LMFDB - Embedded newform 462.2.w.a.239.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(29,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("462.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			239.5
Character	$\chi$	$=$	462.239
Dual form			462.2.w.a.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.911344 + 1.47291i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.04373 - 2.81296i) q^{5} +(-0.128460 - 1.72728i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.33891 - 2.68465i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.911344 + 1.47291i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.04373 - 2.81296i) q^{5} +(-0.128460 - 1.72728i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.33891 - 2.68465i) q^{9} +3.47700i q^{10} +(-2.97640 - 1.46323i) q^{11} +(1.11920 + 1.32189i) q^{12} +(-2.76587 - 3.80689i) q^{13} +(-0.951057 + 0.309017i) q^{14} +(2.28068 + 5.57379i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.89787 - 4.28505i) q^{17} +(2.66119 + 1.38494i) q^{18} +(-2.19110 + 0.711931i) q^{19} +(-2.04373 - 2.81296i) q^{20} +(-1.32189 + 1.11920i) q^{21} +(3.26802 - 0.565707i) q^{22} +0.430436i q^{23} +(-1.68244 - 0.411586i) q^{24} +(-2.19079 - 6.74257i) q^{25} +(4.47527 + 1.45410i) q^{26} +(5.17444 + 0.474553i) q^{27} +(0.587785 - 0.809017i) q^{28} +(-0.591869 + 1.82159i) q^{29} +(-5.12130 - 3.16875i) q^{30} +(-1.01888 + 0.740257i) q^{31} +1.00000 q^{32} +(4.86772 - 3.05045i) q^{33} +7.29017 q^{34} +(2.81296 - 2.04373i) q^{35} +(-2.96700 + 0.443773i) q^{36} +(0.840914 - 2.58807i) q^{37} +(1.35417 - 1.86386i) q^{38} +(8.12785 - 0.604479i) q^{39} +(3.30683 + 1.07445i) q^{40} +(2.21735 + 6.82429i) q^{41} +(0.411586 - 1.68244i) q^{42} -11.3359i q^{43} +(-2.31137 + 2.37856i) q^{44} +(-10.2882 - 1.72042i) q^{45} +(-0.253004 - 0.348230i) q^{46} +(10.3469 - 3.36191i) q^{47} +(1.60305 - 0.655932i) q^{48} +(0.809017 + 0.587785i) q^{49} +(5.73557 + 4.16714i) q^{50} +(11.6865 - 4.78186i) q^{51} +(-4.47527 + 1.45410i) q^{52} +(4.44566 + 6.11893i) q^{53} +(-4.46514 + 2.65754i) q^{54} +(-10.1990 + 5.38203i) q^{55} +1.00000i q^{56} +(0.948236 - 3.87610i) q^{57} +(-0.591869 - 1.82159i) q^{58} +(7.64560 + 2.48420i) q^{59} +(6.00576 - 0.446656i) q^{60} +(5.23127 - 7.20022i) q^{61} +(0.389176 - 1.19776i) q^{62} +(-0.443773 - 2.96700i) q^{63} +(-0.809017 + 0.587785i) q^{64} -16.3613 q^{65} +(-2.14506 + 5.32905i) q^{66} -3.79606 q^{67} +(-5.89787 + 4.28505i) q^{68} +(-0.633992 - 0.392275i) q^{69} +(-1.07445 + 3.30683i) q^{70} +(-8.84298 + 12.1713i) q^{71} +(2.13951 - 2.10298i) q^{72} +(0.238803 + 0.0775919i) q^{73} +(0.840914 + 2.58807i) q^{74} +(11.9277 + 2.91796i) q^{75} +2.30386i q^{76} +(-2.37856 - 2.31137i) q^{77} +(-6.22026 + 5.26646i) q^{78} +(4.38751 + 6.03889i) q^{79} +(-3.30683 + 1.07445i) q^{80} +(-5.41466 + 7.18898i) q^{81} +(-5.80509 - 4.21765i) q^{82} +(-12.9687 - 9.42229i) q^{83} +(0.655932 + 1.60305i) q^{84} +(-24.1073 + 7.83295i) q^{85} +(6.66306 + 9.17091i) q^{86} +(-2.14363 - 2.53186i) q^{87} +(0.471856 - 3.28289i) q^{88} -14.0143i q^{89} +(9.33453 - 4.65538i) q^{90} +(-1.45410 - 4.47527i) q^{91} +(0.409369 + 0.133012i) q^{92} +(-0.161783 - 2.17534i) q^{93} +(-6.39473 + 8.80159i) q^{94} +(-2.47539 + 7.61846i) q^{95} +(-0.911344 + 1.47291i) q^{96} +(3.63725 - 2.64262i) q^{97} -1.00000 q^{98} +(0.0568642 + 9.94971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) $ 48 * q - 12 * q^2 - 4 * q^3 - 12 * q^4 + 6 * q^6 - 12 * q^8 + 10 * q^9	$ 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9} - 8 q^{11} + 6 q^{12} + 36 q^{15} - 12 q^{16} - 24 q^{17} + 30 q^{19} - 8 q^{22} - 4 q^{24} + 18 q^{25} - 20 q^{26} - 22 q^{27} + 8 q^{29} - 24 q^{30} - 32 q^{31} + 48 q^{32} - 14 q^{33} - 4 q^{34} + 6 q^{35} - 10 q^{36} - 20 q^{37} + 20 q^{38} - 6 q^{39} + 22 q^{44} + 12 q^{45} + 20 q^{46} + 20 q^{47} - 4 q^{48} + 12 q^{49} + 28 q^{50} + 8 q^{51} + 20 q^{52} + 20 q^{53} + 18 q^{54} + 16 q^{55} - 2 q^{57} + 8 q^{58} + 30 q^{59} - 4 q^{60} - 20 q^{61} + 8 q^{62} + 4 q^{63} - 12 q^{64} - 14 q^{66} + 36 q^{67} - 24 q^{68} - 70 q^{69} - 4 q^{70} + 10 q^{72} - 20 q^{73} - 20 q^{74} - 30 q^{75} - 16 q^{77} - 16 q^{78} - 20 q^{79} + 26 q^{81} - 10 q^{82} - 46 q^{83} - 10 q^{84} + 10 q^{85} - 30 q^{86} + 8 q^{87} - 8 q^{88} - 38 q^{90} - 36 q^{91} + 10 q^{92} - 36 q^{93} + 50 q^{95} - 4 q^{96} - 2 q^{97} - 48 q^{98} + 70 q^{99}+O(q^{100}) $ 48 * q - 12 * q^2 - 4 * q^3 - 12 * q^4 + 6 * q^6 - 12 * q^8 + 10 * q^9 - 8 * q^11 + 6 * q^12 + 36 * q^15 - 12 * q^16 - 24 * q^17 + 30 * q^19 - 8 * q^22 - 4 * q^24 + 18 * q^25 - 20 * q^26 - 22 * q^27 + 8 * q^29 - 24 * q^30 - 32 * q^31 + 48 * q^32 - 14 * q^33 - 4 * q^34 + 6 * q^35 - 10 * q^36 - 20 * q^37 + 20 * q^38 - 6 * q^39 + 22 * q^44 + 12 * q^45 + 20 * q^46 + 20 * q^47 - 4 * q^48 + 12 * q^49 + 28 * q^50 + 8 * q^51 + 20 * q^52 + 20 * q^53 + 18 * q^54 + 16 * q^55 - 2 * q^57 + 8 * q^58 + 30 * q^59 - 4 * q^60 - 20 * q^61 + 8 * q^62 + 4 * q^63 - 12 * q^64 - 14 * q^66 + 36 * q^67 - 24 * q^68 - 70 * q^69 - 4 * q^70 + 10 * q^72 - 20 * q^73 - 20 * q^74 - 30 * q^75 - 16 * q^77 - 16 * q^78 - 20 * q^79 + 26 * q^81 - 10 * q^82 - 46 * q^83 - 10 * q^84 + 10 * q^85 - 30 * q^86 + 8 * q^87 - 8 * q^88 - 38 * q^90 - 36 * q^91 + 10 * q^92 - 36 * q^93 + 50 * q^95 - 4 * q^96 - 2 * q^97 - 48 * q^98 + 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.911344	+	1.47291i	−0.526164	+	0.850383i
$3$	−0.911344	+	1.47291i	−0.526164	+	0.850383i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.04373	−	2.81296i	0.913985	−	1.25799i	−0.0518030	−	0.998657i	$-0.516497\pi$
$5$	2.04373	−	2.81296i	0.913985	−	1.25799i	0.965788	−	0.259335i	$-0.0835032\pi$
$6$	−0.128460	−	1.72728i	−0.0524436	−	0.705159i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−1.33891	−	2.68465i	−0.446302	−	0.894882i
$10$			3.47700i			1.09953i
$11$	−2.97640	−	1.46323i	−0.897418	−	0.441180i
$11$	−2.97640	−	1.46323i	−0.897418	−	0.441180i
$12$	1.11920	+	1.32189i	0.323084	+	0.381597i
$13$	−2.76587	−	3.80689i	−0.767114	−	1.05584i	−0.996589	−	0.0825268i	$-0.973701\pi$
$13$	−2.76587	−	3.80689i	−0.767114	−	1.05584i	0.229475	−	0.973315i	$-0.426299\pi$
$14$	−0.951057	+	0.309017i	−0.254181	+	0.0825883i
$15$	2.28068	+	5.57379i	0.588868	+	1.43915i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−5.89787	−	4.28505i	−1.43044	−	1.03928i	−0.989934	−	0.141531i	$-0.954798\pi$
$17$	−5.89787	−	4.28505i	−1.43044	−	1.03928i	−0.440510	−	0.897748i	$-0.645202\pi$
$18$	2.66119	+	1.38494i	0.627249	+	0.326433i
$19$	−2.19110	+	0.711931i	−0.502672	+	0.163328i	−0.549367	−	0.835581i	$-0.685131\pi$
$19$	−2.19110	+	0.711931i	−0.502672	+	0.163328i	0.0466948	+	0.998909i	$0.485131\pi$
$20$	−2.04373	−	2.81296i	−0.456992	−	0.628996i
$21$	−1.32189	+	1.11920i	−0.288461	+	0.244229i
$22$	3.26802	−	0.565707i	0.696745	−	0.120609i
$23$			0.430436i			0.0897521i	0.998993	+	0.0448761i	$0.0142893\pi$
$23$			0.430436i			0.0897521i	−0.998993	+	0.0448761i	$0.985711\pi$
$24$	−1.68244	−	0.411586i	−0.343426	−	0.0840147i
$25$	−2.19079	−	6.74257i	−0.438159	−	1.34851i
$26$	4.47527	+	1.45410i	0.877672	+	0.285173i
$27$	5.17444	+	0.474553i	0.995821	+	0.0913279i
$28$	0.587785	−	0.809017i	0.111081	−	0.152890i
$29$	−0.591869	+	1.82159i	−0.109907	+	0.338260i	−0.990851	−	0.134961i	$-0.956909\pi$
$29$	−0.591869	+	1.82159i	−0.109907	+	0.338260i	0.880944	+	0.473221i	$0.156909\pi$
$30$	−5.12130	−	3.16875i	−0.935017	−	0.578531i
$31$	−1.01888	+	0.740257i	−0.182996	+	0.132954i	−0.675512	−	0.737349i	$-0.736077\pi$
$31$	−1.01888	+	0.740257i	−0.182996	+	0.132954i	0.492516	+	0.870303i	$0.336077\pi$
$32$	1.00000			0.176777
$33$	4.86772	−	3.05045i	0.847362	−	0.531016i
$34$	7.29017			1.25025
$35$	2.81296	−	2.04373i	0.475476	−	0.345454i
$36$	−2.96700	+	0.443773i	−0.494499	+	0.0739622i
$37$	0.840914	−	2.58807i	0.138245	−	0.425476i	−0.857835	−	0.513925i	$-0.828191\pi$
$37$	0.840914	−	2.58807i	0.138245	−	0.425476i	0.996081	+	0.0884491i	$0.0281910\pi$
$38$	1.35417	−	1.86386i	0.219676	−	0.302358i
$39$	8.12785	−	0.604479i	1.30150	−	0.0967941i
$40$	3.30683	+	1.07445i	0.522855	+	0.169886i
$41$	2.21735	+	6.82429i	0.346291	+	1.06578i	0.960889	+	0.276935i	$0.0893185\pi$
$41$	2.21735	+	6.82429i	0.346291	+	1.06578i	−0.614597	+	0.788841i	$0.710681\pi$
$42$	0.411586	−	1.68244i	0.0635091	−	0.259606i
$43$		−	11.3359i		−	1.72870i	−0.502888	−	0.864352i	$-0.667729\pi$
$43$		−	11.3359i		−	1.72870i	0.502888	−	0.864352i	$-0.332271\pi$
$44$	−2.31137	+	2.37856i	−0.348452	+	0.358582i
$45$	−10.2882	−	1.72042i	−1.53367	−	0.256465i
$46$	−0.253004	−	0.348230i	−0.0373034	−	0.0513437i
$47$	10.3469	−	3.36191i	1.50925	−	0.490385i	0.566550	−	0.824027i	$-0.308278\pi$
$47$	10.3469	−	3.36191i	1.50925	−	0.490385i	0.942700	+	0.333642i	$0.108278\pi$
$48$	1.60305	−	0.655932i	0.231380	−	0.0946756i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	5.73557	+	4.16714i	0.811132	+	0.589322i
$51$	11.6865	−	4.78186i	1.63643	−	0.669594i
$52$	−4.47527	+	1.45410i	−0.620608	+	0.201648i
$53$	4.44566	+	6.11893i	0.610659	+	0.840499i	0.996631	−	0.0820107i	$-0.0261342\pi$
$53$	4.44566	+	6.11893i	0.610659	+	0.840499i	−0.385973	+	0.922510i	$0.626134\pi$
$54$	−4.46514	+	2.65754i	−0.607629	+	0.361645i
$55$	−10.1990	+	5.38203i	−1.37523	+	0.725713i
$56$			1.00000i			0.133631i
$57$	0.948236	−	3.87610i	0.125597	−	0.513401i
$58$	−0.591869	−	1.82159i	−0.0777162	−	0.239186i
$59$	7.64560	+	2.48420i	0.995372	+	0.323416i	0.761015	−	0.648735i	$-0.224701\pi$
$59$	7.64560	+	2.48420i	0.995372	+	0.323416i	0.234357	+	0.972151i	$0.424701\pi$
$60$	6.00576	−	0.446656i	0.775340	−	0.0576631i
$61$	5.23127	−	7.20022i	0.669795	−	0.921894i	−0.329961	−	0.943995i	$-0.607036\pi$
$61$	5.23127	−	7.20022i	0.669795	−	0.921894i	0.999756	+	0.0221009i	$0.00703550\pi$
$62$	0.389176	−	1.19776i	0.0494254	−	0.152116i
$63$	−0.443773	−	2.96700i	−0.0559102	−	0.373806i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−16.3613			−2.02937
$66$	−2.14506	+	5.32905i	−0.264039	+	0.655960i
$67$	−3.79606			−0.463762			−0.231881	−	0.972744i	$-0.574488\pi$
$67$	−3.79606			−0.463762			−0.231881	+	0.972744i	$0.574488\pi$
$68$	−5.89787	+	4.28505i	−0.715222	+	0.519639i
$69$	−0.633992	−	0.392275i	−0.0763237	−	0.0472244i
$70$	−1.07445	+	3.30683i	−0.128422	+	0.395241i
$71$	−8.84298	+	12.1713i	−1.04947	+	1.44447i	−0.160201	+	0.987084i	$0.551214\pi$
$71$	−8.84298	+	12.1713i	−1.04947	+	1.44447i	−0.889268	+	0.457386i	$0.848786\pi$
$72$	2.13951	−	2.10298i	0.252143	−	0.247838i
$73$	0.238803	+	0.0775919i	0.0279498	+	0.00908145i	0.322959	−	0.946413i	$-0.395323\pi$
$73$	0.238803	+	0.0775919i	0.0279498	+	0.00908145i	−0.295009	+	0.955495i	$0.595323\pi$
$74$	0.840914	+	2.58807i	0.0977543	+	0.300857i
$75$	11.9277	+	2.91796i	1.37730	+	0.336937i
$76$			2.30386i			0.264270i
$77$	−2.37856	−	2.31137i	−0.271062	−	0.263405i
$78$	−6.22026	+	5.26646i	−0.704306	+	0.596309i
$79$	4.38751	+	6.03889i	0.493633	+	0.679428i	0.981053	−	0.193740i	$-0.0620618\pi$
$79$	4.38751	+	6.03889i	0.493633	+	0.679428i	−0.487420	+	0.873168i	$0.662062\pi$
$80$	−3.30683	+	1.07445i	−0.369715	+	0.120128i
$81$	−5.41466	+	7.18898i	−0.601629	+	0.798776i
$82$	−5.80509	−	4.21765i	−0.641065	−	0.465761i
$83$	−12.9687	−	9.42229i	−1.42350	−	1.03423i	−0.991182	−	0.132508i	$-0.957697\pi$
$83$	−12.9687	−	9.42229i	−1.42350	−	1.03423i	−0.432315	−	0.901723i	$-0.642303\pi$
$84$	0.655932	+	1.60305i	0.0715680	+	0.174907i
$85$	−24.1073	+	7.83295i	−2.61481	+	0.849602i
$86$	6.66306	+	9.17091i	0.718496	+	0.988925i
$87$	−2.14363	−	2.53186i	−0.229821	−	0.271444i
$88$	0.471856	−	3.28289i	0.0503000	−	0.349957i
$89$		−	14.0143i		−	1.48551i	−0.669562	−	0.742756i	$-0.733518\pi$
$89$		−	14.0143i		−	1.48551i	0.669562	−	0.742756i	$-0.266482\pi$
$90$	9.33453	−	4.65538i	0.983946	−	0.490720i
$91$	−1.45410	−	4.47527i	−0.152431	−	0.469136i
$92$	0.409369	+	0.133012i	0.0426797	+	0.0138675i
$93$	−0.161783	−	2.17534i	−0.0167761	−	0.225572i
$94$	−6.39473	+	8.80159i	−0.659566	+	0.907815i
$95$	−2.47539	+	7.61846i	−0.253969	+	0.781637i
$96$	−0.911344	+	1.47291i	−0.0930136	+	0.150328i
$97$	3.63725	−	2.64262i	0.369307	−	0.268317i	−0.387617	−	0.921821i	$-0.626702\pi$
$97$	3.63725	−	2.64262i	0.369307	−	0.268317i	0.756923	+	0.653504i	$0.226702\pi$
$98$	−1.00000			−0.101015
$99$	0.0568642	+	9.94971i	0.00571507	+	0.999984i
$100$	−7.08956			−0.708956
$101$	3.07121	−	2.23137i	0.305597	−	0.222029i	−0.424408	−	0.905471i	$-0.639518\pi$
$101$	3.07121	−	2.23137i	0.305597	−	0.222029i	0.730005	+	0.683442i	$0.239518\pi$
$102$	−6.64385	+	10.7377i	−0.657839	+	1.06319i
$103$	1.71131	−	5.26688i	0.168621	−	0.518961i	−0.830664	−	0.556774i	$-0.812039\pi$
$103$	1.71131	−	5.26688i	0.168621	−	0.518961i	0.999285	+	0.0378128i	$0.0120391\pi$
$104$	2.76587	−	3.80689i	0.271216	−	0.373296i
$105$	0.446656	+	6.00576i	0.0435892	+	0.586102i
$106$	−7.19323	−	2.33722i	−0.698668	−	0.227011i
$107$	3.41117	+	10.4985i	0.329771	+	1.01493i	0.969241	+	0.246114i	$0.0791537\pi$
$107$	3.41117	+	10.4985i	0.329771	+	1.01493i	−0.639470	+	0.768816i	$0.720846\pi$
$108$	2.05032	−	4.77454i	0.197292	−	0.459430i
$109$			8.16265i			0.781840i	0.920425	+	0.390920i	$0.127843\pi$
$109$			8.16265i			0.781840i	−0.920425	+	0.390920i	$0.872157\pi$
$110$	5.08766	−	10.3490i	0.485089	−	0.986734i
$111$	3.04562	+	3.59721i	0.289077	+	0.341432i
$112$	−0.587785	−	0.809017i	−0.0555405	−	0.0764449i
$113$	6.92308	−	2.24945i	0.651269	−	0.211610i	0.0352953	−	0.999377i	$-0.488763\pi$
$113$	6.92308	−	2.24945i	0.651269	−	0.211610i	0.615974	+	0.787767i	$0.288763\pi$
$114$	1.51117	+	3.69319i	0.141534	+	0.345899i
$115$	1.21080	+	0.879696i	0.112907	+	0.0820321i
$116$	1.54953	+	1.12580i	0.143871	+	0.104528i
$117$	−6.51692	+	12.5224i	−0.602490	+	1.15770i
$118$	−7.64560	+	2.48420i	−0.703834	+	0.228690i
$119$	−4.28505	−	5.89787i	−0.392810	−	0.540657i
$120$	−4.59622	+	3.89145i	−0.419576	+	0.355239i
$121$	6.71792	+	8.71031i	0.610720	+	0.791847i
$122$			8.89996i			0.805765i
$123$	−12.0723	−	2.95333i	−1.08852	−	0.266293i
$124$	0.389176	+	1.19776i	0.0349490	+	0.107562i
$125$	−6.90980	−	2.24513i	−0.618032	−	0.200811i
$126$	2.10298	+	2.13951i	0.187348	+	0.190602i
$127$	−1.55587	+	2.14147i	−0.138061	+	0.190025i	−0.872449	−	0.488705i	$-0.837469\pi$
$127$	−1.55587	+	2.14147i	−0.138061	+	0.190025i	0.734388	+	0.678730i	$0.237469\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	16.6967	+	10.3309i	1.47006	+	0.909582i
$130$	13.2366	−	9.61693i	1.16092	−	0.843461i
$131$	4.57260			0.399510			0.199755	−	0.979846i	$-0.435985\pi$
$131$	4.57260			0.399510			0.199755	+	0.979846i	$0.435985\pi$
$132$	−1.39694	−	5.57212i	−0.121588	−	0.484991i
$133$	−2.30386			−0.199770
$134$	3.07107	−	2.23127i	0.265300	−	0.192752i
$135$	11.9101	−	13.5856i	1.02505	−	1.16926i
$136$	2.25279	−	6.93336i	0.193175	−	0.594531i
$137$	9.34209	−	12.8583i	0.798149	−	1.09856i	−0.194897	−	0.980824i	$-0.562437\pi$
$137$	9.34209	−	12.8583i	0.798149	−	1.09856i	0.993045	−	0.117734i	$-0.0375629\pi$
$138$	0.743484	−	0.0552939i	0.0632896	−	0.00470693i
$139$	11.0082	+	3.57678i	0.933702	+	0.303378i	0.736076	−	0.676899i	$-0.236677\pi$
$139$	11.0082	+	3.57678i	0.933702	+	0.303378i	0.197627	+	0.980277i	$0.436677\pi$
$140$	−1.07445	−	3.30683i	−0.0908079	−	0.279478i
$141$	−4.47780	+	18.3039i	−0.377099	+	1.54146i
$142$		−	15.0446i		−	1.26251i
$143$	2.66198	+	15.3779i	0.222606	+	1.28597i
$144$	−0.494799	+	2.95891i	−0.0412332	+	0.246576i
$145$	3.91442	+	5.38773i	0.325075	+	0.447427i
$146$	−0.238803	+	0.0775919i	−0.0197635	+	0.00642155i
$147$	−1.60305	+	0.655932i	−0.132217	+	0.0541004i
$148$	−2.20154	−	1.59951i	−0.180966	−	0.131479i
$149$	0.621116	+	0.451267i	0.0508838	+	0.0369692i	0.612936	−	0.790132i	$-0.289988\pi$
$149$	0.621116	+	0.451267i	0.0508838	+	0.0369692i	−0.562053	+	0.827101i	$0.689988\pi$
$150$	−11.3649	+	4.65027i	−0.927938	+	0.379693i
$151$	−6.94425	+	2.25632i	−0.565115	+	0.183617i	−0.577621	−	0.816305i	$-0.696019\pi$
$151$	−6.94425	+	2.25632i	−0.565115	+	0.183617i	0.0125065	+	0.999922i	$0.496019\pi$
$152$	−1.35417	−	1.86386i	−0.109838	−	0.151179i
$153$	−3.60717	+	21.5710i	−0.291622	+	1.74391i
$154$	3.28289	+	0.471856i	0.264543	+	0.0380232i
$155$			4.37894i			0.351725i
$156$	1.93675	−	7.91684i	0.155064	−	0.633854i
$157$	−3.21682	−	9.90035i	−0.256730	−	0.790134i	−0.993484	−	0.113973i	$-0.963642\pi$
$157$	−3.21682	−	9.90035i	−0.256730	−	0.790134i	0.736754	−	0.676161i	$-0.236358\pi$
$158$	−7.09914	−	2.30665i	−0.564777	−	0.183507i
$159$	−13.0641	+	0.971597i	−1.03605	+	0.0770526i
$160$	2.04373	−	2.81296i	0.161571	−	0.222384i
$161$	−0.133012	+	0.409369i	−0.0104828	+	0.0322628i
$162$	0.154978	−	8.99867i	0.0121762	−	0.707002i
$163$	11.3183	−	8.22324i	0.886519	−	0.644094i	−0.0484489	−	0.998826i	$-0.515428\pi$
$163$	11.3183	−	8.22324i	0.886519	−	0.644094i	0.934968	+	0.354732i	$0.115428\pi$
$164$	7.17549			0.560311
$165$	1.36753	−	19.9270i	0.106462	−	1.55131i
$166$	16.0302			1.24418
$167$	7.74189	−	5.62481i	0.599085	−	0.435261i	−0.246469	−	0.969151i	$-0.579270\pi$
$167$	7.74189	−	5.62481i	0.599085	−	0.435261i	0.845554	+	0.533890i	$0.179270\pi$
$168$	−1.47291	−	0.911344i	−0.113637	−	0.0703117i
$169$	−2.82517	+	8.69497i	−0.217321	+	0.668844i
$170$	14.8992	−	20.5069i	1.14271	−	1.57281i
$171$	4.84496	+	4.92912i	0.370503	+	0.376939i
$172$	−10.7811	−	3.50298i	−0.822047	−	0.267099i
$173$	−4.67855	−	14.3991i	−0.355704	−	1.09474i	−0.955600	−	0.294666i	$-0.904792\pi$
$173$	−4.67855	−	14.3991i	−0.355704	−	1.09474i	0.599896	−	0.800078i	$-0.295208\pi$
$174$	3.22242	+	0.788323i	0.244291	+	0.0597626i
$175$		−	7.08956i		−	0.535920i
$176$	1.54789	+	2.93326i	0.116677	+	0.221103i
$177$	−10.6268	+	8.99728i	−0.798757	+	0.676277i
$178$	8.23739	+	11.3378i	0.617419	+	0.849804i
$179$	1.99067	−	0.646807i	0.148789	−	0.0483446i	−0.233675	−	0.972315i	$-0.575075\pi$
$179$	1.99067	−	0.646807i	0.148789	−	0.0483446i	0.382465	+	0.923970i	$0.375075\pi$
$180$	−4.81543	+	9.25298i	−0.358921	+	0.689676i
$181$	−6.35936	−	4.62035i	−0.472687	−	0.343428i	0.325800	−	0.945439i	$-0.394366\pi$
$181$	−6.35936	−	4.62035i	−0.472687	−	0.343428i	−0.798488	+	0.602011i	$0.794366\pi$
$182$	3.80689	+	2.76587i	0.282185	+	0.205020i
$183$	5.83777	+	14.2670i	0.431540	+	1.05465i
$184$	−0.409369	+	0.133012i	−0.0301791	+	0.00980578i
$185$	−5.56152	−	7.65477i	−0.408891	−	0.562790i
$186$	1.40952	+	1.66479i	0.103351	+	0.122068i
$187$	11.2844	+	21.3840i	0.825198	+	1.56375i
$188$		−	10.8794i		−	0.793460i
$189$	4.77454	+	2.05032i	0.347296	+	0.149139i
$190$	−2.47539	−	7.61846i	−0.179583	−	0.552701i
$191$	−14.2728	−	4.63750i	−1.03274	−	0.335558i	−0.256867	−	0.966447i	$-0.582690\pi$
$191$	−14.2728	−	4.63750i	−1.03274	−	0.335558i	−0.775873	+	0.630889i	$0.782690\pi$
$192$	−0.128460	−	1.72728i	−0.00927081	−	0.124656i
$193$	−13.6774	+	18.8253i	−0.984521	+	1.35508i	−0.0501637	+	0.998741i	$0.515974\pi$
$193$	−13.6774	+	18.8253i	−0.984521	+	1.35508i	−0.934358	+	0.356336i	$0.884026\pi$
$194$	−1.38931	+	4.27585i	−0.0997464	+	0.306988i
$195$	14.9108	−	24.0987i	1.06778	−	1.72574i
$196$	0.809017	−	0.587785i	0.0577869	−	0.0419847i
$197$	−11.5478			−0.822743			−0.411372	−	0.911468i	$-0.634950\pi$
$197$	−11.5478			−0.822743			−0.411372	+	0.911468i	$0.634950\pi$
$198$	−5.89430	−	8.01606i	−0.418890	−	0.569677i
$199$	2.17863			0.154439			0.0772196	−	0.997014i	$-0.475396\pi$
$199$	2.17863			0.154439			0.0772196	+	0.997014i	$0.475396\pi$
$200$	5.73557	−	4.16714i	0.405566	−	0.294661i
$201$	3.45951	−	5.59123i	0.244015	−	0.394375i
$202$	−1.17310	+	3.61043i	−0.0825390	+	0.254029i
$203$	−1.12580	+	1.54953i	−0.0790158	+	0.108756i
$204$	−0.936496	−	12.5922i	−0.0655679	−	0.881628i
$205$	23.7281	+	7.70973i	1.65724	+	0.538471i
$206$	1.71131	+	5.26688i	0.119233	+	0.366961i
$207$	1.15557	−	0.576313i	0.0803176	−	0.0400566i
$208$			4.70557i			0.326273i
$209$	7.56330	+	1.08709i	0.523165	+	0.0751954i
$210$	−3.89145	−	4.59622i	−0.268536	−	0.317170i
$211$	−11.2182	−	15.4405i	−0.772290	−	1.06297i	−0.996091	−	0.0883315i	$-0.971847\pi$
$211$	−11.2182	−	15.4405i	−0.772290	−	1.06297i	0.223801	−	0.974635i	$-0.428153\pi$
$212$	7.19323	−	2.33722i	0.494033	−	0.160521i
$213$	−9.86822	−	24.1171i	−0.676159	−	1.65248i
$214$	−8.93057	−	6.48844i	−0.610481	−	0.443541i
$215$	−31.8873	−	23.1675i	−2.17470	−	1.58001i
$216$	1.14766	+	5.06783i	0.0780885	+	0.344822i
$217$	−1.19776	+	0.389176i	−0.0813093	+	0.0264190i
$218$	−4.79789	−	6.60372i	−0.324954	−	0.447261i
$219$	−0.331918	+	0.281022i	−0.0224289	+	0.0189897i
$220$	1.96696	+	11.3629i	0.132613	+	0.766089i
$221$			34.3044i			2.30757i
$222$	−4.57834	−	1.12003i	−0.307278	−	0.0751716i
$223$	1.70015	+	5.23252i	0.113850	+	0.350395i	0.991706	−	0.128531i	$-0.0410262\pi$
$223$	1.70015	+	5.23252i	0.113850	+	0.350395i	−0.877855	+	0.478926i	$0.841026\pi$
$224$	0.951057	+	0.309017i	0.0635451	+	0.0206471i
$225$	−15.1682	+	14.9092i	−1.01121	+	0.993945i
$226$	−4.27870	+	5.88913i	−0.284615	+	0.391739i
$227$	−5.15058	+	15.8519i	−0.341856	+	1.05213i	0.621389	+	0.783502i	$0.286569\pi$
$227$	−5.15058	+	15.8519i	−0.341856	+	1.05213i	−0.963245	+	0.268623i	$0.913431\pi$
$228$	−3.39337	−	2.09961i	−0.224731	−	0.139050i
$229$	16.0183	−	11.6380i	1.05852	−	0.769060i	0.0847066	−	0.996406i	$-0.473005\pi$
$229$	16.0183	−	11.6380i	1.05852	−	0.769060i	0.973814	+	0.227346i	$0.0730047\pi$
$230$	−1.49663			−0.0986847
$231$	5.57212	−	1.39694i	0.366619	−	0.0919122i
$232$	−1.91533			−0.125747
$233$	−0.760078	+	0.552229i	−0.0497944	+	0.0361777i	−0.612404	−	0.790545i	$-0.709797\pi$
$233$	−0.760078	+	0.552229i	−0.0497944	+	0.0361777i	0.562610	+	0.826723i	$0.309797\pi$
$234$	−2.08821	−	13.9614i	−0.136510	−	0.912687i
$235$	11.6894	−	35.9762i	0.762531	−	2.34683i
$236$	4.72524	−	6.50373i	0.307587	−	0.423357i
$237$	−12.8932	+	0.958888i	−0.837506	+	0.0622864i
$238$	6.93336	+	2.25279i	0.449423	+	0.146026i
$239$	0.403177	+	1.24085i	0.0260793	+	0.0802639i	0.963249	−	0.268610i	$-0.0865642\pi$
$239$	0.403177	+	1.24085i	0.0260793	+	0.0802639i	−0.937170	+	0.348874i	$0.886564\pi$
$240$	1.43109	−	5.84984i	0.0923763	−	0.377606i
$241$			16.3202i			1.05128i	0.850709	+	0.525638i	$0.176173\pi$
$241$			16.3202i			1.05128i	−0.850709	+	0.525638i	$0.823827\pi$
$242$	−10.5547	−	3.09810i	−0.678482	−	0.199153i
$243$	−5.65407	−	14.5269i	−0.362709	−	0.931902i
$244$	−5.23127	−	7.20022i	−0.334898	−	0.460947i
$245$	3.30683	−	1.07445i	0.211265	−	0.0686443i
$246$	11.5026	−	4.70663i	0.733381	−	0.300084i
$247$	8.77053	+	6.37216i	0.558055	+	0.405451i
$248$	−1.01888	−	0.740257i	−0.0646987	−	0.0470064i
$249$	25.6971	−	10.5147i	1.62849	−	0.666342i
$250$	6.90980	−	2.24513i	0.437014	−	0.141995i
$251$	10.5125	+	14.4692i	0.663544	+	0.913291i	0.999592	−	0.0285543i	$-0.00909036\pi$
$251$	10.5125	+	14.4692i	0.663544	+	0.913291i	−0.336048	+	0.941845i	$0.609090\pi$
$252$	−2.95891	−	0.494799i	−0.186394	−	0.0311694i
$253$	0.629827	−	1.28115i	0.0395969	−	0.0805452i
$254$		−	2.64700i		−	0.166088i
$255$	10.4329	−	42.6464i	0.653331	−	2.67062i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−7.21157	−	2.34318i	−0.449846	−	0.146164i	0.0753280	−	0.997159i	$-0.476000\pi$
$257$	−7.21157	−	2.34318i	−0.449846	−	0.146164i	−0.525174	+	0.850995i	$0.676000\pi$
$258$	−19.5802	+	1.45621i	−1.21901	+	0.0906595i
$259$	1.59951	−	2.20154i	0.0993889	−	0.136797i
$260$	−5.05592	+	15.5605i	−0.313555	+	0.965023i
$261$	5.68277	−	0.849972i	0.351755	−	0.0526119i
$262$	−3.69931	+	2.68771i	−0.228544	+	0.166047i
$263$	−1.81575			−0.111964			−0.0559821	−	0.998432i	$-0.517829\pi$
$263$	−1.81575			−0.111964			−0.0559821	+	0.998432i	$0.517829\pi$
$264$	4.40536	+	3.68684i	0.271131	+	0.226909i
$265$	26.2980			1.61547
$266$	1.86386	−	1.35417i	0.114281	−	0.0830297i
$267$	20.6417	+	12.7718i	1.26325	+	0.781624i
$268$	−1.17305	+	3.61026i	−0.0716552	+	0.220532i
$269$	13.1502	−	18.0997i	0.801783	−	1.10356i	−0.190757	−	0.981637i	$-0.561094\pi$
$269$	13.1502	−	18.0997i	0.801783	−	1.10356i	0.992540	−	0.121922i	$-0.0389057\pi$
$270$	−1.65002	+	17.9915i	−0.100417	+	1.09493i
$271$	−16.5899	−	5.39039i	−1.00777	−	0.327443i	−0.241802	−	0.970326i	$-0.577738\pi$
$271$	−16.5899	−	5.39039i	−1.00777	−	0.327443i	−0.765965	+	0.642883i	$0.777738\pi$
$272$	2.25279	+	6.93336i	0.136595	+	0.420397i
$273$	7.91684	+	1.93675i	0.479149	+	0.117217i
$274$			15.8937i			0.960174i
$275$	−3.34525	+	23.2742i	−0.201726	+	1.40349i
$276$	−0.568990	+	0.481743i	−0.0342492	+	0.0289975i
$277$	9.05405	+	12.4618i	0.544005	+	0.748759i	0.989184	−	0.146683i	$-0.0468597\pi$
$277$	9.05405	+	12.4618i	0.544005	+	0.748759i	−0.445178	+	0.895442i	$0.646860\pi$
$278$	−11.0082	+	3.57678i	−0.660227	+	0.214521i
$279$	3.35151	+	1.74419i	0.200650	+	0.104422i
$280$	2.81296	+	2.04373i	0.168106	+	0.122136i
$281$	−12.3306	−	8.95874i	−0.735585	−	0.534433i	0.155741	−	0.987798i	$-0.450224\pi$
$281$	−12.3306	−	8.95874i	−0.735585	−	0.534433i	−0.891325	+	0.453364i	$0.850224\pi$
$282$	−7.13613	−	17.4401i	−0.424950	−	1.03854i
$283$	12.9352	−	4.20290i	0.768918	−	0.249837i	0.101816	−	0.994803i	$-0.467535\pi$
$283$	12.9352	−	4.20290i	0.768918	−	0.249837i	0.667102	+	0.744967i	$0.267535\pi$
$284$	8.84298	+	12.1713i	0.524735	+	0.722235i
$285$	−8.96534	−	10.5890i	−0.531061	−	0.627241i
$286$	−11.1925	−	10.8763i	−0.661827	−	0.643131i
$287$			7.17549i			0.423556i
$288$	−1.33891	−	2.68465i	−0.0788958	−	0.158194i
$289$	11.1699	+	34.3774i	0.657053	+	2.02220i
$290$	−6.33366	−	2.05793i	−0.371925	−	0.120846i
$291$	0.577543	+	7.76566i	0.0338562	+	0.455231i
$292$	0.147589	−	0.203138i	0.00863697	−	0.0118878i
$293$	5.12208	−	15.7642i	0.299235	−	0.920952i	−0.682531	−	0.730857i	$-0.739121\pi$
$293$	5.12208	−	15.7642i	0.299235	−	0.920952i	0.981766	−	0.190094i	$-0.0608794\pi$
$294$	0.911344	−	1.47291i	0.0531506	−	0.0859016i
$295$	22.6135	−	16.4297i	1.31661	−	0.956572i
$296$	2.72126			0.158170
$297$	−14.7068	−	8.98385i	−0.853376	−	0.521296i
$298$	−0.767741			−0.0444741
$299$	1.63862	−	1.19053i	0.0947640	−	0.0688501i
$300$	6.46102	−	10.4423i	0.373027	−	0.602884i
$301$	3.50298	−	10.7811i	0.201908	−	0.621409i
$302$	4.29178	−	5.90713i	0.246964	−	0.339917i
$303$	0.487664	+	6.55715i	0.0280156	+	0.376698i
$304$	2.19110	+	0.711931i	0.125668	+	0.0408320i
$305$	−9.56259	−	29.4306i	−0.547553	−	1.68519i
$306$	−9.76085	−	19.5715i	−0.557991	−	1.11883i
$307$		−	25.1222i		−	1.43380i	−0.697176	−	0.716900i	$-0.745560\pi$
$307$		−	25.1222i		−	1.43380i	0.697176	−	0.716900i	$-0.254440\pi$
$308$	−2.93326	+	1.54789i	−0.167138	+	0.0881994i
$309$	6.19802	+	7.32054i	0.352593	+	0.416451i
$310$	−2.57388	−	3.54264i	−0.146186	−	0.201208i
$311$	−5.25510	+	1.70749i	−0.297990	+	0.0968227i	−0.454196	−	0.890902i	$-0.650073\pi$
$311$	−5.25510	+	1.70749i	−0.297990	+	0.0968227i	0.156207	+	0.987724i	$0.450073\pi$
$312$	3.08654	+	7.54325i	0.174741	+	0.427052i
$313$	−25.6773	−	18.6557i	−1.45137	−	1.05448i	−0.985509	−	0.169621i	$-0.945746\pi$
$313$	−25.6773	−	18.6557i	−1.45137	−	1.05448i	−0.465859	−	0.884859i	$-0.654254\pi$
$314$	8.42174	+	6.11875i	0.475266	+	0.345301i
$315$	−9.25298	−	4.81543i	−0.521346	−	0.271319i
$316$	7.09914	−	2.30665i	0.399358	−	0.129759i
$317$	−3.60469	−	4.96143i	−0.202459	−	0.278662i	0.695699	−	0.718333i	$-0.255095\pi$
$317$	−3.60469	−	4.96143i	−0.202459	−	0.278662i	−0.898158	+	0.439672i	$0.855095\pi$
$318$	9.99801	−	8.46494i	0.560661	−	0.474690i
$319$	4.42704	−	4.55573i	0.247866	−	0.255072i
$320$			3.47700i			0.194370i
$321$	−18.5721	−	4.54341i	−1.03659	−	0.253589i
$322$	−0.133012	−	0.409369i	−0.00741247	−	0.0228132i
$323$	15.9735	+	5.19010i	0.888788	+	0.288785i
$324$	5.16390	+	7.37117i	0.286884	+	0.409509i
$325$	−19.6088	+	26.9892i	−1.08770	+	1.49709i
$326$	−4.32321	+	13.3055i	−0.239441	+	0.736923i
$327$	−12.0228	−	7.43898i	−0.664863	−	0.411376i
$328$	−5.80509	+	4.21765i	−0.320533	+	0.232881i
$329$	10.8794			0.599799
$330$	10.6064	+	16.9251i	0.583865	+	0.931696i
$331$	−22.4313			−1.23293			−0.616467	−	0.787381i	$-0.711437\pi$
$331$	−22.4313			−1.23293			−0.616467	+	0.787381i	$0.711437\pi$
$332$	−12.9687	+	9.42229i	−0.711748	+	0.517115i
$333$	−8.07395	+	1.20762i	−0.442450	+	0.0661772i
$334$	−2.95714	+	9.10113i	−0.161807	+	0.497992i
$335$	−7.75812	+	10.6781i	−0.423871	+	0.583409i
$336$	1.72728	−	0.128460i	0.0942309	−	0.00700808i
$337$	−4.91450	−	1.59682i	−0.267710	−	0.0869842i	0.172086	−	0.985082i	$-0.444949\pi$
$337$	−4.91450	−	1.59682i	−0.267710	−	0.0869842i	−0.439796	+	0.898098i	$0.644949\pi$
$338$	−2.82517	−	8.69497i	−0.153669	−	0.472944i
$339$	−2.99608	+	12.2471i	−0.162725	+	0.665170i
$340$			25.3480i			1.37469i
$341$	4.11575	−	0.712451i	0.222880	−	0.0385814i
$342$	−6.81691	−	1.13995i	−0.368617	−	0.0616412i
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	10.7811	−	3.50298i	0.581275	−	0.188868i
$345$	−2.39916	+	0.981686i	−0.129167	+	0.0528522i
$346$	12.2486	+	8.89914i	0.658490	+	0.478421i
$347$	6.31587	+	4.58875i	0.339054	+	0.246337i	0.744263	−	0.667887i	$-0.232801\pi$
$347$	6.31587	+	4.58875i	0.339054	+	0.246337i	−0.405209	+	0.914224i	$0.632801\pi$
$348$	−3.07036	+	1.25632i	−0.164588	+	0.0673461i
$349$	27.4437	−	8.91700i	1.46903	−	0.477316i	0.538213	−	0.842809i	$-0.319099\pi$
$349$	27.4437	−	8.91700i	1.46903	−	0.477316i	0.930814	+	0.365493i	$0.119099\pi$
$350$	4.16714	+	5.73557i	0.222743	+	0.306579i
$351$	−12.5052	−	21.0111i	−0.667480	−	1.12149i
$352$	−2.97640	−	1.46323i	−0.158643	−	0.0779904i
$353$			14.0181i			0.746110i	0.927809	+	0.373055i	$0.121690\pi$
$353$			14.0181i			0.746110i	−0.927809	+	0.373055i	$0.878310\pi$
$354$	3.30876	−	13.5252i	0.175859	−	0.718857i
$355$	16.1647	+	49.7498i	0.857933	+	2.64045i
$356$	−13.3284	−	4.33065i	−0.706403	−	0.229524i
$357$	12.5922	−	0.936496i	0.666448	−	0.0495646i
$358$	−1.23030	+	1.69336i	−0.0650234	+	0.0894970i
$359$	3.56032	−	10.9575i	0.187906	−	0.578317i	−0.812080	−	0.583546i	$-0.801665\pi$
$359$	3.56032	−	10.9575i	0.187906	−	0.578317i	0.999986	+	0.00522975i	$0.00166469\pi$
$360$	−1.54300	−	10.3163i	−0.0813233	−	0.543714i
$361$	−11.0773	+	8.04810i	−0.583014	+	0.423584i
$362$	7.86060			0.413144
$363$	−18.9518	+	1.95678i	−0.994712	+	0.102704i
$364$	−4.70557			−0.246639
$365$	0.706313	−	0.513166i	0.0369701	−	0.0268603i
$366$	−13.1088	−	8.11092i	−0.685208	−	0.423965i
$367$	−10.6782	+	32.8640i	−0.557396	+	1.71549i	0.132136	+	0.991232i	$0.457816\pi$
$367$	−10.6782	+	32.8640i	−0.557396	+	1.71549i	−0.689532	+	0.724256i	$0.742184\pi$
$368$	0.253004	−	0.348230i	0.0131887	−	0.0181528i
$369$	15.3520	−	15.0899i	0.799193	−	0.785548i
$370$	8.99872	+	2.92386i	0.467821	+	0.152004i
$371$	2.33722	+	7.19323i	0.121343	+	0.373454i
$372$	−2.11886	−	0.518352i	−0.109858	−	0.0268753i
$373$			5.24728i			0.271694i	0.990730	+	0.135847i	$0.0433755\pi$
$373$			5.24728i			0.271694i	−0.990730	+	0.135847i	$0.956624\pi$
$374$	−21.6985	−	10.6672i	−1.12200	−	0.551587i
$375$	9.60407	−	8.13141i	0.495952	−	0.419904i
$376$	6.39473	+	8.80159i	0.329783	+	0.453908i
$377$	8.57161	−	2.78508i	0.441460	−	0.143439i
$378$	−5.06783	+	1.14766i	−0.260661	+	0.0590294i
$379$	2.57187	+	1.86857i	0.132108	+	0.0959820i	0.651877	−	0.758325i	$-0.273982\pi$
$379$	2.57187	+	1.86857i	0.132108	+	0.0959820i	−0.519769	+	0.854307i	$0.673982\pi$
$380$	6.48065	+	4.70847i	0.332450	+	0.241539i
$381$	−1.73625	−	4.24326i	−0.0889510	−	0.217389i
$382$	14.2728	−	4.63750i	0.730258	−	0.237275i
$383$	15.9342	+	21.9316i	0.814200	+	1.12065i	0.990662	+	0.136343i	$0.0435349\pi$
$383$	15.9342	+	21.9316i	0.814200	+	1.12065i	−0.176461	+	0.984308i	$0.556465\pi$
$384$	1.11920	+	1.32189i	0.0571138	+	0.0674575i
$385$	−11.3629	+	1.96696i	−0.579109	+	0.100246i
$386$		−	23.2694i		−	1.18438i
$387$	−30.4328	+	15.1777i	−1.54699	+	0.771524i
$388$	−1.38931	−	4.27585i	−0.0705314	−	0.217073i
$389$	14.3831	+	4.67335i	0.729252	+	0.236948i	0.650030	−	0.759909i	$-0.274756\pi$
$389$	14.3831	+	4.67335i	0.729252	+	0.236948i	0.0792221	+	0.996857i	$0.474756\pi$
$390$	2.10178	+	28.2606i	0.106428	+	1.43103i
$391$	1.84444	−	2.53866i	0.0932775	−	0.128385i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$	−4.16721	+	6.73502i	−0.210208	+	0.339737i
$394$	9.34233	−	6.78760i	0.470660	−	0.341954i
$395$	25.9540			1.30589
$396$	9.48031	+	3.02055i	0.476404	+	0.151788i
$397$	−19.5845			−0.982916			−0.491458	−	0.870901i	$-0.663536\pi$
$397$	−19.5845			−0.982916			−0.491458	+	0.870901i	$0.663536\pi$
$398$	−1.76255	+	1.28057i	−0.0883487	+	0.0641891i
$399$	2.09961	−	3.39337i	0.105112	−	0.169881i
$400$	−2.19079	+	6.74257i	−0.109540	+	0.337128i
$401$	16.4177	−	22.5971i	0.819863	−	1.12844i	−0.169863	−	0.985468i	$-0.554332\pi$
$401$	16.4177	−	22.5971i	0.819863	−	1.12844i	0.989726	−	0.142977i	$-0.0456675\pi$
$402$	0.487642	+	6.55685i	0.0243214	+	0.327026i
$403$	5.63615	+	1.83130i	0.280757	+	0.0912234i
$404$	−1.17310	−	3.61043i	−0.0583639	−	0.179625i
$405$	9.15616	+	29.9235i	0.454973	+	1.48691i
$406$		−	1.91533i		−	0.0950562i
$407$	−6.28983	+	6.47267i	−0.311776	+	0.320839i
$408$	8.15913	+	9.63682i	0.403937	+	0.477094i
$409$	−7.60600	−	10.4688i	−0.376092	−	0.517647i	0.578452	−	0.815717i	$-0.303657\pi$
$409$	−7.60600	−	10.4688i	−0.376092	−	0.517647i	−0.954544	+	0.298070i	$0.903657\pi$
$410$	−23.7281	+	7.70973i	−1.17185	+	0.380756i
$411$	10.4252	+	25.4783i	0.514237	+	1.25675i
$412$	−4.48027	−	3.25511i	−0.220727	−	0.160368i
$413$	6.50373	+	4.72524i	0.320028	+	0.232514i
$414$	−0.596127	+	1.14547i	−0.0292980	+	0.0562970i
$415$	−53.0090	+	17.2237i	−2.60211	+	0.845476i
$416$	−2.76587	−	3.80689i	−0.135608	−	0.186648i
$417$	−15.3005	+	12.9544i	−0.749269	+	0.634378i
$418$	−6.75782	+	3.56613i	−0.330536	+	0.174425i
$419$		−	18.9138i		−	0.923999i	−0.886880	−	0.462000i	$-0.847132\pi$
$419$		−	18.9138i		−	0.923999i	0.886880	−	0.462000i	$-0.152868\pi$
$420$	5.84984	+	1.43109i	0.285443	+	0.0698299i
$421$	−2.88958	−	8.89320i	−0.140829	−	0.433428i	0.855622	−	0.517602i	$-0.173175\pi$
$421$	−2.88958	−	8.89320i	−0.140829	−	0.433428i	−0.996451	+	0.0841734i	$0.973175\pi$
$422$	18.1514	+	5.89774i	0.883595	+	0.287097i
$423$	−22.8791	−	23.2765i	−1.11242	−	1.13174i
$424$	−4.44566	+	6.11893i	−0.215900	+	0.297161i
$425$	−15.9713	+	49.1545i	−0.774720	+	2.38434i
$426$	22.1593	+	13.7108i	1.07362	+	0.664290i
$427$	7.20022	−	5.23127i	0.348443	−	0.253159i
$428$	11.0388			0.533580
$429$	−25.0762	−	10.0937i	−1.21069	−	0.487330i
$430$	39.4149			1.90075
$431$	7.65444	−	5.56128i	0.368702	−	0.267877i	−0.387971	−	0.921672i	$-0.626824\pi$
$431$	7.65444	−	5.56128i	0.368702	−	0.267877i	0.756672	+	0.653794i	$0.226824\pi$
$432$	−3.90727	−	3.42538i	−0.187989	−	0.164804i
$433$	−0.201415	+	0.619892i	−0.00967940	+	0.0297901i	−0.955780	−	0.294084i	$-0.904985\pi$
$433$	−0.201415	+	0.619892i	−0.00967940	+	0.0297901i	0.946100	+	0.323874i	$0.104985\pi$
$434$	0.740257	−	1.01888i	0.0355335	−	0.0489076i
$435$	−11.5030	+	0.855494i	−0.551527	+	0.0410178i
$436$	7.76314	+	2.52240i	0.371787	+	0.120801i
$437$	−0.306441	−	0.943128i	−0.0146591	−	0.0451159i
$438$	0.103346	−	0.422448i	0.00493808	−	0.0201853i
$439$			20.9119i			0.998072i	0.866581	+	0.499036i	$0.166312\pi$
$439$			20.9119i			0.998072i	−0.866581	+	0.499036i	$0.833688\pi$
$440$	−8.27027	−	8.03665i	−0.394270	−	0.383132i
$441$	0.494799	−	2.95891i	0.0235618	−	0.140901i
$442$	−20.1636	−	27.7529i	−0.959087	−	1.32007i
$443$	−33.3503	+	10.8362i	−1.58452	+	0.514842i	−0.963216	−	0.268727i	$-0.913397\pi$
$443$	−33.3503	+	10.8362i	−1.58452	+	0.514842i	−0.621305	+	0.783569i	$0.713397\pi$
$444$	4.36229	−	1.78496i	0.207025	−	0.0847104i
$445$	−39.4216	−	28.6414i	−1.86876	−	1.35773i
$446$	−4.45104	−	3.23387i	−0.210763	−	0.153128i
$447$	−1.23072	+	0.503586i	−0.0582112	+	0.0238188i
$448$	−0.951057	+	0.309017i	−0.0449332	+	0.0145997i
$449$	3.44351	+	4.73959i	0.162509	+	0.223675i	0.882504	−	0.470304i	$-0.155856\pi$
$449$	3.44351	+	4.73959i	0.162509	+	0.223675i	−0.719995	+	0.693979i	$0.755856\pi$
$450$	3.50790	−	20.9774i	0.165364	−	0.988884i
$451$	3.38579	−	23.5563i	0.159431	−	1.10922i
$452$		−	7.27936i		−	0.342392i
$453$	3.00524	−	12.2845i	0.141199	−	0.577177i
$454$	−5.15058	−	15.8519i	−0.241729	−	0.743965i
$455$	−15.5605	−	5.05592i	−0.729489	−	0.237025i
$456$	3.97941	−	0.295954i	0.186353	−	0.0138593i
$457$	9.11211	−	12.5417i	0.426247	−	0.586678i	−0.540840	−	0.841126i	$-0.681894\pi$
$457$	9.11211	−	12.5417i	0.426247	−	0.586678i	0.967087	+	0.254447i	$0.0818935\pi$
$458$	−6.11846	+	18.8307i	−0.285897	+	0.879899i
$459$	−28.4847	−	24.9716i	−1.32955	−	1.16557i
$460$	1.21080	−	0.879696i	0.0564537	−	0.0410160i
$461$	8.41171			0.391772			0.195886	−	0.980627i	$-0.437242\pi$
$461$	8.41171			0.391772			0.195886	+	0.980627i	$0.437242\pi$
$462$	−3.68684	+	4.40536i	−0.171527	+	0.204956i
$463$	17.1707			0.797991			0.398996	−	0.916953i	$-0.369359\pi$
$463$	17.1707			0.797991			0.398996	+	0.916953i	$0.369359\pi$
$464$	1.54953	−	1.12580i	0.0719353	−	0.0522640i
$465$	−6.44977	−	3.99072i	−0.299101	−	0.185065i
$466$	0.290324	−	0.893525i	0.0134490	−	0.0413918i
$467$	11.1110	−	15.2930i	0.514158	−	0.707677i	−0.470456	−	0.882424i	$-0.655911\pi$
$467$	11.1110	−	15.2930i	0.514158	−	0.707677i	0.984613	+	0.174746i	$0.0559105\pi$
$468$	9.89571	+	10.0676i	0.457430	+	0.465375i
$469$	−3.61026	−	1.17305i	−0.166706	−	0.0541662i
$470$	11.6894	+	35.9762i	0.539191	+	1.65946i
$471$	17.5139	+	4.28455i	0.806998	+	0.197421i
$472$			8.03906i			0.370028i
$473$	−16.5870	+	33.7401i	−0.762670	+	1.55137i
$474$	9.86723	−	8.35421i	0.453217	−	0.383722i
$475$	9.60049	+	13.2139i	0.440501	+	0.606297i
$476$	−6.93336	+	2.25279i	−0.317790	+	0.103256i
$477$	10.4748	−	20.1277i	0.479610	−	0.921584i
$478$	−1.05553	−	0.766888i	−0.0482788	−	0.0350766i
$479$	12.1583	+	8.83351i	0.555526	+	0.403613i	0.829819	−	0.558033i	$-0.188444\pi$
$479$	12.1583	+	8.83351i	0.555526	+	0.403613i	−0.274293	+	0.961646i	$0.588444\pi$
$480$	2.28068	+	5.57379i	0.104098	+	0.254408i
$481$	−12.1783	+	3.95698i	−0.555285	+	0.180423i
$482$	−9.59276	−	13.2033i	−0.436938	−	0.601394i
$483$	−0.481743	−	0.568990i	−0.0219200	−	0.0258900i
$484$	10.3600	−	3.69749i	0.470907	−	0.168068i
$485$		−	15.6322i		−	0.709823i
$486$	13.1130	+	8.42914i	0.594816	+	0.382354i
$487$	−2.06526	−	6.35621i	−0.0935858	−	0.288028i	0.893297	−	0.449467i	$-0.148386\pi$
$487$	−2.06526	−	6.35621i	−0.0935858	−	0.288028i	−0.986883	+	0.161440i	$0.948386\pi$
$488$	8.46437	+	2.75024i	0.383164	+	0.124497i
$489$	1.79718	+	24.1650i	0.0812715	+	1.09278i
$490$	−2.04373	+	2.81296i	−0.0923264	+	0.127076i
$491$	6.11100	−	18.8077i	0.275786	−	0.848781i	−0.713225	−	0.700935i	$-0.752766\pi$
$491$	6.11100	−	18.8077i	0.275786	−	0.848781i	0.989010	−	0.147846i	$-0.0472338\pi$
$492$	−6.53933	+	10.5688i	−0.294816	+	0.476479i
$493$	11.2964	−	8.20729i	0.508763	−	0.369638i
$494$	−10.8410			−0.487758
$495$	28.1043	+	20.1746i	1.26319	+	0.906780i
$496$	1.25940			0.0565488
$497$	−12.1713	+	8.84298i	−0.545958	+	0.396662i
$498$	−14.6090	+	23.6109i	−0.654644	+	1.05803i
$499$	−5.31910	+	16.3705i	−0.238116	+	0.732845i	0.758577	+	0.651583i	$0.225895\pi$
$499$	−5.31910	+	16.3705i	−0.238116	+	0.732845i	−0.996693	+	0.0812616i	$0.974105\pi$
$500$	−4.27049	+	5.87783i	−0.190982	+	0.262865i
$501$	1.22930	+	16.5292i	0.0549210	+	0.738470i
$502$	−17.0096	−	5.52676i	−0.759176	−	0.246671i
$503$	9.95220	+	30.6297i	0.443747	+	1.36571i	0.883853	+	0.467766i	$0.154941\pi$
$503$	9.95220	+	30.6297i	0.443747	+	1.36571i	−0.440106	+	0.897946i	$0.645059\pi$
$504$	2.68465	−	1.33891i	0.119584	−	0.0596396i
$505$		−	13.1995i		−	0.587370i
$506$	0.243501	+	1.40668i	0.0108249	+	0.0625343i
$507$	−10.2322	−	12.0853i	−0.454427	−	0.536728i
$508$	1.55587	+	2.14147i	0.0690305	+	0.0950124i
$509$	32.9150	−	10.6947i	1.45893	−	0.474036i	0.531190	−	0.847253i	$-0.321745\pi$
$509$	32.9150	−	10.6947i	1.45893	−	0.474036i	0.927744	+	0.373217i	$0.121745\pi$
$510$	16.6265	+	40.6339i	0.736235	+	1.79930i
$511$	0.203138	+	0.147589i	0.00898631	+	0.00652893i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−11.6755	+	2.64405i	−0.515488	+	0.116738i
$514$	7.21157	−	2.34318i	0.318089	−	0.103353i
$515$	−11.3180	−	15.5779i	−0.498732	−	0.686446i
$516$	14.9848	−	12.6871i	0.659669	−	0.558517i
$517$	−35.7157	−	5.13349i	−1.57078	−	0.225771i
$518$			2.72126i			0.119565i
$519$	25.4723	+	6.23146i	1.11811	+	0.273531i
$520$	−5.05592	−	15.5605i	−0.221717	−	0.682374i
$521$	−37.0963	−	12.0533i	−1.62522	−	0.528066i	−0.652054	−	0.758172i	$-0.726092\pi$
$521$	−37.0963	−	12.0533i	−1.62522	−	0.528066i	−0.973165	+	0.230107i	$0.926092\pi$
$522$	−4.09786	+	4.02789i	−0.179358	+	0.176296i
$523$	15.9371	−	21.9355i	0.696881	−	0.959174i	−0.303100	−	0.952959i	$-0.598022\pi$
$523$	15.9371	−	21.9355i	0.696881	−	0.959174i	0.999981	−	0.00621559i	$-0.00197850\pi$
$524$	1.41301	−	4.34880i	0.0617277	−	0.189978i
$525$	10.4423	+	6.46102i	0.455737	+	0.281982i
$526$	1.46898	−	1.06727i	0.0640504	−	0.0465353i
$527$	9.18124			0.399941
$528$	−5.73108	−	0.393307i	−0.249413	−	0.0171165i
$529$	22.8147			0.991945
$530$	−21.2755	+	15.4576i	−0.924150	+	0.671434i
$531$	−3.56752	−	23.8518i	−0.154817	−	1.03508i
$532$	−0.711931	+	2.19110i	−0.0308661	+	0.0949961i
$533$	19.8464	−	27.3163i	0.859645	−	1.18320i
$534$	−24.2066	+	1.80028i	−1.04752	+	0.0779056i
$535$	36.5034	+	11.8607i	1.57818	+	0.512781i
$536$	−1.17305	−	3.61026i	−0.0506679	−	0.155940i
$537$	−0.861496	+	3.52153i	−0.0371763	+	0.151965i
$538$			22.3725i			0.964546i
$539$	−1.54789	−	2.93326i	−0.0666725	−	0.126345i
$540$	−9.24026	−	15.5253i	−0.397638	−	0.668103i
$541$	1.91615	+	2.63736i	0.0823819	+	0.113389i	0.848219	−	0.529646i	$-0.177675\pi$
$541$	1.91615	+	2.63736i	0.0823819	+	0.113389i	−0.765837	+	0.643035i	$0.777675\pi$
$542$	16.5899	−	5.39039i	0.712598	−	0.231537i
$543$	12.6009	−	5.15602i	0.540756	−	0.221266i
$544$	−5.89787	−	4.28505i	−0.252869	−	0.183720i
$545$	22.9612	+	16.6823i	0.983548	+	0.714590i
$546$	−7.54325	+	3.08654i	−0.322821	+	0.132092i
$547$	33.2442	−	10.8017i	1.42142	−	0.461847i	0.505366	−	0.862905i	$-0.331357\pi$
$547$	33.2442	−	10.8017i	1.42142	−	0.461847i	0.916053	+	0.401058i	$0.131357\pi$
$548$	−9.34209	−	12.8583i	−0.399074	−	0.549279i
$549$	−26.3342	−	4.40369i	−1.12392	−	0.187945i
$550$	−10.9739	−	20.7955i	−0.467928	−	0.886724i
$551$		−	4.41264i		−	0.187985i
$552$	0.177162	−	0.724182i	0.00754050	−	0.0308232i
$553$	2.30665	+	7.09914i	0.0980887	+	0.301886i
$554$	−14.6498	−	4.76000i	−0.622409	−	0.202233i
$555$	16.3432	−	1.21547i	0.693731	−	0.0515937i
$556$	6.80343	−	9.36412i	0.288530	−	0.397127i
$557$	12.4590	−	38.3447i	0.527903	−	1.62472i	−0.230600	−	0.973049i	$-0.574069\pi$
$557$	12.4590	−	38.3447i	0.527903	−	1.62472i	0.758503	−	0.651670i	$-0.225931\pi$
$558$	−3.73664	+	0.558888i	−0.158184	+	0.0236596i
$559$	−43.1544	+	31.3535i	−1.82524	+	1.32611i
$560$	−3.47700			−0.146930
$561$	−41.7806	−	2.86727i	−1.76398	−	0.121056i
$562$	15.2415			0.642925
$563$	−2.35244	+	1.70915i	−0.0991437	+	0.0720321i	−0.636253	−	0.771481i	$-0.719516\pi$
$563$	−2.35244	+	1.70915i	−0.0991437	+	0.0720321i	0.537109	+	0.843513i	$0.319516\pi$
$564$	16.0243	+	9.91484i	0.674744	+	0.417490i
$565$	7.82133	−	24.0716i	0.329046	−	1.01270i
$566$	−7.99439	+	11.0033i	−0.336029	+	0.462505i
$567$	−7.37117	+	5.16390i	−0.309560	+	0.216864i
$568$	−14.3082	−	4.64903i	−0.600361	−	0.195069i
$569$	13.7244	+	42.2394i	0.575357	+	1.77077i	0.634961	+	0.772544i	$0.281016\pi$
$569$	13.7244	+	42.2394i	0.575357	+	1.77077i	−0.0596043	+	0.998222i	$0.518984\pi$
$570$	13.4772	+	3.29702i	0.564498	+	0.138097i
$571$			4.53675i			0.189857i	0.995484	+	0.0949285i	$0.0302622\pi$
$571$			4.53675i			0.189857i	−0.995484	+	0.0949285i	$0.969738\pi$
$572$	15.4479	+	2.22035i	0.645908	+	0.0928376i
$573$	19.8380	−	16.7961i	0.828744	−	0.701666i
$574$	−4.21765	−	5.80509i	−0.176041	−	0.242300i
$575$	2.90225	−	0.942997i	0.121032	−	0.0393257i
$576$	2.66119	+	1.38494i	0.110883	+	0.0577057i
$577$	16.9618	+	12.3235i	0.706129	+	0.513033i	0.881923	−	0.471394i	$-0.156249\pi$
$577$	16.9618	+	12.3235i	0.706129	+	0.513033i	−0.175793	+	0.984427i	$0.556249\pi$
$578$	−29.2432	−	21.2464i	−1.21636	−	0.883735i
$579$	−15.2631	−	37.3019i	−0.634314	−	1.55021i
$580$	6.33366	−	2.05793i	0.262991	−	0.0854509i
$581$	−9.42229	−	12.9687i	−0.390903	−	0.538031i
$582$	−5.03178	−	5.94308i	−0.208574	−	0.246349i
$583$	−4.27867	−	24.7174i	−0.177204	−	1.02369i
$584$			0.251093i			0.0103903i
$585$	21.9062	+	43.9243i	0.905712	+	1.81605i
$586$	5.12208	+	15.7642i	0.211591	+	0.651211i
$587$	13.2337	+	4.29989i	0.546213	+	0.177476i	0.569109	−	0.822262i	$-0.307288\pi$
$587$	13.2337	+	4.29989i	0.546213	+	0.177476i	−0.0228952	+	0.999738i	$0.507288\pi$
$588$	0.128460	+	1.72728i	0.00529761	+	0.0712318i
$589$	1.70545	−	2.34735i	0.0702717	−	0.0967207i
$590$	−8.63759	+	26.5838i	−0.355604	+	1.09444i
$591$	10.5240	−	17.0088i	0.432898	−	0.699647i
$592$	−2.20154	+	1.59951i	−0.0904828	+	0.0657396i
$593$	10.0326			0.411990			0.205995	−	0.978553i	$-0.433957\pi$
$593$	10.0326			0.411990			0.205995	+	0.978553i	$0.433957\pi$
$594$	17.1786	−	1.37636i	0.704848	−	0.0564728i
$595$	−25.3480			−1.03916
$596$	0.621116	−	0.451267i	0.0254419	−	0.0184846i
$597$	−1.98548	+	3.20892i	−0.0812604	+	0.131332i
$598$	−0.625898	+	1.92632i	−0.0255949	+	0.0787730i
$599$	5.84937	−	8.05097i	0.238999	−	0.328954i	−0.672622	−	0.739986i	$-0.734832\pi$
$599$	5.84937	−	8.05097i	0.238999	−	0.328954i	0.911621	+	0.411033i	$0.134832\pi$
$600$	0.910725	+	12.2457i	0.0371802	+	0.499927i
$601$	25.6939	+	8.34845i	1.04808	+	0.340540i	0.781913	−	0.623388i	$-0.214244\pi$
$601$	25.6939	+	8.34845i	1.04808	+	0.340540i	0.266163	+	0.963928i	$0.414244\pi$
$602$	3.50298	+	10.7811i	0.142771	+	0.439403i
$603$	5.08256	+	10.1911i	0.206978	+	0.415012i
$604$			7.30161i			0.297098i
$605$	38.2313	−	1.09566i	1.55433	−	0.0445449i
$606$	−4.24872	−	5.01820i	−0.172593	−	0.203851i
$607$	−16.8040	−	23.1288i	−0.682055	−	0.938768i	0.317901	−	0.948124i	$-0.397022\pi$
$607$	−16.8040	−	23.1288i	−0.682055	−	0.938768i	−0.999956	+	0.00935560i	$0.997022\pi$
$608$	−2.19110	+	0.711931i	−0.0888608	+	0.0288726i
$609$	−1.25632	−	3.07036i	−0.0509089	−	0.124417i
$610$	25.0352	+	18.1891i	1.01365	+	0.736457i
$611$	−41.4166	−	30.0909i	−1.67553	−	1.21735i
$612$	19.4006	+	10.0964i	0.784221	+	0.408124i
$613$	−20.8547	+	6.77610i	−0.842313	+	0.273684i	−0.698223	−	0.715880i	$-0.746026\pi$
$613$	−20.8547	+	6.77610i	−0.842313	+	0.273684i	−0.144090	+	0.989565i	$0.546026\pi$
$614$	14.7665	+	20.3243i	0.595926	+	0.820221i
$615$	−32.9802	+	27.9231i	−1.32989	+	1.12597i
$616$	1.46323	−	2.97640i	0.0589552	−	0.119923i
$617$		−	23.3682i		−	0.940766i	−0.882462	−	0.470383i	$-0.844116\pi$
$617$		−	23.3682i		−	0.940766i	0.882462	−	0.470383i	$-0.155884\pi$
$618$	−9.31721	−	2.27933i	−0.374793	−	0.0916882i
$619$	6.81490	+	20.9741i	0.273914	+	0.843020i	0.989505	+	0.144500i	$0.0461575\pi$
$619$	6.81490	+	20.9741i	0.273914	+	0.843020i	−0.715591	+	0.698520i	$0.753842\pi$
$620$	4.16462	+	1.35317i	0.167255	+	0.0543445i
$621$	−0.204265	+	2.22726i	−0.00819687	+	0.0893771i
$622$	3.24783	−	4.47026i	0.130226	−	0.179241i
$623$	4.33065	−	13.3284i	0.173504	−	0.533990i
$624$	−6.93087	−	4.28840i	−0.277457	−	0.171673i
$625$	8.24062	−	5.98716i	0.329625	−	0.239486i
$626$	31.7389			1.26854
$627$	−8.49395	+	10.1493i	−0.339216	+	0.405325i
$628$	−10.4098			−0.415398
$629$	−16.0496	+	11.6607i	−0.639940	+	0.464944i
$630$	10.3163	−	1.54300i	0.411010	−	0.0614747i
$631$	−6.46229	+	19.8889i	−0.257260	+	0.791765i	0.736116	+	0.676855i	$0.236658\pi$
$631$	−6.46229	+	19.8889i	−0.257260	+	0.791765i	−0.993376	+	0.114909i	$0.963342\pi$
$632$	−4.38751	+	6.03889i	−0.174526	+	0.240214i
$633$	32.9660	−	2.45172i	1.31028	−	0.0974473i
$634$	5.83251	+	1.89510i	0.231639	+	0.0752639i
$635$	2.84408	+	8.75318i	0.112864	+	0.347359i
$636$	−3.11300	+	12.7250i	−0.123438	+	0.504578i
$637$		−	4.70557i		−	0.186442i
$638$	−0.903759	+	6.28781i	−0.0357801	+	0.248937i
$639$	44.5156	+	7.44404i	1.76101	+	0.294482i
$640$	−2.04373	−	2.81296i	−0.0807856	−	0.111192i
$641$	−18.5243	+	6.01892i	−0.731667	+	0.237733i	−0.651074	−	0.759014i	$-0.725681\pi$
$641$	−18.5243	+	6.01892i	−0.731667	+	0.237733i	−0.0805929	+	0.996747i	$0.525681\pi$
$642$	17.6957	−	7.24069i	0.698393	−	0.285767i
$643$	−36.1336	−	26.2526i	−1.42497	−	1.03530i	−0.990926	−	0.134410i	$-0.957086\pi$
$643$	−36.1336	−	26.2526i	−1.42497	−	1.03530i	−0.434044	−	0.900891i	$-0.642914\pi$
$644$	0.348230	+	0.253004i	0.0137222	+	0.00996975i
$645$	63.1838	−	25.8535i	2.48786	−	1.01798i
$646$	−15.9735	+	5.19010i	−0.628468	+	0.204202i
$647$	−7.14772	−	9.83799i	−0.281006	−	0.386771i	0.645061	−	0.764131i	$-0.276832\pi$
$647$	−7.14772	−	9.83799i	−0.281006	−	0.386771i	−0.926067	+	0.377360i	$0.876832\pi$
$648$	−8.51035	−	2.92813i	−0.334318	−	0.115028i
$649$	−19.1214	−	18.5812i	−0.750580	−	0.729378i
$650$		−	33.3604i		−	1.30850i
$651$	0.518352	−	2.11886i	0.0203158	−	0.0830448i
$652$	−4.32321	−	13.3055i	−0.169310	−	0.521083i
$653$	18.1613	+	5.90096i	0.710706	+	0.230922i	0.641989	−	0.766714i	$-0.278109\pi$
$653$	18.1613	+	5.90096i	0.710706	+	0.230922i	0.0687169	+	0.997636i	$0.478109\pi$
$654$	14.0992	−	1.04858i	0.551322	−	0.0410025i
$655$	9.34518	−	12.8625i	0.365146	−	0.502581i
$656$	2.21735	−	6.82429i	0.0865729	−	0.266444i
$657$	−0.111428	−	0.744991i	−0.00434723	−	0.0290649i
$658$	−8.80159	+	6.39473i	−0.343122	+	0.249293i
$659$	2.36741			0.0922211			0.0461106	−	0.998936i	$-0.485317\pi$
$659$	2.36741			0.0922211			0.0461106	+	0.998936i	$0.485317\pi$
$660$	−18.5291	−	7.45838i	−0.721245	−	0.290317i
$661$	−32.1595			−1.25086			−0.625430	−	0.780280i	$-0.715076\pi$
$661$	−32.1595			−1.25086			−0.625430	+	0.780280i	$0.715076\pi$
$662$	18.1473	−	13.1848i	0.705314	−	0.512441i
$663$	−50.5272	−	31.2631i	−1.96231	−	1.21416i
$664$	4.95359	−	15.2456i	0.192237	−	0.591644i
$665$	−4.70847	+	6.48065i	−0.182586	+	0.251309i
$666$	5.82214	−	5.72274i	0.225603	−	0.221752i
$667$	−0.784076	−	0.254762i	−0.0303596	−	0.00986442i
$668$	−2.95714	−	9.10113i	−0.114415	−	0.352133i
$669$	−9.25643	−	2.26446i	−0.357874	−	0.0875492i
$670$		−	13.1989i		−	0.509918i
$671$	−26.1059	+	13.7762i	−1.00781	+	0.531824i
$672$	−1.32189	+	1.11920i	−0.0509931	+	0.0431739i
$673$	−9.80807	−	13.4997i	−0.378073	−	0.520373i	0.576999	−	0.816745i	$-0.304223\pi$
$673$	−9.80807	−	13.4997i	−0.378073	−	0.520373i	−0.955073	+	0.296371i	$0.904223\pi$
$674$	4.91450	−	1.59682i	0.189300	−	0.0615071i
$675$	−8.13641	−	35.9286i	−0.313171	−	1.38289i
$676$	7.39639	+	5.37379i	0.284476	+	0.206684i
$677$	9.67974	+	7.03274i	0.372023	+	0.270290i	0.758049	−	0.652197i	$-0.226153\pi$
$677$	9.67974	+	7.03274i	0.372023	+	0.270290i	−0.386026	+	0.922488i	$0.626153\pi$
$678$	−4.77476	−	11.6691i	−0.183374	−	0.448151i
$679$	4.27585	−	1.38931i	0.164092	−	0.0533167i
$680$	−14.8992	−	20.5069i	−0.571356	−	0.786405i
$681$	−18.6544	−	22.0328i	−0.714837	−	0.844300i
$682$	−2.91094	+	2.99556i	−0.111466	+	0.114706i
$683$			34.6159i			1.32454i	0.749265	+	0.662271i	$0.230407\pi$
$683$			34.6159i			1.32454i	−0.749265	+	0.662271i	$0.769593\pi$
$684$	6.18504	−	3.08465i	0.236491	−	0.117944i
$685$	−17.0771	−	52.5578i	−0.652481	−	2.00813i
$686$	−0.951057	−	0.309017i	−0.0363115	−	0.0117983i
$687$	2.54348	+	34.1997i	0.0970397	+	1.30480i
$688$	−6.66306	+	9.17091i	−0.254027	+	0.349638i
$689$	10.9980	−	33.8483i	0.418990	−	1.28952i
$690$	1.36394	−	2.20439i	0.0519244	−	0.0839198i
$691$	−19.2382	+	13.9773i	−0.731854	+	0.531723i	−0.890149	−	0.455669i	$-0.849400\pi$
$691$	−19.2382	+	13.9773i	−0.731854	+	0.531723i	0.158295	+	0.987392i	$0.449400\pi$
$692$	−15.1401			−0.575541
$693$	−3.02055	+	9.48031i	−0.114741	+	0.360127i
$694$	−7.80685			−0.296344
$695$	32.5591	−	23.6556i	1.23504	−	0.897307i
$696$	1.74552	−	2.82110i	0.0661638	−	0.106933i
$697$	16.1648	−	49.7503i	0.612287	−	1.88443i
$698$	−16.9611	+	23.3450i	−0.641989	+	0.883621i
$699$	−0.120689	−	1.62279i	−0.00456489	−	0.0613797i
$700$	−6.74257	−	2.19079i	−0.254845	−	0.0828042i
$701$	−9.90694	−	30.4904i	−0.374180	−	1.15161i	−0.944030	−	0.329859i	$-0.892999\pi$
$701$	−9.90694	−	30.4904i	−0.374180	−	1.15161i	0.569851	−	0.821748i	$-0.307001\pi$
$702$	22.4669	+	9.64792i	0.847960	+	0.364137i
$703$			6.26938i			0.236454i
$704$	3.26802	−	0.565707i	0.123168	−	0.0213209i
$705$	42.3365	+	50.0040i	1.59449	+	1.88326i
$706$	−8.23965	−	11.3409i	−0.310103	−	0.426821i
$707$	3.61043	−	1.17310i	0.135784	−	0.0441189i
$708$	5.27307	+	12.8870i	0.198174	+	0.484322i
$709$	27.7379	+	20.1528i	1.04172	+	0.756853i	0.970620	−	0.240616i	$-0.0773495\pi$
$709$	27.7379	+	20.1528i	1.04172	+	0.756853i	0.0710988	+	0.997469i	$0.477349\pi$
$710$	−42.3197	−	30.7471i	−1.58823	−	1.15392i
$711$	10.3378	−	19.8644i	0.387699	−	0.744974i
$712$	13.3284	−	4.33065i	0.499502	−	0.162298i
$713$	−0.318633	−	0.438561i	−0.0119329	−	0.0164242i
$714$	−9.63682	+	8.15913i	−0.360649	+	0.305348i
$715$	48.6978	+	23.9403i	1.82119	+	0.895318i
$716$		−	2.09311i		−	0.0782232i
$717$	−2.19509	−	0.537000i	−0.0819771	−	0.0200546i
$718$	3.56032	+	10.9575i	0.132870	+	0.408932i
$719$	−33.7565	−	10.9681i	−1.25890	−	0.409043i	−0.397800	−	0.917472i	$-0.630226\pi$
$719$	−33.7565	−	10.9681i	−1.25890	−	0.409043i	−0.861104	+	0.508429i	$0.830226\pi$
$720$	7.31206	+	7.43907i	0.272504	+	0.277238i
$721$	3.25511	−	4.48027i	0.121227	−	0.166854i
$722$	4.23114	−	13.0221i	0.157467	−	0.484632i
$723$	−24.0381	−	14.8733i	−0.893986	−	0.553144i
$724$	−6.35936	+	4.62035i	−0.236344	+	0.171714i
$725$	13.5788			0.504305
$726$	14.1822	−	12.7227i	0.526350	−	0.472182i
$727$	−4.37387			−0.162218			−0.0811089	−	0.996705i	$-0.525846\pi$
$727$	−4.37387			−0.162218			−0.0811089	+	0.996705i	$0.525846\pi$
$728$	3.80689	−	2.76587i	0.141093	−	0.102510i
$729$	26.5496	+	4.91109i	0.983318	+	0.181892i
$730$	−0.269787	+	0.830320i	−0.00998528	+	0.0307315i
$731$	−48.5748	+	66.8575i	−1.79660	+	2.47281i
$732$	15.3727	−	1.14329i	0.568192	−	0.0422572i
$733$	42.8328	+	13.9172i	1.58207	+	0.514044i	0.962588	−	0.270970i	$-0.0873446\pi$
$733$	42.8328	+	13.9172i	1.58207	+	0.514044i	0.619477	+	0.785015i	$0.287345\pi$
$734$	−10.6782	−	32.8640i	−0.394138	−	1.21303i
$735$	−1.43109	+	5.84984i	−0.0527864	+	0.215775i
$736$			0.430436i			0.0158661i
$737$	11.2986	+	5.55450i	0.416189	+	0.204603i
$738$	−3.55042	+	21.2317i	−0.130693	+	0.781548i
$739$	8.93407	+	12.2967i	0.328645	+	0.452341i	0.941082	−	0.338178i	$-0.109811\pi$
$739$	8.93407	+	12.2967i	0.328645	+	0.452341i	−0.612437	+	0.790519i	$0.709811\pi$
$740$	−8.99872	+	2.92386i	−0.330800	+	0.107483i
$741$	−17.3786	+	7.11094i	−0.638418	+	0.261227i
$742$	−6.11893	−	4.44566i	−0.224633	−	0.163205i
$743$	−21.4316	−	15.5710i	−0.786249	−	0.571243i	0.120599	−	0.992701i	$-0.461519\pi$
$743$	−21.4316	−	15.5710i	−0.786249	−	0.571243i	−0.906848	+	0.421458i	$0.861519\pi$
$744$	2.01888	−	0.826081i	0.0740156	−	0.0302856i
$745$	2.53879	−	0.824902i	0.0930140	−	0.0302221i
$746$	−3.08427	−	4.24514i	−0.112923	−	0.155426i
$747$	−7.93170	+	47.4319i	−0.290206	+	1.73544i
$748$	23.8244	−	4.12410i	0.871108	−	0.150792i
$749$			11.0388i			0.403349i
$750$	−2.99034	+	12.2236i	−0.109192	+	0.446342i
$751$	9.56906	+	29.4505i	0.349180	+	1.07467i	0.959308	+	0.282362i	$0.0911180\pi$
$751$	9.56906	+	29.4505i	0.349180	+	1.07467i	−0.610128	+	0.792303i	$0.708882\pi$
$752$	−10.3469	−	3.36191i	−0.377312	−	0.122596i
$753$	−30.8924	+	2.29751i	−1.12578	+	0.0837258i
$754$	−5.29754	+	7.29144i	−0.192925	+	0.265539i
$755$	−7.84524	+	24.1452i	−0.285518	+	0.878733i
$756$	3.42538	−	3.90727i	0.124580	−	0.142106i
$757$	1.86077	−	1.35193i	0.0676310	−	0.0491368i	−0.553456	−	0.832878i	$-0.686691\pi$
$757$	1.86077	−	1.35193i	0.0676310	−	0.0491368i	0.621087	+	0.783742i	$0.286691\pi$
$758$	−3.17900			−0.115467
$759$	1.31303	+	2.09524i	0.0476598	+	0.0760525i
$760$	−8.01052			−0.290572
$761$	−14.2045	+	10.3202i	−0.514914	+	0.374107i	−0.814685	−	0.579904i	$-0.803090\pi$
$761$	−14.2045	+	10.3202i	−0.514914	+	0.374107i	0.299770	+	0.954011i	$0.403090\pi$
$762$	3.89879	+	2.41233i	0.141238	+	0.0873894i
$763$	−2.52240	+	7.76314i	−0.0913169	+	0.281045i
$764$	−8.82105	+	12.1411i	−0.319134	+	0.439251i
$765$	53.3062	+	54.2321i	1.92729	+	1.96077i
$766$	−25.7821	−	8.37711i	−0.931545	−	0.302677i
$767$	−11.6896	−	35.9769i	−0.422087	−	1.29905i
$768$	−1.68244	−	0.411586i	−0.0607097	−	0.0148518i
$769$			27.2055i			0.981057i	0.871425	+	0.490528i	$0.163196\pi$
$769$			27.2055i			0.981057i	−0.871425	+	0.490528i	$0.836804\pi$
$770$	8.03665	−	8.27027i	0.289621	−	0.298040i
$771$	10.0235	−	8.48653i	0.360988	−	0.305635i
$772$	13.6774	+	18.8253i	0.492261	+	0.677539i
$773$	31.0664	−	10.0941i	1.11738	−	0.363060i	0.308614	−	0.951187i	$-0.400135\pi$
$773$	31.0664	−	10.0941i	1.11738	−	0.363060i	0.808768	+	0.588128i	$0.200135\pi$
$774$	15.6995	−	30.1669i	0.564305	−	1.08433i
$775$	7.22338	+	5.24809i	0.259472	+	0.188517i
$776$	3.63725	+	2.64262i	0.130570	+	0.0948645i
$777$	1.78496	+	4.36229i	0.0640350	+	0.156496i
$778$	−14.3831	+	4.67335i	−0.515659	+	0.167548i
$779$	−9.71685	−	13.3741i	−0.348142	−	0.479177i
$780$	−18.3115	−	21.6279i	−0.655657	−	0.774402i
$781$	44.1297	−	23.2874i	1.57908	−	0.833289i
$782$			3.13795i			0.112213i
$783$	−3.92703	+	9.14481i	−0.140341	+	0.326809i
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	−34.4235	−	11.1849i	−1.22863	−	0.399206i
$786$	−0.587397	−	7.89817i	−0.0209518	−	0.281718i
$787$	22.9363	−	31.5691i	0.817591	−	1.12532i	−0.172516	−	0.985007i	$-0.555190\pi$
$787$	22.9363	−	31.5691i	0.817591	−	1.12532i	0.990107	−	0.140311i	$-0.0448104\pi$
$788$	−3.56845	+	10.9826i	−0.127121	+	0.391238i
$789$	1.65478	−	2.67444i	0.0589116	−	0.0952124i
$790$	−20.9972	+	15.2554i	−0.747048	+	0.542762i
$791$	7.27936			0.258824
$792$	−9.44517	+	3.12871i	−0.335619	+	0.111174i
$793$	−41.8794			−1.48718
$794$	15.8442	−	11.5115i	0.562288	−	0.408526i
$795$	−23.9665	+	38.7345i	−0.850005	+	1.37377i
$796$	0.673235	−	2.07200i	0.0238622	−	0.0734402i
$797$	17.0819	−	23.5113i	0.605074	−	0.832812i	−0.391087	−	0.920354i	$-0.627901\pi$
$797$	17.0819	−	23.5113i	0.605074	−	0.832812i	0.996161	+	0.0875413i	$0.0279010\pi$
$798$	0.295954	+	3.97941i	0.0104766	+	0.140869i
$799$	−75.4306	−	24.5089i	−2.66854	−	0.867062i
$800$	−2.19079	−	6.74257i	−0.0774562	−	0.238386i
$801$	−37.6234	+	18.7638i	−1.32936	+	0.662987i
$802$			27.9315i			0.986297i
$803$	−0.597240	−	0.580369i	−0.0210761	−	0.0204808i
$804$	−4.24853	−	5.01798i	−0.149834	−	0.176970i
$805$	0.879696	+	1.21080i	0.0310052	+	0.0426750i
$806$	−5.63615	+	1.83130i	−0.198525	+	0.0645047i
$807$	14.6748	+	35.8641i	0.516578	+	1.26248i
$808$	3.07121	+	2.23137i	0.108045	+	0.0784992i
$809$	8.75423	+	6.36032i	0.307782	+	0.223617i	0.730944	−	0.682437i	$-0.239080\pi$
$809$	8.75423	+	6.36032i	0.307782	+	0.223617i	−0.423162	+	0.906054i	$0.639080\pi$
$810$	−24.9961	−	18.8268i	−0.878274	−	0.661506i
$811$	−24.7704	+	8.04840i	−0.869807	+	0.282618i	−0.709719	−	0.704485i	$-0.751178\pi$
$811$	−24.7704	+	8.04840i	−0.869807	+	0.282618i	−0.160089	+	0.987103i	$0.551178\pi$
$812$	1.12580	+	1.54953i	0.0395079	+	0.0543780i
$813$	23.0587	−	19.5229i	0.808703	−	0.684698i
$814$	1.28404	−	8.93358i	0.0450056	−	0.313122i
$815$		−	48.6440i		−	1.70393i
$816$	−12.2653	−	3.00053i	−0.429370	−	0.105040i
$817$	8.07035	+	24.8380i	0.282346	+	0.868972i
$818$	12.3068	+	3.99871i	0.430296	+	0.139812i
$819$	−10.0676	+	9.89571i	−0.351791	+	0.345784i
$820$	14.6648	−	20.1843i	0.512116	−	0.704867i
$821$	1.92295	−	5.91824i	0.0671115	−	0.206548i	−0.911877	−	0.410464i	$-0.865367\pi$
$821$	1.92295	−	5.91824i	0.0671115	−	0.206548i	0.978988	+	0.203916i	$0.0653668\pi$
$822$	−23.4099	−	14.4846i	−0.816516	−	0.505210i
$823$	36.3950	−	26.4425i	1.26865	−	0.921727i	0.269501	−	0.963000i	$-0.413141\pi$
$823$	36.3950	−	26.4425i	1.26865	−	0.921727i	0.999148	+	0.0412731i	$0.0131414\pi$
$824$	5.53792			0.192923
$825$	−31.2321	−	26.1380i	−1.08736	−	0.910010i
$826$	−8.03906			−0.279715
$827$	−6.30883	+	4.58363i	−0.219379	+	0.159388i	−0.692047	−	0.721852i	$-0.743291\pi$
$827$	−6.30883	+	4.58363i	−0.219379	+	0.159388i	0.472668	+	0.881241i	$0.343291\pi$
$828$	−0.191016	−	1.27710i	−0.00663827	−	0.0443824i
$829$	−3.68637	+	11.3455i	−0.128033	+	0.394045i	−0.994441	−	0.105291i	$-0.966423\pi$
$829$	−3.68637	+	11.3455i	−0.128033	+	0.394045i	0.866408	+	0.499336i	$0.166423\pi$
$830$	32.7613	−	45.0921i	1.13716	−	1.56517i
$831$	−26.6065	+	1.97876i	−0.922968	+	0.0686424i
$832$	4.47527	+	1.45410i	0.155152	+	0.0504119i
$833$	−2.25279	−	6.93336i	−0.0780544	−	0.240227i
$834$	4.76398	−	19.4737i	0.164963	−	0.674319i
$835$		−	33.2732i		−	1.15147i
$836$	3.37107	−	6.85720i	0.116591	−	0.237161i
$837$	−5.62340	+	3.34690i	−0.194373	+	0.115686i
$838$	11.1172	+	15.3016i	0.384039	+	0.528584i
$839$	25.7870	−	8.37869i	0.890265	−	0.289265i	0.172052	−	0.985088i	$-0.444960\pi$
$839$	25.7870	−	8.37869i	0.890265	−	0.289265i	0.718213	+	0.695823i	$0.244960\pi$
$840$	−5.57379	+	2.28068i	−0.192314	+	0.0786909i
$841$	20.4936	+	14.8895i	0.706677	+	0.513431i
$842$	7.56501	+	5.49630i	0.260707	+	0.189415i
$843$	24.4328	−	9.99740i	0.841512	−	0.344329i
$844$	−18.1514	+	5.89774i	−0.624796	+	0.203009i
$845$	18.6847	+	25.7173i	0.642773	+	0.884701i
$846$	32.1911	+	5.38310i	1.10675	+	0.185075i
$847$	3.69749	+	10.3600i	0.127047	+	0.355972i
$848$		−	7.56341i		−	0.259729i
$849$	−5.59793	+	22.8826i	−0.192121	+	0.785330i
$850$	−15.9713	−	49.1545i	−0.547810	−	1.68598i
$851$	1.11400	+	0.361960i	0.0381874	+	0.0124078i
$852$	−25.9862	+	1.93263i	−0.890273	+	0.0662108i
$853$	10.2822	−	14.1522i	0.352055	−	0.484562i	−0.595859	−	0.803089i	$-0.703188\pi$
$853$	10.2822	−	14.1522i	0.352055	−	0.484562i	0.947914	+	0.318527i	$0.103188\pi$
$854$	−2.75024	+	8.46437i	−0.0941113	+	0.289645i
$855$	23.7672	−	3.55486i	0.812820	−	0.121573i
$856$	−8.93057	+	6.48844i	−0.305241	+	0.221770i
$857$	6.27737			0.214431			0.107215	−	0.994236i	$-0.465807\pi$
$857$	6.27737			0.214431			0.107215	+	0.994236i	$0.465807\pi$
$858$	26.2200	−	6.57343i	0.895137	−	0.224413i
$859$	−39.2930			−1.34066			−0.670329	−	0.742064i	$-0.733847\pi$
$859$	−39.2930			−1.34066			−0.670329	+	0.742064i	$0.733847\pi$
$860$	−31.8873	+	23.1675i	−1.08735	+	0.790004i
$861$	−10.5688	−	6.53933i	−0.360184	−	0.222860i
$862$	−2.92374	+	8.99834i	−0.0995829	+	0.306485i
$863$	−18.0328	+	24.8200i	−0.613842	+	0.844881i	−0.996887	−	0.0788488i	$-0.974876\pi$
$863$	−18.0328	+	24.8200i	−0.613842	+	0.844881i	0.383045	+	0.923730i	$0.374876\pi$
$864$	5.17444	+	0.474553i	0.176038	+	0.0161446i
$865$	−50.0658	−	16.2674i	−1.70229	−	0.553107i
$866$	−0.201415	−	0.619892i	−0.00684437	−	0.0210648i
$867$	−60.8144	−	14.8774i	−2.06536	−	0.505264i
$868$			1.25940i			0.0427468i
$869$	−4.22270	−	24.3941i	−0.143245	−	0.827512i
$870$	8.80328	−	7.45341i	0.298459	−	0.252694i
$871$	10.4994	+	14.4512i	0.355758	+	0.489659i
$872$	−7.76314	+	2.52240i	−0.262893	+	0.0854192i
$873$	−11.9644	−	6.22652i	−0.404935	−	0.210736i
$874$	0.802272	+	0.582885i	0.0271373	+	0.0197164i
$875$	−5.87783	−	4.27049i	−0.198707	−	0.144369i
$876$	0.164700	+	0.402513i	0.00556469	+	0.0135997i
$877$	29.6401	−	9.63064i	1.00087	−	0.325204i	0.237659	−	0.971349i	$-0.423620\pi$
$877$	29.6401	−	9.63064i	1.00087	−	0.325204i	0.763215	+	0.646145i	$0.223620\pi$
$878$	−12.2917	−	16.9181i	−0.414826	−	0.570959i
$879$	18.5511	+	21.9109i	0.625714	+	0.739037i
$880$	11.4146	+	1.64064i	0.384787	+	0.0553061i
$881$			52.8843i			1.78172i	0.454282	+	0.890858i	$0.349896\pi$
$881$			52.8843i			1.78172i	−0.454282	+	0.890858i	$0.650104\pi$
$882$	1.33891	+	2.68465i	0.0450833	+	0.0903968i
$883$	−1.18335	−	3.64198i	−0.0398229	−	0.122562i	0.929169	−	0.369656i	$-0.120524\pi$
$883$	−1.18335	−	3.64198i	−0.0398229	−	0.122562i	−0.968992	+	0.247094i	$0.920524\pi$
$884$	32.6255	+	10.6007i	1.09731	+	0.356539i
$885$	3.59070	+	48.2806i	0.120700	+	1.62294i
$886$	20.6116	−	28.3695i	0.692461	−	0.953091i
$887$	−7.43685	+	22.8883i	−0.249705	+	0.768513i	0.745122	+	0.666928i	$0.232391\pi$
$887$	−7.43685	+	22.8883i	−0.249705	+	0.768513i	−0.994827	+	0.101585i	$0.967609\pi$
$888$	−2.48000	+	4.00815i	−0.0832233	+	0.134505i
$889$	−2.14147	+	1.55587i	−0.0718226	+	0.0521822i
$890$	48.7277			1.63336
$891$	26.6353	−	13.4744i	0.892317	−	0.451409i
$892$	5.50179			0.184214
$893$	−20.2776	+	14.7325i	−0.678564	+	0.493006i
$894$	0.699676	−	1.13081i	0.0234007	−	0.0378200i
$895$	2.24895	−	6.92156i	0.0751741	−	0.231362i
$896$	0.587785	−	0.809017i	0.0196365	−	0.0270274i
$897$	0.260190	+	3.49852i	0.00868748	+	0.116812i
$898$	−5.57172	−	1.81036i	−0.185931	−	0.0604125i
$899$	−0.745400	−	2.29411i	−0.0248605	−	0.0765127i
$900$	9.49225	+	19.0330i	0.316408	+	0.634432i
$901$		−	55.1386i		−	1.83693i
$902$	11.1069	+	21.0476i	0.369819	+	0.700808i
$903$	12.6871	+	14.9848i	0.422199	+	0.498663i
$904$	4.27870	+	5.88913i	0.142307	+	0.195869i
$905$	−25.9936	+	8.44585i	−0.864058	+	0.280750i
$906$	4.78936	+	11.7048i	0.159116	+	0.388866i
$907$	−0.409271	−	0.297353i	−0.0135896	−	0.00987344i	0.580970	−	0.813925i	$-0.302673\pi$
$907$	−0.409271	−	0.297353i	−0.0135896	−	0.00987344i	−0.594559	+	0.804052i	$0.702673\pi$
$908$	13.4844	+	9.79699i	0.447496	+	0.325125i
$909$	−10.1025	−	5.25753i	−0.335079	−	0.174381i
$910$	15.5605	−	5.05592i	0.515826	−	0.167602i
$911$	−2.07918	−	2.86174i	−0.0688862	−	0.0948137i	0.773184	−	0.634182i	$-0.218663\pi$
$911$	−2.07918	−	2.86174i	−0.0688862	−	0.0948137i	−0.842070	+	0.539368i	$0.818663\pi$
$912$	−3.04545	+	2.57847i	−0.100845	+	0.0853816i
$913$	24.8130	+	47.0207i	0.821190	+	1.55616i
$914$			15.5025i			0.512776i
$915$	52.0634	+	12.7366i	1.72116	+	0.421060i
$916$	−6.11846	−	18.8307i	−0.202159	−	0.622183i
$917$	4.34880	+	1.41301i	0.143610	+	0.0466618i
$918$	37.7225	+	3.45958i	1.24503	+	0.114183i
$919$	21.1774	−	29.1482i	0.698578	−	0.961510i	−0.301390	−	0.953501i	$-0.597451\pi$
$919$	21.1774	−	29.1482i	0.698578	−	0.961510i	0.999968	−	0.00800903i	$-0.00254938\pi$
$920$	−0.462484	+	1.42338i	−0.0152476	+	0.0469274i
$921$	37.0026	+	22.8950i	1.21928	+	0.754414i
$922$	−6.80522	+	4.94428i	−0.224118	+	0.162831i
$923$	70.7934			2.33019
$924$	0.393307	−	5.73108i	0.0129388	−	0.188539i
$925$	−19.2925			−0.634333
$926$	−13.8914	+	10.0927i	−0.456500	+	0.331667i
$927$	−16.4310	+	2.45758i	−0.539665	+	0.0807176i
$928$	−0.591869	+	1.82159i	−0.0194291	+	0.0597965i
$929$	20.6806	−	28.4644i	0.678509	−	0.933888i	−0.321406	−	0.946942i	$-0.604155\pi$
$929$	20.6806	−	28.4644i	0.678509	−	0.933888i	0.999915	+	0.0130538i	$0.00415526\pi$
$930$	7.56366	−	0.562519i	0.248022	−	0.0184457i
$931$	−2.19110	−	0.711931i	−0.0718103	−	0.0233326i
$932$	0.290324	+	0.893525i	0.00950988	+	0.0292684i
$933$	2.27424	−	9.29638i	0.0744552	−	0.304350i
$934$			18.9032i			0.618533i
$935$	83.2145	+	11.9606i	2.72140	+	0.391153i
$936$	−13.9234	−	2.32831i	−0.455100	−	0.0761033i
$937$	2.98860	+	4.11345i	0.0976332	+	0.134381i	0.855039	−	0.518564i	$-0.173533\pi$
$937$	2.98860	+	4.11345i	0.0976332	+	0.134381i	−0.757405	+	0.652945i	$0.773533\pi$
$938$	3.61026	−	1.17305i	0.117879	−	0.0383013i
$939$	50.8789	−	20.8186i	1.66037	−	0.679388i
$940$	−30.6032	−	22.2345i	−0.998166	−	0.725210i
$941$	10.4150	+	7.56693i	0.339519	+	0.246675i	0.744459	−	0.667668i	$-0.232708\pi$
$941$	10.4150	+	7.56693i	0.339519	+	0.246675i	−0.404940	+	0.914343i	$0.632708\pi$
$942$	−16.6874	+	6.82815i	−0.543706	+	0.222473i
$943$	−2.93742	+	0.954426i	−0.0956556	+	0.0310804i
$944$	−4.72524	−	6.50373i	−0.153793	−	0.211678i
$945$	15.5253	−	9.24026i	0.505039	−	0.300586i
$946$	−6.41278	−	37.0459i	−0.208497	−	1.20447i
$947$			0.702703i			0.0228348i	0.999935	+	0.0114174i	$0.00363435\pi$
$947$			0.702703i			0.0228348i	−0.999935	+	0.0114174i	$0.996366\pi$
$948$	−3.07227	+	12.5585i	−0.0997829	+	0.407882i
$949$	−0.365115	−	1.12371i	−0.0118521	−	0.0364771i
$950$	−15.5339	−	5.04727i	−0.503987	−	0.163755i
$951$	10.5928	−	0.787803i	0.343496	−	0.0255463i
$952$	4.28505	−	5.89787i	0.138879	−	0.191151i
$953$	−2.98770	+	9.19520i	−0.0967811	+	0.297862i	−0.987714	−	0.156274i	$-0.950052\pi$
$953$	−2.98770	+	9.19520i	−0.0967811	+	0.297862i	0.890933	+	0.454135i	$0.150052\pi$
$954$	3.35644	+	22.4406i	0.108669	+	0.726542i
$955$	−42.2148	+	30.6708i	−1.36604	+	0.992484i
$956$	1.30471			0.0421973
$957$	2.67561	+	10.6724i	0.0864901	+	0.344991i
$958$	−15.0285			−0.485548
$959$	12.8583	−	9.34209i	0.415216	−	0.301672i
$960$	−5.12130	−	3.16875i	−0.165289	−	0.102271i
$961$	−9.08940	+	27.9743i	−0.293206	+	0.902396i
$962$	7.52663	−	10.3595i	0.242668	−	0.334004i
$963$	23.6176	−	23.2143i	0.761065	−	0.748071i
$964$	15.5214	+	5.04321i	0.499911	+	0.162431i
$965$	25.0019	+	76.9479i	0.804839	+	2.47704i
$966$	0.724182	+	0.177162i	0.0233002	+	0.00570008i
$967$		−	7.58960i		−	0.244065i	−0.992526	−	0.122033i	$-0.961059\pi$
$967$		−	7.58960i		−	0.244065i	0.992526	−	0.122033i	$-0.0389412\pi$
$968$	−6.20805	+	9.08076i	−0.199534	+	0.291867i
$969$	−22.2019	+	18.7975i	−0.713226	+	0.603862i
$970$	9.18839	+	12.6467i	0.295022	+	0.406062i
$971$	0.649473	−	0.211027i	0.0208426	−	0.00677217i	−0.298577	−	0.954386i	$-0.596512\pi$
$971$	0.649473	−	0.211027i	0.0208426	−	0.00677217i	0.319420	+	0.947613i	$0.396512\pi$
$972$	−15.5631	+	0.888279i	−0.499188	+	0.0284916i
$973$	9.36412	+	6.80343i	0.300200	+	0.218108i
$974$	5.40692	+	3.92836i	0.173249	+	0.125873i
$975$	−21.8822	−	53.4783i	−0.700791	−	1.71268i
$976$	−8.46437	+	2.75024i	−0.270938	+	0.0880330i
$977$	27.5216	+	37.8802i	0.880494	+	1.21190i	0.976284	+	0.216495i	$0.0694623\pi$
$977$	27.5216	+	37.8802i	0.880494	+	1.21190i	−0.0957898	+	0.995402i	$0.530538\pi$
$978$	−15.6578	−	18.4936i	−0.500681	−	0.591359i
$979$	−20.5061	+	41.7121i	−0.655379	+	1.33313i
$980$		−	3.47700i		−	0.111069i
$981$	21.9138	−	10.9290i	0.699655	−	0.348937i
$982$	6.11100	+	18.8077i	0.195010	+	0.600179i
$983$	−46.1059	−	14.9807i	−1.47055	−	0.477811i	−0.539276	−	0.842129i	$-0.681302\pi$
$983$	−46.1059	−	14.9807i	−1.47055	−	0.477811i	−0.931274	+	0.364318i	$0.881302\pi$
$984$	−0.921764	−	12.3941i	−0.0293848	−	0.395109i
$985$	−23.6005	+	32.4833i	−0.751975	+	1.03500i
$986$	−4.31483	+	13.2797i	−0.137412	+	0.422911i
$987$	−9.91484	+	16.0243i	−0.315593	+	0.510059i
$988$	8.77053	−	6.37216i	0.279028	−	0.202726i
$989$	4.87937			0.155155
$990$	−34.5952	+	0.197717i	−1.09951	+	0.00628386i
$991$	17.8508			0.567050			0.283525	−	0.958965i	$-0.408496\pi$
$991$	17.8508			0.567050			0.283525	+	0.958965i	$0.408496\pi$
$992$	−1.01888	+	0.740257i	−0.0323494	+	0.0235032i
$993$	20.4426	−	33.0392i	0.648726	−	1.04847i
$994$	4.64903	−	14.3082i	0.147458	−	0.453830i
$995$	4.45254	−	6.12840i	0.141155	−	0.194283i
$996$	−2.05924	−	27.6886i	−0.0652494	−	0.877346i
$997$	−44.6109	−	14.4950i	−1.41284	−	0.459060i	−0.499521	−	0.866302i	$-0.666490\pi$
$997$	−44.6109	−	14.4950i	−1.41284	−	0.459060i	−0.913320	+	0.407242i	$0.866490\pi$
$998$	−5.31910	−	16.3705i	−0.168373	−	0.518200i
$999$	5.57943	−	12.9927i	0.176525	−	0.411072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.w.a.239.5	yes	48
3.2	odd	2		462.2.w.b.239.10	yes	48
11.7	odd	10		462.2.w.b.29.10	yes	48
33.29	even	10	inner	462.2.w.a.29.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.w.a.29.5	✓	48	33.29	even	10	inner
462.2.w.a.239.5	yes	48	1.1	even	1	trivial
462.2.w.b.29.10	yes	48	11.7	odd	10
462.2.w.b.239.10	yes	48	3.2	odd	2

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.911344 + 1.47291i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.04373 - 2.81296i) q^{5} +(-0.128460 - 1.72728i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.33891 - 2.68465i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.911344 + 1.47291i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.04373 - 2.81296i) q^{5} +(-0.128460 - 1.72728i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.33891 - 2.68465i) q^{9} +3.47700i q^{10} +(-2.97640 - 1.46323i) q^{11} +(1.11920 + 1.32189i) q^{12} +(-2.76587 - 3.80689i) q^{13} +(-0.951057 + 0.309017i) q^{14} +(2.28068 + 5.57379i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.89787 - 4.28505i) q^{17} +(2.66119 + 1.38494i) q^{18} +(-2.19110 + 0.711931i) q^{19} +(-2.04373 - 2.81296i) q^{20} +(-1.32189 + 1.11920i) q^{21} +(3.26802 - 0.565707i) q^{22} +0.430436i q^{23} +(-1.68244 - 0.411586i) q^{24} +(-2.19079 - 6.74257i) q^{25} +(4.47527 + 1.45410i) q^{26} +(5.17444 + 0.474553i) q^{27} +(0.587785 - 0.809017i) q^{28} +(-0.591869 + 1.82159i) q^{29} +(-5.12130 - 3.16875i) q^{30} +(-1.01888 + 0.740257i) q^{31} +1.00000 q^{32} +(4.86772 - 3.05045i) q^{33} +7.29017 q^{34} +(2.81296 - 2.04373i) q^{35} +(-2.96700 + 0.443773i) q^{36} +(0.840914 - 2.58807i) q^{37} +(1.35417 - 1.86386i) q^{38} +(8.12785 - 0.604479i) q^{39} +(3.30683 + 1.07445i) q^{40} +(2.21735 + 6.82429i) q^{41} +(0.411586 - 1.68244i) q^{42} -11.3359i q^{43} +(-2.31137 + 2.37856i) q^{44} +(-10.2882 - 1.72042i) q^{45} +(-0.253004 - 0.348230i) q^{46} +(10.3469 - 3.36191i) q^{47} +(1.60305 - 0.655932i) q^{48} +(0.809017 + 0.587785i) q^{49} +(5.73557 + 4.16714i) q^{50} +(11.6865 - 4.78186i) q^{51} +(-4.47527 + 1.45410i) q^{52} +(4.44566 + 6.11893i) q^{53} +(-4.46514 + 2.65754i) q^{54} +(-10.1990 + 5.38203i) q^{55} +1.00000i q^{56} +(0.948236 - 3.87610i) q^{57} +(-0.591869 - 1.82159i) q^{58} +(7.64560 + 2.48420i) q^{59} +(6.00576 - 0.446656i) q^{60} +(5.23127 - 7.20022i) q^{61} +(0.389176 - 1.19776i) q^{62} +(-0.443773 - 2.96700i) q^{63} +(-0.809017 + 0.587785i) q^{64} -16.3613 q^{65} +(-2.14506 + 5.32905i) q^{66} -3.79606 q^{67} +(-5.89787 + 4.28505i) q^{68} +(-0.633992 - 0.392275i) q^{69} +(-1.07445 + 3.30683i) q^{70} +(-8.84298 + 12.1713i) q^{71} +(2.13951 - 2.10298i) q^{72} +(0.238803 + 0.0775919i) q^{73} +(0.840914 + 2.58807i) q^{74} +(11.9277 + 2.91796i) q^{75} +2.30386i q^{76} +(-2.37856 - 2.31137i) q^{77} +(-6.22026 + 5.26646i) q^{78} +(4.38751 + 6.03889i) q^{79} +(-3.30683 + 1.07445i) q^{80} +(-5.41466 + 7.18898i) q^{81} +(-5.80509 - 4.21765i) q^{82} +(-12.9687 - 9.42229i) q^{83} +(0.655932 + 1.60305i) q^{84} +(-24.1073 + 7.83295i) q^{85} +(6.66306 + 9.17091i) q^{86} +(-2.14363 - 2.53186i) q^{87} +(0.471856 - 3.28289i) q^{88} -14.0143i q^{89} +(9.33453 - 4.65538i) q^{90} +(-1.45410 - 4.47527i) q^{91} +(0.409369 + 0.133012i) q^{92} +(-0.161783 - 2.17534i) q^{93} +(-6.39473 + 8.80159i) q^{94} +(-2.47539 + 7.61846i) q^{95} +(-0.911344 + 1.47291i) q^{96} +(3.63725 - 2.64262i) q^{97} -1.00000 q^{98} +(0.0568642 + 9.94971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 48 * q - 12 * q^2 - 4 * q^3 - 12 * q^4 + 6 * q^6 - 12 * q^8 + 10 * q^9	\( 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9} - 8 q^{11} + 6 q^{12} + 36 q^{15} - 12 q^{16} - 24 q^{17} + 30 q^{19} - 8 q^{22} - 4 q^{24} + 18 q^{25} - 20 q^{26} - 22 q^{27} + 8 q^{29} - 24 q^{30} - 32 q^{31} + 48 q^{32} - 14 q^{33} - 4 q^{34} + 6 q^{35} - 10 q^{36} - 20 q^{37} + 20 q^{38} - 6 q^{39} + 22 q^{44} + 12 q^{45} + 20 q^{46} + 20 q^{47} - 4 q^{48} + 12 q^{49} + 28 q^{50} + 8 q^{51} + 20 q^{52} + 20 q^{53} + 18 q^{54} + 16 q^{55} - 2 q^{57} + 8 q^{58} + 30 q^{59} - 4 q^{60} - 20 q^{61} + 8 q^{62} + 4 q^{63} - 12 q^{64} - 14 q^{66} + 36 q^{67} - 24 q^{68} - 70 q^{69} - 4 q^{70} + 10 q^{72} - 20 q^{73} - 20 q^{74} - 30 q^{75} - 16 q^{77} - 16 q^{78} - 20 q^{79} + 26 q^{81} - 10 q^{82} - 46 q^{83} - 10 q^{84} + 10 q^{85} - 30 q^{86} + 8 q^{87} - 8 q^{88} - 38 q^{90} - 36 q^{91} + 10 q^{92} - 36 q^{93} + 50 q^{95} - 4 q^{96} - 2 q^{97} - 48 q^{98} + 70 q^{99}+O(q^{100}) \) 48 * q - 12 * q^2 - 4 * q^3 - 12 * q^4 + 6 * q^6 - 12 * q^8 + 10 * q^9 - 8 * q^11 + 6 * q^12 + 36 * q^15 - 12 * q^16 - 24 * q^17 + 30 * q^19 - 8 * q^22 - 4 * q^24 + 18 * q^25 - 20 * q^26 - 22 * q^27 + 8 * q^29 - 24 * q^30 - 32 * q^31 + 48 * q^32 - 14 * q^33 - 4 * q^34 + 6 * q^35 - 10 * q^36 - 20 * q^37 + 20 * q^38 - 6 * q^39 + 22 * q^44 + 12 * q^45 + 20 * q^46 + 20 * q^47 - 4 * q^48 + 12 * q^49 + 28 * q^50 + 8 * q^51 + 20 * q^52 + 20 * q^53 + 18 * q^54 + 16 * q^55 - 2 * q^57 + 8 * q^58 + 30 * q^59 - 4 * q^60 - 20 * q^61 + 8 * q^62 + 4 * q^63 - 12 * q^64 - 14 * q^66 + 36 * q^67 - 24 * q^68 - 70 * q^69 - 4 * q^70 + 10 * q^72 - 20 * q^73 - 20 * q^74 - 30 * q^75 - 16 * q^77 - 16 * q^78 - 20 * q^79 + 26 * q^81 - 10 * q^82 - 46 * q^83 - 10 * q^84 + 10 * q^85 - 30 * q^86 + 8 * q^87 - 8 * q^88 - 38 * q^90 - 36 * q^91 + 10 * q^92 - 36 * q^93 + 50 * q^95 - 4 * q^96 - 2 * q^97 - 48 * q^98 + 70 * q^99

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