LMFDB - Embedded newform 380.2.k.c.267.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (of order $4$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.21
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707119i) q^{2} +(-1.27216 - 1.27216i) q^{3} +(0.999965 + 1.73207i) q^{4} +(2.08931 - 0.796745i) q^{5} +(-0.658494 - 2.45763i) q^{6} +(0.691067 - 0.691067i) q^{7} +(-8.52354e-5 + 2.82843i) q^{8} +0.236784i q^{9} +O(q^{10})$	\(q+(1.22474 + 0.707119i) q^{2} +(-1.27216 - 1.27216i) q^{3} +(0.999965 + 1.73207i) q^{4} +(2.08931 - 0.796745i) q^{5} +(-0.658494 - 2.45763i) q^{6} +(0.691067 - 0.691067i) q^{7} +(-8.52354e-5 + 2.82843i) q^{8} +0.236784i q^{9} +(3.12224 + 0.501584i) q^{10} -2.48162i q^{11} +(0.931356 - 3.47559i) q^{12} +(0.299596 - 0.299596i) q^{13} +(1.33504 - 0.357709i) q^{14} +(-3.67152 - 1.64434i) q^{15} +(-2.00014 + 3.46402i) q^{16} +(1.98979 + 1.98979i) q^{17} +(-0.167434 + 0.289998i) q^{18} +1.00000 q^{19} +(3.46925 + 2.82211i) q^{20} -1.75830 q^{21} +(1.75480 - 3.03934i) q^{22} +(3.56603 + 3.56603i) q^{23} +(3.59832 - 3.59810i) q^{24} +(3.73039 - 3.32929i) q^{25} +(0.578776 - 0.155076i) q^{26} +(-3.51525 + 3.51525i) q^{27} +(1.88802 + 0.505934i) q^{28} -5.50279i q^{29} +(-3.33390 - 4.61009i) q^{30} -1.55566i q^{31} +(-4.89912 + 2.82818i) q^{32} +(-3.15702 + 3.15702i) q^{33} +(1.02995 + 3.84398i) q^{34} +(0.893246 - 1.99446i) q^{35} +(-0.410126 + 0.236775i) q^{36} +(1.57326 + 1.57326i) q^{37} +(1.22474 + 0.707119i) q^{38} -0.762268 q^{39} +(2.25336 + 5.90952i) q^{40} -8.98970 q^{41} +(-2.15345 - 1.24333i) q^{42} +(0.612449 + 0.612449i) q^{43} +(4.29835 - 2.48154i) q^{44} +(0.188656 + 0.494713i) q^{45} +(1.84584 + 6.88905i) q^{46} +(-7.25685 + 7.25685i) q^{47} +(6.95129 - 1.86229i) q^{48} +6.04485i q^{49} +(6.92296 - 1.43967i) q^{50} -5.06266i q^{51} +(0.818507 + 0.219336i) q^{52} +(0.698187 - 0.698187i) q^{53} +(-6.79097 + 1.81956i) q^{54} +(-1.97722 - 5.18487i) q^{55} +(1.95457 + 1.95469i) q^{56} +(-1.27216 - 1.27216i) q^{57} +(3.89113 - 6.73948i) q^{58} -6.30971 q^{59} +(-0.823271 - 8.00362i) q^{60} -10.9589 q^{61} +(1.10004 - 1.90528i) q^{62} +(0.163633 + 0.163633i) q^{63} +(-8.00000 - 0.000482164i) q^{64} +(0.387246 - 0.864649i) q^{65} +(-6.09891 + 1.63413i) q^{66} +(-9.08244 + 9.08244i) q^{67} +(-1.45673 + 5.43617i) q^{68} -9.07312i q^{69} +(2.50431 - 1.81105i) q^{70} -7.70738i q^{71} +(-0.669725 - 2.01824e-5i) q^{72} +(-1.79811 + 1.79811i) q^{73} +(0.814347 + 3.03931i) q^{74} +(-8.98105 - 0.510271i) q^{75} +(0.999965 + 1.73207i) q^{76} +(-1.71497 - 1.71497i) q^{77} +(-0.933579 - 0.539014i) q^{78} +0.823249 q^{79} +(-1.41896 + 8.83100i) q^{80} +9.65428 q^{81} +(-11.0100 - 6.35679i) q^{82} +(0.768276 + 0.768276i) q^{83} +(-1.75824 - 3.04549i) q^{84} +(5.74263 + 2.57192i) q^{85} +(0.317015 + 1.18316i) q^{86} +(-7.00043 + 7.00043i) q^{87} +(7.01909 + 0.000211522i) q^{88} +10.3379i q^{89} +(-0.118767 + 0.739296i) q^{90} -0.414082i q^{91} +(-2.61071 + 9.74252i) q^{92} +(-1.97905 + 1.97905i) q^{93} +(-14.0192 + 3.75628i) q^{94} +(2.08931 - 0.796745i) q^{95} +(9.83037 + 2.63457i) q^{96} +(-5.43484 - 5.43484i) q^{97} +(-4.27443 + 7.40336i) q^{98} +0.587608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.22474	+	0.707119i	0.866020	+	0.500009i
$2$	1.22474	+	0.707119i	0.866020	+	0.500009i
$3$	−1.27216	−	1.27216i	−0.734482	−	0.734482i	0.237022	−	0.971504i	$-0.423829\pi$
$3$	−1.27216	−	1.27216i	−0.734482	−	0.734482i	−0.971504	+	0.237022i	$0.923829\pi$
$4$	0.999965	+	1.73207i	0.499983	+	0.866035i
$5$	2.08931	−	0.796745i	0.934366	−	0.356315i
$5$	2.08931	−	0.796745i	0.934366	−	0.356315i
$6$	−0.658494	−	2.45763i	−0.268829	−	1.00332i
$7$	0.691067	−	0.691067i	0.261199	−	0.261199i	−0.564342	−	0.825541i	$-0.690870\pi$
$7$	0.691067	−	0.691067i	0.261199	−	0.261199i	0.825541	+	0.564342i	$0.190870\pi$
$8$	−8.52354e−5		2.82843i	−3.01353e−5		1.00000i
$9$			0.236784i			0.0789279i
$10$	3.12224	+	0.501584i	0.987341	+	0.158615i
$11$		−	2.48162i		−	0.748237i	−0.927381	−	0.374119i	$-0.877945\pi$
$11$		−	2.48162i		−	0.748237i	0.927381	−	0.374119i	$-0.122055\pi$
$12$	0.931356	−	3.47559i	0.268859	−	1.00332i
$13$	0.299596	−	0.299596i	0.0830930	−	0.0830930i	−0.664339	−	0.747432i	$-0.731287\pi$
$13$	0.299596	−	0.299596i	0.0830930	−	0.0830930i	0.747432	+	0.664339i	$0.231287\pi$
$14$	1.33504	−	0.357709i	0.356805	−	0.0956018i
$15$	−3.67152	−	1.64434i	−0.947982	−	0.424568i
$16$	−2.00014	+	3.46402i	−0.500035	+	0.866005i
$17$	1.98979	+	1.98979i	0.482594	+	0.482594i	0.905959	−	0.423365i	$-0.139151\pi$
$17$	1.98979	+	1.98979i	0.482594	+	0.482594i	−0.423365	+	0.905959i	$0.639151\pi$
$18$	−0.167434	+	0.289998i	−0.0394646	+	0.0683531i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	3.46925	+	2.82211i	0.775748	+	0.631042i
$21$	−1.75830			−0.383692
$22$	1.75480	−	3.03934i	0.374125	−	0.647989i
$23$	3.56603	+	3.56603i	0.743568	+	0.743568i	0.973263	−	0.229695i	$-0.0737727\pi$
$23$	3.56603	+	3.56603i	0.743568	+	0.743568i	−0.229695	+	0.973263i	$0.573773\pi$
$24$	3.59832	−	3.59810i	0.734504	−	0.734460i
$25$	3.73039	−	3.32929i	0.746079	−	0.665858i
$26$	0.578776	−	0.155076i	0.113507	−	0.0304130i
$27$	−3.51525	+	3.51525i	−0.676511	+	0.676511i
$28$	1.88802	+	0.505934i	0.356802	+	0.0956126i
$29$		−	5.50279i		−	1.02184i	−0.859627	−	0.510921i	$-0.829304\pi$
$29$		−	5.50279i		−	1.02184i	0.859627	−	0.510921i	$-0.170696\pi$
$30$	−3.33390	−	4.61009i	−0.608684	−	0.841684i
$31$		−	1.55566i		−	0.279405i	−0.990193	−	0.139703i	$-0.955385\pi$
$31$		−	1.55566i		−	0.279405i	0.990193	−	0.139703i	$-0.0446147\pi$
$32$	−4.89912	+	2.82818i	−0.866051	+	0.499957i
$33$	−3.15702	+	3.15702i	−0.549567	+	0.549567i
$34$	1.02995	+	3.84398i	0.176635	+	0.659238i
$35$	0.893246	−	1.99446i	0.150986	−	0.337124i
$36$	−0.410126	+	0.236775i	−0.0683543	+	0.0394626i
$37$	1.57326	+	1.57326i	0.258642	+	0.258642i	0.824502	−	0.565860i	$-0.191456\pi$
$37$	1.57326	+	1.57326i	0.258642	+	0.258642i	−0.565860	+	0.824502i	$0.691456\pi$
$38$	1.22474	+	0.707119i	0.198679	+	0.114710i
$39$	−0.762268			−0.122061
$40$	2.25336	+	5.90952i	0.356287	+	0.934377i
$41$	−8.98970			−1.40395			−0.701977	−	0.712199i	$-0.747699\pi$
$41$	−8.98970			−1.40395			−0.701977	+	0.712199i	$0.747699\pi$
$42$	−2.15345	−	1.24333i	−0.332285	−	0.191849i
$43$	0.612449	+	0.612449i	0.0933977	+	0.0933977i	0.752262	−	0.658864i	$-0.228963\pi$
$43$	0.612449	+	0.612449i	0.0933977	+	0.0933977i	−0.658864	+	0.752262i	$0.728963\pi$
$44$	4.29835	−	2.48154i	0.648000	−	0.374106i
$45$	0.188656	+	0.494713i	0.0281232	+	0.0737475i
$46$	1.84584	+	6.88905i	0.272155	+	1.01574i
$47$	−7.25685	+	7.25685i	−1.05852	+	1.05852i	−0.0603431	+	0.998178i	$0.519219\pi$
$47$	−7.25685	+	7.25685i	−1.05852	+	1.05852i	−0.998178	+	0.0603431i	$0.980781\pi$
$48$	6.95129	−	1.86229i	1.00333	−	0.268799i
$49$			6.04485i			0.863550i
$50$	6.92296	−	1.43967i	0.979054	−	0.203600i
$51$		−	5.06266i		−	0.708914i
$52$	0.818507	+	0.219336i	0.113506	+	0.0304164i
$53$	0.698187	−	0.698187i	0.0959034	−	0.0959034i	−0.657527	−	0.753431i	$-0.728398\pi$
$53$	0.698187	−	0.698187i	0.0959034	−	0.0959034i	0.753431	+	0.657527i	$0.228398\pi$
$54$	−6.79097	+	1.81956i	−0.924134	+	0.247611i
$55$	−1.97722	−	5.18487i	−0.266608	−	0.699127i
$56$	1.95457	+	1.95469i	0.261191	+	0.261207i
$57$	−1.27216	−	1.27216i	−0.168502	−	0.168502i
$58$	3.89113	−	6.73948i	0.510930	−	0.884937i
$59$	−6.30971			−0.821454			−0.410727	−	0.911758i	$-0.634725\pi$
$59$	−6.30971			−0.821454			−0.410727	+	0.911758i	$0.634725\pi$
$60$	−0.823271	−	8.00362i	−0.106284	−	1.03326i
$61$	−10.9589			−1.40315			−0.701575	−	0.712596i	$-0.747519\pi$
$61$	−10.9589			−1.40315			−0.701575	+	0.712596i	$0.747519\pi$
$62$	1.10004	−	1.90528i	0.139705	−	0.241971i
$63$	0.163633	+	0.163633i	0.0206159	+	0.0206159i
$64$	−8.00000		0.000482164i	−1.00000		6.02705e-5i
$65$	0.387246	−	0.864649i	0.0480319	−	0.107247i
$66$	−6.09891	+	1.63413i	−0.750724	+	0.201148i
$67$	−9.08244	+	9.08244i	−1.10960	+	1.10960i	−0.116393	+	0.993203i	$0.537133\pi$
$67$	−9.08244	+	9.08244i	−1.10960	+	1.10960i	−0.993203	+	0.116393i	$0.962867\pi$
$68$	−1.45673	+	5.43617i	−0.176655	+	0.659232i
$69$		−	9.07312i		−	1.09227i
$70$	2.50431	−	1.81105i	0.299322	−	0.216462i
$71$		−	7.70738i		−	0.914698i	−0.889287	−	0.457349i	$-0.848799\pi$
$71$		−	7.70738i		−	0.914698i	0.889287	−	0.457349i	$-0.151201\pi$
$72$	−0.669725		2.01824e-5i	−0.0789279		2.37851e-6i
$73$	−1.79811	+	1.79811i	−0.210453	+	0.210453i	−0.804460	−	0.594007i	$-0.797545\pi$
$73$	−1.79811	+	1.79811i	−0.210453	+	0.210453i	0.594007	+	0.804460i	$0.297545\pi$
$74$	0.814347	+	3.03931i	0.0946660	+	0.353312i
$75$	−8.98105	−	0.510271i	−1.03704	−	0.0589210i
$76$	0.999965	+	1.73207i	0.114704	+	0.198682i
$77$	−1.71497	−	1.71497i	−0.195439	−	0.195439i
$78$	−0.933579	−	0.539014i	−0.105707	−	0.0610314i
$79$	0.823249			0.0926228			0.0463114	−	0.998927i	$-0.485253\pi$
$79$	0.823249			0.0926228			0.0463114	+	0.998927i	$0.485253\pi$
$80$	−1.41896	+	8.83100i	−0.158644	+	0.987336i
$81$	9.65428			1.07270
$82$	−11.0100	−	6.35679i	−1.21585	−	0.701990i
$83$	0.768276	+	0.768276i	0.0843293	+	0.0843293i	0.748013	−	0.663684i	$-0.231008\pi$
$83$	0.768276	+	0.768276i	0.0843293	+	0.0843293i	−0.663684	+	0.748013i	$0.731008\pi$
$84$	−1.75824	−	3.04549i	−0.191839	−	0.332291i
$85$	5.74263	+	2.57192i	0.622875	+	0.278964i
$86$	0.317015	+	1.18316i	0.0341846	+	0.127584i
$87$	−7.00043	+	7.00043i	−0.750525	+	0.750525i
$88$	7.01909		0.000211522i	0.748237		2.25483e-5i
$89$			10.3379i			1.09582i	0.836538	+	0.547909i	$0.184576\pi$
$89$			10.3379i			1.09582i	−0.836538	+	0.547909i	$0.815424\pi$
$90$	−0.118767	+	0.739296i	−0.0125191	+	0.0779287i
$91$		−	0.414082i		−	0.0434076i
$92$	−2.61071	+	9.74252i	−0.272185	+	1.01573i
$93$	−1.97905	+	1.97905i	−0.205218	+	0.205218i
$94$	−14.0192	+	3.75628i	−1.44597	+	0.387431i
$95$	2.08931	−	0.796745i	0.214358	−	0.0817443i
$96$	9.83037	+	2.63457i	1.00331	+	0.268889i
$97$	−5.43484	−	5.43484i	−0.551825	−	0.551825i	0.375142	−	0.926967i	$-0.377594\pi$
$97$	−5.43484	−	5.43484i	−0.551825	−	0.551825i	−0.926967	+	0.375142i	$0.877594\pi$
$98$	−4.27443	+	7.40336i	−0.431783	+	0.747852i
$99$	0.587608			0.0590568
$100$	9.49683	+	3.13213i	0.949683	+	0.313213i
$101$	14.5693			1.44970			0.724849	−	0.688908i	$-0.241909\pi$
$101$	14.5693			1.44970			0.724849	+	0.688908i	$0.241909\pi$
$102$	3.57990	−	6.20043i	0.354463	−	0.613934i
$103$	6.64745	+	6.64745i	0.654992	+	0.654992i	0.954191	−	0.299199i	$-0.0967193\pi$
$103$	6.64745	+	6.64745i	0.654992	+	0.654992i	−0.299199	+	0.954191i	$0.596719\pi$
$104$	0.847360	+	0.847411i	0.0830905	+	0.0830955i
$105$	−3.67362	+	1.40091i	−0.358508	+	0.136715i
$106$	1.34880	−	0.361395i	0.131007	−	0.0351018i
$107$	12.1231	−	12.1231i	1.17199	−	1.17199i	0.190254	−	0.981735i	$-0.439069\pi$
$107$	12.1231	−	12.1231i	1.17199	−	1.17199i	0.981735	−	0.190254i	$-0.0609312\pi$
$108$	−9.60380	−	2.57354i	−0.924126	−	0.247639i
$109$		−	10.7770i		−	1.03225i	−0.856513	−	0.516125i	$-0.827374\pi$
$109$		−	10.7770i		−	1.03225i	0.856513	−	0.516125i	$-0.172626\pi$
$110$	1.24474	−	7.74823i	0.118681	−	0.738765i
$111$		−	4.00287i		−	0.379936i
$112$	1.01164	+	3.77610i	0.0955911	+	0.356808i
$113$	−5.29688	+	5.29688i	−0.498289	+	0.498289i	−0.910905	−	0.412616i	$-0.864615\pi$
$113$	−5.29688	+	5.29688i	−0.498289	+	0.498289i	0.412616	+	0.910905i	$0.364615\pi$
$114$	−0.658494	−	2.45763i	−0.0616736	−	0.230178i
$115$	10.2917	+	4.60931i	0.959709	+	0.429820i
$116$	9.53123	−	5.50260i	0.884952	−	0.510904i
$117$	0.0709394	+	0.0709394i	0.00655835	+	0.00655835i
$118$	−7.72774	−	4.46171i	−0.711396	−	0.410734i
$119$	2.75015			0.252106
$120$	4.65122	−	10.3845i	0.424596	−	0.947969i
$121$	4.84155			0.440141
$122$	−13.4218	−	7.74928i	−1.21516	−	0.701587i
$123$	11.4363	+	11.4363i	1.03118	+	1.03118i
$124$	2.69452	−	1.55561i	0.241975	−	0.139698i
$125$	5.14134	−	9.92807i	0.459855	−	0.887994i
$126$	0.0846997	+	0.316116i	0.00754565	+	0.0281619i
$127$	−1.41770	+	1.41770i	−0.125801	+	0.125801i	−0.767204	−	0.641403i	$-0.778353\pi$
$127$	−1.41770	+	1.41770i	−0.125801	+	0.125801i	0.641403	+	0.767204i	$0.278353\pi$
$128$	−9.79756	−	5.65754i	−0.865990	−	0.500061i
$129$		−	1.55827i		−	0.137198i
$130$	1.08568	−	0.785139i	0.0952208	−	0.0688613i
$131$		−	17.6596i		−	1.54292i	−0.636275	−	0.771462i	$-0.719526\pi$
$131$		−	17.6596i		−	1.54292i	0.636275	−	0.771462i	$-0.280474\pi$
$132$	−8.62510	−	2.31127i	−0.750718	−	0.201171i
$133$	0.691067	−	0.691067i	0.0599231	−	0.0599231i
$134$	−17.5460	+	4.70124i	−1.51574	+	0.406125i
$135$	−4.54368	+	10.1452i	−0.391058	+	0.873160i
$136$	−5.62814	+	5.62780i	−0.482609	+	0.482580i
$137$	−1.63956	−	1.63956i	−0.140077	−	0.140077i	0.633591	−	0.773668i	$-0.281580\pi$
$137$	−1.63956	−	1.63956i	−0.140077	−	0.140077i	−0.773668	+	0.633591i	$0.781580\pi$
$138$	6.41577	−	11.1122i	0.546147	−	0.945932i
$139$	20.3321			1.72454			0.862272	−	0.506446i	$-0.169041\pi$
$139$	20.3321			1.72454			0.862272	+	0.506446i	$0.169041\pi$
$140$	4.34775	−	0.447220i	0.367452	−	0.0377970i
$141$	18.4638			1.55493
$142$	5.45004	−	9.43952i	0.457357	−	0.792147i
$143$	−0.743484	−	0.743484i	−0.0621733	−	0.0621733i
$144$	−0.820224	−	0.473600i	−0.0683520	−	0.0394667i
$145$	−4.38432	−	11.4970i	−0.364098	−	0.954775i
$146$	−3.47369	+	0.930736i	−0.287485	+	0.0770282i
$147$	7.69002	−	7.69002i	0.634262	−	0.634262i
$148$	−1.15179	+	4.29820i	−0.0946766	+	0.353309i
$149$			4.00501i			0.328104i	0.986452	+	0.164052i	$0.0524564\pi$
$149$			4.00501i			0.328104i	−0.986452	+	0.164052i	$0.947544\pi$
$150$	−10.6386	−	6.97562i	−0.868639	−	0.569557i
$151$			18.6011i			1.51373i	0.653569	+	0.756867i	$0.273271\pi$
$151$			18.6011i			1.51373i	−0.653569	+	0.756867i	$0.726729\pi$
$152$	−8.52354e−5		2.82843i	−6.91351e−6		0.229416i
$153$	−0.471149	+	0.471149i	−0.0380901	+	0.0380901i
$154$	−0.887700	−	3.31307i	−0.0715329	−	0.266975i
$155$	−1.23947	−	3.25026i	−0.0995564	−	0.261067i
$156$	−0.762242	−	1.32030i	−0.0610282	−	0.105709i
$157$	−3.87088	−	3.87088i	−0.308930	−	0.308930i	0.535564	−	0.844494i	$-0.320099\pi$
$157$	−3.87088	−	3.87088i	−0.308930	−	0.308930i	−0.844494	+	0.535564i	$0.820099\pi$
$158$	1.00826	+	0.582135i	0.0802132	+	0.0463122i
$159$	−1.77641			−0.140879
$160$	−7.98242	+	9.81229i	−0.631066	+	0.775729i
$161$	4.92873			0.388438
$162$	11.8240	+	6.82673i	0.928979	+	0.536358i
$163$	5.65655	+	5.65655i	0.443056	+	0.443056i	0.893038	−	0.449982i	$-0.148570\pi$
$163$	5.65655	+	5.65655i	0.443056	+	0.443056i	−0.449982	+	0.893038i	$0.648570\pi$
$164$	−8.98938	−	15.5708i	−0.701953	−	1.21587i
$165$	−4.08064	+	9.11133i	−0.317677	+	0.709316i
$166$	0.397674	+	1.48420i	0.0308655	+	0.115196i
$167$	−7.37211	+	7.37211i	−0.570471	+	0.570471i	−0.932260	−	0.361789i	$-0.882166\pi$
$167$	−7.37211	+	7.37211i	−0.570471	+	0.570471i	0.361789	+	0.932260i	$0.382166\pi$
$168$	0.000149869	−	4.97321i	1.15627e−5	−	0.383692i
$169$			12.8205i			0.986191i
$170$	5.21456	+	7.21065i	0.399938	+	0.553031i
$171$			0.236784i			0.0181073i
$172$	−0.448378	+	1.67323i	−0.0341885	+	0.127583i
$173$	−5.10352	+	5.10352i	−0.388013	+	0.388013i	−0.873978	−	0.485965i	$-0.838468\pi$
$173$	−5.10352	+	5.10352i	−0.388013	+	0.388013i	0.485965	+	0.873978i	$0.338468\pi$
$174$	−13.5238	+	3.62355i	−1.02524	+	0.274701i
$175$	0.277191	−	4.87872i	0.0209537	−	0.368796i
$176$	8.59639	+	4.96359i	0.647978	+	0.374145i
$177$	8.02696	+	8.02696i	0.603343	+	0.603343i
$178$	−7.31014	+	12.6612i	−0.547918	+	0.949000i
$179$	22.0833			1.65059			0.825293	−	0.564705i	$-0.191010\pi$
$179$	22.0833			1.65059			0.825293	+	0.564705i	$0.191010\pi$
$180$	−0.668229	+	0.821462i	−0.0498068	+	0.0612282i
$181$	−22.6670			−1.68483			−0.842414	−	0.538831i	$-0.818866\pi$
$181$	−22.6670			−1.68483			−0.842414	+	0.538831i	$0.818866\pi$
$182$	0.292805	−	0.507142i	0.0217042	−	0.0375918i
$183$	13.9415	+	13.9415i	1.03059	+	1.03059i
$184$	−10.0866	+	10.0859i	−0.743591	+	0.743546i
$185$	4.54050	+	2.03353i	0.333824	+	0.149508i
$186$	−3.82325	+	1.02440i	−0.280334	+	0.0751123i
$187$	4.93790	−	4.93790i	0.361095	−	0.361095i
$188$	−19.8260	−	5.31278i	−1.44596	−	0.387475i
$189$			4.85855i			0.353408i
$190$	3.12224	+	0.501584i	0.226511	+	0.0363887i
$191$		−	27.4882i		−	1.98898i	−0.104855	−	0.994488i	$-0.533438\pi$
$191$		−	27.4882i		−	1.98898i	0.104855	−	0.994488i	$-0.466562\pi$
$192$	10.1767	+	10.1779i	0.734438	+	0.734526i
$193$	−12.4032	+	12.4032i	−0.892805	+	0.892805i	−0.994786	−	0.101981i	$-0.967482\pi$
$193$	−12.4032	+	12.4032i	−0.892805	+	0.892805i	0.101981	+	0.994786i	$0.467482\pi$
$194$	−2.81318	−	10.4993i	−0.201974	−	0.753809i
$195$	−1.59261	+	0.607333i	−0.114049	+	0.0434921i
$196$	−10.4701	+	6.04464i	−0.747865	+	0.431760i
$197$	−0.0500370	−	0.0500370i	−0.00356499	−	0.00356499i	0.705322	−	0.708887i	$-0.250802\pi$
$197$	−0.0500370	−	0.0500370i	−0.00356499	−	0.00356499i	−0.708887	+	0.705322i	$0.750802\pi$
$198$	0.719665	+	0.415509i	0.0511444	+	0.0295289i
$199$	−11.8498			−0.840007			−0.420003	−	0.907523i	$-0.637971\pi$
$199$	−11.8498			−0.840007			−0.420003	+	0.907523i	$0.637971\pi$
$200$	9.41633	+	10.5514i	0.665835	+	0.746099i
$201$	23.1086			1.62996
$202$	17.8436	+	10.3022i	1.25547	+	0.724862i
$203$	−3.80280	−	3.80280i	−0.266904	−	0.266904i
$204$	8.76888	−	5.06248i	0.613944	−	0.354444i
$205$	−18.7822	+	7.16250i	−1.31181	+	0.500251i
$206$	3.44084	+	12.8419i	0.239735	+	0.894739i
$207$	−0.844377	+	0.844377i	−0.0586883	+	0.0586883i
$208$	0.438573	+	1.63704i	0.0304096	+	0.113508i
$209$		−	2.48162i		−	0.171657i
$210$	−5.48983	−	0.881933i	−0.378834	−	0.0608592i
$211$			1.91064i			0.131534i	0.997835	+	0.0657669i	$0.0209494\pi$
$211$			1.91064i			0.131534i	−0.997835	+	0.0657669i	$0.979051\pi$
$212$	1.90747	+	0.511147i	0.131006	+	0.0351057i
$213$	−9.80503	+	9.80503i	−0.671829	+	0.671829i
$214$	23.4202	−	6.27517i	1.60097	−	0.428962i
$215$	1.76756	+	0.791628i	0.120547	+	0.0539886i
$216$	−9.94234	−	9.94294i	−0.676491	−	0.676531i
$217$	−1.07507	−	1.07507i	−0.0729804	−	0.0729804i
$218$	7.62063	−	13.1990i	0.516134	−	0.893950i
$219$	4.57497			0.309148
$220$	7.00341	−	8.60937i	0.472170	−	0.580444i
$221$	1.19226			0.0802004
$222$	2.83051	−	4.90247i	0.189971	−	0.329032i
$223$	5.24961	+	5.24961i	0.351540	+	0.351540i	0.860682	−	0.509142i	$-0.170037\pi$
$223$	5.24961	+	5.24961i	0.351540	+	0.351540i	−0.509142	+	0.860682i	$0.670037\pi$
$224$	−1.43116	+	5.34009i	−0.0956233	+	0.356799i
$225$	0.788321	+	0.883296i	0.0525547	+	0.0588864i
$226$	−10.2328	+	2.74176i	−0.680677	+	0.182379i
$227$	17.1089	−	17.1089i	1.13556	−	1.13556i	0.146322	−	0.989237i	$-0.453257\pi$
$227$	17.1089	−	17.1089i	1.13556	−	1.13556i	0.989237	−	0.146322i	$-0.0467435\pi$
$228$	0.931356	−	3.47559i	0.0616805	−	0.230176i
$229$		−	1.80492i		−	0.119272i	−0.998220	−	0.0596361i	$-0.981006\pi$
$229$		−	1.80492i		−	0.119272i	0.998220	−	0.0596361i	$-0.0189940\pi$
$230$	9.34535	+	12.9227i	0.616214	+	0.852096i
$231$			4.36343i			0.287093i
$232$	15.5642		0.000469033i	1.02184		3.07935e-5i
$233$	9.46726	−	9.46726i	0.620221	−	0.620221i	−0.325367	−	0.945588i	$-0.605488\pi$
$233$	9.46726	−	9.46726i	0.620221	−	0.620221i	0.945588	+	0.325367i	$0.105488\pi$
$234$	0.0367196	+	0.137045i	0.00240043	+	0.00895890i
$235$	−9.37992	+	20.9436i	−0.611878	+	1.36621i
$236$	−6.30949	−	10.9289i	−0.410713	−	0.711408i
$237$	−1.04731	−	1.04731i	−0.0680298	−	0.0680298i
$238$	3.36822	+	1.94469i	0.218329	+	0.126055i
$239$	−14.3398			−0.927565			−0.463782	−	0.885949i	$-0.653508\pi$
$239$	−14.3398			−0.927565			−0.463782	+	0.885949i	$0.653508\pi$
$240$	13.0396	−	9.42930i	0.841702	−	0.608659i
$241$	−10.9568			−0.705791			−0.352895	−	0.935663i	$-0.614803\pi$
$241$	−10.9568			−0.705791			−0.352895	+	0.935663i	$0.614803\pi$
$242$	5.92963	+	3.42355i	0.381171	+	0.220074i
$243$	−1.73603	−	1.73603i	−0.111367	−	0.111367i
$244$	−10.9586	−	18.9817i	−0.701550	−	1.21518i
$245$	4.81621	+	12.6295i	0.307696	+	0.806872i
$246$	5.91966	+	22.0934i	0.377424	+	1.40862i
$247$	0.299596	−	0.299596i	0.0190628	−	0.0190628i
$248$	4.40008		0.000132598i	0.279405		8.41996e-6i
$249$		−	1.95474i		−	0.123877i
$250$	13.3171	−	8.52375i	0.842249	−	0.539089i
$251$		−	31.0139i		−	1.95758i	−0.204859	−	0.978791i	$-0.565674\pi$
$251$		−	31.0139i		−	1.95758i	0.204859	−	0.978791i	$-0.434326\pi$
$252$	−0.119797	+	0.447052i	−0.00754650	+	0.0281617i
$253$	8.84954	−	8.84954i	0.556366	−	0.556366i
$254$	−2.73880	+	0.733830i	−0.171848	+	0.0460446i
$255$	−4.03365	−	10.5774i	−0.252597	−	0.662385i
$256$	−7.99889	−	13.8570i	−0.499930	−	0.866066i
$257$	−11.4696	−	11.4696i	−0.715454	−	0.715454i	0.252217	−	0.967671i	$-0.418840\pi$
$257$	−11.4696	−	11.4696i	−0.715454	−	0.715454i	−0.967671	+	0.252217i	$0.918840\pi$
$258$	1.10188	−	1.90847i	0.0686001	−	0.118816i
$259$	2.17445			0.135114
$260$	1.88487	−	0.193882i	0.116894	−	0.0120240i
$261$	1.30297			0.0806519
$262$	12.4874	−	21.6283i	0.771475	−	1.33620i
$263$	6.91740	+	6.91740i	0.426545	+	0.426545i	0.887450	−	0.460905i	$-0.152475\pi$
$263$	6.91740	+	6.91740i	0.426545	+	0.426545i	−0.460905	+	0.887450i	$0.652475\pi$
$264$	−8.92914	−	8.92968i	−0.549550	−	0.549584i
$265$	0.902449	−	2.01500i	0.0554370	−	0.123781i
$266$	1.33504	−	0.357709i	0.0818567	−	0.0219326i
$267$	13.1515	−	13.1515i	0.804858	−	0.804858i
$268$	−24.8135	−	6.64930i	−1.51573	−	0.406171i
$269$			7.30112i			0.445157i	0.974915	+	0.222579i	$0.0714474\pi$
$269$			7.30112i			0.445157i	−0.974915	+	0.222579i	$0.928553\pi$
$270$	−12.7387	+	9.21229i	−0.775251	+	0.560642i
$271$			8.35803i			0.507714i	0.967242	+	0.253857i	$0.0816992\pi$
$271$			8.35803i			0.507714i	−0.967242	+	0.253857i	$0.918301\pi$
$272$	−10.8725	+	2.91281i	−0.659243	+	0.176615i
$273$	−0.526779	+	0.526779i	−0.0318821	+	0.0318821i
$274$	−0.848666	−	3.16739i	−0.0512698	−	0.191349i
$275$	−8.26204	−	9.25743i	−0.498220	−	0.558244i
$276$	15.7153	−	9.07280i	0.945949	−	0.546118i
$277$	20.0525	+	20.0525i	1.20484	+	1.20484i	0.972677	+	0.232161i	$0.0745798\pi$
$277$	20.0525	+	20.0525i	1.20484	+	1.20484i	0.232161	+	0.972677i	$0.425420\pi$
$278$	24.9015	+	14.3772i	1.49349	+	0.862287i
$279$	0.368356			0.0220529
$280$	5.64109	+	2.52665i	0.337120	+	0.150996i
$281$	10.6639			0.636158			0.318079	−	0.948064i	$-0.396962\pi$
$281$	10.6639			0.636158			0.318079	+	0.948064i	$0.396962\pi$
$282$	22.6133	+	13.0561i	1.34660	+	0.777478i
$283$	−0.153098	−	0.153098i	−0.00910071	−	0.00910071i	0.702542	−	0.711642i	$-0.252048\pi$
$283$	−0.153098	−	0.153098i	−0.00910071	−	0.00910071i	−0.711642	+	0.702542i	$0.752048\pi$
$284$	13.3497	−	7.70712i	0.792161	−	0.457333i
$285$	−3.67152	−	1.64434i	−0.217482	−	0.0974025i
$286$	−0.384841	−	1.43630i	−0.0227561	−	0.0849305i
$287$	−6.21248	+	6.21248i	−0.366711	+	0.366711i
$288$	−0.669667	−	1.16003i	−0.0394605	−	0.0683555i
$289$		−	9.08150i		−	0.534206i
$290$	2.76011	−	17.1811i	0.162079	−	1.00891i
$291$			13.8280i			0.810611i
$292$	−4.91250	−	1.31641i	−0.287483	−	0.0770369i
$293$	14.1434	−	14.1434i	0.826264	−	0.826264i	−0.160734	−	0.986998i	$-0.551386\pi$
$293$	14.1434	−	14.1434i	0.826264	−	0.826264i	0.986998	+	0.160734i	$0.0513861\pi$
$294$	14.8560	−	3.98050i	0.866421	−	0.232147i
$295$	−13.1829	+	5.02723i	−0.767538	+	0.292697i
$296$	−4.44998	+	4.44971i	−0.258650	+	0.258634i
$297$	8.72353	+	8.72353i	0.506191	+	0.506191i
$298$	−2.83202	+	4.90509i	−0.164055	+	0.284144i
$299$	2.13673			0.123571
$300$	−8.09691	−	16.0661i	−0.467475	−	0.927575i
$301$	0.846487			0.0487907
$302$	−13.1532	+	22.7814i	−0.756880	+	1.31092i
$303$	−18.5345	−	18.5345i	−1.06478	−	1.06478i
$304$	−2.00014	+	3.46402i	−0.114716	+	0.198675i
$305$	−22.8966	+	8.73149i	−1.31105	+	0.499964i
$306$	−0.910192	+	0.243876i	−0.0520322	+	0.0139414i
$307$	−3.16288	+	3.16288i	−0.180515	+	0.180515i	−0.791580	−	0.611065i	$-0.790741\pi$
$307$	−3.16288	+	3.16288i	−0.180515	+	0.180515i	0.611065	+	0.791580i	$0.290741\pi$
$308$	1.25554	−	4.68536i	0.0715409	−	0.266973i
$309$		−	16.9132i		−	0.962160i
$310$	0.780296	−	4.85716i	0.0443178	−	0.275868i
$311$		−	9.01815i		−	0.511372i	−0.966760	−	0.255686i	$-0.917699\pi$
$311$		−	9.01815i		−	0.511372i	0.966760	−	0.255686i	$-0.0823014\pi$
$312$	6.49722e−5	−	2.15602i	3.67833e−6	−	0.122061i
$313$	23.6184	−	23.6184i	1.33499	−	1.33499i	0.434154	−	0.900839i	$-0.357048\pi$
$313$	23.6184	−	23.6184i	1.33499	−	1.33499i	0.900839	−	0.434154i	$-0.142952\pi$
$314$	−2.00364	−	7.47799i	−0.113072	−	0.422007i
$315$	0.472254	+	0.211506i	0.0266085	+	0.0119170i
$316$	0.823221	+	1.42593i	0.0463098	+	0.0802146i
$317$	−20.2187	−	20.2187i	−1.13559	−	1.13559i	−0.989231	−	0.146362i	$-0.953243\pi$
$317$	−20.2187	−	20.2187i	−1.13559	−	1.13559i	−0.146362	−	0.989231i	$-0.546757\pi$
$318$	−2.17564	−	1.25614i	−0.122004	−	0.0704406i
$319$	−13.6559			−0.764581
$320$	−16.7148	+	6.37295i	−0.934387	+	0.356259i
$321$	−30.8452			−1.72161
$322$	6.03640	+	3.48520i	0.336395	+	0.194223i
$323$	1.98979	+	1.98979i	0.110715	+	0.110715i
$324$	9.65395	+	16.7219i	0.536330	+	0.928995i
$325$	0.120170	−	2.11505i	0.00666582	−	0.117322i
$326$	2.92794	+	10.9277i	0.162163	+	0.605227i
$327$	−13.7101	+	13.7101i	−0.758170	+	0.758170i
$328$	0.000766241	−	25.4267i	4.23086e−5	−	1.40395i
$329$			10.0299i			0.552969i
$330$	−11.4405	+	8.27349i	−0.629779	+	0.455440i
$331$			3.28873i			0.180765i	0.995907	+	0.0903826i	$0.0288090\pi$
$331$			3.28873i			0.180765i	−0.995907	+	0.0903826i	$0.971191\pi$
$332$	−0.562460	+	2.09896i	−0.0308690	+	0.115195i
$333$	−0.372522	+	0.372522i	−0.0204141	+	0.0204141i
$334$	−14.2419	+	3.81594i	−0.779280	+	0.208799i
$335$	−11.7396	+	26.2124i	−0.641403	+	1.43214i
$336$	3.51684	−	6.09078i	0.191859	−	0.332279i
$337$	11.8124	+	11.8124i	0.643461	+	0.643461i	0.951405	−	0.307943i	$-0.0996407\pi$
$337$	11.8124	+	11.8124i	0.643461	+	0.643461i	−0.307943	+	0.951405i	$0.599641\pi$
$338$	−9.06561	+	15.7017i	−0.493104	+	0.854062i
$339$	13.4770			0.731968
$340$	1.28768	+	12.5185i	0.0698342	+	0.678909i
$341$	−3.86057			−0.209062
$342$	−0.167434	+	0.289998i	−0.00905381	+	0.0156813i
$343$	9.01487	+	9.01487i	0.486757	+	0.486757i
$344$	−1.73232	+	1.73222i	−0.0934005	+	0.0933948i
$345$	−7.22896	−	18.9565i	−0.389194	−	1.02058i
$346$	−9.85927	+	2.64168i	−0.530038	+	0.142017i
$347$	−13.4846	+	13.4846i	−0.723889	+	0.723889i	−0.969395	−	0.245506i	$-0.921046\pi$
$347$	−13.4846	+	13.4846i	−0.723889	+	0.723889i	0.245506	+	0.969395i	$0.421046\pi$
$348$	−19.1254	−	5.12506i	−1.02523	−	0.274732i
$349$			19.5025i			1.04394i	0.852962	+	0.521972i	$0.174804\pi$
$349$			19.5025i			1.04394i	−0.852962	+	0.521972i	$0.825196\pi$
$350$	3.78932	−	5.77914i	0.202548	−	0.308908i
$351$			2.10631i			0.112427i
$352$	7.01848	+	12.1578i	0.374086	+	0.648011i
$353$	15.5965	−	15.5965i	0.830117	−	0.830117i	−0.157415	−	0.987533i	$-0.550316\pi$
$353$	15.5965	−	15.5965i	0.830117	−	0.830117i	0.987533	+	0.157415i	$0.0503161\pi$
$354$	4.15490	+	15.5069i	0.220831	+	0.824184i
$355$	−6.14082	−	16.1031i	−0.325921	−	0.854663i
$356$	−17.9060	+	10.3376i	−0.949017	+	0.547890i
$357$	−3.49864	−	3.49864i	−0.185167	−	0.185167i
$358$	27.0463	+	15.6156i	1.42944	+	0.825308i
$359$	0.969375			0.0511616			0.0255808	−	0.999673i	$-0.491856\pi$
$359$	0.969375			0.0511616			0.0255808	+	0.999673i	$0.491856\pi$
$360$	−1.39928	+	0.533558i	−0.0737484	+	0.0281210i
$361$	1.00000			0.0526316
$362$	−27.7612	−	16.0283i	−1.45910	−	0.842428i
$363$	−6.15923	−	6.15923i	−0.323275	−	0.323275i
$364$	0.717219	−	0.414067i	0.0375925	−	0.0217030i
$365$	−2.32417	+	5.18944i	−0.121652	+	0.271628i
$366$	7.21640	+	26.9331i	0.377207	+	1.40781i
$367$	−14.7490	+	14.7490i	−0.769891	+	0.769891i	−0.978087	−	0.208196i	$-0.933241\pi$
$367$	−14.7490	+	14.7490i	−0.769891	+	0.769891i	0.208196	+	0.978087i	$0.433241\pi$
$368$	−19.4853	+	5.22024i	−1.01574	+	0.272124i
$369$		−	2.12861i		−	0.110811i
$370$	4.12297	+	5.70121i	0.214343	+	0.296392i
$371$		−	0.964989i		−	0.0500997i
$372$	−5.40685	−	1.44888i	−0.280332	−	0.0751207i
$373$	9.84863	−	9.84863i	0.509943	−	0.509943i	−0.404566	−	0.914509i	$-0.632577\pi$
$373$	9.84863	−	9.84863i	0.509943	−	0.509943i	0.914509	+	0.404566i	$0.132577\pi$
$374$	9.53932	−	2.55595i	0.493266	−	0.132165i
$375$	−19.1707	+	6.08949i	−0.989971	+	0.314460i
$376$	−20.5249	−	20.5261i	−1.05849	−	1.05855i
$377$	−1.64861	−	1.64861i	−0.0849079	−	0.0849079i
$378$	−3.43558	+	5.95045i	−0.176707	+	0.306058i
$379$	30.5819			1.57089			0.785443	−	0.618934i	$-0.212435\pi$
$379$	30.5819			1.57089			0.785443	+	0.618934i	$0.212435\pi$
$380$	3.46925	+	2.82211i	0.177969	+	0.144771i
$381$	3.60709			0.184797
$382$	19.4374	−	33.6658i	0.994505	−	1.72249i
$383$	−16.6482	−	16.6482i	−0.850683	−	0.850683i	0.139534	−	0.990217i	$-0.455440\pi$
$383$	−16.6482	−	16.6482i	−0.850683	−	0.850683i	−0.990217	+	0.139534i	$0.955440\pi$
$384$	5.26677	+	19.6614i	0.268769	+	1.00334i
$385$	−4.94949	−	2.21670i	−0.252249	−	0.112973i
$386$	−23.9613	+	6.42015i	−1.21960	+	0.326777i
$387$	−0.145018	+	0.145018i	−0.00737168	+	0.00737168i
$388$	3.97888	−	14.8482i	0.201997	−	0.753803i
$389$		−	1.92974i		−	0.0978417i	−0.998803	−	0.0489209i	$-0.984422\pi$
$389$		−	1.92974i		−	0.0978417i	0.998803	−	0.0489209i	$-0.0155782\pi$
$390$	−2.37999	−	0.382341i	−0.120515	−	0.0193606i
$391$			14.1913i			0.717683i
$392$	−17.0974		0.000515236i	−0.863550		2.60233e-5i
$393$	−22.4658	+	22.4658i	−1.13325	+	1.13325i
$394$	−0.0259001	−	0.0966643i	−0.00130483	−	0.00486988i
$395$	1.72002	−	0.655920i	0.0865436	−	0.0330029i
$396$	0.587587	+	1.01778i	0.0295274	+	0.0511453i
$397$	−0.961967	−	0.961967i	−0.0482797	−	0.0482797i	0.682555	−	0.730834i	$-0.260869\pi$
$397$	−0.961967	−	0.961967i	−0.0482797	−	0.0482797i	−0.730834	+	0.682555i	$0.760869\pi$
$398$	−14.5128	−	8.37918i	−0.727463	−	0.420011i
$399$	−1.75830			−0.0880249
$400$	4.07142	+	19.5812i	0.203571	+	0.979060i
$401$	31.1787			1.55699			0.778496	−	0.627649i	$-0.215983\pi$
$401$	31.1787			1.55699			0.778496	+	0.627649i	$0.215983\pi$
$402$	28.3020	+	16.3406i	1.41158	+	0.814993i
$403$	−0.466071	−	0.466071i	−0.0232166	−	0.0232166i
$404$	14.5688	+	25.2350i	0.724824	+	1.25549i
$405$	20.1707	−	7.69200i	1.00229	−	0.382219i
$406$	−1.96840	−	7.34646i	−0.0976900	−	0.364599i
$407$	3.90423	−	3.90423i	0.193526	−	0.193526i
$408$	14.3194		0.000431518i	0.708914		2.13633e-5i
$409$			4.25198i			0.210247i	0.994459	+	0.105123i	$0.0335238\pi$
$409$			4.25198i			0.210247i	−0.994459	+	0.105123i	$0.966476\pi$
$410$	−28.0680	−	4.50909i	−1.38618	−	0.222688i
$411$			4.17156i			0.205768i
$412$	−4.86663	+	18.1611i	−0.239762	+	0.894731i
$413$	−4.36043	+	4.36043i	−0.214563	+	0.214563i
$414$	−1.63122	+	0.437065i	−0.0801699	+	0.0214806i
$415$	2.21728	+	0.993044i	0.108842	+	0.0487466i
$416$	−0.620445	+	2.31507i	−0.0304198	+	0.113506i
$417$	−25.8656	−	25.8656i	−1.26665	−	1.26665i
$418$	1.75480	−	3.03934i	0.0858302	−	0.148659i
$419$	−26.0973			−1.27493			−0.637467	−	0.770477i	$-0.720018\pi$
$419$	−26.0973			−1.27493			−0.637467	+	0.770477i	$0.720018\pi$
$420$	−6.09997	−	4.96210i	−0.297648	−	0.242126i
$421$	−24.1130			−1.17520			−0.587599	−	0.809152i	$-0.699927\pi$
$421$	−24.1130			−1.17520			−0.587599	+	0.809152i	$0.699927\pi$
$422$	−1.35105	+	2.34003i	−0.0657681	+	0.113911i
$423$	−1.71830	−	1.71830i	−0.0835468	−	0.0835468i
$424$	1.97471	+	1.97483i	0.0959005	+	0.0959063i
$425$	14.0473	+	0.798116i	0.681392	+	0.0387143i
$426$	−18.9419	+	5.07527i	−0.917739	+	0.245897i
$427$	−7.57337	+	7.57337i	−0.366501	+	0.366501i
$428$	33.1209	+	8.87543i	1.60096	+	0.429010i
$429$			1.89166i			0.0913303i
$430$	1.60502	+	2.21941i	0.0774010	+	0.107030i
$431$		−	1.00295i		−	0.0483106i	−0.999708	−	0.0241553i	$-0.992310\pi$
$431$		−	1.00295i		−	0.0483106i	0.999708	−	0.0241553i	$-0.00768962\pi$
$432$	−5.14592	−	19.2079i	−0.247583	−	0.924141i
$433$	−5.47457	+	5.47457i	−0.263091	+	0.263091i	−0.826309	−	0.563218i	$-0.809563\pi$
$433$	−5.47457	+	5.47457i	−0.263091	+	0.263091i	0.563218	+	0.826309i	$0.309563\pi$
$434$	−0.556475	−	2.07688i	−0.0267117	−	0.0996933i
$435$	−9.04848	+	20.2036i	−0.433841	+	0.968689i
$436$	18.6666	−	10.7766i	0.893966	−	0.516107i
$437$	3.56603	+	3.56603i	0.170586	+	0.170586i
$438$	5.60314	+	3.23505i	0.267728	+	0.154577i
$439$	−27.5639			−1.31555			−0.657777	−	0.753213i	$-0.728503\pi$
$439$	−27.5639			−1.31555			−0.657777	+	0.753213i	$0.728503\pi$
$440$	14.6652	−	5.59198i	0.699135	−	0.266587i
$441$	−1.43132			−0.0681582
$442$	1.46021	+	0.843073i	0.0694552	+	0.0401009i
$443$	−24.8144	−	24.8144i	−1.17897	−	1.17897i	−0.980008	−	0.198960i	$-0.936244\pi$
$443$	−24.8144	−	24.8144i	−1.17897	−	1.17897i	−0.198960	−	0.980008i	$-0.563756\pi$
$444$	6.93326	−	4.00273i	0.329038	−	0.189961i
$445$	8.23669	+	21.5991i	0.390457	+	1.02389i
$446$	2.71730	+	10.1415i	0.128668	+	0.480214i
$447$	5.09502	−	5.09502i	0.240986	−	0.240986i
$448$	−5.52887	+	5.52820i	−0.261215	+	0.261183i
$449$		−	17.5308i		−	0.827330i	−0.910429	−	0.413665i	$-0.864248\pi$
$449$		−	17.5308i		−	0.827330i	0.910429	−	0.413665i	$-0.135752\pi$
$450$	0.340891	+	1.63924i	0.0160697	+	0.0772747i
$451$			22.3090i			1.05049i
$452$	−14.4713	−	3.87788i	−0.680671	−	0.182400i
$453$	23.6636	−	23.6636i	1.11181	−	1.11181i
$454$	33.0520	−	8.85590i	1.55121	−	0.415628i
$455$	−0.329918	−	0.865143i	−0.0154668	−	0.0405586i
$456$	3.59832	−	3.59810i	0.168507	−	0.168497i
$457$	−13.8122	−	13.8122i	−0.646107	−	0.646107i	0.305943	−	0.952050i	$-0.401028\pi$
$457$	−13.8122	−	13.8122i	−0.646107	−	0.646107i	−0.952050	+	0.305943i	$0.901028\pi$
$458$	1.27629	−	2.21055i	0.0596371	−	0.103292i
$459$	−13.9892			−0.652961
$460$	2.30773	+	22.4352i	0.107599	+	1.04604i
$461$	−20.4762			−0.953670			−0.476835	−	0.878993i	$-0.658216\pi$
$461$	−20.4762			−0.953670			−0.476835	+	0.878993i	$0.658216\pi$
$462$	−3.08546	+	5.34406i	−0.143549	+	0.248628i
$463$	−28.9404	−	28.9404i	−1.34497	−	1.34497i	−0.891032	−	0.453941i	$-0.850018\pi$
$463$	−28.9404	−	28.9404i	−1.34497	−	1.34497i	−0.453941	−	0.891032i	$-0.649982\pi$
$464$	19.0618	+	11.0063i	0.884921	+	0.510957i
$465$	−2.55805	+	5.71165i	−0.118627	+	0.264871i
$466$	18.2894	−	4.90043i	0.847239	−	0.227008i
$467$	0.271431	−	0.271431i	0.0125603	−	0.0125603i	−0.700799	−	0.713359i	$-0.747173\pi$
$467$	0.271431	−	0.271431i	0.0125603	−	0.0125603i	0.713359	+	0.700799i	$0.247173\pi$
$468$	−0.0519351	+	0.193809i	−0.00240070	+	0.00895883i
$469$			12.5532i			0.579651i
$470$	−26.2976	+	19.0178i	−1.21302	+	0.877224i
$471$			9.84876i			0.453807i
$472$	0.000537811	−	17.8465i	2.47547e−5	−	0.821454i
$473$	1.51987	−	1.51987i	0.0698836	−	0.0698836i
$474$	−0.542105	−	2.02324i	−0.0248997	−	0.0929307i
$475$	3.73039	−	3.32929i	0.171162	−	0.152758i
$476$	2.75006	+	4.76346i	0.126049	+	0.218333i
$477$	0.165319	+	0.165319i	0.00756945	+	0.00756945i
$478$	−17.5625	−	10.1399i	−0.803290	−	0.463790i
$479$	2.06918			0.0945434			0.0472717	−	0.998882i	$-0.484947\pi$
$479$	2.06918			0.0945434			0.0472717	+	0.998882i	$0.484947\pi$
$480$	22.6377	−	2.32788i	1.03327	−	0.106253i
$481$	0.942683			0.0429826
$482$	−13.4192	−	7.74778i	−0.611229	−	0.352902i
$483$	−6.27013	−	6.27013i	−0.285301	−	0.285301i
$484$	4.84138	+	8.38590i	0.220063	+	0.381177i
$485$	−15.6852	−	7.02486i	−0.712230	−	0.318983i
$486$	−0.898604	−	3.35377i	−0.0407615	−	0.152130i
$487$	3.83141	−	3.83141i	0.173618	−	0.173618i	−0.614949	−	0.788567i	$-0.710823\pi$
$487$	3.83141	−	3.83141i	0.173618	−	0.173618i	0.788567	+	0.614949i	$0.210823\pi$
$488$	0.000934091	−	30.9966i	4.22843e−5	−	1.40315i
$489$		−	14.3921i		−	0.650833i
$490$	−3.03200	+	18.8735i	−0.136972	+	0.852618i
$491$		−	7.97842i		−	0.360061i	−0.983661	−	0.180030i	$-0.942380\pi$
$491$		−	7.97842i		−	0.360061i	0.983661	−	0.180030i	$-0.0576196\pi$
$492$	−8.37261	+	31.2445i	−0.377466	+	1.40861i
$493$	10.9494	−	10.9494i	0.493135	−	0.493135i
$494$	0.578776	−	0.155076i	0.0260404	−	0.00697722i
$495$	1.22769	−	0.468174i	0.0551806	−	0.0210428i
$496$	5.38885	+	3.11154i	0.241967	+	0.139712i
$497$	−5.32632	−	5.32632i	−0.238918	−	0.238918i
$498$	1.38224	−	2.39405i	0.0619394	−	0.107280i
$499$	23.9622			1.07270			0.536349	−	0.843996i	$-0.319803\pi$
$499$	23.9622			1.07270			0.536349	+	0.843996i	$0.319803\pi$
$500$	22.3373	−	1.02257i	0.998954	−	0.0457305i
$501$	18.7570			0.838002
$502$	21.9306	−	37.9840i	0.978808	−	1.69531i
$503$	11.9399	+	11.9399i	0.532373	+	0.532373i	0.921278	−	0.388905i	$-0.127147\pi$
$503$	11.9399	+	11.9399i	0.532373	+	0.532373i	−0.388905	+	0.921278i	$0.627147\pi$
$504$	−0.462839	+	0.462811i	−0.0206165	+	0.0206153i
$505$	30.4397	−	11.6080i	1.35455	−	0.516550i
$506$	17.0960	−	4.58068i	0.760011	−	0.203636i
$507$	16.3097	−	16.3097i	0.724340	−	0.724340i
$508$	−3.87322	−	1.03791i	−0.171846	−	0.0460498i
$509$			23.3369i			1.03439i	0.855868	+	0.517195i	$0.173024\pi$
$509$			23.3369i			1.03439i	−0.855868	+	0.517195i	$0.826976\pi$
$510$	2.53935	−	15.8069i	0.112444	−	0.699939i
$511$			2.48523i			0.109940i
$512$	0.00204565	−	22.6274i	9.04058e−5	−	1.00000i
$513$	−3.51525	+	3.51525i	−0.155202	+	0.155202i
$514$	−5.93688	−	22.1576i	−0.261864	−	0.977331i
$515$	19.1849	+	8.59222i	0.845386	+	0.378619i
$516$	2.69903	−	1.55821i	0.118818	−	0.0685965i
$517$	18.0088	+	18.0088i	0.792025	+	0.792025i
$518$	2.66313	+	1.53760i	0.117011	+	0.0675581i
$519$	12.9850			0.569978
$520$	2.44556	+	1.09537i	0.107245	+	0.0480352i
$521$	28.6568			1.25548			0.627739	−	0.778424i	$-0.283981\pi$
$521$	28.6568			1.25548			0.627739	+	0.778424i	$0.283981\pi$
$522$	1.59580	+	0.921356i	0.0698462	+	0.0403266i
$523$	−17.5067	−	17.5067i	−0.765515	−	0.765515i	0.211798	−	0.977313i	$-0.432068\pi$
$523$	−17.5067	−	17.5067i	−0.765515	−	0.765515i	−0.977313	+	0.211798i	$0.932068\pi$
$524$	30.5876	−	17.6590i	1.33623	−	0.771435i
$525$	−6.55914	+	5.85388i	−0.286264	+	0.255484i
$526$	3.58057	+	13.3634i	0.156120	+	0.582673i
$527$	3.09544	−	3.09544i	0.134839	−	0.134839i
$528$	−4.62151	−	17.2505i	−0.201125	−	0.750731i
$529$			2.43310i			0.105787i
$530$	2.53011	−	1.82971i	0.109901	−	0.0794776i
$531$		−	1.49404i		−	0.0648356i
$532$	1.88802	+	0.505934i	0.0818561	+	0.0219350i
$533$	−2.69328	+	2.69328i	−0.116659	+	0.116659i
$534$	25.4068	−	6.80746i	1.09946	−	0.294588i
$535$	15.6699	−	34.9880i	0.677469	−	1.51266i
$536$	−25.6882	−	25.6898i	−1.10956	−	1.10963i
$537$	−28.0935	−	28.0935i	−1.21233	−	1.21233i
$538$	−5.16276	+	8.94196i	−0.222583	+	0.385515i
$539$	15.0010			0.646141
$540$	−22.1157	+	2.27488i	−0.951709	+	0.0978951i
$541$	−25.5607			−1.09894			−0.549470	−	0.835513i	$-0.685170\pi$
$541$	−25.5607			−1.09894			−0.549470	+	0.835513i	$0.685170\pi$
$542$	−5.91012	+	10.2364i	−0.253861	+	0.439691i
$543$	28.8361	+	28.8361i	1.23748	+	1.23748i
$544$	−15.3757	−	4.12073i	−0.659227	−	0.176675i
$545$	−8.58653	−	22.5165i	−0.367807	−	0.964500i
$546$	−1.01766	+	0.272670i	−0.0435519	+	0.0116692i
$547$	19.9090	−	19.9090i	0.851245	−	0.851245i	−0.139041	−	0.990287i	$-0.544402\pi$
$547$	19.9090	−	19.9090i	0.851245	−	0.851245i	0.990287	+	0.139041i	$0.0444020\pi$
$548$	1.20033	−	4.47933i	0.0512755	−	0.191348i
$549$		−	2.59490i		−	0.110748i
$550$	−3.57272	−	17.1802i	−0.152341	−	0.732565i
$551$		−	5.50279i		−	0.234427i
$552$	25.6627		0.000773351i	1.09227		3.29160e-5i
$553$	0.568921	−	0.568921i	0.0241930	−	0.0241930i
$554$	10.3796	+	38.7386i	0.440985	+	1.64584i
$555$	−3.18927	−	8.36322i	−0.135377	−	0.354999i
$556$	20.3314	+	35.2166i	0.862242	+	1.49352i
$557$	23.1882	+	23.1882i	0.982517	+	0.982517i	0.999850	−	0.0173329i	$-0.00551751\pi$
$557$	23.1882	+	23.1882i	0.982517	+	0.982517i	−0.0173329	+	0.999850i	$0.505518\pi$
$558$	0.451139	+	0.260471i	0.0190982	+	0.0110266i
$559$	0.366975			0.0155214
$560$	5.12222	+	7.08341i	0.216453	+	0.299329i
$561$	−12.5636			−0.530436
$562$	13.0605	+	7.54068i	0.550925	+	0.318084i
$563$	−28.9631	−	28.9631i	−1.22065	−	1.22065i	−0.967402	−	0.253245i	$-0.918502\pi$
$563$	−28.9631	−	28.9631i	−1.22065	−	1.22065i	−0.253245	−	0.967402i	$-0.581498\pi$
$564$	18.4631	+	31.9805i	0.777437	+	1.34662i
$565$	−6.84654	+	15.2871i	−0.288036	+	0.643132i
$566$	−0.0792462	−	0.295763i	−0.00333097	−	0.0124318i
$567$	6.67176	−	6.67176i	0.280188	−	0.280188i
$568$	21.7998		0.000656942i	0.914698		2.75647e-5i
$569$			28.7179i			1.20392i	0.798528	+	0.601958i	$0.205612\pi$
$569$			28.7179i			1.20392i	−0.798528	+	0.601958i	$0.794388\pi$
$570$	−3.33390	−	4.61009i	−0.139642	−	0.193095i
$571$			22.1834i			0.928346i	0.885744	+	0.464173i	$0.153648\pi$
$571$			22.1834i			0.928346i	−0.885744	+	0.464173i	$0.846352\pi$
$572$	0.544309	−	2.03123i	0.0227587	−	0.0849298i
$573$	−34.9694	+	34.9694i	−1.46087	+	1.46087i
$574$	−12.0016	+	3.21570i	−0.500938	+	0.134221i
$575$	25.1750	+	1.43036i	1.04987	+	0.0596499i
$576$	0.000114169	−	1.89427i	4.75703e−6	−	0.0789279i
$577$	26.4141	+	26.4141i	1.09963	+	1.09963i	0.994453	+	0.105178i	$0.0335413\pi$
$577$	26.4141	+	26.4141i	1.09963	+	1.09963i	0.105178	+	0.994453i	$0.466459\pi$
$578$	6.42170	−	11.1225i	0.267107	−	0.462633i
$579$	31.5578			1.31150
$580$	15.5295	−	19.0906i	0.644826	−	0.792693i
$581$	1.06186			0.0440534
$582$	−9.77803	+	16.9357i	−0.405313	+	0.702006i
$583$	−1.73264	−	1.73264i	−0.0717585	−	0.0717585i
$584$	−5.08567	−	5.08598i	−0.210447	−	0.210459i
$585$	0.204735	+	0.0916935i	0.00846474	+	0.00379106i
$586$	27.3229	−	7.32087i	1.12870	−	0.302422i
$587$	−10.1922	+	10.1922i	−0.420676	+	0.420676i	−0.885436	−	0.464760i	$-0.846140\pi$
$587$	−10.1922	+	10.1922i	−0.420676	+	0.420676i	0.464760	+	0.885436i	$0.346140\pi$
$588$	21.0094	+	5.62991i	0.866414	+	0.232173i
$589$		−	1.55566i		−	0.0641000i
$590$	−19.7005	−	3.16485i	−0.811055	−	0.130295i
$591$			0.127310i			0.00523684i
$592$	−8.59653	+	2.30306i	−0.353315	+	0.0946553i
$593$	−22.1089	+	22.1089i	−0.907903	+	0.907903i	−0.996103	−	0.0881994i	$-0.971889\pi$
$593$	−22.1089	+	22.1089i	−0.907903	+	0.907903i	0.0881994	+	0.996103i	$0.471889\pi$
$594$	4.51546	+	16.8526i	0.185272	+	0.691471i
$595$	5.74591	−	2.19117i	0.235559	−	0.0898293i
$596$	−6.93697	+	4.00487i	−0.284149	+	0.164046i
$597$	15.0748	+	15.0748i	0.616970	+	0.616970i
$598$	2.61694	+	1.51093i	0.107015	+	0.0617864i
$599$	27.0682			1.10598			0.552988	−	0.833189i	$-0.313488\pi$
$599$	27.0682			1.10598			0.552988	+	0.833189i	$0.313488\pi$
$600$	1.44403	−	25.4022i	0.0589523	−	1.03704i
$601$	2.99835			0.122305			0.0611527	−	0.998128i	$-0.480522\pi$
$601$	2.99835			0.122305			0.0611527	+	0.998128i	$0.480522\pi$
$602$	1.03673	+	0.598567i	0.0422538	+	0.0243958i
$603$	−2.15057	−	2.15057i	−0.0875781	−	0.0875781i
$604$	−32.2184	+	18.6004i	−1.31095	+	0.756841i
$605$	10.1155	−	3.85748i	0.411252	−	0.156829i
$606$	−9.59379	−	35.8059i	−0.389721	−	1.45452i
$607$	12.4030	−	12.4030i	0.503421	−	0.503421i	−0.409078	−	0.912499i	$-0.634150\pi$
$607$	12.4030	−	12.4030i	0.503421	−	0.503421i	0.912499	+	0.409078i	$0.134150\pi$
$608$	−4.89912	+	2.82818i	−0.198686	+	0.114698i
$609$			9.67554i			0.392073i
$610$	−34.2165	−	5.49683i	−1.38539	−	0.222560i
$611$			4.34825i			0.175911i
$612$	−1.28720	−	0.344931i	−0.0520318	−	0.0139430i
$613$	−33.4675	+	33.4675i	−1.35174	+	1.35174i	−0.468026	+	0.883715i	$0.655034\pi$
$613$	−33.4675	+	33.4675i	−1.35174	+	1.35174i	−0.883715	+	0.468026i	$0.844966\pi$
$614$	−6.11023	+	1.63716i	−0.246589	+	0.0660706i
$615$	33.0058	+	14.7822i	1.33092	+	0.596074i
$616$	4.85081	−	4.85052i	0.195445	−	0.195433i
$617$	11.4592	+	11.4592i	0.461329	+	0.461329i	0.899091	−	0.437762i	$-0.144229\pi$
$617$	11.4592	+	11.4592i	0.461329	+	0.461329i	−0.437762	+	0.899091i	$0.644229\pi$
$618$	11.9597	−	20.7143i	0.481088	−	0.833250i
$619$	−21.9269			−0.881318			−0.440659	−	0.897675i	$-0.645255\pi$
$619$	−21.9269			−0.881318			−0.440659	+	0.897675i	$0.645255\pi$
$620$	4.39025	−	5.39699i	0.176317	−	0.216748i
$621$	−25.0710			−1.00606
$622$	6.37691	−	11.0449i	0.255691	−	0.442859i
$623$	7.14420	+	7.14420i	0.286226	+	0.286226i
$624$	1.52464	−	2.64051i	0.0610345	−	0.105705i
$625$	2.83168	−	24.8391i	0.113267	−	0.993565i
$626$	45.6274	−	12.2253i	1.82364	−	0.488623i
$627$	−3.15702	+	3.15702i	−0.126079	+	0.126079i
$628$	2.83389	−	10.5754i	0.113085	−	0.422004i
$629$			6.26089i			0.249638i
$630$	0.428828	+	0.592979i	0.0170849	+	0.0236249i
$631$			8.55264i			0.340475i	0.985403	+	0.170238i	$0.0544535\pi$
$631$			8.55264i			0.340475i	−0.985403	+	0.170238i	$0.945546\pi$
$632$	−7.01700e−5		2.32850i	−2.79121e−6		0.0926228i
$633$	2.43064	−	2.43064i	0.0966093	−	0.0966093i
$634$	−10.4656	−	39.0596i	−0.415640	−	1.55125i
$635$	−1.83247	+	4.09156i	−0.0727192	+	0.162369i
$636$	−1.77635	−	3.07687i	−0.0704369	−	0.122006i
$637$	1.81101	+	1.81101i	0.0717550	+	0.0717550i
$638$	−16.7248	−	9.65631i	−0.662143	−	0.382297i
$639$	1.82498			0.0721952
$640$	−24.9777	−	4.01418i	−0.987331	−	0.158674i
$641$	1.23653			0.0488399			0.0244199	−	0.999702i	$-0.492226\pi$
$641$	1.23653			0.0488399			0.0244199	+	0.999702i	$0.492226\pi$
$642$	−37.7773	−	21.8112i	−1.49095	−	0.860820i
$643$	2.39601	+	2.39601i	0.0944892	+	0.0944892i	0.752771	−	0.658282i	$-0.228717\pi$
$643$	2.39601	+	2.39601i	0.0944892	+	0.0944892i	−0.658282	+	0.752771i	$0.728717\pi$
$644$	4.92856	+	8.53691i	0.194212	+	0.336401i
$645$	−1.24154	−	3.25570i	−0.0488857	−	0.128193i
$646$	1.02995	+	3.84398i	0.0405229	+	0.151240i
$647$	−10.7242	+	10.7242i	−0.421611	+	0.421611i	−0.885758	−	0.464147i	$-0.846361\pi$
$647$	−10.7242	+	10.7242i	−0.421611	+	0.421611i	0.464147	+	0.885758i	$0.346361\pi$
$648$	−0.000822887		27.3064i	−3.23261e−5		1.07270i
$649$			15.6583i			0.614643i
$650$	1.64277	−	2.50541i	0.0644347	−	0.0982703i
$651$			2.73532i			0.107206i
$652$	−4.14120	+	15.4539i	−0.162182	+	0.605222i
$653$	30.3297	−	30.3297i	1.18689	−	1.18689i	0.208969	−	0.977922i	$-0.432989\pi$
$653$	30.3297	−	30.3297i	1.18689	−	1.18689i	0.977922	−	0.208969i	$-0.0670108\pi$
$654$	−26.4859	+	7.09660i	−1.03568	+	0.277499i
$655$	−14.0702	−	36.8962i	−0.549767	−	1.44166i
$656$	17.9806	−	31.1405i	0.702026	−	1.21583i
$657$	−0.425763	−	0.425763i	−0.0166106	−	0.0166106i
$658$	−7.09237	+	12.2841i	−0.276489	+	0.478882i
$659$	−8.59030			−0.334631			−0.167315	−	0.985903i	$-0.553510\pi$
$659$	−8.59030			−0.334631			−0.167315	+	0.985903i	$0.553510\pi$
$660$	−19.8620	+	2.04305i	−0.773126	+	0.0795256i
$661$	35.7451			1.39032			0.695161	−	0.718854i	$-0.255333\pi$
$661$	35.7451			1.39032			0.695161	+	0.718854i	$0.255333\pi$
$662$	−2.32553	+	4.02784i	−0.0903841	+	0.156546i
$663$	−1.51675	−	1.51675i	−0.0589057	−	0.0589057i
$664$	−2.17308	+	2.17295i	−0.0843318	+	0.0843268i
$665$	0.893246	−	1.99446i	0.0346386	−	0.0773416i
$666$	−0.719658	+	0.192824i	−0.0278862	+	0.00747178i
$667$	19.6231	−	19.6231i	0.759810	−	0.759810i
$668$	−20.1409	−	5.39717i	−0.779274	−	0.208823i
$669$		−	13.3567i		−	0.516399i
$670$	−32.9132	+	23.8020i	−1.27155	+	0.919551i
$671$			27.1960i			1.04989i
$672$	8.61411	−	4.97278i	0.332296	−	0.191829i
$673$	12.6420	−	12.6420i	0.487314	−	0.487314i	−0.420144	−	0.907458i	$-0.638020\pi$
$673$	12.6420	−	12.6420i	0.487314	−	0.487314i	0.907458	+	0.420144i	$0.138020\pi$
$674$	6.11431	+	22.8198i	0.235514	+	0.878987i
$675$	−1.40999	+	24.8166i	−0.0542705	+	0.955191i
$676$	−22.2060	+	12.8200i	−0.854076	+	0.493078i
$677$	27.3948	+	27.3948i	1.05287	+	1.05287i	0.998522	+	0.0543454i	$0.0173072\pi$
$677$	27.3948	+	27.3948i	1.05287	+	1.05287i	0.0543454	+	0.998522i	$0.482693\pi$
$678$	16.5057	+	9.52982i	0.633899	+	0.365990i
$679$	−7.51169			−0.288272
$680$	−7.27498	+	16.2424i	−0.278983	+	0.622867i
$681$	−43.5306			−1.66810
$682$	−4.72819	−	2.72988i	−0.181052	−	0.104533i
$683$	−7.17226	−	7.17226i	−0.274439	−	0.274439i	0.556445	−	0.830884i	$-0.312165\pi$
$683$	−7.17226	−	7.17226i	−0.274439	−	0.274439i	−0.830884	+	0.556445i	$0.812165\pi$
$684$	−0.410126	+	0.236775i	−0.0156816	+	0.00905333i
$685$	−4.73185	−	2.11923i	−0.180795	−	0.0809715i
$686$	4.66627	+	17.4154i	0.178159	+	0.664925i
$687$	−2.29614	+	2.29614i	−0.0876033	+	0.0876033i
$688$	−3.34652	+	0.896554i	−0.127585	+	0.0341808i
$689$		−	0.418348i		−	0.0159378i
$690$	4.55093	−	28.3285i	0.173251	−	1.07845i
$691$			28.5788i			1.08719i	0.839348	+	0.543594i	$0.182937\pi$
$691$			28.5788i			1.08719i	−0.839348	+	0.543594i	$0.817063\pi$
$692$	−13.9430	−	3.73632i	−0.530033	−	0.142033i
$693$	0.406076	−	0.406076i	0.0154256	−	0.0154256i
$694$	−26.0502	+	6.97986i	−0.988853	+	0.264952i
$695$	42.4799	−	16.1995i	1.61135	−	0.614481i
$696$	−19.7996	−	19.8008i	−0.750503	−	0.750548i
$697$	−17.8876	−	17.8876i	−0.677540	−	0.677540i
$698$	−13.7906	+	23.8854i	−0.521981	+	0.904077i
$699$	−24.0877			−0.911082
$700$	8.72746	−	4.39843i	0.329867	−	0.166245i
$701$	−27.2769			−1.03023			−0.515117	−	0.857120i	$-0.672251\pi$
$701$	−27.2769			−1.03023			−0.515117	+	0.857120i	$0.672251\pi$
$702$	−1.48941	+	2.57968i	−0.0562143	+	0.0973637i
$703$	1.57326	+	1.57326i	0.0593365	+	0.0593365i
$704$	−0.00119655	+	19.8530i	−4.50967e−5	+	0.748237i
$705$	38.5764	−	14.7109i	1.45287	−	0.554045i
$706$	30.1302	−	8.07303i	1.13396	−	0.303833i
$707$	10.0684	−	10.0684i	0.378660	−	0.378660i
$708$	−5.87658	+	21.9299i	−0.220856	+	0.824178i
$709$		−	36.6344i		−	1.37583i	−0.725789	−	0.687917i	$-0.758525\pi$
$709$		−	36.6344i		−	1.37583i	0.725789	−	0.687917i	$-0.241475\pi$
$710$	3.86590	−	24.0643i	0.145085	−	0.903119i
$711$			0.194932i			0.00731052i
$712$	−29.2401		0.000881157i	−1.09582		3.30228e-5i
$713$	5.54754	−	5.54754i	0.207757	−	0.207757i
$714$	−1.81096	−	6.75886i	−0.0677734	−	0.252944i
$715$	−2.14573	−	0.960998i	−0.0802459	−	0.0359393i
$716$	22.0826	+	38.2499i	0.825264	+	1.42947i
$717$	18.2425	+	18.2425i	0.681280	+	0.681280i
$718$	1.18723	+	0.685463i	0.0443070	+	0.0255813i
$719$	−25.4725			−0.949964			−0.474982	−	0.879996i	$-0.657545\pi$
$719$	−25.4725			−0.949964			−0.474982	+	0.879996i	$0.657545\pi$
$720$	−2.09104	−	0.335986i	−0.0779283	−	0.0125215i
$721$	9.18766			0.342166
$722$	1.22474	+	0.707119i	0.0455800	+	0.0263162i
$723$	13.9388	+	13.9388i	0.518391	+	0.518391i
$724$	−22.6662	−	39.2609i	−0.842384	−	1.45912i
$725$	−18.3204	−	20.5276i	−0.680402	−	0.762375i
$726$	−3.18813	−	11.8987i	−0.118323	−	0.441604i
$727$	−5.51517	+	5.51517i	−0.204547	+	0.204547i	−0.801945	−	0.597398i	$-0.796201\pi$
$727$	−5.51517	+	5.51517i	−0.204547	+	0.204547i	0.597398	+	0.801945i	$0.296201\pi$
$728$	1.17120		3.52944e-5i	0.0434076		1.30810e-6i
$729$		−	24.5458i		−	0.909105i
$730$	−6.51605	+	4.71224i	−0.241170	+	0.174408i
$731$			2.43729i			0.0901463i
$732$	−10.2067	+	38.0888i	−0.377250	+	1.40780i
$733$	20.2773	−	20.2773i	0.748959	−	0.748959i	−0.225325	−	0.974284i	$-0.572344\pi$
$733$	20.2773	−	20.2773i	0.748959	−	0.748959i	0.974284	+	0.225325i	$0.0723443\pi$
$734$	−28.4929	+	7.63435i	−1.05169	+	0.281789i
$735$	9.93981	−	22.1938i	0.366636	−	0.818630i
$736$	−27.5558	−	7.38503i	−1.01572	−	0.272216i
$737$	22.5392	+	22.5392i	0.830242	+	0.830242i
$738$	1.50518	−	2.60699i	0.0554065	−	0.0959647i
$739$	37.1286			1.36580			0.682899	−	0.730513i	$-0.260719\pi$
$739$	37.1286			1.36580			0.682899	+	0.730513i	$0.260719\pi$
$740$	1.01812	+	9.89793i	0.0374270	+	0.363855i
$741$	−0.762268			−0.0280026
$742$	0.682362	−	1.18186i	0.0250503	−	0.0433874i
$743$	33.2064	+	33.2064i	1.21822	+	1.21822i	0.968254	+	0.249970i	$0.0804208\pi$
$743$	33.2064	+	33.2064i	1.21822	+	1.21822i	0.249970	+	0.968254i	$0.419579\pi$
$744$	−5.59744	−	5.59778i	−0.205212	−	0.205225i
$745$	3.19098	+	8.36770i	0.116908	+	0.306569i
$746$	19.0261	−	5.09783i	0.696596	−	0.186645i
$747$	−0.181915	+	0.181915i	−0.00665593	+	0.00665593i
$748$	13.4905	+	3.61507i	0.493262	+	0.132180i
$749$		−	16.7558i		−	0.612244i
$750$	−27.7851	−	6.09794i	−1.01457	−	0.222665i
$751$		−	40.6688i		−	1.48403i	−0.670385	−	0.742013i	$-0.733871\pi$
$751$		−	40.6688i		−	1.48403i	0.670385	−	0.742013i	$-0.266129\pi$
$752$	−10.6232	−	39.6526i	−0.387387	−	1.44598i
$753$	−39.4547	+	39.4547i	−1.43781	+	1.43781i
$754$	−0.853353	−	3.18489i	−0.0310773	−	0.115987i
$755$	14.8203	+	38.8633i	0.539367	+	1.41438i
$756$	−8.41536	+	4.85838i	−0.306064	+	0.176698i
$757$	−17.2071	−	17.2071i	−0.625401	−	0.625401i	0.321506	−	0.946907i	$-0.395811\pi$
$757$	−17.2071	−	17.2071i	−0.625401	−	0.625401i	−0.946907	+	0.321506i	$0.895811\pi$
$758$	37.4548	+	21.6250i	1.36042	+	0.785457i
$759$	−22.5161			−0.817281
$760$	2.25336	+	5.90952i	0.0817379	+	0.214361i
$761$	25.4641			0.923073			0.461537	−	0.887121i	$-0.347298\pi$
$761$	25.4641			0.923073			0.461537	+	0.887121i	$0.347298\pi$
$762$	4.41774	+	2.55064i	0.160038	+	0.0924001i
$763$	−7.44764	−	7.44764i	−0.269623	−	0.269623i
$764$	47.6115	−	27.4872i	1.72252	−	0.994453i
$765$	−0.608988	+	1.35976i	−0.0220180	+	0.0491622i
$766$	−8.61742	−	32.1619i	−0.311360	−	1.16206i
$767$	−1.89036	+	1.89036i	−0.0682570	+	0.0682570i
$768$	−7.45252	+	27.8043i	−0.268920	+	1.00330i
$769$		−	14.3062i		−	0.515897i	−0.966159	−	0.257948i	$-0.916954\pi$
$769$		−	14.3062i		−	0.515897i	0.966159	−	0.257948i	$-0.0830464\pi$

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707119i) q^{2} +(-1.27216 - 1.27216i) q^{3} +(0.999965 + 1.73207i) q^{4} +(2.08931 - 0.796745i) q^{5} +(-0.658494 - 2.45763i) q^{6} +(0.691067 - 0.691067i) q^{7} +(-8.52354e-5 + 2.82843i) q^{8} +0.236784i q^{9} +O(q^{10})\)	\(q+(1.22474 + 0.707119i) q^{2} +(-1.27216 - 1.27216i) q^{3} +(0.999965 + 1.73207i) q^{4} +(2.08931 - 0.796745i) q^{5} +(-0.658494 - 2.45763i) q^{6} +(0.691067 - 0.691067i) q^{7} +(-8.52354e-5 + 2.82843i) q^{8} +0.236784i q^{9} +(3.12224 + 0.501584i) q^{10} -2.48162i q^{11} +(0.931356 - 3.47559i) q^{12} +(0.299596 - 0.299596i) q^{13} +(1.33504 - 0.357709i) q^{14} +(-3.67152 - 1.64434i) q^{15} +(-2.00014 + 3.46402i) q^{16} +(1.98979 + 1.98979i) q^{17} +(-0.167434 + 0.289998i) q^{18} +1.00000 q^{19} +(3.46925 + 2.82211i) q^{20} -1.75830 q^{21} +(1.75480 - 3.03934i) q^{22} +(3.56603 + 3.56603i) q^{23} +(3.59832 - 3.59810i) q^{24} +(3.73039 - 3.32929i) q^{25} +(0.578776 - 0.155076i) q^{26} +(-3.51525 + 3.51525i) q^{27} +(1.88802 + 0.505934i) q^{28} -5.50279i q^{29} +(-3.33390 - 4.61009i) q^{30} -1.55566i q^{31} +(-4.89912 + 2.82818i) q^{32} +(-3.15702 + 3.15702i) q^{33} +(1.02995 + 3.84398i) q^{34} +(0.893246 - 1.99446i) q^{35} +(-0.410126 + 0.236775i) q^{36} +(1.57326 + 1.57326i) q^{37} +(1.22474 + 0.707119i) q^{38} -0.762268 q^{39} +(2.25336 + 5.90952i) q^{40} -8.98970 q^{41} +(-2.15345 - 1.24333i) q^{42} +(0.612449 + 0.612449i) q^{43} +(4.29835 - 2.48154i) q^{44} +(0.188656 + 0.494713i) q^{45} +(1.84584 + 6.88905i) q^{46} +(-7.25685 + 7.25685i) q^{47} +(6.95129 - 1.86229i) q^{48} +6.04485i q^{49} +(6.92296 - 1.43967i) q^{50} -5.06266i q^{51} +(0.818507 + 0.219336i) q^{52} +(0.698187 - 0.698187i) q^{53} +(-6.79097 + 1.81956i) q^{54} +(-1.97722 - 5.18487i) q^{55} +(1.95457 + 1.95469i) q^{56} +(-1.27216 - 1.27216i) q^{57} +(3.89113 - 6.73948i) q^{58} -6.30971 q^{59} +(-0.823271 - 8.00362i) q^{60} -10.9589 q^{61} +(1.10004 - 1.90528i) q^{62} +(0.163633 + 0.163633i) q^{63} +(-8.00000 - 0.000482164i) q^{64} +(0.387246 - 0.864649i) q^{65} +(-6.09891 + 1.63413i) q^{66} +(-9.08244 + 9.08244i) q^{67} +(-1.45673 + 5.43617i) q^{68} -9.07312i q^{69} +(2.50431 - 1.81105i) q^{70} -7.70738i q^{71} +(-0.669725 - 2.01824e-5i) q^{72} +(-1.79811 + 1.79811i) q^{73} +(0.814347 + 3.03931i) q^{74} +(-8.98105 - 0.510271i) q^{75} +(0.999965 + 1.73207i) q^{76} +(-1.71497 - 1.71497i) q^{77} +(-0.933579 - 0.539014i) q^{78} +0.823249 q^{79} +(-1.41896 + 8.83100i) q^{80} +9.65428 q^{81} +(-11.0100 - 6.35679i) q^{82} +(0.768276 + 0.768276i) q^{83} +(-1.75824 - 3.04549i) q^{84} +(5.74263 + 2.57192i) q^{85} +(0.317015 + 1.18316i) q^{86} +(-7.00043 + 7.00043i) q^{87} +(7.01909 + 0.000211522i) q^{88} +10.3379i q^{89} +(-0.118767 + 0.739296i) q^{90} -0.414082i q^{91} +(-2.61071 + 9.74252i) q^{92} +(-1.97905 + 1.97905i) q^{93} +(-14.0192 + 3.75628i) q^{94} +(2.08931 - 0.796745i) q^{95} +(9.83037 + 2.63457i) q^{96} +(-5.43484 - 5.43484i) q^{97} +(-4.27443 + 7.40336i) q^{98} +0.587608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

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