LMFDB - Embedded newform 770.2.n.g.421.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 10 x^{10} - 9 x^{9} + 27 x^{8} - 26 x^{7} + 47 x^{6} + 46 x^{5} + 137 x^{4} + \cdots + 1 $ x^12 - 2x^11 + 10x^10 - 9x^9 + 27x^8 - 26x^7 + 47x^6 + 46x^5 + 137x^4 - 57x^3 + 113x^2 - 17*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.3
Root			$-0.594776 - 1.83053i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.g.631.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.594776 + 1.83053i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.55714 - 1.13133i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.570037 + 0.414156i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.594776 + 1.83053i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.55714 - 1.13133i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.570037 + 0.414156i) q^{9} +1.00000 q^{10} +(3.24871 - 0.667752i) q^{11} +1.92474 q^{12} +(4.24320 - 3.08287i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.594776 - 1.83053i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.48621 + 2.53288i) q^{17} +(0.217735 - 0.670119i) q^{18} +(-0.228868 - 0.704384i) q^{19} +(-0.809017 + 0.587785i) q^{20} -1.92474 q^{21} +(-2.23577 + 2.44977i) q^{22} -0.856965 q^{23} +(-1.55714 + 1.13133i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-1.62076 + 4.98818i) q^{26} +(3.57426 + 2.59685i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-2.58821 + 7.96570i) q^{29} +(0.594776 + 1.83053i) q^{30} +(-0.892330 + 0.648316i) q^{31} +1.00000 q^{32} +(3.15459 + 5.54970i) q^{33} -4.30919 q^{34} +(0.809017 - 0.587785i) q^{35} +(0.217735 + 0.670119i) q^{36} +(-0.549806 + 1.69213i) q^{37} +(0.599184 + 0.435333i) q^{38} +(8.16704 + 5.93370i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-3.31266 - 10.1953i) q^{41} +(1.55714 - 1.13133i) q^{42} +1.13472 q^{43} +(0.368836 - 3.29605i) q^{44} +0.704605 q^{45} +(0.693299 - 0.503711i) q^{46} +(2.59627 + 7.99051i) q^{47} +(0.594776 - 1.83053i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-2.56300 + 7.88811i) q^{51} +(-1.62076 - 4.98818i) q^{52} +(7.12469 - 5.17639i) q^{53} -4.41803 q^{54} +(-3.02076 - 1.36932i) q^{55} -1.00000 q^{56} +(1.15327 - 0.837901i) q^{57} +(-2.58821 - 7.96570i) q^{58} +(-4.01222 + 12.3483i) q^{59} +(-1.55714 - 1.13133i) q^{60} +(-10.5890 - 7.69336i) q^{61} +(0.340840 - 1.04900i) q^{62} +(-0.217735 - 0.670119i) q^{63} +(-0.809017 + 0.587785i) q^{64} -5.24489 q^{65} +(-5.81415 - 2.63558i) q^{66} +8.93617 q^{67} +(3.48621 - 2.53288i) q^{68} +(-0.509702 - 1.56870i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(3.64664 + 2.64944i) q^{71} +(-0.570037 - 0.414156i) q^{72} +(-1.03030 + 3.17094i) q^{73} +(-0.549806 - 1.69213i) q^{74} +(-1.55714 + 1.13133i) q^{75} -0.740633 q^{76} +(-0.368836 + 3.29605i) q^{77} -10.0950 q^{78} +(1.26355 - 0.918019i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-3.28094 + 10.0977i) q^{81} +(8.67265 + 6.30105i) q^{82} +(-0.492865 - 0.358088i) q^{83} +(-0.594776 + 1.83053i) q^{84} +(-1.33161 - 4.09828i) q^{85} +(-0.918010 + 0.666974i) q^{86} -16.1209 q^{87} +(1.63898 + 2.88336i) q^{88} +1.46836 q^{89} +(-0.570037 + 0.414156i) q^{90} +(1.62076 + 4.98818i) q^{91} +(-0.264817 + 0.815022i) q^{92} +(-1.71750 - 1.24784i) q^{93} +(-6.79713 - 4.93840i) q^{94} +(-0.228868 + 0.704384i) q^{95} +(0.594776 + 1.83053i) q^{96} +(-6.80954 + 4.94742i) q^{97} +1.00000 q^{98} +(-1.57533 + 1.72612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9	\( 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9} + 12 q^{10} + 7 q^{11} - 2 q^{12} + 8 q^{13} + 3 q^{14} - 2 q^{15} - 3 q^{16} + 8 q^{17} + 8 q^{18} + 11 q^{19} - 3 q^{20} + 2 q^{21} - 3 q^{22} - 20 q^{23} + 3 q^{24} - 3 q^{25} - 2 q^{26} + 7 q^{27} + 3 q^{28} + 20 q^{29} - 2 q^{30} + 2 q^{31} + 12 q^{32} + 33 q^{33} - 42 q^{34} + 3 q^{35} + 8 q^{36} - 4 q^{37} - 14 q^{38} + 18 q^{39} - 3 q^{40} - 14 q^{41} - 3 q^{42} - 38 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 10 q^{47} - 2 q^{48} - 3 q^{49} - 3 q^{50} + 13 q^{51} - 2 q^{52} + 8 q^{53} - 8 q^{54} - 3 q^{55} - 12 q^{56} + 33 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} - 34 q^{61} + 2 q^{62} - 8 q^{63} - 3 q^{64} - 12 q^{65} - 12 q^{66} - 54 q^{67} + 8 q^{68} + 38 q^{69} + 3 q^{70} + 18 q^{71} - 7 q^{72} + 24 q^{73} - 4 q^{74} + 3 q^{75} + 6 q^{76} - 2 q^{77} - 52 q^{78} + 2 q^{79} - 3 q^{80} + 2 q^{81} + 21 q^{82} + 33 q^{83} + 2 q^{84} + 13 q^{85} + 7 q^{86} - 16 q^{87} - 3 q^{88} + 2 q^{89} - 7 q^{90} + 2 q^{91} - 10 q^{92} - 32 q^{93} + 11 q^{95} - 2 q^{96} - q^{97} + 12 q^{98} - 47 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9 + 12 * q^10 + 7 * q^11 - 2 * q^12 + 8 * q^13 + 3 * q^14 - 2 * q^15 - 3 * q^16 + 8 * q^17 + 8 * q^18 + 11 * q^19 - 3 * q^20 + 2 * q^21 - 3 * q^22 - 20 * q^23 + 3 * q^24 - 3 * q^25 - 2 * q^26 + 7 * q^27 + 3 * q^28 + 20 * q^29 - 2 * q^30 + 2 * q^31 + 12 * q^32 + 33 * q^33 - 42 * q^34 + 3 * q^35 + 8 * q^36 - 4 * q^37 - 14 * q^38 + 18 * q^39 - 3 * q^40 - 14 * q^41 - 3 * q^42 - 38 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 10 * q^47 - 2 * q^48 - 3 * q^49 - 3 * q^50 + 13 * q^51 - 2 * q^52 + 8 * q^53 - 8 * q^54 - 3 * q^55 - 12 * q^56 + 33 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 - 34 * q^61 + 2 * q^62 - 8 * q^63 - 3 * q^64 - 12 * q^65 - 12 * q^66 - 54 * q^67 + 8 * q^68 + 38 * q^69 + 3 * q^70 + 18 * q^71 - 7 * q^72 + 24 * q^73 - 4 * q^74 + 3 * q^75 + 6 * q^76 - 2 * q^77 - 52 * q^78 + 2 * q^79 - 3 * q^80 + 2 * q^81 + 21 * q^82 + 33 * q^83 + 2 * q^84 + 13 * q^85 + 7 * q^86 - 16 * q^87 - 3 * q^88 + 2 * q^89 - 7 * q^90 + 2 * q^91 - 10 * q^92 - 32 * q^93 + 11 * q^95 - 2 * q^96 - q^97 + 12 * q^98 - 47 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.594776	+	1.83053i	0.343394	+	1.05686i	0.962438	+	0.271502i	$0.0875203\pi$
$3$	0.594776	+	1.83053i	0.343394	+	1.05686i	−0.619044	+	0.785356i	$0.712480\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	−1.55714	−	1.13133i	−0.635701	−	0.461864i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.570037	+	0.414156i	−0.190012	+	0.138052i
$10$	1.00000			0.316228
$11$	3.24871	−	0.667752i	0.979522	−	0.201335i
$11$	3.24871	−	0.667752i	0.979522	−	0.201335i
$12$	1.92474			0.555623
$13$	4.24320	−	3.08287i	1.17685	−	0.855033i	0.185039	−	0.982731i	$-0.440759\pi$
$13$	4.24320	−	3.08287i	1.17685	−	0.855033i	0.991813	+	0.127698i	$0.0407588\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	0.594776	−	1.83053i	0.153570	−	0.472641i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	3.48621	+	2.53288i	0.845530	+	0.614313i	0.923910	−	0.382610i	$-0.124975\pi$
$17$	3.48621	+	2.53288i	0.845530	+	0.614313i	−0.0783802	+	0.996924i	$0.524975\pi$
$18$	0.217735	−	0.670119i	0.0513206	−	0.157949i
$19$	−0.228868	−	0.704384i	−0.0525059	−	0.161597i	0.921365	−	0.388698i	$-0.127075\pi$
$19$	−0.228868	−	0.704384i	−0.0525059	−	0.161597i	−0.973871	+	0.227101i	$0.927075\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	−1.92474			−0.420012
$22$	−2.23577	+	2.44977i	−0.476667	+	0.522292i
$23$	−0.856965			−0.178689			−0.0893447	−	0.996001i	$-0.528477\pi$
$23$	−0.856965			−0.178689			−0.0893447	+	0.996001i	$0.528477\pi$
$24$	−1.55714	+	1.13133i	−0.317851	+	0.230932i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−1.62076	+	4.98818i	−0.317857	+	0.978263i
$27$	3.57426	+	2.59685i	0.687866	+	0.499764i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	−2.58821	+	7.96570i	−0.480619	+	1.47919i	0.357607	+	0.933872i	$0.383593\pi$
$29$	−2.58821	+	7.96570i	−0.480619	+	1.47919i	−0.838227	+	0.545322i	$0.816407\pi$
$30$	0.594776	+	1.83053i	0.108591	+	0.334208i
$31$	−0.892330	+	0.648316i	−0.160267	+	0.116441i	−0.665028	−	0.746818i	$-0.731581\pi$
$31$	−0.892330	+	0.648316i	−0.160267	+	0.116441i	0.504761	+	0.863259i	$0.331581\pi$
$32$	1.00000			0.176777
$33$	3.15459	+	5.54970i	0.549144	+	0.966079i
$34$	−4.30919			−0.739020
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	0.217735	+	0.670119i	0.0362892	+	0.111687i
$37$	−0.549806	+	1.69213i	−0.0903876	+	0.278184i	−0.986024	−	0.166602i	$-0.946720\pi$
$37$	−0.549806	+	1.69213i	−0.0903876	+	0.278184i	0.895637	+	0.444787i	$0.146720\pi$
$38$	0.599184	+	0.435333i	0.0972006	+	0.0706203i
$39$	8.16704	+	5.93370i	1.30777	+	0.950153i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	−3.31266	−	10.1953i	−0.517350	−	1.59224i	−0.778965	−	0.627067i	$-0.784255\pi$
$41$	−3.31266	−	10.1953i	−0.517350	−	1.59224i	0.261615	−	0.965172i	$-0.415745\pi$
$42$	1.55714	−	1.13133i	0.240272	−	0.174568i
$43$	1.13472			0.173044			0.0865218	−	0.996250i	$-0.472425\pi$
$43$	1.13472			0.173044			0.0865218	+	0.996250i	$0.472425\pi$
$44$	0.368836	−	3.29605i	0.0556041	−	0.496899i
$45$	0.704605			0.105036
$46$	0.693299	−	0.503711i	0.102221	−	0.0742682i
$47$	2.59627	+	7.99051i	0.378705	+	1.16554i	0.940945	+	0.338561i	$0.109940\pi$
$47$	2.59627	+	7.99051i	0.378705	+	1.16554i	−0.562239	+	0.826975i	$0.690060\pi$
$48$	0.594776	−	1.83053i	0.0858485	−	0.264215i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	−2.56300	+	7.88811i	−0.358892	+	1.10456i
$52$	−1.62076	−	4.98818i	−0.224759	−	0.691736i
$53$	7.12469	−	5.17639i	0.978652	−	0.711032i	0.0212451	−	0.999774i	$-0.493237\pi$
$53$	7.12469	−	5.17639i	0.978652	−	0.711032i	0.957407	+	0.288742i	$0.0932370\pi$
$54$	−4.41803			−0.601217
$55$	−3.02076	−	1.36932i	−0.407319	−	0.184639i
$56$	−1.00000			−0.133631
$57$	1.15327	−	0.837901i	0.152755	−	0.110983i
$58$	−2.58821	−	7.96570i	−0.339849	−	1.04595i
$59$	−4.01222	+	12.3483i	−0.522347	+	1.60762i	0.247157	+	0.968975i	$0.420504\pi$
$59$	−4.01222	+	12.3483i	−0.522347	+	1.60762i	−0.769504	+	0.638642i	$0.779496\pi$
$60$	−1.55714	−	1.13133i	−0.201026	−	0.146054i
$61$	−10.5890	−	7.69336i	−1.35578	−	0.985034i	−0.998701	−	0.0509613i	$-0.983772\pi$
$61$	−10.5890	−	7.69336i	−1.35578	−	0.985034i	−0.357082	−	0.934073i	$-0.616228\pi$
$62$	0.340840	−	1.04900i	0.0432867	−	0.133223i
$63$	−0.217735	−	0.670119i	−0.0274320	−	0.0844271i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−5.24489			−0.650548
$66$	−5.81415	−	2.63558i	−0.715673	−	0.324417i
$67$	8.93617			1.09173			0.545864	−	0.837874i	$-0.316202\pi$
$67$	8.93617			1.09173			0.545864	+	0.837874i	$0.316202\pi$
$68$	3.48621	−	2.53288i	0.422765	−	0.307157i
$69$	−0.509702	−	1.56870i	−0.0613609	−	0.188849i
$70$	−0.309017	+	0.951057i	−0.0369346	+	0.113673i
$71$	3.64664	+	2.64944i	0.432777	+	0.314431i	0.782758	−	0.622326i	$-0.213812\pi$
$71$	3.64664	+	2.64944i	0.432777	+	0.314431i	−0.349981	+	0.936757i	$0.613812\pi$
$72$	−0.570037	−	0.414156i	−0.0671796	−	0.0488088i
$73$	−1.03030	+	3.17094i	−0.120588	+	0.371131i	−0.993071	−	0.117512i	$-0.962508\pi$
$73$	−1.03030	+	3.17094i	−0.120588	+	0.371131i	0.872484	+	0.488643i	$0.162508\pi$
$74$	−0.549806	−	1.69213i	−0.0639137	−	0.196706i
$75$	−1.55714	+	1.13133i	−0.179803	+	0.130635i
$76$	−0.740633			−0.0849564
$77$	−0.368836	+	3.29605i	−0.0420328	+	0.375620i
$78$	−10.0950			−1.14304
$79$	1.26355	−	0.918019i	0.142160	−	0.103285i	−0.514432	−	0.857531i	$-0.671997\pi$
$79$	1.26355	−	0.918019i	0.142160	−	0.103285i	0.656592	+	0.754246i	$0.271997\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	−3.28094	+	10.0977i	−0.364549	+	1.12197i
$82$	8.67265	+	6.30105i	0.957734	+	0.695834i
$83$	−0.492865	−	0.358088i	−0.0540990	−	0.0393052i	0.560407	−	0.828217i	$-0.310645\pi$
$83$	−0.492865	−	0.358088i	−0.0540990	−	0.0393052i	−0.614506	+	0.788912i	$0.710645\pi$
$84$	−0.594776	+	1.83053i	−0.0648954	+	0.199727i
$85$	−1.33161	−	4.09828i	−0.144434	−	0.444521i
$86$	−0.918010	+	0.666974i	−0.0989916	+	0.0719216i
$87$	−16.1209			−1.72834
$88$	1.63898	+	2.88336i	0.174715	+	0.307367i
$89$	1.46836			0.155646			0.0778228	−	0.996967i	$-0.475203\pi$
$89$	1.46836			0.155646			0.0778228	+	0.996967i	$0.475203\pi$
$90$	−0.570037	+	0.414156i	−0.0600872	+	0.0436559i
$91$	1.62076	+	4.98818i	0.169902	+	0.522904i
$92$	−0.264817	+	0.815022i	−0.0276090	+	0.0849719i
$93$	−1.71750	−	1.24784i	−0.178096	−	0.129395i
$94$	−6.79713	−	4.93840i	−0.701070	−	0.509358i
$95$	−0.228868	+	0.704384i	−0.0234814	+	0.0722682i
$96$	0.594776	+	1.83053i	0.0607041	+	0.186828i
$97$	−6.80954	+	4.94742i	−0.691404	+	0.502334i	−0.877121	−	0.480269i	$-0.840539\pi$
$97$	−6.80954	+	4.94742i	−0.691404	+	0.502334i	0.185718	+	0.982603i	$0.440539\pi$
$98$	1.00000			0.101015
$99$	−1.57533	+	1.72612i	−0.158327	+	0.173481i
$100$	1.00000			0.100000
$101$	8.92309	−	6.48300i	0.887881	−	0.645083i	−0.0474439	−	0.998874i	$-0.515108\pi$
$101$	8.92309	−	6.48300i	0.887881	−	0.645083i	0.935325	+	0.353791i	$0.115108\pi$
$102$	−2.56300	−	7.88811i	−0.253775	−	0.781039i
$103$	1.81379	−	5.58226i	0.178718	−	0.550036i	−0.821066	−	0.570833i	$-0.806620\pi$
$103$	1.81379	−	5.58226i	0.178718	−	0.550036i	0.999784	+	0.0207969i	$0.00662034\pi$
$104$	4.24320	+	3.08287i	0.416080	+	0.302300i
$105$	1.55714	+	1.13133i	0.151962	+	0.110407i
$106$	−2.72139	+	8.37558i	−0.264325	+	0.813508i
$107$	2.11109	+	6.49726i	0.204086	+	0.628114i	0.999750	+	0.0223743i	$0.00712254\pi$
$107$	2.11109	+	6.49726i	0.204086	+	0.628114i	−0.795663	+	0.605739i	$0.792877\pi$
$108$	3.57426	−	2.59685i	0.343933	−	0.249882i
$109$	−7.76784			−0.744025			−0.372012	−	0.928228i	$-0.621332\pi$
$109$	−7.76784			−0.744025			−0.372012	+	0.928228i	$0.621332\pi$
$110$	3.24871	−	0.667752i	0.309752	−	0.0636677i
$111$	−3.42451			−0.325040
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	1.43368	+	4.41241i	0.134869	+	0.415085i	0.995570	−	0.0940270i	$-0.0299740\pi$
$113$	1.43368	+	4.41241i	0.134869	+	0.415085i	−0.860700	+	0.509112i	$0.829974\pi$
$114$	−0.440510	+	1.35575i	−0.0412576	+	0.126978i
$115$	0.693299	+	0.503711i	0.0646505	+	0.0469713i
$116$	6.77603	+	4.92308i	0.629139	+	0.457096i
$117$	−1.14199	+	3.51470i	−0.105577	+	0.324934i
$118$	−4.01222	−	12.3483i	−0.369355	−	1.13676i
$119$	−3.48621	+	2.53288i	−0.319580	+	0.232189i
$120$	1.92474			0.175703
$121$	10.1082	−	4.33866i	0.918929	−	0.394424i
$122$	13.0887			1.18500
$123$	16.6925	−	12.1278i	1.50512	−	1.09353i
$124$	0.340840	+	1.04900i	0.0306083	+	0.0942027i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	0.570037	+	0.414156i	0.0507830	+	0.0368960i
$127$	−7.62146	−	5.53732i	−0.676296	−	0.491357i	0.195831	−	0.980638i	$-0.437260\pi$
$127$	−7.62146	−	5.53732i	−0.676296	−	0.491357i	−0.872127	+	0.489280i	$0.837260\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	0.674906	+	2.07715i	0.0594222	+	0.182883i
$130$	4.24320	−	3.08287i	0.372153	−	0.270385i
$131$	−0.862825			−0.0753854			−0.0376927	−	0.999289i	$-0.512001\pi$
$131$	−0.862825			−0.0753854			−0.0376927	+	0.999289i	$0.512001\pi$
$132$	6.25290	−	1.28525i	0.544245	−	0.111866i
$133$	0.740633			0.0642210
$134$	−7.22952	+	5.25255i	−0.624535	+	0.453751i
$135$	−1.36525	−	4.20179i	−0.117502	−	0.361633i
$136$	−1.33161	+	4.09828i	−0.114185	+	0.351425i
$137$	13.9530	+	10.1375i	1.19209	+	0.866103i	0.993483	−	0.113977i	$-0.0363590\pi$
$137$	13.9530	+	10.1375i	1.19209	+	0.866103i	0.198605	+	0.980080i	$0.436359\pi$
$138$	1.33442	+	0.969511i	0.113593	+	0.0825302i
$139$	6.31780	−	19.4442i	0.535869	−	1.64924i	−0.205894	−	0.978574i	$-0.566010\pi$
$139$	6.31780	−	19.4442i	0.535869	−	1.64924i	0.741764	−	0.670661i	$-0.233990\pi$
$140$	−0.309017	−	0.951057i	−0.0261167	−	0.0803789i
$141$	−13.0827	+	9.50512i	−1.10176	+	0.800476i
$142$	−4.50750			−0.378261
$143$	11.7263	−	12.8487i	0.980605	−	1.07447i
$144$	0.704605			0.0587171
$145$	6.77603	−	4.92308i	0.562719	−	0.408839i
$146$	−1.03030	−	3.17094i	−0.0852683	−	0.262429i
$147$	0.594776	−	1.83053i	0.0490563	−	0.150980i
$148$	1.43941	+	1.04579i	0.118319	+	0.0859637i
$149$	−1.52336	−	1.10679i	−0.124799	−	0.0906716i	0.523635	−	0.851943i	$-0.324576\pi$
$149$	−1.52336	−	1.10679i	−0.124799	−	0.0906716i	−0.648434	+	0.761271i	$0.724576\pi$
$150$	0.594776	−	1.83053i	0.0485632	−	0.149462i
$151$	1.68444	+	5.18416i	0.137077	+	0.421881i	0.995907	−	0.0903799i	$-0.0288081\pi$
$151$	1.68444	+	5.18416i	0.137077	+	0.421881i	−0.858830	+	0.512261i	$0.828808\pi$
$152$	0.599184	−	0.435333i	0.0486003	−	0.0353102i
$153$	−3.03628			−0.245468
$154$	−1.63898	−	2.88336i	−0.132072	−	0.232348i
$155$	1.10298			0.0885935
$156$	8.16704	−	5.93370i	0.653886	−	0.475076i
$157$	−3.70139	−	11.3917i	−0.295403	−	0.909157i	−0.983086	−	0.183145i	$-0.941372\pi$
$157$	−3.70139	−	11.3917i	−0.295403	−	0.909157i	0.687683	−	0.726011i	$-0.258628\pi$
$158$	−0.482631	+	1.48539i	−0.0383961	+	0.118171i
$159$	13.7131	+	9.96319i	1.08752	+	0.790132i
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	0.264817	−	0.815022i	0.0208705	−	0.0642327i
$162$	−3.28094	−	10.0977i	−0.257775	−	0.793350i
$163$	12.5837	−	9.14257i	0.985629	−	0.716101i	0.0266693	−	0.999644i	$-0.491510\pi$
$163$	12.5837	−	9.14257i	0.985629	−	0.716101i	0.958960	+	0.283543i	$0.0915099\pi$
$164$	−10.7200			−0.837090
$165$	0.709912	−	6.34403i	0.0552666	−	0.493882i
$166$	0.609215			0.0472843
$167$	−14.6006	+	10.6080i	−1.12983	+	0.820871i	−0.985670	−	0.168684i	$-0.946048\pi$
$167$	−14.6006	+	10.6080i	−1.12983	+	0.820871i	−0.144161	+	0.989554i	$0.546048\pi$
$168$	−0.594776	−	1.83053i	−0.0458880	−	0.141229i
$169$	4.48347	−	13.7987i	0.344882	−	1.06144i
$170$	3.48621	+	2.53288i	0.267380	+	0.194263i
$171$	0.422188	+	0.306738i	0.0322856	+	0.0234568i
$172$	0.350649	−	1.07919i	0.0267367	−	0.0822872i
$173$	−2.96862	−	9.13646i	−0.225700	−	0.694632i	−0.998220	−	0.0596421i	$-0.981004\pi$
$173$	−2.96862	−	9.13646i	−0.225700	−	0.694632i	0.772520	−	0.634990i	$-0.218996\pi$
$174$	13.0421	−	9.47562i	0.988716	−	0.718345i
$175$	−1.00000			−0.0755929
$176$	−3.02076	−	1.36932i	−0.227698	−	0.103216i
$177$	−24.9904			−1.87839
$178$	−1.18793	+	0.863078i	−0.0890388	+	0.0646905i
$179$	4.09982	+	12.6179i	0.306435	+	0.943109i	0.979138	+	0.203196i	$0.0651330\pi$
$179$	4.09982	+	12.6179i	0.306435	+	0.943109i	−0.672703	+	0.739912i	$0.734867\pi$
$180$	0.217735	−	0.670119i	0.0162290	−	0.0499477i
$181$	−15.8434	−	11.5109i	−1.17763	−	0.855598i	−0.185727	−	0.982601i	$-0.559464\pi$
$181$	−15.8434	−	11.5109i	−1.17763	−	0.855598i	−0.991902	+	0.127004i	$0.959464\pi$
$182$	−4.24320	−	3.08287i	−0.314527	−	0.228517i
$183$	7.78486	−	23.9593i	0.575473	−	1.77113i
$184$	−0.264817	−	0.815022i	−0.0195225	−	0.0600842i
$185$	1.43941	−	1.04579i	0.105828	−	0.0768883i
$186$	2.12295			0.155662
$187$	13.0170	+	5.90066i	0.951898	+	0.431499i
$188$	8.40172			0.612758
$189$	−3.57426	+	2.59685i	−0.259989	+	0.188893i
$190$	−0.228868	−	0.704384i	−0.0166038	−	0.0511014i
$191$	−3.94166	+	12.1312i	−0.285208	+	0.877781i	0.701128	+	0.713036i	$0.252680\pi$
$191$	−3.94166	+	12.1312i	−0.285208	+	0.877781i	−0.986336	+	0.164746i	$0.947320\pi$
$192$	−1.55714	−	1.13133i	−0.112377	−	0.0816468i
$193$	−9.56974	−	6.95282i	−0.688845	−	0.500475i	0.187435	−	0.982277i	$-0.439982\pi$
$193$	−9.56974	−	6.95282i	−0.688845	−	0.500475i	−0.876280	+	0.481802i	$0.839982\pi$
$194$	2.60101	−	8.00509i	0.186742	−	0.574732i
$195$	−3.11953	−	9.60093i	−0.223394	−	0.687537i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−21.9105			−1.56106			−0.780528	−	0.625121i	$-0.785050\pi$
$197$	−21.9105			−1.56106			−0.780528	+	0.625121i	$0.785050\pi$
$198$	0.259884	−	2.32241i	0.0184691	−	0.165047i
$199$	10.3121			0.731006			0.365503	−	0.930810i	$-0.380897\pi$
$199$	10.3121			0.731006			0.365503	+	0.930810i	$0.380897\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	5.31502	+	16.3579i	0.374893	+	1.15380i
$202$	−3.40832	+	10.4897i	−0.239808	+	0.738054i
$203$	−6.77603	−	4.92308i	−0.475584	−	0.345532i
$204$	6.71003	+	4.87512i	0.469796	+	0.341327i
$205$	−3.31266	+	10.1953i	−0.231366	+	0.712071i
$206$	1.81379	+	5.58226i	0.126372	+	0.388934i
$207$	0.488502	−	0.354917i	0.0339532	−	0.0246685i
$208$	−5.24489			−0.363667
$209$	−1.21388	−	2.13551i	−0.0839658	−	0.147716i
$210$	−1.92474			−0.132819
$211$	20.1004	−	14.6038i	1.38377	−	1.00537i	0.387254	−	0.921973i	$-0.373424\pi$
$211$	20.1004	−	14.6038i	1.38377	−	1.00537i	0.996517	−	0.0833948i	$-0.0265763\pi$
$212$	−2.72139	−	8.37558i	−0.186906	−	0.575237i
$213$	−2.68095	+	8.25112i	−0.183696	+	0.565357i
$214$	−5.52690	−	4.01553i	−0.377811	−	0.274496i
$215$	−0.918010	−	0.666974i	−0.0626078	−	0.0454872i
$216$	−1.36525	+	4.20179i	−0.0928932	+	0.285896i
$217$	−0.340840	−	1.04900i	−0.0231377	−	0.0712106i
$218$	6.28432	−	4.56582i	0.425628	−	0.309237i
$219$	−6.41731			−0.433641
$220$	−2.23577	+	2.44977i	−0.150735	+	0.165163i
$221$	22.6012			1.52032
$222$	2.77049	−	2.01288i	0.185943	−	0.135095i
$223$	−6.25433	−	19.2489i	−0.418821	−	1.28900i	−0.908788	−	0.417258i	$-0.862991\pi$
$223$	−6.25433	−	19.2489i	−0.418821	−	1.28900i	0.489967	−	0.871741i	$-0.337009\pi$
$224$	−0.309017	+	0.951057i	−0.0206471	+	0.0635451i
$225$	−0.570037	−	0.414156i	−0.0380025	−	0.0276104i
$226$	−3.75342	−	2.72702i	−0.249674	−	0.181399i
$227$	3.64919	−	11.2310i	0.242205	−	0.745431i	−0.753878	−	0.657014i	$-0.771819\pi$
$227$	3.64919	−	11.2310i	0.242205	−	0.745431i	0.996084	−	0.0884168i	$-0.0281807\pi$
$228$	−0.440510	−	1.35575i	−0.0291735	−	0.0897869i
$229$	−1.35839	+	0.986925i	−0.0897647	+	0.0652179i	−0.631762	−	0.775162i	$-0.717668\pi$
$229$	−1.35839	+	0.986925i	−0.0897647	+	0.0652179i	0.541998	+	0.840380i	$0.317668\pi$
$230$	−0.856965			−0.0565066
$231$	−6.25290	+	1.28525i	−0.411411	+	0.0845630i
$232$	−8.37564			−0.549887
$233$	12.5576	−	9.12361i	0.822674	−	0.597707i	−0.0948035	−	0.995496i	$-0.530222\pi$
$233$	12.5576	−	9.12361i	0.822674	−	0.597707i	0.917477	+	0.397789i	$0.130222\pi$
$234$	−1.14199	−	3.51470i	−0.0746545	−	0.229763i
$235$	2.59627	−	7.99051i	0.169362	−	0.521243i
$236$	10.5041	+	7.63170i	0.683761	+	0.496781i
$237$	2.43199	+	1.76694i	0.157975	+	0.114775i
$238$	1.33161	−	4.09828i	0.0863156	−	0.265652i
$239$	−6.79953	−	20.9268i	−0.439825	−	1.35364i	−0.888060	−	0.459727i	$-0.847947\pi$
$239$	−6.79953	−	20.9268i	−0.439825	−	1.35364i	0.448235	−	0.893916i	$-0.352053\pi$
$240$	−1.55714	+	1.13133i	−0.100513	+	0.0730271i
$241$	−23.8155			−1.53409			−0.767047	−	0.641591i	$-0.778274\pi$
$241$	−23.8155			−1.53409			−0.767047	+	0.641591i	$0.778274\pi$
$242$	−5.62751	+	9.45151i	−0.361750	+	0.607566i
$243$	−7.18150			−0.460693
$244$	−10.5890	+	7.69336i	−0.677892	+	0.492517i
$245$	0.309017	+	0.951057i	0.0197424	+	0.0607608i
$246$	−6.37599	+	19.6233i	−0.406518	+	1.25113i
$247$	−3.14265	−	2.28327i	−0.199962	−	0.145281i
$248$	−0.892330	−	0.648316i	−0.0566630	−	0.0411681i
$249$	0.362346	−	1.11519i	0.0229628	−	0.0706721i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−23.0637	+	16.7568i	−1.45577	+	1.05768i	−0.471330	+	0.881957i	$0.656226\pi$
$251$	−23.0637	+	16.7568i	−1.45577	+	1.05768i	−0.984440	+	0.175722i	$0.943774\pi$
$252$	−0.704605			−0.0443859
$253$	−2.78403	+	0.572240i	−0.175030	+	0.0359764i
$254$	9.42065			0.591104
$255$	6.71003	−	4.87512i	0.420198	−	0.305292i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	9.15288	−	28.1697i	0.570941	−	1.75718i	−0.0786605	−	0.996901i	$-0.525064\pi$
$257$	9.15288	−	28.1697i	0.570941	−	1.75718i	0.649602	−	0.760275i	$-0.274936\pi$
$258$	−1.76693	−	1.28375i	−0.110004	−	0.0799226i
$259$	−1.43941	−	1.04579i	−0.0894407	−	0.0649825i
$260$	−1.62076	+	4.98818i	−0.100515	+	0.309354i
$261$	−1.82367	−	5.61267i	−0.112882	−	0.347416i
$262$	0.698040	−	0.507156i	0.0431251	−	0.0313322i
$263$	4.09184			0.252314			0.126157	−	0.992010i	$-0.459736\pi$
$263$	4.09184			0.252314			0.126157	+	0.992010i	$0.459736\pi$
$264$	−4.30326	+	4.71515i	−0.264847	+	0.290197i
$265$	−8.80661			−0.540986
$266$	−0.599184	+	0.435333i	−0.0367384	+	0.0266920i
$267$	0.873343	+	2.68787i	0.0534477	+	0.164495i
$268$	2.76143	−	8.49881i	0.168681	−	0.519147i
$269$	−2.42491	−	1.76180i	−0.147849	−	0.107419i	0.511402	−	0.859342i	$-0.329126\pi$
$269$	−2.42491	−	1.76180i	−0.147849	−	0.107419i	−0.659251	+	0.751923i	$0.729126\pi$
$270$	3.57426	+	2.59685i	0.217522	+	0.158039i
$271$	7.63319	−	23.4925i	0.463683	−	1.42707i	−0.396947	−	0.917841i	$-0.629930\pi$
$271$	7.63319	−	23.4925i	0.463683	−	1.42707i	0.860631	−	0.509229i	$-0.170070\pi$
$272$	−1.33161	−	4.09828i	−0.0807409	−	0.248495i
$273$	−8.16704	+	5.93370i	−0.494292	+	0.359124i
$274$	−17.2469			−1.04192
$275$	1.63898	+	2.88336i	0.0988340	+	0.173873i
$276$	−1.64943			−0.0992840
$277$	−2.16702	+	1.57443i	−0.130204	+	0.0945985i	−0.650981	−	0.759094i	$-0.725642\pi$
$277$	−2.16702	+	1.57443i	−0.130204	+	0.0945985i	0.520777	+	0.853693i	$0.325642\pi$
$278$	6.31780	+	19.4442i	0.378917	+	1.16619i
$279$	0.240157	−	0.739128i	0.0143778	−	0.0442505i
$280$	0.809017	+	0.587785i	0.0483480	+	0.0351269i
$281$	9.40186	+	6.83085i	0.560868	+	0.407494i	0.831777	−	0.555111i	$-0.187324\pi$
$281$	9.40186	+	6.83085i	0.560868	+	0.407494i	−0.270908	+	0.962605i	$0.587324\pi$
$282$	4.99714	−	15.3796i	0.297575	−	0.915842i
$283$	5.60439	+	17.2485i	0.333146	+	1.02532i	0.967628	+	0.252381i	$0.0812137\pi$
$283$	5.60439	+	17.2485i	0.333146	+	1.02532i	−0.634481	+	0.772938i	$0.718786\pi$
$284$	3.64664	−	2.64944i	0.216388	−	0.157215i
$285$	−1.42552			−0.0844406
$286$	−1.93450	+	17.2874i	−0.114390	+	1.02223i
$287$	10.7200			0.632781
$288$	−0.570037	+	0.414156i	−0.0335898	+	0.0244044i
$289$	0.484884	+	1.49232i	0.0285226	+	0.0877835i
$290$	−2.58821	+	7.96570i	−0.151985	+	0.467762i
$291$	−13.1066	−	9.52247i	−0.768320	−	0.558217i
$292$	2.69736	+	1.95975i	0.157851	+	0.114686i
$293$	−7.06723	+	21.7507i	−0.412872	+	1.27069i	0.501269	+	0.865292i	$0.332867\pi$
$293$	−7.06723	+	21.7507i	−0.412872	+	1.27069i	−0.914140	+	0.405398i	$0.867133\pi$
$294$	0.594776	+	1.83053i	0.0346880	+	0.106759i
$295$	10.5041	−	7.63170i	0.611574	−	0.444335i
$296$	−1.77921			−0.103415
$297$	13.3458	+	6.04969i	0.774401	+	0.351039i
$298$	1.88298			0.109078
$299$	−3.63627	+	2.64191i	−0.210291	+	0.152785i
$300$	0.594776	+	1.83053i	0.0343394	+	0.105686i
$301$	−0.350649	+	1.07919i	−0.0202111	+	0.0622032i
$302$	−4.40991	−	3.20399i	−0.253762	−	0.184369i
$303$	17.1746	+	12.4781i	0.986654	+	0.716846i
$304$	−0.228868	+	0.704384i	−0.0131265	+	0.0403992i
$305$	4.04464	+	12.4481i	0.231595	+	0.712777i
$306$	2.45640	−	1.78468i	0.140423	−	0.102023i
$307$	−19.9326			−1.13761			−0.568806	−	0.822472i	$-0.692594\pi$
$307$	−19.9326			−1.13761			−0.568806	+	0.822472i	$0.692594\pi$
$308$	3.02076	+	1.36932i	0.172124	+	0.0780243i
$309$	11.2973			0.642681
$310$	−0.892330	+	0.648316i	−0.0506809	+	0.0368219i
$311$	−0.396892	−	1.22151i	−0.0225057	−	0.0692653i	0.939173	−	0.343445i	$-0.111594\pi$
$311$	−0.396892	−	1.22151i	−0.0225057	−	0.0692653i	−0.961679	+	0.274179i	$0.911594\pi$
$312$	−3.11953	+	9.60093i	−0.176609	+	0.543546i
$313$	10.8379	+	7.87422i	0.612596	+	0.445077i	0.850328	−	0.526254i	$-0.176404\pi$
$313$	10.8379	+	7.87422i	0.612596	+	0.445077i	−0.237731	+	0.971331i	$0.576404\pi$
$314$	9.69036	+	7.04046i	0.546859	+	0.397316i
$315$	−0.217735	+	0.670119i	−0.0122680	+	0.0377569i
$316$	−0.482631	−	1.48539i	−0.0271501	−	0.0835595i
$317$	−13.4814	+	9.79483i	−0.757192	+	0.550132i	−0.898048	−	0.439898i	$-0.855015\pi$
$317$	−13.4814	+	9.79483i	−0.757192	+	0.550132i	0.140855	+	0.990030i	$0.455015\pi$
$318$	−16.9504			−0.950530
$319$	−3.08924	+	27.6065i	−0.172964	+	1.54567i
$320$	1.00000			0.0559017
$321$	−10.6378	+	7.72882i	−0.593745	+	0.431381i
$322$	0.264817	+	0.815022i	0.0147577	+	0.0454194i
$323$	0.986236	−	3.03532i	0.0548756	−	0.168890i
$324$	8.58961	+	6.24072i	0.477201	+	0.346707i
$325$	4.24320	+	3.08287i	0.235370	+	0.171007i
$326$	−4.80653	+	14.7930i	−0.266209	+	0.819308i
$327$	−4.62013	−	14.2193i	−0.255494	−	0.786328i
$328$	8.67265	−	6.30105i	0.478867	−	0.347917i
$329$	−8.40172			−0.463202
$330$	3.15459	+	5.54970i	0.173655	+	0.305501i
$331$	11.1340			0.611979			0.305989	−	0.952035i	$-0.401013\pi$
$331$	11.1340			0.611979			0.305989	+	0.952035i	$0.401013\pi$
$332$	−0.492865	+	0.358088i	−0.0270495	+	0.0196526i
$333$	−0.387396	−	1.19228i	−0.0212292	−	0.0653367i
$334$	5.57695	−	17.1641i	0.305157	−	0.939177i
$335$	−7.22952	−	5.25255i	−0.394991	−	0.286977i
$336$	1.55714	+	1.13133i	0.0849491	+	0.0617192i
$337$	−2.07609	+	6.38956i	−0.113092	+	0.348062i	−0.991544	−	0.129769i	$-0.958577\pi$
$337$	−2.07609	+	6.38956i	−0.113092	+	0.348062i	0.878452	+	0.477830i	$0.158577\pi$
$338$	4.48347	+	13.7987i	0.243869	+	0.750551i
$339$	−7.22434	+	5.24879i	−0.392372	+	0.285075i
$340$	−4.30919			−0.233699
$341$	−2.46601	+	2.70204i	−0.133542	+	0.146324i
$342$	−0.521854			−0.0282186
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	0.350649	+	1.07919i	0.0189057	+	0.0581858i
$345$	−0.509702	+	1.56870i	−0.0274414	+	0.0844560i
$346$	7.77194	+	5.64664i	0.417822	+	0.303565i
$347$	15.7032	+	11.4091i	0.842995	+	0.612471i	0.923206	−	0.384306i	$-0.125559\pi$
$347$	15.7032	+	11.4091i	0.842995	+	0.612471i	−0.0802110	+	0.996778i	$0.525559\pi$
$348$	−4.98163	+	15.3319i	−0.267043	+	0.821874i
$349$	8.27194	+	25.4584i	0.442787	+	1.36276i	0.884893	+	0.465794i	$0.154231\pi$
$349$	8.27194	+	25.4584i	0.442787	+	1.36276i	−0.442106	+	0.896963i	$0.645769\pi$
$350$	0.809017	−	0.587785i	0.0432438	−	0.0314184i
$351$	23.1720			1.23683
$352$	3.24871	−	0.667752i	0.173157	−	0.0355913i
$353$	−32.9268			−1.75252			−0.876259	−	0.481841i	$-0.839968\pi$
$353$	−32.9268			−1.75252			−0.876259	+	0.481841i	$0.839968\pi$
$354$	20.2177	−	14.6890i	1.07456	−	0.780711i
$355$	−1.39289	−	4.28689i	−0.0739271	−	0.227524i
$356$	0.453747	−	1.39649i	0.0240486	−	0.0740138i
$357$	−6.71003	−	4.87512i	−0.355132	−	0.258019i
$358$	−10.7335	−	7.79831i	−0.567281	−	0.412154i
$359$	11.1607	−	34.3490i	0.589038	−	1.81287i	0.00662506	−	0.999978i	$-0.497891\pi$
$359$	11.1607	−	34.3490i	0.589038	−	1.81287i	0.582413	−	0.812893i	$-0.302109\pi$
$360$	0.217735	+	0.670119i	0.0114756	+	0.0353184i
$361$	14.9275	−	10.8455i	0.785660	−	0.570816i
$362$	19.5835			1.02929
$363$	13.9542	+	15.9229i	0.732405	+	0.835734i
$364$	5.24489			0.274907
$365$	2.69736	−	1.95975i	0.141186	−	0.102578i
$366$	7.78486	+	23.9593i	0.406921	+	1.25237i
$367$	−2.58237	+	7.94771i	−0.134798	+	0.414867i	−0.995559	−	0.0941437i	$-0.969989\pi$
$367$	−2.58237	+	7.94771i	−0.134798	+	0.414867i	0.860760	+	0.509011i	$0.169989\pi$
$368$	0.693299	+	0.503711i	0.0361407	+	0.0262578i
$369$	6.11079	+	4.43975i	0.318115	+	0.231124i
$370$	−0.549806	+	1.69213i	−0.0285831	+	0.0879697i
$371$	2.72139	+	8.37558i	0.141288	+	0.434838i
$372$	−1.71750	+	1.24784i	−0.0890482	+	0.0646973i
$373$	−16.0205			−0.829509			−0.414755	−	0.909933i	$-0.636133\pi$
$373$	−16.0205			−0.829509			−0.414755	+	0.909933i	$0.636133\pi$
$374$	−13.9993	+	2.87747i	−0.723887	+	0.148790i
$375$	1.92474			0.0993929
$376$	−6.79713	+	4.93840i	−0.350535	+	0.254679i
$377$	13.5749	+	41.7792i	0.699142	+	2.15174i
$378$	1.36525	−	4.20179i	0.0702207	−	0.216117i
$379$	−20.5387	−	14.9222i	−1.05500	−	0.766503i	−0.0818443	−	0.996645i	$-0.526081\pi$
$379$	−20.5387	−	14.9222i	−1.05500	−	0.766503i	−0.973157	+	0.230142i	$0.926081\pi$
$380$	0.599184	+	0.435333i	0.0307375	+	0.0223321i
$381$	5.60317	−	17.2448i	0.287059	−	0.883478i
$382$	−3.94166	−	12.1312i	−0.201673	−	0.620685i
$383$	0.245390	−	0.178286i	0.0125388	−	0.00910999i	−0.581498	−	0.813548i	$-0.697533\pi$
$383$	0.245390	−	0.178286i	0.0125388	−	0.00910999i	0.594037	+	0.804438i	$0.297533\pi$
$384$	1.92474			0.0982212
$385$	2.23577	−	2.44977i	0.113945	−	0.124852i
$386$	11.8288			0.602072
$387$	−0.646835	+	0.469953i	−0.0328805	+	0.0238891i
$388$	2.60101	+	8.00509i	0.132046	+	0.406397i
$389$	−2.08295	+	6.41067i	−0.105610	+	0.325034i	−0.989873	−	0.141955i	$-0.954661\pi$
$389$	−2.08295	+	6.41067i	−0.105610	+	0.325034i	0.884263	+	0.466989i	$0.154661\pi$
$390$	8.16704	+	5.93370i	0.413554	+	0.300465i
$391$	−2.98756	−	2.17059i	−0.151087	−	0.109771i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	−0.513188	−	1.57943i	−0.0258869	−	0.0796717i
$394$	17.7259	−	12.8786i	0.893020	−	0.648817i
$395$	−1.56183			−0.0785841
$396$	1.15483	+	2.03163i	0.0580324	+	0.102093i
$397$	−19.9230			−0.999904			−0.499952	−	0.866053i	$-0.666649\pi$
$397$	−19.9230			−0.999904			−0.499952	+	0.866053i	$0.666649\pi$
$398$	−8.34267	+	6.06130i	−0.418180	+	0.303826i
$399$	0.440510	+	1.35575i	0.0220531	+	0.0678725i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	−27.5782	−	20.0368i	−1.37719	−	1.00059i	−0.997136	−	0.0756247i	$-0.975905\pi$
$401$	−27.5782	−	20.0368i	−1.37719	−	1.00059i	−0.380055	−	0.924964i	$-0.624095\pi$
$402$	−13.9149	−	10.1098i	−0.694012	−	0.504229i
$403$	−1.78767	+	5.50187i	−0.0890500	+	0.274068i
$404$	−3.40832	−	10.4897i	−0.169570	−	0.521883i
$405$	8.58961	−	6.24072i	0.426821	−	0.310104i
$406$	8.37564			0.415676
$407$	−0.656237	+	5.86437i	−0.0325285	+	0.290686i
$408$	−8.29405			−0.410617
$409$	−6.55037	+	4.75912i	−0.323895	+	0.235323i	−0.737836	−	0.674980i	$-0.764152\pi$
$409$	−6.55037	+	4.75912i	−0.323895	+	0.235323i	0.413941	+	0.910304i	$0.364152\pi$
$410$	−3.31266	−	10.1953i	−0.163600	−	0.503510i
$411$	−10.2580	+	31.5710i	−0.505992	+	1.55728i
$412$	−4.74855	−	3.45002i	−0.233944	−	0.169971i
$413$	−10.5041	−	7.63170i	−0.516874	−	0.375531i
$414$	−0.186591	+	0.574268i	−0.00917045	+	0.0282238i
$415$	0.188258	+	0.579398i	0.00924121	+	0.0284415i
$416$	4.24320	−	3.08287i	0.208040	−	0.151150i
$417$	39.3509			1.92702
$418$	2.23727	+	1.01416i	0.109428	+	0.0496043i
$419$	−24.0686			−1.17583			−0.587915	−	0.808923i	$-0.700051\pi$
$419$	−24.0686			−1.17583			−0.587915	+	0.808923i	$0.700051\pi$
$420$	1.55714	−	1.13133i	0.0759808	−	0.0552033i
$421$	4.26045	+	13.1123i	0.207642	+	0.639055i	0.999595	+	0.0284730i	$0.00906447\pi$
$421$	4.26045	+	13.1123i	0.207642	+	0.639055i	−0.791953	+	0.610582i	$0.790936\pi$
$422$	−7.67768	+	23.6295i	−0.373744	+	1.15026i
$423$	−4.78929	−	3.47962i	−0.232863	−	0.169185i
$424$	7.12469	+	5.17639i	0.346006	+	0.251388i
$425$	−1.33161	+	4.09828i	−0.0645927	+	0.198796i
$426$	−2.68095	−	8.25112i	−0.129893	−	0.399768i
$427$	10.5890	−	7.69336i	0.512438	−	0.372308i
$428$	6.83162			0.330219
$429$	30.4946	+	13.8233i	1.47229	+	0.667396i
$430$	1.13472			0.0547212
$431$	7.05467	−	5.12552i	0.339811	−	0.246887i	−0.404771	−	0.914418i	$-0.632649\pi$
$431$	7.05467	−	5.12552i	0.339811	−	0.246887i	0.744582	+	0.667531i	$0.232649\pi$
$432$	−1.36525	−	4.20179i	−0.0656854	−	0.202159i
$433$	−2.63249	+	8.10197i	−0.126509	+	0.389356i	−0.994173	−	0.107796i	$-0.965621\pi$
$433$	−2.63249	+	8.10197i	−0.126509	+	0.389356i	0.867664	+	0.497152i	$0.165621\pi$
$434$	0.892330	+	0.648316i	0.0428332	+	0.0311202i
$435$	13.0421	+	9.47562i	0.625319	+	0.454321i
$436$	−2.40040	+	7.38766i	−0.114958	+	0.353805i
$437$	0.196132	+	0.603632i	0.00938226	+	0.0288756i
$438$	5.19171	−	3.77200i	0.248070	−	0.180233i
$439$	−22.5402			−1.07579			−0.537894	−	0.843013i	$-0.680780\pi$
$439$	−22.5402			−1.07579			−0.537894	+	0.843013i	$0.680780\pi$
$440$	0.368836	−	3.29605i	0.0175836	−	0.157133i
$441$	0.704605			0.0335526
$442$	−18.2848	+	13.2847i	−0.869717	+	0.631887i
$443$	11.7145	+	36.0535i	0.556572	+	1.71295i	0.691756	+	0.722131i	$0.256837\pi$
$443$	11.7145	+	36.0535i	0.556572	+	1.71295i	−0.135185	+	0.990820i	$0.543163\pi$
$444$	−1.05823	+	3.25690i	−0.0502215	+	0.154566i
$445$	−1.18793	−	0.863078i	−0.0563131	−	0.0409138i
$446$	16.3741	+	11.8964i	0.775334	+	0.563313i
$447$	1.11995	−	3.44686i	0.0529719	−	0.163031i
$448$	−0.309017	−	0.951057i	−0.0145997	−	0.0449332i
$449$	25.9331	−	18.8415i	1.22386	−	0.889186i	0.227445	−	0.973791i	$-0.426963\pi$
$449$	25.9331	−	18.8415i	1.22386	−	0.889186i	0.996415	+	0.0846050i	$0.0269628\pi$
$450$	0.704605			0.0332154
$451$	−17.5698	−	30.9096i	−0.827329	−	1.45547i
$452$	4.63948			0.218223
$453$	−8.48790	+	6.16682i	−0.398797	+	0.289743i
$454$	3.64919	+	11.2310i	0.171265	+	0.527099i
$455$	1.62076	−	4.98818i	0.0759823	−	0.233850i
$456$	1.15327	+	0.837901i	0.0540069	+	0.0392383i
$457$	−19.8406	−	14.4150i	−0.928104	−	0.674307i	0.0174242	−	0.999848i	$-0.494453\pi$
$457$	−19.8406	−	14.4150i	−0.928104	−	0.674307i	−0.945528	+	0.325541i	$0.894453\pi$
$458$	0.518857	−	1.59688i	0.0242446	−	0.0746172i
$459$	5.88310	+	18.1063i	0.274600	+	0.845131i
$460$	0.693299	−	0.503711i	0.0323252	−	0.0234857i
$461$	−0.188328			−0.00877132			−0.00438566	−	0.999990i	$-0.501396\pi$
$461$	−0.188328			−0.00877132			−0.00438566	+	0.999990i	$0.501396\pi$
$462$	4.30326	−	4.71515i	0.200206	−	0.219369i
$463$	−9.40956			−0.437299			−0.218650	−	0.975803i	$-0.570165\pi$
$463$	−9.40956			−0.437299			−0.218650	+	0.975803i	$0.570165\pi$
$464$	6.77603	−	4.92308i	0.314569	−	0.228548i
$465$	0.656026	+	2.01904i	0.0304225	+	0.0936308i
$466$	−4.79656	+	14.7623i	−0.222197	+	0.683851i
$467$	−1.49441	−	1.08576i	−0.0691532	−	0.0502427i	0.552672	−	0.833399i	$-0.313608\pi$
$467$	−1.49441	−	1.08576i	−0.0691532	−	0.0502427i	−0.621825	+	0.783156i	$0.713608\pi$
$468$	2.98978	+	2.17220i	0.138203	+	0.100410i
$469$	−2.76143	+	8.49881i	−0.127511	+	0.392438i
$470$	2.59627	+	7.99051i	0.119757	+	0.368575i
$471$	18.6514	−	13.5510i	0.859410	−	0.624398i
$472$	−12.9838			−0.597629
$473$	3.68639	−	0.757714i	0.169500	−	0.0348397i
$474$	−3.00610			−0.138075
$475$	0.599184	−	0.435333i	0.0274925	−	0.0199744i
$476$	1.33161	+	4.09828i	0.0610344	+	0.187844i
$477$	−1.91751	+	5.90148i	−0.0877966	+	0.270210i
$478$	17.8014	+	12.9335i	0.814217	+	0.591564i
$479$	−26.9812	−	19.6030i	−1.23280	−	0.895683i	−0.235705	−	0.971825i	$-0.575740\pi$
$479$	−26.9812	−	19.6030i	−1.23280	−	0.895683i	−0.997097	+	0.0761421i	$0.975740\pi$
$480$	0.594776	−	1.83053i	0.0271477	−	0.0835520i
$481$	2.88367	+	8.87503i	0.131484	+	0.404666i
$482$	19.2672	−	13.9984i	0.877595	−	0.637610i
$483$	1.64943			0.0750517
$484$	−1.00271	−	10.9542i	−0.0455775	−	0.497918i
$485$	8.41705			0.382198
$486$	5.80995	−	4.22118i	0.263545	−	0.191477i
$487$	4.36136	+	13.4229i	0.197632	+	0.608249i	0.999936	+	0.0113327i	$0.00360738\pi$
$487$	4.36136	+	13.4229i	0.197632	+	0.608249i	−0.802304	+	0.596916i	$0.796393\pi$
$488$	4.04464	−	12.4481i	0.183092	−	0.563500i
$489$	24.2202	+	17.5970i	1.09528	+	0.795765i
$490$	−0.809017	−	0.587785i	−0.0365477	−	0.0265534i
$491$	−2.59847	+	7.99726i	−0.117267	+	0.360911i	−0.992413	−	0.122948i	$-0.960765\pi$
$491$	−2.59847	+	7.99726i	−0.117267	+	0.360911i	0.875146	+	0.483859i	$0.160765\pi$
$492$	−6.37599	−	19.6233i	−0.287452	−	0.884685i
$493$	−29.1992	+	21.2145i	−1.31507	+	0.955451i
$494$	3.88453			0.174773
$495$	2.28906	−	0.470502i	0.102885	−	0.0211475i
$496$	1.10298			0.0495253
$497$	−3.64664	+	2.64944i	−0.163574	+	0.118844i
$498$	0.362346	+	1.11519i	0.0162371	+	0.0499727i
$499$	−7.04828	+	21.6924i	−0.315524	+	0.971084i	0.660014	+	0.751254i	$0.270550\pi$
$499$	−7.04828	+	21.6924i	−0.315524	+	0.971084i	−0.975538	+	0.219831i	$0.929450\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−28.1024	−	20.4176i	−1.25552	−	0.912189i
$502$	8.80956	−	27.1130i	0.393190	−	1.21011i
$503$	−6.99949	−	21.5422i	−0.312092	−	0.960520i	−0.976935	−	0.213537i	$-0.931502\pi$
$503$	−6.99949	−	21.5422i	−0.312092	−	0.960520i	0.664843	−	0.746983i	$-0.268498\pi$
$504$	0.570037	−	0.414156i	0.0253915	−	0.0184480i
$505$	−11.0295			−0.490808
$506$	1.91597	−	2.09936i	0.0851753	−	0.0933281i
$507$	27.9256			1.24022
$508$	−7.62146	+	5.53732i	−0.338148	+	0.245679i
$509$	−4.65171	−	14.3165i	−0.206184	−	0.634568i	−0.999663	−	0.0259704i	$-0.991732\pi$
$509$	−4.65171	−	14.3165i	−0.206184	−	0.634568i	0.793479	−	0.608597i	$-0.208268\pi$
$510$	−2.56300	+	7.88811i	−0.113492	+	0.349291i
$511$	−2.69736	−	1.95975i	−0.119324	−	0.0866942i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	1.01115	−	3.11199i	0.0446432	−	0.137398i
$514$	9.15288	+	28.1697i	0.403716	+	1.24251i
$515$	−4.74855	+	3.45002i	−0.209246	+	0.152026i
$516$	2.18404			0.0961471
$517$	13.7702	+	24.2252i	0.605613	+	1.06542i
$518$	1.77921			0.0781740
$519$	14.9589	−	10.8683i	0.656624	−	0.477065i
$520$	−1.62076	−	4.98818i	−0.0710750	−	0.218746i
$521$	−2.31138	+	7.11369i	−0.101263	+	0.311656i	−0.988835	−	0.149013i	$-0.952390\pi$
$521$	−2.31138	+	7.11369i	−0.101263	+	0.311656i	0.887572	+	0.460669i	$0.152390\pi$
$522$	4.77443	+	3.46882i	0.208971	+	0.151826i
$523$	4.16267	+	3.02436i	0.182021	+	0.132246i	0.675065	−	0.737759i	$-0.264116\pi$
$523$	4.16267	+	3.02436i	0.182021	+	0.132246i	−0.493044	+	0.870005i	$0.664116\pi$
$524$	−0.266628	+	0.820596i	−0.0116477	+	0.0358479i
$525$	−0.594776	−	1.83053i	−0.0259581	−	0.0798910i
$526$	−3.31037	+	2.40512i	−0.144339	+	0.104868i
$527$	−4.75295			−0.207042
$528$	0.709912	−	6.34403i	0.0308949	−	0.276088i
$529$	−22.2656			−0.968070
$530$	7.12469	−	5.17639i	0.309477	−	0.224848i
$531$	−2.82703	−	8.70071i	−0.122683	−	0.377578i
$532$	0.228868	−	0.704384i	0.00992269	−	0.0305389i
$533$	−45.4870	−	33.0483i	−1.97026	−	1.43148i
$534$	−2.28644	−	1.66120i	−0.0989440	−	0.0718870i
$535$	2.11109	−	6.49726i	0.0912702	−	0.280901i
$536$	2.76143	+	8.49881i	0.119276	+	0.367092i
$537$	−20.6591	+	15.0097i	−0.891504	+	0.647716i
$538$	2.99735			0.129225
$539$	−3.02076	−	1.36932i	−0.130113	−	0.0589808i
$540$	−4.41803			−0.190122
$541$	1.55376	−	1.12887i	0.0668013	−	0.0485340i	−0.553883	−	0.832594i	$-0.686855\pi$
$541$	1.55376	−	1.12887i	0.0668013	−	0.0485340i	0.620685	+	0.784060i	$0.286855\pi$
$542$	7.63319	+	23.4925i	0.327874	+	1.00909i
$543$	11.6478	−	35.8482i	0.499854	−	1.53839i
$544$	3.48621	+	2.53288i	0.149470	+	0.108596i
$545$	6.28432	+	4.56582i	0.269191	+	0.195578i
$546$	3.11953	−	9.60093i	0.133504	−	0.410882i
$547$	0.0806399	+	0.248184i	0.00344791	+	0.0106116i	0.952766	−	0.303706i	$-0.0982242\pi$
$547$	0.0806399	+	0.248184i	0.00344791	+	0.0106116i	−0.949318	+	0.314318i	$0.898224\pi$
$548$	13.9530	−	10.1375i	0.596044	−	0.433051i
$549$	9.22238			0.393602
$550$	−3.02076	−	1.36932i	−0.128805	−	0.0583880i
$551$	6.20327			0.264268
$552$	1.33442	−	0.969511i	0.0567965	−	0.0412651i
$553$	0.482631	+	1.48539i	0.0205236	+	0.0631651i
$554$	0.827728	−	2.54748i	0.0351668	−	0.108232i
$555$	2.77049	+	2.01288i	0.117601	+	0.0854418i
$556$	−16.5402	−	12.0172i	−0.701462	−	0.509642i
$557$	−1.95258	+	6.00942i	−0.0827334	+	0.254627i	−0.983863	−	0.178922i	$-0.942739\pi$
$557$	−1.95258	+	6.00942i	−0.0827334	+	0.254627i	0.901130	+	0.433549i	$0.142739\pi$
$558$	0.240157	+	0.739128i	0.0101667	+	0.0312898i
$559$	4.81486	−	3.49820i	0.203647	−	0.147958i
$560$	−1.00000			−0.0422577
$561$	−3.05914	+	27.3376i	−0.129157	+	1.15420i
$562$	−11.6213			−0.490217
$563$	−0.775602	+	0.563508i	−0.0326877	+	0.0237490i	−0.604009	−	0.796977i	$-0.706431\pi$
$563$	−0.775602	+	0.563508i	−0.0326877	+	0.0237490i	0.571321	+	0.820726i	$0.306431\pi$
$564$	4.99714	+	15.3796i	0.210417	+	0.647598i
$565$	1.43368	−	4.41241i	0.0603153	−	0.185632i
$566$	−14.6725	−	10.6602i	−0.616731	−	0.448081i
$567$	−8.58961	−	6.24072i	−0.360730	−	0.262086i
$568$	−1.39289	+	4.28689i	−0.0584445	+	0.179874i
$569$	−2.19958	−	6.76961i	−0.0922112	−	0.283797i	0.894306	−	0.447457i	$-0.147670\pi$
$569$	−2.19958	−	6.76961i	−0.0922112	−	0.283797i	−0.986517	+	0.163660i	$0.947670\pi$
$570$	1.15327	−	0.837901i	0.0483052	−	0.0350958i
$571$	−27.1751			−1.13724			−0.568621	−	0.822599i	$-0.692523\pi$
$571$	−27.1751			−1.13724			−0.568621	+	0.822599i	$0.692523\pi$
$572$	−8.59624	−	15.1229i	−0.359427	−	0.632320i
$573$	−24.5509			−1.02563
$574$	−8.67265	+	6.30105i	−0.361989	+	0.263001i
$575$	−0.264817	−	0.815022i	−0.0110436	−	0.0339888i
$576$	0.217735	−	0.670119i	0.00907229	−	0.0279216i
$577$	26.1881	+	19.0268i	1.09022	+	0.792094i	0.979437	−	0.201750i	$-0.0646629\pi$
$577$	26.1881	+	19.0268i	1.09022	+	0.792094i	0.110787	+	0.993844i	$0.464663\pi$
$578$	−1.26944	−	0.922304i	−0.0528018	−	0.0383628i
$579$	7.03551	−	21.6531i	0.292386	−	0.899871i
$580$	−2.58821	−	7.96570i	−0.107470	−	0.330758i
$581$	0.492865	−	0.358088i	0.0204475	−	0.0148560i
$582$	16.2006			0.671536
$583$	19.6895	−	21.5741i	0.815456	−	0.893509i
$584$	−3.33413			−0.137967
$585$	2.98978	−	2.17220i	0.123612	−	0.0898095i
$586$	−7.06723	−	21.7507i	−0.291945	−	0.898513i
$587$	−2.48724	+	7.65494i	−0.102659	+	0.315953i	−0.989174	−	0.146748i	$-0.953120\pi$
$587$	−2.48724	+	7.65494i	−0.102659	+	0.315953i	0.886515	+	0.462701i	$0.153120\pi$
$588$	−1.55714	−	1.13133i	−0.0642155	−	0.0466553i
$589$	0.660889	+	0.480164i	0.0272315	+	0.0197848i
$590$	−4.01222	+	12.3483i	−0.165181	+	0.508373i
$591$	−13.0318	−	40.1078i	−0.536057	−	1.64981i
$592$	1.43941	−	1.04579i	0.0591595	−	0.0429819i
$593$	−39.8151			−1.63501			−0.817506	−	0.575920i	$-0.804644\pi$
$593$	−39.8151			−1.63501			−0.817506	+	0.575920i	$0.804644\pi$
$594$	−14.3529	+	2.95015i	−0.588906	+	0.121046i
$595$	4.30919			0.176660
$596$	−1.52336	+	1.10679i	−0.0623994	+	0.0453358i
$597$	6.13339	+	18.8766i	0.251023	+	0.772569i
$598$	1.38893	−	4.27470i	0.0567977	−	0.174805i
$599$	−24.9117	−	18.0994i	−1.01786	−	0.739521i	−0.0520190	−	0.998646i	$-0.516566\pi$
$599$	−24.9117	−	18.0994i	−1.01786	−	0.739521i	−0.965844	+	0.259126i	$0.916566\pi$
$600$	−1.55714	−	1.13133i	−0.0635701	−	0.0461864i
$601$	10.2946	−	31.6835i	0.419926	−	1.29240i	−0.487845	−	0.872930i	$-0.662217\pi$
$601$	10.2946	−	31.6835i	0.419926	−	1.29240i	0.907770	−	0.419468i	$-0.137783\pi$
$602$	−0.350649	−	1.07919i	−0.0142914	−	0.0439843i
$603$	−5.09395	+	3.70097i	−0.207442	+	0.150715i
$604$	5.45095			0.221796
$605$	−10.7279	−	2.43141i	−0.436152	−	0.0988507i
$606$	−21.2290			−0.862367
$607$	13.6520	−	9.91875i	0.554117	−	0.402590i	−0.275184	−	0.961392i	$-0.588739\pi$
$607$	13.6520	−	9.91875i	0.554117	−	0.402590i	0.829301	+	0.558802i	$0.188739\pi$
$608$	−0.228868	−	0.704384i	−0.00928183	−	0.0285665i
$609$	4.98163	−	15.3319i	0.201866	−	0.621279i
$610$	−10.5890	−	7.69336i	−0.428736	−	0.311495i
$611$	35.6502	+	25.9014i	1.44225	+	1.04786i
$612$	−0.938261	+	2.88767i	−0.0379270	+	0.116727i
$613$	8.26848	+	25.4478i	0.333961	+	1.02783i	0.967232	+	0.253895i	$0.0817119\pi$
$613$	8.26848	+	25.4478i	0.333961	+	1.02783i	−0.633271	+	0.773930i	$0.718288\pi$
$614$	16.1258	−	11.7161i	0.650784	−	0.472822i
$615$	−20.6331			−0.832008
$616$	−3.24871	+	0.667752i	−0.130894	+	0.0269045i
$617$	32.5387			1.30996			0.654979	−	0.755647i	$-0.272677\pi$
$617$	32.5387			1.30996			0.654979	+	0.755647i	$0.272677\pi$
$618$	−9.13970	+	6.64038i	−0.367653	+	0.267115i
$619$	−4.30312	−	13.2436i	−0.172957	−	0.532307i	0.826577	−	0.562823i	$-0.190285\pi$
$619$	−4.30312	−	13.2436i	−0.172957	−	0.532307i	−0.999534	+	0.0305162i	$0.990285\pi$
$620$	0.340840	−	1.04900i	0.0136885	−	0.0421287i
$621$	−3.06301	−	2.22541i	−0.122915	−	0.0893026i
$622$	1.03908	+	0.754933i	0.0416631	+	0.0302700i
$623$	−0.453747	+	1.39649i	−0.0181790	+	0.0559492i
$624$	−3.11953	−	9.60093i	−0.124881	−	0.384345i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−13.3964			−0.535429
$627$	3.18713	−	3.49219i	0.127282	−	0.139465i
$628$	−11.9779			−0.477972
$629$	−6.20270	+	4.50652i	−0.247318	+	0.179687i
$630$	−0.217735	−	0.670119i	−0.00867477	−	0.0266982i
$631$	−3.96624	+	12.2068i	−0.157893	+	0.485946i	−0.998443	−	0.0557894i	$-0.982232\pi$
$631$	−3.96624	+	12.2068i	−0.157893	+	0.485946i	0.840549	+	0.541735i	$0.182232\pi$
$632$	1.26355	+	0.918019i	0.0502611	+	0.0365168i
$633$	38.6880	+	28.1085i	1.53771	+	1.11721i
$634$	5.14945	−	15.8484i	0.204511	−	0.629419i
$635$	2.91114	+	8.95957i	0.115525	+	0.355550i
$636$	13.7131	−	9.96319i	0.543762	−	0.395066i
$637$	−5.24489			−0.207810
$638$	−13.7275	−	24.1500i	−0.543476	−	0.956106i
$639$	−3.17601			−0.125641
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−15.0067	−	46.1860i	−0.592731	−	1.82424i	−0.565711	−	0.824603i	$-0.691398\pi$
$641$	−15.0067	−	46.1860i	−0.592731	−	1.82424i	−0.0270198	−	0.999635i	$-0.508602\pi$
$642$	4.06328	−	12.5055i	0.160365	−	0.493553i
$643$	11.4679	+	8.33189i	0.452248	+	0.328578i	0.790483	−	0.612484i	$-0.209830\pi$
$643$	11.4679	+	8.33189i	0.452248	+	0.328578i	−0.338235	+	0.941062i	$0.609830\pi$
$644$	−0.693299	−	0.503711i	−0.0273198	−	0.0198490i
$645$	0.674906	−	2.07715i	0.0265744	−	0.0817876i
$646$	0.986236	+	3.03532i	0.0388029	+	0.119423i
$647$	20.0622	−	14.5760i	0.788725	−	0.573042i	−0.118860	−	0.992911i	$-0.537924\pi$
$647$	20.0622	−	14.5760i	0.788725	−	0.573042i	0.907585	+	0.419869i	$0.137924\pi$
$648$	−10.6173			−0.417089
$649$	−4.78890	+	42.7953i	−0.187981	+	1.67986i
$650$	−5.24489			−0.205721
$651$	1.71750	−	1.24784i	0.0673141	−	0.0489066i
$652$	−4.80653	−	14.7930i	−0.188238	−	0.579338i
$653$	−8.97871	+	27.6336i	−0.351364	+	1.08139i	0.606724	+	0.794913i	$0.292483\pi$
$653$	−8.97871	+	27.6336i	−0.351364	+	1.08139i	−0.958088	+	0.286475i	$0.907517\pi$
$654$	12.0956	+	8.78800i	0.472977	+	0.343638i
$655$	0.698040	+	0.507156i	0.0272747	+	0.0198162i
$656$	−3.31266	+	10.1953i	−0.129338	+	0.398060i
$657$	−0.725955	−	2.23426i	−0.0283222	−	0.0871668i
$658$	6.79713	−	4.93840i	0.264980	−	0.192519i
$659$	44.0463			1.71580			0.857899	−	0.513818i	$-0.171769\pi$
$659$	44.0463			1.71580			0.857899	+	0.513818i	$0.171769\pi$
$660$	−5.81415	−	2.63558i	−0.226316	−	0.102590i
$661$	−0.575059			−0.0223672			−0.0111836	−	0.999937i	$-0.503560\pi$
$661$	−0.575059			−0.0223672			−0.0111836	+	0.999937i	$0.503560\pi$
$662$	−9.00758	+	6.54439i	−0.350090	+	0.254355i
$663$	13.4427	+	41.3722i	0.522069	+	1.60676i
$664$	0.188258	−	0.579398i	0.00730582	−	0.0224850i
$665$	−0.599184	−	0.435333i	−0.0232354	−	0.0168815i
$666$	1.01422	+	0.736872i	0.0393001	+	0.0285532i
$667$	2.21801	−	6.82633i	0.0858816	−	0.264316i
$668$	5.57695	+	17.1641i	0.215779	+	0.664098i
$669$	31.5157	−	22.8975i	1.21847	−	0.885269i
$670$	8.93617			0.345234
$671$	−39.5378	−	17.9227i	−1.52634	−	0.691897i
$672$	−1.92474			−0.0742483
$673$	22.4558	−	16.3151i	0.865606	−	0.628899i	−0.0637984	−	0.997963i	$-0.520321\pi$
$673$	22.4558	−	16.3151i	0.865606	−	0.628899i	0.929404	+	0.369063i	$0.120321\pi$
$674$	−2.07609	−	6.38956i	−0.0799682	−	0.246117i
$675$	−1.36525	+	4.20179i	−0.0525483	+	0.161727i
$676$	−11.7379	−	8.52807i	−0.451457	−	0.328003i
$677$	−41.4103	−	30.0863i	−1.59153	−	1.15631i	−0.901724	−	0.432312i	$-0.857698\pi$
$677$	−41.4103	−	30.0863i	−1.59153	−	1.15631i	−0.689801	−	0.723999i	$-0.742302\pi$
$678$	2.75945	−	8.49272i	0.105976	−	0.326161i
$679$	−2.60101	−	8.00509i	−0.0998176	−	0.307207i
$680$	3.48621	−	2.53288i	0.133690	−	0.0971314i
$681$	22.7292			0.870986
$682$	0.406819	−	3.63548i	0.0155779	−	0.139210i
$683$	−1.55522			−0.0595090			−0.0297545	−	0.999557i	$-0.509473\pi$
$683$	−1.55522			−0.0595090			−0.0297545	+	0.999557i	$0.509473\pi$
$684$	0.422188	−	0.306738i	0.0161428	−	0.0117284i
$685$	−5.32959	−	16.4028i	−0.203633	−	0.626718i
$686$	−0.309017	+	0.951057i	−0.0117983	+	0.0363115i
$687$	−2.61453	−	1.89957i	−0.0997507	−	0.0724731i
$688$	−0.918010	−	0.666974i	−0.0349988	−	0.0254281i
$689$	14.2734	−	43.9290i	0.543773	−	1.67356i
$690$	−0.509702	−	1.56870i	−0.0194040	−	0.0597194i
$691$	−3.72545	+	2.70670i	−0.141723	+	0.102968i	−0.656388	−	0.754424i	$-0.727916\pi$
$691$	−3.72545	+	2.70670i	−0.141723	+	0.102968i	0.514665	+	0.857392i	$0.327916\pi$
$692$	−9.60665			−0.365190
$693$	−1.15483	−	2.03163i	−0.0438684	−	0.0771752i
$694$	−19.4103			−0.736804
$695$	−16.5402	+	12.0172i	−0.627407	+	0.455838i
$696$	−4.98163	−	15.3319i	−0.188828	−	0.581153i
$697$	14.2749	−	43.9335i	0.540699	−	1.66410i
$698$	−21.6562	−	15.7342i	−0.819700	−	0.595547i
$699$	24.1700	+	17.5605i	0.914193	+	0.664200i
$700$	−0.309017	+	0.951057i	−0.0116797	+	0.0359466i
$701$	−0.900736	−	2.77218i	−0.0340203	−	0.104704i	0.932604	−	0.360900i	$-0.117531\pi$
$701$	−0.900736	−	2.77218i	−0.0340203	−	0.104704i	−0.966625	+	0.256197i	$0.917531\pi$
$702$	−18.7466	+	13.6202i	−0.707544	+	0.514061i
$703$	1.31774			0.0496996
$704$	−2.23577	+	2.44977i	−0.0842636	+	0.0923290i
$705$	16.1711			0.609038
$706$	26.6383	−	19.3539i	1.00255	−	0.728393i
$707$	3.40832	+	10.4897i	0.128183	+	0.394507i
$708$	−7.72246	+	23.7673i	−0.290228	+	0.893230i
$709$	−2.93153	−	2.12988i	−0.110096	−	0.0799893i	0.531375	−	0.847137i	$-0.321676\pi$
$709$	−2.93153	−	2.12988i	−0.110096	−	0.0799893i	−0.641471	+	0.767147i	$0.721676\pi$
$710$	3.64664	+	2.64944i	0.136856	+	0.0994317i
$711$	−0.340064	+	1.04661i	−0.0127534	+	0.0392510i
$712$	0.453747	+	1.39649i	0.0170049	+	0.0523357i
$713$	0.764695	−	0.555584i	0.0286381	−	0.0208068i
$714$	8.29405			0.310397
$715$	−17.0391	+	3.50228i	−0.637226	+	0.130978i
$716$	13.2673			0.495822
$717$	34.2630	−	24.8935i	1.27957	−	0.929666i
$718$	11.1607	+	34.3490i	0.416512	+	1.28189i
$719$	−2.69552	+	8.29597i	−0.100526	+	0.309388i	−0.988654	−	0.150208i	$-0.952006\pi$
$719$	−2.69552	+	8.29597i	−0.100526	+	0.309388i	0.888128	+	0.459596i	$0.152006\pi$
$720$	−0.570037	−	0.414156i	−0.0212440	−	0.0154347i
$721$	4.74855	+	3.45002i	0.176845	+	0.128486i
$722$	−5.70182	+	17.5484i	−0.212200	+	0.653083i
$723$	−14.1649	−	43.5951i	−0.526798	−	1.62132i
$724$	−15.8434	+	11.5109i	−0.588815	+	0.427799i
$725$	−8.37564			−0.311063
$726$	−20.6484	−	4.67981i	−0.766334	−	0.173684i
$727$	37.3206			1.38415			0.692073	−	0.721828i	$-0.256698\pi$
$727$	37.3206			1.38415			0.692073	+	0.721828i	$0.256698\pi$
$728$	−4.24320	+	3.08287i	−0.157264	+	0.114259i
$729$	5.57144	+	17.1471i	0.206350	+	0.635079i
$730$	−1.03030	+	3.17094i	−0.0381332	+	0.117362i
$731$	3.95588	+	2.87412i	0.146314	+	0.106303i
$732$	−20.3810	−	14.8077i	−0.753304	−	0.547308i
$733$	2.72016	−	8.37179i	0.100471	−	0.309219i	−0.888170	−	0.459516i	$-0.848023\pi$
$733$	2.72016	−	8.37179i	0.100471	−	0.309219i	0.988641	+	0.150297i	$0.0480230\pi$
$734$	−2.58237	−	7.94771i	−0.0953169	−	0.293355i
$735$	−1.55714	+	1.13133i	−0.0574361	+	0.0417298i
$736$	−0.856965			−0.0315881
$737$	29.0310	−	5.96715i	1.06937	−	0.219803i
$738$	−7.55335			−0.278043
$739$	−40.9634	+	29.7616i	−1.50686	+	1.09480i	−0.539316	+	0.842103i	$0.681317\pi$
$739$	−40.9634	+	29.7616i	−1.50686	+	1.09480i	−0.967546	+	0.252696i	$0.918683\pi$
$740$	−0.549806	−	1.69213i	−0.0202113	−	0.0622039i
$741$	2.31043	−	7.11076i	0.0848756	−	0.261220i
$742$	−7.12469	−	5.17639i	−0.261556	−	0.190031i
$743$	40.8144	+	29.6534i	1.49733	+	1.08788i	0.971428	+	0.237335i	$0.0762740\pi$
$743$	40.8144	+	29.6534i	1.49733	+	1.08788i	0.525907	+	0.850542i	$0.323726\pi$
$744$	0.656026	−	2.01904i	0.0240511	−	0.0740216i
$745$	0.581873	+	1.79082i	0.0213182	+	0.0656106i
$746$	12.9608	−	9.41660i	0.474530	−	0.344766i
$747$	0.429256			0.0157057
$748$	9.63434	−	10.5565i	0.352266	−	0.385984i
$749$	−6.83162			−0.249622
$750$	−1.55714	+	1.13133i	−0.0568588	+	0.0413104i
$751$	−7.40574	−	22.7925i	−0.270239	−	0.831711i	−0.990440	−	0.137945i	$-0.955950\pi$
$751$	−7.40574	−	22.7925i	−0.270239	−	0.831711i	0.720201	−	0.693766i	$-0.244050\pi$
$752$	2.59627	−	7.99051i	0.0946763	−	0.291384i
$753$	−44.3916	−	32.2524i	−1.61772	−	1.17534i
$754$	−35.5395	−	25.8210i	−1.29427	−	0.940344i
$755$	1.68444	−	5.18416i	0.0613029	−	0.188671i
$756$	1.36525	+	4.20179i	0.0496535	+	0.152818i
$757$	3.94533	−	2.86645i	0.143396	−	0.104183i	−0.513775	−	0.857925i	$-0.671753\pi$
$757$	3.94533	−	2.86645i	0.143396	−	0.104183i	0.657170	+	0.753742i	$0.271753\pi$
$758$	25.3872			0.922105
$759$	−2.70338	−	4.75590i	−0.0981263	−	0.172628i
$760$	−0.740633			−0.0268656
$761$	36.1527	−	26.2665i	1.31054	−	0.952160i	0.310537	−	0.950561i	$-0.399491\pi$
$761$	36.1527	−	26.2665i	1.31054	−	0.952160i	0.999999	−	0.00159812i	$-0.000508698\pi$
$762$	5.60317	+	17.2448i	0.202982	+	0.624713i
$763$	2.40040	−	7.38766i	0.0869002	−	0.267451i
$764$	10.3194	+	7.49748i	0.373343	+	0.271249i
$765$	2.45640	+	1.78468i	0.0888113	+	0.0645252i
$766$	−0.0937305	+	0.288473i	−0.00338662	+	0.0104229i
$767$	21.0436	+	64.7657i	0.759842	+	2.33855i
$768$	−1.55714	+	1.13133i	−0.0561886	+	0.0408234i
$769$	52.9611			1.90983			0.954914	−	0.296884i	$-0.0959474\pi$
$769$	52.9611			1.90983			0.954914	+	0.296884i	$0.0959474\pi$
$770$	−0.368836	+	3.29605i	−0.0132919	+	0.118781i
$771$	57.0094			2.05314
$772$	−9.56974	+	6.95282i	−0.344422	+	0.250237i
$773$	11.8778	+	36.5560i	0.427213	+	1.31483i	0.900859	+	0.434112i	$0.142938\pi$
$773$	11.8778	+	36.5560i	0.427213	+	1.31483i	−0.473646	+	0.880716i	$0.657062\pi$
$774$	0.247069	−	0.760400i	0.00888071	−	0.0273320i
$775$	−0.892330	−	0.648316i	−0.0320534	−	0.0232882i
$776$	−6.80954	−	4.94742i	−0.244448	−	0.177602i
$777$	1.05823	−	3.25690i	0.0379638	−	0.116841i
$778$	−2.08295	−	6.41067i	−0.0746775	−	0.229834i
$779$	−6.42325	+	4.66676i	−0.230137	+	0.167204i
$780$	−10.0950			−0.361459
$781$	13.6160	+	6.17221i	0.487221	+	0.220859i
$782$	3.69282			0.132055
$783$	−29.9367	+	21.7503i	−1.06985	+	0.777292i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−3.70139	+	11.3917i	−0.132108	+	0.406587i
$786$	1.34354	+	0.976141i	0.0479226	+	0.0348178i
$787$	9.63340	+	6.99907i	0.343394	+	0.249490i	0.746092	−	0.665843i	$-0.231928\pi$
$787$	9.63340	+	6.99907i	0.343394	+	0.249490i	−0.402699	+	0.915333i	$0.631928\pi$
$788$	−6.77071	+	20.8381i	−0.241196	+	0.742326i
$789$	2.43373	+	7.49024i	0.0866430	+	0.266660i
$790$	1.26355	−	0.918019i	0.0449549	−	0.0326617i
$791$	−4.63948			−0.164961
$792$	−2.12844	−	0.964830i	−0.0756308	−	0.0342837i
$793$	−68.6489			−2.43779
$794$	16.1180	−	11.7104i	0.572007	−	0.415587i
$795$	−5.23796	−	16.1208i	−0.185771	−	0.571745i
$796$	3.18661	−	9.80739i	0.112947	−	0.347614i
$797$	1.69730	+	1.23316i	0.0601215	+	0.0436808i	0.617440	−	0.786618i	$-0.288170\pi$
$797$	1.69730	+	1.23316i	0.0601215	+	0.0436808i	−0.557319	+	0.830299i	$0.688170\pi$
$798$	−1.15327	−	0.837901i	−0.0408254	−	0.0296614i
$799$	−11.1878	+	34.4326i	−0.395797	+	1.21814i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$	−0.837018	+	0.608129i	−0.0295746	+	0.0214872i
$802$	34.0886			1.20371
$803$	−1.22975	+	10.9895i	−0.0433968	+	0.387809i
$804$	17.1998			0.606589
$805$	−0.693299	+	0.503711i	−0.0244356	+	0.0177535i
$806$	−1.78767	−	5.50187i	−0.0629678	−	0.193795i
$807$	1.78275	−	5.48675i	0.0627559	−	0.193143i
$808$	8.92309	+	6.48300i	0.313913	+	0.228071i
$809$	9.73369	+	7.07194i	0.342218	+	0.248636i	0.745597	−	0.666397i	$-0.232164\pi$
$809$	9.73369	+	7.07194i	0.342218	+	0.248636i	−0.403379	+	0.915033i	$0.632164\pi$
$810$	−3.28094	+	10.0977i	−0.115281	+	0.354797i
$811$	−2.63589	−	8.11243i	−0.0925586	−	0.284866i	0.894051	−	0.447965i	$-0.147851\pi$
$811$	−2.63589	−	8.11243i	−0.0925586	−	0.284866i	−0.986610	+	0.163099i	$0.947851\pi$
$812$	−6.77603	+	4.92308i	−0.237792	+	0.172766i
$813$	47.5439			1.66744
$814$	−2.91608	−	5.13010i	−0.102209	−	0.179810i
$815$	−15.5543			−0.544842
$816$	6.71003	−	4.87512i	0.234898	−	0.170663i
$817$	−0.259702	−	0.799281i	−0.00908582	−	0.0279633i
$818$	2.50202	−	7.70042i	0.0874810	−	0.269239i
$819$	−2.98978	−	2.17220i	−0.104471	−	0.0759029i
$820$	8.67265	+	6.30105i	0.302862	+	0.220042i
$821$	15.3986	−	47.3919i	0.537414	−	1.65399i	−0.200962	−	0.979599i	$-0.564407\pi$
$821$	15.3986	−	47.3919i	0.537414	−	1.65399i	0.738375	−	0.674390i	$-0.235593\pi$
$822$	−10.2580	−	31.5710i	−0.357790	−	1.10117i
$823$	12.0111	−	8.72654i	0.418679	−	0.304188i	−0.358427	−	0.933558i	$-0.616687\pi$
$823$	12.0111	−	8.72654i	0.418679	−	0.304188i	0.777106	+	0.629370i	$0.216687\pi$
$824$	5.86953			0.204475
$825$	−4.30326	+	4.71515i	−0.149820	+	0.164160i
$826$	12.9838			0.451765
$827$	1.22976	−	0.893474i	0.0427630	−	0.0310691i	−0.566198	−	0.824269i	$-0.691586\pi$
$827$	1.22976	−	0.893474i	0.0427630	−	0.0310691i	0.608961	+	0.793200i	$0.291586\pi$
$828$	−0.186591	−	0.574268i	−0.00648449	−	0.0199572i
$829$	−3.22967	+	9.93991i	−0.112171	+	0.345227i	−0.991347	−	0.131271i	$-0.958094\pi$
$829$	−3.22967	+	9.93991i	−0.112171	+	0.345227i	0.879175	+	0.476498i	$0.158094\pi$
$830$	−0.492865	−	0.358088i	−0.0171076	−	0.0124294i
$831$	−4.17094	−	3.03036i	−0.144688	−	0.105122i
$832$	−1.62076	+	4.98818i	−0.0561897	+	0.172934i
$833$	−1.33161	−	4.09828i	−0.0461377	−	0.141997i
$834$	−31.8356	+	23.1299i	−1.10238	+	0.800922i
$835$	18.0474			0.624555
$836$	−2.40610	+	0.494559i	−0.0832167	+	0.0171047i
$837$	−4.87300			−0.168435
$838$	19.4719	−	14.1472i	0.672646	−	0.488706i
$839$	−12.3533	−	38.0195i	−0.426483	−	1.31258i	−0.901567	−	0.432639i	$-0.857582\pi$
$839$	−12.3533	−	38.0195i	−0.426483	−	1.31258i	0.475084	−	0.879940i	$-0.342418\pi$
$840$	−0.594776	+	1.83053i	−0.0205217	+	0.0631593i
$841$	−33.2921	−	24.1881i	−1.14800	−	0.834073i
$842$	−11.1540	−	8.10386i	−0.384392	−	0.279277i
$843$	−6.91209	+	21.2732i	−0.238065	+	0.732689i
$844$	−7.67768	−	23.6295i	−0.264277	−	0.813360i
$845$	−11.7379	+	8.52807i	−0.403795	+	0.293375i
$846$	5.91989			0.203530
$847$	1.00271	+	10.9542i	0.0344534	+	0.376391i
$848$	−8.80661			−0.302420
$849$	−28.2406	+	20.5180i	−0.969217	+	0.704177i
$850$	−1.33161	−	4.09828i	−0.0456739	−	0.140570i
$851$	0.471165	−	1.45010i	0.0161513	−	0.0497086i
$852$	7.01882	+	5.09947i	0.240461	+	0.174705i
$853$	17.9786	+	13.0622i	0.615575	+	0.447241i	0.851373	−	0.524561i	$-0.175770\pi$
$853$	17.9786	+	13.0622i	0.615575	+	0.447241i	−0.235798	+	0.971802i	$0.575770\pi$
$854$	−4.04464	+	12.4481i	−0.138405	+	0.425966i
$855$	−0.161262	−	0.496312i	−0.00551503	−	0.0169735i
$856$	−5.52690	+	4.01553i	−0.188905	+	0.137248i
$857$	−15.8282			−0.540681			−0.270340	−	0.962765i	$-0.587136\pi$
$857$	−15.8282			−0.540681			−0.270340	+	0.962765i	$0.587136\pi$
$858$	−32.7958	+	6.74097i	−1.11963	+	0.230133i
$859$	−20.7983			−0.709628			−0.354814	−	0.934937i	$-0.615456\pi$
$859$	−20.7983			−0.709628			−0.354814	+	0.934937i	$0.615456\pi$
$860$	−0.918010	+	0.666974i	−0.0313039	+	0.0227436i
$861$	6.37599	+	19.6233i	0.217293	+	0.668759i
$862$	−2.69464	+	8.29326i	−0.0917799	+	0.282470i
$863$	15.2352	+	11.0690i	0.518612	+	0.376794i	0.816081	−	0.577938i	$-0.196142\pi$
$863$	15.2352	+	11.0690i	0.518612	+	0.376794i	−0.297469	+	0.954732i	$0.596142\pi$
$864$	3.57426	+	2.59685i	0.121599	+	0.0883467i
$865$	−2.96862	+	9.13646i	−0.100936	+	0.310649i
$866$	−2.63249	−	8.10197i	−0.0894557	−	0.275316i
$867$	−2.44334	+	1.77519i	−0.0829802	+	0.0602886i
$868$	−1.10298			−0.0374376
$869$	3.49188	−	3.82611i	0.118454	−	0.129792i
$870$	−16.1209			−0.546549
$871$	37.9180	−	27.5490i	1.28480	−	0.933463i
$872$	−2.40040	−	7.38766i	−0.0812877	−	0.250178i
$873$	1.83269	−	5.64043i	0.0620270	−	0.190899i
$874$	−0.513480	−	0.373065i	−0.0173687	−	0.0126191i
$875$	0.809017	+	0.587785i	0.0273498	+	0.0198708i
$876$	−1.98306	+	6.10322i	−0.0670013	+	0.206209i
$877$	−5.13513	−	15.8043i	−0.173401	−	0.533673i	0.826156	−	0.563442i	$-0.190523\pi$
$877$	−5.13513	−	15.8043i	−0.173401	−	0.533673i	−0.999557	+	0.0297682i	$0.990523\pi$
$878$	18.2354	−	13.2488i	0.615416	−	0.447126i
$879$	−44.0188			−1.48472
$880$	1.63898	+	2.88336i	0.0552499	+	0.0971980i
$881$	21.6943			0.730901			0.365450	−	0.930831i	$-0.380915\pi$
$881$	21.6943			0.730901			0.365450	+	0.930831i	$0.380915\pi$
$882$	−0.570037	+	0.414156i	−0.0191942	+	0.0139454i
$883$	10.1635	+	31.2799i	0.342028	+	1.05265i	0.963156	+	0.268944i	$0.0866746\pi$
$883$	10.1635	+	31.2799i	0.342028	+	1.05265i	−0.621128	+	0.783709i	$0.713325\pi$
$884$	6.98416	−	21.4950i	0.234903	−	0.722956i
$885$	20.2177	+	14.6890i	0.679609	+	0.493765i
$886$	−30.6689	−	22.2823i	−1.03034	−	0.748587i
$887$	1.24345	−	3.82694i	0.0417509	−	0.128496i	−0.928008	−	0.372559i	$-0.878480\pi$
$887$	1.24345	−	3.82694i	0.0417509	−	0.128496i	0.969759	+	0.244063i	$0.0784804\pi$
$888$	−1.05823	−	3.25690i	−0.0355119	−	0.109294i
$889$	7.62146	−	5.53732i	0.255616	−	0.185716i
$890$	1.46836			0.0492194
$891$	−3.91606	+	34.9953i	−0.131193	+	1.17239i
$892$	−20.2394			−0.677667
$893$	5.03418	−	3.65754i	0.168462	−	0.122395i
$894$	1.11995	+	3.44686i	0.0374568	+	0.115280i
$895$	4.09982	−	12.6179i	0.137042	−	0.421771i
$896$	0.809017	+	0.587785i	0.0270274	+	0.0196365i
$897$	−6.99886	−	5.08497i	−0.233685	−	0.169782i
$898$	−9.90557	+	30.4862i	−0.330553	+	1.01734i
$899$	−2.85475	−	8.78602i	−0.0952112	−	0.293030i
$900$	−0.570037	+	0.414156i	−0.0190012	+	0.0138052i
$901$	37.9493			1.26428
$902$	32.3824	+	14.6791i	1.07822	+	0.488760i
$903$	−2.18404			−0.0726804
$904$	−3.75342	+	2.72702i	−0.124837	+	0.0906993i
$905$	6.05163	+	18.6250i	0.201163	+	0.619116i
$906$	3.24209	−	9.97813i	0.107711	−	0.331501i
$907$	−16.5476	−	12.0225i	−0.549453	−	0.399201i	0.278130	−	0.960543i	$-0.410285\pi$
$907$	−16.5476	−	12.0225i	−0.549453	−	0.399201i	−0.827584	+	0.561342i	$0.810285\pi$
$908$	−9.55370	−	6.94117i	−0.317051	−	0.230351i
$909$	−2.40152	+	7.39111i	−0.0796533	+	0.245148i
$910$	1.62076	+	4.98818i	0.0537276	+	0.165357i
$911$	−22.5945	+	16.4158i	−0.748588	+	0.543881i	−0.895389	−	0.445285i	$-0.853102\pi$
$911$	−22.5945	+	16.4158i	−0.748588	+	0.543881i	0.146801	+	0.989166i	$0.453102\pi$
$912$	−1.42552			−0.0472037
$913$	−1.84029	−	0.834210i	−0.0609047	−	0.0276083i
$914$	24.5243			0.811192
$915$	−20.3810	+	14.8077i	−0.673776	+	0.489527i
$916$	0.518857	+	1.59688i	0.0171435	+	0.0527624i
$917$	0.266628	−	0.820596i	0.00880482	−	0.0270985i
$918$	−15.4022	−	11.1903i	−0.508347	−	0.369336i
$919$	10.7763	+	7.82944i	0.355477	+	0.258269i	0.751163	−	0.660117i	$-0.229493\pi$
$919$	10.7763	+	7.82944i	0.355477	+	0.258269i	−0.395686	+	0.918386i	$0.629493\pi$
$920$	−0.264817	+	0.815022i	−0.00873075	+	0.0268705i
$921$	−11.8554	−	36.4872i	−0.390649	−	1.20229i
$922$	0.152361	−	0.110697i	0.00501774	−	0.00364560i
$923$	23.6413			0.778163
$924$	−0.709912	+	6.34403i	−0.0233544	+	0.208703i
$925$	−1.77921			−0.0585001
$926$	7.61249	−	5.53080i	0.250162	−	0.181753i
$927$	1.27800	+	3.93329i	0.0419751	+	0.129186i
$928$	−2.58821	+	7.96570i	−0.0849623	+	0.261487i
$929$	−31.7226	−	23.0478i	−1.04078	−	0.756174i	−0.0703460	−	0.997523i	$-0.522410\pi$
$929$	−31.7226	−	23.0478i	−1.04078	−	0.756174i	−0.970439	+	0.241348i	$0.922410\pi$
$930$	−1.71750	−	1.24784i	−0.0563190	−	0.0409182i
$931$	−0.228868	+	0.704384i	−0.00750085	+	0.0230852i
$932$	−4.79656	−	14.7623i	−0.157117	−	0.483555i
$933$	1.99995	−	1.45305i	0.0654753	−	0.0475706i
$934$	1.84720			0.0604421
$935$	−7.06266	−	12.4249i	−0.230974	−	0.406339i
$936$	−3.69557			−0.120794
$937$	17.5883	−	12.7786i	0.574584	−	0.417460i	−0.262184	−	0.965018i	$-0.584443\pi$
$937$	17.5883	−	12.7786i	0.574584	−	0.417460i	0.836767	+	0.547558i	$0.184443\pi$
$938$	−2.76143	−	8.49881i	−0.0901639	−	0.277496i
$939$	−7.96787	+	24.5226i	−0.260021	+	0.800264i
$940$	−6.79713	−	4.93840i	−0.221698	−	0.161073i
$941$	−13.2780	−	9.64704i	−0.432851	−	0.314484i	0.349937	−	0.936773i	$-0.386203\pi$
$941$	−13.2780	−	9.64704i	−0.432851	−	0.314484i	−0.782788	+	0.622289i	$0.786203\pi$
$942$	−7.12419	+	21.9260i	−0.232119	+	0.714388i
$943$	2.83883	+	8.73702i	0.0924450	+	0.284516i
$944$	10.5041	−	7.63170i	0.341880	−	0.248391i
$945$	4.41803			0.143718
$946$	−2.53698	+	2.77981i	−0.0824842	+	0.0903793i
$947$	−45.1297			−1.46652			−0.733259	−	0.679949i	$-0.762002\pi$
$947$	−45.1297			−1.46652			−0.733259	+	0.679949i	$0.762002\pi$
$948$	2.43199	−	1.76694i	0.0789874	−	0.0573877i
$949$	5.40381	+	16.6312i	0.175415	+	0.539872i
$950$	−0.228868	+	0.704384i	−0.00742546	+	0.0228532i
$951$	−25.9482	−	18.8525i	−0.841427	−	0.611333i
$952$	−3.48621	−	2.53288i	−0.112989	−	0.0820911i
$953$	−14.4676	+	44.5267i	−0.468651	+	1.44236i	0.385681	+	0.922632i	$0.373967\pi$
$953$	−14.4676	+	44.5267i	−0.468651	+	1.44236i	−0.854332	+	0.519728i	$0.826033\pi$
$954$	−1.91751	−	5.90148i	−0.0620815	−	0.191067i
$955$	10.3194	−	7.49748i	0.333928	−	0.242613i
$956$	−22.0037			−0.711652
$957$	−52.3720	+	10.7648i	−1.69295	+	0.347975i
$958$	33.3506			1.07751
$959$	−13.9530	+	10.1375i	−0.450567	+	0.327356i
$960$	0.594776	+	1.83053i	0.0191963	+	0.0590802i
$961$	−9.20359	+	28.3257i	−0.296890	+	0.913733i
$962$	−7.54955	−	5.48507i	−0.243407	−	0.176846i
$963$	−3.89428	−	2.82936i	−0.125491	−	0.0911748i
$964$	−7.35940	+	22.6499i	−0.237030	+	0.729505i
$965$	3.65531	+	11.2499i	0.117669	+	0.362147i
$966$	−1.33442	+	0.969511i	−0.0429342	+	0.0311935i
$967$	−57.9645			−1.86401			−0.932007	−	0.362441i	$-0.881943\pi$
$967$	−57.9645			−1.86401			−0.932007	+	0.362441i	$0.881943\pi$
$968$	7.24992	+	8.27276i	0.233021	+	0.265897i
$969$	6.14284			0.197337
$970$	−6.80954	+	4.94742i	−0.218641	+	0.158852i
$971$	−3.28375	−	10.1064i	−0.105381	−	0.324328i	0.884439	−	0.466656i	$-0.154541\pi$
$971$	−3.28375	−	10.1064i	−0.105381	−	0.324328i	−0.989820	+	0.142328i	$0.954541\pi$
$972$	−2.21920	+	6.83001i	−0.0711810	+	0.219073i
$973$	16.5402	+	12.0172i	0.530255	+	0.385253i
$974$	−11.4182	−	8.29579i	−0.365862	−	0.265814i
$975$	−3.11953	+	9.60093i	−0.0999049	+	0.307476i
$976$	4.04464	+	12.4481i	0.129466	+	0.398455i
$977$	27.1993	−	19.7615i	0.870183	−	0.632225i	−0.0604530	−	0.998171i	$-0.519255\pi$
$977$	27.1993	−	19.7615i	0.870183	−	0.632225i	0.930636	+	0.365946i	$0.119255\pi$
$978$	−29.9378			−0.957307
$979$	4.77026	−	0.980498i	0.152458	−	0.0313369i
$980$	1.00000			0.0319438
$981$	4.42796	−	3.21710i	0.141374	−	0.102714i
$982$	−2.59847	−	7.99726i	−0.0829204	−	0.255203i
$983$	11.8555	−	36.4875i	0.378132	−	1.16377i	−0.563210	−	0.826314i	$-0.690434\pi$
$983$	11.8555	−	36.4875i	0.378132	−	1.16377i	0.941341	−	0.337455i	$-0.109566\pi$
$984$	16.6925	+	12.1278i	0.532139	+	0.386622i
$985$	17.7259	+	12.8786i	0.564795	+	0.410348i
$986$	11.1531	−	34.3257i	0.355187	−	1.09315i
$987$	−4.99714	−	15.3796i	−0.159061	−	0.489538i
$988$	−3.14265	+	2.28327i	−0.0999811	+	0.0726405i
$989$	−0.972418			−0.0309211
$990$	−1.57533	+	1.72612i	−0.0500673	+	0.0548596i
$991$	55.5999			1.76619			0.883094	−	0.469196i	$-0.155456\pi$
$991$	55.5999			1.76619			0.883094	+	0.469196i	$0.155456\pi$
$992$	−0.892330	+	0.648316i	−0.0283315	+	0.0205840i
$993$	6.62222	+	20.3811i	0.210150	+	0.646775i
$994$	1.39289	−	4.28689i	0.0441799	−	0.135972i
$995$	−8.34267	−	6.06130i	−0.264480	−	0.192156i
$996$	−0.948635	−	0.689224i	−0.0300587	−	0.0218389i
$997$	7.09807	−	21.8456i	0.224798	−	0.691857i	−0.773514	−	0.633779i	$-0.781503\pi$
$997$	7.09807	−	21.8456i	0.224798	−	0.691857i	0.998312	−	0.0580779i	$-0.0184972\pi$
$998$	−7.04828	−	21.6924i	−0.223109	−	0.686660i
$999$	−6.35936	+	4.62035i	−0.201201	+	0.146181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.g.421.3	✓	12
11.2	odd	10		8470.2.a.cv.1.6		6
11.4	even	5	inner	770.2.n.g.631.3	yes	12
11.9	even	5		8470.2.a.db.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.g.421.3	✓	12	1.1	even	1	trivial
770.2.n.g.631.3	yes	12	11.4	even	5	inner
8470.2.a.cv.1.6		6	11.2	odd	10
8470.2.a.db.1.6		6	11.9	even	5

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.594776 + 1.83053i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.55714 - 1.13133i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.570037 + 0.414156i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.594776 + 1.83053i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.55714 - 1.13133i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.570037 + 0.414156i) q^{9} +1.00000 q^{10} +(3.24871 - 0.667752i) q^{11} +1.92474 q^{12} +(4.24320 - 3.08287i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.594776 - 1.83053i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.48621 + 2.53288i) q^{17} +(0.217735 - 0.670119i) q^{18} +(-0.228868 - 0.704384i) q^{19} +(-0.809017 + 0.587785i) q^{20} -1.92474 q^{21} +(-2.23577 + 2.44977i) q^{22} -0.856965 q^{23} +(-1.55714 + 1.13133i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-1.62076 + 4.98818i) q^{26} +(3.57426 + 2.59685i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-2.58821 + 7.96570i) q^{29} +(0.594776 + 1.83053i) q^{30} +(-0.892330 + 0.648316i) q^{31} +1.00000 q^{32} +(3.15459 + 5.54970i) q^{33} -4.30919 q^{34} +(0.809017 - 0.587785i) q^{35} +(0.217735 + 0.670119i) q^{36} +(-0.549806 + 1.69213i) q^{37} +(0.599184 + 0.435333i) q^{38} +(8.16704 + 5.93370i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-3.31266 - 10.1953i) q^{41} +(1.55714 - 1.13133i) q^{42} +1.13472 q^{43} +(0.368836 - 3.29605i) q^{44} +0.704605 q^{45} +(0.693299 - 0.503711i) q^{46} +(2.59627 + 7.99051i) q^{47} +(0.594776 - 1.83053i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-2.56300 + 7.88811i) q^{51} +(-1.62076 - 4.98818i) q^{52} +(7.12469 - 5.17639i) q^{53} -4.41803 q^{54} +(-3.02076 - 1.36932i) q^{55} -1.00000 q^{56} +(1.15327 - 0.837901i) q^{57} +(-2.58821 - 7.96570i) q^{58} +(-4.01222 + 12.3483i) q^{59} +(-1.55714 - 1.13133i) q^{60} +(-10.5890 - 7.69336i) q^{61} +(0.340840 - 1.04900i) q^{62} +(-0.217735 - 0.670119i) q^{63} +(-0.809017 + 0.587785i) q^{64} -5.24489 q^{65} +(-5.81415 - 2.63558i) q^{66} +8.93617 q^{67} +(3.48621 - 2.53288i) q^{68} +(-0.509702 - 1.56870i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(3.64664 + 2.64944i) q^{71} +(-0.570037 - 0.414156i) q^{72} +(-1.03030 + 3.17094i) q^{73} +(-0.549806 - 1.69213i) q^{74} +(-1.55714 + 1.13133i) q^{75} -0.740633 q^{76} +(-0.368836 + 3.29605i) q^{77} -10.0950 q^{78} +(1.26355 - 0.918019i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-3.28094 + 10.0977i) q^{81} +(8.67265 + 6.30105i) q^{82} +(-0.492865 - 0.358088i) q^{83} +(-0.594776 + 1.83053i) q^{84} +(-1.33161 - 4.09828i) q^{85} +(-0.918010 + 0.666974i) q^{86} -16.1209 q^{87} +(1.63898 + 2.88336i) q^{88} +1.46836 q^{89} +(-0.570037 + 0.414156i) q^{90} +(1.62076 + 4.98818i) q^{91} +(-0.264817 + 0.815022i) q^{92} +(-1.71750 - 1.24784i) q^{93} +(-6.79713 - 4.93840i) q^{94} +(-0.228868 + 0.704384i) q^{95} +(0.594776 + 1.83053i) q^{96} +(-6.80954 + 4.94742i) q^{97} +1.00000 q^{98} +(-1.57533 + 1.72612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9	\( 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9} + 12 q^{10} + 7 q^{11} - 2 q^{12} + 8 q^{13} + 3 q^{14} - 2 q^{15} - 3 q^{16} + 8 q^{17} + 8 q^{18} + 11 q^{19} - 3 q^{20} + 2 q^{21} - 3 q^{22} - 20 q^{23} + 3 q^{24} - 3 q^{25} - 2 q^{26} + 7 q^{27} + 3 q^{28} + 20 q^{29} - 2 q^{30} + 2 q^{31} + 12 q^{32} + 33 q^{33} - 42 q^{34} + 3 q^{35} + 8 q^{36} - 4 q^{37} - 14 q^{38} + 18 q^{39} - 3 q^{40} - 14 q^{41} - 3 q^{42} - 38 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 10 q^{47} - 2 q^{48} - 3 q^{49} - 3 q^{50} + 13 q^{51} - 2 q^{52} + 8 q^{53} - 8 q^{54} - 3 q^{55} - 12 q^{56} + 33 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} - 34 q^{61} + 2 q^{62} - 8 q^{63} - 3 q^{64} - 12 q^{65} - 12 q^{66} - 54 q^{67} + 8 q^{68} + 38 q^{69} + 3 q^{70} + 18 q^{71} - 7 q^{72} + 24 q^{73} - 4 q^{74} + 3 q^{75} + 6 q^{76} - 2 q^{77} - 52 q^{78} + 2 q^{79} - 3 q^{80} + 2 q^{81} + 21 q^{82} + 33 q^{83} + 2 q^{84} + 13 q^{85} + 7 q^{86} - 16 q^{87} - 3 q^{88} + 2 q^{89} - 7 q^{90} + 2 q^{91} - 10 q^{92} - 32 q^{93} + 11 q^{95} - 2 q^{96} - q^{97} + 12 q^{98} - 47 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9 + 12 * q^10 + 7 * q^11 - 2 * q^12 + 8 * q^13 + 3 * q^14 - 2 * q^15 - 3 * q^16 + 8 * q^17 + 8 * q^18 + 11 * q^19 - 3 * q^20 + 2 * q^21 - 3 * q^22 - 20 * q^23 + 3 * q^24 - 3 * q^25 - 2 * q^26 + 7 * q^27 + 3 * q^28 + 20 * q^29 - 2 * q^30 + 2 * q^31 + 12 * q^32 + 33 * q^33 - 42 * q^34 + 3 * q^35 + 8 * q^36 - 4 * q^37 - 14 * q^38 + 18 * q^39 - 3 * q^40 - 14 * q^41 - 3 * q^42 - 38 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 10 * q^47 - 2 * q^48 - 3 * q^49 - 3 * q^50 + 13 * q^51 - 2 * q^52 + 8 * q^53 - 8 * q^54 - 3 * q^55 - 12 * q^56 + 33 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 - 34 * q^61 + 2 * q^62 - 8 * q^63 - 3 * q^64 - 12 * q^65 - 12 * q^66 - 54 * q^67 + 8 * q^68 + 38 * q^69 + 3 * q^70 + 18 * q^71 - 7 * q^72 + 24 * q^73 - 4 * q^74 + 3 * q^75 + 6 * q^76 - 2 * q^77 - 52 * q^78 + 2 * q^79 - 3 * q^80 + 2 * q^81 + 21 * q^82 + 33 * q^83 + 2 * q^84 + 13 * q^85 + 7 * q^86 - 16 * q^87 - 3 * q^88 + 2 * q^89 - 7 * q^90 + 2 * q^91 - 10 * q^92 - 32 * q^93 + 11 * q^95 - 2 * q^96 - q^97 + 12 * q^98 - 47 * q^99

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