LMFDB - Embedded newform 273.2.k.d.22.2

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			22.2
Root			$-0.688601 + 1.19269i$ of defining polynomial
Character	$\chi$	$=$	273.22
Dual form			273.2.k.d.211.2

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

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

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	−0.548022	−	0.836464i	$-0.684619\pi$
$2$	0.636945	−	1.10322i	0.450388	−	0.780095i	0.998410	+	0.0563687i	$0.0179522\pi$
$3$	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	−0.838527	−	0.544860i	$-0.816583\pi$
$11$	0.174453	−	0.302162i	0.0525996	−	0.0911053i	0.891126	+	0.453755i	$0.149916\pi$
$12$	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	0.818635	−	0.574315i	$-0.194731\pi$
$17$	−0.363055	−	0.628829i	−0.0880537	−	0.152513i	−0.906688	+	0.421801i	$0.861398\pi$
$18$	−1.27389			−0.300259
$19$	−1.15109	−	1.99375i	−0.264079	−	0.457398i	0.703243	−	0.710950i	$-0.251735\pi$
$19$	−1.15109	−	1.99375i	−0.264079	−	0.457398i	−0.967322	+	0.253551i	$0.918401\pi$
$20$	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	−0.869909	−	0.493212i	$-0.835823\pi$
$23$	−0.0375080	+	0.0649658i	−0.00782096	+	0.0135463i	0.862088	+	0.506758i	$0.169156\pi$
$24$	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	−0.887470	−	0.460865i	$-0.847539\pi$
$29$	−0.240258	+	0.416138i	−0.0446147	+	0.0772749i	0.842856	+	0.538140i	$0.180873\pi$
$30$	−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	−0.817111	−	0.576481i	$-0.804426\pi$
$37$	0.551656	−	0.955496i	0.0906917	−	0.157083i	0.907802	+	0.419398i	$0.137759\pi$
$38$	−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	−0.961205	−	0.275835i	$-0.911046\pi$
$41$	−1.54778	+	2.68084i	−0.241723	+	0.418676i	0.719482	+	0.694511i	$0.244379\pi$
$42$	0.636945	−	1.10322i	0.0982828	−	0.170231i
$43$	2.31140	+	4.00346i	0.352485	+	0.610522i	0.986684	−	0.162648i	$-0.0520034\pi$
$43$	2.31140	+	4.00346i	0.352485	+	0.610522i	−0.634199	+	0.773170i	$0.718670\pi$
$44$	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	0.965030	−	0.262140i	$-0.0844283\pi$
$59$	1.96249	+	3.39914i	0.255495	+	0.442530i	−0.709535	+	0.704670i	$0.751095\pi$
$60$	0.416173			0.0537276
$61$	−2.77389	−	4.80452i	−0.355160	−	0.615156i	0.631985	−	0.774981i	$-0.282240\pi$
$61$	−2.77389	−	4.80452i	−0.355160	−	0.615156i	−0.987145	+	0.159825i	$0.948907\pi$
$62$	−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	−0.999991	−	0.00433206i	$-0.998621\pi$
$67$	−4.06193	+	7.03547i	−0.496244	+	0.859519i	0.503747	+	0.863851i	$0.331954\pi$
$68$	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	0.997006	+	0.0773189i	$0.0246360\pi$
$71$	4.76468	+	8.25267i	0.565463	+	0.979411i	−0.431543	+	0.902092i	$0.642031\pi$
$72$	−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	−0.352807	−	0.935696i	$-0.614773\pi$
$89$	5.98052	−	10.3586i	0.633933	−	1.09800i	0.986740	−	0.162309i	$-0.0518940\pi$
$90$	−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	−0.999888	−	0.0149812i	$-0.995231\pi$
$97$	−5.05166	−	8.74973i	−0.512918	−	0.888400i	0.486970	−	0.873419i	$-0.338102\pi$
$98$	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	−0.949410	−	0.314039i	$-0.898318\pi$
$101$	−2.03751	+	3.52907i	−0.202740	+	0.351155i	0.746671	+	0.665194i	$0.231651\pi$
$102$	−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	−0.677473	−	0.735547i	$-0.736925\pi$
$107$	3.08529	−	5.34388i	0.298266	−	0.516612i	0.975739	+	0.218935i	$0.0702584\pi$
$108$	−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	−0.997059	−	0.0766343i	$-0.975583\pi$
$113$	−6.00494	−	10.4009i	−0.564897	−	0.978430i	0.432162	−	0.901796i	$-0.357751\pi$
$114$	−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	−0.706319	−	0.707894i	$-0.749646\pi$
$127$	2.92886	−	5.07293i	0.259894	−	0.450150i	0.966213	+	0.257744i	$0.0829790\pi$
$128$	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	−0.868750	−	0.495251i	$-0.835076\pi$
$137$	−10.1044	−	17.5013i	−0.863275	−	1.49524i	0.00547505	−	0.999985i	$-0.498257\pi$
$138$	0.0955622			0.00813480
$139$	−2.13695	−	3.70130i	−0.181253	−	0.313940i	0.761054	−	0.648688i	$-0.224682\pi$
$139$	−2.13695	−	3.70130i	−0.181253	−	0.313940i	−0.942308	+	0.334748i	$0.891349\pi$
$140$	−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	0.948714	−	0.316135i	$-0.102385\pi$
$149$	2.44834	+	4.24066i	0.200576	+	0.347408i	−0.748138	+	0.663543i	$0.769052\pi$
$150$	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	0.992165	−	0.124933i	$-0.0398715\pi$
$163$	4.95222	+	8.57749i	0.387888	+	0.671841i	−0.604277	+	0.796774i	$0.706538\pi$
$164$	−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	−0.335192	−	0.942150i	$-0.608801\pi$
$167$	8.37826	−	14.5116i	0.648330	−	1.12294i	0.983522	−	0.180790i	$-0.0578654\pi$
$168$	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	−0.999687	−	0.0249993i	$-0.992042\pi$
$173$	−6.85918	−	11.8804i	−0.521494	−	0.903254i	0.478194	−	0.878254i	$-0.341292\pi$
$174$	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	−0.0798846	−	0.996804i	$-0.525455\pi$
$179$	11.0152	−	19.0789i	0.823315	−	1.42602i	0.903200	−	0.429220i	$-0.141211\pi$
$180$	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	0.920628	−	0.390440i	$-0.127677\pi$
$191$	1.68860	+	2.92474i	0.122183	+	0.211627i	−0.798445	+	0.602067i	$0.794344\pi$
$192$	4.44301	−	7.69551i	0.320646	−	0.555376i
$193$	−11.1614	+	19.3321i	−0.803413	+	1.39155i	0.113945	+	0.993487i	$0.463651\pi$
$193$	−11.1614	+	19.3321i	−0.803413	+	1.39155i	−0.917357	+	0.398065i	$0.869682\pi$
$194$	−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	0.0880085	−	0.996120i	$-0.471950\pi$
$197$	12.7257	−	22.0416i	0.906669	−	1.57040i	0.818661	−	0.574277i	$-0.194717\pi$
$198$	−0.222234	+	0.384921i	−0.0157935	+	0.0273552i
$199$	11.1702	+	19.3473i	0.791833	+	1.37149i	0.924831	+	0.380379i	$0.124206\pi$
$199$	11.1702	+	19.3473i	0.791833	+	1.37149i	−0.132998	+	0.991116i	$0.542460\pi$
$200$	−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	−0.985450	−	0.169968i	$-0.945634\pi$
$211$	−5.01908	+	8.69331i	−0.345528	+	0.598472i	0.639922	+	0.768440i	$0.278967\pi$
$212$	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	−0.767173	−	0.641440i	$-0.778337\pi$
$223$	2.56727	−	4.44664i	0.171917	−	0.297769i	0.939090	+	0.343671i	$0.111671\pi$
$224$	−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	0.718907	+	0.695106i	$0.244643\pi$
$227$	14.4855	+	25.0895i	0.961433	+	1.66525i	0.242526	+	0.970145i	$0.422024\pi$
$228$	−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	0.999997	−	0.00230736i	$-0.000734455\pi$
$241$	7.73105	+	13.3906i	0.498000	+	0.862562i	−0.501997	+	0.864869i	$0.667401\pi$
$242$	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	0.966712	−	0.255866i	$-0.0823604\pi$
$251$	4.14722	+	7.18319i	0.261770	+	0.453399i	−0.704942	+	0.709265i	$0.749027\pi$
$252$	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	−0.530346	−	0.847782i	$-0.677938\pi$
$257$	7.51908	−	13.0234i	0.469028	−	0.812380i	0.999373	+	0.0354019i	$0.0112711\pi$
$258$	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	−0.467636	−	0.883921i	$-0.654894\pi$
$263$	8.62240	−	14.9344i	0.531680	−	0.920896i	0.999316	−	0.0369754i	$-0.0117723\pi$
$264$	−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	0.952209	+	0.305446i	$0.0988057\pi$
$269$	12.1472	+	21.0396i	0.740629	+	1.28281i	−0.211580	+	0.977361i	$0.567861\pi$
$270$	−0.702750	+	1.21720i	−0.0427680	+	0.0740763i
$271$	−9.16630	+	15.8765i	−0.556813	+	0.964429i	0.440947	+	0.897533i	$0.354643\pi$
$271$	−9.16630	+	15.8765i	−0.556813	+	0.964429i	−0.997760	+	0.0668956i	$0.978691\pi$
$272$	−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	0.710634	−	0.703562i	$-0.248408\pi$
$277$	−4.22717	−	7.32167i	−0.253986	−	0.439917i	−0.964620	+	0.263646i	$0.915075\pi$
$278$	−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	0.108443	+	0.994103i	$0.465414\pi$
$283$	−13.5707	+	23.5052i	−0.806697	+	1.39724i	−0.915140	+	0.403137i	$0.867920\pi$
$284$	−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	0.977898	−	0.209083i	$-0.0670479\pi$
$293$	5.27002	+	9.12793i	0.307878	+	0.533260i	−0.670020	+	0.742343i	$0.733715\pi$
$294$	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	0.623538	−	0.781793i	$-0.285695\pi$
$331$	−6.64576	−	11.5108i	−0.365284	−	0.632690i	−0.988822	+	0.149103i	$0.952361\pi$
$332$	−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	0.828599	+	0.559842i	$0.189138\pi$
$347$	16.7491	+	29.0102i	0.899137	+	1.55735i	0.0705378	+	0.997509i	$0.477528\pi$
$348$	−0.0906258	+	0.156969i	−0.00485806	+	0.00841440i
$349$	14.0902	−	24.4050i	0.754232	−	1.30637i	−0.191523	−	0.981488i	$-0.561342\pi$
$349$	14.0902	−	24.4050i	0.754232	−	1.30637i	0.945755	−	0.324881i	$-0.105324\pi$
$350$	−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	−0.823460	−	0.567374i	$-0.807959\pi$
$353$	1.49612	−	2.59136i	0.0796307	−	0.137924i	0.903091	+	0.429450i	$0.141293\pi$
$354$	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	−0.281338	−	0.959609i	$-0.590778\pi$
$367$	13.2257	−	22.9076i	0.690376	−	1.19577i	0.971715	−	0.236158i	$-0.0758884\pi$
$368$	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	0.837113	−	0.547030i	$-0.184242\pi$
$373$	−1.06580	−	1.84603i	−0.0551853	−	0.0955837i	−0.892298	+	0.451446i	$0.850908\pi$
$374$	−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	−0.629533	−	0.776974i	$-0.716754\pi$
$379$	6.97170	−	12.0753i	0.358112	−	0.620269i	0.987645	+	0.156705i	$0.0500871\pi$
$380$	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	0.999600	−	0.0282678i	$-0.00899913\pi$
$383$	9.30219	+	16.1119i	0.475320	+	0.823278i	−0.524281	+	0.851545i	$0.675666\pi$
$384$	−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	−0.951055	−	0.309022i	$-0.899998\pi$
$397$	−14.8071	−	25.6467i	−0.743148	−	1.28717i	0.207907	−	0.978149i	$-0.433335\pi$
$398$	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	−0.949895	−	0.312568i	$-0.898811\pi$
$401$	−4.09023	+	7.08448i	−0.204256	+	0.353782i	0.745639	+	0.666350i	$0.232144\pi$
$402$	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	0.714323	−	0.699816i	$-0.246735\pi$
$409$	−5.03363	−	8.71851i	−0.248897	−	0.431102i	−0.963220	+	0.268714i	$0.913401\pi$
$410$	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	−0.958125	−	0.286351i	$-0.907558\pi$
$419$	−4.72998	+	8.19257i	−0.231075	+	0.400233i	0.727050	+	0.686585i	$0.240891\pi$
$420$	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	−0.384303	−	0.923207i	$-0.625558\pi$
$431$	12.6093	−	21.8400i	0.607369	−	1.05199i	0.991672	−	0.128787i	$-0.0411084\pi$
$432$	−1.55166	+	2.68755i	−0.0746541	+	0.129305i
$433$	−1.88495	−	3.26483i	−0.0905851	−	0.156898i	0.817172	−	0.576393i	$-0.195540\pi$
$433$	−1.88495	−	3.26483i	−0.0905851	−	0.156898i	−0.907757	+	0.419495i	$0.862207\pi$
$434$	−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	−0.458745	−	0.888568i	$-0.651701\pi$
$439$	11.3174	−	19.6023i	0.540150	−	0.935567i	0.998895	−	0.0469991i	$-0.0149658\pi$
$440$	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	0.733170	−	0.680046i	$-0.238040\pi$
$449$	−4.71156	−	8.16066i	−0.222352	−	0.385125i	−0.955522	+	0.294920i	$0.904707\pi$
$450$	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	−0.975545	−	0.219800i	$-0.929460\pi$
$457$	−6.35812	+	11.0126i	−0.297420	+	0.515147i	0.678125	+	0.734947i	$0.262793\pi$
$458$	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	0.971108	+	0.238641i	$0.0767018\pi$
$461$	14.8627	+	25.7429i	0.692223	+	1.19897i	−0.278885	+	0.960324i	$0.589965\pi$
$462$	−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	−0.492524	−	0.870299i	$-0.663926\pi$
$479$	11.1058	−	19.2359i	0.507439	−	0.878909i	0.999963	−	0.00861072i	$-0.00274091\pi$
$480$	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	0.876824	−	0.480812i	$-0.159658\pi$
$487$	0.485852	+	0.841520i	0.0220160	+	0.0381329i	−0.854807	+	0.518945i	$0.826325\pi$
$488$	−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	0.383830	+	0.923404i	$0.374605\pi$
$491$	−13.4674	+	23.3263i	−0.607777	+	1.05270i	−0.991606	+	0.129296i	$0.958728\pi$
$492$	−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	0.691285	−	0.722582i	$-0.257045\pi$
$503$	−6.28270	−	10.8820i	−0.280132	−	0.485203i	−0.971417	+	0.237379i	$0.923712\pi$
$504$	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	0.379116	+	0.925349i	$0.376228\pi$
$509$	−13.8032	+	23.9079i	−0.611818	+	1.05970i	−0.990934	+	0.134351i	$0.957105\pi$
$510$	−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	0.303389	+	0.952867i	$0.401882\pi$
$523$	−15.4027	+	26.6782i	−0.673512	+	1.16656i	−0.976901	+	0.213691i	$0.931451\pi$
$524$	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	0.350440	+	0.936585i	$0.386032\pi$
$557$	−15.0075	+	25.9937i	−0.635886	+	1.10139i	−0.986327	+	0.164803i	$0.947301\pi$
$558$	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	−0.998510	−	0.0545676i	$-0.982622\pi$
$563$	−12.9674	−	22.4602i	−0.546512	−	0.946586i	0.451998	−	0.892019i	$-0.350711\pi$
$564$	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	−0.788966	−	0.614437i	$-0.789383\pi$
$569$	3.28310	−	5.68650i	0.137635	−	0.238390i	0.926601	+	0.376046i	$0.122717\pi$
$570$	−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	−0.866347	−	0.499442i	$-0.833538\pi$
$587$	−0.0156098	+	0.0270370i	−0.000644286	+	0.00111594i	0.865703	+	0.500558i	$0.166872\pi$
$588$	−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	−0.912891	−	0.408204i	$-0.866155\pi$
$601$	−2.52336	+	4.37059i	−0.102930	+	0.178280i	0.809961	+	0.586484i	$0.199488\pi$
$602$	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	0.646167	−	0.763196i	$-0.276371\pi$
$607$	−8.32409	−	14.4177i	−0.337864	−	0.585198i	−0.984031	+	0.177998i	$0.943038\pi$
$608$	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	0.171192	+	0.985238i	$0.445238\pi$
$613$	−19.0060	+	32.9194i	−0.767645	+	1.32960i	−0.938837	+	0.344362i	$0.888095\pi$
$614$	−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	0.664157	−	0.747593i	$-0.268791\pi$
$617$	−7.83330	−	13.5677i	−0.315357	−	0.546214i	−0.979513	+	0.201380i	$0.935457\pi$
$618$	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	0.849667	−	0.527319i	$-0.176803\pi$
$631$	−0.799773	−	1.38525i	−0.0318385	−	0.0551459i	−0.881506	+	0.472174i	$0.843470\pi$
$632$	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	−0.989625	−	0.143678i	$-0.954107\pi$
$641$	−15.6779	−	27.1550i	−0.619241	−	1.07256i	0.370384	−	0.928879i	$-0.379226\pi$
$642$	−7.86064			−0.310235
$643$	9.33154	+	16.1627i	0.368000	+	0.637395i	0.989253	−	0.146215i	$-0.0467092\pi$
$643$	9.33154	+	16.1627i	0.368000	+	0.637395i	−0.621253	+	0.783610i	$0.713376\pi$
$644$	−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	−0.923096	−	0.384570i	$-0.874350\pi$
$647$	−3.26855	+	5.66130i	−0.128500	+	0.222569i	0.794596	+	0.607139i	$0.207683\pi$
$648$	−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	−0.978399	−	0.206725i	$-0.933719\pi$
$653$	−7.92605	+	13.7283i	−0.310170	+	0.537230i	0.668229	+	0.743956i	$0.267053\pi$
$654$	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	0.695784	+	0.718251i	$0.255057\pi$
$659$	24.8987	+	43.1258i	0.969916	+	1.67994i	0.274132	+	0.961692i	$0.411610\pi$
$660$	0.0726027	−	0.125752i	0.00282606	−	0.00489487i
$661$	−1.78552	+	3.09260i	−0.0694485	+	0.120288i	−0.898659	−	0.438649i	$-0.855457\pi$
$661$	−1.78552	+	3.09260i	−0.0694485	+	0.120288i	0.829210	+	0.558937i	$0.188791\pi$
$662$	−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	−0.956665	−	0.291191i	$-0.905948\pi$
$673$	−5.86693	+	10.1618i	−0.226154	+	0.391709i	0.730511	+	0.682901i	$0.239282\pi$
$674$	−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	0.656868	−	0.754005i	$-0.271881\pi$
$683$	−8.48198	−	14.6912i	−0.324554	−	0.562144i	−0.981422	+	0.191862i	$0.938547\pi$
$684$	−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	0.272537	+	0.962145i	$0.412137\pi$
$691$	−18.3213	+	31.7334i	−0.696974	+	1.20719i	−0.969511	+	0.245049i	$0.921196\pi$
$692$	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	0.997903	−	0.0647290i	$-0.0206183\pi$
$709$	11.7930	+	20.4260i	0.442894	+	0.767116i	−0.555008	+	0.831845i	$0.687285\pi$
$710$	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	−0.986198	−	0.165570i	$-0.947054\pi$
$719$	−17.0669	−	29.5607i	−0.636487	−	1.10243i	0.349711	−	0.936857i	$-0.386280\pi$
$720$	−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	−0.756035	−	0.654531i	$-0.772866\pi$
$739$	5.13307	−	8.89074i	0.188823	−	0.327051i	0.944858	+	0.327480i	$0.106199\pi$
$740$	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	−0.0647549	−	0.997901i	$-0.520627\pi$
$743$	22.6741	−	39.2726i	0.831830	−	1.44077i	0.896585	−	0.442871i	$-0.146040\pi$
$744$	−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	−0.458622	−	0.888631i	$-0.651657\pi$
$751$	14.8057	−	25.6442i	0.540266	−	0.935769i	0.998888	−	0.0471372i	$-0.0150098\pi$
$752$	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	−0.527334	−	0.849658i	$-0.676808\pi$
$757$	12.9908	−	22.5007i	0.472158	−	0.817802i	0.999492	+	0.0318559i	$0.0101418\pi$
$758$	−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	0.662510	+	0.749053i	$0.269491\pi$
$761$	27.0332	+	46.8229i	0.979954	+	1.69733i	0.317444	+	0.948277i	$0.397176\pi$
$762$	−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	−0.999205	−	0.0398785i	$-0.987303\pi$
$769$	−12.8967	+	22.3377i	−0.465066	+	0.805519i	0.534138	+	0.845397i	$0.320636\pi$
$770$	0.245194	−	0.424688i	0.00883618	−	0.0153047i
$771$	−7.51908	−	13.0234i	−0.270793	−	0.469028i
$772$	−8.42020			−0.303050
$773$	0.0608679	+	0.105426i	0.00218927	+	0.00379192i	0.867118	−	0.498103i	$-0.165970\pi$
$773$	0.0608679	+	0.105426i	0.00218927	+	0.00379192i	−0.864929	+	0.501895i	$0.832636\pi$
$774$	−2.94447	−	5.09997i	−0.105837	−	0.183315i
$775$	25.9407			0.931818
$776$	−15.2979	−	26.4968i	−0.549163	−	0.951178i
$777$	0.551656	−	0.955496i	0.0197906	−	0.0342782i
$778$	−0.783503	+	1.35707i	−0.0280899	+	0.0486532i
$779$	7.12656			0.255336
$780$	−1.44688	+	0.397651i	−0.0518067	+	0.0142382i
$781$	3.32486			0.118973
$782$	0.0346943	−	0.0600923i	0.00124067	−	0.00214890i
$783$	0.240258	−	0.416138i	0.00858611	−	0.0148716i
$784$	1.55166	+	2.68755i	0.0554163	+	0.0959838i
$785$	7.27579			0.259684
$786$	−14.2711	−	24.7182i	−0.509032	−	0.881670i
$787$	10.1108	+	17.5124i	0.360410	+	0.624249i	0.988028	−	0.154273i	$-0.0493034\pi$
$787$	10.1108	+	17.5124i	0.360410	+	0.624249i	−0.627618	+	0.778521i	$0.715970\pi$
$788$	9.60035			0.341998
$789$	−8.62240	−	14.9344i	−0.306965	−	0.531680i
$790$	12.0208	−	20.8207i	0.427682	−	0.740767i
$791$	6.00494	−	10.4009i	0.213511	−	0.369812i
$792$	−1.05659			−0.0375444
$793$	14.2345	+	14.0531i	0.505483	+	0.499042i
$794$	−37.7253			−1.33882
$795$	3.06047	−	5.30089i	0.108544	−	0.188003i
$796$	−4.21342	+	7.29786i	−0.149341	+	0.258666i
$797$	−16.2062	−	28.0700i	−0.574054	−	0.994291i	−0.996144	−	0.0877365i	$-0.972037\pi$
$797$	−16.2062	−	28.0700i	−0.574054	−	0.994291i	0.422090	−	0.906554i	$-0.361297\pi$
$798$	−2.93273			−0.103818
$799$	−1.70915	−	2.96033i	−0.0604653	−	0.104729i
$800$	−3.97810	−	6.89027i	−0.140647	−	0.243608i
$801$	−11.9610			−0.422622
$802$	5.21050	+	9.02485i	0.183989	+	0.318679i
$803$	−1.82021	+	3.15270i	−0.0642338	+	0.111256i
$804$	−1.53217	+	2.65380i	−0.0540355	+	0.0935923i
$805$	−0.0827661			−0.00291712
$806$	7.95705	−	30.4764i	0.280275	−	1.07349i
$807$	24.2944			0.855205
$808$	−6.17018	+	10.6871i	−0.217066	+	0.375970i
$809$	−12.2314	+	21.1855i	−0.430035	+	0.744842i	−0.996876	−	0.0789852i	$-0.974832\pi$
$809$	−12.2314	+	21.1855i	−0.430035	+	0.744842i	0.566841	+	0.823827i	$0.308165\pi$
$810$	0.702750	+	1.21720i	0.0246921	+	0.0427680i
$811$	−45.2448			−1.58876			−0.794380	−	0.607421i	$-0.792204\pi$
$811$	−45.2448			−1.58876			−0.794380	+	0.607421i	$0.792204\pi$
$812$	−0.0906258	−	0.156969i	−0.00318034	−	0.00550852i
$813$	9.16630	+	15.8765i	0.321476	+	0.556813i
$814$	−0.490388			−0.0171881
$815$	5.46384	+	9.46366i	0.191390	+	0.331497i
$816$	−1.12667	+	1.95145i	−0.0394414	+	0.0683145i
$817$	5.32127	−	9.21671i	0.186168	−	0.322452i
$818$	−12.8246			−0.448401
$819$	−0.910836	+	3.48861i	−0.0318272	+	0.121902i
$820$	−1.28829			−0.0449890
$821$	−18.3665	+	31.8118i	−0.640996	+	1.11024i	0.344214	+	0.938891i	$0.388145\pi$
$821$	−18.3665	+	31.8118i	−0.640996	+	1.11024i	−0.985211	+	0.171347i	$0.945188\pi$
$822$	−12.8719	+	22.2947i	−0.448958	+	0.777618i
$823$	−21.3238	−	36.9339i	−0.743301	−	1.28743i	−0.950984	−	0.309239i	$-0.899926\pi$
$823$	−21.3238	−	36.9339i	−0.743301	−	1.28743i	0.207684	−	0.978196i	$-0.433408\pi$
$824$	−12.4495			−0.433699
$825$	0.659905	+	1.14299i	0.0229749	+	0.0397938i
$826$	2.50000	+	4.33013i	0.0869861	+	0.150664i
$827$	−50.0635			−1.74088			−0.870440	−	0.492275i	$-0.836166\pi$
$827$	−50.0635			−1.74088			−0.870440	+	0.492275i	$0.836166\pi$
$828$	0.0141481	+	0.0245053i	0.000491682	+	0.000851617i
$829$	−12.9455	+	22.4223i	−0.449617	+	0.778759i	−0.998361	−	0.0572312i	$-0.981773\pi$
$829$	−12.9455	+	22.4223i	−0.449617	+	0.778759i	0.548744	+	0.835990i	$0.315106\pi$
$830$	−8.37278	+	14.5021i	−0.290623	+	0.503374i
$831$	−8.45434			−0.293278
$832$	−30.8935	+	8.49056i	−1.07104	+	0.294357i
$833$	0.726109			0.0251582
$834$	−2.72223	+	4.71505i	−0.0942633	+	0.163269i
$835$	9.24384	−	16.0108i	0.319896	−	0.554077i
$836$	−0.151494	−	0.262395i	−0.00523952	−	0.00907512i
$837$	6.85772			0.237037
$838$	6.02548	+	10.4364i	0.208147	+	0.360521i
$839$	14.4674	+	25.0583i	0.499471	+	0.865109i	1.00000		0.000610619i	$-0.000194366\pi$
$839$	14.4674	+	25.0583i	0.499471	+	0.865109i	−0.500529	+	0.865720i	$0.666861\pi$
$840$	3.34116			0.115281
$841$	14.3846	+	24.9148i	0.496019	+	0.859130i
$842$	19.7863	−	34.2709i	0.681880	−	1.18105i
$843$	−12.5060	+	21.6610i	−0.430729	+	0.746045i
$844$	−3.78643			−0.130334
$845$	12.3285	−	7.33022i	0.424112	−	0.252167i
$846$	−5.99708			−0.206184
$847$	−5.43913	+	9.42085i	−0.186891	+	0.323704i
$848$	8.60825	−	14.9099i	0.295608	−	0.512009i
$849$	13.5707	+	23.5052i	0.465747	+	0.806697i
$850$	3.49894			0.120013
$851$	0.0413831	+	0.0716776i	0.00141859	+	0.00245708i
$852$	1.79725	+	3.11293i	0.0615728	+	0.106647i
$853$	40.3094			1.38017			0.690083	−	0.723730i	$-0.257574\pi$
$853$	40.3094			1.38017			0.690083	+	0.723730i	$0.257574\pi$
$854$	−3.53363	−	6.12043i	−0.120918	−	0.209437i
$855$	−1.27002	+	2.19973i	−0.0434336	+	0.0752292i
$856$	9.34317	−	16.1828i	0.319343	−	0.553118i
$857$	40.0459			1.36794			0.683971	−	0.729509i	$-0.260251\pi$
$857$	40.0459			1.36794			0.683971	+	0.729509i	$0.260251\pi$
$858$	1.54526	−	0.424688i	0.0527542	−	0.0144986i
$859$	6.66659			0.227461			0.113731	−	0.993512i	$-0.463720\pi$
$859$	6.66659			0.227461			0.113731	+	0.993512i	$0.463720\pi$
$860$	−0.961941	+	1.66613i	−0.0328019	+	0.0568146i
$861$	−1.54778	+	2.68084i	−0.0527482	+	0.0913626i
$862$	−16.0629	−	27.8217i	−0.547104	−	0.947612i
$863$	−5.85289			−0.199235			−0.0996174	−	0.995026i	$-0.531762\pi$
$863$	−5.85289			−0.199235			−0.0996174	+	0.995026i	$0.531762\pi$
$864$	−1.05166	−	1.82152i	−0.0357781	−	0.0619694i
$865$	−7.56782	−	13.1078i	−0.257314	−	0.445680i
$866$	−4.80245			−0.163194
$867$	−8.23638	−	14.2658i	−0.279722	−	0.484493i
$868$	1.29338	−	2.24019i	0.0439000	−	0.0760371i
$869$	2.98410	−	5.16861i	0.101229	−	0.175333i
$870$	0.675364			0.0228970
$871$	7.39950	−	28.3409i	0.250723	−	0.960296i
$872$	−26.7146			−0.904672
$873$	−5.05166	+	8.74973i	−0.170973	+	0.296133i
$874$	0.110001	−	0.190527i	0.00372084	−	0.00644469i
$875$	−4.84503	−	8.39184i	−0.163792	−	0.283696i
$876$	−3.93566			−0.132974
$877$	−2.18367	−	3.78222i	−0.0737371	−	0.127716i	0.826799	−	0.562497i	$-0.190159\pi$
$877$	−2.18367	−	3.78222i	−0.0737371	−	0.127716i	−0.900536	+	0.434781i	$0.856826\pi$
$878$	−14.4171	−	24.9712i	−0.486554	−	0.842737i
$879$	10.5400			0.355506
$880$	−0.597315	−	1.03458i	−0.0201355	−	0.0348757i
$881$	−1.57366	+	2.72567i	−0.0530181	+	0.0918300i	−0.891316	−	0.453382i	$-0.850217\pi$
$881$	−1.57366	+	2.72567i	−0.0530181	+	0.0918300i	0.838298	+	0.545212i	$0.183551\pi$
$882$	0.636945	−	1.10322i	0.0214471	−	0.0371474i
$883$	14.9554			0.503289			0.251645	−	0.967820i	$-0.419029\pi$
$883$	14.9554			0.503289			0.251645	+	0.967820i	$0.419029\pi$
$884$	−0.249469	+	0.955496i	−0.00839056	+	0.0321368i
$885$	4.33048			0.145568
$886$	2.95756	−	5.12264i	0.0993610	−	0.172098i
$887$	−11.2632	+	19.5085i	−0.378182	+	0.655030i	−0.990798	−	0.135351i	$-0.956784\pi$
$887$	−11.2632	+	19.5085i	−0.378182	+	0.655030i	0.612616	+	0.790381i	$0.290117\pi$
$888$	−1.67058	−	2.89353i	−0.0560609	−	0.0971004i
$889$	5.85772			0.196462
$890$	−8.40561	−	14.5589i	−0.281757	−	0.488017i
$891$	0.174453	+	0.302162i	0.00584441	+	0.0101228i
$892$	1.93676			0.0648475
$893$	−5.41899	−	9.38596i	−0.181339	−	0.314089i
$894$	3.11892	−	5.40213i	0.104312	−	0.180674i
$895$	12.1532	−	21.0500i	0.406237	−	0.703623i
$896$	7.11319			0.237635
$897$	−0.192476	−	0.190024i	−0.00642660	−	0.00634471i
$898$	−12.0040			−0.400580
$899$	1.64762	−	2.85376i	0.0549512	−	0.0951782i
$900$	−0.713423	+	1.23568i	−0.0237808	+	0.0411895i
$901$	−2.01415	−	3.48861i	−0.0671010	−	0.116222i
$902$	1.37588			0.0458118
$903$	2.31140	+	4.00346i	0.0769185	+	0.133227i
$904$	−18.1847	−	31.4969i	−0.604815	−	1.04757i
$905$	10.4084			0.345988
$906$	5.69781	+	9.86890i	0.189297	+	0.327872i
$907$	9.32661	−	16.1542i	0.309685	−	0.536390i	−0.668608	−	0.743615i	$-0.733110\pi$
$907$	9.32661	−	16.1542i	0.309685	−	0.536390i	0.978293	+	0.207225i	$0.0664431\pi$
$908$	−5.46395	+	9.46385i	−0.181328	+	0.314069i
$909$	4.07502			0.135160
$910$	−4.88641	+	1.34295i	−0.161983	+	0.0445183i
$911$	18.3278			0.607226			0.303613	−	0.952795i	$-0.401807\pi$
$911$	18.3278			0.607226			0.303613	+	0.952795i	$0.401807\pi$
$912$	−3.57220	+	6.18724i	−0.118287	+	0.204880i
$913$	−2.07849	+	3.60005i	−0.0687880	+	0.119144i
$914$	8.09955	+	14.0288i	0.267909	+	0.464032i
$915$	−6.12094			−0.202352
$916$	0.128134	+	0.221934i	0.00423366	+	0.00733292i
$917$	11.2027	+	19.4037i	0.369947	+	0.640768i
$918$	0.924984			0.0305290
$919$	−7.55272	−	13.0817i	−0.249141	−	0.431525i	0.714147	−	0.699996i	$-0.246815\pi$
$919$	−7.55272	−	13.0817i	−0.249141	−	0.431525i	−0.963288	+	0.268471i	$0.913482\pi$
$920$	−0.125320	+	0.217061i	−0.00413168	+	0.00715629i
$921$	−2.20421	+	3.81781i	−0.0726312	+	0.125801i
$922$	37.8668			1.24708
$923$	−24.4505	−	24.1389i	−0.804797	−	0.794542i
$924$	0.131609			0.00432960
$925$	−2.08675	+	3.61436i	−0.0686119	+	0.118839i
$926$	−9.73492	+	16.8614i	−0.319909	+	0.554099i
$927$	2.05553	+	3.56028i	0.0675125	+	0.116935i
$928$	−1.01067			−0.0331770
$929$	3.12909	+	5.41974i	0.102662	+	0.177816i	0.912781	−	0.408450i	$-0.133931\pi$
$929$	3.12909	+	5.41974i	0.102662	+	0.177816i	−0.810119	+	0.586266i	$0.800597\pi$
$930$	4.81926	+	8.34720i	0.158030	+	0.273715i
$931$	2.30219			0.0754511
$932$	−3.45182	−	5.97873i	−0.113068	−	0.195840i
$933$	−1.16418	+	2.01642i	−0.0381135	+	0.0660146i
$934$	−16.9748	+	29.4012i	−0.555432	+	0.962036i
$935$	−0.279518			−0.00914121
$936$	7.77002	+	7.67101i	0.253971	+	0.250735i
$937$	−22.6610			−0.740301			−0.370151	−	0.928972i	$-0.620694\pi$
$937$	−22.6610			−0.740301			−0.370151	+	0.928972i	$0.620694\pi$
$938$	−5.17445	+	8.96242i	−0.168952	+	0.292633i
$939$	6.33436	−	10.9714i	0.206714	−	0.358039i
$940$	0.979605	+	1.69673i	0.0319512	+	0.0553411i
$941$	17.2944			0.563783			0.281891	−	0.959446i	$-0.409038\pi$
$941$	17.2944			0.563783			0.281891	+	0.959446i	$0.409038\pi$
$942$	−4.20034	−	7.27520i	−0.136854	−	0.237039i
$943$	−0.116108	−	0.201106i	−0.00378101	−	0.00654890i
$944$	12.1805			0.396440
$945$	−0.551656	−	0.955496i	−0.0179454	−	0.0310823i
$946$	1.02734	−	1.77941i	0.0334019	−	0.0578537i
$947$	13.8061	−	23.9128i	0.448637	−	0.777062i	−0.549661	−	0.835388i	$-0.685243\pi$
$947$	13.8061	−	23.9128i	0.448637	−	0.777062i	0.998298	+	0.0583263i	$0.0185764\pi$
$948$	6.45222			0.209558
$949$	36.2746	−	9.96945i	1.17752	−	0.323622i
$950$	11.0937			0.359926
$951$	−6.14576	+	10.6448i	−0.199290	+	0.345180i
$952$	1.09944	−	1.90428i	0.0356330	−	0.0617181i
$953$	−2.19540	−	3.80254i	−0.0711160	−	0.123176i	0.828275	−	0.560322i	$-0.189323\pi$
$953$	−2.19540	−	3.80254i	−0.0711160	−	0.123176i	−0.899391	+	0.437146i	$0.855989\pi$
$954$	−7.06727			−0.228811
$955$	1.86305	+	3.22691i	0.0602870	+	0.104420i
$956$	−1.02830	−	1.78106i	−0.0332575	−	0.0576036i
$957$	0.167655			0.00541951
$958$	−14.1476	−	24.5044i	−0.457089	−	0.791701i
$959$	10.1044	−	17.5013i	0.326287	−	0.565146i
$960$	4.90202	−	8.49056i	0.158212	−	0.274031i
$961$	16.0283			0.517042
$962$	3.60624	+	3.56028i	0.116270	+	0.114788i
$963$	−6.17058			−0.198844
$964$	−2.91617	+	5.05096i	−0.0939236	+	0.162680i
$965$	−12.3145	+	21.3293i	−0.396417	+	0.686614i
$966$	0.0477811	+	0.0827593i	0.00153733	+	0.00266274i
$967$	−18.4875			−0.594517			−0.297258	−	0.954797i	$-0.596072\pi$
$967$	−18.4875			−0.594517			−0.297258	+	0.954797i	$0.596072\pi$
$968$	16.4713	+	28.5291i	0.529408	+	0.916961i
$969$	0.835820	+	1.44768i	0.0268504	+	0.0465063i
$970$	−14.2002			−0.455941
$971$	26.1687	+	45.3255i	0.839794	+	1.45457i	0.890067	+	0.455830i	$0.150658\pi$
$971$	26.1687	+	45.3255i	0.839794	+	1.45457i	−0.0502726	+	0.998736i	$0.516009\pi$
$972$	−0.188601	+	0.326667i	−0.00604939	+	0.0104779i
$973$	2.13695	−	3.70130i	0.0685073	−	0.118658i
$974$	1.23784			0.0396631
$975$	3.44542	−	13.1964i	0.110342	−	0.422622i
$976$	−17.2165			−0.551087
$977$	−25.8223	+	44.7256i	−0.826130	+	1.43090i	0.0749233	+	0.997189i	$0.476129\pi$
$977$	−25.8223	+	44.7256i	−0.826130	+	1.43090i	−0.901053	+	0.433709i	$0.857205\pi$
$978$	6.30858	−	10.9268i	0.201726	−	0.349400i
$979$	−2.08664	−	3.61417i	−0.0666893	−	0.115509i
$980$	−0.416173			−0.0132941
$981$	4.41084	+	7.63979i	0.140827	+	0.243920i
$982$	17.1560	+	29.7151i	0.547471	+	0.948247i
$983$	37.5419			1.19740			0.598701	−	0.800973i	$-0.295684\pi$
$983$	37.5419			1.19740			0.598701	+	0.800973i	$0.295684\pi$
$984$	4.68714	+	8.11836i	0.149421	+	0.258804i
$985$	14.0404	−	24.3187i	0.447365	−	0.774860i
$986$	0.222234	−	0.384921i	0.00707739	−	0.0122584i
$987$	4.70769			0.149847
$988$	−0.790962	+	3.02948i	−0.0251639	+	0.0963805i
$989$	−0.346784			−0.0110271
$990$	−0.245194	+	0.424688i	−0.00779278	+	0.0134975i
$991$	25.2862	−	43.7969i	0.803242	−	1.39126i	−0.114230	−	0.993454i	$-0.536440\pi$
$991$	25.2862	−	43.7969i	0.803242	−	1.39126i	0.917472	−	0.397801i	$-0.130227\pi$
$992$	−7.21196	−	12.4915i	−0.228980	−	0.396605i
$993$	−13.2915			−0.421793
$994$	6.06968	+	10.5130i	0.192519	+	0.333452i
$995$	12.3242	+	21.3461i	0.390703	+	0.676718i
$996$	−4.49411			−0.142401
$997$	12.9610	+	22.4492i	0.410480	+	0.710972i	0.994942	−	0.100449i	$-0.0320278\pi$
$997$	12.9610	+	22.4492i	0.410480	+	0.710972i	−0.584462	+	0.811421i	$0.698695\pi$
$998$	−13.4547	+	23.3043i	−0.425902	+	0.737685i
$999$	−0.551656	+	0.955496i	−0.0174536	+	0.0302306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.k.d.22.2	✓	6
3.2	odd	2		819.2.o.d.568.2		6
13.3	even	3	inner	273.2.k.d.211.2	yes	6
13.4	even	6		3549.2.a.s.1.2		3
13.9	even	3		3549.2.a.h.1.2		3
39.29	odd	6		819.2.o.d.757.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.d.22.2	✓	6	1.1	even	1	trivial
273.2.k.d.211.2	yes	6	13.3	even	3	inner
819.2.o.d.568.2		6	3.2	odd	2
819.2.o.d.757.2		6	39.29	odd	6
3549.2.a.h.1.2		3	13.9	even	3
3549.2.a.s.1.2		3	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
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

Introduction

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