LMFDB - Embedded newform 380.2.k.d.267.18

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			267.18
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707119 + 1.22474i) q^{2} +(1.27216 + 1.27216i) q^{3} +(-0.999965 + 1.73207i) q^{4} +(2.08931 - 0.796745i) q^{5} +(-0.658494 + 2.45763i) q^{6} +(-0.691067 + 0.691067i) q^{7} +(-2.82843 + 8.52354e-5i) q^{8} +0.236784i q^{9} +O(q^{10})$	\(q+(0.707119 + 1.22474i) 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} +(-2.82843 + 8.52354e-5i) q^{8} +0.236784i q^{9} +(2.45319 + 1.99546i) q^{10} +2.48162i q^{11} +(-3.47559 + 0.931356i) 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} +(-0.289998 + 0.167434i) q^{18} -1.00000 q^{19} +(-0.709214 + 4.41554i) q^{20} -1.75830 q^{21} +(-3.03934 + 1.75480i) 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} +(-0.505934 - 1.88802i) q^{28} -5.50279i q^{29} +(0.582311 + 5.65939i) q^{30} +1.55566i q^{31} +(2.82818 - 4.89912i) 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} +(-0.707119 - 1.22474i) q^{38} +0.762268 q^{39} +(-5.90938 + 2.25371i) q^{40} -8.98970 q^{41} +(-1.24333 - 2.15345i) 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} +(1.86229 - 6.95129i) q^{48} +6.04485i q^{49} +(6.71534 + 2.21455i) q^{50} +5.06266i q^{51} +(0.219336 + 0.818507i) 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} +(6.73948 - 3.89113i) q^{58} +6.30971 q^{59} +(-6.51951 + 4.71504i) q^{60} -10.9589 q^{61} +(-1.90528 + 1.10004i) 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} +(-5.43617 + 1.45673i) q^{68} -9.07312i q^{69} +(-3.07432 + 0.316325i) q^{70} +7.70738i q^{71} +(-2.01824e-5 - 0.669725i) 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} +(0.539014 + 0.933579i) q^{78} -0.823249 q^{79} +(-6.93884 - 5.64380i) q^{80} +9.65428 q^{81} +(-6.35679 - 11.0100i) 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} +(-0.000211522 - 7.01909i) q^{88} +10.3379i q^{89} +(-0.472492 + 0.580876i) q^{90} +0.414082i q^{91} +(9.74252 - 2.61071i) 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} +(-7.40336 + 4.27443i) 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} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 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 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * 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 $

$2$	0.707119	+	1.22474i	0.500009	+	0.866020i
$2$	0.707119	+	1.22474i	0.500009	+	0.866020i
$3$	1.27216	+	1.27216i	0.734482	+	0.734482i	0.971504	−	0.237022i	$-0.0761714\pi$
$3$	1.27216	+	1.27216i	0.734482	+	0.734482i	−0.237022	+	0.971504i	$0.576171\pi$
$4$	−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	−0.825541	−	0.564342i	$-0.809130\pi$
$7$	−0.691067	+	0.691067i	−0.261199	+	0.261199i	0.564342	+	0.825541i	$0.309130\pi$
$8$	−2.82843		8.52354e-5i	−1.00000		3.01353e-5i
$9$			0.236784i			0.0789279i
$10$	2.45319	+	1.99546i	0.775767	+	0.631019i
$11$			2.48162i			0.748237i	0.927381	+	0.374119i	$0.122055\pi$
$11$			2.48162i			0.748237i	−0.927381	+	0.374119i	$0.877945\pi$
$12$	−3.47559	+	0.931356i	−1.00332	+	0.268859i
$13$	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	$0.639151\pi$
$18$	−0.289998	+	0.167434i	−0.0683531	+	0.0394646i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−0.709214	+	4.41554i	−0.158585	+	0.987345i
$21$	−1.75830			−0.383692
$22$	−3.03934	+	1.75480i	−0.647989	+	0.374125i
$23$	−3.56603	−	3.56603i	−0.743568	−	0.743568i	0.229695	−	0.973263i	$-0.426227\pi$
$23$	−3.56603	−	3.56603i	−0.743568	−	0.743568i	−0.973263	+	0.229695i	$0.926227\pi$
$24$	−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
$28$	−0.505934	−	1.88802i	−0.0956126	−	0.356802i
$29$		−	5.50279i		−	1.02184i	−0.859627	−	0.510921i	$-0.829304\pi$
$29$		−	5.50279i		−	1.02184i	0.859627	−	0.510921i	$-0.170696\pi$
$30$	0.582311	+	5.65939i	0.106315	+	1.03326i
$31$			1.55566i			0.279405i	0.990193	+	0.139703i	$0.0446147\pi$
$31$			1.55566i			0.279405i	−0.990193	+	0.139703i	$0.955385\pi$
$32$	2.82818	−	4.89912i	0.499957	−	0.866051i
$33$	−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	$0.691456\pi$
$38$	−0.707119	−	1.22474i	−0.114710	−	0.198679i
$39$	0.762268			0.122061
$40$	−5.90938	+	2.25371i	−0.934355	+	0.356343i
$41$	−8.98970			−1.40395			−0.701977	−	0.712199i	$-0.747699\pi$
$41$	−8.98970			−1.40395			−0.701977	+	0.712199i	$0.747699\pi$
$42$	−1.24333	−	2.15345i	−0.191849	−	0.332285i
$43$	−0.612449	−	0.612449i	−0.0933977	−	0.0933977i	0.658864	−	0.752262i	$-0.271037\pi$
$43$	−0.612449	−	0.612449i	−0.0933977	−	0.0933977i	−0.752262	+	0.658864i	$0.771037\pi$
$44$	−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	$-0.480781\pi$
$47$	7.25685	−	7.25685i	1.05852	−	1.05852i	0.998178	−	0.0603431i	$-0.0192195\pi$
$48$	1.86229	−	6.95129i	0.268799	−	1.00333i
$49$			6.04485i			0.863550i
$50$	6.71534	+	2.21455i	0.949692	+	0.313185i
$51$			5.06266i			0.708914i
$52$	0.219336	+	0.818507i	0.0304164	+	0.113506i
$53$	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
$58$	6.73948	−	3.89113i	0.884937	−	0.510930i
$59$	6.30971			0.821454			0.410727	−	0.911758i	$-0.365275\pi$
$59$	6.30971			0.821454			0.410727	+	0.911758i	$0.365275\pi$
$60$	−6.51951	+	4.71504i	−0.841665	+	0.608710i
$61$	−10.9589			−1.40315			−0.701575	−	0.712596i	$-0.747519\pi$
$61$	−10.9589			−1.40315			−0.701575	+	0.712596i	$0.747519\pi$
$62$	−1.90528	+	1.10004i	−0.241971	+	0.139705i
$63$	−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	$-0.462867\pi$
$67$	9.08244	−	9.08244i	1.10960	−	1.10960i	0.993203	−	0.116393i	$-0.0371333\pi$
$68$	−5.43617	+	1.45673i	−0.659232	+	0.176655i
$69$		−	9.07312i		−	1.09227i
$70$	−3.07432	+	0.316325i	−0.367451	+	0.0378081i
$71$			7.70738i			0.914698i	0.889287	+	0.457349i	$0.151201\pi$
$71$			7.70738i			0.914698i	−0.889287	+	0.457349i	$0.848799\pi$
$72$	−2.01824e−5	−	0.669725i	−2.37851e−6	−	0.0789279i
$73$	−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
$78$	0.539014	+	0.933579i	0.0610314	+	0.105707i
$79$	−0.823249			−0.0926228			−0.0463114	−	0.998927i	$-0.514747\pi$
$79$	−0.823249			−0.0926228			−0.0463114	+	0.998927i	$0.514747\pi$
$80$	−6.93884	−	5.64380i	−0.775786	−	0.630996i
$81$	9.65428			1.07270
$82$	−6.35679	−	11.0100i	−0.701990	−	1.21585i
$83$	−0.768276	−	0.768276i	−0.0843293	−	0.0843293i	0.663684	−	0.748013i	$-0.268992\pi$
$83$	−0.768276	−	0.768276i	−0.0843293	−	0.0843293i	−0.748013	+	0.663684i	$0.768992\pi$
$84$	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
$88$	−0.000211522	−	7.01909i	−2.25483e−5	−	0.748237i
$89$			10.3379i			1.09582i	0.836538	+	0.547909i	$0.184576\pi$
$89$			10.3379i			1.09582i	−0.836538	+	0.547909i	$0.815424\pi$
$90$	−0.472492	+	0.580876i	−0.0498050	+	0.0612297i
$91$			0.414082i			0.0434076i
$92$	9.74252	−	2.61071i	1.01573	−	0.272185i
$93$	−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	$0.877594\pi$
$98$	−7.40336	+	4.27443i	−0.747852	+	0.431783i
$99$	−0.587608			−0.0590568
$100$	2.03630	+	9.79048i	0.203630	+	0.979048i
$101$	14.5693			1.44970			0.724849	−	0.688908i	$-0.241909\pi$
$101$	14.5693			1.44970			0.724849	+	0.688908i	$0.241909\pi$
$102$	−6.20043	+	3.57990i	−0.613934	+	0.354463i
$103$	−6.64745	−	6.64745i	−0.654992	−	0.654992i	0.299199	−	0.954191i	$-0.403281\pi$
$103$	−6.64745	−	6.64745i	−0.654992	−	0.654992i	−0.954191	+	0.299199i	$0.903281\pi$
$104$	−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	$0.560931\pi$
$107$	−12.1231	+	12.1231i	−1.17199	+	1.17199i	−0.981735	+	0.190254i	$0.939069\pi$
$108$	2.57354	+	9.60380i	0.247639	+	0.924126i
$109$		−	10.7770i		−	1.03225i	−0.856513	−	0.516125i	$-0.827374\pi$
$109$		−	10.7770i		−	1.03225i	0.856513	−	0.516125i	$-0.172626\pi$
$110$	−4.95197	+	6.08790i	−0.472152	+	0.580458i
$111$			4.00287i			0.379936i
$112$	3.77610	+	1.01164i	0.356808	+	0.0955911i
$113$	−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
$118$	4.46171	+	7.72774i	0.410734	+	0.711396i
$119$	−2.75015			−0.252106
$120$	−10.3848	−	4.65059i	−0.947995	−	0.424539i
$121$	4.84155			0.440141
$122$	−7.74928	−	13.4218i	−0.701587	−	1.21516i
$123$	−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	−0.641403	−	0.767204i	$-0.721647\pi$
$127$	1.41770	−	1.41770i	0.125801	−	0.125801i	0.767204	+	0.641403i	$0.221647\pi$
$128$	5.65754	+	9.79756i	0.500061	+	0.865990i
$129$		−	1.55827i		−	0.137198i
$130$	1.33280	−	0.137135i	0.116894	−	0.0120276i
$131$			17.6596i			1.54292i	0.636275	+	0.771462i	$0.280474\pi$
$131$			17.6596i			1.54292i	−0.636275	+	0.771462i	$0.719526\pi$
$132$	−2.31127	−	8.62510i	−0.201171	−	0.750718i
$133$	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	$0.781580\pi$
$138$	11.1122	−	6.41577i	0.945932	−	0.546147i
$139$	−20.3321			−1.72454			−0.862272	−	0.506446i	$-0.830959\pi$
$139$	−20.3321			−1.72454			−0.862272	+	0.506446i	$0.830959\pi$
$140$	−2.56132	−	3.54155i	−0.216471	−	0.299316i
$141$	18.4638			1.55493
$142$	−9.43952	+	5.45004i	−0.792147	+	0.457357i
$143$	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
$148$	−4.29820	+	1.15179i	−0.353309	+	0.0946766i
$149$			4.00501i			0.328104i	0.986452	+	0.164052i	$0.0524564\pi$
$149$			4.00501i			0.328104i	−0.986452	+	0.164052i	$0.947544\pi$
$150$	5.72572	+	11.3603i	0.467503	+	0.927561i
$151$		−	18.6011i		−	1.51373i	−0.653569	−	0.756867i	$-0.726729\pi$
$151$		−	18.6011i		−	1.51373i	0.653569	−	0.756867i	$-0.273271\pi$
$152$	2.82843		8.52354e-5i	0.229416		6.91351e-6i
$153$	−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	$0.820099\pi$
$158$	−0.582135	−	1.00826i	−0.0463122	−	0.0802132i
$159$	1.77641			0.140879
$160$	2.00558	−	12.4891i	0.158555	−	0.987350i
$161$	4.92873			0.388438
$162$	6.82673	+	11.8240i	0.536358	+	0.928979i
$163$	−5.65655	−	5.65655i	−0.443056	−	0.443056i	0.449982	−	0.893038i	$-0.351430\pi$
$163$	−5.65655	−	5.65655i	−0.443056	−	0.443056i	−0.893038	+	0.449982i	$0.851430\pi$
$164$	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	−0.361789	−	0.932260i	$-0.617834\pi$
$167$	7.37211	−	7.37211i	0.570471	−	0.570471i	0.932260	+	0.361789i	$0.117834\pi$
$168$	4.97321		0.000149869i	0.383692		1.15627e-5i
$169$			12.8205i			0.986191i
$170$	0.910794	+	8.85186i	0.0698547	+	0.678907i
$171$		−	0.236784i		−	0.0181073i
$172$	1.67323	−	0.448378i	0.127583	−	0.0341885i
$173$	−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
$178$	−12.6612	+	7.31014i	−0.949000	+	0.547918i
$179$	−22.0833			−1.65059			−0.825293	−	0.564705i	$-0.808990\pi$
$179$	−22.0833			−1.65059			−0.825293	+	0.564705i	$0.808990\pi$
$180$	−1.04553	−	0.167930i	−0.0779291	−	0.0125168i
$181$	−22.6670			−1.68483			−0.842414	−	0.538831i	$-0.818866\pi$
$181$	−22.6670			−1.68483			−0.842414	+	0.538831i	$0.818866\pi$
$182$	−0.507142	+	0.292805i	−0.0375918	+	0.0217042i
$183$	−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
$188$	5.31278	+	19.8260i	0.387475	+	1.44596i
$189$			4.85855i			0.353408i
$190$	−2.45319	−	1.99546i	−0.177973	−	0.144766i
$191$			27.4882i			1.98898i	0.104855	+	0.994488i	$0.466562\pi$
$191$			27.4882i			1.98898i	−0.104855	+	0.994488i	$0.533438\pi$
$192$	10.1779	+	10.1767i	0.734526	+	0.734438i
$193$	−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	$0.750802\pi$
$198$	−0.415509	−	0.719665i	−0.0295289	−	0.0511444i
$199$	11.8498			0.840007			0.420003	−	0.907523i	$-0.362029\pi$
$199$	11.8498			0.840007			0.420003	+	0.907523i	$0.362029\pi$
$200$	−10.5509	+	9.41697i	−0.746059	+	0.665880i
$201$	23.1086			1.62996
$202$	10.3022	+	17.8436i	0.724862	+	1.25547i
$203$	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
$208$	−1.63704	−	0.438573i	−0.113508	−	0.0304096i
$209$		−	2.48162i		−	0.171657i
$210$	−4.31344	−	3.50861i	−0.297656	−	0.242117i
$211$		−	1.91064i		−	0.131534i	−0.997835	−	0.0657669i	$-0.979051\pi$
$211$		−	1.91064i		−	0.131534i	0.997835	−	0.0657669i	$-0.0209494\pi$
$212$	0.511147	+	1.90747i	0.0351057	+	0.131006i
$213$	−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
$218$	13.1990	−	7.62063i	0.893950	−	0.516134i
$219$	−4.57497			−0.309148
$220$	−10.9577	−	1.76000i	−0.738769	−	0.118659i
$221$	1.19226			0.0802004
$222$	−4.90247	+	2.83051i	−0.329032	+	0.189971i
$223$	−5.24961	−	5.24961i	−0.351540	−	0.351540i	0.509142	−	0.860682i	$-0.329963\pi$
$223$	−5.24961	−	5.24961i	−0.351540	−	0.351540i	−0.860682	+	0.509142i	$0.829963\pi$
$224$	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	$0.546743\pi$
$227$	−17.1089	+	17.1089i	−1.13556	+	1.13556i	−0.989237	+	0.146322i	$0.953257\pi$
$228$	3.47559	−	0.931356i	0.230176	−	0.0616805i
$229$		−	1.80492i		−	0.119272i	−0.998220	−	0.0596361i	$-0.981006\pi$
$229$		−	1.80492i		−	0.119272i	0.998220	−	0.0596361i	$-0.0189940\pi$
$230$	−1.63229	−	15.8640i	−0.107630	−	1.04604i
$231$		−	4.36343i		−	0.287093i
$232$	0.000469033		15.5642i	3.07935e−5		1.02184i
$233$	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
$238$	−1.94469	−	3.36822i	−0.126055	−	0.218329i
$239$	14.3398			0.927565			0.463782	−	0.885949i	$-0.346492\pi$
$239$	14.3398			0.927565			0.463782	+	0.885949i	$0.346492\pi$
$240$	−1.64751	−	16.0071i	−0.106346	−	1.03326i
$241$	−10.9568			−0.705791			−0.352895	−	0.935663i	$-0.614803\pi$
$241$	−10.9568			−0.705791			−0.352895	+	0.935663i	$0.614803\pi$
$242$	3.42355	+	5.92963i	0.220074	+	0.381171i
$243$	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
$248$	−0.000132598	−	4.40008i	−8.41996e−6	−	0.279405i
$249$		−	1.95474i		−	0.123877i
$250$	15.7948	−	0.723539i	0.998952	−	0.0457606i
$251$			31.0139i			1.95758i	0.204859	+	0.978791i	$0.434326\pi$
$251$			31.0139i			1.95758i	−0.204859	+	0.978791i	$0.565674\pi$
$252$	0.447052	−	0.119797i	0.0281617	−	0.00754650i
$253$	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	$0.918840\pi$
$258$	1.90847	−	1.10188i	0.118816	−	0.0686001i
$259$	−2.17445			−0.135114
$260$	1.11040	+	1.53536i	0.0688642	+	0.0952187i
$261$	1.30297			0.0806519
$262$	−21.6283	+	12.4874i	−1.33620	+	0.771475i
$263$	−6.91740	−	6.91740i	−0.426545	−	0.426545i	0.460905	−	0.887450i	$-0.347525\pi$
$263$	−6.91740	−	6.91740i	−0.426545	−	0.426545i	−0.887450	+	0.460905i	$0.847525\pi$
$264$	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
$268$	6.64930	+	24.8135i	0.406171	+	1.51573i
$269$			7.30112i			0.445157i	0.974915	+	0.222579i	$0.0714474\pi$
$269$			7.30112i			0.445157i	−0.974915	+	0.222579i	$0.928553\pi$
$270$	15.6381	−	1.60905i	0.951706	−	0.0979238i
$271$		−	8.35803i		−	0.507714i	−0.967242	−	0.253857i	$-0.918301\pi$
$271$		−	8.35803i		−	0.507714i	0.967242	−	0.253857i	$-0.0816992\pi$
$272$	2.91281	−	10.8725i	0.176615	−	0.659243i
$273$	−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	$0.425420\pi$
$278$	−14.3772	−	24.9015i	−0.862287	−	1.49349i
$279$	−0.368356			−0.0220529
$280$	2.52631	−	5.64125i	0.150976	−	0.337129i
$281$	10.6639			0.636158			0.318079	−	0.948064i	$-0.396962\pi$
$281$	10.6639			0.636158			0.318079	+	0.948064i	$0.396962\pi$
$282$	13.0561	+	22.6133i	0.777478	+	1.34660i
$283$	0.153098	+	0.153098i	0.00910071	+	0.00910071i	0.711642	−	0.702542i	$-0.247952\pi$
$283$	0.153098	+	0.153098i	0.00910071	+	0.00910071i	−0.702542	+	0.711642i	$0.747952\pi$
$284$	−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
$288$	1.16003	+	0.669667i	0.0683555	+	0.0394605i
$289$		−	9.08150i		−	0.534206i
$290$	10.9806	−	13.4994i	0.644802	−	0.792712i
$291$		−	13.8280i		−	0.810611i
$292$	−1.31641	−	4.91250i	−0.0770369	−	0.287483i
$293$	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
$298$	−4.90509	+	2.83202i	−0.284144	+	0.164055i
$299$	−2.13673			−0.123571
$300$	−9.86456	+	15.0456i	−0.569531	+	0.868656i
$301$	0.846487			0.0487907
$302$	22.7814	−	13.1532i	1.31092	−	0.756880i
$303$	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	−0.611065	−	0.791580i	$-0.709259\pi$
$307$	3.16288	−	3.16288i	0.180515	−	0.180515i	0.791580	+	0.611065i	$0.209259\pi$
$308$	4.68536	−	1.25554i	0.266973	−	0.0715409i
$309$		−	16.9132i		−	0.962160i
$310$	−3.10426	+	3.81634i	−0.176310	+	0.216754i
$311$			9.01815i			0.511372i	0.966760	+	0.255686i	$0.0823014\pi$
$311$			9.01815i			0.511372i	−0.966760	+	0.255686i	$0.917699\pi$
$312$	−2.15602		6.49722e-5i	−0.122061		3.67833e-6i
$313$	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	$-0.546757\pi$
$318$	1.25614	+	2.17564i	0.0704406	+	0.122004i
$319$	13.6559			0.764581
$320$	16.7141	−	6.37497i	0.934344	−	0.356372i
$321$	−30.8452			−1.72161
$322$	3.48520	+	6.03640i	0.194223	+	0.336395i
$323$	−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
$328$	25.4267		0.000766241i	1.40395		4.23086e-5i
$329$			10.0299i			0.552969i
$330$	−14.0445	+	1.44508i	−0.773123	+	0.0795489i
$331$		−	3.28873i		−	0.180765i	−0.995907	−	0.0903826i	$-0.971191\pi$
$331$		−	3.28873i		−	0.180765i	0.995907	−	0.0903826i	$-0.0288090\pi$
$332$	2.09896	−	0.562460i	0.115195	−	0.0308690i
$333$	−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	$0.599641\pi$
$338$	−15.7017	+	9.06561i	−0.854062	+	0.493104i
$339$	−13.4770			−0.731968
$340$	−10.1972	+	7.37481i	−0.553019	+	0.399955i
$341$	−3.86057			−0.209062
$342$	0.289998	−	0.167434i	0.0156813	−	0.00905381i
$343$	−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	−0.245506	−	0.969395i	$-0.578954\pi$
$347$	13.4846	−	13.4846i	0.723889	−	0.723889i	0.969395	+	0.245506i	$0.0789541\pi$
$348$	5.12506	+	19.1254i	0.274732	+	1.02523i
$349$			19.5025i			1.04394i	0.852962	+	0.521972i	$0.174804\pi$
$349$			19.5025i			1.04394i	−0.852962	+	0.521972i	$0.825196\pi$
$350$	−6.17115	+	3.11035i	−0.329862	+	0.166255i
$351$		−	2.10631i		−	0.112427i
$352$	12.1578	+	7.01848i	0.648011	+	0.374086i
$353$	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
$358$	−15.6156	−	27.0463i	−0.825308	−	1.42944i
$359$	−0.969375			−0.0511616			−0.0255808	−	0.999673i	$-0.508144\pi$
$359$	−0.969375			−0.0511616			−0.0255808	+	0.999673i	$0.508144\pi$
$360$	−0.533643	−	1.39924i	−0.0281254	−	0.0737467i
$361$	1.00000			0.0526316
$362$	−16.0283	−	27.7612i	−0.842428	−	1.45910i
$363$	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	−0.208196	−	0.978087i	$-0.566759\pi$
$367$	14.7490	−	14.7490i	0.769891	−	0.769891i	0.978087	+	0.208196i	$0.0667593\pi$
$368$	−5.22024	+	19.4853i	−0.272124	+	1.01574i
$369$		−	2.12861i		−	0.110811i
$370$	0.720134	+	6.99887i	0.0374380	+	0.363854i
$371$			0.964989i			0.0500997i
$372$	−1.44888	−	5.40685i	−0.0751207	−	0.280332i
$373$	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
$378$	−5.95045	+	3.43558i	−0.306058	+	0.176707i
$379$	−30.5819			−1.57089			−0.785443	−	0.618934i	$-0.787565\pi$
$379$	−30.5819			−1.57089			−0.785443	+	0.618934i	$0.787565\pi$
$380$	0.709214	−	4.41554i	0.0363819	−	0.226513i
$381$	3.60709			0.184797
$382$	−33.6658	+	19.4374i	−1.72249	+	0.994505i
$383$	16.6482	+	16.6482i	0.850683	+	0.850683i	0.990217	−	0.139534i	$-0.0445604\pi$
$383$	16.6482	+	16.6482i	0.850683	+	0.850683i	−0.139534	+	0.990217i	$0.544560\pi$
$384$	−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
$388$	14.8482	−	3.97888i	0.753803	−	0.201997i
$389$		−	1.92974i		−	0.0978417i	−0.998803	−	0.0489209i	$-0.984422\pi$
$389$		−	1.92974i		−	0.0978417i	0.998803	−	0.0489209i	$-0.0155782\pi$
$390$	1.86999	+	1.52107i	0.0946906	+	0.0770226i
$391$		−	14.1913i		−	0.717683i
$392$	−0.000515236	−	17.0974i	−2.60233e−5	−	0.863550i
$393$	−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	$0.760869\pi$
$398$	8.37918	+	14.5128i	0.420011	+	0.727463i
$399$	1.75830			0.0880249
$400$	−18.9940	−	6.26312i	−0.949702	−	0.313156i
$401$	31.1787			1.55699			0.778496	−	0.627649i	$-0.215983\pi$
$401$	31.1787			1.55699			0.778496	+	0.627649i	$0.215983\pi$
$402$	16.3406	+	28.3020i	0.814993	+	1.41158i
$403$	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
$408$	−0.000431518	−	14.3194i	−2.13633e−5	−	0.708914i
$409$			4.25198i			0.210247i	0.994459	+	0.105123i	$0.0335238\pi$
$409$			4.25198i			0.210247i	−0.994459	+	0.105123i	$0.966476\pi$
$410$	−22.0534	−	17.9386i	−1.08914	−	0.885922i
$411$		−	4.17156i		−	0.205768i
$412$	18.1611	−	4.86663i	0.894731	−	0.239762i
$413$	−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
$418$	3.03934	−	1.75480i	0.148659	−	0.0858302i
$419$	26.0973			1.27493			0.637467	−	0.770477i	$-0.279982\pi$
$419$	26.0973			1.27493			0.637467	+	0.770477i	$0.279982\pi$
$420$	1.24701	−	7.76383i	0.0608477	−	0.378836i
$421$	−24.1130			−1.17520			−0.587599	−	0.809152i	$-0.699927\pi$
$421$	−24.1130			−1.17520			−0.587599	+	0.809152i	$0.699927\pi$
$422$	2.34003	−	1.35105i	0.113911	−	0.0657681i
$423$	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
$428$	−8.87543	−	33.1209i	−0.429010	−	1.60096i
$429$			1.89166i			0.0913303i
$430$	−0.280339	−	2.72457i	−0.0135191	−	0.131391i
$431$			1.00295i			0.0483106i	0.999708	+	0.0241553i	$0.00768962\pi$
$431$			1.00295i			0.0483106i	−0.999708	+	0.0241553i	$0.992310\pi$
$432$	−19.2079	−	5.14592i	−0.924141	−	0.247583i
$433$	−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
$438$	−3.23505	−	5.60314i	−0.154577	−	0.267728i
$439$	27.5639			1.31555			0.657777	−	0.753213i	$-0.271497\pi$
$439$	27.5639			1.31555			0.657777	+	0.753213i	$0.271497\pi$
$440$	−5.59287	−	14.6649i	−0.266630	−	0.699119i
$441$	−1.43132			−0.0681582
$442$	0.843073	+	1.46021i	0.0401009	+	0.0694552i
$443$	24.8144	+	24.8144i	1.17897	+	1.17897i	0.980008	+	0.198960i	$0.0637563\pi$
$443$	24.8144	+	24.8144i	1.17897	+	1.17897i	0.198960	+	0.980008i	$0.436244\pi$
$444$	−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
$448$	−5.52820	+	5.52887i	−0.261183	+	0.261215i
$449$		−	17.5308i		−	0.827330i	−0.910429	−	0.413665i	$-0.864248\pi$
$449$		−	17.5308i		−	0.827330i	0.910429	−	0.413665i	$-0.135752\pi$
$450$	−0.524370	+	1.59008i	−0.0247190	+	0.0749572i
$451$		−	22.3090i		−	1.05049i
$452$	−3.87788	−	14.4713i	−0.182400	−	0.680671i
$453$	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	$0.901028\pi$
$458$	2.21055	−	1.27629i	0.103292	−	0.0596371i
$459$	13.9892			0.652961
$460$	18.2750	−	13.2169i	0.852077	−	0.616240i
$461$	−20.4762			−0.953670			−0.476835	−	0.878993i	$-0.658216\pi$
$461$	−20.4762			−0.953670			−0.476835	+	0.878993i	$0.658216\pi$
$462$	5.34406	−	3.08546i	0.248628	−	0.143549i
$463$	28.9404	+	28.9404i	1.34497	+	1.34497i	0.891032	+	0.453941i	$0.149982\pi$
$463$	28.9404	+	28.9404i	1.34497	+	1.34497i	0.453941	+	0.891032i	$0.350018\pi$
$464$	−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	−0.713359	−	0.700799i	$-0.752827\pi$
$467$	−0.271431	+	0.271431i	−0.0125603	+	0.0125603i	0.700799	+	0.713359i	$0.252827\pi$
$468$	−0.193809	+	0.0519351i	−0.00895883	+	0.00240070i
$469$			12.5532i			0.579651i
$470$	32.2832	−	3.32171i	1.48911	−	0.153219i
$471$		−	9.84876i		−	0.453807i
$472$	−17.8465		0.000537811i	−0.821454		2.47547e-5i
$473$	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
$478$	10.1399	+	17.5625i	0.463790	+	0.803290i
$479$	−2.06918			−0.0945434			−0.0472717	−	0.998882i	$-0.515053\pi$
$479$	−2.06918			−0.0945434			−0.0472717	+	0.998882i	$0.515053\pi$
$480$	18.4396	−	13.3367i	0.841647	−	0.608735i
$481$	0.942683			0.0429826
$482$	−7.74778	−	13.4192i	−0.352902	−	0.611229i
$483$	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	−0.788567	−	0.614949i	$-0.789177\pi$
$487$	−3.83141	+	3.83141i	−0.173618	+	0.173618i	0.614949	+	0.788567i	$0.289177\pi$
$488$	30.9966		0.000934091i	1.40315		4.22843e-5i
$489$		−	14.3921i		−	0.650833i
$490$	−12.0622	+	14.8292i	−0.544917	+	0.669914i
$491$			7.97842i			0.360061i	0.983661	+	0.180030i	$0.0576196\pi$
$491$			7.97842i			0.360061i	−0.983661	+	0.180030i	$0.942380\pi$
$492$	31.2445	−	8.37261i	1.40861	−	0.377466i
$493$	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
$498$	2.39405	−	1.38224i	0.107280	−	0.0619394i
$499$	−23.9622			−1.07270			−0.536349	−	0.843996i	$-0.680197\pi$
$499$	−23.9622			−1.07270			−0.536349	+	0.843996i	$0.680197\pi$
$500$	12.0550	+	18.8329i	0.539115	+	0.842232i
$501$	18.7570			0.838002
$502$	−37.9840	+	21.9306i	−1.69531	+	0.978808i
$503$	−11.9399	−	11.9399i	−0.532373	−	0.532373i	0.388905	−	0.921278i	$-0.372853\pi$
$503$	−11.9399	−	11.9399i	−0.532373	−	0.532373i	−0.921278	+	0.388905i	$0.872853\pi$
$504$	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
$508$	1.03791	+	3.87322i	0.0460498	+	0.171846i
$509$			23.3369i			1.03439i	0.855868	+	0.517195i	$0.173024\pi$
$509$			23.3369i			1.03439i	−0.855868	+	0.517195i	$0.826976\pi$
$510$	−10.1023	+	12.4197i	−0.447338	+	0.549952i
$511$		−	2.48523i		−	0.109940i
$512$	−22.6274	+	0.00204565i	−1.00000	+	9.04058e-5i
$513$	−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
$518$	−1.53760	−	2.66313i	−0.0675581	−	0.117011i
$519$	−12.9850			−0.569978
$520$	−1.09522	+	2.44563i	−0.0480287	+	0.107248i
$521$	28.6568			1.25548			0.627739	−	0.778424i	$-0.283981\pi$
$521$	28.6568			1.25548			0.627739	+	0.778424i	$0.283981\pi$
$522$	0.921356	+	1.59580i	0.0403266	+	0.0698462i
$523$	17.5067	+	17.5067i	0.765515	+	0.765515i	0.977313	−	0.211798i	$-0.0679319\pi$
$523$	17.5067	+	17.5067i	0.765515	+	0.765515i	−0.211798	+	0.977313i	$0.567932\pi$
$524$	−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
$528$	17.2505	+	4.62151i	0.750731	+	0.201125i
$529$			2.43310i			0.105787i
$530$	3.10599	−	0.319584i	0.134916	−	0.0138819i
$531$			1.49404i			0.0648356i
$532$	0.505934	+	1.88802i	0.0219350	+	0.0818561i
$533$	−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
$538$	−8.94196	+	5.16276i	−0.385515	+	0.222583i
$539$	−15.0010			−0.646141
$540$	13.0287	+	18.0148i	0.560665	+	0.775234i
$541$	−25.5607			−1.09894			−0.549470	−	0.835513i	$-0.685170\pi$
$541$	−25.5607			−1.09894			−0.549470	+	0.835513i	$0.685170\pi$
$542$	10.2364	−	5.91012i	0.439691	−	0.253861i
$543$	−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	−0.990287	−	0.139041i	$-0.955598\pi$
$547$	−19.9090	+	19.9090i	−0.851245	+	0.851245i	0.139041	+	0.990287i	$0.455598\pi$
$548$	4.47933	−	1.20033i	0.191348	−	0.0512755i
$549$		−	2.59490i		−	0.110748i
$550$	−5.49568	+	16.6649i	−0.234337	+	0.710595i
$551$			5.50279i			0.234427i
$552$	0.000773351		25.6627i	3.29160e−5		1.09227i
$553$	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	$0.505518\pi$
$558$	−0.260471	−	0.451139i	−0.0110266	−	0.0190982i
$559$	−0.366975			−0.0155214
$560$	8.69545	−	0.894964i	0.367450	−	0.0378192i
$561$	−12.5636			−0.530436
$562$	7.54068	+	13.0605i	0.318084	+	0.550925i
$563$	28.9631	+	28.9631i	1.22065	+	1.22065i	0.967402	+	0.253245i	$0.0814978\pi$
$563$	28.9631	+	28.9631i	1.22065	+	1.22065i	0.253245	+	0.967402i	$0.418502\pi$
$564$	−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
$568$	−0.000656942	−	21.7998i	−2.75647e−5	−	0.914698i
$569$			28.7179i			1.20392i	0.798528	+	0.601958i	$0.205612\pi$
$569$			28.7179i			1.20392i	−0.798528	+	0.601958i	$0.794388\pi$
$570$	−0.582311	−	5.65939i	−0.0243903	−	0.237046i
$571$		−	22.1834i		−	0.928346i	−0.885744	−	0.464173i	$-0.846352\pi$
$571$		−	22.1834i		−	0.928346i	0.885744	−	0.464173i	$-0.153648\pi$
$572$	−2.03123	+	0.544309i	−0.0849298	+	0.0227587i
$573$	−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	$0.466459\pi$
$578$	11.1225	−	6.42170i	0.462633	−	0.267107i
$579$	−31.5578			−1.31150
$580$	24.2978	+	3.90265i	1.00891	+	0.162049i
$581$	1.06186			0.0440534
$582$	16.9357	−	9.77803i	0.702006	−	0.405313i
$583$	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	−0.464760	−	0.885436i	$-0.653860\pi$
$587$	10.1922	−	10.1922i	0.420676	−	0.420676i	0.885436	+	0.464760i	$0.153860\pi$
$588$	−5.62991	−	21.0094i	−0.232173	−	0.866414i
$589$		−	1.55566i		−	0.0641000i
$590$	15.4789	+	12.5908i	0.637257	+	0.518353i
$591$		−	0.127310i		−	0.00523684i
$592$	2.30306	−	8.59653i	0.0946553	−	0.353315i
$593$	−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
$598$	−1.51093	−	2.61694i	−0.0617864	−	0.107015i
$599$	−27.0682			−1.10598			−0.552988	−	0.833189i	$-0.686512\pi$
$599$	−27.0682			−1.10598			−0.552988	+	0.833189i	$0.686512\pi$
$600$	−25.4023	−	1.44250i	−1.03704	−	0.0588898i
$601$	2.99835			0.122305			0.0611527	−	0.998128i	$-0.480522\pi$
$601$	2.99835			0.122305			0.0611527	+	0.998128i	$0.480522\pi$
$602$	0.598567	+	1.03673i	0.0243958	+	0.0422538i
$603$	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	−0.912499	−	0.409078i	$-0.865850\pi$
$607$	−12.4030	+	12.4030i	−0.503421	+	0.503421i	0.409078	+	0.912499i	$0.365850\pi$
$608$	−2.82818	+	4.89912i	−0.114698	+	0.198686i
$609$			9.67554i			0.392073i
$610$	−26.8844	−	21.8681i	−1.08852	−	0.885414i
$611$		−	4.34825i		−	0.175911i
$612$	−0.344931	−	1.28720i	−0.0139430	−	0.0520318i
$613$	−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	$0.644229\pi$
$618$	20.7143	−	11.9597i	0.833250	−	0.481088i
$619$	21.9269			0.881318			0.440659	−	0.897675i	$-0.354745\pi$
$619$	21.9269			0.881318			0.440659	+	0.897675i	$0.354745\pi$
$620$	−6.86910	−	1.10330i	−0.275870	−	0.0443095i
$621$	−25.0710			−1.00606
$622$	−11.0449	+	6.37691i	−0.442859	+	0.255691i
$623$	−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
$628$	10.5754	−	2.83389i	0.422004	−	0.113085i
$629$			6.26089i			0.249638i
$630$	−0.0749006	−	0.727948i	−0.00298411	−	0.0290021i
$631$		−	8.55264i		−	0.340475i	−0.985403	−	0.170238i	$-0.945546\pi$
$631$		−	8.55264i		−	0.340475i	0.985403	−	0.170238i	$-0.0544535\pi$
$632$	2.32850		7.01700e-5i	0.0926228		2.79121e-6i
$633$	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
$638$	9.65631	+	16.7248i	0.382297	+	0.662143i
$639$	−1.82498			−0.0721952
$640$	19.6265	+	15.9625i	0.775805	+	0.630972i
$641$	1.23653			0.0488399			0.0244199	−	0.999702i	$-0.492226\pi$
$641$	1.23653			0.0488399			0.0244199	+	0.999702i	$0.492226\pi$
$642$	−21.8112	−	37.7773i	−0.860820	−	1.49095i
$643$	−2.39601	−	2.39601i	−0.0944892	−	0.0944892i	0.658282	−	0.752771i	$-0.271283\pi$
$643$	−2.39601	−	2.39601i	−0.0944892	−	0.0944892i	−0.752771	+	0.658282i	$0.771283\pi$
$644$	−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	−0.464147	−	0.885758i	$-0.653639\pi$
$647$	10.7242	−	10.7242i	0.421611	−	0.421611i	0.885758	+	0.464147i	$0.153639\pi$
$648$	−27.3064		0.000822887i	−1.07270		3.23261e-5i
$649$			15.6583i			0.614643i
$650$	2.67536	−	1.34842i	0.104936	−	0.0528893i
$651$		−	2.73532i		−	0.107206i
$652$	15.4539	−	4.14120i	0.605222	−	0.162182i
$653$	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
$658$	−12.2841	+	7.09237i	−0.478882	+	0.276489i
$659$	8.59030			0.334631			0.167315	−	0.985903i	$-0.446490\pi$
$659$	8.59030			0.334631			0.167315	+	0.985903i	$0.446490\pi$
$660$	−11.7010	−	16.1790i	−0.455459	−	0.629765i
$661$	35.7451			1.39032			0.695161	−	0.718854i	$-0.255333\pi$
$661$	35.7451			1.39032			0.695161	+	0.718854i	$0.255333\pi$
$662$	4.02784	−	2.32553i	0.156546	−	0.0903841i
$663$	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
$668$	5.39717	+	20.1409i	0.208823	+	0.779274i
$669$		−	13.3567i		−	0.516399i
$670$	40.4046	−	4.15734i	1.56097	−	0.160612i
$671$		−	27.1960i		−	1.04989i
$672$	−4.97278	+	8.61411i	−0.191829	+	0.332296i
$673$	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	$0.482693\pi$
$678$	−9.52982	−	16.5057i	−0.365990	−	0.633899i
$679$	7.51169			0.288272
$680$	−16.2428	−	7.27400i	−0.622884	−	0.278945i
$681$	−43.5306			−1.66810
$682$	−2.72988	−	4.72819i	−0.104533	−	0.181052i
$683$	7.17226	+	7.17226i	0.274439	+	0.274439i	0.830884	−	0.556445i	$-0.187835\pi$
$683$	7.17226	+	7.17226i	0.274439	+	0.274439i	−0.556445	+	0.830884i	$0.687835\pi$
$684$	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
$688$	−0.896554	+	3.34652i	−0.0341808	+	0.127585i
$689$		−	0.418348i		−	0.0159378i
$690$	18.1050	−	22.2581i	0.689246	−	0.847351i
$691$		−	28.5788i		−	1.08719i	−0.839348	−	0.543594i	$-0.817063\pi$
$691$		−	28.5788i		−	1.08719i	0.839348	−	0.543594i	$-0.182937\pi$
$692$	−3.73632	−	13.9430i	−0.142033	−	0.530033i
$693$	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
$698$	−23.8854	+	13.7906i	−0.904077	+	0.521981i
$699$	24.0877			0.911082
$700$	−8.17310	−	5.35866i	−0.308914	−	0.202538i
$701$	−27.2769			−1.03023			−0.515117	−	0.857120i	$-0.672251\pi$
$701$	−27.2769			−1.03023			−0.515117	+	0.857120i	$0.672251\pi$
$702$	2.57968	−	1.48941i	0.0973637	−	0.0562143i
$703$	−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
$708$	−21.9299	+	5.87658i	−0.824178	+	0.220856i
$709$		−	36.6344i		−	1.37583i	−0.725789	−	0.687917i	$-0.758525\pi$
$709$		−	36.6344i		−	1.37583i	0.725789	−	0.687917i	$-0.241475\pi$
$710$	−15.3798	+	18.9077i	−0.577192	+	0.709593i
$711$		−	0.194932i		−	0.00731052i
$712$	−0.000881157	−	29.2401i	−3.30228e−5	−	1.09582i
$713$	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
$718$	−0.685463	−	1.18723i	−0.0255813	−	0.0443070i
$719$	25.4725			0.949964			0.474982	−	0.879996i	$-0.342455\pi$
$719$	25.4725			0.949964			0.474982	+	0.879996i	$0.342455\pi$
$720$	1.33636	−	1.64300i	0.0498031	−	0.0612312i
$721$	9.18766			0.342166
$722$	0.707119	+	1.22474i	0.0263162	+	0.0455800i
$723$	−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	−0.597398	−	0.801945i	$-0.703799\pi$
$727$	5.51517	−	5.51517i	0.204547	−	0.204547i	0.801945	+	0.597398i	$0.203799\pi$
$728$	−3.52944e−5	−	1.17120i	−1.30810e−6	−	0.0434076i
$729$		−	24.5458i		−	0.909105i
$730$	−7.99916	+	0.823057i	−0.296062	+	0.0304627i
$731$		−	2.43729i		−	0.0901463i
$732$	38.0888	−	10.2067i	1.40780	−	0.377250i
$733$	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
$738$	2.60699	−	1.50518i	0.0959647	−	0.0554065i
$739$	−37.1286			−1.36580			−0.682899	−	0.730513i	$-0.739281\pi$
$739$	−37.1286			−1.36580			−0.682899	+	0.730513i	$0.739281\pi$
$740$	−8.06256	+	5.83101i	−0.296386	+	0.214352i
$741$	−0.762268			−0.0280026
$742$	−1.18186	+	0.682362i	−0.0433874	+	0.0250503i
$743$	−33.2064	−	33.2064i	−1.21822	−	1.21822i	−0.968254	−	0.249970i	$-0.919579\pi$
$743$	−33.2064	−	33.2064i	−1.21822	−	1.21822i	−0.249970	−	0.968254i	$-0.580421\pi$
$744$	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
$748$	−3.61507	−	13.4905i	−0.132180	−	0.493262i
$749$		−	16.7558i		−	0.612244i
$750$	21.0140	+	19.1731i	0.767323	+	0.700102i
$751$			40.6688i			1.48403i	0.670385	+	0.742013i	$0.266129\pi$
$751$			40.6688i			1.48403i	−0.670385	+	0.742013i	$0.733871\pi$
$752$	−39.6526	−	10.6232i	−1.44598	−	0.387387i
$753$	−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	$0.895811\pi$
$758$	−21.6250	−	37.4548i	−0.785457	−	1.36042i
$759$	22.5161			0.817281
$760$	5.90938	−	2.25371i	0.214356	−	0.0817508i
$761$	25.4641			0.923073			0.461537	−	0.887121i	$-0.347298\pi$
$761$	25.4641			0.923073			0.461537	+	0.887121i	$0.347298\pi$
$762$	2.55064	+	4.41774i	0.0924001	+	0.160038i
$763$	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
$768$	−27.8043	+	7.45252i	−1.00330	+	0.268920i
$769$		−	14.3062i		−	0.515897i	−0.966159	−	0.257948i	$-0.916954\pi$
$769$		−	14.3062i		−	0.515897i	0.966159	−	0.257948i	$-0.0830464\pi$
$770$	−0.785000	−	7.62929i	−0.0282894	−	0.274941i
$771$

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)

\(f(q)\)	\(=\)	\(q+(0.707119 + 1.22474i) q^{2} +(1.27216 + 1.27216i) q^{3} +(-0.999965 + 1.73207i) q^{4} +(2.08931 - 0.796745i) q^{5} +(-0.658494 + 2.45763i) q^{6} +(-0.691067 + 0.691067i) q^{7} +(-2.82843 + 8.52354e-5i) q^{8} +0.236784i q^{9} +O(q^{10})\)	\(q+(0.707119 + 1.22474i) 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} +(-2.82843 + 8.52354e-5i) q^{8} +0.236784i q^{9} +(2.45319 + 1.99546i) q^{10} +2.48162i q^{11} +(-3.47559 + 0.931356i) 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} +(-0.289998 + 0.167434i) q^{18} -1.00000 q^{19} +(-0.709214 + 4.41554i) q^{20} -1.75830 q^{21} +(-3.03934 + 1.75480i) 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} +(-0.505934 - 1.88802i) q^{28} -5.50279i q^{29} +(0.582311 + 5.65939i) q^{30} +1.55566i q^{31} +(2.82818 - 4.89912i) 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} +(-0.707119 - 1.22474i) q^{38} +0.762268 q^{39} +(-5.90938 + 2.25371i) q^{40} -8.98970 q^{41} +(-1.24333 - 2.15345i) 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} +(1.86229 - 6.95129i) q^{48} +6.04485i q^{49} +(6.71534 + 2.21455i) q^{50} +5.06266i q^{51} +(0.219336 + 0.818507i) 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} +(6.73948 - 3.89113i) q^{58} +6.30971 q^{59} +(-6.51951 + 4.71504i) q^{60} -10.9589 q^{61} +(-1.90528 + 1.10004i) 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} +(-5.43617 + 1.45673i) q^{68} -9.07312i q^{69} +(-3.07432 + 0.316325i) q^{70} +7.70738i q^{71} +(-2.01824e-5 - 0.669725i) 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} +(0.539014 + 0.933579i) q^{78} -0.823249 q^{79} +(-6.93884 - 5.64380i) q^{80} +9.65428 q^{81} +(-6.35679 - 11.0100i) 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} +(-0.000211522 - 7.01909i) q^{88} +10.3379i q^{89} +(-0.472492 + 0.580876i) q^{90} +0.414082i q^{91} +(9.74252 - 2.61071i) 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} +(-7.40336 + 4.27443i) 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	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more