LMFDB - Embedded newform 345.2.m.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (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:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	345.121
Dual form			345.2.m.c.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.831671 + 1.82111i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.31503 - 1.51762i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(1.31105 - 1.51303i) q^{6} +(0.450906 - 3.13612i) q^{7} +(0.0155624 - 0.00456953i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.831671 + 1.82111i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.31503 - 1.51762i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(1.31105 - 1.51303i) q^{6} +(0.450906 - 3.13612i) q^{7} +(0.0155624 - 0.00456953i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.284918 - 1.98165i) q^{10} +(-0.0600131 - 0.131410i) q^{11} +(0.834196 + 1.82663i) q^{12} +(-0.435665 - 3.03012i) q^{13} +(5.33619 + 3.42936i) q^{14} +(0.959493 - 0.281733i) q^{15} +(0.566944 - 3.94318i) q^{16} +(4.78394 - 5.52096i) q^{17} +(-1.68421 + 1.08238i) q^{18} +(2.03744 + 2.35133i) q^{19} +(1.92676 + 0.565748i) q^{20} +(-1.31619 + 2.88205i) q^{21} +0.289223 q^{22} +(-2.97924 + 3.75820i) q^{23} -0.0162194 q^{24} +(0.415415 - 0.909632i) q^{25} +(5.88050 + 1.72667i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-5.35239 + 3.43977i) q^{28} +(1.17385 - 1.35469i) q^{29} +(-0.284918 + 1.98165i) q^{30} +(9.74845 - 2.86240i) q^{31} +(6.73673 + 4.32943i) q^{32} +(0.0205596 + 0.142995i) q^{33} +(6.07559 + 13.3037i) q^{34} +(1.31619 + 2.88205i) q^{35} +(-0.285783 - 1.98766i) q^{36} +(-8.11745 - 5.21677i) q^{37} +(-5.97650 + 1.75486i) q^{38} +(-0.435665 + 3.03012i) q^{39} +(-0.0106214 + 0.0122578i) q^{40} +(-3.39768 + 2.18356i) q^{41} +(-4.15388 - 4.79383i) q^{42} +(-3.77244 - 1.10769i) q^{43} +(-0.120512 + 0.263885i) q^{44} -1.00000 q^{45} +(-4.36634 - 8.55111i) q^{46} +5.23591 q^{47} +(-1.65490 + 3.62373i) q^{48} +(-2.91546 - 0.856057i) q^{49} +(1.31105 + 1.51303i) q^{50} +(-6.14559 + 3.94953i) q^{51} +(-4.02566 + 4.64586i) q^{52} +(1.58011 - 10.9899i) q^{53} +(1.92093 - 0.564035i) q^{54} +(0.121532 + 0.0781039i) q^{55} +(-0.00731341 - 0.0508659i) q^{56} +(-1.29246 - 2.83010i) q^{57} +(1.49078 + 3.26436i) q^{58} +(-0.377507 - 2.62562i) q^{59} +(-1.68932 - 1.08566i) q^{60} +(-2.51599 + 0.738761i) q^{61} +(-2.89476 + 20.1335i) q^{62} +(2.07484 - 2.39449i) q^{63} +(-6.78444 + 4.36010i) q^{64} +(2.00471 + 2.31356i) q^{65} +(-0.277508 - 0.0814836i) q^{66} +(0.210047 - 0.459939i) q^{67} -14.6697 q^{68} +(3.91737 - 2.76662i) q^{69} -6.34315 q^{70} +(4.77711 - 10.4604i) q^{71} +(0.0155624 + 0.00456953i) q^{72} +(-3.60546 - 4.16092i) q^{73} +(16.2513 - 10.4441i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.889143 - 6.18412i) q^{76} +(-0.439178 + 0.128954i) q^{77} +(-5.15584 - 3.31345i) q^{78} +(0.0815122 + 0.566930i) q^{79} +(1.65490 + 3.62373i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-1.15073 - 8.00353i) q^{82} +(-2.83850 - 1.82419i) q^{83} +(6.10468 - 1.79250i) q^{84} +(-1.03965 + 7.23093i) q^{85} +(5.15465 - 5.94878i) q^{86} +(-1.50796 + 0.969106i) q^{87} +(-0.00153443 - 0.00177083i) q^{88} +(-15.3685 - 4.51259i) q^{89} +(0.831671 - 1.82111i) q^{90} -9.69925 q^{91} +(9.62132 - 0.420774i) q^{92} -10.1600 q^{93} +(-4.35456 + 9.53515i) q^{94} +(-2.98523 - 0.876542i) q^{95} +(-5.24410 - 6.05202i) q^{96} +(6.32673 - 4.06594i) q^{97} +(3.98367 - 4.59741i) q^{98} +(0.0205596 - 0.142995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) $ 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.831671	+	1.82111i	−0.588080	+	1.28772i	0.348515	+	0.937303i	$0.386686\pi$
$2$	−0.831671	+	1.82111i	−0.588080	+	1.28772i	−0.936595	+	0.350413i	$0.886041\pi$
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−1.31503	−	1.51762i	−0.657513	−	0.758811i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$6$	1.31105	−	1.51303i	0.535233	−	0.617692i
$7$	0.450906	−	3.13612i	0.170426	−	1.18534i	−0.707559	−	0.706654i	$-0.750204\pi$
$7$	0.450906	−	3.13612i	0.170426	−	1.18534i	0.877986	−	0.478687i	$-0.158887\pi$
$8$	0.0155624	−	0.00456953i	0.00550213	−	0.00161557i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.284918	−	1.98165i	−0.0900989	−	0.626652i
$11$	−0.0600131	−	0.131410i	−0.0180946	−	0.0396217i	0.900369	−	0.435127i	$-0.143297\pi$
$11$	−0.0600131	−	0.131410i	−0.0180946	−	0.0396217i	−0.918464	+	0.395506i	$0.870569\pi$
$12$	0.834196	+	1.82663i	0.240812	+	0.527304i
$13$	−0.435665	−	3.03012i	−0.120832	−	0.840404i	−0.956617	−	0.291348i	$-0.905896\pi$
$13$	−0.435665	−	3.03012i	−0.120832	−	0.840404i	0.835785	−	0.549056i	$-0.185013\pi$
$14$	5.33619	+	3.42936i	1.42616	+	0.916536i
$15$	0.959493	−	0.281733i	0.247740	−	0.0727430i
$16$	0.566944	−	3.94318i	0.141736	−	0.985796i
$17$	4.78394	−	5.52096i	1.16028	−	1.33903i	0.229558	−	0.973295i	$-0.426272\pi$
$17$	4.78394	−	5.52096i	1.16028	−	1.33903i	0.930719	−	0.365735i	$-0.119182\pi$
$18$	−1.68421	+	1.08238i	−0.396972	+	0.255118i
$19$	2.03744	+	2.35133i	0.467420	+	0.539432i	0.939692	−	0.342021i	$-0.111111\pi$
$19$	2.03744	+	2.35133i	0.467420	+	0.539432i	−0.472272	+	0.881453i	$0.656566\pi$
$20$	1.92676	+	0.565748i	0.430836	+	0.126505i
$21$	−1.31619	+	2.88205i	−0.287216	+	0.628914i
$22$	0.289223			0.0616626
$23$	−2.97924	+	3.75820i	−0.621215	+	0.783640i
$23$	−2.97924	+	3.75820i	−0.621215	+	0.783640i
$24$	−0.0162194			−0.00331077
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	5.88050	+	1.72667i	1.15326	+	0.338628i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−5.35239	+	3.43977i	−1.01151	+	0.650056i
$29$	1.17385	−	1.35469i	0.217978	−	0.251560i	−0.636220	−	0.771507i	$-0.719503\pi$
$29$	1.17385	−	1.35469i	0.217978	−	0.251560i	0.854198	+	0.519948i	$0.174049\pi$
$30$	−0.284918	+	1.98165i	−0.0520186	+	0.361798i
$31$	9.74845	−	2.86240i	1.75087	−	0.514103i	0.760120	−	0.649783i	$-0.225140\pi$
$31$	9.74845	−	2.86240i	1.75087	−	0.514103i	0.990753	+	0.135680i	$0.0433219\pi$
$32$	6.73673	+	4.32943i	1.19090	+	0.765343i
$33$	0.0205596	+	0.142995i	0.00357896	+	0.0248922i
$34$	6.07559	+	13.3037i	1.04196	+	2.28156i
$35$	1.31619	+	2.88205i	0.222476	+	0.487155i
$36$	−0.285783	−	1.98766i	−0.0476304	−	0.331277i
$37$	−8.11745	−	5.21677i	−1.33450	−	0.857632i	−0.337995	−	0.941148i	$-0.609749\pi$
$37$	−8.11745	−	5.21677i	−1.33450	−	0.857632i	−0.996506	+	0.0835160i	$0.973385\pi$
$38$	−5.97650	+	1.75486i	−0.969516	+	0.284676i
$39$	−0.435665	+	3.03012i	−0.0697623	+	0.485207i
$40$	−0.0106214	+	0.0122578i	−0.00167940	+	0.00193813i
$41$	−3.39768	+	2.18356i	−0.530628	+	0.341014i	−0.778364	−	0.627814i	$-0.783950\pi$
$41$	−3.39768	+	2.18356i	−0.530628	+	0.341014i	0.247735	+	0.968828i	$0.420314\pi$
$42$	−4.15388	−	4.79383i	−0.640957	−	0.739704i
$43$	−3.77244	−	1.10769i	−0.575292	−	0.168921i	−0.0188716	−	0.999822i	$-0.506007\pi$
$43$	−3.77244	−	1.10769i	−0.575292	−	0.168921i	−0.556420	+	0.830901i	$0.687826\pi$
$44$	−0.120512	+	0.263885i	−0.0181679	+	0.0397822i
$45$	−1.00000			−0.149071
$46$	−4.36634	−	8.55111i	−0.643781	−	1.26079i
$47$	5.23591			0.763736			0.381868	−	0.924217i	$-0.375281\pi$
$47$	5.23591			0.763736			0.381868	+	0.924217i	$0.375281\pi$
$48$	−1.65490	+	3.62373i	−0.238865	+	0.523040i
$49$	−2.91546	−	0.856057i	−0.416495	−	0.122294i
$50$	1.31105	+	1.51303i	0.185410	+	0.213975i
$51$	−6.14559	+	3.94953i	−0.860555	+	0.553045i
$52$	−4.02566	+	4.64586i	−0.558259	+	0.644265i
$53$	1.58011	−	10.9899i	0.217045	−	1.50958i	−0.531822	−	0.846856i	$-0.678492\pi$
$53$	1.58011	−	10.9899i	0.217045	−	1.50958i	0.748866	−	0.662721i	$-0.230599\pi$
$54$	1.92093	−	0.564035i	0.261405	−	0.0767555i
$55$	0.121532	+	0.0781039i	0.0163874	+	0.0105315i
$56$	−0.00731341	−	0.0508659i	−0.000977295	−	0.00679724i
$57$	−1.29246	−	2.83010i	−0.171191	−	0.374855i
$58$	1.49078	+	3.26436i	0.195749	+	0.428631i
$59$	−0.377507	−	2.62562i	−0.0491473	−	0.341827i	−0.999528	−	0.0307361i	$-0.990215\pi$
$59$	−0.377507	−	2.62562i	−0.0491473	−	0.341827i	0.950380	−	0.311091i	$-0.100694\pi$
$60$	−1.68932	−	1.08566i	−0.218091	−	0.140158i
$61$	−2.51599	+	0.738761i	−0.322140	+	0.0945887i	−0.438804	−	0.898583i	$-0.644598\pi$
$61$	−2.51599	+	0.738761i	−0.322140	+	0.0945887i	0.116665	+	0.993171i	$0.462780\pi$
$62$	−2.89476	+	20.1335i	−0.367635	+	2.55696i
$63$	2.07484	−	2.39449i	0.261405	−	0.301678i
$64$	−6.78444	+	4.36010i	−0.848055	+	0.545012i
$65$	2.00471	+	2.31356i	0.248654	+	0.286962i
$66$	−0.277508	−	0.0814836i	−0.0341588	−	0.0100299i
$67$	0.210047	−	0.459939i	0.0256613	−	0.0561905i	−0.896367	−	0.443312i	$-0.853803\pi$
$67$	0.210047	−	0.459939i	0.0256613	−	0.0561905i	0.922029	+	0.387122i	$0.126531\pi$
$68$	−14.6697			−1.77897
$69$	3.91737	−	2.76662i	0.471596	−	0.333062i
$70$	−6.34315			−0.758151
$71$	4.77711	−	10.4604i	0.566939	−	1.24142i	−0.381473	−	0.924380i	$-0.624583\pi$
$71$	4.77711	−	10.4604i	0.566939	−	1.24142i	0.948411	−	0.317043i	$-0.102690\pi$
$72$	0.0155624	+	0.00456953i	0.00183404	+	0.000538524i
$73$	−3.60546	−	4.16092i	−0.421987	−	0.486999i	0.504454	−	0.863438i	$-0.331694\pi$
$73$	−3.60546	−	4.16092i	−0.421987	−	0.486999i	−0.926441	+	0.376439i	$0.877148\pi$
$74$	16.2513	−	10.4441i	1.88918	−	1.21410i
$75$	−0.654861	+	0.755750i	−0.0756168	+	0.0872664i
$76$	0.889143	−	6.18412i	0.101992	−	0.709368i
$77$	−0.439178	+	0.128954i	−0.0500490	+	0.0146957i
$78$	−5.15584	−	3.31345i	−0.583784	−	0.375175i
$79$	0.0815122	+	0.566930i	0.00917084	+	0.0637846i	0.993893	−	0.110349i	$-0.0351967\pi$
$79$	0.0815122	+	0.566930i	0.00917084	+	0.0637846i	−0.984722	+	0.174133i	$0.944288\pi$
$80$	1.65490	+	3.62373i	0.185024	+	0.405145i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−1.15073	−	8.00353i	−0.127077	−	0.883842i
$83$	−2.83850	−	1.82419i	−0.311565	−	0.200231i	0.375508	−	0.926819i	$-0.377468\pi$
$83$	−2.83850	−	1.82419i	−0.311565	−	0.200231i	−0.687073	+	0.726588i	$0.741105\pi$
$84$	6.10468	−	1.79250i	0.666075	−	0.195577i
$85$	−1.03965	+	7.23093i	−0.112766	+	0.784304i
$86$	5.15465	−	5.94878i	0.555840	−	0.641474i
$87$	−1.50796	+	0.969106i	−0.161670	+	0.103899i
$88$	−0.00153443	−	0.00177083i	−0.000163571	−	0.000188771i
$89$	−15.3685	−	4.51259i	−1.62905	−	0.478333i	−0.665622	−	0.746289i	$-0.731834\pi$
$89$	−15.3685	−	4.51259i	−1.62905	−	0.478333i	−0.963431	+	0.267955i	$0.913652\pi$
$90$	0.831671	−	1.82111i	0.0876658	−	0.191961i
$91$	−9.69925			−1.01676
$92$	9.62132	−	0.420774i	1.00309	−	0.0438687i
$93$	−10.1600			−1.05354
$94$	−4.35456	+	9.53515i	−0.449138	+	0.983475i
$95$	−2.98523	−	0.876542i	−0.306278	−	0.0899313i
$96$	−5.24410	−	6.05202i	−0.535224	−	0.617681i
$97$	6.32673	−	4.06594i	0.642382	−	0.412834i	−0.178493	−	0.983941i	$-0.557122\pi$
$97$	6.32673	−	4.06594i	0.642382	−	0.412834i	0.820875	+	0.571107i	$0.193486\pi$
$98$	3.98367	−	4.59741i	0.402412	−	0.464408i
$99$	0.0205596	−	0.142995i	0.00206631	−	0.0143715i
$100$	−1.92676	+	0.565748i	−0.192676	+	0.0565748i
$101$	−8.69123	−	5.58551i	−0.864810	−	0.555779i	0.0313513	−	0.999508i	$-0.490019\pi$
$101$	−8.69123	−	5.58551i	−0.864810	−	0.555779i	−0.896161	+	0.443729i	$0.853655\pi$
$102$	−2.08140	−	14.4765i	−0.206090	−	1.43339i
$103$	5.58258	+	12.2241i	0.550068	+	1.20448i	0.956750	+	0.290911i	$0.0939584\pi$
$103$	5.58258	+	12.2241i	0.550068	+	1.20448i	−0.406682	+	0.913570i	$0.633314\pi$
$104$	−0.0206262	−	0.0451651i	−0.00202257	−	0.00442880i
$105$	−0.450906	−	3.13612i	−0.0440039	−	0.306054i
$106$	18.6996	+	12.0175i	1.81627	+	1.16724i
$107$	−3.96293	+	1.16362i	−0.383111	+	0.112492i	−0.467617	−	0.883931i	$-0.654887\pi$
$107$	−3.96293	+	1.16362i	−0.383111	+	0.112492i	0.0845053	+	0.996423i	$0.473069\pi$
$108$	−0.285783	+	1.98766i	−0.0274994	+	0.191263i
$109$	9.54820	−	11.0192i	0.914552	−	1.05545i	−0.0837084	−	0.996490i	$-0.526676\pi$
$109$	9.54820	−	11.0192i	0.914552	−	1.05545i	0.998260	−	0.0589590i	$-0.0187781\pi$
$110$	−0.243310	+	0.156366i	−0.0231987	+	0.0149089i
$111$	6.31891	+	7.29241i	0.599764	+	0.692165i
$112$	−12.1106	−	3.55601i	−1.14435	−	0.336011i
$113$	−6.06969	+	13.2908i	−0.570989	+	1.25029i	0.375281	+	0.926911i	$0.377546\pi$
$113$	−6.06969	+	13.2908i	−0.570989	+	1.25029i	−0.946269	+	0.323379i	$0.895181\pi$
$114$	6.22881			0.583381
$115$	0.474461	−	4.77230i	0.0442437	−	0.445020i
$116$	−3.59955			−0.334210
$117$	1.27170	−	2.78464i	0.117569	−	0.257440i
$118$	5.09549	+	1.49617i	0.469078	+	0.137734i
$119$	−15.1573	−	17.4924i	−1.38947	−	1.60353i
$120$	0.0136446	−	0.00876886i	0.00124558	−	0.000800484i
$121$	7.18980	−	8.29747i	0.653618	−	0.754316i
$122$	0.747114	−	5.19629i	0.0676405	−	0.470450i
$123$	3.87523	−	1.13787i	0.349418	−	0.102598i
$124$	−17.1635	−	11.0303i	−1.54133	−	0.990552i
$125$	0.142315	+	0.989821i	0.0127290	+	0.0885323i
$126$	2.63504	+	5.76993i	0.234748	+	0.514026i
$127$	5.16198	+	11.3032i	0.458052	+	1.00299i	0.987927	+	0.154918i	$0.0495113\pi$
$127$	5.16198	+	11.3032i	0.458052	+	1.00299i	−0.529876	+	0.848075i	$0.677761\pi$
$128$	−0.0184659	−	0.128433i	−0.00163217	−	0.0113520i
$129$	3.30756	+	2.12564i	0.291214	+	0.187152i
$130$	−5.88050	+	1.72667i	−0.515754	+	0.151439i
$131$	−3.15496	+	21.9432i	−0.275650	+	1.91719i	0.108845	+	0.994059i	$0.465285\pi$
$131$	−3.15496	+	21.9432i	−0.275650	+	1.91719i	−0.384494	+	0.923127i	$0.625624\pi$
$132$	0.189976	−	0.219244i	0.0165353	−	0.0190827i
$133$	8.29274	−	5.32942i	0.719071	−	0.462119i
$134$	0.662908	+	0.765036i	0.0572665	+	0.0660891i
$135$	0.959493	+	0.281733i	0.0825800	+	0.0242477i
$136$	0.0492213	−	0.107780i	0.00422069	−	0.00924203i
$137$	9.70217			0.828913			0.414456	−	0.910069i	$-0.363972\pi$
$137$	9.70217			0.828913			0.414456	+	0.910069i	$0.363972\pi$
$138$	1.78034	+	9.43487i	0.151553	+	0.803149i
$139$	−11.1029			−0.941738			−0.470869	−	0.882203i	$-0.656060\pi$
$139$	−11.1029			−0.941738			−0.470869	+	0.882203i	$0.656060\pi$
$140$	2.64304	−	5.78744i	0.223377	−	0.489128i
$141$	−5.02382	−	1.47513i	−0.423082	−	0.124228i
$142$	15.0765	+	17.3992i	1.26519	+	1.46011i
$143$	−0.372043	+	0.239098i	−0.0311118	+	0.0199944i
$144$	2.60879	−	3.01070i	0.217399	−	0.250892i
$145$	−0.255101	+	1.77427i	−0.0211850	+	0.147345i
$146$	10.5760	−	3.10540i	0.875279	−	0.257005i
$147$	2.55619	+	1.64276i	0.210831	+	0.135493i
$148$	2.75758	+	19.1794i	0.226672	+	1.57654i
$149$	−2.31117	−	5.06077i	−0.189339	−	0.414594i	0.791027	−	0.611781i	$-0.209547\pi$
$149$	−2.31117	−	5.06077i	−0.189339	−	0.414594i	−0.980366	+	0.197187i	$0.936819\pi$
$150$	−0.831671	−	1.82111i	−0.0679057	−	0.148693i
$151$	3.07036	+	21.3548i	0.249862	+	1.73783i	0.598993	+	0.800755i	$0.295568\pi$
$151$	3.07036	+	21.3548i	0.249862	+	1.73783i	−0.349130	+	0.937074i	$0.613523\pi$
$152$	0.0424519	+	0.0272822i	0.00344330	+	0.00221287i
$153$	7.00937	−	2.05814i	0.566674	−	0.166390i
$154$	0.130412	−	0.907038i	0.0105089	−	0.0730912i
$155$	−6.65338	+	7.67842i	−0.534413	+	0.616745i
$156$	5.17149	−	3.32351i	0.414050	−	0.266094i
$157$	7.02138	+	8.10310i	0.560367	+	0.646698i	0.963267	−	0.268546i	$-0.0865431\pi$
$157$	7.02138	+	8.10310i	0.560367	+	0.646698i	−0.402900	+	0.915244i	$0.631998\pi$
$158$	−1.10023	−	0.323057i	−0.0875296	−	0.0257010i
$159$	−4.61231	+	10.0996i	−0.365780	+	0.800947i
$160$	−8.00797			−0.633085
$161$	10.4428	+	11.0379i	0.823009	+	0.869905i
$162$	−2.00202			−0.157294
$163$	−4.64175	+	10.1640i	−0.363570	+	0.796108i	0.636129	+	0.771583i	$0.280535\pi$
$163$	−4.64175	+	10.1640i	−0.363570	+	0.796108i	−0.999699	+	0.0245251i	$0.992193\pi$
$164$	7.78185	+	2.28496i	0.607660	+	0.178425i
$165$	−0.0946047	−	0.109180i	−0.00736497	−	0.00849963i
$166$	5.68274	−	3.65207i	0.441066	−	0.283456i
$167$	−3.93156	+	4.53726i	−0.304233	+	0.351104i	−0.887194	−	0.461396i	$-0.847349\pi$
$167$	−3.93156	+	4.53726i	−0.304233	+	0.351104i	0.582961	+	0.812500i	$0.301894\pi$
$168$	−0.00731341	+	0.0508659i	−0.000564242	+	0.00392439i
$169$	3.48159	−	1.02229i	0.267815	−	0.0786375i
$170$	−12.3036	−	7.90706i	−0.943645	−	0.606444i
$171$	0.442778	+	3.07959i	0.0338601	+	0.235502i
$172$	3.27981	+	7.18178i	0.250083	+	0.547606i
$173$	3.75019	+	8.21176i	0.285121	+	0.624329i	0.996952	−	0.0780229i	$-0.0248607\pi$
$173$	3.75019	+	8.21176i	0.285121	+	0.624329i	−0.711830	+	0.702352i	$0.752133\pi$
$174$	−0.510719	−	3.55213i	−0.0387175	−	0.269286i
$175$	−2.66540	−	1.71295i	−0.201485	−	0.129487i
$176$	−0.552199	+	0.162140i	−0.0416236	+	0.0122218i
$177$	−0.377507	+	2.62562i	−0.0283752	+	0.197354i
$178$	20.9994	−	24.2346i	1.57397	−	1.81646i
$179$	−0.0296546	+	0.0190579i	−0.00221649	+	0.00142445i	−0.541749	−	0.840541i	$-0.682238\pi$
$179$	−0.0296546	+	0.0190579i	−0.00221649	+	0.00142445i	0.539532	+	0.841965i	$0.318601\pi$
$180$	1.31503	+	1.51762i	0.0980163	+	0.113117i
$181$	16.8274	+	4.94097i	1.25077	+	0.367260i	0.839052	−	0.544051i	$-0.183110\pi$
$181$	16.8274	+	4.94097i	1.25077	+	0.367260i	0.411720	+	0.911311i	$0.364928\pi$
$182$	8.06659	−	17.6634i	0.597935	−	1.30930i
$183$	2.62221			0.193839
$184$	−0.0291909	+	0.0721004i	−0.00215198	+	0.00531531i
$185$	9.64924			0.709426
$186$	8.44978	−	18.5024i	0.619568	−	1.35666i
$187$	−1.01261	−	0.297329i	−0.0740495	−	0.0217429i
$188$	−6.88536	−	7.94613i	−0.502167	−	0.579531i
$189$	−2.66540	+	1.71295i	−0.193879	+	0.124599i
$190$	4.07900	−	4.70742i	0.295922	−	0.341512i
$191$	1.31931	−	9.17601i	0.0954620	−	0.663953i	−0.884759	−	0.466048i	$-0.845677\pi$
$191$	1.31931	−	9.17601i	0.0954620	−	0.663953i	0.980221	−	0.197904i	$-0.0634136\pi$
$192$	7.73800	−	2.27208i	0.558442	−	0.163973i
$193$	12.6544	+	8.13248i	0.910883	+	0.585389i	0.909999	−	0.414611i	$-0.136082\pi$
$193$	12.6544	+	8.13248i	0.910883	+	0.585389i	0.000883857		1.00000i	$0.499719\pi$
$194$	2.14275	+	14.9032i	0.153841	+	1.06999i
$195$	−1.27170	−	2.78464i	−0.0910684	−	0.199412i
$196$	2.53474	+	5.55031i	0.181053	+	0.396450i
$197$	−1.29891	−	9.03410i	−0.0925434	−	0.643653i	−0.982313	−	0.187244i	$-0.940044\pi$
$197$	−1.29891	−	9.03410i	−0.0925434	−	0.643653i	0.889770	−	0.456409i	$-0.150865\pi$
$198$	0.243310	+	0.156366i	0.0172913	+	0.0111124i
$199$	−19.6771	+	5.77771i	−1.39487	+	0.409571i	−0.890920	−	0.454160i	$-0.849939\pi$
$199$	−19.6771	+	5.77771i	−1.39487	+	0.409571i	−0.503952	+	0.863732i	$0.668121\pi$
$200$	0.00230826	−	0.0160543i	0.000163219	−	0.00113521i
$201$	−0.331119	+	0.382131i	−0.0233553	+	0.0269535i
$202$	17.4001	−	11.1823i	1.22426	−	0.786786i
$203$	−3.71918	−	4.29216i	−0.261035	−	0.301250i
$204$	14.0755	+	4.13295i	0.985484	+	0.289364i
$205$	1.67779	−	3.67385i	0.117182	−	0.256593i
$206$	−26.9043			−1.87451
$207$	−4.53814	+	1.55090i	−0.315422	+	0.107795i
$208$	−12.1953			−0.845593
$209$	0.186716	−	0.408851i	0.0129154	−	0.0282808i
$210$	6.08620	+	1.78707i	0.419988	+	0.123320i
$211$	10.2715	+	11.8539i	0.707117	+	0.816056i	0.989696	−	0.143188i	$-0.0457353\pi$
$211$	10.2715	+	11.8539i	0.707117	+	0.816056i	−0.282579	+	0.959244i	$0.591190\pi$
$212$	−18.7564	+	12.0540i	−1.28819	+	0.827872i
$213$	−7.53064	+	8.69083i	−0.515991	+	0.595486i
$214$	1.17678	−	8.18467i	0.0804429	−	0.559493i
$215$	3.77244	−	1.10769i	0.257278	−	0.0755438i
$216$	−0.0136446	−	0.00876886i	−0.000928398	−	0.000596645i
$217$	−4.58120	−	31.8629i	−0.310992	−	2.16300i
$218$	12.1262	+	26.5526i	0.821289	+	1.79837i
$219$	2.28715	+	5.00815i	0.154551	+	0.338419i
$220$	−0.0412857	−	0.287148i	−0.00278348	−	0.0193595i
$221$	−18.8134	−	12.0906i	−1.26552	−	0.813303i
$222$	−18.5355	+	5.44251i	−1.24402	+	0.365277i
$223$	2.20557	−	15.3401i	0.147696	−	1.02725i	−0.772282	−	0.635280i	$-0.780885\pi$
$223$	2.20557	−	15.3401i	0.147696	−	1.02725i	0.919978	−	0.391970i	$-0.128206\pi$
$224$	16.6152	−	19.1750i	1.11015	−	1.28118i
$225$	0.841254	−	0.540641i	0.0560836	−	0.0360427i
$226$	−19.1559	−	22.1071i	−1.27423	−	1.47054i
$227$	3.05971	+	0.898413i	0.203080	+	0.0596298i	0.381691	−	0.924290i	$-0.375342\pi$
$227$	3.05971	+	0.898413i	0.203080	+	0.0596298i	−0.178610	+	0.983920i	$0.557160\pi$
$228$	−2.59539	+	5.68312i	−0.171884	+	0.376374i
$229$	−9.17037			−0.605995			−0.302998	−	0.952991i	$-0.597987\pi$
$229$	−9.17037			−0.605995			−0.302998	+	0.952991i	$0.597987\pi$
$230$	8.29627	+	4.83303i	0.547040	+	0.318681i
$231$	0.457719			0.0301157
$232$	0.0120775	−	0.0264461i	0.000792930	−	0.00173627i
$233$	−7.53281	−	2.21183i	−0.493491	−	0.144902i	0.0255118	−	0.999675i	$-0.491878\pi$
$233$	−7.53281	−	2.21183i	−0.493491	−	0.144902i	−0.519003	+	0.854772i	$0.673697\pi$
$234$	4.01348	+	4.63180i	0.262369	+	0.302790i
$235$	−4.40473	+	2.83075i	−0.287333	+	0.184658i
$236$	−3.48827	+	4.02567i	−0.227067	+	0.262049i
$237$	0.0815122	−	0.566930i	0.00529479	−	0.0368260i
$238$	44.4614	−	13.0551i	2.88201	−	0.846234i
$239$	−1.70710	−	1.09709i	−0.110423	−	0.0709646i	0.484264	−	0.874922i	$-0.339088\pi$
$239$	−1.70710	−	1.09709i	−0.110423	−	0.0709646i	−0.594687	+	0.803958i	$0.702724\pi$
$240$	−0.566944	−	3.94318i	−0.0365961	−	0.254531i
$241$	0.447732	+	0.980397i	0.0288410	+	0.0631529i	0.923504	−	0.383588i	$-0.125312\pi$
$241$	0.447732	+	0.980397i	0.0288410	+	0.0631529i	−0.894663	+	0.446741i	$0.852585\pi$
$242$	9.13102	+	19.9942i	0.586964	+	1.28527i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	4.42975	+	2.84683i	0.283586	+	0.182250i
$245$	2.91546	−	0.856057i	0.186262	−	0.0546915i
$246$	−1.15073	+	8.00353i	−0.0733681	+	0.510287i
$247$	6.23717	−	7.19808i	0.396861	−	0.458003i
$248$	0.138629	−	0.0890916i	0.00880296	−	0.00565732i
$249$	2.20958	+	2.54999i	0.140027	+	0.161599i
$250$	−1.92093	−	0.564035i	−0.121490	−	0.0356727i
$251$	3.74638	−	8.20344i	0.236470	−	0.517796i	−0.753776	−	0.657132i	$-0.771769\pi$
$251$	3.74638	−	8.20344i	0.236470	−	0.517796i	0.990245	+	0.139336i	$0.0444967\pi$
$252$	−6.36240			−0.400794
$253$	0.672661	+	0.165962i	0.0422898	+	0.0104339i
$254$	−24.8773			−1.56094
$255$	3.03472	−	6.64512i	0.190042	−	0.416133i
$256$	−15.2268	−	4.47098i	−0.951672	−	0.279436i
$257$	13.5785	+	15.6704i	0.847005	+	0.977496i	0.999942	−	0.0107401i	$-0.00341875\pi$
$257$	13.5785	+	15.6704i	0.847005	+	0.977496i	−0.152937	+	0.988236i	$0.548873\pi$
$258$	−6.62181	+	4.25558i	−0.412256	+	0.264941i
$259$	−20.0206	+	23.1050i	−1.24402	+	1.43568i
$260$	0.874860	−	6.08479i	0.0542565	−	0.377362i
$261$	1.71990	−	0.505009i	0.106459	−	0.0312593i
$262$	−37.3370	−	23.9950i	−2.30669	−	1.48242i
$263$	−3.76303	−	26.1724i	−0.232038	−	1.61386i	−0.689263	−	0.724511i	$-0.742066\pi$
$263$	−3.76303	−	26.1724i	−0.232038	−	1.61386i	0.457225	−	0.889351i	$-0.348843\pi$
$264$	0.000973375		0.00213139i	5.99071e−5		0.000131178i
$265$	4.61231	+	10.0996i	0.283332	+	0.620411i
$266$	2.80860	+	19.5343i	0.172207	+	1.19772i
$267$	13.4746	+	8.65959i	0.824631	+	0.529958i
$268$	−0.974231	+	0.286060i	−0.0595107	+	0.0174739i
$269$	0.517276	−	3.59774i	0.0315389	−	0.219358i	−0.967957	−	0.251117i	$-0.919202\pi$
$269$	0.517276	−	3.59774i	0.0315389	−	0.219358i	0.999496	+	0.0317595i	$0.0101111\pi$
$270$	−1.31105	+	1.51303i	−0.0797878	+	0.0920800i
$271$	0.161878	−	0.104033i	0.00983341	−	0.00631955i	−0.535715	−	0.844399i	$-0.679958\pi$
$271$	0.161878	−	0.104033i	0.00983341	−	0.00631955i	0.545548	+	0.838079i	$0.316321\pi$
$272$	−19.0579	−	21.9940i	−1.15556	−	1.33358i
$273$	9.30636	+	2.73260i	0.563247	+	0.165384i
$274$	−8.06902	+	17.6687i	−0.487467	+	1.06740i
$275$	−0.144465			−0.00871159
$276$	−9.35013	−	2.30691i	−0.562812	−	0.138860i
$277$	5.61028			0.337089			0.168545	−	0.985694i	$-0.446093\pi$
$277$	5.61028			0.337089			0.168545	+	0.985694i	$0.446093\pi$
$278$	9.23398	−	20.2196i	0.553817	−	1.21269i
$279$	9.74845	+	2.86240i	0.583624	+	0.171368i
$280$	0.0336526	+	0.0388372i	0.00201113	+	0.00232096i
$281$	17.9895	−	11.5611i	1.07316	−	0.689679i	0.120194	−	0.992750i	$-0.461648\pi$
$281$	17.9895	−	11.5611i	1.07316	−	0.689679i	0.952968	+	0.303071i	$0.0980119\pi$
$282$	6.86453	−	7.92209i	0.408777	−	0.471753i
$283$	0.151034	−	1.05046i	0.00897802	−	0.0624435i	−0.984840	−	0.173466i	$-0.944503\pi$
$283$	0.151034	−	1.05046i	0.00897802	−	0.0624435i	0.993818	+	0.111022i	$0.0354125\pi$
$284$	−22.1570	+	6.50588i	−1.31477	+	0.386053i
$285$	2.61735	+	1.68207i	0.155039	+	0.0996373i
$286$	−0.126005	−	0.876381i	−0.00745081	−	0.0518215i
$287$	5.31585	+	11.6401i	0.313785	+	0.687093i
$288$	3.32663	+	7.28430i	0.196024	+	0.429232i
$289$	−5.17559	−	35.9970i	−0.304446	−	2.11747i
$290$	−3.01897	−	1.94017i	−0.177280	−	0.113931i
$291$	−7.21596	+	2.11880i	−0.423007	+	0.124206i
$292$	−1.57343	+	10.9434i	−0.0920780	+	0.640417i
$293$	−16.0873	+	18.5658i	−0.939832	+	1.08462i	0.0564441	+	0.998406i	$0.482024\pi$
$293$	−16.0873	+	18.5658i	−0.939832	+	1.08462i	−0.996276	+	0.0862183i	$0.972522\pi$
$294$	−5.11755	+	3.28885i	−0.298461	+	0.191809i
$295$	1.73710	+	2.00472i	0.101138	+	0.116719i
$296$	−0.150165	−	0.0440924i	−0.00872817	−	0.00256282i
$297$	−0.0600131	+	0.131410i	−0.00348231	+	0.00762520i
$298$	11.1383			0.645226
$299$	12.6858	+	7.39015i	0.733637	+	0.427383i
$300$	2.00810			0.115938
$301$	−5.17486	+	11.3314i	−0.298274	+	0.653128i
$302$	−41.4429	−	12.1687i	−2.38477	−	0.700231i
$303$	6.76555	+	7.80786i	0.388671	+	0.448550i
$304$	10.4268	−	6.70092i	0.598020	−	0.384324i
$305$	1.71718	−	1.98173i	0.0983255	−	0.113474i
$306$	−2.08140	+	14.4765i	−0.118986	+	0.827566i
$307$	15.2801	−	4.48663i	0.872079	−	0.256066i	0.185080	−	0.982723i	$-0.440746\pi$
$307$	15.2801	−	4.48663i	0.872079	−	0.256066i	0.687000	+	0.726658i	$0.258927\pi$
$308$	0.773235	+	0.496928i	0.0440592	+	0.0283151i
$309$	−1.91251	−	13.3018i	−0.108799	−	0.756712i
$310$	−8.44978	−	18.5024i	−0.479915	−	1.05087i
$311$	0.487360	+	1.06717i	0.0276357	+	0.0605137i	0.922946	−	0.384928i	$-0.125774\pi$
$311$	0.487360	+	1.06717i	0.0276357	+	0.0605137i	−0.895311	+	0.445442i	$0.853047\pi$
$312$	0.00706622	+	0.0491467i	0.000400046	+	0.00278238i
$313$	−0.680470	−	0.437311i	−0.0384624	−	0.0247183i	0.521268	−	0.853393i	$-0.325459\pi$
$313$	−0.680470	−	0.437311i	−0.0384624	−	0.0247183i	−0.559731	+	0.828675i	$0.689095\pi$
$314$	−20.5961	+	6.04756i	−1.16230	+	0.341283i
$315$	−0.450906	+	3.13612i	−0.0254056	+	0.176700i
$316$	0.753194	−	0.869232i	0.0423705	−	0.0488981i
$317$	19.0703	−	12.2557i	1.07109	−	0.688350i	0.118611	−	0.992941i	$-0.462156\pi$
$317$	19.0703	−	12.2557i	1.07109	−	0.688350i	0.952483	+	0.304591i	$0.0985196\pi$
$318$	−14.5564	−	16.7990i	−0.816284	−	0.942042i
$319$	−0.248467	−	0.0729564i	−0.0139115	−	0.00408477i
$320$	3.35019	−	7.33589i	0.187281	−	0.410089i
$321$	4.13024			0.230527
$322$	−28.7861	+	9.83760i	−1.60419	+	0.548228i
$323$	22.7286			1.26465
$324$	0.834196	−	1.82663i	0.0463442	−	0.101480i
$325$	−2.93728	−	0.862462i	−0.162931	−	0.0478408i
$326$	−14.6493	−	16.9062i	−0.811352	−	0.936351i
$327$	−12.2659	+	7.88282i	−0.678306	+	0.435921i
$328$	−0.0428982	+	0.0495071i	−0.00236865	+	0.00273357i
$329$	2.36090	−	16.4204i	0.130161	−	0.905287i
$330$	0.277508	−	0.0814836i	0.0152763	−	0.00448552i
$331$	−10.0195	−	6.43917i	−0.550724	−	0.353929i	0.235496	−	0.971875i	$-0.424328\pi$
$331$	−10.0195	−	6.43917i	−0.550724	−	0.353929i	−0.786220	+	0.617947i	$0.787965\pi$
$332$	0.964267	+	6.70662i	0.0529210	+	0.368074i
$333$	−4.00844	−	8.77725i	−0.219661	−	0.480991i
$334$	−4.99307	−	10.9333i	−0.273208	−	0.598243i
$335$	0.0719590	+	0.500486i	0.00393154	+	0.0273444i
$336$	10.6182	+	6.82393i	0.579272	+	0.372276i
$337$	−15.4570	+	4.53860i	−0.841998	+	0.247233i	−0.674164	−	0.738582i	$-0.735496\pi$
$337$	−15.4570	+	4.53860i	−0.841998	+	0.247233i	−0.167835	+	0.985815i	$0.553678\pi$
$338$	−1.03384	+	7.19055i	−0.0562337	+	0.391114i
$339$	9.56827	−	11.0424i	0.519677	−	0.599739i
$340$	12.3410	−	7.93106i	0.669283	−	0.430122i
$341$	−0.961184	−	1.10927i	−0.0520510	−	0.0600701i
$342$	−5.97650	−	1.75486i	−0.323172	−	0.0948919i
$343$	5.21402	−	11.4171i	0.281530	−	0.616466i
$344$	−0.0637698			−0.00343824
$345$	−1.79976	+	4.44532i	−0.0968956	+	0.239328i
$346$	−18.0734			−0.971632
$347$	−9.55826	+	20.9297i	−0.513114	+	1.12356i	0.458867	+	0.888505i	$0.348256\pi$
$347$	−9.55826	+	20.9297i	−0.513114	+	1.12356i	−0.971981	+	0.235059i	$0.924472\pi$
$348$	3.45374	+	1.01411i	0.185140	+	0.0543620i
$349$	−1.41411	−	1.63197i	−0.0756955	−	0.0873572i	0.716639	−	0.697445i	$-0.245680\pi$
$349$	−1.41411	−	1.63197i	−0.0756955	−	0.0873572i	−0.792334	+	0.610087i	$0.791134\pi$
$350$	5.33619	−	3.42936i	0.285232	−	0.183307i
$351$	−2.00471	+	2.31356i	−0.107004	+	0.123489i
$352$	0.164640	−	1.14510i	0.00877536	−	0.0610340i
$353$	−26.2875	+	7.71872i	−1.39914	+	0.410826i	−0.892390	−	0.451264i	$-0.850973\pi$
$353$	−26.2875	+	7.71872i	−1.39914	+	0.410826i	−0.506754	+	0.862090i	$0.669155\pi$
$354$	−4.46757	−	2.87113i	−0.237449	−	0.152599i
$355$	1.63657	+	11.3826i	0.0868599	+	0.604124i
$356$	13.3615	+	29.2577i	0.708160	+	1.55065i
$357$	9.61512	+	21.0542i	0.508886	+	1.11430i
$358$	−0.0100435	−	0.0698540i	−0.000530815	−	0.00369190i
$359$	16.3280	+	10.4934i	0.861758	+	0.553818i	0.895221	−	0.445622i	$-0.147017\pi$
$359$	16.3280	+	10.4934i	0.861758	+	0.553818i	−0.0334637	+	0.999440i	$0.510654\pi$
$360$	−0.0155624	+	0.00456953i	−0.000820209	+	0.000240835i
$361$	1.32639	−	9.22523i	0.0698099	−	0.485538i
$362$	−22.9929	+	26.5352i	−1.20848	+	1.39466i
$363$	−9.23623	+	5.93577i	−0.484776	+	0.311547i
$364$	12.7548	+	14.7198i	0.668532	+	0.771527i
$365$	5.28267	+	1.55113i	0.276508	+	0.0811899i
$366$	−2.18081	+	4.77532i	−0.113993	+	0.249610i
$367$	22.2192			1.15983			0.579917	−	0.814675i	$-0.303085\pi$
$367$	22.2192			1.15983			0.579917	+	0.814675i	$0.303085\pi$
$368$	13.1302	+	13.8784i	0.684460	+	0.723461i
$369$	−4.03883			−0.210253
$370$	−8.02499	+	17.5723i	−0.417199	+	0.913539i
$371$	−33.7531	−	9.91081i	−1.75237	−	0.514543i
$372$	13.3607	+	15.4190i	0.692719	+	0.799440i
$373$	4.92183	−	3.16307i	0.254843	−	0.163777i	−0.406982	−	0.913436i	$-0.633419\pi$
$373$	4.92183	−	3.16307i	0.254843	−	0.163777i	0.661824	+	0.749659i	$0.269782\pi$
$374$	1.38363	−	1.59679i	0.0715457	−	0.0825681i
$375$	0.142315	−	0.989821i	0.00734911	−	0.0511142i
$376$	0.0814832	−	0.0239256i	0.00420218	−	0.00123387i
$377$	−4.61628	−	2.96670i	−0.237751	−	0.152793i
$378$	−0.902724	−	6.27858i	−0.0464311	−	0.322935i
$379$	6.89318	+	15.0940i	0.354079	+	0.775325i	0.999930	+	0.0118610i	$0.00377557\pi$
$379$	6.89318	+	15.0940i	0.354079	+	0.775325i	−0.645851	+	0.763464i	$0.723497\pi$
$380$	2.59539	+	5.68312i	0.133141	+	0.291538i
$381$	−1.76842	−	12.2996i	−0.0905987	−	0.630128i
$382$	15.6132	+	10.0340i	0.798843	+	0.513385i
$383$	14.0636	−	4.12946i	0.718618	−	0.211005i	0.0980767	−	0.995179i	$-0.468731\pi$
$383$	14.0636	−	4.12946i	0.718618	−	0.211005i	0.620542	+	0.784173i	$0.286913\pi$
$384$	−0.0184659	+	0.128433i	−0.000942335	+	0.00655408i
$385$	0.299742	−	0.345921i	0.0152763	−	0.0176298i
$386$	−25.3344	+	16.2814i	−1.28949	+	0.828703i
$387$	−2.57472	−	2.97138i	−0.130880	−	0.151044i
$388$	−14.4904	−	4.25476i	−0.735638	−	0.216003i
$389$	−3.99439	+	8.74650i	−0.202524	+	0.443465i	−0.983455	−	0.181152i	$-0.942018\pi$
$389$	−3.99439	+	8.74650i	−0.202524	+	0.443465i	0.780931	+	0.624617i	$0.214745\pi$
$390$	6.12875			0.310342
$391$	6.49638	+	34.4273i	0.328536	+	1.74107i
$392$	−0.0492833			−0.00248918
$393$	9.20927	−	20.1655i	0.464546	−	1.01721i
$394$	17.5323	+	5.14795i	0.883265	+	0.259350i
$395$	−0.375078	−	0.432863i	−0.0188722	−	0.0217797i
$396$	−0.244049	+	0.156841i	−0.0122639	+	0.00788153i
$397$	−20.3735	+	23.5123i	−1.02252	+	1.18005i	−0.0389991	+	0.999239i	$0.512417\pi$
$397$	−20.3735	+	23.5123i	−1.02252	+	1.18005i	−0.983518	+	0.180809i	$0.942129\pi$
$398$	5.84304	−	40.6392i	0.292885	−	2.03706i
$399$	−9.45829	+	2.77721i	−0.473507	+	0.139034i
$400$	−3.35133	−	2.15377i	−0.167566	−	0.107688i
$401$	−1.23437	−	8.58523i	−0.0616415	−	0.428726i	−0.997151	−	0.0754255i	$-0.975968\pi$
$401$	−1.23437	−	8.58523i	−0.0616415	−	0.428726i	0.935510	−	0.353300i	$-0.114941\pi$
$402$	−0.420520	−	0.920809i	−0.0209736	−	0.0459258i
$403$	−12.9205	−	28.2919i	−0.643615	−	1.40932i
$404$	2.95250	+	20.5351i	0.146892	+	1.02166i
$405$	−0.841254	−	0.540641i	−0.0418022	−	0.0268647i
$406$	10.9096	−	3.20335i	0.541434	−	0.158979i
$407$	−0.198384	+	1.37979i	−0.00983354	+	0.0683938i
$408$	−0.0775926	+	0.0895466i	−0.00384141	+	0.00443322i
$409$	−3.17451	+	2.04014i	−0.156970	+	0.100878i	−0.616768	−	0.787145i	$-0.711558\pi$
$409$	−3.17451	+	2.04014i	−0.156970	+	0.100878i	0.459798	+	0.888024i	$0.347922\pi$
$410$	5.29510	+	6.11087i	0.261506	+	0.301794i
$411$	−9.30917	−	2.73342i	−0.459187	−	0.134830i
$412$	11.2104	−	24.5473i	0.552296	−	1.20936i
$413$	−8.40447			−0.413557
$414$	0.949882	−	9.55427i	0.0466842	−	0.469567i
$415$	3.37413			0.165629
$416$	10.1837	−	22.2993i	0.499299	−	1.09331i
$417$	10.6532	+	3.12806i	0.521688	+	0.153182i
$418$	0.589275	+	0.680059i	0.0288224	+	0.0332628i
$419$	20.4284	−	13.1285i	0.997993	−	0.641371i	0.0637340	−	0.997967i	$-0.479699\pi$
$419$	20.4284	−	13.1285i	0.997993	−	0.641371i	0.934259	+	0.356596i	$0.116063\pi$
$420$	−4.16649	+	4.80838i	−0.203304	+	0.234625i
$421$	−2.88668	+	20.0773i	−0.140688	+	0.978507i	0.790108	+	0.612968i	$0.210024\pi$
$421$	−2.88668	+	20.0773i	−0.140688	+	0.978507i	−0.930796	+	0.365539i	$0.880885\pi$
$422$	−30.1297	+	8.84687i	−1.46669	+	0.430659i
$423$	4.40473	+	2.83075i	0.214165	+	0.137636i
$424$	−0.0256284	−	0.178249i	−0.00124462	−	0.00865655i
$425$	−3.03472	−	6.64512i	−0.147206	−	0.322336i
$426$	−9.56389	−	20.9420i	−0.463372	−	1.01464i
$427$	1.18237	+	8.22355i	0.0572188	+	0.397966i
$428$	6.97730	+	4.48404i	0.337261	+	0.216744i
$429$	0.424335	−	0.124596i	0.0204871	−	0.00601555i
$430$	−1.12021	+	7.79125i	−0.0540214	+	0.375727i
$431$	22.1154	−	25.5225i	1.06526	−	1.22938i	0.0929544	−	0.995670i	$-0.470369\pi$
$431$	22.1154	−	25.5225i	1.06526	−	1.22938i	0.972307	−	0.233707i	$-0.0750856\pi$
$432$	−3.35133	+	2.15377i	−0.161241	+	0.103623i
$433$	25.7136	+	29.6751i	1.23572	+	1.42609i	0.868301	+	0.496038i	$0.165212\pi$
$433$	25.7136	+	29.6751i	1.23572	+	1.42609i	0.367417	+	0.930056i	$0.380242\pi$
$434$	61.8358	+	18.1566i	2.96821	+	0.871547i
$435$	0.744637	−	1.63053i	0.0357026	−	0.0781778i
$436$	−29.2791			−1.40222
$437$	−14.9068	+	0.651927i	−0.713089	+	0.0311859i
$438$	−11.0225			−0.526676
$439$	−5.99464	+	13.1264i	−0.286109	+	0.626491i	−0.997050	−	0.0767612i	$-0.975542\pi$
$439$	−5.99464	+	13.1264i	−0.286109	+	0.626491i	0.710941	+	0.703252i	$0.248269\pi$
$440$	0.00224823		0.000660139i	0.000107180		3.14709e-5i
$441$	−1.98982	−	2.29638i	−0.0947535	−	0.109351i
$442$	37.6648	−	24.2057i	1.79153	−	1.15135i
$443$	−12.9287	+	14.9205i	−0.614260	+	0.708894i	−0.974607	−	0.223924i	$-0.928113\pi$
$443$	−12.9287	+	14.9205i	−0.614260	+	0.708894i	0.360346	+	0.932819i	$0.382659\pi$
$444$	2.75758	−	19.1794i	0.130869	−	0.910215i
$445$	15.3685	−	4.51259i	0.728535	−	0.213917i
$446$	26.1016	+	16.7745i	1.23595	+	0.794296i
$447$	0.791773	+	5.50690i	0.0374496	+	0.260468i
$448$	10.6146	+	23.2428i	0.501494	+	1.09812i
$449$	9.86776	+	21.6074i	0.465689	+	1.01972i	0.986154	+	0.165833i	$0.0530312\pi$
$449$	9.86776	+	21.6074i	0.465689	+	1.01972i	−0.520465	+	0.853883i	$0.674241\pi$
$450$	0.284918	+	1.98165i	0.0134312	+	0.0934157i
$451$	0.490847	+	0.315448i	0.0231131	+	0.0148539i
$452$	28.1522	−	8.26622i	1.32417	−	0.388810i
$453$	3.07036	−	21.3548i	0.144258	−	1.00334i
$454$	−4.18078	+	4.82488i	−0.196214	+	0.226443i
$455$	8.15953	−	5.24381i	0.382525	−	0.245834i
$456$	−0.0330460	−	0.0381371i	−0.00154752	−	0.00178593i
$457$	−29.8463	−	8.76366i	−1.39615	−	0.409947i	−0.504790	−	0.863242i	$-0.668430\pi$
$457$	−29.8463	−	8.76366i	−1.39615	−	0.409947i	−0.891360	+	0.453296i	$0.850248\pi$
$458$	7.62673	−	16.7002i	0.356374	−	0.780350i
$459$	−7.30528			−0.340981
$460$	−7.86648	+	5.55566i	−0.366777	+	0.259034i
$461$	−12.7086			−0.591900			−0.295950	−	0.955203i	$-0.595636\pi$
$461$	−12.7086			−0.591900			−0.295950	+	0.955203i	$0.595636\pi$
$462$	−0.380672	+	0.833555i	−0.0177105	+	0.0387805i
$463$	−33.4930	−	9.83445i	−1.55655	−	0.457045i	−0.613503	−	0.789693i	$-0.710240\pi$
$463$	−33.4930	−	9.83445i	−1.55655	−	0.457045i	−0.943051	+	0.332647i	$0.892058\pi$
$464$	−4.67629	−	5.39673i	−0.217091	−	0.250537i
$465$	8.54714	−	5.49291i	0.396364	−	0.254728i
$466$	10.2928	−	11.8785i	0.476805	−	0.550262i
$467$	2.09278	−	14.5556i	0.0968421	−	0.673552i	−0.882347	−	0.470600i	$-0.844037\pi$
$467$	2.09278	−	14.5556i	0.0968421	−	0.673552i	0.979189	−	0.202952i	$-0.0650535\pi$
$468$	−5.89835	+	1.73191i	−0.272651	+	0.0800576i
$469$	−1.34771	−	0.866122i	−0.0622315	−	0.0399938i
$470$	−1.49180	−	10.3757i	−0.0688118	−	0.478597i
$471$	−4.45406	−	9.75302i	−0.205232	−	0.449396i
$472$	−0.0178728	−	0.0391359i	−0.000822660	−	0.00180137i
$473$	0.0808341	+	0.562214i	0.00371676	+	0.0258506i
$474$	0.964647	+	0.619941i	0.0443077	+	0.0284748i
$475$	2.98523	−	0.876542i	0.136972	−	0.0402185i
$476$	−6.61467	+	46.0060i	−0.303183	+	2.10868i
$477$	7.27086	−	8.39101i	0.332910	−	0.384198i
$478$	3.41765	−	2.19639i	0.156320	−	0.100461i
$479$	−1.49091	−	1.72060i	−0.0681213	−	0.0786161i	0.720666	−	0.693282i	$-0.243836\pi$
$479$	−1.49091	−	1.72060i	−0.0681213	−	0.0786161i	−0.788787	+	0.614666i	$0.789291\pi$
$480$	7.68359	+	2.25610i	0.350706	+	0.102977i
$481$	−12.2709	+	26.8696i	−0.559507	+	1.22515i
$482$	−2.15777			−0.0982838
$483$	−6.91008	−	13.5328i	−0.314420	−	0.615765i
$484$	−22.0472			−1.00215
$485$	−3.12417	+	6.84098i	−0.141861	+	0.310633i
$486$	1.92093	+	0.564035i	0.0871351	+	0.0255852i
$487$	25.7440	+	29.7102i	1.16657	+	1.34630i	0.926839	+	0.375460i	$0.122515\pi$
$487$	25.7440	+	29.7102i	1.16657	+	1.34630i	0.239736	+	0.970838i	$0.422939\pi$
$488$	−0.0357790	+	0.0229938i	−0.00161964	+	0.00104088i
$489$	7.31727	−	8.44458i	0.330898	−	0.381877i
$490$	−0.865735	+	6.02132i	−0.0391099	+	0.272016i
$491$	−5.35356	+	1.57195i	−0.241603	+	0.0709410i	−0.400292	−	0.916388i	$-0.631091\pi$
$491$	−5.35356	+	1.57195i	−0.241603	+	0.0709410i	0.158689	+	0.987329i	$0.449273\pi$
$492$	−6.82288	−	4.38480i	−0.307599	−	0.197682i
$493$	−1.86359	−	12.9615i	−0.0839317	−	0.583758i
$494$	7.92118	+	17.3450i	0.356391	+	0.780387i
$495$	0.0600131	+	0.131410i	0.00269739	+	0.00590646i
$496$	−5.76015	−	40.0627i	−0.258638	−	1.79887i
$497$	−30.6511	−	19.6982i	−1.37489	−	0.883587i
$498$	−6.48145	+	1.90313i	−0.290441	+	0.0852812i
$499$	1.87481	−	13.0396i	0.0839279	−	0.583732i	−0.903848	−	0.427853i	$-0.859270\pi$
$499$	1.87481	−	13.0396i	0.0839279	−	0.583732i	0.987776	−	0.155879i	$-0.0498208\pi$
$500$	1.31503	−	1.51762i	0.0588098	−	0.0678701i
$501$	5.05060	−	3.24582i	0.225644	−	0.145013i
$502$	11.8236	+	13.6451i	0.527711	+	0.609012i
$503$	21.3992	+	6.28338i	0.954144	+	0.280162i	0.721511	−	0.692403i	$-0.243448\pi$
$503$	21.3992	+	6.28338i	0.954144	+	0.280162i	0.232633	+	0.972565i	$0.425266\pi$
$504$	0.0213477	−	0.0467450i	0.000950904	−	0.00208219i
$505$	10.3313			0.459736
$506$	−0.861667	+	1.08696i	−0.0383058	+	0.0483213i
$507$	−3.62857			−0.161151
$508$	10.3658	−	22.6979i	0.459907	−	1.00706i
$509$	42.2662	+	12.4105i	1.87342	+	0.550084i	0.997741	+	0.0671828i	$0.0214011\pi$
$509$	42.2662	+	12.4105i	1.87342	+	0.550084i	0.875675	+	0.482902i	$0.160417\pi$
$510$	9.57757	+	11.0531i	0.424102	+	0.489440i
$511$	−14.6749	+	9.43096i	−0.649177	+	0.417201i
$512$	20.9757	−	24.2073i	0.927005	−	1.06982i
$513$	0.442778	−	3.07959i	0.0195491	−	0.135967i
$514$	−39.8304	+	11.6953i	−1.75684	+	0.515856i
$515$	−11.3052	−	7.26543i	−0.498168	−	0.320153i
$516$	−1.12361	−	7.81490i	−0.0494643	−	0.344032i
$517$	−0.314223	−	0.688053i	−0.0138195	−	0.0302605i
$518$	−25.4261	−	55.6754i	−1.11716	−	2.44624i
$519$	−1.28476	−	8.93568i	−0.0563946	−	0.392233i
$520$	0.0417700	+	0.0268439i	0.00183173	+	0.00117718i
$521$	−0.121714	+	0.0357383i	−0.00533237	+	0.00156572i	−0.284398	−	0.958706i	$-0.591794\pi$
$521$	−0.121714	+	0.0357383i	−0.00533237	+	0.00156572i	0.279065	+	0.960272i	$0.409975\pi$
$522$	−0.510719	+	3.55213i	−0.0223536	+	0.155472i
$523$	10.4785	−	12.0929i	0.458194	−	0.528784i	−0.478896	−	0.877872i	$-0.658963\pi$
$523$	10.4785	−	12.0929i	0.458194	−	0.528784i	0.937090	+	0.349088i	$0.113508\pi$
$524$	37.4503	−	24.0679i	1.63603	−	1.05141i
$525$	2.07484	+	2.39449i	0.0905534	+	0.104504i
$526$	50.7924	+	14.9140i	2.21465	+	0.650281i
$527$	30.8328	−	67.5144i	1.34310	−	2.94097i
$528$	0.575511			0.0250459
$529$	−5.24821	−	22.3932i	−0.228183	−	0.973618i
$530$	−22.2283			−0.965535
$531$	1.10194	−	2.41291i	0.0478201	−	0.104711i
$532$	−18.9932	−	5.57691i	−0.823460	−	0.241790i
$533$	8.09669	+	9.34407i	0.350706	+	0.404737i
$534$	−26.9765	+	17.3367i	−1.16739	+	0.750233i
$535$	2.70473	−	3.12143i	0.116936	−	0.134951i
$536$	0.00116713	−	0.00811756i	5.04123e−5	−	0.000350625i
$537$	0.0338226	−	0.00993121i	0.00145955	−	0.000428563i
$538$	6.12165	+	3.93415i	0.263923	+	0.169613i
$539$	0.0624712	+	0.434497i	0.00269082	+	0.0187151i
$540$	−0.834196	−	1.82663i	−0.0358981	−	0.0786058i
$541$	−5.46011	−	11.9560i	−0.234748	−	0.514027i	0.755194	−	0.655502i	$-0.227543\pi$
$541$	−5.46011	−	11.9560i	−0.234748	−	0.514027i	−0.989942	+	0.141475i	$0.954816\pi$
$542$	0.0548254	+	0.381319i	0.00235495	+	0.0163790i
$543$	−14.7538	−	9.48166i	−0.633144	−	0.406897i
$544$	56.1308	−	16.4815i	2.40659	−	0.706638i
$545$	−2.07502	+	14.4321i	−0.0888842	+	0.618203i
$546$	−12.7162	+	14.6753i	−0.544202	+	0.628043i
$547$	−22.6407	+	14.5503i	−0.968046	+	0.622126i	−0.926214	−	0.376999i	$-0.876956\pi$
$547$	−22.6407	+	14.5503i	−0.968046	+	0.622126i	−0.0418326	+	0.999125i	$0.513320\pi$
$548$	−12.7586	−	14.7242i	−0.545021	−	0.628988i
$549$	−2.51599	−	0.738761i	−0.107380	−	0.0315296i
$550$	0.120148	−	0.263087i	0.00512311	−	0.0112181i
$551$	5.57696			0.237587
$552$	0.0483215	−	0.0609557i	0.00205670	−	0.00259445i
$553$	1.81471			0.0771694
$554$	−4.66591	+	10.2169i	−0.198235	+	0.434075i
$555$	−9.25837	−	2.71850i	−0.392996	−	0.115394i
$556$	14.6006	+	16.8500i	0.619205	+	0.714601i
$557$	34.8370	−	22.3884i	1.47609	−	0.948625i	0.478584	−	0.878042i	$-0.341150\pi$
$557$	34.8370	−	22.3884i	1.47609	−	0.948625i	0.997506	−	0.0705835i	$-0.0224861\pi$
$558$	−13.3202	+	15.3724i	−0.563891	+	0.650764i
$559$	−1.71291	+	11.9135i	−0.0724482	+	0.503889i
$560$	12.1106	−	3.55601i	0.511768	−	0.150269i
$561$	0.887826	+	0.570571i	0.0374840	+	0.0240895i
$562$	6.09272	+	42.3758i	0.257006	+	1.78751i
$563$	−1.83635	−	4.02104i	−0.0773927	−	0.169466i	0.866981	−	0.498342i	$-0.166058\pi$
$563$	−1.83635	−	4.02104i	−0.0773927	−	0.169466i	−0.944373	+	0.328876i	$0.893330\pi$
$564$	4.36777	+	9.56409i	0.183916	+	0.402721i
$565$	−2.07938	−	14.4624i	−0.0874803	−	0.608439i
$566$	1.78739	+	1.14869i	0.0751297	+	0.0482829i
$567$	3.04003	−	0.892632i	0.127669	−	0.0374870i
$568$	0.0265441	−	0.184618i	0.00111376	−	0.00774640i
$569$	−10.3320	+	11.9238i	−0.433140	+	0.499871i	−0.929795	−	0.368078i	$-0.880016\pi$
$569$	−10.3320	+	11.9238i	−0.433140	+	0.499871i	0.496655	+	0.867948i	$0.334562\pi$
$570$	−5.24001	+	3.36755i	−0.219480	+	0.141051i
$571$	−14.1857	−	16.3711i	−0.593652	−	0.685111i	0.376831	−	0.926282i	$-0.377014\pi$
$571$	−14.1857	−	16.3711i	−0.593652	−	0.685111i	−0.970483	+	0.241171i	$0.922468\pi$
$572$	0.852107	+	0.250201i	0.0356284	+	0.0104614i
$573$	−3.85105	+	8.43262i	−0.160880	+	0.352278i
$574$	−25.6189			−1.06931
$575$	2.18096	+	4.27123i	0.0909523	+	0.178123i
$576$	−8.06468			−0.336028
$577$	−0.639377	+	1.40004i	−0.0266176	+	0.0582844i	−0.922474	−	0.386060i	$-0.873836\pi$
$577$	−0.639377	+	1.40004i	−0.0266176	+	0.0582844i	0.895856	+	0.444344i	$0.146563\pi$
$578$	69.8587	+	20.5124i	2.90574	+	0.853202i
$579$	−9.85061	−	11.3682i	−0.409377	−	0.472447i
$580$	3.02813	−	1.94606i	0.125736	−	0.0808059i
$581$	−7.00077	+	8.07932i	−0.290441	+	0.335187i
$582$	2.14275	−	14.9032i	0.0888199	−	0.617756i
$583$	−1.53901	+	0.451895i	−0.0637394	+	0.0187156i
$584$	−0.0751230	−	0.0482786i	−0.00310861	−	0.00199778i
$585$	0.435665	+	3.03012i	0.0180125	+	0.125280i
$586$	−20.4309	−	44.7373i	−0.843991	−	1.84808i
$587$	8.19483	+	17.9442i	0.338237	+	0.740635i	0.999958	−	0.00911429i	$-0.00290121\pi$
$587$	8.19483	+	17.9442i	0.338237	+	0.740635i	−0.661722	+	0.749750i	$0.730174\pi$
$588$	−0.868363	−	6.03960i	−0.0358107	−	0.249069i
$589$	26.5923	+	17.0898i	1.09572	+	0.704175i
$590$	−5.09549	+	1.49617i	−0.209778	+	0.0615964i
$591$	−1.29891	+	9.03410i	−0.0534299	+	0.371613i
$592$	−25.1728	+	29.0510i	−1.03460	+	1.19399i
$593$	15.6893	−	10.0829i	0.644281	−	0.414054i	−0.177291	−	0.984158i	$-0.556734\pi$
$593$	15.6893	−	10.0829i	0.644281	−	0.414054i	0.821572	+	0.570104i	$0.193097\pi$
$594$	−0.189401	−	0.218580i	−0.00777122	−	0.00896846i
$595$	22.2082	+	6.52093i	0.910449	+	0.267332i
$596$	−4.64107	+	10.1625i	−0.190106	+	0.416274i
$597$	20.5078			0.839328
$598$	−24.0086	+	16.9559i	−0.981785	+	0.693380i
$599$	37.7276			1.54151			0.770753	−	0.637134i	$-0.219880\pi$
$599$	37.7276			1.54151			0.770753	+	0.637134i	$0.219880\pi$
$600$	−0.00673777	+	0.0147537i	−0.000275068	+	0.000602316i
$601$	−16.7824	−	4.92776i	−0.684568	−	0.201007i	−0.0790879	−	0.996868i	$-0.525201\pi$
$601$	−16.7824	−	4.92776i	−0.684568	−	0.201007i	−0.605480	+	0.795860i	$0.707019\pi$
$602$	−16.3318	−	18.8479i	−0.665635	−	0.768184i
$603$	0.425365	−	0.273365i	0.0173222	−	0.0111323i
$604$	28.3709	−	32.7418i	1.15440	−	1.33224i
$605$	−1.56249	+	10.8674i	−0.0635244	+	0.441822i
$606$	−19.8457	+	5.82721i	−0.806175	+	0.236714i
$607$	−15.4988	−	9.96049i	−0.629078	−	0.404284i	0.186890	−	0.982381i	$-0.440159\pi$
$607$	−15.4988	−	9.96049i	−0.629078	−	0.404284i	−0.815968	+	0.578097i	$0.803796\pi$
$608$	3.54575	+	24.6612i	0.143799	+	1.00014i
$609$	2.35928	+	5.16611i	0.0956029	+	0.209341i
$610$	2.18081	+	4.77532i	0.0882986	+	0.193347i
$611$	−2.28111	−	15.8654i	−0.0922836	−	0.641847i
$612$	−12.3410	−	7.93106i	−0.498854	−	0.320594i
$613$	−40.9929	+	12.0366i	−1.65569	+	0.486154i	−0.970276	−	0.242000i	$-0.922196\pi$
$613$	−40.9929	+	12.0366i	−1.65569	+	0.486154i	−0.685413	+	0.728155i	$0.740378\pi$
$614$	−4.53736	+	31.5580i	−0.183113	+	1.27358i
$615$	−2.64487	+	3.05234i	−0.106651	+	0.123082i
$616$	−0.00624540	+	0.00401368i	−0.000251634	+	0.000161716i
$617$	−14.6416	−	16.8973i	−0.589447	−	0.680258i	0.380161	−	0.924920i	$-0.375868\pi$
$617$	−14.6416	−	16.8973i	−0.589447	−	0.680258i	−0.969608	+	0.244662i	$0.921323\pi$
$618$	25.8145	+	7.57982i	1.03841	+	0.304905i
$619$	−10.7610	+	23.5634i	−0.432523	+	0.947093i	0.560388	+	0.828230i	$0.310652\pi$
$619$	−10.7610	+	23.5634i	−0.432523	+	0.947093i	−0.992911	+	0.118863i	$0.962075\pi$
$620$	20.4023			0.819376
$621$	4.79125	−	0.209538i	0.192266	−	0.00840848i
$622$	−2.34875			−0.0941764
$623$	−21.0817	+	46.1625i	−0.844622	+	1.84946i
$624$	11.7013	+	3.43582i	0.468428	+	0.137543i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	1.36232	−	0.875508i	0.0544491	−	0.0349923i
$627$	−0.294339	+	0.339686i	−0.0117548	+	0.0135657i
$628$	3.06415	−	21.3116i	0.122273	−	0.850425i
$629$	−67.6350	+	19.8594i	−2.69679	+	0.791848i
$630$	−5.33619	−	3.42936i	−0.212599	−	0.136629i
$631$	−0.761945	−	5.29944i	−0.0303325	−	0.210967i	0.969019	−	0.246988i	$-0.0794409\pi$
$631$	−0.761945	−	5.29944i	−0.0303325	−	0.210967i	−0.999351	+	0.0360207i	$0.988532\pi$
$632$	0.00385912	+	0.00845030i	0.000153508	+	0.000336135i
$633$	−6.51577	−	14.2675i	−0.258979	−	0.567084i
$634$	6.45877	+	44.9217i	0.256511	+	1.78407i
$635$	−10.4535	−	6.71805i	−0.414834	−	0.266598i
$636$	21.3926	−	6.28144i	0.848273	−	0.249075i
$637$	−1.32379	+	9.20715i	−0.0524504	+	0.364801i
$638$	0.339504	−	0.391808i	0.0134411	−	0.0155118i
$639$	9.67409	−	6.21716i	0.382701	−	0.245947i
$640$	0.0849708	+	0.0980615i	0.00335876	+	0.00387622i
$641$	−5.82223	−	1.70956i	−0.229964	−	0.0675236i	0.164720	−	0.986340i	$-0.447328\pi$
$641$	−5.82223	−	1.70956i	−0.229964	−	0.0675236i	−0.394684	+	0.918817i	$0.629146\pi$
$642$	−3.43500	+	7.52160i	−0.135569	+	0.296854i
$643$	−32.6471			−1.28747			−0.643737	−	0.765247i	$-0.722617\pi$
$643$	−32.6471			−1.28747			−0.643737	+	0.765247i	$0.722617\pi$
$644$	3.01871	−	30.3633i	0.118954	−	1.19648i
$645$	−3.93170			−0.154811
$646$	−18.9027	+	41.3912i	−0.743717	+	1.62851i
$647$	−1.13184	−	0.332339i	−0.0444973	−	0.0130656i	0.259408	−	0.965768i	$-0.416473\pi$
$647$	−1.13184	−	0.332339i	−0.0444973	−	0.0130656i	−0.303905	+	0.952702i	$0.598291\pi$
$648$	0.0106214	+	0.0122578i	0.000417249	+	0.000481531i
$649$	−0.322378	+	0.207180i	−0.0126545	+	0.00813253i
$650$	4.01348	−	4.63180i	0.157422	−	0.181674i
$651$	−4.58120	+	31.8629i	−0.179551	+	1.24881i
$652$	21.5292	−	6.32154i	0.843148	−	0.247571i
$653$	22.6864	+	14.5796i	0.887786	+	0.570545i	0.903144	−	0.429337i	$-0.141253\pi$
$653$	22.6864	+	14.5796i	0.887786	+	0.570545i	−0.0153589	+	0.999882i	$0.504889\pi$
$654$	−4.15425	−	28.8934i	−0.162444	−	1.12982i
$655$	−9.20927	−	20.1655i	−0.359836	−	0.787931i
$656$	6.68387	+	14.6356i	0.260961	+	0.571425i
$657$	−0.783541	−	5.44965i	−0.0305688	−	0.212611i
$658$	27.9398	+	17.9558i	1.08921	+	0.699992i
$659$	26.3213	−	7.72865i	1.02533	−	0.301065i	0.274522	−	0.961581i	$-0.411480\pi$
$659$	26.3213	−	7.72865i	1.02533	−	0.301065i	0.750812	+	0.660516i	$0.229662\pi$
$660$	−0.0412857	+	0.287148i	−0.00160704	+	0.0111772i
$661$	17.4697	−	20.1611i	0.679494	−	0.784177i	−0.306337	−	0.951923i	$-0.599103\pi$
$661$	17.4697	−	20.1611i	0.679494	−	0.784177i	0.985830	+	0.167746i	$0.0536488\pi$
$662$	20.0594	−	12.8914i	0.779629	−	0.501037i
$663$	14.6450	+	16.9012i	0.568764	+	0.656389i
$664$	−0.0525094	−	0.0154182i	−0.00203776	−	0.000598341i
$665$	−4.09499	+	8.96678i	−0.158797	+	0.347717i
$666$	19.3180			0.748558
$667$	1.59403	+	8.44751i	0.0617211	+	0.327089i
$668$	12.0560			0.466459
$669$	−6.43804	+	14.0973i	−0.248909	+	0.545035i
$670$	−0.971283	−	0.285194i	−0.0375239	−	0.0110180i
$671$	0.248073	+	0.286292i	0.00957676	+	0.0110522i
$672$	−21.3444	+	13.7172i	−0.823379	+	0.529154i
$673$	4.75919	−	5.49239i	0.183453	−	0.211716i	−0.656572	−	0.754263i	$-0.727994\pi$
$673$	4.75919	−	5.49239i	0.183453	−	0.211716i	0.840026	+	0.542547i	$0.182540\pi$
$674$	4.58991	−	31.9235i	0.176797	−	1.22965i
$675$	−0.959493	+	0.281733i	−0.0369309	+	0.0108439i
$676$	−6.12983	−	3.93940i	−0.235763	−	0.151515i
$677$	3.26168	+	22.6855i	0.125357	+	0.871874i	0.951332	+	0.308168i	$0.0997158\pi$
$677$	3.26168	+	22.6855i	0.125357	+	0.871874i	−0.825976	+	0.563706i	$0.809375\pi$
$678$	12.1517	+	26.6084i	0.466682	+	1.02189i
$679$	−9.89851	−	21.6747i	−0.379870	−	0.831799i
$680$	0.0168625	+	0.117281i	0.000646647	+	0.00449753i
$681$	−2.68266	−	1.72404i	−0.102800	−	0.0660654i
$682$	2.81948	−	0.827873i	0.107963	−	0.0317009i
$683$	−3.18544	+	22.1552i	−0.121887	+	0.847746i	0.833527	+	0.552479i	$0.186318\pi$
$683$	−3.18544	+	22.1552i	−0.121887	+	0.847746i	−0.955415	+	0.295268i	$0.904591\pi$
$684$	4.09138	−	4.72171i	0.156438	−	0.180539i
$685$	−8.16199	+	5.24539i	−0.311854	+	0.200416i
$686$	16.4554	+	18.9905i	0.628270	+	0.725062i
$687$	8.79891	+	2.58359i	0.335699	+	0.0985702i
$688$	−6.50658	+	14.2474i	−0.248061	+	0.543178i
$689$	−33.9891			−1.29488
$690$	−6.59859	−	6.97459i	−0.251204	−	0.265518i
$691$	15.8222			0.601905			0.300953	−	0.953639i	$-0.402695\pi$
$691$	15.8222			0.601905			0.300953	+	0.953639i	$0.402695\pi$
$692$	7.53075	−	16.4901i	0.286276	−	0.626858i
$693$	−0.439178	−	0.128954i	−0.0166830	−	0.00489857i
$694$	−30.1658	−	34.8132i	−1.14508	−	1.32149i
$695$	9.34038	−	6.00269i	0.354301	−	0.227695i
$696$	−0.0190391	+	0.0219722i	−0.000721674	+	0.000832856i
$697$	−4.19897	+	29.2045i	−0.159047	+	1.10620i
$698$	4.14806	−	1.21798i	0.157006	−	0.0461012i
$699$	6.60454	+	4.24448i	0.249807	+	0.160541i
$700$	0.905464	+	6.29764i	0.0342233	+	0.238028i
$701$	−2.59366	−	5.67933i	−0.0979613	−	0.214505i	0.854306	−	0.519770i	$-0.173982\pi$
$701$	−2.59366	−	5.67933i	−0.0979613	−	0.214505i	−0.952268	+	0.305265i	$0.901255\pi$
$702$	−2.54598	−	5.57491i	−0.0960917	−	0.210411i
$703$	−4.27247	−	29.7157i	−0.161139	−	1.12075i
$704$	0.980117	+	0.629883i	0.0369395	+	0.0237396i
$705$	5.02382	−	1.47513i	0.189208	−	0.0555565i
$706$	7.80599	−	54.2918i	0.293782	−	2.04330i
$707$	−21.4357	+	24.7382i	−0.806174	+	0.930375i
$708$	4.48113	−	2.87985i	0.168411	−	0.108231i
$709$	17.3477	+	20.0203i	0.651506	+	0.751878i	0.981365	−	0.192152i	$-0.0615466\pi$
$709$	17.3477	+	20.0203i	0.651506	+	0.751878i	−0.329859	+	0.944030i	$0.607001\pi$
$710$	−22.0899	−	6.48619i	−0.829020	−	0.243422i
$711$	−0.237933	+	0.521000i	−0.00892318	+	0.0195390i
$712$	−0.259790			−0.00973605
$713$	−18.2855	+	45.1645i	−0.684798	+	1.69142i
$714$	−46.3385			−1.73417
$715$	0.183717	−	0.402284i	0.00687062	−	0.0150446i
$716$	0.0679192	+	0.0199429i	0.00253826	+	0.000745300i
$717$	1.32886	+	1.53359i	0.0496273	+	0.0572730i
$718$	−32.6890	+	21.0079i	−1.21994	+	0.784010i
$719$	−33.2908	+	38.4197i	−1.24154	+	1.43281i	−0.380103	+	0.924944i	$0.624111\pi$
$719$	−33.2908	+	38.4197i	−1.24154	+	1.43281i	−0.861435	+	0.507867i	$0.830434\pi$
$720$	−0.566944	+	3.94318i	−0.0211288	+	0.146954i
$721$	40.8536	−	11.9957i	1.52147	−	0.446743i
$722$	15.6970	+	10.0878i	0.584182	+	0.375431i
$723$	−0.153386	−	1.06682i	−0.00570450	−	0.0396756i
$724$	−14.6300	−	32.0352i	−0.543718	−	1.19058i
$725$	−0.744637	−	1.63053i	−0.0276551	−	0.0605563i
$726$	−3.12815	−	21.7568i	−0.116097	−	0.807469i
$727$	14.0145	+	9.00654i	0.519767	+	0.334034i	0.774080	−	0.633088i	$-0.218213\pi$
$727$	14.0145	+	9.00654i	0.519767	+	0.334034i	−0.254313	+	0.967122i	$0.581849\pi$
$728$	−0.150943	+	0.0443210i	−0.00559434	+	0.00164265i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−7.21822	+	8.33026i	−0.267158	+	0.308317i
$731$	−24.1627	+	15.5284i	−0.893688	+	0.574338i
$732$	−3.44827	−	3.97952i	−0.127452	−	0.147087i
$733$	27.7841	+	8.15814i	1.02623	+	0.301328i	0.751176	−	0.660101i	$-0.229487\pi$
$733$	27.7841	+	8.15814i	1.02623	+	0.301328i	0.275052	+	0.961429i	$0.411305\pi$
$734$	−18.4791	+	40.4636i	−0.682076	+	1.49354i
$735$	−3.03854			−0.112078
$736$	−36.3413	+	12.4196i	−1.33956	+	0.457791i
$737$	−0.0730464			−0.00269070
$738$	3.35898	−	7.35513i	0.123646	−	0.270746i
$739$	−44.9513	−	13.1989i	−1.65356	−	0.485530i	−0.683818	−	0.729653i	$-0.739682\pi$
$739$	−44.9513	−	13.1989i	−1.65356	−	0.485530i	−0.969744	+	0.244123i	$0.921500\pi$
$740$	−12.6890	−	14.6439i	−0.466457	−	0.538320i
$741$	−8.01245	+	5.14929i	−0.294345	+	0.189164i
$742$	46.1201	−	53.2254i	1.69312	−	1.95397i
$743$	−0.0547942	+	0.381102i	−0.00201020	+	0.0139813i	−0.990802	−	0.135321i	$-0.956794\pi$
$743$	−0.0547942	+	0.381102i	−0.00201020	+	0.0139813i	0.988792	+	0.149302i	$0.0477026\pi$
$744$	−0.158114	+	0.0464264i	−0.00579673	+	0.00170207i
$745$	4.68034	+	3.00787i	0.171474	+	0.110200i
$746$	1.66694	+	11.5938i	0.0610309	+	0.424479i
$747$	−1.40166	−	3.06921i	−0.0512842	−	0.112297i
$748$	0.880377	+	1.92776i	0.0321898	+	0.0704858i
$749$	1.86235	+	12.9529i	0.0680487	+	0.473289i
$750$	1.68421	+	1.08238i	0.0614987	+	0.0395228i
$751$	38.6387	−	11.3453i	1.40995	−	0.413998i	0.513859	−	0.857875i	$-0.328215\pi$
$751$	38.6387	−	11.3453i	1.40995	−	0.413998i	0.896088	+	0.443877i	$0.146397\pi$
$752$	2.96847	−	20.6462i	0.108249	−	0.752888i
$753$	−5.90580	+	6.81566i	−0.215219	+	0.248377i
$754$	9.24190	−	5.93941i	0.336570	−	0.216301i
$755$	−14.1282	−	16.3048i	−0.514179	−	0.593394i
$756$	6.10468	+	1.79250i	0.222025	+	0.0651924i
$757$	20.3656	−	44.5944i	0.740200	−	1.62081i	−0.0430243	−	0.999074i	$-0.513699\pi$
$757$	20.3656	−	44.5944i	0.740200	−	1.62081i	0.783225	−	0.621739i	$-0.213573\pi$
$758$	−33.2206			−1.20662
$759$	−0.598656	−	0.348750i	−0.0217298	−	0.0126588i
$760$	−0.0504626			−0.00183047
$761$	15.9150	−	34.8489i	0.576917	−	1.26327i	−0.366115	−	0.930570i	$-0.619312\pi$
$761$	15.9150	−	34.8489i	0.576917	−	1.26327i	0.943032	−	0.332702i	$-0.107960\pi$
$762$	23.8696	+	7.00875i	0.864705	+	0.253900i
$763$	−30.2522	−	34.9129i	−1.09520	−	1.26393i
$764$	−15.6606	+	10.0645i	−0.566582	+	0.364120i
$765$	−4.78394	+	5.52096i	−0.172964	+	0.199611i
$766$	−4.17614	+	29.0457i	−0.150890	+	1.04946i
$767$	−7.79148	+	2.28778i	−0.281334	+	0.0826071i
$768$	13.3503	+	8.57975i	0.481739	+	0.309595i
$769$	−4.79239	−	33.3318i	−0.172818	−	1.20198i	−0.872895	−	0.487908i	$-0.837760\pi$
$769$	−4.79239	−	33.3318i	−0.172818	−	1.20198i	0.700077	−	0.714067i	$-0.253149\pi$
$770$	0.380672	+	0.833555i	0.0137185	+	0.0300392i
$771$	−8.61362	−	18.8612i	−0.310212	−	0.679269i
$772$	−4.29883	−	29.8990i	−0.154718	−	1.07609i
$773$	42.4037	+	27.2512i	1.52516	+	0.980158i	0.990865	+	0.134857i	$0.0430574\pi$
$773$	42.4037	+	27.2512i	1.52516	+	0.980158i	0.534290	+	0.845301i	$0.320579\pi$
$774$	7.55252	−	2.21762i	0.271470	−	0.0797107i
$775$	1.44592	−	10.0566i	0.0519389	−	0.361243i
$776$	0.0798795	−	0.0921859i	0.00286751	−	0.00330928i
$777$	25.7191	−	16.5286i	0.922666	−	0.592962i
$778$	−12.6063	−	14.5484i	−0.451957	−	0.521586i
$779$	−12.0568	−	3.54020i	−0.431980	−	0.126841i
$780$	−2.55371	+	5.59183i	−0.0914373	+	0.200220i
$781$	−1.66130			−0.0594458
$782$	−68.0987	−	16.8016i	−2.43520	−	0.600825i
$783$	−1.79251			−0.0640592
$784$	−5.02849	+	11.0109i	−0.179589	+	0.393245i
$785$	−10.2876	−	3.02072i	−0.367181	−	0.107814i
$786$	29.0644	+	33.5421i	1.03669	+	1.19641i
$787$	−19.0144	+	12.2198i	−0.677789	+	0.435589i	−0.833726	−	0.552178i	$-0.813797\pi$
$787$	−19.0144	+	12.2198i	−0.677789	+	0.435589i	0.155937	+	0.987767i	$0.450160\pi$
$788$	−12.0023	+	13.8513i	−0.427563	+	0.493433i
$789$	−3.76303	+	26.1724i	−0.133967	+	0.931764i
$790$	1.10023	−	0.323057i	0.0391444	−	0.0114938i
$791$	38.9446	+	25.0281i	1.38471	+	0.889898i
$792$	−0.000333463	−	0.00231929i	−1.18491e−5	−	8.24124e-5i
$793$	3.33466	+	7.30190i	0.118417	+	0.259298i
$794$	−25.8743	−	56.6568i	−0.918244	−	2.01067i
$795$	−1.58011	−	10.9899i	−0.0560407	−	0.389771i
$796$	34.6443	+	22.2645i	1.22793	+	0.789145i
$797$	−30.5818	+	8.97963i	−1.08326	+	0.318075i	−0.774183	−	0.632961i	$-0.781839\pi$
$797$	−30.5818	+	8.97963i	−1.08326	+	0.318075i	−0.309080	+	0.951036i	$0.600021\pi$
$798$	2.80860	−	19.5343i	0.0994235	−	0.691506i
$799$	25.0483	−	28.9073i	0.886145	−	1.02267i
$800$	6.73673	−	4.32943i	0.238179	−	0.153069i
$801$	−10.4891	−	12.1050i	−0.370614	−	0.427711i
$802$	16.6612	+	4.89217i	0.588327	+	0.172748i
$803$	−0.330413	+	0.723504i	−0.0116600	+	0.0255319i
$804$	1.01536			0.0358090
$805$	−14.7526	−	3.63982i	−0.519960	−	0.128287i
$806$	62.2681			2.19330
$807$	−1.50992	+	3.30627i	−0.0531518	+	0.116386i
$808$	−0.160779	−	0.0472091i	−0.00565620	−	0.00166081i
$809$	2.96061	+	3.41672i	0.104089	+	0.120126i	0.805404	−	0.592727i	$-0.201949\pi$
$809$	2.96061	+	3.41672i	0.104089	+	0.120126i	−0.701314	+	0.712852i	$0.747403\pi$
$810$	1.68421	−	1.08238i	0.0591771	−	0.0380308i
$811$	3.65249	−	4.21519i	0.128256	−	0.148016i	−0.687989	−	0.725721i	$-0.741506\pi$
$811$	3.65249	−	4.21519i	0.128256	−	0.148016i	0.816245	+	0.577706i	$0.196052\pi$
$812$	−1.62306	+	11.2886i	−0.0569581	+	0.396152i
$813$	−0.184631	+	0.0542124i	−0.00647528	+	0.00190131i
$814$	−2.34776	−	1.50881i	−0.0822888	−	0.0528838i
$815$	−1.59019	−	11.0600i	−0.0557021	−	0.387416i
$816$	12.0895	+	26.4724i	0.423218	+	0.926718i
$817$	−5.08158	−	11.1271i	−0.177782	−	0.389288i
$818$	−1.07515	−	7.47785i	−0.0375918	−	0.261457i
$819$	−8.15953	−	5.24381i	−0.285117	−	0.183234i
$820$	−7.78185	+	2.28496i	−0.271754	+	0.0797942i
$821$	5.62251	−	39.1055i	0.196227	−	1.36479i	−0.618883	−	0.785483i	$-0.712414\pi$
$821$	5.62251	−	39.1055i	0.196227	−	1.36479i	0.815110	−	0.579306i	$-0.196676\pi$
$822$	12.7200	−	14.6797i	0.443661	−	0.512012i
$823$	−8.92314	+	5.73455i	−0.311041	+	0.199894i	−0.686843	−	0.726806i	$-0.741004\pi$
$823$	−8.92314	+	5.73455i	−0.311041	+	0.199894i	0.375802	+	0.926700i	$0.377367\pi$
$824$	0.142737	+	0.164727i	0.00497247	+	0.00573854i
$825$	0.138614	+	0.0407006i	0.00482590	+	0.00141701i
$826$	6.98976	−	15.3054i	0.243205	−	0.532544i
$827$	26.0245			0.904960			0.452480	−	0.891775i	$-0.350539\pi$
$827$	26.0245			0.904960			0.452480	+	0.891775i	$0.350539\pi$
$828$	8.32146	+	4.84770i	0.289191	+	0.168469i
$829$	−37.9375			−1.31762			−0.658812	−	0.752308i	$-0.728941\pi$
$829$	−37.9375			−1.31762			−0.658812	+	0.752308i	$0.728941\pi$
$830$	−2.80616	+	6.14464i	−0.0974033	+	0.213284i
$831$	−5.38302	−	1.58060i	−0.186735	−	0.0548304i
$832$	16.1674	+	18.6581i	0.560502	+	0.646854i
$833$	−18.6737	+	12.0008i	−0.647004	+	0.415804i
$834$	−14.5565	+	16.7990i	−0.504049	+	0.581704i
$835$	0.854409	−	5.94255i	0.0295681	−	0.205650i
$836$	−0.866018	+	0.254286i	−0.0299519	+	0.00879466i
$837$	−8.54714	−	5.49291i	−0.295432	−	0.189863i
$838$	6.91874	+	48.1209i	0.239004	+	1.66231i
$839$	−20.2780	−	44.4026i	−0.700074	−	1.53295i	−0.839882	−	0.542769i	$-0.817376\pi$
$839$	−20.2780	−	44.4026i	−0.700074	−	1.53295i	0.139808	−	0.990179i	$-0.455352\pi$
$840$	−0.0213477	−	0.0467450i	−0.000736567	−	0.00161286i
$841$	3.66986	+	25.5244i	0.126547	+	0.880153i
$842$	−34.1621	−	21.9546i	−1.17730	−	0.756607i
$843$	−20.5179	+	6.02461i	−0.706675	+	0.207498i
$844$	4.48249	−	31.1764i	0.154294	−	1.07314i
$845$	−2.37621	+	2.74229i	−0.0817441	+	0.0943377i
$846$	−8.81837	+	5.66722i	−0.303182	+	0.194843i
$847$	−22.7799	−	26.2894i	−0.782727	−	0.903316i
$848$	−42.4393	−	12.4613i	−1.45737	−	0.427923i
$849$	−0.440865	+	0.965360i	−0.0151305	+	0.0331311i
$850$	14.6254			0.501645
$851$	43.7896	−	14.9650i	1.50109	−	0.512994i
$852$	23.0924			0.791132
$853$	13.1004	−	28.6858i	0.448548	−	0.982183i	−0.541402	−	0.840764i	$-0.682106\pi$
$853$	13.1004	−	28.6858i	0.448548	−	0.982183i	0.989950	−	0.141419i	$-0.0451665\pi$
$854$	−15.9593	−	4.68607i	−0.546116	−	0.160354i
$855$	−2.03744	−	2.35133i	−0.0696789	−	0.0804138i
$856$	−0.0563555	+	0.0362175i	−0.00192619	+	0.00123789i
$857$	−23.5728	+	27.2044i	−0.805230	+	0.929285i	−0.998656	−	0.0518297i	$-0.983495\pi$
$857$	−23.5728	+	27.2044i	−0.805230	+	0.929285i	0.193426	+	0.981115i	$0.438040\pi$
$858$	−0.126005	+	0.876381i	−0.00430172	+	0.0299192i
$859$	4.57211	−	1.34249i	0.155998	−	0.0458053i	−0.202801	−	0.979220i	$-0.565004\pi$
$859$	4.57211	−	1.34249i	0.155998	−	0.0458053i	0.358799	+	0.933415i	$0.383186\pi$
$860$	−6.64191	−	4.26850i	−0.226487	−	0.145555i
$861$	−1.82113	−	12.6662i	−0.0620640	−	0.431664i
$862$	28.0865	+	61.5008i	0.956630	+	2.09473i
$863$	−20.0987	−	44.0099i	−0.684166	−	1.49812i	−0.858167	−	0.513370i	$-0.828397\pi$
$863$	−20.0987	−	44.0099i	−0.684166	−	1.49812i	0.174001	−	0.984745i	$-0.444330\pi$
$864$	−1.13965	−	7.92646i	−0.0387718	−	0.269664i
$865$	−7.59447	−	4.88067i	−0.258220	−	0.165948i
$866$	−75.4268	+	22.1473i	−2.56311	+	0.752596i
$867$	−5.17559	+	35.9970i	−0.175772	+	1.22252i
$868$	−42.3315	+	48.8532i	−1.43682	+	1.65818i
$869$	0.0696086	−	0.0447348i	0.00236131	−	0.00151752i
$870$	2.35007	+	2.71212i	0.0796748	+	0.0919496i
$871$	−1.48518	−	0.436088i	−0.0503234	−	0.0147763i
$872$	0.0982402	−	0.215116i	0.00332683	−	0.00728475i
$873$	7.52060			0.254534
$874$	11.2103	−	27.6891i	0.379195	−	0.936596i
$875$	3.16837			0.107110
$876$	4.59282	−	10.0569i	0.155177	−	0.339790i
$877$	−45.9007	−	13.4777i	−1.54996	−	0.455108i	−0.608869	−	0.793271i	$-0.708377\pi$
$877$	−45.9007	−	13.4777i	−1.54996	−	0.455108i	−0.941088	+	0.338162i	$0.890195\pi$
$878$	−18.9191	−	21.8338i	−0.638487	−	0.736853i
$879$	20.6663	−	13.2814i	0.697056	−	0.447971i
$880$	0.376880	−	0.434942i	0.0127046	−	0.0146619i
$881$	−1.91542	+	13.3220i	−0.0645320	+	0.448830i	0.931780	+	0.363024i	$0.118256\pi$
$881$	−1.91542	+	13.3220i	−0.0645320	+	0.448830i	−0.996312	+	0.0858062i	$0.972653\pi$
$882$	5.83683	−	1.71385i	0.196536	−	0.0577082i
$883$	48.6049	+	31.2365i	1.63568	+	1.05119i	0.944499	+	0.328514i	$0.106548\pi$
$883$	48.6049	+	31.2365i	1.63568	+	1.05119i	0.691186	+	0.722677i	$0.257089\pi$
$884$	6.39110	+	44.4511i	0.214956	+	1.49505i
$885$	−1.10194	−	2.41291i	−0.0370413	−	0.0811090i
$886$	−16.4194	−	35.9534i	−0.551620	−	1.20788i
$887$	4.51924	+	31.4320i	0.151741	+	1.05538i	0.913300	+	0.407288i	$0.133525\pi$
$887$	4.51924	+	31.4320i	0.151741	+	1.05538i	−0.761559	+	0.648096i	$0.775566\pi$
$888$	0.131660	+	0.0846128i	0.00441822	+	0.00283942i
$889$	37.7756	−	11.0919i	1.26695	−	0.372011i
$890$	−4.56361	+	31.7406i	−0.152972	+	1.06395i
$891$	0.0946047	−	0.109180i	0.00316938	−	0.00365766i
$892$	−26.1809	+	16.8254i	−0.876601	+	0.563357i
$893$	10.6678	+	12.3114i	0.356986	+	0.411984i
$894$	−10.6871	−	3.13803i	−0.357432	−	0.104951i
$895$	0.0146436	−	0.0320650i	0.000489481	−	0.00107181i
$896$	−0.411108			−0.0137342
$897$	−10.0899	−	10.6648i	−0.336890	−	0.356087i
$898$	−47.5561			−1.58697
$899$	7.56551	−	16.5662i	0.252324	−	0.552512i
$900$	−1.92676	−	0.565748i	−0.0642253	−	0.0188583i
$901$	−53.1157	−	61.2987i	−1.76954	−	2.04216i
$902$	−0.982688	+	0.631535i	−0.0327199	+	0.0210278i
$903$	8.15765	−	9.41443i	0.271470	−	0.313293i
$904$	−0.0337263	+	0.234572i	−0.00112172	+	0.00780174i
$905$	−16.8274	+	4.94097i	−0.559362	+	0.164244i
$906$	36.3358	+	23.3516i	1.20718	+	0.775805i
$907$	8.08820	+	56.2547i	0.268564	+	1.86791i	0.462122	+	0.886816i	$0.347088\pi$
$907$	8.08820	+	56.2547i	0.268564	+	1.86791i	−0.193558	+	0.981089i	$0.562003\pi$
$908$	−2.66015	−	5.82493i	−0.0882803	−	0.193307i
$909$	−4.29177	−	9.39767i	−0.142349	−	0.311701i
$910$	2.76349	+	19.2205i	0.0916088	+	0.637153i
$911$	−26.9380	−	17.3120i	−0.892496	−	0.573572i	0.0120600	−	0.999927i	$-0.496161\pi$
$911$	−26.9380	−	17.3120i	−0.892496	−	0.573572i	−0.904556	+	0.426355i	$0.859797\pi$
$912$	−11.8923	+	3.49191i	−0.393795	+	0.115629i
$913$	−0.0693706	+	0.482483i	−0.00229583	+	0.0159679i
$914$	40.7818	−	47.0647i	1.34894	−	1.55676i
$915$	−2.20594	+	1.41767i	−0.0729262	+	0.0468668i
$916$	12.0593	+	13.9172i	0.398450	+	0.459836i
$917$	67.3938	+	19.7886i	2.22554	+	0.653478i
$918$	6.07559	−	13.3037i	0.200524	−	0.439087i
$919$	27.6087			0.910727			0.455363	−	0.890306i	$-0.349509\pi$
$919$	27.6087			0.910727			0.455363	+	0.890306i	$0.349509\pi$
$920$	−0.0144234	−	0.0764365i	−0.000475527	−	0.00252004i
$921$	−15.9251			−0.524751
$922$	10.5694	−	23.1437i	0.348085	−	0.762199i
$923$	−33.7775	−	9.91798i	−1.11180	−	0.326454i
$924$	−0.601913	−	0.694645i	−0.0198015	−	0.0228521i
$925$	−8.11745	+	5.21677i	−0.266900	+	0.171526i
$926$	45.7648	−	52.8153i	1.50392	−	1.73562i
$927$	−1.91251	+	13.3018i	−0.0628150	+	0.436888i
$928$	13.7729	−	4.04410i	0.452119	−	0.132754i
$929$	28.6574	+	18.4170i	0.940220	+	0.604242i	0.918457	−	0.395521i	$-0.129436\pi$
$929$	28.6574	+	18.4170i	0.940220	+	0.604242i	0.0217625	+	0.999763i	$0.493072\pi$
$930$	2.89476	+	20.1335i	0.0949231	+	0.660204i
$931$	−3.92720	−	8.59938i	−0.128709	−	0.281833i
$932$	6.54913	+	14.3406i	0.214524	+	0.469741i
$933$	−0.166962	−	1.16125i	−0.00546610	−	0.0380175i
$934$	24.7667	+	15.9166i	0.810393	+	0.520808i
$935$	1.01261	−	0.297329i	0.0331159	−	0.00972371i
$936$	0.00706622	−	0.0491467i	0.000230967	−	0.00160641i
$937$	−21.5400	+	24.8585i	−0.703680	+	0.812090i	−0.989245	−	0.146269i	$-0.953273\pi$
$937$	−21.5400	+	24.8585i	−0.703680	+	0.812090i	0.285564	+	0.958360i	$0.407819\pi$
$938$	2.69815	−	1.73400i	0.0880978	−	0.0566170i
$939$	0.529701	+	0.611308i	0.0172861	+	0.0199493i
$940$	10.0883	+	2.96220i	0.329045	+	0.0966164i
$941$	12.0322	−	26.3468i	0.392238	−	0.858882i	−0.605760	−	0.795647i	$-0.707131\pi$
$941$	12.0322	−	26.3468i	0.392238	−	0.858882i	0.997999	−	0.0632352i	$-0.0201418\pi$
$942$	21.4656			0.699387
$943$	1.91627	−	19.2745i	0.0624022	−	0.627665i
$944$	−10.5673			−0.343937
$945$	1.31619	−	2.88205i	0.0428156	−	0.0937530i
$946$	−1.09108	−	0.320369i	−0.0354740	−	0.0104161i
$947$	9.44791	+	10.9035i	0.307016	+	0.354315i	0.888200	−	0.459457i	$-0.151956\pi$
$947$	9.44791	+	10.9035i	0.307016	+	0.354315i	−0.581184	+	0.813772i	$0.697410\pi$
$948$	−0.967576	+	0.621823i	−0.0314254	+	0.0201959i
$949$	−11.0373	+	12.7377i	−0.358286	+	0.413485i
$950$	−0.886452	+	6.16541i	−0.0287603	+	0.200032i
$951$	−21.7506	+	6.38656i	−0.705313	+	0.207099i
$952$	−0.315816	−	0.202962i	−0.0102356	−	0.00657805i
$953$	−1.07089	−	7.44822i	−0.0346896	−	0.241272i	0.965098	−	0.261890i	$-0.0843457\pi$
$953$	−1.07089	−	7.44822i	−0.0346896	−	0.241272i	−0.999787	+	0.0206181i	$0.993437\pi$
$954$	9.23396	+	20.2196i	0.298961	+	0.654632i
$955$	3.85105	+	8.43262i	0.124617	+	0.272873i
$956$	0.579919	+	4.03343i	0.0187559	+	0.130450i
$957$	0.217848	+	0.140002i	0.00704202	+	0.00452563i
$958$	4.37333	−	1.28413i	0.141296	−	0.0414883i
$959$	4.37476	−	30.4271i	0.141268	−	0.982544i
$960$	−5.28124	+	6.09488i	−0.170451	+	0.196711i
$961$	60.7600	−	39.0481i	1.96000	−	1.25962i
$962$	−38.7270	−	44.6934i	−1.24861	−	1.44097i
$963$	−3.96293	−	1.16362i	−0.127704	−	0.0374972i
$964$	0.899092	−	1.96874i	0.0289578	−	0.0634087i
$965$	−15.0423			−0.484229
$966$	30.3916	−	1.32913i	0.977834	−	0.0427641i
$967$	−0.625139			−0.0201031			−0.0100516	−	0.999949i	$-0.503200\pi$
$967$	−0.625139			−0.0201031			−0.0100516	+	0.999949i	$0.503200\pi$
$968$	0.0739749	−	0.161982i	0.00237764	−	0.00520631i
$969$	−21.8079	−	6.40339i	−0.700572	−	0.205706i
$970$	−9.85986	−	11.3789i	−0.316581	−	0.365354i
$971$	23.8450	−	15.3243i	0.765223	−	0.491779i	−0.0988769	−	0.995100i	$-0.531525\pi$
$971$	23.8450	−	15.3243i	0.765223	−	0.491779i	0.864100	+	0.503321i	$0.167889\pi$
$972$	−1.31503	+	1.51762i	−0.0421795	+	0.0486777i
$973$	−5.00637	+	34.8201i	−0.160497	+	1.11628i
$974$	−75.5160	+	22.1735i	−2.41969	+	0.710485i
$975$	2.57531	+	1.65505i	0.0824760	+	0.0530041i
$976$	1.48665	+	10.3398i	0.0475864	+	0.330970i
$977$	−14.1024	−	30.8800i	−0.451177	−	0.987939i	−0.989411	−	0.145144i	$-0.953636\pi$
$977$	−14.1024	−	30.8800i	−0.451177	−	0.987939i	0.538234	−	0.842795i	$-0.319092\pi$
$978$	9.29291	+	20.3486i	0.297154	+	0.650677i
$979$	0.329308	+	2.29039i	0.0105247	+	0.0732012i
$980$	−5.13308	−	3.29883i	−0.163970	−	0.105377i
$981$	13.9899	−	4.10780i	0.446663	−	0.131152i
$982$	1.58972	−	11.0567i	0.0507300	−	0.352835i
$983$	23.5142	−	27.1369i	0.749987	−	0.865531i	−0.244580	−	0.969629i	$-0.578650\pi$
$983$	23.5142	−	27.1369i	0.749987	−	0.865531i	0.994567	+	0.104098i	$0.0331955\pi$
$984$	0.0551082	−	0.0354159i	0.00175679	−	0.00112902i
$985$	5.97692	+	6.89773i	0.190440	+	0.219780i
$986$	25.1542	+	7.38594i	0.801073	+	0.235216i
$987$	−6.89144	+	15.0901i	−0.219357	+	0.480325i
$988$	−19.1260			−0.608479
$989$	15.4019	−	10.8775i	0.489753	−	0.345885i
$990$	−0.289223			−0.00919212
$991$	−5.29050	+	11.5846i	−0.168058	+	0.367996i	−0.974857	−	0.222830i	$-0.928471\pi$
$991$	−5.29050	+	11.5846i	−0.168058	+	0.367996i	0.806799	+	0.590826i	$0.201198\pi$
$992$	78.0652	+	22.9220i	2.47857	+	0.727775i
$993$	7.79956	+	9.00117i	0.247511	+	0.285643i
$994$	61.3642	−	39.4363i	1.94635	−	1.25084i
$995$	13.4298	−	15.4988i	0.425752	−	0.491344i
$996$	0.964267	−	6.70662i	0.0305540	−	0.212507i
$997$	16.3397	−	4.79778i	0.517485	−	0.151947i	−0.0125530	−	0.999921i	$-0.503996\pi$
$997$	16.3397	−	4.79778i	0.517485	−	0.151947i	0.530038	+	0.847974i	$0.322178\pi$
$998$	22.1872	+	14.2589i	0.702324	+	0.451356i
$999$	1.37323	+	9.55102i	0.0434471	+	0.302181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.c.121.1	✓	50
23.2	even	11		7935.2.a.bv.1.4		25
23.4	even	11	inner	345.2.m.c.211.1	yes	50
23.21	odd	22		7935.2.a.bw.1.4		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.121.1	✓	50	1.1	even	1	trivial
345.2.m.c.211.1	yes	50	23.4	even	11	inner
7935.2.a.bv.1.4		25	23.2	even	11
7935.2.a.bw.1.4		25	23.21	odd	22

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.831671 + 1.82111i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.31503 - 1.51762i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(1.31105 - 1.51303i) q^{6} +(0.450906 - 3.13612i) q^{7} +(0.0155624 - 0.00456953i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.831671 + 1.82111i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.31503 - 1.51762i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(1.31105 - 1.51303i) q^{6} +(0.450906 - 3.13612i) q^{7} +(0.0155624 - 0.00456953i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.284918 - 1.98165i) q^{10} +(-0.0600131 - 0.131410i) q^{11} +(0.834196 + 1.82663i) q^{12} +(-0.435665 - 3.03012i) q^{13} +(5.33619 + 3.42936i) q^{14} +(0.959493 - 0.281733i) q^{15} +(0.566944 - 3.94318i) q^{16} +(4.78394 - 5.52096i) q^{17} +(-1.68421 + 1.08238i) q^{18} +(2.03744 + 2.35133i) q^{19} +(1.92676 + 0.565748i) q^{20} +(-1.31619 + 2.88205i) q^{21} +0.289223 q^{22} +(-2.97924 + 3.75820i) q^{23} -0.0162194 q^{24} +(0.415415 - 0.909632i) q^{25} +(5.88050 + 1.72667i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-5.35239 + 3.43977i) q^{28} +(1.17385 - 1.35469i) q^{29} +(-0.284918 + 1.98165i) q^{30} +(9.74845 - 2.86240i) q^{31} +(6.73673 + 4.32943i) q^{32} +(0.0205596 + 0.142995i) q^{33} +(6.07559 + 13.3037i) q^{34} +(1.31619 + 2.88205i) q^{35} +(-0.285783 - 1.98766i) q^{36} +(-8.11745 - 5.21677i) q^{37} +(-5.97650 + 1.75486i) q^{38} +(-0.435665 + 3.03012i) q^{39} +(-0.0106214 + 0.0122578i) q^{40} +(-3.39768 + 2.18356i) q^{41} +(-4.15388 - 4.79383i) q^{42} +(-3.77244 - 1.10769i) q^{43} +(-0.120512 + 0.263885i) q^{44} -1.00000 q^{45} +(-4.36634 - 8.55111i) q^{46} +5.23591 q^{47} +(-1.65490 + 3.62373i) q^{48} +(-2.91546 - 0.856057i) q^{49} +(1.31105 + 1.51303i) q^{50} +(-6.14559 + 3.94953i) q^{51} +(-4.02566 + 4.64586i) q^{52} +(1.58011 - 10.9899i) q^{53} +(1.92093 - 0.564035i) q^{54} +(0.121532 + 0.0781039i) q^{55} +(-0.00731341 - 0.0508659i) q^{56} +(-1.29246 - 2.83010i) q^{57} +(1.49078 + 3.26436i) q^{58} +(-0.377507 - 2.62562i) q^{59} +(-1.68932 - 1.08566i) q^{60} +(-2.51599 + 0.738761i) q^{61} +(-2.89476 + 20.1335i) q^{62} +(2.07484 - 2.39449i) q^{63} +(-6.78444 + 4.36010i) q^{64} +(2.00471 + 2.31356i) q^{65} +(-0.277508 - 0.0814836i) q^{66} +(0.210047 - 0.459939i) q^{67} -14.6697 q^{68} +(3.91737 - 2.76662i) q^{69} -6.34315 q^{70} +(4.77711 - 10.4604i) q^{71} +(0.0155624 + 0.00456953i) q^{72} +(-3.60546 - 4.16092i) q^{73} +(16.2513 - 10.4441i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.889143 - 6.18412i) q^{76} +(-0.439178 + 0.128954i) q^{77} +(-5.15584 - 3.31345i) q^{78} +(0.0815122 + 0.566930i) q^{79} +(1.65490 + 3.62373i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-1.15073 - 8.00353i) q^{82} +(-2.83850 - 1.82419i) q^{83} +(6.10468 - 1.79250i) q^{84} +(-1.03965 + 7.23093i) q^{85} +(5.15465 - 5.94878i) q^{86} +(-1.50796 + 0.969106i) q^{87} +(-0.00153443 - 0.00177083i) q^{88} +(-15.3685 - 4.51259i) q^{89} +(0.831671 - 1.82111i) q^{90} -9.69925 q^{91} +(9.62132 - 0.420774i) q^{92} -10.1600 q^{93} +(-4.35456 + 9.53515i) q^{94} +(-2.98523 - 0.876542i) q^{95} +(-5.24410 - 6.05202i) q^{96} +(6.32673 - 4.06594i) q^{97} +(3.98367 - 4.59741i) q^{98} +(0.0205596 - 0.142995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Introduction

L-functions

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