LMFDB - Embedded newform 273.2.t.c.205.1

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			205.1
Root			$0.874681 - 1.11128i$ of defining polynomial
Character	$\chi$	$=$	273.205
Dual form			273.2.t.c.4.6

$q$-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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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	$-0.712257\pi$
$2$		−	2.22255i		−	1.57158i	0.618493	−	0.785790i	$-0.287743\pi$
$3$	−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	0.334891	−	0.942257i	$-0.391301\pi$
$5$	−0.701414	−	0.404962i	−0.313682	−	0.181104i	−0.648573	+	0.761153i	$0.724634\pi$
$6$	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	0.0411755	−	0.999152i	$-0.486890\pi$
$11$	−2.66500	−	1.53864i	−0.803528	−	0.463917i	−0.844703	+	0.535235i	$0.820223\pi$
$12$	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	−0.862851	−	0.505458i	$-0.831324\pi$
$19$	−3.73356	+	2.15557i	−0.856538	+	0.494522i	0.00631355	+	0.999980i	$0.497990\pi$
$20$	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	−0.999431	−	0.0337339i	$-0.989260\pi$
$29$	−2.84837	−	4.93353i	−0.528930	−	0.916133i	0.470501	−	0.882399i	$-0.344073\pi$
$30$	−0.900048	−	1.55893i	−0.164325	−	0.284620i
$31$	2.93282	−	1.69327i	0.526750	−	0.304119i	−0.212942	−	0.977065i	$-0.568304\pi$
$31$	2.93282	−	1.69327i	0.526750	−	0.304119i	0.739692	+	0.672945i	$0.234971\pi$
$32$			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	$-0.705127\pi$
$37$		−	9.72567i		−	1.59889i	0.600740	−	0.799445i	$-0.294873\pi$
$38$	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	0.340865	−	0.940112i	$-0.389280\pi$
$41$	8.48708	−	4.90002i	1.32546	−	0.765254i	0.984594	+	0.174858i	$0.0559468\pi$
$42$	−3.58733	−	4.65931i	−0.553538	−	0.718947i
$43$	−2.85083	+	4.93777i	−0.434747	+	0.753003i	−0.997275	−	0.0737747i	$-0.976495\pi$
$43$	−2.85083	+	4.93777i	−0.434747	+	0.753003i	0.562528	+	0.826778i	$0.309829\pi$
$44$	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	0.0595130	−	0.998228i	$-0.481045\pi$
$47$	−5.31465	−	3.06841i	−0.775221	−	0.447574i	−0.834734	+	0.550654i	$0.814379\pi$
$48$	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	0.992401	−	0.123050i	$-0.0392675\pi$
$53$	2.83659	+	4.91312i	0.389636	+	0.674870i	−0.602764	+	0.797919i	$0.705934\pi$
$54$		−	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	$-0.895882\pi$
$59$		−	4.93584i		−	0.642592i	0.946979	−	0.321296i	$-0.104118\pi$
$60$	−2.06197	+	1.19048i	−0.266199	+	0.153690i
$61$	1.51741	+	2.62824i	0.194285	+	0.336511i	0.946666	−	0.322217i	$-0.104428\pi$
$61$	1.51741	+	2.62824i	0.194285	+	0.336511i	−0.752381	+	0.658728i	$0.771095\pi$
$62$	−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	−0.127452	−	0.991845i	$-0.540680\pi$
$67$	−8.59577	−	4.96277i	−1.05014	−	0.606299i	−0.922689	+	0.385546i	$0.874013\pi$
$68$	−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	−0.0436133	−	0.999048i	$-0.513887\pi$
$71$	−7.84155	−	4.52732i	−0.930621	−	0.537294i	−0.887008	+	0.461754i	$0.847220\pi$
$72$	1.80878	−	1.04430i	0.213166	−	0.123072i
$73$	−2.75318	+	1.58955i	−0.322235	+	0.186043i	−0.652388	−	0.757885i	$-0.726233\pi$
$73$	−2.75318	+	1.58955i	−0.322235	+	0.186043i	0.330153	+	0.943927i	$0.392900\pi$
$74$	−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	−0.794768	−	0.606914i	$-0.792407\pi$
$79$	1.13963	−	1.97390i	0.128219	−	0.222082i	0.922987	+	0.384832i	$0.125741\pi$
$80$	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	$-0.973258\pi$
$83$		−	1.52896i		−	0.167825i	0.996473	−	0.0839126i	$-0.0267417\pi$
$84$	−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	$-0.943679\pi$
$89$		−	3.32107i		−	0.352032i	0.984387	−	0.176016i	$-0.0563211\pi$
$90$	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	0.941460	−	0.337125i	$-0.109454\pi$
$97$	11.0330	+	6.36990i	1.12023	+	0.646766i	0.178771	+	0.983891i	$0.442788\pi$
$98$	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	−0.190365	−	0.981713i	$-0.560967\pi$
$101$	7.58772	−	13.1423i	0.755006	−	1.30771i	0.945371	−	0.325996i	$-0.105700\pi$
$102$	5.38837	+	3.11098i	0.533528	+	0.308033i
$103$	−4.00749	+	6.94118i	−0.394870	+	0.683935i	−0.993085	−	0.117401i	$-0.962544\pi$
$103$	−4.00749	+	6.94118i	−0.394870	+	0.683935i	0.598214	+	0.801336i	$0.295877\pi$
$104$	−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	−0.369799	−	0.929112i	$-0.620573\pi$
$109$	2.60941	−	1.50655i	0.249937	−	0.144301i	0.619735	+	0.784811i	$0.287240\pi$
$110$	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	−0.923199	−	0.384323i	$-0.874435\pi$
$113$	−1.36880	+	2.37084i	−0.128766	+	0.223030i	0.794433	+	0.607352i	$0.207768\pi$
$114$	−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	0.981588	+	0.191010i	$0.0611763\pi$
$127$	7.39515	+	12.8088i	0.656214	+	1.13660i	−0.325374	+	0.945585i	$0.605490\pi$
$128$		−	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	−0.911842	−	0.410540i	$-0.865340\pi$
$131$	−1.14893	+	1.99001i	−0.100383	+	0.173868i	0.811460	+	0.584408i	$0.198673\pi$
$132$	−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	$0.232968\pi$
$137$			15.6440i			1.33655i	−0.743913	+	0.668276i	$0.767032\pi$
$138$	9.53209	+	5.50335i	0.811425	+	0.468477i
$139$	−11.2601	+	19.5030i	−0.955068	+	1.65423i	−0.220855	+	0.975307i	$0.570885\pi$
$139$	−11.2601	+	19.5030i	−0.955068	+	1.65423i	−0.734213	+	0.678919i	$0.762449\pi$
$140$	−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	0.0650716	−	0.997881i	$-0.479272\pi$
$149$	11.7402	−	6.77823i	0.961797	−	0.555294i	0.896726	+	0.442587i	$0.145939\pi$
$150$		−	9.65481i		−	0.788312i
$151$	7.26064	−	4.19193i	0.590863	−	0.341135i	−0.174576	−	0.984644i	$-0.555855\pi$
$151$	7.26064	−	4.19193i	0.590863	−	0.341135i	0.765439	+	0.643509i	$0.222522\pi$
$152$	−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	0.798077	−	0.602556i	$-0.205851\pi$
$157$	−1.53856	−	2.66486i	−0.122790	−	0.212679i	−0.920867	+	0.389877i	$0.872518\pi$
$158$	−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	−0.693835	−	0.720134i	$-0.744080\pi$
$163$	−5.32516	+	3.07448i	−0.417099	+	0.240812i	0.276736	+	0.960946i	$0.410747\pi$
$164$	−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	−0.924235	−	0.381825i	$-0.875296\pi$
$167$	−13.6424	+	7.87645i	−1.05568	+	0.609498i	−0.131447	+	0.991323i	$0.541962\pi$
$168$	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	−0.989488	−	0.144614i	$-0.953806\pi$
$173$	−8.15461	−	14.1242i	−0.619983	−	1.07384i	0.369505	−	0.929229i	$-0.379527\pi$
$174$		−	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	−0.180617	−	0.983553i	$-0.557810\pi$
$179$	10.1878	−	17.6458i	0.761473	−	1.31891i	0.942091	−	0.335357i	$-0.108857\pi$
$180$		−	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	−0.929276	−	0.369386i	$-0.879568\pi$
$191$	−10.8425	−	18.7798i	−0.784536	−	1.35886i	0.144740	−	0.989470i	$-0.453765\pi$
$192$	−6.46089	+	11.1906i	−0.466275	+	0.807612i
$193$	−0.0438086	−	0.0252929i	−0.00315341	−	0.00182062i	0.498422	−	0.866934i	$-0.333913\pi$
$193$	−0.0438086	−	0.0252929i	−0.00315341	−	0.00182062i	−0.501576	+	0.865114i	$0.667246\pi$
$194$	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	0.166207	−	0.986091i	$-0.446848\pi$
$197$	15.4854	−	8.94051i	1.10329	−	0.636985i	0.937083	+	0.349106i	$0.113515\pi$
$198$	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	0.758435	−	0.651748i	$-0.225964\pi$
$211$	−2.69037	−	4.65986i	−0.185213	−	0.320798i	−0.943648	+	0.330950i	$0.892631\pi$
$212$	−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	−0.927663	−	0.373418i	$-0.878186\pi$
$223$	−15.9502	+	9.20887i	−1.06811	+	0.616671i	−0.140443	+	0.990089i	$0.544853\pi$
$224$	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	$0.279279\pi$
$227$			23.1743i			1.53813i	−0.639168	+	0.769067i	$0.720721\pi$
$228$			12.6736i			0.839330i
$229$	−23.0419	−	13.3032i	−1.52265	−	0.879103i	−0.999641	−	0.0267760i	$-0.991476\pi$
$229$	−23.0419	−	13.3032i	−1.52265	−	0.879103i	−0.523009	−	0.852327i	$-0.675191\pi$
$230$	−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	0.246358	+	0.969179i	$0.420766\pi$
$233$	−10.9316	+	18.9341i	−0.716155	+	1.24042i	−0.962512	+	0.271238i	$0.912567\pi$
$234$	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	$-0.741669\pi$
$239$		−	22.4279i		−	1.45074i	0.688360	−	0.725370i	$-0.258331\pi$
$240$	−0.867965	+	0.501120i	−0.0560269	+	0.0323472i
$241$		−	1.58785i		−	0.102282i	−0.998691	−	0.0511411i	$-0.983714\pi$
$241$		−	1.58785i		−	0.102282i	0.998691	−	0.0511411i	$-0.0162858\pi$
$242$	−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	−0.860362	−	0.509684i	$-0.829762\pi$
$251$	0.177730	−	0.307837i	0.0112182	−	0.0194305i	0.871580	+	0.490253i	$0.163096\pi$
$252$	−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	−0.325673	−	0.945482i	$-0.605591\pi$
$263$	10.6381	−	18.4258i	0.655975	−	1.13618i	0.981648	−	0.190700i	$-0.0610758\pi$
$264$	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	$0.291263\pi$
$271$			26.0950i			1.58516i	−0.609767	+	0.792581i	$0.708737\pi$
$272$	−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	$0.00910643\pi$
$281$			0.959007i			0.0572096i	−0.999591	+	0.0286048i	$0.990894\pi$
$282$	−6.81970	−	11.8121i	−0.406107	−	0.703398i
$283$	1.12986	−	1.95698i	0.0671635	−	0.116331i	−0.830488	−	0.557036i	$-0.811938\pi$
$283$	1.12986	−	1.95698i	0.0671635	−	0.116331i	0.897652	+	0.440706i	$0.145272\pi$
$284$	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	0.629538	−	0.776970i	$-0.283244\pi$
$293$	4.64615	+	2.68246i	0.271431	+	0.156711i	−0.358107	+	0.933681i	$0.616578\pi$
$294$	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	$-0.983618\pi$
$307$		−	1.80266i		−	0.102883i	0.998676	−	0.0514415i	$-0.0163816\pi$
$308$	−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	−0.997978	−	0.0635652i	$-0.979753\pi$
$311$	−9.77057	−	16.9231i	−0.554038	−	0.959622i	0.443940	−	0.896057i	$-0.353580\pi$
$312$	7.51855	−	0.424826i	0.425654	−	0.0240510i
$313$	15.4409	−	26.7444i	0.872770	−	1.51168i	0.0136500	−	0.999907i	$-0.495655\pi$
$313$	15.4409	−	26.7444i	0.872770	−	1.51168i	0.859120	−	0.511775i	$-0.171012\pi$
$314$	−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	−0.0290082	−	0.999579i	$-0.509235\pi$
$317$	−16.1874	−	9.34578i	−0.909173	−	0.524911i	−0.880165	+	0.474668i	$0.842568\pi$
$318$			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	0.159312	−	0.987228i	$-0.449072\pi$
$331$	19.9024	−	11.4906i	1.09393	−	0.631582i	0.934621	+	0.355646i	$0.115739\pi$
$332$			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	−0.0256163	−	0.999672i	$-0.508155\pi$
$349$	15.4556	−	8.92327i	0.827317	−	0.477652i	0.852933	+	0.522020i	$0.174821\pi$
$350$	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	0.505801	−	0.862650i	$-0.331197\pi$
$353$	0.218397	+	0.126091i	0.0116241	+	0.00671117i	−0.494177	+	0.869361i	$0.664530\pi$
$354$	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	0.204860	−	0.978791i	$-0.434326\pi$
$359$	−10.2385	−	5.91120i	−0.540368	−	0.311981i	−0.745228	+	0.666810i	$0.767659\pi$
$360$	−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	−0.619410	−	0.785068i	$-0.712628\pi$
$367$	7.09169	−	12.2832i	0.370183	−	0.641176i	0.989594	+	0.143891i	$0.0459615\pi$
$368$	−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	0.965530	−	0.260291i	$-0.0838185\pi$
$373$	4.97018	+	8.60861i	0.257346	+	0.445737i	−0.708184	+	0.706028i	$0.750485\pi$
$374$	−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	−0.282691	−	0.959211i	$-0.591227\pi$
$379$	7.91690	−	4.57083i	0.406664	−	0.234788i	0.689355	+	0.724423i	$0.257894\pi$
$380$	−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	0.126747	−	0.991935i	$-0.459546\pi$
$383$	20.5325	−	11.8544i	1.04916	−	0.605734i	0.922414	+	0.386202i	$0.126213\pi$
$384$	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	−0.999715	−	0.0238784i	$-0.992399\pi$
$389$	−10.2666	−	17.7823i	−0.520537	−	0.901596i	0.479178	−	0.877718i	$-0.340935\pi$
$390$	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	−0.950294	−	0.311355i	$-0.899217\pi$
$397$	−23.0291	+	13.2959i	−1.15580	+	0.667301i	−0.205505	+	0.978656i	$0.565884\pi$
$398$		−	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	$0.211310\pi$
$401$			24.6769i			1.23231i	−0.787627	+	0.616153i	$0.788690\pi$
$402$	−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	$-0.648167\pi$
$409$		−	36.1441i		−	1.78721i	0.448851	−	0.893607i	$-0.351833\pi$
$410$			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	0.896555	−	0.442932i	$-0.146062\pi$
$419$	1.32411	+	2.29343i	0.0646872	+	0.112042i	−0.831868	+	0.554974i	$0.812728\pi$
$420$	6.24417	−	0.832453i	0.304684	−	0.0406195i
$421$			4.51819i			0.220203i	0.993920	+	0.110102i	$0.0351176\pi$
$421$			4.51819i			0.220203i	−0.993920	+	0.110102i	$0.964882\pi$
$422$	−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	0.757710	−	0.652592i	$-0.226318\pi$
$431$	11.8626	+	6.84890i	0.571404	+	0.329900i	−0.186306	+	0.982492i	$0.559652\pi$
$432$	−1.23745			−0.0595368
$433$	−11.1388	+	19.2929i	−0.535296	+	0.927159i	0.463853	+	0.885912i	$0.346466\pi$
$433$	−11.1388	+	19.2929i	−0.535296	+	0.927159i	−0.999149	+	0.0412471i	$0.986867\pi$
$434$	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	−0.772750	−	0.634710i	$-0.781120\pi$
$443$	3.43706	−	5.95317i	0.163300	−	0.282844i	0.936050	+	0.351866i	$0.114453\pi$
$444$	−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	−0.244428	−	0.969667i	$-0.578600\pi$
$449$	−25.5631	−	14.7589i	−1.20640	−	0.696515i	−0.961971	+	0.273152i	$0.911934\pi$
$450$	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	$-0.886726\pi$
$457$		−	14.8958i		−	0.696794i	0.937347	−	0.348397i	$-0.113274\pi$
$458$	−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	0.911077	−	0.412236i	$-0.135252\pi$
$461$	21.6772	+	12.5154i	1.00961	+	0.582898i	0.0985319	+	0.995134i	$0.468585\pi$
$462$	2.39126	+	17.9367i	0.111251	+	0.834489i
$463$		−	34.2885i		−	1.59352i	−0.604295	−	0.796761i	$-0.706545\pi$
$463$		−	34.2885i		−	1.59352i	0.604295	−	0.796761i	$-0.293455\pi$
$464$	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	−0.830190	−	0.557480i	$-0.811768\pi$
$467$	1.46293	−	2.53387i	0.0676964	−	0.117254i	0.897887	+	0.440226i	$0.145102\pi$
$468$	−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	0.983449	−	0.181186i	$-0.0579936\pi$
$479$	28.8516	+	16.6575i	1.31826	+	0.761099i	0.334813	+	0.942285i	$0.391327\pi$
$480$	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	$-0.889672\pi$
$487$		−	14.9934i		−	0.679416i	0.940531	−	0.339708i	$-0.110328\pi$
$488$	−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	0.800939	+	0.598746i	$0.204334\pi$
$491$	20.3637	+	35.2709i	0.918999	+	1.59175i	0.118060	+	0.993006i	$0.462333\pi$
$492$		−	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	0.521025	−	0.853541i	$-0.325550\pi$
$499$	0.946024	+	0.546187i	0.0423498	+	0.0244507i	−0.478676	+	0.877992i	$0.658883\pi$
$500$		−	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	−0.0995283	−	0.995035i	$-0.531733\pi$
$503$	18.2104	−	31.5413i	0.811961	−	1.40636i	0.911489	−	0.411323i	$-0.134933\pi$
$504$	−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	$0.0565881\pi$
$509$			7.97946i			0.353684i	−0.984239	+	0.176842i	$0.943412\pi$
$510$	−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	0.792014	−	0.610503i	$-0.209033\pi$
$521$	−3.02902	−	5.24643i	−0.132704	−	0.229850i	−0.924718	+	0.380653i	$0.875699\pi$
$522$	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	0.881616	−	0.471968i	$-0.156456\pi$
$541$	21.2518	+	12.2697i	0.913687	+	0.527517i	0.0320714	+	0.999486i	$0.489790\pi$
$542$	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	0.104135	−	0.994563i	$-0.466793\pi$
$557$	−16.6413	−	9.60786i	−0.705115	−	0.407098i	−0.809250	+	0.587465i	$0.800126\pi$
$558$	−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	0.899383	−	0.437161i	$-0.144016\pi$
$571$	1.69895	+	2.94266i	0.0710987	+	0.123147i	−0.828284	+	0.560308i	$0.810683\pi$
$572$	−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	−0.641352	−	0.767247i	$-0.721626\pi$
$577$	−7.14796	+	4.12687i	−0.297573	+	0.171804i	0.343779	+	0.939051i	$0.388293\pi$
$578$			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	−0.865014	−	0.501748i	$-0.832690\pi$
$587$	−20.9087	+	12.0716i	−0.862994	+	0.498250i	0.00201975	+	0.999998i	$0.499357\pi$
$588$	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	0.343874	−	0.939016i	$-0.388261\pi$
$593$	−7.24219	−	4.18128i	−0.297401	−	0.171705i	−0.641275	+	0.767311i	$0.721594\pi$
$594$	−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	0.765799	−	0.643080i	$-0.222344\pi$
$599$	−4.25916	−	7.37709i	−0.174025	−	0.301420i	−0.939823	+	0.341661i	$0.889011\pi$
$600$			9.07291i			0.370400i
$601$	0.714622	+	1.23776i	0.0291500	+	0.0504894i	0.880232	−	0.474543i	$-0.157387\pi$
$601$	0.714622	+	1.23776i	0.0291500	+	0.0504894i	−0.851082	+	0.525032i	$0.824053\pi$
$602$	−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	0.672225	−	0.740347i	$-0.265339\pi$
$607$	−7.51555	−	13.0173i	−0.305047	−	0.528357i	−0.977272	+	0.211990i	$0.932005\pi$
$608$	−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	0.153005	−	0.988225i	$-0.451105\pi$
$613$	−15.5070	−	8.95295i	−0.626320	−	0.361606i	−0.779326	+	0.626619i	$0.784438\pi$
$614$	−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	0.991966	−	0.126509i	$-0.0403771\pi$
$617$	34.2385	+	19.7676i	1.37839	+	0.795813i	0.386423	+	0.922322i	$0.373710\pi$
$618$	−15.4271	+	8.90686i	−0.620570	+	0.358286i
$619$	−23.1290	+	13.3535i	−0.929634	+	0.536724i	−0.886696	−	0.462354i	$-0.847005\pi$
$619$	−23.1290	+	13.3535i	−0.929634	+	0.536724i	−0.0429379	+	0.999078i	$0.513672\pi$
$620$	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	0.781000	−	0.624531i	$-0.214710\pi$
$631$	15.8415	+	9.14610i	0.630640	+	0.364100i	−0.150360	+	0.988631i	$0.548043\pi$
$632$	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	0.672436	−	0.740156i	$-0.265248\pi$
$643$	9.32291	+	5.38258i	0.367660	+	0.212268i	−0.304776	+	0.952424i	$0.598582\pi$
$644$	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	−0.799525	−	0.600633i	$-0.794915\pi$
$647$	3.06254	−	5.30447i	0.120401	−	0.208540i	0.919926	+	0.392093i	$0.128249\pi$
$648$	−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	−0.979973	−	0.199128i	$-0.936189\pi$
$659$	−8.15148	+	14.1188i	−0.317537	+	0.549989i	0.662437	+	0.749118i	$0.269522\pi$
$660$	7.32686			0.285198
$661$	−41.6539	−	24.0489i	−1.62015	−	0.935394i	−0.986879	−	0.161464i	$-0.948378\pi$
$661$	−41.6539	−	24.0489i	−1.62015	−	0.935394i	−0.633271	−	0.773930i	$-0.718288\pi$
$662$	−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	−0.881760	−	0.471698i	$-0.843641\pi$
$673$	−22.0349	−	38.1655i	−0.849382	−	1.47117i	0.0323778	−	0.999476i	$-0.489692\pi$
$674$		−	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	−0.919246	−	0.393683i	$-0.871201\pi$
$677$	−3.08805	+	5.34866i	−0.118684	+	0.205566i	0.800563	+	0.599249i	$0.204534\pi$
$678$	−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	$-0.912422\pi$
$683$		−	14.2002i		−	0.543354i	0.962389	−	0.271677i	$-0.0875782\pi$
$684$	−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	$0.00235591\pi$
$691$			0.389112i			0.0148025i	−0.999973	+	0.00740126i	$0.997644\pi$
$692$	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	0.362965	−	0.931803i	$-0.381765\pi$
$709$	35.9841	−	20.7754i	1.35141	−	0.780238i	0.988447	+	0.151565i	$0.0484312\pi$
$710$	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	−0.947141	−	0.320818i	$-0.896042\pi$
$719$	−20.1484	−	34.8980i	−0.751407	−	1.30147i	0.195734	−	0.980657i	$-0.437291\pi$
$720$		−	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	0.722220	−	0.691664i	$-0.243122\pi$
$733$	13.1128	+	7.57067i	0.484332	+	0.279629i	−0.237888	+	0.971293i	$0.576455\pi$
$734$	−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	0.0729037	−	0.997339i	$-0.476773\pi$
$739$	−20.5071	−	11.8398i	−0.754365	−	0.435533i	−0.827269	+	0.561806i	$0.810107\pi$
$740$	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	0.399370	−	0.916790i	$-0.369229\pi$
$743$	37.9709	−	21.9225i	1.39302	−	0.804260i	0.993648	+	0.112530i	$0.0358954\pi$
$744$	−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	0.676101	−	0.736809i	$-0.263668\pi$
$757$	−8.25531	−	14.2986i	−0.300044	−	0.519692i	−0.976146	+	0.217117i	$0.930335\pi$
$758$	−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	−0.783797	−	0.621017i	$-0.786720\pi$
$761$	−17.5967	+	10.1595i	−0.637880	+	0.368280i	0.145917	+	0.989297i	$0.453387\pi$
$762$			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	−0.924837	−	0.380364i	$-0.875799\pi$
$769$	−29.3351	+	16.9366i	−1.05785	+	0.610750i	−0.133013	+	0.991114i	$0.542465\pi$
$770$	−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	$0.0782715\pi$
$773$			13.5359i			0.486853i	−0.969919	+	0.243426i	$0.921729\pi$
$774$		−	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	$0.304215\pi$
$787$			45.8242i			1.63346i	−0.577022	+	0.816729i	$0.695785\pi$
$788$	−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	−0.938313	−	0.345786i	$-0.887612\pi$
$797$	−4.79076	+	8.29783i	−0.169697	+	0.293924i	0.768616	+	0.639710i	$0.220946\pi$
$798$	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	−0.0238512	+	0.999716i	$0.507593\pi$
$809$	−24.9645	+	43.2398i	−0.877705	+	1.52023i	−0.853853	+	0.520514i	$0.825741\pi$
$810$	−0.900048	−	1.55893i	−0.0316245	−	0.0547752i
$811$		−	12.4298i		−	0.436470i	−0.975896	−	0.218235i	$-0.929970\pi$
$811$		−	12.4298i		−	0.436470i	0.975896	−	0.218235i	$-0.0700299\pi$
$812$	−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	$0.141588\pi$
$821$			24.6582i			0.860576i	−0.902692	+	0.430288i	$0.858412\pi$
$822$	−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	$0.0293646\pi$
$827$			5.29835i			0.184242i	−0.995748	+	0.0921208i	$0.970635\pi$
$828$	7.27919	+	12.6079i	0.252969	+	0.438156i
$829$	7.56579	−	13.1043i	0.262771	−	0.455133i	−0.704206	−	0.709995i	$-0.748697\pi$
$829$	7.56579	−	13.1043i	0.262771	−	0.455133i	0.966977	+	0.254863i	$0.0820303\pi$
$830$	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	−0.147000	−	0.989136i	$-0.546962\pi$
$839$	−31.1992	−	18.0129i	−1.07712	−	0.621874i	−0.930117	+	0.367262i	$0.880295\pi$
$840$	−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	$0.184712\pi$
$853$			32.0255i			1.09653i	−0.836304	+	0.548266i	$0.815288\pi$
$854$	−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	0.928756	−	0.370693i	$-0.120880\pi$
$857$	4.19647	+	7.26850i	0.143349	+	0.248287i	−0.785407	+	0.618980i	$0.787546\pi$
$858$	22.0176	+	11.1055i	0.751668	+	0.379136i
$859$	8.88475	−	15.3888i	0.303144	−	0.525060i	−0.673703	−	0.739003i	$-0.735297\pi$
$859$	8.88475	−	15.3888i	0.303144	−	0.525060i	0.976846	+	0.213942i	$0.0686304\pi$
$860$	−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	0.519470	−	0.854489i	$-0.326129\pi$
$863$	1.15148	+	0.664805i	0.0391967	+	0.0226302i	−0.480274	+	0.877119i	$0.659463\pi$
$864$			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	−0.551396	+	0.834244i	$0.685905\pi$
$877$	−45.8893	+	26.4942i	−1.54957	+	0.894645i	−0.998174	+	0.0604010i	$0.980762\pi$
$878$		−	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	−0.989951	−	0.141408i	$-0.954837\pi$
$881$	−18.3266	−	31.7426i	−0.617439	−	1.06944i	0.372512	−	0.928027i	$-0.378496\pi$
$882$	−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	0.0852307	+	0.996361i	$0.472837\pi$
$907$	−24.7033	+	42.7873i	−0.820259	+	1.42073i	−0.905489	+	0.424369i	$0.860496\pi$
$908$		−	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	−0.995692	−	0.0927197i	$-0.970444\pi$
$919$	−17.5264	−	30.3567i	−0.578144	−	1.00137i	0.417549	−	0.908655i	$-0.362889\pi$
$920$	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	−0.551627	+	0.834091i	$0.685993\pi$
$929$	−47.2367	+	27.2721i	−1.54978	+	0.894768i	−0.998157	+	0.0606776i	$0.980674\pi$
$930$	−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	−0.802659	−	0.596438i	$-0.796582\pi$
$941$	−21.0883	+	12.1753i	−0.687459	+	0.396905i	0.115201	+	0.993342i	$0.463249\pi$
$942$		−	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	$-0.868719\pi$
$947$		−	24.6702i		−	0.801675i	0.916149	−	0.400838i	$-0.131281\pi$
$948$	−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	−0.807327	−	0.590104i	$-0.799087\pi$
$953$	3.31494	−	5.74164i	0.107381	−	0.185990i	0.914709	+	0.404114i	$0.132420\pi$
$954$	−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	$0.280632\pi$
$967$			47.9993i			1.54355i	−0.635893	+	0.771777i	$0.719368\pi$
$968$	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	−0.991760	−	0.128107i	$-0.959110\pi$
$971$	−18.9092	−	32.7516i	−0.606824	−	1.05105i	0.384936	−	0.922943i	$-0.374223\pi$
$972$	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	0.840751	−	0.541422i	$-0.182114\pi$
$977$	24.7631	+	14.2970i	0.792241	+	0.457400i	−0.0485100	+	0.998823i	$0.515447\pi$
$978$	−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	−0.459717	−	0.888065i	$-0.652049\pi$
$983$	2.49292	−	1.43929i	0.0795118	−	0.0459061i	0.539229	+	0.842159i	$0.318716\pi$
$984$	−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	−0.982524	−	0.186134i	$-0.940404\pi$
$991$	−10.3905	+	17.9969i	−0.330065	+	0.571690i	0.652459	+	0.757824i	$0.273737\pi$
$992$	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.205.1	yes	12
3.2	odd	2		819.2.bm.e.478.6		12
7.4	even	3		273.2.bl.c.88.6	yes	12
13.4	even	6		273.2.bl.c.121.6	yes	12
21.11	odd	6		819.2.do.f.361.1		12
39.17	odd	6		819.2.do.f.667.1		12
91.4	even	6	inner	273.2.t.c.4.6	✓	12
273.95	odd	6		819.2.bm.e.550.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.6	✓	12	91.4	even	6	inner
273.2.t.c.205.1	yes	12	1.1	even	1	trivial
273.2.bl.c.88.6	yes	12	7.4	even	3
273.2.bl.c.121.6	yes	12	13.4	even	6
819.2.bm.e.478.6		12	3.2	odd	2
819.2.bm.e.550.1		12	273.95	odd	6
819.2.do.f.361.1		12	21.11	odd	6
819.2.do.f.667.1		12	39.17	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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