LMFDB - Embedded newform 847.2.e.d.606.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(485,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("847.485");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			606.1
Root			$0.356769 - 0.617942i$ of defining polynomial
Character	$\chi$	$=$	847.606
Dual form			847.2.e.d.485.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24543 - 2.15715i) q^{2} +(0.356769 - 0.617942i) q^{3} +(-2.10220 + 3.64112i) q^{4} +(-1.10220 - 1.90907i) q^{5} -1.77733 q^{6} +(1.10220 + 2.40523i) q^{7} +5.49086 q^{8} +(1.24543 + 2.15715i) q^{9} +O(q^{10})$	\(q+(-1.24543 - 2.15715i) q^{2} +(0.356769 - 0.617942i) q^{3} +(-2.10220 + 3.64112i) q^{4} +(-1.10220 - 1.90907i) q^{5} -1.77733 q^{6} +(1.10220 + 2.40523i) q^{7} +5.49086 q^{8} +(1.24543 + 2.15715i) q^{9} +(-2.74543 + 4.75523i) q^{10} +(1.50000 + 2.59808i) q^{12} +3.28646 q^{13} +(3.81574 - 5.37317i) q^{14} -1.57292 q^{15} +(-2.63409 - 4.56239i) q^{16} +(0.745432 - 1.29113i) q^{17} +(3.10220 - 5.37317i) q^{18} +(-3.45897 - 5.99111i) q^{19} +9.26819 q^{20} +(1.87953 + 0.177017i) q^{21} +(-3.24543 - 5.62125i) q^{23} +(1.95897 - 3.39304i) q^{24} +(0.0703069 - 0.121775i) q^{25} +(-4.09306 - 7.08940i) q^{26} +3.91794 q^{27} +(-11.0748 - 1.04304i) q^{28} +1.64975 q^{29} +(1.95897 + 3.39304i) q^{30} +(1.17512 - 2.03538i) q^{31} +(-1.07031 + 1.85383i) q^{32} -3.71354 q^{34} +(3.37691 - 4.75523i) q^{35} -10.4726 q^{36} +(2.77733 + 4.81047i) q^{37} +(-8.61582 + 14.9230i) q^{38} +(1.17251 - 2.03084i) q^{39} +(-6.05203 - 10.4824i) q^{40} +11.2499 q^{41} +(-1.95897 - 4.27489i) q^{42} -5.26819 q^{43} +(2.74543 - 4.75523i) q^{45} +(-8.08393 + 14.0018i) q^{46} +(-0.745432 - 1.29113i) q^{47} -3.75905 q^{48} +(-4.57031 + 5.30210i) q^{49} -0.350250 q^{50} +(-0.531894 - 0.921267i) q^{51} +(-6.90880 + 11.9664i) q^{52} +(-0.152367 + 0.263908i) q^{53} +(-4.87953 - 8.45159i) q^{54} +(6.05203 + 13.2068i) q^{56} -4.93621 q^{57} +(-2.05465 - 3.55876i) q^{58} +(6.32936 - 10.9628i) q^{59} +(3.30660 - 5.72720i) q^{60} +(-6.49086 - 11.2425i) q^{61} -5.85415 q^{62} +(-3.81574 + 5.37317i) q^{63} -5.20440 q^{64} +(-3.62234 - 6.27408i) q^{65} +(2.28646 - 3.96027i) q^{67} +(3.13409 + 5.42841i) q^{68} -4.63148 q^{69} +(-14.4635 - 1.36219i) q^{70} +11.3267 q^{71} +(6.83850 + 11.8446i) q^{72} +(-4.28384 + 7.41984i) q^{73} +(6.91794 - 11.9822i) q^{74} +(-0.0501666 - 0.0868912i) q^{75} +29.0858 q^{76} -5.84111 q^{78} +(2.31574 + 4.01098i) q^{79} +(-5.80660 + 10.0573i) q^{80} +(-2.33850 + 4.05039i) q^{81} +(-14.0110 - 24.2678i) q^{82} +1.93621 q^{83} +(-4.59568 + 6.47145i) q^{84} -3.28646 q^{85} +(6.56117 + 11.3643i) q^{86} +(0.588580 - 1.01945i) q^{87} +(-1.60220 - 2.77509i) q^{89} -13.6770 q^{90} +(3.62234 + 7.90471i) q^{91} +27.2902 q^{92} +(-0.838496 - 1.45232i) q^{93} +(-1.85677 + 3.21602i) q^{94} +(-7.62496 + 13.2068i) q^{95} +(0.763705 + 1.32278i) q^{96} +1.85939 q^{97} +(17.1294 + 3.25544i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} - 4 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8}+O(q^{10}) $ 6 * q + q^3 - 4 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8	$ 6 q + q^{3} - 4 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 9 q^{10} + 9 q^{12} + 22 q^{13} + 12 q^{14} - 14 q^{15} - 2 q^{16} - 3 q^{17} + 10 q^{18} - 11 q^{19} + 28 q^{20} - 10 q^{21} - 12 q^{23} + 2 q^{24} - 3 q^{25} - q^{26} + 4 q^{27} - 13 q^{28} + 18 q^{29} + 2 q^{30} + 3 q^{31} - 3 q^{32} - 20 q^{34} - 9 q^{35} - 18 q^{36} + 4 q^{37} - 8 q^{38} - 5 q^{39} - 3 q^{40} + 10 q^{41} - 2 q^{42} - 4 q^{43} + 9 q^{45} - 10 q^{46} + 3 q^{47} + 20 q^{48} - 24 q^{49} + 6 q^{50} + 2 q^{51} - 7 q^{52} - 17 q^{53} - 8 q^{54} + 3 q^{56} - 40 q^{57} + 13 q^{58} - 8 q^{59} - 6 q^{60} - 24 q^{61} - 26 q^{62} - 12 q^{63} - 14 q^{64} + 15 q^{65} + 16 q^{67} + 5 q^{68} - 6 q^{69} - 27 q^{70} + 14 q^{71} + 10 q^{72} - 20 q^{73} + 22 q^{74} - 25 q^{75} + 78 q^{76} - 12 q^{78} + 3 q^{79} - 9 q^{80} + 17 q^{81} - 41 q^{82} + 22 q^{83} - 12 q^{84} - 22 q^{85} + 21 q^{86} + 30 q^{87} - q^{89} - 20 q^{90} - 15 q^{91} + 50 q^{92} + 26 q^{93} - 10 q^{94} - 17 q^{95} + 27 q^{96} + 18 q^{97} + 24 q^{98}+O(q^{100}) $ 6 * q + q^3 - 4 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 9 * q^10 + 9 * q^12 + 22 * q^13 + 12 * q^14 - 14 * q^15 - 2 * q^16 - 3 * q^17 + 10 * q^18 - 11 * q^19 + 28 * q^20 - 10 * q^21 - 12 * q^23 + 2 * q^24 - 3 * q^25 - q^26 + 4 * q^27 - 13 * q^28 + 18 * q^29 + 2 * q^30 + 3 * q^31 - 3 * q^32 - 20 * q^34 - 9 * q^35 - 18 * q^36 + 4 * q^37 - 8 * q^38 - 5 * q^39 - 3 * q^40 + 10 * q^41 - 2 * q^42 - 4 * q^43 + 9 * q^45 - 10 * q^46 + 3 * q^47 + 20 * q^48 - 24 * q^49 + 6 * q^50 + 2 * q^51 - 7 * q^52 - 17 * q^53 - 8 * q^54 + 3 * q^56 - 40 * q^57 + 13 * q^58 - 8 * q^59 - 6 * q^60 - 24 * q^61 - 26 * q^62 - 12 * q^63 - 14 * q^64 + 15 * q^65 + 16 * q^67 + 5 * q^68 - 6 * q^69 - 27 * q^70 + 14 * q^71 + 10 * q^72 - 20 * q^73 + 22 * q^74 - 25 * q^75 + 78 * q^76 - 12 * q^78 + 3 * q^79 - 9 * q^80 + 17 * q^81 - 41 * q^82 + 22 * q^83 - 12 * q^84 - 22 * q^85 + 21 * q^86 + 30 * q^87 - q^89 - 20 * q^90 - 15 * q^91 + 50 * q^92 + 26 * q^93 - 10 * q^94 - 17 * q^95 + 27 * q^96 + 18 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.24543	−	2.15715i	−0.880653	−	1.52534i	−0.850616	−	0.525787i	$-0.823771\pi$
$2$	−1.24543	−	2.15715i	−0.880653	−	1.52534i	−0.0300373	−	0.999549i	$-0.509563\pi$
$3$	0.356769	−	0.617942i	0.205981	−	0.356769i	−0.744464	−	0.667663i	$-0.767295\pi$
$3$	0.356769	−	0.617942i	0.205981	−	0.356769i	0.950445	+	0.310894i	$0.100628\pi$
$4$	−2.10220	+	3.64112i	−1.05110	+	1.82056i
$5$	−1.10220	−	1.90907i	−0.492919	−	0.853761i	0.507048	−	0.861918i	$-0.330737\pi$
$5$	−1.10220	−	1.90907i	−0.492919	−	0.853761i	−0.999967	+	0.00815703i	$0.997404\pi$
$6$	−1.77733			−0.725590
$7$	1.10220	+	2.40523i	0.416593	+	0.909093i
$7$	1.10220	+	2.40523i	0.416593	+	0.909093i
$8$	5.49086			1.94131
$9$	1.24543	+	2.15715i	0.415144	+	0.719050i
$10$	−2.74543	+	4.75523i	−0.868182	+	1.50373i
$11$		0			0
$11$		0			0
$12$	1.50000	+	2.59808i	0.433013	+	0.750000i
$13$	3.28646			0.911501			0.455750	−	0.890108i	$-0.349371\pi$
$13$	3.28646			0.911501			0.455750	+	0.890108i	$0.349371\pi$
$14$	3.81574	−	5.37317i	1.01980	−	1.43604i
$15$	−1.57292			−0.406127
$16$	−2.63409	−	4.56239i	−0.658524	−	1.14060i
$17$	0.745432	−	1.29113i	0.180794	−	0.313144i	−0.761357	−	0.648333i	$-0.775467\pi$
$17$	0.745432	−	1.29113i	0.180794	−	0.313144i	0.942151	+	0.335189i	$0.108800\pi$
$18$	3.10220	−	5.37317i	0.731196	−	1.26647i
$19$	−3.45897	−	5.99111i	−0.793542	−	1.37446i	−0.923761	−	0.382970i	$-0.874901\pi$
$19$	−3.45897	−	5.99111i	−0.793542	−	1.37446i	0.130219	−	0.991485i	$-0.458432\pi$
$20$	9.26819			2.07243
$21$	1.87953	+	0.177017i	0.410146	+	0.0386283i
$22$		0			0
$23$	−3.24543	−	5.62125i	−0.676719	−	1.17211i	−0.975963	−	0.217936i	$-0.930068\pi$
$23$	−3.24543	−	5.62125i	−0.676719	−	1.17211i	0.299244	−	0.954177i	$-0.403266\pi$
$24$	1.95897	−	3.39304i	0.399873	−	0.692600i
$25$	0.0703069	−	0.121775i	0.0140614	−	0.0243550i
$26$	−4.09306	−	7.08940i	−0.802716	−	1.39034i
$27$	3.91794			0.754008
$28$	−11.0748	−	1.04304i	−2.09294	−	0.197116i
$29$	1.64975			0.306351			0.153175	−	0.988199i	$-0.451050\pi$
$29$	1.64975			0.306351			0.153175	+	0.988199i	$0.451050\pi$
$30$	1.95897	+	3.39304i	0.357657	+	0.619481i
$31$	1.17512	−	2.03538i	0.211059	−	0.365564i	−0.740987	−	0.671519i	$-0.765642\pi$
$31$	1.17512	−	2.03538i	0.211059	−	0.365564i	0.952046	+	0.305955i	$0.0989756\pi$
$32$	−1.07031	+	1.85383i	−0.189205	+	0.327713i
$33$		0			0
$34$	−3.71354			−0.636867
$35$	3.37691	−	4.75523i	0.570802	−	0.803780i
$36$	−10.4726			−1.74543
$37$	2.77733	+	4.81047i	0.456590	+	0.790836i	0.998778	−	0.0494206i	$-0.0157375\pi$
$37$	2.77733	+	4.81047i	0.456590	+	0.790836i	−0.542189	+	0.840257i	$0.682404\pi$
$38$	−8.61582	+	14.9230i	−1.39767	+	2.42084i
$39$	1.17251	−	2.03084i	0.187751	−	0.325195i
$40$	−6.05203	−	10.4824i	−0.956911	−	1.65742i
$41$	11.2499			1.75694			0.878471	−	0.477796i	$-0.158564\pi$
$41$	11.2499			1.75694			0.878471	+	0.477796i	$0.158564\pi$
$42$	−1.95897	−	4.27489i	−0.302276	−	0.659629i
$43$	−5.26819			−0.803391			−0.401696	−	0.915773i	$-0.631579\pi$
$43$	−5.26819			−0.803391			−0.401696	+	0.915773i	$0.631579\pi$
$44$		0			0
$45$	2.74543	−	4.75523i	0.409265	−	0.708867i
$46$	−8.08393	+	14.0018i	−1.19191	+	2.06445i
$47$	−0.745432	−	1.29113i	−0.108732	−	0.188330i	0.806525	−	0.591201i	$-0.201346\pi$
$47$	−0.745432	−	1.29113i	−0.108732	−	0.188330i	−0.915257	+	0.402871i	$0.868012\pi$
$48$	−3.75905			−0.542573
$49$	−4.57031	+	5.30210i	−0.652901	+	0.757443i
$50$	−0.350250			−0.0495328
$51$	−0.531894	−	0.921267i	−0.0744800	−	0.129003i
$52$	−6.90880	+	11.9664i	−0.958079	+	1.65944i
$53$	−0.152367	+	0.263908i	−0.0209293	+	0.0362506i	−0.876300	−	0.481765i	$-0.839996\pi$
$53$	−0.152367	+	0.263908i	−0.0209293	+	0.0362506i	0.855371	+	0.518016i	$0.173329\pi$
$54$	−4.87953	−	8.45159i	−0.664019	−	1.15012i
$55$		0			0
$56$	6.05203	+	13.2068i	0.808737	+	1.76483i
$57$	−4.93621			−0.653817
$58$	−2.05465	−	3.55876i	−0.269789	−	0.467288i
$59$	6.32936	−	10.9628i	0.824012	−	1.42723i	−0.0786592	−	0.996902i	$-0.525064\pi$
$59$	6.32936	−	10.9628i	0.824012	−	1.42723i	0.902672	−	0.430330i	$-0.141603\pi$
$60$	3.30660	−	5.72720i	0.426881	−	0.739379i
$61$	−6.49086	−	11.2425i	−0.831070	−	1.43946i	−0.897191	−	0.441644i	$-0.854396\pi$
$61$	−6.49086	−	11.2425i	−0.831070	−	1.43946i	0.0661206	−	0.997812i	$-0.478938\pi$
$62$	−5.85415			−0.743478
$63$	−3.81574	+	5.37317i	−0.480738	+	0.676956i
$64$	−5.20440			−0.650550
$65$	−3.62234	−	6.27408i	−0.449296	−	0.778204i
$66$		0			0
$67$	2.28646	−	3.96027i	0.279336	−	0.483824i	−0.691884	−	0.722009i	$-0.743219\pi$
$67$	2.28646	−	3.96027i	0.279336	−	0.483824i	0.971220	+	0.238185i	$0.0765524\pi$
$68$	3.13409	+	5.42841i	0.380065	+	0.658292i
$69$	−4.63148			−0.557564
$70$	−14.4635	−	1.36219i	−1.72871	−	0.162813i
$71$	11.3267			1.34424			0.672119	−	0.740444i	$-0.265385\pi$
$71$	11.3267			1.34424			0.672119	+	0.740444i	$0.265385\pi$
$72$	6.83850	+	11.8446i	0.805925	+	1.39590i
$73$	−4.28384	+	7.41984i	−0.501386	+	0.868426i	0.498613	+	0.866825i	$0.333843\pi$
$73$	−4.28384	+	7.41984i	−0.501386	+	0.868426i	−0.999999	+	0.00160129i	$0.999490\pi$
$74$	6.91794	−	11.9822i	0.804194	−	1.39291i
$75$	−0.0501666	−	0.0868912i	−0.00579274	−	0.0100333i
$76$	29.0858			3.33637
$77$		0			0
$78$	−5.84111			−0.661376
$79$	2.31574	+	4.01098i	0.260541	+	0.451270i	0.966386	−	0.257096i	$-0.0827658\pi$
$79$	2.31574	+	4.01098i	0.260541	+	0.451270i	−0.705845	+	0.708366i	$0.749432\pi$
$80$	−5.80660	+	10.0573i	−0.649198	+	1.12444i
$81$	−2.33850	+	4.05039i	−0.259833	+	0.450044i
$82$	−14.0110	−	24.2678i	−1.54726	−	2.67993i
$83$	1.93621			0.212527			0.106263	−	0.994338i	$-0.466111\pi$
$83$	1.93621			0.212527			0.106263	+	0.994338i	$0.466111\pi$
$84$	−4.59568	+	6.47145i	−0.501430	+	0.706093i
$85$	−3.28646			−0.356467
$86$	6.56117	+	11.3643i	0.707509	+	1.22544i
$87$	0.588580	−	1.01945i	0.0631024	−	0.109297i
$88$		0			0
$89$	−1.60220	−	2.77509i	−0.169833	−	0.294159i	0.768528	−	0.639816i	$-0.220989\pi$
$89$	−1.60220	−	2.77509i	−0.169833	−	0.294159i	−0.938361	+	0.345657i	$0.887656\pi$
$90$	−13.6770			−1.44168
$91$	3.62234	+	7.90471i	0.379725	+	0.828639i
$92$	27.2902			2.84520
$93$	−0.838496	−	1.45232i	−0.0869480	−	0.150598i
$94$	−1.85677	+	3.21602i	−0.191511	+	0.331707i
$95$	−7.62496	+	13.2068i	−0.782304	+	1.35499i
$96$	0.763705	+	1.32278i	0.0779453	+	0.135005i
$97$	1.85939			0.188792			0.0943960	−	0.995535i	$-0.469908\pi$
$97$	1.85939			0.188792			0.0943960	+	0.995535i	$0.469908\pi$
$98$	17.1294	+	3.25544i	1.73034	+	0.328849i
$99$		0			0
$100$	0.295598	+	0.511992i	0.0295598	+	0.0511992i
$101$	3.02276	−	5.23557i	0.300776	−	0.520959i	−0.675536	−	0.737327i	$-0.736088\pi$
$101$	3.02276	−	5.23557i	0.300776	−	0.520959i	0.976312	+	0.216368i	$0.0694211\pi$
$102$	−1.32488	+	2.29475i	−0.131182	+	0.227214i
$103$	0.531894	+	0.921267i	0.0524091	+	0.0907752i	0.891040	−	0.453925i	$-0.149977\pi$
$103$	0.531894	+	0.921267i	0.0524091	+	0.0907752i	−0.838631	+	0.544700i	$0.816643\pi$
$104$	18.0455			1.76951
$105$	−1.73368	−	3.78325i	−0.169190	−	0.369208i
$106$	0.759053			0.0737257
$107$	−3.16599	−	5.48365i	−0.306068	−	0.530125i	0.671431	−	0.741067i	$-0.265680\pi$
$107$	−3.16599	−	5.48365i	−0.306068	−	0.530125i	−0.977498	+	0.210943i	$0.932347\pi$
$108$	−8.23630	+	14.2657i	−0.792538	+	1.37272i
$109$	−1.40694	+	2.43688i	−0.134760	+	0.233411i	−0.925506	−	0.378734i	$-0.876360\pi$
$109$	−1.40694	+	2.43688i	−0.134760	+	0.233411i	0.790746	+	0.612145i	$0.209693\pi$
$110$		0			0
$111$	3.96345			0.376194
$112$	8.07031	−	11.3643i	0.762572	−	1.07382i
$113$	−12.7538			−1.19978			−0.599889	−	0.800083i	$-0.704789\pi$
$113$	−12.7538			−1.19978			−0.599889	+	0.800083i	$0.704789\pi$
$114$	6.14772	+	10.6482i	0.575786	+	0.997291i
$115$	−7.15423	+	12.3915i	−0.667136	+	1.15551i
$116$	−3.46811	+	6.00694i	−0.322006	+	0.557730i
$117$	4.09306	+	7.08940i	0.378404	+	0.655415i
$118$	−31.5311			−2.90268
$119$	3.92708	+	0.369859i	0.359994	+	0.0339049i
$120$	−8.63671			−0.788420
$121$		0			0
$122$	−16.1679	+	28.0035i	−1.46377	+	2.53532i
$123$	4.01362	−	6.95180i	0.361896	−	0.626822i
$124$	4.94070	+	8.55754i	0.443688	+	0.768490i
$125$	−11.3320			−1.01356
$126$	16.3430	+	1.53921i	1.45595	+	0.137124i
$127$	12.3775			1.09832			0.549162	−	0.835716i	$-0.314947\pi$
$127$	12.3775			1.09832			0.549162	+	0.835716i	$0.314947\pi$
$128$	8.62234	+	14.9343i	0.762114	+	1.32002i
$129$	−1.87953	+	3.25544i	−0.165483	+	0.286625i
$130$	−9.02276	+	15.6279i	−0.791348	+	1.37066i
$131$	0.379526	+	0.657359i	0.0331594	+	0.0574337i	0.882129	−	0.471008i	$-0.156110\pi$
$131$	0.379526	+	0.657359i	0.0331594	+	0.0574337i	−0.848969	+	0.528442i	$0.822776\pi$
$132$		0			0
$133$	10.5975	−	14.9230i	0.918924	−	1.29399i
$134$	−11.3905			−0.983992
$135$	−4.31836	−	7.47961i	−0.371665	−	0.643742i
$136$	4.09306	−	7.08940i	0.350977	−	0.607911i
$137$	2.92056	−	5.05855i	0.249520	−	0.432181i	−0.713873	−	0.700275i	$-0.753060\pi$
$137$	2.92056	−	5.05855i	0.249520	−	0.432181i	0.963393	+	0.268094i	$0.0863938\pi$
$138$	5.76819	+	9.99080i	0.491021	+	0.850473i
$139$	5.57292			0.472689			0.236345	−	0.971669i	$-0.424051\pi$
$139$	5.57292			0.472689			0.236345	+	0.971669i	$0.424051\pi$
$140$	10.2154	+	22.2922i	0.863359	+	1.88403i
$141$	−1.06379			−0.0895871
$142$	−14.1067	−	24.4335i	−1.18381	−	2.05041i
$143$		0			0
$144$	6.56117	−	11.3643i	0.546764	−	0.947023i
$145$	−1.81836	−	3.14948i	−0.151006	−	0.261550i
$146$	21.3409			1.76619
$147$	1.64585	+	4.71581i	0.135747	+	0.388953i
$148$	−23.3540			−1.91969
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$	−0.124958	+	0.216434i	−0.0102028	+	0.0176718i
$151$	7.42056	−	12.8528i	0.603876	−	1.04594i	−0.388352	−	0.921511i	$-0.626955\pi$
$151$	7.42056	−	12.8528i	0.603876	−	1.04594i	0.992228	−	0.124433i	$-0.0397113\pi$
$152$	−18.9927	−	32.8964i	−1.54051	−	2.66825i
$153$	3.71354			0.300222
$154$		0			0
$155$	−5.18089			−0.416139
$156$	4.92969	+	8.53848i	0.394691	+	0.683625i
$157$	−3.19527	+	5.53436i	−0.255010	+	0.441690i	−0.964898	−	0.262624i	$-0.915412\pi$
$157$	−3.19527	+	5.53436i	−0.255010	+	0.441690i	0.709888	+	0.704314i	$0.248745\pi$
$158$	5.76819	−	9.99080i	0.458893	−	0.794825i
$159$	0.108720	+	0.188308i	0.00862205	+	0.0149338i
$160$	4.71877			0.373052
$161$	9.94331	−	14.0018i	0.783643	−	1.10349i
$162$	11.6498			0.915291
$163$	−4.97259	−	8.61278i	−0.389483	−	0.674605i	0.602897	−	0.797819i	$-0.294013\pi$
$163$	−4.97259	−	8.61278i	−0.389483	−	0.674605i	−0.992380	+	0.123214i	$0.960680\pi$
$164$	−23.6496	+	40.9623i	−1.84672	+	3.19862i
$165$		0			0
$166$	−2.41142	−	4.17670i	−0.187163	−	0.324175i
$167$	1.94145			0.150234			0.0751168	−	0.997175i	$-0.476067\pi$
$167$	1.94145			0.150234			0.0751168	+	0.997175i	$0.476067\pi$
$168$	10.3202	+	0.971976i	0.796223	+	0.0749896i
$169$	−2.19917			−0.169167
$170$	4.09306	+	7.08940i	0.313924	+	0.543732i
$171$	8.61582	−	14.9230i	0.658868	−	1.14119i
$172$	11.0748	−	19.1821i	0.844445	−	1.46262i
$173$	3.21616	+	5.57054i	0.244520	+	0.423521i	0.961996	−	0.273062i	$-0.0880364\pi$
$173$	3.21616	+	5.57054i	0.244520	+	0.423521i	−0.717477	+	0.696582i	$0.754703\pi$
$174$	−2.93214			−0.222285
$175$	0.370390	+	0.0348840i	0.0279989	+	0.00263698i
$176$		0			0
$177$	−4.51624	−	7.82235i	−0.339461	−	0.587964i
$178$	−3.99086	+	6.91238i	−0.299128	+	0.518105i
$179$	1.79298	−	3.10553i	0.134014	−	0.232119i	−0.791207	−	0.611549i	$-0.790547\pi$
$179$	1.79298	−	3.10553i	0.134014	−	0.232119i	0.925220	+	0.379430i	$0.123880\pi$
$180$	11.5429	+	19.9929i	0.860357	+	1.49018i
$181$	12.2134			0.907813			0.453906	−	0.891049i	$-0.350030\pi$
$181$	12.2134			0.907813			0.453906	+	0.891049i	$0.350030\pi$
$182$	12.5403	−	17.6587i	0.929547	−	1.30895i
$183$	−9.26295			−0.684737
$184$	−17.8202	−	30.8655i	−1.31372	−	2.27544i
$185$	6.12234	−	10.6042i	0.450123	−	0.779637i
$186$	−2.08858	+	3.61753i	−0.153142	+	0.265250i
$187$		0			0
$188$	6.26819			0.457155
$189$	4.31836	+	9.42356i	0.314114	+	0.685463i
$190$	37.9855			2.75576
$191$	−6.05465	−	10.4870i	−0.438099	−	0.758810i	0.559444	−	0.828868i	$-0.311015\pi$
$191$	−6.05465	−	10.4870i	−0.438099	−	0.758810i	−0.997543	+	0.0700583i	$0.977681\pi$
$192$	−1.85677	+	3.21602i	−0.134001	+	0.232096i
$193$	−5.96997	+	10.3403i	−0.429728	+	0.744311i	−0.996849	−	0.0793237i	$-0.974724\pi$
$193$	−5.96997	+	10.3403i	−0.429728	+	0.744311i	0.567121	+	0.823635i	$0.308057\pi$
$194$	−2.31574	−	4.01098i	−0.166260	−	0.287971i
$195$	−5.16936			−0.370185
$196$	−9.69788	−	27.7871i	−0.692706	−	1.98479i
$197$	−12.1626			−0.866551			−0.433275	−	0.901262i	$-0.642642\pi$
$197$	−12.1626			−0.866551			−0.433275	+	0.901262i	$0.642642\pi$
$198$		0			0
$199$	−0.952451	+	1.64969i	−0.0675174	+	0.116944i	−0.897808	−	0.440387i	$-0.854841\pi$
$199$	−0.952451	+	1.64969i	−0.0675174	+	0.116944i	0.830290	+	0.557331i	$0.188174\pi$
$200$	0.386046	−	0.668651i	0.0272975	−	0.0472807i
$201$	−1.63148	−	2.82580i	−0.115076	−	0.199317i
$202$	−15.0586			−1.05952
$203$	1.81836	+	3.96804i	0.127624	+	0.278502i
$204$	4.47259			0.313144
$205$	−12.3997	−	21.4769i	−0.866030	−	1.50001i
$206$	1.32488	−	2.29475i	0.0923084	−	0.159883i
$207$	8.08393	−	14.0018i	0.561872	−	0.973191i
$208$	−8.65685	−	14.9941i	−0.600245	−	1.03965i
$209$		0			0
$210$	−6.00187	+	8.45159i	−0.414168	+	0.583215i
$211$	16.2447			1.11833			0.559165	−	0.829056i	$-0.311122\pi$
$211$	16.2447			1.11833			0.559165	+	0.829056i	$0.311122\pi$
$212$	−0.640614	−	1.10958i	−0.0439975	−	0.0762060i
$213$	4.04103	−	6.99927i	0.276887	−	0.479582i
$214$	−7.88605	+	13.6590i	−0.539079	+	0.933712i
$215$	5.80660	+	10.0573i	0.396007	+	0.685904i
$216$	21.5129			1.46377
$217$	6.19078	+	0.583058i	0.420258	+	0.0395806i
$218$	7.00897			0.474707
$219$	3.05669	+	5.29434i	0.206552	+	0.357758i
$220$		0			0
$221$	2.44983	−	4.24324i	0.164794	−	0.285431i
$222$	−4.93621	−	8.54977i	−0.331297	−	0.573823i
$223$	3.03655			0.203342			0.101671	−	0.994818i	$-0.467581\pi$
$223$	3.03655			0.203342			0.101671	+	0.994818i	$0.467581\pi$
$224$	−5.63858	−	0.531051i	−0.376743	−	0.0354823i
$225$	0.350250			0.0233500
$226$	15.8840	+	27.5119i	1.05659	+	1.83007i
$227$	9.22454	−	15.9774i	0.612254	−	1.06046i	−0.378605	−	0.925558i	$-0.623596\pi$
$227$	9.22454	−	15.9774i	0.612254	−	1.06046i	0.990860	−	0.134897i	$-0.0430705\pi$
$228$	10.3769	−	17.9733i	0.687228	−	1.19031i
$229$	12.7499	+	22.0835i	0.842538	+	1.45932i	0.887742	+	0.460341i	$0.152273\pi$
$229$	12.7499	+	22.0835i	0.842538	+	1.45932i	−0.0452039	+	0.998978i	$0.514394\pi$
$230$	35.6404			2.35006
$231$		0			0
$232$	9.05855			0.594723
$233$	1.90880	+	3.30614i	0.125050	+	0.216593i	0.921752	−	0.387779i	$-0.126758\pi$
$233$	1.90880	+	3.30614i	0.125050	+	0.216593i	−0.796703	+	0.604372i	$0.793424\pi$
$234$	10.1953	−	17.6587i	0.666485	−	1.15439i
$235$	−1.64323	+	2.84616i	−0.107193	+	0.185663i
$236$	26.6112	+	46.0919i	1.73224	+	3.00033i
$237$	3.30473			0.214666
$238$	−4.09306	−	8.93193i	−0.265314	−	0.578971i
$239$	−13.0037			−0.841142			−0.420571	−	0.907260i	$-0.638170\pi$
$239$	−13.0037			−0.841142			−0.420571	+	0.907260i	$0.638170\pi$
$240$	4.14323	+	7.17629i	0.267444	+	0.463227i
$241$	−0.225292	+	0.390216i	−0.0145123	+	0.0251360i	−0.873190	−	0.487379i	$-0.837953\pi$
$241$	−0.225292	+	0.390216i	−0.0145123	+	0.0251360i	0.858678	+	0.512515i	$0.171286\pi$
$242$		0			0
$243$	7.54551	+	13.0692i	0.484045	+	0.838391i
$244$	54.5804			3.49415
$245$	15.1595	+	2.88104i	0.968503	+	0.184063i
$246$	−19.9948			−1.27482
$247$	−11.3678	−	19.6896i	−0.723314	−	1.25282i
$248$	6.45245	−	11.1760i	0.409731	−	0.709675i
$249$	0.690780	−	1.19647i	0.0437764	−	0.0758230i
$250$	14.1132	+	24.4448i	0.892597	+	1.54602i
$251$	1.11861			0.0706058			0.0353029	−	0.999377i	$-0.488760\pi$
$251$	1.11861			0.0706058			0.0353029	+	0.999377i	$0.488760\pi$
$252$	−11.5429	−	25.1890i	−0.727134	−	1.58676i
$253$		0			0
$254$	−15.4153	−	26.7001i	−0.967243	−	1.67531i
$255$	−1.17251	+	2.03084i	−0.0734253	+	0.127176i
$256$	16.2727	−	28.1851i	1.01704	−	1.76157i
$257$	11.4198	+	19.7797i	0.712348	+	1.23382i	0.963974	+	0.265998i	$0.0857015\pi$
$257$	11.4198	+	19.7797i	0.712348	+	1.23382i	−0.251626	+	0.967825i	$0.580965\pi$
$258$	9.36329			0.582933
$259$	−8.50914	+	11.9822i	−0.528732	+	0.744539i
$260$	30.4596			1.88902
$261$	2.05465	+	3.55876i	0.127180	+	0.220282i
$262$	0.945349	−	1.63739i	0.0584038	−	0.101158i
$263$	−4.59568	+	7.95995i	−0.283382	+	0.490832i	−0.972215	−	0.234088i	$-0.924790\pi$
$263$	−4.59568	+	7.95995i	−0.283382	+	0.490832i	0.688834	+	0.724919i	$0.258123\pi$
$264$		0			0
$265$	0.671758			0.0412658
$266$	−45.3898	−	4.27489i	−2.78303	−	0.262110i
$267$	−2.28646			−0.139929
$268$	9.61320	+	16.6506i	0.587220	+	1.01709i
$269$	7.80660	−	13.5214i	0.475977	−	0.824416i	−0.523644	−	0.851937i	$-0.675428\pi$
$269$	7.80660	−	13.5214i	0.475977	−	0.824416i	0.999621	+	0.0275208i	$0.00876123\pi$
$270$	−10.7564	+	18.6307i	−0.654616	+	1.13383i
$271$	13.8723	+	24.0275i	0.842680	+	1.45956i	0.887621	+	0.460574i	$0.152357\pi$
$271$	13.8723	+	24.0275i	0.842680	+	1.45956i	−0.0449415	+	0.998990i	$0.514310\pi$
$272$	−7.85415			−0.476228
$273$	6.17699	+	0.581759i	0.373849	+	0.0352097i
$274$	−14.5494			−0.878962
$275$		0			0
$276$	9.73630	−	16.8638i	0.586056	−	1.01508i
$277$	7.40619	−	12.8279i	0.444995	−	0.770753i	−0.553057	−	0.833143i	$-0.686539\pi$
$277$	7.40619	−	12.8279i	0.444995	−	0.770753i	0.998052	+	0.0623900i	$0.0198723\pi$
$278$	−6.94070	−	12.0216i	−0.416275	−	0.721010i
$279$	5.85415			0.350479
$280$	18.5421	−	26.1103i	1.10811	−	1.56039i
$281$	−15.2227			−0.908109			−0.454054	−	0.890974i	$-0.650023\pi$
$281$	−15.2227			−0.908109			−0.454054	+	0.890974i	$0.650023\pi$
$282$	1.32488	+	2.29475i	0.0788952	+	0.136650i
$283$	10.8586	−	18.8077i	0.645479	−	1.11800i	−0.338712	−	0.940890i	$-0.609991\pi$
$283$	10.8586	−	18.8077i	0.645479	−	1.11800i	0.984191	−	0.177112i	$-0.0566755\pi$
$284$	−23.8111	+	41.2420i	−1.41293	+	2.44726i
$285$	5.44070	+	9.42356i	0.322279	+	0.558204i
$286$		0			0
$287$	12.3997	+	27.0587i	0.731929	+	1.59722i
$288$	−5.33198			−0.314190
$289$	7.38866	+	12.7975i	0.434627	+	0.752796i
$290$	−4.52928	+	7.84494i	−0.265968	+	0.460671i
$291$	0.663371	−	1.14899i	0.0388875	−	0.0673551i
$292$	−18.0110	−	31.1960i	−1.05401	−	1.82561i
$293$	−11.1276			−0.650080			−0.325040	−	0.945700i	$-0.605378\pi$
$293$	−11.1276			−0.650080			−0.325040	+	0.945700i	$0.605378\pi$
$294$	8.12292	−	9.42356i	0.473739	−	0.549593i
$295$	−27.9049			−1.62469
$296$	15.2499	+	26.4136i	0.886383	+	1.53526i
$297$		0			0
$298$	−1.24543	+	2.15715i	−0.0721459	+	0.124960i
$299$	−10.6660	−	18.4740i	−0.616830	−	1.06838i
$300$	0.421841			0.0243550
$301$	−5.80660	−	12.6712i	−0.334687	−	0.730358i
$302$	−36.9672			−2.12722
$303$	−2.15685	−	3.73578i	−0.123908	−	0.214615i
$304$	−18.2225	+	31.5623i	−1.04513	+	1.81022i
$305$	−14.3085	+	24.7830i	−0.819301	+	1.41907i
$306$	−4.62496	−	8.01066i	−0.264391	−	0.457939i
$307$	−24.9855			−1.42600			−0.712998	−	0.701166i	$-0.752663\pi$
$307$	−24.9855			−1.42600			−0.712998	+	0.701166i	$0.752663\pi$
$308$		0			0
$309$	0.759053			0.0431810
$310$	6.45245	+	11.1760i	0.366475	+	0.634753i
$311$	−17.3704	+	30.0864i	−0.984984	+	1.70604i	−0.342979	+	0.939343i	$0.611436\pi$
$311$	−17.3704	+	30.0864i	−0.984984	+	1.70604i	−0.642005	+	0.766700i	$0.721897\pi$
$312$	6.43808	−	11.1511i	0.364484	−	0.631306i
$313$	−11.8547	−	20.5330i	−0.670069	−	1.16059i	−0.977884	−	0.209148i	$-0.932931\pi$
$313$	−11.8547	−	20.5330i	−0.670069	−	1.16059i	0.307815	−	0.951446i	$-0.400402\pi$
$314$	15.9179			0.898301
$315$	14.4635	+	1.36219i	0.814923	+	0.0767508i
$316$	−19.4726			−1.09542
$317$	−9.83850	−	17.0408i	−0.552585	−	0.957105i	−0.998087	−	0.0618244i	$-0.980308\pi$
$317$	−9.83850	−	17.0408i	−0.552585	−	0.957105i	0.445502	−	0.895281i	$-0.353025\pi$
$318$	0.270807	−	0.469051i	0.0151861	−	0.0263031i
$319$		0			0
$320$	5.73630	+	9.93556i	0.320669	+	0.555414i
$321$	−4.51811			−0.252176
$322$	−42.5877	−	4.01098i	−2.37332	−	0.223523i
$323$	−10.3137			−0.573870
$324$	−9.83198	−	17.0295i	−0.546221	−	0.946082i
$325$	0.231061	−	0.400209i	0.0128170	−	0.0221996i
$326$	−12.3860	+	21.4533i	−0.686000	+	1.18819i
$327$	1.00390	+	1.73881i	0.0555159	+	0.0961564i
$328$	61.7718			3.41077
$329$	2.28384	−	3.21602i	0.125912	−	0.177305i
$330$		0			0
$331$	14.0949	+	24.4131i	0.774728	+	1.34187i	0.934947	+	0.354786i	$0.115446\pi$
$331$	14.0949	+	24.4131i	0.774728	+	1.34187i	−0.160220	+	0.987081i	$0.551220\pi$
$332$	−4.07031	+	7.04998i	−0.223387	+	0.386918i
$333$	−6.91794	+	11.9822i	−0.379101	+	0.656622i
$334$	−2.41794	−	4.18799i	−0.132304	−	0.229157i
$335$	−10.0806			−0.550760
$336$	−4.14323	−	9.04140i	−0.226032	−	0.493249i
$337$	−21.7460			−1.18458			−0.592290	−	0.805725i	$-0.701776\pi$
$337$	−21.7460			−1.18458			−0.592290	+	0.805725i	$0.701776\pi$
$338$	2.73891	+	4.74394i	0.148977	+	0.258036i
$339$	−4.55017	+	7.88112i	−0.247131	+	0.428044i
$340$	6.90880	−	11.9664i	0.374682	−	0.648969i
$341$		0			0
$342$	−42.9217			−2.32094
$343$	−17.7902	−	5.14868i	−0.960580	−	0.278003i
$344$	−28.9269			−1.55963
$345$	5.10482	+	8.84180i	0.274834	+	0.476027i
$346$	8.01100	−	13.8755i	0.430674	−	0.745950i
$347$	−1.97072	+	3.41339i	−0.105794	+	0.183241i	−0.914062	−	0.405574i	$-0.867072\pi$
$347$	−1.97072	+	3.41339i	−0.105794	+	0.183241i	0.808268	+	0.588814i	$0.200405\pi$
$348$	2.47463	+	4.28618i	0.132654	+	0.229763i
$349$	14.1093			0.755254			0.377627	−	0.925958i	$-0.376740\pi$
$349$	14.1093			0.755254			0.377627	+	0.925958i	$0.376740\pi$
$350$	−0.386046	−	0.842433i	−0.0206350	−	0.0450299i
$351$	12.8762			0.687279
$352$		0			0
$353$	2.48434	−	4.30301i	0.132228	−	0.229026i	−0.792307	−	0.610123i	$-0.791120\pi$
$353$	2.48434	−	4.30301i	0.132228	−	0.229026i	0.924535	+	0.381097i	$0.124453\pi$
$354$	−11.2493	+	19.4844i	−0.597895	+	1.03559i
$355$	−12.4843	−	21.6235i	−0.662600	−	1.14766i
$356$	13.4726			0.714046
$357$	1.62961	−	2.29475i	0.0862481	−	0.121451i
$358$	−8.93214			−0.472078
$359$	−2.03580	−	3.52610i	−0.107445	−	0.186101i	0.807289	−	0.590156i	$-0.200934\pi$
$359$	−2.03580	−	3.52610i	−0.107445	−	0.186101i	−0.914735	+	0.404055i	$0.867600\pi$
$360$	15.0748	−	26.1103i	0.794511	−	1.37613i
$361$	−14.4289	+	24.9917i	−0.759418	+	1.31535i
$362$	−15.2109	−	26.3461i	−0.799468	−	1.38472i
$363$		0			0
$364$	−36.3969	−	3.42792i	−1.90772	−	0.179672i
$365$	18.8866			0.988571
$366$	11.5364	+	19.9816i	0.603016	+	1.04445i
$367$	9.01100	−	15.6075i	0.470371	−	0.814706i	−0.529055	−	0.848587i	$-0.677454\pi$
$367$	9.01100	−	15.6075i	0.470371	−	0.814706i	0.999426	+	0.0338816i	$0.0107869\pi$
$368$	−17.0975	+	29.6138i	−0.891271	+	1.54373i
$369$	14.0110	+	24.2678i	0.729384	+	1.26333i
$370$	−30.4998			−1.58561
$371$	−0.802700	−	0.0755997i	−0.0416741	−	0.00392494i
$372$	7.05075			0.365564
$373$	14.4582	+	25.0424i	0.748618	+	1.29664i	0.948485	+	0.316822i	$0.102616\pi$
$373$	14.4582	+	25.0424i	0.748618	+	1.29664i	−0.199867	+	0.979823i	$0.564051\pi$
$374$		0			0
$375$	−4.04290	+	7.00250i	−0.208774	+	0.361608i
$376$	−4.09306	−	7.08940i	−0.211084	−	0.365608i
$377$	5.42184			0.279239
$378$	14.9498	−	21.0518i	0.768936	−	1.08279i
$379$	4.30847			0.221311			0.110656	−	0.993859i	$-0.464705\pi$
$379$	4.30847			0.221311			0.110656	+	0.993859i	$0.464705\pi$
$380$	−32.0584	−	55.5268i	−1.64456	−	2.84846i
$381$	4.41591	−	7.64857i	0.226234	−	0.391848i
$382$	−15.0813	+	26.1216i	−0.771627	+	1.33650i
$383$	6.17438	+	10.6943i	0.315496	+	0.546455i	0.979543	−	0.201236i	$-0.0644958\pi$
$383$	6.17438	+	10.6943i	0.315496	+	0.546455i	−0.664047	+	0.747691i	$0.731163\pi$
$384$	12.3047			0.627923
$385$		0			0
$386$	29.7408			1.51377
$387$	−6.56117	−	11.3643i	−0.333523	−	0.577679i
$388$	−3.90880	+	6.77025i	−0.198439	+	0.343707i
$389$	−14.7115	+	25.4811i	−0.745903	+	1.29194i	0.203869	+	0.978998i	$0.434648\pi$
$389$	−14.7115	+	25.4811i	−0.745903	+	1.29194i	−0.949772	+	0.312943i	$0.898685\pi$
$390$	6.43808	+	11.1511i	0.326005	+	0.564657i
$391$	−9.67699			−0.489387
$392$	−25.0949	+	29.1131i	−1.26749	+	1.47043i
$393$	0.541613			0.0273208
$394$	15.1477	+	26.2366i	0.763131	+	1.32178i
$395$	5.10482	−	8.84180i	0.256851	−	0.444879i
$396$		0			0
$397$	8.64975	+	14.9818i	0.434119	+	0.751915i	0.997223	−	0.0744702i	$-0.0237266\pi$
$397$	8.64975	+	14.9818i	0.434119	+	0.751915i	−0.563105	+	0.826386i	$0.690393\pi$
$398$	4.74485			0.237838
$399$	−5.44070	−	11.8727i	−0.272376	−	0.594381i
$400$	−0.740780			−0.0370390
$401$	12.4752	+	21.6077i	0.622982	+	1.07904i	0.988927	+	0.148400i	$0.0474124\pi$
$401$	12.4752	+	21.6077i	0.622982	+	1.07904i	−0.365945	+	0.930636i	$0.619254\pi$
$402$	−4.06379	+	7.03869i	−0.202683	+	0.351058i
$403$	3.86200	−	6.68919i	0.192380	−	0.333212i
$404$	12.7089	+	22.0124i	0.632291	+	1.09516i
$405$	10.3100			0.512306
$406$	6.29502	−	8.86439i	0.312416	−	0.439932i
$407$		0			0
$408$	−2.92056	−	5.05855i	−0.144589	−	0.250436i
$409$	−19.2792	+	33.3925i	−0.953295	+	1.65115i	−0.215072	+	0.976598i	$0.568999\pi$
$409$	−19.2792	+	33.3925i	−0.953295	+	1.65115i	−0.738223	+	0.674557i	$0.764335\pi$
$410$	−30.8859	+	53.4959i	−1.52534	+	2.64197i
$411$	−2.08393	−	3.60947i	−0.102793	−	0.178042i
$412$	−4.47259			−0.220349
$413$	33.3443	+	3.14042i	1.64076	+	0.154530i
$414$	−40.2719			−1.97926
$415$	−2.13409	−	3.69636i	−0.104759	−	0.181447i
$416$	−3.51752	+	6.09253i	−0.172461	+	0.298711i
$417$	1.98825	−	3.44374i	0.0973648	−	0.168641i
$418$		0			0
$419$	0.908970			0.0444061			0.0222030	−	0.999753i	$-0.492932\pi$
$419$	0.908970			0.0444061			0.0222030	+	0.999753i	$0.492932\pi$
$420$	17.4198	+	1.64063i	0.850000	+	0.0800544i
$421$	15.5532			0.758014			0.379007	−	0.925394i	$-0.376266\pi$
$421$	15.5532			0.758014			0.379007	+	0.925394i	$0.376266\pi$
$422$	−20.2316	−	35.0422i	−0.984861	−	1.70583i
$423$	1.85677	−	3.21602i	0.0902792	−	0.156368i
$424$	−0.836629	+	1.44908i	−0.0406303	+	0.0703737i
$425$	−0.104818	−	0.181550i	−0.00508442	−	0.00880647i
$426$	−20.1313			−0.975365
$427$	19.8866	−	28.0035i	0.962381	−	1.35519i
$428$	26.6222			1.28683
$429$		0			0
$430$	14.4635	−	25.0514i	0.697490	−	1.20809i
$431$	1.76819	−	3.06259i	0.0851707	−	0.147520i	−0.820293	−	0.571943i	$-0.806190\pi$
$431$	1.76819	−	3.06259i	0.0851707	−	0.147520i	0.905464	+	0.424423i	$0.139523\pi$
$432$	−10.3202	−	17.8752i	−0.496532	−	0.860019i
$433$	17.6457			0.847997			0.423999	−	0.905663i	$-0.360626\pi$
$433$	17.6457			0.847997			0.423999	+	0.905663i	$0.360626\pi$
$434$	−6.45245	−	14.0806i	−0.309728	−	0.675891i
$435$	−2.59493			−0.124417
$436$	−5.91532	−	10.2456i	−0.283293	−	0.490677i
$437$	−22.4517	+	38.8875i	−1.07401	+	1.86024i
$438$	7.61379	−	13.1875i	0.363801	−	0.630122i
$439$	7.51362	+	13.0140i	0.358606	+	0.621123i	0.987728	−	0.156183i	$-0.0499190\pi$
$439$	7.51362	+	13.0140i	0.358606	+	0.621123i	−0.629123	+	0.777306i	$0.716586\pi$
$440$		0			0
$441$	−17.1294	−	3.25544i	−0.815688	−	0.155021i
$442$	−12.2044			−0.580504
$443$	−6.61134	−	11.4512i	−0.314114	−	0.544062i	0.665135	−	0.746723i	$-0.268374\pi$
$443$	−6.61134	−	11.4512i	−0.314114	−	0.544062i	−0.979249	+	0.202662i	$0.935041\pi$
$444$	−8.33198	+	14.4314i	−0.395418	+	0.684884i
$445$	−3.53189	+	6.11742i	−0.167428	+	0.289994i
$446$	−3.78181	−	6.55029i	−0.179074	−	0.310165i
$447$	−0.713538			−0.0337492
$448$	−5.73630	−	12.5178i	−0.271014	−	0.591411i
$449$	−9.90864			−0.467617			−0.233809	−	0.972283i	$-0.575119\pi$
$449$	−9.90864			−0.467617			−0.233809	+	0.972283i	$0.575119\pi$
$450$	−0.436212	−	0.755542i	−0.0205632	−	0.0356166i
$451$		0			0
$452$	26.8111	−	46.4382i	1.26109	−	2.18427i
$453$	−5.29485	−	9.17095i	−0.248774	−	0.430889i
$454$	−45.9542			−2.15674
$455$	11.0981	−	15.6279i	0.520286	−	0.732646i
$456$	−27.1041			−1.26926
$457$	5.17251	+	8.95905i	0.241960	+	0.419087i	0.961272	−	0.275600i	$-0.0888765\pi$
$457$	5.17251	+	8.95905i	0.241960	+	0.419087i	−0.719313	+	0.694686i	$0.755543\pi$
$458$	31.7583	−	55.0070i	1.48397	−	2.57031i
$459$	2.92056	−	5.05855i	0.136320	−	0.236113i
$460$	−30.0793	−	52.0988i	−1.40245	−	2.42912i
$461$	15.3372			0.714325			0.357163	−	0.934042i	$-0.383744\pi$
$461$	15.3372			0.714325			0.357163	+	0.934042i	$0.383744\pi$
$462$		0			0
$463$	−25.1313			−1.16795			−0.583976	−	0.811771i	$-0.698504\pi$
$463$	−25.1313			−1.16795			−0.583976	+	0.811771i	$0.698504\pi$
$464$	−4.34560	−	7.52680i	−0.201739	−	0.349423i
$465$	−1.84838	+	3.20149i	−0.0857167	+	0.148466i
$466$	4.75457	−	8.23515i	0.220251	−	0.381486i
$467$	0.373007	+	0.646068i	0.0172607	+	0.0298964i	0.874527	−	0.484977i	$-0.161172\pi$
$467$	0.373007	+	0.646068i	0.0172607	+	0.0298964i	−0.857266	+	0.514874i	$0.827839\pi$
$468$	−34.4178			−1.59096
$469$	12.0455	+	1.13447i	0.556210	+	0.0523848i
$470$	8.18613			0.377598
$471$	2.27994	+	3.94898i	0.105054	+	0.181959i
$472$	34.7537	−	60.1951i	1.59967	−	2.77070i
$473$		0			0
$474$	−4.11582	−	7.12881i	−0.189046	−	0.327437i
$475$	−0.972758			−0.0446332
$476$	−9.60220	+	13.5214i	−0.440116	+	0.619754i
$477$	−0.759053			−0.0347546
$478$	16.1953	+	28.0510i	0.740754	+	1.28302i
$479$	−10.0565	+	17.4184i	−0.459494	+	0.795867i	−0.998934	−	0.0461569i	$-0.985303\pi$
$479$	−10.0565	+	17.4184i	−0.459494	+	0.795867i	0.539440	+	0.842024i	$0.318636\pi$
$480$	1.68351	−	2.91593i	0.0768414	−	0.133093i
$481$	9.12758	+	15.8094i	0.416182	+	0.720848i
$482$	1.12234			0.0511212
$483$	−5.10482	−	11.1398i	−0.232277	−	0.506878i
$484$		0			0
$485$	−2.04942	−	3.54969i	−0.0930592	−	0.161183i
$486$	18.7948	−	32.5536i	0.852552	−	1.47666i
$487$	2.12496	−	3.68054i	0.0962911	−	0.166781i	−0.813856	−	0.581067i	$-0.802635\pi$
$487$	2.12496	−	3.68054i	0.0962911	−	0.166781i	0.910147	+	0.414286i	$0.135969\pi$
$488$	−35.6404	−	61.7311i	−1.61337	−	2.79443i
$489$	−7.09626			−0.320904
$490$	−12.6652	−	36.2894i	−0.572157	−	1.63939i
$491$	−30.3279			−1.36868			−0.684340	−	0.729163i	$-0.739909\pi$
$491$	−30.3279			−1.36868			−0.684340	+	0.729163i	$0.739909\pi$
$492$	16.8749	+	29.2281i	0.760778	+	1.31771i
$493$	1.22978	−	2.13003i	0.0553863	−	0.0959320i
$494$	−28.3156	+	49.0440i	−1.27398	+	2.20659i
$495$		0			0
$496$	−12.3816			−0.555948
$497$	12.4843	+	27.2435i	0.559999	+	1.22204i
$498$	−3.44128			−0.154207
$499$	−7.22064	−	12.5065i	−0.323240	−	0.559869i	0.657914	−	0.753093i	$-0.271439\pi$
$499$	−7.22064	−	12.5065i	−0.323240	−	0.559869i	−0.981155	+	0.193224i	$0.938106\pi$
$500$	23.8221	−	41.2611i	1.06536	−	1.84525i
$501$	0.692648	−	1.19970i	0.0309452	−	0.0535987i
$502$	−1.39315	−	2.41300i	−0.0621792	−	0.107698i
$503$	2.95822			0.131901			0.0659503	−	0.997823i	$-0.478992\pi$
$503$	2.95822			0.131901			0.0659503	+	0.997823i	$0.478992\pi$
$504$	−20.9517	+	29.5033i	−0.933263	+	1.31418i
$505$	−13.3267			−0.593032
$506$		0			0
$507$	−0.784595	+	1.35896i	−0.0348451	+	0.0603534i
$508$	−26.0200	+	45.0679i	−1.15445	+	1.99957i
$509$	12.4953	+	21.6426i	0.553847	+	0.959290i	0.997992	+	0.0633358i	$0.0201739\pi$
$509$	12.4953	+	21.6426i	0.553847	+	0.959290i	−0.444146	+	0.895955i	$0.646493\pi$
$510$	5.84111			0.258649
$511$	−22.5681	−	2.12550i	−0.998354	−	0.0940267i
$512$	−46.5767			−2.05842
$513$	−13.5520	−	23.4728i	−0.598337	−	1.03635i
$514$	28.4452	−	49.2685i	1.25466	−	2.17314i
$515$	1.17251	−	2.03084i	0.0516669	−	0.0894896i
$516$	−7.90228	−	13.6872i	−0.347879	−	0.602544i
$517$		0			0
$518$	36.4450	+	3.43245i	1.60130	+	0.150813i
$519$	4.58970			0.201465
$520$	−19.8898	−	34.4501i	−0.872225	−	1.51074i
$521$	−14.4316	+	24.9962i	−0.632258	+	1.09510i	0.354831	+	0.934931i	$0.384538\pi$
$521$	−14.4316	+	24.9962i	−0.632258	+	1.09510i	−0.987089	+	0.160173i	$0.948795\pi$
$522$	5.11786	−	8.86439i	0.224002	−	0.387984i
$523$	0.236295	+	0.409276i	0.0103325	+	0.0178964i	0.871145	−	0.491025i	$-0.163378\pi$
$523$	0.236295	+	0.409276i	0.0103325	+	0.0178964i	−0.860813	+	0.508921i	$0.830044\pi$
$524$	−3.19136			−0.139415
$525$	0.153700	−	0.216434i	0.00670802	−	0.00944596i
$526$	22.8944			0.998245
$527$	−1.75195	−	3.03447i	−0.0763162	−	0.132184i
$528$		0			0
$529$	−9.56566	+	16.5682i	−0.415898	+	0.720357i
$530$	−0.836629	−	1.44908i	−0.0363408	−	0.0629442i
$531$	31.5311			1.36834
$532$	32.0584	+	69.9582i	1.38991	+	3.03307i
$533$	36.9724			1.60145
$534$	2.84763	+	4.93224i	0.123229	+	0.213439i
$535$	−6.97911	+	12.0882i	−0.301733	+	0.522617i
$536$	12.5547	−	21.7453i	0.542278	−	0.939254i
$537$	−1.27936	−	2.21592i	−0.0552085	−	0.0956239i
$538$	−38.8904			−1.67668
$539$		0			0
$540$	36.3122			1.56263
$541$	7.72978	+	13.3884i	0.332329	+	0.575611i	0.982968	−	0.183776i	$-0.0588322\pi$
$541$	7.72978	+	13.3884i	0.332329	+	0.575611i	−0.650639	+	0.759387i	$0.725499\pi$
$542$	34.5539	−	59.8491i	1.48422	−	2.57074i
$543$	4.35735	−	7.54715i	0.186992	−	0.323879i
$544$	1.59568	+	2.76380i	0.0684143	+	0.118497i
$545$	6.20290			0.265703
$546$	−6.43808	−	14.0492i	−0.275524	−	0.601252i
$547$	35.0440			1.49837			0.749187	−	0.662359i	$-0.230444\pi$
$547$	35.0440			1.49837			0.749187	+	0.662359i	$0.230444\pi$
$548$	12.2792	+	21.2682i	0.524541	+	0.908532i
$549$	16.1679	−	28.0035i	0.690027	−	1.19516i
$550$		0			0
$551$	−5.70644	−	9.88384i	−0.243102	−	0.421066i
$552$	−25.4308			−1.08241
$553$	−7.09493	+	9.99080i	−0.301707	+	0.424852i
$554$	−36.8956			−1.56754
$555$	−4.36852	−	7.56650i	−0.185433	−	0.321180i
$556$	−11.7154	+	20.2917i	−0.496844	+	0.860559i
$557$	5.26632	−	9.12154i	0.223141	−	0.386492i	−0.732619	−	0.680639i	$-0.761702\pi$
$557$	5.26632	−	9.12154i	0.223141	−	0.386492i	0.955760	+	0.294147i	$0.0950356\pi$
$558$	−7.29095	−	12.6283i	−0.308650	−	0.534598i
$559$	−17.3137			−0.732292
$560$	−30.5903	−	2.88104i	−1.29268	−	0.121746i
$561$		0			0
$562$	18.9588	+	32.8376i	0.799729	+	1.38517i
$563$	−15.3574	+	26.5997i	−0.647235	+	1.12104i	0.336545	+	0.941667i	$0.390742\pi$
$563$	−15.3574	+	26.5997i	−0.647235	+	1.12104i	−0.983780	+	0.179377i	$0.942592\pi$
$564$	2.23630	−	3.87338i	0.0941650	−	0.163099i
$565$	14.0573	+	24.3479i	0.591394	+	1.02432i
$566$	−54.0948			−2.27377
$567$	−12.3196	−	1.16028i	−0.517376	−	0.0487274i
$568$	62.1936			2.60959
$569$	−15.3860	−	26.6494i	−0.645017	−	1.11720i	−0.984298	−	0.176516i	$-0.943517\pi$
$569$	−15.3860	−	26.6494i	−0.645017	−	1.11720i	0.339281	−	0.940685i	$-0.389816\pi$
$570$	13.5520	−	23.4728i	0.567632	−	0.983168i
$571$	−3.75847	+	6.50986i	−0.157287	+	0.272429i	−0.933889	−	0.357562i	$-0.883608\pi$
$571$	−3.75847	+	6.50986i	−0.157287	+	0.272429i	0.776602	+	0.629991i	$0.216941\pi$
$572$		0			0
$573$	−8.64045			−0.360960
$574$	42.9267	−	60.4477i	1.79173	−	2.52304i
$575$	−0.912705			−0.0380624
$576$	−6.48173	−	11.2267i	−0.270072	−	0.467778i
$577$	−13.8092	+	23.9183i	−0.574885	+	0.995731i	0.421169	+	0.906982i	$0.361620\pi$
$577$	−13.8092	+	23.9183i	−0.574885	+	0.995731i	−0.996054	+	0.0887483i	$0.971713\pi$
$578$	18.4042	−	31.8769i	0.765512	−	1.32591i
$579$	4.25980	+	7.37819i	0.177031	+	0.306627i
$580$	15.2902			0.634891
$581$	2.13409	+	4.65704i	0.0885372	+	0.193207i
$582$	−3.30473			−0.136986
$583$		0			0
$584$	−23.5220	+	40.7413i	−0.973348	+	1.68589i
$585$	9.02276	−	15.6279i	0.373045	−	0.646133i
$586$	13.8586	+	24.0039i	0.572495	+	0.991590i
$587$	−29.9582			−1.23651			−0.618254	−	0.785978i	$-0.712160\pi$
$587$	−29.9582			−1.23651			−0.618254	+	0.785978i	$0.712160\pi$
$588$	−20.6307	−	3.92085i	−0.850797	−	0.161693i
$589$	−16.2589			−0.669936
$590$	34.7537	+	60.1951i	1.43079	+	2.47819i
$591$	−4.33925	+	7.51579i	−0.178493	+	0.309158i
$592$	14.6315	−	25.3425i	0.601350	−	1.04157i
$593$	6.33401	+	10.9708i	0.260107	+	0.450518i	0.966270	−	0.257531i	$-0.0829089\pi$
$593$	6.33401	+	10.9708i	0.260107	+	0.450518i	−0.706163	+	0.708049i	$0.749576\pi$
$594$		0			0
$595$	−3.62234	−	7.90471i	−0.148502	−	0.324062i
$596$	4.20440			0.172219
$597$	0.679610	+	1.17712i	0.0278146	+	0.0481762i
$598$	−26.5675	+	46.0163i	−1.08643	+	1.88175i
$599$	−0.647133	+	1.12087i	−0.0264411	+	0.0457974i	−0.878943	−	0.476926i	$-0.841751\pi$
$599$	−0.647133	+	1.12087i	−0.0264411	+	0.0457974i	0.852502	+	0.522724i	$0.175084\pi$
$600$	−0.275458	−	0.477108i	−0.0112455	−	0.0194778i
$601$	41.0220			1.67332			0.836661	−	0.547721i	$-0.184504\pi$
$601$	41.0220			1.67332			0.836661	+	0.547721i	$0.184504\pi$
$602$	−20.1020	+	28.3069i	−0.819298	+	1.15370i
$603$	11.3905			0.463858
$604$	31.1990	+	54.0383i	1.26947	+	2.19879i
$605$		0			0
$606$	−5.37242	+	9.30531i	−0.218240	+	0.378002i
$607$	−10.5884	−	18.3397i	−0.429770	−	0.744384i	0.567082	−	0.823661i	$-0.308072\pi$
$607$	−10.5884	−	18.3397i	−0.429770	−	0.744384i	−0.996853	+	0.0792770i	$0.974739\pi$
$608$	14.8086			0.600570
$609$	3.10075	+	0.292034i	0.125649	+	0.0118338i
$610$	71.2809			2.88608
$611$	−2.44983	−	4.24324i	−0.0991096	−	0.171663i
$612$	−7.80660	+	13.5214i	−0.315563	+	0.546571i
$613$	3.38156	−	5.85704i	0.136580	−	0.236563i	−0.789620	−	0.613596i	$-0.789722\pi$
$613$	3.38156	−	5.85704i	0.136580	−	0.236563i	0.926200	+	0.377033i	$0.123056\pi$
$614$	31.1177	+	53.8974i	1.25581	+	2.17512i
$615$	−17.6953			−0.713542
$616$		0			0
$617$	−41.0728			−1.65353			−0.826763	−	0.562550i	$-0.809820\pi$
$617$	−41.0728			−1.65353			−0.826763	+	0.562550i	$0.809820\pi$
$618$	−0.945349	−	1.63739i	−0.0380275	−	0.0658656i
$619$	15.2134	−	26.3503i	0.611477	−	1.05911i	−0.379515	−	0.925186i	$-0.623909\pi$
$619$	15.2134	−	26.3503i	0.611477	−	1.05911i	0.990992	−	0.133924i	$-0.0427577\pi$
$620$	10.8913	−	18.8643i	0.437404	−	0.757607i
$621$	−12.7154	−	22.0237i	−0.510252	−	0.883782i
$622$	86.5345			3.46972
$623$	4.90880	−	6.91238i	0.196667	−	0.276939i
$624$	−12.3540			−0.494555
$625$	12.1386	+	21.0246i	0.485543	+	0.840985i
$626$	−29.5285	+	51.1449i	−1.18020	+	2.04416i
$627$		0			0
$628$	−13.4342	−	23.2687i	−0.536082	−	0.928521i
$629$	8.28123			0.330194
$630$	−15.0748	−	32.8964i	−0.600594	−	1.31062i
$631$	12.3670			0.492323			0.246162	−	0.969229i	$-0.420831\pi$
$631$	12.3670			0.492323			0.246162	+	0.969229i	$0.420831\pi$
$632$	12.7154	+	22.0237i	0.505792	+	0.876057i
$633$	5.79560	−	10.0383i	0.230354	−	0.398985i
$634$	−24.5064	+	42.4462i	−0.973272	+	1.68576i
$635$	−13.6425	−	23.6295i	−0.541385	−	0.937707i
$636$	−0.914205			−0.0362506
$637$	−15.0201	+	17.4252i	−0.595120	+	0.690410i
$638$		0			0
$639$	14.1067	+	24.4335i	0.558052	+	0.966574i
$640$	19.0071	−	32.9213i	0.751322	−	1.30133i
$641$	23.5657	−	40.8169i	0.930787	−	1.61217i	0.148809	−	0.988866i	$-0.452456\pi$
$641$	23.5657	−	40.8169i	0.930787	−	1.61217i	0.781979	−	0.623305i	$-0.214211\pi$
$642$	5.62699	+	9.74624i	0.222080	+	0.384653i
$643$	1.87242			0.0738412			0.0369206	−	0.999318i	$-0.488245\pi$
$643$	1.87242			0.0738412			0.0369206	+	0.999318i	$0.488245\pi$
$644$	30.0793	+	65.6393i	1.18529	+	2.58655i
$645$	8.28646			0.326279
$646$	12.8450	+	22.2482i	0.505380	+	0.875344i
$647$	0.917939	−	1.58992i	0.0360879	−	0.0625061i	−0.847417	−	0.530927i	$-0.821844\pi$
$647$	0.917939	−	1.58992i	0.0360879	−	0.0625061i	0.883505	+	0.468421i	$0.155177\pi$
$648$	−12.8404	+	22.2402i	−0.504417	+	0.873676i
$649$		0			0
$650$	−1.15108			−0.0451492
$651$	2.56897	−	3.61753i	0.100686	−	0.141782i
$652$	41.8135			1.63754
$653$	9.08858	+	15.7419i	0.355664	+	0.616027i	0.987231	−	0.159293i	$-0.0509216\pi$
$653$	9.08858	+	15.7419i	0.355664	+	0.616027i	−0.631568	+	0.775321i	$0.717588\pi$
$654$	2.50058	−	4.33114i	0.0977805	−	0.169361i
$655$	0.836629	−	1.44908i	0.0326898	−	0.0566204i
$656$	−29.6333	−	51.3265i	−1.15699	−	2.00396i
$657$	−21.3409			−0.832590
$658$	−9.78181	−	0.921267i	−0.381335	−	0.0359147i
$659$	16.8997			0.658318			0.329159	−	0.944275i	$-0.393235\pi$
$659$	16.8997			0.658318			0.329159	+	0.944275i	$0.393235\pi$
$660$		0			0
$661$	22.6516	−	39.2338i	0.881046	−	1.52602i	0.0308661	−	0.999524i	$-0.490173\pi$
$661$	22.6516	−	39.2338i	0.881046	−	1.52602i	0.850180	−	0.526493i	$-0.176493\pi$
$662$	35.1086	−	60.8098i	1.36453	−	2.36344i
$663$	−1.74805	−	3.02771i	−0.0678886	−	0.117587i
$664$	10.6315			0.412581
$665$	−40.1697	−	3.78325i	−1.55772	−	0.146708i
$666$	34.4633			1.33543
$667$	−5.35415	−	9.27366i	−0.207314	−	0.359078i
$668$	−4.08131	+	7.06904i	−0.157911	+	0.273509i
$669$	1.08335	−	1.87641i	0.0418845	−	0.0725462i
$670$	12.5547	+	21.7453i	0.485028	+	0.840094i
$671$		0			0
$672$	−2.33983	+	3.29485i	−0.0902609	+	0.127102i
$673$	−39.5076			−1.52291			−0.761454	−	0.648219i	$-0.775514\pi$
$673$	−39.5076			−1.52291			−0.761454	+	0.648219i	$0.775514\pi$
$674$	27.0832	+	46.9094i	1.04321	+	1.80688i
$675$	0.275458	−	0.477108i	0.0106024	−	0.0183639i
$676$	4.62309	−	8.00743i	0.177811	−	0.307978i
$677$	−17.0669	−	29.5608i	−0.655936	−	1.13611i	−0.981658	−	0.190649i	$-0.938941\pi$
$677$	−17.0669	−	29.5608i	−0.655936	−	1.13611i	0.325723	−	0.945465i	$-0.394392\pi$
$678$	22.6677			0.870547
$679$	2.04942	+	4.47226i	0.0786494	+	0.171630i
$680$	−18.0455			−0.692014
$681$	−6.58206	−	11.4005i	−0.252225	−	0.436867i
$682$		0			0
$683$	−11.8931	+	20.5995i	−0.455079	+	0.788219i	−0.998693	−	0.0511160i	$-0.983722\pi$
$683$	−11.8931	+	20.5995i	−0.455079	+	0.788219i	0.543614	+	0.839335i	$0.317056\pi$
$684$	36.2244	+	62.7425i	1.38507	+	2.39902i
$685$	−12.8762			−0.491973
$686$	11.0500	+	44.7885i	0.421891	+	1.71003i
$687$	18.1951			0.694186
$688$	13.8769	+	24.0355i	0.529052	+	0.916345i
$689$	−0.500750	+	0.867324i	−0.0190770	+	0.0330424i
$690$	12.7154	−	22.0237i	0.484067	−	0.838429i
$691$	10.2812	+	17.8076i	0.391116	+	0.677433i	0.992597	−	0.121454i	$-0.0387557\pi$
$691$	10.2812	+	17.8076i	0.391116	+	0.677433i	−0.601481	+	0.798887i	$0.705422\pi$
$692$	−27.0440			−1.02806
$693$		0			0
$694$	9.81761			0.372671
$695$	−6.14248	−	10.6391i	−0.232998	−	0.403564i
$696$	3.23181	−	5.59766i	0.122501	−	0.212179i
$697$	8.38605	−	14.5251i	0.317644	−	0.550176i
$698$	−17.5722	−	30.4359i	−0.665117	−	1.15202i
$699$	2.72401			0.103031
$700$	−0.905651	+	1.27530i	−0.0342304	+	0.0482019i
$701$	23.9907			0.906116			0.453058	−	0.891481i	$-0.350333\pi$
$701$	23.9907			0.906116			0.453058	+	0.891481i	$0.350333\pi$
$702$	−16.0364	−	27.7758i	−0.605254	−	1.04833i
$703$	19.2134	−	33.2785i	0.724646	−	1.25512i
$704$		0			0
$705$	1.17251	+	2.03084i	0.0441592	+	0.0764860i
$706$	−12.3763			−0.465789
$707$	15.9245	+	1.49979i	0.598901	+	0.0564055i
$708$	37.9762			1.42723
$709$	25.8559	+	44.7836i	0.971037	+	1.68189i	0.692437	+	0.721478i	$0.256537\pi$
$709$	25.8559	+	44.7836i	0.971037	+	1.68189i	0.278599	+	0.960407i	$0.410130\pi$
$710$	−31.0968	+	53.8612i	−1.16704	+	2.02138i
$711$	−5.76819	+	9.99080i	−0.216324	+	0.374684i
$712$	−8.79747	−	15.2377i	−0.329699	−	0.571055i
$713$	−15.2552			−0.571310
$714$	−6.97969	−	0.657359i	−0.261208	−	0.0246010i
$715$		0			0
$716$	7.53841	+	13.0569i	0.281724	+	0.487960i
$717$	−4.63933	+	8.03555i	−0.173259	+	0.300093i
$718$	−5.07089	+	8.78304i	−0.189244	+	0.327780i
$719$	−12.8926	−	22.3306i	−0.480812	−	0.832790i	0.518946	−	0.854807i	$-0.326325\pi$
$719$	−12.8926	−	22.3306i	−0.480812	−	0.832790i	−0.999758	+	0.0220170i	$0.992991\pi$
$720$	−28.9269			−1.07804
$721$	−1.62961	+	2.29475i	−0.0606898	+	0.0854610i
$722$	71.8811			2.67514
$723$	0.160754	+	0.278434i	0.00597851	+	0.0103551i
$724$	−25.6750	+	44.4703i	−0.954202	+	1.65273i
$725$	0.115989	−	0.200899i	0.00430772	−	0.00746118i
$726$		0			0
$727$	32.7330			1.21400			0.606999	−	0.794702i	$-0.292373\pi$
$727$	32.7330			1.21400			0.606999	+	0.794702i	$0.292373\pi$
$728$	19.8898	+	43.4037i	0.737164	+	1.60865i
$729$	−3.26295			−0.120850
$730$	−23.5220	−	40.7413i	−0.870589	−	1.50790i
$731$	−3.92708	+	6.80189i	−0.145248	+	0.251577i
$732$	19.4726	−	33.7275i	0.719728	−	1.24660i
$733$	−4.64136	−	8.03908i	−0.171433	−	0.296930i	0.767488	−	0.641063i	$-0.221506\pi$
$733$	−4.64136	−	8.03908i	−0.171433	−	0.296930i	−0.938921	+	0.344133i	$0.888173\pi$
$734$	−44.8904			−1.65693
$735$	7.18875	−	8.33981i	0.265161	−	0.307618i
$736$	13.8944			0.512156
$737$		0			0
$738$	34.8995	−	60.4477i	1.28467	−	2.22511i
$739$	−25.0466	+	43.3820i	−0.921355	+	1.59583i	−0.124035	+	0.992278i	$0.539583\pi$
$739$	−25.0466	+	43.3820i	−0.921355	+	1.59583i	−0.797320	+	0.603556i	$0.793750\pi$
$740$	25.7408	+	44.5843i	0.946250	+	1.63895i
$741$	−16.2227			−0.595955
$742$	0.836629	+	1.82570i	0.0307136	+	0.0670236i
$743$	−13.1679			−0.483082			−0.241541	−	0.970391i	$-0.577653\pi$
$743$	−13.1679			−0.483082			−0.241541	+	0.970391i	$0.577653\pi$
$744$	−4.60407	−	7.97448i	−0.168793	−	0.292359i
$745$	−1.10220	+	1.90907i	−0.0403815	+	0.0699428i
$746$	36.0135	−	62.3771i	1.31855	−	2.28379i
$747$	2.41142	+	4.17670i	0.0882293	+	0.152818i
$748$		0			0
$749$	9.69992	−	13.6590i	0.354427	−	0.499090i
$750$	20.1406			0.735431
$751$	−20.6569	−	35.7787i	−0.753779	−	1.30558i	−0.945979	−	0.324228i	$-0.894895\pi$
$751$	−20.6569	−	35.7787i	−0.753779	−	1.30558i	0.192200	−	0.981356i	$-0.438438\pi$
$752$	−3.92708	+	6.80189i	−0.143206	+	0.248040i
$753$	0.399084	−	0.691234i	0.0145434	−	0.0251900i
$754$	−6.75253	−	11.6957i	−0.245913	−	0.425933i
$755$	−32.7158			−1.19065
$756$	−43.3904	−	4.08658i	−1.57809	−	0.148627i
$757$	−45.5114			−1.65414			−0.827069	−	0.562100i	$-0.809994\pi$
$757$	−45.5114			−1.65414			−0.827069	+	0.562100i	$0.809994\pi$
$758$	−5.36591	−	9.29402i	−0.194898	−	0.337574i
$759$		0			0
$760$	−41.8676	+	72.5168i	−1.51870	+	2.63046i
$761$	15.6360	+	27.0823i	0.566803	+	0.981732i	0.996879	+	0.0789393i	$0.0251533\pi$
$761$	15.6360	+	27.0823i	0.566803	+	0.981732i	−0.430076	+	0.902793i	$0.641513\pi$
$762$	−21.9988			−0.796934
$763$	−7.41200	−	0.698075i	−0.268333	−	0.0252720i
$764$	50.9124			1.84194
$765$	−4.09306	−	7.08940i	−0.147985	−	0.256318i
$766$	15.3795	−	26.6381i	0.555685	−	0.962474i
$767$	20.8012	−	36.0287i	0.751088	−	1.30092i
$768$	−11.6112	−	20.1111i	−0.418982	−	0.725698i
$769$	−42.0467			−1.51624			−0.758121	−	0.652114i	$-0.773882\pi$
$769$	−42.0467			−1.51624			−0.758121	+	0.652114i	$0.773882\pi$
$770$		0			0
$771$	16.2969			0.586920
$772$	−25.1002	−	43.4748i	−0.903375	−	1.56469i
$773$	−3.82226	+	6.62034i	−0.137477	+	0.238117i	−0.926541	−	0.376194i	$-0.877233\pi$
$773$	−3.82226	+	6.62034i	−0.137477	+	0.238117i	0.789064	+	0.614311i	$0.210566\pi$
$774$	−16.3430	+	28.3069i	−0.587436	+	1.01747i
$775$	−0.165239	−	0.286202i	−0.00593555	−	0.0102807i
$776$	10.2096			0.366505
$777$	4.36852	+	9.53304i	0.156720	+	0.341996i
$778$	73.2887			2.62753
$779$	−38.9131	−	67.3995i	−1.39421	−	2.41484i
$780$	10.8670	−	18.8222i	0.389102	−	0.673944i
$781$		0			0
$782$	12.0520	+	20.8747i	0.430980	+	0.746479i
$783$	6.46362			0.230991
$784$	36.2289	+	6.88526i	1.29389	+	0.245902i
$785$	14.0873			0.502797
$786$	−0.674542	−	1.16834i	−0.0240601	−	0.0416734i
$787$	−13.9517	+	24.1651i	−0.497324	+	0.861391i	−0.999995	−	0.00308674i	$-0.999017\pi$
$787$	−13.9517	+	24.1651i	−0.497324	+	0.861391i	0.502671	+	0.864478i	$0.332351\pi$
$788$	25.5683	−	44.2855i	0.910832	−	1.57761i
$789$	3.27919	+	5.67973i	0.116742	+	0.202204i
$790$	−25.4308			−0.904788
$791$	−14.0573	−	30.6759i	−0.499819	−	1.09071i
$792$		0			0
$793$	−21.3320	−	36.9481i	−0.757521	−	1.31206i
$794$	21.5453	−	37.3176i	0.764616	−	1.32435i
$795$	0.239662	−	0.415107i	0.00849995	−	0.0147223i
$796$	−4.00448	−	6.93597i	−0.141935	−	0.245839i
$797$	10.0560			0.356201			0.178101	−	0.984012i	$-0.443005\pi$
$797$	10.0560			0.356201			0.178101	+	0.984012i	$0.443005\pi$
$798$	−18.8353	+	26.5231i	−0.666762	+	0.938908i
$799$	−2.22267			−0.0786326
$800$	0.150500	+	0.260674i	0.00532098	+	0.00921620i
$801$	3.99086	−	6.91238i	0.141010	−	0.244237i
$802$	31.0740	−	53.8218i	1.09726	−	1.90051i
$803$		0			0
$804$	13.7188			0.483824
$805$	−37.6899	−	3.54969i	−1.32839	−	0.125110i
$806$	−19.2394			−0.677681
$807$	−5.57031	−	9.64805i	−0.196084	−	0.339628i
$808$	16.5975	−	28.7478i	0.583900	−	1.01134i
$809$	19.2863	−	33.4048i	0.678070	−	1.17445i	−0.297491	−	0.954725i	$-0.596150\pi$
$809$	19.2863	−	33.4048i	0.678070	−	1.17445i	0.975561	−	0.219727i	$-0.0705167\pi$
$810$	−12.8404	−	22.2402i	−0.451164	−	0.781440i
$811$	−12.3760			−0.434580			−0.217290	−	0.976107i	$-0.569722\pi$
$811$	−12.3760			−0.434580			−0.217290	+	0.976107i	$0.569722\pi$
$812$	−18.2706	−	1.72076i	−0.641174	−	0.0603868i
$813$	19.7968			0.694303
$814$		0			0
$815$	−10.9616	+	18.9860i	−0.383968	+	0.665051i
$816$	−2.80212	+	4.85341i	−0.0980937	+	0.169903i
$817$	18.2225	+	31.5623i	0.637525	+	1.10423i
$818$	96.0437			3.35809
$819$	−12.5403	+	17.6587i	−0.438193	+	0.617046i
$820$	104.266			3.64114
$821$	14.8691	+	25.7540i	0.518934	+	0.898820i	0.999758	+	0.0220025i	$0.00700418\pi$
$821$	14.8691	+	25.7540i	0.518934	+	0.898820i	−0.480824	+	0.876817i	$0.659662\pi$
$822$	−5.19078	+	8.99070i	−0.181049	+	0.313587i
$823$	−20.3885	+	35.3139i	−0.710698	+	1.23097i	0.253897	+	0.967231i	$0.418288\pi$
$823$	−20.3885	+	35.3139i	−0.710698	+	1.23097i	−0.964595	+	0.263734i	$0.915046\pi$
$824$	2.92056	+	5.05855i	0.101742	+	0.176223i
$825$		0			0
$826$	−34.7537	−	75.8398i	−1.20923	−	2.63880i
$827$	18.8411			0.655170			0.327585	−	0.944822i	$-0.393765\pi$
$827$	18.8411			0.655170			0.327585	+	0.944822i	$0.393765\pi$
$828$	33.9881	+	58.8691i	1.18117	+	2.04584i
$829$	15.5703	−	26.9686i	0.540779	−	0.936657i	−0.458080	−	0.888911i	$-0.651463\pi$
$829$	15.5703	−	26.9686i	0.540779	−	0.936657i	0.998860	−	0.0477461i	$-0.0152038\pi$
$830$	−5.31574	+	9.20713i	−0.184512	+	0.319584i
$831$	−5.28459	−	9.15319i	−0.183321	−	0.317521i
$832$	−17.1041			−0.592977
$833$	3.43883	+	9.85320i	0.119148	+	0.341393i
$834$	−9.90490			−0.342979
$835$	−2.13986	−	3.70635i	−0.0740530	−	0.128264i
$836$		0			0
$837$	4.60407	−	7.97448i	0.159140	−	0.275638i
$838$	−1.13206	−	1.96079i	−0.0391064	−	0.0677342i
$839$	10.2589			0.354176			0.177088	−	0.984195i	$-0.443332\pi$
$839$	10.2589			0.354176			0.177088	+	0.984195i	$0.443332\pi$
$840$	−9.51939	−	20.7733i	−0.328450	−	0.716748i
$841$	−26.2783			−0.906149
$842$	−19.3704	−	33.5505i	−0.667548	−	1.15623i
$843$	−5.43098	+	9.40673i	−0.187053	+	0.323985i
$844$	−34.1496	+	59.1488i	−1.17548	+	2.03599i
$845$	2.42392	+	4.19836i	0.0833855	+	0.144428i
$846$	−9.24992			−0.318019
$847$		0			0
$848$	1.60540			0.0551297
$849$	−7.74805	−	13.4200i	−0.265912	−	0.460574i
$850$	−0.261087	+	0.452217i	−0.00895522	+	0.0155109i
$851$	18.0272	−	31.2241i	0.617966	−	1.07035i
$852$	16.9901	+	29.4277i	0.582072	+	1.00818i
$853$	−3.04435			−0.104237			−0.0521183	−	0.998641i	$-0.516597\pi$
$853$	−3.04435			−0.104237			−0.0521183	+	0.998641i	$0.516597\pi$
$854$	−85.1753	−	8.02195i	−2.91464	−	0.274506i
$855$	−37.9855			−1.29908
$856$	−17.3840	−	30.1100i	−0.594173	−	1.02914i
$857$	24.7766	−	42.9143i	0.846352	−	1.46592i	−0.0380904	−	0.999274i	$-0.512127\pi$
$857$	24.7766	−	42.9143i	0.846352	−	1.46592i	0.884442	−	0.466650i	$-0.154539\pi$
$858$		0			0
$859$	−18.4373	−	31.9344i	−0.629074	−	1.08959i	−0.987738	−	0.156121i	$-0.950101\pi$
$859$	−18.4373	−	31.9344i	−0.629074	−	1.08959i	0.358664	−	0.933467i	$-0.383232\pi$
$860$	−48.8266			−1.66497
$861$	21.1445	+	1.99143i	0.720603	+	0.0678676i
$862$	−8.80864			−0.300023
$863$	23.2115	+	40.2035i	0.790129	+	1.36854i	0.925887	+	0.377801i	$0.123320\pi$
$863$	23.2115	+	40.2035i	0.790129	+	1.36854i	−0.135758	+	0.990742i	$0.543347\pi$
$864$	−4.19340	+	7.26318i	−0.142662	+	0.247098i
$865$	7.08970	−	12.2797i	0.241057	−	0.417523i
$866$	−21.9765	−	38.0644i	−0.746792	−	1.29348i
$867$	10.5442			0.358099
$868$	−15.1372	+	21.3157i	−0.513792	+	0.723501i
$869$		0			0
$870$	3.23181	+	5.59766i	0.109569	+	0.189778i
$871$	7.51437	−	13.0153i	0.254615	−	0.441006i
$872$	−7.72529	+	13.3806i	−0.261611	+	0.453124i
$873$	2.31574	+	4.01098i	0.0783759	+	0.135751i
$874$	111.848			3.78332
$875$	−12.4901	−	27.2561i	−0.422243	−	0.921423i
$876$	−25.7031			−0.868426
$877$	19.5155	+	33.8018i	0.658991	+	1.14141i	0.980877	+	0.194628i	$0.0623499\pi$
$877$	19.5155	+	33.8018i	0.658991	+	1.14141i	−0.321886	+	0.946778i	$0.604317\pi$
$878$	18.7154	−	32.4160i	0.631614	−	1.09399i
$879$	−3.96997	+	6.87620i	−0.133904	+	0.231928i
$880$		0			0
$881$	−44.0049			−1.48256			−0.741281	−	0.671194i	$-0.765782\pi$
$881$	−44.0049			−1.48256			−0.741281	+	0.671194i	$0.765782\pi$
$882$	14.3111	+	41.0052i	0.481879	+	1.38072i
$883$	−23.3596			−0.786112			−0.393056	−	0.919515i	$-0.628582\pi$
$883$	−23.3596			−0.786112			−0.393056	+	0.919515i	$0.628582\pi$
$884$	10.3001	+	17.8403i	0.346429	+	0.600033i
$885$	−9.95560	+	17.2436i	−0.334654	+	0.579638i
$886$	−16.4679	+	28.5233i	−0.553251	+	0.958259i
$887$	20.9588	+	36.3017i	0.703728	+	1.21889i	0.967149	+	0.254211i	$0.0818158\pi$
$887$	20.9588	+	36.3017i	0.703728	+	1.21889i	−0.263421	+	0.964681i	$0.584851\pi$
$888$	21.7628			0.730311
$889$	13.6425	+	29.7708i	0.457554	+	0.998480i
$890$	17.5949			0.589783
$891$		0			0
$892$	−6.38343	+	11.0564i	−0.213733	+	0.370196i
$893$	−5.15685	+	8.93193i	−0.172567	+	0.298896i
$894$	0.888663	+	1.53921i	0.0297213	+	0.0514789i
$895$	−7.90490			−0.264232
$896$	−26.4170	+	37.1994i	−0.882531	+	1.24274i
$897$	−15.2212			−0.508220
$898$	12.3405	+	21.3744i	0.411809	+	0.713274i
$899$	1.93866	−	3.35786i	0.0646580	−	0.111991i
$900$	−0.736295	+	1.27530i	−0.0245432	+	0.0425100i
$901$	0.227159	+	0.393451i	0.00756776	+	0.0131078i
$902$		0			0
$903$	−9.90170	−	0.932559i	−0.329508	−	0.0310336i
$904$	−70.0295			−2.32915
$905$	−13.4616	−	23.3162i	−0.447478	−	0.775055i
$906$	−13.1887	+	22.8436i	−0.438167	+	0.758927i
$907$	10.2591	−	17.7692i	0.340646	−	0.590017i	−0.643907	−	0.765104i	$-0.722687\pi$
$907$	10.2591	−	17.7692i	0.340646	−	0.590017i	0.984553	+	0.175087i	$0.0560208\pi$
$908$	38.7837	+	67.1753i	1.28708	+	2.22929i
$909$	15.0586			0.499461
$910$	−47.5336	−	4.47679i	−1.57572	−	0.148404i
$911$	27.6755			0.916930			0.458465	−	0.888712i	$-0.348399\pi$
$911$	27.6755			0.916930			0.458465	+	0.888712i	$0.348399\pi$
$912$	13.0025	+	22.5209i	0.430554	+	0.745742i
$913$		0			0
$914$	12.8840	−	22.3158i	0.426165	−	0.738140i
$915$	10.2096	+	17.6836i	0.337520	+	0.584602i
$916$	−107.212			−3.54237
$917$	−1.16279	+	1.63739i	−0.0383987	+	0.0540714i
$918$	−14.5494			−0.480202
$919$	0.481727	+	0.834376i	0.0158907	+	0.0275235i	0.873861	−	0.486175i	$-0.161608\pi$
$919$	0.481727	+	0.834376i	0.0158907	+	0.0275235i	−0.857971	+	0.513699i	$0.828275\pi$
$920$	−39.2829	+	68.0400i	−1.29512	+	2.24321i
$921$	−8.91404	+	15.4396i	−0.293728	+	0.508751i
$922$	−19.1015	−	33.0847i	−0.629073	−	1.08959i
$923$	37.2249			1.22527
$924$		0			0
$925$	0.781061			0.0256811
$926$	31.2993	+	54.2120i	1.02856	+	1.78152i
$927$	−1.32488	+	2.29475i	−0.0435146	+	0.0753695i
$928$	−1.76574	+	3.05835i	−0.0579632	+	0.100395i
$929$	−13.1660	−	22.8042i	−0.431962	−	0.748180i	0.565080	−	0.825036i	$-0.308845\pi$
$929$	−13.1660	−	22.8042i	−0.431962	−	0.748180i	−0.997042	+	0.0768558i	$0.975512\pi$
$930$	9.20814			0.301947
$931$	47.5740	+	9.04140i	1.55918	+	0.296320i
$932$	−16.0507			−0.525760
$933$	12.3944	+	21.4678i	0.405775	+	0.702824i
$934$	0.929110	−	1.60927i	0.0304014	−	0.0526568i
$935$		0			0
$936$	22.4745	+	38.9269i	0.734601	+	1.27237i
$937$	21.3865			0.698665			0.349333	−	0.936999i	$-0.386408\pi$
$937$	21.3865			0.698665			0.349333	+	0.936999i	$0.386408\pi$
$938$	−12.5547	−	27.3969i	−0.409924	−	0.894540i
$939$	−16.9176			−0.552085
$940$	−6.90880	−	11.9664i	−0.225340	−	0.390301i
$941$	7.41142	−	12.8370i	0.241605	−	0.418473i	−0.719566	−	0.694424i	$-0.755659\pi$
$941$	7.41142	−	12.8370i	0.241605	−	0.418473i	0.961172	+	0.275951i	$0.0889927\pi$
$942$	5.67903	−	9.83636i	0.185033	−	0.320486i
$943$	−36.5108	−	63.2386i	−1.18896	−	2.05933i
$944$	−66.6885			−2.17053
$945$	13.2305	−	18.6307i	0.430389	−	0.606056i
$946$		0			0
$947$	−15.8560	−	27.4634i	−0.515251	−	0.892442i	−0.999843	−	0.0177013i	$-0.994365\pi$
$947$	−15.8560	−	27.4634i	−0.515251	−	0.892442i	0.484592	−	0.874740i	$-0.338968\pi$
$948$	−6.94722	+	12.0329i	−0.225635	+	0.390811i
$949$	−14.0787	+	24.3850i	−0.457014	+	0.791571i
$950$	1.21150	+	2.09839i	0.0393064	+	0.0680806i
$951$	−14.0403			−0.455287
$952$	21.5630	+	2.03084i	0.698862	+	0.0658200i
$953$	−49.9620			−1.61843			−0.809213	−	0.587515i	$-0.800106\pi$
$953$	−49.9620			−1.61843			−0.809213	+	0.587515i	$0.800106\pi$
$954$	0.945349	+	1.63739i	0.0306068	+	0.0530125i
$955$	−13.3469	+	23.1175i	−0.431895	+	0.748064i
$956$	27.3365	−	47.3481i	0.884124	−	1.53135i
$957$		0			0
$958$	50.0988			1.61862
$959$	15.3860	+	1.44908i	0.496841	+	0.0467933i
$960$	8.18613			0.264206
$961$	12.7382	+	22.0631i	0.410908	+	0.711714i
$962$	22.7355	−	39.3791i	0.733023	−	1.26963i
$963$	7.88605	−	13.6590i	0.254124	−	0.440156i
$964$	−0.947216	−	1.64063i	−0.0305078	−	0.0528410i
$965$	26.3204			0.847285
$966$	−17.6725	+	24.8857i	−0.568604	+	0.800685i
$967$	52.4581			1.68694			0.843469	−	0.537178i	$-0.180510\pi$
$967$	52.4581			1.68694			0.843469	+	0.537178i	$0.180510\pi$
$968$		0			0
$969$	−3.67961	+	6.37327i	−0.118206	+	0.204739i
$970$	−5.10482	+	8.84180i	−0.163906	+	0.283893i
$971$	−15.4133	−	26.6966i	−0.494636	−	0.856735i	0.505345	−	0.862917i	$-0.331365\pi$
$971$	−15.4133	−	26.6966i	−0.494636	−	0.856735i	−0.999981	+	0.00618284i	$0.998032\pi$
$972$	−63.4487			−2.03512
$973$	6.14248	+	13.4042i	0.196919	+	0.429719i
$974$	−10.5860			−0.339196
$975$	−0.164871	−	0.285565i	−0.00528009	−	0.00914538i
$976$	−34.1951	+	59.2276i	−1.09456	+	1.89583i
$977$	−12.3678	+	21.4216i	−0.395680	+	0.685338i	−0.993188	−	0.116525i	$-0.962824\pi$
$977$	−12.3678	+	21.4216i	−0.395680	+	0.685338i	0.597508	+	0.801863i	$0.296158\pi$
$978$	8.83791	+	15.3077i	0.282605	+	0.489487i
$979$		0			0
$980$	−42.3585	+	49.1409i	−1.35309	+	1.56975i
$981$	−7.00897			−0.223779
$982$	37.7713	+	65.4219i	1.20533	+	2.08770i
$983$	−6.11192	+	10.5862i	−0.194940	+	0.337646i	−0.946881	−	0.321585i	$-0.895785\pi$
$983$	−6.11192	+	10.5862i	−0.194940	+	0.337646i	0.751941	+	0.659231i	$0.229118\pi$
$984$	22.0382	−	38.1714i	0.702554	−	1.21686i
$985$	13.4057	+	23.2193i	0.427140	+	0.739827i
$986$	−6.12641			−0.195105
$987$	−1.17251	−	2.55866i	−0.0373213	−	0.0814430i
$988$	95.5894			3.04110
$989$	17.0975	+	29.6138i	0.543670	+	0.941665i
$990$		0			0
$991$	−2.30008	+	3.98386i	−0.0730645	+	0.126552i	−0.900243	−	0.435388i	$-0.856611\pi$
$991$	−2.30008	+	3.98386i	−0.0730645	+	0.126552i	0.827178	+	0.561939i	$0.189945\pi$
$992$	2.51549	+	4.35695i	0.0798668	+	0.138333i
$993$	20.1145			0.638316
$994$	43.2199	−	60.8605i	1.37085	−	1.93038i
$995$	4.19917			0.133123
$996$	2.90432	+	5.03043i	0.0920268	+	0.159395i
$997$	−17.2382	+	29.8574i	−0.545938	+	0.945593i	0.452609	+	0.891709i	$0.350493\pi$
$997$	−17.2382	+	29.8574i	−0.545938	+	0.945593i	−0.998547	+	0.0538835i	$0.982840\pi$
$998$	−17.9856	+	31.1520i	−0.569325	+	0.986100i
$999$	10.8814	+	18.8471i	0.344272	+	0.596297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.e.d.606.1		6
7.2	even	3	inner	847.2.e.d.485.1		6
7.3	odd	6		5929.2.a.w.1.3		3
7.4	even	3		5929.2.a.v.1.3		3
11.2	odd	10		847.2.n.e.81.3		24
11.3	even	5		847.2.n.d.130.1		24
11.4	even	5		847.2.n.d.753.3		24
11.5	even	5		847.2.n.d.487.3		24
11.6	odd	10		847.2.n.e.487.1		24
11.7	odd	10		847.2.n.e.753.1		24
11.8	odd	10		847.2.n.e.130.3		24
11.9	even	5		847.2.n.d.81.1		24
11.10	odd	2		77.2.e.b.67.3	yes	6
33.32	even	2		693.2.i.g.298.1		6
44.43	even	2		1232.2.q.k.529.2		6
77.2	odd	30		847.2.n.e.807.1		24
77.9	even	15		847.2.n.d.807.3		24
77.10	even	6		539.2.a.i.1.1		3
77.16	even	15		847.2.n.d.366.1		24
77.30	odd	30		847.2.n.e.9.1		24
77.32	odd	6		539.2.a.h.1.1		3
77.37	even	15		847.2.n.d.632.1		24
77.51	odd	30		847.2.n.e.632.3		24
77.54	even	6		539.2.e.l.177.3		6
77.58	even	15		847.2.n.d.9.3		24
77.65	odd	6		77.2.e.b.23.3	✓	6
77.72	odd	30		847.2.n.e.366.3		24
77.76	even	2		539.2.e.l.67.3		6
231.32	even	6		4851.2.a.bo.1.3		3
231.65	even	6		693.2.i.g.100.1		6
231.164	odd	6		4851.2.a.bn.1.3		3
308.87	odd	6		8624.2.a.ck.1.2		3
308.219	even	6		1232.2.q.k.177.2		6
308.263	even	6		8624.2.a.cl.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.3	✓	6	77.65	odd	6
77.2.e.b.67.3	yes	6	11.10	odd	2
539.2.a.h.1.1		3	77.32	odd	6
539.2.a.i.1.1		3	77.10	even	6
539.2.e.l.67.3		6	77.76	even	2
539.2.e.l.177.3		6	77.54	even	6
693.2.i.g.100.1		6	231.65	even	6
693.2.i.g.298.1		6	33.32	even	2
847.2.e.d.485.1		6	7.2	even	3	inner
847.2.e.d.606.1		6	1.1	even	1	trivial
847.2.n.d.9.3		24	77.58	even	15
847.2.n.d.81.1		24	11.9	even	5
847.2.n.d.130.1		24	11.3	even	5
847.2.n.d.366.1		24	77.16	even	15
847.2.n.d.487.3		24	11.5	even	5
847.2.n.d.632.1		24	77.37	even	15
847.2.n.d.753.3		24	11.4	even	5
847.2.n.d.807.3		24	77.9	even	15
847.2.n.e.9.1		24	77.30	odd	30
847.2.n.e.81.3		24	11.2	odd	10
847.2.n.e.130.3		24	11.8	odd	10
847.2.n.e.366.3		24	77.72	odd	30
847.2.n.e.487.1		24	11.6	odd	10
847.2.n.e.632.3		24	77.51	odd	30
847.2.n.e.753.1		24	11.7	odd	10
847.2.n.e.807.1		24	77.2	odd	30
1232.2.q.k.177.2		6	308.219	even	6
1232.2.q.k.529.2		6	44.43	even	2
4851.2.a.bn.1.3		3	231.164	odd	6
4851.2.a.bo.1.3		3	231.32	even	6
5929.2.a.v.1.3		3	7.4	even	3
5929.2.a.w.1.3		3	7.3	odd	6
8624.2.a.ck.1.2		3	308.87	odd	6
8624.2.a.cl.1.2		3	308.263	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24543 - 2.15715i) q^{2} +(0.356769 - 0.617942i) q^{3} +(-2.10220 + 3.64112i) q^{4} +(-1.10220 - 1.90907i) q^{5} -1.77733 q^{6} +(1.10220 + 2.40523i) q^{7} +5.49086 q^{8} +(1.24543 + 2.15715i) q^{9} +O(q^{10})\)	\(q+(-1.24543 - 2.15715i) q^{2} +(0.356769 - 0.617942i) q^{3} +(-2.10220 + 3.64112i) q^{4} +(-1.10220 - 1.90907i) q^{5} -1.77733 q^{6} +(1.10220 + 2.40523i) q^{7} +5.49086 q^{8} +(1.24543 + 2.15715i) q^{9} +(-2.74543 + 4.75523i) q^{10} +(1.50000 + 2.59808i) q^{12} +3.28646 q^{13} +(3.81574 - 5.37317i) q^{14} -1.57292 q^{15} +(-2.63409 - 4.56239i) q^{16} +(0.745432 - 1.29113i) q^{17} +(3.10220 - 5.37317i) q^{18} +(-3.45897 - 5.99111i) q^{19} +9.26819 q^{20} +(1.87953 + 0.177017i) q^{21} +(-3.24543 - 5.62125i) q^{23} +(1.95897 - 3.39304i) q^{24} +(0.0703069 - 0.121775i) q^{25} +(-4.09306 - 7.08940i) q^{26} +3.91794 q^{27} +(-11.0748 - 1.04304i) q^{28} +1.64975 q^{29} +(1.95897 + 3.39304i) q^{30} +(1.17512 - 2.03538i) q^{31} +(-1.07031 + 1.85383i) q^{32} -3.71354 q^{34} +(3.37691 - 4.75523i) q^{35} -10.4726 q^{36} +(2.77733 + 4.81047i) q^{37} +(-8.61582 + 14.9230i) q^{38} +(1.17251 - 2.03084i) q^{39} +(-6.05203 - 10.4824i) q^{40} +11.2499 q^{41} +(-1.95897 - 4.27489i) q^{42} -5.26819 q^{43} +(2.74543 - 4.75523i) q^{45} +(-8.08393 + 14.0018i) q^{46} +(-0.745432 - 1.29113i) q^{47} -3.75905 q^{48} +(-4.57031 + 5.30210i) q^{49} -0.350250 q^{50} +(-0.531894 - 0.921267i) q^{51} +(-6.90880 + 11.9664i) q^{52} +(-0.152367 + 0.263908i) q^{53} +(-4.87953 - 8.45159i) q^{54} +(6.05203 + 13.2068i) q^{56} -4.93621 q^{57} +(-2.05465 - 3.55876i) q^{58} +(6.32936 - 10.9628i) q^{59} +(3.30660 - 5.72720i) q^{60} +(-6.49086 - 11.2425i) q^{61} -5.85415 q^{62} +(-3.81574 + 5.37317i) q^{63} -5.20440 q^{64} +(-3.62234 - 6.27408i) q^{65} +(2.28646 - 3.96027i) q^{67} +(3.13409 + 5.42841i) q^{68} -4.63148 q^{69} +(-14.4635 - 1.36219i) q^{70} +11.3267 q^{71} +(6.83850 + 11.8446i) q^{72} +(-4.28384 + 7.41984i) q^{73} +(6.91794 - 11.9822i) q^{74} +(-0.0501666 - 0.0868912i) q^{75} +29.0858 q^{76} -5.84111 q^{78} +(2.31574 + 4.01098i) q^{79} +(-5.80660 + 10.0573i) q^{80} +(-2.33850 + 4.05039i) q^{81} +(-14.0110 - 24.2678i) q^{82} +1.93621 q^{83} +(-4.59568 + 6.47145i) q^{84} -3.28646 q^{85} +(6.56117 + 11.3643i) q^{86} +(0.588580 - 1.01945i) q^{87} +(-1.60220 - 2.77509i) q^{89} -13.6770 q^{90} +(3.62234 + 7.90471i) q^{91} +27.2902 q^{92} +(-0.838496 - 1.45232i) q^{93} +(-1.85677 + 3.21602i) q^{94} +(-7.62496 + 13.2068i) q^{95} +(0.763705 + 1.32278i) q^{96} +1.85939 q^{97} +(17.1294 + 3.25544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} - 4 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8}+O(q^{10}) \) 6 * q + q^3 - 4 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8	\( 6 q + q^{3} - 4 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 9 q^{10} + 9 q^{12} + 22 q^{13} + 12 q^{14} - 14 q^{15} - 2 q^{16} - 3 q^{17} + 10 q^{18} - 11 q^{19} + 28 q^{20} - 10 q^{21} - 12 q^{23} + 2 q^{24} - 3 q^{25} - q^{26} + 4 q^{27} - 13 q^{28} + 18 q^{29} + 2 q^{30} + 3 q^{31} - 3 q^{32} - 20 q^{34} - 9 q^{35} - 18 q^{36} + 4 q^{37} - 8 q^{38} - 5 q^{39} - 3 q^{40} + 10 q^{41} - 2 q^{42} - 4 q^{43} + 9 q^{45} - 10 q^{46} + 3 q^{47} + 20 q^{48} - 24 q^{49} + 6 q^{50} + 2 q^{51} - 7 q^{52} - 17 q^{53} - 8 q^{54} + 3 q^{56} - 40 q^{57} + 13 q^{58} - 8 q^{59} - 6 q^{60} - 24 q^{61} - 26 q^{62} - 12 q^{63} - 14 q^{64} + 15 q^{65} + 16 q^{67} + 5 q^{68} - 6 q^{69} - 27 q^{70} + 14 q^{71} + 10 q^{72} - 20 q^{73} + 22 q^{74} - 25 q^{75} + 78 q^{76} - 12 q^{78} + 3 q^{79} - 9 q^{80} + 17 q^{81} - 41 q^{82} + 22 q^{83} - 12 q^{84} - 22 q^{85} + 21 q^{86} + 30 q^{87} - q^{89} - 20 q^{90} - 15 q^{91} + 50 q^{92} + 26 q^{93} - 10 q^{94} - 17 q^{95} + 27 q^{96} + 18 q^{97} + 24 q^{98}+O(q^{100}) \) 6 * q + q^3 - 4 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 9 * q^10 + 9 * q^12 + 22 * q^13 + 12 * q^14 - 14 * q^15 - 2 * q^16 - 3 * q^17 + 10 * q^18 - 11 * q^19 + 28 * q^20 - 10 * q^21 - 12 * q^23 + 2 * q^24 - 3 * q^25 - q^26 + 4 * q^27 - 13 * q^28 + 18 * q^29 + 2 * q^30 + 3 * q^31 - 3 * q^32 - 20 * q^34 - 9 * q^35 - 18 * q^36 + 4 * q^37 - 8 * q^38 - 5 * q^39 - 3 * q^40 + 10 * q^41 - 2 * q^42 - 4 * q^43 + 9 * q^45 - 10 * q^46 + 3 * q^47 + 20 * q^48 - 24 * q^49 + 6 * q^50 + 2 * q^51 - 7 * q^52 - 17 * q^53 - 8 * q^54 + 3 * q^56 - 40 * q^57 + 13 * q^58 - 8 * q^59 - 6 * q^60 - 24 * q^61 - 26 * q^62 - 12 * q^63 - 14 * q^64 + 15 * q^65 + 16 * q^67 + 5 * q^68 - 6 * q^69 - 27 * q^70 + 14 * q^71 + 10 * q^72 - 20 * q^73 + 22 * q^74 - 25 * q^75 + 78 * q^76 - 12 * q^78 + 3 * q^79 - 9 * q^80 + 17 * q^81 - 41 * q^82 + 22 * q^83 - 12 * q^84 - 22 * q^85 + 21 * q^86 + 30 * q^87 - q^89 - 20 * q^90 - 15 * q^91 + 50 * q^92 + 26 * q^93 - 10 * q^94 - 17 * q^95 + 27 * q^96 + 18 * q^97 + 24 * q^98

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