LMFDB - Embedded newform 273.2.i.b.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(79,273)]

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, 2, 0]))

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

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

chi := DirichletCharacter("273.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.i (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:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	273.79
Dual form			273.2.i.b.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.300767i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.939693 + 1.62760i) q^{4} +(-0.326352 + 0.565258i) q^{5} +0.347296 q^{6} +(-2.05303 + 1.66885i) q^{7} +1.34730 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.300767i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.939693 + 1.62760i) q^{4} +(-0.326352 + 0.565258i) q^{5} +0.347296 q^{6} +(-2.05303 + 1.66885i) q^{7} +1.34730 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.113341 + 0.196312i) q^{10} +(-0.266044 - 0.460802i) q^{11} +(-0.939693 + 1.62760i) q^{12} +1.00000 q^{13} +(0.145430 + 0.907278i) q^{14} -0.652704 q^{15} +(-1.64543 + 2.84997i) q^{16} +(-0.560307 - 0.970481i) q^{17} +(0.173648 + 0.300767i) q^{18} +(-0.152704 + 0.264490i) q^{19} -1.22668 q^{20} +(-2.47178 - 0.943555i) q^{21} -0.184793 q^{22} +(4.00387 - 6.93491i) q^{23} +(0.673648 + 1.16679i) q^{24} +(2.28699 + 3.96118i) q^{25} +(0.173648 - 0.300767i) q^{26} -1.00000 q^{27} +(-4.64543 - 1.77330i) q^{28} +7.78106 q^{29} +(-0.113341 + 0.196312i) q^{30} +(-0.294263 - 0.509678i) q^{31} +(1.91875 + 3.32337i) q^{32} +(0.266044 - 0.460802i) q^{33} -0.389185 q^{34} +(-0.273318 - 1.70513i) q^{35} -1.87939 q^{36} +(1.43969 - 2.49362i) q^{37} +(0.0530334 + 0.0918566i) q^{38} +(0.500000 + 0.866025i) q^{39} +(-0.439693 + 0.761570i) q^{40} -1.04189 q^{41} +(-0.713011 + 0.579585i) q^{42} +2.94356 q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.326352 - 0.565258i) q^{45} +(-1.39053 - 2.40847i) q^{46} +(2.06418 - 3.57526i) q^{47} -3.29086 q^{48} +(1.42989 - 6.85240i) q^{49} +1.58853 q^{50} +(0.560307 - 0.970481i) q^{51} +(0.939693 + 1.62760i) q^{52} +(1.26604 + 2.19285i) q^{53} +(-0.173648 + 0.300767i) q^{54} +0.347296 q^{55} +(-2.76604 + 2.24843i) q^{56} -0.305407 q^{57} +(1.35117 - 2.34029i) q^{58} +(-7.19119 - 12.4555i) q^{59} +(-0.613341 - 1.06234i) q^{60} +(-3.92989 + 6.80677i) q^{61} -0.204393 q^{62} +(-0.418748 - 2.61240i) q^{63} -5.24897 q^{64} +(-0.326352 + 0.565258i) q^{65} +(-0.0923963 - 0.160035i) q^{66} +(-2.33022 - 4.03606i) q^{67} +(1.05303 - 1.82391i) q^{68} +8.00774 q^{69} +(-0.560307 - 0.213887i) q^{70} -3.92902 q^{71} +(-0.673648 + 1.16679i) q^{72} +(-5.81180 - 10.0663i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(-2.28699 + 3.96118i) q^{75} -0.573978 q^{76} +(1.31521 + 0.502055i) q^{77} +0.347296 q^{78} +(-1.46451 + 2.53660i) q^{79} +(-1.07398 - 1.86018i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.180922 + 0.313366i) q^{82} -2.46791 q^{83} +(-0.786989 - 4.90971i) q^{84} +0.731429 q^{85} +(0.511144 - 0.885328i) q^{86} +(3.89053 + 6.73859i) q^{87} +(-0.358441 - 0.620838i) q^{88} +(-5.49273 + 9.51368i) q^{89} -0.226682 q^{90} +(-2.05303 + 1.66885i) q^{91} +15.0496 q^{92} +(0.294263 - 0.509678i) q^{93} +(-0.716881 - 1.24168i) q^{94} +(-0.0996702 - 0.172634i) q^{95} +(-1.91875 + 3.32337i) q^{96} +10.2686 q^{97} +(-1.81268 - 1.61997i) q^{98} +0.532089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 3 q^{5} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 3 * q^5 + 6 * q^8 - 3 * q^9	$ 6 q + 3 q^{3} - 3 q^{5} + 6 q^{8} - 3 q^{9} - 6 q^{10} + 3 q^{11} + 6 q^{13} - 15 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} - 3 q^{19} + 6 q^{20} + 6 q^{22} + 3 q^{24} + 6 q^{25} - 6 q^{27} - 12 q^{28} + 12 q^{29} + 6 q^{30} - 12 q^{31} + 9 q^{32} - 3 q^{33} + 6 q^{34} - 15 q^{35} + 3 q^{37} - 12 q^{38} + 3 q^{39} + 3 q^{40} - 12 q^{42} - 12 q^{43} + 3 q^{44} - 3 q^{45} + 9 q^{46} - 6 q^{47} + 12 q^{48} + 30 q^{50} + 9 q^{51} + 3 q^{53} - 12 q^{56} - 6 q^{57} - 18 q^{58} + 3 q^{59} + 3 q^{60} - 15 q^{61} - 6 q^{64} - 3 q^{65} + 3 q^{66} + 9 q^{67} - 6 q^{68} - 9 q^{70} + 42 q^{71} - 3 q^{72} - 3 q^{74} - 6 q^{75} + 12 q^{76} + 15 q^{77} + 24 q^{79} + 9 q^{80} - 3 q^{81} - 18 q^{82} - 24 q^{83} + 3 q^{84} + 24 q^{85} - 3 q^{86} + 6 q^{87} + 6 q^{88} - 15 q^{89} + 12 q^{90} + 36 q^{92} + 12 q^{93} + 12 q^{94} - 15 q^{95} - 9 q^{96} + 42 q^{97} - 33 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 3 * q^5 + 6 * q^8 - 3 * q^9 - 6 * q^10 + 3 * q^11 + 6 * q^13 - 15 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 - 3 * q^19 + 6 * q^20 + 6 * q^22 + 3 * q^24 + 6 * q^25 - 6 * q^27 - 12 * q^28 + 12 * q^29 + 6 * q^30 - 12 * q^31 + 9 * q^32 - 3 * q^33 + 6 * q^34 - 15 * q^35 + 3 * q^37 - 12 * q^38 + 3 * q^39 + 3 * q^40 - 12 * q^42 - 12 * q^43 + 3 * q^44 - 3 * q^45 + 9 * q^46 - 6 * q^47 + 12 * q^48 + 30 * q^50 + 9 * q^51 + 3 * q^53 - 12 * q^56 - 6 * q^57 - 18 * q^58 + 3 * q^59 + 3 * q^60 - 15 * q^61 - 6 * q^64 - 3 * q^65 + 3 * q^66 + 9 * q^67 - 6 * q^68 - 9 * q^70 + 42 * q^71 - 3 * q^72 - 3 * q^74 - 6 * q^75 + 12 * q^76 + 15 * q^77 + 24 * q^79 + 9 * q^80 - 3 * q^81 - 18 * q^82 - 24 * q^83 + 3 * q^84 + 24 * q^85 - 3 * q^86 + 6 * q^87 + 6 * q^88 - 15 * q^89 + 12 * q^90 + 36 * q^92 + 12 * q^93 + 12 * q^94 - 15 * q^95 - 9 * q^96 + 42 * q^97 - 33 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.173648	−	0.300767i	0.122788	−	0.212675i	−0.798078	−	0.602554i	$-0.794150\pi$
$2$	0.173648	−	0.300767i	0.122788	−	0.212675i	0.920866	+	0.389879i	$0.127483\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.939693	+	1.62760i	0.469846	+	0.813798i
$5$	−0.326352	+	0.565258i	−0.145949	+	0.252791i	−0.929727	−	0.368251i	$-0.879957\pi$
$5$	−0.326352	+	0.565258i	−0.145949	+	0.252791i	0.783778	+	0.621042i	$0.213290\pi$
$6$	0.347296			0.141783
$7$	−2.05303	+	1.66885i	−0.775974	+	0.630765i
$7$	−2.05303	+	1.66885i	−0.775974	+	0.630765i
$8$	1.34730			0.476341
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.113341	+	0.196312i	0.0358415	+	0.0620793i
$11$	−0.266044	−	0.460802i	−0.0802154	−	0.138937i	0.823127	−	0.567857i	$-0.192227\pi$
$11$	−0.266044	−	0.460802i	−0.0802154	−	0.138937i	−0.903342	+	0.428920i	$0.858894\pi$
$12$	−0.939693	+	1.62760i	−0.271266	+	0.469846i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	0.145430	+	0.907278i	0.0388677	+	0.242480i
$15$	−0.652704			−0.168527
$16$	−1.64543	+	2.84997i	−0.411357	+	0.712492i
$17$	−0.560307	−	0.970481i	−0.135895	−	0.235376i	0.790044	−	0.613050i	$-0.210057\pi$
$17$	−0.560307	−	0.970481i	−0.135895	−	0.235376i	−0.925939	+	0.377674i	$0.876724\pi$
$18$	0.173648	+	0.300767i	0.0409293	+	0.0708916i
$19$	−0.152704	+	0.264490i	−0.0350326	+	0.0606783i	−0.883010	−	0.469354i	$-0.844487\pi$
$19$	−0.152704	+	0.264490i	−0.0350326	+	0.0606783i	0.847978	+	0.530032i	$0.177820\pi$
$20$	−1.22668			−0.274294
$21$	−2.47178	−	0.943555i	−0.539387	−	0.205901i
$22$	−0.184793			−0.0393979
$23$	4.00387	−	6.93491i	0.834865	−	1.44603i	−0.0592759	−	0.998242i	$-0.518879\pi$
$23$	4.00387	−	6.93491i	0.834865	−	1.44603i	0.894141	−	0.447786i	$-0.147788\pi$
$24$	0.673648	+	1.16679i	0.137508	+	0.238171i
$25$	2.28699	+	3.96118i	0.457398	+	0.792236i
$26$	0.173648	−	0.300767i	0.0340552	−	0.0589854i
$27$	−1.00000			−0.192450
$28$	−4.64543	−	1.77330i	−0.877904	−	0.335123i
$29$	7.78106			1.44491			0.722453	−	0.691420i	$-0.243014\pi$
$29$	7.78106			1.44491			0.722453	+	0.691420i	$0.243014\pi$
$30$	−0.113341	+	0.196312i	−0.0206931	+	0.0358415i
$31$	−0.294263	−	0.509678i	−0.0528512	−	0.0915409i	0.838389	−	0.545072i	$-0.183498\pi$
$31$	−0.294263	−	0.509678i	−0.0528512	−	0.0915409i	−0.891241	+	0.453531i	$0.850164\pi$
$32$	1.91875	+	3.32337i	0.339190	+	0.587494i
$33$	0.266044	−	0.460802i	0.0463124	−	0.0802154i
$34$	−0.389185			−0.0667447
$35$	−0.273318	−	1.70513i	−0.0461992	−	0.288219i
$36$	−1.87939			−0.313231
$37$	1.43969	−	2.49362i	0.236684	−	0.409949i	−0.723077	−	0.690768i	$-0.757273\pi$
$37$	1.43969	−	2.49362i	0.236684	−	0.409949i	0.959761	+	0.280819i	$0.0906061\pi$
$38$	0.0530334	+	0.0918566i	0.00860316	+	0.0149011i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	−0.439693	+	0.761570i	−0.0695215	+	0.120415i
$41$	−1.04189			−0.162716			−0.0813579	−	0.996685i	$-0.525926\pi$
$41$	−1.04189			−0.162716			−0.0813579	+	0.996685i	$0.525926\pi$
$42$	−0.713011	+	0.579585i	−0.110020	+	0.0894319i
$43$	2.94356			0.448889			0.224445	−	0.974487i	$-0.427943\pi$
$43$	2.94356			0.448889			0.224445	+	0.974487i	$0.427943\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	−0.326352	−	0.565258i	−0.0486497	−	0.0842637i
$46$	−1.39053	−	2.40847i	−0.205022	−	0.355109i
$47$	2.06418	−	3.57526i	0.301091	−	0.521505i	−0.675292	−	0.737550i	$-0.735982\pi$
$47$	2.06418	−	3.57526i	0.301091	−	0.521505i	0.976383	+	0.216045i	$0.0693158\pi$
$48$	−3.29086			−0.474995
$49$	1.42989	−	6.85240i	0.204270	−	0.978915i
$50$	1.58853			0.224651
$51$	0.560307	−	0.970481i	0.0784587	−	0.135895i
$52$	0.939693	+	1.62760i	0.130312	+	0.225707i
$53$	1.26604	+	2.19285i	0.173905	+	0.301212i	0.939782	−	0.341775i	$-0.111028\pi$
$53$	1.26604	+	2.19285i	0.173905	+	0.301212i	−0.765877	+	0.642987i	$0.777695\pi$
$54$	−0.173648	+	0.300767i	−0.0236305	+	0.0409293i
$55$	0.347296			0.0468294
$56$	−2.76604	+	2.24843i	−0.369628	+	0.300459i
$57$	−0.305407			−0.0404522
$58$	1.35117	−	2.34029i	0.177417	−	0.307295i
$59$	−7.19119	−	12.4555i	−0.936213	−	1.62157i	−0.772456	−	0.635068i	$-0.780972\pi$
$59$	−7.19119	−	12.4555i	−0.936213	−	1.62157i	−0.163757	−	0.986501i	$-0.552361\pi$
$60$	−0.613341	−	1.06234i	−0.0791820	−	0.137147i
$61$	−3.92989	+	6.80677i	−0.503171	+	0.871518i	0.496822	+	0.867852i	$0.334500\pi$
$61$	−3.92989	+	6.80677i	−0.503171	+	0.871518i	−0.999993	+	0.00366563i	$0.998833\pi$
$62$	−0.204393			−0.0259579
$63$	−0.418748	−	2.61240i	−0.0527573	−	0.329132i
$64$	−5.24897			−0.656121
$65$	−0.326352	+	0.565258i	−0.0404790	+	0.0701116i
$66$	−0.0923963	−	0.160035i	−0.0113732	−	0.0196989i
$67$	−2.33022	−	4.03606i	−0.284682	−	0.493084i	0.687850	−	0.725853i	$-0.258555\pi$
$67$	−2.33022	−	4.03606i	−0.284682	−	0.493084i	−0.972532	+	0.232769i	$0.925221\pi$
$68$	1.05303	−	1.82391i	0.127699	−	0.221181i
$69$	8.00774			0.964019
$70$	−0.560307	−	0.213887i	−0.0669695	−	0.0255643i
$71$	−3.92902			−0.466288			−0.233144	−	0.972442i	$-0.574901\pi$
$71$	−3.92902			−0.466288			−0.233144	+	0.972442i	$0.574901\pi$
$72$	−0.673648	+	1.16679i	−0.0793902	+	0.137508i
$73$	−5.81180	−	10.0663i	−0.680220	−	1.17818i	−0.974914	−	0.222584i	$-0.928551\pi$
$73$	−5.81180	−	10.0663i	−0.680220	−	1.17818i	0.294693	−	0.955592i	$-0.404783\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$	−2.28699	+	3.96118i	−0.264079	+	0.457398i
$76$	−0.573978			−0.0658398
$77$	1.31521	+	0.502055i	0.149882	+	0.0572145i
$78$	0.347296			0.0393236
$79$	−1.46451	+	2.53660i	−0.164770	+	0.285390i	−0.936574	−	0.350471i	$-0.886022\pi$
$79$	−1.46451	+	2.53660i	−0.164770	+	0.285390i	0.771804	+	0.635861i	$0.219355\pi$
$80$	−1.07398	−	1.86018i	−0.120074	−	0.207975i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.180922	+	0.313366i	−0.0199795	+	0.0346055i
$83$	−2.46791			−0.270888			−0.135444	−	0.990785i	$-0.543246\pi$
$83$	−2.46791			−0.270888			−0.135444	+	0.990785i	$0.543246\pi$
$84$	−0.786989	−	4.90971i	−0.0858675	−	0.535693i
$85$	0.731429			0.0793347
$86$	0.511144	−	0.885328i	0.0551181	−	0.0954674i
$87$	3.89053	+	6.73859i	0.417109	+	0.722453i
$88$	−0.358441	−	0.620838i	−0.0382099	−	0.0661815i
$89$	−5.49273	+	9.51368i	−0.582228	+	1.00845i	0.412987	+	0.910737i	$0.364485\pi$
$89$	−5.49273	+	9.51368i	−0.582228	+	1.00845i	−0.995215	+	0.0977112i	$0.968848\pi$
$90$	−0.226682			−0.0238943
$91$	−2.05303	+	1.66885i	−0.215216	+	0.174943i
$92$	15.0496			1.56903
$93$	0.294263	−	0.509678i	0.0305136	−	0.0528512i
$94$	−0.716881	−	1.24168i	−0.0739407	−	0.128069i
$95$	−0.0996702	−	0.172634i	−0.0102259	−	0.0177119i
$96$	−1.91875	+	3.32337i	−0.195831	+	0.339190i
$97$	10.2686			1.04262			0.521308	−	0.853369i	$-0.325444\pi$
$97$	10.2686			1.04262			0.521308	+	0.853369i	$0.325444\pi$
$98$	−1.81268	−	1.61997i	−0.183108	−	0.163642i
$99$	0.532089			0.0534769
$100$	−4.29813	+	7.44459i	−0.429813	+	0.744459i
$101$	−6.67365	−	11.5591i	−0.664053	−	1.15017i	−0.979541	−	0.201244i	$-0.935502\pi$
$101$	−6.67365	−	11.5591i	−0.664053	−	1.15017i	0.315488	−	0.948929i	$-0.397832\pi$
$102$	−0.194593	−	0.337044i	−0.0192675	−	0.0333724i
$103$	−3.62061	+	6.27109i	−0.356750	+	0.617909i	−0.987416	−	0.158146i	$-0.949448\pi$
$103$	−3.62061	+	6.27109i	−0.356750	+	0.617909i	0.630666	+	0.776054i	$0.282782\pi$
$104$	1.34730			0.132113
$105$	1.34002	−	1.08926i	0.130773	−	0.106301i
$106$	0.879385			0.0854134
$107$	3.59240	−	6.22221i	0.347290	−	0.601524i	−0.638477	−	0.769641i	$-0.720435\pi$
$107$	3.59240	−	6.22221i	0.347290	−	0.601524i	0.985767	+	0.168117i	$0.0537686\pi$
$108$	−0.939693	−	1.62760i	−0.0904220	−	0.156615i
$109$	8.62108	+	14.9322i	0.825750	+	1.43024i	0.901345	+	0.433102i	$0.142581\pi$
$109$	8.62108	+	14.9322i	0.825750	+	1.43024i	−0.0755950	+	0.997139i	$0.524086\pi$
$110$	0.0603074	−	0.104455i	0.00575008	−	0.00995944i
$111$	2.87939			0.273299
$112$	−1.37804	−	8.59705i	−0.130213	−	0.812345i
$113$	11.3523			1.06794			0.533970	−	0.845504i	$-0.320700\pi$
$113$	11.3523			1.06794			0.533970	+	0.845504i	$0.320700\pi$
$114$	−0.0530334	+	0.0918566i	−0.00496703	+	0.00860316i
$115$	2.61334	+	4.52644i	0.243695	+	0.422093i
$116$	7.31180	+	12.6644i	0.678884	+	1.17586i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	−4.99495			−0.459822
$119$	2.76991	+	1.05736i	0.253918	+	0.0969282i
$120$	−0.879385			−0.0802765
$121$	5.35844	−	9.28109i	0.487131	−	0.843736i
$122$	1.36484	+	2.36397i	0.123567	+	0.214024i
$123$	−0.520945	−	0.902302i	−0.0469720	−	0.0813579i
$124$	0.553033	−	0.957882i	0.0496639	−	0.0860203i
$125$	−6.24897			−0.558925
$126$	−0.858441	−	0.327693i	−0.0764760	−	0.0291932i
$127$	−3.55169			−0.315161			−0.157581	−	0.987506i	$-0.550369\pi$
$127$	−3.55169			−0.315161			−0.157581	+	0.987506i	$0.550369\pi$
$128$	−4.74897	+	8.22546i	−0.419754	+	0.727035i
$129$	1.47178	+	2.54920i	0.129583	+	0.224445i
$130$	0.113341	+	0.196312i	0.00994065	+	0.0172177i
$131$	−7.77244	+	13.4623i	−0.679081	+	1.17620i	0.296177	+	0.955133i	$0.404288\pi$
$131$	−7.77244	+	13.4623i	−0.679081	+	1.17620i	−0.975258	+	0.221070i	$0.929045\pi$
$132$	1.00000			0.0870388
$133$	−0.127889	−	0.797847i	−0.0110894	−	0.0691821i
$134$	−1.61856			−0.139822
$135$	0.326352	−	0.565258i	0.0280879	−	0.0486497i
$136$	−0.754900	−	1.30753i	−0.0647321	−	0.112119i
$137$	−4.06031	−	7.03266i	−0.346895	−	0.600841i	0.638801	−	0.769372i	$-0.279431\pi$
$137$	−4.06031	−	7.03266i	−0.346895	−	0.600841i	−0.985696	+	0.168532i	$0.946097\pi$
$138$	1.39053	−	2.40847i	0.118370	−	0.205022i
$139$	16.0223			1.35899			0.679496	−	0.733679i	$-0.262198\pi$
$139$	16.0223			1.35899			0.679496	+	0.733679i	$0.262198\pi$
$140$	2.51842	−	2.04715i	0.212845	−	0.173015i
$141$	4.12836			0.347670
$142$	−0.682266	+	1.18172i	−0.0572545	+	0.0991677i
$143$	−0.266044	−	0.460802i	−0.0222478	−	0.0385342i
$144$	−1.64543	−	2.84997i	−0.137119	−	0.237497i
$145$	−2.53936	+	4.39831i	−0.210883	+	0.365259i
$146$	−4.03684			−0.334091
$147$	6.64930	−	2.18788i	0.548425	−	0.180453i
$148$	5.41147			0.444820
$149$	−11.9436	+	20.6869i	−0.978455	+	1.69473i	−0.310427	+	0.950597i	$0.600472\pi$
$149$	−11.9436	+	20.6869i	−0.978455	+	1.69473i	−0.668028	+	0.744136i	$0.732861\pi$
$150$	0.794263	+	1.37570i	0.0648513	+	0.112326i
$151$	2.45336	+	4.24935i	0.199652	+	0.345807i	0.948416	−	0.317030i	$-0.102686\pi$
$151$	2.45336	+	4.24935i	0.199652	+	0.345807i	−0.748764	+	0.662837i	$0.769352\pi$
$152$	−0.205737	+	0.356347i	−0.0166875	+	0.0289036i
$153$	1.12061			0.0905963
$154$	0.379385	−	0.308391i	0.0305717	−	0.0248508i
$155$	0.384133			0.0308543
$156$	−0.939693	+	1.62760i	−0.0752356	+	0.130312i
$157$	3.45471	+	5.98373i	0.275716	+	0.477554i	0.970315	−	0.241843i	$-0.0777518\pi$
$157$	3.45471	+	5.98373i	0.275716	+	0.477554i	−0.694600	+	0.719396i	$0.744419\pi$
$158$	0.508618	+	0.880952i	0.0404635	+	0.0700848i
$159$	−1.26604	+	2.19285i	−0.100404	+	0.173905i
$160$	−2.50475			−0.198018
$161$	3.35323	+	20.9194i	0.264271	+	1.64868i
$162$	−0.347296			−0.0272862
$163$	7.16385	−	12.4081i	0.561116	−	0.971881i	−0.436284	−	0.899809i	$-0.643706\pi$
$163$	7.16385	−	12.4081i	0.561116	−	0.971881i	0.997399	−	0.0720720i	$-0.0229611\pi$
$164$	−0.979055	−	1.69577i	−0.0764514	−	0.132418i
$165$	0.173648	+	0.300767i	0.0135185	+	0.0234147i
$166$	−0.428548	+	0.742267i	−0.0332618	+	0.0576111i
$167$	−11.4979			−0.889737			−0.444869	−	0.895596i	$-0.646750\pi$
$167$	−11.4979			−0.889737			−0.444869	+	0.895596i	$0.646750\pi$
$168$	−3.33022	−	1.27125i	−0.256932	−	0.0980789i
$169$	1.00000			0.0769231
$170$	0.127011	−	0.219990i	0.00974133	−	0.0168725i
$171$	−0.152704	−	0.264490i	−0.0116775	−	0.0202261i
$172$	2.76604	+	4.79093i	0.210909	+	0.365305i
$173$	−7.71213	+	13.3578i	−0.586343	+	1.01558i	0.408364	+	0.912819i	$0.366099\pi$
$173$	−7.71213	+	13.3578i	−0.586343	+	1.01558i	−0.994707	+	0.102756i	$0.967234\pi$
$174$	2.70233			0.204863
$175$	−11.3059	−	4.31580i	−0.854644	−	0.326244i
$176$	1.75103			0.131989
$177$	7.19119	−	12.4555i	0.540523	−	0.936213i
$178$	1.90760	+	3.30407i	0.142981	+	0.247650i
$179$	−12.5744	−	21.7796i	−0.939858	−	1.62788i	−0.765733	−	0.643158i	$-0.777624\pi$
$179$	−12.5744	−	21.7796i	−0.939858	−	1.62788i	−0.174125	−	0.984724i	$-0.555710\pi$
$180$	0.613341	−	1.06234i	0.0457157	−	0.0791820i
$181$	13.4584			1.00036			0.500178	−	0.865923i	$-0.333268\pi$
$181$	13.4584			1.00036			0.500178	+	0.865923i	$0.333268\pi$
$182$	0.145430	+	0.907278i	0.0107800	+	0.0672519i
$183$	−7.85978			−0.581012
$184$	5.39440	−	9.34337i	0.397680	−	0.688803i
$185$	0.939693	+	1.62760i	0.0690876	+	0.119663i
$186$	−0.102196	−	0.177009i	−0.00749341	−	0.0129790i
$187$	−0.298133	+	0.516382i	−0.0218017	+	0.0377616i
$188$	7.75877			0.565866
$189$	2.05303	−	1.66885i	0.149336	−	0.121391i
$190$	−0.0692302			−0.00502249
$191$	−8.35369	+	14.4690i	−0.604452	+	1.04694i	0.387686	+	0.921792i	$0.373275\pi$
$191$	−8.35369	+	14.4690i	−0.604452	+	1.04694i	−0.992138	+	0.125150i	$0.960059\pi$
$192$	−2.62449	−	4.54574i	−0.189406	−	0.328061i
$193$	−9.13088	−	15.8152i	−0.657255	−	1.13840i	−0.981323	−	0.192366i	$-0.938384\pi$
$193$	−9.13088	−	15.8152i	−0.657255	−	1.13840i	0.324068	−	0.946034i	$-0.394949\pi$
$194$	1.78312	−	3.08845i	0.128020	−	0.221738i
$195$	−0.652704			−0.0467411
$196$	12.4966	−	4.11186i	0.892614	−	0.293705i
$197$	17.1702			1.22333			0.611665	−	0.791117i	$-0.290500\pi$
$197$	17.1702			1.22333			0.611665	+	0.791117i	$0.290500\pi$
$198$	0.0923963	−	0.160035i	0.00656632	−	0.0113732i
$199$	2.53936	+	4.39831i	0.180011	+	0.311788i	0.941884	−	0.335939i	$-0.109053\pi$
$199$	2.53936	+	4.39831i	0.180011	+	0.311788i	−0.761873	+	0.647726i	$0.775720\pi$
$200$	3.08125	+	5.33688i	0.217877	+	0.377375i
$201$	2.33022	−	4.03606i	0.164361	−	0.284682i
$202$	−4.63547			−0.326150
$203$	−15.9748	+	12.9854i	−1.12121	+	0.911397i
$204$	2.10607			0.147454
$205$	0.340022	−	0.588936i	0.0237482	−	0.0411331i
$206$	1.25743	+	2.17793i	0.0876090	+	0.151743i
$207$	4.00387	+	6.93491i	0.278288	+	0.482009i
$208$	−1.64543	+	2.84997i	−0.114090	+	0.197610i
$209$	0.162504			0.0112406
$210$	−0.0949225	−	0.592184i	−0.00655027	−	0.0408646i
$211$	−23.4243			−1.61259			−0.806297	−	0.591512i	$-0.798531\pi$
$211$	−23.4243			−1.61259			−0.806297	+	0.591512i	$0.798531\pi$
$212$	−2.37939	+	4.12122i	−0.163417	+	0.283046i
$213$	−1.96451	−	3.40263i	−0.134606	−	0.233144i
$214$	−1.24763	−	2.16095i	−0.0852860	−	0.147720i
$215$	−0.960637	+	1.66387i	−0.0655149	+	0.113475i
$216$	−1.34730			−0.0916719
$217$	1.45471	+	0.555307i	0.0987520	+	0.0376967i
$218$	5.98814			0.405568
$219$	5.81180	−	10.0663i	0.392725	−	0.680220i
$220$	0.326352	+	0.565258i	0.0220026	+	0.0381097i
$221$	−0.560307	−	0.970481i	−0.0376904	−	0.0652816i
$222$	0.500000	−	0.866025i	0.0335578	−	0.0581238i
$223$	−12.5202			−0.838417			−0.419208	−	0.907890i	$-0.637692\pi$
$223$	−12.5202			−0.838417			−0.419208	+	0.907890i	$0.637692\pi$
$224$	−9.48545	−	3.62089i	−0.633773	−	0.241931i
$225$	−4.57398			−0.304932
$226$	1.97131	−	3.41442i	0.131130	−	0.227124i
$227$	−3.90167	−	6.75790i	−0.258963	−	0.448537i	0.707001	−	0.707212i	$-0.250048\pi$
$227$	−3.90167	−	6.75790i	−0.258963	−	0.448537i	−0.965964	+	0.258675i	$0.916714\pi$
$228$	−0.286989	−	0.497079i	−0.0190063	−	0.0329199i
$229$	10.3229	−	17.8799i	0.682160	−	1.18154i	−0.292161	−	0.956369i	$-0.594374\pi$
$229$	10.3229	−	17.8799i	0.682160	−	1.18154i	0.974320	−	0.225166i	$-0.0722924\pi$
$230$	1.81521			0.119691
$231$	0.222811	+	1.39003i	0.0146599	+	0.0914573i
$232$	10.4834			0.688268
$233$	−4.80928	+	8.32991i	−0.315066	+	0.545711i	−0.979452	−	0.201679i	$-0.935360\pi$
$233$	−4.80928	+	8.32991i	−0.315066	+	0.545711i	0.664385	+	0.747390i	$0.268693\pi$
$234$	0.173648	+	0.300767i	0.0113517	+	0.0196618i
$235$	1.34730	+	2.33359i	0.0878879	+	0.152226i
$236$	13.5150	−	23.4087i	0.879753	−	1.52378i
$237$	−2.92902			−0.190260
$238$	0.799011	−	0.649491i	0.0517922	−	0.0421003i
$239$	2.35235			0.152161			0.0760804	−	0.997102i	$-0.475759\pi$
$239$	2.35235			0.152161			0.0760804	+	0.997102i	$0.475759\pi$
$240$	1.07398	−	1.86018i	0.0693250	−	0.120074i
$241$	7.86618	+	13.6246i	0.506705	+	0.877639i	0.999970	+	0.00775999i	$0.00247011\pi$
$241$	7.86618	+	13.6246i	0.506705	+	0.877639i	−0.493265	+	0.869879i	$0.664197\pi$
$242$	−1.86097	−	3.22329i	−0.119627	−	0.207201i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−14.7716			−0.945652
$245$	3.40673	+	3.04455i	0.217648	+	0.194509i
$246$	−0.361844			−0.0230703
$247$	−0.152704	+	0.264490i	−0.00971630	+	0.0168291i
$248$	−0.396459	−	0.686688i	−0.0251752	−	0.0436047i
$249$	−1.23396	−	2.13727i	−0.0781988	−	0.135444i
$250$	−1.08512	+	1.87949i	−0.0686292	+	0.118869i
$251$	−21.8161			−1.37702			−0.688511	−	0.725226i	$-0.741735\pi$
$251$	−21.8161			−1.37702			−0.688511	+	0.725226i	$0.741735\pi$
$252$	3.85844	−	3.13641i	0.243059	−	0.197575i
$253$	−4.26083			−0.267876
$254$	−0.616744	+	1.06823i	−0.0386980	+	0.0670269i
$255$	0.365715	+	0.633436i	0.0229019	+	0.0396673i
$256$	−3.59967	−	6.23481i	−0.224979	−	0.389676i
$257$	11.6386	−	20.1587i	0.725997	−	1.25746i	−0.232565	−	0.972581i	$-0.574712\pi$
$257$	11.6386	−	20.1587i	0.725997	−	1.25746i	0.958562	−	0.284883i	$-0.0919549\pi$
$258$	1.02229			0.0636449
$259$	1.20574	+	7.52211i	0.0749209	+	0.467401i
$260$	−1.22668			−0.0760756
$261$	−3.89053	+	6.73859i	−0.240818	+	0.417109i
$262$	2.69934	+	4.67539i	0.166766	+	0.288847i
$263$	−1.37551	−	2.38246i	−0.0848179	−	0.146909i	0.820496	−	0.571653i	$-0.193698\pi$
$263$	−1.37551	−	2.38246i	−0.0848179	−	0.146909i	−0.905314	+	0.424744i	$0.860364\pi$
$264$	0.358441	−	0.620838i	0.0220605	−	0.0382099i
$265$	−1.65270			−0.101525
$266$	−0.262174	−	0.100080i	−0.0160749	−	0.00613629i
$267$	−10.9855			−0.672299
$268$	4.37939	−	7.58532i	0.267514	−	0.463347i
$269$	−2.71167	−	4.69674i	−0.165333	−	0.286366i	0.771440	−	0.636302i	$-0.219537\pi$
$269$	−2.71167	−	4.69674i	−0.165333	−	0.286366i	−0.936774	+	0.349936i	$0.886203\pi$
$270$	−0.113341	−	0.196312i	−0.00689770	−	0.0119472i
$271$	−0.807934	+	1.39938i	−0.0490785	+	0.0850064i	−0.889521	−	0.456894i	$-0.848962\pi$
$271$	−0.807934	+	1.39938i	−0.0490785	+	0.0850064i	0.840443	+	0.541901i	$0.182295\pi$
$272$	3.68779			0.223605
$273$	−2.47178	−	0.943555i	−0.149599	−	0.0571066i
$274$	−2.82026			−0.170378
$275$	1.21688	−	2.10770i	0.0733807	−	0.127099i
$276$	7.52481	+	13.0334i	0.452941	+	0.784516i
$277$	−3.92514	−	6.79855i	−0.235839	−	0.408485i	0.723677	−	0.690139i	$-0.242450\pi$
$277$	−3.92514	−	6.79855i	−0.235839	−	0.408485i	−0.959516	+	0.281653i	$0.909117\pi$
$278$	2.78224	−	4.81898i	0.166868	−	0.289023i
$279$	0.588526			0.0352341
$280$	−0.368241	−	2.29731i	−0.0220066	−	0.137290i
$281$	−19.0428			−1.13600			−0.568000	−	0.823029i	$-0.692283\pi$
$281$	−19.0428			−1.13600			−0.568000	+	0.823029i	$0.692283\pi$
$282$	0.716881	−	1.24168i	0.0426897	−	0.0739407i
$283$	−11.6434	−	20.1669i	−0.692127	−	1.19880i	−0.971140	−	0.238511i	$-0.923341\pi$
$283$	−11.6434	−	20.1669i	−0.692127	−	1.19880i	0.279013	−	0.960287i	$-0.409993\pi$
$284$	−3.69207	−	6.39485i	−0.219084	−	0.379464i
$285$	0.0996702	−	0.172634i	0.00590395	−	0.0102259i
$286$	−0.184793			−0.0109270
$287$	2.13903	−	1.73875i	0.126263	−	0.102635i
$288$	−3.83750			−0.226127
$289$	7.87211	−	13.6349i	0.463065	−	0.802053i
$290$	0.881911	+	1.52752i	0.0517876	+	0.0896988i
$291$	5.13429	+	8.89284i	0.300977	+	0.521308i
$292$	10.9226	−	18.9185i	0.639198	−	1.10712i
$293$	26.9736			1.57581			0.787907	−	0.615794i	$-0.211165\pi$
$293$	26.9736			1.57581			0.787907	+	0.615794i	$0.211165\pi$
$294$	0.496596	−	2.37981i	0.0289621	−	0.138794i
$295$	9.38743			0.546557
$296$	1.93969	−	3.35965i	0.112742	−	0.195275i
$297$	0.266044	+	0.460802i	0.0154375	+	0.0267385i
$298$	4.14796	+	7.18447i	0.240285	+	0.416185i
$299$	4.00387	−	6.93491i	0.231550	−	0.401056i
$300$	−8.59627			−0.496306
$301$	−6.04323	+	4.91236i	−0.348326	+	0.283144i
$302$	1.70409			0.0980593
$303$	6.67365	−	11.5591i	0.383391	−	0.664053i
$304$	−0.502526	−	0.870401i	−0.0288219	−	0.0499209i
$305$	−2.56506	−	4.44281i	−0.146875	−	0.254394i
$306$	0.194593	−	0.337044i	0.0111241	−	0.0192675i
$307$	6.28405			0.358650			0.179325	−	0.983790i	$-0.442609\pi$
$307$	6.28405			0.358650			0.179325	+	0.983790i	$0.442609\pi$
$308$	0.418748	+	2.61240i	0.0238604	+	0.148855i
$309$	−7.24123			−0.411939
$310$	0.0667040	−	0.115535i	0.00378853	−	0.00656193i
$311$	−1.11334	−	1.92836i	−0.0631318	−	0.109347i	0.832732	−	0.553676i	$-0.186776\pi$
$311$	−1.11334	−	1.92836i	−0.0631318	−	0.109347i	−0.895864	+	0.444329i	$0.853442\pi$
$312$	0.673648	+	1.16679i	0.0381378	+	0.0660566i
$313$	−9.91060	+	17.1657i	−0.560180	+	0.970260i	0.437300	+	0.899316i	$0.355935\pi$
$313$	−9.91060	+	17.1657i	−0.560180	+	0.970260i	−0.997480	+	0.0709447i	$0.977399\pi$
$314$	2.39961			0.135418
$315$	1.61334	+	0.615862i	0.0909015	+	0.0346999i
$316$	−5.50475			−0.309666
$317$	5.85117	−	10.1345i	0.328634	−	0.569211i	−0.653607	−	0.756834i	$-0.726745\pi$
$317$	5.85117	−	10.1345i	0.328634	−	0.569211i	0.982241	+	0.187623i	$0.0600783\pi$
$318$	0.439693	+	0.761570i	0.0246567	+	0.0427067i
$319$	−2.07011	−	3.58553i	−0.115904	−	0.200751i
$320$	1.71301	−	2.96702i	0.0957602	−	0.165862i
$321$	7.18479			0.401016
$322$	6.87417	+	2.62408i	0.383083	+	0.146234i
$323$	0.342244			0.0190430
$324$	0.939693	−	1.62760i	0.0522051	−	0.0904220i
$325$	2.28699	+	3.96118i	0.126859	+	0.219727i
$326$	−2.48798	−	4.30930i	−0.137796	−	0.238670i
$327$	−8.62108	+	14.9322i	−0.476747	+	0.825750i
$328$	−1.40373			−0.0775082
$329$	1.72874	+	10.7849i	0.0953086	+	0.594592i
$330$	0.120615			0.00663962
$331$	−10.4559	+	18.1101i	−0.574708	+	0.995423i	0.421366	+	0.906891i	$0.361551\pi$
$331$	−10.4559	+	18.1101i	−0.574708	+	0.995423i	−0.996073	+	0.0885320i	$0.971782\pi$
$332$	−2.31908	−	4.01676i	−0.127276	−	0.220448i
$333$	1.43969	+	2.49362i	0.0788947	+	0.136650i
$334$	−1.99660	+	3.45821i	−0.109249	+	0.189225i
$335$	3.04189			0.166196
$336$	6.75624	−	5.49194i	0.368583	−	0.299610i
$337$	−16.0419			−0.873857			−0.436929	−	0.899496i	$-0.643934\pi$
$337$	−16.0419			−0.873857			−0.436929	+	0.899496i	$0.643934\pi$
$338$	0.173648	−	0.300767i	0.00944522	−	0.0163596i
$339$	5.67617	+	9.83142i	0.308287	+	0.533970i
$340$	0.687319	+	1.19047i	0.0372751	+	0.0645624i
$341$	−0.156574	+	0.271194i	−0.00847896	+	0.0146860i
$342$	−0.106067			−0.00573544
$343$	8.50000	+	16.4545i	0.458957	+	0.888459i
$344$	3.96585			0.213824
$345$	−2.61334	+	4.52644i	−0.140698	+	0.243695i
$346$	2.67840	+	4.63912i	0.143991	+	0.249401i
$347$	−9.29339	−	16.0966i	−0.498895	−	0.864112i	0.501104	−	0.865387i	$-0.332927\pi$
$347$	−9.29339	−	16.0966i	−0.498895	−	0.864112i	−0.999999	+	0.00127538i	$0.999594\pi$
$348$	−7.31180	+	12.6644i	−0.391954	+	0.678884i
$349$	15.2267			0.815066			0.407533	−	0.913191i	$-0.366389\pi$
$349$	15.2267			0.815066			0.407533	+	0.913191i	$0.366389\pi$
$350$	−3.26130	+	2.65101i	−0.174324	+	0.141702i
$351$	−1.00000			−0.0533761
$352$	1.02094	−	1.76833i	0.0544165	−	0.0942522i
$353$	2.95471	+	5.11770i	0.157263	+	0.272388i	0.933881	−	0.357584i	$-0.116400\pi$
$353$	2.95471	+	5.11770i	0.157263	+	0.272388i	−0.776618	+	0.629972i	$0.783066\pi$
$354$	−2.49747	−	4.32575i	−0.132739	−	0.229911i
$355$	1.28224	−	2.22091i	0.0680543	−	0.117874i
$356$	−20.6459			−1.09423
$357$	0.469255	+	2.92750i	0.0248356	+	0.154940i
$358$	−8.73412			−0.461612
$359$	−5.19506	+	8.99811i	−0.274185	+	0.474902i	−0.969929	−	0.243388i	$-0.921741\pi$
$359$	−5.19506	+	8.99811i	−0.274185	+	0.474902i	0.695744	+	0.718289i	$0.255075\pi$
$360$	−0.439693	−	0.761570i	−0.0231738	−	0.0401383i
$361$	9.45336	+	16.3737i	0.497545	+	0.861774i
$362$	2.33703	−	4.04785i	0.122832	−	0.212750i
$363$	10.7169			0.562490
$364$	−4.64543	−	1.77330i	−0.243487	−	0.0929464i
$365$	7.58677			0.397110
$366$	−1.36484	+	2.36397i	−0.0713412	+	0.123567i
$367$	12.0902	+	20.9408i	0.631102	+	1.09310i	0.987327	+	0.158700i	$0.0507304\pi$
$367$	12.0902	+	20.9408i	0.631102	+	1.09310i	−0.356225	+	0.934400i	$0.615936\pi$
$368$	13.1762	+	22.8218i	0.686856	+	1.18967i
$369$	0.520945	−	0.902302i	0.0271193	−	0.0469720i
$370$	0.652704			0.0339324
$371$	−6.25877	−	2.38917i	−0.324939	−	0.124039i
$372$	1.10607			0.0573469
$373$	−3.25103	+	5.63095i	−0.168332	+	0.291559i	−0.937834	−	0.347085i	$-0.887171\pi$
$373$	−3.25103	+	5.63095i	−0.168332	+	0.291559i	0.769502	+	0.638645i	$0.220505\pi$
$374$	0.103541	+	0.179338i	0.00535396	+	0.00927333i
$375$	−3.12449	−	5.41177i	−0.161348	−	0.279462i
$376$	2.78106	−	4.81694i	0.143422	−	0.248414i
$377$	7.78106			0.400745
$378$	−0.145430	−	0.907278i	−0.00748010	−	0.0466653i
$379$	−17.7915			−0.913887			−0.456944	−	0.889496i	$-0.651056\pi$
$379$	−17.7915			−0.913887			−0.456944	+	0.889496i	$0.651056\pi$
$380$	0.187319	−	0.324446i	0.00960925	−	0.0166437i
$381$	−1.77584	−	3.07585i	−0.0909793	−	0.157581i
$382$	2.90121	+	5.02504i	0.148439	+	0.257103i
$383$	4.98158	−	8.62835i	0.254547	−	0.440888i	−0.710225	−	0.703974i	$-0.751407\pi$
$383$	4.98158	−	8.62835i	0.254547	−	0.440888i	0.964772	+	0.263086i	$0.0847403\pi$
$384$	−9.49794			−0.484690
$385$	−0.713011	+	0.579585i	−0.0363384	+	0.0295384i
$386$	−6.34224			−0.322812
$387$	−1.47178	+	2.54920i	−0.0748149	+	0.129583i
$388$	9.64930	+	16.7131i	0.489869	+	0.848478i
$389$	1.95084	+	3.37895i	0.0989114	+	0.171320i	0.911234	−	0.411888i	$-0.135131\pi$
$389$	1.95084	+	3.37895i	0.0989114	+	0.171320i	−0.812323	+	0.583208i	$0.801797\pi$
$390$	−0.113341	+	0.196312i	−0.00573923	+	0.00994065i
$391$	−8.97359			−0.453814
$392$	1.92649	−	9.23222i	0.0973024	−	0.466297i
$393$	−15.5449			−0.784136
$394$	2.98158	−	5.16425i	0.150210	−	0.260171i
$395$	−0.955889	−	1.65565i	−0.0480960	−	0.0833047i
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	16.9500	−	29.3582i	0.850694	−	1.47345i	−0.0298888	−	0.999553i	$-0.509515\pi$
$397$	16.9500	−	29.3582i	0.850694	−	1.47345i	0.880583	−	0.473892i	$-0.157151\pi$
$398$	1.76382			0.0884125
$399$	0.627011	−	0.509678i	0.0313898	−	0.0255158i
$400$	−15.0523			−0.752616
$401$	−16.4290	+	28.4559i	−0.820426	+	1.42102i	0.0849396	+	0.996386i	$0.472930\pi$
$401$	−16.4290	+	28.4559i	−0.820426	+	1.42102i	−0.905365	+	0.424633i	$0.860403\pi$
$402$	−0.809278	−	1.40171i	−0.0403631	−	0.0699109i
$403$	−0.294263	−	0.509678i	−0.0146583	−	0.0253889i
$404$	12.5424	−	21.7240i	0.624006	−	1.08081i
$405$	0.652704			0.0324331
$406$	1.13160	+	7.05958i	0.0561602	+	0.350361i
$407$	−1.53209			−0.0759428
$408$	0.754900	−	1.30753i	0.0373731	−	0.0647321i
$409$	−1.81908	−	3.15074i	−0.0899476	−	0.155794i	0.817541	−	0.575870i	$-0.195337\pi$
$409$	−1.81908	−	3.15074i	−0.0899476	−	0.155794i	−0.907489	+	0.420076i	$0.862003\pi$
$410$	−0.118089	−	0.204535i	−0.00583198	−	0.0101013i
$411$	4.06031	−	7.03266i	0.200280	−	0.346895i
$412$	−13.6091			−0.670470
$413$	35.5501	+	13.5706i	1.74931	+	0.667764i
$414$	2.78106			0.136682
$415$	0.805407	−	1.39501i	0.0395359	−	0.0684782i
$416$	1.91875	+	3.32337i	0.0940744	+	0.162942i
$417$	8.01114	+	13.8757i	0.392307	+	0.679496i
$418$	0.0282185	−	0.0488759i	0.00138021	−	0.00239060i
$419$	16.6905			0.815383			0.407692	−	0.913120i	$-0.366334\pi$
$419$	16.6905			0.815383			0.407692	+	0.913120i	$0.366334\pi$
$420$	3.03209	+	1.15744i	0.147951	+	0.0564774i
$421$	−21.5425			−1.04992			−0.524959	−	0.851127i	$-0.675919\pi$
$421$	−21.5425			−1.04992			−0.524959	+	0.851127i	$0.675919\pi$
$422$	−4.06758	+	7.04526i	−0.198007	+	0.342958i
$423$	2.06418	+	3.57526i	0.100364	+	0.173835i
$424$	1.70574	+	2.95442i	0.0828379	+	0.143479i
$425$	2.56283	−	4.43896i	0.124316	−	0.215321i
$426$	−1.36453			−0.0661118
$427$	−3.29127	−	20.5329i	−0.159276	−	0.993658i
$428$	13.5030			0.652692
$429$	0.266044	−	0.460802i	0.0128447	−	0.0222478i
$430$	0.333626	+	0.577857i	0.0160889	+	0.0278667i
$431$	−5.17365	−	8.96102i	−0.249206	−	0.431637i	0.714100	−	0.700044i	$-0.246836\pi$
$431$	−5.17365	−	8.96102i	−0.249206	−	0.431637i	−0.963306	+	0.268407i	$0.913503\pi$
$432$	1.64543	−	2.84997i	0.0791658	−	0.137119i
$433$	−3.22399			−0.154935			−0.0774676	−	0.996995i	$-0.524683\pi$
$433$	−3.22399			−0.154935			−0.0774676	+	0.996995i	$0.524683\pi$
$434$	0.419625	−	0.341101i	0.0201427	−	0.0163734i
$435$	−5.07873			−0.243506
$436$	−16.2023	+	28.0633i	−0.775951	+	1.34399i
$437$	1.22281	+	2.11797i	0.0584950	+	0.101316i
$438$	−2.01842	−	3.49600i	−0.0964438	−	0.167045i
$439$	−14.2494	+	24.6807i	−0.680089	+	1.17795i	0.294865	+	0.955539i	$0.404725\pi$
$439$	−14.2494	+	24.6807i	−0.680089	+	1.17795i	−0.974953	+	0.222409i	$0.928608\pi$
$440$	0.467911			0.0223068
$441$	5.21941	+	4.66452i	0.248543	+	0.222120i
$442$	−0.389185			−0.0185117
$443$	10.5667	−	18.3021i	0.502039	−	0.869558i	−0.497958	−	0.867201i	$-0.665917\pi$
$443$	10.5667	−	18.3021i	0.502039	−	0.869558i	0.999997	−	0.00235633i	$-0.000750045\pi$
$444$	2.70574	+	4.68647i	0.128409	+	0.222410i
$445$	−3.58512	−	6.20961i	−0.169951	−	0.294364i
$446$	−2.17412	+	3.76568i	−0.102947	+	0.178310i
$447$	−23.8871			−1.12982
$448$	10.7763	−	8.75973i	0.509133	−	0.413859i
$449$	25.6468			1.21035			0.605174	−	0.796093i	$-0.293103\pi$
$449$	25.6468			1.21035			0.605174	+	0.796093i	$0.293103\pi$
$450$	−0.794263	+	1.37570i	−0.0374419	+	0.0648513i
$451$	0.277189	+	0.480105i	0.0130523	+	0.0226073i
$452$	10.6677	+	18.4770i	0.501767	+	0.869086i
$453$	−2.45336	+	4.24935i	−0.115269	+	0.199652i
$454$	−2.71007			−0.127190
$455$	−0.273318	−	1.70513i	−0.0128134	−	0.0799375i
$456$	−0.411474			−0.0192690
$457$	−16.8293	+	29.1493i	−0.787244	+	1.36355i	0.140406	+	0.990094i	$0.455159\pi$
$457$	−16.8293	+	29.1493i	−0.787244	+	1.36355i	−0.927650	+	0.373452i	$0.878174\pi$
$458$	−3.58512	−	6.20961i	−0.167522	−	0.290156i
$459$	0.560307	+	0.970481i	0.0261529	+	0.0452982i
$460$	−4.91147	+	8.50692i	−0.228999	+	0.396637i
$461$	9.85710			0.459091			0.229545	−	0.973298i	$-0.426276\pi$
$461$	9.85710			0.459091			0.229545	+	0.973298i	$0.426276\pi$
$462$	0.456767	+	0.174362i	0.0212507	+	0.00811205i
$463$	2.39693			0.111395			0.0556973	−	0.998448i	$-0.482262\pi$
$463$	2.39693			0.111395			0.0556973	+	0.998448i	$0.482262\pi$
$464$	−12.8032	+	22.1758i	−0.594373	+	1.02948i
$465$	0.192066	+	0.332669i	0.00890687	+	0.0154272i
$466$	1.67024	+	2.89295i	0.0773726	+	0.134013i
$467$	13.6395	−	23.6243i	0.631161	−	1.09320i	−0.356154	−	0.934427i	$-0.615912\pi$
$467$	13.6395	−	23.6243i	0.631161	−	1.09320i	0.987315	−	0.158775i	$-0.0507545\pi$
$468$	−1.87939			−0.0868746
$469$	11.5196	+	4.39739i	0.531926	+	0.203052i
$470$	0.935822			0.0431663
$471$	−3.45471	+	5.98373i	−0.159185	+	0.275716i
$472$	−9.68866	−	16.7813i	−0.445957	−	0.772420i
$473$	−0.783119	−	1.35640i	−0.0360078	−	0.0623674i
$474$	−0.508618	+	0.880952i	−0.0233616	+	0.0404635i
$475$	−1.39693			−0.0640954
$476$	0.881911	+	5.50190i	0.0404223	+	0.252179i
$477$	−2.53209			−0.115936
$478$	0.408481	−	0.707510i	0.0186835	−	0.0323608i
$479$	20.4106	+	35.3522i	0.932584	+	1.61528i	0.778887	+	0.627165i	$0.215785\pi$
$479$	20.4106	+	35.3522i	0.932584	+	1.61528i	0.153697	+	0.988118i	$0.450882\pi$
$480$	−1.25237	−	2.16918i	−0.0571628	−	0.0990088i
$481$	1.43969	−	2.49362i	0.0656443	−	0.113699i
$482$	5.46379			0.248869
$483$	−16.4402	+	13.3637i	−0.748053	+	0.608070i
$484$	20.1411			0.915507
$485$	−3.35117	+	5.80439i	−0.152169	+	0.263564i
$486$	−0.173648	−	0.300767i	−0.00787684	−	0.0136431i
$487$	9.61381	+	16.6516i	0.435643	+	0.754556i	0.997348	−	0.0727816i	$-0.0231876\pi$
$487$	9.61381	+	16.6516i	0.435643	+	0.754556i	−0.561705	+	0.827338i	$0.689854\pi$
$488$	−5.29473	+	9.17074i	−0.239681	+	0.415140i
$489$	14.3277			0.647921
$490$	1.50727	−	0.495952i	0.0680917	−	0.0224048i
$491$	−7.54219			−0.340374			−0.170187	−	0.985412i	$-0.554437\pi$
$491$	−7.54219			−0.340374			−0.170187	+	0.985412i	$0.554437\pi$
$492$	0.979055	−	1.69577i	0.0441392	−	0.0764514i
$493$	−4.35978	−	7.55137i	−0.196355	−	0.340097i
$494$	0.0530334	+	0.0918566i	0.00238609	+	0.00413282i
$495$	−0.173648	+	0.300767i	−0.00780491	+	0.0135185i
$496$	1.93676			0.0869629
$497$	8.06640	−	6.55693i	0.361827	−	0.294118i
$498$	−0.857097			−0.0384074
$499$	15.4979	−	26.8432i	0.693783	−	1.20167i	−0.276806	−	0.960926i	$-0.589276\pi$
$499$	15.4979	−	26.8432i	0.693783	−	1.20167i	0.970589	−	0.240742i	$-0.0773907\pi$
$500$	−5.87211	−	10.1708i	−0.262609	−	0.454852i
$501$	−5.74897	−	9.95751i	−0.256845	−	0.444869i
$502$	−3.78833	+	6.56159i	−0.169082	+	0.292858i
$503$	18.4861			0.824254			0.412127	−	0.911126i	$-0.364786\pi$
$503$	18.4861			0.824254			0.412127	+	0.911126i	$0.364786\pi$
$504$	−0.564178	−	3.51968i	−0.0251305	−	0.156779i
$505$	8.71183			0.387671
$506$	−0.739885	+	1.28152i	−0.0328919	+	0.0569705i
$507$	0.500000	+	0.866025i	0.0222058	+	0.0384615i
$508$	−3.33750	−	5.78071i	−0.148077	−	0.256478i
$509$	18.0868	−	31.3272i	0.801682	−	1.38855i	−0.116826	−	0.993152i	$-0.537272\pi$
$509$	18.0868	−	31.3272i	0.801682	−	1.38855i	0.918508	−	0.395402i	$-0.129395\pi$
$510$	0.254023			0.0112483
$511$	28.7310	+	10.9675i	1.27099	+	0.485174i
$512$	−21.4962			−0.950006
$513$	0.152704	−	0.264490i	0.00674203	−	0.0116775i
$514$	−4.04205	−	7.00104i	−0.178287	−	0.308803i
$515$	−2.36319	−	4.09316i	−0.104135	−	0.180366i
$516$	−2.76604	+	4.79093i	−0.121768	+	0.210909i
$517$	−2.19665			−0.0966086
$518$	2.47178	+	0.943555i	0.108604	+	0.0414574i
$519$	−15.4243			−0.677050
$520$	−0.439693	+	0.761570i	−0.0192818	+	0.0333971i
$521$	−13.2430	−	22.9376i	−0.580188	−	1.00492i	−0.995457	−	0.0952164i	$-0.969646\pi$
$521$	−13.2430	−	22.9376i	−0.580188	−	1.00492i	0.415268	−	0.909699i	$-0.363688\pi$
$522$	1.35117	+	2.34029i	0.0591390	+	0.102432i
$523$	5.49794	−	9.52271i	0.240408	−	0.416399i	−0.720422	−	0.693536i	$-0.756052\pi$
$523$	5.49794	−	9.52271i	0.240408	−	0.416399i	0.960831	+	0.277136i	$0.0893854\pi$
$524$	−29.2148			−1.27626
$525$	−1.91534	−	11.9491i	−0.0835925	−	0.521500i
$526$	−0.955423			−0.0416584
$527$	−0.329755	+	0.571153i	−0.0143644	+	0.0248798i
$528$	0.875515	+	1.51644i	0.0381019	+	0.0659944i
$529$	−20.5620	−	35.6144i	−0.893998	−	1.54845i
$530$	−0.286989	+	0.497079i	−0.0124660	+	0.0215918i
$531$	14.3824			0.624142
$532$	1.17840	−	0.957882i	0.0510899	−	0.0415295i
$533$	−1.04189			−0.0451292
$534$	−1.90760	+	3.30407i	−0.0825501	+	0.142981i
$535$	2.34477	+	4.06126i	0.101373	+	0.175584i
$536$	−3.13950	−	5.43777i	−0.135606	−	0.234876i
$537$	12.5744	−	21.7796i	0.542627	−	0.939858i
$538$	−1.88350			−0.0812036
$539$	−3.53802	+	1.16415i	−0.152393	+	0.0501433i
$540$	1.22668			0.0527880
$541$	1.69253	−	2.93155i	0.0727677	−	0.126037i	−0.827346	−	0.561693i	$-0.810150\pi$
$541$	1.69253	−	2.93155i	0.0727677	−	0.126037i	0.900113	+	0.435656i	$0.143484\pi$
$542$	0.280592	+	0.486000i	0.0120525	+	0.0208755i
$543$	6.72921	+	11.6553i	0.288778	+	0.500178i
$544$	2.15018	−	3.72422i	0.0921881	−	0.159674i
$545$	−11.2540			−0.482069
$546$	−0.713011	+	0.579585i	−0.0305141	+	0.0248039i
$547$	−8.37464			−0.358074			−0.179037	−	0.983842i	$-0.557298\pi$
$547$	−8.37464			−0.358074			−0.179037	+	0.983842i	$0.557298\pi$
$548$	7.63088	−	13.2171i	0.325975	−	0.564605i
$549$	−3.92989	−	6.80677i	−0.167724	−	0.290506i
$550$	−0.422618	−	0.731997i	−0.0180205	−	0.0312124i
$551$	−1.18820	+	2.05802i	−0.0506189	+	0.0876744i
$552$	10.7888			0.459202
$553$	−1.22652	−	7.65177i	−0.0521569	−	0.325386i
$554$	−2.72638			−0.115833
$555$	−0.939693	+	1.62760i	−0.0398877	+	0.0690876i
$556$	15.0560	+	26.0778i	0.638518	+	1.10595i
$557$	−18.1827	−	31.4934i	−0.770427	−	1.33442i	−0.937329	−	0.348445i	$-0.886710\pi$
$557$	−18.1827	−	31.4934i	−0.770427	−	1.33442i	0.166902	−	0.985974i	$-0.446624\pi$
$558$	0.102196	−	0.177009i	0.00432632	−	0.00749341i
$559$	2.94356			0.124499
$560$	5.30928	+	2.02671i	0.224358	+	0.0856443i
$561$	−0.596267			−0.0251744
$562$	−3.30675	+	5.72746i	−0.139487	+	0.241598i
$563$	−2.62314	−	4.54341i	−0.110552	−	0.191482i	0.805441	−	0.592676i	$-0.201929\pi$
$563$	−2.62314	−	4.54341i	−0.110552	−	0.191482i	−0.915993	+	0.401194i	$0.868595\pi$
$564$	3.87939	+	6.71929i	0.163352	+	0.282933i
$565$	−3.70486	+	6.41701i	−0.155865	+	0.269965i
$566$	−8.08740			−0.339939
$567$	2.47178	+	0.943555i	0.103805	+	0.0396256i
$568$	−5.29355			−0.222112
$569$	10.7429	−	18.6072i	0.450365	−	0.780055i	−0.548044	−	0.836450i	$-0.684627\pi$
$569$	10.7429	−	18.6072i	0.450365	−	0.780055i	0.998409	+	0.0563949i	$0.0179606\pi$
$570$	−0.0346151	−	0.0599551i	−0.00144987	−	0.00251124i
$571$	−16.5804	−	28.7181i	−0.693867	−	1.20181i	−0.970561	−	0.240855i	$-0.922572\pi$
$571$	−16.5804	−	28.7181i	−0.693867	−	1.20181i	0.276694	−	0.960958i	$-0.410761\pi$
$572$	0.500000	−	0.866025i	0.0209061	−	0.0362103i
$573$	−16.7074			−0.697961
$574$	−0.151522	−	0.945283i	−0.00632439	−	0.0394554i
$575$	36.6272			1.52746
$576$	2.62449	−	4.54574i	0.109354	−	0.189406i
$577$	−13.5890	−	23.5368i	−0.565717	−	0.979851i	−0.996983	−	0.0776258i	$-0.975266\pi$
$577$	−13.5890	−	23.5368i	−0.565717	−	0.979851i	0.431265	−	0.902225i	$-0.358067\pi$
$578$	−2.73396	−	4.73535i	−0.113718	−	0.196965i
$579$	9.13088	−	15.8152i	0.379466	−	0.657255i
$580$	−9.54488			−0.396330
$581$	5.06670	−	4.11857i	0.210202	−	0.170867i
$582$	3.56624			0.147825
$583$	0.673648	−	1.16679i	0.0278997	−	0.0483236i
$584$	−7.83022	−	13.5623i	−0.324017	−	0.561214i
$585$	−0.326352	−	0.565258i	−0.0134930	−	0.0233705i
$586$	4.68392	−	8.11278i	0.193491	−	0.335136i
$587$	−30.8280			−1.27241			−0.636204	−	0.771521i	$-0.719496\pi$
$587$	−30.8280			−1.27241			−0.636204	+	0.771521i	$0.719496\pi$
$588$	9.80928	+	8.76644i	0.404528	+	0.361522i
$589$	0.179740			0.00740606
$590$	1.63011	−	2.82343i	0.0671106	−	0.116239i
$591$	8.58512	+	14.8699i	0.353145	+	0.611665i
$592$	4.73783	+	8.20616i	0.194723	+	0.337271i
$593$	−20.0364	+	34.7041i	−0.822797	+	1.42513i	0.0807937	+	0.996731i	$0.474255\pi$
$593$	−20.0364	+	34.7041i	−0.822797	+	1.42513i	−0.903591	+	0.428396i	$0.859079\pi$
$594$	0.184793			0.00758213
$595$	−1.50165	+	1.22064i	−0.0615616	+	0.0500415i
$596$	−44.8931			−1.83889
$597$	−2.53936	+	4.39831i	−0.103929	+	0.180011i
$598$	−1.39053	−	2.40847i	−0.0568630	−	0.0984896i
$599$	−15.4226	−	26.7128i	−0.630151	−	1.09145i	−0.987520	−	0.157491i	$-0.949660\pi$
$599$	−15.4226	−	26.7128i	−0.630151	−	1.09145i	0.357369	−	0.933963i	$-0.383674\pi$
$600$	−3.08125	+	5.33688i	−0.125792	+	0.217877i
$601$	−9.85803			−0.402117			−0.201059	−	0.979579i	$-0.564438\pi$
$601$	−9.85803			−0.402117			−0.201059	+	0.979579i	$0.564438\pi$
$602$	0.428081	+	2.67063i	0.0174473	+	0.108847i
$603$	4.66044			0.189788
$604$	−4.61081	+	7.98617i	−0.187611	+	0.324952i
$605$	3.49747	+	6.05780i	0.142193	+	0.246285i
$606$	−2.31773	−	4.01443i	−0.0941515	−	0.163075i
$607$	15.6643	−	27.1314i	0.635795	−	1.10123i	−0.350551	−	0.936544i	$-0.614006\pi$
$607$	15.6643	−	27.1314i	0.635795	−	1.10123i	0.986346	−	0.164686i	$-0.0526609\pi$
$608$	−1.17200			−0.0475308
$609$	−19.2331	−	7.34186i	−0.779364	−	0.297507i
$610$	−1.78167			−0.0721377
$611$	2.06418	−	3.57526i	0.0835077	−	0.144640i
$612$	1.05303	+	1.82391i	0.0425664	+	0.0737271i
$613$	2.30928	+	3.99979i	0.0932708	+	0.161550i	0.908886	−	0.417045i	$-0.136934\pi$
$613$	2.30928	+	3.99979i	0.0932708	+	0.161550i	−0.815615	+	0.578595i	$0.803601\pi$
$614$	1.09121	−	1.89004i	0.0440378	−	0.0762757i
$615$	0.680045			0.0274221
$616$	1.77197	+	0.676417i	0.0713949	+	0.0272536i
$617$	−14.5648			−0.586357			−0.293179	−	0.956058i	$-0.594713\pi$
$617$	−14.5648			−0.586357			−0.293179	+	0.956058i	$0.594713\pi$
$618$	−1.25743	+	2.17793i	−0.0505811	+	0.0876090i
$619$	24.7067	+	42.7932i	0.993045	+	1.72000i	0.598485	+	0.801134i	$0.295770\pi$
$619$	24.7067	+	42.7932i	0.993045	+	1.72000i	0.394560	+	0.918870i	$0.370897\pi$
$620$	0.360967	+	0.625213i	0.0144968	+	0.0251092i
$621$	−4.00387	+	6.93491i	−0.160670	+	0.278288i
$622$	−0.773318			−0.0310072
$623$	−4.60014	−	28.6984i	−0.184301	−	1.14978i
$624$	−3.29086			−0.131740
$625$	−9.39558	+	16.2736i	−0.375823	+	0.650945i
$626$	3.44191	+	5.96157i	0.137567	+	0.238272i
$627$	0.0812519	+	0.140732i	0.00324489	+	0.00562031i
$628$	−6.49273	+	11.2457i	−0.259088	+	0.448754i
$629$	−3.22668			−0.128656
$630$	0.465385	−	0.378297i	0.0185414	−	0.0150717i
$631$	0.529401			0.0210751			0.0105376	−	0.999944i	$-0.496646\pi$
$631$	0.529401			0.0210751			0.0105376	+	0.999944i	$0.496646\pi$
$632$	−1.97313	+	3.41755i	−0.0784867	+	0.135943i
$633$	−11.7121	−	20.2860i	−0.465516	−	0.806297i
$634$	−2.03209	−	3.51968i	−0.0807046	−	0.139784i
$635$	1.15910	−	2.00762i	0.0459975	−	0.0796700i
$636$	−4.75877			−0.188698
$637$	1.42989	−	6.85240i	0.0566544	−	0.271502i
$638$	−1.43788			−0.0569263
$639$	1.96451	−	3.40263i	0.0777147	−	0.134606i
$640$	−3.09967	−	5.36879i	−0.122525	−	0.212220i
$641$	16.0556	+	27.8090i	0.634156	+	1.09839i	0.986693	+	0.162593i	$0.0519858\pi$
$641$	16.0556	+	27.8090i	0.634156	+	1.09839i	−0.352537	+	0.935798i	$0.614681\pi$
$642$	1.24763	−	2.16095i	0.0492399	−	0.0852860i
$643$	23.5740			0.929667			0.464833	−	0.885398i	$-0.346114\pi$
$643$	23.5740			0.929667			0.464833	+	0.885398i	$0.346114\pi$
$644$	−30.8974	+	25.1155i	−1.21753	+	0.989691i
$645$	−1.92127			−0.0756501
$646$	0.0594300	−	0.102936i	0.00233824	−	0.00404996i
$647$	7.87598	+	13.6416i	0.309637	+	0.536307i	0.978283	−	0.207274i	$-0.0664592\pi$
$647$	7.87598	+	13.6416i	0.309637	+	0.536307i	−0.668646	+	0.743581i	$0.733126\pi$
$648$	−0.673648	−	1.16679i	−0.0264634	−	0.0458360i
$649$	−3.82635	+	6.62744i	−0.150197	+	0.260150i
$650$	1.58853			0.0623071
$651$	0.246444	+	1.53747i	0.00965891	+	0.0602581i
$652$	26.9273			1.05455
$653$	15.5337	−	26.9052i	0.607882	−	1.05288i	−0.383707	−	0.923455i	$-0.625353\pi$
$653$	15.5337	−	26.9052i	0.607882	−	1.05288i	0.991589	−	0.129428i	$-0.0413140\pi$
$654$	2.99407	+	5.18588i	0.117077	+	0.202784i
$655$	−5.07310	−	8.78687i	−0.198222	−	0.343331i
$656$	1.71436	−	2.96935i	0.0669343	−	0.115934i
$657$	11.6236			0.453480
$658$	3.54395	+	1.35283i	0.138157	+	0.0527390i
$659$	19.9162			0.775826			0.387913	−	0.921696i	$-0.373196\pi$
$659$	19.9162			0.775826			0.387913	+	0.921696i	$0.373196\pi$
$660$	−0.326352	+	0.565258i	−0.0127032	+	0.0220026i
$661$	−12.1361	−	21.0203i	−0.472039	−	0.817596i	0.527449	−	0.849587i	$-0.323149\pi$
$661$	−12.1361	−	21.0203i	−0.472039	−	0.817596i	−0.999488	+	0.0319906i	$0.989815\pi$
$662$	3.63129	+	6.28958i	0.141134	+	0.244452i
$663$	0.560307	−	0.970481i	0.0217605	−	0.0376904i
$664$	−3.32501			−0.129035
$665$	0.492726	+	0.188089i	0.0191071	+	0.00729377i
$666$	1.00000			0.0387492
$667$	31.1544	−	53.9609i	1.20630	−	2.08938i
$668$	−10.8045	−	18.7140i	−0.418040	−	0.724066i
$669$	−6.26011	−	10.8428i	−0.242030	−	0.419208i
$670$	0.528218	−	0.914901i	0.0204069	−	0.0353457i
$671$	4.18210			0.161448
$672$	−1.60694	−	10.0251i	−0.0619892	−	0.386726i
$673$	23.2668			0.896870			0.448435	−	0.893815i	$-0.351982\pi$
$673$	23.2668			0.896870			0.448435	+	0.893815i	$0.351982\pi$
$674$	−2.78564	+	4.82488i	−0.107299	+	0.185847i
$675$	−2.28699	−	3.96118i	−0.0880262	−	0.152466i
$676$	0.939693	+	1.62760i	0.0361420	+	0.0625998i
$677$	−11.0248	+	19.0955i	−0.423718	+	0.733901i	−0.996300	−	0.0859465i	$-0.972609\pi$
$677$	−11.0248	+	19.0955i	−0.423718	+	0.733901i	0.572582	+	0.819848i	$0.305942\pi$
$678$	3.94263			0.151416
$679$	−21.0817	+	17.1367i	−0.809042	+	0.657646i
$680$	0.985452			0.0377904
$681$	3.90167	−	6.75790i	0.149512	−	0.258963i
$682$	0.0543776	+	0.0941848i	0.00208223	+	0.00360652i
$683$	3.73829	+	6.47491i	0.143042	+	0.247756i	0.928641	−	0.370980i	$-0.120978\pi$
$683$	3.73829	+	6.47491i	0.143042	+	0.247756i	−0.785599	+	0.618736i	$0.787645\pi$
$684$	0.286989	−	0.497079i	0.0109733	−	0.0190063i
$685$	5.30035			0.202516
$686$	6.42498	+	0.300767i	0.245307	+	0.0114834i
$687$	20.6459			0.787690
$688$	−4.84343	+	8.38906i	−0.184654	+	0.319830i
$689$	1.26604	+	2.19285i	0.0482325	+	0.0835411i
$690$	0.907604	+	1.57202i	0.0345519	+	0.0598456i
$691$	−5.66637	+	9.81445i	−0.215559	+	0.373359i	−0.953445	−	0.301566i	$-0.902491\pi$
$691$	−5.66637	+	9.81445i	−0.215559	+	0.373359i	0.737886	+	0.674925i	$0.235824\pi$
$692$	−28.9881			−1.10196
$693$	−1.09240	+	0.887975i	−0.0414967	+	0.0337314i
$694$	−6.45512			−0.245033
$695$	−5.22890	+	9.05673i	−0.198344	+	0.343541i
$696$	5.24170	+	9.07888i	0.198686	+	0.344134i
$697$	0.583778	+	1.01113i	0.0221122	+	0.0382994i
$698$	2.64409	−	4.57969i	0.100080	−	0.173344i
$699$	−9.61856			−0.363807
$700$	−3.59967	−	22.4569i	−0.136055	−	0.848792i
$701$	−15.8135			−0.597266			−0.298633	−	0.954368i	$-0.596531\pi$
$701$	−15.8135			−0.597266			−0.298633	+	0.954368i	$0.596531\pi$
$702$	−0.173648	+	0.300767i	−0.00655393	+	0.0113517i
$703$	0.439693	+	0.761570i	0.0165833	+	0.0287232i
$704$	1.39646	+	2.41874i	0.0526310	+	0.0911596i
$705$	−1.34730	+	2.33359i	−0.0507421	+	0.0878879i
$706$	2.05232			0.0772400
$707$	32.9916	+	12.5939i	1.24078	+	0.473643i
$708$	27.0300			1.01585
$709$	−21.1618	+	36.6533i	−0.794748	+	1.37654i	0.128252	+	0.991742i	$0.459063\pi$
$709$	−21.1618	+	36.6533i	−0.794748	+	1.37654i	−0.922999	+	0.384802i	$0.874270\pi$
$710$	−0.445318	−	0.771313i	−0.0167125	−	0.0289469i
$711$	−1.46451	−	2.53660i	−0.0549233	−	0.0951300i
$712$	−7.40033	+	12.8177i	−0.277339	+	0.480365i
$713$	−4.71276			−0.176494
$714$	0.961981	+	0.367218i	0.0360012	+	0.0137428i
$715$	0.347296			0.0129881
$716$	23.6322	−	40.9322i	0.883178	−	1.52971i
$717$	1.17617	+	2.03719i	0.0439250	+	0.0760804i
$718$	1.80423	+	3.12501i	0.0673331	+	0.116624i
$719$	−13.7870	+	23.8798i	−0.514168	+	0.890565i	0.485697	+	0.874127i	$0.338566\pi$
$719$	−13.7870	+	23.8798i	−0.514168	+	0.890565i	−0.999865	+	0.0164377i	$0.994767\pi$
$720$	2.14796			0.0800496
$721$	−3.03225	−	18.9170i	−0.112927	−	0.704506i
$722$	6.56624			0.244370
$723$	−7.86618	+	13.6246i	−0.292546	+	0.506705i
$724$	12.6468	+	21.9049i	0.470014	+	0.814088i
$725$	17.7952	+	30.8222i	0.660897	+	1.14471i
$726$	1.86097	−	3.22329i	0.0690670	−	0.119627i
$727$	20.5844			0.763433			0.381717	−	0.924279i	$-0.375333\pi$
$727$	20.5844			0.763433			0.381717	+	0.924279i	$0.375333\pi$
$728$	−2.76604	+	2.24843i	−0.102516	+	0.0833325i
$729$	1.00000			0.0370370
$730$	1.31743	−	2.28185i	0.0487602	−	0.0844552i
$731$	−1.64930	−	2.85667i	−0.0610016	−	0.105658i
$732$	−7.38578	−	12.7925i	−0.272986	−	0.472826i
$733$	5.80810	−	10.0599i	0.214527	−	0.371572i	−0.738599	−	0.674145i	$-0.764512\pi$
$733$	5.80810	−	10.0599i	0.214527	−	0.371572i	0.953126	+	0.302573i	$0.0978457\pi$
$734$	8.39775			0.309967
$735$	−0.933296	+	4.47259i	−0.0344251	+	0.164974i
$736$	30.7297			1.13271
$737$	−1.23989	+	2.14754i	−0.0456718	+	0.0791058i
$738$	−0.180922	−	0.313366i	−0.00665984	−	0.0115352i
$739$	4.30675	+	7.45951i	0.158426	+	0.274403i	0.934301	−	0.356484i	$-0.116025\pi$
$739$	4.30675	+	7.45951i	0.158426	+	0.274403i	−0.775875	+	0.630887i	$0.782691\pi$
$740$	−1.76604	+	3.05888i	−0.0649211	+	0.112447i
$741$	−0.305407			−0.0112194
$742$	−1.80541	+	1.46756i	−0.0662786	+	0.0538758i
$743$	23.9828			0.879842			0.439921	−	0.898036i	$-0.355006\pi$
$743$	23.9828			0.879842			0.439921	+	0.898036i	$0.355006\pi$
$744$	0.396459	−	0.686688i	0.0145349	−	0.0251752i
$745$	−7.79561	−	13.5024i	−0.285609	−	0.494689i
$746$	1.12907	+	1.95561i	0.0413382	+	0.0715999i
$747$	1.23396	−	2.13727i	0.0451481	−	0.0781988i
$748$	−1.12061			−0.0409737
$749$	3.00862	+	18.7696i	0.109933	+	0.685825i
$750$	−2.17024			−0.0792461
$751$	4.56149	−	7.90073i	0.166451	−	0.288302i	−0.770719	−	0.637176i	$-0.780103\pi$
$751$	4.56149	−	7.90073i	0.166451	−	0.288302i	0.937170	+	0.348874i	$0.113436\pi$
$752$	6.79292	+	11.7657i	0.247712	+	0.429050i
$753$	−10.9081	−	18.8933i	−0.397512	−	0.688511i
$754$	1.35117	−	2.34029i	0.0492066	−	0.0852283i
$755$	−3.20264			−0.116556
$756$	4.64543	+	1.77330i	0.168953	+	0.0644944i
$757$	−26.4979			−0.963084			−0.481542	−	0.876423i	$-0.659923\pi$
$757$	−26.4979			−0.963084			−0.481542	+	0.876423i	$0.659923\pi$
$758$	−3.08946	+	5.35110i	−0.112214	+	0.194361i
$759$	−2.13041	−	3.68999i	−0.0773292	−	0.133938i
$760$	−0.134285	−	0.232589i	−0.00487104	−	0.00843689i
$761$	−26.1498	+	45.2927i	−0.947928	+	1.64186i	−0.198149	+	0.980172i	$0.563493\pi$
$761$	−26.1498	+	45.2927i	−0.947928	+	1.64186i	−0.749779	+	0.661688i	$0.769840\pi$
$762$	−1.23349			−0.0446846
$763$	−42.6189	−	16.2689i	−1.54291	−	0.588975i
$764$	−31.3996			−1.13600
$765$	−0.365715	+	0.633436i	−0.0132224	+	0.0229019i
$766$	−1.73009	−	2.99660i	−0.0625105	−	0.108271i
$767$	−7.19119	−	12.4555i	−0.259659	−	0.449742i
$768$	3.59967	−	6.23481i	0.129892	−	0.224979i
$769$	44.9436			1.62071			0.810353	−	0.585942i	$-0.199275\pi$
$769$	44.9436			1.62071			0.810353	+	0.585942i	$0.199275\pi$
$770$	0.0505072	+	0.315094i	0.00182015	+	0.0113552i

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

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.300767i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.939693 + 1.62760i) q^{4} +(-0.326352 + 0.565258i) q^{5} +0.347296 q^{6} +(-2.05303 + 1.66885i) q^{7} +1.34730 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.300767i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.939693 + 1.62760i) q^{4} +(-0.326352 + 0.565258i) q^{5} +0.347296 q^{6} +(-2.05303 + 1.66885i) q^{7} +1.34730 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.113341 + 0.196312i) q^{10} +(-0.266044 - 0.460802i) q^{11} +(-0.939693 + 1.62760i) q^{12} +1.00000 q^{13} +(0.145430 + 0.907278i) q^{14} -0.652704 q^{15} +(-1.64543 + 2.84997i) q^{16} +(-0.560307 - 0.970481i) q^{17} +(0.173648 + 0.300767i) q^{18} +(-0.152704 + 0.264490i) q^{19} -1.22668 q^{20} +(-2.47178 - 0.943555i) q^{21} -0.184793 q^{22} +(4.00387 - 6.93491i) q^{23} +(0.673648 + 1.16679i) q^{24} +(2.28699 + 3.96118i) q^{25} +(0.173648 - 0.300767i) q^{26} -1.00000 q^{27} +(-4.64543 - 1.77330i) q^{28} +7.78106 q^{29} +(-0.113341 + 0.196312i) q^{30} +(-0.294263 - 0.509678i) q^{31} +(1.91875 + 3.32337i) q^{32} +(0.266044 - 0.460802i) q^{33} -0.389185 q^{34} +(-0.273318 - 1.70513i) q^{35} -1.87939 q^{36} +(1.43969 - 2.49362i) q^{37} +(0.0530334 + 0.0918566i) q^{38} +(0.500000 + 0.866025i) q^{39} +(-0.439693 + 0.761570i) q^{40} -1.04189 q^{41} +(-0.713011 + 0.579585i) q^{42} +2.94356 q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.326352 - 0.565258i) q^{45} +(-1.39053 - 2.40847i) q^{46} +(2.06418 - 3.57526i) q^{47} -3.29086 q^{48} +(1.42989 - 6.85240i) q^{49} +1.58853 q^{50} +(0.560307 - 0.970481i) q^{51} +(0.939693 + 1.62760i) q^{52} +(1.26604 + 2.19285i) q^{53} +(-0.173648 + 0.300767i) q^{54} +0.347296 q^{55} +(-2.76604 + 2.24843i) q^{56} -0.305407 q^{57} +(1.35117 - 2.34029i) q^{58} +(-7.19119 - 12.4555i) q^{59} +(-0.613341 - 1.06234i) q^{60} +(-3.92989 + 6.80677i) q^{61} -0.204393 q^{62} +(-0.418748 - 2.61240i) q^{63} -5.24897 q^{64} +(-0.326352 + 0.565258i) q^{65} +(-0.0923963 - 0.160035i) q^{66} +(-2.33022 - 4.03606i) q^{67} +(1.05303 - 1.82391i) q^{68} +8.00774 q^{69} +(-0.560307 - 0.213887i) q^{70} -3.92902 q^{71} +(-0.673648 + 1.16679i) q^{72} +(-5.81180 - 10.0663i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(-2.28699 + 3.96118i) q^{75} -0.573978 q^{76} +(1.31521 + 0.502055i) q^{77} +0.347296 q^{78} +(-1.46451 + 2.53660i) q^{79} +(-1.07398 - 1.86018i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.180922 + 0.313366i) q^{82} -2.46791 q^{83} +(-0.786989 - 4.90971i) q^{84} +0.731429 q^{85} +(0.511144 - 0.885328i) q^{86} +(3.89053 + 6.73859i) q^{87} +(-0.358441 - 0.620838i) q^{88} +(-5.49273 + 9.51368i) q^{89} -0.226682 q^{90} +(-2.05303 + 1.66885i) q^{91} +15.0496 q^{92} +(0.294263 - 0.509678i) q^{93} +(-0.716881 - 1.24168i) q^{94} +(-0.0996702 - 0.172634i) q^{95} +(-1.91875 + 3.32337i) q^{96} +10.2686 q^{97} +(-1.81268 - 1.61997i) q^{98} +0.532089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 3 q^{5} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 3 * q^5 + 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 3 q^{5} + 6 q^{8} - 3 q^{9} - 6 q^{10} + 3 q^{11} + 6 q^{13} - 15 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} - 3 q^{19} + 6 q^{20} + 6 q^{22} + 3 q^{24} + 6 q^{25} - 6 q^{27} - 12 q^{28} + 12 q^{29} + 6 q^{30} - 12 q^{31} + 9 q^{32} - 3 q^{33} + 6 q^{34} - 15 q^{35} + 3 q^{37} - 12 q^{38} + 3 q^{39} + 3 q^{40} - 12 q^{42} - 12 q^{43} + 3 q^{44} - 3 q^{45} + 9 q^{46} - 6 q^{47} + 12 q^{48} + 30 q^{50} + 9 q^{51} + 3 q^{53} - 12 q^{56} - 6 q^{57} - 18 q^{58} + 3 q^{59} + 3 q^{60} - 15 q^{61} - 6 q^{64} - 3 q^{65} + 3 q^{66} + 9 q^{67} - 6 q^{68} - 9 q^{70} + 42 q^{71} - 3 q^{72} - 3 q^{74} - 6 q^{75} + 12 q^{76} + 15 q^{77} + 24 q^{79} + 9 q^{80} - 3 q^{81} - 18 q^{82} - 24 q^{83} + 3 q^{84} + 24 q^{85} - 3 q^{86} + 6 q^{87} + 6 q^{88} - 15 q^{89} + 12 q^{90} + 36 q^{92} + 12 q^{93} + 12 q^{94} - 15 q^{95} - 9 q^{96} + 42 q^{97} - 33 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 3 * q^5 + 6 * q^8 - 3 * q^9 - 6 * q^10 + 3 * q^11 + 6 * q^13 - 15 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 - 3 * q^19 + 6 * q^20 + 6 * q^22 + 3 * q^24 + 6 * q^25 - 6 * q^27 - 12 * q^28 + 12 * q^29 + 6 * q^30 - 12 * q^31 + 9 * q^32 - 3 * q^33 + 6 * q^34 - 15 * q^35 + 3 * q^37 - 12 * q^38 + 3 * q^39 + 3 * q^40 - 12 * q^42 - 12 * q^43 + 3 * q^44 - 3 * q^45 + 9 * q^46 - 6 * q^47 + 12 * q^48 + 30 * q^50 + 9 * q^51 + 3 * q^53 - 12 * q^56 - 6 * q^57 - 18 * q^58 + 3 * q^59 + 3 * q^60 - 15 * q^61 - 6 * q^64 - 3 * q^65 + 3 * q^66 + 9 * q^67 - 6 * q^68 - 9 * q^70 + 42 * q^71 - 3 * q^72 - 3 * q^74 - 6 * q^75 + 12 * q^76 + 15 * q^77 + 24 * q^79 + 9 * q^80 - 3 * q^81 - 18 * q^82 - 24 * q^83 + 3 * q^84 + 24 * q^85 - 3 * q^86 + 6 * q^87 + 6 * q^88 - 15 * q^89 + 12 * q^90 + 36 * q^92 + 12 * q^93 + 12 * q^94 - 15 * q^95 - 9 * q^96 + 42 * q^97 - 33 * q^98 - 6 * q^99

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