LMFDB - Embedded newform 273.2.k.d.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(22,273)]

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, 0, 4]))

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

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

chi := DirichletCharacter("273.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.771147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 6x^{3} + 15x^{2} + 4x + 1 $ x^6 - x^5 + 5x^4 + 6x^3 + 15x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$-0.688601 - 1.19269i$ of defining polynomial
Character	$\chi$	$=$	273.211
Dual form			273.2.k.d.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.636945 + 1.10322i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.188601 - 0.326667i) q^{4} +1.10331 q^{5} +(-0.636945 + 1.10322i) q^{6} +(0.500000 - 0.866025i) q^{7} +3.02830 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.636945 + 1.10322i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.188601 - 0.326667i) q^{4} +1.10331 q^{5} +(-0.636945 + 1.10322i) q^{6} +(0.500000 - 0.866025i) q^{7} +3.02830 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.702750 + 1.21720i) q^{10} +(0.174453 + 0.302162i) q^{11} +0.377203 q^{12} +(-3.47664 - 0.955496i) q^{13} +1.27389 q^{14} +(0.551656 + 0.955496i) q^{15} +(1.55166 + 2.68755i) q^{16} +(-0.363055 + 0.628829i) q^{17} -1.27389 q^{18} +(-1.15109 + 1.99375i) q^{19} +(0.208086 - 0.360416i) q^{20} +1.00000 q^{21} +(-0.222234 + 0.384921i) q^{22} +(-0.0375080 - 0.0649658i) q^{23} +(1.51415 + 2.62258i) q^{24} -3.78270 q^{25} +(-1.16031 - 4.44410i) q^{26} -1.00000 q^{27} +(-0.188601 - 0.326667i) q^{28} +(-0.240258 - 0.416138i) q^{29} +(-0.702750 + 1.21720i) q^{30} -6.85772 q^{31} +(1.05166 - 1.82152i) q^{32} +(-0.174453 + 0.302162i) q^{33} -0.924984 q^{34} +(0.551656 - 0.955496i) q^{35} +(0.188601 + 0.326667i) q^{36} +(0.551656 + 0.955496i) q^{37} -2.93273 q^{38} +(-0.910836 - 3.48861i) q^{39} +3.34116 q^{40} +(-1.54778 - 2.68084i) q^{41} +(0.636945 + 1.10322i) q^{42} +(2.31140 - 4.00346i) q^{43} +0.131609 q^{44} +(-0.551656 + 0.955496i) q^{45} +(0.0477811 - 0.0827593i) q^{46} +4.70769 q^{47} +(-1.55166 + 2.68755i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.40937 - 4.17316i) q^{50} -0.726109 q^{51} +(-0.967829 + 0.955496i) q^{52} +5.54778 q^{53} +(-0.636945 - 1.10322i) q^{54} +(0.192476 + 0.333379i) q^{55} +(1.51415 - 2.62258i) q^{56} -2.30219 q^{57} +(0.306062 - 0.530115i) q^{58} +(1.96249 - 3.39914i) q^{59} +0.416173 q^{60} +(-2.77389 + 4.80452i) q^{61} +(-4.36799 - 7.56558i) q^{62} +(0.500000 + 0.866025i) q^{63} +8.88601 q^{64} +(-3.83582 - 1.05421i) q^{65} -0.444469 q^{66} +(-4.06193 - 7.03547i) q^{67} +(0.136945 + 0.237196i) q^{68} +(0.0375080 - 0.0649658i) q^{69} +1.40550 q^{70} +(4.76468 - 8.25267i) q^{71} +(-1.51415 + 2.62258i) q^{72} -10.4338 q^{73} +(-0.702750 + 1.21720i) q^{74} +(-1.89135 - 3.27592i) q^{75} +(0.434196 + 0.752049i) q^{76} +0.348907 q^{77} +(3.26855 - 3.22691i) q^{78} +17.1054 q^{79} +(1.71196 + 2.96520i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.97170 - 3.41509i) q^{82} -11.9143 q^{83} +(0.188601 - 0.326667i) q^{84} +(-0.400563 + 0.693795i) q^{85} +5.88894 q^{86} +(0.240258 - 0.416138i) q^{87} +(0.528296 + 0.915036i) q^{88} +(5.98052 + 10.3586i) q^{89} -1.40550 q^{90} +(-2.56580 + 2.53311i) q^{91} -0.0282963 q^{92} +(-3.42886 - 5.93896i) q^{93} +(2.99854 + 5.19362i) q^{94} +(-1.27002 + 2.19973i) q^{95} +2.10331 q^{96} +(-5.05166 + 8.74973i) q^{97} +(0.636945 - 1.10322i) q^{98} -0.348907 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} - 13 q^{10} + 8 q^{11} - 8 q^{12} + 4 q^{14} + 6 q^{16} - 4 q^{17} - 4 q^{18} + 7 q^{19} + 13 q^{20} + 6 q^{21} - q^{22} - 9 q^{23} - 3 q^{24} + 22 q^{25} - 26 q^{26} - 6 q^{27} + 4 q^{28} + 7 q^{29} + 13 q^{30} - 14 q^{31} + 3 q^{32} - 8 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{38} + 26 q^{40} - 2 q^{41} + 2 q^{42} + 19 q^{43} - 30 q^{44} - 7 q^{46} - 34 q^{47} - 6 q^{48} - 3 q^{49} + 16 q^{50} - 8 q^{51} - 26 q^{52} + 26 q^{53} - 2 q^{54} - 3 q^{56} + 14 q^{57} - 22 q^{58} + 3 q^{59} + 26 q^{60} - 13 q^{61} + 17 q^{62} + 3 q^{63} + 2 q^{64} - 2 q^{66} - 5 q^{67} - q^{68} + 9 q^{69} - 26 q^{70} - 8 q^{71} + 3 q^{72} - 4 q^{73} + 13 q^{74} + 11 q^{75} + 18 q^{76} + 16 q^{77} - 13 q^{78} - 2 q^{79} + 26 q^{80} - 3 q^{81} + 36 q^{82} + 4 q^{83} - 4 q^{84} - 13 q^{85} + 34 q^{86} - 7 q^{87} - 21 q^{88} + 19 q^{89} + 26 q^{90} + 24 q^{92} - 7 q^{93} - 7 q^{94} + 6 q^{96} - 27 q^{97} + 2 q^{98} - 16 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 - 13 * q^10 + 8 * q^11 - 8 * q^12 + 4 * q^14 + 6 * q^16 - 4 * q^17 - 4 * q^18 + 7 * q^19 + 13 * q^20 + 6 * q^21 - q^22 - 9 * q^23 - 3 * q^24 + 22 * q^25 - 26 * q^26 - 6 * q^27 + 4 * q^28 + 7 * q^29 + 13 * q^30 - 14 * q^31 + 3 * q^32 - 8 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^38 + 26 * q^40 - 2 * q^41 + 2 * q^42 + 19 * q^43 - 30 * q^44 - 7 * q^46 - 34 * q^47 - 6 * q^48 - 3 * q^49 + 16 * q^50 - 8 * q^51 - 26 * q^52 + 26 * q^53 - 2 * q^54 - 3 * q^56 + 14 * q^57 - 22 * q^58 + 3 * q^59 + 26 * q^60 - 13 * q^61 + 17 * q^62 + 3 * q^63 + 2 * q^64 - 2 * q^66 - 5 * q^67 - q^68 + 9 * q^69 - 26 * q^70 - 8 * q^71 + 3 * q^72 - 4 * q^73 + 13 * q^74 + 11 * q^75 + 18 * q^76 + 16 * q^77 - 13 * q^78 - 2 * q^79 + 26 * q^80 - 3 * q^81 + 36 * q^82 + 4 * q^83 - 4 * q^84 - 13 * q^85 + 34 * q^86 - 7 * q^87 - 21 * q^88 + 19 * q^89 + 26 * q^90 + 24 * q^92 - 7 * q^93 - 7 * q^94 + 6 * q^96 - 27 * q^97 + 2 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.636945	+	1.10322i	0.450388	+	0.780095i	0.998410	−	0.0563687i	$-0.0179522\pi$
$2$	0.636945	+	1.10322i	0.450388	+	0.780095i	−0.548022	+	0.836464i	$0.684619\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.188601	−	0.326667i	0.0943007	−	0.163334i
$5$	1.10331			0.493416			0.246708	−	0.969090i	$-0.420651\pi$
$5$	1.10331			0.493416			0.246708	+	0.969090i	$0.420651\pi$
$6$	−0.636945	+	1.10322i	−0.260032	+	0.450388i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	3.02830			1.07066
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.702750	+	1.21720i	0.222229	+	0.384912i
$11$	0.174453	+	0.302162i	0.0525996	+	0.0911053i	0.891126	−	0.453755i	$-0.149916\pi$
$11$	0.174453	+	0.302162i	0.0525996	+	0.0911053i	−0.838527	+	0.544860i	$0.816583\pi$
$12$	0.377203			0.108889
$13$	−3.47664	−	0.955496i	−0.964246	−	0.265007i
$13$	−3.47664	−	0.955496i	−0.964246	−	0.265007i
$14$	1.27389			0.340462
$15$	0.551656	+	0.955496i	0.142437	+	0.246708i
$16$	1.55166	+	2.68755i	0.387914	+	0.671887i
$17$	−0.363055	+	0.628829i	−0.0880537	+	0.152513i	−0.906688	−	0.421801i	$-0.861398\pi$
$17$	−0.363055	+	0.628829i	−0.0880537	+	0.152513i	0.818635	+	0.574315i	$0.194731\pi$
$18$	−1.27389			−0.300259
$19$	−1.15109	+	1.99375i	−0.264079	+	0.457398i	−0.967322	−	0.253551i	$-0.918401\pi$
$19$	−1.15109	+	1.99375i	−0.264079	+	0.457398i	0.703243	+	0.710950i	$0.251735\pi$
$20$	0.208086	−	0.360416i	0.0465295	−	0.0805915i
$21$	1.00000			0.218218
$22$	−0.222234	+	0.384921i	−0.0473805	+	0.0820655i
$23$	−0.0375080	−	0.0649658i	−0.00782096	−	0.0135463i	0.862088	−	0.506758i	$-0.169156\pi$
$23$	−0.0375080	−	0.0649658i	−0.00782096	−	0.0135463i	−0.869909	+	0.493212i	$0.835823\pi$
$24$	1.51415	+	2.62258i	0.309074	+	0.535332i
$25$	−3.78270			−0.756540
$26$	−1.16031	−	4.44410i	−0.227555	−	0.871560i
$27$	−1.00000			−0.192450
$28$	−0.188601	−	0.326667i	−0.0356423	−	0.0617343i
$29$	−0.240258	−	0.416138i	−0.0446147	−	0.0772749i	0.842856	−	0.538140i	$-0.180873\pi$
$29$	−0.240258	−	0.416138i	−0.0446147	−	0.0772749i	−0.887470	+	0.460865i	$0.847539\pi$
$30$	−0.702750	+	1.21720i	−0.128304	+	0.222229i
$31$	−6.85772			−1.23168			−0.615841	−	0.787870i	$-0.711184\pi$
$31$	−6.85772			−1.23168			−0.615841	+	0.787870i	$0.711184\pi$
$32$	1.05166	−	1.82152i	0.185908	−	0.322003i
$33$	−0.174453	+	0.302162i	−0.0303684	+	0.0525996i
$34$	−0.924984			−0.158633
$35$	0.551656	−	0.955496i	0.0932469	−	0.161508i
$36$	0.188601	+	0.326667i	0.0314336	+	0.0544445i
$37$	0.551656	+	0.955496i	0.0906917	+	0.157083i	0.907802	−	0.419398i	$-0.137759\pi$
$37$	0.551656	+	0.955496i	0.0906917	+	0.157083i	−0.817111	+	0.576481i	$0.804426\pi$
$38$	−2.93273			−0.475752
$39$	−0.910836	−	3.48861i	−0.145850	−	0.558624i
$40$	3.34116			0.528283
$41$	−1.54778	−	2.68084i	−0.241723	−	0.418676i	0.719482	−	0.694511i	$-0.244379\pi$
$41$	−1.54778	−	2.68084i	−0.241723	−	0.418676i	−0.961205	+	0.275835i	$0.911046\pi$
$42$	0.636945	+	1.10322i	0.0982828	+	0.170231i
$43$	2.31140	−	4.00346i	0.352485	−	0.610522i	−0.634199	−	0.773170i	$-0.718670\pi$
$43$	2.31140	−	4.00346i	0.352485	−	0.610522i	0.986684	+	0.162648i	$0.0520034\pi$
$44$	0.131609			0.0198407
$45$	−0.551656	+	0.955496i	−0.0822360	+	0.142437i
$46$	0.0477811	−	0.0827593i	0.00704494	−	0.0122022i
$47$	4.70769			0.686687			0.343343	−	0.939210i	$-0.388441\pi$
$47$	4.70769			0.686687			0.343343	+	0.939210i	$0.388441\pi$
$48$	−1.55166	+	2.68755i	−0.223962	+	0.387914i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.40937	−	4.17316i	−0.340737	−	0.590174i
$51$	−0.726109			−0.101676
$52$	−0.967829	+	0.955496i	−0.134214	+	0.132504i
$53$	5.54778			0.762046			0.381023	−	0.924565i	$-0.375572\pi$
$53$	5.54778			0.762046			0.381023	+	0.924565i	$0.375572\pi$
$54$	−0.636945	−	1.10322i	−0.0866773	−	0.150129i
$55$	0.192476	+	0.333379i	0.0259535	+	0.0449528i
$56$	1.51415	−	2.62258i	0.202337	−	0.350457i
$57$	−2.30219			−0.304932
$58$	0.306062	−	0.530115i	0.0401879	−	0.0696075i
$59$	1.96249	−	3.39914i	0.255495	−	0.442530i	−0.709535	−	0.704670i	$-0.751095\pi$
$59$	1.96249	−	3.39914i	0.255495	−	0.442530i	0.965030	+	0.262140i	$0.0844283\pi$
$60$	0.416173			0.0537276
$61$	−2.77389	+	4.80452i	−0.355160	+	0.615156i	−0.987145	−	0.159825i	$-0.948907\pi$
$61$	−2.77389	+	4.80452i	−0.355160	+	0.615156i	0.631985	+	0.774981i	$0.282240\pi$
$62$	−4.36799	−	7.56558i	−0.554735	−	0.960830i
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	8.88601			1.11075
$65$	−3.83582	−	1.05421i	−0.475775	−	0.130759i
$66$	−0.444469			−0.0547103
$67$	−4.06193	−	7.03547i	−0.496244	−	0.859519i	0.503747	−	0.863851i	$-0.331954\pi$
$67$	−4.06193	−	7.03547i	−0.496244	−	0.859519i	−0.999991	+	0.00433206i	$0.998621\pi$
$68$	0.136945	+	0.237196i	0.0166071	+	0.0287643i
$69$	0.0375080	−	0.0649658i	0.00451543	−	0.00782096i
$70$	1.40550			0.167989
$71$	4.76468	−	8.25267i	0.565463	−	0.979411i	−0.431543	−	0.902092i	$-0.642031\pi$
$71$	4.76468	−	8.25267i	0.565463	−	0.979411i	0.997006	−	0.0773189i	$-0.0246360\pi$
$72$	−1.51415	+	2.62258i	−0.178444	+	0.309074i
$73$	−10.4338			−1.22118			−0.610592	−	0.791946i	$-0.709068\pi$
$73$	−10.4338			−1.22118			−0.610592	+	0.791946i	$0.709068\pi$
$74$	−0.702750	+	1.21720i	−0.0816930	+	0.141496i
$75$	−1.89135	−	3.27592i	−0.218394	−	0.378270i
$76$	0.434196	+	0.752049i	0.0498057	+	0.0862659i
$77$	0.348907			0.0397616
$78$	3.26855	−	3.22691i	0.370091	−	0.365375i
$79$	17.1054			1.92451			0.962256	−	0.272146i	$-0.0877335\pi$
$79$	17.1054			1.92451			0.962256	+	0.272146i	$0.0877335\pi$
$80$	1.71196	+	2.96520i	0.191403	+	0.331520i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.97170	−	3.41509i	0.217738	−	0.377134i
$83$	−11.9143			−1.30777			−0.653883	−	0.756596i	$-0.726861\pi$
$83$	−11.9143			−1.30777			−0.653883	+	0.756596i	$0.726861\pi$
$84$	0.188601	−	0.326667i	0.0205781	−	0.0356423i
$85$	−0.400563	+	0.693795i	−0.0434471	+	0.0752526i
$86$	5.88894			0.635020
$87$	0.240258	−	0.416138i	0.0257583	−	0.0446147i
$88$	0.528296	+	0.915036i	0.0563166	+	0.0975432i
$89$	5.98052	+	10.3586i	0.633933	+	1.09800i	0.986740	+	0.162309i	$0.0518940\pi$
$89$	5.98052	+	10.3586i	0.633933	+	1.09800i	−0.352807	+	0.935696i	$0.614773\pi$
$90$	−1.40550			−0.148153
$91$	−2.56580	+	2.53311i	−0.268969	+	0.265542i
$92$	−0.0282963			−0.00295009
$93$	−3.42886	−	5.93896i	−0.355556	−	0.615841i
$94$	2.99854	+	5.19362i	0.309276	+	0.535681i
$95$	−1.27002	+	2.19973i	−0.130301	+	0.225688i
$96$	2.10331			0.214668
$97$	−5.05166	+	8.74973i	−0.512918	+	0.888400i	0.486970	+	0.873419i	$0.338102\pi$
$97$	−5.05166	+	8.74973i	−0.512918	+	0.888400i	−0.999888	+	0.0149812i	$0.995231\pi$
$98$	0.636945	−	1.10322i	0.0643412	−	0.111442i
$99$	−0.348907			−0.0350664
$100$	−0.713423	+	1.23568i	−0.0713423	+	0.123568i
$101$	−2.03751	−	3.52907i	−0.202740	−	0.351155i	0.746671	−	0.665194i	$-0.231651\pi$
$101$	−2.03751	−	3.52907i	−0.202740	−	0.351155i	−0.949410	+	0.314039i	$0.898318\pi$
$102$	−0.462492	−	0.801060i	−0.0457935	−	0.0793167i
$103$	−4.11106			−0.405075			−0.202538	−	0.979275i	$-0.564919\pi$
$103$	−4.11106			−0.405075			−0.202538	+	0.979275i	$0.564919\pi$
$104$	−10.5283	−	2.89353i	−1.03238	−	0.283734i
$105$	1.10331			0.107672
$106$	3.53363	+	6.12043i	0.343217	+	0.594469i
$107$	3.08529	+	5.34388i	0.298266	+	0.516612i	0.975739	−	0.218935i	$-0.0702584\pi$
$107$	3.08529	+	5.34388i	0.298266	+	0.516612i	−0.677473	+	0.735547i	$0.736925\pi$
$108$	−0.188601	+	0.326667i	−0.0181482	+	0.0314336i
$109$	−8.82167			−0.844963			−0.422481	−	0.906372i	$-0.638841\pi$
$109$	−8.82167			−0.844963			−0.422481	+	0.906372i	$0.638841\pi$
$110$	−0.245194	+	0.424688i	−0.0233783	+	0.0404924i
$111$	−0.551656	+	0.955496i	−0.0523609	+	0.0906917i
$112$	3.10331			0.293235
$113$	−6.00494	+	10.4009i	−0.564897	+	0.978430i	0.432162	+	0.901796i	$0.357751\pi$
$113$	−6.00494	+	10.4009i	−0.564897	+	0.978430i	−0.997059	+	0.0766343i	$0.975583\pi$
$114$	−1.46637	−	2.53982i	−0.137338	−	0.237876i
$115$	−0.0413831	−	0.0716776i	−0.00385899	−	0.00668397i
$116$	−0.181252			−0.0168288
$117$	2.56580	−	2.53311i	0.237209	−	0.234186i
$118$	5.00000			0.460287
$119$	0.363055	+	0.628829i	0.0332812	+	0.0576447i
$120$	1.67058	+	2.89353i	0.152502	+	0.264142i
$121$	5.43913	−	9.42085i	0.494467	−	0.856441i
$122$	−7.06727			−0.639840
$123$	1.54778	−	2.68084i	0.139559	−	0.241723i
$124$	−1.29338	+	2.24019i	−0.116149	+	0.201175i
$125$	−9.69006			−0.866706
$126$	−0.636945	+	1.10322i	−0.0567436	+	0.0982828i
$127$	2.92886	+	5.07293i	0.259894	+	0.450150i	0.966213	−	0.257744i	$-0.0829790\pi$
$127$	2.92886	+	5.07293i	0.259894	+	0.450150i	−0.706319	+	0.707894i	$0.749646\pi$
$128$	3.55659	+	6.16020i	0.314361	+	0.544490i
$129$	4.62280			0.407015
$130$	−1.28018	−	4.90323i	−0.112279	−	0.430042i
$131$	22.4055			1.95758			0.978789	−	0.204872i	$-0.0656778\pi$
$131$	22.4055			1.95758			0.978789	+	0.204872i	$0.0656778\pi$
$132$	0.0658043	+	0.113976i	0.00572753	+	0.00992037i
$133$	1.15109	+	1.99375i	0.0998125	+	0.172880i
$134$	5.17445	−	8.96242i	0.447005	−	0.774235i
$135$	−1.10331			−0.0949580
$136$	−1.09944	+	1.90428i	−0.0942760	+	0.163291i
$137$	−10.1044	+	17.5013i	−0.863275	+	1.49524i	0.00547505	+	0.999985i	$0.498257\pi$
$137$	−10.1044	+	17.5013i	−0.863275	+	1.49524i	−0.868750	+	0.495251i	$0.835076\pi$
$138$	0.0955622			0.00813480
$139$	−2.13695	+	3.70130i	−0.181253	+	0.313940i	−0.942308	−	0.334748i	$-0.891349\pi$
$139$	−2.13695	+	3.70130i	−0.181253	+	0.313940i	0.761054	+	0.648688i	$0.224682\pi$
$140$	−0.208086	−	0.360416i	−0.0175865	−	0.0304607i
$141$	2.35384	+	4.07698i	0.198229	+	0.343343i
$142$	12.1394			1.01871
$143$	−0.317797	−	1.21720i	−0.0265755	−	0.101787i
$144$	−3.10331			−0.258609
$145$	−0.265079	−	0.459131i	−0.0220136	−	0.0381287i
$146$	−6.64576	−	11.5108i	−0.550007	−	0.952640i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$	0.416173			0.0342092
$149$	2.44834	−	4.24066i	0.200576	−	0.347408i	−0.748138	−	0.663543i	$-0.769052\pi$
$149$	2.44834	−	4.24066i	0.200576	−	0.347408i	0.948714	+	0.316135i	$0.102385\pi$
$150$	2.40937	−	4.17316i	0.196725	−	0.340737i
$151$	−8.94553			−0.727977			−0.363988	−	0.931403i	$-0.618585\pi$
$151$	−8.94553			−0.727977			−0.363988	+	0.931403i	$0.618585\pi$
$152$	−3.48585	+	6.03767i	−0.282740	+	0.489720i
$153$	−0.363055	−	0.628829i	−0.0293512	−	0.0508378i
$154$	0.222234	+	0.384921i	0.0179082	+	0.0310178i
$155$	−7.56620			−0.607732
$156$	−1.31140	−	0.360416i	−0.104996	−	0.0288564i
$157$	6.59450			0.526298			0.263149	−	0.964755i	$-0.415239\pi$
$157$	6.59450			0.526298			0.263149	+	0.964755i	$0.415239\pi$
$158$	10.8952	+	18.8711i	0.866778	+	1.50130i
$159$	2.77389	+	4.80452i	0.219984	+	0.381023i
$160$	1.16031	−	2.00971i	0.0917302	−	0.158881i
$161$	−0.0750160			−0.00591209
$162$	0.636945	−	1.10322i	0.0500431	−	0.0866773i
$163$	4.95222	−	8.57749i	0.387888	−	0.671841i	−0.604277	−	0.796774i	$-0.706538\pi$
$163$	4.95222	−	8.57749i	0.387888	−	0.671841i	0.992165	+	0.124933i	$0.0398715\pi$
$164$	−1.16765			−0.0911785
$165$	−0.192476	+	0.333379i	−0.0149843	+	0.0259535i
$166$	−7.58876	−	13.1441i	−0.589002	−	1.02018i
$167$	8.37826	+	14.5116i	0.648330	+	1.12294i	0.983522	+	0.180790i	$0.0578654\pi$
$167$	8.37826	+	14.5116i	0.648330	+	1.12294i	−0.335192	+	0.942150i	$0.608801\pi$
$168$	3.02830			0.233638
$169$	11.1741	+	6.64383i	0.859543	+	0.511064i
$170$	−1.02055			−0.0782723
$171$	−1.15109	−	1.99375i	−0.0880263	−	0.152466i
$172$	−0.871866	−	1.51012i	−0.0664792	−	0.115145i
$173$	−6.85918	+	11.8804i	−0.521494	+	0.903254i	0.478194	+	0.878254i	$0.341292\pi$
$173$	−6.85918	+	11.8804i	−0.521494	+	0.903254i	−0.999687	+	0.0249993i	$0.992042\pi$
$174$	0.612124			0.0464050
$175$	−1.89135	+	3.27592i	−0.142973	+	0.247636i
$176$	−0.541383	+	0.937703i	−0.0408083	+	0.0706820i
$177$	3.92498			0.295020
$178$	−7.61852	+	13.1957i	−0.571032	+	0.989057i
$179$	11.0152	+	19.0789i	0.823315	+	1.42602i	0.903200	+	0.429220i	$0.141211\pi$
$179$	11.0152	+	19.0789i	0.823315	+	1.42602i	−0.0798846	+	0.996804i	$0.525455\pi$
$180$	0.208086	+	0.360416i	0.0155098	+	0.0268638i
$181$	9.43380			0.701208			0.350604	−	0.936524i	$-0.385976\pi$
$181$	9.43380			0.701208			0.350604	+	0.936524i	$0.385976\pi$
$182$	−4.42886	−	1.21720i	−0.328289	−	0.0902247i
$183$	−5.54778			−0.410104
$184$	−0.113585	−	0.196736i	−0.00837363	−	0.0145035i
$185$	0.608649	+	1.05421i	0.0447488	+	0.0775071i
$186$	4.36799	−	7.56558i	0.320277	−	0.554735i
$187$	−0.253344			−0.0185264
$188$	0.887876	−	1.53785i	0.0647550	−	0.112159i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	−3.23572			−0.234744
$191$	1.68860	−	2.92474i	0.122183	−	0.211627i	−0.798445	−	0.602067i	$-0.794344\pi$
$191$	1.68860	−	2.92474i	0.122183	−	0.211627i	0.920628	+	0.390440i	$0.127677\pi$
$192$	4.44301	+	7.69551i	0.320646	+	0.555376i
$193$	−11.1614	−	19.3321i	−0.803413	−	1.39155i	−0.917357	−	0.398065i	$-0.869682\pi$
$193$	−11.1614	−	19.3321i	−0.803413	−	1.39155i	0.113945	−	0.993487i	$-0.463651\pi$
$194$	−12.8705			−0.924049
$195$	−1.00494	−	3.84902i	−0.0719650	−	0.275634i
$196$	−0.377203			−0.0269431
$197$	12.7257	+	22.0416i	0.906669	+	1.57040i	0.818661	+	0.574277i	$0.194717\pi$
$197$	12.7257	+	22.0416i	0.906669	+	1.57040i	0.0880085	+	0.996120i	$0.471950\pi$
$198$	−0.222234	−	0.384921i	−0.0157935	−	0.0273552i
$199$	11.1702	−	19.3473i	0.791833	−	1.37149i	−0.132998	−	0.991116i	$-0.542460\pi$
$199$	11.1702	−	19.3473i	0.791833	−	1.37149i	0.924831	−	0.380379i	$-0.124206\pi$
$200$	−11.4551			−0.810001
$201$	4.06193	−	7.03547i	0.286506	−	0.496244i
$202$	2.59556	−	4.49565i	0.182623	−	0.316313i
$203$	−0.480515			−0.0337256
$204$	−0.136945	+	0.237196i	−0.00958809	+	0.0166071i
$205$	−1.70769	−	2.95780i	−0.119270	−	0.206582i
$206$	−2.61852	−	4.53541i	−0.182441	−	0.315997i
$207$	0.0750160			0.00521397
$208$	−2.82661	−	10.8262i	−0.195990	−	0.750664i
$209$	−0.803248			−0.0555618
$210$	0.702750	+	1.21720i	0.0484943	+	0.0839946i
$211$	−5.01908	−	8.69331i	−0.345528	−	0.598472i	0.639922	−	0.768440i	$-0.278967\pi$
$211$	−5.01908	−	8.69331i	−0.345528	−	0.598472i	−0.985450	+	0.169968i	$0.945634\pi$
$212$	1.04632	−	1.81228i	0.0718615	−	0.124468i
$213$	9.52936			0.652941
$214$	−3.93032	+	6.80752i	−0.268671	+	0.465352i
$215$	2.55019	−	4.41707i	0.173922	−	0.301241i
$216$	−3.02830			−0.206049
$217$	−3.42886	+	5.93896i	−0.232766	+	0.403163i
$218$	−5.61892	−	9.73226i	−0.380561	−	0.659152i
$219$	−5.21690	−	9.03593i	−0.352525	−	0.610592i
$220$	0.145205			0.00978974
$221$	1.86305	−	1.83932i	0.125323	−	0.123726i
$222$	−1.40550			−0.0943309
$223$	2.56727	+	4.44664i	0.171917	+	0.297769i	0.939090	−	0.343671i	$-0.111671\pi$
$223$	2.56727	+	4.44664i	0.171917	+	0.297769i	−0.767173	+	0.641440i	$0.778337\pi$
$224$	−1.05166	−	1.82152i	−0.0702667	−	0.121706i
$225$	1.89135	−	3.27592i	0.126090	−	0.218394i
$226$	−15.2993			−1.01769
$227$	14.4855	−	25.0895i	0.961433	−	1.66525i	0.242526	−	0.970145i	$-0.422024\pi$
$227$	14.4855	−	25.0895i	0.961433	−	1.66525i	0.718907	−	0.695106i	$-0.244643\pi$
$228$	−0.434196	+	0.752049i	−0.0287553	+	0.0498057i
$229$	0.679390			0.0448953			0.0224477	−	0.999748i	$-0.492854\pi$
$229$	0.679390			0.0448953			0.0224477	+	0.999748i	$0.492854\pi$
$230$	0.0527175	−	0.0913094i	0.00347609	−	0.00602076i
$231$	0.174453	+	0.302162i	0.0114782	+	0.0198808i
$232$	−0.727571	−	1.26019i	−0.0477674	−	0.0827355i
$233$	−18.3022			−1.19902			−0.599508	−	0.800369i	$-0.704637\pi$
$233$	−18.3022			−1.19902			−0.599508	+	0.800369i	$0.704637\pi$
$234$	4.42886	+	1.21720i	0.289524	+	0.0795707i
$235$	5.19405			0.338822
$236$	−0.740258	−	1.28216i	−0.0481867	−	0.0834618i
$237$	8.55272	+	14.8137i	0.555559	+	0.962256i
$238$	−0.462492	+	0.801060i	−0.0299789	+	0.0519250i
$239$	−5.45222			−0.352675			−0.176337	−	0.984330i	$-0.556425\pi$
$239$	−5.45222			−0.352675			−0.176337	+	0.984330i	$0.556425\pi$
$240$	−1.71196	+	2.96520i	−0.110507	+	0.191403i
$241$	7.73105	−	13.3906i	0.498000	−	0.862562i	−0.501997	−	0.864869i	$-0.667401\pi$
$241$	7.73105	−	13.3906i	0.498000	−	0.862562i	0.999997	+	0.00230736i	$0.000734455\pi$
$242$	13.8577			0.890808
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.04632	+	1.81228i	0.0669837	+	0.116019i
$245$	−0.551656	−	0.955496i	−0.0352440	−	0.0610444i
$246$	3.94341			0.251422
$247$	5.90696	−	5.83169i	0.375851	−	0.371062i
$248$	−20.7672			−1.31872
$249$	−5.95716	−	10.3181i	−0.377519	−	0.653883i
$250$	−6.17204	−	10.6903i	−0.390354	−	0.676113i
$251$	4.14722	−	7.18319i	0.261770	−	0.453399i	−0.704942	−	0.709265i	$-0.749027\pi$
$251$	4.14722	−	7.18319i	0.261770	−	0.453399i	0.966712	+	0.255866i	$0.0823604\pi$
$252$	0.377203			0.0237615
$253$	0.0130868	−	0.0226670i	0.000822760	−	0.00142506i
$254$	−3.73105	+	6.46236i	−0.234107	+	0.405485i
$255$	−0.801125			−0.0501684
$256$	4.35530	−	7.54361i	0.272207	−	0.471476i
$257$	7.51908	+	13.0234i	0.469028	+	0.812380i	0.999373	−	0.0354019i	$-0.0112711\pi$
$257$	7.51908	+	13.0234i	0.469028	+	0.812380i	−0.530346	+	0.847782i	$0.677938\pi$
$258$	2.94447	+	5.09997i	0.183315	+	0.317510i
$259$	1.10331			0.0685565
$260$	−1.06782	+	1.05421i	−0.0662232	+	0.0653794i
$261$	0.480515			0.0297431
$262$	14.2711	+	24.7182i	0.881670	+	1.52710i
$263$	8.62240	+	14.9344i	0.531680	+	0.920896i	0.999316	+	0.0369754i	$0.0117723\pi$
$263$	8.62240	+	14.9344i	0.531680	+	0.920896i	−0.467636	+	0.883921i	$0.654894\pi$
$264$	−0.528296	+	0.915036i	−0.0325144	+	0.0563166i
$265$	6.12094			0.376006
$266$	−1.46637	+	2.53982i	−0.0899087	+	0.155726i
$267$	−5.98052	+	10.3586i	−0.366002	+	0.633933i
$268$	−3.06434			−0.187185
$269$	12.1472	−	21.0396i	0.740629	−	1.28281i	−0.211580	−	0.977361i	$-0.567861\pi$
$269$	12.1472	−	21.0396i	0.740629	−	1.28281i	0.952209	−	0.305446i	$-0.0988057\pi$
$270$	−0.702750	−	1.21720i	−0.0427680	−	0.0740763i
$271$	−9.16630	−	15.8765i	−0.556813	−	0.964429i	−0.997760	−	0.0668956i	$-0.978691\pi$
$271$	−9.16630	−	15.8765i	−0.556813	−	0.964429i	0.440947	−	0.897533i	$-0.354643\pi$
$272$	−2.25334			−0.136629
$273$	−3.47664	−	0.955496i	−0.210416	−	0.0578293i
$274$	−25.7437			−1.55524
$275$	−0.659905	−	1.14299i	−0.0397938	−	0.0689248i
$276$	−0.0141481	−	0.0245053i	−0.000851617	−	0.00147504i
$277$	−4.22717	+	7.32167i	−0.253986	+	0.439917i	−0.964620	−	0.263646i	$-0.915075\pi$
$277$	−4.22717	+	7.32167i	−0.253986	+	0.439917i	0.710634	+	0.703562i	$0.248408\pi$
$278$	−5.44447			−0.326538
$279$	3.42886	−	5.93896i	0.205280	−	0.355556i
$280$	1.67058	−	2.89353i	0.0998361	−	0.172921i
$281$	−25.0120			−1.49209			−0.746045	−	0.665895i	$-0.768050\pi$
$281$	−25.0120			−1.49209			−0.746045	+	0.665895i	$0.768050\pi$
$282$	−2.99854	+	5.19362i	−0.178560	+	0.309276i
$283$	−13.5707	−	23.5052i	−0.806697	−	1.39724i	−0.915140	−	0.403137i	$-0.867920\pi$
$283$	−13.5707	−	23.5052i	−0.806697	−	1.39724i	0.108443	−	0.994103i	$-0.465414\pi$
$284$	−1.79725	−	3.11293i	−0.106647	−	0.184718i
$285$	−2.54003			−0.150458
$286$	1.14042	−	1.12589i	0.0674344	−	0.0665752i
$287$	−3.09556			−0.182725
$288$	1.05166	+	1.82152i	0.0619694	+	0.107334i
$289$	8.23638	+	14.2658i	0.484493	+	0.839167i
$290$	0.337682	−	0.584882i	0.0198294	−	0.0343455i
$291$	−10.1033			−0.592267
$292$	−1.96783	+	3.40838i	−0.115158	+	0.199460i
$293$	5.27002	−	9.12793i	0.307878	−	0.533260i	−0.670020	−	0.742343i	$-0.733715\pi$
$293$	5.27002	−	9.12793i	0.307878	−	0.533260i	0.977898	+	0.209083i	$0.0670479\pi$
$294$	1.27389			0.0742948
$295$	2.16524	−	3.75031i	0.126065	−	0.218351i
$296$	1.67058	+	2.89353i	0.0971004	+	0.168183i
$297$	−0.174453	−	0.302162i	−0.0101228	−	0.0175332i
$298$	6.23784			0.361349
$299$	0.0683273	+	0.261701i	0.00395147	+	0.0151346i
$300$	−1.42685			−0.0823790
$301$	−2.31140	−	4.00346i	−0.133227	−	0.230756i
$302$	−5.69781	−	9.86890i	−0.327872	−	0.567891i
$303$	2.03751	−	3.52907i	0.117052	−	0.202740i
$304$	−7.14440			−0.409760
$305$	−3.06047	+	5.30089i	−0.175242	+	0.303528i
$306$	0.462492	−	0.801060i	0.0264389	−	0.0457935i
$307$	−4.40842			−0.251602			−0.125801	−	0.992055i	$-0.540150\pi$
$307$	−4.40842			−0.251602			−0.125801	+	0.992055i	$0.540150\pi$
$308$	0.0658043	−	0.113976i	0.00374955	−	0.00649441i
$309$	−2.05553	−	3.56028i	−0.116935	−	0.202538i
$310$	−4.81926	−	8.34720i	−0.273715	−	0.474089i
$311$	−2.32836			−0.132029			−0.0660146	−	0.997819i	$-0.521028\pi$
$311$	−2.32836			−0.132029			−0.0660146	+	0.997819i	$0.521028\pi$
$312$	−2.75828	−	10.5645i	−0.156157	−	0.598099i
$313$	12.6687			0.716078			0.358039	−	0.933707i	$-0.383445\pi$
$313$	12.6687			0.716078			0.358039	+	0.933707i	$0.383445\pi$
$314$	4.20034	+	7.27520i	0.237039	+	0.410563i
$315$	0.551656	+	0.955496i	0.0310823	+	0.0538361i
$316$	3.22611	−	5.58779i	0.181483	−	0.314337i
$317$	−12.2915			−0.690360			−0.345180	−	0.938536i	$-0.612182\pi$
$317$	−12.2915			−0.690360			−0.345180	+	0.938536i	$0.612182\pi$
$318$	−3.53363	+	6.12043i	−0.198156	+	0.343217i
$319$	0.0838275	−	0.145193i	0.00469344	−	0.00812927i
$320$	9.80405			0.548063
$321$	−3.08529	+	5.34388i	−0.172204	+	0.298266i
$322$	−0.0477811	−	0.0827593i	−0.00266274	−	0.00461200i
$323$	−0.835820	−	1.44768i	−0.0465063	−	0.0805512i
$324$	−0.377203			−0.0209557
$325$	13.1511	+	3.61436i	0.729491	+	0.200489i
$326$	12.6172			0.698800
$327$	−4.41084	−	7.63979i	−0.243920	−	0.422481i
$328$	−4.68714	−	8.11836i	−0.258804	−	0.448262i
$329$	2.35384	−	4.07698i	0.129772	−	0.224771i
$330$	−0.490388			−0.0269950
$331$	−6.64576	+	11.5108i	−0.365284	+	0.632690i	−0.988822	−	0.149103i	$-0.952361\pi$
$331$	−6.64576	+	11.5108i	−0.365284	+	0.632690i	0.623538	+	0.781793i	$0.285695\pi$
$332$	−2.24706	+	3.89202i	−0.123323	+	0.213602i
$333$	−1.10331			−0.0604611
$334$	−10.6730	+	18.4862i	−0.584000	+	1.01152i
$335$	−4.48158	−	7.76232i	−0.244855	−	0.424101i
$336$	1.55166	+	2.68755i	0.0846498	+	0.146618i
$337$	−3.40550			−0.185509			−0.0927547	−	0.995689i	$-0.529567\pi$
$337$	−3.40550			−0.185509			−0.0927547	+	0.995689i	$0.529567\pi$
$338$	−0.212362	+	16.5592i	−0.0115510	+	0.900703i
$339$	−12.0099			−0.652287
$340$	0.151093	+	0.261701i	0.00819419	+	0.0141928i
$341$	−1.19635	−	2.07214i	−0.0647861	−	0.112213i
$342$	1.46637	−	2.53982i	0.0792920	−	0.137338i
$343$	−1.00000			−0.0539949
$344$	6.99960	−	12.1237i	0.377393	−	0.653664i
$345$	0.0413831	−	0.0716776i	0.00222799	−	0.00385899i
$346$	−17.4757			−0.939499
$347$	16.7491	−	29.0102i	0.899137	−	1.55735i	0.0705378	−	0.997509i	$-0.477528\pi$
$347$	16.7491	−	29.0102i	0.899137	−	1.55735i	0.828599	−	0.559842i	$-0.189138\pi$
$348$	−0.0906258	−	0.156969i	−0.00485806	−	0.00841440i
$349$	14.0902	+	24.4050i	0.754232	+	1.30637i	0.945755	+	0.324881i	$0.105324\pi$
$349$	14.0902	+	24.4050i	0.754232	+	1.30637i	−0.191523	+	0.981488i	$0.561342\pi$
$350$	−4.81875			−0.257573
$351$	3.47664	+	0.955496i	0.185569	+	0.0510006i
$352$	0.733860			0.0391148
$353$	1.49612	+	2.59136i	0.0796307	+	0.137924i	0.903091	−	0.429450i	$-0.141293\pi$
$353$	1.49612	+	2.59136i	0.0796307	+	0.137924i	−0.823460	+	0.567374i	$0.807959\pi$
$354$	2.50000	+	4.33013i	0.132874	+	0.230144i
$355$	5.25693	−	9.10527i	0.279009	−	0.483257i
$356$	4.51173			0.239121
$357$	−0.363055	+	0.628829i	−0.0192149	+	0.0332812i
$358$	−14.0322	+	24.3044i	−0.741623	+	1.28453i
$359$	3.80888			0.201025			0.100512	−	0.994936i	$-0.467952\pi$
$359$	3.80888			0.201025			0.100512	+	0.994936i	$0.467952\pi$
$360$	−1.67058	+	2.89353i	−0.0880472	+	0.152502i
$361$	6.84997	+	11.8645i	0.360525	+	0.624447i
$362$	6.00881	+	10.4076i	0.315816	+	0.547010i
$363$	10.8783			0.570961
$364$	0.343570	+	1.31591i	0.0180080	+	0.0689726i
$365$	−11.5117			−0.602552
$366$	−3.53363	−	6.12043i	−0.184706	−	0.319920i
$367$	13.2257	+	22.9076i	0.690376	+	1.19577i	0.971715	+	0.236158i	$0.0758884\pi$
$367$	13.2257	+	22.9076i	0.690376	+	1.19577i	−0.281338	+	0.959609i	$0.590778\pi$
$368$	0.116399	−	0.201609i	0.00606772	−	0.0105096i
$369$	3.09556			0.161149
$370$	−0.775352	+	1.34295i	−0.0403086	+	0.0698166i
$371$	2.77389	−	4.80452i	0.144013	−	0.249438i
$372$	−2.58675			−0.134117
$373$	−1.06580	+	1.84603i	−0.0551853	+	0.0955837i	−0.892298	−	0.451446i	$-0.850908\pi$
$373$	−1.06580	+	1.84603i	−0.0551853	+	0.0955837i	0.837113	+	0.547030i	$0.184242\pi$
$374$	−0.161367	−	0.279495i	−0.00834406	−	0.0144523i
$375$	−4.84503	−	8.39184i	−0.250196	−	0.433353i
$376$	14.2563			0.735211
$377$	0.437670	+	1.67633i	0.0225412	+	0.0863353i
$378$	−1.27389			−0.0655219
$379$	6.97170	+	12.0753i	0.358112	+	0.620269i	0.987645	−	0.156705i	$-0.0500871\pi$
$379$	6.97170	+	12.0753i	0.358112	+	0.620269i	−0.629533	+	0.776974i	$0.716754\pi$
$380$	0.479053	+	0.829745i	0.0245749	+	0.0425650i
$381$	−2.92886	+	5.07293i	−0.150050	+	0.259894i
$382$	4.30219			0.220119
$383$	9.30219	−	16.1119i	0.475320	−	0.823278i	−0.524281	−	0.851545i	$-0.675666\pi$
$383$	9.30219	−	16.1119i	0.475320	−	0.823278i	0.999600	+	0.0282678i	$0.00899913\pi$
$384$	−3.55659	+	6.16020i	−0.181497	+	0.314361i
$385$	0.384953			0.0196190
$386$	14.2184	−	24.6269i	0.723695	−	1.25348i
$387$	2.31140	+	4.00346i	0.117495	+	0.203507i
$388$	1.90550	+	3.30042i	0.0967371	+	0.167554i
$389$	−1.23009			−0.0623682			−0.0311841	−	0.999514i	$-0.509928\pi$
$389$	−1.23009			−0.0623682			−0.0311841	+	0.999514i	$0.509928\pi$
$390$	3.60624	−	3.56028i	0.182609	−	0.180282i
$391$	0.0544699			0.00275466
$392$	−1.51415	−	2.62258i	−0.0764760	−	0.132460i
$393$	11.2027	+	19.4037i	0.565104	+	0.978789i
$394$	−16.2112	+	28.0786i	−0.816706	+	1.41458i
$395$	18.8726			0.949585
$396$	−0.0658043	+	0.113976i	−0.00330679	+	0.00572753i
$397$	−14.8071	+	25.6467i	−0.743148	+	1.28717i	0.207907	+	0.978149i	$0.433335\pi$
$397$	−14.8071	+	25.6467i	−0.743148	+	1.28717i	−0.951055	+	0.309022i	$0.899998\pi$
$398$	28.4592			1.42653
$399$	−1.15109	+	1.99375i	−0.0576267	+	0.0998125i
$400$	−5.86945	−	10.1662i	−0.293473	−	0.508310i
$401$	−4.09023	−	7.08448i	−0.204256	−	0.353782i	0.745639	−	0.666350i	$-0.232144\pi$
$401$	−4.09023	−	7.08448i	−0.204256	−	0.353782i	−0.949895	+	0.312568i	$0.898811\pi$
$402$	10.3489			0.516157
$403$	23.8418	+	6.55253i	1.18765	+	0.326405i
$404$	−1.53711			−0.0764740
$405$	−0.551656	−	0.955496i	−0.0274120	−	0.0474790i
$406$	−0.306062	−	0.530115i	−0.0151896	−	0.0263092i
$407$	−0.192476	+	0.333379i	−0.00954070	+	0.0165250i
$408$	−2.19887			−0.108861
$409$	−5.03363	+	8.71851i	−0.248897	+	0.431102i	−0.963220	−	0.268714i	$-0.913401\pi$
$409$	−5.03363	+	8.71851i	−0.248897	+	0.431102i	0.714323	+	0.699816i	$0.246735\pi$
$410$	2.17540	−	3.76791i	0.107436	−	0.186084i
$411$	−20.2087			−0.996824
$412$	−0.775352	+	1.34295i	−0.0381989	+	0.0661624i
$413$	−1.96249	−	3.39914i	−0.0965679	−	0.167261i
$414$	0.0477811	+	0.0827593i	0.00234831	+	0.00406740i
$415$	−13.1452			−0.645273
$416$	−5.39669	+	5.32792i	−0.264594	+	0.261223i
$417$	−4.27389			−0.209293
$418$	−0.511625	−	0.886161i	−0.0250244	−	0.0433435i
$419$	−4.72998	−	8.19257i	−0.231075	−	0.400233i	0.727050	−	0.686585i	$-0.240891\pi$
$419$	−4.72998	−	8.19257i	−0.231075	−	0.400233i	−0.958125	+	0.286351i	$0.907558\pi$
$420$	0.208086	−	0.360416i	0.0101536	−	0.0175865i
$421$	31.0643			1.51398			0.756992	−	0.653424i	$-0.226668\pi$
$421$	31.0643			1.51398			0.756992	+	0.653424i	$0.226668\pi$
$422$	6.39376	−	11.0743i	0.311244	−	0.539090i
$423$	−2.35384	+	4.07698i	−0.114448	+	0.198229i
$424$	16.8003			0.815896
$425$	1.37333	−	2.37867i	0.0666162	−	0.115383i
$426$	6.06968	+	10.5130i	0.294077	+	0.509356i
$427$	2.77389	+	4.80452i	0.134238	+	0.232507i
$428$	2.32756			0.112507
$429$	0.895226	−	0.883819i	0.0432219	−	0.0426712i
$430$	6.49734			0.313329
$431$	12.6093	+	21.8400i	0.607369	+	1.05199i	0.991672	+	0.128787i	$0.0411084\pi$
$431$	12.6093	+	21.8400i	0.607369	+	1.05199i	−0.384303	+	0.923207i	$0.625558\pi$
$432$	−1.55166	−	2.68755i	−0.0746541	−	0.129305i
$433$	−1.88495	+	3.26483i	−0.0905851	+	0.156898i	−0.907757	−	0.419495i	$-0.862207\pi$
$433$	−1.88495	+	3.26483i	−0.0905851	+	0.156898i	0.817172	+	0.576393i	$0.195540\pi$
$434$	−8.73598			−0.419341
$435$	0.265079	−	0.459131i	0.0127096	−	0.0220136i
$436$	−1.66378	+	2.88175i	−0.0796806	+	0.138011i
$437$	0.172701			0.00826141
$438$	6.64576	−	11.5108i	0.317547	−	0.550007i
$439$	11.3174	+	19.6023i	0.540150	+	0.935567i	0.998895	+	0.0469991i	$0.0149658\pi$
$439$	11.3174	+	19.6023i	0.540150	+	0.935567i	−0.458745	+	0.888568i	$0.651701\pi$
$440$	0.582876	+	1.00957i	0.0277875	+	0.0481294i
$441$	1.00000			0.0476190
$442$	3.21584	+	0.883819i	0.152962	+	0.0420390i
$443$	4.64334			0.220612			0.110306	−	0.993898i	$-0.464817\pi$
$443$	4.64334			0.220612			0.110306	+	0.993898i	$0.464817\pi$
$444$	0.208086	+	0.360416i	0.00987534	+	0.0171046i
$445$	6.59838	+	11.4287i	0.312793	+	0.541773i
$446$	−3.27042	+	5.66453i	−0.154859	+	0.268223i
$447$	4.89669			0.231605
$448$	4.44301	−	7.69551i	0.209912	−	0.363579i
$449$	−4.71156	+	8.16066i	−0.222352	+	0.385125i	−0.955522	−	0.294920i	$-0.904707\pi$
$449$	−4.71156	+	8.16066i	−0.222352	+	0.385125i	0.733170	+	0.680046i	$0.238040\pi$
$450$	4.81875			0.227158
$451$	0.540031	−	0.935361i	0.0254291	−	0.0440444i
$452$	2.26508	+	3.92323i	0.106540	+	0.184533i
$453$	−4.47277	−	7.74706i	−0.210149	−	0.363988i
$454$	36.9058			1.73207
$455$	−2.83088	+	2.79481i	−0.132714	+	0.131023i
$456$	−6.97170			−0.326480
$457$	−6.35812	−	11.0126i	−0.297420	−	0.515147i	0.678125	−	0.734947i	$-0.262793\pi$
$457$	−6.35812	−	11.0126i	−0.297420	−	0.515147i	−0.975545	+	0.219800i	$0.929460\pi$
$458$	0.432734	+	0.749517i	0.0202203	+	0.0350226i
$459$	0.363055	−	0.628829i	0.0169459	−	0.0293512i
$460$	−0.0312196			−0.00145562
$461$	14.8627	−	25.7429i	0.692223	−	1.19897i	−0.278885	−	0.960324i	$-0.589965\pi$
$461$	14.8627	−	25.7429i	0.692223	−	1.19897i	0.971108	−	0.238641i	$-0.0767018\pi$
$462$	−0.222234	+	0.384921i	−0.0103393	+	0.0179082i
$463$	−15.2838			−0.710297			−0.355148	−	0.934810i	$-0.615570\pi$
$463$	−15.2838			−0.710297			−0.355148	+	0.934810i	$0.615570\pi$
$464$	0.745594	−	1.29141i	0.0346133	−	0.0599521i
$465$	−3.78310	−	6.55253i	−0.175437	−	0.303866i
$466$	−11.6575	−	20.1914i	−0.540023	−	0.935347i
$467$	−26.6503			−1.23323			−0.616614	−	0.787265i	$-0.711496\pi$
$467$	−26.6503			−1.23323			−0.616614	+	0.787265i	$0.711496\pi$
$468$	−0.343570	−	1.31591i	−0.0158815	−	0.0608281i
$469$	−8.12386			−0.375125
$470$	3.30832	+	5.73019i	0.152602	+	0.264314i
$471$	3.29725	+	5.71101i	0.151929	+	0.263149i
$472$	5.94301	−	10.2936i	0.273549	−	0.473801i
$473$	1.61292			0.0741623
$474$	−10.8952	+	18.8711i	−0.500434	+	0.866778i
$475$	4.35424	−	7.54177i	0.199786	−	0.346040i
$476$	0.273891			0.0125538
$477$	−2.77389	+	4.80452i	−0.127008	+	0.219984i
$478$	−3.47277	−	6.01501i	−0.158841	−	0.275120i
$479$	11.1058	+	19.2359i	0.507439	+	0.878909i	0.999963	+	0.00861072i	$0.00274091\pi$
$479$	11.1058	+	19.2359i	0.507439	+	0.878909i	−0.492524	+	0.870299i	$0.663926\pi$
$480$	2.32061			0.105921
$481$	−1.00494	−	3.84902i	−0.0458212	−	0.175500i
$482$	19.6970			0.897174
$483$	−0.0375080	−	0.0649658i	−0.00170667	−	0.00295605i
$484$	−2.05166	−	3.55357i	−0.0932571	−	0.161526i
$485$	−5.57355	+	9.65368i	−0.253082	+	0.438351i
$486$	1.27389			0.0577848
$487$	0.485852	−	0.841520i	0.0220160	−	0.0381329i	−0.854807	−	0.518945i	$-0.826325\pi$
$487$	0.485852	−	0.841520i	0.0220160	−	0.0381329i	0.876824	+	0.480812i	$0.159658\pi$
$488$	−8.40016	+	14.5495i	−0.380257	+	0.658625i
$489$	9.90444			0.447894
$490$	0.702750	−	1.21720i	0.0317470	−	0.0549874i
$491$	−13.4674	−	23.3263i	−0.607777	−	1.05270i	−0.991606	−	0.129296i	$-0.958728\pi$
$491$	−13.4674	−	23.3263i	−0.607777	−	1.05270i	0.383830	−	0.923404i	$-0.374605\pi$
$492$	−0.583827	−	1.01122i	−0.0263210	−	0.0455893i
$493$	0.348907			0.0157140
$494$	10.1961	+	2.80222i	0.458742	+	0.126078i
$495$	−0.384953			−0.0173023
$496$	−10.6408	−	18.4304i	−0.477787	−	0.827551i
$497$	−4.76468	−	8.25267i	−0.213725	−	0.370183i
$498$	7.58876	−	13.1441i	0.340061	−	0.589002i
$499$	−21.1239			−0.945634			−0.472817	−	0.881161i	$-0.656763\pi$
$499$	−21.1239			−0.945634			−0.472817	+	0.881161i	$0.656763\pi$
$500$	−1.82756	+	3.16543i	−0.0817310	+	0.141562i
$501$	−8.37826	+	14.5116i	−0.374313	+	0.648330i
$502$	10.5662			0.471593
$503$	−6.28270	+	10.8820i	−0.280132	+	0.485203i	−0.971417	−	0.237379i	$-0.923712\pi$
$503$	−6.28270	+	10.8820i	−0.280132	+	0.485203i	0.691285	+	0.722582i	$0.257045\pi$
$504$	1.51415	+	2.62258i	0.0674455	+	0.116819i
$505$	−2.24801	−	3.89366i	−0.100035	−	0.173266i
$506$	0.0333423			0.00148225
$507$	−0.166703	+	12.9989i	−0.00740355	+	0.577303i
$508$	2.20955			0.0980328
$509$	−13.8032	−	23.9079i	−0.611818	−	1.05970i	−0.990934	−	0.134351i	$-0.957105\pi$
$509$	−13.8032	−	23.9079i	−0.611818	−	1.05970i	0.379116	−	0.925349i	$-0.376228\pi$
$510$	−0.510273	−	0.883819i	−0.0225953	−	0.0391362i
$511$	−5.21690	+	9.03593i	−0.230782	+	0.399726i
$512$	25.3227			1.11912
$513$	1.15109	−	1.99375i	0.0508220	−	0.0880263i
$514$	−9.57849	+	16.5904i	−0.422489	+	0.731773i
$515$	−4.53579			−0.199871
$516$	0.871866	−	1.51012i	0.0383818	−	0.0664792i
$517$	0.821271	+	1.42248i	0.0361195	+	0.0625608i
$518$	0.702750	+	1.21720i	0.0308770	+	0.0534806i
$519$	−13.7184			−0.602169
$520$	−11.6160	−	3.19246i	−0.509395	−	0.139999i
$521$	−36.8783			−1.61567			−0.807833	−	0.589411i	$-0.799360\pi$
$521$	−36.8783			−1.61567			−0.807833	+	0.589411i	$0.799360\pi$
$522$	0.306062	+	0.530115i	0.0133960	+	0.0232025i
$523$	−15.4027	−	26.6782i	−0.673512	−	1.16656i	−0.976901	−	0.213691i	$-0.931451\pi$
$523$	−15.4027	−	26.6782i	−0.673512	−	1.16656i	0.303389	−	0.952867i	$-0.401882\pi$
$524$	4.22571	−	7.31914i	0.184601	−	0.319738i
$525$	−3.78270			−0.165091
$526$	−10.9840	+	19.0248i	−0.478925	+	0.829522i
$527$	2.48973	−	4.31233i	0.108454	−	0.187848i
$528$	−1.08277			−0.0471213
$529$	11.4972	−	19.9137i	0.499878	−	0.865814i
$530$	3.89870	+	6.75275i	0.169349	+	0.293321i
$531$	1.96249	+	3.39914i	0.0851649	+	0.147510i
$532$	0.868391			0.0376495
$533$	2.81955	+	10.7992i	0.122128	+	0.467765i
$534$	−15.2370			−0.659371
$535$	3.40404	+	5.89597i	0.147169	+	0.254905i
$536$	−12.3007	−	21.3055i	−0.531310	−	0.920257i
$537$	−11.0152	+	19.0789i	−0.475341	+	0.823315i
$538$	30.9485			1.33428
$539$	0.174453	−	0.302162i	0.00751424	−	0.0130150i
$540$	−0.208086	+	0.360416i	−0.00895461	+	0.0155098i
$541$	−41.4981			−1.78414			−0.892072	−	0.451893i	$-0.850749\pi$
$541$	−41.4981			−1.78414			−0.892072	+	0.451893i	$0.850749\pi$
$542$	11.6769	−	20.2249i	0.501564	−	0.868735i
$543$	4.71690	+	8.16991i	0.202421	+	0.350604i
$544$	0.763617	+	1.32262i	0.0327398	+	0.0567070i
$545$	−9.73306			−0.416918
$546$	−1.16031	−	4.44410i	−0.0496565	−	0.190190i
$547$	−41.3716			−1.76892			−0.884460	−	0.466615i	$-0.845473\pi$
$547$	−41.3716			−1.76892			−0.884460	+	0.466615i	$0.845473\pi$
$548$	3.81140	+	6.60154i	0.162815	+	0.282004i
$549$	−2.77389	−	4.80452i	−0.118387	−	0.205052i
$550$	0.840647	−	1.45604i	0.0358453	−	0.0620859i
$551$	1.10624			0.0471272
$552$	0.113585	−	0.196736i	0.00483452	−	0.00837363i
$553$	8.55272	−	14.8137i	0.363699	−	0.629944i
$554$	−10.7699			−0.457569
$555$	−0.608649	+	1.05421i	−0.0258357	+	0.0447488i
$556$	0.806062	+	1.39614i	0.0341846	+	0.0592095i
$557$	−15.0075	−	25.9937i	−0.635886	−	1.10139i	−0.986327	−	0.164803i	$-0.947301\pi$
$557$	−15.0075	−	25.9937i	−0.635886	−	1.10139i	0.350440	−	0.936585i	$-0.386032\pi$
$558$	8.73598			0.369824
$559$	−11.8612	+	11.7101i	−0.501675	+	0.495283i
$560$	3.42392			0.144687
$561$	−0.126672	−	0.219403i	−0.00534810	−	0.00926319i
$562$	−15.9313	−	27.5938i	−0.672020	−	1.16397i
$563$	−12.9674	+	22.4602i	−0.546512	+	0.946586i	0.451998	+	0.892019i	$0.350711\pi$
$563$	−12.9674	+	22.4602i	−0.546512	+	0.946586i	−0.998510	+	0.0545676i	$0.982622\pi$
$564$	1.77575			0.0747727
$565$	−6.62532	+	11.4754i	−0.278729	+	0.482773i
$566$	17.2876	−	29.9431i	0.726654	−	1.25860i
$567$	−1.00000			−0.0419961
$568$	14.4289	−	24.9915i	0.605421	−	1.04862i
$569$	3.28310	+	5.68650i	0.137635	+	0.238390i	0.926601	−	0.376046i	$-0.122717\pi$
$569$	3.28310	+	5.68650i	0.137635	+	0.238390i	−0.788966	+	0.614437i	$0.789383\pi$
$570$	−1.61786	−	2.80222i	−0.0677647	−	0.117372i
$571$	−30.0539			−1.25772			−0.628858	−	0.777520i	$-0.716477\pi$
$571$	−30.0539			−1.25772			−0.628858	+	0.777520i	$0.716477\pi$
$572$	−0.457556	−	0.125752i	−0.0191314	−	0.00525794i
$573$	3.37720			0.141085
$574$	−1.97170	−	3.41509i	−0.0822973	−	0.142543i
$575$	0.141882	+	0.245746i	0.00591687	+	0.0102483i
$576$	−4.44301	+	7.69551i	−0.185125	+	0.320646i
$577$	21.1706			0.881343			0.440671	−	0.897669i	$-0.354740\pi$
$577$	21.1706			0.881343			0.440671	+	0.897669i	$0.354740\pi$
$578$	−10.4922	+	18.1731i	−0.436420	+	0.755902i
$579$	11.1614	−	19.3321i	0.463851	−	0.803413i
$580$	−0.199977			−0.00830360
$581$	−5.95716	+	10.3181i	−0.247144	+	0.428067i
$582$	−6.43526	−	11.1462i	−0.266750	−	0.462025i
$583$	0.967829	+	1.67633i	0.0400834	+	0.0694264i
$584$	−31.5966			−1.30748
$585$	2.83088	−	2.79481i	0.117043	−	0.115551i
$586$	13.4268			0.554658
$587$	−0.0156098	−	0.0270370i	−0.000644286	−	0.00111594i	0.865703	−	0.500558i	$-0.166872\pi$
$587$	−0.0156098	−	0.0270370i	−0.000644286	−	0.00111594i	−0.866347	+	0.499442i	$0.833538\pi$
$588$	−0.188601	−	0.326667i	−0.00777779	−	0.0134715i
$589$	7.89387	−	13.6726i	0.325261	−	0.563369i
$590$	5.51656			0.227113
$591$	−12.7257	+	22.0416i	−0.523466	+	0.906669i
$592$	−1.71196	+	2.96520i	−0.0703612	+	0.121869i
$593$	−10.3150			−0.423586			−0.211793	−	0.977315i	$-0.567930\pi$
$593$	−10.3150			−0.423586			−0.211793	+	0.977315i	$0.567930\pi$
$594$	0.222234	−	0.384921i	0.00911839	−	0.0157935i
$595$	0.400563	+	0.693795i	0.0164215	+	0.0284428i
$596$	−0.923522	−	1.59959i	−0.0378289	−	0.0655217i
$597$	22.3404			0.914330
$598$	−0.245194	+	0.242070i	−0.0100267	+	0.00989896i
$599$	44.0176			1.79851			0.899256	−	0.437423i	$-0.144109\pi$
$599$	44.0176			1.79851			0.899256	+	0.437423i	$0.144109\pi$
$600$	−5.72757	−	9.92044i	−0.233827	−	0.405000i
$601$	−2.52336	−	4.37059i	−0.102930	−	0.178280i	0.809961	−	0.586484i	$-0.199488\pi$
$601$	−2.52336	−	4.37059i	−0.102930	−	0.178280i	−0.912891	+	0.408204i	$0.866155\pi$
$602$	2.94447	−	5.09997i	0.120008	−	0.207859i
$603$	8.12386			0.330829
$604$	−1.68714	+	2.92221i	−0.0686487	+	0.118903i
$605$	6.00106	−	10.3941i	0.243978	−	0.422582i
$606$	5.19112			0.210875
$607$	−8.32409	+	14.4177i	−0.337864	+	0.585198i	−0.984031	−	0.177998i	$-0.943038\pi$
$607$	−8.32409	+	14.4177i	−0.337864	+	0.585198i	0.646167	+	0.763196i	$0.276371\pi$
$608$	2.42111	+	4.19348i	0.0981889	+	0.170068i
$609$	−0.240258	−	0.416138i	−0.00973573	−	0.0168628i
$610$	−7.79740			−0.315708
$611$	−16.3669	−	4.49818i	−0.662135	−	0.181977i
$612$	−0.273891			−0.0110714
$613$	−19.0060	−	32.9194i	−0.767645	−	1.32960i	−0.938837	−	0.344362i	$-0.888095\pi$
$613$	−19.0060	−	32.9194i	−0.767645	−	1.32960i	0.171192	−	0.985238i	$-0.445238\pi$
$614$	−2.80792	−	4.86347i	−0.113319	−	0.196274i
$615$	1.70769	−	2.95780i	0.0688605	−	0.119270i
$616$	1.05659			0.0425713
$617$	−7.83330	+	13.5677i	−0.315357	+	0.546214i	−0.979513	−	0.201380i	$-0.935457\pi$
$617$	−7.83330	+	13.5677i	−0.315357	+	0.546214i	0.664157	+	0.747593i	$0.268791\pi$
$618$	2.61852	−	4.53541i	0.105332	−	0.182441i
$619$	3.26109			0.131074			0.0655372	−	0.997850i	$-0.479124\pi$
$619$	3.26109			0.131074			0.0655372	+	0.997850i	$0.479124\pi$
$620$	−1.42700	+	2.47163i	−0.0573096	+	0.0992631i
$621$	0.0375080	+	0.0649658i	0.00150514	+	0.00260699i
$622$	−1.48304	−	2.56870i	−0.0594644	−	0.102995i
$623$	11.9610			0.479209
$624$	7.96249	−	7.86103i	0.318755	−	0.314693i
$625$	8.22234			0.328894
$626$	8.06928	+	13.9764i	0.322513	+	0.558609i
$627$	−0.401624	−	0.695633i	−0.0160393	−	0.0277809i
$628$	1.24373	−	2.15421i	0.0496303	−	0.0859622i
$629$	−0.801125			−0.0319430
$630$	−0.702750	+	1.21720i	−0.0279982	+	0.0484943i
$631$	−0.799773	+	1.38525i	−0.0318385	+	0.0551459i	−0.881506	−	0.472174i	$-0.843470\pi$
$631$	−0.799773	+	1.38525i	−0.0318385	+	0.0551459i	0.849667	+	0.527319i	$0.176803\pi$
$632$	51.8003			2.06051
$633$	5.01908	−	8.69331i	0.199491	−	0.345528i
$634$	−7.82902	−	13.5603i	−0.310930	−	0.538547i
$635$	3.23145	+	5.59703i	0.128236	+	0.222111i
$636$	2.09264			0.0829785
$637$	0.910836	+	3.48861i	0.0360886	+	0.138224i
$638$	0.213574			0.00845548
$639$	4.76468	+	8.25267i	0.188488	+	0.326470i
$640$	3.92403	+	6.79662i	0.155111	+	0.268660i
$641$	−15.6779	+	27.1550i	−0.619241	+	1.07256i	0.370384	+	0.928879i	$0.379226\pi$
$641$	−15.6779	+	27.1550i	−0.619241	+	1.07256i	−0.989625	+	0.143678i	$0.954107\pi$
$642$	−7.86064			−0.310235
$643$	9.33154	−	16.1627i	0.368000	−	0.637395i	−0.621253	−	0.783610i	$-0.713376\pi$
$643$	9.33154	−	16.1627i	0.368000	−	0.637395i	0.989253	+	0.146215i	$0.0467092\pi$
$644$	−0.0141481	+	0.0245053i	−0.000557514	+	0.000965643i
$645$	5.10039			0.200828
$646$	1.06474	−	1.84419i	0.0418918	−	0.0725586i
$647$	−3.26855	−	5.66130i	−0.128500	−	0.222569i	0.794596	−	0.607139i	$-0.207683\pi$
$647$	−3.26855	−	5.66130i	−0.128500	−	0.222569i	−0.923096	+	0.384570i	$0.874350\pi$
$648$	−1.51415	−	2.62258i	−0.0594814	−	0.103025i
$649$	1.36945			0.0537557
$650$	4.38909	+	16.8107i	0.172154	+	0.659371i
$651$	−6.85772			−0.268775
$652$	−1.86799	−	3.23546i	−0.0731562	−	0.126710i
$653$	−7.92605	−	13.7283i	−0.310170	−	0.537230i	0.668229	−	0.743956i	$-0.267053\pi$
$653$	−7.92605	−	13.7283i	−0.310170	−	0.537230i	−0.978399	+	0.206725i	$0.933719\pi$
$654$	5.61892	−	9.73226i	0.219717	−	0.380561i
$655$	24.7203			0.965901
$656$	4.80325	−	8.31947i	0.187535	−	0.324821i
$657$	5.21690	−	9.03593i	0.203531	−	0.352525i
$658$	5.99708			0.233790
$659$	24.8987	−	43.1258i	0.969916	−	1.67994i	0.274132	−	0.961692i	$-0.411610\pi$
$659$	24.8987	−	43.1258i	0.969916	−	1.67994i	0.695784	−	0.718251i	$-0.255057\pi$
$660$	0.0726027	+	0.125752i	0.00282606	+	0.00489487i
$661$	−1.78552	−	3.09260i	−0.0694485	−	0.120288i	0.829210	−	0.558937i	$-0.188791\pi$
$661$	−1.78552	−	3.09260i	−0.0694485	−	0.120288i	−0.898659	+	0.438649i	$0.855457\pi$
$662$	−16.9319			−0.658078
$663$	2.52442	+	0.693795i	0.0980404	+	0.0269448i
$664$	−36.0801			−1.40018
$665$	1.27002	+	2.19973i	0.0492491	+	0.0853019i
$666$	−0.702750	−	1.21720i	−0.0272310	−	0.0471655i
$667$	−0.0180232	+	0.0312170i	−0.000697860	+	0.00120873i
$668$	6.32061			0.244552
$669$	−2.56727	+	4.44664i	−0.0992562	+	0.171917i
$670$	5.70904	−	9.88834i	0.220559	−	0.382020i
$671$	−1.93566			−0.0747252
$672$	1.05166	−	1.82152i	0.0405685	−	0.0702667i
$673$	−5.86693	−	10.1618i	−0.226154	−	0.391709i	0.730511	−	0.682901i	$-0.239282\pi$
$673$	−5.86693	−	10.1618i	−0.226154	−	0.391709i	−0.956665	+	0.291191i	$0.905948\pi$
$674$	−2.16912	−	3.75702i	−0.0835512	−	0.144715i
$675$	3.78270			0.145596
$676$	4.27777	−	2.39716i	0.164529	−	0.0921985i
$677$	17.3326			0.666146			0.333073	−	0.942901i	$-0.391914\pi$
$677$	17.3326			0.666146			0.333073	+	0.942901i	$0.391914\pi$
$678$	−7.64963	−	13.2496i	−0.293782	−	0.508846i
$679$	5.05166	+	8.74973i	0.193865	+	0.335784i
$680$	−1.21302	+	2.10102i	−0.0465173	+	0.0805703i
$681$	28.9709			1.11017
$682$	1.52402	−	2.63968i	0.0583578	−	0.101079i
$683$	−8.48198	+	14.6912i	−0.324554	+	0.562144i	−0.981422	−	0.191862i	$-0.938547\pi$
$683$	−8.48198	+	14.6912i	−0.324554	+	0.562144i	0.656868	+	0.754005i	$0.271881\pi$
$684$	−0.868391			−0.0332038
$685$	−11.1483	+	19.3094i	−0.425954	+	0.737774i
$686$	−0.636945	−	1.10322i	−0.0243187	−	0.0421212i
$687$	0.339695	+	0.588369i	0.0129602	+	0.0224477i
$688$	14.3460			0.546935
$689$	−19.2876	−	5.30089i	−0.734801	−	0.201948i
$690$	0.105435			0.00401384
$691$	−18.3213	−	31.7334i	−0.696974	−	1.20719i	−0.969511	−	0.245049i	$-0.921196\pi$
$691$	−18.3213	−	31.7334i	−0.696974	−	1.20719i	0.272537	−	0.962145i	$-0.412137\pi$
$692$	2.58730	+	4.48134i	0.0983545	+	0.170355i
$693$	−0.174453	+	0.302162i	−0.00662693	+	0.0114782i
$694$	42.6730			1.61984
$695$	−2.35772	+	4.08369i	−0.0894333	+	0.154903i
$696$	0.727571	−	1.26019i	0.0275785	−	0.0477674i
$697$	2.24772			0.0851384
$698$	−17.9494	+	31.0893i	−0.679395	+	1.17675i
$699$	−9.15109	−	15.8502i	−0.346126	−	0.599508i
$700$	0.713423	+	1.23568i	0.0269649	+	0.0467045i
$701$	−14.6092			−0.551782			−0.275891	−	0.961189i	$-0.588973\pi$
$701$	−14.6092			−0.551782			−0.275891	+	0.961189i	$0.588973\pi$
$702$	1.16031	+	4.44410i	0.0437929	+	0.167732i
$703$	−2.54003			−0.0957991
$704$	1.55019	+	2.68502i	0.0584252	+	0.101195i
$705$	2.59702	+	4.49818i	0.0978096	+	0.169411i
$706$	−1.90590	+	3.30111i	−0.0717295	+	0.124239i
$707$	−4.07502			−0.153257
$708$	0.740258	−	1.28216i	0.0278206	−	0.0481867i
$709$	11.7930	−	20.4260i	0.442894	−	0.767116i	−0.555008	−	0.831845i	$-0.687285\pi$
$709$	11.7930	−	20.4260i	0.442894	−	0.767116i	0.997903	+	0.0647290i	$0.0206183\pi$
$710$	13.3935			0.502649
$711$	−8.55272	+	14.8137i	−0.320752	+	0.555559i
$712$	18.1108	+	31.3688i	0.678730	+	1.17559i
$713$	0.257219	+	0.445517i	0.00963294	+	0.0166847i
$714$	−0.924984			−0.0346167
$715$	−0.350629	−	1.34295i	−0.0131128	−	0.0502235i
$716$	8.30994			0.310557
$717$	−2.72611	−	4.72176i	−0.101808	−	0.176337i
$718$	2.42605	+	4.20203i	0.0905392	+	0.156819i
$719$	−17.0669	+	29.5607i	−0.636487	+	1.10243i	0.349711	+	0.936857i	$0.386280\pi$
$719$	−17.0669	+	29.5607i	−0.636487	+	1.10243i	−0.986198	+	0.165570i	$0.947054\pi$
$720$	−3.42392			−0.127602
$721$	−2.05553	+	3.56028i	−0.0765520	+	0.132592i
$722$	−8.72611	+	15.1141i	−0.324752	+	0.562487i
$723$	15.4621			0.575041
$724$	1.77923	−	3.08171i	0.0661245	−	0.114531i
$725$	0.908823	+	1.57413i	0.0337528	+	0.0584616i
$726$	6.92886	+	12.0011i	0.257154	+	0.445404i
$727$	−15.3481			−0.569230			−0.284615	−	0.958642i	$-0.591866\pi$
$727$	−15.3481			−0.569230			−0.284615	+	0.958642i	$0.591866\pi$
$728$	−7.77002	+	7.67101i	−0.287976	+	0.284307i
$729$	1.00000			0.0370370
$730$	−7.33235	−	12.7000i	−0.271382	−	0.470048i
$731$	1.67833	+	2.90695i	0.0620752	+	0.107517i
$732$	−1.04632	+	1.81228i	−0.0386731	+	0.0669837i
$733$	23.2894			0.860213			0.430107	−	0.902778i	$-0.358476\pi$
$733$	23.2894			0.860213			0.430107	+	0.902778i	$0.358476\pi$
$734$	−16.8481	+	29.1818i	−0.621875	+	1.07712i
$735$	0.551656	−	0.955496i	0.0203481	−	0.0352440i
$736$	−0.157782			−0.00581593
$737$	1.41723	−	2.45472i	0.0522045	−	0.0904208i
$738$	1.97170	+	3.41509i	0.0725794	+	0.125711i
$739$	5.13307	+	8.89074i	0.188823	+	0.327051i	0.944858	−	0.327480i	$-0.106199\pi$
$739$	5.13307	+	8.89074i	0.188823	+	0.327051i	−0.756035	+	0.654531i	$0.772866\pi$
$740$	0.459168			0.0168794
$741$	8.00388	+	2.19973i	0.294030	+	0.0808092i
$742$	7.06727			0.259447
$743$	22.6741	+	39.2726i	0.831830	+	1.44077i	0.896585	+	0.442871i	$0.146040\pi$
$743$	22.6741	+	39.2726i	0.831830	+	1.44077i	−0.0647549	+	0.997901i	$0.520627\pi$
$744$	−10.3836	−	17.9849i	−0.380681	−	0.659359i
$745$	2.70129	−	4.67877i	0.0989675	−	0.171417i
$746$	−2.71544			−0.0994192
$747$	5.95716	−	10.3181i	0.217961	−	0.377519i
$748$	−0.0477811	+	0.0827593i	−0.00174705	+	0.00302598i
$749$	6.17058			0.225468
$750$	6.17204	−	10.6903i	0.225371	−	0.390354i
$751$	14.8057	+	25.6442i	0.540266	+	0.935769i	0.998888	+	0.0471372i	$0.0150098\pi$
$751$	14.8057	+	25.6442i	0.540266	+	0.935769i	−0.458622	+	0.888631i	$0.651657\pi$
$752$	7.30471	+	12.6521i	0.266375	+	0.461376i
$753$	8.29444			0.302266
$754$	−1.57059	+	1.55058i	−0.0571975	+	0.0564687i
$755$	−9.86971			−0.359196
$756$	0.188601	+	0.326667i	0.00685937	+	0.0118808i
$757$	12.9908	+	22.5007i	0.472158	+	0.817802i	0.999492	−	0.0318559i	$-0.0101418\pi$
$757$	12.9908	+	22.5007i	0.472158	+	0.817802i	−0.527334	+	0.849658i	$0.676808\pi$
$758$	−8.88119	+	15.3827i	−0.322579	+	0.558724i
$759$	0.0261736			0.000950041
$760$	−3.84598	+	6.66144i	−0.139508	+	0.241636i
$761$	27.0332	−	46.8229i	0.979954	−	1.69733i	0.317444	−	0.948277i	$-0.397176\pi$
$761$	27.0332	−	46.8229i	0.979954	−	1.69733i	0.662510	−	0.749053i	$-0.269491\pi$
$762$	−7.46209			−0.270323
$763$	−4.41084	+	7.63979i	−0.159683	+	0.276579i
$764$	−0.636945	−	1.10322i	−0.0230439	−	0.0399132i
$765$	−0.400563	−	0.693795i	−0.0144824	−	0.0250842i
$766$	23.6999			0.856313
$767$	−10.0707	+	9.94242i	−0.363633	+	0.359000i
$768$	8.71061			0.314317
$769$	−12.8967	−	22.3377i	−0.465066	−	0.805519i	0.534138	−	0.845397i	$-0.320636\pi$
$769$	−12.8967	−	22.3377i	−0.465066	−	0.805519i	−0.999205	+	0.0398785i	$0.987303\pi$
$770$	0.245194	+	0.424688i	0.00883618	+	0.0153047i

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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.636945 + 1.10322i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.188601 - 0.326667i) q^{4} +1.10331 q^{5} +(-0.636945 + 1.10322i) q^{6} +(0.500000 - 0.866025i) q^{7} +3.02830 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.636945 + 1.10322i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.188601 - 0.326667i) q^{4} +1.10331 q^{5} +(-0.636945 + 1.10322i) q^{6} +(0.500000 - 0.866025i) q^{7} +3.02830 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.702750 + 1.21720i) q^{10} +(0.174453 + 0.302162i) q^{11} +0.377203 q^{12} +(-3.47664 - 0.955496i) q^{13} +1.27389 q^{14} +(0.551656 + 0.955496i) q^{15} +(1.55166 + 2.68755i) q^{16} +(-0.363055 + 0.628829i) q^{17} -1.27389 q^{18} +(-1.15109 + 1.99375i) q^{19} +(0.208086 - 0.360416i) q^{20} +1.00000 q^{21} +(-0.222234 + 0.384921i) q^{22} +(-0.0375080 - 0.0649658i) q^{23} +(1.51415 + 2.62258i) q^{24} -3.78270 q^{25} +(-1.16031 - 4.44410i) q^{26} -1.00000 q^{27} +(-0.188601 - 0.326667i) q^{28} +(-0.240258 - 0.416138i) q^{29} +(-0.702750 + 1.21720i) q^{30} -6.85772 q^{31} +(1.05166 - 1.82152i) q^{32} +(-0.174453 + 0.302162i) q^{33} -0.924984 q^{34} +(0.551656 - 0.955496i) q^{35} +(0.188601 + 0.326667i) q^{36} +(0.551656 + 0.955496i) q^{37} -2.93273 q^{38} +(-0.910836 - 3.48861i) q^{39} +3.34116 q^{40} +(-1.54778 - 2.68084i) q^{41} +(0.636945 + 1.10322i) q^{42} +(2.31140 - 4.00346i) q^{43} +0.131609 q^{44} +(-0.551656 + 0.955496i) q^{45} +(0.0477811 - 0.0827593i) q^{46} +4.70769 q^{47} +(-1.55166 + 2.68755i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.40937 - 4.17316i) q^{50} -0.726109 q^{51} +(-0.967829 + 0.955496i) q^{52} +5.54778 q^{53} +(-0.636945 - 1.10322i) q^{54} +(0.192476 + 0.333379i) q^{55} +(1.51415 - 2.62258i) q^{56} -2.30219 q^{57} +(0.306062 - 0.530115i) q^{58} +(1.96249 - 3.39914i) q^{59} +0.416173 q^{60} +(-2.77389 + 4.80452i) q^{61} +(-4.36799 - 7.56558i) q^{62} +(0.500000 + 0.866025i) q^{63} +8.88601 q^{64} +(-3.83582 - 1.05421i) q^{65} -0.444469 q^{66} +(-4.06193 - 7.03547i) q^{67} +(0.136945 + 0.237196i) q^{68} +(0.0375080 - 0.0649658i) q^{69} +1.40550 q^{70} +(4.76468 - 8.25267i) q^{71} +(-1.51415 + 2.62258i) q^{72} -10.4338 q^{73} +(-0.702750 + 1.21720i) q^{74} +(-1.89135 - 3.27592i) q^{75} +(0.434196 + 0.752049i) q^{76} +0.348907 q^{77} +(3.26855 - 3.22691i) q^{78} +17.1054 q^{79} +(1.71196 + 2.96520i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.97170 - 3.41509i) q^{82} -11.9143 q^{83} +(0.188601 - 0.326667i) q^{84} +(-0.400563 + 0.693795i) q^{85} +5.88894 q^{86} +(0.240258 - 0.416138i) q^{87} +(0.528296 + 0.915036i) q^{88} +(5.98052 + 10.3586i) q^{89} -1.40550 q^{90} +(-2.56580 + 2.53311i) q^{91} -0.0282963 q^{92} +(-3.42886 - 5.93896i) q^{93} +(2.99854 + 5.19362i) q^{94} +(-1.27002 + 2.19973i) q^{95} +2.10331 q^{96} +(-5.05166 + 8.74973i) q^{97} +(0.636945 - 1.10322i) q^{98} -0.348907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} - 13 q^{10} + 8 q^{11} - 8 q^{12} + 4 q^{14} + 6 q^{16} - 4 q^{17} - 4 q^{18} + 7 q^{19} + 13 q^{20} + 6 q^{21} - q^{22} - 9 q^{23} - 3 q^{24} + 22 q^{25} - 26 q^{26} - 6 q^{27} + 4 q^{28} + 7 q^{29} + 13 q^{30} - 14 q^{31} + 3 q^{32} - 8 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{38} + 26 q^{40} - 2 q^{41} + 2 q^{42} + 19 q^{43} - 30 q^{44} - 7 q^{46} - 34 q^{47} - 6 q^{48} - 3 q^{49} + 16 q^{50} - 8 q^{51} - 26 q^{52} + 26 q^{53} - 2 q^{54} - 3 q^{56} + 14 q^{57} - 22 q^{58} + 3 q^{59} + 26 q^{60} - 13 q^{61} + 17 q^{62} + 3 q^{63} + 2 q^{64} - 2 q^{66} - 5 q^{67} - q^{68} + 9 q^{69} - 26 q^{70} - 8 q^{71} + 3 q^{72} - 4 q^{73} + 13 q^{74} + 11 q^{75} + 18 q^{76} + 16 q^{77} - 13 q^{78} - 2 q^{79} + 26 q^{80} - 3 q^{81} + 36 q^{82} + 4 q^{83} - 4 q^{84} - 13 q^{85} + 34 q^{86} - 7 q^{87} - 21 q^{88} + 19 q^{89} + 26 q^{90} + 24 q^{92} - 7 q^{93} - 7 q^{94} + 6 q^{96} - 27 q^{97} + 2 q^{98} - 16 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 - 13 * q^10 + 8 * q^11 - 8 * q^12 + 4 * q^14 + 6 * q^16 - 4 * q^17 - 4 * q^18 + 7 * q^19 + 13 * q^20 + 6 * q^21 - q^22 - 9 * q^23 - 3 * q^24 + 22 * q^25 - 26 * q^26 - 6 * q^27 + 4 * q^28 + 7 * q^29 + 13 * q^30 - 14 * q^31 + 3 * q^32 - 8 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^38 + 26 * q^40 - 2 * q^41 + 2 * q^42 + 19 * q^43 - 30 * q^44 - 7 * q^46 - 34 * q^47 - 6 * q^48 - 3 * q^49 + 16 * q^50 - 8 * q^51 - 26 * q^52 + 26 * q^53 - 2 * q^54 - 3 * q^56 + 14 * q^57 - 22 * q^58 + 3 * q^59 + 26 * q^60 - 13 * q^61 + 17 * q^62 + 3 * q^63 + 2 * q^64 - 2 * q^66 - 5 * q^67 - q^68 + 9 * q^69 - 26 * q^70 - 8 * q^71 + 3 * q^72 - 4 * q^73 + 13 * q^74 + 11 * q^75 + 18 * q^76 + 16 * q^77 - 13 * q^78 - 2 * q^79 + 26 * q^80 - 3 * q^81 + 36 * q^82 + 4 * q^83 - 4 * q^84 - 13 * q^85 + 34 * q^86 - 7 * q^87 - 21 * q^88 + 19 * q^89 + 26 * q^90 + 24 * q^92 - 7 * q^93 - 7 * q^94 + 6 * q^96 - 27 * q^97 + 2 * q^98 - 16 * q^99

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