LMFDB - Embedded newform 1089.2.e.o.727.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			727.1
Character	$\chi$	$=$	1089.727
Dual form			1089.2.e.o.364.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30084 + 2.25313i) q^{2} +(1.22607 - 1.22342i) q^{3} +(-2.38439 - 4.12988i) q^{4} +(-1.02604 - 1.77715i) q^{5} +(1.16159 + 4.35397i) q^{6} +(1.59481 - 2.76230i) q^{7} +7.20347 q^{8} +(0.00649615 - 2.99999i) q^{9} +O(q^{10})$	\(q+(-1.30084 + 2.25313i) q^{2} +(1.22607 - 1.22342i) q^{3} +(-2.38439 - 4.12988i) q^{4} +(-1.02604 - 1.77715i) q^{5} +(1.16159 + 4.35397i) q^{6} +(1.59481 - 2.76230i) q^{7} +7.20347 q^{8} +(0.00649615 - 2.99999i) q^{9} +5.33887 q^{10} +(-7.97599 - 2.14642i) q^{12} +(-0.696927 - 1.20711i) q^{13} +(4.14920 + 7.18663i) q^{14} +(-3.43220 - 0.923639i) q^{15} +(-4.60181 + 7.97058i) q^{16} +1.35103 q^{17} +(6.75091 + 3.91716i) q^{18} +2.66386 q^{19} +(-4.89295 + 8.47484i) q^{20} +(-1.42409 - 5.33789i) q^{21} +(0.810671 + 1.40412i) q^{23} +(8.83196 - 8.81286i) q^{24} +(0.394484 - 0.683266i) q^{25} +3.62637 q^{26} +(-3.66228 - 3.68615i) q^{27} -15.2106 q^{28} +(-4.60138 + 7.96982i) q^{29} +(6.54583 - 6.53167i) q^{30} +(-3.55780 - 6.16230i) q^{31} +(-4.76900 - 8.26016i) q^{32} +(-1.75748 + 3.04404i) q^{34} -6.54537 q^{35} +(-12.4051 + 7.12631i) q^{36} -0.749192 q^{37} +(-3.46526 + 6.00200i) q^{38} +(-2.33129 - 0.627372i) q^{39} +(-7.39105 - 12.8017i) q^{40} +(-3.02102 - 5.23256i) q^{41} +(13.8795 + 3.73510i) q^{42} +(-3.54650 + 6.14271i) q^{43} +(-5.33811 + 3.06657i) q^{45} -4.21822 q^{46} +(2.86508 - 4.96246i) q^{47} +(4.10920 + 15.4024i) q^{48} +(-1.58685 - 2.74851i) q^{49} +(1.02632 + 1.77764i) q^{50} +(1.65646 - 1.65288i) q^{51} +(-3.32348 + 5.75644i) q^{52} +0.473715 q^{53} +(13.0694 - 3.45648i) q^{54} +(11.4882 - 19.8981i) q^{56} +(3.26607 - 3.25901i) q^{57} +(-11.9713 - 20.7350i) q^{58} +(0.772218 + 1.33752i) q^{59} +(4.36917 + 16.3769i) q^{60} +(4.69496 - 8.13191i) q^{61} +18.5126 q^{62} +(-8.27651 - 4.80237i) q^{63} +6.40765 q^{64} +(-1.43015 + 2.47709i) q^{65} +(-3.69864 - 6.40624i) q^{67} +(-3.22138 - 5.57959i) q^{68} +(2.71177 + 0.729764i) q^{69} +(8.51449 - 14.7475i) q^{70} +1.57051 q^{71} +(0.0467948 - 21.6104i) q^{72} -9.61801 q^{73} +(0.974582 - 1.68803i) q^{74} +(-0.352255 - 1.32035i) q^{75} +(-6.35166 - 11.0014i) q^{76} +(4.44618 - 4.43657i) q^{78} +(1.15608 - 2.00238i) q^{79} +18.8866 q^{80} +(-8.99992 - 0.0389768i) q^{81} +15.7195 q^{82} +(-3.81234 + 6.60316i) q^{83} +(-18.6492 + 18.6089i) q^{84} +(-1.38621 - 2.40099i) q^{85} +(-9.22687 - 15.9814i) q^{86} +(4.10881 + 15.4010i) q^{87} +14.6343 q^{89} +(0.0346821 - 16.0166i) q^{90} -4.44587 q^{91} +(3.86590 - 6.69594i) q^{92} +(-11.9012 - 3.20273i) q^{93} +(7.45404 + 12.9108i) q^{94} +(-2.73322 - 4.73408i) q^{95} +(-15.9528 - 4.29305i) q^{96} +(-3.46356 + 5.99906i) q^{97} +8.25699 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9}+O(q^{10}) $ 36 * q - 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 + q^6 + q^7 + 12 * q^8 - q^9	$ 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} + 3 q^{13} - 5 q^{15} + 8 q^{16} + 40 q^{17} - 17 q^{18} + 6 q^{19} + 5 q^{20} + 8 q^{21} + 10 q^{23} + 57 q^{24} - 7 q^{25} + 4 q^{26} - 9 q^{27} - 38 q^{28} - 21 q^{29} - 12 q^{30} - 6 q^{31} - 9 q^{32} + 4 q^{34} + 76 q^{35} - 65 q^{36} + 14 q^{37} - 13 q^{38} - 42 q^{39} - 20 q^{41} + 18 q^{42} + 4 q^{43} + 20 q^{45} - 16 q^{46} - 7 q^{47} + 10 q^{48} - 7 q^{49} - 25 q^{50} + 4 q^{51} - 19 q^{52} + 62 q^{53} - 17 q^{54} + 57 q^{56} + 18 q^{57} - 12 q^{58} + 12 q^{59} + 11 q^{60} - 16 q^{61} + 38 q^{62} - 5 q^{63} - 32 q^{64} - 42 q^{65} + 5 q^{67} - 51 q^{68} + 31 q^{69} - 8 q^{70} + 26 q^{71} - 51 q^{72} - 9 q^{74} - 16 q^{75} - 8 q^{76} - 32 q^{78} - 2 q^{79} + 92 q^{80} + 47 q^{81} - 68 q^{82} - 36 q^{83} - 60 q^{84} + 25 q^{85} - 26 q^{86} + 60 q^{87} - 28 q^{89} - 163 q^{90} - 30 q^{91} + 15 q^{92} - 39 q^{93} + 4 q^{94} - 64 q^{95} + 21 q^{96} + 16 q^{97} + 164 q^{98}+O(q^{100}) $ 36 * q - 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 + q^6 + q^7 + 12 * q^8 - q^9 + 4 * q^10 - 8 * q^12 + 3 * q^13 - 5 * q^15 + 8 * q^16 + 40 * q^17 - 17 * q^18 + 6 * q^19 + 5 * q^20 + 8 * q^21 + 10 * q^23 + 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 - 38 * q^28 - 21 * q^29 - 12 * q^30 - 6 * q^31 - 9 * q^32 + 4 * q^34 + 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 - 42 * q^39 - 20 * q^41 + 18 * q^42 + 4 * q^43 + 20 * q^45 - 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 - 25 * q^50 + 4 * q^51 - 19 * q^52 + 62 * q^53 - 17 * q^54 + 57 * q^56 + 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 - 16 * q^61 + 38 * q^62 - 5 * q^63 - 32 * q^64 - 42 * q^65 + 5 * q^67 - 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 - 51 * q^72 - 9 * q^74 - 16 * q^75 - 8 * q^76 - 32 * q^78 - 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 - 36 * q^83 - 60 * q^84 + 25 * q^85 - 26 * q^86 + 60 * q^87 - 28 * q^89 - 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 + 4 * q^94 - 64 * q^95 + 21 * q^96 + 16 * q^97 + 164 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.30084	+	2.25313i	−0.919835	+	1.59320i	−0.120171	+	0.992753i	$0.538344\pi$
$2$	−1.30084	+	2.25313i	−0.919835	+	1.59320i	−0.799664	+	0.600448i	$0.794989\pi$
$3$	1.22607	−	1.22342i	0.707872	−	0.706341i
$3$	1.22607	−	1.22342i	0.707872	−	0.706341i
$4$	−2.38439	−	4.12988i	−1.19219	−	2.06494i
$5$	−1.02604	−	1.77715i	−0.458859	−	0.794767i	0.540042	−	0.841638i	$-0.318408\pi$
$5$	−1.02604	−	1.77715i	−0.458859	−	0.794767i	−0.998901	+	0.0468709i	$0.985075\pi$
$6$	1.16159	+	4.35397i	0.474217	+	1.77750i
$7$	1.59481	−	2.76230i	0.602782	−	1.04405i	−0.389615	−	0.920978i	$-0.627392\pi$
$7$	1.59481	−	2.76230i	0.602782	−	1.04405i	0.992398	−	0.123072i	$-0.0392747\pi$
$8$	7.20347			2.54681
$9$	0.00649615	−	2.99999i	0.00216538	−	0.999998i
$10$	5.33887			1.68830
$11$		0			0
$11$		0			0
$12$	−7.97599	−	2.14642i	−2.30247	−	0.619617i
$13$	−0.696927	−	1.20711i	−0.193293	−	0.334793i	0.753047	−	0.657967i	$-0.228583\pi$
$13$	−0.696927	−	1.20711i	−0.193293	−	0.334793i	−0.946340	+	0.323174i	$0.895250\pi$
$14$	4.14920	+	7.18663i	1.10892	+	1.92071i
$15$	−3.43220	−	0.923639i	−0.886190	−	0.238483i
$16$	−4.60181	+	7.97058i	−1.15045	+	1.99264i
$17$	1.35103			0.327673			0.163837	−	0.986488i	$-0.447613\pi$
$17$	1.35103			0.327673			0.163837	+	0.986488i	$0.447613\pi$
$18$	6.75091	+	3.91716i	1.59121	+	0.923283i
$19$	2.66386			0.611130			0.305565	−	0.952171i	$-0.401155\pi$
$19$	2.66386			0.611130			0.305565	+	0.952171i	$0.401155\pi$
$20$	−4.89295	+	8.47484i	−1.09410	+	1.89503i
$21$	−1.42409	−	5.33789i	−0.310762	−	1.16482i
$22$		0			0
$23$	0.810671	+	1.40412i	0.169037	+	0.292780i	0.938081	−	0.346415i	$-0.112601\pi$
$23$	0.810671	+	1.40412i	0.169037	+	0.292780i	−0.769045	+	0.639195i	$0.779268\pi$
$24$	8.83196	−	8.81286i	1.80282	−	1.79892i
$25$	0.394484	−	0.683266i	0.0788967	−	0.136653i
$26$	3.62637			0.711190
$27$	−3.66228	−	3.68615i	−0.704806	−	0.709400i
$28$	−15.2106			−2.87453
$29$	−4.60138	+	7.96982i	−0.854454	+	1.47996i	0.0226967	+	0.999742i	$0.492775\pi$
$29$	−4.60138	+	7.96982i	−0.854454	+	1.47996i	−0.877151	+	0.480215i	$0.840559\pi$
$30$	6.54583	−	6.53167i	1.19510	−	1.19251i
$31$	−3.55780	−	6.16230i	−0.639000	−	1.10678i	−0.985652	−	0.168787i	$-0.946015\pi$
$31$	−3.55780	−	6.16230i	−0.639000	−	1.10678i	0.346652	−	0.937994i	$-0.387318\pi$
$32$	−4.76900	−	8.26016i	−0.843049	−	1.46020i
$33$		0			0
$34$	−1.75748	+	3.04404i	−0.301405	+	0.522049i
$35$	−6.54537			−1.10637
$36$	−12.4051	+	7.12631i	−2.06751	+	1.18772i
$37$	−0.749192			−0.123166			−0.0615832	−	0.998102i	$-0.519615\pi$
$37$	−0.749192			−0.123166			−0.0615832	+	0.998102i	$0.519615\pi$
$38$	−3.46526	+	6.00200i	−0.562139	+	0.973653i
$39$	−2.33129	−	0.627372i	−0.373304	−	0.100460i
$40$	−7.39105	−	12.8017i	−1.16863	−	2.02412i
$41$	−3.02102	−	5.23256i	−0.471804	−	0.817189i	0.527676	−	0.849446i	$-0.323064\pi$
$41$	−3.02102	−	5.23256i	−0.471804	−	0.817189i	−0.999480	+	0.0322574i	$0.989730\pi$
$42$	13.8795	+	3.73510i	2.14165	+	0.576339i
$43$	−3.54650	+	6.14271i	−0.540836	+	0.936755i	0.458021	+	0.888942i	$0.348559\pi$
$43$	−3.54650	+	6.14271i	−0.540836	+	0.936755i	−0.998856	+	0.0478134i	$0.984775\pi$
$44$		0			0
$45$	−5.33811	+	3.06657i	−0.795759	+	0.457137i
$46$	−4.21822			−0.621943
$47$	2.86508	−	4.96246i	0.417915	−	0.723850i	−0.577815	−	0.816168i	$-0.696094\pi$
$47$	2.86508	−	4.96246i	0.417915	−	0.723850i	0.995730	+	0.0923182i	$0.0294277\pi$
$48$	4.10920	+	15.4024i	0.593112	+	2.22315i
$49$	−1.58685	−	2.74851i	−0.226693	−	0.392644i
$50$	1.02632	+	1.77764i	0.145144	+	0.251397i
$51$	1.65646	−	1.65288i	0.231951	−	0.231449i
$52$	−3.32348	+	5.75644i	−0.460884	+	0.798275i
$53$	0.473715			0.0650698			0.0325349	−	0.999471i	$-0.489642\pi$
$53$	0.473715			0.0650698			0.0325349	+	0.999471i	$0.489642\pi$
$54$	13.0694	−	3.45648i	1.77852	−	0.470367i
$55$		0			0
$56$	11.4882	−	19.8981i	1.53517	−	2.65900i
$57$	3.26607	−	3.25901i	0.432602	−	0.431666i
$58$	−11.9713	−	20.7350i	−1.57191	−	2.72263i
$59$	0.772218	+	1.33752i	0.100534	+	0.174130i	0.911905	−	0.410402i	$-0.134611\pi$
$59$	0.772218	+	1.33752i	0.100534	+	0.174130i	−0.811371	+	0.584532i	$0.801278\pi$
$60$	4.36917	+	16.3769i	0.564057	+	2.11424i
$61$	4.69496	−	8.13191i	0.601128	−	1.04118i	−0.391523	−	0.920169i	$-0.628052\pi$
$61$	4.69496	−	8.13191i	0.601128	−	1.04118i	0.992651	−	0.121016i	$-0.0386152\pi$
$62$	18.5126			2.35110
$63$	−8.27651	−	4.80237i	−1.04274	−	0.605042i
$64$	6.40765			0.800956
$65$	−1.43015	+	2.47709i	−0.177388	+	0.307246i
$66$		0			0
$67$	−3.69864	−	6.40624i	−0.451861	−	0.782647i	0.546640	−	0.837367i	$-0.315906\pi$
$67$	−3.69864	−	6.40624i	−0.451861	−	0.782647i	−0.998502	+	0.0547207i	$0.982573\pi$
$68$	−3.22138	−	5.57959i	−0.390649	−	0.676625i
$69$	2.71177	+	0.729764i	0.326459	+	0.0878533i
$70$	8.51449	−	14.7475i	1.01768	−	1.76267i
$71$	1.57051			0.186385			0.0931927	−	0.995648i	$-0.470293\pi$
$71$	1.57051			0.186385			0.0931927	+	0.995648i	$0.470293\pi$
$72$	0.0467948	−	21.6104i	0.00551482	−	2.54681i
$73$	−9.61801			−1.12570			−0.562852	−	0.826558i	$-0.690296\pi$
$73$	−9.61801			−1.12570			−0.562852	+	0.826558i	$0.690296\pi$
$74$	0.974582	−	1.68803i	0.113293	−	0.196229i
$75$	−0.352255	−	1.32035i	−0.0406749	−	0.152461i
$76$	−6.35166	−	11.0014i	−0.728585	−	1.26195i
$77$		0			0
$78$	4.44618	−	4.43657i	0.503431	−	0.502342i
$79$	1.15608	−	2.00238i	0.130069	−	0.225286i	−0.793634	−	0.608395i	$-0.791814\pi$
$79$	1.15608	−	2.00238i	0.130069	−	0.225286i	0.923703	+	0.383110i	$0.125147\pi$
$80$	18.8866			2.11158
$81$	−8.99992	−	0.0389768i	−0.999991	−	0.00433076i
$82$	15.7195			1.73593
$83$	−3.81234	+	6.60316i	−0.418458	+	0.724791i	−0.995785	−	0.0917226i	$-0.970763\pi$
$83$	−3.81234	+	6.60316i	−0.418458	+	0.724791i	0.577326	+	0.816513i	$0.304096\pi$
$84$	−18.6492	+	18.6089i	−2.03480	+	2.03040i
$85$	−1.38621	−	2.40099i	−0.150356	−	0.260424i
$86$	−9.22687	−	15.9814i	−0.994959	−	1.72332i
$87$	4.10881	+	15.4010i	0.440510	+	1.65116i
$88$		0			0
$89$	14.6343			1.55124			0.775619	−	0.631202i	$-0.217438\pi$
$89$	14.6343			1.55124			0.775619	+	0.631202i	$0.217438\pi$
$90$	0.0346821	−	16.0166i	0.00365581	−	1.68829i
$91$	−4.44587			−0.466054
$92$	3.86590	−	6.69594i	0.403048	−	0.698100i
$93$	−11.9012	−	3.20273i	−1.23410	−	0.332107i
$94$	7.45404	+	12.9108i	0.768825	+	1.33164i
$95$	−2.73322	−	4.73408i	−0.280423	−	0.485706i
$96$	−15.9528	−	4.29305i	−1.62817	−	0.438157i
$97$	−3.46356	+	5.99906i	−0.351671	+	0.609112i	−0.986542	−	0.163506i	$-0.947720\pi$
$97$	−3.46356	+	5.99906i	−0.351671	+	0.609112i	0.634871	+	0.772618i	$0.281053\pi$
$98$	8.25699			0.834082
$99$		0			0
$100$	−3.76240			−0.376240
$101$	0.696022	−	1.20554i	0.0692567	−	0.119956i	−0.829318	−	0.558778i	$-0.811271\pi$
$101$	0.696022	−	1.20554i	0.0692567	−	0.119956i	0.898574	+	0.438821i	$0.144604\pi$
$102$	1.56934	+	5.88234i	0.155388	+	0.582439i
$103$	−5.55221	−	9.61671i	−0.547076	−	0.947563i	−0.998473	−	0.0552398i	$-0.982408\pi$
$103$	−5.55221	−	9.61671i	−0.547076	−	0.947563i	0.451397	−	0.892323i	$-0.350926\pi$
$104$	−5.02029	−	8.69540i	−0.492280	−	0.852654i
$105$	−8.02508	+	8.00772i	−0.783167	+	0.781473i
$106$	−0.616229	+	1.06734i	−0.0598535	+	0.103669i
$107$	−11.6162			−1.12298			−0.561488	−	0.827485i	$-0.689771\pi$
$107$	−11.6162			−1.12298			−0.561488	+	0.827485i	$0.689771\pi$
$108$	−6.49105	+	23.9140i	−0.624602	+	2.30112i
$109$	8.56778			0.820645			0.410322	−	0.911941i	$-0.365416\pi$
$109$	8.56778			0.820645			0.410322	+	0.911941i	$0.365416\pi$
$110$		0			0
$111$	−0.918563	+	0.916576i	−0.0871861	+	0.0869975i
$112$	14.6781	+	25.4231i	1.38695	+	2.40226i
$113$	6.91295	+	11.9736i	0.650315	+	1.12638i	0.983046	+	0.183357i	$0.0586965\pi$
$113$	6.91295	+	11.9736i	0.650315	+	1.12638i	−0.332731	+	0.943022i	$0.607970\pi$
$114$	3.09431	+	11.5983i	0.289809	+	1.08628i
$115$	1.66356	−	2.88137i	0.155128	−	0.268690i
$116$	43.8858			4.07469
$117$	−3.62586	+	2.08293i	−0.335211	+	0.192567i
$118$	−4.01814			−0.369899
$119$	2.15464	−	3.73195i	0.197516	−	0.342107i
$120$	−24.7237	−	6.65341i	−2.25696	−	0.607370i
$121$		0			0
$122$	12.2148	+	21.1567i	1.10588	+	1.91544i
$123$	−10.1056	−	2.71952i	−0.911191	−	0.245210i
$124$	−16.9663	+	29.3866i	−1.52362	+	2.63899i
$125$	−11.8794			−1.06253
$126$	21.5868	−	12.4009i	1.92310	−	1.10476i
$127$	10.8293			0.960941			0.480471	−	0.877011i	$-0.340466\pi$
$127$	10.8293			0.960941			0.480471	+	0.877011i	$0.340466\pi$
$128$	1.20266	−	2.08308i	0.106302	−	0.184120i
$129$	3.16685	+	11.8702i	0.278826	+	1.04512i
$130$	−3.72080	−	6.44462i	−0.326336	−	0.565230i
$131$	−2.95131	−	5.11182i	−0.257857	−	0.446622i	0.707810	−	0.706403i	$-0.249683\pi$
$131$	−2.95131	−	5.11182i	−0.257857	−	0.446622i	−0.965668	+	0.259780i	$0.916350\pi$
$132$		0			0
$133$	4.24835	−	7.35836i	0.368379	−	0.638051i
$134$	19.2454			1.66255
$135$	−2.79321	+	10.2906i	−0.240401	+	0.885671i
$136$	9.73211			0.834521
$137$	−0.588661	+	1.01959i	−0.0502927	+	0.0871095i	−0.890076	−	0.455813i	$-0.849349\pi$
$137$	−0.588661	+	1.01959i	−0.0502927	+	0.0871095i	0.839783	+	0.542922i	$0.182682\pi$
$138$	−5.17184	+	5.16065i	−0.440256	+	0.439304i
$139$	1.36592	+	2.36584i	0.115856	+	0.200668i	0.918122	−	0.396299i	$-0.129706\pi$
$139$	1.36592	+	2.36584i	0.115856	+	0.200668i	−0.802266	+	0.596967i	$0.796372\pi$
$140$	15.6067	+	27.0315i	1.31900	+	2.28458i
$141$	−2.55838	−	9.58952i	−0.215454	−	0.807583i
$142$	−2.04299	+	3.53856i	−0.171444	+	0.296949i
$143$		0			0
$144$	23.8818	+	13.8572i	1.99015	+	1.15477i
$145$	18.8848			1.56830
$146$	12.5115	−	21.6706i	1.03546	−	1.79347i
$147$	−5.30817	−	1.42848i	−0.437811	−	0.117819i
$148$	1.78636	+	3.09407i	0.146838	+	0.254331i
$149$	2.24062	+	3.88086i	0.183558	+	0.317932i	0.943090	−	0.332538i	$-0.107905\pi$
$149$	2.24062	+	3.88086i	0.183558	+	0.317932i	−0.759531	+	0.650471i	$0.774572\pi$
$150$	3.43314	+	0.923893i	0.280315	+	0.0754356i
$151$	−11.2546	+	19.4936i	−0.915890	+	1.58637i	−0.110296	+	0.993899i	$0.535180\pi$
$151$	−11.2546	+	19.4936i	−0.915890	+	1.58637i	−0.805593	+	0.592469i	$0.798153\pi$
$152$	19.1890			1.55643
$153$	0.00877650	−	4.05308i	0.000709538	−	0.327672i
$154$		0			0
$155$	−7.30090	+	12.6455i	−0.586422	+	1.01571i
$156$	2.96771	+	11.1238i	0.237607	+	0.890618i
$157$	8.54241	+	14.7959i	0.681758	+	1.18084i	0.974444	+	0.224631i	$0.0721177\pi$
$157$	8.54241	+	14.7959i	0.681758	+	1.18084i	−0.292686	+	0.956209i	$0.594549\pi$
$158$	3.00775	+	5.20957i	0.239284	+	0.414451i
$159$	0.580808	−	0.579552i	0.0460611	−	0.0459614i
$160$	−9.78638	+	16.9505i	−0.773681	+	1.34006i
$161$	5.17147			0.407569
$162$	11.7953	−	20.2272i	0.926726	−	1.58920i
$163$	18.9397			1.48347			0.741737	−	0.670691i	$-0.234002\pi$
$163$	18.9397			1.48347			0.741737	+	0.670691i	$0.234002\pi$
$164$	−14.4066	+	24.9529i	−1.12496	+	1.94849i
$165$		0			0
$166$	−9.91850	−	17.1793i	−0.769825	−	1.33338i
$167$	−2.48591	−	4.30572i	−0.192365	−	0.333186i	0.753668	−	0.657255i	$-0.228282\pi$
$167$	−2.48591	−	4.30572i	−0.192365	−	0.333186i	−0.946034	+	0.324069i	$0.894949\pi$
$168$	−10.2584	−	38.4513i	−0.791453	−	2.96659i
$169$	5.52859	−	9.57579i	0.425276	−	0.736599i
$170$	7.21297			0.553210
$171$	0.0173048	−	7.99155i	0.00132333	−	0.611129i
$172$	33.8249			2.57912
$173$	7.11680	−	12.3267i	0.541080	−	0.937179i	−0.457762	−	0.889075i	$-0.651349\pi$
$173$	7.11680	−	12.3267i	0.541080	−	0.937179i	0.998842	−	0.0481040i	$-0.0153179\pi$
$174$	−40.0452	−	10.7766i	−3.03582	−	0.816969i
$175$	−1.25825	−	2.17936i	−0.0951151	−	0.164744i
$176$		0			0
$177$	2.58314	+	0.695149i	0.194161	+	0.0522506i
$178$	−19.0370	+	32.9730i	−1.42688	+	2.47143i
$179$	−7.87324			−0.588473			−0.294237	−	0.955733i	$-0.595065\pi$
$179$	−7.87324			−0.588473			−0.294237	+	0.955733i	$0.595065\pi$
$180$	25.3927	+	14.7339i	1.89266	+	1.09820i
$181$	−14.3567			−1.06712			−0.533561	−	0.845762i	$-0.679147\pi$
$181$	−14.3567			−1.06712			−0.533561	+	0.845762i	$0.679147\pi$
$182$	5.78338	−	10.0171i	0.428693	−	0.742518i
$183$	−4.19237	−	15.7142i	−0.309909	−	1.16163i
$184$	5.83965	+	10.1146i	0.430504	+	0.745655i
$185$	0.768702	+	1.33143i	0.0565161	+	0.0978887i
$186$	22.6977	−	22.6486i	1.66428	−	1.66068i
$187$		0			0
$188$	−27.3258			−1.99294
$189$	−16.0229	+	4.23759i	−1.16549	+	0.308239i
$190$	14.2220			1.03177
$191$	6.23892	−	10.8061i	0.451433	−	0.781904i	−0.547043	−	0.837105i	$-0.684246\pi$
$191$	6.23892	−	10.8061i	0.451433	−	0.781904i	0.998475	+	0.0552003i	$0.0175797\pi$
$192$	7.85623	−	7.83923i	0.566974	−	0.565748i
$193$	−2.81958	−	4.88365i	−0.202958	−	0.351533i	0.746523	−	0.665360i	$-0.231722\pi$
$193$	−2.81958	−	4.88365i	−0.202958	−	0.351533i	−0.949480	+	0.313827i	$0.898389\pi$
$194$	−9.01110	−	15.6077i	−0.646959	−	1.12057i
$195$	1.27706	+	4.78676i	0.0914519	+	0.342787i
$196$	−7.56734	+	13.1070i	−0.540524	+	0.936216i
$197$	1.45201			0.103451			0.0517257	−	0.998661i	$-0.483528\pi$
$197$	1.45201			0.103451			0.0517257	+	0.998661i	$0.483528\pi$
$198$		0			0
$199$	26.2193			1.85864			0.929319	−	0.369278i	$-0.120395\pi$
$199$	26.2193			1.85864			0.929319	+	0.369278i	$0.120395\pi$
$200$	2.84165	−	4.92188i	0.200935	−	0.348030i
$201$	−12.3723	−	3.32951i	−0.872675	−	0.234846i
$202$	1.81083	+	3.13645i	0.127410	+	0.220680i
$203$	14.6767	+	25.4207i	1.03010	+	1.78419i
$204$	−10.7758	−	2.89988i	−0.754457	−	0.203032i
$205$	−6.19938	+	10.7376i	−0.432983	+	0.749949i
$206$	28.8902			2.01288
$207$	4.21763	−	2.42289i	0.293145	−	0.168402i
$208$	12.8285			0.889497
$209$		0			0
$210$	−7.60304	−	28.4983i	−0.524659	−	1.96657i
$211$	−3.19724	−	5.53778i	−0.220107	−	0.381237i	0.734733	−	0.678356i	$-0.237307\pi$
$211$	−3.19724	−	5.53778i	−0.220107	−	0.381237i	−0.954840	+	0.297119i	$0.903974\pi$
$212$	−1.12952	−	1.95638i	−0.0775757	−	0.134365i
$213$	1.92556	−	1.92139i	0.131937	−	0.131652i
$214$	15.1108	−	26.1727i	1.03295	−	1.78913i
$215$	14.5554			0.992670
$216$	−26.3811	−	26.5531i	−1.79501	−	1.80671i
$217$	−22.6961			−1.54071
$218$	−11.1453	+	19.3043i	−0.754858	+	1.30745i
$219$	−11.7924	+	11.7669i	−0.796854	+	0.795130i
$220$		0			0
$221$	−0.941570	−	1.63085i	−0.0633368	−	0.109703i
$222$	−0.870255	−	3.26196i	−0.0584077	−	0.218928i
$223$	8.57320	−	14.8492i	0.574104	−	0.994377i	−0.422035	−	0.906580i	$-0.638684\pi$
$223$	8.57320	−	14.8492i	0.574104	−	0.994377i	0.996138	−	0.0877972i	$-0.0279827\pi$
$224$	−30.4227			−2.03270
$225$	−2.04723	−	1.18789i	−0.136482	−	0.0791924i
$226$	−35.9706			−2.39273
$227$	2.71734	−	4.70656i	0.180356	−	0.312386i	−0.761646	−	0.647994i	$-0.775608\pi$
$227$	2.71734	−	4.70656i	0.180356	−	0.312386i	0.942002	+	0.335608i	$0.108942\pi$
$228$	−21.2469	−	5.71775i	−1.40711	−	0.378667i
$229$	7.24615	+	12.5507i	0.478839	+	0.829374i	0.999706	−	0.0242643i	$-0.00772432\pi$
$229$	7.24615	+	12.5507i	0.478839	+	0.829374i	−0.520866	+	0.853638i	$0.674391\pi$
$230$	4.32807	+	7.49643i	0.285384	+	0.494300i
$231$		0			0
$232$	−33.1459	+	57.4103i	−2.17613	+	3.76917i
$233$	−1.12468			−0.0736801			−0.0368400	−	0.999321i	$-0.511729\pi$
$233$	−1.12468			−0.0736801			−0.0368400	+	0.999321i	$0.511729\pi$
$234$	0.0235574	−	10.8791i	0.00154000	−	0.711188i
$235$	−11.7587			−0.767056
$236$	3.68253	−	6.37833i	0.239712	−	0.415194i
$237$	−1.03232	−	3.86943i	−0.0670565	−	0.251346i
$238$	5.60570	+	9.70935i	0.363363	+	0.629364i
$239$	−10.9951	−	19.0441i	−0.711213	−	1.23186i	−0.964402	−	0.264441i	$-0.914813\pi$
$239$	−10.9951	−	19.0441i	−0.711213	−	1.23186i	0.253189	−	0.967417i	$-0.418521\pi$
$240$	23.1563	−	23.1062i	1.49473	−	1.49150i
$241$	−5.58129	+	9.66707i	−0.359522	+	0.622711i	−0.987881	−	0.155213i	$-0.950394\pi$
$241$	−5.58129	+	9.66707i	−0.359522	+	0.622711i	0.628359	+	0.777924i	$0.283727\pi$
$242$		0			0
$243$	−11.0822	+	10.9629i	−0.710924	+	0.703269i
$244$	−44.7784			−2.86664
$245$	−3.25635	+	5.64017i	−0.208041	+	0.360337i
$246$	19.2732	−	19.2315i	1.22881	−	1.22616i
$247$	−1.85651	−	3.21557i	−0.118127	−	0.204602i
$248$	−25.6285	−	44.3899i	−1.62741	−	2.81876i
$249$	3.40423	+	12.7600i	0.215735	+	0.808633i
$250$	15.4533	−	26.7658i	0.977350	−	1.69282i
$251$	−13.3561			−0.843028			−0.421514	−	0.906822i	$-0.638501\pi$
$251$	−13.3561			−0.843028			−0.421514	+	0.906822i	$0.638501\pi$
$252$	−0.0988102	+	45.6317i	−0.00622446	+	2.87452i
$253$		0			0
$254$	−14.0872	+	24.3997i	−0.883907	+	1.53097i
$255$	−4.63701	−	1.24786i	−0.290381	−	0.0781443i
$256$	9.53660	+	16.5179i	0.596038	+	1.03237i
$257$	6.24610	+	10.8186i	0.389621	+	0.674843i	0.992398	−	0.123066i	$-0.0392727\pi$
$257$	6.24610	+	10.8186i	0.389621	+	0.674843i	−0.602778	+	0.797909i	$0.705939\pi$
$258$	−30.8647	−	8.30601i	−1.92155	−	0.517110i
$259$	−1.19482	+	2.06949i	−0.0742426	+	0.128592i
$260$	13.6401			0.845924
$261$	23.8795	+	13.8559i	1.47810	+	0.857657i
$262$	15.3568			0.948745
$263$	2.66017	−	4.60756i	0.164033	−	0.284114i	−0.772278	−	0.635284i	$-0.780883\pi$
$263$	2.66017	−	4.60756i	0.164033	−	0.284114i	0.936312	+	0.351170i	$0.114216\pi$
$264$		0			0
$265$	−0.486051	−	0.841865i	−0.0298579	−	0.0517153i
$266$	11.0529	+	19.1441i	0.677695	+	1.17380i
$267$	17.9427	−	17.9039i	1.09808	−	1.09570i
$268$	−17.6380	+	30.5499i	−1.07741	+	1.86613i
$269$	−8.54830			−0.521199			−0.260599	−	0.965447i	$-0.583920\pi$
$269$	−8.54830			−0.521199			−0.260599	+	0.965447i	$0.583920\pi$
$270$	−19.5524	−	19.6799i	−1.18992	−	1.19768i
$271$	7.48115			0.454447			0.227224	−	0.973843i	$-0.427035\pi$
$271$	7.48115			0.454447			0.227224	+	0.973843i	$0.427035\pi$
$272$	−6.21719	+	10.7685i	−0.376973	+	0.652936i
$273$	−5.45095	+	5.43916i	−0.329907	+	0.329193i
$274$	−1.53151	−	2.65265i	−0.0925219	−	0.160253i
$275$		0			0
$276$	−3.45207	−	12.9393i	−0.207790	−	0.778855i
$277$	6.39318	−	11.0733i	0.384129	−	0.665331i	−0.607519	−	0.794305i	$-0.707835\pi$
$277$	6.39318	−	11.0733i	0.384129	−	0.665331i	0.991648	+	0.128974i	$0.0411684\pi$
$278$	−7.10739			−0.426273
$279$	−18.5100	+	10.6334i	−1.10816	+	0.636602i
$280$	−47.1493			−2.81771
$281$	−10.3973	+	18.0087i	−0.620253	+	1.07431i	0.369185	+	0.929356i	$0.379637\pi$
$281$	−10.3973	+	18.0087i	−0.620253	+	1.07431i	−0.989438	+	0.144954i	$0.953697\pi$
$282$	24.9344	+	6.71011i	1.48482	+	0.399581i
$283$	6.27243	+	10.8642i	0.372857	+	0.645808i	0.990004	−	0.141040i	$-0.0450447\pi$
$283$	6.27243	+	10.8642i	0.372857	+	0.645808i	−0.617146	+	0.786848i	$0.711711\pi$
$284$	−3.74470	−	6.48601i	−0.222207	−	0.384874i
$285$	−9.14288	−	2.46044i	−0.541578	−	0.145744i
$286$		0			0
$287$	−19.2718			−1.13758
$288$	−24.8114	+	14.2533i	−1.46203	+	0.839885i
$289$	−15.1747			−0.892630
$290$	−24.5661	+	42.5498i	−1.44257	+	2.49861i
$291$	3.09279	+	11.5927i	0.181303	+	0.679573i
$292$	22.9330	+	39.7212i	1.34206	+	2.32451i
$293$	−8.00414	−	13.8636i	−0.467607	−	0.809919i	0.531708	−	0.846928i	$-0.321550\pi$
$293$	−8.00414	−	13.8636i	−0.467607	−	0.809919i	−0.999315	+	0.0370086i	$0.988217\pi$
$294$	10.1236	−	10.1018i	0.590423	−	0.589146i
$295$	1.58465	−	2.74470i	0.0922620	−	0.159803i
$296$	−5.39679			−0.313682
$297$		0			0
$298$	−11.6588			−0.675374
$299$	1.12996	−	1.95714i	0.0653471	−	0.113185i
$300$	−4.61297	+	4.60299i	−0.266330	+	0.265754i
$301$	11.3120	+	19.5930i	0.652013	+	1.12932i
$302$	−29.2810	−	50.7163i	−1.68493	−	2.91839i
$303$	−0.621514	−	2.32961i	−0.0357050	−	0.133832i
$304$	−12.2586	+	21.2325i	−0.703077	+	1.21777i
$305$	−19.2689			−1.10333
$306$	9.12069	+	5.29220i	0.521395	+	0.302535i
$307$	22.5571			1.28740			0.643702	−	0.765276i	$-0.277398\pi$
$307$	22.5571			1.28740			0.643702	+	0.765276i	$0.277398\pi$
$308$		0			0
$309$	−18.5727	−	4.99809i	−1.05656	−	0.284331i
$310$	−18.9946	−	32.8997i	−1.07882	−	1.86858i
$311$	−14.3699	−	24.8894i	−0.814841	−	1.41135i	−0.909442	−	0.415831i	$-0.863491\pi$
$311$	−14.3699	−	24.8894i	−0.814841	−	1.41135i	0.0946007	−	0.995515i	$-0.469843\pi$
$312$	−16.7933	−	4.51926i	−0.950736	−	0.255853i
$313$	12.3764	−	21.4365i	0.699554	−	1.21166i	−0.269068	−	0.963121i	$-0.586716\pi$
$313$	12.3764	−	21.4365i	0.699554	−	1.21166i	0.968621	−	0.248541i	$-0.0799511\pi$
$314$	−44.4493			−2.50842
$315$	−0.0425197	+	19.6361i	−0.00239571	+	1.10637i
$316$	−11.0261			−0.620268
$317$	13.2131	−	22.8857i	0.742120	−	1.28539i	−0.209409	−	0.977828i	$-0.567154\pi$
$317$	13.2131	−	22.8857i	0.742120	−	1.28539i	0.951528	−	0.307561i	$-0.0995128\pi$
$318$	0.550263	+	2.06254i	0.0308572	+	0.115661i
$319$		0			0
$320$	−6.57450	−	11.3874i	−0.367526	−	0.636574i
$321$	−14.2422	+	14.2114i	−0.794924	+	0.793204i
$322$	−6.72728	+	11.6520i	−0.374896	+	0.649340i
$323$	3.59895			0.200251
$324$	21.2983	+	37.2615i	1.18324	+	2.07008i
$325$	−1.09971			−0.0610007
$326$	−24.6376	+	42.6736i	−1.36455	+	2.36347i
$327$	10.5047	−	10.4820i	0.580911	−	0.579655i
$328$	−21.7618	−	37.6926i	−1.20160	−	2.08123i
$329$	−9.13853	−	15.8284i	−0.503824	−	0.872648i
$330$		0			0
$331$	13.0617	−	22.6235i	0.717934	−	1.24350i	−0.243882	−	0.969805i	$-0.578421\pi$
$331$	13.0617	−	22.6235i	0.717934	−	1.24350i	0.961817	−	0.273694i	$-0.0882456\pi$
$332$	36.3603			1.99553
$333$	−0.00486687	+	2.24757i	−0.000266703	+	0.123166i
$334$	12.9351			0.707777
$335$	−7.58991	+	13.1461i	−0.414681	+	0.718249i
$336$	49.0995	+	13.2132i	2.67860	+	0.720837i
$337$	0.764836	+	1.32473i	0.0416633	+	0.0721629i	0.886105	−	0.463484i	$-0.153401\pi$
$337$	0.764836	+	1.32473i	0.0416633	+	0.0721629i	−0.844442	+	0.535647i	$0.820068\pi$
$338$	14.3836	+	24.9132i	0.782367	+	1.35510i
$339$	23.1244	+	6.22302i	1.25595	+	0.337988i
$340$	−6.61052	+	11.4498i	−0.358506	+	0.620951i
$341$		0			0
$342$	17.9835	+	10.4347i	0.972434	+	0.564246i
$343$	12.2044			0.658978
$344$	−25.5471	+	44.2489i	−1.37741	+	2.38574i
$345$	−1.48548	−	5.56800i	−0.0799756	−	0.299771i
$346$	18.5157	+	32.0701i	0.995409	+	1.72410i
$347$	9.05374	+	15.6815i	0.486030	+	0.841829i	0.999871	−	0.0160565i	$-0.00511116\pi$
$347$	9.05374	+	15.6815i	0.486030	+	0.841829i	−0.513841	+	0.857886i	$0.671778\pi$
$348$	53.8071	−	53.6907i	2.88436	−	2.87812i
$349$	6.20159	−	10.7415i	0.331964	−	0.574978i	−0.650933	−	0.759135i	$-0.725622\pi$
$349$	6.20159	−	10.7415i	0.331964	−	0.574978i	0.982897	+	0.184157i	$0.0589556\pi$
$350$	6.54717			0.349961
$351$	−1.89726	+	6.98976i	−0.101268	+	0.373086i
$352$		0			0
$353$	13.2943	−	23.0264i	0.707585	−	1.22557i	−0.258165	−	0.966101i	$-0.583118\pi$
$353$	13.2943	−	23.0264i	0.707585	−	1.22557i	0.965750	−	0.259473i	$-0.0835489\pi$
$354$	−4.92652	+	4.91586i	−0.261841	+	0.261275i
$355$	−1.61141	−	2.79104i	−0.0855246	−	0.148133i
$356$	−34.8939	−	60.4380i	−1.84937	−	3.20321i
$357$	−1.92399	−	7.21166i	−0.101828	−	0.381681i
$358$	10.2418	−	17.7394i	0.541298	−	0.937556i
$359$	−27.0587			−1.42810			−0.714051	−	0.700094i	$-0.753141\pi$
$359$	−27.0587			−1.42810			−0.714051	+	0.700094i	$0.753141\pi$
$360$	−38.4529	+	22.0899i	−2.02665	+	1.16424i
$361$	−11.9039			−0.626520
$362$	18.6758	−	32.3474i	0.981576	−	1.70014i
$363$		0			0
$364$	10.6007	+	18.3609i	0.555626	+	0.962373i
$365$	9.86847	+	17.0927i	0.516539	+	0.894672i
$366$	40.8597	+	10.9957i	2.13577	+	0.574757i
$367$	5.03001	−	8.71224i	0.262565	−	0.454775i	−0.704358	−	0.709845i	$-0.748765\pi$
$367$	5.03001	−	8.71224i	0.262565	−	0.454775i	0.966923	+	0.255070i	$0.0820984\pi$
$368$	−14.9222			−0.777875
$369$	−15.7173	+	9.02905i	−0.818208	+	0.470033i
$370$	−3.99984			−0.207942
$371$	0.755487	−	1.30854i	0.0392229	−	0.0679361i
$372$	15.1501	+	56.7869i	0.785498	+	2.94427i
$373$	−10.7033	−	18.5386i	−0.554195	−	0.959894i	−0.997966	−	0.0637534i	$-0.979693\pi$
$373$	−10.7033	−	18.5386i	−0.554195	−	0.959894i	0.443771	−	0.896140i	$-0.353640\pi$
$374$		0			0
$375$	−14.5650	+	14.5335i	−0.752134	+	0.750507i
$376$	20.6385	−	35.7470i	1.06435	−	1.84351i
$377$	12.8273			0.660639
$378$	11.2954	−	41.6140i	0.580975	−	2.14039i
$379$	16.2996			0.837252			0.418626	−	0.908159i	$-0.362512\pi$
$379$	16.2996			0.837252			0.418626	+	0.908159i	$0.362512\pi$
$380$	−13.0341	+	22.5757i	−0.668636	+	1.15811i
$381$	13.2774	−	13.2487i	0.680223	−	0.678752i
$382$	16.2317	+	28.1142i	0.830487	+	1.43845i
$383$	7.97631	+	13.8154i	0.407570	+	0.705932i	0.994617	−	0.103621i	$-0.0330428\pi$
$383$	7.97631	+	13.8154i	0.407570	+	0.705932i	−0.587047	+	0.809553i	$0.699709\pi$
$384$	−1.07392	−	4.02536i	−0.0548033	−	0.205418i
$385$		0			0
$386$	14.6713			0.746750
$387$	18.4051	+	10.6794i	0.935582	+	0.542863i
$388$	33.0338			1.67704
$389$	−12.2041	+	21.1381i	−0.618772	+	1.07174i	0.370939	+	0.928657i	$0.379036\pi$
$389$	−12.2041	+	21.1381i	−0.618772	+	1.07174i	−0.989710	+	0.143086i	$0.954297\pi$
$390$	−12.4464	−	3.34946i	−0.630249	−	0.169606i
$391$	1.09524	+	1.89701i	0.0553887	+	0.0959361i
$392$	−11.4309	−	19.7988i	−0.577345	−	0.999991i
$393$	−9.87241	−	2.65676i	−0.497997	−	0.134016i
$394$	−1.88884	+	3.27156i	−0.0951582	+	0.164819i
$395$	−4.74472			−0.238733
$396$		0			0
$397$	0.870040			0.0436661			0.0218330	−	0.999762i	$-0.493050\pi$
$397$	0.870040			0.0436661			0.0218330	+	0.999762i	$0.493050\pi$
$398$	−34.1072	+	59.0754i	−1.70964	+	2.96118i
$399$	−3.79357	−	14.2194i	−0.189916	−	0.711859i
$400$	3.63068	+	6.28852i	0.181534	+	0.314426i
$401$	17.6307	+	30.5373i	0.880437	+	1.52496i	0.850856	+	0.525400i	$0.176084\pi$
$401$	17.6307	+	30.5373i	0.880437	+	1.52496i	0.0295816	+	0.999562i	$0.490583\pi$
$402$	23.5962	−	23.5452i	1.17687	−	1.17433i
$403$	−4.95906	+	8.58934i	−0.247028	+	0.427866i
$404$	−6.63833			−0.330269
$405$	9.16501	+	16.0342i	0.455413	+	0.796747i
$406$	−76.3681			−3.79009
$407$		0			0
$408$	11.9322	−	11.9064i	0.590734	−	0.589457i
$409$	3.37326	+	5.84265i	0.166797	+	0.288901i	0.937292	−	0.348545i	$-0.113324\pi$
$409$	3.37326	+	5.84265i	0.166797	+	0.288901i	−0.770495	+	0.637446i	$0.779991\pi$
$410$	−16.1288	−	27.9359i	−0.796546	−	1.37966i
$411$	0.525646	+	1.97027i	0.0259282	+	0.0971861i
$412$	−26.4772	+	45.8599i	−1.30444	+	2.25935i
$413$	4.92617			0.242401
$414$	−0.0274022	+	12.6546i	−0.00134675	+	0.621942i
$415$	15.6464			0.768053
$416$	−6.64730	+	11.5135i	−0.325910	+	0.564494i
$417$	4.56913	+	1.22960i	0.223751	+	0.0602137i
$418$		0			0
$419$	−0.479668	−	0.830810i	−0.0234333	−	0.0405877i	0.854071	−	0.520157i	$-0.174126\pi$
$419$	−0.479668	−	0.830810i	−0.0234333	−	0.0405877i	−0.877504	+	0.479569i	$0.840793\pi$
$420$	52.2058	+	14.0491i	2.54738	+	0.685525i
$421$	3.61615	−	6.26335i	0.176240	−	0.305257i	−0.764350	−	0.644802i	$-0.776940\pi$
$421$	3.61615	−	6.26335i	0.176240	−	0.305257i	0.940590	+	0.339545i	$0.110273\pi$
$422$	16.6364			0.809849
$423$	−14.8687	−	8.62746i	−0.722943	−	0.419481i
$424$	3.41239			0.165720
$425$	0.532959	−	0.923113i	0.0258523	−	0.0447776i
$426$	1.82429	+	6.83795i	0.0883872	+	0.331300i
$427$	−14.9752	−	25.9377i	−0.724699	−	1.25522i
$428$	27.6974	+	47.9733i	1.33880	+	2.31888i
$429$		0			0
$430$	−18.9343	+	32.7951i	−0.913092	+	1.58152i
$431$	18.9008			0.910418			0.455209	−	0.890385i	$-0.349565\pi$
$431$	18.9008			0.910418			0.455209	+	0.890385i	$0.349565\pi$
$432$	46.2339	−	12.2275i	2.22443	−	0.588297i
$433$	16.5351			0.794625			0.397313	−	0.917683i	$-0.369943\pi$
$433$	16.5351			0.794625			0.397313	+	0.917683i	$0.369943\pi$
$434$	29.5241	−	51.1372i	1.41720	−	2.45466i
$435$	23.1541	−	23.1040i	1.11015	−	1.10775i
$436$	−20.4289	−	35.3839i	−0.978366	−	1.69458i
$437$	2.15951	+	3.74038i	0.103303	+	0.178927i
$438$	−11.1722	−	41.8765i	−0.533828	−	2.00094i
$439$	8.66007	−	14.9997i	0.413323	−	0.715896i	−0.581928	−	0.813240i	$-0.697701\pi$
$439$	8.66007	−	14.9997i	0.413323	−	0.715896i	0.995251	+	0.0973443i	$0.0310348\pi$
$440$		0			0
$441$	−8.25582	+	4.74270i	−0.393134	+	0.225843i
$442$	4.89934			0.233038
$443$	−12.0644	+	20.8962i	−0.573198	+	0.992809i	0.423036	+	0.906113i	$0.360964\pi$
$443$	−12.0644	+	20.8962i	−0.573198	+	0.992809i	−0.996235	+	0.0866960i	$0.972369\pi$
$444$	5.97555	+	1.60808i	0.283587	+	0.0763161i
$445$	−15.0154	−	26.0075i	−0.711799	−	1.23287i
$446$	22.3048	+	38.6330i	1.05616	+	1.82933i
$447$	7.49507	+	2.01700i	0.354504	+	0.0954007i
$448$	10.2190	−	17.6998i	0.482802	−	0.836238i
$449$	6.00580			0.283431			0.141716	−	0.989907i	$-0.454738\pi$
$449$	6.00580			0.283431			0.141716	+	0.989907i	$0.454738\pi$
$450$	5.33958	−	3.06741i	0.251710	−	0.144599i
$451$		0			0
$452$	32.9663	−	57.0992i	1.55060	−	2.68572i
$453$	10.0499	+	37.6697i	0.472183	+	1.76988i
$454$	7.06966	+	12.2450i	0.331795	+	0.574686i
$455$	4.56164	+	7.90100i	0.213853	+	0.370404i
$456$	23.5271	−	23.4762i	1.10176	−	1.09937i
$457$	16.2962	−	28.2258i	0.762302	−	1.32035i	−0.179359	−	0.983784i	$-0.557402\pi$
$457$	16.2962	−	28.2258i	0.762302	−	1.32035i	0.941661	−	0.336562i	$-0.109264\pi$
$458$	−37.7044			−1.76181
$459$	−4.94785	−	4.98010i	−0.230946	−	0.232451i
$460$	−15.8663			−0.739770
$461$	2.94681	−	5.10403i	0.137247	−	0.237718i	−0.789207	−	0.614128i	$-0.789508\pi$
$461$	2.94681	−	5.10403i	0.137247	−	0.237718i	0.926453	+	0.376409i	$0.122841\pi$
$462$		0			0
$463$	19.3992	+	33.6004i	0.901558	+	1.56155i	0.825471	+	0.564444i	$0.190909\pi$
$463$	19.3992	+	33.6004i	0.901558	+	1.56155i	0.0760871	+	0.997101i	$0.475757\pi$
$464$	−42.3493	−	73.3512i	−1.96602	−	3.40524i
$465$	6.51935	+	24.4364i	0.302328	+	1.13321i
$466$	1.46303	−	2.53404i	0.0677735	−	0.117387i
$467$	27.1388			1.25584			0.627918	−	0.778279i	$-0.283907\pi$
$467$	27.1388			1.25584			0.627918	+	0.778279i	$0.283907\pi$
$468$	17.2477	+	10.0078i	0.797275	+	0.462612i
$469$	−23.5946			−1.08950
$470$	15.2963	−	26.4939i	0.705565	−	1.22207i
$471$	28.5751	+	7.68985i	1.31667	+	0.354330i
$472$	5.56265	+	9.63479i	0.256042	+	0.443477i
$473$		0			0
$474$	10.0612	+	2.70757i	0.462126	+	0.124363i
$475$	1.05085	−	1.82012i	0.0482162	−	0.0835129i
$476$	−20.5500			−0.941906
$477$	0.00307732	−	1.42114i	0.000140901	−	0.0650696i
$478$	57.2116			2.61680
$479$	5.12044	−	8.86886i	0.233959	−	0.405229i	−0.725011	−	0.688738i	$-0.758165\pi$
$479$	5.12044	−	8.86886i	0.233959	−	0.405229i	0.958970	+	0.283509i	$0.0914986\pi$
$480$	8.73877	+	32.7553i	0.398868	+	1.49507i
$481$	0.522132	+	0.904360i	0.0238072	+	0.0412353i
$482$	−14.5208	−	25.1507i	−0.661402	−	1.14558i
$483$	6.34059	−	6.32687i	0.288507	−	0.287883i
$484$		0			0
$485$	14.2150			0.645470
$486$	−10.2845	−	39.2306i	−0.466515	−	1.77954i
$487$	−24.5418			−1.11210			−0.556048	−	0.831150i	$-0.687683\pi$
$487$	−24.5418			−1.11210			−0.556048	+	0.831150i	$0.687683\pi$
$488$	33.8200	−	58.5780i	1.53096	−	2.65170i
$489$	23.2214	−	23.1712i	1.05011	−	1.04784i
$490$	−8.47200	−	14.6739i	−0.382726	−	0.662901i
$491$	20.6688	+	35.7994i	0.932769	+	1.61560i	0.778564	+	0.627565i	$0.215948\pi$
$491$	20.6688	+	35.7994i	0.932769	+	1.61560i	0.154205	+	0.988039i	$0.450718\pi$
$492$	12.8644	+	48.2192i	0.579970	+	2.17389i
$493$	−6.21660	+	10.7675i	−0.279982	+	0.484942i
$494$	9.66013			0.434630
$495$		0			0
$496$	65.4894			2.94056
$497$	2.50467	−	4.33822i	0.112350	−	0.194596i
$498$	−33.1783	−	8.92861i	−1.48676	−	0.400101i
$499$	19.7655	+	34.2348i	0.884823	+	1.53256i	0.845916	+	0.533316i	$0.179054\pi$
$499$	19.7655	+	34.2348i	0.884823	+	1.53256i	0.0389075	+	0.999243i	$0.487612\pi$
$500$	28.3251	+	49.0606i	1.26674	+	2.19405i
$501$	−8.31559	−	2.23781i	−0.371513	−	0.0999779i
$502$	17.3742	−	30.0929i	0.775447	−	1.34311i
$503$	14.3871			0.641488			0.320744	−	0.947166i	$-0.396067\pi$
$503$	14.3871			0.641488			0.320744	+	0.947166i	$0.396067\pi$
$504$	−59.6196	−	34.5937i	−2.65567	−	1.54093i
$505$	−2.85658			−0.127116
$506$		0			0
$507$	−4.93676	−	18.5044i	−0.219249	−	0.821808i
$508$	−25.8211	−	44.7235i	−1.14563	−	1.98428i
$509$	1.36053	+	2.35651i	0.0603044	+	0.104450i	0.894601	−	0.446865i	$-0.147460\pi$
$509$	1.36053	+	2.35651i	0.0603044	+	0.104450i	−0.834297	+	0.551315i	$0.814126\pi$
$510$	8.84361	−	8.82448i	0.391602	−	0.390755i
$511$	−15.3389	+	26.5678i	−0.678554	+	1.17529i
$512$	−44.8118			−1.98042
$513$	−9.75579	−	9.81937i	−0.430729	−	0.433536i
$514$	−32.5008			−1.43355
$515$	−11.3936	+	19.7343i	−0.502061	+	0.869596i
$516$	41.4717	−	41.3819i	1.82569	−	1.82174i
$517$		0			0
$518$	−3.10855	−	5.38417i	−0.136582	−	0.236567i
$519$	−6.35496	−	23.8202i	−0.278952	−	1.04559i
$520$	−10.3020	+	17.8437i	−0.451774	+	0.782496i
$521$	−9.52745			−0.417405			−0.208703	−	0.977979i	$-0.566924\pi$
$521$	−9.52745			−0.417405			−0.208703	+	0.977979i	$0.566924\pi$
$522$	−62.2825	+	35.7792i	−2.72603	+	1.56601i
$523$	−6.54000			−0.285974			−0.142987	−	0.989725i	$-0.545671\pi$
$523$	−6.54000			−0.285974			−0.142987	+	0.989725i	$0.545671\pi$
$524$	−14.0741	+	24.3771i	−0.614831	+	1.06492i
$525$	−4.20898	−	1.13268i	−0.183695	−	0.0494341i
$526$	6.92094	+	11.9874i	0.301767	+	0.522676i
$527$	−4.80670	−	8.32545i	−0.209383	−	0.362662i
$528$		0			0
$529$	10.1856	−	17.6420i	0.442853	−	0.767044i
$530$	2.52910			0.109857
$531$	4.01757	−	2.30796i	0.174348	−	0.100157i
$532$	−40.5188			−1.75671
$533$	−4.21086	+	7.29343i	−0.182393	+	0.315913i
$534$	16.9991	+	63.7174i	0.735624	+	2.75732i
$535$	11.9186	+	20.6437i	0.515288	+	0.892505i
$536$	−26.6431	−	46.1472i	−1.15081	−	1.99325i
$537$	−9.65314	+	9.63226i	−0.416564	+	0.415663i
$538$	11.1200	−	19.2604i	0.479417	−	0.830374i
$539$		0			0
$540$	49.1589	−	13.0011i	2.11546	−	0.559478i
$541$	7.15503			0.307619			0.153809	−	0.988101i	$-0.450846\pi$
$541$	7.15503			0.307619			0.153809	+	0.988101i	$0.450846\pi$
$542$	−9.73180	+	16.8560i	−0.418017	+	0.724026i
$543$	−17.6023	+	17.5642i	−0.755386	+	0.753752i
$544$	−6.44307	−	11.1597i	−0.276244	−	0.478469i
$545$	−8.79089	−	15.2263i	−0.376560	−	0.652221i
$546$	−5.16428	−	19.3572i	−0.221011	−	0.828411i
$547$	−4.58910	+	7.94856i	−0.196216	+	0.339856i	−0.947298	−	0.320352i	$-0.896199\pi$
$547$	−4.58910	+	7.94856i	−0.196216	+	0.339856i	0.751083	+	0.660208i	$0.229532\pi$
$548$	5.61437			0.239834
$549$	−24.3652	−	14.1377i	−1.03988	−	0.603381i
$550$		0			0
$551$	−12.2574	+	21.2304i	−0.522183	+	0.904447i
$552$	19.5342	+	5.25684i	0.831429	+	0.223746i
$553$	−3.68745	−	6.38685i	−0.156806	−	0.271597i
$554$	16.6331	+	28.8093i	0.706671	+	1.22399i
$555$	2.57138	+	0.691983i	0.109149	+	0.0293731i
$556$	6.51376	−	11.2822i	0.276245	−	0.478470i
$557$	−5.27246			−0.223401			−0.111701	−	0.993742i	$-0.535630\pi$
$557$	−5.27246			−0.223401			−0.111701	+	0.993742i	$0.535630\pi$
$558$	0.120260	−	55.5376i	0.00509103	−	2.35109i
$559$	9.88660			0.418159
$560$	30.1206	−	52.1703i	1.27283	−	2.20460i
$561$		0			0
$562$	−27.0506	−	46.8530i	−1.14106	−	1.97638i
$563$	−17.3513	−	30.0533i	−0.731269	−	1.26659i	−0.956341	−	0.292252i	$-0.905595\pi$
$563$	−17.3513	−	30.0533i	−0.731269	−	1.26659i	0.225073	−	0.974342i	$-0.427738\pi$
$564$	−33.5034	+	33.4309i	−1.41075	+	1.40769i
$565$	14.1859	−	24.5707i	0.596806	−	1.03370i
$566$	−32.6378			−1.37187
$567$	−14.4608	+	24.7983i	−0.607298	+	1.04143i
$568$	11.3131			0.474688
$569$	−10.9498	+	18.9656i	−0.459038	+	0.795077i	−0.998910	−	0.0466697i	$-0.985139\pi$
$569$	−10.9498	+	18.9656i	−0.459038	+	0.795077i	0.539872	+	0.841747i	$0.318473\pi$
$570$	17.4371	−	17.3994i	0.730361	−	0.728781i
$571$	15.4685	+	26.7922i	0.647335	+	1.12122i	0.983757	+	0.179506i	$0.0574498\pi$
$571$	15.4685	+	26.7922i	0.647335	+	1.12122i	−0.336422	+	0.941711i	$0.609217\pi$
$572$		0			0
$573$	−5.57106	−	20.8819i	−0.232734	−	0.872354i
$574$	25.0696	−	43.4219i	1.04639	−	1.81239i
$575$	1.27919			0.0533457
$576$	0.0416250	−	19.2229i	0.00173438	−	0.800954i
$577$	17.7082			0.737201			0.368600	−	0.929588i	$-0.379837\pi$
$577$	17.7082			0.737201			0.368600	+	0.929588i	$0.379837\pi$
$578$	19.7399	−	34.1906i	0.821073	−	1.42214i
$579$	−9.43174	−	2.53818i	−0.391970	−	0.105483i
$580$	−45.0286	−	77.9918i	−1.86971	−	3.23843i
$581$	12.1599	+	21.0616i	0.504479	+	0.873782i
$582$	−30.1429	−	8.11177i	−1.24947	−	0.336244i
$583$		0			0
$584$	−69.2831			−2.86695
$585$	7.42197	+	4.30653i	0.306861	+	0.178053i
$586$	41.6485			1.72049
$587$	2.11902	−	3.67024i	0.0874612	−	0.151487i	−0.818976	−	0.573828i	$-0.805458\pi$
$587$	2.11902	−	3.67024i	0.0874612	−	0.151487i	0.906437	+	0.422340i	$0.138791\pi$
$588$	6.75727	+	25.3281i	0.278665	+	1.04452i
$589$	−9.47747	−	16.4155i	−0.390513	−	0.676387i
$590$	4.12277	+	7.14084i	0.169732	+	0.293984i
$591$	1.78026	−	1.77641i	0.0732303	−	0.0730719i
$592$	3.44764	−	5.97150i	0.141697	−	0.245427i
$593$	−47.0032			−1.93019			−0.965095	−	0.261898i	$-0.915652\pi$
$593$	−47.0032			−1.93019			−0.965095	+	0.261898i	$0.915652\pi$
$594$		0			0
$595$	−8.84299			−0.362527
$596$	10.6850	−	18.5069i	0.437674	−	0.758073i
$597$	32.1467	−	32.0772i	1.31568	−	1.31283i
$598$	2.93979	+	5.09187i	0.120217	+	0.208222i
$599$	0.984547	+	1.70529i	0.0402275	+	0.0696761i	0.885438	−	0.464757i	$-0.153858\pi$
$599$	0.984547	+	1.70529i	0.0402275	+	0.0696761i	−0.845211	+	0.534433i	$0.820525\pi$
$600$	−2.53746	−	9.51110i	−0.103591	−	0.388289i
$601$	16.2871	−	28.2100i	0.664363	−	1.15071i	−0.315095	−	0.949060i	$-0.602036\pi$
$601$	16.2871	−	28.2100i	0.664363	−	1.15071i	0.979458	−	0.201650i	$-0.0646303\pi$
$602$	−58.8605			−2.39898
$603$	−19.2427	+	11.0543i	−0.783623	+	0.450166i
$604$	107.342			4.36767
$605$		0			0
$606$	6.05739	+	1.63010i	0.246065	+	0.0662185i
$607$	2.60474	+	4.51155i	0.105723	+	0.183118i	0.914034	−	0.405639i	$-0.132951\pi$
$607$	2.60474	+	4.51155i	0.105723	+	0.183118i	−0.808310	+	0.588757i	$0.799618\pi$
$608$	−12.7039	−	22.0039i	−0.515213	−	0.892375i
$609$	49.0948	+	13.2119i	1.98942	+	0.535373i
$610$	25.0658	−	43.4152i	1.01488	−	1.75783i
$611$	−7.98701			−0.323120
$612$	−16.7597	+	9.62786i	−0.677469	+	0.389183i
$613$	19.9361			0.805212			0.402606	−	0.915373i	$-0.368104\pi$
$613$	19.9361			0.805212			0.402606	+	0.915373i	$0.368104\pi$
$614$	−29.3433	+	50.8241i	−1.18420	+	2.05109i
$615$	5.53575	+	20.7495i	0.223223	+	0.836701i
$616$		0			0
$617$	9.04507	+	15.6665i	0.364141	+	0.630710i	0.988638	−	0.150317i	$-0.0480294\pi$
$617$	9.04507	+	15.6665i	0.364141	+	0.630710i	−0.624497	+	0.781027i	$0.714696\pi$
$618$	35.4214	−	35.3448i	1.42486	−	1.42178i
$619$	−4.44152	+	7.69294i	−0.178520	+	0.309206i	−0.941374	−	0.337365i	$-0.890464\pi$
$619$	−4.44152	+	7.69294i	−0.178520	+	0.309206i	0.762854	+	0.646571i	$0.223798\pi$
$620$	69.6326			2.79651
$621$	2.20690	−	8.13055i	0.0885600	−	0.326268i
$622$	74.7718			2.99808
$623$	23.3390	−	40.4244i	0.935059	−	1.61957i
$624$	15.7287	−	15.6946i	0.629650	−	0.628288i
$625$	10.2163	+	17.6952i	0.408654	+	0.707809i
$626$	32.1994	+	55.7710i	1.28695	+	2.22906i
$627$		0			0
$628$	40.7368	−	70.5582i	1.62557	−	2.81558i
$629$	−1.01218			−0.0403583
$630$	−44.1872	−	25.6392i	−1.76046	−	1.02149i
$631$	7.00816			0.278990			0.139495	−	0.990223i	$-0.455452\pi$
$631$	7.00816			0.278990			0.139495	+	0.990223i	$0.455452\pi$
$632$	8.32776	−	14.4241i	0.331261	−	0.573760i
$633$	−10.6951	−	2.87815i	−0.425091	−	0.114396i
$634$	34.3763	+	59.5414i	1.36526	+	2.36469i
$635$	−11.1113	−	19.2453i	−0.440937	−	0.763725i
$636$	−3.77835	−	1.01679i	−0.149821	−	0.0403184i
$637$	−2.21184	+	3.83102i	−0.0876364	+	0.151791i
$638$		0			0
$639$	0.0102023	−	4.71152i	0.000403596	−	0.186385i
$640$	−4.93593			−0.195110
$641$	3.92536	−	6.79892i	0.155042	−	0.268541i	−0.778032	−	0.628224i	$-0.783782\pi$
$641$	3.92536	−	6.79892i	0.155042	−	0.268541i	0.933074	+	0.359683i	$0.117115\pi$
$642$	−13.4932	−	50.5764i	−0.532535	−	1.99609i
$643$	2.76317	+	4.78595i	0.108969	+	0.188739i	0.915353	−	0.402653i	$-0.131912\pi$
$643$	2.76317	+	4.78595i	0.108969	+	0.188739i	−0.806384	+	0.591392i	$0.798579\pi$
$644$	−12.3308	−	21.3575i	−0.485901	−	0.841605i
$645$	17.8459	−	17.8073i	0.702683	−	0.701163i
$646$	−4.68167	+	8.10889i	−0.184198	+	0.319040i
$647$	5.85350			0.230125			0.115062	−	0.993358i	$-0.463293\pi$
$647$	5.85350			0.230125			0.115062	+	0.993358i	$0.463293\pi$
$648$	−64.8306	−	0.280768i	−2.54679	−	0.0110296i
$649$		0			0
$650$	1.43054	−	2.47777i	0.0561105	−	0.0971863i
$651$	−27.8270	+	27.7668i	−1.09063	+	1.08827i
$652$	−45.1596	−	78.2188i	−1.76859	−	3.06328i
$653$	−1.76788	−	3.06206i	−0.0691824	−	0.119827i	0.829359	−	0.558716i	$-0.188706\pi$
$653$	−1.76788	−	3.06206i	−0.0691824	−	0.119827i	−0.898542	+	0.438888i	$0.855372\pi$
$654$	9.95225	+	37.3038i	0.389164	+	1.45870i
$655$	−6.05633	+	10.4899i	−0.236640	+	0.409873i
$656$	55.6087			2.17115
$657$	−0.0624801	+	28.8540i	−0.00243758	+	1.12570i
$658$	47.5512			1.85374
$659$	−1.11686	+	1.93445i	−0.0435066	+	0.0753556i	−0.886959	−	0.461849i	$-0.847186\pi$
$659$	−1.11686	+	1.93445i	−0.0435066	+	0.0753556i	0.843452	+	0.537204i	$0.180520\pi$
$660$		0			0
$661$	5.80090	+	10.0475i	0.225629	+	0.390801i	0.956508	−	0.291706i	$-0.0942230\pi$
$661$	5.80090	+	10.0475i	0.225629	+	0.390801i	−0.730879	+	0.682507i	$0.760890\pi$
$662$	33.9824	+	58.8592i	1.32076	+	2.28763i
$663$	−3.14964	−	0.847599i	−0.122322	−	0.0329180i
$664$	−27.4620	+	47.5657i	−1.06573	+	1.84591i
$665$	−17.4359			−0.676136
$666$	−5.05773	−	2.93470i	−0.195983	−	0.113717i
$667$	−14.9208			−0.577736
$668$	−11.8547	+	20.5330i	−0.458673	+	0.794445i
$669$	−7.65546	−	28.6948i	−0.295977	−	1.10940i
$670$	−19.7466	−	34.2021i	−0.762877	−	1.32134i
$671$		0			0
$672$	−37.3003	+	37.2196i	−1.43889	+	1.43578i
$673$	−22.8392	+	39.5587i	−0.880387	+	1.52488i	−0.0294763	+	0.999565i	$0.509384\pi$
$673$	−22.8392	+	39.5587i	−0.880387	+	1.52488i	−0.850911	+	0.525310i	$0.823949\pi$
$674$	−3.97972			−0.153293
$675$	−3.96333	+	1.04819i	−0.152549	+	0.0403447i
$676$	−52.7291			−2.02804
$677$	13.0528	−	22.6082i	0.501661	−	0.868903i	−0.498337	−	0.866983i	$-0.666056\pi$
$677$	13.0528	−	22.6082i	0.501661	−	0.868903i	0.999998	−	0.00191927i	$-0.000610924\pi$
$678$	−44.1025	+	44.0071i	−1.69375	+	1.69008i
$679$	11.0475	+	19.1348i	0.423963	+	0.734325i
$680$	−9.98553	−	17.2955i	−0.382928	−	0.663250i
$681$	−2.42645	−	9.09502i	−0.0929818	−	0.348522i
$682$		0			0
$683$	24.9486			0.954631			0.477315	−	0.878732i	$-0.341610\pi$
$683$	24.9486			0.954631			0.477315	+	0.878732i	$0.341610\pi$
$684$	−33.0454	+	18.9835i	−1.26352	+	0.725851i
$685$	2.41596			0.0923090
$686$	−15.8761	+	27.4981i	−0.606151	+	1.04988i
$687$	24.2391	+	6.52297i	0.924778	+	0.248867i
$688$	−32.6406	−	56.5352i	−1.24441	−	2.15539i
$689$	−0.330145	−	0.571828i	−0.0125775	−	0.0217849i
$690$	14.4778	+	3.89612i	0.551160	+	0.148323i
$691$	−10.3287	+	17.8899i	−0.392924	+	0.680564i	−0.992834	−	0.119504i	$-0.961870\pi$
$691$	−10.3287	+	17.8899i	−0.392924	+	0.680564i	0.599910	+	0.800067i	$0.295203\pi$
$692$	−67.8768			−2.58029
$693$		0			0
$694$	−47.1100			−1.78827
$695$	2.80298	−	4.85490i	0.106323	−	0.184157i
$696$	29.5977	+	110.940i	1.12190	+	4.20518i
$697$	−4.08149	−	7.06935i	−0.154597	−	0.267771i
$698$	16.1346	+	27.9459i	0.610703	+	1.05777i
$699$	−1.37893	+	1.37595i	−0.0521561	+	0.0520432i
$700$	−6.00033	+	10.3929i	−0.226791	+	0.392814i
$701$	17.8736			0.675076			0.337538	−	0.941312i	$-0.390406\pi$
$701$	17.8736			0.675076			0.337538	+	0.941312i	$0.390406\pi$
$702$	−13.2808	−	13.3673i	−0.501251	−	0.504518i
$703$	−1.99574			−0.0752708
$704$		0			0
$705$	−14.4170	+	14.3859i	−0.542978	+	0.541803i
$706$	34.5877	+	59.9076i	1.30172	+	2.25465i
$707$	−2.22005	−	3.84524i	−0.0834935	−	0.144615i
$708$	−3.28832	−	12.3255i	−0.123583	−	0.463222i
$709$	−25.0974	+	43.4700i	−0.942554	+	1.63255i	−0.181978	+	0.983303i	$0.558250\pi$
$709$	−25.0974	+	43.4700i	−0.942554	+	1.63255i	−0.760576	+	0.649249i	$0.775083\pi$
$710$	8.38475			0.314674
$711$	−5.99963	−	3.48123i	−0.225004	−	0.130556i
$712$	105.418			3.95071
$713$	5.76842	−	9.99119i	0.216029	−	0.374173i
$714$	18.7516	+	5.04624i	0.701760	+	0.188851i
$715$		0			0
$716$	18.7728	+	32.5155i	0.701574	+	1.21516i
$717$	−36.7796	−	9.89776i	−1.37356	−	0.369638i
$718$	35.1991	−	60.9666i	1.31362	−	2.27525i
$719$	20.9041			0.779590			0.389795	−	0.920902i	$-0.372546\pi$
$719$	20.9041			0.779590			0.389795	+	0.920902i	$0.372546\pi$
$720$	0.122690	−	56.6596i	0.00457239	−	2.11158i
$721$	−35.4189			−1.31907
$722$	15.4851	−	26.8209i	0.576295	−	0.998172i
$723$	4.98382	+	18.6808i	0.185350	+	0.694745i
$724$	34.2318	+	59.2912i	1.27221	+	2.20354i
$725$	3.63033	+	6.28792i	0.134827	+	0.233528i
$726$		0			0
$727$	8.77099	−	15.1918i	0.325298	−	0.563433i	−0.656274	−	0.754522i	$-0.727869\pi$
$727$	8.77099	−	15.1918i	0.325298	−	0.563433i	0.981573	+	0.191089i	$0.0612020\pi$
$728$	−32.0257			−1.18695
$729$	−0.175395	+	26.9994i	−0.00649611	+	0.999979i
$730$	−51.3493			−1.90052
$731$	−4.79143	+	8.29899i	−0.177217	+	0.306949i
$732$	−54.9014	+	54.7827i	−2.02921	+	2.02483i
$733$	−5.14380	−	8.90932i	−0.189990	−	0.329073i	0.755256	−	0.655430i	$-0.227512\pi$
$733$	−5.14380	−	8.90932i	−0.189990	−	0.329073i	−0.945247	+	0.326356i	$0.894179\pi$
$734$	13.0865	+	22.6665i	0.483032	+	0.836636i
$735$	2.90777	+	10.8991i	0.107255	+	0.402020i
$736$	7.73219	−	13.3925i	0.285012	−	0.493656i
$737$		0			0
$738$	0.102116	−	47.1584i	0.00375895	−	1.73592i
$739$	50.1213			1.84374			0.921871	−	0.387496i	$-0.126660\pi$
$739$	50.1213			1.84374			0.921871	+	0.387496i	$0.126660\pi$
$740$	3.66576	−	6.34928i	0.134756	−	0.233404i
$741$	−6.21021	−	1.67123i	−0.228138	−	0.0613941i
$742$	1.96554	+	3.40441i	0.0721572	+	0.124980i
$743$	1.02057	+	1.76767i	0.0374409	+	0.0648496i	0.884139	−	0.467225i	$-0.154746\pi$
$743$	1.02057	+	1.76767i	0.0374409	+	0.0648496i	−0.846698	+	0.532074i	$0.821413\pi$
$744$	−85.7298	−	23.0707i	−3.14301	−	0.845815i
$745$	4.59792	−	7.96383i	0.168455	−	0.291772i
$746$	55.6932			2.03907
$747$	19.7847	+	11.4799i	0.723883	+	0.420027i
$748$		0			0
$749$	−18.5256	+	32.0873i	−0.676911	+	1.17244i
$750$	−13.7990	−	51.7226i	−0.503869	−	1.88864i
$751$	16.8601	+	29.2025i	0.615234	+	1.06562i	0.990343	+	0.138635i	$0.0442716\pi$
$751$	16.8601	+	29.2025i	0.615234	+	1.06562i	−0.375110	+	0.926980i	$0.622395\pi$
$752$	26.3691	+	45.6727i	0.961583	+	1.66551i
$753$	−16.3755	+	16.3401i	−0.596756	+	0.595465i
$754$	−16.6863	+	28.9015i	−0.607679	+	1.05253i
$755$	46.1909			1.68106
$756$	55.7054	+	56.0685i	2.02599	+	2.03919i
$757$	−28.6697			−1.04202			−0.521009	−	0.853551i	$-0.674444\pi$
$757$	−28.6697			−1.04202			−0.521009	+	0.853551i	$0.674444\pi$
$758$	−21.2032	+	36.7250i	−0.770134	+	1.33391i
$759$		0			0
$760$	−19.6887	−	34.1018i	−0.714184	−	1.23700i
$761$	−15.4164	−	26.7020i	−0.558845	−	0.967947i	−0.997593	−	0.0693374i	$-0.977911\pi$
$761$	−15.4164	−	26.7020i	−0.558845	−	0.967947i	0.438749	−	0.898610i	$-0.355422\pi$
$762$	12.5792	+	47.1502i	0.455695	+	1.70807i
$763$	13.6640	−	23.6668i	0.494670	−	0.856794i
$764$	−59.5040			−2.15278
$765$	−7.21195	+	4.14303i	−0.260749	+	0.149791i
$766$	−41.5037			−1.49959
$767$	1.07636	−	1.86431i	0.0388651	−	0.0673163i
$768$	31.9008	+	8.58483i	1.15112	+	0.309778i
$769$	−15.3073	−	26.5131i	−0.551997	−	0.956086i	−0.998130	−	0.0611200i	$-0.980533\pi$
$769$	−15.3073	−	26.5131i	−0.551997	−	0.956086i	0.446134	−	0.894966i	$-0.352801\pi$
$770$		0			0
$771$	20.8938	+	5.62272i	0.752471	+	0.202497i
$772$	−13.4459	+	23.2890i	−0.483929	+	0.838190i
$773$	51.8254			1.86403			0.932015	−	0.362420i	$-0.118049\pi$
$773$	51.8254			1.86403			0.932015	+	0.362420i	$0.118049\pi$
$774$	−48.0041	+	27.5767i	−1.72547	+	0.991225i
$775$	−5.61398			−0.201660
$776$	−24.9497	+	43.2141i	−0.895640	+	1.55129i
$777$	1.06692	+	3.99911i	0.0382755	+	0.143467i
$778$	−31.7512	−	54.9947i	−1.13834	−	1.97165i
$779$	−8.04756	−	13.9388i	−0.288334	−	0.499409i
$780$	16.7237	−	16.6876i	0.598806	−	0.597511i
$781$		0			0
$782$	−5.69895			−0.203794
$783$	46.2295	−	12.2263i	1.65211	−	0.436934i
$784$	29.2096			1.04320
$785$	17.5297	−	30.3623i	0.625662	−	1.08368i
$786$	18.8285	−	18.7878i	0.671590	−	0.670137i
$787$	25.5940	+	44.3302i	0.912329	+	1.58020i	0.810766	+	0.585371i	$0.199051\pi$
$787$	25.5940	+	44.3302i	0.912329	+	1.58020i	0.101563	+	0.994829i	$0.467616\pi$
$788$	−3.46215	−	5.99662i	−0.123334	−	0.213621i
$789$	−2.37541	−	8.90369i	−0.0845667	−	0.316980i
$790$	6.17214	−	10.6905i	0.219595	−	0.380350i
$791$	44.0994			1.56799
$792$		0			0
$793$	−13.0882			−0.464775
$794$	−1.13179	+	1.96031i	−0.0401656	+	0.0695688i
$795$	−1.62588	−	0.437542i	−0.0576642	−	0.0155180i
$796$	−62.5169	−	108.283i	−2.21585	−	3.83797i
$797$	−6.89488	−	11.9423i	−0.244229	−	0.423017i	0.717685	−	0.696367i	$-0.245202\pi$
$797$	−6.89488	−	11.9423i	−0.244229	−	0.423017i	−0.961915	+	0.273350i	$0.911868\pi$
$798$	36.9729	+	9.94977i	1.30883	+	0.352218i
$799$	3.87081	−	6.70444i	0.136939	−	0.237186i
$800$	−7.52518			−0.266055
$801$	0.0950669	−	43.9029i	0.00335902	−	1.55123i
$802$	−91.7393			−3.23943
$803$		0			0
$804$	15.7499	+	59.0349i	0.555455	+	2.08200i
$805$	−5.30614	−	9.19050i	−0.187017	−	0.323923i
$806$	−12.9019	−	22.3468i	−0.454451	−	0.787131i
$807$	−10.4808	+	10.4581i	−0.368942	+	0.368144i
$808$	5.01377	−	8.68410i	0.176384	−	0.305506i
$809$	9.88328			0.347478			0.173739	−	0.984792i	$-0.444415\pi$
$809$	9.88328			0.347478			0.173739	+	0.984792i	$0.444415\pi$
$810$	−48.0494	−	0.208092i	−1.68828	−	0.00731161i
$811$	19.8171			0.695871			0.347936	−	0.937518i	$-0.386883\pi$
$811$	19.8171			0.695871			0.347936	+	0.937518i	$0.386883\pi$
$812$	69.9896	−	121.226i	2.45615	−	4.25418i
$813$	9.17241	−	9.15257i	0.321691	−	0.320995i
$814$		0			0
$815$	−19.4329	−	33.6588i	−0.680706	−	1.17902i
$816$	5.55165	+	20.8092i	0.194347	+	0.728466i
$817$	−9.44736	+	16.3633i	−0.330521	+	0.572479i
$818$	−17.5523			−0.613702
$819$	−0.0288810	+	13.3376i	−0.00100919	+	0.466053i
$820$	59.1268			2.06480
$821$	−4.59294	+	7.95520i	−0.160295	+	0.277639i	−0.934974	−	0.354715i	$-0.884578\pi$
$821$	−4.59294	+	7.95520i	−0.160295	+	0.277639i	0.774680	+	0.632354i	$0.217911\pi$
$822$	−5.12304	−	1.37866i	−0.178687	−	0.0480864i
$823$	−5.64006	−	9.76886i	−0.196600	−	0.340521i	0.750824	−	0.660502i	$-0.229657\pi$
$823$	−5.64006	−	9.76886i	−0.196600	−	0.340521i	−0.947424	+	0.319981i	$0.896323\pi$
$824$	−39.9952	−	69.2737i	−1.39330	−	2.41326i
$825$		0			0
$826$	−6.40817	+	11.0993i	−0.222969	+	0.386193i
$827$	−17.7324			−0.616616			−0.308308	−	0.951287i	$-0.599763\pi$
$827$	−17.7324			−0.616616			−0.308308	+	0.951287i	$0.599763\pi$
$828$	−20.0627	−	11.6412i	−0.697226	−	0.404559i
$829$	−39.7321			−1.37995			−0.689976	−	0.723832i	$-0.742379\pi$
$829$	−39.7321			−1.37995			−0.689976	+	0.723832i	$0.742379\pi$
$830$	−20.3536	+	35.2534i	−0.706482	+	1.22366i
$831$	−5.70881	−	21.3982i	−0.198036	−	0.742295i
$832$	−4.46566	−	7.73476i	−0.154819	−	0.268154i
$833$	−2.14389	−	3.71332i	−0.0742813	−	0.128659i
$834$	−8.71416	+	8.69531i	−0.301747	+	0.301094i
$835$	−5.10128	+	8.83568i	−0.176537	+	0.305771i
$836$		0			0
$837$	−9.68547	+	35.6827i	−0.334779	+	1.23337i
$838$	2.49589			0.0862192
$839$	−6.29907	+	10.9103i	−0.217468	+	0.376666i	−0.954033	−	0.299701i	$-0.903113\pi$
$839$	−6.29907	+	10.9103i	−0.217468	+	0.376666i	0.736565	+	0.676367i	$0.236446\pi$
$840$	−57.8084	+	57.6834i	−1.99458	+	1.99027i
$841$	−27.8453	−	48.2295i	−0.960183	−	1.66309i
$842$	9.40807	+	16.2953i	0.324224	+	0.561572i
$843$	9.28433	+	34.8002i	0.319769	+	1.19858i
$844$	−15.2469	+	26.4084i	−0.524820	+	0.909015i
$845$	−22.6902			−0.780567
$846$	38.7807	−	22.2782i	1.33331	−	0.765940i
$847$		0			0
$848$	−2.17995	+	3.77578i	−0.0748598	+	0.129661i
$849$	20.9819	+	5.64643i	0.720096	+	0.193785i
$850$	1.38659	+	2.40165i	0.0475598	+	0.0823759i
$851$	−0.607349	−	1.05196i	−0.0208196	−	0.0360607i
$852$	−12.5264	−	3.37097i	−0.429147	−	0.115488i
$853$	1.72933	−	2.99528i	0.0592110	−	0.102556i	−0.834900	−	0.550401i	$-0.814475\pi$
$853$	1.72933	−	2.99528i	0.0592110	−	0.102556i	0.894111	+	0.447845i	$0.147808\pi$
$854$	77.9213			2.66641
$855$	−14.2200	+	8.16889i	−0.486312	+	0.279370i
$856$	−83.6767			−2.86001
$857$	25.3321	−	43.8764i	0.865327	−	1.49879i	−0.00139610	−	0.999999i	$-0.500444\pi$
$857$	25.3321	−	43.8764i	0.865327	−	1.49879i	0.866723	−	0.498790i	$-0.166222\pi$
$858$		0			0
$859$	−15.9394	−	27.6079i	−0.543846	−	0.941969i	−0.998679	−	0.0513919i	$-0.983634\pi$
$859$	−15.9394	−	27.6079i	−0.543846	−	0.941969i	0.454833	−	0.890577i	$-0.349699\pi$
$860$	−34.7057	−	60.1120i	−1.18345	−	2.04980i
$861$	−23.6286	+	23.5775i	−0.805262	+	0.803520i
$862$	−24.5869	+	42.5858i	−0.837434	+	1.45048i
$863$	18.3852			0.625840			0.312920	−	0.949780i	$-0.398693\pi$
$863$	18.3852			0.625840			0.312920	+	0.949780i	$0.398693\pi$
$864$	−12.9827	+	47.8303i	−0.441682	+	1.62722i
$865$	−29.2085			−0.993119
$866$	−21.5095	+	37.2556i	−0.730924	+	1.26600i
$867$	−18.6053	+	18.5650i	−0.631868	+	0.630501i
$868$	54.1163	+	93.7322i	1.83683	+	3.18148i
$869$		0			0
$870$	21.9364	+	82.2237i	0.743713	+	2.78764i
$871$	−5.15537	+	8.92936i	−0.174683	+	0.302560i
$872$	61.7178			2.09003
$873$	17.9746	+	10.4296i	0.608350	+	0.352989i
$874$	−11.2367			−0.380088
$875$	−18.9455	+	32.8145i	−0.640473	+	1.10933i
$876$	76.7132	+	20.6443i	2.59190	+	0.697506i
$877$	−3.29425	−	5.70580i	−0.111239	−	0.192671i	0.805031	−	0.593232i	$-0.202149\pi$
$877$	−3.29425	−	5.70580i	−0.111239	−	0.192671i	−0.916270	+	0.400561i	$0.868815\pi$
$878$	22.5308	+	39.0245i	0.760377	+	1.31701i
$879$	−26.7746	−	7.20531i	−0.903085	−	0.243029i
$880$		0			0
$881$	−57.1119			−1.92415			−0.962074	−	0.272788i	$-0.912054\pi$
$881$	−57.1119			−1.92415			−0.962074	+	0.272788i	$0.912054\pi$
$882$	0.0536386	−	24.7709i	0.00180611	−	0.834080i
$883$	−44.4245			−1.49500			−0.747501	−	0.664261i	$-0.768746\pi$
$883$	−44.4245			−1.49500			−0.747501	+	0.664261i	$0.768746\pi$
$884$	−4.49013	+	7.77713i	−0.151019	+	0.261573i
$885$	−1.41502	−	5.30389i	−0.0475653	−	0.178288i
$886$	−31.3879	−	54.3654i	−1.05450	−	1.82644i
$887$	−16.2326	−	28.1156i	−0.545036	−	0.944030i	−0.998605	−	0.0528086i	$-0.983183\pi$
$887$	−16.2326	−	28.1156i	−0.545036	−	0.944030i	0.453569	−	0.891221i	$-0.350151\pi$
$888$	−6.61684	+	6.60253i	−0.222047	+	0.221566i
$889$	17.2706	−	29.9136i	0.579239	−	1.00327i
$890$	78.1309			2.61895
$891$		0			0
$892$	−81.7672			−2.73777
$893$	7.63216	−	13.2193i	0.255400	−	0.442367i
$894$	−14.2945	+	14.2635i	−0.478078	+	0.477044i
$895$	8.07826	+	13.9920i	0.270026	+	0.467699i
$896$	−3.83605	−	6.64423i	−0.128153	−	0.221968i
$897$	−1.00900	−	3.78201i	−0.0336895	−	0.126277i
$898$	−7.81260	+	13.5318i	−0.260710	+	0.451563i
$899$	65.4832			2.18399
$900$	−0.0244411	+	11.2872i	−0.000814704	+	0.376239i
$901$	0.640004			0.0213216
$902$		0			0
$903$	37.8397	+	10.1830i	1.25923	+	0.338870i
$904$	49.7972	+	86.2513i	1.65623	+	2.86867i
$905$	14.7305	+	25.5140i	0.489659	+	0.848114i
$906$	−97.9478	−	26.3587i	−3.25410	−	0.875710i
$907$	12.8187	−	22.2026i	0.425637	−	0.737226i	−0.570842	−	0.821060i	$-0.693383\pi$
$907$	12.8187	−	22.2026i	0.425637	−	0.737226i	0.996480	+	0.0838341i	$0.0267166\pi$
$908$	−25.9167			−0.860076
$909$	−3.61210	−	2.09589i	−0.119806	−	0.0695163i
$910$	−23.7359			−0.786838
$911$	−5.55313	+	9.61831i	−0.183984	+	0.318669i	−0.943234	−	0.332130i	$-0.892233\pi$
$911$	−5.55313	+	9.61831i	−0.183984	+	0.318669i	0.759250	+	0.650799i	$0.225566\pi$
$912$	10.9463	+	41.0298i	0.362469	+	1.35863i
$913$		0			0
$914$	42.3975	+	73.4346i	1.40238	+	2.42900i
$915$	−23.6250	+	23.5739i	−0.781018	+	0.779329i
$916$	34.5552	−	59.8514i	1.14174	−	1.97755i
$917$	−18.8272			−0.621728
$918$	17.6572	−	4.66981i	0.582774	−	0.154127i
$919$	20.6612			0.681550			0.340775	−	0.940145i	$-0.389310\pi$
$919$	20.6612			0.681550			0.340775	+	0.940145i	$0.389310\pi$
$920$	11.9834	−	20.7559i	0.395082	−	0.684302i
$921$	27.6566	−	27.5968i	0.911317	−	0.909346i
$922$	7.66668	+	13.2791i	0.252489	+	0.437323i
$923$	−1.09453	−	1.89578i	−0.0360269	−	0.0624005i
$924$		0			0
$925$	−0.295544	+	0.511898i	−0.00971743	+	0.0168311i
$926$	−100.941			−3.31714
$927$	−28.8861	+	16.5941i	−0.948745	+	0.545023i
$928$	87.7759			2.88139
$929$	5.78263	−	10.0158i	0.189722	−	0.328608i	−0.755436	−	0.655223i	$-0.772575\pi$
$929$	5.78263	−	10.0158i	0.189722	−	0.328608i	0.945157	+	0.326615i	$0.105908\pi$
$930$	−63.5388	−	17.0989i	−2.08352	−	0.560696i
$931$	−4.22715	−	7.32164i	−0.138539	−	0.239957i
$932$	2.68166	+	4.64478i	0.0878408	+	0.152145i
$933$	−48.0686	−	12.9357i	−1.57369	−	0.423497i
$934$	−35.3034	+	61.1472i	−1.15516	+	2.00080i
$935$		0			0
$936$	−26.1188	+	15.0044i	−0.853718	+	0.490433i
$937$	−13.8102			−0.451160			−0.225580	−	0.974225i	$-0.572428\pi$
$937$	−13.8102			−0.451160			−0.225580	+	0.974225i	$0.572428\pi$
$938$	30.6928	−	53.1616i	1.00216	−	1.73579i
$939$	−11.0515	−	41.4241i	−0.360652	−	1.35182i
$940$	28.0374	+	48.5622i	0.914479	+	1.58392i
$941$	−10.5015	−	18.1891i	−0.342338	−	0.592946i	0.642529	−	0.766262i	$-0.277885\pi$
$941$	−10.5015	−	18.1891i	−0.342338	−	0.592946i	−0.984866	+	0.173315i	$0.944552\pi$
$942$	−54.4980	+	54.3801i	−1.77564	+	1.77180i
$943$	4.89811	−	8.48377i	0.159504	−	0.276270i
$944$	−14.2144			−0.462640
$945$	23.9710	+	24.1272i	0.779776	+	0.784858i
$946$		0			0
$947$	22.0312	−	38.1592i	0.715919	−	1.24001i	−0.246686	−	0.969096i	$-0.579341\pi$
$947$	22.0312	−	38.1592i	0.715919	−	1.24001i	0.962604	−	0.270912i	$-0.0873252\pi$
$948$	−13.5188	+	13.4896i	−0.439070	+	0.438121i
$949$	6.70305	+	11.6100i	0.217590	+	0.376878i
$950$	2.73397	+	4.73538i	0.0887019	+	0.153636i
$951$	−11.7986	−	44.2246i	−0.382597	−	1.43408i
$952$	15.5209	−	26.8830i	0.503035	−	0.871282i
$953$	−19.8460			−0.642876			−0.321438	−	0.946931i	$-0.604166\pi$
$953$	−19.8460			−0.642876			−0.321438	+	0.946931i	$0.604166\pi$
$954$	3.19801	+	1.85562i	0.103539	+	0.0600778i
$955$	−25.6055			−0.828576
$956$	−52.4331	+	90.8167i	−1.69581	+	2.93722i
$957$		0			0
$958$	13.3218	+	23.0740i	0.430407	+	0.745487i
$959$	1.87761	+	3.25211i	0.0606311	+	0.105016i
$960$	−21.9923	−	5.91835i	−0.709799	−	0.191014i
$961$	−9.81593	+	17.0017i	−0.316643	+	0.548442i
$962$	−2.71685			−0.0875947
$963$	−0.0754603	+	34.8484i	−0.00243168	+	1.12297i
$964$	53.2318			1.71448
$965$	−5.78600	+	10.0216i	−0.186258	+	0.322608i
$966$	6.00714	+	22.5164i	0.193276	+	0.724454i
$967$	21.7498	+	37.6718i	0.699427	+	1.21144i	0.968665	+	0.248370i	$0.0798949\pi$
$967$	21.7498	+	37.6718i	0.699427	+	1.21144i	−0.269238	+	0.963074i	$0.586772\pi$
$968$		0			0
$969$	4.41257	−	4.40302i	0.141752	−	0.141445i
$970$	−18.4915	+	32.0282i	−0.593726	+	1.02836i
$971$	−4.46699			−0.143352			−0.0716762	−	0.997428i	$-0.522835\pi$
$971$	−4.46699			−0.143352			−0.0716762	+	0.997428i	$0.522835\pi$
$972$	71.6996	+	19.6285i	2.29976	+	0.629583i
$973$	8.71355			0.279344
$974$	31.9250	−	55.2958i	1.02294	−	1.77179i
$975$	−1.34832	+	1.34540i	−0.0431807	+	0.0430873i
$976$	43.2107	+	74.8431i	1.38314	+	2.39567i
$977$	−23.0232	−	39.8774i	−0.736578	−	1.27579i	−0.954027	−	0.299720i	$-0.903107\pi$
$977$	−23.0232	−	39.8774i	−0.736578	−	1.27579i	0.217449	−	0.976072i	$-0.430226\pi$
$978$	22.0002	+	82.4630i	0.703489	+	2.63687i
$979$		0			0
$980$	31.0576			0.992098
$981$	0.0556576	−	25.7033i	0.00177701	−	0.820643i
$982$	−107.547			−3.43198
$983$	27.8071	−	48.1633i	0.886909	−	1.53617i	0.0433983	−	0.999058i	$-0.486182\pi$
$983$	27.8071	−	48.1633i	0.886909	−	1.53617i	0.843510	−	0.537113i	$-0.180485\pi$
$984$	−72.7953	−	19.5899i	−2.32063	−	0.624505i
$985$	−1.48982	−	2.58044i	−0.0474696	−	0.0822197i
$986$	−16.1736	−	28.0136i	−0.515074	−	0.892134i
$987$	−30.5692	−	8.22648i	−0.973029	−	0.261852i
$988$	−8.85328	+	15.3343i	−0.281660	+	0.487850i
$989$	−11.5002			−0.365684
$990$		0			0
$991$	−54.8380			−1.74199			−0.870993	−	0.491295i	$-0.836524\pi$
$991$	−54.8380			−1.74199			−0.870993	+	0.491295i	$0.836524\pi$
$992$	−33.9344	+	58.7760i	−1.07742	+	1.86614i
$993$	−11.6634	−	43.7179i	−0.370128	−	1.38734i
$994$	6.51636	+	11.2867i	0.206687	+	0.357992i
$995$	−26.9021	−	46.5958i	−0.852853	−	1.47718i
$996$	44.5803	−	44.4839i	1.41258	−	1.40952i
$997$	24.1955	−	41.9079i	0.766280	−	1.32724i	−0.173287	−	0.984871i	$-0.555439\pi$
$997$	24.1955	−	41.9079i	0.766280	−	1.32724i	0.939567	−	0.342365i	$-0.111228\pi$
$998$	−102.847			−3.25557
$999$	2.74375	+	2.76164i	0.0868085	+	0.0873743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.o.727.1		36
9.2	odd	6		9801.2.a.cn.1.1		18
9.4	even	3	inner	1089.2.e.o.364.1		36
9.7	even	3		9801.2.a.co.1.18		18
11.7	odd	10		99.2.m.b.16.9	✓	72
11.8	odd	10		99.2.m.b.97.1	yes	72
11.10	odd	2		1089.2.e.p.727.18		36
33.8	even	10		297.2.n.b.262.9		72
33.29	even	10		297.2.n.b.181.1		72
99.7	odd	30		891.2.f.f.82.1		36
99.29	even	30		891.2.f.e.82.9		36
99.40	odd	30		99.2.m.b.49.1	yes	72
99.41	even	30		297.2.n.b.64.1		72
99.43	odd	6		9801.2.a.cm.1.1		18
99.52	odd	30		891.2.f.f.163.1		36
99.65	even	6		9801.2.a.cp.1.18		18
99.74	even	30		891.2.f.e.163.9		36
99.76	odd	6		1089.2.e.p.364.18		36
99.85	odd	30		99.2.m.b.31.9	yes	72
99.95	even	30		297.2.n.b.280.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.9	✓	72	11.7	odd	10
99.2.m.b.31.9	yes	72	99.85	odd	30
99.2.m.b.49.1	yes	72	99.40	odd	30
99.2.m.b.97.1	yes	72	11.8	odd	10
297.2.n.b.64.1		72	99.41	even	30
297.2.n.b.181.1		72	33.29	even	10
297.2.n.b.262.9		72	33.8	even	10
297.2.n.b.280.9		72	99.95	even	30
891.2.f.e.82.9		36	99.29	even	30
891.2.f.e.163.9		36	99.74	even	30
891.2.f.f.82.1		36	99.7	odd	30
891.2.f.f.163.1		36	99.52	odd	30
1089.2.e.o.364.1		36	9.4	even	3	inner
1089.2.e.o.727.1		36	1.1	even	1	trivial
1089.2.e.p.364.18		36	99.76	odd	6
1089.2.e.p.727.18		36	11.10	odd	2
9801.2.a.cm.1.1		18	99.43	odd	6
9801.2.a.cn.1.1		18	9.2	odd	6
9801.2.a.co.1.18		18	9.7	even	3
9801.2.a.cp.1.18		18	99.65	even	6

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:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30084 + 2.25313i) q^{2} +(1.22607 - 1.22342i) q^{3} +(-2.38439 - 4.12988i) q^{4} +(-1.02604 - 1.77715i) q^{5} +(1.16159 + 4.35397i) q^{6} +(1.59481 - 2.76230i) q^{7} +7.20347 q^{8} +(0.00649615 - 2.99999i) q^{9} +O(q^{10})\)	\(q+(-1.30084 + 2.25313i) q^{2} +(1.22607 - 1.22342i) q^{3} +(-2.38439 - 4.12988i) q^{4} +(-1.02604 - 1.77715i) q^{5} +(1.16159 + 4.35397i) q^{6} +(1.59481 - 2.76230i) q^{7} +7.20347 q^{8} +(0.00649615 - 2.99999i) q^{9} +5.33887 q^{10} +(-7.97599 - 2.14642i) q^{12} +(-0.696927 - 1.20711i) q^{13} +(4.14920 + 7.18663i) q^{14} +(-3.43220 - 0.923639i) q^{15} +(-4.60181 + 7.97058i) q^{16} +1.35103 q^{17} +(6.75091 + 3.91716i) q^{18} +2.66386 q^{19} +(-4.89295 + 8.47484i) q^{20} +(-1.42409 - 5.33789i) q^{21} +(0.810671 + 1.40412i) q^{23} +(8.83196 - 8.81286i) q^{24} +(0.394484 - 0.683266i) q^{25} +3.62637 q^{26} +(-3.66228 - 3.68615i) q^{27} -15.2106 q^{28} +(-4.60138 + 7.96982i) q^{29} +(6.54583 - 6.53167i) q^{30} +(-3.55780 - 6.16230i) q^{31} +(-4.76900 - 8.26016i) q^{32} +(-1.75748 + 3.04404i) q^{34} -6.54537 q^{35} +(-12.4051 + 7.12631i) q^{36} -0.749192 q^{37} +(-3.46526 + 6.00200i) q^{38} +(-2.33129 - 0.627372i) q^{39} +(-7.39105 - 12.8017i) q^{40} +(-3.02102 - 5.23256i) q^{41} +(13.8795 + 3.73510i) q^{42} +(-3.54650 + 6.14271i) q^{43} +(-5.33811 + 3.06657i) q^{45} -4.21822 q^{46} +(2.86508 - 4.96246i) q^{47} +(4.10920 + 15.4024i) q^{48} +(-1.58685 - 2.74851i) q^{49} +(1.02632 + 1.77764i) q^{50} +(1.65646 - 1.65288i) q^{51} +(-3.32348 + 5.75644i) q^{52} +0.473715 q^{53} +(13.0694 - 3.45648i) q^{54} +(11.4882 - 19.8981i) q^{56} +(3.26607 - 3.25901i) q^{57} +(-11.9713 - 20.7350i) q^{58} +(0.772218 + 1.33752i) q^{59} +(4.36917 + 16.3769i) q^{60} +(4.69496 - 8.13191i) q^{61} +18.5126 q^{62} +(-8.27651 - 4.80237i) q^{63} +6.40765 q^{64} +(-1.43015 + 2.47709i) q^{65} +(-3.69864 - 6.40624i) q^{67} +(-3.22138 - 5.57959i) q^{68} +(2.71177 + 0.729764i) q^{69} +(8.51449 - 14.7475i) q^{70} +1.57051 q^{71} +(0.0467948 - 21.6104i) q^{72} -9.61801 q^{73} +(0.974582 - 1.68803i) q^{74} +(-0.352255 - 1.32035i) q^{75} +(-6.35166 - 11.0014i) q^{76} +(4.44618 - 4.43657i) q^{78} +(1.15608 - 2.00238i) q^{79} +18.8866 q^{80} +(-8.99992 - 0.0389768i) q^{81} +15.7195 q^{82} +(-3.81234 + 6.60316i) q^{83} +(-18.6492 + 18.6089i) q^{84} +(-1.38621 - 2.40099i) q^{85} +(-9.22687 - 15.9814i) q^{86} +(4.10881 + 15.4010i) q^{87} +14.6343 q^{89} +(0.0346821 - 16.0166i) q^{90} -4.44587 q^{91} +(3.86590 - 6.69594i) q^{92} +(-11.9012 - 3.20273i) q^{93} +(7.45404 + 12.9108i) q^{94} +(-2.73322 - 4.73408i) q^{95} +(-15.9528 - 4.29305i) q^{96} +(-3.46356 + 5.99906i) q^{97} +8.25699 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9}+O(q^{10}) \) 36 * q - 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 + q^6 + q^7 + 12 * q^8 - q^9	\( 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} + 3 q^{13} - 5 q^{15} + 8 q^{16} + 40 q^{17} - 17 q^{18} + 6 q^{19} + 5 q^{20} + 8 q^{21} + 10 q^{23} + 57 q^{24} - 7 q^{25} + 4 q^{26} - 9 q^{27} - 38 q^{28} - 21 q^{29} - 12 q^{30} - 6 q^{31} - 9 q^{32} + 4 q^{34} + 76 q^{35} - 65 q^{36} + 14 q^{37} - 13 q^{38} - 42 q^{39} - 20 q^{41} + 18 q^{42} + 4 q^{43} + 20 q^{45} - 16 q^{46} - 7 q^{47} + 10 q^{48} - 7 q^{49} - 25 q^{50} + 4 q^{51} - 19 q^{52} + 62 q^{53} - 17 q^{54} + 57 q^{56} + 18 q^{57} - 12 q^{58} + 12 q^{59} + 11 q^{60} - 16 q^{61} + 38 q^{62} - 5 q^{63} - 32 q^{64} - 42 q^{65} + 5 q^{67} - 51 q^{68} + 31 q^{69} - 8 q^{70} + 26 q^{71} - 51 q^{72} - 9 q^{74} - 16 q^{75} - 8 q^{76} - 32 q^{78} - 2 q^{79} + 92 q^{80} + 47 q^{81} - 68 q^{82} - 36 q^{83} - 60 q^{84} + 25 q^{85} - 26 q^{86} + 60 q^{87} - 28 q^{89} - 163 q^{90} - 30 q^{91} + 15 q^{92} - 39 q^{93} + 4 q^{94} - 64 q^{95} + 21 q^{96} + 16 q^{97} + 164 q^{98}+O(q^{100}) \) 36 * q - 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 + q^6 + q^7 + 12 * q^8 - q^9 + 4 * q^10 - 8 * q^12 + 3 * q^13 - 5 * q^15 + 8 * q^16 + 40 * q^17 - 17 * q^18 + 6 * q^19 + 5 * q^20 + 8 * q^21 + 10 * q^23 + 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 - 38 * q^28 - 21 * q^29 - 12 * q^30 - 6 * q^31 - 9 * q^32 + 4 * q^34 + 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 - 42 * q^39 - 20 * q^41 + 18 * q^42 + 4 * q^43 + 20 * q^45 - 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 - 25 * q^50 + 4 * q^51 - 19 * q^52 + 62 * q^53 - 17 * q^54 + 57 * q^56 + 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 - 16 * q^61 + 38 * q^62 - 5 * q^63 - 32 * q^64 - 42 * q^65 + 5 * q^67 - 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 - 51 * q^72 - 9 * q^74 - 16 * q^75 - 8 * q^76 - 32 * q^78 - 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 - 36 * q^83 - 60 * q^84 + 25 * q^85 - 26 * q^86 + 60 * q^87 - 28 * q^89 - 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 + 4 * q^94 - 64 * q^95 + 21 * q^96 + 16 * q^97 + 164 * q^98

Introduction

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