LMFDB - Embedded newform 93.2.m.b.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(7,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 28]))

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

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

chi := DirichletCharacter("93.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.m (of order $15$, degree $8$, 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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			82.1
Character	$\chi$	$=$	93.82
Dual form			93.2.m.b.76.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.418031 - 1.28657i) q^{2} +(0.669131 + 0.743145i) q^{3} +(0.137526 - 0.0999185i) q^{4} +(1.63328 + 2.82893i) q^{5} +(0.676389 - 1.17154i) q^{6} +(-0.149090 - 1.41850i) q^{7} +(-2.37488 - 1.72545i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.418031 - 1.28657i) q^{2} +(0.669131 + 0.743145i) q^{3} +(0.137526 - 0.0999185i) q^{4} +(1.63328 + 2.82893i) q^{5} +(0.676389 - 1.17154i) q^{6} +(-0.149090 - 1.41850i) q^{7} +(-2.37488 - 1.72545i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(2.95685 - 3.28391i) q^{10} +(-4.38826 - 1.95378i) q^{11} +(0.166277 + 0.0353432i) q^{12} +(3.02956 - 0.643952i) q^{13} +(-1.76267 + 0.784793i) q^{14} +(-1.00942 + 3.10669i) q^{15} +(-1.12208 + 3.45340i) q^{16} +(-3.32456 + 1.48019i) q^{17} +(1.32322 - 0.281258i) q^{18} +(-3.39558 - 0.721752i) q^{19} +(0.507281 + 0.225856i) q^{20} +(0.954391 - 1.05996i) q^{21} +(-0.679240 + 6.46254i) q^{22} +(6.09693 + 4.42968i) q^{23} +(-0.306845 - 2.91944i) q^{24} +(-2.83523 + 4.91076i) q^{25} +(-2.09494 - 3.62854i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.162238 - 0.180184i) q^{28} +(-0.609968 - 1.87729i) q^{29} +4.41894 q^{30} +(-4.70038 - 2.98436i) q^{31} -0.958934 q^{32} +(-1.48438 - 4.56845i) q^{33} +(3.29413 + 3.65850i) q^{34} +(3.76933 - 2.73858i) q^{35} +(0.0849957 + 0.147217i) q^{36} +(-4.53564 + 7.85596i) q^{37} +(0.490874 + 4.67035i) q^{38} +(2.50572 + 1.82051i) q^{39} +(1.00233 - 9.53653i) q^{40} +(3.43795 - 3.81823i) q^{41} +(-1.76267 - 0.784793i) q^{42} +(4.10301 + 0.872121i) q^{43} +(-0.798719 + 0.169773i) q^{44} +(-2.98416 + 1.32863i) q^{45} +(3.15038 - 9.69586i) q^{46} +(3.27633 - 10.0835i) q^{47} +(-3.31719 + 1.47691i) q^{48} +(4.85712 - 1.03241i) q^{49} +(7.50325 + 1.59486i) q^{50} +(-3.32456 - 1.48019i) q^{51} +(0.352300 - 0.391269i) q^{52} +(-0.0300848 + 0.286238i) q^{53} +(1.09442 + 0.795143i) q^{54} +(-1.64017 - 15.6052i) q^{55} +(-2.09349 + 3.62602i) q^{56} +(-1.73572 - 3.00635i) q^{57} +(-2.16027 + 1.56953i) q^{58} +(2.55052 + 2.83264i) q^{59} +(0.171594 + 0.528111i) q^{60} -6.98631 q^{61} +(-1.87468 + 7.29492i) q^{62} +1.42631 q^{63} +(2.64502 + 8.14054i) q^{64} +(6.76982 + 7.51865i) q^{65} +(-5.25710 + 3.81951i) q^{66} +(4.01427 + 6.95292i) q^{67} +(-0.309315 + 0.535749i) q^{68} +(0.787750 + 7.49494i) q^{69} +(-5.09907 - 3.70469i) q^{70} +(1.00247 - 9.53784i) q^{71} +(1.96424 - 2.18151i) q^{72} +(10.4141 + 4.63666i) q^{73} +(12.0033 + 2.55137i) q^{74} +(-5.54655 + 1.17895i) q^{75} +(-0.539096 + 0.240021i) q^{76} +(-2.11719 + 6.51605i) q^{77} +(1.29474 - 3.98481i) q^{78} +(-8.15681 + 3.63165i) q^{79} +(-11.6021 + 2.46610i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-6.34959 - 2.82702i) q^{82} +(-4.38393 + 4.86884i) q^{83} +(0.0253441 - 0.241133i) q^{84} +(-9.61729 - 6.98737i) q^{85} +(-0.593142 - 5.64337i) q^{86} +(0.986948 - 1.70944i) q^{87} +(7.05045 + 12.2117i) q^{88} +(-1.18956 + 0.864265i) q^{89} +(2.95685 + 3.28391i) q^{90} +(-1.36513 - 4.20142i) q^{91} +1.28109 q^{92} +(-0.927353 - 5.48999i) q^{93} -14.3427 q^{94} +(-3.50415 - 10.7847i) q^{95} +(-0.641652 - 0.712627i) q^{96} +(7.55896 - 5.49190i) q^{97} +(-3.35870 - 5.81743i) q^{98} +(2.40178 - 4.16000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.418031	−	1.28657i	−0.295593	−	0.909741i	−0.983022	−	0.183489i	$-0.941261\pi$
$2$	−0.418031	−	1.28657i	−0.295593	−	0.909741i	0.687429	−	0.726252i	$-0.258739\pi$
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$4$	0.137526	−	0.0999185i	0.0687630	−	0.0499592i
$5$	1.63328	+	2.82893i	0.730427	+	1.26514i	0.956701	+	0.291072i	$0.0940120\pi$
$5$	1.63328	+	2.82893i	0.730427	+	1.26514i	−0.226274	+	0.974064i	$0.572655\pi$
$6$	0.676389	−	1.17154i	0.276135	−	0.478279i
$7$	−0.149090	−	1.41850i	−0.0563509	−	0.536143i	−0.985887	−	0.167412i	$-0.946459\pi$
$7$	−0.149090	−	1.41850i	−0.0563509	−	0.536143i	0.929536	−	0.368731i	$-0.120208\pi$
$8$	−2.37488	−	1.72545i	−0.839648	−	0.610040i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	2.95685	−	3.28391i	0.935038	−	1.03846i
$11$	−4.38826	−	1.95378i	−1.32311	−	0.589087i	−0.381058	−	0.924551i	$-0.624440\pi$
$11$	−4.38826	−	1.95378i	−1.32311	−	0.589087i	−0.942053	+	0.335464i	$0.891107\pi$
$12$	0.166277	+	0.0353432i	0.0480000	+	0.0102027i
$13$	3.02956	−	0.643952i	0.840248	−	0.178600i	0.232367	−	0.972628i	$-0.425353\pi$
$13$	3.02956	−	0.643952i	0.840248	−	0.178600i	0.607881	+	0.794028i	$0.292020\pi$
$14$	−1.76267	+	0.784793i	−0.471094	+	0.209745i
$15$	−1.00942	+	3.10669i	−0.260632	+	0.802144i
$16$	−1.12208	+	3.45340i	−0.280519	+	0.863350i
$17$	−3.32456	+	1.48019i	−0.806323	+	0.358998i	−0.768148	−	0.640273i	$-0.778821\pi$
$17$	−3.32456	+	1.48019i	−0.806323	+	0.358998i	−0.0381758	+	0.999271i	$0.512155\pi$
$18$	1.32322	−	0.281258i	0.311885	−	0.0662932i
$19$	−3.39558	−	0.721752i	−0.778998	−	0.165581i	−0.198782	−	0.980044i	$-0.563699\pi$
$19$	−3.39558	−	0.721752i	−0.778998	−	0.165581i	−0.580216	+	0.814462i	$0.697032\pi$
$20$	0.507281	+	0.225856i	0.113432	+	0.0505030i
$21$	0.954391	−	1.05996i	0.208265	−	0.231302i
$22$	−0.679240	+	6.46254i	−0.144815	+	1.37782i
$23$	6.09693	+	4.42968i	1.27130	+	0.923652i	0.999253	−	0.0386325i	$-0.0123002\pi$
$23$	6.09693	+	4.42968i	1.27130	+	0.923652i	0.272045	+	0.962285i	$0.412300\pi$
$24$	−0.306845	−	2.91944i	−0.0626345	−	0.595927i
$25$	−2.83523	+	4.91076i	−0.567046	+	0.982153i
$26$	−2.09494	−	3.62854i	−0.410851	−	0.711615i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−0.162238	−	0.180184i	−0.0306602	−	0.0340515i
$29$	−0.609968	−	1.87729i	−0.113268	−	0.348604i	0.878314	−	0.478085i	$-0.158669\pi$
$29$	−0.609968	−	1.87729i	−0.113268	−	0.348604i	−0.991582	+	0.129481i	$0.958669\pi$
$30$	4.41894			0.806784
$31$	−4.70038	−	2.98436i	−0.844213	−	0.536008i
$31$	−4.70038	−	2.98436i	−0.844213	−	0.536008i
$32$	−0.958934			−0.169517
$33$	−1.48438	−	4.56845i	−0.258397	−	0.795265i
$34$	3.29413	+	3.65850i	0.564939	+	0.627428i
$35$	3.76933	−	2.73858i	0.637134	−	0.462905i
$36$	0.0849957	+	0.147217i	0.0141660	+	0.0245362i
$37$	−4.53564	+	7.85596i	−0.745654	+	1.29151i	0.204234	+	0.978922i	$0.434530\pi$
$37$	−4.53564	+	7.85596i	−0.745654	+	1.29151i	−0.949888	+	0.312589i	$0.898804\pi$
$38$	0.490874	+	4.67035i	0.0796303	+	0.757632i
$39$	2.50572	+	1.82051i	0.401236	+	0.291515i
$40$	1.00233	−	9.53653i	0.158482	−	1.50786i
$41$	3.43795	−	3.81823i	0.536918	−	0.596308i	−0.412253	−	0.911070i	$-0.635258\pi$
$41$	3.43795	−	3.81823i	0.536918	−	0.596308i	0.949171	+	0.314762i	$0.101925\pi$
$42$	−1.76267	−	0.784793i	−0.271987	−	0.121096i
$43$	4.10301	+	0.872121i	0.625703	+	0.132997i	0.509842	−	0.860268i	$-0.329704\pi$
$43$	4.10301	+	0.872121i	0.625703	+	0.132997i	0.115861	+	0.993265i	$0.463037\pi$
$44$	−0.798719	+	0.169773i	−0.120411	+	0.0255942i
$45$	−2.98416	+	1.32863i	−0.444852	+	0.198061i
$46$	3.15038	−	9.69586i	0.464498	−	1.42958i
$47$	3.27633	−	10.0835i	0.477901	−	1.47083i	−0.364104	−	0.931358i	$-0.618625\pi$
$47$	3.27633	−	10.0835i	0.477901	−	1.47083i	0.842005	−	0.539470i	$-0.181375\pi$
$48$	−3.31719	+	1.47691i	−0.478796	+	0.213174i
$49$	4.85712	−	1.03241i	0.693874	−	0.147487i
$50$	7.50325	+	1.59486i	1.06112	+	0.225548i
$51$	−3.32456	−	1.48019i	−0.465531	−	0.207268i
$52$	0.352300	−	0.391269i	0.0488552	−	0.0542592i
$53$	−0.0300848	+	0.286238i	−0.00413247	+	0.0393178i	−0.996394	−	0.0848491i	$-0.972959\pi$
$53$	−0.0300848	+	0.286238i	−0.00413247	+	0.0393178i	0.992261	+	0.124167i	$0.0396258\pi$
$54$	1.09442	+	0.795143i	0.148932	+	0.108205i
$55$	−1.64017	−	15.6052i	−0.221160	−	2.10420i
$56$	−2.09349	+	3.62602i	−0.279754	+	0.484548i
$57$	−1.73572	−	3.00635i	−0.229901	−	0.398201i
$58$	−2.16027	+	1.56953i	−0.283658	+	0.206089i
$59$	2.55052	+	2.83264i	0.332050	+	0.368779i	0.885931	−	0.463817i	$-0.153520\pi$
$59$	2.55052	+	2.83264i	0.332050	+	0.368779i	−0.553881	+	0.832596i	$0.686854\pi$
$60$	0.171594	+	0.528111i	0.0221526	+	0.0681788i
$61$	−6.98631			−0.894505			−0.447252	−	0.894408i	$-0.647597\pi$
$61$	−6.98631			−0.894505			−0.447252	+	0.894408i	$0.647597\pi$
$62$	−1.87468	+	7.29492i	−0.238085	+	0.926456i
$63$	1.42631			0.179699
$64$	2.64502	+	8.14054i	0.330628	+	1.01757i
$65$	6.76982	+	7.51865i	0.839693	+	0.932574i
$66$	−5.25710	+	3.81951i	−0.647105	+	0.470149i
$67$	4.01427	+	6.95292i	0.490421	+	0.849435i	0.999939	−	0.0110253i	$-0.00350955\pi$
$67$	4.01427	+	6.95292i	0.490421	+	0.849435i	−0.509518	+	0.860460i	$0.670176\pi$
$68$	−0.309315	+	0.535749i	−0.0375099	+	0.0649691i
$69$	0.787750	+	7.49494i	0.0948339	+	0.902284i
$70$	−5.09907	−	3.70469i	−0.609456	−	0.442795i
$71$	1.00247	−	9.53784i	0.118971	−	1.13193i	−0.758289	−	0.651918i	$-0.773964\pi$
$71$	1.00247	−	9.53784i	0.118971	−	1.13193i	0.877260	−	0.480015i	$-0.159369\pi$
$72$	1.96424	−	2.18151i	0.231488	−	0.257094i
$73$	10.4141	+	4.63666i	1.21888	+	0.542680i	0.912440	−	0.409210i	$-0.134196\pi$
$73$	10.4141	+	4.63666i	1.21888	+	0.542680i	0.306439	+	0.951890i	$0.400862\pi$
$74$	12.0033	+	2.55137i	1.39535	+	0.296591i
$75$	−5.54655	+	1.17895i	−0.640460	+	0.136134i
$76$	−0.539096	+	0.240021i	−0.0618386	+	0.0275323i
$77$	−2.11719	+	6.51605i	−0.241276	+	0.742572i
$78$	1.29474	−	3.98481i	0.146601	−	0.451191i
$79$	−8.15681	+	3.63165i	−0.917713	+	0.408592i	−0.810563	−	0.585651i	$-0.800839\pi$
$79$	−8.15681	+	3.63165i	−0.917713	+	0.408592i	−0.107149	+	0.994243i	$0.534172\pi$
$80$	−11.6021	+	2.46610i	−1.29715	+	0.275719i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−6.34959	−	2.82702i	−0.701195	−	0.312192i
$83$	−4.38393	+	4.86884i	−0.481198	+	0.534425i	−0.934041	−	0.357165i	$-0.883743\pi$
$83$	−4.38393	+	4.86884i	−0.481198	+	0.534425i	0.452843	+	0.891590i	$0.350410\pi$
$84$	0.0253441	−	0.241133i	0.00276527	−	0.0263098i
$85$	−9.61729	−	6.98737i	−1.04314	−	0.757887i
$86$	−0.593142	−	5.64337i	−0.0639602	−	0.608541i
$87$	0.986948	−	1.70944i	0.105812	−	0.183272i
$88$	7.05045	+	12.2117i	0.751581	+	1.30178i
$89$	−1.18956	+	0.864265i	−0.126093	+	0.0916119i	−0.649044	−	0.760751i	$-0.724831\pi$
$89$	−1.18956	+	0.864265i	−0.126093	+	0.0916119i	0.522951	+	0.852363i	$0.324831\pi$
$90$	2.95685	+	3.28391i	0.311679	+	0.346155i
$91$	−1.36513	−	4.20142i	−0.143104	−	0.440429i
$92$	1.28109			0.133563
$93$	−0.927353	−	5.48999i	−0.0961620	−	0.569286i
$94$	−14.3427			−1.47934
$95$	−3.50415	−	10.7847i	−0.359518	−	1.10648i
$96$	−0.641652	−	0.712627i	−0.0654884	−	0.0727322i
$97$	7.55896	−	5.49190i	0.767496	−	0.557618i	−0.133704	−	0.991021i	$-0.542687\pi$
$97$	7.55896	−	5.49190i	0.767496	−	0.557618i	0.901200	+	0.433403i	$0.142687\pi$
$98$	−3.35870	−	5.81743i	−0.339279	−	0.587649i
$99$	2.40178	−	4.16000i	0.241388	−	0.418095i
$100$	0.100758	+	0.958649i	0.0100758	+	0.0958649i
$101$	10.2342	+	7.43558i	1.01834	+	0.739867i	0.965942	−	0.258759i	$-0.0833135\pi$
$101$	10.2342	+	7.43558i	1.01834	+	0.739867i	0.0523982	+	0.998626i	$0.483313\pi$
$102$	−0.514594	+	4.89603i	−0.0509524	+	0.484780i
$103$	2.06380	−	2.29208i	0.203352	−	0.225845i	−0.632839	−	0.774283i	$-0.718111\pi$
$103$	2.06380	−	2.29208i	0.203352	−	0.225845i	0.836191	+	0.548438i	$0.184777\pi$
$104$	−8.30595	−	3.69805i	−0.814466	−	0.362624i
$105$	4.55734	+	0.968692i	0.444751	+	0.0945347i
$106$	0.380841	−	0.0809502i	0.0369905	−	0.00786258i
$107$	9.90377	−	4.40944i	0.957434	−	0.426277i	0.132297	−	0.991210i	$-0.457765\pi$
$107$	9.90377	−	4.40944i	0.957434	−	0.426277i	0.825137	+	0.564933i	$0.191098\pi$
$108$	−0.0525303	+	0.161671i	−0.00505473	+	0.0155568i
$109$	5.12929	−	15.7863i	0.491297	−	1.51206i	−0.331353	−	0.943507i	$-0.607505\pi$
$109$	5.12929	−	15.7863i	0.491297	−	1.51206i	0.822649	−	0.568549i	$-0.192495\pi$
$110$	−19.3915	+	8.63364i	−1.84890	+	0.823185i
$111$	−8.87305	+	1.88602i	−0.842192	+	0.179014i
$112$	5.06594	+	1.07680i	0.478687	+	0.101748i
$113$	−4.73374	−	2.10760i	−0.445313	−	0.198266i	0.171814	−	0.985129i	$-0.445037\pi$
$113$	−4.73374	−	2.10760i	−0.445313	−	0.198266i	−0.617127	+	0.786863i	$0.711704\pi$
$114$	−3.14229	+	3.48987i	−0.294303	+	0.326856i
$115$	−2.57324	+	24.4827i	−0.239956	+	2.28303i
$116$	−0.271462	−	0.197229i	−0.0252046	−	0.0183122i
$117$	0.323750	+	3.08027i	0.0299307	+	0.284771i
$118$	2.57819	−	4.46556i	0.237342	−	0.411088i
$119$	2.59531	+	4.49521i	0.237912	+	0.412075i
$120$	7.75771	−	5.63631i	0.708179	−	0.514522i
$121$	8.07915	+	8.97281i	0.734469	+	0.815710i
$122$	2.92050	+	8.98836i	0.264409	+	0.813768i
$123$	5.13794			0.463273
$124$	−0.944617	+	0.0592271i	−0.0848292	+	0.00531875i
$125$	−2.19010			−0.195889
$126$	−0.596244	−	1.83505i	−0.0531177	−	0.163479i
$127$	1.84302	+	2.04688i	0.163542	+	0.181631i	0.819346	−	0.573300i	$-0.194337\pi$
$127$	1.84302	+	2.04688i	0.163542	+	0.181631i	−0.655804	+	0.754931i	$0.727670\pi$
$128$	7.81607	−	5.67870i	0.690849	−	0.501931i
$129$	2.09734	+	3.63269i	0.184660	+	0.319841i
$130$	6.84326	−	11.8529i	0.600193	−	1.03957i
$131$	−1.20921	−	11.5049i	−0.105650	−	1.00519i	−0.911005	−	0.412396i	$-0.864692\pi$
$131$	−1.20921	−	11.5049i	−0.105650	−	1.00519i	0.805355	−	0.592792i	$-0.201975\pi$
$132$	−0.660613	−	0.479964i	−0.0574990	−	0.0417755i
$133$	−0.517558	+	4.92423i	−0.0448780	+	0.426985i
$134$	7.26732	−	8.07118i	0.627801	−	0.697243i
$135$	−2.98416	−	1.32863i	−0.256835	−	0.114350i
$136$	10.4494	+	2.22109i	0.896031	+	0.190457i
$137$	−6.63206	+	1.40969i	−0.566615	+	0.120438i	−0.482307	−	0.876002i	$-0.660201\pi$
$137$	−6.63206	+	1.40969i	−0.566615	+	0.120438i	−0.0843076	+	0.996440i	$0.526868\pi$
$138$	9.31345	−	4.14661i	0.792813	−	0.352983i
$139$	2.16472	−	6.66232i	0.183609	−	0.565091i	−0.816313	−	0.577611i	$-0.803985\pi$
$139$	2.16472	−	6.66232i	0.183609	−	0.565091i	0.999922	+	0.0125197i	$0.00398526\pi$
$140$	0.244746	−	0.753252i	0.0206848	−	0.0636614i
$141$	9.68578	−	4.31239i	0.815690	−	0.363169i
$142$	−12.6902	+	2.69737i	−1.06493	+	0.226359i
$143$	−14.5526	−	3.09326i	−1.21695	−	0.258671i
$144$	−3.31719	−	1.47691i	−0.276433	−	0.123076i
$145$	4.31446	−	4.79170i	0.358297	−	0.397929i
$146$	1.61196	−	15.3367i	0.133406	−	1.26928i
$147$	4.01728	+	2.91872i	0.331339	+	0.240732i
$148$	0.161187	+	1.53359i	0.0132495	+	0.126061i
$149$	−7.31915	+	12.6771i	−0.599608	+	1.03855i	0.393271	+	0.919423i	$0.371343\pi$
$149$	−7.31915	+	12.6771i	−0.599608	+	1.03855i	−0.992879	+	0.119129i	$0.961990\pi$
$150$	3.83544	+	6.64317i	0.313162	+	0.542413i
$151$	−13.6986	+	9.95262i	−1.11478	+	0.809933i	−0.983409	−	0.181401i	$-0.941937\pi$
$151$	−13.6986	+	9.95262i	−1.11478	+	0.809933i	−0.131367	+	0.991334i	$0.541937\pi$
$152$	6.81874	+	7.57298i	0.553073	+	0.614250i
$153$	−1.12457	−	3.46107i	−0.0909160	−	0.279811i
$154$	9.26839			0.746868
$155$	0.765505	−	18.1714i	0.0614869	−	1.45956i
$156$	0.526504			0.0421541
$157$	5.09238	+	15.6727i	0.406416	+	1.25082i	0.919707	+	0.392605i	$0.128426\pi$
$157$	5.09238	+	15.6727i	0.406416	+	1.25082i	−0.513291	+	0.858215i	$0.671574\pi$
$158$	8.08216	+	8.97615i	0.642982	+	0.714104i
$159$	−0.232847	+	0.169173i	−0.0184660	+	0.0134163i
$160$	−1.56621	−	2.71276i	−0.123820	−	0.214462i
$161$	5.37451	−	9.30893i	0.423571	−	0.733646i
$162$	0.141404	+	1.34537i	0.0111097	+	0.105702i
$163$	−8.56703	−	6.22431i	−0.671022	−	0.487526i	0.199345	−	0.979929i	$-0.436118\pi$
$163$	−8.56703	−	6.22431i	−0.671022	−	0.487526i	−0.870367	+	0.492403i	$0.836118\pi$
$164$	0.0912958	−	0.868622i	0.00712900	−	0.0678279i
$165$	10.4994	−	11.6608i	0.817378	−	0.907790i
$166$	8.09672	+	3.60489i	0.628427	+	0.279794i
$167$	−0.486959	−	0.103506i	−0.0376820	−	0.00800956i	0.189032	−	0.981971i	$-0.439465\pi$
$167$	−0.486959	−	0.103506i	−0.0376820	−	0.00800956i	−0.226714	+	0.973961i	$0.572798\pi$
$168$	−4.09548	+	0.870520i	−0.315973	+	0.0671621i
$169$	−3.11255	+	1.38580i	−0.239427	+	0.106600i
$170$	−4.96940	+	15.2942i	−0.381136	+	1.17302i
$171$	1.07273	−	3.30153i	0.0820339	−	0.252474i
$172$	0.651411	−	0.290027i	0.0496696	−	0.0221143i
$173$	−16.4460	+	3.49571i	−1.25037	+	0.265774i	−0.785085	−	0.619388i	$-0.787381\pi$
$173$	−16.4460	+	3.49571i	−1.25037	+	0.265774i	−0.465283	+	0.885162i	$0.654047\pi$
$174$	−2.61189	−	0.555175i	−0.198007	−	0.0420877i
$175$	7.38863	+	3.28963i	0.558528	+	0.248673i
$176$	11.6712	−	12.9621i	0.879747	−	0.977058i
$177$	−0.398431	+	3.79082i	−0.0299479	+	0.284935i
$178$	1.60921	+	1.16916i	0.120615	+	0.0876322i
$179$	2.15541	+	20.5074i	0.161103	+	1.53279i	0.714358	+	0.699780i	$0.246719\pi$
$179$	2.15541	+	20.5074i	0.161103	+	1.53279i	−0.553255	+	0.833012i	$0.686615\pi$
$180$	−0.277644	+	0.480894i	−0.0206944	+	0.0358437i
$181$	−11.7207	−	20.3009i	−0.871194	−	1.50895i	−0.860763	−	0.509006i	$-0.830013\pi$
$181$	−11.7207	−	20.3009i	−0.871194	−	1.50895i	−0.0104307	−	0.999946i	$-0.503320\pi$
$182$	−4.83475	+	3.51265i	−0.358376	+	0.260375i
$183$	−4.67475	−	5.19184i	−0.345568	−	0.383792i
$184$	−6.83629	−	21.0399i	−0.503978	−	1.55109i
$185$	−29.6319			−2.17858
$186$	−6.67559	+	3.48809i	−0.489478	+	0.255759i
$187$	17.4810			1.27834
$188$	−0.556947	−	1.71411i	−0.0406196	−	0.125014i
$189$	0.954391	+	1.05996i	0.0694217	+	0.0771006i
$190$	−12.4104	+	9.01666i	−0.900343	+	0.654137i
$191$	−5.91834	−	10.2509i	−0.428236	−	0.741727i	0.568480	−	0.822697i	$-0.307532\pi$
$191$	−5.91834	−	10.2509i	−0.428236	−	0.741727i	−0.996717	+	0.0809700i	$0.974198\pi$
$192$	−4.27973	+	7.41271i	−0.308863	+	0.534967i
$193$	0.605204	+	5.75813i	0.0435635	+	0.414479i	0.994472	+	0.105006i	$0.0334861\pi$
$193$	0.605204	+	5.75813i	0.0435635	+	0.414479i	−0.950908	+	0.309473i	$0.899847\pi$
$194$	−10.2256	−	7.42933i	−0.734155	−	0.533395i
$195$	−1.05755	+	10.0619i	−0.0757327	+	0.720549i
$196$	0.564823	−	0.627299i	0.0403445	−	0.0448071i
$197$	14.7208	+	6.55412i	1.04881	+	0.466962i	0.857455	−	0.514558i	$-0.172044\pi$
$197$	14.7208	+	6.55412i	1.04881	+	0.466962i	0.191358	+	0.981520i	$0.438711\pi$
$198$	−6.35614	−	1.35104i	−0.451711	−	0.0960142i
$199$	−9.00185	+	1.91340i	−0.638124	+	0.135638i	−0.515602	−	0.856828i	$-0.672432\pi$
$199$	−9.00185	+	1.91340i	−0.638124	+	0.135638i	−0.122522	+	0.992466i	$0.539098\pi$
$200$	15.2066	−	6.77043i	1.07527	−	0.478742i
$201$	−2.48096	+	7.63560i	−0.174993	+	0.538574i
$202$	5.28816	−	16.2753i	0.372074	−	1.14513i
$203$	−2.57199	+	1.14513i	−0.180519	+	0.0803721i
$204$	−0.605111	+	0.128620i	−0.0423662	+	0.00900522i
$205$	16.4167	+	3.48947i	1.14659	+	0.243715i
$206$	−3.81165	−	1.69706i	−0.265570	−	0.118240i
$207$	−5.04272	+	5.60050i	−0.350493	+	0.389262i
$208$	−1.17557	+	11.1848i	−0.0815114	+	0.775529i
$209$	13.4905	+	9.80144i	0.933160	+	0.677980i
$210$	−0.658822	−	6.26827i	−0.0454630	−	0.432552i
$211$	−6.75600	+	11.7017i	−0.465102	+	0.805581i	−0.999206	−	0.0398381i	$-0.987316\pi$
$211$	−6.75600	+	11.7017i	−0.465102	+	0.805581i	0.534104	+	0.845419i	$0.320649\pi$
$212$	0.0244630	+	0.0423712i	0.00168013	+	0.00291006i
$213$	7.75878	−	5.63708i	0.531623	−	0.386247i
$214$	−9.81314	−	10.8986i	−0.670812	−	0.745013i
$215$	4.23420	+	13.0315i	0.288770	+	0.888744i
$216$	2.93552			0.199737
$217$	−3.53254	+	7.11243i	−0.239805	+	0.482823i
$218$	−22.4544			−1.52080
$219$	3.52269	+	10.8417i	0.238041	+	0.732616i
$220$	−1.78481	−	1.98223i	−0.120332	−	0.133642i
$221$	−9.11876	+	6.62517i	−0.613394	+	0.445657i
$222$	6.13571	+	10.6274i	0.411802	+	0.713262i
$223$	2.14570	−	3.71646i	0.143687	−	0.248872i	−0.785196	−	0.619248i	$-0.787438\pi$
$223$	2.14570	−	3.71646i	0.143687	−	0.248872i	0.928882	+	0.370375i	$0.120771\pi$
$224$	0.142968	+	1.36025i	0.00955245	+	0.0908855i
$225$	−4.58750	−	3.33301i	−0.305833	−	0.222201i
$226$	−0.732716	+	6.97132i	−0.0487395	+	0.463726i
$227$	−5.10824	+	5.67327i	−0.339046	+	0.376548i	−0.888423	−	0.459026i	$-0.848198\pi$
$227$	−5.10824	+	5.67327i	−0.339046	+	0.376548i	0.549377	+	0.835575i	$0.314865\pi$
$228$	−0.539096	−	0.240021i	−0.0357025	−	0.0158958i
$229$	−13.1494	−	2.79498i	−0.868935	−	0.184698i	−0.248191	−	0.968711i	$-0.579836\pi$
$229$	−13.1494	−	2.79498i	−0.868935	−	0.184698i	−0.620744	+	0.784013i	$0.713169\pi$
$230$	32.5744	−	6.92390i	2.14789	−	0.456548i
$231$	−6.25904	+	2.78671i	−0.411815	+	0.183352i
$232$	−1.79057	+	5.51081i	−0.117557	+	0.361802i
$233$	−4.54128	+	13.9766i	−0.297509	+	0.915640i	0.684858	+	0.728677i	$0.259864\pi$
$233$	−4.54128	+	13.9766i	−0.297509	+	0.915640i	−0.982367	+	0.186963i	$0.940136\pi$
$234$	3.82764	−	1.70418i	0.250221	−	0.111406i
$235$	33.8767	−	7.20071i	2.20987	−	0.469722i
$236$	0.633797	+	0.134718i	0.0412566	+	0.00876937i
$237$	−8.15681	−	3.63165i	−0.529842	−	0.235901i
$238$	4.69847	−	5.21818i	0.304557	−	0.338244i
$239$	−0.487058	+	4.63405i	−0.0315052	+	0.299752i	0.967411	+	0.253211i	$0.0814865\pi$
$239$	−0.487058	+	4.63405i	−0.0315052	+	0.299752i	−0.998916	+	0.0465412i	$0.985180\pi$
$240$	−9.59599	−	6.97190i	−0.619419	−	0.450034i
$241$	−1.42086	−	13.5186i	−0.0915259	−	0.870811i	−0.939908	−	0.341427i	$-0.889090\pi$
$241$	−1.42086	−	13.5186i	−0.0915259	−	0.870811i	0.848382	−	0.529384i	$-0.177577\pi$
$242$	8.16679	−	14.1453i	0.524981	−	0.909294i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.960799	+	0.698061i	−0.0615088	+	0.0446888i
$245$	10.8537	+	12.0542i	0.693415	+	0.770116i
$246$	−2.14782	−	6.61031i	−0.136940	−	0.421458i
$247$	−10.7519			−0.684125
$248$	6.01347	+	15.1978i	0.381856	+	0.965061i
$249$	−6.55167			−0.415195
$250$	0.915532	+	2.81772i	0.0579033	+	0.178208i
$251$	14.2768	+	15.8560i	0.901147	+	1.00082i	0.999984	+	0.00572108i	$0.00182109\pi$
$251$	14.2768	+	15.8560i	0.901147	+	1.00082i	−0.0988370	+	0.995104i	$0.531512\pi$
$252$	0.196155	−	0.142515i	0.0123566	−	0.00897761i
$253$	−18.1003	−	31.3507i	−1.13796	−	1.97100i
$254$	1.86301	−	3.22683i	0.116896	−	0.202470i
$255$	−1.24260	−	11.8225i	−0.0778143	−	0.740354i
$256$	3.27610	+	2.38023i	0.204756	+	0.148764i
$257$	2.21124	−	21.0386i	0.137934	−	1.31235i	−0.678367	−	0.734723i	$-0.737312\pi$
$257$	2.21124	−	21.0386i	0.137934	−	1.31235i	0.816301	−	0.577627i	$-0.196021\pi$
$258$	3.79695	−	4.21694i	0.236388	−	0.262535i
$259$	11.8199	+	5.26256i	0.734453	+	0.327000i
$260$	1.68228	+	0.357579i	0.104330	+	0.0221761i
$261$	1.93076	−	0.410396i	0.119511	−	0.0254029i
$262$	−14.2964	+	6.36515i	−0.883232	+	0.393240i
$263$	2.70179	−	8.31526i	0.166600	−	0.512741i	−0.832551	−	0.553948i	$-0.813120\pi$
$263$	2.70179	−	8.31526i	0.166600	−	0.512741i	0.999151	+	0.0412075i	$0.0131205\pi$
$264$	−4.35742	+	13.4108i	−0.268181	+	0.825375i
$265$	−0.858884	+	0.382400i	−0.0527608	+	0.0234906i
$266$	6.55172	−	1.39261i	0.401712	−	0.0853864i
$267$	−1.43824	−	0.305708i	−0.0880192	−	0.0187090i
$268$	1.24679	+	0.555108i	0.0761600	+	0.0339086i
$269$	8.97841	−	9.97154i	0.547423	−	0.607975i	−0.404415	−	0.914576i	$-0.632525\pi$
$269$	8.97841	−	9.97154i	0.547423	−	0.607975i	0.951838	+	0.306600i	$0.0991915\pi$
$270$	−0.461905	+	4.39473i	−0.0281106	+	0.267455i
$271$	18.1022	+	13.1520i	1.09963	+	0.798929i	0.981000	−	0.194009i	$-0.0621490\pi$
$271$	18.1022	+	13.1520i	1.09963	+	0.798929i	0.118632	+	0.992938i	$0.462149\pi$
$272$	−1.38127	−	13.1419i	−0.0837518	−	0.796845i
$273$	2.20882	−	3.82579i	0.133684	−	0.231547i
$274$	4.58607	+	7.94330i	0.277055	+	0.479872i
$275$	22.0363	−	16.0103i	1.32884	−	0.965457i
$276$	0.857219	+	0.952038i	0.0515985	+	0.0573059i
$277$	−5.61898	−	17.2935i	−0.337612	−	1.03906i	−0.965421	−	0.260696i	$-0.916048\pi$
$277$	−5.61898	−	17.2935i	−0.337612	−	1.03906i	0.627809	−	0.778367i	$-0.283952\pi$
$278$	−9.47645			−0.568360
$279$	3.45934	−	4.36268i	0.207105	−	0.261187i
$280$	−13.6770			−0.817358
$281$	−1.95900	−	6.02919i	−0.116864	−	0.359671i	0.875467	−	0.483278i	$-0.160554\pi$
$281$	−1.95900	−	6.02919i	−0.116864	−	0.359671i	−0.992331	+	0.123607i	$0.960554\pi$
$282$	−9.59715	−	10.6587i	−0.571502	−	0.634717i
$283$	−17.5987	+	12.7862i	−1.04613	+	0.760059i	−0.971473	−	0.237150i	$-0.923787\pi$
$283$	−17.5987	+	12.7862i	−1.04613	+	0.760059i	−0.0746584	+	0.997209i	$0.523787\pi$
$284$	−0.815141	−	1.41187i	−0.0483697	−	0.0837788i
$285$	5.66984	−	9.82044i	0.335852	−	0.581713i
$286$	2.10377	+	20.0160i	0.124399	+	1.18357i
$287$	−5.92874	−	4.30748i	−0.349962	−	0.254262i
$288$	0.100236	−	0.953681i	0.00590646	−	0.0561962i
$289$	−2.51350	+	2.79152i	−0.147853	+	0.164207i
$290$	−7.96843	−	3.54777i	−0.467922	−	0.208332i
$291$	9.13921	+	1.94260i	0.535750	+	0.113877i
$292$	1.89550	−	0.402901i	0.110926	−	0.0235780i
$293$	−16.1026	+	7.16932i	−0.940721	+	0.418836i	−0.819042	−	0.573733i	$-0.805495\pi$
$293$	−16.1026	+	7.16932i	−0.940721	+	0.418836i	−0.121679	+	0.992569i	$0.538828\pi$
$294$	2.07579	−	6.38862i	0.121062	−	0.372592i
$295$	−3.84762	+	11.8418i	−0.224017	+	0.689454i
$296$	24.3267	−	10.8309i	1.41396	−	0.629536i
$297$	4.69858	−	0.998714i	0.272639	−	0.0579513i
$298$	19.3696	+	4.11714i	1.12205	+	0.238500i
$299$	21.3235	+	9.49384i	1.23317	+	0.549043i
$300$	−0.644995	+	0.716339i	−0.0372388	+	0.0413579i
$301$	0.625385	−	5.95014i	0.0360466	−	0.342961i
$302$	18.5312	+	13.4637i	1.06635	+	0.774748i
$303$	1.32230	+	12.5809i	0.0759642	+	0.722751i
$304$	6.30260	−	10.9164i	0.361479	−	0.626100i
$305$	−11.4106	−	19.7638i	−0.653370	−	1.13167i
$306$	−3.98279	+	2.89367i	−0.227681	+	0.165420i
$307$	−2.52181	−	2.80076i	−0.143927	−	0.159848i	0.666871	−	0.745173i	$-0.267633\pi$
$307$	−2.52181	−	2.80076i	−0.143927	−	0.159848i	−0.810798	+	0.585326i	$0.800967\pi$
$308$	0.359904	+	1.10767i	0.0205075	+	0.0631155i
$309$	3.08430			0.175460
$310$	−23.6987	+	6.61132i	−1.34600	+	0.375498i
$311$	−3.50161			−0.198558			−0.0992792	−	0.995060i	$-0.531654\pi$
$311$	−3.50161			−0.198558			−0.0992792	+	0.995060i	$0.531654\pi$
$312$	−2.80958	−	8.64700i	−0.159061	−	0.489540i
$313$	−11.7841	−	13.0876i	−0.666076	−	0.739752i	0.311521	−	0.950239i	$-0.399162\pi$
$313$	−11.7841	−	13.0876i	−0.666076	−	0.739752i	−0.977597	+	0.210487i	$0.932495\pi$
$314$	18.0353	−	13.1034i	1.01779	−	0.739467i
$315$	2.32958	+	4.03494i	0.131257	+	0.227343i
$316$	−0.758905	+	1.31446i	−0.0426917	+	0.0739442i
$317$	−2.05768	−	19.5776i	−0.115571	−	1.09959i	−0.886521	−	0.462689i	$-0.846885\pi$
$317$	−2.05768	−	19.5776i	−0.115571	−	1.09959i	0.770950	−	0.636896i	$-0.219782\pi$
$318$	0.314990	+	0.228854i	0.0176638	+	0.0128335i
$319$	−0.991109	+	9.42977i	−0.0554915	+	0.527966i
$320$	−18.7089	+	20.7784i	−1.04586	+	1.16155i
$321$	9.90377	+	4.40944i	0.552775	+	0.246111i
$322$	−14.2233	−	3.02325i	−0.792633	−	0.168479i
$323$	12.3571	−	2.62658i	0.687568	−	0.146147i
$324$	−0.155295	+	0.0691418i	−0.00862750	+	0.00384121i
$325$	−5.42719	+	16.7032i	−0.301047	+	0.926526i
$326$	−4.42672	+	13.6240i	−0.245173	+	0.754565i
$327$	15.1637	−	6.75131i	0.838554	−	0.373348i
$328$	−14.7529	+	3.13583i	−0.814594	+	0.173147i
$329$	−14.7919	−	3.14412i	−0.815505	−	0.173341i
$330$	−19.3915	−	8.63364i	−1.06747	−	0.475266i
$331$	9.75171	−	10.8304i	0.536003	−	0.595291i	−0.412933	−	0.910761i	$-0.635496\pi$
$331$	9.75171	−	10.8304i	0.536003	−	0.595291i	0.948935	+	0.315470i	$0.102162\pi$
$332$	−0.116416	+	1.10763i	−0.00638918	+	0.0607890i
$333$	−7.33882	−	5.33196i	−0.402165	−	0.292190i
$334$	0.0703961	+	0.669775i	0.00385191	+	0.0366484i
$335$	−13.1129	+	22.7122i	−0.716434	+	1.24090i
$336$	2.58956	+	4.48525i	0.141272	+	0.244690i
$337$	21.3763	−	15.5308i	1.16444	−	0.846018i	0.174110	−	0.984726i	$-0.444295\pi$
$337$	21.3763	−	15.5308i	1.16444	−	0.846018i	0.990333	+	0.138708i	$0.0442950\pi$
$338$	3.08407	+	3.42520i	0.167751	+	0.186306i
$339$	−1.60124	−	4.92811i	−0.0869675	−	0.267658i
$340$	−2.02080			−0.109593
$341$	14.7957	+	22.2797i	0.801232	+	1.20651i
$342$	−4.69608			−0.253935
$343$	−5.27392	−	16.2314i	−0.284765	−	0.876415i
$344$	−8.23936	−	9.15073i	−0.444236	−	0.493374i
$345$	−19.9160	+	14.4698i	−1.07224	+	0.779030i
$346$	11.3724	+	19.6976i	0.611385	+	1.05895i
$347$	0.862463	−	1.49383i	0.0462994	−	0.0801930i	−0.841947	−	0.539560i	$-0.818590\pi$
$347$	0.862463	−	1.49383i	0.0462994	−	0.0801930i	0.888246	+	0.459367i	$0.151924\pi$
$348$	−0.0350741	−	0.333707i	−0.00188017	−	0.0178886i
$349$	−0.201963	−	0.146735i	−0.0108108	−	0.00785452i	0.582367	−	0.812926i	$-0.302127\pi$
$349$	−0.201963	−	0.146735i	−0.0108108	−	0.00785452i	−0.593178	+	0.805072i	$0.702127\pi$
$350$	1.14365	−	10.8811i	0.0611309	−	0.581622i
$351$	−2.07246	+	2.30170i	−0.110620	+	0.122856i
$352$	4.20806	+	1.87355i	0.224290	+	0.0998604i
$353$	−3.38702	−	0.719933i	−0.180273	−	0.0383182i	0.116891	−	0.993145i	$-0.462707\pi$
$353$	−3.38702	−	0.719933i	−0.180273	−	0.0383182i	−0.297163	+	0.954827i	$0.596041\pi$
$354$	5.04370	−	1.07207i	0.268070	−	0.0569800i
$355$	28.6192	−	12.7421i	1.51895	−	0.676280i
$356$	−0.0772392	+	0.237718i	−0.00409367	+	0.0125990i
$357$	−1.60399	+	4.93657i	−0.0848921	+	0.261271i
$358$	25.4831	−	11.3458i	1.34682	−	0.599644i
$359$	−27.7672	+	5.90211i	−1.46550	+	0.311501i	−0.870477	−	0.492209i	$-0.836190\pi$
$359$	−27.7672	+	5.90211i	−1.46550	+	0.311501i	−0.595021	+	0.803710i	$0.702856\pi$
$360$	9.37952	+	1.99368i	0.494344	+	0.105076i
$361$	−6.34836	−	2.82647i	−0.334124	−	0.148762i
$362$	−21.2188	+	23.5659i	−1.11524	+	1.23860i
$363$	−1.26209	+	12.0080i	−0.0662424	+	0.630255i
$364$	−0.607540	−	0.441404i	−0.0318437	−	0.0231358i
$365$	3.89240	+	37.0338i	0.203738	+	1.93844i
$366$	−4.72546	+	8.18474i	−0.247004	+	0.427823i
$367$	0.174051	+	0.301464i	0.00908537	+	0.0157363i	0.870532	−	0.492111i	$-0.163775\pi$
$367$	0.174051	+	0.301464i	0.00908537	+	0.0157363i	−0.861447	+	0.507848i	$0.830441\pi$
$368$	−22.1387	+	16.0847i	−1.15406	+	0.838473i
$369$	3.43795	+	3.81823i	0.178973	+	0.198769i
$370$	12.3871	+	38.1235i	0.643974	+	1.98195i
$371$	0.410514			0.0213128
$372$	−0.676087	−	0.662357i	−0.0350535	−	0.0343416i
$373$	34.9539			1.80984			0.904922	−	0.425577i	$-0.139929\pi$
$373$	34.9539			1.80984			0.904922	+	0.425577i	$0.139929\pi$
$374$	−7.30760	−	22.4905i	−0.377867	−	1.16296i
$375$	−1.46547	−	1.62756i	−0.0756763	−	0.0840470i
$376$	−25.1795	+	18.2940i	−1.29853	+	0.943439i
$377$	−3.05682	−	5.29456i	−0.157434	−	0.272684i
$378$	0.964744	−	1.67098i	0.0496211	−	0.0859462i
$379$	1.69389	+	16.1163i	0.0870095	+	0.827840i	0.947797	+	0.318875i	$0.103305\pi$
$379$	1.69389	+	16.1163i	0.0870095	+	0.827840i	−0.860787	+	0.508965i	$0.830028\pi$
$380$	−1.55950	−	1.13304i	−0.0800006	−	0.0581239i
$381$	−0.287908	+	2.73926i	−0.0147500	+	0.140337i
$382$	−10.7144	+	11.8995i	−0.548196	+	0.608833i
$383$	−22.5923	−	10.0587i	−1.15441	−	0.513978i	−0.261942	−	0.965084i	$-0.584363\pi$
$383$	−22.5923	−	10.0587i	−1.15441	−	0.513978i	−0.892470	+	0.451106i	$0.851030\pi$
$384$	9.45007	+	2.00867i	0.482247	+	0.102505i
$385$	−21.8914	+	4.65316i	−1.11569	+	0.237147i
$386$	7.15523	−	3.18571i	0.364192	−	0.162149i
$387$	−1.29622	+	3.98937i	−0.0658908	+	0.202791i
$388$	0.490810	−	1.51056i	0.0249171	−	0.0766870i
$389$	0.912340	−	0.406200i	0.0462575	−	0.0205952i	−0.383478	−	0.923550i	$-0.625274\pi$
$389$	0.912340	−	0.406200i	0.0462575	−	0.0205952i	0.429735	+	0.902955i	$0.358607\pi$
$390$	13.3874	−	2.84559i	0.677899	−	0.144092i
$391$	−26.8264	−	5.70212i	−1.35667	−	0.288368i
$392$	−13.3165	−	5.92887i	−0.672583	−	0.299453i
$393$	7.74069	−	8.59690i	0.390466	−	0.433656i
$394$	2.27857	−	21.6791i	0.114793	−	1.09218i
$395$	−23.5961	−	17.1435i	−1.18725	−	0.862585i
$396$	−0.0853540	−	0.812089i	−0.00428920	−	0.0408090i
$397$	6.79946	−	11.7770i	0.341255	−	0.591071i	−0.643411	−	0.765521i	$-0.722481\pi$
$397$	6.79946	−	11.7770i	0.341255	−	0.591071i	0.984666	+	0.174450i	$0.0558147\pi$
$398$	6.22478	+	10.7816i	0.312020	+	0.540434i
$399$	−4.00573	+	2.91033i	−0.200537	+	0.145699i
$400$	−13.7775	−	15.3014i	−0.688874	−	0.765072i
$401$	0.712040	+	2.19143i	0.0355576	+	0.109435i	0.967260	−	0.253788i	$-0.0816764\pi$
$401$	0.712040	+	2.19143i	0.0355576	+	0.109435i	−0.931702	+	0.363223i	$0.881676\pi$
$402$	10.8608			0.541689
$403$	−16.1619	−	6.01448i	−0.805079	−	0.299603i
$404$	2.15042			0.106987
$405$	−1.00942	−	3.10669i	−0.0501587	−	0.154373i
$406$	2.54846	+	2.83035i	0.126478	+	0.140468i
$407$	35.2524	−	25.6124i	1.74740	−	1.26956i
$408$	5.34144	+	9.25164i	0.264441	+	0.458025i
$409$	3.07389	−	5.32413i	0.151994	−	0.263261i	−0.779966	−	0.625821i	$-0.784764\pi$
$409$	3.07389	−	5.32413i	0.151994	−	0.263261i	0.931960	+	0.362560i	$0.118097\pi$
$410$	−2.37324	−	22.5799i	−0.117206	−	1.11514i
$411$	−5.48532	−	3.98531i	−0.270571	−	0.196581i
$412$	0.0548047	−	0.521432i	0.00270004	−	0.0256891i
$413$	3.63785	−	4.04024i	0.179007	−	0.198807i
$414$	9.31345	+	4.14661i	0.457731	+	0.203795i
$415$	−20.9338	−	4.44962i	−1.02760	−	0.218423i
$416$	−2.90515	+	0.617508i	−0.142437	+	0.0302758i
$417$	6.39955	−	2.84926i	0.313387	−	0.139529i
$418$	6.97076	−	21.4538i	0.340951	−	1.04934i
$419$	1.41520	−	4.35554i	0.0691370	−	0.212782i	−0.910519	−	0.413468i	$-0.864317\pi$
$419$	1.41520	−	4.35554i	0.0691370	−	0.212782i	0.979656	+	0.200686i	$0.0643172\pi$
$420$	0.723543	−	0.322142i	0.0353053	−	0.0157189i
$421$	25.5370	−	5.42805i	1.24460	−	0.264547i	0.461890	−	0.886937i	$-0.347172\pi$
$421$	25.5370	−	5.42805i	1.24460	−	0.264547i	0.782707	+	0.622390i	$0.213838\pi$
$422$	17.8793	+	3.80036i	0.870351	+	0.184999i
$423$	9.68578	+	4.31239i	0.470939	+	0.209676i
$424$	0.565338	−	0.627871i	0.0274552	−	0.0304921i
$425$	2.15703	−	20.5228i	0.104631	−	0.995501i
$426$	−10.4959	−	7.62572i	−0.508528	−	0.369468i
$427$	1.04159	+	9.91008i	0.0504062	+	0.479582i
$428$	0.921441	−	1.59598i	0.0445395	−	0.0771447i
$429$	−7.43887	−	12.8845i	−0.359152	−	0.622070i
$430$	14.9959	−	10.8952i	0.723168	−	0.525413i
$431$	−7.96657	−	8.84778i	−0.383736	−	0.426182i	0.520070	−	0.854123i	$-0.325906\pi$
$431$	−7.96657	−	8.84778i	−0.383736	−	0.426182i	−0.903807	+	0.427941i	$0.859239\pi$
$432$	−1.12208	−	3.45340i	−0.0539860	−	0.166152i
$433$	33.6810			1.61861			0.809304	−	0.587391i	$-0.199845\pi$
$433$	33.6810			1.61861			0.809304	+	0.587391i	$0.199845\pi$
$434$	10.6273	+	1.57164i	0.510129	+	0.0754410i
$435$	6.44787			0.309152
$436$	−0.871935	−	2.68354i	−0.0417581	−	0.128518i
$437$	−17.5055	−	19.4418i	−0.837400	−	0.930027i
$438$	12.4760	−	9.06436i	0.596127	−	0.433112i
$439$	0.385671	+	0.668002i	0.0184071	+	0.0318820i	0.875082	−	0.483974i	$-0.160807\pi$
$439$	0.385671	+	0.668002i	0.0184071	+	0.0318820i	−0.856675	+	0.515856i	$0.827474\pi$
$440$	−23.0308	+	39.8905i	−1.09795	+	1.90170i
$441$	0.519049	+	4.93842i	0.0247166	+	0.235163i
$442$	12.3357	+	8.96238i	0.586748	+	0.426297i
$443$	−3.74931	+	35.6723i	−0.178135	+	1.69484i	0.431462	+	0.902131i	$0.357998\pi$
$443$	−3.74931	+	35.6723i	−0.178135	+	1.69484i	−0.609597	+	0.792711i	$0.708669\pi$
$444$	−1.03183	+	1.14596i	−0.0489683	+	0.0543848i
$445$	−4.38783	−	1.95359i	−0.208003	−	0.0926090i
$446$	−5.67845	−	1.20699i	−0.268882	−	0.0571527i
$447$	−14.3184	+	3.04347i	−0.677238	+	0.143951i
$448$	11.1530	−	4.96564i	0.526930	−	0.234604i
$449$	−2.17372	+	6.69002i	−0.102584	+	0.315722i	−0.989156	−	0.146870i	$-0.953080\pi$
$449$	−2.17372	+	6.69002i	−0.102584	+	0.315722i	0.886572	+	0.462591i	$0.153080\pi$
$450$	−2.37043	+	7.29543i	−0.111743	+	0.343910i
$451$	−22.5466	+	10.0384i	−1.06168	+	0.472690i
$452$	−0.861600	+	0.183139i	−0.0405263	+	0.00861413i
$453$	−16.5624	−	3.52044i	−0.778169	−	0.165405i
$454$	9.43446	+	4.20049i	0.442781	+	0.197139i
$455$	9.65590	−	10.7240i	0.452675	−	0.502747i
$456$	−1.06519	+	10.1346i	−0.0498822	+	0.474598i
$457$	−2.60474	−	1.89245i	−0.121844	−	0.0885251i	0.525194	−	0.850982i	$-0.323993\pi$
$457$	−2.60474	−	1.89245i	−0.121844	−	0.0885251i	−0.647039	+	0.762457i	$0.723993\pi$
$458$	1.90091	+	18.0860i	0.0888237	+	0.845101i
$459$	1.81959	−	3.15162i	0.0849312	−	0.147105i
$460$	2.09239	+	3.62412i	0.0975581	+	0.168976i
$461$	10.0142	−	7.27572i	0.466406	−	0.338864i	−0.329633	−	0.944109i	$-0.606925\pi$
$461$	10.0142	−	7.27572i	0.466406	−	0.338864i	0.796039	+	0.605245i	$0.206925\pi$
$462$	6.20176	+	6.88776i	0.288532	+	0.320447i
$463$	2.08682	+	6.42257i	0.0969828	+	0.298482i	0.987765	−	0.155947i	$-0.0498431\pi$
$463$	2.08682	+	6.42257i	0.0969828	+	0.298482i	−0.890783	+	0.454430i	$0.849843\pi$
$464$	7.16746			0.332741
$465$	14.0162	−	11.5901i	0.649985	−	0.537479i
$466$	19.8803			0.920937
$467$	4.34942	+	13.3861i	0.201267	+	0.619436i	0.999846	+	0.0175461i	$0.00558537\pi$
$467$	4.34942	+	13.3861i	0.201267	+	0.619436i	−0.798579	+	0.601890i	$0.794415\pi$
$468$	0.352300	+	0.391269i	0.0162851	+	0.0180864i
$469$	9.26424	−	6.73086i	0.427783	−	0.310802i
$470$	−23.4257	−	40.5745i	−1.08055	−	1.87156i
$471$	−8.23964	+	14.2715i	−0.379663	+	0.657595i
$472$	−1.16960	−	11.1280i	−0.0538352	−	0.512208i
$473$	−16.3011	−	11.8435i	−0.749527	−	0.544563i
$474$	−1.26256	+	12.0124i	−0.0579912	+	0.551749i
$475$	13.1716	−	14.6285i	0.604354	−	0.671203i
$476$	0.806076	+	0.358888i	0.0369464	+	0.0164496i
$477$	−0.281525	−	0.0598400i	−0.0128901	−	0.00273989i
$478$	6.16563	−	1.31054i	0.282009	−	0.0599429i
$479$	12.7647	−	5.68321i	0.583234	−	0.259672i	−0.0938404	−	0.995587i	$-0.529914\pi$
$479$	12.7647	−	5.68321i	0.583234	−	0.259672i	0.677074	+	0.735915i	$0.263248\pi$
$480$	0.967972	−	2.97911i	0.0441817	−	0.135977i
$481$	−8.68212	+	26.7208i	−0.395870	+	1.21836i
$482$	−16.7987	+	7.47924i	−0.765158	+	0.340670i
$483$	10.5141	−	2.23485i	0.478410	−	0.101689i
$484$	2.00764	+	0.426738i	0.0912565	+	0.0193972i
$485$	27.8821	+	12.4139i	1.26606	+	0.563687i
$486$	−0.905185	+	1.00531i	−0.0410600	+	0.0456018i
$487$	0.945188	−	8.99286i	0.0428305	−	0.407505i	−0.952011	−	0.306064i	$-0.900988\pi$
$487$	0.945188	−	8.99286i	0.0428305	−	0.407505i	0.994842	−	0.101441i	$-0.0323455\pi$
$488$	16.5917	+	12.0545i	0.751069	+	0.545684i
$489$	−1.10690	−	10.5314i	−0.0500556	−	0.476247i
$490$	10.9714	−	19.0030i	0.495638	−	0.858469i
$491$	8.41149	+	14.5691i	0.379605	+	0.657496i	0.991005	−	0.133826i	$-0.0427265\pi$
$491$	8.41149	+	14.5691i	0.379605	+	0.657496i	−0.611399	+	0.791322i	$0.709393\pi$
$492$	0.706600	−	0.513375i	0.0318560	−	0.0231447i
$493$	4.80661	+	5.33828i	0.216479	+	0.240424i
$494$	4.49462	+	13.8330i	0.202222	+	0.622376i
$495$	15.6911			0.705264
$496$	15.5804	−	12.8836i	0.699580	−	0.578491i
$497$	−13.6789			−0.613582
$498$	2.73881	+	8.42918i	0.122729	+	0.377720i
$499$	−2.73113	−	3.03322i	−0.122262	−	0.135786i	0.678906	−	0.734225i	$-0.262454\pi$
$499$	−2.73113	−	3.03322i	−0.122262	−	0.135786i	−0.801168	+	0.598439i	$0.795788\pi$
$500$	−0.301196	+	0.218832i	−0.0134699	+	0.00978645i
$501$	−0.248919	−	0.431140i	−0.0111209	−	0.0192619i
$502$	14.4317	−	24.9965i	0.644119	−	1.11565i
$503$	−0.779835	−	7.41963i	−0.0347711	−	0.330825i	−0.998055	−	0.0623400i	$-0.980144\pi$
$503$	−0.779835	−	7.41963i	−0.0347711	−	0.330825i	0.963284	−	0.268485i	$-0.0865230\pi$
$504$	−3.38733	−	2.46104i	−0.150884	−	0.109623i
$505$	−4.31939	+	41.0962i	−0.192210	+	1.82876i
$506$	−32.7683	+	36.3929i	−1.45673	+	1.61786i
$507$	−3.11255	−	1.38580i	−0.138233	−	0.0615454i
$508$	0.457985	+	0.0973476i	0.0203198	+	0.00431910i
$509$	−13.3996	+	2.84817i	−0.593926	+	0.126243i	−0.495062	−	0.868858i	$-0.664854\pi$
$509$	−13.3996	+	2.84817i	−0.593926	+	0.126243i	−0.0988649	+	0.995101i	$0.531521\pi$
$510$	−14.6910	+	6.54086i	−0.650529	+	0.289634i
$511$	5.02446	−	15.4637i	0.222269	−	0.684074i
$512$	7.66376	−	23.5866i	0.338693	−	1.04239i
$513$	3.17131	−	1.41196i	0.140017	−	0.0623395i
$514$	−27.9919	+	5.94987i	−1.23467	+	0.262437i
$515$	9.85490	+	2.09472i	0.434259	+	0.0923046i
$516$	0.651411	+	0.290027i	0.0286768	+	0.0127677i
$517$	−34.0783	+	37.8478i	−1.49876	+	1.66454i
$518$	1.82955	−	17.4070i	0.0803859	−	0.764821i
$519$	−13.6024	−	9.88269i	−0.597077	−	0.433802i
$520$	−3.10446	−	29.5369i	−0.136139	−	1.29528i
$521$	9.22884	−	15.9848i	0.404323	−	0.700307i	−0.589920	−	0.807462i	$-0.700841\pi$
$521$	9.22884	−	15.9848i	0.404323	−	0.700307i	0.994242	+	0.107155i	$0.0341740\pi$
$522$	−1.33512	−	2.31250i	−0.0584367	−	0.101215i
$523$	−25.9172	+	18.8299i	−1.13328	+	0.823376i	−0.986169	−	0.165744i	$-0.946997\pi$
$523$	−25.9172	+	18.8299i	−1.13328	+	0.823376i	−0.147111	+	0.989120i	$0.546997\pi$
$524$	−1.31585	−	1.46140i	−0.0574832	−	0.0638416i
$525$	2.49929	+	7.69201i	0.109078	+	0.335707i
$526$	−11.8276			−0.515707
$527$	20.0441	+	2.96424i	0.873135	+	0.129124i
$528$	17.4423			0.759077
$529$	10.4431	+	32.1406i	0.454049	+	1.39742i
$530$	0.851024	+	0.945158i	0.0369661	+	0.0410550i
$531$	−3.08373	+	2.24046i	−0.133822	+	0.0972277i
$532$	0.420844	+	0.728924i	0.0182459	+	0.0316028i
$533$	7.95672	−	13.7814i	0.344644	−	0.596940i
$534$	0.207917	+	1.97820i	0.00899744	+	0.0856049i
$535$	28.6497	+	20.8152i	1.23863	+	0.899920i
$536$	2.46352	−	23.4388i	0.106408	−	1.01240i
$537$	−13.7977	+	15.3239i	−0.595414	+	0.661274i
$538$	−16.5823	−	7.38293i	−0.714915	−	0.318301i
$539$	−23.3314	−	4.95924i	−1.00495	−	0.213610i
$540$	−0.543154	+	0.115451i	−0.0233736	+	0.00496822i
$541$	−26.7744	+	11.9207i	−1.15112	+	0.512513i	−0.891421	−	0.453176i	$-0.850291\pi$
$541$	−26.7744	+	11.9207i	−1.15112	+	0.512513i	−0.259702	+	0.965689i	$0.583624\pi$
$542$	9.35370	−	28.7877i	0.401776	−	1.23654i
$543$	7.24380	−	22.2941i	0.310861	−	0.956732i
$544$	3.18803	−	1.41940i	0.136686	−	0.0608564i
$545$	53.0360	−	11.2732i	2.27181	−	0.482889i
$546$	−5.84549	−	1.24250i	−0.250164	−	0.0531740i
$547$	−9.53909	−	4.24708i	−0.407862	−	0.181592i	0.192542	−	0.981289i	$-0.438327\pi$
$547$	−9.53909	−	4.24708i	−0.407862	−	0.181592i	−0.600404	+	0.799697i	$0.704994\pi$
$548$	−0.771227	+	0.856534i	−0.0329452	+	0.0365893i
$549$	0.730268	−	6.94803i	0.0311671	−	0.296535i
$550$	−29.8102	−	21.6584i	−1.27111	−	0.923516i
$551$	0.716256	+	6.81472i	0.0305135	+	0.290317i
$552$	11.0614	−	19.1588i	0.470802	−	0.815454i
$553$	6.36760	+	11.0290i	0.270778	+	0.469001i
$554$	−19.9003	+	14.4584i	−0.845483	+	0.614279i
$555$	−19.8276	−	22.0208i	−0.841636	−	0.934732i
$556$	−0.367984	−	1.13254i	−0.0156060	−	0.0480303i
$557$	−32.9017			−1.39409			−0.697044	−	0.717028i	$-0.745502\pi$
$557$	−32.9017			−1.39409			−0.697044	+	0.717028i	$0.745502\pi$
$558$	−7.05900	−	2.62694i	−0.298831	−	0.111207i
$559$	12.9919			0.549499
$560$	5.22793	+	16.0899i	0.220920	+	0.679923i
$561$	11.6971	+	12.9909i	0.493850	+	0.548477i
$562$	−6.93804	+	5.04078i	−0.292663	+	0.212632i
$563$	16.3035	+	28.2386i	0.687113	+	1.19011i	0.972768	+	0.231781i	$0.0744554\pi$
$563$	16.3035	+	28.2386i	0.687113	+	1.19011i	−0.285655	+	0.958332i	$0.592211\pi$
$564$	0.901160	−	1.56085i	0.0379457	−	0.0657238i
$565$	−1.76930	−	16.8337i	−0.0744348	−	0.708200i
$566$	23.8071	+	17.2969i	1.00069	+	0.727041i
$567$	−0.149090	+	1.41850i	−0.00626121	+	0.0595714i
$568$	−18.8378	+	20.9216i	−0.790419	+	0.877849i
$569$	18.4304	+	8.20573i	0.772642	+	0.344002i	0.754900	−	0.655840i	$-0.227686\pi$
$569$	18.4304	+	8.20573i	0.772642	+	0.344002i	0.0177420	+	0.999843i	$0.494352\pi$
$570$	−15.0048	−	3.18938i	−0.628484	−	0.133588i
$571$	−23.4135	+	4.97670i	−0.979826	+	0.208268i	−0.669867	−	0.742481i	$-0.733649\pi$
$571$	−23.4135	+	4.97670i	−0.979826	+	0.208268i	−0.309959	+	0.950750i	$0.600315\pi$
$572$	−2.31044	+	1.02867i	−0.0966043	+	0.0430110i
$573$	3.65774	−	11.2574i	0.152804	−	0.470283i
$574$	−3.06347	+	9.42839i	−0.127867	+	0.393533i
$575$	−39.0393	+	17.3814i	−1.62805	+	0.724855i
$576$	−8.37242	+	1.77961i	−0.348851	+	0.0741505i
$577$	−34.4064	−	7.31330i	−1.43236	−	0.304457i	−0.574566	−	0.818458i	$-0.694829\pi$
$577$	−34.4064	−	7.31330i	−1.43236	−	0.304457i	−0.857789	+	0.514001i	$0.828163\pi$
$578$	4.64221	+	2.06684i	0.193090	+	0.0859694i
$579$	−3.87416	+	4.30269i	−0.161005	+	0.178814i
$580$	0.114572	−	1.09008i	0.00475733	−	0.0452630i
$581$	7.56006	+	5.49271i	0.313644	+	0.227876i
$582$	−1.32119	−	12.5703i	−0.0547651	−	0.521055i
$583$	0.691266	−	1.19731i	0.0286293	−	0.0495874i
$584$	−16.7319	−	28.9806i	−0.692373	−	1.19922i
$585$	−8.18510	+	5.94682i	−0.338412	+	0.245871i
$586$	15.9552	+	17.7200i	0.659103	+	0.732008i
$587$	−3.53695	−	10.8856i	−0.145986	−	0.449297i	0.851151	−	0.524921i	$-0.175905\pi$
$587$	−3.53695	−	10.8856i	−0.145986	−	0.449297i	−0.997136	+	0.0756239i	$0.975905\pi$
$588$	0.844114			0.0348107
$589$	13.8065	+	13.5261i	0.568888	+	0.557335i
$590$	16.8437			0.693443
$591$	4.97947	+	15.3252i	0.204828	+	0.630396i
$592$	−22.0404	−	24.4784i	−0.905856	−	1.00605i
$593$	31.4634	−	22.8595i	1.29205	−	0.938727i	0.292202	−	0.956357i	$-0.405612\pi$
$593$	31.4634	−	22.8595i	1.29205	−	0.938727i	0.999845	+	0.0176300i	$0.00561211\pi$
$594$	−3.24907	−	5.62755i	−0.133311	−	0.230901i
$595$	−8.47775	+	14.6839i	−0.347554	+	0.601981i
$596$	0.260107	+	2.47475i	0.0106544	+	0.101370i
$597$	−7.44535	−	5.40936i	−0.304718	−	0.221390i
$598$	3.30057	−	31.4029i	0.134971	−	1.28416i
$599$	11.3133	−	12.5647i	0.462248	−	0.513379i	−0.466281	−	0.884636i	$-0.654407\pi$
$599$	11.3133	−	12.5647i	0.462248	−	0.513379i	0.928530	+	0.371257i	$0.121073\pi$
$600$	15.2066	+	6.77043i	0.620808	+	0.276402i
$601$	−12.0115	−	2.55312i	−0.489959	−	0.104144i	−0.0436944	−	0.999045i	$-0.513913\pi$
$601$	−12.0115	−	2.55312i	−0.489959	−	0.104144i	−0.446265	+	0.894901i	$0.647246\pi$
$602$	−7.91670	+	1.68275i	−0.322661	+	0.0685836i
$603$	−7.33444	+	3.26550i	−0.298681	+	0.132982i
$604$	−0.889463	+	2.73749i	−0.0361918	+	0.111387i
$605$	−12.1879	+	37.5105i	−0.495509	+	1.52502i
$606$	15.6334	−	6.96043i	0.635062	−	0.282748i
$607$	15.0377	−	3.19636i	0.610360	−	0.129736i	0.107647	−	0.994189i	$-0.465668\pi$
$607$	15.0377	−	3.19636i	0.610360	−	0.129736i	0.502713	+	0.864453i	$0.332335\pi$
$608$	3.25613	+	0.692113i	0.132054	+	0.0280689i
$609$	−2.57199	−	1.14513i	−0.104222	−	0.0464028i
$610$	−20.6574	+	22.9424i	−0.836396	+	0.928911i
$611$	3.43253	−	32.6583i	0.138865	−	1.32121i
$612$	−0.500482	−	0.363621i	−0.0202308	−	0.0146985i
$613$	2.00947	+	19.1189i	0.0811619	+	0.772204i	0.957096	+	0.289772i	$0.0935796\pi$
$613$	2.00947	+	19.1189i	0.0811619	+	0.772204i	−0.875934	+	0.482432i	$0.839754\pi$
$614$	−2.54917	+	4.41529i	−0.102876	+	0.178187i
$615$	8.39171	+	14.5349i	0.338387	+	0.586103i
$616$	16.2712	−	11.8217i	0.655586	−	0.476311i
$617$	7.11429	+	7.90122i	0.286411	+	0.318091i	0.869131	−	0.494581i	$-0.164679\pi$
$617$	7.11429	+	7.90122i	0.286411	+	0.318091i	−0.582721	+	0.812672i	$0.698012\pi$
$618$	−1.28933	−	3.96816i	−0.0518646	−	0.159623i
$619$	22.7175			0.913093			0.456546	−	0.889700i	$-0.349086\pi$
$619$	22.7175			0.913093			0.456546	+	0.889700i	$0.349086\pi$
$620$	−1.71038	−	2.57552i	−0.0686904	−	0.103435i
$621$	−7.53622			−0.302418
$622$	1.46379	+	4.50507i	0.0586924	+	0.180637i
$623$	1.40331	+	1.55854i	0.0562226	+	0.0624415i
$624$	−9.09857	+	6.61050i	−0.364234	+	0.264632i
$625$	10.5991	+	18.3582i	0.423964	+	0.734327i
$626$	−11.9119	+	20.6320i	−0.476096	+	0.824622i
$627$	1.74303	+	16.5839i	0.0696101	+	0.662296i
$628$	2.26633	+	1.64658i	0.0904364	+	0.0657059i
$629$	3.45070	−	32.8312i	0.137588	−	1.30906i
$630$	4.21740	−	4.68389i	0.168025	−	0.186611i
$631$	−13.8808	−	6.18014i	−0.552587	−	0.246027i	0.111395	−	0.993776i	$-0.464468\pi$
$631$	−13.8808	−	6.18014i	−0.552587	−	0.246027i	−0.663982	+	0.747749i	$0.731135\pi$
$632$	25.6377	+	5.44946i	1.01981	+	0.216768i
$633$	−13.2167	+	2.80930i	−0.525318	+	0.111660i
$634$	−24.3277	+	10.8314i	−0.966176	+	0.430169i
$635$	−2.78031	+	8.55692i	−0.110333	+	0.339571i
$636$	−0.0151190	+	0.0465314i	−0.000599506	+	0.00184509i
$637$	14.0501	−	6.25550i	0.556685	−	0.247852i
$638$	12.5464	−	2.66681i	0.496715	−	0.105580i
$639$	9.38081	+	1.99395i	0.371099	+	0.0788795i
$640$	28.8305	+	12.8362i	1.13963	+	0.507394i
$641$	−14.5229	+	16.1294i	−0.573622	+	0.637072i	−0.958227	−	0.286010i	$-0.907671\pi$
$641$	−14.5229	+	16.1294i	−0.573622	+	0.637072i	0.384605	+	0.923081i	$0.374338\pi$
$642$	1.53296	−	14.5852i	0.0605012	−	0.575631i
$643$	−27.3906	−	19.9004i	−1.08018	−	0.784796i	−0.102465	−	0.994737i	$-0.532673\pi$
$643$	−27.3906	−	19.9004i	−1.08018	−	0.784796i	−0.977714	+	0.209940i	$0.932673\pi$
$644$	−0.190999	−	1.81723i	−0.00752641	−	0.0716090i
$645$	−6.85109	+	11.8664i	−0.269761	+	0.467240i
$646$	−8.54494	−	14.8003i	−0.336196	−	0.582309i
$647$	−8.83959	+	6.42234i	−0.347520	+	0.252488i	−0.747828	−	0.663893i	$-0.768903\pi$
$647$	−8.83959	+	6.42234i	−0.347520	+	0.252488i	0.400308	+	0.916381i	$0.368903\pi$
$648$	1.96424	+	2.18151i	0.0771628	+	0.0856980i
$649$	−5.65800	−	17.4135i	−0.222096	−	0.683541i
$650$	23.7585			0.931886
$651$	−7.64930	+	2.13396i	−0.299800	+	0.0836364i
$652$	−1.80011			−0.0704979
$653$	11.3941	+	35.0673i	0.445884	+	1.37229i	0.881511	+	0.472163i	$0.156527\pi$
$653$	11.3941	+	35.0673i	0.445884	+	1.37229i	−0.435627	+	0.900127i	$0.643473\pi$
$654$	−15.0249	−	16.6869i	−0.587521	−	0.652508i
$655$	30.5716	−	22.2115i	1.19453	−	0.867877i
$656$	9.32824	+	16.1570i	0.364207	+	0.630824i
$657$	−5.69983	+	9.87239i	−0.222372	+	0.385159i
$658$	2.13836	+	20.3451i	0.0833620	+	0.793136i
$659$	17.0295	+	12.3726i	0.663374	+	0.481970i	0.867801	−	0.496912i	$-0.165533\pi$
$659$	17.0295	+	12.3726i	0.663374	+	0.481970i	−0.204426	+	0.978882i	$0.565533\pi$
$660$	0.278815	−	2.65274i	0.0108528	−	0.103258i
$661$	17.9476	−	19.9328i	0.698080	−	0.775297i	−0.284989	−	0.958531i	$-0.591990\pi$
$661$	17.9476	−	19.9328i	0.698080	−	0.775297i	0.983069	+	0.183234i	$0.0586566\pi$
$662$	−18.0105	−	8.01881i	−0.700000	−	0.311660i
$663$	−11.0251	−	2.34346i	−0.428180	−	0.0910124i
$664$	18.8123	−	3.99867i	0.730058	−	0.155179i
$665$	−14.7756	+	6.57853i	−0.572974	+	0.255105i
$666$	−3.79208	+	11.6708i	−0.146940	+	0.452235i
$667$	4.59685	−	14.1477i	0.177991	−	0.547799i
$668$	−0.0773117	+	0.0344214i	−0.00299128	+	0.00133180i
$669$	4.19762	−	0.892231i	0.162289	−	0.0344956i
$670$	34.7024	+	7.37622i	1.34067	+	0.284968i
$671$	30.6577	+	13.6497i	1.18353	+	0.526941i
$672$	−0.915198	+	1.01643i	−0.0353045	+	0.0392097i
$673$	2.63640	−	25.0837i	0.101626	−	0.966905i	−0.818294	−	0.574799i	$-0.805080\pi$
$673$	2.63640	−	25.0837i	0.101626	−	0.966905i	0.919920	−	0.392105i	$-0.128253\pi$
$674$	−28.9175	−	21.0098i	−1.11386	−	0.809266i
$675$	−0.592724	−	5.63940i	−0.0228140	−	0.217060i
$676$	−0.289590	+	0.501584i	−0.0111381	+	0.0192917i
$677$	−5.01179	−	8.68068i	−0.192619	−	0.333626i	0.753499	−	0.657450i	$-0.228365\pi$
$677$	−5.01179	−	8.68068i	−0.192619	−	0.333626i	−0.946117	+	0.323824i	$0.895031\pi$
$678$	−5.67099	+	4.12021i	−0.217793	+	0.158236i
$679$	−8.91724	−	9.90360i	−0.342212	−	0.380065i
$680$	10.7836	+	33.1884i	0.413531	+	1.27272i
$681$	−7.63414			−0.292541
$682$	22.4793	−	28.3493i	0.860776	−	1.08555i
$683$	37.1303			1.42075			0.710375	−	0.703823i	$-0.248525\pi$
$683$	37.1303			1.42075			0.710375	+	0.703823i	$0.248525\pi$
$684$	−0.182355	−	0.561232i	−0.00697253	−	0.0214592i
$685$	−14.8199	−	16.4592i	−0.566241	−	0.628874i
$686$	−18.6782	+	13.5705i	−0.713137	+	0.518124i
$687$	−6.72157	−	11.6421i	−0.256444	−	0.444174i
$688$	−7.61568	+	13.1907i	−0.290345	+	0.502892i
$689$	0.0931799	+	0.886547i	0.00354987	+	0.0337748i
$690$	26.9420	+	19.5745i	1.02566	+	0.745188i
$691$	0.647258	−	6.15824i	0.0246228	−	0.234271i	−0.975288	−	0.220936i	$-0.929089\pi$
$691$	0.647258	−	6.15824i	0.0246228	−	0.234271i	0.999911	−	0.0133344i	$-0.00424460\pi$
$692$	−1.91247	+	2.12401i	−0.0727012	+	0.0807428i
$693$	−6.25904	−	2.78671i	−0.237761	−	0.105858i
$694$	−2.28245	−	0.485150i	−0.0866406	−	0.0184160i
$695$	22.3828	−	4.75762i	0.849030	−	0.180467i
$696$	−5.29345	+	2.35680i	−0.200648	+	0.0893342i
$697$	−5.77797	+	17.7828i	−0.218856	+	0.673570i
$698$	−0.104357	+	0.321179i	−0.00394998	+	0.0121568i
$699$	−13.4254	+	5.97736i	−0.507794	+	0.226085i
$700$	1.34482	−	0.285851i	0.0508295	−	0.0108042i
$701$	−0.809388	−	0.172041i	−0.0305702	−	0.00649789i	0.192601	−	0.981277i	$-0.438308\pi$
$701$	−0.809388	−	0.172041i	−0.0305702	−	0.00649789i	−0.223171	+	0.974779i	$0.571641\pi$
$702$	3.82764	+	1.70418i	0.144465	+	0.0643200i
$703$	21.0712	−	23.4019i	0.794714	−	0.882619i
$704$	4.29777	−	40.8906i	0.161978	−	1.54112i
$705$	28.0191	+	20.3571i	1.05526	+	0.766691i
$706$	0.489637	+	4.65858i	0.0184277	+	0.175328i
$707$	9.02155	−	15.6258i	0.339290	−	0.587668i
$708$	0.323978	+	0.561146i	0.0121758	+	0.0210892i
$709$	19.8174	−	14.3982i	0.744260	−	0.540736i	−0.149783	−	0.988719i	$-0.547857\pi$
$709$	19.8174	−	14.3982i	0.744260	−	0.540736i	0.894042	+	0.447983i	$0.147857\pi$
$710$	−28.3573	−	31.4940i	−1.06423	−	1.18195i
$711$	−2.75913	−	8.49174i	−0.103476	−	0.318465i
$712$	4.31631			0.161761
$713$	−15.4381	−	39.0166i	−0.578162	−	1.46118i
$714$	7.02175			0.262782
$715$	−15.0180	−	46.2205i	−0.561640	−	1.72855i
$716$	2.34549	+	2.60493i	0.0876550	+	0.0973508i
$717$	−3.76968	+	2.73883i	−0.140781	+	0.102283i
$718$	19.2010	+	33.2572i	0.716577	+	1.24115i
$719$	−7.08615	+	12.2736i	−0.264269	+	0.457727i	−0.967372	−	0.253361i	$-0.918464\pi$
$719$	−7.08615	+	12.2736i	−0.264269	+	0.457727i	0.703103	+	0.711088i	$0.251797\pi$
$720$	−1.23984	−	11.7963i	−0.0462062	−	0.439623i
$721$	−3.55901	−	2.58577i	−0.132544	−	0.0962992i
$722$	−0.982635	+	9.34915i	−0.0365699	+	0.347939i
$723$	9.09555	−	10.1016i	0.338267	−	0.375684i
$724$	−3.64033	−	1.62078i	−0.135292	−	0.0602359i
$725$	10.9483	+	2.32714i	0.406610	+	0.0864276i
$726$	15.9767	−	3.39594i	0.592949	−	0.126035i
$727$	−31.2480	+	13.9125i	−1.15893	+	0.515987i	−0.893905	−	0.448256i	$-0.852045\pi$
$727$	−31.2480	+	13.9125i	−1.15893	+	0.515987i	−0.265020	+	0.964243i	$0.585379\pi$
$728$	−4.00735	+	12.3333i	−0.148522	+	0.457104i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	46.0193	−	20.4891i	1.70325	−	0.758336i
$731$	−14.9316	+	3.17381i	−0.552265	+	0.117387i
$732$	−1.16166	−	0.246918i	−0.0429362	−	0.00912637i
$733$	−13.6813	−	6.09132i	−0.505332	−	0.224988i	0.138205	−	0.990404i	$-0.455867\pi$
$733$	−13.6813	−	6.09132i	−0.505332	−	0.224988i	−0.643536	+	0.765415i	$0.722534\pi$
$734$	0.315096	−	0.349950i	0.0116304	−	0.0129169i
$735$	−1.69551	+	16.1317i	−0.0625398	+	0.595027i
$736$	−5.84656	−	4.24777i	−0.215507	−	0.156575i
$737$	−4.03119	−	38.3543i	−0.148491	−	1.41280i
$738$	3.47525	−	6.01930i	0.127926	−	0.221574i
$739$	10.0421	+	17.3934i	0.369404	+	0.639827i	0.989473	−	0.144721i	$-0.0462284\pi$
$739$	10.0421	+	17.3934i	0.369404	+	0.639827i	−0.620068	+	0.784548i	$0.712895\pi$
$740$	−4.07516	+	2.96078i	−0.149806	+	0.108840i
$741$	−7.19440	−	7.99019i	−0.264293	−	0.293527i
$742$	−0.171608	−	0.528154i	−0.00629992	−	0.0193892i
$743$	−16.3801			−0.600928			−0.300464	−	0.953793i	$-0.597141\pi$
$743$	−16.3801			−0.600928			−0.300464	+	0.953793i	$0.597141\pi$
$744$	−7.27037	+	14.6382i	−0.266545	+	0.536662i
$745$	−47.8170			−1.75188
$746$	−14.6118	−	44.9706i	−0.534977	−	1.64649i
$747$	−4.38393	−	4.86884i	−0.160399	−	0.178142i
$748$	2.40409	−	1.74667i	0.0879022	−	0.0638647i
$749$	−7.73136	−	13.3911i	−0.282498	−	0.489300i
$750$	−1.48136	+	2.56579i	−0.0540917	+	0.0936895i
$751$	−2.67660	−	25.4661i	−0.0976705	−	0.929272i	−0.928146	−	0.372217i	$-0.878598\pi$
$751$	−2.67660	−	25.4661i	−0.0976705	−	0.929272i	0.830475	−	0.557055i	$-0.188069\pi$
$752$	31.1460	+	22.6289i	1.13578	+	0.825192i
$753$	−2.23026	+	21.2195i	−0.0812753	+	0.773283i
$754$	−5.53397	+	6.14609i	−0.201535	+	0.223828i
$755$	−50.5290	−	22.4969i	−1.83894	−	0.818748i
$756$	0.237163	+	0.0504105i	0.00862553	+	0.00183341i
$757$	30.1887	−	6.41681i	1.09723	−	0.233223i	0.376482	−	0.926424i	$-0.377134\pi$
$757$	30.1887	−	6.41681i	1.09723	−	0.233223i	0.720744	+	0.693201i	$0.243800\pi$
$758$	20.0267	−	8.91644i	0.727401	−	0.323860i
$759$	11.1866	−	34.4288i	0.406048	−	1.24969i
$760$	−10.2865	+	31.6586i	−0.373130	+	1.14838i
$761$	18.9916	−	8.45560i	0.688445	−	0.306515i	−0.0325360	−	0.999471i	$-0.510358\pi$
$761$	18.9916	−	8.45560i	0.688445	−	0.306515i	0.720981	+	0.692955i	$0.243692\pi$
$762$	3.64460	−	0.774684i	0.132030	−	0.0280639i
$763$	−23.1577	−	4.92231i	−0.838363	−	0.178200i
$764$	−1.83818	−	0.818409i	−0.0665029	−	0.0296090i
$765$	7.95437	−	8.83423i	0.287591	−	0.319402i
$766$	−3.49697	+	33.2714i	−0.126351	+	1.20214i
$767$	9.55104	+	6.93924i	0.344868	+	0.250561i
$768$	0.423287	+	4.02730i	0.0152740	+	0.145323i
$769$	−8.70269	+	15.0735i	−0.313827	+	0.543565i	−0.979187	−	0.202958i	$-0.934945\pi$
$769$	−8.70269	+	15.0735i	−0.313827	+	0.543565i	0.665360	+	0.746522i	$0.268278\pi$
$770$	15.1379	+	26.2196i	0.545532	+	0.944890i
$771$	17.1143	−	12.4343i	0.616357	−	0.447810i
$772$	0.658575	+	0.731421i	0.0237026	+	0.0263244i
$773$	9.26303	+	28.5087i	0.333168	+	1.02539i	0.967617	+	0.252421i	$0.0812268\pi$
$773$	9.26303	+	28.5087i	0.333168	+	1.02539i	−0.634450	+	0.772964i	$0.718773\pi$
$774$	5.67446			0.203964
$775$	27.9822	−	14.6211i	1.00515	−	0.525205i
$776$	−27.4277			−0.984596
$777$	3.99821	+	12.3052i	0.143435	+	0.441448i
$778$	−0.903991	−	1.00398i	−0.0324097	−	0.0359946i
$779$	−14.4296	+	10.4838i	−0.516996	+	0.375619i
$780$	0.859931	+	1.48944i	0.0307905	+	0.0533306i
$781$	−23.0339	+	39.8960i	−0.824219	+	1.42759i
$782$	3.87809	+	36.8976i	0.138680	+	1.31946i
$783$	1.59692	+	1.16023i	0.0570691	+	0.0414631i
$784$	−1.88473	+	17.9320i	−0.0673118	+	0.640429i
$785$	−36.0198	+	40.0040i	−1.28560	+	1.42780i
$786$	−14.2964	−	6.36515i	−0.509934	−	0.227037i
$787$	39.4672	+	8.38902i	1.40686	+	0.299036i	0.847898	−	0.530160i	$-0.177868\pi$
$787$	39.4672	+	8.38902i	1.40686	+	0.299036i	0.558958	+	0.829196i	$0.311201\pi$
$788$	2.67937	−	0.569518i	0.0954486	−	0.0202882i
$789$	7.98730	−	3.55617i	0.284355	−	0.126603i
$790$	−12.1924	+	37.5245i	−0.433788	+	1.33506i
$791$	−2.28387	+	7.02904i	−0.0812052	+	0.249924i
$792$	−12.8818	+	5.73536i	−0.457735	+	0.203797i
$793$	−21.1654	+	4.49885i	−0.751606	+	0.159759i
$794$	−17.9943	−	3.82481i	−0.638594	−	0.135737i
$795$	−0.858884	−	0.382400i	−0.0304615	−	0.0135623i
$796$	−1.04680	+	1.16259i	−0.0371030	+	0.0412070i
$797$	−1.07763	+	10.2530i	−0.0381716	+	0.363179i	0.958717	+	0.284361i	$0.0917813\pi$
$797$	−1.07763	+	10.2530i	−0.0381716	+	0.363179i	−0.996889	+	0.0788180i	$0.974885\pi$
$798$	5.41887	+	3.93704i	0.191826	+	0.139370i
$799$	4.03314	+	38.3727i	0.142682	+	1.35753i
$800$	2.71880	−	4.70910i	0.0961241	−	0.166492i
$801$	−0.735188	−	1.27338i	−0.0259766	−	0.0449928i
$802$	2.52177	−	1.83218i	0.0890469	−	0.0646964i
$803$	−36.6408	−	40.6938i	−1.29303	−	1.43605i
$804$	0.421741	+	1.29799i	0.0148737	+	0.0457765i
$805$	35.1124			1.23755
$806$	−0.981879	+	23.3076i	−0.0345852	+	0.820974i
$807$	13.4180			0.472337
$808$	−11.4753	−	35.3172i	−0.403699	−	1.24246i
$809$	14.9350	+	16.5870i	0.525086	+	0.583167i	0.946095	−	0.323889i	$-0.104991\pi$
$809$	14.9350	+	16.5870i	0.525086	+	0.583167i	−0.421009	+	0.907056i	$0.638324\pi$
$810$	−3.57500	+	2.59739i	−0.125613	+	0.0912629i
$811$	19.3338	+	33.4871i	0.678901	+	1.17589i	0.975312	+	0.220830i	$0.0708766\pi$
$811$	19.3338	+	33.4871i	0.678901	+	1.17589i	−0.296412	+	0.955060i	$0.595790\pi$
$812$	−0.239297	+	0.414474i	−0.00839767	+	0.0145452i
$813$	2.33889	+	22.2530i	0.0820283	+	0.780447i
$814$	−47.6887	−	34.6478i	−1.67149	−	1.21441i
$815$	3.61575	−	34.4016i	0.126654	−	1.20504i
$816$	8.84209	−	9.82014i	0.309535	−	0.343774i
$817$	−13.3026	−	5.92271i	−0.465400	−	0.207209i
$818$	−8.13484	−	1.72911i	−0.284428	−	0.0604570i
$819$	4.32110	−	0.918478i	0.150992	−	0.0320942i
$820$	2.60638	−	1.16044i	0.0910188	−	0.0405242i
$821$	11.1023	−	34.1693i	0.387472	−	1.19252i	−0.547199	−	0.837002i	$-0.684306\pi$
$821$	11.1023	−	34.1693i	0.387472	−	1.19252i	0.934671	−	0.355513i	$-0.115694\pi$
$822$	−2.83435	+	8.72322i	−0.0988592	+	0.304257i
$823$	−2.48601	+	1.10684i	−0.0866568	+	0.0385821i	−0.449607	−	0.893226i	$-0.648436\pi$
$823$	−2.48601	+	1.10684i	−0.0866568	+	0.0385821i	0.362951	+	0.931808i	$0.381769\pi$
$824$	−8.85616	+	1.88243i	−0.308519	+	0.0655777i
$825$	26.6431	+	5.66317i	0.927595	+	0.197166i
$826$	−6.71878	−	2.99139i	−0.233776	−	0.104084i
$827$	−9.01033	+	10.0070i	−0.313320	+	0.347977i	−0.879150	−	0.476545i	$-0.841889\pi$
$827$	−9.01033	+	10.0070i	−0.313320	+	0.347977i	0.565830	+	0.824522i	$0.308556\pi$
$828$	−0.133911	+	1.27408i	−0.00465372	+	0.0442772i
$829$	27.0794	+	19.6744i	0.940507	+	0.683319i	0.948543	−	0.316649i	$-0.102558\pi$
$829$	27.0794	+	19.6744i	0.940507	+	0.683319i	−0.00803530	+	0.999968i	$0.502558\pi$
$830$	3.02625	+	28.7929i	0.105043	+	0.999415i
$831$	9.09171	−	15.7473i	0.315388	−	0.546268i
$832$	13.2554	+	22.9589i	0.459547	+	0.795958i
$833$	−14.6196	+	10.6218i	−0.506539	+	0.368022i
$834$	−6.34099	−	7.04238i	−0.219570	−	0.243858i
$835$	−0.502530	−	1.54663i	−0.0173908	−	0.0535232i
$836$	2.83464			0.0980382
$837$	5.55685	−	0.348412i	0.192073	−	0.0120429i
$838$	−6.19529			−0.214013
$839$	−3.92752	−	12.0876i	−0.135593	−	0.417312i	0.860089	−	0.510144i	$-0.170408\pi$
$839$	−3.92752	−	12.0876i	−0.135593	−	0.417312i	−0.995682	+	0.0928322i	$0.970408\pi$
$840$	−9.15171	−	10.1640i	−0.315764	−	0.350692i
$841$	20.3093	−	14.7556i	0.700322	−	0.508814i
$842$	−17.6588	−	30.5860i	−0.608563	−	1.05406i
$843$	3.16973	−	5.49014i	0.109171	−	0.189090i
$844$	0.240094	+	2.28434i	0.00826438	+	0.0786303i
$845$	−9.00400	−	6.54179i	−0.309747	−	0.225044i
$846$	1.49922	−	14.2641i	0.0515443	−	0.490411i
$847$	11.5234	−	12.7980i	0.395949	−	0.439746i
$848$	−0.954736	−	0.425076i	−0.0327858	−	0.0145972i
$849$	−21.2778	−	4.52273i	−0.730251	−	0.155220i
$850$	−27.3057	+	5.80400i	−0.936577	+	0.199076i
$851$	−62.4529	+	27.8058i	−2.14086	+	0.953171i
$852$	0.503785	−	1.55049i	0.0172594	−	0.0531189i
$853$	5.65126	−	17.3928i	0.193496	−	0.595518i	−0.806495	−	0.591241i	$-0.798638\pi$
$853$	5.65126	−	17.3928i	0.193496	−	0.595518i	0.999991	−	0.00427758i	$-0.00136160\pi$
$854$	12.3146	−	5.48280i	0.421396	−	0.187618i
$855$	11.0919	−	2.35765i	0.379334	−	0.0806299i
$856$	−31.1286	−	6.61659i	−1.06395	−	0.226150i
$857$	28.3569	+	12.6253i	0.968652	+	0.431272i	0.829197	−	0.558957i	$-0.188798\pi$
$857$	28.3569	+	12.6253i	0.968652	+	0.431272i	0.139455	+	0.990228i	$0.455465\pi$
$858$	−13.4671	+	14.9567i	−0.459760	+	0.510615i
$859$	1.49681	−	14.2412i	0.0510704	−	0.485902i	−0.938855	−	0.344313i	$-0.888112\pi$
$859$	1.49681	−	14.2412i	0.0510704	−	0.485902i	0.989925	−	0.141590i	$-0.0452214\pi$
$860$	1.88440	+	1.36910i	0.0642577	+	0.0466859i
$861$	−0.766018	−	7.28818i	−0.0261058	−	0.248380i
$862$	−8.05299	+	13.9482i	−0.274286	+	0.475077i
$863$	0.752888	+	1.30404i	0.0256286	+	0.0443900i	0.878555	−	0.477641i	$-0.158508\pi$
$863$	0.752888	+	1.30404i	0.0256286	+	0.0443900i	−0.852927	+	0.522031i	$0.825175\pi$
$864$	0.775794	−	0.563647i	0.0263931	−	0.0191757i
$865$	−36.7501	−	40.8152i	−1.24954	−	1.38776i
$866$	−14.0797	−	43.3330i	−0.478449	−	1.47251i
$867$	−3.75637			−0.127573
$868$	0.224847	+	1.33111i	0.00763181	+	0.0451808i
$869$	42.8897			1.45493
$870$	−2.69541	−	8.29562i	−0.0913830	−	0.281248i
$871$	16.6388	+	18.4793i	0.563785	+	0.626146i
$872$	−39.4200	+	28.6403i	−1.33493	+	0.969884i
$873$	4.67169	+	8.09161i	0.158113	+	0.273859i
$874$	−17.6954	+	30.6492i	−0.598554	+	1.03673i
$875$	0.326524	+	3.10666i	0.0110385	+	0.105024i
$876$	1.56775	+	1.13904i	0.0529693	+	0.0384845i
$877$	−3.62842	+	34.5221i	−0.122523	+	1.16573i	0.744556	+	0.667560i	$0.232661\pi$
$877$	−3.62842	+	34.5221i	−0.122523	+	1.16573i	−0.867079	+	0.498170i	$0.834005\pi$
$878$	0.698208	−	0.775438i	0.0235634	−	0.0261698i
$879$	−16.1026	−	7.16932i	−0.543126	−	0.241815i
$880$	55.7313	+	11.8460i	1.87870	+	0.399330i
$881$	35.8985	−	7.63046i	1.20945	−	0.257077i	0.441308	−	0.897356i	$-0.354515\pi$
$881$	35.8985	−	7.63046i	1.20945	−	0.257077i	0.768143	+	0.640279i	$0.221181\pi$
$882$	6.13664	−	2.73221i	0.206631	−	0.0919983i
$883$	2.49000	−	7.66344i	0.0837953	−	0.257895i	−0.900377	−	0.435111i	$-0.856709\pi$
$883$	2.49000	−	7.66344i	0.0837953	−	0.257895i	0.984172	+	0.177216i	$0.0567091\pi$
$884$	−0.592090	+	1.82227i	−0.0199141	+	0.0612894i
$885$	−11.3747	+	5.06434i	−0.382357	+	0.170236i
$886$	47.4622	−	10.0884i	1.59452	−	0.338926i
$887$	−12.7888	−	2.71834i	−0.429406	−	0.0912730i	−0.0118617	−	0.999930i	$-0.503776\pi$
$887$	−12.7888	−	2.71834i	−0.429406	−	0.0912730i	−0.417544	+	0.908657i	$0.637109\pi$
$888$	24.3267	+	10.8309i	0.816351	+	0.363463i
$889$	2.62873	−	2.91950i	0.0881647	−	0.0979168i
$890$	−0.679174	+	6.46191i	−0.0227660	+	0.216604i
$891$	3.88615	+	2.82346i	0.130191	+	0.0945894i
$892$	−0.0762536	−	0.725504i	−0.00255316	−	0.0242917i
$893$	−18.4028	+	31.8746i	−0.615826	+	1.06664i
$894$	9.90118	+	17.1494i	0.331145	+	0.573560i
$895$	−54.4935	+	39.5918i	−1.82152	+	1.32341i
$896$	−9.22055	−	10.2405i	−0.308037	−	0.342110i
$897$	7.21291	+	22.1991i	0.240832	+	0.741205i
$898$	9.51585			0.317548
$899$	−2.73543	+	10.6443i	−0.0912317	+	0.355008i
$900$	−0.963930			−0.0321310
$901$	−0.323667	−	0.996145i	−0.0107829	−	0.0331864i
$902$	22.3403	+	24.8114i	0.743851	+	0.826130i
$903$	4.84028	−	3.51667i	0.161075	−	0.117028i
$904$	7.60552	+	13.1731i	0.252956	+	0.438132i
$905$	38.2865	−	66.3141i	1.27269	−	2.20436i
$906$	2.39431	+	22.7803i	0.0795455	+	0.756825i
$907$	29.3669	+	21.3363i	0.975112	+	0.708461i	0.956611	−	0.291368i	$-0.0941105\pi$
$907$	29.3669	+	21.3363i	0.975112	+	0.708461i	0.0185014	+	0.999829i	$0.494110\pi$
$908$	−0.135651	+	1.29063i	−0.00450173	+	0.0428311i
$909$	−8.46461	+	9.40090i	−0.280753	+	0.311808i
$910$	−17.8336	−	7.94002i	−0.591177	−	0.263209i
$911$	−40.9081	−	8.69528i	−1.35535	−	0.288088i	−0.527744	−	0.849403i	$-0.676962\pi$
$911$	−40.9081	−	8.69528i	−1.35535	−	0.288088i	−0.827602	+	0.561316i	$0.810295\pi$
$912$	12.3297	−	2.62077i	0.408279	−	0.0867823i
$913$	28.7505	−	12.8005i	0.951502	−	0.423636i
$914$	−1.34591	+	4.14227i	−0.0445186	+	0.137014i
$915$	7.05215	−	21.7043i	0.233137	−	0.717522i
$916$	−2.08765	+	0.929482i	−0.0689779	+	0.0307109i
$917$	−16.1394	+	3.43054i	−0.532971	+	0.113286i
$918$	−4.81542	−	1.02355i	−0.158933	−	0.0337822i
$919$	−32.0815	−	14.2836i	−1.05827	−	0.471172i	−0.197572	−	0.980288i	$-0.563306\pi$
$919$	−32.0815	−	14.2836i	−1.05827	−	0.471172i	−0.860698	+	0.509116i	$0.829972\pi$
$920$	48.3549	−	53.7036i	1.59421	−	1.77055i
$921$	0.393946	−	3.74815i	0.0129810	−	0.123506i
$922$	−13.5469	−	9.84243i	−0.446145	−	0.324143i
$923$	−3.10488	−	29.5410i	−0.102198	−	0.972353i
$924$	−0.582338	+	1.00864i	−0.0191575	+	0.0331818i
$925$	−25.7192	−	44.5469i	−0.845641	−	1.46469i
$926$	7.39072	−	5.36967i	0.242874	−	0.176458i
$927$	2.06380	+	2.29208i	0.0677840	+	0.0752818i
$928$	0.584919	+	1.80020i	0.0192009	+	0.0590943i
$929$	−16.5352			−0.542501			−0.271251	−	0.962509i	$-0.587437\pi$
$929$	−16.5352			−0.542501			−0.271251	+	0.962509i	$0.587437\pi$
$930$	−20.7707	−	13.1877i	−0.681098	−	0.432443i
$931$	−17.2378			−0.564948
$932$	0.771979	+	2.37591i	0.0252870	+	0.0778255i
$933$	−2.34304	−	2.60221i	−0.0767076	−	0.0851924i
$934$	15.4040	−	11.1916i	0.504033	−	0.366202i
$935$	28.5514	+	49.4525i	0.933731	+	1.61727i
$936$	4.54600	−	7.87390i	0.148591	−	0.257367i
$937$	−1.85306	−	17.6307i	−0.0605368	−	0.575969i	−0.982182	−	0.187934i	$-0.939821\pi$
$937$	−1.85306	−	17.6307i	−0.0605368	−	0.575969i	0.921645	−	0.388034i	$-0.126846\pi$
$938$	−12.5325	−	9.10537i	−0.409199	−	0.297301i
$939$	1.84085	−	17.5146i	0.0600740	−	0.571566i
$940$	3.93944	−	4.37519i	0.128490	−	0.142703i
$941$	3.05750	+	1.36129i	0.0996718	+	0.0443767i	0.455967	−	0.889997i	$-0.349294\pi$
$941$	3.05750	+	1.36129i	0.0996718	+	0.0443767i	−0.356295	+	0.934373i	$0.615960\pi$
$942$	21.8057	+	4.63494i	0.710467	+	0.151014i
$943$	37.8745	−	8.05048i	1.23336	−	0.262160i
$944$	−12.6441	+	5.62953i	−0.411532	+	0.183226i
$945$	−1.43976	+	4.43112i	−0.0468353	+	0.144144i
$946$	−8.42305	+	25.9235i	−0.273857	+	0.842845i
$947$	6.18026	−	2.75163i	0.200832	−	0.0894160i	−0.303856	−	0.952718i	$-0.598274\pi$
$947$	6.18026	−	2.75163i	0.200832	−	0.0894160i	0.504688	+	0.863302i	$0.331608\pi$
$948$	−1.48464	+	0.315570i	−0.0482189	+	0.0102492i
$949$	34.5359	+	7.34084i	1.12108	+	0.238294i
$950$	−24.3267	−	10.8310i	−0.789264	−	0.351403i
$951$	13.1721	−	14.6291i	0.427135	−	0.474381i
$952$	1.59271	−	15.1537i	0.0516202	−	0.491133i
$953$	−5.64439	−	4.10089i	−0.182840	−	0.132841i	0.492601	−	0.870256i	$-0.336046\pi$
$953$	−5.64439	−	4.10089i	−0.182840	−	0.132841i	−0.675440	+	0.737415i	$0.736046\pi$
$954$	0.0406981	+	0.387216i	0.00131765	+	0.0125366i
$955$	19.3327	−	33.4852i	0.625590	−	1.08355i
$956$	0.396044	+	0.685968i	0.0128090	+	0.0221858i
$957$	−7.67087	+	5.57321i	−0.247964	+	0.180156i
$958$	−12.6479	−	14.0469i	−0.408634	−	0.453834i
$959$	2.98842	+	9.19741i	0.0965011	+	0.297000i
$960$	−27.9601			−0.902407
$961$	13.1871	+	28.0553i	0.425392	+	0.905009i
$962$	38.0075			1.22541
$963$	3.35006	+	10.3104i	0.107954	+	0.332249i
$964$	−1.54617	−	1.71719i	−0.0497986	−	0.0553070i
$965$	−15.3009	+	11.1167i	−0.492553	+	0.357860i
$966$	−7.27052	−	12.5929i	−0.233925	−	0.405170i
$967$	6.36487	−	11.0243i	0.204680	−	0.354517i	−0.745351	−	0.666673i	$-0.767718\pi$
$967$	6.36487	−	11.0243i	0.204680	−	0.354517i	0.950031	+	0.312156i	$0.101051\pi$
$968$	−3.70488	−	35.2496i	−0.119079	−	1.13296i
$969$	10.2205	+	7.42559i	0.328328	+	0.238544i
$970$	4.31576	−	41.0617i	0.138571	−	1.31841i
$971$	27.9118	−	30.9992i	0.895734	−	0.994813i	−0.104266	−	0.994549i	$-0.533249\pi$
$971$	27.9118	−	30.9992i	0.895734	−	0.994813i	1.00000		0.000263577i	$-8.38991e-5\pi$
$972$	−0.155295	−	0.0691418i	−0.00498109	−	0.00221772i
$973$	−9.77325	−	2.07737i	−0.313316	−	0.0665974i
$974$	−11.9650	+	2.54325i	−0.383385	+	0.0814910i
$975$	−16.0444	+	7.14342i	−0.513832	+	0.228773i
$976$	7.83918	−	24.1265i	0.250926	−	0.772271i
$977$	4.56051	−	14.0358i	0.145904	−	0.449045i	−0.851222	−	0.524805i	$-0.824138\pi$
$977$	4.56051	−	14.0358i	0.145904	−	0.449045i	0.997126	+	0.0757598i	$0.0241382\pi$
$978$	−13.0867	+	5.82656i	−0.418466	+	0.186313i
$979$	6.90868	−	1.46849i	0.220802	−	0.0469330i
$980$	2.69710	+	0.573286i	0.0861557	+	0.0183130i
$981$	15.1637	+	6.75131i	0.484139	+	0.215553i
$982$	15.2279	−	16.9123i	0.485942	−	0.539694i
$983$	−4.81179	+	45.7812i	−0.153472	+	1.46019i	0.598566	+	0.801073i	$0.295737\pi$
$983$	−4.81179	+	45.7812i	−0.153472	+	1.46019i	−0.752039	+	0.659119i	$0.770929\pi$
$984$	−12.2020	−	8.86528i	−0.388986	−	0.282615i
$985$	5.50209	+	52.3488i	0.175311	+	1.66797i
$986$	4.85875	−	8.41560i	0.154734	−	0.268007i
$987$	−7.56119	−	13.0964i	−0.240675	−	0.416862i
$988$	−1.47866	+	1.07431i	−0.0470425	+	0.0341783i
$989$	21.1525	+	23.4923i	0.672611	+	0.747011i
$990$	−6.55938	−	20.1877i	−0.208471	−	0.641607i
$991$	−6.23101			−0.197934			−0.0989672	−	0.995091i	$-0.531554\pi$
$991$	−6.23101			−0.197934			−0.0989672	+	0.995091i	$0.531554\pi$
$992$	4.50736	+	2.86181i	0.143109	+	0.0908625i
$993$	14.5737			0.462483
$994$	5.71821	+	17.5988i	0.181371	+	0.558201i
$995$	−20.1155	−	22.3405i	−0.637703	−	0.708241i
$996$	−0.901025	+	0.654633i	−0.0285501	+	0.0207428i
$997$	−6.97285	−	12.0773i	−0.220832	−	0.382493i	0.734229	−	0.678902i	$-0.237544\pi$
$997$	−6.97285	−	12.0773i	−0.220832	−	0.382493i	−0.955061	+	0.296410i	$0.904211\pi$
$998$	−2.76075	+	4.78176i	−0.0873901	+	0.151364i
$999$	−0.948207	−	9.02158i	−0.0299999	−	0.285430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.m.b.82.1	yes	24
3.2	odd	2		279.2.y.d.82.3		24
31.13	odd	30		2883.2.a.s.1.2		12
31.14	even	15	inner	93.2.m.b.76.1	✓	24
31.18	even	15		2883.2.a.t.1.2		12
93.14	odd	30		279.2.y.d.262.3		24
93.44	even	30		8649.2.a.bl.1.11		12
93.80	odd	30		8649.2.a.bk.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.76.1	✓	24	31.14	even	15	inner
93.2.m.b.82.1	yes	24	1.1	even	1	trivial
279.2.y.d.82.3		24	3.2	odd	2
279.2.y.d.262.3		24	93.14	odd	30
2883.2.a.s.1.2		12	31.13	odd	30
2883.2.a.t.1.2		12	31.18	even	15
8649.2.a.bk.1.11		12	93.80	odd	30
8649.2.a.bl.1.11		12	93.44	even	30

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.418031 - 1.28657i) q^{2} +(0.669131 + 0.743145i) q^{3} +(0.137526 - 0.0999185i) q^{4} +(1.63328 + 2.82893i) q^{5} +(0.676389 - 1.17154i) q^{6} +(-0.149090 - 1.41850i) q^{7} +(-2.37488 - 1.72545i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.418031 - 1.28657i) q^{2} +(0.669131 + 0.743145i) q^{3} +(0.137526 - 0.0999185i) q^{4} +(1.63328 + 2.82893i) q^{5} +(0.676389 - 1.17154i) q^{6} +(-0.149090 - 1.41850i) q^{7} +(-2.37488 - 1.72545i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(2.95685 - 3.28391i) q^{10} +(-4.38826 - 1.95378i) q^{11} +(0.166277 + 0.0353432i) q^{12} +(3.02956 - 0.643952i) q^{13} +(-1.76267 + 0.784793i) q^{14} +(-1.00942 + 3.10669i) q^{15} +(-1.12208 + 3.45340i) q^{16} +(-3.32456 + 1.48019i) q^{17} +(1.32322 - 0.281258i) q^{18} +(-3.39558 - 0.721752i) q^{19} +(0.507281 + 0.225856i) q^{20} +(0.954391 - 1.05996i) q^{21} +(-0.679240 + 6.46254i) q^{22} +(6.09693 + 4.42968i) q^{23} +(-0.306845 - 2.91944i) q^{24} +(-2.83523 + 4.91076i) q^{25} +(-2.09494 - 3.62854i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.162238 - 0.180184i) q^{28} +(-0.609968 - 1.87729i) q^{29} +4.41894 q^{30} +(-4.70038 - 2.98436i) q^{31} -0.958934 q^{32} +(-1.48438 - 4.56845i) q^{33} +(3.29413 + 3.65850i) q^{34} +(3.76933 - 2.73858i) q^{35} +(0.0849957 + 0.147217i) q^{36} +(-4.53564 + 7.85596i) q^{37} +(0.490874 + 4.67035i) q^{38} +(2.50572 + 1.82051i) q^{39} +(1.00233 - 9.53653i) q^{40} +(3.43795 - 3.81823i) q^{41} +(-1.76267 - 0.784793i) q^{42} +(4.10301 + 0.872121i) q^{43} +(-0.798719 + 0.169773i) q^{44} +(-2.98416 + 1.32863i) q^{45} +(3.15038 - 9.69586i) q^{46} +(3.27633 - 10.0835i) q^{47} +(-3.31719 + 1.47691i) q^{48} +(4.85712 - 1.03241i) q^{49} +(7.50325 + 1.59486i) q^{50} +(-3.32456 - 1.48019i) q^{51} +(0.352300 - 0.391269i) q^{52} +(-0.0300848 + 0.286238i) q^{53} +(1.09442 + 0.795143i) q^{54} +(-1.64017 - 15.6052i) q^{55} +(-2.09349 + 3.62602i) q^{56} +(-1.73572 - 3.00635i) q^{57} +(-2.16027 + 1.56953i) q^{58} +(2.55052 + 2.83264i) q^{59} +(0.171594 + 0.528111i) q^{60} -6.98631 q^{61} +(-1.87468 + 7.29492i) q^{62} +1.42631 q^{63} +(2.64502 + 8.14054i) q^{64} +(6.76982 + 7.51865i) q^{65} +(-5.25710 + 3.81951i) q^{66} +(4.01427 + 6.95292i) q^{67} +(-0.309315 + 0.535749i) q^{68} +(0.787750 + 7.49494i) q^{69} +(-5.09907 - 3.70469i) q^{70} +(1.00247 - 9.53784i) q^{71} +(1.96424 - 2.18151i) q^{72} +(10.4141 + 4.63666i) q^{73} +(12.0033 + 2.55137i) q^{74} +(-5.54655 + 1.17895i) q^{75} +(-0.539096 + 0.240021i) q^{76} +(-2.11719 + 6.51605i) q^{77} +(1.29474 - 3.98481i) q^{78} +(-8.15681 + 3.63165i) q^{79} +(-11.6021 + 2.46610i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-6.34959 - 2.82702i) q^{82} +(-4.38393 + 4.86884i) q^{83} +(0.0253441 - 0.241133i) q^{84} +(-9.61729 - 6.98737i) q^{85} +(-0.593142 - 5.64337i) q^{86} +(0.986948 - 1.70944i) q^{87} +(7.05045 + 12.2117i) q^{88} +(-1.18956 + 0.864265i) q^{89} +(2.95685 + 3.28391i) q^{90} +(-1.36513 - 4.20142i) q^{91} +1.28109 q^{92} +(-0.927353 - 5.48999i) q^{93} -14.3427 q^{94} +(-3.50415 - 10.7847i) q^{95} +(-0.641652 - 0.712627i) q^{96} +(7.55896 - 5.49190i) q^{97} +(-3.35870 - 5.81743i) q^{98} +(2.40178 - 4.16000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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