LMFDB - Embedded newform 287.2.r.a.214.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(9,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("287.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.r (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			214.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	287.214
Dual form			287.2.r.a.114.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.133975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-0.366025 + 0.366025i) q^{6} +(2.50000 + 0.866025i) q^{7} +3.00000i q^{8} +(-2.36603 + 1.36603i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.133975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-0.366025 + 0.366025i) q^{6} +(2.50000 + 0.866025i) q^{7} +3.00000i q^{8} +(-2.36603 + 1.36603i) q^{9} +(-0.866025 + 1.50000i) q^{10} +(-2.86603 + 0.767949i) q^{11} +(0.133975 - 0.500000i) q^{12} +(1.73205 + 1.73205i) q^{13} +(2.59808 - 0.500000i) q^{14} +(0.633975 - 0.633975i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.464102 - 1.73205i) q^{17} +(-1.36603 + 2.36603i) q^{18} +(6.59808 + 1.76795i) q^{19} -1.73205i q^{20} +(-1.36603 - 0.0980762i) q^{21} +(-2.09808 + 2.09808i) q^{22} +(-0.267949 - 0.464102i) q^{23} +(-0.401924 - 1.50000i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(2.36603 + 0.633975i) q^{26} +(2.09808 - 2.09808i) q^{27} +(-2.00000 + 1.73205i) q^{28} +(3.26795 + 3.26795i) q^{29} +(0.232051 - 0.866025i) q^{30} +(1.36603 - 2.36603i) q^{31} +(-4.33013 - 2.50000i) q^{32} +(1.33013 - 0.767949i) q^{33} +(-1.26795 - 1.26795i) q^{34} +(-4.50000 + 0.866025i) q^{35} -2.73205i q^{36} +(-3.73205 - 6.46410i) q^{37} +(6.59808 - 1.76795i) q^{38} +(-1.09808 - 0.633975i) q^{39} +(-2.59808 - 4.50000i) q^{40} +(4.00000 - 5.00000i) q^{41} +(-1.23205 + 0.598076i) q^{42} -1.46410i q^{43} +(0.767949 - 2.86603i) q^{44} +(2.36603 - 4.09808i) q^{45} +(-0.464102 - 0.267949i) q^{46} +(-3.36603 - 0.901924i) q^{47} +(-0.366025 - 0.366025i) q^{48} +(5.50000 + 4.33013i) q^{49} +2.00000i q^{50} +(0.464102 + 0.803848i) q^{51} +(-2.36603 + 0.633975i) q^{52} +(-1.36603 + 0.366025i) q^{53} +(0.767949 - 2.86603i) q^{54} +(3.63397 - 3.63397i) q^{55} +(-2.59808 + 7.50000i) q^{56} -3.53590 q^{57} +(4.46410 + 1.19615i) q^{58} +(-3.63397 + 6.29423i) q^{59} +(0.232051 + 0.866025i) q^{60} +(6.06218 - 3.50000i) q^{61} -2.73205i q^{62} +(-7.09808 + 1.36603i) q^{63} -7.00000 q^{64} +(-4.09808 - 1.09808i) q^{65} +(0.767949 - 1.33013i) q^{66} +(0.633975 + 2.36603i) q^{67} +(1.73205 + 0.464102i) q^{68} +(0.196152 + 0.196152i) q^{69} +(-3.46410 + 3.00000i) q^{70} +(8.36603 + 8.36603i) q^{71} +(-4.09808 - 7.09808i) q^{72} +(9.92820 + 5.73205i) q^{73} +(-6.46410 - 3.73205i) q^{74} +(0.267949 - 1.00000i) q^{75} +(-4.83013 + 4.83013i) q^{76} +(-7.83013 - 0.562178i) q^{77} -1.26795 q^{78} +(1.66987 - 6.23205i) q^{79} +(-1.50000 - 0.866025i) q^{80} +(3.33013 - 5.76795i) q^{81} +(0.964102 - 6.33013i) q^{82} -2.73205 q^{83} +(0.767949 - 1.13397i) q^{84} +(2.19615 + 2.19615i) q^{85} +(-0.732051 - 1.26795i) q^{86} +(-2.07180 - 1.19615i) q^{87} +(-2.30385 - 8.59808i) q^{88} +(1.83013 - 6.83013i) q^{89} -4.73205i q^{90} +(2.83013 + 5.83013i) q^{91} +0.535898 q^{92} +(-0.366025 + 1.36603i) q^{93} +(-3.36603 + 0.901924i) q^{94} +(-11.4282 + 3.06218i) q^{95} +(2.50000 + 0.669873i) q^{96} +(1.46410 - 1.46410i) q^{97} +(6.92820 + 1.00000i) q^{98} +(5.73205 - 5.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^9	$ 4 q - 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{9} - 8 q^{11} + 4 q^{12} + 6 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} + 16 q^{19} - 2 q^{21} + 2 q^{22} - 8 q^{23} - 12 q^{24} - 4 q^{25} + 6 q^{26} - 2 q^{27} - 8 q^{28} + 20 q^{29} - 6 q^{30} + 2 q^{31} - 12 q^{33} - 12 q^{34} - 18 q^{35} - 8 q^{37} + 16 q^{38} + 6 q^{39} + 16 q^{41} + 2 q^{42} + 10 q^{44} + 6 q^{45} + 12 q^{46} - 10 q^{47} + 2 q^{48} + 22 q^{49} - 12 q^{51} - 6 q^{52} - 2 q^{53} + 10 q^{54} + 18 q^{55} - 28 q^{57} + 4 q^{58} - 18 q^{59} - 6 q^{60} - 18 q^{63} - 28 q^{64} - 6 q^{65} + 10 q^{66} + 6 q^{67} - 20 q^{69} + 30 q^{71} - 6 q^{72} + 12 q^{73} - 12 q^{74} + 8 q^{75} - 2 q^{76} - 14 q^{77} - 12 q^{78} + 24 q^{79} - 6 q^{80} - 4 q^{81} - 10 q^{82} - 4 q^{83} + 10 q^{84} - 12 q^{85} + 4 q^{86} - 36 q^{87} - 30 q^{88} - 10 q^{89} - 6 q^{91} + 16 q^{92} + 2 q^{93} - 10 q^{94} - 18 q^{95} + 10 q^{96} - 8 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^9 - 8 * q^11 + 4 * q^12 + 6 * q^15 + 2 * q^16 + 12 * q^17 - 2 * q^18 + 16 * q^19 - 2 * q^21 + 2 * q^22 - 8 * q^23 - 12 * q^24 - 4 * q^25 + 6 * q^26 - 2 * q^27 - 8 * q^28 + 20 * q^29 - 6 * q^30 + 2 * q^31 - 12 * q^33 - 12 * q^34 - 18 * q^35 - 8 * q^37 + 16 * q^38 + 6 * q^39 + 16 * q^41 + 2 * q^42 + 10 * q^44 + 6 * q^45 + 12 * q^46 - 10 * q^47 + 2 * q^48 + 22 * q^49 - 12 * q^51 - 6 * q^52 - 2 * q^53 + 10 * q^54 + 18 * q^55 - 28 * q^57 + 4 * q^58 - 18 * q^59 - 6 * q^60 - 18 * q^63 - 28 * q^64 - 6 * q^65 + 10 * q^66 + 6 * q^67 - 20 * q^69 + 30 * q^71 - 6 * q^72 + 12 * q^73 - 12 * q^74 + 8 * q^75 - 2 * q^76 - 14 * q^77 - 12 * q^78 + 24 * q^79 - 6 * q^80 - 4 * q^81 - 10 * q^82 - 4 * q^83 + 10 * q^84 - 12 * q^85 + 4 * q^86 - 36 * q^87 - 30 * q^88 - 10 * q^89 - 6 * q^91 + 16 * q^92 + 2 * q^93 - 10 * q^94 - 18 * q^95 + 10 * q^96 - 8 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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	−0.161521	−	0.986869i	$-0.551640\pi$
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i	0.773893	+	0.633316i	$0.218307\pi$
$3$	−0.500000	+	0.133975i	−0.288675	+	0.0773503i	−0.400251	−	0.916406i	$-0.631077\pi$
$3$	−0.500000	+	0.133975i	−0.288675	+	0.0773503i	0.111576	+	0.993756i	$0.464410\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$	−0.366025	+	0.366025i	−0.149429	+	0.149429i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$			3.00000i			1.06066i
$9$	−2.36603	+	1.36603i	−0.788675	+	0.455342i
$10$	−0.866025	+	1.50000i	−0.273861	+	0.474342i
$11$	−2.86603	+	0.767949i	−0.864139	+	0.231545i	−0.663552	−	0.748130i	$-0.730952\pi$
$11$	−2.86603	+	0.767949i	−0.864139	+	0.231545i	−0.200587	+	0.979676i	$0.564285\pi$
$12$	0.133975	−	0.500000i	0.0386751	−	0.144338i
$13$	1.73205	+	1.73205i	0.480384	+	0.480384i	0.905254	−	0.424870i	$-0.139680\pi$
$13$	1.73205	+	1.73205i	0.480384	+	0.480384i	−0.424870	+	0.905254i	$0.639680\pi$
$14$	2.59808	−	0.500000i	0.694365	−	0.133631i
$15$	0.633975	−	0.633975i	0.163692	−	0.163692i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.464102	−	1.73205i	−0.112561	−	0.420084i	0.886532	−	0.462668i	$-0.153108\pi$
$17$	−0.464102	−	1.73205i	−0.112561	−	0.420084i	−0.999093	+	0.0425838i	$0.986441\pi$
$18$	−1.36603	+	2.36603i	−0.321975	+	0.557678i
$19$	6.59808	+	1.76795i	1.51370	+	0.405595i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	6.59808	+	1.76795i	1.51370	+	0.405595i	0.596040	+	0.802955i	$0.296740\pi$
$20$		−	1.73205i		−	0.387298i
$21$	−1.36603	−	0.0980762i	−0.298091	−	0.0214020i
$22$	−2.09808	+	2.09808i	−0.447311	+	0.447311i
$23$	−0.267949	−	0.464102i	−0.0558713	−	0.0967719i	0.836737	−	0.547605i	$-0.184460\pi$
$23$	−0.267949	−	0.464102i	−0.0558713	−	0.0967719i	−0.892608	+	0.450833i	$0.851127\pi$
$24$	−0.401924	−	1.50000i	−0.0820423	−	0.306186i
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	2.36603	+	0.633975i	0.464016	+	0.124333i
$27$	2.09808	−	2.09808i	0.403775	−	0.403775i
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	3.26795	+	3.26795i	0.606843	+	0.606843i	0.942120	−	0.335277i	$-0.108830\pi$
$29$	3.26795	+	3.26795i	0.606843	+	0.606843i	−0.335277	+	0.942120i	$0.608830\pi$
$30$	0.232051	−	0.866025i	0.0423665	−	0.158114i
$31$	1.36603	−	2.36603i	0.245345	−	0.424951i	−0.716883	−	0.697193i	$-0.754432\pi$
$31$	1.36603	−	2.36603i	0.245345	−	0.424951i	0.962229	+	0.272243i	$0.0877653\pi$
$32$	−4.33013	−	2.50000i	−0.765466	−	0.441942i
$33$	1.33013	−	0.767949i	0.231545	−	0.133683i
$34$	−1.26795	−	1.26795i	−0.217451	−	0.217451i
$35$	−4.50000	+	0.866025i	−0.760639	+	0.146385i
$36$		−	2.73205i		−	0.455342i
$37$	−3.73205	−	6.46410i	−0.613545	−	1.06269i	−0.990638	−	0.136516i	$-0.956409\pi$
$37$	−3.73205	−	6.46410i	−0.613545	−	1.06269i	0.377092	−	0.926176i	$-0.376924\pi$
$38$	6.59808	−	1.76795i	1.07035	−	0.286799i
$39$	−1.09808	−	0.633975i	−0.175833	−	0.101517i
$40$	−2.59808	−	4.50000i	−0.410792	−	0.711512i
$41$	4.00000	−	5.00000i	0.624695	−	0.780869i
$41$	4.00000	−	5.00000i	0.624695	−	0.780869i
$42$	−1.23205	+	0.598076i	−0.190110	+	0.0922852i
$43$		−	1.46410i		−	0.223273i	−0.993749	−	0.111637i	$-0.964391\pi$
$43$		−	1.46410i		−	0.223273i	0.993749	−	0.111637i	$-0.0356093\pi$
$44$	0.767949	−	2.86603i	0.115773	−	0.432070i
$45$	2.36603	−	4.09808i	0.352706	−	0.610905i
$46$	−0.464102	−	0.267949i	−0.0684280	−	0.0395070i
$47$	−3.36603	−	0.901924i	−0.490985	−	0.131559i	0.00482786	−	0.999988i	$-0.498463\pi$
$47$	−3.36603	−	0.901924i	−0.490985	−	0.131559i	−0.495813	+	0.868429i	$0.665130\pi$
$48$	−0.366025	−	0.366025i	−0.0528312	−	0.0528312i
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$			2.00000i			0.282843i
$51$	0.464102	+	0.803848i	0.0649872	+	0.112561i
$52$	−2.36603	+	0.633975i	−0.328109	+	0.0879165i
$53$	−1.36603	+	0.366025i	−0.187638	+	0.0502775i	−0.351414	−	0.936220i	$-0.614299\pi$
$53$	−1.36603	+	0.366025i	−0.187638	+	0.0502775i	0.163776	+	0.986498i	$0.447632\pi$
$54$	0.767949	−	2.86603i	0.104505	−	0.390017i
$55$	3.63397	−	3.63397i	0.490005	−	0.490005i
$56$	−2.59808	+	7.50000i	−0.347183	+	1.00223i
$57$	−3.53590			−0.468341
$58$	4.46410	+	1.19615i	0.586165	+	0.157063i
$59$	−3.63397	+	6.29423i	−0.473103	+	0.819439i	−0.999526	−	0.0307841i	$-0.990200\pi$
$59$	−3.63397	+	6.29423i	−0.473103	+	0.819439i	0.526423	+	0.850223i	$0.323533\pi$
$60$	0.232051	+	0.866025i	0.0299576	+	0.111803i
$61$	6.06218	−	3.50000i	0.776182	−	0.448129i	−0.0588933	−	0.998264i	$-0.518757\pi$
$61$	6.06218	−	3.50000i	0.776182	−	0.448129i	0.835076	+	0.550135i	$0.185424\pi$
$62$		−	2.73205i		−	0.346971i
$63$	−7.09808	+	1.36603i	−0.894274	+	0.172103i
$64$	−7.00000			−0.875000
$65$	−4.09808	−	1.09808i	−0.508304	−	0.136200i
$66$	0.767949	−	1.33013i	0.0945280	−	0.163727i
$67$	0.633975	+	2.36603i	0.0774523	+	0.289056i	0.993778	−	0.111377i	$-0.0355262\pi$
$67$	0.633975	+	2.36603i	0.0774523	+	0.289056i	−0.916326	+	0.400433i	$0.868860\pi$
$68$	1.73205	+	0.464102i	0.210042	+	0.0562806i
$69$	0.196152	+	0.196152i	0.0236140	+	0.0236140i
$70$	−3.46410	+	3.00000i	−0.414039	+	0.358569i
$71$	8.36603	+	8.36603i	0.992865	+	0.992865i	0.999975	−	0.00711017i	$-0.00226326\pi$
$71$	8.36603	+	8.36603i	0.992865	+	0.992865i	−0.00711017	+	0.999975i	$0.502263\pi$
$72$	−4.09808	−	7.09808i	−0.482963	−	0.836516i
$73$	9.92820	+	5.73205i	1.16201	+	0.670886i	0.951784	−	0.306767i	$-0.0992474\pi$
$73$	9.92820	+	5.73205i	1.16201	+	0.670886i	0.210224	+	0.977653i	$0.432581\pi$
$74$	−6.46410	−	3.73205i	−0.751437	−	0.433842i
$75$	0.267949	−	1.00000i	0.0309401	−	0.115470i
$76$	−4.83013	+	4.83013i	−0.554054	+	0.554054i
$77$	−7.83013	−	0.562178i	−0.892326	−	0.0640661i
$78$	−1.26795			−0.143567
$79$	1.66987	−	6.23205i	0.187875	−	0.701160i	−0.806121	−	0.591750i	$-0.798437\pi$
$79$	1.66987	−	6.23205i	0.187875	−	0.701160i	0.993997	−	0.109410i	$-0.0348962\pi$
$80$	−1.50000	−	0.866025i	−0.167705	−	0.0968246i
$81$	3.33013	−	5.76795i	0.370014	−	0.640883i
$82$	0.964102	−	6.33013i	0.106467	−	0.699046i
$83$	−2.73205			−0.299882			−0.149941	−	0.988695i	$-0.547908\pi$
$83$	−2.73205			−0.299882			−0.149941	+	0.988695i	$0.547908\pi$
$84$	0.767949	−	1.13397i	0.0837901	−	0.123727i
$85$	2.19615	+	2.19615i	0.238206	+	0.238206i
$86$	−0.732051	−	1.26795i	−0.0789391	−	0.136726i
$87$	−2.07180	−	1.19615i	−0.222120	−	0.128241i
$88$	−2.30385	−	8.59808i	−0.245591	−	0.916558i
$89$	1.83013	−	6.83013i	0.193993	−	0.723992i	−0.798532	−	0.601952i	$-0.794390\pi$
$89$	1.83013	−	6.83013i	0.193993	−	0.723992i	0.992525	−	0.122040i	$-0.0389436\pi$
$90$		−	4.73205i		−	0.498802i
$91$	2.83013	+	5.83013i	0.296678	+	0.611163i
$92$	0.535898			0.0558713
$93$	−0.366025	+	1.36603i	−0.0379551	+	0.141650i
$94$	−3.36603	+	0.901924i	−0.347179	+	0.0930263i
$95$	−11.4282	+	3.06218i	−1.17251	+	0.314173i
$96$	2.50000	+	0.669873i	0.255155	+	0.0683686i
$97$	1.46410	−	1.46410i	0.148657	−	0.148657i	−0.628861	−	0.777518i	$-0.716478\pi$
$97$	1.46410	−	1.46410i	0.148657	−	0.148657i	0.777518	+	0.628861i	$0.216478\pi$
$98$	6.92820	+	1.00000i	0.699854	+	0.101015i
$99$	5.73205	−	5.73205i	0.576093	−	0.576093i
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	1.53590	+	5.73205i	0.152828	+	0.570360i	0.999282	+	0.0378985i	$0.0120664\pi$
$101$	1.53590	+	5.73205i	0.152828	+	0.570360i	−0.846454	+	0.532462i	$0.821267\pi$
$102$	0.803848	+	0.464102i	0.0795928	+	0.0459529i
$103$	4.56218	−	2.63397i	0.449525	−	0.259533i	−0.258105	−	0.966117i	$-0.583098\pi$
$103$	4.56218	−	2.63397i	0.449525	−	0.259533i	0.707629	+	0.706584i	$0.249765\pi$
$104$	−5.19615	+	5.19615i	−0.509525	+	0.509525i
$105$	2.13397	−	1.03590i	0.208255	−	0.101093i
$106$	−1.00000	+	1.00000i	−0.0971286	+	0.0971286i
$107$	9.02628	+	15.6340i	0.872603	+	1.51139i	0.859294	+	0.511482i	$0.170903\pi$
$107$	9.02628	+	15.6340i	0.872603	+	1.51139i	0.0133093	+	0.999911i	$0.495763\pi$
$108$	0.767949	+	2.86603i	0.0738959	+	0.275783i
$109$	2.53590	+	9.46410i	0.242895	+	0.906497i	0.974430	+	0.224692i	$0.0721377\pi$
$109$	2.53590	+	9.46410i	0.242895	+	0.906497i	−0.731535	+	0.681804i	$0.761196\pi$
$110$	1.33013	−	4.96410i	0.126823	−	0.473309i
$111$	2.73205	+	2.73205i	0.259315	+	0.259315i
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$	11.5885			1.09015			0.545075	−	0.838387i	$-0.316501\pi$
$113$	11.5885			1.09015			0.545075	+	0.838387i	$0.316501\pi$
$114$	−3.06218	+	1.76795i	−0.286799	+	0.165584i
$115$	0.803848	+	0.464102i	0.0749592	+	0.0432777i
$116$	−4.46410	+	1.19615i	−0.414481	+	0.111060i
$117$	−6.46410	−	1.73205i	−0.597606	−	0.160128i
$118$			7.26795i			0.669069i
$119$	0.339746	−	4.73205i	0.0311445	−	0.433786i
$120$	1.90192	+	1.90192i	0.173621	+	0.173621i
$121$	−1.90192	+	1.09808i	−0.172902	+	0.0998251i
$122$	3.50000	−	6.06218i	0.316875	−	0.548844i
$123$	−1.33013	+	3.03590i	−0.119934	+	0.273738i
$124$	1.36603	+	2.36603i	0.122673	+	0.212475i
$125$		−	12.1244i		−	1.08444i
$126$	−5.46410	+	4.73205i	−0.486781	+	0.421565i
$127$	−7.12436			−0.632184			−0.316092	−	0.948728i	$-0.602371\pi$
$127$	−7.12436			−0.632184			−0.316092	+	0.948728i	$0.602371\pi$
$128$	2.59808	−	1.50000i	0.229640	−	0.132583i
$129$	0.196152	+	0.732051i	0.0172703	+	0.0644535i
$130$	−4.09808	+	1.09808i	−0.359425	+	0.0963077i
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$			1.53590i			0.133683i
$133$	14.9641	+	10.1340i	1.29755	+	0.878727i
$134$	1.73205	+	1.73205i	0.149626	+	0.149626i
$135$	−1.33013	+	4.96410i	−0.114479	+	0.427242i
$136$	5.19615	−	1.39230i	0.445566	−	0.119389i
$137$	−2.90192	−	10.8301i	−0.247928	−	0.925280i	−0.971889	−	0.235439i	$-0.924347\pi$
$137$	−2.90192	−	10.8301i	−0.247928	−	0.925280i	0.723961	−	0.689841i	$-0.242320\pi$
$138$	0.267949	+	0.0717968i	0.0228093	+	0.00611175i
$139$	−23.5167			−1.99466			−0.997329	−	0.0730462i	$-0.976728\pi$
$139$	−23.5167			−1.99466			−0.997329	+	0.0730462i	$0.976728\pi$
$140$	1.50000	−	4.33013i	0.126773	−	0.365963i
$141$	1.80385			0.151911
$142$	11.4282	+	3.06218i	0.959034	+	0.256972i
$143$	−6.29423	−	3.63397i	−0.526350	−	0.303888i
$144$	−2.36603	−	1.36603i	−0.197169	−	0.113835i
$145$	−7.73205	−	2.07180i	−0.642112	−	0.172053i
$146$	11.4641			0.948776
$147$	−3.33013	−	1.42820i	−0.274664	−	0.117796i
$148$	7.46410			0.613545
$149$	−7.09808	−	1.90192i	−0.581497	−	0.155812i	−0.0439329	−	0.999034i	$-0.513989\pi$
$149$	−7.09808	−	1.90192i	−0.581497	−	0.155812i	−0.537564	+	0.843223i	$0.680655\pi$
$150$	−0.267949	−	1.00000i	−0.0218780	−	0.0816497i
$151$	1.36603	−	0.366025i	0.111166	−	0.0297867i	−0.202807	−	0.979219i	$-0.565007\pi$
$151$	1.36603	−	0.366025i	0.111166	−	0.0297867i	0.313973	+	0.949432i	$0.398340\pi$
$152$	−5.30385	+	19.7942i	−0.430199	+	1.60552i
$153$	3.46410	+	3.46410i	0.280056	+	0.280056i
$154$	−7.06218	+	3.42820i	−0.569087	+	0.276252i
$155$			4.73205i			0.380087i
$156$	1.09808	−	0.633975i	0.0879165	−	0.0507586i
$157$	15.1962	−	4.07180i	1.21278	−	0.324965i	0.404931	−	0.914347i	$-0.367296\pi$
$157$	15.1962	−	4.07180i	1.21278	−	0.324965i	0.807854	+	0.589383i	$0.200629\pi$
$158$	−1.66987	−	6.23205i	−0.132848	−	0.495795i
$159$	0.633975	−	0.366025i	0.0502775	−	0.0290277i
$160$	8.66025			0.684653
$161$	−0.267949	−	1.39230i	−0.0211174	−	0.109729i
$162$		−	6.66025i		−	0.523279i
$163$	12.0981	+	20.9545i	0.947594	+	1.64128i	0.750471	+	0.660903i	$0.229827\pi$
$163$	12.0981	+	20.9545i	0.947594	+	1.64128i	0.197123	+	0.980379i	$0.436840\pi$
$164$	2.33013	+	5.96410i	0.181952	+	0.465718i
$165$	−1.33013	+	2.30385i	−0.103550	+	0.179354i
$166$	−2.36603	+	1.36603i	−0.183639	+	0.106024i
$167$	−11.9282	−	11.9282i	−0.923032	−	0.923032i	0.0742105	−	0.997243i	$-0.476356\pi$
$167$	−11.9282	−	11.9282i	−0.923032	−	0.923032i	−0.997243	+	0.0742105i	$0.976356\pi$
$168$	0.294229	−	4.09808i	0.0227002	−	0.316173i
$169$		−	7.00000i		−	0.538462i
$170$	3.00000	+	0.803848i	0.230089	+	0.0616523i
$171$	−18.0263	+	4.83013i	−1.37850	+	0.369369i
$172$	1.26795	+	0.732051i	0.0966802	+	0.0558184i
$173$	12.0622	−	6.96410i	0.917070	−	0.529471i	0.0343711	−	0.999409i	$-0.489057\pi$
$173$	12.0622	−	6.96410i	0.917070	−	0.529471i	0.882699	+	0.469938i	$0.155724\pi$
$174$	−2.39230			−0.181360
$175$	−4.00000	+	3.46410i	−0.302372	+	0.261861i
$176$	−2.09808	−	2.09808i	−0.158148	−	0.158148i
$177$	0.973721	−	3.63397i	0.0731893	−	0.273146i
$178$	−1.83013	−	6.83013i	−0.137174	−	0.511940i
$179$	0.330127	+	1.23205i	0.0246749	+	0.0920878i	0.977165	−	0.212481i	$-0.0681543\pi$
$179$	0.330127	+	1.23205i	0.0246749	+	0.0920878i	−0.952490	+	0.304569i	$0.901488\pi$
$180$	2.36603	+	4.09808i	0.176353	+	0.305453i
$181$	4.26795	−	4.26795i	0.317234	−	0.317234i	−0.530470	−	0.847704i	$-0.677984\pi$
$181$	4.26795	−	4.26795i	0.317234	−	0.317234i	0.847704	+	0.530470i	$0.177984\pi$
$182$	5.36603	+	3.63397i	0.397756	+	0.269368i
$183$	−2.56218	+	2.56218i	−0.189402	+	0.189402i
$184$	1.39230	−	0.803848i	0.102642	−	0.0592604i
$185$	11.1962	+	6.46410i	0.823157	+	0.475250i
$186$	0.366025	+	1.36603i	0.0268383	+	0.100162i
$187$	2.66025	+	4.60770i	0.194537	+	0.336948i
$188$	2.46410	−	2.46410i	0.179713	−	0.179713i
$189$	7.06218	−	3.42820i	0.513698	−	0.249365i
$190$	−8.36603	+	8.36603i	−0.606935	+	0.606935i
$191$	−21.0263	−	5.63397i	−1.52141	−	0.407660i	−0.601203	−	0.799096i	$-0.705312\pi$
$191$	−21.0263	−	5.63397i	−1.52141	−	0.407660i	−0.920205	+	0.391436i	$0.871978\pi$
$192$	3.50000	−	0.937822i	0.252591	−	0.0676815i
$193$	−0.633975	+	0.169873i	−0.0456345	+	0.0122277i	−0.281564	−	0.959542i	$-0.590853\pi$
$193$	−0.633975	+	0.169873i	−0.0456345	+	0.0122277i	0.235930	+	0.971770i	$0.424187\pi$
$194$	0.535898	−	2.00000i	0.0384753	−	0.143592i
$195$	2.19615			0.157270
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$			13.9282i			0.992343i	0.868224	+	0.496172i	$0.165261\pi$
$197$			13.9282i			0.992343i	−0.868224	+	0.496172i	$0.834739\pi$
$198$	2.09808	−	7.83013i	0.149104	−	0.556463i
$199$	3.29423	+	12.2942i	0.233522	+	0.871515i	0.978810	+	0.204772i	$0.0656453\pi$
$199$	3.29423	+	12.2942i	0.233522	+	0.871515i	−0.745288	+	0.666743i	$0.767688\pi$
$200$	−5.19615	−	3.00000i	−0.367423	−	0.212132i
$201$	−0.633975	−	1.09808i	−0.0447171	−	0.0774523i
$202$	4.19615	+	4.19615i	0.295240	+	0.295240i
$203$	5.33975	+	11.0000i	0.374777	+	0.772049i
$204$	−0.928203			−0.0649872
$205$	−1.66987	+	10.9641i	−0.116629	+	0.765766i
$206$	2.63397	−	4.56218i	0.183518	−	0.317862i
$207$	1.26795	+	0.732051i	0.0881286	+	0.0508810i
$208$	−0.633975	+	2.36603i	−0.0439582	+	0.164054i
$209$	−20.2679			−1.40196
$210$	1.33013	−	1.96410i	0.0917875	−	0.135536i
$211$	−13.8301	+	13.8301i	−0.952105	+	0.952105i	−0.998904	−	0.0467991i	$-0.985098\pi$
$211$	−13.8301	+	13.8301i	−0.952105	+	0.952105i	0.0467991	+	0.998904i	$0.485098\pi$
$212$	0.366025	−	1.36603i	0.0251387	−	0.0938190i
$213$	−5.30385	−	3.06218i	−0.363414	−	0.209817i
$214$	15.6340	+	9.02628i	1.06872	+	0.617024i
$215$	1.26795	+	2.19615i	0.0864734	+	0.149776i
$216$	6.29423	+	6.29423i	0.428268	+	0.428268i
$217$	5.46410	−	4.73205i	0.370927	−	0.321233i
$218$	6.92820	+	6.92820i	0.469237	+	0.469237i
$219$	−5.73205	−	1.53590i	−0.387336	−	0.103786i
$220$	1.33013	+	4.96410i	0.0896771	+	0.334680i
$221$	2.19615	−	3.80385i	0.147729	−	0.255874i
$222$	3.73205	+	1.00000i	0.250479	+	0.0671156i
$223$	−4.92820			−0.330017			−0.165008	−	0.986292i	$-0.552765\pi$
$223$	−4.92820			−0.330017			−0.165008	+	0.986292i	$0.552765\pi$
$224$	−8.66025	−	10.0000i	−0.578638	−	0.668153i
$225$		−	5.46410i		−	0.364273i
$226$	10.0359	−	5.79423i	0.667578	−	0.385426i
$227$	−1.57180	−	5.86603i	−0.104324	−	0.389342i	0.893944	−	0.448179i	$-0.147927\pi$
$227$	−1.57180	−	5.86603i	−0.104324	−	0.389342i	−0.998268	+	0.0588374i	$0.981261\pi$
$228$	1.76795	−	3.06218i	0.117085	−	0.202798i
$229$	11.1962	+	3.00000i	0.739863	+	0.198246i	0.609017	−	0.793157i	$-0.291564\pi$
$229$	11.1962	+	3.00000i	0.739863	+	0.198246i	0.130846	+	0.991403i	$0.458231\pi$
$230$	0.928203			0.0612039
$231$	3.99038	−	0.767949i	0.262548	−	0.0505273i
$232$	−9.80385	+	9.80385i	−0.643654	+	0.643654i
$233$	7.36603	−	27.4904i	0.482564	−	1.80095i	−0.108222	−	0.994127i	$-0.534516\pi$
$233$	7.36603	−	27.4904i	0.482564	−	1.80095i	0.590786	−	0.806828i	$-0.298818\pi$
$234$	−6.46410	+	1.73205i	−0.422572	+	0.113228i
$235$	5.83013	−	1.56218i	0.380316	−	0.101905i
$236$	−3.63397	−	6.29423i	−0.236552	−	0.409719i
$237$			3.33975i			0.216940i
$238$	−2.07180	−	4.26795i	−0.134295	−	0.276650i
$239$	−19.7583	−	19.7583i	−1.27806	−	1.27806i	−0.941752	−	0.336308i	$-0.890822\pi$
$239$	−19.7583	−	19.7583i	−1.27806	−	1.27806i	−0.336308	−	0.941752i	$-0.609178\pi$
$240$	0.866025	+	0.232051i	0.0559017	+	0.0149788i
$241$	−22.0526	−	12.7321i	−1.42053	−	0.820143i	−0.424186	−	0.905575i	$-0.639440\pi$
$241$	−22.0526	−	12.7321i	−1.42053	−	0.820143i	−0.996344	+	0.0854315i	$0.972773\pi$
$242$	−1.09808	+	1.90192i	−0.0705870	+	0.122260i
$243$	−3.19615	+	11.9282i	−0.205033	+	0.765195i
$244$			7.00000i			0.448129i
$245$	−12.0000	−	1.73205i	−0.766652	−	0.110657i
$246$	0.366025	+	3.29423i	0.0233369	+	0.210032i
$247$	8.36603	+	14.4904i	0.532317	+	0.922001i
$248$	7.09808	+	4.09808i	0.450728	+	0.260228i
$249$	1.36603	−	0.366025i	0.0865683	−	0.0231959i
$250$	−6.06218	−	10.5000i	−0.383406	−	0.664078i
$251$		−	1.26795i		−	0.0800322i	−0.999199	−	0.0400161i	$-0.987259\pi$
$251$		−	1.26795i		−	0.0800322i	0.999199	−	0.0400161i	$-0.0127409\pi$
$252$	2.36603	−	6.83013i	0.149046	−	0.430258i
$253$	1.12436	+	1.12436i	0.0706876	+	0.0706876i
$254$	−6.16987	+	3.56218i	−0.387132	+	0.223511i
$255$	−1.39230	−	0.803848i	−0.0871895	−	0.0503389i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	6.53590	−	24.3923i	0.407698	−	1.52155i	−0.391327	−	0.920252i	$-0.627984\pi$
$257$	6.53590	−	24.3923i	0.407698	−	1.52155i	0.799025	−	0.601298i	$-0.205350\pi$
$258$	0.535898	+	0.535898i	0.0333636	+	0.0333636i
$259$	−3.73205	−	19.3923i	−0.231898	−	1.20498i
$260$	3.00000	−	3.00000i	0.186052	−	0.186052i
$261$	−12.1962	−	3.26795i	−0.754923	−	0.202281i
$262$		0			0
$263$	−0.758330	−	2.83013i	−0.0467606	−	0.174513i	0.938596	−	0.345017i	$-0.112127\pi$
$263$	−0.758330	−	2.83013i	−0.0467606	−	0.174513i	−0.985357	+	0.170504i	$0.945460\pi$
$264$	2.30385	+	3.99038i	0.141792	+	0.245591i
$265$	1.73205	−	1.73205i	0.106399	−	0.106399i
$266$	18.0263	+	1.29423i	1.10526	+	0.0793542i
$267$			3.66025i			0.224004i
$268$	−2.36603	−	0.633975i	−0.144528	−	0.0387262i
$269$	−5.50000	+	9.52628i	−0.335341	+	0.580828i	−0.983550	−	0.180635i	$-0.942185\pi$
$269$	−5.50000	+	9.52628i	−0.335341	+	0.580828i	0.648209	+	0.761462i	$0.275518\pi$
$270$	1.33013	+	4.96410i	0.0809490	+	0.302106i
$271$	6.73205	+	11.6603i	0.408943	+	0.708310i	0.994772	−	0.102125i	$-0.0325642\pi$
$271$	6.73205	+	11.6603i	0.408943	+	0.708310i	−0.585829	+	0.810435i	$0.699231\pi$
$272$	1.26795	−	1.26795i	0.0768807	−	0.0768807i
$273$	−2.19615	−	2.53590i	−0.132917	−	0.153480i
$274$	−7.92820	−	7.92820i	−0.478960	−	0.478960i
$275$	1.53590	−	5.73205i	0.0926182	−	0.345656i
$276$	−0.267949	+	0.0717968i	−0.0161286	+	0.00432166i
$277$	12.7942	−	22.1603i	0.768731	−	1.33148i	−0.169521	−	0.985527i	$-0.554222\pi$
$277$	12.7942	−	22.1603i	0.768731	−	1.33148i	0.938251	−	0.345954i	$-0.112445\pi$
$278$	−20.3660	+	11.7583i	−1.22147	+	0.705218i
$279$			7.46410i			0.446864i
$280$	−2.59808	−	13.5000i	−0.155265	−	0.806779i
$281$	10.1962	−	10.1962i	0.608251	−	0.608251i	−0.334237	−	0.942489i	$-0.608479\pi$
$281$	10.1962	−	10.1962i	0.608251	−	0.608251i	0.942489	+	0.334237i	$0.108479\pi$
$282$	1.56218	−	0.901924i	0.0930263	−	0.0537088i
$283$	7.09808	−	12.2942i	0.421937	−	0.730816i	−0.574192	−	0.818721i	$-0.694684\pi$
$283$	7.09808	−	12.2942i	0.421937	−	0.730816i	0.996129	+	0.0879046i	$0.0280171\pi$
$284$	−11.4282	+	3.06218i	−0.678139	+	0.181707i
$285$	5.30385	−	3.06218i	0.314173	−	0.181388i
$286$	−7.26795			−0.429763
$287$	14.3301	−	9.03590i	0.845881	−	0.533372i
$288$	13.6603			0.804938
$289$	11.9378	−	6.89230i	0.702225	−	0.405430i
$290$	−7.73205	+	2.07180i	−0.454042	+	0.121660i
$291$	−0.535898	+	0.928203i	−0.0314149	+	0.0544122i
$292$	−9.92820	+	5.73205i	−0.581004	+	0.335443i
$293$	−17.1244	+	17.1244i	−1.00042	+	1.00042i	−0.000415626		1.00000i	$0.500132\pi$
$293$	−17.1244	+	17.1244i	−1.00042	+	1.00042i	−1.00000		0.000415626i	$0.999868\pi$
$294$	−3.59808	+	0.428203i	−0.209844	+	0.0249733i
$295$		−	12.5885i		−	0.732928i
$296$	19.3923	−	11.1962i	1.12715	−	0.650763i
$297$	−4.40192	+	7.62436i	−0.255426	+	0.442410i
$298$	−7.09808	+	1.90192i	−0.411181	+	0.110175i
$299$	0.339746	−	1.26795i	0.0196480	−	0.0733274i
$300$	0.732051	+	0.732051i	0.0422650	+	0.0422650i
$301$	1.26795	−	3.66025i	0.0730834	−	0.210974i
$302$	1.00000	−	1.00000i	0.0575435	−	0.0575435i
$303$	−1.53590	−	2.66025i	−0.0882351	−	0.152828i
$304$	1.76795	+	6.59808i	0.101399	+	0.378426i
$305$	−6.06218	+	10.5000i	−0.347119	+	0.601228i
$306$	4.73205	+	1.26795i	0.270513	+	0.0724838i
$307$		−	22.0000i		−	1.25561i	−0.778372	−	0.627803i	$-0.783954\pi$
$307$		−	22.0000i		−	1.25561i	0.778372	−	0.627803i	$-0.216046\pi$
$308$	4.40192	−	6.50000i	0.250823	−	0.370372i
$309$	−1.92820	+	1.92820i	−0.109692	+	0.109692i
$310$	2.36603	+	4.09808i	0.134381	+	0.232755i
$311$	0.366025	+	1.36603i	0.0207554	+	0.0774602i	0.975527	−	0.219881i	$-0.0705668\pi$
$311$	0.366025	+	1.36603i	0.0207554	+	0.0774602i	−0.954771	+	0.297341i	$0.903900\pi$
$312$	1.90192	−	3.29423i	0.107675	−	0.186499i
$313$	−32.0526	−	8.58846i	−1.81172	−	0.485448i	−0.816013	−	0.578034i	$-0.803820\pi$
$313$	−32.0526	−	8.58846i	−1.81172	−	0.485448i	−0.995705	+	0.0925853i	$0.970487\pi$
$314$	11.1244	−	11.1244i	0.627784	−	0.627784i
$315$	9.46410	−	8.19615i	0.533242	−	0.461801i
$316$	4.56218	+	4.56218i	0.256643	+	0.256643i
$317$	−8.53590	+	31.8564i	−0.479424	+	1.78923i	0.124531	+	0.992216i	$0.460257\pi$
$317$	−8.53590	+	31.8564i	−0.479424	+	1.78923i	−0.603955	+	0.797018i	$0.706409\pi$
$318$	0.366025	−	0.633975i	0.0205257	−	0.0355515i
$319$	−11.8756	−	6.85641i	−0.664908	−	0.383885i
$320$	10.5000	−	6.06218i	0.586968	−	0.338886i
$321$	−6.60770	−	6.60770i	−0.368806	−	0.368806i
$322$	−0.928203	−	1.07180i	−0.0517267	−	0.0597289i
$323$		−	12.2487i		−	0.681537i
$324$	3.33013	+	5.76795i	0.185007	+	0.320442i
$325$	−4.73205	+	1.26795i	−0.262487	+	0.0703332i
$326$	20.9545	+	12.0981i	1.16056	+	0.670050i
$327$	−2.53590	−	4.39230i	−0.140236	−	0.242895i
$328$	15.0000	+	12.0000i	0.828236	+	0.662589i
$329$	−7.63397	−	5.16987i	−0.420875	−	0.285024i
$330$			2.66025i			0.146442i
$331$	−3.49038	+	13.0263i	−0.191849	+	0.715989i	0.801211	+	0.598381i	$0.204189\pi$
$331$	−3.49038	+	13.0263i	−0.191849	+	0.715989i	−0.993060	+	0.117608i	$0.962477\pi$
$332$	1.36603	−	2.36603i	0.0749704	−	0.129853i
$333$	17.6603	+	10.1962i	0.967776	+	0.558746i
$334$	−16.2942	−	4.36603i	−0.891581	−	0.238898i
$335$	−3.00000	−	3.00000i	−0.163908	−	0.163908i
$336$	−0.598076	−	1.23205i	−0.0326277	−	0.0672139i
$337$		−	21.1962i		−	1.15463i	−0.816522	−	0.577314i	$-0.804101\pi$
$337$		−	21.1962i		−	1.15463i	0.816522	−	0.577314i	$-0.195899\pi$
$338$	−3.50000	−	6.06218i	−0.190375	−	0.329739i
$339$	−5.79423	+	1.55256i	−0.314699	+	0.0843234i
$340$	−3.00000	+	0.803848i	−0.162698	+	0.0435948i
$341$	−2.09808	+	7.83013i	−0.113617	+	0.424025i
$342$	−13.1962	+	13.1962i	−0.713566	+	0.713566i
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	4.39230			0.236817
$345$	−0.464102	−	0.124356i	−0.0249864	−	0.00669508i
$346$	6.96410	−	12.0622i	0.374392	−	0.648467i
$347$	−4.30385	−	16.0622i	−0.231043	−	0.862263i	−0.979893	−	0.199524i	$-0.936060\pi$
$347$	−4.30385	−	16.0622i	−0.231043	−	0.862263i	0.748850	−	0.662739i	$-0.230606\pi$
$348$	2.07180	−	1.19615i	0.111060	−	0.0641205i
$349$			3.46410i			0.185429i	0.995693	+	0.0927146i	$0.0295544\pi$
$349$			3.46410i			0.185429i	−0.995693	+	0.0927146i	$0.970446\pi$
$350$	−1.73205	+	5.00000i	−0.0925820	+	0.267261i
$351$	7.26795			0.387934
$352$	14.3301	+	3.83975i	0.763798	+	0.204659i
$353$	1.66987	−	2.89230i	0.0888784	−	0.153942i	−0.818159	−	0.574992i	$-0.805005\pi$
$353$	1.66987	−	2.89230i	0.0888784	−	0.153942i	0.907037	+	0.421050i	$0.138338\pi$
$354$	−0.973721	−	3.63397i	−0.0517527	−	0.193144i
$355$	−19.7942	−	5.30385i	−1.05057	−	0.281499i
$356$	5.00000	+	5.00000i	0.264999	+	0.264999i
$357$	0.464102	+	2.41154i	0.0245629	+	0.127632i
$358$	0.901924	+	0.901924i	0.0476682	+	0.0476682i
$359$	−9.29423	−	16.0981i	−0.490531	−	0.849624i	0.509410	−	0.860524i	$-0.329864\pi$
$359$	−9.29423	−	16.0981i	−0.490531	−	0.849624i	−0.999941	+	0.0109000i	$0.996530\pi$
$360$	12.2942	+	7.09808i	0.647963	+	0.374101i
$361$	23.9545	+	13.8301i	1.26076	+	0.727901i
$362$	1.56218	−	5.83013i	0.0821062	−	0.306425i
$363$	0.803848	−	0.803848i	0.0421911	−	0.0421911i
$364$	−6.46410	−	0.464102i	−0.338811	−	0.0243255i
$365$	−19.8564			−1.03933
$366$	−0.937822	+	3.50000i	−0.0490208	+	0.182948i
$367$	−28.6865	−	16.5622i	−1.49742	−	0.864539i	−0.497429	−	0.867505i	$-0.665723\pi$
$367$	−28.6865	−	16.5622i	−1.49742	−	0.864539i	−0.999996	+	0.00296590i	$0.999056\pi$
$368$	0.267949	−	0.464102i	0.0139678	−	0.0241930i
$369$	−2.63397	+	17.2942i	−0.137119	+	0.900302i
$370$	12.9282			0.672105
$371$	−3.73205	−	0.267949i	−0.193758	−	0.0139112i
$372$	−1.00000	−	1.00000i	−0.0518476	−	0.0518476i
$373$	6.42820	+	11.1340i	0.332840	+	0.576495i	0.983067	−	0.183244i	$-0.0586598\pi$
$373$	6.42820	+	11.1340i	0.332840	+	0.576495i	−0.650228	+	0.759739i	$0.725327\pi$
$374$	4.60770	+	2.66025i	0.238258	+	0.137558i
$375$	1.62436	+	6.06218i	0.0838814	+	0.313050i
$376$	2.70577	−	10.0981i	0.139540	−	0.520769i
$377$			11.3205i			0.583036i
$378$	4.40192	−	6.50000i	0.226411	−	0.334324i
$379$	16.5885			0.852092			0.426046	−	0.904702i	$-0.359906\pi$
$379$	16.5885			0.852092			0.426046	+	0.904702i	$0.359906\pi$
$380$	3.06218	−	11.4282i	0.157086	−	0.586254i
$381$	3.56218	−	0.954483i	0.182496	−	0.0488996i
$382$	−21.0263	+	5.63397i	−1.07580	+	0.288259i
$383$	14.1603	+	3.79423i	0.723555	+	0.193876i	0.601757	−	0.798679i	$-0.294467\pi$
$383$	14.1603	+	3.79423i	0.723555	+	0.193876i	0.121798	+	0.992555i	$0.461134\pi$
$384$	−1.09808	+	1.09808i	−0.0560360	+	0.0560360i
$385$	12.2321	−	5.93782i	0.623403	−	0.302619i
$386$	−0.464102	+	0.464102i	−0.0236222	+	0.0236222i
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$	0.535898	+	2.00000i	0.0272061	+	0.101535i
$389$	12.4019	+	7.16025i	0.628802	+	0.363039i	0.780288	−	0.625420i	$-0.215072\pi$
$389$	12.4019	+	7.16025i	0.628802	+	0.363039i	−0.151486	+	0.988459i	$0.548406\pi$
$390$	1.90192	−	1.09808i	0.0963077	−	0.0556033i
$391$	−0.679492	+	0.679492i	−0.0343634	+	0.0343634i
$392$	−12.9904	+	16.5000i	−0.656113	+	0.833376i
$393$		0			0
$394$	6.96410	+	12.0622i	0.350846	+	0.607684i
$395$	2.89230	+	10.7942i	0.145528	+	0.543117i
$396$	2.09808	+	7.83013i	0.105432	+	0.393479i
$397$	−3.29423	+	12.2942i	−0.165333	+	0.617030i	0.832665	+	0.553777i	$0.186814\pi$
$397$	−3.29423	+	12.2942i	−0.165333	+	0.617030i	−0.997998	+	0.0632526i	$0.979853\pi$
$398$	9.00000	+	9.00000i	0.451129	+	0.451129i
$399$	−8.83975	−	3.06218i	−0.442541	−	0.153301i
$400$	−2.00000			−0.100000
$401$	−26.5526	+	15.3301i	−1.32597	+	0.765550i	−0.984674	−	0.174405i	$-0.944200\pi$
$401$	−26.5526	+	15.3301i	−1.32597	+	0.765550i	−0.341298	+	0.939955i	$0.610866\pi$
$402$	−1.09808	−	0.633975i	−0.0547671	−	0.0316198i
$403$	6.46410	−	1.73205i	0.322000	−	0.0862796i
$404$	−5.73205	−	1.53590i	−0.285180	−	0.0764138i
$405$			11.5359i			0.573223i
$406$	10.1244	+	6.85641i	0.502463	+	0.340278i
$407$	15.6603	+	15.6603i	0.776250	+	0.776250i
$408$	−2.41154	+	1.39230i	−0.119389	+	0.0689294i
$409$	−8.99038	+	15.5718i	−0.444546	+	0.769976i	−0.998020	−	0.0628902i	$-0.979968\pi$
$409$	−8.99038	+	15.5718i	−0.444546	+	0.769976i	0.553475	+	0.832866i	$0.313302\pi$
$410$	4.03590	+	10.3301i	0.199319	+	0.510169i
$411$	2.90192	+	5.02628i	0.143141	+	0.247928i
$412$			5.26795i			0.259533i
$413$	−14.5359	+	12.5885i	−0.715265	+	0.619437i
$414$	1.46410			0.0719567
$415$	4.09808	−	2.36603i	0.201167	−	0.116144i
$416$	−3.16987	−	11.8301i	−0.155416	−	0.580020i
$417$	11.7583	−	3.15064i	0.575808	−	0.154287i
$418$	−17.5526	+	10.1340i	−0.858524	+	0.495669i
$419$		−	12.9282i		−	0.631584i	−0.948828	−	0.315792i	$-0.897730\pi$
$419$		−	12.9282i		−	0.631584i	0.948828	−	0.315792i	$-0.102270\pi$
$420$	−0.169873	+	2.36603i	−0.00828895	+	0.115450i
$421$	−26.3205	−	26.3205i	−1.28278	−	1.28278i	−0.939077	−	0.343706i	$-0.888318\pi$
$421$	−26.3205	−	26.3205i	−1.28278	−	1.28278i	−0.343706	−	0.939077i	$-0.611682\pi$
$422$	−5.06218	+	18.8923i	−0.246423	+	0.919663i
$423$	9.19615	−	2.46410i	0.447132	−	0.119809i
$424$	−1.09808	−	4.09808i	−0.0533273	−	0.199020i
$425$	3.46410	+	0.928203i	0.168034	+	0.0450245i
$426$	−6.12436			−0.296726
$427$	18.1865	−	3.50000i	0.880108	−	0.169377i
$428$	−18.0526			−0.872603
$429$	3.63397	+	0.973721i	0.175450	+	0.0470117i
$430$	2.19615	+	1.26795i	0.105908	+	0.0611459i
$431$	27.4641	+	15.8564i	1.32290	+	0.763776i	0.984190	−	0.177115i	$-0.0566764\pi$
$431$	27.4641	+	15.8564i	1.32290	+	0.763776i	0.338709	+	0.940891i	$0.390010\pi$
$432$	2.86603	+	0.767949i	0.137892	+	0.0369480i
$433$	33.2487			1.59783			0.798916	−	0.601443i	$-0.205407\pi$
$433$	33.2487			1.59783			0.798916	+	0.601443i	$0.205407\pi$
$434$	2.36603	−	6.83013i	0.113573	−	0.327857i
$435$	4.14359			0.198670
$436$	−9.46410	−	2.53590i	−0.453248	−	0.121448i
$437$	−0.947441	−	3.53590i	−0.0453223	−	0.169145i
$438$	−5.73205	+	1.53590i	−0.273888	+	0.0733881i
$439$	−9.59808	+	35.8205i	−0.458091	+	1.70962i	0.220747	+	0.975331i	$0.429151\pi$
$439$	−9.59808	+	35.8205i	−0.458091	+	1.70962i	−0.678838	+	0.734288i	$0.737516\pi$
$440$	10.9019	+	10.9019i	0.519729	+	0.519729i
$441$	−18.9282	−	2.73205i	−0.901343	−	0.130098i
$442$		−	4.39230i		−	0.208921i
$443$	−5.07180	+	2.92820i	−0.240968	+	0.139123i	−0.615622	−	0.788042i	$-0.711095\pi$
$443$	−5.07180	+	2.92820i	−0.240968	+	0.139123i	0.374653	+	0.927165i	$0.377762\pi$
$444$	−3.73205	+	1.00000i	−0.177115	+	0.0474579i
$445$	3.16987	+	11.8301i	0.150266	+	0.560802i
$446$	−4.26795	+	2.46410i	−0.202093	+	0.116679i
$447$	3.80385			0.179916
$448$	−17.5000	−	6.06218i	−0.826797	−	0.286411i
$449$		−	13.1436i		−	0.620285i	−0.950690	−	0.310142i	$-0.899623\pi$
$449$		−	13.1436i		−	0.620285i	0.950690	−	0.310142i	$-0.100377\pi$
$450$	−2.73205	−	4.73205i	−0.128790	−	0.223071i
$451$	−7.62436	+	17.4019i	−0.359017	+	0.819425i
$452$	−5.79423	+	10.0359i	−0.272538	+	0.472049i
$453$	−0.633975	+	0.366025i	−0.0297867	+	0.0171974i
$454$	−4.29423	−	4.29423i	−0.201538	−	0.201538i
$455$	−9.29423	−	6.29423i	−0.435720	−	0.295078i
$456$		−	10.6077i		−	0.496751i
$457$	−27.1244	−	7.26795i	−1.26882	−	0.339980i	−0.439244	−	0.898368i	$-0.644754\pi$
$457$	−27.1244	−	7.26795i	−1.26882	−	0.339980i	−0.829580	+	0.558388i	$0.811420\pi$
$458$	11.1962	−	3.00000i	0.523162	−	0.140181i
$459$	−4.60770	−	2.66025i	−0.215069	−	0.124170i
$460$	−0.803848	+	0.464102i	−0.0374796	+	0.0216388i
$461$	41.5885			1.93697			0.968484	−	0.249077i	$-0.0801271\pi$
$461$	41.5885			1.93697			0.968484	+	0.249077i	$0.0801271\pi$
$462$	3.07180	−	2.66025i	0.142913	−	0.123766i
$463$	11.2942	+	11.2942i	0.524887	+	0.524887i	0.919043	−	0.394156i	$-0.128963\pi$
$463$	11.2942	+	11.2942i	0.524887	+	0.524887i	−0.394156	+	0.919043i	$0.628963\pi$
$464$	−1.19615	+	4.46410i	−0.0555300	+	0.207241i
$465$	−0.633975	−	2.36603i	−0.0293999	−	0.109722i
$466$	−7.36603	−	27.4904i	−0.341225	−	1.27347i
$467$	3.00000	+	5.19615i	0.138823	+	0.240449i	0.927052	−	0.374934i	$-0.122335\pi$
$467$	3.00000	+	5.19615i	0.138823	+	0.240449i	−0.788228	+	0.615383i	$0.789001\pi$
$468$	4.73205	−	4.73205i	0.218739	−	0.218739i
$469$	−0.464102	+	6.46410i	−0.0214302	+	0.298484i
$470$	4.26795	−	4.26795i	0.196866	−	0.196866i
$471$	−7.05256	+	4.07180i	−0.324965	+	0.187618i
$472$	−18.8827	−	10.9019i	−0.869146	−	0.501802i
$473$	1.12436	+	4.19615i	0.0516979	+	0.192939i
$474$	1.66987	+	2.89230i	0.0766998	+	0.132848i
$475$	−9.66025	+	9.66025i	−0.443243	+	0.443243i
$476$	3.92820	+	2.66025i	0.180049	+	0.121933i
$477$	2.73205	−	2.73205i	0.125092	−	0.125092i
$478$	−26.9904	−	7.23205i	−1.23451	−	0.330786i
$479$	2.40192	−	0.643594i	0.109747	−	0.0294065i	−0.203528	−	0.979069i	$-0.565241\pi$
$479$	2.40192	−	0.643594i	0.109747	−	0.0294065i	0.313274	+	0.949663i	$0.398574\pi$
$480$	−4.33013	+	1.16025i	−0.197642	+	0.0529581i
$481$	4.73205	−	17.6603i	0.215763	−	0.805238i
$482$	−25.4641			−1.15986
$483$	0.320508	+	0.660254i	0.0145836	+	0.0300426i
$484$		−	2.19615i		−	0.0998251i
$485$	−0.928203	+	3.46410i	−0.0421475	+	0.157297i
$486$	3.19615	+	11.9282i	0.144980	+	0.541074i
$487$	29.4904	+	17.0263i	1.33634	+	0.771534i	0.986262	−	0.165187i	$-0.0528229\pi$
$487$	29.4904	+	17.0263i	1.33634	+	0.771534i	0.350075	+	0.936722i	$0.386156\pi$
$488$	10.5000	+	18.1865i	0.475313	+	0.823266i
$489$	−8.85641	−	8.85641i	−0.400501	−	0.400501i
$490$	−11.2583	+	4.50000i	−0.508600	+	0.203289i
$491$	19.1244			0.863070			0.431535	−	0.902096i	$-0.357972\pi$
$491$	19.1244			0.863070			0.431535	+	0.902096i	$0.357972\pi$
$492$	−1.96410	−	2.66987i	−0.0885485	−	0.120367i
$493$	4.14359	−	7.17691i	0.186618	−	0.323232i
$494$	14.4904	+	8.36603i	0.651953	+	0.376405i
$495$	−3.63397	+	13.5622i	−0.163335	+	0.609575i
$496$	2.73205			0.122673
$497$	13.6699	+	28.1603i	0.613178	+	1.26316i
$498$	1.00000	−	1.00000i	0.0448111	−	0.0448111i
$499$	7.90192	−	29.4904i	0.353739	−	1.32017i	−0.528326	−	0.849042i	$-0.677180\pi$
$499$	7.90192	−	29.4904i	0.353739	−	1.32017i	0.882064	−	0.471129i	$-0.156153\pi$
$500$	10.5000	+	6.06218i	0.469574	+	0.271109i
$501$	7.56218	+	4.36603i	0.337853	+	0.195060i
$502$	−0.633975	−	1.09808i	−0.0282957	−	0.0490095i
$503$	21.5622	+	21.5622i	0.961410	+	0.961410i	0.999283	−	0.0378726i	$-0.0120581\pi$
$503$	21.5622	+	21.5622i	0.961410	+	0.961410i	−0.0378726	+	0.999283i	$0.512058\pi$
$504$	−4.09808	−	21.2942i	−0.182543	−	0.948520i
$505$	−7.26795	−	7.26795i	−0.323419	−	0.323419i
$506$	1.53590	+	0.411543i	0.0682790	+	0.0182953i
$507$	0.937822	+	3.50000i	0.0416501	+	0.155440i
$508$	3.56218	−	6.16987i	0.158046	−	0.273744i
$509$	11.1962	+	3.00000i	0.496261	+	0.132973i	0.498264	−	0.867025i	$-0.333971\pi$
$509$	11.1962	+	3.00000i	0.496261	+	0.132973i	−0.00200333	+	0.999998i	$0.500638\pi$
$510$	−1.60770			−0.0711899
$511$	19.8564	+	22.9282i	0.878396	+	1.01428i
$512$		−	11.0000i		−	0.486136i
$513$	17.5526	−	10.1340i	0.774964	−	0.447426i
$514$	−6.53590	−	24.3923i	−0.288286	−	1.07590i
$515$	−4.56218	+	7.90192i	−0.201034	+	0.348200i
$516$	−0.732051	−	0.196152i	−0.0322267	−	0.00863513i
$517$	10.3397			0.454742
$518$	−12.9282	−	14.9282i	−0.568033	−	0.655908i
$519$	−5.09808	+	5.09808i	−0.223781	+	0.223781i
$520$	3.29423	−	12.2942i	0.144461	−	0.539138i
$521$	10.0263	−	2.68653i	0.439259	−	0.117699i	−0.0324101	−	0.999475i	$-0.510318\pi$
$521$	10.0263	−	2.68653i	0.439259	−	0.117699i	0.471669	+	0.881775i	$0.343652\pi$
$522$	−12.1962	+	3.26795i	−0.533811	+	0.143034i
$523$	−14.2679	−	24.7128i	−0.623894	−	1.08062i	−0.988754	−	0.149553i	$-0.952216\pi$
$523$	−14.2679	−	24.7128i	−0.623894	−	1.08062i	0.364860	−	0.931062i	$-0.381117\pi$
$524$		0			0
$525$	1.53590	−	2.26795i	0.0670321	−	0.0989814i
$526$	−2.07180	−	2.07180i	−0.0903346	−	0.0903346i
$527$	−4.73205	−	1.26795i	−0.206131	−	0.0552327i
$528$	1.33013	+	0.767949i	0.0578863	+	0.0334207i
$529$	11.3564	−	19.6699i	0.493757	−	0.855212i
$530$	0.633975	−	2.36603i	0.0275381	−	0.102774i
$531$		−	19.8564i		−	0.861695i
$532$	−16.2583	+	7.89230i	−0.704888	+	0.342175i
$533$	15.5885	−	1.73205i	0.675211	−	0.0750234i
$534$	1.83013	+	3.16987i	0.0791973	+	0.137174i
$535$	−27.0788	−	15.6340i	−1.17072	−	0.675916i
$536$	−7.09808	+	1.90192i	−0.306590	+	0.0821506i
$537$	−0.330127	−	0.571797i	−0.0142460	−	0.0246749i
$538$			11.0000i			0.474244i
$539$	−19.0885	−	8.18653i	−0.822198	−	0.352619i
$540$	−3.63397	−	3.63397i	−0.156381	−	0.156381i
$541$	−12.1244	+	7.00000i	−0.521267	+	0.300954i	−0.737453	−	0.675399i	$-0.763972\pi$
$541$	−12.1244	+	7.00000i	−0.521267	+	0.300954i	0.216186	+	0.976352i	$0.430638\pi$
$542$	11.6603	+	6.73205i	0.500851	+	0.289166i
$543$	−1.56218	+	2.70577i	−0.0670395	+	0.116116i
$544$	−2.32051	+	8.66025i	−0.0994910	+	0.371305i
$545$	−12.0000	−	12.0000i	−0.514024	−	0.514024i
$546$	−3.16987	−	1.09808i	−0.135658	−	0.0469933i
$547$	−17.5359	+	17.5359i	−0.749781	+	0.749781i	−0.974438	−	0.224657i	$-0.927874\pi$
$547$	−17.5359	+	17.5359i	−0.749781	+	0.749781i	0.224657	+	0.974438i	$0.427874\pi$
$548$	10.8301	+	2.90192i	0.462640	+	0.123964i
$549$	−9.56218	+	16.5622i	−0.408104	+	0.706857i
$550$	−1.53590	−	5.73205i	−0.0654909	−	0.244415i
$551$	15.7846	+	27.3397i	0.672447	+	1.16471i
$552$	−0.588457	+	0.588457i	−0.0250464	+	0.0250464i
$553$	9.57180	−	14.1340i	0.407034	−	0.601038i
$554$		−	25.5885i		−	1.08715i
$555$	−6.46410	−	1.73205i	−0.274386	−	0.0735215i
$556$	11.7583	−	20.3660i	0.498664	−	0.863712i
$557$	−4.43782	−	16.5622i	−0.188037	−	0.701762i	−0.993960	−	0.109742i	$-0.964997\pi$
$557$	−4.43782	−	16.5622i	−0.188037	−	0.701762i	0.805924	−	0.592020i	$-0.201669\pi$
$558$	3.73205	+	6.46410i	0.157990	+	0.273647i
$559$	2.53590	−	2.53590i	0.107257	−	0.107257i
$560$	−3.00000	−	3.46410i	−0.126773	−	0.146385i
$561$	−1.94744	−	1.94744i	−0.0822210	−	0.0822210i
$562$	3.73205	−	13.9282i	0.157427	−	0.587526i
$563$	−12.1603	+	3.25833i	−0.512494	+	0.137322i	−0.505792	−	0.862655i	$-0.668800\pi$
$563$	−12.1603	+	3.25833i	−0.512494	+	0.137322i	−0.00670132	+	0.999978i	$0.502133\pi$
$564$	−0.901924	+	1.56218i	−0.0379778	+	0.0657796i
$565$	−17.3827	+	10.0359i	−0.731295	+	0.422213i
$566$		−	14.1962i		−	0.596709i
$567$	13.3205	−	11.5359i	0.559409	−	0.484462i
$568$	−25.0981	+	25.0981i	−1.05309	+	1.05309i
$569$	−13.3923	+	7.73205i	−0.561435	+	0.324144i	−0.753721	−	0.657194i	$-0.771743\pi$
$569$	−13.3923	+	7.73205i	−0.561435	+	0.324144i	0.192286	+	0.981339i	$0.438410\pi$
$570$	3.06218	−	5.30385i	0.128261	−	0.222154i
$571$	−4.50000	+	1.20577i	−0.188319	+	0.0504600i	−0.351746	−	0.936095i	$-0.614412\pi$
$571$	−4.50000	+	1.20577i	−0.188319	+	0.0504600i	0.163427	+	0.986555i	$0.447745\pi$
$572$	6.29423	−	3.63397i	0.263175	−	0.151944i
$573$	11.2679			0.470725
$574$	7.89230	−	14.9904i	0.329418	−	0.625686i
$575$	1.07180			0.0446970
$576$	16.5622	−	9.56218i	0.690091	−	0.398424i
$577$	22.2942	−	5.97372i	0.928121	−	0.248689i	0.237068	−	0.971493i	$-0.423814\pi$
$577$	22.2942	−	5.97372i	0.928121	−	0.248689i	0.691053	+	0.722804i	$0.257147\pi$
$578$	6.89230	−	11.9378i	0.286682	−	0.496548i
$579$	0.294229	−	0.169873i	0.0122277	−	0.00705968i
$580$	5.66025	−	5.66025i	0.235029	−	0.235029i
$581$	−6.83013	−	2.36603i	−0.283361	−	0.0981593i
$582$			1.07180i			0.0444274i
$583$	3.63397	−	2.09808i	0.150504	−	0.0868934i
$584$	−17.1962	+	29.7846i	−0.711582	+	1.23250i
$585$	11.1962	−	3.00000i	0.462904	−	0.124035i
$586$	−6.26795	+	23.3923i	−0.258927	+	0.966327i
$587$	1.56218	+	1.56218i	0.0644780	+	0.0644780i	0.738610	−	0.674132i	$-0.235482\pi$
$587$	1.56218	+	1.56218i	0.0644780	+	0.0644780i	−0.674132	+	0.738610i	$0.735482\pi$
$588$	2.90192	−	2.16987i	0.119673	−	0.0894841i
$589$	13.1962	−	13.1962i	0.543738	−	0.543738i
$590$	−6.29423	−	10.9019i	−0.259129	−	0.448825i
$591$	−1.86603	−	6.96410i	−0.0767580	−	0.286465i
$592$	3.73205	−	6.46410i	0.153386	−	0.265673i
$593$	16.9282	+	4.53590i	0.695158	+	0.186267i	0.589061	−	0.808089i	$-0.299498\pi$
$593$	16.9282	+	4.53590i	0.695158	+	0.186267i	0.106097	+	0.994356i	$0.466165\pi$
$594$			8.80385i			0.361226i
$595$	3.58846	+	7.39230i	0.147112	+	0.303055i
$596$	5.19615	−	5.19615i	0.212843	−	0.212843i
$597$	−3.29423	−	5.70577i	−0.134824	−	0.233522i
$598$	−0.339746	−	1.26795i	−0.0138932	−	0.0518503i
$599$	−5.85641	+	10.1436i	−0.239286	+	0.414456i	−0.960510	−	0.278247i	$-0.910247\pi$
$599$	−5.85641	+	10.1436i	−0.239286	+	0.414456i	0.721223	+	0.692703i	$0.243580\pi$
$600$	3.00000	+	0.803848i	0.122474	+	0.0328169i
$601$	4.26795	−	4.26795i	0.174093	−	0.174093i	−0.614682	−	0.788775i	$-0.710716\pi$
$601$	4.26795	−	4.26795i	0.174093	−	0.174093i	0.788775	+	0.614682i	$0.210716\pi$
$602$	−0.732051	−	3.80385i	−0.0298362	−	0.155033i
$603$	−4.73205	−	4.73205i	−0.192704	−	0.192704i
$604$	−0.366025	+	1.36603i	−0.0148934	+	0.0555828i
$605$	1.90192	−	3.29423i	0.0773242	−	0.133929i
$606$	−2.66025	−	1.53590i	−0.108065	−	0.0623916i
$607$	35.0263	−	20.2224i	1.42167	−	0.820803i	0.425231	−	0.905085i	$-0.360193\pi$
$607$	35.0263	−	20.2224i	1.42167	−	0.820803i	0.996442	+	0.0842817i	$0.0268596\pi$
$608$	−24.1506	−	24.1506i	−0.979438	−	0.979438i
$609$	−4.14359	−	4.78461i	−0.167907	−	0.193882i
$610$			12.1244i			0.490901i
$611$	−4.26795	−	7.39230i	−0.172663	−	0.299061i
$612$	−4.73205	+	1.26795i	−0.191282	+	0.0512538i
$613$	−9.23205	−	5.33013i	−0.372879	−	0.215282i	0.301836	−	0.953360i	$-0.402400\pi$
$613$	−9.23205	−	5.33013i	−0.372879	−	0.215282i	−0.674715	+	0.738078i	$0.735734\pi$
$614$	−11.0000	−	19.0526i	−0.443924	−	0.768899i
$615$	−0.633975	−	5.70577i	−0.0255643	−	0.230079i
$616$	1.68653	−	23.4904i	0.0679524	−	0.946454i
$617$		−	9.67949i		−	0.389682i	−0.980835	−	0.194841i	$-0.937581\pi$
$617$		−	9.67949i		−	0.389682i	0.980835	−	0.194841i	$-0.0624190\pi$
$618$	−0.705771	+	2.63397i	−0.0283903	+	0.105954i
$619$	22.2224	−	38.4904i	0.893195	−	1.54706i	0.0571721	−	0.998364i	$-0.481792\pi$
$619$	22.2224	−	38.4904i	0.893195	−	1.54706i	0.836023	−	0.548695i	$-0.184875\pi$
$620$	−4.09808	−	2.36603i	−0.164583	−	0.0950219i
$621$	−1.53590	−	0.411543i	−0.0616335	−	0.0165146i
$622$	1.00000	+	1.00000i	0.0400963	+	0.0400963i
$623$	10.4904	−	15.4904i	0.420288	−	0.620609i
$624$		−	1.26795i		−	0.0507586i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	−32.0526	+	8.58846i	−1.28108	+	0.343264i
$627$	10.1340	−	2.71539i	0.404712	−	0.108442i
$628$	−4.07180	+	15.1962i	−0.162482	+	0.606392i
$629$	−9.46410	+	9.46410i	−0.377358	+	0.377358i
$630$	4.09808	−	11.8301i	0.163271	−	0.471324i
$631$	−38.0526			−1.51485			−0.757424	−	0.652923i	$-0.773542\pi$
$631$	−38.0526			−1.51485			−0.757424	+	0.652923i	$0.773542\pi$
$632$	18.6962	+	5.00962i	0.743693	+	0.199272i
$633$	5.06218	−	8.76795i	0.201204	−	0.348495i
$634$	8.53590	+	31.8564i	0.339004	+	1.26518i
$635$	10.6865	−	6.16987i	0.424082	−	0.244844i
$636$			0.732051i			0.0290277i
$637$	2.02628	+	17.0263i	0.0802841	+	0.674606i
$638$	−13.7128			−0.542895
$639$	−31.2224	−	8.36603i	−1.23514	−	0.330955i
$640$	−2.59808	+	4.50000i	−0.102698	+	0.177878i
$641$	−2.04552	−	7.63397i	−0.0807931	−	0.301524i	0.913691	−	0.406409i	$-0.133219\pi$
$641$	−2.04552	−	7.63397i	−0.0807931	−	0.301524i	−0.994484	+	0.104885i	$0.966553\pi$
$642$	−9.02628	−	2.41858i	−0.356239	−	0.0954539i
$643$	−3.63397	−	3.63397i	−0.143310	−	0.143310i	0.631812	−	0.775122i	$-0.282312\pi$
$643$	−3.63397	−	3.63397i	−0.143310	−	0.143310i	−0.775122	+	0.631812i	$0.782312\pi$
$644$	1.33975	+	0.464102i	0.0527934	+	0.0182882i
$645$	−0.928203	−	0.928203i	−0.0365480	−	0.0365480i
$646$	−6.12436	−	10.6077i	−0.240960	−	0.417354i
$647$	23.6147	+	13.6340i	0.928391	+	0.536007i	0.886302	−	0.463107i	$-0.153265\pi$
$647$	23.6147	+	13.6340i	0.928391	+	0.536007i	0.0420887	+	0.999114i	$0.486599\pi$
$648$	17.3038	+	9.99038i	0.679759	+	0.392459i
$649$	5.58142	−	20.8301i	0.219090	−	0.817654i
$650$	−3.46410	+	3.46410i	−0.135873	+	0.135873i
$651$	−2.09808	+	3.09808i	−0.0822301	+	0.121423i
$652$	−24.1962			−0.947594
$653$	−5.39230	+	20.1244i	−0.211017	+	0.787527i	0.776514	+	0.630101i	$0.216986\pi$
$653$	−5.39230	+	20.1244i	−0.211017	+	0.787527i	−0.987531	+	0.157426i	$0.949680\pi$
$654$	−4.39230	−	2.53590i	−0.171753	−	0.0991615i
$655$		0			0
$656$	6.33013	+	0.964102i	0.247150	+	0.0376418i
$657$	−31.3205			−1.22193
$658$	−9.19615	−	0.660254i	−0.358503	−	0.0257394i
$659$	27.5359	+	27.5359i	1.07265	+	1.07265i	0.997146	+	0.0755005i	$0.0240555\pi$
$659$	27.5359	+	27.5359i	1.07265	+	1.07265i	0.0755005	+	0.997146i	$0.475945\pi$
$660$	−1.33013	−	2.30385i	−0.0517751	−	0.0896771i
$661$	−3.23205	−	1.86603i	−0.125712	−	0.0725800i	0.435825	−	0.900031i	$-0.356457\pi$
$661$	−3.23205	−	1.86603i	−0.125712	−	0.0725800i	−0.561537	+	0.827451i	$0.689790\pi$
$662$	3.49038	+	13.0263i	0.135658	+	0.506281i
$663$	−0.588457	+	2.19615i	−0.0228538	+	0.0852915i
$664$		−	8.19615i		−	0.318072i
$665$	−31.2224	−	2.24167i	−1.21075	−	0.0869282i
$666$	20.3923			0.790186
$667$	0.641016	−	2.39230i	0.0248202	−	0.0926304i
$668$	16.2942	−	4.36603i	0.630443	−	0.168927i
$669$	2.46410	−	0.660254i	0.0952677	−	0.0255269i
$670$	−4.09808	−	1.09808i	−0.158322	−	0.0424224i
$671$	−14.6865	+	14.6865i	−0.566967	+	0.566967i
$672$	5.66987	+	3.83975i	0.218720	+	0.148121i
$673$	−9.33975	+	9.33975i	−0.360021	+	0.360021i	−0.863820	−	0.503800i	$-0.831935\pi$
$673$	−9.33975	+	9.33975i	−0.360021	+	0.360021i	0.503800	+	0.863820i	$0.331935\pi$
$674$	−10.5981	−	18.3564i	−0.408223	−	0.707062i
$675$	1.53590	+	5.73205i	0.0591168	+	0.220627i
$676$	6.06218	+	3.50000i	0.233161	+	0.134615i
$677$	10.2846	−	5.93782i	0.395270	−	0.228209i	−0.289171	−	0.957277i	$-0.593380\pi$
$677$	10.2846	−	5.93782i	0.395270	−	0.228209i	0.684441	+	0.729068i	$0.260046\pi$
$678$	−4.24167	+	4.24167i	−0.162900	+	0.162900i
$679$	4.92820	−	2.39230i	0.189127	−	0.0918082i
$680$	−6.58846	+	6.58846i	−0.252656	+	0.252656i
$681$	1.57180	+	2.72243i	0.0602314	+	0.104324i
$682$	2.09808	+	7.83013i	0.0803395	+	0.299831i
$683$	−1.22243	−	4.56218i	−0.0467751	−	0.174567i	0.938587	−	0.345044i	$-0.112136\pi$
$683$	−1.22243	−	4.56218i	−0.0467751	−	0.174567i	−0.985362	+	0.170477i	$0.945469\pi$
$684$	4.83013	−	18.0263i	0.184685	−	0.689252i
$685$	13.7321	+	13.7321i	0.524675	+	0.524675i
$686$	16.4545	+	8.50000i	0.628235	+	0.324532i
$687$	−6.00000			−0.228914
$688$	1.26795	−	0.732051i	0.0483401	−	0.0279092i
$689$	−3.00000	−	1.73205i	−0.114291	−	0.0659859i
$690$	−0.464102	+	0.124356i	−0.0176680	+	0.00473414i
$691$	−34.2846	−	9.18653i	−1.30425	−	0.349472i	−0.461193	−	0.887300i	$-0.652578\pi$
$691$	−34.2846	−	9.18653i	−1.30425	−	0.349472i	−0.843055	+	0.537828i	$0.819245\pi$
$692$			13.9282i			0.529471i
$693$	19.2942	−	9.36603i	0.732927	−	0.355786i
$694$	−11.7583	−	11.7583i	−0.446340	−	0.446340i
$695$	35.2750	−	20.3660i	1.33806	−	0.772527i
$696$	3.58846	−	6.21539i	0.136020	−	0.235594i
$697$	−10.5167	−	4.60770i	−0.398347	−	0.174529i
$698$	1.73205	+	3.00000i	0.0655591	+	0.113552i
$699$			14.7321i			0.557217i
$700$	−1.00000	−	5.19615i	−0.0377964	−	0.196396i
$701$	−13.0526			−0.492988			−0.246494	−	0.969144i	$-0.579279\pi$
$701$	−13.0526			−0.492988			−0.246494	+	0.969144i	$0.579279\pi$
$702$	6.29423	−	3.63397i	0.237560	−	0.137156i
$703$	−13.1962	−	49.2487i	−0.497702	−	1.85745i
$704$	20.0622	−	5.37564i	0.756122	−	0.202602i
$705$	−2.70577	+	1.56218i	−0.101905	+	0.0588350i
$706$		−	3.33975i		−	0.125693i
$707$	−1.12436	+	15.6603i	−0.0422857	+	0.588964i
$708$	2.66025	+	2.66025i	0.0999785	+	0.0999785i
$709$	−9.80385	+	36.5885i	−0.368191	+	1.37411i	0.494852	+	0.868978i	$0.335222\pi$
$709$	−9.80385	+	36.5885i	−0.368191	+	1.37411i	−0.863043	+	0.505131i	$0.831444\pi$
$710$	−19.7942	+	5.30385i	−0.742864	+	0.199050i
$711$	4.56218	+	17.0263i	0.171095	+	0.638535i
$712$	20.4904	+	5.49038i	0.767909	+	0.205761i
$713$	−1.46410			−0.0548310
$714$	1.60770	+	1.85641i	0.0601665	+	0.0694743i
$715$	12.5885			0.470782
$716$	−1.23205	−	0.330127i	−0.0460439	−	0.0123374i
$717$	12.5263	+	7.23205i	0.467802	+	0.270086i
$718$	−16.0981	−	9.29423i	−0.600775	−	0.346858i
$719$	−38.9186	−	10.4282i	−1.45142	−	0.388906i	−0.554901	−	0.831916i	$-0.687244\pi$
$719$	−38.9186	−	10.4282i	−1.45142	−	0.388906i	−0.896517	+	0.443010i	$0.853911\pi$
$720$	4.73205			0.176353
$721$	13.6865	−	2.63397i	0.509713	−	0.0980943i
$722$	27.6603			1.02941
$723$	12.7321	+	3.41154i	0.473510	+	0.126877i
$724$	1.56218	+	5.83013i	0.0580579	+	0.216675i
$725$	−8.92820	+	2.39230i	−0.331585	+	0.0888480i
$726$	0.294229	−	1.09808i	0.0109198	−	0.0407534i
$727$	−3.00000	−	3.00000i	−0.111264	−	0.111264i	0.649283	−	0.760547i	$-0.275069\pi$
$727$	−3.00000	−	3.00000i	−0.111264	−	0.111264i	−0.760547	+	0.649283i	$0.775069\pi$
$728$	−17.4904	+	8.49038i	−0.648237	+	0.314674i
$729$			13.5885i			0.503276i
$730$	−17.1962	+	9.92820i	−0.636458	+	0.367459i
$731$	−2.53590	+	0.679492i	−0.0937936	+	0.0251319i
$732$	−0.937822	−	3.50000i	−0.0346629	−	0.129364i
$733$	10.0526	−	5.80385i	0.371300	−	0.214370i	−0.302726	−	0.953078i	$-0.597897\pi$
$733$	10.0526	−	5.80385i	0.371300	−	0.214370i	0.674026	+	0.738708i	$0.264564\pi$
$734$	−33.1244			−1.22264
$735$	6.23205	−	0.741670i	0.229873	−	0.0273569i
$736$			2.67949i			0.0987674i
$737$	−3.63397	−	6.29423i	−0.133859	−	0.231851i
$738$	6.36603	+	16.2942i	0.234337	+	0.599799i
$739$	−3.97372	+	6.88269i	−0.146176	+	0.253184i	−0.929811	−	0.368037i	$-0.880030\pi$
$739$	−3.97372	+	6.88269i	−0.146176	+	0.253184i	0.783635	+	0.621221i	$0.213363\pi$
$740$	−11.1962	+	6.46410i	−0.411579	+	0.237625i
$741$	−6.12436	−	6.12436i	−0.224984	−	0.224984i
$742$	−3.36603	+	1.63397i	−0.123571	+	0.0599851i
$743$		−	11.8564i		−	0.434969i	−0.976064	−	0.217485i	$-0.930215\pi$
$743$		−	11.8564i		−	0.434969i	0.976064	−	0.217485i	$-0.0697852\pi$
$744$	−4.09808	−	1.09808i	−0.150243	−	0.0402574i
$745$	12.2942	−	3.29423i	0.450426	−	0.120691i
$746$	11.1340	+	6.42820i	0.407644	+	0.235353i
$747$	6.46410	−	3.73205i	0.236509	−	0.136549i
$748$	−5.32051			−0.194537
$749$	9.02628	+	46.9019i	0.329813	+	1.71376i
$750$	4.43782	+	4.43782i	0.162046	+	0.162046i
$751$	−2.08846	+	7.79423i	−0.0762089	+	0.284415i	−0.993505	−	0.113791i	$-0.963701\pi$
$751$	−2.08846	+	7.79423i	−0.0762089	+	0.284415i	0.917296	+	0.398206i	$0.130367\pi$
$752$	−0.901924	−	3.36603i	−0.0328898	−	0.122746i
$753$	0.169873	+	0.633975i	0.00619052	+	0.0231033i
$754$	5.66025	+	9.80385i	0.206134	+	0.357035i
$755$	−1.73205	+	1.73205i	−0.0630358	+	0.0630358i
$756$	−0.562178	+	7.83013i	−0.0204462	+	0.284779i
$757$	9.80385	−	9.80385i	0.356327	−	0.356327i	−0.506130	−	0.862457i	$-0.668924\pi$
$757$	9.80385	−	9.80385i	0.356327	−	0.356327i	0.862457	+	0.506130i	$0.168924\pi$
$758$	14.3660	−	8.29423i	0.521798	−	0.301260i
$759$	−0.712813	−	0.411543i	−0.0258735	−	0.0149381i
$760$	−9.18653	−	34.2846i	−0.333231	−	1.24363i
$761$	−12.1244	−	21.0000i	−0.439508	−	0.761249i	0.558144	−	0.829744i	$-0.311514\pi$
$761$	−12.1244	−	21.0000i	−0.439508	−	0.761249i	−0.997651	+	0.0684947i	$0.978180\pi$
$762$	2.60770	−	2.60770i	0.0944668	−	0.0944668i
$763$	−1.85641	+	25.8564i	−0.0672064	+	0.936065i
$764$	15.3923	−	15.3923i	0.556874	−	0.556874i
$765$	−8.19615	−	2.19615i	−0.296333	−	0.0794021i
$766$	14.1603	−	3.79423i	0.511631	−	0.137091i
$767$	−17.1962	+	4.60770i	−0.620917	+	0.166374i
$768$	−2.27757	+	8.50000i	−0.0821847	+	0.306717i
$769$	−0.751289			−0.0270922			−0.0135461	−	0.999908i	$-0.504312\pi$
$769$	−0.751289			−0.0270922			−0.0135461	+	0.999908i	$0.504312\pi$
$770$	7.62436	−	11.2583i	0.274763	−	0.405722i
$771$			13.0718i			0.470769i
$772$	0.169873	−	0.633975i	0.00611386	−	0.0228172i
$773$	4.36603	+	16.2942i	0.157035	+	0.586063i	0.998922	+	0.0464096i	$0.0147779\pi$
$773$	4.36603	+	16.2942i	0.157035	+	0.586063i	−0.841887	+	0.539653i	$0.818555\pi$
$774$	3.46410	+	2.00000i	0.124515	+	0.0718885i
$775$	2.73205	+	4.73205i	0.0981382	+	0.169980i
$776$	4.39230	+	4.39230i	0.157675	+	0.157675i
$777$	4.46410	+	9.19615i	0.160149	+	0.329910i
$778$	14.3205			0.513415
$779$	35.2321	−	25.9186i	1.26232	−	0.928630i
$780$	−1.09808	+	1.90192i	−0.0393174	+	0.0680998i
$781$	−30.4019	−	17.5526i	−1.08787	−	0.628080i
$782$	−0.248711	+	0.928203i	−0.00889390	+	0.0331925i
$783$	13.7128			0.490056
$784$	−1.00000	+	6.92820i	−0.0357143	+	0.247436i
$785$	−19.2679	+	19.2679i	−0.687703	+	0.687703i
$786$		0			0
$787$	13.2679	+	7.66025i	0.472951	+	0.273059i	0.717474	−	0.696585i	$-0.245298\pi$
$787$	13.2679	+	7.66025i	0.472951	+	0.273059i	−0.244523	+	0.969643i	$0.578631\pi$
$788$	−12.0622	−	6.96410i	−0.429697	−	0.248086i
$789$	0.758330	+	1.31347i	0.0269973	+	0.0467606i
$790$	7.90192	+	7.90192i	0.281138	+	0.281138i
$791$	28.9711	+	10.0359i	1.03010	+	0.356835i
$792$	17.1962	+	17.1962i	0.611039	+	0.611039i
$793$	16.5622	+	4.43782i	0.588140	+	0.157592i
$794$	3.29423	+	12.2942i	0.116908	+	0.436306i
$795$	−0.633975	+	1.09808i	−0.0224848	+	0.0389447i
$796$	−12.2942	−	3.29423i	−0.435757	−	0.116761i
$797$	20.7846			0.736229			0.368114	−	0.929781i	$-0.380004\pi$
$797$	20.7846			0.736229			0.368114	+	0.929781i	$0.380004\pi$
$798$	−9.18653	+	1.76795i	−0.325200	+	0.0625847i
$799$			6.24871i			0.221064i
$800$	8.66025	−	5.00000i	0.306186	−	0.176777i
$801$	5.00000	+	18.6603i	0.176666	+	0.659328i
$802$	−15.3301	+	26.5526i	−0.541326	+	0.937603i
$803$	−32.8564	−	8.80385i	−1.15948	−	0.310681i
$804$	1.26795			0.0447171
$805$	1.60770	+	1.85641i	0.0566638	+	0.0654297i
$806$	4.73205	−	4.73205i	0.166679	−	0.166679i
$807$	1.47372	−	5.50000i	0.0518774	−	0.193609i
$808$	−17.1962	+	4.60770i	−0.604959	+	0.162098i
$809$	−14.9282	+	4.00000i	−0.524848	+	0.140633i	−0.511508	−	0.859279i	$-0.670913\pi$
$809$	−14.9282	+	4.00000i	−0.524848	+	0.140633i	−0.0133397	+	0.999911i	$0.504246\pi$
$810$	5.76795	+	9.99038i	0.202665	+	0.351026i
$811$		−	31.8038i		−	1.11678i	−0.829577	−	0.558392i	$-0.811418\pi$
$811$		−	31.8038i		−	1.11678i	0.829577	−	0.558392i	$-0.188582\pi$
$812$	−12.1962	−	0.875644i	−0.428001	−	0.0307291i
$813$	−4.92820	−	4.92820i	−0.172840	−	0.172840i
$814$	21.3923	+	5.73205i	0.749800	+	0.200908i
$815$	−36.2942	−	20.9545i	−1.27133	−	0.734004i
$816$	−0.464102	+	0.803848i	−0.0162468	+	0.0281403i
$817$	2.58846	−	9.66025i	0.0905587	−	0.337970i
$818$			17.9808i			0.628683i
$819$	−14.6603	−	9.92820i	−0.512271	−	0.346919i
$820$	−8.66025	−	6.92820i	−0.302429	−	0.241943i
$821$	19.8660	+	34.4090i	0.693329	+	1.20088i	0.970741	+	0.240130i	$0.0771901\pi$
$821$	19.8660	+	34.4090i	0.693329	+	1.20088i	−0.277412	+	0.960751i	$0.589477\pi$
$822$	5.02628	+	2.90192i	0.175312	+	0.101216i
$823$	36.3827	−	9.74871i	1.26822	−	0.339819i	0.438872	−	0.898550i	$-0.355378\pi$
$823$	36.3827	−	9.74871i	1.26822	−	0.339819i	0.829349	+	0.558731i	$0.188712\pi$
$824$	7.90192	+	13.6865i	0.275277	+	0.476793i
$825$			3.07180i			0.106946i
$826$	−6.29423	+	18.1699i	−0.219004	+	0.632211i
$827$	25.0526	+	25.0526i	0.871163	+	0.871163i	0.992599	−	0.121436i	$-0.0387500\pi$
$827$	25.0526	+	25.0526i	0.871163	+	0.871163i	−0.121436	+	0.992599i	$0.538750\pi$
$828$	−1.26795	+	0.732051i	−0.0440643	+	0.0254405i
$829$	−34.1769	−	19.7321i	−1.18701	−	0.685322i	−0.229387	−	0.973335i	$-0.573672\pi$
$829$	−34.1769	−	19.7321i	−1.18701	−	0.685322i	−0.957627	+	0.288013i	$0.907005\pi$
$830$	2.36603	−	4.09808i	0.0821259	−	0.142246i
$831$	−3.42820	+	12.7942i	−0.118923	+	0.443827i
$832$	−12.1244	−	12.1244i	−0.420336	−	0.420336i
$833$	4.94744	−	11.5359i	0.171419	−	0.399695i
$834$	8.60770	−	8.60770i	0.298060	−	0.298060i
$835$	28.2224	+	7.56218i	0.976678	+	0.261700i
$836$	10.1340	−	17.5526i	0.350491	−	0.607068i
$837$	−2.09808	−	7.83013i	−0.0725201	−	0.270649i
$838$	−6.46410	−	11.1962i	−0.223299	−	0.386765i
$839$	37.0070	−	37.0070i	1.27762	−	1.27762i	0.335632	−	0.941993i	$-0.391050\pi$
$839$	37.0070	−	37.0070i	1.27762	−	1.27762i	0.941993	−	0.335632i	$-0.108950\pi$
$840$	3.10770	+	6.40192i	0.107226	+	0.220887i
$841$		−	7.64102i		−	0.263483i
$842$	−35.9545	−	9.63397i	−1.23907	−	0.332009i
$843$	−3.73205	+	6.46410i	−0.128539	+	0.222635i
$844$	−5.06218	−	18.8923i	−0.174247	−	0.650300i
$845$	6.06218	+	10.5000i	0.208545	+	0.361211i
$846$	6.73205	−	6.73205i	0.231453	−	0.231453i
$847$	−5.70577	+	1.09808i	−0.196053	+	0.0377303i
$848$	−1.00000	−	1.00000i	−0.0343401	−	0.0343401i
$849$	−1.90192	+	7.09808i	−0.0652739	+	0.243605i
$850$	3.46410	−	0.928203i	0.118818	−	0.0318371i
$851$	−2.00000	+	3.46410i	−0.0685591	+	0.118748i
$852$	5.30385	−	3.06218i	0.181707	−	0.104908i
$853$		−	53.2487i		−	1.82320i	−0.411077	−	0.911601i	$-0.634847\pi$
$853$		−	53.2487i		−	1.82320i	0.411077	−	0.911601i	$-0.365153\pi$
$854$	14.0000	−	12.1244i	0.479070	−	0.414887i
$855$	22.8564	−	22.8564i	0.781673	−	0.781673i
$856$	−46.9019	+	27.0788i	−1.60307	+	0.925536i
$857$	−26.1147	+	45.2321i	−0.892062	+	1.54510i	−0.0546637	+	0.998505i	$0.517409\pi$
$857$	−26.1147	+	45.2321i	−0.892062	+	1.54510i	−0.837399	+	0.546593i	$0.815925\pi$
$858$	3.63397	−	0.973721i	0.124062	−	0.0332423i
$859$	−20.9545	+	12.0981i	−0.714958	+	0.412781i	−0.812894	−	0.582412i	$-0.802109\pi$
$859$	−20.9545	+	12.0981i	−0.714958	+	0.412781i	0.0979363	+	0.995193i	$0.468776\pi$
$860$	−2.53590			−0.0864734
$861$	−5.95448	+	6.43782i	−0.202928	+	0.219400i
$862$	31.7128			1.08014
$863$	28.6865	−	16.5622i	0.976501	−	0.563783i	0.0752890	−	0.997162i	$-0.476012\pi$
$863$	28.6865	−	16.5622i	0.976501	−	0.563783i	0.901212	+	0.433379i	$0.142679\pi$
$864$	−14.3301	+	3.83975i	−0.487521	+	0.130631i
$865$	−12.0622	+	20.8923i	−0.410126	+	0.710360i
$866$	28.7942	−	16.6244i	0.978468	−	0.564919i
$867$	−5.04552	+	5.04552i	−0.171355	+	0.171355i
$868$	1.36603	+	7.09808i	0.0463659	+	0.240924i
$869$			19.1436i			0.649402i
$870$	3.58846	−	2.07180i	0.121660	−	0.0702405i
$871$	−3.00000	+	5.19615i	−0.101651	+	0.176065i
$872$	−28.3923	+	7.60770i	−0.961485	+	0.257629i
$873$	−1.46410	+	5.46410i	−0.0495523	+	0.184932i
$874$	−2.58846	−	2.58846i	−0.0875559	−	0.0875559i
$875$	10.5000	−	30.3109i	0.354965	−	1.02470i
$876$	4.19615	−	4.19615i	0.141775	−	0.141775i
$877$	11.4282	+	19.7942i	0.385903	+	0.668404i	0.991894	−	0.127068i	$-0.0405566\pi$
$877$	11.4282	+	19.7942i	0.385903	+	0.668404i	−0.605991	+	0.795471i	$0.707223\pi$
$878$	9.59808	+	35.8205i	0.323919	+	1.20888i
$879$	6.26795	−	10.8564i	0.211413	−	0.366178i
$880$	4.96410	+	1.33013i	0.167340	+	0.0448386i
$881$			22.0718i			0.743618i	0.928309	+	0.371809i	$0.121262\pi$
$881$			22.0718i			0.743618i	−0.928309	+	0.371809i	$0.878738\pi$
$882$	−17.7583	+	7.09808i	−0.597954	+	0.239005i
$883$	−10.4641	+	10.4641i	−0.352145	+	0.352145i	−0.860907	−	0.508762i	$-0.830103\pi$
$883$	−10.4641	+	10.4641i	−0.352145	+	0.352145i	0.508762	+	0.860907i	$0.330103\pi$
$884$	2.19615	+	3.80385i	0.0738646	+	0.127937i
$885$	1.68653	+	6.29423i	0.0566922	+	0.211578i
$886$	−2.92820	+	5.07180i	−0.0983749	+	0.170390i
$887$	−12.7942	−	3.42820i	−0.429588	−	0.115108i	0.0375447	−	0.999295i	$-0.488046\pi$
$887$	−12.7942	−	3.42820i	−0.429588	−	0.115108i	−0.467133	+	0.884187i	$0.654713\pi$
$888$	−8.19615	+	8.19615i	−0.275045	+	0.275045i
$889$	−17.8109	−	6.16987i	−0.597358	−	0.206931i
$890$	8.66025	+	8.66025i	0.290292	+	0.290292i
$891$	−5.11474	+	19.0885i	−0.171350	+	0.639487i
$892$	2.46410	−	4.26795i	0.0825042	−	0.142902i
$893$	−20.6147	−	11.9019i	−0.689846	−	0.398283i
$894$	3.29423	−	1.90192i	0.110175	−	0.0636098i
$895$	−1.56218	−	1.56218i	−0.0522178	−	0.0522178i
$896$	7.79423	−	1.50000i	0.260387	−	0.0501115i
$897$			0.679492i			0.0226876i
$898$	−6.57180	−	11.3827i	−0.219304	−	0.379845i
$899$	12.1962	−	3.26795i	0.406764	−	0.108992i
$900$	4.73205	+	2.73205i	0.157735	+	0.0910684i
$901$	1.26795	+	2.19615i	0.0422415	+	0.0731644i
$902$	2.09808	+	18.8827i	0.0698583	+	0.628725i
$903$	−0.143594	+	2.00000i	−0.00477849	+	0.0665558i
$904$			34.7654i			1.15628i
$905$	−2.70577	+	10.0981i	−0.0899429	+	0.335671i
$906$	−0.366025	+	0.633975i	−0.0121604	+	0.0210624i
$907$	−16.2224	−	9.36603i	−0.538657	−	0.310994i	0.205877	−	0.978578i	$-0.433995\pi$
$907$	−16.2224	−	9.36603i	−0.538657	−	0.310994i	−0.744534	+	0.667584i	$0.767328\pi$
$908$	5.86603	+	1.57180i	0.194671	+	0.0521619i
$909$	−11.4641	−	11.4641i	−0.380240	−	0.380240i
$910$	−11.1962	−	0.803848i	−0.371149	−	0.0266473i
$911$			19.8564i			0.657872i	0.944352	+	0.328936i	$0.106690\pi$
$911$			19.8564i			0.657872i	−0.944352	+	0.328936i	$0.893310\pi$
$912$	−1.76795	−	3.06218i	−0.0585426	−	0.101399i
$913$	7.83013	−	2.09808i	0.259139	−	0.0694362i
$914$	−27.1244	+	7.26795i	−0.897194	+	0.240402i
$915$	1.62436	−	6.06218i	0.0536995	−	0.200409i
$916$	−8.19615	+	8.19615i	−0.270808	+	0.270808i
$917$		0			0
$918$	−5.32051			−0.175603
$919$	−24.5263	−	6.57180i	−0.809047	−	0.216784i	−0.169495	−	0.985531i	$-0.554214\pi$
$919$	−24.5263	−	6.57180i	−0.809047	−	0.216784i	−0.639552	+	0.768747i	$0.720880\pi$
$920$	−1.39230	+	2.41154i	−0.0459029	+	0.0795062i
$921$	2.94744	+	11.0000i	0.0971215	+	0.362462i
$922$	36.0167	−	20.7942i	1.18615	−	0.684821i
$923$			28.9808i			0.953913i
$924$	−1.33013	+	3.83975i	−0.0437580	+	0.126318i
$925$	14.9282			0.490836
$926$	15.4282	+	4.13397i	0.507002	+	0.135851i
$927$	−7.19615	+	12.4641i	−0.236353	+	0.409375i
$928$	−5.98076	−	22.3205i	−0.196328	−	0.732707i
$929$	43.1506	+	11.5622i	1.41573	+	0.379343i	0.883966	−	0.467552i	$-0.154864\pi$
$929$	43.1506	+	11.5622i	1.41573	+	0.379343i	0.531761	+	0.846895i	$0.321531\pi$
$930$	−1.73205	−	1.73205i	−0.0567962	−	0.0567962i
$931$	28.6340	+	38.2942i	0.938441	+	1.25504i
$932$	20.1244	+	20.1244i	0.659195	+	0.659195i
$933$	−0.366025	−	0.633975i	−0.0119831	−	0.0207554i
$934$	5.19615	+	3.00000i	0.170023	+	0.0981630i
$935$	−7.98076	−	4.60770i	−0.260999	−	0.150688i
$936$	5.19615	−	19.3923i	0.169842	−	0.633857i
$937$	16.5359	−	16.5359i	0.540204	−	0.540204i	−0.383385	−	0.923589i	$-0.625242\pi$
$937$	16.5359	−	16.5359i	0.540204	−	0.540204i	0.923589	+	0.383385i	$0.125242\pi$
$938$	2.83013	+	5.83013i	0.0924069	+	0.190360i
$939$	17.1769			0.560547
$940$	−1.56218	+	5.83013i	−0.0509526	+	0.190158i
$941$	−9.99038	−	5.76795i	−0.325677	−	0.188030i	0.328243	−	0.944593i	$-0.393543\pi$
$941$	−9.99038	−	5.76795i	−0.325677	−	0.188030i	−0.653920	+	0.756564i	$0.726877\pi$
$942$	−4.07180	+	7.05256i	−0.132666	+	0.229785i
$943$	−3.39230	−	0.516660i	−0.110469	−	0.0168248i
$944$	−7.26795			−0.236552
$945$	−7.62436	+	11.2583i	−0.248020	+	0.366234i
$946$	3.07180	+	3.07180i	0.0998727	+	0.0998727i
$947$	−1.33975	−	2.32051i	−0.0435359	−	0.0754064i	0.843436	−	0.537229i	$-0.180529\pi$
$947$	−1.33975	−	2.32051i	−0.0435359	−	0.0754064i	−0.886972	+	0.461823i	$0.847196\pi$
$948$	−2.89230	−	1.66987i	−0.0939377	−	0.0542350i
$949$	7.26795	+	27.1244i	0.235928	+	0.880494i
$950$	−3.53590	+	13.1962i	−0.114720	+	0.428140i
$951$		−	17.0718i		−	0.553591i
$952$	14.1962	+	1.01924i	0.460100	+	0.0330337i
$953$	−57.7128			−1.86950			−0.934751	−	0.355304i	$-0.884377\pi$
$953$	−57.7128			−1.86950			−0.934751	+	0.355304i	$0.884377\pi$
$954$	1.00000	−	3.73205i	0.0323762	−	0.120830i
$955$	36.4186	−	9.75833i	1.17848	−	0.315772i
$956$	26.9904	−	7.23205i	0.872931	−	0.233901i
$957$	6.85641	+	1.83717i	0.221636	+	0.0593872i
$958$	1.75833	−	1.75833i	0.0568091	−	0.0568091i
$959$	2.12436	−	29.5885i	0.0685990	−	0.955461i
$960$	−4.43782	+	4.43782i	−0.143230	+	0.143230i
$961$	11.7679	+	20.3827i	0.379611	+	0.657506i
$962$	−4.73205	−	17.6603i	−0.152567	−	0.569389i
$963$	−42.7128	−	24.6603i	−1.37640	−	0.794666i
$964$	22.0526	−	12.7321i	0.710265	−	0.410072i
$965$	0.803848	−	0.803848i	0.0258768	−	0.0258768i
$966$	0.607695	+	0.411543i	0.0195523	+	0.0132412i
$967$	−20.1506	+	20.1506i	−0.648001	+	0.648001i	−0.952510	−	0.304509i	$-0.901508\pi$
$967$	−20.1506	+	20.1506i	−0.648001	+	0.648001i	0.304509	+	0.952510i	$0.401508\pi$
$968$	−3.29423	−	5.70577i	−0.105881	−	0.183390i
$969$	1.64102	+	6.12436i	0.0527170	+	0.196743i
$970$	0.928203	+	3.46410i	0.0298028	+	0.111226i
$971$	7.29423	−	27.2224i	0.234083	−	0.873609i	−0.744477	−	0.667648i	$-0.767301\pi$
$971$	7.29423	−	27.2224i	0.234083	−	0.873609i	0.978560	−	0.205961i	$-0.0660322\pi$
$972$	−8.73205	−	8.73205i	−0.280081	−	0.280081i
$973$	−58.7917	−	20.3660i	−1.88477	−	0.652905i
$974$	34.0526			1.09111
$975$	2.19615	−	1.26795i	0.0703332	−	0.0406069i
$976$	6.06218	+	3.50000i	0.194046	+	0.112032i
$977$	44.4186	−	11.9019i	1.42108	−	0.380776i	0.535211	−	0.844718i	$-0.320232\pi$
$977$	44.4186	−	11.9019i	1.42108	−	0.380776i	0.885865	+	0.463942i	$0.153565\pi$
$978$	−12.0981	−	3.24167i	−0.386854	−	0.103657i
$979$			20.9808i			0.670548i
$980$	7.50000	−	9.52628i	0.239579	−	0.304306i
$981$	−18.9282	−	18.9282i	−0.604331	−	0.604331i
$982$	16.5622	−	9.56218i	0.528520	−	0.305141i
$983$	9.19615	−	15.9282i	0.293312	−	0.508031i	−0.681279	−	0.732024i	$-0.738576\pi$
$983$	9.19615	−	15.9282i	0.293312	−	0.508031i	0.974591	+	0.223993i	$0.0719093\pi$
$984$	−9.10770	−	3.99038i	−0.290343	−	0.127209i
$985$	−12.0622	−	20.8923i	−0.384333	−	0.665684i
$986$		−	8.28719i		−	0.263918i
$987$	4.50962	+	1.56218i	0.143543	+	0.0497247i
$988$	−16.7321			−0.532317
$989$	−0.679492	+	0.392305i	−0.0216066	+	0.0124746i
$990$	3.63397	+	13.5622i	0.115495	+	0.431034i
$991$	−25.7942	+	6.91154i	−0.819381	+	0.219552i	−0.644076	−	0.764962i	$-0.722758\pi$
$991$	−25.7942	+	6.91154i	−0.819381	+	0.219552i	−0.175305	+	0.984514i	$0.556091\pi$
$992$	−11.8301	+	6.83013i	−0.375607	+	0.216857i
$993$		−	6.98076i		−	0.221528i
$994$	25.9186	+	17.5526i	0.822088	+	0.556733i
$995$	−15.5885	−	15.5885i	−0.494187	−	0.494187i
$996$	−0.366025	+	1.36603i	−0.0115980	+	0.0432842i
$997$	45.8827	−	12.2942i	1.45312	−	0.389362i	0.556012	−	0.831174i	$-0.312331\pi$
$997$	45.8827	−	12.2942i	1.45312	−	0.389362i	0.897108	+	0.441812i	$0.145664\pi$
$998$	−7.90192	−	29.4904i	−0.250131	−	0.933502i
$999$	−21.3923	−	5.73205i	−0.676823	−	0.181354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.r.a.214.1	yes	4
7.2	even	3		287.2.r.b.9.1	yes	4
41.32	even	4		287.2.r.b.32.1	yes	4
287.114	even	12	inner	287.2.r.a.114.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.r.a.114.1	✓	4	287.114	even	12	inner
287.2.r.a.214.1	yes	4	1.1	even	1	trivial
287.2.r.b.9.1	yes	4	7.2	even	3
287.2.r.b.32.1	yes	4	41.32	even	4

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.133975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-0.366025 + 0.366025i) q^{6} +(2.50000 + 0.866025i) q^{7} +3.00000i q^{8} +(-2.36603 + 1.36603i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.133975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-0.366025 + 0.366025i) q^{6} +(2.50000 + 0.866025i) q^{7} +3.00000i q^{8} +(-2.36603 + 1.36603i) q^{9} +(-0.866025 + 1.50000i) q^{10} +(-2.86603 + 0.767949i) q^{11} +(0.133975 - 0.500000i) q^{12} +(1.73205 + 1.73205i) q^{13} +(2.59808 - 0.500000i) q^{14} +(0.633975 - 0.633975i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.464102 - 1.73205i) q^{17} +(-1.36603 + 2.36603i) q^{18} +(6.59808 + 1.76795i) q^{19} -1.73205i q^{20} +(-1.36603 - 0.0980762i) q^{21} +(-2.09808 + 2.09808i) q^{22} +(-0.267949 - 0.464102i) q^{23} +(-0.401924 - 1.50000i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(2.36603 + 0.633975i) q^{26} +(2.09808 - 2.09808i) q^{27} +(-2.00000 + 1.73205i) q^{28} +(3.26795 + 3.26795i) q^{29} +(0.232051 - 0.866025i) q^{30} +(1.36603 - 2.36603i) q^{31} +(-4.33013 - 2.50000i) q^{32} +(1.33013 - 0.767949i) q^{33} +(-1.26795 - 1.26795i) q^{34} +(-4.50000 + 0.866025i) q^{35} -2.73205i q^{36} +(-3.73205 - 6.46410i) q^{37} +(6.59808 - 1.76795i) q^{38} +(-1.09808 - 0.633975i) q^{39} +(-2.59808 - 4.50000i) q^{40} +(4.00000 - 5.00000i) q^{41} +(-1.23205 + 0.598076i) q^{42} -1.46410i q^{43} +(0.767949 - 2.86603i) q^{44} +(2.36603 - 4.09808i) q^{45} +(-0.464102 - 0.267949i) q^{46} +(-3.36603 - 0.901924i) q^{47} +(-0.366025 - 0.366025i) q^{48} +(5.50000 + 4.33013i) q^{49} +2.00000i q^{50} +(0.464102 + 0.803848i) q^{51} +(-2.36603 + 0.633975i) q^{52} +(-1.36603 + 0.366025i) q^{53} +(0.767949 - 2.86603i) q^{54} +(3.63397 - 3.63397i) q^{55} +(-2.59808 + 7.50000i) q^{56} -3.53590 q^{57} +(4.46410 + 1.19615i) q^{58} +(-3.63397 + 6.29423i) q^{59} +(0.232051 + 0.866025i) q^{60} +(6.06218 - 3.50000i) q^{61} -2.73205i q^{62} +(-7.09808 + 1.36603i) q^{63} -7.00000 q^{64} +(-4.09808 - 1.09808i) q^{65} +(0.767949 - 1.33013i) q^{66} +(0.633975 + 2.36603i) q^{67} +(1.73205 + 0.464102i) q^{68} +(0.196152 + 0.196152i) q^{69} +(-3.46410 + 3.00000i) q^{70} +(8.36603 + 8.36603i) q^{71} +(-4.09808 - 7.09808i) q^{72} +(9.92820 + 5.73205i) q^{73} +(-6.46410 - 3.73205i) q^{74} +(0.267949 - 1.00000i) q^{75} +(-4.83013 + 4.83013i) q^{76} +(-7.83013 - 0.562178i) q^{77} -1.26795 q^{78} +(1.66987 - 6.23205i) q^{79} +(-1.50000 - 0.866025i) q^{80} +(3.33013 - 5.76795i) q^{81} +(0.964102 - 6.33013i) q^{82} -2.73205 q^{83} +(0.767949 - 1.13397i) q^{84} +(2.19615 + 2.19615i) q^{85} +(-0.732051 - 1.26795i) q^{86} +(-2.07180 - 1.19615i) q^{87} +(-2.30385 - 8.59808i) q^{88} +(1.83013 - 6.83013i) q^{89} -4.73205i q^{90} +(2.83013 + 5.83013i) q^{91} +0.535898 q^{92} +(-0.366025 + 1.36603i) q^{93} +(-3.36603 + 0.901924i) q^{94} +(-11.4282 + 3.06218i) q^{95} +(2.50000 + 0.669873i) q^{96} +(1.46410 - 1.46410i) q^{97} +(6.92820 + 1.00000i) q^{98} +(5.73205 - 5.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^9	\( 4 q - 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{9} - 8 q^{11} + 4 q^{12} + 6 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} + 16 q^{19} - 2 q^{21} + 2 q^{22} - 8 q^{23} - 12 q^{24} - 4 q^{25} + 6 q^{26} - 2 q^{27} - 8 q^{28} + 20 q^{29} - 6 q^{30} + 2 q^{31} - 12 q^{33} - 12 q^{34} - 18 q^{35} - 8 q^{37} + 16 q^{38} + 6 q^{39} + 16 q^{41} + 2 q^{42} + 10 q^{44} + 6 q^{45} + 12 q^{46} - 10 q^{47} + 2 q^{48} + 22 q^{49} - 12 q^{51} - 6 q^{52} - 2 q^{53} + 10 q^{54} + 18 q^{55} - 28 q^{57} + 4 q^{58} - 18 q^{59} - 6 q^{60} - 18 q^{63} - 28 q^{64} - 6 q^{65} + 10 q^{66} + 6 q^{67} - 20 q^{69} + 30 q^{71} - 6 q^{72} + 12 q^{73} - 12 q^{74} + 8 q^{75} - 2 q^{76} - 14 q^{77} - 12 q^{78} + 24 q^{79} - 6 q^{80} - 4 q^{81} - 10 q^{82} - 4 q^{83} + 10 q^{84} - 12 q^{85} + 4 q^{86} - 36 q^{87} - 30 q^{88} - 10 q^{89} - 6 q^{91} + 16 q^{92} + 2 q^{93} - 10 q^{94} - 18 q^{95} + 10 q^{96} - 8 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^9 - 8 * q^11 + 4 * q^12 + 6 * q^15 + 2 * q^16 + 12 * q^17 - 2 * q^18 + 16 * q^19 - 2 * q^21 + 2 * q^22 - 8 * q^23 - 12 * q^24 - 4 * q^25 + 6 * q^26 - 2 * q^27 - 8 * q^28 + 20 * q^29 - 6 * q^30 + 2 * q^31 - 12 * q^33 - 12 * q^34 - 18 * q^35 - 8 * q^37 + 16 * q^38 + 6 * q^39 + 16 * q^41 + 2 * q^42 + 10 * q^44 + 6 * q^45 + 12 * q^46 - 10 * q^47 + 2 * q^48 + 22 * q^49 - 12 * q^51 - 6 * q^52 - 2 * q^53 + 10 * q^54 + 18 * q^55 - 28 * q^57 + 4 * q^58 - 18 * q^59 - 6 * q^60 - 18 * q^63 - 28 * q^64 - 6 * q^65 + 10 * q^66 + 6 * q^67 - 20 * q^69 + 30 * q^71 - 6 * q^72 + 12 * q^73 - 12 * q^74 + 8 * q^75 - 2 * q^76 - 14 * q^77 - 12 * q^78 + 24 * q^79 - 6 * q^80 - 4 * q^81 - 10 * q^82 - 4 * q^83 + 10 * q^84 - 12 * q^85 + 4 * q^86 - 36 * q^87 - 30 * q^88 - 10 * q^89 - 6 * q^91 + 16 * q^92 + 2 * q^93 - 10 * q^94 - 18 * q^95 + 10 * q^96 - 8 * q^97 + 16 * q^99

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