LMFDB - Embedded newform 273.2.i.b.79.1

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			79.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	273.79
Dual form			273.2.i.b.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 1.62760i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.766044 - 1.32683i) q^{4} +(-1.43969 + 2.49362i) q^{5} -1.87939 q^{6} +(2.47178 + 0.943555i) q^{7} -0.879385 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 1.62760i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.766044 - 1.32683i) q^{4} +(-1.43969 + 2.49362i) q^{5} -1.87939 q^{6} +(2.47178 + 0.943555i) q^{7} -0.879385 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.70574 - 4.68647i) q^{10} +(0.326352 + 0.565258i) q^{11} +(0.766044 - 1.32683i) q^{12} +1.00000 q^{13} +(-3.85844 + 3.13641i) q^{14} -2.87939 q^{15} +(2.35844 - 4.08494i) q^{16} +(-2.26604 - 3.92490i) q^{17} +(-0.939693 - 1.62760i) q^{18} +(-2.37939 + 4.12122i) q^{19} +4.41147 q^{20} +(0.418748 + 2.61240i) q^{21} -1.22668 q^{22} +(-0.0714517 + 0.123758i) q^{23} +(-0.439693 - 0.761570i) q^{24} +(-1.64543 - 2.84997i) q^{25} +(-0.939693 + 1.62760i) q^{26} -1.00000 q^{27} +(-0.641559 - 4.00243i) q^{28} +5.26857 q^{29} +(2.70574 - 4.68647i) q^{30} +(-2.59240 - 4.49016i) q^{31} +(3.55303 + 6.15403i) q^{32} +(-0.326352 + 0.565258i) q^{33} +8.51754 q^{34} +(-5.91147 + 4.80526i) q^{35} +1.53209 q^{36} +(-0.266044 + 0.460802i) q^{37} +(-4.47178 - 7.74535i) q^{38} +(0.500000 + 0.866025i) q^{39} +(1.26604 - 2.19285i) q^{40} +5.63816 q^{41} +(-4.64543 - 1.77330i) q^{42} -2.83750 q^{43} +(0.500000 - 0.866025i) q^{44} +(-1.43969 - 2.49362i) q^{45} +(-0.134285 - 0.232589i) q^{46} +(-0.305407 + 0.528981i) q^{47} +4.71688 q^{48} +(5.21941 + 4.66452i) q^{49} +6.18479 q^{50} +(2.26604 - 3.92490i) q^{51} +(-0.766044 - 1.32683i) q^{52} +(0.673648 + 1.16679i) q^{53} +(0.939693 - 1.62760i) q^{54} -1.87939 q^{55} +(-2.17365 - 0.829748i) q^{56} -4.75877 q^{57} +(-4.95084 + 8.57510i) q^{58} +(7.56805 + 13.1082i) q^{59} +(2.20574 + 3.82045i) q^{60} +(-7.71941 + 13.3704i) q^{61} +9.74422 q^{62} +(-2.05303 + 1.66885i) q^{63} -3.92127 q^{64} +(-1.43969 + 2.49362i) q^{65} +(-0.613341 - 1.06234i) q^{66} +(0.631759 + 1.09424i) q^{67} +(-3.47178 + 6.01330i) q^{68} -0.142903 q^{69} +(-2.26604 - 14.1370i) q^{70} +14.3131 q^{71} +(0.439693 - 0.761570i) q^{72} +(5.53596 + 9.58856i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(1.64543 - 2.84997i) q^{75} +7.29086 q^{76} +(0.273318 + 1.70513i) q^{77} -1.87939 q^{78} +(7.65657 - 13.2616i) q^{79} +(6.79086 + 11.7621i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.29813 + 9.17664i) q^{82} -3.65270 q^{83} +(3.14543 - 2.55682i) q^{84} +13.0496 q^{85} +(2.66637 - 4.61830i) q^{86} +(2.63429 + 4.56272i) q^{87} +(-0.286989 - 0.497079i) q^{88} +(0.737826 - 1.27795i) q^{89} +5.41147 q^{90} +(2.47178 + 0.943555i) q^{91} +0.218941 q^{92} +(2.59240 - 4.49016i) q^{93} +(-0.573978 - 0.994159i) q^{94} +(-6.85117 - 11.8666i) q^{95} +(-3.55303 + 6.15403i) q^{96} -2.04963 q^{97} +(-12.4966 + 4.11186i) q^{98} -0.652704 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 $

$2$	−0.939693	+	1.62760i	−0.664463	+	1.15088i	0.314968	+	0.949102i	$0.398006\pi$
$2$	−0.939693	+	1.62760i	−0.664463	+	1.15088i	−0.979431	+	0.201781i	$0.935327\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.766044	−	1.32683i	−0.383022	−	0.663414i
$5$	−1.43969	+	2.49362i	−0.643850	+	1.11518i	0.340716	+	0.940166i	$0.389331\pi$
$5$	−1.43969	+	2.49362i	−0.643850	+	1.11518i	−0.984566	+	0.175015i	$0.944003\pi$
$6$	−1.87939			−0.767256
$7$	2.47178	+	0.943555i	0.934246	+	0.356630i
$7$	2.47178	+	0.943555i	0.934246	+	0.356630i
$8$	−0.879385			−0.310910
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.70574	−	4.68647i	−0.855629	−	1.48199i
$11$	0.326352	+	0.565258i	0.0983988	+	0.170432i	0.911022	−	0.412358i	$-0.135295\pi$
$11$	0.326352	+	0.565258i	0.0983988	+	0.170432i	−0.812623	+	0.582789i	$0.801961\pi$
$12$	0.766044	−	1.32683i	0.221138	−	0.383022i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−3.85844	+	3.13641i	−1.03121	+	0.838240i
$15$	−2.87939			−0.743454
$16$	2.35844	−	4.08494i	0.589610	−	1.02123i
$17$	−2.26604	−	3.92490i	−0.549597	−	0.951929i	−0.998302	−	0.0582494i	$-0.981448\pi$
$17$	−2.26604	−	3.92490i	−0.549597	−	0.951929i	0.448706	−	0.893680i	$-0.351885\pi$
$18$	−0.939693	−	1.62760i	−0.221488	−	0.383628i
$19$	−2.37939	+	4.12122i	−0.545868	+	0.945472i	0.452683	+	0.891671i	$0.350467\pi$
$19$	−2.37939	+	4.12122i	−0.545868	+	0.945472i	−0.998552	+	0.0538005i	$0.982867\pi$
$20$	4.41147			0.986436
$21$	0.418748	+	2.61240i	0.0913783	+	0.570073i
$22$	−1.22668			−0.261529
$23$	−0.0714517	+	0.123758i	−0.0148987	+	0.0258053i	−0.873379	−	0.487042i	$-0.838076\pi$
$23$	−0.0714517	+	0.123758i	−0.0148987	+	0.0258053i	0.858480	+	0.512847i	$0.171409\pi$
$24$	−0.439693	−	0.761570i	−0.0897519	−	0.155455i
$25$	−1.64543	−	2.84997i	−0.329086	−	0.569994i
$26$	−0.939693	+	1.62760i	−0.184289	+	0.319198i
$27$	−1.00000			−0.192450
$28$	−0.641559	−	4.00243i	−0.121243	−	0.756389i
$29$	5.26857			0.978349			0.489175	−	0.872186i	$-0.337298\pi$
$29$	5.26857			0.978349			0.489175	+	0.872186i	$0.337298\pi$
$30$	2.70574	−	4.68647i	0.493998	−	0.855629i
$31$	−2.59240	−	4.49016i	−0.465608	−	0.806457i	0.533621	−	0.845724i	$-0.320831\pi$
$31$	−2.59240	−	4.49016i	−0.465608	−	0.806457i	−0.999229	+	0.0392670i	$0.987498\pi$
$32$	3.55303	+	6.15403i	0.628094	+	1.08789i
$33$	−0.326352	+	0.565258i	−0.0568106	+	0.0983988i
$34$	8.51754			1.46075
$35$	−5.91147	+	4.80526i	−0.999222	+	0.812237i
$36$	1.53209			0.255348
$37$	−0.266044	+	0.460802i	−0.0437374	+	0.0757555i	−0.887065	−	0.461644i	$-0.847260\pi$
$37$	−0.266044	+	0.460802i	−0.0437374	+	0.0757555i	0.843328	+	0.537399i	$0.180593\pi$
$38$	−4.47178	−	7.74535i	−0.725419	−	1.25646i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	1.26604	−	2.19285i	0.200179	−	0.346721i
$41$	5.63816			0.880532			0.440266	−	0.897867i	$-0.354884\pi$
$41$	5.63816			0.880532			0.440266	+	0.897867i	$0.354884\pi$
$42$	−4.64543	−	1.77330i	−0.716805	−	0.273627i
$43$	−2.83750			−0.432714			−0.216357	−	0.976314i	$-0.569418\pi$
$43$	−2.83750			−0.432714			−0.216357	+	0.976314i	$0.569418\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	−1.43969	−	2.49362i	−0.214617	−	0.371727i
$46$	−0.134285	−	0.232589i	−0.0197993	−	0.0342934i
$47$	−0.305407	+	0.528981i	−0.0445482	+	0.0771598i	−0.887440	−	0.460924i	$-0.847518\pi$
$47$	−0.305407	+	0.528981i	−0.0445482	+	0.0771598i	0.842892	+	0.538084i	$0.180852\pi$
$48$	4.71688			0.680823
$49$	5.21941	+	4.66452i	0.745630	+	0.666361i
$50$	6.18479			0.874662
$51$	2.26604	−	3.92490i	0.317310	−	0.549597i
$52$	−0.766044	−	1.32683i	−0.106231	−	0.183998i
$53$	0.673648	+	1.16679i	0.0925327	+	0.160271i	0.908576	−	0.417719i	$-0.137170\pi$
$53$	0.673648	+	1.16679i	0.0925327	+	0.160271i	−0.816044	+	0.577990i	$0.803837\pi$
$54$	0.939693	−	1.62760i	0.127876	−	0.221488i
$55$	−1.87939			−0.253416
$56$	−2.17365	−	0.829748i	−0.290466	−	0.110880i
$57$	−4.75877			−0.630315
$58$	−4.95084	+	8.57510i	−0.650077	+	1.12597i
$59$	7.56805	+	13.1082i	0.985276	+	1.70655i	0.640704	+	0.767788i	$0.278643\pi$
$59$	7.56805	+	13.1082i	0.985276	+	1.70655i	0.344572	+	0.938760i	$0.388024\pi$
$60$	2.20574	+	3.82045i	0.284759	+	0.493218i
$61$	−7.71941	+	13.3704i	−0.988369	+	1.71191i	−0.362483	+	0.931990i	$0.618071\pi$
$61$	−7.71941	+	13.3704i	−0.988369	+	1.71191i	−0.625886	+	0.779915i	$0.715262\pi$
$62$	9.74422			1.23752
$63$	−2.05303	+	1.66885i	−0.258658	+	0.210255i
$64$	−3.92127			−0.490159
$65$	−1.43969	+	2.49362i	−0.178572	+	0.309296i
$66$	−0.613341	−	1.06234i	−0.0754970	−	0.130765i
$67$	0.631759	+	1.09424i	0.0771817	+	0.133683i	0.902033	−	0.431667i	$-0.142075\pi$
$67$	0.631759	+	1.09424i	0.0771817	+	0.133683i	−0.824851	+	0.565350i	$0.808741\pi$
$68$	−3.47178	+	6.01330i	−0.421015	+	0.729220i
$69$	−0.142903			−0.0172036
$70$	−2.26604	−	14.1370i	−0.270844	−	1.68969i
$71$	14.3131			1.69866			0.849329	−	0.527864i	$-0.177007\pi$
$71$	14.3131			1.69866			0.849329	+	0.527864i	$0.177007\pi$
$72$	0.439693	−	0.761570i	0.0518183	−	0.0897519i
$73$	5.53596	+	9.58856i	0.647935	+	1.12226i	0.983615	+	0.180280i	$0.0577005\pi$
$73$	5.53596	+	9.58856i	0.647935	+	1.12226i	−0.335680	+	0.941976i	$0.608966\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$	1.64543	−	2.84997i	0.189998	−	0.329086i
$76$	7.29086			0.836319
$77$	0.273318	+	1.70513i	0.0311475	+	0.194317i
$78$	−1.87939			−0.212798
$79$	7.65657	−	13.2616i	0.861432	−	1.49204i	−0.00911509	−	0.999958i	$-0.502901\pi$
$79$	7.65657	−	13.2616i	0.861432	−	1.49204i	0.870547	−	0.492085i	$-0.163765\pi$
$80$	6.79086	+	11.7621i	0.759241	+	1.31504i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.29813	+	9.17664i	−0.585081	+	1.01339i
$83$	−3.65270			−0.400936			−0.200468	−	0.979700i	$-0.564246\pi$
$83$	−3.65270			−0.400936			−0.200468	+	0.979700i	$0.564246\pi$
$84$	3.14543	−	2.55682i	0.343195	−	0.278972i
$85$	13.0496			1.41543
$86$	2.66637	−	4.61830i	0.287523	−	0.498004i
$87$	2.63429	+	4.56272i	0.282425	+	0.489175i
$88$	−0.286989	−	0.497079i	−0.0305931	−	0.0529889i
$89$	0.737826	−	1.27795i	0.0782094	−	0.135463i	−0.824268	−	0.566200i	$-0.808413\pi$
$89$	0.737826	−	1.27795i	0.0782094	−	0.135463i	0.902477	+	0.430737i	$0.141746\pi$
$90$	5.41147			0.570419
$91$	2.47178	+	0.943555i	0.259113	+	0.0989114i
$92$	0.218941			0.0228262
$93$	2.59240	−	4.49016i	0.268819	−	0.465608i
$94$	−0.573978	−	0.994159i	−0.0592013	−	0.102540i
$95$	−6.85117	−	11.8666i	−0.702915	−	1.21748i
$96$	−3.55303	+	6.15403i	−0.362630	+	0.628094i
$97$	−2.04963			−0.208108			−0.104054	−	0.994572i	$-0.533182\pi$
$97$	−2.04963			−0.208108			−0.104054	+	0.994572i	$0.533182\pi$
$98$	−12.4966	+	4.11186i	−1.26235	+	0.415361i
$99$	−0.652704			−0.0655992
$100$	−2.52094	+	4.36640i	−0.252094	+	0.436640i
$101$	−5.56031	−	9.63073i	−0.553271	−	0.958294i	−0.998036	−	0.0626464i	$-0.980046\pi$
$101$	−5.56031	−	9.63073i	−0.553271	−	0.958294i	0.444765	−	0.895648i	$-0.353287\pi$
$102$	4.25877	+	7.37641i	0.421681	+	0.730373i
$103$	−7.03209	+	12.1799i	−0.692892	+	1.20012i	0.277994	+	0.960583i	$0.410331\pi$
$103$	−7.03209	+	12.1799i	−0.692892	+	1.20012i	−0.970886	+	0.239542i	$0.923003\pi$
$104$	−0.879385			−0.0862308
$105$	−7.11721	−	2.71686i	−0.694569	−	0.265138i
$106$	−2.53209			−0.245938
$107$	4.11334	−	7.12452i	0.397652	−	0.688753i	−0.595784	−	0.803145i	$-0.703159\pi$
$107$	4.11334	−	7.12452i	0.397652	−	0.688753i	0.993436	+	0.114392i	$0.0364919\pi$
$108$	0.766044	+	1.32683i	0.0737127	+	0.127674i
$109$	−2.34864	−	4.06796i	−0.224959	−	0.389640i	0.731348	−	0.682004i	$-0.238891\pi$
$109$	−2.34864	−	4.06796i	−0.224959	−	0.389640i	−0.956307	+	0.292364i	$0.905558\pi$
$110$	1.76604	−	3.05888i	0.168386	−	0.291653i
$111$	−0.532089			−0.0505036
$112$	9.68392	−	7.87176i	0.915044	−	0.743811i
$113$	−14.3259			−1.34767			−0.673836	−	0.738881i	$-0.735354\pi$
$113$	−14.3259			−1.34767			−0.673836	+	0.738881i	$0.735354\pi$
$114$	4.47178	−	7.74535i	0.418821	−	0.725419i
$115$	−0.205737	−	0.356347i	−0.0191851	−	0.0332295i
$116$	−4.03596	−	6.99049i	−0.374729	−	0.649050i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	−28.4466			−2.61872
$119$	−1.89780	−	11.8396i	−0.173971	−	1.08534i
$120$	2.53209			0.231147
$121$	5.28699	−	9.15733i	0.480635	−	0.832485i
$122$	−14.5077	−	25.1281i	−1.31347	−	2.27500i
$123$	2.81908	+	4.88279i	0.254188	+	0.440266i
$124$	−3.97178	+	6.87933i	−0.356677	+	0.617782i
$125$	−4.92127			−0.440172
$126$	−0.786989	−	4.90971i	−0.0701106	−	0.437392i
$127$	8.62361			0.765221			0.382611	−	0.923910i	$-0.375025\pi$
$127$	8.62361			0.765221			0.382611	+	0.923910i	$0.375025\pi$
$128$	−3.42127	+	5.92582i	−0.302401	+	0.523774i
$129$	−1.41875	−	2.45734i	−0.124914	−	0.216357i
$130$	−2.70574	−	4.68647i	−0.237309	−	0.411031i
$131$	8.62108	−	14.9322i	0.753227	−	1.30463i	−0.193023	−	0.981194i	$-0.561829\pi$
$131$	8.62108	−	14.9322i	0.753227	−	1.30463i	0.946251	−	0.323434i	$-0.104837\pi$
$132$	1.00000			0.0870388
$133$	−9.76991	+	7.94166i	−0.847159	+	0.688630i
$134$	−2.37464			−0.205137
$135$	1.43969	−	2.49362i	0.123909	−	0.214617i
$136$	1.99273	+	3.45150i	0.170875	+	0.295964i
$137$	−5.76604	−	9.98708i	−0.492626	−	0.853254i	0.507338	−	0.861747i	$-0.330630\pi$
$137$	−5.76604	−	9.98708i	−0.492626	−	0.853254i	−0.999964	+	0.00849345i	$0.997296\pi$
$138$	0.134285	−	0.232589i	0.0114311	−	0.0197993i
$139$	20.3327			1.72460			0.862301	−	0.506397i	$-0.169023\pi$
$139$	20.3327			1.72460			0.862301	+	0.506397i	$0.169023\pi$
$140$	10.9042	+	4.16247i	0.921573	+	0.351793i
$141$	−0.610815			−0.0514399
$142$	−13.4500	+	23.2960i	−1.12870	+	1.95496i
$143$	0.326352	+	0.565258i	0.0272909	+	0.0472692i
$144$	2.35844	+	4.08494i	0.196537	+	0.340412i
$145$	−7.58512	+	13.1378i	−0.629910	+	1.09104i
$146$	−20.8084			−1.72212
$147$	−1.42989	+	6.85240i	−0.117936	+	0.565177i
$148$	0.815207			0.0670096
$149$	−6.16250	+	10.6738i	−0.504852	+	0.874429i	0.495132	+	0.868818i	$0.335120\pi$
$149$	−6.16250	+	10.6738i	−0.504852	+	0.874429i	−0.999984	+	0.00561168i	$0.998214\pi$
$150$	3.09240	+	5.35619i	0.252493	+	0.437331i
$151$	−8.82295	−	15.2818i	−0.718001	−	1.24361i	−0.961790	−	0.273787i	$-0.911724\pi$
$151$	−8.82295	−	15.2818i	−0.718001	−	1.24361i	0.243789	−	0.969828i	$-0.421610\pi$
$152$	2.09240	−	3.62414i	0.169716	−	0.293956i
$153$	4.53209			0.366398
$154$	−3.03209	−	1.15744i	−0.244333	−	0.0932693i
$155$	14.9290			1.19913
$156$	0.766044	−	1.32683i	0.0613326	−	0.106231i
$157$	−0.171122	−	0.296392i	−0.0136570	−	0.0236547i	0.859116	−	0.511781i	$-0.171014\pi$
$157$	−0.171122	−	0.296392i	−0.0136570	−	0.0236547i	−0.872773	+	0.488126i	$0.837681\pi$
$158$	14.3897	+	24.9236i	1.14478	+	1.98282i
$159$	−0.673648	+	1.16679i	−0.0534238	+	0.0925327i
$160$	−20.4611			−1.61759
$161$	−0.293386	+	0.238484i	−0.0231220	+	0.0187952i
$162$	1.87939			0.147658
$163$	11.5458	−	19.9978i	0.904334	−	1.56635i	0.0825245	−	0.996589i	$-0.473702\pi$
$163$	11.5458	−	19.9978i	0.904334	−	1.56635i	0.821809	−	0.569763i	$-0.192965\pi$
$164$	−4.31908	−	7.48086i	−0.337263	−	0.584157i
$165$	−0.939693	−	1.62760i	−0.0731550	−	0.126708i
$166$	3.43242	−	5.94512i	0.266407	−	0.461431i
$167$	−8.84255			−0.684257			−0.342128	−	0.939653i	$-0.611148\pi$
$167$	−8.84255			−0.684257			−0.342128	+	0.939653i	$0.611148\pi$
$168$	−0.368241	−	2.29731i	−0.0284104	−	0.177241i
$169$	1.00000			0.0769231
$170$	−12.2626	+	21.2395i	−0.940502	+	1.62900i
$171$	−2.37939	−	4.12122i	−0.181956	−	0.315157i
$172$	2.17365	+	3.76487i	0.165739	+	0.287069i
$173$	10.3871	−	17.9910i	0.789719	−	1.36783i	−0.136421	−	0.990651i	$-0.543560\pi$
$173$	10.3871	−	17.9910i	0.789719	−	1.36783i	0.926139	−	0.377182i	$-0.123107\pi$
$174$	−9.90167			−0.750644
$175$	−1.37804	−	8.59705i	−0.104170	−	0.649876i
$176$	3.07873			0.232068
$177$	−7.56805	+	13.1082i	−0.568849	+	0.985276i
$178$	1.38666	+	2.40176i	0.103935	+	0.180020i
$179$	9.67159	+	16.7517i	0.722888	+	1.25208i	0.959837	+	0.280557i	$0.0905193\pi$
$179$	9.67159	+	16.7517i	0.722888	+	1.25208i	−0.236949	+	0.971522i	$0.576147\pi$
$180$	−2.20574	+	3.82045i	−0.164406	+	0.284759i
$181$	−21.2695			−1.58095			−0.790475	−	0.612494i	$-0.790166\pi$
$181$	−21.2695			−1.58095			−0.790475	+	0.612494i	$0.790166\pi$
$182$	−3.85844	+	3.13641i	−0.286007	+	0.232486i
$183$	−15.4388			−1.14127
$184$	0.0628336	−	0.108831i	0.00463215	−	0.00802313i
$185$	−0.766044	−	1.32683i	−0.0563207	−	0.0975503i
$186$	4.87211	+	8.43874i	0.357241	+	0.618759i
$187$	1.47906	−	2.56180i	0.108159	−	0.187337i
$188$	0.935822			0.0682519
$189$	−2.47178	−	0.943555i	−0.179796	−	0.0686335i
$190$	25.7520			1.86824
$191$	9.67412	−	16.7561i	0.699994	−	1.21243i	−0.268473	−	0.963287i	$-0.586519\pi$
$191$	9.67412	−	16.7561i	0.699994	−	1.21243i	0.968468	−	0.249139i	$-0.0801475\pi$
$192$	−1.96064	−	3.39592i	−0.141497	−	0.245080i
$193$	7.33409	+	12.7030i	0.527920	+	0.914383i	0.999470	+	0.0325445i	$0.0103611\pi$
$193$	7.33409	+	12.7030i	0.527920	+	0.914383i	−0.471551	+	0.881839i	$0.656306\pi$
$194$	1.92602	−	3.33597i	0.138280	−	0.239509i
$195$	−2.87939			−0.206197
$196$	2.19072	−	10.4985i	0.156480	−	0.749892i
$197$	5.75103			0.409744			0.204872	−	0.978789i	$-0.434322\pi$
$197$	5.75103			0.409744			0.204872	+	0.978789i	$0.434322\pi$
$198$	0.613341	−	1.06234i	0.0435882	−	0.0754970i
$199$	7.58512	+	13.1378i	0.537695	+	0.931315i	0.999028	+	0.0440879i	$0.0140382\pi$
$199$	7.58512	+	13.1378i	0.537695	+	0.931315i	−0.461333	+	0.887227i	$0.652629\pi$
$200$	1.44697	+	2.50622i	0.102316	+	0.177216i
$201$	−0.631759	+	1.09424i	−0.0445609	+	0.0771817i
$202$	20.8999			1.47051
$203$	13.0228	+	4.97119i	0.914018	+	0.348909i
$204$	−6.94356			−0.486147
$205$	−8.11721	+	14.0594i	−0.566931	+	0.981953i
$206$	−13.2160	−	22.8908i	−0.920803	−	1.59488i
$207$	−0.0714517	−	0.123758i	−0.00496624	−	0.00860178i
$208$	2.35844	−	4.08494i	0.163528	−	0.283240i
$209$	−3.10607			−0.214851
$210$	11.1099	−	9.03093i	0.766659	−	0.623193i
$211$	12.7743			0.879416			0.439708	−	0.898141i	$-0.355082\pi$
$211$	12.7743			0.879416			0.439708	+	0.898141i	$0.355082\pi$
$212$	1.03209	−	1.78763i	0.0708842	−	0.122775i
$213$	7.15657	+	12.3955i	0.490360	+	0.849329i
$214$	7.73055	+	13.3897i	0.528450	+	0.915302i
$215$	4.08512	−	7.07564i	0.278603	−	0.482555i
$216$	0.879385			0.0598346
$217$	−2.17112	−	13.5448i	−0.147385	−	0.919479i
$218$	8.82800			0.597908
$219$	−5.53596	+	9.58856i	−0.374085	+	0.647935i
$220$	1.43969	+	2.49362i	0.0970641	+	0.168120i
$221$	−2.26604	−	3.92490i	−0.152431	−	0.264018i
$222$	0.500000	−	0.866025i	0.0335578	−	0.0581238i
$223$	−14.1753			−0.949248			−0.474624	−	0.880189i	$-0.657416\pi$
$223$	−14.1753			−0.949248			−0.474624	+	0.880189i	$0.657416\pi$
$224$	2.97565	+	18.5639i	0.198819	+	1.24035i
$225$	3.29086			0.219391
$226$	13.4620	−	23.3168i	0.895478	−	1.55101i
$227$	−4.80066	−	8.31499i	−0.318631	−	0.551885i	0.661572	−	0.749882i	$-0.269890\pi$
$227$	−4.80066	−	8.31499i	−0.318631	−	0.551885i	−0.980203	+	0.197997i	$0.936556\pi$
$228$	3.64543	+	6.31407i	0.241424	+	0.418159i
$229$	1.13041	−	1.95794i	0.0746999	−	0.129384i	−0.826256	−	0.563295i	$-0.809533\pi$
$229$	1.13041	−	1.95794i	0.0746999	−	0.129384i	0.900956	+	0.433911i	$0.142867\pi$
$230$	0.773318			0.0509911
$231$	−1.34002	+	1.08926i	−0.0881670	+	0.0716683i
$232$	−4.63310			−0.304178
$233$	−5.18732	+	8.98470i	−0.339833	+	0.588607i	−0.984401	−	0.175939i	$-0.943704\pi$
$233$	−5.18732	+	8.98470i	−0.339833	+	0.588607i	0.644568	+	0.764547i	$0.277037\pi$
$234$	−0.939693	−	1.62760i	−0.0614296	−	0.106399i
$235$	−0.879385	−	1.52314i	−0.0573648	−	0.0993587i
$236$	11.5949	−	20.0830i	0.754765	−	1.30729i
$237$	15.3131			0.994696
$238$	21.0535	+	8.03677i	1.36470	+	0.520946i
$239$	−23.3259			−1.50883			−0.754415	−	0.656398i	$-0.772079\pi$
$239$	−23.3259			−1.50883			−0.754415	+	0.656398i	$0.772079\pi$
$240$	−6.79086	+	11.7621i	−0.438348	+	0.759241i
$241$	−0.355914	−	0.616462i	−0.0229265	−	0.0397098i	0.854335	−	0.519723i	$-0.173965\pi$
$241$	−0.355914	−	0.616462i	−0.0229265	−	0.0397098i	−0.877261	+	0.480014i	$0.840632\pi$
$242$	9.93629	+	17.2102i	0.638729	+	1.10631i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	23.6536			1.51427
$245$	−19.1459	+	6.29974i	−1.22319	+	0.402476i
$246$	−10.5963			−0.675593
$247$	−2.37939	+	4.12122i	−0.151397	+	0.262227i
$248$	2.27972	+	3.94858i	0.144762	+	0.250735i
$249$	−1.82635	−	3.16333i	−0.115740	−	0.200468i
$250$	4.62449	−	8.00984i	0.292478	−	0.506587i
$251$	7.98814			0.504207			0.252103	−	0.967700i	$-0.418878\pi$
$251$	7.98814			0.504207			0.252103	+	0.967700i	$0.418878\pi$
$252$	3.78699	+	1.44561i	0.238558	+	0.0910649i
$253$	−0.0932736			−0.00586406
$254$	−8.10354	+	14.0357i	−0.508461	+	0.880681i
$255$	6.52481	+	11.3013i	0.408600	+	0.707716i
$256$	−10.3512	−	17.9287i	−0.646948	−	1.12055i
$257$	−12.9770	+	22.4768i	−0.809483	+	1.40207i	0.103740	+	0.994604i	$0.466919\pi$
$257$	−12.9770	+	22.4768i	−0.809483	+	1.40207i	−0.913223	+	0.407461i	$0.866414\pi$
$258$	5.33275			0.332002
$259$	−1.09240	+	0.887975i	−0.0678782	+	0.0551761i
$260$	4.41147			0.273588
$261$	−2.63429	+	4.56272i	−0.163058	+	0.282425i
$262$	16.2023	+	28.0633i	1.00098	+	1.73375i
$263$	−2.03936	−	3.53228i	−0.125753	−	0.217810i	0.796274	−	0.604936i	$-0.206801\pi$
$263$	−2.03936	−	3.53228i	−0.125753	−	0.217810i	−0.922027	+	0.387126i	$0.873468\pi$
$264$	0.286989	−	0.497079i	0.0176630	−	0.0305931i
$265$	−3.87939			−0.238309
$266$	−3.74510	−	23.3642i	−0.229627	−	1.43255i
$267$	1.47565			0.0903084
$268$	0.967911	−	1.67647i	0.0591246	−	0.102407i
$269$	1.00640	+	1.74313i	0.0613611	+	0.106281i	0.895074	−	0.445918i	$-0.147123\pi$
$269$	1.00640	+	1.74313i	0.0613611	+	0.106281i	−0.833713	+	0.552198i	$0.813789\pi$
$270$	2.70574	+	4.68647i	0.164666	+	0.285210i
$271$	6.46451	−	11.1969i	0.392691	−	0.680161i	−0.600113	−	0.799916i	$-0.704878\pi$
$271$	6.46451	−	11.1969i	0.392691	−	0.680161i	0.992803	+	0.119755i	$0.0382109\pi$
$272$	−21.3773			−1.29619
$273$	0.418748	+	2.61240i	0.0253438	+	0.158110i
$274$	21.6732			1.30933
$275$	1.07398	−	1.86018i	0.0647633	−	0.112173i
$276$	0.109470	+	0.189608i	0.00658934	+	0.0114131i
$277$	10.2417	+	17.7391i	0.615364	+	1.06584i	0.990321	+	0.138799i	$0.0443243\pi$
$277$	10.2417	+	17.7391i	0.615364	+	1.06584i	−0.374957	+	0.927042i	$0.622342\pi$
$278$	−19.1065	+	33.0935i	−1.14593	+	1.98482i
$279$	5.18479			0.310405
$280$	5.19846	−	4.22567i	0.310668	−	0.252532i
$281$	16.3996			0.978319			0.489159	−	0.872194i	$-0.337304\pi$
$281$	16.3996			0.978319			0.489159	+	0.872194i	$0.337304\pi$
$282$	0.573978	−	0.994159i	0.0341799	−	0.0592013i
$283$	−4.98411	−	8.63273i	−0.296274	−	0.513162i	0.679006	−	0.734133i	$-0.262411\pi$
$283$	−4.98411	−	8.63273i	−0.296274	−	0.513162i	−0.975281	+	0.220970i	$0.929078\pi$
$284$	−10.9645	−	18.9911i	−0.650624	−	1.12691i
$285$	6.85117	−	11.8666i	0.405828	−	0.702915i
$286$	−1.22668			−0.0725352
$287$	13.9363	+	5.31991i	0.822633	+	0.314024i
$288$	−7.10607			−0.418729
$289$	−1.76991	+	3.06558i	−0.104113	+	0.180328i
$290$	−14.2554	−	24.6910i	−0.837104	−	1.44991i
$291$	−1.02481	−	1.77503i	−0.0600757	−	0.104054i
$292$	8.48158	−	14.6905i	0.496347	−	0.859698i
$293$	17.3523			1.01374			0.506868	−	0.862024i	$-0.330803\pi$
$293$	17.3523			1.01374			0.506868	+	0.862024i	$0.330803\pi$
$294$	−9.80928	−	8.76644i	−0.572089	−	0.511269i
$295$	−43.5827			−2.53748
$296$	0.233956	−	0.405223i	0.0135984	−	0.0235531i
$297$	−0.326352	−	0.565258i	−0.0189369	−	0.0327996i
$298$	−11.5817	−	20.0601i	−0.670911	−	1.16205i
$299$	−0.0714517	+	0.123758i	−0.00413216	+	0.00715711i
$300$	−5.04189			−0.291094
$301$	−7.01367	−	2.67733i	−0.404261	−	0.154319i
$302$	33.1634			1.90834
$303$	5.56031	−	9.63073i	0.319431	−	0.553271i
$304$	11.2233	+	19.4393i	0.643699	+	1.11492i
$305$	−22.2271	−	38.4986i	−1.27272	−	2.20442i
$306$	−4.25877	+	7.37641i	−0.243458	+	0.421681i
$307$	−22.3354			−1.27475			−0.637375	−	0.770553i	$-0.719980\pi$
$307$	−22.3354			−1.27475			−0.637375	+	0.770553i	$0.719980\pi$
$308$	2.05303	−	1.66885i	0.116982	−	0.0950914i
$309$	−14.0642			−0.800083
$310$	−14.0287	+	24.2984i	−0.796776	+	1.38006i
$311$	1.70574	+	2.95442i	0.0967235	+	0.167530i	0.910327	−	0.413891i	$-0.135830\pi$
$311$	1.70574	+	2.95442i	0.0967235	+	0.167530i	−0.813603	+	0.581421i	$0.802497\pi$
$312$	−0.439693	−	0.761570i	−0.0248927	−	0.0431154i
$313$	16.7173	−	28.9553i	0.944920	−	1.63665i	0.189010	−	0.981975i	$-0.439472\pi$
$313$	16.7173	−	28.9553i	0.944920	−	1.63665i	0.755911	−	0.654675i	$-0.227194\pi$
$314$	0.643208			0.0362983
$315$	−1.20574	−	7.52211i	−0.0679356	−	0.423823i
$316$	−23.4611			−1.31979
$317$	−0.450837	+	0.780873i	−0.0253215	+	0.0438582i	−0.878408	−	0.477911i	$-0.841394\pi$
$317$	−0.450837	+	0.780873i	−0.0253215	+	0.0438582i	0.853087	+	0.521769i	$0.174728\pi$
$318$	−1.26604	−	2.19285i	−0.0709962	−	0.122969i
$319$	1.71941	+	2.97810i	0.0962683	+	0.166742i
$320$	5.64543	−	9.77817i	0.315589	−	0.546616i
$321$	8.22668			0.459169
$322$	−0.112463	−	0.701615i	−0.00626734	−	0.0390995i
$323$	21.5672			1.20003
$324$	−0.766044	+	1.32683i	−0.0425580	+	0.0737127i
$325$	−1.64543	−	2.84997i	−0.0912720	−	0.158088i
$326$	21.6989	+	37.5836i	1.20179	+	2.08157i
$327$	2.34864	−	4.06796i	0.129880	−	0.224959i
$328$	−4.95811			−0.273766
$329$	−1.25402	+	1.01936i	−0.0691365	+	0.0561990i
$330$	3.53209			0.194435
$331$	12.5462	−	21.7307i	0.689603	−	1.19443i	−0.282363	−	0.959308i	$-0.591118\pi$
$331$	12.5462	−	21.7307i	0.689603	−	1.19443i	0.971966	−	0.235120i	$-0.0755483\pi$
$332$	2.79813	+	4.84651i	0.153568	+	0.265987i
$333$	−0.266044	−	0.460802i	−0.0145791	−	0.0252518i
$334$	8.30928	−	14.3921i	0.454663	−	0.787500i
$335$	−3.63816			−0.198774
$336$	11.6591	+	4.45064i	0.636056	+	0.242802i
$337$	−9.36184			−0.509972			−0.254986	−	0.966945i	$-0.582071\pi$
$337$	−9.36184			−0.509972			−0.254986	+	0.966945i	$0.582071\pi$
$338$	−0.939693	+	1.62760i	−0.0511125	+	0.0885295i
$339$	−7.16297	−	12.4066i	−0.389039	−	0.673836i
$340$	−9.99660	−	17.3146i	−0.542142	−	0.939017i
$341$	1.69207	−	2.93075i	0.0916305	−	0.158709i
$342$	8.94356			0.483613
$343$	8.50000	+	16.4545i	0.458957	+	0.888459i
$344$	2.49525			0.134535
$345$	0.205737	−	0.356347i	0.0110765	−	0.0191851i
$346$	19.5214	+	33.8121i	1.04948	+	1.81775i
$347$	10.4402	+	18.0829i	0.560457	+	0.970740i	0.997456	+	0.0712784i	$0.0227079\pi$
$347$	10.4402	+	18.0829i	0.560457	+	0.970740i	−0.436999	+	0.899462i	$0.643959\pi$
$348$	4.03596	−	6.99049i	0.216350	−	0.374729i
$349$	9.58853			0.513262			0.256631	−	0.966509i	$-0.417387\pi$
$349$	9.58853			0.513262			0.256631	+	0.966509i	$0.417387\pi$
$350$	15.2875	+	5.83569i	0.817149	+	0.311931i
$351$	−1.00000			−0.0533761
$352$	−2.31908	+	4.01676i	−0.123607	+	0.214094i
$353$	−0.671122	−	1.16242i	−0.0357202	−	0.0618692i	0.847613	−	0.530616i	$-0.178039\pi$
$353$	−0.671122	−	1.16242i	−0.0357202	−	0.0618692i	−0.883333	+	0.468746i	$0.844706\pi$
$354$	−14.2233	−	24.6354i	−0.755959	−	1.30936i
$355$	−20.6065	+	35.6916i	−1.09368	+	1.89431i
$356$	−2.26083			−0.119824
$357$	9.30453	−	7.56337i	0.492448	−	0.400296i
$358$	−36.3533			−1.92133
$359$	13.6395	−	23.6243i	0.719865	−	1.24684i	−0.241188	−	0.970479i	$-0.577537\pi$
$359$	13.6395	−	23.6243i	0.719865	−	1.24684i	0.961053	−	0.276365i	$-0.0891298\pi$
$360$	1.26604	+	2.19285i	0.0667264	+	0.115574i
$361$	−1.82295	−	3.15744i	−0.0959446	−	0.166181i
$362$	19.9868	−	34.6181i	1.05048	−	1.81949i
$363$	10.5740			0.554990
$364$	−0.641559	−	4.00243i	−0.0336268	−	0.209785i
$365$	−31.8803			−1.66869
$366$	14.5077	−	25.1281i	0.758332	−	1.31347i
$367$	−17.0710	−	29.5679i	−0.891101	−	1.54343i	−0.838557	−	0.544814i	$-0.816600\pi$
$367$	−17.0710	−	29.5679i	−0.891101	−	1.54343i	−0.0525440	−	0.998619i	$-0.516733\pi$
$368$	0.337029	+	0.583752i	0.0175689	+	0.0304302i
$369$	−2.81908	+	4.88279i	−0.146755	+	0.254188i
$370$	2.87939			0.149692
$371$	0.564178	+	3.51968i	0.0292907	+	0.182733i
$372$	−7.94356			−0.411855
$373$	−4.57873	+	7.93059i	−0.237077	+	0.410630i	−0.959874	−	0.280430i	$-0.909523\pi$
$373$	−4.57873	+	7.93059i	−0.237077	+	0.410630i	0.722797	+	0.691060i	$0.242856\pi$
$374$	2.77972	+	4.81461i	0.143736	+	0.248957i
$375$	−2.46064	−	4.26195i	−0.127067	−	0.220086i
$376$	0.268571	−	0.465178i	0.0138505	−	0.0239897i
$377$	5.26857			0.271345
$378$	3.85844	−	3.13641i	0.198457	−	0.161319i
$379$	−22.4293			−1.15212			−0.576058	−	0.817409i	$-0.695410\pi$
$379$	−22.4293			−1.15212			−0.576058	+	0.817409i	$0.695410\pi$
$380$	−10.4966	+	18.1806i	−0.538464	+	0.932647i
$381$	4.31180	+	7.46826i	0.220900	+	0.382611i
$382$	18.1814	+	31.4911i	0.930241	+	1.61122i
$383$	−3.40420	+	5.89625i	−0.173947	+	0.301284i	−0.939796	−	0.341735i	$-0.888985\pi$
$383$	−3.40420	+	5.89625i	−0.173947	+	0.301284i	0.765850	+	0.643020i	$0.222319\pi$
$384$	−6.84255			−0.349182
$385$	−4.64543	−	1.77330i	−0.236753	−	0.0903759i
$386$	−27.5672			−1.40313
$387$	1.41875	−	2.45734i	0.0721190	−	0.124914i
$388$	1.57011	+	2.71951i	0.0797101	+	0.138062i
$389$	2.40033	+	4.15749i	0.121702	+	0.210793i	0.920439	−	0.390887i	$-0.127832\pi$
$389$	2.40033	+	4.15749i	0.121702	+	0.210793i	−0.798737	+	0.601680i	$0.794498\pi$
$390$	2.70574	−	4.68647i	0.137010	−	0.237309i
$391$	0.647651			0.0327531
$392$	−4.58987	−	4.10191i	−0.231823	−	0.207178i
$393$	17.2422			0.869752
$394$	−5.40420	+	9.36035i	−0.272260	+	0.471568i
$395$	22.0462	+	38.1852i	1.10927	+	1.92131i
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	−4.63223	+	8.02325i	−0.232485	+	0.402675i	−0.958539	−	0.284962i	$-0.908019\pi$
$397$	−4.63223	+	8.02325i	−0.232485	+	0.402675i	0.726054	+	0.687638i	$0.241352\pi$
$398$	−28.5107			−1.42911
$399$	−11.7626	−	4.49016i	−0.588869	−	0.224789i
$400$	−15.5226			−0.776130
$401$	1.81315	−	3.14046i	0.0905443	−	0.156827i	−0.817196	−	0.576360i	$-0.804473\pi$
$401$	1.81315	−	3.14046i	0.0905443	−	0.156827i	0.907740	+	0.419533i	$0.137806\pi$
$402$	−1.18732	−	2.05650i	−0.0592181	−	0.102569i
$403$	−2.59240	−	4.49016i	−0.129136	−	0.223671i
$404$	−8.51889	+	14.7551i	−0.423830	+	0.734096i
$405$	2.87939			0.143078
$406$	−20.3285	+	16.5244i	−1.00888	+	0.820092i
$407$	−0.347296			−0.0172148
$408$	−1.99273	+	3.45150i	−0.0986546	+	0.170875i
$409$	3.29813	+	5.71253i	0.163082	+	0.282467i	0.935973	−	0.352073i	$-0.114523\pi$
$409$	3.29813	+	5.71253i	0.163082	+	0.282467i	−0.772890	+	0.634540i	$0.781190\pi$
$410$	−15.2554	−	26.4231i	−0.753409	−	1.30494i
$411$	5.76604	−	9.98708i	0.284418	−	0.492626i
$412$	21.5476			1.06157
$413$	6.33821	+	39.5416i	0.311883	+	1.94571i
$414$	0.268571			0.0131995
$415$	5.25877	−	9.10846i	0.258143	−	0.447117i
$416$	3.55303	+	6.15403i	0.174202	+	0.301726i
$417$	10.1664	+	17.6087i	0.497849	+	0.862301i
$418$	2.91875	−	5.05542i	0.142761	−	0.247269i
$419$	6.92633			0.338373			0.169187	−	0.985584i	$-0.445886\pi$
$419$	6.92633			0.338373			0.169187	+	0.985584i	$0.445886\pi$
$420$	1.84730	+	11.5245i	0.0901388	+	0.562340i
$421$	−27.5080			−1.34066			−0.670330	−	0.742063i	$-0.733847\pi$
$421$	−27.5080			−1.34066			−0.670330	+	0.742063i	$0.733847\pi$
$422$	−12.0039	+	20.7913i	−0.584339	+	1.01211i
$423$	−0.305407	−	0.528981i	−0.0148494	−	0.0257199i
$424$	−0.592396	−	1.02606i	−0.0287693	−	0.0498299i
$425$	−7.45723	+	12.9163i	−0.361729	+	0.626533i
$426$	−26.8999			−1.30331
$427$	−31.6964	+	25.7650i	−1.53390	+	1.24686i
$428$	−12.6040			−0.609238
$429$	−0.326352	+	0.565258i	−0.0157564	+	0.0272909i
$430$	7.67752	+	13.2979i	0.370243	+	0.641279i
$431$	−4.06031	−	7.03266i	−0.195578	−	0.338751i	0.751512	−	0.659720i	$-0.229325\pi$
$431$	−4.06031	−	7.03266i	−0.195578	−	0.338751i	−0.947090	+	0.320968i	$0.895992\pi$
$432$	−2.35844	+	4.08494i	−0.113471	+	0.196537i
$433$	17.7151			0.851335			0.425667	−	0.904880i	$-0.360039\pi$
$433$	17.7151			0.851335			0.425667	+	0.904880i	$0.360039\pi$
$434$	24.0856	+	9.19421i	1.15615	+	0.441336i
$435$	−15.1702			−0.727358
$436$	−3.59833	+	6.23248i	−0.172329	+	0.298482i
$437$	−0.340022	−	0.588936i	−0.0162655	−	0.0281726i
$438$	−10.4042	−	18.0206i	−0.497132	−	0.861058i
$439$	1.45946	−	2.52785i	0.0696560	−	0.120648i	−0.829094	−	0.559109i	$-0.811143\pi$
$439$	1.45946	−	2.52785i	0.0696560	−	0.120648i	0.898750	+	0.438462i	$0.144477\pi$
$440$	1.65270			0.0787896
$441$	−6.64930	+	2.18788i	−0.316633	+	0.104185i
$442$	8.51754			0.405138
$443$	−3.52869	+	6.11186i	−0.167653	+	0.290383i	−0.937594	−	0.347731i	$-0.886952\pi$
$443$	−3.52869	+	6.11186i	−0.167653	+	0.290383i	0.769941	+	0.638115i	$0.220285\pi$
$444$	0.407604	+	0.705990i	0.0193440	+	0.0335048i
$445$	2.12449	+	3.67972i	0.100710	+	0.174435i
$446$	13.3204	−	23.0716i	0.630740	−	1.09247i
$447$	−12.3250			−0.582953
$448$	−9.69253	−	3.69994i	−0.457929	−	0.174806i
$449$	−21.5006			−1.01468			−0.507339	−	0.861747i	$-0.669371\pi$
$449$	−21.5006			−1.01468			−0.507339	+	0.861747i	$0.669371\pi$
$450$	−3.09240	+	5.35619i	−0.145777	+	0.252493i
$451$	1.84002	+	3.18701i	0.0866433	+	0.150071i
$452$	10.9743	+	19.0081i	0.516188	+	0.894064i
$453$	8.82295	−	15.2818i	0.414538	−	0.718001i
$454$	18.0446			0.846874
$455$	−5.91147	+	4.80526i	−0.277134	+	0.225274i
$456$	4.18479			0.195971
$457$	8.16431	−	14.1410i	0.381911	−	0.661488i	−0.609425	−	0.792844i	$-0.708600\pi$
$457$	8.16431	−	14.1410i	0.381911	−	0.661488i	0.991335	+	0.131355i	$0.0419329\pi$
$458$	2.12449	+	3.67972i	0.0992707	+	0.171942i
$459$	2.26604	+	3.92490i	0.105770	+	0.183199i
$460$	−0.315207	+	0.545955i	−0.0146966	+	0.0254553i
$461$	2.13516			0.0994444			0.0497222	−	0.998763i	$-0.484166\pi$
$461$	2.13516			0.0994444			0.0497222	+	0.998763i	$0.484166\pi$
$462$	−0.513671	−	3.20459i	−0.0238981	−	0.149091i
$463$	−14.6604			−0.681329			−0.340664	−	0.940185i	$-0.610652\pi$
$463$	−14.6604			−0.681329			−0.340664	+	0.940185i	$0.610652\pi$
$464$	12.4256	−	21.5218i	0.576845	−	0.999124i
$465$	7.46451	+	12.9289i	0.346158	+	0.599564i
$466$	−9.74897	−	16.8857i	−0.451612	−	0.782215i
$467$	11.0556	−	19.1488i	0.511590	−	0.886100i	−0.488319	−	0.872665i	$-0.662390\pi$
$467$	11.0556	−	19.1488i	0.511590	−	0.886100i	0.999910	−	0.0134354i	$-0.00427676\pi$
$468$	1.53209			0.0708208
$469$	0.529096	+	3.30082i	0.0244314	+	0.152418i
$470$	3.30541			0.152467
$471$	0.171122	−	0.296392i	0.00788488	−	0.0136570i
$472$	−6.65523	−	11.5272i	−0.306332	−	0.530582i
$473$	−0.926022	−	1.60392i	−0.0425785	−	0.0737482i
$474$	−14.3897	+	24.9236i	−0.660939	+	1.14478i
$475$	15.6604			0.718550
$476$	−14.2554	+	11.5878i	−0.653394	+	0.531124i
$477$	−1.34730			−0.0616885
$478$	21.9192	−	37.9652i	1.00256	−	1.73649i
$479$	−6.21735	−	10.7688i	−0.284078	−	0.492037i	0.688307	−	0.725419i	$-0.258354\pi$
$479$	−6.21735	−	10.7688i	−0.284078	−	0.492037i	−0.972385	+	0.233382i	$0.925021\pi$
$480$	−10.2306	−	17.7198i	−0.466959	−	0.808796i
$481$	−0.266044	+	0.460802i	−0.0121306	+	0.0210108i
$482$	1.33780			0.0609352
$483$	−0.353226	−	0.134837i	−0.0160723	−	0.00613531i
$484$	−16.2003			−0.736376
$485$	2.95084	−	5.11100i	0.133991	−	0.232079i
$486$	0.939693	+	1.62760i	0.0426253	+	0.0738292i
$487$	−7.58647	−	13.1401i	−0.343776	−	0.595437i	0.641355	−	0.767244i	$-0.278373\pi$
$487$	−7.58647	−	13.1401i	−0.343776	−	0.595437i	−0.985131	+	0.171807i	$0.945039\pi$
$488$	6.78833	−	11.7577i	0.307293	−	0.532248i
$489$	23.0915			1.04423
$490$	7.73783	−	37.0816i	0.349559	−	1.67518i
$491$	40.5458			1.82981			0.914904	−	0.403673i	$-0.132266\pi$
$491$	40.5458			1.82981			0.914904	+	0.403673i	$0.132266\pi$
$492$	4.31908	−	7.48086i	0.194719	−	0.337263i
$493$	−11.9388	−	20.6786i	−0.537697	−	0.931319i
$494$	−4.47178	−	7.74535i	−0.201195	−	0.348480i
$495$	0.939693	−	1.62760i	0.0422360	−	0.0731550i
$496$	−24.4561			−1.09811
$497$	35.3790	+	13.5052i	1.58696	+	0.605793i
$498$	6.86484			0.307621
$499$	12.8425	−	22.2439i	0.574911	−	0.995776i	−0.421140	−	0.906996i	$-0.638370\pi$
$499$	12.8425	−	22.2439i	0.574911	−	0.995776i	0.996051	−	0.0887801i	$-0.0282968\pi$
$500$	3.76991	+	6.52968i	0.168596	+	0.292016i
$501$	−4.42127	−	7.65787i	−0.197528	−	0.342128i
$502$	−7.50640	+	13.0015i	−0.335027	+	0.580284i
$503$	18.6705			0.832479			0.416239	−	0.909255i	$-0.363348\pi$
$503$	18.6705			0.832479			0.416239	+	0.909255i	$0.363348\pi$
$504$	1.80541	−	1.46756i	0.0804192	−	0.0653703i
$505$	32.0205			1.42490
$506$	0.0876485	−	0.151812i	0.00389645	−	0.00674885i
$507$	0.500000	+	0.866025i	0.0222058	+	0.0384615i
$508$	−6.60607	−	11.4420i	−0.293097	−	0.507659i
$509$	−21.3803	+	37.0318i	−0.947666	+	1.64141i	−0.197343	+	0.980335i	$0.563231\pi$
$509$	−21.3803	+	37.0318i	−0.947666	+	1.64141i	−0.750323	+	0.661071i	$0.770102\pi$
$510$	−24.5253			−1.08600
$511$	4.63634	+	28.9243i	0.205100	+	1.27954i
$512$	25.2226			1.11469
$513$	2.37939	−	4.12122i	0.105052	−	0.181956i
$514$	−24.3888	−	42.2426i	−1.07574	−	1.86324i
$515$	−20.2481	−	35.0707i	−0.892238	−	1.54540i
$516$	−2.17365	+	3.76487i	−0.0956895	+	0.165739i
$517$	−0.398681			−0.0175340
$518$	−0.418748	−	2.61240i	−0.0183987	−	0.114782i
$519$	20.7743			0.911888
$520$	1.26604	−	2.19285i	0.0555197	−	0.0961630i
$521$	−13.3353	−	23.0974i	−0.584229	−	1.01191i	−0.994971	−	0.100163i	$-0.968064\pi$
$521$	−13.3353	−	23.0974i	−0.584229	−	1.01191i	0.410742	−	0.911752i	$-0.365270\pi$
$522$	−4.95084	−	8.57510i	−0.216692	−	0.375322i
$523$	2.84255	−	4.92344i	0.124296	−	0.215287i	−0.797162	−	0.603766i	$-0.793666\pi$
$523$	2.84255	−	4.92344i	0.124296	−	0.215287i	0.921458	+	0.388479i	$0.126999\pi$
$524$	−26.4165			−1.15401
$525$	6.75624	−	5.49194i	0.294867	−	0.239688i
$526$	7.66550			0.334232
$527$	−11.7490	+	20.3498i	−0.511793	+	0.886452i
$528$	1.53936	+	2.66625i	0.0669922	+	0.116034i
$529$	11.4898	+	19.9009i	0.499556	+	0.865256i
$530$	3.64543	−	6.31407i	0.158347	−	0.274266i
$531$	−15.1361			−0.656851
$532$	18.0214	+	6.87933i	0.781327	+	0.298257i
$533$	5.63816			0.244216
$534$	−1.38666	+	2.40176i	−0.0600066	+	0.103935i
$535$	11.8439	+	20.5142i	0.512056	+	0.886907i
$536$	−0.555560	−	0.962258i	−0.0239965	−	0.0415632i
$537$	−9.67159	+	16.7517i	−0.417360	+	0.722888i
$538$	−3.78281			−0.163089
$539$	−0.933296	+	4.47259i	−0.0401999	+	0.192648i
$540$	−4.41147			−0.189840
$541$	−5.41622	+	9.38117i	−0.232862	+	0.403328i	−0.958649	−	0.284591i	$-0.908142\pi$
$541$	−5.41622	+	9.38117i	−0.232862	+	0.403328i	0.725787	+	0.687919i	$0.241476\pi$
$542$	12.1493	+	21.0432i	0.521857	+	0.903883i
$543$	−10.6348	−	18.4199i	−0.456381	−	0.790475i
$544$	16.1027	−	27.8906i	0.690396	−	1.19580i
$545$	13.5253			0.579359
$546$	−4.64543	−	1.77330i	−0.198806	−	0.0758904i
$547$	12.9932			0.555549			0.277774	−	0.960646i	$-0.410403\pi$
$547$	12.9932			0.555549			0.277774	+	0.960646i	$0.410403\pi$
$548$	−8.83409	+	15.3011i	−0.377374	+	0.653630i
$549$	−7.71941	−	13.3704i	−0.329456	−	0.570635i
$550$	2.01842	+	3.49600i	0.0860656	+	0.149070i
$551$	−12.5360	+	21.7129i	−0.534050	+	0.925001i
$552$	0.125667			0.00534875
$553$	31.4384	−	25.5553i	1.33690	−	1.08672i
$554$	−38.4962			−1.63555
$555$	0.766044	−	1.32683i	0.0325168	−	0.0563207i
$556$	−15.5758	−	26.9781i	−0.660561	−	1.14412i
$557$	−16.5692	−	28.6987i	−0.702061	−	1.21601i	−0.967742	−	0.251944i	$-0.918930\pi$
$557$	−16.5692	−	28.6987i	−0.702061	−	1.21601i	0.265681	−	0.964061i	$-0.414403\pi$
$558$	−4.87211	+	8.43874i	−0.206253	+	0.357241i
$559$	−2.83750			−0.120013
$560$	5.68732	+	35.4809i	0.240333	+	1.49934i
$561$	2.95811			0.124892
$562$	−15.4106	+	26.6919i	−0.650057	+	1.12593i
$563$	5.69119	+	9.85743i	0.239855	+	0.415441i	0.960673	−	0.277684i	$-0.0895668\pi$
$563$	5.69119	+	9.85743i	0.239855	+	0.415441i	−0.720817	+	0.693125i	$0.756233\pi$
$564$	0.467911	+	0.810446i	0.0197026	+	0.0341259i
$565$	20.6250	−	35.7235i	0.867698	−	1.50290i
$566$	18.7341			0.787454
$567$	−0.418748	−	2.61240i	−0.0175858	−	0.109711i
$568$	−12.5868			−0.528129
$569$	−16.1917	+	28.0448i	−0.678790	+	1.17570i	0.296556	+	0.955015i	$0.404162\pi$
$569$	−16.1917	+	28.0448i	−0.678790	+	1.17570i	−0.975346	+	0.220683i	$0.929172\pi$
$570$	12.8760	+	22.3019i	0.539316	+	0.934122i
$571$	7.08559	+	12.2726i	0.296523	+	0.513592i	0.975338	−	0.220717i	$-0.0708396\pi$
$571$	7.08559	+	12.2726i	0.296523	+	0.513592i	−0.678815	+	0.734309i	$0.737506\pi$
$572$	0.500000	−	0.866025i	0.0209061	−	0.0362103i
$573$	19.3482			0.808284
$574$	−21.7545	+	17.6836i	−0.908015	+	0.738097i
$575$	0.470275			0.0196118
$576$	1.96064	−	3.39592i	0.0816932	−	0.141497i
$577$	−3.80406	−	6.58883i	−0.158365	−	0.274297i	0.775914	−	0.630839i	$-0.217289\pi$
$577$	−3.80406	−	6.58883i	−0.158365	−	0.274297i	−0.934279	+	0.356542i	$0.883956\pi$
$578$	−3.32635	−	5.76141i	−0.138358	−	0.239643i
$579$	−7.33409	+	12.7030i	−0.304794	+	0.527920i
$580$	23.2422			0.965078
$581$	−9.02869	−	3.44653i	−0.374573	−	0.142986i
$582$	3.85204			0.159672
$583$	−0.439693	+	0.761570i	−0.0182102	+	0.0315410i
$584$	−4.86824	−	8.43204i	−0.201449	−	0.348920i
$585$	−1.43969	−	2.49362i	−0.0595240	−	0.103099i
$586$	−16.3059	+	28.2426i	−0.673589	+	1.16669i
$587$	1.81614			0.0749602			0.0374801	−	0.999297i	$-0.488067\pi$
$587$	1.81614			0.0749602			0.0374801	+	0.999297i	$0.488067\pi$
$588$	10.1873	−	3.35202i	0.420118	−	0.138235i
$589$	24.6732			1.01664
$590$	40.9543	−	70.9349i	1.68606	−	2.92034i
$591$	2.87551	+	4.98054i	0.118283	+	0.204872i
$592$	1.25490	+	2.17355i	0.0515761	+	0.0893324i
$593$	−0.395115	+	0.684360i	−0.0162254	+	0.0281033i	−0.874024	−	0.485883i	$-0.838498\pi$
$593$	−0.395115	+	0.684360i	−0.0162254	+	0.0281033i	0.857799	+	0.513986i	$0.171832\pi$
$594$	1.22668			0.0503314
$595$	32.2558	+	12.3130i	1.32236	+	0.504786i
$596$	18.8830			0.773478
$597$	−7.58512	+	13.1378i	−0.310438	+	0.537695i
$598$	−0.134285	−	0.232589i	−0.00549134	−	0.00951127i
$599$	−12.9816	−	22.4848i	−0.530413	−	0.918702i	−0.999370	−	0.0354815i	$-0.988704\pi$
$599$	−12.9816	−	22.4848i	−0.530413	−	0.918702i	0.468957	−	0.883221i	$-0.344630\pi$
$600$	−1.44697	+	2.50622i	−0.0590722	+	0.102316i
$601$	26.6263			1.08611			0.543055	−	0.839697i	$-0.317268\pi$
$601$	26.6263			1.08611			0.543055	+	0.839697i	$0.317268\pi$
$602$	10.9483	−	8.89955i	0.446220	−	0.362718i
$603$	−1.26352			−0.0514544
$604$	−13.5175	+	23.4131i	−0.550021	+	0.952664i
$605$	15.2233	+	26.3675i	0.618914	+	1.07199i
$606$	10.4500	+	18.0999i	0.424501	+	0.735257i
$607$	5.66503	−	9.81212i	0.229936	−	0.398262i	−0.727853	−	0.685734i	$-0.759481\pi$
$607$	5.66503	−	9.81212i	0.229936	−	0.398262i	0.957789	+	0.287472i	$0.0928148\pi$
$608$	−33.8161			−1.37143
$609$	2.20620	+	13.7636i	0.0893999	+	0.557730i
$610$	83.5467			3.38271
$611$	−0.305407	+	0.528981i	−0.0123555	+	0.0214003i
$612$	−3.47178	−	6.01330i	−0.140338	−	0.243073i
$613$	2.68732	+	4.65457i	0.108540	+	0.187996i	0.915179	−	0.403048i	$-0.132049\pi$
$613$	2.68732	+	4.65457i	0.108540	+	0.187996i	−0.806639	+	0.591044i	$0.798716\pi$
$614$	20.9884	−	36.3531i	0.847025	−	1.46709i
$615$	−16.2344			−0.654635
$616$	−0.240352	−	1.49946i	−0.00968406	−	0.0604150i
$617$	−24.8408			−1.00005			−0.500026	−	0.866010i	$-0.666676\pi$
$617$	−24.8408			−1.00005			−0.500026	+	0.866010i	$0.666676\pi$
$618$	13.2160	−	22.8908i	0.531626	−	0.920803i
$619$	−6.35386	−	11.0052i	−0.255383	−	0.442336i	0.709616	−	0.704588i	$-0.248868\pi$
$619$	−6.35386	−	11.0052i	−0.255383	−	0.442336i	−0.964999	+	0.262252i	$0.915535\pi$
$620$	−11.4363	−	19.8082i	−0.459292	−	0.795518i
$621$	0.0714517	−	0.123758i	0.00286726	−	0.00496624i
$622$	−6.41147			−0.257077
$623$	3.02956	−	2.46264i	0.121377	−	0.0986635i
$624$	4.71688			0.188826
$625$	15.3123	−	26.5216i	0.612491	−	1.06087i
$626$	31.4183	+	54.4182i	1.25573	+	2.17499i
$627$	−1.55303	−	2.68993i	−0.0620222	−	0.107426i
$628$	−0.262174	+	0.454099i	−0.0104619	+	0.0181205i
$629$	2.41147			0.0961518
$630$	13.3760	+	5.10602i	0.532912	+	0.203429i
$631$	−15.9564			−0.635213			−0.317606	−	0.948223i	$-0.602879\pi$
$631$	−15.9564			−0.635213			−0.317606	+	0.948223i	$0.602879\pi$
$632$	−6.73308	+	11.6620i	−0.267827	+	0.463891i
$633$	6.38713	+	11.0628i	0.253865	+	0.439708i
$634$	−0.847296	−	1.46756i	−0.0336504	−	0.0582843i
$635$	−12.4153	+	21.5040i	−0.492688	+	0.853361i
$636$	2.06418			0.0818500
$637$	5.21941	+	4.66452i	0.206800	+	0.184815i
$638$	−6.46286			−0.255867
$639$	−7.15657	+	12.3955i	−0.283110	+	0.490360i
$640$	−9.85117	−	17.0627i	−0.389402	−	0.674463i
$641$	−0.195060	−	0.337853i	−0.00770439	−	0.0133444i	0.862148	−	0.506657i	$-0.169119\pi$
$641$	−0.195060	−	0.337853i	−0.00770439	−	0.0133444i	−0.869852	+	0.493313i	$0.835786\pi$
$642$	−7.73055	+	13.3897i	−0.305101	+	0.528450i
$643$	15.7091			0.619508			0.309754	−	0.950817i	$-0.399753\pi$
$643$	15.7091			0.619508			0.309754	+	0.950817i	$0.399753\pi$
$644$	0.541174	+	0.206583i	0.0213252	+	0.00814050i
$645$	8.17024			0.321703
$646$	−20.2665	+	35.1026i	−0.797375	+	1.38109i
$647$	−5.84137	−	10.1175i	−0.229648	−	0.397762i	0.728056	−	0.685518i	$-0.240424\pi$
$647$	−5.84137	−	10.1175i	−0.229648	−	0.397762i	−0.957704	+	0.287756i	$0.907091\pi$
$648$	0.439693	+	0.761570i	0.0172728	+	0.0299173i
$649$	−4.93969	+	8.55580i	−0.193900	+	0.335844i
$650$	6.18479			0.242588
$651$	10.6446	−	8.65263i	0.417193	−	0.339123i
$652$	−35.3783			−1.38552
$653$	−19.4085	+	33.6166i	−0.759515	+	1.31552i	0.183584	+	0.983004i	$0.441230\pi$
$653$	−19.4085	+	33.6166i	−0.759515	+	1.31552i	−0.943098	+	0.332514i	$0.892103\pi$
$654$	4.41400	+	7.64527i	0.172601	+	0.298954i
$655$	24.8234	+	42.9954i	0.969931	+	1.67997i
$656$	13.2973	−	23.0315i	0.519171	−	0.899230i
$657$	−11.0719			−0.431957
$658$	−0.480704	−	2.99892i	−0.0187398	−	0.116910i
$659$	33.2763			1.29626			0.648131	−	0.761529i	$-0.275551\pi$
$659$	33.2763			1.29626			0.648131	+	0.761529i	$0.275551\pi$
$660$	−1.43969	+	2.49362i	−0.0560400	+	0.0970641i
$661$	0.753718	+	1.30548i	0.0293162	+	0.0507772i	0.880311	−	0.474396i	$-0.157334\pi$
$661$	0.753718	+	1.30548i	0.0293162	+	0.0507772i	−0.850995	+	0.525174i	$0.824000\pi$
$662$	23.5792	+	40.8404i	0.916431	+	1.58731i
$663$	2.26604	−	3.92490i	0.0880059	−	0.152431i
$664$	3.21213			0.124655
$665$	−5.73783	−	35.7960i	−0.222503	−	1.38811i
$666$	1.00000			0.0387492
$667$	−0.376449	+	0.652028i	−0.0145761	+	0.0252466i
$668$	6.77379	+	11.7325i	0.262086	+	0.453946i
$669$	−7.08765	−	12.2762i	−0.274024	−	0.474624i
$670$	3.41875	−	5.92145i	0.132078	−	0.228765i
$671$	−10.0770			−0.389017
$672$	−14.5890	+	11.8589i	−0.562783	+	0.457469i
$673$	−33.1147			−1.27648			−0.638240	−	0.769838i	$-0.720337\pi$
$673$	−33.1147			−1.27648			−0.638240	+	0.769838i	$0.720337\pi$
$674$	8.79726	−	15.2373i	0.338858	−	0.586919i
$675$	1.64543	+	2.84997i	0.0633326	+	0.109695i
$676$	−0.766044	−	1.32683i	−0.0294632	−	0.0510318i
$677$	−3.60947	+	6.25179i	−0.138723	+	0.240276i	−0.927014	−	0.375028i	$-0.877633\pi$
$677$	−3.60947	+	6.25179i	−0.138723	+	0.240276i	0.788290	+	0.615303i	$0.210967\pi$
$678$	26.9240			1.03401
$679$	−5.06624	−	1.93394i	−0.194424	−	0.0742178i
$680$	−11.4757			−0.440071
$681$	4.80066	−	8.31499i	0.183962	−	0.318631i
$682$	3.18004	+	5.50800i	0.121770	+	0.210912i
$683$	−14.1258	−	24.4667i	−0.540510	−	0.936191i	−0.998875	−	0.0474264i	$-0.984898\pi$
$683$	−14.1258	−	24.4667i	−0.540510	−	0.936191i	0.458365	−	0.888764i	$-0.348435\pi$
$684$	−3.64543	+	6.31407i	−0.139386	+	0.241424i
$685$	33.2053			1.26871
$686$	−34.7686	−	1.62760i	−1.32747	−	0.0621419i
$687$	2.26083			0.0862560
$688$	−6.69207	+	11.5910i	−0.255133	+	0.441903i
$689$	0.673648	+	1.16679i	0.0256640	+	0.0444513i
$690$	0.386659	+	0.669713i	0.0147199	+	0.0254956i
$691$	1.67752	−	2.90555i	0.0638158	−	0.110532i	−0.832352	−	0.554247i	$-0.813006\pi$
$691$	1.67752	−	2.90555i	0.0638158	−	0.110532i	0.896168	+	0.443715i	$0.146340\pi$
$692$	−31.8280			−1.20992
$693$	−1.61334	−	0.615862i	−0.0612857	−	0.0233947i
$694$	−39.2422			−1.48961
$695$	−29.2729	+	50.7022i	−1.11038	+	1.92324i
$696$	−2.31655	−	4.01239i	−0.0878087	−	0.152089i
$697$	−12.7763	−	22.1292i	−0.483937	−	0.838204i
$698$	−9.01027	+	15.6062i	−0.341044	+	0.590705i
$699$	−10.3746			−0.392405
$700$	−10.3512	+	8.41415i	−0.391237	+	0.318025i
$701$	29.2918			1.10634			0.553168	−	0.833070i	$-0.313419\pi$
$701$	29.2918			1.10634			0.553168	+	0.833070i	$0.313419\pi$
$702$	0.939693	−	1.62760i	0.0354664	−	0.0614296i
$703$	−1.26604	−	2.19285i	−0.0477498	−	0.0827050i
$704$	−1.27972	−	2.21653i	−0.0482311	−	0.0835387i
$705$	0.879385	−	1.52314i	0.0331196	−	0.0573648i
$706$	2.52259			0.0949391
$707$	−4.65674	−	29.0515i	−0.175135	−	1.09260i
$708$	23.1898			0.871528
$709$	−22.8883	+	39.6437i	−0.859588	+	1.48885i	0.0127335	+	0.999919i	$0.495947\pi$
$709$	−22.8883	+	39.6437i	−0.859588	+	1.48885i	−0.872322	+	0.488932i	$0.837387\pi$
$710$	−38.7276	−	67.0782i	−1.45342	−	2.51740i
$711$	7.65657	+	13.2616i	0.287144	+	0.497348i
$712$	−0.648833	+	1.12381i	−0.0243161	+	0.0421166i
$713$	0.740925			0.0277479
$714$	3.56670	+	22.2513i	0.133481	+	0.832732i
$715$	−1.87939			−0.0702850
$716$	14.8177	−	25.6651i	0.553765	−	0.959149i
$717$	−11.6630	−	20.2009i	−0.435562	−	0.754415i
$718$	25.6339	+	44.3992i	0.956648	+	1.65696i
$719$	−9.85457	+	17.0686i	−0.367513	+	0.636552i	−0.989176	−	0.146733i	$-0.953124\pi$
$719$	−9.85457	+	17.0686i	−0.367513	+	0.636552i	0.621663	+	0.783285i	$0.286457\pi$
$720$	−13.5817			−0.506161
$721$	−28.8742	+	23.4710i	−1.07533	+	0.874105i
$722$	6.85204			0.255007
$723$	0.355914	−	0.616462i	0.0132366	−	0.0229265i
$724$	16.2934	+	28.2210i	0.605539	+	1.04882i
$725$	−8.66906	−	15.0153i	−0.321961	−	0.557653i
$726$	−9.93629	+	17.2102i	−0.368770	+	0.638729i
$727$	19.8699			0.736933			0.368467	−	0.929641i	$-0.379883\pi$
$727$	19.8699			0.736933			0.368467	+	0.929641i	$0.379883\pi$
$728$	−2.17365	−	0.829748i	−0.0805608	−	0.0307525i
$729$	1.00000			0.0370370
$730$	29.9577	−	51.8883i	1.10878	−	1.92047i
$731$	6.42989	+	11.1369i	0.237818	+	0.411913i
$732$	11.8268	+	20.4847i	0.437132	+	0.757134i
$733$	25.5624	−	44.2754i	0.944170	−	1.63535i	0.186764	−	0.982405i	$-0.440200\pi$
$733$	25.5624	−	44.2754i	0.944170	−	1.63535i	0.757405	−	0.652945i	$-0.226467\pi$
$734$	64.1661			2.36841
$735$	−15.0287	−	13.4310i	−0.554341	−	0.495408i
$736$	−1.01548			−0.0374311
$737$	−0.412351	+	0.714214i	−0.0151892	+	0.0263084i
$738$	−5.29813	−	9.17664i	−0.195027	−	0.337797i
$739$	16.4106	+	28.4240i	0.603674	+	1.04559i	0.992260	+	0.124181i	$0.0396303\pi$
$739$	16.4106	+	28.4240i	0.603674	+	1.04559i	−0.388586	+	0.921412i	$0.627036\pi$
$740$	−1.17365	+	2.03282i	−0.0431442	+	0.0747279i
$741$	−4.75877			−0.174818
$742$	−6.25877	−	2.38917i	−0.229767	−	0.0877090i
$743$	−3.77930			−0.138649			−0.0693246	−	0.997594i	$-0.522084\pi$
$743$	−3.77930			−0.138649			−0.0693246	+	0.997594i	$0.522084\pi$
$744$	−2.27972	+	3.94858i	−0.0835784	+	0.144762i
$745$	−17.7442	−	30.7339i	−0.650098	−	1.12600i
$746$	−8.60519	−	14.9046i	−0.315058	−	0.545697i
$747$	1.82635	−	3.16333i	0.0668227	−	0.115740i
$748$	−4.53209			−0.165710
$749$	16.8897	−	13.7291i	0.617134	−	0.501650i
$750$	9.24897			0.337725
$751$	−13.1091	+	22.7056i	−0.478356	+	0.828538i	−0.999692	−	0.0248141i	$-0.992101\pi$
$751$	−13.1091	+	22.7056i	−0.478356	+	0.828538i	0.521336	+	0.853352i	$0.325434\pi$
$752$	1.44057	+	2.49514i	0.0525322	+	0.0909884i
$753$	3.99407	+	6.91793i	0.145552	+	0.252103i
$754$	−4.95084	+	8.57510i	−0.180299	+	0.312287i
$755$	50.8093			1.84914
$756$	0.641559	+	4.00243i	0.0233333	+	0.145567i
$757$	−23.8425			−0.866572			−0.433286	−	0.901256i	$-0.642646\pi$
$757$	−23.8425			−0.866572			−0.433286	+	0.901256i	$0.642646\pi$
$758$	21.0767	−	36.5059i	0.765539	−	1.32595i
$759$	−0.0466368	−	0.0807773i	−0.00169281	−	0.00293203i
$760$	6.02481	+	10.4353i	0.218543	+	0.378528i
$761$	−3.68938	+	6.39019i	−0.133740	+	0.231644i	−0.925115	−	0.379686i	$-0.876032\pi$
$761$	−3.68938	+	6.39019i	−0.133740	+	0.231644i	0.791376	+	0.611330i	$0.209365\pi$
$762$	−16.2071			−0.587121
$763$	−1.96698	−	12.2712i	−0.0712094	−	0.444247i
$764$	−29.6432			−1.07245
$765$	−6.52481	+	11.3013i	−0.235905	+	0.408600i
$766$	−6.39780	−	11.0813i	−0.231162	−	0.400384i
$767$	7.56805	+	13.1082i	0.273266	+	0.473311i
$768$	10.3512	−	17.9287i	0.373516	−	0.646948i
$769$	39.1625			1.41224			0.706118	−	0.708094i	$-0.250445\pi$
$769$	39.1625			1.41224			0.706118	+	0.708094i	$0.250445\pi$
$770$	7.25150	−	5.89452i	0.261326	−	0.212424i
$771$	−25.

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)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 1.62760i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.766044 - 1.32683i) q^{4} +(-1.43969 + 2.49362i) q^{5} -1.87939 q^{6} +(2.47178 + 0.943555i) q^{7} -0.879385 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 1.62760i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.766044 - 1.32683i) q^{4} +(-1.43969 + 2.49362i) q^{5} -1.87939 q^{6} +(2.47178 + 0.943555i) q^{7} -0.879385 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.70574 - 4.68647i) q^{10} +(0.326352 + 0.565258i) q^{11} +(0.766044 - 1.32683i) q^{12} +1.00000 q^{13} +(-3.85844 + 3.13641i) q^{14} -2.87939 q^{15} +(2.35844 - 4.08494i) q^{16} +(-2.26604 - 3.92490i) q^{17} +(-0.939693 - 1.62760i) q^{18} +(-2.37939 + 4.12122i) q^{19} +4.41147 q^{20} +(0.418748 + 2.61240i) q^{21} -1.22668 q^{22} +(-0.0714517 + 0.123758i) q^{23} +(-0.439693 - 0.761570i) q^{24} +(-1.64543 - 2.84997i) q^{25} +(-0.939693 + 1.62760i) q^{26} -1.00000 q^{27} +(-0.641559 - 4.00243i) q^{28} +5.26857 q^{29} +(2.70574 - 4.68647i) q^{30} +(-2.59240 - 4.49016i) q^{31} +(3.55303 + 6.15403i) q^{32} +(-0.326352 + 0.565258i) q^{33} +8.51754 q^{34} +(-5.91147 + 4.80526i) q^{35} +1.53209 q^{36} +(-0.266044 + 0.460802i) q^{37} +(-4.47178 - 7.74535i) q^{38} +(0.500000 + 0.866025i) q^{39} +(1.26604 - 2.19285i) q^{40} +5.63816 q^{41} +(-4.64543 - 1.77330i) q^{42} -2.83750 q^{43} +(0.500000 - 0.866025i) q^{44} +(-1.43969 - 2.49362i) q^{45} +(-0.134285 - 0.232589i) q^{46} +(-0.305407 + 0.528981i) q^{47} +4.71688 q^{48} +(5.21941 + 4.66452i) q^{49} +6.18479 q^{50} +(2.26604 - 3.92490i) q^{51} +(-0.766044 - 1.32683i) q^{52} +(0.673648 + 1.16679i) q^{53} +(0.939693 - 1.62760i) q^{54} -1.87939 q^{55} +(-2.17365 - 0.829748i) q^{56} -4.75877 q^{57} +(-4.95084 + 8.57510i) q^{58} +(7.56805 + 13.1082i) q^{59} +(2.20574 + 3.82045i) q^{60} +(-7.71941 + 13.3704i) q^{61} +9.74422 q^{62} +(-2.05303 + 1.66885i) q^{63} -3.92127 q^{64} +(-1.43969 + 2.49362i) q^{65} +(-0.613341 - 1.06234i) q^{66} +(0.631759 + 1.09424i) q^{67} +(-3.47178 + 6.01330i) q^{68} -0.142903 q^{69} +(-2.26604 - 14.1370i) q^{70} +14.3131 q^{71} +(0.439693 - 0.761570i) q^{72} +(5.53596 + 9.58856i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(1.64543 - 2.84997i) q^{75} +7.29086 q^{76} +(0.273318 + 1.70513i) q^{77} -1.87939 q^{78} +(7.65657 - 13.2616i) q^{79} +(6.79086 + 11.7621i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.29813 + 9.17664i) q^{82} -3.65270 q^{83} +(3.14543 - 2.55682i) q^{84} +13.0496 q^{85} +(2.66637 - 4.61830i) q^{86} +(2.63429 + 4.56272i) q^{87} +(-0.286989 - 0.497079i) q^{88} +(0.737826 - 1.27795i) q^{89} +5.41147 q^{90} +(2.47178 + 0.943555i) q^{91} +0.218941 q^{92} +(2.59240 - 4.49016i) q^{93} +(-0.573978 - 0.994159i) q^{94} +(-6.85117 - 11.8666i) q^{95} +(-3.55303 + 6.15403i) q^{96} -2.04963 q^{97} +(-12.4966 + 4.11186i) q^{98} -0.652704 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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