LMFDB - Embedded newform 507.2.q.b.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

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

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.48128 - 0.200310i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(4.14255 + 0.673230i) q^{4} +(1.36223 + 1.20683i) q^{5} +(1.99010 + 1.49546i) q^{6} +(-0.288513 + 0.300373i) q^{7} +(-5.30995 - 1.30878i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-3.13834 - 3.26736i) q^{10} +(-1.77558 + 3.74196i) q^{11} +(-3.14142 - 2.78306i) q^{12} +(0.792477 + 3.51738i) q^{13} +(0.776050 - 0.687520i) q^{14} +(-0.506334 - 1.74807i) q^{15} +(4.95150 + 1.65305i) q^{16} +(-3.70811 + 3.86055i) q^{17} +(-0.882738 - 2.32759i) q^{18} +(3.81106 - 6.60095i) q^{19} +(4.83063 + 5.91645i) q^{20} +(0.404387 - 0.0996725i) q^{21} +(5.15528 - 8.92921i) q^{22} +(-3.75359 - 6.50141i) q^{23} +(3.78841 + 3.94416i) q^{24} +(-0.203452 - 1.67558i) q^{25} +(-1.26180 - 8.88637i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-1.39740 + 1.05008i) q^{28} +(-6.01096 - 0.485255i) q^{29} +(0.906203 + 4.43888i) q^{30} +(-0.756841 + 6.23315i) q^{31} +(-1.89249 - 0.806313i) q^{32} +(3.50066 - 2.21368i) q^{33} +(9.97418 - 8.83635i) q^{34} +(-0.755521 + 0.0609919i) q^{35} +(1.16765 + 4.03120i) q^{36} +(-8.29979 + 3.53621i) q^{37} +(-10.7786 + 15.6154i) q^{38} +(1.21013 - 3.39641i) q^{39} +(-5.65389 - 8.19107i) q^{40} +(4.53244 + 2.86614i) q^{41} +(-1.02337 + 0.166313i) q^{42} +(0.270753 + 0.115357i) q^{43} +(-9.87464 + 14.3059i) q^{44} +(-0.506334 + 1.74807i) q^{45} +(8.01143 + 16.8837i) q^{46} +(-1.26330 + 3.33106i) q^{47} +(-3.30146 - 4.04355i) q^{48} +(0.274877 + 6.82100i) q^{49} +(0.169187 + 4.19834i) q^{50} +(5.19739 - 1.28104i) q^{51} +(0.914870 + 15.1044i) q^{52} +(-9.03181 - 2.22614i) q^{53} +(-0.497935 + 2.43905i) q^{54} +(-6.93467 + 2.95459i) q^{55} +(1.92511 - 1.21737i) q^{56} +(-6.74905 + 3.54218i) q^{57} +(14.8177 + 2.40811i) q^{58} +(5.84033 - 1.94979i) q^{59} +(-0.920662 - 7.58233i) q^{60} +(-1.61099 + 5.56177i) q^{61} +(3.12650 - 15.3146i) q^{62} +(-0.395056 - 0.131889i) q^{63} +(-4.71014 - 2.47207i) q^{64} +(-3.16535 + 5.74787i) q^{65} +(-9.12955 + 4.79156i) q^{66} +(-11.3169 + 1.83918i) q^{67} +(-17.9601 + 13.4961i) q^{68} +(-0.302284 + 7.50110i) q^{69} +1.88688 q^{70} +(-0.115478 + 2.86555i) q^{71} +(-1.09391 - 5.35834i) q^{72} +(-6.79584 - 9.84547i) q^{73} +(21.3025 - 7.11181i) q^{74} +(-0.723584 + 1.52492i) q^{75} +(20.2315 - 24.7790i) q^{76} +(-0.611708 - 1.61294i) q^{77} +(-3.68300 + 8.18506i) q^{78} +(-0.661667 + 1.74467i) q^{79} +(4.75013 + 8.22747i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-10.6721 - 8.01960i) q^{82} +(11.4130 + 5.98999i) q^{83} +(1.74230 - 0.140653i) q^{84} +(-9.71033 + 0.783899i) q^{85} +(-0.648709 - 0.340469i) q^{86} +(4.82105 + 3.62278i) q^{87} +(14.3257 - 17.5458i) q^{88} +(1.14250 + 1.97887i) q^{89} +(1.60651 - 4.23603i) q^{90} +(-1.28517 - 0.776770i) q^{91} +(-11.1725 - 29.4595i) q^{92} +(3.97108 - 4.86369i) q^{93} +(3.80186 - 8.01225i) q^{94} +(13.1578 - 4.39271i) q^{95} +(1.16856 + 1.69296i) q^{96} +(2.10735 + 10.3225i) q^{97} +(0.684267 - 16.9799i) q^{98} -4.14186 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

Coefficient data

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

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

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

$2$	−2.48128	−	0.200310i	−1.75453	−	0.141641i	−0.839065	−	0.544031i	$-0.816897\pi$
$2$	−2.48128	−	0.200310i	−1.75453	−	0.141641i	−0.915468	+	0.402391i	$0.868179\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	4.14255	+	0.673230i	2.07127	+	0.336615i
$5$	1.36223	+	1.20683i	0.609208	+	0.539711i	0.910335	−	0.413873i	$-0.135824\pi$
$5$	1.36223	+	1.20683i	0.609208	+	0.539711i	−0.301127	+	0.953584i	$0.597363\pi$
$6$	1.99010	+	1.49546i	0.812454	+	0.610520i
$7$	−0.288513	+	0.300373i	−0.109048	+	0.113530i	−0.773489	−	0.633810i	$-0.781490\pi$
$7$	−0.288513	+	0.300373i	−0.109048	+	0.113530i	0.664441	+	0.747341i	$0.268670\pi$
$8$	−5.30995	−	1.30878i	−1.87735	−	0.462725i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−3.13834	−	3.26736i	−0.992431	−	1.03323i
$11$	−1.77558	+	3.74196i	−0.535359	+	1.12824i	0.438004	+	0.898973i	$0.355686\pi$
$11$	−1.77558	+	3.74196i	−0.535359	+	1.12824i	−0.973363	+	0.229271i	$0.926366\pi$
$12$	−3.14142	−	2.78306i	−0.906851	−	0.803400i
$13$	0.792477	+	3.51738i	0.219794	+	0.975546i
$13$	0.792477	+	3.51738i	0.219794	+	0.975546i
$14$	0.776050	−	0.687520i	0.207408	−	0.183747i
$15$	−0.506334	−	1.74807i	−0.130735	−	0.451349i
$16$	4.95150	+	1.65305i	1.23788	+	0.413264i
$17$	−3.70811	+	3.86055i	−0.899349	+	0.936321i	−0.998271	−	0.0587741i	$-0.981281\pi$
$17$	−3.70811	+	3.86055i	−0.899349	+	0.936321i	0.0989228	+	0.995095i	$0.468460\pi$
$18$	−0.882738	−	2.32759i	−0.208063	−	0.548618i
$19$	3.81106	−	6.60095i	0.874317	−	1.51436i	0.0168294	−	0.999858i	$-0.494643\pi$
$19$	3.81106	−	6.60095i	0.874317	−	1.51436i	0.857488	−	0.514504i	$-0.172024\pi$
$20$	4.83063	+	5.91645i	1.08016	+	1.32296i
$21$	0.404387	−	0.0996725i	0.0882446	−	0.0217503i
$22$	5.15528	−	8.92921i	1.09911	−	1.90371i
$23$	−3.75359	−	6.50141i	−0.782678	−	1.35564i	−0.930376	−	0.366606i	$-0.880520\pi$
$23$	−3.75359	−	6.50141i	−0.782678	−	1.35564i	0.147698	−	0.989032i	$-0.452814\pi$
$24$	3.78841	+	3.94416i	0.773307	+	0.805097i
$25$	−0.203452	−	1.67558i	−0.0406904	−	0.335116i
$26$	−1.26180	−	8.88637i	−0.247458	−	1.74276i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−1.39740	+	1.05008i	−0.264083	+	0.198446i
$29$	−6.01096	−	0.485255i	−1.11621	−	0.0901095i	−0.491433	−	0.870915i	$-0.663527\pi$
$29$	−6.01096	−	0.485255i	−1.11621	−	0.0901095i	−0.624774	+	0.780806i	$0.714809\pi$
$30$	0.906203	+	4.43888i	0.165449	+	0.810424i
$31$	−0.756841	+	6.23315i	−0.135933	+	1.11951i	0.751879	+	0.659301i	$0.229148\pi$
$31$	−0.756841	+	6.23315i	−0.135933	+	1.11951i	−0.887812	+	0.460206i	$0.847776\pi$
$32$	−1.89249	−	0.806313i	−0.334548	−	0.142537i
$33$	3.50066	−	2.21368i	0.609386	−	0.385353i
$34$	9.97418	−	8.83635i	1.71056	−	1.51542i
$35$	−0.755521	+	0.0609919i	−0.127706	+	0.0103095i
$36$	1.16765	+	4.03120i	0.194608	+	0.671866i
$37$	−8.29979	+	3.53621i	−1.36448	+	0.581349i	−0.945195	−	0.326507i	$-0.894128\pi$
$37$	−8.29979	+	3.53621i	−1.36448	+	0.581349i	−0.419282	+	0.907856i	$0.637718\pi$
$38$	−10.7786	+	15.6154i	−1.74851	+	2.53316i
$39$	1.21013	−	3.39641i	0.193775	−	0.543861i
$40$	−5.65389	−	8.19107i	−0.893959	−	1.29512i
$41$	4.53244	+	2.86614i	0.707847	+	0.447616i	0.839273	−	0.543710i	$-0.182981\pi$
$41$	4.53244	+	2.86614i	0.707847	+	0.447616i	−0.131425	+	0.991326i	$0.541955\pi$
$42$	−1.02337	+	0.166313i	−0.157909	+	0.0256627i
$43$	0.270753	+	0.115357i	0.0412895	+	0.0175918i	0.412513	−	0.910952i	$-0.364651\pi$
$43$	0.270753	+	0.115357i	0.0412895	+	0.0175918i	−0.371223	+	0.928544i	$0.621062\pi$
$44$	−9.87464	+	14.3059i	−1.48866	+	2.15669i
$45$	−0.506334	+	1.74807i	−0.0754798	+	0.260587i
$46$	8.01143	+	16.8837i	1.18122	+	2.48937i
$47$	−1.26330	+	3.33106i	−0.184272	+	0.485884i	−0.995039	−	0.0994838i	$-0.968281\pi$
$47$	−1.26330	+	3.33106i	−0.184272	+	0.485884i	0.810768	+	0.585368i	$0.199050\pi$
$48$	−3.30146	−	4.04355i	−0.476525	−	0.583637i
$49$	0.274877	+	6.82100i	0.0392681	+	0.974429i
$50$	0.169187	+	4.19834i	0.0239267	+	0.593735i
$51$	5.19739	−	1.28104i	0.727780	−	0.179382i
$52$	0.914870	+	15.1044i	0.126870	+	2.09461i
$53$	−9.03181	−	2.22614i	−1.24061	−	0.305784i	−0.436198	−	0.899851i	$-0.643675\pi$
$53$	−9.03181	−	2.22614i	−1.24061	−	0.305784i	−0.804416	+	0.594067i	$0.797521\pi$
$54$	−0.497935	+	2.43905i	−0.0677604	+	0.331912i
$55$	−6.93467	+	2.95459i	−0.935071	+	0.398397i
$56$	1.92511	−	1.21737i	0.257254	−	0.162677i
$57$	−6.74905	+	3.54218i	−0.893934	+	0.469173i
$58$	14.8177	+	2.40811i	1.94566	+	0.316200i
$59$	5.84033	−	1.94979i	0.760346	−	0.253841i	0.0900524	−	0.995937i	$-0.471297\pi$
$59$	5.84033	−	1.94979i	0.760346	−	0.253841i	0.670293	+	0.742096i	$0.266168\pi$
$60$	−0.920662	−	7.58233i	−0.118857	−	0.978875i
$61$	−1.61099	+	5.56177i	−0.206266	+	0.712112i	0.788954	+	0.614452i	$0.210623\pi$
$61$	−1.61099	+	5.56177i	−0.206266	+	0.712112i	−0.995220	+	0.0976599i	$0.968864\pi$
$62$	3.12650	−	15.3146i	0.397066	−	1.94496i
$63$	−0.395056	−	0.131889i	−0.0497723	−	0.0166164i
$64$	−4.71014	−	2.47207i	−0.588768	−	0.309009i
$65$	−3.16535	+	5.74787i	−0.392613	+	0.712936i
$66$	−9.12955	+	4.79156i	−1.12377	+	0.589800i
$67$	−11.3169	+	1.83918i	−1.38258	+	0.224691i	−0.805790	−	0.592202i	$-0.798259\pi$
$67$	−11.3169	+	1.83918i	−1.38258	+	0.224691i	−0.576790	+	0.816893i	$0.695695\pi$
$68$	−17.9601	+	13.4961i	−2.17798	+	1.63664i
$69$	−0.302284	+	7.50110i	−0.0363907	+	0.903026i
$70$	1.88688			0.225525
$71$	−0.115478	+	2.86555i	−0.0137047	+	0.340078i	0.977762	+	0.209718i	$0.0672545\pi$
$71$	−0.115478	+	2.86555i	−0.0137047	+	0.340078i	−0.991467	+	0.130361i	$0.958386\pi$
$72$	−1.09391	−	5.35834i	−0.128919	−	0.631486i
$73$	−6.79584	−	9.84547i	−0.795393	−	1.15233i	−0.985352	−	0.170533i	$-0.945451\pi$
$73$	−6.79584	−	9.84547i	−0.795393	−	1.15233i	0.189959	−	0.981792i	$-0.439164\pi$
$74$	21.3025	−	7.11181i	2.47636	−	0.826731i
$75$	−0.723584	+	1.52492i	−0.0835523	+	0.176083i
$76$	20.2315	−	24.7790i	2.32071	−	2.84235i
$77$	−0.611708	−	1.61294i	−0.0697106	−	0.183812i
$78$	−3.68300	+	8.18506i	−0.417018	+	0.926775i
$79$	−0.661667	+	1.74467i	−0.0744434	+	0.196291i	−0.967073	−	0.254500i	$-0.918089\pi$
$79$	−0.661667	+	1.74467i	−0.0744434	+	0.196291i	0.892629	+	0.450791i	$0.148858\pi$
$80$	4.75013	+	8.22747i	0.531081	+	0.919859i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	−10.6721	−	8.01960i	−1.17854	−	0.885616i
$83$	11.4130	+	5.98999i	1.25274	+	0.657487i	0.954843	−	0.297112i	$-0.0960233\pi$
$83$	11.4130	+	5.98999i	1.25274	+	0.657487i	0.297894	+	0.954599i	$0.403716\pi$
$84$	1.74230	−	0.140653i	0.190100	−	0.0153465i
$85$	−9.71033	+	0.783899i	−1.05323	+	0.0850258i
$86$	−0.648709	−	0.340469i	−0.0699521	−	0.0367137i
$87$	4.82105	+	3.62278i	0.516871	+	0.388403i
$88$	14.3257	−	17.5458i	1.52712	−	1.87039i
$89$	1.14250	+	1.97887i	0.121105	+	0.209760i	0.920204	−	0.391440i	$-0.128023\pi$
$89$	1.14250	+	1.97887i	0.121105	+	0.209760i	−0.799099	+	0.601200i	$0.794690\pi$
$90$	1.60651	−	4.23603i	0.169341	−	0.446517i
$91$	−1.28517	−	0.776770i	−0.134722	−	0.0814276i
$92$	−11.1725	−	29.4595i	−1.16481	−	3.07136i
$93$	3.97108	−	4.86369i	0.411782	−	0.504341i
$94$	3.80186	−	8.01225i	0.392132	−	0.826400i
$95$	13.1578	−	4.39271i	1.34996	−	0.450683i
$96$	1.16856	+	1.69296i	0.119266	+	0.172787i
$97$	2.10735	+	10.3225i	0.213968	+	1.04809i	0.934854	+	0.355033i	$0.115530\pi$
$97$	2.10735	+	10.3225i	0.213968	+	1.04809i	−0.720885	+	0.693054i	$0.756265\pi$
$98$	0.684267	−	16.9799i	0.0691214	−	1.71523i
$99$	−4.14186			−0.416272
$100$	0.285239	−	7.07814i	0.0285239	−	0.707814i
$101$	6.74459	−	5.06823i	0.671111	−	0.504307i	−0.209706	−	0.977765i	$-0.567251\pi$
$101$	6.74459	−	5.06823i	0.671111	−	0.504307i	0.880817	+	0.473457i	$0.156994\pi$
$102$	−13.1528	+	2.13754i	−1.30232	+	0.211648i
$103$	−0.437302	+	0.229514i	−0.0430886	+	0.0226147i	−0.486130	−	0.873887i	$-0.661592\pi$
$103$	−0.437302	+	0.229514i	−0.0430886	+	0.0226147i	0.443041	+	0.896501i	$0.353900\pi$
$104$	0.395482	−	19.7143i	0.0387802	−	1.93315i
$105$	0.671157	+	0.352250i	0.0654982	+	0.0343761i
$106$	21.9646	+	7.33285i	2.13339	+	0.712229i
$107$	−0.375398	+	1.83882i	−0.0362911	+	0.177766i	−0.993896	−	0.110318i	$-0.964813\pi$
$107$	−0.375398	+	1.83882i	−0.0362911	+	0.177766i	0.957605	+	0.288084i	$0.0930182\pi$
$108$	1.16765	−	4.03120i	0.112357	−	0.387902i
$109$	1.06775	+	8.79373i	0.102272	+	0.842287i	0.950085	+	0.311991i	$0.100996\pi$
$109$	1.06775	+	8.79373i	0.102272	+	0.842287i	−0.847813	+	0.530296i	$0.822081\pi$
$110$	17.7987	−	5.94209i	1.69704	−	0.566556i
$111$	8.90488	+	1.44718i	0.845214	+	0.137361i
$112$	−1.92510	+	1.01037i	−0.181905	+	0.0954713i
$113$	−14.3740	+	9.08958i	−1.35219	+	0.855076i	−0.996823	−	0.0796496i	$-0.974620\pi$
$113$	−14.3740	+	9.08958i	−1.35219	+	0.855076i	−0.355371	+	0.934725i	$0.615646\pi$
$114$	17.4559	−	7.43725i	1.63489	−	0.696562i
$115$	2.73285	−	13.3864i	0.254839	−	1.24829i
$116$	−24.5740	−	6.05694i	−2.28164	−	0.562373i
$117$	−2.83805	+	2.22384i	−0.262378	+	0.205594i
$118$	−14.8821	+	3.66810i	−1.37001	+	0.337676i
$119$	−0.0897706	−	2.22763i	−0.00822926	−	0.204207i
$120$	0.400763	+	9.94483i	0.0365845	+	0.907834i
$121$	−3.89270	−	4.76769i	−0.353881	−	0.433426i
$122$	5.11140	−	13.4776i	0.462764	−	1.22021i
$123$	−2.29892	−	4.84486i	−0.207286	−	0.436847i
$124$	−7.33159	+	25.3116i	−0.658396	+	2.27305i
$125$	6.91416	−	10.0169i	0.618421	−	0.895938i
$126$	0.953827	+	0.406388i	0.0849737	+	0.0362039i
$127$	6.11044	−	0.993043i	0.542214	−	0.0881183i	0.116865	−	0.993148i	$-0.462716\pi$
$127$	6.11044	−	0.993043i	0.542214	−	0.0881183i	0.425349	+	0.905029i	$0.360151\pi$
$128$	14.6693	+	9.27630i	1.29660	+	0.819917i
$129$	−0.167184	−	0.242207i	−0.0147197	−	0.0213251i
$130$	9.00549	−	13.6281i	0.789834	−	1.19526i
$131$	−0.294473	+	0.426617i	−0.0257282	+	0.0372737i	−0.835637	−	0.549282i	$-0.814901\pi$
$131$	−0.294473	+	0.426617i	−0.0257282	+	0.0372737i	0.809909	+	0.586556i	$0.199517\pi$
$132$	15.9920	−	6.81354i	1.39192	−	0.593042i
$133$	0.883211	+	3.04920i	0.0765841	+	0.264399i
$134$	28.4489	−	2.29663i	2.45761	−	0.198399i
$135$	1.36223	−	1.20683i	0.117242	−	0.103867i
$136$	24.7425	−	15.6462i	2.12165	−	1.34165i
$137$	2.00167	+	0.852834i	0.171015	+	0.0728625i	0.475777	−	0.879566i	$-0.342167\pi$
$137$	2.00167	+	0.852834i	0.171015	+	0.0728625i	−0.304763	+	0.952428i	$0.598577\pi$
$138$	2.25260	−	18.5518i	0.191754	−	1.57923i
$139$	1.41936	+	6.95247i	0.120388	+	0.589701i	0.994567	+	0.104097i	$0.0331952\pi$
$139$	1.41936	+	6.95247i	0.120388	+	0.589701i	−0.874179	+	0.485604i	$0.838600\pi$
$140$	−3.17084	−	0.255977i	−0.267985	−	0.0216340i
$141$	2.84807	−	2.14018i	0.239850	−	0.180236i
$142$	0.860532	−	7.08712i	0.0722142	−	0.594738i
$143$	−14.5690	−	3.27999i	−1.21832	−	0.274286i
$144$	0.629220	+	5.18209i	0.0524350	+	0.431841i
$145$	−7.60269	−	7.91524i	−0.631369	−	0.657325i
$146$	14.8903	+	25.7907i	1.23233	+	2.13445i
$147$	3.41327	−	5.91195i	0.281522	−	0.487610i
$148$	−36.7630	+	9.06126i	−3.02190	+	0.744831i
$149$	−6.37397	−	7.80670i	−0.522176	−	0.639549i	0.444431	−	0.895813i	$-0.353406\pi$
$149$	−6.37397	−	7.80670i	−0.522176	−	0.639549i	−0.966607	+	0.256264i	$0.917508\pi$
$150$	2.10087	−	3.63882i	0.171536	−	0.297109i
$151$	1.72236	+	4.54148i	0.140163	+	0.369581i	0.986656	−	0.162820i	$-0.0520591\pi$
$151$	1.72236	+	4.54148i	0.140163	+	0.369581i	−0.846492	+	0.532401i	$0.821290\pi$
$152$	−28.8757	+	30.0628i	−2.34213	+	2.43842i
$153$	−5.07745	−	1.69510i	−0.410488	−	0.137041i
$154$	1.19473	+	4.12470i	0.0962744	+	0.332378i
$155$	−8.55335	+	7.57761i	−0.687022	+	0.608648i
$156$	7.29957	−	13.2551i	0.584433	−	1.06126i
$157$	−9.05134	−	8.01878i	−0.722375	−	0.639969i	0.219624	−	0.975585i	$-0.429517\pi$
$157$	−9.05134	−	8.01878i	−0.722375	−	0.639969i	−0.941999	+	0.335616i	$0.891056\pi$
$158$	1.99126	−	4.19649i	0.158416	−	0.333855i
$159$	6.44380	+	6.70870i	0.511026	+	0.532035i
$160$	−1.60492	−	3.38230i	−0.126880	−	0.267394i
$161$	3.03581	+	0.748260i	0.239255	+	0.0589712i
$162$	1.72444	−	1.79533i	0.135485	−	0.141054i
$163$	12.2046	+	9.17113i	0.955935	+	0.718339i	0.959516	−	0.281655i	$-0.0908834\pi$
$163$	12.2046	+	9.17113i	0.955935	+	0.718339i	−0.00358075	+	0.999994i	$0.501140\pi$
$164$	16.8463	+	14.9245i	1.31547	+	1.16541i
$165$	7.44024	+	1.20916i	0.579222	+	0.0941328i
$166$	−27.1190	−	17.1490i	−2.10484	−	1.33102i
$167$	5.58863	+	0.451161i	0.432461	+	0.0349119i	0.294781	−	0.955565i	$-0.404753\pi$
$167$	5.58863	+	0.451161i	0.432461	+	0.0349119i	0.137680	+	0.990477i	$0.456035\pi$
$168$	−2.27772			−0.175730
$169$	−11.7440	+	5.57489i	−0.903381	+	0.428838i
$170$	24.2511			1.85998
$171$	7.59741	+	0.613326i	0.580988	+	0.0469022i
$172$	1.04395	+	0.660152i	0.0796002	+	0.0503361i
$173$	10.8360	+	1.76102i	0.823846	+	0.133888i	0.557698	−	0.830044i	$-0.311685\pi$
$173$	10.8360	+	1.76102i	0.823846	+	0.133888i	0.266148	+	0.963932i	$0.414249\pi$
$174$	−11.2367	−	9.95486i	−0.851853	−	0.754676i
$175$	0.561998	+	0.422314i	0.0424830	+	0.0319239i
$176$	−14.9775	+	15.5932i	−1.12897	+	1.17538i
$177$	−5.97828	−	1.47351i	−0.449355	−	0.110756i
$178$	−2.43848	−	5.13899i	−0.182772	−	0.385184i
$179$	−13.5239	−	14.0798i	−1.01082	−	1.05238i	−0.998623	−	0.0524513i	$-0.983297\pi$
$179$	−13.5239	−	14.0798i	−1.01082	−	1.05238i	−0.0121982	−	0.999926i	$-0.503883\pi$
$180$	−3.27436	+	6.90058i	−0.244057	+	0.514339i
$181$	3.51560	+	3.11455i	0.261313	+	0.231503i	0.783598	−	0.621268i	$-0.213382\pi$
$181$	3.51560	+	3.11455i	0.261313	+	0.231503i	−0.522286	+	0.852771i	$0.674921\pi$
$182$	3.03327	+	2.18482i	0.224841	+	0.161950i
$183$	4.33417	−	3.83974i	0.320391	−	0.283842i
$184$	11.4224	+	39.4348i	0.842073	+	2.90717i
$185$	−15.5738	−	5.19931i	−1.14501	−	0.382261i
$186$	−10.8276	+	11.2728i	−0.793920	+	0.826558i
$187$	−7.86198	−	20.7303i	−0.574925	−	1.51595i
$188$	−7.47586	+	12.9486i	−0.545233	+	0.944371i
$189$	0.263407	+	0.322615i	0.0191600	+	0.0234668i
$190$	−33.5281	+	8.26394i	−2.43238	+	0.599529i
$191$	6.87924	−	11.9152i	0.497764	−	0.862153i	−0.502232	−	0.864733i	$-0.667488\pi$
$191$	6.87924	−	11.9152i	0.497764	−	0.862153i	0.999997	+	0.00257954i	$0.000821095\pi$
$192$	2.65973	+	4.60678i	0.191949	+	0.332466i
$193$	12.4061	+	12.9161i	0.893009	+	0.929721i	0.997901	−	0.0647629i	$-0.0206291\pi$
$193$	12.4061	+	12.9161i	0.893009	+	0.929721i	−0.104892	+	0.994484i	$0.533450\pi$
$194$	−3.16123	−	26.0351i	−0.226963	−	1.86921i
$195$	5.74736	−	3.16627i	0.411577	−	0.226742i
$196$	−3.45341	+	28.4414i	−0.246672	+	2.03153i
$197$	10.4242	−	7.83324i	0.742690	−	0.558095i	−0.160655	−	0.987011i	$-0.551361\pi$
$197$	10.4242	−	7.83324i	0.742690	−	0.558095i	0.903345	+	0.428915i	$0.141104\pi$
$198$	10.2771	+	0.829656i	0.730364	+	0.0589611i
$199$	−4.29914	−	21.0586i	−0.304758	−	1.49280i	−0.787103	−	0.616822i	$-0.788420\pi$
$199$	−4.29914	−	21.0586i	−0.304758	−	1.49280i	0.482345	−	0.875982i	$-0.339785\pi$
$200$	−1.11265	+	9.16351i	−0.0786763	+	0.647958i
$201$	10.5479	+	4.49404i	0.743992	+	0.316985i
$202$	−17.7505	+	11.2247i	−1.24892	+	0.789768i
$203$	1.87999	−	1.66553i	0.131950	−	0.116897i
$204$	22.3929	−	1.80774i	1.56781	−	0.126567i
$205$	2.71528	+	9.37423i	0.189643	+	0.654724i
$206$	1.13104	−	0.481893i	0.0788036	−	0.0335751i
$207$	4.26457	−	6.17829i	0.296408	−	0.429421i
$208$	−1.89047	+	18.7263i	−0.131081	+	1.29844i
$209$	17.9337	+	25.9814i	1.24050	+	1.79717i
$210$	−1.59477	−	1.00847i	−0.110050	−	0.0695912i
$211$	−14.9238	+	2.42536i	−1.02740	+	0.166969i	−0.650675	−	0.759357i	$-0.725514\pi$
$211$	−14.9238	+	2.42536i	−1.02740	+	0.166969i	−0.376725	+	0.926325i	$0.622950\pi$
$212$	−35.9160	−	15.3024i	−2.46672	−	1.05097i
$213$	1.62914	−	2.36022i	0.111627	−	0.161719i
$214$	1.29980	−	4.48745i	0.0888528	−	0.306755i
$215$	0.229612	+	0.483897i	0.0156594	+	0.0330015i
$216$	−1.93928	+	5.11347i	−0.131952	+	0.347928i
$217$	−1.65391	−	2.02568i	−0.112275	−	0.137512i
$218$	−0.887925	−	22.0336i	−0.0601379	−	1.49231i
$219$	0.481707	+	11.9534i	0.0325507	+	0.807738i
$220$	−30.7163	+	7.57090i	−2.07090	+	0.510430i
$221$	−16.5176	−	9.98344i	−1.11110	−	0.671559i
$222$	−21.8057	−	5.37461i	−1.46350	−	0.360720i
$223$	1.08946	−	5.33652i	0.0729555	−	0.357360i	−0.926883	−	0.375351i	$-0.877522\pi$
$223$	1.08946	−	5.33652i	0.0729555	−	0.357360i	0.999838	+	0.0179915i	$0.00572718\pi$
$224$	0.788201	−	0.335821i	0.0526639	−	0.0224380i
$225$	1.42658	−	0.902117i	0.0951056	−	0.0601411i
$226$	37.4868	−	19.6746i	2.49358	−	1.30873i
$227$	−29.6644	−	4.82093i	−1.96889	−	0.319976i	−0.996091	−	0.0883366i	$-0.971845\pi$
$227$	−29.6644	−	4.82093i	−1.96889	−	0.319976i	−0.972802	−	0.231640i	$-0.925591\pi$
$228$	−30.3430	+	10.1300i	−2.00951	+	0.670874i
$229$	2.20456	+	18.1562i	0.145681	+	1.19979i	0.863786	+	0.503859i	$0.168087\pi$
$229$	2.20456	+	18.1562i	0.145681	+	1.19979i	−0.718105	+	0.695935i	$0.754990\pi$
$230$	−9.46240	+	32.6680i	−0.623932	+	2.15406i
$231$	−0.345053	+	1.69018i	−0.0227028	+	0.111206i
$232$	31.2828	+	10.4437i	2.05381	+	0.685664i
$233$	16.5557	+	8.68909i	1.08460	+	0.569241i	0.909667	−	0.415339i	$-0.136337\pi$
$233$	16.5557	+	8.68909i	1.08460	+	0.569241i	0.174932	+	0.984581i	$0.444030\pi$
$234$	7.48747	−	4.94949i	0.489471	−	0.323558i
$235$	−5.74093	+	3.01307i	−0.374497	+	0.196551i
$236$	25.5065	−	4.14521i	1.66033	−	0.269830i
$237$	1.49170	−	1.12094i	0.0968965	−	0.0728130i
$238$	−0.223471	+	5.54538i	−0.0144855	+	0.359453i
$239$	−2.14255			−0.138590			−0.0692951	−	0.997596i	$-0.522075\pi$
$239$	−2.14255			−0.138590			−0.0692951	+	0.997596i	$0.522075\pi$
$240$	0.382537	−	9.49256i	0.0246927	−	0.612742i
$241$	−0.617327	−	3.02387i	−0.0397655	−	0.194784i	0.955055	−	0.296427i	$-0.0957952\pi$
$241$	−0.617327	−	3.02387i	−0.0397655	−	0.194784i	−0.994821	+	0.101643i	$0.967590\pi$
$242$	8.70387	+	12.6097i	0.559506	+	0.810584i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−10.4179	+	21.9554i	−0.666941	+	1.40555i
$245$	−7.85735	+	9.62351i	−0.501988	+	0.614823i
$246$	4.73379	+	12.4820i	0.301815	+	0.795822i
$247$	26.2383	+	8.17386i	1.66950	+	0.520090i
$248$	12.1766	−	32.1071i	0.773217	−	2.03881i
$249$	−6.44469	−	11.1625i	−0.408416	−	0.707397i
$250$	−19.1625	+	23.4698i	−1.21194	+	1.48436i
$251$	2.24324	+	1.68568i	0.141592	+	0.106399i	0.669178	−	0.743102i	$-0.266646\pi$
$251$	2.24324	+	1.68568i	0.141592	+	0.106399i	−0.527586	+	0.849502i	$0.676903\pi$
$252$	−1.54775	−	0.812320i	−0.0974988	−	0.0511713i
$253$	30.9929	−	2.50200i	1.94851	−	0.157300i
$254$	−15.3607	+	1.24004i	−0.963813	+	0.0778071i
$255$	8.62605	+	4.52730i	0.540184	+	0.283510i
$256$	−26.0354	−	19.5643i	−1.62721	−	1.22277i
$257$	−9.92828	+	12.1599i	−0.619309	+	0.758516i	−0.985063	−	0.172196i	$-0.944914\pi$
$257$	−9.92828	+	12.1599i	−0.619309	+	0.758516i	0.365754	+	0.930712i	$0.380811\pi$
$258$	0.366313	+	0.634473i	0.0228057	+	0.0395006i
$259$	1.33241	−	3.51328i	0.0827920	−	0.218304i
$260$	−16.9823	+	21.6798i	−1.05319	+	1.34453i
$261$	−2.13845	−	5.63863i	−0.132367	−	0.349022i
$262$	0.816126	−	0.999573i	0.0504204	−	0.0617538i
$263$	3.00248	−	6.32759i	0.185141	−	0.390176i	−0.789565	−	0.613666i	$-0.789694\pi$
$263$	3.00248	−	6.32759i	0.185141	−	0.390176i	0.974706	+	0.223491i	$0.0717453\pi$
$264$	−21.4855	+	7.17292i	−1.32234	+	0.441463i
$265$	−9.61683	−	13.9324i	−0.590757	−	0.855859i
$266$	−1.58071	−	7.74285i	−0.0969198	−	0.474744i
$267$	0.0920077	−	2.28315i	0.00563078	−	0.139726i
$268$	−48.1190			−2.93934
$269$	−0.910793	+	22.6011i	−0.0555320	+	1.37801i	0.695870	+	0.718168i	$0.255019\pi$
$269$	−0.910793	+	22.6011i	−0.0555320	+	1.37801i	−0.751402	+	0.659845i	$0.770622\pi$
$270$	−3.62182	+	2.72162i	−0.220417	+	0.165633i
$271$	−18.0561	+	2.93441i	−1.09683	+	0.178252i	−0.681788	−	0.731549i	$-0.738798\pi$
$271$	−18.0561	+	2.93441i	−1.09683	+	0.178252i	−0.415043	+	0.909802i	$0.636233\pi$
$272$	−24.7424	+	12.9858i	−1.50023	+	0.787381i
$273$	0.671054	+	1.34340i	0.0406141	+	0.0813061i
$274$	−4.79589	−	2.51708i	−0.289730	−	0.152062i
$275$	6.63120	+	2.21382i	0.399876	+	0.133498i
$276$	−6.30219	+	30.8702i	−0.379347	+	1.85816i
$277$	3.41920	−	11.8044i	0.205440	−	0.709260i	−0.789935	−	0.613191i	$-0.789886\pi$
$277$	3.41920	−	11.8044i	0.205440	−	0.709260i	0.995375	−	0.0960696i	$-0.0306271\pi$
$278$	−2.12918	−	17.5354i	−0.127700	−	1.05170i
$279$	−5.95579	+	1.98834i	−0.356564	+	0.119039i
$280$	4.09160	+	0.664950i	0.244520	+	0.0397383i
$281$	17.2694	−	9.06368i	1.03021	−	0.540694i	0.137108	−	0.990556i	$-0.456219\pi$
$281$	17.2694	−	9.06368i	1.03021	−	0.540694i	0.893098	+	0.449862i	$0.148527\pi$
$282$	−7.49556	+	4.73991i	−0.446354	+	0.282257i
$283$	23.4872	−	10.0069i	1.39617	−	0.594851i	0.442788	−	0.896626i	$-0.353990\pi$
$283$	23.4872	−	10.0069i	1.39617	−	0.594851i	0.953379	+	0.301775i	$0.0975793\pi$
$284$	−2.40755	+	11.7929i	−0.142862	+	0.699782i
$285$	−13.4686	−	3.31971i	−0.797810	−	0.196642i
$286$	35.4929	+	11.0569i	2.09874	+	0.653808i
$287$	−2.16858	+	0.534506i	−0.128007	+	0.0315509i
$288$	−0.0828309	−	2.05543i	−0.00488086	−	0.121117i
$289$	−0.469256	−	11.6445i	−0.0276033	−	0.684969i
$290$	17.2789	+	21.1629i	1.01465	+	1.24273i
$291$	3.73589	−	9.85074i	0.219002	−	0.577461i
$292$	−21.5238	−	45.3605i	−1.25959	−	2.65452i
$293$	3.30230	−	11.4009i	0.192923	−	0.666046i	−0.804477	−	0.593983i	$-0.797555\pi$
$293$	3.30230	−	11.4009i	0.192923	−	0.666046i	0.997400	−	0.0720630i	$-0.0229583\pi$
$294$	−9.65351	+	13.9855i	−0.563004	+	0.815653i
$295$	10.3089	+	4.39223i	0.600209	+	0.255725i
$296$	48.6996	−	7.91445i	2.83060	−	0.460018i
$297$	3.50066	+	2.21368i	0.203129	+	0.128451i
$298$	14.2519	+	20.6474i	0.825589	+	1.19607i
$299$	19.8933	−	18.3550i	1.15046	−	1.06150i
$300$	−4.02410	+	5.82992i	−0.232332	+	0.336591i
$301$	−0.112766	+	0.0480451i	−0.00649972	+	0.00276927i
$302$	−3.36396	−	11.6137i	−0.193574	−	0.668295i
$303$	−8.40925	+	0.678865i	−0.483099	+	0.0389998i
$304$	29.7822	−	26.3847i	1.70813	−	1.51327i
$305$	−8.90666	+	5.63223i	−0.509994	+	0.322501i
$306$	12.2591	+	5.22310i	0.700804	+	0.298585i
$307$	0.802604	−	6.61004i	0.0458070	−	0.377255i	−0.951720	−	0.306968i	$-0.900686\pi$
$307$	0.802604	−	6.61004i	0.0458070	−	0.377255i	0.997527	−	0.0702866i	$-0.0223914\pi$
$308$	−1.44815	−	7.09351i	−0.0825160	−	0.404190i
$309$	0.492270	+	0.0397402i	0.0280043	+	0.00226074i
$310$	22.7412	−	17.0889i	1.29161	−	0.970583i
$311$	−0.910333	+	7.49727i	−0.0516203	+	0.425131i	0.943874	+	0.330306i	$0.107152\pi$
$311$	−0.910333	+	7.49727i	−0.0516203	+	0.425131i	−0.995494	+	0.0948246i	$0.969771\pi$
$312$	−10.8709	+	16.4510i	−0.615442	+	0.931352i
$313$	0.542101	+	4.46461i	0.0306414	+	0.252354i	0.999978	+	0.00661815i	$0.00210664\pi$
$313$	0.542101	+	4.46461i	0.0306414	+	0.252354i	−0.969337	+	0.245736i	$0.920970\pi$
$314$	20.8527	+	21.7100i	1.17679	+	1.22516i
$315$	−0.378989	−	0.656429i	−0.0213536	−	0.0369856i
$316$	−3.91555	+	6.78194i	−0.220267	+	0.381514i
$317$	−9.02074	+	2.22341i	−0.506655	+	0.124879i	−0.484354	−	0.874872i	$-0.660945\pi$
$317$	−9.02074	+	2.22341i	−0.506655	+	0.124879i	−0.0223012	+	0.999751i	$0.507099\pi$
$318$	−14.6451	−	17.9370i	−0.821255	−	1.00585i
$319$	12.4888	−	21.6312i	0.699236	−	1.21111i
$320$	−3.43293	−	9.05188i	−0.191906	−	0.506016i
$321$	1.30007	−	1.35352i	0.0725629	−	0.0755459i
$322$	−7.38283	−	2.46475i	−0.411429	−	0.137355i
$323$	11.3515	+	39.1898i	0.631613	+	2.18058i
$324$	−3.14142	+	2.78306i	−0.174523	+	0.154614i
$325$	5.73242	−	2.04348i	0.317977	−	0.113352i
$326$	−28.4459	−	25.2009i	−1.57547	−	1.39575i
$327$	3.79750	−	8.00305i	0.210002	−	0.442570i
$328$	−20.3158	−	21.1510i	−1.12175	−	1.16787i
$329$	−0.636082	−	1.34051i	−0.0350683	−	0.0739049i
$330$	−18.2192	−	4.49062i	−1.00293	−	0.247200i
$331$	−11.5194	+	11.9930i	−0.633164	+	0.659193i	−0.958064	−	0.286555i	$-0.907490\pi$
$331$	−11.5194	+	11.9930i	−0.633164	+	0.659193i	0.324900	+	0.945748i	$0.394669\pi$
$332$	43.2462	+	32.4974i	2.37344	+	1.78353i
$333$	−6.75285	−	5.98250i	−0.370054	−	0.327839i
$334$	−13.7766	−	2.23892i	−0.753823	−	0.122508i
$335$	−17.6358	−	11.1522i	−0.963547	−	0.609310i
$336$	2.16709	+	0.174946i	0.118224	+	0.00954406i
$337$	32.6144			1.77662			0.888310	−	0.459244i	$-0.151880\pi$
$337$	32.6144			1.77662			0.888310	+	0.459244i	$0.151880\pi$
$338$	30.2568	−	11.4805i	1.64575	−	0.624455i
$339$	17.0068			0.923685
$340$	−40.7533	−	3.28994i	−2.21016	−	0.178422i
$341$	−21.9804	−	13.8996i	−1.19030	−	0.752703i
$342$	−18.7285	−	3.04367i	−1.01272	−	0.164583i
$343$	−4.31038	−	3.81867i	−0.232739	−	0.206189i
$344$	−1.28671	−	0.966898i	−0.0693746	−	0.0521316i
$345$	−9.46434	+	9.85342i	−0.509543	+	0.530490i
$346$	−26.5345	−	6.54016i	−1.42650	−	0.351601i
$347$	−2.57468	−	5.42603i	−0.138216	−	0.291285i	0.822526	−	0.568728i	$-0.192564\pi$
$347$	−2.57468	−	5.42603i	−0.138216	−	0.291285i	−0.960742	+	0.277443i	$0.910513\pi$
$348$	17.5325	+	18.2532i	0.939839	+	0.978476i
$349$	−7.59540	+	16.0070i	−0.406573	+	0.856834i	0.592127	+	0.805845i	$0.298289\pi$
$349$	−7.59540	+	16.0070i	−0.406573	+	0.856834i	−0.998699	+	0.0509888i	$0.983763\pi$
$350$	−1.30988	−	1.16045i	−0.0700162	−	0.0620289i
$351$	3.58726	−	0.362726i	0.191474	−	0.0193609i
$352$	6.37746	−	5.64994i	0.339920	−	0.301143i
$353$	6.75565	+	23.3232i	0.359567	+	1.24137i	0.912822	+	0.408358i	$0.133898\pi$
$353$	6.75565	+	23.3232i	0.359567	+	1.24137i	−0.553255	+	0.833012i	$0.686614\pi$
$354$	14.5387	+	4.85372i	0.772721	+	0.257972i
$355$	−3.61555	+	3.76418i	−0.191893	+	0.199782i
$356$	3.40063	+	8.96673i	0.180233	+	0.475236i
$357$	−1.11472	+	1.93075i	−0.0589973	+	0.102186i
$358$	30.7362	+	37.6451i	1.62446	+	1.98960i
$359$	−6.25564	+	1.54188i	−0.330160	+	0.0813772i	−0.400911	−	0.916117i	$-0.631306\pi$
$359$	−6.25564	+	1.54188i	−0.330160	+	0.0813772i	0.0707513	+	0.997494i	$0.477460\pi$
$360$	4.97645	−	8.61946i	0.262282	−	0.454286i
$361$	−19.5484	−	33.8588i	−1.02886	−	1.78204i
$362$	−8.09934	−	8.43230i	−0.425692	−	0.443192i
$363$	0.741902	+	6.11011i	0.0389398	+	0.320698i
$364$	−4.80093	−	4.08302i	−0.251637	−	0.214008i
$365$	2.62432	−	21.6132i	0.137363	−	1.13129i
$366$	−11.5234	+	8.65931i	−0.602340	+	0.452629i
$367$	20.2885	+	1.63786i	1.05905	+	0.0854953i	0.597698	−	0.801722i	$-0.296082\pi$
$367$	20.2885	+	1.63786i	1.05905	+	0.0854953i	0.461352	+	0.887217i	$0.347364\pi$
$368$	−7.83874	−	38.3967i	−0.408622	−	2.00156i
$369$	−0.646393	+	5.32352i	−0.0336499	+	0.277132i
$370$	37.6017	+	16.0206i	1.95482	+	0.832870i
$371$	3.27446	−	2.07064i	0.170002	−	0.107503i
$372$	19.7248	−	17.4746i	1.02268	−	0.906017i
$373$	−16.1657	+	1.30503i	−0.837026	+	0.0675718i	−0.491543	−	0.870853i	$-0.663567\pi$
$373$	−16.1657	+	1.30503i	−0.837026	+	0.0675718i	−0.345483	+	0.938425i	$0.612285\pi$
$374$	15.3553	+	53.0127i	0.794005	+	2.74122i
$375$	−11.1975	+	4.77079i	−0.578234	+	0.246363i
$376$	11.0677	−	16.0343i	0.570773	−	0.826908i
$377$	−3.05672	−	21.5274i	−0.157429	−	1.10872i
$378$	−0.588965	−	0.853263i	−0.0302931	−	0.0438871i
$379$	18.2364	+	11.5320i	0.936743	+	0.592360i	0.913266	−	0.407364i	$-0.133552\pi$
$379$	18.2364	+	11.5320i	0.936743	+	0.592360i	0.0234769	+	0.999724i	$0.492526\pi$
$380$	57.4640	−	9.33882i	2.94784	−	0.479071i
$381$	−5.69523	−	2.42651i	−0.291776	−	0.124314i
$382$	−19.4561	+	28.1870i	−0.995460	+	1.44217i
$383$	−2.05144	+	7.08241i	−0.104824	+	0.361894i	−0.995732	−	0.0922890i	$-0.970582\pi$
$383$	−2.05144	+	7.08241i	−0.104824	+	0.361894i	0.890908	+	0.454183i	$0.150069\pi$
$384$	−7.44048	−	15.6805i	−0.379695	−	0.800191i
$385$	1.11326	−	2.93543i	0.0567370	−	0.149603i
$386$	−28.1958	−	34.5336i	−1.43513	−	1.75771i
$387$	0.0118504	+	0.294065i	0.000602390	+	0.0149482i
$388$	1.78039	+	44.1800i	0.0903858	+	2.24290i
$389$	15.6974	−	3.86906i	0.795889	−	0.196169i	0.179652	−	0.983730i	$-0.442503\pi$
$389$	15.6974	−	3.86906i	0.795889	−	0.196169i	0.616237	+	0.787561i	$0.288657\pi$
$390$	−14.8951	+	6.70517i	−0.754242	+	0.339530i
$391$	39.0178	+	9.61702i	1.97321	+	0.486353i
$392$	7.46763	−	36.5789i	0.377172	−	1.84751i
$393$	0.476898	−	0.203187i	0.0240563	−	0.0102494i
$394$	−27.4344	+	17.3484i	−1.38212	+	0.874002i
$395$	−3.00687	+	1.57813i	−0.151292	+	0.0794042i
$396$	−17.1578	−	2.78842i	−0.862214	−	0.140123i
$397$	−25.5123	+	8.51725i	−1.28042	+	0.427468i	−0.873871	−	0.486159i	$-0.838398\pi$
$397$	−25.5123	+	8.51725i	−1.28042	+	0.427468i	−0.406554	+	0.913627i	$0.633270\pi$
$398$	6.44915	+	53.1135i	0.323267	+	2.66234i
$399$	0.883211	−	3.04920i	0.0442159	−	0.152651i
$400$	1.76243	−	8.63295i	0.0881215	−	0.431648i
$401$	−16.4084	−	5.47792i	−0.819395	−	0.273554i	−0.124092	−	0.992271i	$-0.539602\pi$
$401$	−16.4084	−	5.47792i	−0.819395	−	0.273554i	−0.695303	+	0.718717i	$0.744730\pi$
$402$	−25.2722	−	13.2639i	−1.26046	−	0.661541i
$403$	−22.5242	+	2.27753i	−1.12201	+	0.113452i
$404$	31.3519	−	16.4547i	1.55981	−	0.818653i
$405$	−1.79635	+	0.291936i	−0.0892616	+	0.0145064i
$406$	−4.99842	+	3.75607i	−0.248068	+	0.186411i
$407$	1.50460	−	37.3363i	0.0745804	−	1.85069i
$408$	−29.2745			−1.44930
$409$	0.191419	−	4.75002i	0.00946508	−	0.234874i	−0.987531	−	0.157424i	$-0.949681\pi$
$409$	0.191419	−	4.75002i	0.00946508	−	0.234874i	0.996996	−	0.0774499i	$-0.0246778\pi$
$410$	−4.85963	−	23.8040i	−0.240000	−	1.17560i
$411$	−1.23598	−	1.79063i	−0.0609666	−	0.0883254i
$412$	−1.96606	+	0.656367i	−0.0968608	+	0.0323369i
$413$	−1.09934	+	2.31682i	−0.0540951	+	0.114003i
$414$	−11.8192	+	14.4759i	−0.580881	+	0.711450i
$415$	8.31820	+	21.9333i	0.408324	+	1.07666i
$416$	1.33636	−	7.29559i	0.0655204	−	0.357696i
$417$	2.51623	−	6.63476i	0.123220	−	0.324905i
$418$	−39.2942	−	68.0595i	−1.92194	−	3.32890i
$419$	3.57628	−	4.38015i	0.174713	−	0.213984i	−0.679824	−	0.733375i	$-0.737944\pi$
$419$	3.57628	−	4.38015i	0.174713	−	0.213984i	0.854537	+	0.519391i	$0.173841\pi$
$420$	2.54315	+	1.91106i	0.124093	+	0.0932500i
$421$	−21.6903	−	11.3840i	−1.05712	−	0.554821i	−0.155719	−	0.987801i	$-0.549770\pi$
$421$	−21.6903	−	11.3840i	−1.05712	−	0.554821i	−0.901403	+	0.432981i	$0.857462\pi$
$422$	37.5161	−	3.02861i	1.82626	−	0.147431i
$423$	−3.55101	+	0.286667i	−0.172656	+	0.0139382i
$424$	45.0449	+	23.6414i	2.18757	+	1.14813i
$425$	7.22308	+	5.42779i	0.350371	+	0.263287i
$426$	−4.51514	+	5.53004i	−0.218759	+	0.267931i
$427$	−1.20582	−	2.08854i	−0.0583537	−	0.101072i
$428$	−2.79306	+	7.36468i	−0.135007	+	0.355985i
$429$	10.5606	+	10.5589i	0.509869	+	0.509787i
$430$	−0.472803	−	1.24668i	−0.0228006	−	0.0601202i
$431$	15.0686	−	18.4557i	0.725829	−	0.888979i	−0.271469	−	0.962447i	$-0.587509\pi$
$431$	15.0686	−	18.4557i	0.725829	−	0.888979i	0.997298	+	0.0734684i	$0.0234068\pi$
$432$	2.23784	−	4.71615i	0.107668	−	0.226906i
$433$	38.3379	−	12.7991i	1.84240	−	0.615084i	0.845726	−	0.533617i	$-0.179168\pi$
$433$	38.3379	−	12.7991i	1.84240	−	0.615084i	0.996676	−	0.0814676i	$-0.0259607\pi$
$434$	3.69807	+	5.35758i	0.177513	+	0.257172i
$435$	2.19529	+	10.7533i	0.105256	+	0.515579i
$436$	−1.49699	+	37.1473i	−0.0716926	+	1.77903i
$437$	−57.2207			−2.73724
$438$	1.19914	−	29.7564i	0.0572972	−	1.42181i
$439$	20.5709	−	15.4581i	0.981798	−	0.737773i	0.0167532	−	0.999860i	$-0.494667\pi$
$439$	20.5709	−	15.4581i	0.981798	−	0.737773i	0.965044	+	0.262087i	$0.0844106\pi$
$440$	40.6897	−	6.61271i	1.93980	−	0.315249i
$441$	−6.04460	+	3.17245i	−0.287838	+	0.151069i
$442$	38.9851	+	28.0804i	1.85433	+	1.33565i
$443$	24.6393	+	12.9317i	1.17065	+	0.614403i	0.934028	−	0.357199i	$-0.116268\pi$
$443$	24.6393	+	12.9317i	1.17065	+	0.614403i	0.236619	+	0.971602i	$0.423961\pi$
$444$	35.9146	+	11.9901i	1.70443	+	0.569023i
$445$	−0.831812	+	4.07448i	−0.0394317	+	0.193149i
$446$	−3.77221	+	13.0232i	−0.178620	+	0.616666i
$447$	1.21480	+	10.0048i	0.0574583	+	0.473211i
$448$	2.10148	−	0.701577i	0.0992856	−	0.0331464i
$449$	22.0889	+	3.58980i	1.04244	+	0.169413i	0.657443	−	0.753505i	$-0.271638\pi$
$449$	22.0889	+	3.58980i	1.04244	+	0.169413i	0.384998	+	0.922918i	$0.374202\pi$
$450$	−3.72046	+	1.95265i	−0.175384	+	0.0920488i
$451$	−18.7727	+	11.8711i	−0.883972	+	0.558990i
$452$	−65.6644	+	27.9770i	−3.08860	+	1.31593i
$453$	0.971548	−	4.75896i	0.0456473	−	0.223595i
$454$	72.6400	+	17.9042i	3.40917	+	0.840284i
$455$	−0.813265	−	2.60912i	−0.0381265	−	0.122317i
$456$	40.4731	−	9.97571i	1.89532	−	0.467156i
$457$	−1.57145	−	38.9951i	−0.0735093	−	1.82411i	−0.444837	−	0.895612i	$-0.646738\pi$
$457$	−1.57145	−	38.9951i	−0.0735093	−	1.82411i	0.371327	−	0.928502i	$-0.378903\pi$
$458$	−1.83327	−	45.4922i	−0.0856633	−	2.12571i
$459$	3.38544	+	4.14641i	0.158019	+	0.193538i
$460$	20.3331	−	53.6139i	0.948034	−	2.49976i
$461$	12.7487	+	26.8672i	0.593764	+	1.25133i	0.948622	+	0.316411i	$0.102478\pi$
$461$	12.7487	+	26.8672i	0.593764	+	1.25133i	−0.354858	+	0.934920i	$0.615471\pi$
$462$	1.19473	−	4.12470i	0.0555840	−	0.191898i
$463$	−1.73685	+	2.51626i	−0.0807182	+	0.116940i	−0.861263	−	0.508159i	$-0.830326\pi$
$463$	−1.73685	+	2.51626i	−0.0807182	+	0.116940i	0.780545	+	0.625099i	$0.214942\pi$
$464$	−28.9611	−	12.3392i	−1.34449	−	0.572832i
$465$	11.2792	−	1.83305i	0.523060	−	0.0850054i
$466$	−39.3388	−	24.8764i	−1.82234	−	1.15238i
$467$	−5.85096	−	8.47658i	−0.270750	−	0.392249i	0.663898	−	0.747823i	$-0.268901\pi$
$467$	−5.85096	−	8.47658i	−0.270750	−	0.392249i	−0.934648	+	0.355574i	$0.884285\pi$
$468$	−13.2539	+	7.30170i	−0.612663	+	0.337521i
$469$	2.71263	−	3.92992i	0.125258	−	0.181467i
$470$	14.8484	−	6.32633i	0.684907	−	0.291812i
$471$	3.36433	+	11.6150i	0.155020	+	0.535192i
$472$	−33.5637	+	2.70954i	−1.54489	+	0.124717i
$473$	−0.912408	+	0.808323i	−0.0419525	+	0.0371667i
$474$	−3.92587	+	2.48257i	−0.180321	+	0.114028i
$475$	−11.8358	−	5.04276i	−0.543063	−	0.231378i
$476$	1.12783	−	9.28852i	0.0516940	−	0.425739i
$477$	−1.86066	−	9.11412i	−0.0851938	−	0.417307i
$478$	5.31628	+	0.429174i	0.243161	+	0.0196300i
$479$	9.45775	−	7.10704i	0.432136	−	0.324729i	−0.362317	−	0.932055i	$-0.618014\pi$
$479$	9.45775	−	7.10704i	0.432136	−	0.324729i	0.794453	+	0.607326i	$0.207758\pi$
$480$	−0.451260	+	3.71646i	−0.0205971	+	0.169632i
$481$	−19.0156	−	26.3912i	−0.867037	−	1.20333i
$482$	0.926053	+	7.62674i	0.0421806	+	0.347388i
$483$	−2.16592	−	2.25496i	−0.0985527	−	0.102604i
$484$	−12.9159	−	22.3710i	−0.587088	−	1.01687i
$485$	−9.58678	+	16.6048i	−0.435313	+	0.753984i
$486$	−2.41702	+	0.595742i	−0.109638	+	0.0270234i
$487$	11.0415	+	13.5233i	0.500336	+	0.612801i	0.961597	−	0.274464i	$-0.0885003\pi$
$487$	11.0415	+	13.5233i	0.500336	+	0.612801i	−0.461261	+	0.887264i	$0.652603\pi$
$488$	15.8334	−	27.4243i	0.716745	−	1.24144i
$489$	−5.41352	−	14.2743i	−0.244808	−	0.645505i
$490$	21.4240	−	22.3048i	0.967838	−	1.00763i
$491$	−4.91906	−	1.64222i	−0.221994	−	0.0741125i	0.203495	−	0.979076i	$-0.434770\pi$
$491$	−4.91906	−	1.64222i	−0.221994	−	0.0741125i	−0.425489	+	0.904963i	$0.639898\pi$
$492$	−6.26167	−	21.6178i	−0.282298	−	0.974605i
$493$	24.1626	−	21.4062i	1.08823	−	0.964088i
$494$	−63.4673	−	25.5374i	−2.85553	−	1.14898i
$495$	−5.64217	−	4.99852i	−0.253597	−	0.224667i
$496$	−14.0512	+	29.6124i	−0.630919	+	1.32963i
$497$	−0.827419	−	0.861434i	−0.0371148	−	0.0386406i
$498$	13.7551	+	28.9884i	0.616383	+	1.29900i
$499$	22.7347	+	5.60360i	1.01774	+	0.250852i	0.712687	−	0.701482i	$-0.247478\pi$
$499$	22.7347	+	5.60360i	1.01774	+	0.250852i	0.305058	+	0.952334i	$0.401324\pi$
$500$	35.3859	−	36.8406i	1.58251	−	1.64756i
$501$	−4.48233	−	3.36825i	−0.200256	−	0.150482i
$502$	−5.22845	−	4.63200i	−0.233357	−	0.206736i
$503$	13.8994	+	2.25888i	0.619746	+	0.100718i	0.462174	−	0.886789i	$-0.347069\pi$
$503$	13.8994	+	2.25888i	0.619746	+	0.100718i	0.157571	+	0.987508i	$0.449634\pi$
$504$	1.92511	+	1.21737i	0.0857512	+	0.0542258i
$505$	15.3042	+	1.23548i	0.681027	+	0.0549782i
$506$	−77.4033			−3.44100
$507$	12.9055	+	1.56490i	0.573152	+	0.0694997i
$508$	25.9813			1.15274
$509$	−13.1332	−	1.06022i	−0.582118	−	0.0469934i	−0.214099	−	0.976812i	$-0.568682\pi$
$509$	−13.1332	−	1.06022i	−0.582118	−	0.0469934i	−0.368018	+	0.929819i	$0.619964\pi$
$510$	−20.4968	−	12.9614i	−0.907614	−	0.573940i
$511$	4.91800	+	0.799253i	0.217560	+	0.0353569i
$512$	34.6996	+	30.7412i	1.53352	+	1.35858i
$513$	−6.09345	−	4.57893i	−0.269032	−	0.202165i
$514$	27.0706	−	28.1835i	1.19403	−	1.24312i
$515$	−0.872690	−	0.215099i	−0.0384553	−	0.00947839i
$516$	−0.529505	−	1.11591i	−0.0233101	−	0.0491251i
$517$	−10.2216	−	10.6418i	−0.449545	−	0.468026i
$518$	−4.00983	+	8.45055i	−0.176182	+	0.371296i
$519$	−8.21728	−	7.27987i	−0.360698	−	0.319551i
$520$	24.3306	−	26.3781i	1.06697	−	1.15676i
$521$	23.2951	−	20.6376i	1.02058	−	0.904151i	0.0251489	−	0.999684i	$-0.491994\pi$
$521$	23.2951	−	20.6376i	1.02058	−	0.904151i	0.995426	+	0.0955330i	$0.0304556\pi$
$522$	4.17663	+	14.4194i	0.182806	+	0.631119i
$523$	−29.3820	−	9.80916i	−1.28479	−	0.428925i	−0.409403	−	0.912354i	$-0.634263\pi$
$523$	−29.3820	−	9.80916i	−1.28479	−	0.428925i	−0.875384	+	0.483429i	$0.839391\pi$
$524$	−1.50708	+	1.56903i	−0.0658370	+	0.0685436i
$525$	−0.249283	−	0.657304i	−0.0108796	−	0.0286871i
$526$	−8.71748	+	15.0991i	−0.380100	+	0.658353i
$527$	−21.2569	−	26.0350i	−0.925967	−	1.13410i
$528$	20.9929	−	5.17427i	0.913597	−	0.225181i
$529$	−16.6789	+	28.8887i	−0.725170	+	1.25603i
$530$	21.0713	+	36.4965i	0.915278	+	1.58531i
$531$	4.26524	+	4.44059i	0.185096	+	0.192705i
$532$	1.60593	+	13.2261i	0.0696261	+	0.573422i
$533$	−6.48945	+	18.2137i	−0.281089	+	0.788921i
$534$	−0.685635	+	5.64671i	−0.0296703	+	0.244357i
$535$	−2.73053	+	2.05186i	−0.118051	+	0.0887096i
$536$	62.4992	+	5.04546i	2.69955	+	0.217931i
$537$	3.90505	+	19.1282i	0.168515	+	0.825442i
$538$	6.78716	−	55.8973i	0.292615	−	2.40990i
$539$	−26.0120	−	11.0827i	−1.12042	−	0.477365i
$540$	6.45558	−	4.08226i	0.277804	−	0.175673i
$541$	−31.3900	+	27.8091i	−1.34956	+	1.19561i	−0.387790	+	0.921748i	$0.626761\pi$
$541$	−31.3900	+	27.8091i	−1.34956	+	1.19561i	−0.961770	+	0.273858i	$0.911700\pi$
$542$	45.3902	−	3.66427i	1.94967	−	0.157394i
$543$	−1.30673	−	4.51136i	−0.0560772	−	0.193601i
$544$	10.1304	−	4.31614i	0.434336	−	0.185053i
$545$	−9.15803	+	13.2677i	−0.392287	+	0.568326i
$546$	−1.39598	−	3.46777i	−0.0597425	−	0.148407i
$547$	22.5421	+	32.6579i	0.963831	+	1.39635i	0.917638	+	0.397417i	$0.130093\pi$
$547$	22.5421	+	32.6579i	0.963831	+	1.39635i	0.0461929	+	0.998933i	$0.485291\pi$
$548$	7.71788	+	4.88049i	0.329691	+	0.208484i
$549$	−5.71540	+	0.928844i	−0.243928	+	0.0396421i
$550$	−16.0104	−	6.82141i	−0.682688	−	0.290866i
$551$	−26.1113	+	37.8287i	−1.11238	+	1.61156i
$552$	11.4224	−	39.4348i	0.486171	−	1.67846i
$553$	−0.333154	−	0.702107i	−0.0141672	−	0.0298566i
$554$	−10.8486	+	28.6053i	−0.460911	+	1.21532i
$555$	10.3840	+	12.7181i	0.440776	+	0.539853i
$556$	1.19915	+	29.7565i	0.0508551	+	1.26196i
$557$	0.518692	+	12.8712i	0.0219777	+	0.545370i	0.972249	+	0.233948i	$0.0751644\pi$
$557$	0.518692	+	12.8712i	0.0219777	+	0.545370i	−0.950272	+	0.311423i	$0.899195\pi$
$558$	15.1763	−	3.74062i	0.642464	−	0.158353i
$559$	−0.191190	+	1.04376i	−0.00808645	+	0.0441464i
$560$	−3.84179	−	0.946915i	−0.162345	−	0.0400145i
$561$	−4.43479	+	21.7230i	−0.187237	+	0.917147i
$562$	−44.6659	+	19.0303i	−1.88412	+	0.802747i
$563$	−29.7404	+	18.8067i	−1.25341	+	0.792608i	−0.985309	−	0.170783i	$-0.945370\pi$
$563$	−29.7404	+	18.8067i	−1.25341	+	0.792608i	−0.268100	+	0.963391i	$0.586396\pi$
$564$	13.2391	−	6.94841i	0.557466	−	0.292581i
$565$	−30.5503	−	4.96491i	−1.28526	−	0.208875i
$566$	−60.2828	+	20.1254i	−2.53388	+	0.845932i
$567$	−0.0502023	−	0.413453i	−0.00210830	−	0.0173634i
$568$	4.36357	−	15.0648i	0.183091	−	0.632104i
$569$	−4.86116	+	23.8116i	−0.203791	+	0.998232i	0.741237	+	0.671243i	$0.234239\pi$
$569$	−4.86116	+	23.8116i	−0.203791	+	0.998232i	−0.945028	+	0.326989i	$0.893966\pi$
$570$	32.7544	+	10.9350i	1.37193	+	0.458018i
$571$	30.2464	+	15.8745i	1.26577	+	0.664329i	0.957901	−	0.287099i	$-0.0926908\pi$
$571$	30.2464	+	15.8745i	1.26577	+	0.664329i	0.307872	+	0.951428i	$0.400383\pi$
$572$	−58.1447	−	23.3958i	−2.43115	−	0.978228i
$573$	−12.1825	+	6.39389i	−0.508933	+	0.267108i
$574$	5.48792	−	0.891874i	0.229061	−	0.0372261i
$575$	−10.1300	+	7.61217i	−0.422448	+	0.317449i
$576$	0.214193	−	5.31514i	0.00892470	−	0.221464i
$577$	22.9318			0.954663			0.477332	−	0.878723i	$-0.341604\pi$
$577$	22.9318			0.954663			0.477332	+	0.878723i	$0.341604\pi$
$578$	−1.16815	+	28.9872i	−0.0485885	+	1.20571i
$579$	−3.58228	−	17.5472i	−0.148875	−	0.729236i
$580$	−26.1657	−	37.9076i	−1.08647	−	1.57403i
$581$	−5.09202	+	1.69997i	−0.211253	+	0.0705265i
$582$	−11.2430	+	23.6942i	−0.466038	+	0.982155i
$583$	24.3669	−	29.8440i	1.00917	−	1.23601i
$584$	23.1999	+	61.1732i	0.960020	+	2.53136i
$585$	−6.54988	−	0.395666i	−0.270804	−	0.0163588i
$586$	−10.4777	+	27.6273i	−0.432828	+	1.14127i
$587$	4.81313	+	8.33658i	0.198659	+	0.344088i	0.948094	−	0.317991i	$-0.103008\pi$
$587$	4.81313	+	8.33658i	0.198659	+	0.344088i	−0.749435	+	0.662078i	$0.769675\pi$
$588$	18.1197	−	22.1926i	0.747245	−	0.915209i
$589$	38.2604	+	28.7508i	1.57649	+	1.18466i
$590$	−24.6996	−	12.9633i	−1.01687	−	0.533693i
$591$	−12.9970	+	1.04923i	−0.534625	+	0.0431594i
$592$	−46.9420	+	3.78955i	−1.92930	+	0.155750i
$593$	39.6542	+	20.8121i	1.62840	+	0.854652i	0.996849	+	0.0793212i	$0.0252753\pi$
$593$	39.6542	+	20.8121i	1.62840	+	0.854652i	0.631555	+	0.775331i	$0.282417\pi$
$594$	−8.24270	−	6.19399i	−0.338202	−	0.254143i
$595$	2.56609	−	3.14289i	0.105199	−	0.128846i
$596$	−21.1488	−	36.6308i	−0.866288	−	1.50045i
$597$	−7.62150	+	20.0963i	−0.311927	+	0.822485i
$598$	−53.0377	+	41.5593i	−2.16887	+	1.69948i
$599$	−2.55196	−	6.72898i	−0.104270	−	0.274938i	0.872720	−	0.488221i	$-0.162354\pi$
$599$	−2.55196	−	6.72898i	−0.104270	−	0.274938i	−0.976991	+	0.213282i	$0.931585\pi$
$600$	5.83798	−	7.15023i	0.238335	−	0.291907i
$601$	−12.7172	+	26.8009i	−0.518744	+	1.09323i	0.459957	+	0.887941i	$0.347865\pi$
$601$	−12.7172	+	26.8009i	−0.518744	+	1.09323i	−0.978701	+	0.205289i	$0.934187\pi$
$602$	0.289428	−	0.0966254i	0.0117962	−	0.00393816i
$603$	−6.51308	−	9.43582i	−0.265233	−	0.384256i
$604$	4.07749	+	19.9729i	0.165911	+	0.812684i
$605$	0.451043	−	11.1925i	0.0183375	−	0.455040i
$606$	21.0017			0.853137
$607$	−0.160162	+	3.97439i	−0.00650079	+	0.161315i	0.992678	+	0.120792i	$0.0385435\pi$
$607$	−0.160162	+	3.97439i	−0.00650079	+	0.161315i	−0.999179	+	0.0405232i	$0.987098\pi$
$608$	−12.5348	+	9.41931i	−0.508354	+	0.382003i
$609$	−2.47912	+	0.402896i	−0.100459	+	0.0163262i
$610$	23.2281	−	12.1911i	0.940480	−	0.493602i
$611$	−12.7177	−	1.80373i	−0.514505	−	0.0729712i
$612$	−19.8924	−	10.4403i	−0.804103	−	0.422026i
$613$	9.26687	+	3.09374i	0.374285	+	0.124955i	0.497586	−	0.867415i	$-0.334220\pi$
$613$	9.26687	+	3.09374i	0.374285	+	0.124955i	−0.123301	+	0.992369i	$0.539348\pi$
$614$	−3.31554	+	16.2406i	−0.133804	+	0.655418i
$615$	2.71528	−	9.37423i	0.109491	−	0.378005i
$616$	1.13714	+	9.36523i	0.0458169	+	0.377336i
$617$	3.43202	−	1.14578i	0.138168	−	0.0461272i	−0.246743	−	0.969081i	$-0.579360\pi$
$617$	3.43202	−	1.14578i	0.138168	−	0.0461272i	0.384911	+	0.922954i	$0.374232\pi$
$618$	−1.21350	−	0.197213i	−0.0488142	−	0.00793308i
$619$	26.9674	−	14.1536i	1.08391	−	0.568881i	0.174449	−	0.984666i	$-0.444185\pi$
$619$	26.9674	−	14.1536i	1.08391	−	0.568881i	0.909463	+	0.415785i	$0.136493\pi$
$620$	−40.5341	+	25.6322i	−1.62789	+	1.02942i
$621$	−6.90646	+	2.94257i	−0.277147	+	0.118081i
$622$	3.76057	−	18.4205i	0.150785	−	0.738595i
$623$	−0.924026	−	0.227752i	−0.0370203	−	0.00912469i
$624$	11.6064	−	14.8169i	0.464628	−	0.593152i
$625$	13.3132	−	3.28140i	0.532527	−	0.131256i
$626$	−0.450802	−	11.1865i	−0.0180177	−	0.447104i
$627$	−1.27119	−	31.5442i	−0.0507663	−	1.25975i
$628$	−32.0971	−	39.3118i	−1.28081	−	1.56871i
$629$	17.1248	−	45.1544i	0.682811	−	1.80042i
$630$	0.808891	+	1.70470i	0.0322270	+	0.0679170i
$631$	6.61424	−	22.8350i	0.263309	−	0.909048i	−0.714515	−	0.699620i	$-0.753353\pi$
$631$	6.61424	−	22.8350i	0.263309	−	0.909048i	0.977824	−	0.209428i	$-0.0671602\pi$
$632$	5.79682	−	8.39814i	0.230585	−	0.334060i
$633$	13.9098	+	5.92639i	0.552863	+	0.235553i
$634$	22.8284	−	3.70998i	0.906632	−	0.147342i
$635$	9.52227	+	6.02152i	0.377880	+	0.238957i
$636$	22.1772	+	32.1293i	0.879385	+	1.27401i
$637$	−23.7742	+	6.37234i	−0.941969	+	0.252481i
$638$	−35.3211	+	51.1715i	−1.39838	+	2.02590i
$639$	−2.63839	+	1.12411i	−0.104373	+	0.0444692i
$640$	8.78804	+	30.3398i	0.347378	+	1.19929i
$641$	−36.3222	+	2.93223i	−1.43464	+	0.115816i	−0.773191	−	0.634173i	$-0.781341\pi$
$641$	−36.3222	+	2.93223i	−1.43464	+	0.115816i	−0.661450	+	0.749989i	$0.730059\pi$
$642$	−3.49697	+	3.09804i	−0.138014	+	0.122270i
$643$	−25.7573	+	16.2879i	−1.01577	+	0.642334i	−0.935091	−	0.354407i	$-0.884683\pi$
$643$	−25.7573	+	16.2879i	−1.01577	+	0.642334i	−0.0806778	+	0.996740i	$0.525708\pi$
$644$	12.0722	+	5.14350i	0.475713	+	0.202682i
$645$	0.0645606	−	0.531704i	0.00254207	−	0.0209358i
$646$	−20.3161	−	99.5150i	−0.799327	−	3.91536i
$647$	−27.2324	−	2.19842i	−1.07061	−	0.0864289i	−0.467430	−	0.884030i	$-0.654820\pi$
$647$	−27.2324	−	2.19842i	−1.07061	−	0.0864289i	−0.603185	+	0.797601i	$0.706102\pi$
$648$	4.37204	−	3.28538i	0.171750	−	0.129062i
$649$	−3.07395	+	25.3163i	−0.120663	+	0.993752i
$650$	−14.6331	+	3.92219i	−0.573957	+	0.153841i
$651$	0.315217	+	2.59604i	0.0123543	+	0.101747i
$652$	44.3837	+	46.2083i	1.73820	+	1.80966i
$653$	21.9273	+	37.9793i	0.858083	+	1.48624i	0.873755	+	0.486366i	$0.161678\pi$
$653$	21.9273	+	37.9793i	0.858083	+	1.48624i	−0.0156725	+	0.999877i	$0.504989\pi$
$654$	−11.0258	+	19.0972i	−0.431141	+	0.746759i
$655$	−0.915994	+	0.225772i	−0.0357909	+	0.00882166i
$656$	17.7045	+	21.6841i	0.691244	+	0.846620i
$657$	5.98157	−	10.3604i	0.233363	−	0.404197i
$658$	1.30978	+	3.45361i	0.0510606	+	0.134636i
$659$	−1.58778	+	1.65306i	−0.0618512	+	0.0643939i	−0.751409	−	0.659837i	$-0.770625\pi$
$659$	−1.58778	+	1.65306i	−0.0618512	+	0.0643939i	0.689558	+	0.724231i	$0.257805\pi$
$660$	30.0075	+	10.0180i	1.16804	+	0.389950i
$661$	−6.94545	−	23.9785i	−0.270147	−	0.932655i	−0.974796	−	0.223099i	$-0.928383\pi$
$661$	−6.94545	−	23.9785i	−0.270147	−	0.932655i	0.704649	−	0.709556i	$-0.251104\pi$
$662$	30.9852	−	27.4505i	1.20427	−	1.06689i
$663$	8.62473	+	17.2660i	0.334957	+	0.670556i
$664$	−52.7627	−	46.7437i	−2.04759	−	1.81401i
$665$	−2.47673	+	5.21960i	−0.0960435	+	0.202407i
$666$	15.5574	+	16.1970i	0.602836	+	0.627619i
$667$	19.4078	+	40.9012i	0.751475	+	1.58370i
$668$	22.8474	+	5.63139i	0.883994	+	0.217885i
$669$	−3.77299	+	3.92810i	−0.145872	+	0.151869i
$670$	41.5256	+	31.2044i	1.60427	+	1.20553i
$671$	−17.9515	−	15.9037i	−0.693010	−	0.613954i
$672$	−0.845665	−	0.137434i	−0.0326222	−	0.00530163i
$673$	22.3927	+	14.1603i	0.863173	+	0.545838i	0.891118	−	0.453772i	$-0.149922\pi$
$673$	22.3927	+	14.1603i	0.863173	+	0.545838i	−0.0279446	+	0.999609i	$0.508896\pi$
$674$	−80.9257	−	6.53299i	−3.11714	−	0.251642i
$675$	−1.68789			−0.0649667
$676$	−52.4031	+	15.1879i	−2.01550	+	0.584149i
$677$	18.5746			0.713879			0.356940	−	0.934127i	$-0.383820\pi$
$677$	18.5746			0.713879			0.356940	+	0.934127i	$0.383820\pi$
$678$	−42.1988	−	3.40664i	−1.62064	−	0.130831i
$679$	−3.70859	−	2.34517i	−0.142323	−	0.0899993i
$680$	52.5873	+	8.54627i	2.01663	+	0.327734i
$681$	22.4954	+	19.9292i	0.862026	+	0.763688i
$682$	51.7554	+	38.8916i	1.98182	+	1.48924i
$683$	−13.4843	+	14.0387i	−0.515964	+	0.537175i	−0.927305	−	0.374306i	$-0.877881\pi$
$683$	−13.4843	+	14.0387i	−0.515964	+	0.537175i	0.411342	+	0.911481i	$0.365060\pi$
$684$	31.0597	+	7.65553i	1.18760	+	0.292717i
$685$	1.69752	+	3.57744i	0.0648587	+	0.136687i
$686$	9.93037	+	10.3386i	0.379143	+	0.394730i
$687$	7.84059	−	16.5237i	0.299137	−	0.630418i
$688$	1.14994	+	1.01876i	0.0438412	+	0.0388399i
$689$	0.672684	−	33.5325i	0.0256272	−	1.27749i
$690$	25.4575	−	22.5533i	0.969149	−	0.858591i
$691$	−5.21666	−	18.0100i	−0.198451	−	0.685133i	−0.996579	−	0.0826447i	$-0.973663\pi$
$691$	−5.21666	−	18.0100i	−0.198451	−	0.685133i	0.798128	−	0.602488i	$-0.205824\pi$
$692$	43.7031	+	14.5902i	1.66134	+	0.554638i
$693$	1.19498	−	1.24410i	0.0453935	−	0.0472596i
$694$	5.30163	+	13.9793i	0.201247	+	0.530645i
$695$	−6.45697	+	11.1838i	−0.244927	+	0.424226i
$696$	−20.8581	−	25.5465i	−0.790623	−	0.968337i
$697$	−27.8716	+	6.86974i	−1.05571	+	0.260210i
$698$	22.0527	−	38.1964i	0.834708	−	1.44576i
$699$	−9.34867	−	16.1924i	−0.353599	−	0.612452i
$700$	2.04379	+	2.12781i	0.0772480	+	0.0804236i
$701$	−2.94668	−	24.2681i	−0.111295	−	0.916594i	−0.936235	−	0.351374i	$-0.885715\pi$
$701$	−2.94668	−	24.2681i	−0.111295	−	0.916594i	0.824941	−	0.565219i	$-0.191209\pi$
$702$	−8.97367	+	0.181462i	−0.338689	+	0.00684884i
$703$	−8.28866	+	68.2632i	−0.312613	+	2.57460i
$704$	17.6137	−	13.2358i	0.663840	−	0.498843i
$705$	6.46256	+	0.521712i	0.243394	+	0.0196488i
$706$	−12.0908	−	59.2248i	−0.455044	−	2.22895i
$707$	−0.423537	+	3.48814i	−0.0159288	+	0.131185i
$708$	−23.7733	−	10.1289i	−0.893455	−	0.380666i
$709$	−1.68462	+	1.06529i	−0.0632673	+	0.0400078i	−0.565725	−	0.824594i	$-0.691404\pi$
$709$	−1.68462	+	1.06529i	−0.0632673	+	0.0400078i	0.502458	+	0.864602i	$0.332429\pi$
$710$	9.72520	−	8.61577i	0.364980	−	0.323344i
$711$	−1.85988	+	0.150145i	−0.0697508	+	0.00563087i
$712$	−3.47670	−	12.0030i	−0.130295	−	0.449831i
$713$	43.3652	−	18.4762i	1.62404	−	0.691938i
$714$	3.15269	−	4.56746i	0.117986	−	0.170933i
$715$	−15.8880	−	22.0505i	−0.594177	−	0.824640i
$716$	−46.5443	−	67.4311i	−1.73944	−	2.52002i
$717$	1.81086	+	1.14512i	0.0676279	+	0.0427653i
$718$	15.8309	−	2.57277i	0.590803	−	0.0960149i
$719$	0.407666	+	0.173690i	0.0152034	+	0.00647755i	0.399555	−	0.916709i	$-0.369165\pi$
$719$	0.407666	+	0.173690i	0.0152034	+	0.00647755i	−0.384352	+	0.923187i	$0.625575\pi$
$720$	−5.39677	+	7.81857i	−0.201126	+	0.291381i
$721$	0.0572273	−	0.197571i	0.00213125	−	0.00735794i
$722$	41.7228	+	87.9290i	1.55276	+	3.27238i
$723$	−1.09440	+	2.88568i	−0.0407010	+	0.107320i
$724$	12.4667	+	15.2690i	0.463323	+	0.567468i
$725$	0.409859	+	10.1706i	0.0152218	+	0.377725i
$726$	−0.616953	−	15.3095i	−0.0228973	−	0.568190i
$727$	−27.5472	+	6.78978i	−1.02167	+	0.251819i	−0.714351	−	0.699788i	$-0.753278\pi$
$727$	−27.5472	+	6.78978i	−1.02167	+	0.251819i	−0.307319	+	0.951607i	$0.599432\pi$
$728$	5.80755	+	5.80661i	0.215242	+	0.215207i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−10.8410	+	53.1029i	−0.401245	+	1.96543i
$731$	−1.44932	+	0.617500i	−0.0536052	+	0.0228390i
$732$	20.5395	−	12.9884i	0.759163	−	0.480065i
$733$	7.60504	−	3.99143i	0.280899	−	0.147427i	−0.318390	−	0.947960i	$-0.603142\pi$
$733$	7.60504	−	3.99143i	0.280899	−	0.147427i	0.599289	+	0.800533i	$0.295450\pi$
$734$	−50.0134	−	8.12797i	−1.84603	−	0.300009i
$735$	11.7844	−	3.93421i	0.434674	−	0.145115i
$736$	1.86145	+	15.3304i	0.0686139	+	0.565087i
$737$	13.2120	−	45.6130i	0.486670	−	1.68018i
$738$	2.67024	−	13.0797i	0.0982929	−	0.481470i
$739$	−29.6243	−	9.89005i	−1.08975	−	0.363811i	−0.285665	−	0.958329i	$-0.592215\pi$
$739$	−29.6243	−	9.89005i	−1.08975	−	0.363811i	−0.804082	+	0.594518i	$0.797343\pi$
$740$	−61.0150	−	32.0232i	−2.24296	−	1.17720i
$741$	−17.8077	−	20.9319i	−0.654181	−	0.768953i
$742$	−8.53965	+	4.48195i	−0.313500	+	0.164538i
$743$	−40.5802	+	6.59492i	−1.48874	+	0.241944i	−0.849716	−	0.527241i	$-0.823227\pi$
$743$	−40.5802	+	6.59492i	−1.48874	+	0.241944i	−0.639026	+	0.769185i	$0.720663\pi$
$744$	−27.4517	+	20.6286i	−1.00643	+	0.756283i
$745$	0.738546	−	18.3268i	0.0270582	−	0.671443i
$746$	40.3730			1.47816
$747$	−0.519003	+	12.8789i	−0.0189893	+	0.471215i
$748$	−18.6124	−	91.1694i	−0.680535	−	3.33348i
$749$	−0.444026	−	0.643283i	−0.0162244	−	0.0235051i
$750$	28.7397	−	9.59473i	1.04943	−	0.350350i
$751$	20.4832	−	43.1673i	0.747441	−	1.57520i	−0.0688963	−	0.997624i	$-0.521948\pi$
$751$	20.4832	−	43.1673i	0.747441	−	1.57520i	0.816338	−	0.577575i	$-0.196001\pi$
$752$	−11.7617	+	14.4054i	−0.428904	+	0.525312i
$753$	−0.995022	−	2.62366i	−0.0362606	−	0.0956113i
$754$	3.27244	+	54.0279i	0.119175	+	1.96758i
$755$	−3.13456	+	8.26515i	−0.114078	+	0.300799i
$756$	0.873982	+	1.51378i	0.0317864	+	0.0550557i
$757$	6.94217	−	8.50261i	0.252317	−	0.309033i	−0.632879	−	0.774251i	$-0.718127\pi$
$757$	6.94217	−	8.50261i	0.252317	−	0.309033i	0.885196	+	0.465218i	$0.154024\pi$
$758$	−42.9398	−	32.2672i	−1.55964	−	1.17200i
$759$	−27.5321	−	14.4500i	−0.999352	−	0.524500i
$760$	−75.6162	+	6.10437i	−2.74289	+	0.221429i
$761$	21.0164	−	1.69662i	0.761845	−	0.0615025i	0.306564	−	0.951850i	$-0.400821\pi$
$761$	21.0164	−	1.69662i	0.761845	−	0.0615025i	0.455281	+	0.890348i	$0.349539\pi$
$762$	13.6454	+	7.16168i	0.494322	+	0.259440i
$763$	−2.94946	−	2.21638i	−0.106778	−	0.0802383i
$764$	36.5192	−	44.7280i	1.32122	−	1.61820i
$765$	−4.87096	−	8.43675i	−0.176110	−	0.305031i
$766$	6.50889	−	17.1625i	0.235176	−	0.620108i
$767$	11.4865	+	18.9975i	0.414752	+	0.685960i
$768$	11.5484	+	30.4506i	0.416716	+	1.09879i
$769$	−11.7808	+	14.4288i	−0.424826	+	0.520318i	−0.942023	−

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.48128 - 0.200310i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(4.14255 + 0.673230i) q^{4} +(1.36223 + 1.20683i) q^{5} +(1.99010 + 1.49546i) q^{6} +(-0.288513 + 0.300373i) q^{7} +(-5.30995 - 1.30878i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-3.13834 - 3.26736i) q^{10} +(-1.77558 + 3.74196i) q^{11} +(-3.14142 - 2.78306i) q^{12} +(0.792477 + 3.51738i) q^{13} +(0.776050 - 0.687520i) q^{14} +(-0.506334 - 1.74807i) q^{15} +(4.95150 + 1.65305i) q^{16} +(-3.70811 + 3.86055i) q^{17} +(-0.882738 - 2.32759i) q^{18} +(3.81106 - 6.60095i) q^{19} +(4.83063 + 5.91645i) q^{20} +(0.404387 - 0.0996725i) q^{21} +(5.15528 - 8.92921i) q^{22} +(-3.75359 - 6.50141i) q^{23} +(3.78841 + 3.94416i) q^{24} +(-0.203452 - 1.67558i) q^{25} +(-1.26180 - 8.88637i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-1.39740 + 1.05008i) q^{28} +(-6.01096 - 0.485255i) q^{29} +(0.906203 + 4.43888i) q^{30} +(-0.756841 + 6.23315i) q^{31} +(-1.89249 - 0.806313i) q^{32} +(3.50066 - 2.21368i) q^{33} +(9.97418 - 8.83635i) q^{34} +(-0.755521 + 0.0609919i) q^{35} +(1.16765 + 4.03120i) q^{36} +(-8.29979 + 3.53621i) q^{37} +(-10.7786 + 15.6154i) q^{38} +(1.21013 - 3.39641i) q^{39} +(-5.65389 - 8.19107i) q^{40} +(4.53244 + 2.86614i) q^{41} +(-1.02337 + 0.166313i) q^{42} +(0.270753 + 0.115357i) q^{43} +(-9.87464 + 14.3059i) q^{44} +(-0.506334 + 1.74807i) q^{45} +(8.01143 + 16.8837i) q^{46} +(-1.26330 + 3.33106i) q^{47} +(-3.30146 - 4.04355i) q^{48} +(0.274877 + 6.82100i) q^{49} +(0.169187 + 4.19834i) q^{50} +(5.19739 - 1.28104i) q^{51} +(0.914870 + 15.1044i) q^{52} +(-9.03181 - 2.22614i) q^{53} +(-0.497935 + 2.43905i) q^{54} +(-6.93467 + 2.95459i) q^{55} +(1.92511 - 1.21737i) q^{56} +(-6.74905 + 3.54218i) q^{57} +(14.8177 + 2.40811i) q^{58} +(5.84033 - 1.94979i) q^{59} +(-0.920662 - 7.58233i) q^{60} +(-1.61099 + 5.56177i) q^{61} +(3.12650 - 15.3146i) q^{62} +(-0.395056 - 0.131889i) q^{63} +(-4.71014 - 2.47207i) q^{64} +(-3.16535 + 5.74787i) q^{65} +(-9.12955 + 4.79156i) q^{66} +(-11.3169 + 1.83918i) q^{67} +(-17.9601 + 13.4961i) q^{68} +(-0.302284 + 7.50110i) q^{69} +1.88688 q^{70} +(-0.115478 + 2.86555i) q^{71} +(-1.09391 - 5.35834i) q^{72} +(-6.79584 - 9.84547i) q^{73} +(21.3025 - 7.11181i) q^{74} +(-0.723584 + 1.52492i) q^{75} +(20.2315 - 24.7790i) q^{76} +(-0.611708 - 1.61294i) q^{77} +(-3.68300 + 8.18506i) q^{78} +(-0.661667 + 1.74467i) q^{79} +(4.75013 + 8.22747i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-10.6721 - 8.01960i) q^{82} +(11.4130 + 5.98999i) q^{83} +(1.74230 - 0.140653i) q^{84} +(-9.71033 + 0.783899i) q^{85} +(-0.648709 - 0.340469i) q^{86} +(4.82105 + 3.62278i) q^{87} +(14.3257 - 17.5458i) q^{88} +(1.14250 + 1.97887i) q^{89} +(1.60651 - 4.23603i) q^{90} +(-1.28517 - 0.776770i) q^{91} +(-11.1725 - 29.4595i) q^{92} +(3.97108 - 4.86369i) q^{93} +(3.80186 - 8.01225i) q^{94} +(13.1578 - 4.39271i) q^{95} +(1.16856 + 1.69296i) q^{96} +(2.10735 + 10.3225i) q^{97} +(0.684267 - 16.9799i) q^{98} -4.14186 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

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