LMFDB - Embedded newform 126.2.h.c.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(67,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("126.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.h (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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	126.79
Dual form			126.2.h.c.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.73025 + 0.0789082i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.460505 q^{5} +(-0.796790 - 1.53790i) q^{6} +(2.25729 - 1.38008i) q^{7} +1.00000 q^{8} +(2.98755 + 0.273062i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.73025 + 0.0789082i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.460505 q^{5} +(-0.796790 - 1.53790i) q^{6} +(2.25729 - 1.38008i) q^{7} +1.00000 q^{8} +(2.98755 + 0.273062i) q^{9} +(0.230252 + 0.398809i) q^{10} -3.64766 q^{11} +(-0.933463 + 1.45899i) q^{12} +(0.730252 + 1.26483i) q^{13} +(-2.32383 - 1.26483i) q^{14} +(-0.796790 - 0.0363376i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.86693 - 3.23361i) q^{17} +(-1.25729 - 2.72382i) q^{18} +(-2.02704 + 3.51094i) q^{19} +(0.230252 - 0.398809i) q^{20} +(4.01459 - 2.20977i) q^{21} +(1.82383 + 3.15897i) q^{22} +1.13307 q^{23} +(1.73025 + 0.0789082i) q^{24} -4.78794 q^{25} +(0.730252 - 1.26483i) q^{26} +(5.14766 + 0.708209i) q^{27} +(0.0665372 + 2.64491i) q^{28} +(-4.48755 + 7.77266i) q^{29} +(0.366926 + 0.708209i) q^{30} +(0.257295 - 0.445647i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.31138 - 0.287831i) q^{33} +(-1.86693 + 3.23361i) q^{34} +(-1.03950 + 0.635534i) q^{35} +(-1.73025 + 2.45076i) q^{36} +(-4.55408 + 7.88791i) q^{37} +4.05408 q^{38} +(1.16372 + 2.24611i) q^{39} -0.460505 q^{40} +(-0.472958 - 0.819187i) q^{41} +(-3.92101 - 2.37185i) q^{42} +(4.66372 - 8.07779i) q^{43} +(1.82383 - 3.15897i) q^{44} +(-1.37578 - 0.125747i) q^{45} +(-0.566537 - 0.981271i) q^{46} +(-1.16372 - 2.01561i) q^{47} +(-0.796790 - 1.53790i) q^{48} +(3.19076 - 6.23049i) q^{49} +(2.39397 + 4.14647i) q^{50} +(-2.97509 - 5.74228i) q^{51} -1.46050 q^{52} +(6.21780 + 10.7695i) q^{53} +(-1.96050 - 4.81211i) q^{54} +1.67977 q^{55} +(2.25729 - 1.38008i) q^{56} +(-3.78434 + 5.91486i) q^{57} +8.97509 q^{58} +(6.44805 - 11.1684i) q^{59} +(0.429864 - 0.671871i) q^{60} +(-6.04163 - 10.4644i) q^{61} -0.514589 q^{62} +(7.12062 - 3.50667i) q^{63} +1.00000 q^{64} +(-0.336285 - 0.582462i) q^{65} +(2.90642 + 5.60973i) q^{66} +(1.16012 - 2.00938i) q^{67} +3.73385 q^{68} +(1.96050 + 0.0894089i) q^{69} +(1.07014 + 0.582462i) q^{70} +1.67977 q^{71} +(2.98755 + 0.273062i) q^{72} +(-6.62062 - 11.4673i) q^{73} +9.10817 q^{74} +(-8.28434 - 0.377808i) q^{75} +(-2.02704 - 3.51094i) q^{76} +(-8.23385 + 5.03407i) q^{77} +(1.36333 - 2.13086i) q^{78} +(2.50360 + 4.33636i) q^{79} +(0.230252 + 0.398809i) q^{80} +(8.85087 + 1.63157i) q^{81} +(-0.472958 + 0.819187i) q^{82} +(3.32383 - 5.75705i) q^{83} +(-0.0935793 + 4.58162i) q^{84} +(0.859728 + 1.48909i) q^{85} -9.32743 q^{86} +(-8.37792 + 13.0946i) q^{87} -3.64766 q^{88} +(-1.36333 + 2.36135i) q^{89} +(0.578990 + 1.25433i) q^{90} +(3.39397 + 1.84730i) q^{91} +(-0.566537 + 0.981271i) q^{92} +(0.480350 - 0.750780i) q^{93} +(-1.16372 + 2.01561i) q^{94} +(0.933463 - 1.61680i) q^{95} +(-0.933463 + 1.45899i) q^{96} +(-5.59358 + 9.68836i) q^{97} +(-6.99115 + 0.351971i) q^{98} +(-10.8976 - 0.996040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9	\( 6 q - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9} - 5 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} - 4 q^{17} + 8 q^{18} - 3 q^{19} - 5 q^{20} - 7 q^{21} - q^{22} + 14 q^{23} + 4 q^{24} + 4 q^{25} - 2 q^{26} + 7 q^{27} + 4 q^{28} - 5 q^{29} - 5 q^{30} - 14 q^{31} - 3 q^{32} - 4 q^{33} - 4 q^{34} - 19 q^{35} - 4 q^{36} - 9 q^{37} + 6 q^{38} - 3 q^{39} + 10 q^{40} - 12 q^{41} + 2 q^{42} + 18 q^{43} - q^{44} - 31 q^{45} - 7 q^{46} + 3 q^{47} - 2 q^{48} - 2 q^{50} + 26 q^{51} + 4 q^{52} + 9 q^{53} + q^{54} + 14 q^{55} - 2 q^{56} + 2 q^{57} + 10 q^{58} + 4 q^{59} + 7 q^{60} + 4 q^{61} + 28 q^{62} + 28 q^{63} + 6 q^{64} - 12 q^{65} + 23 q^{66} + 5 q^{67} + 8 q^{68} - q^{69} + 2 q^{70} + 14 q^{71} - 4 q^{72} - 25 q^{73} + 18 q^{74} - 25 q^{75} - 3 q^{76} - 35 q^{77} + 9 q^{78} + 7 q^{79} - 5 q^{80} + 32 q^{81} - 12 q^{82} + 8 q^{83} + 5 q^{84} + 14 q^{85} - 36 q^{86} - 20 q^{87} + 2 q^{88} - 9 q^{89} + 29 q^{90} + 4 q^{91} - 7 q^{92} - 3 q^{93} + 3 q^{94} + 2 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 41 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9 - 5 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 - 4 * q^17 + 8 * q^18 - 3 * q^19 - 5 * q^20 - 7 * q^21 - q^22 + 14 * q^23 + 4 * q^24 + 4 * q^25 - 2 * q^26 + 7 * q^27 + 4 * q^28 - 5 * q^29 - 5 * q^30 - 14 * q^31 - 3 * q^32 - 4 * q^33 - 4 * q^34 - 19 * q^35 - 4 * q^36 - 9 * q^37 + 6 * q^38 - 3 * q^39 + 10 * q^40 - 12 * q^41 + 2 * q^42 + 18 * q^43 - q^44 - 31 * q^45 - 7 * q^46 + 3 * q^47 - 2 * q^48 - 2 * q^50 + 26 * q^51 + 4 * q^52 + 9 * q^53 + q^54 + 14 * q^55 - 2 * q^56 + 2 * q^57 + 10 * q^58 + 4 * q^59 + 7 * q^60 + 4 * q^61 + 28 * q^62 + 28 * q^63 + 6 * q^64 - 12 * q^65 + 23 * q^66 + 5 * q^67 + 8 * q^68 - q^69 + 2 * q^70 + 14 * q^71 - 4 * q^72 - 25 * q^73 + 18 * q^74 - 25 * q^75 - 3 * q^76 - 35 * q^77 + 9 * q^78 + 7 * q^79 - 5 * q^80 + 32 * q^81 - 12 * q^82 + 8 * q^83 + 5 * q^84 + 14 * q^85 - 36 * q^86 - 20 * q^87 + 2 * q^88 - 9 * q^89 + 29 * q^90 + 4 * q^91 - 7 * q^92 - 3 * q^93 + 3 * q^94 + 2 * q^95 - 2 * q^96 - 28 * q^97 - 12 * q^98 - 41 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.73025	+	0.0789082i	0.998962	+	0.0455577i
$3$	1.73025	+	0.0789082i	0.998962	+	0.0455577i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.460505			−0.205944			−0.102972	−	0.994684i	$-0.532835\pi$
$5$	−0.460505			−0.205944			−0.102972	+	0.994684i	$0.532835\pi$
$6$	−0.796790	−	1.53790i	−0.325288	−	0.627844i
$7$	2.25729	−	1.38008i	0.853177	−	0.521621i
$7$	2.25729	−	1.38008i	0.853177	−	0.521621i
$8$	1.00000			0.353553
$9$	2.98755	+	0.273062i	0.995849	+	0.0910208i
$10$	0.230252	+	0.398809i	0.0728122	+	0.126114i
$11$	−3.64766			−1.09981			−0.549906	−	0.835227i	$-0.685336\pi$
$11$	−3.64766			−1.09981			−0.549906	+	0.835227i	$0.685336\pi$
$12$	−0.933463	+	1.45899i	−0.269467	+	0.421174i
$13$	0.730252	+	1.26483i	0.202536	+	0.350802i	0.949345	−	0.314236i	$-0.101748\pi$
$13$	0.730252	+	1.26483i	0.202536	+	0.350802i	−0.746809	+	0.665038i	$0.768415\pi$
$14$	−2.32383	−	1.26483i	−0.621070	−	0.338041i
$15$	−0.796790	−	0.0363376i	−0.205730	−	0.00938234i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.86693	−	3.23361i	−0.452796	−	0.784266i	0.545763	−	0.837940i	$-0.316240\pi$
$17$	−1.86693	−	3.23361i	−0.452796	−	0.784266i	−0.998558	+	0.0536743i	$0.982907\pi$
$18$	−1.25729	−	2.72382i	−0.296347	−	0.642011i
$19$	−2.02704	+	3.51094i	−0.465035	+	0.805465i	−0.999203	−	0.0399136i	$-0.987292\pi$
$19$	−2.02704	+	3.51094i	−0.465035	+	0.805465i	0.534168	+	0.845378i	$0.320625\pi$
$20$	0.230252	−	0.398809i	0.0514860	−	0.0891764i
$21$	4.01459	−	2.20977i	0.876055	−	0.482211i
$22$	1.82383	+	3.15897i	0.388842	+	0.673495i
$23$	1.13307			0.236262			0.118131	−	0.992998i	$-0.462310\pi$
$23$	1.13307			0.236262			0.118131	+	0.992998i	$0.462310\pi$
$24$	1.73025	+	0.0789082i	0.353186	+	0.0161071i
$25$	−4.78794			−0.957587
$26$	0.730252	−	1.26483i	0.143214	−	0.248054i
$27$	5.14766	+	0.708209i	0.990668	+	0.136295i
$28$	0.0665372	+	2.64491i	0.0125744	+	0.499842i
$29$	−4.48755	+	7.77266i	−0.833317	+	1.44335i	0.0620772	+	0.998071i	$0.480228\pi$
$29$	−4.48755	+	7.77266i	−0.833317	+	1.44335i	−0.895394	+	0.445275i	$0.853106\pi$
$30$	0.366926	+	0.708209i	0.0669911	+	0.129301i
$31$	0.257295	−	0.445647i	0.0462115	−	0.0800406i	−0.841994	−	0.539486i	$-0.818619\pi$
$31$	0.257295	−	0.445647i	0.0462115	−	0.0800406i	0.888206	+	0.459446i	$0.151952\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−6.31138	−	0.287831i	−1.09867	−	0.0501049i
$34$	−1.86693	+	3.23361i	−0.320175	+	0.554560i
$35$	−1.03950	+	0.635534i	−0.175707	+	0.107425i
$36$	−1.73025	+	2.45076i	−0.288375	+	0.408460i
$37$	−4.55408	+	7.88791i	−0.748687	+	1.29676i	0.199765	+	0.979844i	$0.435982\pi$
$37$	−4.55408	+	7.88791i	−0.748687	+	1.29676i	−0.948452	+	0.316920i	$0.897351\pi$
$38$	4.05408			0.657659
$39$	1.16372	+	2.24611i	0.186344	+	0.359665i
$40$	−0.460505			−0.0728122
$41$	−0.472958	−	0.819187i	−0.0738636	−	0.127936i	0.826728	−	0.562602i	$-0.190200\pi$
$41$	−0.472958	−	0.819187i	−0.0738636	−	0.127936i	−0.900592	+	0.434666i	$0.856866\pi$
$42$	−3.92101	−	2.37185i	−0.605025	−	0.365985i
$43$	4.66372	−	8.07779i	0.711210	−	1.23185i	−0.253193	−	0.967416i	$-0.581481\pi$
$43$	4.66372	−	8.07779i	0.711210	−	1.23185i	0.964403	−	0.264436i	$-0.0851858\pi$
$44$	1.82383	−	3.15897i	0.274953	−	0.476233i
$45$	−1.37578	−	0.125747i	−0.205089	−	0.0187452i
$46$	−0.566537	−	0.981271i	−0.0835314	−	0.144681i
$47$	−1.16372	−	2.01561i	−0.169745	−	0.294007i	0.768585	−	0.639748i	$-0.220961\pi$
$47$	−1.16372	−	2.01561i	−0.169745	−	0.294007i	−0.938330	+	0.345740i	$0.887628\pi$
$48$	−0.796790	−	1.53790i	−0.115007	−	0.221976i
$49$	3.19076	−	6.23049i	0.455822	−	0.890071i
$50$	2.39397	+	4.14647i	0.338558	+	0.586400i
$51$	−2.97509	−	5.74228i	−0.416596	−	0.804080i
$52$	−1.46050			−0.202536
$53$	6.21780	+	10.7695i	0.854080	+	1.47931i	0.877495	+	0.479585i	$0.159213\pi$
$53$	6.21780	+	10.7695i	0.854080	+	1.47931i	−0.0234151	+	0.999726i	$0.507454\pi$
$54$	−1.96050	−	4.81211i	−0.266791	−	0.654845i
$55$	1.67977			0.226500
$56$	2.25729	−	1.38008i	0.301644	−	0.184421i
$57$	−3.78434	+	5.91486i	−0.501248	+	0.783443i
$58$	8.97509			1.17849
$59$	6.44805	−	11.1684i	0.839465	−	1.45400i	−0.0508779	−	0.998705i	$-0.516202\pi$
$59$	6.44805	−	11.1684i	0.839465	−	1.45400i	0.890343	−	0.455291i	$-0.150465\pi$
$60$	0.429864	−	0.671871i	0.0554952	−	0.0867382i
$61$	−6.04163	−	10.4644i	−0.773552	−	1.33983i	−0.935605	−	0.353049i	$-0.885145\pi$
$61$	−6.04163	−	10.4644i	−0.773552	−	1.33983i	0.162053	−	0.986782i	$-0.448188\pi$
$62$	−0.514589			−0.0653529
$63$	7.12062	−	3.50667i	0.897114	−	0.441799i
$64$	1.00000			0.125000
$65$	−0.336285	−	0.582462i	−0.0417110	−	0.0722456i
$66$	2.90642	+	5.60973i	0.357756	+	0.690510i
$67$	1.16012	−	2.00938i	0.141731	−	0.245485i	−0.786418	−	0.617695i	$-0.788067\pi$
$67$	1.16012	−	2.00938i	0.141731	−	0.245485i	0.928148	+	0.372210i	$0.121400\pi$
$68$	3.73385			0.452796
$69$	1.96050	+	0.0894089i	0.236017	+	0.0107636i
$70$	1.07014	+	0.582462i	0.127906	+	0.0696176i
$71$	1.67977			0.199352			0.0996758	−	0.995020i	$-0.468219\pi$
$71$	1.67977			0.199352			0.0996758	+	0.995020i	$0.468219\pi$
$72$	2.98755	+	0.273062i	0.352086	+	0.0321807i
$73$	−6.62062	−	11.4673i	−0.774885	−	1.34214i	−0.934859	−	0.355019i	$-0.884474\pi$
$73$	−6.62062	−	11.4673i	−0.774885	−	1.34214i	0.159974	−	0.987121i	$-0.448859\pi$
$74$	9.10817			1.05880
$75$	−8.28434	−	0.377808i	−0.956593	−	0.0436255i
$76$	−2.02704	−	3.51094i	−0.232518	−	0.402732i
$77$	−8.23385	+	5.03407i	−0.938334	+	0.573685i
$78$	1.36333	−	2.13086i	0.154366	−	0.241272i
$79$	2.50360	+	4.33636i	0.281677	+	0.487879i	0.971798	−	0.235815i	$-0.0757761\pi$
$79$	2.50360	+	4.33636i	0.281677	+	0.487879i	−0.690121	+	0.723694i	$0.742443\pi$
$80$	0.230252	+	0.398809i	0.0257430	+	0.0445882i
$81$	8.85087	+	1.63157i	0.983430	+	0.181286i
$82$	−0.472958	+	0.819187i	−0.0522295	+	0.0904641i
$83$	3.32383	−	5.75705i	0.364838	−	0.631918i	−0.623912	−	0.781494i	$-0.714458\pi$
$83$	3.32383	−	5.75705i	0.364838	−	0.631918i	0.988750	+	0.149577i	$0.0477911\pi$
$84$	−0.0935793	+	4.58162i	−0.0102103	+	0.499896i
$85$	0.859728	+	1.48909i	0.0932506	+	0.161515i
$86$	−9.32743			−1.00580
$87$	−8.37792	+	13.0946i	−0.898207	+	1.40388i
$88$	−3.64766			−0.388842
$89$	−1.36333	+	2.36135i	−0.144512	+	0.250303i	−0.929191	−	0.369600i	$-0.879495\pi$
$89$	−1.36333	+	2.36135i	−0.144512	+	0.250303i	0.784679	+	0.619903i	$0.212828\pi$
$90$	0.578990	+	1.25433i	0.0610309	+	0.132218i
$91$	3.39397	+	1.84730i	0.355784	+	0.193649i
$92$	−0.566537	+	0.981271i	−0.0590656	+	0.102305i
$93$	0.480350	−	0.750780i	0.0498099	−	0.0778522i
$94$	−1.16372	+	2.01561i	−0.120028	+	0.207895i
$95$	0.933463	−	1.61680i	0.0957713	−	0.165881i
$96$	−0.933463	+	1.45899i	−0.0952711	+	0.148907i
$97$	−5.59358	+	9.68836i	−0.567942	+	0.983704i	0.428827	+	0.903386i	$0.358927\pi$
$97$	−5.59358	+	9.68836i	−0.567942	+	0.983704i	−0.996769	+	0.0803178i	$0.974406\pi$
$98$	−6.99115	+	0.351971i	−0.706212	+	0.0355544i
$99$	−10.8976	−	0.996040i	−1.09525	−	0.100106i
$100$	2.39397	−	4.14647i	0.239397	−	0.414647i
$101$	13.7558			1.36876			0.684378	−	0.729127i	$-0.260074\pi$
$101$	13.7558			1.36876			0.684378	+	0.729127i	$0.260074\pi$
$102$	−3.48541	+	5.44765i	−0.345107	+	0.539397i
$103$	11.1623			1.09985			0.549925	−	0.835214i	$-0.314656\pi$
$103$	11.1623			1.09985			0.549925	+	0.835214i	$0.314656\pi$
$104$	0.730252	+	1.26483i	0.0716071	+	0.124027i
$105$	−1.84874	+	1.01761i	−0.180418	+	0.0993085i
$106$	6.21780	−	10.7695i	0.603926	−	1.04603i
$107$	−3.89037	+	6.73832i	−0.376096	+	0.651418i	−0.990490	−	0.137581i	$-0.956067\pi$
$107$	−3.89037	+	6.73832i	−0.376096	+	0.651418i	0.614394	+	0.788999i	$0.289400\pi$
$108$	−3.18716	+	4.10390i	−0.306684	+	0.394898i
$109$	−3.75729	−	6.50783i	−0.359884	−	0.623337i	0.628058	−	0.778167i	$-0.283850\pi$
$109$	−3.75729	−	6.50783i	−0.359884	−	0.623337i	−0.987941	+	0.154830i	$0.950517\pi$
$110$	−0.839883	−	1.45472i	−0.0800797	−	0.138702i
$111$	−8.50214	+	13.2887i	−0.806987	+	1.26131i
$112$	−2.32383	−	1.26483i	−0.219581	−	0.119516i
$113$	3.03064	+	5.24922i	0.285099	+	0.493805i	0.972633	−	0.232346i	$-0.0746403\pi$
$113$	3.03064	+	5.24922i	0.285099	+	0.493805i	−0.687534	+	0.726152i	$0.741307\pi$
$114$	7.01459	+	0.319901i	0.656976	+	0.0299614i
$115$	−0.521786			−0.0486568
$116$	−4.48755	−	7.77266i	−0.416658	−	0.721673i
$117$	1.83628	+	3.97816i	0.169765	+	0.367781i
$118$	−12.8961			−1.18718
$119$	−8.67684	−	4.72270i	−0.795405	−	0.432929i
$120$	−0.796790	−	0.0363376i	−0.0727366	−	0.00331716i
$121$	2.30545			0.209586
$122$	−6.04163	+	10.4644i	−0.546984	+	0.947403i
$123$	−0.753696	−	1.45472i	−0.0679585	−	0.131168i
$124$	0.257295	+	0.445647i	0.0231057	+	0.0400203i
$125$	4.50739			0.403153
$126$	−6.59718	−	4.41330i	−0.587723	−	0.393168i
$127$	8.80992			0.781754			0.390877	−	0.920443i	$-0.372172\pi$
$127$	8.80992			0.781754			0.390877	+	0.920443i	$0.372172\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	8.70681	−	13.6086i	0.766592	−	1.19817i
$130$	−0.336285	+	0.582462i	−0.0294941	+	0.0510853i
$131$	21.1373			1.84678			0.923389	−	0.383865i	$-0.125407\pi$
$131$	21.1373			1.84678			0.923389	+	0.383865i	$0.125407\pi$
$132$	3.40496	−	5.32190i	0.296364	−	0.463212i
$133$	0.269748	+	10.7227i	0.0233901	+	0.929777i
$134$	−2.32023			−0.200438
$135$	−2.37052	−	0.326134i	−0.204022	−	0.0280691i
$136$	−1.86693	−	3.23361i	−0.160088	−	0.277280i
$137$	−4.40642			−0.376466			−0.188233	−	0.982124i	$-0.560276\pi$
$137$	−4.40642			−0.376466			−0.188233	+	0.982124i	$0.560276\pi$
$138$	−0.902822	−	1.74255i	−0.0768533	−	0.148336i
$139$	−1.01245	−	1.75362i	−0.0858751	−	0.148740i	0.819889	−	0.572523i	$-0.194035\pi$
$139$	−1.01245	−	1.75362i	−0.0858751	−	0.148740i	−0.905764	+	0.423783i	$0.860702\pi$
$140$	−0.0306407	−	1.21800i	−0.00258961	−	0.102939i
$141$	−1.85447	−	3.57935i	−0.156175	−	0.301435i
$142$	−0.839883	−	1.45472i	−0.0704815	−	0.122077i
$143$	−2.66372	−	4.61369i	−0.222751	−	0.385816i
$144$	−1.25729	−	2.72382i	−0.104775	−	0.226985i
$145$	2.06654	−	3.57935i	0.171617	−	0.297249i
$146$	−6.62062	+	11.4673i	−0.547927	+	0.949037i
$147$	6.01245	−	10.5286i	0.495899	−	0.868380i
$148$	−4.55408	−	7.88791i	−0.374343	−	0.648382i
$149$	−9.16225			−0.750601			−0.375300	−	0.926903i	$-0.622460\pi$
$149$	−9.16225			−0.750601			−0.375300	+	0.926903i	$0.622460\pi$
$150$	3.81498	+	7.36335i	0.311492	+	0.601215i
$151$	−0.103896			−0.00845496			−0.00422748	−	0.999991i	$-0.501346\pi$
$151$	−0.103896			−0.00845496			−0.00422748	+	0.999991i	$0.501346\pi$
$152$	−2.02704	+	3.51094i	−0.164415	+	0.284775i
$153$	−4.69455	−	10.1703i	−0.379532	−	0.822224i
$154$	8.47656	+	4.61369i	0.683060	+	0.371782i
$155$	−0.118485	+	0.205223i	−0.00951698	+	0.0164839i
$156$	−2.52704	−	0.115246i	−0.202325	−	0.00922705i
$157$	−10.4911	+	18.1712i	−0.837285	+	1.45022i	0.0548721	+	0.998493i	$0.482525\pi$
$157$	−10.4911	+	18.1712i	−0.837285	+	1.45022i	−0.892157	+	0.451726i	$0.850808\pi$
$158$	2.50360	−	4.33636i	0.199176	−	0.344982i
$159$	9.90856	+	19.1247i	0.785800	+	1.51668i
$160$	0.230252	−	0.398809i	0.0182031	−	0.0315286i
$161$	2.55768	−	1.56373i	0.201574	−	0.123239i
$162$	−3.01245	−	8.48087i	−0.236681	−	0.666320i
$163$	−11.5182	+	19.9501i	−0.902174	+	1.56261i	−0.0775078	+	0.996992i	$0.524696\pi$
$163$	−11.5182	+	19.9501i	−0.902174	+	1.56261i	−0.824666	+	0.565620i	$0.808637\pi$
$164$	0.945916			0.0738636
$165$	2.90642	+	0.132547i	0.226265	+	0.0103188i
$166$	−6.64766			−0.515959
$167$	−5.31498	−	9.20581i	−0.411285	−	0.712367i	0.583745	−	0.811937i	$-0.301587\pi$
$167$	−5.31498	−	9.20581i	−0.411285	−	0.712367i	−0.995031	+	0.0995698i	$0.968253\pi$
$168$	4.01459	−	2.20977i	0.309732	−	0.170487i
$169$	5.43346	−	9.41103i	0.417959	−	0.723926i
$170$	0.859728	−	1.48909i	0.0659382	−	0.114208i
$171$	−7.01459	+	9.93559i	−0.536419	+	0.759793i
$172$	4.66372	+	8.07779i	0.355605	+	0.615926i
$173$	−1.46936	−	2.54500i	−0.111713	−	0.193493i	0.804748	−	0.593617i	$-0.202301\pi$
$173$	−1.46936	−	2.54500i	−0.111713	−	0.193493i	−0.916461	+	0.400124i	$0.868967\pi$
$174$	15.5292	+	0.708209i	1.17726	+	0.0536892i
$175$	−10.8078	+	6.60773i	−0.816991	+	0.499498i
$176$	1.82383	+	3.15897i	0.137476	+	0.238116i
$177$	12.0380	−	18.8153i	0.904834	−	1.41424i
$178$	2.72665			0.204371
$179$	−4.58113	−	7.93474i	−0.342409	−	0.593071i	0.642470	−	0.766311i	$-0.277910\pi$
$179$	−4.58113	−	7.93474i	−0.342409	−	0.593071i	−0.984880	+	0.173240i	$0.944576\pi$
$180$	0.796790	−	1.12859i	0.0593892	−	0.0841199i
$181$	22.4284			1.66709			0.833545	−	0.552452i	$-0.186308\pi$
$181$	22.4284			1.66709			0.833545	+	0.552452i	$0.186308\pi$
$182$	−0.0971780	−	3.86291i	−0.00720331	−	0.286338i
$183$	−9.62782	−	18.5828i	−0.711709	−	1.37368i
$184$	1.13307			0.0835314
$185$	2.09718	−	3.63242i	0.154188	−	0.267061i
$186$	−0.890369	−	0.0406053i	−0.0652850	−	0.00297733i
$187$	6.80992	+	11.7951i	0.497990	+	0.862545i
$188$	2.32743			0.169745
$189$	12.5972	−	5.50555i	0.916310	−	0.400470i
$190$	−1.86693			−0.135441
$191$	−1.24484	−	2.15613i	−0.0900736	−	0.156012i	0.817468	−	0.575974i	$-0.195377\pi$
$191$	−1.24484	−	2.15613i	−0.0900736	−	0.156012i	−0.907542	+	0.419962i	$0.862044\pi$
$192$	1.73025	+	0.0789082i	0.124870	+	0.00569471i
$193$	−2.24484	+	3.88818i	−0.161587	+	0.279877i	−0.935438	−	0.353491i	$-0.884995\pi$
$193$	−2.24484	+	3.88818i	−0.161587	+	0.279877i	0.773851	+	0.633368i	$0.218328\pi$
$194$	11.1872			0.803191
$195$	−0.535897	−	1.03434i	−0.0383763	−	0.0740708i
$196$	3.80039	+	5.87852i	0.271456	+	0.419895i
$197$	12.7339			0.907249			0.453625	−	0.891193i	$-0.350131\pi$
$197$	12.7339			0.907249			0.453625	+	0.891193i	$0.350131\pi$
$198$	4.58619	+	9.93559i	0.325926	+	0.706092i
$199$	−1.47296	−	2.55124i	−0.104415	−	0.180852i	0.809084	−	0.587693i	$-0.199964\pi$
$199$	−1.47296	−	2.55124i	−0.104415	−	0.180852i	−0.913499	+	0.406841i	$0.866630\pi$
$200$	−4.78794			−0.338558
$201$	2.16585	−	3.38519i	0.152767	−	0.238773i
$202$	−6.87792	−	11.9129i	−0.483928	−	0.838189i
$203$	0.597178	+	23.7384i	0.0419137	+	1.66611i
$204$	6.46050	+	0.294632i	0.452326	+	0.0206283i
$205$	0.217799	+	0.377240i	0.0152118	+	0.0263476i
$206$	−5.58113	−	9.66679i	−0.388855	−	0.673517i
$207$	3.38511	+	0.309400i	0.235282	+	0.0215048i
$208$	0.730252	−	1.26483i	0.0506339	−	0.0877005i
$209$	7.39397	−	12.8067i	0.511451	−	0.885860i
$210$	1.80564	+	1.09225i	0.124601	+	0.0753724i
$211$	−0.608168	−	1.05338i	−0.0418680	−	0.0725176i	0.844332	−	0.535820i	$-0.179998\pi$
$211$	−0.608168	−	1.05338i	−0.0418680	−	0.0725176i	−0.886200	+	0.463303i	$0.846664\pi$
$212$	−12.4356			−0.854080
$213$	2.90642	+	0.132547i	0.199145	+	0.00908200i
$214$	7.78074			0.531880
$215$	−2.14766	+	3.71986i	−0.146469	+	0.253693i
$216$	5.14766	+	0.708209i	0.350254	+	0.0481875i
$217$	−0.0342393	−	1.36104i	−0.00232432	−	0.0923937i
$218$	−3.75729	+	6.50783i	−0.254476	+	0.440766i
$219$	−10.5505	−	20.3637i	−0.712936	−	1.37605i
$220$	−0.839883	+	1.45472i	−0.0566249	+	0.0980773i
$221$	2.72665	−	4.72270i	0.183415	−	0.317683i
$222$	15.7594	+	0.718710i	1.05770	+	0.0482366i
$223$	−0.445916	+	0.772349i	−0.0298607	+	0.0517203i	−0.880570	−	0.473917i	$-0.842840\pi$
$223$	−0.445916	+	0.772349i	−0.0298607	+	0.0517203i	0.850709	+	0.525637i	$0.176173\pi$
$224$	0.0665372	+	2.64491i	0.00444571	+	0.176721i
$225$	−14.3042	−	1.30740i	−0.953612	−	0.0871603i
$226$	3.03064	−	5.24922i	0.201595	−	0.349173i
$227$	−14.6519			−0.972483			−0.486242	−	0.873824i	$-0.661632\pi$
$227$	−14.6519			−0.972483			−0.486242	+	0.873824i	$0.661632\pi$
$228$	−3.23025	−	6.23476i	−0.213929	−	0.412907i
$229$	−9.57587			−0.632791			−0.316396	−	0.948627i	$-0.602473\pi$
$229$	−9.57587			−0.632791			−0.316396	+	0.948627i	$0.602473\pi$
$230$	0.260893	+	0.451880i	0.0172028	+	0.0297961i
$231$	−14.6439	+	8.06049i	−0.963496	+	0.530341i
$232$	−4.48755	+	7.77266i	−0.294622	+	0.510300i
$233$	7.21420	−	12.4954i	0.472618	−	0.818598i	−0.526891	−	0.849933i	$-0.676642\pi$
$233$	7.21420	−	12.4954i	0.472618	−	0.818598i	0.999509	+	0.0313345i	$0.00997571\pi$
$234$	2.52704	−	3.57935i	0.165198	−	0.233989i
$235$	0.535897	+	0.928200i	0.0349580	+	0.0605491i
$236$	6.44805	+	11.1684i	0.419732	+	0.726998i
$237$	3.98968	+	7.70055i	0.259158	+	0.500205i
$238$	0.248440	+	9.87572i	0.0161040	+	0.640148i
$239$	−9.15486	−	15.8567i	−0.592179	−	1.02568i	−0.993938	−	0.109938i	$-0.964935\pi$
$239$	−9.15486	−	15.8567i	−0.592179	−	1.02568i	0.401760	−	0.915745i	$-0.368399\pi$
$240$	0.366926	+	0.708209i	0.0236849	+	0.0457147i
$241$	0.0933847			0.00601544			0.00300772	−	0.999995i	$-0.499043\pi$
$241$	0.0933847			0.00601544			0.00300772	+	0.999995i	$0.499043\pi$
$242$	−1.15272	−	1.99658i	−0.0741000	−	0.128345i
$243$	15.1855	+	3.52144i	0.974150	+	0.225901i
$244$	12.0833			0.773552
$245$	−1.46936	+	2.86917i	−0.0938739	+	0.183305i
$246$	−0.882977	+	1.38008i	−0.0562966	+	0.0879907i
$247$	−5.92101			−0.376745
$248$	0.257295	−	0.445647i	0.0163382	−	0.0282986i
$249$	6.20535	−	9.69886i	0.393248	−	0.614641i
$250$	−2.25370	−	3.90352i	−0.142536	−	0.246880i
$251$	−18.2733			−1.15340			−0.576702	−	0.816955i	$-0.695661\pi$
$251$	−18.2733			−1.15340			−0.576702	+	0.816955i	$0.695661\pi$
$252$	−0.523443	+	7.91998i	−0.0329738	+	0.498912i
$253$	−4.13307			−0.259844
$254$	−4.40496	−	7.62961i	−0.276392	−	0.478724i
$255$	1.37005	+	2.64435i	0.0857956	+	0.165595i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−21.0512			−1.31314			−0.656568	−	0.754267i	$-0.727992\pi$
$257$	−21.0512			−1.31314			−0.656568	+	0.754267i	$0.727992\pi$
$258$	−16.1388	−	0.736011i	−1.00476	−	0.0458221i
$259$	0.606032	+	24.0903i	0.0376570	+	1.49690i
$260$	0.672570			0.0417110
$261$	−15.5292	+	21.9958i	−0.961232	+	1.36151i
$262$	−10.5687	−	18.3055i	−0.652935	−	1.13092i
$263$	−5.16518			−0.318499			−0.159249	−	0.987238i	$-0.550907\pi$
$263$	−5.16518			−0.318499			−0.159249	+	0.987238i	$0.550907\pi$
$264$	−6.31138	−	0.287831i	−0.388439	−	0.0177148i
$265$	−2.86333	−	4.95943i	−0.175893	−	0.304655i
$266$	9.15126	−	5.59496i	0.561100	−	0.343049i
$267$	−2.54523	+	3.97816i	−0.155766	+	0.243459i
$268$	1.16012	+	2.00938i	0.0708654	+	0.122742i
$269$	8.42840	+	14.5984i	0.513889	+	0.890081i	0.999870	+	0.0161123i	$0.00512891\pi$
$269$	8.42840	+	14.5984i	0.513889	+	0.890081i	−0.485981	+	0.873969i	$0.661538\pi$
$270$	0.902822	+	2.21600i	0.0549440	+	0.134862i
$271$	12.5562	−	21.7480i	0.762736	−	1.32110i	−0.178699	−	0.983904i	$-0.557189\pi$
$271$	12.5562	−	21.7480i	0.762736	−	1.32110i	0.941435	−	0.337194i	$-0.109478\pi$
$272$	−1.86693	+	3.23361i	−0.113199	+	0.196066i
$273$	5.72665	+	3.46410i	0.346593	+	0.209657i
$274$	2.20321	+	3.81607i	0.133101	+	0.230537i
$275$	17.4648			1.05317
$276$	−1.05768	+	1.65314i	−0.0636650	+	0.0995075i
$277$	3.38151			0.203176			0.101588	−	0.994827i	$-0.467608\pi$
$277$	3.38151			0.203176			0.101588	+	0.994827i	$0.467608\pi$
$278$	−1.01245	+	1.75362i	−0.0607229	+	0.105175i
$279$	0.890369	−	1.26113i	0.0533050	−	0.0755022i
$280$	−1.03950	+	0.635534i	−0.0621217	+	0.0379804i
$281$	−10.1388	+	17.5609i	−0.604831	+	1.04760i	0.387248	+	0.921976i	$0.373426\pi$
$281$	−10.1388	+	17.5609i	−0.604831	+	1.04760i	−0.992078	+	0.125622i	$0.959907\pi$
$282$	−2.17257	+	3.39569i	−0.129375	+	0.202211i
$283$	−8.67471	+	15.0250i	−0.515658	+	0.893145i	0.484177	+	0.874970i	$0.339119\pi$
$283$	−8.67471	+	15.0250i	−0.515658	+	0.893145i	−0.999835	+	0.0181754i	$0.994214\pi$
$284$	−0.839883	+	1.45472i	−0.0498379	+	0.0863218i
$285$	1.74271	−	2.72382i	0.103229	−	0.161345i
$286$	−2.66372	+	4.61369i	−0.157509	+	0.272813i
$287$	−2.19815	−	1.19643i	−0.129753	−	0.0706228i
$288$	−1.73025	+	2.45076i	−0.101956	+	0.144412i
$289$	1.52918	−	2.64861i	0.0899517	−	0.155801i
$290$	−4.13307			−0.242702
$291$	−10.4428	+	16.3219i	−0.612168	+	0.956809i
$292$	13.2412			0.774885
$293$	−4.93560	−	8.54871i	−0.288341	−	0.499421i	0.685073	−	0.728474i	$-0.259770\pi$
$293$	−4.93560	−	8.54871i	−0.288341	−	0.499421i	−0.973414	+	0.229054i	$0.926437\pi$
$294$	−12.1242	+	0.0573390i	−0.707099	+	0.00334408i
$295$	−2.96936	+	5.14308i	−0.172883	+	0.299442i
$296$	−4.55408	+	7.88791i	−0.264701	+	0.458475i
$297$	−18.7769	−	2.58331i	−1.08955	−	0.149899i
$298$	4.58113	+	7.93474i	0.265378	+	0.459647i
$299$	0.827430	+	1.43315i	0.0478515	+	0.0828813i
$300$	4.46936	−	6.98554i	0.258039	−	0.403310i
$301$	−0.620621	−	24.6703i	−0.0357720	−	1.42197i
$302$	0.0519482	+	0.0899768i	0.00298928	+	0.00517759i
$303$	23.8011	+	1.08545i	1.36734	+	0.0623574i
$304$	4.05408			0.232518
$305$	2.78220	+	4.81891i	0.159308	+	0.275930i
$306$	−6.46050	+	9.15077i	−0.369322	+	0.523115i
$307$	7.78794			0.444481			0.222240	−	0.974992i	$-0.428663\pi$
$307$	7.78794			0.444481			0.222240	+	0.974992i	$0.428663\pi$
$308$	−0.242705	−	9.64776i	−0.0138294	−	0.549732i
$309$	19.3135	+	0.880794i	1.09871	+	0.0501066i
$310$	0.236971			0.0134590
$311$	−7.70535	+	13.3461i	−0.436930	+	0.756785i	−0.997451	−	0.0713552i	$-0.977268\pi$
$311$	−7.70535	+	13.3461i	−0.436930	+	0.756785i	0.560521	+	0.828140i	$0.310601\pi$
$312$	1.16372	+	2.24611i	0.0658824	+	0.127161i
$313$	−4.24844	−	7.35851i	−0.240136	−	0.415928i	0.720617	−	0.693334i	$-0.243859\pi$
$313$	−4.24844	−	7.35851i	−0.240136	−	0.415928i	−0.960753	+	0.277406i	$0.910525\pi$
$314$	20.9823			1.18410
$315$	−3.27908	+	1.61484i	−0.184755	+	0.0909859i
$316$	−5.00720			−0.281677
$317$	7.05262	+	12.2155i	0.396115	+	0.686091i	0.993243	−	0.116055i	$-0.0370249\pi$
$317$	7.05262	+	12.2155i	0.396115	+	0.686091i	−0.597128	+	0.802146i	$0.703692\pi$
$318$	11.6082	−	18.1434i	0.650954	−	1.01743i
$319$	16.3691	−	28.3520i	0.916491	−	1.58741i
$320$	−0.460505			−0.0257430
$321$	−7.26303	+	11.3520i	−0.405383	+	0.633607i
$322$	−2.63307	−	1.43315i	−0.146736	−	0.0798664i
$323$	15.1373			0.842264
$324$	−5.83842	+	6.84929i	−0.324357	+	0.380516i
$325$	−3.49640	−	6.05594i	−0.193945	−	0.335923i
$326$	23.0364			1.27587
$327$	−5.98755	−	11.5567i	−0.331112	−	0.639085i
$328$	−0.472958	−	0.819187i	−0.0261147	−	0.0452320i
$329$	−5.40856	−	2.94381i	−0.298183	−	0.162298i
$330$	−1.33842	−	2.58331i	−0.0736776	−	0.142206i
$331$	−13.7719	−	23.8536i	−0.756971	−	1.31111i	−0.944388	−	0.328832i	$-0.893345\pi$
$331$	−13.7719	−	23.8536i	−0.756971	−	1.31111i	0.187417	−	0.982280i	$-0.439988\pi$
$332$	3.32383	+	5.75705i	0.182419	+	0.315959i
$333$	−15.7594	+	22.3219i	−0.863611	+	1.22323i
$334$	−5.31498	+	9.20581i	−0.290823	+	0.503720i
$335$	−0.534239	+	0.925330i	−0.0291886	+	0.0505562i
$336$	−3.92101	−	2.37185i	−0.213909	−	0.129395i
$337$	0.748440	+	1.29634i	0.0407701	+	0.0706159i	0.885690	−	0.464276i	$-0.153686\pi$
$337$	0.748440	+	1.29634i	0.0407701	+	0.0706159i	−0.844920	+	0.534892i	$0.820352\pi$
$338$	−10.8669			−0.591083
$339$	4.82957	+	9.32162i	0.262306	+	0.506281i
$340$	−1.71946			−0.0932506
$341$	−0.938524	+	1.62557i	−0.0508239	+	0.0880296i
$342$	12.1118	+	1.10702i	0.654929	+	0.0598607i
$343$	−1.39610	−	18.4676i	−0.0753825	−	0.997155i
$344$	4.66372	−	8.07779i	0.251451	−	0.435525i
$345$	−0.902822	−	0.0411732i	−0.0486063	−	0.00221669i
$346$	−1.46936	+	2.54500i	−0.0789932	+	0.136820i
$347$	9.14406	−	15.8380i	0.490879	−	0.850228i	−0.509066	−	0.860728i	$-0.670009\pi$
$347$	9.14406	−	15.8380i	0.490879	−	0.850228i	0.999945	+	0.0105001i	$0.00334233\pi$
$348$	−7.15126	−	13.8028i	−0.383348	−	0.739906i
$349$	−3.90136	+	6.75735i	−0.208835	+	0.361713i	−0.951348	−	0.308119i	$-0.900300\pi$
$349$	−3.90136	+	6.75735i	−0.208835	+	0.361713i	0.742513	+	0.669832i	$0.233634\pi$
$350$	11.1264	+	6.05594i	0.594729	+	0.323704i
$351$	2.86333	+	7.02811i	0.152833	+	0.375133i
$352$	1.82383	−	3.15897i	0.0972106	−	0.168374i
$353$	26.9253			1.43309			0.716544	−	0.697542i	$-0.245723\pi$
$353$	26.9253			1.43309			0.716544	+	0.697542i	$0.245723\pi$
$354$	−22.3135	−	1.01761i	−1.18595	−	0.0540853i
$355$	−0.773541			−0.0410553
$356$	−1.36333	−	2.36135i	−0.0722562	−	0.125151i
$357$	−14.6405	−	8.85614i	−0.774856	−	0.468717i
$358$	−4.58113	+	7.93474i	−0.242120	+	0.419364i
$359$	−3.13161	+	5.42411i	−0.165280	+	0.286274i	−0.936755	−	0.349987i	$-0.886186\pi$
$359$	−3.13161	+	5.42411i	−0.165280	+	0.286274i	0.771475	+	0.636260i	$0.219519\pi$
$360$	−1.37578	−	0.125747i	−0.0725100	−	0.00662743i
$361$	1.28220	+	2.22084i	0.0674842	+	0.116886i
$362$	−11.2142	−	19.4236i	−0.589405	−	1.02088i
$363$	3.98901	+	0.181919i	0.209369	+	0.00954827i
$364$	−3.29679	+	2.01561i	−0.172799	+	0.105647i
$365$	3.04883	+	5.28073i	0.159583	+	0.276406i
$366$	−11.2793	+	17.6293i	−0.589577	+	0.921500i
$367$	29.2733			1.52806			0.764028	−	0.645183i	$-0.223219\pi$
$367$	29.2733			1.52806			0.764028	+	0.645183i	$0.223219\pi$
$368$	−0.566537	−	0.981271i	−0.0295328	−	0.0511523i
$369$	−1.18929	−	2.57651i	−0.0619122	−	0.134128i
$370$	−4.19436			−0.218054
$371$	28.8982	+	15.7290i	1.50032	+	0.816608i
$372$	0.410019	+	0.791385i	0.0212585	+	0.0410314i
$373$	17.8597			0.924742			0.462371	−	0.886687i	$-0.346999\pi$
$373$	17.8597			0.924742			0.462371	+	0.886687i	$0.346999\pi$
$374$	6.80992	−	11.7951i	0.352132	−	0.609911i
$375$	7.79893	+	0.355670i	0.402735	+	0.0183667i
$376$	−1.16372	−	2.01561i	−0.0600140	−	0.103947i
$377$	−13.1082			−0.675105
$378$	−11.0665	−	8.15670i	−0.569201	−	0.419535i
$379$	−22.4255			−1.15192			−0.575960	−	0.817478i	$-0.695371\pi$
$379$	−22.4255			−1.15192			−0.575960	+	0.817478i	$0.695371\pi$
$380$	0.933463	+	1.61680i	0.0478856	+	0.0829403i
$381$	15.2434	+	0.695175i	0.780942	+	0.0356149i
$382$	−1.24484	+	2.15613i	−0.0636916	+	0.110317i
$383$	−14.1403			−0.722534			−0.361267	−	0.932462i	$-0.617656\pi$
$383$	−14.1403			−0.722534			−0.361267	+	0.932462i	$0.617656\pi$
$384$	−0.796790	−	1.53790i	−0.0406610	−	0.0784805i
$385$	3.79173	−	2.31821i	0.193244	−	0.118147i
$386$	4.48968			0.228519
$387$	16.1388	−	22.8593i	0.820382	−	1.16200i
$388$	−5.59358	−	9.68836i	−0.283971	−	0.491852i
$389$	−23.1301			−1.17275			−0.586373	−	0.810041i	$-0.699445\pi$
$389$	−23.1301			−1.17275			−0.586373	+	0.810041i	$0.699445\pi$
$390$	−0.627819	+	0.981271i	−0.0317908	+	0.0496886i
$391$	−2.11537	−	3.66392i	−0.106979	−	0.185292i
$392$	3.19076	−	6.23049i	0.161158	−	0.314688i
$393$	36.5729	+	1.66791i	1.84486	+	0.0841350i
$394$	−6.36693	−	11.0278i	−0.320761	−	0.555574i
$395$	−1.15292	−	1.99691i	−0.0580097	−	0.100476i
$396$	6.31138	−	8.93955i	0.317159	−	0.449229i
$397$	−5.13307	+	8.89075i	−0.257622	+	0.446214i	−0.965604	−	0.260016i	$-0.916272\pi$
$397$	−5.13307	+	8.89075i	−0.257622	+	0.446214i	0.707983	+	0.706230i	$0.249605\pi$
$398$	−1.47296	+	2.55124i	−0.0738327	+	0.127882i
$399$	−0.379379	+	18.5743i	−0.0189927	+	0.929877i
$400$	2.39397	+	4.14647i	0.119698	+	0.207324i
$401$	34.0335			1.69955			0.849775	−	0.527146i	$-0.176738\pi$
$401$	34.0335			1.69955			0.849775	+	0.527146i	$0.176738\pi$
$402$	−4.01459	−	0.183086i	−0.200230	−	0.00913148i
$403$	0.751560			0.0374379
$404$	−6.87792	+	11.9129i	−0.342189	+	0.592689i
$405$	−4.07587	−	0.751347i	−0.202532	−	0.0373348i
$406$	20.2594	−	12.3863i	1.00546	−	0.614724i
$407$	16.6118	−	28.7724i	0.823415	−	1.42620i
$408$	−2.97509	−	5.74228i	−0.147289	−	0.284285i
$409$	1.74484	−	3.02215i	0.0862769	−	0.149436i	−0.819658	−	0.572854i	$-0.805836\pi$
$409$	1.74484	−	3.02215i	0.0862769	−	0.149436i	0.905935	+	0.423418i	$0.139170\pi$
$410$	0.217799	−	0.377240i	0.0107563	−	0.0186305i
$411$	−7.62422	−	0.347703i	−0.376075	−	0.0171509i
$412$	−5.58113	+	9.66679i	−0.274962	+	0.476249i
$413$	−0.858071	−	34.1091i	−0.0422229	−	1.67840i
$414$	−1.42461	−	3.08629i	−0.0700157	−	0.151683i
$415$	−1.53064	+	2.65115i	−0.0751362	+	0.130140i
$416$	−1.46050			−0.0716071
$417$	−1.61342	−	3.11410i	−0.0790097	−	0.152498i
$418$	−14.7879			−0.723302
$419$	14.4897	+	25.0969i	0.707867	+	1.22606i	0.965647	+	0.259858i	$0.0836759\pi$
$419$	14.4897	+	25.0969i	0.707867	+	1.22606i	−0.257779	+	0.966204i	$0.582991\pi$
$420$	0.0430937	−	2.10986i	0.00210276	−	0.102951i
$421$	−1.06128	+	1.83819i	−0.0517237	+	0.0895881i	−0.890728	−	0.454537i	$-0.849805\pi$
$421$	−1.06128	+	1.83819i	−0.0517237	+	0.0895881i	0.839004	+	0.544125i	$0.183138\pi$
$422$	−0.608168	+	1.05338i	−0.0296052	+	0.0512777i
$423$	−2.92627	−	6.33951i	−0.142280	−	0.308237i
$424$	6.21780	+	10.7695i	0.301963	+	0.523015i
$425$	8.93872	+	15.4823i	0.433592	+	0.751003i
$426$	−1.33842	−	2.58331i	−0.0648467	−	0.125162i
$427$	−28.0795	−	15.2833i	−1.35886	−	0.739612i
$428$	−3.89037	−	6.73832i	−0.188048	−	0.325709i
$429$	−4.24484	−	8.19304i	−0.204943	−	0.395564i
$430$	4.29533			0.207139
$431$	10.9356	+	18.9410i	0.526749	+	0.912356i	0.999514	+	0.0311679i	$0.00992265\pi$
$431$	10.9356	+	18.9410i	0.526749	+	0.912356i	−0.472765	+	0.881189i	$0.656744\pi$
$432$	−1.96050	−	4.81211i	−0.0943248	−	0.231523i
$433$	−13.0512			−0.627199			−0.313599	−	0.949555i	$-0.601535\pi$
$433$	−13.0512			−0.627199			−0.313599	+	0.949555i	$0.601535\pi$
$434$	−1.16158	+	0.710174i	−0.0557576	+	0.0340895i
$435$	3.85807	−	6.03011i	0.184980	−	0.289122i
$436$	7.51459			0.359884
$437$	−2.29679	+	3.97816i	−0.109870	+	0.190301i
$438$	−12.3602	+	19.3188i	−0.590594	+	0.923089i
$439$	−2.43200	−	4.21235i	−0.116073	−	0.201044i	0.802135	−	0.597143i	$-0.203697\pi$
$439$	−2.43200	−	4.21235i	−0.116073	−	0.201044i	−0.918208	+	0.396098i	$0.870364\pi$
$440$	1.67977			0.0800797
$441$	11.2339	−	17.7426i	0.534945	−	0.844887i
$442$	−5.45331			−0.259387
$443$	5.76975	+	9.99350i	0.274129	+	0.474805i	0.969915	−	0.243444i	$-0.0782771\pi$
$443$	5.76975	+	9.99350i	0.274129	+	0.474805i	−0.695786	+	0.718249i	$0.744944\pi$
$444$	−7.25729	−	14.0074i	−0.344416	−	0.664763i
$445$	0.627819	−	1.08741i	0.0297615	−	0.0515484i
$446$	0.891832			0.0422294
$447$	−15.8530	−	0.722977i	−0.749822	−	0.0341957i
$448$	2.25729	−	1.38008i	0.106647	−	0.0652027i
$449$	−26.4251			−1.24708			−0.623538	−	0.781793i	$-0.714306\pi$
$449$	−26.4251			−1.24708			−0.623538	+	0.781793i	$0.714306\pi$
$450$	6.01984	+	13.0415i	0.283778	+	0.614782i
$451$	1.72519	+	2.98812i	0.0812361	+	0.140705i
$452$	−6.06128			−0.285099
$453$	−0.179767	−	0.00819828i	−0.00844618	−	0.000385189i
$454$	7.32597	+	12.6889i	0.343825	+	0.595522i
$455$	−1.56294	−	0.850689i	−0.0732717	−	0.0398809i
$456$	−3.78434	+	5.91486i	−0.177218	+	0.276989i
$457$	1.86906	+	3.23731i	0.0874310	+	0.151435i	0.906425	−	0.422368i	$-0.138801\pi$
$457$	1.86906	+	3.23731i	0.0874310	+	0.151435i	−0.818994	+	0.573803i	$0.805468\pi$
$458$	4.78794	+	8.29295i	0.223726	+	0.387504i
$459$	−7.32023	−	17.9677i	−0.341679	−	0.838661i
$460$	0.260893	−	0.451880i	0.0121642	−	0.0210690i
$461$	−7.90496	+	13.6918i	−0.368171	+	0.637690i	−0.989280	−	0.146034i	$-0.953349\pi$
$461$	−7.90496	+	13.6918i	−0.368171	+	0.637690i	0.621109	+	0.783724i	$0.286682\pi$
$462$	14.3025	+	8.65172i	0.665414	+	0.402514i
$463$	19.1965	+	33.2493i	0.892137	+	1.54523i	0.837309	+	0.546730i	$0.184128\pi$
$463$	19.1965	+	33.2493i	0.892137	+	1.54523i	0.0548278	+	0.998496i	$0.482539\pi$
$464$	8.97509			0.416658
$465$	−0.221203	+	0.345738i	−0.0102581	+	0.0160332i
$466$	−14.4284			−0.668383
$467$	3.15652	−	5.46725i	0.146066	−	0.252994i	−0.783704	−	0.621134i	$-0.786672\pi$
$467$	3.15652	−	5.46725i	0.146066	−	0.252994i	0.929770	+	0.368140i	$0.120005\pi$
$468$	−4.36333	−	0.398809i	−0.201695	−	0.0184349i
$469$	−0.154382	−	6.13682i	−0.00712869	−	0.283372i
$470$	0.535897	−	0.928200i	0.0247191	−	0.0428147i
$471$	−19.5862	+	30.6129i	−0.902484	+	1.41057i
$472$	6.44805	−	11.1684i	0.296796	−	0.514065i
$473$	−17.0117	+	29.4651i	−0.782197	+	1.35481i
$474$	4.67403	−	7.30544i	0.214685	−	0.335550i
$475$	9.70535	−	16.8102i	0.445312	−	0.771303i
$476$	8.42840	−	5.15301i	0.386315	−	0.236188i
$477$	15.6352	+	33.8724i	0.715887	+	1.55091i
$478$	−9.15486	+	15.8567i	−0.418734	+	0.725268i
$479$	−20.4136			−0.932722			−0.466361	−	0.884594i	$-0.654435\pi$
$479$	−20.4136			−0.932722			−0.466361	+	0.884594i	$0.654435\pi$
$480$	0.429864	−	0.671871i	0.0196205	−	0.0306666i
$481$	−13.3025			−0.606543
$482$	−0.0466924	−	0.0808735i	−0.00212678	−	0.00368369i
$483$	4.54883	−	2.50383i	0.206979	−	0.113928i
$484$	−1.15272	+	1.99658i	−0.0523966	+	0.0907535i
$485$	2.57587	−	4.46154i	0.116964	−	0.202588i
$486$	−4.54309	−	14.9118i	−0.206079	−	0.676411i
$487$	6.18190	+	10.7074i	0.280129	+	0.485197i	0.971416	−	0.237383i	$-0.0762895\pi$
$487$	6.18190	+	10.7074i	0.280129	+	0.485197i	−0.691287	+	0.722580i	$0.742956\pi$
$488$	−6.04163	−	10.4644i	−0.273492	−	0.473702i
$489$	−21.5036	+	33.6098i	−0.972426	+	1.51989i
$490$	3.21946	−	0.162084i	0.145440	−	0.00732222i
$491$	0.207004	+	0.358541i	0.00934194	+	0.0161807i	0.870659	−	0.491888i	$-0.163693\pi$
$491$	0.207004	+	0.358541i	0.00934194	+	0.0161807i	−0.861317	+	0.508069i	$0.830360\pi$
$492$	1.63667	+	0.0746406i	0.0737869	+	0.00336506i
$493$	33.5117			1.50929
$494$	2.96050	+	5.12774i	0.133199	+	0.230708i
$495$	5.01838	+	0.458681i	0.225560	+	0.0206162i
$496$	−0.514589			−0.0231057
$497$	3.79173	−	2.31821i	0.170082	−	0.103986i
$498$	−11.5021	−	0.524555i	−0.515423	−	0.0235059i
$499$	−0.923935			−0.0413610			−0.0206805	−	0.999786i	$-0.506583\pi$
$499$	−0.923935			−0.0413610			−0.0206805	+	0.999786i	$0.506583\pi$
$500$	−2.25370	+	3.90352i	−0.100788	+	0.174571i
$501$	−8.46984	−	16.3478i	−0.378404	−	0.730365i
$502$	9.13667	+	15.8252i	0.407790	+	0.706312i
$503$	−23.8142			−1.06182			−0.530911	−	0.847428i	$-0.678150\pi$
$503$	−23.8142			−1.06182			−0.530911	+	0.847428i	$0.678150\pi$
$504$	7.12062	−	3.50667i	0.317178	−	0.156200i
$505$	−6.33463			−0.281887
$506$	2.06654	+	3.57935i	0.0918688	+	0.159121i
$507$	10.1439	−	15.8547i	0.450505	−	0.704133i
$508$	−4.40496	+	7.62961i	−0.195438	+	0.338509i
$509$	−30.6342			−1.35784			−0.678919	−	0.734213i	$-0.737551\pi$
$509$	−30.6342			−1.35784			−0.678919	+	0.734213i	$0.737551\pi$
$510$	1.60505	−	2.50867i	0.0710728	−	0.111086i
$511$	−30.7704	−	16.7480i	−1.36120	−	0.740887i
$512$	1.00000			0.0441942
$513$	−12.9210	+	16.6376i	−0.570477	+	0.734567i
$514$	10.5256	+	18.2308i	0.464263	+	0.804128i
$515$	−5.14027			−0.226507
$516$	7.43200	+	14.3446i	0.327176	+	0.631487i
$517$	4.24484	+	7.35228i	0.186688	+	0.323353i
$518$	20.5598	−	12.5700i	0.903347	−	0.552294i
$519$	−2.34154	−	4.51945i	−0.102782	−	0.198382i
$520$	−0.336285	−	0.582462i	−0.0147471	−	0.0255427i
$521$	−13.4518	−	23.2993i	−0.589336	−	1.02076i	−0.994320	−	0.106436i	$-0.966056\pi$
$521$	−13.4518	−	23.2993i	−0.589336	−	1.02076i	0.404984	−	0.914324i	$-0.367277\pi$
$522$	26.8135	+	2.45076i	1.17360	+	0.107267i
$523$	−7.85301	+	13.6018i	−0.343388	+	0.594766i	−0.985060	−	0.172214i	$-0.944908\pi$
$523$	−7.85301	+	13.6018i	−0.343388	+	0.594766i	0.641671	+	0.766980i	$0.278241\pi$
$524$	−10.5687	+	18.3055i	−0.461695	+	0.799679i
$525$	−19.2216	+	10.5802i	−0.838899	+	0.461759i
$526$	2.58259	+	4.47318i	0.112606	+	0.195040i
$527$	−1.92140			−0.0836975
$528$	2.90642	+	5.60973i	0.126486	+	0.244132i
$529$	−21.7161			−0.944180
$530$	−2.86333	+	4.95943i	−0.124375	+	0.215424i
$531$	22.3135	−	31.6053i	0.968324	−	1.37155i
$532$	−9.42101	−	5.12774i	−0.408453	−	0.222316i
$533$	0.690757	−	1.19643i	0.0299200	−	0.0518230i
$534$	4.71780	+	0.215155i	0.204159	+	0.00931069i
$535$	1.79153	−	3.10303i	0.0774548	−	0.134156i
$536$	1.16012	−	2.00938i	0.0501094	−	0.0867920i
$537$	−7.30039	−	14.0906i	−0.315035	−	0.608054i
$538$	8.42840	−	14.5984i	0.363374	−	0.629383i
$539$	−11.6388	+	22.7267i	−0.501319	+	0.978910i
$540$	1.46770	−	1.88987i	0.0631598	−	0.0813269i
$541$	−2.05934	+	3.56688i	−0.0885379	+	0.153352i	−0.906893	−	0.421360i	$-0.861553\pi$
$541$	−2.05934	+	3.56688i	−0.0885379	+	0.153352i	0.818355	+	0.574713i	$0.194886\pi$
$542$	−25.1124			−1.07867
$543$	38.8068	+	1.76979i	1.66536	+	0.0759488i
$544$	3.73385			0.160088
$545$	1.73025	+	2.99689i	0.0741159	+	0.128372i
$546$	0.136673	−	6.69148i	0.00584907	−	0.286369i
$547$	−11.8602	+	20.5425i	−0.507106	+	0.878333i	0.492860	+	0.870108i	$0.335951\pi$
$547$	−11.8602	+	20.5425i	−0.507106	+	0.878333i	−0.999966	+	0.00822465i	$0.997382\pi$
$548$	2.20321	−	3.81607i	0.0941165	−	0.163015i
$549$	−15.1922	−	32.9127i	−0.648388	−	1.40468i
$550$	−8.73239	−	15.1249i	−0.372350	−	0.644930i
$551$	−18.1929	−	31.5110i	−0.775043	−	1.34241i
$552$	1.96050	+	0.0894089i	0.0834446	+	0.00380550i
$553$	11.6359	+	6.33327i	0.494808	+	0.269318i
$554$	−1.69076	−	2.92848i	−0.0718334	−	0.124419i
$555$	3.91528	−	6.11952i	0.166194	−	0.259759i
$556$	2.02491			0.0858751
$557$	−21.0313	−	36.4273i	−0.891125	−	1.54347i	−0.838528	−	0.544859i	$-0.816583\pi$
$557$	−21.0313	−	36.4273i	−0.891125	−	1.54347i	−0.0525975	−	0.998616i	$-0.516750\pi$
$558$	−1.53736	−	0.140515i	−0.0650816	−	0.00594847i
$559$	13.6228			0.576181
$560$	1.07014	+	0.582462i	0.0452215	+	0.0246135i
$561$	10.8521	+	20.9459i	0.458178	+	0.884336i
$562$	20.2776			0.855360
$563$	−5.91216	+	10.2402i	−0.249168	+	0.431571i	−0.963295	−	0.268445i	$-0.913490\pi$
$563$	−5.91216	+	10.2402i	−0.249168	+	0.431571i	0.714127	+	0.700016i	$0.246824\pi$
$564$	4.02704	+	0.183653i	0.169569	+	0.00773321i
$565$	−1.39562	−	2.41729i	−0.0587144	−	0.101696i
$566$	17.3494			0.729250
$567$	22.2307	−	8.53197i	0.933603	−	0.358309i
$568$	1.67977			0.0704815
$569$	−7.10078	−	12.2989i	−0.297680	−	0.515597i	0.677925	−	0.735131i	$-0.262880\pi$
$569$	−7.10078	−	12.2989i	−0.297680	−	0.515597i	−0.975605	+	0.219534i	$0.929546\pi$
$570$	−3.23025	−	0.147316i	−0.135300	−	0.00617038i
$571$	−5.97869	+	10.3554i	−0.250200	+	0.433360i	−0.963581	−	0.267417i	$-0.913830\pi$
$571$	−5.97869	+	10.3554i	−0.250200	+	0.433360i	0.713380	+	0.700777i	$0.247163\pi$
$572$	5.32743			0.222751
$573$	−1.98375	−	3.82888i	−0.0828725	−	0.159954i
$574$	0.0629386	+	2.50187i	0.00262701	+	0.104426i
$575$	−5.42509			−0.226242
$576$	2.98755	+	0.273062i	0.124481	+	0.0113776i
$577$	21.3135	+	36.9161i	0.887293	+	1.53684i	0.843062	+	0.537816i	$0.180750\pi$
$577$	21.3135	+	36.9161i	0.887293	+	1.53684i	0.0442307	+	0.999021i	$0.485916\pi$
$578$	−3.05836			−0.127211
$579$	−4.19095	+	6.55040i	−0.174170	+	0.272225i
$580$	2.06654	+	3.57935i	0.0858083	+	0.148624i
$581$	−0.442317	−	17.5825i	−0.0183504	−	0.729445i
$582$	19.3566	+	0.882759i	0.802357	+	0.0365915i
$583$	−22.6804	−	39.2837i	−0.939328	−	1.62696i
$584$	−6.62062	−	11.4673i	−0.273963	−	0.474518i
$585$	−0.845618	−	1.83196i	−0.0349620	−	0.0757422i
$586$	−4.93560	+	8.54871i	−0.203888	+	0.353144i
$587$	20.5328	−	35.5638i	0.847478	−	1.46788i	−0.0359730	−	0.999353i	$-0.511453\pi$
$587$	20.5328	−	35.5638i	0.847478	−	1.46788i	0.883451	−	0.468523i	$-0.155214\pi$
$588$	6.11177	+	10.4712i	0.252045	+	0.431826i
$589$	1.04309	+	1.80669i	0.0429799	+	0.0744434i
$590$	5.93872			0.244493
$591$	22.0328	+	1.00481i	0.906307	+	0.0413322i
$592$	9.10817			0.374343
$593$	16.1008	−	27.8874i	0.661180	−	1.14520i	−0.319126	−	0.947712i	$-0.603389\pi$
$593$	16.1008	−	27.8874i	0.661180	−	1.14520i	0.980306	−	0.197485i	$-0.0632772\pi$
$594$	7.15126	+	17.5530i	0.293420	+	0.720207i
$595$	3.99573	+	2.17483i	0.163809	+	0.0891592i
$596$	4.58113	−	7.93474i	0.187650	−	0.325020i
$597$	−2.34728	−	4.53051i	−0.0960676	−	0.185422i
$598$	0.827430	−	1.43315i	0.0338361	−	0.0586059i
$599$	−9.53590	+	16.5167i	−0.389626	+	0.674852i	−0.992399	−	0.123060i	$-0.960729\pi$
$599$	−9.53590	+	16.5167i	−0.389626	+	0.674852i	0.602773	+	0.797913i	$0.294062\pi$
$600$	−8.28434	−	0.377808i	−0.338207	−	0.0154239i
$601$	4.27188	−	7.39912i	0.174254	−	0.301816i	−0.765649	−	0.643259i	$-0.777582\pi$
$601$	4.27188	−	7.39912i	0.174254	−	0.301816i	0.939903	+	0.341442i	$0.110915\pi$
$602$	−21.0548	+	12.8726i	−0.858128	+	0.524648i
$603$	4.01459	−	5.68634i	0.163487	−	0.231565i
$604$	0.0519482	−	0.0899768i	0.00211374	−	0.00366111i
$605$	−1.06167			−0.0431631
$606$	−10.9605	−	21.1550i	−0.445240	−	0.859365i
$607$	38.0115			1.54284			0.771419	−	0.636328i	$-0.219547\pi$
$607$	38.0115			1.54284			0.771419	+	0.636328i	$0.219547\pi$
$608$	−2.02704	−	3.51094i	−0.0822074	−	0.142387i
$609$	−0.839883	+	41.1205i	−0.0340338	+	1.66629i
$610$	2.78220	−	4.81891i	0.112648	−	0.195112i
$611$	1.69961	−	2.94381i	0.0687589	−	0.119094i
$612$	11.1551	+	1.01957i	0.450916	+	0.0412138i
$613$	11.3296	+	19.6234i	0.457597	+	0.792581i	0.998833	−	0.0482894i	$-0.0153770\pi$
$613$	11.3296	+	19.6234i	0.457597	+	0.792581i	−0.541237	+	0.840870i	$0.682044\pi$
$614$	−3.89397	−	6.74455i	−0.157148	−	0.272188i
$615$	0.347081	+	0.669906i	0.0139956	+	0.0270132i
$616$	−8.23385	+	5.03407i	−0.331751	+	0.202828i
$617$	−10.1388	−	17.5609i	−0.408173	−	0.706977i	0.586512	−	0.809941i	$-0.300501\pi$
$617$	−10.1388	−	17.5609i	−0.408173	−	0.706977i	−0.994685	+	0.102964i	$0.967167\pi$
$618$	−8.89397	−	17.1664i	−0.357768	−	0.690534i
$619$	2.06128			0.0828499			0.0414249	−	0.999142i	$-0.486810\pi$
$619$	2.06128			0.0828499			0.0414249	+	0.999142i	$0.486810\pi$
$620$	−0.118485	−	0.205223i	−0.00475849	−	0.00824194i
$621$	5.83269	+	0.802453i	0.234058	+	0.0322013i
$622$	15.4107			0.617912
$623$	0.181424	+	7.21177i	0.00726860	+	0.288933i
$624$	1.36333	−	2.13086i	0.0545768	−	0.0853027i
$625$	21.8640			0.874560
$626$	−4.24844	+	7.35851i	−0.169802	+	0.294105i
$627$	13.8040	−	21.5754i	0.551278	−	0.861640i
$628$	−10.4911	−	18.1712i	−0.418642	−	0.725110i
$629$	34.0085			1.35601
$630$	3.03803	+	2.03235i	0.121038	+	0.0809707i
$631$	1.63715			0.0651740			0.0325870	−	0.999469i	$-0.489625\pi$
$631$	1.63715			0.0651740			0.0325870	+	0.999469i	$0.489625\pi$
$632$	2.50360	+	4.33636i	0.0995878	+	0.172491i
$633$	−0.969165	−	1.87060i	−0.0385208	−	0.0743497i
$634$	7.05262	−	12.2155i	0.280095	−	0.485139i
$635$	−4.05701			−0.160998
$636$	−21.5167	−	0.981271i	−0.853194	−	0.0389099i
$637$	10.2106	−	0.514055i	0.404559	−	0.0203676i
$638$	−32.7381			−1.29611
$639$	5.01838	+	0.458681i	0.198524	+	0.0181451i
$640$	0.230252	+	0.398809i	0.00910153	+	0.0157643i
$641$	21.9325			0.866281			0.433140	−	0.901326i	$-0.357405\pi$
$641$	21.9325			0.866281			0.433140	+	0.901326i	$0.357405\pi$
$642$	13.4626	+	0.613964i	0.531328	+	0.0242312i
$643$	−14.1819	−	24.5638i	−0.559280	−	0.968701i	−0.997557	−	0.0698609i	$-0.977744\pi$
$643$	−14.1819	−	24.5638i	−0.559280	−	0.968701i	0.438277	−	0.898840i	$-0.355589\pi$
$644$	0.0753916	+	2.99689i	0.00297085	+	0.118094i
$645$	−4.00953	+	6.26683i	−0.157875	+	0.246756i
$646$	−7.56867	−	13.1093i	−0.297785	−	0.515780i
$647$	17.3904	+	30.1210i	0.683686	+	1.18418i	0.973848	+	0.227201i	$0.0729575\pi$
$647$	17.3904	+	30.1210i	0.683686	+	1.18418i	−0.290162	+	0.956978i	$0.593709\pi$
$648$	8.85087	+	1.63157i	0.347695	+	0.0640943i
$649$	−23.5203	+	40.7384i	−0.923253	+	1.59912i
$650$	−3.49640	+	6.05594i	−0.137140	+	0.237534i
$651$	0.0481549	−	2.35765i	0.00188734	−	0.0924037i
$652$	−11.5182	−	19.9501i	−0.451087	−	0.781306i
$653$	−3.19863			−0.125172			−0.0625860	−	0.998040i	$-0.519935\pi$
$653$	−3.19863			−0.125172			−0.0625860	+	0.998040i	$0.519935\pi$
$654$	−7.01459	+	10.9637i	−0.274292	+	0.428715i
$655$	−9.73385			−0.380333
$656$	−0.472958	+	0.819187i	−0.0184659	+	0.0319839i
$657$	−16.6481	−	36.0668i	−0.649506	−	1.40710i
$658$	0.154861	+	6.15585i	0.00603710	+	0.239980i
$659$	5.30418	−	9.18711i	0.206622	−	0.357879i	−0.744027	−	0.668150i	$-0.767086\pi$
$659$	5.30418	−	9.18711i	0.206622	−	0.357879i	0.950648	+	0.310271i	$0.100420\pi$
$660$	−1.56800	+	2.45076i	−0.0610343	+	0.0953957i
$661$	−5.06507	+	8.77297i	−0.197009	+	0.341229i	−0.947557	−	0.319586i	$-0.896456\pi$
$661$	−5.06507	+	8.77297i	−0.197009	+	0.341229i	0.750549	+	0.660815i	$0.229789\pi$
$662$	−13.7719	+	23.8536i	−0.535259	+	0.927097i
$663$	5.09046	−	7.95631i	0.197697	−	0.308998i
$664$	3.32383	−	5.75705i	0.128990	−	0.223417i
$665$	−0.124220	−	4.93786i	−0.00481705	−	0.191482i
$666$	27.2111	+	2.48710i	1.05441	+	0.0963731i
$667$	−5.08472	+	8.80700i	−0.196881	+	0.341008i
$668$	10.6300			0.411285
$669$	−0.832492	+	1.30117i	−0.0321860	+	0.0503062i
$670$	1.06848			0.0412789
$671$	22.0378	+	38.1707i	0.850761	+	1.47356i
$672$	−0.0935793	+	4.58162i	−0.00360990	+	0.176740i
$673$	1.60817	−	2.78543i	0.0619903	−	0.107370i	−0.833365	−	0.552724i	$-0.813589\pi$
$673$	1.60817	−	2.78543i	0.0619903	−	0.107370i	0.895355	+	0.445353i	$0.146922\pi$
$674$	0.748440	−	1.29634i	0.0288288	−	0.0499330i
$675$	−24.6467	−	3.39086i	−0.948651	−	0.130514i
$676$	5.43346	+	9.41103i	0.208979	+	0.361963i
$677$	14.6819	+	25.4298i	0.564271	+	0.977347i	0.997117	+	0.0758786i	$0.0241762\pi$
$677$	14.6819	+	25.4298i	0.564271	+	0.977347i	−0.432846	+	0.901468i	$0.642491\pi$
$678$	5.65798	−	8.84334i	0.217293	−	0.339626i
$679$	0.744363	+	29.5891i	0.0285660	+	1.13552i
$680$	0.859728	+	1.48909i	0.0329691	+	0.0571041i
$681$	−25.3515	−	1.15616i	−0.971473	−	0.0443041i
$682$	1.87705			0.0718759
$683$	12.6278	+	21.8720i	0.483190	+	0.836910i	0.999814	−	0.0193029i	$-0.00614468\pi$
$683$	12.6278	+	21.8720i	0.483190	+	0.836910i	−0.516624	+	0.856213i	$0.672811\pi$
$684$	−5.09718	−	11.0426i	−0.194895	−	0.422225i
$685$	2.02918			0.0775309
$686$	−15.2953	+	10.4428i	−0.583978	+	0.398710i
$687$	−16.5687	−	0.755615i	−0.632134	−	0.0288285i
$688$	−9.32743			−0.355605
$689$	−9.08113	+	15.7290i	−0.345963	+	0.599226i
$690$	0.415754	+	0.802453i	0.0158275	+	0.0305489i
$691$	7.68190	+	13.3054i	0.292233	+	0.506163i	0.974338	−	0.225092i	$-0.0722683\pi$
$691$	7.68190	+	13.3054i	0.292233	+	0.506163i	−0.682104	+	0.731255i	$0.738935\pi$
$692$	2.93872			0.111713
$693$	−25.9736	+	12.7912i	−0.986657	+	0.485896i
$694$	−18.2881			−0.694208
$695$	0.466240	+	0.807551i	0.0176855	+	0.0306321i
$696$	−8.37792	+	13.0946i	−0.317564	+	0.496348i
$697$	−1.76595	+	3.05872i	−0.0668903	+	0.115857i
$698$	7.80272			0.295337
$699$	13.4684	−	21.0509i	0.509421	−	0.796217i
$700$	−0.318576	−	12.6637i	−0.0120410	−	0.478642i
$701$	−13.3700			−0.504980			−0.252490	−	0.967600i	$-0.581249\pi$
$701$	−13.3700			−0.504980			−0.252490	+	0.967600i	$0.581249\pi$
$702$	4.65486	−	5.99377i	0.175686	−	0.226220i
$703$	−18.4626	−	31.9782i	−0.696332	−	1.20608i
$704$	−3.64766			−0.137476
$705$	0.853994	+	1.64831i	0.0321633	+	0.0620788i
$706$	−13.4626	−	23.3180i	−0.506673	−	0.877584i
$707$	31.0510	−	18.9842i	1.16779	−	0.713972i
$708$	10.2755	+	19.8329i	0.386176	+	0.745365i
$709$	0.562939	+	0.975038i	0.0211416	+	0.0366183i	0.876403	−	0.481579i	$-0.159937\pi$
$709$	0.562939	+	0.975038i	0.0211416	+	0.0366183i	−0.855261	+	0.518197i	$0.826603\pi$
$710$	0.386770	+	0.669906i	0.0145152	+	0.0251411i
$711$	6.29552	+	13.6387i	0.236101	+	0.511492i
$712$	−1.36333	+	2.36135i	−0.0510928	+	0.0884954i
$713$	0.291534	−	0.504951i	0.0109180	−	0.0189106i
$714$	−0.349411	+	17.1071i	−0.0130764	+	0.640217i
$715$	1.22665	+	2.12463i	0.0458743	+	0.0794565i
$716$	9.16225			0.342409
$717$	−14.5890	−	28.1585i	−0.544836	−	1.05160i
$718$	6.26322			0.233741
$719$	9.13667	−	15.8252i	0.340740	−	0.590180i	−0.643830	−	0.765169i	$-0.722656\pi$
$719$	9.13667	−	15.8252i	0.340740	−	0.590180i	0.984570	+	0.174989i	$0.0559889\pi$
$720$	0.578990	+	1.25433i	0.0215777	+	0.0467463i
$721$	25.1965	−	15.4048i	0.938366	−	0.573705i
$722$	1.28220	−	2.22084i	0.0477186	−	0.0826510i
$723$	0.161579	+	0.00736882i	0.00600919	+	0.000274050i
$724$	−11.2142	+	19.4236i	−0.416772	+	0.721871i
$725$	21.4861	−	37.2150i	0.797973	−	1.38213i
$726$	−1.83696	−	3.54554i	−0.0681759	−	0.131587i
$727$	−14.8478	+	25.7171i	−0.550673	+	0.953793i	0.447553	+	0.894257i	$0.352295\pi$
$727$	−14.8478	+	25.7171i	−0.550673	+	0.953793i	−0.998226	+	0.0595359i	$0.981038\pi$
$728$	3.39397	+	1.84730i	0.125789	+	0.0684654i
$729$	25.9969	+	7.29124i	0.962847	+	0.270046i
$730$	3.04883	−	5.28073i	0.112842	−	0.195448i
$731$	−34.8272			−1.28813
$732$	20.9071	+	0.953469i	0.772748	+	0.0352412i
$733$	19.2278			0.710195			0.355098	−	0.934829i	$-0.384448\pi$
$733$	19.2278			0.710195			0.355098	+	0.934829i	$0.384448\pi$
$734$	−14.6367	−	25.3515i	−0.540249	−	0.935740i
$735$	−2.76876	+	4.84845i	−0.102127	+	0.178838i
$736$	−0.566537	+	0.981271i	−0.0208828	+	0.0361701i
$737$	−4.23171	+	7.32955i	−0.155877	+	0.269987i
$738$	−1.63667	+	2.31821i	−0.0602468	+	0.0853346i
$739$	−15.1336	−	26.2121i	−0.556697	−	0.964227i	−0.997769	−	0.0667556i	$-0.978735\pi$
$739$	−15.1336	−	26.2121i	−0.556697	−	0.964227i	0.441073	−	0.897471i	$-0.354598\pi$
$740$	2.09718	+	3.63242i	0.0770938	+	0.133530i
$741$	−10.2448	−	0.467216i	−0.376354	−	0.0171636i
$742$	−0.827430	−	32.8911i	−0.0303759	−	1.20747i
$743$	−11.8815	−	20.5794i	−0.435890	−	0.754984i	0.561477	−	0.827492i	$-0.310233\pi$
$743$	−11.8815	−	20.5794i	−0.435890	−	0.754984i	−0.997368	+	0.0725076i	$0.976900\pi$
$744$	0.480350	−	0.750780i	0.0176105	−	0.0275249i
$745$	4.21926			0.154582
$746$	−8.92986	−	15.4670i	−0.326946	−	0.566286i
$747$	11.5021	−	16.2918i	0.420841	−	0.596087i
$748$	−13.6198			−0.497990
$749$	0.517709	+	20.5794i	0.0189167	+	0.751954i
$750$	−3.59144	−	6.93190i	−0.131141	−	0.253117i
$751$	12.6683			0.462273			0.231136	−	0.972921i	$-0.425756\pi$
$751$	12.6683			0.462273			0.231136	+	0.972921i	$0.425756\pi$
$752$	−1.16372	+	2.01561i	−0.0424363	+	0.0735019i
$753$	−31.6175	−	1.44192i	−1.15221	−	0.0525464i
$754$	6.55408	+	11.3520i	0.238686	+	0.413416i
$755$	0.0478448			0.00174125
$756$	−1.53064	+	13.6623i	−0.0556689	+	0.496891i
$757$	−29.0799			−1.05693			−0.528464	−	0.848955i	$-0.677232\pi$
$757$	−29.0799			−1.05693			−0.528464	+	0.848955i	$0.677232\pi$
$758$	11.2127	+	19.4210i	0.407265	+	0.705404i
$759$	−7.15126	−	0.326134i	−0.259574	−	0.0118379i
$760$	0.933463	−	1.61680i	0.0338603	−	0.0586477i
$761$	29.2029			1.05860			0.529302	−	0.848433i	$-0.322454\pi$
$761$	29.2029			1.05860			0.529302	+	0.848433i	$0.322454\pi$
$762$	−7.01965	−	13.5487i	−0.254295	−	0.490819i
$763$	−17.4626	−	9.50471i	−0.632190	−	0.344094i
$764$	2.48968			0.0900736
$765$	2.16186	+	4.68350i	0.0781623	+	0.169332i
$766$	7.07014	+	12.2458i	0.255454	+	0.442460i
$767$	18.8348			0.680086
$768$	−0.933463	+	1.45899i	−0.0336834	+	0.0526467i
$769$	12.5869	+	21.8011i	0.453894	+	0.786167i	0.998624	−	0.0524443i	$-0.0167012\pi$
$769$	12.5869	+	21.8011i	0.453894	+	0.786167i	−0.544730	+	0.838611i	$0.683368\pi$
$770$	−3.90350	−	2.12463i	−0.140672	−	0.0765662i
$771$	−36.4238	−	1.66111i	−1.31177	−	0.0598234i
$772$	−2.24484	−	3.88818i	−0.0807936	−	0.139939i
$773$	−0.752039	−	1.30257i	−0.0270490	−	0.0468502i	0.852184	−	0.523242i	$-0.175278\pi$
$773$	−0.752039	−	1.30257i	−0.0270490	−	0.0468502i	−0.879233	+	0.476392i	$0.841944\pi$
$774$	−27.8661	−	2.54697i	−1.00163	−	0.0915490i
$775$	−1.23191	+	2.13373i	−0.0442515	+	0.0766458i
$776$	−5.59358	+	9.68836i	−0.200798	+	0.347792i
$777$	−0.852336	+	41.7302i	−0.0305774	+	1.49706i
$778$	11.5651	+	20.0313i	0.414628	+	0.718157i
$779$	3.83482			0.137397
$780$	1.16372	+	0.0530713i	0.0416677	+	0.00190026i
$781$	−6.12722			−0.219249
$782$	−2.11537	+	3.66392i	−0.0756453	+	0.131022i
$783$	−28.6050	+	36.8329i	−1.02226	+	1.31630i
$784$	−6.99115	+	0.351971i	−0.249684	+	0.0125704i
$785$	4.83122	−	8.36792i	0.172434	−	0.298664i
$786$	−16.8420	−	32.5071i	−0.600735	−	1.15949i
$787$	7.47656	−	12.9498i	0.266510	−	0.461610i	−0.701448	−	0.712721i	$-0.747463\pi$
$787$	7.47656	−	12.9498i	0.266510	−	0.461610i	0.967958	+	0.251111i	$0.0807960\pi$
$788$	−6.36693	+	11.0278i	−0.226812	+	0.392850i
$789$	−8.93706	−	0.407575i	−0.318168	−	0.0145101i
$790$	−1.15292	+	1.99691i	−0.0410190	+	0.0710470i
$791$	14.0854	+	7.66652i	0.500819	+	0.272590i
$792$	−10.8976	−	0.996040i	−0.387228	−	0.0353927i
$793$	8.82383	−	15.2833i	0.313343	−	0.542727i
$794$	10.2661			0.364332
$795$	−4.56294	−	8.80700i	−0.161831	−	0.312352i
$796$	2.94592			0.104415
$797$	−4.56294	−	7.90324i	−0.161628	−	0.279947i	0.773825	−	0.633400i	$-0.218341\pi$
$797$	−4.56294	−	7.90324i	−0.161628	−	0.279947i	−0.935453	+	0.353452i	$0.885008\pi$
$798$	16.2755	−	8.95859i	0.576146	−	0.317130i
$799$	−4.34514	+	7.52600i	−0.153720	+	0.266251i
$800$	2.39397	−	4.14647i	0.0846395	−	0.146600i
$801$	−4.71780	+	6.68238i	−0.166695	+	0.236110i
$802$	−17.0167	−	29.4738i	−0.600881	−	1.04076i
$803$	24.1498	+	41.8287i	0.852228	+	1.47610i
$804$	1.84874	+	3.56828i	0.0652000	+	0.125843i
$805$	−1.17783	+	0.720107i	−0.0415129	+	0.0253804i
$806$	−0.375780	−	0.650870i	−0.0132363	−	0.0229259i
$807$	13.4313	+	25.9240i	0.472805	+	0.912569i
$808$	13.7558			0.483928
$809$	17.7755	+	30.7880i	0.624953	+	1.08245i	0.988550	+	0.150894i	$0.0482151\pi$
$809$	17.7755	+	30.7880i	0.624953	+	1.08245i	−0.363597	+	0.931556i	$0.618452\pi$
$810$	1.38725	+	3.90548i	0.0487430	+	0.137225i
$811$	−13.5070			−0.474295			−0.237148	−	0.971474i	$-0.576212\pi$
$811$	−13.5070			−0.474295			−0.237148	+	0.971474i	$0.576212\pi$
$812$	−20.8566	−	11.3520i	−0.731923	−	0.398377i
$813$	23.4415	−	36.6388i	0.822130	−	1.28498i
$814$	−33.2235			−1.16448
$815$	5.30418	−	9.18711i	0.185797	−	0.321810i
$816$	−3.48541	+	5.44765i	−0.122014	+	0.190706i
$817$	18.9071	+	32.7480i	0.661475	+	1.14571i
$818$	−3.48968			−0.122014
$819$	9.63521	+	6.44565i	0.336682	+	0.225229i
$820$	−0.435599			−0.0152118
$821$	−10.8114	−	18.7259i	−0.377320	−	0.653537i	0.613352	−	0.789810i	$-0.289821\pi$
$821$	−10.8114	−	18.7259i	−0.377320	−	0.653537i	−0.990671	+	0.136273i	$0.956488\pi$
$822$	3.51099	+	6.77662i	0.122460	+	0.236362i
$823$	0.753501	−	1.30510i	0.0262654	−	0.0454930i	−0.852594	−	0.522574i	$-0.824972\pi$
$823$	0.753501	−	1.30510i	0.0262654	−	0.0454930i	0.878859	+	0.477081i	$0.158305\pi$
$824$	11.1623			0.388855
$825$	30.2185	+	1.37811i	1.05207	+	0.0479798i
$826$	−29.1103	+	17.7977i	−1.01288	+	0.619260i
$827$	23.3786			0.812953			0.406477	−	0.913661i	$-0.366757\pi$
$827$	23.3786			0.812953			0.406477	+	0.913661i	$0.366757\pi$
$828$	−1.96050	+	2.77689i	−0.0681323	+	0.0965037i
$829$	−11.0095	−	19.0691i	−0.382377	−	0.662296i	0.609025	−	0.793151i	$-0.291561\pi$
$829$	−11.0095	−	19.0691i	−0.382377	−	0.662296i	−0.991401	+	0.130855i	$0.958228\pi$
$830$	3.06128			0.106259
$831$	5.85087	+	0.266829i	0.202965	+	0.00925621i
$832$	0.730252	+	1.26483i	0.0253169	+	0.0438502i
$833$	−26.1039	+	1.31421i	−0.904446	+	0.0455345i
$834$	−1.89017	+	2.95431i	−0.0654514	+	0.102300i
$835$	2.44757	+	4.23932i	0.0847018	+	0.146708i
$836$	7.39397	+	12.8067i	0.255726	+	0.442930i
$837$	1.64008	−	2.11182i	0.0566894	−	0.0729953i
$838$	14.4897	−	25.0969i	0.500538	−	0.866957i
$839$	−1.06507	+	1.84476i	−0.0367705	+	0.0636883i	−0.883825	−	0.467818i	$-0.845040\pi$
$839$	−1.06507	+	1.84476i	−0.0367705	+	0.0636883i	0.847055	+	0.531506i	$0.178374\pi$
$840$	−1.84874	+	1.01761i	−0.0637875	+	0.0351108i
$841$	−25.7762	−	44.6456i	−0.888833	−	1.53950i
$842$	2.12256			0.0731483
$843$	−18.9284	+	29.5848i	−0.651929	+	1.01896i
$844$	1.21634			0.0418680
$845$	−2.50214	+	4.33383i	−0.0860761	+	0.149088i
$846$	−4.02704	+	5.70397i	−0.138453	+	0.196107i
$847$	5.20408	−	3.18171i	0.178814	−	0.109325i
$848$	6.21780	−	10.7695i	0.213520	−	0.369828i
$849$	−16.1950	+	25.3126i	−0.555812	+	0.868726i
$850$	8.93872	−	15.4823i	0.306596	−	0.531039i
$851$	−5.16012	+	8.93758i	−0.176887	+	0.306376i
$852$	−1.56800	+	2.45076i	−0.0537188	+	0.0839617i
$853$	−3.50146	+	6.06471i	−0.119888	+	0.207652i	−0.919723	−	0.392568i	$-0.871587\pi$
$853$	−3.50146	+	6.06471i	−0.119888	+	0.207652i	0.799835	+	0.600220i	$0.204920\pi$
$854$	0.803987	+	31.9592i	0.0275119	+	1.09362i
$855$	3.23025	−	4.57539i	0.110472	−	0.156475i
$856$	−3.89037	+	6.73832i	−0.132970	+	0.230311i
$857$	10.9282			0.373300			0.186650	−	0.982426i	$-0.440237\pi$
$857$	10.9282			0.373300			0.186650	+	0.982426i	$0.440237\pi$
$858$	−4.97296	+	7.77266i	−0.169774	+	0.265354i
$859$	−13.9076			−0.474520			−0.237260	−	0.971446i	$-0.576249\pi$
$859$	−13.9076			−0.474520			−0.237260	+	0.971446i	$0.576249\pi$
$860$	−2.14766	−	3.71986i	−0.0732347	−	0.126846i
$861$	−3.70895	−	2.24357i	−0.126401	−	0.0764607i
$862$	10.9356	−	18.9410i	0.372468	−	0.645133i
$863$	−18.4231	+	31.9098i	−0.627131	+	1.08622i	0.360993	+	0.932568i	$0.382438\pi$
$863$	−18.4231	+	31.9098i	−0.627131	+	1.08622i	−0.988125	+	0.153655i	$0.950896\pi$
$864$	−3.18716	+	4.10390i	−0.108429	+	0.139618i
$865$	0.676647	+	1.17199i	0.0230067	+	0.0398488i
$866$	6.52558	+	11.3026i	0.221748	+	0.384079i
$867$	2.85486	−	4.46211i	0.0969562	−	0.151541i
$868$	1.19582	+	0.650870i	0.0405887	+	0.0220920i
$869$	−9.13229	−	15.8176i	−0.309792	−	0.536575i
$870$	−7.15126	−	0.326134i	−0.242450	−	0.0110570i
$871$	3.38871			0.114822
$872$	−3.75729	−	6.50783i	−0.127238	−	0.220383i
$873$	−19.3566	+	27.4170i	−0.655122	+	0.927926i
$874$	4.59358			0.155380
$875$	10.1745	−	6.22056i	0.343961	−	0.210293i
$876$	22.9107	+	1.04484i	0.774081	+	0.0353020i
$877$	−10.3595			−0.349817			−0.174908	−	0.984585i	$-0.555963\pi$
$877$	−10.3595			−0.349817			−0.174908	+	0.984585i	$0.555963\pi$
$878$	−2.43200	+	4.21235i	−0.0820760	+	0.142160i
$879$	−7.86527	−	15.1809i	−0.265289	−	0.512038i
$880$	−0.839883	−	1.45472i	−0.0283125	−	0.0490386i
$881$	9.34806			0.314944			0.157472	−	0.987523i	$-0.449666\pi$
$881$	9.34806			0.314944			0.157472	+	0.987523i	$0.449666\pi$
$882$	−20.9825	−	0.857490i	−0.706517	−	0.0288732i
$883$	2.29494			0.0772308			0.0386154	−	0.999254i	$-0.487705\pi$
$883$	2.29494			0.0772308			0.0386154	+	0.999254i	$0.487705\pi$
$884$	2.72665	+	4.72270i	0.0917073	+	0.158842i
$885$	−5.54357	+	8.66452i	−0.186345	+	0.291255i
$886$	5.76975	−	9.99350i	0.193838	−	0.335738i
$887$	−27.6726			−0.929154			−0.464577	−	0.885533i	$-0.653794\pi$
$887$	−27.6726			−0.929154			−0.464577	+	0.885533i	$0.653794\pi$
$888$	−8.50214	+	13.2887i	−0.285313	+	0.445940i
$889$	19.8866	−	12.1584i	0.666974	−	0.407779i
$890$	−1.25564			−0.0420891
$891$	−32.2850	−	5.95143i	−1.08159	−	0.199380i
$892$	−0.445916	−	0.772349i	−0.0149304	−	0.0258602i
$893$	9.43560			0.315750
$894$	7.30039	+	14.0906i	0.244162	+	0.471260i
$895$	2.10963	+	3.65399i	0.0705172	+	0.122139i
$896$	−2.32383	−	1.26483i	−0.0776338	−	0.0422551i
$897$	1.31858	+	2.54500i	0.0440260	+	0.0849752i
$898$	13.2125	+	22.8848i	0.440908	+	0.763676i
$899$	2.30924	+	3.99973i	0.0770176	+	0.133398i
$900$	8.28434	−	11.7341i	0.276145	−	0.391136i
$901$	23.2163	−	40.2119i	0.773448	−	1.33965i
$902$	1.72519	−	2.98812i	0.0574426	−	0.0994935i
$903$	0.872855	−	42.7347i	0.0290468	−	1.42212i
$904$	3.03064	+	5.24922i	0.100798	+	0.174587i
$905$	−10.3284			−0.343327
$906$	0.0827835	+	0.159782i	0.00275030	+	0.00530839i
$907$	−2.93152			−0.0973396			−0.0486698	−	0.998815i	$-0.515498\pi$
$907$	−2.93152			−0.0973396			−0.0486698	+	0.998815i	$0.515498\pi$
$908$	7.32597	−	12.6889i	0.243121	−	0.421098i
$909$	41.0962	+	3.75620i	1.36307	+	0.124585i
$910$	0.0447509	+	1.77889i	0.00148348	+	0.0589696i
$911$	15.3171	−	26.5300i	0.507479	−	0.878979i	−0.492484	−	0.870322i	$-0.663911\pi$
$911$	15.3171	−	26.5300i	0.507479	−	0.878979i	0.999963	−	0.00865719i	$-0.00275570\pi$
$912$	7.01459	+	0.319901i	0.232276	+	0.0105930i
$913$	−12.1242	+	20.9998i	−0.401253	+	0.694991i
$914$	1.86906	−	3.23731i	0.0618231	−	0.107081i
$915$	4.43366	+	8.55747i	0.146572	+	0.282901i
$916$	4.78794	−	8.29295i	0.158198	−	0.274007i
$917$	47.7132	−	29.1712i	1.57563	−	0.963319i
$918$	−11.9004	+	15.3234i	−0.392771	+	0.505746i
$919$	13.1857	−	22.8383i	0.434956	−	0.753366i	−0.562336	−	0.826909i	$-0.690097\pi$
$919$	13.1857	−	22.8383i	0.434956	−	0.753366i	0.997292	+	0.0735429i	$0.0234306\pi$
$920$	−0.521786			−0.0172028
$921$	13.4751	+	0.614532i	0.444019	+	0.0202495i
$922$	15.8099			0.520672
$923$	1.22665	+	2.12463i	0.0403758	+	0.0699329i
$924$	0.341346	−	16.7122i	0.0112295	−	0.549791i
$925$	21.8047	−	37.7668i	0.716933	−	1.24176i
$926$	19.1965	−	33.2493i	0.630836	−	1.09264i
$927$	33.3478	+	3.04799i	1.09528	+	0.100109i
$928$	−4.48755	−	7.77266i	−0.147311	−	0.255150i
$929$	−8.93706	−	15.4794i	−0.293215	−	0.507864i	0.681353	−	0.731955i	$-0.261392\pi$
$929$	−8.93706	−	15.4794i	−0.293215	−	0.507864i	−0.974568	+	0.224091i	$0.928059\pi$
$930$	0.410019	+	0.0186989i	0.0134451	+	0.000613163i
$931$	15.4071	+	23.8320i	0.504947	+	0.781063i
$932$	7.21420	+	12.4954i	0.236309	+	0.409299i
$933$	−14.3853	+	22.4840i	−0.470954	+	0.736094i
$934$	−6.31304			−0.206569
$935$	−3.13600	−	5.43171i	−0.102558	−	0.177636i
$936$	1.83628	+	3.97816i	0.0600208	+	0.130030i
$937$	15.9134			0.519869			0.259934	−	0.965626i	$-0.416299\pi$
$937$	15.9134			0.519869			0.259934	+	0.965626i	$0.416299\pi$
$938$	−5.23745	+	3.20211i	−0.171009	+	0.104553i
$939$	−6.77023	−	13.0673i	−0.220938	−	0.426436i
$940$	−1.07179			−0.0349580
$941$	8.14027	−	14.0994i	0.265365	−	0.459626i	−0.702294	−	0.711887i	$-0.747841\pi$
$941$	8.14027	−	14.0994i	0.265365	−	0.459626i	0.967659	+	0.252261i	$0.0811741\pi$
$942$	36.3047	+	1.65568i	1.18287	+	0.0539448i
$943$	−0.535897	−	0.928200i	−0.0174512	−	0.0302264i
$944$	−12.8961			−0.419732
$945$	−5.80106	+	2.53533i	−0.188709	+	0.0824744i
$946$	34.0233			1.10619
$947$	14.2951	+	24.7599i	0.464529	+	0.804589i	0.999180	−	0.0404846i	$-0.0128902\pi$
$947$	14.2951	+	24.7599i	0.464529	+	0.804589i	−0.534651	+	0.845073i	$0.679557\pi$
$948$	−8.66372	−	0.395109i	−0.281384	−	0.0128325i
$949$	9.66945	−	16.7480i	0.313884	−	0.543662i
$950$	−19.4107			−0.629766
$951$	11.2389	+	21.6924i	0.364447	+	0.703424i
$952$	−8.67684	−	4.72270i	−0.281218	−	0.153064i
$953$	−29.3537			−0.950859			−0.475430	−	0.879754i	$-0.657707\pi$
$953$	−29.3537			−0.950859			−0.475430	+	0.879754i	$0.657707\pi$
$954$	21.5167	−	30.4767i	0.696630	−	0.986719i
$955$	0.573256	+	0.992908i	0.0185501	+	0.0321297i
$956$	18.3097			0.592179
$957$	30.5598	−	47.7645i	0.987859	−	1.54401i
$958$	10.2068	+	17.6787i	0.329767	+	0.571173i
$959$	−9.94659	+	6.08121i	−0.321192	+	0.196373i
$960$	−0.796790	−	0.0363376i	−0.0257163	−	0.00117279i
$961$	15.3676	+	26.6175i	0.495729	+	0.858628i
$962$	6.65126	+	11.5203i	0.214445	+	0.371430i
$963$	−13.4626	+	19.0687i	−0.433828	+	0.614481i
$964$	−0.0466924	+	0.0808735i	−0.00150386	+	0.00260476i
$965$	1.03376	−	1.79053i	0.0332779	−	0.0576391i
$966$	−4.44280	−	2.68749i	−0.142945	−	0.0864684i
$967$	−4.69815	−	8.13743i	−0.151082	−	0.261682i	0.780543	−	0.625102i	$-0.214943\pi$
$967$	−4.69815	−	8.13743i	−0.151082	−	0.261682i	−0.931626	+	0.363419i	$0.881609\pi$
$968$	2.30545			0.0741000
$969$	26.1914	+	1.19446i	0.841390	+	0.0383716i
$970$	−5.15174			−0.165412
$971$	7.77335	−	13.4638i	0.249459	−	0.432075i	−0.713917	−	0.700230i	$-0.753081\pi$
$971$	7.77335	−	13.4638i	0.249459	−	0.432075i	0.963376	+	0.268155i	$0.0864140\pi$
$972$	−10.6424	+	11.3903i	−0.341355	+	0.365344i
$973$	−4.70554	−	2.56117i	−0.150853	−	0.0821074i
$974$	6.18190	−	10.7074i	0.198081	−	0.343086i
$975$	−5.57179	−	10.7542i	−0.178440	−	0.344410i
$976$	−6.04163	+	10.4644i	−0.193388	+	0.334958i
$977$	4.79893	−	8.31198i	0.153531	−	0.265924i	−0.778992	−	0.627034i	$-0.784269\pi$
$977$	4.79893	−	8.31198i	0.153531	−	0.265924i	0.932523	+	0.361110i	$0.117602\pi$
$978$	39.8587	+	1.81776i	1.27454	+	0.0581256i
$979$	4.97296	−	8.61342i	0.158936	−	0.275286i
$980$	−1.75010	−	2.70709i	−0.0559048	−	0.0864748i
$981$	−9.44805	−	20.4684i	−0.301653	−	0.653506i
$982$	0.207004	−	0.358541i	0.00660575	−	0.0114415i
$983$	−46.8535			−1.49439			−0.747197	−	0.664603i	$-0.768601\pi$
$983$	−46.8535			−1.49439			−0.747197	+	0.664603i	$0.768601\pi$
$984$	−0.753696	−	1.45472i	−0.0240269	−	0.0463748i
$985$	−5.86400			−0.186843
$986$	−16.7558	−	29.0220i	−0.533614	−	0.924247i
$987$	−9.12588	−	5.52032i	−0.290480	−	0.175714i
$988$	2.96050	−	5.12774i	0.0941862	−	0.163135i
$989$	5.28434	−	9.15274i	0.168032	−	0.291040i
$990$	−2.11196	−	4.57539i	−0.0671225	−	0.145415i
$991$	10.8260	+	18.7511i	0.343898	+	0.595649i	0.985153	−	0.171679i	$-0.0549192\pi$
$991$	10.8260	+	18.7511i	0.343898	+	0.595649i	−0.641255	+	0.767328i	$0.721586\pi$
$992$	0.257295	+	0.445647i	0.00816911	+	0.0141493i
$993$	−21.9466	−	42.3595i	−0.696454	−	1.34424i
$994$	−3.90350	−	2.12463i	−0.123811	−	0.0673891i
$995$	0.678304	+	1.17486i	0.0215037	+	0.0372455i
$996$	5.29679	+	10.2234i	0.167835	+	0.323941i
$997$	−57.2379			−1.81274			−0.906372	−	0.422481i	$-0.861159\pi$
$997$	−57.2379			−1.81274			−0.906372	+	0.422481i	$0.861159\pi$
$998$	0.461967	+	0.800151i	0.0146233	+	0.0253283i
$999$	−29.0292	+	37.3790i	−0.918443	+	1.18262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.h.c.79.3	yes	6
3.2	odd	2		378.2.h.d.289.3		6
4.3	odd	2		1008.2.t.g.961.1		6
7.2	even	3		882.2.f.l.295.2		6
7.3	odd	6		882.2.e.p.655.2		6
7.4	even	3		126.2.e.d.25.2	✓	6
7.5	odd	6		882.2.f.m.295.2		6
7.6	odd	2		882.2.h.o.79.1		6
9.2	odd	6		1134.2.g.n.163.1		6
9.4	even	3		126.2.e.d.121.2	yes	6
9.5	odd	6		378.2.e.c.37.1		6
9.7	even	3		1134.2.g.k.163.3		6
12.11	even	2		3024.2.t.g.289.3		6
21.2	odd	6		2646.2.f.o.883.1		6
21.5	even	6		2646.2.f.n.883.3		6
21.11	odd	6		378.2.e.c.235.1		6
21.17	even	6		2646.2.e.o.2125.3		6
21.20	even	2		2646.2.h.p.667.1		6
28.11	odd	6		1008.2.q.h.529.2		6
36.23	even	6		3024.2.q.h.2305.1		6
36.31	odd	6		1008.2.q.h.625.2		6
63.2	odd	6		7938.2.a.bu.1.3		3
63.4	even	3	inner	126.2.h.c.67.3	yes	6
63.5	even	6		2646.2.f.n.1765.3		6
63.11	odd	6		1134.2.g.n.487.1		6
63.13	odd	6		882.2.e.p.373.2		6
63.16	even	3		7938.2.a.cb.1.1		3
63.23	odd	6		2646.2.f.o.1765.1		6
63.25	even	3		1134.2.g.k.487.3		6
63.31	odd	6		882.2.h.o.67.1		6
63.32	odd	6		378.2.h.d.361.3		6
63.40	odd	6		882.2.f.m.589.2		6
63.41	even	6		2646.2.e.o.1549.3		6
63.47	even	6		7938.2.a.bx.1.1		3
63.58	even	3		882.2.f.l.589.2		6
63.59	even	6		2646.2.h.p.361.1		6
63.61	odd	6		7938.2.a.by.1.3		3
84.11	even	6		3024.2.q.h.2881.1		6
252.67	odd	6		1008.2.t.g.193.1		6
252.95	even	6		3024.2.t.g.1873.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.2	✓	6	7.4	even	3
126.2.e.d.121.2	yes	6	9.4	even	3
126.2.h.c.67.3	yes	6	63.4	even	3	inner
126.2.h.c.79.3	yes	6	1.1	even	1	trivial
378.2.e.c.37.1		6	9.5	odd	6
378.2.e.c.235.1		6	21.11	odd	6
378.2.h.d.289.3		6	3.2	odd	2
378.2.h.d.361.3		6	63.32	odd	6
882.2.e.p.373.2		6	63.13	odd	6
882.2.e.p.655.2		6	7.3	odd	6
882.2.f.l.295.2		6	7.2	even	3
882.2.f.l.589.2		6	63.58	even	3
882.2.f.m.295.2		6	7.5	odd	6
882.2.f.m.589.2		6	63.40	odd	6
882.2.h.o.67.1		6	63.31	odd	6
882.2.h.o.79.1		6	7.6	odd	2
1008.2.q.h.529.2		6	28.11	odd	6
1008.2.q.h.625.2		6	36.31	odd	6
1008.2.t.g.193.1		6	252.67	odd	6
1008.2.t.g.961.1		6	4.3	odd	2
1134.2.g.k.163.3		6	9.7	even	3
1134.2.g.k.487.3		6	63.25	even	3
1134.2.g.n.163.1		6	9.2	odd	6
1134.2.g.n.487.1		6	63.11	odd	6
2646.2.e.o.1549.3		6	63.41	even	6
2646.2.e.o.2125.3		6	21.17	even	6
2646.2.f.n.883.3		6	21.5	even	6
2646.2.f.n.1765.3		6	63.5	even	6
2646.2.f.o.883.1		6	21.2	odd	6
2646.2.f.o.1765.1		6	63.23	odd	6
2646.2.h.p.361.1		6	63.59	even	6
2646.2.h.p.667.1		6	21.20	even	2
3024.2.q.h.2305.1		6	36.23	even	6
3024.2.q.h.2881.1		6	84.11	even	6
3024.2.t.g.289.3		6	12.11	even	2
3024.2.t.g.1873.3		6	252.95	even	6
7938.2.a.bu.1.3		3	63.2	odd	6
7938.2.a.bx.1.1		3	63.47	even	6
7938.2.a.by.1.3		3	63.61	odd	6
7938.2.a.cb.1.1		3	63.16	even	3

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.73025 + 0.0789082i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.460505 q^{5} +(-0.796790 - 1.53790i) q^{6} +(2.25729 - 1.38008i) q^{7} +1.00000 q^{8} +(2.98755 + 0.273062i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.73025 + 0.0789082i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.460505 q^{5} +(-0.796790 - 1.53790i) q^{6} +(2.25729 - 1.38008i) q^{7} +1.00000 q^{8} +(2.98755 + 0.273062i) q^{9} +(0.230252 + 0.398809i) q^{10} -3.64766 q^{11} +(-0.933463 + 1.45899i) q^{12} +(0.730252 + 1.26483i) q^{13} +(-2.32383 - 1.26483i) q^{14} +(-0.796790 - 0.0363376i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.86693 - 3.23361i) q^{17} +(-1.25729 - 2.72382i) q^{18} +(-2.02704 + 3.51094i) q^{19} +(0.230252 - 0.398809i) q^{20} +(4.01459 - 2.20977i) q^{21} +(1.82383 + 3.15897i) q^{22} +1.13307 q^{23} +(1.73025 + 0.0789082i) q^{24} -4.78794 q^{25} +(0.730252 - 1.26483i) q^{26} +(5.14766 + 0.708209i) q^{27} +(0.0665372 + 2.64491i) q^{28} +(-4.48755 + 7.77266i) q^{29} +(0.366926 + 0.708209i) q^{30} +(0.257295 - 0.445647i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.31138 - 0.287831i) q^{33} +(-1.86693 + 3.23361i) q^{34} +(-1.03950 + 0.635534i) q^{35} +(-1.73025 + 2.45076i) q^{36} +(-4.55408 + 7.88791i) q^{37} +4.05408 q^{38} +(1.16372 + 2.24611i) q^{39} -0.460505 q^{40} +(-0.472958 - 0.819187i) q^{41} +(-3.92101 - 2.37185i) q^{42} +(4.66372 - 8.07779i) q^{43} +(1.82383 - 3.15897i) q^{44} +(-1.37578 - 0.125747i) q^{45} +(-0.566537 - 0.981271i) q^{46} +(-1.16372 - 2.01561i) q^{47} +(-0.796790 - 1.53790i) q^{48} +(3.19076 - 6.23049i) q^{49} +(2.39397 + 4.14647i) q^{50} +(-2.97509 - 5.74228i) q^{51} -1.46050 q^{52} +(6.21780 + 10.7695i) q^{53} +(-1.96050 - 4.81211i) q^{54} +1.67977 q^{55} +(2.25729 - 1.38008i) q^{56} +(-3.78434 + 5.91486i) q^{57} +8.97509 q^{58} +(6.44805 - 11.1684i) q^{59} +(0.429864 - 0.671871i) q^{60} +(-6.04163 - 10.4644i) q^{61} -0.514589 q^{62} +(7.12062 - 3.50667i) q^{63} +1.00000 q^{64} +(-0.336285 - 0.582462i) q^{65} +(2.90642 + 5.60973i) q^{66} +(1.16012 - 2.00938i) q^{67} +3.73385 q^{68} +(1.96050 + 0.0894089i) q^{69} +(1.07014 + 0.582462i) q^{70} +1.67977 q^{71} +(2.98755 + 0.273062i) q^{72} +(-6.62062 - 11.4673i) q^{73} +9.10817 q^{74} +(-8.28434 - 0.377808i) q^{75} +(-2.02704 - 3.51094i) q^{76} +(-8.23385 + 5.03407i) q^{77} +(1.36333 - 2.13086i) q^{78} +(2.50360 + 4.33636i) q^{79} +(0.230252 + 0.398809i) q^{80} +(8.85087 + 1.63157i) q^{81} +(-0.472958 + 0.819187i) q^{82} +(3.32383 - 5.75705i) q^{83} +(-0.0935793 + 4.58162i) q^{84} +(0.859728 + 1.48909i) q^{85} -9.32743 q^{86} +(-8.37792 + 13.0946i) q^{87} -3.64766 q^{88} +(-1.36333 + 2.36135i) q^{89} +(0.578990 + 1.25433i) q^{90} +(3.39397 + 1.84730i) q^{91} +(-0.566537 + 0.981271i) q^{92} +(0.480350 - 0.750780i) q^{93} +(-1.16372 + 2.01561i) q^{94} +(0.933463 - 1.61680i) q^{95} +(-0.933463 + 1.45899i) q^{96} +(-5.59358 + 9.68836i) q^{97} +(-6.99115 + 0.351971i) q^{98} +(-10.8976 - 0.996040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9	\( 6 q - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9} - 5 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} - 4 q^{17} + 8 q^{18} - 3 q^{19} - 5 q^{20} - 7 q^{21} - q^{22} + 14 q^{23} + 4 q^{24} + 4 q^{25} - 2 q^{26} + 7 q^{27} + 4 q^{28} - 5 q^{29} - 5 q^{30} - 14 q^{31} - 3 q^{32} - 4 q^{33} - 4 q^{34} - 19 q^{35} - 4 q^{36} - 9 q^{37} + 6 q^{38} - 3 q^{39} + 10 q^{40} - 12 q^{41} + 2 q^{42} + 18 q^{43} - q^{44} - 31 q^{45} - 7 q^{46} + 3 q^{47} - 2 q^{48} - 2 q^{50} + 26 q^{51} + 4 q^{52} + 9 q^{53} + q^{54} + 14 q^{55} - 2 q^{56} + 2 q^{57} + 10 q^{58} + 4 q^{59} + 7 q^{60} + 4 q^{61} + 28 q^{62} + 28 q^{63} + 6 q^{64} - 12 q^{65} + 23 q^{66} + 5 q^{67} + 8 q^{68} - q^{69} + 2 q^{70} + 14 q^{71} - 4 q^{72} - 25 q^{73} + 18 q^{74} - 25 q^{75} - 3 q^{76} - 35 q^{77} + 9 q^{78} + 7 q^{79} - 5 q^{80} + 32 q^{81} - 12 q^{82} + 8 q^{83} + 5 q^{84} + 14 q^{85} - 36 q^{86} - 20 q^{87} + 2 q^{88} - 9 q^{89} + 29 q^{90} + 4 q^{91} - 7 q^{92} - 3 q^{93} + 3 q^{94} + 2 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 41 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9 - 5 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 - 4 * q^17 + 8 * q^18 - 3 * q^19 - 5 * q^20 - 7 * q^21 - q^22 + 14 * q^23 + 4 * q^24 + 4 * q^25 - 2 * q^26 + 7 * q^27 + 4 * q^28 - 5 * q^29 - 5 * q^30 - 14 * q^31 - 3 * q^32 - 4 * q^33 - 4 * q^34 - 19 * q^35 - 4 * q^36 - 9 * q^37 + 6 * q^38 - 3 * q^39 + 10 * q^40 - 12 * q^41 + 2 * q^42 + 18 * q^43 - q^44 - 31 * q^45 - 7 * q^46 + 3 * q^47 - 2 * q^48 - 2 * q^50 + 26 * q^51 + 4 * q^52 + 9 * q^53 + q^54 + 14 * q^55 - 2 * q^56 + 2 * q^57 + 10 * q^58 + 4 * q^59 + 7 * q^60 + 4 * q^61 + 28 * q^62 + 28 * q^63 + 6 * q^64 - 12 * q^65 + 23 * q^66 + 5 * q^67 + 8 * q^68 - q^69 + 2 * q^70 + 14 * q^71 - 4 * q^72 - 25 * q^73 + 18 * q^74 - 25 * q^75 - 3 * q^76 - 35 * q^77 + 9 * q^78 + 7 * q^79 - 5 * q^80 + 32 * q^81 - 12 * q^82 + 8 * q^83 + 5 * q^84 + 14 * q^85 - 36 * q^86 - 20 * q^87 + 2 * q^88 - 9 * q^89 + 29 * q^90 + 4 * q^91 - 7 * q^92 - 3 * q^93 + 3 * q^94 + 2 * q^95 - 2 * q^96 - 28 * q^97 - 12 * q^98 - 41 * q^99

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