LMFDB - Embedded newform 380.2.be.b.51.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(51,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 5]))

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

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

chi := DirichletCharacter("380.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.be (of order $18$, degree $6$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			51.17
Character	$\chi$	$=$	380.51
Dual form			380.2.be.b.231.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10357 - 0.884387i) q^{2} +(-1.09042 - 0.396882i) q^{3} +(0.435721 - 1.95196i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-1.55435 + 0.526371i) q^{6} +(-1.28762 - 0.743405i) q^{7} +(-1.24544 - 2.53946i) q^{8} +(-1.26662 - 1.06282i) q^{9} +O(q^{10})$	\(q+(1.10357 - 0.884387i) q^{2} +(-1.09042 - 0.396882i) q^{3} +(0.435721 - 1.95196i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-1.55435 + 0.526371i) q^{6} +(-1.28762 - 0.743405i) q^{7} +(-1.24544 - 2.53946i) q^{8} +(-1.26662 - 1.06282i) q^{9} +(-1.06258 - 0.933229i) q^{10} +(-1.42203 + 0.821011i) q^{11} +(-1.24982 + 1.95553i) q^{12} +(1.15465 + 3.17238i) q^{13} +(-2.07843 + 0.318352i) q^{14} +(-0.201502 + 1.14278i) q^{15} +(-3.62029 - 1.70102i) q^{16} +(4.95639 - 4.15890i) q^{17} +(-2.33775 - 0.0527121i) q^{18} +(-4.22466 - 1.07343i) q^{19} +(-1.99797 - 0.0901470i) q^{20} +(1.10900 + 1.32166i) q^{21} +(-0.843218 + 2.16367i) q^{22} +(-3.40987 - 0.601253i) q^{23} +(0.350190 + 3.26339i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(4.07985 + 2.47978i) q^{26} +(2.69995 + 4.67645i) q^{27} +(-2.01214 + 2.18946i) q^{28} +(6.47232 - 7.71340i) q^{29} +(0.788285 + 1.43934i) q^{30} +(4.32540 - 7.49181i) q^{31} +(-5.49960 + 1.32455i) q^{32} +(1.87646 - 0.330871i) q^{33} +(1.79163 - 8.97299i) q^{34} +(-0.508519 + 1.39714i) q^{35} +(-2.62648 + 2.00930i) q^{36} +3.04067i q^{37} +(-5.61152 + 2.55163i) q^{38} -3.91750i q^{39} +(-2.28462 + 1.66749i) q^{40} +(-3.24473 + 8.91482i) q^{41} +(2.39272 + 0.477751i) q^{42} +(7.05877 - 1.24465i) q^{43} +(0.982972 + 3.13348i) q^{44} +(-0.826730 + 1.43194i) q^{45} +(-4.29476 + 2.35212i) q^{46} +(-2.48880 + 2.96604i) q^{47} +(3.27255 + 3.29166i) q^{48} +(-2.39470 - 4.14774i) q^{49} +(-0.734536 + 1.20849i) q^{50} +(-7.05516 + 2.56787i) q^{51} +(6.69546 - 0.871562i) q^{52} +(7.22408 + 1.27380i) q^{53} +(7.11536 + 2.77298i) q^{54} +(1.05547 + 1.25786i) q^{55} +(-0.284203 + 4.19572i) q^{56} +(4.18065 + 2.84719i) q^{57} +(0.321003 - 14.2363i) q^{58} +(10.9843 - 9.21690i) q^{59} +(2.14285 + 0.891256i) q^{60} +(0.623080 - 3.53366i) q^{61} +(-1.85229 - 12.0930i) q^{62} +(0.840816 + 2.31012i) q^{63} +(-4.89776 + 6.32550i) q^{64} +(2.92368 - 1.68799i) q^{65} +(1.77819 - 2.02466i) q^{66} +(1.24980 + 1.04871i) q^{67} +(-5.95841 - 11.4868i) q^{68} +(3.47958 + 2.00894i) q^{69} +(0.674431 + 1.99157i) q^{70} +(0.521605 + 2.95817i) q^{71} +(-1.12150 + 4.54023i) q^{72} +(4.79480 + 1.74516i) q^{73} +(2.68913 + 3.35559i) q^{74} +1.16041 q^{75} +(-3.93607 + 7.77865i) q^{76} +2.44138 q^{77} +(-3.46458 - 4.32322i) q^{78} +(2.65944 + 0.967958i) q^{79} +(-1.04652 + 3.86067i) q^{80} +(-0.226731 - 1.28586i) q^{81} +(4.30337 + 12.7077i) q^{82} +(13.2534 + 7.65186i) q^{83} +(3.06304 - 1.58886i) q^{84} +(-4.95639 - 4.15890i) q^{85} +(6.68907 - 7.61624i) q^{86} +(-10.1189 + 5.84214i) q^{87} +(3.85599 + 2.58868i) q^{88} +(-4.19047 - 11.5132i) q^{89} +(0.354035 + 2.31139i) q^{90} +(0.871616 - 4.94318i) q^{91} +(-2.65937 + 6.39396i) q^{92} +(-7.68989 + 6.45258i) q^{93} +(-0.123435 + 5.47428i) q^{94} +(-0.323519 + 4.34688i) q^{95} +(6.52258 + 0.738368i) q^{96} +(-5.45126 - 6.49656i) q^{97} +(-6.31091 - 2.45947i) q^{98} +(2.67377 + 0.471458i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.10357	−	0.884387i	0.780340	−	0.625356i
$2$	1.10357	−	0.884387i	0.780340	−	0.625356i
$3$	−1.09042	−	0.396882i	−0.629557	−	0.229140i	0.00748161	−	0.999972i	$-0.497619\pi$
$3$	−1.09042	−	0.396882i	−0.629557	−	0.229140i	−0.637038	+	0.770832i	$0.719841\pi$
$4$	0.435721	−	1.95196i	0.217860	−	0.975980i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	−1.55435	+	0.526371i	−0.634562	+	0.214890i
$7$	−1.28762	−	0.743405i	−0.486673	−	0.280981i	0.236520	−	0.971627i	$-0.423993\pi$
$7$	−1.28762	−	0.743405i	−0.486673	−	0.280981i	−0.723193	+	0.690646i	$0.757326\pi$
$8$	−1.24544	−	2.53946i	−0.440330	−	0.897836i
$9$	−1.26662	−	1.06282i	−0.422208	−	0.354274i
$10$	−1.06258	−	0.933229i	−0.336018	−	0.295113i
$11$	−1.42203	+	0.821011i	−0.428759	+	0.247544i	−0.698818	−	0.715300i	$-0.746290\pi$
$11$	−1.42203	+	0.821011i	−0.428759	+	0.247544i	0.270059	+	0.962844i	$0.412957\pi$
$12$	−1.24982	+	1.95553i	−0.360791	+	0.564514i
$13$	1.15465	+	3.17238i	0.320243	+	0.879860i	0.990473	+	0.137707i	$0.0439731\pi$
$13$	1.15465	+	3.17238i	0.320243	+	0.879860i	−0.670230	+	0.742153i	$0.733805\pi$
$14$	−2.07843	+	0.318352i	−0.555483	+	0.0850833i
$15$	−0.201502	+	1.14278i	−0.0520277	+	0.295064i
$16$	−3.62029	−	1.70102i	−0.905074	−	0.425255i
$17$	4.95639	−	4.15890i	1.20210	−	1.00868i	0.202533	−	0.979275i	$-0.435083\pi$
$17$	4.95639	−	4.15890i	1.20210	−	1.00868i	0.999568	−	0.0294069i	$-0.00936187\pi$
$18$	−2.33775	−	0.0527121i	−0.551013	−	0.0124244i
$19$	−4.22466	−	1.07343i	−0.969203	−	0.246262i
$19$	−4.22466	−	1.07343i	−0.969203	−	0.246262i
$20$	−1.99797	−	0.0901470i	−0.446759	−	0.0201575i
$21$	1.10900	+	1.32166i	0.242004	+	0.288410i
$22$	−0.843218	+	2.16367i	−0.179775	+	0.461296i
$23$	−3.40987	−	0.601253i	−0.711008	−	0.125370i	−0.193565	−	0.981088i	$-0.562005\pi$
$23$	−3.40987	−	0.601253i	−0.711008	−	0.125370i	−0.517443	+	0.855718i	$0.673116\pi$
$24$	0.350190	+	3.26339i	0.0714823	+	0.666136i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	4.07985	+	2.47978i	0.800123	+	0.486324i
$27$	2.69995	+	4.67645i	0.519606	+	0.899983i
$28$	−2.01214	+	2.18946i	−0.380258	+	0.413768i
$29$	6.47232	−	7.71340i	1.20188	−	1.43234i	0.329053	−	0.944311i	$-0.393271\pi$
$29$	6.47232	−	7.71340i	1.20188	−	1.43234i	0.872826	−	0.488032i	$-0.162285\pi$
$30$	0.788285	+	1.43934i	0.143920	+	0.262786i
$31$	4.32540	−	7.49181i	0.776865	−	1.34557i	−0.156876	−	0.987618i	$-0.550142\pi$
$31$	4.32540	−	7.49181i	0.776865	−	1.34557i	0.933741	−	0.357951i	$-0.116524\pi$
$32$	−5.49960	+	1.32455i	−0.972201	+	0.234150i
$33$	1.87646	−	0.330871i	0.326650	−	0.0575973i
$34$	1.79163	−	8.97299i	0.307262	−	1.53886i
$35$	−0.508519	+	1.39714i	−0.0859554	+	0.236161i
$36$	−2.62648	+	2.00930i	−0.437747	+	0.334884i
$37$			3.04067i			0.499883i	0.968261	+	0.249942i	$0.0804115\pi$
$37$			3.04067i			0.499883i	−0.968261	+	0.249942i	$0.919589\pi$
$38$	−5.61152	+	2.55163i	−0.910309	+	0.413929i
$39$		−	3.91750i		−	0.627302i
$40$	−2.28462	+	1.66749i	−0.361229	+	0.263654i
$41$	−3.24473	+	8.91482i	−0.506741	+	1.39226i	0.377839	+	0.925872i	$0.376667\pi$
$41$	−3.24473	+	8.91482i	−0.506741	+	1.39226i	−0.884580	+	0.466389i	$0.845555\pi$
$42$	2.39272	+	0.477751i	0.369204	+	0.0737186i
$43$	7.05877	−	1.24465i	1.07645	−	0.189808i	0.392806	−	0.919621i	$-0.371504\pi$
$43$	7.05877	−	1.24465i	1.07645	−	0.189808i	0.683646	+	0.729814i	$0.260393\pi$
$44$	0.982972	+	3.13348i	0.148189	+	0.472390i
$45$	−0.826730	+	1.43194i	−0.123242	+	0.213461i
$46$	−4.29476	+	2.35212i	−0.633228	+	0.346802i
$47$	−2.48880	+	2.96604i	−0.363029	+	0.432641i	−0.916381	−	0.400306i	$-0.868904\pi$
$47$	−2.48880	+	2.96604i	−0.363029	+	0.432641i	0.553353	+	0.832947i	$0.313348\pi$
$48$	3.27255	+	3.29166i	0.472352	+	0.475111i
$49$	−2.39470	−	4.14774i	−0.342100	−	0.592534i
$50$	−0.734536	+	1.20849i	−0.103879	+	0.170907i
$51$	−7.05516	+	2.56787i	−0.987920	+	0.359574i
$52$	6.69546	−	0.871562i	0.928494	−	0.120864i
$53$	7.22408	+	1.27380i	0.992304	+	0.174970i	0.646152	−	0.763209i	$-0.276377\pi$
$53$	7.22408	+	1.27380i	0.992304	+	0.174970i	0.346152	+	0.938179i	$0.387488\pi$
$54$	7.11536	+	2.77298i	0.968279	+	0.377354i
$55$	1.05547	+	1.25786i	0.142320	+	0.169610i
$56$	−0.284203	+	4.19572i	−0.0379782	+	0.560677i
$57$	4.18065	+	2.84719i	0.553740	+	0.377119i
$58$	0.321003	−	14.2363i	0.0421497	−	1.86932i
$59$	10.9843	−	9.21690i	1.43003	−	1.19994i	0.484335	−	0.874882i	$-0.339062\pi$
$59$	10.9843	−	9.21690i	1.43003	−	1.19994i	0.945695	−	0.325055i	$-0.105383\pi$
$60$	2.14285	+	0.891256i	0.276641	+	0.115061i
$61$	0.623080	−	3.53366i	0.0797772	−	0.452439i	−0.918585	−	0.395224i	$-0.870667\pi$
$61$	0.623080	−	3.53366i	0.0797772	−	0.452439i	0.998362	−	0.0572149i	$-0.0182220\pi$
$62$	−1.85229	−	12.0930i	−0.235241	−	1.53582i
$63$	0.840816	+	2.31012i	0.105933	+	0.291048i
$64$	−4.89776	+	6.32550i	−0.612220	+	0.790688i
$65$	2.92368	−	1.68799i	0.362638	−	0.209369i
$66$	1.77819	−	2.02466i	0.218880	−	0.249218i
$67$	1.24980	+	1.04871i	0.152688	+	0.128120i	0.715931	−	0.698171i	$-0.246002\pi$
$67$	1.24980	+	1.04871i	0.152688	+	0.128120i	−0.563244	+	0.826291i	$0.690447\pi$
$68$	−5.95841	−	11.4868i	−0.722564	−	1.39298i
$69$	3.47958	+	2.00894i	0.418892	+	0.241848i
$70$	0.674431	+	1.99157i	0.0806099	+	0.238038i
$71$	0.521605	+	2.95817i	0.0619031	+	0.351070i	0.999989	+	0.00466749i	$0.00148571\pi$
$71$	0.521605	+	2.95817i	0.0619031	+	0.351070i	−0.938086	+	0.346402i	$0.887403\pi$
$72$	−1.12150	+	4.54023i	−0.132170	+	0.535071i
$73$	4.79480	+	1.74516i	0.561189	+	0.204256i	0.607011	−	0.794694i	$-0.292368\pi$
$73$	4.79480	+	1.74516i	0.561189	+	0.204256i	−0.0458219	+	0.998950i	$0.514591\pi$
$74$	2.68913	+	3.35559i	0.312605	+	0.390079i
$75$	1.16041			0.133992
$76$	−3.93607	+	7.77865i	−0.451498	+	0.892272i
$77$	2.44138			0.278221
$78$	−3.46458	−	4.32322i	−0.392287	−	0.489509i
$79$	2.65944	+	0.967958i	0.299211	+	0.108904i	0.487263	−	0.873255i	$-0.337995\pi$
$79$	2.65944	+	0.967958i	0.299211	+	0.108904i	−0.188052	+	0.982159i	$0.560217\pi$
$80$	−1.04652	+	3.86067i	−0.117004	+	0.431636i
$81$	−0.226731	−	1.28586i	−0.0251924	−	0.142873i
$82$	4.30337	+	12.7077i	0.475228	+	1.40333i
$83$	13.2534	+	7.65186i	1.45475	+	0.839901i	0.998745	−	0.0500754i	$-0.0159462\pi$
$83$	13.2534	+	7.65186i	1.45475	+	0.839901i	0.456006	+	0.889977i	$0.349280\pi$
$84$	3.06304	−	1.58886i	0.334205	−	0.173358i
$85$	−4.95639	−	4.15890i	−0.537596	−	0.451096i
$86$	6.68907	−	7.61624i	0.721301	−	0.821280i
$87$	−10.1189	+	5.84214i	−1.08486	+	0.626343i
$88$	3.85599	+	2.58868i	0.411049	+	0.275954i
$89$	−4.19047	−	11.5132i	−0.444189	−	1.22040i	−0.936712	−	0.350100i	$-0.886148\pi$
$89$	−4.19047	−	11.5132i	−0.444189	−	1.22040i	0.492523	−	0.870299i	$-0.336075\pi$
$90$	0.354035	+	2.31139i	0.0373186	+	0.243642i
$91$	0.871616	−	4.94318i	0.0913702	−	0.518186i
$92$	−2.65937	+	6.39396i	−0.277259	+	0.666616i
$93$	−7.68989	+	6.45258i	−0.797404	+	0.669101i
$94$	−0.123435	+	5.47428i	−0.0127314	+	0.564629i
$95$	−0.323519	+	4.34688i	−0.0331923	+	0.445980i
$96$	6.52258	+	0.738368i	0.665708	+	0.0753594i
$97$	−5.45126	−	6.49656i	−0.553492	−	0.659626i	0.414664	−	0.909975i	$-0.363899\pi$
$97$	−5.45126	−	6.49656i	−0.553492	−	0.659626i	−0.968156	+	0.250349i	$0.919455\pi$
$98$	−6.31091	−	2.45947i	−0.637498	−	0.248444i
$99$	2.67377	+	0.471458i	0.268724	+	0.0473833i
$100$	0.258166	+	1.98327i	0.0258166	+	0.198327i
$101$	−3.16019	+	1.15022i	−0.314451	+	0.114451i	−0.494424	−	0.869221i	$-0.664621\pi$
$101$	−3.16019	+	1.15022i	−0.314451	+	0.114451i	0.179973	+	0.983672i	$0.442399\pi$
$102$	−5.51485	+	9.07330i	−0.546052	+	0.898391i
$103$	−2.23597	−	3.87282i	−0.220317	−	0.381600i	0.734587	−	0.678514i	$-0.237376\pi$
$103$	−2.23597	−	3.87282i	−0.220317	−	0.381600i	−0.954904	+	0.296914i	$0.904042\pi$
$104$	6.61809	−	6.88320i	0.648958	−	0.674954i
$105$	1.10900	−	1.32166i	0.108228	−	0.128981i
$106$	9.09879	−	4.98316i	0.883753	−	0.484007i
$107$	−2.76272	+	4.78516i	−0.267082	+	0.462599i	−0.968107	−	0.250537i	$-0.919393\pi$
$107$	−2.76272	+	4.78516i	−0.267082	+	0.462599i	0.701025	+	0.713137i	$0.252726\pi$
$108$	10.3047	−	3.23257i	0.991567	−	0.311054i
$109$	−15.4950	+	2.73219i	−1.48415	+	0.261696i	−0.856236	−	0.516585i	$-0.827203\pi$
$109$	−15.4950	+	2.73219i	−1.48415	+	0.261696i	−0.627916	+	0.778281i	$0.716092\pi$
$110$	2.27722	+	0.454690i	0.217124	+	0.0433530i
$111$	1.20679	−	3.31562i	0.114543	−	0.314705i
$112$	3.39700	+	4.88160i	0.320986	+	0.461268i
$113$			4.23571i			0.398462i	0.979953	+	0.199231i	$0.0638444\pi$
$113$			4.23571i			0.398462i	−0.979953	+	0.199231i	$0.936156\pi$
$114$	7.13164	−	0.555246i	0.667939	−	0.0520035i
$115$			3.46248i			0.322878i
$116$	−12.2361	−	15.9946i	−1.13610	−	1.48506i
$117$	1.90917	−	5.24540i	0.176503	−	0.484937i
$118$	3.97058	−	19.8858i	0.365521	−	1.83064i
$119$	−9.47367	+	1.67046i	−0.868450	+	0.153131i
$120$	3.15300	−	0.911551i	0.287828	−	0.0832129i
$121$	−4.15188	+	7.19127i	−0.377444	+	0.653752i
$122$	−2.43751	−	4.45068i	−0.220682	−	0.402945i
$123$	7.07626	−	8.43316i	0.638045	−	0.760392i
$124$	−12.7390	−	11.7073i	−1.14400	−	1.05135i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	2.97094	+	1.80577i	0.264672	+	0.160871i
$127$	0.393633	−	0.143271i	0.0349293	−	0.0127132i	−0.324496	−	0.945887i	$-0.605195\pi$
$127$	0.393633	−	0.143271i	0.0349293	−	0.0127132i	0.359426	+	0.933174i	$0.382973\pi$
$128$	0.189182	+	11.3121i	0.0167215	+	0.999860i
$129$	−8.19103	−	1.44430i	−0.721180	−	0.127164i
$130$	1.73364	−	4.44847i	0.152051	−	0.390157i
$131$	7.47927	+	8.91345i	0.653467	+	0.778772i	0.986433	−	0.164167i	$-0.0524937\pi$
$131$	7.47927	+	8.91345i	0.653467	+	0.778772i	−0.332965	+	0.942939i	$0.608049\pi$
$132$	0.171767	−	3.80695i	0.0149504	−	0.331352i
$133$	4.64174	+	4.52280i	0.402490	+	0.392177i
$134$	2.30670	+	0.0520120i	0.199269	+	0.00449315i
$135$	4.13656	−	3.47099i	0.356019	−	0.298735i
$136$	−16.7343	−	7.40691i	−1.43495	−	0.635137i
$137$	−1.07288	+	6.08458i	−0.0916620	+	0.519841i	0.904057	+	0.427411i	$0.140574\pi$
$137$	−1.07288	+	6.08458i	−0.0916620	+	0.519841i	−0.995719	+	0.0924297i	$0.970537\pi$
$138$	5.61663	−	0.860298i	0.478119	−	0.0732334i
$139$	−2.64065	−	7.25513i	−0.223977	−	0.615372i	0.775903	−	0.630852i	$-0.217295\pi$
$139$	−2.64065	−	7.25513i	−0.223977	−	0.615372i	−0.999880	+	0.0154801i	$0.995072\pi$
$140$	2.50560	+	1.60137i	0.211762	+	0.135341i
$141$	3.89102	−	2.24648i	0.327683	−	0.189188i
$142$	3.19179	+	2.80324i	0.267849	+	0.235242i
$143$	−4.24651	−	3.56325i	−0.355111	−	0.297974i
$144$	2.77767	+	6.00228i	0.231472	+	0.500190i
$145$	−8.72013	−	5.03457i	−0.724167	−	0.418098i
$146$	6.83478	−	2.31455i	0.565651	−	0.191554i
$147$	0.965074	+	5.47321i	0.0795980	+	0.451422i
$148$	5.93527	+	1.32488i	0.487876	+	0.108905i
$149$	−1.48289	−	0.539727i	−0.121483	−	0.0442162i	0.280563	−	0.959835i	$-0.409479\pi$
$149$	−1.48289	−	0.539727i	−0.121483	−	0.0442162i	−0.402046	+	0.915619i	$0.631701\pi$
$150$	1.28059	−	1.02625i	0.104559	−	0.0837927i
$151$	−19.4799			−1.58525			−0.792625	−	0.609709i	$-0.791286\pi$
$151$	−19.4799			−1.58525			−0.792625	+	0.609709i	$0.791286\pi$
$152$	2.53562	+	12.0653i	0.205666	+	0.978622i
$153$	−10.6981			−0.864887
$154$	2.69422	−	2.15912i	0.217107	−	0.173987i
$155$	−8.12909	−	2.95875i	−0.652944	−	0.237652i
$156$	−7.64680	−	1.70694i	−0.612234	−	0.136664i
$157$	1.35863	+	7.70517i	0.108430	+	0.614939i	0.989795	+	0.142502i	$0.0455147\pi$
$157$	1.35863	+	7.70517i	0.108430	+	0.614939i	−0.881364	+	0.472438i	$0.843374\pi$
$158$	3.79092	−	1.28377i	0.301590	−	0.102131i
$159$	−7.37177	−	4.25609i	−0.584619	−	0.337530i
$160$	2.25942	+	5.18604i	0.178623	+	0.409992i
$161$	3.94363	+	3.30910i	0.310802	+	0.260794i
$162$	−1.38741	−	1.21851i	−0.109005	−	0.0957353i
$163$	−9.40645	+	5.43082i	−0.736770	+	0.425374i	−0.820894	−	0.571081i	$-0.806524\pi$
$163$	−9.40645	+	5.43082i	−0.736770	+	0.425374i	0.0841236	+	0.996455i	$0.473191\pi$
$164$	15.9876	+	10.2179i	1.24842	+	0.797888i
$165$	−0.651689	−	1.79050i	−0.0507339	−	0.139390i
$166$	21.3932	−	3.27680i	1.66044	−	0.254329i
$167$	3.41386	−	19.3610i	0.264173	−	1.49820i	−0.507208	−	0.861823i	$-0.669323\pi$
$167$	3.41386	−	19.3610i	0.264173	−	1.49820i	0.771381	−	0.636374i	$-0.219566\pi$
$168$	1.97511	−	4.46232i	0.152383	−	0.344276i
$169$	1.22781	−	1.03025i	0.0944468	−	0.0792503i
$170$	−9.14779	−	0.206266i	−0.701603	−	0.0158199i
$171$	4.21019	+	5.84970i	0.321961	+	0.447338i
$172$	0.646143	−	14.3208i	0.0492679	−	1.09195i
$173$	1.67641	+	1.99786i	0.127455	+	0.151895i	0.825998	−	0.563673i	$-0.190612\pi$
$173$	1.67641	+	1.99786i	0.127455	+	0.151895i	−0.698543	+	0.715568i	$0.746168\pi$
$174$	−6.00016	+	15.3962i	−0.454871	+	1.16718i
$175$	1.46422	+	0.258182i	0.110685	+	0.0195167i
$176$	6.54473	−	0.553397i	0.493328	−	0.0417139i
$177$	−15.6355	+	5.69087i	−1.17524	+	0.427752i
$178$	−14.8066	−	8.99962i	−1.10980	−	0.674550i
$179$	12.6648	+	21.9361i	0.946611	+	1.63958i	0.752493	+	0.658600i	$0.228851\pi$
$179$	12.6648	+	21.9361i	0.946611	+	1.63958i	0.194118	+	0.980978i	$0.437816\pi$
$180$	2.43486	+	2.23767i	0.181484	+	0.166786i
$181$	9.04302	−	10.7771i	0.672162	−	0.801052i	−0.316914	−	0.948454i	$-0.602647\pi$
$181$	9.04302	−	10.7771i	0.672162	−	0.801052i	0.989077	+	0.147402i	$0.0470912\pi$
$182$	−3.40979	−	6.22598i	−0.252751	−	0.461500i
$183$	−2.08187	+	3.60590i	−0.153896	+	0.266556i
$184$	2.71993	+	9.40808i	0.200516	+	0.693573i
$185$	2.99448	−	0.528007i	0.220158	−	0.0388199i
$186$	−2.77973	+	13.9217i	−0.203820	+	1.02079i
$187$	−3.63364	+	9.98335i	−0.265718	+	0.730055i
$188$	4.70516	+	6.15040i	0.343159	+	0.448564i
$189$		−	8.02863i		−	0.583997i
$190$	3.48729	+	5.08319i	0.252995	+	0.368773i
$191$		−	16.5323i		−	1.19624i	−0.801408	−	0.598118i	$-0.795916\pi$
$191$		−	16.5323i		−	1.19624i	0.801408	−	0.598118i	$-0.204084\pi$
$192$	7.85111	−	4.95365i	0.566605	−	0.357499i
$193$	−5.01066	+	13.7667i	−0.360675	+	0.990947i	0.618116	+	0.786087i	$0.287896\pi$
$193$	−5.01066	+	13.7667i	−0.360675	+	0.990947i	−0.978791	+	0.204860i	$0.934326\pi$
$194$	−11.7613	−	2.34837i	−0.844413	−	0.168603i
$195$	−3.85798	+	0.680267i	−0.276276	+	0.0487149i
$196$	−9.13964	+	2.86710i	−0.652831	+	0.204793i
$197$	−9.52561	+	16.4988i	−0.678672	+	1.17549i	0.296709	+	0.954968i	$0.404111\pi$
$197$	−9.52561	+	16.4988i	−0.678672	+	1.17549i	−0.975381	+	0.220526i	$0.929223\pi$
$198$	3.36764	−	1.84436i	0.239327	−	0.131073i
$199$	4.35301	−	5.18772i	0.308577	−	0.367748i	−0.589361	−	0.807870i	$-0.700620\pi$
$199$	4.35301	−	5.18772i	0.308577	−	0.367748i	0.897938	+	0.440122i	$0.145065\pi$
$200$	2.03888	+	1.96035i	0.144170	+	0.138618i
$201$	−0.946600	−	1.63956i	−0.0667680	−	0.115646i
$202$	−2.47025	+	4.06418i	−0.173806	+	0.285954i
$203$	−14.0680	+	5.12035i	−0.987383	+	0.359378i
$204$	1.93830	+	14.8903i	0.135708	+	1.04253i
$205$	9.34282	+	1.64739i	0.652531	+	0.115059i
$206$	−5.89261	−	2.29645i	−0.410558	−	0.160001i
$207$	3.68000	+	4.38565i	0.255778	+	0.304824i
$208$	1.21610	−	13.4490i	0.0843213	−	0.932523i
$209$	6.88890	−	1.94204i	0.476515	−	0.134334i
$210$	0.0550024	−	2.43933i	0.00379553	−	0.168330i
$211$	−0.354765	+	0.297683i	−0.0244230	+	0.0204933i	−0.654917	−	0.755700i	$-0.727297\pi$
$211$	−0.354765	+	0.297683i	−0.0244230	+	0.0204933i	0.630494	+	0.776194i	$0.282852\pi$
$212$	5.63409	−	13.5461i	0.386951	−	0.930350i
$213$	0.605273	−	3.43267i	0.0414726	−	0.235203i
$214$	1.18309	+	7.72406i	0.0808745	+	0.528006i
$215$	−2.45148	−	6.73540i	−0.167190	−	0.459350i
$216$	8.51305	−	12.6807i	0.579240	−	0.862810i
$217$	−11.1389	+	6.43105i	−0.756158	+	0.436568i
$218$	−14.6835	+	16.7187i	−0.994490	+	1.13233i
$219$	−4.53574	−	3.80594i	−0.306497	−	0.257182i
$220$	2.91519	−	1.51216i	0.196542	−	0.101950i
$221$	18.9165	+	10.9215i	1.27246	+	0.734657i
$222$	−1.60052	−	4.72628i	−0.107420	−	0.317207i
$223$	−3.42824	−	19.4425i	−0.229572	−	1.30197i	−0.853750	−	0.520684i	$-0.825677\pi$
$223$	−3.42824	−	19.4425i	−0.229572	−	1.30197i	0.624178	−	0.781282i	$-0.285434\pi$
$224$	8.06605	+	2.38292i	0.538935	+	0.159215i
$225$	1.55374	+	0.565516i	0.103583	+	0.0377011i
$226$	3.74601	+	4.67439i	0.249181	+	0.310936i
$227$	3.86097			0.256261			0.128131	−	0.991757i	$-0.459102\pi$
$227$	3.86097			0.256261			0.128131	+	0.991757i	$0.459102\pi$
$228$	7.37919	−	6.91987i	0.488699	−	0.458280i
$229$	−21.6315			−1.42945			−0.714725	−	0.699405i	$-0.753448\pi$
$229$	−21.6315			−1.42945			−0.714725	+	0.699405i	$0.753448\pi$
$230$	3.06217	+	3.82107i	0.201913	+	0.251954i
$231$	−2.66214	−	0.968938i	−0.175156	−	0.0637515i
$232$	−27.6488	−	6.82963i	−1.81523	−	0.448387i
$233$	1.81178	+	10.2751i	0.118694	+	0.673146i	0.984855	+	0.173381i	$0.0554692\pi$
$233$	1.81178	+	10.2751i	0.118694	+	0.673146i	−0.866161	+	0.499765i	$0.833420\pi$
$234$	−2.53206	−	7.47710i	−0.165526	−	0.488793i
$235$	3.35315	+	1.93594i	0.218736	+	0.126287i
$236$	−13.2049	−	25.4568i	−0.859568	−	1.65710i
$237$	−2.51576	−	2.11097i	−0.163416	−	0.137122i
$238$	−8.97750	+	10.2219i	−0.581925	+	0.662585i
$239$	−1.58969	+	0.917810i	−0.102829	+	0.0593682i	−0.550532	−	0.834814i	$-0.685575\pi$
$239$	−1.58969	+	0.917810i	−0.102829	+	0.0593682i	0.447704	+	0.894182i	$0.352242\pi$
$240$	2.67338	−	3.79443i	0.172566	−	0.244929i
$241$	−0.0378910	−	0.104105i	−0.00244077	−	0.00670597i	0.938466	−	0.345371i	$-0.112247\pi$
$241$	−0.0378910	−	0.104105i	−0.00244077	−	0.00670597i	−0.940907	+	0.338665i	$0.890025\pi$
$242$	1.77798	+	11.6079i	0.114293	+	0.746185i
$243$	2.54995	−	14.4615i	0.163579	−	0.927704i
$244$	−6.62608	−	2.75592i	−0.424191	−	0.176430i
$245$	−3.66889	+	3.07856i	−0.234397	+	0.196682i
$246$	0.350956	−	15.5647i	0.0223761	−	0.992369i
$247$	−1.47268	−	14.6417i	−0.0937044	−	0.931627i
$248$	−24.4122	−	1.65360i	−1.55018	−	0.105003i
$249$	−11.4150	−	13.6038i	−0.723394	−	0.862107i
$250$	1.31768	+	0.513524i	0.0833377	+	0.0324781i
$251$	24.0654	+	4.24338i	1.51899	+	0.267840i	0.870038	−	0.492985i	$-0.164094\pi$
$251$	24.0654	+	4.24338i	1.51899	+	0.267840i	0.648957	+	0.760825i	$0.275206\pi$
$252$	4.87563	−	0.634670i	0.307136	−	0.0399805i
$253$	5.34259	−	1.94454i	0.335886	−	0.122252i
$254$	0.307694	−	0.506232i	0.0193064	−	0.0317638i
$255$	3.75397	+	6.50207i	0.235083	+	0.407175i
$256$	10.2131	+	12.3164i	0.638317	+	0.769774i
$257$	12.8246	−	15.2838i	0.799977	−	0.953376i	−0.199672	−	0.979863i	$-0.563988\pi$
$257$	12.8246	−	15.2838i	0.799977	−	0.953376i	0.999649	+	0.0264869i	$0.00843202\pi$
$258$	−10.3167	+	5.65016i	−0.642288	+	0.351763i
$259$	2.26045	−	3.91522i	0.140458	−	0.243280i
$260$	−2.02098	−	6.44240i	−0.125336	−	0.399541i
$261$	−16.3960	+	2.89105i	−1.01489	+	0.178952i
$262$	16.1368	+	3.22202i	0.996936	+	0.199057i
$263$	−2.20159	+	6.04882i	−0.135756	+	0.372986i	−0.988879	−	0.148724i	$-0.952483\pi$
$263$	−2.20159	+	6.04882i	−0.135756	+	0.372986i	0.853123	+	0.521710i	$0.174706\pi$
$264$	−3.17726	−	4.35313i	−0.195547	−	0.267917i
$265$		−	7.33553i		−	0.450618i
$266$	9.12238	+	0.886118i	0.559329	+	0.0543314i
$267$			14.2174i			0.870092i
$268$	2.59160	−	1.98262i	0.158307	−	0.121108i
$269$	−2.24420	+	6.16588i	−0.136831	+	0.375941i	−0.989116	−	0.147137i	$-0.952994\pi$
$269$	−2.24420	+	6.16588i	−0.136831	+	0.375941i	0.852285	+	0.523078i	$0.175216\pi$
$270$	1.49528	−	7.48879i	0.0909998	−	0.455753i
$271$	5.70109	−	1.00526i	0.346317	−	0.0610649i	0.00221542	−	0.999998i	$-0.499295\pi$
$271$	5.70109	−	1.00526i	0.346317	−	0.0610649i	0.344101	+	0.938933i	$0.388184\pi$
$272$	−25.0180	+	6.62555i	−1.51694	+	0.401733i
$273$	−2.91229	+	5.04423i	−0.176260	+	0.305291i
$274$	4.19713	+	7.66359i	0.253558	+	0.462974i
$275$	1.05547	−	1.25786i	0.0636473	−	0.0758519i
$276$	5.43749	−	5.91667i	0.327299	−	0.356142i
$277$	−2.08135	−	3.60501i	−0.125056	−	0.216604i	0.796699	−	0.604377i	$-0.206578\pi$
$277$	−2.08135	−	3.60501i	−0.125056	−	0.216604i	−0.921755	+	0.387773i	$0.873245\pi$
$278$	−9.33047	−	5.67117i	−0.559605	−	0.340134i
$279$	−13.4411	+	4.89217i	−0.804699	+	0.292886i
$280$	4.18133	−	0.448694i	0.249882	−	0.0268146i
$281$	7.69542	+	1.35691i	0.459070	+	0.0809465i	0.398401	−	0.917211i	$-0.369565\pi$
$281$	7.69542	+	1.35691i	0.459070	+	0.0809465i	0.0606696	+	0.998158i	$0.480676\pi$
$282$	2.30724	−	5.92030i	0.137394	−	0.352549i
$283$	−2.81414	−	3.35376i	−0.167283	−	0.199361i	0.675890	−	0.737003i	$-0.263760\pi$
$283$	−2.81414	−	3.35376i	−0.167283	−	0.199361i	−0.843173	+	0.537642i	$0.819315\pi$
$284$	6.00150	+	0.270784i	0.356123	+	0.0160681i
$285$	2.07797	−	4.61154i	0.123088	−	0.273164i
$286$	−7.83760	−	0.176724i	−0.463447	−	0.0104499i
$287$	10.8053	−	9.06671i	0.637816	−	0.535191i
$288$	8.37368	+	4.16739i	0.493424	+	0.245566i
$289$	4.31729	−	24.4846i	0.253958	−	1.44027i
$290$	−14.0757	+	2.15598i	−0.826556	+	0.126603i
$291$	3.36582	+	9.24752i	0.197308	+	0.542099i
$292$	5.49569	−	8.59885i	0.321611	−	0.503210i
$293$	13.7066	−	7.91351i	0.800748	−	0.462312i	−0.0429845	−	0.999076i	$-0.513687\pi$
$293$	13.7066	−	7.91351i	0.800748	−	0.462312i	0.843733	+	0.536764i	$0.180353\pi$
$294$	5.90545	+	5.18655i	0.344413	+	0.302486i
$295$	−10.9843	−	9.21690i	−0.639529	−	0.536629i
$296$	7.72168	−	3.78697i	0.448813	−	0.220113i
$297$	−7.67884	−	4.43338i	−0.445571	−	0.257251i
$298$	−2.11379	+	0.715821i	−0.122449	+	0.0414664i
$299$	−2.02981	−	11.5116i	−0.117387	−	0.665736i
$300$	0.505613	−	2.26506i	0.0291916	−	0.130774i
$301$	−10.0143	−	3.64489i	−0.577212	−	0.210088i
$302$	−21.4974	+	17.2277i	−1.23703	+	0.991345i
$303$	3.90245			0.224190
$304$	13.4686	+	11.0724i	0.772476	+	0.635044i
$305$	−3.58818			−0.205458
$306$	−11.8060	+	9.46122i	−0.674906	+	0.540862i
$307$	5.14410	+	1.87230i	0.293589	+	0.106858i	0.484616	−	0.874727i	$-0.338959\pi$
$307$	5.14410	+	1.87230i	0.293589	+	0.106858i	−0.191026	+	0.981585i	$0.561182\pi$
$308$	1.06376	−	4.76547i	0.0606133	−	0.271538i
$309$	0.901107	+	5.11043i	0.0512622	+	0.290722i
$310$	−11.5877	+	3.92408i	−0.658136	+	0.222873i
$311$	8.49640	+	4.90540i	0.481787	+	0.278160i	0.721161	−	0.692768i	$-0.243609\pi$
$311$	8.49640	+	4.90540i	0.481787	+	0.278160i	−0.239374	+	0.970927i	$0.576942\pi$
$312$	−9.94835	+	4.87901i	−0.563214	+	0.276220i
$313$	6.89812	+	5.78821i	0.389905	+	0.327169i	0.816576	−	0.577238i	$-0.195869\pi$
$313$	6.89812	+	5.78821i	0.389905	+	0.327169i	−0.426671	+	0.904407i	$0.640314\pi$
$314$	8.31369	+	7.30162i	0.469168	+	0.412054i
$315$	2.12902	−	1.22919i	0.119957	−	0.0692570i
$316$	3.04819	−	4.76937i	0.171474	−	0.268298i
$317$	−4.72964	−	12.9946i	−0.265643	−	0.729848i	−0.998762	−	0.0497476i	$-0.984158\pi$
$317$	−4.72964	−	12.9946i	−0.265643	−	0.729848i	0.733119	−	0.680101i	$-0.238064\pi$
$318$	−11.8993	+	1.82261i	−0.667278	+	0.102207i
$319$	−2.87105	+	16.2826i	−0.160748	+	0.911648i
$320$	7.07989	+	3.72494i	0.395778	+	0.208230i
$321$	4.91168	−	4.12139i	0.274143	−	0.230033i
$322$	7.27859	+	0.164119i	0.405620	+	0.00914599i
$323$	−25.4033	+	12.2496i	−1.41348	+	0.681587i
$324$	−2.60873	−	0.117704i	−0.144930	−	0.00653913i
$325$	−2.17004	−	2.58615i	−0.120372	−	0.143454i
$326$	−5.57771	+	14.3122i	−0.308921	+	0.792680i
$327$	17.9805	+	3.17044i	0.994323	+	0.175326i
$328$	26.6800	−	2.86300i	1.47315	−	0.158083i
$329$	5.40959	−	1.96893i	0.298240	−	0.108551i
$330$	−2.30268	−	1.39959i	−0.126758	−	0.0770451i
$331$	8.70826	+	15.0831i	0.478649	+	0.829044i	0.999700	−	0.0244809i	$-0.00779329\pi$
$331$	8.70826	+	15.0831i	0.478649	+	0.829044i	−0.521051	+	0.853525i	$0.674460\pi$
$332$	20.7109	−	22.5361i	1.13666	−	1.23683i
$333$	3.23170	−	3.85139i	0.177096	−	0.211055i
$334$	−13.3552	−	24.3853i	−0.730762	−	1.33430i
$335$	0.815750	−	1.41292i	0.0445692	−	0.0771961i
$336$	−1.76675	−	6.67123i	−0.0963842	−	0.363945i
$337$	19.3795	−	3.41713i	1.05567	−	0.186143i	0.381235	−	0.924478i	$-0.375499\pi$
$337$	19.3795	−	3.41713i	1.05567	−	0.186143i	0.674434	+	0.738335i	$0.264388\pi$
$338$	0.443827	−	2.22281i	0.0241410	−	0.120905i
$339$	1.68108	−	4.61872i	0.0913036	−	0.250855i
$340$	−10.2776	+	7.86255i	−0.557382	+	0.426407i
$341$			14.2048i			0.769233i
$342$	9.81962	+	2.73210i	0.530984	+	0.147735i
$343$			17.5286i			0.946455i
$344$	−11.9520	−	16.3754i	−0.644410	−	0.882900i
$345$	1.37419	−	3.77557i	0.0739841	−	0.203270i
$346$	3.61691	+	0.722184i	0.194446	+	0.0388249i
$347$	7.35622	−	1.29710i	0.394903	−	0.0696320i	0.0273292	−	0.999626i	$-0.491300\pi$
$347$	7.35622	−	1.29710i	0.394903	−	0.0696320i	0.367573	+	0.929994i	$0.380189\pi$
$348$	6.99461	+	22.2972i	0.374951	+	1.19525i
$349$	7.36902	−	12.7635i	0.394455	−	0.683215i	−0.598577	−	0.801065i	$-0.704267\pi$
$349$	7.36902	−	12.7635i	0.394455	−	0.683215i	0.993031	+	0.117850i	$0.0376002\pi$
$350$	1.84420	−	1.01002i	0.0985767	−	0.0539877i
$351$	−11.7180	+	13.9649i	−0.625459	+	0.745393i
$352$	6.73314	−	6.39879i	0.358877	−	0.341056i
$353$	17.6079	+	30.4978i	0.937176	+	1.62324i	0.770707	+	0.637189i	$0.219903\pi$
$353$	17.6079	+	30.4978i	0.937176	+	1.62324i	0.166468	+	0.986047i	$0.446764\pi$
$354$	−12.2219	+	20.1081i	−0.649589	+	1.06873i
$355$	2.82265	−	1.02736i	0.149811	−	0.0545267i
$356$	−24.2992	+	3.16308i	−1.28786	+	0.167643i
$357$	10.9933	+	1.93842i	0.581827	+	0.102592i
$358$	33.3764	+	13.0073i	1.76400	+	0.687460i
$359$	14.7931	+	17.6297i	0.780750	+	0.930462i	0.998967	−	0.0454384i	$-0.0144685\pi$
$359$	14.7931	+	17.6297i	0.780750	+	0.930462i	−0.218217	+	0.975900i	$0.570024\pi$
$360$	4.66600	+	0.316058i	0.245920	+	0.0166577i
$361$	16.6955	+	9.06976i	0.878710	+	0.477356i
$362$	0.448500	−	19.8907i	0.0235726	−	1.04543i
$363$	7.38140	−	6.19373i	0.387423	−	0.325086i
$364$	−9.26911	−	3.85521i	−0.485833	−	0.202068i
$365$	0.886043	−	5.02500i	0.0463776	−	0.263021i
$366$	0.891530	+	5.82053i	0.0466010	+	0.304244i
$367$	−8.29186	−	22.7817i	−0.432832	−	1.18920i	−0.944067	−	0.329755i	$-0.893034\pi$
$367$	−8.29186	−	22.7817i	−0.432832	−	1.18920i	0.511235	−	0.859441i	$-0.329188\pi$
$368$	11.3220	+	7.97697i	0.590200	+	0.415828i
$369$	13.5847	−	7.84314i	0.707192	−	0.408298i
$370$	2.83764	−	3.23097i	0.147522	−	0.167970i
$371$	−8.35489	−	7.01059i	−0.433764	−	0.363971i
$372$	9.24453	+	17.8219i	0.479307	+	0.924021i
$373$	−5.06853	−	2.92632i	−0.262438	−	0.151519i	0.363008	−	0.931786i	$-0.381750\pi$
$373$	−5.06853	−	2.92632i	−0.262438	−	0.151519i	−0.625446	+	0.780267i	$0.715083\pi$
$374$	4.81917	+	14.2308i	0.249193	+	0.735859i
$375$	−0.201502	−	1.14278i	−0.0104055	−	0.0590127i
$376$	10.6318	+	2.62620i	0.548293	+	0.135436i
$377$	31.9431	+	11.6263i	1.64515	+	0.598787i
$378$	−7.10041	−	8.86013i	−0.365206	−	0.455716i
$379$	−1.32383			−0.0680007			−0.0340004	−	0.999422i	$-0.510825\pi$
$379$	−1.32383			−0.0680007			−0.0340004	+	0.999422i	$0.510825\pi$
$380$	8.34396	+	2.52552i	0.428036	+	0.129556i
$381$	−0.486088			−0.0249031
$382$	−14.6209	−	18.2445i	−0.748072	−	0.933470i
$383$	2.20706	+	0.803306i	0.112776	+	0.0410470i	0.397792	−	0.917476i	$-0.369777\pi$
$383$	2.20706	+	0.803306i	0.112776	+	0.0410470i	−0.285016	+	0.958523i	$0.591999\pi$
$384$	4.28329	−	12.4101i	0.218581	−	0.633300i
$385$	−0.423941	−	2.40429i	−0.0216060	−	0.122534i
$386$	6.64546	+	19.6238i	0.338245	+	0.998825i
$387$	−10.2636	−	5.92572i	−0.521730	−	0.301221i
$388$	−15.0563	+	7.80996i	−0.764366	+	0.396491i
$389$	9.97296	+	8.36830i	0.505649	+	0.424290i	0.859595	−	0.510976i	$-0.170716\pi$
$389$	9.97296	+	8.36830i	0.505649	+	0.424290i	−0.353946	+	0.935266i	$0.615160\pi$
$390$	−3.65593	+	4.16267i	−0.185125	+	0.210785i
$391$	−19.4012	+	11.2013i	−0.981161	+	0.566474i
$392$	−7.55058	+	11.2470i	−0.381362	+	0.568060i
$393$	−4.61799	−	12.6878i	−0.232947	−	0.640016i
$394$	4.07920	+	26.6319i	0.205507	+	1.34170i
$395$	0.491445	−	2.78712i	0.0247273	−	0.140235i
$396$	2.08528	−	5.01367i	0.104789	−	0.251946i
$397$	−5.91636	+	4.96442i	−0.296934	+	0.249157i	−0.779067	−	0.626941i	$-0.784307\pi$
$397$	−5.91636	+	4.96442i	−0.296934	+	0.249157i	0.482133	+	0.876098i	$0.339862\pi$
$398$	0.215893	−	9.57474i	0.0108217	−	0.479938i
$399$	−3.26645	−	6.77400i	−0.163527	−	0.339124i
$400$	3.98375	+	0.360221i	0.199187	+	0.0180111i
$401$	−9.81825	−	11.7009i	−0.490300	−	0.584317i	0.462994	−	0.886362i	$-0.346775\pi$
$401$	−9.81825	−	11.7009i	−0.490300	−	0.584317i	−0.953294	+	0.302045i	$0.902331\pi$
$402$	−2.49464	−	0.972204i	−0.124421	−	0.0484891i
$403$	28.7612	+	5.07137i	1.43270	+	0.252623i
$404$	0.868214	+	6.66975i	0.0431953	+	0.331832i
$405$	−1.22695	+	0.446573i	−0.0609676	+	0.0221904i
$406$	−10.9967	+	18.0922i	−0.545755	+	0.897902i
$407$	−2.49643	−	4.32394i	−0.123743	−	0.214330i
$408$	15.3078	+	14.7182i	0.757848	+	0.728660i
$409$	−8.95297	+	10.6697i	−0.442696	+	0.527585i	−0.940540	−	0.339682i	$-0.889681\pi$
$409$	−8.95297	+	10.6697i	−0.442696	+	0.527585i	0.497844	+	0.867266i	$0.334125\pi$
$410$	11.7674	−	6.44466i	0.581149	−	0.318279i
$411$	3.58475	−	6.20897i	0.176823	−	0.306266i
$412$	−8.53384	+	2.67706i	−0.420432	+	0.131889i
$413$	−20.9954	+	3.70206i	−1.03312	+	0.182166i
$414$	7.93974	+	1.58532i	0.390217	+	0.0779142i
$415$	5.23418	−	14.3808i	0.256936	−	0.705926i
$416$	−10.5521	−	15.9174i	−0.517359	−	0.780415i
$417$			8.95920i			0.438734i
$418$	5.88486	−	8.23562i	0.287838	−	0.402818i
$419$			35.8074i			1.74931i	0.484749	+	0.874653i	$0.338911\pi$
$419$			35.8074i			1.74931i	−0.484749	+	0.874653i	$0.661089\pi$
$420$	−2.09661	−	2.74060i	−0.102304	−	0.133728i
$421$	11.6482	−	32.0031i	0.567698	−	1.55974i	−0.240390	−	0.970676i	$-0.577275\pi$
$421$	11.6482	−	32.0031i	0.567698	−	1.55974i	0.808088	−	0.589061i	$-0.200502\pi$
$422$	−0.128240	+	0.642262i	−0.00624262	+	0.0312648i
$423$	6.30475	−	1.11170i	0.306547	−	0.0540525i
$424$	−5.76239	−	19.9317i	−0.279846	−	0.967971i
$425$	−3.23505	+	5.60328i	−0.156923	+	0.271799i
$426$	−2.36785	−	4.32348i	−0.114723	−	0.209473i
$427$	−3.42923	+	4.08680i	−0.165952	+	0.197774i
$428$	8.13668	+	7.47771i	0.393301	+	0.361449i
$429$	3.21631	+	5.57081i	0.155285	+	0.268961i
$430$	−8.66207	−	5.26490i	−0.417722	−	0.253896i
$431$	4.38855	−	1.59730i	0.211389	−	0.0769394i	−0.234155	−	0.972199i	$-0.575232\pi$
$431$	4.38855	−	1.59730i	0.211389	−	0.0769394i	0.445544	+	0.895260i	$0.353010\pi$
$432$	−1.81988	−	21.5228i	−0.0875592	−	1.03552i
$433$	17.4415	+	3.07541i	0.838185	+	0.147795i	0.576232	−	0.817286i	$-0.304522\pi$
$433$	17.4415	+	3.07541i	0.838185	+	0.147795i	0.261953	+	0.965081i	$0.415634\pi$
$434$	−6.60499	+	16.9482i	−0.317050	+	0.813539i
$435$	7.51051	+	8.95068i	0.360101	+	0.429152i
$436$	−1.41838	+	31.4361i	−0.0679279	+	1.50552i
$437$	13.7601	+	6.20035i	0.658237	+	0.296603i
$438$	−8.37142	−	0.188760i	−0.400002	−	0.00901932i
$439$	−2.02242	+	1.69701i	−0.0965248	+	0.0809939i	−0.689773	−	0.724026i	$-0.742290\pi$
$439$	−2.02242	+	1.69701i	−0.0965248	+	0.0809939i	0.593248	+	0.805020i	$0.297845\pi$
$440$	1.87977	−	4.24692i	0.0896145	−	0.202464i
$441$	−1.37513	+	7.79876i	−0.0654825	+	0.371370i
$442$	30.5344	−	4.67695i	1.45238	−	0.222460i
$443$	0.537838	+	1.47770i	0.0255534	+	0.0702075i	0.951813	−	0.306678i	$-0.0992174\pi$
$443$	0.537838	+	1.47770i	0.0255534	+	0.0702075i	−0.926260	+	0.376885i	$0.876995\pi$
$444$	−5.94614	−	3.80029i	−0.282191	−	0.180354i
$445$	−10.6106	+	6.12606i	−0.502993	+	0.290403i
$446$	−20.9780	−	18.4242i	−0.993336	−	0.872412i
$447$	1.40277	+	1.17706i	0.0663487	+	0.0556732i
$448$	11.0088	−	4.50379i	0.520119	−	0.212784i
$449$	20.7458	+	11.9776i	0.979054	+	0.565257i	0.901984	−	0.431768i	$-0.142110\pi$
$449$	20.7458	+	11.9776i	0.979054	+	0.565257i	0.0770698	+	0.997026i	$0.475444\pi$
$450$	2.21480	−	0.750025i	0.104406	−	0.0353565i
$451$	−2.70505	−	15.3411i	−0.127376	−	0.722385i
$452$	8.26794	+	1.84559i	0.388891	+	0.0868091i
$453$	21.2413	+	7.73121i	0.998005	+	0.363244i
$454$	4.26084	−	3.41459i	0.199971	−	0.160255i
$455$	−5.01944			−0.235315
$456$	2.02359	−	14.1626i	0.0947631	−	0.663225i
$457$	1.60386			0.0750254			0.0375127	−	0.999296i	$-0.488057\pi$
$457$	1.60386			0.0750254			0.0375127	+	0.999296i	$0.488057\pi$
$458$	−23.8718	+	19.1306i	−1.11546	+	0.893915i
$459$	32.8309	+	11.9495i	1.53242	+	0.557754i
$460$	6.75861	+	1.50867i	0.315122	+	0.0703422i
$461$	1.79183	+	10.1620i	0.0834537	+	0.473290i	0.997680	+	0.0680845i	$0.0216888\pi$
$461$	1.79183	+	10.1620i	0.0834537	+	0.473290i	−0.914226	+	0.405205i	$0.867200\pi$
$462$	−3.79476	+	1.28507i	−0.176548	+	0.0597868i
$463$	−5.79397	−	3.34515i	−0.269269	−	0.155462i	0.359286	−	0.933227i	$-0.383020\pi$
$463$	−5.79397	−	3.34515i	−0.269269	−	0.155462i	−0.628555	+	0.777765i	$0.716353\pi$
$464$	−36.5523	+	16.9153i	−1.69690	+	0.785272i
$465$	7.68989	+	6.45258i	0.356610	+	0.299231i
$466$	11.0866	+	9.73698i	0.513577	+	0.451057i
$467$	−8.68064	+	5.01177i	−0.401692	+	0.231917i	−0.687214	−	0.726455i	$-0.741166\pi$
$467$	−8.68064	+	5.01177i	−0.401692	+	0.231917i	0.285522	+	0.958372i	$0.407833\pi$
$468$	−9.40695	−	6.01215i	−0.434836	−	0.277912i
$469$	−0.829649	−	2.27944i	−0.0383096	−	0.105255i
$470$	5.41255	−	0.829039i	0.249662	−	0.0382407i
$471$	1.57656	−	8.94112i	0.0726441	−	0.411985i
$472$	−37.0862	−	16.4151i	−1.70703	−	0.755565i
$473$	−9.01593	+	7.56526i	−0.414553	+	0.347851i
$474$	−4.64322	−	0.104696i	−0.213270	−	0.00480886i
$475$	4.33702	−	0.436223i	0.198996	−	0.0200153i
$476$	−0.867198	+	19.2201i	−0.0397479	+	0.880951i
$477$	−7.79637	−	9.29135i	−0.356971	−	0.425422i
$478$	−0.942634	+	2.41877i	−0.0431151	+	0.110632i
$479$	−26.4306	−	4.66043i	−1.20765	−	0.212940i	−0.466645	−	0.884445i	$-0.654537\pi$
$479$	−26.4306	−	4.66043i	−1.20765	−	0.212940i	−0.741001	+	0.671504i	$0.765648\pi$
$480$	−0.405484	−	6.55171i	−0.0185077	−	0.299043i
$481$	−9.64617	+	3.51092i	−0.439827	+	0.160084i
$482$	−0.133884	−	0.0813762i	−0.00609825	−	0.00370658i
$483$	−2.98691	−	5.17348i	−0.135909	−	0.235401i
$484$	12.2280	+	11.2377i	0.555819	+	0.510804i
$485$	−5.45126	+	6.49656i	−0.247529	+	0.294994i
$486$	−9.97549	−	18.2143i	−0.452498	−	0.826219i
$487$	16.8981	−	29.2685i	0.765728	−	1.32628i	−0.174132	−	0.984722i	$-0.555712\pi$
$487$	16.8981	−	29.2685i	0.765728	−	1.32628i	0.939861	−	0.341558i	$-0.110955\pi$
$488$	−9.74962	+	2.81868i	−0.441345	+	0.127595i
$489$	12.4124	−	2.18864i	0.561309	−	0.0989739i
$490$	−1.32623	+	6.64212i	−0.0599127	+	0.300060i
$491$	10.5587	−	29.0097i	0.476506	−	1.30919i	−0.435935	−	0.899978i	$-0.643582\pi$
$491$	10.5587	−	29.0097i	0.476506	−	1.30919i	0.912440	−	0.409210i	$-0.134196\pi$
$492$	−13.3779	−	17.4871i	−0.603123	−	0.788378i
$493$		−	65.1484i		−	2.93413i
$494$	−14.5741	−	14.8556i	−0.655719	−	0.668387i
$495$		−	2.71502i		−	0.122031i
$496$	−28.4029	+	19.7650i	−1.27533	+	0.887474i
$497$	1.52749	−	4.19675i	0.0685173	−	0.188250i
$498$	−24.6282	−	4.91749i	−1.10362	−	0.220358i
$499$	−35.1489	+	6.19771i	−1.57348	+	0.277447i	−0.891189	−	0.453631i	$-0.850128\pi$
$499$	−35.1489	+	6.19771i	−1.57348	+	0.277447i	−0.682293	+	0.731079i	$0.739017\pi$
$500$	1.90831	−	0.598635i	0.0853421	−	0.0267718i
$501$	−11.4066	+	19.7568i	−0.509608	+	0.882668i
$502$	30.3106	−	16.6003i	1.35283	−	0.740906i
$503$	−11.3744	+	13.5555i	−0.507160	+	0.604409i	−0.957495	−	0.288450i	$-0.906860\pi$
$503$	−11.3744	+	13.5555i	−0.507160	+	0.604409i	0.450335	+	0.892860i	$0.351304\pi$
$504$	4.81929	−	5.01234i	0.214668	−	0.223267i
$505$	1.68150	+	2.91245i	0.0748260	+	0.129602i
$506$	4.17618	−	6.87085i	0.185654	−	0.305446i
$507$	−1.74772	+	0.636118i	−0.0776190	+	0.0282510i
$508$	−0.108145	−	0.830782i	−0.00479814	−	0.0368600i
$509$	20.2161	+	3.56464i	0.896062	+	0.158000i	0.602668	−	0.797992i	$-0.294104\pi$
$509$	20.2161	+	3.56464i	0.896062	+	0.158000i	0.293394	+	0.955992i	$0.405215\pi$
$510$	9.89310	+	3.85551i	0.438074	+	0.170725i
$511$	−4.87650	−	5.81158i	−0.215723	−	0.257089i
$512$	22.1632	+	4.55965i	0.979486	+	0.201510i
$513$	−6.38652	−	22.6546i	−0.281972	−	1.00023i
$514$	0.636053	−	28.2086i	0.0280551	−	1.24423i
$515$	−3.42571	+	2.87451i	−0.150955	+	0.126666i
$516$	−6.38822	+	15.3593i	−0.281226	+	0.676153i
$517$	1.10401	−	6.26114i	0.0485542	−	0.275364i
$518$	−0.968005	−	6.31982i	−0.0425317	−	0.277677i
$519$	−1.03508	−	2.84385i	−0.0454349	−	0.124831i
$520$	−7.92785	−	5.32230i	−0.347659	−	0.233398i
$521$	−24.7963	+	14.3162i	−1.08635	+	0.627202i	−0.932601	−	0.360909i	$-0.882467\pi$
$521$	−24.7963	+	14.3162i	−1.08635	+	0.627202i	−0.153745	+	0.988111i	$0.549133\pi$
$522$	−15.5372	+	17.6908i	−0.680047	+	0.774307i
$523$	32.6152	+	27.3674i	1.42616	+	1.19669i	0.947939	+	0.318453i	$0.103163\pi$
$523$	32.6152	+	27.3674i	1.42616	+	1.19669i	0.478223	+	0.878239i	$0.341281\pi$
$524$	20.6576	−	10.7155i	0.902430	−	0.468107i
$525$	−1.49416	−	0.862651i	−0.0652103	−	0.0376492i
$526$	2.91989	+	8.62233i	0.127313	+	0.375952i
$527$	−9.71936	−	55.1212i	−0.423382	−	2.40112i
$528$	−7.35617	−	1.99405i	−0.320136	−	0.0867799i
$529$	−10.3472	−	3.76607i	−0.449878	−	0.163742i
$530$	−6.48744	−	8.09524i	−0.281796	−	0.351635i
$531$	−23.7089			−1.02888
$532$	10.8508	−	7.08982i	0.470443	−	0.307383i
$533$	−32.0277			−1.38727
$534$	12.5737	+	15.6899i	0.544117	+	0.678967i
$535$	5.19221	+	1.88981i	0.224479	+	0.0817036i
$536$	1.10660	−	4.47993i	0.0477980	−	0.193503i
$537$	−5.10397	−	28.9460i	−0.220253	−	1.24911i
$538$	2.97640	+	8.78921i	0.128322	+	0.378930i
$539$	6.81068	+	3.93215i	0.293357	+	0.169370i
$540$	−4.97284	−	9.58679i	−0.213997	−	0.412550i
$541$	−1.78514	−	1.49791i	−0.0767493	−	0.0644003i	0.603606	−	0.797283i	$-0.293730\pi$
$541$	−1.78514	−	1.49791i	−0.0767493	−	0.0644003i	−0.680355	+	0.732882i	$0.738174\pi$
$542$	5.40250	−	6.15133i	0.232057	−	0.264222i
$543$	−14.1379	+	8.16255i	−0.606717	+	0.350288i
$544$	−21.7495	+	29.4373i	−0.932500	+	1.26211i
$545$	5.38136	+	14.7852i	0.230512	+	0.633326i
$546$	1.24715	+	8.14224i	0.0533729	+	0.348456i
$547$	−1.83718	+	10.4191i	−0.0785519	+	0.445490i	0.920011	+	0.391893i	$0.128180\pi$
$547$	−1.83718	+	10.4191i	−0.0785519	+	0.445490i	−0.998563	+	0.0535970i	$0.982931\pi$
$548$	11.4094	+	4.74539i	0.487385	+	0.202713i
$549$	−4.54487	+	3.81360i	−0.193970	+	0.162760i
$550$	0.0523475	−	2.32158i	0.00223210	−	0.0989925i
$551$	−35.6231	+	25.6389i	−1.51760	+	1.09225i
$552$	0.768015	−	11.3383i	0.0326889	−	0.482590i
$553$	−2.70476	−	3.22340i	−0.115018	−	0.137073i
$554$	−5.48514	−	2.13765i	−0.233041	−	0.0908200i
$555$	−3.47481	−	0.612702i	−0.147497	−	0.0260078i
$556$	−15.3123	+	1.99323i	−0.649386	+	0.0845319i
$557$	21.6399	−	7.87628i	0.916912	−	0.333729i	0.159903	−	0.987133i	$-0.448882\pi$
$557$	21.6399	−	7.87628i	0.916912	−	0.333729i	0.757009	+	0.653404i	$0.226660\pi$
$558$	−10.5066	+	17.2860i	−0.444780	+	0.731774i
$559$	12.0989	+	20.9559i	0.511730	+	0.886342i
$560$	4.21756	−	4.19308i	0.178224	−	0.177190i
$561$	7.92442	−	9.44396i	0.334569	−	0.398724i
$562$	9.69245	−	5.30829i	0.408851	−	0.223917i
$563$	15.3295	−	26.5515i	0.646062	−	1.11901i	−0.337993	−	0.941149i	$-0.609748\pi$
$563$	15.3295	−	26.5515i	0.646062	−	1.11901i	0.984055	−	0.177864i	$-0.0569187\pi$
$564$	−2.68964	−	8.57394i	−0.113254	−	0.361028i
$565$	4.17136	−	0.735523i	0.175490	−	0.0309437i
$566$	−6.07162	−	1.21231i	−0.255209	−	0.0509573i
$567$	−0.663970	+	1.82424i	−0.0278841	+	0.0766110i
$568$	6.86253	−	5.00882i	0.287946	−	0.210165i
$569$		−	3.29242i		−	0.138025i	−0.997616	−	0.0690127i	$-0.978015\pi$
$569$		−	3.29242i		−	0.138025i	0.997616	−	0.0690127i	$-0.0219849\pi$
$570$	−1.78521	−	6.92687i	−0.0747740	−	0.290135i
$571$			26.9222i			1.12666i	0.826233	+	0.563329i	$0.190480\pi$
$571$			26.9222i			1.12666i	−0.826233	+	0.563329i	$0.809520\pi$
$572$	−8.80561	+	6.73644i	−0.368181	+	0.281665i
$573$	−6.56137	+	18.0272i	−0.274105	+	0.753098i
$574$	3.90588	−	19.5618i	0.163028	−	0.816492i
$575$	3.40987	−	0.601253i	0.142202	−	0.0250740i
$576$	12.9265	−	2.80658i	0.538604	−	0.116941i
$577$	−12.5874	+	21.8020i	−0.524020	+	0.907629i	0.475589	+	0.879668i	$0.342235\pi$
$577$	−12.5874	+	21.8020i	−0.524020	+	0.907629i	−0.999609	+	0.0279617i	$0.991098\pi$
$578$	−16.8894	−	30.8385i	−0.702506	−	1.28271i
$579$	10.9275	−	13.0229i	0.454131	−	0.541212i
$580$	−13.6268	+	14.8277i	−0.565823	+	0.615686i
$581$	−11.3769	−	19.7053i	−0.471992	−	0.817514i
$582$	11.8928	+	7.22857i	0.492972	+	0.299634i
$583$	−11.3187	+	4.11967i	−0.468772	+	0.170619i
$584$	−1.53985	−	14.3497i	−0.0637196	−	0.593796i
$585$	−5.49723	−	0.969311i	−0.227283	−	0.0400761i
$586$	8.12755	−	20.8550i	0.335746	−	0.861513i
$587$	−21.2670	−	25.3450i	−0.877784	−	1.04610i	−0.998572	−	0.0534234i	$-0.982987\pi$
$587$	−21.2670	−	25.3450i	−0.877784	−	1.04610i	0.120788	−	0.992678i	$-0.461458\pi$
$588$	11.1040	+	0.501004i	0.457920	+	0.0206611i
$589$	−26.3153	+	27.0073i	−1.08430	+	1.11282i
$590$	−20.2732	−	0.457124i	−0.834634	−	0.0188195i
$591$	16.9351	−	14.2102i	0.696615	−	0.584529i
$592$	5.17224	−	11.0081i	0.212578	−	0.452431i
$593$	7.74163	−	43.9050i	0.317911	−	1.80296i	−0.237504	−	0.971387i	$-0.576329\pi$
$593$	7.74163	−	43.9050i	0.317911	−	1.80296i	0.555414	−	0.831574i	$-0.312560\pi$
$594$	−12.3949	+	1.89853i	−0.508570	+	0.0778976i
$595$	3.29017	+	9.03967i	0.134884	+	0.370591i
$596$	−1.69965	+	2.65937i	−0.0696204	+	0.108932i
$597$	−6.80554	+	3.92918i	−0.278532	+	0.160811i
$598$	−12.4208	−	10.9087i	−0.507924	−	0.446091i
$599$	−34.2707	−	28.7565i	−1.40026	−	1.17496i	−0.960982	−	0.276609i	$-0.910789\pi$
$599$	−34.2707	−	28.7565i	−1.40026	−	1.17496i	−0.439280	−	0.898350i	$-0.644766\pi$
$600$	−1.44522	−	2.94681i	−0.0590007	−	0.120303i
$601$	9.91544	+	5.72468i	0.404459	+	0.233515i	0.688406	−	0.725325i	$-0.258311\pi$
$601$	9.91544	+	5.72468i	0.404459	+	0.233515i	−0.283947	+	0.958840i	$0.591644\pi$
$602$	−14.2749	+	4.83409i	−0.581802	+	0.197023i
$603$	−0.468436	−	2.65664i	−0.0190762	−	0.108187i
$604$	−8.48779	+	38.0239i	−0.345363	+	1.54717i
$605$	7.80298	+	2.84005i	0.317236	+	0.115465i
$606$	4.30662	−	3.45128i	0.174944	−	0.140199i
$607$	20.3855			0.827423			0.413712	−	0.910408i	$-0.364232\pi$
$607$	20.3855			0.827423			0.413712	+	0.910408i	$0.364232\pi$
$608$	24.6557	+	0.307659i	0.999922	+	0.0124772i
$609$	17.3723			0.703961
$610$	−3.95979	+	3.17333i	−0.160327	+	0.128485i
$611$	−12.2831	−	4.47068i	−0.496921	−	0.180864i
$612$	−4.66137	+	20.8822i	−0.188425	+	0.844112i
$613$	5.38626	+	30.5470i	0.217549	+	1.23378i	0.876428	+	0.481533i	$0.159920\pi$
$613$	5.38626	+	30.5470i	0.217549	+	1.23378i	−0.658879	+	0.752249i	$0.728969\pi$
$614$	7.33270	−	2.48317i	0.295924	−	0.100212i
$615$	−9.53382	−	5.50435i	−0.384441	−	0.221957i
$616$	−3.04059	−	6.19979i	−0.122509	−	0.249797i
$617$	−28.3732	−	23.8079i	−1.14226	−	0.958470i	−0.142750	−	0.989759i	$-0.545595\pi$
$617$	−28.3732	−	23.8079i	−1.14226	−	0.958470i	−0.999510	+	0.0312884i	$0.990039\pi$
$618$	5.51403	+	4.84278i	0.221807	+	0.194805i
$619$	6.33070	−	3.65503i	0.254452	−	0.146908i	−0.367349	−	0.930083i	$-0.619735\pi$
$619$	6.33070	−	3.65503i	0.254452	−	0.146908i	0.621801	+	0.783175i	$0.286401\pi$
$620$	−9.31737	+	14.5785i	−0.374195	+	0.585486i
$621$	−6.39476	−	17.5695i	−0.256613	−	0.705038i
$622$	13.7146	−	2.10067i	0.549906	−	0.0842290i
$623$	−3.16328	+	17.9398i	−0.126734	+	0.718744i
$624$	−6.66374	+	14.1825i	−0.266763	+	0.567755i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	12.7316	+	0.287074i	0.508855	+	0.0114738i
$627$	−8.28259	−	0.616436i	−0.330775	−	0.0246181i
$628$	15.6322	+	0.705313i	0.623791	+	0.0281450i
$629$	12.6459	+	15.0708i	0.504224	+	0.600910i
$630$	1.26244	−	3.23937i	0.0502967	−	0.129060i
$631$	37.5384	+	6.61903i	1.49438	+	0.263500i	0.860308	−	0.509774i	$-0.170271\pi$
$631$	37.5384	+	6.61903i	1.49438	+	0.263500i	0.634072	+	0.773274i	$0.281382\pi$
$632$	−0.854082	−	7.95910i	−0.0339735	−	0.316596i
$633$	0.504989	−	0.183801i	0.0200715	−	0.00730543i
$634$	−16.7117	−	10.1576i	−0.663707	−	0.403408i
$635$	−0.209448	−	0.362774i	−0.00831168	−	0.0143962i
$636$	−11.5198	+	12.5349i	−0.456788	+	0.497042i
$637$	10.3932	−	12.3861i	0.411792	−	0.490754i
$638$	11.2317	+	20.5080i	0.444666	+	0.811920i
$639$	2.48333	−	4.30126i	0.0982391	−	0.170155i
$640$	11.1074	−	2.15064i	0.439059	−	0.0850114i
$641$	−7.53685	+	1.32895i	−0.297688	+	0.0524904i	−0.320497	−	0.947249i	$-0.603850\pi$
$641$	−7.53685	+	1.32895i	−0.297688	+	0.0524904i	0.0228095	+	0.999740i	$0.492739\pi$
$642$	1.77547	−	8.89205i	0.0700721	−	0.350941i
$643$	2.13572	−	5.86783i	0.0842244	−	0.231405i	−0.890430	−	0.455120i	$-0.849596\pi$
$643$	2.13572	−	5.86783i	0.0842244	−	0.231405i	0.974655	+	0.223715i	$0.0718186\pi$
$644$	8.17755	−	6.25597i	0.322241	−	0.246520i
$645$			8.31739i			0.327497i
$646$	−17.2009	+	35.9846i	−0.676761	+	1.41580i
$647$			42.4622i			1.66936i	0.550735	+	0.834680i	$0.314347\pi$
$647$			42.4622i			1.66936i	−0.550735	+	0.834680i	$0.685653\pi$
$648$	−2.98301	+	2.17723i	−0.117184	+	0.0855298i
$649$	−8.05282	+	22.1249i	−0.316101	+	0.868480i
$650$	−4.68193	−	0.934837i	−0.183641	−	0.0366673i
$651$	14.6985	−	2.59174i	0.576080	−	0.101578i
$652$	6.50215	+	20.7273i	0.254644	+	0.811745i
$653$	15.5069	−	26.8587i	0.606830	−	1.05106i	−0.384929	−	0.922946i	$-0.625774\pi$
$653$	15.5069	−	26.8587i	0.606830	−	1.05106i	0.991759	−	0.128115i	$-0.0408926\pi$
$654$	22.6466	−	12.4029i	0.885551	−	0.484992i
$655$	7.47927	−	8.91345i	0.292239	−	0.348277i
$656$	26.9111	−	26.7549i	1.05070	−	1.04460i
$657$	−4.21841	−	7.30649i	−0.164576	−	0.285053i
$658$	4.22855	−	6.95701i	0.164846	−	0.271212i
$659$	28.7932	−	10.4799i	1.12162	−	0.408238i	0.286380	−	0.958116i	$-0.407548\pi$
$659$	28.7932	−	10.4799i	1.12162	−	0.408238i	0.835245	+	0.549878i	$0.185326\pi$
$660$	−3.77894	+	0.491912i	−0.147095	+	0.0191477i
$661$	−26.5597	−	4.68319i	−1.03305	−	0.182155i	−0.368680	−	0.929556i	$-0.620190\pi$
$661$	−26.5597	−	4.68319i	−1.03305	−	0.182155i	−0.664373	+	0.747401i	$0.731301\pi$
$662$	22.9495	+	8.94380i	0.891957	+	0.347610i
$663$	−16.2925	−	19.4167i	−0.632748	−	0.754080i
$664$	2.92530	−	43.1865i	0.113524	−	1.67596i
$665$	3.64806	−	5.35660i	0.141466	−	0.207720i
$666$	0.160280	−	7.10833i	0.00621073	−	0.275442i
$667$	−26.7075	+	22.4102i	−1.03412	+	0.867728i
$668$	−36.3044	−	15.0997i	−1.40466	−	0.584225i
$669$	−3.97814	+	22.5612i	−0.153804	+	0.872266i
$670$	−0.349333	−	2.28069i	−0.0134959	−	0.0881107i
$671$	2.01514	+	5.53654i	0.0777935	+	0.213736i
$672$	−7.84968	−	5.79966i	−0.302808	−	0.223727i
$673$	−10.6681	+	6.15921i	−0.411223	+	0.237420i	−0.691315	−	0.722553i	$-0.742968\pi$
$673$	−10.6681	+	6.15921i	−0.411223	+	0.237420i	0.280092	+	0.959973i	$0.409635\pi$
$674$	18.3645	−	20.9100i	0.707375	−	0.805423i
$675$	−4.13656	−	3.47099i	−0.159216	−	0.133598i
$676$	−1.47603	−	2.84554i	−0.0567705	−	0.109444i
$677$	−35.9972	−	20.7830i	−1.38348	−	0.798755i	−0.390914	−	0.920427i	$-0.627841\pi$
$677$	−35.9972	−	20.7830i	−1.38348	−	0.798755i	−0.992570	+	0.121672i	$0.961174\pi$
$678$	−2.22955	−	6.58379i	−0.0856255	−	0.252849i
$679$	2.18955	+	12.4176i	0.0840274	+	0.476543i
$680$	−4.38850	+	17.7662i	−0.168291	+	0.681304i
$681$	−4.21009	−	1.53235i	−0.161331	−	0.0587197i
$682$	12.5625	+	15.6760i	0.481044	+	0.600263i
$683$	−19.5329			−0.747407			−0.373703	−	0.927548i	$-0.621912\pi$
$683$	−19.5329			−0.747407			−0.373703	+	0.927548i	$0.621912\pi$
$684$	13.2528	−	5.66928i	0.506735	−	0.216770i
$685$	6.17845			0.236066
$686$	15.5021	+	19.3440i	0.591871	+	0.738557i
$687$	23.5875	+	8.58516i	0.899920	+	0.327544i
$688$	−27.6720	−	7.50109i	−1.05498	−	0.285977i
$689$	4.30032	+	24.3883i	0.163829	+	0.929121i
$690$	−1.82255	−	5.38191i	−0.0693831	−	0.204886i
$691$	−11.8501	−	6.84167i	−0.450800	−	0.260269i	0.257368	−	0.966313i	$-0.417145\pi$
$691$	−11.8501	−	6.84167i	−0.450800	−	0.260269i	−0.708168	+	0.706044i	$0.750478\pi$
$692$	4.63019	−	2.40177i	0.176013	−	0.0913014i
$693$	−3.09230	−	2.59475i	−0.117467	−	0.0985665i
$694$	6.97095	−	7.93718i	0.264613	−	0.301291i
$695$	−6.68636	+	3.86037i	−0.253628	+	0.146432i
$696$	27.4384	+	18.4205i	1.04005	+	0.698227i
$697$	20.9937	+	57.6798i	0.795194	+	2.18478i
$698$	−3.15567	−	20.6025i	−0.119444	−	0.779815i
$699$	2.10240	−	11.9233i	0.0795202	−	0.450981i
$700$	1.14195	−	2.74561i	0.0431618	−	0.103774i
$701$	11.3948	−	9.56134i	0.430374	−	0.361127i	−0.401719	−	0.915763i	$-0.631587\pi$
$701$	11.3948	−	9.56134i	0.430374	−	0.361127i	0.832093	+	0.554636i	$0.187143\pi$
$702$	−0.581168	+	25.7745i	−0.0219348	+	0.972794i
$703$	3.26395	−	12.8458i	0.123102	−	0.484489i
$704$	1.77147	−	13.0162i	0.0667647	−	0.490566i
$705$	−2.88802	−	3.44180i	−0.108769	−	0.129626i
$706$	46.4034	+	18.0842i	1.74642	+	0.680607i
$707$	4.92419	+	0.868268i	0.185193	+	0.0326546i
$708$	4.29562	+	32.9996i	0.161439	+	1.24020i
$709$	−33.0292	+	12.0216i	−1.24044	+	0.451482i	−0.877159	−	0.480200i	$-0.840564\pi$
$709$	−33.0292	+	12.0216i	−1.24044	+	0.451482i	−0.363277	+	0.931681i	$0.618342\pi$
$710$	2.20640	−	3.63008i	0.0828047	−	0.136234i
$711$	−2.33974	−	4.05256i	−0.0877473	−	0.151983i
$712$	−24.0184	+	24.9806i	−0.900129	+	0.936187i
$713$	−19.2535	+	22.9455i	−0.721050	+	0.859314i
$714$	13.8462	−	7.58316i	0.518179	−	0.283793i
$715$	−2.77171	+	4.80075i	−0.103656	+	0.179538i
$716$	48.3366	−	15.1632i	1.80642	−	0.566674i
$717$	2.09770	−	0.369881i	0.0783401	−	0.0138135i
$718$	31.9167	+	6.37277i	1.19112	+	0.237830i
$719$	−5.36937	+	14.7522i	−0.200244	+	0.550165i	−0.998649	−	0.0519546i	$-0.983455\pi$
$719$	−5.36937	+	14.7522i	−0.200244	+	0.550165i	0.798406	+	0.602120i	$0.205677\pi$
$720$	5.42876	−	3.77775i	0.202318	−	0.140789i
$721$			6.64893i			0.247619i
$722$	26.4458	−	4.75618i	0.984210	−	0.177007i
$723$			0.128556i			0.00478107i
$724$	−17.0961	−	22.3474i	−0.635373	−	0.830535i
$725$	−3.44385	+	9.46189i	−0.127901	+	0.351406i
$726$	2.66822	−	13.3632i	0.0990269	−	0.495955i
$727$	−44.8976	+	7.91666i	−1.66516	+	0.293613i	−0.925325	−	0.379175i	$-0.876208\pi$
$727$	−44.8976	+	7.91666i	−1.66516	+	0.293613i	−0.739836	+	0.672788i	$0.765097\pi$
$728$	−13.6386	+	3.94300i	−0.505479	+	0.146137i
$729$	−10.4786	+	18.1494i	−0.388095	+	0.672200i
$730$	−3.46624	−	6.32903i	−0.128291	−	0.234248i
$731$	29.8096	−	35.5257i	1.10255	−	1.31397i
$732$	6.13146	+	5.63489i	0.226625	+	0.208272i
$733$	−8.34222	−	14.4491i	−0.308127	−	0.533691i	0.669826	−	0.742518i	$-0.266369\pi$
$733$	−8.34222	−	14.4491i	−0.308127	−	0.533691i	−0.977953	+	0.208827i	$0.933035\pi$
$734$	−29.2985	−	17.8079i	−1.08143	−	0.657303i
$735$	5.22247	−	1.90082i	0.192634	−	0.0701130i
$736$	19.5493	−	1.20990i	0.720597	−	0.0445977i
$737$	−2.63826	−	0.465196i	−0.0971815	−	0.0171357i
$738$	8.05528	−	20.6696i	0.296519	−	0.760858i
$739$	−11.5448	−	13.7586i	−0.424682	−	0.506117i	0.510698	−	0.859760i	$-0.329387\pi$
$739$	−11.5448	−	13.7586i	−0.424682	−	0.506117i	−0.935380	+	0.353643i	$0.884943\pi$
$740$	0.274107	−	6.07516i	0.0100764	−	0.223327i
$741$	−4.20517	+	16.5501i	−0.154481	+	0.607983i
$742$	−15.4203	−	0.347699i	−0.566095	−	0.0127644i
$743$	−18.7297	+	15.7161i	−0.687128	+	0.576568i	−0.918079	−	0.396397i	$-0.870260\pi$
$743$	−18.7297	+	15.7161i	−0.687128	+	0.576568i	0.230952	+	0.972965i	$0.425816\pi$
$744$	25.9634	+	11.4919i	0.951864	+	0.421313i
$745$	−0.274027	+	1.55408i	−0.0100396	+	0.0569372i
$746$	−8.18146	+	1.25315i	−0.299544	+	0.0458812i
$747$	−8.65451	−	23.7781i	−0.316652	−	0.869994i
$748$	17.9038	+	11.4427i	0.654629	+	0.418386i
$749$	7.11463	−	4.10764i	0.259963	−	0.150090i
$750$	−1.23303	−	1.08292i	−0.0450238	−	0.0395428i
$751$	−9.62096	−	8.07295i	−0.351074	−	0.294586i	0.450147	−	0.892954i	$-0.351372\pi$
$751$	−9.62096	−	8.07295i	−0.351074	−	0.294586i	−0.801221	+	0.598368i	$0.795816\pi$
$752$	14.0555	−	6.50443i	0.512550	−	0.237192i
$753$	−24.5574	−	14.1782i	−0.894920	−	0.516683i
$754$	45.5336	−	15.4196i	1.65823	−	0.561549i
$755$	3.38265	+	19.1839i	0.123107	+	0.698175i
$756$	−15.6716	−	3.49824i	−0.569969	−	0.127230i
$757$	−23.7043	−	8.62765i	−0.861546	−	0.313577i	−0.126807	−	0.991927i	$-0.540473\pi$
$757$	−23.7043	−	8.62765i	−0.861546	−	0.313577i	−0.734739	+	0.678350i	$0.762695\pi$
$758$	−1.46094	+	1.17078i	−0.0530637	+	0.0425246i
$759$	−6.59744			−0.239472
$760$	11.4417	−	4.59221i	0.415033	−	0.166577i
$761$	34.4285			1.24803			0.624016	−	0.781411i	$-0.285500\pi$
$761$	34.4285			1.24803			0.624016	+	0.781411i	$0.285500\pi$
$762$	−0.536431	+	0.429890i	−0.0194329	+	0.0155733i
$763$	21.9827	+	8.00106i	0.795828	+	0.289658i
$764$	−32.2704	−	7.20347i	−1.16750	−	0.260612i
$765$	1.85770	+	10.5355i	0.0671652	+	0.380913i
$766$	3.14608	−	1.06540i	0.113672	−	0.0384943i
$767$	41.9225	+	24.2040i	1.51373	+	0.873955i
$768$	−6.24843	−	17.4835i	−0.225471	−	0.630880i
$769$	5.83882	+	4.89935i	0.210553	+	0.176675i	0.741965	−	0.670438i	$-0.233894\pi$
$769$	5.83882	+	4.89935i	0.210553	+	0.176675i	−0.531412	+	0.847113i	$0.678338\pi$
$770$	−2.59417	−	2.27836i	−0.0934872	−	0.0821065i
$771$	−20.0501	+	11.5759i	−0.722088	+	0.416898i
$772$	24.6887	+	15.7790i	0.888567	+	0.567900i
$773$	−3.62869	−	9.96974i	−0.130515	−	0.358587i	0.857172	−	0.515030i	$-0.172219\pi$
$773$	−3.62869	−	9.96974i	−0.130515	−	0.358587i	−0.987687	+	0.156443i	$0.949997\pi$
$774$	−16.5672	+	2.53760i	−0.595497	+	0.0912122i
$775$	−1.50220	+	8.51937i	−0.0539604	+	0.306025i
$776$	−9.70857	+	21.9344i	−0.348517	+	0.787398i
$777$	−4.01873	+	3.37212i	−0.144171	+	0.120974i
$778$	18.4066	+	0.415037i	0.659910	+	0.0148798i
$779$	23.2773	−	34.1791i	0.833996	−	1.22459i
$780$	−0.353151	+	7.82704i	−0.0126448	+	0.280253i
$781$	−3.17043	−	3.77837i	−0.113447	−	0.135201i
$782$	−11.5043	+	29.5195i	−0.411392	+	1.05562i
$783$	53.5463	+	9.44165i	1.91359	+	0.337417i
$784$	1.61413	+	19.0895i	0.0576475	+	0.681766i
$785$	7.35219	−	2.67598i	0.262411	−	0.0955097i
$786$	−16.3172	−	9.91778i	−0.582016	−	0.353756i
$787$	17.3047	+	29.9726i	0.616846	+	1.06841i	0.990058	+	0.140663i	$0.0449233\pi$
$787$	17.3047	+	29.9726i	0.616846	+	1.06841i	−0.373211	+	0.927746i	$0.621743\pi$
$788$	28.0546	+	25.7825i	0.999403	+	0.918464i
$789$	4.80133	−	5.72201i	0.170932	−	0.203709i
$790$	−1.92255	−	3.51041i	−0.0684014	−	0.124895i
$791$	3.14885	−	5.45397i	0.111960	−	0.193921i
$792$	−2.13277	−	7.37712i	−0.0757847	−	0.262134i
$793$	11.9296	−	2.10350i	0.423631	−	0.0746976i
$794$	−2.13864	+	10.7109i	−0.0758974	+	0.380116i
$795$	−2.91134	+	7.99883i	−0.103255	+	0.283689i
$796$	−8.22952	−	10.7573i	−0.291688	−	0.381283i
$797$			38.7364i			1.37211i	0.727547	+	0.686057i	$0.240660\pi$
$797$			38.7364i			1.37211i	−0.727547	+	0.686057i	$0.759340\pi$
$798$	−9.59558	−	4.58675i	−0.339680	−	0.162369i
$799$			25.0515i			0.886259i
$800$	4.71491	−	3.12564i	0.166697	−	0.110508i
$801$	−6.92877	+	19.0366i	−0.244816	+	0.672627i
$802$	−21.1832	−	4.22964i	−0.748006	−	0.149354i
$803$	−8.25117	+	1.45490i	−0.291177	+	0.0513424i
$804$	−3.61281	+	1.13334i	−0.127414	+	0.0399697i
$805$	2.57402	−	4.45834i	0.0907224	−	0.157136i
$806$	36.2250	−	19.8394i	1.27597	−	0.698813i
$807$	4.89426	−	5.83275i	0.172286	−	0.205322i
$808$	6.85677	+	6.59268i	0.241220	+	0.231930i
$809$	−15.9201	−	27.5744i	−0.559721	−	0.969465i	−0.997519	−	0.0703918i	$-0.977575\pi$
$809$	−15.9201	−	27.5744i	−0.559721	−	0.969465i	0.437799	−	0.899073i	$-0.355758\pi$
$810$	−0.959078	+	1.57792i	−0.0336986	+	0.0554425i
$811$	−38.3784	+	13.9686i	−1.34765	+	0.490504i	−0.912213	−	0.409716i	$-0.865628\pi$
$811$	−38.3784	+	13.9686i	−1.34765	+	0.490504i	−0.435435	+	0.900220i	$0.643405\pi$
$812$	3.86498	+	29.6913i	0.135634	+	1.04196i
$813$	−6.61557	−	1.16650i	−0.232018	−	0.0409111i
$814$	−6.57901	−	2.56395i	−0.230594	−	0.0898664i
$815$	6.98172	+	8.32050i	0.244559	+	0.291454i
$816$	29.9098	+	2.70452i	1.04705	+	0.0946772i
$817$	−31.1569	−	2.31887i	−1.09004	−	0.0811271i
$818$	−0.444034	+	19.6927i	−0.0155253	+	0.688538i
$819$	−6.35773	+	5.33477i	−0.222157	+	0.186412i
$820$	7.28650	−	17.5190i	0.254456	−	0.611790i
$821$	−0.0376541	+	0.213547i	−0.00131414	+	0.00745285i	−0.985458	−	0.169921i	$-0.945649\pi$
$821$	−0.0376541	+	0.213547i	−0.00131414	+	0.00745285i	0.984144	+	0.177373i	$0.0567600\pi$
$822$	−1.53512	−	10.0223i	−0.0535434	−	0.349569i
$823$	−2.30681	−	6.33791i	−0.0804104	−	0.220926i	0.892972	−	0.450112i	$-0.148616\pi$
$823$	−2.30681	−	6.33791i	−0.0804104	−	0.220926i	−0.973383	+	0.229186i	$0.926394\pi$
$824$	−7.05011	+	10.5015i	−0.245602	+	0.365838i
$825$	−1.65013	+	0.952706i	−0.0574503	+	0.0331690i
$826$	−19.8958	+	22.6535i	−0.692263	+	0.788217i
$827$	21.9139	+	18.3879i	0.762020	+	0.639411i	0.938652	−	0.344866i	$-0.112076\pi$
$827$	21.9139	+	18.3879i	0.762020	+	0.639411i	−0.176632	+	0.984277i	$0.556520\pi$
$828$	10.1641	−	5.27229i	0.353226	−	0.183225i
$829$	44.0510	+	25.4329i	1.52995	+	0.883320i	0.999363	+	0.0356918i	$0.0113635\pi$
$829$	44.0510	+	25.4329i	1.52995	+	0.883320i	0.530591	+	0.847628i	$0.321970\pi$
$830$	−6.94191	−	20.4992i	−0.240957	−	0.711538i
$831$	0.838795	+	4.75704i	0.0290975	+	0.165020i
$832$	−25.7221	−	8.23380i	−0.891753	−	0.285456i
$833$	−29.1191	−	10.5985i	−1.00892	−	0.367216i
$834$	7.92339	+	9.88707i	0.274365	+	0.342361i
$835$	−19.6596			−0.680350
$836$	−0.789142	−	14.2931i	−0.0272930	−	0.494336i
$837$	46.7134			1.61465
$838$	31.6676	+	39.5159i	1.09394	+	1.36505i
$839$	−4.83067	−	1.75822i	−0.166773	−	0.0607005i	0.257284	−	0.966336i	$-0.417172\pi$
$839$	−4.83067	−	1.75822i	−0.166773	−	0.0607005i	−0.424057	+	0.905635i	$0.639395\pi$
$840$	−4.73750	−	1.17023i	−0.163459	−	0.0403767i
$841$	−12.5700	−	71.2877i	−0.433447	−	2.45820i
$842$	−15.4486	−	45.6191i	−0.532393	−	1.57214i
$843$	−7.85274	−	4.53378i	−0.270463	−	0.156152i
$844$	0.426487	+	0.822193i	0.0146803	+	0.0283010i
$845$	−1.22781	−	1.03025i	−0.0422379	−	0.0354418i
$846$	5.97454	−	6.80266i	0.205409	−	0.233880i
$847$	10.6921	−	6.17306i	0.367383	−	0.212109i
$848$	−23.9865	−	16.8998i	−0.823701	−	0.580343i
$849$	1.73756	+	4.77391i	0.0596329	+	0.163840i
$850$	1.38536	+	9.04463i	0.0475176	+	0.310228i
$851$	1.82821	−	10.3683i	0.0626703	−	0.355421i
$852$	−6.43671	−	2.67716i	−0.220518	−	0.0917178i
$853$	−10.3278	+	8.66609i	−0.353619	+	0.296721i	−0.802241	−	0.597000i	$-0.796359\pi$
$853$	−10.3278	+	8.66609i	−0.353619	+	0.296721i	0.448622	+	0.893721i	$0.351915\pi$
$854$	−0.170077	+	7.54282i	−0.00581992	+	0.258110i
$855$	5.02974	−	5.16201i	0.172013	−	0.176537i
$856$	15.5926	+	1.05618i	0.532942	+	0.0360996i
$857$	−14.6909	−	17.5079i	−0.501832	−	0.598060i	0.454354	−	0.890821i	$-0.349870\pi$
$857$	−14.6909	−	17.5079i	−0.501832	−	0.598060i	−0.956186	+	0.292761i	$0.905426\pi$
$858$	8.47617	+	3.30331i	0.289372	+	0.112773i
$859$	39.4484	+	6.95582i	1.34596	+	0.237330i	0.799758	−	0.600322i	$-0.204961\pi$
$859$	39.4484	+	6.95582i	1.34596	+	0.237330i	0.546205	+	0.837652i	$0.316072\pi$
$860$	−14.2154	+	1.85045i	−0.484741	+	0.0630997i
$861$	−15.3808	+	5.59814i	−0.524175	+	0.190784i
$862$	3.43043	−	5.64391i	0.116841	−	0.192232i
$863$	12.5590	+	21.7528i	0.427513	+	0.740474i	0.996651	−	0.0817676i	$-0.0260565\pi$
$863$	12.5590	+	21.7528i	0.427513	+	0.740474i	−0.569139	+	0.822242i	$0.692723\pi$
$864$	−21.0428	−	22.1424i	−0.715892	−	0.753299i
$865$	1.67641	−	1.99786i	0.0569995	−	0.0679293i
$866$	21.9677	−	12.0311i	0.746493	−	0.408834i
$867$	−14.4252	+	24.9851i	−0.489904	+	0.848538i
$868$	7.69970	+	24.5448i	0.261345	+	0.833106i
$869$	−4.57652	+	0.806964i	−0.155248	+	0.0273744i
$870$	16.2042	+	3.23548i	0.549374	+	0.109693i
$871$	−1.88381	+	5.17573i	−0.0638306	+	0.175373i
$872$	26.2364	+	35.9462i	0.888476	+	1.21729i
$873$			14.0224i			0.474587i
$874$	20.6688	−	5.32679i	0.699131	−	0.180181i
$875$		−	1.48681i		−	0.0502634i
$876$	−9.40536	+	7.19526i	−0.317778	+	0.243105i
$877$	−9.60639	+	26.3933i	−0.324385	+	0.891240i	0.665120	+	0.746737i	$0.268381\pi$
$877$	−9.60639	+	26.3933i	−0.324385	+	0.891240i	−0.989504	+	0.144503i	$0.953842\pi$
$878$	−0.731061	+	3.66137i	−0.0246721	+	0.123565i
$879$	−18.0867	+	3.18918i	−0.610051	+	0.107568i
$880$	−1.68147	−	6.34921i	−0.0566824	−	0.214032i
$881$	4.96529	−	8.60014i	0.167285	−	0.289746i	−0.770179	−	0.637827i	$-0.779833\pi$
$881$	4.96529	−	8.60014i	0.167285	−	0.289746i	0.937464	+	0.348081i	$0.113167\pi$
$882$	5.37957	+	9.82261i	0.181140	+	0.330744i
$883$	−28.2729	+	33.6944i	−0.951460	+	1.13391i	0.0394284	+	0.999222i	$0.487446\pi$
$883$	−28.2729	+	33.6944i	−0.951460	+	1.13391i	−0.990889	+	0.134684i	$0.956998\pi$
$884$	29.5606	−	32.1656i	0.994230	−	1.08185i
$885$	8.31950	+	14.4098i	0.279657	+	0.484380i
$886$	1.90040	+	1.15508i	0.0638450	+	0.0388057i
$887$	9.93520	−	3.61612i	0.333591	−	0.121417i	−0.169793	−	0.985480i	$-0.554310\pi$
$887$	9.93520	−	3.61612i	0.333591	−	0.121417i	0.503385	+	0.864062i	$0.332088\pi$
$888$	−9.92289	+	1.06481i	−0.332990	+	0.0357328i
$889$	−0.613356	−	0.108151i	−0.0205713	−	0.00362728i
$890$	−6.29175	+	16.1444i	−0.210900	+	0.541162i
$891$	1.37812	+	1.64238i	0.0461688	+	0.0550219i
$892$	−39.4447	−	1.77972i	−1.32071	−	0.0595894i
$893$	13.6982	−	9.85894i	0.458392	−	0.329917i
$894$	2.58903	+	0.0583779i	0.0865901	+	0.00195245i
$895$	19.4036	−	16.2815i	0.648590	−	0.544232i
$896$	8.16590	−	14.7063i	0.272804	−	0.491303i
$897$	−2.35541	+	13.3582i	−0.0786448	+	0.446017i
$898$	33.4872	−	5.12923i	1.11748	−	0.171164i
$899$	−29.7920	−	81.8529i	−0.993620	−	2.72995i
$900$	1.78086	−	2.78644i	0.0593621	−	0.0928813i
$901$	41.1030	−	23.7308i	1.36934	−	0.790588i
$902$	−16.5527	−	14.5376i	−0.551144	−	0.484051i
$903$	9.47320	+	7.94896i	0.315248	+	0.264525i
$904$	10.7564	−	5.27532i	0.357754	−	0.175455i
$905$	−12.1836	−	7.03422i	−0.404998	−	0.233825i
$906$	30.2786	−	10.2536i	1.00594	−	0.340654i
$907$	−0.872873	−	4.95031i	−0.0289833	−	0.164372i	0.966881	−	0.255229i	$-0.0821507\pi$
$907$	−0.872873	−	4.95031i	−0.0289833	−	0.164372i	−0.995864	+	0.0908563i	$0.971040\pi$
$908$	1.68230	−	7.53645i	0.0558292	−	0.250106i
$909$	5.22525	+	1.90184i	0.173311	+	0.0630800i
$910$	−5.53928	+	4.43912i	−0.183625	+	0.147155i
$911$	42.6375			1.41264			0.706322	−	0.707891i	$-0.250353\pi$
$911$	42.6375			1.41264			0.706322	+	0.707891i	$0.250353\pi$
$912$	−10.2921	−	17.4190i	−0.340804	−	0.576801i
$913$	−25.1291			−0.831651
$914$	1.76997	−	1.41843i	0.0585453	−	0.0469176i
$915$	3.91263	+	1.42408i	0.129348	+	0.0470787i
$916$	−9.42530	+	42.2238i	−0.311421	+	1.39511i
$917$	−3.00412	−	17.0372i	−0.0992049	−	0.562619i
$918$	46.7991	−	15.8482i	1.54460	−	0.523067i
$919$	17.4585	+	10.0797i	0.575902	+	0.332497i	0.759503	−	0.650504i	$-0.225442\pi$
$919$	17.4585	+	10.0797i	0.575902	+	0.332497i	−0.183601	+	0.983001i	$0.558775\pi$
$920$	8.79283	−	4.31231i	0.289891	−	0.142173i
$921$	−4.86617	−	4.08320i	−0.160346	−	0.134546i
$922$	10.9645	+	9.62973i	0.361097	+	0.317138i
$923$	−8.78216	+	5.07038i	−0.289068	+	0.166894i
$924$	−3.05128	+	4.77420i	−0.100380	+	0.157060i
$925$	−1.03997	−	2.85730i	−0.0341940	−	0.0939474i
$926$	−9.35245	+	1.43251i	−0.307341	+	0.0470753i
$927$	−1.28399	+	7.28184i	−0.0421716	+	0.239167i
$928$	−25.3783	+	50.9935i	−0.833084	+	1.67394i
$929$	−10.6198	+	8.91110i	−0.348426	+	0.292364i	−0.800158	−	0.599790i	$-0.795251\pi$
$929$	−10.6198	+	8.91110i	−0.348426	+	0.292364i	0.451732	+	0.892154i	$0.350806\pi$
$930$	14.1929	+	0.320024i	0.465403	+	0.0104940i
$931$	5.66447	+	20.0933i	0.185646	+	0.658532i
$932$	20.8461	+	0.940561i	0.682836	+	0.0308091i
$933$	−7.31782	−	8.72103i	−0.239575	−	0.285514i
$934$	−5.14733	+	13.2079i	−0.168426	+	0.432174i
$935$	10.4627	+	1.84485i	0.342165	+	0.0603330i
$936$	−15.6983	+	1.68456i	−0.513114	+	0.0550617i
$937$	−13.7001	+	4.98642i	−0.447562	+	0.162899i	−0.555961	−	0.831208i	$-0.687650\pi$
$937$	−13.7001	+	4.98642i	−0.447562	+	0.162899i	0.108399	+	0.994107i	$0.465428\pi$
$938$	−2.93148	−	1.78179i	−0.0957162	−	0.0581774i
$939$	−5.22464	−	9.04935i	−0.170500	−	0.295314i
$940$	5.23992	−	5.70169i	0.170907	−	0.185969i
$941$	−1.05177	+	1.25345i	−0.0342868	+	0.0408614i	−0.782915	−	0.622128i	$-0.786268\pi$
$941$	−1.05177	+	1.25345i	−0.0342868	+	0.0408614i	0.748629	+	0.662990i	$0.230713\pi$
$942$	−6.16756	−	11.2614i	−0.200950	−	0.366917i
$943$	16.4242	−	28.4475i	0.534844	−	0.926378i
$944$	−55.4444	+	14.6834i	−1.80456	+	0.477905i
$945$	−7.90665	+	1.39416i	−0.257203	+	0.0453519i
$946$	−3.25907	+	16.3223i	−0.105961	+	0.530685i
$947$	−5.59611	+	15.3752i	−0.181849	+	0.499626i	−0.996803	−	0.0798995i	$-0.974540\pi$
$947$	−5.59611	+	15.3752i	−0.181849	+	0.499626i	0.814954	+	0.579526i	$0.196762\pi$
$948$	−5.21670	+	3.99086i	−0.169430	+	0.129617i
$949$			17.2260i			0.559179i
$950$	4.40040	−	4.31700i	0.142768	−	0.140062i
$951$			16.0467i			0.520350i
$952$	16.0410	+	21.9776i	0.519891	+	0.712298i
$953$	19.0106	−	52.2313i	0.615815	−	1.69194i	−0.101189	−	0.994867i	$-0.532265\pi$
$953$	19.0106	−	52.2313i	0.615815	−	1.69194i	0.717004	−	0.697069i	$-0.245513\pi$
$954$	−16.8210	−	3.35862i	−0.544599	−	0.108739i
$955$	−16.2811	+	2.87080i	−0.526845	+	0.0928970i
$956$	1.09887	+	3.50293i	0.0355398	+	0.113293i
$957$	9.59292	−	16.6154i	0.310095	−	0.537101i
$958$	−33.2896	+	18.2318i	−1.07554	+	0.589042i
$959$	5.90476	−	7.03702i	0.190675	−	0.227237i
$960$	−6.24172	−	6.87164i	−0.201451	−	0.221781i
$961$	−21.9182	−	37.9634i	−0.707037	−	1.22462i
$962$	−7.54018	+	12.4055i	−0.243105	+	0.399968i
$963$	8.58511	−	3.12472i	0.276651	−	0.100693i
$964$	−0.219718	+	0.0286011i	−0.00707664	+	0.000921180i
$965$	14.4276	+	2.54398i	0.464441	+	0.0818935i
$966$	−7.87161	−	3.06770i	−0.253265	−	0.0987016i
$967$	−5.46898	−	6.51767i	−0.175870	−	0.209594i	0.670907	−	0.741541i	$-0.265905\pi$
$967$	−5.46898	−	6.51767i	−0.175870	−	0.209594i	−0.846778	+	0.531947i	$0.821460\pi$
$968$	23.4329	+	1.58726i	0.753162	+	0.0510165i
$969$	32.5621	−	3.27514i	1.04604	−	0.105213i
$970$	−0.270362	+	11.9904i	−0.00868081	+	0.384989i
$971$	36.7959	−	30.8754i	1.18084	−	0.990840i	0.180864	−	0.983508i	$-0.442111\pi$
$971$	36.7959	−	30.8754i	1.18084	−	0.990840i	0.999973	−	0.00733152i	$-0.00233372\pi$
$972$	−27.1171	−	11.2786i	−0.869783	−	0.361760i
$973$	−1.99336	+	11.3049i	−0.0639041	+	0.362418i
$974$	−7.23638	−	47.2442i	−0.231869	−	1.51380i
$975$	1.33986	+	3.68125i	0.0429100	+	0.117894i
$976$	−8.26656	+	11.7330i	−0.264606	+	0.375565i
$977$	4.39393	−	2.53684i	0.140574	−	0.0811606i	−0.428063	−	0.903749i	$-0.640804\pi$
$977$	4.39393	−	2.53684i	0.140574	−	0.0811606i	0.568638	+	0.822588i	$0.307471\pi$
$978$	11.7623	−	13.3927i	0.376118	−	0.428251i
$979$	15.4115	+	12.9318i	0.492553	+	0.413301i
$980$	4.41062	+	8.50292i	0.140892	+	0.271616i
$981$	22.5302	+	13.0078i	0.719333	+	0.415307i
$982$	−14.0036	−	41.3521i	−0.446872	−	1.31960i
$983$	−6.80743	−	38.6069i	−0.217123	−	1.23137i	−0.877184	−	0.480155i	$-0.840580\pi$
$983$	−6.80743	−	38.6069i	−0.217123	−	1.23137i	0.660060	−	0.751213i	$-0.270531\pi$
$984$	−30.2288	−	7.46692i	−0.963658	−	0.238037i
$985$	17.9023	+	6.51590i	0.570415	+	0.207614i
$986$	−57.6163	−	71.8956i	−1.83488	−	2.28962i
$987$	−6.68018			−0.212632
$988$	−29.2216	−	3.50506i	−0.929663	−	0.111511i
$989$	−24.8179			−0.789162
$990$	−2.40113	−	2.99620i	−0.0763128	−	0.0952256i
$991$	−30.4217	−	11.0726i	−0.966378	−	0.351733i	−0.189848	−	0.981813i	$-0.560800\pi$
$991$	−30.4217	−	11.0726i	−0.966378	−	0.351733i	−0.776530	+	0.630081i	$0.783022\pi$
$992$	−13.8647	+	46.9312i	−0.440203	+	1.49007i
$993$	−3.50947	−	19.9032i	−0.111370	−	0.631608i
$994$	−2.02586	−	5.98228i	−0.0642563	−	0.189747i
$995$	−5.86480	−	3.38604i	−0.185927	−	0.107345i
$996$	−31.5278	+	16.3541i	−0.998998	+	0.518199i
$997$	35.8962	+	30.1205i	1.13684	+	0.953925i	0.999331	−	0.0365753i	$-0.0116449\pi$
$997$	35.8962	+	30.1205i	1.13684	+	0.953925i	0.137512	+	0.990500i	$0.456089\pi$
$998$	−33.3080	+	37.9248i	−1.05435	+	1.20049i
$999$	−14.2196	+	8.20966i	−0.449887	+	0.259742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.be.b.51.17	yes	120
4.3	odd	2	inner	380.2.be.b.51.4	✓	120
19.3	odd	18	inner	380.2.be.b.231.4	yes	120
76.3	even	18	inner	380.2.be.b.231.17	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.be.b.51.4	✓	120	4.3	odd	2	inner
380.2.be.b.51.17	yes	120	1.1	even	1	trivial
380.2.be.b.231.4	yes	120	19.3	odd	18	inner
380.2.be.b.231.17	yes	120	76.3	even	18	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10357 - 0.884387i) q^{2} +(-1.09042 - 0.396882i) q^{3} +(0.435721 - 1.95196i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-1.55435 + 0.526371i) q^{6} +(-1.28762 - 0.743405i) q^{7} +(-1.24544 - 2.53946i) q^{8} +(-1.26662 - 1.06282i) q^{9} +O(q^{10})\)	\(q+(1.10357 - 0.884387i) q^{2} +(-1.09042 - 0.396882i) q^{3} +(0.435721 - 1.95196i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-1.55435 + 0.526371i) q^{6} +(-1.28762 - 0.743405i) q^{7} +(-1.24544 - 2.53946i) q^{8} +(-1.26662 - 1.06282i) q^{9} +(-1.06258 - 0.933229i) q^{10} +(-1.42203 + 0.821011i) q^{11} +(-1.24982 + 1.95553i) q^{12} +(1.15465 + 3.17238i) q^{13} +(-2.07843 + 0.318352i) q^{14} +(-0.201502 + 1.14278i) q^{15} +(-3.62029 - 1.70102i) q^{16} +(4.95639 - 4.15890i) q^{17} +(-2.33775 - 0.0527121i) q^{18} +(-4.22466 - 1.07343i) q^{19} +(-1.99797 - 0.0901470i) q^{20} +(1.10900 + 1.32166i) q^{21} +(-0.843218 + 2.16367i) q^{22} +(-3.40987 - 0.601253i) q^{23} +(0.350190 + 3.26339i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(4.07985 + 2.47978i) q^{26} +(2.69995 + 4.67645i) q^{27} +(-2.01214 + 2.18946i) q^{28} +(6.47232 - 7.71340i) q^{29} +(0.788285 + 1.43934i) q^{30} +(4.32540 - 7.49181i) q^{31} +(-5.49960 + 1.32455i) q^{32} +(1.87646 - 0.330871i) q^{33} +(1.79163 - 8.97299i) q^{34} +(-0.508519 + 1.39714i) q^{35} +(-2.62648 + 2.00930i) q^{36} +3.04067i q^{37} +(-5.61152 + 2.55163i) q^{38} -3.91750i q^{39} +(-2.28462 + 1.66749i) q^{40} +(-3.24473 + 8.91482i) q^{41} +(2.39272 + 0.477751i) q^{42} +(7.05877 - 1.24465i) q^{43} +(0.982972 + 3.13348i) q^{44} +(-0.826730 + 1.43194i) q^{45} +(-4.29476 + 2.35212i) q^{46} +(-2.48880 + 2.96604i) q^{47} +(3.27255 + 3.29166i) q^{48} +(-2.39470 - 4.14774i) q^{49} +(-0.734536 + 1.20849i) q^{50} +(-7.05516 + 2.56787i) q^{51} +(6.69546 - 0.871562i) q^{52} +(7.22408 + 1.27380i) q^{53} +(7.11536 + 2.77298i) q^{54} +(1.05547 + 1.25786i) q^{55} +(-0.284203 + 4.19572i) q^{56} +(4.18065 + 2.84719i) q^{57} +(0.321003 - 14.2363i) q^{58} +(10.9843 - 9.21690i) q^{59} +(2.14285 + 0.891256i) q^{60} +(0.623080 - 3.53366i) q^{61} +(-1.85229 - 12.0930i) q^{62} +(0.840816 + 2.31012i) q^{63} +(-4.89776 + 6.32550i) q^{64} +(2.92368 - 1.68799i) q^{65} +(1.77819 - 2.02466i) q^{66} +(1.24980 + 1.04871i) q^{67} +(-5.95841 - 11.4868i) q^{68} +(3.47958 + 2.00894i) q^{69} +(0.674431 + 1.99157i) q^{70} +(0.521605 + 2.95817i) q^{71} +(-1.12150 + 4.54023i) q^{72} +(4.79480 + 1.74516i) q^{73} +(2.68913 + 3.35559i) q^{74} +1.16041 q^{75} +(-3.93607 + 7.77865i) q^{76} +2.44138 q^{77} +(-3.46458 - 4.32322i) q^{78} +(2.65944 + 0.967958i) q^{79} +(-1.04652 + 3.86067i) q^{80} +(-0.226731 - 1.28586i) q^{81} +(4.30337 + 12.7077i) q^{82} +(13.2534 + 7.65186i) q^{83} +(3.06304 - 1.58886i) q^{84} +(-4.95639 - 4.15890i) q^{85} +(6.68907 - 7.61624i) q^{86} +(-10.1189 + 5.84214i) q^{87} +(3.85599 + 2.58868i) q^{88} +(-4.19047 - 11.5132i) q^{89} +(0.354035 + 2.31139i) q^{90} +(0.871616 - 4.94318i) q^{91} +(-2.65937 + 6.39396i) q^{92} +(-7.68989 + 6.45258i) q^{93} +(-0.123435 + 5.47428i) q^{94} +(-0.323519 + 4.34688i) q^{95} +(6.52258 + 0.738368i) q^{96} +(-5.45126 - 6.49656i) q^{97} +(-6.31091 - 2.45947i) q^{98} +(2.67377 + 0.471458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Introduction

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