LMFDB - Embedded newform 75.2.g.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(16,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("75.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.1
Root			$1.40799 + 0.132563i$ of defining polynomial
Character	$\chi$	$=$	75.31
Dual form			75.2.g.b.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.346820 - 1.06740i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.598970 - 0.435177i) q^{4} +(0.407987 - 2.19853i) q^{5} +(0.907987 + 0.659691i) q^{6} +1.11373 q^{7} +(-2.48822 - 1.80780i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.346820 - 1.06740i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.598970 - 0.435177i) q^{4} +(0.407987 - 2.19853i) q^{5} +(0.907987 + 0.659691i) q^{6} +1.11373 q^{7} +(-2.48822 - 1.80780i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-2.48822 + 0.327009i) q^{10} +(1.13412 + 3.49045i) q^{11} +(-0.228786 + 0.704131i) q^{12} +(-1.25215 + 3.85372i) q^{13} +(-0.386266 - 1.18880i) q^{14} +(0.962197 + 2.01846i) q^{15} +(-0.609110 + 1.87465i) q^{16} +(-1.71700 - 1.24748i) q^{17} -1.12233 q^{18} +(3.28513 + 2.38678i) q^{19} +(-0.712379 - 1.49440i) q^{20} +(-0.901030 + 0.654637i) q^{21} +(3.33238 - 2.42112i) q^{22} +(1.90799 + 5.87218i) q^{23} +3.07561 q^{24} +(-4.66709 - 1.79395i) q^{25} +4.54774 q^{26} +(0.309017 + 0.951057i) q^{27} +(0.667093 - 0.484672i) q^{28} +(1.82808 - 1.32818i) q^{29} +(1.82080 - 1.72709i) q^{30} +(-8.13227 - 5.90844i) q^{31} -3.93896 q^{32} +(-2.96915 - 2.15722i) q^{33} +(-0.736068 + 2.26538i) q^{34} +(0.454389 - 2.44858i) q^{35} +(-0.228786 - 0.704131i) q^{36} +(2.27817 - 7.01149i) q^{37} +(1.40831 - 4.33434i) q^{38} +(-1.25215 - 3.85372i) q^{39} +(-4.98966 + 4.73287i) q^{40} +(-2.30902 + 7.10642i) q^{41} +(1.01126 + 0.734721i) q^{42} +9.24998 q^{43} +(2.19826 + 1.59713i) q^{44} +(-1.96485 - 1.06740i) q^{45} +(5.60625 - 4.07318i) q^{46} +(2.53032 - 1.83839i) q^{47} +(-0.609110 - 1.87465i) q^{48} -5.75960 q^{49} +(-0.296220 + 5.60384i) q^{50} +2.12233 q^{51} +(0.927051 + 2.85317i) q^{52} +(2.83934 - 2.06290i) q^{53} +(0.907987 - 0.659691i) q^{54} +(8.13657 - 1.06933i) q^{55} +(-2.77121 - 2.01340i) q^{56} -4.06064 q^{57} +(-2.05172 - 1.49066i) q^{58} +(-2.03760 + 6.27109i) q^{59} +(1.45471 + 0.790270i) q^{60} +(-2.81332 - 8.65850i) q^{61} +(-3.48625 + 10.7296i) q^{62} +(0.344163 - 1.05922i) q^{63} +(2.58433 + 7.95375i) q^{64} +(7.96167 + 4.32516i) q^{65} +(-1.27286 + 3.91745i) q^{66} +(-2.12499 - 1.54390i) q^{67} -1.57131 q^{68} +(-4.99517 - 3.62921i) q^{69} +(-2.77121 + 0.364201i) q^{70} +(-0.534620 + 0.388424i) q^{71} +(-2.48822 + 1.80780i) q^{72} +(2.31003 + 7.10955i) q^{73} -8.27420 q^{74} +(4.83021 - 1.29192i) q^{75} +3.00637 q^{76} +(1.26310 + 3.88743i) q^{77} +(-3.67920 + 2.67310i) q^{78} +(-6.90667 + 5.01799i) q^{79} +(3.87297 + 2.10398i) q^{80} +(-0.809017 - 0.587785i) q^{81} +8.38623 q^{82} +(-9.92170 - 7.20854i) q^{83} +(-0.254807 + 0.784215i) q^{84} +(-3.44313 + 3.26594i) q^{85} +(-3.20808 - 9.87345i) q^{86} +(-0.698265 + 2.14904i) q^{87} +(3.48809 - 10.7352i) q^{88} +(-4.72429 - 14.5399i) q^{89} +(-0.457897 + 2.46749i) q^{90} +(-1.39456 + 4.29202i) q^{91} +(3.69826 + 2.68695i) q^{92} +10.0520 q^{93} +(-2.83986 - 2.06328i) q^{94} +(6.58771 - 6.24868i) q^{95} +(3.18668 - 2.31526i) q^{96} +(-10.9217 + 7.93508i) q^{97} +(1.99754 + 6.14781i) q^{98} +3.67008 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q - q^2 - 2 * q^3 + q^4 - 5 * q^5 - q^6 + 4 * q^7 - 2 * q^9	\( 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9} + 16 q^{11} - 9 q^{12} - 8 q^{13} - 8 q^{14} + 5 q^{15} - 17 q^{16} - q^{17} + 4 q^{18} - 5 q^{19} - 10 q^{20} - 11 q^{21} + 13 q^{22} + 7 q^{23} + 30 q^{24} - 15 q^{25} + 6 q^{26} - 2 q^{27} - 17 q^{28} + 5 q^{29} + 30 q^{30} - 19 q^{31} + 24 q^{32} - 9 q^{33} + 12 q^{34} - 10 q^{35} - 9 q^{36} - q^{37} - 10 q^{38} - 8 q^{39} + 25 q^{40} - 14 q^{41} - 8 q^{42} + 32 q^{43} - 3 q^{44} - 5 q^{45} + 16 q^{46} - q^{47} - 17 q^{48} + 16 q^{49} + 10 q^{50} + 4 q^{51} - 6 q^{52} - 3 q^{53} - q^{54} + 15 q^{55} - 15 q^{56} + 10 q^{57} + 5 q^{58} + 30 q^{59} - 15 q^{60} - 14 q^{61} - 17 q^{62} + 9 q^{63} - 44 q^{64} + 25 q^{65} - 7 q^{66} + 4 q^{67} - 22 q^{68} - 8 q^{69} - 15 q^{70} + 21 q^{71} + 2 q^{73} - 38 q^{74} - 15 q^{75} + 80 q^{76} - 37 q^{77} - 14 q^{78} - 30 q^{79} - 50 q^{80} - 2 q^{81} - 12 q^{82} + 2 q^{83} + 8 q^{84} - 30 q^{85} - 34 q^{86} + 15 q^{87} + 70 q^{88} - 5 q^{90} + 21 q^{91} + 9 q^{92} + 46 q^{93} - 33 q^{94} + 65 q^{95} + 34 q^{96} - 6 q^{97} + 73 q^{98} - 14 q^{99}+O(q^{100}) \) 8 * q - q^2 - 2 * q^3 + q^4 - 5 * q^5 - q^6 + 4 * q^7 - 2 * q^9 + 16 * q^11 - 9 * q^12 - 8 * q^13 - 8 * q^14 + 5 * q^15 - 17 * q^16 - q^17 + 4 * q^18 - 5 * q^19 - 10 * q^20 - 11 * q^21 + 13 * q^22 + 7 * q^23 + 30 * q^24 - 15 * q^25 + 6 * q^26 - 2 * q^27 - 17 * q^28 + 5 * q^29 + 30 * q^30 - 19 * q^31 + 24 * q^32 - 9 * q^33 + 12 * q^34 - 10 * q^35 - 9 * q^36 - q^37 - 10 * q^38 - 8 * q^39 + 25 * q^40 - 14 * q^41 - 8 * q^42 + 32 * q^43 - 3 * q^44 - 5 * q^45 + 16 * q^46 - q^47 - 17 * q^48 + 16 * q^49 + 10 * q^50 + 4 * q^51 - 6 * q^52 - 3 * q^53 - q^54 + 15 * q^55 - 15 * q^56 + 10 * q^57 + 5 * q^58 + 30 * q^59 - 15 * q^60 - 14 * q^61 - 17 * q^62 + 9 * q^63 - 44 * q^64 + 25 * q^65 - 7 * q^66 + 4 * q^67 - 22 * q^68 - 8 * q^69 - 15 * q^70 + 21 * q^71 + 2 * q^73 - 38 * q^74 - 15 * q^75 + 80 * q^76 - 37 * q^77 - 14 * q^78 - 30 * q^79 - 50 * q^80 - 2 * q^81 - 12 * q^82 + 2 * q^83 + 8 * q^84 - 30 * q^85 - 34 * q^86 + 15 * q^87 + 70 * q^88 - 5 * q^90 + 21 * q^91 + 9 * q^92 + 46 * q^93 - 33 * q^94 + 65 * q^95 + 34 * q^96 - 6 * q^97 + 73 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.346820	−	1.06740i	−0.245239	−	0.754768i	−0.995597	−	0.0937362i	$-0.970119\pi$
$2$	−0.346820	−	1.06740i	−0.245239	−	0.754768i	0.750358	−	0.661031i	$-0.229881\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	0.598970	−	0.435177i	0.299485	−	0.217589i
$5$	0.407987	−	2.19853i	0.182457	−	0.983214i
$5$	0.407987	−	2.19853i	0.182457	−	0.983214i
$6$	0.907987	+	0.659691i	0.370684	+	0.269318i
$7$	1.11373			0.420952			0.210476	−	0.977599i	$-0.432499\pi$
$7$	1.11373			0.420952			0.210476	+	0.977599i	$0.432499\pi$
$8$	−2.48822	−	1.80780i	−0.879718	−	0.639152i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−2.48822	+	0.327009i	−0.786844	+	0.103409i
$11$	1.13412	+	3.49045i	0.341949	+	1.05241i	0.963197	+	0.268796i	$0.0866258\pi$
$11$	1.13412	+	3.49045i	0.341949	+	1.05241i	−0.621248	+	0.783614i	$0.713374\pi$
$12$	−0.228786	+	0.704131i	−0.0660449	+	0.203265i
$13$	−1.25215	+	3.85372i	−0.347284	+	1.06883i	0.613066	+	0.790032i	$0.289936\pi$
$13$	−1.25215	+	3.85372i	−0.347284	+	1.06883i	−0.960350	+	0.278798i	$0.910064\pi$
$14$	−0.386266	−	1.18880i	−0.103234	−	0.317721i
$15$	0.962197	+	2.01846i	0.248438	+	0.521164i
$16$	−0.609110	+	1.87465i	−0.152277	+	0.468662i
$17$	−1.71700	−	1.24748i	−0.416435	−	0.302557i	0.359767	−	0.933042i	$-0.382856\pi$
$17$	−1.71700	−	1.24748i	−0.416435	−	0.302557i	−0.776202	+	0.630485i	$0.782856\pi$
$18$	−1.12233			−0.264537
$19$	3.28513	+	2.38678i	0.753660	+	0.547566i	0.896959	−	0.442113i	$-0.145771\pi$
$19$	3.28513	+	2.38678i	0.753660	+	0.547566i	−0.143299	+	0.989679i	$0.545771\pi$
$20$	−0.712379	−	1.49440i	−0.159293	−	0.334158i
$21$	−0.901030	+	0.654637i	−0.196621	+	0.142853i
$22$	3.33238	−	2.42112i	0.710466	−	0.516184i
$23$	1.90799	+	5.87218i	0.397843	+	1.22443i	0.926725	+	0.375739i	$0.122611\pi$
$23$	1.90799	+	5.87218i	0.397843	+	1.22443i	−0.528883	+	0.848695i	$0.677389\pi$
$24$	3.07561			0.627806
$25$	−4.66709	−	1.79395i	−0.933419	−	0.358789i
$26$	4.54774			0.891886
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	0.667093	−	0.484672i	0.126069	−	0.0915943i
$29$	1.82808	−	1.32818i	0.339466	−	0.246637i	−0.404970	−	0.914330i	$-0.632718\pi$
$29$	1.82808	−	1.32818i	0.339466	−	0.246637i	0.744437	+	0.667693i	$0.232718\pi$
$30$	1.82080	−	1.72709i	0.332431	−	0.315323i
$31$	−8.13227	−	5.90844i	−1.46060	−	1.06119i	−0.983206	−	0.182498i	$-0.941582\pi$
$31$	−8.13227	−	5.90844i	−1.46060	−	1.06119i	−0.477393	−	0.878690i	$-0.658418\pi$
$32$	−3.93896			−0.696316
$33$	−2.96915	−	2.15722i	−0.516863	−	0.375523i
$34$	−0.736068	+	2.26538i	−0.126235	+	0.388510i
$35$	0.454389	−	2.44858i	0.0768058	−	0.413886i
$36$	−0.228786	−	0.704131i	−0.0381310	−	0.117355i
$37$	2.27817	−	7.01149i	0.374529	−	1.15268i	−0.569267	−	0.822153i	$-0.692773\pi$
$37$	2.27817	−	7.01149i	0.374529	−	1.15268i	0.943796	−	0.330529i	$-0.107227\pi$
$38$	1.40831	−	4.33434i	0.228458	−	0.703123i
$39$	−1.25215	−	3.85372i	−0.200504	−	0.617089i
$40$	−4.98966	+	4.73287i	−0.788934	+	0.748333i
$41$	−2.30902	+	7.10642i	−0.360608	+	1.10984i	0.592078	+	0.805881i	$0.298308\pi$
$41$	−2.30902	+	7.10642i	−0.360608	+	1.10984i	−0.952686	+	0.303956i	$0.901692\pi$
$42$	1.01126	+	0.734721i	0.156040	+	0.113370i
$43$	9.24998			1.41061			0.705304	−	0.708905i	$-0.250810\pi$
$43$	9.24998			1.41061			0.705304	+	0.708905i	$0.250810\pi$
$44$	2.19826	+	1.59713i	0.331401	+	0.240777i
$45$	−1.96485	−	1.06740i	−0.292903	−	0.159119i
$46$	5.60625	−	4.07318i	0.826597	−	0.600558i
$47$	2.53032	−	1.83839i	0.369085	−	0.268156i	−0.387746	−	0.921766i	$-0.626746\pi$
$47$	2.53032	−	1.83839i	0.369085	−	0.268156i	0.756831	+	0.653610i	$0.226746\pi$
$48$	−0.609110	−	1.87465i	−0.0879174	−	0.270582i
$49$	−5.75960			−0.822799
$50$	−0.296220	+	5.60384i	−0.0418918	+	0.792503i
$51$	2.12233			0.297186
$52$	0.927051	+	2.85317i	0.128559	+	0.395663i
$53$	2.83934	−	2.06290i	0.390013	−	0.283361i	−0.375448	−	0.926844i	$-0.622511\pi$
$53$	2.83934	−	2.06290i	0.390013	−	0.283361i	0.765461	+	0.643483i	$0.222511\pi$
$54$	0.907987	−	0.659691i	0.123561	−	0.0897726i
$55$	8.13657	−	1.06933i	1.09714	−	0.144189i
$56$	−2.77121	−	2.01340i	−0.370319	−	0.269053i
$57$	−4.06064			−0.537845
$58$	−2.05172	−	1.49066i	−0.269404	−	0.195733i
$59$	−2.03760	+	6.27109i	−0.265273	+	0.816427i	0.726357	+	0.687317i	$0.241212\pi$
$59$	−2.03760	+	6.27109i	−0.265273	+	0.816427i	−0.991630	+	0.129110i	$0.958788\pi$
$60$	1.45471	+	0.790270i	0.187803	+	0.102023i
$61$	−2.81332	−	8.65850i	−0.360208	−	1.10861i	−0.952928	−	0.303198i	$-0.901946\pi$
$61$	−2.81332	−	8.65850i	−0.360208	−	1.10861i	0.592719	−	0.805409i	$-0.298054\pi$
$62$	−3.48625	+	10.7296i	−0.442754	+	1.36266i
$63$	0.344163	−	1.05922i	0.0433604	−	0.133450i
$64$	2.58433	+	7.95375i	0.323041	+	0.994219i
$65$	7.96167	+	4.32516i	0.987524	+	0.536470i
$66$	−1.27286	+	3.91745i	−0.156678	+	0.482205i
$67$	−2.12499	−	1.54390i	−0.259609	−	0.188617i	0.450366	−	0.892844i	$-0.351294\pi$
$67$	−2.12499	−	1.54390i	−0.259609	−	0.188617i	−0.709975	+	0.704227i	$0.751294\pi$
$68$	−1.57131			−0.190549
$69$	−4.99517	−	3.62921i	−0.601348	−	0.436905i
$70$	−2.77121	+	0.364201i	−0.331223	+	0.0435304i
$71$	−0.534620	+	0.388424i	−0.0634477	+	0.0460975i	−0.619057	−	0.785346i	$-0.712485\pi$
$71$	−0.534620	+	0.388424i	−0.0634477	+	0.0460975i	0.555609	+	0.831443i	$0.312485\pi$
$72$	−2.48822	+	1.80780i	−0.293239	+	0.213051i
$73$	2.31003	+	7.10955i	0.270369	+	0.832110i	0.990408	+	0.138176i	$0.0441239\pi$
$73$	2.31003	+	7.10955i	0.270369	+	0.832110i	−0.720039	+	0.693934i	$0.755876\pi$
$74$	−8.27420			−0.961856
$75$	4.83021	−	1.29192i	0.557745	−	0.149178i
$76$	3.00637			0.344854
$77$	1.26310	+	3.88743i	0.143944	+	0.443014i
$78$	−3.67920	+	2.67310i	−0.416587	+	0.302668i
$79$	−6.90667	+	5.01799i	−0.777061	+	0.564568i	−0.904096	−	0.427330i	$-0.859454\pi$
$79$	−6.90667	+	5.01799i	−0.777061	+	0.564568i	0.127034	+	0.991898i	$0.459454\pi$
$80$	3.87297	+	2.10398i	0.433011	+	0.235232i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	8.38623			0.926104
$83$	−9.92170	−	7.20854i	−1.08905	−	0.791240i	−0.109810	−	0.993953i	$-0.535024\pi$
$83$	−9.92170	−	7.20854i	−1.08905	−	0.791240i	−0.979238	+	0.202713i	$0.935024\pi$
$84$	−0.254807	+	0.784215i	−0.0278017	+	0.0855649i
$85$	−3.44313	+	3.26594i	−0.373460	+	0.354240i
$86$	−3.20808	−	9.87345i	−0.345936	−	1.06468i
$87$	−0.698265	+	2.14904i	−0.0748618	+	0.230401i
$88$	3.48809	−	10.7352i	0.371832	−	1.14438i
$89$	−4.72429	−	14.5399i	−0.500773	−	1.54122i	−0.807762	−	0.589509i	$-0.799321\pi$
$89$	−4.72429	−	14.5399i	−0.500773	−	1.54122i	0.306989	−	0.951713i	$-0.400679\pi$
$90$	−0.457897	+	2.46749i	−0.0482666	+	0.260096i
$91$	−1.39456	+	4.29202i	−0.146190	+	0.449926i
$92$	3.69826	+	2.68695i	0.385571	+	0.280134i
$93$	10.0520			1.04235
$94$	−2.83986	−	2.06328i	−0.292910	−	0.212811i
$95$	6.58771	−	6.24868i	0.675885	−	0.641101i
$96$	3.18668	−	2.31526i	0.325240	−	0.236300i
$97$	−10.9217	+	7.93508i	−1.10893	+	0.805685i	−0.982495	−	0.186290i	$-0.940354\pi$
$97$	−10.9217	+	7.93508i	−1.10893	+	0.805685i	−0.126436	+	0.991975i	$0.540354\pi$
$98$	1.99754	+	6.14781i	0.201782	+	0.621022i
$99$	3.67008			0.368856
$100$	−3.57613	+	0.956493i	−0.357613	+	0.0956493i
$101$	7.22642			0.719055			0.359528	−	0.933134i	$-0.382938\pi$
$101$	7.22642			0.719055			0.359528	+	0.933134i	$0.382938\pi$
$102$	−0.736068	−	2.26538i	−0.0728816	−	0.224306i
$103$	−4.26957	+	3.10203i	−0.420693	+	0.305652i	−0.777917	−	0.628367i	$-0.783723\pi$
$103$	−4.26957	+	3.10203i	−0.420693	+	0.305652i	0.357223	+	0.934019i	$0.383723\pi$
$104$	10.0824	−	7.32526i	0.988657	−	0.718301i
$105$	1.07163	+	2.24803i	0.104581	+	0.219385i
$106$	−3.18668	−	2.31526i	−0.309518	−	0.224878i
$107$	5.46682			0.528498			0.264249	−	0.964455i	$-0.414876\pi$
$107$	5.46682			0.528498			0.264249	+	0.964455i	$0.414876\pi$
$108$	0.598970	+	0.435177i	0.0576359	+	0.0418749i
$109$	3.50410	−	10.7845i	0.335632	−	1.03297i	−0.630778	−	0.775963i	$-0.717264\pi$
$109$	3.50410	−	10.7845i	0.335632	−	1.03297i	0.966410	−	0.257005i	$-0.0827358\pi$
$110$	−3.96334	−	8.31413i	−0.377889	−	0.792721i
$111$	2.27817	+	7.01149i	0.216234	+	0.665501i
$112$	−0.678387	+	2.08786i	−0.0641015	+	0.197284i
$113$	1.49416	−	4.59855i	0.140559	−	0.432595i	−0.855854	−	0.517217i	$-0.826968\pi$
$113$	1.49416	−	4.59855i	0.140559	−	0.432595i	0.996413	+	0.0846215i	$0.0269681\pi$
$114$	1.40831	+	4.33434i	0.131900	+	0.405948i
$115$	13.6886	−	1.79900i	1.27647	−	0.167758i
$116$	0.516973	−	1.59108i	0.0479997	−	0.147728i
$117$	3.27817	+	2.38173i	0.303067	+	0.220191i
$118$	7.40046			0.681268
$119$	−1.91229	−	1.38936i	−0.175299	−	0.127362i
$120$	1.25481	−	6.76182i	0.114548	−	0.617267i
$121$	−1.99783	+	1.45151i	−0.181621	+	0.131955i
$122$	−8.26639	+	6.00588i	−0.748404	+	0.543747i
$123$	−2.30902	−	7.10642i	−0.208197	−	0.640765i
$124$	−7.44220			−0.668330
$125$	−5.84816	+	9.52885i	−0.523075	+	0.852286i
$126$	−1.24998			−0.111357
$127$	0.234728	+	0.722418i	0.0208287	+	0.0641043i	0.960931	−	0.276789i	$-0.0892704\pi$
$127$	0.234728	+	0.722418i	0.0208287	+	0.0641043i	−0.940102	+	0.340894i	$0.889270\pi$
$128$	1.22019	−	0.886518i	0.107850	−	0.0783578i
$129$	−7.48339	+	5.43700i	−0.658876	+	0.478701i
$130$	1.85542	−	9.99836i	0.162731	−	0.876914i
$131$	−11.8562	−	8.61406i	−1.03588	−	0.752614i	−0.0664061	−	0.997793i	$-0.521153\pi$
$131$	−11.8562	−	8.61406i	−1.03588	−	0.752614i	−0.969478	+	0.245179i	$0.921153\pi$
$132$	−2.71720			−0.236502
$133$	3.65876	+	2.65824i	0.317255	+	0.230499i
$134$	−0.910969	+	2.80367i	−0.0786958	+	0.242201i
$135$	2.21700	−	0.291365i	0.190809	−	0.0250767i
$136$	2.01710	+	6.20799i	0.172965	+	0.532330i
$137$	3.79825	−	11.6898i	0.324506	−	0.998728i	−0.647157	−	0.762357i	$-0.724042\pi$
$137$	3.79825	−	11.6898i	0.324506	−	0.998728i	0.971663	−	0.236371i	$-0.0759580\pi$
$138$	−2.14140	+	6.59054i	−0.182288	+	0.561024i
$139$	4.55306	+	14.0129i	0.386185	+	1.18856i	0.935617	+	0.353017i	$0.114844\pi$
$139$	4.55306	+	14.0129i	0.386185	+	1.18856i	−0.549432	+	0.835539i	$0.685156\pi$
$140$	−0.793401	−	1.66437i	−0.0670547	−	0.140665i
$141$	−0.966496	+	2.97457i	−0.0813937	+	0.250504i
$142$	0.600022	+	0.435941i	0.0503527	+	0.0365834i
$143$	−14.8713			−1.24360
$144$	1.59467	+	1.15860i	0.132889	+	0.0965497i
$145$	−2.17421	−	4.56098i	−0.180558	−	0.378768i
$146$	6.78758	−	4.93147i	0.561744	−	0.408131i
$147$	4.65961	−	3.38541i	0.384318	−	0.279224i
$148$	−1.68668	−	5.19108i	−0.138645	−	0.426704i
$149$	15.6498			1.28208			0.641041	−	0.767507i	$-0.278503\pi$
$149$	15.6498			1.28208			0.641041	+	0.767507i	$0.278503\pi$
$150$	−3.05421	−	4.70772i	−0.249375	−	0.384384i
$151$	3.95819			0.322113			0.161056	−	0.986945i	$-0.448510\pi$
$151$	3.95819			0.322113			0.161056	+	0.986945i	$0.448510\pi$
$152$	−3.85929	−	11.8777i	−0.313030	−	0.963407i
$153$	−1.71700	+	1.24748i	−0.138812	+	0.100852i
$154$	3.71139	−	2.69648i	0.299072	−	0.217289i
$155$	−16.3078	+	15.4685i	−1.30987	+	1.24246i
$156$	−2.42705	−	1.76336i	−0.194320	−	0.141181i
$157$	−4.50061			−0.359188			−0.179594	−	0.983741i	$-0.557478\pi$
$157$	−4.50061			−0.359188			−0.179594	+	0.983741i	$0.557478\pi$
$158$	7.75159	+	5.63186i	0.616683	+	0.448047i
$159$	−1.08453	+	3.33784i	−0.0860089	+	0.264708i
$160$	−1.60704	+	8.65993i	−0.127048	+	0.684627i
$161$	2.12499	+	6.54005i	0.167473	+	0.515428i
$162$	−0.346820	+	1.06740i	−0.0272488	+	0.0838631i
$163$	−0.758292	+	2.33378i	−0.0593940	+	0.182796i	−0.976352	−	0.216189i	$-0.930637\pi$
$163$	−0.758292	+	2.33378i	−0.0593940	+	0.182796i	0.916958	+	0.398985i	$0.130637\pi$
$164$	1.70952	+	5.26137i	0.133491	+	0.410844i
$165$	−5.95409	+	5.64767i	−0.463525	+	0.439670i
$166$	−4.25337	+	13.0905i	−0.330125	+	1.01602i
$167$	2.47824	+	1.80055i	0.191772	+	0.139331i	0.679528	−	0.733649i	$-0.262184\pi$
$167$	2.47824	+	1.80055i	0.191772	+	0.139331i	−0.487756	+	0.872980i	$0.662184\pi$
$168$	3.42541			0.264276
$169$	−2.76606	−	2.00966i	−0.212774	−	0.154589i
$170$	4.68022	+	2.54252i	0.358956	+	0.195002i
$171$	3.28513	−	2.38678i	0.251220	−	0.182522i
$172$	5.54046	−	4.02538i	0.422456	−	0.306932i
$173$	3.47942	+	10.7085i	0.264535	+	0.814156i	0.991800	+	0.127799i	$0.0407912\pi$
$173$	3.47942	+	10.7085i	0.264535	+	0.814156i	−0.727265	+	0.686357i	$0.759209\pi$
$174$	2.53606			0.192258
$175$	−5.19790	−	1.99798i	−0.392925	−	0.151033i
$176$	−7.23416			−0.545296
$177$	−2.03760	−	6.27109i	−0.153156	−	0.471364i
$178$	−13.8814	+	10.0854i	−1.04046	+	0.755935i
$179$	−8.13657	+	5.91157i	−0.608156	+	0.441851i	−0.848764	−	0.528771i	$-0.822653\pi$
$179$	−8.13657	+	5.91157i	−0.608156	+	0.441851i	0.240609	+	0.970622i	$0.422653\pi$
$180$	−1.64140	+	0.215717i	−0.122343	+	0.0160786i
$181$	15.7503	+	11.4433i	1.17071	+	0.850571i	0.991094	−	0.133165i	$-0.0425141\pi$
$181$	15.7503	+	11.4433i	1.17071	+	0.850571i	0.179617	+	0.983737i	$0.442514\pi$
$182$	5.06498			0.375441
$183$	7.36536	+	5.35125i	0.544463	+	0.395575i
$184$	5.86822	−	18.0605i	0.432611	−	1.33144i
$185$	−14.4855	−	7.86923i	−1.06500	−	0.578557i
$186$	−3.48625	−	10.7296i	−0.255624	−	0.786731i
$187$	2.40697	−	7.40790i	0.176015	−	0.541719i
$188$	0.715563	−	2.20227i	0.0521878	−	0.160617i
$189$	0.344163	+	1.05922i	0.0250342	+	0.0770472i
$190$	−8.95461	−	4.86457i	−0.649636	−	0.352913i
$191$	−3.58739	+	11.0408i	−0.259574	+	0.798888i	0.733320	+	0.679884i	$0.237970\pi$
$191$	−3.58739	+	11.0408i	−0.259574	+	0.798888i	−0.992894	+	0.119003i	$0.962030\pi$
$192$	−6.76586	−	4.91569i	−0.488284	−	0.354759i
$193$	−3.38156			−0.243410			−0.121705	−	0.992566i	$-0.538836\pi$
$193$	−3.38156			−0.243410			−0.121705	+	0.992566i	$0.538836\pi$
$194$	12.2578	+	8.90581i	0.880058	+	0.639400i
$195$	−8.98339	+	1.18062i	−0.643314	+	0.0845463i
$196$	−3.44982	+	2.50644i	−0.246416	+	0.179032i
$197$	14.2291	−	10.3380i	1.01378	−	0.736554i	0.0487811	−	0.998809i	$-0.484466\pi$
$197$	14.2291	−	10.3380i	1.01378	−	0.736554i	0.964998	+	0.262256i	$0.0844663\pi$
$198$	−1.27286	−	3.91745i	−0.0904579	−	0.278401i
$199$	20.0102			1.41849			0.709244	−	0.704963i	$-0.249037\pi$
$199$	20.0102			1.41849			0.709244	+	0.704963i	$0.249037\pi$
$200$	8.36966	+	12.9009i	0.591824	+	0.912230i
$201$	2.62663			0.185268
$202$	−2.50627	−	7.71350i	−0.176340	−	0.542720i
$203$	2.03600	−	1.47924i	0.142899	−	0.103822i
$204$	1.27121	−	0.923591i	0.0890028	−	0.0646643i
$205$	14.6817	+	7.97578i	1.02541	+	0.557052i
$206$	4.79188	+	3.48151i	0.333866	+	0.242568i
$207$	6.17438			0.429149
$208$	−6.46167	−	4.69468i	−0.448036	−	0.325517i
$209$	−4.60524	+	14.1735i	−0.318551	+	0.980399i
$210$	2.02789	−	1.92352i	0.139937	−	0.132736i
$211$	0.754807	+	2.32306i	0.0519631	+	0.159926i	0.973671	−	0.227960i	$-0.0732055\pi$
$211$	0.754807	+	2.32306i	0.0519631	+	0.159926i	−0.921707	+	0.387886i	$0.873206\pi$
$212$	0.802951	−	2.47123i	0.0551469	−	0.169725i
$213$	0.204207	−	0.628483i	0.0139920	−	0.0430630i
$214$	−1.89600	−	5.83530i	−0.129608	−	0.398893i
$215$	3.77387	−	20.3364i	0.257376	−	1.38693i
$216$	0.950415	−	2.92508i	0.0646675	−	0.199026i
$217$	−9.05719	−	6.58044i	−0.614842	−	0.446709i
$218$	−12.7267			−0.861961
$219$	−6.04774	−	4.39394i	−0.408669	−	0.296915i
$220$	4.40821	−	4.18135i	0.297202	−	0.281906i
$221$	6.95737	−	5.05483i	0.468003	−	0.340024i
$222$	6.69397	−	4.86345i	0.449270	−	0.326413i
$223$	−7.92223	−	24.3821i	−0.530511	−	1.63275i	−0.753153	−	0.657846i	$-0.771468\pi$
$223$	−7.92223	−	24.3821i	−0.530511	−	1.63275i	0.222641	−	0.974900i	$-0.428532\pi$
$224$	−4.38695			−0.293116
$225$	−3.14835	+	3.88431i	−0.209890	+	0.258954i
$226$	−5.42671			−0.360979
$227$	2.02819	+	6.24212i	0.134616	+	0.414304i	0.995530	−	0.0944455i	$-0.0301078\pi$
$227$	2.02819	+	6.24212i	0.134616	+	0.414304i	−0.860914	+	0.508750i	$0.830108\pi$
$228$	−2.43220	+	1.76710i	−0.161076	+	0.117029i
$229$	6.44293	−	4.68106i	0.425761	−	0.309333i	−0.354191	−	0.935173i	$-0.615244\pi$
$229$	6.44293	−	4.68106i	0.425761	−	0.309333i	0.779952	+	0.625840i	$0.215244\pi$
$230$	−6.66774	−	13.9873i	−0.439658	−	0.922297i
$231$	−3.30685	−	2.40257i	−0.217575	−	0.158077i
$232$	−6.94974			−0.456273
$233$	7.62181	+	5.53757i	0.499321	+	0.362778i	0.808758	−	0.588142i	$-0.200140\pi$
$233$	7.62181	+	5.53757i	0.499321	+	0.362778i	−0.309436	+	0.950920i	$0.600140\pi$
$234$	1.40533	−	4.32516i	0.0918693	−	0.282745i
$235$	−3.00941	−	6.31303i	−0.196312	−	0.411817i
$236$	1.50857	+	4.64291i	0.0981998	+	0.302228i
$237$	2.63811	−	8.11928i	0.171364	−	0.527404i
$238$	−0.819784	+	2.52304i	−0.0531387	+	0.163544i
$239$	−3.46814	−	10.6738i	−0.224335	−	0.690433i	−0.998358	−	0.0572756i	$-0.981759\pi$
$239$	−3.46814	−	10.6738i	−0.224335	−	0.690433i	0.774023	−	0.633157i	$-0.218241\pi$
$240$	−4.36998	+	0.574317i	−0.282081	+	0.0370720i
$241$	7.00879	−	21.5708i	0.451476	−	1.38950i	−0.423748	−	0.905780i	$-0.639286\pi$
$241$	7.00879	−	21.5708i	0.451476	−	1.38950i	0.875223	−	0.483719i	$-0.160714\pi$
$242$	2.24223	+	1.62908i	0.144136	+	0.104721i
$243$	1.00000			0.0641500
$244$	−5.45307	−	3.96189i	−0.349097	−	0.253634i
$245$	−2.34984	+	12.6627i	−0.150126	+	0.808988i
$246$	−6.78460	+	4.92930i	−0.432570	+	0.314281i
$247$	−13.3115	+	9.67135i	−0.846989	+	0.615373i
$248$	9.55361	+	29.4030i	0.606655	+	1.86709i
$249$	12.2639			0.777193
$250$	12.1994	+	2.93754i	0.771557	+	0.185787i
$251$	−6.76819			−0.427205			−0.213602	−	0.976921i	$-0.568520\pi$
$251$	−6.76819			−0.427205			−0.213602	+	0.976921i	$0.568520\pi$
$252$	−0.254807	−	0.784215i	−0.0160513	−	0.0494009i
$253$	−18.3327	+	13.3195i	−1.15257	+	0.837387i
$254$	0.689703	−	0.501098i	0.0432758	−	0.0314417i
$255$	0.865884	−	4.66602i	0.0542238	−	0.292198i
$256$	12.1623	+	8.83640i	0.760142	+	0.552275i
$257$	−14.7934			−0.922786			−0.461393	−	0.887196i	$-0.652650\pi$
$257$	−14.7934			−0.922786			−0.461393	+	0.887196i	$0.652650\pi$
$258$	8.39886	+	6.10213i	0.522890	+	0.379902i
$259$	2.53728	−	7.80894i	0.157659	−	0.485224i
$260$	6.65101	−	0.874096i	0.412478	−	0.0542092i
$261$	−0.698265	−	2.14904i	−0.0432215	−	0.133022i
$262$	−5.08269	+	15.6429i	−0.314009	+	0.966422i
$263$	6.17070	−	18.9915i	0.380502	−	1.17106i	−0.559189	−	0.829040i	$-0.688887\pi$
$263$	6.17070	−	18.9915i	0.380502	−	1.17106i	0.939691	−	0.342024i	$-0.111113\pi$
$264$	3.48809	+	10.7352i	0.214677	+	0.660709i
$265$	−3.37694	−	7.08401i	−0.207444	−	0.435167i
$266$	1.56849	−	4.82730i	0.0961700	−	0.295981i
$267$	12.3683	+	8.98613i	0.756930	+	0.549942i
$268$	−1.94467			−0.118790
$269$	8.28280	+	6.01780i	0.505011	+	0.366912i	0.810928	−	0.585146i	$-0.198963\pi$
$269$	8.28280	+	6.01780i	0.505011	+	0.366912i	−0.305917	+	0.952058i	$0.598963\pi$
$270$	−1.07991	−	2.26538i	−0.0657210	−	0.137867i
$271$	−9.95701	+	7.23419i	−0.604845	+	0.439446i	−0.847595	−	0.530643i	$-0.821950\pi$
$271$	−9.95701	+	7.23419i	−0.604845	+	0.439446i	0.242750	+	0.970089i	$0.421950\pi$
$272$	3.38442	−	2.45893i	0.205211	−	0.149094i
$273$	−1.39456	−	4.29202i	−0.0844028	−	0.259765i
$274$	−13.7950			−0.833389
$275$	0.968651	−	18.3248i	0.0584118	−	1.10503i
$276$	−4.57131			−0.275160
$277$	9.75011	+	30.0077i	0.585827	+	1.80299i	0.595923	+	0.803041i	$0.296786\pi$
$277$	9.75011	+	30.0077i	0.585827	+	1.80299i	−0.0100963	+	0.999949i	$0.503214\pi$
$278$	13.3783	−	9.71989i	0.802376	−	0.582960i
$279$	−8.13227	+	5.90844i	−0.486866	+	0.353729i
$280$	−5.55716	+	5.27116i	−0.332104	+	0.315012i
$281$	17.2417	+	12.5268i	1.02855	+	0.747288i	0.968019	−	0.250878i	$-0.0807192\pi$
$281$	17.2417	+	12.5268i	1.02855	+	0.747288i	0.0605353	+	0.998166i	$0.480719\pi$
$282$	3.51026			0.209033
$283$	0.699317	+	0.508083i	0.0415701	+	0.0302024i	0.608376	−	0.793649i	$-0.291821\pi$
$283$	0.699317	+	0.508083i	0.0415701	+	0.0302024i	−0.566806	+	0.823851i	$0.691821\pi$
$284$	−0.151188	+	0.465309i	−0.00897135	+	0.0276110i
$285$	−1.65669	+	8.92745i	−0.0981337	+	0.528817i
$286$	5.15767	+	15.8737i	0.304979	+	0.938629i
$287$	−2.57163	+	7.91467i	−0.151799	+	0.467188i
$288$	−1.21720	+	3.74617i	−0.0717245	+	0.220745i
$289$	−3.86138	−	11.8841i	−0.227140	−	0.699066i
$290$	−4.11434	+	3.90260i	−0.241602	+	0.229168i
$291$	4.17172	−	12.8392i	0.244550	−	0.752649i
$292$	4.47755	+	3.25313i	0.262029	+	0.190375i
$293$	3.17701			0.185603			0.0928014	−	0.995685i	$-0.470418\pi$
$293$	3.17701			0.185603			0.0928014	+	0.995685i	$0.470418\pi$
$294$	−5.22964	−	3.79955i	−0.304999	−	0.221594i
$295$	12.9559	+	7.03826i	0.754321	+	0.409783i
$296$	−18.3439	+	13.3276i	−1.06622	+	0.774653i
$297$	−2.96915	+	2.15722i	−0.172288	+	0.125174i
$298$	−5.42766	−	16.7046i	−0.314416	−	0.967673i
$299$	−25.0188			−1.44688
$300$	2.33094	−	2.87582i	0.134577	−	0.166035i
$301$	10.3020			0.593799
$302$	−1.37278	−	4.22498i	−0.0789945	−	0.243120i
$303$	−5.84629	+	4.24758i	−0.335861	+	0.244017i
$304$	−6.47538	+	4.70464i	−0.371389	+	0.269830i
$305$	−20.1838	+	2.65262i	−1.15572	+	0.151888i
$306$	1.92705	+	1.40008i	0.110162	+	0.0800375i
$307$	−0.507986			−0.0289923			−0.0144961	−	0.999895i	$-0.504614\pi$
$307$	−0.507986			−0.0289923			−0.0144961	+	0.999895i	$0.504614\pi$
$308$	2.44828	+	1.77878i	0.139504	+	0.101356i
$309$	1.63083	−	5.01918i	0.0927747	−	0.285531i
$310$	22.1670	+	12.0422i	1.25900	+	0.683949i
$311$	−4.52519	−	13.9271i	−0.256600	−	0.789734i	−0.993510	−	0.113743i	$-0.963716\pi$
$311$	−4.52519	−	13.9271i	−0.256600	−	0.789734i	0.736910	−	0.675991i	$-0.236284\pi$
$312$	−3.85112	+	11.8525i	−0.218027	+	0.671017i
$313$	−4.62171	+	14.2241i	−0.261234	+	0.803996i	0.731303	+	0.682053i	$0.238913\pi$
$313$	−4.62171	+	14.2241i	−0.261234	+	0.803996i	−0.992537	+	0.121943i	$0.961087\pi$
$314$	1.56090	+	4.80397i	0.0880869	+	0.271103i
$315$	−2.18833	−	1.18880i	−0.123298	−	0.0669815i
$316$	−1.95317	+	6.01125i	−0.109875	+	0.338159i
$317$	−14.6586	−	10.6501i	−0.823310	−	0.598170i	0.0943487	−	0.995539i	$-0.469923\pi$
$317$	−14.6586	−	10.6501i	−0.823310	−	0.598170i	−0.917659	+	0.397369i	$0.869923\pi$
$318$	3.93896			0.220886
$319$	6.70920	+	4.87452i	0.375643	+	0.272921i
$320$	18.5409	−	2.43671i	1.03647	−	0.136216i
$321$	−4.42275	+	3.21332i	−0.246854	+	0.179350i
$322$	6.24388	−	4.53644i	0.347958	−	0.252806i
$323$	−2.66312	−	8.19624i	−0.148180	−	0.456051i
$324$	−0.740367			−0.0411315
$325$	12.7573	−	15.7394i	0.707646	−	0.873064i
$326$	2.75408			0.152534
$327$	3.50410	+	10.7845i	0.193777	+	0.596385i
$328$	18.5923	−	13.5081i	1.02659	−	0.745860i
$329$	2.81811	−	2.04747i	0.155367	−	0.112881i
$330$	8.09333	+	4.39668i	0.445523	+	0.242029i
$331$	−21.3188	−	15.4890i	−1.17178	−	0.851351i	−0.180563	−	0.983563i	$-0.557792\pi$
$331$	−21.3188	−	15.4890i	−1.17178	−	0.851351i	−0.991221	+	0.132212i	$0.957792\pi$
$332$	−9.07979			−0.498318
$333$	−5.96433	−	4.33334i	−0.326843	−	0.237465i
$334$	1.06241	−	3.26975i	0.0581322	−	0.178913i
$335$	−4.26127	+	4.04197i	−0.232818	+	0.220837i
$336$	−0.678387	−	2.08786i	−0.0370090	−	0.113902i
$337$	−3.30488	+	10.1714i	−0.180028	+	0.554070i	−0.999827	−	0.0185811i	$-0.994085\pi$
$337$	−3.30488	+	10.1714i	−0.180028	+	0.554070i	0.819799	+	0.572651i	$0.194085\pi$
$338$	−1.18579	+	3.64949i	−0.0644986	+	0.198506i
$339$	1.49416	+	4.59855i	0.0811516	+	0.249759i
$340$	−0.641073	+	3.45457i	−0.0347670	+	0.187350i
$341$	11.4002	−	35.0861i	0.617354	−	1.90002i
$342$	−3.68701	−	2.67877i	−0.199371	−	0.144851i
$343$	−14.2108			−0.767311
$344$	−23.0160	−	16.7221i	−1.24094	−	0.901594i
$345$	−10.0169	+	9.50139i	−0.539292	+	0.511537i
$346$	10.2236	−	7.42788i	0.549624	−	0.399325i
$347$	−13.0850	+	9.50682i	−0.702441	+	0.510353i	−0.880726	−	0.473626i	$-0.842945\pi$
$347$	−13.0850	+	9.50682i	−0.702441	+	0.510353i	0.178286	+	0.983979i	$0.442945\pi$
$348$	0.516973	+	1.59108i	0.0277126	+	0.0852907i
$349$	15.2383			0.815688			0.407844	−	0.913052i	$-0.366281\pi$
$349$	15.2383			0.815688			0.407844	+	0.913052i	$0.366281\pi$
$350$	−0.329910	+	6.24119i	−0.0176344	+	0.333606i
$351$	−4.05204			−0.216282
$352$	−4.46723	−	13.7487i	−0.238104	−	0.732810i
$353$	23.8970	−	17.3622i	1.27191	−	0.924097i	0.272633	−	0.962118i	$-0.412106\pi$
$353$	23.8970	−	17.3622i	1.27191	−	0.924097i	0.999277	+	0.0380214i	$0.0121055\pi$
$354$	−5.98710	+	4.34988i	−0.318211	+	0.231194i
$355$	0.635845	+	1.33385i	0.0337472	+	0.0707935i
$356$	−9.15712	−	6.65304i	−0.485326	−	0.352610i
$357$	2.36372			0.125101
$358$	9.13195	+	6.63475i	0.482638	+	0.350657i
$359$	−4.06875	+	12.5223i	−0.214740	+	0.660903i	0.784431	+	0.620216i	$0.212955\pi$
$359$	−4.06875	+	12.5223i	−0.214740	+	0.660903i	−0.999172	+	0.0406876i	$0.987045\pi$
$360$	2.95934	+	6.20799i	0.155971	+	0.327190i
$361$	−0.776002	−	2.38829i	−0.0408422	−	0.125699i
$362$	6.75205	−	20.7807i	0.354880	−	1.09221i
$363$	0.763104	−	2.34859i	0.0400526	−	0.123269i
$364$	1.03249	+	3.17767i	0.0541171	+	0.166555i
$365$	16.5730	−	2.17808i	0.867472	−	0.114006i
$366$	3.15748	−	9.71772i	0.165044	−	0.507953i
$367$	3.14622	+	2.28586i	0.164232	+	0.119321i	0.666865	−	0.745178i	$-0.267636\pi$
$367$	3.14622	+	2.28586i	0.164232	+	0.119321i	−0.502634	+	0.864499i	$0.667636\pi$
$368$	−12.1704			−0.634428
$369$	6.04508	+	4.39201i	0.314695	+	0.228639i
$370$	−3.37576	+	18.1911i	−0.175498	+	0.945710i
$371$	3.16227	−	2.29752i	0.164177	−	0.119281i
$372$	6.02087	−	4.37442i	0.312168	−	0.226803i
$373$	−2.51641	−	7.74470i	−0.130295	−	0.401006i	0.864534	−	0.502575i	$-0.167614\pi$
$373$	−2.51641	−	7.74470i	−0.130295	−	0.401006i	−0.994829	+	0.101569i	$0.967614\pi$
$374$	−8.74200			−0.452038
$375$	−0.869658	−	11.1465i	−0.0449089	−	0.575601i
$376$	−9.61941			−0.496083
$377$	2.82940	+	8.70799i	0.145721	+	0.448484i
$378$	1.01126	−	0.734721i	0.0520134	−	0.0377900i
$379$	−8.01509	+	5.82330i	−0.411708	+	0.299123i	−0.774293	−	0.632828i	$-0.781894\pi$
$379$	−8.01509	+	5.82330i	−0.411708	+	0.299123i	0.362585	+	0.931951i	$0.381894\pi$
$380$	1.22656	−	6.60960i	0.0629211	−	0.339065i
$381$	−0.614526	−	0.446479i	−0.0314831	−	0.0228738i
$382$	13.0292			0.666632
$383$	4.22481	+	3.06951i	0.215878	+	0.156844i	0.690469	−	0.723362i	$-0.257404\pi$
$383$	4.22481	+	3.06951i	0.215878	+	0.156844i	−0.474591	+	0.880206i	$0.657404\pi$
$384$	−0.466070	+	1.43442i	−0.0237840	+	0.0731997i
$385$	9.06198	−	1.19095i	0.461841	−	0.0606966i
$386$	1.17279	+	3.60949i	0.0596937	+	0.183718i
$387$	2.85840	−	8.79726i	0.145301	−	0.447190i
$388$	−3.08860	+	9.50575i	−0.156800	+	0.482581i
$389$	−1.15255	−	3.54719i	−0.0584367	−	0.179850i	0.917577	−	0.397557i	$-0.130142\pi$
$389$	−1.15255	−	3.54719i	−0.0584367	−	0.179850i	−0.976014	+	0.217708i	$0.930142\pi$
$390$	4.37582	+	9.17943i	0.221578	+	0.464819i
$391$	4.04938	−	12.4627i	0.204786	−	0.630267i
$392$	14.3311	+	10.4122i	0.723831	+	0.525894i
$393$	14.6551			0.739253
$394$	−15.9698	−	11.6027i	−0.804545	−	0.584536i
$395$	8.21438	+	17.2318i	0.413310	+	0.867027i
$396$	2.19826	−	1.59713i	0.110467	−	0.0802589i
$397$	−3.24870	+	2.36032i	−0.163048	+	0.118461i	−0.666317	−	0.745668i	$-0.732130\pi$
$397$	−3.24870	+	2.36032i	−0.163048	+	0.118461i	0.503270	+	0.864130i	$0.332130\pi$
$398$	−6.93995	−	21.3590i	−0.347868	−	1.07063i
$399$	−4.52248			−0.226407
$400$	6.20579	−	7.65645i	0.310289	−	0.382822i
$401$	−24.9890			−1.24789			−0.623945	−	0.781468i	$-0.714471\pi$
$401$	−24.9890			−1.24789			−0.623945	+	0.781468i	$0.714471\pi$
$402$	−0.910969	−	2.80367i	−0.0454350	−	0.139835i
$403$	32.9523	−	23.9413i	1.64147	−	1.19260i
$404$	4.32841	−	3.14477i	0.215346	−	0.156458i
$405$	−1.62233	+	1.53884i	−0.0806144	+	0.0764657i
$406$	−2.28507	−	1.66020i	−0.113406	−	0.0823943i
$407$	27.0570			1.34116
$408$	−5.28083	−	3.83675i	−0.261440	−	0.189947i
$409$	−7.84186	+	24.1348i	−0.387755	+	1.19339i	0.546707	+	0.837324i	$0.315881\pi$
$409$	−7.84186	+	24.1348i	−0.387755	+	1.19339i	−0.934462	+	0.356063i	$0.884119\pi$
$410$	3.42147	−	18.4374i	0.168974	−	0.910558i
$411$	3.79825	+	11.6898i	0.187354	+	0.576616i
$412$	−1.20741	+	3.71604i	−0.0594850	+	0.183076i
$413$	−2.26935	+	6.98433i	−0.111667	+	0.343677i
$414$	−2.14140	−	6.59054i	−0.105244	−	0.323908i
$415$	−19.8961	+	18.8722i	−0.976663	+	0.926400i
$416$	4.93216	−	15.1796i	0.241819	−	0.744243i
$417$	−11.9201	−	8.66043i	−0.583728	−	0.424103i
$418$	16.7260			0.818094
$419$	24.9354	+	18.1166i	1.21817	+	0.885056i	0.995947	−	0.0899392i	$-0.0286673\pi$
$419$	24.9354	+	18.1166i	1.21817	+	0.885056i	0.222227	+	0.974995i	$0.428667\pi$
$420$	1.62017	+	0.880151i	0.0790560	+	0.0429470i
$421$	−6.91425	+	5.02350i	−0.336980	+	0.244830i	−0.743387	−	0.668862i	$-0.766782\pi$
$421$	−6.91425	+	5.02350i	−0.336980	+	0.244830i	0.406406	+	0.913692i	$0.366782\pi$
$422$	2.21785	−	1.61137i	0.107963	−	0.0784401i
$423$	−0.966496	−	2.97457i	−0.0469927	−	0.144629i
$424$	−10.7942			−0.524212
$425$	5.77551	+	8.90230i	0.280154	+	0.431825i
$426$	−0.741668			−0.0359339
$427$	−3.13329	−	9.64327i	−0.151630	−	0.466670i
$428$	3.27446	−	2.37904i	0.158277	−	0.114995i
$429$	12.0311	−	8.74113i	0.580869	−	0.422026i
$430$	−23.0160	+	3.02483i	−1.10993	+	0.145870i
$431$	21.3431	+	15.5067i	1.02806	+	0.746929i	0.967919	−	0.251261i	$-0.0808452\pi$
$431$	21.3431	+	15.5067i	1.02806	+	0.746929i	0.0601403	+	0.998190i	$0.480845\pi$
$432$	−1.97112			−0.0948356
$433$	7.58269	+	5.50914i	0.364401	+	0.264753i	0.754885	−	0.655857i	$-0.227693\pi$
$433$	7.58269	+	5.50914i	0.364401	+	0.264753i	−0.390485	+	0.920609i	$0.627693\pi$
$434$	−3.88276	+	11.9499i	−0.186378	+	0.573613i
$435$	4.43985	+	2.41194i	0.212874	+	0.115644i
$436$	−2.59432	−	7.98450i	−0.124245	−	0.382388i
$437$	−7.74765	+	23.8448i	−0.370620	+	1.14065i
$438$	−2.59263	+	7.97928i	−0.123880	+	0.381265i
$439$	−0.159447	−	0.490727i	−0.00760998	−	0.0234211i	0.947179	−	0.320704i	$-0.103920\pi$
$439$	−0.159447	−	0.490727i	−0.00760998	−	0.0234211i	−0.954789	+	0.297283i	$0.903920\pi$
$440$	−22.1787	−	12.0485i	−1.05733	−	0.574391i
$441$	−1.77981	+	5.47770i	−0.0847530	+	0.260843i
$442$	−7.80849	−	5.67320i	−0.371412	−	0.269847i
$443$	−17.8348			−0.847357			−0.423678	−	0.905813i	$-0.639261\pi$
$443$	−17.8348			−0.847357			−0.423678	+	0.905813i	$0.639261\pi$
$444$	4.41579	+	3.20826i	0.209564	+	0.152257i
$445$	−33.8938	+	4.45443i	−1.60672	+	0.211160i
$446$	−23.2779	+	16.9124i	−1.10224	+	0.800826i
$447$	−12.6610	+	9.19872i	−0.598842	+	0.435084i
$448$	2.87826	+	8.85836i	0.135985	+	0.418518i
$449$	−4.16533			−0.196574			−0.0982870	−	0.995158i	$-0.531336\pi$
$449$	−4.16533			−0.196574			−0.0982870	+	0.995158i	$0.531336\pi$
$450$	5.23804	+	2.01340i	0.246923	+	0.0949128i
$451$	−27.4233			−1.29131
$452$	−1.10623	−	3.40462i	−0.0520325	−	0.160140i
$453$	−3.20224	+	2.32656i	−0.150454	+	0.109311i
$454$	5.95944	−	4.32979i	0.279691	−	0.203207i
$455$	8.86719	+	4.81708i	0.415700	+	0.225828i
$456$	10.1038	+	7.34081i	0.473152	+	0.343765i
$457$	−17.6734			−0.826725			−0.413362	−	0.910567i	$-0.635646\pi$
$457$	−17.6734			−0.826725			−0.413362	+	0.910567i	$0.635646\pi$
$458$	−7.23112	−	5.25371i	−0.337888	−	0.245490i
$459$	0.655837	−	2.01846i	0.0306119	−	0.0942136i
$460$	7.41618	−	7.03452i	0.345781	−	0.327986i
$461$	−0.0633350	−	0.194925i	−0.00294981	−	0.00907857i	0.949571	−	0.313553i	$-0.101519\pi$
$461$	−0.0633350	−	0.194925i	−0.00294981	−	0.00907857i	−0.952521	+	0.304474i	$0.901519\pi$
$462$	−1.41762	+	4.36300i	−0.0659538	+	0.202985i
$463$	−3.96084	+	12.1902i	−0.184076	+	0.566528i	−0.999931	−	0.0117286i	$-0.996267\pi$
$463$	−3.96084	+	12.1902i	−0.184076	+	0.566528i	0.815855	+	0.578256i	$0.196267\pi$
$464$	1.37636	+	4.23601i	0.0638961	+	0.196652i
$465$	4.10110	−	22.0997i	0.190184	−	1.02485i
$466$	3.26742	−	10.0561i	0.151360	−	0.465839i
$467$	−0.901030	−	0.654637i	−0.0416947	−	0.0302930i	0.566743	−	0.823895i	$-0.308203\pi$
$467$	−0.901030	−	0.654637i	−0.0416947	−	0.0302930i	−0.608437	+	0.793602i	$0.708203\pi$
$468$	3.00000			0.138675
$469$	−2.36668	−	1.71949i	−0.109283	−	0.0793987i
$470$	−5.69482	+	5.40174i	−0.262682	+	0.249164i
$471$	3.64107	−	2.64539i	0.167772	−	0.121893i
$472$	16.4069	−	11.9203i	0.755187	−	0.548675i
$473$	10.4905	+	32.2866i	0.482356	+	1.48454i
$474$	−9.58149			−0.440092
$475$	−11.0502	−	17.0327i	−0.507020	−	0.781513i
$476$	−1.75002			−0.0802120
$477$	−1.08453	−	3.33784i	−0.0496572	−	0.152829i
$478$	−10.1905	+	7.40380i	−0.466101	+	0.338642i
$479$	20.3670	−	14.7975i	0.930590	−	0.676113i	−0.0155470	−	0.999879i	$-0.504949\pi$
$479$	20.3670	−	14.7975i	0.930590	−	0.676113i	0.946137	+	0.323766i	$0.104949\pi$
$480$	−3.79005	−	7.95062i	−0.172991	−	0.362895i
$481$	24.1677	+	17.5589i	1.10195	+	0.800615i
$482$	−25.4555			−1.15947
$483$	−5.56330	−	4.04197i	−0.253139	−	0.183916i
$484$	−0.564977	+	1.73882i	−0.0256808	+	0.0790373i
$485$	12.9896	+	27.2491i	0.589828	+	1.23732i
$486$	−0.346820	−	1.06740i	−0.0157321	−	0.0484184i
$487$	3.20135	−	9.85274i	0.145067	−	0.446470i	−0.851953	−	0.523619i	$-0.824582\pi$
$487$	3.20135	−	9.85274i	0.145067	−	0.446470i	0.997020	+	0.0771487i	$0.0245816\pi$
$488$	−8.65265	+	26.6301i	−0.391687	+	1.20549i
$489$	−0.758292	−	2.33378i	−0.0342912	−	0.105537i
$490$	14.3311	−	1.88344i	0.647414	−	0.0850852i
$491$	−4.83831	+	14.8908i	−0.218350	+	0.672012i	0.780549	+	0.625095i	$0.214940\pi$
$491$	−4.83831	+	14.8908i	−0.218350	+	0.672012i	−0.998899	+	0.0469170i	$0.985060\pi$
$492$	−4.47558	−	3.25170i	−0.201775	−	0.146598i
$493$	−4.79569			−0.215987
$494$	14.9399	+	10.8545i	0.672178	+	0.488366i
$495$	1.49734	−	8.06878i	0.0673006	−	0.362665i
$496$	16.0297	−	11.6463i	0.719754	−	0.522932i
$497$	−0.595425	+	0.432601i	−0.0267084	+	0.0194048i
$498$	−4.25337	−	13.0905i	−0.190598	−	0.586600i
$499$	35.7864			1.60202			0.801010	−	0.598651i	$-0.204296\pi$
$499$	35.7864			1.60202			0.801010	+	0.598651i	$0.204296\pi$
$500$	0.643866	+	8.25248i	0.0287946	+	0.369062i
$501$	−3.06328			−0.136857
$502$	2.34735	+	7.22439i	0.104767	+	0.322440i
$503$	9.52947	−	6.92356i	0.424898	−	0.308706i	−0.354708	−	0.934977i	$-0.615420\pi$
$503$	9.52947	−	6.92356i	0.424898	−	0.308706i	0.779606	+	0.626271i	$0.215420\pi$
$504$	−2.77121	+	2.01340i	−0.123440	+	0.0896842i
$505$	2.94828	−	15.8875i	0.131197	−	0.706985i
$506$	20.5754	+	14.9489i	0.914687	+	0.664559i
$507$	3.41904			0.151845
$508$	0.454975	+	0.330559i	0.0201862	+	0.0146662i
$509$	10.3986	−	32.0037i	0.460912	−	1.41854i	−0.403141	−	0.915138i	$-0.632082\pi$
$509$	10.3986	−	32.0037i	0.460912	−	1.41854i	0.864052	−	0.503402i	$-0.167918\pi$
$510$	−5.28083	+	0.694023i	−0.233839	+	0.0307318i
$511$	2.57276	+	7.91815i	0.113812	+	0.350278i
$512$	6.14602	−	18.9155i	0.271618	−	0.835955i
$513$	−1.25481	+	3.86190i	−0.0554011	+	0.170507i
$514$	5.13064	+	15.7905i	0.226303	+	0.696489i
$515$	5.07798	+	10.6524i	0.223762	+	0.469400i
$516$	−2.11627	+	6.51320i	−0.0931635	+	0.286728i
$517$	9.28647	+	6.74701i	0.408418	+	0.296733i
$518$	−9.21526			−0.404895
$519$	−9.10923	−	6.61825i	−0.399851	−	0.290509i
$520$	−11.9914	−	25.1550i	−0.525856	−	1.10312i
$521$	9.58263	−	6.96219i	0.419823	−	0.305019i	−0.357744	−	0.933820i	$-0.616454\pi$
$521$	9.58263	−	6.96219i	0.419823	−	0.305019i	0.777566	+	0.628801i	$0.216454\pi$
$522$	−2.05172	+	1.49066i	−0.0898012	+	0.0652444i
$523$	1.26602	+	3.89642i	0.0553593	+	0.170379i	0.974913	−	0.222586i	$-0.0714497\pi$
$523$	1.26602	+	3.89642i	0.0553593	+	0.170379i	−0.919554	+	0.392964i	$0.871450\pi$
$524$	−10.8502			−0.473992
$525$	5.37957	−	1.43885i	0.234784	−	0.0627967i
$526$	−22.4117			−0.977195
$527$	6.59250	+	20.2896i	0.287174	+	0.883830i
$528$	5.85256	−	4.25213i	0.254700	−	0.185050i
$529$	−12.2347	+	8.88902i	−0.531943	+	0.386479i
$530$	−6.39030	+	6.06143i	−0.277577	+	0.263292i
$531$	5.33451	+	3.87575i	0.231498	+	0.168193i
$532$	3.34829			0.145167
$533$	−24.4949	−	17.7966i	−1.06099	−	0.770857i
$534$	5.30222	−	16.3186i	0.229450	−	0.706174i
$535$	2.23039	−	12.0190i	0.0964282	−	0.519626i
$536$	2.49639	+	7.68310i	0.107828	+	0.331859i
$537$	3.10789	−	9.56511i	0.134116	−	0.412765i
$538$	3.55078	−	10.9282i	0.153085	−	0.471147i
$539$	−6.53205	−	20.1036i	−0.281355	−	0.865922i
$540$	1.20112	−	1.13931i	0.0516881	−	0.0490280i
$541$	4.31332	−	13.2750i	0.185444	−	0.570738i	−0.814512	−	0.580147i	$-0.802995\pi$
$541$	4.31332	−	13.2750i	0.185444	−	0.570738i	0.999956	+	0.00940920i	$0.00299509\pi$
$542$	11.1751	+	8.11917i	0.480011	+	0.348748i
$543$	−19.4684			−0.835471
$544$	6.76321	+	4.91376i	0.289970	+	0.210676i
$545$	−22.2805	−	12.1038i	−0.954390	−	0.518470i
$546$	−4.09765	+	2.97712i	−0.175363	+	0.127409i
$547$	21.4426	−	15.5789i	0.916818	−	0.666107i	−0.0259119	−	0.999664i	$-0.508249\pi$
$547$	21.4426	−	15.5789i	0.916818	−	0.666107i	0.942730	+	0.333557i	$0.108249\pi$
$548$	−2.81210	−	8.65476i	−0.120127	−	0.369713i
$549$	−9.10408			−0.388553
$550$	−19.8959	+	5.32147i	−0.848363	+	0.226908i
$551$	9.17556			0.390892
$552$	5.86822	+	18.0605i	0.249768	+	0.768706i
$553$	−7.69220	+	5.58871i	−0.327105	+	0.237656i
$554$	28.6488	−	20.8146i	1.21717	−	0.884327i
$555$	16.3445	−	2.14804i	0.693783	−	0.0911791i
$556$	8.82522	+	6.41190i	0.374273	+	0.271925i
$557$	10.6860			0.452781			0.226391	−	0.974037i	$-0.427307\pi$
$557$	10.6860			0.452781			0.226391	+	0.974037i	$0.427307\pi$
$558$	9.12712	+	6.63124i	0.386382	+	0.280723i
$559$	−11.5824	+	35.6468i	−0.489882	+	1.50770i
$560$	4.31345	+	2.34327i	0.182277	+	0.0990214i
$561$	2.40697	+	7.40790i	0.101622	+	0.312762i
$562$	7.39140	−	22.7484i	0.311788	−	0.959583i
$563$	−7.90310	+	24.3232i	−0.333076	+	1.02510i	0.634586	+	0.772852i	$0.281171\pi$
$563$	−7.90310	+	24.3232i	−0.333076	+	1.02510i	−0.967662	+	0.252250i	$0.918829\pi$
$564$	0.715563	+	2.20227i	0.0301306	+	0.0927325i
$565$	−9.50047	−	5.16111i	−0.399688	−	0.217129i
$566$	0.299792	−	0.922666i	0.0126012	−	0.0387825i
$567$	−0.901030	−	0.654637i	−0.0378397	−	0.0274922i
$568$	2.03244			0.0852794
$569$	−4.93670	−	3.58672i	−0.206957	−	0.150363i	0.479479	−	0.877554i	$-0.340826\pi$
$569$	−4.93670	−	3.58672i	−0.206957	−	0.150363i	−0.686436	+	0.727190i	$0.740826\pi$
$570$	10.1038	−	1.32787i	0.423200	−	0.0556182i
$571$	−19.2058	+	13.9538i	−0.803737	+	0.583949i	−0.912008	−	0.410173i	$-0.865468\pi$
$571$	−19.2058	+	13.9538i	−0.803737	+	0.583949i	0.108271	+	0.994121i	$0.465468\pi$
$572$	−8.90746	+	6.47165i	−0.372440	+	0.270593i
$573$	−3.58739	−	11.0408i	−0.149865	−	0.461238i
$574$	9.34003			0.389845
$575$	1.62962	−	30.8288i	0.0679597	−	1.28565i
$576$	8.36307			0.348461
$577$	−13.6474	−	42.0024i	−0.568149	−	1.74858i	−0.658405	−	0.752664i	$-0.728769\pi$
$577$	−13.6474	−	42.0024i	−0.568149	−	1.74858i	0.0902565	−	0.995919i	$-0.471231\pi$
$578$	−11.3459	+	8.24330i	−0.471929	+	0.342876i
$579$	2.73574	−	1.98763i	0.113694	−	0.0826032i
$580$	−3.28712	−	1.78572i	−0.136490	−	0.0741480i
$581$	−11.0501	−	8.02840i	−0.458437	−	0.333074i
$582$	−15.1515			−0.628048
$583$	10.4206	+	7.57100i	0.431576	+	0.313559i
$584$	7.10475	−	21.8662i	0.293997	−	0.904828i
$585$	6.57376	−	6.23545i	0.271792	−	0.257804i
$586$	−1.10185	−	3.39115i	−0.0455170	−	0.140087i
$587$	0.158206	−	0.486909i	0.00652987	−	0.0200969i	−0.947738	−	0.319048i	$-0.896637\pi$
$587$	0.158206	−	0.486909i	0.00652987	−	0.0200969i	0.954268	+	0.298951i	$0.0966368\pi$
$588$	1.31772	−	4.05551i	0.0543417	−	0.167246i
$589$	−12.6134	−	38.8200i	−0.519725	−	1.59955i
$590$	3.01929	−	16.2702i	0.124302	−	0.669832i
$591$	−5.43502	+	16.7273i	−0.223567	+	0.688068i
$592$	11.7564	+	8.54153i	0.483186	+	0.351055i
$593$	−18.8405			−0.773687			−0.386844	−	0.922145i	$-0.626435\pi$
$593$	−18.8405			−0.773687			−0.386844	+	0.922145i	$0.626435\pi$
$594$	3.33238	+	2.42112i	0.136729	+	0.0993396i
$595$	−3.83474	+	3.63738i	−0.157209	+	0.149118i
$596$	9.37376	−	6.81043i	0.383964	−	0.278966i
$597$	−16.1886	+	11.7617i	−0.662556	+	0.481375i
$598$	8.67703	+	26.7052i	0.354830	+	1.09206i
$599$	6.20712			0.253616			0.126808	−	0.991927i	$-0.459527\pi$
$599$	6.20712			0.253616			0.126808	+	0.991927i	$0.459527\pi$
$600$	−14.3541	−	5.51747i	−0.586005	−	0.225250i
$601$	34.0303			1.38813			0.694063	−	0.719915i	$-0.255819\pi$
$601$	34.0303			1.38813			0.694063	+	0.719915i	$0.255819\pi$
$602$	−3.57295	−	10.9964i	−0.145623	−	0.448180i
$603$	−2.12499	+	1.54390i	−0.0865363	+	0.0628723i
$604$	2.37083	−	1.72251i	0.0964679	−	0.0700880i
$605$	2.37610	+	4.98450i	0.0966023	+	0.202649i
$606$	6.56149	+	4.76720i	0.266542	+	0.193654i
$607$	16.2488			0.659518			0.329759	−	0.944065i	$-0.393032\pi$
$607$	16.2488			0.659518			0.329759	+	0.944065i	$0.393032\pi$
$608$	−12.9400	−	9.40144i	−0.524785	−	0.381279i
$609$	−0.777682	+	2.39346i	−0.0315132	+	0.0969878i
$610$	9.83155	+	20.6242i	0.398068	+	0.835051i
$611$	3.91628	+	12.0531i	0.158436	+	0.487615i
$612$	−0.485560	+	1.49440i	−0.0196276	+	0.0604076i
$613$	−0.0210086	+	0.0646578i	−0.000848529	+	0.00261150i	−0.951480	−	0.307711i	$-0.900437\pi$
$613$	−0.0210086	+	0.0646578i	−0.000848529	+	0.00261150i	0.950631	+	0.310322i	$0.100437\pi$
$614$	0.176180	+	0.542225i	0.00711004	+	0.0218824i
$615$	−16.5658	+	2.17712i	−0.667996	+	0.0877900i
$616$	3.88481	−	11.9562i	0.156523	−	0.481730i
$617$	−26.5445	−	19.2857i	−1.06864	−	0.776413i	−0.0929733	−	0.995669i	$-0.529637\pi$
$617$	−26.5445	−	19.2857i	−1.06864	−	0.776413i	−0.975667	+	0.219256i	$0.929637\pi$
$618$	−5.92309			−0.238262
$619$	5.48280	+	3.98349i	0.220372	+	0.160110i	0.692494	−	0.721423i	$-0.256512\pi$
$619$	5.48280	+	3.98349i	0.220372	+	0.160110i	−0.472122	+	0.881533i	$0.656512\pi$
$620$	−3.03632	+	16.3619i	−0.121942	+	0.657111i
$621$	−4.99517	+	3.62921i	−0.200449	+	0.145635i
$622$	−13.2964	+	9.66040i	−0.533137	+	0.387347i
$623$	−5.26160	−	16.1935i	−0.210802	−	0.648780i
$624$	7.98706			0.319738
$625$	18.5635	+	16.7450i	0.742541	+	0.669801i
$626$	16.7858			0.670895
$627$	−4.60524	−	14.1735i	−0.183915	−	0.566034i
$628$	−2.69573	+	1.95856i	−0.107571	+	0.0781552i
$629$	−12.6583	+	9.19679i	−0.504719	+	0.366700i
$630$	−0.509976	+	2.74813i	−0.0203179	+	0.109488i
$631$	6.20352	+	4.50712i	0.246958	+	0.179426i	0.704378	−	0.709825i	$-0.251226\pi$
$631$	6.20352	+	4.50712i	0.246958	+	0.179426i	−0.457419	+	0.889251i	$0.651226\pi$
$632$	26.2568			1.04444
$633$	−1.97611	−	1.43573i	−0.0785433	−	0.0570651i
$634$	−6.28405	+	19.3403i	−0.249572	+	0.768102i
$635$	1.68403	−	0.221320i	0.0668285	−	0.00878281i
$636$	0.802951	+	2.47123i	0.0318391	+	0.0979906i
$637$	7.21188	−	22.1959i	0.285745	−	0.879432i
$638$	2.87619	−	8.85199i	0.113869	−	0.350454i
$639$	0.204207	+	0.628483i	0.00807829	+	0.0248624i
$640$	−1.45122	−	3.04431i	−0.0573644	−	0.120337i
$641$	−7.32096	+	22.5316i	−0.289161	+	0.889945i	0.695960	+	0.718081i	$0.254979\pi$
$641$	−7.32096	+	22.5316i	−0.289161	+	0.889945i	−0.985121	+	0.171864i	$0.945021\pi$
$642$	4.96380	+	3.60641i	0.195906	+	0.142334i
$643$	2.16861			0.0855218			0.0427609	−	0.999085i	$-0.486385\pi$
$643$	2.16861			0.0855218			0.0427609	+	0.999085i	$0.486385\pi$
$644$	4.11889	+	2.99255i	0.162307	+	0.117923i
$645$	8.90030	+	18.6707i	0.350449	+	0.735158i
$646$	−7.82506	+	5.68524i	−0.307873	+	0.223683i
$647$	−2.06737	+	1.50203i	−0.0812767	+	0.0590510i	−0.627682	−	0.778470i	$-0.715996\pi$
$647$	−2.06737	+	1.50203i	−0.0812767	+	0.0590510i	0.546405	+	0.837521i	$0.315996\pi$
$648$	0.950415	+	2.92508i	0.0373358	+	0.114908i
$649$	−24.1998			−0.949926
$650$	−21.2247	−	8.15840i	−0.832503	−	0.319999i
$651$	11.1953			0.438779
$652$	0.561415	+	1.72786i	0.0219867	+	0.0676681i
$653$	−26.2233	+	19.0523i	−1.02620	+	0.745575i	−0.967544	−	0.252704i	$-0.918680\pi$
$653$	−26.2233	+	19.0523i	−1.02620	+	0.745575i	−0.0586517	+	0.998279i	$0.518680\pi$
$654$	10.2961	−	7.48057i	0.402610	−	0.292513i
$655$	−23.7755	+	22.5519i	−0.928985	+	0.881175i
$656$	−11.9156	−	8.65719i	−0.465226	−	0.338006i
$657$	7.47542			0.291644
$658$	−3.16285	−	2.29795i	−0.123301	−	0.0895833i
$659$	0.139043	−	0.427929i	0.00541633	−	0.0166697i	−0.948312	−	0.317340i	$-0.897210\pi$
$659$	0.139043	−	0.427929i	0.00541633	−	0.0166697i	0.953728	+	0.300670i	$0.0972104\pi$
$660$	−1.10858	+	5.97386i	−0.0431516	+	0.232532i
$661$	−8.33812	−	25.6621i	−0.324315	−	0.998140i	−0.971749	−	0.236018i	$-0.924158\pi$
$661$	−8.33812	−	25.6621i	−0.324315	−	0.998140i	0.647433	−	0.762122i	$-0.275842\pi$
$662$	−9.13921	+	28.1276i	−0.355205	+	1.09321i
$663$	−2.65748	+	8.17888i	−0.103208	+	0.317641i
$664$	11.6558	+	35.8728i	0.452332	+	1.39214i
$665$	7.33696	−	6.95937i	0.284515	−	0.269873i
$666$	−2.55687	+	7.86923i	−0.0990766	+	0.304926i
$667$	11.2873	+	8.20067i	0.437044	+	0.317531i
$668$	2.26795			0.0877496
$669$	20.7407	+	15.0690i	0.801880	+	0.582600i
$670$	5.79231	+	3.14666i	0.223776	+	0.121566i
$671$	27.0314	−	19.6395i	1.04354	−	0.758174i
$672$	3.54912	−	2.57859i	0.136910	−	0.0994711i
$673$	5.44561	+	16.7599i	0.209913	+	0.646046i	0.999476	+	0.0323758i	$0.0103073\pi$
$673$	5.44561	+	16.7599i	0.209913	+	0.646046i	−0.789563	+	0.613670i	$0.789693\pi$
$674$	12.0032			0.462344
$675$	0.263932	−	4.99303i	0.0101587	−	0.192182i
$676$	−2.53135			−0.0973595
$677$	−5.97899	−	18.4014i	−0.229791	−	0.707225i	−0.997770	−	0.0667494i	$-0.978737\pi$
$677$	−5.97899	−	18.4014i	−0.229791	−	0.707225i	0.767978	−	0.640476i	$-0.221263\pi$
$678$	4.39030	−	3.18974i	0.168608	−	0.122501i
$679$	−12.1639	+	8.83757i	−0.466807	+	0.339155i
$680$	14.4714	−	1.90188i	0.554953	−	0.0729336i
$681$	−5.30987	−	3.85784i	−0.203475	−	0.147833i
$682$	−41.4049			−1.58547
$683$	24.2268	+	17.6018i	0.927015	+	0.673515i	0.945260	−	0.326318i	$-0.105808\pi$
$683$	24.2268	+	17.6018i	0.927015	+	0.673515i	−0.0182455	+	0.999834i	$0.505808\pi$
$684$	0.929018	−	2.85922i	0.0355219	−	0.109325i
$685$	−24.1508	−	13.1199i	−0.922755	−	0.501284i
$686$	4.92859	+	15.1686i	0.188175	+	0.579142i
$687$	−2.46098	+	7.57412i	−0.0938923	+	0.288971i
$688$	−5.63426	+	17.3405i	−0.214804	+	0.661099i
$689$	4.39456	+	13.5251i	0.167419	+	0.515264i
$690$	13.6159	+	7.39679i	0.518347	+	0.281591i
$691$	−6.16024	+	18.9593i	−0.234346	+	0.721244i	0.762861	+	0.646563i	$0.223794\pi$
$691$	−6.16024	+	18.9593i	−0.234346	+	0.721244i	−0.997207	+	0.0746817i	$0.976206\pi$
$692$	6.74418	+	4.89993i	0.256375	+	0.186268i
$693$	4.08749			0.155271
$694$	14.6858	+	10.6698i	0.557464	+	0.405021i
$695$	32.6653	−	4.29298i	1.23907	−	0.162842i
$696$	5.62246	−	4.08495i	0.213119	−	0.154840i
$697$	12.8297	−	9.32131i	0.485959	−	0.353070i
$698$	−5.28495	−	16.2654i	−0.200038	−	0.615655i
$699$	−9.42107			−0.356338
$700$	−3.98286	+	1.06528i	−0.150538	+	0.0402638i
$701$	−49.0150			−1.85127			−0.925636	−	0.378415i	$-0.876469\pi$
$701$	−49.0150			−1.85127			−0.925636	+	0.378415i	$0.876469\pi$
$702$	1.40533	+	4.32516i	0.0530407	+	0.163243i
$703$	24.2190	−	17.5961i	0.913437	−	0.663651i
$704$	−24.8312	+	18.0409i	−0.935862	+	0.679944i
$705$	6.14537	+	3.33846i	0.231448	+	0.125734i
$706$	−26.8204	−	19.4862i	−1.00940	−	0.733372i
$707$	8.04831			0.302688
$708$	−3.94950	−	2.86948i	−0.148431	−	0.107842i
$709$	−1.48744	+	4.57788i	−0.0558621	+	0.171926i	−0.975095	−	0.221789i	$-0.928810\pi$
$709$	−1.48744	+	4.57788i	−0.0558621	+	0.171926i	0.919233	+	0.393715i	$0.128810\pi$
$710$	1.20323	−	1.14131i	0.0451565	−	0.0428326i
$711$	2.63811	+	8.11928i	0.0989370	+	0.304497i
$712$	−14.5300	+	44.7189i	−0.544536	+	1.67591i
$713$	19.1792	−	59.0274i	0.718265	−	2.21059i
$714$	−0.819784	−	2.52304i	−0.0306797	−	0.0944223i
$715$	−6.06730	+	32.6950i	−0.226904	+	1.22273i
$716$	−2.30098	+	7.08170i	−0.0859918	+	0.264656i
$717$	9.07970	+	6.59679i	0.339088	+	0.246362i
$718$	14.7775			0.551491
$719$	−26.0917	−	18.9568i	−0.973058	−	0.706968i	−0.0169113	−	0.999857i	$-0.505383\pi$
$719$	−26.0917	−	18.9568i	−0.973058	−	0.706968i	−0.956146	+	0.292889i	$0.905383\pi$
$720$	3.19782	−	3.03324i	0.119176	−	0.113042i
$721$	−4.75517	+	3.45483i	−0.177092	+	0.128665i
$722$	−2.28013	+	1.65661i	−0.0848578	+	0.0616528i
$723$	7.00879	+	21.5708i	0.260660	+	0.802228i
$724$	14.4138			0.535685
$725$	−10.9145	+	2.91926i	−0.405355	+	0.108418i
$726$	−2.77155			−0.102862
$727$	−9.01548	−	27.7468i	−0.334366	−	1.02907i	−0.967034	−	0.254648i	$-0.918040\pi$
$727$	−9.01548	−	27.7468i	−0.334366	−	1.02907i	0.632668	−	0.774423i	$-0.281960\pi$
$728$	11.2291	−	8.15840i	0.416177	−	0.302370i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−8.07275	−	16.9347i	−0.298786	−	0.626781i
$731$	−15.8823	−	11.5391i	−0.587426	−	0.426790i
$732$	6.74037			0.249131
$733$	−4.20771	−	3.05708i	−0.155415	−	0.112916i	0.507360	−	0.861734i	$-0.330622\pi$
$733$	−4.20771	−	3.05708i	−0.155415	−	0.112916i	−0.662775	+	0.748818i	$0.730622\pi$
$734$	1.34876	−	4.15107i	0.0497838	−	0.153219i
$735$	−5.54186	−	11.6255i	−0.204415	−	0.428813i
$736$	−7.51548	−	23.1303i	−0.277024	−	0.852593i
$737$	2.97891	−	9.16813i	0.109729	−	0.337712i
$738$	2.59149	−	7.97578i	0.0953940	−	0.293592i
$739$	−5.04334	−	15.5218i	−0.185522	−	0.570979i	0.814435	−	0.580255i	$-0.197047\pi$
$739$	−5.04334	−	15.5218i	−0.185522	−	0.570979i	−0.999957	+	0.00927620i	$0.997047\pi$
$740$	−12.1009	+	1.59034i	−0.444838	+	0.0584620i
$741$	5.08453	−	15.6486i	0.186785	−	0.574865i
$742$	−3.54912	−	2.57859i	−0.130292	−	0.0946629i
$743$	53.4487			1.96084			0.980421	−	0.196914i	$-0.0630919\pi$
$743$	53.4487			1.96084			0.980421	+	0.196914i	$0.0630919\pi$
$744$	−25.0117	−	18.1720i	−0.916972	−	0.666219i
$745$	6.38491	−	34.4066i	0.233925	−	1.26056i
$746$	−7.39398	+	5.37204i	−0.270713	+	0.196684i
$747$	−9.92170	+	7.20854i	−0.363016	+	0.263747i
$748$	−1.78204	−	5.48457i	−0.0651580	−	0.200536i
$749$	6.08859			0.222472
$750$	−11.5962	+	4.79409i	−0.423432	+	0.175056i
$751$	−0.566970			−0.0206890			−0.0103445	−	0.999946i	$-0.503293\pi$
$751$	−0.566970			−0.0206890			−0.0103445	+	0.999946i	$0.503293\pi$
$752$	1.90508	+	5.86324i	0.0694712	+	0.213810i
$753$	5.47558	−	3.97824i	0.199541	−	0.144975i
$754$	8.31364	−	6.04021i	0.302765	−	0.219972i
$755$	1.61489	−	8.70220i	0.0587718	−	0.316706i
$756$	0.667093	+	0.484672i	0.0242620	+	0.0176273i
$757$	53.0708			1.92889			0.964445	−	0.264282i	$-0.0851350\pi$
$757$	53.0708			1.92889			0.964445	+	0.264282i	$0.0851350\pi$
$758$	8.99560	+	6.53569i	0.326735	+	0.237387i
$759$	7.00246	−	21.5513i	0.254173	−	0.782264i
$760$	−27.6880	+	3.63884i	−1.00435	+	0.131995i
$761$	−8.49970	−	26.1594i	−0.308114	−	0.948277i	−0.978497	−	0.206262i	$-0.933870\pi$
$761$	−8.49970	−	26.1594i	−0.308114	−	0.948277i	0.670383	−	0.742015i	$-0.266130\pi$
$762$	−0.263443	+	0.810794i	−0.00954353	+	0.0293720i
$763$	3.90264	−	12.0111i	0.141285	−	0.434830i
$764$	2.65599	+	8.17428i	0.0960902	+	0.295735i
$765$	2.04210	+	4.28384i	0.0738324	+	0.154883i
$766$	1.81115	−	5.57414i	0.0654394	−	0.201402i
$767$	−21.6157	−	15.7047i	−0.780496	−	0.567064i
$768$	−15.0334			−0.542471
$769$	−12.1123	−	8.80007i	−0.436779	−	0.317339i	0.347575	−	0.937652i	$-0.387005\pi$
$769$	−12.1123	−	8.80007i	−0.436779	−	0.317339i	−0.784354	+	0.620314i	$0.787005\pi$
$770$	−4.41410	−	9.25974i	−0.159073	−	0.333698i
$771$	11.9681	−	8.69533i	0.431021	−	0.313155i
$772$	−2.02546	+	1.47158i	−0.0728977	+	0.0529633i
$773$	−0.634806	−	1.95373i	−0.0228324	−	0.0702708i	0.938991	−	0.343941i	$-0.111762\pi$
$773$	−0.634806	−	1.95373i	−0.0228324	−	0.0702708i	−0.961823	+	0.273671i	$0.911762\pi$
$774$	−10.3816			−0.373158
$775$	27.3547	+	42.1641i	0.982608	+	1.51458i
$776$	41.5206			1.49050
$777$	2.53728	+	7.80894i	0.0910243	+	0.280144i
$778$	−3.38655	+	2.46048i	−0.121414	+	0.0882123i
$779$	−24.5469	+	17.8344i	−0.879485	+	0.638983i
$780$	−4.86700	+	4.61653i	−0.174267	+	0.165298i
$781$	−1.96210	−	1.42555i	−0.0702093	−	0.0510100i
$782$	−14.7072			−0.525927
$783$	1.82808	+	1.32818i	0.0653303	+	0.0474652i
$784$	3.50823	−	10.7972i	0.125294	−	0.385615i
$785$	−1.83619	+	9.89475i	−0.0655365	+	0.353159i
$786$	−5.08269	−	15.6429i	−0.181293	−	0.557964i
$787$	−5.19981	+	16.0034i	−0.185353	+	0.570458i	−0.999954	−	0.00956327i	$-0.996956\pi$
$787$	−5.19981	+	16.0034i	−0.185353	+	0.570458i	0.814601	+	0.580022i	$0.196956\pi$
$788$	4.02391	−	12.3843i	0.143346	−	0.441174i
$789$	6.17070	+	18.9915i	0.219683	+	0.676114i
$790$	15.5444	−	14.7444i	0.553044	−	0.524582i
$791$	1.66410	−	5.12156i	0.0591685	−	0.182102i
$792$	−9.13195	−	6.63475i	−0.324490	−	0.235756i
$793$	36.8901			1.31001
$794$	3.64613	+	2.64907i	0.129396	+	0.0940118i
$795$	6.89588	+	3.74617i	0.244572	+	0.132863i
$796$	11.9855	−	8.70799i	0.424816	−	0.308647i
$797$	0.168996	−	0.122783i	0.00598616	−	0.00434920i	−0.584788	−	0.811186i	$-0.698822\pi$
$797$	0.168996	−	0.122783i	0.00598616	−	0.00434920i	0.590774	+	0.806837i	$0.298822\pi$
$798$	1.56849	+	4.82730i	0.0555238	+	0.170885i
$799$	−6.63791			−0.234832
$800$	18.3835	+	7.06627i	0.649954	+	0.249830i
$801$	−15.2881			−0.540179
$802$	8.66668	+	26.6733i	0.306031	+	0.941867i
$803$	−22.1957	+	16.1261i	−0.783268	+	0.569078i
$804$	1.57327	−	1.14305i	0.0554851	−	0.0403123i
$805$	15.2455	−	2.00361i	0.537333	−	0.0706179i
$806$	−36.9835	−	26.8701i	−1.30269	−	0.946458i
$807$	−10.2381			−0.360398
$808$	−17.9809	−	13.0639i	−0.632566	−	0.459586i
$809$	−5.24264	+	16.1352i	−0.184321	+	0.567283i	−0.999936	−	0.0113128i	$-0.996399\pi$
$809$	−5.24264	+	16.1352i	−0.184321	+	0.567283i	0.815615	+	0.578595i	$0.196399\pi$
$810$	2.20522	+	1.19798i	0.0774836	+	0.0420928i
$811$	−6.32508	−	19.4666i	−0.222103	−	0.683564i	−0.998573	−	0.0534090i	$-0.982991\pi$
$811$	−6.32508	−	19.4666i	−0.222103	−	0.683564i	0.776469	−	0.630155i	$-0.217009\pi$
$812$	0.575770	−	1.77204i	0.0202056	−	0.0621864i
$813$	3.80324	−	11.7052i	0.133385	−	0.410518i
$814$	−9.38390	−	28.8807i	−0.328905	−	1.01227i
$815$	4.82153	+	2.61928i	0.168891	+	0.0917495i
$816$	−1.29273	+	3.97863i	−0.0452548	+	0.139280i
$817$	30.3874	+	22.0777i	1.06312	+	0.772401i
$818$	28.4812			0.995822
$819$	3.65101	+	2.65262i	0.127577	+	0.0926899i
$820$	12.2647	−	1.61187i	0.428304	−	0.0562890i
$821$	−31.0368	+	22.5496i	−1.08319	+	0.786985i	−0.978237	−	0.207492i	$-0.933470\pi$
$821$	−31.0368	+	22.5496i	−1.08319	+	0.786985i	−0.104955	+	0.994477i	$0.533470\pi$
$822$	11.1604	−	8.10852i	0.389265	−	0.282817i
$823$	−8.96451	−	27.5899i	−0.312483	−	0.961725i	−0.976778	−	0.214254i	$-0.931268\pi$
$823$	−8.96451	−	27.5899i	−0.312483	−	0.961725i	0.664295	−	0.747471i	$-0.268732\pi$
$824$	16.2315			0.565449
$825$	9.98739	+	15.3944i	0.347716	+	0.535965i
$826$	8.24215			0.286781
$827$	4.43648	+	13.6541i	0.154271	+	0.474799i	0.998086	−	0.0618356i	$-0.0196955\pi$
$827$	4.43648	+	13.6541i	0.154271	+	0.474799i	−0.843815	+	0.536634i	$0.819695\pi$
$828$	3.69826	−	2.68695i	0.128524	−	0.0933779i
$829$	−3.75031	+	2.72476i	−0.130254	+	0.0946347i	−0.651004	−	0.759074i	$-0.725652\pi$
$829$	−3.75031	+	2.72476i	−0.130254	+	0.0946347i	0.520751	+	0.853709i	$0.325652\pi$
$830$	27.0446	+	14.6919i	0.938732	+	0.509964i
$831$	−25.5261	−	18.5458i	−0.885491	−	0.643347i
$832$	−33.8875			−1.17484
$833$	9.88925	+	7.18496i	0.342642	+	0.248944i
$834$	−5.11005	+	15.7271i	−0.176946	+	0.544585i
$835$	4.96965	−	4.71390i	0.171982	−	0.163131i
$836$	3.40957	+	10.4936i	0.117922	+	0.362928i
$837$	3.10625	−	9.56006i	0.107368	−	0.330444i
$838$	10.6896	−	32.8993i	0.369268	−	1.13649i
$839$	1.52235	+	4.68531i	0.0525573	+	0.161755i	0.973890	−	0.227020i	$-0.0728983\pi$
$839$	1.52235	+	4.68531i	0.0525573	+	0.161755i	−0.921333	+	0.388775i	$0.872898\pi$
$840$	1.39752	−	7.53087i	0.0482191	−	0.259840i
$841$	−7.38367	+	22.7246i	−0.254609	+	0.783607i
$842$	7.76010	+	5.63804i	0.267431	+	0.194300i
$843$	−21.3119			−0.734022
$844$	1.46305	+	1.06297i	0.0503602	+	0.0365888i
$845$	−5.54683	+	5.26137i	−0.190817	+	0.180996i
$846$	−2.83986	+	2.06328i	−0.0976365	+	0.0709371i
$847$	−2.22505	+	1.61660i	−0.0764538	+	0.0555469i
$848$	2.13774	+	6.57929i	0.0734103	+	0.225934i
$849$	−0.864403			−0.0296662
$850$	7.49927	−	9.25229i	0.257223	−	0.317351i
$851$	45.5194			1.56039
$852$	−0.151188	−	0.465309i	−0.00517961	−	0.0159412i
$853$	−43.4018	+	31.5333i	−1.48605	+	1.07968i	−0.510507	+	0.859874i	$0.670542\pi$
$853$	−43.4018	+	31.5333i	−1.48605	+	1.07968i	−0.975544	+	0.219805i	$0.929458\pi$
$854$	−9.20656	+	6.68896i	−0.315042	+	0.228891i
$855$	−3.90714	−	8.19624i	−0.133621	−	0.280305i
$856$	−13.6026	−	9.88290i	−0.464929	−	0.337790i
$857$	−27.1144			−0.926210			−0.463105	−	0.886303i	$-0.653265\pi$
$857$	−27.1144			−0.926210			−0.463105	+	0.886303i	$0.653265\pi$
$858$	−13.5029	−	9.81046i	−0.460983	−	0.334924i
$859$	3.21966	−	9.90910i	0.109853	−	0.338094i	−0.880985	−	0.473143i	$-0.843119\pi$
$859$	3.21966	−	9.90910i	0.109853	−	0.338094i	0.990839	+	0.135049i	$0.0431193\pi$
$860$	−6.58950	−	13.8232i	−0.224700	−	0.471367i
$861$	−2.57163	−	7.91467i	−0.0876410	−	0.269731i
$862$	9.14963	−	28.1597i	0.311638	−	0.959122i
$863$	−13.4865	+	41.5072i	−0.459086	+	1.41292i	0.407185	+	0.913346i	$0.366510\pi$
$863$	−13.4865	+	41.5072i	−0.459086	+	1.41292i	−0.866271	+	0.499575i	$0.833490\pi$
$864$	−1.21720	−	3.74617i	−0.0414101	−	0.127447i
$865$	24.9626	−	3.28067i	0.848756	−	0.111546i
$866$	3.25065	−	10.0045i	0.110461	−	0.339965i
$867$	10.1092	+	7.34479i	0.343328	+	0.249442i
$868$	−8.28864			−0.281335
$869$	−25.3480	−	18.4164i	−0.859872	−	0.624734i
$870$	1.03468	−	5.57561i	0.0350789	−	0.189031i
$871$	8.61055	−	6.25593i	0.291757	−	0.211974i
$872$	−28.2151	+	20.4995i	−0.955485	+	0.694201i
$873$	4.17172	+	12.8392i	0.141191	+	0.434542i
$874$	28.1391			0.951818
$875$	−6.51330	+	10.6126i	−0.220190	+	0.358772i
$876$	−5.53456			−0.186995
$877$	16.5767	+	51.0180i	0.559757	+	1.72275i	0.683038	+	0.730383i	$0.260658\pi$
$877$	16.5767	+	51.0180i	0.559757	+	1.72275i	−0.123281	+	0.992372i	$0.539342\pi$
$878$	−0.468503	+	0.340388i	−0.0158112	+	0.0114875i
$879$	−2.57025	+	1.86740i	−0.0866925	+	0.0629858i
$880$	−2.95144	+	15.9045i	−0.0994931	+	0.536142i
$881$	44.4110	+	32.2665i	1.49625	+	1.08709i	0.971847	+	0.235613i	$0.0757097\pi$
$881$	44.4110	+	32.2665i	1.49625	+	1.08709i	0.524398	+	0.851473i	$0.324290\pi$
$882$	6.46419			0.217661
$883$	15.4483	+	11.2239i	0.519877	+	0.377713i	0.816558	−	0.577264i	$-0.195880\pi$
$883$	15.4483	+	11.2239i	0.519877	+	0.377713i	−0.296681	+	0.954977i	$0.595880\pi$
$884$	1.96751	−	6.05538i	0.0661746	−	0.203664i
$885$	−14.6185	+	1.92121i	−0.491396	+	0.0645808i
$886$	6.18547	+	19.0369i	0.207805	+	0.639558i
$887$	−3.46598	+	10.6672i	−0.116376	+	0.358170i	−0.992232	−	0.124404i	$-0.960298\pi$
$887$	−3.46598	+	10.6672i	−0.116376	+	0.358170i	0.875855	+	0.482574i	$0.160298\pi$
$888$	7.00676	−	21.5646i	0.235131	−	0.723660i
$889$	0.261425	+	0.804582i	0.00876790	+	0.0269848i
$890$	16.5097	+	34.6334i	0.553407	+	1.16092i
$891$	1.13412	−	3.49045i	0.0379943	−	0.116934i
$892$	−15.3557	−	11.1566i	−0.514147	−	0.373550i
$893$	12.7003			0.424998
$894$	14.2098	+	10.3240i	0.475247	+	0.345287i
$895$	9.67716	+	20.3004i	0.323472	+	0.678566i
$896$	1.35896	−	0.987345i	0.0453998	−	0.0329849i
$897$	20.2407	−	14.7057i	0.675816	−	0.491009i
$898$	1.44462	+	4.44608i	0.0482076	+	0.148368i
$899$	−22.7139			−0.757552
$900$	−0.195407	+	3.69668i	−0.00651356	+	0.123223i
$901$	−7.44857			−0.248148
$902$	9.51095	+	29.2717i	0.316680	+	0.974641i
$903$	−8.33451	+	6.05538i	−0.277355	+	0.201510i
$904$	−12.0310	+	8.74106i	−0.400146	+	0.290723i
$905$	31.5843	−	29.9589i	1.04990	−	0.995866i
$906$	3.59398	+	2.61118i	0.119402	+	0.0867506i
$907$	−36.4513			−1.21034			−0.605172	−	0.796095i	$-0.706896\pi$
$907$	−36.4513			−1.21034			−0.605172	+	0.796095i	$0.706896\pi$
$908$	3.93125	+	2.85622i	0.130463	+	0.0947871i
$909$	2.23309	−	6.87273i	0.0740668	−	0.227954i
$910$	2.06644	−	11.1355i	0.0685020	−	0.369139i
$911$	0.360106	+	1.10829i	0.0119309	+	0.0367194i	0.956845	−	0.290600i	$-0.0938548\pi$
$911$	0.360106	+	1.10829i	0.0119309	+	0.0367194i	−0.944914	+	0.327319i	$0.893855\pi$
$912$	2.47338	−	7.61227i	0.0819017	−	0.252067i
$913$	13.9087	−	42.8065i	0.460310	−	1.41669i
$914$	6.12948	+	18.8646i	0.202745	+	0.623985i
$915$	14.7699	−	14.0097i	0.488276	−	0.463148i
$916$	1.82203	−	5.60763i	0.0602016	−	0.185281i
$917$	−13.2047	−	9.59377i	−0.436057	−	0.316814i
$918$	−2.38197			−0.0786166
$919$	−35.5543	−	25.8317i	−1.17283	−	0.852109i	−0.181482	−	0.983394i	$-0.558089\pi$
$919$	−35.5543	−	25.8317i	−1.17283	−	0.852109i	−0.991345	+	0.131286i	$0.958089\pi$
$920$	−37.3125	−	20.2699i	−1.23016	−	0.668279i
$921$	0.410969	−	0.298587i	0.0135419	−	0.00983876i
$922$	−0.186098	+	0.135208i	−0.00612880	+	0.00445283i
$923$	−0.827454	−	2.54664i	−0.0272360	−	0.0838237i
$924$	−3.02624			−0.0995561
$925$	−23.2107	+	28.6364i	−0.763162	+	0.941558i
$926$	14.3856			0.472739
$927$	1.63083	+	5.01918i	0.0535635	+	0.164852i
$928$	−7.20073	+	5.23164i	−0.236376	+	0.171737i
$929$	−25.2512	+	18.3460i	−0.828464	+	0.601914i	−0.919124	−	0.393968i	$-0.871102\pi$
$929$	−25.2512	+	18.3460i	−0.828464	+	0.601914i	0.0906606	+	0.995882i	$0.471102\pi$
$930$	−25.0117	+	3.28711i	−0.820165	+	0.107789i
$931$	−18.9210	−	13.7469i	−0.620111	−	0.450537i
$932$	6.97506			0.228476
$933$	11.8471	+	8.60743i	0.387857	+	0.281795i
$934$	−0.386266	+	1.18880i	−0.0126390	+	0.0388988i
$935$	−15.3045	−	8.31413i	−0.500510	−	0.271901i
$936$	−3.85112	−	11.8525i	−0.125878	−	0.387412i
$937$	−13.9385	+	42.8983i	−0.455351	+	1.40143i	0.415371	+	0.909652i	$0.363652\pi$
$937$	−13.9385	+	42.8983i	−0.455351	+	1.40143i	−0.870722	+	0.491775i	$0.836348\pi$
$938$	−1.01458	+	3.12255i	−0.0331271	+	0.101955i
$939$	−4.62171	−	14.2241i	−0.150824	−	0.464188i
$940$	−4.54983	−	2.47169i	−0.148399	−	0.0806175i
$941$	−12.0931	+	37.2187i	−0.394224	+	1.21330i	0.535341	+	0.844636i	$0.320183\pi$
$941$	−12.0931	+	37.2187i	−0.394224	+	1.21330i	−0.929565	+	0.368659i	$0.879817\pi$
$942$	−4.08650	−	2.96901i	−0.133145	−	0.0967357i
$943$	−46.1358			−1.50239
$944$	−10.5150	−	7.63957i	−0.342233	−	0.248647i
$945$	2.46915	−	0.324504i	0.0803216	−	0.0105561i
$946$	30.8245	−	22.3953i	1.00219	−	0.728133i
$947$	39.5235	−	28.7155i	1.28434	−	0.933128i	0.284665	−	0.958627i	$-0.408117\pi$
$947$	39.5235	−	28.7155i	1.28434	−	0.933128i	0.999675	+	0.0254991i	$0.00811748\pi$
$948$	−1.95317	−	6.01125i	−0.0634361	−	0.195236i
$949$	−30.2907			−0.983278
$950$	−14.3483	+	17.7023i	−0.465520	+	0.574339i
$951$	18.1190			0.587550
$952$	2.24651	+	6.91405i	0.0728098	+	0.224086i
$953$	−18.4314	+	13.3912i	−0.597051	+	0.433783i	−0.844831	−	0.535034i	$-0.820299\pi$
$953$	−18.4314	+	13.3912i	−0.597051	+	0.433783i	0.247780	+	0.968816i	$0.420299\pi$
$954$	−3.18668	+	2.31526i	−0.103173	+	0.0749593i
$955$	22.8101	+	12.3915i	0.738116	+	0.400980i
$956$	−6.72232	−	4.88405i	−0.217415	−	0.157961i
$957$	−8.29302			−0.268075
$958$	−22.8585	−	16.6077i	−0.738525	−	0.536570i
$959$	4.23024	−	13.0193i	0.136602	−	0.420417i
$960$	−13.5677	+	12.8694i	−0.437895	+	0.415359i
$961$	21.6446	+	66.6154i	0.698214	+	2.14888i
$962$	10.3605	−	31.8864i	0.334037	−	1.02806i
$963$	1.68934	−	5.19926i	0.0544382	−	0.167544i
$964$	−5.18908	−	15.9703i	−0.167129	−	0.514370i
$965$	−1.37963	+	7.43448i	−0.0444120	+	0.239324i
$966$	−2.38495	+	7.34012i	−0.0767345	+	0.236164i
$967$	−34.9436	−	25.3880i	−1.12371	−	0.816425i	−0.138944	−	0.990300i	$-0.544371\pi$
$967$	−34.9436	−	25.3880i	−1.12371	−	0.816425i	−0.984768	+	0.173876i	$0.944371\pi$
$968$	7.59507			0.244115
$969$	6.97214	+	5.06555i	0.223977	+	0.162729i
$970$	24.5807	−	23.3157i	0.789239	−	0.748622i
$971$	25.9089	−	18.8239i	0.831457	−	0.604089i	−0.0885142	−	0.996075i	$-0.528212\pi$
$971$	25.9089	−	18.8239i	0.831457	−	0.604089i	0.919971	+	0.391986i	$0.128212\pi$
$972$	0.598970	−	0.435177i	0.0192120	−	0.0139583i
$973$	5.07090	+	15.6066i	0.162565	+	0.500325i
$974$	−11.6271			−0.372557
$975$	−1.06946	+	20.2320i	−0.0342502	+	0.647941i
$976$	17.9452			0.574413
$977$	−2.24659	−	6.91428i	−0.0718747	−	0.221208i	0.908666	−	0.417524i	$-0.137102\pi$
$977$	−2.24659	−	6.91428i	−0.0718747	−	0.221208i	−0.980541	+	0.196316i	$0.937102\pi$
$978$	−2.22810	+	1.61881i	−0.0712467	+	0.0517637i
$979$	45.3927	−	32.9798i	1.45076	−	1.05404i
$980$	4.10302	+	8.60715i	0.131066	+	0.274945i
$981$	−9.17385	−	6.66519i	−0.292898	−	0.212803i
$982$	17.5725			0.560760
$983$	4.11915	+	2.99274i	0.131380	+	0.0954535i	0.651535	−	0.758619i	$-0.274126\pi$
$983$	4.11915	+	2.99274i	0.131380	+	0.0954535i	−0.520154	+	0.854072i	$0.674126\pi$
$984$	−7.10163	+	21.8566i	−0.226392	+	0.696762i
$985$	−16.9232	−	35.5009i	−0.539219	−	1.13115i
$986$	1.66324	+	5.11894i	0.0529685	+	0.163020i
$987$	−1.07642	+	3.31288i	−0.0342628	+	0.105450i
$988$	−3.76442	+	11.5857i	−0.119762	+	0.368590i
$989$	17.6488	+	54.3176i	0.561201	+	1.72720i
$990$	−9.13195	+	1.20015i	−0.290232	+	0.0381432i
$991$	−19.1826	+	59.0380i	−0.609356	+	1.87540i	−0.145859	+	0.989305i	$0.546594\pi$
$991$	−19.1826	+	59.0380i	−0.609356	+	1.87540i	−0.463497	+	0.886098i	$0.653406\pi$
$992$	32.0327	+	23.2731i	1.01704	+	0.738922i
$993$	26.3514			0.836237
$994$	0.668265	+	0.485523i	0.0211961	+	0.0153999i
$995$	8.16391	−	43.9931i	0.258813	−	1.39468i
$996$	7.34570	−	5.33697i	0.232758	−	0.169108i
$997$	−2.07832	+	1.50999i	−0.0658212	+	0.0478219i	−0.620209	−	0.784436i	$-0.712952\pi$
$997$	−2.07832	+	1.50999i	−0.0658212	+	0.0478219i	0.554388	+	0.832258i	$0.312952\pi$
$998$	−12.4114	−	38.1985i	−0.392878	−	1.20915i
$999$	7.37232			0.233250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.g.b.31.1	✓	8
3.2	odd	2		225.2.h.c.181.2		8
5.2	odd	4		375.2.i.b.349.3		16
5.3	odd	4		375.2.i.b.349.2		16
5.4	even	2		375.2.g.b.151.2		8
25.2	odd	20		1875.2.b.c.1249.4		8
25.3	odd	20		375.2.i.b.274.3		16
25.4	even	10		375.2.g.b.226.2		8
25.11	even	5		1875.2.a.h.1.2		4
25.14	even	10		1875.2.a.e.1.3		4
25.21	even	5	inner	75.2.g.b.46.1	yes	8
25.22	odd	20		375.2.i.b.274.2		16
25.23	odd	20		1875.2.b.c.1249.5		8
75.11	odd	10		5625.2.a.i.1.3		4
75.14	odd	10		5625.2.a.n.1.2		4
75.71	odd	10		225.2.h.c.46.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.31.1	✓	8	1.1	even	1	trivial
75.2.g.b.46.1	yes	8	25.21	even	5	inner
225.2.h.c.46.2		8	75.71	odd	10
225.2.h.c.181.2		8	3.2	odd	2
375.2.g.b.151.2		8	5.4	even	2
375.2.g.b.226.2		8	25.4	even	10
375.2.i.b.274.2		16	25.22	odd	20
375.2.i.b.274.3		16	25.3	odd	20
375.2.i.b.349.2		16	5.3	odd	4
375.2.i.b.349.3		16	5.2	odd	4
1875.2.a.e.1.3		4	25.14	even	10
1875.2.a.h.1.2		4	25.11	even	5
1875.2.b.c.1249.4		8	25.2	odd	20
1875.2.b.c.1249.5		8	25.23	odd	20
5625.2.a.i.1.3		4	75.11	odd	10
5625.2.a.n.1.2		4	75.14	odd	10

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.346820 - 1.06740i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.598970 - 0.435177i) q^{4} +(0.407987 - 2.19853i) q^{5} +(0.907987 + 0.659691i) q^{6} +1.11373 q^{7} +(-2.48822 - 1.80780i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.346820 - 1.06740i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.598970 - 0.435177i) q^{4} +(0.407987 - 2.19853i) q^{5} +(0.907987 + 0.659691i) q^{6} +1.11373 q^{7} +(-2.48822 - 1.80780i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-2.48822 + 0.327009i) q^{10} +(1.13412 + 3.49045i) q^{11} +(-0.228786 + 0.704131i) q^{12} +(-1.25215 + 3.85372i) q^{13} +(-0.386266 - 1.18880i) q^{14} +(0.962197 + 2.01846i) q^{15} +(-0.609110 + 1.87465i) q^{16} +(-1.71700 - 1.24748i) q^{17} -1.12233 q^{18} +(3.28513 + 2.38678i) q^{19} +(-0.712379 - 1.49440i) q^{20} +(-0.901030 + 0.654637i) q^{21} +(3.33238 - 2.42112i) q^{22} +(1.90799 + 5.87218i) q^{23} +3.07561 q^{24} +(-4.66709 - 1.79395i) q^{25} +4.54774 q^{26} +(0.309017 + 0.951057i) q^{27} +(0.667093 - 0.484672i) q^{28} +(1.82808 - 1.32818i) q^{29} +(1.82080 - 1.72709i) q^{30} +(-8.13227 - 5.90844i) q^{31} -3.93896 q^{32} +(-2.96915 - 2.15722i) q^{33} +(-0.736068 + 2.26538i) q^{34} +(0.454389 - 2.44858i) q^{35} +(-0.228786 - 0.704131i) q^{36} +(2.27817 - 7.01149i) q^{37} +(1.40831 - 4.33434i) q^{38} +(-1.25215 - 3.85372i) q^{39} +(-4.98966 + 4.73287i) q^{40} +(-2.30902 + 7.10642i) q^{41} +(1.01126 + 0.734721i) q^{42} +9.24998 q^{43} +(2.19826 + 1.59713i) q^{44} +(-1.96485 - 1.06740i) q^{45} +(5.60625 - 4.07318i) q^{46} +(2.53032 - 1.83839i) q^{47} +(-0.609110 - 1.87465i) q^{48} -5.75960 q^{49} +(-0.296220 + 5.60384i) q^{50} +2.12233 q^{51} +(0.927051 + 2.85317i) q^{52} +(2.83934 - 2.06290i) q^{53} +(0.907987 - 0.659691i) q^{54} +(8.13657 - 1.06933i) q^{55} +(-2.77121 - 2.01340i) q^{56} -4.06064 q^{57} +(-2.05172 - 1.49066i) q^{58} +(-2.03760 + 6.27109i) q^{59} +(1.45471 + 0.790270i) q^{60} +(-2.81332 - 8.65850i) q^{61} +(-3.48625 + 10.7296i) q^{62} +(0.344163 - 1.05922i) q^{63} +(2.58433 + 7.95375i) q^{64} +(7.96167 + 4.32516i) q^{65} +(-1.27286 + 3.91745i) q^{66} +(-2.12499 - 1.54390i) q^{67} -1.57131 q^{68} +(-4.99517 - 3.62921i) q^{69} +(-2.77121 + 0.364201i) q^{70} +(-0.534620 + 0.388424i) q^{71} +(-2.48822 + 1.80780i) q^{72} +(2.31003 + 7.10955i) q^{73} -8.27420 q^{74} +(4.83021 - 1.29192i) q^{75} +3.00637 q^{76} +(1.26310 + 3.88743i) q^{77} +(-3.67920 + 2.67310i) q^{78} +(-6.90667 + 5.01799i) q^{79} +(3.87297 + 2.10398i) q^{80} +(-0.809017 - 0.587785i) q^{81} +8.38623 q^{82} +(-9.92170 - 7.20854i) q^{83} +(-0.254807 + 0.784215i) q^{84} +(-3.44313 + 3.26594i) q^{85} +(-3.20808 - 9.87345i) q^{86} +(-0.698265 + 2.14904i) q^{87} +(3.48809 - 10.7352i) q^{88} +(-4.72429 - 14.5399i) q^{89} +(-0.457897 + 2.46749i) q^{90} +(-1.39456 + 4.29202i) q^{91} +(3.69826 + 2.68695i) q^{92} +10.0520 q^{93} +(-2.83986 - 2.06328i) q^{94} +(6.58771 - 6.24868i) q^{95} +(3.18668 - 2.31526i) q^{96} +(-10.9217 + 7.93508i) q^{97} +(1.99754 + 6.14781i) q^{98} +3.67008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q - q^2 - 2 * q^3 + q^4 - 5 * q^5 - q^6 + 4 * q^7 - 2 * q^9	\( 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9} + 16 q^{11} - 9 q^{12} - 8 q^{13} - 8 q^{14} + 5 q^{15} - 17 q^{16} - q^{17} + 4 q^{18} - 5 q^{19} - 10 q^{20} - 11 q^{21} + 13 q^{22} + 7 q^{23} + 30 q^{24} - 15 q^{25} + 6 q^{26} - 2 q^{27} - 17 q^{28} + 5 q^{29} + 30 q^{30} - 19 q^{31} + 24 q^{32} - 9 q^{33} + 12 q^{34} - 10 q^{35} - 9 q^{36} - q^{37} - 10 q^{38} - 8 q^{39} + 25 q^{40} - 14 q^{41} - 8 q^{42} + 32 q^{43} - 3 q^{44} - 5 q^{45} + 16 q^{46} - q^{47} - 17 q^{48} + 16 q^{49} + 10 q^{50} + 4 q^{51} - 6 q^{52} - 3 q^{53} - q^{54} + 15 q^{55} - 15 q^{56} + 10 q^{57} + 5 q^{58} + 30 q^{59} - 15 q^{60} - 14 q^{61} - 17 q^{62} + 9 q^{63} - 44 q^{64} + 25 q^{65} - 7 q^{66} + 4 q^{67} - 22 q^{68} - 8 q^{69} - 15 q^{70} + 21 q^{71} + 2 q^{73} - 38 q^{74} - 15 q^{75} + 80 q^{76} - 37 q^{77} - 14 q^{78} - 30 q^{79} - 50 q^{80} - 2 q^{81} - 12 q^{82} + 2 q^{83} + 8 q^{84} - 30 q^{85} - 34 q^{86} + 15 q^{87} + 70 q^{88} - 5 q^{90} + 21 q^{91} + 9 q^{92} + 46 q^{93} - 33 q^{94} + 65 q^{95} + 34 q^{96} - 6 q^{97} + 73 q^{98} - 14 q^{99}+O(q^{100}) \) 8 * q - q^2 - 2 * q^3 + q^4 - 5 * q^5 - q^6 + 4 * q^7 - 2 * q^9 + 16 * q^11 - 9 * q^12 - 8 * q^13 - 8 * q^14 + 5 * q^15 - 17 * q^16 - q^17 + 4 * q^18 - 5 * q^19 - 10 * q^20 - 11 * q^21 + 13 * q^22 + 7 * q^23 + 30 * q^24 - 15 * q^25 + 6 * q^26 - 2 * q^27 - 17 * q^28 + 5 * q^29 + 30 * q^30 - 19 * q^31 + 24 * q^32 - 9 * q^33 + 12 * q^34 - 10 * q^35 - 9 * q^36 - q^37 - 10 * q^38 - 8 * q^39 + 25 * q^40 - 14 * q^41 - 8 * q^42 + 32 * q^43 - 3 * q^44 - 5 * q^45 + 16 * q^46 - q^47 - 17 * q^48 + 16 * q^49 + 10 * q^50 + 4 * q^51 - 6 * q^52 - 3 * q^53 - q^54 + 15 * q^55 - 15 * q^56 + 10 * q^57 + 5 * q^58 + 30 * q^59 - 15 * q^60 - 14 * q^61 - 17 * q^62 + 9 * q^63 - 44 * q^64 + 25 * q^65 - 7 * q^66 + 4 * q^67 - 22 * q^68 - 8 * q^69 - 15 * q^70 + 21 * q^71 + 2 * q^73 - 38 * q^74 - 15 * q^75 + 80 * q^76 - 37 * q^77 - 14 * q^78 - 30 * q^79 - 50 * q^80 - 2 * q^81 - 12 * q^82 + 2 * q^83 + 8 * q^84 - 30 * q^85 - 34 * q^86 + 15 * q^87 + 70 * q^88 - 5 * q^90 + 21 * q^91 + 9 * q^92 + 46 * q^93 - 33 * q^94 + 65 * q^95 + 34 * q^96 - 6 * q^97 + 73 * q^98 - 14 * q^99

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