LMFDB - Embedded newform 390.2.bd.b.223.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(7,390)]

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, 11]))

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

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

chi := DirichletCharacter("390.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bd (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			223.4
Root			$-1.09227 + 0.838128i$ of defining polynomial
Character	$\chi$	$=$	390.223
Dual form			390.2.bd.b.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.17085 + 1.90502i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(1.97220 - 3.41596i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.17085 + 1.90502i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(1.97220 - 3.41596i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.96650 + 1.06437i) q^{10} +(-1.48984 + 5.56016i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(0.730685 - 3.53074i) q^{13} -3.94441i q^{14} +(2.14315 - 0.637899i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.85935 - 1.03411i) q^{17} -1.00000 q^{18} +(-2.08506 + 0.558691i) q^{19} +(2.23522 - 0.0614757i) q^{20} +(-2.78912 - 2.78912i) q^{21} +(1.48984 + 5.56016i) q^{22} +(-4.18221 - 1.12062i) 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} +(-1.97220 - 3.41596i) q^{28} +(5.04514 - 2.91282i) q^{29} +(1.53707 - 1.62401i) q^{30} +(-2.83191 + 2.83191i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.98511 + 2.87815i) q^{33} +(2.82524 - 2.82524i) q^{34} +(8.81663 - 0.242485i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-1.82494 - 3.16089i) 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} +(-3.81000 - 1.02089i) q^{42} +(2.76364 + 10.3141i) q^{43} +(4.07032 + 4.07032i) q^{44} +(-0.0614757 - 2.23522i) q^{45} +(-4.18221 + 1.12062i) q^{46} -13.4556 q^{47} +(-0.965926 + 0.258819i) q^{48} +(-4.27917 - 7.41174i) q^{49} +(0.274824 + 4.99244i) q^{50} -3.99550i q^{51} +(-2.69236 - 2.39816i) q^{52} +(4.15062 + 4.15062i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(-12.3366 + 3.67194i) q^{55} +(-3.41596 - 1.97220i) q^{56} +2.15862i q^{57} +(2.91282 - 5.04514i) q^{58} +(0.509008 + 1.89964i) q^{59} +(0.519137 - 2.17497i) q^{60} +(-1.42948 + 2.47593i) q^{61} +(-1.03655 + 3.86846i) q^{62} +(-3.41596 + 1.97220i) q^{63} -1.00000 q^{64} +(7.58165 - 2.74199i) q^{65} +5.75631 q^{66} +(-2.35978 + 1.36242i) q^{67} +(1.03411 - 3.85935i) q^{68} +(-2.16487 + 3.74966i) q^{69} +(7.51418 - 4.61831i) q^{70} +(3.31290 + 12.3639i) q^{71} +(-0.500000 + 0.866025i) q^{72} +4.59815i q^{73} +(-3.16089 - 1.82494i) q^{74} +(3.72452 + 3.33586i) q^{75} +(-0.558691 + 2.08506i) q^{76} +(16.0550 + 16.0550i) q^{77} +(-3.59954 + 0.208034i) q^{78} -2.49954i q^{79} +(1.06437 - 1.96650i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.0577328 + 0.0154695i) q^{82} +12.0125 q^{83} +(-3.81000 + 1.02089i) q^{84} +(6.48873 + 6.14136i) q^{85} +(7.55042 + 7.55042i) q^{86} +(-1.50778 - 5.62713i) q^{87} +(5.56016 + 1.48984i) 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} +(2.00246 + 3.46837i) q^{93} +(-11.6529 + 6.72781i) q^{94} +(-3.50562 - 3.31795i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(8.26098 + 4.76948i) q^{97} +(-7.41174 - 4.27917i) q^{98} +(4.07032 - 4.07032i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7	$ 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7} + 12 q^{11} - 8 q^{13} + 12 q^{15} - 8 q^{16} + 16 q^{17} - 16 q^{18} + 4 q^{19} - 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{28} + 48 q^{29} - 8 q^{30} + 16 q^{31} + 20 q^{34} + 12 q^{35} + 20 q^{37} - 4 q^{38} - 4 q^{39} - 12 q^{41} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 64 q^{47} + 4 q^{49} + 16 q^{50} - 16 q^{52} + 32 q^{53} - 44 q^{55} - 24 q^{56} - 12 q^{58} - 4 q^{59} + 12 q^{60} + 4 q^{61} - 20 q^{62} - 24 q^{63} - 16 q^{64} - 8 q^{65} + 32 q^{66} - 36 q^{67} - 4 q^{68} - 4 q^{69} - 36 q^{71} - 8 q^{72} - 12 q^{74} + 8 q^{76} - 4 q^{77} - 12 q^{78} - 8 q^{80} + 8 q^{81} - 12 q^{82} + 24 q^{83} - 52 q^{85} + 16 q^{86} - 12 q^{87} + 24 q^{89} - 4 q^{90} - 8 q^{92} - 36 q^{94} - 44 q^{95} + 60 q^{97} + 12 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7 + 12 * q^11 - 8 * q^13 + 12 * q^15 - 8 * q^16 + 16 * q^17 - 16 * q^18 + 4 * q^19 - 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^28 + 48 * q^29 - 8 * q^30 + 16 * q^31 + 20 * q^34 + 12 * q^35 + 20 * q^37 - 4 * q^38 - 4 * q^39 - 12 * q^41 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 64 * q^47 + 4 * q^49 + 16 * q^50 - 16 * q^52 + 32 * q^53 - 44 * q^55 - 24 * q^56 - 12 * q^58 - 4 * q^59 + 12 * q^60 + 4 * q^61 - 20 * q^62 - 24 * q^63 - 16 * q^64 - 8 * q^65 + 32 * q^66 - 36 * q^67 - 4 * q^68 - 4 * q^69 - 36 * q^71 - 8 * q^72 - 12 * q^74 + 8 * q^76 - 4 * q^77 - 12 * q^78 - 8 * q^80 + 8 * q^81 - 12 * q^82 + 24 * q^83 - 52 * q^85 + 16 * q^86 - 12 * q^87 + 24 * q^89 - 4 * q^90 - 8 * q^92 - 36 * q^94 - 44 * q^95 + 60 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.17085	+	1.90502i	0.523620	+	0.851952i
$5$	1.17085	+	1.90502i	0.523620	+	0.851952i
$6$	−0.258819	−	0.965926i	−0.105662	−	0.394338i
$7$	1.97220	−	3.41596i	0.745423	−	1.29111i	−0.204574	−	0.978851i	$-0.565581\pi$
$7$	1.97220	−	3.41596i	0.745423	−	1.29111i	0.949997	−	0.312259i	$-0.101086\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	1.96650	+	1.06437i	0.621861	+	0.336584i
$11$	−1.48984	+	5.56016i	−0.449204	+	1.67645i	0.255387	+	0.966839i	$0.417797\pi$
$11$	−1.48984	+	5.56016i	−0.449204	+	1.67645i	−0.704591	+	0.709614i	$0.748870\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	0.730685	−	3.53074i	0.202656	−	0.979250i
$13$	0.730685	−	3.53074i	0.202656	−	0.979250i
$14$		−	3.94441i		−	1.05419i
$15$	2.14315	−	0.637899i	0.553359	−	0.164705i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.85935	−	1.03411i	0.936031	−	0.250809i	0.241606	−	0.970374i	$-0.422326\pi$
$17$	3.85935	−	1.03411i	0.936031	−	0.250809i	0.694424	+	0.719566i	$0.255659\pi$
$18$	−1.00000			−0.235702
$19$	−2.08506	+	0.558691i	−0.478347	+	0.128173i	−0.489933	−	0.871760i	$-0.662979\pi$
$19$	−2.08506	+	0.558691i	−0.478347	+	0.128173i	0.0115860	+	0.999933i	$0.496312\pi$
$20$	2.23522	−	0.0614757i	0.499811	−	0.0137464i
$21$	−2.78912	−	2.78912i	−0.608635	−	0.608635i
$22$	1.48984	+	5.56016i	0.317635	+	1.18543i
$23$	−4.18221	−	1.12062i	−0.872050	−	0.233665i	−0.205076	−	0.978746i	$-0.565744\pi$
$23$	−4.18221	−	1.12062i	−0.872050	−	0.233665i	−0.666974	+	0.745081i	$0.732411\pi$
$24$	−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
$28$	−1.97220	−	3.41596i	−0.372711	−	0.645555i
$29$	5.04514	−	2.91282i	0.936860	−	0.540896i	0.0478852	−	0.998853i	$-0.484752\pi$
$29$	5.04514	−	2.91282i	0.936860	−	0.540896i	0.888975	+	0.457957i	$0.151419\pi$
$30$	1.53707	−	1.62401i	0.280630	−	0.296502i
$31$	−2.83191	+	2.83191i	−0.508627	+	0.508627i	−0.914105	−	0.405478i	$-0.867105\pi$
$31$	−2.83191	+	2.83191i	−0.508627	+	0.508627i	0.405478	+	0.914105i	$0.367105\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	4.98511	+	2.87815i	0.867796	+	0.501022i
$34$	2.82524	−	2.82524i	0.484525	−	0.484525i
$35$	8.81663	−	0.242485i	1.49028	−	0.0409875i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−1.82494	−	3.16089i	−0.300018	−	0.519647i	0.676121	−	0.736790i	$-0.263660\pi$
$37$	−1.82494	−	3.16089i	−0.300018	−	0.519647i	−0.976140	+	0.217143i	$0.930326\pi$
$38$	−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	0.254308	−	0.967123i	$-0.418152\pi$
$41$	−0.0577328	−	0.0154695i	−0.00901635	−	0.00241592i	−0.263324	+	0.964707i	$0.584819\pi$
$42$	−3.81000	−	1.02089i	−0.587896	−	0.157526i
$43$	2.76364	+	10.3141i	0.421452	+	1.57288i	0.771551	+	0.636167i	$0.219481\pi$
$43$	2.76364	+	10.3141i	0.421452	+	1.57288i	−0.350100	+	0.936712i	$0.613852\pi$
$44$	4.07032	+	4.07032i	0.613624	+	0.613624i
$45$	−0.0614757	−	2.23522i	−0.00916425	−	0.333207i
$46$	−4.18221	+	1.12062i	−0.616633	+	0.165226i
$47$	−13.4556			−1.96270			−0.981352	−	0.192222i	$-0.938431\pi$
$47$	−13.4556			−1.96270			−0.981352	+	0.192222i	$0.938431\pi$
$48$	−0.965926	+	0.258819i	−0.139419	+	0.0373573i
$49$	−4.27917	−	7.41174i	−0.611310	−	1.05882i
$50$	0.274824	+	4.99244i	0.0388659	+	0.706038i
$51$		−	3.99550i		−	0.559481i
$52$	−2.69236	−	2.39816i	−0.373364	−	0.332565i
$53$	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
$55$	−12.3366	+	3.67194i	−1.66347	+	0.495125i
$56$	−3.41596	−	1.97220i	−0.456476	−	0.263547i
$57$			2.15862i			0.285916i
$58$	2.91282	−	5.04514i	0.382471	−	0.662460i
$59$	0.509008	+	1.89964i	0.0662671	+	0.247312i	0.991112	−	0.133033i	$-0.0424717\pi$
$59$	0.509008	+	1.89964i	0.0662671	+	0.247312i	−0.924844	+	0.380346i	$0.875805\pi$
$60$	0.519137	−	2.17497i	0.0670203	−	0.280787i
$61$	−1.42948	+	2.47593i	−0.183026	+	0.317010i	−0.942910	−	0.333049i	$-0.891923\pi$
$61$	−1.42948	+	2.47593i	−0.183026	+	0.317010i	0.759884	+	0.650059i	$0.225256\pi$
$62$	−1.03655	+	3.86846i	−0.131642	+	0.491296i
$63$	−3.41596	+	1.97220i	−0.430370	+	0.248474i
$64$	−1.00000			−0.125000
$65$	7.58165	−	2.74199i	0.940388	−	0.340103i
$66$	5.75631			0.708552
$67$	−2.35978	+	1.36242i	−0.288293	+	0.166446i	−0.637172	−	0.770722i	$-0.719896\pi$
$67$	−2.35978	+	1.36242i	−0.288293	+	0.166446i	0.348879	+	0.937168i	$0.386562\pi$
$68$	1.03411	−	3.85935i	0.125404	−	0.468015i
$69$	−2.16487	+	3.74966i	−0.260620	+	0.451406i
$70$	7.51418	−	4.61831i	0.898116	−	0.551994i
$71$	3.31290	+	12.3639i	0.393169	+	1.46733i	0.824876	+	0.565313i	$0.191245\pi$
$71$	3.31290	+	12.3639i	0.393169	+	1.46733i	−0.431707	+	0.902014i	$0.642089\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$			4.59815i			0.538173i	0.963116	+	0.269087i	$0.0867218\pi$
$73$			4.59815i			0.538173i	−0.963116	+	0.269087i	$0.913278\pi$
$74$	−3.16089	−	1.82494i	−0.367446	−	0.212145i
$75$	3.72452	+	3.33586i	0.430070	+	0.385192i
$76$	−0.558691	+	2.08506i	−0.0640863	+	0.239173i
$77$	16.0550	+	16.0550i	1.82964	+	1.82964i
$78$	−3.59954	+	0.208034i	−0.407568	+	0.0235552i
$79$		−	2.49954i		−	0.281220i	−0.990065	−	0.140610i	$-0.955094\pi$
$79$		−	2.49954i		−	0.281220i	0.990065	−	0.140610i	$-0.0449063\pi$
$80$	1.06437	−	1.96650i	0.119000	−	0.219861i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−0.0577328	+	0.0154695i	−0.00637552	+	0.00170832i
$83$	12.0125			1.31855			0.659274	−	0.751903i	$-0.270864\pi$
$83$	12.0125			1.31855			0.659274	+	0.751903i	$0.270864\pi$
$84$	−3.81000	+	1.02089i	−0.415706	+	0.111388i
$85$	6.48873	+	6.14136i	0.703802	+	0.666124i
$86$	7.55042	+	7.55042i	0.814182	+	0.814182i
$87$	−1.50778	−	5.62713i	−0.161651	−	0.603291i
$88$	5.56016	+	1.48984i	0.592715	+	0.158818i
$89$	−8.00537	−	2.14503i	−0.848567	−	0.227373i	−0.191770	−	0.981440i	$-0.561423\pi$
$89$	−8.00537	−	2.14503i	−0.848567	−	0.227373i	−0.656798	+	0.754067i	$0.728089\pi$
$90$	−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
$93$	2.00246	+	3.46837i	0.207646	+	0.359653i
$94$	−11.6529	+	6.72781i	−1.20191	+	0.693920i
$95$	−3.50562	−	3.31795i	−0.359669	−	0.340414i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	8.26098	+	4.76948i	0.838776	+	0.484267i	0.856848	−	0.515569i	$-0.172420\pi$
$97$	8.26098	+	4.76948i	0.838776	+	0.484267i	−0.0180722	+	0.999837i	$0.505753\pi$
$98$	−7.41174	−	4.27917i	−0.748699	−	0.432262i
$99$	4.07032	−	4.07032i	0.409083	−	0.409083i
$100$	2.73423	+	4.18617i	0.273423	+	0.418617i
$101$	−5.66842	+	3.27266i	−0.564029	+	0.325642i	−0.754761	−	0.656000i	$-0.772247\pi$
$101$	−5.66842	+	3.27266i	−0.564029	+	0.325642i	0.190732	+	0.981642i	$0.438914\pi$
$102$	−1.99775	−	3.46020i	−0.197807	−	0.342611i
$103$	5.76194	−	5.76194i	0.567741	−	0.567741i	−0.363754	−	0.931495i	$-0.618505\pi$
$103$	5.76194	−	5.76194i	0.567741	−	0.567741i	0.931495	+	0.363754i	$0.118505\pi$
$104$	−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
$107$	−12.0481	−	3.22828i	−1.16474	−	0.312090i	−0.375880	−	0.926668i	$-0.622659\pi$
$107$	−12.0481	−	3.22828i	−1.16474	−	0.312090i	−0.788856	+	0.614578i	$0.789326\pi$
$108$	0.258819	+	0.965926i	0.0249049	+	0.0929463i
$109$	−1.07788	−	1.07788i	−0.103242	−	0.103242i	0.653599	−	0.756841i	$-0.273258\pi$
$109$	−1.07788	−	1.07788i	−0.103242	−	0.103242i	−0.756841	+	0.653599i	$0.773258\pi$
$110$	−8.84785	+	9.34830i	−0.843610	+	0.891326i
$111$	−3.52552	+	0.944659i	−0.334627	+	0.0896631i
$112$	−3.94441			−0.372711
$113$	−8.17239	+	2.18978i	−0.768793	+	0.205998i	−0.621838	−	0.783146i	$-0.713614\pi$
$113$	−8.17239	+	2.18978i	−0.768793	+	0.205998i	−0.146955	+	0.989143i	$0.546947\pi$
$114$	1.07931	+	1.86942i	0.101087	+	0.175087i
$115$	−2.76194	−	9.27927i	−0.257552	−	0.865297i
$116$		−	5.82563i		−	0.540896i
$117$	−2.39816	+	2.69236i	−0.221710	+	0.248909i
$118$	1.39063	+	1.39063i	0.128018	+	0.128018i
$119$	4.07895	−	15.2229i	0.373917	−	1.39548i
$120$	−0.637899	−	2.14315i	−0.0582320	−	0.195642i
$121$	−19.1695	−	11.0675i	−1.74268	−	1.00614i
$122$			2.85896i			0.258838i
$123$	−0.0298847	+	0.0517618i	−0.00269461	+	0.00466721i
$124$	1.03655	+	3.86846i	0.0930851	+	0.347398i
$125$	−11.1423	+	0.921206i	−0.996600	+	0.0823952i
$126$	−1.97220	+	3.41596i	−0.175698	+	0.304318i
$127$	3.31300	−	12.3643i	0.293981	−	1.09715i	−0.648043	−	0.761604i	$-0.724412\pi$
$127$	3.31300	−	12.3643i	0.293981	−	1.09715i	0.942023	−	0.335547i	$-0.108921\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	10.6779			0.940137
$130$	5.19491	−	6.16546i	0.455623	−	0.540747i
$131$	13.9900			1.22231			0.611156	−	0.791510i	$-0.290705\pi$
$131$	13.9900			1.22231			0.611156	+	0.791510i	$0.290705\pi$
$132$	4.98511	−	2.87815i	0.433898	−	0.250511i
$133$	−2.20371	+	8.22434i	−0.191086	+	0.713141i
$134$	−1.36242	+	2.35978i	−0.117695	+	0.203854i
$135$	−2.17497	−	0.519137i	−0.187192	−	0.0446802i
$136$	−1.03411	−	3.85935i	−0.0886742	−	0.330937i
$137$	−4.16740	+	7.21815i	−0.356045	+	0.616688i	−0.987296	−	0.158890i	$-0.949208\pi$
$137$	−4.16740	+	7.21815i	−0.356045	+	0.616688i	0.631251	+	0.775579i	$0.282542\pi$
$138$			4.32974i			0.368572i
$139$	−1.77925	−	1.02725i	−0.150914	−	0.0871305i	0.422641	−	0.906297i	$-0.361103\pi$
$139$	−1.77925	−	1.02725i	−0.150914	−	0.0871305i	−0.573556	+	0.819167i	$0.694436\pi$
$140$	4.19832	−	7.75667i	0.354822	−	0.655558i
$141$	−3.48257	+	12.9971i	−0.293285	+	1.09456i
$142$	9.05102	+	9.05102i	0.759545	+	0.759545i
$143$	18.5429	+	9.32297i	1.55063	+	0.779626i
$144$			1.00000i			0.0833333i
$145$	11.4561	+	6.20064i	0.951376	+	0.514935i
$146$	2.29908	+	3.98212i	0.190273	+	0.329562i
$147$	−8.26673	+	2.21506i	−0.681828	+	0.182695i
$148$	−3.64988			−0.300018
$149$	17.1570	−	4.59720i	1.40555	−	0.376617i	0.525218	−	0.850968i	$-0.323984\pi$
$149$	17.1570	−	4.59720i	1.40555	−	0.376617i	0.880336	+	0.474351i	$0.157317\pi$
$150$	4.89346	+	1.02668i	0.399549	+	0.0838280i
$151$	−10.3481	−	10.3481i	−0.842114	−	0.842114i	0.147019	−	0.989134i	$-0.453032\pi$
$151$	−10.3481	−	10.3481i	−0.842114	−	0.842114i	−0.989134	+	0.147019i	$0.953032\pi$
$152$	0.558691	+	2.08506i	0.0453159	+	0.169121i
$153$	−3.85935	−	1.03411i	−0.312010	−	0.0836029i
$154$	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	$0.00227725\pi$
$158$	−1.24977	−	2.16466i	−0.0994262	−	0.172211i
$159$	5.08345	−	2.93493i	0.403144	−	0.232755i
$160$	−0.0614757	−	2.23522i	−0.00486008	−	0.176710i
$161$	−12.0761	+	12.0761i	−0.951734	+	0.951734i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−19.4367	−	11.2218i	−1.52240	−	0.878957i	−0.999650	−	0.0264701i	$-0.991573\pi$
$163$	−19.4367	−	11.2218i	−1.52240	−	0.878957i	−0.522749	−	0.852487i	$-0.675093\pi$
$164$	−0.0422634	+	0.0422634i	−0.00330021	+	0.00330021i
$165$	0.353873	+	12.8666i	0.0275490	+	1.00167i
$166$	10.4032	−	6.00627i	0.807442	−	0.466177i
$167$	−7.16686	−	12.4134i	−0.554589	−	0.960576i	−0.997935	−	0.0642254i	$-0.979542\pi$
$167$	−7.16686	−	12.4134i	−0.554589	−	0.960576i	0.443347	−	0.896350i	$-0.353791\pi$
$168$	−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
$172$	10.3141	+	2.76364i	0.786440	+	0.210726i
$173$	−2.31128	−	8.62581i	−0.175723	−	0.655808i	−0.996427	−	0.0844546i	$-0.973085\pi$
$173$	−2.31128	−	8.62581i	−0.175723	−	0.655808i	0.820704	−	0.571353i	$-0.193581\pi$
$174$	−4.11934	−	4.11934i	−0.312287	−	0.312287i
$175$	10.7849	+	16.5120i	0.815261	+	1.24819i
$176$	5.56016	−	1.48984i	0.419113	−	0.112301i
$177$	1.96665			0.147823
$178$	−8.00537	+	2.14503i	−0.600028	+	0.160777i
$179$	−4.09709	−	7.09637i	−0.306231	−	0.530408i	0.671304	−	0.741182i	$-0.265735\pi$
$179$	−4.09709	−	7.09637i	−0.306231	−	0.530408i	−0.977535	+	0.210775i	$0.932401\pi$
$180$	−1.96650	−	1.06437i	−0.146574	−	0.0793336i
$181$		−	14.8291i		−	1.10224i	−0.834426	−	0.551120i	$-0.814201\pi$
$181$		−	14.8291i		−	1.10224i	0.834426	−	0.551120i	$-0.185799\pi$
$182$	−13.9267	−	2.88212i	−1.03231	−	0.213637i
$183$	2.02159	+	2.02159i	0.149440	+	0.149440i
$184$	−1.12062	+	4.18221i	−0.0826131	+	0.308316i
$185$	3.88483	−	7.17748i	0.285619	−	0.527699i
$186$	3.46837	+	2.00246i	0.254313	+	0.146828i
$187$			22.9993i			1.68188i
$188$	−6.72781	+	11.6529i	−0.490676	+	0.849875i
$189$	1.02089	+	3.81000i	0.0742586	+	0.277137i
$190$	−4.69493	−	1.12062i	−0.340606	−	0.0812982i
$191$	7.09233	−	12.2843i	0.513183	−	0.888859i	−0.486700	−	0.873569i	$-0.661799\pi$
$191$	7.09233	−	12.2843i	0.513183	−	0.888859i	0.999883	−	0.0152901i	$-0.00486717\pi$
$192$	−0.258819	+	0.965926i	−0.0186787	+	0.0697097i
$193$	16.4778	−	9.51346i	1.18610	−	0.684794i	0.228680	−	0.973502i	$-0.426559\pi$
$193$	16.4778	−	9.51346i	1.18610	−	0.684794i	0.957417	+	0.288708i	$0.0932256\pi$
$194$	9.53896			0.684857
$195$	−0.686287	−	8.03300i	−0.0491461	−	0.575255i
$196$	−8.55834			−0.611310
$197$	−2.51498	+	1.45202i	−0.179185	+	0.103452i	−0.586910	−	0.809652i	$-0.699656\pi$
$197$	−2.51498	+	1.45202i	−0.179185	+	0.103452i	0.407725	+	0.913105i	$0.366322\pi$
$198$	1.48984	−	5.56016i	0.105878	−	0.395144i
$199$	4.54977	−	7.88044i	0.322525	−	0.558630i	−0.658483	−	0.752595i	$-0.728802\pi$
$199$	4.54977	−	7.88044i	0.322525	−	0.558630i	0.981008	+	0.193966i	$0.0621351\pi$
$200$	4.46099	+	2.25822i	0.315440	+	0.159680i
$201$	0.705239	+	2.63199i	0.0497437	+	0.185646i
$202$	−3.27266	+	5.66842i	−0.230264	+	0.398829i
$203$		−	22.9787i		−	1.61279i
$204$	−3.46020	−	1.99775i	−0.242263	−	0.139870i
$205$	−0.0381269	−	0.128095i	−0.00266290	−	0.00894652i
$206$	2.10902	−	7.87096i	0.146942	−	0.548396i
$207$	3.06159	+	3.06159i	0.212795	+	0.212795i
$208$	−3.42305	+	1.13258i	−0.237346	+	0.0785300i
$209$		−	12.4257i		−	0.859501i
$210$	−2.51613	−	8.45345i	−0.173630	−	0.583343i
$211$	−0.853215	−	1.47781i	−0.0587377	−	0.101737i	0.835161	−	0.550005i	$-0.185374\pi$
$211$	−0.853215	−	1.47781i	−0.0587377	−	0.101737i	−0.893899	+	0.448268i	$0.852041\pi$
$212$	5.66985	−	1.51923i	0.389407	−	0.104341i
$213$	12.8001			0.877046
$214$	−12.0481	+	3.22828i	−0.823592	+	0.220681i
$215$	−16.4127	+	17.3410i	−1.11934	+	1.18265i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	4.08858	+	15.2588i	0.277551	+	1.03583i
$218$	−1.47241	−	0.394532i	−0.0997244	−	0.0267211i
$219$	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
$223$	13.0458	+	22.5960i	0.873613	+	1.51314i	0.858233	+	0.513261i	$0.171563\pi$
$223$	13.0458	+	22.5960i	0.873613	+	1.51314i	0.0153806	+	0.999882i	$0.495104\pi$
$224$	−3.41596	+	1.97220i	−0.228238	+	0.131773i
$225$	4.18617	−	2.73423i	0.279078	−	0.182282i
$226$	−5.98260	+	5.98260i	−0.397957	+	0.397957i
$227$	3.98974	+	2.30348i	0.264808	+	0.152887i	0.626526	−	0.779401i	$-0.284476\pi$
$227$	3.98974	+	2.30348i	0.264808	+	0.152887i	−0.361718	+	0.932288i	$0.617810\pi$
$228$	1.86942	+	1.07931i	0.123805	+	0.0714790i
$229$	−3.74685	+	3.74685i	−0.247599	+	0.247599i	−0.819985	−	0.572386i	$-0.806018\pi$
$229$	−3.74685	+	3.74685i	−0.247599	+	0.247599i	0.572386	+	0.819985i	$0.306018\pi$
$230$	−7.03154	−	6.65512i	−0.463646	−	0.438825i
$231$	19.6633	−	11.3526i	1.29375	−	0.746947i
$232$	−2.91282	−	5.04514i	−0.191236	−	0.331230i
$233$	−8.41343	+	8.41343i	−0.551182	+	0.551182i	−0.926782	−	0.375600i	$-0.877437\pi$
$233$	−8.41343	+	8.41343i	−0.551182	+	0.551182i	0.375600	+	0.926782i	$0.377437\pi$
$234$	−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
$237$	−2.41437	−	0.646927i	−0.156830	−	0.0420224i
$238$	−4.07895	−	15.2229i	−0.264399	−	0.986751i
$239$	−4.88289	−	4.88289i	−0.315848	−	0.315848i	0.531322	−	0.847170i	$-0.321695\pi$
$239$	−4.88289	−	4.88289i	−0.315848	−	0.315848i	−0.847170	+	0.531322i	$0.821695\pi$
$240$	−1.62401	−	1.53707i	−0.104829	−	0.0992175i
$241$	8.02186	−	2.14945i	0.516733	−	0.138458i	0.00897808	−	0.999960i	$-0.497142\pi$
$241$	8.02186	−	2.14945i	0.516733	−	0.138458i	0.507755	+	0.861501i	$0.330475\pi$
$242$	−22.1351			−1.42289
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	1.42948	+	2.47593i	0.0915130	+	0.158505i
$245$	9.10926	−	16.8300i	0.581969	−	1.07523i
$246$			0.0597694i			0.00381076i
$247$	0.449066	+	7.77004i	0.0285734	+	0.494396i
$248$	2.83191	+	2.83191i	0.179827	+	0.179827i
$249$	3.10907	−	11.6032i	0.197030	−	0.735324i
$250$	−9.18893	+	6.36895i	−0.581159	+	0.402808i
$251$	22.9835	+	13.2695i	1.45071	+	0.837565i	0.998521	−	0.0543591i	$-0.0173116\pi$
$251$	22.9835	+	13.2695i	1.45071	+	0.837565i	0.452184	+	0.891924i	$0.350645\pi$
$252$			3.94441i			0.248474i
$253$	12.4616	−	21.5842i	0.783457	−	1.35699i
$254$	−3.31300	−	12.3643i	−0.207876	−	0.775803i
$255$	7.61151	−	4.67813i	0.476651	−	0.292956i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.18509	−	19.3510i	0.323437	−	1.20708i	−0.592437	−	0.805617i	$-0.701834\pi$
$257$	5.18509	−	19.3510i	0.323437	−	1.20708i	0.915874	−	0.401466i	$-0.131499\pi$
$258$	9.24733	−	5.33895i	0.575714	−	0.332389i
$259$	−14.3966			−0.894562
$260$	1.41619	−	7.93690i	0.0878283	−	0.492226i
$261$	−5.82563			−0.360597
$262$	12.1157	−	6.99500i	0.748510	−	0.432153i
$263$	−4.06256	+	15.1617i	−0.250508	+	0.934910i	0.720026	+	0.693947i	$0.244130\pi$
$263$	−4.06256	+	15.1617i	−0.250508	+	0.934910i	−0.970534	+	0.240963i	$0.922537\pi$
$264$	2.87815	−	4.98511i	0.177138	−	0.306812i
$265$	−3.04727	+	12.7668i	−0.187192	+	0.784257i
$266$	2.20371	+	8.22434i	0.135118	+	0.504267i
$267$	−4.14388	+	7.17742i	−0.253602	+	0.439251i
$268$			2.72484i			0.166446i
$269$	−7.38580	−	4.26419i	−0.450320	−	0.259992i	0.257645	−	0.966240i	$-0.417053\pi$
$269$	−7.38580	−	4.26419i	−0.450320	−	0.259992i	−0.707965	+	0.706247i	$0.750387\pi$
$270$	−2.14315	+	0.637899i	−0.130428	+	0.0388213i
$271$	−5.38936	+	20.1134i	−0.327380	+	1.22180i	0.584517	+	0.811382i	$0.301284\pi$
$271$	−5.38936	+	20.1134i	−0.327380	+	1.22180i	−0.911897	+	0.410419i	$0.865383\pi$
$272$	−2.82524	−	2.82524i	−0.171305	−	0.171305i
$273$	−11.8856	+	7.80967i	−0.719349	+	0.472663i
$274$			8.33481i			0.503524i
$275$	−21.4395	−	19.2022i	−1.29285	−	1.15794i
$276$	2.16487	+	3.74966i	0.130310	+	0.225703i
$277$	26.8528	−	7.19517i	1.61343	−	0.432316i	0.664365	−	0.747409i	$-0.268702\pi$
$277$	26.8528	−	7.19517i	1.61343	−	0.432316i	0.949061	+	0.315093i	$0.102036\pi$
$278$	−2.05451			−0.123221
$279$	3.86846	−	1.03655i	0.231599	−	0.0620567i
$280$	−0.242485	−	8.81663i	−0.0144913	−	0.526894i
$281$	2.84766	+	2.84766i	0.169877	+	0.169877i	0.786925	−	0.617048i	$-0.211672\pi$
$281$	2.84766	+	2.84766i	0.169877	+	0.169877i	−0.617048	+	0.786925i	$0.711672\pi$
$282$	3.48257	+	12.9971i	0.207384	+	0.773968i
$283$	−27.4548	−	7.35650i	−1.63202	−	0.437299i	−0.677519	−	0.735505i	$-0.736945\pi$
$283$	−27.4548	−	7.35650i	−1.63202	−	0.437299i	−0.954501	+	0.298207i	$0.903612\pi$
$284$	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
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−0.897213	+	0.518006i	−0.0527772	+	0.0304709i
$290$	13.0216	−	0.358135i	0.764654	−	0.0210304i
$291$	6.74506	−	6.74506i	0.395403	−	0.395403i
$292$	3.98212	+	2.29908i	0.233036	+	0.134543i
$293$	2.70934	+	1.56424i	0.158281	+	0.0913838i	0.577049	−	0.816710i	$-0.304204\pi$
$293$	2.70934	+	1.56424i	0.158281	+	0.0913838i	−0.418767	+	0.908094i	$0.637538\pi$
$294$	−6.05166	+	6.05166i	−0.352940	+	0.352940i
$295$	−3.02289	+	3.19387i	−0.175999	+	0.185954i
$296$	−3.16089	+	1.82494i	−0.183723	+	0.106073i
$297$	−2.87815	−	4.98511i	−0.167007	−	0.289265i
$298$	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
$302$	−14.1357	−	3.78766i	−0.813420	−	0.217955i
$303$	1.69406	+	6.32230i	0.0973209	+	0.363207i
$304$	1.52637	+	1.52637i	0.0875435	+	0.0875435i
$305$	−6.39040	+	0.175756i	−0.365914	+	0.0100638i
$306$	−3.85935	+	1.03411i	−0.220625	+	0.0591162i
$307$	27.4796			1.56835			0.784173	−	0.620542i	$-0.213088\pi$
$307$	27.4796			1.56835			0.784173	+	0.620542i	$0.213088\pi$
$308$	21.9315	−	5.87654i	1.24967	−	0.334847i
$309$	−4.07431	−	7.05691i	−0.231779	−	0.401454i
$310$	−8.58316	+	2.55474i	−0.487491	+	0.145100i
$311$		−	8.90153i		−	0.504759i	−0.967628	−	0.252380i	$-0.918787\pi$
$311$		−	8.90153i		−	0.504759i	0.967628	−	0.252380i	$-0.0812132\pi$
$312$	−1.61961	+	3.22131i	−0.0916923	+	0.182371i
$313$	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
$315$	−7.75667	−	4.19832i	−0.437039	−	0.236548i
$316$	−2.16466	−	1.24977i	−0.121772	−	0.0703049i
$317$			16.5893i			0.931750i	0.884850	+	0.465875i	$0.154260\pi$
$317$			16.5893i			0.931750i	−0.884850	+	0.465875i	$0.845740\pi$
$318$	2.93493	−	5.08345i	0.164583	−	0.285066i
$319$	8.67927	+	32.3915i	0.485946	+	1.81357i
$320$	−1.17085	−	1.90502i	−0.0654526	−	0.106494i
$321$	−6.23657	+	10.8020i	−0.348091	+	0.602912i
$322$	−4.42018	+	16.4963i	−0.246327	+	0.919304i
$323$	−7.46925	+	4.31237i	−0.415600	+	0.239947i
$324$	1.00000			0.0555556
$325$	14.1005	+	11.2327i	0.782158	+	0.623081i
$326$	−22.4435			−1.24303
$327$	−1.32013	+	0.762177i	−0.0730033	+	0.0421485i
$328$	−0.0154695	+	0.0577328i	−0.000854158	+	0.00318776i
$329$	−26.5372	+	45.9638i	−1.46304	+	2.53407i
$330$	6.73978	+	10.9659i	0.371012	+	0.603652i
$331$	−1.64893	−	6.15390i	−0.0906335	−	0.338249i	0.905688	−	0.423945i	$-0.139355\pi$
$331$	−1.64893	−	6.15390i	−0.0906335	−	0.338249i	−0.996321	+	0.0856964i	$0.972688\pi$
$332$	6.00627	−	10.4032i	0.329637	−	0.570948i
$333$			3.64988i			0.200012i
$334$	−12.4134	−	7.16686i	−0.679229	−	0.392153i
$335$	−5.35838	−	2.90024i	−0.292760	−	0.158457i
$336$	−1.02089	+	3.81000i	−0.0556940	+	0.207853i
$337$	−15.8216	−	15.8216i	−0.861857	−	0.861857i	0.129697	−	0.991554i	$-0.458600\pi$
$337$	−15.8216	−	15.8216i	−0.861857	−	0.861857i	−0.991554	+	0.129697i	$0.958600\pi$
$338$	−12.9134	+	1.49766i	−0.702399	+	0.0814618i
$339$			8.46068i			0.459521i
$340$	8.56294	−	2.54872i	0.464391	−	0.138224i
$341$	−11.5268	−	19.9650i	−0.624211	−	1.08117i
$342$	2.08506	−	0.558691i	0.112747	−	0.0302106i
$343$	−6.14674			−0.331893
$344$	10.3141	−	2.76364i	0.556097	−	0.149006i
$345$	−9.67793	+	0.266174i	−0.521042	+	0.0143303i
$346$	−6.31453	−	6.31453i	−0.339471	−	0.339471i
$347$	−6.79115	−	25.3449i	−0.364568	−	1.36059i	−0.868006	−	0.496554i	$-0.834598\pi$
$347$	−6.79115	−	25.3449i	−0.364568	−	1.36059i	0.503438	−	0.864031i	$-0.332068\pi$
$348$	−5.62713	−	1.50778i	−0.301646	−	0.0808257i
$349$	21.6505	+	5.80122i	1.15892	+	0.310532i	0.786535	−	0.617545i	$-0.211873\pi$
$349$	21.6505	+	5.80122i	1.15892	+	0.310532i	0.372387	+	0.928078i	$0.378539\pi$
$350$	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
$353$	6.91152	+	11.9711i	0.367863	+	0.637157i	0.989231	−	0.146361i	$-0.0467562\pi$
$353$	6.91152	+	11.9711i	0.367863	+	0.637157i	−0.621368	+	0.783519i	$0.713423\pi$
$354$	1.70317	−	0.983327i	0.0905226	−	0.0522632i
$355$	−19.6746	+	20.7875i	−1.04422	+	1.10328i
$356$	−5.86034	+	5.86034i	−0.310597	+	0.310597i
$357$	−13.6484	−	7.87993i	−0.722352	−	0.417050i
$358$	−7.09637	−	4.09709i	−0.375055	−	0.216538i
$359$	−4.57733	+	4.57733i	−0.241582	+	0.241582i	−0.817504	−	0.575922i	$-0.804643\pi$
$359$	−4.57733	+	4.57733i	−0.241582	+	0.241582i	0.575922	+	0.817504i	$0.304643\pi$
$360$	−2.23522	+	0.0614757i	−0.117807	+	0.00324005i
$361$	−12.4191	+	7.17019i	−0.653638	+	0.377378i
$362$	−7.41456	−	12.8424i	−0.389700	−	0.674981i
$363$	−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
$367$	−16.0270	−	4.29441i	−0.836601	−	0.224167i	−0.185010	−	0.982737i	$-0.559232\pi$
$367$	−16.0270	−	4.29441i	−0.836601	−	0.224167i	−0.651591	+	0.758570i	$0.725898\pi$
$368$	1.12062	+	4.18221i	0.0584163	+	0.218013i
$369$	0.0422634	+	0.0422634i	0.00220014	+	0.00220014i
$370$	−0.224379	−	8.15830i	−0.0116649	−	0.424130i
$371$	22.3642	−	5.99247i	1.16109	−	0.311114i
$372$	4.00493			0.207646
$373$	−8.78910	+	2.35503i	−0.455082	+	0.121939i	−0.479077	−	0.877773i	$-0.659028\pi$
$373$	−8.78910	+	2.35503i	−0.455082	+	0.121939i	0.0239941	+	0.999712i	$0.492362\pi$
$374$	11.4996	+	19.9180i	0.594633	+	1.02993i
$375$	−1.99403	+	11.0011i	−0.102971	+	0.568094i
$376$			13.4556i			0.693920i
$377$	−6.59797	−	19.9414i	−0.339813	−	1.02704i
$378$	2.78912	+	2.78912i	0.143457	+	0.143457i
$379$	2.63393	−	9.82994i	0.135296	−	0.504930i	−0.864701	−	0.502287i	$-0.832492\pi$
$379$	2.63393	−	9.82994i	0.135296	−	0.504930i	0.999997	−	0.00264304i	$-0.000841308\pi$
$380$	−4.62624	+	1.37698i	−0.237321	+	0.0706376i
$381$	−11.0855	−	6.40022i	−0.567927	−	0.327893i
$382$		−	14.1847i		−	0.725751i
$383$	11.4734	−	19.8726i	0.586266	−	1.01544i	−0.408451	−	0.912780i	$-0.633931\pi$
$383$	11.4734	−	19.8726i	0.586266	−	1.01544i	0.994716	−	0.102661i	$-0.0327358\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	−11.7871	+	49.3832i	−0.600727	+	2.51680i
$386$	9.51346	−	16.4778i	0.484222	−	0.838698i
$387$	2.76364	−	10.3141i	0.140484	−	0.524293i
$388$	8.26098	−	4.76948i	0.419388	−	0.242134i
$389$	−4.23516			−0.214731			−0.107366	−	0.994220i	$-0.534242\pi$
$389$	−4.23516			−0.214731			−0.107366	+	0.994220i	$0.534242\pi$
$390$	−4.61084	−	6.61363i	−0.233479	−	0.334894i
$391$	−17.2995			−0.874871
$392$	−7.41174	+	4.27917i	−0.374350	+	0.216131i
$393$	3.62088	−	13.5133i	0.182649	−	0.681656i
$394$	−1.45202	+	2.51498i	−0.0731519	+	0.126703i
$395$	4.76167	−	2.92658i	0.239586	−	0.147252i
$396$	−1.48984	−	5.56016i	−0.0748673	−	0.279409i
$397$	−8.54497	+	14.8003i	−0.428860	+	0.742807i	−0.996772	−	0.0802821i	$-0.974418\pi$
$397$	−8.54497	+	14.8003i	−0.428860	+	0.742807i	0.567912	+	0.823089i	$0.307751\pi$
$398$		−	9.09955i		−	0.456119i
$399$	7.37374	+	4.25723i	0.369149	+	0.213128i
$400$	4.99244	−	0.274824i	0.249622	−	0.0137412i
$401$	−2.85538	+	10.6564i	−0.142591	+	0.532156i	0.857260	+	0.514884i	$0.172165\pi$
$401$	−2.85538	+	10.6564i	−0.142591	+	0.532156i	−0.999851	+	0.0172721i	$0.994502\pi$
$402$	1.92675	+	1.92675i	0.0960975	+	0.0960975i
$403$	7.92950	+	12.0680i	0.394997	+	0.601149i
$404$			6.54533i			0.325642i
$405$	−1.06437	+	1.96650i	−0.0528891	+	0.0977160i
$406$	−11.4893	−	19.9001i	−0.570206	−	0.987625i
$407$	20.2939	−	5.43775i	1.00593	−	0.269539i
$408$	−3.99550			−0.197807
$409$	10.1249	−	2.71296i	0.500645	−	0.134147i	0.000345561	−	1.00000i	$-0.499890\pi$
$409$	10.1249	−	2.71296i	0.500645	−	0.134147i	0.500299	+	0.865853i	$0.333223\pi$
$410$	−0.0970662	−	0.0918698i	−0.00479376	−	0.00453713i
$411$	5.89360	+	5.89360i	0.290710	+	0.290710i
$412$	−2.10902	−	7.87096i	−0.103904	−	0.387774i
$413$	7.49296	+	2.00773i	0.368705	+	0.0987941i
$414$	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
$418$	−6.21283	−	10.7609i	−0.303879	−	0.526335i
$419$	−31.2083	+	18.0181i	−1.52462	+	0.880242i	−0.525049	+	0.851072i	$0.675953\pi$
$419$	−31.2083	+	18.0181i	−1.52462	+	0.880242i	−0.999574	+	0.0291695i	$0.990714\pi$
$420$	−6.40576	−	6.06283i	−0.312569	−	0.295836i
$421$	11.8375	−	11.8375i	0.576926	−	0.576926i	−0.357129	−	0.934055i	$-0.616244\pi$
$421$	11.8375	−	11.8375i	0.576926	−	0.576926i	0.934055	+	0.357129i	$0.116244\pi$
$422$	−1.47781	−	0.853215i	−0.0719388	−	0.0415339i
$423$	11.6529	+	6.72781i	0.566584	+	0.327117i
$424$	4.15062	−	4.15062i	0.201572	−	0.201572i
$425$	−4.10209	+	19.5518i	−0.198981	+	0.948401i
$426$	11.0852	−	6.40004i	0.537079	−	0.310083i
$427$	5.63844	+	9.76607i	0.272863	+	0.472613i
$428$	−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	−0.181378	−	0.983413i	$-0.558056\pi$
$431$	−17.2346	−	4.61800i	−0.830163	−	0.222441i	−0.648785	+	0.760972i	$0.724722\pi$
$432$	0.965926	+	0.258819i	0.0464731	+	0.0124524i
$433$	−9.11056	−	34.0011i	−0.437826	−	1.63399i	−0.734213	−	0.678920i	$-0.762448\pi$
$433$	−9.11056	−	34.0011i	−0.437826	−	1.63399i	0.296387	−	0.955068i	$-0.404218\pi$
$434$	11.1702	+	11.1702i	0.536188	+	0.536188i
$435$	8.95441	−	9.46089i	0.429331	−	0.453615i
$436$	−1.47241	+	0.394532i	−0.0705158	+	0.0188947i
$437$	9.34625			0.447092
$438$	4.44148	−	1.19009i	0.212222	−	0.0568647i
$439$	10.6384	+	18.4262i	0.507743	+	0.879436i	0.999960	+	0.00896365i	$0.00285326\pi$
$439$	10.6384	+	18.4262i	0.507743	+	0.879436i	−0.492217	+	0.870472i	$0.663813\pi$
$440$	3.67194	+	12.3366i	0.175053	+	0.588125i
$441$			8.55834i			0.407540i
$442$	−7.91082	−	12.0395i	−0.376279	−	0.572663i
$443$	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
$445$	−5.28676	−	17.7619i	−0.250616	−	0.841996i
$446$	22.5960	+	13.0458i	1.06995	+	0.617738i
$447$		−	17.7622i		−	0.840124i
$448$	−1.97220	+	3.41596i	−0.0931779	+	0.161389i
$449$	6.95367	+	25.9514i	0.328164	+	1.22472i	0.911093	+	0.412201i	$0.135240\pi$
$449$	6.95367	+	25.9514i	0.328164	+	1.22472i	−0.582929	+	0.812523i	$0.698093\pi$
$450$	2.25822	−	4.46099i	0.106453	−	0.210293i
$451$	0.172025	−	0.297957i	0.00810036	−	0.0140302i
$452$	−2.18978	+	8.17239i	−0.102999	+	0.384397i
$453$	−12.6737	+	7.31719i	−0.595465	+	0.343792i
$454$	4.60695			0.216215
$455$	5.58603	−	31.3064i	0.261877	−	1.46767i
$456$	2.15862			0.101087
$457$	−4.90777	+	2.83350i	−0.229576	+	0.132546i	−0.610376	−	0.792111i	$-0.708982\pi$
$457$	−4.90777	+	2.83350i	−0.229576	+	0.132546i	0.380800	+	0.924657i	$0.375648\pi$
$458$	−1.37144	+	5.11829i	−0.0640833	+	0.239162i
$459$	−1.99775	+	3.46020i	−0.0932469	+	0.161508i
$460$	−9.41705	−	2.24773i	−0.439072	−	0.104801i
$461$	9.72828	+	36.3064i	0.453091	+	1.69096i	0.693639	+	0.720322i	$0.256006\pi$
$461$	9.72828	+	36.3064i	0.453091	+	1.69096i	−0.240548	+	0.970637i	$0.577327\pi$
$462$	11.3526	−	19.6633i	0.528171	−	0.914819i
$463$			14.2949i			0.664342i	0.943219	+	0.332171i	$0.107781\pi$
$463$			14.2949i			0.664342i	−0.943219	+	0.332171i	$0.892219\pi$
$464$	−5.04514	−	2.91282i	−0.234215	−	0.135224i
$465$	−4.26273	+	7.87568i	−0.197680	+	0.365226i
$466$	−3.07953	+	11.4930i	−0.142657	+	0.532401i
$467$	13.2534	+	13.2534i	0.613296	+	0.613296i	0.943803	−	0.330507i	$-0.107220\pi$
$467$	13.2534	+	13.2534i	0.613296	+	0.613296i	−0.330507	+	0.943803i	$0.607220\pi$
$468$	1.13258	+	3.42305i	0.0523534	+	0.158231i
$469$			10.7479i			0.496290i
$470$	−26.4604	−	14.3218i	−1.22053	−	0.660614i
$471$	−8.79641	−	15.2358i	−0.405317	−	0.702030i
$472$	1.89964	−	0.509008i	0.0874381	−	0.0234290i
$473$	−61.4653			−2.82618
$474$	−2.41437	+	0.646927i	−0.110895	+	0.0297144i
$475$	2.21621	−	10.5631i	0.101687	−	0.484668i
$476$	−11.1439	−	11.1439i	−0.510780	−	0.510780i
$477$	−1.51923	−	5.66985i	−0.0695609	−	0.259605i
$478$	−6.67015	−	1.78726i	−0.305086	−	0.0817475i
$479$	−8.14759	−	2.18314i	−0.372273	−	0.0997503i	0.0678315	−	0.997697i	$-0.478392\pi$
$479$	−8.14759	−	2.18314i	−0.372273	−	0.0997503i	−0.440105	+	0.897947i	$0.645059\pi$
$480$	−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
$483$	8.53912	+	14.7902i	0.388544	+	0.672977i
$484$	−19.1695	+	11.0675i	−0.871342	+	0.503069i
$485$	0.586414	+	21.3217i	0.0266277	+	0.968169i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	−25.6419	−	14.8044i	−1.16195	−	0.670850i	−0.210176	−	0.977664i	$-0.567404\pi$
$487$	−25.6419	−	14.8044i	−1.16195	−	0.670850i	−0.951770	+	0.306814i	$0.900737\pi$
$488$	2.47593	+	1.42948i	0.112080	+	0.0647094i
$489$	−15.8700	+	15.8700i	−0.717665	+	0.717665i
$490$	−0.526130	−	19.1298i	−0.0237681	−	0.864197i
$491$	−14.1073	+	8.14488i	−0.636656	+	0.367573i	−0.783325	−	0.621612i	$-0.786478\pi$
$491$	−14.1073	+	8.14488i	−0.636656	+	0.367573i	0.146669	+	0.989186i	$0.453145\pi$
$492$	0.0298847	+	0.0517618i	0.00134731	+	0.00233360i
$493$	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
$497$	48.7683	+	13.0674i	2.18756	+	0.586155i
$498$	−3.10907	−	11.6032i	−0.139321	−	0.519953i
$499$	7.03621	+	7.03621i	0.314984	+	0.314984i	0.846837	−	0.531853i	$-0.178504\pi$
$499$	7.03621	+	7.03621i	0.314984	+	0.314984i	−0.531853	+	0.846837i	$0.678504\pi$
$500$	−4.77337	+	10.1101i	−0.213472	+	0.452139i
$501$	−13.8453	+	3.70984i	−0.618563	+	0.165743i
$502$	26.5391			1.18450
$503$	29.7889	−	7.98192i	1.32822	−	0.355896i	0.476171	−	0.879353i	$-0.342024\pi$
$503$	29.7889	−	7.98192i	1.32822	−	0.355896i	0.852052	+	0.523456i	$0.175358\pi$
$504$	1.97220	+	3.41596i	0.0878489	+	0.152159i
$505$	−12.8714	−	6.96666i	−0.572768	−	0.310012i
$506$		−	24.9233i		−	1.10798i
$507$	−8.07218	+	10.1902i	−0.358498	+	0.452562i
$508$	−9.05127	−	9.05127i	−0.401585	−	0.401585i
$509$	−0.529872	+	1.97751i	−0.0234862	+	0.0876516i	−0.976674	−	0.214727i	$-0.931114\pi$
$509$	−0.529872	+	1.97751i	−0.0234862	+	0.0876516i	0.953188	+	0.302378i	$0.0977806\pi$
$510$	4.25269	−	7.85713i	0.188312	−	0.347920i
$511$	15.7071	+	9.06849i	0.694841	+	0.401167i
$512$			1.00000i			0.0441942i
$513$	1.07931	−	1.86942i	0.0476526	−	0.0825368i
$514$	−5.18509	−	19.3510i	−0.228704	−	0.853536i
$515$	17.7230	+	4.23025i	0.780969	+	0.186407i
$516$	5.33895	−	9.24733i	0.235034	−	0.407091i
$517$	20.0467	−	74.8154i	0.881654	−	3.29038i
$518$	−12.4678	+	7.19831i	−0.547805	+	0.316276i
$519$	−8.93009			−0.391988
$520$	−2.74199	−	7.58165i	−0.120244	−	0.332477i
$521$	19.0196			0.833265			0.416632	−	0.909075i	$-0.363210\pi$
$521$	19.0196			0.833265			0.416632	+	0.909075i	$0.363210\pi$
$522$	−5.04514	+	2.91282i	−0.220820	+	0.127490i
$523$	7.13496	−	26.6281i	0.311990	−	1.16436i	−0.614769	−	0.788707i	$-0.710751\pi$
$523$	7.13496	−	26.6281i	0.311990	−	1.16436i	0.926759	−	0.375656i	$-0.122583\pi$
$524$	6.99500	−	12.1157i	0.305578	−	0.529277i
$525$	18.7407	−	6.14380i	0.817909	−	0.268137i
$526$	4.06256	+	15.1617i	0.177136	+	0.661081i
$527$	−8.00084	+	13.8579i	−0.348522	+	0.603658i
$528$		−	5.75631i		−	0.250511i
$529$	−3.68352	−	2.12668i	−0.160153	−	0.0924644i
$530$	3.74438	+	12.5800i	0.162646	+	0.546440i
$531$	0.509008	−	1.89964i	0.0220890	−	0.0824374i
$532$	6.02064	+	6.02064i	0.261028	+	0.261028i
$533$	−0.0968031	+	0.192536i	−0.00419301	+	0.00833966i
$534$			8.28777i			0.358647i
$535$	−7.95660	−	26.7318i	−0.343994	−	1.15572i
$536$	1.36242	+	2.35978i	0.0588475	+	0.101927i
$537$	−7.91497	+	2.12081i	−0.341556	+	0.0915197i
$538$	−8.52839			−0.367685
$539$	47.5858	−	12.7506i	2.04967	−	0.549206i
$540$	−1.53707	+	1.62401i	−0.0661450	+	0.0698863i
$541$	−13.9866	−	13.9866i	−0.601331	−	0.601331i	0.339335	−	0.940666i	$-0.389798\pi$
$541$	−13.9866	−	13.9866i	−0.601331	−	0.601331i	−0.940666	+	0.339335i	$0.889798\pi$
$542$	5.38936	+	20.1134i	0.231493	+	0.863943i
$543$	−14.3238	−	3.83806i	−0.614694	−	0.164707i
$544$	−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	$0.133860\pi$
$548$	4.16740	+	7.21815i	0.178023	+	0.308344i
$549$	2.47593	−	1.42948i	0.105670	−	0.0610086i
$550$	−28.1682	−	5.90988i	−1.20110	−	0.251998i
$551$	−8.89209	+	8.89209i	−0.378816	+	0.378816i
$552$	3.74966	+	2.16487i	0.159596	+	0.0921430i
$553$	−8.53830	−	4.92959i	−0.363086	−	0.209628i
$554$	19.6576	−	19.6576i	0.835171	−	0.835171i
$555$	−5.92745	−	5.61013i	−0.251606	−	0.238137i
$556$	−1.77925	+	1.02725i	−0.0754572	+	0.0435652i
$557$	4.03120	+	6.98225i	0.170807	+	0.295847i	0.938702	−	0.344729i	$-0.112029\pi$
$557$	4.03120	+	6.98225i	0.170807	+	0.295847i	−0.767895	+	0.640576i	$0.778696\pi$
$558$	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
$562$	3.88997	+	1.04231i	0.164089	+	0.0439674i
$563$	5.99845	+	22.3865i	0.252804	+	0.943479i	0.969299	+	0.245886i	$0.0790788\pi$
$563$	5.99845	+	22.3865i	0.252804	+	0.943479i	−0.716494	+	0.697593i	$0.754254\pi$
$564$	9.51456	+	9.51456i	0.400635	+	0.400635i
$565$	−13.7402	−	13.0047i	−0.578056	−	0.547110i
$566$	−27.4548	+	7.35650i	−1.15401	+	0.309217i
$567$	3.94441			0.165650
$568$	12.3639	−	3.31290i	0.518779	−	0.139006i
$569$	−3.87731	−	6.71570i	−0.162545	−	0.281537i	0.773236	−	0.634119i	$-0.218637\pi$
$569$	−3.87731	−	6.71570i	−0.162545	−	0.281537i	−0.935781	+	0.352582i	$0.885304\pi$
$570$	−2.29757	+	4.24492i	−0.0962347	+	0.177800i
$571$		−	6.07789i		−	0.254352i	−0.991880	−	0.127176i	$-0.959409\pi$
$571$		−	6.07789i		−	0.254352i	0.991880	−	0.127176i	$-0.0405913\pi$
$572$	17.3454	−	11.3971i	0.725246	−	0.476537i
$573$	−10.0301	−	10.0301i	−0.419012	−	0.419012i
$574$	−0.0610179	+	0.227722i	−0.00254684	+	0.00950492i
$575$	14.4434	−	16.1262i	0.602331	−	0.672509i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$		−	10.5553i		−	0.439421i	−0.975565	−	0.219711i	$-0.929489\pi$
$577$		−	10.5553i		−	0.439421i	0.975565	−	0.219711i	$-0.0705113\pi$
$578$	−0.518006	+	0.897213i	−0.0215462	+	0.0373191i
$579$	−4.92453	−	18.3786i	−0.204656	−	0.763788i
$580$	11.0980	−	6.82094i	0.460817	−	0.283224i
$581$	23.6912	−	41.0343i	0.982875	−	1.70239i
$582$	2.46886	−	9.21393i	0.102338	−	0.381930i
$583$	−29.2619	+	16.8944i	−1.21190	+	0.699693i
$584$	4.59815			0.190273
$585$	−7.93690	−	1.41619i	−0.328150	−	0.0585522i
$586$	3.12848			0.129236
$587$	−19.3484	+	11.1708i	−0.798596	+	0.461070i	−0.842980	−	0.537945i	$-0.819201\pi$
$587$	−19.3484	+	11.1708i	−0.798596	+	0.461070i	0.0443840	+	0.999015i	$0.485867\pi$
$588$	−2.21506	+	8.26673i	−0.0913476	+	0.340914i
$589$	4.32256	−	7.48689i	0.178108	−	0.308492i
$590$	−1.02096	+	4.27741i	−0.0420324	+	0.176098i
$591$	0.751622	+	2.80509i	0.0309176	+	0.115386i
$592$	−1.82494	+	3.16089i	−0.0750046	+	0.129912i
$593$		−	44.2328i		−	1.81642i	−0.418510	−	0.908212i	$-0.637447\pi$
$593$		−	44.2328i		−	1.81642i	0.418510	−	0.908212i	$-0.362553\pi$
$594$	−4.98511	−	2.87815i	−0.204541	−	0.118092i
$595$	33.7757	−	10.0532i	1.38467	−	0.412141i
$596$	4.59720	−	17.1570i	0.188309	−	0.702777i
$597$	−6.43435	−	6.43435i	−0.263340	−	0.263340i
$598$	0.900734	+	15.5851i	0.0368337	+	0.637322i
$599$			14.7411i			0.602305i	0.953576	+	0.301153i	$0.0973714\pi$
$599$			14.7411i			0.602305i	−0.953576	+	0.301153i	$0.902629\pi$
$600$	3.33586	−	3.72452i	0.136186	−	0.152053i
$601$	9.96571	+	17.2611i	0.406510	+	0.704096i	0.994496	−	0.104775i	$-0.0334123\pi$
$601$	9.96571	+	17.2611i	0.406510	+	0.704096i	−0.587986	+	0.808871i	$0.700079\pi$
$602$	40.6829	−	10.9009i	1.65811	−	0.444289i
$603$	2.72484			0.110964
$604$	−14.1357	+	3.78766i	−0.575175	+	0.154118i
$605$	−1.36077	−	49.4768i	−0.0553231	−	2.01152i
$606$	4.62825	+	4.62825i	0.188010	+	0.188010i
$607$	10.3477	+	38.6181i	0.420000	+	1.56746i	0.774605	+	0.632446i	$0.217949\pi$
$607$	10.3477	+	38.6181i	0.420000	+	1.56746i	−0.354604	+	0.935016i	$0.615384\pi$
$608$	2.08506	+	0.558691i	0.0845605	+	0.0226579i
$609$	−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
$613$	−14.5815	−	25.2559i	−0.588940	−	1.02007i	−0.994372	−	0.105949i	$-0.966212\pi$
$613$	−14.5815	−	25.2559i	−0.588940	−	1.02007i	0.405431	−	0.914126i	$-0.367121\pi$
$614$	23.7981	−	13.7398i	0.960412	−	0.554494i
$615$	−0.133598	+	0.00367437i	−0.00538719	+	0.000148165i
$616$	16.0550	−	16.0550i	0.646875	−	0.646875i
$617$	14.5620	+	8.40738i	0.586244	+	0.338468i	0.763611	−	0.645677i	$-0.223425\pi$
$617$	14.5620	+	8.40738i	0.586244	+	0.338468i	−0.177367	+	0.984145i	$0.556758\pi$
$618$	−7.05691	−	4.07431i	−0.283871	−	0.163893i
$619$	2.38716	−	2.38716i	0.0959482	−	0.0959482i	−0.657503	−	0.753452i	$-0.728387\pi$
$619$	2.38716	−	2.38716i	0.0959482	−	0.0959482i	0.753452	+	0.657503i	$0.228387\pi$
$620$	−6.15586	+	6.50405i	−0.247225	+	0.261209i
$621$	3.74966	−	2.16487i	0.150469	−	0.0868732i
$622$	−4.45076	−	7.70895i	−0.178459	−	0.309101i
$623$	−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
$627$	−12.0023	−	3.21600i	−0.479324	−	0.128435i
$628$	−4.55336	−	16.9934i	−0.181699	−	0.678109i
$629$	−10.3118	−	10.3118i	−0.411158	−	0.411158i
$630$	−8.81663	+	0.242485i	−0.351263	+	0.00966084i
$631$	14.9043	−	3.99359i	0.593331	−	0.158982i	0.0503556	−	0.998731i	$-0.483965\pi$
$631$	14.9043	−	3.99359i	0.593331	−	0.158982i	0.542975	+	0.839749i	$0.317298\pi$
$632$	−2.49954			−0.0994262
$633$	−1.64828	+	0.441657i	−0.0655134	+	0.0175543i
$634$	8.29467	+	14.3668i	0.329423	+	0.570578i
$635$	27.4332	−	8.16539i	1.08865	−	0.324033i
$636$		−	5.86986i		−	0.232755i
$637$	−29.2956	+	9.69298i	−1.16074	+	0.384050i
$638$	23.7122	+	23.7122i	0.938775	+	0.938775i
$639$	3.31290	−	12.3639i	0.131056	−	0.489109i
$640$	−1.96650	−	1.06437i	−0.0777326	−	0.0420730i
$641$	−14.7904	−	8.53924i	−0.584185	−	0.337280i	0.178610	−	0.983920i	$-0.442840\pi$
$641$	−14.7904	−	8.53924i	−0.584185	−	0.337280i	−0.762795	+	0.646640i	$0.776173\pi$
$642$			12.4731i			0.492275i
$643$	−1.15712	+	2.00420i	−0.0456325	+	0.0790379i	−0.887940	−	0.459960i	$-0.847864\pi$
$643$	−1.15712	+	2.00420i	−0.0456325	+	0.0790379i	0.842307	+	0.538998i	$0.181197\pi$
$644$	4.42018	+	16.4963i	0.174179	+	0.650046i
$645$	12.5022	+	20.3416i	0.492275	+	0.800951i
$646$	−4.31237	+	7.46925i	−0.169668	+	0.293874i
$647$	5.79616	−	21.6316i	0.227871	−	0.850425i	−0.753363	−	0.657604i	$-0.771570\pi$
$647$	5.79616	−	21.6316i	0.227871	−	0.850425i	0.981234	−	0.192820i	$-0.0617635\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−11.3207			−0.444375
$650$	17.8278	+	2.67757i	0.699264	+	0.105023i
$651$	15.7971			0.619136
$652$	−19.4367	+	11.2218i	−0.761199	+	0.439479i
$653$	0.855924	−	3.19435i	0.0334949	−	0.125005i	−0.947154	−	0.320779i	$-0.896055\pi$
$653$	0.855924	−	3.19435i	0.0334949	−	0.125005i	0.980649	+	0.195774i	$0.0627220\pi$
$654$	−0.762177	+	1.32013i	−0.0298035	+	0.0516212i
$655$	16.3802	+	26.6513i	0.640028	+	1.04135i
$656$	0.0154695	+	0.0577328i	0.000603981	+	0.00225409i
$657$	2.29908	−	3.98212i	0.0896955	−	0.155357i
$658$			53.0744i			2.06906i
$659$	7.45456	+	4.30389i	0.290388	+	0.167656i	0.638117	−	0.769939i	$-0.279714\pi$
$659$	7.45456	+	4.30389i	0.290388	+	0.167656i	−0.347729	+	0.937595i	$0.613047\pi$
$660$	11.3198	+	6.12685i	0.440621	+	0.238487i
$661$	11.1441	−	41.5904i	0.433456	−	1.61768i	−0.311280	−	0.950318i	$-0.600758\pi$
$661$	11.1441	−	41.5904i	0.433456	−	1.61768i	0.744735	−	0.667360i	$-0.232576\pi$
$662$	−4.50497	−	4.50497i	−0.175091	−	0.175091i
$663$	−14.1070	−	2.91945i	−0.547872	−	0.113382i
$664$		−	12.0125i		−	0.466177i
$665$	−18.2478	+	5.43137i	−0.707618	+	0.210620i
$666$	1.82494	+	3.16089i	0.0707150	+	0.122482i
$667$	−24.3640	+	6.52831i	−0.943377	+	0.252777i
$668$	−14.3337			−0.554589
$669$	25.2026	−	6.75302i	0.974389	−	0.261087i
$670$	−6.09061	+	0.167511i	−0.235301	+	0.00647152i
$671$	−11.6369	−	11.6369i	−0.449237	−	0.449237i
$672$	1.02089	+	3.81000i	0.0393816	+	0.146974i
$673$	16.2251	+	4.34750i	0.625431	+	0.167584i	0.557596	−	0.830113i	$-0.311724\pi$
$673$	16.2251	+	4.34750i	0.625431	+	0.167584i	0.0678355	+	0.997697i	$0.478391\pi$
$674$	−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	$0.406067\pi$
$678$	4.23034	+	7.32716i	0.162465	+	0.281398i
$679$	32.5847	−	18.8128i	1.25048	−	0.721968i
$680$	6.14136	−	6.48873i	0.235510	−	0.248831i
$681$	3.25761	−	3.25761i	0.124832	−	0.124832i
$682$	−19.9650	−	11.5268i	−0.764499	−	0.441384i
$683$	14.1912	+	8.19327i	0.543010	+	0.313507i	0.746298	−	0.665612i	$-0.231829\pi$
$683$	14.1912	+	8.19327i	0.543010	+	0.313507i	−0.203288	+	0.979119i	$0.565163\pi$
$684$	1.52637	−	1.52637i	0.0583623	−	0.0583623i
$685$	−18.6301	+	0.512388i	−0.711821	+	0.0195773i
$686$	−5.32324	+	3.07337i	−0.203242	+	0.117342i
$687$	2.64942	+	4.58894i	0.101082	+	0.175079i
$688$	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	0.721298	−	0.692625i	$-0.243546\pi$
$691$	26.2776	+	7.04106i	0.999647	+	0.267855i	0.278350	+	0.960480i	$0.410213\pi$
$692$	−8.62581	−	2.31128i	−0.327904	−	0.0878616i
$693$	−5.87654	−	21.9315i	−0.223231	−	0.833111i
$694$	−18.5538	−	18.5538i	−0.704291	−	0.704291i
$695$	−0.126302	−	4.59228i	−0.00479092	−	0.174195i
$696$	−5.62713	+	1.50778i	−0.213296	+	0.0571524i
$697$	−0.238808			−0.00904552
$698$	21.6505	−	5.80122i	0.819482	−	0.219579i
$699$	5.94920	+	10.3043i	0.225019	+	0.389745i
$700$	19.6922	−	1.08402i	0.744296	−	0.0409720i
$701$		−	24.9044i		−	0.940628i	−0.882499	−	0.470314i	$-0.844141\pi$
$701$		−	24.9044i		−	0.940628i	0.882499	−	0.470314i	$-0.155859\pi$
$702$	3.22131	+	1.61961i	0.121581	+	0.0611282i
$703$	5.57108	+	5.57108i	0.210117	+	0.210117i
$704$	1.48984	−	5.56016i	0.0561505	−	0.209557i
$705$	−28.8374	+	8.58333i	−1.08608	+	0.323267i
$706$	11.9711	+	6.91152i	0.450538	+	0.260118i
$707$			25.8174i			0.970964i
$708$	0.983327	−	1.70317i	0.0369557	−	0.0640091i
$709$	9.12847	+	34.0679i	0.342827	+	1.27945i	0.895130	+	0.445804i	$0.147082\pi$
$709$	9.12847	+	34.0679i	0.342827	+	1.27945i	−0.552303	+	0.833643i	$0.686251\pi$
$710$	−6.64499	+	27.8398i	−0.249382	+	1.04481i
$711$	−1.24977	+	2.16466i	−0.0468699	+	0.0811811i
$712$	−2.14503	+	8.00537i	−0.0803885	+	0.300014i
$713$	15.0171	−	8.67015i	0.562396	−	0.324700i
$714$	−15.7599			−0.589798
$715$	3.95048	+	46.2404i	0.147740	+	1.72929i
$716$	−8.19418			−0.306231
$717$	−5.98030	+	3.45273i	−0.223338	+	0.128944i
$718$	−1.67542	+	6.25274i	−0.0625260	+	0.233350i
$719$	21.1479	−	36.6293i	0.788685	−	1.36604i	−0.138088	−	0.990420i	$-0.544096\pi$
$719$	21.1479	−	36.6293i	0.788685	−	1.36604i	0.926773	−	0.375622i	$-0.122571\pi$
$720$	−1.90502	+	1.17085i	−0.0709960	+	0.0436350i
$721$	−8.31882	−	31.0463i	−0.309809	−	1.15622i
$722$	−7.17019	+	12.4191i	−0.266847	+	0.462192i
$723$		−	8.30484i		−	0.308860i
$724$	−12.8424	−	7.41456i	−0.477284	−	0.275560i
$725$	1.60102	+	29.0841i	0.0594604	+	1.08016i
$726$	−5.72897	+	21.3808i	−0.212622	+	0.793517i
$727$	14.2431	+	14.2431i	0.528248	+	0.528248i	0.920050	−	0.391802i	$-0.128148\pi$
$727$	14.2431	+	14.2431i	0.528248	+	0.528248i	−0.391802	+	0.920050i	$0.628148\pi$
$728$	−9.45932	+	10.6198i	−0.350586	+	0.393595i
$729$		−	1.00000i		−	0.0370370i
$730$	−4.89415	+	9.04226i	−0.181140	+	0.334669i
$731$	21.3318	+	36.9477i	0.788983	+	1.36656i
$732$	2.76154	−	0.739952i	0.102069	−	0.0273494i
$733$	15.0682			0.556556			0.278278	−	0.960501i	$-0.410236\pi$
$733$	15.0682			0.556556			0.278278	+	0.960501i	$0.410236\pi$
$734$	−16.0270	+	4.29441i	−0.591566	+	0.158510i
$735$	−13.8988	−	13.1548i	−0.512667	−	0.485222i
$736$	3.06159	+	3.06159i	0.112852	+	0.112852i
$737$	−4.05957	−	15.1505i	−0.149536	−	0.558077i
$738$	0.0577328	+	0.0154695i	0.00212517	+	0.000569439i
$739$	−22.6190	−	6.06075i	−0.832054	−	0.222948i	−0.182445	−	0.983216i	$-0.558401\pi$
$739$	−22.6190	−	6.06075i	−0.832054	−	0.222948i	−0.649610	+	0.760268i	$0.725068\pi$
$740$	−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
$743$	−13.5979	−	23.5522i	−0.498857	−	0.864045i	0.501142	−	0.865365i	$-0.332913\pi$
$743$	−13.5979	−	23.5522i	−0.498857	−	0.864045i	−0.999999	+	0.00131959i	$0.999580\pi$
$744$	3.46837	−	2.00246i	0.127157	−	0.0734139i
$745$	28.8460	+	27.3018i	1.05684	+	1.00026i
$746$	−6.43407	+	6.43407i	−0.235568	+	0.235568i
$747$	−10.4032	−	6.00627i	−0.380632	−	0.219758i
$748$	19.9180	+	11.4996i	0.728273	+	0.420469i
$749$	−34.7890	+	34.7890i	−1.27116	+	1.27116i
$750$	3.77366	+	10.5242i	0.137795	+	0.384291i
$751$	19.3349	−	11.1630i	0.705540	−	0.407344i	−0.103867	−	0.994591i	$-0.533122\pi$
$751$	19.3349	−	11.1630i	0.705540	−	0.407344i	0.809407	+	0.587247i	$0.199788\pi$
$752$	6.72781	+	11.6529i	0.245338	+	0.424938i
$753$	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
$757$	46.1673	+	12.3705i	1.67798	+	0.449613i	0.967245	−	0.253846i	$-0.0816956\pi$
$757$	46.1673	+	12.3705i	1.67798	+	0.449613i	0.710736	+	0.703459i	$0.248362\pi$
$758$	−2.63393	−	9.82994i	−0.0956685	−	0.357040i
$759$	−17.6234	−	17.6234i	−0.639690	−	0.639690i
$760$	−3.31795	+	3.50562i	−0.120355	+	0.127162i
$761$	−32.4685	+	8.69990i	−1.17698	+	0.315371i	−0.793728	−	0.608272i	$-0.791863\pi$
$761$	−32.4685	+	8.69990i	−1.17698	+	0.315371i	−0.383253	+	0.923643i	$0.625196\pi$
$762$	−12.8004			−0.463711
$763$	−5.80780	+	1.55619i	−0.210256	+	0.0563380i
$764$	−7.09233	−	12.2843i	−0.256592	−	0.444430i
$765$	−2.54872	−	8.56294i	−0.0921493	−	0.309594i
$766$		−	22.9469i		−	0.829105i
$767$	7.07906	−	0.409131i	0.255610	−	0.0147729i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−0.495133	+	1.84786i	−0.0178550	+	0.0666356i	−0.974279	−	0.225347i	$-0.927648\pi$
$769$	−0.495133	+	1.84786i	−0.0178550	+	0.0666356i	0.956424	+	0.291983i	$0.0943150\pi$
$770$	14.4836	+	48.6606i	0.521954	+	1.75361i
$771$	−17.3496	−	10.0168i	−0.624832	−	0.360747i
$772$		−	19.0269i		−	0.684794i
$773$	−21.1102	+	36.5639i	−0.759280	+	1.31511i	0.183939	+	0.982938i	$0.441115\pi$
$773$	−21.1102	+	36.5639i	−0.759280	+	1.31511i	−0.943218	+	0.332173i	$0.892218\pi$
$774$	−2.76364	−	10.3141i	−0.0993371	−	0.370731i
$775$	−6.23807	−	19.0282i	−0.224078	−	0.683514i
$776$	4.76948	−	8.26098i	0.171214	−	0.296552i
$777$	−3.72612	+	13.9061i	−0.133674	+	0.498877i
$778$	−3.66776	+	2.11758i	−0.131495	+	0.0759189i
$779$	0.129019			0.00462260
$780$	−7.29992	−	3.42216i	−0.261379	−	0.122533i
$781$	−73.6811			−2.63652
$782$	−14.9818	+	8.64973i	−0.535747	+	0.309314i
$783$	−1.50778	+	5.62713i	−0.0538838	+	0.201097i
$784$	−4.27917	+	7.41174i	−0.152828	+	0.264705i
$785$	38.2639	+	9.13309i	1.36570	+	0.325974i
$786$	−3.62088	−	13.5133i	−0.129153	−	0.482004i
$787$	6.69792	−	11.6011i	0.238755	−	0.413536i	−0.721602	−	0.692308i	$-0.756594\pi$
$787$	6.69792	−	11.6011i	0.238755	−	0.413536i	0.960357	+	0.278772i	$0.0899274\pi$
$788$			2.90405i			0.103452i
$789$	13.5936	+	7.84827i	0.483945	+	0.279406i
$790$	2.66043	−	4.91533i	0.0946540	−	0.174880i
$791$	−8.63740	+	32.2352i	−0.307111	+	1.14615i
$792$	−4.07032	−	4.07032i	−0.144633	−	0.144633i
$793$	7.69735	+	6.85624i	0.273341	+	0.243472i
$794$			17.0899i			0.606499i
$795$	11.5431	+	6.24772i	0.409391	+	0.221584i
$796$	−4.54977	−	7.88044i	−0.161262	−	0.279315i
$797$	−33.1733	+	8.88876i	−1.17506	+	0.314856i	−0.792965	−	0.609268i	$-0.791463\pi$
$797$	−33.1733	+	8.88876i	−1.17506	+	0.314856i	−0.382094	+	0.924124i	$0.624797\pi$
$798$	8.51447			0.301409
$799$	−51.9300	+	13.9146i	−1.83715	+	0.492263i
$800$	4.18617	−	2.73423i	0.148003	−	0.0966695i
$801$	5.86034	+	5.86034i	0.207065	+	0.207065i
$802$	2.85538	+	10.6564i	0.100827	+	0.376291i
$803$	−25.5665	−	6.85052i	−0.902222	−	0.241750i
$804$	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
$808$	3.27266	+	5.66842i	0.115132	+	0.199414i
$809$	−33.1559	+	19.1426i	−1.16570	+	0.673018i	−0.952664	−	0.304026i	$-0.901669\pi$
$809$	−33.1559	+	19.1426i	−1.16570	+	0.673018i	−0.213037	+	0.977044i	$0.568336\pi$
$810$	0.0614757	+	2.23522i	0.00216004	+	0.0785377i
$811$	−13.2953	+	13.2953i	−0.466860	+	0.466860i	−0.900896	−	0.434036i	$-0.857089\pi$
$811$	−13.2953	+	13.2953i	−0.466860	+	0.466860i	0.434036	+	0.900896i	$0.357089\pi$
$812$	−19.9001	−	11.4893i	−0.698357	−	0.403196i
$813$	18.0332	+	10.4114i	0.632450	+	0.365145i
$814$	14.8562	−	14.8562i	0.520709	−	0.520709i
$815$	−1.37973	−	50.1663i	−0.0483299	−	1.75725i
$816$	−3.46020	+	1.99775i	−0.121131	+	0.0699352i
$817$	−11.5248	−	19.9615i	−0.403200	−	0.698363i
$818$	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	−0.317498	−	0.948259i	$-0.602843\pi$
$821$	−30.5611	−	8.18882i	−1.06659	−	0.285792i	−0.749091	+	0.662467i	$0.769509\pi$
$822$	8.05080	+	2.15721i	0.280804	+	0.0752412i
$823$	−5.20135	−	19.4117i	−0.181308	−	0.676649i	−0.995391	−	0.0959011i	$-0.969427\pi$
$823$	−5.20135	−	19.4117i	−0.181308	−	0.676649i	0.814083	−	0.580748i	$-0.197240\pi$
$824$	−5.76194	−	5.76194i	−0.200727	−	0.200727i
$825$	−24.0969	+	15.7390i	−0.838945	+	0.547963i
$826$	7.49296	−	2.00773i	0.260713	−	0.0698580i
$827$	24.4431			0.849970			0.424985	−	0.905200i	$-0.360279\pi$
$827$	24.4431			0.849970			0.424985	+	0.905200i	$0.360279\pi$
$828$	4.18221	−	1.12062i	0.145342	−	0.0389442i
$829$	14.4413	+	25.0131i	0.501568	+	0.868741i	0.999998	+	0.00181104i	$0.000576474\pi$
$829$	14.4413	+	25.0131i	0.501568	+	0.868741i	−0.498431	+	0.866930i	$0.666090\pi$
$830$	23.6226	+	12.7858i	0.819953	+	0.443802i
$831$		−	27.8000i		−	0.964372i
$832$	−0.730685	+	3.53074i	−0.0253319	+	0.122406i
$833$	−24.1794	−	24.1794i	−0.837766	−	0.837766i
$834$	−0.531745	+	1.98450i	−0.0184128	+	0.0687177i
$835$	15.2564	−	28.1872i	0.527970	−	0.975460i
$836$	−10.7609	−	6.21283i	−0.372175	−	0.214875i
$837$		−	4.00493i		−	0.138431i
$838$	−18.0181	+	31.2083i	−0.622425	+	1.07807i
$839$	5.22644	+	19.5054i	0.180437	+	0.673400i	0.995561	+	0.0941139i	$0.0300018\pi$
$839$	5.22644	+	19.5054i	0.180437	+	0.673400i	−0.815125	+	0.579286i	$0.803332\pi$
$840$	−8.57897	−	2.04769i	−0.296003	−	0.0706520i
$841$	2.46899	−	4.27641i	0.0851375	−	0.147462i
$842$	4.33284	−	16.1704i	0.149320	−	0.557268i
$843$	3.48765	−	2.01360i	0.120121	−	0.0693520i
$844$	−1.70643			−0.0587377
$845$	−4.14146	−	28.7724i	−0.142471	−	0.989799i
$846$	13.4556			0.462614
$847$	−75.6124	+	43.6548i	−2.59807	+	1.50000i
$848$	1.51923	−	5.66985i	0.0521707	−	0.194704i
$849$	−14.2117	+	24.6153i	−0.487743	+	0.844796i
$850$	6.22338	+	18.9834i	0.213460	+	0.651125i
$851$	4.09013	+	15.2646i	0.140208	+	0.523262i
$852$	6.40004	−	11.0852i	0.219262	−	0.379772i
$853$			12.5604i			0.430059i	0.976608	+	0.215030i	$0.0689848\pi$
$853$			12.5604i			0.430059i	−0.976608	+	0.215030i	$0.931015\pi$
$854$	9.76607	+	5.63844i	0.334188	+	0.192944i
$855$	1.37698	+	4.62624i	0.0470917	+	0.158214i
$856$	−3.22828	+	12.0481i	−0.110340	+	0.411796i
$857$	15.6057	+	15.6057i	0.533079	+	0.533079i	0.921487	−	0.388408i	$-0.126975\pi$
$857$	15.6057	+	15.6057i	0.533079	+	0.533079i	−0.388408	+	0.921487i	$0.626975\pi$
$858$	4.20605	−	20.3240i	0.143592	−	0.693850i
$859$		−	27.8178i		−	0.949132i	−0.880220	−	0.474566i	$-0.842605\pi$
$859$		−	27.8178i		−	0.949132i	0.880220	−	0.474566i	$-0.157395\pi$
$860$	6.81142	+	22.8843i	0.232268	+	0.780349i
$861$	0.117877	+	0.204170i	0.00401725	+	0.00695809i
$862$	−17.2346	+	4.61800i	−0.587014	+	0.157290i
$863$	8.10977			0.276060			0.138030	−	0.990428i	$-0.455923\pi$
$863$	8.10977			0.276060			0.138030	+	0.990428i	$0.455923\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	13.7262	−	14.5026i	0.466705	−	0.493102i
$866$	−24.8905	−	24.8905i	−0.845814	−	0.845814i
$867$	0.268140	+	1.00071i	0.00910650	+	0.0339859i
$868$	15.2588	+	4.08858i	0.517917	+	0.138776i
$869$	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
$873$	−4.76948	−	8.26098i	−0.161422	−	0.279592i
$874$	8.09409	−	4.67312i	0.273787	−	0.158071i
$875$	−18.8281	+	39.8785i	−0.636507	+	1.34814i
$876$	3.25139	−	3.25139i	0.109854	−	0.109854i
$877$	33.4115	+	19.2902i	1.12823	+	0.651382i	0.943488	−	0.331405i	$-0.107523\pi$
$877$	33.4115	+	19.2902i	1.12823	+	0.651382i	0.184739	+	0.982788i	$0.440856\pi$
$878$	18.4262	+	10.6384i	0.621855	+	0.359028i
$879$	2.21217	−	2.21217i	0.0746146	−	0.0746146i
$880$	9.34830	+	8.84785i	0.315131	+	0.298261i
$881$	−36.9213	+	21.3165i	−1.24391	+	0.718172i	−0.969888	−	0.243552i	$-0.921687\pi$
$881$	−36.9213	+	21.3165i	−1.24391	+	0.718172i	−0.274022	+	0.961723i	$0.588354\pi$
$882$	4.27917	+	7.41174i	0.144087	+	0.249566i
$883$	−6.29479	+	6.29479i	−0.211837	+	0.211837i	−0.805047	−	0.593211i	$-0.797860\pi$
$883$	−6.29479	+	6.29479i	−0.211837	+	0.211837i	0.593211	+	0.805047i	$0.297860\pi$
$884$	−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
$887$	−14.2396	−	3.81548i	−0.478117	−	0.128111i	0.0117085	−	0.999931i	$-0.496273\pi$
$887$	−14.2396	−	3.81548i	−0.478117	−	0.128111i	−0.489826	+	0.871820i	$0.662940\pi$
$888$	0.944659	+	3.52552i	0.0317007	+	0.118309i
$889$	−35.7019	−	35.7019i	−1.19740	−	1.19740i
$890$	−13.4594	−	12.7389i	−0.451161	−	0.427009i
$891$	−5.56016	+	1.48984i	−0.186273	+	0.0499116i
$892$	26.0917			0.873613
$893$	28.0558	−	7.51754i	0.938852	−	0.251565i
$894$	−8.88110	−	15.3825i	−0.297029	−	0.514468i
$895$	8.72166	−	16.1138i	0.291533	−	0.538626i
$896$			3.94441i			0.131773i
$897$	11.6572	+	10.3834i	0.389224	+	0.346692i
$898$	18.9978	+	18.9978i	0.633964	+	0.633964i
$899$	−6.03857	+	22.5362i	−0.201398	+	0.751626i
$900$	−0.274824	−	4.99244i	−0.00916079	−	0.166415i
$901$	20.3109	+	11.7265i	0.676654	+	0.390667i
$902$		−	0.344051i		−	0.0114556i
$903$	21.0590	−	36.4752i	0.700799	−	1.21382i
$904$	2.18978	+	8.17239i	0.0728311	+	0.271810i
$905$	28.2498	−	17.3627i	0.939055	−	0.577155i
$906$	−7.31719	+	12.6737i	−0.243097	+	0.421057i
$907$	−8.01244	+	29.9028i	−0.266049	+	0.992907i	0.695557	+	0.718471i	$0.255158\pi$
$907$	−8.01244	+	29.9028i	−0.266049	+	0.992907i	−0.961605	+	0.274436i	$0.911509\pi$
$908$	3.98974	−	2.30348i	0.132404	−	0.0764435i
$909$	6.54533			0.217095
$910$	−10.8155	−	29.9051i	−0.358532	−	0.991345i
$911$	13.4035			0.444077			0.222038	−	0.975038i	$-0.428729\pi$
$911$	13.4035			0.444077			0.222038	+	0.975038i	$0.428729\pi$
$912$	1.86942	−	1.07931i	0.0619026	−	0.0357395i
$913$	−17.8968	+	66.7917i	−0.592297	+	2.21048i
$914$	−2.83350	+	4.90777i	−0.0937240	+	0.162335i
$915$	−1.48419	+	6.21815i	−0.0490658	+	0.205566i
$916$	1.37144	+	5.11829i	0.0453137	+	0.169113i
$917$	27.5911	−	47.7892i	0.911140	−	1.57814i
$918$			3.99550i			0.131871i
$919$	−32.8083	−	18.9419i	−1.08224	−	0.624834i	−0.150744	−	0.988573i	$-0.548167\pi$
$919$	−32.8083	−	18.9419i	−1.08224	−	0.624834i	−0.931501	+	0.363739i	$0.881500\pi$
$920$	−9.27927	+	2.76194i	−0.305929	+	0.0910584i
$921$	7.11225	−	26.5433i	0.234357	−	0.874631i
$922$	26.5782	+	26.5782i	0.875305	+	0.875305i
$923$	46.0744	−	2.66285i	1.51656	−	0.0876489i
$924$		−	22.7052i		−	0.746947i
$925$	18.2218	−	1.00307i	0.599130	−	0.0329809i
$926$	7.14747	+	12.3798i	0.234880	+	0.406825i
$927$	−7.87096	+	2.10902i	−0.258516	+	0.0692692i
$928$	−5.82563			−0.191236
$929$	−37.8082	+	10.1307i	−1.24045	+	0.332376i	−0.818638	−	0.574309i	$-0.805271\pi$
$929$	−37.8082	+	10.1307i	−1.24045	+	0.332376i	−0.421807	+	0.906686i	$0.638604\pi$
$930$	0.246206	+	8.95191i	0.00807341	+	0.293545i
$931$	13.0632	+	13.0632i	0.428130	+	0.428130i
$932$	3.07953	+	11.4930i	0.100873	+	0.376465i
$933$	−8.59821	−	2.30388i	−0.281493	−	0.0754258i
$934$	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	$0.963639\pi$
$938$	5.37393	+	9.30792i	0.175465	+	0.303914i
$939$	12.4702	−	7.19968i	0.406950	−	0.234953i
$940$	−30.0763	+	0.827193i	−0.980981	+	0.0269801i
$941$	33.2518	−	33.2518i	1.08398	−	1.08398i	0.0878430	−	0.996134i	$-0.472003\pi$
$941$	33.2518	−	33.2518i	1.08398	−	1.08398i	0.996134	−	0.0878430i	$-0.0279974\pi$
$942$	−15.2358	−	8.79641i	−0.496410	−	0.286603i
$943$	0.224115	+	0.129393i	0.00729819	+	0.00421361i
$944$	1.39063	−	1.39063i	0.0452613	−	0.0452613i
$945$	−6.06283	+	6.40576i	−0.197224	+	0.208379i
$946$	−53.2305	+	30.7326i	−1.73067	+	0.999204i
$947$	−30.0812	−	52.1022i	−0.977507	−	1.69309i	−0.671400	−	0.741096i	$-0.734307\pi$
$947$	−30.0812	−	52.1022i	−0.977507	−	1.69309i	−0.306108	−	0.951997i	$-0.599027\pi$
$948$	−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
$952$	−15.2229	−	4.07895i	−0.493376	−	0.132200i
$953$	2.65433	+	9.90608i	0.0859821	+	0.320890i	0.995498	−	0.0947788i	$-0.0302144\pi$
$953$	2.65433	+	9.90608i	0.0859821	+	0.320890i	−0.909516	+	0.415668i	$0.863548\pi$
$954$	−4.15062	−	4.15062i	−0.134381	−	0.134381i
$955$	31.7059	−	0.872012i	1.02598	−	0.0282176i
$956$	−6.67015	+	1.78726i	−0.215728	+	0.0578042i
$957$	33.5341			1.08400
$958$	−8.14759	+	2.18314i	−0.263237	+	0.0705341i
$959$	16.4379	+	28.4713i	0.530808	+	0.919387i
$960$	−2.14315	+	0.637899i	−0.0691698	+	0.0205881i
$961$			14.9605i			0.482598i
$962$	−8.75300	+	9.82682i	−0.282208	+	0.316829i
$963$	8.81983	+	8.81983i	0.284215	+	0.284215i
$964$	2.14945	−	8.02186i	0.0692291	−	0.258367i
$965$	37.4164	+	20.2517i	1.20448	+	0.651926i
$966$	14.7902	+	8.53912i	0.475867	+	0.274742i
$967$		−	28.1172i		−	0.904190i	−0.891970	−	0.452095i	$-0.850677\pi$
$967$		−	28.1172i		−	0.904190i	0.891970	−	0.452095i	$-0.149323\pi$
$968$	−11.0675	+	19.1695i	−0.355724	+	0.616132i
$969$	2.23225	+	8.33087i	0.0717102	+	0.267626i
$970$	11.1687	+	18.1719i	0.358605	+	0.583465i
$971$	9.68270	−	16.7709i	0.310733	−	0.538205i	−0.667789	−	0.744351i	$-0.732759\pi$
$971$	9.68270	−	16.7709i	0.310733	−	0.538205i	0.978521	+	0.206146i	$0.0660923\pi$
$972$	0.258819	−	0.965926i	0.00830162	−	0.0309821i
$973$	−7.01811	+	4.05190i	−0.224990	+	0.129898i
$974$	−29.6087			−0.948725
$975$	14.4995	−	10.7128i	0.464355	−	0.343085i
$976$	2.85896			0.0915130
$977$	−37.0322	+	21.3806i	−1.18477	+	0.684025i	−0.957112	−	0.289717i	$-0.906439\pi$
$977$	−37.0322	+	21.3806i	−1.18477	+	0.684025i	−0.227653	+	0.973742i	$0.573105\pi$
$978$	−5.80882	+	21.6788i	−0.185745	+	0.693212i
$979$	23.8535	−	41.3154i	0.762360	−	1.32045i
$980$	−10.0205	−	16.3038i	−0.320095	−	0.520807i
$981$	0.394532	+	1.47241i	0.0125964	+	0.0470105i
$982$	−8.14488	+	14.1073i	−0.259914	+	0.450184i
$983$			25.0799i			0.799926i	0.916531	+	0.399963i	$0.130977\pi$
$983$			25.0799i			0.799926i	−0.916531	+	0.399963i	$0.869023\pi$
$984$	0.0517618	+	0.0298847i	0.00165011	+	0.000952690i
$985$	−5.71080	−	3.09098i	−0.181961	−	0.0984870i
$986$	6.02435	−	22.4832i	0.191854	−	0.716010i
$987$	37.5293	+	37.5293i	1.19457	+	1.19457i
$988$	6.95359	+	3.49612i	0.221223	+	0.111226i
$989$		−	46.2325i		−	1.47011i
$990$	12.3366	−	3.67194i	0.392083	−	0.116702i
$991$	15.7008	+	27.1946i	0.498753	+	0.863865i	0.999999	−	0.00143950i	$-0.000458209\pi$
$991$	15.7008	+	27.1946i	0.498753	+	0.863865i	−0.501246	+	0.865305i	$0.667125\pi$
$992$	3.86846	−	1.03655i	0.122824	−	0.0329106i
$993$	−6.37099			−0.202177
$994$	48.7683	−	13.0674i	1.54684	−	0.414474i
$995$	20.3395	−	0.559401i	0.644806	−	0.0177342i
$996$	−8.49415	−	8.49415i	−0.269147	−	0.269147i
$997$	8.49960	+	31.7209i	0.269185	+	1.00461i	0.959639	+	0.281236i	$0.0907443\pi$
$997$	8.49960	+	31.7209i	0.269185	+	1.00461i	−0.690454	+	0.723377i	$0.742589\pi$
$998$	9.61164	+	2.57543i	0.304251	+	0.0815238i
$999$	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.bd.b.223.4	yes	16
5.2	odd	4		390.2.bn.b.67.1	yes	16
13.7	odd	12		390.2.bn.b.163.1	yes	16
65.7	even	12	inner	390.2.bd.b.7.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.b.7.4	✓	16	65.7	even	12	inner
390.2.bd.b.223.4	yes	16	1.1	even	1	trivial
390.2.bn.b.67.1	yes	16	5.2	odd	4
390.2.bn.b.163.1	yes	16	13.7	odd	12

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.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.17085 + 1.90502i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(1.97220 - 3.41596i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.17085 + 1.90502i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(1.97220 - 3.41596i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.96650 + 1.06437i) q^{10} +(-1.48984 + 5.56016i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(0.730685 - 3.53074i) q^{13} -3.94441i q^{14} +(2.14315 - 0.637899i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.85935 - 1.03411i) q^{17} -1.00000 q^{18} +(-2.08506 + 0.558691i) q^{19} +(2.23522 - 0.0614757i) q^{20} +(-2.78912 - 2.78912i) q^{21} +(1.48984 + 5.56016i) q^{22} +(-4.18221 - 1.12062i) 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} +(-1.97220 - 3.41596i) q^{28} +(5.04514 - 2.91282i) q^{29} +(1.53707 - 1.62401i) q^{30} +(-2.83191 + 2.83191i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.98511 + 2.87815i) q^{33} +(2.82524 - 2.82524i) q^{34} +(8.81663 - 0.242485i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-1.82494 - 3.16089i) 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} +(-3.81000 - 1.02089i) q^{42} +(2.76364 + 10.3141i) q^{43} +(4.07032 + 4.07032i) q^{44} +(-0.0614757 - 2.23522i) q^{45} +(-4.18221 + 1.12062i) q^{46} -13.4556 q^{47} +(-0.965926 + 0.258819i) q^{48} +(-4.27917 - 7.41174i) q^{49} +(0.274824 + 4.99244i) q^{50} -3.99550i q^{51} +(-2.69236 - 2.39816i) q^{52} +(4.15062 + 4.15062i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(-12.3366 + 3.67194i) q^{55} +(-3.41596 - 1.97220i) q^{56} +2.15862i q^{57} +(2.91282 - 5.04514i) q^{58} +(0.509008 + 1.89964i) q^{59} +(0.519137 - 2.17497i) q^{60} +(-1.42948 + 2.47593i) q^{61} +(-1.03655 + 3.86846i) q^{62} +(-3.41596 + 1.97220i) q^{63} -1.00000 q^{64} +(7.58165 - 2.74199i) q^{65} +5.75631 q^{66} +(-2.35978 + 1.36242i) q^{67} +(1.03411 - 3.85935i) q^{68} +(-2.16487 + 3.74966i) q^{69} +(7.51418 - 4.61831i) q^{70} +(3.31290 + 12.3639i) q^{71} +(-0.500000 + 0.866025i) q^{72} +4.59815i q^{73} +(-3.16089 - 1.82494i) q^{74} +(3.72452 + 3.33586i) q^{75} +(-0.558691 + 2.08506i) q^{76} +(16.0550 + 16.0550i) q^{77} +(-3.59954 + 0.208034i) q^{78} -2.49954i q^{79} +(1.06437 - 1.96650i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.0577328 + 0.0154695i) q^{82} +12.0125 q^{83} +(-3.81000 + 1.02089i) q^{84} +(6.48873 + 6.14136i) q^{85} +(7.55042 + 7.55042i) q^{86} +(-1.50778 - 5.62713i) q^{87} +(5.56016 + 1.48984i) 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} +(2.00246 + 3.46837i) q^{93} +(-11.6529 + 6.72781i) q^{94} +(-3.50562 - 3.31795i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(8.26098 + 4.76948i) q^{97} +(-7.41174 - 4.27917i) q^{98} +(4.07032 - 4.07032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7	\( 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7} + 12 q^{11} - 8 q^{13} + 12 q^{15} - 8 q^{16} + 16 q^{17} - 16 q^{18} + 4 q^{19} - 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{28} + 48 q^{29} - 8 q^{30} + 16 q^{31} + 20 q^{34} + 12 q^{35} + 20 q^{37} - 4 q^{38} - 4 q^{39} - 12 q^{41} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 64 q^{47} + 4 q^{49} + 16 q^{50} - 16 q^{52} + 32 q^{53} - 44 q^{55} - 24 q^{56} - 12 q^{58} - 4 q^{59} + 12 q^{60} + 4 q^{61} - 20 q^{62} - 24 q^{63} - 16 q^{64} - 8 q^{65} + 32 q^{66} - 36 q^{67} - 4 q^{68} - 4 q^{69} - 36 q^{71} - 8 q^{72} - 12 q^{74} + 8 q^{76} - 4 q^{77} - 12 q^{78} - 8 q^{80} + 8 q^{81} - 12 q^{82} + 24 q^{83} - 52 q^{85} + 16 q^{86} - 12 q^{87} + 24 q^{89} - 4 q^{90} - 8 q^{92} - 36 q^{94} - 44 q^{95} + 60 q^{97} + 12 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7 + 12 * q^11 - 8 * q^13 + 12 * q^15 - 8 * q^16 + 16 * q^17 - 16 * q^18 + 4 * q^19 - 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^28 + 48 * q^29 - 8 * q^30 + 16 * q^31 + 20 * q^34 + 12 * q^35 + 20 * q^37 - 4 * q^38 - 4 * q^39 - 12 * q^41 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 64 * q^47 + 4 * q^49 + 16 * q^50 - 16 * q^52 + 32 * q^53 - 44 * q^55 - 24 * q^56 - 12 * q^58 - 4 * q^59 + 12 * q^60 + 4 * q^61 - 20 * q^62 - 24 * q^63 - 16 * q^64 - 8 * q^65 + 32 * q^66 - 36 * q^67 - 4 * q^68 - 4 * q^69 - 36 * q^71 - 8 * q^72 - 12 * q^74 + 8 * q^76 - 4 * q^77 - 12 * q^78 - 8 * q^80 + 8 * q^81 - 12 * q^82 + 24 * q^83 - 52 * q^85 + 16 * q^86 - 12 * q^87 + 24 * q^89 - 4 * q^90 - 8 * q^92 - 36 * q^94 - 44 * q^95 + 60 * q^97 + 12 * q^99

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