LMFDB - Embedded newform 126.2.e.d.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(25,126)]

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([4, 4]))

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

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

chi := DirichletCharacter("126.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.00611506547$
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			121.2
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	126.121
Dual form			126.2.e.d.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.796790 + 1.53790i) q^{3} +1.00000 q^{4} +(0.230252 + 0.398809i) q^{5} +(-0.796790 + 1.53790i) q^{6} +(0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +(-1.73025 - 2.45076i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.796790 + 1.53790i) q^{3} +1.00000 q^{4} +(0.230252 + 0.398809i) q^{5} +(-0.796790 + 1.53790i) q^{6} +(0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +(-1.73025 - 2.45076i) q^{9} +(0.230252 + 0.398809i) q^{10} +(1.82383 - 3.15897i) q^{11} +(-0.796790 + 1.53790i) q^{12} +(0.730252 - 1.26483i) q^{13} +(0.0665372 + 2.64491i) q^{14} +(-0.796790 + 0.0363376i) q^{15} +1.00000 q^{16} +(-1.86693 - 3.23361i) q^{17} +(-1.73025 - 2.45076i) q^{18} +(-2.02704 + 3.51094i) q^{19} +(0.230252 + 0.398809i) q^{20} +(-4.12062 - 2.00511i) q^{21} +(1.82383 - 3.15897i) q^{22} +(-0.566537 - 0.981271i) q^{23} +(-0.796790 + 1.53790i) q^{24} +(2.39397 - 4.14647i) 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} +(-0.796790 + 0.0363376i) q^{30} -0.514589 q^{31} +1.00000 q^{32} +(3.40496 + 5.32190i) 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} +(-2.02704 + 3.51094i) q^{38} +(1.36333 + 2.13086i) q^{39} +(0.230252 + 0.398809i) q^{40} +(-0.472958 + 0.819187i) q^{41} +(-4.12062 - 2.00511i) q^{42} +(4.66372 + 8.07779i) q^{43} +(1.82383 - 3.15897i) q^{44} +(0.578990 - 1.25433i) q^{45} +(-0.566537 - 0.981271i) q^{46} +2.32743 q^{47} +(-0.796790 + 1.53790i) q^{48} +(-6.99115 + 0.351971i) q^{49} +(2.39397 - 4.14647i) q^{50} +(6.46050 - 0.294632i) q^{51} +(0.730252 - 1.26483i) q^{52} +(6.21780 + 10.7695i) q^{53} +(5.14766 - 0.708209i) q^{54} +1.67977 q^{55} +(0.0665372 + 2.64491i) q^{56} +(-3.78434 - 5.91486i) q^{57} +(-4.48755 - 7.77266i) q^{58} -12.8961 q^{59} +(-0.796790 + 0.0363376i) q^{60} +12.0833 q^{61} -0.514589 q^{62} +(6.36693 - 4.73944i) q^{63} +1.00000 q^{64} +0.672570 q^{65} +(3.40496 + 5.32190i) q^{66} -2.32023 q^{67} +(-1.86693 - 3.23361i) q^{68} +(1.96050 - 0.0894089i) q^{69} +(-1.03950 + 0.635534i) q^{70} +1.67977 q^{71} +(-1.73025 - 2.45076i) q^{72} +(-6.62062 - 11.4673i) q^{73} +(-4.55408 + 7.88791i) q^{74} +(4.46936 + 6.98554i) q^{75} +(-2.02704 + 3.51094i) q^{76} +(8.47656 + 4.61369i) q^{77} +(1.36333 + 2.13086i) q^{78} -5.00720 q^{79} +(0.230252 + 0.398809i) q^{80} +(-3.01245 + 8.48087i) q^{81} +(-0.472958 + 0.819187i) q^{82} +(3.32383 + 5.75705i) q^{83} +(-4.12062 - 2.00511i) q^{84} +(0.859728 - 1.48909i) q^{85} +(4.66372 + 8.07779i) q^{86} +(15.5292 - 0.708209i) q^{87} +(1.82383 - 3.15897i) 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} +(0.410019 - 0.791385i) q^{93} +2.32743 q^{94} -1.86693 q^{95} +(-0.796790 + 1.53790i) 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 + 6 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 - 4 * q^9	\( 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} - 4 q^{9} - 5 q^{10} - q^{11} - 2 q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{15} + 6 q^{16} - 4 q^{17} - 4 q^{18} - 3 q^{19} - 5 q^{20} - 10 q^{21} - q^{22} - 7 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 7 q^{27} + 4 q^{28} - 5 q^{29} - 2 q^{30} + 28 q^{31} + 6 q^{32} - 19 q^{33} - 4 q^{34} - 19 q^{35} - 4 q^{36} - 9 q^{37} - 3 q^{38} + 9 q^{39} - 5 q^{40} - 12 q^{41} - 10 q^{42} + 18 q^{43} - q^{44} + 29 q^{45} - 7 q^{46} - 6 q^{47} - 2 q^{48} - 12 q^{49} - 2 q^{50} + 26 q^{51} - 2 q^{52} + 9 q^{53} + 7 q^{54} + 14 q^{55} + 4 q^{56} + 2 q^{57} - 5 q^{58} - 8 q^{59} - 2 q^{60} - 8 q^{61} + 28 q^{62} + 31 q^{63} + 6 q^{64} + 24 q^{65} - 19 q^{66} - 10 q^{67} - 4 q^{68} - q^{69} - 19 q^{70} + 14 q^{71} - 4 q^{72} - 25 q^{73} - 9 q^{74} + 44 q^{75} - 3 q^{76} + 52 q^{77} + 9 q^{78} - 14 q^{79} - 5 q^{80} - 40 q^{81} - 12 q^{82} + 8 q^{83} - 10 q^{84} + 14 q^{85} + 18 q^{86} + 31 q^{87} - q^{88} - 9 q^{89} + 29 q^{90} + 4 q^{91} - 7 q^{92} - 6 q^{94} - 4 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 41 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 - 4 * q^9 - 5 * q^10 - q^11 - 2 * q^12 - 2 * q^13 + 4 * q^14 - 2 * q^15 + 6 * q^16 - 4 * q^17 - 4 * q^18 - 3 * q^19 - 5 * q^20 - 10 * q^21 - q^22 - 7 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^26 + 7 * q^27 + 4 * q^28 - 5 * q^29 - 2 * q^30 + 28 * q^31 + 6 * q^32 - 19 * q^33 - 4 * q^34 - 19 * q^35 - 4 * q^36 - 9 * q^37 - 3 * q^38 + 9 * q^39 - 5 * q^40 - 12 * q^41 - 10 * q^42 + 18 * q^43 - q^44 + 29 * q^45 - 7 * q^46 - 6 * q^47 - 2 * q^48 - 12 * q^49 - 2 * q^50 + 26 * q^51 - 2 * q^52 + 9 * q^53 + 7 * q^54 + 14 * q^55 + 4 * q^56 + 2 * q^57 - 5 * q^58 - 8 * q^59 - 2 * q^60 - 8 * q^61 + 28 * q^62 + 31 * q^63 + 6 * q^64 + 24 * q^65 - 19 * q^66 - 10 * q^67 - 4 * q^68 - q^69 - 19 * q^70 + 14 * q^71 - 4 * q^72 - 25 * q^73 - 9 * q^74 + 44 * q^75 - 3 * q^76 + 52 * q^77 + 9 * q^78 - 14 * q^79 - 5 * q^80 - 40 * q^81 - 12 * q^82 + 8 * q^83 - 10 * q^84 + 14 * q^85 + 18 * q^86 + 31 * q^87 - q^88 - 9 * q^89 + 29 * q^90 + 4 * q^91 - 7 * q^92 - 6 * q^94 - 4 * 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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.796790	+	1.53790i	−0.460027	+	0.887905i
$3$	−0.796790	+	1.53790i	−0.460027	+	0.887905i
$4$	1.00000			0.500000
$5$	0.230252	+	0.398809i	0.102972	+	0.178353i	0.912908	−	0.408166i	$-0.133831\pi$
$5$	0.230252	+	0.398809i	0.102972	+	0.178353i	−0.809936	+	0.586519i	$0.800498\pi$
$6$	−0.796790	+	1.53790i	−0.325288	+	0.627844i
$7$	0.0665372	+	2.64491i	0.0251487	+	0.999684i
$7$	0.0665372	+	2.64491i	0.0251487	+	0.999684i
$8$	1.00000			0.353553
$9$	−1.73025	−	2.45076i	−0.576751	−	0.816920i
$10$	0.230252	+	0.398809i	0.0728122	+	0.126114i
$11$	1.82383	−	3.15897i	0.549906	−	0.952465i	−0.448374	−	0.893846i	$-0.647997\pi$
$11$	1.82383	−	3.15897i	0.549906	−	0.952465i	0.998280	−	0.0586193i	$-0.0186698\pi$
$12$	−0.796790	+	1.53790i	−0.230013	+	0.443953i
$13$	0.730252	−	1.26483i	0.202536	−	0.350802i	−0.746809	−	0.665038i	$-0.768415\pi$
$13$	0.730252	−	1.26483i	0.202536	−	0.350802i	0.949345	+	0.314236i	$0.101748\pi$
$14$	0.0665372	+	2.64491i	0.0177828	+	0.706883i
$15$	−0.796790	+	0.0363376i	−0.205730	+	0.00938234i
$16$	1.00000			0.250000
$17$	−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	$0.982907\pi$
$18$	−1.73025	−	2.45076i	−0.407824	−	0.577650i
$19$	−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
$21$	−4.12062	−	2.00511i	−0.899193	−	0.437552i
$22$	1.82383	−	3.15897i	0.388842	−	0.673495i
$23$	−0.566537	−	0.981271i	−0.118131	−	0.204609i	0.800896	−	0.598804i	$-0.204357\pi$
$23$	−0.566537	−	0.981271i	−0.118131	−	0.204609i	−0.919027	+	0.394194i	$0.871024\pi$
$24$	−0.796790	+	1.53790i	−0.162644	+	0.313922i
$25$	2.39397	−	4.14647i	0.478794	−	0.829295i
$26$	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	−0.895394	−	0.445275i	$-0.853106\pi$
$29$	−4.48755	−	7.77266i	−0.833317	−	1.44335i	0.0620772	−	0.998071i	$-0.480228\pi$
$30$	−0.796790	+	0.0363376i	−0.145473	+	0.00663431i
$31$	−0.514589			−0.0924229			−0.0462115	−	0.998932i	$-0.514715\pi$
$31$	−0.514589			−0.0924229			−0.0462115	+	0.998932i	$0.514715\pi$
$32$	1.00000			0.176777
$33$	3.40496	+	5.32190i	0.592727	+	0.926424i
$34$	−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	$0.897351\pi$
$38$	−2.02704	+	3.51094i	−0.328830	+	0.569550i
$39$	1.36333	+	2.13086i	0.218307	+	0.341211i
$40$	0.230252	+	0.398809i	0.0364061	+	0.0630572i
$41$	−0.472958	+	0.819187i	−0.0738636	+	0.127936i	−0.900592	−	0.434666i	$-0.856866\pi$
$41$	−0.472958	+	0.819187i	−0.0738636	+	0.127936i	0.826728	+	0.562602i	$0.190200\pi$
$42$	−4.12062	−	2.00511i	−0.635826	−	0.309396i
$43$	4.66372	+	8.07779i	0.711210	+	1.23185i	0.964403	+	0.264436i	$0.0851858\pi$
$43$	4.66372	+	8.07779i	0.711210	+	1.23185i	−0.253193	+	0.967416i	$0.581481\pi$
$44$	1.82383	−	3.15897i	0.274953	−	0.476233i
$45$	0.578990	−	1.25433i	0.0863108	−	0.186985i
$46$	−0.566537	−	0.981271i	−0.0835314	−	0.144681i
$47$	2.32743			0.339491			0.169745	−	0.985488i	$-0.445705\pi$
$47$	2.32743			0.339491			0.169745	+	0.985488i	$0.445705\pi$
$48$	−0.796790	+	1.53790i	−0.115007	+	0.221976i
$49$	−6.99115	+	0.351971i	−0.998735	+	0.0502815i
$50$	2.39397	−	4.14647i	0.338558	−	0.586400i
$51$	6.46050	−	0.294632i	0.904652	−	0.0412567i
$52$	0.730252	−	1.26483i	0.101268	−	0.175401i
$53$	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	$0.507454\pi$
$54$	5.14766	−	0.708209i	0.700508	−	0.0963750i
$55$	1.67977			0.226500
$56$	0.0665372	+	2.64491i	0.00889141	+	0.353442i
$57$	−3.78434	−	5.91486i	−0.501248	−	0.783443i
$58$	−4.48755	−	7.77266i	−0.589244	−	1.02060i
$59$	−12.8961			−1.67893			−0.839465	−	0.543414i	$-0.817131\pi$
$59$	−12.8961			−1.67893			−0.839465	+	0.543414i	$0.817131\pi$
$60$	−0.796790	+	0.0363376i	−0.102865	+	0.00469117i
$61$	12.0833			1.54710			0.773552	−	0.633733i	$-0.218478\pi$
$61$	12.0833			1.54710			0.773552	+	0.633733i	$0.218478\pi$
$62$	−0.514589			−0.0653529
$63$	6.36693	−	4.73944i	0.802157	−	0.597113i
$64$	1.00000			0.125000
$65$	0.672570			0.0834220
$66$	3.40496	+	5.32190i	0.419121	+	0.655080i
$67$	−2.32023			−0.283462			−0.141731	−	0.989905i	$-0.545267\pi$
$67$	−2.32023			−0.283462			−0.141731	+	0.989905i	$0.545267\pi$
$68$	−1.86693	−	3.23361i	−0.226398	−	0.392133i
$69$	1.96050	−	0.0894089i	0.236017	−	0.0107636i
$70$	−1.03950	+	0.635534i	−0.124243	+	0.0759608i
$71$	1.67977			0.199352			0.0996758	−	0.995020i	$-0.468219\pi$
$71$	1.67977			0.199352			0.0996758	+	0.995020i	$0.468219\pi$
$72$	−1.73025	−	2.45076i	−0.203912	−	0.288825i
$73$	−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	$-0.448859\pi$
$74$	−4.55408	+	7.88791i	−0.529402	+	0.916950i
$75$	4.46936	+	6.98554i	0.516077	+	0.806621i
$76$	−2.02704	+	3.51094i	−0.232518	+	0.402732i
$77$	8.47656	+	4.61369i	0.965993	+	0.525779i
$78$	1.36333	+	2.13086i	0.154366	+	0.241272i
$79$	−5.00720			−0.563354			−0.281677	−	0.959509i	$-0.590891\pi$
$79$	−5.00720			−0.563354			−0.281677	+	0.959509i	$0.590891\pi$
$80$	0.230252	+	0.398809i	0.0257430	+	0.0445882i
$81$	−3.01245	+	8.48087i	−0.334717	+	0.942319i
$82$	−0.472958	+	0.819187i	−0.0522295	+	0.0904641i
$83$	3.32383	+	5.75705i	0.364838	+	0.631918i	0.988750	−	0.149577i	$-0.0477911\pi$
$83$	3.32383	+	5.75705i	0.364838	+	0.631918i	−0.623912	+	0.781494i	$0.714458\pi$
$84$	−4.12062	−	2.00511i	−0.449597	−	0.218776i
$85$	0.859728	−	1.48909i	0.0932506	−	0.161515i
$86$	4.66372	+	8.07779i	0.502901	+	0.871051i
$87$	15.5292	−	0.708209i	1.66490	−	0.0759280i
$88$	1.82383	−	3.15897i	0.194421	−	0.336747i
$89$	−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
$93$	0.410019	−	0.791385i	0.0425170	−	0.0820628i
$94$	2.32743			0.240056
$95$	−1.86693			−0.191543
$96$	−0.796790	+	1.53790i	−0.0813220	+	0.156961i
$97$	−5.59358	−	9.68836i	−0.567942	−	0.983704i	−0.996769	−	0.0803178i	$-0.974406\pi$
$97$	−5.59358	−	9.68836i	−0.567942	−	0.983704i	0.428827	−	0.903386i	$-0.358927\pi$
$98$	−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
$101$	−6.87792	+	11.9129i	−0.684378	+	1.18538i	0.289254	+	0.957253i	$0.406593\pi$
$101$	−6.87792	+	11.9129i	−0.684378	+	1.18538i	−0.973632	+	0.228125i	$0.926740\pi$
$102$	6.46050	−	0.294632i	0.639685	−	0.0291729i
$103$	−5.58113	−	9.66679i	−0.549925	−	0.952498i	−0.998279	−	0.0586417i	$-0.981323\pi$
$103$	−5.58113	−	9.66679i	−0.549925	−	0.952498i	0.448354	−	0.893856i	$-0.352010\pi$
$104$	0.730252	−	1.26483i	0.0716071	−	0.124027i
$105$	−0.149126	−	2.10502i	−0.0145532	−	0.205429i
$106$	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	$0.289400\pi$
$108$	5.14766	−	0.708209i	0.495334	−	0.0681474i
$109$	−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	$0.950517\pi$
$110$	1.67977			0.160159
$111$	−8.50214	−	13.2887i	−0.806987	−	1.26131i
$112$	0.0665372	+	2.64491i	0.00628718	+	0.249921i
$113$	3.03064	−	5.24922i	0.285099	−	0.493805i	−0.687534	−	0.726152i	$-0.741307\pi$
$113$	3.03064	−	5.24922i	0.285099	−	0.493805i	0.972633	+	0.232346i	$0.0746403\pi$
$114$	−3.78434	−	5.91486i	−0.354436	−	0.553978i
$115$	0.260893	−	0.451880i	0.0243284	−	0.0421380i
$116$	−4.48755	−	7.77266i	−0.416658	−	0.721673i
$117$	−4.36333	+	0.398809i	−0.403390	+	0.0368699i
$118$	−12.8961			−1.18718
$119$	8.42840	−	5.15301i	0.772630	−	0.472376i
$120$	−0.796790	+	0.0363376i	−0.0727366	+	0.00331716i
$121$	−1.15272	−	1.99658i	−0.104793	−	0.181507i
$122$	12.0833			1.09397
$123$	−0.882977	−	1.38008i	−0.0796154	−	0.124438i
$124$	−0.514589			−0.0462115
$125$	4.50739			0.403153
$126$	6.36693	−	4.73944i	0.567211	−	0.422223i
$127$	8.80992			0.781754			0.390877	−	0.920443i	$-0.372172\pi$
$127$	8.80992			0.781754			0.390877	+	0.920443i	$0.372172\pi$
$128$	1.00000			0.0883883
$129$	−16.1388	+	0.736011i	−1.42094	+	0.0648022i
$130$	0.672570			0.0589883
$131$	−10.5687	−	18.3055i	−0.923389	−	1.59936i	−0.794131	−	0.607746i	$-0.792074\pi$
$131$	−10.5687	−	18.3055i	−0.923389	−	1.59936i	−0.129258	−	0.991611i	$-0.541260\pi$
$132$	3.40496	+	5.32190i	0.296364	+	0.463212i
$133$	−9.42101	−	5.12774i	−0.816905	−	0.444632i
$134$	−2.32023			−0.200438
$135$	1.46770	+	1.88987i	0.126320	+	0.162654i
$136$	−1.86693	−	3.23361i	−0.160088	−	0.277280i
$137$	2.20321	−	3.81607i	0.188233	−	0.326029i	−0.756428	−	0.654077i	$-0.773057\pi$
$137$	2.20321	−	3.81607i	0.188233	−	0.326029i	0.944661	+	0.328048i	$0.106391\pi$
$138$	1.96050	−	0.0894089i	0.166889	−	0.00761099i
$139$	−1.01245	+	1.75362i	−0.0858751	+	0.148740i	−0.905764	−	0.423783i	$-0.860702\pi$
$139$	−1.01245	+	1.75362i	−0.0858751	+	0.148740i	0.819889	+	0.572523i	$0.194035\pi$
$140$	−1.03950	+	0.635534i	−0.0878534	+	0.0537124i
$141$	−1.85447	+	3.57935i	−0.156175	+	0.301435i
$142$	1.67977			0.140963
$143$	−2.66372	−	4.61369i	−0.222751	−	0.385816i
$144$	−1.73025	−	2.45076i	−0.144188	−	0.204230i
$145$	2.06654	−	3.57935i	0.171617	−	0.297249i
$146$	−6.62062	−	11.4673i	−0.547927	−	0.949037i
$147$	5.02918	−	11.0321i	0.414800	−	0.909913i
$148$	−4.55408	+	7.88791i	−0.374343	+	0.648382i
$149$	4.58113	+	7.93474i	0.375300	+	0.650040i	0.990372	−	0.138432i	$-0.0442062\pi$
$149$	4.58113	+	7.93474i	0.375300	+	0.650040i	−0.615071	+	0.788471i	$0.710873\pi$
$150$	4.46936	+	6.98554i	0.364922	+	0.570367i
$151$	0.0519482	−	0.0899768i	0.00422748	−	0.00732221i	−0.863904	−	0.503657i	$-0.831988\pi$
$151$	0.0519482	−	0.0899768i	0.00422748	−	0.00732221i	0.868131	+	0.496334i	$0.165321\pi$
$152$	−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
$156$	1.36333	+	2.13086i	0.109154	+	0.170605i
$157$	20.9823			1.67457			0.837285	−	0.546767i	$-0.184142\pi$
$157$	20.9823			1.67457			0.837285	+	0.546767i	$0.184142\pi$
$158$	−5.00720			−0.398351
$159$	−21.5167	+	0.981271i	−1.70639	+	0.0778199i
$160$	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	$0.808637\pi$
$164$	−0.472958	+	0.819187i	−0.0369318	+	0.0639678i
$165$	−1.33842	+	2.58331i	−0.104196	+	0.201110i
$166$	3.32383	+	5.75705i	0.257979	+	0.446833i
$167$	−5.31498	+	9.20581i	−0.411285	+	0.712367i	−0.995031	−	0.0995698i	$-0.968253\pi$
$167$	−5.31498	+	9.20581i	−0.411285	+	0.712367i	0.583745	+	0.811937i	$0.301587\pi$
$168$	−4.12062	−	2.00511i	−0.317913	−	0.154698i
$169$	5.43346	+	9.41103i	0.417959	+	0.723926i
$170$	0.859728	−	1.48909i	0.0659382	−	0.114208i
$171$	12.1118	−	1.10702i	0.926210	−	0.0846558i
$172$	4.66372	+	8.07779i	0.355605	+	0.615926i
$173$	2.93872			0.223427			0.111713	−	0.993740i	$-0.464366\pi$
$173$	2.93872			0.223427			0.111713	+	0.993740i	$0.464366\pi$
$174$	15.5292	−	0.708209i	1.17726	−	0.0536892i
$175$	11.1264	+	6.05594i	0.841073	+	0.457786i
$176$	1.82383	−	3.15897i	0.137476	−	0.238116i
$177$	10.2755	−	19.8329i	0.772353	−	1.49073i
$178$	−1.36333	+	2.36135i	−0.102186	+	0.176991i
$179$	−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	$0.944576\pi$
$180$	0.578990	−	1.25433i	0.0431554	−	0.0934925i
$181$	22.4284			1.66709			0.833545	−	0.552452i	$-0.186308\pi$
$181$	22.4284			1.66709			0.833545	+	0.552452i	$0.186308\pi$
$182$	3.39397	+	1.84730i	0.251578	+	0.136931i
$183$	−9.62782	+	18.5828i	−0.711709	+	1.37368i
$184$	−0.566537	−	0.981271i	−0.0417657	−	0.0723403i
$185$	−4.19436			−0.308375
$186$	0.410019	−	0.791385i	0.0300641	−	0.0580272i
$187$	−13.6198			−0.995981
$188$	2.32743			0.169745
$189$	2.21566	+	13.5680i	0.161166	+	0.986927i
$190$	−1.86693			−0.135441
$191$	2.48968			0.180147			0.0900736	−	0.995935i	$-0.471290\pi$
$191$	2.48968			0.180147			0.0900736	+	0.995935i	$0.471290\pi$
$192$	−0.796790	+	1.53790i	−0.0575033	+	0.110988i
$193$	4.48968			0.323174			0.161587	−	0.986858i	$-0.448339\pi$
$193$	4.48968			0.323174			0.161587	+	0.986858i	$0.448339\pi$
$194$	−5.59358	−	9.68836i	−0.401596	−	0.695584i
$195$	−0.535897	+	1.03434i	−0.0383763	+	0.0740708i
$196$	−6.99115	+	0.351971i	−0.499368	+	0.0251408i
$197$	12.7339			0.907249			0.453625	−	0.891193i	$-0.350131\pi$
$197$	12.7339			0.907249			0.453625	+	0.891193i	$0.350131\pi$
$198$	−10.8976	+	0.996040i	−0.774456	+	0.0707855i
$199$	−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	$0.866630\pi$
$200$	2.39397	−	4.14647i	0.169279	−	0.293200i
$201$	1.84874	−	3.56828i	0.130400	−	0.251687i
$202$	−6.87792	+	11.9129i	−0.483928	+	0.838189i
$203$	20.2594	−	12.3863i	1.42193	−	0.869351i
$204$	6.46050	−	0.294632i	0.452326	−	0.0206283i
$205$	−0.435599			−0.0304235
$206$	−5.58113	−	9.66679i	−0.388855	−	0.673517i
$207$	−1.42461	+	3.08629i	−0.0990171	+	0.214512i
$208$	0.730252	−	1.26483i	0.0506339	−	0.0877005i
$209$	7.39397	+	12.8067i	0.511451	+	0.885860i
$210$	−0.149126	−	2.10502i	−0.0102907	−	0.145260i
$211$	−0.608168	+	1.05338i	−0.0418680	+	0.0725176i	−0.886200	−	0.463303i	$-0.846664\pi$
$211$	−0.608168	+	1.05338i	−0.0418680	+	0.0725176i	0.844332	+	0.535820i	$0.179998\pi$
$212$	6.21780	+	10.7695i	0.427040	+	0.739655i
$213$	−1.33842	+	2.58331i	−0.0917071	+	0.177005i
$214$	−3.89037	+	6.73832i	−0.265940	+	0.460622i
$215$	−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
$219$	22.9107	−	1.04484i	1.54816	−	0.0706040i
$220$	1.67977			0.113250
$221$	−5.45331			−0.366829
$222$	−8.50214	−	13.2887i	−0.570626	−	0.891880i
$223$	−0.445916	−	0.772349i	−0.0298607	−	0.0517203i	0.850709	−	0.525637i	$-0.176173\pi$
$223$	−0.445916	−	0.772349i	−0.0298607	−	0.0517203i	−0.880570	+	0.473917i	$0.842840\pi$
$224$	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
$227$	7.32597	−	12.6889i	0.486242	−	0.842195i	−0.513633	−	0.858010i	$-0.671701\pi$
$227$	7.32597	−	12.6889i	0.486242	−	0.842195i	0.999875	+	0.0158147i	$0.00503418\pi$
$228$	−3.78434	−	5.91486i	−0.250624	−	0.391721i
$229$	4.78794	+	8.29295i	0.316396	+	0.548013i	0.979733	−	0.200307i	$-0.0641939\pi$
$229$	4.78794	+	8.29295i	0.316396	+	0.548013i	−0.663338	+	0.748320i	$0.730861\pi$
$230$	0.260893	−	0.451880i	0.0172028	−	0.0297961i
$231$	−13.8494	+	9.35993i	−0.911224	+	0.615838i
$232$	−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	$0.00997571\pi$
$234$	−4.36333	+	0.398809i	−0.285240	+	0.0260710i
$235$	0.535897	+	0.928200i	0.0349580	+	0.0605491i
$236$	−12.8961			−0.839465
$237$	3.98968	−	7.70055i	0.259158	−	0.500205i
$238$	8.42840	−	5.15301i	0.546332	−	0.334020i
$239$	−9.15486	+	15.8567i	−0.592179	+	1.02568i	0.401760	+	0.915745i	$0.368399\pi$
$239$	−9.15486	+	15.8567i	−0.592179	+	1.02568i	−0.993938	+	0.109938i	$0.964935\pi$
$240$	−0.796790	+	0.0363376i	−0.0514326	+	0.00234558i
$241$	−0.0466924	+	0.0808735i	−0.00300772	+	0.00520952i	−0.867525	−	0.497393i	$-0.834291\pi$
$241$	−0.0466924	+	0.0808735i	−0.00300772	+	0.00520952i	0.864518	+	0.502602i	$0.167624\pi$
$242$	−1.15272	−	1.99658i	−0.0741000	−	0.128345i
$243$	−10.6424	−	11.3903i	−0.682711	−	0.730689i
$244$	12.0833			0.773552
$245$	−1.75010	−	2.70709i	−0.111810	−	0.172950i
$246$	−0.882977	−	1.38008i	−0.0562966	−	0.0879907i
$247$	2.96050	+	5.12774i	0.188372	+	0.326271i
$248$	−0.514589			−0.0326764
$249$	−11.5021	+	0.524555i	−0.728918	+	0.0332424i
$250$	4.50739			0.285072
$251$	−18.2733			−1.15340			−0.576702	−	0.816955i	$-0.695661\pi$
$251$	−18.2733			−1.15340			−0.576702	+	0.816955i	$0.695661\pi$
$252$	6.36693	−	4.73944i	0.401079	−	0.298556i
$253$	−4.13307			−0.259844
$254$	8.80992			0.552783
$255$	1.60505	+	2.50867i	0.100512	+	0.157099i
$256$	1.00000			0.0625000
$257$	10.5256	+	18.2308i	0.656568	+	1.13721i	0.981498	+	0.191471i	$0.0613257\pi$
$257$	10.5256	+	18.2308i	0.656568	+	1.13721i	−0.324931	+	0.945738i	$0.605341\pi$
$258$	−16.1388	+	0.736011i	−1.00476	+	0.0458221i
$259$	−21.1659	−	11.5203i	−1.31518	−	0.715838i
$260$	0.672570			0.0417110
$261$	−11.2843	+	24.4466i	−0.698483	+	1.51320i
$262$	−10.5687	−	18.3055i	−0.652935	−	1.13092i
$263$	2.58259	−	4.47318i	0.159249	−	0.275828i	−0.775349	−	0.631533i	$-0.782426\pi$
$263$	2.58259	−	4.47318i	0.159249	−	0.275828i	0.934598	+	0.355705i	$0.115759\pi$
$264$	3.40496	+	5.32190i	0.209561	+	0.327540i
$265$	−2.86333	+	4.95943i	−0.175893	+	0.304655i
$266$	−9.42101	−	5.12774i	−0.577639	−	0.314402i
$267$	−2.54523	−	3.97816i	−0.155766	−	0.243459i
$268$	−2.32023			−0.141731
$269$	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	$0.661538\pi$
$270$	1.46770	+	1.88987i	0.0893215	+	0.115014i
$271$	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
$273$	−5.54523	+	3.74766i	−0.335613	+	0.226819i
$274$	2.20321	−	3.81607i	0.133101	−	0.230537i
$275$	−8.73239	−	15.1249i	−0.526583	−	0.912068i
$276$	1.96050	−	0.0894089i	0.118009	−	0.00538178i
$277$	−1.69076	+	2.92848i	−0.101588	+	0.175955i	−0.912339	−	0.409436i	$-0.865726\pi$
$277$	−1.69076	+	2.92848i	−0.101588	+	0.175955i	0.810751	+	0.585391i	$0.199059\pi$
$278$	−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	−0.992078	−	0.125622i	$-0.959907\pi$
$281$	−10.1388	−	17.5609i	−0.604831	−	1.04760i	0.387248	−	0.921976i	$-0.373426\pi$
$282$	−1.85447	+	3.57935i	−0.110432	+	0.213147i
$283$	17.3494			1.03132			0.515658	−	0.856795i	$-0.327548\pi$
$283$	17.3494			1.03132			0.515658	+	0.856795i	$0.327548\pi$
$284$	1.67977			0.0996758
$285$	1.48755	−	2.87114i	0.0881147	−	0.170072i
$286$	−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
$290$	2.06654	−	3.57935i	0.121351	−	0.210187i
$291$	19.3566	−	0.882759i	1.13470	−	0.0517483i
$292$	−6.62062	−	11.4673i	−0.387443	−	0.671070i
$293$	−4.93560	+	8.54871i	−0.288341	+	0.499421i	−0.973414	−	0.229054i	$-0.926437\pi$
$293$	−4.93560	+	8.54871i	−0.288341	+	0.499421i	0.685073	+	0.728474i	$0.259770\pi$
$294$	5.02918	−	11.0321i	0.293308	−	0.643405i
$295$	−2.96936	−	5.14308i	−0.172883	−	0.299442i
$296$	−4.55408	+	7.88791i	−0.264701	+	0.458475i
$297$	7.15126	−	17.5530i	0.414958	−	1.01853i
$298$	4.58113	+	7.93474i	0.265378	+	0.459647i
$299$	−1.65486			−0.0957031
$300$	4.46936	+	6.98554i	0.258039	+	0.403310i
$301$	−21.0548	+	12.8726i	−1.21358	+	0.741964i
$302$	0.0519482	−	0.0899768i	0.00298928	−	0.00517759i
$303$	−12.8406	−	20.0696i	−0.737671	−	1.15297i
$304$	−2.02704	+	3.51094i	−0.116259	+	0.201366i
$305$	2.78220	+	4.81891i	0.159308	+	0.275930i
$306$	−4.69455	+	10.1703i	−0.268370	+	0.581400i
$307$	7.78794			0.444481			0.222240	−	0.974992i	$-0.428663\pi$
$307$	7.78794			0.444481			0.222240	+	0.974992i	$0.428663\pi$
$308$	8.47656	+	4.61369i	0.482997	+	0.262889i
$309$	19.3135	−	0.880794i	1.09871	−	0.0501066i
$310$	−0.118485	−	0.205223i	−0.00672952	−	0.0116559i
$311$	15.4107			0.873860			0.436930	−	0.899495i	$-0.356066\pi$
$311$	15.4107			0.873860			0.436930	+	0.899495i	$0.356066\pi$
$312$	1.36333	+	2.13086i	0.0771832	+	0.120636i
$313$	8.49688			0.480272			0.240136	−	0.970739i	$-0.422808\pi$
$313$	8.49688			0.480272			0.240136	+	0.970739i	$0.422808\pi$
$314$	20.9823			1.18410
$315$	3.35613	+	1.44792i	0.189096	+	0.0815810i
$316$	−5.00720			−0.281677
$317$	−14.1052			−0.792229			−0.396115	−	0.918201i	$-0.629642\pi$
$317$	−14.1052			−0.792229			−0.396115	+	0.918201i	$0.629642\pi$
$318$	−21.5167	+	0.981271i	−1.20660	+	0.0550270i
$319$	−32.7381			−1.83298
$320$	0.230252	+	0.398809i	0.0128715	+	0.0222941i
$321$	−7.26303	−	11.3520i	−0.405383	−	0.633607i
$322$	2.55768	−	1.56373i	0.142534	−	0.0871435i
$323$	15.1373			0.842264
$324$	−3.01245	+	8.48087i	−0.167359	+	0.471159i
$325$	−3.49640	−	6.05594i	−0.193945	−	0.335923i
$326$	−11.5182	+	19.9501i	−0.637933	+	1.10493i
$327$	13.0021	−	0.592963i	0.719020	−	0.0327909i
$328$	−0.472958	+	0.819187i	−0.0261147	+	0.0452320i
$329$	0.154861	+	6.15585i	0.00853775	+	0.339383i
$330$	−1.33842	+	2.58331i	−0.0736776	+	0.142206i
$331$	27.5438			1.51394			0.756971	−	0.653448i	$-0.226678\pi$
$331$	27.5438			1.51394			0.756971	+	0.653448i	$0.226678\pi$
$332$	3.32383	+	5.75705i	0.182419	+	0.315959i
$333$	27.2111	−	2.48710i	1.49116	−	0.136292i
$334$	−5.31498	+	9.20581i	−0.290823	+	0.503720i
$335$	−0.534239	−	0.925330i	−0.0291886	−	0.0505562i
$336$	−4.12062	−	2.00511i	−0.224798	−	0.109388i
$337$	0.748440	−	1.29634i	0.0407701	−	0.0706159i	−0.844920	−	0.534892i	$-0.820352\pi$
$337$	0.748440	−	1.29634i	0.0407701	−	0.0706159i	0.885690	+	0.464276i	$0.153686\pi$
$338$	5.43346	+	9.41103i	0.295541	+	0.511893i
$339$	5.65798	+	8.84334i	0.307299	+	0.480304i
$340$	0.859728	−	1.48909i	0.0466253	−	0.0807574i
$341$	−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
$345$	0.487068	+	0.761280i	0.0262229	+	0.0409859i
$346$	2.93872			0.157986
$347$	−18.2881			−0.981758			−0.490879	−	0.871228i	$-0.663324\pi$
$347$	−18.2881			−0.981758			−0.490879	+	0.871228i	$0.663324\pi$
$348$	15.5292	−	0.708209i	0.832451	−	0.0379640i
$349$	−3.90136	−	6.75735i	−0.208835	−	0.361713i	0.742513	−	0.669832i	$-0.233634\pi$
$349$	−3.90136	−	6.75735i	−0.208835	−	0.361713i	−0.951348	+	0.308119i	$0.900300\pi$
$350$	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
$353$	−13.4626	+	23.3180i	−0.716544	+	1.24109i	0.245817	+	0.969316i	$0.420944\pi$
$353$	−13.4626	+	23.3180i	−0.716544	+	1.24109i	−0.962361	+	0.271774i	$0.912390\pi$
$354$	10.2755	−	19.8329i	0.546136	−	1.05411i
$355$	0.386770	+	0.669906i	0.0205276	+	0.0355549i
$356$	−1.36333	+	2.36135i	−0.0722562	+	0.125151i
$357$	1.20914	+	17.0679i	0.0639945	+	0.903328i
$358$	−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	$0.219519\pi$
$360$	0.578990	−	1.25433i	0.0305155	−	0.0661092i
$361$	1.28220	+	2.22084i	0.0674842	+	0.116886i
$362$	22.4284			1.17881
$363$	3.98901	−	0.181919i	0.209369	−	0.00954827i
$364$	3.39397	+	1.84730i	0.177892	+	0.0968247i
$365$	3.04883	−	5.28073i	0.159583	−	0.276406i
$366$	−9.62782	+	18.5828i	−0.503254	+	0.971339i
$367$	−14.6367	+	25.3515i	−0.764028	+	1.32334i	0.176731	+	0.984259i	$0.443448\pi$
$367$	−14.6367	+	25.3515i	−0.764028	+	1.32334i	−0.940759	+	0.339076i	$0.889886\pi$
$368$	−0.566537	−	0.981271i	−0.0295328	−	0.0511523i
$369$	2.82597	−	0.258294i	0.147114	−	0.0134462i
$370$	−4.19436			−0.218054
$371$	−28.0708	+	17.1621i	−1.45736	+	0.891013i
$372$	0.410019	−	0.791385i	0.0212585	−	0.0410314i
$373$	−8.92986	−	15.4670i	−0.462371	−	0.800850i	0.536708	−	0.843768i	$-0.319668\pi$
$373$	−8.92986	−	15.4670i	−0.462371	−	0.800850i	−0.999079	+	0.0429184i	$0.986334\pi$
$374$	−13.6198			−0.704265
$375$	−3.59144	+	6.93190i	−0.185461	+	0.357962i
$376$	2.32743			0.120028
$377$	−13.1082			−0.675105
$378$	2.21566	+	13.5680i	0.113961	+	0.697863i
$379$	−22.4255			−1.15192			−0.575960	−	0.817478i	$-0.695371\pi$
$379$	−22.4255			−1.15192			−0.575960	+	0.817478i	$0.695371\pi$
$380$	−1.86693			−0.0957713
$381$	−7.01965	+	13.5487i	−0.359628	+	0.694123i
$382$	2.48968			0.127383
$383$	7.07014	+	12.2458i	0.361267	+	0.625733i	0.988170	−	0.153365i	$-0.0490109\pi$
$383$	7.07014	+	12.2458i	0.361267	+	0.625733i	−0.626903	+	0.779098i	$0.715678\pi$
$384$	−0.796790	+	1.53790i	−0.0406610	+	0.0784805i
$385$	0.111767	+	4.44284i	0.00569618	+	0.226428i
$386$	4.48968			0.228519
$387$	11.7273	−	25.4063i	0.596134	−	1.29147i
$388$	−5.59358	−	9.68836i	−0.283971	−	0.491852i
$389$	11.5651	−	20.0313i	0.586373	−	1.01563i	−0.408330	−	0.912834i	$-0.633889\pi$
$389$	11.5651	−	20.0313i	0.586373	−	1.01563i	0.994703	−	0.102793i	$-0.0327779\pi$
$390$	−0.535897	+	1.03434i	−0.0271362	+	0.0523760i
$391$	−2.11537	+	3.66392i	−0.106979	+	0.185292i
$392$	−6.99115	+	0.351971i	−0.353106	+	0.0177772i
$393$	36.5729	−	1.66791i	1.84486	−	0.0841350i
$394$	12.7339			0.641522
$395$	−1.15292	−	1.99691i	−0.0580097	−	0.100476i
$396$	−10.8976	+	0.996040i	−0.547623	+	0.0500529i
$397$	−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
$399$	15.3925	−	10.4028i	0.770589	−	0.520792i
$400$	2.39397	−	4.14647i	0.119698	−	0.207324i
$401$	−17.0167	−	29.4738i	−0.849775	−	1.47185i	−0.881409	−	0.472353i	$-0.843405\pi$
$401$	−17.0167	−	29.4738i	−0.849775	−	1.47185i	0.0316345	−	0.999500i	$-0.489929\pi$
$402$	1.84874	−	3.56828i	0.0922067	−	0.177970i
$403$	−0.375780	+	0.650870i	−0.0187189	+	0.0324221i
$404$	−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
$408$	6.46050	−	0.294632i	0.319843	−	0.0145864i
$409$	−3.48968			−0.172554			−0.0862769	−	0.996271i	$-0.527497\pi$
$409$	−3.48968			−0.172554			−0.0862769	+	0.996271i	$0.527497\pi$
$410$	−0.435599			−0.0215127
$411$	4.11323	+	6.42892i	0.202891	+	0.317115i
$412$	−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
$416$	0.730252	−	1.26483i	0.0358036	−	0.0620136i
$417$	−1.89017	−	2.95431i	−0.0925622	−	0.144673i
$418$	7.39397	+	12.8067i	0.361651	+	0.626398i
$419$	14.4897	−	25.0969i	0.707867	−	1.22606i	−0.257779	−	0.966204i	$-0.582991\pi$
$419$	14.4897	−	25.0969i	0.707867	−	1.22606i	0.965647	−	0.259858i	$-0.0836759\pi$
$420$	−0.149126	−	2.10502i	−0.00727661	−	0.102715i
$421$	−1.06128	−	1.83819i	−0.0517237	−	0.0895881i	0.839004	−	0.544125i	$-0.183138\pi$
$421$	−1.06128	−	1.83819i	−0.0517237	−	0.0895881i	−0.890728	+	0.454537i	$0.849805\pi$
$422$	−0.608168	+	1.05338i	−0.0296052	+	0.0512777i
$423$	−4.02704	−	5.70397i	−0.195801	−	0.277337i
$424$	6.21780	+	10.7695i	0.301963	+	0.523015i
$425$	−17.8774			−0.867183
$426$	−1.33842	+	2.58331i	−0.0648467	+	0.125162i
$427$	0.803987	+	31.9592i	0.0389077	+	1.54661i
$428$	−3.89037	+	6.73832i	−0.188048	+	0.325709i
$429$	9.21780	−	0.420378i	0.445040	−	0.0202960i
$430$	−2.14766	+	3.71986i	−0.103570	+	0.179388i
$431$	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	$0.656744\pi$
$432$	5.14766	−	0.708209i	0.247667	−	0.0340737i
$433$	−13.0512			−0.627199			−0.313599	−	0.949555i	$-0.601535\pi$
$433$	−13.0512			−0.627199			−0.313599	+	0.949555i	$0.601535\pi$
$434$	−0.0342393	−	1.36104i	−0.00164354	−	0.0653322i
$435$	3.85807	+	6.03011i	0.184980	+	0.289122i
$436$	−3.75729	−	6.50783i	−0.179942	−	0.311668i
$437$	4.59358			0.219741
$438$	22.9107	−	1.04484i	1.09472	−	0.0499245i
$439$	4.86400			0.232146			0.116073	−	0.993241i	$-0.462969\pi$
$439$	4.86400			0.232146			0.116073	+	0.993241i	$0.462969\pi$
$440$	1.67977			0.0800797
$441$	12.9590	+	16.5246i	0.617097	+	0.786887i
$442$	−5.45331			−0.259387
$443$	−11.5395			−0.548258			−0.274129	−	0.961693i	$-0.588390\pi$
$443$	−11.5395			−0.548258			−0.274129	+	0.961693i	$0.588390\pi$
$444$	−8.50214	−	13.2887i	−0.403494	−	0.630654i
$445$	−1.25564			−0.0595229
$446$	−0.445916	−	0.772349i	−0.0211147	−	0.0365718i
$447$	−15.8530	+	0.722977i	−0.749822	+	0.0341957i
$448$	0.0665372	+	2.64491i	0.00314359	+	0.124960i
$449$	−26.4251			−1.24708			−0.623538	−	0.781793i	$-0.714306\pi$
$449$	−26.4251			−1.24708			−0.623538	+	0.781793i	$0.714306\pi$
$450$	−14.3042	+	1.30740i	−0.674306	+	0.0616317i
$451$	1.72519	+	2.98812i	0.0812361	+	0.140705i
$452$	3.03064	−	5.24922i	0.142549	−	0.246903i
$453$	0.0969833	+	0.151584i	0.00455667	+	0.00712201i
$454$	7.32597	−	12.6889i	0.343825	−	0.595522i
$455$	0.0447509	+	1.77889i	0.00209796	+	0.0833956i
$456$	−3.78434	−	5.91486i	−0.177218	−	0.276989i
$457$	−3.73812			−0.174862			−0.0874310	−	0.996171i	$-0.527866\pi$
$457$	−3.73812			−0.174862			−0.0874310	+	0.996171i	$0.527866\pi$
$458$	4.78794	+	8.29295i	0.223726	+	0.387504i
$459$	−11.9004	−	15.3234i	−0.555462	−	0.715233i
$460$	0.260893	−	0.451880i	0.0121642	−	0.0210690i
$461$	−7.90496	−	13.6918i	−0.368171	−	0.637690i	0.621109	−	0.783724i	$-0.286682\pi$
$461$	−7.90496	−	13.6918i	−0.368171	−	0.637690i	−0.989280	+	0.146034i	$0.953349\pi$
$462$	−13.8494	+	9.35993i	−0.644333	+	0.435463i
$463$	19.1965	−	33.2493i	0.892137	−	1.54523i	0.0548278	−	0.998496i	$-0.482539\pi$
$463$	19.1965	−	33.2493i	0.892137	−	1.54523i	0.837309	−	0.546730i	$-0.184128\pi$
$464$	−4.48755	−	7.77266i	−0.208329	−	0.360837i
$465$	0.410019	−	0.0186989i	0.0190142	−	0.000867143i
$466$	7.21420	−	12.4954i	0.334191	−	0.578836i
$467$	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
$471$	−16.7185	+	32.2686i	−0.770347	+	1.48686i
$472$	−12.8961			−0.593591
$473$	34.0233			1.56439
$474$	3.98968	−	7.70055i	0.183252	−	0.353698i
$475$	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
$479$	10.2068	−	17.6787i	0.466361	−	0.807761i	−0.532901	−	0.846178i	$-0.678898\pi$
$479$	10.2068	−	17.6787i	0.466361	−	0.807761i	0.999262	+	0.0384168i	$0.0122314\pi$
$480$	−0.796790	+	0.0363376i	−0.0363683	+	0.00165858i
$481$	6.65126	+	11.5203i	0.303271	+	0.525282i
$482$	−0.0466924	+	0.0808735i	−0.00212678	+	0.00368369i
$483$	0.366926	+	5.17942i	0.0166957	+	0.235672i
$484$	−1.15272	−	1.99658i	−0.0523966	−	0.0907535i
$485$	2.57587	−	4.46154i	0.116964	−	0.202588i
$486$	−10.6424	−	11.3903i	−0.482749	−	0.516675i
$487$	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	$0.742956\pi$
$488$	12.0833			0.546984
$489$	−21.5036	−	33.6098i	−0.972426	−	1.51989i
$490$	−1.75010	−	2.70709i	−0.0790613	−	0.122294i
$491$	0.207004	−	0.358541i	0.00934194	−	0.0161807i	−0.861317	−	0.508069i	$-0.830360\pi$
$491$	0.207004	−	0.358541i	0.00934194	−	0.0161807i	0.870659	+	0.491888i	$0.163693\pi$
$492$	−0.882977	−	1.38008i	−0.0398077	−	0.0622188i
$493$	−16.7558	+	29.0220i	−0.754645	+	1.30708i
$494$	2.96050	+	5.12774i	0.133199	+	0.230708i
$495$	−2.90642	−	4.11671i	−0.130634	−	0.185032i
$496$	−0.514589			−0.0231057
$497$	0.111767	+	4.44284i	0.00501344	+	0.199289i
$498$	−11.5021	+	0.524555i	−0.515423	+	0.0235059i
$499$	0.461967	+	0.800151i	0.0206805	+	0.0358197i	0.876180	−	0.481983i	$-0.160083\pi$
$499$	0.461967	+	0.800151i	0.0206805	+	0.0358197i	−0.855500	+	0.517803i	$0.826750\pi$
$500$	4.50739			0.201577
$501$	−9.92267	−	15.5090i	−0.443312	−	0.692890i
$502$	−18.2733			−0.815579
$503$	−23.8142			−1.06182			−0.530911	−	0.847428i	$-0.678150\pi$
$503$	−23.8142			−1.06182			−0.530911	+	0.847428i	$0.678150\pi$
$504$	6.36693	−	4.73944i	0.283605	−	0.211111i
$505$	−6.33463			−0.281887
$506$	−4.13307			−0.183738
$507$	−18.8025	+	0.857490i	−0.835049	+	0.0380825i
$508$	8.80992			0.390877
$509$	15.3171	+	26.5300i	0.678919	+	1.17592i	0.975307	+	0.220855i	$0.0708846\pi$
$509$	15.3171	+	26.5300i	0.678919	+	1.17592i	−0.296388	+	0.955068i	$0.595782\pi$
$510$	1.60505	+	2.50867i	0.0710728	+	0.111086i
$511$	29.8894	−	18.2740i	1.32223	−	0.808393i
$512$	1.00000			0.0441942
$513$	−7.94805	+	19.5087i	−0.350915	+	0.861330i
$514$	10.5256	+	18.2308i	0.464263	+	0.804128i
$515$	2.57014	−	4.45161i	0.113254	−	0.196161i
$516$	−16.1388	+	0.736011i	−0.710471	+	0.0324011i
$517$	4.24484	−	7.35228i	0.186688	−	0.323353i
$518$	−21.1659	−	11.5203i	−0.929974	−	0.506174i
$519$	−2.34154	+	4.51945i	−0.102782	+	0.198382i
$520$	0.672570			0.0294941
$521$	−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	$-0.367277\pi$
$522$	−11.2843	+	24.4466i	−0.493902	+	1.07000i
$523$	−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
$525$	−18.1788	+	12.2859i	−0.793387	+	0.536199i
$526$	2.58259	−	4.47318i	0.112606	−	0.195040i
$527$	0.960699	+	1.66398i	0.0418487	+	0.0724841i
$528$	3.40496	+	5.32190i	0.148182	+	0.231606i
$529$	10.8581	−	18.8067i	0.472090	−	0.817684i
$530$	−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
$534$	−2.54523	−	3.97816i	−0.110143	−	0.172152i
$535$	−3.58307			−0.154910
$536$	−2.32023			−0.100219
$537$	15.8530	−	0.722977i	0.684108	−	0.0311988i
$538$	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	$0.194886\pi$
$542$	12.5562	−	21.7480i	0.539336	−	0.934157i
$543$	−17.8707	+	34.4926i	−0.766906	+	1.48022i
$544$	−1.86693	−	3.23361i	−0.0800438	−	0.138640i
$545$	1.73025	−	2.99689i	0.0741159	−	0.128372i
$546$	−5.54523	+	3.74766i	−0.237314	+	0.160385i
$547$	−11.8602	−	20.5425i	−0.507106	−	0.878333i	−0.999966	−	0.00822465i	$-0.997382\pi$
$547$	−11.8602	−	20.5425i	−0.507106	−	0.878333i	0.492860	−	0.870108i	$-0.335951\pi$
$548$	2.20321	−	3.81607i	0.0941165	−	0.163015i
$549$	−20.9071	−	29.6132i	−0.892293	−	1.26386i
$550$	−8.73239	−	15.1249i	−0.372350	−	0.644930i
$551$	36.3858			1.55009
$552$	1.96050	−	0.0894089i	0.0834446	−	0.00380550i
$553$	−0.333165	−	13.2436i	−0.0141676	−	0.563176i
$554$	−1.69076	+	2.92848i	−0.0718334	+	0.124419i
$555$	3.34202	−	6.45049i	0.141861	−	0.273808i
$556$	−1.01245	+	1.75362i	−0.0429376	+	0.0743701i
$557$	−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	$-0.516750\pi$
$558$	0.890369	+	1.26113i	0.0376923	+	0.0533881i
$559$	13.6228			0.576181
$560$	−1.03950	+	0.635534i	−0.0439267	+	0.0268562i
$561$	10.8521	−	20.9459i	0.458178	−	0.884336i
$562$	−10.1388	−	17.5609i	−0.427680	−	0.740763i
$563$	11.8243			0.498335			0.249168	−	0.968460i	$-0.419843\pi$
$563$	11.8243			0.498335			0.249168	+	0.968460i	$0.419843\pi$
$564$	−1.85447	+	3.57935i	−0.0780874	+	0.150718i
$565$	2.79125			0.117429
$566$	17.3494			0.729250
$567$	−22.6316	−	7.40339i	−0.950438	−	0.310913i
$568$	1.67977			0.0704815
$569$	14.2016			0.595360			0.297680	−	0.954666i	$-0.403787\pi$
$569$	14.2016			0.595360			0.297680	+	0.954666i	$0.403787\pi$
$570$	1.48755	−	2.87114i	0.0623065	−	0.120259i
$571$	11.9574			0.500401			0.250200	−	0.968194i	$-0.419503\pi$
$571$	11.9574			0.500401			0.250200	+	0.968194i	$0.419503\pi$
$572$	−2.66372	−	4.61369i	−0.111376	−	0.192908i
$573$	−1.98375	+	3.82888i	−0.0828725	+	0.159954i
$574$	−2.19815	−	1.19643i	−0.0917490	−	0.0499379i
$575$	−5.42509			−0.226242
$576$	−1.73025	−	2.45076i	−0.0720939	−	0.102115i
$577$	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	$0.485916\pi$
$578$	1.52918	−	2.64861i	0.0636054	−	0.110168i
$579$	−3.57733	+	6.90467i	−0.148669	+	0.286948i
$580$	2.06654	−	3.57935i	0.0858083	−	0.148624i
$581$	−15.0057	+	9.17431i	−0.622543	+	0.380614i
$582$	19.3566	−	0.882759i	0.802357	−	0.0365915i
$583$	45.3609			1.87866
$584$	−6.62062	−	11.4673i	−0.273963	−	0.474518i
$585$	−1.16372	−	1.64831i	−0.0481137	−	0.0681491i
$586$	−4.93560	+	8.54871i	−0.203888	+	0.353144i
$587$	20.5328	+	35.5638i	0.847478	+	1.46788i	0.883451	+	0.468523i	$0.155214\pi$
$587$	20.5328	+	35.5638i	0.847478	+	1.46788i	−0.0359730	+	0.999353i	$0.511453\pi$
$588$	5.02918	−	11.0321i	0.207400	−	0.454956i
$589$	1.04309	−	1.80669i	0.0429799	−	0.0744434i
$590$	−2.96936	−	5.14308i	−0.122247	−	0.211737i
$591$	−10.1462	+	19.5833i	−0.417359	+	0.805551i
$592$	−4.55408	+	7.88791i	−0.187172	+	0.324191i
$593$	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
$597$	5.09718	−	0.232457i	0.208614	−	0.00951383i
$598$	−1.65486			−0.0676723
$599$	19.0718			0.779252			0.389626	−	0.920973i	$-0.372604\pi$
$599$	19.0718			0.779252			0.389626	+	0.920973i	$0.372604\pi$
$600$	4.46936	+	6.98554i	0.182461	+	0.285184i
$601$	4.27188	+	7.39912i	0.174254	+	0.301816i	0.939903	−	0.341442i	$-0.110915\pi$
$601$	4.27188	+	7.39912i	0.174254	+	0.301816i	−0.765649	+	0.643259i	$0.777582\pi$
$602$	−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
$605$	0.530835	−	0.919434i	0.0215815	−	0.0373803i
$606$	−12.8406	−	20.0696i	−0.521612	−	0.815272i
$607$	−19.0057	−	32.9189i	−0.771419	−	1.33614i	−0.936785	−	0.349905i	$-0.886214\pi$
$607$	−19.0057	−	32.9189i	−0.771419	−	1.33614i	0.165366	−	0.986232i	$-0.447119\pi$
$608$	−2.02704	+	3.51094i	−0.0822074	+	0.142387i
$609$	2.90642	+	41.0262i	0.117774	+	1.66247i
$610$	2.78220	+	4.81891i	0.112648	+	0.195112i
$611$	1.69961	−	2.94381i	0.0687589	−	0.119094i
$612$	−4.69455	+	10.1703i	−0.189766	+	0.411112i
$613$	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	$0.682044\pi$
$614$	7.78794			0.314295
$615$	0.347081	−	0.669906i	0.0139956	−	0.0270132i
$616$	8.47656	+	4.61369i	0.341530	+	0.185891i
$617$	−10.1388	+	17.5609i	−0.408173	+	0.706977i	−0.994685	−	0.102964i	$-0.967167\pi$
$617$	−10.1388	+	17.5609i	−0.408173	+	0.706977i	0.586512	+	0.809941i	$0.300501\pi$
$618$	19.3135	−	0.880794i	0.776904	−	0.0354307i
$619$	−1.03064	+	1.78512i	−0.0414249	+	0.0717501i	−0.885994	−	0.463696i	$-0.846523\pi$
$619$	−1.03064	+	1.78512i	−0.0414249	+	0.0717501i	0.844570	+	0.535446i	$0.179856\pi$
$620$	−0.118485	−	0.205223i	−0.00475849	−	0.00824194i
$621$	−3.61129	−	4.65003i	−0.144916	−	0.186599i
$622$	15.4107			0.617912
$623$	−6.33628	−	3.44877i	−0.253858	−	0.138172i
$624$	1.36333	+	2.13086i	0.0545768	+	0.0853027i
$625$	−10.9320	−	18.9348i	−0.437280	−	0.757391i
$626$	8.49688			0.339604
$627$	−25.5869	+	1.16689i	−1.02184	+	0.0466011i
$628$	20.9823			0.837285
$629$	34.0085			1.35601
$630$	3.35613	+	1.44792i	0.133711	+	0.0576865i
$631$	1.63715			0.0651740			0.0325870	−	0.999469i	$-0.489625\pi$
$631$	1.63715			0.0651740			0.0325870	+	0.999469i	$0.489625\pi$
$632$	−5.00720			−0.199176
$633$	−1.13541	−	1.77462i	−0.0451283	−	0.0705349i
$634$	−14.1052			−0.560191
$635$	2.02850	+	3.51347i	0.0804988	+	0.139428i
$636$	−21.5167	+	0.981271i	−0.853194	+	0.0389099i
$637$	−4.66012	+	9.09967i	−0.184641	+	0.360542i
$638$	−32.7381			−1.29611
$639$	−2.90642	−	4.11671i	−0.114976	−	0.162854i
$640$	0.230252	+	0.398809i	0.00910153	+	0.0157643i
$641$	−10.9662	+	18.9941i	−0.433140	+	0.750221i	−0.997142	−	0.0755526i	$-0.975928\pi$
$641$	−10.9662	+	18.9941i	−0.433140	+	0.750221i	0.564001	+	0.825774i	$0.309261\pi$
$642$	−7.26303	−	11.3520i	−0.286649	−	0.448028i
$643$	−14.1819	+	24.5638i	−0.559280	+	0.968701i	0.438277	+	0.898840i	$0.355589\pi$
$643$	−14.1819	+	24.5638i	−0.559280	+	0.968701i	−0.997557	+	0.0698609i	$0.977744\pi$
$644$	2.55768	−	1.56373i	0.100787	−	0.0616197i
$645$	−4.00953	−	6.26683i	−0.157875	−	0.246756i
$646$	15.1373			0.595571
$647$	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	$0.593709\pi$
$648$	−3.01245	+	8.48087i	−0.118340	+	0.333160i
$649$	−23.5203	+	40.7384i	−0.923253	+	1.59912i
$650$	−3.49640	−	6.05594i	−0.137140	−	0.237534i
$651$	2.12043	+	1.03181i	0.0831061	+	0.0404398i
$652$	−11.5182	+	19.9501i	−0.451087	+	0.781306i
$653$	1.59931	+	2.77009i	0.0625860	+	0.108402i	0.895621	−	0.444819i	$-0.146732\pi$
$653$	1.59931	+	2.77009i	0.0625860	+	0.108402i	−0.833035	+	0.553221i	$0.813399\pi$
$654$	13.0021	−	0.592963i	0.508424	−	0.0231867i
$655$	4.86693	−	8.42976i	0.190167	−	0.329378i
$656$	−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	0.950648	−	0.310271i	$-0.100420\pi$
$659$	5.30418	+	9.18711i	0.206622	+	0.357879i	−0.744027	+	0.668150i	$0.767086\pi$
$660$	−1.33842	+	2.58331i	−0.0520980	+	0.100555i
$661$	10.1301			0.394017			0.197009	−	0.980402i	$-0.436877\pi$
$661$	10.1301			0.394017			0.197009	+	0.980402i	$0.436877\pi$
$662$	27.5438			1.07052
$663$	4.34514	−	8.38662i	0.168751	−	0.325709i
$664$	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
$668$	−5.31498	+	9.20581i	−0.205643	+	0.356184i
$669$	1.54309	−	0.0703729i	0.0596595	−	0.00272077i
$670$	−0.534239	−	0.925330i	−0.0206395	−	0.0357486i
$671$	22.0378	−	38.1707i	0.850761	−	1.47356i
$672$	−4.12062	−	2.00511i	−0.158956	−	0.0773489i
$673$	1.60817	+	2.78543i	0.0619903	+	0.107370i	0.895355	−	0.445353i	$-0.146922\pi$
$673$	1.60817	+	2.78543i	0.0619903	+	0.107370i	−0.833365	+	0.552724i	$0.813589\pi$
$674$	0.748440	−	1.29634i	0.0288288	−	0.0499330i
$675$	9.38677	−	23.0401i	0.361297	−	0.886813i
$676$	5.43346	+	9.41103i	0.208979	+	0.361963i
$677$	−29.3638			−1.12854			−0.564271	−	0.825589i	$-0.690843\pi$
$677$	−29.3638			−1.12854			−0.564271	+	0.825589i	$0.690843\pi$
$678$	5.65798	+	8.84334i	0.217293	+	0.339626i
$679$	25.2527	−	15.4392i	0.969110	−	0.592501i
$680$	0.859728	−	1.48909i	0.0329691	−	0.0571041i
$681$	13.6770	+	21.3770i	0.524105	+	0.819169i
$682$	−0.938524	+	1.62557i	−0.0359379	+	0.0622463i
$683$	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	$0.672811\pi$
$684$	12.1118	−	1.10702i	0.463105	−	0.0423279i
$685$	2.02918			0.0775309
$686$	−1.39610	−	18.4676i	−0.0533035	−	0.705095i
$687$	−16.5687	+	0.755615i	−0.632134	+	0.0288285i
$688$	4.66372	+	8.07779i	0.177802	+	0.307963i
$689$	18.1623			0.691927
$690$	0.487068	+	0.761280i	0.0185424	+	0.0289814i
$691$	−15.3638			−0.584467			−0.292233	−	0.956347i	$-0.594398\pi$
$691$	−15.3638			−0.584467			−0.292233	+	0.956347i	$0.594398\pi$
$692$	2.93872			0.111713
$693$	−3.35953	−	28.7569i	−0.127618	−	1.09238i
$694$	−18.2881			−0.694208
$695$	−0.932479			−0.0353709
$696$	15.5292	−	0.708209i	0.588632	−	0.0268446i
$697$	3.53191			0.133781
$698$	−3.90136	−	6.75735i	−0.147669	−	0.255770i
$699$	13.4684	+	21.0509i	0.509421	+	0.796217i
$700$	11.1264	+	6.05594i	0.420537	+	0.228893i
$701$	−13.3700			−0.504980			−0.252490	−	0.967600i	$-0.581249\pi$
$701$	−13.3700			−0.504980			−0.252490	+	0.967600i	$0.581249\pi$
$702$	2.86333	−	7.02811i	0.108069	−	0.265259i
$703$	−18.4626	−	31.9782i	−0.696332	−	1.20608i
$704$	1.82383	−	3.15897i	0.0687382	−	0.119058i
$705$	−1.85447	+	0.0845733i	−0.0698435	+	0.00318522i
$706$	−13.4626	+	23.3180i	−0.506673	+	0.877584i
$707$	−31.9662	−	17.3988i	−1.20221	−	0.654351i
$708$	10.2755	−	19.8329i	0.386176	−	0.745365i
$709$	−1.12588			−0.0422832			−0.0211416	−	0.999776i	$-0.506730\pi$
$709$	−1.12588			−0.0422832			−0.0211416	+	0.999776i	$0.506730\pi$
$710$	0.386770	+	0.669906i	0.0145152	+	0.0251411i
$711$	8.66372	+	12.2714i	0.324915	+	0.460215i
$712$	−1.36333	+	2.36135i	−0.0510928	+	0.0884954i
$713$	0.291534	+	0.504951i	0.0109180	+	0.0189106i
$714$	1.20914	+	17.0679i	0.0452509	+	0.638749i
$715$	1.22665	−	2.12463i	0.0458743	−	0.0794565i
$716$	−4.58113	−	7.93474i	−0.171205	−	0.296535i
$717$	−17.0914	−	26.7137i	−0.638292	−	0.997640i
$718$	−3.13161	+	5.42411i	−0.116871	+	0.202426i
$719$	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
$723$	−0.0871712	−	0.136247i	−0.00324193	−	0.00506709i
$724$	22.4284			0.833545
$725$	−42.9722			−1.59595
$726$	3.98901	−	0.181919i	0.148046	−	0.00675165i
$727$	−14.8478	−	25.7171i	−0.550673	−	0.953793i	−0.998226	−	0.0595359i	$-0.981038\pi$
$727$	−14.8478	−	25.7171i	−0.550673	−	0.953793i	0.447553	−	0.894257i	$-0.352295\pi$
$728$	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
$731$	17.4136	−	30.1613i	0.644066	−	1.11555i
$732$	−9.62782	+	18.5828i	−0.355854	+	0.686840i
$733$	−9.61390	−	16.6518i	−0.355098	−	0.615047i	0.632037	−	0.774938i	$-0.282219\pi$
$733$	−9.61390	−	16.6518i	−0.355098	−	0.615047i	−0.987135	+	0.159891i	$0.948886\pi$
$734$	−14.6367	+	25.3515i	−0.540249	+	0.935740i
$735$	5.55768	−	0.534488i	0.204998	−	0.0197149i
$736$	−0.566537	−	0.981271i	−0.0208828	−	0.0361701i
$737$	−4.23171	+	7.32955i	−0.155877	+	0.269987i
$738$	2.82597	−	0.258294i	0.104025	−	0.00950793i
$739$	−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	$-0.354598\pi$
$740$	−4.19436			−0.154188
$741$	−10.2448	+	0.467216i	−0.376354	+	0.0171636i
$742$	−28.0708	+	17.1621i	−1.03051	+	0.630041i
$743$	−11.8815	+	20.5794i	−0.435890	+	0.754984i	−0.997368	−	0.0725076i	$-0.976900\pi$
$743$	−11.8815	+	20.5794i	−0.435890	+	0.754984i	0.561477	+	0.827492i	$0.310233\pi$
$744$	0.410019	−	0.791385i	0.0150320	−	0.0290136i
$745$	−2.10963	+	3.65399i	−0.0772909	+	0.133872i
$746$	−8.92986	−	15.4670i	−0.326946	−	0.566286i
$747$	8.35807	−	18.1071i	0.305806	−	0.662503i
$748$	−13.6198			−0.497990
$749$	−18.0811	−	9.84134i	−0.660670	−	0.359595i
$750$	−3.59144	+	6.93190i	−0.131141	+	0.253117i
$751$	−6.33415	−	10.9711i	−0.231136	−	0.400340i	0.727006	−	0.686631i	$-0.240911\pi$
$751$	−6.33415	−	10.9711i	−0.231136	−	0.400340i	−0.958143	+	0.286291i	$0.907578\pi$
$752$	2.32743			0.0848727
$753$	14.5600	−	28.1025i	0.530596	−	1.02411i
$754$	−13.1082			−0.477371
$755$	0.0478448			0.00174125
$756$	2.21566	+	13.5680i	0.0805829	+	0.493464i
$757$	−29.0799			−1.05693			−0.528464	−	0.848955i	$-0.677232\pi$
$757$	−29.0799			−1.05693			−0.528464	+	0.848955i	$0.677232\pi$
$758$	−22.4255			−0.814530
$759$	3.29319	−	6.35624i	0.119535	−	0.230717i
$760$	−1.86693			−0.0677205
$761$	−14.6015	−	25.2905i	−0.529302	−	0.916778i	−0.999416	−	0.0341724i	$-0.989120\pi$
$761$	−14.6015	−	25.2905i	−0.529302	−	0.916778i	0.470114	−	0.882606i	$-0.344213\pi$
$762$	−7.01965	+	13.5487i	−0.254295	+	0.490819i
$763$	16.9626	−	10.3707i	0.614089	−	0.375446i
$764$	2.48968			0.0900736
$765$	−5.13696	+	0.469519i	−0.185727	+	0.0169755i
$766$	7.07014	+	12.2458i	0.255454	+	0.442460i
$767$	−9.41741	+	16.3114i	−0.340043	+	0.588972i
$768$	−0.796790	+	1.53790i	−0.0287517	+	0.0554941i
$769$	12.5869	−	21.8011i	0.453894	−	0.786167i	−0.544730	−	0.838611i	$-0.683368\pi$
$769$	12.5869	−	21.8011i	0.453894	−	0.786167i	0.998624	+	0.0524443i	$0.0167012\pi$
$770$	0.111767	+	4.44284i	0.00402780	+	0.160109i
$771$	−36.4238	+	1.66111i	−1.31177	+	0.0598234i
$772$	4.48968			0.161587
$773$	−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	$0.841944\pi$
$774$	11.7273	−	25.4063i	0.421530	−	0.913209i
$775$	−1.23191	+	2.13373i	−0.0442515	+	0.0766458i
$776$	−5.59358	−	9.68836i	−0.200798	−	0.347792i
$777$	34.5818	−	23.3716i	1.24062	−	0.838452i
$778$	11.5651	−	20.0313i	0.414628	−	0.718157i
$779$	−1.91741	−	3.32105i	−0.0686984	−	0.118989i
$780$	−0.535897	+	1.03434i	−0.0191882	+	0.0370354i
$781$	3.06361	−	5.30633i	0.109625	−	0.189875i
$782$	−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
$786$	36.5729	−	1.66791i	1.30451	−	0.0594924i
$787$	−14.9531			−0.533021			−0.266510	−	0.963832i	$-0.585871\pi$
$787$	−14.9531			−0.533021			−0.266510	+	0.963832i	$0.585871\pi$
$788$	12.7339			0.453625
$789$	4.82150	+	7.53593i	0.171650	+	0.268286i
$790$	−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
$794$	−5.13307	+	8.89075i	−0.182166	+	0.315521i
$795$	−5.34562	−	8.35512i	−0.189590	−	0.296326i
$796$	−1.47296	−	2.55124i	−0.0522076	−	0.0904262i
$797$	−4.56294	+	7.90324i	−0.161628	+	0.279947i	−0.935453	−	0.353452i	$-0.885008\pi$
$797$	−4.56294	+	7.90324i	−0.161628	+	0.279947i	0.773825	+	0.633400i	$0.218341\pi$
$798$	15.3925	−	10.4028i	0.544889	−	0.368255i
$799$	−4.34514	−	7.52600i	−0.153720	−	0.266251i
$800$	2.39397	−	4.14647i	0.0846395	−	0.146600i
$801$	8.14601	−	0.744547i	0.287825	−	0.0263073i
$802$	−17.0167	−	29.4738i	−0.600881	−	1.04076i
$803$	−48.2996			−1.70446
$804$	1.84874	−	3.56828i	0.0652000	−	0.125843i
$805$	1.21254	+	0.659973i	0.0427365	+	0.0232610i
$806$	−0.375780	+	0.650870i	−0.0132363	+	0.0229259i
$807$	−29.1665	+	1.33014i	−1.02671	+	0.0468232i
$808$	−6.87792	+	11.9129i	−0.241964	+	0.419094i
$809$	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	$0.618452\pi$
$810$	−4.07587	+	0.751347i	−0.143211	+	0.0263997i
$811$	−13.5070			−0.474295			−0.237148	−	0.971474i	$-0.576212\pi$
$811$	−13.5070			−0.474295			−0.237148	+	0.971474i	$0.576212\pi$
$812$	20.2594	−	12.3863i	0.710967	−	0.434676i
$813$	23.4415	+	36.6388i	0.822130	+	1.28498i
$814$	16.6118	+	28.7724i	0.582242	+	1.00847i
$815$	−10.6084			−0.371595
$816$	6.46050	−	0.294632i	0.226163	−	0.0103142i
$817$	−37.8142			−1.32295
$818$	−3.48968			−0.122014
$819$	−1.34514	−	11.5141i	−0.0470030	−	0.402335i
$820$	−0.435599			−0.0152118
$821$	21.6228			0.754639			0.377320	−	0.926083i	$-0.376846\pi$
$821$	21.6228			0.754639			0.377320	+	0.926083i	$0.376846\pi$
$822$	4.11323	+	6.42892i	0.143465	+	0.224234i
$823$	−1.50700			−0.0525308			−0.0262654	−	0.999655i	$-0.508361\pi$
$823$	−1.50700			−0.0525308			−0.0262654	+	0.999655i	$0.508361\pi$
$824$	−5.58113	−	9.66679i	−0.194428	−	0.336759i
$825$	30.2185	−	1.37811i	1.05207	−	0.0479798i
$826$	−0.858071	−	34.1091i	−0.0298561	−	1.18681i
$827$	23.3786			0.812953			0.406477	−	0.913661i	$-0.366757\pi$
$827$	23.3786			0.812953			0.406477	+	0.913661i	$0.366757\pi$
$828$	−1.42461	+	3.08629i	−0.0495086	+	0.107256i
$829$	−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	$0.958228\pi$
$830$	−1.53064	+	2.65115i	−0.0531293	+	0.0920227i
$831$	−3.15652	−	4.93359i	−0.109498	−	0.171144i
$832$	0.730252	−	1.26483i	0.0253169	−	0.0438502i
$833$	14.1901	+	21.9495i	0.491657	+	0.760506i
$834$	−1.89017	−	2.95431i	−0.0654514	−	0.102300i
$835$	−4.89515			−0.169404
$836$	7.39397	+	12.8067i	0.255726	+	0.442930i
$837$	−2.64893	+	0.364437i	−0.0915605	+	0.0125968i
$838$	14.4897	−	25.0969i	0.500538	−	0.866957i
$839$	−1.06507	−	1.84476i	−0.0367705	−	0.0636883i	0.847055	−	0.531506i	$-0.178374\pi$
$839$	−1.06507	−	1.84476i	−0.0367705	−	0.0636883i	−0.883825	+	0.467818i	$0.845040\pi$
$840$	−0.149126	−	2.10502i	−0.00514534	−	0.0726302i
$841$	−25.7762	+	44.6456i	−0.888833	+	1.53950i
$842$	−1.06128	−	1.83819i	−0.0365742	−	0.0633483i
$843$	35.0854	−	1.60007i	1.20841	−	0.0551094i
$844$	−0.608168	+	1.05338i	−0.0209340	+	0.0362588i
$845$	−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
$849$	−13.8238	+	26.6816i	−0.474433	+	0.915710i
$850$	−17.8774			−0.613191
$851$	10.3202			0.353773
$852$	−1.33842	+	2.58331i	−0.0458535	+	0.0885027i
$853$	−3.50146	−	6.06471i	−0.119888	−	0.207652i	0.799835	−	0.600220i	$-0.204920\pi$
$853$	−3.50146	−	6.06471i	−0.119888	−	0.207652i	−0.919723	+	0.392568i	$0.871587\pi$
$854$	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
$857$	−5.46410	+	9.46410i	−0.186650	+	0.323288i	−0.944131	−	0.329569i	$-0.893096\pi$
$857$	−5.46410	+	9.46410i	−0.186650	+	0.323288i	0.757481	+	0.652857i	$0.226430\pi$
$858$	9.21780	−	0.420378i	0.314690	−	0.0143515i
$859$	6.95379	+	12.0443i	0.237260	+	0.410947i	0.959927	−	0.280250i	$-0.0904173\pi$
$859$	6.95379	+	12.0443i	0.237260	+	0.410947i	−0.722667	+	0.691196i	$0.757084\pi$
$860$	−2.14766	+	3.71986i	−0.0732347	+	0.126846i
$861$	3.59144	−	2.42723i	0.122396	−	0.0827196i
$862$	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	$0.950896\pi$
$864$	5.14766	−	0.708209i	0.175127	−	0.0240938i
$865$	0.676647	+	1.17199i	0.0230067	+	0.0398488i
$866$	−13.0512			−0.443496
$867$	2.85486	+	4.46211i	0.0969562	+	0.151541i
$868$	−0.0342393	−	1.36104i	−0.00116216	−	0.0461968i
$869$	−9.13229	+	15.8176i	−0.309792	+	0.536575i
$870$	3.85807	+	6.03011i	0.130801	+	0.204440i
$871$	−1.69436	+	2.93471i	−0.0574111	+	0.0994389i
$872$	−3.75729	−	6.50783i	−0.127238	−	0.220383i
$873$	−14.0656	+	30.4718i	−0.476047	+	1.03132i
$874$	4.59358			0.155380
$875$	0.299909	+	11.9217i	0.0101388	+	0.403026i
$876$	22.9107	−	1.04484i	0.774081	−	0.0353020i
$877$	5.17977	+	8.97162i	0.174908	+	0.302950i	0.940130	−	0.340817i	$-0.110704\pi$
$877$	5.17977	+	8.97162i	0.174908	+	0.302950i	−0.765221	+	0.643767i	$0.777370\pi$
$878$	4.86400			0.164152
$879$	−9.21440	−	14.4020i	−0.310794	−	0.485766i
$880$	1.67977			0.0566249
$881$	9.34806			0.314944			0.157472	−	0.987523i	$-0.449666\pi$
$881$	9.34806			0.314944			0.157472	+	0.987523i	$0.449666\pi$
$882$	12.9590	+	16.5246i	0.436354	+	0.556413i
$883$	2.29494			0.0772308			0.0386154	−	0.999254i	$-0.487705\pi$
$883$	2.29494			0.0772308			0.0386154	+	0.999254i	$0.487705\pi$
$884$	−5.45331			−0.183415
$885$	10.2755	−	0.468614i	0.345407	−	0.0157523i
$886$	−11.5395			−0.387677
$887$	13.8363	+	23.9651i	0.464577	+	0.804671i	0.999182	−	0.0404309i	$-0.0128731\pi$
$887$	13.8363	+	23.9651i	0.464577	+	0.804671i	−0.534605	+	0.845102i	$0.679540\pi$
$888$	−8.50214	−	13.2887i	−0.285313	−	0.445940i
$889$	0.586187	+	23.3015i	0.0196601	+	0.781506i
$890$	−1.25564			−0.0420891
$891$	21.2966	+	24.9839i	0.713463	+	0.836993i
$892$	−0.445916	−	0.772349i	−0.0149304	−	0.0258602i
$893$	−4.71780	+	8.17147i	−0.157875	+	0.273448i
$894$	−15.8530	+	0.722977i	−0.530204	+	0.0241800i
$895$	2.10963	−	3.65399i	0.0705172	−	0.122139i
$896$	0.0665372	+	2.64491i	0.00222285	+	0.0883604i
$897$	1.31858	−	2.54500i	0.0440260	−	0.0849752i
$898$	−26.4251			−0.881817
$899$	2.30924	+	3.99973i	0.0770176	+	0.133398i
$900$	−14.3042	+	1.30740i	−0.476806	+	0.0435802i
$901$	23.2163	−	40.2119i	0.773448	−	1.33965i
$902$	1.72519	+	2.98812i	0.0574426	+	0.0994935i
$903$	−3.02052	−	42.6368i	−0.100517	−	1.41886i
$904$	3.03064	−	5.24922i	0.100798	−	0.174587i
$905$	5.16419	+	8.94465i	0.171664	+	0.297330i
$906$	0.0969833	+	0.151584i	0.00322206	+	0.00503602i
$907$	1.46576	−	2.53877i	0.0486698	−	0.0842985i	−0.840664	−	0.541557i	$-0.817835\pi$
$907$	1.46576	−	2.53877i	0.0486698	−	0.0842985i	0.889334	+	0.457258i	$0.151168\pi$
$908$	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	0.999963	+	0.00865719i	$0.00275570\pi$
$911$	15.3171	+	26.5300i	0.507479	+	0.878979i	−0.492484	+	0.870322i	$0.663911\pi$
$912$	−3.78434	−	5.91486i	−0.125312	−	0.195861i
$913$	24.2484			0.802506
$914$	−3.73812			−0.123646
$915$	−9.62782	+	0.439077i	−0.318286	+	0.0145154i
$916$	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	$0.0234306\pi$
$920$	0.260893	−	0.451880i	0.00860139	−	0.0148980i
$921$	−6.20535	+	11.9770i	−0.204473	+	0.394657i
$922$	−7.90496	−	13.6918i	−0.260336	−	0.450915i
$923$	1.22665	−	2.12463i	0.0403758	−	0.0699329i
$924$	−13.8494	+	9.35993i	−0.455612	+	0.307919i
$925$	21.8047	+	37.7668i	0.716933	+	1.24176i
$926$	19.1965	−	33.2493i	0.630836	−	1.09264i
$927$	−14.0342	+	30.4040i	−0.460945	+	0.998598i
$928$	−4.48755	−	7.77266i	−0.147311	−	0.255150i
$929$	17.8741			0.586431			0.293215	−	0.956046i	$-0.405275\pi$
$929$	17.8741			0.586431			0.293215	+	0.956046i	$0.405275\pi$
$930$	0.410019	−	0.0186989i	0.0134451	−	0.000613163i
$931$	12.9356	−	25.2590i	0.423947	−	0.827829i
$932$	7.21420	−	12.4954i	0.236309	−	0.409299i
$933$	−12.2791	+	23.7001i	−0.401999	+	0.775905i
$934$	3.15652	−	5.46725i	0.103284	−	0.178894i
$935$	−3.13600	−	5.43171i	−0.102558	−	0.177636i
$936$	−4.36333	+	0.398809i	−0.142620	+	0.0130355i
$937$	15.9134			0.519869			0.259934	−	0.965626i	$-0.416299\pi$
$937$	15.9134			0.519869			0.259934	+	0.965626i	$0.416299\pi$
$938$	−0.154382	−	6.13682i	−0.00504075	−	0.200374i
$939$	−6.77023	+	13.0673i	−0.220938	+	0.426436i
$940$	0.535897	+	0.928200i	0.0174790	+	0.0302745i
$941$	−16.2805			−0.530731			−0.265365	−	0.964148i	$-0.585493\pi$
$941$	−16.2805			−0.530731			−0.265365	+	0.964148i	$0.585493\pi$
$942$	−16.7185	+	32.2686i	−0.544717	+	1.05137i
$943$	1.07179			0.0349024
$944$	−12.8961			−0.419732
$945$	−4.90088	+	4.00769i	−0.159426	+	0.130370i
$946$	34.0233			1.10619
$947$	−28.5903			−0.929059			−0.464529	−	0.885558i	$-0.653776\pi$
$947$	−28.5903			−0.929059			−0.464529	+	0.885558i	$0.653776\pi$
$948$	3.98968	−	7.70055i	0.129579	−	0.250102i
$949$	−19.3389			−0.627767
$950$	9.70535	+	16.8102i	0.314883	+	0.545393i
$951$	11.2389	−	21.6924i	0.364447	−	0.703424i
$952$	8.42840	−	5.15301i	0.273166	−	0.167010i
$953$	−29.3537			−0.950859			−0.475430	−	0.879754i	$-0.657707\pi$
$953$	−29.3537			−0.950859			−0.475430	+	0.879754i	$0.657707\pi$
$954$	15.6352	−	33.8724i	0.506209	−	1.09666i
$955$	0.573256	+	0.992908i	0.0185501	+	0.0321297i
$956$	−9.15486	+	15.8567i	−0.296089	+	0.512842i
$957$	26.0854	−	50.3479i	0.843221	−	1.62751i
$958$	10.2068	−	17.6787i	0.329767	−	0.571173i
$959$	10.2398	+	5.57339i	0.330660	+	0.179974i
$960$	−0.796790	+	0.0363376i	−0.0257163	+	0.00117279i
$961$	−30.7352			−0.991458
$962$	6.65126	+	11.5203i	0.214445	+	0.371430i
$963$	23.2453	−	2.12463i	0.749070	−	0.0684651i
$964$	−0.0466924	+	0.0808735i	−0.00150386	+	0.00260476i
$965$	1.03376	+	1.79053i	0.0332779	+	0.0576391i
$966$	0.366926	+	5.17942i	0.0118056	+	0.166645i
$967$	−4.69815	+	8.13743i	−0.151082	+	0.261682i	−0.931626	−	0.363419i	$-0.881609\pi$
$967$	−4.69815	+	8.13743i	−0.151082	+	0.261682i	0.780543	+	0.625102i	$0.214943\pi$
$968$	−1.15272	−	1.99658i	−0.0370500	−	0.0641724i
$969$	−12.0613	+	23.2797i	−0.387464	+	0.747851i
$970$	2.57587	−	4.46154i	0.0827062	−	0.143251i
$971$	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
$975$	12.0993	−	0.551790i	0.387488	−	0.0176714i
$976$	12.0833			0.386776
$977$	−9.59785			−0.307062			−0.153531	−	0.988144i	$-0.549065\pi$
$977$	−9.59785			−0.307062			−0.153531	+	0.988144i	$0.549065\pi$
$978$	−21.5036	−	33.6098i	−0.687609	−	1.07472i
$979$	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
$983$	23.4267	−	40.5763i	0.747197	−	1.29418i	−0.201964	−	0.979393i	$-0.564732\pi$
$983$	23.4267	−	40.5763i	0.747197	−	1.29418i	0.949161	−	0.314790i	$-0.101934\pi$
$984$	−0.882977	−	1.38008i	−0.0281483	−	0.0439953i
$985$	2.93200	+	5.07837i	0.0934213	+	0.161810i
$986$	−16.7558	+	29.0220i	−0.533614	+	0.924247i
$987$	−9.59046	−	4.66676i	−0.305268	−	0.148545i
$988$	2.96050	+	5.12774i	0.0941862	+	0.163135i
$989$	5.28434	−	9.15274i	0.168032	−	0.291040i
$990$	−2.90642	−	4.11671i	−0.0923721	−	0.130838i
$991$	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	$0.721586\pi$
$992$	−0.514589			−0.0163382
$993$	−21.9466	+	42.3595i	−0.696454	+	1.34424i
$994$	0.111767	+	4.44284i	0.00354504	+	0.140918i
$995$	0.678304	−	1.17486i	0.0215037	−	0.0372455i
$996$	−11.5021	+	0.524555i	−0.364459	+	0.0166212i
$997$	28.6190	−	49.5695i	0.906372	−	1.56988i	0.0873064	−	0.996182i	$-0.472174\pi$
$997$	28.6190	−	49.5695i	0.906372	−	1.56988i	0.819065	−	0.573700i	$-0.194493\pi$
$998$	0.461967	+	0.800151i	0.0146233	+	0.0253283i
$999$	−17.8566	+	43.8295i	−0.564958	+	1.38670i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.2	✓	6	63.25	even	3	inner
126.2.e.d.121.2	yes	6	1.1	even	1	trivial
126.2.h.c.67.3	yes	6	7.4	even	3
126.2.h.c.79.3	yes	6	9.7	even	3
378.2.e.c.37.1		6	3.2	odd	2
378.2.e.c.235.1		6	63.11	odd	6
378.2.h.d.289.3		6	9.2	odd	6
378.2.h.d.361.3		6	21.11	odd	6
882.2.e.p.373.2		6	7.6	odd	2
882.2.e.p.655.2		6	63.52	odd	6
882.2.f.l.295.2		6	63.16	even	3
882.2.f.l.589.2		6	7.2	even	3
882.2.f.m.295.2		6	63.61	odd	6
882.2.f.m.589.2		6	7.5	odd	6
882.2.h.o.67.1		6	7.3	odd	6
882.2.h.o.79.1		6	63.34	odd	6
1008.2.q.h.529.2		6	252.151	odd	6
1008.2.q.h.625.2		6	4.3	odd	2
1008.2.t.g.193.1		6	28.11	odd	6
1008.2.t.g.961.1		6	36.7	odd	6
1134.2.g.k.163.3		6	9.4	even	3
1134.2.g.k.487.3		6	63.4	even	3
1134.2.g.n.163.1		6	9.5	odd	6
1134.2.g.n.487.1		6	63.32	odd	6
2646.2.e.o.1549.3		6	21.20	even	2
2646.2.e.o.2125.3		6	63.38	even	6
2646.2.f.n.883.3		6	63.47	even	6
2646.2.f.n.1765.3		6	21.5	even	6
2646.2.f.o.883.1		6	63.2	odd	6
2646.2.f.o.1765.1		6	21.2	odd	6
2646.2.h.p.361.1		6	21.17	even	6
2646.2.h.p.667.1		6	63.20	even	6
3024.2.q.h.2305.1		6	12.11	even	2
3024.2.q.h.2881.1		6	252.11	even	6
3024.2.t.g.289.3		6	36.11	even	6
3024.2.t.g.1873.3		6	84.11	even	6
7938.2.a.bu.1.3		3	63.23	odd	6
7938.2.a.bx.1.1		3	63.5	even	6
7938.2.a.by.1.3		3	63.40	odd	6
7938.2.a.cb.1.1		3	63.58	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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.796790 + 1.53790i) q^{3} +1.00000 q^{4} +(0.230252 + 0.398809i) q^{5} +(-0.796790 + 1.53790i) q^{6} +(0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +(-1.73025 - 2.45076i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.796790 + 1.53790i) q^{3} +1.00000 q^{4} +(0.230252 + 0.398809i) q^{5} +(-0.796790 + 1.53790i) q^{6} +(0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +(-1.73025 - 2.45076i) q^{9} +(0.230252 + 0.398809i) q^{10} +(1.82383 - 3.15897i) q^{11} +(-0.796790 + 1.53790i) q^{12} +(0.730252 - 1.26483i) q^{13} +(0.0665372 + 2.64491i) q^{14} +(-0.796790 + 0.0363376i) q^{15} +1.00000 q^{16} +(-1.86693 - 3.23361i) q^{17} +(-1.73025 - 2.45076i) q^{18} +(-2.02704 + 3.51094i) q^{19} +(0.230252 + 0.398809i) q^{20} +(-4.12062 - 2.00511i) q^{21} +(1.82383 - 3.15897i) q^{22} +(-0.566537 - 0.981271i) q^{23} +(-0.796790 + 1.53790i) q^{24} +(2.39397 - 4.14647i) 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} +(-0.796790 + 0.0363376i) q^{30} -0.514589 q^{31} +1.00000 q^{32} +(3.40496 + 5.32190i) 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} +(-2.02704 + 3.51094i) q^{38} +(1.36333 + 2.13086i) q^{39} +(0.230252 + 0.398809i) q^{40} +(-0.472958 + 0.819187i) q^{41} +(-4.12062 - 2.00511i) q^{42} +(4.66372 + 8.07779i) q^{43} +(1.82383 - 3.15897i) q^{44} +(0.578990 - 1.25433i) q^{45} +(-0.566537 - 0.981271i) q^{46} +2.32743 q^{47} +(-0.796790 + 1.53790i) q^{48} +(-6.99115 + 0.351971i) q^{49} +(2.39397 - 4.14647i) q^{50} +(6.46050 - 0.294632i) q^{51} +(0.730252 - 1.26483i) q^{52} +(6.21780 + 10.7695i) q^{53} +(5.14766 - 0.708209i) q^{54} +1.67977 q^{55} +(0.0665372 + 2.64491i) q^{56} +(-3.78434 - 5.91486i) q^{57} +(-4.48755 - 7.77266i) q^{58} -12.8961 q^{59} +(-0.796790 + 0.0363376i) q^{60} +12.0833 q^{61} -0.514589 q^{62} +(6.36693 - 4.73944i) q^{63} +1.00000 q^{64} +0.672570 q^{65} +(3.40496 + 5.32190i) q^{66} -2.32023 q^{67} +(-1.86693 - 3.23361i) q^{68} +(1.96050 - 0.0894089i) q^{69} +(-1.03950 + 0.635534i) q^{70} +1.67977 q^{71} +(-1.73025 - 2.45076i) q^{72} +(-6.62062 - 11.4673i) q^{73} +(-4.55408 + 7.88791i) q^{74} +(4.46936 + 6.98554i) q^{75} +(-2.02704 + 3.51094i) q^{76} +(8.47656 + 4.61369i) q^{77} +(1.36333 + 2.13086i) q^{78} -5.00720 q^{79} +(0.230252 + 0.398809i) q^{80} +(-3.01245 + 8.48087i) q^{81} +(-0.472958 + 0.819187i) q^{82} +(3.32383 + 5.75705i) q^{83} +(-4.12062 - 2.00511i) q^{84} +(0.859728 - 1.48909i) q^{85} +(4.66372 + 8.07779i) q^{86} +(15.5292 - 0.708209i) q^{87} +(1.82383 - 3.15897i) 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} +(0.410019 - 0.791385i) q^{93} +2.32743 q^{94} -1.86693 q^{95} +(-0.796790 + 1.53790i) q^{96} +(-5.59358 - 9.68836i) q^{97} +(-6.99115 + 0.351971i) q^{98} +(-10.8976 + 0.996040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 - 4 * q^9	\( 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} - 4 q^{9} - 5 q^{10} - q^{11} - 2 q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{15} + 6 q^{16} - 4 q^{17} - 4 q^{18} - 3 q^{19} - 5 q^{20} - 10 q^{21} - q^{22} - 7 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 7 q^{27} + 4 q^{28} - 5 q^{29} - 2 q^{30} + 28 q^{31} + 6 q^{32} - 19 q^{33} - 4 q^{34} - 19 q^{35} - 4 q^{36} - 9 q^{37} - 3 q^{38} + 9 q^{39} - 5 q^{40} - 12 q^{41} - 10 q^{42} + 18 q^{43} - q^{44} + 29 q^{45} - 7 q^{46} - 6 q^{47} - 2 q^{48} - 12 q^{49} - 2 q^{50} + 26 q^{51} - 2 q^{52} + 9 q^{53} + 7 q^{54} + 14 q^{55} + 4 q^{56} + 2 q^{57} - 5 q^{58} - 8 q^{59} - 2 q^{60} - 8 q^{61} + 28 q^{62} + 31 q^{63} + 6 q^{64} + 24 q^{65} - 19 q^{66} - 10 q^{67} - 4 q^{68} - q^{69} - 19 q^{70} + 14 q^{71} - 4 q^{72} - 25 q^{73} - 9 q^{74} + 44 q^{75} - 3 q^{76} + 52 q^{77} + 9 q^{78} - 14 q^{79} - 5 q^{80} - 40 q^{81} - 12 q^{82} + 8 q^{83} - 10 q^{84} + 14 q^{85} + 18 q^{86} + 31 q^{87} - q^{88} - 9 q^{89} + 29 q^{90} + 4 q^{91} - 7 q^{92} - 6 q^{94} - 4 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 41 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 - 4 * q^9 - 5 * q^10 - q^11 - 2 * q^12 - 2 * q^13 + 4 * q^14 - 2 * q^15 + 6 * q^16 - 4 * q^17 - 4 * q^18 - 3 * q^19 - 5 * q^20 - 10 * q^21 - q^22 - 7 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^26 + 7 * q^27 + 4 * q^28 - 5 * q^29 - 2 * q^30 + 28 * q^31 + 6 * q^32 - 19 * q^33 - 4 * q^34 - 19 * q^35 - 4 * q^36 - 9 * q^37 - 3 * q^38 + 9 * q^39 - 5 * q^40 - 12 * q^41 - 10 * q^42 + 18 * q^43 - q^44 + 29 * q^45 - 7 * q^46 - 6 * q^47 - 2 * q^48 - 12 * q^49 - 2 * q^50 + 26 * q^51 - 2 * q^52 + 9 * q^53 + 7 * q^54 + 14 * q^55 + 4 * q^56 + 2 * q^57 - 5 * q^58 - 8 * q^59 - 2 * q^60 - 8 * q^61 + 28 * q^62 + 31 * q^63 + 6 * q^64 + 24 * q^65 - 19 * q^66 - 10 * q^67 - 4 * q^68 - q^69 - 19 * q^70 + 14 * q^71 - 4 * q^72 - 25 * q^73 - 9 * q^74 + 44 * q^75 - 3 * q^76 + 52 * q^77 + 9 * q^78 - 14 * q^79 - 5 * q^80 - 40 * q^81 - 12 * q^82 + 8 * q^83 - 10 * q^84 + 14 * q^85 + 18 * q^86 + 31 * q^87 - q^88 - 9 * q^89 + 29 * q^90 + 4 * q^91 - 7 * q^92 - 6 * q^94 - 4 * q^95 - 2 * q^96 - 28 * q^97 - 12 * q^98 - 41 * q^99

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