LMFDB - Embedded newform 416.2.bd.a.83.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

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

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.1
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41400 - 0.0247176i) q^{2} +(1.03934 + 0.430508i) q^{3} +(1.99878 + 0.0699014i) q^{4} +(-0.387075 + 0.934483i) q^{5} +(-1.45898 - 0.634427i) q^{6} -4.00321i q^{7} +(-2.82454 - 0.148245i) q^{8} +(-1.22643 - 1.22643i) q^{9} +O(q^{10})$	\(q+(-1.41400 - 0.0247176i) q^{2} +(1.03934 + 0.430508i) q^{3} +(1.99878 + 0.0699014i) q^{4} +(-0.387075 + 0.934483i) q^{5} +(-1.45898 - 0.634427i) q^{6} -4.00321i q^{7} +(-2.82454 - 0.148245i) q^{8} +(-1.22643 - 1.22643i) q^{9} +(0.570422 - 1.31179i) q^{10} +(-5.03511 - 2.08561i) q^{11} +(2.04731 + 0.933141i) q^{12} +(-3.26904 - 1.52098i) q^{13} +(-0.0989499 + 5.66053i) q^{14} +(-0.804604 + 0.804604i) q^{15} +(3.99023 + 0.279435i) q^{16} -1.31652 q^{17} +(1.70386 + 1.76449i) q^{18} +(-1.63531 - 3.94798i) q^{19} +(-0.838999 + 1.84077i) q^{20} +(1.72341 - 4.16069i) q^{21} +(7.06808 + 3.07350i) q^{22} +(2.48957 + 2.48957i) q^{23} +(-2.87183 - 1.37006i) q^{24} +(2.81210 + 2.81210i) q^{25} +(4.58482 + 2.23147i) q^{26} +(-2.03821 - 4.92068i) q^{27} +(0.279830 - 8.00152i) q^{28} +(-0.417444 + 1.00780i) q^{29} +(1.15760 - 1.11782i) q^{30} +(4.10888 + 4.10888i) q^{31} +(-5.63527 - 0.493749i) q^{32} +(-4.33531 - 4.33531i) q^{33} +(1.86155 + 0.0325412i) q^{34} +(3.74093 + 1.54954i) q^{35} +(-2.36564 - 2.53710i) q^{36} +(-1.34477 - 0.557021i) q^{37} +(2.21473 + 5.62285i) q^{38} +(-2.74284 - 2.98816i) q^{39} +(1.23184 - 2.58210i) q^{40} +0.321682 q^{41} +(-2.53974 + 5.84060i) q^{42} +(-2.08238 - 5.02730i) q^{43} +(-9.91827 - 4.52063i) q^{44} +(1.62080 - 0.671359i) q^{45} +(-3.45871 - 3.58178i) q^{46} +(6.70557 + 6.70557i) q^{47} +(4.02690 + 2.00825i) q^{48} -9.02567 q^{49} +(-3.90680 - 4.04582i) q^{50} +(-1.36831 - 0.566771i) q^{51} +(-6.42776 - 3.26862i) q^{52} +(-3.64238 - 8.79347i) q^{53} +(2.76040 + 7.00821i) q^{54} +(3.89793 - 3.89793i) q^{55} +(-0.593457 + 11.3072i) q^{56} -4.80730i q^{57} +(0.615176 - 1.41471i) q^{58} +(2.38670 - 5.76200i) q^{59} +(-1.66447 + 1.55198i) q^{60} +(-1.26927 + 3.06430i) q^{61} +(-5.70839 - 5.91151i) q^{62} +(-4.90967 + 4.90967i) q^{63} +(7.95605 + 0.837450i) q^{64} +(2.68670 - 2.46612i) q^{65} +(6.02295 + 6.23727i) q^{66} +(8.05384 - 3.33601i) q^{67} +(-2.63143 - 0.0920264i) q^{68} +(1.51572 + 3.65928i) q^{69} +(-5.25136 - 2.28352i) q^{70} +8.00373 q^{71} +(3.28230 + 3.64593i) q^{72} -10.6425i q^{73} +(1.88773 + 0.820866i) q^{74} +(1.71209 + 4.13336i) q^{75} +(-2.99265 - 8.00544i) q^{76} +(-8.34913 + 20.1566i) q^{77} +(3.80451 + 4.29305i) q^{78} +0.399083 q^{79} +(-1.80565 + 3.62064i) q^{80} -0.788397i q^{81} +(-0.454858 - 0.00795122i) q^{82} +(-1.49038 - 3.59810i) q^{83} +(3.73556 - 8.19582i) q^{84} +(0.509592 - 1.23026i) q^{85} +(2.82021 + 7.16007i) q^{86} +(-0.867731 + 0.867731i) q^{87} +(13.9127 + 6.63732i) q^{88} -8.13354 q^{89} +(-2.30841 + 0.909238i) q^{90} +(-6.08881 + 13.0866i) q^{91} +(4.80207 + 5.15012i) q^{92} +(2.50161 + 6.03942i) q^{93} +(-9.31592 - 9.64741i) q^{94} +4.32230 q^{95} +(-5.64438 - 2.93920i) q^{96} +(-7.10314 + 7.10314i) q^{97} +(12.7623 + 0.223093i) q^{98} +(3.61736 + 8.73309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.41400	−	0.0247176i	−0.999847	−	0.0174780i
$2$	−1.41400	−	0.0247176i	−0.999847	−	0.0174780i
$3$	1.03934	+	0.430508i	0.600062	+	0.248554i	0.661973	−	0.749528i	$-0.269719\pi$
$3$	1.03934	+	0.430508i	0.600062	+	0.248554i	−0.0619108	+	0.998082i	$0.519719\pi$
$4$	1.99878	+	0.0699014i	0.999389	+	0.0349507i
$5$	−0.387075	+	0.934483i	−0.173105	+	0.417913i	−0.986492	−	0.163810i	$-0.947622\pi$
$5$	−0.387075	+	0.934483i	−0.173105	+	0.417913i	0.813386	+	0.581724i	$0.197622\pi$
$6$	−1.45898	−	0.634427i	−0.595626	−	0.259004i
$7$		−	4.00321i		−	1.51307i	−0.653953	−	0.756535i	$-0.726891\pi$
$7$		−	4.00321i		−	1.51307i	0.653953	−	0.756535i	$-0.273109\pi$
$8$	−2.82454	−	0.148245i	−0.998626	−	0.0524127i
$9$	−1.22643	−	1.22643i	−0.408811	−	0.408811i
$10$	0.570422	−	1.31179i	0.180383	−	0.414824i
$11$	−5.03511	−	2.08561i	−1.51814	−	0.628835i	−0.540924	−	0.841072i	$-0.681925\pi$
$11$	−5.03511	−	2.08561i	−1.51814	−	0.628835i	−0.977218	+	0.212237i	$0.931925\pi$
$12$	2.04731	+	0.933141i	0.591008	+	0.269375i
$13$	−3.26904	−	1.52098i	−0.906668	−	0.421845i
$13$	−3.26904	−	1.52098i	−0.906668	−	0.421845i
$14$	−0.0989499	+	5.66053i	−0.0264455	+	1.51284i
$15$	−0.804604	+	0.804604i	−0.207748	+	0.207748i
$16$	3.99023	+	0.279435i	0.997557	+	0.0698587i
$17$	−1.31652			−0.319303			−0.159651	−	0.987173i	$-0.551037\pi$
$17$	−1.31652			−0.319303			−0.159651	+	0.987173i	$0.551037\pi$
$18$	1.70386	+	1.76449i	0.401604	+	0.415894i
$19$	−1.63531	−	3.94798i	−0.375165	−	0.905728i	−0.992857	−	0.119309i	$-0.961932\pi$
$19$	−1.63531	−	3.94798i	−0.375165	−	0.905728i	0.617692	−	0.786420i	$-0.288068\pi$
$20$	−0.838999	+	1.84077i	−0.187606	+	0.411608i
$21$	1.72341	−	4.16069i	0.376079	−	0.907936i
$22$	7.06808	+	3.07350i	1.50692	+	0.655273i
$23$	2.48957	+	2.48957i	0.519111	+	0.519111i	0.917302	−	0.398192i	$-0.130362\pi$
$23$	2.48957	+	2.48957i	0.519111	+	0.519111i	−0.398192	+	0.917302i	$0.630362\pi$
$24$	−2.87183	−	1.37006i	−0.586210	−	0.279663i
$25$	2.81210	+	2.81210i	0.562421	+	0.562421i
$26$	4.58482	+	2.23147i	0.899156	+	0.437627i
$27$	−2.03821	−	4.92068i	−0.392254	−	0.946986i
$28$	0.279830	−	8.00152i	0.0528828	−	1.51215i
$29$	−0.417444	+	1.00780i	−0.0775175	+	0.187144i	−0.957888	−	0.287144i	$-0.907294\pi$
$29$	−0.417444	+	1.00780i	−0.0775175	+	0.187144i	0.880370	+	0.474287i	$0.157294\pi$
$30$	1.15760	−	1.11782i	0.211347	−	0.204085i
$31$	4.10888	+	4.10888i	0.737977	+	0.737977i	0.972186	−	0.234209i	$-0.0752501\pi$
$31$	4.10888	+	4.10888i	0.737977	+	0.737977i	−0.234209	+	0.972186i	$0.575250\pi$
$32$	−5.63527	−	0.493749i	−0.996184	−	0.0872833i
$33$	−4.33531	−	4.33531i	−0.754680	−	0.754680i
$34$	1.86155	+	0.0325412i	0.319254	+	0.00558077i
$35$	3.74093	+	1.54954i	0.632332	+	0.261921i
$36$	−2.36564	−	2.53710i	−0.394273	−	0.422850i
$37$	−1.34477	−	0.557021i	−0.221078	−	0.0915737i	0.269395	−	0.963030i	$-0.413176\pi$
$37$	−1.34477	−	0.557021i	−0.221078	−	0.0915737i	−0.490474	+	0.871456i	$0.663176\pi$
$38$	2.21473	+	5.62285i	0.359277	+	0.912147i
$39$	−2.74284	−	2.98816i	−0.439206	−	0.478489i
$40$	1.23184	−	2.58210i	0.194771	−	0.408266i
$41$	0.321682			0.0502383			0.0251192	−	0.999684i	$-0.492003\pi$
$41$	0.321682			0.0502383			0.0251192	+	0.999684i	$0.492003\pi$
$42$	−2.53974	+	5.84060i	−0.391891	+	0.901224i
$43$	−2.08238	−	5.02730i	−0.317560	−	0.766657i	−0.999382	−	0.0351393i	$-0.988813\pi$
$43$	−2.08238	−	5.02730i	−0.317560	−	0.766657i	0.681823	−	0.731517i	$-0.261187\pi$
$44$	−9.91827	−	4.52063i	−1.49524	−	0.681511i
$45$	1.62080	−	0.671359i	0.241615	−	0.100080i
$46$	−3.45871	−	3.58178i	−0.509958	−	0.528104i
$47$	6.70557	+	6.70557i	0.978108	+	0.978108i	0.999765	−	0.0216571i	$-0.00689422\pi$
$47$	6.70557	+	6.70557i	0.978108	+	0.978108i	−0.0216571	+	0.999765i	$0.506894\pi$
$48$	4.02690	+	2.00825i	0.581232	+	0.289866i
$49$	−9.02567			−1.28938
$50$	−3.90680	−	4.04582i	−0.552505	−	0.572165i
$51$	−1.36831	−	0.566771i	−0.191601	−	0.0793638i
$52$	−6.42776	−	3.26862i	−0.891370	−	0.453276i
$53$	−3.64238	−	8.79347i	−0.500319	−	1.20788i	−0.949310	−	0.314340i	$-0.898217\pi$
$53$	−3.64238	−	8.79347i	−0.500319	−	1.20788i	0.448992	−	0.893536i	$-0.351783\pi$
$54$	2.76040	+	7.00821i	0.375643	+	0.953697i
$55$	3.89793	−	3.89793i	0.525597	−	0.525597i
$56$	−0.593457	+	11.3072i	−0.0793041	+	1.51099i
$57$		−	4.80730i		−	0.636742i
$58$	0.615176	−	1.41471i	0.0807765	−	0.185760i
$59$	2.38670	−	5.76200i	0.310722	−	0.750148i	−0.688957	−	0.724802i	$-0.741931\pi$
$59$	2.38670	−	5.76200i	0.310722	−	0.750148i	0.999679	−	0.0253461i	$-0.00806879\pi$
$60$	−1.66447	+	1.55198i	−0.214882	+	0.200360i
$61$	−1.26927	+	3.06430i	−0.162514	+	0.392343i	−0.984069	−	0.177785i	$-0.943107\pi$
$61$	−1.26927	+	3.06430i	−0.162514	+	0.392343i	0.821555	+	0.570129i	$0.193107\pi$
$62$	−5.70839	−	5.91151i	−0.724966	−	0.750762i
$63$	−4.90967	+	4.90967i	−0.618560	+	0.618560i
$64$	7.95605	+	0.837450i	0.994506	+	0.104681i
$65$	2.68670	−	2.46612i	0.333244	−	0.305885i
$66$	6.02295	+	6.23727i	0.741374	+	0.767755i
$67$	8.05384	−	3.33601i	0.983933	−	0.407558i	0.168052	−	0.985778i	$-0.446252\pi$
$67$	8.05384	−	3.33601i	0.983933	−	0.407558i	0.815881	+	0.578220i	$0.196252\pi$
$68$	−2.63143	−	0.0920264i	−0.319107	−	0.0111598i
$69$	1.51572	+	3.65928i	0.182472	+	0.440526i
$70$	−5.25136	−	2.28352i	−0.627658	−	0.272933i
$71$	8.00373			0.949868			0.474934	−	0.880022i	$-0.342472\pi$
$71$	8.00373			0.949868			0.474934	+	0.880022i	$0.342472\pi$
$72$	3.28230	+	3.64593i	0.386823	+	0.429676i
$73$		−	10.6425i		−	1.24561i	−0.782376	−	0.622807i	$-0.785992\pi$
$73$		−	10.6425i		−	1.24561i	0.782376	−	0.622807i	$-0.214008\pi$
$74$	1.88773	+	0.820866i	0.219444	+	0.0954237i
$75$	1.71209	+	4.13336i	0.197695	+	0.477279i
$76$	−2.99265	−	8.00544i	−0.343280	−	0.918287i
$77$	−8.34913	+	20.1566i	−0.951472	+	2.29706i
$78$	3.80451	+	4.29305i	0.430776	+	0.486092i
$79$	0.399083			0.0449004			0.0224502	−	0.999748i	$-0.492853\pi$
$79$	0.399083			0.0449004			0.0224502	+	0.999748i	$0.492853\pi$
$80$	−1.80565	+	3.62064i	−0.201877	+	0.404799i
$81$		−	0.788397i		−	0.0875997i
$82$	−0.454858	−	0.00795122i	−0.0502306	−	0.000878066i
$83$	−1.49038	−	3.59810i	−0.163591	−	0.394942i	0.820734	−	0.571311i	$-0.193565\pi$
$83$	−1.49038	−	3.59810i	−0.163591	−	0.394942i	−0.984324	+	0.176368i	$0.943565\pi$
$84$	3.73556	−	8.19582i	0.407583	−	0.894237i
$85$	0.509592	−	1.23026i	0.0552730	−	0.133441i
$86$	2.82021	+	7.16007i	0.304111	+	0.772090i
$87$	−0.867731	+	0.867731i	−0.0930306	+	0.0930306i
$88$	13.9127	+	6.63732i	1.48310	+	0.707540i
$89$	−8.13354			−0.862153			−0.431077	−	0.902315i	$-0.641866\pi$
$89$	−8.13354			−0.862153			−0.431077	+	0.902315i	$0.641866\pi$
$90$	−2.30841	+	0.909238i	−0.243328	+	0.0958421i
$91$	−6.08881	+	13.0866i	−0.638281	+	1.37185i
$92$	4.80207	+	5.15012i	0.500650	+	0.536937i
$93$	2.50161	+	6.03942i	0.259405	+	0.626259i
$94$	−9.31592	−	9.64741i	−0.960864	−	0.995054i
$95$	4.32230			0.443459
$96$	−5.64438	−	2.93920i	−0.576077	−	0.299981i
$97$	−7.10314	+	7.10314i	−0.721214	+	0.721214i	−0.968853	−	0.247638i	$-0.920346\pi$
$97$	−7.10314	+	7.10314i	−0.721214	+	0.721214i	0.247638	+	0.968853i	$0.420346\pi$
$98$	12.7623	+	0.223093i	1.28919	+	0.0225358i
$99$	3.61736	+	8.73309i	0.363559	+	0.877709i
$100$	5.42420	+	5.81734i	0.542420	+	0.581734i
$101$	6.49575	+	15.6821i	0.646351	+	1.56043i	0.817967	+	0.575265i	$0.195101\pi$
$101$	6.49575	+	15.6821i	0.646351	+	1.56043i	−0.171616	+	0.985164i	$0.554899\pi$
$102$	1.92077	+	0.835234i	0.190185	+	0.0827005i
$103$	9.90285	−	9.90285i	0.975756	−	0.975756i	−0.0239566	−	0.999713i	$-0.507626\pi$
$103$	9.90285	−	9.90285i	0.975756	−	0.975756i	0.999713	+	0.0239566i	$0.00762635\pi$
$104$	9.00805	+	4.78070i	0.883312	+	0.468786i
$105$	3.22100	+	3.22100i	0.314337	+	0.314337i
$106$	4.93296	+	12.5240i	0.479131	+	1.21644i
$107$	13.1702	−	5.45527i	1.27321	−	0.527381i	0.359272	−	0.933233i	$-0.383025\pi$
$107$	13.1702	−	5.45527i	1.27321	−	0.527381i	0.913939	+	0.405852i	$0.133025\pi$
$108$	−3.72997	−	9.97783i	−0.358917	−	0.960117i
$109$	−5.08877	+	2.10784i	−0.487415	+	0.201894i	−0.612837	−	0.790210i	$-0.709972\pi$
$109$	−5.08877	+	2.10784i	−0.487415	+	0.201894i	0.125421	+	0.992104i	$0.459972\pi$
$110$	−5.60801	+	5.41532i	−0.534703	+	0.516330i
$111$	−1.15787	−	1.15787i	−0.109900	−	0.109900i
$112$	1.11863	−	15.9737i	0.105701	−	1.50937i
$113$			1.15881i			0.109012i	0.998513	+	0.0545060i	$0.0173584\pi$
$113$			1.15881i			0.109012i	−0.998513	+	0.0545060i	$0.982642\pi$
$114$	−0.118825	+	6.79750i	−0.0111290	+	0.636645i
$115$	−3.29011	+	1.36281i	−0.306804	+	0.127082i
$116$	−0.904825	+	1.98519i	−0.0840109	+	0.184320i
$117$	2.14387	+	5.87465i	0.198201	+	0.543111i
$118$	−3.51721	+	8.08846i	−0.323785	+	0.744603i
$119$			5.27030i			0.483127i
$120$	2.39192	−	2.15336i	0.218351	−	0.196574i
$121$	13.2244	+	13.2244i	1.20221	+	1.20221i
$122$	1.87049	−	4.30154i	0.169346	−	0.389443i
$123$	0.334336	+	0.138487i	0.0301461	+	0.0124869i
$124$	7.92552	+	8.49996i	0.711733	+	0.763319i
$125$	−8.38877	+	3.47474i	−0.750315	+	0.310790i
$126$	7.06362	−	6.82091i	0.629277	−	0.607655i
$127$	−1.79658			−0.159420			−0.0797102	−	0.996818i	$-0.525399\pi$
$127$	−1.79658			−0.159420			−0.0797102	+	0.996818i	$0.525399\pi$
$128$	−11.2291	−	1.38081i	−0.992524	−	0.122047i
$129$		−	6.12155i		−	0.538972i
$130$	−3.85994	+	3.42068i	−0.338539	+	0.300014i
$131$	−18.0536	−	7.47805i	−1.57735	−	0.653360i	−0.589360	−	0.807870i	$-0.700620\pi$
$131$	−18.0536	−	7.47805i	−1.57735	−	0.653360i	−0.987991	+	0.154510i	$0.950620\pi$
$132$	−8.36227	−	8.96836i	−0.727842	−	0.780595i
$133$	−15.8046	+	6.54647i	−1.37043	+	0.567651i
$134$	−11.4706	+	4.51804i	−0.990906	+	0.390299i
$135$	5.38724			0.463659
$136$	3.71856	+	0.195168i	0.318864	+	0.0167355i
$137$		−	13.2194i		−	1.12941i	−0.825292	−	0.564706i	$-0.808989\pi$
$137$		−	13.2194i		−	1.12941i	0.825292	−	0.564706i	$-0.191011\pi$
$138$	−2.05278	−	5.21168i	−0.174744	−	0.443647i
$139$	14.0734	−	5.82937i	1.19369	−	0.494441i	0.304732	−	0.952438i	$-0.401433\pi$
$139$	14.0734	−	5.82937i	1.19369	−	0.494441i	0.888954	+	0.457997i	$0.151433\pi$
$140$	7.36897	+	3.35869i	0.622792	+	0.283861i
$141$	4.08255	+	9.85616i	0.343813	+	0.830038i
$142$	−11.3173	−	0.197833i	−0.949723	−	0.0166018i
$143$	13.2878	+	14.4763i	1.11118	+	1.21057i
$144$	−4.55104	−	5.23646i	−0.379254	−	0.436372i
$145$	−0.780189	−	0.780189i	−0.0647912	−	0.0647912i
$146$	−0.263058	+	15.0485i	−0.0217708	+	1.24542i
$147$	−9.38072	−	3.88562i	−0.773709	−	0.320481i
$148$	−2.64896	−	1.20736i	−0.217743	−	0.0992446i
$149$	1.05215	+	0.435816i	0.0861957	+	0.0357034i	0.425365	−	0.905022i	$-0.360146\pi$
$149$	1.05215	+	0.435816i	0.0861957	+	0.0357034i	−0.339169	+	0.940725i	$0.610146\pi$
$150$	−2.31873	−	5.88688i	−0.189323	−	0.480661i
$151$	−17.9914			−1.46412			−0.732058	−	0.681242i	$-0.761440\pi$
$151$	−17.9914			−1.46412			−0.732058	+	0.681242i	$0.761440\pi$
$152$	4.03372	+	11.3936i	0.327178	+	0.924147i
$153$	1.61462	+	1.61462i	0.130535	+	0.130535i
$154$	12.3039	−	28.2950i	0.991474	−	2.28007i
$155$	−5.43012	+	2.24923i	−0.436158	+	0.180663i
$156$	−5.27345	−	6.16440i	−0.422214	−	0.493547i
$157$	5.83646	−	14.0905i	0.465800	−	1.12454i	−0.500179	−	0.865922i	$-0.666732\pi$
$157$	5.83646	−	14.0905i	0.465800	−	1.12454i	0.965979	−	0.258619i	$-0.0832675\pi$
$158$	−0.564303	−	0.00986440i	−0.0448935	−	0.000784769i
$159$		−	10.7075i		−	0.849157i
$160$	2.64267	−	5.07494i	0.208922	−	0.401209i
$161$	9.96626	−	9.96626i	0.785451	−	0.785451i
$162$	−0.0194873	+	1.11479i	−0.00153107	+	0.0875863i
$163$	0.476411	+	1.15016i	0.0373154	+	0.0900873i	0.941439	−	0.337185i	$-0.109475\pi$
$163$	0.476411	+	1.15016i	0.0373154	+	0.0900873i	−0.904123	+	0.427272i	$0.859475\pi$
$164$	0.642971	+	0.0224860i	0.0502076	+	0.00175586i
$165$	5.72936	−	2.37318i	0.446030	−	0.184752i
$166$	2.01846	+	5.12454i	0.156663	+	0.397741i
$167$		−	0.981684i		−	0.0759650i	−0.999278	−	0.0379825i	$-0.987907\pi$
$167$		−	0.981684i		−	0.0759650i	0.999278	−	0.0379825i	$-0.0120931\pi$
$168$	−5.48465	+	11.4965i	−0.423150	+	0.886977i
$169$	8.37322	+	9.94431i	0.644094	+	0.764947i
$170$	−0.750971	+	1.72699i	−0.0575968	+	0.132454i
$171$	−2.83634	+	6.84753i	−0.216900	+	0.523644i
$172$	−3.81079	−	10.1940i	−0.290570	−	0.777287i
$173$	3.76378	−	9.08658i	0.286155	−	0.690840i	−0.713800	−	0.700350i	$-0.753027\pi$
$173$	3.76378	−	9.08658i	0.286155	−	0.690840i	0.999955	+	0.00951042i	$0.00302730\pi$
$174$	1.24842	−	1.20552i	0.0946423	−	0.0913904i
$175$	11.2574	−	11.2574i	0.850982	−	0.850982i
$176$	−19.5084	−	9.72904i	−1.47050	−	0.733354i
$177$	4.96117	−	4.96117i	0.372904	−	0.372904i
$178$	11.5008	+	0.201042i	0.862021	+	0.0150687i
$179$	−13.9701	−	5.78662i	−1.04418	−	0.432512i	−0.206367	−	0.978475i	$-0.566164\pi$
$179$	−13.9701	−	5.78662i	−1.04418	−	0.432512i	−0.837809	+	0.545963i	$0.816164\pi$
$180$	3.28656	−	1.22860i	0.244966	−	0.0915745i
$181$	−15.1205	+	6.26312i	−1.12390	+	0.465534i	−0.865703	−	0.500558i	$-0.833128\pi$
$181$	−15.1205	+	6.26312i	−1.12390	+	0.465534i	−0.258196	+	0.966093i	$0.583128\pi$
$182$	8.93304	−	18.3540i	0.662161	−	1.36049i
$183$	−2.63841	+	2.63841i	−0.195037	+	0.195037i
$184$	−6.66282	−	7.40095i	−0.491189	−	0.545605i
$185$	1.04105	−	1.04105i	0.0765397	−	0.0765397i
$186$	−3.38799	−	8.60156i	−0.248419	−	0.630697i
$187$	6.62881	+	2.74574i	0.484746	+	0.200789i
$188$	12.9342	+	13.8717i	0.943325	+	1.01170i
$189$	−19.6985	+	8.15939i	−1.43286	+	0.593508i
$190$	−6.11173	−	0.106837i	−0.443391	−	0.00775078i
$191$		−	8.25717i		−	0.597468i	−0.954336	−	0.298734i	$-0.903436\pi$
$191$		−	8.25717i		−	0.597468i	0.954336	−	0.298734i	$-0.0965644\pi$
$192$	7.90849	+	4.29553i	0.570746	+	0.310003i
$193$	−12.6912	−	12.6912i	−0.913531	−	0.913531i	0.0830171	−	0.996548i	$-0.473544\pi$
$193$	−12.6912	−	12.6912i	−0.913531	−	0.913531i	−0.996548	+	0.0830171i	$0.973544\pi$
$194$	10.2194	−	9.86825i	0.733710	−	0.708499i
$195$	3.85407	−	1.40649i	0.275996	−	0.100721i
$196$	−18.0403	−	0.630907i	−1.28859	−	0.0450648i
$197$	4.96803	−	11.9939i	0.353958	−	0.854530i	−0.642166	−	0.766566i	$-0.721964\pi$
$197$	4.96803	−	11.9939i	0.353958	−	0.854530i	0.996124	−	0.0879640i	$-0.0280361\pi$
$198$	−4.89908	−	12.4380i	−0.348163	−	0.883929i
$199$	17.9928	−	17.9928i	1.27548	−	1.27548i	0.332307	−	0.943171i	$-0.392173\pi$
$199$	17.9928	−	17.9928i	1.27548	−	1.27548i	0.943171	−	0.332307i	$-0.107827\pi$
$200$	−7.52602	−	8.35978i	−0.532170	−	0.591126i
$201$	9.80684			0.691721
$202$	−8.79735	−	22.3350i	−0.618979	−	1.57149i
$203$	4.03443	+	1.67112i	0.283162	+	0.117289i
$204$	−2.69532	−	1.22850i	−0.188710	−	0.0860120i
$205$	−0.124515	+	0.300606i	−0.00869652	+	0.0209953i
$206$	−14.2474	+	13.7578i	−0.992662	+	0.958553i
$207$		−	6.10658i		−	0.424437i
$208$	−12.6192	−	6.98255i	−0.874983	−	0.484153i
$209$			23.2891i			1.61094i
$210$	−4.47487	−	4.63410i	−0.308795	−	0.319783i
$211$	−9.28690	+	22.4205i	−0.639336	+	1.54349i	0.188229	+	0.982125i	$0.439725\pi$
$211$	−9.28690	+	22.4205i	−0.639336	+	1.54349i	−0.827565	+	0.561369i	$0.810275\pi$
$212$	−6.66563	−	17.8308i	−0.457797	−	1.22462i
$213$	8.31858	+	3.44567i	0.569979	+	0.236093i
$214$	−18.7575	+	7.38821i	−1.28223	+	0.505047i
$215$	5.50397			0.375367
$216$	5.02755	+	14.2008i	0.342081	+	0.966243i
$217$	16.4487	−	16.4487i	1.11661	−	1.11661i
$218$	7.24760	−	2.85469i	0.490870	−	0.193344i
$219$	4.58169	−	11.0612i	0.309602	−	0.747445i
$220$	8.06357	−	7.51863i	0.543646	−	0.506906i
$221$	4.30375	+	2.00240i	0.289501	+	0.134696i
$222$	1.60860	+	1.66584i	0.107962	+	0.111804i
$223$	16.1248	+	16.1248i	1.07980	+	1.07980i	0.996527	+	0.0832723i	$0.0265371\pi$
$223$	16.1248	+	16.1248i	1.07980	+	1.07980i	0.0832723	+	0.996527i	$0.473463\pi$
$224$	−1.97658	+	22.5591i	−0.132066	+	1.50730i
$225$		−	6.89772i		−	0.459848i
$226$	0.0286431	−	1.63856i	0.00190531	−	0.108995i
$227$	−7.59392	+	3.14551i	−0.504026	+	0.208775i	−0.620184	−	0.784456i	$-0.712942\pi$
$227$	−7.59392	+	3.14551i	−0.504026	+	0.208775i	0.116158	+	0.993231i	$0.462942\pi$
$228$	0.336037	−	9.60872i	0.0222546	−	0.636353i
$229$	−4.81266	−	1.99347i	−0.318030	−	0.131732i	0.217958	−	0.975958i	$-0.430061\pi$
$229$	−4.81266	−	1.99347i	−0.318030	−	0.131732i	−0.535987	+	0.844226i	$0.680061\pi$
$230$	4.68589	−	1.84568i	0.308978	−	0.121701i
$231$	−17.3551	+	17.3551i	−1.14188	+	1.14188i
$232$	1.32849	−	2.78469i	0.0872196	−	0.182824i
$233$	−17.8948	+	17.8948i	−1.17233	+	1.17233i	−0.190677	+	0.981653i	$0.561068\pi$
$233$	−17.8948	+	17.8948i	−1.17233	+	1.17233i	−0.981653	+	0.190677i	$0.938932\pi$
$234$	−2.88622	−	8.35973i	−0.188678	−	0.546493i
$235$	−8.86180	+	3.67068i	−0.578080	+	0.239449i
$236$	5.17325	−	11.3501i	0.336750	−	0.738830i
$237$	0.414782	+	0.171808i	0.0269430	+	0.0111602i
$238$	0.130269	−	7.45218i	0.00844410	−	0.483053i
$239$	−20.7919	+	20.7919i	−1.34492	+	1.34492i	−0.453829	+	0.891089i	$0.649942\pi$
$239$	−20.7919	+	20.7919i	−1.34492	+	1.34492i	−0.891089	+	0.453829i	$0.850058\pi$
$240$	−3.43539	+	2.98572i	−0.221753	+	0.192727i
$241$	−8.68365	+	8.68365i	−0.559363	+	0.559363i	−0.929126	−	0.369763i	$-0.879439\pi$
$241$	−8.68365	+	8.68365i	−0.559363	+	0.559363i	0.369763	+	0.929126i	$0.379439\pi$
$242$	−18.3723	−	19.0261i	−1.18102	−	1.22304i
$243$	−5.77523	+	13.9426i	−0.370481	+	0.894421i
$244$	−2.75120	+	6.03613i	−0.176127	+	0.386424i
$245$	3.49362	−	8.43434i	0.223199	−	0.538850i
$246$	−0.469328	−	0.204084i	−0.0299232	−	0.0130119i
$247$	−0.658933	+	15.3934i	−0.0419269	+	0.979456i
$248$	−10.9966	−	12.2148i	−0.698283	−	0.775642i
$249$		−	4.38126i		−	0.277651i
$250$	11.9476	−	4.70593i	0.755632	−	0.297629i
$251$	9.46757	−	3.92160i	0.597588	−	0.247529i	−0.0633234	−	0.997993i	$-0.520170\pi$
$251$	9.46757	−	3.92160i	0.597588	−	0.247529i	0.660911	+	0.750464i	$0.270170\pi$
$252$	−10.1565	+	9.47015i	−0.639802	+	0.596563i
$253$	−7.34297	−	17.7275i	−0.461649	−	1.11452i
$254$	2.54036	+	0.0444071i	0.159396	+	0.00278635i
$255$	1.05928	−	1.05928i	0.0663344	−	0.0663344i
$256$	15.8438	+	2.23002i	0.990240	+	0.139376i
$257$		−	21.9735i		−	1.37067i	−0.728229	−	0.685334i	$-0.759656\pi$
$257$		−	21.9735i		−	1.37067i	0.728229	−	0.685334i	$-0.240344\pi$
$258$	−0.151310	+	8.65585i	−0.00942016	+	0.538890i
$259$	−2.22987	+	5.38338i	−0.138557	+	0.334507i
$260$	5.54250	−	4.74143i	0.343731	−	0.294051i
$261$	1.74797	−	0.724032i	0.108197	−	0.0448165i
$262$	25.3429	+	11.0202i	1.56569	+	0.680830i
$263$	−4.69386	−	4.69386i	−0.289436	−	0.289436i	0.547421	−	0.836857i	$-0.315610\pi$
$263$	−4.69386	−	4.69386i	−0.289436	−	0.289436i	−0.836857	+	0.547421i	$0.815610\pi$
$264$	11.6026	+	12.8879i	0.714088	+	0.793197i
$265$	9.62722			0.591396
$266$	22.5095	−	8.86604i	1.38014	−	0.543612i
$267$	−8.45349	−	3.50155i	−0.517345	−	0.214291i
$268$	16.3310	−	6.10497i	0.997576	−	0.372920i
$269$	3.50289	+	1.45094i	0.213575	+	0.0884656i	0.486906	−	0.873454i	$-0.338125\pi$
$269$	3.50289	+	1.45094i	0.213575	+	0.0884656i	−0.273331	+	0.961920i	$0.588125\pi$
$270$	−7.61754	−	0.133160i	−0.463589	−	0.00810384i
$271$	11.8900	+	11.8900i	0.722267	+	0.722267i	0.969066	−	0.246800i	$-0.0793790\pi$
$271$	11.8900	+	11.8900i	0.722267	+	0.722267i	−0.246800	+	0.969066i	$0.579379\pi$
$272$	−5.25321	−	0.367881i	−0.318522	−	0.0223060i
$273$	−11.9622	+	10.9802i	−0.723987	+	0.664549i
$274$	−0.326753	+	18.6923i	−0.0197399	+	1.12924i
$275$	−8.29429	−	20.0242i	−0.500165	−	1.20750i
$276$	2.77381	+	7.42004i	0.166964	+	0.446634i
$277$	13.6789	−	5.66597i	0.821883	−	0.340435i	0.0681988	−	0.997672i	$-0.478275\pi$
$277$	13.6789	−	5.66597i	0.821883	−	0.340435i	0.753684	+	0.657237i	$0.228275\pi$
$278$	−20.0438	+	7.89486i	−1.20215	+	0.473502i
$279$		−	10.0785i		−	0.603387i
$280$	−10.3367	−	4.93132i	−0.617735	−	0.294703i
$281$	13.8765			0.827804			0.413902	−	0.910321i	$-0.364166\pi$
$281$	13.8765			0.827804			0.413902	+	0.910321i	$0.364166\pi$
$282$	−5.52910	−	14.0375i	−0.329253	−	0.835920i
$283$	−8.02276	+	3.32314i	−0.476904	+	0.197540i	−0.608169	−	0.793807i	$-0.708096\pi$
$283$	−8.02276	+	3.32314i	−0.476904	+	0.197540i	0.131266	+	0.991347i	$0.458096\pi$
$284$	15.9977	+	0.559471i	0.949287	+	0.0331985i
$285$	4.49233	+	1.86079i	0.266103	+	0.110223i
$286$	−18.4311	−	20.7978i	−1.08985	−	1.22980i
$287$		−	1.28776i		−	0.0760141i
$288$	6.30573	+	7.51683i	0.371569	+	0.442934i
$289$	−15.2668			−0.898046
$290$	1.08390	+	1.12247i	0.0636489	+	0.0659137i
$291$	−10.4405	+	4.32460i	−0.612034	+	0.253513i
$292$	0.743927	−	21.2720i	0.0435350	−	1.24485i
$293$	30.0013	+	12.4270i	1.75270	+	0.725990i	0.997514	+	0.0704751i	$0.0224515\pi$
$293$	30.0013	+	12.4270i	1.75270	+	0.725990i	0.755182	+	0.655515i	$0.227548\pi$
$294$	13.1683	+	5.72613i	0.767989	+	0.333955i
$295$	4.46066	+	4.46066i	0.259709	+	0.259709i
$296$	3.71577	+	1.77268i	0.215975	+	0.103035i
$297$			29.0271i			1.68432i
$298$	−1.47697	−	0.642249i	−0.0855585	−	0.0372045i
$299$	−4.35190	−	11.9251i	−0.251677	−	0.689645i
$300$	3.13317	+	8.38134i	0.180893	+	0.483897i
$301$	−20.1253	+	8.33619i	−1.16001	+	0.480490i
$302$	25.4397	+	0.444704i	1.46389	+	0.0255898i
$303$			19.0955i			1.09701i
$304$	−5.42204	−	16.2103i	−0.310975	−	0.929724i
$305$	−2.37223	−	2.37223i	−0.135833	−	0.135833i
$306$	−2.24316	−	2.32298i	−0.128233	−	0.132796i
$307$	27.1657	−	11.2524i	1.55043	−	0.642208i	0.567034	−	0.823694i	$-0.308091\pi$
$307$	27.1657	−	11.2524i	1.55043	−	0.642208i	0.983393	+	0.181486i	$0.0580908\pi$
$308$	−18.0970	+	39.7049i	−1.03117	+	2.26240i
$309$	14.5557	−	6.02915i	0.828042	−	0.342986i
$310$	7.73378	−	3.04619i	0.439249	−	0.173012i
$311$	−14.8173	−	14.8173i	−0.840213	−	0.840213i	0.148673	−	0.988886i	$-0.452500\pi$
$311$	−14.8173	−	14.8173i	−0.840213	−	0.840213i	−0.988886	+	0.148673i	$0.952500\pi$
$312$	7.30428	+	8.84680i	0.413523	+	0.500851i
$313$	12.6396	−	12.6396i	0.714431	−	0.714431i	−0.253028	−	0.967459i	$-0.581426\pi$
$313$	12.6396	−	12.6396i	0.714431	−	0.714431i	0.967459	+	0.253028i	$0.0814265\pi$
$314$	−8.60102	+	19.7796i	−0.485384	+	1.11623i
$315$	−2.68759	−	6.48842i	−0.151429	−	0.365581i
$316$	0.797679	+	0.0278965i	0.0448729	+	0.00156930i
$317$	3.17537	+	7.66601i	0.178346	+	0.430566i	0.987620	−	0.156866i	$-0.0501390\pi$
$317$	3.17537	+	7.66601i	0.178346	+	0.430566i	−0.809274	+	0.587432i	$0.800139\pi$
$318$	−0.264663	+	15.1403i	−0.0148416	+	0.849027i
$319$	4.20375	−	4.20375i	0.235365	−	0.235365i
$320$	−3.86217	+	7.11063i	−0.215902	+	0.397496i
$321$	16.0368			0.895088
$322$	−14.3386	+	13.8459i	−0.799059	+	0.771603i
$323$	2.15291	+	5.19758i	0.119791	+	0.289201i
$324$	0.0551100	−	1.57583i	0.00306167	−	0.0875462i
$325$	−4.91571	−	13.4700i	−0.272674	−	0.747183i
$326$	−0.645215	−	1.63810i	−0.0357351	−	0.0907258i
$327$	−6.19639			−0.342661
$328$	−0.908604	−	0.0476879i	−0.0501693	−	0.00263312i
$329$	26.8438	−	26.8438i	1.47995	−	1.47995i
$330$	−8.15996	+	3.21405i	−0.449191	+	0.176928i
$331$	−7.82394	+	18.8887i	−0.430042	+	1.03821i	0.549231	+	0.835671i	$0.314921\pi$
$331$	−7.82394	+	18.8887i	−0.430042	+	1.03821i	−0.979273	+	0.202543i	$0.935079\pi$
$332$	−2.72743	−	7.29598i	−0.149687	−	0.400419i
$333$	0.966119	+	2.33242i	0.0529430	+	0.127816i
$334$	−0.0242649	+	1.38810i	−0.00132772	+	0.0759534i
$335$			8.81746i			0.481749i
$336$	8.03945	−	16.1205i	0.438588	−	0.879445i
$337$	26.7270			1.45591			0.727957	−	0.685623i	$-0.240470\pi$
$337$	26.7270			1.45591			0.727957	+	0.685623i	$0.240470\pi$
$338$	−11.5939	−	14.2682i	−0.630625	−	0.776087i
$339$	−0.498878	+	1.20440i	−0.0270953	+	0.0654139i
$340$	1.10456	−	2.42340i	0.0599031	−	0.131427i
$341$	−12.1191	−	29.2582i	−0.656288	−	1.58442i
$342$	4.17983	−	9.61229i	0.226020	−	0.519773i
$343$			8.10919i			0.437855i
$344$	5.13648	+	14.5085i	0.276941	+	0.782247i
$345$	−4.00623			−0.215688
$346$	−5.54658	+	12.7554i	−0.298186	+	0.685733i
$347$	−8.86026	−	21.3906i	−0.475644	−	1.14831i	−0.961633	−	0.274340i	$-0.911541\pi$
$347$	−8.86026	−	21.3906i	−0.475644	−	1.14831i	0.485989	−	0.873965i	$-0.338459\pi$
$348$	−1.79506	+	1.67375i	−0.0962252	+	0.0897223i
$349$	4.30549	−	1.78339i	0.230468	−	0.0954628i	−0.264461	−	0.964396i	$-0.585194\pi$
$349$	4.30549	−	1.78339i	0.230468	−	0.0954628i	0.494929	+	0.868934i	$0.335194\pi$
$350$	−16.1962	+	15.6397i	−0.865726	+	0.835979i
$351$	−0.821281	+	19.1860i	−0.0438367	+	1.02407i
$352$	27.3444	+	14.2390i	1.45746	+	0.758943i
$353$	−0.687334	+	0.687334i	−0.0365831	+	0.0365831i	−0.725162	−	0.688579i	$-0.758235\pi$
$353$	−0.687334	+	0.687334i	−0.0365831	+	0.0365831i	0.688579	+	0.725162i	$0.258235\pi$
$354$	−7.13771	+	6.89245i	−0.379365	+	0.366330i
$355$	−3.09805	+	7.47934i	−0.164427	+	0.396962i
$356$	−16.2571	−	0.568545i	−0.861626	−	0.0301328i
$357$	−2.26890	+	5.47762i	−0.120083	+	0.289906i
$358$	19.6107	+	8.52757i	1.03646	+	0.450696i
$359$		−	26.0218i		−	1.37338i	−0.726952	−	0.686688i	$-0.759064\pi$
$359$		−	26.0218i		−	1.37338i	0.726952	−	0.686688i	$-0.240936\pi$
$360$	−4.67755	+	1.65600i	−0.246529	+	0.0872791i
$361$	0.522720	−	0.522720i	0.0275116	−	0.0275116i
$362$	21.5352	−	8.48229i	1.13186	−	0.445819i
$363$	8.05139	+	19.4378i	0.422588	+	1.02022i
$364$	−13.0850	+	25.7317i	−0.685838	+	1.34871i
$365$	9.94526	+	4.11946i	0.520559	+	0.215622i
$366$	3.79592	−	3.66549i	0.198416	−	0.191598i
$367$	−2.67219			−0.139487			−0.0697436	−	0.997565i	$-0.522218\pi$
$367$	−2.67219			−0.139487			−0.0697436	+	0.997565i	$0.522218\pi$
$368$	9.23827	+	10.6296i	0.481578	+	0.554107i
$369$	−0.394522	−	0.394522i	−0.0205380	−	0.0205380i
$370$	−1.49778	+	1.44631i	−0.0778658	+	0.0751903i
$371$	−35.2021	+	14.5812i	−1.82760	+	0.757018i
$372$	4.57800	+	12.2463i	0.237358	+	0.634942i
$373$	13.6983	+	33.0707i	0.709272	+	1.71233i	0.701813	+	0.712361i	$0.252374\pi$
$373$	13.6983	+	33.0707i	0.709272	+	1.71233i	0.00745886	+	0.999972i	$0.497626\pi$
$374$	−9.30525	−	4.04632i	−0.481163	−	0.209230i
$375$	−10.2147			−0.527483
$376$	−17.9461	−	19.9342i	−0.925499	−	1.02803i
$377$	2.89749	−	2.65961i	0.149228	−	0.136977i
$378$	28.0553	−	11.0505i	1.44301	−	0.568374i
$379$	17.3836	+	7.20052i	0.892936	+	0.369866i	0.781500	−	0.623906i	$-0.214455\pi$
$379$	17.3836	+	7.20052i	0.892936	+	0.369866i	0.111436	+	0.993772i	$0.464455\pi$
$380$	8.63933	+	0.302135i	0.443188	+	0.0154992i
$381$	−1.86725	−	0.773440i	−0.0956621	−	0.0396246i
$382$	−0.204098	+	11.6756i	−0.0104426	+	0.597377i
$383$	−4.76778	−	4.76778i	−0.243622	−	0.243622i	0.574725	−	0.818347i	$-0.305109\pi$
$383$	−4.76778	−	4.76778i	−0.243622	−	0.243622i	−0.818347	+	0.574725i	$0.805109\pi$
$384$	−11.0764	−	6.26935i	−0.565241	−	0.319932i
$385$	−15.6042	−	15.6042i	−0.795265	−	0.795265i
$386$	17.6316	+	18.2590i	0.897425	+	0.929358i
$387$	−3.61176	+	8.71956i	−0.183596	+	0.443240i
$388$	−14.6941	+	13.7011i	−0.745981	+	0.695567i
$389$	−8.28986	−	20.0135i	−0.420313	−	1.01472i	−0.982255	−	0.187549i	$-0.939946\pi$
$389$	−8.28986	−	20.0135i	−0.420313	−	1.01472i	0.561943	−	0.827176i	$-0.310054\pi$
$390$	−5.48441	+	1.89351i	−0.277714	+	0.0958817i
$391$	−3.27756	−	3.27756i	−0.165753	−	0.165753i
$392$	25.4934	+	1.33801i	1.28761	+	0.0675800i
$393$	−15.5444	−	15.5444i	−0.784113	−	0.784113i
$394$	−7.32125	+	16.8365i	−0.368839	+	0.848213i
$395$	−0.154475	+	0.372936i	−0.00777250	+	0.0187645i
$396$	6.61985	+	17.7084i	0.332660	+	0.889879i
$397$	9.40202	+	22.6985i	0.471874	+	1.13920i	0.963334	+	0.268304i	$0.0864633\pi$
$397$	9.40202	+	22.6985i	0.471874	+	1.13920i	−0.491460	+	0.870900i	$0.663537\pi$
$398$	−25.8866	+	24.9971i	−1.29758	+	1.25299i
$399$	−19.2446			−0.963435
$400$	10.4351	+	12.0067i	0.521757	+	0.600337i
$401$	15.2537	−	15.2537i	0.761733	−	0.761733i	−0.214903	−	0.976635i	$-0.568943\pi$
$401$	15.2537	−	15.2537i	0.761733	−	0.761733i	0.976635	+	0.214903i	$0.0689435\pi$
$402$	−13.8668	−	0.242402i	−0.691615	−	0.0120899i
$403$	−7.18255	−	19.6816i	−0.357788	−	0.980412i
$404$	11.8874	+	31.7991i	0.591418	+	1.58207i
$405$	0.736744	+	0.305169i	0.0366091	+	0.0151640i
$406$	−5.66337	−	2.46268i	−0.281068	−	0.122221i
$407$	5.60932	+	5.60932i	0.278044	+	0.278044i
$408$	3.78082	+	1.80371i	0.187178	+	0.0892971i
$409$			1.52450i			0.0753819i	0.999289	+	0.0376909i	$0.0120002\pi$
$409$			1.52450i			0.0753819i	−0.999289	+	0.0376909i	$0.988000\pi$
$410$	0.183495	−	0.421979i	0.00906215	−	0.0208401i
$411$	5.69107	−	13.7395i	0.280720	−	0.677718i
$412$	20.4858	−	19.1014i	1.00926	−	0.941057i
$413$	−23.0665	−	9.55445i	−1.13503	−	0.470144i
$414$	−0.150940	+	8.63469i	−0.00741831	+	0.424372i
$415$	3.93925			0.193370
$416$	17.6709	+	10.1852i	0.866388	+	0.499372i
$417$	17.1366			0.839181
$418$	0.575652	−	32.9307i	0.0281560	−	1.61070i
$419$	0.842029	+	0.348780i	0.0411358	+	0.0170390i	0.403156	−	0.915131i	$-0.367913\pi$
$419$	0.842029	+	0.348780i	0.0411358	+	0.0170390i	−0.362021	+	0.932170i	$0.617913\pi$
$420$	6.21291	+	6.66321i	0.303159	+	0.325131i
$421$	−11.2248	+	27.0991i	−0.547064	+	1.32073i	0.372589	+	0.927996i	$0.378470\pi$
$421$	−11.2248	+	27.0991i	−0.547064	+	1.32073i	−0.919653	+	0.392732i	$0.871530\pi$
$422$	13.6858	−	31.4731i	0.666216	−	1.53208i
$423$		−	16.4479i		−	0.799724i
$424$	8.98444	+	25.3775i	0.436323	+	1.23244i
$425$	−3.70218	−	3.70218i	−0.179582	−	0.179582i
$426$	−11.6773	−	5.07778i	−0.565766	−	0.246019i
$427$	12.2670	+	5.08117i	0.593643	+	0.245895i
$428$	26.7056	−	9.98327i	1.29087	−	0.482559i
$429$	7.57835	+	20.7662i	0.365886	+	1.00260i
$430$	−7.78259	−	0.136045i	−0.375310	−	0.00656067i
$431$	19.0693	−	19.0693i	0.918537	−	0.918537i	−0.0783860	−	0.996923i	$-0.524977\pi$
$431$	19.0693	−	19.0693i	0.918537	−	0.918537i	0.996923	+	0.0783860i	$0.0249767\pi$
$432$	−6.75793	−	20.2042i	−0.325141	−	0.972075i
$433$	−28.1205			−1.35138			−0.675692	−	0.737184i	$-0.736155\pi$
$433$	−28.1205			−1.35138			−0.675692	+	0.737184i	$0.736155\pi$
$434$	−23.6650	+	22.8519i	−1.13596	+	1.09692i
$435$	−0.475003	−	1.14676i	−0.0227746	−	0.0549828i
$436$	−10.3187	+	3.85738i	−0.494174	+	0.184735i
$437$	5.75755	−	13.9000i	0.275421	−	0.664926i
$438$	−6.75191	+	15.5272i	−0.322619	+	0.741920i
$439$	−9.30428	−	9.30428i	−0.444069	−	0.444069i	0.449308	−	0.893377i	$-0.351671\pi$
$439$	−9.30428	−	9.30428i	−0.444069	−	0.444069i	−0.893377	+	0.449308i	$0.851671\pi$
$440$	−11.5877	+	10.4320i	−0.552423	+	0.497327i
$441$	11.0694	+	11.0694i	0.527114	+	0.527114i
$442$	−6.03599	−	2.93777i	−0.287103	−	0.139735i
$443$	−15.6473	−	37.7760i	−0.743427	−	1.79479i	−0.591337	−	0.806424i	$-0.701400\pi$
$443$	−15.6473	−	37.7760i	−0.743427	−	1.79479i	−0.152090	−	0.988367i	$-0.548600\pi$
$444$	−2.23338	−	2.39525i	−0.105992	−	0.113674i
$445$	3.14829	−	7.60065i	0.149243	−	0.360305i
$446$	−22.4019	−	23.1991i	−1.06076	−	1.09851i
$447$	0.905919	+	0.905919i	0.0428485	+	0.0428485i
$448$	3.35249	−	31.8497i	0.158390	−	1.50476i
$449$	13.1722	+	13.1722i	0.621637	+	0.621637i	0.945950	−	0.324313i	$-0.105133\pi$
$449$	13.1722	+	13.1722i	0.621637	+	0.621637i	−0.324313	+	0.945950i	$0.605133\pi$
$450$	−0.170495	+	9.75336i	−0.00803723	+	0.459778i
$451$	−1.61970	−	0.670903i	−0.0762689	−	0.0315916i
$452$	−0.0810026	+	2.31621i	−0.00381004	+	0.108945i
$453$	−18.6991	−	7.74542i	−0.878560	−	0.363911i
$454$	10.8155	−	4.26003i	0.507598	−	0.199933i
$455$	−9.87241	−	10.7554i	−0.462826	−	0.504221i
$456$	−0.712660	+	13.5784i	−0.0333733	+	0.635867i
$457$	−25.9365			−1.21326			−0.606630	−	0.794984i	$-0.707479\pi$
$457$	−25.9365			−1.21326			−0.606630	+	0.794984i	$0.707479\pi$
$458$	6.75582	+	2.93772i	0.315679	+	0.137271i
$459$	2.68334	+	6.47817i	0.125248	+	0.302375i
$460$	−6.67146	+	2.49397i	−0.311058	+	0.116282i
$461$	12.7293	−	5.27264i	0.592862	−	0.245571i	−0.0660195	−	0.997818i	$-0.521030\pi$
$461$	12.7293	−	5.27264i	0.592862	−	0.245571i	0.658881	+	0.752247i	$0.271030\pi$
$462$	24.9691	−	24.1111i	1.16167	−	1.12175i
$463$	−10.5771	−	10.5771i	−0.491559	−	0.491559i	0.417238	−	0.908797i	$-0.362998\pi$
$463$	−10.5771	−	10.5771i	−0.491559	−	0.491559i	−0.908797	+	0.417238i	$0.862998\pi$
$464$	−1.94731	+	3.90470i	−0.0904017	+	0.181271i
$465$	−6.61205			−0.306626
$466$	25.7456	−	24.8609i	1.19264	−	1.15166i
$467$	−15.7453	−	6.52190i	−0.728603	−	0.301797i	−0.0126254	−	0.999920i	$-0.504019\pi$
$467$	−15.7453	−	6.52190i	−0.728603	−	0.301797i	−0.715978	+	0.698123i	$0.754019\pi$
$468$	3.87448	+	11.8920i	0.179098	+	0.549707i
$469$	−13.3547	−	32.2412i	−0.616665	−	1.48876i
$470$	12.6213	−	4.97129i	0.582177	−	0.229308i
$471$	12.1321	−	12.1321i	0.559018	−	0.559018i
$472$	−7.59551	+	15.9212i	−0.349612	+	0.732831i
$473$			29.6560i			1.36359i
$474$	−0.582254	−	0.253189i	−0.0267438	−	0.0116294i
$475$	6.50347	−	15.7008i	0.298400	−	0.720401i
$476$	−0.368401	+	10.5342i	−0.0168856	+	0.482832i
$477$	−6.31748	+	15.2518i	−0.289258	+	0.698330i
$478$	29.9137	−	28.8858i	1.36822	−	1.32121i
$479$	6.23873	−	6.23873i	0.285055	−	0.285055i	−0.550066	−	0.835121i	$-0.685398\pi$
$479$	6.23873	−	6.23873i	0.285055	−	0.285055i	0.835121	+	0.550066i	$0.185398\pi$
$480$	4.93143	−	4.13689i	0.225088	−	0.188822i
$481$	3.54888	+	3.86629i	0.161815	+	0.176288i
$482$	12.4933	−	12.0640i	0.569054	−	0.549501i
$483$	14.6489	−	6.06776i	0.666546	−	0.276092i
$484$	25.5082	+	27.3570i	1.15946	+	1.24350i
$485$	−3.88831	−	9.38721i	−0.176559	−	0.426251i
$486$	8.51079	−	19.5721i	0.386057	−	0.887809i
$487$	−35.4651			−1.60708			−0.803538	−	0.595253i	$-0.797052\pi$
$487$	−35.4651			−1.60708			−0.803538	+	0.595253i	$0.797052\pi$
$488$	4.03938	−	8.46707i	0.182854	−	0.383286i
$489$			1.40050i			0.0633329i
$490$	−5.14844	+	11.8398i	−0.232583	+	0.534867i
$491$	10.4198	+	25.1556i	0.470238	+	1.13526i	0.964058	+	0.265692i	$0.0856003\pi$
$491$	10.4198	+	25.1556i	0.470238	+	1.13526i	−0.493820	+	0.869564i	$0.664400\pi$
$492$	0.658584	+	0.300175i	0.0296912	+	0.0135329i
$493$	0.549573	−	1.32679i	0.0247515	−	0.0597555i
$494$	1.31222	−	21.7499i	0.0590395	−	0.978574i
$495$	−9.56112			−0.429740
$496$	15.2472	+	17.5435i	0.684620	+	0.787728i
$497$		−	32.0406i		−	1.43722i
$498$	−0.108294	+	6.19509i	−0.00485279	+	0.277609i
$499$	10.2090	+	24.6468i	0.457019	+	1.10334i	0.969598	+	0.244702i	$0.0786902\pi$
$499$	10.2090	+	24.6468i	0.457019	+	1.10334i	−0.512579	+	0.858640i	$0.671310\pi$
$500$	−17.0102	+	6.35885i	−0.760718	+	0.284377i
$501$	0.422623	−	1.02030i	0.0188814	−	0.0455837i
$502$	−13.4841	+	5.31111i	−0.601823	+	0.237047i
$503$	−3.01334	+	3.01334i	−0.134358	+	0.134358i	−0.771087	−	0.636729i	$-0.780287\pi$
$503$	−3.01334	+	3.01334i	−0.134358	+	0.134358i	0.636729	+	0.771087i	$0.280287\pi$
$504$	14.5954	−	13.1397i	0.650131	−	0.585290i
$505$	−17.1690			−0.764011
$506$	9.94476	+	25.2482i	0.442099	+	1.12242i
$507$	4.42150	+	13.9402i	0.196366	+	0.619107i
$508$	−3.59096	−	0.125583i	−0.159323	−	0.00557185i
$509$	4.35853	+	10.5224i	0.193188	+	0.466398i	0.990558	−	0.137093i	$-0.0437759\pi$
$509$	4.35853	+	10.5224i	0.193188	+	0.466398i	−0.797370	+	0.603491i	$0.793776\pi$
$510$	−1.52400	+	1.47163i	−0.0674837	+	0.0651649i
$511$	−42.6042			−1.88470
$512$	−22.3480	−	3.54486i	−0.987652	−	0.156662i
$513$	−16.0936	+	16.0936i	−0.710552	+	0.710552i
$514$	−0.543132	+	31.0704i	−0.0239565	+	1.37046i
$515$	5.42089	+	13.0872i	0.238873	+	0.576690i
$516$	0.427904	−	12.2356i	0.0188374	−	0.538643i
$517$	−19.7781	−	47.7485i	−0.869838	−	2.09998i
$518$	3.28610	−	7.55697i	0.144383	−	0.332034i
$519$	7.82368	−	7.82368i	0.343422	−	0.343422i
$520$	−7.95427	+	6.56737i	−0.348818	+	0.287998i
$521$	23.1735	+	23.1735i	1.01525	+	1.01525i	0.999882	+	0.0153654i	$0.00489114\pi$
$521$	23.1735	+	23.1735i	1.01525	+	1.01525i	0.0153654	+	0.999882i	$0.495109\pi$
$522$	−2.48952	+	0.980574i	−0.108963	+	0.0429186i
$523$	11.2484	−	4.65925i	0.491860	−	0.203735i	−0.122946	−	0.992413i	$-0.539234\pi$
$523$	11.2484	−	4.65925i	0.491860	−	0.203735i	0.614806	+	0.788678i	$0.289234\pi$
$524$	−35.5624	−	16.2089i	−1.55355	−	0.708091i
$525$	16.5467	−	6.85386i	0.722157	−	0.299127i
$526$	6.52109	+	6.75313i	0.284333	+	0.294450i
$527$	−5.40942	−	5.40942i	−0.235638	−	0.235638i
$528$	−16.0874	−	18.5103i	−0.700115	−	0.805557i
$529$		−	10.6041i		−	0.461048i
$530$	−13.6129	−	0.237962i	−0.591305	−	0.0103364i
$531$	−9.99384	+	4.13958i	−0.433696	+	0.179643i
$532$	−32.0475	+	11.9802i	−1.38943	+	0.519407i
$533$	−1.05159	−	0.489273i	−0.0455495	−	0.0211928i
$534$	11.8667	+	5.16013i	0.513521	+	0.223301i
$535$			14.4189i			0.623384i
$536$	−23.2429	+	8.22875i	−1.00394	+	0.355428i
$537$	−12.0285	−	12.0285i	−0.519068	−	0.519068i
$538$	−4.91721	−	2.13821i	−0.211996	−	0.0921850i
$539$	45.4452	+	18.8240i	1.95746	+	0.810808i
$540$	10.7679	+	0.376575i	0.463376	+	0.0162052i
$541$	14.7592	−	6.11348i	0.634549	−	0.262839i	−0.0421354	−	0.999112i	$-0.513416\pi$
$541$	14.7592	−	6.11348i	0.634549	−	0.262839i	0.676685	+	0.736273i	$0.263416\pi$
$542$	−16.5185	−	17.1063i	−0.709532	−	0.734780i
$543$	−18.4116			−0.790119
$544$	7.41893	+	0.650029i	0.318084	+	0.0278698i
$545$		−	5.57125i		−	0.238646i
$546$	17.1860	−	15.2302i	0.735492	−	0.651794i
$547$	−0.191386	−	0.0792748i	−0.00818308	−	0.00338954i	0.378588	−	0.925565i	$-0.376410\pi$
$547$	−0.191386	−	0.0792748i	−0.00818308	−	0.00338954i	−0.386771	+	0.922176i	$0.626410\pi$
$548$	0.924057	−	26.4227i	0.0394737	−	1.12872i
$549$	5.31484	−	2.20148i	0.226832	−	0.0939569i
$550$	11.2332	+	28.5192i	0.478983	+	1.21606i
$551$	4.66142			0.198583
$552$	−3.73875	−	10.5605i	−0.159132	−	0.449484i
$553$		−	1.59761i		−	0.0679374i
$554$	−19.4819	+	7.67356i	−0.827708	+	0.326018i
$555$	1.53019	−	0.633824i	0.0649528	−	0.0269043i
$556$	28.5370	−	10.6679i	1.21024	−	0.452419i
$557$	6.88896	+	16.6314i	0.291895	+	0.704696i	0.999999	−	0.00141156i	$-0.000449315\pi$
$557$	6.88896	+	16.6314i	0.291895	+	0.704696i	−0.708104	+	0.706108i	$0.750449\pi$
$558$	−0.249118	+	14.2510i	−0.0105460	+	0.603295i
$559$	−0.839077	+	19.6017i	−0.0354892	+	0.829064i
$560$	14.4942	+	7.22838i	0.612490	+	0.305455i
$561$	5.70751	+	5.70751i	0.240971	+	0.240971i
$562$	−19.6214	−	0.342995i	−0.827678	−	0.0144684i
$563$	38.2612	+	15.8483i	1.61252	+	0.667927i	0.993115	−	0.117146i	$-0.0373745\pi$
$563$	38.2612	+	15.8483i	1.61252	+	0.667927i	0.619403	+	0.785073i	$0.287375\pi$
$564$	7.47116	+	19.9856i	0.314593	+	0.841547i
$565$	−1.08289	−	0.448548i	−0.0455575	−	0.0188706i
$566$	11.4263	−	4.50060i	0.480283	−	0.189174i
$567$	−3.15612			−0.132545
$568$	−22.6068	−	1.18652i	−0.948562	−	0.0497851i
$569$	9.95156	+	9.95156i	0.417191	+	0.417191i	0.884234	−	0.467043i	$-0.154681\pi$
$569$	9.95156	+	9.95156i	0.417191	+	0.417191i	−0.467043	+	0.884234i	$0.654681\pi$
$570$	−6.30616	−	2.74219i	−0.264136	−	0.114858i
$571$	21.1867	−	8.77582i	0.886636	−	0.367257i	0.107569	−	0.994198i	$-0.465693\pi$
$571$	21.1867	−	8.77582i	0.886636	−	0.367257i	0.779067	+	0.626941i	$0.215693\pi$
$572$	25.5474	+	29.8636i	1.06819	+	1.24866i
$573$	3.55478	−	8.58199i	0.148503	−	0.358518i
$574$	−0.0318304	+	1.82089i	−0.00132858	+	0.0760025i
$575$			14.0018i			0.583917i
$576$	−8.73049	−	10.7846i	−0.363770	−	0.449360i
$577$	10.3609	−	10.3609i	0.431329	−	0.431329i	−0.457752	−	0.889080i	$-0.651345\pi$
$577$	10.3609	−	10.3609i	0.431329	−	0.431329i	0.889080	+	0.457752i	$0.151345\pi$
$578$	21.5872	+	0.377359i	0.897909	+	0.0156961i
$579$	−7.72677	−	18.6541i	−0.321114	−	0.775237i
$580$	−1.50489	−	1.61396i	−0.0624871	−	0.0670161i
$581$	−14.4039	+	5.96630i	−0.597576	+	0.247524i
$582$	14.8698	−	5.85691i	0.616371	−	0.242777i
$583$			51.8727i			2.14835i
$584$	−1.57771	+	30.0602i	−0.0652859	+	1.24390i
$585$	−6.31960	−	0.270519i	−0.261283	−	0.0111846i
$586$	−42.1146	−	18.3132i	−1.73974	−	0.756513i
$587$	4.84590	−	11.6990i	0.200012	−	0.482871i	−0.791769	−	0.610821i	$-0.790840\pi$
$587$	4.84590	−	11.6990i	0.200012	−	0.482871i	0.991781	+	0.127950i	$0.0408397\pi$
$588$	−18.4784	−	8.42222i	−0.762035	−	0.347327i
$589$	9.50249	−	22.9411i	0.391543	−	0.945270i
$590$	−6.19710	−	6.41761i	−0.255131	−	0.264209i
$591$	10.3269	−	10.3269i	0.424793	−	0.424793i
$592$	−5.21028	−	2.59841i	−0.214141	−	0.106794i
$593$	17.3002	−	17.3002i	0.710434	−	0.710434i	−0.256192	−	0.966626i	$-0.582468\pi$
$593$	17.3002	−	17.3002i	0.710434	−	0.710434i	0.966626	+	0.256192i	$0.0824679\pi$
$594$	0.717481	−	41.0442i	0.0294386	−	1.68406i
$595$	−4.92500	−	2.04000i	−0.201905	−	0.0836319i
$596$	2.07255	+	0.944646i	0.0848951	+	0.0386942i
$597$	26.4467	−	10.9546i	1.08239	−	0.448341i
$598$	5.85881	+	16.9696i	0.239585	+	0.693939i
$599$	21.2291	−	21.2291i	0.867400	−	0.867400i	−0.124784	−	0.992184i	$-0.539824\pi$
$599$	21.2291	−	21.2291i	0.867400	−	0.867400i	0.992184	+	0.124784i	$0.0398239\pi$
$600$	−4.22312	−	11.9286i	−0.172408	−	0.486985i
$601$	−17.0759	+	17.0759i	−0.696540	+	0.696540i	−0.963662	−	0.267123i	$-0.913927\pi$
$601$	−17.0759	+	17.0759i	−0.696540	+	0.696540i	0.267123	+	0.963662i	$0.413927\pi$
$602$	28.6632	−	11.2899i	1.16823	−	0.460142i
$603$	−13.9689	−	5.78611i	−0.568858	−	0.235629i
$604$	−35.9607	−	1.25762i	−1.46322	−	0.0511718i
$605$	−17.4768	+	7.23911i	−0.710531	+	0.294312i
$606$	0.471995	−	27.0010i	0.0191735	−	1.09684i
$607$		−	24.1177i		−	0.978909i	−0.872029	−	0.489455i	$-0.837196\pi$
$607$		−	24.1177i		−	0.978909i	0.872029	−	0.489455i	$-0.162804\pi$
$608$	7.26607	+	23.0553i	0.294678	+	0.935017i
$609$	3.47371	+	3.47371i	0.140762	+	0.140762i
$610$	3.29569	+	3.41296i	0.133439	+	0.138187i
$611$	−11.7217	−	32.1198i	−0.474209	−	1.29943i
$612$	3.11441	+	3.34014i	0.125892	+	0.135017i
$613$	10.6617	−	25.7397i	0.430623	−	1.03962i	−0.548464	−	0.836174i	$-0.684787\pi$
$613$	10.6617	−	25.7397i	0.430623	−	1.03962i	0.979087	−	0.203442i	$-0.0652129\pi$
$614$	−38.6903	+	15.2394i	−1.56142	+	0.615012i
$615$	−0.258827	+	0.258827i	−0.0104369	+	0.0104369i
$616$	26.5706	−	55.6953i	1.07056	−	2.24403i
$617$	−28.6911			−1.15506			−0.577531	−	0.816369i	$-0.695984\pi$
$617$	−28.6911			−1.15506			−0.577531	+	0.816369i	$0.695984\pi$
$618$	−20.7307	+	8.16542i	−0.833910	+	0.328461i
$619$	−18.0497	−	7.47645i	−0.725481	−	0.300504i	−0.0107872	−	0.999942i	$-0.503434\pi$
$619$	−18.0497	−	7.47645i	−0.725481	−	0.300504i	−0.714693	+	0.699438i	$0.753434\pi$
$620$	−11.0108	+	4.11614i	−0.442206	+	0.165308i
$621$	7.17610	−	17.3246i	0.287967	−	0.695214i
$622$	20.5854	+	21.3179i	0.825400	+	0.854770i
$623$			32.5602i			1.30450i
$624$	−10.1096	−	12.6899i	−0.404706	−	0.508002i
$625$			10.7004i			0.428017i
$626$	−18.1847	+	17.5599i	−0.726809	+	0.701835i
$627$	−10.0261	+	24.2052i	−0.400406	+	0.966664i
$628$	12.6507	−	27.7557i	0.504819	−	1.10757i
$629$	1.77041	+	0.733328i	0.0705909	+	0.0292397i
$630$	3.63987	+	9.24104i	0.145016	+	0.368172i
$631$	1.25528			0.0499718			0.0249859	−	0.999688i	$-0.492046\pi$
$631$	1.25528			0.0499718			0.0249859	+	0.999688i	$0.492046\pi$
$632$	−1.12723	−	0.0591623i	−0.0448387	−	0.00235335i
$633$	−19.3044	+	19.3044i	−0.767283	+	0.767283i
$634$	−4.30047	−	10.9182i	−0.170794	−	0.433618i
$635$	0.695411	−	1.67887i	0.0275965	−	0.0666239i
$636$	0.748466	−	21.4018i	0.0296786	−	0.848638i
$637$	29.5053	+	13.7279i	1.16904	+	0.543919i
$638$	−6.04800	+	5.84019i	−0.239443	+	0.231215i
$639$	−9.81605	−	9.81605i	−0.388317	−	0.388317i
$640$	5.63686	−	9.95895i	0.222816	−	0.393662i
$641$			14.5355i			0.574120i	0.957913	+	0.287060i	$0.0926779\pi$
$641$			14.5355i			0.574120i	−0.957913	+	0.287060i	$0.907322\pi$
$642$	−22.6760	−	0.396392i	−0.894951	−	0.0156444i
$643$	−1.63693	+	0.678037i	−0.0645540	+	0.0267392i	−0.414727	−	0.909946i	$-0.636123\pi$
$643$	−1.63693	+	0.678037i	−0.0645540	+	0.0267392i	0.350173	+	0.936685i	$0.386123\pi$
$644$	20.6170	−	19.2237i	0.812423	−	0.757519i
$645$	5.72048	+	2.36950i	0.225244	+	0.0932990i
$646$	−2.91574	−	7.40259i	−0.114718	−	0.291251i
$647$	−4.16077	+	4.16077i	−0.163577	+	0.163577i	−0.784149	−	0.620572i	$-0.786900\pi$
$647$	−4.16077	+	4.16077i	−0.163577	+	0.163577i	0.620572	+	0.784149i	$0.286900\pi$
$648$	−0.116876	+	2.22686i	−0.00459133	+	0.0874793i
$649$	−24.0346	+	24.0346i	−0.943439	+	0.943439i
$650$	6.61785	+	19.1681i	0.259574	+	0.751835i
$651$	24.1771	−	10.0145i	0.947573	−	0.392498i
$652$	0.871842	+	2.33221i	0.0341440	+	0.0913365i
$653$	19.6786	+	8.15115i	0.770084	+	0.318979i	0.732906	−	0.680330i	$-0.238163\pi$
$653$	19.6786	+	8.15115i	0.770084	+	0.318979i	0.0371773	+	0.999309i	$0.488163\pi$
$654$	8.76167	+	0.153160i	0.342609	+	0.00598903i
$655$	13.9762	−	13.9762i	0.546096	−	0.546096i
$656$	1.28358	+	0.0898891i	0.0501156	+	0.00350958i
$657$	−13.0524	+	13.0524i	−0.509221	+	0.509221i
$658$	−38.6206	+	37.2936i	−1.50559	+	1.45385i
$659$	3.28764	−	7.93707i	0.128068	−	0.309184i	−0.846820	−	0.531880i	$-0.821486\pi$
$659$	3.28764	−	7.93707i	0.128068	−	0.309184i	0.974888	+	0.222696i	$0.0714857\pi$
$660$	11.6176	−	4.34297i	0.452215	−	0.169050i
$661$	2.80839	−	6.78006i	0.109234	−	0.263714i	−0.859805	−	0.510623i	$-0.829415\pi$
$661$	2.80839	−	6.78006i	0.109234	−	0.263714i	0.969039	+	0.246909i	$0.0794148\pi$
$662$	11.5299	−	26.5151i	0.448123	−	1.03054i
$663$	3.61100	+	3.93397i	0.140239	+	0.152783i
$664$	3.67624	+	10.3839i	0.142666	+	0.402974i
$665$		−	17.3031i		−	0.670985i
$666$	−1.30844	−	3.32191i	−0.0507010	−	0.128722i
$667$	−3.54824	+	1.46973i	−0.137388	+	0.0569082i
$668$	0.0686211	−	1.96217i	0.00265503	−	0.0759186i
$669$	9.81729	+	23.7010i	0.379558	+	0.916335i
$670$	0.217947	−	12.4679i	0.00842002	−	0.481676i
$671$	12.7819	−	12.7819i	0.493438	−	0.493438i
$672$	−11.7662	+	22.5956i	−0.453892	+	0.871645i
$673$			30.7329i			1.18466i	0.805694	+	0.592332i	$0.201793\pi$
$673$			30.7329i			1.18466i	−0.805694	+	0.592332i	$0.798207\pi$
$674$	−37.7919	−	0.660629i	−1.45569	−	0.0254465i
$675$	8.10580	−	19.5691i	0.311992	−	0.753216i
$676$	16.0411	+	20.4618i	0.616965	+	0.786991i
$677$	−15.5734	+	6.45073i	−0.598536	+	0.247922i	−0.661318	−	0.750105i	$-0.730003\pi$
$677$	−15.5734	+	6.45073i	−0.598536	+	0.247922i	0.0627820	+	0.998027i	$0.480003\pi$
$678$	0.735182	−	1.69068i	0.0282345	−	0.0649303i
$679$	28.4353	+	28.4353i	1.09125	+	1.09125i
$680$	−1.62174	+	3.39938i	−0.0621910	+	0.130360i
$681$	−9.24682			−0.354339
$682$	16.4132	+	41.6705i	0.628495	+	1.59565i
$683$	−23.9817	−	9.93354i	−0.917633	−	0.380096i	−0.126660	−	0.991946i	$-0.540426\pi$
$683$	−23.9817	−	9.93354i	−0.917633	−	0.380096i	−0.790974	+	0.611850i	$0.790426\pi$
$684$	−6.14787	+	13.4884i	−0.235070	+	0.515743i
$685$	12.3533	+	5.11692i	0.471997	+	0.195507i
$686$	0.200440	−	11.4664i	0.00765284	−	0.437788i
$687$	−4.14378	−	4.14378i	−0.158095	−	0.158095i
$688$	−6.90436	−	20.6420i	−0.263226	−	0.786968i
$689$	−1.46767	+	34.2862i	−0.0559136	+	1.30620i
$690$	5.66480	+	0.0990246i	0.215655	+	0.00376980i
$691$	0.533717	+	1.28851i	0.0203036	+	0.0490171i	0.933706	−	0.358040i	$-0.116555\pi$
$691$	0.533717	+	1.28851i	0.0203036	+	0.0490171i	−0.913403	+	0.407057i	$0.866555\pi$
$692$	8.15813	−	17.8990i	0.310126	−	0.680416i
$693$	34.9604	−	14.4811i	1.32804	−	0.550090i
$694$	11.9997	+	30.4652i	0.455501	+	1.15644i
$695$			15.4077i			0.584448i
$696$	2.57958	−	2.32230i	0.0977787	−	0.0880267i
$697$	−0.423500			−0.0160412
$698$	−6.13203	+	2.41529i	−0.232101	+	0.0914201i
$699$	−26.3026	+	10.8949i	−0.994857	+	0.412083i
$700$	23.2880	−	21.7142i	0.880205	−	0.820720i
$701$	−8.80288	−	3.64627i	−0.332480	−	0.137718i	0.210197	−	0.977659i	$-0.432589\pi$
$701$	−8.80288	−	3.64627i	−0.332480	−	0.137718i	−0.542677	+	0.839941i	$0.682589\pi$
$702$	1.63552	−	27.1086i	0.0617288	−	1.02315i
$703$			6.22001i			0.234592i
$704$	−38.3130	−	20.8099i	−1.44397	−	0.784301i
$705$	−10.7907			−0.406400
$706$	0.988877	−	0.954899i	0.0372169	−	0.0359381i
$707$	62.7788	−	26.0038i	2.36104	−	0.977975i
$708$	10.2631	−	9.56948i	0.385710	−	0.359643i
$709$	33.1544	+	13.7330i	1.24514	+	0.515753i	0.905317	−	0.424737i	$-0.139633\pi$
$709$	33.1544	+	13.7330i	1.24514	+	0.515753i	0.339822	+	0.940490i	$0.389633\pi$
$710$	4.56550	−	10.4992i	0.171340	−	0.394028i
$711$	−0.489449	−	0.489449i	−0.0183558	−	0.0183558i
$712$	22.9735	+	1.20576i	0.860968	+	0.0451878i
$713$			20.4587i			0.766183i
$714$	3.34362	−	7.68925i	0.125132	−	0.287763i
$715$	−18.6712	+	6.81380i	−0.698263	+	0.254822i
$716$	−27.5187	−	12.5427i	−1.02842	−	0.468742i
$717$	−30.5609	+	12.6587i	−1.14132	+	0.472750i
$718$	−0.643196	+	36.7947i	−0.0240039	+	1.37317i
$719$		−	21.5035i		−	0.801944i	−0.916090	−	0.400972i	$-0.868673\pi$
$719$		−	21.5035i		−	0.801944i	0.916090	−	0.400972i	$-0.131327\pi$
$720$	6.65498	−	2.22597i	0.248016	−	0.0829569i
$721$	−39.6432	−	39.6432i	−1.47639	−	1.47639i
$722$	−0.752045	+	0.726204i	−0.0279882	+	0.0270265i
$723$	−12.7636	+	5.28687i	−0.474684	+	0.196621i
$724$	−30.6603	+	11.4616i	−1.13948	+	0.425969i
$725$	−4.00793	+	1.66014i	−0.148851	+	0.0616561i
$726$	−10.9042	−	27.6840i	−0.404692	−	1.02745i
$727$	−28.4471	−	28.4471i	−1.05504	−	1.05504i	−0.998394	−	0.0566487i	$-0.981959\pi$
$727$	−28.4471	−	28.4471i	−1.05504	−	1.05504i	−0.0566487	−	0.998394i	$-0.518041\pi$
$728$	19.1381	−	36.0611i	0.709306	−	1.33651i
$729$	−13.6773	+	13.6773i	−0.506566	+	0.506566i
$730$	−13.9607	−	6.07073i	−0.516710	−	0.224688i
$731$	2.74149	+	6.61854i	0.101398	+	0.244795i
$732$	−5.45802	+	5.08917i	−0.201734	+	0.188101i
$733$	−1.14575	−	2.76609i	−0.0423194	−	0.102168i	0.901306	−	0.433182i	$-0.142609\pi$
$733$	−1.14575	−	2.76609i	−0.0423194	−	0.102168i	−0.943626	+	0.331014i	$0.892609\pi$
$734$	3.77847	+	0.0660502i	0.139466	+	0.00243796i
$735$	7.26210	−	7.26210i	0.267866	−	0.267866i
$736$	−12.8002	−	15.2586i	−0.471820	−	0.562439i
$737$	−47.5096			−1.75004
$738$	0.548101	+	0.567605i	0.0201759	+	0.0208938i
$739$	5.98303	+	14.4443i	0.220089	+	0.531342i	0.994902	−	0.100849i	$-0.0321558\pi$
$739$	5.98303	+	14.4443i	0.220089	+	0.531342i	−0.774813	+	0.632191i	$0.782156\pi$
$740$	2.15360	−	2.00806i	0.0791681	−	0.0738179i
$741$	−7.31182	+	15.7152i	−0.268606	+	0.577313i
$742$	50.1361	−	19.7477i	1.84055	−	0.724959i
$743$	13.9428			0.511510			0.255755	−	0.966742i	$-0.417676\pi$
$743$	13.9428			0.511510			0.255755	+	0.966742i	$0.417676\pi$
$744$	−6.17058	−	17.4294i	−0.226224	−	0.638994i
$745$	−0.814525	+	0.814525i	−0.0298419	+	0.0298419i
$746$	−18.5520	−	47.1004i	−0.679235	−	1.72447i
$747$	−2.58498	+	6.24068i	−0.0945793	+	0.228335i
$748$	13.0576	+	5.95149i	0.477433	+	0.217608i
$749$	−21.8386	−	52.7230i	−0.797965	−	1.92646i
$750$	14.4435	+	0.252483i	0.527403	+	0.00921936i
$751$			2.86826i			0.104664i	0.998630	+	0.0523321i	$0.0166654\pi$
$751$			2.86826i			0.104664i	−0.998630	+	0.0523321i	$0.983335\pi$
$752$	24.8830	+	28.6305i	0.907389	+	1.04405i
$753$	11.5283			0.420114
$754$	−4.16278	+	3.68906i	−0.151600	+	0.134348i
$755$	6.96401	−	16.8126i	0.253446	−	0.611874i
$756$	−39.9433	+	14.9319i	−1.45272	+	0.543067i
$757$	5.19822	+	12.5496i	0.188933	+	0.456123i	0.989755	−	0.142779i	$-0.0456038\pi$
$757$	5.19822	+	12.5496i	0.188933	+	0.456123i	−0.800822	+	0.598902i	$0.795604\pi$
$758$	−24.4024	−	10.6112i	−0.886335	−	0.385416i
$759$		−	21.5861i		−	0.783525i
$760$	−12.2085	−	0.640762i	−0.442850	−	0.0232429i
$761$	50.3148			1.82391			0.911955	−	0.410291i	$-0.134573\pi$
$761$	50.3148			1.82391			0.911955	+	0.410291i	$0.134573\pi$
$762$	2.62117	+	1.13980i	0.0949550	+	0.0412905i
$763$	8.43810	+	20.3714i	0.305480	+	0.737494i
$764$	0.577188	−	16.5043i	0.0208819	−	0.597103i
$765$	−2.13382	+	0.883856i	−0.0771484	+	0.0319559i
$766$	6.62379	+	6.85948i	0.239327	+	0.247843i
$767$	−16.5661	+	15.2061i	−0.598168	+	0.549059i
$768$	15.5071	+	9.13863i	0.559563	+	0.329762i
$769$	−20.2223	+	20.2223i	−0.729235

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41400 - 0.0247176i) q^{2} +(1.03934 + 0.430508i) q^{3} +(1.99878 + 0.0699014i) q^{4} +(-0.387075 + 0.934483i) q^{5} +(-1.45898 - 0.634427i) q^{6} -4.00321i q^{7} +(-2.82454 - 0.148245i) q^{8} +(-1.22643 - 1.22643i) q^{9} +O(q^{10})\)	\(q+(-1.41400 - 0.0247176i) q^{2} +(1.03934 + 0.430508i) q^{3} +(1.99878 + 0.0699014i) q^{4} +(-0.387075 + 0.934483i) q^{5} +(-1.45898 - 0.634427i) q^{6} -4.00321i q^{7} +(-2.82454 - 0.148245i) q^{8} +(-1.22643 - 1.22643i) q^{9} +(0.570422 - 1.31179i) q^{10} +(-5.03511 - 2.08561i) q^{11} +(2.04731 + 0.933141i) q^{12} +(-3.26904 - 1.52098i) q^{13} +(-0.0989499 + 5.66053i) q^{14} +(-0.804604 + 0.804604i) q^{15} +(3.99023 + 0.279435i) q^{16} -1.31652 q^{17} +(1.70386 + 1.76449i) q^{18} +(-1.63531 - 3.94798i) q^{19} +(-0.838999 + 1.84077i) q^{20} +(1.72341 - 4.16069i) q^{21} +(7.06808 + 3.07350i) q^{22} +(2.48957 + 2.48957i) q^{23} +(-2.87183 - 1.37006i) q^{24} +(2.81210 + 2.81210i) q^{25} +(4.58482 + 2.23147i) q^{26} +(-2.03821 - 4.92068i) q^{27} +(0.279830 - 8.00152i) q^{28} +(-0.417444 + 1.00780i) q^{29} +(1.15760 - 1.11782i) q^{30} +(4.10888 + 4.10888i) q^{31} +(-5.63527 - 0.493749i) q^{32} +(-4.33531 - 4.33531i) q^{33} +(1.86155 + 0.0325412i) q^{34} +(3.74093 + 1.54954i) q^{35} +(-2.36564 - 2.53710i) q^{36} +(-1.34477 - 0.557021i) q^{37} +(2.21473 + 5.62285i) q^{38} +(-2.74284 - 2.98816i) q^{39} +(1.23184 - 2.58210i) q^{40} +0.321682 q^{41} +(-2.53974 + 5.84060i) q^{42} +(-2.08238 - 5.02730i) q^{43} +(-9.91827 - 4.52063i) q^{44} +(1.62080 - 0.671359i) q^{45} +(-3.45871 - 3.58178i) q^{46} +(6.70557 + 6.70557i) q^{47} +(4.02690 + 2.00825i) q^{48} -9.02567 q^{49} +(-3.90680 - 4.04582i) q^{50} +(-1.36831 - 0.566771i) q^{51} +(-6.42776 - 3.26862i) q^{52} +(-3.64238 - 8.79347i) q^{53} +(2.76040 + 7.00821i) q^{54} +(3.89793 - 3.89793i) q^{55} +(-0.593457 + 11.3072i) q^{56} -4.80730i q^{57} +(0.615176 - 1.41471i) q^{58} +(2.38670 - 5.76200i) q^{59} +(-1.66447 + 1.55198i) q^{60} +(-1.26927 + 3.06430i) q^{61} +(-5.70839 - 5.91151i) q^{62} +(-4.90967 + 4.90967i) q^{63} +(7.95605 + 0.837450i) q^{64} +(2.68670 - 2.46612i) q^{65} +(6.02295 + 6.23727i) q^{66} +(8.05384 - 3.33601i) q^{67} +(-2.63143 - 0.0920264i) q^{68} +(1.51572 + 3.65928i) q^{69} +(-5.25136 - 2.28352i) q^{70} +8.00373 q^{71} +(3.28230 + 3.64593i) q^{72} -10.6425i q^{73} +(1.88773 + 0.820866i) q^{74} +(1.71209 + 4.13336i) q^{75} +(-2.99265 - 8.00544i) q^{76} +(-8.34913 + 20.1566i) q^{77} +(3.80451 + 4.29305i) q^{78} +0.399083 q^{79} +(-1.80565 + 3.62064i) q^{80} -0.788397i q^{81} +(-0.454858 - 0.00795122i) q^{82} +(-1.49038 - 3.59810i) q^{83} +(3.73556 - 8.19582i) q^{84} +(0.509592 - 1.23026i) q^{85} +(2.82021 + 7.16007i) q^{86} +(-0.867731 + 0.867731i) q^{87} +(13.9127 + 6.63732i) q^{88} -8.13354 q^{89} +(-2.30841 + 0.909238i) q^{90} +(-6.08881 + 13.0866i) q^{91} +(4.80207 + 5.15012i) q^{92} +(2.50161 + 6.03942i) q^{93} +(-9.31592 - 9.64741i) q^{94} +4.32230 q^{95} +(-5.64438 - 2.93920i) q^{96} +(-7.10314 + 7.10314i) q^{97} +(12.7623 + 0.223093i) q^{98} +(3.61736 + 8.73309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

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