LMFDB - Embedded newform 77.2.e.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(23,77)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("77.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.e (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:	$0.614848095564$
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			67.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	77.67
Dual form			77.2.e.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 1.62760i) q^{2} +(-0.326352 + 0.565258i) q^{3} +(-0.766044 + 1.32683i) q^{4} +(-1.76604 - 3.05888i) q^{5} +1.22668 q^{6} +(0.418748 - 2.61240i) q^{7} -0.879385 q^{8} +(1.28699 + 2.22913i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 1.62760i) q^{2} +(-0.326352 + 0.565258i) q^{3} +(-0.766044 + 1.32683i) q^{4} +(-1.76604 - 3.05888i) q^{5} +1.22668 q^{6} +(0.418748 - 2.61240i) q^{7} -0.879385 q^{8} +(1.28699 + 2.22913i) q^{9} +(-3.31908 + 5.74881i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +4.41147 q^{13} +(-4.64543 + 1.77330i) q^{14} +2.30541 q^{15} +(2.35844 + 4.08494i) q^{16} +(2.62449 - 4.54574i) q^{17} +(2.41875 - 4.18939i) q^{18} +(-0.907604 - 1.57202i) q^{19} +5.41147 q^{20} +(1.34002 + 1.08926i) q^{21} +1.87939 q^{22} +(3.16637 + 5.48432i) q^{23} +(0.286989 - 0.497079i) q^{24} +(-3.73783 + 6.47410i) q^{25} +(-4.14543 - 7.18009i) q^{26} -3.63816 q^{27} +(3.14543 + 2.55682i) q^{28} +1.92127 q^{29} +(-2.16637 - 3.75227i) q^{30} +(-0.733956 + 1.27125i) q^{31} +(3.55303 - 6.15403i) q^{32} +(-0.326352 - 0.565258i) q^{33} -9.86484 q^{34} +(-8.73055 + 3.33272i) q^{35} -3.94356 q^{36} +(-2.22668 - 3.85673i) q^{37} +(-1.70574 + 2.95442i) q^{38} +(-1.43969 + 2.49362i) q^{39} +(1.55303 + 2.68993i) q^{40} +0.283119 q^{41} +(0.513671 - 3.20459i) q^{42} -3.41147 q^{43} +(-0.766044 - 1.32683i) q^{44} +(4.54576 - 7.87349i) q^{45} +(5.95084 - 10.3072i) q^{46} +(2.27719 + 3.94421i) q^{47} -3.07873 q^{48} +(-6.64930 - 2.18788i) q^{49} +14.0496 q^{50} +(1.71301 + 2.96702i) q^{51} +(-3.37939 + 5.85327i) q^{52} +(3.61721 - 6.26519i) q^{53} +(3.41875 + 5.92145i) q^{54} +3.53209 q^{55} +(-0.368241 + 2.29731i) q^{56} +1.18479 q^{57} +(-1.80541 - 3.12706i) q^{58} +(-4.76991 + 8.26173i) q^{59} +(-1.76604 + 3.05888i) q^{60} +(0.573978 + 0.994159i) q^{61} +2.75877 q^{62} +(6.36231 - 2.42869i) q^{63} -3.92127 q^{64} +(-7.79086 - 13.4942i) q^{65} +(-0.613341 + 1.06234i) q^{66} +(0.347296 - 0.601535i) q^{67} +(4.02094 + 6.96448i) q^{68} -4.13341 q^{69} +(13.6284 + 11.0781i) q^{70} +9.46110 q^{71} +(-1.13176 - 1.96026i) q^{72} +(-1.17365 + 2.03282i) q^{73} +(-4.18479 + 7.24827i) q^{74} +(-2.43969 - 4.22567i) q^{75} +2.78106 q^{76} +(2.05303 + 1.66885i) q^{77} +5.41147 q^{78} +(6.20961 + 10.7554i) q^{79} +(8.33022 - 14.4284i) q^{80} +(-2.67365 + 4.63089i) q^{81} +(-0.266044 - 0.460802i) q^{82} -11.3327 q^{83} +(-2.47178 + 0.943555i) q^{84} -18.5398 q^{85} +(3.20574 + 5.55250i) q^{86} +(-0.627011 + 1.08602i) q^{87} +(0.439693 - 0.761570i) q^{88} +(1.73396 + 3.00330i) q^{89} -17.0865 q^{90} +(1.84730 - 11.5245i) q^{91} -9.70233 q^{92} +(-0.479055 - 0.829748i) q^{93} +(4.27972 - 7.41268i) q^{94} +(-3.20574 + 5.55250i) q^{95} +(2.31908 + 4.01676i) q^{96} +15.3473 q^{97} +(2.68732 + 12.8783i) q^{98} -2.57398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 6 q^{5} - 6 q^{6} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^3 - 6 * q^5 - 6 * q^6 + 6 * q^8	$ 6 q - 3 q^{3} - 6 q^{5} - 6 q^{6} + 6 q^{8} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{16} + 3 q^{17} + 12 q^{18} - 9 q^{19} + 12 q^{20} - 12 q^{21} - 6 q^{24} - 3 q^{25} - 9 q^{26} + 12 q^{27} + 3 q^{28} - 6 q^{29} + 6 q^{30} - 9 q^{31} + 9 q^{32} - 3 q^{33} - 12 q^{34} - 15 q^{35} + 6 q^{36} - 3 q^{39} - 3 q^{40} + 18 q^{41} - 18 q^{42} - 3 q^{45} + 24 q^{46} + 3 q^{47} - 36 q^{48} + 30 q^{50} + 18 q^{51} - 9 q^{52} - 9 q^{53} + 18 q^{54} + 12 q^{55} + 3 q^{56} - 15 q^{58} - 6 q^{60} - 12 q^{61} - 6 q^{62} + 6 q^{63} - 6 q^{64} - 15 q^{65} + 3 q^{66} + 21 q^{68} + 42 q^{69} + 45 q^{70} - 18 q^{71} - 12 q^{72} - 6 q^{73} - 18 q^{74} - 9 q^{75} - 18 q^{76} + 12 q^{78} + 3 q^{79} + 27 q^{80} - 15 q^{81} + 3 q^{82} - 30 q^{83} - 54 q^{85} + 9 q^{86} + 24 q^{87} - 3 q^{88} + 15 q^{89} - 72 q^{90} + 9 q^{91} - 6 q^{92} - 6 q^{93} - 9 q^{95} - 3 q^{96} + 90 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q - 3 * q^3 - 6 * q^5 - 6 * q^6 + 6 * q^8 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^16 + 3 * q^17 + 12 * q^18 - 9 * q^19 + 12 * q^20 - 12 * q^21 - 6 * q^24 - 3 * q^25 - 9 * q^26 + 12 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 - 9 * q^31 + 9 * q^32 - 3 * q^33 - 12 * q^34 - 15 * q^35 + 6 * q^36 - 3 * q^39 - 3 * q^40 + 18 * q^41 - 18 * q^42 - 3 * q^45 + 24 * q^46 + 3 * q^47 - 36 * q^48 + 30 * q^50 + 18 * q^51 - 9 * q^52 - 9 * q^53 + 18 * q^54 + 12 * q^55 + 3 * q^56 - 15 * q^58 - 6 * q^60 - 12 * q^61 - 6 * q^62 + 6 * q^63 - 6 * q^64 - 15 * q^65 + 3 * q^66 + 21 * q^68 + 42 * q^69 + 45 * q^70 - 18 * q^71 - 12 * q^72 - 6 * q^73 - 18 * q^74 - 9 * q^75 - 18 * q^76 + 12 * q^78 + 3 * q^79 + 27 * q^80 - 15 * q^81 + 3 * q^82 - 30 * q^83 - 54 * q^85 + 9 * q^86 + 24 * q^87 - 3 * q^88 + 15 * q^89 - 72 * q^90 + 9 * q^91 - 6 * q^92 - 6 * q^93 - 9 * q^95 - 3 * q^96 + 90 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.939693	−	1.62760i	−0.664463	−	1.15088i	−0.979431	−	0.201781i	$-0.935327\pi$
$2$	−0.939693	−	1.62760i	−0.664463	−	1.15088i	0.314968	−	0.949102i	$-0.398006\pi$
$3$	−0.326352	+	0.565258i	−0.188419	+	0.326352i	−0.944723	−	0.327868i	$-0.893670\pi$
$3$	−0.326352	+	0.565258i	−0.188419	+	0.326352i	0.756304	+	0.654220i	$0.227003\pi$
$4$	−0.766044	+	1.32683i	−0.383022	+	0.663414i
$5$	−1.76604	−	3.05888i	−0.789799	−	1.36797i	−0.926090	−	0.377303i	$-0.876851\pi$
$5$	−1.76604	−	3.05888i	−0.789799	−	1.36797i	0.136291	−	0.990669i	$-0.456482\pi$
$6$	1.22668			0.500791
$7$	0.418748	−	2.61240i	0.158272	−	0.987396i
$7$	0.418748	−	2.61240i	0.158272	−	0.987396i
$8$	−0.879385			−0.310910
$9$	1.28699	+	2.22913i	0.428996	+	0.743043i
$10$	−3.31908	+	5.74881i	−1.04958	+	1.81793i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	4.41147			1.22352			0.611761	−	0.791042i	$-0.290461\pi$
$13$	4.41147			1.22352			0.611761	+	0.791042i	$0.290461\pi$
$14$	−4.64543	+	1.77330i	−1.24154	+	0.473935i
$15$	2.30541			0.595254
$16$	2.35844	+	4.08494i	0.589610	+	1.02123i
$17$	2.62449	−	4.54574i	0.636531	−	1.10250i	−0.349657	−	0.936878i	$-0.613702\pi$
$17$	2.62449	−	4.54574i	0.636531	−	1.10250i	0.986189	−	0.165627i	$-0.0529647\pi$
$18$	2.41875	−	4.18939i	0.570104	−	0.987450i
$19$	−0.907604	−	1.57202i	−0.208219	−	0.360645i	0.742935	−	0.669364i	$-0.233433\pi$
$19$	−0.907604	−	1.57202i	−0.208219	−	0.360645i	−0.951153	+	0.308719i	$0.900100\pi$
$20$	5.41147			1.21004
$21$	1.34002	+	1.08926i	0.292417	+	0.237697i
$22$	1.87939			0.400686
$23$	3.16637	+	5.48432i	0.660235	+	1.14356i	0.980554	+	0.196250i	$0.0628765\pi$
$23$	3.16637	+	5.48432i	0.660235	+	1.14356i	−0.320319	+	0.947310i	$0.603790\pi$
$24$	0.286989	−	0.497079i	0.0585814	−	0.101466i
$25$	−3.73783	+	6.47410i	−0.747565	+	1.29482i
$26$	−4.14543	−	7.18009i	−0.812986	−	1.40813i
$27$	−3.63816			−0.700163
$28$	3.14543	+	2.55682i	0.594430	+	0.483194i
$29$	1.92127			0.356772			0.178386	−	0.983961i	$-0.442912\pi$
$29$	1.92127			0.356772			0.178386	+	0.983961i	$0.442912\pi$
$30$	−2.16637	−	3.75227i	−0.395524	−	0.685068i
$31$	−0.733956	+	1.27125i	−0.131822	+	0.228323i	−0.924379	−	0.381475i	$-0.875416\pi$
$31$	−0.733956	+	1.27125i	−0.131822	+	0.228323i	0.792557	+	0.609798i	$0.208749\pi$
$32$	3.55303	−	6.15403i	0.628094	−	1.08789i
$33$	−0.326352	−	0.565258i	−0.0568106	−	0.0983988i
$34$	−9.86484			−1.69181
$35$	−8.73055	+	3.33272i	−1.47573	+	0.563333i
$36$	−3.94356			−0.657261
$37$	−2.22668	−	3.85673i	−0.366064	−	0.634042i	0.622882	−	0.782316i	$-0.285962\pi$
$37$	−2.22668	−	3.85673i	−0.366064	−	0.634042i	−0.988946	+	0.148274i	$0.952628\pi$
$38$	−1.70574	+	2.95442i	−0.276707	+	0.479271i
$39$	−1.43969	+	2.49362i	−0.230535	+	0.399299i
$40$	1.55303	+	2.68993i	0.245556	+	0.425316i
$41$	0.283119			0.0442157			0.0221078	−	0.999756i	$-0.492962\pi$
$41$	0.283119			0.0442157			0.0221078	+	0.999756i	$0.492962\pi$
$42$	0.513671	−	3.20459i	0.0792611	−	0.494478i
$43$	−3.41147			−0.520245			−0.260122	−	0.965576i	$-0.583763\pi$
$43$	−3.41147			−0.520245			−0.260122	+	0.965576i	$0.583763\pi$
$44$	−0.766044	−	1.32683i	−0.115486	−	0.200027i
$45$	4.54576	−	7.87349i	0.677642	−	1.17371i
$46$	5.95084	−	10.3072i	0.877403	−	1.51971i
$47$	2.27719	+	3.94421i	0.332162	+	0.575322i	0.982936	−	0.183950i	$-0.0588886\pi$
$47$	2.27719	+	3.94421i	0.332162	+	0.575322i	−0.650773	+	0.759272i	$0.725555\pi$
$48$	−3.07873			−0.444376
$49$	−6.64930	−	2.18788i	−0.949900	−	0.312554i
$50$	14.0496			1.98692
$51$	1.71301	+	2.96702i	0.239870	+	0.415466i
$52$	−3.37939	+	5.85327i	−0.468636	+	0.811702i
$53$	3.61721	−	6.26519i	0.496862	−	0.860591i	−0.503131	−	0.864210i	$-0.667819\pi$
$53$	3.61721	−	6.26519i	0.496862	−	0.860591i	0.999993	+	0.00361947i	$0.00115212\pi$
$54$	3.41875	+	5.92145i	0.465233	+	0.805807i
$55$	3.53209			0.476267
$56$	−0.368241	+	2.29731i	−0.0492083	+	0.306991i
$57$	1.18479			0.156930
$58$	−1.80541	−	3.12706i	−0.237062	−	0.410603i
$59$	−4.76991	+	8.26173i	−0.620990	+	1.07559i	0.368312	+	0.929702i	$0.379936\pi$
$59$	−4.76991	+	8.26173i	−0.620990	+	1.07559i	−0.989302	+	0.145884i	$0.953397\pi$
$60$	−1.76604	+	3.05888i	−0.227995	+	0.394900i
$61$	0.573978	+	0.994159i	0.0734903	+	0.127289i	0.900429	−	0.435003i	$-0.143253\pi$
$61$	0.573978	+	0.994159i	0.0734903	+	0.127289i	−0.826938	+	0.562292i	$0.809920\pi$
$62$	2.75877			0.350364
$63$	6.36231	−	2.42869i	0.801576	−	0.305986i
$64$	−3.92127			−0.490159
$65$	−7.79086	−	13.4942i	−0.966337	−	1.67375i
$66$	−0.613341	+	1.06234i	−0.0754970	+	0.130765i
$67$	0.347296	−	0.601535i	0.0424290	−	0.0734892i	−0.844031	−	0.536294i	$-0.819824\pi$
$67$	0.347296	−	0.601535i	0.0424290	−	0.0734892i	0.886460	+	0.462805i	$0.153157\pi$
$68$	4.02094	+	6.96448i	0.487611	+	0.844567i
$69$	−4.13341			−0.497604
$70$	13.6284	+	11.0781i	1.62890	+	1.32408i
$71$	9.46110			1.12283			0.561413	−	0.827536i	$-0.310258\pi$
$71$	9.46110			1.12283			0.561413	+	0.827536i	$0.310258\pi$
$72$	−1.13176	−	1.96026i	−0.133379	−	0.231019i
$73$	−1.17365	+	2.03282i	−0.137365	+	0.237923i	−0.926498	−	0.376299i	$-0.877197\pi$
$73$	−1.17365	+	2.03282i	−0.137365	+	0.237923i	0.789133	+	0.614222i	$0.210530\pi$
$74$	−4.18479	+	7.24827i	−0.486472	+	0.842595i
$75$	−2.43969	−	4.22567i	−0.281711	−	0.487939i
$76$	2.78106			0.319009
$77$	2.05303	+	1.66885i	0.233965	+	0.190183i
$78$	5.41147			0.612729
$79$	6.20961	+	10.7554i	0.698635	+	1.21007i	0.968940	+	0.247297i	$0.0795424\pi$
$79$	6.20961	+	10.7554i	0.698635	+	1.21007i	−0.270304	+	0.962775i	$0.587124\pi$
$80$	8.33022	−	14.4284i	0.931347	−	1.61314i
$81$	−2.67365	+	4.63089i	−0.297072	+	0.514544i
$82$	−0.266044	−	0.460802i	−0.0293797	−	0.0508871i
$83$	−11.3327			−1.24393			−0.621965	−	0.783045i	$-0.713666\pi$
$83$	−11.3327			−1.24393			−0.621965	+	0.783045i	$0.713666\pi$
$84$	−2.47178	+	0.943555i	−0.269693	+	0.102950i
$85$	−18.5398			−2.01093
$86$	3.20574	+	5.55250i	0.345684	+	0.598741i
$87$	−0.627011	+	1.08602i	−0.0672227	+	0.116433i
$88$	0.439693	−	0.761570i	0.0468714	−	0.0811836i
$89$	1.73396	+	3.00330i	0.183799	+	0.318349i	0.943171	−	0.332307i	$-0.107827\pi$
$89$	1.73396	+	3.00330i	0.183799	+	0.318349i	−0.759372	+	0.650656i	$0.774494\pi$
$90$	−17.0865			−1.80107
$91$	1.84730	−	11.5245i	0.193649	−	1.20810i
$92$	−9.70233			−1.01154
$93$	−0.479055	−	0.829748i	−0.0496757	−	0.0860409i
$94$	4.27972	−	7.41268i	0.441419	−	0.764560i
$95$	−3.20574	+	5.55250i	−0.328902	+	0.569674i
$96$	2.31908	+	4.01676i	0.236690	+	0.409959i
$97$	15.3473			1.55828			0.779141	−	0.626849i	$-0.215656\pi$
$97$	15.3473			1.55828			0.779141	+	0.626849i	$0.215656\pi$
$98$	2.68732	+	12.8783i	0.271460	+	1.30090i
$99$	−2.57398			−0.258695
$100$	−5.72668	−	9.91890i	−0.572668	−	0.991890i
$101$	−3.35117	+	5.80439i	−0.333454	+	0.577558i	−0.983187	−	0.182604i	$-0.941547\pi$
$101$	−3.35117	+	5.80439i	−0.333454	+	0.577558i	0.649733	+	0.760163i	$0.274881\pi$
$102$	3.21941	−	5.57618i	0.318769	−	0.552124i
$103$	−1.12449	−	1.94767i	−0.110799	−	0.191909i	0.805294	−	0.592876i	$-0.202008\pi$
$103$	−1.12449	−	1.94767i	−0.110799	−	0.191909i	−0.916093	+	0.400967i	$0.868674\pi$
$104$	−3.87939			−0.380405
$105$	0.965385	−	6.02265i	0.0942119	−	0.587751i
$106$	−13.5963			−1.32059
$107$	5.76604	+	9.98708i	0.557425	+	0.965488i	0.997710	+	0.0676300i	$0.0215438\pi$
$107$	5.76604	+	9.98708i	0.557425	+	0.965488i	−0.440286	+	0.897858i	$0.645123\pi$
$108$	2.78699	−	4.82721i	0.268178	−	0.464498i
$109$	5.99273	−	10.3797i	0.573999	−	0.994196i	−0.422151	−	0.906526i	$-0.638725\pi$
$109$	5.99273	−	10.3797i	0.573999	−	0.994196i	0.996150	−	0.0876698i	$-0.0279420\pi$
$110$	−3.31908	−	5.74881i	−0.316462	−	0.548128i
$111$	2.90673			0.275894
$112$	11.6591	−	4.45064i	1.10168	−	0.420546i
$113$	5.00774			0.471089			0.235544	−	0.971864i	$-0.424313\pi$
$113$	5.00774			0.471089			0.235544	+	0.971864i	$0.424313\pi$
$114$	−1.11334	−	1.92836i	−0.104274	−	0.180608i
$115$	11.1839	−	19.3711i	1.04291	−	1.80637i
$116$	−1.47178	+	2.54920i	−0.136651	+	0.236687i
$117$	5.67752	+	9.83375i	0.524887	+	0.909131i
$118$	17.9290			1.65050
$119$	−10.7763	−	8.75973i	−0.987863	−	0.803003i
$120$	−2.02734			−0.185070
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	1.07873	−	1.86841i	0.0976632	−	0.169158i
$123$	−0.0923963	+	0.160035i	−0.00833109	+	0.0144299i
$124$	−1.12449	−	1.94767i	−0.100982	−	0.174906i
$125$	8.74422			0.782107
$126$	−9.93154	−	8.07305i	−0.884772	−	0.719204i
$127$	−14.2344			−1.26310			−0.631550	−	0.775335i	$-0.717581\pi$
$127$	−14.2344			−1.26310			−0.631550	+	0.775335i	$0.717581\pi$
$128$	−3.42127	−	5.92582i	−0.302401	−	0.523774i
$129$	1.11334	−	1.92836i	0.0980242	−	0.169783i
$130$	−14.6420	+	25.3607i	−1.28419	+	2.22428i
$131$	−2.55690	−	4.42869i	−0.223398	−	0.386936i	0.732440	−	0.680832i	$-0.238382\pi$
$131$	−2.55690	−	4.42869i	−0.223398	−	0.386936i	−0.955838	+	0.293896i	$0.905048\pi$
$132$	1.00000			0.0870388
$133$	−4.48680	+	1.71275i	−0.389055	+	0.148514i
$134$	−1.30541			−0.112770
$135$	6.42514	+	11.1287i	0.552988	+	0.957804i
$136$	−2.30793	+	3.99746i	−0.197904	+	0.342779i
$137$	−9.85369	+	17.0671i	−0.841858	+	1.45814i	0.0464645	+	0.998920i	$0.485205\pi$
$137$	−9.85369	+	17.0671i	−0.841858	+	1.45814i	−0.888322	+	0.459221i	$0.848129\pi$
$138$	3.88413	+	6.72752i	0.330639	+	0.572684i
$139$	−5.28581			−0.448336			−0.224168	−	0.974550i	$-0.571966\pi$
$139$	−5.28581			−0.448336			−0.224168	+	0.974550i	$0.571966\pi$
$140$	2.26604	−	14.1370i	0.191516	−	1.19479i
$141$	−2.97266			−0.250343
$142$	−8.89053	−	15.3988i	−0.746077	−	1.29224i
$143$	−2.20574	+	3.82045i	−0.184453	+	0.319482i
$144$	−6.07057	+	10.5145i	−0.505881	+	0.876212i
$145$	−3.39306	−	5.87695i	−0.281778	−	0.488054i
$146$	4.41147			0.365096
$147$	3.40673	−	3.04455i	0.280982	−	0.251110i
$148$	6.82295			0.560843
$149$	8.50774	+	14.7358i	0.696981	+	1.20721i	0.969508	+	0.245059i	$0.0788073\pi$
$149$	8.50774	+	14.7358i	0.696981	+	1.20721i	−0.272527	+	0.962148i	$0.587859\pi$
$150$	−4.58512	+	7.94166i	−0.374374	+	0.648434i
$151$	−0.651359	+	1.12819i	−0.0530069	+	0.0918106i	−0.891311	−	0.453392i	$-0.850214\pi$
$151$	−0.651359	+	1.12819i	−0.0530069	+	0.0918106i	0.838304	+	0.545202i	$0.183547\pi$
$152$	0.798133	+	1.38241i	0.0647372	+	0.112128i
$153$	13.5107			1.09228
$154$	0.786989	−	4.90971i	0.0634174	−	0.395636i
$155$	5.18479			0.416453
$156$	−2.20574	−	3.82045i	−0.176600	−	0.305881i
$157$	−6.84730	+	11.8599i	−0.546474	+	0.946520i	0.452039	+	0.891998i	$0.350697\pi$
$157$	−6.84730	+	11.8599i	−0.546474	+	0.946520i	−0.998513	+	0.0545220i	$0.982636\pi$
$158$	11.6702	−	20.2135i	0.928435	−	1.60810i
$159$	2.36097	+	4.08931i	0.187237	+	0.324304i
$160$	−25.0993			−1.98427
$161$	15.6532	−	5.97530i	1.23364	−	0.470919i
$162$	10.0496			0.789573
$163$	−8.20233	−	14.2069i	−0.642456	−	1.11277i	−0.984883	−	0.173222i	$-0.944582\pi$
$163$	−8.20233	−	14.2069i	−0.642456	−	1.11277i	0.342426	−	0.939545i	$-0.388751\pi$
$164$	−0.216881	+	0.375650i	−0.0169356	+	0.0293333i
$165$	−1.15270	+	1.99654i	−0.0897379	+	0.155431i
$166$	10.6493	+	18.4451i	0.826546	+	1.43162i
$167$	−8.24628			−0.638116			−0.319058	−	0.947735i	$-0.603367\pi$
$167$	−8.24628			−0.638116			−0.319058	+	0.947735i	$0.603367\pi$
$168$	−1.17840	−	0.957882i	−0.0909152	−	0.0739022i
$169$	6.46110			0.497008
$170$	17.4217	+	30.1753i	1.33619	+	2.31434i
$171$	2.33615	−	4.04633i	0.178650	−	0.309431i
$172$	2.61334	−	4.52644i	0.199265	−	0.345138i
$173$	−9.61721	−	16.6575i	−0.731183	−	1.26645i	−0.956378	−	0.292132i	$-0.905635\pi$
$173$	−9.61721	−	16.6575i	−0.731183	−	1.26645i	0.225195	−	0.974314i	$-0.427698\pi$
$174$	2.35679			0.178668
$175$	15.3478	+	12.4757i	1.16018	+	0.943076i
$176$	−4.71688			−0.355548
$177$	−3.11334	−	5.39246i	−0.234013	−	0.405322i
$178$	3.25877	−	5.64436i	0.244255	−	0.423062i
$179$	0.663848	−	1.14982i	0.0496183	−	0.0859415i	−0.840150	−	0.542355i	$-0.817533\pi$
$179$	0.663848	−	1.14982i	0.0496183	−	0.0859415i	0.889768	+	0.456413i	$0.150866\pi$
$180$	6.96451	+	12.0629i	0.519104	+	0.899114i
$181$	17.6527			1.31212			0.656058	−	0.754711i	$-0.272223\pi$
$181$	17.6527			1.31212			0.656058	+	0.754711i	$0.272223\pi$
$182$	−20.4932	+	7.82288i	−1.51906	+	0.579871i
$183$	−0.749275			−0.0553880
$184$	−2.78446	−	4.82283i	−0.205273	−	0.355544i
$185$	−7.86484	+	13.6223i	−0.578234	+	1.00153i
$186$	−0.900330	+	1.55942i	−0.0660154	+	0.114342i
$187$	2.62449	+	4.54574i	0.191921	+	0.332418i
$188$	−6.97771			−0.508902
$189$	−1.52347	+	9.50433i	−0.110816	+	0.691338i
$190$	12.0496			0.874172
$191$	−7.77631	−	13.4690i	−0.562674	−	0.974580i	−0.997262	−	0.0739507i	$-0.976439\pi$
$191$	−7.77631	−	13.4690i	−0.562674	−	0.974580i	0.434588	−	0.900629i	$-0.356894\pi$
$192$	1.27972	−	2.21653i	0.0923555	−	0.159964i
$193$	2.60947	−	4.51974i	0.187834	−	0.325338i	−0.756694	−	0.653769i	$-0.773187\pi$
$193$	2.60947	−	4.51974i	0.187834	−	0.325338i	0.944528	+	0.328432i	$0.106520\pi$
$194$	−14.4217	−	24.9792i	−1.03542	−	1.79340i
$195$	10.1702			0.728306
$196$	7.99660	−	7.14647i	0.571185	−	0.510462i
$197$	−4.61856			−0.329058			−0.164529	−	0.986372i	$-0.552610\pi$
$197$	−4.61856			−0.329058			−0.164529	+	0.986372i	$0.552610\pi$
$198$	2.41875	+	4.18939i	0.171893	+	0.297727i
$199$	3.02481	−	5.23913i	0.214423	−	0.371392i	−0.738671	−	0.674067i	$-0.764546\pi$
$199$	3.02481	−	5.23913i	0.214423	−	0.371392i	0.953094	+	0.302674i	$0.0978794\pi$
$200$	3.28699	−	5.69323i	0.232425	−	0.402572i
$201$	0.226682	+	0.392624i	0.0159889	+	0.0276936i
$202$	12.5963			0.886270
$203$	0.804530	−	5.01914i	0.0564669	−	0.352275i
$204$	−5.24897			−0.367501
$205$	−0.500000	−	0.866025i	−0.0349215	−	0.0604858i
$206$	−2.11334	+	3.66041i	−0.147243	+	0.255033i
$207$	−8.15018	+	14.1165i	−0.566476	+	0.981166i
$208$	10.4042	+	18.0206i	0.721401	+	1.24950i
$209$	1.81521			0.125561
$210$	−10.7096	+	4.08819i	−0.739033	+	0.282112i
$211$	8.69459			0.598560			0.299280	−	0.954165i	$-0.403253\pi$
$211$	8.69459			0.598560			0.299280	+	0.954165i	$0.403253\pi$
$212$	5.54189	+	9.59883i	0.380619	+	0.659251i
$213$	−3.08765	+	5.34796i	−0.211562	+	0.366436i
$214$	10.8366	−	18.7696i	0.740776	−	1.28306i
$215$	6.02481	+	10.4353i	0.410889	+	0.711681i
$216$	3.19934			0.217688
$217$	3.01367	+	2.44972i	0.204581	+	0.166298i
$218$	−22.5253			−1.52560
$219$	−0.766044	−	1.32683i	−0.0517645	−	0.0896587i
$220$	−2.70574	+	4.68647i	−0.182421	+	0.315962i
$221$	11.5778	−	20.0534i	0.778810	−	1.34894i
$222$	−2.73143	−	4.73097i	−0.183322	−	0.317522i
$223$	−0.221629			−0.0148414			−0.00742069	−	0.999972i	$-0.502362\pi$
$223$	−0.221629			−0.0148414			−0.00742069	+	0.999972i	$0.502362\pi$
$224$	−14.5890	−	11.8589i	−0.974768	−	0.792359i
$225$	−19.2422			−1.28281
$226$	−4.70574	−	8.15058i	−0.313021	−	0.542168i
$227$	4.84982	−	8.40014i	0.321894	−	0.557537i	−0.658985	−	0.752156i	$-0.729014\pi$
$227$	4.84982	−	8.40014i	0.321894	−	0.557537i	0.980879	+	0.194619i	$0.0623472\pi$
$228$	−0.907604	+	1.57202i	−0.0601075	+	0.104109i
$229$	−11.8473	−	20.5201i	−0.782891	−	1.35601i	−0.930251	−	0.366925i	$-0.880411\pi$
$229$	−11.8473	−	20.5201i	−0.782891	−	1.35601i	0.147359	−	0.989083i	$-0.452923\pi$
$230$	−42.0378			−2.77189
$231$	−1.61334	+	0.615862i	−0.106150	+	0.0405207i
$232$	−1.68954			−0.110924
$233$	−10.4436	−	18.0888i	−0.684181	−	1.18504i	−0.973694	−	0.227861i	$-0.926827\pi$
$233$	−10.4436	−	18.0888i	−0.684181	−	1.18504i	0.289513	−	0.957174i	$-0.406507\pi$
$234$	10.6702	−	18.4814i	0.697536	−	1.20817i
$235$	8.04323	−	13.9313i	0.524683	−	0.908777i
$236$	−7.30793	−	12.6577i	−0.475706	−	0.823947i
$237$	−8.10607			−0.526546
$238$	−4.13088	+	25.7709i	−0.267765	+	1.67048i
$239$	15.0300			0.972212			0.486106	−	0.873900i	$-0.338417\pi$
$239$	15.0300			0.972212			0.486106	+	0.873900i	$0.338417\pi$
$240$	5.43717	+	9.41745i	0.350968	+	0.607894i
$241$	−14.7699	+	25.5822i	−0.951414	+	1.64790i	−0.209045	+	0.977906i	$0.567035\pi$
$241$	−14.7699	+	25.5822i	−0.951414	+	1.64790i	−0.742369	+	0.669991i	$0.766298\pi$
$242$	−0.939693	+	1.62760i	−0.0604057	+	0.104626i
$243$	−7.20233	−	12.4748i	−0.462030	−	0.800259i
$244$	−1.75877			−0.112594
$245$	5.05051	+	24.2033i	0.322665	+	1.54629i
$246$	0.347296			0.0221428
$247$	−4.00387	−	6.93491i	−0.254760	−	0.441258i
$248$	0.645430	−	1.11792i	0.0409848	−	0.0709878i
$249$	3.69846	−	6.40593i	0.234381	−	0.405959i
$250$	−8.21688	−	14.2321i	−0.519681	−	0.900114i
$251$	3.77063			0.238000			0.119000	−	0.992894i	$-0.462031\pi$
$251$	3.77063			0.238000			0.119000	+	0.992894i	$0.462031\pi$
$252$	−1.65136	+	10.3022i	−0.104026	+	0.648976i
$253$	−6.33275			−0.398136
$254$	13.3760	+	23.1679i	0.839284	+	1.45368i
$255$	6.05051	−	10.4798i	0.378897	−	0.656270i
$256$	−10.3512	+	17.9287i	−0.646948	+	1.12055i
$257$	4.33022	+	7.50016i	0.270112	+	0.467847i	0.968890	−	0.247491i	$-0.0796060\pi$
$257$	4.33022	+	7.50016i	0.270112	+	0.467847i	−0.698778	+	0.715338i	$0.746273\pi$
$258$	−4.18479			−0.260534
$259$	−11.0077	+	4.20199i	−0.683988	+	0.261099i
$260$	23.8726			1.48051
$261$	2.47266	+	4.28277i	0.153054	+	0.265097i
$262$	−4.80541	+	8.32321i	−0.296879	+	0.514210i
$263$	2.91740	−	5.05309i	0.179895	−	0.311587i	−0.761950	−	0.647636i	$-0.775758\pi$
$263$	2.91740	−	5.05309i	0.179895	−	0.311587i	0.941844	+	0.336049i	$0.109091\pi$
$264$	0.286989	+	0.497079i	0.0176630	+	0.0305931i
$265$	−25.5526			−1.56969
$266$	7.00387	+	5.69323i	0.429435	+	0.349074i
$267$	−2.26352			−0.138525
$268$	0.532089	+	0.921605i	0.0325025	+	0.0562960i
$269$	10.9907	−	19.0364i	0.670113	−	1.16067i	−0.307759	−	0.951464i	$-0.599579\pi$
$269$	10.9907	−	19.0364i	0.670113	−	1.16067i	0.977872	−	0.209205i	$-0.0670876\pi$
$270$	12.0753	−	20.9151i	0.734881	−	1.27285i
$271$	−4.92602	−	8.53212i	−0.299235	−	0.518289i	0.676727	−	0.736235i	$-0.263398\pi$
$271$	−4.92602	−	8.53212i	−0.299235	−	0.518289i	−0.975961	+	0.217945i	$0.930065\pi$
$272$	24.7588			1.50122
$273$	5.91147	+	4.80526i	0.357779	+	0.290827i
$274$	37.0378			2.23753
$275$	−3.73783	−	6.47410i	−0.225399	−	0.390403i
$276$	3.16637	−	5.48432i	0.190593	−	0.330117i
$277$	−11.8195	+	20.4721i	−0.710168	+	1.23005i	0.254626	+	0.967040i	$0.418048\pi$
$277$	−11.8195	+	20.4721i	−0.710168	+	1.23005i	−0.964794	+	0.263007i	$0.915286\pi$
$278$	4.96703	+	8.60315i	0.297903	+	0.515983i
$279$	−3.77837			−0.226205
$280$	7.67752	−	2.93075i	0.458819	−	0.175146i
$281$	16.2713			0.970662			0.485331	−	0.874331i	$-0.338699\pi$
$281$	16.2713			0.970662			0.485331	+	0.874331i	$0.338699\pi$
$282$	2.79339	+	4.83829i	0.166344	+	0.288116i
$283$	−8.49912	+	14.7209i	−0.505220	+	0.875067i	0.494761	+	0.869029i	$0.335255\pi$
$283$	−8.49912	+	14.7209i	−0.505220	+	0.875067i	−0.999982	+	0.00603853i	$0.998078\pi$
$284$	−7.24763	+	12.5533i	−0.430067	+	0.744899i
$285$	−2.09240	−	3.62414i	−0.123943	−	0.214675i
$286$	8.29086			0.490249
$287$	0.118555	−	0.739620i	0.00699810	−	0.0436584i
$288$	18.2909			1.07780
$289$	−5.27584	−	9.13803i	−0.310344	−	0.537531i
$290$	−6.37686	+	11.0450i	−0.374462	+	0.648587i
$291$	−5.00862	+	8.67518i	−0.293610	+	0.508548i
$292$	−1.79813	−	3.11446i	−0.105228	−	0.182260i
$293$	−13.7784			−0.804941			−0.402471	−	0.915433i	$-0.631848\pi$
$293$	−13.7784			−0.804941			−0.402471	+	0.915433i	$0.631848\pi$
$294$	−8.15657	−	2.68383i	−0.475701	−	0.156524i
$295$	33.6955			1.96183
$296$	1.95811	+	3.39155i	0.113813	+	0.197130i
$297$	1.81908	−	3.15074i	0.105554	−	0.182824i
$298$	15.9893	−	27.6943i	0.926237	−	1.60429i
$299$	13.9684	+	24.1939i	0.807812	+	1.39917i
$300$	7.47565			0.431607
$301$	−1.42855	+	8.91215i	−0.0823402	+	0.513688i
$302$	2.44831			0.140884
$303$	−2.18732	−	3.78855i	−0.125658	−	0.217646i
$304$	4.28106	−	7.41501i	0.245536	−	0.425280i
$305$	2.02734	−	3.51146i	0.116085	−	0.201065i
$306$	−12.6959	−	21.9900i	−0.725778	−	1.25709i
$307$	−11.6159			−0.662953			−0.331476	−	0.943464i	$-0.607547\pi$
$307$	−11.6159			−0.662953			−0.331476	+	0.943464i	$0.607547\pi$
$308$	−3.78699	+	1.44561i	−0.215784	+	0.0823713i
$309$	1.46791			0.0835065
$310$	−4.87211	−	8.43874i	−0.276717	−	0.479288i
$311$	−1.72416	+	2.98632i	−0.0977679	+	0.169339i	−0.910760	−	0.412935i	$-0.864504\pi$
$311$	−1.72416	+	2.98632i	−0.0977679	+	0.169339i	0.812993	+	0.582274i	$0.197837\pi$
$312$	1.26604	−	2.19285i	0.0716757	−	0.124146i
$313$	9.71095	+	16.8199i	0.548895	+	0.950715i	0.998351	+	0.0574119i	$0.0182848\pi$
$313$	9.71095	+	16.8199i	0.548895	+	0.950715i	−0.449455	+	0.893303i	$0.648382\pi$
$314$	25.7374			1.45245
$315$	−18.6652	−	15.1724i	−1.05166	−	0.854866i
$316$	−19.0273			−1.07037
$317$	16.4081	+	28.4196i	0.921569	+	1.59620i	0.796988	+	0.603995i	$0.206425\pi$
$317$	16.4081	+	28.4196i	0.921569	+	1.59620i	0.124581	+	0.992209i	$0.460241\pi$
$318$	4.43717	−	7.68540i	0.248824	−	0.430976i
$319$	−0.960637	+	1.66387i	−0.0537854	+	0.0931590i
$320$	6.92514	+	11.9947i	0.387127	+	0.670524i
$321$	−7.52704			−0.420118
$322$	−24.4345	−	19.8621i	−1.36168	−	1.10687i
$323$	−9.52797			−0.530150
$324$	−4.09627	−	7.09494i	−0.227570	−	0.394163i
$325$	−16.4893	+	28.5603i	−0.914663	+	1.58424i
$326$	−15.4153	+	26.7002i	−0.853777	+	1.47879i
$327$	3.91147	+	6.77487i	0.216305	+	0.374651i
$328$	−0.248970			−0.0137471
$329$	11.2574	−	4.29731i	0.620642	−	0.236918i
$330$	4.33275			0.238510
$331$	3.18004	+	5.50800i	0.174791	+	0.302747i	0.940089	−	0.340929i	$-0.110742\pi$
$331$	3.18004	+	5.50800i	0.174791	+	0.302747i	−0.765298	+	0.643676i	$0.777408\pi$
$332$	8.68139	−	15.0366i	0.476453	−	0.825241i
$333$	5.73143	−	9.92713i	0.314080	−	0.544003i
$334$	7.74897	+	13.4216i	0.424005	+	0.734398i
$335$	−2.45336			−0.134042
$336$	−1.28921	+	8.04287i	−0.0703322	+	0.438775i
$337$	−15.5449			−0.846784			−0.423392	−	0.905947i	$-0.639161\pi$
$337$	−15.5449			−0.846784			−0.423392	+	0.905947i	$0.639161\pi$
$338$	−6.07145	−	10.5161i	−0.330243	−	0.571998i
$339$	−1.63429	+	2.83067i	−0.0887622	+	0.153741i
$340$	14.2023	−	24.5992i	0.770230	−	1.33408i
$341$	−0.733956	−	1.27125i	−0.0397459	−	0.0688420i
$342$	−8.78106			−0.474825
$343$	−8.50000	+	16.4545i	−0.458957	+	0.888459i
$344$	3.00000			0.161749
$345$	7.29978	+	12.6436i	0.393007	+	0.680708i
$346$	−18.0744	+	31.3059i	−0.971688	+	1.68301i
$347$	9.86231	−	17.0820i	0.529437	−	0.917011i	−0.469974	−	0.882680i	$-0.655737\pi$
$347$	9.86231	−	17.0820i	0.529437	−	0.917011i	0.999411	−	0.0343308i	$-0.0109300\pi$
$348$	−0.960637	−	1.66387i	−0.0514956	−	0.0891929i
$349$	−5.79385			−0.310138			−0.155069	−	0.987904i	$-0.549560\pi$
$349$	−5.79385			−0.310138			−0.155069	+	0.987904i	$0.549560\pi$
$350$	5.88326	−	36.7033i	0.314473	−	1.96187i
$351$	−16.0496			−0.856666
$352$	3.55303	+	6.15403i	0.189377	+	0.328011i
$353$	−16.5831	+	28.7227i	−0.882627	+	1.52876i	−0.0342183	+	0.999414i	$0.510894\pi$
$353$	−16.5831	+	28.7227i	−0.882627	+	1.52876i	−0.848409	+	0.529341i	$0.822439\pi$
$354$	−5.85117	+	10.1345i	−0.310986	+	0.538644i
$355$	−16.7087	−	28.9404i	−0.886807	−	1.53600i
$356$	−5.31315			−0.281596
$357$	8.46838	−	3.23264i	0.448194	−	0.171089i
$358$	−2.49525			−0.131878
$359$	−2.10488	−	3.64577i	−0.111092	−	0.192416i	0.805119	−	0.593113i	$-0.202101\pi$
$359$	−2.10488	−	3.64577i	−0.111092	−	0.192416i	−0.916211	+	0.400697i	$0.868768\pi$
$360$	−3.99747	+	6.92383i	−0.210685	+	0.364918i
$361$	7.85251	−	13.6009i	0.413290	−	0.715839i
$362$	−16.5881	−	28.7315i	−0.871852	−	1.51009i
$363$	0.652704			0.0342581
$364$	13.8760	+	11.2794i	0.727299	+	0.591199i
$365$	8.29086			0.433963
$366$	0.704088	+	1.21952i	0.0368033	+	0.0637451i
$367$	9.71941	−	16.8345i	0.507349	−	0.878754i	−0.492615	−	0.870247i	$-0.663959\pi$
$367$	9.71941	−	16.8345i	0.507349	−	0.878754i	0.999964	−	0.00850673i	$-0.00270781\pi$
$368$	−14.9354	+	25.8689i	−0.778562	+	1.34851i
$369$	0.364370	+	0.631108i	0.0189684	+	0.0328542i
$370$	29.5621			1.53686
$371$	−14.8525	−	12.0732i	−0.771104	−	0.626807i
$372$	1.46791			0.0761076
$373$	−6.35710	−	11.0108i	−0.329158	−	0.570118i	0.653187	−	0.757197i	$-0.273432\pi$
$373$	−6.35710	−	11.0108i	−0.329158	−	0.570118i	−0.982345	+	0.187078i	$0.940098\pi$
$374$	4.93242	−	8.54320i	0.255049	−	0.441758i
$375$	−2.85369	+	4.94274i	−0.147364	+	0.255242i
$376$	−2.00253	−	3.46848i	−0.103272	−	0.178873i
$377$	8.47565			0.436518
$378$	16.9008	−	6.45155i	0.869283	−	0.331832i
$379$	−22.8111			−1.17173			−0.585863	−	0.810410i	$-0.699245\pi$
$379$	−22.8111			−1.17173			−0.585863	+	0.810410i	$0.699245\pi$
$380$	−4.91147	−	8.50692i	−0.251953	−	0.436396i
$381$	4.64543	−	8.04612i	0.237993	−	0.412215i
$382$	−14.6147	+	25.3134i	−0.747752	+	1.29515i
$383$	−4.14930	−	7.18680i	−0.212019	−	0.367228i	0.740327	−	0.672247i	$-0.234671\pi$
$383$	−4.14930	−	7.18680i	−0.212019	−	0.367228i	−0.952346	+	0.305019i	$0.901337\pi$
$384$	4.46616			0.227913
$385$	1.47906	−	9.22724i	0.0753796	−	0.470264i
$386$	−9.80840			−0.499234
$387$	−4.39053	−	7.60462i	−0.223183	−	0.386565i
$388$	−11.7567	+	20.3632i	−0.596857	+	1.03379i
$389$	−5.69981	+	9.87236i	−0.288992	+	0.500548i	−0.973569	−	0.228392i	$-0.926653\pi$
$389$	−5.69981	+	9.87236i	−0.288992	+	0.500548i	0.684578	+	0.728940i	$0.259987\pi$
$390$	−9.55690	−	16.5530i	−0.483933	−	0.838196i
$391$	33.2404			1.68104
$392$	5.84730	+	1.92399i	0.295333	+	0.0971760i
$393$	3.33780			0.168370
$394$	4.34002	+	7.51714i	0.218647	+	0.378708i
$395$	21.9329	−	37.9889i	1.10356	−	1.91143i
$396$	1.97178	−	3.41523i	0.0990857	−	0.171622i
$397$	−3.29086	−	5.69994i	−0.165163	−	0.286072i	0.771550	−	0.636169i	$-0.219482\pi$
$397$	−3.29086	−	5.69994i	−0.165163	−	0.286072i	−0.936713	+	0.350097i	$0.886149\pi$
$398$	−11.3696			−0.569906
$399$	0.496130	−	3.09516i	0.0248375	−	0.154952i
$400$	−35.2618			−1.76309
$401$	−2.09492	−	3.62851i	−0.104615	−	0.181199i	0.808966	−	0.587856i	$-0.200028\pi$
$401$	−2.09492	−	3.62851i	−0.104615	−	0.181199i	−0.913581	+	0.406657i	$0.866695\pi$
$402$	0.426022	−	0.737892i	0.0212480	−	0.0368027i
$403$	−3.23783	+	5.60808i	−0.161288	+	0.279358i
$404$	−5.13429	−	8.89284i	−0.255440	−	0.442435i
$405$	18.8871			0.938509
$406$	−8.92514	+	3.40700i	−0.442947	+	0.169087i
$407$	4.45336			0.220745
$408$	−1.50640	−	2.60916i	−0.0745777	−	0.129172i
$409$	−0.386659	+	0.669713i	−0.0191191	+	0.0331152i	−0.875427	−	0.483351i	$-0.839419\pi$
$409$	−0.386659	+	0.669713i	−0.0191191	+	0.0331152i	0.856308	+	0.516466i	$0.172753\pi$
$410$	−0.939693	+	1.62760i	−0.0464081	+	0.0803812i
$411$	−6.43154	−	11.1398i	−0.317245	−	0.549484i
$412$	3.44562			0.169754
$413$	19.5856	+	15.9205i	0.963744	+	0.783398i
$414$	30.6346			1.50561
$415$	20.0141	+	34.6655i	0.982455	+	1.70166i
$416$	15.6741	−	27.1484i	0.768487	−	1.33106i
$417$	1.72503	−	2.98784i	0.0844752	−	0.146315i
$418$	−1.70574	−	2.95442i	−0.0834303	−	0.144506i
$419$	13.7547			0.671959			0.335979	−	0.941869i	$-0.390933\pi$
$419$	13.7547			0.671959			0.335979	+	0.941869i	$0.390933\pi$
$420$	7.25150	+	5.89452i	0.353837	+	0.287623i
$421$	−5.80571			−0.282953			−0.141477	−	0.989942i	$-0.545185\pi$
$421$	−5.80571			−0.282953			−0.141477	+	0.989942i	$0.545185\pi$
$422$	−8.17024	−	14.1513i	−0.397721	−	0.688873i
$423$	−5.86143	+	10.1523i	−0.284993	+	0.493622i
$424$	−3.18092	+	5.50952i	−0.154479	+	0.267566i
$425$	19.6197	+	33.9824i	0.951697	+	1.64839i
$426$	11.6058			0.562301
$427$	2.83750	−	1.08316i	0.137316	−	0.0524178i
$428$	−17.6682			−0.854024
$429$	−1.43969	−	2.49362i	−0.0695090	−	0.120393i
$430$	11.3229	−	19.6119i	0.546041	−	0.945771i
$431$	9.00299	−	15.5936i	0.433659	−	0.751119i	−0.563526	−	0.826098i	$-0.690556\pi$
$431$	9.00299	−	15.5936i	0.433659	−	0.751119i	0.997185	+	0.0749789i	$0.0238889\pi$
$432$	−8.58037	−	14.8616i	−0.412823	−	0.715031i
$433$	2.34049			0.112477			0.0562384	−	0.998417i	$-0.482089\pi$
$433$	2.34049			0.112477			0.0562384	+	0.998417i	$0.482089\pi$
$434$	1.15523	−	7.20702i	0.0554528	−	0.345948i
$435$	4.42932			0.212370
$436$	9.18139	+	15.9026i	0.439709	+	0.761598i
$437$	5.74763	−	9.95518i	0.274946	−	0.476221i
$438$	−1.43969	+	2.49362i	−0.0687912	+	0.119150i
$439$	20.0167	+	34.6699i	0.955343	+	1.65470i	0.733581	+	0.679602i	$0.237848\pi$
$439$	20.0167	+	34.6699i	0.955343	+	1.65470i	0.221762	+	0.975101i	$0.428819\pi$
$440$	−3.10607			−0.148076
$441$	−3.68051	−	17.6379i	−0.175262	−	0.839901i
$442$	−43.5185			−2.06996
$443$	−9.48798	−	16.4337i	−0.450787	−	0.780787i	0.547648	−	0.836709i	$-0.315523\pi$
$443$	−9.48798	−	16.4337i	−0.450787	−	0.780787i	−0.998435	+	0.0559223i	$0.982190\pi$
$444$	−2.22668	+	3.85673i	−0.105674	+	0.183032i
$445$	6.12449	−	10.6079i	0.290328	−	0.502864i
$446$	0.208263	+	0.360723i	0.00986155	+	0.0170807i
$447$	−11.1061			−0.525299
$448$	−1.64203	+	10.2439i	−0.0775784	+	0.483981i
$449$	−31.5371			−1.48833			−0.744165	−	0.667996i	$-0.767152\pi$
$449$	−31.5371			−1.48833			−0.744165	+	0.667996i	$0.767152\pi$
$450$	18.0817	+	31.3185i	0.852380	+	1.47637i
$451$	−0.141559	+	0.245188i	−0.00666577	+	0.0115454i
$452$	−3.83615	+	6.64441i	−0.180437	+	0.312527i
$453$	−0.425145	−	0.736372i	−0.0199750	−	0.0345978i
$454$	−18.2294			−0.855547
$455$	−38.5146	+	14.7022i	−1.80559	+	0.689250i
$456$	−1.04189			−0.0487909
$457$	−5.80928	−	10.0620i	−0.271747	−	0.470679i	0.697563	−	0.716524i	$-0.254268\pi$
$457$	−5.80928	−	10.0620i	−0.271747	−	0.470679i	−0.969309	+	0.245845i	$0.920935\pi$
$458$	−22.2656	+	38.5652i	−1.04040	+	1.80203i
$459$	−9.54829	+	16.5381i	−0.445676	+	0.771933i
$460$	17.1348	+	29.6783i	0.798912	+	1.38376i
$461$	−12.9786			−0.604476			−0.302238	−	0.953233i	$-0.597734\pi$
$461$	−12.9786			−0.604476			−0.302238	+	0.953233i	$0.597734\pi$
$462$	2.51842	+	2.04715i	0.117167	+	0.0952418i
$463$	35.3705			1.64381			0.821904	−	0.569626i	$-0.192912\pi$
$463$	35.3705			1.64381			0.821904	+	0.569626i	$0.192912\pi$
$464$	4.53121	+	7.84829i	0.210356	+	0.364348i
$465$	−1.69207	+	2.93075i	−0.0784677	+	0.135910i
$466$	−19.6275	+	33.9958i	−0.909225	+	1.57482i
$467$	19.9329	+	34.5248i	0.922384	+	1.59762i	0.795715	+	0.605671i	$0.207095\pi$
$467$	19.9329	+	34.5248i	0.922384	+	1.59762i	0.126669	+	0.991945i	$0.459572\pi$
$468$	−17.3969			−0.804173
$469$	−1.42602	−	1.15917i	−0.0658476	−	0.0535255i
$470$	−30.2327			−1.39453
$471$	−4.46926	−	7.74098i	−0.205932	−	0.356685i
$472$	4.19459	−	7.26525i	0.193072	−	0.334410i
$473$	1.70574	−	2.95442i	0.0784299	−	0.135845i
$474$	7.61721	+	13.1934i	0.349870	+	0.605993i
$475$	13.5699			0.622628
$476$	19.8778	−	7.58797i	0.911097	−	0.347794i
$477$	18.6212			0.852608
$478$	−14.1236	−	24.4628i	−0.645999	−	1.11890i
$479$	15.1900	−	26.3099i	0.694049	−	1.20213i	−0.276451	−	0.961028i	$-0.589158\pi$
$479$	15.1900	−	26.3099i	0.694049	−	1.20213i	0.970500	−	0.241100i	$-0.0775083\pi$
$480$	8.19119	−	14.1876i	0.373875	−	0.647570i
$481$	−9.82295	−	17.0138i	−0.447888	−	0.775765i
$482$	55.5167			2.52872
$483$	−1.73086	+	10.7981i	−0.0787567	+	0.491332i
$484$	1.53209			0.0696404
$485$	−27.1040	−	46.9455i	−1.23073	−	2.13169i
$486$	−13.5360	+	23.4450i	−0.614004	+	1.06349i
$487$	5.21554	−	9.03358i	0.236339	−	0.409350i	−0.723322	−	0.690511i	$-0.757386\pi$
$487$	5.21554	−	9.03358i	0.236339	−	0.409350i	0.959661	+	0.281160i	$0.0907192\pi$
$488$	−0.504748	−	0.874249i	−0.0228489	−	0.0395754i
$489$	10.7074			0.484205
$490$	34.6472	−	30.9638i	1.56520	−	1.39880i
$491$	−10.2763			−0.463763			−0.231882	−	0.972744i	$-0.574488\pi$
$491$	−10.2763			−0.463763			−0.231882	+	0.972744i	$0.574488\pi$
$492$	−0.141559	−	0.245188i	−0.00638199	−	0.0110539i
$493$	5.04236	−	8.73362i	0.227096	−	0.393342i
$494$	−7.52481	+	13.0334i	−0.338557	+	0.586399i
$495$	4.54576	+	7.87349i	0.204317	+	0.353887i
$496$	−6.92396			−0.310895
$497$	3.96182	−	24.7162i	0.177712	−	1.10867i
$498$	−13.9017			−0.622949
$499$	18.2592	+	31.6259i	0.817396	+	1.41577i	0.907595	+	0.419847i	$0.137916\pi$
$499$	18.2592	+	31.6259i	0.817396	+	1.41577i	−0.0901991	+	0.995924i	$0.528750\pi$
$500$	−6.69846	+	11.6021i	−0.299564	+	0.518861i
$501$	2.69119	−	4.66128i	0.120233	−	0.208250i
$502$	−3.54323	−	6.13706i	−0.158142	−	0.273910i
$503$	−31.3628			−1.39840			−0.699199	−	0.714928i	$-0.746460\pi$
$503$	−31.3628			−1.39840			−0.699199	+	0.714928i	$0.746460\pi$
$504$	−5.59492	+	2.13575i	−0.249218	+	0.0951340i
$505$	23.6732			1.05345
$506$	5.95084	+	10.3072i	0.264547	+	0.458209i
$507$	−2.10859	+	3.65219i	−0.0936459	+	0.162199i
$508$	10.9042	−	18.8866i	0.483796	−	0.837959i
$509$	5.78224	+	10.0151i	0.256293	+	0.443913i	0.965246	−	0.261343i	$-0.0841654\pi$
$509$	5.78224	+	10.0151i	0.256293	+	0.443913i	−0.708953	+	0.705256i	$0.750832\pi$
$510$	−22.7425			−1.00705
$511$	4.81908	+	3.91728i	0.213183	+	0.173290i
$512$	25.2226			1.11469
$513$	3.30200	+	5.71924i	0.145787	+	0.252511i
$514$	8.13816	−	14.0957i	0.358959	−	0.621735i
$515$	−3.97178	+	6.87933i	−0.175018	+	0.303139i
$516$	1.70574	+	2.95442i	0.0750909	+	0.130061i
$517$	−4.55438			−0.200301
$518$	17.1830	+	13.9676i	0.754979	+	0.613700i
$519$	12.5544			0.551076
$520$	6.85117	+	11.8666i	0.300444	+	0.520383i
$521$	15.2802	−	26.4661i	0.669437	−	1.15950i	−0.308625	−	0.951184i	$-0.599869\pi$
$521$	15.2802	−	26.4661i	0.669437	−	1.15950i	0.978062	−	0.208315i	$-0.0667979\pi$
$522$	4.64708	−	8.04898i	0.203397	−	0.352294i
$523$	2.22756	+	3.85825i	0.0974044	+	0.168709i	0.910610	−	0.413268i	$-0.135613\pi$
$523$	2.22756	+	3.85825i	0.0974044	+	0.168709i	−0.813205	+	0.581977i	$0.802279\pi$
$524$	7.83481			0.342265
$525$	−12.0608	+	4.60397i	−0.526375	+	0.200934i
$526$	−10.9659			−0.478134
$527$	3.85251	+	6.67274i	0.167818	+	0.290669i
$528$	1.53936	−	2.66625i	0.0669922	−	0.116034i
$529$	−8.55185	+	14.8122i	−0.371820	+	0.644010i
$530$	24.0116	+	41.5893i	1.04300	+	1.80653i
$531$	−24.5553			−1.06561
$532$	1.16456	−	7.26525i	0.0504902	−	0.314988i
$533$	1.24897			0.0540989
$534$	2.12701	+	3.68409i	0.0920448	+	0.159426i
$535$	20.3662	−	35.2753i	0.880507	−	1.52508i
$536$	−0.305407	+	0.528981i	−0.0131916	+	0.0228485i
$537$	0.433296	+	0.750491i	0.0186981	+	0.0323861i
$538$	−41.3114			−1.78106
$539$	5.21941	−	4.66452i	0.224816	−	0.200915i
$540$	−19.6878			−0.847227
$541$	8.33527	+	14.4371i	0.358361	+	0.620700i	0.987687	−	0.156441i	$-0.0500022\pi$
$541$	8.33527	+	14.4371i	0.358361	+	0.620700i	−0.629326	+	0.777142i	$0.716669\pi$
$542$	−9.25789	+	16.0351i	−0.397661	+	0.688768i
$543$	−5.76099	+	9.97833i	−0.247228	+	0.428211i
$544$	−18.6498	−	32.3023i	−0.799602	−	1.38495i
$545$	−42.3337			−1.81338
$546$	2.26604	−	14.1370i	0.0969777	−	0.605006i
$547$	36.2080			1.54814			0.774071	−	0.633098i	$-0.218217\pi$
$547$	36.2080			1.54814			0.774071	+	0.633098i	$0.218217\pi$
$548$	−15.0967	−	26.1483i	−0.644900	−	1.11700i
$549$	−1.47741	+	2.55894i	−0.0630542	+	0.109213i
$550$	−7.02481	+	12.1673i	−0.299539	+	0.518817i
$551$	−1.74376	−	3.02027i	−0.0742865	−	0.128668i
$552$	3.63486			0.154710
$553$	30.6976	−	11.7182i	1.30539	−	0.498309i
$554$	44.4270			1.88752
$555$	−5.13341	−	8.89132i	−0.217901	−	0.377416i
$556$	4.04916	−	7.01336i	0.171723	−	0.297433i
$557$	0.334970	−	0.580185i	0.0141931	−	0.0245832i	−0.858842	−	0.512241i	$-0.828815\pi$
$557$	0.334970	−	0.580185i	0.0141931	−	0.0245832i	0.873035	+	0.487658i	$0.162149\pi$
$558$	3.55051	+	6.14966i	0.150305	+	0.260336i
$559$	−15.0496			−0.636532
$560$	−34.2044	−	27.8038i	−1.44540	−	1.17492i
$561$	−3.42602			−0.144647
$562$	−15.2900	−	26.4830i	−0.644969	−	1.11712i
$563$	6.51707	−	11.2879i	0.274662	−	0.475728i	−0.695388	−	0.718635i	$-0.744767\pi$
$563$	6.51707	−	11.2879i	0.274662	−	0.475728i	0.970050	+	0.242906i	$0.0781007\pi$
$564$	2.27719	−	3.94421i	0.0958869	−	0.166081i
$565$	−8.84389	−	15.3181i	−0.372065	−	0.644436i
$566$	31.9463			1.34280
$567$	10.9782	+	8.92383i	0.461040	+	0.374765i
$568$	−8.31996			−0.349098
$569$	−13.7208	−	23.7650i	−0.575204	−	0.996282i	−0.996019	−	0.0891361i	$-0.971589\pi$
$569$	−13.7208	−	23.7650i	−0.575204	−	0.996282i	0.420816	−	0.907146i	$-0.361744\pi$
$570$	−3.93242	+	6.81115i	−0.164711	+	0.285288i
$571$	−8.11974	+	14.0638i	−0.339800	+	0.588552i	−0.984395	−	0.175973i	$-0.943693\pi$
$571$	−8.11974	+	14.0638i	−0.339800	+	0.588552i	0.644595	+	0.764525i	$0.277026\pi$
$572$	−3.37939	−	5.85327i	−0.141299	−	0.244737i
$573$	10.1513			0.424075
$574$	−1.31521	+	0.502055i	−0.0548957	+	0.0209554i
$575$	−47.3414			−1.97427
$576$	−5.04664	−	8.74103i	−0.210277	−	0.364210i
$577$	−11.8589	+	20.5402i	−0.493693	+	0.855101i	−0.999974	−	0.00726770i	$-0.997687\pi$
$577$	−11.8589	+	20.5402i	−0.493693	+	0.855101i	0.506281	+	0.862369i	$0.331020\pi$
$578$	−9.91534	+	17.1739i	−0.412424	+	0.714339i
$579$	1.70321	+	2.95005i	0.0707830	+	0.122600i
$580$	10.3969			0.431709
$581$	−4.74557	+	29.6057i	−0.196879	+	1.22825i
$582$	18.8262			0.780373
$583$	3.61721	+	6.26519i	0.149810	+	0.259478i
$584$	1.03209	−	1.78763i	0.0427081	−	0.0739727i
$585$	20.0535	−	34.7337i	0.829110	−	1.43606i
$586$	12.9474	+	22.4256i	0.534854	+	0.926394i
$587$	−44.5904			−1.84044			−0.920221	−	0.391399i	$-0.871991\pi$
$587$	−44.5904			−1.84044			−0.920221	+	0.391399i	$0.871991\pi$
$588$	1.42989	+	6.85240i	0.0589678	+	0.282588i
$589$	2.66456			0.109791
$590$	−31.6634	−	54.8427i	−1.30356	−	2.25784i
$591$	1.50727	−	2.61068i	0.0620010	−	0.107389i
$592$	10.5030	−	18.1917i	0.431670	−	0.747675i
$593$	21.4217	+	37.1035i	0.879685	+	1.52366i	0.851686	+	0.524052i	$0.175580\pi$
$593$	21.4217	+	37.1035i	0.879685	+	1.52366i	0.0279992	+	0.999608i	$0.491086\pi$
$594$	−6.83750			−0.280546
$595$	−7.76352	+	48.4335i	−0.318273	+	1.98558i
$596$	−26.0692			−1.06784
$597$	1.97431	+	3.41960i	0.0808030	+	0.139955i
$598$	26.2520	−	45.4697i	1.07352	−	1.85940i
$599$	0.316552	−	0.548284i	0.0129339	−	0.0224023i	−0.859486	−	0.511159i	$-0.829216\pi$
$599$	0.316552	−	0.548284i	0.0129339	−	0.0224023i	0.872420	+	0.488757i	$0.162550\pi$
$600$	2.14543	+	3.71599i	0.0875868	+	0.151705i
$601$	−3.45842			−0.141072			−0.0705359	−	0.997509i	$-0.522471\pi$
$601$	−3.45842			−0.141072			−0.0705359	+	0.997509i	$0.522471\pi$
$602$	15.8478	−	6.04958i	0.645907	−	0.246562i
$603$	1.78787			0.0728075
$604$	−0.997941	−	1.72848i	−0.0406056	−	0.0703310i
$605$	−1.76604	+	3.05888i	−0.0717999	+	0.124361i
$606$	−4.11081	+	7.12014i	−0.166990	+	0.289236i
$607$	−24.1374	−	41.8073i	−0.979708	−	1.69690i	−0.663430	−	0.748239i	$-0.730900\pi$
$607$	−24.1374	−	41.8073i	−0.979708	−	1.69690i	−0.316279	−	0.948666i	$-0.602433\pi$
$608$	−12.8990			−0.523123
$609$	2.57455	+	2.09277i	0.104326	+	0.0848035i
$610$	−7.62031			−0.308537
$611$	10.0458	+	17.3998i	0.406408	+	0.703919i
$612$	−10.3498	+	17.9264i	−0.418367	+	0.724633i
$613$	10.6578	−	18.4598i	0.430463	−	0.745583i	−0.566450	−	0.824096i	$-0.691684\pi$
$613$	10.6578	−	18.4598i	0.430463	−	0.745583i	0.996913	+	0.0785125i	$0.0250171\pi$
$614$	10.9153	+	18.9059i	0.440507	+	0.762981i
$615$	0.652704			0.0263196
$616$	−1.80541	−	1.46756i	−0.0727419	−	0.0591297i
$617$	−12.4243			−0.500182			−0.250091	−	0.968222i	$-0.580461\pi$
$617$	−12.4243			−0.500182			−0.250091	+	0.968222i	$0.580461\pi$
$618$	−1.37939	−	2.38917i	−0.0554870	−	0.0961063i
$619$	−18.1702	+	31.4718i	−0.730324	+	1.26496i	0.226421	+	0.974030i	$0.427297\pi$
$619$	−18.1702	+	31.4718i	−0.730324	+	1.26496i	−0.956745	+	0.290928i	$0.906036\pi$
$620$	−3.97178	+	6.87933i	−0.159511	+	0.276280i
$621$	−11.5198	−	19.9528i	−0.462272	−	0.800679i
$622$	6.48070			0.259853
$623$	8.57192	−	3.27217i	0.343427	−	0.131097i
$624$	−13.5817			−0.543704
$625$	3.24644	+	5.62301i	0.129858	+	0.224920i
$626$	18.2506	−	31.6110i	0.729441	−	1.26343i
$627$	−0.592396	+	1.02606i	−0.0236580	+	0.0409769i
$628$	−10.4907	−	18.1704i	−0.418623	−	0.725077i
$629$	−23.3756			−0.932045
$630$	−7.15493	+	44.6367i	−0.285059	+	1.77837i
$631$	15.9195			0.633746			0.316873	−	0.948468i	$-0.397367\pi$
$631$	15.9195			0.633746			0.316873	+	0.948468i	$0.397367\pi$
$632$	−5.46064	−	9.45810i	−0.217212	−	0.376223i
$633$	−2.83750	+	4.91469i	−0.112780	+	0.195341i
$634$	30.8371	−	53.4114i	1.22470	−	2.12124i
$635$	25.1386	+	43.5414i	0.997596	+	1.72789i
$636$	−7.23442			−0.286864
$637$	−29.3332	−	9.65177i	−1.16222	−	0.382417i
$638$	3.61081			0.142954
$639$	12.1763	+	21.0900i	0.481688	+	0.834309i
$640$	−12.0842	+	20.9305i	−0.477672	+	0.827352i
$641$	6.23695	−	10.8027i	0.246345	−	0.426681i	−0.716164	−	0.697932i	$-0.754104\pi$
$641$	6.23695	−	10.8027i	0.246345	−	0.426681i	0.962509	+	0.271250i	$0.0874372\pi$
$642$	7.07310	+	12.2510i	0.279153	+	0.483507i
$643$	−36.8331			−1.45255			−0.726277	−	0.687402i	$-0.758751\pi$
$643$	−36.8331			−1.45255			−0.726277	+	0.687402i	$0.758751\pi$
$644$	−4.06283	+	25.3464i	−0.160098	+	0.998788i
$645$	−7.86484			−0.309678
$646$	8.95336	+	15.5077i	0.352265	+	0.610142i
$647$	−10.2294	+	17.7178i	−0.402158	+	0.696558i	−0.993986	−	0.109506i	$-0.965073\pi$
$647$	−10.2294	+	17.7178i	−0.402158	+	0.696558i	0.591828	+	0.806064i	$0.298406\pi$
$648$	2.35117	−	4.07234i	0.0923626	−	0.159977i
$649$	−4.76991	−	8.26173i	−0.187236	−	0.324301i
$650$	61.9796			2.43104
$651$	−2.36824	+	0.904030i	−0.0928187	+	0.0354317i
$652$	25.1334			0.984300
$653$	7.77972	+	13.4749i	0.304444	+	0.527312i	0.977137	−	0.212609i	$-0.0681961\pi$
$653$	7.77972	+	13.4749i	0.304444	+	0.527312i	−0.672694	+	0.739921i	$0.734863\pi$
$654$	7.35117	−	12.7326i	0.287453	−	0.497884i
$655$	−9.03121	+	15.6425i	−0.352879	+	0.611204i
$656$	0.667718	+	1.15652i	0.0260700	+	0.0451546i
$657$	−6.04189			−0.235717
$658$	−17.5728	−	14.2844i	−0.685059	−	0.556863i
$659$	−23.6673			−0.921945			−0.460973	−	0.887414i	$-0.652499\pi$
$659$	−23.6673			−0.921945			−0.460973	+	0.887414i	$0.652499\pi$
$660$	−1.76604	−	3.05888i	−0.0687432	−	0.119067i
$661$	−10.0988	+	17.4916i	−0.392798	+	0.680345i	−0.992817	−	0.119640i	$-0.961826\pi$
$661$	−10.0988	+	17.4916i	−0.392798	+	0.680345i	0.600020	+	0.799985i	$0.295159\pi$
$662$	5.97653	−	10.3517i	0.232284	−	0.402328i
$663$	7.55690	+	13.0889i	0.293486	+	0.508332i
$664$	9.96585			0.386750
$665$	13.1630	+	10.6998i	0.510438	+	0.414920i
$666$	−21.5431			−0.834779
$667$	6.08347	+	10.5369i	0.235553	+	0.407990i
$668$	6.31702	−	10.9414i	0.244413	−	0.423335i
$669$	0.0723291	−	0.125278i	0.00279640	−	0.00484351i
$670$	2.30541	+	3.99308i	0.0890657	+	0.154266i
$671$	−1.14796			−0.0443163
$672$	11.4645	−	4.37636i	0.442253	−	0.168822i
$673$	7.92633			0.305537			0.152769	−	0.988262i	$-0.451181\pi$
$673$	7.92633			0.305537			0.152769	+	0.988262i	$0.451181\pi$
$674$	14.6074	+	25.3008i	0.562656	+	0.974550i
$675$	13.5988	−	23.5538i	0.523418	−	0.906586i
$676$	−4.94949	+	8.57277i	−0.190365	+	0.329722i
$677$	−18.0282	−	31.2258i	−0.692881	−	1.20010i	−0.970890	−	0.239526i	$-0.923008\pi$
$677$	−18.0282	−	31.2258i	−0.692881	−	1.20010i	0.278009	−	0.960578i	$-0.410325\pi$
$678$	6.14290			0.235917
$679$	6.42665	−	40.0933i	0.246632	−	1.53864i
$680$	16.3037			0.625217
$681$	3.16550	+	5.48280i	0.121302	+	0.210101i
$682$	−1.37939	+	2.38917i	−0.0528194	+	0.0914859i
$683$	6.17840	−	10.7013i	0.236410	−	0.409474i	−0.723272	−	0.690564i	$-0.757363\pi$
$683$	6.17840	−	10.7013i	0.236410	−	0.409474i	0.959681	+	0.281090i	$0.0906959\pi$
$684$	3.57919	+	6.19934i	0.136854	+	0.237038i
$685$	69.6082			2.65959
$686$	34.7686	−	1.62760i	1.32747	−	0.0621419i
$687$	15.4655			0.590047
$688$	−8.04576	−	13.9357i	−0.306742	−	0.531292i
$689$	15.9572	−	27.6387i	0.607922	−	1.05295i
$690$	13.7191	−	23.7622i	0.522277	−	0.904611i
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	29.4688			1.12024
$693$	−1.07785	+	6.72427i	−0.0409441	+	0.255434i
$694$	−37.0702			−1.40716
$695$	9.33497	+	16.1686i	0.354096	+	0.613312i
$696$	0.551385	−	0.955026i	0.0209002	−	0.0362002i
$697$	0.743041	−	1.28698i	0.0281447	−	0.0487480i
$698$	5.44444	+	9.43005i	0.206075	+	0.356933i
$699$	13.6331			0.515651
$700$	−28.3102	+	10.8069i	−1.07003	+	0.408462i
$701$	12.7611			0.481981			0.240991	−	0.970527i	$-0.422528\pi$
$701$	12.7611			0.481981			0.240991	+	0.970527i	$0.422528\pi$
$702$	15.0817	+	26.1223i	0.569223	+	0.985923i
$703$	−4.04189	+	7.00076i	−0.152443	+	0.264039i
$704$	1.96064	−	3.39592i	0.0738943	−	0.127989i
$705$	5.24985	+	9.09300i	0.197721	+	0.342462i
$706$	62.3319			2.34589
$707$	13.7601	+	11.1852i	0.517502	+	0.420662i
$708$	9.53983			0.358529
$709$	−2.35251	−	4.07467i	−0.0883504	−	0.153027i	0.818464	−	0.574558i	$-0.194826\pi$
$709$	−2.35251	−	4.07467i	−0.0883504	−	0.153027i	−0.906814	+	0.421531i	$0.861493\pi$
$710$	−31.4021	+	54.3901i	−1.17850	+	2.04122i
$711$	−15.9834	+	27.6840i	−0.599424	+	1.03823i
$712$	−1.52481	−	2.64106i	−0.0571449	−	0.0989778i
$713$	−9.29591			−0.348135
$714$	−13.2191	−	10.7454i	−0.494712	−	0.402137i
$715$	15.5817			0.582723
$716$	1.01707	+	1.76162i	0.0380098	+	0.0658350i
$717$	−4.90508	+	8.49584i	−0.183183	+	0.317283i
$718$	−3.95589	+	6.85180i	−0.147632	+	0.255707i
$719$	−26.3109	−	45.5719i	−0.981232	−	1.69954i	−0.657613	−	0.753356i	$-0.728434\pi$
$719$	−26.3109	−	45.5719i	−0.981232	−	1.69954i	−0.323619	−	0.946187i	$-0.604900\pi$
$720$	42.8836			1.59818
$721$	−5.55896	+	2.12203i	−0.207027	+	0.0790284i
$722$	−29.5158			−1.09846
$723$	−9.64038	−	16.6976i	−0.358529	−	0.620991i
$724$	−13.5228	+	23.4221i	−0.502569	+	0.870475i
$725$	−7.18139	+	12.4385i	−0.266710	+	0.461955i
$726$	−0.613341	−	1.06234i	−0.0227632	−	0.0394270i
$727$	−22.3901			−0.830404			−0.415202	−	0.909729i	$-0.636289\pi$
$727$	−22.3901			−0.830404			−0.415202	+	0.909729i	$0.636289\pi$
$728$	−1.62449	+	10.1345i	−0.0602074	+	0.375610i
$729$	−6.63991			−0.245923
$730$	−7.79086	−	13.4942i	−0.288353	−	0.499441i
$731$	−8.95336	+	15.5077i	−0.331152	+	0.573572i
$732$	0.573978	−	0.994159i	0.0212148	−	0.0367452i
$733$	15.1079	+	26.1676i	0.558022	+	0.966523i	0.997662	+	0.0683484i	$0.0217729\pi$
$733$	15.1079	+	26.1676i	0.558022	+	0.966523i	−0.439639	+	0.898174i	$0.644894\pi$
$734$	−36.5330			−1.34846
$735$	−15.3293	−	5.04395i	−0.565431	−	0.186049i
$736$	45.0009			1.65876
$737$	0.347296	+	0.601535i	0.0127928	+	0.0221578i
$738$	0.684793	−	1.18610i	0.0252076	−	0.0436608i
$739$	−6.38578	+	11.0605i	−0.234905	+	0.406867i	−0.959245	−	0.282576i	$-0.908811\pi$
$739$	−6.38578	+	11.0605i	−0.234905	+	0.406867i	0.724340	+	0.689443i	$0.242145\pi$
$740$	−12.0496	−	20.8706i	−0.442953	−	0.767217i
$741$	5.22668			0.192007
$742$	−5.69341	+	35.5189i	−0.209012	+	1.30394i
$743$	−37.4989			−1.37570			−0.687850	−	0.725853i	$-0.741445\pi$
$743$	−37.4989			−1.37570			−0.687850	+	0.725853i	$0.741445\pi$
$744$	0.421274	+	0.729669i	0.0154447	+	0.0267509i
$745$	30.0501	−	52.0483i	1.10095	−	1.90690i
$746$	−11.9474	+	20.6936i	−0.437427	+	0.757645i
$747$	−14.5851	−	25.2622i	−0.533642	−	0.924295i
$748$	−8.04189			−0.294041
$749$	28.5048	−	10.8812i	1.04154	−	0.397589i
$750$	10.7264			0.391672
$751$	−18.3923	−	31.8565i	−0.671146	−	1.16246i	−0.977579	−	0.210567i	$-0.932469\pi$
$751$	−18.3923	−	31.8565i	−0.671146	−	1.16246i	0.306433	−	0.951892i	$-0.400864\pi$
$752$	−10.7412	+	18.6044i	−0.391692	+	0.678431i
$753$	−1.23055	+	2.13138i	−0.0448438	+	0.0776718i
$754$	−7.96451	−	13.7949i	−0.290050	−	0.502382i
$755$	4.60132			0.167459
$756$	−11.4436	−	9.30212i	−0.416198	−	0.338315i
$757$	−2.27126			−0.0825503			−0.0412752	−	0.999148i	$-0.513142\pi$
$757$	−2.27126			−0.0825503			−0.0412752	+	0.999148i	$0.513142\pi$
$758$	21.4354	+	37.1272i	0.778569	+	1.34852i
$759$	2.06670	−	3.57964i	0.0750166	−	0.129933i
$760$	2.81908	−	4.88279i	0.102259	−	0.177117i
$761$	−5.09539	−	8.82547i	−0.184708	−	0.319923i	0.758770	−	0.651358i	$-0.225801\pi$
$761$	−5.09539	−	8.82547i	−0.184708	−	0.319923i	−0.943478	+	0.331435i	$0.892467\pi$
$762$	−17.4611			−0.632549
$763$	−24.6065	−	20.0019i	−0.890816	−	0.724117i
$764$	23.8280			0.862067
$765$	−23.8606	−	41.3277i	−0.862680	−	1.49421i
$766$	−7.79813	+	13.5068i	−0.281758	+	0.488019i
$767$	−21.0424	+	36.4464i	−0.759795	+	1.31600i
$768$	−6.75624	−	11.7022i	−0.243795	−	0.422265i
$769$	−27.7802			−1.00178			−0.500891	−	0.865511i	$-0.666994\pi$
$769$	−27.7802			−1.00178			−0.500891	+	0.865511i	$0.666994\pi$
$770$	−16.4081	+	6.26347i	−0.591306	+	0.225720i
$771$	−5.65270			−0.203577
$772$	3.99794	+	6.92464i	0.143889	+	0.249223i
$773$	5.39100	−	9.33748i	0.193901	−	0.335846i	−0.752639	−	0.658433i	$-0.771219\pi$
$773$	5.39100	−	9.33748i	0.193901	−	0.335846i	0.946540	+	0.322588i	$0.104553\pi$
$774$	−8.25150	+	14.2920i	−0.296594	+	0.513716i
$775$	−5.48680	−	9.50341i	−0.197092	−	0.341373i
$776$	−13.4962			−0.484485
$777$	1.21719	−	7.59354i	0.0436663	−	0.272417i
$778$	21.4243			0.768097
$779$	−0.256959	−	0.445067i	−0.00920653	−	0.0159462i
$780$	−7.79086	+	13.4942i	−0.278958	+	0.483169i
$781$	−4.73055	+	8.19356i	−0.169272	+	0.293188i
$782$	−31.2358	−	54.1019i	−1.11699	−	1.93468i
$783$	−6.98990			−0.249798
$784$	−6.74463	−	32.3220i	−0.240880	−	1.15436i
$785$	48.3705			1.72642
$786$	−3.13651	−	5.43259i	−0.111875	−	0.193774i
$787$	10.6736	−	18.4873i	0.380474	−	0.659001i	−0.610656	−	0.791896i	$-0.709094\pi$
$787$	10.6736	−	18.4873i	0.380474	−	0.659001i	0.991130	+	0.132895i	$0.0424274\pi$
$788$	3.53802	−	6.12803i	0.126037	−	0.218302i
$789$	1.90420	+	3.29817i	0.0677913	+	0.117418i
$790$	−82.4407			−2.93311
$791$	2.09698	−	13.0822i	0.0745601	−	0.465151i
$792$	2.26352			0.0804306
$793$	2.53209	+	4.38571i	0.0899171	+	0.155741i
$794$	−6.18479	+	10.7124i	−0.219490	+	0.380168i
$795$	8.33915	−	14.4438i	0.295759	−	0.512270i
$796$	4.63429	+	8.02682i	0.164258	+	0.284503i
$797$	39.3096			1.39242			0.696209	−	0.717839i	$-0.254868\pi$
$797$	39.3096			1.39242			0.696209	+	0.717839i	$0.254868\pi$
$798$	−5.50387	+	2.10100i	−0.194835	+	0.0743745i
$799$	23.9058			0.845726
$800$	26.5612	+	46.0054i	0.939082	+	1.62654i
$801$	−4.46316	+	7.73043i	−0.157698	+	0.273141i
$802$	−3.93717	+	6.81937i	−0.139026	+	0.240800i
$803$	−1.17365	−	2.03282i	−0.0414171	−	0.0717366i
$804$	−0.694593			−0.0244964
$805$	−45.9219	−	37.3285i	−1.61853	−	1.31566i
$806$	12.1702			0.428679
$807$	7.17365	+	12.4251i	0.252524	+	0.437385i
$808$	2.94697	−	5.10430i	0.103674	−	0.179569i
$809$	−1.62330	+	2.81164i	−0.0570723	+	0.0988521i	−0.893150	−	0.449759i	$-0.851510\pi$
$809$	−1.62330	+	2.81164i	−0.0570723	+	0.0988521i	0.836078	+	0.548611i	$0.184843\pi$
$810$	−17.7481	−	30.7406i	−0.623604	−	1.08011i
$811$	33.4056			1.17303			0.586515	−	0.809939i	$-0.300500\pi$
$811$	33.4056			1.17303			0.586515	+	0.809939i	$0.300500\pi$
$812$	6.04323	+	4.91236i	0.212076	+	0.172390i
$813$	6.43047			0.225526
$814$	−4.18479	−	7.24827i	−0.146677	−	0.254052i
$815$	−28.9714	+	50.1799i	−1.01482	+	1.75772i
$816$	−8.08007	+	13.9951i	−0.282859	+	0.489926i
$817$	3.09627	+	5.36289i	0.108325	+	0.187624i
$818$	1.45336			0.0508157
$819$	28.0672	−	10.7141i	0.980746	−	0.374381i
$820$	1.53209			0.0535029
$821$	12.0988	+	20.9557i	0.422251	+	0.731360i	0.996159	−	0.0875596i	$-0.0279068\pi$
$821$	12.0988	+	20.9557i	0.422251	+	0.731360i	−0.573908	+	0.818919i	$0.694573\pi$
$822$	−12.0873	+	20.9359i	−0.421595	+	0.730223i
$823$	23.3576	−	40.4565i	0.814193	−	1.41022i	−0.0957121	−	0.995409i	$-0.530513\pi$
$823$	23.3576	−	40.4565i	0.814193	−	1.41022i	0.909906	−	0.414815i	$-0.136154\pi$
$824$	0.988856	+	1.71275i	0.0344484	+	0.0596664i
$825$	4.87939			0.169878
$826$	7.50774	−	46.8378i	0.261228	−	1.62970i
$827$	1.89992			0.0660667			0.0330333	−	0.999454i	$-0.489483\pi$
$827$	1.89992			0.0660667			0.0330333	+	0.999454i	$0.489483\pi$
$828$	−12.4868	−	21.6278i	−0.433946	−	0.751617i
$829$	−25.4850	+	44.1414i	−0.885132	+	1.53309i	−0.0395699	+	0.999217i	$0.512599\pi$
$829$	−25.4850	+	44.1414i	−0.885132	+	1.53309i	−0.845562	+	0.533877i	$0.820735\pi$
$830$	37.6143	−	65.1498i	1.30561	−	2.26138i
$831$	−7.71466	−	13.3622i	−0.267619	−	0.463529i
$832$	−17.2986			−0.599721
$833$	−27.3965	+	24.4839i	−0.949233	+	0.848319i
$834$	−6.48400			−0.224523
$835$	14.5633	+	25.2244i	0.503984	+	0.872926i
$836$	−1.39053	+	2.40847i	−0.0480925	+	0.0832986i
$837$	2.67024	−	4.62500i	0.0922972	−	0.159863i
$838$	−12.9251	−	22.3870i	−0.446492	−	0.773346i
$839$	42.9368			1.48234			0.741171	−	0.671317i	$-0.234271\pi$
$839$	42.9368			1.48234			0.741171	+	0.671317i	$0.234271\pi$
$840$	−0.848945	+	5.29623i	−0.0292914	+	0.182737i
$841$	−25.3087			−0.872714
$842$	5.45558	+	9.44935i	0.188012	+	0.325646i
$843$	−5.31016	+	9.19746i	−0.182891	+	0.316777i
$844$	−6.66044	+	11.5362i	−0.229262	+	0.397093i
$845$	−11.4106	−	19.7637i	−0.392536	−	0.679893i
$846$	22.0318			0.757468
$847$	−2.47178	+	0.943555i	−0.0849314	+	0.0324209i
$848$	34.1239			1.17182
$849$	−5.54741	−	9.60839i	−0.190387	−	0.329759i
$850$	36.8730	−	63.8660i	1.26474	−	2.19059i
$851$	14.1010	−	24.4237i	0.483377	−	0.837233i
$852$	−4.73055	−	8.19356i	−0.162066	−	0.280707i
$853$	52.3560			1.79263			0.896317	−	0.443414i	$-0.146233\pi$
$853$	52.3560			1.79263			0.896317	+	0.443414i	$0.146233\pi$
$854$	−4.42932	−	3.60046i	−0.151568	−	0.123205i
$855$	−16.5030			−0.564390
$856$	−5.07057	−	8.78249i	−0.173309	−	0.300179i
$857$	0.489018	−	0.847004i	0.0167045	−	0.0289331i	−0.857552	−	0.514397i	$-0.828016\pi$
$857$	0.489018	−	0.847004i	0.0167045	−	0.0289331i	0.874257	+	0.485464i	$0.161349\pi$
$858$	−2.70574	+	4.68647i	−0.0923723	+	0.159994i
$859$	17.0073	+	29.4576i	0.580283	+	1.00508i	0.995446	+	0.0953319i	$0.0303912\pi$
$859$	17.0073	+	29.4576i	0.580283	+	1.00508i	−0.415163	+	0.909747i	$0.636275\pi$
$860$	−18.4611			−0.629518
$861$	0.379385	+	0.308391i	0.0129294	+	0.0105099i
$862$	−33.8402			−1.15260
$863$	11.3478	+	19.6549i	0.386282	+	0.669061i	0.991946	−	0.126660i	$-0.0404257\pi$
$863$	11.3478	+	19.6549i	0.386282	+	0.669061i	−0.605664	+	0.795721i	$0.707092\pi$
$864$	−12.9265	+	22.3893i	−0.439768	+	0.761701i
$865$	−33.9688	+	58.8358i	−1.15498	+	2.00048i
$866$	−2.19934	−	3.80937i	−0.0747366	−	0.129448i
$867$	6.88713			0.233899
$868$	−5.55896	+	2.12203i	−0.188684	+	0.0720263i
$869$	−12.4192			−0.421293
$870$	−4.16220	−	7.20914i	−0.141112	−	0.244413i
$871$	1.53209	−	2.65366i	0.0519129	−	0.0899157i
$872$	−5.26991	+	9.12776i	−0.178462	+	0.309105i
$873$	19.7518	+	34.2111i	0.668497	+	1.15787i
$874$	−21.6040			−0.730766
$875$	3.66163	−	22.8434i	0.123786	−	0.772249i
$876$	2.34730			0.0793078
$877$	0.614218	+	1.06386i	0.0207407	+	0.0359239i	0.876209	−	0.481930i	$-0.160064\pi$
$877$	0.614218	+	1.06386i	0.0207407	+	0.0359239i	−0.855469	+	0.517854i	$0.826731\pi$
$878$	37.6190	−	65.1581i	1.26958	−	2.19898i
$879$	4.49660	−	7.78833i	0.151666	−	0.262694i
$880$	8.33022	+	14.4284i	0.280812	+	0.486380i
$881$	9.13516			0.307771			0.153886	−	0.988089i	$-0.450821\pi$
$881$	9.13516			0.307771			0.153886	+	0.988089i	$0.450821\pi$
$882$	−25.2489	+	22.5646i	−0.850173	+	0.759790i
$883$	44.8256			1.50850			0.754251	−	0.656586i	$-0.228000\pi$
$883$	44.8256			1.50850			0.754251	+	0.656586i	$0.228000\pi$
$884$	17.7383	+	30.7236i	0.596603	+	1.03335i
$885$	−10.9966	+	19.0467i	−0.369647	+	0.640247i
$886$	−17.8316	+	30.8852i	−0.599063	+	1.03761i
$887$	11.5089	+	19.9340i	0.386432	+	0.669320i	0.991967	−	0.126499i	$-0.0403741\pi$
$887$	11.5089	+	19.9340i	0.386432	+	0.669320i	−0.605535	+	0.795819i	$0.707041\pi$
$888$	−2.55613			−0.0857782
$889$	−5.96064	+	37.1860i	−0.199913	+	1.24718i
$890$	−23.0205			−0.771650
$891$	−2.67365	−	4.63089i	−0.0895706	−	0.155141i
$892$	0.169778	−	0.294064i	0.00568458	−	0.00984598i
$893$	4.13357	−	7.15955i	0.138325	−	0.239585i
$894$	10.4363	+	18.0762i	0.349042	+	0.604558i
$895$	−4.68954			−0.156754
$896$	−16.9133	+	6.45632i	−0.565033	+	0.215691i
$897$	−18.2344			−0.608830
$898$	29.6352	+	51.3297i	0.988940	+	1.71289i
$899$	−1.41013	+	2.44242i	−0.0470305	+	0.0814592i
$900$	14.7404	−	25.5310i	0.491345	−	0.851035i
$901$	−18.9866	−	32.8858i	−0.632536	−	1.09559i
$902$	0.532089			0.0177166
$903$	−4.57145	−	3.71599i	−0.152128	−	0.123661i
$904$	−4.40373			−0.146466
$905$	−31.1755	−	53.9975i	−1.03631	−	1.79494i
$906$	−0.799011	+	1.38393i	−0.0265454	+	0.0459779i
$907$	14.1604	−	24.5266i	0.470190	−	0.814393i	−0.529229	−	0.848479i	$-0.677519\pi$
$907$	14.1604	−	24.5266i	0.470190	−	0.814393i	0.999419	+	0.0340863i	$0.0108521\pi$
$908$	7.43036	+	12.8698i	0.246585	+	0.427098i
$909$	−17.2517			−0.572201
$910$	60.1211	+	48.8706i	1.99300	+	1.62005i
$911$	2.97596			0.0985978			0.0492989	−	0.998784i	$-0.484301\pi$
$911$	2.97596			0.0985978			0.0492989	+	0.998784i	$0.484301\pi$
$912$	2.79426	+	4.83981i	0.0925273	+	0.160262i
$913$	5.66637	−	9.81445i	0.187530	−	0.324811i
$914$	−10.9179	+	18.9103i	−0.361131	+	0.625497i
$915$	1.32325	+	2.29194i	0.0437454	+	0.0757692i
$916$	36.3022			1.19946
$917$	−12.6402	+	4.82516i	−0.417417	+	0.159341i
$918$	35.8898			1.18454
$919$	−10.8969	−	18.8740i	−0.359456	−	0.622597i	0.628414	−	0.777879i	$-0.283705\pi$
$919$	−10.8969	−	18.8740i	−0.359456	−	0.622597i	−0.987870	+	0.155283i	$0.950371\pi$
$920$	−9.83497	+	17.0347i	−0.324249	+	0.561616i
$921$	3.79086	−	6.56596i	0.124913	−	0.216356i
$922$	12.1959	+	21.1240i	0.401652	+	0.695681i
$923$	41.7374			1.37380
$924$	0.418748	−	2.61240i	0.0137758	−	0.0859418i
$925$	33.2918			1.09463
$926$	−33.2374	−	57.5689i	−1.09225	−	1.89183i
$927$	2.89440	−	5.01325i	0.0950646	−	0.164657i
$928$	6.82635	−	11.8236i	0.224086	−	0.388128i
$929$	−18.5326	−	32.0993i	−0.608033	−	1.05314i	−0.991564	−	0.129617i	$-0.958625\pi$
$929$	−18.5326	−	32.0993i	−0.608033	−	1.05314i	0.383531	−	0.923528i	$-0.374708\pi$
$930$	6.36009			0.208556
$931$	2.59555	+	12.4385i	0.0850658	+	0.407656i
$932$	32.0009			1.04823
$933$	−1.12536	−	1.94919i	−0.0368427	−	0.0638135i
$934$	37.4616	−	64.8853i	1.22578	−	2.12311i
$935$	9.26991	−	16.0560i	0.303159	−	0.525086i
$936$	−4.99273	−	8.64766i	−0.163192	−	0.282657i
$937$	39.8340			1.30132			0.650660	−	0.759369i	$-0.274492\pi$
$937$	39.8340			1.30132			0.650660	+	0.759369i	$0.274492\pi$
$938$	−0.546637	+	3.41025i	−0.0178483	+	0.111349i
$939$	−12.6767			−0.413690
$940$	12.3229	+	21.3440i	0.401930	+	0.696164i
$941$	−6.84595	+	11.8575i	−0.223172	+	0.386545i	−0.955769	−	0.294117i	$-0.904974\pi$
$941$	−6.84595	+	11.8575i	−0.223172	+	0.386545i	0.732598	+	0.680662i	$0.238308\pi$
$942$	−8.39945	+	14.5483i	−0.273669	+	0.474009i
$943$	0.896459	+	1.55271i	0.0291927	+	0.0505633i
$944$	−44.9982			−1.46457
$945$	31.7631	−	12.1250i	1.03325	−	0.394425i
$946$	−6.41147			−0.208455
$947$	23.5667	+	40.8187i	0.765815	+	1.32643i	0.939815	+	0.341685i	$0.110998\pi$
$947$	23.5667	+	40.8187i	0.765815	+	1.32643i	−0.174000	+	0.984746i	$0.555669\pi$
$948$	6.20961	−	10.7554i	0.201679	−	0.349318i
$949$	−5.17752	+	8.96773i	−0.168069	+	0.291105i
$950$	−12.7515	−	22.0862i	−0.413713	−	0.716572i
$951$	−21.4192			−0.694566
$952$	9.47653	+	7.70318i	0.307136	+	0.249662i
$953$	−26.8990			−0.871344			−0.435672	−	0.900106i	$-0.643489\pi$
$953$	−26.8990			−0.871344			−0.435672	+	0.900106i	$0.643489\pi$
$954$	−17.4982	−	30.3078i	−0.566527	−	0.981253i
$955$	−27.4666	+	47.5736i	−0.888799	+	1.53945i
$956$	−11.5137	+	19.9423i	−0.372379	+	0.644979i
$957$	−0.627011	−	1.08602i	−0.0202684	−	0.0351059i
$958$	−57.0958			−1.84468
$959$	40.4599	+	32.8886i	1.30652	+	1.06203i
$960$	−9.04013			−0.291769
$961$	14.4226	+	24.9807i	0.465246	+	0.805829i
$962$	−18.4611	+	31.9756i	−0.595210	+	1.03093i
$963$	−14.8417	+	25.7065i	−0.478266	+	0.828381i
$964$	−22.6288	−	39.1943i	−0.728825	−	1.26236i
$965$	−18.4338			−0.593404
$966$	19.2015	−	7.32979i	0.617797	−	0.235832i
$967$	−39.4270			−1.26789			−0.633943	−	0.773380i	$-0.718565\pi$
$967$	−39.4270			−1.26789			−0.633943	+	0.773380i	$0.718565\pi$
$968$	0.439693	+	0.761570i	0.0141323	+	0.0244778i
$969$	3.10947	−	5.38576i	0.0998906	−	0.173016i
$970$	−50.9389	+	88.2287i	−1.63555	+	2.83285i
$971$	−8.04071	−	13.9269i	−0.258039	−	0.446936i	0.707678	−	0.706535i	$-0.249743\pi$
$971$	−8.04071	−	13.9269i	−0.258039	−	0.446936i	−0.965716	+	0.259599i	$0.916409\pi$
$972$	22.0692			0.707871
$973$	−2.21342	+	13.8087i	−0.0709590	+	0.442685i
$974$	−19.6040			−0.628153
$975$	−10.7626	−	18.6414i	−0.344680	−	0.597004i
$976$	−2.70739	+	4.68933i	−0.0866613	+	0.150102i
$977$	−13.7139	+	23.7532i	−0.438748	+	0.759934i	−0.997593	−	0.0693382i	$-0.977911\pi$
$977$	−13.7139	+	23.7532i	−0.438748	+	0.759934i	0.558845	+	0.829272i	$0.311245\pi$
$978$	−10.0617	−	17.4273i	−0.321736	−	0.557263i
$979$	−3.46791			−0.110835
$980$	−35.9825	−	11.8396i	−1.14942	−	0.378204i
$981$	30.8503			0.984974
$982$	9.65657	+	16.7257i	0.308154	+	0.533738i
$983$	3.73308	−	6.46588i	0.119067	−	0.206230i	−0.800331	−	0.599558i	$-0.795343\pi$
$983$	3.73308	−	6.46588i	0.119067	−	0.206230i	0.919398	+	0.393328i	$0.128676\pi$
$984$	0.0812519	−	0.140732i	0.00259022	−	0.00448639i
$985$	8.15657	+	14.1276i	0.259890	+	0.450143i
$986$	−18.9531			−0.603588
$987$	−1.24480	+	7.76578i	−0.0396223	+	0.247188i
$988$	12.2686			0.390315
$989$	−10.8020	−	18.7096i	−0.343484	−	0.594931i
$990$	8.54323	−	14.7973i	0.271522	−	0.470290i
$991$	12.1352	−	21.0188i	0.385488	−	0.667685i	−0.606349	−	0.795199i	$-0.707366\pi$
$991$	12.1352	−	21.0188i	0.385488	−	0.667685i	0.991837	+	0.127514i	$0.0406998\pi$
$992$	5.21554	+	9.03358i	0.165593	+	0.286816i
$993$	−4.15125			−0.131736
$994$	−43.9509	+	16.7774i	−1.39404	+	0.532147i
$995$	−21.3678			−0.677406
$996$	5.66637	+	9.81445i	0.179546	+	0.310983i
$997$	16.5581	−	28.6794i	0.524400	−	0.908287i	−0.475197	−	0.879880i	$-0.657623\pi$
$997$	16.5581	−	28.6794i	0.524400	−	0.908287i	0.999596	−	0.0284075i	$-0.00904361\pi$
$998$	34.3161	−	59.4373i	1.08626	−	1.88145i
$999$	8.10101	+	14.0314i	0.256305	+	0.443933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.e.a.67.1	yes	6
3.2	odd	2		693.2.i.h.298.3		6
4.3	odd	2		1232.2.q.m.529.2		6
7.2	even	3	inner	77.2.e.a.23.1	✓	6
7.3	odd	6		539.2.a.g.1.3		3
7.4	even	3		539.2.a.j.1.3		3
7.5	odd	6		539.2.e.m.177.1		6
7.6	odd	2		539.2.e.m.67.1		6
11.2	odd	10		847.2.n.f.81.3		24
11.3	even	5		847.2.n.g.130.1		24
11.4	even	5		847.2.n.g.753.3		24
11.5	even	5		847.2.n.g.487.3		24
11.6	odd	10		847.2.n.f.487.1		24
11.7	odd	10		847.2.n.f.753.1		24
11.8	odd	10		847.2.n.f.130.3		24
11.9	even	5		847.2.n.g.81.1		24
11.10	odd	2		847.2.e.c.606.3		6
21.2	odd	6		693.2.i.h.100.3		6
21.11	odd	6		4851.2.a.bj.1.1		3
21.17	even	6		4851.2.a.bk.1.1		3
28.3	even	6		8624.2.a.co.1.2		3
28.11	odd	6		8624.2.a.ch.1.2		3
28.23	odd	6		1232.2.q.m.177.2		6
77.2	odd	30		847.2.n.f.807.1		24
77.9	even	15		847.2.n.g.807.3		24
77.10	even	6		5929.2.a.u.1.1		3
77.16	even	15		847.2.n.g.366.1		24
77.30	odd	30		847.2.n.f.9.1		24
77.32	odd	6		5929.2.a.x.1.1		3
77.37	even	15		847.2.n.g.632.1		24
77.51	odd	30		847.2.n.f.632.3		24
77.58	even	15		847.2.n.g.9.3		24
77.65	odd	6		847.2.e.c.485.3		6
77.72	odd	30		847.2.n.f.366.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.1	✓	6	7.2	even	3	inner
77.2.e.a.67.1	yes	6	1.1	even	1	trivial
539.2.a.g.1.3		3	7.3	odd	6
539.2.a.j.1.3		3	7.4	even	3
539.2.e.m.67.1		6	7.6	odd	2
539.2.e.m.177.1		6	7.5	odd	6
693.2.i.h.100.3		6	21.2	odd	6
693.2.i.h.298.3		6	3.2	odd	2
847.2.e.c.485.3		6	77.65	odd	6
847.2.e.c.606.3		6	11.10	odd	2
847.2.n.f.9.1		24	77.30	odd	30
847.2.n.f.81.3		24	11.2	odd	10
847.2.n.f.130.3		24	11.8	odd	10
847.2.n.f.366.3		24	77.72	odd	30
847.2.n.f.487.1		24	11.6	odd	10
847.2.n.f.632.3		24	77.51	odd	30
847.2.n.f.753.1		24	11.7	odd	10
847.2.n.f.807.1		24	77.2	odd	30
847.2.n.g.9.3		24	77.58	even	15
847.2.n.g.81.1		24	11.9	even	5
847.2.n.g.130.1		24	11.3	even	5
847.2.n.g.366.1		24	77.16	even	15
847.2.n.g.487.3		24	11.5	even	5
847.2.n.g.632.1		24	77.37	even	15
847.2.n.g.753.3		24	11.4	even	5
847.2.n.g.807.3		24	77.9	even	15
1232.2.q.m.177.2		6	28.23	odd	6
1232.2.q.m.529.2		6	4.3	odd	2
4851.2.a.bj.1.1		3	21.11	odd	6
4851.2.a.bk.1.1		3	21.17	even	6
5929.2.a.u.1.1		3	77.10	even	6
5929.2.a.x.1.1		3	77.32	odd	6
8624.2.a.ch.1.2		3	28.11	odd	6
8624.2.a.co.1.2		3	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 1.62760i) q^{2} +(-0.326352 + 0.565258i) q^{3} +(-0.766044 + 1.32683i) q^{4} +(-1.76604 - 3.05888i) q^{5} +1.22668 q^{6} +(0.418748 - 2.61240i) q^{7} -0.879385 q^{8} +(1.28699 + 2.22913i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 1.62760i) q^{2} +(-0.326352 + 0.565258i) q^{3} +(-0.766044 + 1.32683i) q^{4} +(-1.76604 - 3.05888i) q^{5} +1.22668 q^{6} +(0.418748 - 2.61240i) q^{7} -0.879385 q^{8} +(1.28699 + 2.22913i) q^{9} +(-3.31908 + 5.74881i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +4.41147 q^{13} +(-4.64543 + 1.77330i) q^{14} +2.30541 q^{15} +(2.35844 + 4.08494i) q^{16} +(2.62449 - 4.54574i) q^{17} +(2.41875 - 4.18939i) q^{18} +(-0.907604 - 1.57202i) q^{19} +5.41147 q^{20} +(1.34002 + 1.08926i) q^{21} +1.87939 q^{22} +(3.16637 + 5.48432i) q^{23} +(0.286989 - 0.497079i) q^{24} +(-3.73783 + 6.47410i) q^{25} +(-4.14543 - 7.18009i) q^{26} -3.63816 q^{27} +(3.14543 + 2.55682i) q^{28} +1.92127 q^{29} +(-2.16637 - 3.75227i) q^{30} +(-0.733956 + 1.27125i) q^{31} +(3.55303 - 6.15403i) q^{32} +(-0.326352 - 0.565258i) q^{33} -9.86484 q^{34} +(-8.73055 + 3.33272i) q^{35} -3.94356 q^{36} +(-2.22668 - 3.85673i) q^{37} +(-1.70574 + 2.95442i) q^{38} +(-1.43969 + 2.49362i) q^{39} +(1.55303 + 2.68993i) q^{40} +0.283119 q^{41} +(0.513671 - 3.20459i) q^{42} -3.41147 q^{43} +(-0.766044 - 1.32683i) q^{44} +(4.54576 - 7.87349i) q^{45} +(5.95084 - 10.3072i) q^{46} +(2.27719 + 3.94421i) q^{47} -3.07873 q^{48} +(-6.64930 - 2.18788i) q^{49} +14.0496 q^{50} +(1.71301 + 2.96702i) q^{51} +(-3.37939 + 5.85327i) q^{52} +(3.61721 - 6.26519i) q^{53} +(3.41875 + 5.92145i) q^{54} +3.53209 q^{55} +(-0.368241 + 2.29731i) q^{56} +1.18479 q^{57} +(-1.80541 - 3.12706i) q^{58} +(-4.76991 + 8.26173i) q^{59} +(-1.76604 + 3.05888i) q^{60} +(0.573978 + 0.994159i) q^{61} +2.75877 q^{62} +(6.36231 - 2.42869i) q^{63} -3.92127 q^{64} +(-7.79086 - 13.4942i) q^{65} +(-0.613341 + 1.06234i) q^{66} +(0.347296 - 0.601535i) q^{67} +(4.02094 + 6.96448i) q^{68} -4.13341 q^{69} +(13.6284 + 11.0781i) q^{70} +9.46110 q^{71} +(-1.13176 - 1.96026i) q^{72} +(-1.17365 + 2.03282i) q^{73} +(-4.18479 + 7.24827i) q^{74} +(-2.43969 - 4.22567i) q^{75} +2.78106 q^{76} +(2.05303 + 1.66885i) q^{77} +5.41147 q^{78} +(6.20961 + 10.7554i) q^{79} +(8.33022 - 14.4284i) q^{80} +(-2.67365 + 4.63089i) q^{81} +(-0.266044 - 0.460802i) q^{82} -11.3327 q^{83} +(-2.47178 + 0.943555i) q^{84} -18.5398 q^{85} +(3.20574 + 5.55250i) q^{86} +(-0.627011 + 1.08602i) q^{87} +(0.439693 - 0.761570i) q^{88} +(1.73396 + 3.00330i) q^{89} -17.0865 q^{90} +(1.84730 - 11.5245i) q^{91} -9.70233 q^{92} +(-0.479055 - 0.829748i) q^{93} +(4.27972 - 7.41268i) q^{94} +(-3.20574 + 5.55250i) q^{95} +(2.31908 + 4.01676i) q^{96} +15.3473 q^{97} +(2.68732 + 12.8783i) q^{98} -2.57398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 6 q^{5} - 6 q^{6} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^3 - 6 * q^5 - 6 * q^6 + 6 * q^8	\( 6 q - 3 q^{3} - 6 q^{5} - 6 q^{6} + 6 q^{8} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{16} + 3 q^{17} + 12 q^{18} - 9 q^{19} + 12 q^{20} - 12 q^{21} - 6 q^{24} - 3 q^{25} - 9 q^{26} + 12 q^{27} + 3 q^{28} - 6 q^{29} + 6 q^{30} - 9 q^{31} + 9 q^{32} - 3 q^{33} - 12 q^{34} - 15 q^{35} + 6 q^{36} - 3 q^{39} - 3 q^{40} + 18 q^{41} - 18 q^{42} - 3 q^{45} + 24 q^{46} + 3 q^{47} - 36 q^{48} + 30 q^{50} + 18 q^{51} - 9 q^{52} - 9 q^{53} + 18 q^{54} + 12 q^{55} + 3 q^{56} - 15 q^{58} - 6 q^{60} - 12 q^{61} - 6 q^{62} + 6 q^{63} - 6 q^{64} - 15 q^{65} + 3 q^{66} + 21 q^{68} + 42 q^{69} + 45 q^{70} - 18 q^{71} - 12 q^{72} - 6 q^{73} - 18 q^{74} - 9 q^{75} - 18 q^{76} + 12 q^{78} + 3 q^{79} + 27 q^{80} - 15 q^{81} + 3 q^{82} - 30 q^{83} - 54 q^{85} + 9 q^{86} + 24 q^{87} - 3 q^{88} + 15 q^{89} - 72 q^{90} + 9 q^{91} - 6 q^{92} - 6 q^{93} - 9 q^{95} - 3 q^{96} + 90 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q - 3 * q^3 - 6 * q^5 - 6 * q^6 + 6 * q^8 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^16 + 3 * q^17 + 12 * q^18 - 9 * q^19 + 12 * q^20 - 12 * q^21 - 6 * q^24 - 3 * q^25 - 9 * q^26 + 12 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 - 9 * q^31 + 9 * q^32 - 3 * q^33 - 12 * q^34 - 15 * q^35 + 6 * q^36 - 3 * q^39 - 3 * q^40 + 18 * q^41 - 18 * q^42 - 3 * q^45 + 24 * q^46 + 3 * q^47 - 36 * q^48 + 30 * q^50 + 18 * q^51 - 9 * q^52 - 9 * q^53 + 18 * q^54 + 12 * q^55 + 3 * q^56 - 15 * q^58 - 6 * q^60 - 12 * q^61 - 6 * q^62 + 6 * q^63 - 6 * q^64 - 15 * q^65 + 3 * q^66 + 21 * q^68 + 42 * q^69 + 45 * q^70 - 18 * q^71 - 12 * q^72 - 6 * q^73 - 18 * q^74 - 9 * q^75 - 18 * q^76 + 12 * q^78 + 3 * q^79 + 27 * q^80 - 15 * q^81 + 3 * q^82 - 30 * q^83 - 54 * q^85 + 9 * q^86 + 24 * q^87 - 3 * q^88 + 15 * q^89 - 72 * q^90 + 9 * q^91 - 6 * q^92 - 6 * q^93 - 9 * q^95 - 3 * q^96 + 90 * q^97 - 6 * q^98

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