LMFDB - Embedded newform 507.2.p.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

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

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	507.25
Dual form			507.2.p.a.142.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.41243 - 0.914913i) q^{2} +(0.568065 + 0.822984i) q^{3} +(3.48572 + 3.08808i) q^{4} +(-3.08975 - 0.375164i) q^{5} +(-0.617456 - 2.50512i) q^{6} +(-0.149094 - 0.284076i) q^{7} +(-3.18567 - 6.06979i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(7.11057 + 3.73191i) q^{10} +(-0.968722 + 0.367388i) q^{11} +(-0.561324 + 4.62292i) q^{12} +(0.206269 - 3.59965i) q^{13} +(0.0997749 + 0.821720i) q^{14} +(-1.44643 - 2.75594i) q^{15} +(1.00922 + 8.31169i) q^{16} +(2.88757 - 1.51551i) q^{17} +(1.71092 - 1.93123i) q^{18} +1.14795i q^{19} +(-9.61148 - 10.8491i) q^{20} +(0.149094 - 0.284076i) q^{21} +2.67310 q^{22} +7.25822 q^{23} +(3.18567 - 6.06979i) q^{24} +(4.55112 + 1.12175i) q^{25} +(-3.79097 + 8.49517i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(0.357546 - 1.45062i) q^{28} +(-3.47071 + 9.15150i) q^{29} +(0.967958 + 7.97185i) q^{30} +(1.05559 + 4.28271i) q^{31} +(1.88879 - 7.66312i) q^{32} +(-0.852651 - 0.588542i) q^{33} +(-8.35261 + 1.01419i) q^{34} +(0.354090 + 0.933658i) q^{35} +(-4.12346 + 2.16416i) q^{36} +(1.85815 + 7.53882i) q^{37} +(1.05027 - 2.76934i) q^{38} +(3.07963 - 1.87508i) q^{39} +(7.56577 + 19.9493i) q^{40} +(3.92138 - 2.70674i) q^{41} +(-0.619584 + 0.548903i) q^{42} +(-2.51080 - 0.618857i) q^{43} +(-4.51122 - 1.71088i) q^{44} +(1.44643 - 2.75594i) q^{45} +(-17.5099 - 6.64064i) q^{46} +(7.85034 + 8.86121i) q^{47} +(-6.26708 + 5.55215i) q^{48} +(3.91798 - 5.67618i) q^{49} +(-9.95295 - 6.87002i) q^{50} +(2.88757 + 1.51551i) q^{51} +(11.8350 - 11.9104i) q^{52} +(6.05895 - 3.17998i) q^{53} +(2.56128 + 0.310996i) q^{54} +(3.13094 - 0.771708i) q^{55} +(-1.24931 + 1.80994i) q^{56} +(-0.944742 + 0.652108i) q^{57} +(16.7457 - 18.9019i) q^{58} +(5.17654 + 0.628546i) q^{59} +(3.46871 - 14.0731i) q^{60} +(-2.99585 - 1.57234i) q^{61} +(1.37177 - 11.2975i) q^{62} +(0.318485 - 0.0386711i) q^{63} +(-2.05515 + 2.97740i) q^{64} +(-1.98778 + 11.0446i) q^{65} +(1.51849 + 2.19992i) q^{66} +(5.68622 + 6.41841i) q^{67} +(14.7453 + 3.63439i) q^{68} +(4.12314 + 5.97339i) q^{69} -2.57634i q^{70} +(6.11068 - 4.21790i) q^{71} +(6.80500 - 0.826277i) q^{72} +(0.635825 - 0.241137i) q^{73} +(2.41471 - 19.8869i) q^{74} +(1.66215 + 4.38273i) q^{75} +(-3.54495 + 4.00142i) q^{76} +(0.248797 + 0.220415i) q^{77} +(-9.14491 + 1.70590i) q^{78} +(-3.16272 + 2.80193i) q^{79} -26.0597i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-11.9365 + 2.94208i) q^{82} +(-0.209763 - 0.144789i) q^{83} +(1.39695 - 0.529793i) q^{84} +(-9.49044 + 3.59925i) q^{85} +(5.49093 + 3.79011i) q^{86} +(-9.50312 + 2.34231i) q^{87} +(5.31599 + 4.70956i) q^{88} -16.8423i q^{89} +(-6.01084 + 5.32514i) q^{90} +(-1.05332 + 0.478091i) q^{91} +(25.3001 + 22.4139i) q^{92} +(-2.92496 + 3.30160i) q^{93} +(-10.8312 - 28.5594i) q^{94} +(0.430668 - 3.54687i) q^{95} +(7.37958 - 2.79871i) q^{96} +(15.0456 - 1.82687i) q^{97} +(-14.6451 + 10.1088i) q^{98} -1.03605i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

Coefficient data

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

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

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

$2$	−2.41243	−	0.914913i	−1.70584	−	0.646941i	−0.707625	−	0.706589i	$-0.750233\pi$
$2$	−2.41243	−	0.914913i	−1.70584	−	0.646941i	−0.998220	+	0.0596471i	$0.981002\pi$
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$4$	3.48572	+	3.08808i	1.74286	+	1.54404i
$5$	−3.08975	−	0.375164i	−1.38178	−	0.167778i	−0.604335	−	0.796730i	$-0.706561\pi$
$5$	−3.08975	−	0.375164i	−1.38178	−	0.167778i	−0.777444	+	0.628952i	$0.783484\pi$
$6$	−0.617456	−	2.50512i	−0.252076	−	1.02271i
$7$	−0.149094	−	0.284076i	−0.0563524	−	0.107370i	0.855651	−	0.517553i	$-0.173157\pi$
$7$	−0.149094	−	0.284076i	−0.0563524	−	0.107370i	−0.912003	+	0.410183i	$0.865465\pi$
$8$	−3.18567	−	6.06979i	−1.12630	−	2.14599i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	7.11057	+	3.73191i	2.24856	+	1.18013i
$11$	−0.968722	+	0.367388i	−0.292081	+	0.110772i	−0.496293	−	0.868155i	$-0.665306\pi$
$11$	−0.968722	+	0.367388i	−0.292081	+	0.110772i	0.204213	+	0.978927i	$0.434537\pi$
$12$	−0.561324	+	4.62292i	−0.162040	+	1.33452i
$13$	0.206269	−	3.59965i	0.0572088	−	0.998362i
$13$	0.206269	−	3.59965i	0.0572088	−	0.998362i
$14$	0.0997749	+	0.821720i	0.0266660	+	0.219614i
$15$	−1.44643	−	2.75594i	−0.373466	−	0.711579i
$16$	1.00922	+	8.31169i	0.252305	+	2.07792i
$17$	2.88757	−	1.51551i	0.700338	−	0.367566i	−0.0766698	−	0.997057i	$-0.524429\pi$
$17$	2.88757	−	1.51551i	0.700338	−	0.367566i	0.777008	+	0.629491i	$0.216736\pi$
$18$	1.71092	−	1.93123i	0.403267	−	0.455194i
$19$			1.14795i			0.263357i	0.991292	+	0.131679i	$0.0420367\pi$
$19$			1.14795i			0.263357i	−0.991292	+	0.131679i	$0.957963\pi$
$20$	−9.61148	−	10.8491i	−2.14919	−	2.42594i
$21$	0.149094	−	0.284076i	0.0325350	−	0.0619904i
$22$	2.67310			0.569907
$23$	7.25822			1.51344			0.756721	−	0.653738i	$-0.226800\pi$
$23$	7.25822			1.51344			0.756721	+	0.653738i	$0.226800\pi$
$24$	3.18567	−	6.06979i	0.650272	−	1.23899i
$25$	4.55112	+	1.12175i	0.910224	+	0.224350i
$26$	−3.79097	+	8.49517i	−0.743471	+	1.66604i
$27$	−0.970942	+	0.239316i	−0.186858	+	0.0460563i
$28$	0.357546	−	1.45062i	0.0675699	−	0.274142i
$29$	−3.47071	+	9.15150i	−0.644494	+	1.69939i	0.0679748	+	0.997687i	$0.478346\pi$
$29$	−3.47071	+	9.15150i	−0.644494	+	1.69939i	−0.712469	+	0.701704i	$0.752423\pi$
$30$	0.967958	+	7.97185i	0.176724	+	1.45545i
$31$	1.05559	+	4.28271i	0.189590	+	0.769198i	0.986317	+	0.164859i	$0.0527168\pi$
$31$	1.05559	+	4.28271i	0.189590	+	0.769198i	−0.796727	+	0.604340i	$0.793437\pi$
$32$	1.88879	−	7.66312i	0.333894	−	1.35466i
$33$	−0.852651	−	0.588542i	−0.148427	−	0.102452i
$34$	−8.35261	+	1.01419i	−1.43246	+	0.173932i
$35$	0.354090	+	0.933658i	0.0598521	+	0.157817i
$36$	−4.12346	+	2.16416i	−0.687243	+	0.360693i
$37$	1.85815	+	7.53882i	0.305478	+	1.23937i	0.900212	+	0.435451i	$0.143411\pi$
$37$	1.85815	+	7.53882i	0.305478	+	1.23937i	−0.594734	+	0.803923i	$0.702743\pi$
$38$	1.05027	−	2.76934i	0.170377	−	0.449246i
$39$	3.07963	−	1.87508i	0.493135	−	0.300252i
$40$	7.56577	+	19.9493i	1.19625	+	3.15426i
$41$	3.92138	−	2.70674i	0.612417	−	0.422721i	−0.221071	−	0.975258i	$-0.570955\pi$
$41$	3.92138	−	2.70674i	0.612417	−	0.422721i	0.833489	+	0.552536i	$0.186340\pi$
$42$	−0.619584	+	0.548903i	−0.0956039	+	0.0846976i
$43$	−2.51080	−	0.618857i	−0.382894	−	0.0943748i	0.0431706	−	0.999068i	$-0.486254\pi$
$43$	−2.51080	−	0.618857i	−0.382894	−	0.0943748i	−0.426064	+	0.904693i	$0.640100\pi$
$44$	−4.51122	−	1.71088i	−0.680091	−	0.257925i
$45$	1.44643	−	2.75594i	0.215620	−	0.410831i
$46$	−17.5099	−	6.64064i	−2.58170	−	0.979109i
$47$	7.85034	+	8.86121i	1.14509	+	1.29254i	0.950174	+	0.311720i	$0.100905\pi$
$47$	7.85034	+	8.86121i	1.14509	+	1.29254i	0.194916	+	0.980820i	$0.437556\pi$
$48$	−6.26708	+	5.55215i	−0.904575	+	0.801384i
$49$	3.91798	−	5.67618i	0.559712	−	0.810883i
$50$	−9.95295	−	6.87002i	−1.40756	−	0.971568i
$51$	2.88757	+	1.51551i	0.404340	+	0.212214i
$52$	11.8350	−	11.9104i	1.64122	−	1.65167i
$53$	6.05895	−	3.17998i	0.832261	−	0.436804i	0.00592575	−	0.999982i	$-0.498114\pi$
$53$	6.05895	−	3.17998i	0.832261	−	0.436804i	0.826336	+	0.563178i	$0.190421\pi$
$54$	2.56128	+	0.310996i	0.348546	+	0.0423212i
$55$	3.13094	−	0.771708i	0.422176	−	0.104057i
$56$	−1.24931	+	1.80994i	−0.166946	+	0.241864i
$57$	−0.944742	+	0.652108i	−0.125134	+	0.0863738i
$58$	16.7457	−	18.9019i	2.19881	−	2.48195i
$59$	5.17654	+	0.628546i	0.673929	+	0.0818297i	0.450344	−	0.892855i	$-0.351301\pi$
$59$	5.17654	+	0.628546i	0.673929	+	0.0818297i	0.223584	+	0.974685i	$0.428224\pi$
$60$	3.46871	−	14.0731i	0.447808	−	1.81683i
$61$	−2.99585	−	1.57234i	−0.383579	−	0.201318i	0.261902	−	0.965095i	$-0.415650\pi$
$61$	−2.99585	−	1.57234i	−0.383579	−	0.201318i	−0.645480	+	0.763777i	$0.723343\pi$
$62$	1.37177	−	11.2975i	0.174215	−	1.43479i
$63$	0.318485	−	0.0386711i	0.0401253	−	0.00487209i
$64$	−2.05515	+	2.97740i	−0.256894	+	0.372175i
$65$	−1.98778	+	11.0446i	−0.246554	+	1.36992i
$66$	1.51849	+	2.19992i	0.186914	+	0.270791i
$67$	5.68622	+	6.41841i	0.694682	+	0.784134i	0.984955	−	0.172810i	$-0.0552847\pi$
$67$	5.68622	+	6.41841i	0.694682	+	0.784134i	−0.290273	+	0.956944i	$0.593746\pi$
$68$	14.7453	+	3.63439i	1.78813	+	0.440734i
$69$	4.12314	+	5.97339i	0.496367	+	0.719112i
$70$		−	2.57634i		−	0.307932i
$71$	6.11068	−	4.21790i	0.725204	−	0.500572i	−0.147353	−	0.989084i	$-0.547075\pi$
$71$	6.11068	−	4.21790i	0.725204	−	0.500572i	0.872557	+	0.488511i	$0.162460\pi$
$72$	6.80500	−	0.826277i	0.801977	−	0.0973777i
$73$	0.635825	−	0.241137i	0.0744177	−	0.0282229i	−0.317115	−	0.948387i	$-0.602714\pi$
$73$	0.635825	−	0.241137i	0.0744177	−	0.0282229i	0.391533	+	0.920164i	$0.371945\pi$
$74$	2.41471	−	19.8869i	0.280704	−	2.31181i
$75$	1.66215	+	4.38273i	0.191928	+	0.506074i
$76$	−3.54495	+	4.00142i	−0.406634	+	0.458995i
$77$	0.248797	+	0.220415i	0.0283530	+	0.0251186i
$78$	−9.14491	+	1.70590i	−1.03546	+	0.193155i
$79$	−3.16272	+	2.80193i	−0.355834	+	0.315241i	−0.822034	−	0.569438i	$-0.807161\pi$
$79$	−3.16272	+	2.80193i	−0.355834	+	0.315241i	0.466201	+	0.884679i	$0.345622\pi$
$80$		−	26.0597i		−	2.91356i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	−11.9365	+	2.94208i	−1.31816	+	0.324898i
$83$	−0.209763	−	0.144789i	−0.0230245	−	0.0158927i	0.556497	−	0.830850i	$-0.312145\pi$
$83$	−0.209763	−	0.144789i	−0.0230245	−	0.0158927i	−0.579521	+	0.814957i	$0.696760\pi$
$84$	1.39695	−	0.529793i	0.152420	−	0.0578051i
$85$	−9.49044	+	3.59925i	−1.02938	+	0.390393i
$86$	5.49093	+	3.79011i	0.592102	+	0.408698i
$87$	−9.50312	+	2.34231i	−1.01884	+	0.251122i
$88$	5.31599	+	4.70956i	0.566687	+	0.502040i
$89$		−	16.8423i		−	1.78528i	−0.450770	−	0.892640i	$-0.648851\pi$
$89$		−	16.8423i		−	1.78528i	0.450770	−	0.892640i	$-0.351149\pi$
$90$	−6.01084	+	5.32514i	−0.633598	+	0.561319i
$91$	−1.05332	+	0.478091i	−0.110418	+	0.0501175i
$92$	25.3001	+	22.4139i	2.63772	+	2.33682i
$93$	−2.92496	+	3.30160i	−0.303304	+	0.342360i
$94$	−10.8312	−	28.5594i	−1.11715	−	2.94568i
$95$	0.430668	−	3.54687i	0.0441856	−	0.363901i
$96$	7.37958	−	2.79871i	0.753175	−	0.285642i
$97$	15.0456	−	1.82687i	1.52765	−	0.185490i	0.686834	−	0.726814i	$-0.259000\pi$
$97$	15.0456	−	1.82687i	1.52765	−	0.185490i	0.840814	+	0.541324i	$0.182077\pi$
$98$	−14.6451	+	10.1088i	−1.47937	+	1.02114i
$99$		−	1.03605i		−	0.104127i
$100$	12.3999	+	17.9643i	1.23999	+	1.79643i
$101$	−11.4054	−	2.81117i	−1.13488	−	0.279722i	−0.373246	−	0.927733i	$-0.621755\pi$
$101$	−11.4054	−	2.81117i	−1.13488	−	0.279722i	−0.761631	+	0.648010i	$0.775601\pi$
$102$	−5.57949	−	6.29794i	−0.552452	−	0.623589i
$103$	5.45299	+	7.90002i	0.537299	+	0.778412i	0.993785	−	0.111319i	$-0.0355074\pi$
$103$	5.45299	+	7.90002i	0.537299	+	0.778412i	−0.456486	+	0.889731i	$0.650892\pi$
$104$	−22.5062	+	10.2153i	−2.20691	+	1.00169i
$105$	−0.567240	+	0.821789i	−0.0553569	+	0.0801984i
$106$	−17.5262	+	2.12807i	−1.70230	+	0.206696i
$107$	−0.303440	+	2.49905i	−0.0293346	+	0.241592i	0.970665	+	0.240437i	$0.0772908\pi$
$107$	−0.303440	+	2.49905i	−0.0293346	+	0.241592i	−0.999999	+	0.00115519i	$0.999632\pi$
$108$	−4.12346	−	2.16416i	−0.396780	−	0.208246i
$109$	−1.07000	+	4.34117i	−0.102488	+	0.415809i	−0.999666	−	0.0258606i	$-0.991767\pi$
$109$	−1.07000	+	4.34117i	−0.102488	+	0.415809i	0.897178	+	0.441669i	$0.145614\pi$
$110$	−8.25922	−	1.00285i	−0.787486	−	0.0956181i
$111$	−5.14877	+	5.81177i	−0.488700	+	0.551628i
$112$	2.21068	−	1.52592i	0.208889	−	0.144186i
$113$	−8.10208	+	11.7379i	−0.762180	+	1.10421i	0.229224	+	0.973374i	$0.426381\pi$
$113$	−8.10208	+	11.7379i	−0.762180	+	1.10421i	−0.991404	+	0.130835i	$0.958234\pi$
$114$	2.87574	−	0.708807i	0.269338	−	0.0663859i
$115$	−22.4261	−	2.72302i	−2.09124	−	0.253923i
$116$	−40.3585	+	21.1818i	−3.74719	+	1.96668i
$117$	3.29258	+	1.46932i	0.304399	+	0.135838i
$118$	−11.9130	−	6.25241i	−1.09668	−	0.575581i
$119$	−0.861040	−	0.594333i	−0.0789314	−	0.0544824i
$120$	−12.1201	+	17.5590i	−1.10641	+	1.60291i
$121$	−7.43017	+	6.58256i	−0.675470	+	0.598414i
$122$	5.78871	+	6.53410i	0.524085	+	0.591570i
$123$	4.45520	+	1.68963i	0.401712	+	0.152349i
$124$	−9.54586	+	18.1881i	−0.857243	+	1.63334i
$125$	0.909938	+	0.345094i	0.0813874	+	0.0308662i
$126$	−0.803702	−	0.198095i	−0.0715995	−	0.0176477i
$127$	13.0314	−	11.5448i	1.15635	−	1.02444i	0.157027	−	0.987594i	$-0.449809\pi$
$127$	13.0314	−	11.5448i	1.15635	−	1.02444i	0.999321	−	0.0368411i	$-0.0117295\pi$
$128$	−5.30877	+	3.66438i	−0.469234	+	0.323889i
$129$	−0.916988	−	2.41790i	−0.0807363	−	0.212884i
$130$	14.9003	−	24.8257i	1.30684	−	2.17736i
$131$	−1.79987	+	4.74588i	−0.157256	+	0.414649i	−0.990369	−	0.138453i	$-0.955787\pi$
$131$	−1.79987	+	4.74588i	−0.157256	+	0.414649i	0.833113	+	0.553102i	$0.186556\pi$
$132$	−1.15464	−	4.68455i	−0.100498	−	0.407738i
$133$	0.326104	−	0.171152i	0.0282768	−	0.0148408i
$134$	−7.84530	−	20.6863i	−0.677730	−	1.78703i
$135$	3.08975	−	0.375164i	0.265924	−	0.0322890i
$136$	−18.3977	−	12.6990i	−1.57759	−	1.08893i
$137$	1.52491	−	6.18679i	0.130282	−	0.528573i	−0.869140	−	0.494566i	$-0.835327\pi$
$137$	1.52491	−	6.18679i	0.130282	−	0.528573i	0.999422	−	0.0340070i	$-0.0108268\pi$
$138$	−4.48163	−	18.1827i	−0.381502	−	1.54781i
$139$	0.0844675	+	0.695653i	0.00716444	+	0.0590045i	0.995853	−	0.0909812i	$-0.0290003\pi$
$139$	0.0844675	+	0.695653i	0.00716444	+	0.0590045i	−0.988688	+	0.149986i	$0.952077\pi$
$140$	−1.64895	+	4.34793i	−0.139362	+	0.367467i
$141$	−2.83313	+	11.4944i	−0.238592	+	0.968007i
$142$	−18.6006	+	4.58463i	−1.56093	+	0.384734i
$143$	1.12265	+	3.56284i	0.0938805	+	0.297939i
$144$	−8.12944	−	2.00373i	−0.677453	−	0.166977i
$145$	14.1569	−	26.9738i	1.17567	−	2.24005i
$146$	−1.75450			−0.145204
$147$	6.89707			0.568861
$148$	−16.8035	+	32.0163i	−1.38124	+	2.63173i
$149$	12.6635	+	14.2942i	1.03744	+	1.17102i	0.985027	+	0.172398i	$0.0551516\pi$
$149$	12.6635	+	14.2942i	1.03744	+	1.17102i	0.0524093	+	0.998626i	$0.483310\pi$
$150$		−	12.0937i		−	0.987449i
$151$	−9.71859	+	10.9700i	−0.790888	+	0.892728i	−0.996300	−	0.0859478i	$-0.972608\pi$
$151$	−9.71859	+	10.9700i	−0.790888	+	0.892728i	0.205412	+	0.978676i	$0.434147\pi$
$152$	6.96779	−	3.65698i	0.565162	−	0.296620i
$153$	0.393083	+	3.23733i	0.0317789	+	0.261723i
$154$	−0.398544	−	0.759362i	−0.0321156	−	0.0611911i
$155$	−1.65481	−	13.6286i	−0.132917	−	1.09467i
$156$	16.5251	+	2.97414i	1.32307	+	0.238121i
$157$	2.03119	−	16.7284i	0.162107	−	1.33507i	−0.653704	−	0.756751i	$-0.726786\pi$
$157$	2.03119	−	16.7284i	0.162107	−	1.33507i	0.815810	−	0.578319i	$-0.196291\pi$
$158$	10.1934	−	3.86583i	0.810940	−	0.307549i
$159$	6.05895	+	3.17998i	0.480506	+	0.252189i
$160$	−8.71082	+	22.9686i	−0.688651	+	1.81582i
$161$	−1.08216	−	2.06188i	−0.0852861	−	0.162499i
$162$	1.19903	+	2.28456i	0.0942046	+	0.179492i
$163$	−5.48778	−	22.2648i	−0.429836	−	1.74391i	−0.642023	−	0.766686i	$-0.721904\pi$
$163$	−5.48778	−	22.2648i	−0.429836	−	1.74391i	0.212186	−	0.977229i	$-0.431942\pi$
$164$	22.0275	+	2.67462i	1.72006	+	0.208853i
$165$	2.41368	+	2.13833i	0.187905	+	0.166469i
$166$	0.373569	+	0.541208i	0.0289946	+	0.0420059i
$167$	−8.54970	−	3.24247i	−0.661595	−	0.250910i	0.000873323	−	1.00000i	$-0.499722\pi$
$167$	−8.54970	−	3.24247i	−0.661595	−	0.250910i	−0.662469	+	0.749090i	$0.730491\pi$
$168$	−2.19924			−0.169675
$169$	−12.9149	−	1.48499i	−0.993454	−	0.114230i
$170$	26.1880			2.00853
$171$	−1.07335	−	0.407068i	−0.0820810	−	0.0311292i
$172$	−6.84087	−	9.91072i	−0.521612	−	0.755685i
$173$	1.63673	+	1.45002i	0.124438	+	0.110243i	0.723047	−	0.690799i	$-0.242741\pi$
$173$	1.63673	+	1.45002i	0.124438	+	0.110243i	−0.598609	+	0.801042i	$0.704280\pi$
$174$	25.0686	+	3.04388i	1.90045	+	0.230756i
$175$	−0.359885	−	1.46011i	−0.0272047	−	0.110374i
$176$	−4.03127	−	7.68094i	−0.303868	−	0.578972i
$177$	2.42333	+	4.61727i	0.182149	+	0.347055i
$178$	−15.4092	+	40.6308i	−1.15497	+	3.04541i
$179$	−0.181304	−	0.0951558i	−0.0135513	−	0.00711228i	0.457934	−	0.888986i	$-0.348590\pi$
$179$	−0.181304	−	0.0951558i	−0.0135513	−	0.00711228i	−0.471485	+	0.881874i	$0.656282\pi$
$180$	13.5524	−	5.13974i	1.01014	−	0.383094i
$181$	−1.84418	+	15.1882i	−0.137077	+	1.12893i	0.748070	+	0.663620i	$0.230981\pi$
$181$	−1.84418	+	15.1882i	−0.137077	+	1.12893i	−0.885147	+	0.465312i	$0.845942\pi$
$182$	2.97848	−	0.189659i	0.220780	−	0.0140584i
$183$	−0.407823	−	3.35872i	−0.0301471	−	0.248284i
$184$	−23.1223	−	44.0558i	−1.70460	−	3.24784i
$185$	−2.91294	−	23.9902i	−0.214163	−	1.76379i
$186$	10.0769	−	5.28878i	0.738876	−	0.387792i
$187$	−2.24047	+	2.52897i	−0.163839	+	0.184936i
$188$			55.1302i			4.02078i
$189$	0.212746	+	0.240140i	0.0154750	+	0.0174676i
$190$	−4.28404	+	8.16255i	−0.310797	+	0.592174i
$191$	−5.74593			−0.415761			−0.207880	−	0.978154i	$-0.566656\pi$
$191$	−5.74593			−0.415761			−0.207880	+	0.978154i	$0.566656\pi$
$192$	−3.61781			−0.261093
$193$	7.08551	−	13.5003i	0.510026	−	0.971774i	−0.485221	−	0.874392i	$-0.661261\pi$
$193$	7.08551	−	13.5003i	0.510026	−	0.971774i	0.995247	−	0.0973824i	$-0.0310470\pi$
$194$	−37.9678	−	9.35823i	−2.72593	−	0.671882i
$195$	−10.2187	+	4.63816i	−0.731779	+	0.332145i
$196$	31.1855	−	7.68653i	2.22753	−	0.549038i
$197$	−2.41627	+	9.80321i	−0.172152	+	0.698450i	0.819887	+	0.572525i	$0.194036\pi$
$197$	−2.41627	+	9.80321i	−0.172152	+	0.698450i	−0.992040	+	0.125925i	$0.959810\pi$
$198$	−0.947894	+	2.49939i	−0.0673639	+	0.177624i
$199$	1.76194	+	14.5108i	0.124900	+	1.02865i	0.911534	+	0.411226i	$0.134899\pi$
$199$	1.76194	+	14.5108i	0.124900	+	1.02865i	−0.786633	+	0.617421i	$0.788178\pi$
$200$	−7.68958	−	31.1979i	−0.543736	−	2.20602i
$201$	−2.05211	+	8.32574i	−0.144745	+	0.587252i
$202$	24.9427	+	17.2167i	1.75496	+	1.21136i
$203$	3.11718	−	0.378494i	0.218783	−	0.0265651i
$204$	5.38523	+	14.1997i	0.377042	+	0.994178i
$205$	−13.1316	+	6.89199i	−0.917150	+	0.481357i
$206$	−5.92711	−	24.0472i	−0.412962	−	1.67545i
$207$	−2.57380	+	6.78655i	−0.178891	+	0.471698i
$208$	30.1273	−	1.91840i	2.08895	−	0.133017i
$209$	−0.421741	−	1.11204i	−0.0291725	−	0.0769215i
$210$	2.12029	−	1.46353i	0.146314	−	0.100993i
$211$	18.5795	−	16.4600i	1.27906	−	1.13315i	0.294970	−	0.955507i	$-0.404690\pi$
$211$	18.5795	−	16.4600i	1.27906	−	1.13315i	0.984095	−	0.177645i	$-0.0568480\pi$
$212$	30.9399	+	7.62599i	2.12496	+	0.523755i
$213$	6.94253	+	2.63295i	0.475694	+	0.180407i
$214$	3.01844	−	5.75116i	0.206336	−	0.393141i
$215$	7.52559	+	2.85408i	0.513241	+	0.194647i
$216$	4.54569	+	5.13103i	0.309295	+	0.349122i
$217$	1.05923	−	0.938397i	0.0719053	−	0.0637025i
$218$	6.55310	−	9.49380i	0.443832	−	0.643001i
$219$	0.559642	+	0.386293i	0.0378171	+	0.0261032i
$220$	13.2967	+	6.97864i	0.896462	+	0.470500i
$221$	−4.85969	−	10.7068i	−0.326898	−	0.720219i
$222$	17.7383	−	9.30978i	1.19052	−	0.624832i
$223$	−4.22037	−	0.512445i	−0.282617	−	0.0343159i	−0.0219990	−	0.999758i	$-0.507003\pi$
$223$	−4.22037	−	0.512445i	−0.282617	−	0.0343159i	−0.260618	+	0.965442i	$0.583926\pi$
$224$	−2.45851	+	0.605969i	−0.164266	+	0.0404880i
$225$	−2.66271	+	3.85759i	−0.177514	+	0.257173i
$226$	30.2849	−	20.9041i	2.01452	−	1.39052i
$227$	12.4904	−	14.0988i	0.829020	−	0.935770i	−0.169743	−	0.985488i	$-0.554294\pi$
$227$	12.4904	−	14.0988i	0.829020	−	0.935770i	0.998763	+	0.0497183i	$0.0158324\pi$
$228$	−5.30687	−	0.644370i	−0.351456	−	0.0426745i
$229$	−2.22185	+	9.01441i	−0.146824	+	0.595689i	0.850718	+	0.525622i	$0.176167\pi$
$229$	−2.22185	+	9.01441i	−0.146824	+	0.595689i	−0.997542	+	0.0700669i	$0.977679\pi$
$230$	51.6100	+	27.0870i	3.40306	+	1.78607i
$231$	−0.0400651	+	0.329966i	−0.00263609	+	0.0217101i
$232$	66.6042	−	8.08721i	4.37278	−	0.530951i
$233$	−8.45073	+	12.2430i	−0.553626	+	0.802065i	−0.995475	−	0.0950242i	$-0.969707\pi$
$233$	−8.45073	+	12.2430i	−0.553626	+	0.802065i	0.441849	+	0.897089i	$0.354323\pi$
$234$	−6.59882	−	6.55705i	−0.431379	−	0.428648i
$235$	−20.9312	−	30.3241i	−1.36540	−	1.97813i
$236$	16.1030	+	18.1765i	1.04822	+	1.18319i
$237$	−4.10257	−	1.01119i	−0.266491	−	0.0656840i
$238$	1.53343	+	2.22156i	0.0993978	+	0.144003i
$239$		−	12.9876i		−	0.840097i	−0.907502	−	0.420048i	$-0.862013\pi$
$239$		−	12.9876i		−	0.840097i	0.907502	−	0.420048i	$-0.137987\pi$
$240$	21.4467	−	14.8036i	1.38438	−	0.955568i
$241$	−0.120149	+	0.0145887i	−0.00773948	+	0.000939743i	−0.124406	−	0.992231i	$-0.539702\pi$
$241$	−0.120149	+	0.0145887i	−0.00773948	+	0.000939743i	0.116666	+	0.993171i	$0.462779\pi$
$242$	23.9472	−	9.08198i	1.53939	−	0.583812i
$243$	0.120537	−	0.992709i	0.00773243	−	0.0636823i
$244$	−5.58717	−	14.7322i	−0.357682	−	0.943129i
$245$	−14.2351	+	16.0681i	−0.909447	+	1.02655i
$246$	−9.20198	−	8.15224i	−0.586697	−	0.519768i
$247$	4.13220	+	0.236786i	0.262926	+	0.0150663i
$248$	22.6324	−	20.0505i	1.43716	−	1.27321i
$249$		−	0.254881i		−	0.0161524i
$250$	−1.87943	−	1.66503i	−0.118866	−	0.105306i
$251$	2.64246	−	0.651308i	0.166791	−	0.0411102i	−0.155036	−	0.987909i	$-0.549549\pi$
$251$	2.64246	−	0.651308i	0.166791	−	0.0411102i	0.321827	+	0.946799i	$0.395703\pi$
$252$	1.22957	+	0.848710i	0.0774555	+	0.0534637i
$253$	−7.03119	+	2.66658i	−0.442047	+	0.167646i
$254$	−41.9998	+	15.9284i	−2.63530	+	0.999437i
$255$	−8.35331	−	5.76587i	−0.523105	−	0.361073i
$256$	23.1850	−	5.71459i	1.44906	−	0.357162i
$257$	−14.2807	−	12.6516i	−0.890804	−	0.789183i	0.0875419	−	0.996161i	$-0.472099\pi$
$257$	−14.2807	−	12.6516i	−0.890804	−	0.789183i	−0.978346	+	0.206978i	$0.933637\pi$
$258$			6.67197i			0.415379i
$259$	1.86455	−	1.65185i	0.115858	−	0.102641i
$260$	−41.0356	+	32.3601i	−2.54492	+	2.00689i
$261$	−7.32607	−	6.49033i	−0.453472	−	0.401742i
$262$	8.68414	−	9.80236i	0.536508	−	0.605592i
$263$	−7.92928	−	20.9078i	−0.488941	−	1.28923i	−0.921764	−	0.387752i	$-0.873252\pi$
$263$	−7.92928	−	20.9078i	−0.488941	−	1.28923i	0.432823	−	0.901479i	$-0.357517\pi$
$264$	−0.856062	+	7.05031i	−0.0526870	+	0.433916i
$265$	−19.9137	+	7.55227i	−1.22329	+	0.463932i
$266$	−0.943291	+	0.114536i	−0.0578369	+	0.00702267i
$267$	13.8609	−	9.56752i	0.848276	−	0.585523i
$268$			39.9323i			2.43925i
$269$	15.1481	+	21.9458i	0.923595	+	1.33806i	0.941070	+	0.338211i	$0.109822\pi$
$269$	15.1481	+	21.9458i	0.923595	+	1.33806i	−0.0174759	+	0.999847i	$0.505563\pi$
$270$	−7.79705	−	1.92180i	−0.474513	−	0.116957i
$271$	12.1860	+	13.7551i	0.740245	+	0.835563i	0.991191	−	0.132437i	$-0.0422804\pi$
$271$	12.1860	+	13.7551i	0.740245	+	0.835563i	−0.250947	+	0.968001i	$0.580742\pi$
$272$	15.5107	+	22.4711i	0.940472	+	1.36251i
$273$	−0.991818	−	0.595283i	−0.0600275	−	0.0360282i
$274$	−9.33910	+	13.5300i	−0.564196	+	0.817379i
$275$	−4.82089	+	0.585362i	−0.290710	+	0.0352986i
$276$	−4.07421	+	33.5542i	−0.245239	+	2.01972i
$277$	−1.17139	−	0.614791i	−0.0703818	−	0.0369392i	0.429165	−	0.903226i	$-0.358808\pi$
$277$	−1.17139	−	0.614791i	−0.0703818	−	0.0369392i	−0.499547	+	0.866287i	$0.666500\pi$
$278$	0.432690	−	1.75549i	0.0259510	−	0.105287i
$279$	−4.37873	−	0.531674i	−0.262148	−	0.0318305i
$280$	4.53909	−	5.12358i	0.271263	−	0.306192i
$281$	−16.9796	+	11.7202i	−1.01292	+	0.699168i	−0.954219	−	0.299108i	$-0.903311\pi$
$281$	−16.9796	+	11.7202i	−1.01292	+	0.699168i	−0.0587005	+	0.998276i	$0.518696\pi$
$282$	17.3511	−	25.1375i	1.03324	−	1.49691i
$283$	2.06326	−	0.508549i	0.122648	−	0.0302301i	−0.177514	−	0.984118i	$-0.556805\pi$
$283$	2.06326	−	0.508549i	0.122648	−	0.0302301i	0.300162	+	0.953888i	$0.402959\pi$
$284$	34.3253	+	4.16785i	2.03683	+	0.247316i
$285$	3.16367	−	1.66042i	0.187399	−	0.0983548i
$286$	0.551378	−	9.62221i	0.0326037	−	0.568973i
$287$	−1.35357	−	0.710410i	−0.0798989	−	0.0419342i
$288$	6.49537	+	4.48343i	0.382743	+	0.264189i
$289$	−3.61583	+	5.23843i	−0.212696	+	0.308143i
$290$	−58.8313	+	52.1200i	−3.45469	+	3.06059i
$291$	10.0504	+	11.3445i	0.589162	+	0.665027i
$292$	2.96096	+	1.12294i	0.173277	+	0.0657153i
$293$	−2.63151	+	5.01393i	−0.153735	+	0.292917i	−0.950127	−	0.311864i	$-0.899047\pi$
$293$	−2.63151	+	5.01393i	−0.153735	+	0.292917i	0.796392	+	0.604780i	$0.206739\pi$
$294$	−16.6387	−	6.31022i	−0.970388	−	0.368020i
$295$	−15.7584	−	3.88411i	−0.917492	−	0.226141i
$296$	39.8395	−	35.2948i	2.31563	−	2.05147i
$297$	0.852651	−	0.588542i	0.0494758	−	0.0341507i
$298$	−17.4719	−	46.0697i	−1.01212	−	2.66875i
$299$	1.49715	−	26.1270i	0.0865822	−	1.51096i
$300$	−7.74042	+	20.4098i	−0.446893	+	1.17836i
$301$	0.198544	+	0.805525i	0.0114439	+	0.0464297i
$302$	33.4820	−	17.5727i	1.92667	−	1.01120i
$303$	−4.16544	−	10.9834i	−0.239298	−	0.630978i
$304$	−9.54138	+	1.15853i	−0.547235	+	0.0664464i
$305$	8.66654	+	5.98208i	0.496245	+	0.342533i
$306$	2.01359	−	8.16947i	0.115109	−	0.467017i
$307$	0.239913	+	0.973364i	0.0136925	+	0.0555528i	0.977391	−	0.211441i	$-0.0678157\pi$
$307$	0.239913	+	0.973364i	0.0136925	+	0.0555528i	−0.963698	+	0.266994i	$0.913970\pi$
$308$	0.186578	+	1.53661i	0.0106313	+	0.0875564i
$309$	−3.40394	+	8.97545i	−0.193643	+	0.510595i
$310$	−8.47685	+	34.3919i	−0.481452	+	1.95333i
$311$	16.1625	−	3.98369i	0.916490	−	0.225894i	0.247259	−	0.968949i	$-0.420470\pi$
$311$	16.1625	−	3.98369i	0.916490	−	0.225894i	0.669230	+	0.743055i	$0.266624\pi$
$312$	−21.1920	−	12.7193i	−1.19976	−	0.720088i
$313$	−8.43792	−	2.07976i	−0.476939	−	0.117555i	−0.00648427	−	0.999979i	$-0.502064\pi$
$313$	−8.43792	−	2.07976i	−0.476939	−	0.117555i	−0.470455	+	0.882424i	$0.655910\pi$
$314$	−20.2051	+	38.4976i	−1.14024	+	2.17255i
$315$	−0.998548			−0.0562618
$316$	−19.6769			−1.10691
$317$	−10.7262	+	20.4371i	−0.602445	+	1.14786i	0.373043	+	0.927814i	$0.378314\pi$
$317$	−10.7262	+	20.4371i	−0.602445	+	1.14786i	−0.975489	+	0.220050i	$0.929378\pi$
$318$	−11.7074	−	13.2149i	−0.656517	−	0.741055i
$319$		−	10.1404i		−	0.567751i
$320$	7.46693	−	8.42842i	0.417414	−	0.471163i
$321$	−2.22905	+	1.16990i	−0.124414	+	0.0652973i
$322$	0.724188	+	5.96422i	0.0403574	+	0.332373i
$323$	1.73973	+	3.31477i	0.0968011	+	0.184439i
$324$	−0.561324	−	4.62292i	−0.0311847	−	0.256829i
$325$	4.97666	−	16.1510i	0.276056	−	0.895899i
$326$	−7.13149	+	58.7331i	−0.394977	+	3.25293i
$327$	−4.18054	+	1.58547i	−0.231185	+	0.0876767i
$328$	−28.9215	−	15.1792i	−1.59693	−	0.838131i
$329$	1.34681	−	3.55125i	0.0742520	−	0.195787i
$330$	−3.86644	−	7.36689i	−0.212841	−	0.405534i
$331$	−10.7878	−	20.5545i	−0.592952	−	1.12978i	−0.978337	−	0.207020i	$-0.933624\pi$
$331$	−10.7878	−	20.5545i	−0.592952	−	1.12978i	0.385385	−	0.922756i	$-0.374069\pi$
$332$	−0.284056	−	1.15246i	−0.0155896	−	0.0632494i
$333$	−7.70783	−	0.935900i	−0.422386	−	0.0512870i
$334$	17.6589	+	15.6445i	0.966255	+	0.856027i
$335$	−15.1611	−	21.9646i	−0.828337	−	1.20005i
$336$	2.51162	+	0.952530i	0.137020	+	0.0519648i
$337$	33.5818			1.82932			0.914660	−	0.404224i	$-0.132458\pi$
$337$	33.5818			1.82932			0.914660	+	0.404224i	$0.132458\pi$
$338$	29.7976	+	15.3985i	1.62078	+	0.837566i
$339$	−14.2626			−0.774638
$340$	−44.1958	−	16.7613i	−2.39685	−	0.909007i
$341$	−2.59599	−	3.76095i	−0.140581	−	0.203667i
$342$	2.21695	+	1.96404i	0.119879	+	0.106203i
$343$	−4.42601	−	0.537414i	−0.238982	−	0.0290177i
$344$	4.24225	+	17.2115i	0.228727	+	0.927982i
$345$	−10.4985	−	20.0032i	−0.565219	−	1.07693i
$346$	−2.62185	−	4.99552i	−0.140952	−	0.268561i
$347$	9.70124	−	25.5801i	0.520790	−	1.37321i	−0.374293	−	0.927310i	$-0.622115\pi$
$347$	9.70124	−	25.5801i	0.520790	−	1.37321i	0.895083	−	0.445899i	$-0.147116\pi$
$348$	−40.3585	−	21.1818i	−2.16344	−	1.13546i
$349$	16.7920	−	6.36836i	0.898855	−	0.340891i	0.138472	−	0.990366i	$-0.455781\pi$
$349$	16.7920	−	6.36836i	0.898855	−	0.340891i	0.760382	+	0.649476i	$0.225012\pi$
$350$	−0.467677	+	3.85167i	−0.0249984	+	0.205880i
$351$	0.661176	+	3.54441i	0.0352910	+	0.189187i
$352$	0.985625	+	8.11735i	0.0525340	+	0.432656i
$353$	15.8439	+	30.1881i	0.843287	+	1.60675i	0.793963	+	0.607966i	$0.208014\pi$
$353$	15.8439	+	30.1881i	0.843287	+	1.60675i	0.0493239	+	0.998783i	$0.484293\pi$
$354$	−1.62171	−	13.3560i	−0.0861927	−	0.709861i
$355$	−20.4629	+	10.7398i	−1.08606	+	0.570007i
$356$	52.0104	−	58.7076i	2.75654	−	3.11149i
$357$		−	1.04624i		−	0.0553730i
$358$	0.350324	+	0.395434i	0.0185152	+	0.0208993i
$359$	−7.66113	+	14.5971i	−0.404339	+	0.770404i	−0.999447	−	0.0332417i	$-0.989417\pi$
$359$	−7.66113	+	14.5971i	−0.404339	+	0.770404i	0.595108	+	0.803646i	$0.297109\pi$
$360$	−21.3358			−1.12449
$361$	17.6822			0.930643
$362$	18.3449	−	34.9532i	0.964185	−	1.83710i
$363$	−9.63816	−	2.37559i	−0.505872	−	0.124686i
$364$	−5.14798	−	1.58626i	−0.269827	−	0.0831426i
$365$	−2.05501	+	0.506514i	−0.107564	+	0.0265122i
$366$	−2.08910	+	8.47580i	−0.109199	+	0.443037i
$367$	−5.67052	+	14.9519i	−0.295999	+	0.780484i	0.701687	+	0.712485i	$0.252431\pi$
$367$	−5.67052	+	14.9519i	−0.295999	+	0.780484i	−0.997685	+	0.0679985i	$0.978339\pi$
$368$	7.32515	+	60.3280i	0.381850	+	3.14482i
$369$	1.14030	+	4.62638i	0.0593617	+	0.240840i
$370$	−14.9217	+	60.5397i	−0.775742	+	3.14731i
$371$	−1.80671	−	1.24708i	−0.0937998	−	0.0647453i
$372$	−20.3912	+	2.47594i	−1.05723	+	0.128371i
$373$	−0.602893	−	1.58970i	−0.0312166	−	0.0823115i	0.918502	−	0.395417i	$-0.129400\pi$
$373$	−0.602893	−	1.58970i	−0.0312166	−	0.0823115i	−0.949718	+	0.313105i	$0.898631\pi$
$374$	7.71876	−	4.05112i	0.399127	−	0.209478i
$375$	0.232897	+	0.944900i	0.0120267	+	0.0487944i
$376$	28.7770	−	75.8788i	1.48406	−	3.91315i
$377$	32.2263	+	14.3810i	1.65974	+	0.740659i
$378$	−0.293526	−	0.773965i	−0.0150974	−	0.0398084i
$379$	−24.4733	+	16.8927i	−1.25711	+	0.867719i	−0.995247	−	0.0973862i	$-0.968952\pi$
$379$	−24.4733	+	16.8927i	−1.25711	+	0.867719i	−0.261862	+	0.965105i	$0.584336\pi$
$380$	12.4542	−	11.0335i	0.638888	−	0.566005i
$381$	16.9039	+	4.16643i	0.866011	+	0.213452i
$382$	13.8616	+	5.25703i	0.709223	+	0.268973i
$383$	15.4242	−	29.3883i	0.788137	−	1.50167i	−0.0752702	−	0.997163i	$-0.523982\pi$
$383$	15.4242	−	29.3883i	0.788137	−	1.50167i	0.863408	−	0.504507i	$-0.168326\pi$
$384$	−6.03145	−	2.28743i	−0.307791	−	0.116730i
$385$	−0.686029	−	0.774367i	−0.0349633	−	0.0394654i
$386$	−29.4449	+	26.0859i	−1.49871	+	1.32774i
$387$	1.46898	−	2.12819i	0.0746726	−	0.108182i
$388$	58.0862	+	40.0940i	2.94888	+	2.03547i
$389$	13.6420	+	7.15986i	0.691675	+	0.363019i	0.773648	−	0.633615i	$-0.218430\pi$
$389$	13.6420	+	7.15986i	0.691675	+	0.363019i	−0.0819728	+	0.996635i	$0.526122\pi$
$390$	28.8955	−	1.83996i	1.46318	−	0.0931699i
$391$	20.9586	−	10.9999i	1.05992	−	0.556290i
$392$	−46.9346	−	5.69889i	−2.37055	−	0.287837i
$393$	−4.92823	+	1.21470i	−0.248596	+	0.0612735i
$394$	14.7982	−	21.4389i	0.745521	−	1.08007i
$395$	10.8232	−	7.47072i	0.544575	−	0.375893i
$396$	3.19940	−	3.61137i	0.160776	−	0.181478i
$397$	1.09245	+	0.132647i	0.0548283	+	0.00665737i	0.147905	−	0.989002i	$-0.452747\pi$
$397$	1.09245	+	0.132647i	0.0548283	+	0.00665737i	−0.0930765	+	0.995659i	$0.529670\pi$
$398$	9.02562	−	36.6184i	0.452413	−	1.83551i
$399$	0.326104	+	0.171152i	0.0163256	+	0.00856833i
$400$	−4.73055	+	38.9596i	−0.236528	+	1.94798i
$401$	−32.7441	+	3.97585i	−1.63516	+	0.198545i	−0.885948	−	0.463784i	$-0.846491\pi$
$401$	−32.7441	+	3.97585i	−1.63516	+	0.198545i	−0.749214	+	0.662329i	$0.769568\pi$
$402$	12.5679	−	18.2077i	0.626830	−	0.908119i
$403$	15.6340	−	2.91637i	0.778785	−	0.145275i
$404$	−31.0748	−	45.0197i	−1.54603	−	2.23981i
$405$	2.06393	+	2.32970i	0.102558	+	0.115764i
$406$	−7.86626	−	1.93886i	−0.390396	−	0.0962240i
$407$	−4.56970	−	6.62035i	−0.226512	−	0.328159i
$408$		−	22.3548i		−	1.10673i
$409$	−20.4544	+	14.1186i	−1.01140	+	0.698121i	−0.953869	−	0.300222i	$-0.902939\pi$
$409$	−20.4544	+	14.1186i	−1.01140	+	0.698121i	−0.0575341	+	0.998344i	$0.518324\pi$
$410$	37.9846	−	4.61216i	1.87592	−	0.227778i
$411$	5.95787	−	2.25952i	0.293880	−	0.111454i
$412$	−5.38829	+	44.3765i	−0.265462	+	2.18628i
$413$	−0.593239	−	1.56424i	−0.0291914	−	0.0769713i
$414$	12.4182	−	14.0173i	0.610322	−	0.688911i
$415$	0.593797	+	0.526058i	0.0291483	+	0.0258232i
$416$	−27.1949	−	8.37964i	−1.33334	−	0.410846i
$417$	−0.524528	+	0.464691i	−0.0256862	+	0.0227560i
$418$			3.06858i			0.150089i
$419$	25.5936	+	22.6739i	1.25033	+	1.10769i	0.989835	+	0.142218i	$0.0454235\pi$
$419$	25.5936	+	22.6739i	1.25033	+	1.10769i	0.260493	+	0.965476i	$0.416115\pi$
$420$	−4.51499	+	1.11284i	−0.220309	+	0.0543013i
$421$	11.8917	+	8.20824i	0.579566	+	0.400045i	0.821467	−	0.570255i	$-0.193156\pi$
$421$	11.8917	+	8.20824i	0.579566	+	0.400045i	−0.241902	+	0.970301i	$0.577771\pi$
$422$	−59.8811	+	22.7099i	−2.91497	+	1.10550i
$423$	−11.0691	+	4.19797i	−0.538200	+	0.204112i
$424$	−38.6036	−	26.6462i	−1.87476	−	1.29405i
$425$	14.8417	−	3.65815i	0.719928	−	0.177446i
$426$	−14.3394	−	12.7036i	−0.694747	−	0.615492i
$427$			1.08547i			0.0525298i
$428$	−8.77497	+	7.77395i	−0.424154	+	0.375768i
$429$	−2.29442	+	2.94784i	−0.110776	+	0.142323i
$430$	−15.5437	−	13.7705i	−0.749584	−	0.664073i
$431$	13.7931	−	15.5692i	0.664392	−	0.749944i	−0.315619	−	0.948886i	$-0.602212\pi$
$431$	13.7931	−	15.5692i	0.664392	−	0.749944i	0.980011	+	0.198942i	$0.0637506\pi$
$432$	−2.96901	−	7.82864i	−0.142847	−	0.376656i
$433$	1.93164	−	15.9085i	0.0928286	−	0.764513i	−0.869747	−	0.493498i	$-0.835718\pi$
$433$	1.93164	−	15.9085i	0.0928286	−	0.764513i	0.962575	−	0.271014i	$-0.0873590\pi$
$434$	−3.41387	+	1.29471i	−0.163871	+	0.0621481i
$435$	30.2411	−	3.67193i	1.44995	−	0.176056i
$436$	−17.1356	+	11.8279i	−0.820647	+	0.566451i
$437$			8.33204i			0.398576i
$438$	−0.996671	−	1.44393i	−0.0476228	−	0.0689935i
$439$	−0.968162	−	0.238630i	−0.0462078	−	0.0113892i	0.216144	−	0.976362i	$-0.430652\pi$
$439$	−0.968162	−	0.238630i	−0.0462078	−	0.0113892i	−0.262352	+	0.964972i	$0.584498\pi$
$440$	−14.6582	−	16.5457i	−0.698804	−	0.788787i
$441$	3.91798	+	5.67618i	0.186571	+	0.270294i
$442$	1.92784	+	30.2757i	0.0916981	+	1.44007i
$443$	−22.4688	+	32.5517i	−1.06752	+	1.54658i	−0.252110	+	0.967699i	$0.581124\pi$
$443$	−22.4688	+	32.5517i	−1.06752	+	1.54658i	−0.815415	+	0.578877i	$0.803491\pi$
$444$	−35.8944	+	4.35837i	−1.70347	+	0.206839i
$445$	−6.31863	+	52.0386i	−0.299532	+	2.46686i
$446$	9.71248	+	5.09750i	0.459899	+	0.241374i
$447$	−4.57017	+	18.5419i	−0.216161	+	0.877001i
$448$	1.15222	+	0.139905i	0.0544372	+	0.00660987i
$449$	19.7414	−	22.2834i	0.931654	−	1.05162i	−0.0668944	−	0.997760i	$-0.521309\pi$
$449$	19.7414	−	22.2834i	0.931654	−	1.05162i	0.998548	−	0.0538600i	$-0.0171525\pi$
$450$	9.95295	−	6.87002i	0.469186	−	0.323856i
$451$	−2.80431	+	4.06274i	−0.132050	+	0.191307i
$452$	−64.4892	+	15.8951i	−3.03331	+	0.747645i
$453$	−14.5489	−	1.76656i	−0.683569	−	0.0830003i
$454$	−43.0315	+	22.5847i	−2.01957	+	1.05995i
$455$	3.43388	−	1.08201i	0.160983	−	0.0507256i
$456$	6.96779	+	3.65698i	0.326297	+	0.171254i
$457$	23.0685	+	15.9231i	1.07910	+	0.744849i	0.968499	−	0.249016i	$-0.0801071\pi$
$457$	23.0685	+	15.9231i	1.07910	+	0.744849i	0.110601	+	0.993865i	$0.464723\pi$
$458$	13.6075	−	19.7138i	0.635835	−	0.921166i
$459$	−2.44098	+	2.16252i	−0.113935	+	0.100938i
$460$	−69.7622	−	78.7453i	−3.25268	−	3.67152i
$461$	−30.5561	−	11.5884i	−1.42314	−	0.539725i	−0.481528	−	0.876431i	$-0.659918\pi$
$461$	−30.5561	−	11.5884i	−1.42314	−	0.539725i	−0.941610	+	0.336706i	$0.890687\pi$
$462$	0.398544	−	0.759362i	0.0185419	−	0.0353287i
$463$	−23.2495	−	8.81739i	−1.08050	−	0.409779i	−0.250827	−	0.968032i	$-0.580703\pi$
$463$	−23.2495	−	8.81739i	−1.08050	−	0.409779i	−0.829671	+	0.558253i	$0.811472\pi$
$464$	−79.5671	−	19.6115i	−3.69381	−	0.910443i
$465$	10.2760	−	9.10378i	0.476540	−	0.422178i
$466$	31.5880	−	21.8037i	1.46329	−	1.01003i
$467$	0.407888	+	1.07551i	0.0188748	+	0.0497687i	0.944122	−	0.329595i	$-0.106912\pi$
$467$	0.407888	+	1.07551i	0.0188748	+	0.0497687i	−0.925248	+	0.379364i	$0.876143\pi$
$468$	6.93966	+	15.2894i	0.320786	+	0.706752i
$469$	0.975531	−	2.57226i	0.0450458	−	0.118776i
$470$	22.7511	+	92.3050i	1.04943	+	4.25771i
$471$	14.9210	−	7.83116i	0.687525	−	0.360841i
$472$	−12.6756	−	33.4228i	−0.583442	−	1.53841i
$473$	2.65963	−	0.322937i	0.122290	−	0.0148487i
$474$	8.97200	+	6.19292i	0.412098	+	0.284450i
$475$	−1.28771	+	5.22444i	−0.0590842	+	0.239714i
$476$	−1.16600	−	4.73064i	−0.0534434	−	0.216829i
$477$	0.824802	+	6.79286i	0.0377651	+	0.311024i
$478$	−11.8825	+	31.3316i	−0.543493	+	1.43307i
$479$	9.49945	−	38.5408i	0.434041	−	1.76097i	−0.192212	−	0.981353i	$-0.561566\pi$
$479$	9.49945	−	38.5408i	0.434041	−	1.76097i	0.626253	−	0.779620i	$-0.284588\pi$
$480$	−23.8511	+	5.87876i	−1.08865	+	0.268327i
$481$	27.5204	−	5.13366i	1.25482	−	0.234075i
$482$	0.303198	+	0.0747317i	0.0138103	+	0.00340393i
$483$	1.08216	−	2.06188i	0.0492399	−	0.0938188i
$484$	−46.2270			−2.10123
$485$	−47.1726			−2.14200
$486$	−1.19903	+	2.28456i	−0.0543890	+	0.103630i
$487$	11.8843	+	13.4146i	0.538529	+	0.607874i	0.953290	−	0.302057i	$-0.0976733\pi$
$487$	11.8843	+	13.4146i	0.538529	+	0.607874i	−0.414761	+	0.909930i	$0.636135\pi$
$488$			23.1931i			1.04990i
$489$	15.2062	−	17.1642i	0.687647	−	0.776193i
$490$	49.0421	−	25.7393i	2.21550	−	1.16278i
$491$	1.52639	+	12.5710i	0.0688850	+	0.567319i	0.985762	+	0.168149i	$0.0537788\pi$
$491$	1.52639	+	12.5710i	0.0688850	+	0.567319i	−0.916877	+	0.399171i	$0.869298\pi$
$492$	10.3119	+	19.6476i	0.464895	+	0.885783i
$493$	3.84731	+	31.6855i	0.173274	+	1.42704i
$494$	−9.75200	−	4.35184i	−0.438763	−	0.195798i
$495$	−0.388688	+	3.20113i	−0.0174702	+	0.143880i
$496$	−34.5313	+	13.0960i	−1.55050	+	0.588027i
$497$	−2.10927	−	1.10703i	−0.0946137	−	0.0496571i
$498$	−0.233194	+	0.614883i	−0.0104497	+	0.0275536i
$499$	0.991903	+	1.88991i	0.0444037	+	0.0846042i	0.906647	−	0.421890i	$-0.138633\pi$
$499$	0.991903	+	1.88991i	0.0444037	+	0.0846042i	−0.862243	+	0.506495i	$0.830941\pi$
$500$	2.10611	+	4.01286i	0.0941882	+	0.179461i
$501$	−2.18828	−	8.87820i	−0.0977651	−	0.396649i
$502$	−6.97064	−	0.846389i	−0.311115	−	0.0377762i
$503$	−13.8459	−	12.2664i	−0.617358	−	0.546931i	0.295430	−	0.955364i	$-0.404537\pi$
$503$	−13.8459	−	12.2664i	−0.617358	−	0.546931i	−0.912788	+	0.408433i	$0.866075\pi$
$504$	−1.24931	−	1.80994i	−0.0556488	−	0.0806212i
$505$	34.1851	+	12.9647i	1.52122	+	0.576922i
$506$	19.4019			0.862521
$507$	−6.11438	−	11.4723i	−0.271549	−	0.509504i
$508$	81.0750			3.59712
$509$	−18.6029	−	7.05516i	−0.824561	−	0.312715i	−0.0940085	−	0.995571i	$-0.529968\pi$
$509$	−18.6029	−	7.05516i	−0.824561	−	0.312715i	−0.730552	+	0.682857i	$0.760737\pi$
$510$	14.8765	+	21.5523i	0.658742	+	0.954352i
$511$	−0.163299	−	0.144670i	−0.00722392	−	0.00639984i
$512$	−48.3533	−	5.87115i	−2.13693	−	0.259471i
$513$	−0.274722	−	1.11459i	−0.0121293	−	0.0492103i
$514$	22.8760	+	43.5866i	1.00902	+	1.92252i
$515$	−13.8846	−	26.4549i	−0.611828	−	1.16574i
$516$	4.27030	−	11.2599i	0.187990	−	0.495688i
$517$	−10.8603	−	5.69992i	−0.477635	−	0.250682i
$518$	−6.00940	+	2.27907i	−0.264038	+	0.100136i
$519$	−0.263571	+	2.17070i	−0.0115695	+	0.0952833i
$520$	73.3710	−	23.1192i	3.21753	−	1.01384i
$521$	2.30250	+	18.9628i	0.100874	+	0.830775i	0.952060	+	0.305911i	$0.0989608\pi$
$521$	2.30250	+	18.9628i	0.100874	+	0.830775i	−0.851186	+	0.524864i	$0.824116\pi$
$522$	11.7355	+	22.3602i	0.513650	+	0.978679i
$523$	−3.99043	−	32.8641i	−0.174489	−	1.43705i	−0.772222	−	0.635353i	$-0.780855\pi$
$523$	−3.99043	−	32.8641i	−0.174489	−	1.43705i	0.597733	−	0.801695i	$-0.296068\pi$
$524$	−20.9295	+	10.9847i	−0.914310	+	0.479867i
$525$	0.997208	−	1.12562i	0.0435217	−	0.0491259i
$526$			57.6932i			2.51554i
$527$	9.53861	+	10.7669i	0.415508	+	0.469012i
$528$	4.03127	−	7.68094i	0.175438	−	0.334270i
$529$	29.6817			1.29051
$530$	54.9500			2.38688
$531$	−2.42333	+	4.61727i	−0.105163	+	0.200372i
$532$	1.66524	+	0.410444i	0.0721972	+	0.0177950i
$533$	−8.93443	−	14.6739i	−0.386993	−	0.635598i
$534$	−42.1920	+	10.3994i	−1.82583	+	0.450025i
$535$	1.87511	−	7.60761i	0.0810680	−	0.328906i
$536$	20.8440	−	54.9610i	0.900323	−	2.37396i
$537$	−0.0246808	−	0.203265i	−0.00106506	−	0.00877154i
$538$	−16.4652	−	66.8018i	−0.709864	−	2.88003i
$539$	−1.71008	+	6.93806i	−0.0736582	+	0.298843i
$540$	11.9286	+	8.23369i	0.513323	+	0.354322i
$541$	−25.3880	+	3.08266i	−1.09152	+	0.132534i	−0.646445	−	0.762961i	$-0.723745\pi$
$541$	−25.3880	+	3.08266i	−1.09152	+	0.132534i	−0.445072	+	0.895495i	$0.646822\pi$
$542$	−16.8130	−	44.3323i	−0.722181	−	1.90424i
$543$	−13.5473	+	7.11016i	−0.581369	+	0.305126i
$544$	−6.15955	−	24.9903i	−0.264089	−	1.07145i
$545$	4.93469	−	13.0117i	0.211379	−	0.557361i
$546$	1.84806	+	2.34350i	0.0790895	+	0.100293i
$547$	6.91945	+	18.2451i	0.295854	+	0.780104i	0.997701	+	0.0677753i	$0.0215901\pi$
$547$	6.91945	+	18.2451i	0.295854	+	0.780104i	−0.701846	+	0.712328i	$0.747641\pi$
$548$	24.4207	−	16.8564i	1.04320	−	0.720069i
$549$	2.53251	−	2.24360i	0.108085	−	0.0957547i
$550$	12.1656	+	2.99855i	0.518743	+	0.127859i
$551$	−10.5054	−	3.98419i	−0.447547	−	0.169732i
$552$	23.1223	−	44.0558i	0.984149	−	1.87514i
$553$	1.26750	+	0.480700i	0.0538997	+	0.0204414i
$554$	2.26340	+	2.55486i	0.0961628	+	0.108545i
$555$	18.0888	−	16.0253i	0.767827	−	0.680236i
$556$	−1.85380	+	2.68569i	−0.0786187	+	0.113899i
$557$	2.41475	+	1.66678i	0.102316	+	0.0706238i	0.618124	−	0.786080i	$-0.287893\pi$
$557$	2.41475	+	1.66678i	0.102316	+	0.0706238i	−0.515808	+	0.856704i	$0.672508\pi$
$558$	10.0769	+	5.28878i	0.426590	+	0.223892i
$559$	−2.74557	+	8.91035i	−0.116125	+	0.376867i
$560$	−7.40292	+	3.88535i	−0.312831	+	0.164186i
$561$	−3.35403	−	0.407253i	−0.141607	−	0.0171942i
$562$	51.6851	−	12.7392i	2.18020	−	0.537372i
$563$	19.3272	−	28.0002i	0.814542	−	1.18007i	−0.166455	−	0.986049i	$-0.553232\pi$
$563$	19.3272	−	28.0002i	0.814542	−	1.18007i	0.980998	−	0.194019i	$-0.0621525\pi$
$564$	−45.3712	+	31.3175i	−1.91047	+	1.31871i
$565$	29.4371	−	33.2276i	1.23843	−	1.39790i
$566$	−5.44275	−	0.660870i	−0.228776	−	0.0277784i
$567$	−0.0767782	+	0.311501i	−0.00322438	+	0.0130818i
$568$	−45.0683	−	23.6537i	−1.89103	−	0.992487i
$569$	2.77364	−	22.8430i	0.116277	−	0.957629i	−0.811463	−	0.584403i	$-0.801329\pi$
$569$	2.77364	−	22.8430i	0.116277	−	0.957629i	0.927741	−	0.373226i	$-0.121748\pi$
$570$	−9.15126	+	1.11116i	−0.383304	+	0.0465415i
$571$	−8.97922	+	13.0087i	−0.375769	+	0.544395i	−0.964551	−	0.263897i	$-0.914992\pi$
$571$	−8.97922	+	13.0087i	−0.375769	+	0.544395i	0.588782	+	0.808292i	$0.299608\pi$
$572$	−7.08908	+	15.8859i	−0.296409	+	0.664222i
$573$	−3.26406	−	4.72881i	−0.136358	−	0.197549i
$574$	2.61544	+	2.95222i	0.109166	+	0.123223i
$575$	33.0330	+	8.14191i	1.37757	+	0.339541i
$576$	−2.05515	−	2.97740i	−0.0856313	−	0.124058i
$577$			27.9621i			1.16408i	0.813161	+	0.582039i	$0.197745\pi$
$577$			27.9621i			1.16408i	−0.813161	+	0.582039i	$0.802255\pi$
$578$	13.5156	−	9.32917i	0.562176	−	0.388042i
$579$	15.1356	−	1.83779i	0.629013	−	0.0763760i
$580$	132.644	−	50.3054i	5.50776	−	2.08882i
$581$	−0.00985653	+	0.0811758i	−0.000408918	+	0.00336774i
$582$	−13.8665	−	36.5630i	−0.574786	−	1.51558i
$583$	−4.70115	+	5.30650i	−0.194702	+	0.219773i
$584$	−3.48918	−	3.09114i	−0.144383	−	0.127912i
$585$	−9.62204	−	5.77509i	−0.397822	−	0.238770i
$586$	10.9356	−	9.68814i	0.451747	−	0.400213i
$587$		−	32.2243i		−	1.33004i	−0.746825	−	0.665020i	$-0.768423\pi$
$587$		−	32.2243i		−	1.33004i	0.746825	−	0.665020i	$-0.231577\pi$
$588$	24.0413	+	21.2987i	0.991445	+	0.878344i
$589$	−4.91633	+	1.21177i	−0.202574	+	0.0499300i
$590$	34.4625	+	23.7877i	1.41880	+	0.979325i
$591$	−9.44049	+	3.58030i	−0.388330	+	0.147274i
$592$	−60.7850	+	23.0527i	−2.49825	+	0.947461i
$593$	9.31998	+	6.43312i	0.382726	+	0.264176i	0.743857	−	0.668338i	$-0.232994\pi$
$593$	9.31998	+	6.43312i	0.382726	+	0.264176i	−0.361132	+	0.932515i	$0.617610\pi$
$594$	−2.59542	+	0.639714i	−0.106492	+	0.0262478i
$595$	2.43743	+	2.15937i	0.0999249	+	0.0885257i
$596$			88.9315i			3.64277i
$597$	−10.9413	+	9.69314i	−0.447797	+	0.396714i
$598$	−27.5157	+	61.6598i	−1.12520	+	2.52146i
$599$	−18.6827	−	16.5515i	−0.763356	−	0.676274i	0.188756	−	0.982024i	$-0.439554\pi$
$599$	−18.6827	−	16.5515i	−0.763356	−	0.676274i	−0.952112	+	0.305750i	$0.901093\pi$
$600$	21.3072	−	24.0508i	0.869861	−	0.981870i
$601$	14.7808	+	38.9737i	0.602920	+	1.58977i	0.793815	+	0.608160i	$0.208092\pi$
$601$	14.7808	+	38.9737i	0.602920	+	1.58977i	−0.190894	+	0.981611i	$0.561139\pi$
$602$	0.258012	−	2.12492i	0.0105158	−	0.0866054i
$603$	−8.01768	+	3.04070i	−0.326505	+	0.123827i
$604$	−67.7526	+	8.22666i	−2.75681	+	0.334738i
$605$	25.4269	−	17.5509i	1.03375	−	0.713547i
$606$			30.3076i			1.23116i
$607$	−6.12256	−	8.87006i	−0.248507	−	0.360025i	0.678802	−	0.734321i	$-0.262500\pi$
$607$	−6.12256	−	8.87006i	−0.248507	−	0.360025i	−0.927309	+	0.374297i	$0.877884\pi$
$608$	8.79686	+	2.16823i	0.356760	+	0.0879334i
$609$	2.08225	+	2.35038i	0.0843772	+	0.0952422i
$610$	−15.4343	−	22.3605i	−0.624917	−	0.905349i
$611$	33.5165	−	26.4307i	1.35593	−	1.06927i
$612$	−8.62696	+	12.4983i	−0.348724	+	0.505214i
$613$	−8.31869	+	1.01007i	−0.335989	+	0.0407964i	−0.286793	−	0.957993i	$-0.592589\pi$
$613$	−8.31869	+	1.01007i	−0.335989	+	0.0407964i	−0.0491963	+	0.998789i	$0.515666\pi$
$614$	0.311772	−	2.56767i	0.0125821	−	0.103623i
$615$	−13.1316	−	6.89199i	−0.529517	−	0.277912i
$616$	0.545286	−	2.21231i	0.0219702	−	0.0891365i
$617$	21.8249	+	2.65002i	0.878637	+	0.106686i	0.547409	−	0.836865i	$-0.315614\pi$
$617$	21.8249	+	2.65002i	0.878637	+	0.106686i	0.331228	+	0.943551i	$0.392537\pi$
$618$	16.4235	−	18.5383i	0.660651	−	0.745720i
$619$	−9.73114	+	6.71692i	−0.391128	+	0.269976i	−0.747357	−	0.664423i	$-0.768678\pi$
$619$	−9.73114	+	6.71692i	−0.391128	+	0.269976i	0.356230	+	0.934398i	$0.384062\pi$
$620$	36.3179	−	52.6155i	1.45856	−	2.11309i
$621$	−7.04731	+	1.73700i	−0.282799	+	0.0697036i
$622$	−42.6355	−	5.17689i	−1.70953	−	0.207574i
$623$	−4.78449	+	2.51109i	−0.191686	+	0.100605i
$624$	18.6931	+	23.7045i	0.748322	+	0.948940i
$625$	−23.4341	−	12.2992i	−0.937365	−	0.491967i
$626$	18.4531	+	12.7372i	0.737533	+	0.509082i
$627$	0.675615	−	0.978798i	0.0269815	−	0.0390894i
$628$	58.7387	−	52.0380i	2.34393	−	2.07654i
$629$	16.7907	+	18.9528i	0.669490	+	0.755698i
$630$	2.40892	+	0.913584i	0.0959738	+	0.0363981i
$631$	−8.83481	+	16.8333i	−0.351708	+	0.670124i	−0.995467	−	0.0951042i	$-0.969682\pi$
$631$	−8.83481	+	16.8333i	−0.351708	+	0.670124i	0.643759	+	0.765228i	$0.277374\pi$
$632$	27.0825	+	10.2710i	1.07728	+	0.408559i
$633$	24.1006	+	5.94028i	0.957915	+	0.236105i
$634$	44.5745	−	39.4895i	1.77028	−	1.56833i
$635$	−44.5950	+	30.7817i	−1.76970	+	1.22153i
$636$	11.2998	+	29.7951i	0.448065	+	1.18145i
$637$	−19.6241	−	15.2742i	−0.777534	−	0.605185i
$638$	−9.27754	+	24.4629i	−0.367301	+	0.968494i
$639$	1.77693	+	7.20927i	0.0702941	+	0.285194i
$640$	17.7775	−	9.33037i	0.702719	−	0.368815i
$641$	−14.5268	−	38.3041i	−0.573775	−	1.51292i	−0.836454	−	0.548037i	$-0.815375\pi$
$641$	−14.5268	−	38.3041i	−0.573775	−	1.51292i	0.262679	−	0.964883i	$-0.415394\pi$
$642$	6.44778	−	0.782902i	0.254474	−	0.0308987i
$643$	1.60166	+	1.10555i	0.0631634	+	0.0435986i	0.599228	−	0.800578i	$-0.295474\pi$
$643$	1.60166	+	1.10555i	0.0631634	+	0.0435986i	−0.536065	+	0.844177i	$0.680090\pi$
$644$	2.59515	−	10.5289i	0.102263	−	0.414898i
$645$	1.92616	+	7.81474i	0.0758425	+	0.307705i
$646$	−1.16424	−	9.58836i	−0.0458063	−	0.377249i
$647$	−10.9417	+	28.8509i	−0.430162	+	1.13424i	0.528309	+	0.849052i	$0.322826\pi$
$647$	−10.9417	+	28.8509i	−0.430162	+	1.13424i	−0.958471	+	0.285192i	$0.907943\pi$
$648$	−1.64050	+	6.65579i	−0.0644451	+	0.261464i
$649$	−5.24555	+	1.29291i	−0.205906	+	0.0507512i
$650$	−26.7826	+	34.4100i	−1.05050	+	1.34967i
$651$	1.37400	+	0.338660i	0.0538512	+	0.0132731i
$652$	49.6266	−	94.5557i	1.94353	−	3.70309i
$653$	−19.0073			−0.743814			−0.371907	−	0.928270i	$-0.621296\pi$
$653$	−19.0073			−0.743814			−0.371907	+	0.928270i	$0.621296\pi$
$654$	11.5358			0.451087
$655$	7.34165	−	13.9883i	0.286862	−	0.546570i
$656$	26.4551	+	29.8616i	1.03290	+	1.16590i
$657$			0.680015i			0.0265299i
$658$	−6.49816	+	7.33491i	−0.253325	+	0.285945i
$659$	−7.48018	+	3.92590i	−0.291386	+	0.152931i	−0.604082	−	0.796922i	$-0.706460\pi$
$659$	−7.48018	+	3.92590i	−0.291386	+	0.152931i	0.312696	+	0.949853i	$0.398768\pi$
$660$	1.81007	+	14.9073i	0.0704569	+	0.580265i
$661$	0.144085	+	0.274532i	0.00560428	+	0.0106781i	0.888242	−	0.459376i	$-0.151927\pi$
$661$	0.144085	+	0.274532i	0.00560428	+	0.0106781i	−0.882638	+	0.470054i	$0.844235\pi$
$662$	7.21928	+	59.4561i	0.280585	+	2.31083i
$663$	6.05093	−	10.0816i	0.234999	−	0.391538i
$664$	−0.210603	+	1.73447i	−0.00817296	+	0.0673104i
$665$	−1.07179	+	0.406476i	−0.0415622	+	0.0157625i
$666$	17.7383	+	9.30978i	0.687346	+	0.360747i
$667$	−25.1911	+	66.4236i	−0.975405	+	2.57193i
$668$	−19.7888	−	37.7045i	−0.765653	−	1.45883i
$669$	−1.97571	−	3.76439i	−0.0763852	−	0.145540i
$670$	16.4793	+	66.8590i	0.636649	+	2.58299i
$671$	3.47980	+	0.422524i	0.134336	+	0.0163114i
$672$	−1.89530	−	1.67909i	−0.0731127	−	0.0647722i
$673$	5.69267	+	8.24725i	0.219436	+	0.317908i	0.917206	−	0.398414i	$-0.130439\pi$
$673$	5.69267	+	8.24725i	0.219436	+	0.317908i	−0.697769	+	0.716322i	$0.745824\pi$
$674$	−81.0138	−	30.7245i	−3.12053	−	1.18346i
$675$	−4.68733			−0.180415
$676$	−40.4320	−	45.0585i	−1.55508	−	1.73302i
$677$	−29.9657			−1.15168			−0.575838	−	0.817564i	$-0.695324\pi$
$677$	−29.9657			−1.15168			−0.575838	+	0.817564i	$0.695324\pi$
$678$	34.4075	+	13.0490i	1.32141	+	0.501146i
$679$	−2.76218	−	4.00171i	−0.106003	−	0.153572i
$680$	52.0801	+	46.1389i	1.99718	+	1.76935i
$681$	18.6985	+	2.27040i	0.716527	+	0.0870021i
$682$	2.82171	+	11.4481i	0.108049	+	0.438371i
$683$	−16.8737	−	32.1502i	−0.645656	−	1.23019i	−0.959764	−	0.280807i	$-0.909398\pi$
$683$	−16.8737	−	32.1502i	−0.645656	−	1.23019i	0.314108	−	0.949387i	$-0.398294\pi$
$684$	−2.48434	−	4.73351i	−0.0949910	−	0.180990i
$685$	−7.03265	+	18.5436i	−0.268704	+	0.708513i
$686$	10.1857	+	5.34589i	0.388893	+	0.204107i
$687$	−8.68087	+	3.29222i	−0.331196	+	0.125606i
$688$	2.60979	−	21.4936i	0.0994974	−	0.819434i
$689$	−10.1970	−	22.4660i	−0.388476	−	0.855887i
$690$	7.02565	+	57.8614i	0.267462	+	2.20275i
$691$	−12.5917	−	23.9915i	−0.479011	−	0.912678i	−0.998312	−	0.0580870i	$-0.981500\pi$
$691$	−12.5917	−	23.9915i	−0.479011	−	0.912678i	0.519301	−	0.854591i	$-0.326192\pi$
$692$	1.22742	+	10.1087i	0.0466594	+	0.384275i
$693$	−0.294316	+	0.154469i	−0.0111801	+	0.00586779i
$694$	−46.8071	+	52.8343i	−1.77677	+	2.00556i
$695$		−	2.18109i		−	0.0827333i
$696$	44.4911	+	50.2201i	1.68643	+	1.90359i
$697$	7.22117	−	13.7588i	0.273521	−	0.521152i
$698$	−46.3360			−1.75384
$699$	−14.8763			−0.562675
$700$	3.25447	−	6.20088i	0.123008	−	0.234371i
$701$	13.8292	+	3.40859i	0.522322	+	0.128741i	0.491657	−	0.870789i	$-0.336391\pi$
$701$	13.8292	+	3.40859i	0.522322	+	0.128741i	0.0306650	+	0.999530i	$0.490238\pi$
$702$	1.64779	−	9.15555i	0.0621917	−	0.345554i
$703$	−8.65416	+	2.13306i	−0.326398	+	0.0804498i
$704$	0.897009	−	3.63931i	0.0338073	−	0.137162i
$705$	13.0660	−	34.4521i	0.492093	−	1.29754i
$706$	−10.6029	−	87.3224i	−0.399044	−	3.28642i
$707$	0.901891	+	3.65912i	0.0339191	+	0.137615i
$708$	−5.81144	+	23.5779i	−0.218407	+	0.886113i
$709$	24.9600	+	17.2287i	0.937394	+	0.647036i	0.935638	−	0.352962i	$-0.114826\pi$
$709$	24.9600	+	17.2287i	0.937394	+	0.647036i	0.00175608	+	0.999998i	$0.499441\pi$
$710$	59.1912	−	7.18712i	2.22141	−	0.269728i
$711$	−1.49833	−	3.95077i	−0.0561918	−	0.148166i
$712$	−102.229	+	53.6540i	−3.83120	+	2.01077i
$713$	7.66173	+	31.0849i	0.286934	+	1.16414i
$714$	−0.957221	+	2.52398i	−0.0358231	+	0.0944577i
$715$	−2.13206	−	11.4295i	−0.0797345	−	0.427438i
$716$	−0.338127	−	0.891568i	−0.0126364	−	0.0333195i
$717$	10.6886	−	7.37779i	0.399172	−	0.275529i
$718$	31.8370	−	28.2051i	1.18815	−	1.05261i
$719$	29.2181	+	7.20161i	1.08965	+	0.268575i	0.742913	−	0.669388i	$-0.233443\pi$
$719$	29.2181	+	7.20161i	1.08965	+	0.268575i	0.346737	+	0.937962i	$0.387290\pi$
$720$	24.3662	+	9.24090i	0.908076	+	0.344388i
$721$	1.43119	−	2.72691i	0.0533004	−	0.101555i
$722$	−42.6571	−	16.1777i	−1.58753	−	0.602072i
$723$	−0.0802587	−	0.0905933i	−0.00298485	−	0.00336920i
$724$	−53.3308	+	47.2469i	−1.98202	+	1.75592i
$725$	−26.0613	+	37.7563i	−0.967893	+	1.40223i
$726$	21.0779	+	14.5490i	0.782274	+	0.539965i
$727$	18.5485	+	9.73502i	0.687927	+	0.361052i	0.772190	−	0.635392i	$-0.219161\pi$
$727$	18.5485	+	9.73502i	0.687927	+	0.361052i	−0.0842630	+	0.996444i	$0.526854\pi$
$728$	6.25745	+	4.87042i	0.231917	+	0.180510i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	5.42098	+	0.658226i	0.200639	+	0.0243620i
$731$	−8.18800	+	2.01816i	−0.302844	+	0.0746443i
$732$	8.95045	−	12.9670i	0.330818	−	0.479273i
$733$	−27.6756	+	19.1031i	−1.02222	+	0.705590i	−0.956346	−	0.292238i	$-0.905600\pi$
$733$	−27.6756	+	19.1031i	−1.02222	+	0.705590i	−0.0658777	+	0.997828i	$0.520985\pi$
$734$	27.3594	−	30.8824i	1.00985	−	1.13989i
$735$	−21.3103	−	2.58753i	−0.786041	−	0.0954426i
$736$	13.7092	−	55.6206i	0.505330	−	2.05020i
$737$	−7.86641	−	4.12861i	−0.289763	−	0.152079i
$738$	1.48184	−	12.2041i	0.0545474	−	0.449239i
$739$	24.2966	−	2.95014i	0.893766	−	0.108523i	0.339250	−	0.940696i	$-0.389827\pi$
$739$	24.2966	−	2.95014i	0.893766	−	0.108523i	0.554515	+	0.832173i	$0.312904\pi$
$740$	63.9300	−	92.6185i	2.35011	−	3.40473i
$741$	2.15249	+	3.53525i	0.0790736	+	0.129870i
$742$	3.21759	+	4.66148i	0.118121	+	0.171128i
$743$	5.13975	+	5.80158i	0.188559	+	0.212839i	0.835187	−	0.549967i	$-0.185360\pi$
$743$	5.13975	+	5.80158i	0.188559	+	0.212839i	−0.646627	+	0.762806i	$0.723821\pi$
$744$	29.3579	+	7.23608i	1.07631	+	0.265288i
$745$	−33.7645	−	48.9164i	−1.23704	−	1.79216i
$746$			4.38663i			0.160606i
$747$	0.209763	−	0.144789i	0.00767483	−	0.00529756i
$748$	−15.6193	+	1.89653i	−0.571098	+	0.0693439i
$749$	0.755160	−	0.286394i	0.0275930	−	0.0104646i
$750$	0.302655	−	2.49258i	0.0110514	−	0.0910163i
$751$	−3.90630	−	10.3001i	−0.142543	−	0.375855i	0.844664	−	0.535296i	$-0.179800\pi$
$751$	−3.90630	−	10.3001i	−0.142543	−	0.375855i	−0.987207	+	0.159441i	$0.949031\pi$
$752$	−65.7289	+	74.1925i	−2.39688	+	2.70552i
$753$	2.03711	+	1.80472i	0.0742362	+	0.0657676i
$754$	−64.5862	−	64.1773i	−2.35209	−	2.33720i
$755$	34.1436	−	30.2486i	1.24261	−	1.10086i
$756$			1.49404i			0.0543376i
$757$	−16.7150	−	14.8082i	−0.607518	−	0.538214i	0.302305	−	0.953211i	$-0.402244\pi$
$757$	−16.7150	−	14.8082i	−0.607518	−	0.538214i	−0.909823	+	0.414997i	$0.863782\pi$
$758$	74.4954	−	18.3615i	2.70579	−	0.666918i
$759$	−6.18872	−	4.27177i	−0.224636	−	0.155055i
$760$	−22.9007	+	8.68510i	−0.830697	+	0.315042i
$761$	−2.10860	+	0.799687i	−0.0764368	+	0.0289886i	−0.392527	−	0.919741i	$-0.628399\pi$
$761$	−2.10860	+	0.799687i	−0.0764368	+	0.0289886i	0.316090	+	0.948729i	$0.397630\pi$
$762$	−36.9674	−	25.5168i	−1.33919	−	0.924375i
$763$	1.39275	−	0.343282i	0.0504210	−	0.0124277i
$764$	−20.0287	−	17.7439i	−0.724613	−	0.641951i
$765$		−	10.1500i		−	0.366975i
$766$	−64.0974	+	56.7853i	−2.31593	+	2.05174i
$767$	3.33031	−	18.5041i	0.120250	−	0.668143i
$768$	17.8736	+	15.8346i	0.644958	+	0.571383i
$769$	−3.49063	+	3.94011i	−0.125875	+	0.142084i	−0.808069	−	0.589087i	$-0.799487\pi$
$769$	−3.49063	+	3.94011i	−0.125875	+	0.142084i	0.682194	+	0.731171i	$0.261026\pi$

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.41243 - 0.914913i) q^{2} +(0.568065 + 0.822984i) q^{3} +(3.48572 + 3.08808i) q^{4} +(-3.08975 - 0.375164i) q^{5} +(-0.617456 - 2.50512i) q^{6} +(-0.149094 - 0.284076i) q^{7} +(-3.18567 - 6.06979i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(7.11057 + 3.73191i) q^{10} +(-0.968722 + 0.367388i) q^{11} +(-0.561324 + 4.62292i) q^{12} +(0.206269 - 3.59965i) q^{13} +(0.0997749 + 0.821720i) q^{14} +(-1.44643 - 2.75594i) q^{15} +(1.00922 + 8.31169i) q^{16} +(2.88757 - 1.51551i) q^{17} +(1.71092 - 1.93123i) q^{18} +1.14795i q^{19} +(-9.61148 - 10.8491i) q^{20} +(0.149094 - 0.284076i) q^{21} +2.67310 q^{22} +7.25822 q^{23} +(3.18567 - 6.06979i) q^{24} +(4.55112 + 1.12175i) q^{25} +(-3.79097 + 8.49517i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(0.357546 - 1.45062i) q^{28} +(-3.47071 + 9.15150i) q^{29} +(0.967958 + 7.97185i) q^{30} +(1.05559 + 4.28271i) q^{31} +(1.88879 - 7.66312i) q^{32} +(-0.852651 - 0.588542i) q^{33} +(-8.35261 + 1.01419i) q^{34} +(0.354090 + 0.933658i) q^{35} +(-4.12346 + 2.16416i) q^{36} +(1.85815 + 7.53882i) q^{37} +(1.05027 - 2.76934i) q^{38} +(3.07963 - 1.87508i) q^{39} +(7.56577 + 19.9493i) q^{40} +(3.92138 - 2.70674i) q^{41} +(-0.619584 + 0.548903i) q^{42} +(-2.51080 - 0.618857i) q^{43} +(-4.51122 - 1.71088i) q^{44} +(1.44643 - 2.75594i) q^{45} +(-17.5099 - 6.64064i) q^{46} +(7.85034 + 8.86121i) q^{47} +(-6.26708 + 5.55215i) q^{48} +(3.91798 - 5.67618i) q^{49} +(-9.95295 - 6.87002i) q^{50} +(2.88757 + 1.51551i) q^{51} +(11.8350 - 11.9104i) q^{52} +(6.05895 - 3.17998i) q^{53} +(2.56128 + 0.310996i) q^{54} +(3.13094 - 0.771708i) q^{55} +(-1.24931 + 1.80994i) q^{56} +(-0.944742 + 0.652108i) q^{57} +(16.7457 - 18.9019i) q^{58} +(5.17654 + 0.628546i) q^{59} +(3.46871 - 14.0731i) q^{60} +(-2.99585 - 1.57234i) q^{61} +(1.37177 - 11.2975i) q^{62} +(0.318485 - 0.0386711i) q^{63} +(-2.05515 + 2.97740i) q^{64} +(-1.98778 + 11.0446i) q^{65} +(1.51849 + 2.19992i) q^{66} +(5.68622 + 6.41841i) q^{67} +(14.7453 + 3.63439i) q^{68} +(4.12314 + 5.97339i) q^{69} -2.57634i q^{70} +(6.11068 - 4.21790i) q^{71} +(6.80500 - 0.826277i) q^{72} +(0.635825 - 0.241137i) q^{73} +(2.41471 - 19.8869i) q^{74} +(1.66215 + 4.38273i) q^{75} +(-3.54495 + 4.00142i) q^{76} +(0.248797 + 0.220415i) q^{77} +(-9.14491 + 1.70590i) q^{78} +(-3.16272 + 2.80193i) q^{79} -26.0597i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-11.9365 + 2.94208i) q^{82} +(-0.209763 - 0.144789i) q^{83} +(1.39695 - 0.529793i) q^{84} +(-9.49044 + 3.59925i) q^{85} +(5.49093 + 3.79011i) q^{86} +(-9.50312 + 2.34231i) q^{87} +(5.31599 + 4.70956i) q^{88} -16.8423i q^{89} +(-6.01084 + 5.32514i) q^{90} +(-1.05332 + 0.478091i) q^{91} +(25.3001 + 22.4139i) q^{92} +(-2.92496 + 3.30160i) q^{93} +(-10.8312 - 28.5594i) q^{94} +(0.430668 - 3.54687i) q^{95} +(7.37958 - 2.79871i) q^{96} +(15.0456 - 1.82687i) q^{97} +(-14.6451 + 10.1088i) q^{98} -1.03605i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

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