LMFDB - Embedded newform 494.2.m.a.381.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [494,2,Mod(153,494)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(494, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("494.153");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 494 = 2 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	494.m (of order $6$, 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:	$3.94460985985$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 198x^{12} + 718x^{10} + 1229x^{8} + 990x^{6} + 373x^{4} + 64x^{2} + 4 $ x^16 + 24x^14 + 198x^12 + 718x^10 + 1229x^8 + 990x^6 + 373x^4 + 64*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			381.1
Root			$-1.40354i$ of defining polynomial
Character	$\chi$	$=$	494.381
Dual form			494.2.m.a.153.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.701771 + 1.21550i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.425845i q^{5} +(1.21550 - 0.701771i) q^{6} +(-2.53322 + 1.46256i) q^{7} -1.00000i q^{8} +(0.515036 + 0.892068i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.701771 + 1.21550i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.425845i q^{5} +(1.21550 - 0.701771i) q^{6} +(-2.53322 + 1.46256i) q^{7} -1.00000i q^{8} +(0.515036 + 0.892068i) q^{9} +(-0.212922 + 0.368793i) q^{10} +(-5.41504 - 3.12637i) q^{11} -1.40354 q^{12} +(3.34419 - 1.34773i) q^{13} +2.92512 q^{14} +(0.517616 + 0.298846i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.18343 - 3.78180i) q^{17} -1.03007i q^{18} +(-0.866025 + 0.500000i) q^{19} +(0.368793 - 0.212922i) q^{20} -4.10552i q^{21} +(3.12637 + 5.41504i) q^{22} +(1.12225 - 1.94379i) q^{23} +(1.21550 + 0.701771i) q^{24} +4.81866 q^{25} +(-3.57002 - 0.504926i) q^{26} -5.65637 q^{27} +(-2.53322 - 1.46256i) q^{28} +(-0.197114 + 0.341411i) q^{29} +(-0.298846 - 0.517616i) q^{30} -4.46367i q^{31} +(0.866025 - 0.500000i) q^{32} +(7.60023 - 4.38799i) q^{33} +4.36685i q^{34} +(0.622823 + 1.07876i) q^{35} +(-0.515036 + 0.892068i) q^{36} +(-5.53194 - 3.19387i) q^{37} +1.00000 q^{38} +(-0.708685 + 5.01067i) q^{39} -0.425845 q^{40} +(-3.92169 - 2.26419i) q^{41} +(-2.05276 + 3.55549i) q^{42} +(-4.45097 - 7.70930i) q^{43} -6.25275i q^{44} +(0.379883 - 0.219325i) q^{45} +(-1.94379 + 1.12225i) q^{46} -7.29953i q^{47} +(-0.701771 - 1.21550i) q^{48} +(0.778151 - 1.34780i) q^{49} +(-4.17308 - 2.40933i) q^{50} +6.12906 q^{51} +(2.83927 + 2.22229i) q^{52} -4.60396 q^{53} +(4.89856 + 2.82819i) q^{54} +(-1.33135 + 2.30597i) q^{55} +(1.46256 + 2.53322i) q^{56} -1.40354i q^{57} +(0.341411 - 0.197114i) q^{58} +(-0.884781 + 0.510829i) q^{59} +0.597691i q^{60} +(1.82701 + 3.16448i) q^{61} +(-2.23183 + 3.86565i) q^{62} +(-2.60940 - 1.50654i) q^{63} -1.00000 q^{64} +(-0.573925 - 1.42411i) q^{65} -8.77599 q^{66} +(-7.12906 - 4.11596i) q^{67} +(2.18343 - 3.78180i) q^{68} +(1.57513 + 2.72820i) q^{69} -1.24565i q^{70} +(-4.25637 + 2.45742i) q^{71} +(0.892068 - 0.515036i) q^{72} +10.5155i q^{73} +(3.19387 + 5.53194i) q^{74} +(-3.38159 + 5.85709i) q^{75} +(-0.866025 - 0.500000i) q^{76} +18.2900 q^{77} +(3.11908 - 3.98503i) q^{78} +7.39511 q^{79} +(0.368793 + 0.212922i) q^{80} +(2.42437 - 4.19913i) q^{81} +(2.26419 + 3.92169i) q^{82} +9.79541i q^{83} +(3.55549 - 2.05276i) q^{84} +(-1.61046 + 0.929801i) q^{85} +8.90193i q^{86} +(-0.276657 - 0.479184i) q^{87} +(-3.12637 + 5.41504i) q^{88} +(-0.478479 - 0.276250i) q^{89} -0.438651 q^{90} +(-6.50045 + 8.30518i) q^{91} +2.24450 q^{92} +(5.42560 + 3.13247i) q^{93} +(-3.64976 + 6.32158i) q^{94} +(0.212922 + 0.368793i) q^{95} +1.40354i q^{96} +(-4.22473 + 2.43915i) q^{97} +(-1.34780 + 0.778151i) q^{98} -6.44077i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 8 q^{4}+O(q^{10}) $ 16 * q + 4 * q^3 + 8 * q^4	$ 16 q + 4 q^{3} + 8 q^{4} - 2 q^{10} - 6 q^{11} + 8 q^{12} - 4 q^{14} - 18 q^{15} - 8 q^{16} + 2 q^{17} + 10 q^{22} - 8 q^{23} + 28 q^{25} - 14 q^{26} - 44 q^{27} - 8 q^{29} + 30 q^{33} + 10 q^{35} + 6 q^{37} + 16 q^{38} - 34 q^{39} - 4 q^{40} + 6 q^{41} - 12 q^{42} - 16 q^{43} - 30 q^{45} + 12 q^{46} + 4 q^{48} - 14 q^{49} + 12 q^{50} + 44 q^{51} - 48 q^{53} - 36 q^{54} + 10 q^{55} - 2 q^{56} - 6 q^{58} + 84 q^{59} + 26 q^{61} - 12 q^{62} + 12 q^{63} - 16 q^{64} - 30 q^{65} + 8 q^{66} - 18 q^{67} - 2 q^{68} + 6 q^{69} - 6 q^{71} + 12 q^{72} + 6 q^{75} + 24 q^{77} - 30 q^{78} - 44 q^{79} - 36 q^{81} + 2 q^{82} + 12 q^{84} + 48 q^{85} + 38 q^{87} - 10 q^{88} + 36 q^{89} + 24 q^{90} - 28 q^{91} - 16 q^{92} + 54 q^{93} - 12 q^{94} + 2 q^{95} + 12 q^{97} + 24 q^{98}+O(q^{100}) $ 16 * q + 4 * q^3 + 8 * q^4 - 2 * q^10 - 6 * q^11 + 8 * q^12 - 4 * q^14 - 18 * q^15 - 8 * q^16 + 2 * q^17 + 10 * q^22 - 8 * q^23 + 28 * q^25 - 14 * q^26 - 44 * q^27 - 8 * q^29 + 30 * q^33 + 10 * q^35 + 6 * q^37 + 16 * q^38 - 34 * q^39 - 4 * q^40 + 6 * q^41 - 12 * q^42 - 16 * q^43 - 30 * q^45 + 12 * q^46 + 4 * q^48 - 14 * q^49 + 12 * q^50 + 44 * q^51 - 48 * q^53 - 36 * q^54 + 10 * q^55 - 2 * q^56 - 6 * q^58 + 84 * q^59 + 26 * q^61 - 12 * q^62 + 12 * q^63 - 16 * q^64 - 30 * q^65 + 8 * q^66 - 18 * q^67 - 2 * q^68 + 6 * q^69 - 6 * q^71 + 12 * q^72 + 6 * q^75 + 24 * q^77 - 30 * q^78 - 44 * q^79 - 36 * q^81 + 2 * q^82 + 12 * q^84 + 48 * q^85 + 38 * q^87 - 10 * q^88 + 36 * q^89 + 24 * q^90 - 28 * q^91 - 16 * q^92 + 54 * q^93 - 12 * q^94 + 2 * q^95 + 12 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/494\mathbb{Z}\right)^\times$.

$n$	$287$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.701771	+	1.21550i	−0.405168	+	0.701771i	−0.994341	−	0.106236i	$-0.966120\pi$
$3$	−0.701771	+	1.21550i	−0.405168	+	0.701771i	0.589173	+	0.808007i	$0.299453\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	0.425845i		−	0.190444i	−0.995456	−	0.0952218i	$-0.969644\pi$
$5$		−	0.425845i		−	0.190444i	0.995456	−	0.0952218i	$-0.0303560\pi$
$6$	1.21550	−	0.701771i	0.496227	−	0.286497i
$7$	−2.53322	+	1.46256i	−0.957469	+	0.552795i	−0.895393	−	0.445277i	$-0.853105\pi$
$7$	−2.53322	+	1.46256i	−0.957469	+	0.552795i	−0.0620757	+	0.998071i	$0.519772\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.515036	+	0.892068i	0.171679	+	0.297356i
$10$	−0.212922	+	0.368793i	−0.0673320	+	0.116622i
$11$	−5.41504	−	3.12637i	−1.63270	−	0.942637i	−0.983257	−	0.182222i	$-0.941671\pi$
$11$	−5.41504	−	3.12637i	−1.63270	−	0.942637i	−0.649438	−	0.760415i	$-0.724996\pi$
$12$	−1.40354			−0.405168
$13$	3.34419	−	1.34773i	0.927512	−	0.373794i
$13$	3.34419	−	1.34773i	0.927512	−	0.373794i
$14$	2.92512			0.781770
$15$	0.517616	+	0.298846i	0.133648	+	0.0771616i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.18343	−	3.78180i	−0.529559	−	0.917222i	−0.999406	−	0.0344744i	$-0.989024\pi$
$17$	−2.18343	−	3.78180i	−0.529559	−	0.917222i	0.469847	−	0.882748i	$-0.344309\pi$
$18$		−	1.03007i		−	0.242790i
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$20$	0.368793	−	0.212922i	0.0824645	−	0.0476109i
$21$		−	4.10552i		−	0.895898i
$22$	3.12637	+	5.41504i	0.666545	+	1.15449i
$23$	1.12225	−	1.94379i	0.234005	−	0.405309i	−0.724978	−	0.688772i	$-0.758150\pi$
$23$	1.12225	−	1.94379i	0.234005	−	0.405309i	0.958983	+	0.283463i	$0.0914833\pi$
$24$	1.21550	+	0.701771i	0.248113	+	0.143248i
$25$	4.81866			0.963731
$26$	−3.57002	−	0.504926i	−0.700139	−	0.0990242i
$27$	−5.65637			−1.08857
$28$	−2.53322	−	1.46256i	−0.478734	−	0.276397i
$29$	−0.197114	+	0.341411i	−0.0366031	+	0.0633984i	−0.883747	−	0.467966i	$-0.844987\pi$
$29$	−0.197114	+	0.341411i	−0.0366031	+	0.0633984i	0.847144	+	0.531364i	$0.178320\pi$
$30$	−0.298846	−	0.517616i	−0.0545615	−	0.0945033i
$31$		−	4.46367i		−	0.801698i	−0.916144	−	0.400849i	$-0.868715\pi$
$31$		−	4.46367i		−	0.801698i	0.916144	−	0.400849i	$-0.131285\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	7.60023	−	4.38799i	1.32303	−	0.763852i
$34$			4.36685i			0.748909i
$35$	0.622823	+	1.07876i	0.105276	+	0.182344i
$36$	−0.515036	+	0.892068i	−0.0858393	+	0.148678i
$37$	−5.53194	−	3.19387i	−0.909446	−	0.525069i	−0.0291931	−	0.999574i	$-0.509294\pi$
$37$	−5.53194	−	3.19387i	−0.909446	−	0.525069i	−0.880253	+	0.474505i	$0.842627\pi$
$38$	1.00000			0.162221
$39$	−0.708685	+	5.01067i	−0.113480	+	0.802350i
$40$	−0.425845			−0.0673320
$41$	−3.92169	−	2.26419i	−0.612465	−	0.353607i	0.161465	−	0.986879i	$-0.448378\pi$
$41$	−3.92169	−	2.26419i	−0.612465	−	0.353607i	−0.773930	+	0.633272i	$0.781712\pi$
$42$	−2.05276	+	3.55549i	−0.316748	+	0.548623i
$43$	−4.45097	−	7.70930i	−0.678766	−	1.17566i	−0.975353	−	0.220651i	$-0.929182\pi$
$43$	−4.45097	−	7.70930i	−0.678766	−	1.17566i	0.296587	−	0.955006i	$-0.404152\pi$
$44$		−	6.25275i		−	0.942637i
$45$	0.379883	−	0.219325i	0.0566295	−	0.0326951i
$46$	−1.94379	+	1.12225i	−0.286597	+	0.165467i
$47$		−	7.29953i		−	1.06475i	−0.846510	−	0.532373i	$-0.821301\pi$
$47$		−	7.29953i		−	1.06475i	0.846510	−	0.532373i	$-0.178699\pi$
$48$	−0.701771	−	1.21550i	−0.101292	−	0.175443i
$49$	0.778151	−	1.34780i	0.111164	−	0.192542i
$50$	−4.17308	−	2.40933i	−0.590162	−	0.340730i
$51$	6.12906			0.858240
$52$	2.83927	+	2.22229i	0.393735	+	0.308176i
$53$	−4.60396			−0.632402			−0.316201	−	0.948692i	$-0.602407\pi$
$53$	−4.60396			−0.632402			−0.316201	+	0.948692i	$0.602407\pi$
$54$	4.89856	+	2.82819i	0.666610	+	0.384867i
$55$	−1.33135	+	2.30597i	−0.179519	+	0.310936i
$56$	1.46256	+	2.53322i	0.195443	+	0.338516i
$57$		−	1.40354i		−	0.185904i
$58$	0.341411	−	0.197114i	0.0448294	−	0.0258823i
$59$	−0.884781	+	0.510829i	−0.115189	+	0.0665042i	−0.556487	−	0.830856i	$-0.687851\pi$
$59$	−0.884781	+	0.510829i	−0.115189	+	0.0665042i	0.441299	+	0.897360i	$0.354518\pi$
$60$			0.597691i			0.0771616i
$61$	1.82701	+	3.16448i	0.233925	+	0.405170i	0.958960	−	0.283542i	$-0.0915096\pi$
$61$	1.82701	+	3.16448i	0.233925	+	0.405170i	−0.725035	+	0.688712i	$0.758176\pi$
$62$	−2.23183	+	3.86565i	−0.283443	+	0.490938i
$63$	−2.60940	−	1.50654i	−0.328754	−	0.189806i
$64$	−1.00000			−0.125000
$65$	−0.573925	−	1.42411i	−0.0711866	−	0.176639i
$66$	−8.77599			−1.08025
$67$	−7.12906	−	4.11596i	−0.870953	−	0.502845i	−0.00328842	−	0.999995i	$-0.501047\pi$
$67$	−7.12906	−	4.11596i	−0.870953	−	0.502845i	−0.867665	+	0.497149i	$0.834380\pi$
$68$	2.18343	−	3.78180i	0.264779	−	0.458611i
$69$	1.57513	+	2.72820i	0.189623	+	0.328436i
$70$		−	1.24565i		−	0.148883i
$71$	−4.25637	+	2.45742i	−0.505138	+	0.291642i	−0.730833	−	0.682556i	$-0.760868\pi$
$71$	−4.25637	+	2.45742i	−0.505138	+	0.291642i	0.225695	+	0.974198i	$0.427535\pi$
$72$	0.892068	−	0.515036i	0.105131	−	0.0606975i
$73$			10.5155i			1.23075i	0.788236	+	0.615373i	$0.210995\pi$
$73$			10.5155i			1.23075i	−0.788236	+	0.615373i	$0.789005\pi$
$74$	3.19387	+	5.53194i	0.371280	+	0.643075i
$75$	−3.38159	+	5.85709i	−0.390473	+	0.676318i
$76$	−0.866025	−	0.500000i	−0.0993399	−	0.0573539i
$77$	18.2900			2.08434
$78$	3.11908	−	3.98503i	0.353166	−	0.451216i
$79$	7.39511			0.832014			0.416007	−	0.909361i	$-0.363429\pi$
$79$	7.39511			0.832014			0.416007	+	0.909361i	$0.363429\pi$
$80$	0.368793	+	0.212922i	0.0412323	+	0.0238055i
$81$	2.42437	−	4.19913i	0.269374	−	0.466570i
$82$	2.26419	+	3.92169i	0.250038	+	0.433078i
$83$			9.79541i			1.07519i	0.843205	+	0.537593i	$0.180666\pi$
$83$			9.79541i			1.07519i	−0.843205	+	0.537593i	$0.819334\pi$
$84$	3.55549	−	2.05276i	0.387935	−	0.223975i
$85$	−1.61046	+	0.929801i	−0.174679	+	0.100851i
$86$			8.90193i			0.959920i
$87$	−0.276657	−	0.479184i	−0.0296608	−	0.0513739i
$88$	−3.12637	+	5.41504i	−0.333273	+	0.577245i
$89$	−0.478479	−	0.276250i	−0.0507187	−	0.0292824i	0.474426	−	0.880295i	$-0.342656\pi$
$89$	−0.478479	−	0.276250i	−0.0507187	−	0.0292824i	−0.525145	+	0.851013i	$0.675989\pi$
$90$	−0.438651			−0.0462378
$91$	−6.50045	+	8.30518i	−0.681433	+	0.870619i
$92$	2.24450			0.234005
$93$	5.42560	+	3.13247i	0.562608	+	0.324822i
$94$	−3.64976	+	6.32158i	−0.376444	+	0.652021i
$95$	0.212922	+	0.368793i	0.0218454	+	0.0378373i
$96$			1.40354i			0.143248i
$97$	−4.22473	+	2.43915i	−0.428956	+	0.247658i	−0.698902	−	0.715218i	$-0.746328\pi$
$97$	−4.22473	+	2.43915i	−0.428956	+	0.247658i	0.269946	+	0.962876i	$0.412994\pi$
$98$	−1.34780	+	0.778151i	−0.136148	+	0.0786051i
$99$		−	6.44077i		−	0.647322i
$100$	2.40933	+	4.17308i	0.240933	+	0.417308i
$101$	−3.87341	+	6.70895i	−0.385419	+	0.667565i	−0.991827	−	0.127588i	$-0.959276\pi$
$101$	−3.87341	+	6.70895i	−0.385419	+	0.667565i	0.606408	+	0.795153i	$0.292610\pi$
$102$	−5.30792	−	3.06453i	−0.525562	−	0.303434i
$103$	5.07181			0.499740			0.249870	−	0.968279i	$-0.419612\pi$
$103$	5.07181			0.499740			0.249870	+	0.968279i	$0.419612\pi$
$104$	−1.34773	−	3.34419i	−0.132156	−	0.327925i
$105$	−1.74832			−0.170618
$106$	3.98714	+	2.30198i	0.387266	+	0.223588i
$107$	4.85997	−	8.41771i	0.469831	−	0.813771i	−0.529574	−	0.848264i	$-0.677648\pi$
$107$	4.85997	−	8.41771i	0.469831	−	0.813771i	0.999405	+	0.0344928i	$0.0109816\pi$
$108$	−2.82819	−	4.89856i	−0.272142	−	0.471364i
$109$			8.51312i			0.815409i	0.913114	+	0.407705i	$0.133671\pi$
$109$			8.51312i			0.815409i	−0.913114	+	0.407705i	$0.866329\pi$
$110$	2.30597	−	1.33135i	0.219865	−	0.126939i
$111$	7.76431	−	4.48273i	0.736956	−	0.425482i
$112$		−	2.92512i		−	0.276397i
$113$	−10.4443	−	18.0901i	−0.982517	−	1.70177i	−0.652490	−	0.757797i	$-0.726276\pi$
$113$	−10.4443	−	18.0901i	−0.982517	−	1.70177i	−0.330027	−	0.943972i	$-0.607058\pi$
$114$	−0.701771	+	1.21550i	−0.0657269	+	0.113842i
$115$	−0.827755	−	0.477905i	−0.0771886	−	0.0445648i
$116$	−0.394227			−0.0366031
$117$	2.92465	+	2.28912i	0.270384	+	0.211629i
$118$	1.02166			0.0940512
$119$	11.0622	+	6.38677i	1.01407	+	0.585474i
$120$	0.298846	−	0.517616i	0.0272807	−	0.0472516i
$121$	14.0484	+	24.3326i	1.27713	+	2.21205i
$122$		−	3.65403i		−	0.330820i
$123$	5.50425	−	3.17788i	0.496302	−	0.286540i
$124$	3.86565	−	2.23183i	0.347145	−	0.200424i
$125$		−	4.18123i		−	0.373980i
$126$	1.50654	+	2.60940i	0.134213	+	0.232464i
$127$	−7.72008	+	13.3716i	−0.685046	+	1.18653i	0.288376	+	0.957517i	$0.406885\pi$
$127$	−7.72008	+	13.3716i	−0.685046	+	1.18653i	−0.973422	+	0.229017i	$0.926449\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	12.4942			1.10006
$130$	−0.215020	+	1.52028i	−0.0188585	+	0.133337i
$131$	19.5021			1.70390			0.851952	−	0.523619i	$-0.175419\pi$
$131$	19.5021			1.70390			0.851952	+	0.523619i	$0.175419\pi$
$132$	7.60023	+	4.38799i	0.661515	+	0.381926i
$133$	1.46256	−	2.53322i	0.126820	−	0.219658i
$134$	4.11596	+	7.12906i	0.355565	+	0.615857i
$135$			2.40874i			0.207311i
$136$	−3.78180	+	2.18343i	−0.324287	+	0.187227i
$137$	7.22366	−	4.17058i	0.617159	−	0.356317i	−0.158603	−	0.987342i	$-0.550699\pi$
$137$	7.22366	−	4.17058i	0.617159	−	0.356317i	0.775762	+	0.631026i	$0.217366\pi$
$138$		−	3.15025i		−	0.268167i
$139$	4.32142	+	7.48491i	0.366538	+	0.634862i	0.989022	−	0.147771i	$-0.0472097\pi$
$139$	4.32142	+	7.48491i	0.366538	+	0.634862i	−0.622484	+	0.782633i	$0.713876\pi$
$140$	−0.622823	+	1.07876i	−0.0526381	+	0.0911719i
$141$	8.87259	+	5.12259i	0.747207	+	0.431400i
$142$	4.91483			0.412444
$143$	−22.3224	−	3.15717i	−1.86670	−	0.264016i
$144$	−1.03007			−0.0858393
$145$	0.145388	+	0.0839398i	0.0120738	+	0.00697082i
$146$	5.25775	−	9.10669i	0.435135	−	0.753675i
$147$	1.09217	+	1.89169i	0.0900804	+	0.156024i
$148$		−	6.38774i		−	0.525069i
$149$	6.31582	−	3.64644i	0.517412	−	0.298728i	−0.218463	−	0.975845i	$-0.570104\pi$
$149$	6.31582	−	3.64644i	0.517412	−	0.298728i	0.735875	+	0.677117i	$0.236771\pi$
$150$	5.85709	−	3.38159i	0.478229	−	0.276106i
$151$		−	0.0688467i		−	0.00560267i	−0.999996	−	0.00280133i	$-0.999108\pi$
$151$		−	0.0688467i		−	0.00560267i	0.999996	−	0.00280133i	$-0.000891693\pi$
$152$	0.500000	+	0.866025i	0.0405554	+	0.0702439i
$153$	2.24908	−	3.89553i	0.181828	−	0.314935i
$154$	−15.8396	−	9.14500i	−1.27639	−	0.736925i
$155$	−1.90083			−0.152678
$156$	−4.69371	+	1.89160i	−0.375798	+	0.151449i
$157$	−10.5441			−0.841510			−0.420755	−	0.907174i	$-0.638235\pi$
$157$	−10.5441			−0.841510			−0.420755	+	0.907174i	$0.638235\pi$
$158$	−6.40435	−	3.69755i	−0.509503	−	0.294162i
$159$	3.23092	−	5.59612i	0.256229	−	0.443801i
$160$	−0.212922	−	0.368793i	−0.0168330	−	0.0291556i
$161$			6.56542i			0.517428i
$162$	−4.19913	+	2.42437i	−0.329915	+	0.190477i
$163$	−5.21619	+	3.01157i	−0.408564	+	0.235884i	−0.690172	−	0.723645i	$-0.742465\pi$
$163$	−5.21619	+	3.01157i	−0.408564	+	0.235884i	0.281609	+	0.959529i	$0.409132\pi$
$164$		−	4.52838i		−	0.353607i
$165$	−1.86861	−	3.23652i	−0.145471	−	0.251963i
$166$	4.89770	−	8.48307i	0.380136	−	0.658414i
$167$	−8.07622	−	4.66281i	−0.624956	−	0.360819i	0.153840	−	0.988096i	$-0.450836\pi$
$167$	−8.07622	−	4.66281i	−0.624956	−	0.360819i	−0.778796	+	0.627277i	$0.784169\pi$
$168$	−4.10552			−0.316748
$169$	9.36724	−	9.01415i	0.720557	−	0.693396i
$170$	1.85960			0.142625
$171$	−0.892068	−	0.515036i	−0.0682181	−	0.0393858i
$172$	4.45097	−	7.70930i	0.339383	−	0.587829i
$173$	−9.33088	−	16.1616i	−0.709414	−	1.22874i	−0.965075	−	0.261974i	$-0.915627\pi$
$173$	−9.33088	−	16.1616i	−0.709414	−	1.22874i	0.255661	−	0.966766i	$-0.417707\pi$
$174$			0.553314i			0.0419466i
$175$	−12.2067	+	7.04756i	−0.922743	+	0.532746i
$176$	5.41504	−	3.12637i	0.408174	−	0.235659i
$177$		−	1.43394i		−	0.107781i
$178$	0.276250	+	0.478479i	0.0207058	+	0.0358635i
$179$	−12.2124	+	21.1525i	−0.912799	+	1.58101i	−0.102707	+	0.994712i	$0.532750\pi$
$179$	−12.2124	+	21.1525i	−0.912799	+	1.58101i	−0.810092	+	0.586303i	$0.800583\pi$
$180$	0.379883	+	0.219325i	0.0283148	+	0.0163475i
$181$	−26.4469			−1.96579			−0.982893	−	0.184179i	$-0.941037\pi$
$181$	−26.4469			−1.96579			−0.982893	+	0.184179i	$0.941037\pi$
$182$	9.78215	−	3.94227i	0.725101	−	0.292221i
$183$	−5.12858			−0.379115
$184$	−1.94379	−	1.12225i	−0.143298	−	0.0827334i
$185$	−1.36009	+	2.35575i	−0.0999960	+	0.173198i
$186$	−3.13247	−	5.42560i	−0.229684	−	0.397824i
$187$			27.3048i			1.99673i
$188$	6.32158	−	3.64976i	0.461048	−	0.266186i
$189$	14.3289	−	8.27277i	1.04227	−	0.601756i
$190$		−	0.425845i		−	0.0308940i
$191$	7.70178	+	13.3399i	0.557281	+	0.965239i	0.997722	+	0.0674577i	$0.0214888\pi$
$191$	7.70178	+	13.3399i	0.557281	+	0.965239i	−0.440441	+	0.897782i	$0.645178\pi$
$192$	0.701771	−	1.21550i	0.0506459	−	0.0877213i
$193$	−8.35286	−	4.82253i	−0.601252	−	0.347133i	0.168282	−	0.985739i	$-0.446178\pi$
$193$	−8.35286	−	4.82253i	−0.601252	−	0.347133i	−0.769534	+	0.638606i	$0.779511\pi$
$194$	4.87829			0.350241
$195$	2.13377	+	0.301790i	0.152802	+	0.0216116i
$196$	1.55630			0.111164
$197$	−7.65834	−	4.42154i	−0.545634	−	0.315022i	0.201725	−	0.979442i	$-0.435345\pi$
$197$	−7.65834	−	4.42154i	−0.545634	−	0.315022i	−0.747359	+	0.664420i	$0.768679\pi$
$198$	−3.22039	+	5.57787i	−0.228863	+	0.396402i
$199$	−7.63434	−	13.2231i	−0.541184	−	0.937358i	−0.998836	−	0.0482272i	$-0.984643\pi$
$199$	−7.63434	−	13.2231i	−0.541184	−	0.937358i	0.457652	−	0.889131i	$-0.348690\pi$
$200$		−	4.81866i		−	0.340730i
$201$	10.0059	−	5.77693i	0.705764	−	0.407473i
$202$	6.70895	−	3.87341i	0.472040	−	0.272532i
$203$		−	1.15316i		−	0.0809360i
$204$	3.06453	+	5.30792i	0.214560	+	0.371629i
$205$	−0.964193	+	1.67003i	−0.0673422	+	0.116640i
$206$	−4.39232	−	2.53591i	−0.306027	−	0.176685i
$207$	2.31200			0.160695
$208$	−0.504926	+	3.57002i	−0.0350103	+	0.247536i
$209$	6.25275			0.432512
$210$	1.51409	+	0.874158i	0.104482	+	0.0603226i
$211$	−8.41601	+	14.5770i	−0.579382	+	1.00352i	0.416168	+	0.909288i	$0.363373\pi$
$211$	−8.41601	+	14.5770i	−0.579382	+	1.00352i	−0.995550	+	0.0942315i	$0.969961\pi$
$212$	−2.30198	−	3.98714i	−0.158101	−	0.273838i
$213$		−	6.89817i		−	0.472655i
$214$	−8.41771	+	4.85997i	−0.575423	+	0.332221i
$215$	−3.28297	+	1.89542i	−0.223896	+	0.129267i
$216$			5.65637i			0.384867i
$217$	6.52837	+	11.3075i	0.443175	+	0.767601i
$218$	4.25656	−	7.37258i	0.288291	−	0.499334i
$219$	−12.7816	−	7.37947i	−0.863702	−	0.498659i
$220$	−2.66270			−0.179519
$221$	−12.3987	−	9.70441i	−0.834024	−	0.652789i
$222$	−8.96546			−0.601722
$223$	−1.14874	−	0.663223i	−0.0769250	−	0.0444127i	0.461044	−	0.887377i	$-0.347475\pi$
$223$	−1.14874	−	0.663223i	−0.0769250	−	0.0444127i	−0.537969	+	0.842965i	$0.680808\pi$
$224$	−1.46256	+	2.53322i	−0.0977213	+	0.169258i
$225$	2.48178	+	4.29857i	0.165452	+	0.286571i
$226$			20.8886i			1.38949i
$227$	19.4571	−	11.2336i	1.29142	−	0.745599i	0.312510	−	0.949914i	$-0.398830\pi$
$227$	19.4571	−	11.2336i	1.29142	−	0.745599i	0.978905	+	0.204315i	$0.0654967\pi$
$228$	1.21550	−	0.701771i	0.0804986	−	0.0464759i
$229$		−	19.4946i		−	1.28824i	−0.764925	−	0.644119i	$-0.777224\pi$
$229$		−	19.4946i		−	1.28824i	0.764925	−	0.644119i	$-0.222776\pi$
$230$	0.477905	+	0.827755i	0.0315121	+	0.0545806i
$231$	−12.8354	+	22.2316i	−0.844507	+	1.46273i
$232$	0.341411	+	0.197114i	0.0224147	+	0.0129411i
$233$	18.1804			1.19103			0.595517	−	0.803342i	$-0.296947\pi$
$233$	18.1804			1.19103			0.595517	+	0.803342i	$0.296947\pi$
$234$	−1.38826	−	3.44476i	−0.0907534	−	0.225191i
$235$	−3.10847			−0.202774
$236$	−0.884781	−	0.510829i	−0.0575943	−	0.0332521i
$237$	−5.18967	+	8.98877i	−0.337105	+	0.583883i
$238$	−6.38677	−	11.0622i	−0.413993	−	0.717057i
$239$			28.3307i			1.83256i	0.400541	+	0.916279i	$0.368822\pi$
$239$			28.3307i			1.83256i	−0.400541	+	0.916279i	$0.631178\pi$
$240$	−0.517616	+	0.298846i	−0.0334119	+	0.0192904i
$241$	8.45430	−	4.88109i	0.544589	−	0.314419i	−0.202348	−	0.979314i	$-0.564857\pi$
$241$	8.45430	−	4.88109i	0.544589	−	0.314419i	0.746937	+	0.664895i	$0.231524\pi$
$242$		−	28.0968i		−	1.80613i
$243$	−5.08185	−	8.80203i	−0.326001	−	0.564650i
$244$	−1.82701	+	3.16448i	−0.116963	+	0.202585i
$245$	−0.573952	−	0.331372i	−0.0366685	−	0.0211705i
$246$	−6.35577			−0.405229
$247$	−2.22229	+	2.83927i	−0.141401	+	0.180658i
$248$	−4.46367			−0.283443
$249$	−11.9063	−	6.87413i	−0.754534	−	0.435630i
$250$	−2.09061	+	3.62105i	−0.132222	+	0.229015i
$251$	−8.37372	−	14.5037i	−0.528544	−	0.915466i	−0.999446	−	0.0332802i	$-0.989405\pi$
$251$	−8.37372	−	14.5037i	−0.528544	−	0.915466i	0.470902	−	0.882186i	$-0.343929\pi$
$252$		−	3.01308i		−	0.189806i
$253$	−12.1541	+	7.01715i	−0.764119	+	0.441164i
$254$	13.3716	−	7.72008i	0.839007	−	0.484401i
$255$		−	2.61003i		−	0.163446i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.45412	+	16.3750i	−0.589732	+	1.02145i	0.404535	+	0.914522i	$0.367433\pi$
$257$	−9.45412	+	16.3750i	−0.589732	+	1.02145i	−0.994267	+	0.106923i	$0.965900\pi$
$258$	−10.8203	−	6.24712i	−0.673644	−	0.388929i
$259$	18.6849			1.16102
$260$	0.946351	−	1.20909i	0.0586902	−	0.0749844i
$261$	−0.406082			−0.0251358
$262$	−16.8893	−	9.75104i	−1.04342	−	0.602421i
$263$	−8.58263	+	14.8656i	−0.529228	+	0.916650i	0.470191	+	0.882565i	$0.344185\pi$
$263$	−8.58263	+	14.8656i	−0.529228	+	0.916650i	−0.999419	+	0.0340849i	$0.989148\pi$
$264$	−4.38799	−	7.60023i	−0.270062	−	0.467762i
$265$			1.96057i			0.120437i
$266$	−2.53322	+	1.46256i	−0.155322	+	0.0896752i
$267$	0.671565	−	0.387728i	0.0410991	−	0.0237286i
$268$		−	8.23193i		−	0.502845i
$269$	−11.9147	−	20.6368i	−0.726451	−	1.25825i	−0.958374	−	0.285516i	$-0.907835\pi$
$269$	−11.9147	−	20.6368i	−0.726451	−	1.25825i	0.231923	−	0.972734i	$-0.425498\pi$
$270$	1.20437	−	2.08603i	0.0732956	−	0.126952i
$271$	10.8006	+	6.23575i	0.656092	+	0.378795i	0.790786	−	0.612093i	$-0.209672\pi$
$271$	10.8006	+	6.23575i	0.656092	+	0.378795i	−0.134695	+	0.990887i	$0.543005\pi$
$272$	4.36685			0.264779
$273$	−5.53314	−	13.7297i	−0.334881	−	0.830956i
$274$	−8.34116			−0.503908
$275$	−26.0932	−	15.0649i	−1.57348	−	0.908449i
$276$	−1.57513	+	2.72820i	−0.0948114	+	0.164218i
$277$	−8.16516	−	14.1425i	−0.490597	−	0.849738i	0.509345	−	0.860563i	$-0.329888\pi$
$277$	−8.16516	−	14.1425i	−0.490597	−	0.849738i	−0.999941	+	0.0108243i	$0.996554\pi$
$278$		−	8.64283i		−	0.518363i
$279$	3.98189	−	2.29895i	0.238390	−	0.137634i
$280$	1.07876	−	0.622823i	0.0644683	−	0.0372208i
$281$		−	19.6635i		−	1.17302i	−0.809940	−	0.586512i	$-0.800501\pi$
$281$		−	19.6635i		−	1.17302i	0.809940	−	0.586512i	$-0.199499\pi$
$282$	−5.12259	−	8.87259i	−0.305046	−	0.528355i
$283$	8.73333	−	15.1266i	0.519142	−	0.899181i	−0.480610	−	0.876934i	$-0.659585\pi$
$283$	8.73333	−	15.1266i	0.519142	−	0.899181i	0.999753	−	0.0222467i	$-0.00708193\pi$
$284$	−4.25637	−	2.45742i	−0.252569	−	0.145821i
$285$	−0.597691			−0.0354042
$286$	17.7532	+	13.8954i	1.04977	+	0.821653i
$287$	13.2460			0.781888
$288$	0.892068	+	0.515036i	0.0525656	+	0.0303488i
$289$	−1.03470	+	1.79215i	−0.0608644	+	0.105420i
$290$	−0.0839398	−	0.145388i	−0.00492912	−	0.00853748i
$291$		−	6.84689i		−	0.401372i
$292$	−9.10669	+	5.25775i	−0.532929	+	0.307687i
$293$	−5.05625	+	2.91922i	−0.295389	+	0.170543i	−0.640370	−	0.768067i	$-0.721219\pi$
$293$	−5.05625	+	2.91922i	−0.295389	+	0.170543i	0.344981	+	0.938610i	$0.387885\pi$
$294$		−	2.18433i		−	0.127393i
$295$	0.217534	+	0.376780i	0.0126653	+	0.0219370i
$296$	−3.19387	+	5.53194i	−0.185640	+	0.321538i
$297$	30.6295	+	17.6839i	1.77730	+	1.02613i
$298$	−7.29288			−0.422465
$299$	1.13331	−	8.01292i	0.0655408	−	0.463399i
$300$	−6.76318			−0.390473
$301$	22.5506	+	13.0196i	1.29979	+	0.750437i
$302$	−0.0344234	+	0.0596230i	−0.00198084	+	0.00343092i
$303$	−5.43649	−	9.41628i	−0.312318	−	0.540951i
$304$		−	1.00000i		−	0.0573539i
$305$	1.34758	−	0.778024i	0.0771621	−	0.0445495i
$306$	−3.89553	+	2.24908i	−0.222692	+	0.128572i
$307$		−	9.68903i		−	0.552982i	−0.961017	−	0.276491i	$-0.910828\pi$
$307$		−	9.68903i		−	0.552982i	0.961017	−	0.276491i	$-0.0891716\pi$
$308$	9.14500	+	15.8396i	0.521085	+	0.902546i
$309$	−3.55925	+	6.16480i	−0.202479	+	0.350703i
$310$	1.64617	+	0.950415i	0.0934960	+	0.0539799i
$311$	1.67689			0.0950877			0.0475439	−	0.998869i	$-0.484861\pi$
$311$	1.67689			0.0950877			0.0475439	+	0.998869i	$0.484861\pi$
$312$	5.01067	+	0.708685i	0.283673	+	0.0401214i
$313$	−12.1187			−0.684991			−0.342496	−	0.939519i	$-0.611272\pi$
$313$	−12.1187			−0.684991			−0.342496	+	0.939519i	$0.611272\pi$
$314$	9.13145	+	5.27205i	0.515318	+	0.297519i
$315$	−0.641552	+	1.11120i	−0.0361474	+	0.0626090i
$316$	3.69755	+	6.40435i	0.208004	+	0.360273i
$317$			10.1049i			0.567549i	0.958891	+	0.283775i	$0.0915868\pi$
$317$			10.1049i			0.567549i	−0.958891	+	0.283775i	$0.908413\pi$
$318$	−5.59612	+	3.23092i	−0.313815	+	0.181181i
$319$	2.13475	−	1.23250i	0.119523	−	0.0690068i
$320$			0.425845i			0.0238055i
$321$	6.82117	+	11.8146i	0.380720	+	0.659427i
$322$	3.28271	−	5.68582i	0.182938	−	0.316859i
$323$	3.78180	+	2.18343i	0.210425	+	0.121489i
$324$	4.84874			0.269374
$325$	16.1145	−	6.49426i	0.893872	−	0.360236i
$326$	6.02314			0.333591
$327$	−10.3477	−	5.97426i	−0.572230	−	0.330377i
$328$	−2.26419	+	3.92169i	−0.125019	+	0.216539i
$329$	10.6760	+	18.4913i	0.588586	+	1.01946i
$330$			3.73721i			0.205727i
$331$	30.8183	−	17.7930i	1.69393	−	0.977989i	0.742636	−	0.669696i	$-0.233575\pi$
$331$	30.8183	−	17.7930i	1.69393	−	0.977989i	0.951291	−	0.308294i	$-0.0997580\pi$
$332$	−8.48307	+	4.89770i	−0.465569	+	0.268796i
$333$		−	6.57982i		−	0.360572i
$334$	4.66281	+	8.07622i	0.255137	+	0.441911i
$335$	−1.75276	+	3.03587i	−0.0957637	+	0.165868i
$336$	3.55549	+	2.05276i	0.193968	+	0.111987i
$337$	22.9814			1.25188			0.625939	−	0.779872i	$-0.284716\pi$
$337$	22.9814			1.25188			0.625939	+	0.779872i	$0.284716\pi$
$338$	−12.6193	+	3.12286i	−0.686402	+	0.169861i
$339$	29.3180			1.59234
$340$	−1.61046	−	0.929801i	−0.0873396	−	0.0504255i
$341$	−13.9551	+	24.1709i	−0.755710	+	1.30893i
$342$	0.515036	+	0.892068i	0.0278499	+	0.0482375i
$343$		−	15.9234i		−	0.859785i
$344$	−7.70930	+	4.45097i	−0.415658	+	0.239980i
$345$	1.16179	−	0.670759i	0.0625486	−	0.0361125i
$346$			18.6618i			1.00326i
$347$	−3.60278	−	6.24019i	−0.193407	−	0.334991i	0.752970	−	0.658055i	$-0.228621\pi$
$347$	−3.60278	−	6.24019i	−0.193407	−	0.334991i	−0.946377	+	0.323064i	$0.895287\pi$
$348$	0.276657	−	0.479184i	0.0148304	−	0.0256870i
$349$	−25.5887	−	14.7736i	−1.36973	−	0.790814i	−0.378836	−	0.925464i	$-0.623676\pi$
$349$	−25.5887	−	14.7736i	−1.36973	−	0.790814i	−0.990893	+	0.134650i	$0.957009\pi$
$350$	14.0951			0.753416
$351$	−18.9160	+	7.62327i	−1.00966	+	0.406900i
$352$	−6.25275			−0.333273
$353$	−1.22667	−	0.708217i	−0.0652889	−	0.0376946i	0.467000	−	0.884257i	$-0.345335\pi$
$353$	−1.22667	−	0.708217i	−0.0652889	−	0.0376946i	−0.532289	+	0.846563i	$0.678668\pi$
$354$	−0.716969	+	1.24183i	−0.0381065	+	0.0660024i
$355$	1.04648	+	1.81255i	0.0555413	+	0.0962004i
$356$		−	0.552500i		−	0.0292824i
$357$	−15.5263	+	8.96410i	−0.821738	+	0.474431i
$358$	21.1525	−	12.2124i	1.11795	−	0.645446i
$359$			2.06385i			0.108926i	0.998516	+	0.0544629i	$0.0173447\pi$
$359$			2.06385i			0.108926i	−0.998516	+	0.0544629i	$0.982655\pi$
$360$	−0.219325	−	0.379883i	−0.0115595	−	0.0200216i
$361$	0.500000	−	0.866025i	0.0263158	−	0.0455803i
$362$	22.9037	+	13.2235i	1.20379	+	0.695010i
$363$	−39.4351			−2.06981
$364$	−10.4427	−	1.47697i	−0.547347	−	0.0774141i
$365$	4.47797			0.234388
$366$	4.44148	+	2.56429i	0.232160	+	0.134038i
$367$	14.0723	−	24.3739i	0.734567	−	1.27231i	−0.220346	−	0.975422i	$-0.570719\pi$
$367$	14.0723	−	24.3739i	0.734567	−	1.27231i	0.954913	−	0.296886i	$-0.0959481\pi$
$368$	1.12225	+	1.94379i	0.0585014	+	0.101327i
$369$		−	4.66455i		−	0.242827i
$370$	2.35575	−	1.36009i	0.122470	−	0.0707079i
$371$	11.6629	−	6.73355i	0.605505	−	0.349589i
$372$			6.26494i			0.324822i
$373$	15.2008	+	26.3285i	0.787067	+	1.36324i	0.927756	+	0.373186i	$0.121735\pi$
$373$	15.2008	+	26.3285i	0.787067	+	1.36324i	−0.140689	+	0.990054i	$0.544932\pi$
$374$	13.6524	−	23.6467i	0.705949	−	1.22274i
$375$	5.08229	+	2.93426i	0.262448	+	0.151525i
$376$	−7.29953			−0.376444
$377$	−0.199056	+	1.40740i	−0.0102519	+	0.0724847i
$378$	−16.5455			−0.851011
$379$	4.27701	+	2.46934i	0.219695	+	0.126841i	0.605809	−	0.795610i	$-0.292849\pi$
$379$	4.27701	+	2.46934i	0.219695	+	0.126841i	−0.386114	+	0.922451i	$0.626183\pi$
$380$	−0.212922	+	0.368793i	−0.0109227	+	0.0189187i
$381$	−10.8354	−	18.7675i	−0.555117	−	0.961490i
$382$		−	15.4036i		−	0.788115i
$383$	−12.3714	+	7.14260i	−0.632146	+	0.364970i	−0.781583	−	0.623801i	$-0.785587\pi$
$383$	−12.3714	+	7.14260i	−0.632146	+	0.364970i	0.149436	+	0.988771i	$0.452254\pi$
$384$	−1.21550	+	0.701771i	−0.0620284	+	0.0358121i
$385$		−	7.78871i		−	0.396949i
$386$	4.82253	+	8.35286i	0.245460	+	0.425149i
$387$	4.58481	−	7.94113i	0.233059	−	0.403670i
$388$	−4.22473	−	2.43915i	−0.214478	−	0.123829i
$389$	−5.81026			−0.294592			−0.147296	−	0.989092i	$-0.547057\pi$
$389$	−5.81026			−0.294592			−0.147296	+	0.989092i	$0.547057\pi$
$390$	−1.69700	−	1.32824i	−0.0859311	−	0.0672582i
$391$	−9.80140			−0.495678
$392$	−1.34780	−	0.778151i	−0.0680740	−	0.0393025i
$393$	−13.6860	+	23.7048i	−0.690367	+	1.19575i
$394$	4.42154	+	7.65834i	0.222754	+	0.385821i
$395$		−	3.14917i		−	0.158452i
$396$	5.57787	−	3.22039i	0.280299	−	0.161831i
$397$	13.4549	−	7.76822i	0.675284	−	0.389876i	−0.122792	−	0.992432i	$-0.539185\pi$
$397$	13.4549	−	7.76822i	0.675284	−	0.389876i	0.798076	+	0.602557i	$0.205851\pi$
$398$			15.2687i			0.765350i
$399$	2.05276	+	3.55549i	0.102767	+	0.177997i
$400$	−2.40933	+	4.17308i	−0.120466	+	0.208654i
$401$	−3.29004	−	1.89951i	−0.164297	−	0.0948568i	0.415597	−	0.909549i	$-0.363573\pi$
$401$	−3.29004	−	1.89951i	−0.164297	−	0.0948568i	−0.579894	+	0.814692i	$0.696906\pi$
$402$	−11.5539			−0.576254
$403$	−6.01582	−	14.9274i	−0.299669	−	0.743584i
$404$	−7.74682			−0.385419
$405$	−1.78818	−	1.03241i	−0.0888553	−	0.0513007i
$406$	−0.576580	+	0.998666i	−0.0286152	+	0.0495630i
$407$	19.9705	+	34.5898i	0.989899	+	1.71455i
$408$		−	6.12906i		−	0.303434i
$409$	18.9897	−	10.9637i	0.938982	−	0.542122i	0.0493410	−	0.998782i	$-0.484288\pi$
$409$	18.9897	−	10.9637i	0.938982	−	0.542122i	0.889641	+	0.456660i	$0.150955\pi$
$410$	1.67003	−	0.964193i	0.0824770	−	0.0476181i
$411$			11.7072i			0.577472i
$412$	2.53591	+	4.39232i	0.124935	+	0.216394i
$413$	1.49423	−	2.58809i	0.0735264	−	0.127351i
$414$	−2.00225	−	1.15600i	−0.0984051	−	0.0568142i
$415$	4.17133			0.204762
$416$	2.22229	−	2.83927i	0.108957	−	0.139206i
$417$	−12.1306			−0.594037
$418$	−5.41504	−	3.12637i	−0.264858	−	0.152916i
$419$	−9.91853	+	17.1794i	−0.484552	+	0.839269i	−0.999843	−	0.0177468i	$-0.994351\pi$
$419$	−9.91853	+	17.1794i	−0.484552	+	0.839269i	0.515290	+	0.857016i	$0.327684\pi$
$420$	−0.874158	−	1.51409i	−0.0426545	−	0.0738798i
$421$		−	15.5001i		−	0.755428i	−0.925922	−	0.377714i	$-0.876710\pi$
$421$		−	15.5001i		−	0.755428i	0.925922	−	0.377714i	$-0.123290\pi$
$422$	14.5770	−	8.41601i	0.709595	−	0.409685i
$423$	6.51167	−	3.75952i	0.316608	−	0.182794i
$424$			4.60396i			0.223588i
$425$	−10.5212	−	18.2232i	−0.510352	−	0.883956i
$426$	−3.44909	+	5.97399i	−0.167109	+	0.289441i
$427$	−9.25647	−	5.34422i	−0.447952	−	0.258625i
$428$	9.71994			0.469831
$429$	19.5028	−	24.9174i	0.941603	−	1.20302i
$430$	3.79084			0.182811
$431$	26.5033	+	15.3017i	1.27662	+	0.737057i	0.976225	−	0.216759i	$-0.0695485\pi$
$431$	26.5033	+	15.3017i	1.27662	+	0.737057i	0.300394	+	0.953815i	$0.402882\pi$
$432$	2.82819	−	4.89856i	0.136071	−	0.235682i
$433$	2.16010	+	3.74140i	0.103808	+	0.179800i	0.913250	−	0.407399i	$-0.133564\pi$
$433$	2.16010	+	3.74140i	0.103808	+	0.179800i	−0.809443	+	0.587199i	$0.800231\pi$
$434$		−	13.0567i		−	0.626743i
$435$	−0.204058	+	0.117813i	−0.00978384	+	0.00564870i
$436$	−7.37258	+	4.25656i	−0.353083	+	0.203852i
$437$			2.24450i			0.107369i
$438$	7.37947	+	12.7816i	0.352605	+	0.610730i
$439$	−9.53612	+	16.5170i	−0.455134	+	0.788316i	−0.998696	−	0.0510536i	$-0.983742\pi$
$439$	−9.53612	+	16.5170i	−0.455134	+	0.788316i	0.543562	+	0.839369i	$0.317075\pi$
$440$	2.30597	+	1.33135i	0.109933	+	0.0634696i
$441$	1.60310			0.0763381
$442$	5.88534	+	14.6036i	0.279937	+	0.694622i
$443$	18.5646			0.882032			0.441016	−	0.897499i	$-0.354618\pi$
$443$	18.5646			0.882032			0.441016	+	0.897499i	$0.354618\pi$
$444$	7.76431	+	4.48273i	0.368478	+	0.212741i
$445$	−0.117640	+	0.203758i	−0.00557666	+	0.00965905i
$446$	0.663223	+	1.14874i	0.0314045	+	0.0543942i
$447$			10.2359i			0.484139i
$448$	2.53322	−	1.46256i	0.119684	−	0.0690994i
$449$	2.28840	−	1.32121i	0.107996	−	0.0623517i	−0.445029	−	0.895516i	$-0.646807\pi$
$449$	2.28840	−	1.32121i	0.107996	−	0.0623517i	0.553025	+	0.833164i	$0.313473\pi$
$450$		−	4.96356i		−	0.233984i
$451$	14.1574	+	24.5213i	0.666646	+	1.15466i
$452$	10.4443	−	18.0901i	0.491258	−	0.850884i
$453$	0.0836834	+	0.0483146i	0.00393179	+	0.00227002i
$454$	−22.4672			−1.05444
$455$	3.53672	+	2.76819i	0.165804	+	0.129775i
$456$	−1.40354			−0.0657269
$457$	34.0304	+	19.6475i	1.59188	+	0.919071i	0.992985	+	0.118241i	$0.0377256\pi$
$457$	34.0304	+	19.6475i	1.59188	+	0.919071i	0.598892	+	0.800830i	$0.295608\pi$
$458$	−9.74729	+	16.8828i	−0.455461	+	0.788882i
$459$	12.3503	+	21.3913i	0.576461	+	0.998460i
$460$		−	0.955809i		−	0.0445648i
$461$	−27.8486	+	16.0784i	−1.29704	+	0.748844i	−0.979891	−	0.199533i	$-0.936058\pi$
$461$	−27.8486	+	16.0784i	−1.29704	+	0.748844i	−0.317145	+	0.948377i	$0.602724\pi$
$462$	22.2316	−	12.8354i	1.03431	−	0.597156i
$463$		−	10.9509i		−	0.508933i	−0.967082	−	0.254466i	$-0.918100\pi$
$463$		−	10.9509i		−	0.508933i	0.967082	−	0.254466i	$-0.0818998\pi$
$464$	−0.197114	−	0.341411i	−0.00915077	−	0.0158496i
$465$	1.33395	−	2.31046i	0.0618603	−	0.107145i
$466$	−15.7446	−	9.09018i	−0.729357	−	0.421094i
$467$	−36.2880			−1.67921			−0.839604	−	0.543199i	$-0.817213\pi$
$467$	−36.2880			−1.67921			−0.839604	+	0.543199i	$0.817213\pi$
$468$	−0.520110	+	3.67738i	−0.0240421	+	0.169987i
$469$	24.0793			1.11188
$470$	2.69201	+	1.55423i	0.124173	+	0.0716914i
$471$	7.39954	−	12.8164i	0.340953	−	0.590547i
$472$	0.510829	+	0.884781i	0.0235128	+	0.0407254i
$473$			55.6615i			2.55932i
$474$	8.98877	−	5.18967i	0.412868	−	0.238369i
$475$	−4.17308	+	2.40933i	−0.191474	+	0.110548i
$476$			12.7735i			0.585474i
$477$	−2.37120	−	4.10704i	−0.108570	−	0.188049i
$478$	14.1653	−	24.5351i	0.647907	−	1.12221i
$479$	7.48161	+	4.31951i	0.341843	+	0.197363i	0.661087	−	0.750309i	$-0.270095\pi$
$479$	7.48161	+	4.31951i	0.341843	+	0.197363i	−0.319243	+	0.947673i	$0.603429\pi$
$480$	0.597691			0.0272807
$481$	−22.8044	−	3.22534i	−1.03979	−	0.147063i
$482$	−9.76218			−0.444655
$483$	−7.98029	−	4.60742i	−0.363116	−	0.209645i
$484$	−14.0484	+	24.3326i	−0.638565	+	1.10603i
$485$	1.03870	+	1.79908i	0.0471649	+	0.0816919i
$486$			10.1637i			0.461035i
$487$	−30.6632	+	17.7034i	−1.38948	+	0.802217i	−0.993257	−	0.115936i	$-0.963013\pi$
$487$	−30.6632	+	17.7034i	−1.38948	+	0.802217i	−0.396225	+	0.918154i	$0.629680\pi$
$488$	3.16448	−	1.82701i	0.143249	−	0.0827050i
$489$		−	8.45372i		−	0.382291i
$490$	0.331372	+	0.573952i	0.0149698	+	0.0259285i
$491$	19.0012	−	32.9110i	0.857512	−	1.48525i	−0.0167834	−	0.999859i	$-0.505343\pi$
$491$	19.0012	−	32.9110i	0.857512	−	1.48525i	0.874295	−	0.485395i	$-0.161324\pi$
$492$	5.50425	+	3.17788i	0.248151	+	0.143270i
$493$	1.72153			0.0775339
$494$	3.34419	−	1.34773i	0.150462	−	0.0606373i
$495$	−2.74277			−0.123278
$496$	3.86565	+	2.23183i	0.173573	+	0.100212i
$497$	7.18823	−	12.4504i	0.322436	−	0.558476i
$498$	6.87413	+	11.9063i	0.308037	+	0.533536i
$499$			5.50496i			0.246436i	0.992380	+	0.123218i	$0.0393214\pi$
$499$			5.50496i			0.246436i	−0.992380	+	0.123218i	$0.960679\pi$
$500$	3.62105	−	2.09061i	0.161938	−	0.0934950i
$501$	11.3353	−	6.54444i	0.506424	−	0.292384i
$502$			16.7474i			0.747475i
$503$	6.92622	+	11.9966i	0.308825	+	0.534900i	0.978106	−	0.208109i	$-0.0667310\pi$
$503$	6.92622	+	11.9966i	0.308825	+	0.534900i	−0.669281	+	0.743010i	$0.733398\pi$
$504$	−1.50654	+	2.60940i	−0.0671066	+	0.116232i
$505$	2.85697	+	1.64947i	0.127134	+	0.0734006i
$506$	14.0343			0.623901
$507$	4.38306	+	17.7118i	0.194659	+	0.786607i
$508$	−15.4402			−0.685046
$509$	9.59340	+	5.53875i	0.425220	+	0.245501i	0.697308	−	0.716772i	$-0.254381\pi$
$509$	9.59340	+	5.53875i	0.425220	+	0.245501i	−0.272088	+	0.962272i	$0.587714\pi$
$510$	−1.30501	+	2.26035i	−0.0577870	+	0.100090i
$511$	−15.3795	−	26.6381i	−0.680350	−	1.17840i
$512$			1.00000i			0.0441942i
$513$	4.89856	−	2.82819i	0.216277	−	0.124867i
$514$	16.3750	−	9.45412i	0.722271	−	0.417003i
$515$		−	2.15981i		−	0.0951724i
$516$	6.24712	+	10.8203i	0.275014	+	0.476338i
$517$	−22.8210	+	39.5272i	−1.00367	+	1.73840i
$518$	−16.1816	−	9.34244i	−0.710978	−	0.410483i
$519$	26.1926			1.14973
$520$	−1.42411	+	0.573925i	−0.0624512	+	0.0251683i
$521$	−23.7563			−1.04078			−0.520392	−	0.853927i	$-0.674214\pi$
$521$	−23.7563			−1.04078			−0.520392	+	0.853927i	$0.674214\pi$
$522$	0.351677	+	0.203041i	0.0153925	+	0.00888686i
$523$	7.80410	−	13.5171i	0.341250	−	0.591062i	−0.643415	−	0.765517i	$-0.722483\pi$
$523$	7.80410	−	13.5171i	0.341250	−	0.591062i	0.984665	+	0.174456i	$0.0558165\pi$
$524$	9.75104	+	16.8893i	0.425976	+	0.737812i
$525$		−	19.7831i		−	0.863405i
$526$	14.8656	−	8.58263i	0.648169	−	0.374221i
$527$	−16.8807	+	9.74608i	−0.735335	+	0.424546i
$528$			8.77599i			0.381926i
$529$	8.98111	+	15.5557i	0.390483	+	0.676336i
$530$	0.980286	−	1.69791i	0.0425809	−	0.0737523i
$531$	−0.911387	−	0.526190i	−0.0395508	−	0.0228347i
$532$	2.92512			0.126820
$533$	−16.1664	−	2.28650i	−0.700245	−	0.0990391i
$534$	−0.775457			−0.0335573
$535$	−3.58464	−	2.06959i	−0.154978	−	0.0894763i
$536$	−4.11596	+	7.12906i	−0.177783	+	0.307929i
$537$	−17.1406	−	29.6885i	−0.739673	−	1.28115i
$538$			23.8294i			1.02736i
$539$	−8.42743	+	4.86558i	−0.362995	+	0.209575i
$540$	−2.08603	+	1.20437i	−0.0897684	+	0.0518278i
$541$		−	22.2684i		−	0.957395i	−0.877980	−	0.478697i	$-0.841109\pi$
$541$		−	22.2684i		−	0.957395i	0.877980	−	0.478697i	$-0.158891\pi$
$542$	−6.23575	−	10.8006i	−0.267848	−	0.463927i
$543$	18.5597	−	32.1463i	0.796472	−	1.37953i
$544$	−3.78180	−	2.18343i	−0.162144	−	0.0936136i
$545$	3.62527			0.155290
$546$	−2.07298	+	14.6568i	−0.0887156	+	0.627253i
$547$	−27.3856			−1.17093			−0.585463	−	0.810699i	$-0.699087\pi$
$547$	−27.3856			−1.17093			−0.585463	+	0.810699i	$0.699087\pi$
$548$	7.22366	+	4.17058i	0.308579	+	0.178158i
$549$	−1.88195	+	3.25964i	−0.0803198	+	0.139118i
$550$	15.0649	+	26.0932i	0.642370	+	1.11262i
$551$		−	0.394227i		−	0.0167946i
$552$	2.72820	−	1.57513i	0.116120	−	0.0670418i
$553$	−18.7335	+	10.8158i	−0.796628	+	0.459933i
$554$			16.3303i			0.693808i
$555$	−1.90895	−	3.30639i	−0.0810303	−	0.140349i
$556$	−4.32142	+	7.48491i	−0.183269	+	0.317431i
$557$	25.9540	+	14.9846i	1.09971	+	0.634917i	0.936144	−	0.351616i	$-0.114368\pi$
$557$	25.9540	+	14.9846i	1.09971	+	0.634917i	0.163564	+	0.986533i	$0.447701\pi$
$558$	−4.59789			−0.194644
$559$	−25.2750	−	19.7827i	−1.06902	−	0.836718i
$560$	−1.24565			−0.0526381
$561$	−33.1891	−	19.1617i	−1.40124	−	0.809009i
$562$	−9.83174	+	17.0291i	−0.414727	+	0.718328i
$563$	−18.3885	−	31.8498i	−0.774983	−	1.34231i	−0.934804	−	0.355164i	$-0.884425\pi$
$563$	−18.3885	−	31.8498i	−0.774983	−	1.34231i	0.159821	−	0.987146i	$-0.448908\pi$
$564$			10.2452i			0.431400i
$565$	−7.70356	+	4.44765i	−0.324091	+	0.187114i
$566$	−15.1266	+	8.73333i	−0.635817	+	0.367089i
$567$			14.1831i			0.595635i
$568$	2.45742	+	4.25637i	0.103111	+	0.178593i
$569$	7.04988	−	12.2107i	0.295546	−	0.511901i	−0.679566	−	0.733615i	$-0.737832\pi$
$569$	7.04988	−	12.2107i	0.295546	−	0.511901i	0.975112	+	0.221714i	$0.0711650\pi$
$570$	0.517616	+	0.298846i	0.0216805	+	0.0125173i
$571$	−17.8101			−0.745330			−0.372665	−	0.927966i	$-0.621556\pi$
$571$	−17.8101			−0.745330			−0.372665	+	0.927966i	$0.621556\pi$
$572$	−8.42702	−	20.9104i	−0.352352	−	0.874307i
$573$	−21.6195			−0.903169
$574$	−11.4714	−	6.62301i	−0.478807	−	0.276439i
$575$	5.40774	−	9.36648i	0.225518	−	0.390609i
$576$	−0.515036	−	0.892068i	−0.0214598	−	0.0371695i
$577$			20.4540i			0.851512i	0.904838	+	0.425756i	$0.139992\pi$
$577$			20.4540i			0.851512i	−0.904838	+	0.425756i	$0.860008\pi$
$578$	1.79215	−	1.03470i	0.0745434	−	0.0430377i
$579$	11.7236	−	6.76862i	0.487216	−	0.281294i
$580$			0.167880i			0.00697082i
$581$	−14.3263	−	24.8140i	−0.594357	−	1.02946i
$582$	−3.42344	+	5.92958i	−0.141906	+	0.245789i
$583$	24.9306	+	14.3937i	1.03252	+	0.596126i
$584$	10.5155			0.435135
$585$	0.974809	−	1.24545i	0.0403034	−	0.0514928i
$586$	5.83845			0.241184
$587$	34.1849	+	19.7367i	1.41096	+	0.814620i	0.995479	−	0.0949809i	$-0.0302790\pi$
$587$	34.1849	+	19.7367i	1.41096	+	0.814620i	0.415484	+	0.909601i	$0.363612\pi$
$588$	−1.09217	+	1.89169i	−0.0450402	+	0.0780119i
$589$	2.23183	+	3.86565i	0.0919611	+	0.159281i
$590$		−	0.435068i		−	0.0179114i
$591$	10.7488	−	6.20582i	0.442146	−	0.255273i
$592$	5.53194	−	3.19387i	0.227361	−	0.131267i
$593$			10.4284i			0.428243i	0.976807	+	0.214122i	$0.0686889\pi$
$593$			10.4284i			0.428243i	−0.976807	+	0.214122i	$0.931311\pi$
$594$	−17.6839	−	30.6295i	−0.725580	−	1.25674i
$595$	2.71977	−	4.71079i	0.111500	−	0.193123i
$596$	6.31582	+	3.64644i	0.258706	+	0.149364i
$597$	21.4302			0.877081
$598$	−4.98793	+	6.37273i	−0.203972	+	0.260601i
$599$	−18.1621			−0.742085			−0.371043	−	0.928616i	$-0.621000\pi$
$599$	−18.1621			−0.742085			−0.371043	+	0.928616i	$0.621000\pi$
$600$	5.85709	+	3.38159i	0.239115	+	0.138053i
$601$	18.4471	−	31.9514i	0.752474	−	1.30332i	−0.194146	−	0.980973i	$-0.562194\pi$
$601$	18.4471	−	31.9514i	0.752474	−	1.30332i	0.946620	−	0.322351i	$-0.104473\pi$
$602$	−13.0196	−	22.5506i	−0.530639	−	0.919094i
$603$		−	8.47947i		−	0.345311i
$604$	0.0596230	−	0.0344234i	0.00242603	−	0.00140067i
$605$	10.3619	−	5.98245i	0.421271	−	0.243221i
$606$			10.8730i			0.441685i
$607$	9.57168	+	16.5786i	0.388502	+	0.672906i	0.992248	−	0.124271i	$-0.0396592\pi$
$607$	9.57168	+	16.5786i	0.388502	+	0.672906i	−0.603746	+	0.797177i	$0.706326\pi$
$608$	−0.500000	+	0.866025i	−0.0202777	+	0.0351220i
$609$	1.40167	+	0.809254i	0.0567985	+	0.0327926i
$610$	−1.55605			−0.0630026
$611$	−9.83780	−	24.4110i	−0.397995	−	0.987564i
$612$	4.49817			0.181828
$613$	−31.6407	−	18.2678i	−1.27796	−	0.737828i	−0.301483	−	0.953472i	$-0.597482\pi$
$613$	−31.6407	−	18.2678i	−1.27796	−	0.737828i	−0.976472	+	0.215644i	$0.930815\pi$
$614$	−4.84451	+	8.39094i	−0.195509	+	0.338631i
$615$	−1.35329	−	2.34396i	−0.0545697	−	0.0945176i
$616$		−	18.2900i		−	0.736925i
$617$	5.86092	−	3.38380i	0.235952	−	0.136227i	−0.377363	−	0.926065i	$-0.623169\pi$
$617$	5.86092	−	3.38380i	0.235952	−	0.136227i	0.613315	+	0.789839i	$0.289836\pi$
$618$	6.16480	−	3.55925i	0.247985	−	0.143174i
$619$			16.1044i			0.647289i	0.946179	+	0.323644i	$0.104908\pi$
$619$			16.1044i			0.647289i	−0.946179	+	0.323644i	$0.895092\pi$
$620$	−0.950415	−	1.64617i	−0.0381696	−	0.0661116i
$621$	−6.34787	+	10.9948i	−0.254731	+	0.441207i
$622$	−1.45223	−	0.838445i	−0.0582291	−	0.0336186i
$623$	1.61613			0.0647487
$624$	−3.98503	−	3.11908i	−0.159529	−	0.124863i
$625$	22.3127			0.892509
$626$	10.4951	+	6.05937i	0.419470	+	0.242181i
$627$	−4.38799	+	7.60023i	−0.175240	+	0.303524i
$628$	−5.27205	−	9.13145i	−0.210378	−	0.364385i
$629$			27.8943i			1.11222i
$630$	1.11120	−	0.641552i	0.0442713	−	0.0255600i
$631$	21.0203	−	12.1361i	0.836804	−	0.483129i	−0.0193724	−	0.999812i	$-0.506167\pi$
$631$	21.0203	−	12.1361i	0.836804	−	0.483129i	0.856177	+	0.516683i	$0.172833\pi$
$632$		−	7.39511i		−	0.294162i
$633$	−11.8122	−	20.4594i	−0.469494	−	0.813187i
$634$	5.05247	−	8.75113i	0.200659	−	0.347552i
$635$	5.69421	+	3.28756i	0.225968	+	0.130463i
$636$	6.46185			0.256229
$637$	0.785817	−	5.55603i	0.0311352	−	0.220138i
$638$	−2.46500			−0.0975904
$639$	−4.38436	−	2.53131i	−0.173443	−	0.100137i
$640$	0.212922	−	0.368793i	0.00841650	−	0.0145778i
$641$	6.86522	+	11.8909i	0.271160	+	0.469663i	0.969159	−	0.246436i	$-0.0792595\pi$
$641$	6.86522	+	11.8909i	0.271160	+	0.469663i	−0.697999	+	0.716098i	$0.745926\pi$
$642$		−	13.6423i		−	0.538420i
$643$	13.0818	−	7.55278i	0.515896	−	0.297852i	−0.219358	−	0.975644i	$-0.570396\pi$
$643$	13.0818	−	7.55278i	0.515896	−	0.297852i	0.735254	+	0.677792i	$0.237063\pi$
$644$	−5.68582	+	3.28271i	−0.224053	+	0.129357i
$645$		−	5.32061i		−	0.209499i
$646$	−2.18343	−	3.78180i	−0.0859057	−	0.148793i
$647$	18.7199	−	32.4237i	0.735953	−	1.27471i	−0.218351	−	0.975870i	$-0.570068\pi$
$647$	18.7199	−	32.4237i	0.735953	−	1.27471i	0.954304	−	0.298838i	$-0.0965991\pi$
$648$	−4.19913	−	2.42437i	−0.164957	−	0.0952383i
$649$	6.38816			0.250757
$650$	−17.2027	−	2.43307i	−0.674746	−	0.0954327i
$651$	−18.3257			−0.718240
$652$	−5.21619	−	3.01157i	−0.204282	−	0.117942i
$653$	14.2303	−	24.6476i	0.556874	−	0.964534i	−0.440881	−	0.897565i	$-0.645334\pi$
$653$	14.2303	−	24.6476i	0.556874	−	0.964534i	0.997755	−	0.0669683i	$-0.0213326\pi$
$654$	5.97426	+	10.3477i	0.233612	+	0.404628i
$655$		−	8.30486i		−	0.324498i
$656$	3.92169	−	2.26419i	0.153116	−	0.0884017i
$657$	−9.38054	+	5.41586i	−0.365970	+	0.211293i
$658$		−	21.3520i		−	0.832386i
$659$	−5.84442	−	10.1228i	−0.227666	−	0.394330i	0.729450	−	0.684034i	$-0.239776\pi$
$659$	−5.84442	−	10.1228i	−0.227666	−	0.394330i	−0.957116	+	0.289705i	$0.906443\pi$
$660$	1.86861	−	3.23652i	0.0727354	−	0.125981i
$661$	−11.6473	−	6.72459i	−0.453029	−	0.261556i	0.256080	−	0.966656i	$-0.417569\pi$
$661$	−11.6473	−	6.72459i	−0.453029	−	0.261556i	−0.709109	+	0.705099i	$0.750902\pi$
$662$	−35.5859			−1.38309
$663$	20.4967	−	8.26032i	0.796028	−	0.320804i
$664$	9.79541			0.380136
$665$	−1.07876	−	0.622823i	−0.0418326	−	0.0241520i
$666$	−3.28991	+	5.69830i	−0.127482	+	0.220804i
$667$	0.442422	+	0.766297i	0.0171306	+	0.0296711i
$668$		−	9.32561i		−	0.360819i
$669$	1.61230	−	0.930861i	0.0623350	−	0.0359892i
$670$	3.03587	−	1.75276i	0.117286	−	0.0677151i
$671$		−	22.8477i		−	0.882026i
$672$	−2.05276	−	3.55549i	−0.0791870	−	0.137156i
$673$	12.8100	−	22.1876i	0.493790	−	0.855269i	−0.506185	−	0.862425i	$-0.668945\pi$
$673$	12.8100	−	22.1876i	0.493790	−	0.855269i	0.999974	+	0.00715623i	$0.00227792\pi$
$674$	−19.9025	−	11.4907i	−0.766615	−	0.442606i
$675$	−27.2561			−1.04909
$676$	12.4901	+	3.60519i	0.480388	+	0.138661i
$677$	−32.2260			−1.23855			−0.619274	−	0.785175i	$-0.712573\pi$
$677$	−32.2260			−1.23855			−0.619274	+	0.785175i	$0.712573\pi$
$678$	−25.3901	−	14.6590i	−0.975102	−	0.562976i
$679$	7.13479	−	12.3578i	0.273808	−	0.474249i
$680$	0.929801	+	1.61046i	0.0356562	+	0.0617584i
$681$			31.5336i			1.20837i
$682$	24.1709	−	13.9551i	0.925552	−	0.534368i
$683$	8.60464	−	4.96789i	0.329247	−	0.190091i	−0.326260	−	0.945280i	$-0.605788\pi$
$683$	8.60464	−	4.96789i	0.329247	−	0.190091i	0.655507	+	0.755189i	$0.272455\pi$
$684$		−	1.03007i		−	0.0393858i
$685$	−1.77602	−	3.07616i	−0.0678583	−	0.117534i
$686$	−7.96172	+	13.7901i	−0.303980	+	0.526509i
$687$	23.6957	+	13.6807i	0.904048	+	0.521953i
$688$	8.90193			0.339383
$689$	−15.3965	+	6.20490i	−0.586561	+	0.236388i
$690$	−1.34152			−0.0510707
$691$	24.2428	+	13.9966i	0.922239	+	0.532455i	0.884349	−	0.466827i	$-0.154603\pi$
$691$	24.2428	+	13.9966i	0.922239	+	0.532455i	0.0378904	+	0.999282i	$0.487936\pi$
$692$	9.33088	−	16.1616i	0.354707	−	0.614370i
$693$	9.42000	+	16.3159i	0.357836	+	0.619791i
$694$			7.20555i			0.273519i
$695$	3.18741	−	1.84025i	0.120905	−	0.0698048i
$696$	−0.479184	+	0.276657i	−0.0181634	+	0.0104867i
$697$			19.7747i			0.749022i
$698$	14.7736	+	25.5887i	0.559190	+	0.968545i
$699$	−12.7584	+	22.0983i	−0.482569	+	0.835833i
$700$	−12.2067	−	7.04756i	−0.461371	−	0.266373i
$701$	32.6718			1.23400			0.616999	−	0.786964i	$-0.288348\pi$
$701$	32.6718			1.23400			0.616999	+	0.786964i	$0.288348\pi$
$702$	20.1934	+	2.85605i	0.762150	+	0.107795i
$703$	6.38774			0.240918
$704$	5.41504	+	3.12637i	0.204087	+	0.117830i
$705$	2.18143	−	3.77835i	0.0821575	−	0.142301i
$706$	0.708217	+	1.22667i	0.0266541	+	0.0461663i
$707$		−	22.6604i		−	0.852230i
$708$	1.24183	−	0.716969i	0.0466707	−	0.0269454i
$709$	−39.7797	+	22.9668i	−1.49396	+	0.862536i	−0.999976	−	0.00693671i	$-0.997792\pi$
$709$	−39.7797	+	22.9668i	−1.49396	+	0.862536i	−0.493981	+	0.869473i	$0.664459\pi$
$710$		−	2.09296i		−	0.0785473i
$711$	3.80874	+	6.59694i	0.142839	+	0.247404i
$712$	−0.276250	+	0.478479i	−0.0103529	+	0.0179318i
$713$	−8.67645	−	5.00935i	−0.324936	−	0.187602i
$714$	17.9282			0.670946
$715$	−1.34447	+	9.50590i	−0.0502802	+	0.355500i
$716$	−24.4248			−0.912799
$717$	−34.4360	−	19.8816i	−1.28604	−	0.742493i
$718$	1.03192	−	1.78735i	0.0385111	−	0.0667032i
$719$	−7.06626	−	12.2391i	−0.263527	−	0.456442i	0.703650	−	0.710547i	$-0.251552\pi$
$719$	−7.06626	−	12.2391i	−0.263527	−	0.456442i	−0.967177	+	0.254105i	$0.918219\pi$
$720$			0.438651i			0.0163475i
$721$	−12.8480	+	7.41782i	−0.478486	+	0.276254i
$722$	−0.866025	+	0.500000i	−0.0322301	+	0.0186081i
$723$			13.7016i			0.509569i
$724$	−13.2235	−	22.9037i	−0.491446	−	0.851210i
$725$	−0.949823	+	1.64514i	−0.0352755	+	0.0610990i
$726$	34.1518	+	19.7175i	1.26749	+	0.731787i
$727$	−15.2232			−0.564598			−0.282299	−	0.959326i	$-0.591097\pi$
$727$	−15.2232			−0.564598			−0.282299	+	0.959326i	$0.591097\pi$
$728$	8.30518	+	6.50045i	0.307810	+	0.240923i
$729$	28.8114			1.06709
$730$	−3.87804	−	2.23899i	−0.143533	−	0.0828686i
$731$	−19.4367	+	33.6654i	−0.718893	+	1.24516i
$732$	−2.56429	−	4.44148i	−0.0947788	−	0.164162i
$733$			6.19770i			0.228917i	0.993428	+	0.114459i	$0.0365133\pi$
$733$			6.19770i			0.228917i	−0.993428	+	0.114459i	$0.963487\pi$
$734$	−24.3739	+	14.0723i	−0.899657	+	0.519417i
$735$	0.805566	−	0.465094i	0.0297137	−	0.0171552i
$736$		−	2.24450i		−	0.0827334i
$737$	25.7361	+	44.5762i	0.948001	+	1.64199i
$738$	−2.33228	+	4.03962i	−0.0858522	+	0.148700i
$739$	−28.0527	−	16.1962i	−1.03193	−	0.595788i	−0.114396	−	0.993435i	$-0.536493\pi$
$739$	−28.0527	−	16.1962i	−1.03193	−	0.595788i	−0.917538	+	0.397648i	$0.869827\pi$
$740$	−2.72019			−0.0999960
$741$	−1.89160	−	4.69371i	−0.0694896	−	0.172428i
$742$	−13.4671			−0.494393
$743$	3.31352	+	1.91306i	0.121561	+	0.0701834i	0.559548	−	0.828798i	$-0.310975\pi$
$743$	3.31352	+	1.91306i	0.121561	+	0.0701834i	−0.437986	+	0.898982i	$0.644308\pi$
$744$	3.13247	−	5.42560i	0.114842	−	0.198912i
$745$	−1.55282	−	2.68956i	−0.0568908	−	0.0985378i
$746$		−	30.4016i		−	1.11308i
$747$	−8.73817	+	5.04498i	−0.319713	+	0.184586i
$748$	−23.6467	+	13.6524i	−0.864608	+	0.499181i
$749$			28.4319i			1.03888i
$750$	−2.93426	−	5.08229i	−0.107144	−	0.185579i
$751$	10.3940	−	18.0030i	0.379284	−	0.656939i	−0.611674	−	0.791110i	$-0.709504\pi$
$751$	10.3940	−	18.0030i	0.379284	−	0.656939i	0.990958	+	0.134171i	$0.0428370\pi$
$752$	6.32158	+	3.64976i	0.230524	+	0.133093i
$753$	23.5057			0.856596
$754$	0.876087	−	1.11932i	0.0319052	−	0.0407631i
$755$	−0.0293180			−0.00106699
$756$	14.3289	+	8.27277i	0.521136	+	0.300878i
$757$	14.7634	−	25.5709i	0.536584	−	0.929390i	−0.462501	−	0.886619i	$-0.653048\pi$
$757$	14.7634	−	25.5709i	0.536584	−	0.929390i	0.999085	−	0.0427714i	$-0.0136187\pi$
$758$	−2.46934	−	4.27701i	−0.0896903	−	0.155348i
$759$		−	19.6977i		−	0.714982i
$760$	0.368793	−	0.212922i	0.0133775	−	0.00772351i
$761$	−14.5730	+	8.41374i	−0.528272	+	0.304998i	−0.740312	−	0.672263i	$-0.765322\pi$
$761$	−14.5730	+	8.41374i	−0.528272	+	0.304998i	0.212041	+	0.977261i	$0.431989\pi$
$762$			21.6709i			0.785054i
$763$	−12.4509	−	21.5656i	−0.450754	−	0.780729i
$764$	−7.70178	+	13.3399i	−0.278641	+	0.482620i
$765$	−1.65889	−	0.957761i	−0.0599773	−	0.0346279i
$766$	14.2852			0.516145
$767$	−2.27042	+	2.90076i	−0.0819800	+	0.104740i
$768$	1.40354			0.0506459
$769$	6.77872	+	3.91369i	0.244447	+	0.141131i	0.617219	−	0.786792i	$-0.288259\pi$
$769$	6.77872	+	3.91369i	0.244447	+	0.141131i	−0.372772	+	0.927923i	$0.621593\pi$
$770$	−3.89435	+	6.74522i	−0.140343	+	0.243081i
$771$	−13.2693	−	22.9830i	−0.477881	−	0.827713i
$772$		−	9.64505i		−	0.347133i
$773$	−17.5991	+	10.1608i	−0.632995	+	0.365460i	−0.781911	−	0.623390i	$-0.785755\pi$
$773$	−17.5991	+	10.1608i	−0.632995	+	0.365460i	0.148916	+	0.988850i	$0.452422\pi$
$774$	−7.94113	+	4.58481i	−0.285438	+	0.164798i
$775$		−	21.5089i		−	0.772621i
$776$	2.43915	+	4.22473i	0.0875603	+	0.151659i
$777$	−13.1125	+	22.7115i	−0.470408	+	0.814771i
$778$	5.03183	+	2.90513i	0.180400	+	0.104154i
$779$	4.52838			0.162246
$780$	0.805527	+	1.99879i	0.0288425	+	0.0715683i
$781$	30.7312			1.09965
$782$	8.48826	+	4.90070i	0.303540	+	0.175249i
$783$	1.11495	−	1.93115i	0.0398450	−	0.0690135i
$784$	0.778151	+	1.34780i	0.0277911	+	0.0481356i
$785$			4.49015i			0.160260i
$786$	23.7048	−	13.6860i	0.845523	−	0.488163i
$787$	28.1107	−	16.2297i	1.00204	−	0.578528i	0.0931882	−	0.995649i	$-0.470294\pi$
$787$	28.1107	−	16.2297i	1.00204	−	0.578528i	0.908851	+	0.417121i	$0.136961\pi$
$788$		−	8.84308i		−	0.315022i
$789$	−12.0461	−	20.8644i	−0.428852	−	0.742793i
$790$	−1.57458	+	2.72726i	−0.0560212	+	0.0970316i
$791$	52.9155	+	30.5508i	1.88146	+	1.08626i
$792$	−6.44077			−0.228863
$793$	10.3748	+	8.12030i	0.368418	+	0.288360i
$794$	−15.5364			−0.551367
$795$	−2.38308	−	1.37587i	−0.0845192	−	0.0487972i
$796$	7.63434	−	13.2231i	0.270592	−	0.468679i
$797$	−1.50719	−	2.61052i	−0.0533873	−	0.0924695i	0.838097	−	0.545522i	$-0.183668\pi$
$797$	−1.50719	−	2.61052i	−0.0533873	−	0.0924695i	−0.891484	+	0.453052i	$0.850335\pi$
$798$		−	4.10552i		−	0.145334i
$799$	−27.6054	+	15.9380i	−0.976608	+	0.563845i
$800$	4.17308	−	2.40933i	0.147541	−	0.0851826i
$801$		−	0.569114i		−	0.0201087i
$802$	1.89951	+	3.29004i	0.0670739	+	0.116175i
$803$	32.8754	−	56.9418i	1.16015	−	2.00943i
$804$	10.0059	+	5.77693i	0.352882	+	0.203737i
$805$	2.79585			0.0985409
$806$	−2.25382	+	15.9354i	−0.0793875	+	0.561300i
$807$	33.4455			1.17734
$808$	6.70895	+	3.87341i	0.236020	+	0.136266i
$809$	−11.1276	+	19.2735i	−0.391224	+	0.677621i	−0.992611	−	0.121337i	$-0.961282\pi$
$809$	−11.1276	+	19.2735i	−0.391224	+	0.677621i	0.601387	+	0.798958i	$0.294615\pi$
$810$	1.03241	+	1.78818i	0.0362750	+	0.0628302i
$811$		−	3.31086i		−	0.116260i	−0.998309	−	0.0581300i	$-0.981486\pi$
$811$		−	3.31086i		−	0.116260i	0.998309	−	0.0581300i	$-0.0185138\pi$
$812$	0.998666	−	0.576580i	0.0350463	−	0.0202340i
$813$	−15.1591	+	8.75213i	−0.531654	+	0.306951i
$814$		−	39.9409i		−	1.39993i
$815$	1.28246	+	2.22129i	0.0449227	+	0.0778083i
$816$	−3.06453	+	5.30792i	−0.107280	+	0.185814i
$817$	7.70930	+	4.45097i	0.269714	+	0.155720i
$818$	−21.9275			−0.766676
$819$	−10.7567	−	1.52138i	−0.375871	−	0.0531614i
$820$	−1.92839			−0.0673422
$821$	−25.8928	−	14.9492i	−0.903664	−	0.521731i	−0.0252770	−	0.999680i	$-0.508047\pi$
$821$	−25.8928	−	14.9492i	−0.903664	−	0.521731i	−0.878387	+	0.477950i	$0.841380\pi$
$822$	5.85358	−	10.1387i	0.204167	−	0.353628i
$823$	−16.3469	−	28.3136i	−0.569817	−	0.986951i	−0.996584	−	0.0825896i	$-0.973681\pi$
$823$	−16.3469	−	28.3136i	−0.569817	−	0.986951i	0.426767	−	0.904362i	$-0.359652\pi$
$824$		−	5.07181i		−	0.176685i
$825$	36.6229	−	21.1442i	1.27505	−	0.736148i
$826$	−2.58809	+	1.49423i	−0.0900511	+	0.0519910i
$827$			6.15194i			0.213924i	0.994263	+	0.106962i	$0.0341123\pi$
$827$			6.15194i			0.213924i	−0.994263	+	0.106962i	$0.965888\pi$
$828$	1.15600	+	2.00225i	0.0401737	+	0.0695829i
$829$	−13.5593	+	23.4854i	−0.470935	+	0.815683i	−0.999447	−	0.0332428i	$-0.989417\pi$
$829$	−13.5593	+	23.4854i	−0.470935	+	0.815683i	0.528513	+	0.848925i	$0.322750\pi$
$830$	−3.61247	−	2.08566i	−0.125391	−	0.0723944i
$831$	22.9203			0.795095
$832$	−3.34419	+	1.34773i	−0.115939	+	0.0467242i
$833$	−6.79614			−0.235472
$834$	10.5054	+	6.06529i	0.363772	+	0.210024i
$835$	−1.98563	+	3.43922i	−0.0687156	+	0.119019i
$836$	3.12637	+	5.41504i	0.108128	+	0.187283i
$837$			25.2482i			0.872704i
$838$	17.1794	−	9.91853i	0.593453	−	0.342630i
$839$	−29.2790	+	16.9042i	−1.01082	+	0.583598i	−0.911432	−	0.411450i	$-0.865022\pi$
$839$	−29.2790	+	16.9042i	−1.01082	+	0.583598i	−0.0993897	+	0.995049i	$0.531689\pi$
$840$			1.74832i			0.0603226i
$841$	14.4223	+	24.9801i	0.497320	+	0.861384i
$842$	−7.75004	+	13.4235i	−0.267084	+	0.462603i
$843$	23.9010	+	13.7993i	0.823195	+	0.475272i
$844$	−16.8320			−0.579382
$845$	−3.83863	−	3.98899i	−0.132053	−	0.137225i
$846$	−7.51903			−0.258510
$847$	−71.1756	−	41.0933i	−2.44562	−	1.41198i
$848$	2.30198	−	3.98714i	0.0790503	−	0.136919i
$849$	12.2576	+	21.2308i	0.420679	+	0.728638i
$850$			21.0424i			0.721747i
$851$	−12.4165	+	7.16864i	−0.425631	+	0.245738i
$852$	5.97399	−	3.44909i	0.204666	−	0.118164i
$853$		−	33.3895i		−	1.14323i	−0.820521	−	0.571617i	$-0.806316\pi$
$853$		−	33.3895i		−	1.14323i	0.820521	−	0.571617i	$-0.193684\pi$
$854$	5.34422	+	9.25647i	0.182876	+	0.316750i
$855$	−0.219325	+	0.379883i	−0.00750077	+	0.0129917i
$856$	−8.41771	−	4.85997i	−0.287711	−	0.166110i
$857$	−34.2122			−1.16867			−0.584333	−	0.811514i	$-0.698644\pi$
$857$	−34.2122			−1.16867			−0.584333	+	0.811514i	$0.698644\pi$
$858$	−29.3486	+	11.8277i	−1.00194	+	0.403790i
$859$	53.0118			1.80874			0.904370	−	0.426750i	$-0.140341\pi$
$859$	53.0118			1.80874			0.904370	+	0.426750i	$0.140341\pi$
$860$	−3.28297	−	1.89542i	−0.111948	−	0.0646334i
$861$	−9.29567	+	16.1006i	−0.316796	+	0.548706i
$862$	−15.3017	−	26.5033i	−0.521178	−	0.902706i
$863$		−	27.2945i		−	0.929115i	−0.885543	−	0.464557i	$-0.846213\pi$
$863$		−	27.2945i		−	0.929115i	0.885543	−	0.464557i	$-0.153787\pi$
$864$	−4.89856	+	2.82819i	−0.166652	+	0.0962168i
$865$	−6.88232	+	3.97351i	−0.234006	+	0.135103i
$866$		−	4.32019i		−	0.146806i
$867$	−1.45224	−	2.51535i	−0.0493206	−	0.0854258i
$868$	−6.52837	+	11.3075i	−0.221587	+	0.383800i
$869$	−40.0448	−	23.1199i	−1.35843	−	0.784288i
$870$	0.235626			0.00798847
$871$	−29.3882	−	4.15652i	−0.995780	−	0.140838i
$872$	8.51312			0.288291
$873$	−4.35177	−	2.51249i	−0.147285	−	0.0850351i
$874$	1.12225	−	1.94379i	0.0379607	−	0.0657498i
$875$	6.11528	+	10.5920i	0.206734	+	0.358074i
$876$		−	14.7589i		−	0.498659i
$877$	30.5114	−	17.6158i	1.03030	−	0.594842i	0.113227	−	0.993569i	$-0.463881\pi$
$877$	30.5114	−	17.6158i	1.03030	−	0.594842i	0.917070	+	0.398727i	$0.130548\pi$
$878$	16.5170	−	9.53612i	0.557423	−	0.321829i
$879$		−	8.19451i		−	0.276394i
$880$	−1.33135	−	2.30597i	−0.0448798	−	0.0777341i
$881$	8.40542	−	14.5586i	0.283186	−	0.490492i	−0.688982	−	0.724779i	$-0.741942\pi$
$881$	8.40542	−	14.5586i	0.283186	−	0.490492i	0.972168	+	0.234286i	$0.0752754\pi$
$882$	−1.38833	−	0.801550i	−0.0467474	−	0.0269896i
$883$	−22.5292			−0.758168			−0.379084	−	0.925362i	$-0.623761\pi$
$883$	−22.5292			−0.758168			−0.379084	+	0.925362i	$0.623761\pi$
$884$	2.20494	−	15.5898i	0.0741601	−	0.524340i
$885$	−0.610635			−0.0205263
$886$	−16.0774	−	9.28231i	−0.540132	−	0.311845i
$887$	−18.7085	+	32.4041i	−0.628171	+	1.08802i	0.359748	+	0.933050i	$0.382863\pi$
$887$	−18.7085	+	32.4041i	−0.628171	+	1.08802i	−0.987919	+	0.154974i	$0.950471\pi$
$888$	−4.48273	−	7.76431i	−0.150431	−	0.260553i
$889$		−	45.1642i		−	1.51476i
$890$	0.203758	−	0.117640i	0.00682998	−	0.00394329i
$891$	−26.2561	+	15.1590i	−0.879613	+	0.507845i
$892$		−	1.32645i		−	0.0444127i
$893$	3.64976	+	6.32158i	0.122135	+	0.211543i
$894$	5.11793	−	8.86451i	0.171169	−	0.296474i
$895$	9.00770	+	5.20060i	0.301094	+	0.173837i
$896$	−2.92512			−0.0977213
$897$	8.94440	+	7.00077i	0.298645	+	0.233749i
$898$	−2.64242			−0.0881786
$899$	1.52394	+	0.879849i	0.0508264	+	0.0293446i
$900$	−2.48178	+	4.29857i	−0.0827260	+	0.143286i
$901$	10.0524	+	17.4113i	0.334894	+	0.580053i
$902$		−	28.3148i		−	0.942780i
$903$	−31.6507	+	18.2735i	−1.05327	+	0.608105i
$904$	−18.0901	+	10.4443i	−0.601666	+	0.347372i
$905$			11.2623i			0.374371i
$906$	−0.0483146	−	0.0836834i	−0.00160515	−	0.00278019i
$907$	−25.3965	+	43.9880i	−0.843276	+	1.46060i	0.0438344	+	0.999039i	$0.486043\pi$
$907$	−25.3965	+	43.9880i	−0.843276	+	1.46060i	−0.887110	+	0.461558i	$0.847291\pi$
$908$	19.4571	+	11.2336i	0.645708	+	0.372800i
$909$	−7.97978			−0.264673
$910$	−1.67880	−	4.16568i	−0.0556516	−	0.138091i
$911$	53.7232			1.77993			0.889964	−	0.456031i	$-0.150729\pi$
$911$	53.7232			1.77993			0.889964	+	0.456031i	$0.150729\pi$
$912$	1.21550	+	0.701771i	0.0402493	+	0.0232380i
$913$	30.6241	−	53.0425i	1.01351	−	1.75545i
$914$	−19.6475	−	34.0304i	−0.649881	−	1.12563i
$915$			2.18398i			0.0722001i
$916$	16.8828	−	9.74729i	0.557824	−	0.322060i
$917$	−49.4032	+	28.5229i	−1.63144	+	0.941910i
$918$		−	24.7005i		−	0.815239i
$919$	3.16773	+	5.48667i	0.104494	+	0.180989i	0.913531	−	0.406768i	$-0.133344\pi$
$919$	3.16773	+	5.48667i	0.104494	+	0.180989i	−0.809037	+	0.587757i	$0.800011\pi$
$920$	−0.477905	+	0.827755i	−0.0157561	+	0.0272903i
$921$	11.7770	+	6.79947i	0.388067	+	0.224050i
$922$	32.1567			1.05903
$923$	−10.9222	+	13.9545i	−0.359508	+	0.459319i
$924$	−25.6708			−0.844507
$925$	−26.6565	−	15.3902i	−0.876461	−	0.506025i
$926$	−5.47546	+	9.48378i	−0.179935	+	0.311656i
$927$	2.61216	+	4.52440i	0.0857947	+	0.148601i
$928$			0.394227i			0.0129411i
$929$	−40.1748	+	23.1950i	−1.31809	+	0.761002i	−0.983422	−	0.181333i	$-0.941959\pi$
$929$	−40.1748	+	23.1950i	−1.31809	+	0.761002i	−0.334672	+	0.942335i	$0.608626\pi$
$930$	−2.31046	+	1.33395i	−0.0757631	+	0.0437418i
$931$			1.55630i			0.0510057i
$932$	9.09018	+	15.7446i	0.297759	+	0.515733i
$933$	−1.17679	+	2.03826i	−0.0385265	+	0.0667298i
$934$	31.4263	+	18.1440i	1.02830	+	0.593690i
$935$	11.6276			0.380264
$936$	2.28912	−	2.92465i	0.0748221	−	0.0955950i
$937$	48.8813			1.59688			0.798441	−	0.602072i	$-0.205658\pi$
$937$	48.8813			1.59688			0.798441	+	0.602072i	$0.205658\pi$
$938$	−20.8533	−	12.0397i	−0.680885	−	0.393109i
$939$	8.50457	−	14.7304i	0.277536	−	0.480707i
$940$	−1.55423	−	2.69201i	−0.0506935	−	0.0878037i
$941$			0.310622i			0.0101260i	0.999987	+	0.00506300i	$0.00161161\pi$
$941$			0.310622i			0.0101260i	−0.999987	+	0.00506300i	$0.998388\pi$
$942$	−12.8164	+	7.39954i	−0.417580	+	0.241090i
$943$	−8.80224	+	5.08197i	−0.286640	+	0.165492i
$944$		−	1.02166i		−	0.0332521i
$945$	−3.52292	−	6.10187i	−0.114601	−	0.198494i
$946$	27.8308	−	48.2043i	0.904856	−	1.56726i
$947$	37.6609	+	21.7435i	1.22382	+	0.706570i	0.965729	−	0.259551i	$-0.0835747\pi$
$947$	37.6609	+	21.7435i	1.22382	+	0.706570i	0.258086	+	0.966122i	$0.416908\pi$
$948$	−10.3793			−0.337105
$949$	14.1721	+	35.1659i	0.460045	+	1.14153i
$950$	4.81866			0.156338
$951$	−12.2826	−	7.09135i	−0.398290	−	0.229953i
$952$	6.38677	−	11.0622i	0.206996	−	0.358528i
$953$	19.7345	+	34.1811i	0.639262	+	1.10723i	0.985595	+	0.169123i	$0.0540934\pi$
$953$	19.7345	+	34.1811i	0.639262	+	1.10723i	−0.346333	+	0.938112i	$0.612573\pi$
$954$			4.74240i			0.153541i
$955$	5.68072	−	3.27976i	0.183824	−	0.106131i
$956$	−24.5351	+	14.1653i	−0.793521	+	0.458139i
$957$			3.45973i			0.111837i
$958$	−4.31951	−	7.48161i	−0.139557	−	0.241720i
$959$	−12.1994	+	21.1300i	−0.393940	+	0.682324i
$960$	−0.517616	−	0.298846i	−0.0167060	−	0.00964520i
$961$	11.0757			0.357280
$962$	18.1365	+	14.1954i	0.584744	+	0.457678i
$963$	10.0122			0.322639
$964$	8.45430	+	4.88109i	0.272295	+	0.157209i
$965$	−2.05365	+	3.55702i	−0.0661093	+	0.114505i
$966$	4.60742	+	7.98029i	0.148241	+	0.256762i
$967$			43.8685i			1.41072i	0.708851	+	0.705358i	$0.249214\pi$
$967$			43.8685i			1.41072i	−0.708851	+	0.705358i	$0.750786\pi$
$968$	24.3326	−	14.0484i	0.782079	−	0.451533i
$969$	−5.30792	+	3.06453i	−0.170515	+	0.0984468i
$970$		−	2.07740i		−	0.0667012i
$971$	−5.28619	−	9.15595i	−0.169642	−	0.293828i	0.768652	−	0.639667i	$-0.220928\pi$
$971$	−5.28619	−	9.15595i	−0.169642	−	0.293828i	−0.938294	+	0.345839i	$0.887594\pi$
$972$	5.08185	−	8.80203i	0.163001	−	0.282325i
$973$	−21.8942	−	12.6406i	−0.701897	−	0.405240i
$974$	35.4068			1.13451
$975$	−3.41491	+	24.1447i	−0.109365	+	0.773250i
$976$	−3.65403			−0.116963
$977$	6.54533	+	3.77895i	0.209404	+	0.120899i	0.601034	−	0.799223i	$-0.294756\pi$
$977$	6.54533	+	3.77895i	0.209404	+	0.120899i	−0.391631	+	0.920123i	$0.628089\pi$
$978$	−4.22686	+	7.32114i	−0.135160	+	0.234104i
$979$	1.72732	+	2.99181i	0.0552054	+	0.0956186i
$980$		−	0.662743i		−	0.0211705i
$981$	−7.59428	+	4.38456i	−0.242467	+	0.139988i
$982$	−32.9110	+	19.0012i	−1.05023	+	0.606352i
$983$		−	6.75818i		−	0.215553i	−0.994175	−	0.107776i	$-0.965627\pi$
$983$		−	6.75818i		−	0.215553i	0.994175	−	0.107776i	$-0.0343730\pi$
$984$	−3.17788	−	5.50425i	−0.101307	−	0.175469i
$985$	−1.88289	+	3.26126i	−0.0599939	+	0.103913i
$986$	−1.49089	−	0.860766i	−0.0474796	−	0.0274124i
$987$	−29.9684			−0.953903
$988$	−3.57002	−	0.504926i	−0.113577	−	0.0160638i
$989$	−19.9804			−0.635340
$990$	2.37531	+	1.37139i	0.0754923	+	0.0435855i
$991$	29.6891	−	51.4230i	0.943105	−	1.63351i	0.183602	−	0.983001i	$-0.441224\pi$
$991$	29.6891	−	51.4230i	0.943105	−	1.63351i	0.759502	−	0.650505i	$-0.225443\pi$
$992$	−2.23183	−	3.86565i	−0.0708608	−	0.122734i
$993$			49.9463i			1.58500i
$994$	−12.4504	+	7.18823i	−0.394902	+	0.227997i
$995$	−5.63098	+	3.25105i	−0.178514	+	0.103065i
$996$		−	13.7483i		−	0.435630i
$997$	23.0431	+	39.9118i	0.729782	+	1.26402i	0.956975	+	0.290169i	$0.0937117\pi$
$997$	23.0431	+	39.9118i	0.729782	+	1.26402i	−0.227194	+	0.973850i	$0.572955\pi$
$998$	2.75248	−	4.76743i	0.0871282	−	0.150910i
$999$	31.2907	+	18.0657i	0.989995	+	0.571574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	494.2.m.a.381.1	yes	16
13.6	odd	12		6422.2.a.bh.1.7		8
13.7	odd	12		6422.2.a.bg.1.7		8
13.10	even	6	inner	494.2.m.a.153.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.m.a.153.1	✓	16	13.10	even	6	inner
494.2.m.a.381.1	yes	16	1.1	even	1	trivial
6422.2.a.bg.1.7		8	13.7	odd	12
6422.2.a.bh.1.7		8	13.6	odd	12

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:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.701771 + 1.21550i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.425845i q^{5} +(1.21550 - 0.701771i) q^{6} +(-2.53322 + 1.46256i) q^{7} -1.00000i q^{8} +(0.515036 + 0.892068i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.701771 + 1.21550i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.425845i q^{5} +(1.21550 - 0.701771i) q^{6} +(-2.53322 + 1.46256i) q^{7} -1.00000i q^{8} +(0.515036 + 0.892068i) q^{9} +(-0.212922 + 0.368793i) q^{10} +(-5.41504 - 3.12637i) q^{11} -1.40354 q^{12} +(3.34419 - 1.34773i) q^{13} +2.92512 q^{14} +(0.517616 + 0.298846i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.18343 - 3.78180i) q^{17} -1.03007i q^{18} +(-0.866025 + 0.500000i) q^{19} +(0.368793 - 0.212922i) q^{20} -4.10552i q^{21} +(3.12637 + 5.41504i) q^{22} +(1.12225 - 1.94379i) q^{23} +(1.21550 + 0.701771i) q^{24} +4.81866 q^{25} +(-3.57002 - 0.504926i) q^{26} -5.65637 q^{27} +(-2.53322 - 1.46256i) q^{28} +(-0.197114 + 0.341411i) q^{29} +(-0.298846 - 0.517616i) q^{30} -4.46367i q^{31} +(0.866025 - 0.500000i) q^{32} +(7.60023 - 4.38799i) q^{33} +4.36685i q^{34} +(0.622823 + 1.07876i) q^{35} +(-0.515036 + 0.892068i) q^{36} +(-5.53194 - 3.19387i) q^{37} +1.00000 q^{38} +(-0.708685 + 5.01067i) q^{39} -0.425845 q^{40} +(-3.92169 - 2.26419i) q^{41} +(-2.05276 + 3.55549i) q^{42} +(-4.45097 - 7.70930i) q^{43} -6.25275i q^{44} +(0.379883 - 0.219325i) q^{45} +(-1.94379 + 1.12225i) q^{46} -7.29953i q^{47} +(-0.701771 - 1.21550i) q^{48} +(0.778151 - 1.34780i) q^{49} +(-4.17308 - 2.40933i) q^{50} +6.12906 q^{51} +(2.83927 + 2.22229i) q^{52} -4.60396 q^{53} +(4.89856 + 2.82819i) q^{54} +(-1.33135 + 2.30597i) q^{55} +(1.46256 + 2.53322i) q^{56} -1.40354i q^{57} +(0.341411 - 0.197114i) q^{58} +(-0.884781 + 0.510829i) q^{59} +0.597691i q^{60} +(1.82701 + 3.16448i) q^{61} +(-2.23183 + 3.86565i) q^{62} +(-2.60940 - 1.50654i) q^{63} -1.00000 q^{64} +(-0.573925 - 1.42411i) q^{65} -8.77599 q^{66} +(-7.12906 - 4.11596i) q^{67} +(2.18343 - 3.78180i) q^{68} +(1.57513 + 2.72820i) q^{69} -1.24565i q^{70} +(-4.25637 + 2.45742i) q^{71} +(0.892068 - 0.515036i) q^{72} +10.5155i q^{73} +(3.19387 + 5.53194i) q^{74} +(-3.38159 + 5.85709i) q^{75} +(-0.866025 - 0.500000i) q^{76} +18.2900 q^{77} +(3.11908 - 3.98503i) q^{78} +7.39511 q^{79} +(0.368793 + 0.212922i) q^{80} +(2.42437 - 4.19913i) q^{81} +(2.26419 + 3.92169i) q^{82} +9.79541i q^{83} +(3.55549 - 2.05276i) q^{84} +(-1.61046 + 0.929801i) q^{85} +8.90193i q^{86} +(-0.276657 - 0.479184i) q^{87} +(-3.12637 + 5.41504i) q^{88} +(-0.478479 - 0.276250i) q^{89} -0.438651 q^{90} +(-6.50045 + 8.30518i) q^{91} +2.24450 q^{92} +(5.42560 + 3.13247i) q^{93} +(-3.64976 + 6.32158i) q^{94} +(0.212922 + 0.368793i) q^{95} +1.40354i q^{96} +(-4.22473 + 2.43915i) q^{97} +(-1.34780 + 0.778151i) q^{98} -6.44077i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 8 q^{4}+O(q^{10}) \) 16 * q + 4 * q^3 + 8 * q^4	\( 16 q + 4 q^{3} + 8 q^{4} - 2 q^{10} - 6 q^{11} + 8 q^{12} - 4 q^{14} - 18 q^{15} - 8 q^{16} + 2 q^{17} + 10 q^{22} - 8 q^{23} + 28 q^{25} - 14 q^{26} - 44 q^{27} - 8 q^{29} + 30 q^{33} + 10 q^{35} + 6 q^{37} + 16 q^{38} - 34 q^{39} - 4 q^{40} + 6 q^{41} - 12 q^{42} - 16 q^{43} - 30 q^{45} + 12 q^{46} + 4 q^{48} - 14 q^{49} + 12 q^{50} + 44 q^{51} - 48 q^{53} - 36 q^{54} + 10 q^{55} - 2 q^{56} - 6 q^{58} + 84 q^{59} + 26 q^{61} - 12 q^{62} + 12 q^{63} - 16 q^{64} - 30 q^{65} + 8 q^{66} - 18 q^{67} - 2 q^{68} + 6 q^{69} - 6 q^{71} + 12 q^{72} + 6 q^{75} + 24 q^{77} - 30 q^{78} - 44 q^{79} - 36 q^{81} + 2 q^{82} + 12 q^{84} + 48 q^{85} + 38 q^{87} - 10 q^{88} + 36 q^{89} + 24 q^{90} - 28 q^{91} - 16 q^{92} + 54 q^{93} - 12 q^{94} + 2 q^{95} + 12 q^{97} + 24 q^{98}+O(q^{100}) \) 16 * q + 4 * q^3 + 8 * q^4 - 2 * q^10 - 6 * q^11 + 8 * q^12 - 4 * q^14 - 18 * q^15 - 8 * q^16 + 2 * q^17 + 10 * q^22 - 8 * q^23 + 28 * q^25 - 14 * q^26 - 44 * q^27 - 8 * q^29 + 30 * q^33 + 10 * q^35 + 6 * q^37 + 16 * q^38 - 34 * q^39 - 4 * q^40 + 6 * q^41 - 12 * q^42 - 16 * q^43 - 30 * q^45 + 12 * q^46 + 4 * q^48 - 14 * q^49 + 12 * q^50 + 44 * q^51 - 48 * q^53 - 36 * q^54 + 10 * q^55 - 2 * q^56 - 6 * q^58 + 84 * q^59 + 26 * q^61 - 12 * q^62 + 12 * q^63 - 16 * q^64 - 30 * q^65 + 8 * q^66 - 18 * q^67 - 2 * q^68 + 6 * q^69 - 6 * q^71 + 12 * q^72 + 6 * q^75 + 24 * q^77 - 30 * q^78 - 44 * q^79 - 36 * q^81 + 2 * q^82 + 12 * q^84 + 48 * q^85 + 38 * q^87 - 10 * q^88 + 36 * q^89 + 24 * q^90 - 28 * q^91 - 16 * q^92 + 54 * q^93 - 12 * q^94 + 2 * q^95 + 12 * q^97 + 24 * q^98

Introduction

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