LMFDB - Embedded newform 126.2.e.d.25.2

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			25.2
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	126.25
Dual form			126.2.e.d.121.2

$q$-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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

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

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	−0.809936	−	0.586519i	$-0.800498\pi$
$5$	0.230252	−	0.398809i	0.102972	−	0.178353i	0.912908	+	0.408166i	$0.133831\pi$
$6$	−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	0.998280	+	0.0586193i	$0.0186698\pi$
$11$	1.82383	+	3.15897i	0.549906	+	0.952465i	−0.448374	+	0.893846i	$0.647997\pi$
$12$	−0.796790	−	1.53790i	−0.230013	−	0.443953i
$13$	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	$0.768415\pi$
$14$	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	−0.998558	−	0.0536743i	$-0.982907\pi$
$17$	−1.86693	+	3.23361i	−0.452796	+	0.784266i	0.545763	+	0.837940i	$0.316240\pi$
$18$	−1.73025	+	2.45076i	−0.407824	+	0.577650i
$19$	−2.02704	−	3.51094i	−0.465035	−	0.805465i	0.534168	−	0.845378i	$-0.320625\pi$
$19$	−2.02704	−	3.51094i	−0.465035	−	0.805465i	−0.999203	+	0.0399136i	$0.987292\pi$
$20$	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	−0.919027	−	0.394194i	$-0.871024\pi$
$23$	−0.566537	+	0.981271i	−0.118131	+	0.204609i	0.800896	+	0.598804i	$0.204357\pi$
$24$	−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	0.0620772	+	0.998071i	$0.480228\pi$
$29$	−4.48755	+	7.77266i	−0.833317	+	1.44335i	−0.895394	+	0.445275i	$0.853106\pi$
$30$	−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	−0.948452	−	0.316920i	$-0.897351\pi$
$37$	−4.55408	−	7.88791i	−0.748687	−	1.29676i	0.199765	−	0.979844i	$-0.435982\pi$
$38$	−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	0.826728	−	0.562602i	$-0.190200\pi$
$41$	−0.472958	−	0.819187i	−0.0738636	−	0.127936i	−0.900592	+	0.434666i	$0.856866\pi$
$42$	−4.12062	+	2.00511i	−0.635826	+	0.309396i
$43$	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
$45$	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	−0.0234151	−	0.999726i	$-0.507454\pi$
$53$	6.21780	−	10.7695i	0.854080	−	1.47931i	0.877495	−	0.479585i	$-0.159213\pi$
$54$	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	0.159974	+	0.987121i	$0.448859\pi$
$73$	−6.62062	+	11.4673i	−0.774885	+	1.34214i	−0.934859	+	0.355019i	$0.884474\pi$
$74$	−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	−0.623912	−	0.781494i	$-0.714458\pi$
$83$	3.32383	−	5.75705i	0.364838	−	0.631918i	0.988750	+	0.149577i	$0.0477911\pi$
$84$	−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	0.784679	−	0.619903i	$-0.212828\pi$
$89$	−1.36333	−	2.36135i	−0.144512	−	0.250303i	−0.929191	+	0.369600i	$0.879495\pi$
$90$	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	0.428827	+	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
$101$	−6.87792	−	11.9129i	−0.684378	−	1.18538i	−0.973632	−	0.228125i	$-0.926740\pi$
$101$	−6.87792	−	11.9129i	−0.684378	−	1.18538i	0.289254	−	0.957253i	$-0.406593\pi$
$102$	6.46050	+	0.294632i	0.639685	+	0.0291729i
$103$	−5.58113	+	9.66679i	−0.549925	+	0.952498i	0.448354	+	0.893856i	$0.352010\pi$
$103$	−5.58113	+	9.66679i	−0.549925	+	0.952498i	−0.998279	+	0.0586417i	$0.981323\pi$
$104$	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	0.614394	−	0.788999i	$-0.289400\pi$
$107$	−3.89037	−	6.73832i	−0.376096	−	0.651418i	−0.990490	+	0.137581i	$0.956067\pi$
$108$	5.14766	+	0.708209i	0.495334	+	0.0681474i
$109$	−3.75729	+	6.50783i	−0.359884	+	0.623337i	−0.987941	−	0.154830i	$-0.950517\pi$
$109$	−3.75729	+	6.50783i	−0.359884	+	0.623337i	0.628058	+	0.778167i	$0.283850\pi$
$110$	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	0.972633	−	0.232346i	$-0.0746403\pi$
$113$	3.03064	+	5.24922i	0.285099	+	0.493805i	−0.687534	+	0.726152i	$0.741307\pi$
$114$	−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	−0.129258	+	0.991611i	$0.541260\pi$
$131$	−10.5687	+	18.3055i	−0.923389	+	1.59936i	−0.794131	+	0.607746i	$0.792074\pi$
$132$	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	0.944661	−	0.328048i	$-0.106391\pi$
$137$	2.20321	+	3.81607i	0.188233	+	0.326029i	−0.756428	+	0.654077i	$0.773057\pi$
$138$	1.96050	+	0.0894089i	0.166889	+	0.00761099i
$139$	−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	$0.860702\pi$
$140$	−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	−0.615071	−	0.788471i	$-0.710873\pi$
$149$	4.58113	−	7.93474i	0.375300	−	0.650040i	0.990372	+	0.138432i	$0.0442062\pi$
$150$	4.46936	−	6.98554i	0.364922	−	0.570367i
$151$	0.0519482	+	0.0899768i	0.00422748	+	0.00732221i	0.868131	−	0.496334i	$-0.165321\pi$
$151$	0.0519482	+	0.0899768i	0.00422748	+	0.00732221i	−0.863904	+	0.503657i	$0.831988\pi$
$152$	−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	−0.824666	−	0.565620i	$-0.808637\pi$
$163$	−11.5182	−	19.9501i	−0.902174	−	1.56261i	−0.0775078	−	0.996992i	$-0.524696\pi$
$164$	−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	0.583745	−	0.811937i	$-0.301587\pi$
$167$	−5.31498	−	9.20581i	−0.411285	−	0.712367i	−0.995031	+	0.0995698i	$0.968253\pi$
$168$	−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	−0.984880	−	0.173240i	$-0.944576\pi$
$179$	−4.58113	+	7.93474i	−0.342409	+	0.593071i	0.642470	+	0.766311i	$0.277910\pi$
$180$	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	−0.913499	−	0.406841i	$-0.866630\pi$
$199$	−1.47296	+	2.55124i	−0.104415	+	0.180852i	0.809084	+	0.587693i	$0.199964\pi$
$200$	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	0.844332	−	0.535820i	$-0.179998\pi$
$211$	−0.608168	−	1.05338i	−0.0418680	−	0.0725176i	−0.886200	+	0.463303i	$0.846664\pi$
$212$	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	−0.880570	−	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
$227$	7.32597	+	12.6889i	0.486242	+	0.842195i	0.999875	−	0.0158147i	$-0.00503418\pi$
$227$	7.32597	+	12.6889i	0.486242	+	0.842195i	−0.513633	+	0.858010i	$0.671701\pi$
$228$	−3.78434	+	5.91486i	−0.250624	+	0.391721i
$229$	4.78794	−	8.29295i	0.316396	−	0.548013i	−0.663338	−	0.748320i	$-0.730861\pi$
$229$	4.78794	−	8.29295i	0.316396	−	0.548013i	0.979733	+	0.200307i	$0.0641939\pi$
$230$	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	0.999509	−	0.0313345i	$-0.00997571\pi$
$233$	7.21420	+	12.4954i	0.472618	+	0.818598i	−0.526891	+	0.849933i	$0.676642\pi$
$234$	−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	−0.993938	−	0.109938i	$-0.964935\pi$
$239$	−9.15486	−	15.8567i	−0.592179	−	1.02568i	0.401760	−	0.915745i	$-0.368399\pi$
$240$	−0.796790	−	0.0363376i	−0.0514326	−	0.00234558i
$241$	−0.0466924	−	0.0808735i	−0.00300772	−	0.00520952i	0.864518	−	0.502602i	$-0.167624\pi$
$241$	−0.0466924	−	0.0808735i	−0.00300772	−	0.00520952i	−0.867525	+	0.497393i	$0.834291\pi$
$242$	−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	−0.324931	−	0.945738i	$-0.605341\pi$
$257$	10.5256	−	18.2308i	0.656568	−	1.13721i	0.981498	−	0.191471i	$-0.0613257\pi$
$258$	−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	0.934598	−	0.355705i	$-0.115759\pi$
$263$	2.58259	+	4.47318i	0.159249	+	0.275828i	−0.775349	+	0.631533i	$0.782426\pi$
$264$	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	−0.485981	−	0.873969i	$-0.661538\pi$
$269$	8.42840	−	14.5984i	0.513889	−	0.890081i	0.999870	−	0.0161123i	$-0.00512891\pi$
$270$	1.46770	−	1.88987i	0.0893215	−	0.115014i
$271$	12.5562	+	21.7480i	0.762736	+	1.32110i	0.941435	+	0.337194i	$0.109478\pi$
$271$	12.5562	+	21.7480i	0.762736	+	1.32110i	−0.178699	+	0.983904i	$0.557189\pi$
$272$	−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	0.810751	−	0.585391i	$-0.199059\pi$
$277$	−1.69076	−	2.92848i	−0.101588	−	0.175955i	−0.912339	+	0.409436i	$0.865726\pi$
$278$	−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	$0.959907\pi$
$282$	−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	0.685073	−	0.728474i	$-0.259770\pi$
$293$	−4.93560	−	8.54871i	−0.288341	−	0.499421i	−0.973414	+	0.229054i	$0.926437\pi$
$294$	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	0.885690	−	0.464276i	$-0.153686\pi$
$337$	0.748440	+	1.29634i	0.0407701	+	0.0706159i	−0.844920	+	0.534892i	$0.820352\pi$
$338$	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	−0.951348	−	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
$353$	−13.4626	−	23.3180i	−0.716544	−	1.24109i	−0.962361	−	0.271774i	$-0.912390\pi$
$353$	−13.4626	−	23.3180i	−0.716544	−	1.24109i	0.245817	−	0.969316i	$-0.420944\pi$
$354$	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	0.771475	−	0.636260i	$-0.219519\pi$
$359$	−3.13161	−	5.42411i	−0.165280	−	0.286274i	−0.936755	+	0.349987i	$0.886186\pi$
$360$	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	−0.940759	−	0.339076i	$-0.889886\pi$
$367$	−14.6367	−	25.3515i	−0.764028	−	1.32334i	0.176731	−	0.984259i	$-0.443448\pi$
$368$	−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	−0.999079	−	0.0429184i	$-0.986334\pi$
$373$	−8.92986	+	15.4670i	−0.462371	+	0.800850i	0.536708	+	0.843768i	$0.319668\pi$
$374$	−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	−0.626903	−	0.779098i	$-0.715678\pi$
$383$	7.07014	−	12.2458i	0.361267	−	0.625733i	0.988170	+	0.153365i	$0.0490109\pi$
$384$	−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	0.994703	+	0.102793i	$0.0327779\pi$
$389$	11.5651	+	20.0313i	0.586373	+	1.01563i	−0.408330	+	0.912834i	$0.633889\pi$
$390$	−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	0.707983	−	0.706230i	$-0.249605\pi$
$397$	−5.13307	−	8.89075i	−0.257622	−	0.446214i	−0.965604	+	0.260016i	$0.916272\pi$
$398$	−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	0.0316345	+	0.999500i	$0.489929\pi$
$401$	−17.0167	+	29.4738i	−0.849775	+	1.47185i	−0.881409	+	0.472353i	$0.843405\pi$
$402$	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	0.965647	+	0.259858i	$0.0836759\pi$
$419$	14.4897	+	25.0969i	0.707867	+	1.22606i	−0.257779	+	0.966204i	$0.582991\pi$
$420$	−0.149126	+	2.10502i	−0.00727661	+	0.102715i
$421$	−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
$423$	−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	−0.472765	−	0.881189i	$-0.656744\pi$
$431$	10.9356	−	18.9410i	0.526749	−	0.912356i	0.999514	−	0.0311679i	$-0.00992265\pi$
$432$	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	−0.989280	−	0.146034i	$-0.953349\pi$
$461$	−7.90496	+	13.6918i	−0.368171	+	0.637690i	0.621109	+	0.783724i	$0.286682\pi$
$462$	−13.8494	−	9.35993i	−0.644333	−	0.435463i
$463$	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	$0.482539\pi$
$464$	−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	0.929770	−	0.368140i	$-0.120005\pi$
$467$	3.15652	+	5.46725i	0.146066	+	0.252994i	−0.783704	+	0.621134i	$0.786672\pi$
$468$	−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	0.999262	−	0.0384168i	$-0.0122314\pi$
$479$	10.2068	+	17.6787i	0.466361	+	0.807761i	−0.532901	+	0.846178i	$0.678898\pi$
$480$	−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	−0.691287	−	0.722580i	$-0.742956\pi$
$487$	6.18190	−	10.7074i	0.280129	−	0.485197i	0.971416	+	0.237383i	$0.0762895\pi$
$488$	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	0.870659	−	0.491888i	$-0.163693\pi$
$491$	0.207004	+	0.358541i	0.00934194	+	0.0161807i	−0.861317	+	0.508069i	$0.830360\pi$
$492$	−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	−0.855500	−	0.517803i	$-0.826750\pi$
$499$	0.461967	−	0.800151i	0.0206805	−	0.0358197i	0.876180	+	0.481983i	$0.160083\pi$
$500$	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	−0.296388	−	0.955068i	$-0.595782\pi$
$509$	15.3171	−	26.5300i	0.678919	−	1.17592i	0.975307	−	0.220855i	$-0.0708846\pi$
$510$	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	0.404984	+	0.914324i	$0.367277\pi$
$521$	−13.4518	+	23.2993i	−0.589336	+	1.02076i	−0.994320	+	0.106436i	$0.966056\pi$
$522$	−11.2843	−	24.4466i	−0.493902	−	1.07000i
$523$	−7.85301	−	13.6018i	−0.343388	−	0.594766i	0.641671	−	0.766980i	$-0.278241\pi$
$523$	−7.85301	−	13.6018i	−0.343388	−	0.594766i	−0.985060	+	0.172214i	$0.944908\pi$
$524$	−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	0.818355	−	0.574713i	$-0.194886\pi$
$541$	−2.05934	−	3.56688i	−0.0885379	−	0.153352i	−0.906893	+	0.421360i	$0.861553\pi$
$542$	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	0.492860	+	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
$549$	−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	−0.0525975	+	0.998616i	$0.516750\pi$
$557$	−21.0313	+	36.4273i	−0.891125	+	1.54347i	−0.838528	+	0.544859i	$0.816583\pi$
$558$	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	0.0442307	−	0.999021i	$-0.485916\pi$
$577$	21.3135	−	36.9161i	0.887293	−	1.53684i	0.843062	−	0.537816i	$-0.180750\pi$
$578$	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	−0.0359730	−	0.999353i	$-0.511453\pi$
$587$	20.5328	−	35.5638i	0.847478	−	1.46788i	0.883451	−	0.468523i	$-0.155214\pi$
$588$	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	0.980306	+	0.197485i	$0.0632772\pi$
$593$	16.1008	+	27.8874i	0.661180	+	1.14520i	−0.319126	+	0.947712i	$0.603389\pi$
$594$	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	−0.765649	−	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
$605$	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	0.165366	+	0.986232i	$0.447119\pi$
$607$	−19.0057	+	32.9189i	−0.771419	+	1.33614i	−0.936785	+	0.349905i	$0.886214\pi$
$608$	−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	−0.541237	−	0.840870i	$-0.682044\pi$
$613$	11.3296	−	19.6234i	0.457597	−	0.792581i	0.998833	+	0.0482894i	$0.0153770\pi$
$614$	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	0.586512	−	0.809941i	$-0.300501\pi$
$617$	−10.1388	−	17.5609i	−0.408173	−	0.706977i	−0.994685	+	0.102964i	$0.967167\pi$
$618$	19.3135	+	0.880794i	0.776904	+	0.0354307i
$619$	−1.03064	−	1.78512i	−0.0414249	−	0.0717501i	0.844570	−	0.535446i	$-0.179856\pi$
$619$	−1.03064	−	1.78512i	−0.0414249	−	0.0717501i	−0.885994	+	0.463696i	$0.846523\pi$
$620$	−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	0.564001	−	0.825774i	$-0.309261\pi$
$641$	−10.9662	−	18.9941i	−0.433140	−	0.750221i	−0.997142	+	0.0755526i	$0.975928\pi$
$642$	−7.26303	+	11.3520i	−0.286649	+	0.448028i
$643$	−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	$-0.355589\pi$
$644$	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	−0.290162	−	0.956978i	$-0.593709\pi$
$647$	17.3904	−	30.1210i	0.683686	−	1.18418i	0.973848	−	0.227201i	$-0.0729575\pi$
$648$	−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	−0.833035	−	0.553221i	$-0.813399\pi$
$653$	1.59931	−	2.77009i	0.0625860	−	0.108402i	0.895621	+	0.444819i	$0.146732\pi$
$654$	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	−0.744027	−	0.668150i	$-0.767086\pi$
$659$	5.30418	−	9.18711i	0.206622	−	0.357879i	0.950648	+	0.310271i	$0.100420\pi$
$660$	−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	−0.833365	−	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
$675$	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	−0.516624	−	0.856213i	$-0.672811\pi$
$683$	12.6278	−	21.8720i	0.483190	−	0.836910i	0.999814	+	0.0193029i	$0.00614468\pi$
$684$	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	0.984570	−	0.174989i	$-0.0559889\pi$
$719$	9.13667	+	15.8252i	0.340740	+	0.590180i	−0.643830	+	0.765169i	$0.722656\pi$
$720$	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	0.447553	+	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
$731$	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	−0.987135	−	0.159891i	$-0.948886\pi$
$733$	−9.61390	+	16.6518i	−0.355098	+	0.615047i	0.632037	+	0.774938i	$0.282219\pi$
$734$	−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	0.441073	+	0.897471i	$0.354598\pi$
$739$	−15.1336	+	26.2121i	−0.556697	+	0.964227i	−0.997769	+	0.0667556i	$0.978735\pi$
$740$	−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	0.561477	−	0.827492i	$-0.310233\pi$
$743$	−11.8815	−	20.5794i	−0.435890	−	0.754984i	−0.997368	+	0.0725076i	$0.976900\pi$
$744$	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	−0.958143	−	0.286291i	$-0.907578\pi$
$751$	−6.33415	+	10.9711i	−0.231136	+	0.400340i	0.727006	+	0.686631i	$0.240911\pi$
$752$	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	0.470114	+	0.882606i	$0.344213\pi$
$761$	−14.6015	+	25.2905i	−0.529302	+	0.916778i	−0.999416	+	0.0341724i	$0.989120\pi$
$762$	−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

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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