LMFDB - Embedded newform 520.2.ca.b.101.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.12
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.b.381.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.417482 + 1.35119i) q^{2} +(-1.00502 + 0.580249i) q^{3} +(-1.65142 - 1.12819i) q^{4} +1.00000 q^{5} +(-0.364447 - 1.60022i) q^{6} +(-2.74313 - 1.58374i) q^{7} +(2.21384 - 1.76037i) q^{8} +(-0.826622 + 1.43175i) q^{9} +O(q^{10})$	\(q+(-0.417482 + 1.35119i) q^{2} +(-1.00502 + 0.580249i) q^{3} +(-1.65142 - 1.12819i) q^{4} +1.00000 q^{5} +(-0.364447 - 1.60022i) q^{6} +(-2.74313 - 1.58374i) q^{7} +(2.21384 - 1.76037i) q^{8} +(-0.826622 + 1.43175i) q^{9} +(-0.417482 + 1.35119i) q^{10} +(-1.23270 - 2.13510i) q^{11} +(2.31434 + 0.175626i) q^{12} +(3.60242 - 0.150193i) q^{13} +(3.28514 - 3.04529i) q^{14} +(-1.00502 + 0.580249i) q^{15} +(1.45435 + 3.72624i) q^{16} +(0.369228 - 0.639522i) q^{17} +(-1.58946 - 1.71465i) q^{18} +(4.31749 - 7.47811i) q^{19} +(-1.65142 - 1.12819i) q^{20} +3.67586 q^{21} +(3.39956 - 0.774244i) q^{22} +(2.88507 + 4.99708i) q^{23} +(-1.20350 + 3.05379i) q^{24} +1.00000 q^{25} +(-1.30101 + 4.93025i) q^{26} -5.40008i q^{27} +(2.74327 + 5.71020i) q^{28} +(1.59257 - 0.919468i) q^{29} +(-0.364447 - 1.60022i) q^{30} -9.05883i q^{31} +(-5.64202 + 0.409467i) q^{32} +(2.47778 + 1.43055i) q^{33} +(0.709967 + 0.765885i) q^{34} +(-2.74313 - 1.58374i) q^{35} +(2.98039 - 1.43183i) q^{36} +(1.35800 + 2.35212i) q^{37} +(8.30185 + 8.95571i) q^{38} +(-3.53336 + 2.24125i) q^{39} +(2.21384 - 1.76037i) q^{40} +(0.165016 - 0.0952718i) q^{41} +(-1.53461 + 4.96678i) q^{42} +(7.43510 + 4.29266i) q^{43} +(-0.373106 + 4.91667i) q^{44} +(-0.826622 + 1.43175i) q^{45} +(-7.95646 + 1.81207i) q^{46} +8.23945i q^{47} +(-3.62380 - 2.90106i) q^{48} +(1.51649 + 2.62664i) q^{49} +(-0.417482 + 1.35119i) q^{50} +0.856977i q^{51} +(-6.11855 - 3.81620i) q^{52} -4.18560i q^{53} +(7.29652 + 2.25444i) q^{54} +(-1.23270 - 2.13510i) q^{55} +(-8.86082 + 1.32277i) q^{56} +10.0209i q^{57} +(0.577506 + 2.53572i) q^{58} +(5.72512 - 9.91620i) q^{59} +(2.31434 + 0.175626i) q^{60} +(-4.03040 - 2.32695i) q^{61} +(12.2402 + 3.78190i) q^{62} +(4.53506 - 2.61832i) q^{63} +(1.80218 - 7.79437i) q^{64} +(3.60242 - 0.150193i) q^{65} +(-2.96737 + 2.75072i) q^{66} +(-1.66496 - 2.88379i) q^{67} +(-1.33125 + 0.639556i) q^{68} +(-5.79911 - 3.34812i) q^{69} +(3.28514 - 3.04529i) q^{70} +(-3.24673 - 1.87450i) q^{71} +(0.690407 + 4.62483i) q^{72} -1.03291i q^{73} +(-3.74510 + 0.852941i) q^{74} +(-1.00502 + 0.580249i) q^{75} +(-15.5667 + 7.47851i) q^{76} +7.80914i q^{77} +(-1.55323 - 5.70991i) q^{78} -9.18672 q^{79} +(1.45435 + 3.72624i) q^{80} +(0.653525 + 1.13194i) q^{81} +(0.0598390 + 0.262741i) q^{82} +1.79420 q^{83} +(-6.07038 - 4.14709i) q^{84} +(0.369228 - 0.639522i) q^{85} +(-8.90422 + 8.25411i) q^{86} +(-1.06704 + 1.84817i) q^{87} +(-6.48758 - 2.55676i) q^{88} +(12.1943 - 7.04039i) q^{89} +(-1.58946 - 1.71465i) q^{90} +(-10.1198 - 5.29332i) q^{91} +(0.873233 - 11.5072i) q^{92} +(5.25638 + 9.10431i) q^{93} +(-11.1330 - 3.43983i) q^{94} +(4.31749 - 7.47811i) q^{95} +(5.43275 - 3.68530i) q^{96} +(-14.8416 - 8.56882i) q^{97} +(-4.18219 + 0.952488i) q^{98} +4.07592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

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 $

$2$	−0.417482	+	1.35119i	−0.295205	+	0.955434i
$2$	−0.417482	+	1.35119i	−0.295205	+	0.955434i
$3$	−1.00502	+	0.580249i	−0.580249	+	0.335007i	−0.761232	−	0.648479i	$-0.775405\pi$
$3$	−1.00502	+	0.580249i	−0.580249	+	0.335007i	0.180983	+	0.983486i	$0.442072\pi$
$4$	−1.65142	−	1.12819i	−0.825708	−	0.564097i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.364447	−	1.60022i	−0.148785	−	0.653285i
$7$	−2.74313	−	1.58374i	−1.03680	−	0.598599i	−0.117878	−	0.993028i	$-0.537609\pi$
$7$	−2.74313	−	1.58374i	−1.03680	−	0.598599i	−0.918926	+	0.394429i	$0.870942\pi$
$8$	2.21384	−	1.76037i	0.782711	−	0.622386i
$9$	−0.826622	+	1.43175i	−0.275541	+	0.477251i
$10$	−0.417482	+	1.35119i	−0.132020	+	0.427283i
$11$	−1.23270	−	2.13510i	−0.371674	−	0.643758i	0.618149	−	0.786061i	$-0.287883\pi$
$11$	−1.23270	−	2.13510i	−0.371674	−	0.643758i	−0.989823	+	0.142303i	$0.954549\pi$
$12$	2.31434	+	0.175626i	0.668093	+	0.0506988i
$13$	3.60242	−	0.150193i	0.999132	−	0.0416560i
$13$	3.60242	−	0.150193i	0.999132	−	0.0416560i
$14$	3.28514	−	3.04529i	0.877991	−	0.813888i
$15$	−1.00502	+	0.580249i	−0.259495	+	0.149820i
$16$	1.45435	+	3.72624i	0.363589	+	0.931560i
$17$	0.369228	−	0.639522i	0.0895509	−	0.155107i	−0.817770	−	0.575544i	$-0.804790\pi$
$17$	0.369228	−	0.639522i	0.0895509	−	0.155107i	0.907321	+	0.420438i	$0.138123\pi$
$18$	−1.58946	−	1.71465i	−0.374640	−	0.404148i
$19$	4.31749	−	7.47811i	0.990499	−	1.71560i	0.376157	−	0.926556i	$-0.377245\pi$
$19$	4.31749	−	7.47811i	0.990499	−	1.71560i	0.614342	−	0.789040i	$-0.289421\pi$
$20$	−1.65142	−	1.12819i	−0.369268	−	0.252272i
$21$	3.67586			0.802139
$22$	3.39956	−	0.774244i	0.724788	−	0.165069i
$23$	2.88507	+	4.99708i	0.601578	+	1.04196i	0.992582	+	0.121575i	$0.0387945\pi$
$23$	2.88507	+	4.99708i	0.601578	+	1.04196i	−0.391004	+	0.920389i	$0.627872\pi$
$24$	−1.20350	+	3.05379i	−0.245664	+	0.623352i
$25$	1.00000			0.200000
$26$	−1.30101	+	4.93025i	−0.255149	+	0.966902i
$27$		−	5.40008i		−	1.03925i
$28$	2.74327	+	5.71020i	0.518430	+	1.07913i
$29$	1.59257	−	0.919468i	0.295732	−	0.170741i	−0.344792	−	0.938679i	$-0.612051\pi$
$29$	1.59257	−	0.919468i	0.295732	−	0.170741i	0.640524	+	0.767938i	$0.278717\pi$
$30$	−0.364447	−	1.60022i	−0.0665386	−	0.292158i
$31$		−	9.05883i		−	1.62701i	−0.581556	−	0.813507i	$-0.697556\pi$
$31$		−	9.05883i		−	1.62701i	0.581556	−	0.813507i	$-0.302444\pi$
$32$	−5.64202	+	0.409467i	−0.997377	+	0.0723842i
$33$	2.47778	+	1.43055i	0.431327	+	0.249027i
$34$	0.709967	+	0.765885i	0.121758	+	0.131348i
$35$	−2.74313	−	1.58374i	−0.463673	−	0.267702i
$36$	2.98039	−	1.43183i	0.496732	−	0.238638i
$37$	1.35800	+	2.35212i	0.223253	+	0.386686i	0.955794	−	0.294037i	$-0.0949989\pi$
$37$	1.35800	+	2.35212i	0.223253	+	0.386686i	−0.732541	+	0.680723i	$0.761666\pi$
$38$	8.30185	+	8.95571i	1.34674	+	1.45281i
$39$	−3.53336	+	2.24125i	−0.565790	+	0.358887i
$40$	2.21384	−	1.76037i	0.350039	−	0.278339i
$41$	0.165016	−	0.0952718i	0.0257711	−	0.0148790i	−0.487059	−	0.873369i	$-0.661930\pi$
$41$	0.165016	−	0.0952718i	0.0257711	−	0.0148790i	0.512830	+	0.858490i	$0.328597\pi$
$42$	−1.53461	+	4.96678i	−0.236795	+	0.766391i
$43$	7.43510	+	4.29266i	1.13384	+	0.654624i	0.944899	−	0.327363i	$-0.106160\pi$
$43$	7.43510	+	4.29266i	1.13384	+	0.654624i	0.188944	+	0.981988i	$0.439493\pi$
$44$	−0.373106	+	4.91667i	−0.0562479	+	0.741216i
$45$	−0.826622	+	1.43175i	−0.123226	+	0.213433i
$46$	−7.95646	+	1.81207i	−1.17312	+	0.267176i
$47$			8.23945i			1.20185i	0.799307	+	0.600923i	$0.205200\pi$
$47$			8.23945i			1.20185i	−0.799307	+	0.600923i	$0.794800\pi$
$48$	−3.62380	−	2.90106i	−0.523051	−	0.418732i
$49$	1.51649	+	2.62664i	0.216642	+	0.375234i
$50$	−0.417482	+	1.35119i	−0.0590409	+	0.191087i
$51$			0.856977i			0.120001i
$52$	−6.11855	−	3.81620i	−0.848490	−	0.529212i
$53$		−	4.18560i		−	0.574936i	−0.957790	−	0.287468i	$-0.907186\pi$
$53$		−	4.18560i		−	0.574936i	0.957790	−	0.287468i	$-0.0928135\pi$
$54$	7.29652	+	2.25444i	0.992931	+	0.306790i
$55$	−1.23270	−	2.13510i	−0.166218	−	0.287897i
$56$	−8.86082	+	1.32277i	−1.18408	+	0.176762i
$57$			10.0209i			1.32730i
$58$	0.577506	+	2.53572i	0.0758302	+	0.332956i
$59$	5.72512	−	9.91620i	0.745347	−	1.29098i	−0.204685	−	0.978828i	$-0.565617\pi$
$59$	5.72512	−	9.91620i	0.745347	−	1.29098i	0.950032	−	0.312151i	$-0.101050\pi$
$60$	2.31434	+	0.175626i	0.298780	+	0.0226732i
$61$	−4.03040	−	2.32695i	−0.516040	−	0.297936i	0.219273	−	0.975664i	$-0.429632\pi$
$61$	−4.03040	−	2.32695i	−0.516040	−	0.297936i	−0.735313	+	0.677728i	$0.762965\pi$
$62$	12.2402	+	3.78190i	1.55450	+	0.480302i
$63$	4.53506	−	2.61832i	0.571363	−	0.329877i
$64$	1.80218	−	7.79437i	0.225272	−	0.974296i
$65$	3.60242	−	0.150193i	0.446825	−	0.0186291i
$66$	−2.96737	+	2.75072i	−0.365258	+	0.338590i
$67$	−1.66496	−	2.88379i	−0.203407	−	0.352311i	0.746217	−	0.665703i	$-0.231868\pi$
$67$	−1.66496	−	2.88379i	−0.203407	−	0.352311i	−0.949624	+	0.313391i	$0.898535\pi$
$68$	−1.33125	+	0.639556i	−0.161438	+	0.0775575i
$69$	−5.79911	−	3.34812i	−0.698130	−	0.403066i
$70$	3.28514	−	3.04529i	0.392650	−	0.363982i
$71$	−3.24673	−	1.87450i	−0.385316	−	0.222462i	0.294813	−	0.955555i	$-0.404743\pi$
$71$	−3.24673	−	1.87450i	−0.385316	−	0.222462i	−0.680129	+	0.733093i	$0.738076\pi$
$72$	0.690407	+	4.62483i	0.0813652	+	0.545042i
$73$		−	1.03291i		−	0.120893i	−0.998171	−	0.0604467i	$-0.980747\pi$
$73$		−	1.03291i		−	0.120893i	0.998171	−	0.0604467i	$-0.0192525\pi$
$74$	−3.74510	+	0.852941i	−0.435359	+	0.0991523i
$75$	−1.00502	+	0.580249i	−0.116050	+	0.0670014i
$76$	−15.5667	+	7.47851i	−1.78563	+	0.857843i
$77$			7.80914i			0.889934i
$78$	−1.55323	−	5.70991i	−0.175869	−	0.646520i
$79$	−9.18672			−1.03359			−0.516793	−	0.856110i	$-0.672874\pi$
$79$	−9.18672			−1.03359			−0.516793	+	0.856110i	$0.672874\pi$
$80$	1.45435	+	3.72624i	0.162602	+	0.416606i
$81$	0.653525	+	1.13194i	0.0726139	+	0.125771i
$82$	0.0598390	+	0.262741i	0.00660811	+	0.0290149i
$83$	1.79420			0.196939			0.0984693	−	0.995140i	$-0.468605\pi$
$83$	1.79420			0.196939			0.0984693	+	0.995140i	$0.468605\pi$
$84$	−6.07038	−	4.14709i	−0.662333	−	0.452485i
$85$	0.369228	−	0.639522i	0.0400484	−	0.0693658i
$86$	−8.90422	+	8.25411i	−0.960166	+	0.890064i
$87$	−1.06704	+	1.84817i	−0.114399	+	0.198145i
$88$	−6.48758	−	2.55676i	−0.691579	−	0.272552i
$89$	12.1943	−	7.04039i	1.29260	−	0.746280i	0.313482	−	0.949594i	$-0.398505\pi$
$89$	12.1943	−	7.04039i	1.29260	−	0.746280i	0.979114	+	0.203314i	$0.0651712\pi$
$90$	−1.58946	−	1.71465i	−0.167544	−	0.180740i
$91$	−10.1198	−	5.29332i	−1.06084	−	0.554890i
$92$	0.873233	−	11.5072i	0.0910409	−	1.19971i
$93$	5.25638	+	9.10431i	0.545061	+	0.944073i
$94$	−11.1330	−	3.43983i	−1.14829	−	0.354791i
$95$	4.31749	−	7.47811i	0.442965	−	0.767238i
$96$	5.43275	−	3.68530i	0.554478	−	0.376129i
$97$	−14.8416	−	8.56882i	−1.50694	−	0.870032i	−0.999967	−	0.00806860i	$-0.997432\pi$
$97$	−14.8416	−	8.56882i	−1.50694	−	0.870032i	−0.506971	−	0.861963i	$-0.669235\pi$
$98$	−4.18219	+	0.952488i	−0.422465	+	0.0962158i
$99$	4.07592			0.409645
$100$	−1.65142	−	1.12819i	−0.165142	−	0.112819i
$101$	4.58812	−	2.64895i	0.456535	−	0.263580i	−0.254051	−	0.967191i	$-0.581763\pi$
$101$	4.58812	−	2.64895i	0.456535	−	0.263580i	0.710586	+	0.703610i	$0.248430\pi$
$102$	−1.15794	−	0.357773i	−0.114653	−	0.0354248i
$103$	−7.06565			−0.696199			−0.348100	−	0.937458i	$-0.613173\pi$
$103$	−7.06565			−0.696199			−0.348100	+	0.937458i	$0.613173\pi$
$104$	7.71079	−	6.67411i	0.756105	−	0.654450i
$105$	3.67586			0.358728
$106$	5.65553	+	1.74741i	0.549314	+	0.169724i
$107$	−10.2327	+	5.90788i	−0.989237	+	0.571136i	−0.905046	−	0.425313i	$-0.860164\pi$
$107$	−10.2327	+	5.90788i	−0.989237	+	0.571136i	−0.0841908	+	0.996450i	$0.526831\pi$
$108$	−6.09234	+	8.91778i	−0.586236	+	0.858114i
$109$	3.12953			0.299754			0.149877	−	0.988705i	$-0.452112\pi$
$109$	3.12953			0.299754			0.149877	+	0.988705i	$0.452112\pi$
$110$	3.39956	−	0.774244i	0.324135	−	0.0738213i
$111$	−2.72963	−	1.57595i	−0.259085	−	0.149583i
$112$	1.91193	−	12.5249i	0.180661	−	1.18349i
$113$	9.72386	−	16.8422i	0.914744	−	1.58438i	0.107468	−	0.994209i	$-0.465726\pi$
$113$	9.72386	−	16.8422i	0.914744	−	1.58438i	0.807276	−	0.590174i	$-0.200941\pi$
$114$	−13.5401	−	4.18354i	−1.26814	−	0.391824i
$115$	2.88507	+	4.99708i	0.269034	+	0.465980i
$116$	−3.66733	−	0.278299i	−0.340503	−	0.0258394i
$117$	−2.76280	+	5.28193i	−0.255421	+	0.488314i
$118$	11.0085	+	11.8756i	1.01342	+	1.09323i
$119$	−2.02568	+	1.16953i	−0.185693	+	0.107210i
$120$	−1.20350	+	3.05379i	−0.109864	+	0.278772i
$121$	2.46089	−	4.26239i	0.223717	−	0.387490i
$122$	4.82677	−	4.47437i	0.436996	−	0.405090i
$123$	−0.110563	+	0.191500i	−0.00996910	+	0.0172670i
$124$	−10.2201	+	14.9599i	−0.917794	+	1.34344i
$125$	1.00000			0.0894427
$126$	1.64453	+	7.22081i	0.146506	+	0.643281i
$127$	−1.96907	−	3.41052i	−0.174726	−	0.302635i	0.765340	−	0.643626i	$-0.222571\pi$
$127$	−1.96907	−	3.41052i	−0.174726	−	0.302635i	−0.940067	+	0.340991i	$0.889237\pi$
$128$	9.77928	+	5.68909i	0.864374	+	0.502849i
$129$	−9.96325			−0.877215
$130$	−1.30101	+	4.93025i	−0.114106	+	0.432412i
$131$		−	9.67553i		−	0.845355i	−0.906280	−	0.422678i	$-0.861090\pi$
$131$		−	9.67553i		−	0.845355i	0.906280	−	0.422678i	$-0.138910\pi$
$132$	−2.47792	−	5.15785i	−0.215675	−	0.448933i
$133$	−23.6868	+	13.6756i	−2.05391	+	1.18582i
$134$	4.59164	−	1.04574i	0.396657	−	0.0903381i
$135$		−	5.40008i		−	0.464765i
$136$	−0.308385	−	2.06578i	−0.0264438	−	0.177139i
$137$	13.2517	+	7.65088i	1.13217	+	0.653659i	0.944480	−	0.328569i	$-0.106566\pi$
$137$	13.2517	+	7.65088i	1.13217	+	0.653659i	0.187691	+	0.982228i	$0.439900\pi$
$138$	6.94496	−	6.43790i	0.591194	−	0.548031i
$139$	7.64524	+	4.41398i	0.648461	+	0.374389i	0.787866	−	0.615846i	$-0.211186\pi$
$139$	7.64524	+	4.41398i	0.648461	+	0.374389i	−0.139406	+	0.990235i	$0.544519\pi$
$140$	2.74327	+	5.71020i	0.231849	+	0.482600i
$141$	−4.78093	−	8.28082i	−0.402627	−	0.697371i
$142$	3.88825	−	3.60437i	0.326295	−	0.302472i
$143$	−4.76139	−	7.50640i	−0.398168	−	0.627717i
$144$	−6.53725	−	0.997917i	−0.544771	−	0.0831597i
$145$	1.59257	−	0.919468i	0.132255	−	0.0763577i
$146$	1.39566	+	0.431223i	0.115506	+	0.0356883i
$147$	−3.04821	−	1.75988i	−0.251412	−	0.145153i
$148$	0.411030	−	5.41642i	0.0337864	−	0.445227i
$149$	−6.58106	+	11.3987i	−0.539141	+	0.933820i	0.459809	+	0.888018i	$0.347918\pi$
$149$	−6.58106	+	11.3987i	−0.539141	+	0.933820i	−0.998951	+	0.0458023i	$0.985416\pi$
$150$	−0.364447	−	1.60022i	−0.0297570	−	0.130657i
$151$			17.2918i			1.40719i	0.710602	+	0.703594i	$0.248422\pi$
$151$			17.2918i			1.40719i	−0.710602	+	0.703594i	$0.751578\pi$
$152$	−3.60603	−	24.1557i	−0.292488	−	1.95929i
$153$	0.610424	+	1.05729i	0.0493499	+	0.0854765i
$154$	−10.5516	−	3.26018i	−0.850273	−	0.262713i
$155$		−	9.05883i		−	0.727623i
$156$	8.36361	+	0.285081i	0.669625	+	0.0228247i
$157$		−	23.8530i		−	1.90367i	−0.306603	−	0.951837i	$-0.599192\pi$
$157$		−	23.8530i		−	1.90367i	0.306603	−	0.951837i	$-0.400808\pi$
$158$	3.83529	−	12.4130i	0.305120	−	0.987524i
$159$	2.42869	+	4.20661i	0.192608	+	0.333606i
$160$	−5.64202	+	0.409467i	−0.446040	+	0.0323712i
$161$		−	18.2768i		−	1.44042i
$162$	−1.80230	+	0.410471i	−0.141602	+	0.0322496i
$163$	1.04268	−	1.80598i	0.0816692	−	0.141455i	−0.822298	−	0.569057i	$-0.807308\pi$
$163$	1.04268	−	1.80598i	0.0816692	−	0.141455i	0.903967	+	0.427602i	$0.140642\pi$
$164$	−0.379995	−	0.0288362i	−0.0296726	−	0.00225173i
$165$	2.47778	+	1.43055i	0.192895	+	0.111368i
$166$	−0.749045	+	2.42429i	−0.0581372	+	0.188162i
$167$	−13.6936	+	7.90603i	−1.05965	+	0.611787i	−0.925334	−	0.379152i	$-0.876216\pi$
$167$	−13.6936	+	7.90603i	−1.05965	+	0.611787i	−0.134312	+	0.990939i	$0.542882\pi$
$168$	8.13777	−	6.47089i	0.627843	−	0.499240i
$169$	12.9549	−	1.08212i	0.996530	−	0.0832398i
$170$	0.709967	+	0.765885i	0.0544520	+	0.0587407i
$171$	7.13786	+	12.3631i	0.545846	+	0.945433i
$172$	−7.43550	−	15.4772i	−0.566952	−	1.18013i
$173$	7.84473	+	4.52916i	0.596424	+	0.344345i	0.767633	−	0.640889i	$-0.221434\pi$
$173$	7.84473	+	4.52916i	0.596424	+	0.344345i	−0.171210	+	0.985235i	$0.554768\pi$
$174$	−2.05175	−	2.21335i	−0.155543	−	0.167794i
$175$	−2.74313	−	1.58374i	−0.207361	−	0.119720i
$176$	6.16312	−	7.69854i	0.464562	−	0.580299i
$177$			13.2880i			0.998786i
$178$	4.42198	+	19.4161i	0.331441	+	1.45530i
$179$	−9.85005	+	5.68693i	−0.736227	+	0.425061i	−0.820696	−	0.571365i	$-0.806414\pi$
$179$	−9.85005	+	5.68693i	−0.736227	+	0.425061i	0.0844689	+	0.996426i	$0.473081\pi$
$180$	2.98039	−	1.43183i	0.222145	−	0.106722i
$181$			17.5350i			1.30337i	0.758490	+	0.651685i	$0.225937\pi$
$181$			17.5350i			1.30337i	−0.758490	+	0.651685i	$0.774063\pi$
$182$	11.3771	−	11.4638i	0.843326	−	0.849756i
$183$	5.40085			0.399242
$184$	15.1838	+	5.98395i	1.11937	+	0.441143i
$185$	1.35800	+	2.35212i	0.0998420	+	0.172931i
$186$	−14.4961	+	3.30146i	−1.06290	+	0.242075i
$187$	−1.82059			−0.133135
$188$	9.29570	−	13.6068i	0.677959	−	0.992375i
$189$	−8.55235	+	14.8131i	−0.622092	+	1.07749i
$190$	8.30185	+	8.95571i	0.602280	+	0.649716i
$191$	0.345693	−	0.598758i	0.0250135	−	0.0433246i	−0.853248	−	0.521506i	$-0.825370\pi$
$191$	0.345693	−	0.598758i	0.0250135	−	0.0433246i	0.878261	+	0.478181i	$0.158704\pi$
$192$	2.71145	+	8.87921i	0.195682	+	0.640802i
$193$	4.73055	−	2.73118i	0.340512	−	0.196595i	−0.319986	−	0.947422i	$-0.603678\pi$
$193$	4.73055	−	2.73118i	0.340512	−	0.196595i	0.660499	+	0.750827i	$0.270345\pi$
$194$	17.7742	−	16.4765i	1.27611	−	1.18294i
$195$	−3.53336	+	2.24125i	−0.253029	+	0.160499i
$196$	0.459001	−	6.04857i	0.0327858	−	0.432041i
$197$	6.97854	+	12.0872i	0.497200	+	0.861176i	0.999995	−	0.00322997i	$-0.00102813\pi$
$197$	6.97854	+	12.0872i	0.497200	+	0.861176i	−0.502795	+	0.864406i	$0.667695\pi$
$198$	−1.70162	+	5.50733i	−0.120929	+	0.391389i
$199$	−12.4653	+	21.5906i	−0.883644	+	1.53052i	−0.0363850	+	0.999338i	$0.511584\pi$
$199$	−12.4653	+	21.5906i	−0.883644	+	1.53052i	−0.847259	+	0.531179i	$0.821749\pi$
$200$	2.21384	−	1.76037i	0.156542	−	0.124477i
$201$	3.34664	+	1.93218i	0.236054	+	0.136286i
$202$	1.66377	+	7.30530i	0.117063	+	0.513999i
$203$	−5.82481			−0.408821
$204$	0.966836	−	1.41523i	0.0676921	−	0.0990856i
$205$	0.165016	−	0.0952718i	0.0115252	−	0.00665407i
$206$	2.94979	−	9.54702i	0.205521	−	0.665172i
$207$	−9.53944			−0.663037
$208$	5.79885	+	13.2050i	0.402078	+	0.915605i
$209$	−21.2887			−1.47257
$210$	−1.53461	+	4.96678i	−0.105898	+	0.342741i
$211$	−7.96783	+	4.60023i	−0.548528	+	0.316693i	−0.748528	−	0.663103i	$-0.769239\pi$
$211$	−7.96783	+	4.60023i	−0.548528	+	0.316693i	0.200000	+	0.979796i	$0.435906\pi$
$212$	−4.72217	+	6.91217i	−0.324320	+	0.474730i
$213$	4.35071			0.298106
$214$	−3.71066	−	16.2928i	−0.253656	−	1.11375i
$215$	7.43510	+	4.29266i	0.507070	+	0.292757i
$216$	−9.50615	−	11.9549i	−0.646812	−	0.813429i
$217$	−14.3469	+	24.8495i	−0.973929	+	1.68689i
$218$	−1.30652	+	4.22858i	−0.0884888	+	0.286395i
$219$	0.599347	+	1.03810i	0.0405001	+	0.0701483i
$220$	−0.373106	+	4.91667i	−0.0251548	+	0.331482i
$221$	1.23406	−	2.35928i	0.0830121	−	0.158702i
$222$	3.26898	−	3.03031i	0.219400	−	0.203381i
$223$	3.64597	−	2.10500i	0.244152	−	0.140961i	−0.372932	−	0.927859i	$-0.621647\pi$
$223$	3.64597	−	2.10500i	0.244152	−	0.140961i	0.617084	+	0.786898i	$0.288314\pi$
$224$	16.1252	+	7.81229i	1.07741	+	0.521981i
$225$	−0.826622	+	1.43175i	−0.0551081	+	0.0954501i
$226$	18.6975	+	20.1701i	1.24374	+	1.34169i
$227$	4.37813	−	7.58314i	0.290587	−	0.503311i	−0.683362	−	0.730080i	$-0.739483\pi$
$227$	4.37813	−	7.58314i	0.290587	−	0.503311i	0.973949	+	0.226769i	$0.0728162\pi$
$228$	11.3055	−	16.5486i	0.748724	−	1.09596i
$229$	−22.6655			−1.49778			−0.748889	−	0.662696i	$-0.769412\pi$
$229$	−22.6655			−1.49778			−0.748889	+	0.662696i	$0.769412\pi$
$230$	−7.95646	+	1.81207i	−0.524634	+	0.119485i
$231$	−4.53125	−	7.84835i	−0.298134	−	0.516383i
$232$	1.90708	−	4.83906i	0.125206	−	0.317700i
$233$	−16.3316			−1.06992			−0.534960	−	0.844877i	$-0.679673\pi$
$233$	−16.3316			−1.06992			−0.534960	+	0.844877i	$0.679673\pi$
$234$	−5.98345	−	5.93818i	−0.391150	−	0.388191i
$235$			8.23945i			0.537482i
$236$	−20.6420	+	9.91673i	−1.34368	+	0.645524i
$237$	9.23284	−	5.33059i	0.599738	−	0.346259i
$238$	−0.734563	−	3.22533i	−0.0476147	−	0.209067i
$239$		−	6.36009i		−	0.411400i	−0.978615	−	0.205700i	$-0.934053\pi$
$239$		−	6.36009i		−	0.411400i	0.978615	−	0.205700i	$-0.0659471\pi$
$240$	−3.62380	−	2.90106i	−0.233915	−	0.187263i
$241$	10.6580	+	6.15341i	0.686543	+	0.396376i	0.802316	−	0.596900i	$-0.203601\pi$
$241$	10.6580	+	6.15341i	0.686543	+	0.396376i	−0.115772	+	0.993276i	$0.536934\pi$
$242$	4.73191	+	5.10460i	0.304178	+	0.328136i
$243$	12.7162	+	7.34171i	0.815745	+	0.470971i
$244$	4.03062	+	8.38985i	0.258034	+	0.537105i
$245$	1.51649	+	2.62664i	0.0968850	+	0.167810i
$246$	−0.212595	−	0.229339i	−0.0135545	−	0.0146221i
$247$	14.4303	−	27.5878i	0.918175	−	1.75537i
$248$	−15.9469	−	20.0548i	−1.01263	−	1.27348i
$249$	−1.80320	+	1.04108i	−0.114273	+	0.0659758i
$250$	−0.417482	+	1.35119i	−0.0264039	+	0.0854566i
$251$	6.06987	+	3.50444i	0.383127	+	0.221198i	0.679178	−	0.733974i	$-0.262337\pi$
$251$	6.06987	+	3.50444i	0.383127	+	0.221198i	−0.296051	+	0.955172i	$0.595670\pi$
$252$	−10.4432	−	0.792495i	−0.657862	−	0.0499225i
$253$	7.11286	−	12.3198i	0.447182	−	0.774541i
$254$	5.43031	−	1.23674i	0.340728	−	0.0776003i
$255$			0.856977i			0.0536660i
$256$	−11.7697	+	10.8385i	−0.735607	+	0.677409i
$257$	9.24502	+	16.0128i	0.576688	+	0.998854i	0.995856	+	0.0909446i	$0.0289886\pi$
$257$	9.24502	+	16.0128i	0.576688	+	0.998854i	−0.419168	+	0.907909i	$0.637678\pi$
$258$	4.15948	−	13.4622i	0.258958	−	0.838121i
$259$		−	8.60288i		−	0.534557i
$260$	−6.11855	−	3.81620i	−0.379456	−	0.236671i
$261$			3.04021i			0.188184i
$262$	13.0735	+	4.03937i	0.807681	+	0.249553i
$263$	13.1616	+	22.7966i	0.811581	+	1.40570i	0.911757	+	0.410730i	$0.134726\pi$
$263$	13.1616	+	22.7966i	0.811581	+	1.40570i	−0.100176	+	0.994970i	$0.531941\pi$
$264$	8.00371	−	1.19482i	0.492595	−	0.0735358i
$265$		−	4.18560i		−	0.257119i
$266$	−8.58946	−	37.7147i	−0.526653	−	2.31243i
$267$	−8.17036	+	14.1515i	−0.500018	+	0.866057i
$268$	−0.503939	+	6.64074i	−0.0307830	+	0.405648i
$269$	4.45389	+	2.57145i	0.271558	+	0.156784i	0.629596	−	0.776923i	$-0.283221\pi$
$269$	4.45389	+	2.57145i	0.271558	+	0.156784i	−0.358037	+	0.933707i	$0.616554\pi$
$270$	7.29652	+	2.25444i	0.444052	+	0.137201i
$271$	19.4600	−	11.2352i	1.18211	−	0.682493i	0.225610	−	0.974218i	$-0.427563\pi$
$271$	19.4600	−	11.2352i	1.18211	−	0.682493i	0.956502	+	0.291725i	$0.0942293\pi$
$272$	2.92000	+	0.445740i	0.177051	+	0.0270270i
$273$	13.2420	−	0.552089i	0.801443	−	0.0334139i
$274$	−15.8701	+	14.7114i	−0.958750	+	0.888751i
$275$	−1.23270	−	2.13510i	−0.0743348	−	0.128752i
$276$	5.79942	+	12.0717i	0.349084	+	0.726628i
$277$	4.75235	+	2.74377i	0.285541	+	0.164857i	0.635929	−	0.771747i	$-0.280617\pi$
$277$	4.75235	+	2.74377i	0.285541	+	0.164857i	−0.350388	+	0.936605i	$0.613950\pi$
$278$	−9.15587	+	8.48739i	−0.549133	+	0.509040i
$279$	12.9700	+	7.48823i	0.776493	+	0.448308i
$280$	−8.86082	+	1.32277i	−0.529535	+	0.0790504i
$281$			6.19365i			0.369482i	0.982787	+	0.184741i	$0.0591447\pi$
$281$			6.19365i			0.369482i	−0.982787	+	0.184741i	$0.940855\pi$
$282$	13.1849	−	3.00284i	0.785149	−	0.178817i
$283$	−16.8496	+	9.72811i	−1.00160	+	0.578276i	−0.908722	−	0.417401i	$-0.862941\pi$
$283$	−16.8496	+	9.72811i	−1.00160	+	0.578276i	−0.0928810	+	0.995677i	$0.529608\pi$
$284$	3.24690	+	6.75852i	0.192668	+	0.401045i
$285$			10.0209i			0.593585i
$286$	12.1304	−	3.29974i	0.717283	−	0.195118i
$287$	−0.603545			−0.0356261
$288$	4.07756	−	8.41644i	0.240273	−	0.495943i
$289$	8.22734	+	14.2502i	0.483961	+	0.838245i
$290$	0.577506	+	2.53572i	0.0339123	+	0.148902i
$291$	19.8882			1.16587
$292$	−1.16533	+	1.70577i	−0.0681956	+	0.0998227i
$293$	16.3593	−	28.3351i	0.955721	−	1.65536i	0.223011	−	0.974816i	$-0.428412\pi$
$293$	16.3593	−	28.3351i	0.955721	−	1.65536i	0.732710	−	0.680541i	$-0.238255\pi$
$294$	3.65051	−	3.38398i	0.212902	−	0.197358i
$295$	5.72512	−	9.91620i	0.333329	−	0.577343i
$296$	7.14700	+	2.81664i	0.415411	+	0.163714i
$297$	−11.5297	+	6.65669i	−0.669023	+	0.386260i
$298$	−12.6543	−	13.6510i	−0.733046	−	0.790782i
$299$	11.1438	+	17.5683i	0.644460	+	1.01600i
$300$	2.31434	+	0.175626i	0.133619	+	0.0101398i
$301$	−13.5969	−	23.5506i	−0.783715	−	1.35743i
$302$	−23.3645	−	7.21903i	−1.34447	−	0.415408i
$303$	−3.07410	+	5.32450i	−0.176603	+	0.305885i
$304$	34.1444	+	5.21217i	1.95831	+	0.298938i
$305$	−4.03040	−	2.32695i	−0.230780	−	0.133241i
$306$	−1.68343	+	0.383399i	−0.0962354	+	0.0219175i
$307$	−21.1733			−1.20842			−0.604212	−	0.796824i	$-0.706512\pi$
$307$	−21.1733			−1.20842			−0.604212	+	0.796824i	$0.706512\pi$
$308$	8.81023	−	12.8961i	0.502009	−	0.734826i
$309$	7.10113	−	4.09984i	0.403969	−	0.233232i
$310$	12.2402	+	3.78190i	0.695195	+	0.214798i
$311$	17.0756			0.968271			0.484136	−	0.874993i	$-0.339134\pi$
$311$	17.0756			0.968271			0.484136	+	0.874993i	$0.339134\pi$
$312$	−3.87686	+	11.1818i	−0.219484	+	0.633045i
$313$	−25.0633			−1.41666			−0.708330	−	0.705881i	$-0.750551\pi$
$313$	−25.0633			−1.41666			−0.708330	+	0.705881i	$0.750551\pi$
$314$	32.2299	+	9.95820i	1.81884	+	0.561974i
$315$	4.53506	−	2.61832i	0.255521	−	0.147525i
$316$	15.1711	+	10.3644i	0.853441	+	0.583043i
$317$	18.2387			1.02439			0.512195	−	0.858869i	$-0.328833\pi$
$317$	18.2387			1.02439			0.512195	+	0.858869i	$0.328833\pi$
$318$	−6.69786	+	1.52543i	−0.375597	+	0.0855418i
$319$	−3.92632	−	2.26686i	−0.219832	−	0.126920i
$320$	1.80218	−	7.79437i	0.100745	−	0.435718i
$321$	6.85608	−	11.8751i	0.382669	−	0.662802i
$322$	24.6954	+	7.63026i	1.37622	+	0.425218i
$323$	−3.18827	−	5.52225i	−0.177400	−	0.307266i
$324$	0.197805	−	2.60661i	0.0109892	−	0.144811i
$325$	3.60242	−	0.150193i	0.199826	−	0.00833121i
$326$	2.00492	+	2.16282i	0.111042	+	0.119788i
$327$	−3.14524	+	1.81590i	−0.173932	+	0.100420i
$328$	0.197604	−	0.501405i	0.0109109	−	0.0276855i
$329$	13.0492	−	22.6018i	0.719424	−	1.24608i
$330$	−2.96737	+	2.75072i	−0.163348	+	0.151422i
$331$	13.4517	−	23.2990i	0.739371	−	1.28063i	−0.213409	−	0.976963i	$-0.568457\pi$
$331$	13.4517	−	23.2990i	0.739371	−	1.28063i	0.952779	−	0.303664i	$-0.0982101\pi$
$332$	−2.96296	−	2.02420i	−0.162614	−	0.111092i
$333$	−4.49020			−0.246062
$334$	−4.96567	−	21.8033i	−0.271710	−	1.19302i
$335$	−1.66496	−	2.88379i	−0.0909664	−	0.157558i
$336$	5.34601	+	13.6971i	0.291649	+	0.747241i
$337$	3.00972			0.163950			0.0819750	−	0.996634i	$-0.473877\pi$
$337$	3.00972			0.163950			0.0819750	+	0.996634i	$0.473877\pi$
$338$	−3.94629	+	17.9562i	−0.214650	+	0.976691i
$339$			22.5690i			1.22578i
$340$	−1.33125	+	0.639556i	−0.0721974	+	0.0346848i
$341$	−19.3415	+	11.1668i	−1.04740	+	0.604718i
$342$	−19.6849	+	4.48320i	−1.06443	+	0.242424i
$343$			12.5655i			0.678472i
$344$	24.0168	−	3.58529i	1.29490	−	0.193306i
$345$	−5.79911	−	3.34812i	−0.312213	−	0.180256i
$346$	−9.39478	+	8.70886i	−0.505066	+	0.468191i
$347$	−2.24508	−	1.29620i	−0.120522	−	0.0695836i	0.438527	−	0.898718i	$-0.355500\pi$
$347$	−2.24508	−	1.29620i	−0.120522	−	0.0695836i	−0.559049	+	0.829134i	$0.688834\pi$
$348$	3.84722	−	1.84827i	0.206233	−	0.0990776i
$349$	−9.78948	−	16.9559i	−0.524019	−	0.907627i	−0.999609	−	0.0279603i	$-0.991099\pi$
$349$	−9.78948	−	16.9559i	−0.524019	−	0.907627i	0.475590	−	0.879667i	$-0.342235\pi$
$350$	3.28514	−	3.04529i	0.175598	−	0.162778i
$351$	−0.811054	−	19.4534i	−0.0432909	−	1.03834i
$352$	7.82918	+	11.5415i	0.417297	+	0.615166i
$353$	−4.69869	+	2.71279i	−0.250086	+	0.144387i	−0.619804	−	0.784757i	$-0.712788\pi$
$353$	−4.69869	+	2.71279i	−0.250086	+	0.144387i	0.369718	+	0.929144i	$0.379454\pi$
$354$	−17.9546	−	5.54750i	−0.954274	−	0.294846i
$355$	−3.24673	−	1.87450i	−0.172319	−	0.0994881i
$356$	−28.0808	−	2.13094i	−1.48828	−	0.112940i
$357$	1.35723	−	2.35079i	0.0718323	−	0.124417i
$358$	−3.57188	−	15.6835i	−0.188780	−	0.828896i
$359$			24.1177i			1.27288i	0.771325	+	0.636442i	$0.219594\pi$
$359$			24.1177i			1.27288i	−0.771325	+	0.636442i	$0.780406\pi$
$360$	0.690407	+	4.62483i	0.0363876	+	0.243750i
$361$	−27.7814	−	48.1188i	−1.46218	−	2.53257i
$362$	−23.6931	−	7.32057i	−1.24528	−	0.384761i
$363$			5.71172i			0.299787i
$364$	10.7401	+	20.1585i	0.562932	+	1.05659i
$365$		−	1.03291i		−	0.0540652i
$366$	−2.25476	+	7.29757i	−0.117858	+	0.381450i
$367$	−1.11654	−	1.93390i	−0.0582827	−	0.100949i	0.835412	−	0.549624i	$-0.185229\pi$
$367$	−1.11654	−	1.93390i	−0.0582827	−	0.100949i	−0.893695	+	0.448676i	$0.851896\pi$
$368$	−14.4244	+	18.0180i	−0.751925	+	0.939252i
$369$			0.315015i			0.0163990i
$370$	−3.74510	+	0.852941i	−0.194698	+	0.0443423i
$371$	−6.62892	+	11.4816i	−0.344156	+	0.596096i
$372$	1.59097	−	20.9652i	0.0824877	−	1.08700i
$373$	−11.6773	−	6.74188i	−0.604627	−	0.349082i	0.166233	−	0.986087i	$-0.446840\pi$
$373$	−11.6773	−	6.74188i	−0.604627	−	0.349082i	−0.770860	+	0.637005i	$0.780173\pi$
$374$	0.760066	−	2.45996i	0.0393021	−	0.127202i
$375$	−1.00502	+	0.580249i	−0.0518991	+	0.0299639i
$376$	14.5045	+	18.2408i	0.748012	+	0.940698i
$377$	5.59900	−	3.55150i	0.288363	−	0.182912i
$378$	−16.4448	−	17.7400i	−0.845830	−	0.912449i
$379$	3.05975	+	5.29964i	0.157169	+	0.272224i	0.933847	−	0.357674i	$-0.116430\pi$
$379$	3.05975	+	5.29964i	0.157169	+	0.272224i	−0.776678	+	0.629898i	$0.783097\pi$
$380$	−15.5667	+	7.47851i	−0.798556	+	0.383639i
$381$	3.95791	+	2.28510i	0.202770	+	0.117069i
$382$	0.664714	+	0.717068i	0.0340097	+	0.0366884i
$383$	18.3627	+	10.6017i	0.938292	+	0.541723i	0.889424	−	0.457082i	$-0.151106\pi$
$383$	18.3627	+	10.6017i	0.938292	+	0.541723i	0.0488673	+	0.998805i	$0.484439\pi$
$384$	−13.1295	−	0.0432384i	−0.670010	−	0.00220650i
$385$			7.80914i			0.397991i
$386$	1.71542	+	7.53208i	0.0873126	+	0.383373i
$387$	−12.2920	+	7.09681i	−0.624840	+	0.360751i
$388$	14.8424	+	30.8949i	0.753510	+	1.56845i
$389$			8.17552i			0.414515i	0.978286	+	0.207258i	$0.0664539\pi$
$389$			8.17552i			0.414515i	−0.978286	+	0.207258i	$0.933546\pi$
$390$	−1.55323	−	5.70991i	−0.0786510	−	0.289133i
$391$	4.26099			0.215488
$392$	7.98113	+	3.14537i	0.403108	+	0.158865i
$393$	5.61422	+	9.72411i	0.283200	+	0.490517i
$394$	−19.2455	+	4.38313i	−0.969573	+	0.220819i
$395$	−9.18672			−0.462234
$396$	−6.73104	−	4.59843i	−0.338247	−	0.231080i
$397$	1.33438	−	2.31122i	0.0669707	−	0.115997i	−0.830596	−	0.556876i	$-0.812000\pi$
$397$	1.33438	−	2.31122i	0.0669707	−	0.115997i	0.897566	+	0.440879i	$0.145333\pi$
$398$	−23.9689	−	25.8567i	−1.20145	−	1.29608i
$399$	15.8705	−	27.4885i	0.794519	−	1.37615i
$400$	1.45435	+	3.72624i	0.0727177	+	0.186312i
$401$	7.61683	−	4.39758i	0.380367	−	0.219605i	−0.297611	−	0.954687i	$-0.596190\pi$
$401$	7.61683	−	4.39758i	0.380367	−	0.219605i	0.677978	+	0.735082i	$0.262857\pi$
$402$	−4.00790	+	3.71528i	−0.199896	+	0.185301i
$403$	−1.36057	−	32.6337i	−0.0677749	−	1.62560i
$404$	−10.5654	−	0.801767i	−0.525650	−	0.0398894i
$405$	0.653525	+	1.13194i	0.0324739	+	0.0562465i
$406$	2.43176	−	7.87041i	0.120686	−	0.390602i
$407$	3.34801	−	5.79893i	0.165955	−	0.287442i
$408$	1.50860	+	1.89721i	0.0746867	+	0.0939258i
$409$	8.07460	+	4.66187i	0.399263	+	0.230515i	0.686166	−	0.727445i	$-0.259292\pi$
$409$	8.07460	+	4.66187i	0.399263	+	0.230515i	−0.286903	+	0.957960i	$0.592626\pi$
$410$	0.0598390	+	0.262741i	0.00295524	+	0.0129759i
$411$	−17.7577			−0.875921
$412$	11.6683	+	7.97143i	0.574858	+	0.392724i
$413$	−31.4094	+	18.1343i	−1.54556	+	0.892328i
$414$	3.98255	−	12.8896i	0.195732	−	0.633488i
$415$	1.79420			0.0880736
$416$	−20.2634	+	2.32246i	−0.993496	+	0.113868i
$417$	−10.2448			−0.501692
$418$	8.88766	−	28.7650i	0.434710	−	1.40694i
$419$	30.8485	−	17.8104i	1.50705	−	0.870094i	0.507081	−	0.861898i	$-0.330724\pi$
$419$	30.8485	−	17.8104i	1.50705	−	0.870094i	0.999966	−	0.00819632i	$-0.00260900\pi$
$420$	−6.07038	−	4.14709i	−0.296204	−	0.202357i
$421$	−0.743378			−0.0362300			−0.0181150	−	0.999836i	$-0.505767\pi$
$421$	−0.743378			−0.0362300			−0.0181150	+	0.999836i	$0.505767\pi$
$422$	−2.88934	−	12.6865i	−0.140651	−	0.617571i
$423$	−11.7968	−	6.81091i	−0.573582	−	0.331158i
$424$	−7.36821	−	9.26625i	−0.357832	−	0.450009i
$425$	0.369228	−	0.639522i	0.0179102	−	0.0310214i
$426$	−1.81634	+	5.87862i	−0.0880022	+	0.284820i
$427$	7.37060	+	12.7663i	0.356688	+	0.617802i
$428$	23.5638	+	1.78816i	1.13900	+	0.0864339i
$429$	9.14088	+	4.78129i	0.441326	+	0.230843i
$430$	−8.90422	+	8.25411i	−0.429399	+	0.398049i
$431$	11.7483	−	6.78289i	0.565896	−	0.326720i	−0.189612	−	0.981859i	$-0.560723\pi$
$431$	11.7483	−	6.78289i	0.565896	−	0.326720i	0.755509	+	0.655139i	$0.227390\pi$
$432$	20.1220	−	7.85363i	0.968120	−	0.377858i
$433$	−12.9676	+	22.4605i	−0.623182	+	1.07938i	0.365707	+	0.930730i	$0.380827\pi$
$433$	−12.9676	+	22.4605i	−0.623182	+	1.07938i	−0.988889	+	0.148653i	$0.952506\pi$
$434$	−27.5868	−	29.7595i	−1.32421	−	1.42850i
$435$	−1.06704	+	1.84817i	−0.0511607	+	0.0886129i
$436$	−5.16815	−	3.53071i	−0.247510	−	0.169090i
$437$	49.8250			2.38345
$438$	−1.65288	+	0.376442i	−0.0789779	+	0.0179871i
$439$	1.85839	+	3.21883i	0.0886962	+	0.153626i	0.906960	−	0.421216i	$-0.138397\pi$
$439$	1.85839	+	3.21883i	0.0886962	+	0.153626i	−0.818264	+	0.574843i	$0.805063\pi$
$440$	−6.48758	−	2.55676i	−0.309283	−	0.121889i
$441$	−5.01426			−0.238774
$442$	2.67263	+	2.65241i	0.127124	+	0.126162i
$443$		−	1.77030i		−	0.0841096i	−0.999115	−	0.0420548i	$-0.986610\pi$
$443$		−	1.77030i		−	0.0841096i	0.999115	−	0.0420548i	$-0.0133904\pi$
$444$	2.72978	+	5.68211i	0.129550	+	0.269661i
$445$	12.1943	−	7.04039i	0.578066	−	0.333747i
$446$	1.32212	+	5.80519i	0.0626043	+	0.274884i
$447$		−	15.2746i		−	0.722464i
$448$	−17.2879	+	18.5267i	−0.816775	+	0.875306i
$449$	−24.6942	−	14.2572i	−1.16539	−	0.672838i	−0.212800	−	0.977096i	$-0.568258\pi$
$449$	−24.6942	−	14.2572i	−1.16539	−	0.672838i	−0.952590	+	0.304258i	$0.901592\pi$
$450$	−1.58946	−	1.71465i	−0.0749281	−	0.0808295i
$451$	−0.406830	−	0.234884i	−0.0191569	−	0.0110602i
$452$	−35.0594	+	16.8431i	−1.64906	+	0.792234i
$453$	−10.0336	−	17.3786i	−0.471418	−	0.816519i
$454$	8.41846	+	9.08151i	0.395098	+	0.426216i
$455$	−10.1198	−	5.29332i	−0.474422	−	0.248154i
$456$	17.6405	+	22.1846i	0.826091	+	1.03889i
$457$	−27.5901	+	15.9291i	−1.29061	+	0.745133i	−0.978762	−	0.204999i	$-0.934281\pi$
$457$	−27.5901	+	15.9291i	−1.29061	+	0.745133i	−0.311846	+	0.950133i	$0.600947\pi$
$458$	9.46244	−	30.6253i	0.442151	−	1.43103i
$459$	−3.45347	−	1.99386i	−0.161194	−	0.0930654i
$460$	0.873233	−	11.5072i	0.0407147	−	0.536525i
$461$	−4.12121	+	7.13815i	−0.191944	+	0.332457i	−0.945894	−	0.324474i	$-0.894813\pi$
$461$	−4.12121	+	7.13815i	−0.191944	+	0.332457i	0.753950	+	0.656931i	$0.228146\pi$
$462$	12.4963	−	2.84602i	0.581381	−	0.132409i
$463$		−	13.2846i		−	0.617390i	−0.951161	−	0.308695i	$-0.900108\pi$
$463$		−	13.2846i		−	0.617390i	0.951161	−	0.308695i	$-0.0998922\pi$
$464$	5.74231	+	4.59705i	0.266580	+	0.213413i
$465$	5.25638	+	9.10431i	0.243759	+	0.422202i
$466$	6.81817	−	22.0671i	0.315846	−	1.02224i
$467$			3.38808i			0.156782i	0.996923	+	0.0783909i	$0.0249782\pi$
$467$			3.38808i			0.156782i	−0.996923	+	0.0783909i	$0.975022\pi$
$468$	10.5216	−	5.60568i	0.486360	−	0.259123i
$469$			10.5475i			0.487037i
$470$	−11.1330	−	3.43983i	−0.513529	−	0.158667i
$471$	13.8407	+	23.9727i	0.637744	+	1.10461i
$472$	−4.78171	−	32.0312i	−0.220096	−	1.47436i
$473$		−	21.1663i		−	0.973227i
$474$	3.34807	+	14.7007i	0.153782	+	0.675227i
$475$	4.31749	−	7.47811i	0.198100	−	0.343119i
$476$	4.66469	+	0.353984i	0.213806	+	0.0162248i
$477$	5.99274	+	3.45991i	0.274389	+	0.158418i
$478$	8.59368	+	2.65523i	0.393066	+	0.121447i
$479$	−29.5093	+	17.0372i	−1.34832	+	0.778450i	−0.988011	−	0.154385i	$-0.950660\pi$
$479$	−29.5093	+	17.0372i	−1.34832	+	0.778450i	−0.360304	+	0.932835i	$0.617327\pi$
$480$	5.43275	−	3.68530i	0.247970	−	0.168210i
$481$	5.24535	+	8.26937i	0.239168	+	0.377051i
$482$	−12.7639	+	11.8320i	−0.581382	+	0.538935i
$483$	10.6051	+	18.3686i	0.482550	+	0.835800i
$484$	−8.87275	+	4.26261i	−0.403307	+	0.193755i
$485$	−14.8416	−	8.56882i	−0.673924	−	0.389090i
$486$	−15.2288	+	14.1170i	−0.690793	+	0.640358i
$487$	8.92075	+	5.15040i	0.404238	+	0.233387i	0.688311	−	0.725416i	$-0.258352\pi$
$487$	8.92075	+	5.15040i	0.404238	+	0.233387i	−0.284073	+	0.958803i	$0.591686\pi$
$488$	−13.0190	+	1.94351i	−0.589341	+	0.0879784i
$489$			2.42006i			0.109439i
$490$	−4.18219	+	0.952488i	−0.188932	+	0.0430290i
$491$	−8.22556	+	4.74903i	−0.371214	+	0.214321i	−0.673989	−	0.738742i	$-0.735420\pi$
$491$	−8.22556	+	4.74903i	−0.371214	+	0.214321i	0.302774	+	0.953062i	$0.402087\pi$
$492$	0.398635	−	0.191510i	0.0179718	−	0.00863396i
$493$		−	1.35797i		−	0.0611600i
$494$	31.2519	+	31.0154i	1.40609	+	1.39545i
$495$	4.07592			0.183199
$496$	33.7554	−	13.1747i	1.51566	−	0.591564i
$497$	5.93746	+	10.2840i	0.266331	+	0.461299i
$498$	−0.653889	−	2.87110i	−0.0293015	−	0.128657i
$499$	−23.3056			−1.04330			−0.521652	−	0.853158i	$-0.674684\pi$
$499$	−23.3056			−1.04330			−0.521652	+	0.853158i	$0.674684\pi$
$500$	−1.65142	−	1.12819i	−0.0738536	−	0.0504544i
$501$	9.17493	−	15.8914i	0.409906	−	0.709978i
$502$	−7.26922	+	6.73849i	−0.324441	+	0.300754i
$503$	−7.62610	+	13.2088i	−0.340031	+	0.588951i	−0.984438	−	0.175732i	$-0.943771\pi$
$503$	−7.62610	+	13.2088i	−0.340031	+	0.588951i	0.644407	+	0.764682i	$0.277104\pi$
$504$	5.43068	−	13.7799i	0.241902	−	0.613806i
$505$	4.58812	−	2.64895i	0.204169	−	0.117877i
$506$	13.6769	+	14.7541i	0.608013	+	0.655901i
$507$	−12.3920	+	8.60461i	−0.550349	+	0.382144i
$508$	−0.595984	+	7.85368i	−0.0264425	+	0.348451i
$509$	−9.44807	−	16.3645i	−0.418778	−	0.725346i	0.577038	−	0.816717i	$-0.304208\pi$
$509$	−9.44807	−	16.3645i	−0.418778	−	0.725346i	−0.995817	+	0.0913714i	$0.970875\pi$
$510$	−1.15794	−	0.357773i	−0.0512743	−	0.0158424i
$511$	−1.63587	+	2.83341i	−0.0723667	+	0.125343i
$512$	−9.73126	−	20.4280i	−0.430065	−	0.902798i
$513$	−40.3824	−	23.3148i	−1.78293	−	1.02937i
$514$	−25.4960	+	5.80667i	−1.12458	+	0.256121i
$515$	−7.06565			−0.311350
$516$	16.4535	+	11.2405i	0.724324	+	0.494835i
$517$	17.5921	−	10.1568i	0.773698	−	0.446695i
$518$	11.6241	+	3.59155i	0.510734	+	0.157804i
$519$	−10.5122			−0.461432
$520$	7.71079	−	6.67411i	0.338141	−	0.292679i
$521$	4.53269			0.198581			0.0992904	−	0.995058i	$-0.468343\pi$
$521$	4.53269			0.198581			0.0992904	+	0.995058i	$0.468343\pi$
$522$	−4.10790	−	1.26923i	−0.179798	−	0.0555529i
$523$	23.1340	−	13.3564i	1.01158	−	0.584036i	0.0999260	−	0.994995i	$-0.468139\pi$
$523$	23.1340	−	13.3564i	1.01158	−	0.584036i	0.911654	+	0.410959i	$0.134806\pi$
$524$	−10.9159	+	15.9783i	−0.476863	+	0.698017i
$525$	3.67586			0.160428
$526$	−36.2973	+	8.26665i	−1.58264	+	0.360443i
$527$	−5.79332	−	3.34477i	−0.252361	−	0.145701i
$528$	−1.72699	+	11.3133i	−0.0751576	+	0.492350i
$529$	−5.14723	+	8.91527i	−0.223793	+	0.387620i
$530$	5.65553	+	1.74741i	0.245661	+	0.0759028i
$531$	9.46502	+	16.3939i	0.410747	+	0.711435i
$532$	54.5455	+	4.13924i	2.36485	+	0.179459i
$533$	0.580147	−	0.367993i	0.0251289	−	0.0159396i
$534$	−15.7103	−	16.9477i	−0.679852	−	0.733398i
$535$	−10.2327	+	5.90788i	−0.442400	+	0.255420i
$536$	−8.76250	−	3.45331i	−0.378483	−	0.149160i
$537$	6.59967	−	11.4310i	0.284797	−	0.493282i
$538$	−5.33394	+	4.94450i	−0.229962	+	0.213173i
$539$	3.73876	−	6.47573i	0.161040	−	0.278929i
$540$	−6.09234	+	8.91778i	−0.262173	+	0.383760i
$541$	10.6452			0.457674			0.228837	−	0.973465i	$-0.426508\pi$
$541$	10.6452			0.457674			0.228837	+	0.973465i	$0.426508\pi$
$542$	7.05671	+	30.9847i	0.303112	+	1.33090i
$543$	−10.1747	−	17.6231i	−0.436638	−	0.756279i
$544$	−1.82133	+	3.75938i	−0.0780887	+	0.161182i
$545$	3.12953			0.134054
$546$	−4.78233	+	18.1229i	−0.204665	+	0.775590i
$547$		−	18.7968i		−	0.803695i	−0.915707	−	0.401847i	$-0.868368\pi$
$547$		−	18.7968i		−	0.803695i	0.915707	−	0.401847i	$-0.131632\pi$
$548$	−13.2524	−	27.5853i	−0.566115	−	1.17839i
$549$	6.66324	−	3.84702i	0.284380	−	0.164187i
$550$	3.39956	−	0.774244i	0.144958	−	0.0330139i
$551$		−	15.8792i		−	0.676475i
$552$	−18.7322	+	2.79640i	−0.797296	+	0.119022i
$553$	25.2003	+	14.5494i	1.07163	+	0.618704i
$554$	−5.69137	+	5.27584i	−0.241803	+	0.224149i
$555$	−2.72963	−	1.57595i	−0.115866	−	0.0668955i
$556$	−7.64565	−	15.9146i	−0.324248	−	0.674931i
$557$	−10.6352	−	18.4206i	−0.450626	−	0.780508i	0.547799	−	0.836610i	$-0.315466\pi$
$557$	−10.6352	−	18.4206i	−0.450626	−	0.780508i	−0.998425	+	0.0561026i	$0.982133\pi$
$558$	−15.5327	+	14.3987i	−0.657554	+	0.609545i
$559$	27.4291	+	14.3473i	1.16013	+	0.606825i
$560$	1.91193	−	12.5249i	0.0807939	−	0.529272i
$561$	1.82973	−	1.05640i	0.0772514	−	0.0446011i
$562$	−8.36879	−	2.58574i	−0.353016	−	0.109073i
$563$	20.4572	+	11.8110i	0.862168	+	0.497773i	0.864738	−	0.502224i	$-0.167485\pi$
$563$	20.4572	+	11.8110i	0.862168	+	0.497773i	−0.00256999	+	0.999997i	$0.500818\pi$
$564$	−1.44706	+	19.0689i	−0.0609322	+	0.802945i
$565$	9.72386	−	16.8422i	0.409086	−	0.708557i
$566$	−6.11010	−	26.8283i	−0.256826	−	1.12768i
$567$		−	4.14007i		−	0.173866i
$568$	−10.4876	+	1.56561i	−0.440048	+	0.0656915i
$569$	−15.0749	−	26.1106i	−0.631974	−	1.09461i	−0.987148	−	0.159811i	$-0.948911\pi$
$569$	−15.0749	−	26.1106i	−0.631974	−	1.09461i	0.355173	−	0.934800i	$-0.384422\pi$
$570$	−13.5401	−	4.18354i	−0.567131	−	0.175229i
$571$			6.49912i			0.271980i	0.990710	+	0.135990i	$0.0434215\pi$
$571$			6.49912i			0.271980i	−0.990710	+	0.135990i	$0.956579\pi$
$572$	−0.605636	+	17.7680i	−0.0253229	+	0.742916i
$573$			0.802353i			0.0335188i
$574$	0.251969	−	0.815502i	0.0105170	−	0.0340384i
$575$	2.88507	+	4.99708i	0.120316	+	0.208393i
$576$	9.66988	+	9.02327i	0.402912	+	0.375969i
$577$		−	4.08088i		−	0.169889i	−0.996386	−	0.0849446i	$-0.972929\pi$
$577$		−	4.08088i		−	0.169889i	0.996386	−	0.0849446i	$-0.0270713\pi$
$578$	−22.6894	+	5.16749i	−0.943756	+	0.214939i
$579$	−3.16953	+	5.48979i	−0.131721	+	0.228148i
$580$	−3.66733	−	0.278299i	−0.152278	−	0.0115557i
$581$	−4.92170	−	2.84155i	−0.204187	−	0.117887i
$582$	−8.30297	+	26.8727i	−0.344169	+	1.11391i
$583$	−8.93668	+	5.15960i	−0.370120	+	0.213689i
$584$	−1.81831	−	2.28671i	−0.0752423	−	0.0946245i
$585$	−2.76280	+	5.28193i	−0.114228	+	0.218381i
$586$	31.4564	+	33.9339i	1.29945	+	1.40180i
$587$	−7.83029	−	13.5625i	−0.323191	−	0.559783i	0.657954	−	0.753058i	$-0.271422\pi$
$587$	−7.83029	−	13.5625i	−0.323191	−	0.559783i	−0.981145	+	0.193275i	$0.938089\pi$
$588$	3.04837	+	6.34527i	0.125713	+	0.261675i
$589$	−67.7429	−	39.1114i	−2.79130	−	1.61156i
$590$	11.0085	+	11.8756i	0.453213	+	0.488909i
$591$	−14.0271	−	8.09858i	−0.577000	−	0.333131i
$592$	−6.78955	+	8.48104i	−0.279049	+	0.348569i
$593$			35.5283i			1.45897i	0.683996	+	0.729486i	$0.260241\pi$
$593$			35.5283i			1.45897i	−0.683996	+	0.729486i	$0.739759\pi$
$594$	−4.18098	−	18.3579i	−0.171548	−	0.753233i
$595$	−2.02568	+	1.16953i	−0.0830447	+	0.0479459i
$596$	23.7280	−	11.3993i	0.971939	−	0.466935i
$597$		−	28.9320i		−	1.18411i
$598$	−28.3904	+	7.72286i	−1.16097	+	0.315811i
$599$	15.0781			0.616075			0.308037	−	0.951374i	$-0.400328\pi$
$599$	15.0781			0.616075			0.308037	+	0.951374i	$0.400328\pi$
$600$	−1.20350	+	3.05379i	−0.0491327	+	0.124670i
$601$	−9.78938	−	16.9557i	−0.399317	−	0.691637i	0.594325	−	0.804225i	$-0.297419\pi$
$601$	−9.78938	−	16.9557i	−0.399317	−	0.691637i	−0.993642	+	0.112588i	$0.964086\pi$
$602$	37.4978	−	8.54006i	1.52830	−	0.348067i
$603$	5.50517			0.224188
$604$	19.5085	−	28.5560i	0.793791	−	1.16193i
$605$	2.46089	−	4.26239i	0.100049	−	0.173291i
$606$	−5.91102	−	6.37658i	−0.240119	−	0.259031i
$607$	12.4880	−	21.6299i	0.506874	−	0.877932i	−0.493094	−	0.869976i	$-0.664134\pi$
$607$	12.4880	−	21.6299i	0.506874	−	0.877932i	0.999968	−	0.00795583i	$-0.00253244\pi$
$608$	−21.2973	+	43.9595i	−0.863719	+	1.78279i
$609$	5.85405	−	3.37984i	0.237218	−	0.136958i
$610$	4.82677	−	4.47437i	0.195430	−	0.181162i
$611$	1.23751	+	29.6820i	0.0500642	+	1.20080i
$612$	0.184759	−	2.43470i	0.00746844	−	0.0984167i
$613$	−5.34922	−	9.26513i	−0.216053	−	0.374215i	0.737545	−	0.675298i	$-0.235985\pi$
$613$	−5.34922	−	9.26513i	−0.216053	−	0.374215i	−0.953598	+	0.301083i	$0.902652\pi$
$614$	8.83948	−	28.6091i	0.356733	−	1.15457i
$615$	−0.110563	+	0.191500i	−0.00445832	+	0.00772204i
$616$	13.7470	+	17.2882i	0.553882	+	0.696561i
$617$	17.2769	+	9.97481i	0.695541	+	0.401571i	0.805685	−	0.592345i	$-0.201798\pi$
$617$	17.2769	+	9.97481i	0.695541	+	0.401571i	−0.110143	+	0.993916i	$0.535131\pi$
$618$	2.57505	+	11.3066i	0.103584	+	0.454817i
$619$	14.3270			0.575850			0.287925	−	0.957653i	$-0.407035\pi$
$619$	14.3270			0.575850			0.287925	+	0.957653i	$0.407035\pi$
$620$	−10.2201	+	14.9599i	−0.410450	+	0.600804i
$621$	26.9847	−	15.5796i	1.08286	−	0.625188i
$622$	−7.12878	+	23.0724i	−0.285838	+	0.925119i
$623$	−44.6007			−1.78689
$624$	−13.4902	−	9.90657i	−0.540040	−	0.396580i
$625$	1.00000			0.0400000
$626$	10.4635	−	33.8652i	0.418205	−	1.35353i
$627$	21.3956	−	12.3528i	0.854458	−	0.493321i
$628$	−26.9108	+	39.3912i	−1.07386	+	1.57188i
$629$	2.00564			0.0799702
$630$	1.64453	+	7.22081i	0.0655196	+	0.287684i
$631$	21.3141	+	12.3057i	0.848500	+	0.489882i	0.860145	−	0.510050i	$-0.170373\pi$
$631$	21.3141	+	12.3057i	0.848500	+	0.489882i	−0.0116443	+	0.999932i	$0.503707\pi$
$632$	−20.3379	+	16.1721i	−0.808999	+	0.643290i
$633$	5.33855	−	9.24665i	0.212188	−	0.367521i
$634$	−7.61435	+	24.6440i	−0.302405	+	0.978737i
$635$	−1.96907	−	3.41052i	−0.0781400	−	0.135342i
$636$	0.735100	−	9.68691i	0.0291486	−	0.384111i
$637$	5.85754	+	9.23449i	0.232084	+	0.365884i
$638$	4.70212	−	4.35882i	0.186159	−	0.172567i
$639$	5.36764	−	3.09901i	0.212340	−	0.122595i
$640$	9.77928	+	5.68909i	0.386560	+	0.224881i
$641$	−10.8642	+	18.8174i	−0.429112	+	0.743243i	−0.996795	−	0.0800040i	$-0.974507\pi$
$641$	−10.8642	+	18.8174i	−0.429112	+	0.743243i	0.567683	+	0.823247i	$0.307840\pi$
$642$	13.1832	+	14.2215i	0.520298	+	0.561278i
$643$	−8.88679	+	15.3924i	−0.350461	+	0.607016i	−0.986330	−	0.164781i	$-0.947308\pi$
$643$	−8.88679	+	15.3924i	−0.350461	+	0.607016i	0.635869	+	0.771797i	$0.280642\pi$
$644$	−20.6198	+	30.1827i	−0.812535	+	1.18936i
$645$	−9.96325			−0.392302
$646$	8.79265	−	2.00251i	0.345942	−	0.0787878i
$647$	19.8313	+	34.3488i	0.779649	+	1.35039i	0.932144	+	0.362088i	$0.117936\pi$
$647$	19.8313	+	34.3488i	0.779649	+	1.35039i	−0.152495	+	0.988304i	$0.548731\pi$
$648$	3.43943	+	1.35548i	0.135114	+	0.0532484i
$649$	−28.2295			−1.10810
$650$	−1.30101	+	4.93025i	−0.0510298	+	0.193380i
$651$		−	33.2990i		−	1.30509i
$652$	−3.75940	+	1.80608i	−0.147229	+	0.0707314i
$653$	−11.7391	+	6.77755i	−0.459385	+	0.265226i	−0.711785	−	0.702397i	$-0.752113\pi$
$653$	−11.7391	+	6.77755i	−0.459385	+	0.265226i	0.252401	+	0.967623i	$0.418780\pi$
$654$	−1.14055	−	5.00792i	−0.0445989	−	0.195825i
$655$		−	9.67553i		−	0.378054i
$656$	0.594997	+	0.476328i	0.0232307	+	0.0185975i
$657$	1.47888	+	0.853829i	0.0576964	+	0.0333111i
$658$	25.0915	+	27.0678i	0.978169	+	1.05521i
$659$	1.49368	+	0.862377i	0.0581856	+	0.0335934i	0.528811	−	0.848740i	$-0.322638\pi$
$659$	1.49368	+	0.862377i	0.0581856	+	0.0335934i	−0.470625	+	0.882333i	$0.655972\pi$
$660$	−2.47792	−	5.15785i	−0.0964527	−	0.200769i
$661$	12.9412	+	22.4148i	0.503355	+	0.871836i	0.999992	+	0.00387783i	$0.00123436\pi$
$661$	12.9412	+	22.4148i	0.503355	+	0.871836i	−0.496638	+	0.867958i	$0.665432\pi$
$662$	25.8655	+	27.9026i	1.00529	+	1.08447i
$663$	0.128712	+	3.08719i	0.00499875	+	0.119897i
$664$	3.97206	−	3.15845i	0.154146	−	0.122572i
$665$	−23.6868	+	13.6756i	−0.918535	+	0.530317i
$666$	1.87458	−	6.06711i	0.0726386	−	0.235096i
$667$	9.18932	+	5.30546i	0.355812	+	0.205428i
$668$	31.5335	+	2.39294i	1.22007	+	0.0925858i
$669$	−2.44285	+	4.23114i	−0.0944460	+	0.163585i
$670$	4.59164	−	1.04574i	0.177390	−	0.0404004i
$671$			11.4738i			0.442940i
$672$	−20.7393	+	1.50514i	−0.800035	+	0.0580622i
$673$	−6.92986	−	12.0029i	−0.267127	−	0.462677i	0.700992	−	0.713169i	$-0.252741\pi$
$673$	−6.92986	−	12.0029i	−0.267127	−	0.462677i	−0.968119	+	0.250492i	$0.919408\pi$
$674$	−1.25651	+	4.06670i	−0.0483988	+	0.156643i
$675$		−	5.40008i		−	0.207849i
$676$	−22.6148	−	12.8286i	−0.869798	−	0.493408i
$677$			32.0465i			1.23165i	0.787884	+	0.615823i	$0.211176\pi$
$677$			32.0465i			1.23165i	−0.787884	+	0.615823i	$0.788824\pi$
$678$	−30.4950	−	9.42218i	−1.17115	−	0.361857i
$679$	27.1416	+	47.0107i	1.04160	+	1.80410i
$680$	−0.308385	−	2.06578i	−0.0118260	−	0.0792189i
$681$			10.1616i			0.389394i
$682$	−7.01374	−	30.7960i	−0.268570	−	1.17924i
$683$	4.02679	−	6.97461i	0.154081	−	0.266876i	−0.778643	−	0.627467i	$-0.784092\pi$
$683$	4.02679	−	6.97461i	0.154081	−	0.266876i	0.932724	+	0.360591i	$0.117425\pi$
$684$	2.16044	−	28.4696i	0.0826065	−	1.08856i
$685$	13.2517	+	7.65088i	0.506322	+	0.292325i
$686$	−16.9783	−	5.24587i	−0.648236	−	0.200288i
$687$	22.7793	−	13.1516i	0.869084	−	0.501766i
$688$	−5.18220	+	33.9480i	−0.197569	+	1.29426i
$689$	−0.628647	−	15.0783i	−0.0239496	−	0.574437i
$690$	6.94496	−	6.43790i	0.264390	−	0.245087i
$691$	9.06234	+	15.6964i	0.344748	+	0.597121i	0.985308	−	0.170787i	$-0.0546311\pi$
$691$	9.06234	+	15.6964i	0.344748	+	0.597121i	−0.640560	+	0.767908i	$0.721298\pi$
$692$	−7.84515	−	16.3299i	−0.298228	−	0.620770i
$693$	−11.1807	−	6.45521i	−0.424722	−	0.245213i
$694$	2.68869	−	2.49239i	0.102061	−	0.0946097i
$695$	7.64524	+	4.41398i	0.290000	+	0.167432i
$696$	0.891208	+	5.96994i	0.0337812	+	0.226290i
$697$		−	0.140708i		−	0.00532970i
$698$	26.9975	−	6.14864i	1.02187	−	0.232730i
$699$	16.4136	−	9.47641i	0.620820	−	0.358431i
$700$	2.74327	+	5.71020i	0.103686	+	0.215825i
$701$		−	0.168502i		−	0.00636422i	−0.999995	−	0.00318211i	$-0.998987\pi$
$701$		−	0.168502i		−	0.00636422i	0.999995	−	0.00318211i	$-0.00101290\pi$
$702$	26.6238	+	7.02555i	1.00485	+	0.265162i
$703$	23.4526			0.884530
$704$	−18.8633	+	5.76030i	−0.710938	+	0.217100i
$705$	−4.78093	−	8.28082i	−0.180060	−	0.311874i
$706$	−1.70387	−	7.48135i	−0.0641258	−	0.281564i
$707$	−16.7810			−0.631116
$708$	14.9914	−	21.9440i	0.563412	−	0.824706i
$709$	13.2652	−	22.9759i	0.498184	−	0.862879i	−0.501814	−	0.864975i	$-0.667334\pi$
$709$	13.2652	−	22.9759i	0.498184	−	0.862879i	0.999998	+	0.00209603i	$0.000667187\pi$
$710$	3.88825	−	3.60437i	0.145924	−	0.135270i
$711$	7.59395	−	13.1531i	0.284795	−	0.493280i
$712$	14.6026	−	37.0529i	0.547254	−	1.38861i
$713$	45.2677	−	26.1353i	1.69529	−	0.978776i
$714$	2.60974	+	2.81529i	0.0976672	+	0.105360i
$715$	−4.76139	−	7.50640i	−0.178066	−	0.280723i
$716$	22.6825	+	1.72128i	0.847684	+	0.0643273i
$717$	3.69044	+	6.39203i	0.137822	+	0.238715i
$718$	−32.5875	−	10.0687i	−1.21616	−	0.375761i
$719$	19.5787	−	33.9113i	0.730163	−	1.26468i	−0.226651	−	0.973976i	$-0.572778\pi$
$719$	19.5787	−	33.9113i	0.730163	−	1.26468i	0.956813	−	0.290703i	$-0.0938890\pi$
$720$	−6.53725	−	0.997917i	−0.243629	−	0.0371902i
$721$	19.3820	+	11.1902i	0.721822	+	0.416744i
$722$	76.6158	−	17.4491i	2.85134	−	0.649389i
$723$	−14.2820			−0.531155
$724$	19.7829	−	28.9577i	0.735227	−	1.07620i
$725$	1.59257	−	0.919468i	0.0591464	−	0.0341482i
$726$	−7.71760	−	2.38454i	−0.286427	−	0.0884986i
$727$	−18.8156			−0.697832			−0.348916	−	0.937154i	$-0.613450\pi$
$727$	−18.8156			−0.697832			−0.348916	+	0.937154i	$0.613450\pi$
$728$	−31.7217	+	6.09600i	−1.17569	+	0.225933i
$729$	−20.9612			−0.776342
$730$	1.39566	+	0.431223i	0.0516557	+	0.0159603i
$731$	5.49050	−	3.16994i	0.203073	−	0.117244i
$732$	−8.91906	−	6.09321i	−0.329658	−	0.225212i
$733$	19.8512			0.733219			0.366610	−	0.930375i	$-0.380518\pi$
$733$	19.8512			0.733219			0.366610	+	0.930375i	$0.380518\pi$
$734$	3.07919	−	0.701281i	0.113655	−	0.0258848i
$735$	−3.04821	−	1.75988i	−0.112435	−	0.0649143i
$736$	−18.3237	−	27.0123i	−0.675422	−	0.995686i
$737$	−4.10480	+	7.10972i	−0.151202	+	0.261890i
$738$	−0.425645	−	0.131513i	−0.0156682	−	0.00484107i
$739$	21.9843	+	38.0780i	0.808707	+	1.40072i	0.913760	+	0.406255i	$0.133166\pi$
$739$	21.9843	+	38.0780i	0.808707	+	1.40072i	−0.105052	+	0.994467i	$0.533501\pi$
$740$	0.411030	−	5.41642i	0.0151098	−	0.199111i
$741$	1.50506	+	36.0994i	0.0552899	+	1.32614i
$742$	−12.7464	−	13.7503i	−0.467934	−	0.504789i
$743$	−17.2021	+	9.93161i	−0.631082	+	0.364356i	−0.781171	−	0.624317i	$-0.785377\pi$
$743$	−17.2021	+	9.93161i	−0.631082	+	0.364356i	0.150089	+	0.988673i	$0.452044\pi$
$744$	27.6638	+	10.9023i	1.01420	+	0.399698i
$745$	−6.58106	+	11.3987i	−0.241111	+	0.417617i
$746$	13.9846	−	12.9636i	0.512013	−	0.474631i
$747$	−1.48312	+	2.56884i	−0.0542646	+	0.0939890i
$748$	3.00656	+	2.05398i	0.109931	+	0.0751010i
$749$	37.4263			1.36753
$750$	−0.364447	−	1.60022i	−0.0133077	−	0.0584316i
$751$	−9.68597	−	16.7766i	−0.353446	−	0.612186i	0.633405	−	0.773821i	$-0.281657\pi$
$751$	−9.68597	−	16.7766i	−0.353446	−	0.612186i	−0.986851	+	0.161634i	$0.948324\pi$
$752$	−30.7021	+	11.9831i	−1.11959	+	0.436978i
$753$	−8.13379			−0.296412
$754$	2.46127	+	9.04798i	0.0896340	+	0.329508i
$755$			17.2918i			0.629313i
$756$	30.8355	−	14.8139i	1.12148	−	0.538776i
$757$	−14.7095	+	8.49256i	−0.534627	+	0.308667i	−0.742899	−	0.669404i	$-0.766550\pi$
$757$	−14.7095	+	8.49256i	−0.534627	+	0.308667i	0.208271	+	0.978071i	$0.433216\pi$
$758$	−8.43819	+	1.92179i	−0.306489	+	0.0698024i
$759$			16.5089i			0.599236i
$760$	−3.60603	−	24.1557i	−0.130804	−	0.876220i
$761$	45.5367	+	26.2906i	1.65070	+	0.953035i	0.976783	+	0.214232i	$0.0687249\pi$
$761$	45.5367	+	26.2906i	1.65070	+	0.953035i	0.673922	+	0.738803i	$0.264608\pi$
$762$	−4.73995	+	4.39389i	−0.171710	+	0.159174i
$763$	−8.58468	−	4.95637i	−0.310786	−	0.179433i
$764$	−1.24640	+	0.598790i	−0.0450932	+	0.0216635i
$765$	0.610424	+	1.05729i	0.0220699	+	0.0382262i
$766$	−21.9910	+	20.3855i	−0.794569	+	0.736557i
$767$	19.1350	−	36.5822i	0.690923	−	1.32091i
$768$	5.53975	−	17.7223i	0.199898	−	0.639499i
$769$	42.8525	−	24.7409i	1.54530	−	0.892181i	0.546812	−	0.837255i

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.417482 + 1.35119i) q^{2} +(-1.00502 + 0.580249i) q^{3} +(-1.65142 - 1.12819i) q^{4} +1.00000 q^{5} +(-0.364447 - 1.60022i) q^{6} +(-2.74313 - 1.58374i) q^{7} +(2.21384 - 1.76037i) q^{8} +(-0.826622 + 1.43175i) q^{9} +O(q^{10})\)	\(q+(-0.417482 + 1.35119i) q^{2} +(-1.00502 + 0.580249i) q^{3} +(-1.65142 - 1.12819i) q^{4} +1.00000 q^{5} +(-0.364447 - 1.60022i) q^{6} +(-2.74313 - 1.58374i) q^{7} +(2.21384 - 1.76037i) q^{8} +(-0.826622 + 1.43175i) q^{9} +(-0.417482 + 1.35119i) q^{10} +(-1.23270 - 2.13510i) q^{11} +(2.31434 + 0.175626i) q^{12} +(3.60242 - 0.150193i) q^{13} +(3.28514 - 3.04529i) q^{14} +(-1.00502 + 0.580249i) q^{15} +(1.45435 + 3.72624i) q^{16} +(0.369228 - 0.639522i) q^{17} +(-1.58946 - 1.71465i) q^{18} +(4.31749 - 7.47811i) q^{19} +(-1.65142 - 1.12819i) q^{20} +3.67586 q^{21} +(3.39956 - 0.774244i) q^{22} +(2.88507 + 4.99708i) q^{23} +(-1.20350 + 3.05379i) q^{24} +1.00000 q^{25} +(-1.30101 + 4.93025i) q^{26} -5.40008i q^{27} +(2.74327 + 5.71020i) q^{28} +(1.59257 - 0.919468i) q^{29} +(-0.364447 - 1.60022i) q^{30} -9.05883i q^{31} +(-5.64202 + 0.409467i) q^{32} +(2.47778 + 1.43055i) q^{33} +(0.709967 + 0.765885i) q^{34} +(-2.74313 - 1.58374i) q^{35} +(2.98039 - 1.43183i) q^{36} +(1.35800 + 2.35212i) q^{37} +(8.30185 + 8.95571i) q^{38} +(-3.53336 + 2.24125i) q^{39} +(2.21384 - 1.76037i) q^{40} +(0.165016 - 0.0952718i) q^{41} +(-1.53461 + 4.96678i) q^{42} +(7.43510 + 4.29266i) q^{43} +(-0.373106 + 4.91667i) q^{44} +(-0.826622 + 1.43175i) q^{45} +(-7.95646 + 1.81207i) q^{46} +8.23945i q^{47} +(-3.62380 - 2.90106i) q^{48} +(1.51649 + 2.62664i) q^{49} +(-0.417482 + 1.35119i) q^{50} +0.856977i q^{51} +(-6.11855 - 3.81620i) q^{52} -4.18560i q^{53} +(7.29652 + 2.25444i) q^{54} +(-1.23270 - 2.13510i) q^{55} +(-8.86082 + 1.32277i) q^{56} +10.0209i q^{57} +(0.577506 + 2.53572i) q^{58} +(5.72512 - 9.91620i) q^{59} +(2.31434 + 0.175626i) q^{60} +(-4.03040 - 2.32695i) q^{61} +(12.2402 + 3.78190i) q^{62} +(4.53506 - 2.61832i) q^{63} +(1.80218 - 7.79437i) q^{64} +(3.60242 - 0.150193i) q^{65} +(-2.96737 + 2.75072i) q^{66} +(-1.66496 - 2.88379i) q^{67} +(-1.33125 + 0.639556i) q^{68} +(-5.79911 - 3.34812i) q^{69} +(3.28514 - 3.04529i) q^{70} +(-3.24673 - 1.87450i) q^{71} +(0.690407 + 4.62483i) q^{72} -1.03291i q^{73} +(-3.74510 + 0.852941i) q^{74} +(-1.00502 + 0.580249i) q^{75} +(-15.5667 + 7.47851i) q^{76} +7.80914i q^{77} +(-1.55323 - 5.70991i) q^{78} -9.18672 q^{79} +(1.45435 + 3.72624i) q^{80} +(0.653525 + 1.13194i) q^{81} +(0.0598390 + 0.262741i) q^{82} +1.79420 q^{83} +(-6.07038 - 4.14709i) q^{84} +(0.369228 - 0.639522i) q^{85} +(-8.90422 + 8.25411i) q^{86} +(-1.06704 + 1.84817i) q^{87} +(-6.48758 - 2.55676i) q^{88} +(12.1943 - 7.04039i) q^{89} +(-1.58946 - 1.71465i) q^{90} +(-10.1198 - 5.29332i) q^{91} +(0.873233 - 11.5072i) q^{92} +(5.25638 + 9.10431i) q^{93} +(-11.1330 - 3.43983i) q^{94} +(4.31749 - 7.47811i) q^{95} +(5.43275 - 3.68530i) q^{96} +(-14.8416 - 8.56882i) q^{97} +(-4.18219 + 0.952488i) q^{98} +4.07592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

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