LMFDB - Embedded newform 483.2.d.b.461.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(461,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.2
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	483.461
Dual form			483.2.d.b.461.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.618034i q^{2} +(1.61803 + 0.618034i) q^{3} +1.61803 q^{4} +0.381966 q^{5} +(0.381966 - 1.00000i) q^{6} +(0.381966 - 2.61803i) q^{7} -2.23607i q^{8} +(2.23607 + 2.00000i) q^{9} +O(q^{10})$	\(q-0.618034i q^{2} +(1.61803 + 0.618034i) q^{3} +1.61803 q^{4} +0.381966 q^{5} +(0.381966 - 1.00000i) q^{6} +(0.381966 - 2.61803i) q^{7} -2.23607i q^{8} +(2.23607 + 2.00000i) q^{9} -0.236068i q^{10} +2.23607i q^{11} +(2.61803 + 1.00000i) q^{12} -0.145898i q^{13} +(-1.61803 - 0.236068i) q^{14} +(0.618034 + 0.236068i) q^{15} +1.85410 q^{16} -7.47214 q^{17} +(1.23607 - 1.38197i) q^{18} -3.47214i q^{19} +0.618034 q^{20} +(2.23607 - 4.00000i) q^{21} +1.38197 q^{22} -1.00000i q^{23} +(1.38197 - 3.61803i) q^{24} -4.85410 q^{25} -0.0901699 q^{26} +(2.38197 + 4.61803i) q^{27} +(0.618034 - 4.23607i) q^{28} +6.23607i q^{29} +(0.145898 - 0.381966i) q^{30} +9.47214i q^{31} -5.61803i q^{32} +(-1.38197 + 3.61803i) q^{33} +4.61803i q^{34} +(0.145898 - 1.00000i) q^{35} +(3.61803 + 3.23607i) q^{36} +10.2361 q^{37} -2.14590 q^{38} +(0.0901699 - 0.236068i) q^{39} -0.854102i q^{40} -4.23607 q^{41} +(-2.47214 - 1.38197i) q^{42} +5.38197 q^{43} +3.61803i q^{44} +(0.854102 + 0.763932i) q^{45} -0.618034 q^{46} -8.00000 q^{47} +(3.00000 + 1.14590i) q^{48} +(-6.70820 - 2.00000i) q^{49} +3.00000i q^{50} +(-12.0902 - 4.61803i) q^{51} -0.236068i q^{52} -6.56231i q^{53} +(2.85410 - 1.47214i) q^{54} +0.854102i q^{55} +(-5.85410 - 0.854102i) q^{56} +(2.14590 - 5.61803i) q^{57} +3.85410 q^{58} +12.5623 q^{59} +(1.00000 + 0.381966i) q^{60} -5.85410i q^{61} +5.85410 q^{62} +(6.09017 - 5.09017i) q^{63} +0.236068 q^{64} -0.0557281i q^{65} +(2.23607 + 0.854102i) q^{66} -8.38197 q^{67} -12.0902 q^{68} +(0.618034 - 1.61803i) q^{69} +(-0.618034 - 0.0901699i) q^{70} +10.3262i q^{71} +(4.47214 - 5.00000i) q^{72} -3.76393i q^{73} -6.32624i q^{74} +(-7.85410 - 3.00000i) q^{75} -5.61803i q^{76} +(5.85410 + 0.854102i) q^{77} +(-0.145898 - 0.0557281i) q^{78} -12.2361 q^{79} +0.708204 q^{80} +(1.00000 + 8.94427i) q^{81} +2.61803i q^{82} +2.70820 q^{83} +(3.61803 - 6.47214i) q^{84} -2.85410 q^{85} -3.32624i q^{86} +(-3.85410 + 10.0902i) q^{87} +5.00000 q^{88} -3.09017 q^{89} +(0.472136 - 0.527864i) q^{90} +(-0.381966 - 0.0557281i) q^{91} -1.61803i q^{92} +(-5.85410 + 15.3262i) q^{93} +4.94427i q^{94} -1.32624i q^{95} +(3.47214 - 9.09017i) q^{96} +15.9443i q^{97} +(-1.23607 + 4.14590i) q^{98} +(-4.47214 + 5.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7	$ 4 q + 2 q^{3} + 2 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{12} - 2 q^{14} - 2 q^{15} - 6 q^{16} - 12 q^{17} - 4 q^{18} - 2 q^{20} + 10 q^{22} + 10 q^{24} - 6 q^{25} + 22 q^{26} + 14 q^{27} - 2 q^{28} + 14 q^{30} - 10 q^{33} + 14 q^{35} + 10 q^{36} + 32 q^{37} - 22 q^{38} - 22 q^{39} - 8 q^{41} + 8 q^{42} + 26 q^{43} - 10 q^{45} + 2 q^{46} - 32 q^{47} + 12 q^{48} - 26 q^{51} - 2 q^{54} - 10 q^{56} + 22 q^{57} + 2 q^{58} + 10 q^{59} + 4 q^{60} + 10 q^{62} + 2 q^{63} - 8 q^{64} - 38 q^{67} - 26 q^{68} - 2 q^{69} + 2 q^{70} - 18 q^{75} + 10 q^{77} - 14 q^{78} - 40 q^{79} - 24 q^{80} + 4 q^{81} - 16 q^{83} + 10 q^{84} + 2 q^{85} - 2 q^{87} + 20 q^{88} + 10 q^{89} - 16 q^{90} - 6 q^{91} - 10 q^{93} - 4 q^{96} + 4 q^{98}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^12 - 2 * q^14 - 2 * q^15 - 6 * q^16 - 12 * q^17 - 4 * q^18 - 2 * q^20 + 10 * q^22 + 10 * q^24 - 6 * q^25 + 22 * q^26 + 14 * q^27 - 2 * q^28 + 14 * q^30 - 10 * q^33 + 14 * q^35 + 10 * q^36 + 32 * q^37 - 22 * q^38 - 22 * q^39 - 8 * q^41 + 8 * q^42 + 26 * q^43 - 10 * q^45 + 2 * q^46 - 32 * q^47 + 12 * q^48 - 26 * q^51 - 2 * q^54 - 10 * q^56 + 22 * q^57 + 2 * q^58 + 10 * q^59 + 4 * q^60 + 10 * q^62 + 2 * q^63 - 8 * q^64 - 38 * q^67 - 26 * q^68 - 2 * q^69 + 2 * q^70 - 18 * q^75 + 10 * q^77 - 14 * q^78 - 40 * q^79 - 24 * q^80 + 4 * q^81 - 16 * q^83 + 10 * q^84 + 2 * q^85 - 2 * q^87 + 20 * q^88 + 10 * q^89 - 16 * q^90 - 6 * q^91 - 10 * q^93 - 4 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	0.618034i		−	0.437016i	−0.975835	−	0.218508i	$-0.929881\pi$
$2$		−	0.618034i		−	0.437016i	0.975835	−	0.218508i	$-0.0701190\pi$
$3$	1.61803	+	0.618034i	0.934172	+	0.356822i
$3$	1.61803	+	0.618034i	0.934172	+	0.356822i
$4$	1.61803			0.809017
$5$	0.381966			0.170820			0.0854102	−	0.996346i	$-0.472780\pi$
$5$	0.381966			0.170820			0.0854102	+	0.996346i	$0.472780\pi$
$6$	0.381966	−	1.00000i	0.155937	−	0.408248i
$7$	0.381966	−	2.61803i	0.144370	−	0.989524i
$7$	0.381966	−	2.61803i	0.144370	−	0.989524i
$8$		−	2.23607i		−	0.790569i
$9$	2.23607	+	2.00000i	0.745356	+	0.666667i
$10$		−	0.236068i		−	0.0746512i
$11$			2.23607i			0.674200i	0.941469	+	0.337100i	$0.109446\pi$
$11$			2.23607i			0.674200i	−0.941469	+	0.337100i	$0.890554\pi$
$12$	2.61803	+	1.00000i	0.755761	+	0.288675i
$13$		−	0.145898i		−	0.0404648i	−0.999795	−	0.0202324i	$-0.993559\pi$
$13$		−	0.145898i		−	0.0404648i	0.999795	−	0.0202324i	$-0.00644062\pi$
$14$	−1.61803	−	0.236068i	−0.432438	−	0.0630918i
$15$	0.618034	+	0.236068i	0.159576	+	0.0609525i
$16$	1.85410			0.463525
$17$	−7.47214			−1.81226			−0.906130	−	0.423000i	$-0.860977\pi$
$17$	−7.47214			−1.81226			−0.906130	+	0.423000i	$0.860977\pi$
$18$	1.23607	−	1.38197i	0.291344	−	0.325733i
$19$		−	3.47214i		−	0.796563i	−0.917263	−	0.398281i	$-0.869607\pi$
$19$		−	3.47214i		−	0.796563i	0.917263	−	0.398281i	$-0.130393\pi$
$20$	0.618034			0.138197
$21$	2.23607	−	4.00000i	0.487950	−	0.872872i
$22$	1.38197			0.294636
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	1.38197	−	3.61803i	0.282093	−	0.738528i
$25$	−4.85410			−0.970820
$26$	−0.0901699			−0.0176838
$27$	2.38197	+	4.61803i	0.458410	+	0.888741i
$28$	0.618034	−	4.23607i	0.116797	−	0.800542i
$29$			6.23607i			1.15801i	0.815324	+	0.579004i	$0.196559\pi$
$29$			6.23607i			1.15801i	−0.815324	+	0.579004i	$0.803441\pi$
$30$	0.145898	−	0.381966i	0.0266372	−	0.0697371i
$31$			9.47214i			1.70125i	0.525776	+	0.850623i	$0.323775\pi$
$31$			9.47214i			1.70125i	−0.525776	+	0.850623i	$0.676225\pi$
$32$		−	5.61803i		−	0.993137i
$33$	−1.38197	+	3.61803i	−0.240569	+	0.629819i
$34$			4.61803i			0.791986i
$35$	0.145898	−	1.00000i	0.0246613	−	0.169031i
$36$	3.61803	+	3.23607i	0.603006	+	0.539345i
$37$	10.2361			1.68280			0.841400	−	0.540413i	$-0.181732\pi$
$37$	10.2361			1.68280			0.841400	+	0.540413i	$0.181732\pi$
$38$	−2.14590			−0.348111
$39$	0.0901699	−	0.236068i	0.0144387	−	0.0378011i
$40$		−	0.854102i		−	0.135045i
$41$	−4.23607			−0.661563			−0.330781	−	0.943707i	$-0.607312\pi$
$41$	−4.23607			−0.661563			−0.330781	+	0.943707i	$0.607312\pi$
$42$	−2.47214	−	1.38197i	−0.381459	−	0.213242i
$43$	5.38197			0.820742			0.410371	−	0.911919i	$-0.365399\pi$
$43$	5.38197			0.820742			0.410371	+	0.911919i	$0.365399\pi$
$44$			3.61803i			0.545439i
$45$	0.854102	+	0.763932i	0.127322	+	0.113880i
$46$	−0.618034			−0.0911241
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	3.00000	+	1.14590i	0.433013	+	0.165396i
$49$	−6.70820	−	2.00000i	−0.958315	−	0.285714i
$50$			3.00000i			0.424264i
$51$	−12.0902	−	4.61803i	−1.69296	−	0.646654i
$52$		−	0.236068i		−	0.0327367i
$53$		−	6.56231i		−	0.901402i	−0.892675	−	0.450701i	$-0.851174\pi$
$53$		−	6.56231i		−	0.901402i	0.892675	−	0.450701i	$-0.148826\pi$
$54$	2.85410	−	1.47214i	0.388394	−	0.200332i
$55$			0.854102i			0.115167i
$56$	−5.85410	−	0.854102i	−0.782287	−	0.114134i
$57$	2.14590	−	5.61803i	0.284231	−	0.744127i
$58$	3.85410			0.506068
$59$	12.5623			1.63547			0.817736	−	0.575593i	$-0.195229\pi$
$59$	12.5623			1.63547			0.817736	+	0.575593i	$0.195229\pi$
$60$	1.00000	+	0.381966i	0.129099	+	0.0493116i
$61$		−	5.85410i		−	0.749541i	−0.927118	−	0.374770i	$-0.877722\pi$
$61$		−	5.85410i		−	0.749541i	0.927118	−	0.374770i	$-0.122278\pi$
$62$	5.85410			0.743472
$63$	6.09017	−	5.09017i	0.767289	−	0.641301i
$64$	0.236068			0.0295085
$65$		−	0.0557281i		−	0.00691222i
$66$	2.23607	+	0.854102i	0.275241	+	0.105133i
$67$	−8.38197			−1.02402			−0.512010	−	0.858979i	$-0.671099\pi$
$67$	−8.38197			−1.02402			−0.512010	+	0.858979i	$0.671099\pi$
$68$	−12.0902			−1.46615
$69$	0.618034	−	1.61803i	0.0744025	−	0.194788i
$70$	−0.618034	−	0.0901699i	−0.0738692	−	0.0107774i
$71$			10.3262i			1.22550i	0.790277	+	0.612749i	$0.209937\pi$
$71$			10.3262i			1.22550i	−0.790277	+	0.612749i	$0.790063\pi$
$72$	4.47214	−	5.00000i	0.527046	−	0.589256i
$73$		−	3.76393i		−	0.440535i	−0.975440	−	0.220267i	$-0.929307\pi$
$73$		−	3.76393i		−	0.440535i	0.975440	−	0.220267i	$-0.0706930\pi$
$74$		−	6.32624i		−	0.735410i
$75$	−7.85410	−	3.00000i	−0.906914	−	0.346410i
$76$		−	5.61803i		−	0.644433i
$77$	5.85410	+	0.854102i	0.667137	+	0.0973340i
$78$	−0.145898	−	0.0557281i	−0.0165197	−	0.00630996i
$79$	−12.2361			−1.37667			−0.688333	−	0.725395i	$-0.741657\pi$
$79$	−12.2361			−1.37667			−0.688333	+	0.725395i	$0.741657\pi$
$80$	0.708204			0.0791796
$81$	1.00000	+	8.94427i	0.111111	+	0.993808i
$82$			2.61803i			0.289113i
$83$	2.70820			0.297264			0.148632	−	0.988893i	$-0.452513\pi$
$83$	2.70820			0.297264			0.148632	+	0.988893i	$0.452513\pi$
$84$	3.61803	−	6.47214i	0.394760	−	0.706168i
$85$	−2.85410			−0.309571
$86$		−	3.32624i		−	0.358677i
$87$	−3.85410	+	10.0902i	−0.413203	+	1.08178i
$88$	5.00000			0.533002
$89$	−3.09017			−0.327557			−0.163779	−	0.986497i	$-0.552368\pi$
$89$	−3.09017			−0.327557			−0.163779	+	0.986497i	$0.552368\pi$
$90$	0.472136	−	0.527864i	0.0497675	−	0.0556418i
$91$	−0.381966	−	0.0557281i	−0.0400409	−	0.00584189i
$92$		−	1.61803i		−	0.168692i
$93$	−5.85410	+	15.3262i	−0.607042	+	1.58926i
$94$			4.94427i			0.509963i
$95$		−	1.32624i		−	0.136069i
$96$	3.47214	−	9.09017i	0.354373	−	0.927762i
$97$			15.9443i			1.61890i	0.587192	+	0.809448i	$0.300233\pi$
$97$			15.9443i			1.61890i	−0.587192	+	0.809448i	$0.699767\pi$
$98$	−1.23607	+	4.14590i	−0.124862	+	0.418799i
$99$	−4.47214	+	5.00000i	−0.449467	+	0.502519i
$100$	−7.85410			−0.785410
$101$	6.09017			0.605995			0.302997	−	0.952991i	$-0.402013\pi$
$101$	6.09017			0.605995			0.302997	+	0.952991i	$0.402013\pi$
$102$	−2.85410	+	7.47214i	−0.282598	+	0.739852i
$103$		−	12.1803i		−	1.20016i	−0.799938	−	0.600082i	$-0.795134\pi$
$103$		−	12.1803i		−	1.20016i	0.799938	−	0.600082i	$-0.204866\pi$
$104$	−0.326238			−0.0319903
$105$	0.854102	−	1.52786i	0.0833518	−	0.149104i
$106$	−4.05573			−0.393927
$107$			9.38197i			0.906989i	0.891259	+	0.453494i	$0.149823\pi$
$107$			9.38197i			0.906989i	−0.891259	+	0.453494i	$0.850177\pi$
$108$	3.85410	+	7.47214i	0.370861	+	0.719007i
$109$	−8.09017			−0.774898			−0.387449	−	0.921891i	$-0.626644\pi$
$109$	−8.09017			−0.774898			−0.387449	+	0.921891i	$0.626644\pi$
$110$	0.527864			0.0503299
$111$	16.5623	+	6.32624i	1.57202	+	0.600460i
$112$	0.708204	−	4.85410i	0.0669190	−	0.458670i
$113$		−	13.7984i		−	1.29804i	−0.760771	−	0.649021i	$-0.775179\pi$
$113$		−	13.7984i		−	1.29804i	0.760771	−	0.649021i	$-0.224821\pi$
$114$	−3.47214	−	1.32624i	−0.325195	−	0.124214i
$115$		−	0.381966i		−	0.0356185i
$116$			10.0902i			0.936849i
$117$	0.291796	−	0.326238i	0.0269766	−	0.0301607i
$118$		−	7.76393i		−	0.714728i
$119$	−2.85410	+	19.5623i	−0.261635	+	1.79327i
$120$	0.527864	−	1.38197i	0.0481872	−	0.126156i
$121$	6.00000			0.545455
$122$	−3.61803			−0.327561
$123$	−6.85410	−	2.61803i	−0.618014	−	0.236060i
$124$			15.3262i			1.37634i
$125$	−3.76393			−0.336656
$126$	−3.14590	−	3.76393i	−0.280259	−	0.335318i
$127$	−16.7984			−1.49061			−0.745307	−	0.666721i	$-0.767697\pi$
$127$	−16.7984			−1.49061			−0.745307	+	0.666721i	$0.767697\pi$
$128$		−	11.3820i		−	1.00603i
$129$	8.70820	+	3.32624i	0.766715	+	0.292859i
$130$	−0.0344419			−0.00302075
$131$	−5.29180			−0.462346			−0.231173	−	0.972913i	$-0.574256\pi$
$131$	−5.29180			−0.462346			−0.231173	+	0.972913i	$0.574256\pi$
$132$	−2.23607	+	5.85410i	−0.194625	+	0.509534i
$133$	−9.09017	−	1.32624i	−0.788218	−	0.114999i
$134$			5.18034i			0.447513i
$135$	0.909830	+	1.76393i	0.0783057	+	0.151815i
$136$			16.7082i			1.43272i
$137$		−	9.76393i		−	0.834189i	−0.908863	−	0.417095i	$-0.863048\pi$
$137$		−	9.76393i		−	0.834189i	0.908863	−	0.417095i	$-0.136952\pi$
$138$	−1.00000	−	0.381966i	−0.0851257	−	0.0325151i
$139$		−	12.0902i		−	1.02547i	−0.858545	−	0.512737i	$-0.828631\pi$
$139$		−	12.0902i		−	1.02547i	0.858545	−	0.512737i	$-0.171369\pi$
$140$	0.236068	−	1.61803i	0.0199514	−	0.136749i
$141$	−12.9443	−	4.94427i	−1.09010	−	0.416383i
$142$	6.38197			0.535563
$143$	0.326238			0.0272814
$144$	4.14590	+	3.70820i	0.345492	+	0.309017i
$145$			2.38197i			0.197812i
$146$	−2.32624			−0.192521
$147$	−9.61803	−	7.38197i	−0.793282	−	0.608854i
$148$	16.5623			1.36141
$149$			5.70820i			0.467634i	0.972281	+	0.233817i	$0.0751217\pi$
$149$			5.70820i			0.467634i	−0.972281	+	0.233817i	$0.924878\pi$
$150$	−1.85410	+	4.85410i	−0.151387	+	0.396336i
$151$	6.47214			0.526695			0.263347	−	0.964701i	$-0.415173\pi$
$151$	6.47214			0.526695			0.263347	+	0.964701i	$0.415173\pi$
$152$	−7.76393			−0.629738
$153$	−16.7082	−	14.9443i	−1.35078	−	1.20817i
$154$	0.527864	−	3.61803i	0.0425365	−	0.291549i
$155$			3.61803i			0.290607i
$156$	0.145898	−	0.381966i	0.0116812	−	0.0305818i
$157$			16.4721i			1.31462i	0.753620	+	0.657310i	$0.228306\pi$
$157$			16.4721i			1.31462i	−0.753620	+	0.657310i	$0.771694\pi$
$158$			7.56231i			0.601625i
$159$	4.05573	−	10.6180i	0.321640	−	0.842065i
$160$		−	2.14590i		−	0.169648i
$161$	−2.61803	−	0.381966i	−0.206330	−	0.0301031i
$162$	5.52786	−	0.618034i	0.434310	−	0.0485573i
$163$	−7.90983			−0.619546			−0.309773	−	0.950811i	$-0.600253\pi$
$163$	−7.90983			−0.619546			−0.309773	+	0.950811i	$0.600253\pi$
$164$	−6.85410			−0.535215
$165$	−0.527864	+	1.38197i	−0.0410942	+	0.107586i
$166$		−	1.67376i		−	0.129909i
$167$	3.18034			0.246102			0.123051	−	0.992400i	$-0.460732\pi$
$167$	3.18034			0.246102			0.123051	+	0.992400i	$0.460732\pi$
$168$	−8.94427	−	5.00000i	−0.690066	−	0.385758i
$169$	12.9787			0.998363
$170$			1.76393i			0.135287i
$171$	6.94427	−	7.76393i	0.531042	−	0.593723i
$172$	8.70820			0.663994
$173$	5.47214			0.416039			0.208019	−	0.978125i	$-0.433298\pi$
$173$	5.47214			0.416039			0.208019	+	0.978125i	$0.433298\pi$
$174$	6.23607	+	2.38197i	0.472755	+	0.180576i
$175$	−1.85410	+	12.7082i	−0.140157	+	0.960650i
$176$			4.14590i			0.312509i
$177$	20.3262	+	7.76393i	1.52781	+	0.583573i
$178$			1.90983i			0.143148i
$179$		−	21.3262i		−	1.59400i	−0.603981	−	0.796999i	$-0.706420\pi$
$179$		−	21.3262i		−	1.59400i	0.603981	−	0.796999i	$-0.293580\pi$
$180$	1.38197	+	1.23607i	0.103006	+	0.0921311i
$181$			6.70820i			0.498617i	0.968424	+	0.249308i	$0.0802033\pi$
$181$			6.70820i			0.498617i	−0.968424	+	0.249308i	$0.919797\pi$
$182$	−0.0344419	+	0.236068i	−0.00255300	+	0.0174985i
$183$	3.61803	−	9.47214i	0.267453	−	0.700200i
$184$	−2.23607			−0.164845
$185$	3.90983			0.287456
$186$	9.47214	+	3.61803i	0.694531	+	0.265287i
$187$		−	16.7082i		−	1.22182i
$188$	−12.9443			−0.944058
$189$	13.0000	−	4.47214i	0.945611	−	0.325300i
$190$	−0.819660			−0.0594644
$191$		−	8.29180i		−	0.599973i	−0.953943	−	0.299987i	$-0.903018\pi$
$191$		−	8.29180i		−	0.599973i	0.953943	−	0.299987i	$-0.0969822\pi$
$192$	0.381966	+	0.145898i	0.0275660	+	0.0105293i
$193$	2.29180			0.164967			0.0824835	−	0.996592i	$-0.473715\pi$
$193$	2.29180			0.164967			0.0824835	+	0.996592i	$0.473715\pi$
$194$	9.85410			0.707483
$195$	0.0344419	−	0.0901699i	0.00246643	−	0.00645720i
$196$	−10.8541	−	3.23607i	−0.775293	−	0.231148i
$197$			14.9098i			1.06228i	0.847284	+	0.531141i	$0.178236\pi$
$197$			14.9098i			1.06228i	−0.847284	+	0.531141i	$0.821764\pi$
$198$	3.09017	+	2.76393i	0.219609	+	0.196424i
$199$			12.3820i			0.877734i	0.898552	+	0.438867i	$0.144620\pi$
$199$			12.3820i			0.877734i	−0.898552	+	0.438867i	$0.855380\pi$
$200$			10.8541i			0.767501i
$201$	−13.5623	−	5.18034i	−0.956611	−	0.365393i
$202$		−	3.76393i		−	0.264829i
$203$	16.3262	+	2.38197i	1.14588	+	0.167181i
$204$	−19.5623	−	7.47214i	−1.36964	−	0.523154i
$205$	−1.61803			−0.113008
$206$	−7.52786			−0.524491
$207$	2.00000	−	2.23607i	0.139010	−	0.155417i
$208$		−	0.270510i		−	0.0187565i
$209$	7.76393			0.537042
$210$	−0.944272	−	0.527864i	−0.0651610	−	0.0364261i
$211$	−3.00000			−0.206529			−0.103264	−	0.994654i	$-0.532929\pi$
$211$	−3.00000			−0.206529			−0.103264	+	0.994654i	$0.532929\pi$
$212$		−	10.6180i		−	0.729250i
$213$	−6.38197	+	16.7082i	−0.437285	+	1.14483i
$214$	5.79837			0.396369
$215$	2.05573			0.140199
$216$	10.3262	−	5.32624i	0.702611	−	0.362405i
$217$	24.7984	+	3.61803i	1.68342	+	0.245608i
$218$			5.00000i			0.338643i
$219$	2.32624	−	6.09017i	0.157193	−	0.411536i
$220$			1.38197i			0.0931721i
$221$			1.09017i			0.0733328i
$222$	3.90983	−	10.2361i	0.262411	−	0.687000i
$223$			5.90983i			0.395751i	0.980227	+	0.197876i	$0.0634043\pi$
$223$			5.90983i			0.395751i	−0.980227	+	0.197876i	$0.936596\pi$
$224$	−14.7082	−	2.14590i	−0.982733	−	0.143379i
$225$	−10.8541	−	9.70820i	−0.723607	−	0.647214i
$226$	−8.52786			−0.567265
$227$	6.67376			0.442953			0.221477	−	0.975166i	$-0.428912\pi$
$227$	6.67376			0.442953			0.221477	+	0.975166i	$0.428912\pi$
$228$	3.47214	−	9.09017i	0.229948	−	0.602011i
$229$		−	22.0902i		−	1.45976i	−0.683576	−	0.729880i	$-0.739576\pi$
$229$		−	22.0902i		−	1.45976i	0.683576	−	0.729880i	$-0.260424\pi$
$230$	−0.236068			−0.0155659
$231$	8.94427	+	5.00000i	0.588490	+	0.328976i
$232$	13.9443			0.915486
$233$		−	29.3262i		−	1.92123i	−0.277890	−	0.960613i	$-0.589635\pi$
$233$		−	29.3262i		−	1.92123i	0.277890	−	0.960613i	$-0.410365\pi$
$234$	−0.201626	−	0.180340i	−0.0131807	−	0.0117892i
$235$	−3.05573			−0.199334
$236$	20.3262			1.32313
$237$	−19.7984	−	7.56231i	−1.28604	−	0.491225i
$238$	12.0902	+	1.76393i	0.783689	+	0.114339i
$239$		−	21.3262i		−	1.37948i	−0.724057	−	0.689740i	$-0.757725\pi$
$239$		−	21.3262i		−	1.37948i	0.724057	−	0.689740i	$-0.242275\pi$
$240$	1.14590	+	0.437694i	0.0739674	+	0.0282530i
$241$			9.47214i			0.610154i	0.952328	+	0.305077i	$0.0986822\pi$
$241$			9.47214i			0.610154i	−0.952328	+	0.305077i	$0.901318\pi$
$242$		−	3.70820i		−	0.238372i
$243$	−3.90983	+	15.0902i	−0.250816	+	0.968035i
$244$		−	9.47214i		−	0.606391i
$245$	−2.56231	−	0.763932i	−0.163700	−	0.0488058i
$246$	−1.61803	+	4.23607i	−0.103162	+	0.270082i
$247$	−0.506578			−0.0322328
$248$	21.1803			1.34495
$249$	4.38197	+	1.67376i	0.277696	+	0.106070i
$250$			2.32624i			0.147124i
$251$	2.47214			0.156040			0.0780199	−	0.996952i	$-0.475140\pi$
$251$	2.47214			0.156040			0.0780199	+	0.996952i	$0.475140\pi$
$252$	9.85410	−	8.23607i	0.620750	−	0.518824i
$253$	2.23607			0.140580
$254$			10.3820i			0.651422i
$255$	−4.61803	−	1.76393i	−0.289193	−	0.110462i
$256$	−6.56231			−0.410144
$257$	13.0557			0.814394			0.407197	−	0.913340i	$-0.366506\pi$
$257$	13.0557			0.814394			0.407197	+	0.913340i	$0.366506\pi$
$258$	2.05573	−	5.38197i	0.127984	−	0.335067i
$259$	3.90983	−	26.7984i	0.242945	−	1.66517i
$260$		−	0.0901699i		−	0.00559210i
$261$	−12.4721	+	13.9443i	−0.772006	+	0.863129i
$262$			3.27051i			0.202053i
$263$		−	0.0557281i		−	0.00343634i	−0.999999	−	0.00171817i	$-0.999453\pi$
$263$		−	0.0557281i		−	0.00343634i	0.999999	−	0.00171817i	$-0.000546911\pi$
$264$	8.09017	+	3.09017i	0.497916	+	0.190187i
$265$		−	2.50658i		−	0.153978i
$266$	−0.819660	+	5.61803i	−0.0502566	+	0.344464i
$267$	−5.00000	−	1.90983i	−0.305995	−	0.116880i
$268$	−13.5623			−0.828450
$269$	−4.14590			−0.252780			−0.126390	−	0.991981i	$-0.540339\pi$
$269$	−4.14590			−0.252780			−0.126390	+	0.991981i	$0.540339\pi$
$270$	1.09017	−	0.562306i	0.0663456	−	0.0342208i
$271$			2.23607i			0.135831i	0.997691	+	0.0679157i	$0.0216349\pi$
$271$			2.23607i			0.135831i	−0.997691	+	0.0679157i	$0.978365\pi$
$272$	−13.8541			−0.840028
$273$	−0.583592	−	0.326238i	−0.0353206	−	0.0197448i
$274$	−6.03444			−0.364554
$275$		−	10.8541i		−	0.654527i
$276$	1.00000	−	2.61803i	0.0601929	−	0.157587i
$277$	13.8541			0.832412			0.416206	−	0.909270i	$-0.363359\pi$
$277$	13.8541			0.832412			0.416206	+	0.909270i	$0.363359\pi$
$278$	−7.47214			−0.448149
$279$	−18.9443	+	21.1803i	−1.13416	+	1.26803i
$280$	−2.23607	−	0.326238i	−0.133631	−	0.0194964i
$281$		−	18.9443i		−	1.13012i	−0.825050	−	0.565060i	$-0.808853\pi$
$281$		−	18.9443i		−	1.13012i	0.825050	−	0.565060i	$-0.191147\pi$
$282$	−3.05573	+	8.00000i	−0.181966	+	0.476393i
$283$		−	15.7984i		−	0.939116i	−0.882902	−	0.469558i	$-0.844413\pi$
$283$		−	15.7984i		−	0.939116i	0.882902	−	0.469558i	$-0.155587\pi$
$284$			16.7082i			0.991449i
$285$	0.819660	−	2.14590i	0.0485525	−	0.127112i
$286$		−	0.201626i		−	0.0119224i
$287$	−1.61803	+	11.0902i	−0.0955095	+	0.654632i
$288$	11.2361	−	12.5623i	0.662092	−	0.740241i
$289$	38.8328			2.28428
$290$	1.47214			0.0864468
$291$	−9.85410	+	25.7984i	−0.577658	+	1.51233i
$292$		−	6.09017i		−	0.356400i
$293$	27.7082			1.61873			0.809365	−	0.587306i	$-0.199811\pi$
$293$	27.7082			1.61873			0.809365	+	0.587306i	$0.199811\pi$
$294$	−4.56231	+	5.94427i	−0.266079	+	0.346677i
$295$	4.79837			0.279372
$296$		−	22.8885i		−	1.33037i
$297$	−10.3262	+	5.32624i	−0.599189	+	0.309060i
$298$	3.52786			0.204364
$299$	−0.145898			−0.00843750
$300$	−12.7082	−	4.85410i	−0.733708	−	0.280252i
$301$	2.05573	−	14.0902i	0.118490	−	0.812144i
$302$		−	4.00000i		−	0.230174i
$303$	9.85410	+	3.76393i	0.566103	+	0.216232i
$304$		−	6.43769i		−	0.369227i
$305$		−	2.23607i		−	0.128037i
$306$	−9.23607	+	10.3262i	−0.527991	+	0.590312i
$307$			12.5279i			0.715003i	0.933913	+	0.357501i	$0.116371\pi$
$307$			12.5279i			0.715003i	−0.933913	+	0.357501i	$0.883629\pi$
$308$	9.47214	+	1.38197i	0.539725	+	0.0787448i
$309$	7.52786	−	19.7082i	0.428245	−	1.12116i
$310$	2.23607			0.127000
$311$	7.67376			0.435139			0.217570	−	0.976045i	$-0.430187\pi$
$311$	7.67376			0.435139			0.217570	+	0.976045i	$0.430187\pi$
$312$	−0.527864	−	0.201626i	−0.0298844	−	0.0114148i
$313$		−	12.1803i		−	0.688474i	−0.938883	−	0.344237i	$-0.888138\pi$
$313$		−	12.1803i		−	0.688474i	0.938883	−	0.344237i	$-0.111862\pi$
$314$	10.1803			0.574510
$315$	2.32624	−	1.94427i	0.131069	−	0.109547i
$316$	−19.7984			−1.11375
$317$			1.61803i			0.0908778i	0.998967	+	0.0454389i	$0.0144686\pi$
$317$			1.61803i			0.0908778i	−0.998967	+	0.0454389i	$0.985531\pi$
$318$	−6.56231	−	2.50658i	−0.367996	−	0.140562i
$319$	−13.9443			−0.780729
$320$	0.0901699			0.00504065
$321$	−5.79837	+	15.1803i	−0.323634	+	0.847284i
$322$	−0.236068	+	1.61803i	−0.0131556	+	0.0901695i
$323$			25.9443i			1.44358i
$324$	1.61803	+	14.4721i	0.0898908	+	0.804008i
$325$			0.708204i			0.0392841i
$326$			4.88854i			0.270751i
$327$	−13.0902	−	5.00000i	−0.723888	−	0.276501i
$328$			9.47214i			0.523011i
$329$	−3.05573	+	20.9443i	−0.168468	+	1.15470i
$330$	0.854102	+	0.326238i	0.0470168	+	0.0179588i
$331$	−22.0689			−1.21302			−0.606508	−	0.795078i	$-0.707430\pi$
$331$	−22.0689			−1.21302			−0.606508	+	0.795078i	$0.707430\pi$
$332$	4.38197			0.240492
$333$	22.8885	+	20.4721i	1.25428	+	1.12187i
$334$		−	1.96556i		−	0.107551i
$335$	−3.20163			−0.174924
$336$	4.14590	−	7.41641i	0.226177	−	0.404598i
$337$	23.4508			1.27745			0.638725	−	0.769435i	$-0.279462\pi$
$337$	23.4508			1.27745			0.638725	+	0.769435i	$0.279462\pi$
$338$		−	8.02129i		−	0.436300i
$339$	8.52786	−	22.3262i	0.463170	−	1.21259i
$340$	−4.61803			−0.250448
$341$	−21.1803			−1.14698
$342$	−4.79837	−	4.29180i	−0.259466	−	0.232074i
$343$	−7.79837	+	16.7984i	−0.421073	+	0.907027i
$344$		−	12.0344i		−	0.648854i
$345$	0.236068	−	0.618034i	0.0127095	−	0.0332738i
$346$		−	3.38197i		−	0.181816i
$347$		−	0.819660i		−	0.0440017i	−0.999758	−	0.0220008i	$-0.992996\pi$
$347$		−	0.819660i		−	0.0440017i	0.999758	−	0.0220008i	$-0.00700365\pi$
$348$	−6.23607	+	16.3262i	−0.334288	+	0.875178i
$349$			25.1459i			1.34603i	0.739629	+	0.673015i	$0.235001\pi$
$349$			25.1459i			1.34603i	−0.739629	+	0.673015i	$0.764999\pi$
$350$	7.85410	+	1.14590i	0.419819	+	0.0612508i
$351$	0.673762	−	0.347524i	0.0359628	−	0.0185495i
$352$	12.5623			0.669573
$353$	35.4721			1.88799			0.943996	−	0.329958i	$-0.107035\pi$
$353$	35.4721			1.88799			0.943996	+	0.329958i	$0.107035\pi$
$354$	4.79837	−	12.5623i	0.255031	−	0.667679i
$355$			3.94427i			0.209340i
$356$	−5.00000			−0.264999
$357$	−16.7082	+	29.8885i	−0.884292	+	1.58187i
$358$	−13.1803			−0.696603
$359$		−	14.0902i		−	0.743651i	−0.928303	−	0.371825i	$-0.878732\pi$
$359$		−	14.0902i		−	0.743651i	0.928303	−	0.371825i	$-0.121268\pi$
$360$	1.70820	−	1.90983i	0.0900303	−	0.100657i
$361$	6.94427			0.365488
$362$	4.14590			0.217904
$363$	9.70820	+	3.70820i	0.509549	+	0.194630i
$364$	−0.618034	−	0.0901699i	−0.0323938	−	0.00472619i
$365$		−	1.43769i		−	0.0752523i
$366$	−5.85410	−	2.23607i	−0.305999	−	0.116881i
$367$			11.2705i			0.588316i	0.955757	+	0.294158i	$0.0950392\pi$
$367$			11.2705i			0.588316i	−0.955757	+	0.294158i	$0.904961\pi$
$368$		−	1.85410i		−	0.0966517i
$369$	−9.47214	−	8.47214i	−0.493100	−	0.441042i
$370$		−	2.41641i		−	0.125623i
$371$	−17.1803	−	2.50658i	−0.891959	−	0.130135i
$372$	−9.47214	+	24.7984i	−0.491107	+	1.28574i
$373$	−1.00000			−0.0517780			−0.0258890	−	0.999665i	$-0.508242\pi$
$373$	−1.00000			−0.0517780			−0.0258890	+	0.999665i	$0.508242\pi$
$374$	−10.3262			−0.533957
$375$	−6.09017	−	2.32624i	−0.314495	−	0.120126i
$376$			17.8885i			0.922531i
$377$	0.909830			0.0468586
$378$	−2.76393	−	8.03444i	−0.142161	−	0.413247i
$379$	15.5279			0.797613			0.398806	−	0.917035i	$-0.369425\pi$
$379$	15.5279			0.797613			0.398806	+	0.917035i	$0.369425\pi$
$380$		−	2.14590i		−	0.110082i
$381$	−27.1803	−	10.3820i	−1.39249	−	0.531884i
$382$	−5.12461			−0.262198
$383$	3.76393			0.192328			0.0961640	−	0.995366i	$-0.469343\pi$
$383$	3.76393			0.192328			0.0961640	+	0.995366i	$0.469343\pi$
$384$	7.03444	−	18.4164i	0.358975	−	0.939808i
$385$	2.23607	+	0.326238i	0.113961	+	0.0166266i
$386$		−	1.41641i		−	0.0720933i
$387$	12.0344	+	10.7639i	0.611745	+	0.547161i
$388$			25.7984i			1.30971i
$389$		−	19.2918i		−	0.978133i	−0.872247	−	0.489066i	$-0.837338\pi$
$389$		−	19.2918i		−	0.978133i	0.872247	−	0.489066i	$-0.162662\pi$
$390$	−0.0557281	−	0.0212862i	−0.00282190	−	0.00107787i
$391$			7.47214i			0.377882i
$392$	−4.47214	+	15.0000i	−0.225877	+	0.757614i
$393$	−8.56231	−	3.27051i	−0.431911	−	0.164975i
$394$	9.21478			0.464234
$395$	−4.67376			−0.235162
$396$	−7.23607	+	8.09017i	−0.363626	+	0.406546i
$397$		−	10.7639i		−	0.540226i	−0.962829	−	0.270113i	$-0.912939\pi$
$397$		−	10.7639i		−	0.540226i	0.962829	−	0.270113i	$-0.0870611\pi$
$398$	7.65248			0.383584
$399$	−13.8885	−	7.76393i	−0.695297	−	0.388683i
$400$	−9.00000			−0.450000
$401$			18.4164i			0.919672i	0.888004	+	0.459836i	$0.152092\pi$
$401$			18.4164i			0.919672i	−0.888004	+	0.459836i	$0.847908\pi$
$402$	−3.20163	+	8.38197i	−0.159683	+	0.418054i
$403$	1.38197			0.0688406
$404$	9.85410			0.490260
$405$	0.381966	+	3.41641i	0.0189800	+	0.169763i
$406$	1.47214	−	10.0902i	0.0730609	−	0.500767i
$407$			22.8885i			1.13454i
$408$	−10.3262	+	27.0344i	−0.511225	+	1.33840i
$409$		−	24.5279i		−	1.21282i	−0.795150	−	0.606412i	$-0.792608\pi$
$409$		−	24.5279i		−	1.21282i	0.795150	−	0.606412i	$-0.207392\pi$
$410$			1.00000i			0.0493865i
$411$	6.03444	−	15.7984i	0.297657	−	0.779276i
$412$		−	19.7082i		−	0.970954i
$413$	4.79837	−	32.8885i	0.236113	−	1.61834i
$414$	−1.38197	−	1.23607i	−0.0679199	−	0.0607494i
$415$	1.03444			0.0507788
$416$	−0.819660			−0.0401871
$417$	7.47214	−	19.5623i	0.365912	−	0.957970i
$418$		−	4.79837i		−	0.234696i
$419$	0.201626			0.00985008			0.00492504	−	0.999988i	$-0.498432\pi$
$419$	0.201626			0.00985008			0.00492504	+	0.999988i	$0.498432\pi$
$420$	1.38197	−	2.47214i	0.0674330	−	0.120628i
$421$	−20.6869			−1.00822			−0.504109	−	0.863640i	$-0.668179\pi$
$421$	−20.6869			−1.00822			−0.504109	+	0.863640i	$0.668179\pi$
$422$			1.85410i			0.0902563i
$423$	−17.8885	−	16.0000i	−0.869771	−	0.777947i
$424$	−14.6738			−0.712621
$425$	36.2705			1.75938
$426$	10.3262	+	3.94427i	0.500308	+	0.191101i
$427$	−15.3262	−	2.23607i	−0.741689	−	0.108211i
$428$			15.1803i			0.733769i
$429$	0.527864	+	0.201626i	0.0254855	+	0.00973460i
$430$		−	1.27051i		−	0.0612694i
$431$			33.0902i			1.59390i	0.604047	+	0.796949i	$0.293554\pi$
$431$			33.0902i			1.59390i	−0.604047	+	0.796949i	$0.706446\pi$
$432$	4.41641	+	8.56231i	0.212485	+	0.411954i
$433$		−	10.4721i		−	0.503259i	−0.967824	−	0.251629i	$-0.919034\pi$
$433$		−	10.4721i		−	0.503259i	0.967824	−	0.251629i	$-0.0809664\pi$
$434$	2.23607	−	15.3262i	0.107335	−	0.735683i
$435$	−1.47214	+	3.85410i	−0.0705835	+	0.184790i
$436$	−13.0902			−0.626905
$437$	−3.47214			−0.166095
$438$	−3.76393	−	1.43769i	−0.179848	−	0.0686957i
$439$			16.5279i			0.788832i	0.918932	+	0.394416i	$0.129053\pi$
$439$			16.5279i			0.788832i	−0.918932	+	0.394416i	$0.870947\pi$
$440$	1.90983			0.0910476
$441$	−11.0000	−	17.8885i	−0.523810	−	0.851835i
$442$	0.673762			0.0320476
$443$		−	0.180340i		−	0.00856821i	−0.999991	−	0.00428410i	$-0.998636\pi$
$443$		−	0.180340i		−	0.00856821i	0.999991	−	0.00428410i	$-0.00136368\pi$
$444$	26.7984	+	10.2361i	1.27179	+	0.485782i
$445$	−1.18034			−0.0559535
$446$	3.65248			0.172950
$447$	−3.52786	+	9.23607i	−0.166862	+	0.436851i
$448$	0.0901699	−	0.618034i	0.00426013	−	0.0291994i
$449$			22.0902i			1.04250i	0.853404	+	0.521250i	$0.174534\pi$
$449$			22.0902i			1.04250i	−0.853404	+	0.521250i	$0.825466\pi$
$450$	−6.00000	+	6.70820i	−0.282843	+	0.316228i
$451$		−	9.47214i		−	0.446025i
$452$		−	22.3262i		−	1.05014i
$453$	10.4721	+	4.00000i	0.492024	+	0.187936i
$454$		−	4.12461i		−	0.193578i
$455$	−0.145898	−	0.0212862i	−0.00683981	−	0.000997914i
$456$	−12.5623	−	4.79837i	−0.588284	−	0.224704i
$457$	−4.56231			−0.213416			−0.106708	−	0.994290i	$-0.534031\pi$
$457$	−4.56231			−0.213416			−0.106708	+	0.994290i	$0.534031\pi$
$458$	−13.6525			−0.637938
$459$	−17.7984	−	34.5066i	−0.830757	−	1.61063i
$460$		−	0.618034i		−	0.0288160i
$461$	35.6869			1.66211			0.831053	−	0.556194i	$-0.187739\pi$
$461$	35.6869			1.66211			0.831053	+	0.556194i	$0.187739\pi$
$462$	3.09017	−	5.52786i	0.143768	−	0.257180i
$463$	−25.4721			−1.18379			−0.591895	−	0.806015i	$-0.701620\pi$
$463$	−25.4721			−1.18379			−0.591895	+	0.806015i	$0.701620\pi$
$464$			11.5623i			0.536767i
$465$	−2.23607	+	5.85410i	−0.103695	+	0.271477i
$466$	−18.1246			−0.839606
$467$	−19.8328			−0.917753			−0.458877	−	0.888500i	$-0.651748\pi$
$467$	−19.8328			−0.917753			−0.458877	+	0.888500i	$0.651748\pi$
$468$	0.472136	−	0.527864i	0.0218245	−	0.0244005i
$469$	−3.20163	+	21.9443i	−0.147837	+	1.01329i
$470$			1.88854i			0.0871120i
$471$	−10.1803	+	26.6525i	−0.469085	+	1.22808i
$472$		−	28.0902i		−	1.29295i
$473$			12.0344i			0.553344i
$474$	−4.67376	+	12.2361i	−0.214673	+	0.562021i
$475$			16.8541i			0.773319i
$476$	−4.61803	+	31.6525i	−0.211667	+	1.45079i
$477$	13.1246	−	14.6738i	0.600935	−	0.671865i
$478$	−13.1803			−0.602855
$479$	5.65248			0.258268			0.129134	−	0.991627i	$-0.458780\pi$
$479$	5.65248			0.258268			0.129134	+	0.991627i	$0.458780\pi$
$480$	1.32624	−	3.47214i	0.0605342	−	0.158481i
$481$		−	1.49342i		−	0.0680942i
$482$	5.85410			0.266647
$483$	−4.00000	−	2.23607i	−0.182006	−	0.101745i
$484$	9.70820			0.441282
$485$			6.09017i			0.276540i
$486$	9.32624	+	2.41641i	0.423047	+	0.109610i
$487$	1.29180			0.0585369			0.0292684	−	0.999572i	$-0.490682\pi$
$487$	1.29180			0.0585369			0.0292684	+	0.999572i	$0.490682\pi$
$488$	−13.0902			−0.592564
$489$	−12.7984	−	4.88854i	−0.578762	−	0.221068i
$490$	−0.472136	+	1.58359i	−0.0213289	+	0.0715394i
$491$			33.0902i			1.49334i	0.665196	+	0.746669i	$0.268348\pi$
$491$			33.0902i			1.49334i	−0.665196	+	0.746669i	$0.731652\pi$
$492$	−11.0902	−	4.23607i	−0.499983	−	0.190977i
$493$		−	46.5967i		−	2.09861i
$494$			0.313082i			0.0140862i
$495$	−1.70820	+	1.90983i	−0.0767781	+	0.0858405i
$496$			17.5623i			0.788571i
$497$	27.0344	+	3.94427i	1.21266	+	0.176925i
$498$	1.03444	−	2.70820i	0.0463544	−	0.121358i
$499$	2.56231			0.114705			0.0573523	−	0.998354i	$-0.481734\pi$
$499$	2.56231			0.114705			0.0573523	+	0.998354i	$0.481734\pi$
$500$	−6.09017			−0.272361
$501$	5.14590	+	1.96556i	0.229902	+	0.0878147i
$502$		−	1.52786i		−	0.0681919i
$503$	−42.7426			−1.90580			−0.952900	−	0.303284i	$-0.901917\pi$
$503$	−42.7426			−1.90580			−0.952900	+	0.303284i	$0.901917\pi$
$504$	−11.3820	−	13.6180i	−0.506993	−	0.606595i
$505$	2.32624			0.103516
$506$		−	1.38197i		−	0.0614359i
$507$	21.0000	+	8.02129i	0.932643	+	0.356238i
$508$	−27.1803			−1.20593
$509$	20.0000			0.886484			0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000			0.886484			0.443242	+	0.896402i	$0.353828\pi$
$510$	−1.09017	+	2.85410i	−0.0482735	+	0.126382i
$511$	−9.85410	−	1.43769i	−0.435920	−	0.0635998i
$512$		−	18.7082i		−	0.826794i
$513$	16.0344	−	8.27051i	0.707938	−	0.365152i
$514$		−	8.06888i		−	0.355903i
$515$		−	4.65248i		−	0.205013i
$516$	14.0902	+	5.38197i	0.620285	+	0.236928i
$517$		−	17.8885i		−	0.786737i
$518$	−16.5623	−	2.41641i	−0.727706	−	0.106171i
$519$	8.85410	+	3.38197i	0.388652	+	0.148452i
$520$	−0.124612			−0.00546459
$521$	−27.5279			−1.20602			−0.603009	−	0.797735i	$-0.706032\pi$
$521$	−27.5279			−1.20602			−0.603009	+	0.797735i	$0.706032\pi$
$522$	8.61803	+	7.70820i	0.377201	+	0.337379i
$523$			23.5967i			1.03181i	0.856645	+	0.515907i	$0.172545\pi$
$523$			23.5967i			1.03181i	−0.856645	+	0.515907i	$0.827455\pi$
$524$	−8.56231			−0.374046
$525$	−10.8541	+	19.4164i	−0.473712	+	0.847402i
$526$	−0.0344419			−0.00150174
$527$		−	70.7771i		−	3.08310i
$528$	−2.56231	+	6.70820i	−0.111510	+	0.291937i
$529$	−1.00000			−0.0434783
$530$	−1.54915			−0.0672908
$531$	28.0902	+	25.1246i	1.21901	+	1.09032i
$532$	−14.7082	−	2.14590i	−0.637682	−	0.0930365i
$533$			0.618034i			0.0267700i
$534$	−1.18034	+	3.09017i	−0.0510783	+	0.133725i
$535$			3.58359i			0.154932i
$536$			18.7426i			0.809559i
$537$	13.1803	−	34.5066i	0.568774	−	1.48907i
$538$			2.56231i			0.110469i
$539$	4.47214	−	15.0000i	0.192629	−	0.646096i
$540$	1.47214	+	2.85410i	0.0633506	+	0.122821i
$541$	−20.7639			−0.892711			−0.446356	−	0.894856i	$-0.647278\pi$
$541$	−20.7639			−0.892711			−0.446356	+	0.894856i	$0.647278\pi$
$542$	1.38197			0.0593605
$543$	−4.14590	+	10.8541i	−0.177918	+	0.465794i
$544$			41.9787i			1.79982i
$545$	−3.09017			−0.132368
$546$	−0.201626	+	0.360680i	−0.00862880	+	0.0154357i
$547$	31.2148			1.33465			0.667324	−	0.744768i	$-0.267440\pi$
$547$	31.2148			1.33465			0.667324	+	0.744768i	$0.267440\pi$
$548$		−	15.7984i		−	0.674873i
$549$	11.7082	−	13.0902i	0.499694	−	0.558675i
$550$	−6.70820			−0.286039
$551$	21.6525			0.922426
$552$	−3.61803	−	1.38197i	−0.153994	−	0.0588204i
$553$	−4.67376	+	32.0344i	−0.198749	+	1.36224i
$554$		−	8.56231i		−	0.363778i
$555$	6.32624	+	2.41641i	0.268534	+	0.102571i
$556$		−	19.5623i		−	0.829627i
$557$		−	26.0689i		−	1.10457i	−0.833654	−	0.552287i	$-0.813755\pi$
$557$		−	26.0689i		−	1.10457i	0.833654	−	0.552287i	$-0.186245\pi$
$558$	13.0902	+	11.7082i	0.554151	+	0.495648i
$559$		−	0.785218i		−	0.0332112i
$560$	0.270510	−	1.85410i	0.0114311	−	0.0783501i
$561$	10.3262	−	27.0344i	0.435974	−	1.14140i
$562$	−11.7082			−0.493881
$563$	−18.1459			−0.764758			−0.382379	−	0.924005i	$-0.624895\pi$
$563$	−18.1459			−0.764758			−0.382379	+	0.924005i	$0.624895\pi$
$564$	−20.9443	−	8.00000i	−0.881913	−	0.336861i
$565$		−	5.27051i		−	0.221732i
$566$	−9.76393			−0.410409
$567$	23.7984	+	0.798374i	0.999438	+	0.0335286i
$568$	23.0902			0.968842
$569$			13.5967i			0.570005i	0.958527	+	0.285003i	$0.0919945\pi$
$569$			13.5967i			0.570005i	−0.958527	+	0.285003i	$0.908006\pi$
$570$	−1.32624	−	0.506578i	−0.0555500	−	0.0212182i
$571$	10.4164			0.435913			0.217957	−	0.975958i	$-0.430061\pi$
$571$	10.4164			0.435913			0.217957	+	0.975958i	$0.430061\pi$
$572$	0.527864			0.0220711
$573$	5.12461	−	13.4164i	0.214084	−	0.560478i
$574$	6.85410	+	1.00000i	0.286085	+	0.0417392i
$575$			4.85410i			0.202430i
$576$	0.527864	+	0.472136i	0.0219943	+	0.0196723i
$577$		−	29.3050i		−	1.21998i	−0.792409	−	0.609991i	$-0.791173\pi$
$577$		−	29.3050i		−	1.21998i	0.792409	−	0.609991i	$-0.208827\pi$
$578$		−	24.0000i		−	0.998268i
$579$	3.70820	+	1.41641i	0.154108	+	0.0588639i
$580$			3.85410i			0.160033i
$581$	1.03444	−	7.09017i	0.0429159	−	0.294150i
$582$	15.9443	+	6.09017i	0.660911	+	0.252446i
$583$	14.6738			0.607725
$584$	−8.41641			−0.348273
$585$	0.111456	−	0.124612i	0.00460815	−	0.00515206i
$586$		−	17.1246i		−	0.707411i
$587$	2.32624			0.0960141			0.0480071	−	0.998847i	$-0.484713\pi$
$587$	2.32624			0.0960141			0.0480071	+	0.998847i	$0.484713\pi$
$588$	−15.5623	−	11.9443i	−0.641779	−	0.492573i
$589$	32.8885			1.35515
$590$		−	2.96556i		−	0.122090i
$591$	−9.21478	+	24.1246i	−0.379045	+	0.992354i
$592$	18.9787			0.780020
$593$	−9.12461			−0.374703			−0.187351	−	0.982293i	$-0.559990\pi$
$593$	−9.12461			−0.374703			−0.187351	+	0.982293i	$0.559990\pi$
$594$	3.29180	+	6.38197i	0.135064	+	0.261855i
$595$	−1.09017	+	7.47214i	−0.0446926	+	0.306328i
$596$			9.23607i			0.378324i
$597$	−7.65248	+	20.0344i	−0.313195	+	0.819955i
$598$			0.0901699i			0.00368732i
$599$			9.85410i			0.402628i	0.979527	+	0.201314i	$0.0645211\pi$
$599$			9.85410i			0.402628i	−0.979527	+	0.201314i	$0.935479\pi$
$600$	−6.70820	+	17.5623i	−0.273861	+	0.716978i
$601$		−	25.3262i		−	1.03308i	−0.856263	−	0.516539i	$-0.827220\pi$
$601$		−	25.3262i		−	1.03308i	0.856263	−	0.516539i	$-0.172780\pi$
$602$	−8.70820	−	1.27051i	−0.354920	−	0.0517821i
$603$	−18.7426	−	16.7639i	−0.763260	−	0.682680i
$604$	10.4721			0.426105
$605$	2.29180			0.0931748
$606$	2.32624	−	6.09017i	0.0944970	−	0.247396i
$607$			14.4377i			0.586008i	0.956111	+	0.293004i	$0.0946549\pi$
$607$			14.4377i			0.586008i	−0.956111	+	0.293004i	$0.905345\pi$
$608$	−19.5066			−0.791096
$609$	24.9443	+	13.9443i	1.01079	+	0.565050i
$610$	−1.38197			−0.0559542
$611$			1.16718i			0.0472192i
$612$	−27.0344	−	24.1803i	−1.09280	−	0.977432i
$613$	3.47214			0.140238			0.0701191	−	0.997539i	$-0.477662\pi$
$613$	3.47214			0.140238			0.0701191	+	0.997539i	$0.477662\pi$
$614$	7.74265			0.312468
$615$	−2.61803	−	1.00000i	−0.105569	−	0.0403239i
$616$	1.90983	−	13.0902i	0.0769492	−	0.527418i
$617$			21.0902i			0.849058i	0.905414	+	0.424529i	$0.139560\pi$
$617$			21.0902i			0.849058i	−0.905414	+	0.424529i	$0.860440\pi$
$618$	−12.1803	−	4.65248i	−0.489965	−	0.187150i
$619$			6.97871i			0.280498i	0.990116	+	0.140249i	$0.0447903\pi$
$619$			6.97871i			0.280498i	−0.990116	+	0.140249i	$0.955210\pi$
$620$			5.85410i			0.235106i
$621$	4.61803	−	2.38197i	0.185315	−	0.0955850i
$622$		−	4.74265i		−	0.190163i
$623$	−1.18034	+	8.09017i	−0.0472893	+	0.324126i
$624$	0.167184	−	0.437694i	0.00669273	−	0.0175218i
$625$	22.8328			0.913313
$626$	−7.52786			−0.300874
$627$	12.5623	+	4.79837i	0.501690	+	0.191629i
$628$			26.6525i			1.06355i
$629$	−76.4853			−3.04967
$630$	−1.20163	−	1.43769i	−0.0478739	−	0.0572791i
$631$	−29.1803			−1.16165			−0.580825	−	0.814028i	$-0.697270\pi$
$631$	−29.1803			−1.16165			−0.580825	+	0.814028i	$0.697270\pi$
$632$			27.3607i			1.08835i
$633$	−4.85410	−	1.85410i	−0.192933	−	0.0736939i
$634$	1.00000			0.0397151
$635$	−6.41641			−0.254627
$636$	6.56231	−	17.1803i	0.260212	−	0.681245i
$637$	−0.291796	+	0.978714i	−0.0115614	+	0.0387781i
$638$			8.61803i			0.341191i
$639$	−20.6525	+	23.0902i	−0.816999	+	0.913433i
$640$		−	4.34752i		−	0.171851i
$641$		−	27.5623i		−	1.08865i	−0.838876	−	0.544323i	$-0.816787\pi$
$641$		−	27.5623i		−	1.08865i	0.838876	−	0.544323i	$-0.183213\pi$
$642$	9.38197	+	3.58359i	0.370277	+	0.141433i
$643$			18.7984i			0.741335i	0.928766	+	0.370668i	$0.120871\pi$
$643$			18.7984i			0.741335i	−0.928766	+	0.370668i	$0.879129\pi$
$644$	−4.23607	−	0.618034i	−0.166924	−	0.0243540i
$645$	3.32624	+	1.27051i	0.130970	+	0.0500263i
$646$	16.0344			0.630867
$647$	4.96556			0.195216			0.0976081	−	0.995225i	$-0.468881\pi$
$647$	4.96556			0.195216			0.0976081	+	0.995225i	$0.468881\pi$
$648$	20.0000	−	2.23607i	0.785674	−	0.0878410i
$649$			28.0902i			1.10264i
$650$	0.437694			0.0171678
$651$	37.8885	+	21.1803i	1.48497	+	0.830123i
$652$	−12.7984			−0.501223
$653$		−	35.5066i		−	1.38948i	−0.719261	−	0.694740i	$-0.755519\pi$
$653$		−	35.5066i		−	1.38948i	0.719261	−	0.694740i	$-0.244481\pi$
$654$	−3.09017	+	8.09017i	−0.120835	+	0.316351i
$655$	−2.02129			−0.0789782
$656$	−7.85410			−0.306651
$657$	7.52786	−	8.41641i	0.293690	−	0.328355i
$658$	12.9443	+	1.88854i	0.504620	+	0.0736231i
$659$			22.4164i			0.873219i	0.899651	+	0.436610i	$0.143821\pi$
$659$			22.4164i			0.873219i	−0.899651	+	0.436610i	$0.856179\pi$
$660$	−0.854102	+	2.23607i	−0.0332459	+	0.0870388i
$661$			33.9443i			1.32028i	0.751143	+	0.660140i	$0.229503\pi$
$661$			33.9443i			1.32028i	−0.751143	+	0.660140i	$0.770497\pi$
$662$			13.6393i			0.530107i
$663$	−0.673762	+	1.76393i	−0.0261668	+	0.0685054i
$664$		−	6.05573i		−	0.235008i
$665$	−3.47214	−	0.506578i	−0.134644	−	0.0196442i
$666$	12.6525	−	14.1459i	0.490273	−	0.548142i
$667$	6.23607			0.241462
$668$	5.14590			0.199101
$669$	−3.65248	+	9.56231i	−0.141213	+	0.369700i
$670$			1.97871i			0.0764444i
$671$	13.0902			0.505340
$672$	−22.4721	−	12.5623i	−0.866881	−	0.484601i
$673$	1.76393			0.0679946			0.0339973	−	0.999422i	$-0.489176\pi$
$673$	1.76393			0.0679946			0.0339973	+	0.999422i	$0.489176\pi$
$674$		−	14.4934i		−	0.558266i
$675$	−11.5623	−	22.4164i	−0.445033	−	0.862808i
$676$	21.0000			0.807692
$677$	−24.5066			−0.941864			−0.470932	−	0.882169i	$-0.656082\pi$
$677$	−24.5066			−0.941864			−0.470932	+	0.882169i	$0.656082\pi$
$678$	−13.7984	−	5.27051i	−0.529923	−	0.202413i
$679$	41.7426	+	6.09017i	1.60194	+	0.233719i
$680$			6.38197i			0.244737i
$681$	10.7984	+	4.12461i	0.413795	+	0.158055i
$682$			13.0902i			0.501249i
$683$			20.5967i			0.788113i	0.919086	+	0.394056i	$0.128929\pi$
$683$			20.5967i			0.788113i	−0.919086	+	0.394056i	$0.871071\pi$
$684$	11.2361	−	12.5623i	0.429622	−	0.480332i
$685$		−	3.72949i		−	0.142496i
$686$	10.3820	+	4.81966i	0.396385	+	0.184015i
$687$	13.6525	−	35.7426i	0.520874	−	1.36367i
$688$	9.97871			0.380435
$689$	−0.957428			−0.0364751
$690$	−0.381966	−	0.145898i	−0.0145412	−	0.00555424i
$691$			3.09017i			0.117556i	0.998271	+	0.0587778i	$0.0187203\pi$
$691$			3.09017i			0.117556i	−0.998271	+	0.0587778i	$0.981280\pi$
$692$	8.85410			0.336582
$693$	11.3820	+	13.6180i	0.432365	+	0.517306i
$694$	−0.506578			−0.0192294
$695$		−	4.61803i		−	0.175172i
$696$	22.5623	+	8.61803i	0.855222	+	0.326666i
$697$	31.6525			1.19892
$698$	15.5410			0.588236
$699$	18.1246	−	47.4508i	0.685536	−	1.79476i
$700$	−3.00000	+	20.5623i	−0.113389	+	0.777182i
$701$			46.6312i			1.76124i	0.473827	+	0.880618i	$0.342872\pi$
$701$			46.6312i			1.76124i	−0.473827	+	0.880618i	$0.657128\pi$
$702$	−0.214782	−	0.416408i	−0.00810641	−	0.0157163i
$703$		−	35.5410i		−	1.34045i
$704$			0.527864i			0.0198946i
$705$	−4.94427	−	1.88854i	−0.186212	−	0.0711267i
$706$		−	21.9230i		−	0.825082i
$707$	2.32624	−	15.9443i	0.0874872	−	0.599646i
$708$	32.8885	+	12.5623i	1.23603	+	0.472120i
$709$	12.4377			0.467107			0.233554	−	0.972344i	$-0.424965\pi$
$709$	12.4377			0.467107			0.233554	+	0.972344i	$0.424965\pi$
$710$	2.43769			0.0914850
$711$	−27.3607	−	24.4721i	−1.02611	−	0.917777i
$712$			6.90983i			0.258957i
$713$	9.47214			0.354734
$714$	18.4721	+	10.3262i	0.691302	+	0.386450i
$715$	0.124612			0.00466022
$716$		−	34.5066i		−	1.28957i
$717$	13.1803	−	34.5066i	0.492229	−	1.28867i
$718$	−8.70820			−0.324987
$719$	−22.2361			−0.829265			−0.414633	−	0.909989i	$-0.636090\pi$
$719$	−22.2361			−0.829265			−0.414633	+	0.909989i	$0.636090\pi$
$720$	1.58359	+	1.41641i	0.0590170	+	0.0527864i
$721$	−31.8885	−	4.65248i	−1.18759	−	0.173267i
$722$		−	4.29180i		−	0.159724i
$723$	−5.85410	+	15.3262i	−0.217716	+	0.569989i
$724$			10.8541i			0.403390i
$725$		−	30.2705i		−	1.12422i
$726$	2.29180	−	6.00000i	0.0850565	−	0.222681i
$727$			11.4721i			0.425478i	0.977109	+	0.212739i	$0.0682384\pi$
$727$			11.4721i			0.425478i	−0.977109	+	0.212739i	$0.931762\pi$
$728$	−0.124612	+	0.854102i	−0.00461842	+	0.0316551i
$729$	−15.6525	+	22.0000i	−0.579721	+	0.814815i
$730$	−0.888544			−0.0328865
$731$	−40.2148			−1.48740
$732$	5.85410	−	15.3262i	0.216374	−	0.566474i
$733$			6.36068i			0.234937i	0.993077	+	0.117469i	$0.0374779\pi$
$733$			6.36068i			0.234937i	−0.993077	+	0.117469i	$0.962522\pi$
$734$	6.96556			0.257103
$735$	−3.67376	−	2.81966i	−0.135509	−	0.104005i
$736$	−5.61803			−0.207083
$737$		−	18.7426i		−	0.690394i
$738$	−5.23607	+	5.85410i	−0.192742	+	0.215492i
$739$	−1.58359			−0.0582534			−0.0291267	−	0.999576i	$-0.509273\pi$
$739$	−1.58359			−0.0582534			−0.0291267	+	0.999576i	$0.509273\pi$
$740$	6.32624			0.232557
$741$	−0.819660	−	0.313082i	−0.0301110	−	0.0115014i
$742$	−1.54915	+	10.6180i	−0.0568711	+	0.389800i
$743$			5.14590i			0.188785i	0.995535	+	0.0943923i	$0.0300908\pi$
$743$			5.14590i			0.188785i	−0.995535	+	0.0943923i	$0.969909\pi$
$744$	34.2705	+	13.0902i	1.25642	+	0.479909i
$745$			2.18034i			0.0798815i
$746$			0.618034i			0.0226278i
$747$	6.05573	+	5.41641i	0.221568	+	0.198176i
$748$		−	27.0344i		−	0.988477i
$749$	24.5623	+	3.58359i	0.897487	+	0.130942i
$750$	−1.43769	+	3.76393i	−0.0524972	+	0.137439i
$751$	14.9656			0.546101			0.273050	−	0.962000i	$-0.411967\pi$
$751$	14.9656			0.546101			0.273050	+	0.962000i	$0.411967\pi$
$752$	−14.8328			−0.540897
$753$	4.00000	+	1.52786i	0.145768	+	0.0556785i
$754$		−	0.562306i		−	0.0204780i
$755$	2.47214			0.0899702
$756$	21.0344	−	7.23607i	0.765015	−	0.263173i
$757$	−17.0000			−0.617876			−0.308938	−	0.951082i	$-0.599973\pi$
$757$	−17.0000			−0.617876			−0.308938	+	0.951082i	$0.599973\pi$
$758$		−	9.59675i		−	0.348570i
$759$	3.61803	+	1.38197i	0.131326	+	0.0501622i
$760$	−2.96556			−0.107572
$761$	−22.0000			−0.797499			−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000			−0.797499			−0.398750	+	0.917060i	$0.630556\pi$
$762$	−6.41641	+	16.7984i	−0.232442	+	0.608541i
$763$	−3.09017	+	21.1803i	−0.111872	+	0.766780i
$764$		−	13.4164i		−	0.485389i
$765$	−6.38197	−	5.70820i	−0.230740	−	0.206381i
$766$		−	2.32624i		−	0.0840504i
$767$		−	1.83282i		−	0.0661791i
$768$	−10.6180	−	4.05573i	−0.383145	−	0.146348i
$769$		−	0.180340i		−	0.00650322i	−0.999995	−	0.00325161i	$-0.998965\pi$
$769$		−	0.180340i		−	0.00650322i	0.999995	−	0.00325161i	$-0.00103502\pi$
$770$	0.201626	−	1.38197i	0.00726610	−	0.0498026i
$771$	21.1246	+	8.06888i	0.760784	+	0.290594i
$772$	3.70820			0.133461
$773$	12.7082			0.457082			0.228541	−	0.973534i	$-0.426604\pi$
$773$	12.7082			0.457082			0.228541	+	0.973534i	$0.426604\pi$
$774$	6.65248	−	7.43769i	0.239118	−	0.267342i
$775$		−	45.9787i		−	1.65160i
$776$	35.6525			1.27985
$777$	22.8885	−	40.9443i	0.821122	−	1.46887i
$778$	−11.9230			−0.427460
$779$			14.7082i			0.526976i
$780$	0.0557281	−	0.145898i	0.00199539	−	0.00522399i
$781$	−23.0902			−0.826231
$782$	4.61803			0.165141
$783$	−28.7984	+	14.8541i	−1.02917	+	0.530842i
$784$	−12.4377	−	3.70820i	−0.444203	−	0.132436i
$785$			6.29180i			0.224564i
$786$	−2.02129	+	5.29180i	−0.0720969	+	0.188752i
$787$		−	19.5066i		−	0.695334i	−0.937618	−	0.347667i	$-0.886974\pi$
$787$		−	19.5066i		−	0.695334i	0.937618	−	0.347667i	$-0.113026\pi$
$788$			24.1246i			0.859404i
$789$	0.0344419	−	0.0901699i	0.00122616	−	0.00321014i
$790$			2.88854i			0.102770i
$791$	−36.1246	−	5.27051i	−1.28444	−	0.187398i
$792$	11.1803	+	10.0000i	0.397276	+	0.355335i
$793$	−0.854102			−0.0303301
$794$	−6.65248			−0.236088
$795$	1.54915	−	4.05573i	0.0549427	−	0.143842i
$796$			20.0344i			0.710102i
$797$	40.5410			1.43604			0.718018	−	0.696024i	$-0.245049\pi$
$797$	40.5410			1.43604			0.718018	+	0.696024i	$0.245049\pi$
$798$	−4.79837	+	8.58359i	−0.169861	+	0.303856i
$799$	59.7771			2.11476
$800$			27.2705i			0.964158i
$801$	−6.90983	−	6.18034i	−0.244147	−	0.218372i
$802$	11.3820			0.401911
$803$	8.41641			0.297009
$804$	−21.9443	−	8.38197i	−0.773915	−	0.295609i
$805$	−1.00000	−	0.145898i	−0.0352454	−	0.00514223i
$806$		−	0.854102i		−	0.0300845i
$807$	−6.70820	−	2.56231i	−0.236140	−	0.0901974i
$808$		−	13.6180i		−	0.479081i
$809$			6.03444i			0.212160i	0.994358	+	0.106080i	$0.0338299\pi$
$809$			6.03444i			0.212160i	−0.994358	+	0.106080i	$0.966170\pi$
$810$	2.11146	−	0.236068i	0.0741890	−	0.00829458i
$811$			9.06888i			0.318452i	0.987242	+	0.159226i	$0.0508998\pi$
$811$			9.06888i			0.318452i	−0.987242	+	0.159226i	$0.949100\pi$
$812$	26.4164	+	3.85410i	0.927034	+	0.135252i
$813$	−1.38197	+	3.61803i	−0.0484677	+	0.126890i
$814$	14.1459			0.495813
$815$	−3.02129			−0.105831
$816$	−22.4164	−	8.56231i	−0.784731	−	0.299741i
$817$		−	18.6869i		−	0.653772i
$818$	−15.1591			−0.530024
$819$	−0.742646	−	0.888544i	−0.0259501	−	0.0310482i
$820$	−2.61803			−0.0914257
$821$			3.81966i			0.133307i	0.997776	+	0.0666535i	$0.0212322\pi$
$821$			3.81966i			0.133307i	−0.997776	+	0.0666535i	$0.978768\pi$
$822$	−9.76393	−	3.72949i	−0.340556	−	0.130081i
$823$	−8.56231			−0.298463			−0.149232	−	0.988802i	$-0.547680\pi$
$823$	−8.56231			−0.298463			−0.149232	+	0.988802i	$0.547680\pi$
$824$	−27.2361			−0.948813
$825$	6.70820	−	17.5623i	0.233550	−	0.611441i
$826$	−20.3262	−	2.96556i	−0.707240	−	0.103185i
$827$		−	25.2148i		−	0.876804i	−0.898779	−	0.438402i	$-0.855545\pi$
$827$		−	25.2148i		−	0.876804i	0.898779	−	0.438402i	$-0.144455\pi$
$828$	3.23607	−	3.61803i	0.112461	−	0.125735i
$829$			1.00000i			0.0347314i	0.999849	+	0.0173657i	$0.00552796\pi$
$829$			1.00000i			0.0347314i	−0.999849	+	0.0173657i	$0.994472\pi$
$830$		−	0.639320i		−	0.0221911i
$831$	22.4164	+	8.56231i	0.777617	+	0.297023i
$832$		−	0.0344419i		−	0.00119406i
$833$	50.1246	+	14.9443i	1.73671	+	0.517788i
$834$	−12.0902	−	4.61803i	−0.418648	−	0.159909i
$835$	1.21478			0.0420393
$836$	12.5623			0.434476
$837$	−43.7426	+	22.5623i	−1.51197	+	0.779867i
$838$		−	0.124612i		−	0.00430464i
$839$	−4.14590			−0.143132			−0.0715661	−	0.997436i	$-0.522800\pi$
$839$	−4.14590			−0.143132			−0.0715661	+	0.997436i	$0.522800\pi$
$840$	−3.41641	−	1.90983i	−0.117877	−	0.0658954i
$841$	−9.88854			−0.340984
$842$			12.7852i			0.440608i
$843$	11.7082	−	30.6525i	0.403252	−	1.05573i
$844$	−4.85410			−0.167085
$845$	4.95743			0.170541
$846$	−9.88854	+	11.0557i	−0.339975	+	0.380104i
$847$	2.29180	−	15.7082i	0.0787470	−	0.539740i
$848$		−	12.1672i		−	0.417823i
$849$	9.76393	−	25.5623i	0.335097	−	0.877296i
$850$		−	22.4164i		−	0.768876i
$851$		−	10.2361i		−	0.350888i
$852$	−10.3262	+	27.0344i	−0.353771	+	0.926185i
$853$		−	36.6525i		−	1.25496i	−0.778634	−	0.627478i	$-0.784087\pi$
$853$		−	36.6525i		−	1.25496i	0.778634	−	0.627478i	$-0.215913\pi$
$854$	−1.38197	+	9.47214i	−0.0472899	+	0.324130i
$855$	2.65248	−	2.96556i	0.0907128	−	0.101420i
$856$	20.9787			0.717038
$857$	17.5279			0.598740			0.299370	−	0.954137i	$-0.403223\pi$
$857$	17.5279			0.598740			0.299370	+	0.954137i	$0.403223\pi$
$858$	0.124612	−	0.326238i	0.00425418	−	0.0111376i
$859$		−	29.5279i		−	1.00748i	−0.863856	−	0.503739i	$-0.831957\pi$
$859$		−	29.5279i		−	1.00748i	0.863856	−	0.503739i	$-0.168043\pi$
$860$	3.32624			0.113424
$861$	−9.47214	+	16.9443i	−0.322810	+	0.577459i
$862$	20.4508			0.696559
$863$			28.3607i			0.965409i	0.875783	+	0.482704i	$0.160345\pi$
$863$			28.3607i			0.965409i	−0.875783	+	0.482704i	$0.839655\pi$
$864$	25.9443	−	13.3820i	0.882642	−	0.455264i
$865$	2.09017			0.0710679
$866$	−6.47214			−0.219932
$867$	62.8328	+	24.0000i	2.13391	+	0.815083i
$868$	40.1246	+	5.85410i	1.36192	+	0.198701i
$869$		−	27.3607i		−	0.928147i
$870$	2.38197	+	0.909830i	0.0807562	+	0.0308461i
$871$			1.22291i			0.0414368i
$872$			18.0902i			0.612610i
$873$	−31.8885	+	35.6525i	−1.07926	+	1.20665i
$874$			2.14590i			0.0725861i
$875$	−1.43769	+	9.85410i	−0.0486029	+	0.333129i
$876$	3.76393	−	9.85410i	0.127171	−	0.332939i
$877$	−3.70820			−0.125217			−0.0626086	−	0.998038i	$-0.519942\pi$
$877$	−3.70820			−0.125217			−0.0626086	+	0.998038i	$0.519942\pi$
$878$	10.2148			0.344732
$879$	44.8328	+	17.1246i	1.51217	+	0.577599i
$880$			1.58359i			0.0533829i
$881$	−9.88854			−0.333154			−0.166577	−	0.986028i	$-0.553271\pi$
$881$	−9.88854			−0.333154			−0.166577	+	0.986028i	$0.553271\pi$
$882$	−11.0557	+	6.79837i	−0.372266	+	0.228913i
$883$	−13.1591			−0.442837			−0.221419	−	0.975179i	$-0.571069\pi$
$883$	−13.1591			−0.442837			−0.221419	+	0.975179i	$0.571069\pi$
$884$			1.76393i			0.0593275i
$885$	7.76393	+	2.96556i	0.260982	+	0.0996861i
$886$	−0.111456			−0.00374444
$887$	−31.0902			−1.04391			−0.521953	−	0.852974i	$-0.674796\pi$
$887$	−31.0902			−1.04391			−0.521953	+	0.852974i	$0.674796\pi$
$888$	14.1459	−	37.0344i	0.474705	−	1.24279i
$889$	−6.41641	+	43.9787i	−0.215199	+	1.47500i
$890$			0.729490i			0.0244526i
$891$	−20.0000	+	2.23607i	−0.670025	+	0.0749111i
$892$			9.56231i			0.320170i
$893$			27.7771i			0.929525i
$894$	5.70820	+	2.18034i	0.190911	+	0.0729215i
$895$		−	8.14590i		−	0.272287i
$896$	−29.7984	−	4.34752i	−0.995494	−	0.145241i
$897$	−0.236068	−	0.0901699i	−0.00788208	−	0.00301069i
$898$	13.6525			0.455589
$899$	−59.0689			−1.97006
$900$	−17.5623	−	15.7082i	−0.585410	−	0.523607i
$901$			49.0344i			1.63357i
$902$	−5.85410			−0.194920
$903$	12.0344	−	21.5279i	0.400481	−	0.716402i
$904$	−30.8541			−1.02619
$905$			2.56231i			0.0851739i
$906$	2.47214	−	6.47214i	0.0821312	−	0.215022i
$907$	25.0344			0.831255			0.415627	−	0.909535i	$-0.363562\pi$
$907$	25.0344			0.831255			0.415627	+	0.909535i	$0.363562\pi$
$908$	10.7984			0.358357
$909$	13.6180	+	12.1803i	0.451682	+	0.403996i
$910$	−0.0131556	+	0.0901699i	−0.000436104	+	0.00298910i
$911$		−	25.1246i		−	0.832416i	−0.909270	−	0.416208i	$-0.863359\pi$
$911$		−	25.1246i		−	0.832416i	0.909270	−	0.416208i	$-0.136641\pi$
$912$	3.97871	−	10.4164i	0.131748	−	0.344922i
$913$			6.05573i			0.200415i
$914$			2.81966i			0.0932661i
$915$	1.38197	−	3.61803i	0.0456864	−	0.119609i
$916$		−	35.7426i		−	1.18097i
$917$	−2.02129	+	13.8541i	−0.0667488	+	0.457503i
$918$	−21.3262	+	11.0000i	−0.703871	+	0.363054i
$919$	−45.6525			−1.50594			−0.752968	−	0.658057i	$-0.771379\pi$
$919$	−45.6525			−1.50594			−0.752968	+	0.658057i	$0.771379\pi$
$920$	−0.854102			−0.0281589
$921$	−7.74265	+	20.2705i	−0.255129	+	0.667936i
$922$		−	22.0557i		−	0.726367i
$923$	1.50658			0.0495896
$924$	14.4721	+	8.09017i	0.476098	+	0.266147i
$925$	−49.6869			−1.63370
$926$			15.7426i			0.517335i
$927$	24.3607	−	27.2361i	0.800110	−	0.894550i
$928$	35.0344			1.15006
$929$	−39.3951			−1.29251			−0.646256	−	0.763121i	$-0.723666\pi$
$929$	−39.3951			−1.29251			−0.646256	+	0.763121i	$0.723666\pi$
$930$	3.61803	+	1.38197i	0.118640	+	0.0453165i
$931$	−6.94427	+	23.2918i	−0.227589	+	0.763358i
$932$		−	47.4508i		−	1.55430i
$933$	12.4164	+	4.74265i	0.406495	+	0.155267i
$934$			12.2574i			0.401073i
$935$		−	6.38197i		−	0.208713i
$936$	−0.729490	−	0.652476i	−0.0238441	−	0.0213268i
$937$			25.2918i			0.826247i	0.910675	+	0.413123i	$0.135562\pi$
$937$			25.2918i			0.826247i	−0.910675	+	0.413123i	$0.864438\pi$
$938$	13.5623	+	1.97871i	0.442825	+	0.0646073i
$939$	7.52786	−	19.7082i	0.245663	−	0.643153i
$940$	−4.94427			−0.161264
$941$	−17.5279			−0.571392			−0.285696	−	0.958320i	$-0.592225\pi$
$941$	−17.5279			−0.571392			−0.285696	+	0.958320i	$0.592225\pi$
$942$	16.4721	+	6.29180i	0.536691	+	0.204998i
$943$			4.23607i			0.137945i
$944$	23.2918			0.758083
$945$	4.96556	−	1.70820i	0.161530	−	0.0555679i
$946$	7.43769			0.241820
$947$		−	48.8328i		−	1.58685i	−0.608666	−	0.793427i	$-0.708295\pi$
$947$		−	48.8328i		−	1.58685i	0.608666	−	0.793427i	$-0.291705\pi$
$948$	−32.0344	−	12.2361i	−1.04043	−	0.397409i
$949$	−0.549150			−0.0178262
$950$	10.4164			0.337953
$951$	−1.00000	+	2.61803i	−0.0324272	+	0.0848956i
$952$	43.7426	+	6.38197i	1.41771	+	0.206841i
$953$		−	26.0344i		−	0.843338i	−0.906750	−	0.421669i	$-0.861444\pi$
$953$		−	26.0344i		−	0.843338i	0.906750	−	0.421669i	$-0.138556\pi$
$954$	−9.06888	−	8.11146i	−0.293616	−	0.262618i
$955$		−	3.16718i		−	0.102488i
$956$		−	34.5066i		−	1.11602i
$957$	−22.5623	−	8.61803i	−0.729336	−	0.278581i
$958$		−	3.49342i		−	0.112867i
$959$	−25.5623	−	3.72949i	−0.825450	−	0.120432i
$960$	0.145898	+	0.0557281i	0.00470884	+	0.00179862i
$961$	−58.7214			−1.89424
$962$	−0.922986			−0.0297583
$963$	−18.7639	+	20.9787i	−0.604659	+	0.676030i
$964$			15.3262i			0.493625i
$965$	0.875388			0.0281797
$966$	−1.38197	+	2.47214i	−0.0444640	+	0.0795397i
$967$	−19.8885			−0.639572			−0.319786	−	0.947490i	$-0.603611\pi$
$967$	−19.8885			−0.639572			−0.319786	+	0.947490i	$0.603611\pi$
$968$		−	13.4164i		−	0.431220i
$969$	−16.0344	+	41.9787i	−0.515100	+	1.34855i
$970$	3.76393			0.120853
$971$	−35.7426			−1.14704			−0.573518	−	0.819193i	$-0.694422\pi$
$971$	−35.7426			−1.14704			−0.573518	+	0.819193i	$0.694422\pi$
$972$	−6.32624	+	24.4164i	−0.202914	+	0.783157i
$973$	−31.6525	−	4.61803i	−1.01473	−	0.148047i
$974$		−	0.798374i		−	0.0255815i
$975$	−0.437694	+	1.14590i	−0.0140174	+	0.0366981i
$976$		−	10.8541i		−	0.347431i
$977$			38.9787i			1.24704i	0.781808	+	0.623520i	$0.214298\pi$
$977$			38.9787i			1.24704i	−0.781808	+	0.623520i	$0.785702\pi$
$978$	−3.02129	+	7.90983i	−0.0966101	+	0.252928i
$979$		−	6.90983i		−	0.220839i
$980$	−4.14590	−	1.23607i	−0.132436	−	0.0394847i
$981$	−18.0902	−	16.1803i	−0.577575	−	0.516598i
$982$	20.4508			0.652613
$983$	−25.1803			−0.803128			−0.401564	−	0.915831i	$-0.631533\pi$
$983$	−25.1803			−0.803128			−0.401564	+	0.915831i	$0.631533\pi$
$984$	−5.85410	+	15.3262i	−0.186622	+	0.488583i
$985$			5.69505i			0.181459i
$986$	−28.7984			−0.917127
$987$	−17.8885	+	32.0000i	−0.569399	+	1.01857i
$988$	−0.819660			−0.0260769
$989$		−	5.38197i		−	0.171137i
$990$	1.18034	+	1.05573i	0.0375137	+	0.0335532i
$991$	26.7984			0.851278			0.425639	−	0.904893i	$-0.360049\pi$
$991$	26.7984			0.851278			0.425639	+	0.904893i	$0.360049\pi$
$992$	53.2148			1.68957
$993$	−35.7082	−	13.6393i	−1.13317	−	0.432831i
$994$	2.43769	−	16.7082i	0.0773190	−	0.529952i
$995$			4.72949i			0.149935i
$996$	7.09017	+	2.70820i	0.224661	+	0.0858127i
$997$			35.9443i			1.13837i	0.822211	+	0.569183i	$0.192741\pi$
$997$			35.9443i			1.13837i	−0.822211	+	0.569183i	$0.807259\pi$
$998$		−	1.58359i		−	0.0501277i
$999$	24.3820	+	47.2705i	0.771411	+	1.49557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.d.b.461.2	yes	4
3.2	odd	2		483.2.d.a.461.3	yes	4
7.6	odd	2		483.2.d.a.461.2	✓	4
21.20	even	2	inner	483.2.d.b.461.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.d.a.461.2	✓	4	7.6	odd	2
483.2.d.a.461.3	yes	4	3.2	odd	2
483.2.d.b.461.2	yes	4	1.1	even	1	trivial
483.2.d.b.461.3	yes	4	21.20	even	2	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.618034i q^{2} +(1.61803 + 0.618034i) q^{3} +1.61803 q^{4} +0.381966 q^{5} +(0.381966 - 1.00000i) q^{6} +(0.381966 - 2.61803i) q^{7} -2.23607i q^{8} +(2.23607 + 2.00000i) q^{9} +O(q^{10})\)	\(q-0.618034i q^{2} +(1.61803 + 0.618034i) q^{3} +1.61803 q^{4} +0.381966 q^{5} +(0.381966 - 1.00000i) q^{6} +(0.381966 - 2.61803i) q^{7} -2.23607i q^{8} +(2.23607 + 2.00000i) q^{9} -0.236068i q^{10} +2.23607i q^{11} +(2.61803 + 1.00000i) q^{12} -0.145898i q^{13} +(-1.61803 - 0.236068i) q^{14} +(0.618034 + 0.236068i) q^{15} +1.85410 q^{16} -7.47214 q^{17} +(1.23607 - 1.38197i) q^{18} -3.47214i q^{19} +0.618034 q^{20} +(2.23607 - 4.00000i) q^{21} +1.38197 q^{22} -1.00000i q^{23} +(1.38197 - 3.61803i) q^{24} -4.85410 q^{25} -0.0901699 q^{26} +(2.38197 + 4.61803i) q^{27} +(0.618034 - 4.23607i) q^{28} +6.23607i q^{29} +(0.145898 - 0.381966i) q^{30} +9.47214i q^{31} -5.61803i q^{32} +(-1.38197 + 3.61803i) q^{33} +4.61803i q^{34} +(0.145898 - 1.00000i) q^{35} +(3.61803 + 3.23607i) q^{36} +10.2361 q^{37} -2.14590 q^{38} +(0.0901699 - 0.236068i) q^{39} -0.854102i q^{40} -4.23607 q^{41} +(-2.47214 - 1.38197i) q^{42} +5.38197 q^{43} +3.61803i q^{44} +(0.854102 + 0.763932i) q^{45} -0.618034 q^{46} -8.00000 q^{47} +(3.00000 + 1.14590i) q^{48} +(-6.70820 - 2.00000i) q^{49} +3.00000i q^{50} +(-12.0902 - 4.61803i) q^{51} -0.236068i q^{52} -6.56231i q^{53} +(2.85410 - 1.47214i) q^{54} +0.854102i q^{55} +(-5.85410 - 0.854102i) q^{56} +(2.14590 - 5.61803i) q^{57} +3.85410 q^{58} +12.5623 q^{59} +(1.00000 + 0.381966i) q^{60} -5.85410i q^{61} +5.85410 q^{62} +(6.09017 - 5.09017i) q^{63} +0.236068 q^{64} -0.0557281i q^{65} +(2.23607 + 0.854102i) q^{66} -8.38197 q^{67} -12.0902 q^{68} +(0.618034 - 1.61803i) q^{69} +(-0.618034 - 0.0901699i) q^{70} +10.3262i q^{71} +(4.47214 - 5.00000i) q^{72} -3.76393i q^{73} -6.32624i q^{74} +(-7.85410 - 3.00000i) q^{75} -5.61803i q^{76} +(5.85410 + 0.854102i) q^{77} +(-0.145898 - 0.0557281i) q^{78} -12.2361 q^{79} +0.708204 q^{80} +(1.00000 + 8.94427i) q^{81} +2.61803i q^{82} +2.70820 q^{83} +(3.61803 - 6.47214i) q^{84} -2.85410 q^{85} -3.32624i q^{86} +(-3.85410 + 10.0902i) q^{87} +5.00000 q^{88} -3.09017 q^{89} +(0.472136 - 0.527864i) q^{90} +(-0.381966 - 0.0557281i) q^{91} -1.61803i q^{92} +(-5.85410 + 15.3262i) q^{93} +4.94427i q^{94} -1.32624i q^{95} +(3.47214 - 9.09017i) q^{96} +15.9443i q^{97} +(-1.23607 + 4.14590i) q^{98} +(-4.47214 + 5.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7	\( 4 q + 2 q^{3} + 2 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{12} - 2 q^{14} - 2 q^{15} - 6 q^{16} - 12 q^{17} - 4 q^{18} - 2 q^{20} + 10 q^{22} + 10 q^{24} - 6 q^{25} + 22 q^{26} + 14 q^{27} - 2 q^{28} + 14 q^{30} - 10 q^{33} + 14 q^{35} + 10 q^{36} + 32 q^{37} - 22 q^{38} - 22 q^{39} - 8 q^{41} + 8 q^{42} + 26 q^{43} - 10 q^{45} + 2 q^{46} - 32 q^{47} + 12 q^{48} - 26 q^{51} - 2 q^{54} - 10 q^{56} + 22 q^{57} + 2 q^{58} + 10 q^{59} + 4 q^{60} + 10 q^{62} + 2 q^{63} - 8 q^{64} - 38 q^{67} - 26 q^{68} - 2 q^{69} + 2 q^{70} - 18 q^{75} + 10 q^{77} - 14 q^{78} - 40 q^{79} - 24 q^{80} + 4 q^{81} - 16 q^{83} + 10 q^{84} + 2 q^{85} - 2 q^{87} + 20 q^{88} + 10 q^{89} - 16 q^{90} - 6 q^{91} - 10 q^{93} - 4 q^{96} + 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^12 - 2 * q^14 - 2 * q^15 - 6 * q^16 - 12 * q^17 - 4 * q^18 - 2 * q^20 + 10 * q^22 + 10 * q^24 - 6 * q^25 + 22 * q^26 + 14 * q^27 - 2 * q^28 + 14 * q^30 - 10 * q^33 + 14 * q^35 + 10 * q^36 + 32 * q^37 - 22 * q^38 - 22 * q^39 - 8 * q^41 + 8 * q^42 + 26 * q^43 - 10 * q^45 + 2 * q^46 - 32 * q^47 + 12 * q^48 - 26 * q^51 - 2 * q^54 - 10 * q^56 + 22 * q^57 + 2 * q^58 + 10 * q^59 + 4 * q^60 + 10 * q^62 + 2 * q^63 - 8 * q^64 - 38 * q^67 - 26 * q^68 - 2 * q^69 + 2 * q^70 - 18 * q^75 + 10 * q^77 - 14 * q^78 - 40 * q^79 - 24 * q^80 + 4 * q^81 - 16 * q^83 + 10 * q^84 + 2 * q^85 - 2 * q^87 + 20 * q^88 + 10 * q^89 - 16 * q^90 - 6 * q^91 - 10 * q^93 - 4 * q^96 + 4 * q^98

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