LMFDB - Embedded newform 520.2.ca.a.101.3

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			101.3
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.a.381.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37890 - 0.314043i) q^{2} +(1.00502 - 0.580249i) q^{3} +(1.80275 + 0.866072i) q^{4} -1.00000 q^{5} +(-1.56805 + 0.484488i) q^{6} +(-2.74313 - 1.58374i) q^{7} +(-2.21384 - 1.76037i) q^{8} +(-0.826622 + 1.43175i) q^{9} +O(q^{10})$	\(q+(-1.37890 - 0.314043i) q^{2} +(1.00502 - 0.580249i) q^{3} +(1.80275 + 0.866072i) q^{4} -1.00000 q^{5} +(-1.56805 + 0.484488i) q^{6} +(-2.74313 - 1.58374i) q^{7} +(-2.21384 - 1.76037i) q^{8} +(-0.826622 + 1.43175i) q^{9} +(1.37890 + 0.314043i) 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} +(2.49984 + 3.12263i) q^{16} +(0.369228 - 0.639522i) q^{17} +(1.58946 - 1.71465i) q^{18} +(-4.31749 + 7.47811i) q^{19} +(-1.80275 - 0.866072i) q^{20} -3.67586 q^{21} +(-1.02926 - 3.33122i) q^{22} +(2.88507 + 4.99708i) q^{23} +(-3.24641 - 0.484633i) q^{24} +1.00000 q^{25} +(5.01456 + 0.924215i) q^{26} +5.40008i q^{27} +(-3.57354 - 5.23084i) q^{28} +(-1.59257 + 0.919468i) q^{29} +(1.56805 - 0.484488i) q^{30} -9.05883i q^{31} +(-2.46640 - 5.09086i) q^{32} +(2.47778 + 1.43055i) q^{33} +(-0.709967 + 0.765885i) q^{34} +(2.74313 + 1.58374i) q^{35} +(-2.73020 + 1.86518i) 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} +(5.06866 + 1.15438i) q^{42} +(-7.43510 - 4.29266i) q^{43} +(0.373106 + 4.91667i) q^{44} +(0.826622 - 1.43175i) q^{45} +(-2.40893 - 7.79654i) q^{46} +8.23945i q^{47} +(4.32429 + 1.68778i) q^{48} +(1.51649 + 2.62664i) q^{49} +(-1.37890 - 0.314043i) q^{50} -0.856977i q^{51} +(-6.62436 - 2.84919i) q^{52} +4.18560i q^{53} +(1.69586 - 7.44619i) q^{54} +(-1.23270 - 2.13510i) q^{55} +(3.28486 + 8.33508i) q^{56} +10.0209i q^{57} +(2.48475 - 0.767724i) q^{58} +(-5.72512 + 9.91620i) q^{59} +(-2.31434 + 0.175626i) q^{60} +(4.03040 + 2.32695i) q^{61} +(-2.84487 + 12.4913i) 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} +(1.21950 - 0.833122i) q^{68} +(5.79911 + 3.34812i) q^{69} +(-3.28514 - 3.04529i) q^{70} +(-3.24673 - 1.87450i) q^{71} +(4.35043 - 1.71451i) q^{72} -1.03291i q^{73} +(1.13388 + 3.66982i) q^{74} +(1.00502 - 0.580249i) q^{75} +(-14.2599 + 9.74193i) q^{76} -7.80914i q^{77} +(5.57601 - 1.98084i) q^{78} -9.18672 q^{79} +(-2.49984 - 3.12263i) q^{80} +(0.653525 + 1.13194i) q^{81} +(-0.257460 + 0.0795486i) q^{82} -1.79420 q^{83} +(-6.62668 - 3.18356i) q^{84} +(-0.369228 + 0.639522i) q^{85} +(8.90422 + 8.25411i) q^{86} +(-1.06704 + 1.84817i) q^{87} +(1.02957 - 6.89679i) 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} +(2.58754 - 11.3614i) q^{94} +(4.31749 - 7.47811i) q^{95} +(-5.43275 - 3.68530i) q^{96} +(-14.8416 - 8.56882i) q^{97} +(-1.26622 - 4.09813i) q^{98} -4.07592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * 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 $

$2$	−1.37890	−	0.314043i	−0.975032	−	0.222062i
$2$	−1.37890	−	0.314043i	−0.975032	−	0.222062i
$3$	1.00502	−	0.580249i	0.580249	−	0.335007i	−0.180983	−	0.983486i	$-0.557928\pi$
$3$	1.00502	−	0.580249i	0.580249	−	0.335007i	0.761232	+	0.648479i	$0.224595\pi$
$4$	1.80275	+	0.866072i	0.901377	+	0.433036i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.56805	+	0.484488i	−0.640154	+	0.197791i
$7$	−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
$10$	1.37890	+	0.314043i	0.436048	+	0.0993093i
$11$	1.23270	+	2.13510i	0.371674	+	0.643758i	0.989823	−	0.142303i	$-0.0454507\pi$
$11$	1.23270	+	2.13510i	0.371674	+	0.643758i	−0.618149	+	0.786061i	$0.712117\pi$
$12$	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
$16$	2.49984	+	3.12263i	0.624960	+	0.780657i
$17$	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	$0.622755\pi$
$19$	−4.31749	+	7.47811i	−0.990499	+	1.71560i	−0.614342	+	0.789040i	$0.710579\pi$
$20$	−1.80275	−	0.866072i	−0.403108	−	0.193660i
$21$	−3.67586			−0.802139
$22$	−1.02926	−	3.33122i	−0.219440	−	0.710220i
$23$	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	$0.627872\pi$
$24$	−3.24641	−	0.484633i	−0.662671	−	0.0989252i
$25$	1.00000			0.200000
$26$	5.01456	+	0.924215i	0.983436	+	0.181254i
$27$			5.40008i			1.03925i
$28$	−3.57354	−	5.23084i	−0.675336	−	0.988536i
$29$	−1.59257	+	0.919468i	−0.295732	+	0.170741i	−0.640524	−	0.767938i	$-0.721283\pi$
$29$	−1.59257	+	0.919468i	−0.295732	+	0.170741i	0.344792	+	0.938679i	$0.387949\pi$
$30$	1.56805	−	0.484488i	0.286286	−	0.0884549i
$31$		−	9.05883i		−	1.62701i	−0.581556	−	0.813507i	$-0.697556\pi$
$31$		−	9.05883i		−	1.62701i	0.581556	−	0.813507i	$-0.302444\pi$
$32$	−2.46640	−	5.09086i	−0.436002	−	0.899946i
$33$	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
$36$	−2.73020	+	1.86518i	−0.455033	+	0.310864i
$37$	−1.35800	−	2.35212i	−0.223253	−	0.386686i	0.732541	−	0.680723i	$-0.238334\pi$
$37$	−1.35800	−	2.35212i	−0.223253	−	0.386686i	−0.955794	+	0.294037i	$0.905001\pi$
$38$	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	$0.328597\pi$
$42$	5.06866	+	1.15438i	0.782112	+	0.178125i
$43$	−7.43510	−	4.29266i	−1.13384	−	0.654624i	−0.188944	−	0.981988i	$-0.560507\pi$
$43$	−7.43510	−	4.29266i	−1.13384	−	0.654624i	−0.944899	+	0.327363i	$0.893840\pi$
$44$	0.373106	+	4.91667i	0.0562479	+	0.741216i
$45$	0.826622	−	1.43175i	0.123226	−	0.213433i
$46$	−2.40893	−	7.79654i	−0.355177	−	1.14954i
$47$			8.23945i			1.20185i	0.799307	+	0.600923i	$0.205200\pi$
$47$			8.23945i			1.20185i	−0.799307	+	0.600923i	$0.794800\pi$
$48$	4.32429	+	1.68778i	0.624158	+	0.243609i
$49$	1.51649	+	2.62664i	0.216642	+	0.375234i
$50$	−1.37890	−	0.314043i	−0.195006	−	0.0444124i
$51$		−	0.856977i		−	0.120001i
$52$	−6.62436	−	2.84919i	−0.918633	−	0.395112i
$53$			4.18560i			0.574936i	0.957790	+	0.287468i	$0.0928135\pi$
$53$			4.18560i			0.574936i	−0.957790	+	0.287468i	$0.907186\pi$
$54$	1.69586	−	7.44619i	0.230777	−	1.01330i
$55$	−1.23270	−	2.13510i	−0.166218	−	0.287897i
$56$	3.28486	+	8.33508i	0.438958	+	1.11382i
$57$			10.0209i			1.32730i
$58$	2.48475	−	0.767724i	0.326263	−	0.100807i
$59$	−5.72512	+	9.91620i	−0.745347	+	1.29098i	0.204685	+	0.978828i	$0.434383\pi$
$59$	−5.72512	+	9.91620i	−0.745347	+	1.29098i	−0.950032	+	0.312151i	$0.898950\pi$
$60$	−2.31434	+	0.175626i	−0.298780	+	0.0226732i
$61$	4.03040	+	2.32695i	0.516040	+	0.297936i	0.735313	−	0.677728i	$-0.237035\pi$
$61$	4.03040	+	2.32695i	0.516040	+	0.297936i	−0.219273	+	0.975664i	$0.570368\pi$
$62$	−2.84487	+	12.4913i	−0.361298	+	1.58639i
$63$	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	0.949624	−	0.313391i	$-0.101465\pi$
$67$	1.66496	+	2.88379i	0.203407	+	0.352311i	−0.746217	+	0.665703i	$0.768132\pi$
$68$	1.21950	−	0.833122i	0.147886	−	0.101031i
$69$	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	$0.738076\pi$
$72$	4.35043	−	1.71451i	0.512703	−	0.202056i
$73$		−	1.03291i		−	0.120893i	−0.998171	−	0.0604467i	$-0.980747\pi$
$73$		−	1.03291i		−	0.120893i	0.998171	−	0.0604467i	$-0.0192525\pi$
$74$	1.13388	+	3.66982i	0.131811	+	0.426608i
$75$	1.00502	−	0.580249i	0.116050	−	0.0670014i
$76$	−14.2599	+	9.74193i	−1.63573	+	1.11748i
$77$		−	7.80914i		−	0.889934i
$78$	5.57601	−	1.98084i	0.631359	−	0.224286i
$79$	−9.18672			−1.03359			−0.516793	−	0.856110i	$-0.672874\pi$
$79$	−9.18672			−1.03359			−0.516793	+	0.856110i	$0.672874\pi$
$80$	−2.49984	−	3.12263i	−0.279491	−	0.349120i
$81$	0.653525	+	1.13194i	0.0726139	+	0.125771i
$82$	−0.257460	+	0.0795486i	−0.0284317	+	0.00878467i
$83$	−1.79420			−0.196939			−0.0984693	−	0.995140i	$-0.531395\pi$
$83$	−1.79420			−0.196939			−0.0984693	+	0.995140i	$0.531395\pi$
$84$	−6.62668	−	3.18356i	−0.723030	−	0.347355i
$85$	−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
$88$	1.02957	−	6.89679i	0.109753	−	0.735201i
$89$	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
$94$	2.58754	−	11.3614i	0.266885	−	1.17184i
$95$	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	$-0.669235\pi$
$98$	−1.26622	−	4.09813i	−0.127907	−	0.413973i
$99$	−4.07592			−0.409645
$100$	1.80275	+	0.866072i	0.180275	+	0.0866072i
$101$	−4.58812	+	2.64895i	−0.456535	+	0.263580i	−0.710586	−	0.703610i	$-0.751570\pi$
$101$	−4.58812	+	2.64895i	−0.456535	+	0.263580i	0.254051	+	0.967191i	$0.418237\pi$
$102$	−0.269128	+	1.18169i	−0.0266476	+	0.117005i
$103$	−7.06565			−0.696199			−0.348100	−	0.937458i	$-0.613173\pi$
$103$	−7.06565			−0.696199			−0.348100	+	0.937458i	$0.613173\pi$
$104$	8.23958	+	6.00910i	0.807957	+	0.589241i
$105$	3.67586			0.358728
$106$	1.31446	−	5.77154i	0.127672	−	0.560581i
$107$	10.2327	−	5.90788i	0.989237	−	0.571136i	0.0841908	−	0.996450i	$-0.473169\pi$
$107$	10.2327	−	5.90788i	0.989237	−	0.571136i	0.905046	+	0.425313i	$0.139836\pi$
$108$	−4.67686	+	9.73501i	−0.450031	+	0.936752i
$109$	−3.12953			−0.299754			−0.149877	−	0.988705i	$-0.547888\pi$
$109$	−3.12953			−0.299754			−0.149877	+	0.988705i	$0.547888\pi$
$110$	1.02926	+	3.33122i	0.0981364	+	0.317620i
$111$	−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	$-0.200941\pi$
$114$	3.14699	−	13.8178i	0.294743	−	1.29416i
$115$	−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
$120$	3.24641	+	0.484633i	0.296355	+	0.0442407i
$121$	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
$124$	7.84559	−	16.3308i	0.704555	−	1.46655i
$125$	−1.00000			−0.0894427
$126$	−7.07567	+	2.18620i	−0.630351	+	0.194762i
$127$	−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	$0.889237\pi$
$128$	−0.0372585	−	11.3136i	−0.00329322	−	0.999995i
$129$	−9.96325			−0.877215
$130$	−5.01456	−	0.924215i	−0.439806	−	0.0810590i
$131$			9.67553i			0.845355i	0.906280	+	0.422678i	$0.138910\pi$
$131$			9.67553i			0.845355i	−0.906280	+	0.422678i	$0.861090\pi$
$132$	3.22787	+	4.72486i	0.280950	+	0.411247i
$133$	23.6868	−	13.6756i	2.05391	−	1.18582i
$134$	−1.39018	−	4.49934i	−0.120093	−	0.388684i
$135$		−	5.40008i		−	0.464765i
$136$	−1.94321	+	0.765820i	−0.166629	+	0.0656685i
$137$	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	0.139406	−	0.990235i	$-0.455481\pi$
$139$	−7.64524	−	4.41398i	−0.648461	−	0.374389i	−0.787866	+	0.615846i	$0.788814\pi$
$140$	3.57354	+	5.23084i	0.302019	+	0.442087i
$141$	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
$146$	−0.324380	+	1.42429i	−0.0268459	+	0.117875i
$147$	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	$-0.652082\pi$
$149$	6.58106	−	11.3987i	0.539141	−	0.933820i	0.998951	−	0.0458023i	$-0.0145844\pi$
$150$	−1.56805	+	0.484488i	−0.128031	+	0.0395582i
$151$			17.2918i			1.40719i	0.710602	+	0.703594i	$0.248422\pi$
$151$			17.2918i			1.40719i	−0.710602	+	0.703594i	$0.751578\pi$
$152$	22.7225	−	8.95495i	1.84304	−	0.726342i
$153$	0.610424	+	1.05729i	0.0493499	+	0.0854765i
$154$	−2.45241	+	10.7681i	−0.197621	+	0.867715i
$155$			9.05883i			0.727623i
$156$	−8.31086	+	0.980277i	−0.665401	+	0.0784849i
$157$			23.8530i			1.90367i	0.306603	+	0.951837i	$0.400808\pi$
$157$			23.8530i			1.90367i	−0.306603	+	0.951837i	$0.599192\pi$
$158$	12.6676	+	2.88503i	1.00778	+	0.229521i
$159$	2.42869	+	4.20661i	0.192608	+	0.333606i
$160$	2.46640	+	5.09086i	0.194986	+	0.402468i
$161$		−	18.2768i		−	1.44042i
$162$	−0.545671	−	1.76607i	−0.0428719	−	0.138756i
$163$	−1.04268	+	1.80598i	−0.0816692	+	0.141455i	−0.903967	−	0.427602i	$-0.859358\pi$
$163$	−1.04268	+	1.80598i	−0.0816692	+	0.141455i	0.822298	+	0.569057i	$0.192692\pi$
$164$	0.379995	−	0.0288362i	0.0296726	−	0.00225173i
$165$	−2.47778	−	1.43055i	−0.192895	−	0.111368i
$166$	2.47402	+	0.563455i	0.192021	+	0.0437326i
$167$	−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
$172$	−9.68591	−	14.1779i	−0.738544	−	1.08106i
$173$	−7.84473	−	4.52916i	−0.596424	−	0.344345i	0.171210	−	0.985235i	$-0.445232\pi$
$173$	−7.84473	−	4.52916i	−0.596424	−	0.344345i	−0.767633	+	0.640889i	$0.778566\pi$
$174$	2.05175	−	2.21335i	0.155543	−	0.167794i
$175$	−2.74313	−	1.58374i	−0.207361	−	0.119720i
$176$	−3.58557	+	9.18669i	−0.270273	+	0.692473i
$177$			13.2880i			0.998786i
$178$	−19.0258	+	5.87848i	−1.42604	+	0.440611i
$179$	9.85005	−	5.68693i	0.736227	−	0.425061i	−0.0844689	−	0.996426i	$-0.526919\pi$
$179$	9.85005	−	5.68693i	0.736227	−	0.425061i	0.820696	+	0.571365i	$0.193586\pi$
$180$	2.73020	−	1.86518i	0.203497	−	0.139022i
$181$		−	17.5350i		−	1.30337i	−0.758490	−	0.651685i	$-0.774063\pi$
$181$		−	17.5350i		−	1.30337i	0.758490	−	0.651685i	$-0.225937\pi$
$182$	−12.2918	−	10.4770i	−0.911132	−	0.776608i
$183$	5.40085			0.399242
$184$	2.40965	−	16.1415i	0.177642	−	1.18997i
$185$	1.35800	+	2.35212i	0.0998420	+	0.172931i
$186$	4.38889	+	14.2047i	0.321809	+	1.04154i
$187$	1.82059			0.133135
$188$	−7.13595	+	14.8537i	−0.520443	+	1.08332i
$189$	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	$0.158704\pi$
$192$	6.33390	+	6.78779i	0.457110	+	0.489867i
$193$	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	0.502795	−	0.864406i	$-0.332305\pi$
$197$	−6.97854	−	12.0872i	−0.497200	−	0.861176i	−0.999995	+	0.00322997i	$0.998972\pi$
$198$	5.62030	+	1.28001i	0.399417	+	0.0909667i
$199$	−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
$202$	7.15846	−	2.21178i	0.503668	−	0.155620i
$203$	5.82481			0.408821
$204$	0.742203	−	1.54492i	0.0519646	−	0.108166i
$205$	−0.165016	+	0.0952718i	−0.0115252	+	0.00665407i
$206$	9.74286	+	2.21892i	0.678817	+	0.154600i
$207$	−9.53944			−0.663037
$208$	−9.47447	−	10.8736i	−0.656937	−	0.753946i
$209$	−21.2887			−1.47257
$210$	−5.06866	−	1.15438i	−0.349771	−	0.0796599i
$211$	7.96783	−	4.60023i	0.548528	−	0.316693i	−0.200000	−	0.979796i	$-0.564094\pi$
$211$	7.96783	−	4.60023i	0.548528	−	0.316693i	0.748528	+	0.663103i	$0.230761\pi$
$212$	−3.62503	+	7.54560i	−0.248968	+	0.518234i
$213$	−4.35071			−0.298106
$214$	−15.9653	+	4.93287i	−1.09137	+	0.337204i
$215$	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
$218$	4.31532	+	0.982807i	0.292270	+	0.0665641i
$219$	−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	$0.288314\pi$
$224$	−1.29698	+	17.8710i	−0.0866582	+	1.19406i
$225$	−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	−0.973949	−	0.226769i	$-0.927184\pi$
$227$	−4.37813	+	7.58314i	−0.290587	+	0.503311i	0.683362	+	0.730080i	$0.260517\pi$
$228$	−8.67879	+	18.0652i	−0.574767	+	1.19639i
$229$	22.6655			1.49778			0.748889	−	0.662696i	$-0.230588\pi$
$229$	22.6655			1.49778			0.748889	+	0.662696i	$0.230588\pi$
$230$	2.40893	+	7.79654i	0.158840	+	0.514088i
$231$	−4.53125	−	7.84835i	−0.298134	−	0.516383i
$232$	5.14429	+	0.767953i	0.337739	+	0.0504186i
$233$	−16.3316			−1.06992			−0.534960	−	0.844877i	$-0.679673\pi$
$233$	−16.3316			−1.06992			−0.534960	+	0.844877i	$0.679673\pi$
$234$	−5.46839	+	6.41563i	−0.357480	+	0.419403i
$235$		−	8.23945i		−	0.537482i
$236$	−18.9091	+	12.9181i	−1.23088	+	0.840897i
$237$	−9.23284	+	5.33059i	−0.599738	+	0.346259i
$238$	3.16050	−	0.976512i	0.204865	−	0.0632979i
$239$		−	6.36009i		−	0.411400i	−0.978615	−	0.205700i	$-0.934053\pi$
$239$		−	6.36009i		−	0.411400i	0.978615	−	0.205700i	$-0.0659471\pi$
$240$	−4.32429	−	1.68778i	−0.279132	−	0.108945i
$241$	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
$244$	5.25051	+	7.68554i	0.336130	+	0.492016i
$245$	−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
$250$	1.37890	+	0.314043i	0.0872096	+	0.0198619i
$251$	−6.06987	−	3.50444i	−0.383127	−	0.221198i	0.296051	−	0.955172i	$-0.404330\pi$
$251$	−6.06987	−	3.50444i	−0.383127	−	0.221198i	−0.679178	+	0.733974i	$0.737663\pi$
$252$	10.4432	−	0.792495i	0.657862	−	0.0499225i
$253$	−7.11286	+	12.3198i	−0.447182	+	0.774541i
$254$	1.64410	+	5.32116i	0.103160	+	0.333879i
$255$			0.856977i			0.0536660i
$256$	−3.50160	+	15.6121i	−0.218850	+	0.975759i
$257$	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	$0.637678\pi$
$258$	13.7384	+	3.12889i	0.855313	+	0.194796i
$259$			8.60288i			0.534557i
$260$	6.62436	+	2.84919i	0.410825	+	0.176700i
$261$		−	3.04021i		−	0.188184i
$262$	3.03854	−	13.3416i	0.187722	−	0.824249i
$263$	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	$0.531941\pi$
$264$	−2.96712	−	7.52883i	−0.182613	−	0.463367i
$265$		−	4.18560i		−	0.257119i
$266$	−36.9566	+	11.4186i	−2.26595	+	0.700122i
$267$	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	0.358037	−	0.933707i	$-0.383446\pi$
$269$	−4.45389	−	2.57145i	−0.271558	−	0.156784i	−0.629596	+	0.776923i	$0.716779\pi$
$270$	−1.69586	+	7.44619i	−0.103207	+	0.453161i
$271$	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
$276$	7.55465	+	11.0583i	0.454737	+	0.665630i
$277$	−4.75235	−	2.74377i	−0.285541	−	0.164857i	0.350388	−	0.936605i	$-0.386050\pi$
$277$	−4.75235	−	2.74377i	−0.285541	−	0.164857i	−0.635929	+	0.771747i	$0.719383\pi$
$278$	9.15587	+	8.48739i	0.549133	+	0.509040i
$279$	12.9700	+	7.48823i	0.776493	+	0.448308i
$280$	−3.28486	−	8.33508i	−0.196308	−	0.498116i
$281$			6.19365i			0.369482i	0.982787	+	0.184741i	$0.0591447\pi$
$281$			6.19365i			0.369482i	−0.982787	+	0.184741i	$0.940855\pi$
$282$	−3.99191	−	12.9199i	−0.237715	−	0.769367i
$283$	16.8496	−	9.72811i	1.00160	−	0.578276i	0.0928810	−	0.995677i	$-0.470392\pi$
$283$	16.8496	−	9.72811i	1.00160	−	0.578276i	0.908722	+	0.417401i	$0.137059\pi$
$284$	−4.22960	−	6.19116i	−0.250981	−	0.367378i
$285$		−	10.0209i		−	0.593585i
$286$	4.20817	+	11.8459i	0.248834	+	0.700462i
$287$	−0.603545			−0.0356261
$288$	9.32763	+	0.676948i	0.549636	+	0.0398896i
$289$	8.22734	+	14.2502i	0.483961	+	0.838245i
$290$	−2.48475	+	0.767724i	−0.145909	+	0.0450823i
$291$	−19.8882			−1.16587
$292$	0.894577	−	1.86209i	0.0523512	−	0.108970i
$293$	−16.3593	+	28.3351i	−0.955721	+	1.65536i	−0.223011	+	0.974816i	$0.571588\pi$
$293$	−16.3593	+	28.3351i	−0.955721	+	1.65536i	−0.732710	+	0.680541i	$0.761745\pi$
$294$	−3.65051	−	3.38398i	−0.212902	−	0.197358i
$295$	5.72512	−	9.91620i	0.333329	−	0.577343i
$296$	−1.13422	+	7.59780i	−0.0659252	+	0.441613i
$297$	−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
$302$	5.43038	−	23.8437i	0.312483	−	1.37205i
$303$	−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
$306$	−0.509683	−	1.64959i	−0.0291366	−	0.0943011i
$307$	21.1733			1.20842			0.604212	−	0.796824i	$-0.293488\pi$
$307$	21.1733			1.20842			0.604212	+	0.796824i	$0.293488\pi$
$308$	6.76327	−	14.0780i	0.385373	−	0.802166i
$309$	−7.10113	+	4.09984i	−0.403969	+	0.233232i
$310$	2.84487	−	12.4913i	0.161577	−	0.709456i
$311$	17.0756			0.968271			0.484136	−	0.874993i	$-0.339134\pi$
$311$	17.0756			0.968271			0.484136	+	0.874993i	$0.339134\pi$
$312$	11.7677	+	1.25826i	0.666216	+	0.0712351i
$313$	−25.0633			−1.41666			−0.708330	−	0.705881i	$-0.750551\pi$
$313$	−25.0633			−1.41666			−0.708330	+	0.705881i	$0.750551\pi$
$314$	7.49087	−	32.8910i	0.422734	−	1.85614i
$315$	−4.53506	+	2.61832i	−0.255521	+	0.147525i
$316$	−16.5614	−	7.95636i	−0.931651	−	0.447580i
$317$	−18.2387			−1.02439			−0.512195	−	0.858869i	$-0.671167\pi$
$317$	−18.2387			−1.02439			−0.512195	+	0.858869i	$0.671167\pi$
$318$	−2.02787	−	6.56323i	−0.113717	−	0.368048i
$319$	−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
$322$	−5.73972	+	25.2020i	−0.319862	+	1.40445i
$323$	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
$328$	−0.533032	−	0.0795724i	−0.0294318	−	0.00439365i
$329$	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	$0.431543\pi$
$331$	−13.4517	+	23.2990i	−0.739371	+	1.28063i	−0.952779	+	0.303664i	$0.901790\pi$
$332$	−3.23449	−	1.55390i	−0.177516	−	0.0852814i
$333$	4.49020			0.246062
$334$	21.3651	−	6.60126i	1.16904	−	0.361205i
$335$	−1.66496	−	2.88379i	−0.0909664	−	0.157558i
$336$	−9.18907	−	11.4784i	−0.501305	−	0.626195i
$337$	3.00972			0.163950			0.0819750	−	0.996634i	$-0.473877\pi$
$337$	3.00972			0.163950			0.0819750	+	0.996634i	$0.473877\pi$
$338$	−18.2034	−	2.57626i	−0.990133	−	0.140130i
$339$		−	22.5690i		−	1.22578i
$340$	−1.21950	+	0.833122i	−0.0661366	+	0.0451824i
$341$	19.3415	−	11.1668i	1.04740	−	0.604718i
$342$	5.95986	+	19.2892i	0.322273	+	1.04304i
$343$			12.5655i			0.678472i
$344$	8.90345	+	22.5918i	0.480042	+	1.21807i
$345$	−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	0.559049	−	0.829134i	$-0.311166\pi$
$347$	2.24508	+	1.29620i	0.120522	+	0.0695836i	−0.438527	+	0.898718i	$0.644500\pi$
$348$	−3.52426	+	2.40766i	−0.188920	+	0.129064i
$349$	9.78948	+	16.9559i	0.524019	+	0.907627i	0.999609	+	0.0279603i	$0.00890119\pi$
$349$	9.78948	+	16.9559i	0.524019	+	0.907627i	−0.475590	+	0.879667i	$0.657765\pi$
$350$	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	$0.379454\pi$
$354$	4.17300	−	18.3229i	0.221793	−	0.973849i
$355$	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
$358$	−15.3682	+	4.74838i	−0.812235	+	0.250960i
$359$			24.1177i			1.27288i	0.771325	+	0.636442i	$0.219594\pi$
$359$			24.1177i			1.27288i	−0.771325	+	0.636442i	$0.780406\pi$
$360$	−4.35043	+	1.71451i	−0.229288	+	0.0903624i
$361$	−27.7814	−	48.1188i	−1.46218	−	2.53257i
$362$	−5.50676	+	24.1791i	−0.289429	+	1.27083i
$363$		−	5.71172i		−	0.299787i
$364$	13.6590	+	18.3070i	0.715928	+	0.959547i
$365$			1.03291i			0.0540652i
$366$	−7.44726	−	1.69610i	−0.389274	−	0.0886567i
$367$	−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	$0.851896\pi$
$368$	−8.39182	+	21.5009i	−0.437454	+	1.12081i
$369$			0.315015i			0.0163990i
$370$	−1.13388	−	3.66982i	−0.0589476	−	0.190785i
$371$	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	0.770860	−	0.637005i	$-0.219827\pi$
$373$	11.6773	+	6.74188i	0.604627	+	0.349082i	−0.166233	+	0.986087i	$0.553160\pi$
$374$	−2.51042	−	0.571745i	−0.129811	−	0.0295642i
$375$	−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	0.776678	−	0.629898i	$-0.216903\pi$
$379$	−3.05975	−	5.29964i	−0.157169	−	0.272224i	−0.933847	+	0.357674i	$0.883570\pi$
$380$	14.2599	−	9.74193i	0.731520	−	0.499750i
$381$	−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	$0.484439\pi$
$384$	−6.60218	−	11.3488i	−0.336916	−	0.579143i
$385$			7.80914i			0.397991i
$386$	−7.38068	+	2.28044i	−0.375667	+	0.116071i
$387$	12.2920	−	7.09681i	0.624840	−	0.360751i
$388$	−19.3346	−	28.3014i	−0.981565	−	1.43678i
$389$		−	8.17552i		−	0.414515i	−0.978286	−	0.207258i	$-0.933546\pi$
$389$		−	8.17552i		−	0.414515i	0.978286	−	0.207258i	$-0.0664539\pi$
$390$	−5.57601	+	1.98084i	−0.282352	+	0.100304i
$391$	4.26099			0.215488
$392$	1.26660	−	8.48455i	0.0639727	−	0.428534i
$393$	5.61422	+	9.72411i	0.283200	+	0.490517i
$394$	5.82683	+	18.8586i	0.293552	+	0.950084i
$395$	9.18672			0.462234
$396$	−7.34787	−	3.53004i	−0.369244	−	0.177391i
$397$	−1.33438	+	2.31122i	−0.0669707	+	0.115997i	−0.897566	−	0.440879i	$-0.854667\pi$
$397$	−1.33438	+	2.31122i	−0.0669707	+	0.115997i	0.830596	+	0.556876i	$0.188000\pi$
$398$	23.9689	−	25.8567i	1.20145	−	1.29608i
$399$	15.8705	−	27.4885i	0.794519	−	1.37615i
$400$	2.49984	+	3.12263i	0.124992	+	0.156131i
$401$	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
$406$	−8.03185	−	1.82924i	−0.398614	−	0.0907838i
$407$	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	$0.592626\pi$
$410$	0.257460	−	0.0795486i	0.0127151	−	0.00392863i
$411$	17.7577			0.875921
$412$	−12.7376	−	6.11936i	−0.627538	−	0.301479i
$413$	31.4094	−	18.1343i	1.54556	−	0.892328i
$414$	13.1540	+	2.99580i	0.646483	+	0.147236i
$415$	1.79420			0.0880736
$416$	9.64962	+	17.9690i	0.473112	+	0.881002i
$417$	−10.2448			−0.501692
$418$	29.3551	+	6.68558i	1.43580	+	0.327002i
$419$	−30.8485	+	17.8104i	−1.50705	+	0.870094i	−0.507081	+	0.861898i	$0.669276\pi$
$419$	−30.8485	+	17.8104i	−1.50705	+	0.870094i	−0.999966	+	0.00819632i	$0.997391\pi$
$420$	6.62668	+	3.18356i	0.323349	+	0.155342i
$421$	0.743378			0.0362300			0.0181150	−	0.999836i	$-0.494233\pi$
$421$	0.743378			0.0362300			0.0181150	+	0.999836i	$0.494233\pi$
$422$	−12.4315	+	3.84103i	−0.605158	+	0.186978i
$423$	−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
$426$	5.99921	+	1.36631i	0.290663	+	0.0661980i
$427$	−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	$0.227390\pi$
$432$	−16.8624	+	13.4993i	−0.811294	+	0.649487i
$433$	−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
$436$	−5.64176	−	2.71039i	−0.270191	−	0.129804i
$437$	−49.8250			−2.38345
$438$	0.500434	+	1.61966i	0.0239117	+	0.0773904i
$439$	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	$0.805063\pi$
$440$	−1.02957	+	6.89679i	−0.0490829	+	0.328792i
$441$	−5.01426			−0.238774
$442$	2.44257	−	2.86567i	0.116181	−	0.136306i
$443$			1.77030i			0.0841096i	0.999115	+	0.0420548i	$0.0133904\pi$
$443$			1.77030i			0.0841096i	−0.999115	+	0.0420548i	$0.986610\pi$
$444$	−3.55596	−	5.20511i	−0.168759	−	0.247024i
$445$	−12.1943	+	7.04039i	−0.578066	+	0.333747i
$446$	−5.68850	+	1.75760i	−0.269358	+	0.0832248i
$447$		−	15.2746i		−	0.722464i
$448$	7.40069	−	24.2351i	0.349650	−	1.14500i
$449$	−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
$452$	32.1163	−	21.9408i	1.51062	−	1.03201i
$453$	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	$0.600947\pi$
$458$	−31.2535	−	7.11795i	−1.46038	−	0.332600i
$459$	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	−0.753950	−	0.656931i	$-0.771854\pi$
$461$	4.12121	−	7.13815i	0.191944	−	0.332457i	0.945894	+	0.324474i	$0.105187\pi$
$462$	3.78343	+	12.2451i	0.176021	+	0.569695i
$463$		−	13.2846i		−	0.617390i	−0.951161	−	0.308695i	$-0.900108\pi$
$463$		−	13.2846i		−	0.617390i	0.951161	−	0.308695i	$-0.0998922\pi$
$464$	−6.85232	−	2.67447i	−0.318111	−	0.124159i
$465$	5.25638	+	9.10431i	0.243759	+	0.422202i
$466$	22.5198	+	5.12884i	1.04321	+	0.237589i
$467$		−	3.38808i		−	0.156782i	−0.996923	−	0.0783909i	$-0.975022\pi$
$467$		−	3.38808i		−	0.156782i	0.996923	−	0.0783909i	$-0.0249782\pi$
$468$	9.55518	−	7.12922i	0.441688	−	0.329549i
$469$		−	10.5475i		−	0.487037i
$470$	−2.58754	+	11.3614i	−0.119355	+	0.524063i
$471$	13.8407	+	23.9727i	0.637744	+	1.10461i
$472$	30.1307	−	11.8745i	1.38688	−	0.546570i
$473$		−	21.1663i		−	0.973227i
$474$	14.4052	−	4.45085i	0.661655	−	0.204434i
$475$	−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
$478$	−1.99735	+	8.76996i	−0.0913565	+	0.401129i
$479$	−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
$484$	8.12791	−	5.55272i	0.369450	−	0.252397i
$485$	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	$0.591686\pi$
$488$	−4.82636	−	12.2465i	−0.218479	−	0.554374i
$489$			2.42006i			0.109439i
$490$	1.26622	+	4.09813i	0.0572018	+	0.185134i
$491$	8.22556	−	4.74903i	0.371214	−	0.214321i	−0.302774	−	0.953062i	$-0.597913\pi$
$491$	8.22556	−	4.74903i	0.371214	−	0.214321i	0.673989	+	0.738742i	$0.264580\pi$
$492$	0.365170	−	0.249473i	0.0164631	−	0.0112471i
$493$			1.35797i			0.0611600i
$494$	−28.5617	+	33.5091i	−1.28505	+	1.50765i
$495$	4.07592			0.183199
$496$	28.2873	−	22.6456i	1.27014	−	1.01682i
$497$	5.93746	+	10.2840i	0.266331	+	0.461299i
$498$	2.81339	−	0.869265i	0.126071	−	0.0389527i
$499$	23.3056			1.04330			0.521652	−	0.853158i	$-0.325316\pi$
$499$	23.3056			1.04330			0.521652	+	0.853158i	$0.325316\pi$
$500$	−1.80275	−	0.866072i	−0.0806216	−	0.0387319i
$501$	−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	$0.277104\pi$
$504$	−14.6491	−	2.18686i	−0.652523	−	0.0974103i
$505$	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	0.995817	−	0.0913714i	$-0.0291251\pi$
$509$	9.44807	+	16.3645i	0.418778	+	0.725346i	−0.577038	+	0.816717i	$0.695792\pi$
$510$	0.269128	−	1.18169i	0.0119172	−	0.0523261i
$511$	−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
$514$	−7.71927	−	24.9835i	−0.340482	−	1.10198i
$515$	7.06565			0.311350
$516$	−17.9613	−	8.62888i	−0.790701	−	0.379865i
$517$	−17.5921	+	10.1568i	−0.773698	+	0.446695i
$518$	2.70168	−	11.8626i	0.118705	−	0.521211i
$519$	−10.5122			−0.461432
$520$	−8.23958	−	6.00910i	−0.361330	−	0.263517i
$521$	4.53269			0.198581			0.0992904	−	0.995058i	$-0.468343\pi$
$521$	4.53269			0.198581			0.0992904	+	0.995058i	$0.468343\pi$
$522$	−0.954758	+	4.19216i	−0.0417886	+	0.183486i
$523$	−23.1340	+	13.3564i	−1.01158	+	0.584036i	−0.911654	−	0.410959i	$-0.865194\pi$
$523$	−23.1340	+	13.3564i	−1.01158	+	0.584036i	−0.0999260	+	0.994995i	$0.531861\pi$
$524$	−8.37971	+	17.4426i	−0.366069	+	0.761984i
$525$	−3.67586			−0.160428
$526$	−10.9895	−	35.5677i	−0.479165	−	1.55082i
$527$	−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
$530$	−1.31446	+	5.77154i	−0.0570965	+	0.250700i
$531$	−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
$536$	1.39060	−	9.31521i	0.0600647	−	0.402356i
$537$	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
$540$	4.67686	−	9.73501i	0.201260	−	0.418928i
$541$	−10.6452			−0.457674			−0.228837	−	0.973465i	$-0.573492\pi$
$541$	−10.6452			−0.457674			−0.228837	+	0.973465i	$0.573492\pi$
$542$	−30.3619	+	9.38104i	−1.30415	+	0.402950i
$543$	−10.1747	−	17.6231i	−0.436638	−	0.756279i
$544$	−4.16638	−	0.302373i	−0.178632	−	0.0129641i
$545$	3.12953			0.134054
$546$	−18.4328	−	3.39729i	−0.788853	−	0.145391i
$547$			18.7968i			0.803695i	0.915707	+	0.401847i	$0.131632\pi$
$547$			18.7968i			0.803695i	−0.915707	+	0.401847i	$0.868368\pi$
$548$	17.2634	+	25.2696i	0.737454	+	1.07946i
$549$	−6.66324	+	3.84702i	−0.284380	+	0.164187i
$550$	−1.02926	−	3.33122i	−0.0438879	−	0.142044i
$551$		−	15.8792i		−	0.676475i
$552$	−6.94436	−	17.6208i	−0.295572	−	0.749990i
$553$	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
$556$	−9.95966	−	14.5786i	−0.422383	−	0.618272i
$557$	10.6352	+	18.4206i	0.450626	+	0.780508i	0.998425	−	0.0561026i	$-0.0178674\pi$
$557$	10.6352	+	18.4206i	0.450626	+	0.780508i	−0.547799	+	0.836610i	$0.684534\pi$
$558$	−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
$562$	1.94508	−	8.54045i	0.0820481	−	0.360257i
$563$	−20.4572	−	11.8110i	−0.862168	−	0.497773i	0.00256999	−	0.999997i	$-0.499182\pi$
$563$	−20.4572	−	11.8110i	−0.862168	−	0.497773i	−0.864738	+	0.502224i	$0.832515\pi$
$564$	1.44706	+	19.0689i	0.0609322	+	0.802945i
$565$	−9.72386	+	16.8422i	−0.409086	+	0.708557i
$566$	−26.2890	+	8.12263i	−1.10501	+	0.341420i
$567$		−	4.14007i		−	0.173866i
$568$	3.88792	+	9.86530i	0.163134	+	0.413939i
$569$	−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	$-0.384422\pi$
$570$	−3.14699	+	13.8178i	−0.131813	+	0.578765i
$571$		−	6.49912i		−	0.271980i	−0.990710	−	0.135990i	$-0.956579\pi$
$571$		−	6.49912i		−	0.271980i	0.990710	−	0.135990i	$-0.0434215\pi$
$572$	−2.08254	−	17.6559i	−0.0870752	−	0.738230i
$573$		−	0.802353i		−	0.0335188i
$574$	0.832230	+	0.189539i	0.0347366	+	0.00791121i
$575$	2.88507	+	4.99708i	0.120316	+	0.208393i
$576$	−12.6493	−	3.86273i	−0.527055	−	0.160947i
$577$		−	4.08088i		−	0.169889i	−0.996386	−	0.0849446i	$-0.972929\pi$
$577$		−	4.08088i		−	0.169889i	0.996386	−	0.0849446i	$-0.0270713\pi$
$578$	−6.86954	−	22.2334i	−0.285735	−	0.924786i
$579$	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
$582$	27.4239	+	6.24576i	1.13676	+	0.258895i
$583$	−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	0.981145	−	0.193275i	$-0.0619111\pi$
$587$	7.83029	+	13.5625i	0.323191	+	0.559783i	−0.657954	+	0.753058i	$0.728578\pi$
$588$	3.97098	+	5.81260i	0.163761	+	0.239708i
$589$	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
$592$	3.95002	−	10.1204i	0.162345	−	0.415948i
$593$			35.5283i			1.45897i	0.683996	+	0.729486i	$0.260241\pi$
$593$			35.5283i			1.45897i	−0.683996	+	0.729486i	$0.739759\pi$
$594$	17.9889	−	5.55811i	0.738093	−	0.228052i
$595$	2.02568	−	1.16953i	0.0830447	−	0.0479459i
$596$	21.7361	−	14.8494i	0.890347	−	0.608256i
$597$			28.9320i			1.18411i
$598$	9.84897	+	27.7246i	0.402754	+	1.13374i
$599$	15.0781			0.616075			0.308037	−	0.951374i	$-0.400328\pi$
$599$	15.0781			0.616075			0.308037	+	0.951374i	$0.400328\pi$
$600$	−3.24641	−	0.484633i	−0.132534	−	0.0197850i
$601$	−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	$0.964086\pi$
$602$	−11.3530	−	36.7441i	−0.462713	−	1.49758i
$603$	−5.50517			−0.224188
$604$	−14.9759	+	31.1729i	−0.609363	+	1.26841i
$605$	−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	$-0.00253244\pi$
$608$	48.7187	+	3.53573i	1.97580	+	0.143393i
$609$	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	0.953598	−	0.301083i	$-0.0973482\pi$
$613$	5.34922	+	9.26513i	0.216053	+	0.374215i	−0.737545	+	0.675298i	$0.764015\pi$
$614$	−29.1960	−	6.64934i	−1.17825	−	0.268345i
$615$	−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	$0.535131\pi$
$618$	11.0793	−	3.42322i	0.445675	−	0.137702i
$619$	−14.3270			−0.575850			−0.287925	−	0.957653i	$-0.592965\pi$
$619$	−14.3270			−0.575850			−0.287925	+	0.957653i	$0.592965\pi$
$620$	−7.84559	+	16.3308i	−0.315087	+	0.655862i
$621$	−26.9847	+	15.5796i	−1.08286	+	0.625188i
$622$	−23.5457	−	5.36249i	−0.944096	−	0.215016i
$623$	−44.6007			−1.78689
$624$	−15.8314	−	5.43060i	−0.633764	−	0.217398i
$625$	1.00000			0.0400000
$626$	34.5599	+	7.87096i	1.38129	+	0.314587i
$627$	−21.3956	+	12.3528i	−0.854458	+	0.493321i
$628$	−20.6584	+	43.0010i	−0.824359	+	1.71593i
$629$	−2.00564			−0.0799702
$630$	7.07567	−	2.18620i	0.281902	−	0.0871004i
$631$	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
$634$	25.1495	+	5.72776i	0.998813	+	0.227478i
$635$	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
$640$	0.0372585	+	11.3136i	0.00147277	+	0.447211i
$641$	−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	−0.635869	−	0.771797i	$-0.719358\pi$
$643$	8.88679	−	15.3924i	0.350461	−	0.607016i	0.986330	+	0.164781i	$0.0526916\pi$
$644$	15.8290	−	32.9486i	0.623752	−	1.29836i
$645$	9.96325			0.392302
$646$	−2.66210	−	8.61591i	−0.104739	−	0.338989i
$647$	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	$0.548731\pi$
$648$	0.545834	−	3.65638i	0.0214424	−	0.143636i
$649$	−28.2295			−1.10810
$650$	5.01456	+	0.924215i	0.196687	+	0.0362507i
$651$			33.2990i			1.30509i
$652$	−3.44381	+	2.35270i	−0.134870	+	0.0921387i
$653$	11.7391	−	6.77755i	0.459385	−	0.265226i	−0.252401	−	0.967623i	$-0.581220\pi$
$653$	11.7391	−	6.77755i	0.459385	−	0.265226i	0.711785	+	0.702397i	$0.247887\pi$
$654$	4.90725	−	1.51622i	0.191889	−	0.0592887i
$655$		−	9.67553i		−	0.378054i
$656$	0.710011	+	0.277118i	0.0277213	+	0.0108196i
$657$	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	0.470625	−	0.882333i	$-0.344028\pi$
$659$	−1.49368	−	0.862377i	−0.0581856	−	0.0335934i	−0.528811	+	0.848740i	$0.677362\pi$
$660$	−3.22787	−	4.72486i	−0.125645	−	0.183915i
$661$	−12.9412	−	22.4148i	−0.503355	−	0.871836i	−0.999992	−	0.00387783i	$-0.998766\pi$
$661$	−12.9412	−	22.4148i	−0.503355	−	0.871836i	0.496638	−	0.867958i	$-0.334568\pi$
$662$	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
$666$	−6.19156	−	1.41012i	−0.239918	−	0.0546410i
$667$	−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
$670$	1.39018	+	4.49934i	0.0537074	+	0.173825i
$671$			11.4738i			0.442940i
$672$	9.06615	+	18.7133i	0.349734	+	0.721882i
$673$	−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	$0.919408\pi$
$674$	−4.15012	−	0.945183i	−0.159857	−	0.0364071i
$675$			5.40008i			0.207849i
$676$	24.2917	+	9.26907i	0.934294	+	0.356503i
$677$		−	32.0465i		−	1.23165i	−0.787884	−	0.615823i	$-0.788824\pi$
$677$		−	32.0465i		−	1.23165i	0.787884	−	0.615823i	$-0.211176\pi$
$678$	−7.08766	+	31.1205i	−0.272200	+	1.19518i
$679$	27.1416	+	47.0107i	1.04160	+	1.80410i
$680$	1.94321	−	0.765820i	0.0745186	−	0.0293678i
$681$			10.1616i			0.389394i
$682$	−30.1770	+	9.32392i	−1.15554	+	0.357031i
$683$	−4.02679	+	6.97461i	−0.154081	+	0.266876i	−0.932724	−	0.360591i	$-0.882575\pi$
$683$	−4.02679	+	6.97461i	−0.154081	+	0.266876i	0.778643	+	0.627467i	$0.215908\pi$
$684$	−2.16044	−	28.4696i	−0.0826065	−	1.08856i
$685$	−13.2517	−	7.65088i	−0.506322	−	0.292325i
$686$	3.94611	−	17.3266i	0.150663	−	0.661533i
$687$	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	0.640560	−	0.767908i	$-0.278702\pi$
$691$	−9.06234	−	15.6964i	−0.344748	−	0.597121i	−0.985308	+	0.170787i	$0.945369\pi$
$692$	−10.2195	−	14.9590i	−0.388489	−	0.568658i
$693$	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
$696$	5.61572	−	2.21316i	0.212864	−	0.0838897i
$697$		−	0.140708i		−	0.00532970i
$698$	−8.17387	−	26.4549i	−0.309386	−	1.00133i
$699$	−16.4136	+	9.47641i	−0.620820	+	0.358431i
$700$	−3.57354	−	5.23084i	−0.135067	−	0.197707i
$701$			0.168502i			0.00636422i	0.999995	+	0.00318211i	$0.00101290\pi$
$701$			0.168502i			0.00636422i	−0.999995	+	0.00318211i	$0.998987\pi$
$702$	−4.99084	+	27.0790i	−0.188367	+	1.02203i
$703$	23.4526			0.884530
$704$	−14.4202	+	13.4560i	−0.543483	+	0.507141i
$705$	−4.78093	−	8.28082i	−0.180060	−	0.311874i
$706$	7.33097	−	2.26508i	0.275905	−	0.0852475i
$707$	16.7810			0.631116
$708$	−11.5083	+	23.9550i	−0.432510	+	0.900282i
$709$	−13.2652	+	22.9759i	−0.498184	+	0.862879i	−0.999998	−	0.00209603i	$-0.999333\pi$
$709$	−13.2652	+	22.9759i	−0.498184	+	0.862879i	0.501814	+	0.864975i	$0.332666\pi$
$710$	−3.88825	−	3.60437i	−0.145924	−	0.135270i
$711$	7.59395	−	13.1531i	0.284795	−	0.493280i
$712$	−39.3900	−	5.88024i	−1.47620	−	0.220371i
$713$	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
$718$	7.57400	−	33.2560i	0.282659	−	1.24110i
$719$	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
$722$	23.1965	+	75.0758i	0.863284	+	2.79403i
$723$	14.2820			0.531155
$724$	15.1866	−	31.6114i	0.564406	−	1.17483i
$725$	−1.59257	+	0.919468i	−0.0591464	+	0.0341482i
$726$	−1.79373	+	7.87591i	−0.0665714	+	0.292302i
$727$	−18.8156			−0.697832			−0.348916	−	0.937154i	$-0.613450\pi$
$727$	−18.8156			−0.697832			−0.348916	+	0.937154i	$0.613450\pi$
$728$	−13.0853	−	29.5331i	−0.484974	−	1.09457i
$729$	−20.9612			−0.776342
$730$	0.324380	−	1.42429i	0.0120058	−	0.0527153i
$731$	−5.49050	+	3.16994i	−0.203073	+	0.117244i
$732$	9.73640	+	4.67752i	0.359868	+	0.172886i
$733$	−19.8512			−0.733219			−0.366610	−	0.930375i	$-0.619482\pi$
$733$	−19.8512			−0.733219			−0.366610	+	0.930375i	$0.619482\pi$
$734$	0.932268	+	3.01730i	0.0344106	+	0.111370i
$735$	−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
$738$	0.0989284	−	0.434376i	0.00364161	−	0.0159896i
$739$	−21.9843	−	38.0780i	−0.808707	−	1.40072i	−0.913760	−	0.406255i	$-0.866834\pi$
$739$	−21.9843	−	38.0780i	−0.808707	−	1.40072i	0.105052	−	0.994467i	$-0.466499\pi$
$740$	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	$0.452044\pi$
$744$	−4.39020	+	29.4087i	−0.160953	+	1.07817i
$745$	−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
$748$	3.28208	+	1.57676i	0.120005	+	0.0576522i
$749$	−37.4263			−1.36753
$750$	1.56805	−	0.484488i	0.0572571	−	0.0176910i
$751$	−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	$0.948324\pi$
$752$	−25.7287	+	20.5973i	−0.938230	+	0.751106i
$753$	−8.13379			−0.296412
$754$	−8.83580	+	3.13886i	−0.321781	+	0.114310i
$755$		−	17.2918i		−	0.629313i
$756$	28.2470	−	19.2974i	1.02733	−	0.701840i
$757$	14.7095	−	8.49256i	0.534627	−	0.308667i	−0.208271	−	0.978071i	$-0.566784\pi$
$757$	14.7095	−	8.49256i	0.534627	−	0.308667i	0.742899	+	0.669404i	$0.233450\pi$
$758$	2.55478	+	8.26858i	0.0927938	+	0.300329i
$759$			16.5089i			0.599236i
$760$	−22.7225	+	8.95495i	−0.824231	+	0.324830i
$761$	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
$764$	1.14177	−	0.780019i	0.0413077	−	0.0282201i
$765$	−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

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)

\(f(q)\)	\(=\)	\(q+(-1.37890 - 0.314043i) q^{2} +(1.00502 - 0.580249i) q^{3} +(1.80275 + 0.866072i) q^{4} -1.00000 q^{5} +(-1.56805 + 0.484488i) q^{6} +(-2.74313 - 1.58374i) q^{7} +(-2.21384 - 1.76037i) q^{8} +(-0.826622 + 1.43175i) q^{9} +O(q^{10})\)	\(q+(-1.37890 - 0.314043i) q^{2} +(1.00502 - 0.580249i) q^{3} +(1.80275 + 0.866072i) q^{4} -1.00000 q^{5} +(-1.56805 + 0.484488i) q^{6} +(-2.74313 - 1.58374i) q^{7} +(-2.21384 - 1.76037i) q^{8} +(-0.826622 + 1.43175i) q^{9} +(1.37890 + 0.314043i) 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} +(2.49984 + 3.12263i) q^{16} +(0.369228 - 0.639522i) q^{17} +(1.58946 - 1.71465i) q^{18} +(-4.31749 + 7.47811i) q^{19} +(-1.80275 - 0.866072i) q^{20} -3.67586 q^{21} +(-1.02926 - 3.33122i) q^{22} +(2.88507 + 4.99708i) q^{23} +(-3.24641 - 0.484633i) q^{24} +1.00000 q^{25} +(5.01456 + 0.924215i) q^{26} +5.40008i q^{27} +(-3.57354 - 5.23084i) q^{28} +(-1.59257 + 0.919468i) q^{29} +(1.56805 - 0.484488i) q^{30} -9.05883i q^{31} +(-2.46640 - 5.09086i) q^{32} +(2.47778 + 1.43055i) q^{33} +(-0.709967 + 0.765885i) q^{34} +(2.74313 + 1.58374i) q^{35} +(-2.73020 + 1.86518i) 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} +(5.06866 + 1.15438i) q^{42} +(-7.43510 - 4.29266i) q^{43} +(0.373106 + 4.91667i) q^{44} +(0.826622 - 1.43175i) q^{45} +(-2.40893 - 7.79654i) q^{46} +8.23945i q^{47} +(4.32429 + 1.68778i) q^{48} +(1.51649 + 2.62664i) q^{49} +(-1.37890 - 0.314043i) q^{50} -0.856977i q^{51} +(-6.62436 - 2.84919i) q^{52} +4.18560i q^{53} +(1.69586 - 7.44619i) q^{54} +(-1.23270 - 2.13510i) q^{55} +(3.28486 + 8.33508i) q^{56} +10.0209i q^{57} +(2.48475 - 0.767724i) q^{58} +(-5.72512 + 9.91620i) q^{59} +(-2.31434 + 0.175626i) q^{60} +(4.03040 + 2.32695i) q^{61} +(-2.84487 + 12.4913i) 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} +(1.21950 - 0.833122i) q^{68} +(5.79911 + 3.34812i) q^{69} +(-3.28514 - 3.04529i) q^{70} +(-3.24673 - 1.87450i) q^{71} +(4.35043 - 1.71451i) q^{72} -1.03291i q^{73} +(1.13388 + 3.66982i) q^{74} +(1.00502 - 0.580249i) q^{75} +(-14.2599 + 9.74193i) q^{76} -7.80914i q^{77} +(5.57601 - 1.98084i) q^{78} -9.18672 q^{79} +(-2.49984 - 3.12263i) q^{80} +(0.653525 + 1.13194i) q^{81} +(-0.257460 + 0.0795486i) q^{82} -1.79420 q^{83} +(-6.62668 - 3.18356i) q^{84} +(-0.369228 + 0.639522i) q^{85} +(8.90422 + 8.25411i) q^{86} +(-1.06704 + 1.84817i) q^{87} +(1.02957 - 6.89679i) 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} +(2.58754 - 11.3614i) q^{94} +(4.31749 - 7.47811i) q^{95} +(-5.43275 - 3.68530i) q^{96} +(-14.8416 - 8.56882i) q^{97} +(-1.26622 - 4.09813i) q^{98} -4.07592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

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