LMFDB - Embedded newform 65.2.m.a.36.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(36,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("65.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.1
Root			$1.20036 + 0.747754i$ of defining polynomial
Character	$\chi$	$=$	65.36
Dual form			65.2.m.a.56.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16117 + 1.24775i) q^{2} +(1.41342 + 2.44811i) q^{3} +(2.11378 - 3.66117i) q^{4} +1.00000i q^{5} +(-6.10929 - 3.52720i) q^{6} +(-1.64996 - 0.952606i) q^{7} +5.55889i q^{8} +(-2.49551 + 4.32235i) q^{9} +O(q^{10})$	\(q+(-2.16117 + 1.24775i) q^{2} +(1.41342 + 2.44811i) q^{3} +(2.11378 - 3.66117i) q^{4} +1.00000i q^{5} +(-6.10929 - 3.52720i) q^{6} +(-1.64996 - 0.952606i) q^{7} +5.55889i q^{8} +(-2.49551 + 4.32235i) q^{9} +(-1.24775 - 2.16117i) q^{10} +(0.926118 - 0.534695i) q^{11} +11.9506 q^{12} +(1.40072 - 3.32235i) q^{13} +4.75447 q^{14} +(-2.44811 + 1.41342i) q^{15} +(-2.70857 - 4.69138i) q^{16} +(0.318632 - 0.551886i) q^{17} -12.4551i q^{18} +(4.96410 + 2.86603i) q^{19} +(3.66117 + 2.11378i) q^{20} -5.38573i q^{21} +(-1.33433 + 2.31114i) q^{22} +(1.90893 + 3.30636i) q^{23} +(-13.6088 + 7.85704i) q^{24} -1.00000 q^{25} +(1.11827 + 8.92792i) q^{26} -5.62828 q^{27} +(-6.97531 + 4.02720i) q^{28} +(-4.72756 - 8.18837i) q^{29} +(3.52720 - 6.10929i) q^{30} +1.46410i q^{31} +(2.07908 + 1.20036i) q^{32} +(2.61799 + 1.51150i) q^{33} +1.59030i q^{34} +(0.952606 - 1.64996i) q^{35} +(10.5499 + 18.2730i) q^{36} +(0.655970 - 0.378725i) q^{37} -14.3044 q^{38} +(10.1133 - 1.26675i) q^{39} -5.55889 q^{40} +(-0.232051 + 0.133975i) q^{41} +(6.72006 + 11.6395i) q^{42} +(0.318632 - 0.551886i) q^{43} -4.52091i q^{44} +(-4.32235 - 2.49551i) q^{45} +(-8.25104 - 4.76374i) q^{46} -9.44613i q^{47} +(7.65668 - 13.2618i) q^{48} +(-1.68508 - 2.91865i) q^{49} +(2.16117 - 1.24775i) q^{50} +1.80144 q^{51} +(-9.20287 - 12.1510i) q^{52} -6.99102 q^{53} +(12.1637 - 7.02271i) q^{54} +(0.534695 + 0.926118i) q^{55} +(5.29543 - 9.17196i) q^{56} +16.2036i q^{57} +(20.4341 + 11.7977i) q^{58} +(-0.641756 - 0.370518i) q^{59} +11.9506i q^{60} +(-2.09928 + 3.63606i) q^{61} +(-1.82684 - 3.16418i) q^{62} +(8.23499 - 4.75447i) q^{63} +4.84325 q^{64} +(3.32235 + 1.40072i) q^{65} -7.54390 q^{66} +(-7.01029 + 4.04739i) q^{67} +(-1.34703 - 2.33313i) q^{68} +(-5.39623 + 9.34654i) q^{69} +4.75447i q^{70} +(8.45663 + 4.88244i) q^{71} +(-24.0274 - 13.8723i) q^{72} -3.71649i q^{73} +(-0.945110 + 1.63698i) q^{74} +(-1.41342 - 2.44811i) q^{75} +(20.9860 - 12.1163i) q^{76} -2.03741 q^{77} +(-20.2760 + 15.3565i) q^{78} -9.31937 q^{79} +(4.69138 - 2.70857i) q^{80} +(-0.468594 - 0.811629i) q^{81} +(0.334335 - 0.579085i) q^{82} -5.11778i q^{83} +(-19.7181 - 11.3842i) q^{84} +(0.551886 + 0.318632i) q^{85} +1.59030i q^{86} +(13.3640 - 23.1472i) q^{87} +(2.97231 + 5.14819i) q^{88} +(-10.8932 + 6.28917i) q^{89} +12.4551 q^{90} +(-5.47602 + 4.14741i) q^{91} +16.1402 q^{92} +(-3.58429 + 2.06939i) q^{93} +(11.7864 + 20.4147i) q^{94} +(-2.86603 + 4.96410i) q^{95} +6.78645i q^{96} +(-3.65597 - 2.11078i) q^{97} +(7.28351 + 4.20514i) q^{98} +5.33734i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 2 q^{4} - 18 q^{6} - 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 2 * q^4 - 18 * q^6 - 6 * q^7 - 4 * q^9	$ 8 q + 2 q^{3} + 2 q^{4} - 18 q^{6} - 6 q^{7} - 4 q^{9} - 2 q^{10} + 20 q^{12} + 4 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + 12 q^{19} + 12 q^{20} - 12 q^{22} - 10 q^{23} - 12 q^{24} - 8 q^{25} + 10 q^{26} - 4 q^{27} - 18 q^{28} - 8 q^{29} + 4 q^{30} + 6 q^{32} + 42 q^{33} + 10 q^{35} + 20 q^{36} + 6 q^{37} - 16 q^{38} - 12 q^{40} + 12 q^{41} + 4 q^{42} - 2 q^{43} - 42 q^{46} + 28 q^{48} + 12 q^{49} - 8 q^{51} - 6 q^{52} - 24 q^{53} + 18 q^{54} + 12 q^{56} + 36 q^{58} - 12 q^{59} - 28 q^{61} + 4 q^{62} - 24 q^{63} - 8 q^{64} - 8 q^{65} + 12 q^{66} + 6 q^{67} - 14 q^{68} - 16 q^{69} - 48 q^{72} + 10 q^{74} - 2 q^{75} + 54 q^{76} - 36 q^{77} - 56 q^{78} - 16 q^{79} + 8 q^{81} + 4 q^{82} - 30 q^{84} + 18 q^{85} + 22 q^{87} - 18 q^{88} + 24 q^{89} + 40 q^{90} + 28 q^{91} + 44 q^{92} + 32 q^{94} - 16 q^{95} - 30 q^{97} + 72 q^{98}+O(q^{100}) $ 8 * q + 2 * q^3 + 2 * q^4 - 18 * q^6 - 6 * q^7 - 4 * q^9 - 2 * q^10 + 20 * q^12 + 4 * q^14 - 6 * q^15 - 2 * q^16 - 2 * q^17 + 12 * q^19 + 12 * q^20 - 12 * q^22 - 10 * q^23 - 12 * q^24 - 8 * q^25 + 10 * q^26 - 4 * q^27 - 18 * q^28 - 8 * q^29 + 4 * q^30 + 6 * q^32 + 42 * q^33 + 10 * q^35 + 20 * q^36 + 6 * q^37 - 16 * q^38 - 12 * q^40 + 12 * q^41 + 4 * q^42 - 2 * q^43 - 42 * q^46 + 28 * q^48 + 12 * q^49 - 8 * q^51 - 6 * q^52 - 24 * q^53 + 18 * q^54 + 12 * q^56 + 36 * q^58 - 12 * q^59 - 28 * q^61 + 4 * q^62 - 24 * q^63 - 8 * q^64 - 8 * q^65 + 12 * q^66 + 6 * q^67 - 14 * q^68 - 16 * q^69 - 48 * q^72 + 10 * q^74 - 2 * q^75 + 54 * q^76 - 36 * q^77 - 56 * q^78 - 16 * q^79 + 8 * q^81 + 4 * q^82 - 30 * q^84 + 18 * q^85 + 22 * q^87 - 18 * q^88 + 24 * q^89 + 40 * q^90 + 28 * q^91 + 44 * q^92 + 32 * q^94 - 16 * q^95 - 30 * q^97 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.16117	+	1.24775i	−1.52818	+	0.882295i	−0.528742	+	0.848783i	$0.677336\pi$
$2$	−2.16117	+	1.24775i	−1.52818	+	0.882295i	−0.999438	+	0.0335125i	$0.989331\pi$
$3$	1.41342	+	2.44811i	0.816038	+	1.41342i	0.908580	+	0.417710i	$0.137167\pi$
$3$	1.41342	+	2.44811i	0.816038	+	1.41342i	−0.0925423	+	0.995709i	$0.529499\pi$
$4$	2.11378	−	3.66117i	1.05689	−	1.83059i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−6.10929	−	3.52720i	−2.49411	−	1.43997i
$7$	−1.64996	−	0.952606i	−0.623627	−	0.360051i	0.154653	−	0.987969i	$-0.450574\pi$
$7$	−1.64996	−	0.952606i	−0.623627	−	0.360051i	−0.778280	+	0.627918i	$0.783907\pi$
$8$			5.55889i			1.96536i
$9$	−2.49551	+	4.32235i	−0.831836	+	1.44078i
$10$	−1.24775	−	2.16117i	−0.394574	−	0.683423i
$11$	0.926118	−	0.534695i	0.279235	−	0.161217i	−0.353842	−	0.935305i	$-0.615125\pi$
$11$	0.926118	−	0.534695i	0.279235	−	0.161217i	0.633077	+	0.774089i	$0.281792\pi$
$12$	11.9506			3.44985
$13$	1.40072	−	3.32235i	0.388490	−	0.921453i
$13$	1.40072	−	3.32235i	0.388490	−	0.921453i
$14$	4.75447			1.27069
$15$	−2.44811	+	1.41342i	−0.632100	+	0.364943i
$16$	−2.70857	−	4.69138i	−0.677142	−	1.17284i
$17$	0.318632	−	0.551886i	0.0772795	−	0.133852i	−0.824796	−	0.565431i	$-0.808710\pi$
$17$	0.318632	−	0.551886i	0.0772795	−	0.133852i	0.902075	+	0.431579i	$0.142043\pi$
$18$		−	12.4551i		−	2.93570i
$19$	4.96410	+	2.86603i	1.13884	+	0.657511i	0.946144	−	0.323747i	$-0.104943\pi$
$19$	4.96410	+	2.86603i	1.13884	+	0.657511i	0.192699	+	0.981258i	$0.438276\pi$
$20$	3.66117	+	2.11378i	0.818663	+	0.472655i
$21$		−	5.38573i		−	1.17526i
$22$	−1.33433	+	2.31114i	−0.284481	+	0.492736i
$23$	1.90893	+	3.30636i	0.398039	+	0.689423i	0.993484	−	0.113973i	$-0.0363576\pi$
$23$	1.90893	+	3.30636i	0.398039	+	0.689423i	−0.595445	+	0.803396i	$0.703024\pi$
$24$	−13.6088	+	7.85704i	−2.77788	+	1.60381i
$25$	−1.00000			−0.200000
$26$	1.11827	+	8.92792i	0.219311	+	1.75091i
$27$	−5.62828			−1.08316
$28$	−6.97531	+	4.02720i	−1.31821	+	0.761069i
$29$	−4.72756	−	8.18837i	−0.877886	−	1.52054i	−0.853657	−	0.520836i	$-0.825620\pi$
$29$	−4.72756	−	8.18837i	−0.877886	−	1.52054i	−0.0242288	−	0.999706i	$-0.507713\pi$
$30$	3.52720	−	6.10929i	0.643975	−	1.11540i
$31$			1.46410i			0.262960i	0.991319	+	0.131480i	$0.0419730\pi$
$31$			1.46410i			0.262960i	−0.991319	+	0.131480i	$0.958027\pi$
$32$	2.07908	+	1.20036i	0.367534	+	0.212196i
$33$	2.61799	+	1.51150i	0.455733	+	0.263118i
$34$			1.59030i			0.272733i
$35$	0.952606	−	1.64996i	0.161020	−	0.278895i
$36$	10.5499	+	18.2730i	1.75832	+	3.04550i
$37$	0.655970	−	0.378725i	0.107841	−	0.0622619i	−0.445110	−	0.895476i	$-0.646835\pi$
$37$	0.655970	−	0.378725i	0.107841	−	0.0622619i	0.552950	+	0.833214i	$0.313502\pi$
$38$	−14.3044			−2.32048
$39$	10.1133	−	1.26675i	1.61942	−	0.202842i
$40$	−5.55889			−0.878938
$41$	−0.232051	+	0.133975i	−0.0362402	+	0.0209233i	−0.518011	−	0.855374i	$-0.673327\pi$
$41$	−0.232051	+	0.133975i	−0.0362402	+	0.0209233i	0.481770	+	0.876297i	$0.339994\pi$
$42$	6.72006	+	11.6395i	1.03693	+	1.79601i
$43$	0.318632	−	0.551886i	0.0485909	−	0.0841618i	−0.840707	−	0.541490i	$-0.817860\pi$
$43$	0.318632	−	0.551886i	0.0485909	−	0.0841618i	0.889298	+	0.457328i	$0.151194\pi$
$44$		−	4.52091i		−	0.681552i
$45$	−4.32235	−	2.49551i	−0.644337	−	0.372008i
$46$	−8.25104	−	4.76374i	−1.21655	−	0.702375i
$47$		−	9.44613i		−	1.37786i	−0.724828	−	0.688930i	$-0.758081\pi$
$47$		−	9.44613i		−	1.37786i	0.724828	−	0.688930i	$-0.241919\pi$
$48$	7.65668	−	13.2618i	1.10515	−	1.91417i
$49$	−1.68508	−	2.91865i	−0.240726	−	0.416950i
$50$	2.16117	−	1.24775i	0.305636	−	0.176459i
$51$	1.80144			0.252252
$52$	−9.20287	−	12.1510i	−1.27621	−	1.68504i
$53$	−6.99102			−0.960290			−0.480145	−	0.877189i	$-0.659416\pi$
$53$	−6.99102			−0.960290			−0.480145	+	0.877189i	$0.659416\pi$
$54$	12.1637	−	7.02271i	1.65527	−	0.955669i
$55$	0.534695	+	0.926118i	0.0720982	+	0.124878i
$56$	5.29543	−	9.17196i	0.707632	−	1.22565i
$57$			16.2036i			2.14622i
$58$	20.4341	+	11.7977i	2.68313	+	1.54911i
$59$	−0.641756	−	0.370518i	−0.0835495	−	0.0482373i	0.457643	−	0.889136i	$-0.348694\pi$
$59$	−0.641756	−	0.370518i	−0.0835495	−	0.0482373i	−0.541193	+	0.840899i	$0.682027\pi$
$60$			11.9506i			1.54282i
$61$	−2.09928	+	3.63606i	−0.268785	+	0.465550i	−0.968548	−	0.248825i	$-0.919956\pi$
$61$	−2.09928	+	3.63606i	−0.268785	+	0.465550i	0.699763	+	0.714375i	$0.253289\pi$
$62$	−1.82684	−	3.16418i	−0.232009	−	0.401851i
$63$	8.23499	−	4.75447i	1.03751	−	0.599007i
$64$	4.84325			0.605406
$65$	3.32235	+	1.40072i	0.412086	+	0.173738i
$66$	−7.54390			−0.928589
$67$	−7.01029	+	4.04739i	−0.856443	+	0.494468i	−0.862820	−	0.505512i	$-0.831304\pi$
$67$	−7.01029	+	4.04739i	−0.856443	+	0.494468i	0.00637624	+	0.999980i	$0.497970\pi$
$68$	−1.34703	−	2.33313i	−0.163352	−	0.282934i
$69$	−5.39623	+	9.34654i	−0.649629	+	1.12519i
$70$			4.75447i			0.568268i
$71$	8.45663	+	4.88244i	1.00362	+	0.579439i	0.909317	−	0.416105i	$-0.136605\pi$
$71$	8.45663	+	4.88244i	1.00362	+	0.579439i	0.0943010	+	0.995544i	$0.469938\pi$
$72$	−24.0274	−	13.8723i	−2.83166	−	1.63486i
$73$		−	3.71649i		−	0.434982i	−0.976062	−	0.217491i	$-0.930213\pi$
$73$		−	3.71649i		−	0.434982i	0.976062	−	0.217491i	$-0.0697873\pi$
$74$	−0.945110	+	1.63698i	−0.109867	+	0.190295i
$75$	−1.41342	−	2.44811i	−0.163208	−	0.282684i
$76$	20.9860	−	12.1163i	2.40726	−	1.38983i
$77$	−2.03741			−0.232185
$78$	−20.2760	+	15.3565i	−2.29580	+	1.73879i
$79$	−9.31937			−1.04851			−0.524255	−	0.851561i	$-0.675656\pi$
$79$	−9.31937			−1.04851			−0.524255	+	0.851561i	$0.675656\pi$
$80$	4.69138	−	2.70857i	0.524512	−	0.302827i
$81$	−0.468594	−	0.811629i	−0.0520660	−	0.0901809i
$82$	0.334335	−	0.579085i	0.0369211	−	0.0639492i
$83$		−	5.11778i		−	0.561749i	−0.959744	−	0.280875i	$-0.909376\pi$
$83$		−	5.11778i		−	0.561749i	0.959744	−	0.280875i	$-0.0906245\pi$
$84$	−19.7181	−	11.3842i	−2.15142	−	1.24212i
$85$	0.551886	+	0.318632i	0.0598605	+	0.0345605i
$86$			1.59030i			0.171486i
$87$	13.3640	−	23.1472i	1.43278	−	2.48164i
$88$	2.97231	+	5.14819i	0.316849	+	0.548799i
$89$	−10.8932	+	6.28917i	−1.15467	+	0.666650i	−0.950021	−	0.312185i	$-0.898939\pi$
$89$	−10.8932	+	6.28917i	−1.15467	+	0.666650i	−0.204651	+	0.978835i	$0.565606\pi$
$90$	12.4551			1.31288
$91$	−5.47602	+	4.14741i	−0.574043	+	0.434767i
$92$	16.1402			1.68273
$93$	−3.58429	+	2.06939i	−0.371673	+	0.214586i
$94$	11.7864	+	20.4147i	1.21568	+	2.10562i
$95$	−2.86603	+	4.96410i	−0.294048	+	0.509306i
$96$			6.78645i			0.692639i
$97$	−3.65597	−	2.11078i	−0.371208	−	0.214317i	0.302778	−	0.953061i	$-0.402086\pi$
$97$	−3.65597	−	2.11078i	−0.371208	−	0.214317i	−0.673986	+	0.738744i	$0.735419\pi$
$98$	7.28351	+	4.20514i	0.735746	+	0.424783i
$99$			5.33734i			0.536423i
$100$	−2.11378	+	3.66117i	−0.211378	+	0.366117i
$101$	−7.62379	−	13.2048i	−0.758595	−	1.31393i	−0.943567	−	0.331181i	$-0.892553\pi$
$101$	−7.62379	−	13.2048i	−0.758595	−	1.31393i	0.184972	−	0.982744i	$-0.440781\pi$
$102$	−3.89322	+	2.24775i	−0.385487	+	0.222561i
$103$	13.5269			1.33285			0.666423	−	0.745574i	$-0.267824\pi$
$103$	13.5269			1.33285			0.666423	+	0.745574i	$0.267824\pi$
$104$	18.4686	+	7.78645i	1.81099	+	0.763524i
$105$	5.38573			0.525593
$106$	15.1088	−	8.72307i	1.46750	−	0.847259i
$107$	3.68137	+	6.37632i	0.355891	+	0.616422i	0.987270	−	0.159053i	$-0.0508440\pi$
$107$	3.68137	+	6.37632i	0.355891	+	0.616422i	−0.631379	+	0.775475i	$0.717511\pi$
$108$	−11.8969	+	20.6061i	−1.14478	+	1.98282i
$109$		−	10.0760i		−	0.965103i	−0.875868	−	0.482551i	$-0.839710\pi$
$109$		−	10.0760i		−	0.965103i	0.875868	−	0.482551i	$-0.160290\pi$
$110$	−2.31114	−	1.33433i	−0.220358	−	0.127224i
$111$	1.85432	+	1.07059i	0.176004	+	0.101616i
$112$			10.3208i			0.975223i
$113$	3.34403	−	5.79203i	0.314580	−	0.544868i	−0.664768	−	0.747050i	$-0.731470\pi$
$113$	3.34403	−	5.79203i	0.314580	−	0.544868i	0.979348	+	0.202181i	$0.0648030\pi$
$114$	−20.2181	−	35.0187i	−1.89360	−	3.27981i
$115$	−3.30636	+	1.90893i	−0.308320	+	0.178008i
$116$	−39.9721			−3.71131
$117$	10.8648	+	14.3453i	1.00445	+	1.32623i
$118$	1.84926			0.170238
$119$	−1.05146	+	0.607061i	−0.0963872	+	0.0556492i
$120$	−7.85704	−	13.6088i	−0.717246	−	1.24231i
$121$	−4.92820	+	8.53590i	−0.448018	+	0.775991i
$122$		−	10.4775i		−	0.948592i
$123$	−0.655970	−	0.378725i	−0.0591468	−	0.0341484i
$124$	5.36033	+	3.09479i	0.481372	+	0.277920i
$125$		−	1.00000i		−	0.0894427i
$126$	−11.8648	+	20.5505i	−1.05700	+	1.83078i
$127$	0.744750	+	1.28994i	0.0660859	+	0.114464i	0.897175	−	0.441675i	$-0.145616\pi$
$127$	0.744750	+	1.28994i	0.0660859	+	0.114464i	−0.831089	+	0.556139i	$0.812282\pi$
$128$	−14.6253	+	8.44391i	−1.29270	+	0.746343i
$129$	1.80144			0.158608
$130$	−8.92792	+	1.11827i	−0.783030	+	0.0980789i
$131$	4.12676			0.360557			0.180278	−	0.983616i	$-0.442300\pi$
$131$	4.12676			0.360557			0.180278	+	0.983616i	$0.442300\pi$
$132$	11.0677	−	6.38994i	0.963319	−	0.556172i
$133$	−5.46039	−	9.45767i	−0.473476	−	0.820084i
$134$	10.1003	−	17.4942i	0.872533	−	1.51127i
$135$		−	5.62828i		−	0.484405i
$136$	3.06787	+	1.77124i	0.263068	+	0.151882i
$137$	17.4155	+	10.0548i	1.48790	+	0.859041i	0.999905	−	0.0138029i	$-0.00439372\pi$
$137$	17.4155	+	10.0548i	1.48790	+	0.859041i	0.487999	+	0.872844i	$0.337727\pi$
$138$		−	26.9327i		−	2.29266i
$139$	−10.4126	+	18.0352i	−0.883189	+	1.52973i	−0.0354130	+	0.999373i	$0.511275\pi$
$139$	−10.4126	+	18.0352i	−0.883189	+	1.52973i	−0.847776	+	0.530355i	$0.822059\pi$
$140$	−4.02720	−	6.97531i	−0.340360	−	0.589521i
$141$	23.1252	−	13.3513i	1.94749	−	1.12439i
$142$	−24.3683			−2.04494
$143$	−0.479208	−	3.82584i	−0.0400734	−	0.319933i
$144$	27.0370			2.25308
$145$	8.18837	−	4.72756i	0.680007	−	0.392602i
$146$	4.63726	+	8.03198i	0.383783	+	0.664731i
$147$	4.76346	−	8.25055i	0.392883	−	0.680494i
$148$		−	3.20216i		−	0.263216i
$149$	11.5768	+	6.68388i	0.948410	+	0.547565i	0.892587	−	0.450876i	$-0.148888\pi$
$149$	11.5768	+	6.68388i	0.948410	+	0.547565i	0.0558233	+	0.998441i	$0.482222\pi$
$150$	6.10929	+	3.52720i	0.498821	+	0.287995i
$151$			18.2984i			1.48910i	0.667567	+	0.744550i	$0.267336\pi$
$151$			18.2984i			1.48910i	−0.667567	+	0.744550i	$0.732664\pi$
$152$	−15.9319	+	27.5949i	−1.29225	+	2.23824i
$153$	1.59030	+	2.75447i	0.128568	+	0.222686i
$154$	4.40320	−	2.54219i	0.354820	−	0.204856i
$155$	−1.46410			−0.117599
$156$	16.7395	−	39.7041i	1.34023	−	3.17887i
$157$	2.42229			0.193320			0.0966599	−	0.995317i	$-0.469184\pi$
$157$	2.42229			0.193320			0.0966599	+	0.995317i	$0.469184\pi$
$158$	20.1408	−	11.6283i	1.60231	−	0.925096i
$159$	−9.88124	−	17.1148i	−0.783633	−	1.35729i
$160$	−1.20036	+	2.07908i	−0.0948968	+	0.164366i
$161$		−	7.27382i		−	0.573258i
$162$	2.02543	+	1.16938i	0.159132	+	0.0918752i
$163$	−13.8416	−	7.99144i	−1.08416	−	0.625938i	−0.152142	−	0.988359i	$-0.548617\pi$
$163$	−13.8416	−	7.99144i	−1.08416	−	0.625938i	−0.932015	+	0.362421i	$0.881950\pi$
$164$			1.13277i			0.0884545i
$165$	−1.51150	+	2.61799i	−0.117670	+	0.203810i
$166$	6.38573	+	11.0604i	0.495629	+	0.858454i
$167$	−12.4648	+	7.19658i	−0.964558	+	0.556888i	−0.897573	−	0.440866i	$-0.854671\pi$
$167$	−12.4648	+	7.19658i	−0.964558	+	0.556888i	−0.0669853	+	0.997754i	$0.521338\pi$
$168$	29.9387			2.30982
$169$	−9.07597	−	9.30735i	−0.698151	−	0.715950i
$170$	−1.59030			−0.121970
$171$	−24.7759	+	14.3044i	−1.89466	+	1.09388i
$172$	−1.34703	−	2.33313i	−0.102710	−	0.177900i
$173$	−12.1745	+	21.0868i	−0.925608	+	1.60320i	−0.135027	+	0.990842i	$0.543112\pi$
$173$	−12.1745	+	21.0868i	−0.925608	+	1.60320i	−0.790581	+	0.612358i	$0.790221\pi$
$174$			66.7001i			5.05653i
$175$	1.64996	+	0.952606i	0.124725	+	0.0720103i
$176$	−5.01691	−	2.89651i	−0.378164	−	0.218333i
$177$		−	2.09479i		−	0.157454i
$178$	15.6947	−	27.1840i	1.17636	−	2.03752i
$179$	1.89414	+	3.28075i	0.141575	+	0.245215i	0.928090	−	0.372356i	$-0.121450\pi$
$179$	1.89414	+	3.28075i	0.141575	+	0.245215i	−0.786515	+	0.617571i	$0.788117\pi$
$180$	−18.2730	+	10.5499i	−1.36199	+	0.786343i
$181$	8.48794			0.630904			0.315452	−	0.948942i	$-0.397844\pi$
$181$	8.48794			0.630904			0.315452	+	0.948942i	$0.397844\pi$
$182$	6.65968	−	15.7960i	0.493649	−	1.17088i
$183$	−11.8687			−0.877356
$184$	−18.3797	+	10.6115i	−1.35497	+	0.782291i
$185$	0.378725	+	0.655970i	0.0278444	+	0.0482279i
$186$	5.16418	−	8.94462i	0.378656	−	0.655851i
$187$		−	0.681482i		−	0.0498349i
$188$	−34.5839	−	19.9670i	−2.52229	−	1.45625i
$189$	9.28645	+	5.36153i	0.675490	+	0.389994i
$190$		−	14.3044i		−	1.03775i
$191$	2.72155	−	4.71386i	0.196924	−	0.341083i	−0.750605	−	0.660751i	$-0.770238\pi$
$191$	2.72155	−	4.71386i	0.196924	−	0.341083i	0.947530	+	0.319668i	$0.103571\pi$
$192$	6.84555	+	11.8568i	0.494035	+	0.855693i
$193$	10.5288	−	6.07880i	0.757879	−	0.437562i	−0.0706548	−	0.997501i	$-0.522509\pi$
$193$	10.5288	−	6.07880i	0.757879	−	0.437562i	0.828534	+	0.559939i	$0.189176\pi$
$194$	10.5349			0.756363
$195$	1.26675	+	10.1133i	0.0907135	+	0.724227i
$196$	−14.2476			−1.01768
$197$	3.79172	−	2.18915i	0.270149	−	0.155970i	−0.358807	−	0.933412i	$-0.616816\pi$
$197$	3.79172	−	2.18915i	0.270149	−	0.155970i	0.628955	+	0.777442i	$0.283483\pi$
$198$	−6.65968	−	11.5349i	−0.473283	−	0.819751i
$199$	10.4186	−	18.0456i	0.738558	−	1.27922i	−0.214586	−	0.976705i	$-0.568840\pi$
$199$	10.4186	−	18.0456i	0.738558	−	1.27922i	0.953144	−	0.302516i	$-0.0978265\pi$
$200$		−	5.55889i		−	0.393073i
$201$	−19.8170	−	11.4413i	−1.39778	−	0.807009i
$202$	32.9526	+	19.0252i	2.31854	+	1.33861i
$203$			18.0140i			1.26434i
$204$	3.80785	−	6.59538i	0.266603	−	0.461769i
$205$	−0.133975	−	0.232051i	−0.00935719	−	0.0162071i
$206$	−29.2340	+	16.8783i	−2.03683	+	1.17596i
$207$	−19.0550			−1.32441
$208$	−19.3803	+	2.42749i	−1.34378	+	0.168316i
$209$	6.12979			0.424007
$210$	−11.6395	+	6.72006i	−0.803201	+	0.463728i
$211$	5.32684	+	9.22635i	0.366715	+	0.635168i	0.989050	−	0.147583i	$-0.0471492\pi$
$211$	5.32684	+	9.22635i	0.366715	+	0.635168i	−0.622335	+	0.782751i	$0.713816\pi$
$212$	−14.7775	+	25.5953i	−1.01492	+	1.75789i
$213$			27.6037i			1.89138i
$214$	−15.9121	−	9.18688i	−1.08773	−	0.628002i
$215$	0.551886	+	0.318632i	0.0376383	+	0.0217305i
$216$		−	31.2870i		−	2.12881i
$217$	1.39471	−	2.41571i	0.0946792	−	0.163989i
$218$	12.5723	+	21.7759i	0.851505	+	1.47485i
$219$	9.09839	−	5.25296i	0.614812	−	0.354962i
$220$	4.52091			0.304799
$221$	−1.38724	−	1.83164i	−0.0933161	−	0.123210i
$222$	−5.34335			−0.358622
$223$	−18.4804	+	10.6697i	−1.23754	+	0.714494i	−0.968591	−	0.248661i	$-0.920010\pi$
$223$	−18.4804	+	10.6697i	−1.23754	+	0.714494i	−0.268949	+	0.963155i	$0.586676\pi$
$224$	−2.28694	−	3.96110i	−0.152803	−	0.264662i
$225$	2.49551	−	4.32235i	0.166367	−	0.288156i
$226$			16.6901i			1.11021i
$227$	13.5842	+	7.84283i	0.901613	+	0.520547i	0.877723	−	0.479168i	$-0.159062\pi$
$227$	13.5842	+	7.84283i	0.901613	+	0.520547i	0.0238900	+	0.999715i	$0.492395\pi$
$228$	59.3241	+	34.2508i	3.92884	+	2.26831i
$229$		−	7.62085i		−	0.503600i	−0.967779	−	0.251800i	$-0.918977\pi$
$229$		−	7.62085i		−	0.503600i	0.967779	−	0.251800i	$-0.0810225\pi$
$230$	4.76374	−	8.25104i	0.314112	−	0.544058i
$231$	−2.87972	−	4.98782i	−0.189472	−	0.328175i
$232$	45.5182	−	26.2800i	2.98842	−	1.72536i
$233$	19.0550			1.24833			0.624166	−	0.781292i	$-0.285439\pi$
$233$	19.0550			1.24833			0.624166	+	0.781292i	$0.285439\pi$
$234$	−41.3802	−	17.4461i	−2.70511	−	1.14049i
$235$	9.44613			0.616198
$236$	−2.71306	+	1.56639i	−0.176605	+	0.101963i
$237$	−13.1722	−	22.8149i	−0.855625	−	1.48199i
$238$	1.51493	−	2.62393i	0.0981980	−	0.170084i
$239$		−	12.7535i		−	0.824954i	−0.910968	−	0.412477i	$-0.864664\pi$
$239$		−	12.7535i		−	0.824954i	0.910968	−	0.412477i	$-0.135336\pi$
$240$	13.2618	+	7.65668i	0.856043	+	0.494237i
$241$	−22.4550	−	12.9644i	−1.44646	−	0.835111i	−0.448187	−	0.893940i	$-0.647930\pi$
$241$	−22.4550	−	12.9644i	−1.44646	−	0.835111i	−0.998268	+	0.0588285i	$0.981263\pi$
$242$		−	24.5967i		−	1.58114i
$243$	−7.11778	+	12.3284i	−0.456606	+	0.790864i
$244$	8.87483	+	15.3717i	0.568153	+	0.984069i
$245$	2.91865	−	1.68508i	0.186466	−	0.107656i
$246$	1.89022			0.120516
$247$	16.4752	−	12.4780i	1.04829	−	0.793954i
$248$	−8.13878			−0.516813
$249$	12.5289	−	7.23357i	0.793987	−	0.458409i
$250$	1.24775	+	2.16117i	0.0789149	+	0.136685i
$251$	3.80593	−	6.59207i	0.240228	−	0.416088i	−0.720551	−	0.693402i	$-0.756111\pi$
$251$	3.80593	−	6.59207i	0.240228	−	0.416088i	0.960779	+	0.277314i	$0.0894444\pi$
$252$		−	40.1996i		−	2.53234i
$253$	3.53578	+	2.04139i	0.222293	+	0.128341i
$254$	−3.21907	−	1.85853i	−0.201982	−	0.116614i
$255$			1.80144i			0.112811i
$256$	16.2286	−	28.1087i	1.01429	−	1.75680i
$257$	0.167891	+	0.290796i	0.0104728	+	0.0181394i	0.871214	−	0.490903i	$-0.163333\pi$
$257$	0.167891	+	0.290796i	0.0104728	+	0.0181394i	−0.860742	+	0.509042i	$0.830000\pi$
$258$	−3.89322	+	2.24775i	−0.242382	+	0.139939i
$259$	−1.44310			−0.0896700
$260$	12.1510	−	9.20287i	0.753572	−	0.570738i
$261$	47.1906			2.92103
$262$	−8.91865	+	5.14918i	−0.550996	+	0.318118i
$263$	2.68795	+	4.65566i	0.165746	+	0.287080i	0.936920	−	0.349544i	$-0.113664\pi$
$263$	2.68795	+	4.65566i	0.165746	+	0.287080i	−0.771174	+	0.636624i	$0.780330\pi$
$264$	−8.40224	+	14.5531i	−0.517122	+	0.895681i
$265$		−	6.99102i		−	0.429455i
$266$	23.6017	+	13.6264i	1.44711	+	0.835491i
$267$	−30.7932	−	17.7785i	−1.88451	−	1.08802i
$268$			34.2212i			2.09039i
$269$	0.655192	−	1.13483i	0.0399478	−	0.0691916i	−0.845360	−	0.534197i	$-0.820614\pi$
$269$	0.655192	−	1.13483i	0.0399478	−	0.0691916i	0.885308	+	0.465005i	$0.153948\pi$
$270$	7.02271	+	12.1637i	0.427388	+	0.740258i
$271$	−10.0851	+	5.82266i	−0.612629	+	0.353701i	−0.773994	−	0.633194i	$-0.781744\pi$
$271$	−10.0851	+	5.82266i	−0.612629	+	0.353701i	0.161365	+	0.986895i	$0.448410\pi$
$272$	−3.45214			−0.209317
$273$	−17.8933	−	7.54390i	−1.08295	−	0.456577i
$274$	−50.1838			−3.03171
$275$	−0.926118	+	0.534695i	−0.0558470	+	0.0322433i
$276$	22.8129	+	39.5130i	1.37317	+	2.37841i
$277$	−10.1581	+	17.5943i	−0.610338	+	1.05714i	0.380845	+	0.924639i	$0.375633\pi$
$277$	−10.1581	+	17.5943i	−0.610338	+	1.05714i	−0.991183	+	0.132498i	$0.957700\pi$
$278$		−	51.9697i		−	3.11693i
$279$	−6.32835	−	3.65368i	−0.378869	−	0.218740i
$280$	9.17196	+	5.29543i	0.548129	+	0.316463i
$281$		−	11.8744i		−	0.708366i	−0.935176	−	0.354183i	$-0.884759\pi$
$281$		−	11.8744i		−	0.708366i	0.935176	−	0.354183i	$-0.115241\pi$
$282$	−33.3184	+	57.7091i	−1.98408	+	3.43653i
$283$	−11.3261	−	19.6173i	−0.673264	−	1.16613i	−0.976973	−	0.213363i	$-0.931558\pi$
$283$	−11.3261	−	19.6173i	−0.673264	−	1.16613i	0.303709	−	0.952765i	$-0.401775\pi$
$284$	35.7509	−	20.6408i	2.12143	−	1.22481i
$285$	−16.2036			−0.959817
$286$	5.80936	+	7.67038i	0.343515	+	0.453559i
$287$	0.510500			0.0301339
$288$	−10.3767	+	5.99102i	−0.611455	+	0.353024i
$289$	8.29695	+	14.3707i	0.488056	+	0.845337i
$290$	−11.7977	+	20.4341i	−0.692782	+	1.19993i
$291$		−	11.9336i		−	0.699562i
$292$	−13.6067	−	7.85584i	−0.796272	−	0.459728i
$293$	−16.1191	−	9.30636i	−0.941687	−	0.543683i	−0.0511983	−	0.998689i	$-0.516304\pi$
$293$	−16.1191	−	9.30636i	−0.941687	−	0.543683i	−0.890489	+	0.455005i	$0.849637\pi$
$294$			23.7745i			1.38656i
$295$	0.370518	−	0.641756i	0.0215724	−	0.0373645i
$296$	2.10529	+	3.64647i	0.122367	+	0.211946i
$297$	−5.21245	+	3.00941i	−0.302457	+	0.174624i
$298$	−33.3593			−1.93245
$299$	13.6587	−	1.71083i	0.789905	−	0.0989400i
$300$	−11.9506			−0.689970
$301$	−1.05146	+	0.607061i	−0.0606052	+	0.0349904i
$302$	−22.8319	−	39.5459i	−1.31383	−	2.27561i
$303$	21.5512	−	37.3278i	1.23808	−	2.14443i
$304$		−	31.0513i		−	1.78091i
$305$	−3.63606	−	2.09928i	−0.208200	−	0.120204i
$306$	−6.87381	−	3.96859i	−0.392949	−	0.226869i
$307$			3.14776i			0.179652i	0.995957	+	0.0898262i	$0.0286311\pi$
$307$			3.14776i			0.179652i	−0.995957	+	0.0898262i	$0.971369\pi$
$308$	−4.30664	+	7.45932i	−0.245394	+	0.425034i
$309$	19.1192	+	33.1154i	1.08765	+	1.88387i
$310$	3.16418	−	1.82684i	0.179713	−	0.103757i
$311$	3.18059			0.180355			0.0901774	−	0.995926i	$-0.471257\pi$
$311$	3.18059			0.180355			0.0901774	+	0.995926i	$0.471257\pi$
$312$	7.04170	+	56.2186i	0.398658	+	3.18275i
$313$	35.3533			1.99829			0.999144	−	0.0413596i	$-0.0131689\pi$
$313$	35.3533			1.99829			0.999144	+	0.0413596i	$0.0131689\pi$
$314$	−5.23499	+	3.02242i	−0.295427	+	0.170565i
$315$	4.75447	+	8.23499i	0.267884	+	0.463989i
$316$	−19.6991	+	34.1198i	−1.10816	+	1.91939i
$317$			13.6357i			0.765858i	0.923778	+	0.382929i	$0.125085\pi$
$317$			13.6357i			0.765858i	−0.923778	+	0.382929i	$0.874915\pi$
$318$	42.7101	+	24.6587i	2.39506	+	1.38279i
$319$	−8.75656	−	5.05560i	−0.490273	−	0.283059i
$320$			4.84325i			0.270746i
$321$	−10.4066	+	18.0248i	−0.580842	+	1.00605i
$322$	9.07594	+	15.7200i	0.505782	+	0.876041i
$323$	3.16344	−	1.82641i	0.176018	−	0.101624i
$324$	−3.96202			−0.220112
$325$	−1.40072	+	3.32235i	−0.0776980	+	0.184291i
$326$	39.8854			2.20905
$327$	24.6671	−	14.2416i	1.36409	−	0.787560i
$328$	−0.744750	−	1.28994i	−0.0411219	−	0.0712253i
$329$	−8.99844	+	15.5858i	−0.496100	+	0.859271i
$330$		−	7.54390i		−	0.415278i
$331$	−24.9380	−	14.3980i	−1.37072	−	0.791383i	−0.379698	−	0.925110i	$-0.623972\pi$
$331$	−24.9380	−	14.3980i	−1.37072	−	0.791383i	−0.991018	+	0.133727i	$0.957305\pi$
$332$	−18.7371	−	10.8179i	−1.02833	−	0.593707i
$333$			3.78044i			0.207167i
$334$	17.9591	−	31.1061i	0.982679	−	1.70205i
$335$	−4.04739	−	7.01029i	−0.221133	−	0.383013i
$336$	−25.2665	+	14.5876i	−1.37840	+	0.795819i
$337$	−11.7493			−0.640026			−0.320013	−	0.947413i	$-0.603687\pi$
$337$	−11.7493			−0.640026			−0.320013	+	0.947413i	$0.603687\pi$
$338$	31.2280	+	8.79023i	1.69858	+	0.478125i
$339$	18.9061			1.02684
$340$	2.33313	−	1.34703i	0.126532	−	0.0730532i
$341$	0.782847	+	1.35593i	0.0423936	+	0.0734278i
$342$	35.6967	−	61.8285i	1.93026	−	3.34330i
$343$			19.7574i			1.06680i
$344$	3.06787	+	1.77124i	0.165409	+	0.0954987i
$345$	−9.34654	−	5.39623i	−0.503201	−	0.290523i
$346$		−	60.7630i		−	3.26664i
$347$	−0.949887	+	1.64525i	−0.0509926	+	0.0883218i	−0.890395	−	0.455189i	$-0.849572\pi$
$347$	−0.949887	+	1.64525i	−0.0509926	+	0.0883218i	0.839402	+	0.543510i	$0.182905\pi$
$348$	−56.4973	−	97.8562i	−3.02857	−	5.24564i
$349$	−8.89329	+	5.13454i	−0.476047	+	0.274846i	−0.718768	−	0.695250i	$-0.755293\pi$
$349$	−8.89329	+	5.13454i	−0.476047	+	0.274846i	0.242721	+	0.970096i	$0.421960\pi$
$350$	−4.75447			−0.254137
$351$	−7.88364	+	18.6991i	−0.420798	+	0.998084i
$352$	2.56730			0.136838
$353$	−0.693330	+	0.400294i	−0.0369022	+	0.0213055i	−0.518338	−	0.855176i	$-0.673449\pi$
$353$	−0.693330	+	0.400294i	−0.0369022	+	0.0213055i	0.481435	+	0.876482i	$0.340116\pi$
$354$	2.61378	+	4.52720i	0.138921	+	0.240618i
$355$	−4.88244	+	8.45663i	−0.259133	+	0.448831i
$356$			53.1756i			2.81830i
$357$	−2.97231	−	1.71606i	−0.157311	−	0.0908237i
$358$	−8.18714	−	4.72685i	−0.432704	−	0.249822i
$359$			8.13272i			0.429228i	0.976699	+	0.214614i	$0.0688494\pi$
$359$			8.13272i			0.429228i	−0.976699	+	0.214614i	$0.931151\pi$
$360$	13.8723	−	24.0274i	0.731132	−	1.26636i
$361$	6.92820	+	12.0000i	0.364642	+	0.631579i
$362$	−18.3439	+	10.5909i	−0.964135	+	0.556643i
$363$	−27.8625			−1.46240
$364$	3.60929	+	28.8154i	0.189178	+	1.51034i
$365$	3.71649			0.194530
$366$	25.6502	−	14.8092i	1.34076	−	0.774087i
$367$	10.2632	+	17.7765i	0.535737	+	0.927924i	0.999127	+	0.0417696i	$0.0132996\pi$
$367$	10.2632	+	17.7765i	0.535737	+	0.927924i	−0.463390	+	0.886154i	$0.653367\pi$
$368$	10.3409	−	17.9110i	0.539057	−	0.933675i
$369$		−	1.33734i		−	0.0696191i
$370$	−1.63698	−	0.945110i	−0.0851025	−	0.0491339i
$371$	11.5349	+	6.65968i	0.598863	+	0.345754i
$372$			17.4969i			0.907173i
$373$	8.90292	−	15.4203i	0.460976	−	0.798433i	−0.538034	−	0.842923i	$-0.680833\pi$
$373$	8.90292	−	15.4203i	0.460976	−	0.798433i	0.999010	+	0.0444897i	$0.0141662\pi$
$374$	0.850322	+	1.47280i	0.0439691	+	0.0761568i
$375$	2.44811	−	1.41342i	0.126420	−	0.0729887i
$376$	52.5100			2.70800
$377$	−33.8266	+	4.23697i	−1.74216	+	0.218215i
$378$	−26.7595			−1.37636
$379$	−1.77150	+	1.02277i	−0.0909956	+	0.0525363i	−0.544807	−	0.838561i	$-0.683397\pi$
$379$	−1.77150	+	1.02277i	−0.0909956	+	0.0525363i	0.453812	+	0.891098i	$0.350064\pi$
$380$	12.1163	+	20.9860i	0.621553	+	1.07656i
$381$	−2.10529	+	3.64647i	−0.107857	+	0.186814i
$382$			13.5833i			0.694982i
$383$	−6.84611	−	3.95261i	−0.349820	−	0.201969i	0.314786	−	0.949163i	$-0.398067\pi$
$383$	−6.84611	−	3.95261i	−0.349820	−	0.201969i	−0.664606	+	0.747194i	$0.731401\pi$
$384$	−41.3433	−	23.8696i	−2.10979	−	1.21809i
$385$		−	2.03741i		−	0.103836i
$386$	−15.1697	+	26.2747i	−0.772117	+	1.33735i
$387$	1.59030	+	2.75447i	0.0808393	+	0.140018i
$388$	−15.4558	+	8.92343i	−0.784651	+	0.453018i
$389$	9.21171			0.467052			0.233526	−	0.972351i	$-0.424974\pi$
$389$	9.21171			0.467052			0.233526	+	0.972351i	$0.424974\pi$
$390$	−15.3565	−	20.2760i	−0.777609	−	1.02671i
$391$	2.43298			0.123041
$392$	16.2244	−	9.36719i	0.819458	−	0.473114i
$393$	5.83285	+	10.1028i	0.294228	+	0.509618i
$394$	−5.46304	+	9.46226i	−0.275224	+	0.476702i
$395$		−	9.31937i		−	0.468908i
$396$	19.5409	+	11.2820i	0.981968	+	0.566940i
$397$	5.50305	+	3.17719i	0.276190	+	0.159458i	0.631697	−	0.775215i	$-0.282359\pi$
$397$	5.50305	+	3.17719i	0.276190	+	0.159458i	−0.355507	+	0.934674i	$0.615692\pi$
$398$			51.9996i			2.60651i
$399$	15.4356	−	26.7353i	0.772748	−	1.33844i
$400$	2.70857	+	4.69138i	0.135428	+	0.234569i
$401$	3.61063	−	2.08460i	0.180306	−	0.104100i	−0.407130	−	0.913370i	$-0.633470\pi$
$401$	3.61063	−	2.08460i	0.180306	−	0.104100i	0.587437	+	0.809270i	$0.300137\pi$
$402$	57.1038			2.84808
$403$	4.86425	+	2.05080i	0.242306	+	0.102157i
$404$	−64.4600			−3.20701
$405$	0.811629	−	0.468594i	0.0403301	−	0.0232846i
$406$	−22.4770	−	38.9314i	−1.11552	−	1.93213i
$407$	0.405004	−	0.701487i	0.0200753	−	0.0347714i
$408$			10.0140i			0.495767i
$409$	8.80580	+	5.08403i	0.435419	+	0.251389i	0.701652	−	0.712519i	$-0.252446\pi$
$409$	8.80580	+	5.08403i	0.435419	+	0.251389i	−0.266234	+	0.963909i	$0.585779\pi$
$410$	0.579085	+	0.334335i	0.0285989	+	0.0165116i
$411$			56.8467i			2.80404i
$412$	28.5929	−	49.5244i	1.40867	−	2.43989i
$413$	0.705915	+	1.22268i	0.0347358	+	0.0601642i
$414$	41.1811	−	23.7759i	2.02394	−	1.16852i
$415$	5.11778			0.251222
$416$	6.90023	−	5.22607i	0.338311	−	0.256229i
$417$	−58.8697			−2.88286
$418$	−13.2475	+	7.64847i	−0.647959	+	0.374099i
$419$	−14.2954	−	24.7604i	−0.698378	−	1.20963i	−0.969029	−	0.246948i	$-0.920572\pi$
$419$	−14.2954	−	24.7604i	−0.698378	−	1.20963i	0.270651	−	0.962677i	$-0.412761\pi$
$420$	11.3842	−	19.7181i	0.555494	−	0.962144i
$421$		−	2.01797i		−	0.0983498i	−0.998790	−	0.0491749i	$-0.984341\pi$
$421$		−	2.01797i		−	0.0983498i	0.998790	−	0.0491749i	$-0.0156592\pi$
$422$	−23.0244	−	13.2932i	−1.12081	−	0.647101i
$423$	40.8295	+	23.5729i	1.98520	+	1.14615i
$424$		−	38.8623i		−	1.88732i
$425$	−0.318632	+	0.551886i	−0.0154559	+	0.0267704i
$426$	−34.4427	−	59.6564i	−1.66875	−	2.89036i
$427$	6.92747	−	3.99957i	0.335244	−	0.193553i
$428$	31.1264			1.50455
$429$	8.68878	−	6.58068i	0.419498	−	0.317718i
$430$	−1.59030			−0.0766908
$431$	17.8508	−	10.3061i	0.859842	−	0.496430i	−0.00411765	−	0.999992i	$-0.501311\pi$
$431$	17.8508	−	10.3061i	0.859842	−	0.496430i	0.863959	+	0.503562i	$0.167977\pi$
$432$	15.2446	+	26.4044i	0.733455	+	1.27038i
$433$	14.7178	−	25.4920i	0.707292	−	1.22507i	−0.258566	−	0.965994i	$-0.583250\pi$
$433$	14.7178	−	25.4920i	0.707292	−	1.22507i	0.965858	−	0.259072i	$-0.0834168\pi$
$434$			6.96103i			0.334140i
$435$	23.1472	+	13.3640i	1.10982	+	0.640757i
$436$	−36.8899	−	21.2984i	−1.76670	−	1.02001i
$437$			21.8841i			1.04686i
$438$	−13.1088	+	22.7051i	−0.626362	+	1.08489i
$439$	8.47602	+	14.6809i	0.404538	+	0.700681i	0.994268	−	0.106920i	$-0.0340988\pi$
$439$	8.47602	+	14.6809i	0.404538	+	0.700681i	−0.589729	+	0.807601i	$0.700765\pi$
$440$	−5.14819	+	2.97231i	−0.245430	+	0.141699i
$441$	16.8205			0.800978
$442$	5.28351	+	2.22756i	0.251311	+	0.105954i
$443$	−24.1399			−1.14692			−0.573461	−	0.819233i	$-0.694400\pi$
$443$	−24.1399			−1.14692			−0.573461	+	0.819233i	$0.694400\pi$
$444$	7.83925	−	4.52599i	0.372034	−	0.214794i
$445$	−6.28917	−	10.8932i	−0.298135	−	0.516385i
$446$	26.6262	−	46.1180i	1.26079	−	2.18375i
$447$			37.7885i			1.78733i
$448$	−7.99118	−	4.61371i	−0.377548	−	0.217977i
$449$	18.0679	+	10.4315i	0.852676	+	0.492293i	0.861553	−	0.507668i	$-0.169492\pi$
$449$	18.0679	+	10.4315i	0.852676	+	0.492293i	−0.00887706	+	0.999961i	$0.502826\pi$
$450$			12.4551i			0.587140i
$451$	−0.143271	+	0.248153i	−0.00674637	+	0.0116851i
$452$	−14.1371	−	24.4861i	−0.664952	−	1.15173i
$453$	−44.7965	+	25.8633i	−2.10472	+	1.21516i
$454$	−39.1437			−1.83710
$455$	−4.14741	−	5.47602i	−0.194434	−	0.256720i
$456$	−90.0739			−4.21810
$457$	26.4708	−	15.2830i	1.23825	−	0.714906i	0.269517	−	0.962996i	$-0.413136\pi$
$457$	26.4708	−	15.2830i	1.23825	−	0.714906i	0.968737	+	0.248089i	$0.0798027\pi$
$458$	9.50894	+	16.4700i	0.444324	+	0.769591i
$459$	−1.79335	+	3.10617i	−0.0837063	+	0.144984i
$460$			16.1402i			0.752541i
$461$	4.05146	+	2.33911i	0.188695	+	0.108943i	0.591372	−	0.806399i	$-0.298587\pi$
$461$	4.05146	+	2.33911i	0.188695	+	0.108943i	−0.402676	+	0.915342i	$0.631920\pi$
$462$	12.4471	+	7.18636i	0.579094	+	0.334340i
$463$		−	14.0011i		−	0.650688i	−0.945596	−	0.325344i	$-0.894520\pi$
$463$		−	14.0011i		−	0.650688i	0.945596	−	0.325344i	$-0.105480\pi$
$464$	−25.6098	+	44.3575i	−1.18891	+	2.05925i
$465$	−2.06939	−	3.58429i	−0.0959656	−	0.166217i
$466$	−41.1811	+	23.7759i	−1.90768	+	1.10140i
$467$	6.98506			0.323230			0.161615	−	0.986854i	$-0.448330\pi$
$467$	6.98506			0.323230			0.161615	+	0.986854i	$0.448330\pi$
$468$	75.4866	−	9.45512i	3.48937	−	0.437063i
$469$	15.4223			0.712135
$470$	−20.4147	+	11.7864i	−0.941661	+	0.543668i
$471$	3.42371	+	5.93004i	0.157756	+	0.273242i
$472$	2.05967	−	3.56745i	0.0948039	−	0.164205i
$473$		−	0.681482i		−	0.0313346i
$474$	56.9347	+	32.8713i	2.61510	+	1.50983i
$475$	−4.96410	−	2.86603i	−0.227769	−	0.131502i
$476$			5.13277i			0.235260i
$477$	17.4461	−	30.2176i	0.798804	−	1.38357i
$478$	15.9132	+	27.5625i	0.727853	+	1.26068i
$479$	−14.1065	+	8.14438i	−0.644542	+	0.372126i	−0.786362	−	0.617766i	$-0.788038\pi$
$479$	−14.1065	+	8.14438i	−0.644542	+	0.372126i	0.141820	+	0.989892i	$0.454704\pi$
$480$	−6.78645			−0.309758
$481$	−0.339423	−	2.70985i	−0.0154764	−	0.123558i
$482$	64.7056			2.94726
$483$	17.8071	−	10.2810i	0.810253	−	0.467800i
$484$	20.8343	+	36.0860i	0.947012	+	1.64027i
$485$	2.11078	−	3.65597i	0.0958454	−	0.166009i
$486$		−	35.5249i		−	1.61144i
$487$	17.3559	+	10.0204i	0.786471	+	0.454069i	0.838719	−	0.544565i	$-0.183305\pi$
$487$	17.3559	+	10.0204i	0.786471	+	0.454069i	−0.0522474	+	0.998634i	$0.516638\pi$
$488$	−20.2125	−	11.6697i	−0.914975	−	0.528261i
$489$		−	45.1810i		−	2.04316i
$490$	−4.20514	+	7.28351i	−0.189969	+	0.329035i
$491$	−7.89916	−	13.6818i	−0.356484	−	0.617449i	0.630887	−	0.775875i	$-0.282691\pi$
$491$	−7.89916	−	13.6818i	−0.356484	−	0.617449i	−0.987371	+	0.158426i	$0.949358\pi$
$492$	−2.77315	+	1.60108i	−0.125023	+	0.0721823i
$493$	−6.02540			−0.271370
$494$	−20.0364	+	47.5241i	−0.901481	+	2.13821i
$495$	−5.33734			−0.239896
$496$	6.86865	−	3.96562i	0.308411	−	0.178061i
$497$	−9.30208	−	16.1117i	−0.417255	−	0.722708i
$498$	−18.0514	+	31.2660i	−0.808903	+	1.40106i
$499$		−	1.24651i		−	0.0558016i	−0.999611	−	0.0279008i	$-0.991118\pi$
$499$		−	1.24651i		−	0.0558016i	0.999611	−	0.0279008i	$-0.00888226\pi$
$500$	−3.66117	−	2.11378i	−0.163733	−	0.0945311i
$501$	−35.2361	−	20.3436i	−1.57423	−	0.908883i
$502$			18.9955i			0.847809i
$503$	3.82672	−	6.62808i	0.170625	−	0.295532i	−0.768013	−	0.640434i	$-0.778755\pi$
$503$	3.82672	−	6.62808i	0.170625	−	0.295532i	0.938639	+	0.344902i	$0.112088\pi$
$504$	26.4296	+	45.7774i	1.17727	+	2.03909i
$505$	13.2048	−	7.62379i	0.587605	−	0.339254i
$506$	−10.1886			−0.452938
$507$	9.95732	−	35.3742i	0.442220	−	1.57102i
$508$	6.29695			0.279382
$509$	−22.2777	+	12.8621i	−0.987444	+	0.570101i	−0.904509	−	0.426454i	$-0.859763\pi$
$509$	−22.2777	+	12.8621i	−0.987444	+	0.570101i	−0.0829345	+	0.996555i	$0.526429\pi$
$510$	−2.24775	−	3.89322i	−0.0995322	−	0.172395i
$511$	−3.54035	+	6.13207i	−0.156616	+	0.271267i
$512$			47.2215i			2.08691i
$513$	−27.9393	−	16.1308i	−1.23355	−	0.712192i
$514$	−0.725685	−	0.418974i	−0.0320086	−	0.0184802i
$515$			13.5269i			0.596067i
$516$	3.80785	−	6.59538i	0.167631	−	0.290346i
$517$	−5.05080	−	8.74824i	−0.222134	−	0.384747i
$518$	3.11879	−	1.80064i	0.137032	−	0.0791154i
$519$	−68.8305			−3.02132
$520$	−7.78645	+	18.4686i	−0.341458	+	0.809900i
$521$	−30.1519			−1.32098			−0.660490	−	0.750835i	$-0.729651\pi$
$521$	−30.1519			−1.32098			−0.660490	+	0.750835i	$0.729651\pi$
$522$	−101.987	+	58.8823i	−4.46386	+	2.57721i
$523$	−1.96876	−	3.41000i	−0.0860880	−	0.149109i	0.819766	−	0.572698i	$-0.194103\pi$
$523$	−1.96876	−	3.41000i	−0.0860880	−	0.149109i	−0.905854	+	0.423589i	$0.860770\pi$
$524$	8.72307	−	15.1088i	0.381069	−	0.660031i
$525$			5.38573i			0.235052i
$526$	−11.6182	−	6.70779i	−0.506579	−	0.292473i
$527$	0.808017	+	0.466509i	0.0351978	+	0.0203215i
$528$		−	16.3759i		−	0.712672i
$529$	4.21200	−	7.29539i	0.183130	−	0.317191i
$530$	8.72307	+	15.1088i	0.378906	+	0.656284i
$531$	3.20301	−	1.84926i	0.138999	−	0.0802510i
$532$	−46.1682			−2.00165
$533$	0.120072	+	0.958614i	0.00520088	+	0.0415222i
$534$	88.7326			3.83983
$535$	−6.37632	+	3.68137i	−0.275672	+	0.159159i
$536$	−22.4990	−	38.9694i	−0.971809	−	1.68322i
$537$	−5.35444	+	9.27415i	−0.231061	+	0.400209i
$538$			3.27007i			0.140983i
$539$	−3.12117	−	1.80201i	−0.134438	−	0.0776180i
$540$	−20.6061	−	11.8969i	−0.886745	−	0.511963i
$541$		−	15.8881i		−	0.683083i	−0.939867	−	0.341541i	$-0.889051\pi$
$541$		−	15.8881i		−	0.683083i	0.939867	−	0.341541i	$-0.110949\pi$
$542$	14.5305	−	25.1675i	0.624138	−	1.08104i
$543$	11.9970	+	20.7795i	0.514842	+	0.891732i
$544$	1.32492	−	0.764945i	0.0568057	−	0.0327968i
$545$	10.0760			0.431607
$546$	48.0833	−	6.02271i	2.05778	−	0.257748i
$547$	−6.56107			−0.280531			−0.140266	−	0.990114i	$-0.544796\pi$
$547$	−6.56107			−0.280531			−0.140266	+	0.990114i	$0.544796\pi$
$548$	73.6249	−	42.5074i	3.14510	−	1.81582i
$549$	−10.4775	−	18.1476i	−0.447170	−	0.774522i
$550$	1.33433	−	2.31114i	0.0568962	−	0.0985471i
$551$		−	54.1972i		−	2.30888i
$552$	−51.9564	−	29.9970i	−2.21141	−	1.27676i
$553$	15.3766	+	8.87769i	0.653880	+	0.377518i
$554$		−	50.6990i		−	2.15399i
$555$	−1.07059	+	1.85432i	−0.0454441	+	0.0787116i
$556$	44.0200	+	76.2450i	1.86687	+	3.23351i
$557$	6.79835	−	3.92503i	0.288055	−	0.166309i	−0.349009	−	0.937119i	$-0.613482\pi$
$557$	6.79835	−	3.92503i	0.288055	−	0.166309i	0.637065	+	0.770810i	$0.280148\pi$
$558$	18.2356			0.771973
$559$	−1.38724	−	1.83164i	−0.0586741	−	0.0774702i
$560$	−10.3208			−0.436133
$561$	1.66835	−	0.963220i	0.0704377	−	0.0406672i
$562$	14.8163	+	25.6626i	0.624988	+	1.08251i
$563$	−7.77976	+	13.4749i	−0.327878	+	0.567901i	−0.982091	−	0.188410i	$-0.939667\pi$
$563$	−7.77976	+	13.4749i	−0.327878	+	0.567901i	0.654213	+	0.756310i	$0.273000\pi$
$564$		−	112.887i		−	4.75341i
$565$	5.79203	+	3.34403i	0.243673	+	0.140684i
$566$	48.9552	+	28.2643i	2.05774	+	1.18804i
$567$			1.78554i			0.0749857i
$568$	−27.1409	+	47.0095i	−1.13881	+	1.97247i
$569$	1.73957	+	3.01303i	0.0729267	+	0.126313i	0.900183	−	0.435512i	$-0.143433\pi$
$569$	1.73957	+	3.01303i	0.0729267	+	0.126313i	−0.827256	+	0.561825i	$0.810099\pi$
$570$	35.0187	−	20.2181i	1.46677	−	0.846842i
$571$	21.5118			0.900240			0.450120	−	0.892968i	$-0.351381\pi$
$571$	21.5118			0.900240			0.450120	+	0.892968i	$0.351381\pi$
$572$	−15.0200	−	6.33252i	−0.628018	−	0.264776i
$573$	15.3868			0.642791
$574$	−1.10328	+	0.636978i	−0.0460500	+	0.0265870i
$575$	−1.90893	−	3.30636i	−0.0796078	−	0.137885i
$576$	−12.0864	+	20.9342i	−0.503599	+	0.872259i
$577$		−	9.97608i		−	0.415310i	−0.978202	−	0.207655i	$-0.933417\pi$
$577$		−	9.97608i		−	0.415310i	0.978202	−	0.207655i	$-0.0665831\pi$
$578$	−35.8623	−	20.7051i	−1.49167	−	0.861218i
$579$	29.7632	+	17.1838i	1.23692	+	0.714134i
$580$		−	39.9721i		−	1.65975i
$581$	−4.87523	+	8.44414i	−0.202259	+	0.350322i
$582$	14.8902	+	25.7907i	0.617221	+	1.06906i
$583$	−6.47451	+	3.73806i	−0.268147	+	0.154815i
$584$	20.6595			0.854898
$585$	−14.3453	+	10.8648i	−0.593107	+	0.449205i
$586$	46.4482			1.91876
$587$	20.8341	−	12.0286i	0.859915	−	0.496472i	−0.00406862	−	0.999992i	$-0.501295\pi$
$587$	20.8341	−	12.0286i	0.859915	−	0.496472i	0.863984	+	0.503519i	$0.167962\pi$
$588$	−20.1378	−	34.8797i	−0.830469	−	1.43841i
$589$	−4.19615	+	7.26795i	−0.172899	+	0.299471i
$590$			1.84926i			0.0761328i
$591$	10.7186	+	6.18837i	0.440903	+	0.254556i
$592$	−3.55348	−	2.05160i	−0.146047	−	0.0843203i
$593$			0.940219i			0.0386102i	0.999814	+	0.0193051i	$0.00614538\pi$
$593$			0.940219i			0.0386102i	−0.999814	+	0.0193051i	$0.993855\pi$
$594$	7.51001	−	13.0077i	0.308139	−	0.533713i
$595$	−0.607061	−	1.05146i	−0.0248871	−	0.0431057i
$596$	48.9417	−	28.2565i	2.00473	−	1.15743i
$597$	58.9037			2.41077
$598$	−27.3842	+	20.7401i	−1.11982	+	0.848128i
$599$	−11.4270			−0.466896			−0.233448	−	0.972369i	$-0.575001\pi$
$599$	−11.4270			−0.466896			−0.233448	+	0.972369i	$0.575001\pi$
$600$	13.6088	−	7.85704i	0.555577	−	0.320762i
$601$	18.0215	+	31.2142i	0.735114	+	1.27325i	0.954674	+	0.297655i	$0.0962045\pi$
$601$	18.0215	+	31.2142i	0.735114	+	1.27325i	−0.219560	+	0.975599i	$0.570462\pi$
$602$	1.51493	−	2.62393i	0.0617437	−	0.106943i
$603$		−	40.4012i		−	1.64526i
$604$	66.9935	+	38.6787i	2.72593	+	1.57381i
$605$	−8.53590	−	4.92820i	−0.347034	−	0.200360i
$606$			107.562i			4.36942i
$607$	−19.9454	+	34.5464i	−0.809557	+	1.40219i	0.103614	+	0.994618i	$0.466959\pi$
$607$	−19.9454	+	34.5464i	−0.809557	+	1.40219i	−0.913171	+	0.407576i	$0.866374\pi$
$608$	6.88052	+	11.9174i	0.279042	+	0.483315i
$609$	−44.1003	+	25.4613i	−1.78704	+	1.03175i
$610$	10.4775			0.424223
$611$	−31.3833	−	13.2314i	−1.26963	−	0.535285i
$612$	13.4461			0.543528
$613$	0.299187	−	0.172736i	0.0120841	−	0.00697673i	−0.493946	−	0.869493i	$-0.664446\pi$
$613$	0.299187	−	0.172736i	0.0120841	−	0.00697673i	0.506030	+	0.862516i	$0.331113\pi$
$614$	−3.92763	−	6.80286i	−0.158506	−	0.274541i
$615$	0.378725	−	0.655970i	0.0152716	−	0.0264513i
$616$		−	11.3258i		−	0.456328i
$617$	33.5022	+	19.3425i	1.34875	+	0.778700i	0.988072	−	0.153991i	$-0.0492128\pi$
$617$	33.5022	+	19.3425i	1.34875	+	0.778700i	0.360676	+	0.932691i	$0.382546\pi$
$618$	−82.6398	−	47.7121i	−3.32426	−	1.91926i
$619$			14.8971i			0.598764i	0.954133	+	0.299382i	$0.0967805\pi$
$619$			14.8971i			0.598764i	−0.954133	+	0.299382i	$0.903219\pi$
$620$	−3.09479	+	5.36033i	−0.124290	+	0.215276i
$621$	−10.7440	−	18.6091i	−0.431141	−	0.746758i
$622$	−6.87381	+	3.96859i	−0.275615	+	0.159126i
$623$	23.9644			0.960113
$624$	−33.3353	−	44.0142i	−1.33448	−	1.76198i
$625$	1.00000			0.0400000
$626$	−76.4047	+	44.1123i	−3.05374	+	1.76308i
$627$	8.66397	+	15.0064i	0.346006	+	0.599299i
$628$	5.12019	−	8.86842i	0.204318	−	0.353889i
$629$		−	0.482694i		−	0.0192463i
$630$	−20.5505	−	11.8648i	−0.818750	−	0.472706i
$631$	33.6408	+	19.4225i	1.33922	+	0.773198i	0.986691	−	0.162604i	$-0.0519893\pi$
$631$	33.6408	+	19.4225i	1.33922	+	0.773198i	0.352526	+	0.935802i	$0.385323\pi$
$632$		−	51.8053i		−	2.06071i
$633$	−15.0581	+	26.0814i	−0.598506	+	1.03664i
$634$	−17.0140	−	29.4691i	−0.675713	−	1.17037i
$635$	−1.28994	+	0.744750i	−0.0511899	+	0.0295545i
$636$	−83.5470			−3.31285
$637$	−12.0571	+	1.51022i	−0.477719	+	0.0598370i
$638$	25.2326			0.998967
$639$	−42.2072	+	24.3683i	−1.66969	+	0.963996i
$640$	−8.44391	−	14.6253i	−0.333775	−	0.578115i
$641$	18.5908	−	32.2003i	0.734293	−	1.27183i	−0.220739	−	0.975333i	$-0.570847\pi$
$641$	18.5908	−	32.2003i	0.734293	−	1.27183i	0.955033	−	0.296501i	$-0.0958197\pi$
$642$		−	51.9397i		−	2.04990i
$643$	7.88410	+	4.55189i	0.310918	+	0.179509i	0.647337	−	0.762204i	$-0.275882\pi$
$643$	7.88410	+	4.55189i	0.310918	+	0.179509i	−0.336419	+	0.941712i	$0.609216\pi$
$644$	−26.6307	−	15.3753i	−1.04940	−	0.605870i
$645$			1.80144i			0.0709316i
$646$	−4.55783	+	7.89439i	−0.179325	+	0.310601i
$647$	−9.56118	−	16.5605i	−0.375889	−	0.651059i	0.614571	−	0.788862i	$-0.289329\pi$
$647$	−9.56118	−	16.5605i	−0.375889	−	0.651059i	−0.990460	+	0.137803i	$0.955996\pi$
$648$	4.51175	−	2.60486i	0.177238	−	0.102329i
$649$	−0.792455			−0.0311066
$650$	−1.11827	−	8.92792i	−0.0438622	−	0.350182i
$651$	7.88525			0.309047
$652$	−58.5161	+	33.7843i	−2.29167	+	1.32309i
$653$	−17.3162	−	29.9926i	−0.677636	−	1.17370i	−0.975691	−	0.219152i	$-0.929671\pi$
$653$	−17.3162	−	29.9926i	−0.677636	−	1.17370i	0.298055	−	0.954549i	$-0.403662\pi$
$654$	−35.5399	+	61.5570i	−1.38972	+	2.40707i
$655$			4.12676i			0.161246i
$656$	1.25705	+	0.725758i	0.0490796	+	0.0283361i
$657$	16.0640	+	9.27453i	0.626714	+	0.361834i
$658$		−	44.9114i		−	1.75083i
$659$	3.34926	−	5.80109i	0.130469	−	0.225978i	−0.793389	−	0.608715i	$-0.791685\pi$
$659$	3.34926	−	5.80109i	0.130469	−	0.225978i	0.923857	+	0.382737i	$0.125018\pi$
$660$	6.38994	+	11.0677i	0.248728	+	0.430809i
$661$	5.22004	−	3.01379i	0.203036	−	0.117223i	−0.395035	−	0.918666i	$-0.629268\pi$
$661$	5.22004	−	3.01379i	0.203036	−	0.117223i	0.598071	+	0.801443i	$0.295934\pi$
$662$	71.8604			2.79294
$663$	2.52331	−	5.98501i	0.0979974	−	0.232438i
$664$	28.4492			1.10404
$665$	9.45767	−	5.46039i	0.366753	−	0.211745i
$666$	−4.71706	−	8.17018i	−0.182782	−	0.316588i
$667$	18.0491	−	31.2620i	0.698865	−	1.21047i
$668$			60.8479i			2.35428i
$669$	−52.2411	−	30.1614i	−2.01976	−	1.16611i
$670$	17.4942	+	10.1003i	0.675861	+	0.390209i
$671$			4.48990i			0.173330i
$672$	6.46481	−	11.1974i	0.249386	−	0.431948i
$673$	11.6784	+	20.2276i	0.450169	+	0.779715i	0.998396	−	0.0566140i	$-0.0180304\pi$
$673$	11.6784	+	20.2276i	0.450169	+	0.779715i	−0.548227	+	0.836329i	$0.684697\pi$
$674$	25.3923	−	14.6603i	0.978075	−	0.564692i
$675$	5.62828			0.216633
$676$	−53.2604	+	13.5550i	−2.04848	+	0.521346i
$677$	−45.4042			−1.74503			−0.872513	−	0.488590i	$-0.837511\pi$
$677$	−45.4042			−1.74503			−0.872513	+	0.488590i	$0.837511\pi$
$678$	−40.8593	+	23.5901i	−1.56919	+	0.905973i
$679$	4.02148	+	6.96540i	0.154330	+	0.267308i
$680$	−1.77124	+	3.06787i	−0.0679239	+	0.117648i
$681$			44.3408i			1.69914i
$682$	−3.38374	−	1.95360i	−0.129570	−	0.0748073i
$683$	22.0817	+	12.7489i	0.844934	+	0.487823i	0.858938	−	0.512079i	$-0.171125\pi$
$683$	22.0817	+	12.7489i	0.844934	+	0.487823i	−0.0140045	+	0.999902i	$0.504458\pi$
$684$			120.945i			4.62445i
$685$	−10.0548	+	17.4155i	−0.384175	+	0.665411i
$686$	−24.6523	−	42.6991i	−0.941230	−	1.63026i
$687$	18.6567	−	10.7715i	0.711798	−	0.410957i
$688$	−3.45214			−0.131612
$689$	−9.79246	+	23.2266i	−0.373063	+	0.884862i
$690$	26.9327			1.02531
$691$	5.71257	−	3.29815i	0.217316	−	0.125468i	−0.387391	−	0.921916i	$-0.626624\pi$
$691$	5.71257	−	3.29815i	0.217316	−	0.125468i	0.604707	+	0.796448i	$0.293290\pi$
$692$	51.4683	+	89.1457i	1.95653	+	3.38881i
$693$	5.08438	−	8.80641i	0.193140	−	0.334528i
$694$		−	4.74090i		−	0.179962i
$695$	−18.0352	−	10.4126i	−0.684115	−	0.394974i
$696$	128.673	+	74.2892i	4.87733	+	2.81593i
$697$			0.170754i			0.00646778i
$698$	12.8133	−	22.1933i	0.484990	−	0.840028i
$699$	26.9327	+	46.6487i	1.01869	+	1.76442i
$700$	6.97531	−	4.02720i	0.263642	−	0.152214i
$701$	−29.2474			−1.10466			−0.552329	−	0.833626i	$-0.686261\pi$
$701$	−29.2474			−1.10466			−0.552329	+	0.833626i	$0.686261\pi$
$702$	−6.29394	−	50.2488i	−0.237550	−	1.89652i
$703$	4.34174			0.163752
$704$	4.48542	−	2.58966i	0.169051	−	0.0976015i
$705$	13.3513	+	23.1252i	0.502841	+	0.870946i
$706$	0.998937	−	1.73021i	0.0375955	−	0.0651173i
$707$			29.0499i			1.09253i
$708$	−7.66938	−	4.42792i	−0.288233	−	0.166411i
$709$	−9.46865	−	5.46673i	−0.355603	−	0.205307i	0.311548	−	0.950231i	$-0.399153\pi$
$709$	−9.46865	−	5.46673i	−0.355603	−	0.205307i	−0.667150	+	0.744923i	$0.732486\pi$
$710$		−	24.3683i		−	0.914527i
$711$	23.2566	−	40.2815i	0.872189	−	1.51068i
$712$	−34.9608	−	60.5538i	−1.31021	−	2.26935i
$713$	−4.84084	+	2.79486i	−0.181291	+	0.104668i
$714$	8.56490			0.320533
$715$	3.82584	−	0.479208i	0.143078	−	0.0179214i
$716$	16.0152			0.598516
$717$	31.2220	−	18.0260i	1.16601	−	0.673194i
$718$	−10.1476	−	17.5762i	−0.378706	−	0.655938i
$719$	8.02989	−	13.9082i	0.299464	−	0.518688i	−0.676549	−	0.736398i	$-0.736525\pi$
$719$	8.02989	−	13.9082i	0.299464	−	0.518688i	0.976014	+	0.217710i	$0.0698587\pi$
$720$			27.0370i			1.00761i
$721$	−22.3189	−	12.8858i	−0.831199	−	0.479893i
$722$	−29.9461	−	17.2894i	−1.11448	−	0.643444i
$723$		−	73.2966i		−	2.72593i
$724$	17.9416	−	31.0758i	0.666796	−	1.15492i
$725$	4.72756	+	8.18837i	0.175577	+	0.304108i
$726$	60.2156	−	34.7655i	2.23481	−	1.29027i
$727$	−51.3754			−1.90541			−0.952704	−	0.303900i	$-0.901711\pi$
$727$	−51.3754			−1.90541			−0.952704	+	0.303900i	$0.901711\pi$
$728$	−23.0550	−	30.4406i	−0.854475	−	1.12820i
$729$	−43.0532			−1.59456
$730$	−8.03198	+	4.63726i	−0.297277	+	0.171633i
$731$	−0.203052	−	0.351697i	−0.00751016	−	0.0130080i
$732$	−25.0877	+	43.4532i	−0.927268	+	1.60608i
$733$			9.82358i			0.362842i	0.983406	+	0.181421i	$0.0580697\pi$
$733$			9.82358i			0.362842i	−0.983406	+	0.181421i	$0.941930\pi$
$734$	−44.3613	−	25.6120i	−1.63741	−	0.945357i
$735$	8.25055	+	4.76346i	0.304326	+	0.175703i
$736$			9.16560i			0.337848i
$737$	−4.32824	+	7.49673i	−0.159433	+	0.276146i
$738$	1.66867	+	2.89022i	0.0614246	+	0.106390i
$739$	42.5082	−	24.5421i	1.56369	−	0.902797i	0.566811	−	0.823848i	$-0.308177\pi$
$739$	42.5082	−	24.5421i	1.56369	−	0.902797i	0.996879	−	0.0789487i	$-0.0251563\pi$
$740$	3.20216			0.117714
$741$	53.8339	+	22.6967i	1.97764	+	0.833783i
$742$	−33.2386			−1.22023
$743$	−35.3663	+	20.4188i	−1.29746	+	0.749091i	−0.979966	−	0.199167i	$-0.936176\pi$
$743$	−35.3663	+	20.4188i	−1.29746	+	0.749091i	−0.317499	+	0.948259i	$0.602843\pi$
$744$	−11.5035	−	19.9247i	−0.421739	−	0.730473i
$745$	−6.68388	+	11.5768i	−0.244878	+	0.424142i
$746$			44.4346i			1.62687i
$747$	22.1208	+	12.7715i	0.809358	+	0.467283i
$748$	−2.49503	−	1.44050i	−0.0912272	−	0.0526700i
$749$		−	14.0276i		−	0.512557i
$750$	−3.52720	+	6.10929i	−0.128795	+	0.223080i
$751$	−1.36340	−	2.36148i	−0.0497512	−	0.0861716i	0.840077	−	0.542467i	$-0.182510\pi$
$751$	−1.36340	−	2.36148i	−0.0497512	−	0.0861716i	−0.889829	+	0.456295i	$0.849176\pi$
$752$	−44.3154	+	25.5855i	−1.61601	+	0.933006i
$753$	21.5175			0.784142
$754$	67.8184	−	51.3641i	2.46980	−	1.87057i
$755$	−18.2984			−0.665946
$756$	39.2590	−	22.6662i	1.42784	−	0.824362i
$757$	−7.40301	−	12.8224i	−0.269067	−	0.466038i	0.699554	−	0.714580i	$-0.253382\pi$
$757$	−7.40301	−	12.8224i	−0.269067	−	0.466038i	−0.968621	+	0.248542i	$0.920049\pi$
$758$	2.55234	−	4.42078i	0.0927051	−	0.160570i
$759$			11.5413i			0.418924i
$760$	−27.5949	−	15.9319i	−1.00097	−	0.577911i
$761$	9.84575	+	5.68445i	0.356908	+	0.206061i	0.667724	−	0.744409i	$-0.267269\pi$
$761$	9.84575	+	5.68445i	0.356908	+	0.206061i	−0.310815	+	0.950470i	$0.600602\pi$
$762$		−	10.5075i		−	0.380647i
$763$	−9.59843	+	16.6250i	−0.347486	+	0.601864i
$764$	−11.5055	−	19.9281i	−0.416255	−	0.720975i
$765$	−2.75447	+	1.59030i	−0.0995882	+	0.0574972i
$766$	19.7275			0.712784
$767$	−2.12991	+	1.61314i	−0.0769065	+	0.0582472i
$768$	91.7512			3.31078
$769$	18.2352	−	10.5281i	0.657579	−	0.379654i	−0.133775	−	0.991012i	$-0.542710\pi$
$769$	18.2352	−	10.5281i	0.657579	−	0.379654i	0.791354	+	0.611358i	$0.209377\pi$
$770$	2.54219	+	4.40320i	0.0916142	+	0.158680i
$771$	−0.474602	+	0.822034i	−0.0170924	+	0.0296048i
$772$		−	51.3970i		−	1.84982i
$773$	12.1961	+	7.04144i	0.438664	+	0.253263i	0.703031	−	0.711159i	$-0.251830\pi$
$773$	12.1961	+	7.04144i	0.438664	+	0.253263i	−0.264367	+	0.964422i	$0.585163\pi$
$774$	−6.87381	−	3.96859i	−0.247074	−	0.142648i
$775$		−	1.46410i		−	0.0525921i
$776$	11.7336	−	20.3231i	0.421210	−	0.729558i
$777$	−2.03971	−	3.53288i	−0.0731741	−	0.126741i
$778$	−19.9081	+	11.4940i	−0.713740	+	0.412078i
$779$	−1.53590			−0.0550293
$780$	39.7041	+	16.7395i	1.42164	+	0.599370i
$781$	10.4425			0.373660
$782$	−5.25809	+	3.03576i	−0.188029	+	0.108558i
$783$	26.6080	+	46.0864i	0.950893	+	1.64699i
$784$	−9.12832	+	15.8107i	−0.326011	+	0.564668i
$785$			2.42229i			0.0864552i
$786$	−25.2116	−	14.5559i	−0.899267	−	0.519192i
$787$	−28.5998	−	16.5121i	−1.01947	−	0.588593i	−0.105522	−	0.994417i	$-0.533651\pi$
$787$	−28.5998	−	16.5121i	−1.01947	−	0.588593i	−0.913951	+	0.405823i	$0.866985\pi$
$788$		−	18.5095i		−	0.659374i
$789$	−7.59839	+	13.1608i	−0.270510	+	0.468537i
$790$	11.6283	+	20.1408i	0.413716	+	0.716576i
$791$	−11.0350	+	6.37109i	−0.392361	+	0.226530i
$792$	−29.6697			−1.05427
$793$	9.13974	+	12.0676i	0.324562	+	0.428534i
$794$	−15.8574			−0.562758
$795$	17.1148	−	9.88124i	0.606999	−	0.350451i
$796$	−44.0454	−	76.2890i	−1.56115	−	2.70399i
$797$	−8.47079	+	14.6718i	−0.300051	+	0.519703i	−0.976147	−	0.217110i	$-0.930337\pi$
$797$	−8.47079	+	14.6718i	−0.300051	+	0.519703i	0.676096	+	0.736813i	$0.263670\pi$
$798$			77.0395i			2.72717i
$799$	−5.21319	−	3.00984i	−0.184429	−	0.106480i
$800$	−2.07908	−	1.20036i	−0.0735067	−	0.0424391i
$801$		−	62.7787i		−	2.21817i
$802$	−5.20213	+	9.01036i	−0.183694	+	0.318167i
$803$	−1.98719	−	3.44191i	−0.0701263	−	0.121462i
$804$	−83.7774	+	48.3689i	−2.95460	+	1.70584i
$805$	7.27382			0.256369
$806$	−13.0714	+	1.63726i	−0.460420	+	0.0576701i
$807$	3.70425			0.130396
$808$	73.4039	−	42.3798i	2.58234	−	1.49092i
$809$	25.8818	+	44.8285i	0.909954	+	1.57609i	0.814125	+	0.580689i	$0.197217\pi$
$809$	25.8818	+	44.8285i	0.909954	+	1.57609i	0.0958292	+	0.995398i	$0.469450\pi$
$810$	−1.16938	+	2.02543i	−0.0410878	+	0.0711662i
$811$		−	22.6699i		−	0.796047i	−0.917375	−	0.398023i	$-0.869696\pi$
$811$		−	22.6699i		−	0.796047i	0.917375	−	0.398023i	$-0.130304\pi$
$812$	65.9524	+	38.0776i	2.31448	+	1.33626i
$813$	−28.5091	−	16.4597i	−0.999856	−	0.577267i
$814$			2.02138i			0.0708494i
$815$	7.99144	−	13.8416i	0.279928	−	0.484849i
$816$	−4.87932	−	8.45123i	−0.170810	−	0.295852i
$817$	3.16344	−	1.82641i	0.110675	−	0.0638981i
$818$	−25.3745			−0.887198
$819$	−4.26109	−	34.0192i	−0.148895	−	1.18873i
$820$	−1.13277			−0.0395581
$821$	−24.8230	+	14.3315i	−0.866328	+	0.500174i	−0.866126	−	0.499826i	$-0.833397\pi$
$821$	−24.8230	+	14.3315i	−0.866328	+	0.500174i	−0.000201482		1.00000i	$0.500064\pi$
$822$	−70.9307	−	122.856i	−2.47399	−	4.28508i
$823$	−12.9164	+	22.3718i	−0.450236	+	0.779831i	−0.998400	−	0.0565391i	$-0.981993\pi$
$823$	−12.9164	+	22.3718i	−0.450236	+	0.779831i	0.548165	+	0.836371i	$0.315327\pi$
$824$			75.1946i			2.61953i
$825$	−2.61799	−	1.51150i	−0.0911466	−	0.0526235i
$826$	−3.05121	−	1.76162i	−0.106165	−	0.0612945i
$827$		−	16.0820i		−	0.559227i	−0.960113	−	0.279613i	$-0.909794\pi$
$827$		−	16.0820i		−	0.559227i	0.960113	−	0.279613i	$-0.0902063\pi$
$828$	−40.2780	+	69.7635i	−1.39976	+	2.42445i
$829$	−11.2909	−	19.5564i	−0.392149	−	0.679222i	0.600584	−	0.799562i	$-0.294935\pi$
$829$	−11.2909	−	19.5564i	−0.392149	−	0.679222i	−0.992733	+	0.120340i	$0.961602\pi$
$830$	−11.0604	+	6.38573i	−0.383912	+	0.221652i
$831$	−57.4304			−1.99224
$832$	6.78404	−	16.0910i	0.235194	−	0.557854i
$833$	−2.14768			−0.0744128
$834$	127.228	−	73.4549i	4.40553	−	2.54354i
$835$	−7.19658	−	12.4648i	−0.249048	−	0.431364i
$836$	12.9570	−	22.4422i	0.448128	−	0.776181i
$837$		−	8.24037i		−	0.284829i
$838$	61.7898	+	35.6744i	2.13449	+	1.23235i
$839$	15.4533	+	8.92198i	0.533508	+	0.308021i	0.742444	−	0.669908i	$-0.233667\pi$
$839$	15.4533	+	8.92198i	0.533508	+	0.308021i	−0.208936	+	0.977929i	$0.567000\pi$
$840$			29.9387i			1.03298i
$841$	−30.1996	+	52.3073i	−1.04137	+	1.80370i
$842$	2.51793	+	4.36118i	0.0867736	+	0.150296i
$843$	29.0698	−	16.7835i	1.00122	−	0.578053i
$844$	45.0390			1.55031
$845$	9.30735	−	9.07597i	0.320183	−	0.312223i
$846$	−117.653			−4.04498
$847$	16.2627	−	9.38927i	0.558793	−	0.322619i
$848$	18.9356	+	32.7975i	0.650252	+	1.12627i
$849$	32.0169	−	55.4550i	1.09882	−	1.90321i
$850$		−	1.59030i		−	0.0545467i
$851$	2.50440	+	1.44591i	0.0858497	+	0.0495653i
$852$	101.062	+	58.3482i	3.46233	+	1.99898i
$853$			19.7936i			0.677720i	0.940837	+	0.338860i	$0.110041\pi$
$853$			19.7936i			0.677720i	−0.940837	+	0.338860i	$0.889959\pi$
$854$	−9.98097	+	17.2875i	−0.341542	+	0.591568i
$855$	−14.3044	−	24.7759i	−0.489199	−	0.847318i
$856$	−35.4452	+	20.4643i	−1.21149	+	0.699456i
$857$	11.7302			0.400696			0.200348	−	0.979725i	$-0.435793\pi$
$857$	11.7302			0.400696			0.200348	+	0.979725i	$0.435793\pi$
$858$	−10.5669	+	25.0634i	−0.360748	+	0.855652i
$859$	5.37452			0.183376			0.0916882	−	0.995788i	$-0.470774\pi$
$859$	5.37452			0.183376			0.0916882	+	0.995788i	$0.470774\pi$
$860$	2.33313	−	1.34703i	0.0795591	−	0.0459335i
$861$	0.721551	+	1.24976i	0.0245904	+	0.0425918i
$862$	−25.7191	+	44.5467i	−0.875995	+	1.51727i
$863$			25.3234i			0.862017i	0.902348	+	0.431008i	$0.141842\pi$
$863$			25.3234i			0.862017i	−0.902348	+	0.431008i	$0.858158\pi$
$864$	−11.7017	−	6.75596i	−0.398099	−	0.229842i
$865$	−21.0868	−	12.1745i	−0.716973	−	0.413944i
$866$			73.4567i			2.49616i
$867$	−23.4541	+	40.6237i	−0.796544	+	1.37965i
$868$	−5.89623	−	10.2126i	−0.200131	−	0.346637i
$869$	−8.63084	+	4.98302i	−0.292781	+	0.169037i
$870$	−66.7001			−2.26135
$871$	3.62739	+	28.9599i	0.122909	+	0.981268i
$872$	56.0112			1.89678
$873$	18.2470	−	10.5349i	0.617567	−	0.356553i
$874$	−27.3060	−	47.2954i	−0.923640	−	1.59979i
$875$	−0.952606	+	1.64996i	−0.0322040	+	0.0557789i
$876$		−	44.4144i		−	1.50062i
$877$	17.9194	+	10.3458i	0.605095	+	0.349352i	0.771043	−	0.636783i	$-0.219735\pi$
$877$	17.9194	+	10.3458i	0.605095	+	0.349352i	−0.165949	+	0.986134i	$0.553069\pi$
$878$	−36.6363	−	21.1520i	−1.23642	−	0.713845i
$879$		−	52.6151i		−	1.77466i
$880$	2.89651	−	5.01691i	0.0976414	−	0.169120i
$881$	24.1997	+	41.9150i	0.815307	+	1.41215i	0.909107	+	0.416562i	$0.136765\pi$
$881$	24.1997	+	41.9150i	0.815307	+	1.41215i	−0.0937999	+	0.995591i	$0.529901\pi$
$882$	−36.3521	+	20.9879i	−1.22404	+	0.706699i
$883$	−45.8550			−1.54314			−0.771572	−	0.636142i	$-0.780529\pi$
$883$	−45.8550			−1.54314			−0.771572	+	0.636142i	$0.780529\pi$
$884$	−9.63829	+	1.20725i	−0.324171	+	0.0406042i
$885$	2.09479			0.0704155
$886$	52.1705	−	30.1207i	1.75270	−	1.01192i
$887$	0.541169	+	0.937332i	0.0181707	+	0.0314725i	0.874968	−	0.484181i	$-0.160882\pi$
$887$	0.541169	+	0.937332i	0.0181707	+	0.0314725i	−0.856797	+	0.515654i	$0.827549\pi$
$888$	−5.95131	+	10.3080i	−0.199713	+	0.345913i
$889$		−	2.83781i		−	0.0951772i
$890$	27.1840	+	15.6947i	0.911208	+	0.526086i
$891$	−0.867947	−	0.501109i	−0.0290773	−	0.0167878i
$892$			90.2133i			3.02056i
$893$	27.0729	−	46.8916i	0.905959	−	1.56917i
$894$	−47.1507	−	81.6675i	−1.57696	−	2.73137i
$895$	−3.28075	+	1.89414i	−0.109663	+	0.0633142i
$896$	32.1749			1.07489
$897$	23.4938	+	31.0200i	0.784436	+	1.03573i
$898$	−52.0637			−1.73739
$899$	11.9886	−	6.92163i	0.399842	−	0.230849i
$900$	−10.5499	−	18.2730i	−0.351663	−	0.609099i
$901$	−2.22756	+	3.85824i	−0.0742107	+	0.128537i
$902$		−	0.715068i		−	0.0238092i
$903$	−2.97231	−	1.71606i	−0.0989122	−	0.0571070i
$904$	32.1973	+	18.5891i	1.07086	+	0.618264i
$905$			8.48794i			0.282149i
$906$	64.5420	−	111.790i	2.14426	−	3.71397i
$907$	−22.7653	−	39.4307i	−0.755910	−	1.30928i	−0.944920	−	0.327300i	$-0.893861\pi$
$907$	−22.7653	−	39.4307i	−0.755910	−	1.30928i	0.189010	−	0.981975i	$-0.439472\pi$
$908$	57.4279	−	33.1560i	1.90581	−	1.10032i
$909$	76.1009			2.52411
$910$	15.7960	+	6.65968i	0.523632	+	0.220766i
$911$	39.7417			1.31670			0.658350	−	0.752712i	$-0.271255\pi$
$911$	39.7417			1.31670			0.658350	+	0.752712i	$0.271255\pi$
$912$	76.0171	−	43.8885i	2.51718	−	1.45329i
$913$	−2.73645	−	4.73967i	−0.0905632	−	0.156860i
$914$	−38.1387	+	66.0582i	−1.26152	+	2.18501i
$915$		−	11.8687i		−	0.392365i
$916$	−27.9012	−	16.1088i	−0.921883	−	0.532250i
$917$	−6.80900	−	3.93118i	−0.224853	−	0.129819i
$918$		−	8.95062i		−	0.295415i
$919$	−23.4969	+	40.6978i	−0.775091	+	1.34250i	0.159653	+	0.987173i	$0.448963\pi$
$919$	−23.4969	+	40.6978i	−0.775091	+	1.34250i	−0.934743	+	0.355323i	$0.884371\pi$
$920$	−10.6115	−	18.3797i	−0.349851	−	0.605960i
$921$	−7.70608	+	4.44911i	−0.253924	+	0.146603i
$922$	−11.6745			−0.384481
$923$	28.0665	−	21.2569i	0.923821	−	0.699680i
$924$	−24.3484			−0.801002
$925$	−0.655970	+	0.378725i	−0.0215682	+	0.0124524i
$926$	17.4700	+	30.2589i	0.574099	+	0.994369i
$927$	−33.7565	+	58.4680i	−1.10871	+	1.92034i
$928$		−	22.6991i		−	0.745134i
$929$	−13.1821	−	7.61066i	−0.432489	−	0.249698i	0.267917	−	0.963442i	$-0.413665\pi$
$929$	−13.1821	−	7.61066i	−0.432489	−	0.249698i	−0.700406	+	0.713744i	$0.746998\pi$
$930$	8.94462	+	5.16418i	0.293306	+	0.169340i
$931$		−	19.3180i		−	0.633121i
$932$	40.2780	−	69.7635i	1.31935	−	2.28518i
$933$	4.49551	+	7.78645i	0.147176	+	0.254917i
$934$	−15.0959	+	8.71564i	−0.493954	+	0.285184i
$935$	0.681482			0.0222869
$936$	−79.7441	+	60.3963i	−2.60652	+	1.97412i
$937$	6.07285			0.198392			0.0991958	−	0.995068i	$-0.468373\pi$
$937$	6.07285			0.198392			0.0991958	+	0.995068i	$0.468373\pi$
$938$	−33.3302	+	19.2432i	−1.08827	+	0.628313i
$939$	49.9691	+	86.5490i	1.63068	+	2.82442i
$940$	19.9670	−	34.5839i	0.651253	−	1.12800i
$941$			0.0496576i			0.00161879i	1.00000		0.000809396i	$0.000257639\pi$
$941$			0.0496576i			0.00161879i	−1.00000		0.000809396i	$0.999742\pi$
$942$	−14.7985	−	8.54390i	−0.482160	−	0.278375i
$943$	−0.885936	−	0.511495i	−0.0288500	−	0.0166566i
$944$			4.01429i			0.130654i
$945$	−5.36153	+	9.28645i	−0.174411	+	0.302088i
$946$	0.850322	+	1.47280i	0.0276464	+	0.0478849i
$947$	−16.1584	+	9.32907i	−0.525078	+	0.303154i	−0.739010	−	0.673695i	$-0.764706\pi$
$947$	−16.1584	+	9.32907i	−0.525078	+	0.303154i	0.213932	+	0.976849i	$0.431373\pi$
$948$	−111.372			−3.61720
$949$	−12.3475	−	5.20576i	−0.400816	−	0.168986i
$950$	14.3044			0.464095
$951$	−33.3818	+	19.2730i	−1.08248	+	0.624969i
$952$	−3.37458	−	5.84495i	−0.109371	−	0.189436i
$953$	−0.764764	+	1.32461i	−0.0247731	+	0.0429083i	−0.878146	−	0.478392i	$-0.841220\pi$
$953$	−0.764764	+	1.32461i	−0.0247731	+	0.0429083i	0.853373	+	0.521301i	$0.174553\pi$
$954$			87.0739i			2.81912i
$955$	4.71386	+	2.72155i	0.152537	+	0.0880673i
$956$	−46.6927	−	26.9581i	−1.51015	−	0.871886i
$957$		−	28.5827i		−	0.923948i
$958$	20.3244	−	35.2028i	0.656650	−	1.13735i
$959$	−19.1566	−	33.1802i	−0.618598	−	1.07144i
$960$	−11.8568	+	6.84555i	−0.382678	+	0.220939i
$961$	28.8564			0.930852
$962$	4.11477	+	5.43293i	0.132666	+	0.175165i
$963$	−36.7475			−1.18417
$964$	−94.9299	+	54.8078i	−3.05749	+	1.76524i
$965$	6.07880	+	10.5288i	0.195683	+	0.338934i
$966$	−25.6562	+	44.4379i	−0.825475	+	1.42976i
$967$		−	32.1716i		−	1.03457i	−0.855813	−	0.517285i	$-0.826943\pi$
$967$		−	32.1716i		−	1.03457i	0.855813	−	0.517285i	$-0.173057\pi$
$968$	−47.4501	−	27.3953i	−1.52510	−	0.880519i
$969$	8.94253	+	5.16297i	0.287276	+	0.165859i
$970$			10.5349i			0.338256i
$971$	8.62705	−	14.9425i	0.276855	−	0.479527i	−0.693746	−	0.720219i	$-0.744041\pi$
$971$	8.62705	−	14.9425i	0.276855	−	0.479527i	0.970601	+	0.240692i	$0.0773745\pi$
$972$	30.0908	+	52.1188i	0.965164	+	1.67171i
$973$	34.3609	−	19.8383i	1.10156	−	0.635986i
$974$	−50.0122			−1.60249
$975$	−10.1133	+	1.26675i	−0.323884	+	0.0405683i
$976$	22.7442			0.728023
$977$	−13.6164	+	7.86142i	−0.435626	+	0.251509i	−0.701741	−	0.712432i	$-0.747593\pi$
$977$	−13.6164	+	7.86142i	−0.435626	+	0.251509i	0.266114	+	0.963942i	$0.414260\pi$
$978$	56.3748	+	97.6440i	1.80267	+	3.12231i
$979$	−6.72557	+	11.6490i	−0.214950	+	0.372304i
$980$		−	14.2476i		−	0.455122i
$981$	43.5518	+	25.1447i	1.39050	+	0.802807i
$982$	34.1429	+	19.7124i	1.08954	+	0.629049i
$983$			38.5356i			1.22910i	0.788880	+	0.614548i	$0.210662\pi$
$983$			38.5356i			1.22910i	−0.788880	+	0.614548i	$0.789338\pi$
$984$	2.10529	−	3.64647i	0.0671141	−	0.116245i
$985$	2.18915	+	3.79172i	0.0697521	+	0.120814i
$986$	13.0219	−	7.51821i	0.414703	−	0.239429i
$987$	−50.8743			−1.61935
$988$	−10.8590	−	86.6944i	−0.345469	−	2.75812i
$989$	2.43298			0.0773642
$990$	11.5349	−	6.65968i	0.366604	−	0.211659i
$991$	−4.29571	−	7.44040i	−0.136458	−	0.236352i	0.789696	−	0.613499i	$-0.210238\pi$
$991$	−4.29571	−	7.44040i	−0.136458	−	0.236352i	−0.926153	+	0.377147i	$0.876905\pi$
$992$	−1.75745	+	3.04399i	−0.0557991	+	0.0966468i
$993$		−	81.4014i		−	2.58320i
$994$	40.2068	+	23.2134i	1.27528	+	0.736285i
$995$	18.0456	+	10.4186i	0.572085	+	0.330293i
$996$		−	61.1606i		−	1.93795i
$997$	10.2687	−	17.7859i	0.325213	−	0.563285i	−0.656343	−	0.754463i	$-0.727897\pi$
$997$	10.2687	−	17.7859i	0.325213	−	0.563285i	0.981555	+	0.191178i	$0.0612308\pi$
$998$	1.55534	+	2.69393i	0.0492335	+	0.0852750i
$999$	−3.69198	+	2.13157i	−0.116809	+	0.0674398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.m.a.36.1	✓	8
3.2	odd	2		585.2.bu.c.361.4		8
4.3	odd	2		1040.2.da.b.881.1		8
5.2	odd	4		325.2.m.b.49.1		8
5.3	odd	4		325.2.m.c.49.4		8
5.4	even	2		325.2.n.d.101.4		8
13.2	odd	12		845.2.a.l.1.1		4
13.3	even	3		845.2.c.g.506.1		8
13.4	even	6	inner	65.2.m.a.56.1	yes	8
13.5	odd	4		845.2.e.n.146.4		8
13.6	odd	12		845.2.e.n.191.4		8
13.7	odd	12		845.2.e.m.191.1		8
13.8	odd	4		845.2.e.m.146.1		8
13.9	even	3		845.2.m.g.316.4		8
13.10	even	6		845.2.c.g.506.8		8
13.11	odd	12		845.2.a.m.1.4		4
13.12	even	2		845.2.m.g.361.4		8
39.2	even	12		7605.2.a.cj.1.4		4
39.11	even	12		7605.2.a.cf.1.1		4
39.17	odd	6		585.2.bu.c.316.4		8
52.43	odd	6		1040.2.da.b.641.1		8
65.4	even	6		325.2.n.d.251.4		8
65.17	odd	12		325.2.m.c.199.4		8
65.24	odd	12		4225.2.a.bi.1.1		4
65.43	odd	12		325.2.m.b.199.1		8
65.54	odd	12		4225.2.a.bl.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.1	✓	8	1.1	even	1	trivial
65.2.m.a.56.1	yes	8	13.4	even	6	inner
325.2.m.b.49.1		8	5.2	odd	4
325.2.m.b.199.1		8	65.43	odd	12
325.2.m.c.49.4		8	5.3	odd	4
325.2.m.c.199.4		8	65.17	odd	12
325.2.n.d.101.4		8	5.4	even	2
325.2.n.d.251.4		8	65.4	even	6
585.2.bu.c.316.4		8	39.17	odd	6
585.2.bu.c.361.4		8	3.2	odd	2
845.2.a.l.1.1		4	13.2	odd	12
845.2.a.m.1.4		4	13.11	odd	12
845.2.c.g.506.1		8	13.3	even	3
845.2.c.g.506.8		8	13.10	even	6
845.2.e.m.146.1		8	13.8	odd	4
845.2.e.m.191.1		8	13.7	odd	12
845.2.e.n.146.4		8	13.5	odd	4
845.2.e.n.191.4		8	13.6	odd	12
845.2.m.g.316.4		8	13.9	even	3
845.2.m.g.361.4		8	13.12	even	2
1040.2.da.b.641.1		8	52.43	odd	6
1040.2.da.b.881.1		8	4.3	odd	2
4225.2.a.bi.1.1		4	65.24	odd	12
4225.2.a.bl.1.4		4	65.54	odd	12
7605.2.a.cf.1.1		4	39.11	even	12
7605.2.a.cj.1.4		4	39.2	even	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16117 + 1.24775i) q^{2} +(1.41342 + 2.44811i) q^{3} +(2.11378 - 3.66117i) q^{4} +1.00000i q^{5} +(-6.10929 - 3.52720i) q^{6} +(-1.64996 - 0.952606i) q^{7} +5.55889i q^{8} +(-2.49551 + 4.32235i) q^{9} +O(q^{10})\)	\(q+(-2.16117 + 1.24775i) q^{2} +(1.41342 + 2.44811i) q^{3} +(2.11378 - 3.66117i) q^{4} +1.00000i q^{5} +(-6.10929 - 3.52720i) q^{6} +(-1.64996 - 0.952606i) q^{7} +5.55889i q^{8} +(-2.49551 + 4.32235i) q^{9} +(-1.24775 - 2.16117i) q^{10} +(0.926118 - 0.534695i) q^{11} +11.9506 q^{12} +(1.40072 - 3.32235i) q^{13} +4.75447 q^{14} +(-2.44811 + 1.41342i) q^{15} +(-2.70857 - 4.69138i) q^{16} +(0.318632 - 0.551886i) q^{17} -12.4551i q^{18} +(4.96410 + 2.86603i) q^{19} +(3.66117 + 2.11378i) q^{20} -5.38573i q^{21} +(-1.33433 + 2.31114i) q^{22} +(1.90893 + 3.30636i) q^{23} +(-13.6088 + 7.85704i) q^{24} -1.00000 q^{25} +(1.11827 + 8.92792i) q^{26} -5.62828 q^{27} +(-6.97531 + 4.02720i) q^{28} +(-4.72756 - 8.18837i) q^{29} +(3.52720 - 6.10929i) q^{30} +1.46410i q^{31} +(2.07908 + 1.20036i) q^{32} +(2.61799 + 1.51150i) q^{33} +1.59030i q^{34} +(0.952606 - 1.64996i) q^{35} +(10.5499 + 18.2730i) q^{36} +(0.655970 - 0.378725i) q^{37} -14.3044 q^{38} +(10.1133 - 1.26675i) q^{39} -5.55889 q^{40} +(-0.232051 + 0.133975i) q^{41} +(6.72006 + 11.6395i) q^{42} +(0.318632 - 0.551886i) q^{43} -4.52091i q^{44} +(-4.32235 - 2.49551i) q^{45} +(-8.25104 - 4.76374i) q^{46} -9.44613i q^{47} +(7.65668 - 13.2618i) q^{48} +(-1.68508 - 2.91865i) q^{49} +(2.16117 - 1.24775i) q^{50} +1.80144 q^{51} +(-9.20287 - 12.1510i) q^{52} -6.99102 q^{53} +(12.1637 - 7.02271i) q^{54} +(0.534695 + 0.926118i) q^{55} +(5.29543 - 9.17196i) q^{56} +16.2036i q^{57} +(20.4341 + 11.7977i) q^{58} +(-0.641756 - 0.370518i) q^{59} +11.9506i q^{60} +(-2.09928 + 3.63606i) q^{61} +(-1.82684 - 3.16418i) q^{62} +(8.23499 - 4.75447i) q^{63} +4.84325 q^{64} +(3.32235 + 1.40072i) q^{65} -7.54390 q^{66} +(-7.01029 + 4.04739i) q^{67} +(-1.34703 - 2.33313i) q^{68} +(-5.39623 + 9.34654i) q^{69} +4.75447i q^{70} +(8.45663 + 4.88244i) q^{71} +(-24.0274 - 13.8723i) q^{72} -3.71649i q^{73} +(-0.945110 + 1.63698i) q^{74} +(-1.41342 - 2.44811i) q^{75} +(20.9860 - 12.1163i) q^{76} -2.03741 q^{77} +(-20.2760 + 15.3565i) q^{78} -9.31937 q^{79} +(4.69138 - 2.70857i) q^{80} +(-0.468594 - 0.811629i) q^{81} +(0.334335 - 0.579085i) q^{82} -5.11778i q^{83} +(-19.7181 - 11.3842i) q^{84} +(0.551886 + 0.318632i) q^{85} +1.59030i q^{86} +(13.3640 - 23.1472i) q^{87} +(2.97231 + 5.14819i) q^{88} +(-10.8932 + 6.28917i) q^{89} +12.4551 q^{90} +(-5.47602 + 4.14741i) q^{91} +16.1402 q^{92} +(-3.58429 + 2.06939i) q^{93} +(11.7864 + 20.4147i) q^{94} +(-2.86603 + 4.96410i) q^{95} +6.78645i q^{96} +(-3.65597 - 2.11078i) q^{97} +(7.28351 + 4.20514i) q^{98} +5.33734i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 2 q^{4} - 18 q^{6} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 2 * q^4 - 18 * q^6 - 6 * q^7 - 4 * q^9	\( 8 q + 2 q^{3} + 2 q^{4} - 18 q^{6} - 6 q^{7} - 4 q^{9} - 2 q^{10} + 20 q^{12} + 4 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + 12 q^{19} + 12 q^{20} - 12 q^{22} - 10 q^{23} - 12 q^{24} - 8 q^{25} + 10 q^{26} - 4 q^{27} - 18 q^{28} - 8 q^{29} + 4 q^{30} + 6 q^{32} + 42 q^{33} + 10 q^{35} + 20 q^{36} + 6 q^{37} - 16 q^{38} - 12 q^{40} + 12 q^{41} + 4 q^{42} - 2 q^{43} - 42 q^{46} + 28 q^{48} + 12 q^{49} - 8 q^{51} - 6 q^{52} - 24 q^{53} + 18 q^{54} + 12 q^{56} + 36 q^{58} - 12 q^{59} - 28 q^{61} + 4 q^{62} - 24 q^{63} - 8 q^{64} - 8 q^{65} + 12 q^{66} + 6 q^{67} - 14 q^{68} - 16 q^{69} - 48 q^{72} + 10 q^{74} - 2 q^{75} + 54 q^{76} - 36 q^{77} - 56 q^{78} - 16 q^{79} + 8 q^{81} + 4 q^{82} - 30 q^{84} + 18 q^{85} + 22 q^{87} - 18 q^{88} + 24 q^{89} + 40 q^{90} + 28 q^{91} + 44 q^{92} + 32 q^{94} - 16 q^{95} - 30 q^{97} + 72 q^{98}+O(q^{100}) \) 8 * q + 2 * q^3 + 2 * q^4 - 18 * q^6 - 6 * q^7 - 4 * q^9 - 2 * q^10 + 20 * q^12 + 4 * q^14 - 6 * q^15 - 2 * q^16 - 2 * q^17 + 12 * q^19 + 12 * q^20 - 12 * q^22 - 10 * q^23 - 12 * q^24 - 8 * q^25 + 10 * q^26 - 4 * q^27 - 18 * q^28 - 8 * q^29 + 4 * q^30 + 6 * q^32 + 42 * q^33 + 10 * q^35 + 20 * q^36 + 6 * q^37 - 16 * q^38 - 12 * q^40 + 12 * q^41 + 4 * q^42 - 2 * q^43 - 42 * q^46 + 28 * q^48 + 12 * q^49 - 8 * q^51 - 6 * q^52 - 24 * q^53 + 18 * q^54 + 12 * q^56 + 36 * q^58 - 12 * q^59 - 28 * q^61 + 4 * q^62 - 24 * q^63 - 8 * q^64 - 8 * q^65 + 12 * q^66 + 6 * q^67 - 14 * q^68 - 16 * q^69 - 48 * q^72 + 10 * q^74 - 2 * q^75 + 54 * q^76 - 36 * q^77 - 56 * q^78 - 16 * q^79 + 8 * q^81 + 4 * q^82 - 30 * q^84 + 18 * q^85 + 22 * q^87 - 18 * q^88 + 24 * q^89 + 40 * q^90 + 28 * q^91 + 44 * q^92 + 32 * q^94 - 16 * q^95 - 30 * q^97 + 72 * q^98

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