LMFDB - Embedded newform 380.2.be.b.51.4

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			51.4
Character	$\chi$	$=$	380.51
Dual form			380.2.be.b.231.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06258 + 0.933229i) q^{2} +(1.09042 + 0.396882i) q^{3} +(0.258166 - 1.98327i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-1.52905 + 0.595896i) q^{6} +(1.28762 + 0.743405i) q^{7} +(1.57652 + 2.34831i) q^{8} +(-1.26662 - 1.06282i) q^{9} +O(q^{10})$	\(q+(-1.06258 + 0.933229i) q^{2} +(1.09042 + 0.396882i) q^{3} +(0.258166 - 1.98327i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-1.52905 + 0.595896i) q^{6} +(1.28762 + 0.743405i) q^{7} +(1.57652 + 2.34831i) q^{8} +(-1.26662 - 1.06282i) q^{9} +(1.10357 + 0.884387i) q^{10} +(1.42203 - 0.821011i) q^{11} +(1.06863 - 2.06014i) q^{12} +(1.15465 + 3.17238i) q^{13} +(-2.06197 + 0.411711i) q^{14} +(0.201502 - 1.14278i) q^{15} +(-3.86670 - 1.02402i) 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} +(-0.744837 + 2.19948i) q^{22} +(3.40987 + 0.601253i) q^{23} +(0.787073 + 3.18635i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-4.18747 - 2.29336i) q^{26} +(-2.69995 - 4.67645i) q^{27} +(1.80679 - 2.36176i) q^{28} +(6.47232 - 7.71340i) q^{29} +(0.852359 + 1.40234i) q^{30} +(-4.32540 + 7.49181i) q^{31} +(5.06434 - 2.52041i) q^{32} +(1.87646 - 0.330871i) q^{33} +(-1.38536 + 9.04463i) q^{34} +(0.508519 - 1.39714i) q^{35} +(-2.43486 + 2.23767i) q^{36} +3.04067i q^{37} +(-5.49081 + 2.80197i) q^{38} +3.91750i q^{39} +(2.03888 - 1.96035i) q^{40} +(-3.24473 + 8.91482i) q^{41} +(-2.41182 - 0.369418i) q^{42} +(-7.05877 + 1.24465i) q^{43} +(-1.26116 - 3.03223i) q^{44} +(-0.826730 + 1.43194i) q^{45} +(-4.18438 + 2.54331i) q^{46} +(2.48880 - 2.96604i) q^{47} +(-3.80993 - 2.65124i) q^{48} +(-2.39470 - 4.14774i) q^{49} +(0.679318 - 1.24037i) q^{50} +(7.05516 - 2.56787i) q^{51} +(6.58977 - 1.47098i) q^{52} +(7.22408 + 1.27380i) q^{53} +(7.23312 + 2.44944i) 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} +(-2.21441 - 0.694659i) q^{60} +(0.623080 - 3.53366i) q^{61} +(-2.39548 - 11.9973i) q^{62} +(-0.840816 - 2.31012i) q^{63} +(-3.02916 + 7.40433i) q^{64} +(2.92368 - 1.68799i) q^{65} +(-1.68512 + 2.10275i) q^{66} +(-1.24980 - 1.04871i) q^{67} +(-6.96865 - 10.9035i) q^{68} +(3.47958 + 2.00894i) q^{69} +(0.763513 + 1.95915i) q^{70} +(-0.521605 - 2.95817i) q^{71} +(0.498986 - 4.64999i) q^{72} +(4.79480 + 1.74516i) q^{73} +(-2.83764 - 3.23097i) q^{74} -1.16041 q^{75} +(3.21956 - 8.10151i) q^{76} +2.44138 q^{77} +(-3.65593 - 4.16267i) q^{78} +(-2.65944 - 0.967958i) q^{79} +(-0.337022 + 3.98578i) q^{80} +(-0.226731 - 1.28586i) q^{81} +(-4.87177 - 12.5008i) q^{82} +(-13.2534 - 7.65186i) q^{83} +(2.90751 - 1.85824i) q^{84} +(-4.95639 - 4.15890i) q^{85} +(6.33898 - 7.90999i) q^{86} +(10.1189 - 5.84214i) q^{87} +(4.16986 + 2.04504i) q^{88} +(-4.19047 - 11.5132i) q^{89} +(-0.457857 - 2.29308i) q^{90} +(-0.871616 + 4.94318i) q^{91} +(2.07276 - 6.60747i) 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} +(6.41536 + 2.17251i) 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 $

$2$	−1.06258	+	0.933229i	−0.751360	+	0.659893i
$2$	−1.06258	+	0.933229i	−0.751360	+	0.659893i
$3$	1.09042	+	0.396882i	0.629557	+	0.229140i	0.637038	−	0.770832i	$-0.280159\pi$
$3$	1.09042	+	0.396882i	0.629557	+	0.229140i	−0.00748161	+	0.999972i	$0.502381\pi$
$4$	0.258166	−	1.98327i	0.129083	−	0.991634i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	−1.52905	+	0.595896i	−0.624231	+	0.243273i
$7$	1.28762	+	0.743405i	0.486673	+	0.280981i	0.723193	−	0.690646i	$-0.242674\pi$
$7$	1.28762	+	0.743405i	0.486673	+	0.280981i	−0.236520	+	0.971627i	$0.576007\pi$
$8$	1.57652	+	2.34831i	0.557384	+	0.830255i
$9$	−1.26662	−	1.06282i	−0.422208	−	0.354274i
$10$	1.10357	+	0.884387i	0.348979	+	0.279668i
$11$	1.42203	−	0.821011i	0.428759	−	0.247544i	−0.270059	−	0.962844i	$-0.587043\pi$
$11$	1.42203	−	0.821011i	0.428759	−	0.247544i	0.698818	+	0.715300i	$0.253710\pi$
$12$	1.06863	−	2.06014i	0.308488	−	0.594712i
$13$	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	$0.733805\pi$
$14$	−2.06197	+	0.411711i	−0.551084	+	0.110034i
$15$	0.201502	−	1.14278i	0.0520277	−	0.295064i
$16$	−3.86670	−	1.02402i	−0.966675	−	0.256006i
$17$	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
$22$	−0.744837	+	2.19948i	−0.158800	+	0.468930i
$23$	3.40987	+	0.601253i	0.711008	+	0.125370i	0.517443	−	0.855718i	$-0.326884\pi$
$23$	3.40987	+	0.601253i	0.711008	+	0.125370i	0.193565	+	0.981088i	$0.437995\pi$
$24$	0.787073	+	3.18635i	0.160661	+	0.650411i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	−4.18747	−	2.29336i	−0.821231	−	0.449765i
$27$	−2.69995	−	4.67645i	−0.519606	−	0.899983i
$28$	1.80679	−	2.36176i	0.341451	−	0.446332i
$29$	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	$-0.162285\pi$
$30$	0.852359	+	1.40234i	0.155619	+	0.256032i
$31$	−4.32540	+	7.49181i	−0.776865	+	1.34557i	0.156876	+	0.987618i	$0.449858\pi$
$31$	−4.32540	+	7.49181i	−0.776865	+	1.34557i	−0.933741	+	0.357951i	$0.883476\pi$
$32$	5.06434	−	2.52041i	0.895257	−	0.445549i
$33$	1.87646	−	0.330871i	0.326650	−	0.0575973i
$34$	−1.38536	+	9.04463i	−0.237588	+	1.55114i
$35$	0.508519	−	1.39714i	0.0859554	−	0.236161i
$36$	−2.43486	+	2.23767i	−0.405810	+	0.372945i
$37$			3.04067i			0.499883i	0.968261	+	0.249942i	$0.0804115\pi$
$37$			3.04067i			0.499883i	−0.968261	+	0.249942i	$0.919589\pi$
$38$	−5.49081	+	2.80197i	−0.890727	+	0.454539i
$39$			3.91750i			0.627302i
$40$	2.03888	−	1.96035i	0.322375	−	0.309959i
$41$	−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	$0.845555\pi$
$42$	−2.41182	−	0.369418i	−0.372152	−	0.0570024i
$43$	−7.05877	+	1.24465i	−1.07645	+	0.189808i	−0.683646	−	0.729814i	$-0.739607\pi$
$43$	−7.05877	+	1.24465i	−1.07645	+	0.189808i	−0.392806	+	0.919621i	$0.628496\pi$
$44$	−1.26116	−	3.03223i	−0.190128	−	0.457126i
$45$	−0.826730	+	1.43194i	−0.123242	+	0.213461i
$46$	−4.18438	+	2.54331i	−0.616953	+	0.374991i
$47$	2.48880	−	2.96604i	0.363029	−	0.432641i	−0.553353	−	0.832947i	$-0.686652\pi$
$47$	2.48880	−	2.96604i	0.363029	−	0.432641i	0.916381	+	0.400306i	$0.131096\pi$
$48$	−3.80993	−	2.65124i	−0.549916	−	0.382674i
$49$	−2.39470	−	4.14774i	−0.342100	−	0.592534i
$50$	0.679318	−	1.24037i	0.0960701	−	0.175415i
$51$	7.05516	−	2.56787i	0.987920	−	0.359574i
$52$	6.58977	−	1.47098i	0.913836	−	0.203989i
$53$	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	$0.387488\pi$
$54$	7.23312	+	2.44944i	0.984303	+	0.333327i
$55$	−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	$0.660938\pi$
$59$	−10.9843	+	9.21690i	−1.43003	+	1.19994i	−0.945695	+	0.325055i	$0.894617\pi$
$60$	−2.21441	−	0.694659i	−0.285879	−	0.0896801i
$61$	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	$-0.0182220\pi$
$62$	−2.39548	−	11.9973i	−0.304226	−	1.52365i
$63$	−0.840816	−	2.31012i	−0.105933	−	0.291048i
$64$	−3.02916	+	7.40433i	−0.378646	+	0.925542i
$65$	2.92368	−	1.68799i	0.362638	−	0.209369i
$66$	−1.68512	+	2.10275i	−0.207424	+	0.258831i
$67$	−1.24980	−	1.04871i	−0.152688	−	0.128120i	0.563244	−	0.826291i	$-0.309553\pi$
$67$	−1.24980	−	1.04871i	−0.152688	−	0.128120i	−0.715931	+	0.698171i	$0.753998\pi$
$68$	−6.96865	−	10.9035i	−0.845073	−	1.32225i
$69$	3.47958	+	2.00894i	0.418892	+	0.241848i
$70$	0.763513	+	1.95915i	0.0912572	+	0.234163i
$71$	−0.521605	−	2.95817i	−0.0619031	−	0.351070i	−0.999989	−	0.00466749i	$-0.998514\pi$
$71$	−0.521605	−	2.95817i	−0.0619031	−	0.351070i	0.938086	−	0.346402i	$-0.112597\pi$
$72$	0.498986	−	4.64999i	0.0588060	−	0.548007i
$73$	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	$0.514591\pi$
$74$	−2.83764	−	3.23097i	−0.329869	−	0.375592i
$75$	−1.16041			−0.133992
$76$	3.21956	−	8.10151i	0.369309	−	0.929307i
$77$	2.44138			0.278221
$78$	−3.65593	−	4.16267i	−0.413952	−	0.471329i
$79$	−2.65944	−	0.967958i	−0.299211	−	0.108904i	0.188052	−	0.982159i	$-0.439783\pi$
$79$	−2.65944	−	0.967958i	−0.299211	−	0.108904i	−0.487263	+	0.873255i	$0.662005\pi$
$80$	−0.337022	+	3.98578i	−0.0376802	+	0.445623i
$81$	−0.226731	−	1.28586i	−0.0251924	−	0.142873i
$82$	−4.87177	−	12.5008i	−0.537998	−	1.38048i
$83$	−13.2534	−	7.65186i	−1.45475	−	0.839901i	−0.456006	−	0.889977i	$-0.650720\pi$
$83$	−13.2534	−	7.65186i	−1.45475	−	0.839901i	−0.998745	+	0.0500754i	$0.984054\pi$
$84$	2.90751	−	1.85824i	0.317235	−	0.202751i
$85$	−4.95639	−	4.15890i	−0.537596	−	0.451096i
$86$	6.33898	−	7.90999i	0.683550	−	0.852957i
$87$	10.1189	−	5.84214i	1.08486	−	0.626343i
$88$	4.16986	+	2.04504i	0.444508	+	0.218002i
$89$	−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	$-0.336075\pi$
$90$	−0.457857	−	2.29308i	−0.0482624	−	0.241712i
$91$	−0.871616	+	4.94318i	−0.0913702	+	0.518186i
$92$	2.07276	−	6.60747i	0.216100	−	0.688876i
$93$	−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	$0.919455\pi$
$98$	6.41536	+	2.17251i	0.648049	+	0.219457i
$99$	−2.67377	−	0.471458i	−0.268724	−	0.0473833i
$100$	0.435721	+	1.95196i	0.0435721	+	0.195196i
$101$	−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	$0.442399\pi$
$102$	−5.10028	+	9.31266i	−0.505003	+	0.922090i
$103$	2.23597	+	3.87282i	0.220317	+	0.381600i	0.954904	−	0.296914i	$-0.0959575\pi$
$103$	2.23597	+	3.87282i	0.220317	+	0.381600i	−0.734587	+	0.678514i	$0.762624\pi$
$104$	−5.62941	+	7.71281i	−0.552009	+	0.756303i
$105$	1.10900	−	1.32166i	0.108228	−	0.128981i
$106$	−8.86494	+	5.38821i	−0.861039	+	0.523349i
$107$	2.76272	−	4.78516i	0.267082	−	0.462599i	−0.701025	−	0.713137i	$-0.747274\pi$
$107$	2.76272	−	4.78516i	0.267082	−	0.462599i	0.968107	+	0.250537i	$0.0806073\pi$
$108$	−9.97169	+	4.14742i	−0.959526	+	0.399086i
$109$	−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	$0.716092\pi$
$110$	2.29540	+	0.351586i	0.218858	+	0.0335224i
$111$	−1.20679	+	3.31562i	−0.114543	+	0.314705i
$112$	−4.21756	−	4.19308i	−0.398522	−	0.396208i
$113$			4.23571i			0.398462i	0.979953	+	0.199231i	$0.0638444\pi$
$113$			4.23571i			0.398462i	−0.979953	+	0.199231i	$0.936156\pi$
$114$	−7.09936	+	0.876129i	−0.664916	+	0.0820570i
$115$		−	3.46248i		−	0.322878i
$116$	−13.6268	−	14.8277i	−1.26522	−	1.37671i
$117$	1.90917	−	5.24540i	0.176503	−	0.484937i
$118$	3.07022	−	20.0446i	0.282637	−	1.84525i
$119$	9.47367	−	1.67046i	0.868450	−	0.153131i
$120$	3.00127	−	1.32842i	0.273977	−	0.121268i
$121$	−4.15188	+	7.19127i	−0.377444	+	0.653752i
$122$	2.63564	+	4.33629i	0.238620	+	0.392589i
$123$	−7.07626	+	8.43316i	−0.638045	+	0.760392i
$124$	13.7416	+	10.5126i	1.23403	+	0.944055i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	3.04931	+	1.67002i	0.271654	+	0.148777i
$127$	−0.393633	+	0.143271i	−0.0349293	+	0.0127132i	−0.359426	−	0.933174i	$-0.617027\pi$
$127$	−0.393633	+	0.143271i	−0.0349293	+	0.0127132i	0.324496	+	0.945887i	$0.394805\pi$
$128$	−3.69120	−	10.6946i	−0.326259	−	0.945280i
$129$	−8.19103	−	1.44430i	−0.721180	−	0.127164i
$130$	−1.53137	+	4.52209i	−0.134310	+	0.396614i
$131$	−7.47927	−	8.91345i	−0.653467	−	0.778772i	0.332965	−	0.942939i	$-0.391951\pi$
$131$	−7.47927	−	8.91345i	−0.653467	−	0.778772i	−0.986433	+	0.164167i	$0.947506\pi$
$132$	−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
$136$	17.5803	+	5.08256i	1.50750	+	0.435826i
$137$	−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	$0.970537\pi$
$138$	−5.57214	+	1.11258i	−0.474332	+	0.0947095i
$139$	2.64065	+	7.25513i	0.223977	+	0.615372i	0.999880	−	0.0154801i	$-0.00492768\pi$
$139$	2.64065	+	7.25513i	0.223977	+	0.615372i	−0.775903	+	0.630852i	$0.782705\pi$
$140$	−2.63963	−	1.36922i	−0.223089	−	0.115721i
$141$	3.89102	−	2.24648i	0.327683	−	0.189188i
$142$	3.31490	+	2.65652i	0.278180	+	0.222930i
$143$	4.24651	+	3.56325i	0.355111	+	0.297974i
$144$	3.80930	+	5.40667i	0.317441	+	0.450556i
$145$	−8.72013	−	5.03457i	−0.724167	−	0.418098i
$146$	−6.72351	+	2.62027i	−0.556442	+	0.216855i
$147$	−0.965074	−	5.47321i	−0.0795980	−	0.451422i
$148$	6.03047	+	0.784998i	0.495701	+	0.0645264i
$149$	−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	$0.631701\pi$
$150$	1.23303	−	1.08292i	0.100676	−	0.0884204i
$151$	19.4799			1.58525			0.792625	−	0.609709i	$-0.208714\pi$
$151$	19.4799			1.58525			0.792625	+	0.609709i	$0.208714\pi$
$152$	4.13951	+	11.6131i	0.335759	+	0.941948i
$153$	−10.6981			−0.864887
$154$	−2.59417	+	2.27836i	−0.209044	+	0.183596i
$155$	8.12909	+	2.95875i	0.652944	+	0.237652i
$156$	7.76945	+	1.01137i	0.622054	+	0.0809740i
$157$	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	$0.843374\pi$
$158$	3.72921	−	1.45333i	0.296680	−	0.115621i
$159$	7.37177	+	4.25609i	0.584619	+	0.337530i
$160$	−3.36153	−	4.54974i	−0.265752	−	0.359688i
$161$	3.94363	+	3.30910i	0.310802	+	0.260794i
$162$	1.44092	+	1.15474i	0.113209	+	0.0907247i
$163$	9.40645	−	5.43082i	0.736770	−	0.425374i	−0.0841236	−	0.996455i	$-0.526809\pi$
$163$	9.40645	−	5.43082i	0.736770	−	0.425374i	0.820894	+	0.571081i	$0.193476\pi$
$164$	16.8428	+	8.73667i	1.31520	+	0.682219i
$165$	−0.651689	−	1.79050i	−0.0507339	−	0.139390i
$166$	21.2238	−	4.23774i	1.64729	−	0.328912i
$167$	−3.41386	+	19.3610i	−0.264173	+	1.49820i	0.507208	+	0.861823i	$0.330677\pi$
$167$	−3.41386	+	19.3610i	−0.264173	+	1.49820i	−0.771381	+	0.636374i	$0.780434\pi$
$168$	−1.35530	+	4.68791i	−0.104564	+	0.361680i
$169$	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	$0.746168\pi$
$174$	−5.30010	+	15.6510i	−0.401799	+	1.18650i
$175$	−1.46422	−	0.258182i	−0.110685	−	0.0195167i
$176$	−6.33931	+	1.71841i	−0.477844	+	0.129530i
$177$	−15.6355	+	5.69087i	−1.17524	+	0.427752i
$178$	15.1972	+	8.32309i	1.13908	+	0.623842i
$179$	−12.6648	−	21.9361i	−0.946611	−	1.63958i	−0.752493	−	0.658600i	$-0.771149\pi$
$179$	−12.6648	−	21.9361i	−0.946611	−	1.63958i	−0.194118	−	0.980978i	$-0.562184\pi$
$180$	2.62648	+	2.00930i	0.195766	+	0.149765i
$181$	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	$0.0470912\pi$
$182$	−3.68696	−	6.06596i	−0.273295	−	0.449639i
$183$	2.08187	−	3.60590i	0.153896	−	0.266556i
$184$	3.96381	+	8.95534i	0.292216	+	0.660197i
$185$	2.99448	−	0.528007i	0.220158	−	0.0388199i
$186$	2.14941	−	14.0328i	0.157602	−	1.02894i
$187$	3.63364	−	9.98335i	0.265718	−	0.730055i
$188$	−5.23992	−	5.70169i	−0.382161	−	0.415838i
$189$		−	8.02863i		−	0.583997i
$190$	3.71287	+	4.92083i	0.269360	+	0.356995i
$191$			16.5323i			1.19624i	0.801408	+	0.598118i	$0.204084\pi$
$191$			16.5323i			1.19624i	−0.801408	+	0.598118i	$0.795916\pi$
$192$	−6.24172	+	6.87164i	−0.450457	+	0.495918i
$193$	−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	$0.934326\pi$
$194$	11.8552	+	1.81586i	0.851154	+	0.130371i
$195$	3.85798	−	0.680267i	0.276276	−	0.0487149i
$196$	−8.84430	+	3.67852i	−0.631736	+	0.262751i
$197$	−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	$0.929223\pi$
$198$	3.28108	−	1.99428i	0.233176	−	0.141727i
$199$	−4.35301	+	5.18772i	−0.308577	+	0.367748i	−0.897938	−	0.440122i	$-0.854935\pi$
$199$	−4.35301	+	5.18772i	−0.308577	+	0.367748i	0.589361	+	0.807870i	$0.299380\pi$
$200$	−2.28462	−	1.66749i	−0.161547	−	0.117910i
$201$	−0.946600	−	1.63956i	−0.0667680	−	0.115646i
$202$	2.28455	−	4.17139i	0.160741	−	0.293498i
$203$	14.0680	−	5.12035i	0.987383	−	0.359378i
$204$	−3.27137	−	14.6552i	−0.229042	−	1.02607i
$205$	9.34282	+	1.64739i	0.652531	+	0.115059i
$206$	−5.99013	−	2.02852i	−0.417352	−	0.141333i
$207$	−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	−0.630494	−	0.776194i	$-0.717148\pi$
$211$	0.354765	−	0.297683i	0.0244230	−	0.0204933i	0.654917	+	0.755700i	$0.272703\pi$
$212$	4.39130	−	13.9984i	0.301596	−	0.961417i
$213$	0.605273	−	3.43267i	0.0414726	−	0.235203i
$214$	1.53004	+	7.66288i	0.104591	+	0.523824i
$215$	2.45148	+	6.73540i	0.167190	+	0.459350i
$216$	6.72525	−	13.7129i	0.457595	−	0.933041i
$217$	−11.1389	+	6.43105i	−0.756158	+	0.436568i
$218$	13.9150	−	17.3636i	0.942441	−	1.17601i
$219$	4.53574	+	3.80594i	0.306497	+	0.257182i
$220$	−2.76716	+	1.76855i	−0.186562	+	0.119235i
$221$	18.9165	+	10.9215i	1.27246	+	0.734657i
$222$	−1.81192	−	4.64934i	−0.121608	−	0.312043i
$223$	3.42824	+	19.4425i	0.229572	+	1.30197i	0.853750	+	0.520684i	$0.174323\pi$
$223$	3.42824	+	19.4425i	0.229572	+	1.30197i	−0.624178	+	0.781282i	$0.714566\pi$
$224$	8.39461	+	0.519541i	0.560888	+	0.0347133i
$225$	1.55374	+	0.565516i	0.103583	+	0.0377011i
$226$	−3.95289	−	4.50079i	−0.262942	−	0.299388i
$227$	−3.86097			−0.256261			−0.128131	−	0.991757i	$-0.540898\pi$
$227$	−3.86097			−0.256261			−0.128131	+	0.991757i	$0.540898\pi$
$228$	6.72603	−	7.55629i	0.445442	−	0.500428i
$229$	−21.6315			−1.42945			−0.714725	−	0.699405i	$-0.753448\pi$
$229$	−21.6315			−1.42945			−0.714725	+	0.699405i	$0.753448\pi$
$230$	3.23128	+	3.67917i	0.213065	+	0.242597i
$231$	2.66214	+	0.968938i	0.175156	+	0.0637515i
$232$	28.3172	+	3.03869i	1.85912	+	0.199500i
$233$	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	$0.833420\pi$
$234$	2.86651	+	7.35537i	0.187390	+	0.480835i
$235$	−3.35315	−	1.93594i	−0.218736	−	0.126287i
$236$	15.4438	+	24.1642i	1.00531	+	1.57296i
$237$	−2.51576	−	2.11097i	−0.163416	−	0.137122i
$238$	−8.50764	+	10.6161i	−0.551468	+	0.688141i
$239$	1.58969	−	0.917810i	0.102829	−	0.0593682i	−0.447704	−	0.894182i	$-0.647758\pi$
$239$	1.58969	−	0.917810i	0.102829	−	0.0593682i	0.550532	+	0.834814i	$0.314425\pi$
$240$	−1.94938	+	4.21243i	−0.125832	+	0.271911i
$241$	−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	$0.890025\pi$
$242$	−2.29938	−	11.5160i	−0.147810	−	0.740275i
$243$	−2.54995	+	14.4615i	−0.163579	+	0.927704i
$244$	−6.84734	−	2.14801i	−0.438356	−	0.137512i
$245$	−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
$250$	−1.33949	−	0.453609i	−0.0847169	−	0.0286888i
$251$	−24.0654	−	4.24338i	−1.51899	−	0.267840i	−0.648957	−	0.760825i	$-0.724794\pi$
$251$	−24.0654	−	4.24338i	−1.51899	−	0.267840i	−0.870038	+	0.492985i	$0.835906\pi$
$252$	−4.79866	+	1.07117i	−0.302287	+	0.0674772i
$253$	5.34259	−	1.94454i	0.335886	−	0.122252i
$254$	0.284563	−	0.519587i	0.0178551	−	0.0326018i
$255$	−3.75397	−	6.50207i	−0.235083	−	0.407175i
$256$	13.9027	+	7.91919i	0.868922	+	0.494949i
$257$	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	$0.00843202\pi$
$258$	10.0515	−	6.10942i	0.625780	−	0.380356i
$259$	−2.26045	+	3.91522i	−0.140458	+	0.243280i
$260$	−2.59294	−	6.23422i	−0.160807	−	0.386630i
$261$	−16.3960	+	2.89105i	−1.01489	+	0.178952i
$262$	16.2656	+	2.49141i	1.00489	+	0.153920i
$263$	2.20159	−	6.04882i	0.135756	−	0.372986i	−0.853123	−	0.521710i	$-0.825294\pi$
$263$	2.20159	−	6.04882i	0.135756	−	0.372986i	0.988879	+	0.148724i	$0.0475165\pi$
$264$	3.73527	+	3.88490i	0.229890	+	0.239099i
$265$		−	7.33553i		−	0.450618i
$266$	−9.15305	−	0.474040i	−0.561209	−	0.0290653i
$267$		−	14.2174i		−	0.870092i
$268$	−2.40252	+	2.20795i	−0.146758	+	0.134872i
$269$	−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	$0.175216\pi$
$270$	1.15621	−	7.54858i	0.0703649	−	0.459392i
$271$	−5.70109	+	1.00526i	−0.346317	+	0.0610649i	−0.344101	−	0.938933i	$-0.611816\pi$
$271$	−5.70109	+	1.00526i	−0.346317	+	0.0610649i	−0.00221542	+	0.999998i	$0.500705\pi$
$272$	−23.4237	+	11.0058i	−1.42027	+	0.667323i
$273$	−2.91229	+	5.04423i	−0.176260	+	0.305291i
$274$	−4.53829	−	7.46662i	−0.274168	−	0.451075i
$275$	−1.05547	+	1.25786i	−0.0636473	+	0.0758519i
$276$	4.88257	−	6.38230i	0.293896	−	0.384170i
$277$	−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	$0.873245\pi$
$278$	−9.57661	−	5.24484i	−0.574367	−	0.314565i
$279$	13.4411	−	4.89217i	0.804699	−	0.292886i
$280$	4.08263	−	1.00846i	0.243984	−	0.0602673i
$281$	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	$0.480676\pi$
$282$	−2.03805	+	6.01828i	−0.121364	+	0.358383i
$283$	2.81414	+	3.35376i	0.167283	+	0.199361i	0.843173	−	0.537642i	$-0.180685\pi$
$283$	2.81414	+	3.35376i	0.167283	+	0.199361i	−0.675890	+	0.737003i	$0.736240\pi$
$284$	−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
$288$	−9.09336	−	2.19009i	−0.535831	−	0.129052i
$289$	4.31729	−	24.4846i	0.253958	−	1.44027i
$290$	13.9643	−	2.78823i	0.820010	−	0.163731i
$291$	−3.36582	−	9.24752i	−0.197308	−	0.542099i
$292$	4.69898	−	9.05883i	0.274987	−	0.530128i
$293$	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	$0.180353\pi$
$294$	6.13323	+	4.91510i	0.357697	+	0.286655i
$295$	10.9843	+	9.21690i	0.639529	+	0.536629i
$296$	−7.14046	+	4.79368i	−0.415031	+	0.278627i
$297$	−7.67884	−	4.43338i	−0.445571	−	0.257251i
$298$	2.07938	−	0.810370i	0.120455	−	0.0469435i
$299$	2.02981	+	11.5116i	0.117387	+	0.665736i
$300$	−0.299577	+	2.30139i	−0.0172961	+	0.132871i
$301$	−10.0143	−	3.64489i	−0.577212	−	0.210088i
$302$	−20.6990	+	18.1792i	−1.19109	+	1.04610i
$303$	−3.90245			−0.224190
$304$	−15.2363	−	8.47679i	−0.873860	−	0.486177i
$305$	−3.58818			−0.205458
$306$	11.3676	−	9.98374i	0.649841	−	0.570733i
$307$	−5.14410	−	1.87230i	−0.293589	−	0.106858i	0.191026	−	0.981585i	$-0.438818\pi$
$307$	−5.14410	−	1.87230i	−0.293589	−	0.106858i	−0.484616	+	0.874727i	$0.661041\pi$
$308$	0.630280	−	4.84190i	0.0359135	−	0.275893i
$309$	0.901107	+	5.11043i	0.0512622	+	0.290722i
$310$	−11.3990	+	4.44239i	−0.647421	+	0.252311i
$311$	−8.49640	−	4.90540i	−0.481787	−	0.278160i	0.239374	−	0.970927i	$-0.423058\pi$
$311$	−8.49640	−	4.90540i	−0.481787	−	0.278160i	−0.721161	+	0.692768i	$0.756391\pi$
$312$	−9.19952	+	6.17602i	−0.520820	+	0.349648i
$313$	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	$0.640314\pi$
$314$	−8.63434	−	6.91947i	−0.487264	−	0.390488i
$315$	−2.12902	+	1.22919i	−0.119957	+	0.0692570i
$316$	−2.60630	+	5.02449i	−0.146616	+	0.282650i
$317$	−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	$-0.238064\pi$
$318$	−11.8050	+	2.35710i	−0.661993	+	0.132179i
$319$	2.87105	−	16.2826i	0.160748	−	0.911648i
$320$	7.81785	+	1.69740i	0.437031	+	0.0948873i
$321$	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
$326$	−4.92694	+	14.5491i	−0.272878	+	0.805799i
$327$	−17.9805	−	3.17044i	−0.994323	−	0.175326i
$328$	−26.0502	+	6.43475i	−1.43838	+	0.355300i
$329$	5.40959	−	1.96893i	0.298240	−	0.108551i
$330$	2.36342	+	1.29438i	0.130102	+	0.0712533i
$331$	−8.70826	−	15.0831i	−0.478649	−	0.829044i	0.521051	−	0.853525i	$-0.325540\pi$
$331$	−8.70826	−	15.0831i	−0.478649	−	0.829044i	−0.999700	+	0.0244809i	$0.992207\pi$
$332$	−18.5973	+	24.3096i	−1.02066	+	1.33416i
$333$	3.23170	−	3.85139i	0.177096	−	0.211055i
$334$	−14.4407	−	23.7586i	−0.790161	−	1.30001i
$335$	−0.815750	+	1.41292i	−0.0445692	+	0.0771961i
$336$	−2.93477	−	6.24610i	−0.160105	−	0.340753i
$337$	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	$0.264388\pi$
$338$	−0.343186	+	2.24056i	−0.0186668	+	0.121870i
$339$	−1.68108	+	4.61872i	−0.0913036	+	0.250855i
$340$	−9.52779	+	8.75616i	−0.516717	+	0.474869i
$341$			14.2048i			0.769233i
$342$	9.93278	+	2.28672i	0.537103	+	0.123652i
$343$		−	17.5286i		−	0.946455i
$344$	−14.0511	−	14.6140i	−0.757586	−	0.787934i
$345$	1.37419	−	3.77557i	0.0739841	−	0.203270i
$346$	−3.64578	−	0.558424i	−0.195999	−	0.0300211i
$347$	−7.35622	+	1.29710i	−0.394903	+	0.0696320i	−0.367573	−	0.929994i	$-0.619811\pi$
$347$	−7.35622	+	1.29710i	−0.394903	+	0.0696320i	−0.0273292	+	0.999626i	$0.508700\pi$
$348$	−8.97417	−	21.5767i	−0.481066	−	1.15663i
$349$	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	$0.0376002\pi$
$350$	1.79680	−	1.09212i	0.0960431	−	0.0583760i
$351$	11.7180	−	13.9649i	0.625459	−	0.745393i
$352$	5.13238	−	7.74198i	0.273557	−	0.412649i
$353$	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	$0.446764\pi$
$354$	11.3032	−	20.6386i	0.600757	−	1.09693i
$355$	−2.82265	+	1.02736i	−0.149811	+	0.0545267i
$356$	−23.9156	+	5.33850i	−1.26753	+	0.282940i
$357$	10.9933	+	1.93842i	0.581827	+	0.102592i
$358$	33.9288	+	11.4897i	1.79319	+	0.607251i
$359$	−14.7931	−	17.6297i	−0.780750	−	0.930462i	0.218217	−	0.975900i	$-0.429976\pi$
$359$	−14.7931	−	17.6297i	−0.780750	−	0.930462i	−0.998967	+	0.0454384i	$0.985532\pi$
$360$	−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
$364$	9.57863	+	3.00481i	0.502056	+	0.157495i
$365$	0.886043	−	5.02500i	0.0463776	−	0.263021i
$366$	1.15298	+	5.77443i	0.0602670	+	0.301834i
$367$	8.29186	+	22.7817i	0.432832	+	1.18920i	0.944067	+	0.329755i	$0.106966\pi$
$367$	8.29186	+	22.7817i	0.432832	+	1.18920i	−0.511235	+	0.859441i	$0.670812\pi$
$368$	−12.5693	−	5.81666i	−0.655218	−	0.303214i
$369$	13.5847	−	7.84314i	0.707192	−	0.408298i
$370$	−2.68913	+	3.35559i	−0.139801	+	0.174449i
$371$	8.35489	+	7.01059i	0.433764	+	0.363971i
$372$	10.8119	+	16.9169i	0.560572	+	0.877102i
$373$	−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	$0.715083\pi$
$374$	5.45571	+	13.9992i	0.282108	+	0.723879i
$375$	0.201502	+	1.14278i	0.0104055	+	0.0590127i
$376$	10.8888	+	1.16847i	0.561549	+	0.0602592i
$377$	31.9431	+	11.6263i	1.64515	+	0.598787i
$378$	7.49255	+	8.53108i	0.385375	+	0.438792i
$379$	1.32383			0.0680007			0.0340004	−	0.999422i	$-0.489175\pi$
$379$	1.32383			0.0680007			0.0340004	+	0.999422i	$0.489175\pi$
$380$	−8.53750	−	1.76384i	−0.437964	−	0.0904831i
$381$	−0.486088			−0.0249031
$382$	−15.4284	−	17.5669i	−0.789387	−	0.898803i
$383$	−2.20706	−	0.803306i	−0.112776	−	0.0410470i	0.285016	−	0.958523i	$-0.408001\pi$
$383$	−2.20706	−	0.803306i	−0.112776	−	0.0410470i	−0.397792	+	0.917476i	$0.630223\pi$
$384$	0.219528	−	13.1267i	0.0112027	−	0.669867i
$385$	−0.423941	−	2.40429i	−0.0216060	−	0.122534i
$386$	−7.52322	−	19.3043i	−0.382922	−	0.982564i
$387$	10.2636	+	5.92572i	0.521730	+	0.301221i
$388$	−14.2918	+	9.13412i	−0.725554	+	0.463715i
$389$	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	$0.615160\pi$
$390$	−3.46458	+	4.32322i	−0.175436	+	0.218915i
$391$	19.4012	−	11.2013i	0.981161	−	0.566474i
$392$	5.96490	−	12.1625i	0.301273	−	0.614299i
$393$	−4.61799	−	12.6878i	−0.232947	−	0.640016i
$394$	−5.27545	−	26.4210i	−0.265773	−	1.33107i
$395$	−0.491445	+	2.78712i	−0.0247273	+	0.140235i
$396$	−1.62530	+	5.18109i	−0.0816746	+	0.260359i
$397$	−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	$0.902331\pi$
$402$	2.53593	+	0.858773i	0.126481	+	0.0428317i
$403$	−28.7612	−	5.07137i	−1.43270	−	0.252623i
$404$	1.46533	+	6.56446i	0.0729030	+	0.326594i
$405$	−1.22695	+	0.446573i	−0.0609676	+	0.0221904i
$406$	−10.1700	+	18.5695i	−0.504729	+	0.921589i
$407$	2.49643	+	4.32394i	0.123743	+	0.214330i
$408$	17.1528	+	12.5194i	0.849189	+	0.619805i
$409$	−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	$0.334125\pi$
$410$	−11.4649	+	6.96850i	−0.566212	+	0.344150i
$411$	−3.58475	+	6.20897i	−0.176823	+	0.306266i
$412$	8.25808	−	3.43470i	0.406847	−	0.169216i
$413$	−20.9954	+	3.70206i	−1.03312	+	0.182166i
$414$	8.00313	+	1.22584i	0.393332	+	0.0602466i
$415$	−5.23418	+	14.3808i	−0.256936	+	0.705926i
$416$	13.8432	+	13.1558i	0.678721	+	0.645017i
$417$			8.95920i			0.438734i
$418$	−5.50767	+	8.49250i	−0.269389	+	0.415382i
$419$		−	35.8074i		−	1.74931i	−0.484749	−	0.874653i	$-0.661089\pi$
$419$		−	35.8074i		−	1.74931i	0.484749	−	0.874653i	$-0.338911\pi$
$420$	−2.33490	−	2.54066i	−0.113931	−	0.123971i
$421$	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	$-0.200502\pi$
$422$	−0.0991605	+	0.647390i	−0.00482706	+	0.0315144i
$423$	−6.30475	+	1.11170i	−0.306547	+	0.0540525i
$424$	8.39763	+	18.9726i	0.407825	+	0.921391i
$425$	−3.23505	+	5.60328i	−0.156923	+	0.271799i
$426$	2.56032	+	4.21236i	0.124048	+	0.204089i
$427$	3.42923	−	4.08680i	0.165952	−	0.197774i
$428$	−8.77702	−	6.71457i	−0.424253	−	0.324561i
$429$	3.21631	+	5.57081i	0.155285	+	0.268961i
$430$	−8.89058	−	4.86912i	−0.428742	−	0.234810i
$431$	−4.38855	+	1.59730i	−0.211389	+	0.0769394i	−0.445544	−	0.895260i	$-0.646990\pi$
$431$	−4.38855	+	1.59730i	−0.211389	+	0.0769394i	0.234155	+	0.972199i	$0.424768\pi$
$432$	5.65110	+	20.8472i	0.271889	+	1.00301i
$433$	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	$0.415634\pi$
$434$	5.83437	−	17.2287i	0.280059	−	0.827003i
$435$	−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	−0.593248	−	0.805020i	$-0.702155\pi$
$439$	2.02242	−	1.69701i	0.0965248	−	0.0809939i	0.689773	+	0.724026i	$0.257710\pi$
$440$	1.28988	−	4.46163i	0.0614928	−	0.212700i
$441$	−1.37513	+	7.79876i	−0.0654825	+	0.371370i
$442$	−30.2926	+	6.04849i	−1.44087	+	0.287698i
$443$	−0.537838	−	1.47770i	−0.0255534	−	0.0702075i	0.926260	−	0.376885i	$-0.123005\pi$
$443$	−0.537838	−	1.47770i	−0.0255534	−	0.0702075i	−0.951813	+	0.306678i	$0.900783\pi$
$444$	6.26422	+	3.24936i	0.297287	+	0.154208i
$445$	−10.6106	+	6.12606i	−0.502993	+	0.290403i
$446$	−21.7871	−	17.4599i	−1.03165	−	0.826752i
$447$	−1.40277	−	1.17706i	−0.0663487	−	0.0556732i
$448$	−9.40482	+	7.28204i	−0.444336	+	0.344044i
$449$	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	$0.475444\pi$
$450$	−2.17874	+	0.849091i	−0.102707	+	0.0400265i
$451$	2.70505	+	15.3411i	0.127376	+	0.722385i
$452$	8.40055	+	1.09352i	0.395129	+	0.0514347i
$453$	21.2413	+	7.73121i	0.998005	+	0.363244i
$454$	4.10260	−	3.60317i	0.192544	−	0.169105i
$455$	5.01944			0.235315
$456$	−0.0952152	+	14.3061i	−0.00445886	+	0.669945i
$457$	1.60386			0.0750254			0.0375127	−	0.999296i	$-0.488057\pi$
$457$	1.60386			0.0750254			0.0375127	+	0.999296i	$0.488057\pi$
$458$	22.9853	−	20.1872i	1.07403	−	0.943284i
$459$	−32.8309	−	11.9495i	−1.53242	−	0.557754i
$460$	−6.86702	−	0.893893i	−0.320176	−	0.0416780i
$461$	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	$0.867200\pi$
$462$	−3.73298	+	1.45481i	−0.173674	+	0.0676837i
$463$	5.79397	+	3.34515i	0.269269	+	0.155462i	0.628555	−	0.777765i	$-0.283647\pi$
$463$	5.79397	+	3.34515i	0.269269	+	0.155462i	−0.359286	+	0.933227i	$0.616980\pi$
$464$	−32.9252	+	23.1976i	−1.52851	+	1.07692i
$465$	7.68989	+	6.45258i	0.356610	+	0.299231i
$466$	−11.5142	−	9.22737i	−0.533386	−	0.427450i
$467$	8.68064	−	5.01177i	0.401692	−	0.231917i	−0.285522	−	0.958372i	$-0.592167\pi$
$467$	8.68064	−	5.01177i	0.401692	−	0.231917i	0.687214	+	0.726455i	$0.258834\pi$
$468$	−9.91015	−	5.14058i	−0.458097	−	0.237623i
$469$	−0.829649	−	2.27944i	−0.0383096	−	0.105255i
$470$	5.36968	−	1.07216i	0.247685	−	0.0494550i
$471$	−1.57656	+	8.94112i	−0.0726441	+	0.411985i
$472$	−38.9611	−	11.2639i	−1.79333	−	0.518463i
$473$	−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
$478$	−0.832654	+	2.45880i	−0.0380847	+	0.112463i
$479$	26.4306	+	4.66043i	1.20765	+	0.212940i	0.741001	−	0.671504i	$-0.234352\pi$
$479$	26.4306	+	4.66043i	1.20765	+	0.212940i	0.466645	+	0.884445i	$0.345463\pi$
$480$	−1.85979	−	6.29528i	−0.0848872	−	0.287339i
$481$	−9.64617	+	3.51092i	−0.439827	+	0.160084i
$482$	0.137416	+	0.0752588i	0.00625912	+	0.00342795i
$483$	2.98691	+	5.17348i	0.135909	+	0.235401i
$484$	13.1903	+	10.0908i	0.599561	+	0.458674i
$485$	−5.45126	+	6.49656i	−0.247529	+	0.294994i
$486$	−10.7863	−	17.7462i	−0.489278	−	0.804984i
$487$	−16.8981	+	29.2685i	−0.765728	+	1.32628i	0.174132	+	0.984722i	$0.444288\pi$
$487$	−16.8981	+	29.2685i	−0.765728	+	1.32628i	−0.939861	+	0.341558i	$0.889045\pi$
$488$	9.28045	−	4.10770i	0.420106	−	0.185947i
$489$	12.4124	−	2.18864i	0.561309	−	0.0989739i
$490$	1.02549	−	6.69514i	0.0463271	−	0.302456i
$491$	−10.5587	+	29.0097i	−0.476506	+	1.30919i	0.435935	+	0.899978i	$0.356418\pi$
$491$	−10.5587	+	29.0097i	−0.476506	+	1.30919i	−0.912440	+	0.409210i	$0.865804\pi$
$492$	14.8984	+	16.2113i	0.671670	+	0.730861i
$493$		−	65.1484i		−	2.93413i
$494$	−15.2289	−	14.1836i	−0.685179	−	0.638152i
$495$			2.71502i			0.122031i
$496$	24.3968	−	24.5393i	1.09545	−	1.10185i
$497$	1.52749	−	4.19675i	0.0685173	−	0.188250i
$498$	24.8248	+	3.80241i	1.11243	+	0.170390i
$499$	35.1489	−	6.19771i	1.57348	−	0.277447i	0.682293	−	0.731079i	$-0.260983\pi$
$499$	35.1489	−	6.19771i	1.57348	−	0.277447i	0.891189	+	0.453631i	$0.149872\pi$
$500$	1.84664	−	0.768056i	0.0825844	−	0.0343485i
$501$	−11.4066	+	19.7568i	−0.509608	+	0.882668i
$502$	29.5315	−	17.9496i	1.31806	−	0.801130i
$503$	11.3744	−	13.5555i	0.507160	−	0.604409i	−0.450335	−	0.892860i	$-0.648696\pi$
$503$	11.3744	−	13.5555i	0.507160	−	0.604409i	0.957495	+	0.288450i	$0.0931400\pi$
$504$	4.09933	−	5.61646i	0.182599	−	0.250177i
$505$	1.68150	+	2.91245i	0.0748260	+	0.129602i
$506$	−3.86224	+	7.05210i	−0.171697	+	0.313504i
$507$	1.74772	−	0.636118i	0.0776190	−	0.0282510i
$508$	0.182521	+	0.817667i	0.00809808	+	0.0362781i
$509$	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	$0.405215\pi$
$510$	10.0568	+	3.40567i	0.445324	+	0.150806i
$511$	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
$516$	−4.97908	+	15.8721i	−0.219192	+	0.698732i
$517$	1.10401	−	6.26114i	0.0485542	−	0.275364i
$518$	−1.25188	−	6.26976i	−0.0550043	−	0.275478i
$519$	1.03508	+	2.84385i	0.0454349	+	0.124831i
$520$	8.57317	+	4.20457i	0.375958	+	0.184383i
$521$	−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	$0.549133\pi$
$522$	14.7241	−	18.3732i	0.644455	−	0.804173i
$523$	−32.6152	−	27.3674i	−1.42616	−	1.19669i	−0.947939	−	0.318453i	$-0.896837\pi$
$523$	−32.6152	−	27.3674i	−1.42616	−	1.19669i	−0.478223	−	0.878239i	$-0.658719\pi$
$524$	−19.6086	+	12.5322i	−0.856608	+	0.547474i
$525$	−1.49416	−	0.862651i	−0.0652103	−	0.0376492i
$526$	3.30556	+	8.48196i	0.144129	+	0.369831i
$527$	9.71936	+	55.1212i	0.423382	+	2.40112i
$528$	−7.59455	−	0.642165i	−0.330510	−	0.0279466i
$529$	−10.3472	−	3.76607i	−0.449878	−	0.163742i
$530$	6.84573	+	7.79461i	0.297359	+	0.338576i
$531$	23.7089			1.02888
$532$	10.1683	−	8.03819i	0.440850	−	0.348500i
$533$	−32.0277			−1.38727
$534$	13.2681	+	15.1072i	0.574167	+	0.653752i
$535$	−5.19221	−	1.88981i	−0.224479	−	0.0817036i
$536$	0.492358	−	4.58824i	0.0212666	−	0.198182i
$537$	−5.10397	−	28.9460i	−0.220253	−	1.24911i
$538$	−3.36954	−	8.64612i	−0.145271	−	0.372761i
$539$	−6.81068	−	3.93215i	−0.293357	−	0.169370i
$540$	5.81598	+	9.10000i	0.250280	+	0.391602i
$541$	−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	$0.738174\pi$
$542$	5.11975	−	6.38859i	0.219912	−	0.274414i
$543$	14.1379	−	8.16255i	0.606717	−	0.350288i
$544$	14.6187	−	33.5542i	0.626772	−	1.43863i
$545$	5.38136	+	14.7852i	0.230512	+	0.633326i
$546$	−1.61288	−	8.07775i	−0.0690248	−	0.345696i
$547$	1.83718	−	10.4191i	0.0785519	−	0.445490i	−0.920011	−	0.391893i	$-0.871820\pi$
$547$	1.83718	−	10.4191i	0.0785519	−	0.445490i	0.998563	−	0.0535970i	$-0.0170686\pi$
$548$	11.7904	+	3.69863i	0.503660	+	0.157998i
$549$	−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
$554$	5.57591	+	1.88824i	0.236898	+	0.0802237i
$555$	3.47481	+	0.612702i	0.147497	+	0.0260078i
$556$	15.0706	−	3.36409i	0.639135	−	0.142669i
$557$	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	$0.226660\pi$
$558$	−9.71680	+	17.7420i	−0.411345	+	0.751078i
$559$	−12.0989	−	20.9559i	−0.511730	−	0.886342i
$560$	−3.39700	+	4.88160i	−0.143550	+	0.206285i
$561$	7.92442	−	9.44396i	0.334569	−	0.398724i
$562$	−9.44334	+	5.73976i	−0.398343	+	0.242117i
$563$	−15.3295	+	26.5515i	−0.646062	+	1.11901i	0.337993	+	0.941149i	$0.390252\pi$
$563$	−15.3295	+	26.5515i	−0.646062	+	1.11901i	−0.984055	+	0.177864i	$0.943081\pi$
$564$	−3.45084	−	8.29689i	−0.145307	−	0.349362i
$565$	4.17136	−	0.735523i	0.175490	−	0.0309437i
$566$	−6.12009	−	0.937413i	−0.257247	−	0.0394024i
$567$	0.663970	−	1.82424i	0.0278841	−	0.0766110i
$568$	6.12439	−	5.88850i	0.256974	−	0.247076i
$569$		−	3.29242i		−	0.138025i	−0.997616	−	0.0690127i	$-0.978015\pi$
$569$		−	3.29242i		−	0.138025i	0.997616	−	0.0690127i	$-0.0219849\pi$
$570$	2.09561	+	6.83937i	0.0877754	+	0.286470i
$571$		−	26.9222i		−	1.12666i	−0.826233	−	0.563329i	$-0.809520\pi$
$571$		−	26.9222i		−	1.12666i	0.826233	−	0.563329i	$-0.190480\pi$
$572$	8.16318	−	7.50206i	0.341320	−	0.313677i
$573$	−6.56137	+	18.0272i	−0.274105	+	0.753098i
$574$	3.02019	−	19.7179i	0.126060	−	0.823011i
$575$	−3.40987	+	0.601253i	−0.142202	+	0.0250740i
$576$	11.7063	−	6.15904i	0.487763	−	0.256627i
$577$	−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	$0.991098\pi$
$578$	18.2622	+	30.0459i	0.759609	+	1.24974i
$579$	−10.9275	+	13.0229i	−0.454131	+	0.541212i
$580$	−12.2361	+	15.9946i	−0.508078	+	0.664139i
$581$	−11.3769	−	19.7053i	−0.471992	−	0.817514i
$582$	12.2065	+	6.68517i	0.505977	+	0.277109i
$583$	11.3187	−	4.11967i	0.468772	−	0.170619i
$584$	3.46091	+	14.0110i	0.143213	+	0.579779i
$585$	−5.49723	−	0.969311i	−0.227283	−	0.0400761i
$586$	−7.17928	+	21.2002i	−0.296574	+	0.875771i
$587$	21.2670	+	25.3450i	0.877784	+	1.04610i	0.998572	+	0.0534234i	$0.0170133\pi$
$587$	21.2670	+	25.3450i	0.877784	+	1.04610i	−0.120788	+	0.992678i	$0.538542\pi$
$588$	−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
$592$	3.11372	−	11.7574i	0.127973	−	0.483225i
$593$	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	$-0.312560\pi$
$594$	12.2968	−	2.45528i	0.504542	−	0.100741i
$595$	−3.29017	−	9.03967i	−0.134884	−	0.370591i
$596$	−1.45325	+	2.80162i	−0.0595276	+	0.114759i
$597$	−6.80554	+	3.92918i	−0.278532	+	0.160811i
$598$	−12.8999	−	10.3378i	−0.527514	−	0.422744i
$599$	34.2707	+	28.7565i	1.40026	+	1.17496i	0.960982	+	0.276609i	$0.0892108\pi$
$599$	34.2707	+	28.7565i	1.40026	+	1.17496i	0.439280	+	0.898350i	$0.355234\pi$
$600$	−1.82940	−	2.72500i	−0.0746851	−	0.111248i
$601$	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	$0.591644\pi$
$602$	14.0425	−	5.47260i	0.572330	−	0.223047i
$603$	0.468436	+	2.65664i	0.0190762	+	0.108187i
$604$	5.02904	−	38.6338i	0.204629	−	1.57199i
$605$	7.80298	+	2.84005i	0.317236	+	0.115465i
$606$	4.14668	−	3.64188i	0.168447	−	0.147941i
$607$	−20.3855			−0.827423			−0.413712	−	0.910408i	$-0.635768\pi$
$607$	−20.3855			−0.827423			−0.413712	+	0.910408i	$0.635768\pi$
$608$	24.1006	−	5.21164i	0.977408	−	0.211360i
$609$	17.3723			0.703961
$610$	3.81273	−	3.34859i	0.154373	−	0.135580i
$611$	12.2831	+	4.47068i	0.496921	+	0.180864i
$612$	−2.76187	+	21.2171i	−0.111642	+	0.857651i
$613$	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	$0.728969\pi$
$614$	7.21332	−	2.81115i	0.291106	−	0.113449i
$615$	9.53382	+	5.50435i	0.384441	+	0.221957i
$616$	3.84888	+	5.73312i	0.155076	+	0.230994i
$617$	−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	$0.990039\pi$
$618$	−5.72671	−	4.58932i	−0.230362	−	0.184609i
$619$	−6.33070	+	3.65503i	−0.254452	+	0.146908i	−0.621801	−	0.783175i	$-0.713599\pi$
$619$	−6.33070	+	3.65503i	−0.254452	+	0.146908i	0.367349	+	0.930083i	$0.380265\pi$
$620$	7.96664	−	15.3583i	0.319948	−	0.616805i
$621$	−6.39476	−	17.5695i	−0.256613	−	0.705038i
$622$	13.6060	−	2.71670i	0.545551	−	0.108930i
$623$	3.16328	−	17.9398i	0.126734	−	0.718744i
$624$	4.01162	−	15.1478i	0.160593	−	0.606397i
$625$	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
$630$	1.11514	−	3.29298i	0.0444284	−	0.131196i
$631$	−37.5384	−	6.61903i	−1.49438	−	0.263500i	−0.634072	−	0.773274i	$-0.718618\pi$
$631$	−37.5384	−	6.61903i	−1.49438	−	0.263500i	−0.860308	+	0.509774i	$0.829729\pi$
$632$	−1.91960	−	7.77122i	−0.0763575	−	0.309122i
$633$	0.504989	−	0.183801i	0.0200715	−	0.00730543i
$634$	17.1526	+	9.39398i	0.681215	+	0.373083i
$635$	0.209448	+	0.362774i	0.00831168	+	0.0143962i
$636$	10.3441	−	13.5214i	0.410171	−	0.536159i
$637$	10.3932	−	12.3861i	0.411792	−	0.490754i
$638$	12.1446	+	19.9809i	0.480810	+	0.791052i
$639$	−2.48333	+	4.30126i	−0.0982391	+	0.170155i
$640$	−9.89118	+	5.49223i	−0.390983	+	0.217099i
$641$	−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	$0.492739\pi$
$642$	−1.37287	+	8.96304i	−0.0541827	+	0.353743i
$643$	−2.13572	+	5.86783i	−0.0842244	+	0.231405i	−0.974655	−	0.223715i	$-0.928181\pi$
$643$	−2.13572	+	5.86783i	−0.0842244	+	0.231405i	0.890430	+	0.455120i	$0.150404\pi$
$644$	7.58094	−	6.96698i	0.298731	−	0.274537i
$645$			8.31739i			0.327497i
$646$	−15.5615	+	36.7234i	−0.612258	+	1.44486i
$647$		−	42.4622i		−	1.66936i	−0.550735	−	0.834680i	$-0.685653\pi$
$647$		−	42.4622i		−	1.66936i	0.550735	−	0.834680i	$-0.314347\pi$
$648$	2.66215	−	2.55962i	0.104579	−	0.100551i
$649$	−8.05282	+	22.1249i	−0.316101	+	0.868480i
$650$	4.71931	+	0.722856i	0.185107	+	0.0283527i
$651$	−14.6985	+	2.59174i	−0.576080	+	0.101578i
$652$	−8.34234	−	20.0576i	−0.326711	−	0.785515i
$653$	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	$-0.0408926\pi$
$654$	22.0645	−	13.4111i	0.862790	−	0.524414i
$655$	−7.47927	+	8.91345i	−0.292239	+	0.348277i
$656$	21.6754	−	31.1482i	0.846281	−	1.21613i
$657$	−4.21841	−	7.30649i	−0.164576	−	0.285053i
$658$	−3.91067	+	7.14053i	−0.152454	+	0.278367i
$659$	−28.7932	+	10.4799i	−1.12162	+	0.408238i	−0.835245	−	0.549878i	$-0.814674\pi$
$659$	−28.7932	+	10.4799i	−1.12162	+	0.408238i	−0.286380	+	0.958116i	$0.592452\pi$
$660$	−3.71929	+	0.830227i	−0.144773	+	0.0323166i
$661$	−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	$0.731301\pi$
$662$	23.3293	+	7.90029i	0.906718	+	0.307054i
$663$	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
$668$	37.5167	+	11.7689i	1.45156	+	0.455354i
$669$	−3.97814	+	22.5612i	−0.153804	+	0.872266i
$670$	−0.451776	−	2.26263i	−0.0174536	−	0.0874129i
$671$	−2.01514	−	5.53654i	−0.0777935	−	0.213736i
$672$	8.94749	+	3.89819i	0.345157	+	0.150376i
$673$	−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	$0.409635\pi$
$674$	−17.4034	+	21.7165i	−0.670353	+	0.836489i
$675$	4.13656	+	3.47099i	0.159216	+	0.133598i
$676$	−1.72629	−	2.70105i	−0.0663958	−	0.103886i
$677$	−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	$0.961174\pi$
$678$	−2.52404	−	6.47661i	−0.0969353	−	0.248733i
$679$	−2.18955	−	12.4176i	−0.0840274	−	0.476543i
$680$	1.95257	−	18.1958i	0.0748775	−	0.697775i
$681$	−4.21009	−	1.53235i	−0.161331	−	0.0587197i
$682$	−13.2563	−	15.0938i	−0.507612	−	0.577971i
$683$	19.5329			0.747407			0.373703	−	0.927548i	$-0.378088\pi$
$683$	19.5329			0.747407			0.373703	+	0.927548i	$0.378088\pi$
$684$	−12.6884	+	6.83973i	−0.485155	+	0.261524i
$685$	6.17845			0.236066
$686$	16.3582	+	18.6256i	0.624559	+	0.711128i
$687$	−23.5875	−	8.58516i	−0.899920	−	0.327544i
$688$	28.5687	+	2.41566i	1.08917	+	0.0920960i
$689$	4.30032	+	24.3883i	0.163829	+	0.929121i
$690$	2.06327	+	5.29429i	0.0785475	+	0.201550i
$691$	11.8501	+	6.84167i	0.450800	+	0.260269i	0.708168	−	0.706044i	$-0.249522\pi$
$691$	11.8501	+	6.84167i	0.450800	+	0.260269i	−0.257368	+	0.966313i	$0.582855\pi$
$692$	4.39509	−	2.80898i	0.167076	−	0.106781i
$693$	−3.09230	−	2.59475i	−0.117467	−	0.0985665i
$694$	6.60610	−	8.24332i	0.250764	−	0.312912i
$695$	6.68636	−	3.86037i	0.253628	−	0.146432i
$696$	29.6718	+	14.5521i	1.12471	+	0.551595i
$697$	20.9937	+	57.6798i	0.795194	+	2.18478i
$698$	4.08109	+	20.4393i	0.154472	+	0.773638i
$699$	−2.10240	+	11.9233i	−0.0795202	+	0.450981i
$700$	−0.890056	+	2.83729i	−0.0336410	+	0.107240i
$701$	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
$706$	−47.1714	−	15.9742i	−1.77532	−	0.601199i
$707$	−4.92419	−	0.868268i	−0.185193	−	0.0326546i
$708$	7.24995	+	32.4786i	0.272470	+	1.22062i
$709$	−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	$0.618342\pi$
$710$	2.04054	−	3.72584i	0.0765800	−	0.139828i
$711$	2.33974	+	4.05256i	0.0877473	+	0.151983i
$712$	20.4303	−	27.9914i	0.765658	−	1.04902i
$713$	−19.2535	+	22.9455i	−0.721050	+	0.859314i
$714$	−13.4903	+	8.19954i	−0.504861	+	0.306860i
$715$	2.77171	−	4.80075i	0.103656	−	0.179538i
$716$	−46.7747	+	19.4545i	−1.74805	+	0.727050i
$717$	2.09770	−	0.369881i	0.0783401	−	0.0138135i
$718$	32.1715	+	4.92770i	1.20063	+	0.183900i
$719$	5.36937	−	14.7522i	0.200244	−	0.550165i	−0.798406	−	0.602120i	$-0.794323\pi$
$719$	5.36937	−	14.7522i	0.200244	−	0.550165i	0.998649	+	0.0519546i	$0.0165451\pi$
$720$	4.66306	−	4.69028i	0.173782	−	0.174797i
$721$			6.64893i			0.247619i
$722$	−26.2045	+	5.94335i	−0.975231	+	0.221189i
$723$		−	0.128556i		−	0.00478107i
$724$	−19.0392	−	20.7170i	−0.707585	−	0.769941i
$725$	−3.44385	+	9.46189i	−0.127901	+	0.351406i
$726$	2.06318	−	13.4699i	0.0765718	−	0.499914i
$727$	44.8976	−	7.91666i	1.66516	−	0.293613i	0.739836	−	0.672788i	$-0.234903\pi$
$727$	44.8976	−	7.91666i	1.66516	−	0.293613i	0.925325	+	0.379175i	$0.123792\pi$
$728$	−12.9823	+	5.74620i	−0.481155	+	0.212968i
$729$	−10.4786	+	18.1494i	−0.388095	+	0.672200i
$730$	3.74798	+	6.16636i	0.138719	+	0.228227i
$731$	−29.8096	+	35.5257i	−1.10255	+	1.31397i
$732$	−6.61400	−	5.05982i	−0.244461	−	0.187016i
$733$	−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	$0.933035\pi$
$734$	−30.0714	−	16.4692i	−1.10995	−	0.607891i
$735$	−5.22247	+	1.90082i	−0.192634	+	0.0701130i
$736$	18.7842	−	5.54932i	0.692393	−	0.204551i
$737$	−2.63826	−	0.465196i	−0.0971815	−	0.0171357i
$738$	−7.11545	+	21.0117i	−0.261923	+	0.773450i
$739$	11.5448	+	13.7586i	0.424682	+	0.506117i	0.935380	−	0.353643i	$-0.115057\pi$
$739$	11.5448	+	13.7586i	0.424682	+	0.506117i	−0.510698	+	0.859760i	$0.670613\pi$
$740$	−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	−0.230952	−	0.972965i	$-0.574184\pi$
$743$	18.7297	−	15.7161i	0.687128	−	0.576568i	0.918079	+	0.396397i	$0.129740\pi$
$744$	−27.2760	−	7.88565i	−0.999985	−	0.289102i
$745$	−0.274027	+	1.55408i	−0.0100396	+	0.0569372i
$746$	8.11666	−	1.62065i	0.297172	−	0.0593360i
$747$	8.65451	+	23.7781i	0.316652	+	0.869994i
$748$	−18.8616	−	9.78385i	−0.689647	−	0.357733i
$749$	7.11463	−	4.10764i	0.259963	−	0.150090i
$750$	−1.28059	−	1.02625i	−0.0467604	−	0.0374732i
$751$	9.62096	+	8.07295i	0.351074	+	0.294586i	0.801221	−	0.598368i	$-0.204184\pi$
$751$	9.62096	+	8.07295i	0.351074	+	0.294586i	−0.450147	+	0.892954i	$0.648628\pi$
$752$	−12.6607	+	8.92018i	−0.461690	+	0.325286i
$753$	−24.5574	−	14.1782i	−0.894920	−	0.516683i
$754$	−44.7923	+	17.4563i	−1.63124	+	0.635721i
$755$	−3.38265	−	19.1839i	−0.123107	−	0.698175i
$756$	−15.9229	−	2.07272i	−0.579111	−	0.0753840i
$757$	−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	$0.762695\pi$
$758$	−1.40668	+	1.23544i	−0.0510930	+	0.0448732i
$759$	6.59744			0.239472
$760$	10.7179	−	6.09322i	0.388778	−	0.221024i
$761$	34.4285			1.24803			0.624016	−	0.781411i	$-0.285500\pi$
$761$	34.4285			1.24803			0.624016	+	0.781411i	$0.285500\pi$
$762$	0.516509	−	0.453632i	0.0187112	−	0.0164334i
$763$	−21.9827	−	8.00106i	−0.795828	−	0.289658i
$764$	32.7880	+	4.26808i	1.18623	+	0.154414i
$765$	1.85770	+	10.5355i	0.0671652	+	0.380913i
$766$	3.09486	−	1.20612i	0.111822	−	0.0435788i
$767$	−41.9225	−	24.2040i	−1.51373	−	0.873955i
$768$	12.0169	+	14.1530i	0.433623	+	0.510703i
$769$	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	$0.678338\pi$
$770$	2.69422	+	2.15912i	0.0970930	+	0.0778093i
$771$	20.0501	−	11.5759i	0.722088	−	0.416898i
$772$	26.0094	+	13.4916i	0.936099	+	0.485572i
$773$	−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	$0.949997\pi$
$774$	−16.4360	+	3.28177i	−0.590781	+	0.117961i
$775$	1.50220	−	8.51937i	0.0539604	−	0.306025i
$776$	6.66195	−	23.0433i	0.239150	−	0.827205i
$777$	−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
$782$	−10.1620	+	30.0081i	−0.363393	+	1.07309i
$783$	−53.5463	−	9.44165i	−1.91359	−	0.337417i
$784$	5.01219	+	18.4903i	0.179007	+	0.660367i
$785$	7.35219	−	2.67598i	0.262411	−	0.0955097i
$786$	16.7477	+	9.17223i	0.597369	+	0.327163i
$787$	−17.3047	−	29.9726i	−0.616846	−	1.06841i	−0.990058	−	0.140663i	$-0.955077\pi$
$787$	−17.3047	−	29.9726i	−0.616846	−	1.06841i	0.373211	−	0.927746i	$-0.378257\pi$
$788$	30.2624	+	23.1513i	1.07805	+	0.824730i
$789$	4.80133	−	5.72201i	0.170932	−	0.203709i
$790$	−2.07883	−	3.42018i	−0.0739613	−	0.121685i
$791$	−3.14885	+	5.45397i	−0.111960	+	0.193921i
$792$	−3.10812	−	7.02212i	−0.110442	−	0.249520i
$793$	11.9296	−	2.10350i	0.423631	−	0.0746976i
$794$	1.65369	−	10.7964i	0.0586871	−	0.383151i
$795$	2.91134	−	7.99883i	0.103255	−	0.283689i
$796$	9.16483	+	9.97248i	0.324839	+	0.353465i
$797$			38.7364i			1.37211i	0.727547	+	0.686057i	$0.240660\pi$
$797$			38.7364i			1.37211i	−0.727547	+	0.686057i	$0.759340\pi$
$798$	−9.79257	−	4.14959i	−0.346653	−	0.146894i
$799$		−	25.0515i		−	0.886259i
$800$	−3.89689	+	4.10051i	−0.137776	+	0.144975i
$801$	−6.92877	+	19.0366i	−0.244816	+	0.672627i
$802$	21.3524	+	3.27054i	0.753978	+	0.115487i
$803$	8.25117	−	1.45490i	0.291177	−	0.0513424i
$804$	−3.49607	+	1.45408i	−0.123297	+	0.0512816i
$805$	2.57402	−	4.45834i	0.0907224	−	0.157136i
$806$	35.2939	−	21.4520i	1.24318	−	0.755616i
$807$	−4.89426	+	5.83275i	−0.172286	+	0.205322i
$808$	−7.68318	−	5.60779i	−0.270293	−	0.197281i
$809$	−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	$-0.355758\pi$
$810$	0.886981	−	1.61955i	0.0311653	−	0.0569051i
$811$	38.3784	−	13.9686i	1.34765	−	0.490504i	0.435435	−	0.900220i	$-0.356595\pi$
$811$	38.3784	−	13.9686i	1.34765	−	0.490504i	0.912213	+	0.409716i	$0.134372\pi$
$812$	−6.52313	−	29.2226i	−0.228917	−	1.02551i
$813$	−6.61557	−	1.16650i	−0.232018	−	0.0409111i
$814$	−6.68788	−	2.26480i	−0.234410	−	0.0793813i
$815$	−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
$820$	5.67922	−	18.1040i	0.198327	−	0.632220i
$821$	−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	$0.0567600\pi$
$822$	−1.98530	−	9.94295i	−0.0692452	−	0.346800i
$823$	2.30681	+	6.33791i	0.0804104	+	0.220926i	0.973383	−	0.229186i	$-0.0736064\pi$
$823$	2.30681	+	6.33791i	0.0804104	+	0.220926i	−0.892972	+	0.450112i	$0.851384\pi$
$824$	−5.56954	+	11.3563i	−0.194024	+	0.395617i
$825$	−1.65013	+	0.952706i	−0.0574503	+	0.0331690i
$826$	18.8545	−	23.5273i	0.656032	−	0.818619i
$827$	−21.9139	−	18.3879i	−0.762020	−	0.639411i	0.176632	−	0.984277i	$-0.443480\pi$
$827$	−21.9139	−	18.3879i	−0.762020	−	0.639411i	−0.938652	+	0.344866i	$0.887924\pi$
$828$	−9.64797	+	6.16620i	−0.335290	+	0.214290i
$829$	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	$0.321970\pi$
$830$	−7.85883	−	20.1655i	−0.272784	−	0.699954i
$831$	−0.838795	−	4.75704i	−0.0290975	−	0.165020i
$832$	−26.9870	−	1.06023i	−0.935605	−	0.0367570i
$833$	−29.1191	−	10.5985i	−1.00892	−	0.367216i
$834$	−8.36098	−	9.51989i	−0.289517	−	0.329647i
$835$	19.6596			0.680350
$836$	−2.07310	−	14.1639i	−0.0716997	−	0.489869i
$837$	46.7134			1.61465
$838$	33.4165	+	38.0483i	1.15435	+	1.31436i
$839$	4.83067	+	1.75822i	0.166773	+	0.0607005i	0.424057	−	0.905635i	$-0.360605\pi$
$839$	4.83067	+	1.75822i	0.166773	+	0.0607005i	−0.257284	+	0.966336i	$0.582828\pi$
$840$	4.85204	+	0.520667i	0.167411	+	0.0179647i
$841$	−12.5700	−	71.2877i	−0.433447	−	2.45820i
$842$	17.4891	+	44.8764i	0.602714	+	1.54654i
$843$	7.85274	+	4.53378i	0.270463	+	0.156152i
$844$	−0.498797	−	0.780445i	−0.0171693	−	0.0268640i
$845$	−1.22781	−	1.03025i	−0.0422379	−	0.0354418i
$846$	5.66185	−	7.06504i	0.194658	−	0.242901i
$847$	−10.6921	+	6.17306i	−0.367383	+	0.212109i
$848$	−26.6290	−	12.3230i	−0.914442	−	0.423175i
$849$	1.73756	+	4.77391i	0.0596329	+	0.163840i
$850$	−1.79163	−	8.97299i	−0.0614524	−	0.307771i
$851$	−1.82821	+	10.3683i	−0.0626703	+	0.355421i
$852$	−6.65165	−	2.08662i	−0.227882	−	0.0714863i
$853$	−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	$0.905426\pi$
$858$	−8.61645	−	2.91790i	−0.294161	−	0.0996154i
$859$	−39.4484	−	6.95582i	−1.34596	−	0.237330i	−0.546205	−	0.837652i	$-0.683928\pi$
$859$	−39.4484	−	6.95582i	−1.34596	−	0.237330i	−0.799758	+	0.600322i	$0.795039\pi$
$860$	13.9910	−	3.12310i	0.477089	−	0.106497i
$861$	−15.3808	+	5.59814i	−0.524175	+	0.190784i
$862$	3.17255	−	5.79279i	0.108058	−	0.197303i
$863$	−12.5590	−	21.7528i	−0.427513	−	0.740474i	0.569139	−	0.822242i	$-0.307277\pi$
$863$	−12.5590	−	21.7528i	−0.427513	−	0.740474i	−0.996651	+	0.0817676i	$0.973943\pi$
$864$	−25.4600	−	16.8782i	−0.866168	−	0.574207i
$865$	1.67641	−	1.99786i	0.0569995	−	0.0679293i
$866$	−21.4031	+	13.0090i	−0.727307	+	0.442065i
$867$	14.4252	−	24.9851i	0.489904	−	0.848538i
$868$	9.87880	+	23.7517i	0.335308	+	0.806185i
$869$	−4.57652	+	0.806964i	−0.155248	+	0.0273744i
$870$	16.3336	+	2.50181i	0.553760	+	0.0848193i
$871$	1.88381	−	5.17573i	0.0638306	−	0.175373i
$872$	−30.8442	−	32.0798i	−1.04452	−	1.08636i
$873$			14.0224i			0.474587i
$874$	−20.4077	+	6.25299i	−0.690299	+	0.211510i
$875$			1.48681i			0.0502634i
$876$	8.71917	−	8.01303i	0.294594	−	0.270735i
$877$	−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	$0.953842\pi$
$878$	−0.565288	+	3.69060i	−0.0190775	+	0.124552i
$879$	18.0867	−	3.18918i	0.610051	−	0.107568i
$880$	2.79311	+	5.94461i	0.0941558	+	0.200393i
$881$	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	$0.113167\pi$
$882$	−5.81684	−	9.57015i	−0.195863	−	0.322244i
$883$	28.2729	−	33.6944i	0.951460	−	1.13391i	−0.0394284	−	0.999222i	$-0.512554\pi$
$883$	28.2729	−	33.6944i	0.951460	−	1.13391i	0.990889	−	0.134684i	$-0.0430019\pi$
$884$	26.5438	−	34.6970i	0.892764	−	1.16699i
$885$	8.31950	+	14.4098i	0.279657	+	0.484380i
$886$	1.95053	+	1.06825i	0.0655293	+	0.0358886i
$887$	−9.93520	+	3.61612i	−0.333591	+	0.121417i	−0.503385	−	0.864062i	$-0.667912\pi$
$887$	−9.93520	+	3.61612i	−0.333591	+	0.121417i	0.169793	+	0.985480i	$0.445690\pi$
$888$	−9.68865	+	2.39323i	−0.325130	+	0.0803115i
$889$	−0.613356	−	0.108151i	−0.0205713	−	0.00362728i
$890$	5.55767	−	16.4116i	0.186294	−	0.550118i
$891$	−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
$896$	3.19759	−	16.5146i	0.106824	−	0.551715i
$897$	−2.35541	+	13.3582i	−0.0786448	+	0.446017i
$898$	−33.2220	+	6.63340i	−1.10863	+	0.221359i
$899$	29.7920	+	81.8529i	0.993620	+	2.72995i
$900$	1.52269	−	2.93549i	0.0507565	−	0.0978497i
$901$	41.1030	−	23.7308i	1.36934	−	0.790588i
$902$	−17.1911	−	13.7768i	−0.572402	−	0.458717i
$903$	−9.47320	−	7.94896i	−0.315248	−	0.264525i
$904$	−9.94678	+	6.67769i	−0.330825	+	0.222097i
$905$	−12.1836	−	7.03422i	−0.404998	−	0.233825i
$906$	−29.7857	+	11.6080i	−0.989563	+	0.385649i
$907$	0.872873	+	4.95031i	0.0289833	+	0.164372i	0.995864	−	0.0908563i	$-0.0289604\pi$
$907$	0.872873	+	4.95031i	0.0289833	+	0.164372i	−0.966881	+	0.255229i	$0.917849\pi$
$908$	−0.996770	+	7.65733i	−0.0330790	+	0.254117i
$909$	5.22525	+	1.90184i	0.173311	+	0.0630800i
$910$	−5.33357	+	4.68428i	−0.176806	+	0.155283i
$911$	−42.6375			−1.41264			−0.706322	−	0.707891i	$-0.749647\pi$
$911$	−42.6375			−1.41264			−0.706322	+	0.707891i	$0.749647\pi$
$912$	−13.2497	−	15.2903i	−0.438742	−	0.506312i
$913$	−25.1291			−0.831651
$914$	−1.70423	+	1.49677i	−0.0563711	+	0.0495087i
$915$	−3.91263	−	1.42408i	−0.129348	−	0.0470787i
$916$	−5.58452	+	42.9011i	−0.184518	+	1.41749i
$917$	−3.00412	−	17.0372i	−0.0992049	−	0.562619i
$918$	46.0372	−	17.9415i	1.51945	−	0.592156i
$919$	−17.4585	−	10.0797i	−0.575902	−	0.332497i	0.183601	−	0.983001i	$-0.441225\pi$
$919$	−17.4585	−	10.0797i	−0.575902	−	0.332497i	−0.759503	+	0.650504i	$0.774558\pi$
$920$	8.13098	−	5.45866i	0.268071	−	0.179967i
$921$	−4.86617	−	4.08320i	−0.160346	−	0.134546i
$922$	−11.3874	−	9.12574i	−0.375024	−	0.300540i
$923$	8.78216	−	5.07038i	0.289068	−	0.166894i
$924$	2.60894	−	5.02958i	0.0858277	−	0.165461i
$925$	−1.03997	−	2.85730i	−0.0341940	−	0.0939474i
$926$	−9.27838	+	1.85260i	−0.304906	+	0.0608804i
$927$	1.28399	−	7.28184i	0.0421716	−	0.239167i
$928$	13.3371	−	55.3762i	0.437811	−	1.81781i
$929$	−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
$934$	−4.54677	+	13.4264i	−0.148775	+	0.439327i
$935$	−10.4627	−	1.84485i	−0.342165	−	0.0603330i
$936$	15.3277	−	3.78615i	0.501001	−	0.123754i
$937$	−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	$0.465428\pi$
$938$	3.00881	+	1.64784i	0.0982412	+	0.0538040i
$939$	5.22464	+	9.04935i	0.170500	+	0.295314i
$940$	−4.70516	+	6.15040i	−0.153465	+	0.200604i
$941$	−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	$0.230713\pi$
$942$	−6.66889	−	10.9720i	−0.217284	−	0.357486i
$943$	−16.4242	+	28.4475i	−0.534844	+	0.926378i
$944$	51.9112	−	24.3908i	1.68957	−	0.793854i
$945$	−7.90665	+	1.39416i	−0.257203	+	0.0453519i
$946$	2.52005	−	16.4527i	0.0819339	−	0.534922i
$947$	5.59611	−	15.3752i	0.181849	−	0.499626i	−0.814954	−	0.579526i	$-0.803238\pi$
$947$	5.59611	−	15.3752i	0.181849	−	0.499626i	0.996803	+	0.0798995i	$0.0254599\pi$
$948$	−4.83610	+	4.44444i	−0.157069	+	0.144349i
$949$			17.2260i			0.559179i
$950$	4.20134	−	4.51095i	0.136310	−	0.146355i
$951$		−	16.0467i		−	0.520350i
$952$	18.8582	+	19.6136i	0.611198	+	0.635682i
$953$	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	$-0.245513\pi$
$954$	16.9552	+	2.59703i	0.548946	+	0.0840820i
$955$	16.2811	−	2.87080i	0.526845	−	0.0928970i
$956$	−1.40986	−	3.38973i	−0.0455981	−	0.109632i
$957$	9.59292	−	16.6154i	0.310095	−	0.537101i
$958$	−32.4340	+	19.7137i	−1.04789	+	0.636922i
$959$	−5.90476	+	7.03702i	−0.190675	+	0.227237i
$960$	7.85111	+	4.95365i	0.253394	+	0.159878i
$961$	−21.9182	−	37.9634i	−0.707037	−	1.22462i
$962$	6.97336	−	12.7327i	0.224830	−	0.410520i
$963$	−8.58511	+	3.12472i	−0.276651	+	0.100693i
$964$	−0.216249	+	0.0482717i	−0.00696493	+	0.00155473i
$965$	14.4276	+	2.54398i	0.464441	+	0.0818935i
$966$	−8.00188	−	2.70978i	−0.257456	−	0.0871857i
$967$	5.46898	+	6.51767i	0.175870	+	0.209594i	0.846778	−	0.531947i	$-0.178540\pi$
$967$	5.46898	+	6.51767i	0.175870	+	0.209594i	−0.670907	+	0.741541i	$0.734095\pi$
$968$	−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	$0.557889\pi$
$971$	−36.7959	+	30.8754i	−1.18084	+	0.990840i	−0.999973	+	0.00733152i	$0.997666\pi$
$972$	28.0227	+	8.79069i	0.898827	+	0.281961i
$973$	−1.99336	+	11.3049i	−0.0639041	+	0.362418i
$974$	−9.35849	−	46.8700i	−0.299865	−	1.50181i
$975$	−1.33986	−	3.68125i	−0.0429100	−	0.117894i
$976$	−6.02782	+	13.0256i	−0.192946	+	0.416938i
$977$	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	$0.307471\pi$
$978$	−11.1467	+	13.9092i	−0.356433	+	0.444769i
$979$	−15.4115	−	12.9318i	−0.492553	−	0.413301i
$980$	5.15843	+	8.07117i	0.164780	+	0.257824i
$981$	22.5302	+	13.0078i	0.719333	+	0.415307i
$982$	−15.8532	−	40.6788i	−0.505897	−	1.29811i
$983$	6.80743	+	38.6069i	0.217123	+	1.23137i	0.877184	+	0.480155i	$0.159420\pi$
$983$	6.80743	+	38.6069i	0.217123	+	1.23137i	−0.660060	+	0.751213i	$0.729469\pi$
$984$	−30.9596	−	3.32224i	−0.986955	−	0.105909i
$985$	17.9023	+	6.51590i	0.570415	+	0.207614i
$986$	60.7984	+	69.2256i	1.93621	+	2.20459i
$987$	6.68018			0.212632
$988$	29.4185	+	0.859260i	0.935928	+	0.0273367i
$989$	−24.8179			−0.789162
$990$	−2.53373	−	2.88493i	−0.0805274	−	0.0916892i
$991$	30.4217	+	11.0726i	0.966378	+	0.351733i	0.776530	−	0.630081i	$-0.216978\pi$
$991$	30.4217	+	11.0726i	0.966378	+	0.351733i	0.189848	+	0.981813i	$0.439200\pi$
$992$	−3.02288	+	48.8429i	−0.0959765	+	1.55076i
$993$	−3.50947	−	19.9032i	−0.111370	−	0.631608i
$994$	2.29344	+	5.88489i	0.0727435	+	0.186657i
$995$	5.86480	+	3.38604i	0.185927	+	0.107345i
$996$	−29.9270	+	19.1269i	−0.948272	+	0.606058i
$997$	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	$0.456089\pi$
$998$	−31.5648	+	39.3876i	−0.999166	+	1.24679i
$999$	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.51.4	✓	120
4.3	odd	2	inner	380.2.be.b.51.17	yes	120
19.3	odd	18	inner	380.2.be.b.231.17	yes	120
76.3	even	18	inner	380.2.be.b.231.4	yes	120

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

\(f(q)\)	\(=\)	\(q+(-1.06258 + 0.933229i) q^{2} +(1.09042 + 0.396882i) q^{3} +(0.258166 - 1.98327i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-1.52905 + 0.595896i) q^{6} +(1.28762 + 0.743405i) q^{7} +(1.57652 + 2.34831i) q^{8} +(-1.26662 - 1.06282i) q^{9} +O(q^{10})\)	\(q+(-1.06258 + 0.933229i) q^{2} +(1.09042 + 0.396882i) q^{3} +(0.258166 - 1.98327i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-1.52905 + 0.595896i) q^{6} +(1.28762 + 0.743405i) q^{7} +(1.57652 + 2.34831i) q^{8} +(-1.26662 - 1.06282i) q^{9} +(1.10357 + 0.884387i) q^{10} +(1.42203 - 0.821011i) q^{11} +(1.06863 - 2.06014i) q^{12} +(1.15465 + 3.17238i) q^{13} +(-2.06197 + 0.411711i) q^{14} +(0.201502 - 1.14278i) q^{15} +(-3.86670 - 1.02402i) 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} +(-0.744837 + 2.19948i) q^{22} +(3.40987 + 0.601253i) q^{23} +(0.787073 + 3.18635i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-4.18747 - 2.29336i) q^{26} +(-2.69995 - 4.67645i) q^{27} +(1.80679 - 2.36176i) q^{28} +(6.47232 - 7.71340i) q^{29} +(0.852359 + 1.40234i) q^{30} +(-4.32540 + 7.49181i) q^{31} +(5.06434 - 2.52041i) q^{32} +(1.87646 - 0.330871i) q^{33} +(-1.38536 + 9.04463i) q^{34} +(0.508519 - 1.39714i) q^{35} +(-2.43486 + 2.23767i) q^{36} +3.04067i q^{37} +(-5.49081 + 2.80197i) q^{38} +3.91750i q^{39} +(2.03888 - 1.96035i) q^{40} +(-3.24473 + 8.91482i) q^{41} +(-2.41182 - 0.369418i) q^{42} +(-7.05877 + 1.24465i) q^{43} +(-1.26116 - 3.03223i) q^{44} +(-0.826730 + 1.43194i) q^{45} +(-4.18438 + 2.54331i) q^{46} +(2.48880 - 2.96604i) q^{47} +(-3.80993 - 2.65124i) q^{48} +(-2.39470 - 4.14774i) q^{49} +(0.679318 - 1.24037i) q^{50} +(7.05516 - 2.56787i) q^{51} +(6.58977 - 1.47098i) q^{52} +(7.22408 + 1.27380i) q^{53} +(7.23312 + 2.44944i) 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} +(-2.21441 - 0.694659i) q^{60} +(0.623080 - 3.53366i) q^{61} +(-2.39548 - 11.9973i) q^{62} +(-0.840816 - 2.31012i) q^{63} +(-3.02916 + 7.40433i) q^{64} +(2.92368 - 1.68799i) q^{65} +(-1.68512 + 2.10275i) q^{66} +(-1.24980 - 1.04871i) q^{67} +(-6.96865 - 10.9035i) q^{68} +(3.47958 + 2.00894i) q^{69} +(0.763513 + 1.95915i) q^{70} +(-0.521605 - 2.95817i) q^{71} +(0.498986 - 4.64999i) q^{72} +(4.79480 + 1.74516i) q^{73} +(-2.83764 - 3.23097i) q^{74} -1.16041 q^{75} +(3.21956 - 8.10151i) q^{76} +2.44138 q^{77} +(-3.65593 - 4.16267i) q^{78} +(-2.65944 - 0.967958i) q^{79} +(-0.337022 + 3.98578i) q^{80} +(-0.226731 - 1.28586i) q^{81} +(-4.87177 - 12.5008i) q^{82} +(-13.2534 - 7.65186i) q^{83} +(2.90751 - 1.85824i) q^{84} +(-4.95639 - 4.15890i) q^{85} +(6.33898 - 7.90999i) q^{86} +(10.1189 - 5.84214i) q^{87} +(4.16986 + 2.04504i) q^{88} +(-4.19047 - 11.5132i) q^{89} +(-0.457857 - 2.29308i) q^{90} +(-0.871616 + 4.94318i) q^{91} +(2.07276 - 6.60747i) 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} +(6.41536 + 2.17251i) 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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