LMFDB - Embedded newform 507.2.p.a.64.5

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			64.5
Character	$\chi$	$=$	507.64
Dual form			507.2.p.a.103.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16970 - 0.142027i) q^{2} +(-0.748511 + 0.663123i) q^{3} +(-0.593855 - 0.146372i) q^{4} +(1.79511 + 3.42030i) q^{5} +(0.969716 - 0.669346i) q^{6} +(2.92200 + 1.10817i) q^{7} +(2.87729 + 1.09121i) q^{8} +(0.120537 - 0.992709i) q^{9} +(-1.61397 - 4.25568i) q^{10} +(-2.60991 + 0.316900i) q^{11} +(0.541569 - 0.284237i) q^{12} +(3.28629 + 1.48333i) q^{13} +(-3.26047 - 1.71123i) q^{14} +(-3.61173 - 1.36975i) q^{15} +(-2.12745 - 1.11657i) q^{16} +(-0.611607 + 1.61268i) q^{17} +(-0.281984 + 1.14405i) q^{18} -7.31198i q^{19} +(-0.565399 - 2.29391i) q^{20} +(-2.92200 + 1.10817i) q^{21} +3.09782 q^{22} +8.64905 q^{23} +(-2.87729 + 1.09121i) q^{24} +(-5.63568 + 8.16469i) q^{25} +(-3.63331 - 2.20180i) q^{26} +(0.568065 + 0.822984i) q^{27} +(-1.57304 - 1.08579i) q^{28} +(-0.653320 + 5.38057i) q^{29} +(4.03011 + 2.11516i) q^{30} +(-7.24520 + 5.00100i) q^{31} +(-2.73518 - 1.88796i) q^{32} +(1.74340 - 1.96789i) q^{33} +(0.944442 - 1.79948i) q^{34} +(1.45505 + 11.9834i) q^{35} +(-0.216886 + 0.571881i) q^{36} +(1.28328 - 0.885784i) q^{37} +(-1.03850 + 8.55283i) q^{38} +(-3.44346 + 1.06893i) q^{39} +(1.43278 + 11.8000i) q^{40} +(1.66641 + 1.88099i) q^{41} +(3.57525 - 0.881221i) q^{42} +(0.399840 - 0.579269i) q^{43} +(1.59629 + 0.193825i) q^{44} +(3.61173 - 1.36975i) q^{45} +(-10.1168 - 1.22840i) q^{46} +(0.852814 + 3.46000i) q^{47} +(2.33284 - 0.574994i) q^{48} +(2.07046 + 1.83427i) q^{49} +(7.75167 - 8.74983i) q^{50} +(-0.611607 - 1.61268i) q^{51} +(-1.73446 - 1.36190i) q^{52} +(-2.08039 + 5.48553i) q^{53} +(-0.547580 - 1.04333i) q^{54} +(-5.76897 - 8.35779i) q^{55} +(7.19819 + 6.37704i) q^{56} +(4.84874 + 5.47309i) q^{57} +(1.52838 - 6.20087i) q^{58} +(2.32799 + 4.43561i) q^{59} +(1.94435 + 1.34209i) q^{60} +(-3.51916 - 9.27926i) q^{61} +(9.18499 - 4.82066i) q^{62} +(1.45230 - 2.76712i) q^{63} +(6.52803 + 5.78333i) q^{64} +(0.825828 + 13.9028i) q^{65} +(-2.31875 + 2.05424i) q^{66} +(-1.27249 - 5.16269i) q^{67} +(0.599256 - 0.868172i) q^{68} +(-6.47391 + 5.73538i) q^{69} -14.2236i q^{70} +(-6.15715 - 6.94998i) q^{71} +(1.43007 - 2.72478i) q^{72} +(-11.4133 + 1.38582i) q^{73} +(-1.62686 + 0.853842i) q^{74} +(-1.19583 - 9.84851i) q^{75} +(-1.07027 + 4.34225i) q^{76} +(-7.97733 - 1.96624i) q^{77} +(4.17963 - 0.761260i) q^{78} +(6.55153 - 1.61481i) q^{79} -9.28087i q^{80} +(-0.970942 - 0.239316i) q^{81} +(-1.68205 - 2.43687i) q^{82} +(3.46761 - 3.91412i) q^{83} +(1.89745 - 0.230392i) q^{84} +(-6.61373 + 0.803052i) q^{85} +(-0.549966 + 0.620783i) q^{86} +(-3.07896 - 4.46065i) q^{87} +(-7.85527 - 1.93615i) q^{88} -3.17610i q^{89} +(-4.41919 + 1.08923i) q^{90} +(7.95877 + 7.97606i) q^{91} +(-5.13628 - 1.26598i) q^{92} +(2.10683 - 8.54775i) q^{93} +(-0.506122 - 4.16829i) q^{94} +(25.0091 - 13.1258i) q^{95} +(3.29926 - 0.400602i) q^{96} +(-2.76441 + 5.26715i) q^{97} +(-2.16131 - 2.43961i) q^{98} +2.62908i 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.16970	−	0.142027i	−0.827104	−	0.100429i	−0.303973	−	0.952681i	$-0.598313\pi$
$2$	−1.16970	−	0.142027i	−0.827104	−	0.100429i	−0.523131	+	0.852252i	$0.675236\pi$
$3$	−0.748511	+	0.663123i	−0.432153	+	0.382854i
$3$	−0.748511	+	0.663123i	−0.432153	+	0.382854i
$4$	−0.593855	−	0.146372i	−0.296927	−	0.0731860i
$5$	1.79511	+	3.42030i	0.802798	+	1.52960i	0.847617	+	0.530608i	$0.178036\pi$
$5$	1.79511	+	3.42030i	0.802798	+	1.52960i	−0.0448200	+	0.998995i	$0.514271\pi$
$6$	0.969716	−	0.669346i	0.395885	−	0.273259i
$7$	2.92200	+	1.10817i	1.10441	+	0.418848i	0.838363	−	0.545112i	$-0.183513\pi$
$7$	2.92200	+	1.10817i	1.10441	+	0.418848i	0.266048	+	0.963960i	$0.414282\pi$
$8$	2.87729	+	1.09121i	1.01728	+	0.385802i
$9$	0.120537	−	0.992709i	0.0401789	−	0.330903i
$10$	−1.61397	−	4.25568i	−0.510381	−	1.34576i
$11$	−2.60991	+	0.316900i	−0.786917	+	0.0955491i	−0.504123	−	0.863632i	$-0.668184\pi$
$11$	−2.60991	+	0.316900i	−0.786917	+	0.0955491i	−0.282794	+	0.959181i	$0.591261\pi$
$12$	0.541569	−	0.284237i	0.156338	−	0.0820523i
$13$	3.28629	+	1.48333i	0.911454	+	0.411402i
$13$	3.28629	+	1.48333i	0.911454	+	0.411402i
$14$	−3.26047	−	1.71123i	−0.871398	−	0.457345i
$15$	−3.61173	−	1.36975i	−0.932546	−	0.353668i
$16$	−2.12745	−	1.11657i	−0.531862	−	0.279143i
$17$	−0.611607	+	1.61268i	−0.148337	+	0.391131i	−0.988504	−	0.151196i	$-0.951688\pi$
$17$	−0.611607	+	1.61268i	−0.148337	+	0.391131i	0.840167	+	0.542327i	$0.182457\pi$
$18$	−0.281984	+	1.14405i	−0.0664642	+	0.269656i
$19$		−	7.31198i		−	1.67748i	−0.544530	−	0.838741i	$-0.683292\pi$
$19$		−	7.31198i		−	1.67748i	0.544530	−	0.838741i	$-0.316708\pi$
$20$	−0.565399	−	2.29391i	−0.126427	−	0.512934i
$21$	−2.92200	+	1.10817i	−0.637632	+	0.241822i
$22$	3.09782			0.660458
$23$	8.64905			1.80345			0.901726	−	0.432308i	$-0.142301\pi$
$23$	8.64905			1.80345			0.901726	+	0.432308i	$0.142301\pi$
$24$	−2.87729	+	1.09121i	−0.587324	+	0.222743i
$25$	−5.63568	+	8.16469i	−1.12714	+	1.63294i
$26$	−3.63331	−	2.20180i	−0.712550	−	0.431808i
$27$	0.568065	+	0.822984i	0.109324	+	0.158383i
$28$	−1.57304	−	1.08579i	−0.297276	−	0.205195i
$29$	−0.653320	+	5.38057i	−0.121318	+	0.999147i	0.797185	+	0.603735i	$0.206321\pi$
$29$	−0.653320	+	5.38057i	−0.121318	+	0.999147i	−0.918504	+	0.395413i	$0.870602\pi$
$30$	4.03011	+	2.11516i	0.735794	+	0.386174i
$31$	−7.24520	+	5.00100i	−1.30128	+	0.898206i	−0.998494	−	0.0548543i	$-0.982531\pi$
$31$	−7.24520	+	5.00100i	−1.30128	+	0.898206i	−0.302781	+	0.953060i	$0.597915\pi$
$32$	−2.73518	−	1.88796i	−0.483516	−	0.333747i
$33$	1.74340	−	1.96789i	0.303487	−	0.342566i
$34$	0.944442	−	1.79948i	0.161970	−	0.308609i
$35$	1.45505	+	11.9834i	0.245948	+	2.02556i
$36$	−0.216886	+	0.571881i	−0.0361477	+	0.0953136i
$37$	1.28328	−	0.885784i	0.210970	−	0.145622i	−0.457894	−	0.889007i	$-0.651396\pi$
$37$	1.28328	−	0.885784i	0.210970	−	0.145622i	0.668864	+	0.743385i	$0.266781\pi$
$38$	−1.03850	+	8.55283i	−0.168467	+	1.38745i
$39$	−3.44346	+	1.06893i	−0.551394	+	0.171165i
$40$	1.43278	+	11.8000i	0.226543	+	1.86575i
$41$	1.66641	+	1.88099i	0.260250	+	0.293762i	0.864083	−	0.503349i	$-0.167899\pi$
$41$	1.66641	+	1.88099i	0.260250	+	0.293762i	−0.603833	+	0.797111i	$0.706361\pi$
$42$	3.57525	−	0.881221i	0.551674	−	0.135975i
$43$	0.399840	−	0.579269i	0.0609751	−	0.0883377i	−0.791310	−	0.611415i	$-0.790601\pi$
$43$	0.399840	−	0.579269i	0.0609751	−	0.0883377i	0.852285	+	0.523077i	$0.175216\pi$
$44$	1.59629	+	0.193825i	0.240650	+	0.0292202i
$45$	3.61173	−	1.36975i	0.538406	−	0.204190i
$46$	−10.1168	−	1.22840i	−1.49164	−	0.181118i
$47$	0.852814	+	3.46000i	0.124396	+	0.504693i	0.999774	+	0.0212549i	$0.00676617\pi$
$47$	0.852814	+	3.46000i	0.124396	+	0.504693i	−0.875378	+	0.483438i	$0.839388\pi$
$48$	2.33284	−	0.574994i	0.336717	−	0.0829932i
$49$	2.07046	+	1.83427i	0.295780	+	0.262038i
$50$	7.75167	−	8.74983i	1.09625	−	1.23741i
$51$	−0.611607	−	1.61268i	−0.0856421	−	0.225820i
$52$	−1.73446	−	1.36190i	−0.240527	−	0.188862i
$53$	−2.08039	+	5.48553i	−0.285763	+	0.753496i	0.712873	+	0.701293i	$0.247394\pi$
$53$	−2.08039	+	5.48553i	−0.285763	+	0.753496i	−0.998636	+	0.0522030i	$0.983376\pi$
$54$	−0.547580	−	1.04333i	−0.0745162	−	0.141979i
$55$	−5.76897	−	8.35779i	−0.777887	−	1.12696i
$56$	7.19819	+	6.37704i	0.961898	+	0.852167i
$57$	4.84874	+	5.47309i	0.642231	+	0.724929i
$58$	1.52838	−	6.20087i	0.200686	−	0.814215i
$59$	2.32799	+	4.43561i	0.303078	+	0.577467i	0.988597	−	0.150588i	$-0.0481168\pi$
$59$	2.32799	+	4.43561i	0.303078	+	0.577467i	−0.685519	+	0.728055i	$0.740424\pi$
$60$	1.94435	+	1.34209i	0.251015	+	0.173263i
$61$	−3.51916	−	9.27926i	−0.450582	−	1.18809i	−0.947349	−	0.320203i	$-0.896249\pi$
$61$	−3.51916	−	9.27926i	−0.450582	−	1.18809i	0.496767	−	0.867884i	$-0.334520\pi$
$62$	9.18499	−	4.82066i	1.16650	−	0.612224i
$63$	1.45230	−	2.76712i	0.182972	−	0.348624i
$64$	6.52803	+	5.78333i	0.816003	+	0.722916i
$65$	0.825828	+	13.9028i	0.102431	+	1.72444i
$66$	−2.31875	+	2.05424i	−0.285419	+	0.252859i
$67$	−1.27249	−	5.16269i	−0.155459	−	0.630723i	−0.996030	−	0.0890206i	$-0.971626\pi$
$67$	−1.27249	−	5.16269i	−0.155459	−	0.630723i	0.840571	−	0.541702i	$-0.182220\pi$
$68$	0.599256	−	0.868172i	0.0726705	−	0.105281i
$69$	−6.47391	+	5.73538i	−0.779367	+	0.690459i
$70$		−	14.2236i		−	1.70005i
$71$	−6.15715	−	6.94998i	−0.730719	−	0.824811i	0.259293	−	0.965799i	$-0.416511\pi$
$71$	−6.15715	−	6.94998i	−0.730719	−	0.824811i	−0.990011	+	0.140988i	$0.954972\pi$
$72$	1.43007	−	2.72478i	0.168536	−	0.321118i
$73$	−11.4133	+	1.38582i	−1.33582	+	0.162198i	−0.757086	−	0.653315i	$-0.773378\pi$
$73$	−11.4133	+	1.38582i	−1.33582	+	0.162198i	−0.578738	+	0.815514i	$0.696454\pi$
$74$	−1.62686	+	0.853842i	−0.189119	+	0.0992571i
$75$	−1.19583	−	9.84851i	−0.138082	−	1.13721i
$76$	−1.07027	+	4.34225i	−0.122768	+	0.498090i
$77$	−7.97733	−	1.96624i	−0.909101	−	0.224073i
$78$	4.17963	−	0.761260i	0.473250	−	0.0861957i
$79$	6.55153	−	1.61481i	0.737104	−	0.181680i	0.147147	−	0.989115i	$-0.452991\pi$
$79$	6.55153	−	1.61481i	0.737104	−	0.181680i	0.589957	+	0.807435i	$0.299145\pi$
$80$		−	9.28087i		−	1.03763i
$81$	−0.970942	−	0.239316i	−0.107882	−	0.0265906i
$82$	−1.68205	−	2.43687i	−0.185752	−	0.269108i
$83$	3.46761	−	3.91412i	0.380620	−	0.429631i	−0.526714	−	0.850043i	$-0.676576\pi$
$83$	3.46761	−	3.91412i	0.380620	−	0.429631i	0.907333	+	0.420412i	$0.138114\pi$
$84$	1.89745	−	0.230392i	0.207028	−	0.0251378i
$85$	−6.61373	+	0.803052i	−0.717360	+	0.0871032i
$86$	−0.549966	+	0.620783i	−0.0593043	+	0.0669408i
$87$	−3.07896	−	4.46065i	−0.330100	−	0.478232i
$88$	−7.85527	−	1.93615i	−0.837374	−	0.206394i
$89$		−	3.17610i		−	0.336666i	−0.985730	−	0.168333i	$-0.946162\pi$
$89$		−	3.17610i		−	0.336666i	0.985730	−	0.168333i	$-0.0538384\pi$
$90$	−4.41919	+	1.08923i	−0.465824	+	0.114815i
$91$	7.95877	+	7.97606i	0.834305	+	0.836118i
$92$	−5.13628	−	1.26598i	−0.535494	−	0.131987i
$93$	2.10683	−	8.54775i	0.218468	−	0.886361i
$94$	−0.506122	−	4.16829i	−0.0522025	−	0.429927i
$95$	25.0091	−	13.1258i	2.56588	−	1.34668i
$96$	3.29926	−	0.400602i	0.336729	−	0.0408863i
$97$	−2.76441	+	5.26715i	−0.280684	+	0.534798i	−0.984457	−	0.175627i	$-0.943805\pi$
$97$	−2.76441	+	5.26715i	−0.280684	+	0.534798i	0.703773	+	0.710425i	$0.251497\pi$
$98$	−2.16131	−	2.43961i	−0.218325	−	0.246438i
$99$			2.62908i			0.264232i
$100$	4.54186	−	4.02373i	0.454186	−	0.402373i
$101$	1.87586	−	2.71766i	0.186655	−	0.270417i	−0.718473	−	0.695554i	$-0.755159\pi$
$101$	1.87586	−	2.71766i	0.186655	−	0.270417i	0.905129	+	0.425137i	$0.139774\pi$
$102$	0.486353	+	1.97321i	0.0481562	+	0.195377i
$103$	3.28646	−	2.91155i	0.323825	−	0.286884i	−0.485510	−	0.874231i	$-0.661366\pi$
$103$	3.28646	−	2.91155i	0.323825	−	0.286884i	0.809335	+	0.587347i	$0.199828\pi$
$104$	7.83699	+	7.85401i	0.768480	+	0.770149i
$105$	−9.03557	−	8.00482i	−0.881781	−	0.781190i
$106$	3.21253	−	6.12096i	0.312028	−	0.594521i
$107$	−14.0175	+	7.35694i	−1.35512	+	0.711222i	−0.976740	−	0.214428i	$-0.931211\pi$
$107$	−14.0175	+	7.35694i	−1.35512	+	0.711222i	−0.378381	+	0.925650i	$0.623519\pi$
$108$	−0.216886	−	0.571881i	−0.0208699	−	0.0550293i
$109$	5.96066	+	4.11435i	0.570928	+	0.394083i	0.818260	−	0.574848i	$-0.194939\pi$
$109$	5.96066	+	4.11435i	0.570928	+	0.394083i	−0.247333	+	0.968931i	$0.579554\pi$
$110$	5.56093	+	10.5955i	0.530214	+	1.01024i
$111$	−0.373165	+	1.51399i	−0.0354193	+	0.143702i
$112$	−4.97905	−	5.62019i	−0.470476	−	0.531058i
$113$	−5.21132	−	4.61683i	−0.490240	−	0.434315i	0.381437	−	0.924395i	$-0.375429\pi$
$113$	−5.21132	−	4.61683i	−0.490240	−	0.434315i	−0.871678	+	0.490080i	$0.836968\pi$
$114$	−4.89424	−	7.09054i	−0.458388	−	0.664090i
$115$	15.5260	+	29.5823i	1.44781	+	2.75857i
$116$	1.17554	−	3.09965i	0.109146	−	0.287795i
$117$	1.86863	−	3.08354i	0.172755	−	0.285073i
$118$	−2.09307	−	5.51897i	−0.192683	−	0.508063i
$119$	−3.57423	+	4.03447i	−0.327649	+	0.369839i
$120$	−8.89731	−	7.88233i	−0.812210	−	0.719555i
$121$	−3.96916	+	0.978309i	−0.360832	+	0.0889372i
$122$	2.79845	+	11.3538i	0.253360	+	1.02792i
$123$	−2.49466	−	0.302906i	−0.224936	−	0.0273121i
$124$	5.03460	−	1.90937i	0.452120	−	0.171467i
$125$	−18.8694	−	2.29116i	−1.68773	−	0.204928i
$126$	−2.09176	+	3.03044i	−0.186349	+	0.269973i
$127$	17.9304	−	4.41944i	1.59106	−	0.392162i	0.658330	−	0.752730i	$-0.271263\pi$
$127$	17.9304	−	4.41944i	1.59106	−	0.392162i	0.932733	+	0.360568i	$0.117417\pi$
$128$	−2.40669	−	2.71659i	−0.212723	−	0.240115i
$129$	0.0848414	+	0.698732i	0.00746987	+	0.0615199i
$130$	1.00861	−	16.3795i	0.0884612	−	1.43657i
$131$	1.56408	−	12.8813i	0.136654	−	1.12545i	−0.749483	−	0.662024i	$-0.769698\pi$
$131$	1.56408	−	12.8813i	0.136654	−	1.12545i	0.886137	−	0.463424i	$-0.153379\pi$
$132$	−1.32337	+	0.913457i	−0.115185	+	0.0795063i
$133$	8.10290	−	21.3656i	0.702610	−	1.85263i
$134$	0.755187	+	6.21953i	0.0652383	+	0.537285i
$135$	−1.79511	+	3.42030i	−0.154498	+	0.294372i
$136$	−3.51954	+	3.97274i	−0.301798	+	0.340660i
$137$	11.7976	+	8.14332i	1.00794	+	0.695731i	0.953066	−	0.302763i	$-0.0979089\pi$
$137$	11.7976	+	8.14332i	1.00794	+	0.695731i	0.0548740	+	0.998493i	$0.482524\pi$
$138$	8.38712	−	5.78921i	0.713959	−	0.492810i
$139$	−0.917058	−	0.481309i	−0.0777839	−	0.0408241i	0.425383	−	0.905014i	$-0.360139\pi$
$139$	−0.917058	−	0.481309i	−0.0777839	−	0.0408241i	−0.503167	+	0.864189i	$0.667832\pi$
$140$	0.889946	−	7.32936i	0.0752141	−	0.619444i
$141$	−2.93275	−	2.02433i	−0.246982	−	0.170479i
$142$	6.21493	+	9.00388i	0.521546	+	0.755589i
$143$	−9.04700	−	2.82993i	−0.756548	−	0.236651i
$144$	−1.36487	+	1.97735i	−0.113739	+	0.164779i
$145$	−19.5759	+	7.42417i	−1.62569	+	0.616544i
$146$	13.5470			1.12115
$147$	−2.76611			−0.228145
$148$	−0.891735	+	0.338191i	−0.0733002	+	0.0277991i
$149$	−1.44917	−	5.87953i	−0.118721	−	0.481670i	−0.999960	−	0.00899823i	$-0.997136\pi$
$149$	−1.44917	−	5.87953i	−0.118721	−	0.481670i	0.881238	−	0.472672i	$-0.156710\pi$
$150$			11.6897i			0.954456i
$151$	4.30382	−	17.4613i	0.350240	−	1.42098i	−0.486644	−	0.873600i	$-0.661779\pi$
$151$	4.30382	−	17.4613i	0.350240	−	1.42098i	0.836884	−	0.547380i	$-0.184375\pi$
$152$	7.97891	−	21.0387i	0.647175	−	1.70646i
$153$	1.52720	+	0.801534i	0.123466	+	0.0648002i
$154$	9.05183	+	3.43291i	0.729418	+	0.276632i
$155$	−30.1108	−	15.8034i	−2.41856	−	1.26936i
$156$	2.20137	−	0.130761i	0.176251	−	0.0104693i
$157$	0.599602	−	0.314696i	0.0478535	−	0.0251154i	−0.440627	−	0.897690i	$-0.645244\pi$
$157$	0.599602	−	0.314696i	0.0478535	−	0.0251154i	0.488480	+	0.872575i	$0.337551\pi$
$158$	−7.89267	+	0.958344i	−0.627907	+	0.0762418i
$159$	−2.08039	−	5.48553i	−0.164986	−	0.435031i
$160$	1.54743	−	12.7442i	0.122335	−	1.00752i
$161$	25.2725	+	9.58460i	1.99175	+	0.755372i
$162$	1.10172	+	0.417828i	0.0865595	+	0.0328277i
$163$	−5.09275	+	3.51527i	−0.398895	+	0.275337i	−0.750578	−	0.660782i	$-0.770225\pi$
$163$	−5.09275	+	3.51527i	−0.398895	+	0.275337i	0.351683	+	0.936119i	$0.385609\pi$
$164$	−0.714283	−	1.36095i	−0.0557761	−	0.106272i
$165$	9.86038	+	2.43036i	0.767629	+	0.189204i
$166$	−4.61198	+	4.08586i	−0.357959	+	0.317124i
$167$	−1.92873	−	0.234190i	−0.149249	−	0.0181221i	0.0455710	−	0.998961i	$-0.485489\pi$
$167$	−1.92873	−	0.234190i	−0.149249	−	0.0181221i	−0.194820	+	0.980839i	$0.562412\pi$
$168$	−9.61668			−0.741943
$169$	8.59946	+	9.74932i	0.661497	+	0.749948i
$170$	7.85014			0.602078
$171$	−7.25866	−	0.881361i	−0.555084	−	0.0673994i
$172$	−0.322236	+	0.285476i	−0.0245702	+	0.0217673i
$173$	2.51164	+	0.619065i	0.190957	+	0.0470666i	0.333634	−	0.942703i	$-0.391725\pi$
$173$	2.51164	+	0.619065i	0.190957	+	0.0470666i	−0.142677	+	0.989769i	$0.545571\pi$
$174$	2.96793	+	5.65492i	0.224998	+	0.428699i
$175$	−25.5153	+	17.6119i	−1.92878	+	1.33134i
$176$	5.90629	+	2.23996i	0.445203	+	0.168843i
$177$	−4.68388	−	1.77636i	−0.352062	−	0.133519i
$178$	−0.451093	+	3.71509i	−0.0338109	+	0.278458i
$179$	1.87346	+	4.93991i	0.140029	+	0.369226i	0.986624	−	0.163011i	$-0.0521206\pi$
$179$	1.87346	+	4.93991i	0.140029	+	0.369226i	−0.846595	+	0.532237i	$0.821351\pi$
$180$	−2.34534	+	0.284776i	−0.174811	+	0.0212259i
$181$	4.01785	−	2.10873i	0.298645	−	0.156741i	−0.308745	−	0.951145i	$-0.599909\pi$
$181$	4.01785	−	2.10873i	0.298645	−	0.156741i	0.607390	+	0.794404i	$0.292217\pi$
$182$	−8.17656	−	10.4600i	−0.606087	−	0.775344i
$183$	8.78741	+	4.61199i	0.649584	+	0.340928i
$184$	24.8858	+	9.43795i	1.83461	+	0.695775i
$185$	5.33327	+	2.79912i	0.392110	+	0.205795i
$186$	−3.67838	+	9.69909i	−0.269712	+	0.711172i
$187$	1.08518	−	4.40276i	0.0793564	−	0.321961i
$188$		−	2.17957i		−	0.158961i
$189$	0.747880	+	3.03427i	0.0544003	+	0.220711i
$190$	−31.1174	+	11.8013i	−2.25750	+	0.856155i
$191$	2.80101			0.202674			0.101337	−	0.994852i	$-0.467688\pi$
$191$	2.80101			0.202674			0.101337	+	0.994852i	$0.467688\pi$
$192$	−8.72135			−0.629410
$193$	20.9085	−	7.92954i	1.50503	−	0.570781i	0.542044	−	0.840350i	$-0.317650\pi$
$193$	20.9085	−	7.92954i	1.50503	−	0.570781i	0.962981	+	0.269569i	$0.0868812\pi$
$194$	3.98162	−	5.76837i	0.285863	−	0.414145i
$195$	−9.83743	−	9.85880i	−0.704473	−	0.706003i
$196$	−0.961067	−	1.39235i	−0.0686477	−	0.0994533i
$197$	−10.2872	−	7.10071i	−0.732930	−	0.505905i	0.142173	−	0.989842i	$-0.454591\pi$
$197$	−10.2872	−	7.10071i	−0.732930	−	0.505905i	−0.875103	+	0.483937i	$0.839206\pi$
$198$	0.373401	−	3.07524i	0.0265365	−	0.218548i
$199$	24.4656	+	12.8405i	1.73432	+	0.910240i	0.961145	+	0.276043i	$0.0890231\pi$
$199$	24.4656	+	12.8405i	1.73432	+	0.910240i	0.773172	+	0.634197i	$0.218669\pi$
$200$	−25.1249	+	17.3425i	−1.77660	+	1.22630i
$201$	4.37597	+	3.02051i	0.308657	+	0.213050i
$202$	−2.58018	+	2.91242i	−0.181541	+	0.204917i
$203$	−7.87158	+	14.9980i	−0.552476	+	1.05266i
$204$	0.127155	+	1.04722i	0.00890264	+	0.0733198i
$205$	−3.44215	+	9.07621i	−0.240410	+	0.633910i
$206$	−4.25770	+	2.93888i	−0.296648	+	0.204761i
$207$	1.04253	−	8.58599i	0.0724607	−	0.596768i
$208$	−5.33517	−	6.82509i	−0.369928	−	0.473235i
$209$	2.31717	+	19.0836i	0.160282	+	1.32004i
$210$	9.43201	+	10.6465i	0.650871	+	0.734681i
$211$	12.9314	−	3.18731i	0.890235	−	0.219423i	0.232432	−	0.972613i	$-0.425332\pi$
$211$	12.9314	−	3.18731i	0.890235	−	0.219423i	0.657804	+	0.753189i	$0.271486\pi$
$212$	2.03838	−	2.95310i	0.139996	−	0.202820i
$213$	9.21738	+	1.11919i	0.631564	+	0.0766858i
$214$	17.4411	−	6.61456i	1.19225	−	0.452162i
$215$	2.69903	+	0.327721i	0.184072	+	0.0223504i
$216$	0.736437	+	2.98784i	0.0501082	+	0.203297i
$217$	−26.7124	+	6.58401i	−1.81336	+	0.446952i
$218$	−6.38784	−	5.65913i	−0.432639	−	0.383285i
$219$	7.62399	−	8.60571i	0.515182	−	0.581520i
$220$	2.20258	+	5.80773i	0.148498	+	0.391557i
$221$	−4.40205	+	4.39251i	−0.296114	+	0.295472i
$222$	0.651520	−	1.71792i	0.0437272	−	0.115299i
$223$	−0.0993413	−	0.189279i	−0.00665239	−	0.0126751i	0.882107	−	0.471049i	$-0.156124\pi$
$223$	−0.0993413	−	0.189279i	−0.00665239	−	0.0126751i	−0.888760	+	0.458374i	$0.848432\pi$
$224$	−5.90001	−	8.54764i	−0.394211	−	0.571113i
$225$	7.42586	+	6.57874i	0.495057	+	0.438582i
$226$	5.43997	+	6.14046i	0.361862	+	0.408457i
$227$	−7.06592	+	28.6676i	−0.468981	+	1.90273i	−0.0405052	+	0.999179i	$0.512897\pi$
$227$	−7.06592	+	28.6676i	−0.468981	+	1.90273i	−0.428476	+	0.903553i	$0.640949\pi$
$228$	−2.07834	−	3.95994i	−0.137641	−	0.262253i
$229$	10.5383	+	7.27407i	0.696391	+	0.480684i	0.862912	−	0.505354i	$-0.168638\pi$
$229$	10.5383	+	7.27407i	0.696391	+	0.480684i	−0.166521	+	0.986038i	$0.553253\pi$
$230$	−13.9593	−	36.8076i	−0.920448	−	2.42702i
$231$	7.27497	−	3.81820i	0.478658	−	0.251219i
$232$	−7.75113	+	14.7686i	−0.508887	+	0.969603i
$233$	1.19800	+	1.06134i	0.0784838	+	0.0695306i	0.701453	−	0.712716i	$-0.252535\pi$
$233$	1.19800	+	1.06134i	0.0784838	+	0.0695306i	−0.622969	+	0.782247i	$0.714074\pi$
$234$	−2.62369	+	3.34142i	−0.171516	+	0.218435i
$235$	−10.3033	+	9.12796i	−0.672116	+	0.595443i
$236$	−0.733237	−	2.97486i	−0.0477296	−	0.193647i
$237$	−3.83307	+	5.55316i	−0.248985	+	0.360717i
$238$	4.75379	−	4.21149i	0.308142	−	0.272990i
$239$		−	10.9969i		−	0.711328i	−0.934614	−	0.355664i	$-0.884255\pi$
$239$		−	10.9969i		−	0.711328i	0.934614	−	0.355664i	$-0.115745\pi$
$240$	6.15435	+	6.94683i	0.397262	+	0.448416i
$241$	0.0182096	−	0.0346955i	0.00117298	−	0.00223493i	−0.884869	−	0.465840i	$-0.845752\pi$
$241$	0.0182096	−	0.0346955i	0.00117298	−	0.00223493i	0.886042	+	0.463605i	$0.153444\pi$
$242$	4.78167	−	0.580600i	0.307378	−	0.0373224i
$243$	0.885456	−	0.464723i	0.0568020	−	0.0298120i
$244$	0.731645	+	6.02563i	0.0468387	+	0.385752i
$245$	−2.55704	+	10.3743i	−0.163363	+	0.662790i
$246$	2.87498	+	0.708619i	0.183302	+	0.0451799i
$247$	10.8461	−	24.0293i	0.690120	−	1.52895i
$248$	−26.3037	+	6.48327i	−1.67028	+	0.411688i
$249$			5.22921i			0.331388i
$250$	21.7462	+	5.35995i	1.37535	+	0.338993i
$251$	−14.3500	−	20.7896i	−0.905767	−	1.31223i	−0.949689	−	0.313195i	$-0.898601\pi$
$251$	−14.3500	−	20.7896i	−0.905767	−	1.31223i	0.0439222	−	0.999035i	$-0.486015\pi$
$252$	−1.26748	+	1.43069i	−0.0798438	+	0.0901250i
$253$	−22.5732	+	2.74089i	−1.41917	+	0.172318i
$254$	−21.6009	+	2.62282i	−1.35536	+	0.164570i
$255$	4.41793	−	4.98681i	0.276661	−	0.312286i
$256$	−7.47931	−	10.8357i	−0.467457	−	0.677228i
$257$	26.4417	+	6.51730i	1.64939	+	0.406538i	0.951003	−	0.309182i	$-0.100055\pi$
$257$	26.4417	+	6.51730i	1.64939	+	0.406538i	0.698387	+	0.715720i	$0.253901\pi$
$258$		−	0.829358i		−	0.0516336i
$259$	4.73134	−	1.16617i	0.293991	−	0.0724623i
$260$	1.54456	−	8.37714i	0.0957899	−	0.519528i
$261$	5.26259	+	1.29711i	0.325746	+	0.0802893i
$262$	−3.65901	+	14.8452i	−0.226054	+	0.917138i
$263$	−2.51195	−	20.6877i	−0.154893	−	1.27566i	−0.838133	−	0.545466i	$-0.816353\pi$
$263$	−2.51195	−	20.6877i	−0.154893	−	1.27566i	0.683240	−	0.730194i	$-0.260570\pi$
$264$	7.16366	−	3.75978i	0.440893	−	0.231398i
$265$	−22.4967	+	2.73159i	−1.38196	+	0.167800i
$266$	−12.5125	+	23.8405i	−0.767188	+	1.46176i
$267$	2.10614	+	2.37735i	0.128894	+	0.145491i
$268$			3.25214i			0.198656i
$269$	−16.4608	+	14.5830i	−1.00363	+	0.889140i	−0.993841	−	0.110812i	$-0.964655\pi$
$269$	−16.4608	+	14.5830i	−1.00363	+	0.889140i	−0.00979002	+	0.999952i	$0.503116\pi$
$270$	2.58552	−	3.74577i	0.157350	−	0.227960i
$271$	0.616730	+	2.50217i	0.0374637	+	0.151996i	0.986695	−	0.162583i	$-0.0519827\pi$
$271$	0.616730	+	2.50217i	0.0374637	+	0.151996i	−0.949231	+	0.314579i	$0.898137\pi$
$272$	3.10183	−	2.74798i	0.188076	−	0.166621i
$273$	−11.2463	−	0.692525i	−0.680659	−	0.0419135i
$274$	−12.6431	−	11.2008i	−0.763800	−	0.676667i
$275$	12.1212	−	23.0951i	0.730937	−	1.39268i
$276$	4.68406	−	2.45838i	0.281947	−	0.147977i
$277$	−10.6711	−	28.1374i	−0.641164	−	1.69061i	−0.720225	−	0.693740i	$-0.755962\pi$
$277$	−10.6711	−	28.1374i	−0.641164	−	1.69061i	0.0790614	−	0.996870i	$-0.474808\pi$
$278$	1.00433	+	0.693236i	0.0602354	+	0.0415775i
$279$	4.09122	+	7.79517i	0.244935	+	0.466685i
$280$	−8.88982	+	36.0674i	−0.531268	+	2.15544i
$281$	−2.56544	−	2.89578i	−0.153041	−	0.172748i	0.666990	−	0.745067i	$-0.267582\pi$
$281$	−2.56544	−	2.89578i	−0.153041	−	0.172748i	−0.820031	+	0.572319i	$0.806044\pi$
$282$	3.14293	+	2.78439i	0.187159	+	0.165808i
$283$	12.1120	+	17.5473i	0.719984	+	1.04308i	0.996624	+	0.0821034i	$0.0261638\pi$
$283$	12.1120	+	17.5473i	0.719984	+	1.04308i	−0.276640	+	0.960974i	$0.589221\pi$
$284$	2.63917	+	5.02851i	0.156606	+	0.298387i
$285$	−10.0156	+	26.4089i	−0.593272	+	1.56433i
$286$	10.1804	+	4.59510i	0.601977	+	0.271714i
$287$	2.78480	+	7.34292i	0.164382	+	0.433439i
$288$	−2.20388	+	2.48767i	−0.129865	+	0.146587i
$289$	10.4980	+	9.30044i	0.617531	+	0.547085i
$290$	23.9524	−	5.90374i	1.40654	−	0.346680i
$291$	−1.42357	−	5.77566i	−0.0834513	−	0.338575i
$292$	6.98067	+	0.847607i	0.408513	+	0.0496025i
$293$	24.1851	−	9.17221i	1.41291	−	0.535846i	0.474158	−	0.880440i	$-0.342752\pi$
$293$	24.1851	−	9.17221i	1.41291	−	0.535846i	0.938752	+	0.344593i	$0.111983\pi$
$294$	3.23552	+	0.392863i	0.188699	+	0.0229123i
$295$	−10.9921	+	15.9248i	−0.639985	+	0.927178i
$296$	4.65894	−	1.14833i	0.270796	−	0.0667451i
$297$	−1.74340	−	1.96789i	−0.101162	−	0.114189i
$298$	0.860046	+	7.08312i	0.0498212	+	0.410314i
$299$	28.4233	+	12.8294i	1.64376	+	0.741944i
$300$	−0.731400	+	6.02362i	−0.0422274	+	0.347774i
$301$	1.81026	−	1.24953i	0.104342	−	0.0720218i
$302$	−7.51417	+	19.8132i	−0.432392	+	1.14012i
$303$	0.398036	+	3.27812i	0.0228666	+	0.188323i
$304$	−8.16434	+	15.5558i	−0.468257	+	0.892189i
$305$	25.4205	−	28.6938i	1.45558	−	1.64300i
$306$	−1.67252	−	1.15446i	−0.0956118	−	0.0659961i
$307$	20.5520	−	14.1860i	1.17296	−	0.809637i	0.187959	−	0.982177i	$-0.439813\pi$
$307$	20.5520	−	14.1860i	1.17296	−	0.809637i	0.985003	+	0.172540i	$0.0551973\pi$
$308$	4.44957	+	2.33532i	0.253538	+	0.133067i
$309$	−0.529236	+	4.35865i	−0.0301072	+	0.247955i
$310$	32.9761	+	22.7618i	1.87292	+	1.29278i
$311$	16.8504	+	24.4121i	0.955501	+	1.38428i	0.922995	+	0.384811i	$0.125733\pi$
$311$	16.8504	+	24.4121i	0.955501	+	1.38428i	0.0325058	+	0.999472i	$0.489651\pi$
$312$	−11.0742	−	0.681929i	−0.626956	−	0.0386066i
$313$	−6.29720	+	9.12307i	−0.355939	+	0.515667i	−0.959522	−	0.281634i	$-0.909124\pi$
$313$	−6.29720	+	9.12307i	−0.355939	+	0.515667i	0.603583	+	0.797300i	$0.293739\pi$
$314$	−0.746051	+	0.282940i	−0.0421021	+	0.0159672i
$315$	12.0714			0.680146
$316$	−4.12702			−0.232163
$317$	−25.4458	+	9.65031i	−1.42918	+	0.542015i	−0.943279	−	0.332000i	$-0.892276\pi$
$317$	−25.4458	+	9.65031i	−1.42918	+	0.542015i	−0.485898	+	0.874016i	$0.661507\pi$
$318$	1.65434	+	6.71191i	0.0927706	+	0.376385i
$319$		−	14.2498i		−	0.797838i
$320$	−8.06217	+	32.7095i	−0.450689	+	1.82852i
$321$	5.61368	−	14.8021i	0.313325	−	0.826170i
$322$	−28.2000	−	14.8005i	−1.57153	−	0.824800i
$323$	11.7918	+	4.47206i	0.656116	+	0.248832i
$324$	0.541569	+	0.284237i	0.0300872	+	0.0157910i
$325$	−30.6315	+	18.4720i	−1.69913	+	1.02464i
$326$	6.45626	−	3.38851i	0.357579	−	0.187672i
$327$	−7.18993	+	0.873016i	−0.397604	+	0.0482779i
$328$	2.74219	+	7.23057i	0.151412	+	0.399241i
$329$	−1.34234	+	11.0552i	−0.0740057	+	0.609492i
$330$	−11.1885	−	4.24324i	−0.615908	−	0.233583i
$331$	−12.3293	−	4.67587i	−0.677677	−	0.257009i	−0.00833715	−	0.999965i	$-0.502654\pi$
$331$	−12.3293	−	4.67587i	−0.677677	−	0.257009i	−0.669340	+	0.742956i	$0.733423\pi$
$332$	−2.63217	+	1.81686i	−0.144459	+	0.0997131i
$333$	−0.724643	−	1.38069i	−0.0397102	−	0.0756615i
$334$	2.22277	+	0.547864i	0.121625	+	0.0299778i
$335$	15.3737	−	13.6199i	0.839953	−	0.744133i
$336$	7.45375	+	0.905049i	0.406635	+	0.0493744i
$337$	17.4959			0.953065			0.476532	−	0.879157i	$-0.341893\pi$
$337$	17.4959			0.953065			0.476532	+	0.879157i	$0.341893\pi$
$338$	−8.67413	−	12.6252i	−0.471810	−	0.686718i
$339$	6.96226			0.378138
$340$	4.04514	+	0.491169i	0.219378	+	0.0266374i
$341$	17.3245	−	15.3482i	0.938174	−	0.831149i
$342$	8.36529	+	2.06186i	0.452343	+	0.111493i
$343$	−6.14886	−	11.7157i	−0.332007	−	0.632587i
$344$	1.78256	−	1.23041i	0.0961092	−	0.0663394i
$345$	−31.2381	−	11.8470i	−1.68180	−	0.637823i
$346$	−2.84995	−	1.08084i	−0.153214	−	0.0581065i
$347$	3.57223	−	29.4200i	0.191768	−	1.57935i	−0.505686	−	0.862718i	$-0.668760\pi$
$347$	3.57223	−	29.4200i	0.191768	−	1.57935i	0.697453	−	0.716630i	$-0.254317\pi$
$348$	1.17554	+	3.09965i	0.0630157	+	0.166159i
$349$	−26.8011	+	3.25425i	−1.43463	+	0.174196i	−0.800641	−	0.599145i	$-0.795507\pi$
$349$	−26.8011	+	3.25425i	−1.43463	+	0.174196i	−0.633991	+	0.773341i	$0.718584\pi$
$350$	32.3467	−	16.9768i	1.72900	−	0.907450i
$351$	0.646070	+	3.54720i	0.0344847	+	0.189335i
$352$	7.73686	+	4.06062i	0.412376	+	0.216432i
$353$	−17.1097	−	6.48886i	−0.910658	−	0.345367i	−0.145611	−	0.989342i	$-0.546515\pi$
$353$	−17.1097	−	6.48886i	−0.910658	−	0.345367i	−0.765047	+	0.643975i	$0.777284\pi$
$354$	5.22644	+	2.74305i	0.277782	+	0.145791i
$355$	12.7182	−	33.5352i	0.675014	−	1.77987i
$356$	−0.464892	+	1.88614i	−0.0246392	+	0.0999653i
$357$		−	5.39000i		−	0.285269i
$358$	−1.48979	−	6.04430i	−0.0787377	−	0.319451i
$359$	22.7071	−	8.61165i	1.19843	−	0.454506i	0.327002	−	0.945024i	$-0.393962\pi$
$359$	22.7071	−	8.61165i	1.19843	−	0.454506i	0.871431	+	0.490518i	$0.163192\pi$
$360$	11.8867			0.626484
$361$	−34.4650			−1.81395
$362$	−4.99919	+	1.89594i	−0.262751	+	0.0996485i
$363$	2.32222	−	3.36431i	0.121885	−	0.176581i
$364$	−3.55888	−	5.90156i	−0.186536	−	0.309326i
$365$	−25.2280	−	36.5491i	−1.32049	−	1.91307i
$366$	−9.62362	−	6.64270i	−0.503035	−	0.347220i
$367$	3.95622	−	32.5824i	0.206513	−	1.70079i	−0.408897	−	0.912580i	$-0.634087\pi$
$367$	3.95622	−	32.5824i	0.206513	−	1.70079i	0.615410	−	0.788207i	$-0.288990\pi$
$368$	−18.4004	−	9.65728i	−0.959187	−	0.503420i
$369$	2.06814	−	1.42753i	0.107663	−	0.0743145i
$370$	−5.84078	−	4.03160i	−0.303648	−	0.209593i
$371$	−12.1578	+	13.7233i	−0.631201	+	0.712478i
$372$	−2.50230	+	4.76774i	−0.129738	+	0.247196i
$373$	−1.66583	−	13.7194i	−0.0862536	−	0.710362i	−0.970121	−	0.242624i	$-0.921992\pi$
$373$	−1.66583	−	13.7194i	−0.0862536	−	0.710362i	0.883867	−	0.467738i	$-0.154931\pi$
$374$	−1.89465	+	4.99578i	−0.0979701	+	0.258326i
$375$	15.6433	−	10.7978i	0.807815	−	0.557594i
$376$	−1.32180	+	10.8860i	−0.0681668	+	0.561404i
$377$	−10.1282	+	16.7131i	−0.521627	+	0.860766i
$378$	−0.443847	−	3.65541i	−0.0228290	−	0.188014i
$379$	−13.3934	−	15.1180i	−0.687973	−	0.776561i	0.295940	−	0.955206i	$-0.404367\pi$
$379$	−13.3934	−	15.1180i	−0.687973	−	0.776561i	−0.983914	+	0.178645i	$0.942829\pi$
$380$	−16.7730	+	4.13418i	−0.860438	+	0.212079i
$381$	−10.4904	+	15.1980i	−0.537442	+	0.778619i
$382$	−3.27635	−	0.397820i	−0.167632	−	0.0203543i
$383$	3.68143	−	1.39618i	0.188112	−	0.0713416i	−0.258750	−	0.965944i	$-0.583311\pi$
$383$	3.68143	−	1.39618i	0.188112	−	0.0713416i	0.446862	+	0.894603i	$0.352541\pi$
$384$	3.60287	+	0.437467i	0.183858	+	0.0223244i
$385$	−7.59508	−	30.8144i	−0.387081	−	1.57045i
$386$	−25.5829	+	6.30562i	−1.30213	+	0.320947i
$387$	−0.526850	−	0.466748i	−0.0267813	−	0.0237261i
$388$	2.41262	−	2.72329i	0.122482	−	0.138254i
$389$	6.79428	+	17.9150i	0.344483	+	0.908328i	0.989548	+	0.144200i	$0.0460610\pi$
$389$	6.79428	+	17.9150i	0.344483	+	0.908328i	−0.645065	+	0.764128i	$0.723170\pi$
$390$	10.1066	+	12.9290i	0.511769	+	0.654687i
$391$	−5.28982	+	13.9481i	−0.267518	+	0.705386i
$392$	3.95574	+	7.53703i	0.199795	+	0.380678i
$393$	7.37118	+	10.6790i	0.371827	+	0.538684i
$394$	11.0244	+	9.76677i	0.555402	+	0.492043i
$395$	17.2838	+	19.5094i	0.869643	+	0.981624i
$396$	0.384823	−	1.56129i	0.0193381	−	0.0784578i
$397$	−9.98322	−	19.0214i	−0.501043	−	0.954658i	−0.996303	−	0.0859132i	$-0.972619\pi$
$397$	−9.98322	−	19.0214i	−0.501043	−	0.954658i	0.495259	−	0.868745i	$-0.335073\pi$
$398$	−26.7937	−	18.4943i	−1.34305	−	0.927038i
$399$	8.10290	+	21.3656i	0.405652	+	1.06962i
$400$	21.1061	−	11.0773i	1.05530	−	0.553866i
$401$	−1.96792	+	3.74957i	−0.0982734	+	0.187244i	−0.929629	−	0.368496i	$-0.879873\pi$
$401$	−1.96792	+	3.74957i	−0.0982734	+	0.187244i	0.831356	+	0.555740i	$0.187565\pi$
$402$	−4.68958	−	4.15460i	−0.233895	−	0.207213i
$403$	−31.2280	+	5.68773i	−1.55558	+	0.283326i
$404$	−1.51178	+	1.33932i	−0.0752138	+	0.0666336i
$405$	−0.924417	−	3.75051i	−0.0459346	−	0.186364i
$406$	11.3375	−	16.4252i	0.562672	−	0.815171i
$407$	−3.06854	+	2.71849i	−0.152102	+	0.134750i
$408$		−	5.30752i		−	0.262762i
$409$	24.4376	+	27.5843i	1.20836	+	1.36396i	0.912682	+	0.408670i	$0.134007\pi$
$409$	24.4376	+	27.5843i	1.20836	+	1.36396i	0.295678	+	0.955288i	$0.404454\pi$
$410$	5.31536	−	10.1276i	0.262507	−	0.500165i
$411$	−14.2307	+	1.72792i	−0.701948	+	0.0852319i
$412$	−2.37785	+	1.24799i	−0.117148	+	0.0614841i
$413$	1.88698	+	15.5406i	0.0928520	+	0.764705i
$414$	−2.43889	+	9.89498i	−0.119865	+	0.486312i
$415$	19.6122	+	4.83397i	0.962725	+	0.237290i
$416$	−6.18813	−	10.2616i	−0.303398	−	0.503114i
$417$	1.00560	−	0.247857i	0.0492442	−	0.0121376i
$418$		−	22.6512i		−	1.10791i
$419$	−14.9376	−	3.68179i	−0.729751	−	0.179867i	−0.143101	−	0.989708i	$-0.545707\pi$
$419$	−14.9376	−	3.68179i	−0.729751	−	0.179867i	−0.586650	+	0.809841i	$0.699554\pi$
$420$	4.19413	+	6.07625i	0.204653	+	0.296491i
$421$	−1.05282	+	1.18839i	−0.0513115	+	0.0579187i	−0.773606	−	0.633667i	$-0.781549\pi$
$421$	−1.05282	+	1.18839i	−0.0513115	+	0.0579187i	0.722295	+	0.691586i	$0.243087\pi$
$422$	−15.5786	+	1.89158i	−0.758353	+	0.0920808i
$423$	3.53757	−	0.429539i	0.172003	−	0.0208849i
$424$	−11.9718	+	13.5133i	−0.581400	+	0.656265i
$425$	−9.72018	−	14.0821i	−0.471498	−	0.683083i
$426$	−10.6226	−	2.61824i	−0.514668	−	0.126854i
$427$		−	31.0138i		−	1.50086i
$428$	9.40119	−	2.31719i	0.454424	−	0.112005i
$429$	8.64837	−	3.88104i	0.417547	−	0.187378i
$430$	−3.11051	−	0.766672i	−0.150002	−	0.0369722i
$431$	−3.62138	+	14.6925i	−0.174436	+	0.707714i	0.816946	+	0.576714i	$0.195665\pi$
$431$	−3.62138	+	14.6925i	−0.174436	+	0.707714i	−0.991382	+	0.131001i	$0.958181\pi$
$432$	−0.289608	−	2.38514i	−0.0139338	−	0.114755i
$433$	24.9603	−	13.1002i	1.19952	−	0.629555i	0.257878	−	0.966178i	$-0.416977\pi$
$433$	24.9603	−	13.1002i	1.19952	−	0.629555i	0.941640	+	0.336622i	$0.109285\pi$
$434$	32.1806	−	3.90744i	1.54472	−	0.187563i
$435$	9.72966	−	18.5383i	0.466502	−	0.888844i
$436$	−2.93754	−	3.31580i	−0.140683	−	0.158798i
$437$		−	63.2417i		−	3.02526i
$438$	−10.1400	+	8.98329i	−0.484510	+	0.429238i
$439$	7.47659	−	10.8317i	0.356838	−	0.516970i	−0.602918	−	0.797803i	$-0.705995\pi$
$439$	7.47659	−	10.8317i	0.356838	−	0.516970i	0.959757	+	0.280833i	$0.0906109\pi$
$440$	−7.47886	−	30.3429i	−0.356541	−	1.44654i
$441$	2.07046	−	1.83427i	0.0985934	−	0.0873461i
$442$	5.77294	−	4.51271i	0.274591	−	0.214648i
$443$	−24.6144	−	21.8065i	−1.16947	−	1.03606i	−0.998712	−	0.0507434i	$-0.983841\pi$
$443$	−24.6144	−	21.8065i	−1.16947	−	1.03606i	−0.170755	−	0.985314i	$-0.554621\pi$
$444$	0.443212	−	0.844469i	0.0210339	−	0.0400767i
$445$	10.8632	−	5.70145i	0.514965	−	0.270275i
$446$	0.0893168	+	0.235509i	0.00422927	+	0.0111517i
$447$	4.98357	+	3.43991i	0.235715	+	0.162702i
$448$	12.6660	+	24.1330i	0.598412	+	1.14018i
$449$	−2.32459	+	9.43124i	−0.109704	+	0.445088i	−0.999946	−	0.0104008i	$-0.996689\pi$
$449$	−2.32459	+	9.43124i	−0.109704	+	0.445088i	0.890242	+	0.455489i	$0.150535\pi$
$450$	−7.75167	−	8.74983i	−0.365417	−	0.412471i
$451$	−4.94528	−	4.38113i	−0.232864	−	0.206299i
$452$	2.41899	+	3.50452i	0.113780	+	0.164839i
$453$	8.35752	+	15.9239i	0.392671	+	0.748172i
$454$	12.3366	−	32.5289i	0.578985	−	1.52666i
$455$	−12.9936	+	41.5392i	−0.609150	+	1.94739i
$456$	7.97891	+	21.0387i	0.373647	+	0.985226i
$457$	−15.4346	+	17.4220i	−0.721998	+	0.814967i	−0.988873	−	0.148764i	$-0.952471\pi$
$457$	−15.4346	+	17.4220i	−0.721998	+	0.814967i	0.266875	+	0.963731i	$0.414009\pi$
$458$	−11.2936	−	10.0052i	−0.527713	−	0.467513i
$459$	−1.67464	+	0.412761i	−0.0781654	+	0.0192660i
$460$	−4.89016	−	19.8402i	−0.228005	−	0.925052i
$461$	−3.65070	−	0.443275i	−0.170030	−	0.0206454i	0.0350789	−	0.999385i	$-0.488832\pi$
$461$	−3.65070	−	0.443275i	−0.170030	−	0.0206454i	−0.205109	+	0.978739i	$0.565755\pi$
$462$	−9.05183	+	3.43291i	−0.421129	+	0.159713i
$463$	38.2367	+	4.64277i	1.77701	+	0.215768i	0.942264	−	0.334870i	$-0.108692\pi$
$463$	38.2367	+	4.64277i	1.77701	+	0.215768i	0.834744	+	0.550638i	$0.185615\pi$
$464$	7.39769	−	10.7174i	0.343429	−	0.497543i
$465$	33.0178	−	8.13817i	1.53117	−	0.377399i
$466$	−1.25057	−	1.41160i	−0.0579314	−	0.0653910i
$467$	1.19113	+	9.80982i	0.0551188	+	0.453945i	0.993973	+	0.109628i	$0.0349661\pi$
$467$	1.19113	+	9.80982i	0.0551188	+	0.453945i	−0.938854	+	0.344316i	$0.888111\pi$
$468$	−1.56104	+	1.55766i	−0.0721591	+	0.0720027i
$469$	2.00292	−	16.4955i	0.0924860	−	0.761691i
$470$	13.3483	−	9.21363i	0.615709	−	0.424993i
$471$	−0.240127	+	0.633163i	−0.0110645	+	0.0291746i
$472$	1.85810	+	15.3028i	0.0855261	+	0.704371i
$473$	−0.859977	+	1.63855i	−0.0395418	+	0.0753406i
$474$	5.27225	−	5.95114i	0.242163	−	0.273345i
$475$	59.7000	+	41.2080i	2.73923	+	1.89075i
$476$	2.71311	−	1.87272i	0.124355	−	0.0858361i
$477$	5.19478	+	2.72643i	0.237852	+	0.124835i
$478$	−1.56186	+	12.8630i	−0.0714377	+	0.588342i
$479$	−19.7835	−	13.6556i	−0.903932	−	0.623939i	0.0227683	−	0.999741i	$-0.492752\pi$
$479$	−19.7835	−	13.6556i	−0.903932	−	0.623939i	−0.926700	+	0.375802i	$0.877367\pi$
$480$	7.29270	+	10.5653i	0.332865	+	0.482238i
$481$	5.53114	−	1.00742i	0.252199	−	0.0459343i
$482$	−0.0262275	+	0.0379971i	−0.00119463	+	0.00173072i
$483$	−25.2725	+	9.58460i	−1.14994	+	0.436114i
$484$	2.50030			0.113650
$485$	−22.9776			−1.04336
$486$	−1.10172	+	0.417828i	−0.0499751	+	0.0189531i
$487$	4.27830	+	17.3577i	0.193868	+	0.786554i	0.984662	+	0.174471i	$0.0558217\pi$
$487$	4.27830	+	17.3577i	0.193868	+	0.786554i	−0.790794	+	0.612082i	$0.790332\pi$
$488$		−	30.5392i		−	1.38245i
$489$	1.48092	−	6.00834i	0.0669696	−	0.271706i
$490$	4.46441	−	11.7717i	0.201681	−	0.531790i
$491$	−30.0546	−	15.7739i	−1.35635	−	0.711866i	−0.379377	−	0.925242i	$-0.623862\pi$
$491$	−30.0546	−	15.7739i	−1.35635	−	0.711866i	−0.976970	+	0.213377i	$0.931554\pi$
$492$	1.43713	+	0.545030i	0.0647907	+	0.0245719i
$493$	−8.27754	−	4.34439i	−0.372802	−	0.195661i
$494$	−16.0995	+	26.5667i	−0.724350	+	1.19529i
$495$	−8.99223	+	4.71949i	−0.404171	+	0.212125i
$496$	20.9977	−	2.54959i	0.942826	−	0.114480i
$497$	−10.2894	−	27.1310i	−0.461544	−	1.21699i
$498$	0.742692	−	6.11662i	0.0332808	−	0.274092i
$499$	−2.64628	−	1.00360i	−0.118464	−	0.0449273i	0.294661	−	0.955602i	$-0.404793\pi$
$499$	−2.64628	−	1.00360i	−0.118464	−	0.0449273i	−0.413124	+	0.910675i	$0.635563\pi$
$500$	10.8703	+	4.12257i	0.486135	+	0.184367i
$501$	1.59897	−	1.10369i	0.0714366	−	0.0493091i
$502$	13.8326	+	26.3558i	0.617378	+	1.17631i
$503$	21.2060	+	5.22681i	0.945529	+	0.233052i	0.681795	−	0.731543i	$-0.261200\pi$
$503$	21.2060	+	5.22681i	0.945529	+	0.233052i	0.263734	+	0.964595i	$0.415046\pi$
$504$	7.19819	−	6.37704i	0.320633	−	0.284056i
$505$	12.6626	+	1.53752i	0.563477	+	0.0684185i
$506$	26.7932			1.19110
$507$	−12.9018	−	1.59498i	−0.572988	−	0.0708355i
$508$	−11.2949			−0.501131
$509$	28.3658	+	3.44423i	1.25729	+	0.152663i	0.721934	−	0.691962i	$-0.243253\pi$
$509$	28.3658	+	3.44423i	1.25729	+	0.152663i	0.535359	+	0.844625i	$0.320176\pi$
$510$	−5.87592	+	5.20561i	−0.260190	+	0.230508i
$511$	−34.8853	−	8.59846i	−1.54324	−	0.380373i
$512$	10.5829	+	20.1640i	0.467701	+	0.891130i
$513$	6.01764	−	4.15368i	0.265685	−	0.183389i
$514$	−30.0033	−	11.3788i	−1.32339	−	0.501895i
$515$	15.8579	+	6.01412i	0.698784	+	0.265014i
$516$	0.0518913	−	0.427364i	0.00228439	−	0.0188136i
$517$	−3.32225	−	8.76004i	−0.146112	−	0.385266i
$518$	−5.69988	+	0.692091i	−0.250438	+	0.0304087i
$519$	−2.29051	+	1.20215i	−0.100542	+	0.0527686i
$520$	−12.7948	+	40.9036i	−0.561089	+	1.79374i
$521$	15.9712	+	8.38235i	0.699712	+	0.367237i	0.776766	−	0.629790i	$-0.216859\pi$
$521$	15.9712	+	8.38235i	0.699712	+	0.367237i	−0.0770535	+	0.997027i	$0.524551\pi$
$522$	−5.97144	−	2.26467i	−0.261363	−	0.0991218i
$523$	21.9005	+	11.4942i	0.957640	+	0.502608i	0.869734	−	0.493520i	$-0.164290\pi$
$523$	21.9005	+	11.4942i	0.957640	+	0.502608i	0.0879060	+	0.996129i	$0.471982\pi$
$524$	−2.81430	+	7.42070i	−0.122943	+	0.324175i
$525$	7.41960	−	30.1025i	0.323818	−	1.31378i
$526$			24.5552i			1.07066i
$527$	−3.63377	−	14.7428i	−0.158290	−	0.642206i
$528$	−5.90629	+	2.23996i	−0.257038	+	0.0974817i
$529$	51.8061			2.25244
$530$	26.7024			1.15988
$531$	4.68388	−	1.77636i	0.203263	−	0.0770874i
$532$	−7.93926	+	11.5020i	−0.344211	+	0.498675i
$533$	2.68619	+	8.65334i	0.116352	+	0.374818i
$534$	−2.12591	−	3.07991i	−0.0919972	−	0.133281i
$535$	−50.3258	−	34.7374i	−2.17578	−	1.50183i
$536$	1.97227	−	16.2431i	0.0851890	−	0.701595i
$537$	−4.67807	−	2.45524i	−0.201874	−	0.105951i
$538$	21.3254	−	14.7198i	0.919402	−	0.634618i
$539$	−5.98500	−	4.13115i	−0.257792	−	0.177941i
$540$	1.56667	−	1.76840i	0.0674187	−	0.0761000i
$541$	−2.67410	+	5.09507i	−0.114968	+	0.219054i	−0.936140	−	0.351627i	$-0.885629\pi$
$541$	−2.67410	+	5.09507i	−0.114968	+	0.219054i	0.821172	+	0.570681i	$0.193321\pi$
$542$	−0.366012	−	3.01438i	−0.0157216	−	0.129479i
$543$	−1.60906	+	4.24274i	−0.0690513	+	0.182073i
$544$	4.71751	−	3.25627i	0.202262	−	0.139611i
$545$	−3.37224	+	27.7729i	−0.144451	+	1.18966i
$546$	13.0565	+	2.40733i	0.558766	+	0.103024i
$547$	1.95354	+	16.0888i	0.0835272	+	0.687909i	0.972981	+	0.230884i	$0.0741618\pi$
$547$	1.95354	+	16.0888i	0.0835272	+	0.687909i	−0.889454	+	0.457025i	$0.848915\pi$
$548$	−5.81413	−	6.56279i	−0.248367	−	0.280349i
$549$	−9.63579	+	2.37501i	−0.411245	+	0.101363i
$550$	−17.4583	+	25.2928i	−0.744426	+	1.07849i
$551$	39.3426	+	4.77706i	1.67605	+	0.203510i
$552$	−24.8858	+	9.43795i	−1.05921	+	0.401706i
$553$	20.9330	+	2.54173i	0.890163	+	0.108085i
$554$	8.48571	+	34.4279i	0.360523	+	1.46270i
$555$	−5.84817	+	1.44144i	−0.248241	+	0.0611859i
$556$	0.474149	+	0.420059i	0.0201084	+	0.0178145i
$557$	−5.59350	+	6.31376i	−0.237004	+	0.267522i	−0.854964	−	0.518687i	$-0.826421\pi$
$557$	−5.59350	+	6.31376i	−0.237004	+	0.267522i	0.617960	+	0.786210i	$0.287959\pi$
$558$	−3.67838	−	9.69909i	−0.155718	−	0.410595i
$559$	2.17324	−	1.31055i	0.0919183	−	0.0554304i
$560$	10.2848	−	27.1187i	0.434610	−	1.14597i
$561$	2.10730	+	4.01512i	0.0889701	+	0.169518i
$562$	2.58951	+	3.75156i	0.109232	+	0.158250i
$563$	13.6507	+	12.0934i	0.575307	+	0.509678i	0.899854	−	0.436192i	$-0.143673\pi$
$563$	13.6507	+	12.0934i	0.575307	+	0.509678i	−0.324546	+	0.945870i	$0.605212\pi$
$564$	1.44532	+	1.63143i	0.0608590	+	0.0686956i
$565$	6.43603	−	26.1120i	0.270766	−	1.09854i
$566$	−11.6752	−	22.2453i	−0.490747	−	0.935040i
$567$	−2.57189	−	1.77525i	−0.108009	−	0.0745533i
$568$	−10.1320	−	26.7158i	−0.425129	−	1.12097i
$569$	22.4897	−	11.8035i	0.942818	−	0.494829i	0.0780214	−	0.996952i	$-0.475140\pi$
$569$	22.4897	−	11.8035i	0.942818	−	0.494829i	0.864796	+	0.502123i	$0.167447\pi$
$570$	15.4660	−	29.4681i	0.647801	−	1.23428i
$571$	−17.8813	−	15.8415i	−0.748310	−	0.662944i	0.200178	−	0.979760i	$-0.435848\pi$
$571$	−17.8813	−	15.8415i	−0.748310	−	0.662944i	−0.948487	+	0.316815i	$0.897386\pi$
$572$	4.95838	+	3.00480i	0.207320	+	0.125637i
$573$	−2.09659	+	1.85741i	−0.0875862	+	0.0775946i
$574$	−2.21449	−	8.98454i	−0.0924310	−	0.375008i
$575$	−48.7433	+	70.6169i	−2.03274	+	2.94493i
$576$	6.52803	−	5.78333i	0.272001	−	0.240972i
$577$		−	21.6360i		−	0.900720i	−0.892847	−	0.450360i	$-0.851296\pi$
$577$		−	21.6360i		−	0.900720i	0.892847	−	0.450360i	$-0.148704\pi$
$578$	−10.9586	−	12.3697i	−0.455819	−	0.514513i
$579$	−10.3920	+	19.8002i	−0.431875	+	0.822870i
$580$	12.7119	−	1.54351i	0.527835	−	0.0640908i
$581$	14.4699	−	7.59437i	0.600311	−	0.315067i
$582$	0.844852	+	6.95799i	0.0350203	+	0.288418i
$583$	3.69126	−	14.9760i	0.152876	−	0.620244i
$584$	−34.3515	−	8.46689i	−1.42148	−	0.350362i
$585$	13.9010	+	0.855996i	0.574736	+	0.0353911i
$586$	−29.5921	+	7.29379i	−1.22244	+	0.301304i
$587$			14.3191i			0.591014i	0.955341	+	0.295507i	$0.0954886\pi$
$587$			14.3191i			0.591014i	−0.955341	+	0.295507i	$0.904511\pi$
$588$	1.64267	+	0.404881i	0.0677424	+	0.0166970i
$589$	36.5672	+	52.9767i	1.50672	+	2.18287i
$590$	15.1192	−	17.0661i	0.622449	−	0.702600i
$591$	12.4087	−	1.50669i	0.510425	−	0.0619769i
$592$	−3.71915	+	0.451587i	−0.152856	+	0.0185601i
$593$	−21.3580	+	24.1082i	−0.877067	+	0.990003i	−0.999997	−	0.00241182i	$-0.999232\pi$
$593$	−21.3580	+	24.1082i	−0.877067	+	0.990003i	0.122931	+	0.992415i	$0.460771\pi$
$594$	1.75976	+	2.54946i	0.0722040	+	0.104606i
$595$	−20.2152	−	4.98260i	−0.828743	−	0.204267i
$596$			3.70371i			0.151710i
$597$	−26.8276	+	6.61240i	−1.09798	+	0.270628i
$598$	−31.4247	−	19.0435i	−1.28505	−	0.778745i
$599$	−3.20926	−	0.791012i	−0.131127	−	0.0323199i	0.173206	−	0.984886i	$-0.444587\pi$
$599$	−3.20926	−	0.791012i	−0.131127	−	0.0323199i	−0.304333	+	0.952566i	$0.598434\pi$
$600$	7.30607	−	29.6419i	0.298269	−	1.21013i
$601$	1.91011	+	15.7312i	0.0779151	+	0.641688i	0.978388	+	0.206777i	$0.0662974\pi$
$601$	1.91011	+	15.7312i	0.0779151	+	0.641688i	−0.900473	+	0.434912i	$0.856780\pi$
$602$	−2.29493	+	1.20447i	−0.0935344	+	0.0490906i
$603$	−5.27843	+	0.640917i	−0.214954	+	0.0261002i
$604$	−5.11169	+	9.73951i	−0.207992	+	0.396295i
$605$	−10.4712	−	11.8195i	−0.425714	−	0.480532i
$606$		−	3.89096i		−	0.158059i
$607$	3.52970	−	3.12704i	0.143266	−	0.126923i	−0.588446	−	0.808536i	$-0.700260\pi$
$607$	3.52970	−	3.12704i	0.143266	−	0.126923i	0.731712	+	0.681614i	$0.238722\pi$
$608$	−13.8047	+	19.9995i	−0.559854	+	0.811089i
$609$	−4.05358	−	16.4460i	−0.164259	−	0.666426i
$610$	−33.8097	+	29.9528i	−1.36892	+	1.21275i
$611$	−2.32973	+	12.6356i	−0.0942509	+	0.511182i
$612$	−0.789610	−	0.699534i	−0.0319181	−	0.0282770i
$613$	−19.1822	+	36.5486i	−0.774762	+	1.47619i	0.101753	+	0.994810i	$0.467555\pi$
$613$	−19.1822	+	36.5486i	−0.774762	+	1.47619i	−0.876514	+	0.481375i	$0.840137\pi$
$614$	−26.0544	+	13.6744i	−1.05147	+	0.551855i
$615$	−3.44215	−	9.07621i	−0.138801	−	0.365988i
$616$	−20.8075	−	14.3624i	−0.838358	−	0.578677i
$617$	−18.8933	−	35.9982i	−0.760617	−	1.44923i	−0.889192	−	0.457535i	$-0.848732\pi$
$617$	−18.8933	−	35.9982i	−0.760617	−	1.44923i	0.128575	−	0.991700i	$-0.458960\pi$
$618$	1.23810	−	5.02316i	0.0498036	−	0.202061i
$619$	−11.0212	−	12.4403i	−0.442978	−	0.500019i	0.484035	−	0.875049i	$-0.339171\pi$
$619$	−11.0212	−	12.4403i	−0.442978	−	0.500019i	−0.927013	+	0.375030i	$0.877632\pi$
$620$	15.5683	+	13.7923i	0.625237	+	0.553912i
$621$	4.91322	+	7.11803i	0.197161	+	0.285637i
$622$	−16.2428	−	30.9481i	−0.651277	−	1.24090i
$623$	3.51965	−	9.28056i	0.141012	−	0.371818i
$624$	8.51931	+	1.57078i	0.341045	+	0.0628814i
$625$	−8.44631	−	22.2711i	−0.337852	−	0.890843i
$626$	8.66157	−	9.77689i	0.346186	−	0.390763i
$627$	−14.3892	−	12.7477i	−0.574649	−	0.509095i
$628$	−0.402139	+	0.0991184i	−0.0160471	+	0.00395526i
$629$	0.643619	+	2.61127i	0.0256628	+	0.104118i
$630$	−14.1199	−	1.71447i	−0.562551	−	0.0683061i
$631$	−13.2039	+	5.00757i	−0.525639	+	0.199348i	−0.603127	−	0.797645i	$-0.706079\pi$
$631$	−13.2039	+	5.00757i	−0.525639	+	0.199348i	0.0774889	+	0.996993i	$0.475310\pi$
$632$	20.6127	+	2.50284i	0.819930	+	0.0995575i
$633$	−7.56573	+	10.9608i	−0.300711	+	0.435655i
$634$	31.1346	−	7.67398i	1.23651	−	0.304773i
$635$	47.3028	+	53.3938i	1.87715	+	2.11887i
$636$	0.432520	+	3.56212i	0.0171505	+	0.141247i
$637$	4.08332	+	9.09913i	0.161787	+	0.360521i
$638$	−2.02387	+	16.6681i	−0.0801258	+	0.659895i
$639$	−7.64147	+	5.27453i	−0.302292	+	0.208657i
$640$	4.97128	−	13.1082i	0.196507	−	0.518146i
$641$	−5.75941	−	47.4330i	−0.227483	−	1.87349i	−0.442343	−	0.896846i	$-0.645853\pi$
$641$	−5.75941	−	47.4330i	−0.227483	−	1.87349i	0.214860	−	0.976645i	$-0.431071\pi$
$642$	−8.66863	+	16.5167i	−0.342123	+	0.651862i
$643$	−1.52751	+	1.72420i	−0.0602391	+	0.0679959i	−0.777858	−	0.628440i	$-0.783694\pi$
$643$	−1.52751	+	1.72420i	−0.0602391	+	0.0679959i	0.717619	+	0.696436i	$0.245232\pi$
$644$	−13.6053	−	9.39105i	−0.536123	−	0.370059i
$645$	−2.23757	+	1.54448i	−0.0881043	+	0.0608140i
$646$	−13.1578	−	6.90574i	−0.517686	−	0.271703i
$647$	0.244193	−	2.01111i	0.00960023	−	0.0790650i	−0.987121	−	0.159974i	$-0.948859\pi$
$647$	0.244193	−	2.01111i	0.00960023	−	0.0790650i	0.996722	+	0.0809086i	$0.0257822\pi$
$648$	−2.53254	−	1.74808i	−0.0994874	−	0.0686712i
$649$	−7.48148	−	10.8388i	−0.293674	−	0.425460i
$650$	38.4532	−	17.2562i	1.50826	−	0.676845i
$651$	15.6285	−	22.6418i	0.612529	−	0.887402i
$652$	3.53889	−	1.34212i	0.138594	−	0.0525616i
$653$	37.0748			1.45085			0.725424	−	0.688303i	$-0.241644\pi$
$653$	37.0748			1.45085			0.725424	+	0.688303i	$0.241644\pi$
$654$	8.53407			0.333708
$655$	46.8657	−	17.7738i	1.83119	−	0.694480i
$656$	−1.44495	−	5.86238i	−0.0564157	−	0.228887i
$657$			11.4971i			0.448545i
$658$	3.14028	−	12.7406i	0.122421	−	0.496681i
$659$	8.06289	−	21.2601i	0.314086	−	0.828176i	−0.681281	−	0.732022i	$-0.738577\pi$
$659$	8.06289	−	21.2601i	0.314086	−	0.828176i	0.995366	−	0.0961537i	$-0.0306540\pi$
$660$	−5.49989	−	2.88657i	−0.214083	−	0.112359i
$661$	5.42872	+	2.05884i	0.211153	+	0.0800797i	0.457914	−	0.888997i	$-0.348597\pi$
$661$	5.42872	+	2.05884i	0.211153	+	0.0800797i	−0.246761	+	0.969076i	$0.579366\pi$
$662$	13.7574	+	7.22046i	0.534698	+	0.280631i
$663$	0.382211	−	6.20694i	0.0148438	−	0.241058i
$664$	14.2485	−	7.47816i	0.552947	−	0.290209i
$665$	87.6222	−	10.6393i	3.39784	−	0.412573i
$666$	0.651520	+	1.71792i	0.0252459	+	0.0665679i
$667$	−5.65060	+	46.5369i	−0.218792	+	1.80191i
$668$	1.11110	+	0.421386i	0.0429899	+	0.0163039i
$669$	0.199873	+	0.0758019i	0.00772755	+	0.00293067i
$670$	−19.9170	+	13.7477i	−0.769460	+	0.531120i
$671$	12.1253	+	23.1028i	0.468091	+	0.891874i
$672$	10.0844	+	2.48557i	0.389012	+	0.0958829i
$673$	−25.4798	+	22.5732i	−0.982175	+	0.870131i	−0.991537	−	0.129825i	$-0.958558\pi$
$673$	−25.4798	+	22.5732i	−0.982175	+	0.870131i	0.00936193	+	0.999956i	$0.497020\pi$
$674$	−20.4650	−	2.48490i	−0.788283	−	0.0957149i
$675$	−9.92084			−0.381853
$676$	−3.67980	−	7.04840i	−0.141531	−	0.271092i
$677$	−25.2846			−0.971767			−0.485884	−	0.874023i	$-0.661502\pi$
$677$	−25.2846			−0.971767			−0.485884	+	0.874023i	$0.661502\pi$
$678$	−8.14376	−	0.988831i	−0.312759	−	0.0379758i
$679$	−13.9145	+	12.3272i	−0.533989	+	0.473073i
$680$	−19.9059	−	4.90637i	−0.763357	−	0.188151i
$681$	−13.7212	−	26.1435i	−0.525797	−	1.00182i
$682$	−22.4443	+	15.4922i	−0.859438	+	0.593227i
$683$	−27.8761	−	10.5720i	−1.06665	−	0.404527i	−0.242062	−	0.970261i	$-0.577824\pi$
$683$	−27.8761	−	10.5720i	−1.06665	−	0.404527i	−0.824588	+	0.565733i	$0.808593\pi$
$684$	4.18158	+	1.58587i	0.159887	+	0.0606371i
$685$	−6.67451	+	54.9696i	−0.255020	+	2.10028i
$686$	5.52838	+	14.5772i	0.211075	+	0.556558i
$687$	−12.7116	+	1.54347i	−0.484979	+	0.0588871i
$688$	−1.49743	+	0.785914i	−0.0570891	+	0.0299627i
$689$	−14.9736	+	14.9412i	−0.570450	+	0.569213i
$690$	34.8566	+	18.2942i	1.32697	+	0.696447i
$691$	−18.0782	−	6.85615i	−0.687726	−	0.260820i	−0.0141088	−	0.999900i	$-0.504491\pi$
$691$	−18.0782	−	6.85615i	−0.687726	−	0.260820i	−0.673617	+	0.739080i	$0.735260\pi$
$692$	−1.40094	−	0.735269i	−0.0532556	−	0.0279507i
$693$	−2.91346	+	7.68216i	−0.110673	+	0.291821i
$694$	−8.35689	+	33.9053i	−0.317223	+	1.28703i
$695$		−	4.00061i		−	0.151752i
$696$	−3.99155	−	16.1944i	−0.151299	−	0.613846i
$697$	−4.05262	+	1.53696i	−0.153504	+	0.0582164i
$698$	31.8115			1.20408
$699$	−1.60052			−0.0605371
$700$	17.7303	−	6.72420i	0.670141	−	0.254151i
$701$	4.56605	−	6.61506i	0.172457	−	0.249847i	−0.727219	−	0.686406i	$-0.759187\pi$
$701$	4.56605	−	6.61506i	0.172457	−	0.249847i	0.899676	+	0.436558i	$0.143803\pi$
$702$	−0.251910	−	4.24092i	−0.00950774	−	0.160063i
$703$	−6.47683	−	9.38331i	−0.244278	−	0.353898i
$704$	−18.8703	−	13.0252i	−0.711201	−	0.490907i
$705$	1.65920	−	13.6648i	0.0624892	−	0.514645i
$706$	19.0917	+	10.0201i	0.718524	+	0.377110i
$707$	8.49289	−	5.86222i	0.319408	−	0.220471i
$708$	2.52153	+	1.74049i	0.0947649	+	0.0654115i
$709$	−0.768649	+	0.867625i	−0.0288672	+	0.0325844i	−0.762767	−	0.646673i	$-0.776160\pi$
$709$	−0.768649	+	0.867625i	−0.0288672	+	0.0325844i	0.733900	+	0.679258i	$0.237698\pi$
$710$	−19.6395	+	37.4199i	−0.737056	+	1.40434i
$711$	−0.813333	−	6.69840i	−0.0305024	−	0.251210i
$712$	3.46580	−	9.13856i	0.129886	−	0.342482i
$713$	−62.6641	+	43.2539i	−2.34679	+	1.61987i
$714$	−0.765528	+	6.30469i	−0.0286491	+	0.235947i
$715$	−6.56115	−	36.0235i	−0.245373	−	1.34720i
$716$	−0.389499	−	3.20781i	−0.0145562	−	0.119881i
$717$	7.29227	+	8.23127i	0.272335	+	0.307402i
$718$	−27.7836	+	6.84803i	−1.03687	+	0.255566i
$719$	−12.2663	+	17.7708i	−0.457456	+	0.662739i	−0.982052	−	0.188612i	$-0.939601\pi$
$719$	−12.2663	+	17.7708i	−0.457456	+	0.662739i	0.524596	+	0.851351i	$0.324216\pi$
$720$	−9.21320	−	1.11868i	−0.343356	−	0.0416909i
$721$	12.8295	−	4.86559i	0.477796	−	0.181204i
$722$	40.3137	+	4.89497i	1.50032	+	0.182172i
$723$	0.00937729	+	0.0380451i	0.000348745	+	0.00141491i
$724$	−2.69468	+	0.664179i	−0.100147	+	0.0246840i
$725$	−40.2488	−	35.6574i	−1.49480	−	1.32428i
$726$	−3.19413	+	3.60542i	−0.118545	+	0.133810i
$727$	−9.96806	−	26.2836i	−0.369695	−	0.974805i	−0.982779	−	0.184787i	$-0.940840\pi$
$727$	−9.96806	−	26.2836i	−0.369695	−	0.974805i	0.613084	−	0.790018i	$-0.289929\pi$
$728$	14.1961	+	31.6341i	0.526142	+	1.17244i
$729$	−0.354605	+	0.935016i	−0.0131335	+	0.0346302i
$730$	24.3183	+	46.3346i	0.900059	+	1.71492i
$731$	0.689627	+	0.999098i	0.0255068	+	0.0369530i
$732$	−4.54338	−	4.02508i	−0.167928	−	0.148771i
$733$	14.9953	+	16.9262i	0.553864	+	0.625183i	0.957046	−	0.289937i	$-0.0936343\pi$
$733$	14.9953	+	16.9262i	0.553864	+	0.625183i	−0.403182	+	0.915120i	$0.632096\pi$
$734$	−9.25519	+	37.5498i	−0.341615	+	1.38599i
$735$	−4.96547	−	9.46091i	−0.183154	−	0.348971i
$736$	−23.6567	−	16.3290i	−0.871997	−	0.601896i
$737$	4.95714	+	13.0709i	0.182598	+	0.481473i
$738$	−2.62186	+	1.37606i	−0.0965119	+	0.0506533i
$739$	2.86119	−	5.45154i	0.105250	−	0.200538i	−0.827135	−	0.562003i	$-0.810031\pi$
$739$	2.86119	−	5.45154i	0.105250	−	0.200538i	0.932386	+	0.361465i	$0.117723\pi$
$740$	−2.75747	−	2.44291i	−0.101367	−	0.0898031i
$741$	7.81597	+	25.1785i	0.287127	+	0.924954i
$742$	16.1701	−	14.3254i	0.593622	−	0.525903i
$743$	6.99855	+	28.3942i	0.256752	+	1.04168i	0.947798	+	0.318872i	$0.103304\pi$
$743$	6.99855	+	28.3942i	0.256752	+	1.04168i	−0.691046	+	0.722811i	$0.742850\pi$
$744$	15.3894	−	22.2954i	0.564202	−	0.817387i
$745$	17.5083	−	15.5110i	0.641455	−	0.568280i
$746$			16.2842i			0.596205i
$747$	−3.46761	−	3.91412i	−0.126873	−	0.143210i
$748$	−1.28888	+	2.45576i	−0.0471261	+	0.0897913i
$749$	−49.1118	+	5.96325i	−1.79451	+	0.217892i
$750$	−19.8315	+	10.4084i	−0.724145	+	0.380061i
$751$	3.91029	+	32.2041i	0.142689	+	1.17515i	0.871487	+	0.490418i	$0.163156\pi$
$751$	3.91029	+	32.2041i	0.142689	+	1.17515i	−0.728799	+	0.684728i	$0.759921\pi$
$752$	2.04902	−	8.31320i	0.0747201	−	0.303151i
$753$	24.5272	+	6.04542i	0.893822	+	0.220307i
$754$	14.2206	−	18.1108i	0.517886	−	0.659557i
$755$	67.4486	−	16.6246i	2.45471	−	0.605031i
$756$		−	1.91138i		−	0.0695163i
$757$	−4.82244	−	1.18862i	−0.175274	−	0.0432013i	0.150702	−	0.988579i	$-0.451847\pi$
$757$	−4.82244	−	1.18862i	−0.175274	−	0.0432013i	−0.325976	+	0.945378i	$0.605693\pi$
$758$	13.5191	+	19.5858i	0.491036	+	0.711389i
$759$	15.0788	−	17.0204i	0.547325	−	0.617802i
$760$	86.2815	−	10.4765i	3.12976	−	0.380021i
$761$	−29.3598	+	3.56493i	−1.06429	+	0.129228i	−0.633901	−	0.773414i	$-0.718547\pi$
$761$	−29.3598	+	3.56493i	−1.06429	+	0.129228i	−0.430391	+	0.902642i	$0.641624\pi$
$762$	14.4292	−	16.2872i	0.522715	−	0.590024i
$763$	12.8577	+	18.6275i	0.465478	+	0.674362i
$764$	−1.66339	−	0.409990i	−0.0601794	−	0.0148329i
$765$			6.66230i			0.240876i
$766$	−4.50447	+	1.11025i	−0.162753	+	0.0401150i
$767$	1.07097	+	18.0299i	0.0386706	+	0.651021i
$768$	12.7837	+	3.15090i	0.461292	+	0.113698i
$769$	0.380960	−	1.54562i	0.0137378	−	0.0557363i	−0.963673	−	0.267085i	$-0.913939\pi$
$769$	0.380960	−	1.54562i	0.0137378	−	0.0557363i	0.977411	+	0.211349i	$0.0677856\pi$

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+(-1.16970 - 0.142027i) q^{2} +(-0.748511 + 0.663123i) q^{3} +(-0.593855 - 0.146372i) q^{4} +(1.79511 + 3.42030i) q^{5} +(0.969716 - 0.669346i) q^{6} +(2.92200 + 1.10817i) q^{7} +(2.87729 + 1.09121i) q^{8} +(0.120537 - 0.992709i) q^{9} +(-1.61397 - 4.25568i) q^{10} +(-2.60991 + 0.316900i) q^{11} +(0.541569 - 0.284237i) q^{12} +(3.28629 + 1.48333i) q^{13} +(-3.26047 - 1.71123i) q^{14} +(-3.61173 - 1.36975i) q^{15} +(-2.12745 - 1.11657i) q^{16} +(-0.611607 + 1.61268i) q^{17} +(-0.281984 + 1.14405i) q^{18} -7.31198i q^{19} +(-0.565399 - 2.29391i) q^{20} +(-2.92200 + 1.10817i) q^{21} +3.09782 q^{22} +8.64905 q^{23} +(-2.87729 + 1.09121i) q^{24} +(-5.63568 + 8.16469i) q^{25} +(-3.63331 - 2.20180i) q^{26} +(0.568065 + 0.822984i) q^{27} +(-1.57304 - 1.08579i) q^{28} +(-0.653320 + 5.38057i) q^{29} +(4.03011 + 2.11516i) q^{30} +(-7.24520 + 5.00100i) q^{31} +(-2.73518 - 1.88796i) q^{32} +(1.74340 - 1.96789i) q^{33} +(0.944442 - 1.79948i) q^{34} +(1.45505 + 11.9834i) q^{35} +(-0.216886 + 0.571881i) q^{36} +(1.28328 - 0.885784i) q^{37} +(-1.03850 + 8.55283i) q^{38} +(-3.44346 + 1.06893i) q^{39} +(1.43278 + 11.8000i) q^{40} +(1.66641 + 1.88099i) q^{41} +(3.57525 - 0.881221i) q^{42} +(0.399840 - 0.579269i) q^{43} +(1.59629 + 0.193825i) q^{44} +(3.61173 - 1.36975i) q^{45} +(-10.1168 - 1.22840i) q^{46} +(0.852814 + 3.46000i) q^{47} +(2.33284 - 0.574994i) q^{48} +(2.07046 + 1.83427i) q^{49} +(7.75167 - 8.74983i) q^{50} +(-0.611607 - 1.61268i) q^{51} +(-1.73446 - 1.36190i) q^{52} +(-2.08039 + 5.48553i) q^{53} +(-0.547580 - 1.04333i) q^{54} +(-5.76897 - 8.35779i) q^{55} +(7.19819 + 6.37704i) q^{56} +(4.84874 + 5.47309i) q^{57} +(1.52838 - 6.20087i) q^{58} +(2.32799 + 4.43561i) q^{59} +(1.94435 + 1.34209i) q^{60} +(-3.51916 - 9.27926i) q^{61} +(9.18499 - 4.82066i) q^{62} +(1.45230 - 2.76712i) q^{63} +(6.52803 + 5.78333i) q^{64} +(0.825828 + 13.9028i) q^{65} +(-2.31875 + 2.05424i) q^{66} +(-1.27249 - 5.16269i) q^{67} +(0.599256 - 0.868172i) q^{68} +(-6.47391 + 5.73538i) q^{69} -14.2236i q^{70} +(-6.15715 - 6.94998i) q^{71} +(1.43007 - 2.72478i) q^{72} +(-11.4133 + 1.38582i) q^{73} +(-1.62686 + 0.853842i) q^{74} +(-1.19583 - 9.84851i) q^{75} +(-1.07027 + 4.34225i) q^{76} +(-7.97733 - 1.96624i) q^{77} +(4.17963 - 0.761260i) q^{78} +(6.55153 - 1.61481i) q^{79} -9.28087i q^{80} +(-0.970942 - 0.239316i) q^{81} +(-1.68205 - 2.43687i) q^{82} +(3.46761 - 3.91412i) q^{83} +(1.89745 - 0.230392i) q^{84} +(-6.61373 + 0.803052i) q^{85} +(-0.549966 + 0.620783i) q^{86} +(-3.07896 - 4.46065i) q^{87} +(-7.85527 - 1.93615i) q^{88} -3.17610i q^{89} +(-4.41919 + 1.08923i) q^{90} +(7.95877 + 7.97606i) q^{91} +(-5.13628 - 1.26598i) q^{92} +(2.10683 - 8.54775i) q^{93} +(-0.506122 - 4.16829i) q^{94} +(25.0091 - 13.1258i) q^{95} +(3.29926 - 0.400602i) q^{96} +(-2.76441 + 5.26715i) q^{97} +(-2.16131 - 2.43961i) q^{98} +2.62908i 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

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