LMFDB - Embedded newform 273.2.t.c.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (of order $6$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.6
Root			$0.874681 + 1.11128i$ of defining polynomial
Character	$\chi$	$=$	273.4
Dual form			273.2.t.c.205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.22255i q^{2} +(-0.500000 - 0.866025i) q^{3} -2.93973 q^{4} +(-0.701414 + 0.404962i) q^{5} +(1.92478 - 1.11128i) q^{6} +(-2.44601 + 1.00849i) q^{7} -2.08860i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+2.22255i q^{2} +(-0.500000 - 0.866025i) q^{3} -2.93973 q^{4} +(-0.701414 + 0.404962i) q^{5} +(1.92478 - 1.11128i) q^{6} +(-2.44601 + 1.00849i) q^{7} -2.08860i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.900048 - 1.55893i) q^{10} +(-2.66500 + 1.53864i) q^{11} +(1.46986 + 2.54588i) q^{12} +(-3.01583 - 1.97606i) q^{13} +(-2.24141 - 5.43638i) q^{14} +(0.701414 + 0.404962i) q^{15} -1.23745 q^{16} +2.79947 q^{17} +(-1.92478 - 1.11128i) q^{18} +(-3.73356 - 2.15557i) q^{19} +(2.06197 - 1.19048i) q^{20} +(2.09638 + 1.61406i) q^{21} +(-3.41970 - 5.92310i) q^{22} +4.95229 q^{23} +(-1.80878 + 1.04430i) q^{24} +(-2.17201 + 3.76204i) q^{25} +(4.39188 - 6.70282i) q^{26} +1.00000 q^{27} +(7.19060 - 2.96468i) q^{28} +(-2.84837 + 4.93353i) q^{29} +(-0.900048 + 1.55893i) q^{30} +(2.93282 + 1.69327i) q^{31} -6.92749i q^{32} +(2.66500 + 1.53864i) q^{33} +6.22195i q^{34} +(1.30727 - 1.69791i) q^{35} +(1.46986 - 2.54588i) q^{36} +9.72567i q^{37} +(4.79087 - 8.29803i) q^{38} +(-0.203402 + 3.59981i) q^{39} +(0.845801 + 1.46497i) q^{40} +(8.48708 + 4.90002i) q^{41} +(-3.58733 + 4.65931i) q^{42} +(-2.85083 - 4.93777i) q^{43} +(7.83438 - 4.52318i) q^{44} -0.809923i q^{45} +11.0067i q^{46} +(-5.31465 + 3.06841i) q^{47} +(0.618725 + 1.07166i) q^{48} +(4.96591 - 4.93353i) q^{49} +(-8.36131 - 4.82741i) q^{50} +(-1.39973 - 2.42441i) q^{51} +(8.86571 + 5.80907i) q^{52} +(2.83659 - 4.91312i) q^{53} +2.22255i q^{54} +(1.24618 - 2.15845i) q^{55} +(2.10632 + 5.10872i) q^{56} +4.31115i q^{57} +(-10.9650 - 6.33066i) q^{58} +4.93584i q^{59} +(-2.06197 - 1.19048i) q^{60} +(1.51741 - 2.62824i) q^{61} +(-3.76337 + 6.51834i) q^{62} +(0.349630 - 2.62255i) q^{63} +12.9218 q^{64} +(2.91557 + 0.164740i) q^{65} +(-3.41970 + 5.92310i) q^{66} +(-8.59577 + 4.96277i) q^{67} -8.22967 q^{68} +(-2.47614 - 4.28881i) q^{69} +(3.77368 + 2.90547i) q^{70} +(-7.84155 + 4.52732i) q^{71} +(1.80878 + 1.04430i) q^{72} +(-2.75318 - 1.58955i) q^{73} -21.6158 q^{74} +4.34402 q^{75} +(10.9757 + 6.33680i) q^{76} +(4.96692 - 6.45114i) q^{77} +(-8.00076 - 0.452072i) q^{78} +(1.13963 + 1.97390i) q^{79} +(0.867965 - 0.501120i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.8905 + 18.8630i) q^{82} +1.52896i q^{83} +(-6.16279 - 4.74491i) q^{84} +(-1.96359 + 1.13368i) q^{85} +(10.9745 - 6.33610i) q^{86} +5.69675 q^{87} +(3.21359 + 5.56611i) q^{88} +3.32107i q^{89} +1.80010 q^{90} +(9.36956 + 1.79203i) q^{91} -14.5584 q^{92} -3.38653i q^{93} +(-6.81970 - 11.8121i) q^{94} +3.49170 q^{95} +(-5.99938 + 3.46374i) q^{96} +(11.0330 - 6.36990i) q^{97} +(10.9650 + 11.0370i) q^{98} -3.07728i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$			2.22255i			1.57158i	0.618493	+	0.785790i	$0.287743\pi$
$2$			2.22255i			1.57158i	−0.618493	+	0.785790i	$0.712257\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−2.93973			−1.46986
$5$	−0.701414	+	0.404962i	−0.313682	+	0.181104i	−0.648573	−	0.761153i	$-0.724634\pi$
$5$	−0.701414	+	0.404962i	−0.313682	+	0.181104i	0.334891	+	0.942257i	$0.391301\pi$
$6$	1.92478	−	1.11128i	0.785790	−	0.453676i
$7$	−2.44601	+	1.00849i	−0.924504	+	0.381172i
$7$	−2.44601	+	1.00849i	−0.924504	+	0.381172i
$8$		−	2.08860i		−	0.738430i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.900048	−	1.55893i	−0.284620	−	0.492976i
$11$	−2.66500	+	1.53864i	−0.803528	+	0.463917i	−0.844703	−	0.535235i	$-0.820223\pi$
$11$	−2.66500	+	1.53864i	−0.803528	+	0.463917i	0.0411755	+	0.999152i	$0.486890\pi$
$12$	1.46986	+	2.54588i	0.424313	+	0.734932i
$13$	−3.01583	−	1.97606i	−0.836439	−	0.548059i
$13$	−3.01583	−	1.97606i	−0.836439	−	0.548059i
$14$	−2.24141	−	5.43638i	−0.599042	−	1.45293i
$15$	0.701414	+	0.404962i	0.181104	+	0.104561i
$16$	−1.23745			−0.309363
$17$	2.79947			0.678970			0.339485	−	0.940611i	$-0.389747\pi$
$17$	2.79947			0.678970			0.339485	+	0.940611i	$0.389747\pi$
$18$	−1.92478	−	1.11128i	−0.453676	−	0.261930i
$19$	−3.73356	−	2.15557i	−0.856538	−	0.494522i	0.00631355	−	0.999980i	$-0.497990\pi$
$19$	−3.73356	−	2.15557i	−0.856538	−	0.494522i	−0.862851	+	0.505458i	$0.831324\pi$
$20$	2.06197	−	1.19048i	0.461070	−	0.266199i
$21$	2.09638	+	1.61406i	0.457467	+	0.352217i
$22$	−3.41970	−	5.92310i	−0.729083	−	1.26281i
$23$	4.95229			1.03262			0.516312	−	0.856401i	$-0.327305\pi$
$23$	4.95229			1.03262			0.516312	+	0.856401i	$0.327305\pi$
$24$	−1.80878	+	1.04430i	−0.369215	+	0.213166i
$25$	−2.17201	+	3.76204i	−0.434402	+	0.752407i
$26$	4.39188	−	6.70282i	0.861319	−	1.31453i
$27$	1.00000			0.192450
$28$	7.19060	−	2.96468i	1.35890	−	0.560271i
$29$	−2.84837	+	4.93353i	−0.528930	+	0.916133i	0.470501	+	0.882399i	$0.344073\pi$
$29$	−2.84837	+	4.93353i	−0.528930	+	0.916133i	−0.999431	+	0.0337339i	$0.989260\pi$
$30$	−0.900048	+	1.55893i	−0.164325	+	0.284620i
$31$	2.93282	+	1.69327i	0.526750	+	0.304119i	0.739692	−	0.672945i	$-0.234971\pi$
$31$	2.93282	+	1.69327i	0.526750	+	0.304119i	−0.212942	+	0.977065i	$0.568304\pi$
$32$		−	6.92749i		−	1.22462i
$33$	2.66500	+	1.53864i	0.463917	+	0.267843i
$34$			6.22195i			1.06706i
$35$	1.30727	−	1.69791i	0.220968	−	0.286999i
$36$	1.46986	−	2.54588i	0.244977	−	0.424313i
$37$			9.72567i			1.59889i	0.600740	+	0.799445i	$0.294873\pi$
$37$			9.72567i			1.59889i	−0.600740	+	0.799445i	$0.705127\pi$
$38$	4.79087	−	8.29803i	0.777182	−	1.34612i
$39$	−0.203402	+	3.59981i	−0.0325705	+	0.576431i
$40$	0.845801	+	1.46497i	0.133733	+	0.231632i
$41$	8.48708	+	4.90002i	1.32546	+	0.765254i	0.984594	−	0.174858i	$-0.0559468\pi$
$41$	8.48708	+	4.90002i	1.32546	+	0.765254i	0.340865	+	0.940112i	$0.389280\pi$
$42$	−3.58733	+	4.65931i	−0.553538	+	0.718947i
$43$	−2.85083	−	4.93777i	−0.434747	−	0.753003i	0.562528	−	0.826778i	$-0.309829\pi$
$43$	−2.85083	−	4.93777i	−0.434747	−	0.753003i	−0.997275	+	0.0737747i	$0.976495\pi$
$44$	7.83438	−	4.52318i	1.18108	−	0.681895i
$45$		−	0.809923i		−	0.120736i
$46$			11.0067i			1.62285i
$47$	−5.31465	+	3.06841i	−0.775221	+	0.447574i	−0.834734	−	0.550654i	$-0.814379\pi$
$47$	−5.31465	+	3.06841i	−0.775221	+	0.447574i	0.0595130	+	0.998228i	$0.481045\pi$
$48$	0.618725	+	1.07166i	0.0893053	+	0.154681i
$49$	4.96591	−	4.93353i	0.709416	−	0.704790i
$50$	−8.36131	−	4.82741i	−1.18247	−	0.682698i
$51$	−1.39973	−	2.42441i	−0.196002	−	0.339485i
$52$	8.86571	+	5.80907i	1.22945	+	0.805573i
$53$	2.83659	−	4.91312i	0.389636	−	0.674870i	−0.602764	−	0.797919i	$-0.705934\pi$
$53$	2.83659	−	4.91312i	0.389636	−	0.674870i	0.992401	+	0.123050i	$0.0392675\pi$
$54$			2.22255i			0.302451i
$55$	1.24618	−	2.15845i	0.168035	−	0.291045i
$56$	2.10632	+	5.10872i	0.281469	+	0.682682i
$57$			4.31115i			0.571025i
$58$	−10.9650	−	6.33066i	−1.43978	−	0.831256i
$59$			4.93584i			0.642592i	0.946979	+	0.321296i	$0.104118\pi$
$59$			4.93584i			0.642592i	−0.946979	+	0.321296i	$0.895882\pi$
$60$	−2.06197	−	1.19048i	−0.266199	−	0.153690i
$61$	1.51741	−	2.62824i	0.194285	−	0.336511i	−0.752381	−	0.658728i	$-0.771095\pi$
$61$	1.51741	−	2.62824i	0.194285	−	0.336511i	0.946666	+	0.322217i	$0.104428\pi$
$62$	−3.76337	+	6.51834i	−0.477948	+	0.827830i
$63$	0.349630	−	2.62255i	0.0440492	−	0.330410i
$64$	12.9218			1.61522
$65$	2.91557	+	0.164740i	0.361632	+	0.0204335i
$66$	−3.41970	+	5.92310i	−0.420936	+	0.729083i
$67$	−8.59577	+	4.96277i	−1.05014	+	0.606299i	−0.922689	−	0.385546i	$-0.874013\pi$
$67$	−8.59577	+	4.96277i	−1.05014	+	0.606299i	−0.127452	+	0.991845i	$0.540680\pi$
$68$	−8.22967			−0.997994
$69$	−2.47614	−	4.28881i	−0.298093	−	0.516312i
$70$	3.77368	+	2.90547i	0.451041	+	0.347270i
$71$	−7.84155	+	4.52732i	−0.930621	+	0.537294i	−0.887008	−	0.461754i	$-0.847220\pi$
$71$	−7.84155	+	4.52732i	−0.930621	+	0.537294i	−0.0436133	+	0.999048i	$0.513887\pi$
$72$	1.80878	+	1.04430i	0.213166	+	0.123072i
$73$	−2.75318	−	1.58955i	−0.322235	−	0.186043i	0.330153	−	0.943927i	$-0.392900\pi$
$73$	−2.75318	−	1.58955i	−0.322235	−	0.186043i	−0.652388	+	0.757885i	$0.726233\pi$
$74$	−21.6158			−2.51278
$75$	4.34402			0.501605
$76$	10.9757	+	6.33680i	1.25899	+	0.726881i
$77$	4.96692	−	6.45114i	0.566033	−	0.735175i
$78$	−8.00076	−	0.452072i	−0.905907	−	0.0511871i
$79$	1.13963	+	1.97390i	0.128219	+	0.222082i	0.922987	−	0.384832i	$-0.125741\pi$
$79$	1.13963	+	1.97390i	0.128219	+	0.222082i	−0.794768	+	0.606914i	$0.792407\pi$
$80$	0.867965	−	0.501120i	0.0970415	−	0.0560269i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.8905	+	18.8630i	−1.20266	+	2.08306i
$83$			1.52896i			0.167825i	0.996473	+	0.0839126i	$0.0267417\pi$
$83$			1.52896i			0.167825i	−0.996473	+	0.0839126i	$0.973258\pi$
$84$	−6.16279	−	4.74491i	−0.672415	−	0.517712i
$85$	−1.96359	+	1.13368i	−0.212981	+	0.122965i
$86$	10.9745	−	6.33610i	1.18341	−	0.683239i
$87$	5.69675			0.610756
$88$	3.21359	+	5.56611i	0.342570	+	0.593349i
$89$			3.32107i			0.352032i	0.984387	+	0.176016i	$0.0563211\pi$
$89$			3.32107i			0.352032i	−0.984387	+	0.176016i	$0.943679\pi$
$90$	1.80010			0.189747
$91$	9.36956	+	1.79203i	0.982197	+	0.187856i
$92$	−14.5584			−1.51782
$93$		−	3.38653i		−	0.351167i
$94$	−6.81970	−	11.8121i	−0.703398	−	1.21832i
$95$	3.49170			0.358241
$96$	−5.99938	+	3.46374i	−0.612309	+	0.353517i
$97$	11.0330	−	6.36990i	1.12023	−	0.646766i	0.178771	−	0.983891i	$-0.442788\pi$
$97$	11.0330	−	6.36990i	1.12023	−	0.646766i	0.941460	+	0.337125i	$0.109454\pi$
$98$	10.9650	+	11.0370i	1.10763	+	1.11490i
$99$		−	3.07728i		−	0.309278i
$100$	6.38513	−	11.0594i	0.638513	−	1.10594i
$101$	7.58772	+	13.1423i	0.755006	+	1.30771i	0.945371	+	0.325996i	$0.105700\pi$
$101$	7.58772	+	13.1423i	0.755006	+	1.30771i	−0.190365	+	0.981713i	$0.560967\pi$
$102$	5.38837	−	3.11098i	0.533528	−	0.308033i
$103$	−4.00749	−	6.94118i	−0.394870	−	0.683935i	0.598214	−	0.801336i	$-0.295877\pi$
$103$	−4.00749	−	6.94118i	−0.394870	−	0.683935i	−0.993085	+	0.117401i	$0.962544\pi$
$104$	−4.12718	+	6.29884i	−0.404704	+	0.617652i
$105$	−2.12406	−	0.283173i	−0.207287	−	0.0276349i
$106$	10.9197	+	6.30447i	1.06061	+	0.612344i
$107$	−9.78649			−0.946095			−0.473048	−	0.881037i	$-0.656846\pi$
$107$	−9.78649			−0.946095			−0.473048	+	0.881037i	$0.656846\pi$
$108$	−2.93973			−0.282876
$109$	2.60941	+	1.50655i	0.249937	+	0.144301i	0.619735	−	0.784811i	$-0.287240\pi$
$109$	2.60941	+	1.50655i	0.249937	+	0.144301i	−0.369799	+	0.929112i	$0.620573\pi$
$110$	4.79725	+	2.76970i	0.457400	+	0.264080i
$111$	8.42267	−	4.86283i	0.799445	−	0.461560i
$112$	3.02681	−	1.24795i	0.286007	−	0.117920i
$113$	−1.36880	−	2.37084i	−0.128766	−	0.223030i	0.794433	−	0.607352i	$-0.207768\pi$
$113$	−1.36880	−	2.37084i	−0.128766	−	0.223030i	−0.923199	+	0.384323i	$0.874435\pi$
$114$	−9.58174			−0.897412
$115$	−3.47361	+	2.00549i	−0.323915	+	0.187013i
$116$	8.37345	−	14.5032i	0.777455	−	1.34659i
$117$	3.21923	−	1.62375i	0.297618	−	0.150116i
$118$	−10.9702			−1.00989
$119$	−6.84752	+	2.82322i	−0.627711	+	0.258804i
$120$	0.845801	−	1.46497i	0.0772107	−	0.133733i
$121$	−0.765183	+	1.32534i	−0.0695621	+	0.120485i
$122$	5.84139	+	3.37253i	0.528855	+	0.305334i
$123$		−	9.80003i		−	0.883639i
$124$	−8.62170	−	4.97774i	−0.774252	−	0.447014i
$125$		−	7.56794i		−	0.676898i
$126$	5.82874	+	0.777070i	0.519266	+	0.0692269i
$127$	7.39515	−	12.8088i	0.656214	−	1.13660i	−0.325374	−	0.945585i	$-0.605490\pi$
$127$	7.39515	−	12.8088i	0.656214	−	1.13660i	0.981588	−	0.191010i	$-0.0611763\pi$
$128$			14.8643i			1.31383i
$129$	−2.85083	+	4.93777i	−0.251001	+	0.434747i
$130$	−0.366144	+	6.48000i	−0.0321129	+	0.568334i
$131$	−1.14893	−	1.99001i	−0.100383	−	0.173868i	0.811460	−	0.584408i	$-0.198673\pi$
$131$	−1.14893	−	1.99001i	−0.100383	−	0.173868i	−0.911842	+	0.410540i	$0.865340\pi$
$132$	−7.83438	−	4.52318i	−0.681895	−	0.393692i
$133$	11.3062	+	1.50730i	0.980371	+	0.130700i
$134$	−11.0300	−	19.1045i	−0.952847	−	1.65038i
$135$	−0.701414	+	0.404962i	−0.0603681	+	0.0348536i
$136$		−	5.84695i		−	0.501372i
$137$		−	15.6440i		−	1.33655i	−0.743913	−	0.668276i	$-0.767032\pi$
$137$		−	15.6440i		−	1.33655i	0.743913	−	0.668276i	$-0.232968\pi$
$138$	9.53209	−	5.50335i	0.811425	−	0.468477i
$139$	−11.2601	−	19.5030i	−0.955068	−	1.65423i	−0.734213	−	0.678919i	$-0.762449\pi$
$139$	−11.2601	−	19.5030i	−0.955068	−	1.65423i	−0.220855	−	0.975307i	$-0.570885\pi$
$140$	−3.84301	+	4.99138i	−0.324794	+	0.421849i
$141$	5.31465	+	3.06841i	0.447574	+	0.258407i
$142$	−10.0622	−	17.4282i	−0.844401	−	1.46255i
$143$	11.0776	+	0.625926i	0.926356	+	0.0523425i
$144$	0.618725	−	1.07166i	0.0515604	−	0.0893053i
$145$		−	4.61393i		−	0.383166i
$146$	3.53285	−	6.11908i	0.292381	−	0.506419i
$147$	−6.75552	−	1.83384i	−0.557186	−	0.151253i
$148$		−	28.5908i		−	2.35015i
$149$	11.7402	+	6.77823i	0.961797	+	0.555294i	0.896726	−	0.442587i	$-0.145939\pi$
$149$	11.7402	+	6.77823i	0.961797	+	0.555294i	0.0650716	+	0.997881i	$0.479272\pi$
$150$			9.65481i			0.788312i
$151$	7.26064	+	4.19193i	0.590863	+	0.341135i	0.765439	−	0.643509i	$-0.222522\pi$
$151$	7.26064	+	4.19193i	0.590863	+	0.341135i	−0.174576	+	0.984644i	$0.555855\pi$
$152$	−4.50212	+	7.79790i	−0.365170	+	0.632493i
$153$	−1.39973	+	2.42441i	−0.113162	+	0.196002i
$154$	14.3380	+	11.0392i	1.15539	+	0.889566i
$155$	−2.74283			−0.220309
$156$	0.597948	−	10.5825i	0.0478742	−	0.847275i
$157$	−1.53856	+	2.66486i	−0.122790	+	0.212679i	−0.920867	−	0.389877i	$-0.872518\pi$
$157$	−1.53856	+	2.66486i	−0.122790	+	0.212679i	0.798077	+	0.602556i	$0.205851\pi$
$158$	−4.38710	+	2.53289i	−0.349019	+	0.201506i
$159$	−5.67319			−0.449913
$160$	2.80537	+	4.85904i	0.221784	+	0.384141i
$161$	−12.1133	+	4.99431i	−0.954665	+	0.393607i
$162$	1.92478	−	1.11128i	0.151225	−	0.0873100i
$163$	−5.32516	−	3.07448i	−0.417099	−	0.240812i	0.276736	−	0.960946i	$-0.410747\pi$
$163$	−5.32516	−	3.07448i	−0.417099	−	0.240812i	−0.693835	+	0.720134i	$0.744080\pi$
$164$	−24.9497	−	14.4047i	−1.94824	−	1.12482i
$165$	−2.49236			−0.194030
$166$	−3.39819			−0.263751
$167$	−13.6424	−	7.87645i	−1.05568	−	0.609498i	−0.131447	−	0.991323i	$-0.541962\pi$
$167$	−13.6424	−	7.87645i	−1.05568	−	0.609498i	−0.924235	+	0.381825i	$0.875296\pi$
$168$	3.37112	−	4.37849i	0.260088	−	0.337808i
$169$	5.19040	+	11.9189i	0.399262	+	0.916837i
$170$	−2.51965	−	4.36417i	−0.193249	−	0.334716i
$171$	3.73356	−	2.15557i	0.285513	−	0.164841i
$172$	8.38065	+	14.5157i	0.639019	+	1.10681i
$173$	−8.15461	+	14.1242i	−0.619983	+	1.07384i	0.369505	+	0.929229i	$0.379527\pi$
$173$	−8.15461	+	14.1242i	−0.619983	+	1.07384i	−0.989488	+	0.144614i	$0.953806\pi$
$174$			12.6613i			0.959851i
$175$	1.51880	−	11.3924i	0.114810	−	0.861185i
$176$	3.29780	−	1.90399i	0.248581	−	0.143519i
$177$	4.27457	−	2.46792i	0.321296	−	0.185500i
$178$	−7.38124			−0.553247
$179$	10.1878	+	17.6458i	0.761473	+	1.31891i	0.942091	+	0.335357i	$0.108857\pi$
$179$	10.1878	+	17.6458i	0.761473	+	1.31891i	−0.180617	+	0.983553i	$0.557810\pi$
$180$			2.38096i			0.177466i
$181$	−22.1726			−1.64808			−0.824039	−	0.566533i	$-0.808285\pi$
$181$	−22.1726			−1.64808			−0.824039	+	0.566533i	$0.808285\pi$
$182$	−3.98288	+	20.8243i	−0.295231	+	1.54360i
$183$	−3.03483			−0.224341
$184$		−	10.3433i		−	0.762520i
$185$	−3.93852	−	6.82172i	−0.289566	−	0.501543i
$186$	7.52673			0.551887
$187$	−7.46058	+	4.30737i	−0.545572	+	0.314986i
$188$	15.6236	−	9.02030i	1.13947	−	0.657873i
$189$	−2.44601	+	1.00849i	−0.177921	+	0.0733566i
$190$			7.76047i			0.563004i
$191$	−10.8425	+	18.7798i	−0.784536	+	1.35886i	0.144740	+	0.989470i	$0.453765\pi$
$191$	−10.8425	+	18.7798i	−0.784536	+	1.35886i	−0.929276	+	0.369386i	$0.879568\pi$
$192$	−6.46089	−	11.1906i	−0.466275	−	0.807612i
$193$	−0.0438086	+	0.0252929i	−0.00315341	+	0.00182062i	−0.501576	−	0.865114i	$-0.667246\pi$
$193$	−0.0438086	+	0.0252929i	−0.00315341	+	0.00182062i	0.498422	+	0.866934i	$0.333913\pi$
$194$	14.1574	+	24.5214i	1.01644	+	1.76053i
$195$	−1.31512	−	2.60733i	−0.0941774	−	0.186715i
$196$	−14.5984	+	14.5032i	−1.04275	+	1.03595i
$197$	15.4854	+	8.94051i	1.10329	+	0.636985i	0.937083	−	0.349106i	$-0.113515\pi$
$197$	15.4854	+	8.94051i	1.10329	+	0.636985i	0.166207	+	0.986091i	$0.446848\pi$
$198$	6.83940			0.486055
$199$	16.1691			1.14620			0.573099	−	0.819486i	$-0.305741\pi$
$199$	16.1691			1.14620			0.573099	+	0.819486i	$0.305741\pi$
$200$	7.85737	+	4.53645i	0.555600	+	0.320776i
$201$	8.59577	+	4.96277i	0.606299	+	0.350047i
$202$	−29.2095	+	16.8641i	−2.05517	+	1.18655i
$203$	1.99175	−	14.9400i	0.139794	−	1.04858i
$204$	4.11484	+	7.12711i	0.288096	+	0.498997i
$205$	−7.93728			−0.554363
$206$	15.4271	−	8.90686i	1.07486	−	0.620570i
$207$	−2.47614	+	4.28881i	−0.172104	+	0.298093i
$208$	3.73193	+	2.44527i	0.258763	+	0.169549i
$209$	13.2666			0.917669
$210$	0.629367	−	4.72084i	0.0434304	−	0.325769i
$211$	−2.69037	+	4.65986i	−0.185213	+	0.320798i	−0.943648	−	0.330950i	$-0.892631\pi$
$211$	−2.69037	+	4.65986i	−0.185213	+	0.320798i	0.758435	+	0.651748i	$0.225964\pi$
$212$	−8.33882	+	14.4433i	−0.572712	+	0.991967i
$213$	7.84155	+	4.52732i	0.537294	+	0.310207i
$214$		−	21.7510i		−	1.48686i
$215$	3.99922	+	2.30895i	0.272744	+	0.157469i
$216$		−	2.08860i		−	0.142111i
$217$	−8.88134	−	1.18403i	−0.602905	−	0.0803773i
$218$	−3.34837	+	5.79955i	−0.226781	+	0.392795i
$219$			3.17910i			0.214824i
$220$	−3.66343	+	6.34525i	−0.246988	+	0.427796i
$221$	−8.44270	−	5.53190i	−0.567918	−	0.372116i
$222$	10.8079	+	18.7198i	0.725378	+	1.25639i
$223$	−15.9502	−	9.20887i	−1.06811	−	0.616671i	−0.140443	−	0.990089i	$-0.544853\pi$
$223$	−15.9502	−	9.20887i	−1.06811	−	0.616671i	−0.927663	+	0.373418i	$0.878186\pi$
$224$	6.98627	+	16.9447i	0.466790	+	1.13216i
$225$	−2.17201	−	3.76204i	−0.144801	−	0.250802i
$226$	5.26931	−	3.04224i	0.350509	−	0.202367i
$227$		−	23.1743i		−	1.53813i	−0.639168	−	0.769067i	$-0.720721\pi$
$227$		−	23.1743i		−	1.53813i	0.639168	−	0.769067i	$-0.279279\pi$
$228$		−	12.6736i		−	0.839330i
$229$	−23.0419	+	13.3032i	−1.52265	+	0.879103i	−0.523009	+	0.852327i	$0.675191\pi$
$229$	−23.0419	+	13.3032i	−1.52265	+	0.879103i	−0.999641	+	0.0267760i	$0.991476\pi$
$230$	−4.45730	−	7.72026i	−0.293905	−	0.509059i
$231$	−8.07031	−	1.07591i	−0.530987	−	0.0707895i
$232$	10.3041	+	5.94910i	0.676500	+	0.390578i
$233$	−10.9316	−	18.9341i	−0.716155	−	1.24042i	−0.962512	−	0.271238i	$-0.912567\pi$
$233$	−10.9316	−	18.9341i	−0.716155	−	1.24042i	0.246358	−	0.969179i	$-0.420766\pi$
$234$	3.60887	+	7.15489i	0.235919	+	0.467730i
$235$	2.48518	−	4.30446i	0.162115	−	0.280792i
$236$		−	14.5100i		−	0.944523i
$237$	1.13963	−	1.97390i	0.0740272	−	0.128219i
$238$	−6.27475	−	15.2190i	−0.406732	−	0.986498i
$239$			22.4279i			1.45074i	0.688360	+	0.725370i	$0.258331\pi$
$239$			22.4279i			1.45074i	−0.688360	+	0.725370i	$0.741669\pi$
$240$	−0.867965	−	0.501120i	−0.0560269	−	0.0323472i
$241$			1.58785i			0.102282i	0.998691	+	0.0511411i	$0.0162858\pi$
$241$			1.58785i			0.102282i	−0.998691	+	0.0511411i	$0.983714\pi$
$242$	−2.94563	−	1.70066i	−0.189352	−	0.109322i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−4.46079	+	7.72631i	−0.285573	+	0.494626i
$245$	−1.48527	+	5.47145i	−0.0948905	+	0.349558i
$246$	21.7811			1.38871
$247$	7.00024	+	13.8786i	0.445414	+	0.883072i
$248$	3.53655	−	6.12548i	0.224571	−	0.388968i
$249$	1.32412	−	0.764480i	0.0839126	−	0.0484470i
$250$	16.8201			1.06380
$251$	0.177730	+	0.307837i	0.0112182	+	0.0194305i	0.871580	−	0.490253i	$-0.163096\pi$
$251$	0.177730	+	0.307837i	0.0112182	+	0.0194305i	−0.860362	+	0.509684i	$0.829762\pi$
$252$	−1.02782	+	7.70958i	−0.0647464	+	0.485658i
$253$	−13.1978	+	7.61978i	−0.829741	+	0.479051i
$254$	28.4682	+	16.4361i	1.78625	+	1.03129i
$255$	1.96359	+	1.13368i	0.122965	+	0.0709936i
$256$	−7.19318			−0.449574
$257$	−5.20848			−0.324896			−0.162448	−	0.986717i	$-0.551939\pi$
$257$	−5.20848			−0.324896			−0.162448	+	0.986717i	$0.551939\pi$
$258$	−10.9745	−	6.33610i	−0.683239	−	0.394468i
$259$	−9.80820	−	23.7891i	−0.609452	−	1.47818i
$260$	−8.57099	−	0.484292i	−0.531550	−	0.0300345i
$261$	−2.84837	−	4.93353i	−0.176310	−	0.305378i
$262$	4.42290	−	2.55356i	0.273247	−	0.157759i
$263$	10.6381	+	18.4258i	0.655975	+	1.13618i	0.981648	+	0.190700i	$0.0610758\pi$
$263$	10.6381	+	18.4258i	0.655975	+	1.13618i	−0.325673	+	0.945482i	$0.605591\pi$
$264$	3.21359	−	5.56611i	0.197783	−	0.342570i
$265$			4.59485i			0.282259i
$266$	−3.35006	+	25.1286i	−0.205405	+	1.54073i
$267$	2.87613	−	1.66053i	0.176016	−	0.101623i
$268$	25.2692	−	14.5892i	1.54356	−	0.891177i
$269$	3.80171			0.231795			0.115897	−	0.993261i	$-0.463026\pi$
$269$	3.80171			0.231795			0.115897	+	0.993261i	$0.463026\pi$
$270$	−0.900048	−	1.55893i	−0.0547752	−	0.0948734i
$271$		−	26.0950i		−	1.58516i	−0.609767	−	0.792581i	$-0.708737\pi$
$271$		−	26.0950i		−	1.58516i	0.609767	−	0.792581i	$-0.291263\pi$
$272$	−3.46420			−0.210048
$273$	−3.13283	−	9.01029i	−0.189608	−	0.545328i
$274$	34.7695			2.10050
$275$		−	13.3678i		−	0.806107i
$276$	7.27919	+	12.6079i	0.438156	+	0.758908i
$277$	28.6852			1.72352			0.861762	−	0.507312i	$-0.169361\pi$
$277$	28.6852			1.72352			0.861762	+	0.507312i	$0.169361\pi$
$278$	43.3465	−	25.0261i	2.59975	−	1.50097i
$279$	−2.93282	+	1.69327i	−0.175583	+	0.101373i
$280$	−3.54624	−	2.73035i	−0.211928	−	0.163170i
$281$		−	0.959007i		−	0.0572096i	−0.999591	−	0.0286048i	$-0.990894\pi$
$281$		−	0.959007i		−	0.0572096i	0.999591	−	0.0286048i	$-0.00910643\pi$
$282$	−6.81970	+	11.8121i	−0.406107	+	0.703398i
$283$	1.12986	+	1.95698i	0.0671635	+	0.116331i	0.897652	−	0.440706i	$-0.145272\pi$
$283$	1.12986	+	1.95698i	0.0671635	+	0.116331i	−0.830488	+	0.557036i	$0.811938\pi$
$284$	23.0520	−	13.3091i	1.36789	−	0.789750i
$285$	−1.74585	−	3.02390i	−0.103415	−	0.179120i
$286$	−1.39115	+	24.6205i	−0.0822605	+	1.45584i
$287$	−25.7011	−	3.42638i	−1.51709	−	0.202253i
$288$	5.99938	+	3.46374i	0.353517	+	0.204103i
$289$	−9.16299			−0.538999
$290$	10.2547			0.602176
$291$	−11.0330	−	6.36990i	−0.646766	−	0.373410i
$292$	8.09360	+	4.67284i	0.473642	+	0.273457i
$293$	4.64615	−	2.68246i	0.271431	−	0.156711i	−0.358107	−	0.933681i	$-0.616578\pi$
$293$	4.64615	−	2.68246i	0.271431	−	0.156711i	0.629538	+	0.776970i	$0.283244\pi$
$294$	4.07581	−	15.0145i	0.237706	−	0.875662i
$295$	−1.99883	−	3.46207i	−0.116376	−	0.201570i
$296$	20.3130			1.18067
$297$	−2.66500	+	1.53864i	−0.154639	+	0.0892809i
$298$	−15.0649	+	26.0933i	−0.872689	+	1.51154i
$299$	−14.9352	−	9.78600i	−0.863727	−	0.565939i
$300$	−12.7703			−0.737291
$301$	11.9528	+	9.20282i	0.688949	+	0.530442i
$302$	−9.31678	+	16.1371i	−0.536121	+	0.928588i
$303$	7.58772	−	13.1423i	0.435903	−	0.755006i
$304$	4.62010	+	2.66741i	0.264981	+	0.152987i
$305$			2.45798i			0.140743i
$306$	−5.38837	−	3.11098i	−0.308033	−	0.177843i
$307$			1.80266i			0.102883i	0.998676	+	0.0514415i	$0.0163816\pi$
$307$			1.80266i			0.102883i	−0.998676	+	0.0514415i	$0.983618\pi$
$308$	−14.6014	+	18.9646i	−0.831991	+	1.08061i
$309$	−4.00749	+	6.94118i	−0.227978	+	0.394870i
$310$		−	6.09608i		−	0.346234i
$311$	−9.77057	+	16.9231i	−0.554038	+	0.959622i	0.443940	+	0.896057i	$0.353580\pi$
$311$	−9.77057	+	16.9231i	−0.554038	+	0.959622i	−0.997978	+	0.0635652i	$0.979753\pi$
$312$	7.51855	+	0.424826i	0.425654	+	0.0240510i
$313$	15.4409	+	26.7444i	0.872770	+	1.51168i	0.859120	+	0.511775i	$0.171012\pi$
$313$	15.4409	+	26.7444i	0.872770	+	1.51168i	0.0136500	+	0.999907i	$0.495655\pi$
$314$	−5.92279	−	3.41952i	−0.334242	−	0.192975i
$315$	0.816796	+	1.98108i	0.0460213	+	0.111621i
$316$	−3.35021	−	5.80274i	−0.188464	−	0.326430i
$317$	−16.1874	+	9.34578i	−0.909173	+	0.524911i	−0.880165	−	0.474668i	$-0.842568\pi$
$317$	−16.1874	+	9.34578i	−0.909173	+	0.524911i	−0.0290082	+	0.999579i	$0.509235\pi$
$318$		−	12.6089i		−	0.707074i
$319$		−	17.5305i		−	0.981518i
$320$	−9.06353	+	5.23283i	−0.506666	+	0.292524i
$321$	4.89324	+	8.47534i	0.273114	+	0.473048i
$322$	−11.1001	−	26.9225i	−0.618585	−	1.50033i
$323$	−10.4520	−	6.03445i	−0.581564	−	0.335766i
$324$	1.46986	+	2.54588i	0.0816591	+	0.141438i
$325$	13.9844	−	7.05362i	0.775715	−	0.391265i
$326$	6.83320	−	11.8354i	0.378456	−	0.655505i
$327$		−	3.01309i		−	0.166624i
$328$	10.2342	−	17.7261i	0.565086	−	0.978758i
$329$	9.90522	−	12.8651i	0.546092	−	0.709276i
$330$		−	5.53939i		−	0.304934i
$331$	19.9024	+	11.4906i	1.09393	+	0.631582i	0.934621	−	0.355646i	$-0.115739\pi$
$331$	19.9024	+	11.4906i	1.09393	+	0.631582i	0.159312	+	0.987228i	$0.449072\pi$
$332$		−	4.49473i		−	0.246680i
$333$	−8.42267	−	4.86283i	−0.461560	−	0.266482i
$334$	17.5058	−	30.3210i	0.957876	−	1.65909i
$335$	4.01946	−	6.96192i	0.219607	−	0.380370i
$336$	−2.59416	−	1.99732i	−0.141523	−	0.108963i
$337$	30.3389			1.65267			0.826333	−	0.563182i	$-0.190423\pi$
$337$	30.3389			1.65267			0.826333	+	0.563182i	$0.190423\pi$
$338$	−26.4903	+	11.5359i	−1.44088	+	0.627472i
$339$	−1.36880	+	2.37084i	−0.0743433	+	0.128766i
$340$	5.77241	−	3.33270i	0.313053	−	0.180741i
$341$	−10.4213			−0.564345
$342$	4.79087	+	8.29803i	0.259061	+	0.448706i
$343$	−7.17127	+	17.0755i	−0.387212	+	0.921991i
$344$	−10.3130	+	5.95422i	−0.556040	+	0.321030i
$345$	3.47361	+	2.00549i	0.187013	+	0.107972i
$346$	−31.3917	−	18.1240i	−1.68763	−	0.974353i
$347$	−0.719982			−0.0386506			−0.0193253	−	0.999813i	$-0.506152\pi$
$347$	−0.719982			−0.0386506			−0.0193253	+	0.999813i	$0.506152\pi$
$348$	−16.7469			−0.897728
$349$	15.4556	+	8.92327i	0.827317	+	0.477652i	0.852933	−	0.522020i	$-0.174821\pi$
$349$	15.4556	+	8.92327i	0.827317	+	0.477652i	−0.0256163	+	0.999672i	$0.508155\pi$
$350$	25.3202	+	3.37561i	1.35342	+	0.180434i
$351$	−3.01583	−	1.97606i	−0.160973	−	0.105474i
$352$	10.6589	+	18.4618i	0.568121	+	0.984015i
$353$	0.218397	−	0.126091i	0.0116241	−	0.00671117i	−0.494177	−	0.869361i	$-0.664530\pi$
$353$	0.218397	−	0.126091i	0.0116241	−	0.00671117i	0.505801	+	0.862650i	$0.331197\pi$
$354$	5.48508	+	9.50044i	0.291529	+	0.504943i
$355$	3.66679	−	6.35106i	0.194613	−	0.337079i
$356$		−	9.76304i		−	0.517440i
$357$	5.86874	+	4.51851i	0.310607	+	0.239145i
$358$	−39.2187	+	22.6429i	−2.07277	+	1.19672i
$359$	−10.2385	+	5.91120i	−0.540368	+	0.311981i	−0.745228	−	0.666810i	$-0.767659\pi$
$359$	−10.2385	+	5.91120i	−0.540368	+	0.311981i	0.204860	+	0.978791i	$0.434326\pi$
$360$	−1.69160			−0.0891553
$361$	−0.207011	−	0.358553i	−0.0108953	−	0.0188712i
$362$		−	49.2798i		−	2.59009i
$363$	1.53037			0.0803234
$364$	−27.5440	−	5.26809i	−1.44370	−	0.276123i
$365$	2.57483			0.134773
$366$		−	6.74506i		−	0.352570i
$367$	7.09169	+	12.2832i	0.370183	+	0.641176i	0.989594	−	0.143891i	$-0.0459615\pi$
$367$	7.09169	+	12.2832i	0.370183	+	0.641176i	−0.619410	+	0.785068i	$0.712628\pi$
$368$	−6.12821			−0.319455
$369$	−8.48708	+	4.90002i	−0.441820	+	0.255085i
$370$	15.1616	−	8.75356i	0.788215	−	0.455076i
$371$	−1.98351	+	14.8782i	−0.102979	+	0.772438i
$372$			9.95548i			0.516168i
$373$	4.97018	−	8.60861i	0.257346	−	0.445737i	−0.708184	−	0.706028i	$-0.750485\pi$
$373$	4.97018	−	8.60861i	0.257346	−	0.445737i	0.965530	+	0.260291i	$0.0838185\pi$
$374$	−9.57334	−	16.5815i	−0.495026	−	0.857409i
$375$	−6.55403	+	3.78397i	−0.338449	+	0.195403i
$376$	6.40867	+	11.1001i	0.330502	+	0.572446i
$377$	18.3391	−	9.25011i	0.944513	−	0.476405i
$378$	−2.24141	−	5.43638i	−0.115286	−	0.279617i
$379$	7.91690	+	4.57083i	0.406664	+	0.234788i	0.689355	−	0.724423i	$-0.257894\pi$
$379$	7.91690	+	4.57083i	0.406664	+	0.234788i	−0.282691	+	0.959211i	$0.591227\pi$
$380$	−10.2646			−0.526565
$381$	−14.7903			−0.757730
$382$	−41.7390	−	24.0980i	−2.13555	−	1.23296i
$383$	20.5325	+	11.8544i	1.04916	+	0.605734i	0.922414	−	0.386202i	$-0.126213\pi$
$383$	20.5325	+	11.8544i	1.04916	+	0.605734i	0.126747	+	0.991935i	$0.459546\pi$
$384$	12.8729	−	7.43217i	0.656917	−	0.379271i
$385$	−0.871403	+	6.53633i	−0.0444108	+	0.333122i
$386$	−0.0562147	−	0.0973667i	−0.00286125	−	0.00495584i
$387$	5.70165			0.289831
$388$	−32.4340	+	18.7258i	−1.64659	+	0.950658i
$389$	−10.2666	+	17.7823i	−0.520537	+	0.901596i	0.479178	+	0.877718i	$0.340935\pi$
$389$	−10.2666	+	17.7823i	−0.520537	+	0.901596i	−0.999715	+	0.0238784i	$0.992399\pi$
$390$	5.79492	−	2.92291i	0.293437	−	0.148007i
$391$	13.8638			0.701121
$392$	−10.3041	−	10.3718i	−0.520438	−	0.523854i
$393$	−1.14893	+	1.99001i	−0.0579560	+	0.100383i
$394$	−19.8707	+	34.4171i	−1.00107	+	1.73391i
$395$	−1.59871	−	0.923016i	−0.0804399	−	0.0464420i
$396$			9.04636i			0.454597i
$397$	−23.0291	−	13.2959i	−1.15580	−	0.667301i	−0.205505	−	0.978656i	$-0.565884\pi$
$397$	−23.0291	−	13.2959i	−1.15580	−	0.667301i	−0.950294	+	0.311355i	$0.899217\pi$
$398$			35.9367i			1.80134i
$399$	−4.34773	−	10.5451i	−0.217659	−	0.527915i
$400$	2.68776	−	4.65533i	0.134388	−	0.232767i
$401$		−	24.6769i		−	1.23231i	−0.787627	−	0.616153i	$-0.788690\pi$
$401$		−	24.6769i		−	1.23231i	0.787627	−	0.616153i	$-0.211310\pi$
$402$	−11.0300	+	19.1045i	−0.550127	+	0.952847i
$403$	−5.49889	−	10.9020i	−0.273919	−	0.543068i
$404$	−22.3058	−	38.6349i	−1.10976	−	1.92216i
$405$	0.701414	+	0.404962i	0.0348536	+	0.0201227i
$406$	33.2049	+	4.42677i	1.64793	+	0.219697i
$407$	−14.9643	−	25.9189i	−0.741752	−	1.28475i
$408$	−5.06361	+	2.92348i	−0.250686	+	0.144734i
$409$			36.1441i			1.78721i	0.448851	+	0.893607i	$0.351833\pi$
$409$			36.1441i			1.78721i	−0.448851	+	0.893607i	$0.648167\pi$
$410$		−	17.6410i		−	0.871227i
$411$	−13.5481	+	7.82198i	−0.668276	+	0.385830i
$412$	11.7809	+	20.4052i	0.580406	+	1.00529i
$413$	−4.97773	−	12.0731i	−0.244938	−	0.594079i
$414$	−9.53209	−	5.50335i	−0.468477	−	0.270475i
$415$	−0.619171	−	1.07243i	−0.0303939	−	0.0526438i
$416$	−13.6891	+	20.8921i	−0.671164	+	1.02432i
$417$	−11.2601	+	19.5030i	−0.551409	+	0.955068i
$418$			29.4857i			1.44219i
$419$	1.32411	−	2.29343i	0.0646872	−	0.112042i	−0.831868	−	0.554974i	$-0.812728\pi$
$419$	1.32411	−	2.29343i	0.0646872	−	0.112042i	0.896555	+	0.442932i	$0.146062\pi$
$420$	6.24417	+	0.832453i	0.304684	+	0.0406195i
$421$		−	4.51819i		−	0.220203i	−0.993920	−	0.110102i	$-0.964882\pi$
$421$		−	4.51819i		−	0.220203i	0.993920	−	0.110102i	$-0.0351176\pi$
$422$	−10.3568	−	5.97948i	−0.504160	−	0.291077i
$423$		−	6.13683i		−	0.298383i
$424$	−10.2615	−	5.92450i	−0.498344	−	0.287719i
$425$	−6.08047	+	10.5317i	−0.294946	+	0.510862i
$426$	−10.0622	+	17.4282i	−0.487515	+	0.844401i
$427$	−1.06107	+	7.95898i	−0.0513486	+	0.385162i
$428$	28.7696			1.39063
$429$	−4.99674	−	9.90646i	−0.241245	−	0.478288i
$430$	−5.13176	+	8.88846i	−0.247475	+	0.428640i
$431$	11.8626	−	6.84890i	0.571404	−	0.329900i	−0.186306	−	0.982492i	$-0.559652\pi$
$431$	11.8626	−	6.84890i	0.571404	−	0.329900i	0.757710	+	0.652592i	$0.226318\pi$
$432$	−1.23745			−0.0595368
$433$	−11.1388	−	19.2929i	−0.535296	−	0.927159i	−0.999149	−	0.0412471i	$-0.986867\pi$
$433$	−11.1388	−	19.2929i	−0.535296	−	0.927159i	0.463853	−	0.885912i	$-0.346466\pi$
$434$	2.63157	−	19.7392i	0.126319	−	0.947513i
$435$	−3.99578	+	2.30697i	−0.191583	+	0.110611i
$436$	−7.67097	−	4.42884i	−0.367373	−	0.212103i
$437$	−18.4897	−	10.6750i	−0.884481	−	0.510655i
$438$	−7.06570			−0.337612
$439$	21.4588			1.02417			0.512086	−	0.858934i	$-0.328873\pi$
$439$	21.4588			1.02417			0.512086	+	0.858934i	$0.328873\pi$
$440$	−4.50812	−	2.60276i	−0.214916	−	0.124082i
$441$	1.78961	+	6.76737i	0.0852193	+	0.322256i
$442$	12.2949	−	18.7643i	0.584810	−	0.892528i
$443$	3.43706	+	5.95317i	0.163300	+	0.282844i	0.936050	−	0.351866i	$-0.114453\pi$
$443$	3.43706	+	5.95317i	0.163300	+	0.282844i	−0.772750	+	0.634710i	$0.781120\pi$
$444$	−24.7604	+	14.2954i	−1.17508	+	0.678430i
$445$	−1.34490	−	2.32944i	−0.0637546	−	0.110426i
$446$	20.4672	−	35.4502i	0.969148	−	1.67861i
$447$		−	13.5565i		−	0.641198i
$448$	−31.6068	+	13.0314i	−1.49328	+	0.615678i
$449$	−25.5631	+	14.7589i	−1.20640	+	0.696515i	−0.961971	−	0.273152i	$-0.911934\pi$
$449$	−25.5631	+	14.7589i	−1.20640	+	0.696515i	−0.244428	+	0.969667i	$0.578600\pi$
$450$	8.36131	−	4.82741i	0.394156	−	0.227566i
$451$	−30.1574			−1.42006
$452$	4.02392	+	6.96963i	0.189269	+	0.327824i
$453$		−	8.38387i		−	0.393908i
$454$	51.5061			2.41730
$455$	−7.29765	+	2.53735i	−0.342119	+	0.118953i
$456$	9.00424			0.421662
$457$			14.8958i			0.696794i	0.937347	+	0.348397i	$0.113274\pi$
$457$			14.8958i			0.696794i	−0.937347	+	0.348397i	$0.886726\pi$
$458$	−29.5671	−	51.2118i	−1.38158	−	2.39297i
$459$	2.79947			0.130668
$460$	10.2115	−	5.89559i	0.476112	−	0.274883i
$461$	21.6772	−	12.5154i	1.00961	−	0.582898i	0.0985319	−	0.995134i	$-0.468585\pi$
$461$	21.6772	−	12.5154i	1.00961	−	0.582898i	0.911077	+	0.412236i	$0.135252\pi$
$462$	2.39126	−	17.9367i	0.111251	−	0.834489i
$463$			34.2885i			1.59352i	0.604295	+	0.796761i	$0.293455\pi$
$463$			34.2885i			1.59352i	−0.604295	+	0.796761i	$0.706545\pi$
$464$	3.52472	−	6.10500i	0.163631	−	0.283417i
$465$	1.37142	+	2.37536i	0.0635979	+	0.110155i
$466$	42.0821	−	24.2961i	1.94941	−	1.12549i
$467$	1.46293	+	2.53387i	0.0676964	+	0.117254i	0.897887	−	0.440226i	$-0.145102\pi$
$467$	1.46293	+	2.53387i	0.0676964	+	0.117254i	−0.830190	+	0.557480i	$0.811768\pi$
$468$	−9.46366	+	4.77339i	−0.437458	+	0.220650i
$469$	16.0204	−	20.8077i	0.739755	−	0.960810i
$470$	9.56687	+	5.52344i	0.441287	+	0.254777i
$471$	3.07712			0.141786
$472$	10.3090			0.474509
$473$	15.1949	+	8.77278i	0.698662	+	0.403373i
$474$	4.38710	+	2.53289i	0.201506	+	0.116340i
$475$	16.2187	−	9.36386i	0.744164	−	0.429643i
$476$	20.1298	−	8.29951i	0.922650	−	0.380407i
$477$	2.83659	+	4.91312i	0.129879	+	0.224957i
$478$	−49.8471			−2.27995
$479$	28.8516	−	16.6575i	1.31826	−	0.761099i	0.334813	−	0.942285i	$-0.391327\pi$
$479$	28.8516	−	16.6575i	1.31826	−	0.761099i	0.983449	+	0.181186i	$0.0579936\pi$
$480$	2.80537	−	4.85904i	0.128047	−	0.221784i
$481$	19.2185	−	29.3309i	0.876286	−	1.33737i
$482$	−3.52907			−0.160745
$483$	10.3819	+	7.99330i	0.472391	+	0.363708i
$484$	2.24943	−	3.89613i	0.102247	−	0.177097i
$485$	−5.15913	+	8.93588i	−0.234264	+	0.405758i
$486$	−1.92478	−	1.11128i	−0.0873100	−	0.0504085i
$487$			14.9934i			0.679416i	0.940531	+	0.339708i	$0.110328\pi$
$487$			14.9934i			0.679416i	−0.940531	+	0.339708i	$0.889672\pi$
$488$	−5.48933	−	3.16926i	−0.248490	−	0.143466i
$489$			6.14897i			0.278066i
$490$	−12.1606	−	3.30109i	−0.549359	−	0.149128i
$491$	20.3637	−	35.2709i	0.918999	−	1.59175i	0.118060	−	0.993006i	$-0.462333\pi$
$491$	20.3637	−	35.2709i	0.918999	−	1.59175i	0.800939	−	0.598746i	$-0.204334\pi$
$492$			28.8094i			1.29883i
$493$	−7.97393	+	13.8112i	−0.359128	+	0.622027i
$494$	−30.8458	+	15.5584i	−1.38782	+	0.700004i
$495$	1.24618	+	2.15845i	0.0560116	+	0.0970149i
$496$	−3.62922	−	2.09533i	−0.162957	−	0.0940831i
$497$	14.6148	−	18.9820i	0.655562	−	0.851458i
$498$	1.69910	+	2.94292i	0.0761383	+	0.131875i
$499$	0.946024	−	0.546187i	0.0423498	−	0.0244507i	−0.478676	−	0.877992i	$-0.658883\pi$
$499$	0.946024	−	0.546187i	0.0423498	−	0.0244507i	0.521025	+	0.853541i	$0.325550\pi$
$500$			22.2477i			0.994948i
$501$			15.7529i			0.703788i
$502$	−0.684183	+	0.395013i	−0.0305366	+	0.0176303i
$503$	18.2104	+	31.5413i	0.811961	+	1.40636i	0.911489	+	0.411323i	$0.134933\pi$
$503$	18.2104	+	31.5413i	0.811961	+	1.40636i	−0.0995283	+	0.995035i	$0.531733\pi$
$504$	−5.47744	−	0.730235i	−0.243985	−	0.0325273i
$505$	−10.6443	−	6.14547i	−0.473664	−	0.273470i
$506$	−16.9353	−	29.3329i	−0.752868	−	1.30401i
$507$	7.72685	−	10.4545i	0.343162	−	0.464299i
$508$	−21.7397	+	37.6543i	−0.964545	+	1.67064i
$509$		−	7.97946i		−	0.353684i	−0.984239	−	0.176842i	$-0.943412\pi$
$509$		−	7.97946i		−	0.353684i	0.984239	−	0.176842i	$-0.0565881\pi$
$510$	−2.51965	+	4.36417i	−0.111572	+	0.193249i
$511$	8.33734	+	1.11151i	0.368822	+	0.0491702i
$512$			13.7415i			0.607294i
$513$	−3.73356	−	2.15557i	−0.164841	−	0.0951709i
$514$		−	11.5761i		−	0.510600i
$515$	5.62183	+	3.24576i	0.247727	+	0.143025i
$516$	8.38065	−	14.5157i	0.368938	−	0.639019i
$517$	9.44236	−	16.3546i	0.415274	−	0.719276i
$518$	52.8724	−	21.7992i	2.32308	−	0.957802i
$519$	16.3092			0.715895
$520$	0.344076	−	6.08945i	0.0150887	−	0.267040i
$521$	−3.02902	+	5.24643i	−0.132704	+	0.229850i	−0.924718	−	0.380653i	$-0.875699\pi$
$521$	−3.02902	+	5.24643i	−0.132704	+	0.229850i	0.792014	+	0.610503i	$0.209033\pi$
$522$	10.9650	−	6.33066i	0.479926	−	0.277085i
$523$	11.4689			0.501501			0.250750	−	0.968052i	$-0.419323\pi$
$523$	11.4689			0.501501			0.250750	+	0.968052i	$0.419323\pi$
$524$	3.37755	+	5.85009i	0.147549	+	0.255562i
$525$	−10.6255	+	4.38089i	−0.463736	+	0.191198i
$526$	−40.9522	+	23.6438i	−1.78560	+	1.03092i
$527$	8.21033	+	4.74024i	0.357648	+	0.206488i
$528$	−3.29780	−	1.90399i	−0.143519	−	0.0828605i
$529$	1.52515			0.0663108
$530$	−10.2123			−0.443593
$531$	−4.27457	−	2.46792i	−0.185500	−	0.107099i
$532$	−33.2371	−	4.43107i	−1.44101	−	0.192111i
$533$	−15.9128	−	31.5485i	−0.689261	−	1.36652i
$534$	3.69062	+	6.39234i	0.159709	+	0.276624i
$535$	6.86438	−	3.96315i	0.296773	−	0.171342i
$536$	10.3652	+	17.9531i	0.447709	+	0.775455i
$537$	10.1878	−	17.6458i	0.439637	−	0.761473i
$538$			8.44950i			0.364284i
$539$	−5.64324	+	20.7886i	−0.243072	+	0.895428i
$540$	2.06197	−	1.19048i	0.0887330	−	0.0512300i
$541$	21.2518	−	12.2697i	0.913687	−	0.527517i	0.0320714	−	0.999486i	$-0.489790\pi$
$541$	21.2518	−	12.2697i	0.913687	−	0.527517i	0.881616	+	0.471968i	$0.156456\pi$
$542$	57.9975			2.49121
$543$	11.0863	+	19.2021i	0.475759	+	0.824039i
$544$		−	19.3933i		−	0.831479i
$545$	−2.44037			−0.104534
$546$	20.0258	−	6.96288i	0.857026	−	0.297984i
$547$	−20.6787			−0.884155			−0.442078	−	0.896977i	$-0.645758\pi$
$547$	−20.6787			−0.884155			−0.442078	+	0.896977i	$0.645758\pi$
$548$			45.9890i			1.96455i
$549$	1.51741	+	2.62824i	0.0647616	+	0.112170i
$550$	29.7105			1.26686
$551$	21.2692	−	12.2798i	0.906097	−	0.523135i
$552$	−8.95758	+	5.17166i	−0.381260	+	0.220121i
$553$	−4.77821	−	3.67888i	−0.203190	−	0.156442i
$554$			63.7542i			2.70866i
$555$	−3.93852	+	6.82172i	−0.167181	+	0.289566i
$556$	33.1016	+	57.3336i	1.40382	+	2.43149i
$557$	−16.6413	+	9.60786i	−0.705115	+	0.407098i	−0.809250	−	0.587465i	$-0.800126\pi$
$557$	−16.6413	+	9.60786i	−0.705115	+	0.407098i	0.104135	+	0.994563i	$0.466793\pi$
$558$	−3.76337	−	6.51834i	−0.159316	−	0.275943i
$559$	−1.15973	+	20.5249i	−0.0490513	+	0.868109i
$560$	−1.61768	+	2.10107i	−0.0683594	+	0.0887866i
$561$	7.46058	+	4.30737i	0.314986	+	0.181857i
$562$	2.13144			0.0899094
$563$	−5.92264			−0.249609			−0.124805	−	0.992181i	$-0.539830\pi$
$563$	−5.92264			−0.249609			−0.124805	+	0.992181i	$0.539830\pi$
$564$	−15.6236	−	9.02030i	−0.657873	−	0.379823i
$565$	1.92020	+	1.10863i	0.0807834	+	0.0466403i
$566$	−4.34949	+	2.51118i	−0.182823	+	0.105553i
$567$	2.09638	+	1.61406i	0.0880396	+	0.0677842i
$568$	9.45575	+	16.3778i	0.396754	+	0.687199i
$569$	35.7698			1.49955			0.749773	−	0.661695i	$-0.230162\pi$
$569$	35.7698			1.49955			0.749773	+	0.661695i	$0.230162\pi$
$570$	6.72077	−	3.88024i	0.281502	−	0.162525i
$571$	1.69895	−	2.94266i	0.0710987	−	0.123147i	−0.828284	−	0.560308i	$-0.810683\pi$
$571$	1.69895	−	2.94266i	0.0710987	−	0.123147i	0.899383	+	0.437161i	$0.144016\pi$
$572$	−32.5652	−	1.84005i	−1.36162	−	0.0769365i
$573$	21.6850			0.905904
$574$	7.61531	−	57.1219i	0.317857	−	2.38422i
$575$	−10.7564	+	18.6307i	−0.448574	+	0.776953i
$576$	−6.46089	+	11.1906i	−0.269204	+	0.466275i
$577$	−7.14796	−	4.12687i	−0.297573	−	0.171804i	0.343779	−	0.939051i	$-0.388293\pi$
$577$	−7.14796	−	4.12687i	−0.297573	−	0.171804i	−0.641352	+	0.767247i	$0.721626\pi$
$578$		−	20.3652i		−	0.847081i
$579$	0.0438086	+	0.0252929i	0.00182062	+	0.00105114i
$580$			13.5637i			0.563202i
$581$	−1.54194	−	3.73985i	−0.0639702	−	0.155155i
$582$	14.1574	−	24.5214i	0.586844	−	1.01644i
$583$			17.4580i			0.723035i
$584$	−3.31992	+	5.75028i	−0.137379	+	0.237948i
$585$	−1.60045	+	2.44259i	−0.0661706	+	0.100989i
$586$	5.96189	+	10.3263i	0.246283	+	0.426576i
$587$	−20.9087	−	12.0716i	−0.862994	−	0.498250i	0.00201975	−	0.999998i	$-0.499357\pi$
$587$	−20.9087	−	12.0716i	−0.862994	−	0.498250i	−0.865014	+	0.501748i	$0.832690\pi$
$588$	19.8594	+	5.39100i	0.818988	+	0.222321i
$589$	−7.29991	−	12.6438i	−0.300788	−	0.520980i
$590$	7.69463	−	4.44249i	0.316783	−	0.182895i
$591$		−	17.8810i		−	0.735527i
$592$		−	12.0350i		−	0.494636i
$593$	−7.24219	+	4.18128i	−0.297401	+	0.171705i	−0.641275	−	0.767311i	$-0.721594\pi$
$593$	−7.24219	+	4.18128i	−0.297401	+	0.171705i	0.343874	+	0.939016i	$0.388261\pi$
$594$	−3.41970	−	5.92310i	−0.140312	−	0.243028i
$595$	3.65965	−	4.75323i	0.150031	−	0.194863i
$596$	−34.5131	−	19.9262i	−1.41371	−	0.816207i
$597$	−8.08456	−	14.0029i	−0.330879	−	0.573099i
$598$	21.7499	−	33.1943i	0.889418	−	1.35742i
$599$	−4.25916	+	7.37709i	−0.174025	+	0.301420i	−0.939823	−	0.341661i	$-0.889011\pi$
$599$	−4.25916	+	7.37709i	−0.174025	+	0.301420i	0.765799	+	0.643080i	$0.222344\pi$
$600$		−	9.07291i		−	0.370400i
$601$	0.714622	−	1.23776i	0.0291500	−	0.0504894i	−0.851082	−	0.525032i	$-0.824053\pi$
$601$	0.714622	−	1.23776i	0.0291500	−	0.0504894i	0.880232	+	0.474543i	$0.157387\pi$
$602$	−20.4537	+	26.5657i	−0.833632	+	1.08274i
$603$		−	9.92554i		−	0.404199i
$604$	−21.3443	−	12.3231i	−0.868488	−	0.501422i
$605$		−	1.23948i		−	0.0503920i
$606$	29.2095	+	16.8641i	1.18655	+	0.685057i
$607$	−7.51555	+	13.0173i	−0.305047	+	0.528357i	−0.977272	−	0.211990i	$-0.932005\pi$
$607$	−7.51555	+	13.0173i	−0.305047	+	0.528357i	0.672225	+	0.740347i	$0.265339\pi$
$608$	−14.9327	+	25.8642i	−0.605601	+	1.04893i
$609$	−13.9343	+	5.74509i	−0.564646	+	0.232803i
$610$	−5.46298			−0.221190
$611$	22.0914	+	1.24825i	0.893722	+	0.0504986i
$612$	4.11484	−	7.12711i	0.166332	−	0.288096i
$613$	−15.5070	+	8.95295i	−0.626320	+	0.361606i	−0.779326	−	0.626619i	$-0.784438\pi$
$613$	−15.5070	+	8.95295i	−0.626320	+	0.361606i	0.153005	+	0.988225i	$0.451105\pi$
$614$	−4.00649			−0.161689
$615$	3.96864	+	6.87388i	0.160031	+	0.277182i
$616$	−13.4738	−	10.3739i	−0.542876	−	0.417976i
$617$	34.2385	−	19.7676i	1.37839	−	0.795813i	0.386423	−	0.922322i	$-0.373710\pi$
$617$	34.2385	−	19.7676i	1.37839	−	0.795813i	0.991966	+	0.126509i	$0.0403771\pi$
$618$	−15.4271	−	8.90686i	−0.620570	−	0.358286i
$619$	−23.1290	−	13.3535i	−0.929634	−	0.536724i	−0.0429379	−	0.999078i	$-0.513672\pi$
$619$	−23.1290	−	13.3535i	−0.929634	−	0.536724i	−0.886696	+	0.462354i	$0.847005\pi$
$620$	8.06318			0.323825
$621$	4.95229			0.198728
$622$	−37.6125	−	21.7156i	−1.50812	−	0.870715i
$623$	−3.34925	−	8.12335i	−0.134185	−	0.325455i
$624$	0.251700	−	4.45458i	0.0100761	−	0.178326i
$625$	−7.79533	−	13.5019i	−0.311813	−	0.540076i
$626$	−59.4407	+	34.3181i	−2.37573	+	1.37163i
$627$	−6.63329	−	11.4892i	−0.264908	−	0.458835i
$628$	4.52294	−	7.83397i	0.180485	−	0.312609i
$629$			27.2267i			1.08560i
$630$	−4.40305	+	1.81537i	−0.175422	+	0.0723261i
$631$	15.8415	−	9.14610i	0.630640	−	0.364100i	−0.150360	−	0.988631i	$-0.548043\pi$
$631$	15.8415	−	9.14610i	0.630640	−	0.364100i	0.781000	+	0.624531i	$0.214710\pi$
$632$	4.12269	−	2.38023i	0.163992	−	0.0946806i
$633$	5.38074			0.213865
$634$	−20.7715	−	35.9772i	−0.824940	−	1.42884i
$635$			11.9790i			0.475373i
$636$	16.6776			0.661311
$637$	−24.7253	+	5.06574i	−0.979650	+	0.200712i
$638$	38.9624			1.54253
$639$		−	9.05465i		−	0.358196i
$640$	−6.01949	−	10.4261i	−0.237941	−	0.412126i
$641$	38.4823			1.51996			0.759981	−	0.649946i	$-0.225208\pi$
$641$	38.4823			1.51996			0.759981	+	0.649946i	$0.225208\pi$
$642$	−18.8369	+	10.8755i	−0.743432	+	0.429221i
$643$	9.32291	−	5.38258i	0.367660	−	0.212268i	−0.304776	−	0.952424i	$-0.598582\pi$
$643$	9.32291	−	5.38258i	0.367660	−	0.212268i	0.672436	+	0.740156i	$0.265248\pi$
$644$	35.6099	−	14.6819i	1.40323	−	0.578549i
$645$		−	4.61790i		−	0.181830i
$646$	13.4119	−	23.2301i	0.527683	−	0.913974i
$647$	3.06254	+	5.30447i	0.120401	+	0.208540i	0.919926	−	0.392093i	$-0.128249\pi$
$647$	3.06254	+	5.30447i	0.120401	+	0.208540i	−0.799525	+	0.600633i	$0.794915\pi$
$648$	−1.80878	+	1.04430i	−0.0710555	+	0.0410239i
$649$	−7.59448	−	13.1540i	−0.298109	−	0.516341i
$650$	15.6770	+	31.0810i	0.614904	+	1.21910i
$651$	3.41527	+	8.28348i	0.133855	+	0.324655i
$652$	15.6545	+	9.03815i	0.613079	+	0.353961i
$653$	23.4205			0.916516			0.458258	−	0.888819i	$-0.348474\pi$
$653$	23.4205			0.916516			0.458258	+	0.888819i	$0.348474\pi$
$654$	6.69675			0.261864
$655$	1.61176	+	0.930547i	0.0629765	+	0.0363595i
$656$	−10.5023	−	6.06352i	−0.410047	−	0.236741i
$657$	2.75318	−	1.58955i	0.107412	−	0.0620142i
$658$	28.5933	+	22.0148i	1.11468	+	0.858228i
$659$	−8.15148	−	14.1188i	−0.317537	−	0.549989i	0.662437	−	0.749118i	$-0.269522\pi$
$659$	−8.15148	−	14.1188i	−0.317537	−	0.549989i	−0.979973	+	0.199128i	$0.936189\pi$
$660$	7.32686			0.285198
$661$	−41.6539	+	24.0489i	−1.62015	+	0.935394i	−0.633271	+	0.773930i	$0.718288\pi$
$661$	−41.6539	+	24.0489i	−1.62015	+	0.935394i	−0.986879	+	0.161464i	$0.948378\pi$
$662$	−25.5385	+	44.2340i	−0.992582	+	1.71920i
$663$	−0.569418	+	10.0775i	−0.0221144	+	0.391379i
$664$	3.19338			0.123927
$665$	−8.54072	+	3.52133i	−0.331195	+	0.136551i
$666$	10.8079	−	18.7198i	0.418797	−	0.725378i
$667$	−14.1060	+	24.4323i	−0.546185	+	0.946021i
$668$	40.1050	+	23.1546i	1.55171	+	0.895880i
$669$			18.4177i			0.712071i
$670$	15.4732	+	8.93346i	0.597782	+	0.345130i
$671$			9.33901i			0.360528i
$672$	11.1814	−	14.5226i	0.431332	−	0.560223i
$673$	−22.0349	+	38.1655i	−0.849382	+	1.47117i	0.0323778	+	0.999476i	$0.489692\pi$
$673$	−22.0349	+	38.1655i	−0.849382	+	1.47117i	−0.881760	+	0.471698i	$0.843641\pi$
$674$			67.4297i			2.59730i
$675$	−2.17201	+	3.76204i	−0.0836008	+	0.144801i
$676$	−15.2584	−	35.0383i	−0.586861	−	1.34763i
$677$	−3.08805	−	5.34866i	−0.118684	−	0.205566i	0.800563	−	0.599249i	$-0.204534\pi$
$677$	−3.08805	−	5.34866i	−0.118684	−	0.205566i	−0.919246	+	0.393683i	$0.871201\pi$
$678$	−5.26931	−	3.04224i	−0.202367	−	0.116836i
$679$	−20.5628	+	26.7075i	−0.789129	+	1.02494i
$680$	2.36779	+	4.10114i	0.0908007	+	0.157271i
$681$	−20.0696	+	11.5872i	−0.769067	+	0.444021i
$682$		−	23.1618i		−	0.886913i
$683$			14.2002i			0.543354i	0.962389	+	0.271677i	$0.0875782\pi$
$683$			14.2002i			0.543354i	−0.962389	+	0.271677i	$0.912422\pi$
$684$	−10.9757	+	6.33680i	−0.419665	+	0.242294i
$685$	6.33520	+	10.9729i	0.242056	+	0.419253i
$686$	−37.9512	−	15.9385i	−1.44898	−	0.608535i
$687$	23.0419	+	13.3032i	0.879103	+	0.507550i
$688$	3.52775	+	6.11025i	0.134494	+	0.232951i
$689$	−18.2633	+	9.21185i	−0.695776	+	0.350944i
$690$	−4.45730	+	7.72026i	−0.169686	+	0.293905i
$691$		−	0.389112i		−	0.0148025i	−0.999973	−	0.00740126i	$-0.997644\pi$
$691$		−	0.389112i		−	0.0148025i	0.999973	−	0.00740126i	$-0.00235591\pi$
$692$	23.9723	−	41.5213i	0.911291	−	1.57840i
$693$	3.10339	+	7.52704i	0.117888	+	0.285929i
$694$		−	1.60020i		−	0.0607426i
$695$	15.7960	+	9.11981i	0.599175	+	0.345934i
$696$		−	11.8982i		−	0.451000i
$697$	23.7593	+	13.7174i	0.899947	+	0.519585i
$698$	−19.8324	+	34.3507i	−0.750668	+	1.30019i
$699$	−10.9316	+	18.9341i	−0.413472	+	0.716155i
$700$	−4.46486	+	33.4906i	−0.168756	+	1.26583i
$701$	−3.60438			−0.136135			−0.0680677	−	0.997681i	$-0.521683\pi$
$701$	−3.60438			−0.136135			−0.0680677	+	0.997681i	$0.521683\pi$
$702$	4.39188	−	6.70282i	0.165761	−	0.252982i
$703$	20.9644	−	36.3114i	0.790687	−	1.36951i
$704$	−34.4366	+	19.8820i	−1.29788	+	0.749329i
$705$	−4.97036			−0.187195
$706$	0.280244	+	0.485397i	0.0105471	+	0.0182682i
$707$	−31.8135	−	24.4941i	−1.19647	−	0.921196i
$708$	−12.5661	+	7.25502i	−0.472262	+	0.272660i
$709$	35.9841	+	20.7754i	1.35141	+	0.780238i	0.988447	−	0.151565i	$-0.0484312\pi$
$709$	35.9841	+	20.7754i	1.35141	+	0.780238i	0.362965	+	0.931803i	$0.381765\pi$
$710$	14.1155	+	8.14962i	0.529747	+	0.305850i
$711$	−2.27927			−0.0854792
$712$	6.93636			0.259951
$713$	14.5242	+	8.38554i	0.543935	+	0.314041i
$714$	−10.0426	+	13.0436i	−0.375836	+	0.488143i
$715$	−8.02347	+	4.04698i	−0.300061	+	0.151348i
$716$	−29.9494	−	51.8739i	−1.11926	−	1.93862i
$717$	19.4231	−	11.2139i	0.725370	−	0.418792i
$718$	−13.1379	−	22.7556i	−0.490304	−	0.849231i
$719$	−20.1484	+	34.8980i	−0.751407	+	1.30147i	0.195734	+	0.980657i	$0.437291\pi$
$719$	−20.1484	+	34.8980i	−0.751407	+	1.30147i	−0.947141	+	0.320818i	$0.896042\pi$
$720$			1.00224i			0.0373513i
$721$	16.8024	+	12.9367i	0.625756	+	0.481788i
$722$	0.796903	−	0.460092i	0.0296577	−	0.0171229i
$723$	1.37512	−	0.793924i	0.0511411	−	0.0295263i
$724$	65.1815			2.42245
$725$	−12.3734	−	21.4314i	−0.459537	−	0.795941i
$726$			3.40132i			0.126235i
$727$	−31.8052			−1.17959			−0.589796	−	0.807553i	$-0.700792\pi$
$727$	−31.8052			−1.17959			−0.589796	+	0.807553i	$0.700792\pi$
$728$	3.74283	−	19.5692i	0.138719	−	0.725283i
$729$	1.00000			0.0370370
$730$			5.72268i			0.211806i
$731$	−7.98079	−	13.8231i	−0.295180	−	0.511267i
$732$	8.92157			0.329751
$733$	13.1128	−	7.57067i	0.484332	−	0.279629i	−0.237888	−	0.971293i	$-0.576455\pi$
$733$	13.1128	−	7.57067i	0.484332	−	0.279629i	0.722220	+	0.691664i	$0.243122\pi$
$734$	−27.3000	+	15.7616i	−1.00766	+	0.581773i
$735$	5.48105	−	1.44944i	0.202172	−	0.0534635i
$736$		−	34.3069i		−	1.26457i
$737$	15.2718	−	26.4516i	0.562545	−	0.974356i
$738$	−10.8905	−	18.8630i	−0.400886	−	0.694355i
$739$	−20.5071	+	11.8398i	−0.754365	+	0.435533i	−0.827269	−	0.561806i	$-0.810107\pi$
$739$	−20.5071	+	11.8398i	−0.754365	+	0.435533i	0.0729037	+	0.997339i	$0.476773\pi$
$740$	11.5782	+	20.0540i	0.425623	+	0.737200i
$741$	8.51907	−	13.0017i	0.312956	−	0.477628i
$742$	−33.0676	−	4.40846i	−1.21395	−	0.161840i
$743$	37.9709	+	21.9225i	1.39302	+	0.804260i	0.993648	−	0.112530i	$-0.0358954\pi$
$743$	37.9709	+	21.9225i	1.39302	+	0.804260i	0.399370	+	0.916790i	$0.369229\pi$
$744$	−7.07309			−0.259312
$745$	−10.9797			−0.402265
$746$	19.1331	+	11.0465i	0.700512	+	0.404441i
$747$	−1.32412	−	0.764480i	−0.0484470	−	0.0279709i
$748$	21.9321	−	12.6625i	0.801916	−	0.462987i
$749$	23.9378	−	9.86953i	0.874669	−	0.360625i
$750$	−8.41007	−	14.5667i	−0.307092	−	0.531899i
$751$	15.0908			0.550673			0.275336	−	0.961348i	$-0.411211\pi$
$751$	15.0908			0.550673			0.275336	+	0.961348i	$0.411211\pi$
$752$	6.57661	−	3.79701i	0.239824	−	0.138463i
$753$	0.177730	−	0.307837i	0.00647683	−	0.0112182i
$754$	20.5588	+	40.7596i	0.748709	+	1.48438i
$755$	−6.79029			−0.247124
$756$	7.19060	−	2.96468i	0.261520	−	0.107824i
$757$	−8.25531	+	14.2986i	−0.300044	+	0.519692i	−0.976146	−	0.217117i	$-0.930335\pi$
$757$	−8.25531	+	14.2986i	−0.300044	+	0.519692i	0.676101	+	0.736809i	$0.263668\pi$
$758$	−10.1589	+	17.5957i	−0.368987	+	0.639105i
$759$	13.1978	+	7.61978i	0.479051	+	0.276580i
$760$		−	7.29275i		−	0.264536i
$761$	−17.5967	−	10.1595i	−0.637880	−	0.368280i	0.145917	−	0.989297i	$-0.453387\pi$
$761$	−17.5967	−	10.1595i	−0.637880	−	0.368280i	−0.783797	+	0.621017i	$0.786720\pi$
$762$		−	32.8722i		−	1.19083i
$763$	−7.90198	−	1.05347i	−0.286071	−	0.0381381i
$764$	31.8740	−	55.2074i	1.15316	−	1.99733i
$765$		−	2.26735i		−	0.0819763i
$766$	−26.3471	+	45.6345i	−0.951959	+	1.64884i
$767$	9.75350	−	14.8856i	0.352179	−	0.537489i
$768$	3.59659	+	6.22948i	0.129781	+	0.224787i
$769$	−29.3351	−	16.9366i	−1.05785	−	0.610750i	−0.133013	−	0.991114i	$-0.542465\pi$
$769$	−29.3351	−	16.9366i	−1.05785	−	0.610750i	−0.924837	+	0.380364i	$0.875799\pi$
$770$	−14.5273	−	1.93674i	−0.523528	−	0.0697951i
$771$	2.60424	+	4.51067i	0.0937894	+	0.162448i
$772$	0.128785	−	0.0743542i	0.00463508	−	0.00267607i
$773$		−	13.5359i		−	0.486853i	−0.969919	−	0.243426i	$-0.921729\pi$
$773$		−	13.5359i		−	0.486853i	0.969919	−	0.243426i	$-0.0782715\pi$
$774$			12.6722i			0.455493i
$775$	−12.7402	+	7.35558i	−0.457643	+	0.264220i
$776$	−13.3042	−	23.0435i	−0.477591	−	0.827212i
$777$	−15.6978	+	20.3887i	−0.563157	+	0.731440i
$778$	−39.5220	−	22.8180i	−1.41693	−	0.818065i
$779$	−21.1247	−	36.5890i	−0.756870	−	1.31094i
$780$	3.86608	+	7.66484i	0.138428	+	0.274445i
$781$	13.9318	−	24.1306i	0.498520	−	0.863462i
$782$			30.8129i			1.10187i
$783$	−2.84837	+	4.93353i	−0.101793	+	0.176310i
$784$	−6.14507	+	6.10500i	−0.219467	+	0.218036i
$785$		−	2.49223i		−	0.0889515i
$786$	−4.42290	−	2.55356i	−0.157759	−	0.0910825i
$787$		−	45.8242i		−	1.63346i	−0.577022	−	0.816729i	$-0.695785\pi$
$787$		−	45.8242i		−	1.63346i	0.577022	−	0.816729i	$-0.304215\pi$
$788$	−45.5230	−	26.2827i	−1.62169	−	0.936282i
$789$	10.6381	−	18.4258i	0.378728	−	0.655975i
$790$	2.05145	−	3.55322i	0.0729873	−	0.126418i
$791$	5.73907	+	4.41867i	0.204058	+	0.157110i
$792$	−6.42719			−0.228380
$793$	−9.76980	+	4.92781i	−0.346936	+	0.174992i
$794$	29.5507	−	51.1834i	1.04872	−	1.81643i
$795$	3.97925	−	2.29742i	0.141130	−	0.0814812i
$796$	−47.5328			−1.68476
$797$	−4.79076	−	8.29783i	−0.169697	−	0.293924i	0.768616	−	0.639710i	$-0.220946\pi$
$797$	−4.79076	−	8.29783i	−0.169697	−	0.293924i	−0.938313	+	0.345786i	$0.887612\pi$
$798$	23.4370	−	9.66305i	0.829661	−	0.342068i
$799$	−14.8782	+	8.58992i	−0.526352	+	0.303889i
$800$	26.0614	+	15.0466i	0.921411	+	0.531977i
$801$	−2.87613	−	1.66053i	−0.101623	−	0.0586720i
$802$	54.8457			1.93667
$803$	9.78296			0.345233
$804$	−25.2692	−	14.5892i	−0.891177	−	0.514521i
$805$	6.47396	−	8.40852i	0.228177	−	0.296361i
$806$	24.2303	−	12.2216i	0.853475	−	0.430486i
$807$	−1.90086	−	3.29238i	−0.0669133	−	0.115897i
$808$	27.4490	−	15.8477i	0.965652	−	0.557519i
$809$	−24.9645	−	43.2398i	−0.877705	−	1.52023i	−0.853853	−	0.520514i	$-0.825741\pi$
$809$	−24.9645	−	43.2398i	−0.877705	−	1.52023i	−0.0238512	−	0.999716i	$-0.507593\pi$
$810$	−0.900048	+	1.55893i	−0.0316245	+	0.0547752i
$811$			12.4298i			0.436470i	0.975896	+	0.218235i	$0.0700299\pi$
$811$			12.4298i			0.436470i	−0.975896	+	0.218235i	$0.929970\pi$
$812$	−5.85521	+	43.9196i	−0.205478	+	1.54127i
$813$	−22.5990	+	13.0475i	−0.792581	+	0.457597i
$814$	57.6061	−	33.2589i	2.01909	−	1.16572i
$815$	4.98019			0.174449
$816$	1.73210	+	3.00009i	0.0606356	+	0.105024i
$817$			24.5806i			0.859968i
$818$	−80.3322			−2.80875
$819$	−6.23673	+	7.21826i	−0.217929	+	0.252226i
$820$	23.3334			0.814839
$821$		−	24.6582i		−	0.860576i	−0.902692	−	0.430288i	$-0.858412\pi$
$821$		−	24.6582i		−	0.860576i	0.902692	−	0.430288i	$-0.141588\pi$
$822$	−17.3847	−	30.1112i	−0.606362	−	1.05025i
$823$	2.48814			0.0867311			0.0433655	−	0.999059i	$-0.486192\pi$
$823$	2.48814			0.0867311			0.0433655	+	0.999059i	$0.486192\pi$
$824$	−14.4973	+	8.37003i	−0.505038	+	0.291584i
$825$	−11.5768	+	6.68388i	−0.403053	+	0.232703i
$826$	26.8331	−	11.0633i	0.933643	−	0.384940i
$827$		−	5.29835i		−	0.184242i	−0.995748	−	0.0921208i	$-0.970635\pi$
$827$		−	5.29835i		−	0.184242i	0.995748	−	0.0921208i	$-0.0293646\pi$
$828$	7.27919	−	12.6079i	0.252969	−	0.438156i
$829$	7.56579	+	13.1043i	0.262771	+	0.455133i	0.966977	−	0.254863i	$-0.0820303\pi$
$829$	7.56579	+	13.1043i	0.262771	+	0.455133i	−0.704206	+	0.709995i	$0.748697\pi$
$830$	2.38354	−	1.37614i	0.0827339	−	0.0477664i
$831$	−14.3426	−	24.8421i	−0.497539	−	0.861762i
$832$	−38.9698	−	25.5342i	−1.35104	−	0.885238i
$833$	13.9019	−	13.8112i	0.481672	−	0.478531i
$834$	−43.3465	−	25.0261i	−1.50097	−	0.866583i
$835$	12.7587			0.441531
$836$	−39.0002			−1.34885
$837$	2.93282	+	1.69327i	0.101373	+	0.0585278i
$838$	5.09727	+	2.94291i	0.176082	+	0.101661i
$839$	−31.1992	+	18.0129i	−1.07712	+	0.621874i	−0.930117	−	0.367262i	$-0.880295\pi$
$839$	−31.1992	+	18.0129i	−1.07712	+	0.621874i	−0.147000	+	0.989136i	$0.546962\pi$
$840$	−0.591435	+	4.43631i	−0.0204064	+	0.153067i
$841$	−1.72648	−	2.99034i	−0.0595336	−	0.103115i
$842$	10.0419			0.346067
$843$	−0.830525	+	0.479504i	−0.0286048	+	0.0165150i
$844$	7.90896	−	13.6987i	0.272238	−	0.471529i
$845$	−8.46731	−	6.25816i	−0.291284	−	0.215287i
$846$	13.6394			0.468932
$847$	0.535061	−	4.01346i	0.0183849	−	0.137904i
$848$	−3.51014	+	6.07975i	−0.120539	+	0.208779i
$849$	1.12986	−	1.95698i	0.0387769	−	0.0671635i
$850$	−23.4072	−	13.5142i	−0.802861	−	0.463532i
$851$			48.1643i			1.65105i
$852$	−23.0520	−	13.3091i	−0.789750	−	0.455962i
$853$		−	32.0255i		−	1.09653i	−0.836304	−	0.548266i	$-0.815288\pi$
$853$		−	32.0255i		−	1.09653i	0.836304	−	0.548266i	$-0.184712\pi$
$854$	−17.6892	−	2.35827i	−0.605313	−	0.0806984i
$855$	−1.74585	+	3.02390i	−0.0597068	+	0.103415i
$856$			20.4400i			0.698625i
$857$	4.19647	−	7.26850i	0.143349	−	0.248287i	−0.785407	−	0.618980i	$-0.787546\pi$
$857$	4.19647	−	7.26850i	0.143349	−	0.248287i	0.928756	+	0.370693i	$0.120880\pi$
$858$	22.0176	−	11.1055i	0.751668	−	0.379136i
$859$	8.88475	+	15.3888i	0.303144	+	0.525060i	0.976846	−	0.213942i	$-0.0686304\pi$
$859$	8.88475	+	15.3888i	0.303144	+	0.525060i	−0.673703	+	0.739003i	$0.735297\pi$
$860$	−11.7566	−	6.78769i	−0.400897	−	0.231458i
$861$	9.88319	+	23.9710i	0.336818	+	0.816928i
$862$	15.2220	+	26.3653i	0.518464	+	0.898007i
$863$	1.15148	−	0.664805i	0.0391967	−	0.0226302i	−0.480274	−	0.877119i	$-0.659463\pi$
$863$	1.15148	−	0.664805i	0.0391967	−	0.0226302i	0.519470	+	0.854489i	$0.326129\pi$
$864$		−	6.92749i		−	0.235678i
$865$		−	13.2092i		−	0.449127i
$866$	42.8795	−	24.7565i	1.45710	−	0.841260i
$867$	4.58149	+	7.93538i	0.155596	+	0.269500i
$868$	26.1087	+	3.48073i	0.886188	+	0.118144i
$869$	−6.07425	−	3.50697i	−0.206055	−	0.118966i
$870$	−5.12735	−	8.88082i	−0.173833	−	0.301088i
$871$	35.7300	+	2.01888i	1.21067	+	0.0684071i
$872$	3.14657	−	5.45001i	0.106556	−	0.184561i
$873$			12.7398i			0.431177i
$874$	23.7258	−	41.0942i	0.802536	−	1.39003i
$875$	7.63216	+	18.5113i	0.258014	+	0.625795i
$876$		−	9.34569i		−	0.315762i
$877$	−45.8893	−	26.4942i	−1.54957	−	0.894645i	−0.998174	−	0.0604010i	$-0.980762\pi$
$877$	−45.8893	−	26.4942i	−1.54957	−	0.894645i	−0.551396	−	0.834244i	$-0.685905\pi$
$878$			47.6932i			1.60957i
$879$	−4.64615	−	2.68246i	−0.156711	−	0.0904770i
$880$	−1.54208	+	2.67097i	−0.0519837	+	0.0900384i
$881$	−18.3266	+	31.7426i	−0.617439	+	1.06944i	0.372512	+	0.928027i	$0.378496\pi$
$881$	−18.3266	+	31.7426i	−0.617439	+	1.06944i	−0.989951	+	0.141408i	$0.954837\pi$
$882$	−15.0408	+	3.97749i	−0.506451	+	0.133929i
$883$	45.3649			1.52665			0.763324	−	0.646015i	$-0.223566\pi$
$883$	45.3649			1.52665			0.763324	+	0.646015i	$0.223566\pi$
$884$	24.8193	+	16.2623i	0.834762	+	0.546960i
$885$	−1.99883	+	3.46207i	−0.0671899	+	0.116376i
$886$	−13.2312	+	7.63905i	−0.444511	+	0.256639i
$887$	29.8206			1.00128			0.500639	−	0.865656i	$-0.333098\pi$
$887$	29.8206			1.00128			0.500639	+	0.865656i	$0.333098\pi$
$888$	−10.1565	−	17.5916i	−0.340830	−	0.590334i
$889$	−5.17113	+	38.7883i	−0.173434	+	1.30092i
$890$	5.17730	−	2.98912i	0.173544	−	0.100195i
$891$	2.66500	+	1.53864i	0.0892809	+	0.0515463i
$892$	46.8893	+	27.0716i	1.56997	+	0.906423i
$893$	26.4567			0.885341
$894$	30.1299			1.00769
$895$	−14.2918	−	8.25136i	−0.477721	−	0.275812i
$896$	−14.9905	−	36.3583i	−0.500797	−	1.21465i
$897$	−1.00731	+	17.8273i	−0.0336330	+	0.595236i
$898$	−32.8024	−	56.8154i	−1.09463	−	1.89595i
$899$	−16.7075	+	9.64611i	−0.557228	+	0.321716i
$900$	6.38513	+	11.0594i	0.212838	+	0.368645i
$901$	7.94095	−	13.7541i	0.264551	−	0.458216i
$902$		−	67.0264i		−	2.23173i
$903$	1.99347	−	14.9529i	0.0663384	−	0.497600i
$904$	−4.95173	+	2.85888i	−0.164692	+	0.0950849i
$905$	15.5522	−	8.97907i	0.516973	−	0.298474i
$906$	18.6336			0.619059
$907$	−24.7033	−	42.7873i	−0.820259	−	1.42073i	−0.905489	−	0.424369i	$-0.860496\pi$
$907$	−24.7033	−	42.7873i	−0.820259	−	1.42073i	0.0852307	−	0.996361i	$-0.472837\pi$
$908$			68.1263i			2.26085i
$909$	−15.1754			−0.503338
$910$	−5.63940	−	16.2194i	−0.186944	−	0.537667i
$911$	−22.3495			−0.740471			−0.370235	−	0.928938i	$-0.620723\pi$
$911$	−22.3495			−0.740471			−0.370235	+	0.928938i	$0.620723\pi$
$912$		−	5.33483i		−	0.176654i
$913$	−2.35252	−	4.07468i	−0.0778570	−	0.134852i
$914$	−33.1066			−1.09507
$915$	2.12867	−	1.22899i	0.0703717	−	0.0406291i
$916$	67.7369	−	39.1079i	2.23809	−	1.29216i
$917$	4.81719	+	3.70890i	0.159078	+	0.122479i
$918$			6.22195i			0.205355i
$919$	−17.5264	+	30.3567i	−0.578144	+	1.00137i	0.417549	+	0.908655i	$0.362889\pi$
$919$	−17.5264	+	30.3567i	−0.578144	+	1.00137i	−0.995692	+	0.0927197i	$0.970444\pi$
$920$	4.18865	+	7.25496i	0.138096	+	0.239189i
$921$	1.56115	−	0.901328i	0.0514415	−	0.0296998i
$922$	27.8160	+	48.1787i	0.916071	+	1.58668i
$923$	32.5950	+	1.84174i	1.07288	+	0.0606215i
$924$	23.7245	+	3.16288i	0.780479	+	0.104051i
$925$	−36.5883	−	21.1243i	−1.20302	−	0.694561i
$926$	−76.2079			−2.50435
$927$	8.01499			0.263247
$928$	34.1770	+	19.7321i	1.12191	+	0.647737i
$929$	−47.2367	−	27.2721i	−1.54978	−	0.894768i	−0.998157	−	0.0606776i	$-0.980674\pi$
$929$	−47.2367	−	27.2721i	−1.54978	−	0.894768i	−0.551627	−	0.834091i	$-0.685993\pi$
$930$	−5.27936	+	3.04804i	−0.173117	+	0.0999491i
$931$	−29.1751	+	7.71525i	−0.956176	+	0.252857i
$932$	32.1360	+	55.6612i	1.05265	+	1.82324i
$933$	19.5411			0.639748
$934$	−5.63166	+	3.25144i	−0.184274	+	0.106390i
$935$	3.48864	−	6.04250i	0.114091	−	0.197611i
$936$	−3.39136	−	6.72366i	−0.110850	−	0.219770i
$937$	−4.92743			−0.160972			−0.0804861	−	0.996756i	$-0.525647\pi$
$937$	−4.92743			−0.160972			−0.0804861	+	0.996756i	$0.525647\pi$
$938$	46.2461	+	35.6062i	1.50999	+	1.16258i
$939$	15.4409	−	26.7444i	0.503894	−	0.872770i
$940$	−7.30575	+	12.6539i	−0.238287	+	0.412726i
$941$	−21.0883	−	12.1753i	−0.687459	−	0.396905i	0.115201	−	0.993342i	$-0.463249\pi$
$941$	−21.0883	−	12.1753i	−0.687459	−	0.396905i	−0.802659	+	0.596438i	$0.796582\pi$
$942$			6.83905i			0.222828i
$943$	42.0304	+	24.2663i	1.36870	+	0.790219i
$944$		−	6.10786i		−	0.198794i
$945$	1.30727	−	1.69791i	0.0425254	−	0.0552329i
$946$	−19.4979	+	33.7714i	−0.633933	+	1.09800i
$947$			24.6702i			0.801675i	0.916149	+	0.400838i	$0.131281\pi$
$947$			24.6702i			0.801675i	−0.916149	+	0.400838i	$0.868719\pi$
$948$	−3.35021	+	5.80274i	−0.108810	+	0.188464i
$949$	5.16207	+	10.2342i	0.167568	+	0.332217i
$950$	20.8116	+	36.0468i	0.675219	+	1.16951i
$951$	16.1874	+	9.34578i	0.524911	+	0.303058i
$952$	5.89657	+	14.3017i	0.191109	+	0.463521i
$953$	3.31494	+	5.74164i	0.107381	+	0.185990i	0.914709	−	0.404114i	$-0.132420\pi$
$953$	3.31494	+	5.74164i	0.107381	+	0.185990i	−0.807327	+	0.590104i	$0.799087\pi$
$954$	−10.9197	+	6.30447i	−0.353537	+	0.204115i
$955$		−	17.5632i		−	0.568332i
$956$		−	65.9319i		−	2.13239i
$957$	−15.1818	+	8.76524i	−0.490759	+	0.283340i
$958$	37.0220	+	64.1241i	1.19613	+	2.07175i
$959$	15.7767	+	38.2652i	0.509456	+	1.23565i
$960$	9.06353	+	5.23283i	0.292524	+	0.168889i
$961$	−9.76571	−	16.9147i	−0.315023	−	0.545635i
$962$	65.1894	+	42.7140i	2.10179	+	1.37715i
$963$	4.89324	−	8.47534i	0.157683	−	0.273114i
$964$		−	4.66784i		−	0.150341i
$965$	0.0204853	−	0.0354816i	0.000659445	−	0.00114219i
$966$	−17.7655	+	23.0742i	−0.571596	+	0.742401i
$967$		−	47.9993i		−	1.54355i	−0.635893	−	0.771777i	$-0.719368\pi$
$967$		−	47.9993i		−	1.54355i	0.635893	−	0.771777i	$-0.280632\pi$
$968$	2.76809	+	1.59816i	0.0889698	+	0.0513667i
$969$			12.0689i			0.387709i
$970$	−19.8604	−	11.4664i	−0.637681	−	0.368165i
$971$	−18.9092	+	32.7516i	−0.606824	+	1.05105i	0.384936	+	0.922943i	$0.374223\pi$
$971$	−18.9092	+	32.7516i	−0.606824	+	1.05105i	−0.991760	+	0.128107i	$0.959110\pi$
$972$	1.46986	−	2.54588i	0.0471459	−	0.0816591i
$973$	47.2108	+	36.3490i	1.51351	+	1.16529i
$974$	−33.3236			−1.06776
$975$	−13.1008	−	8.58404i	−0.419562	−	0.274909i
$976$	−1.87772	+	3.25231i	−0.0601045	+	0.104104i
$977$	24.7631	−	14.2970i	0.792241	−	0.457400i	−0.0485100	−	0.998823i	$-0.515447\pi$
$977$	24.7631	−	14.2970i	0.792241	−	0.457400i	0.840751	+	0.541422i	$0.182114\pi$
$978$	−13.6664			−0.437003
$979$	−5.10992	−	8.85064i	−0.163314	−	0.282868i
$980$	4.36630	−	16.0846i	0.139476	−	0.513803i
$981$	−2.60941	+	1.50655i	−0.0833122	+	0.0481003i
$982$	78.3913	+	45.2592i	2.50157	+	1.44428i
$983$	2.49292	+	1.43929i	0.0795118	+	0.0459061i	0.539229	−	0.842159i	$-0.318716\pi$
$983$	2.49292	+	1.43929i	0.0795118	+	0.0459061i	−0.459717	+	0.888065i	$0.652049\pi$
$984$	−20.4683			−0.652506
$985$	−14.4823			−0.461443
$986$	−30.6962	−	17.7225i	−0.977566	−	0.564398i
$987$	−16.0941	−	2.14562i	−0.512281	−	0.0682957i
$988$	−20.5788	−	40.7992i	−0.654699	−	1.29800i
$989$	−14.1181	−	24.4533i	−0.448930	−	0.777569i
$990$	−4.79725	+	2.76970i	−0.152467	+	0.0880267i
$991$	−10.3905	−	17.9969i	−0.330065	−	0.571690i	0.652459	−	0.757824i	$-0.273737\pi$
$991$	−10.3905	−	17.9969i	−0.330065	−	0.571690i	−0.982524	+	0.186134i	$0.940404\pi$
$992$	11.7301	−	20.3171i	0.372430	−	0.645068i
$993$		−	22.9813i		−	0.729289i
$994$	42.1884	+	32.4820i	1.33813	+	1.03027i
$995$	−11.3412	+	6.54787i	−0.359542	+	0.207582i
$996$	−3.89255	+	2.24737i	−0.123340	+	0.0712105i
$997$	−41.1238			−1.30240			−0.651202	−	0.758904i	$-0.725735\pi$
$997$	−41.1238			−1.30240			−0.651202	+	0.758904i	$0.725735\pi$
$998$	1.21393	+	2.10259i	0.0384262	+	0.0665562i
$999$			9.72567i			0.307706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.c.4.6	✓	12
3.2	odd	2		819.2.bm.e.550.1		12
7.2	even	3		273.2.bl.c.121.6	yes	12
13.10	even	6		273.2.bl.c.88.6	yes	12
21.2	odd	6		819.2.do.f.667.1		12
39.23	odd	6		819.2.do.f.361.1		12
91.23	even	6	inner	273.2.t.c.205.1	yes	12
273.23	odd	6		819.2.bm.e.478.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.6	✓	12	1.1	even	1	trivial
273.2.t.c.205.1	yes	12	91.23	even	6	inner
273.2.bl.c.88.6	yes	12	13.10	even	6
273.2.bl.c.121.6	yes	12	7.2	even	3
819.2.bm.e.478.6		12	273.23	odd	6
819.2.bm.e.550.1		12	3.2	odd	2
819.2.do.f.361.1		12	39.23	odd	6
819.2.do.f.667.1		12	21.2	odd	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.22255i q^{2} +(-0.500000 - 0.866025i) q^{3} -2.93973 q^{4} +(-0.701414 + 0.404962i) q^{5} +(1.92478 - 1.11128i) q^{6} +(-2.44601 + 1.00849i) q^{7} -2.08860i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+2.22255i q^{2} +(-0.500000 - 0.866025i) q^{3} -2.93973 q^{4} +(-0.701414 + 0.404962i) q^{5} +(1.92478 - 1.11128i) q^{6} +(-2.44601 + 1.00849i) q^{7} -2.08860i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.900048 - 1.55893i) q^{10} +(-2.66500 + 1.53864i) q^{11} +(1.46986 + 2.54588i) q^{12} +(-3.01583 - 1.97606i) q^{13} +(-2.24141 - 5.43638i) q^{14} +(0.701414 + 0.404962i) q^{15} -1.23745 q^{16} +2.79947 q^{17} +(-1.92478 - 1.11128i) q^{18} +(-3.73356 - 2.15557i) q^{19} +(2.06197 - 1.19048i) q^{20} +(2.09638 + 1.61406i) q^{21} +(-3.41970 - 5.92310i) q^{22} +4.95229 q^{23} +(-1.80878 + 1.04430i) q^{24} +(-2.17201 + 3.76204i) q^{25} +(4.39188 - 6.70282i) q^{26} +1.00000 q^{27} +(7.19060 - 2.96468i) q^{28} +(-2.84837 + 4.93353i) q^{29} +(-0.900048 + 1.55893i) q^{30} +(2.93282 + 1.69327i) q^{31} -6.92749i q^{32} +(2.66500 + 1.53864i) q^{33} +6.22195i q^{34} +(1.30727 - 1.69791i) q^{35} +(1.46986 - 2.54588i) q^{36} +9.72567i q^{37} +(4.79087 - 8.29803i) q^{38} +(-0.203402 + 3.59981i) q^{39} +(0.845801 + 1.46497i) q^{40} +(8.48708 + 4.90002i) q^{41} +(-3.58733 + 4.65931i) q^{42} +(-2.85083 - 4.93777i) q^{43} +(7.83438 - 4.52318i) q^{44} -0.809923i q^{45} +11.0067i q^{46} +(-5.31465 + 3.06841i) q^{47} +(0.618725 + 1.07166i) q^{48} +(4.96591 - 4.93353i) q^{49} +(-8.36131 - 4.82741i) q^{50} +(-1.39973 - 2.42441i) q^{51} +(8.86571 + 5.80907i) q^{52} +(2.83659 - 4.91312i) q^{53} +2.22255i q^{54} +(1.24618 - 2.15845i) q^{55} +(2.10632 + 5.10872i) q^{56} +4.31115i q^{57} +(-10.9650 - 6.33066i) q^{58} +4.93584i q^{59} +(-2.06197 - 1.19048i) q^{60} +(1.51741 - 2.62824i) q^{61} +(-3.76337 + 6.51834i) q^{62} +(0.349630 - 2.62255i) q^{63} +12.9218 q^{64} +(2.91557 + 0.164740i) q^{65} +(-3.41970 + 5.92310i) q^{66} +(-8.59577 + 4.96277i) q^{67} -8.22967 q^{68} +(-2.47614 - 4.28881i) q^{69} +(3.77368 + 2.90547i) q^{70} +(-7.84155 + 4.52732i) q^{71} +(1.80878 + 1.04430i) q^{72} +(-2.75318 - 1.58955i) q^{73} -21.6158 q^{74} +4.34402 q^{75} +(10.9757 + 6.33680i) q^{76} +(4.96692 - 6.45114i) q^{77} +(-8.00076 - 0.452072i) q^{78} +(1.13963 + 1.97390i) q^{79} +(0.867965 - 0.501120i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.8905 + 18.8630i) q^{82} +1.52896i q^{83} +(-6.16279 - 4.74491i) q^{84} +(-1.96359 + 1.13368i) q^{85} +(10.9745 - 6.33610i) q^{86} +5.69675 q^{87} +(3.21359 + 5.56611i) q^{88} +3.32107i q^{89} +1.80010 q^{90} +(9.36956 + 1.79203i) q^{91} -14.5584 q^{92} -3.38653i q^{93} +(-6.81970 - 11.8121i) q^{94} +3.49170 q^{95} +(-5.99938 + 3.46374i) q^{96} +(11.0330 - 6.36990i) q^{97} +(10.9650 + 11.0370i) q^{98} -3.07728i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

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