LMFDB - Embedded newform 390.2.bn.b.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(67,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("390.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			163.1
Root			$0.277956 - 0.213283i$ of defining polynomial
Character	$\chi$	$=$	390.163
Dual form			390.2.bn.b.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.90502 + 1.17085i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(3.41596 - 1.97220i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.90502 + 1.17085i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(3.41596 - 1.97220i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +(0.0614757 + 2.23522i) q^{10} +(-1.48984 - 5.56016i) q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.53074 + 0.730685i) q^{13} -3.94441i q^{14} +(1.53707 - 1.62401i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.03411 - 3.85935i) q^{17} -1.00000i q^{18} +(2.08506 + 0.558691i) q^{19} +(1.96650 + 1.06437i) q^{20} +(-2.78912 + 2.78912i) q^{21} +(-5.56016 - 1.48984i) q^{22} +(-1.12062 - 4.18221i) q^{23} +(0.965926 - 0.258819i) q^{24} +(2.25822 - 4.46099i) q^{25} +(-1.13258 + 3.42305i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-3.41596 - 1.97220i) q^{28} +(-5.04514 - 2.91282i) q^{29} +(-0.637899 - 2.14315i) q^{30} +(-2.83191 - 2.83191i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.87815 + 4.98511i) q^{33} +(-2.82524 - 2.82524i) q^{34} +(-4.19832 + 7.75667i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(3.16089 + 1.82494i) q^{37} +(1.52637 - 1.52637i) q^{38} +(3.22131 - 1.61961i) q^{39} +(1.90502 - 1.17085i) q^{40} +(-0.0577328 + 0.0154695i) q^{41} +(1.02089 + 3.81000i) q^{42} +(10.3141 + 2.76364i) q^{43} +(-4.07032 + 4.07032i) q^{44} +(-1.06437 + 1.96650i) q^{45} +(-4.18221 - 1.12062i) q^{46} +13.4556i q^{47} +(0.258819 - 0.965926i) q^{48} +(4.27917 - 7.41174i) q^{49} +(-2.73423 - 4.18617i) q^{50} +3.99550i q^{51} +(2.39816 + 2.69236i) q^{52} +(4.15062 + 4.15062i) q^{53} +(0.258819 + 0.965926i) q^{54} +(9.34830 + 8.84785i) q^{55} +(-3.41596 + 1.97220i) q^{56} -2.15862 q^{57} +(-5.04514 + 2.91282i) q^{58} +(-0.509008 + 1.89964i) q^{59} +(-2.17497 - 0.519137i) q^{60} +(-1.42948 - 2.47593i) q^{61} +(-3.86846 + 1.03655i) q^{62} +(1.97220 - 3.41596i) q^{63} +1.00000 q^{64} +(5.87061 - 5.52594i) q^{65} +5.75631 q^{66} +(-1.36242 + 2.35978i) q^{67} +(-3.85935 + 1.03411i) q^{68} +(2.16487 + 3.74966i) q^{69} +(4.61831 + 7.51418i) q^{70} +(3.31290 - 12.3639i) q^{71} +(-0.866025 + 0.500000i) q^{72} +4.59815 q^{73} +(3.16089 - 1.82494i) q^{74} +(-1.02668 + 4.89346i) q^{75} +(-0.558691 - 2.08506i) q^{76} +(-16.0550 - 16.0550i) q^{77} +(0.208034 - 3.59954i) q^{78} -2.49954i q^{79} +(-0.0614757 - 2.23522i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.0154695 + 0.0577328i) q^{82} +12.0125i q^{83} +(3.81000 + 1.02089i) q^{84} +(2.54872 + 8.56294i) q^{85} +(7.55042 - 7.55042i) q^{86} +(5.62713 + 1.50778i) q^{87} +(1.48984 + 5.56016i) q^{88} +(8.00537 - 2.14503i) q^{89} +(1.17085 + 1.90502i) q^{90} +(-10.6198 + 9.45932i) q^{91} +(-3.06159 + 3.06159i) q^{92} +(3.46837 + 2.00246i) q^{93} +(11.6529 + 6.72781i) q^{94} +(-4.62624 + 1.37698i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-4.76948 - 8.26098i) q^{97} +(-4.27917 - 7.41174i) q^{98} +(-4.07032 - 4.07032i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8}+O(q^{10}) $ 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8	$ 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8} + 12 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{19} + 4 q^{23} + 4 q^{25} + 4 q^{26} - 24 q^{28} - 48 q^{29} - 4 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 20 q^{34} - 12 q^{35} + 12 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} + 20 q^{43} - 12 q^{44} + 8 q^{45} - 4 q^{46} - 4 q^{49} - 16 q^{50} - 4 q^{52} + 32 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{57} - 48 q^{58} + 4 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 16 q^{64} - 8 q^{65} + 32 q^{66} - 28 q^{67} - 16 q^{68} + 4 q^{69} - 36 q^{71} + 32 q^{73} + 12 q^{74} - 24 q^{75} + 8 q^{76} + 4 q^{77} + 20 q^{78} + 8 q^{81} - 24 q^{82} + 52 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} - 24 q^{89} + 4 q^{90} - 8 q^{92} + 36 q^{94} - 40 q^{95} - 4 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8 + 12 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^16 - 4 * q^17 - 4 * q^19 + 4 * q^23 + 4 * q^25 + 4 * q^26 - 24 * q^28 - 48 * q^29 - 4 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 20 * q^34 - 12 * q^35 + 12 * q^37 + 4 * q^38 + 4 * q^39 - 12 * q^41 + 20 * q^43 - 12 * q^44 + 8 * q^45 - 4 * q^46 - 4 * q^49 - 16 * q^50 - 4 * q^52 + 32 * q^53 + 16 * q^55 - 24 * q^56 - 8 * q^57 - 48 * q^58 + 4 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 16 * q^64 - 8 * q^65 + 32 * q^66 - 28 * q^67 - 16 * q^68 + 4 * q^69 - 36 * q^71 + 32 * q^73 + 12 * q^74 - 24 * q^75 + 8 * q^76 + 4 * q^77 + 20 * q^78 + 8 * q^81 - 24 * q^82 + 52 * q^85 + 16 * q^86 + 36 * q^87 - 12 * q^88 - 24 * q^89 + 4 * q^90 - 8 * q^92 + 36 * q^94 - 40 * q^95 - 4 * q^97 + 4 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.90502	+	1.17085i	−0.851952	+	0.523620i
$5$	−1.90502	+	1.17085i	−0.851952	+	0.523620i
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	3.41596	−	1.97220i	1.29111	−	0.745423i	0.312259	−	0.949997i	$-0.398914\pi$
$7$	3.41596	−	1.97220i	1.29111	−	0.745423i	0.978851	+	0.204574i	$0.0655810\pi$
$8$	−1.00000			−0.353553
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	0.0614757	+	2.23522i	0.0194403	+	0.706839i
$11$	−1.48984	−	5.56016i	−0.449204	−	1.67645i	−0.704591	−	0.709614i	$-0.748870\pi$
$11$	−1.48984	−	5.56016i	−0.449204	−	1.67645i	0.255387	−	0.966839i	$-0.417797\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−3.53074	+	0.730685i	−0.979250	+	0.202656i
$13$	−3.53074	+	0.730685i	−0.979250	+	0.202656i
$14$		−	3.94441i		−	1.05419i
$15$	1.53707	−	1.62401i	0.396870	−	0.419318i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.03411	−	3.85935i	0.250809	−	0.936031i	−0.719566	−	0.694424i	$-0.755659\pi$
$17$	1.03411	−	3.85935i	0.250809	−	0.936031i	0.970374	−	0.241606i	$-0.0776742\pi$
$18$		−	1.00000i		−	0.235702i
$19$	2.08506	+	0.558691i	0.478347	+	0.128173i	0.489933	−	0.871760i	$-0.337021\pi$
$19$	2.08506	+	0.558691i	0.478347	+	0.128173i	−0.0115860	+	0.999933i	$0.503688\pi$
$20$	1.96650	+	1.06437i	0.439722	+	0.238001i
$21$	−2.78912	+	2.78912i	−0.608635	+	0.608635i
$22$	−5.56016	−	1.48984i	−1.18543	−	0.317635i
$23$	−1.12062	−	4.18221i	−0.233665	−	0.872050i	−0.978746	−	0.205076i	$-0.934256\pi$
$23$	−1.12062	−	4.18221i	−0.233665	−	0.872050i	0.745081	−	0.666974i	$-0.232411\pi$
$24$	0.965926	−	0.258819i	0.197169	−	0.0528312i
$25$	2.25822	−	4.46099i	0.451643	−	0.892199i
$26$	−1.13258	+	3.42305i	−0.222116	+	0.671315i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−3.41596	−	1.97220i	−0.645555	−	0.372711i
$29$	−5.04514	−	2.91282i	−0.936860	−	0.540896i	−0.0478852	−	0.998853i	$-0.515248\pi$
$29$	−5.04514	−	2.91282i	−0.936860	−	0.540896i	−0.888975	+	0.457957i	$0.848581\pi$
$30$	−0.637899	−	2.14315i	−0.116464	−	0.391284i
$31$	−2.83191	−	2.83191i	−0.508627	−	0.508627i	0.405478	−	0.914105i	$-0.367105\pi$
$31$	−2.83191	−	2.83191i	−0.508627	−	0.508627i	−0.914105	+	0.405478i	$0.867105\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.87815	+	4.98511i	0.501022	+	0.867796i
$34$	−2.82524	−	2.82524i	−0.484525	−	0.484525i
$35$	−4.19832	+	7.75667i	−0.709645	+	1.31112i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	3.16089	+	1.82494i	0.519647	+	0.300018i	0.736790	−	0.676121i	$-0.236340\pi$
$37$	3.16089	+	1.82494i	0.519647	+	0.300018i	−0.217143	+	0.976140i	$0.569674\pi$
$38$	1.52637	−	1.52637i	0.247610	−	0.247610i
$39$	3.22131	−	1.61961i	0.515823	−	0.259345i
$40$	1.90502	−	1.17085i	0.301210	−	0.185128i
$41$	−0.0577328	+	0.0154695i	−0.00901635	+	0.00241592i	−0.263324	−	0.964707i	$-0.584819\pi$
$41$	−0.0577328	+	0.0154695i	−0.00901635	+	0.00241592i	0.254308	+	0.967123i	$0.418152\pi$
$42$	1.02089	+	3.81000i	0.157526	+	0.587896i
$43$	10.3141	+	2.76364i	1.57288	+	0.421452i	0.936712	−	0.350100i	$-0.113852\pi$
$43$	10.3141	+	2.76364i	1.57288	+	0.421452i	0.636167	+	0.771551i	$0.280519\pi$
$44$	−4.07032	+	4.07032i	−0.613624	+	0.613624i
$45$	−1.06437	+	1.96650i	−0.158667	+	0.293148i
$46$	−4.18221	−	1.12062i	−0.616633	−	0.165226i
$47$			13.4556i			1.96270i	0.192222	+	0.981352i	$0.438431\pi$
$47$			13.4556i			1.96270i	−0.192222	+	0.981352i	$0.561569\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	4.27917	−	7.41174i	0.611310	−	1.05882i
$50$	−2.73423	−	4.18617i	−0.386678	−	0.592014i
$51$			3.99550i			0.559481i
$52$	2.39816	+	2.69236i	0.332565	+	0.373364i
$53$	4.15062	+	4.15062i	0.570132	+	0.570132i	0.932165	−	0.362034i	$-0.117917\pi$
$53$	4.15062	+	4.15062i	0.570132	+	0.570132i	−0.362034	+	0.932165i	$0.617917\pi$
$54$	0.258819	+	0.965926i	0.0352208	+	0.131446i
$55$	9.34830	+	8.84785i	1.26052	+	1.19304i
$56$	−3.41596	+	1.97220i	−0.456476	+	0.263547i
$57$	−2.15862			−0.285916
$58$	−5.04514	+	2.91282i	−0.662460	+	0.382471i
$59$	−0.509008	+	1.89964i	−0.0662671	+	0.247312i	−0.991112	−	0.133033i	$-0.957528\pi$
$59$	−0.509008	+	1.89964i	−0.0662671	+	0.247312i	0.924844	+	0.380346i	$0.124195\pi$
$60$	−2.17497	−	0.519137i	−0.280787	−	0.0670203i
$61$	−1.42948	−	2.47593i	−0.183026	−	0.317010i	0.759884	−	0.650059i	$-0.225256\pi$
$61$	−1.42948	−	2.47593i	−0.183026	−	0.317010i	−0.942910	+	0.333049i	$0.891923\pi$
$62$	−3.86846	+	1.03655i	−0.491296	+	0.131642i
$63$	1.97220	−	3.41596i	0.248474	−	0.430370i
$64$	1.00000			0.125000
$65$	5.87061	−	5.52594i	0.728159	−	0.685408i
$66$	5.75631			0.708552
$67$	−1.36242	+	2.35978i	−0.166446	+	0.288293i	−0.937168	−	0.348879i	$-0.886562\pi$
$67$	−1.36242	+	2.35978i	−0.166446	+	0.288293i	0.770722	+	0.637172i	$0.219896\pi$
$68$	−3.85935	+	1.03411i	−0.468015	+	0.125404i
$69$	2.16487	+	3.74966i	0.260620	+	0.451406i
$70$	4.61831	+	7.51418i	0.551994	+	0.898116i
$71$	3.31290	−	12.3639i	0.393169	−	1.46733i	−0.431707	−	0.902014i	$-0.642089\pi$
$71$	3.31290	−	12.3639i	0.393169	−	1.46733i	0.824876	−	0.565313i	$-0.191245\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	4.59815			0.538173			0.269087	−	0.963116i	$-0.413278\pi$
$73$	4.59815			0.538173			0.269087	+	0.963116i	$0.413278\pi$
$74$	3.16089	−	1.82494i	0.367446	−	0.212145i
$75$	−1.02668	+	4.89346i	−0.118551	+	0.565048i
$76$	−0.558691	−	2.08506i	−0.0640863	−	0.239173i
$77$	−16.0550	−	16.0550i	−1.82964	−	1.82964i
$78$	0.208034	−	3.59954i	0.0235552	−	0.407568i
$79$		−	2.49954i		−	0.281220i	−0.990065	−	0.140610i	$-0.955094\pi$
$79$		−	2.49954i		−	0.281220i	0.990065	−	0.140610i	$-0.0449063\pi$
$80$	−0.0614757	−	2.23522i	−0.00687319	−	0.249906i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−0.0154695	+	0.0577328i	−0.00170832	+	0.00637552i
$83$			12.0125i			1.31855i	0.751903	+	0.659274i	$0.229136\pi$
$83$			12.0125i			1.31855i	−0.751903	+	0.659274i	$0.770864\pi$
$84$	3.81000	+	1.02089i	0.415706	+	0.111388i
$85$	2.54872	+	8.56294i	0.276448	+	0.928781i
$86$	7.55042	−	7.55042i	0.814182	−	0.814182i
$87$	5.62713	+	1.50778i	0.603291	+	0.161651i
$88$	1.48984	+	5.56016i	0.158818	+	0.592715i
$89$	8.00537	−	2.14503i	0.848567	−	0.227373i	0.191770	−	0.981440i	$-0.438577\pi$
$89$	8.00537	−	2.14503i	0.848567	−	0.227373i	0.656798	+	0.754067i	$0.271911\pi$
$90$	1.17085	+	1.90502i	0.123419	+	0.200807i
$91$	−10.6198	+	9.45932i	−1.11326	+	0.991606i
$92$	−3.06159	+	3.06159i	−0.319193	+	0.319193i
$93$	3.46837	+	2.00246i	0.359653	+	0.207646i
$94$	11.6529	+	6.72781i	1.20191	+	0.693920i
$95$	−4.62624	+	1.37698i	−0.474642	+	0.141275i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−4.76948	−	8.26098i	−0.484267	−	0.838776i	0.515569	−	0.856848i	$-0.327580\pi$
$97$	−4.76948	−	8.26098i	−0.484267	−	0.838776i	−0.999837	+	0.0180722i	$0.994247\pi$
$98$	−4.27917	−	7.41174i	−0.432262	−	0.748699i
$99$	−4.07032	−	4.07032i	−0.409083	−	0.409083i
$100$	−4.99244	+	0.274824i	−0.499244	+	0.0274824i
$101$	−5.66842	−	3.27266i	−0.564029	−	0.325642i	0.190732	−	0.981642i	$-0.438914\pi$
$101$	−5.66842	−	3.27266i	−0.564029	−	0.325642i	−0.754761	+	0.656000i	$0.772247\pi$
$102$	3.46020	+	1.99775i	0.342611	+	0.197807i
$103$	−5.76194	+	5.76194i	−0.567741	+	0.567741i	−0.931495	−	0.363754i	$-0.881495\pi$
$103$	−5.76194	+	5.76194i	−0.567741	+	0.567741i	0.363754	+	0.931495i	$0.381495\pi$
$104$	3.53074	−	0.730685i	0.346217	−	0.0716496i
$105$	2.04769	−	8.57897i	0.199834	−	0.837222i
$106$	5.66985	−	1.51923i	0.550705	−	0.147561i
$107$	3.22828	+	12.0481i	0.312090	+	1.16474i	0.926668	+	0.375880i	$0.122659\pi$
$107$	3.22828	+	12.0481i	0.312090	+	1.16474i	−0.614578	+	0.788856i	$0.710674\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	1.07788	−	1.07788i	0.103242	−	0.103242i	−0.653599	−	0.756841i	$-0.726742\pi$
$109$	1.07788	−	1.07788i	0.103242	−	0.103242i	0.756841	+	0.653599i	$0.226742\pi$
$110$	12.3366	−	3.67194i	1.17625	−	0.350106i
$111$	−3.52552	−	0.944659i	−0.334627	−	0.0896631i
$112$			3.94441i			0.372711i
$113$	2.18978	−	8.17239i	0.205998	−	0.768793i	−0.783146	−	0.621838i	$-0.786386\pi$
$113$	2.18978	−	8.17239i	0.205998	−	0.768793i	0.989143	−	0.146955i	$-0.0469473\pi$
$114$	−1.07931	+	1.86942i	−0.101087	+	0.175087i
$115$	7.03154	+	6.65512i	0.655695	+	0.620593i
$116$			5.82563i			0.540896i
$117$	−2.69236	+	2.39816i	−0.248909	+	0.221710i
$118$	1.39063	+	1.39063i	0.128018	+	0.128018i
$119$	−4.07895	−	15.2229i	−0.373917	−	1.39548i
$120$	−1.53707	+	1.62401i	−0.140315	+	0.148251i
$121$	−19.1695	+	11.0675i	−1.74268	+	1.00614i
$122$	−2.85896			−0.258838
$123$	0.0517618	−	0.0298847i	0.00466721	−	0.00269461i
$124$	−1.03655	+	3.86846i	−0.0930851	+	0.347398i
$125$	0.921206	+	11.1423i	0.0823952	+	0.996600i
$126$	−1.97220	−	3.41596i	−0.175698	−	0.304318i
$127$	12.3643	−	3.31300i	1.09715	−	0.293981i	0.335547	−	0.942023i	$-0.391079\pi$
$127$	12.3643	−	3.31300i	1.09715	−	0.293981i	0.761604	+	0.648043i	$0.224412\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−10.6779			−0.940137
$130$	−1.85030	−	7.84706i	−0.162282	−	0.688233i
$131$	13.9900			1.22231			0.611156	−	0.791510i	$-0.290705\pi$
$131$	13.9900			1.22231			0.611156	+	0.791510i	$0.290705\pi$
$132$	2.87815	−	4.98511i	0.250511	−	0.433898i
$133$	8.22434	−	2.20371i	0.713141	−	0.191086i
$134$	1.36242	+	2.35978i	0.117695	+	0.203854i
$135$	0.519137	−	2.17497i	0.0446802	−	0.187192i
$136$	−1.03411	+	3.85935i	−0.0886742	+	0.330937i
$137$	−7.21815	+	4.16740i	−0.616688	+	0.356045i	−0.775579	−	0.631251i	$-0.782542\pi$
$137$	−7.21815	+	4.16740i	−0.616688	+	0.356045i	0.158890	+	0.987296i	$0.449208\pi$
$138$	4.32974			0.368572
$139$	1.77925	−	1.02725i	0.150914	−	0.0871305i	−0.422641	−	0.906297i	$-0.638897\pi$
$139$	1.77925	−	1.02725i	0.150914	−	0.0871305i	0.573556	+	0.819167i	$0.305564\pi$
$140$	8.81663	−	0.242485i	0.745141	−	0.0204937i
$141$	−3.48257	−	12.9971i	−0.293285	−	1.09456i
$142$	−9.05102	−	9.05102i	−0.759545	−	0.759545i
$143$	9.32297	+	18.5429i	0.779626	+	1.55063i
$144$			1.00000i			0.0833333i
$145$	13.0216	−	0.358135i	1.08138	−	0.0297415i
$146$	2.29908	−	3.98212i	0.190273	−	0.329562i
$147$	−2.21506	+	8.26673i	−0.182695	+	0.681828i
$148$		−	3.64988i		−	0.300018i
$149$	−17.1570	−	4.59720i	−1.40555	−	0.376617i	−0.525218	−	0.850968i	$-0.676016\pi$
$149$	−17.1570	−	4.59720i	−1.40555	−	0.376617i	−0.880336	+	0.474351i	$0.842683\pi$
$150$	3.72452	+	3.33586i	0.304106	+	0.272372i
$151$	−10.3481	+	10.3481i	−0.842114	+	0.842114i	−0.989134	−	0.147019i	$-0.953032\pi$
$151$	−10.3481	+	10.3481i	−0.842114	+	0.842114i	0.147019	+	0.989134i	$0.453032\pi$
$152$	−2.08506	−	0.558691i	−0.169121	−	0.0453159i
$153$	−1.03411	−	3.85935i	−0.0836029	−	0.312010i
$154$	−21.9315	+	5.87654i	−1.76729	+	0.473545i
$155$	8.71060	+	2.07911i	0.699653	+	0.166998i
$156$	−3.01328	−	1.97994i	−0.241255	−	0.158522i
$157$	12.4400	−	12.4400i	0.992820	−	0.992820i	−0.00715412	−	0.999974i	$-0.502277\pi$
$157$	12.4400	−	12.4400i	0.992820	−	0.992820i	0.999974	+	0.00715412i	$0.00227725\pi$
$158$	−2.16466	−	1.24977i	−0.172211	−	0.0994262i
$159$	−5.08345	−	2.93493i	−0.403144	−	0.232755i
$160$	−1.96650	−	1.06437i	−0.155465	−	0.0841460i
$161$	−12.0761	−	12.0761i	−0.951734	−	0.951734i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−11.2218	−	19.4367i	−0.878957	−	1.52240i	−0.852487	−	0.522749i	$-0.824907\pi$
$163$	−11.2218	−	19.4367i	−0.878957	−	1.52240i	−0.0264701	−	0.999650i	$-0.508427\pi$
$164$	0.0422634	+	0.0422634i	0.00330021	+	0.00330021i
$165$	−11.3198	−	6.12685i	−0.881242	−	0.476975i
$166$	10.4032	+	6.00627i	0.807442	+	0.466177i
$167$	12.4134	+	7.16686i	0.960576	+	0.554589i	0.896350	−	0.443347i	$-0.146209\pi$
$167$	12.4134	+	7.16686i	0.960576	+	0.554589i	0.0642254	+	0.997935i	$0.479542\pi$
$168$	2.78912	−	2.78912i	0.215185	−	0.215185i
$169$	11.9322	−	5.15971i	0.917861	−	0.396901i
$170$	8.69009	+	2.07421i	0.666499	+	0.159085i
$171$	2.08506	−	0.558691i	0.159449	−	0.0427242i
$172$	−2.76364	−	10.3141i	−0.210726	−	0.786440i
$173$	−8.62581	−	2.31128i	−0.655808	−	0.175723i	−0.0844546	−	0.996427i	$-0.526915\pi$
$173$	−8.62581	−	2.31128i	−0.655808	−	0.175723i	−0.571353	+	0.820704i	$0.693581\pi$
$174$	4.11934	−	4.11934i	0.312287	−	0.312287i
$175$	−1.08402	−	19.6922i	−0.0819439	−	1.48859i
$176$	5.56016	+	1.48984i	0.419113	+	0.112301i
$177$		−	1.96665i		−	0.147823i
$178$	2.14503	−	8.00537i	0.160777	−	0.600028i
$179$	4.09709	−	7.09637i	0.306231	−	0.530408i	−0.671304	−	0.741182i	$-0.734265\pi$
$179$	4.09709	−	7.09637i	0.306231	−	0.530408i	0.977535	+	0.210775i	$0.0675987\pi$
$180$	2.23522	−	0.0614757i	0.166604	−	0.00458213i
$181$			14.8291i			1.10224i	0.834426	+	0.551120i	$0.185799\pi$
$181$			14.8291i			1.10224i	−0.834426	+	0.551120i	$0.814201\pi$
$182$	2.88212	+	13.9267i	0.213637	+	1.03231i
$183$	2.02159	+	2.02159i	0.149440	+	0.149440i
$184$	1.12062	+	4.18221i	0.0826131	+	0.308316i
$185$	−8.15830	+	0.224379i	−0.599810	+	0.0164967i
$186$	3.46837	−	2.00246i	0.254313	−	0.146828i
$187$	−22.9993			−1.68188
$188$	11.6529	−	6.72781i	0.849875	−	0.490676i
$189$	−1.02089	+	3.81000i	−0.0742586	+	0.277137i
$190$	−1.12062	+	4.69493i	−0.0812982	+	0.340606i
$191$	7.09233	+	12.2843i	0.513183	+	0.888859i	0.999883	+	0.0152901i	$0.00486717\pi$
$191$	7.09233	+	12.2843i	0.513183	+	0.888859i	−0.486700	+	0.873569i	$0.661799\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	−9.51346	+	16.4778i	−0.684794	+	1.18610i	0.288708	+	0.957417i	$0.406774\pi$
$193$	−9.51346	+	16.4778i	−0.684794	+	1.18610i	−0.973502	+	0.228680i	$0.926559\pi$
$194$	−9.53896			−0.684857
$195$	−4.24035	+	6.85707i	−0.303658	+	0.491045i
$196$	−8.55834			−0.611310
$197$	−1.45202	+	2.51498i	−0.103452	+	0.179185i	−0.913105	−	0.407725i	$-0.866322\pi$
$197$	−1.45202	+	2.51498i	−0.103452	+	0.179185i	0.809652	+	0.586910i	$0.199656\pi$
$198$	−5.56016	+	1.48984i	−0.395144	+	0.105878i
$199$	−4.54977	−	7.88044i	−0.322525	−	0.558630i	0.658483	−	0.752595i	$-0.271198\pi$
$199$	−4.54977	−	7.88044i	−0.322525	−	0.558630i	−0.981008	+	0.193966i	$0.937865\pi$
$200$	−2.25822	+	4.46099i	−0.159680	+	0.315440i
$201$	0.705239	−	2.63199i	0.0497437	−	0.185646i
$202$	−5.66842	+	3.27266i	−0.398829	+	0.230264i
$203$	−22.9787			−1.61279
$204$	3.46020	−	1.99775i	0.242263	−	0.139870i
$205$	0.0918698	−	0.0970662i	0.00641647	−	0.00677940i
$206$	2.10902	+	7.87096i	0.146942	+	0.548396i
$207$	−3.06159	−	3.06159i	−0.212795	−	0.212795i
$208$	1.13258	−	3.42305i	0.0785300	−	0.237346i
$209$		−	12.4257i		−	0.859501i
$210$	−6.40576	−	6.06283i	−0.442039	−	0.418375i
$211$	−0.853215	+	1.47781i	−0.0587377	+	0.101737i	−0.893899	−	0.448268i	$-0.852041\pi$
$211$	−0.853215	+	1.47781i	−0.0587377	+	0.101737i	0.835161	+	0.550005i	$0.185374\pi$
$212$	1.51923	−	5.66985i	0.104341	−	0.389407i
$213$			12.8001i			0.877046i
$214$	12.0481	+	3.22828i	0.823592	+	0.220681i
$215$	−22.8843	+	6.81142i	−1.56070	+	0.464535i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−15.2588	−	4.08858i	−1.03583	−	0.277551i
$218$	−0.394532	−	1.47241i	−0.0267211	−	0.0997244i
$219$	−4.44148	+	1.19009i	−0.300127	+	0.0804188i
$220$	2.98831	−	12.5198i	0.201472	−	0.844084i
$221$	−0.831200	+	14.3820i	−0.0559126	+	0.967436i
$222$	−2.58086	+	2.58086i	−0.173216	+	0.173216i
$223$	22.5960	+	13.0458i	1.51314	+	0.873613i	0.999882	+	0.0153806i	$0.00489598\pi$
$223$	22.5960	+	13.0458i	1.51314	+	0.873613i	0.513261	+	0.858233i	$0.328437\pi$
$224$	3.41596	+	1.97220i	0.228238	+	0.131773i
$225$	−0.274824	−	4.99244i	−0.0183216	−	0.332829i
$226$	−5.98260	−	5.98260i	−0.397957	−	0.397957i
$227$	−2.30348	−	3.98974i	−0.152887	−	0.264808i	0.779401	−	0.626526i	$-0.215524\pi$
$227$	−2.30348	−	3.98974i	−0.152887	−	0.264808i	−0.932288	+	0.361718i	$0.882190\pi$
$228$	1.07931	+	1.86942i	0.0714790	+	0.123805i
$229$	3.74685	+	3.74685i	0.247599	+	0.247599i	0.819985	−	0.572386i	$-0.193982\pi$
$229$	3.74685	+	3.74685i	0.247599	+	0.247599i	−0.572386	+	0.819985i	$0.693982\pi$
$230$	9.27927	−	2.76194i	0.611857	−	0.182117i
$231$	19.6633	+	11.3526i	1.29375	+	0.746947i
$232$	5.04514	+	2.91282i	0.331230	+	0.191236i
$233$	8.41343	−	8.41343i	0.551182	−	0.551182i	−0.375600	−	0.926782i	$-0.622563\pi$
$233$	8.41343	−	8.41343i	0.551182	−	0.551182i	0.926782	+	0.375600i	$0.122563\pi$
$234$	0.730685	+	3.53074i	0.0477664	+	0.230811i
$235$	−15.7545	−	25.6332i	−1.02771	−	1.67213i
$236$	1.89964	−	0.509008i	0.123656	−	0.0331336i
$237$	0.646927	+	2.41437i	0.0420224	+	0.156830i
$238$	−15.2229	−	4.07895i	−0.986751	−	0.264399i
$239$	4.88289	−	4.88289i	0.315848	−	0.315848i	−0.531322	−	0.847170i	$-0.678305\pi$
$239$	4.88289	−	4.88289i	0.315848	−	0.315848i	0.847170	+	0.531322i	$0.178305\pi$
$240$	0.637899	+	2.14315i	0.0411762	+	0.138340i
$241$	8.02186	+	2.14945i	0.516733	+	0.138458i	0.507755	−	0.861501i	$-0.330475\pi$
$241$	8.02186	+	2.14945i	0.516733	+	0.138458i	0.00897808	+	0.999960i	$0.497142\pi$
$242$			22.1351i			1.42289i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−1.42948	+	2.47593i	−0.0915130	+	0.158505i
$245$	0.526130	+	19.1298i	0.0336132	+	1.22216i
$246$		−	0.0597694i		−	0.00381076i
$247$	−7.77004	−	0.449066i	−0.494396	−	0.0285734i
$248$	2.83191	+	2.83191i	0.179827	+	0.179827i
$249$	−3.10907	−	11.6032i	−0.197030	−	0.735324i
$250$	10.1101	+	4.77337i	0.639421	+	0.301895i
$251$	22.9835	−	13.2695i	1.45071	−	0.837565i	0.452184	−	0.891924i	$-0.350645\pi$
$251$	22.9835	−	13.2695i	1.45071	−	0.837565i	0.998521	+	0.0543591i	$0.0173116\pi$
$252$	−3.94441			−0.248474
$253$	−21.5842	+	12.4616i	−1.35699	+	0.783457i
$254$	3.31300	−	12.3643i	0.207876	−	0.775803i
$255$	−4.67813	−	7.61151i	−0.292956	−	0.476651i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	19.3510	−	5.18509i	1.20708	−	0.323437i	0.401466	−	0.915874i	$-0.368501\pi$
$257$	19.3510	−	5.18509i	1.20708	−	0.323437i	0.805617	+	0.592437i	$0.201834\pi$
$258$	−5.33895	+	9.24733i	−0.332389	+	0.575714i
$259$	14.3966			0.894562
$260$	−7.72090	−	2.32113i	−0.478830	−	0.143950i
$261$	−5.82563			−0.360597
$262$	6.99500	−	12.1157i	0.432153	−	0.748510i
$263$	15.1617	−	4.06256i	0.934910	−	0.250508i	0.240963	−	0.970534i	$-0.422537\pi$
$263$	15.1617	−	4.06256i	0.934910	−	0.250508i	0.693947	+	0.720026i	$0.255870\pi$
$264$	−2.87815	−	4.98511i	−0.177138	−	0.306812i
$265$	−12.7668	−	3.04727i	−0.784257	−	0.187192i
$266$	2.20371	−	8.22434i	0.135118	−	0.504267i
$267$	−7.17742	+	4.14388i	−0.439251	+	0.253602i
$268$	2.72484			0.166446
$269$	7.38580	−	4.26419i	0.450320	−	0.259992i	−0.257645	−	0.966240i	$-0.582947\pi$
$269$	7.38580	−	4.26419i	0.450320	−	0.259992i	0.707965	+	0.706247i	$0.249613\pi$
$270$	−1.62401	−	1.53707i	−0.0988342	−	0.0935432i
$271$	−5.38936	−	20.1134i	−0.327380	−	1.22180i	−0.911897	−	0.410419i	$-0.865383\pi$
$271$	−5.38936	−	20.1134i	−0.327380	−	1.22180i	0.584517	−	0.811382i	$-0.301284\pi$
$272$	2.82524	+	2.82524i	0.171305	+	0.171305i
$273$	7.80967	−	11.8856i	0.472663	−	0.719349i
$274$			8.33481i			0.503524i
$275$	−28.1682	−	5.90988i	−1.69861	−	0.356379i
$276$	2.16487	−	3.74966i	0.130310	−	0.225703i
$277$	7.19517	−	26.8528i	0.432316	−	1.61343i	−0.315093	−	0.949061i	$-0.602036\pi$
$277$	7.19517	−	26.8528i	0.432316	−	1.61343i	0.747409	−	0.664365i	$-0.231298\pi$
$278$		−	2.05451i		−	0.123221i
$279$	−3.86846	−	1.03655i	−0.231599	−	0.0620567i
$280$	4.19832	−	7.75667i	0.250897	−	0.463549i
$281$	2.84766	−	2.84766i	0.169877	−	0.169877i	−0.617048	−	0.786925i	$-0.711672\pi$
$281$	2.84766	−	2.84766i	0.169877	−	0.169877i	0.786925	+	0.617048i	$0.211672\pi$
$282$	−12.9971	−	3.48257i	−0.773968	−	0.207384i
$283$	−7.35650	−	27.4548i	−0.437299	−	1.63202i	−0.735505	−	0.677519i	$-0.763055\pi$
$283$	−7.35650	−	27.4548i	−0.437299	−	1.63202i	0.298207	−	0.954501i	$-0.403612\pi$
$284$	−12.3639	+	3.31290i	−0.733664	+	0.196585i
$285$	4.11221	−	2.52742i	0.243587	−	0.149711i
$286$	20.7201	+	1.19751i	1.22520	+	0.0708102i
$287$	−0.166704	+	0.166704i	−0.00984022	+	0.00984022i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	0.897213	+	0.518006i	0.0527772	+	0.0304709i
$290$	6.20064	−	11.4561i	0.364114	−	0.672725i
$291$	6.74506	+	6.74506i	0.395403	+	0.395403i
$292$	−2.29908	−	3.98212i	−0.134543	−	0.233036i
$293$	1.56424	+	2.70934i	0.0913838	+	0.158281i	0.908094	−	0.418767i	$-0.137538\pi$
$293$	1.56424	+	2.70934i	0.0913838	+	0.158281i	−0.816710	+	0.577049i	$0.804204\pi$
$294$	6.05166	+	6.05166i	0.352940	+	0.352940i
$295$	−1.25453	−	4.21483i	−0.0730414	−	0.245397i
$296$	−3.16089	−	1.82494i	−0.183723	−	0.106073i
$297$	4.98511	+	2.87815i	0.289265	+	0.167007i
$298$	−12.5598	+	12.5598i	−0.727568	+	0.727568i
$299$	7.01249	+	13.9474i	0.405542	+	0.806602i
$300$	4.75120	−	1.55760i	0.274311	−	0.0899280i
$301$	40.6829	−	10.9009i	2.34492	−	0.628320i
$302$	3.78766	+	14.1357i	0.217955	+	0.813420i
$303$	6.32230	+	1.69406i	0.363207	+	0.0973209i
$304$	−1.52637	+	1.52637i	−0.0875435	+	0.0875435i
$305$	5.62213	+	3.04299i	0.321922	+	0.174241i
$306$	−3.85935	−	1.03411i	−0.220625	−	0.0591162i
$307$		−	27.4796i		−	1.56835i	−0.620542	−	0.784173i	$-0.713088\pi$
$307$		−	27.4796i		−	1.56835i	0.620542	−	0.784173i	$-0.286912\pi$
$308$	−5.87654	+	21.9315i	−0.334847	+	1.24967i
$309$	4.07431	−	7.05691i	0.231779	−	0.401454i
$310$	6.15586	−	6.50405i	0.349629	−	0.369405i
$311$			8.90153i			0.504759i	0.967628	+	0.252380i	$0.0812132\pi$
$311$			8.90153i			0.504759i	−0.967628	+	0.252380i	$0.918787\pi$
$312$	−3.22131	+	1.61961i	−0.182371	+	0.0916923i
$313$	10.1819	+	10.1819i	0.575514	+	0.575514i	0.933664	−	0.358150i	$-0.116592\pi$
$313$	10.1819	+	10.1819i	0.575514	+	0.575514i	−0.358150	+	0.933664i	$0.616592\pi$
$314$	−4.55336	−	16.9934i	−0.256961	−	0.958991i
$315$	0.242485	+	8.81663i	0.0136625	+	0.496761i
$316$	−2.16466	+	1.24977i	−0.121772	+	0.0703049i
$317$	−16.5893			−0.931750			−0.465875	−	0.884850i	$-0.654260\pi$
$317$	−16.5893			−0.931750			−0.465875	+	0.884850i	$0.654260\pi$
$318$	−5.08345	+	2.93493i	−0.285066	+	0.164583i
$319$	−8.67927	+	32.3915i	−0.485946	+	1.81357i
$320$	−1.90502	+	1.17085i	−0.106494	+	0.0654526i
$321$	−6.23657	−	10.8020i	−0.348091	−	0.602912i
$322$	−16.4963	+	4.42018i	−0.919304	+	0.246327i
$323$	4.31237	−	7.46925i	0.239947	−	0.415600i
$324$	−1.00000			−0.0555556
$325$	−4.71359	+	17.4006i	−0.261463	+	0.965214i
$326$	−22.4435			−1.24303
$327$	−0.762177	+	1.32013i	−0.0421485	+	0.0730033i
$328$	0.0577328	−	0.0154695i	0.00318776	−	0.000854158i
$329$	26.5372	+	45.9638i	1.46304	+	2.53407i
$330$	−10.9659	+	6.73978i	−0.603652	+	0.371012i
$331$	−1.64893	+	6.15390i	−0.0906335	+	0.338249i	−0.996321	−	0.0856964i	$-0.972688\pi$
$331$	−1.64893	+	6.15390i	−0.0906335	+	0.338249i	0.905688	+	0.423945i	$0.139355\pi$
$332$	10.4032	−	6.00627i	0.570948	−	0.329637i
$333$	3.64988			0.200012
$334$	12.4134	−	7.16686i	0.679229	−	0.392153i
$335$	−0.167511	−	6.09061i	−0.00915211	−	0.332766i
$336$	−1.02089	−	3.81000i	−0.0556940	−	0.207853i
$337$	15.8216	+	15.8216i	0.861857	+	0.861857i	0.991554	−	0.129697i	$-0.0414004\pi$
$337$	15.8216	+	15.8216i	0.861857	+	0.861857i	−0.129697	+	0.991554i	$0.541400\pi$
$338$	1.49766	−	12.9134i	0.0814618	−	0.702399i
$339$			8.46068i			0.459521i
$340$	6.14136	−	6.48873i	0.333062	−	0.351901i
$341$	−11.5268	+	19.9650i	−0.624211	+	1.08117i
$342$	0.558691	−	2.08506i	0.0302106	−	0.112747i
$343$		−	6.14674i		−	0.331893i
$344$	−10.3141	−	2.76364i	−0.556097	−	0.149006i
$345$	−8.51442	−	4.60845i	−0.458401	−	0.248111i
$346$	−6.31453	+	6.31453i	−0.339471	+	0.339471i
$347$	25.3449	+	6.79115i	1.36059	+	0.364568i	0.864031	−	0.503438i	$-0.167932\pi$
$347$	25.3449	+	6.79115i	1.36059	+	0.364568i	0.496554	+	0.868006i	$0.334598\pi$
$348$	−1.50778	−	5.62713i	−0.0808257	−	0.301646i
$349$	−21.6505	+	5.80122i	−1.15892	+	0.310532i	−0.786535	−	0.617545i	$-0.788127\pi$
$349$	−21.6505	+	5.80122i	−1.15892	+	0.310532i	−0.372387	+	0.928078i	$0.621461\pi$
$350$	−17.5960	−	8.90732i	−0.940544	−	0.476116i
$351$	1.97994	−	3.01328i	0.105681	−	0.160837i
$352$	4.07032	−	4.07032i	0.216949	−	0.216949i
$353$	11.9711	+	6.91152i	0.637157	+	0.367863i	0.783519	−	0.621368i	$-0.213423\pi$
$353$	11.9711	+	6.91152i	0.637157	+	0.367863i	−0.146361	+	0.989231i	$0.546756\pi$
$354$	−1.70317	−	0.983327i	−0.0905226	−	0.0522632i
$355$	8.16516	+	27.4325i	0.433361	+	1.45596i
$356$	−5.86034	−	5.86034i	−0.310597	−	0.310597i
$357$	7.87993	+	13.6484i	0.417050	+	0.722352i
$358$	−4.09709	−	7.09637i	−0.216538	−	0.375055i
$359$	4.57733	+	4.57733i	0.241582	+	0.241582i	0.817504	−	0.575922i	$-0.195357\pi$
$359$	4.57733	+	4.57733i	0.241582	+	0.241582i	−0.575922	+	0.817504i	$0.695357\pi$
$360$	1.06437	−	1.96650i	0.0560973	−	0.103644i
$361$	−12.4191	−	7.17019i	−0.653638	−	0.377378i
$362$	12.8424	+	7.41456i	0.674981	+	0.389700i
$363$	15.6518	−	15.6518i	0.821509	−	0.821509i
$364$	13.5019	+	4.46734i	0.707692	+	0.234152i
$365$	−8.75958	+	5.38375i	−0.458498	+	0.281798i
$366$	2.76154	−	0.739952i	0.144348	−	0.0386779i
$367$	4.29441	+	16.0270i	0.224167	+	0.836601i	0.982737	+	0.185010i	$0.0592317\pi$
$367$	4.29441	+	16.0270i	0.224167	+	0.836601i	−0.758570	+	0.651591i	$0.774102\pi$
$368$	4.18221	+	1.12062i	0.218013	+	0.0584163i
$369$	−0.0422634	+	0.0422634i	−0.00220014	+	0.00220014i
$370$	−3.88483	+	7.17748i	−0.201963	+	0.373140i
$371$	22.3642	+	5.99247i	1.16109	+	0.311114i
$372$		−	4.00493i		−	0.207646i
$373$	2.35503	−	8.78910i	0.121939	−	0.455082i	−0.877773	−	0.479077i	$-0.840972\pi$
$373$	2.35503	−	8.78910i	0.121939	−	0.455082i	0.999712	+	0.0239941i	$0.00763829\pi$
$374$	−11.4996	+	19.9180i	−0.594633	+	1.02993i
$375$	−3.77366	−	10.5242i	−0.194871	−	0.543469i
$376$		−	13.4556i		−	0.693920i
$377$	19.9414	+	6.59797i	1.02704	+	0.339813i
$378$	2.78912	+	2.78912i	0.143457	+	0.143457i
$379$	−2.63393	−	9.82994i	−0.135296	−	0.504930i	−0.999997	−	0.00264304i	$-0.999159\pi$
$379$	−2.63393	−	9.82994i	−0.135296	−	0.504930i	0.864701	−	0.502287i	$-0.167508\pi$
$380$	3.50562	+	3.31795i	0.179834	+	0.170207i
$381$	−11.0855	+	6.40022i	−0.567927	+	0.327893i
$382$	14.1847			0.725751
$383$	−19.8726	+	11.4734i	−1.01544	+	0.586266i	−0.912780	−	0.408451i	$-0.866069\pi$
$383$	−19.8726	+	11.4734i	−1.01544	+	0.586266i	−0.102661	+	0.994716i	$0.532736\pi$
$384$	−0.258819	+	0.965926i	−0.0132078	+	0.0492922i
$385$	49.3832	+	11.7871i	2.51680	+	0.600727i
$386$	9.51346	+	16.4778i	0.484222	+	0.838698i
$387$	10.3141	−	2.76364i	0.524293	−	0.140484i
$388$	−4.76948	+	8.26098i	−0.242134	+	0.419388i
$389$	4.23516			0.214731			0.107366	−	0.994220i	$-0.465758\pi$
$389$	4.23516			0.214731			0.107366	+	0.994220i	$0.465758\pi$
$390$	3.81822	+	7.10079i	0.193343	+	0.359562i
$391$	−17.2995			−0.874871
$392$	−4.27917	+	7.41174i	−0.216131	+	0.374350i
$393$	−13.5133	+	3.62088i	−0.681656	+	0.182649i
$394$	1.45202	+	2.51498i	0.0731519	+	0.126703i
$395$	2.92658	+	4.76167i	0.147252	+	0.239586i
$396$	−1.48984	+	5.56016i	−0.0748673	+	0.279409i
$397$	−14.8003	+	8.54497i	−0.742807	+	0.428860i	−0.823089	−	0.567912i	$-0.807751\pi$
$397$	−14.8003	+	8.54497i	−0.742807	+	0.428860i	0.0802821	+	0.996772i	$0.474418\pi$
$398$	−9.09955			−0.456119
$399$	−7.37374	+	4.25723i	−0.369149	+	0.213128i
$400$	2.73423	+	4.18617i	0.136711	+	0.209308i
$401$	−2.85538	−	10.6564i	−0.142591	−	0.532156i	−0.999851	−	0.0172721i	$-0.994502\pi$
$401$	−2.85538	−	10.6564i	−0.142591	−	0.532156i	0.857260	−	0.514884i	$-0.172165\pi$
$402$	−1.92675	−	1.92675i	−0.0960975	−	0.0960975i
$403$	12.0680	+	7.92950i	0.601149	+	0.394997i
$404$			6.54533i			0.325642i
$405$	0.0614757	+	2.23522i	0.00305475	+	0.111069i
$406$	−11.4893	+	19.9001i	−0.570206	+	0.987625i
$407$	5.43775	−	20.2939i	0.269539	−	1.00593i
$408$		−	3.99550i		−	0.197807i
$409$	−10.1249	−	2.71296i	−0.500645	−	0.134147i	−0.000345561	−	1.00000i	$-0.500110\pi$
$409$	−10.1249	−	2.71296i	−0.500645	−	0.134147i	−0.500299	+	0.865853i	$0.666777\pi$
$410$	−0.0381269	−	0.128095i	−0.00188295	−	0.00632615i
$411$	5.89360	−	5.89360i	0.290710	−	0.290710i
$412$	7.87096	+	2.10902i	0.387774	+	0.103904i
$413$	2.00773	+	7.49296i	0.0987941	+	0.368705i
$414$	−4.18221	+	1.12062i	−0.205544	+	0.0550754i
$415$	−14.0649	−	22.8842i	−0.690418	−	1.12334i
$416$	−2.39816	−	2.69236i	−0.117579	−	0.132004i
$417$	−1.45276	+	1.45276i	−0.0711417	+	0.0711417i
$418$	−10.7609	−	6.21283i	−0.526335	−	0.303879i
$419$	31.2083	+	18.0181i	1.52462	+	0.880242i	0.999574	+	0.0291695i	$0.00928627\pi$
$419$	31.2083	+	18.0181i	1.52462	+	0.880242i	0.525049	+	0.851072i	$0.324047\pi$
$420$	−8.45345	+	2.51613i	−0.412486	+	0.122775i
$421$	11.8375	+	11.8375i	0.576926	+	0.576926i	0.934055	−	0.357129i	$-0.116244\pi$
$421$	11.8375	+	11.8375i	0.576926	+	0.576926i	−0.357129	+	0.934055i	$0.616244\pi$
$422$	0.853215	+	1.47781i	0.0415339	+	0.0719388i
$423$	6.72781	+	11.6529i	0.327117	+	0.566584i
$424$	−4.15062	−	4.15062i	−0.201572	−	0.201572i
$425$	−14.8813	−	13.3284i	−0.721849	−	0.646523i
$426$	11.0852	+	6.40004i	0.537079	+	0.310083i
$427$	−9.76607	−	5.63844i	−0.472613	−	0.272863i
$428$	8.81983	−	8.81983i	0.426323	−	0.426323i
$429$	−13.8045	−	15.4981i	−0.666490	−	0.748254i
$430$	−5.54330	+	23.2241i	−0.267321	+	1.11997i
$431$	−17.2346	+	4.61800i	−0.830163	+	0.222441i	−0.648785	−	0.760972i	$-0.724722\pi$
$431$	−17.2346	+	4.61800i	−0.830163	+	0.222441i	−0.181378	+	0.983413i	$0.558056\pi$
$432$	−0.258819	−	0.965926i	−0.0124524	−	0.0464731i
$433$	−34.0011	−	9.11056i	−1.63399	−	0.437826i	−0.678920	−	0.734213i	$-0.737552\pi$
$433$	−34.0011	−	9.11056i	−1.63399	−	0.437826i	−0.955068	+	0.296387i	$0.904218\pi$
$434$	−11.1702	+	11.1702i	−0.536188	+	0.536188i
$435$	−12.4852	+	3.71616i	−0.598619	+	0.178176i
$436$	−1.47241	−	0.394532i	−0.0705158	−	0.0188947i
$437$		−	9.34625i		−	0.447092i
$438$	−1.19009	+	4.44148i	−0.0568647	+	0.212222i
$439$	−10.6384	+	18.4262i	−0.507743	+	0.879436i	0.492217	+	0.870472i	$0.336187\pi$
$439$	−10.6384	+	18.4262i	−0.507743	+	0.879436i	−0.999960	+	0.00896365i	$0.997147\pi$
$440$	−9.34830	−	8.84785i	−0.445663	−	0.421805i
$441$		−	8.55834i		−	0.407540i
$442$	12.0395	+	7.91082i	0.572663	+	0.376279i
$443$	1.91611	+	1.91611i	0.0910369	+	0.0910369i	0.751159	−	0.660122i	$-0.229495\pi$
$443$	1.91611	+	1.91611i	0.0910369	+	0.0910369i	−0.660122	+	0.751159i	$0.729495\pi$
$444$	0.944659	+	3.52552i	0.0448315	+	0.167314i
$445$	−12.7389	+	13.4594i	−0.603881	+	0.638038i
$446$	22.5960	−	13.0458i	1.06995	−	0.617738i
$447$	17.7622			0.840124
$448$	3.41596	−	1.97220i	0.161389	−	0.0931779i
$449$	−6.95367	+	25.9514i	−0.328164	+	1.22472i	0.582929	+	0.812523i	$0.301907\pi$
$449$	−6.95367	+	25.9514i	−0.328164	+	1.22472i	−0.911093	+	0.412201i	$0.864760\pi$
$450$	−4.46099	−	2.25822i	−0.210293	−	0.106453i
$451$	0.172025	+	0.297957i	0.00810036	+	0.0140302i
$452$	−8.17239	+	2.18978i	−0.384397	+	0.102999i
$453$	7.31719	−	12.6737i	0.343792	−	0.595465i
$454$	−4.60695			−0.216215
$455$	9.15547	−	30.4544i	0.429215	−	1.42772i
$456$	2.15862			0.101087
$457$	−2.83350	+	4.90777i	−0.132546	+	0.229576i	−0.924657	−	0.380800i	$-0.875648\pi$
$457$	−2.83350	+	4.90777i	−0.132546	+	0.229576i	0.792111	+	0.610376i	$0.208982\pi$
$458$	5.11829	−	1.37144i	0.239162	−	0.0640833i
$459$	1.99775	+	3.46020i	0.0932469	+	0.161508i
$460$	2.24773	−	9.41705i	0.104801	−	0.439072i
$461$	9.72828	−	36.3064i	0.453091	−	1.69096i	−0.240548	−	0.970637i	$-0.577327\pi$
$461$	9.72828	−	36.3064i	0.453091	−	1.69096i	0.693639	−	0.720322i	$-0.256006\pi$
$462$	19.6633	−	11.3526i	0.914819	−	0.528171i
$463$	14.2949			0.664342			0.332171	−	0.943219i	$-0.392219\pi$
$463$	14.2949			0.664342			0.332171	+	0.943219i	$0.392219\pi$
$464$	5.04514	−	2.91282i	0.234215	−	0.135224i
$465$	−8.95191	+	0.246206i	−0.415135	+	0.0114175i
$466$	−3.07953	−	11.4930i	−0.142657	−	0.532401i
$467$	−13.2534	−	13.2534i	−0.613296	−	0.613296i	0.330507	−	0.943803i	$-0.392780\pi$
$467$	−13.2534	−	13.2534i	−0.613296	−	0.613296i	−0.943803	+	0.330507i	$0.892780\pi$
$468$	3.42305	+	1.13258i	0.158231	+	0.0523534i
$469$			10.7479i			0.496290i
$470$	−30.0763	+	0.827193i	−1.38732	+	0.0381556i
$471$	−8.79641	+	15.2358i	−0.405317	+	0.702030i
$472$	0.509008	−	1.89964i	0.0234290	−	0.0874381i
$473$		−	61.4653i		−	2.82618i
$474$	2.41437	+	0.646927i	0.110895	+	0.0297144i
$475$	7.20084	−	8.03981i	0.330397	−	0.368892i
$476$	−11.1439	+	11.1439i	−0.510780	+	0.510780i
$477$	5.66985	+	1.51923i	0.259605	+	0.0695609i
$478$	−1.78726	−	6.67015i	−0.0817475	−	0.305086i
$479$	8.14759	−	2.18314i	0.372273	−	0.0997503i	−0.0678315	−	0.997697i	$-0.521608\pi$
$479$	8.14759	−	2.18314i	0.372273	−	0.0997503i	0.440105	+	0.897947i	$0.354941\pi$
$480$	2.17497	+	0.519137i	0.0992734	+	0.0236953i
$481$	−12.4937	−	4.13377i	−0.569665	−	0.188484i
$482$	5.87241	−	5.87241i	0.267481	−	0.267481i
$483$	14.7902	+	8.53912i	0.672977	+	0.388544i
$484$	19.1695	+	11.0675i	0.871342	+	0.503069i
$485$	18.7583	+	10.1530i	0.851772	+	0.461024i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	14.8044	+	25.6419i	0.670850	+	1.16195i	0.977664	+	0.210176i	$0.0674038\pi$
$487$	14.8044	+	25.6419i	0.670850	+	1.16195i	−0.306814	+	0.951770i	$0.599263\pi$
$488$	1.42948	+	2.47593i	0.0647094	+	0.112080i
$489$	15.8700	+	15.8700i	0.717665	+	0.717665i
$490$	16.8300	+	9.10926i	0.760300	+	0.411514i
$491$	−14.1073	−	8.14488i	−0.636656	−	0.367573i	0.146669	−	0.989186i	$-0.453145\pi$
$491$	−14.1073	−	8.14488i	−0.636656	−	0.367573i	−0.783325	+	0.621612i	$0.786478\pi$
$492$	−0.0517618	−	0.0298847i	−0.00233360	−	0.00134731i
$493$	−16.4588	+	16.4588i	−0.741268	+	0.741268i
$494$	−4.27392	+	6.50452i	−0.192293	+	0.292652i
$495$	12.5198	+	2.98831i	0.562723	+	0.134315i
$496$	3.86846	−	1.03655i	0.173699	−	0.0465426i
$497$	−13.0674	−	48.7683i	−0.586155	−	2.18756i
$498$	−11.6032	−	3.10907i	−0.519953	−	0.139321i
$499$	−7.03621	+	7.03621i	−0.314984	+	0.314984i	−0.846837	−	0.531853i	$-0.821496\pi$
$499$	−7.03621	+	7.03621i	−0.314984	+	0.314984i	0.531853	+	0.846837i	$0.321496\pi$
$500$	9.18893	−	6.36895i	0.410942	−	0.284828i
$501$	−13.8453	−	3.70984i	−0.618563	−	0.165743i
$502$		−	26.5391i		−	1.18450i
$503$	−7.98192	+	29.7889i	−0.355896	+	1.32822i	0.523456	+	0.852052i	$0.324642\pi$
$503$	−7.98192	+	29.7889i	−0.355896	+	1.32822i	−0.879353	+	0.476171i	$0.842024\pi$
$504$	−1.97220	+	3.41596i	−0.0878489	+	0.152159i
$505$	14.6303	−	0.402378i	0.651038	−	0.0179056i
$506$			24.9233i			1.10798i
$507$	−10.1902	+	8.07218i	−0.452562	+	0.358498i
$508$	−9.05127	−	9.05127i	−0.401585	−	0.401585i
$509$	0.529872	+	1.97751i	0.0234862	+	0.0876516i	0.976674	−	0.214727i	$-0.0688861\pi$
$509$	0.529872	+	1.97751i	0.0234862	+	0.0876516i	−0.953188	+	0.302378i	$0.902219\pi$
$510$	−8.93082	+	0.245626i	−0.395464	+	0.0108765i
$511$	15.7071	−	9.06849i	0.694841	−	0.401167i
$512$	−1.00000			−0.0441942
$513$	−1.86942	+	1.07931i	−0.0825368	+	0.0476526i
$514$	5.18509	−	19.3510i	0.228704	−	0.853536i
$515$	4.23025	−	17.7230i	0.186407	−	0.780969i
$516$	5.33895	+	9.24733i	0.235034	+	0.407091i
$517$	74.8154	−	20.0467i	3.29038	−	0.881654i
$518$	7.19831	−	12.4678i	0.316276	−	0.547805i
$519$	8.93009			0.391988
$520$	−5.87061	+	5.52594i	−0.257443	+	0.242328i
$521$	19.0196			0.833265			0.416632	−	0.909075i	$-0.363210\pi$
$521$	19.0196			0.833265			0.416632	+	0.909075i	$0.363210\pi$
$522$	−2.91282	+	5.04514i	−0.127490	+	0.220820i
$523$	−26.6281	+	7.13496i	−1.16436	+	0.311990i	−0.788707	−	0.614769i	$-0.789249\pi$
$523$	−26.6281	+	7.13496i	−1.16436	+	0.311990i	−0.375656	+	0.926759i	$0.622583\pi$
$524$	−6.99500	−	12.1157i	−0.305578	−	0.529277i
$525$	6.14380	+	18.7407i	0.268137	+	0.817909i
$526$	4.06256	−	15.1617i	0.177136	−	0.661081i
$527$	−13.8579	+	8.00084i	−0.603658	+	0.348522i
$528$	−5.75631			−0.250511
$529$	3.68352	−	2.12668i	0.160153	−	0.0924644i
$530$	−9.02240	+	9.53272i	−0.391908	+	0.414075i
$531$	0.509008	+	1.89964i	0.0220890	+	0.0824374i
$532$	−6.02064	−	6.02064i	−0.261028	−	0.261028i
$533$	0.192536	−	0.0968031i	0.00833966	−	0.00419301i
$534$			8.28777i			0.358647i
$535$	−20.2565	−	19.1721i	−0.875765	−	0.828882i
$536$	1.36242	−	2.35978i	0.0588475	−	0.101927i
$537$	−2.12081	+	7.91497i	−0.0915197	+	0.341556i
$538$		−	8.52839i		−	0.367685i
$539$	−47.5858	−	12.7506i	−2.04967	−	0.549206i
$540$	−2.14315	+	0.637899i	−0.0922264	+	0.0274508i
$541$	−13.9866	+	13.9866i	−0.601331	+	0.601331i	−0.940666	−	0.339335i	$-0.889798\pi$
$541$	−13.9866	+	13.9866i	−0.601331	+	0.601331i	0.339335	+	0.940666i	$0.389798\pi$
$542$	−20.1134	−	5.38936i	−0.863943	−	0.231493i
$543$	−3.83806	−	14.3238i	−0.164707	−	0.614694i
$544$	3.85935	−	1.03411i	0.165468	−	0.0443371i
$545$	−0.791349	+	3.31543i	−0.0338977	+	0.142017i
$546$	−6.38840	−	12.7062i	−0.273398	−	0.543774i
$547$	11.8022	−	11.8022i	0.504624	−	0.504624i	−0.408247	−	0.912871i	$-0.633860\pi$
$547$	11.8022	−	11.8022i	0.504624	−	0.504624i	0.912871	+	0.408247i	$0.133860\pi$
$548$	7.21815	+	4.16740i	0.308344	+	0.178023i
$549$	−2.47593	−	1.42948i	−0.105670	−	0.0610086i
$550$	−19.2022	+	21.4395i	−0.818786	+	0.914182i
$551$	−8.89209	−	8.89209i	−0.378816	−	0.378816i
$552$	−2.16487	−	3.74966i	−0.0921430	−	0.159596i
$553$	−4.92959	−	8.53830i	−0.209628	−	0.363086i
$554$	−19.6576	−	19.6576i	−0.835171	−	0.835171i
$555$	7.82224	−	2.32826i	0.332036	−	0.0988290i
$556$	−1.77925	−	1.02725i	−0.0754572	−	0.0435652i
$557$	−6.98225	−	4.03120i	−0.295847	−	0.170807i	0.344729	−	0.938702i	$-0.387971\pi$
$557$	−6.98225	−	4.03120i	−0.295847	−	0.170807i	−0.640576	+	0.767895i	$0.721304\pi$
$558$	−2.83191	+	2.83191i	−0.119884	+	0.119884i
$559$	−38.4356	−	2.22137i	−1.62565	−	0.0939539i
$560$	−4.61831	−	7.51418i	−0.195159	−	0.317532i
$561$	22.2156	−	5.95266i	0.937944	−	0.251321i
$562$	−1.04231	−	3.88997i	−0.0439674	−	0.164089i
$563$	22.3865	+	5.99845i	0.943479	+	0.252804i	0.697593	−	0.716494i	$-0.254254\pi$
$563$	22.3865	+	5.99845i	0.943479	+	0.252804i	0.245886	+	0.969299i	$0.420921\pi$
$564$	−9.51456	+	9.51456i	−0.400635	+	0.400635i
$565$	5.39706	+	18.1325i	0.227056	+	0.762839i
$566$	−27.4548	−	7.35650i	−1.15401	−	0.309217i
$567$		−	3.94441i		−	0.165650i
$568$	−3.31290	+	12.3639i	−0.139006	+	0.518779i
$569$	3.87731	−	6.71570i	0.162545	−	0.281537i	−0.773236	−	0.634119i	$-0.781363\pi$
$569$	3.87731	−	6.71570i	0.162545	−	0.281537i	0.935781	+	0.352582i	$0.114696\pi$
$570$	−0.132703	−	4.82499i	−0.00555830	−	0.202097i
$571$			6.07789i			0.254352i	0.991880	+	0.127176i	$0.0405913\pi$
$571$			6.07789i			0.254352i	−0.991880	+	0.127176i	$0.959409\pi$
$572$	11.3971	−	17.3454i	0.476537	−	0.725246i
$573$	−10.0301	−	10.0301i	−0.419012	−	0.419012i
$574$	0.0610179	+	0.227722i	0.00254684	+	0.00950492i
$575$	−21.1874	−	4.44525i	−0.883575	−	0.185380i
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	10.5553			0.439421			0.219711	−	0.975565i	$-0.429489\pi$
$577$	10.5553			0.439421			0.219711	+	0.975565i	$0.429489\pi$
$578$	0.897213	−	0.518006i	0.0373191	−	0.0215462i
$579$	4.92453	−	18.3786i	0.204656	−	0.763788i
$580$	−6.82094	−	11.0980i	−0.283224	−	0.460817i
$581$	23.6912	+	41.0343i	0.982875	+	1.70239i
$582$	9.21393	−	2.46886i	0.381930	−	0.102338i
$583$	16.8944	−	29.2619i	0.699693	−	1.21190i
$584$	−4.59815			−0.190273
$585$	2.32113	−	7.72090i	0.0959668	−	0.319220i
$586$	3.12848			0.129236
$587$	−11.1708	+	19.3484i	−0.461070	+	0.798596i	−0.999015	−	0.0443840i	$-0.985867\pi$
$587$	−11.1708	+	19.3484i	−0.461070	+	0.798596i	0.537945	+	0.842980i	$0.319201\pi$
$588$	8.26673	−	2.21506i	0.340914	−	0.0913476i
$589$	−4.32256	−	7.48689i	−0.178108	−	0.308492i
$590$	−4.27741	−	1.02096i	−0.176098	−	0.0420324i
$591$	0.751622	−	2.80509i	0.0309176	−	0.115386i
$592$	−3.16089	+	1.82494i	−0.129912	+	0.0750046i
$593$	−44.2328			−1.81642			−0.908212	−	0.418510i	$-0.862553\pi$
$593$	−44.2328			−1.81642			−0.908212	+	0.418510i	$0.862553\pi$
$594$	4.98511	−	2.87815i	0.204541	−	0.118092i
$595$	25.5942	+	24.2240i	1.04926	+	0.993088i
$596$	4.59720	+	17.1570i	0.188309	+	0.702777i
$597$	6.43435	+	6.43435i	0.263340	+	0.263340i
$598$	15.5851	+	0.900734i	0.637322	+	0.0368337i
$599$			14.7411i			0.602305i	0.953576	+	0.301153i	$0.0973714\pi$
$599$			14.7411i			0.602305i	−0.953576	+	0.301153i	$0.902629\pi$
$600$	1.02668	−	4.89346i	0.0419140	−	0.199775i
$601$	9.96571	−	17.2611i	0.406510	−	0.704096i	−0.587986	−	0.808871i	$-0.700079\pi$
$601$	9.96571	−	17.2611i	0.406510	−	0.704096i	0.994496	+	0.104775i	$0.0334123\pi$
$602$	10.9009	−	40.6829i	0.444289	−	1.65811i
$603$			2.72484i			0.110964i
$604$	14.1357	+	3.78766i	0.575175	+	0.154118i
$605$	23.5599	−	43.5285i	0.957847	−	1.76969i
$606$	4.62825	−	4.62825i	0.188010	−	0.188010i
$607$	−38.6181	−	10.3477i	−1.56746	−	0.420000i	−0.632446	−	0.774605i	$-0.717949\pi$
$607$	−38.6181	−	10.3477i	−1.56746	−	0.420000i	−0.935016	+	0.354604i	$0.884616\pi$
$608$	0.558691	+	2.08506i	0.0226579	+	0.0845605i
$609$	22.1957	−	5.94731i	0.899414	−	0.240997i
$610$	5.44637	−	3.34741i	0.220517	−	0.135533i
$611$	−9.83182	−	47.5082i	−0.397753	−	1.92198i
$612$	−2.82524	+	2.82524i	−0.114204	+	0.114204i
$613$	−25.2559	−	14.5815i	−1.02007	−	0.588940i	−0.105949	−	0.994372i	$-0.533788\pi$
$613$	−25.2559	−	14.5815i	−1.02007	−	0.588940i	−0.914126	+	0.405431i	$0.867121\pi$
$614$	−23.7981	−	13.7398i	−0.960412	−	0.554494i
$615$	−0.0636169	+	0.117536i	−0.00256528	+	0.00473953i
$616$	16.0550	+	16.0550i	0.646875	+	0.646875i
$617$	−8.40738	−	14.5620i	−0.338468	−	0.586244i	0.645677	−	0.763611i	$-0.276575\pi$
$617$	−8.40738	−	14.5620i	−0.338468	−	0.586244i	−0.984145	+	0.177367i	$0.943242\pi$
$618$	−4.07431	−	7.05691i	−0.163893	−	0.283871i
$619$	−2.38716	−	2.38716i	−0.0959482	−	0.0959482i	0.657503	−	0.753452i	$-0.271613\pi$
$619$	−2.38716	−	2.38716i	−0.0959482	−	0.0959482i	−0.753452	+	0.657503i	$0.771613\pi$
$620$	−2.55474	−	8.58316i	−0.102601	−	0.344708i
$621$	3.74966	+	2.16487i	0.150469	+	0.0868732i
$622$	7.70895	+	4.45076i	0.309101	+	0.178459i
$623$	23.1156	−	23.1156i	0.926105	−	0.926105i
$624$	−0.208034	+	3.59954i	−0.00832804	+	0.144097i
$625$	−14.8009	−	20.1478i	−0.592037	−	0.805911i
$626$	13.9087	−	3.72683i	0.555904	−	0.148954i
$627$	3.21600	+	12.0023i	0.128435	+	0.479324i
$628$	−16.9934	−	4.55336i	−0.678109	−	0.181699i
$629$	10.3118	−	10.3118i	0.411158	−	0.411158i
$630$	7.75667	+	4.19832i	0.309033	+	0.167265i
$631$	14.9043	+	3.99359i	0.593331	+	0.158982i	0.542975	−	0.839749i	$-0.317298\pi$
$631$	14.9043	+	3.99359i	0.593331	+	0.158982i	0.0503556	+	0.998731i	$0.483965\pi$
$632$			2.49954i			0.0994262i
$633$	0.441657	−	1.64828i	0.0175543	−	0.0655134i
$634$	−8.29467	+	14.3668i	−0.329423	+	0.570578i
$635$	−19.6752	+	20.7880i	−0.780786	+	0.824948i
$636$			5.86986i			0.232755i
$637$	−9.69298	+	29.2956i	−0.384050	+	1.16074i
$638$	23.7122	+	23.7122i	0.938775	+	0.938775i
$639$	−3.31290	−	12.3639i	−0.131056	−	0.489109i
$640$	0.0614757	+	2.23522i	0.00243004	+	0.0883549i
$641$	−14.7904	+	8.53924i	−0.584185	+	0.337280i	−0.762795	−	0.646640i	$-0.776173\pi$
$641$	−14.7904	+	8.53924i	−0.584185	+	0.337280i	0.178610	+	0.983920i	$0.442840\pi$
$642$	−12.4731			−0.492275
$643$	2.00420	−	1.15712i	0.0790379	−	0.0456325i	−0.459960	−	0.887940i	$-0.652136\pi$
$643$	2.00420	−	1.15712i	0.0790379	−	0.0456325i	0.538998	+	0.842307i	$0.318803\pi$
$644$	−4.42018	+	16.4963i	−0.174179	+	0.650046i
$645$	20.3416	−	12.5022i	0.800951	−	0.492275i
$646$	−4.31237	−	7.46925i	−0.169668	−	0.293874i
$647$	21.6316	−	5.79616i	0.850425	−	0.227871i	0.192820	−	0.981234i	$-0.438237\pi$
$647$	21.6316	−	5.79616i	0.850425	−	0.227871i	0.657604	+	0.753363i	$0.271570\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	11.3207			0.444375
$650$	12.7126	+	12.7824i	0.498629	+	0.501367i
$651$	15.7971			0.619136
$652$	−11.2218	+	19.4367i	−0.439479	+	0.761199i
$653$	−3.19435	+	0.855924i	−0.125005	+	0.0334949i	−0.320779	−	0.947154i	$-0.603945\pi$
$653$	−3.19435	+	0.855924i	−0.125005	+	0.0334949i	0.195774	+	0.980649i	$0.437278\pi$
$654$	0.762177	+	1.32013i	0.0298035	+	0.0516212i
$655$	−26.6513	+	16.3802i	−1.04135	+	0.640028i
$656$	0.0154695	−	0.0577328i	0.000603981	−	0.00225409i
$657$	3.98212	−	2.29908i	0.155357	−	0.0896955i
$658$	53.0744			2.06906
$659$	−7.45456	+	4.30389i	−0.290388	+	0.167656i	−0.638117	−	0.769939i	$-0.720286\pi$
$659$	−7.45456	+	4.30389i	−0.290388	+	0.167656i	0.347729	+	0.937595i	$0.386953\pi$
$660$	0.353873	+	12.8666i	0.0137745	+	0.500833i
$661$	11.1441	+	41.5904i	0.433456	+	1.61768i	0.744735	+	0.667360i	$0.232576\pi$
$661$	11.1441	+	41.5904i	0.433456	+	1.61768i	−0.311280	+	0.950318i	$0.600758\pi$
$662$	4.50497	+	4.50497i	0.175091	+	0.175091i
$663$	−2.91945	−	14.1070i	−0.113382	−	0.547872i
$664$		−	12.0125i		−	0.466177i
$665$	−13.0873	+	13.8276i	−0.507505	+	0.536211i
$666$	1.82494	−	3.16089i	0.0707150	−	0.122482i
$667$	−6.52831	+	24.3640i	−0.252777	+	0.943377i
$668$		−	14.3337i		−	0.554589i
$669$	−25.2026	−	6.75302i	−0.974389	−	0.261087i
$670$	−5.35838	−	2.90024i	−0.207012	−	0.112046i
$671$	−11.6369	+	11.6369i	−0.449237	+	0.449237i
$672$	−3.81000	−	1.02089i	−0.146974	−	0.0393816i
$673$	4.34750	+	16.2251i	0.167584	+	0.625431i	0.997697	+	0.0678355i	$0.0216093\pi$
$673$	4.34750	+	16.2251i	0.167584	+	0.625431i	−0.830113	+	0.557596i	$0.811724\pi$
$674$	21.6127	−	5.79110i	0.832490	−	0.223065i
$675$	1.55760	+	4.75120i	0.0599520	+	0.182874i
$676$	−10.4345	−	7.75373i	−0.401329	−	0.298220i
$677$	−17.3272	+	17.3272i	−0.665938	+	0.665938i	−0.956773	−	0.290835i	$-0.906067\pi$
$677$	−17.3272	+	17.3272i	−0.665938	+	0.665938i	0.290835	+	0.956773i	$0.406067\pi$
$678$	7.32716	+	4.23034i	0.281398	+	0.162465i
$679$	−32.5847	−	18.8128i	−1.25048	−	0.721968i
$680$	−2.54872	−	8.56294i	−0.0977391	−	0.328374i
$681$	3.25761	+	3.25761i	0.124832	+	0.124832i
$682$	11.5268	+	19.9650i	0.441384	+	0.764499i
$683$	8.19327	+	14.1912i	0.313507	+	0.543010i	0.979119	−	0.203288i	$-0.0651628\pi$
$683$	8.19327	+	14.1912i	0.313507	+	0.543010i	−0.665612	+	0.746298i	$0.731829\pi$
$684$	−1.52637	−	1.52637i	−0.0583623	−	0.0583623i
$685$	8.87133	−	16.3904i	0.338956	−	0.626244i
$686$	−5.32324	−	3.07337i	−0.203242	−	0.117342i
$687$	−4.58894	−	2.64942i	−0.175079	−	0.101082i
$688$	−7.55042	+	7.55042i	−0.287857	+	0.287857i
$689$	−17.6875	−	11.6220i	−0.673842	−	0.442761i
$690$	−8.24825	+	5.06948i	−0.314005	+	0.192992i
$691$	26.2776	−	7.04106i	0.999647	−	0.267855i	0.278350	−	0.960480i	$-0.410213\pi$
$691$	26.2776	−	7.04106i	0.999647	−	0.267855i	0.721298	+	0.692625i	$0.243546\pi$
$692$	2.31128	+	8.62581i	0.0878616	+	0.327904i
$693$	−21.9315	−	5.87654i	−0.833111	−	0.223231i
$694$	18.5538	−	18.5538i	0.704291	−	0.704291i
$695$	−2.18676	+	4.04018i	−0.0829485	+	0.153253i
$696$	−5.62713	−	1.50778i	−0.213296	−	0.0571524i
$697$			0.238808i			0.00904552i
$698$	−5.80122	+	21.6505i	−0.219579	+	0.819482i
$699$	−5.94920	+	10.3043i	−0.225019	+	0.389745i
$700$	−16.5120	+	10.7849i	−0.624093	+	0.407631i
$701$			24.9044i			0.940628i	0.882499	+	0.470314i	$0.155859\pi$
$701$			24.9044i			0.940628i	−0.882499	+	0.470314i	$0.844141\pi$
$702$	−1.61961	−	3.22131i	−0.0611282	−	0.121581i
$703$	5.57108	+	5.57108i	0.210117	+	0.210117i
$704$	−1.48984	−	5.56016i	−0.0561505	−	0.209557i
$705$	21.8521	+	20.6822i	0.822996	+	0.778938i
$706$	11.9711	−	6.91152i	0.450538	−	0.260118i
$707$	−25.8174			−0.970964
$708$	−1.70317	+	0.983327i	−0.0640091	+	0.0369557i
$709$	−9.12847	+	34.0679i	−0.342827	+	1.27945i	0.552303	+	0.833643i	$0.313749\pi$
$709$	−9.12847	+	34.0679i	−0.342827	+	1.27945i	−0.895130	+	0.445804i	$0.852918\pi$
$710$	27.8398	+	6.64499i	1.04481	+	0.249382i
$711$	−1.24977	−	2.16466i	−0.0468699	−	0.0811811i
$712$	−8.00537	+	2.14503i	−0.300014	+	0.0803885i
$713$	−8.67015	+	15.0171i	−0.324700	+	0.562396i
$714$	15.7599			0.589798
$715$	−39.4714	−	24.4088i	−1.47615	−	0.912836i
$716$	−8.19418			−0.306231
$717$	−3.45273	+	5.98030i	−0.128944	+	0.223338i
$718$	6.25274	−	1.67542i	0.233350	−	0.0625260i
$719$	−21.1479	−	36.6293i	−0.788685	−	1.36604i	−0.926773	−	0.375622i	$-0.877429\pi$
$719$	−21.1479	−	36.6293i	−0.788685	−	1.36604i	0.138088	−	0.990420i	$-0.455904\pi$
$720$	−1.17085	−	1.90502i	−0.0436350	−	0.0709960i
$721$	−8.31882	+	31.0463i	−0.309809	+	1.15622i
$722$	−12.4191	+	7.17019i	−0.462192	+	0.266847i
$723$	−8.30484			−0.308860
$724$	12.8424	−	7.41456i	0.477284	−	0.275560i
$725$	−24.3871	+	15.9286i	−0.905713	+	0.591573i
$726$	−5.72897	−	21.3808i	−0.212622	−	0.793517i
$727$	−14.2431	−	14.2431i	−0.528248	−	0.528248i	0.391802	−	0.920050i	$-0.371852\pi$
$727$	−14.2431	−	14.2431i	−0.528248	−	0.528248i	−0.920050	+	0.391802i	$0.871852\pi$
$728$	10.6198	−	9.45932i	0.393595	−	0.350586i
$729$		−	1.00000i		−	0.0370370i
$730$	0.282675	+	10.2779i	0.0104623	+	0.380402i
$731$	21.3318	−	36.9477i	0.788983	−	1.36656i
$732$	0.739952	−	2.76154i	0.0273494	−	0.102069i
$733$			15.0682i			0.556556i	0.960501	+	0.278278i	$0.0897637\pi$
$733$			15.0682i			0.556556i	−0.960501	+	0.278278i	$0.910236\pi$
$734$	16.0270	+	4.29441i	0.591566	+	0.158510i
$735$	−5.45936	−	18.3418i	−0.201372	−	0.676548i
$736$	3.06159	−	3.06159i	0.112852	−	0.112852i
$737$	15.1505	+	4.05957i	0.558077	+	0.149536i
$738$	0.0154695	+	0.0577328i	0.000569439	+	0.00212517i
$739$	22.6190	−	6.06075i	0.832054	−	0.222948i	0.182445	−	0.983216i	$-0.441599\pi$
$739$	22.6190	−	6.06075i	0.832054	−	0.222948i	0.649610	+	0.760268i	$0.274932\pi$
$740$	4.27347	+	6.95311i	0.157096	+	0.255601i
$741$	7.62151	−	1.57727i	0.279983	−	0.0579424i
$742$	16.3717	−	16.3717i	0.601025	−	0.601025i
$743$	−23.5522	−	13.5979i	−0.864045	−	0.498857i	0.00131959	−	0.999999i	$-0.499580\pi$
$743$	−23.5522	−	13.5979i	−0.864045	−	0.498857i	−0.865365	+	0.501142i	$0.832913\pi$
$744$	−3.46837	−	2.00246i	−0.127157	−	0.0734139i
$745$	38.0670	−	11.3305i	1.39467	−	0.415117i
$746$	−6.43407	−	6.43407i	−0.235568	−	0.235568i
$747$	6.00627	+	10.4032i	0.219758	+	0.380632i
$748$	11.4996	+	19.9180i	0.420469	+	0.728273i
$749$	34.7890	+	34.7890i	1.27116	+	1.27116i
$750$	−11.0011	−	1.99403i	−0.401703	−	0.0728116i
$751$	19.3349	+	11.1630i	0.705540	+	0.407344i	0.809407	−	0.587247i	$-0.199788\pi$
$751$	19.3349	+	11.1630i	0.705540	+	0.407344i	−0.103867	+	0.994591i	$0.533122\pi$
$752$	−11.6529	−	6.72781i	−0.424938	−	0.245338i
$753$	−18.7660	+	18.7660i	−0.683869	+	0.683869i
$754$	15.6847	−	13.9708i	0.571204	−	0.508786i
$755$	7.59725	−	31.8294i	0.276492	−	1.15839i
$756$	3.81000	−	1.02089i	0.138569	−	0.0371293i
$757$	−12.3705	−	46.1673i	−0.449613	−	1.67798i	−0.703459	−	0.710736i	$-0.748362\pi$
$757$	−12.3705	−	46.1673i	−0.449613	−	1.67798i	0.253846	−	0.967245i	$-0.418304\pi$
$758$	−9.82994	−	2.63393i	−0.357040	−	0.0956685i
$759$	17.6234	−	17.6234i	0.639690	−	0.639690i
$760$	4.62624	−	1.37698i	0.167811	−	0.0499483i
$761$	−32.4685	−	8.69990i	−1.17698	−	0.315371i	−0.383253	−	0.923643i	$-0.625196\pi$
$761$	−32.4685	−	8.69990i	−1.17698	−	0.315371i	−0.793728	+	0.608272i	$0.791863\pi$
$762$			12.8004i			0.463711i
$763$	1.55619	−	5.80780i	0.0563380	−	0.210256i
$764$	7.09233	−	12.2843i	0.256592	−	0.444430i
$765$	6.48873	+	6.14136i	0.234601	+	0.222041i
$766$			22.9469i			0.829105i
$767$	0.409131	−	7.07906i	0.0147729	−	0.255610i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	0.495133	+	1.84786i	0.0178550	+	0.0666356i	0.974279	−	0.225347i	$-0.0723516\pi$
$769$	0.495133	+	1.84786i	0.0178550	+	0.0666356i	−0.956424	+	0.291983i	$0.905685\pi$
$770$	34.8995	−	36.8735i	1.25769	−	1.32883i
$771$	−17.3496	+	10.0168i	−0.624832	+	0.360747i
$772$	19.0269			0.684794
$773$	36.5639	−	21.1102i	1.31511	−	0.759280i	0.332173	−	0.943218i	$-0.392218\pi$
$773$	36.5639	−	21.1102i	1.31511	−	0.759280i	0.982938	+	0.183939i	$0.0588848\pi$
$774$	2.76364	−	10.3141i	0.0993371	−	0.370731i
$775$	−19.0282	+	6.23807i	−0.683514	+	0.224078i
$776$	4.76948	+	8.26098i	0.171214	+	0.296552i
$777$	−13.9061	+	3.72612i	−0.498877	+	0.133674i
$778$	2.11758	−	3.66776i	0.0759189	−	0.131495i
$779$	−0.129019			−0.00462260
$780$	8.05857	+	0.243718i	0.288543	+	0.00872652i
$781$	−73.6811			−2.63652
$782$	−8.64973	+	14.9818i	−0.309314	+	0.535747i
$783$	5.62713	−	1.50778i	0.201097	−	0.0538838i
$784$	4.27917	+	7.41174i	0.152828	+	0.264705i
$785$	−9.13309	+	38.2639i	−0.325974	+	1.36570i
$786$	−3.62088	+	13.5133i	−0.129153	+	0.482004i
$787$	11.6011	−	6.69792i	0.413536	−	0.238755i	−0.278772	−	0.960357i	$-0.589927\pi$
$787$	11.6011	−	6.69792i	0.413536	−	0.238755i	0.692308	+	0.721602i	$0.256594\pi$
$788$	2.90405			0.103452
$789$	−13.5936	+	7.84827i	−0.483945	+	0.279406i
$790$	5.58702	−	0.153661i	0.198777	−	0.00546700i
$791$	−8.63740	−	32.2352i	−0.307111	−	1.14615i
$792$	4.07032	+	4.07032i	0.144633	+	0.144633i
$793$	6.85624	+	7.69735i	0.243472	+	0.273341i
$794$			17.0899i			0.606499i
$795$	13.1205	−	0.360854i	0.465335	−	0.0127982i
$796$	−4.54977	+	7.88044i	−0.161262	+	0.279315i
$797$	−8.88876	+	33.1733i	−0.314856	+	1.17506i	0.609268	+	0.792965i	$0.291463\pi$
$797$	−8.88876	+	33.1733i	−0.314856	+	1.17506i	−0.924124	+	0.382094i	$0.875203\pi$
$798$			8.51447i			0.301409i
$799$	51.9300	+	13.9146i	1.83715	+	0.492263i
$800$	4.99244	−	0.274824i	0.176509	−	0.00971649i
$801$	5.86034	−	5.86034i	0.207065	−	0.207065i
$802$	−10.6564	−	2.85538i	−0.376291	−	0.100827i
$803$	−6.85052	−	25.5665i	−0.241750	−	0.902222i
$804$	−2.63199	+	0.705239i	−0.0928231	+	0.0248719i
$805$	37.1447	+	8.86596i	1.30918	+	0.312484i
$806$	12.9011	−	6.48642i	0.454423	−	0.228474i
$807$	−6.03048	+	6.03048i	−0.212283	+	0.212283i
$808$	5.66842	+	3.27266i	0.199414	+	0.115132i
$809$	33.1559	+	19.1426i	1.16570	+	0.673018i	0.952664	−	0.304026i	$-0.0983310\pi$
$809$	33.1559	+	19.1426i	1.16570	+	0.673018i	0.213037	+	0.977044i	$0.431664\pi$
$810$	1.96650	+	1.06437i	0.0690957	+	0.0373982i
$811$	−13.2953	−	13.2953i	−0.466860	−	0.466860i	0.434036	−	0.900896i	$-0.357089\pi$
$811$	−13.2953	−	13.2953i	−0.466860	−	0.466860i	−0.900896	+	0.434036i	$0.857089\pi$
$812$	11.4893	+	19.9001i	0.403196	+	0.698357i
$813$	10.4114	+	18.0332i	0.365145	+	0.632450i
$814$	−14.8562	−	14.8562i	−0.520709	−	0.520709i
$815$	44.1352	+	23.8883i	1.54599	+	0.836770i
$816$	−3.46020	−	1.99775i	−0.121131	−	0.0699352i
$817$	19.9615	+	11.5248i	0.698363	+	0.403200i
$818$	−7.41195	+	7.41195i	−0.259153	+	0.259153i
$819$	−4.46734	+	13.5019i	−0.156102	+	0.471795i
$820$	−0.129997	−	0.0310285i	−0.00453968	−	0.00108356i
$821$	−30.5611	+	8.18882i	−1.06659	+	0.285792i	−0.749091	−	0.662467i	$-0.769509\pi$
$821$	−30.5611	+	8.18882i	−1.06659	+	0.285792i	−0.317498	+	0.948259i	$0.602843\pi$
$822$	−2.15721	−	8.05080i	−0.0752412	−	0.280804i
$823$	−19.4117	−	5.20135i	−0.676649	−	0.181308i	−0.0959011	−	0.995391i	$-0.530573\pi$
$823$	−19.4117	−	5.20135i	−0.676649	−	0.181308i	−0.580748	+	0.814083i	$0.697240\pi$
$824$	5.76194	−	5.76194i	0.200727	−	0.200727i
$825$	28.7380	−	1.58197i	1.00053	−	0.0550771i
$826$	7.49296	+	2.00773i	0.260713	+	0.0698580i
$827$		−	24.4431i		−	0.849970i	−0.905200	−	0.424985i	$-0.860279\pi$
$827$		−	24.4431i		−	0.849970i	0.905200	−	0.424985i	$-0.139721\pi$
$828$	−1.12062	+	4.18221i	−0.0389442	+	0.145342i
$829$	−14.4413	+	25.0131i	−0.501568	+	0.868741i	0.498431	+	0.866930i	$0.333910\pi$
$829$	−14.4413	+	25.0131i	−0.501568	+	0.868741i	−0.999998	+	0.00181104i	$0.999424\pi$
$830$	−26.8507	+	0.738479i	−0.932001	+	0.0256330i
$831$			27.8000i			0.964372i
$832$	−3.53074	+	0.730685i	−0.122406	+	0.0253319i
$833$	−24.1794	−	24.1794i	−0.837766	−	0.837766i
$834$	0.531745	+	1.98450i	0.0184128	+	0.0687177i
$835$	−32.0391	+	0.881176i	−1.10876	+	0.0304943i
$836$	−10.7609	+	6.21283i	−0.372175	+	0.214875i
$837$	4.00493			0.138431
$838$	31.2083	−	18.0181i	1.07807	−	0.622425i
$839$	−5.22644	+	19.5054i	−0.180437	+	0.673400i	0.815125	+	0.579286i	$0.196668\pi$
$839$	−5.22644	+	19.5054i	−0.180437	+	0.673400i	−0.995561	+	0.0941139i	$0.969998\pi$
$840$	−2.04769	+	8.57897i	−0.0706520	+	0.296003i
$841$	2.46899	+	4.27641i	0.0851375	+	0.147462i
$842$	16.1704	−	4.33284i	0.557268	−	0.149320i
$843$	−2.01360	+	3.48765i	−0.0693520	+	0.120121i
$844$	1.70643			0.0587377
$845$	−16.6898	+	23.8002i	−0.574148	+	0.818751i
$846$	13.4556			0.462614
$847$	−43.6548	+	75.6124i	−1.50000	+	2.59807i
$848$	−5.66985	+	1.51923i	−0.194704	+	0.0521707i
$849$	14.2117	+	24.6153i	0.487743	+	0.844796i
$850$	−18.9834	+	6.22338i	−0.651125	+	0.213460i
$851$	4.09013	−	15.2646i	0.140208	−	0.523262i
$852$	11.0852	−	6.40004i	0.379772	−	0.219262i
$853$	12.5604			0.430059			0.215030	−	0.976608i	$-0.431015\pi$
$853$	12.5604			0.430059			0.215030	+	0.976608i	$0.431015\pi$
$854$	−9.76607	+	5.63844i	−0.334188	+	0.192944i
$855$	−3.31795	+	3.50562i	−0.113471	+	0.119890i
$856$	−3.22828	−	12.0481i	−0.110340	−	0.411796i
$857$	−15.6057	−	15.6057i	−0.533079	−	0.533079i	0.388408	−	0.921487i	$-0.373025\pi$
$857$	−15.6057	−	15.6057i	−0.533079	−	0.533079i	−0.921487	+	0.388408i	$0.873025\pi$
$858$	−20.3240	+	4.20605i	−0.693850	+	0.143592i
$859$		−	27.8178i		−	0.949132i	−0.880220	−	0.474566i	$-0.842605\pi$
$859$		−	27.8178i		−	0.949132i	0.880220	−	0.474566i	$-0.157395\pi$
$860$	17.3410	+	16.4127i	0.591324	+	0.559668i
$861$	0.117877	−	0.204170i	0.00401725	−	0.00695809i
$862$	−4.61800	+	17.2346i	−0.157290	+	0.587014i
$863$			8.10977i			0.276060i	0.990428	+	0.138030i	$0.0440770\pi$
$863$			8.10977i			0.276060i	−0.990428	+	0.138030i	$0.955923\pi$
$864$	−0.965926	−	0.258819i	−0.0328615	−	0.00880520i
$865$	19.1385	−	5.69650i	0.650729	−	0.193687i
$866$	−24.8905	+	24.8905i	−0.845814	+	0.845814i
$867$	−1.00071	−	0.268140i	−0.0339859	−	0.00910650i
$868$	4.08858	+	15.2588i	0.138776	+	0.517917i
$869$	−13.8978	+	3.72391i	−0.471451	+	0.126325i
$870$	−3.02430	+	12.6706i	−0.102533	+	0.429573i
$871$	3.08608	−	9.32725i	0.104568	−	0.316042i
$872$	−1.07788	+	1.07788i	−0.0365017	+	0.0365017i
$873$	−8.26098	−	4.76948i	−0.279592	−	0.161422i
$874$	−8.09409	−	4.67312i	−0.273787	−	0.158071i
$875$	25.1217	+	36.2449i	0.849269	+	1.22530i
$876$	3.25139	+	3.25139i	0.109854	+	0.109854i
$877$	−19.2902	−	33.4115i	−0.651382	−	1.12823i	−0.982788	−	0.184739i	$-0.940856\pi$
$877$	−19.2902	−	33.4115i	−0.651382	−	1.12823i	0.331405	−	0.943488i	$-0.392477\pi$
$878$	10.6384	+	18.4262i	0.359028	+	0.621855i
$879$	−2.21217	−	2.21217i	−0.0746146	−	0.0746146i
$880$	−12.3366	+	3.67194i	−0.415867	+	0.123781i
$881$	−36.9213	−	21.3165i	−1.24391	−	0.718172i	−0.274022	−	0.961723i	$-0.588354\pi$
$881$	−36.9213	−	21.3165i	−1.24391	−	0.718172i	−0.969888	+	0.243552i	$0.921687\pi$
$882$	−7.41174	−	4.27917i	−0.249566	−	0.144087i
$883$	6.29479	−	6.29479i	0.211837	−	0.211837i	−0.593211	−	0.805047i	$-0.702140\pi$
$883$	6.29479	−	6.29479i	0.211837	−	0.211837i	0.805047	+	0.593211i	$0.202140\pi$
$884$	12.8707	−	6.47114i	0.432890	−	0.217648i
$885$	2.30266	+	3.74652i	0.0774030	+	0.125938i
$886$	2.61745	−	0.701343i	0.0879349	−	0.0235621i
$887$	3.81548	+	14.2396i	0.128111	+	0.478117i	0.999931	−	0.0117085i	$-0.00372701\pi$
$887$	3.81548	+	14.2396i	0.128111	+	0.478117i	−0.871820	+	0.489826i	$0.837060\pi$
$888$	3.52552	+	0.944659i	0.118309	+	0.0317007i
$889$	35.7019	−	35.7019i	1.19740	−	1.19740i
$890$	5.28676	+	17.7619i	0.177213	+	0.595381i
$891$	−5.56016	−	1.48984i	−0.186273	−	0.0499116i
$892$		−	26.0917i		−	0.873613i
$893$	−7.51754	+	28.0558i	−0.251565	+	0.938852i
$894$	8.88110	−	15.3825i	0.297029	−	0.514468i
$895$	0.503743	+	18.3158i	0.0168383	+	0.612230i
$896$		−	3.94441i		−	0.131773i
$897$	−10.3834	−	11.6572i	−0.346692	−	0.389224i
$898$	18.9978	+	18.9978i	0.633964	+	0.633964i
$899$	6.03857	+	22.5362i	0.201398	+	0.751626i
$900$	−4.18617	+	2.73423i	−0.139539	+	0.0911408i
$901$	20.3109	−	11.7265i	0.676654	−	0.390667i
$902$	0.344051			0.0114556
$903$	−36.4752	+	21.0590i	−1.21382	+	0.700799i
$904$	−2.18978	+	8.17239i	−0.0728311	+	0.271810i
$905$	−17.3627	−	28.2498i	−0.577155	−	0.939055i
$906$	−7.31719	−	12.6737i	−0.243097	−	0.421057i
$907$	−29.9028	+	8.01244i	−0.992907	+	0.266049i	−0.718471	−	0.695557i	$-0.755158\pi$
$907$	−29.9028	+	8.01244i	−0.992907	+	0.266049i	−0.274436	+	0.961605i	$0.588491\pi$
$908$	−2.30348	+	3.98974i	−0.0764435	+	0.132404i
$909$	−6.54533			−0.217095
$910$	−21.7965	−	23.1561i	−0.722548	−	0.767616i
$911$	13.4035			0.444077			0.222038	−	0.975038i	$-0.428729\pi$
$911$	13.4035			0.444077			0.222038	+	0.975038i	$0.428729\pi$
$912$	1.07931	−	1.86942i	0.0357395	−	0.0619026i
$913$	66.7917	−	17.8968i	2.21048	−	0.592297i
$914$	2.83350	+	4.90777i	0.0937240	+	0.162335i
$915$	−6.21815	−	1.48419i	−0.205566	−	0.0490658i
$916$	1.37144	−	5.11829i	0.0453137	−	0.169113i
$917$	47.7892	−	27.5911i	1.57814	−	0.911140i
$918$	3.99550			0.131871
$919$	32.8083	−	18.9419i	1.08224	−	0.624834i	0.150744	−	0.988573i	$-0.451833\pi$
$919$	32.8083	−	18.9419i	1.08224	−	0.624834i	0.931501	+	0.363739i	$0.118500\pi$
$920$	−7.03154	−	6.65512i	−0.231823	−	0.219413i
$921$	7.11225	+	26.5433i	0.234357	+	0.874631i
$922$	−26.5782	−	26.5782i	−0.875305	−	0.875305i
$923$	−2.66285	+	46.0744i	−0.0876489	+	1.51656i
$924$		−	22.7052i		−	0.746947i
$925$	15.2790	−	9.97960i	0.502371	−	0.328127i
$926$	7.14747	−	12.3798i	0.234880	−	0.406825i
$927$	−2.10902	+	7.87096i	−0.0692692	+	0.258516i
$928$		−	5.82563i		−	0.191236i
$929$	37.8082	+	10.1307i	1.24045	+	0.332376i	0.818638	−	0.574309i	$-0.194729\pi$
$929$	37.8082	+	10.1307i	1.24045	+	0.332376i	0.421807	+	0.906686i	$0.361396\pi$
$930$	−4.26273	+	7.87568i	−0.139781	+	0.258254i
$931$	13.0632	−	13.0632i	0.428130	−	0.428130i
$932$	−11.4930	−	3.07953i	−0.376465	−	0.100873i
$933$	−2.30388	−	8.59821i	−0.0754258	−	0.281493i
$934$	−18.1045	+	4.85110i	−0.592398	+	0.158733i
$935$	43.8142	−	26.9287i	1.43288	−	0.880664i
$936$	2.69236	−	2.39816i	0.0880027	−	0.0783863i
$937$	−33.9000	+	33.9000i	−1.10747	+	1.10747i	−0.113984	+	0.993483i	$0.536361\pi$
$937$	−33.9000	+	33.9000i	−1.10747	+	1.10747i	−0.993483	+	0.113984i	$0.963639\pi$
$938$	9.30792	+	5.37393i	0.303914	+	0.175465i
$939$	−12.4702	−	7.19968i	−0.406950	−	0.234953i
$940$	−14.3218	+	26.4604i	−0.467125	+	0.863044i
$941$	33.2518	+	33.2518i	1.08398	+	1.08398i	0.996134	+	0.0878430i	$0.0279974\pi$
$941$	33.2518	+	33.2518i	1.08398	+	1.08398i	0.0878430	+	0.996134i	$0.472003\pi$
$942$	8.79641	+	15.2358i	0.286603	+	0.496410i
$943$	0.129393	+	0.224115i	0.00421361	+	0.00729819i
$944$	−1.39063	−	1.39063i	−0.0452613	−	0.0452613i
$945$	−2.51613	−	8.45345i	−0.0818498	−	0.274991i
$946$	−53.2305	−	30.7326i	−1.73067	−	0.999204i
$947$	52.1022	+	30.0812i	1.69309	+	0.977507i	0.951997	+	0.306108i	$0.0990268\pi$
$947$	52.1022	+	30.0812i	1.69309	+	0.977507i	0.741096	+	0.671400i	$0.234307\pi$
$948$	1.76744	−	1.76744i	0.0574037	−	0.0574037i
$949$	−16.2349	+	3.35980i	−0.527006	+	0.109064i
$950$	−3.36226	−	10.2560i	−0.109086	−	0.332749i
$951$	16.0241	−	4.29364i	0.519616	−	0.139231i
$952$	4.07895	+	15.2229i	0.132200	+	0.493376i
$953$	9.90608	+	2.65433i	0.320890	+	0.0859821i	0.415668	−	0.909516i	$-0.363548\pi$
$953$	9.90608	+	2.65433i	0.320890	+	0.0859821i	−0.0947788	+	0.995498i	$0.530214\pi$
$954$	4.15062	−	4.15062i	0.134381	−	0.134381i
$955$	−27.8941	−	15.0978i	−0.902632	−	0.488552i
$956$	−6.67015	−	1.78726i	−0.215728	−	0.0578042i
$957$		−	33.5341i		−	1.08400i
$958$	2.18314	−	8.14759i	0.0705341	−	0.263237i
$959$	−16.4379	+	28.4713i	−0.530808	+	0.919387i
$960$	1.53707	−	1.62401i	0.0496088	−	0.0524147i
$961$		−	14.9605i		−	0.482598i
$962$	−9.82682	+	8.75300i	−0.316829	+	0.282208i
$963$	8.81983	+	8.81983i	0.284215	+	0.284215i
$964$	−2.14945	−	8.02186i	−0.0692291	−	0.258367i
$965$	−1.16969	−	42.5294i	−0.0376537	−	1.36907i
$966$	14.7902	−	8.53912i	0.475867	−	0.274742i
$967$	28.1172			0.904190			0.452095	−	0.891970i	$-0.350677\pi$
$967$	28.1172			0.904190			0.452095	+	0.891970i	$0.350677\pi$
$968$	19.1695	−	11.0675i	0.616132	−	0.355724i
$969$	−2.23225	+	8.33087i	−0.0717102	+	0.267626i
$970$	18.1719	−	11.1687i	0.583465	−	0.358605i
$971$	9.68270	+	16.7709i	0.310733	+	0.538205i	0.978521	−	0.206146i	$-0.0660923\pi$
$971$	9.68270	+	16.7709i	0.310733	+	0.538205i	−0.667789	+	0.744351i	$0.732759\pi$
$972$	0.965926	−	0.258819i	0.0309821	−	0.00830162i
$973$	4.05190	−	7.01811i	0.129898	−	0.224990i
$974$	29.6087			0.948725
$975$	0.0493585	−	18.0277i	0.00158074	−	0.577348i
$976$	2.85896			0.0915130
$977$	−21.3806	+	37.0322i	−0.684025	+	1.18477i	0.289717	+	0.957112i	$0.406439\pi$
$977$	−21.3806	+	37.0322i	−0.684025	+	1.18477i	−0.973742	+	0.227653i	$0.926895\pi$
$978$	21.6788	−	5.80882i	0.693212	−	0.185745i
$979$	−23.8535	−	41.3154i	−0.762360	−	1.32045i
$980$	16.3038	−	10.0205i	0.520807	−	0.320095i
$981$	0.394532	−	1.47241i	0.0125964	−	0.0470105i
$982$	−14.1073	+	8.14488i	−0.450184	+	0.259914i
$983$	25.0799			0.799926			0.399963	−	0.916531i	$-0.369023\pi$
$983$	25.0799			0.799926			0.399963	+	0.916531i	$0.369023\pi$
$984$	−0.0517618	+	0.0298847i	−0.00165011	+	0.000952690i
$985$	−0.178528	−	6.49119i	−0.00568838	−	0.206826i
$986$	6.02435	+	22.4832i	0.191854	+	0.716010i
$987$	−37.5293	−	37.5293i	−1.19457	−	1.19457i
$988$	3.49612	+	6.95359i	0.111226	+	0.221223i
$989$		−	46.2325i		−	1.47011i
$990$	8.84785	−	9.34830i	0.281203	−	0.297109i
$991$	15.7008	−	27.1946i	0.498753	−	0.863865i	−0.501246	−	0.865305i	$-0.667125\pi$
$991$	15.7008	−	27.1946i	0.498753	−	0.863865i	0.999999	+	0.00143950i	$0.000458209\pi$
$992$	1.03655	−	3.86846i	0.0329106	−	0.122824i
$993$		−	6.37099i		−	0.202177i
$994$	−48.7683	−	13.0674i	−1.54684	−	0.414474i
$995$	17.8942	+	9.68530i	0.567285	+	0.307045i
$996$	−8.49415	+	8.49415i	−0.269147	+	0.269147i
$997$	−31.7209	−	8.49960i	−1.00461	−	0.269185i	−0.281236	−	0.959639i	$-0.590744\pi$
$997$	−31.7209	−	8.49960i	−1.00461	−	0.269185i	−0.723377	+	0.690454i	$0.757411\pi$
$998$	2.57543	+	9.61164i	0.0815238	+	0.304251i
$999$	−3.52552	+	0.944659i	−0.111542	+	0.0298877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bn.b.163.1	yes	16
5.2	odd	4		390.2.bd.b.7.4	✓	16
13.2	odd	12		390.2.bd.b.223.4	yes	16
65.2	even	12	inner	390.2.bn.b.67.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.b.7.4	✓	16	5.2	odd	4
390.2.bd.b.223.4	yes	16	13.2	odd	12
390.2.bn.b.67.1	yes	16	65.2	even	12	inner
390.2.bn.b.163.1	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.90502 + 1.17085i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(3.41596 - 1.97220i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.90502 + 1.17085i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(3.41596 - 1.97220i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +(0.0614757 + 2.23522i) q^{10} +(-1.48984 - 5.56016i) q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.53074 + 0.730685i) q^{13} -3.94441i q^{14} +(1.53707 - 1.62401i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.03411 - 3.85935i) q^{17} -1.00000i q^{18} +(2.08506 + 0.558691i) q^{19} +(1.96650 + 1.06437i) q^{20} +(-2.78912 + 2.78912i) q^{21} +(-5.56016 - 1.48984i) q^{22} +(-1.12062 - 4.18221i) q^{23} +(0.965926 - 0.258819i) q^{24} +(2.25822 - 4.46099i) q^{25} +(-1.13258 + 3.42305i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-3.41596 - 1.97220i) q^{28} +(-5.04514 - 2.91282i) q^{29} +(-0.637899 - 2.14315i) q^{30} +(-2.83191 - 2.83191i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.87815 + 4.98511i) q^{33} +(-2.82524 - 2.82524i) q^{34} +(-4.19832 + 7.75667i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(3.16089 + 1.82494i) q^{37} +(1.52637 - 1.52637i) q^{38} +(3.22131 - 1.61961i) q^{39} +(1.90502 - 1.17085i) q^{40} +(-0.0577328 + 0.0154695i) q^{41} +(1.02089 + 3.81000i) q^{42} +(10.3141 + 2.76364i) q^{43} +(-4.07032 + 4.07032i) q^{44} +(-1.06437 + 1.96650i) q^{45} +(-4.18221 - 1.12062i) q^{46} +13.4556i q^{47} +(0.258819 - 0.965926i) q^{48} +(4.27917 - 7.41174i) q^{49} +(-2.73423 - 4.18617i) q^{50} +3.99550i q^{51} +(2.39816 + 2.69236i) q^{52} +(4.15062 + 4.15062i) q^{53} +(0.258819 + 0.965926i) q^{54} +(9.34830 + 8.84785i) q^{55} +(-3.41596 + 1.97220i) q^{56} -2.15862 q^{57} +(-5.04514 + 2.91282i) q^{58} +(-0.509008 + 1.89964i) q^{59} +(-2.17497 - 0.519137i) q^{60} +(-1.42948 - 2.47593i) q^{61} +(-3.86846 + 1.03655i) q^{62} +(1.97220 - 3.41596i) q^{63} +1.00000 q^{64} +(5.87061 - 5.52594i) q^{65} +5.75631 q^{66} +(-1.36242 + 2.35978i) q^{67} +(-3.85935 + 1.03411i) q^{68} +(2.16487 + 3.74966i) q^{69} +(4.61831 + 7.51418i) q^{70} +(3.31290 - 12.3639i) q^{71} +(-0.866025 + 0.500000i) q^{72} +4.59815 q^{73} +(3.16089 - 1.82494i) q^{74} +(-1.02668 + 4.89346i) q^{75} +(-0.558691 - 2.08506i) q^{76} +(-16.0550 - 16.0550i) q^{77} +(0.208034 - 3.59954i) q^{78} -2.49954i q^{79} +(-0.0614757 - 2.23522i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.0154695 + 0.0577328i) q^{82} +12.0125i q^{83} +(3.81000 + 1.02089i) q^{84} +(2.54872 + 8.56294i) q^{85} +(7.55042 - 7.55042i) q^{86} +(5.62713 + 1.50778i) q^{87} +(1.48984 + 5.56016i) q^{88} +(8.00537 - 2.14503i) q^{89} +(1.17085 + 1.90502i) q^{90} +(-10.6198 + 9.45932i) q^{91} +(-3.06159 + 3.06159i) q^{92} +(3.46837 + 2.00246i) q^{93} +(11.6529 + 6.72781i) q^{94} +(-4.62624 + 1.37698i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-4.76948 - 8.26098i) q^{97} +(-4.27917 - 7.41174i) q^{98} +(-4.07032 - 4.07032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8}+O(q^{10}) \) 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8	\( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8} + 12 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{19} + 4 q^{23} + 4 q^{25} + 4 q^{26} - 24 q^{28} - 48 q^{29} - 4 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 20 q^{34} - 12 q^{35} + 12 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} + 20 q^{43} - 12 q^{44} + 8 q^{45} - 4 q^{46} - 4 q^{49} - 16 q^{50} - 4 q^{52} + 32 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{57} - 48 q^{58} + 4 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 16 q^{64} - 8 q^{65} + 32 q^{66} - 28 q^{67} - 16 q^{68} + 4 q^{69} - 36 q^{71} + 32 q^{73} + 12 q^{74} - 24 q^{75} + 8 q^{76} + 4 q^{77} + 20 q^{78} + 8 q^{81} - 24 q^{82} + 52 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} - 24 q^{89} + 4 q^{90} - 8 q^{92} + 36 q^{94} - 40 q^{95} - 4 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8 + 12 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^16 - 4 * q^17 - 4 * q^19 + 4 * q^23 + 4 * q^25 + 4 * q^26 - 24 * q^28 - 48 * q^29 - 4 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 20 * q^34 - 12 * q^35 + 12 * q^37 + 4 * q^38 + 4 * q^39 - 12 * q^41 + 20 * q^43 - 12 * q^44 + 8 * q^45 - 4 * q^46 - 4 * q^49 - 16 * q^50 - 4 * q^52 + 32 * q^53 + 16 * q^55 - 24 * q^56 - 8 * q^57 - 48 * q^58 + 4 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 16 * q^64 - 8 * q^65 + 32 * q^66 - 28 * q^67 - 16 * q^68 + 4 * q^69 - 36 * q^71 + 32 * q^73 + 12 * q^74 - 24 * q^75 + 8 * q^76 + 4 * q^77 + 20 * q^78 + 8 * q^81 - 24 * q^82 + 52 * q^85 + 16 * q^86 + 36 * q^87 - 12 * q^88 - 24 * q^89 + 4 * q^90 - 8 * q^92 + 36 * q^94 - 40 * q^95 - 4 * q^97 + 4 * q^98 - 12 * q^99

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