LMFDB - Embedded newform 416.2.bd.a.83.9

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			83.9
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26014 - 0.641900i) q^{2} +(-0.400717 - 0.165982i) q^{3} +(1.17593 + 1.61777i) q^{4} +(1.56341 - 3.77440i) q^{5} +(0.398417 + 0.466382i) q^{6} -2.76672i q^{7} +(-0.443390 - 2.79346i) q^{8} +(-1.98830 - 1.98830i) q^{9} +O(q^{10})$	\(q+(-1.26014 - 0.641900i) q^{2} +(-0.400717 - 0.165982i) q^{3} +(1.17593 + 1.61777i) q^{4} +(1.56341 - 3.77440i) q^{5} +(0.398417 + 0.466382i) q^{6} -2.76672i q^{7} +(-0.443390 - 2.79346i) q^{8} +(-1.98830 - 1.98830i) q^{9} +(-4.39291 + 3.75274i) q^{10} +(4.68296 + 1.93975i) q^{11} +(-0.202693 - 0.843453i) q^{12} +(-0.679641 + 3.54092i) q^{13} +(-1.77596 + 3.48647i) q^{14} +(-1.25297 + 1.25297i) q^{15} +(-1.23439 + 3.80477i) q^{16} -3.33220 q^{17} +(1.22925 + 3.78183i) q^{18} +(-1.93348 - 4.66783i) q^{19} +(7.94459 - 1.90919i) q^{20} +(-0.459227 + 1.10867i) q^{21} +(-4.65609 - 5.45036i) q^{22} +(2.98467 + 2.98467i) q^{23} +(-0.285991 + 1.19298i) q^{24} +(-8.26634 - 8.26634i) q^{25} +(3.12936 - 4.02580i) q^{26} +(0.964670 + 2.32892i) q^{27} +(4.47593 - 3.25346i) q^{28} +(0.983162 - 2.37356i) q^{29} +(2.38320 - 0.774642i) q^{30} +(5.05908 + 5.05908i) q^{31} +(3.99779 - 4.00221i) q^{32} +(-1.55458 - 1.55458i) q^{33} +(4.19906 + 2.13894i) q^{34} +(-10.4427 - 4.32551i) q^{35} +(0.878520 - 5.55471i) q^{36} +(-8.77750 - 3.63576i) q^{37} +(-0.559818 + 7.12323i) q^{38} +(0.860074 - 1.30610i) q^{39} +(-11.2368 - 2.69378i) q^{40} -0.0305502 q^{41} +(1.29035 - 1.10231i) q^{42} +(-2.60064 - 6.27850i) q^{43} +(2.36876 + 9.85698i) q^{44} +(-10.6132 + 4.39611i) q^{45} +(-1.84525 - 5.67697i) q^{46} +(-2.44565 - 2.44565i) q^{47} +(1.12616 - 1.31975i) q^{48} -0.654734 q^{49} +(5.11062 + 15.7230i) q^{50} +(1.33527 + 0.553088i) q^{51} +(-6.52761 + 3.06436i) q^{52} +(2.04108 + 4.92760i) q^{53} +(0.279310 - 3.55400i) q^{54} +(14.6428 - 14.6428i) q^{55} +(-7.72871 + 1.22674i) q^{56} +2.19140i q^{57} +(-2.76252 + 2.35994i) q^{58} +(-0.589917 + 1.42419i) q^{59} +(-3.50042 - 0.553619i) q^{60} +(-0.595870 + 1.43856i) q^{61} +(-3.12775 - 9.62260i) q^{62} +(-5.50106 + 5.50106i) q^{63} +(-7.60681 + 2.47718i) q^{64} +(12.3023 + 8.10114i) q^{65} +(0.961110 + 2.95688i) q^{66} +(-1.10964 + 0.459627i) q^{67} +(-3.91843 - 5.39075i) q^{68} +(-0.700605 - 1.69141i) q^{69} +(10.3828 + 12.1540i) q^{70} +9.00054 q^{71} +(-4.67263 + 6.43581i) q^{72} -6.79471i q^{73} +(8.72713 + 10.2159i) q^{74} +(1.94040 + 4.68453i) q^{75} +(5.27786 - 8.61696i) q^{76} +(5.36674 - 12.9564i) q^{77} +(-1.92220 + 1.09379i) q^{78} +10.7833 q^{79} +(12.4309 + 10.6075i) q^{80} +7.34227i q^{81} +(0.0384976 + 0.0196102i) q^{82} +(0.681723 + 1.64583i) q^{83} +(-2.33360 + 0.560793i) q^{84} +(-5.20960 + 12.5771i) q^{85} +(-0.752989 + 9.58117i) q^{86} +(-0.787940 + 0.787940i) q^{87} +(3.34222 - 13.9417i) q^{88} +13.6109 q^{89} +(16.1960 + 1.27285i) q^{90} +(9.79672 + 1.88038i) q^{91} +(-1.31876 + 8.33828i) q^{92} +(-1.18754 - 2.86698i) q^{93} +(1.51201 + 4.65174i) q^{94} -20.6411 q^{95} +(-2.26628 + 0.940192i) q^{96} +(7.18176 - 7.18176i) q^{97} +(0.825060 + 0.420274i) q^{98} +(-5.45433 - 13.1679i) 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 $

$2$	−1.26014	−	0.641900i	−0.891057	−	0.453892i
$2$	−1.26014	−	0.641900i	−0.891057	−	0.453892i
$3$	−0.400717	−	0.165982i	−0.231354	−	0.0958300i	0.263995	−	0.964524i	$-0.414960\pi$
$3$	−0.400717	−	0.165982i	−0.231354	−	0.0958300i	−0.495349	+	0.868694i	$0.664960\pi$
$4$	1.17593	+	1.61777i	0.587964	+	0.808887i
$5$	1.56341	−	3.77440i	0.699178	−	1.68796i	−0.0262396	−	0.999656i	$-0.508353\pi$
$5$	1.56341	−	3.77440i	0.699178	−	1.68796i	0.725418	−	0.688309i	$-0.241647\pi$
$6$	0.398417	+	0.466382i	0.162653	+	0.190400i
$7$		−	2.76672i		−	1.04572i	−0.852418	−	0.522861i	$-0.824865\pi$
$7$		−	2.76672i		−	1.04572i	0.852418	−	0.522861i	$-0.175135\pi$
$8$	−0.443390	−	2.79346i	−0.156762	−	0.987636i
$9$	−1.98830	−	1.98830i	−0.662765	−	0.662765i
$10$	−4.39291	+	3.75274i	−1.38916	+	1.18672i
$11$	4.68296	+	1.93975i	1.41197	+	0.584856i	0.952829	−	0.303509i	$-0.0981582\pi$
$11$	4.68296	+	1.93975i	1.41197	+	0.584856i	0.459138	+	0.888365i	$0.348158\pi$
$12$	−0.202693	−	0.843453i	−0.0585123	−	0.243484i
$13$	−0.679641	+	3.54092i	−0.188498	+	0.982073i
$13$	−0.679641	+	3.54092i	−0.188498	+	0.982073i
$14$	−1.77596	+	3.48647i	−0.474645	+	0.931797i
$15$	−1.25297	+	1.25297i	−0.323515	+	0.323515i
$16$	−1.23439	+	3.80477i	−0.308596	+	0.951193i
$17$	−3.33220			−0.808178			−0.404089	−	0.914720i	$-0.632411\pi$
$17$	−3.33220			−0.808178			−0.404089	+	0.914720i	$0.632411\pi$
$18$	1.22925	+	3.78183i	0.289738	+	0.891385i
$19$	−1.93348	−	4.66783i	−0.443570	−	1.07087i	−0.974687	−	0.223574i	$-0.928228\pi$
$19$	−1.93348	−	4.66783i	−0.443570	−	1.07087i	0.531117	−	0.847299i	$-0.321772\pi$
$20$	7.94459	−	1.90919i	1.77646	−	0.426907i
$21$	−0.459227	+	1.10867i	−0.100212	+	0.241932i
$22$	−4.65609	−	5.45036i	−0.992681	−	1.16202i
$23$	2.98467	+	2.98467i	0.622346	+	0.622346i	0.946131	−	0.323784i	$-0.104955\pi$
$23$	2.98467	+	2.98467i	0.622346	+	0.622346i	−0.323784	+	0.946131i	$0.604955\pi$
$24$	−0.285991	+	1.19298i	−0.0583777	+	0.243516i
$25$	−8.26634	−	8.26634i	−1.65327	−	1.65327i
$26$	3.12936	−	4.02580i	0.613718	−	0.789525i
$27$	0.964670	+	2.32892i	0.185651	+	0.448201i
$28$	4.47593	−	3.25346i	0.845871	−	0.614847i
$29$	0.983162	−	2.37356i	0.182569	−	0.440760i	−0.805926	−	0.592016i	$-0.798332\pi$
$29$	0.983162	−	2.37356i	0.182569	−	0.440760i	0.988495	+	0.151257i	$0.0483320\pi$
$30$	2.38320	−	0.774642i	0.435112	−	0.141430i
$31$	5.05908	+	5.05908i	0.908638	+	0.908638i	0.996162	−	0.0875241i	$-0.0278955\pi$
$31$	5.05908	+	5.05908i	0.908638	+	0.908638i	−0.0875241	+	0.996162i	$0.527895\pi$
$32$	3.99779	−	4.00221i	0.706716	−	0.707498i
$33$	−1.55458	−	1.55458i	−0.270618	−	0.270618i
$34$	4.19906	+	2.13894i	0.720133	+	0.366826i
$35$	−10.4427	−	4.32551i	−1.76514	−	0.731145i
$36$	0.878520	−	5.55471i	0.146420	−	0.925785i
$37$	−8.77750	−	3.63576i	−1.44301	−	0.597715i	−0.482486	−	0.875904i	$-0.660266\pi$
$37$	−8.77750	−	3.63576i	−1.44301	−	0.597715i	−0.960527	+	0.278188i	$0.910266\pi$
$38$	−0.559818	+	7.12323i	−0.0908145	+	1.15554i
$39$	0.860074	−	1.30610i	0.137722	−	0.209143i
$40$	−11.2368	−	2.69378i	−1.77670	−	0.425925i
$41$	−0.0305502			−0.00477113			−0.00238557	−	0.999997i	$-0.500759\pi$
$41$	−0.0305502			−0.00477113			−0.00238557	+	0.999997i	$0.500759\pi$
$42$	1.29035	−	1.10231i	0.199105	−	0.170090i
$43$	−2.60064	−	6.27850i	−0.396594	−	0.957463i	−0.988468	−	0.151432i	$-0.951612\pi$
$43$	−2.60064	−	6.27850i	−0.396594	−	0.957463i	0.591874	−	0.806031i	$-0.298388\pi$
$44$	2.36876	+	9.85698i	0.357104	+	1.48600i
$45$	−10.6132	+	4.39611i	−1.58212	+	0.655334i
$46$	−1.84525	−	5.67697i	−0.272068	−	0.837024i
$47$	−2.44565	−	2.44565i	−0.356735	−	0.356735i	0.505873	−	0.862608i	$-0.331171\pi$
$47$	−2.44565	−	2.44565i	−0.356735	−	0.356735i	−0.862608	+	0.505873i	$0.831171\pi$
$48$	1.12616	−	1.31975i	0.162548	−	0.190490i
$49$	−0.654734			−0.0935335
$50$	5.11062	+	15.7230i	0.722751	+	2.22356i
$51$	1.33527	+	0.553088i	0.186975	+	0.0774477i
$52$	−6.52761	+	3.06436i	−0.905217	+	0.424950i
$53$	2.04108	+	4.92760i	0.280364	+	0.676858i	0.999844	−	0.0176550i	$-0.00562005\pi$
$53$	2.04108	+	4.92760i	0.280364	+	0.676858i	−0.719481	+	0.694513i	$0.755620\pi$
$54$	0.279310	−	3.55400i	0.0380093	−	0.483637i
$55$	14.6428	−	14.6428i	1.97443	−	1.97443i
$56$	−7.72871	+	1.22674i	−1.03279	+	0.163930i
$57$			2.19140i			0.290258i
$58$	−2.76252	+	2.35994i	−0.362736	+	0.309875i
$59$	−0.589917	+	1.42419i	−0.0768006	+	0.185413i	−0.957617	−	0.288045i	$-0.906995\pi$
$59$	−0.589917	+	1.42419i	−0.0768006	+	0.185413i	0.880816	+	0.473458i	$0.156995\pi$
$60$	−3.50042	−	0.553619i	−0.451903	−	0.0714719i
$61$	−0.595870	+	1.43856i	−0.0762933	+	0.184188i	−0.957425	−	0.288683i	$-0.906783\pi$
$61$	−0.595870	+	1.43856i	−0.0762933	+	0.184188i	0.881131	+	0.472872i	$0.156783\pi$
$62$	−3.12775	−	9.62260i	−0.397225	−	1.22207i
$63$	−5.50106	+	5.50106i	−0.693068	+	0.693068i
$64$	−7.60681	+	2.47718i	−0.950851	+	0.309648i
$65$	12.3023	+	8.10114i	1.52591	+	1.00482i
$66$	0.961110	+	2.95688i	0.118305	+	0.363967i
$67$	−1.10964	+	0.459627i	−0.135564	+	0.0561524i	−0.449434	−	0.893314i	$-0.648374\pi$
$67$	−1.10964	+	0.459627i	−0.135564	+	0.0561524i	0.313870	+	0.949466i	$0.398374\pi$
$68$	−3.91843	−	5.39075i	−0.475180	−	0.653725i
$69$	−0.700605	−	1.69141i	−0.0843430	−	0.203622i
$70$	10.3828	+	12.1540i	1.24098	+	1.45268i
$71$	9.00054			1.06817			0.534084	−	0.845432i	$-0.320657\pi$
$71$	9.00054			1.06817			0.534084	+	0.845432i	$0.320657\pi$
$72$	−4.67263	+	6.43581i	−0.550675	+	0.758468i
$73$		−	6.79471i		−	0.795261i	−0.917546	−	0.397631i	$-0.869833\pi$
$73$		−	6.79471i		−	0.795261i	0.917546	−	0.397631i	$-0.130167\pi$
$74$	8.72713	+	10.2159i	1.01451	+	1.18757i
$75$	1.94040	+	4.68453i	0.224058	+	0.540923i
$76$	5.27786	−	8.61696i	0.605412	−	0.988433i
$77$	5.36674	−	12.9564i	0.611596	−	1.47652i
$78$	−1.92220	+	1.09379i	−0.217646	+	0.123847i
$79$	10.7833			1.21322			0.606609	−	0.795000i	$-0.292529\pi$
$79$	10.7833			1.21322			0.606609	+	0.795000i	$0.292529\pi$
$80$	12.4309	+	10.6075i	1.38982	+	1.18595i
$81$			7.34227i			0.815808i
$82$	0.0384976	+	0.0196102i	0.00425135	+	0.00216558i
$83$	0.681723	+	1.64583i	0.0748289	+	0.180653i	0.956868	−	0.290524i	$-0.0938295\pi$
$83$	0.681723	+	1.64583i	0.0748289	+	0.180653i	−0.882039	+	0.471176i	$0.843829\pi$
$84$	−2.33360	+	0.560793i	−0.254616	+	0.0611876i
$85$	−5.20960	+	12.5771i	−0.565060	+	1.36418i
$86$	−0.752989	+	9.58117i	−0.0811969	+	1.03316i
$87$	−0.787940	+	0.787940i	−0.0844760	+	0.0844760i
$88$	3.34222	−	13.9417i	0.356282	−	1.48619i
$89$	13.6109			1.44275			0.721376	−	0.692544i	$-0.243510\pi$
$89$	13.6109			1.44275			0.721376	+	0.692544i	$0.243510\pi$
$90$	16.1960	+	1.27285i	1.70721	+	0.134170i
$91$	9.79672	+	1.88038i	1.02698	+	0.197117i
$92$	−1.31876	+	8.33828i	−0.137491	+	0.869325i
$93$	−1.18754	−	2.86698i	−0.123142	−	0.297292i
$94$	1.51201	+	4.65174i	0.155952	+	0.479791i
$95$	−20.6411			−2.11773
$96$	−2.26628	+	0.940192i	−0.231301	+	0.0959579i
$97$	7.18176	−	7.18176i	0.729198	−	0.729198i	−0.241262	−	0.970460i	$-0.577561\pi$
$97$	7.18176	−	7.18176i	0.729198	−	0.729198i	0.970460	+	0.241262i	$0.0775614\pi$
$98$	0.825060	+	0.420274i	0.0833437	+	0.0424541i
$99$	−5.45433	−	13.1679i	−0.548181	−	1.32343i
$100$	3.65245	−	23.0937i	0.365245	−	2.30937i
$101$	−0.915836	−	2.21102i	−0.0911291	−	0.220005i	0.871743	−	0.489964i	$-0.162990\pi$
$101$	−0.915836	−	2.21102i	−0.0911291	−	0.220005i	−0.962872	+	0.269959i	$0.912990\pi$
$102$	−1.32761	−	1.55408i	−0.131453	−	0.153877i
$103$	−8.61029	+	8.61029i	−0.848397	+	0.848397i	−0.989933	−	0.141536i	$-0.954796\pi$
$103$	−8.61029	+	8.61029i	−0.848397	+	0.848397i	0.141536	+	0.989933i	$0.454796\pi$
$104$	10.1927	+	0.328541i	0.999481	+	0.0322161i
$105$	3.46662	+	3.46662i	0.338307	+	0.338307i
$106$	0.590973	−	7.51965i	0.0574004	−	0.730373i
$107$	1.48045	−	0.613222i	0.143120	−	0.0592824i	−0.309974	−	0.950745i	$-0.600320\pi$
$107$	1.48045	−	0.613222i	0.143120	−	0.0592824i	0.453094	+	0.891463i	$0.350320\pi$
$108$	−2.63328	+	4.29926i	−0.253388	+	0.413696i
$109$	−9.79021	+	4.05524i	−0.937732	+	0.388421i	−0.798607	−	0.601853i	$-0.794429\pi$
$109$	−9.79021	+	4.05524i	−0.937732	+	0.388421i	−0.139126	+	0.990275i	$0.544429\pi$
$110$	−27.8512	+	9.05282i	−2.65551	+	0.863152i
$111$	2.91382	+	2.91382i	0.276568	+	0.276568i
$112$	10.5267	+	3.41520i	0.994683	+	0.322706i
$113$		−	10.4501i		−	0.983063i	−0.870860	−	0.491531i	$-0.836437\pi$
$113$		−	10.4501i		−	0.983063i	0.870860	−	0.491531i	$-0.163563\pi$
$114$	1.40666	−	2.76148i	0.131746	−	0.258637i
$115$	15.9316	−	6.59909i	1.48563	−	0.615368i
$116$	4.99602	−	1.20061i	0.463869	−	0.111473i
$117$	8.39172	−	5.68906i	0.775815	−	0.525954i
$118$	1.65757	−	1.41601i	0.152591	−	0.130354i
$119$			9.21927i			0.845129i
$120$	4.05567	+	2.94456i	0.370231	+	0.268801i
$121$	10.3894	+	10.3894i	0.944487	+	0.944487i
$122$	1.67429	−	1.43030i	0.151583	−	0.129493i
$123$	0.0122420	+	0.00507079i	0.00110382	+	0.000457218i
$124$	−2.23533	+	14.1336i	−0.200739	+	1.26923i
$125$	−25.2522	+	10.4598i	−2.25862	+	0.935552i
$126$	10.4633	−	3.40100i	0.932141	−	0.302985i
$127$	19.9532			1.77056			0.885282	−	0.465054i	$-0.153965\pi$
$127$	19.9532			1.77056			0.885282	+	0.465054i	$0.153965\pi$
$128$	11.1758	+	1.76120i	0.987809	+	0.155670i
$129$			2.94757i			0.259519i
$130$	−10.3025	−	18.1055i	−0.903593	−	1.58795i
$131$	−1.82503	−	0.755952i	−0.159454	−	0.0660478i	0.301529	−	0.953457i	$-0.402503\pi$
$131$	−1.82503	−	0.755952i	−0.159454	−	0.0660478i	−0.460983	+	0.887409i	$0.652503\pi$
$132$	0.686884	−	4.34303i	0.0597856	−	0.378013i
$133$	−12.9146	+	5.34939i	−1.11983	+	0.463851i
$134$	1.69334	+	0.133080i	0.146282	+	0.0114964i
$135$	10.2985			0.886350
$136$	1.47747	+	9.30837i	0.126692	+	0.798186i
$137$			14.2779i			1.21984i	0.792463	+	0.609920i	$0.208798\pi$
$137$			14.2779i			1.21984i	−0.792463	+	0.609920i	$0.791202\pi$
$138$	−0.202853	+	2.58114i	−0.0172680	+	0.219721i
$139$	1.75263	−	0.725963i	0.148656	−	0.0615754i	−0.307115	−	0.951672i	$-0.599364\pi$
$139$	1.75263	−	0.725963i	0.148656	−	0.0615754i	0.455771	+	0.890097i	$0.349364\pi$
$140$	−5.28218	−	21.9804i	−0.446426	−	1.85769i
$141$	0.574080	+	1.38595i	0.0483462	+	0.116718i
$142$	−11.3420	−	5.77745i	−0.951798	−	0.484833i
$143$	−10.0512	+	15.2637i	−0.840525	+	1.27641i
$144$	10.0193	−	5.11069i	0.834945	−	0.425891i
$145$	−7.42170	−	7.42170i	−0.616339	−	0.616339i
$146$	−4.36153	+	8.56232i	−0.360963	+	0.708623i
$147$	0.262363	+	0.108674i	0.0216394	+	0.00896332i
$148$	−4.43988	−	18.4754i	−0.364956	−	1.51867i
$149$	6.11550	+	2.53312i	0.501002	+	0.207522i	0.618849	−	0.785510i	$-0.287599\pi$
$149$	6.11550	+	2.53312i	0.501002	+	0.207522i	−0.117847	+	0.993032i	$0.537599\pi$
$150$	0.561822	−	7.14873i	0.0458726	−	0.583691i
$151$	−5.03387			−0.409651			−0.204825	−	0.978799i	$-0.565663\pi$
$151$	−5.03387			−0.409651			−0.204825	+	0.978799i	$0.565663\pi$
$152$	−12.1821	+	7.47075i	−0.988098	+	0.605958i
$153$	6.62541	+	6.62541i	0.535633	+	0.535633i
$154$	−15.0796	+	12.8821i	−1.21515	+	1.03807i
$155$	27.0044	−	11.1856i	2.16905	−	0.898450i
$156$	3.12436	−	0.144472i	0.250149	−	0.0115670i
$157$	−0.398624	+	0.962363i	−0.0318136	+	0.0768049i	−0.938988	−	0.343950i	$-0.888235\pi$
$157$	−0.398624	+	0.962363i	−0.0318136	+	0.0768049i	0.907174	+	0.420755i	$0.138235\pi$
$158$	−13.5885	−	6.92181i	−1.08105	−	0.550670i
$159$		−	2.31336i		−	0.183461i
$160$	−8.85578	−	21.3464i	−0.700111	−	1.68758i
$161$	8.25774	−	8.25774i	0.650801	−	0.650801i
$162$	4.71301	−	9.25232i	0.370289	−	0.726931i
$163$	−0.0922893	−	0.222806i	−0.00722865	−	0.0174515i	0.920224	−	0.391392i	$-0.128006\pi$
$163$	−0.0922893	−	0.222806i	−0.00722865	−	0.0174515i	−0.927453	+	0.373941i	$0.878006\pi$
$164$	−0.0359248	−	0.0494233i	−0.00280526	−	0.00385931i
$165$	−8.29806	+	3.43717i	−0.646003	+	0.267583i
$166$	0.197386	−	2.51158i	0.0153201	−	0.194936i
$167$			15.5075i			1.20000i	0.799998	+	0.600002i	$0.204834\pi$
$167$			15.5075i			1.20000i	−0.799998	+	0.600002i	$0.795166\pi$
$168$	3.30064	+	0.791257i	0.254650	+	0.0610468i
$169$	−12.0762	−	4.81310i	−0.928937	−	0.370239i
$170$	14.6381	−	12.5049i	1.12269	−	0.959082i
$171$	−5.43670	+	13.1253i	−0.415755	+	1.00372i
$172$	7.09903	−	11.5903i	0.541296	−	0.883754i
$173$	7.16012	−	17.2861i	0.544374	−	1.31424i	−0.377236	−	0.926117i	$-0.623125\pi$
$173$	7.16012	−	17.2861i	0.544374	−	1.31424i	0.921610	−	0.388118i	$-0.126875\pi$
$174$	1.49870	−	0.487139i	0.113616	−	0.0369299i
$175$	−22.8706	+	22.8706i	−1.72886	+	1.72886i
$176$	−13.1609	+	15.4232i	−0.992039	+	1.16257i
$177$	0.472780	−	0.472780i	0.0355363	−	0.0355363i
$178$	−17.1517	−	8.73683i	−1.28557	−	0.654853i
$179$	12.0137	+	4.97624i	0.897946	+	0.371941i	0.783430	−	0.621480i	$-0.213468\pi$
$179$	12.0137	+	4.97624i	0.897946	+	0.371941i	0.114516	+	0.993421i	$0.463468\pi$
$180$	−19.5922	−	12.0002i	−1.46032	−	0.894440i
$181$	−7.69007	+	3.18533i	−0.571599	+	0.236764i	−0.649712	−	0.760181i	$-0.725110\pi$
$181$	−7.69007	+	3.18533i	−0.571599	+	0.236764i	0.0781133	+	0.996944i	$0.475110\pi$
$182$	−11.1383	−	8.65806i	−0.825624	−	0.641778i
$183$	0.477551	−	0.477551i	0.0353016	−	0.0353016i
$184$	7.01417	−	9.66092i	0.517092	−	0.712212i
$185$	−27.4457	+	27.4457i	−2.01785	+	2.01785i
$186$	−0.343841	+	4.37509i	−0.0252116	+	0.320797i
$187$	−15.6046	−	6.46363i	−1.14112	−	0.472668i
$188$	1.08060	−	6.83243i	0.0788110	−	0.498306i
$189$	6.44346	−	2.66897i	0.468693	−	0.194139i
$190$	26.0107	+	13.2495i	1.88702	+	0.961221i
$191$			13.8788i			1.00423i	0.864799	+	0.502117i	$0.167445\pi$
$191$			13.8788i			1.00423i	−0.864799	+	0.502117i	$0.832555\pi$
$192$	3.45935	+	0.269947i	0.249657	+	0.0194818i
$193$	−0.907904	−	0.907904i	−0.0653524	−	0.0653524i	0.673675	−	0.739028i	$-0.264715\pi$
$193$	−0.907904	−	0.907904i	−0.0653524	−	0.0653524i	−0.739028	+	0.673675i	$0.764715\pi$
$194$	−13.6600	+	4.44009i	−0.980733	+	0.318780i
$195$	−3.58509	−	5.28823i	−0.256734	−	0.378698i
$196$	−0.769921	−	1.05921i	−0.0549943	−	0.0756580i
$197$	6.59972	−	15.9331i	0.470211	−	1.13519i	−0.493860	−	0.869542i	$-0.664414\pi$
$197$	6.59972	−	15.9331i	0.470211	−	1.13519i	0.964070	−	0.265647i	$-0.0855856\pi$
$198$	−1.57924	+	20.0946i	−0.112232	+	1.42806i
$199$	−4.34166	+	4.34166i	−0.307772	+	0.307772i	−0.844045	−	0.536273i	$-0.819832\pi$
$199$	−4.34166	+	4.34166i	−0.307772	+	0.307772i	0.536273	+	0.844045i	$0.319832\pi$
$200$	−19.4265	+	26.7569i	−1.37366	+	1.89200i
$201$	0.520941			0.0367443
$202$	−0.265171	+	3.37409i	−0.0186574	+	0.237400i
$203$	−6.56698	−	2.72013i	−0.460912	−	0.190916i
$204$	0.675413	+	2.81056i	0.0472884	+	0.196778i
$205$	−0.0477624	+	0.115309i	−0.00333587	+	0.00805351i
$206$	16.3772	−	5.32326i	1.14105	−	0.370889i
$207$		−	11.8688i		−	0.824939i
$208$	−12.6334	−	6.95673i	−0.875972	−	0.482363i
$209$		−	25.6097i		−	1.77146i
$210$	−2.14322	−	6.59366i	−0.147896	−	0.455006i
$211$	2.62957	−	6.34835i	0.181027	−	0.437038i	−0.807152	−	0.590344i	$-0.798992\pi$
$211$	2.62957	−	6.34835i	0.181027	−	0.437038i	0.988179	+	0.153306i	$0.0489920\pi$
$212$	−5.57158	+	9.09650i	−0.382658	+	0.624750i
$213$	−3.60667	−	1.49393i	−0.247125	−	0.102363i
$214$	−2.25921	−	0.177552i	−0.154436	−	0.0121372i
$215$	−27.7635			−1.89345
$216$	6.07801	−	3.72738i	0.413556	−	0.253616i
$217$	13.9971	−	13.9971i	0.950183	−	0.950183i
$218$	14.9401	+	1.17415i	1.01187	+	0.0795236i
$219$	−1.12780	+	2.72276i	−0.0762099	+	0.183987i
$220$	40.9076	+	6.46985i	2.75799	+	0.436197i
$221$	2.26470	−	11.7991i	0.152340	−	0.793690i
$222$	−1.80146	−	5.54222i	−0.120906	−	0.371970i
$223$	3.93888	+	3.93888i	0.263767	+	0.263767i	0.826583	−	0.562816i	$-0.190282\pi$
$223$	3.93888	+	3.93888i	0.263767	+	0.263767i	−0.562816	+	0.826583i	$0.690282\pi$
$224$	−11.0730	−	11.0608i	−0.739845	−	0.739028i
$225$			32.8719i			2.19146i
$226$	−6.70792	+	13.1686i	−0.446204	+	0.875965i
$227$	7.20502	−	2.98442i	0.478214	−	0.198083i	−0.130538	−	0.991443i	$-0.541670\pi$
$227$	7.20502	−	2.98442i	0.478214	−	0.198083i	0.608752	+	0.793361i	$0.291670\pi$
$228$	−3.54519	+	2.57693i	−0.234786	+	0.170661i
$229$	18.5938	+	7.70179i	1.22871	+	0.508949i	0.900169	−	0.435540i	$-0.143443\pi$
$229$	18.5938	+	7.70179i	1.22871	+	0.508949i	0.328542	+	0.944489i	$0.393443\pi$
$230$	−24.3121	−	1.91070i	−1.60309	−	0.125988i
$231$	−4.30109	+	4.30109i	−0.282991	+	0.282991i
$232$	−7.06637	−	1.69401i	−0.463930	−	0.111217i
$233$	9.61063	−	9.61063i	0.629613	−	0.629613i	−0.318358	−	0.947971i	$-0.603131\pi$
$233$	9.61063	−	9.61063i	0.629613	−	0.629613i	0.947971	+	0.318358i	$0.103131\pi$
$234$	−14.2266	+	1.78240i	−0.930021	+	0.116519i
$235$	−13.0544	+	5.40733i	−0.851578	+	0.352735i
$236$	−2.99771	+	0.720388i	−0.195134	+	0.0468932i
$237$	−4.32106	−	1.78984i	−0.280683	−	0.116263i
$238$	5.91785	−	11.6176i	0.383597	−	0.753058i
$239$	20.1563	−	20.1563i	1.30381	−	1.30381i	0.378000	−	0.925806i	$-0.376612\pi$
$239$	20.1563	−	20.1563i	1.30381	−	1.30381i	0.925806	−	0.378000i	$-0.123388\pi$
$240$	−3.22062	−	6.31391i	−0.207890	−	0.407561i
$241$	15.3552	−	15.3552i	0.989112	−	0.989112i	−0.0108292	−	0.999941i	$-0.503447\pi$
$241$	15.3552	−	15.3552i	0.989112	−	0.989112i	0.999941	+	0.0108292i	$0.00344710\pi$
$242$	−6.42316	−	19.7610i	−0.412897	−	1.27029i
$243$	4.11270	−	9.92893i	0.263830	−	0.636941i
$244$	−3.02796	+	0.727657i	−0.193845	+	0.0465835i
$245$	−1.02362	+	2.47123i	−0.0653966	+	0.157881i
$246$	−0.0121717	−	0.0142481i	−0.000776040	−	0.000908423i
$247$	17.8425	−	3.67383i	1.13529	−	0.233760i
$248$	11.8892	−	16.3755i	0.754964	−	1.03984i
$249$		−	0.772665i		−	0.0489656i
$250$	38.5355	+	3.02852i	2.43720	+	0.191541i
$251$	2.13893	−	0.885973i	0.135008	−	0.0559221i	−0.314157	−	0.949371i	$-0.601722\pi$
$251$	2.13893	−	0.885973i	0.135008	−	0.0559221i	0.449165	+	0.893449i	$0.351722\pi$
$252$	−15.3683	−	2.43062i	−0.968113	−	0.153115i
$253$	8.18759	+	19.7666i	0.514750	+	1.24272i
$254$	−25.1440	−	12.8080i	−1.57767	−	0.803645i
$255$	4.17515	−	4.17515i	0.261458	−	0.261458i
$256$	−12.9526	−	9.39311i	−0.809537	−	0.587069i
$257$		−	12.3296i		−	0.769101i	−0.923104	−	0.384551i	$-0.874356\pi$
$257$		−	12.3296i		−	0.769101i	0.923104	−	0.384551i	$-0.125644\pi$
$258$	1.89204	−	3.71436i	0.117793	−	0.231246i
$259$	−10.0591	+	24.2849i	−0.625044	+	1.50899i
$260$	1.36080	+	29.4287i	0.0843931	+	1.82509i
$261$	−6.67416	+	2.76453i	−0.413120	+	0.171120i
$262$	1.81456	+	2.12410i	0.112104	+	0.131227i
$263$	14.2392	+	14.2392i	0.878028	+	0.878028i	0.993330	−	0.115303i	$-0.0367838\pi$
$263$	14.2392	+	14.2392i	0.878028	+	0.878028i	−0.115303	+	0.993330i	$0.536784\pi$
$264$	−3.65337	+	5.03194i	−0.224849	+	0.309694i
$265$	21.7898			1.33854
$266$	19.7080	+	1.54886i	1.20837	+	0.0949667i
$267$	−5.45412	−	2.25917i	−0.333787	−	0.138259i
$268$	−2.04843	−	1.25465i	−0.125128	−	0.0766402i
$269$	−29.3922	−	12.1747i	−1.79208	−	0.742302i	−0.989277	−	0.146051i	$-0.953344\pi$
$269$	−29.3922	−	12.1747i	−1.79208	−	0.742302i	−0.802798	−	0.596251i	$-0.796656\pi$
$270$	−12.9775	−	6.61058i	−0.789788	−	0.402307i
$271$	−7.40382	−	7.40382i	−0.449750	−	0.449750i	0.445521	−	0.895271i	$-0.353018\pi$
$271$	−7.40382	−	7.40382i	−0.449750	−	0.449750i	−0.895271	+	0.445521i	$0.853018\pi$
$272$	4.11322	−	12.6783i	0.249401	−	0.768734i
$273$	−3.61360	−	2.37958i	−0.218705	−	0.144019i
$274$	9.16496	−	17.9922i	0.553675	−	1.08695i
$275$	−22.6764	−	54.7456i	−1.36744	−	3.30128i
$276$	1.91246	−	3.12240i	0.115116	−	0.187946i
$277$	7.54653	−	3.12587i	0.453427	−	0.187816i	−0.144269	−	0.989539i	$-0.546083\pi$
$277$	7.54653	−	3.12587i	0.453427	−	0.187816i	0.597696	+	0.801723i	$0.296083\pi$
$278$	−2.67456	−	0.210195i	−0.160410	−	0.0126067i
$279$		−	20.1179i		−	1.20443i
$280$	−7.45294	+	31.0892i	−0.445399	+	1.85793i
$281$	−4.20469			−0.250831			−0.125416	−	0.992104i	$-0.540026\pi$
$281$	−4.20469			−0.250831			−0.125416	+	0.992104i	$0.540026\pi$
$282$	0.166219	−	2.11500i	0.00989819	−	0.125946i
$283$	−11.0994	+	4.59753i	−0.659792	+	0.273295i	−0.687351	−	0.726325i	$-0.741227\pi$
$283$	−11.0994	+	4.59753i	−0.659792	+	0.273295i	0.0275589	+	0.999620i	$0.491227\pi$
$284$	10.5840	+	14.5608i	0.628044	+	0.864027i
$285$	8.27123	+	3.42606i	0.489946	+	0.202942i
$286$	22.4637	−	12.7825i	1.32831	−	0.755847i
$287$			0.0845237i			0.00498928i
$288$	−15.9064	+	0.00879443i	−0.937292	+	0.000518217i
$289$	−5.89642			−0.346848
$290$	4.58843	+	14.1164i	0.269442	+	0.828944i
$291$	−4.06990	+	1.68581i	−0.238582	+	0.0988239i
$292$	10.9923	−	7.99010i	0.643276	−	0.467585i
$293$	27.7054	+	11.4759i	1.61857	+	0.670432i	0.993882	−	0.110446i	$-0.0352279\pi$
$293$	27.7054	+	11.4759i	1.61857	+	0.670432i	0.624684	+	0.780878i	$0.285228\pi$
$294$	−0.260858	−	0.305357i	−0.0152135	−	0.0178088i
$295$	4.45317	+	4.45317i	0.259274	+	0.259274i
$296$	−6.26449	+	26.1316i	−0.364116	+	1.51887i
$297$			12.7775i			0.741423i
$298$	−6.08041	−	7.11765i	−0.352228	−	0.412314i
$299$	−12.5970	+	8.53996i	−0.728501	+	0.493879i
$300$	−5.29675	+	8.64780i	−0.305808	+	0.499281i
$301$	−17.3709	+	7.19524i	−1.00124	+	0.414727i
$302$	6.34340	+	3.23124i	0.365022	+	0.185937i
$303$			1.03801i			0.0596320i
$304$	20.1467	−	1.59454i	1.15549	−	0.0914534i
$305$	4.49811	+	4.49811i	0.257561	+	0.257561i
$306$	−4.09612	−	12.6018i	−0.234160	−	0.720398i
$307$	−28.6324	+	11.8599i	−1.63414	+	0.676883i	−0.995687	−	0.0927787i	$-0.970425\pi$
$307$	−28.6324	+	11.8599i	−1.63414	+	0.676883i	−0.638452	+	0.769661i	$0.720425\pi$
$308$	27.2715	−	6.55369i	1.55394	−	0.373431i
$309$	4.87945	−	2.02113i	0.277582	−	0.114978i
$310$	−41.2095	−	3.23868i	−2.34055	−	0.183944i
$311$	2.18929	+	2.18929i	0.124143	+	0.124143i	0.766449	−	0.642306i	$-0.222022\pi$
$311$	2.18929	+	2.18929i	0.124143	+	0.124143i	−0.642306	+	0.766449i	$0.722022\pi$
$312$	−4.02988	−	1.82347i	−0.228147	−	0.103234i
$313$	−9.49490	+	9.49490i	−0.536684	+	0.536684i	−0.922553	−	0.385870i	$-0.873901\pi$
$313$	−9.49490	+	9.49490i	−0.536684	+	0.536684i	0.385870	+	0.922553i	$0.373901\pi$
$314$	1.12006	−	0.956840i	0.0632089	−	0.0539976i
$315$	12.1628	+	29.3636i	0.685297	+	1.65445i
$316$	12.6804	+	17.4450i	0.713328	+	0.981356i
$317$	7.73315	+	18.6695i	0.434337	+	1.04858i	0.977874	+	0.209197i	$0.0670850\pi$
$317$	7.73315	+	18.6695i	0.434337	+	1.04858i	−0.543536	+	0.839386i	$0.682915\pi$
$318$	−1.48494	+	2.91516i	−0.0832715	+	0.163474i
$319$	9.20823	−	9.20823i	0.515562	−	0.515562i
$320$	−2.54267	+	32.5840i	−0.142139	+	1.82150i
$321$	−0.695025			−0.0387925
$322$	−15.7066	+	5.10530i	−0.875294	+	0.284507i
$323$	6.44274	+	15.5541i	0.358484	+	0.865456i
$324$	−11.8781	+	8.63398i	−0.659896	+	0.479666i
$325$	34.8886	−	23.6523i	1.93527	−	1.31199i
$326$	−0.0267214	+	0.340008i	−0.00147996	+	0.0188313i
$327$	4.59620			0.254171
$328$	0.0135456	+	0.0853406i	0.000747933	+	0.00471215i
$329$	−6.76644	+	6.76644i	−0.373046	+	0.373046i
$330$	12.6631	+	0.995196i	0.697079	+	0.0547838i
$331$	−3.29463	+	7.95393i	−0.181089	+	0.437188i	−0.988192	−	0.153224i	$-0.951034\pi$
$331$	−3.29463	+	7.95393i	−0.181089	+	0.437188i	0.807102	+	0.590411i	$0.201034\pi$
$332$	−1.86092	+	3.03825i	−0.102131	+	0.166745i
$333$	10.2233	+	24.6813i	0.560234	+	1.35252i
$334$	9.95425	−	19.5417i	0.544672	−	1.06927i
$335$			4.90680i			0.268087i
$336$	−3.65138	−	3.11578i	−0.199199	−	0.169980i
$337$	13.0137			0.708901			0.354450	−	0.935075i	$-0.384668\pi$
$337$	13.0137			0.708901			0.354450	+	0.935075i	$0.384668\pi$
$338$	12.1282	+	13.8169i	0.659687	+	0.751541i
$339$	−1.73453	+	4.18753i	−0.0942069	+	0.227436i
$340$	−26.4730	+	6.36180i	−1.43570	+	0.345017i
$341$	13.8782	+	33.5049i	0.751545	+	1.81439i
$342$	15.2762	−	13.0500i	0.826041	−	0.705664i
$343$		−	17.5556i		−	0.947912i
$344$	−16.3856	+	10.0486i	−0.883454	+	0.541785i
$345$	−7.47940			−0.402677
$346$	−20.1187	+	17.1869i	−1.08159	+	0.923971i
$347$	−11.0791	−	26.7473i	−0.594757	−	1.43587i	−0.878861	−	0.477077i	$-0.841696\pi$
$347$	−11.0791	−	26.7473i	−0.594757	−	1.43587i	0.284104	−	0.958793i	$-0.408304\pi$
$348$	−2.20127	−	0.348148i	−0.118000	−	0.0186627i
$349$	−24.8737	+	10.3030i	−1.33146	+	0.551508i	−0.931071	−	0.364838i	$-0.881124\pi$
$349$	−24.8737	+	10.3030i	−1.33146	+	0.551508i	−0.400387	+	0.916346i	$0.631124\pi$
$350$	43.5010	−	14.1396i	2.32523	−	0.755796i
$351$	−8.90213	+	1.83299i	−0.475161	+	0.0978375i
$352$	26.4848	−	10.9875i	1.41164	−	0.585636i
$353$	12.1165	−	12.1165i	0.644894	−	0.644894i	−0.306860	−	0.951755i	$-0.599278\pi$
$353$	12.1165	−	12.1165i	0.644894	−	0.644894i	0.951755	+	0.306860i	$0.0992784\pi$
$354$	−0.899248	+	0.292293i	−0.0477945	+	0.0155352i
$355$	14.0715	−	33.9717i	0.746839	−	1.80303i
$356$	16.0054	+	22.0193i	0.848286	+	1.16702i
$357$	1.53024	−	3.69432i	0.0809888	−	0.195524i
$358$	−11.9448	−	13.9824i	−0.631300	−	0.738992i
$359$		−	3.06691i		−	0.161865i	−0.996720	−	0.0809327i	$-0.974210\pi$
$359$		−	3.06691i		−	0.161865i	0.996720	−	0.0809327i	$-0.0257899\pi$
$360$	16.9861	+	27.6982i	0.895247	+	1.45982i
$361$	−4.61524	+	4.61524i	−0.242907	+	0.242907i
$362$	11.7353	+	0.922280i	0.616792	+	0.0484740i
$363$	−2.43874	−	5.88765i	−0.128001	−	0.309021i
$364$	8.47822	+	18.0601i	0.444379	+	0.946605i
$365$	−25.6460	−	10.6229i	−1.34237	−	0.556029i
$366$	−0.908323	+	0.295243i	−0.0474788	+	0.0154326i
$367$	−31.3282			−1.63532			−0.817660	−	0.575702i	$-0.804729\pi$
$367$	−31.3282			−1.63532			−0.817660	+	0.575702i	$0.804729\pi$
$368$	−15.0402	+	7.67175i	−0.784025	+	0.399918i
$369$	0.0607428	+	0.0607428i	0.00316214	+	0.00316214i
$370$	52.2029	−	16.9681i	2.71390	−	0.882131i
$371$	13.6333	−	5.64709i	0.707805	−	0.293182i
$372$	3.24166	−	5.29254i	0.168072	−	0.274405i
$373$	−4.75194	−	11.4722i	−0.246046	−	0.594008i	0.751815	−	0.659374i	$-0.229178\pi$
$373$	−4.75194	−	11.4722i	−0.246046	−	0.594008i	−0.997861	+	0.0653661i	$0.979178\pi$
$374$	15.5150	+	18.1617i	0.802263	+	0.939119i
$375$	11.8551			0.612196
$376$	−5.74745	+	7.91621i	−0.296402	+	0.408247i
$377$	7.73639	+	5.09447i	0.398444	+	0.262378i
$378$	−9.83291	−	0.772772i	−0.505750	−	0.0397471i
$379$	15.9148	+	6.59212i	0.817488	+	0.338615i	0.751937	−	0.659235i	$-0.229120\pi$
$379$	15.9148	+	6.59212i	0.817488	+	0.338615i	0.0655507	+	0.997849i	$0.479120\pi$
$380$	−24.2724	−	33.3926i	−1.24515	−	1.71300i
$381$	−7.99561	−	3.31189i	−0.409627	−	0.169673i
$382$	8.90880	−	17.4893i	0.455814	−	0.894830i
$383$	−3.37391	−	3.37391i	−0.172399	−	0.172399i	0.615634	−	0.788033i	$-0.288900\pi$
$383$	−3.37391	−	3.37391i	−0.172399	−	0.172399i	−0.788033	+	0.615634i	$0.788900\pi$
$384$	−4.18600	−	2.56073i	−0.213616	−	0.130677i
$385$	−40.5125	−	40.5125i	−2.06471	−	2.06471i
$386$	0.561306	+	1.72687i	0.0285697	+	0.0878956i
$387$	−7.31268	+	17.6544i	−0.371724	+	0.897422i
$388$	20.0637	+	3.17323i	1.01858	+	0.161096i
$389$	7.62474	+	18.4078i	0.386590	+	0.933310i	0.990657	+	0.136377i	$0.0435458\pi$
$389$	7.62474	+	18.4078i	0.386590	+	0.933310i	−0.604067	+	0.796933i	$0.706454\pi$
$390$	1.12322	+	8.96521i	0.0568763	+	0.453971i
$391$	−9.94553	−	9.94553i	−0.502967	−	0.502967i
$392$	0.290303	+	1.82897i	0.0146625	+	0.0923771i
$393$	0.605846	+	0.605846i	0.0305609	+	0.0305609i
$394$	−18.5441	+	15.8417i	−0.934237	+	0.798093i
$395$	16.8587	−	40.7006i	0.848255	−	2.04787i
$396$	14.8888	−	24.3084i	0.748191	−	1.22154i
$397$	3.56723	+	8.61204i	0.179034	+	0.432226i	0.987764	−	0.155953i	$-0.0498449\pi$
$397$	3.56723	+	8.61204i	0.179034	+	0.432226i	−0.808731	+	0.588179i	$0.799845\pi$
$398$	8.25803	−	2.68421i	0.413938	−	0.134547i
$399$	6.06299			0.303529
$400$	41.6554	−	21.2477i	2.08277	−	1.06239i
$401$	24.7905	−	24.7905i	1.23798	−	1.23798i	0.277155	−	0.960825i	$-0.410608\pi$
$401$	24.7905	−	24.7905i	1.23798	−	1.23798i	0.960825	−	0.277155i	$-0.0893915\pi$
$402$	−0.656461	−	0.334392i	−0.0327413	−	0.0166780i
$403$	−21.3522	+	14.4754i	−1.06363	+	0.721073i
$404$	2.49998	−	4.08162i	0.124379	−	0.203068i
$405$	27.7127	+	11.4790i	1.37705	+	0.570395i
$406$	6.52929	+	7.64311i	0.324043	+	0.379321i
$407$	−34.0523	−	34.0523i	−1.68791	−	1.68791i
$408$	0.952980	−	3.97526i	0.0471796	−	0.196805i
$409$			19.5210i			0.965252i	0.875827	+	0.482626i	$0.160317\pi$
$409$			19.5210i			0.965252i	−0.875827	+	0.482626i	$0.839683\pi$
$410$	0.134204	−	0.114647i	0.00662787	−	0.00566201i
$411$	2.36987	−	5.72138i	0.116897	−	0.282215i
$412$	−24.0546	−	3.80442i	−1.18508	−	0.187430i
$413$	3.94032	+	1.63213i	0.193891	+	0.0803121i
$414$	−7.61859	+	14.9564i	−0.374433	+	0.735068i
$415$	7.27782			0.357254
$416$	11.4544	+	16.8759i	0.561600	+	0.827409i
$417$	−0.822806			−0.0402930
$418$	−16.4389	+	32.2719i	−0.804052	+	1.57847i
$419$	−15.2178	−	6.30342i	−0.743438	−	0.307942i	−0.0213769	−	0.999771i	$-0.506805\pi$
$419$	−15.2178	−	6.30342i	−0.743438	−	0.307942i	−0.722061	+	0.691829i	$0.756805\pi$
$420$	−1.53171	+	9.68469i	−0.0747398	+	0.472565i
$421$	−6.43183	+	15.5278i	−0.313468	+	0.756779i	0.686103	+	0.727504i	$0.259320\pi$
$421$	−6.43183	+	15.5278i	−0.313468	+	0.756779i	−0.999571	+	0.0292751i	$0.990680\pi$
$422$	−7.38865	+	6.31191i	−0.359674	+	0.307259i
$423$			9.72537i			0.472864i
$424$	12.8600	−	7.88651i	0.624539	−	0.383003i
$425$	27.5451	+	27.5451i	1.33614	+	1.33614i
$426$	3.58597	+	4.19769i	0.173741	+	0.203379i
$427$	3.98008	+	1.64860i	0.192610	+	0.0797816i
$428$	2.73296	+	1.67393i	0.132102	+	0.0809123i
$429$	6.56119	−	4.44808i	0.316777	−	0.214755i
$430$	34.9860	+	17.8214i	1.68717	+	0.859423i
$431$	−3.79419	+	3.79419i	−0.182760	+	0.182760i	−0.792557	−	0.609797i	$-0.791251\pi$
$431$	−3.79419	+	3.79419i	−0.182760	+	0.182760i	0.609797	+	0.792557i	$0.291251\pi$
$432$	−10.0518	+	0.795566i	−0.483616	+	0.0382767i
$433$	−33.2223			−1.59656			−0.798280	−	0.602287i	$-0.794256\pi$
$433$	−33.2223			−1.59656			−0.798280	+	0.602287i	$0.794256\pi$
$434$	−26.6230	+	8.65361i	−1.27795	+	0.415386i
$435$	1.74213	+	4.20588i	0.0835288	+	0.201656i
$436$	−18.0730	−	11.0697i	−0.865542	−	0.530141i
$437$	8.16113	−	19.7027i	0.390400	−	0.942508i
$438$	3.16893	−	2.70713i	0.151418	−	0.129352i
$439$	17.2022	+	17.2022i	0.821014	+	0.821014i	0.986254	−	0.165239i	$-0.0528396\pi$
$439$	17.2022	+	17.2022i	0.821014	+	0.821014i	−0.165239	+	0.986254i	$0.552840\pi$
$440$	−47.3965	−	34.4115i	−2.25954	−	1.64050i
$441$	1.30181	+	1.30181i	0.0619908	+	0.0619908i
$442$	−10.4277	+	13.4148i	−0.495994	+	0.638077i
$443$	12.7028	+	30.6673i	0.603530	+	1.45705i	0.869924	+	0.493186i	$0.164168\pi$
$443$	12.7028	+	30.6673i	0.603530	+	1.45705i	−0.266394	+	0.963864i	$0.585832\pi$
$444$	−1.28746	+	8.14036i	−0.0611002	+	0.386324i
$445$	21.2794	−	51.3730i	1.00874	−	2.43531i
$446$	−2.43519	−	7.49193i	−0.115310	−	0.354753i
$447$	−2.03013	−	2.03013i	−0.0960220	−	0.0960220i
$448$	6.85367	+	21.0459i	0.323805	+	0.994326i
$449$	22.9156	+	22.9156i	1.08146	+	1.08146i	0.996374	+	0.0850814i	$0.0271150\pi$
$449$	22.9156	+	22.9156i	1.08146	+	1.08146i	0.0850814	+	0.996374i	$0.472885\pi$
$450$	21.1005	−	41.4233i	0.994685	−	1.95271i
$451$	−0.143065	−	0.0592596i	−0.00673668	−	0.00279043i
$452$	16.9059	−	12.2886i	0.795187	−	0.578006i
$453$	2.01716	+	0.835534i	0.0947744	+	0.0392568i
$454$	−10.9951	−	0.864107i	−0.516024	−	0.0405545i
$455$	22.4136	−	34.0370i	1.05076	−	1.59568i
$456$	6.12159	−	0.971646i	0.286670	−	0.0455015i
$457$	0.0888898			0.00415809			0.00207904	−	0.999998i	$-0.499338\pi$
$457$	0.0888898			0.00415809			0.00207904	+	0.999998i	$0.499338\pi$
$458$	−18.4871	−	21.6407i	−0.863844	−	1.01120i
$459$	−3.21448	−	7.76043i	−0.150039	−	0.362226i
$460$	29.4103	+	18.0137i	1.37126	+	0.839892i
$461$	−12.9297	+	5.35567i	−0.602198	+	0.249438i	−0.662888	−	0.748718i	$-0.730670\pi$
$461$	−12.9297	+	5.35567i	−0.602198	+	0.249438i	0.0606908	+	0.998157i	$0.480670\pi$
$462$	8.18086	−	2.65912i	0.380608	−	0.123714i
$463$	22.1982	+	22.1982i	1.03164	+	1.03164i	0.999483	+	0.0321568i	$0.0102376\pi$
$463$	22.1982	+	22.1982i	1.03164	+	1.03164i	0.0321568	+	0.999483i	$0.489762\pi$
$464$	7.81727	+	6.67060i	0.362908	+	0.309675i
$465$	−12.6778			−0.587917
$466$	−18.2798	+	5.94172i	−0.846797	+	0.275245i
$467$	−5.62561	−	2.33021i	−0.260322	−	0.107829i	0.248705	−	0.968579i	$-0.419995\pi$
$467$	−5.62561	−	2.33021i	−0.260322	−	0.107829i	−0.509028	+	0.860750i	$0.669995\pi$
$468$	19.0717	+	6.88597i	0.881589	+	0.318304i
$469$	1.27166	+	3.07005i	0.0587197	+	0.141762i
$470$	19.9215	+	1.56564i	0.918908	+	0.0722174i
$471$	0.319471	−	0.319471i	0.0147204	−	0.0147204i
$472$	4.23996	+	1.01644i	0.195160	+	0.0467854i
$473$		−	34.4466i		−	1.58386i
$474$	4.29626	+	5.02915i	0.197334	+	0.230996i
$475$	−22.6031	+	54.5686i	−1.03710	+	2.50378i
$476$	−14.9147	+	10.8412i	−0.683614	+	0.496906i
$477$	5.73926	−	13.8558i	0.262783	−	0.634413i
$478$	−38.3383	+	12.4615i	−1.75355	+	0.569978i
$479$	−10.8131	+	10.8131i	−0.494065	+	0.494065i	−0.909584	−	0.415519i	$-0.863600\pi$
$479$	−10.8131	+	10.8131i	−0.494065	+	0.494065i	0.415519	+	0.909584i	$0.363600\pi$
$480$	0.00554201	+	10.0238i	0.000252957	+	0.457520i
$481$	18.8395	−	28.6094i	0.859006	−	1.30448i
$482$	−29.2062	+	9.49323i	−1.33031	+	0.432405i
$483$	−4.67966	+	1.93838i	−0.212932	+	0.0881992i
$484$	−4.59049	+	29.0248i	−0.208659	+	1.31931i
$485$	−15.8788	−	38.3349i	−0.721021	−	1.74070i
$486$	−11.5560	+	9.87194i	−0.524190	+	0.447800i
$487$	10.7050			0.485091			0.242545	−	0.970140i	$-0.422018\pi$
$487$	10.7050			0.485091			0.242545	+	0.970140i	$0.422018\pi$
$488$	4.28275	+	1.02670i	0.193871	+	0.0464763i
$489$			0.104601i			0.00473020i
$490$	2.87619	−	2.45705i	0.129933	−	0.110998i
$491$	−4.53631	−	10.9516i	−0.204721	−	0.494239i	0.787856	−	0.615859i	$-0.211191\pi$
$491$	−4.53631	−	10.9516i	−0.204721	−	0.494239i	−0.992577	+	0.121620i	$0.961191\pi$
$492$	0.00619229	+	0.0257676i	0.000279170	+	0.00116169i
$493$	−3.27610	+	7.90920i	−0.147548	+	0.356212i
$494$	−24.8423	−	6.82351i	−1.11771	−	0.307004i
$495$	−58.2284			−2.61717
$496$	−25.4935	+	13.0038i	−1.14469	+	0.583888i
$497$		−	24.9020i		−	1.11701i
$498$	−0.495974	+	0.973669i	−0.0222251	+	0.0436312i
$499$	0.0771298	+	0.186208i	0.00345280	+	0.00833580i	0.925597	−	0.378512i	$-0.123564\pi$
$499$	0.0771298	+	0.186208i	0.00345280	+	0.00833580i	−0.922144	+	0.386847i	$0.873564\pi$
$500$	−46.6163	−	28.5523i	−2.08475	−	1.27690i
$501$	2.57397	−	6.21411i	0.114996	−	0.277626i
$502$	−3.26406	−	0.256524i	−0.145682	−	0.0114492i
$503$	−14.2199	+	14.2199i	−0.634035	+	0.634035i	−0.949078	−	0.315042i	$-0.897981\pi$
$503$	−14.2199	+	14.2199i	−0.634035	+	0.634035i	0.315042	+	0.949078i	$0.397981\pi$
$504$	17.8061	+	12.9279i	0.793146	+	0.575852i
$505$	−9.77713			−0.435076
$506$	2.37063	−	30.1644i	0.105387	−	1.34097i
$507$	4.04024	+	3.93313i	0.179433	+	0.174676i
$508$	23.4636	+	32.2798i	1.04103	+	1.43219i
$509$	2.35220	+	5.67872i	0.104260	+	0.251705i	0.967397	−	0.253264i	$-0.0815041\pi$
$509$	2.35220	+	5.67872i	0.104260	+	0.251705i	−0.863138	+	0.504969i	$0.831504\pi$
$510$	−7.94132	+	2.58126i	−0.351648	+	0.114300i
$511$	−18.7991			−0.831622
$512$	10.2927	+	20.1509i	0.454877	+	0.890554i
$513$	9.00582	−	9.00582i	0.397617	−	0.397617i
$514$	−7.91439	+	15.5371i	−0.349089	+	0.685313i
$515$	19.0373	+	45.9601i	0.838884	+	2.02525i
$516$	−4.76849	+	3.46613i	−0.209921	+	0.152588i
$517$	−6.70896	−	16.1969i	−0.295060	−	0.712337i
$518$	28.2644	−	24.1455i	1.24187	−	1.06089i
$519$	−5.73837	+	5.73837i	−0.251886	+	0.251886i
$520$	17.1755	−	37.9579i	0.753195	−	1.66456i
$521$	−2.29471	−	2.29471i	−0.100533	−	0.100533i	0.655051	−	0.755584i	$-0.272647\pi$
$521$	−2.29471	−	2.29471i	−0.100533	−	0.100533i	−0.755584	+	0.655051i	$0.772647\pi$
$522$	10.1850	+	0.800441i	0.445784	+	0.0350343i
$523$	0.996233	−	0.412653i	0.0435622	−	0.0180441i	−0.360796	−	0.932645i	$-0.617495\pi$
$523$	0.996233	−	0.412653i	0.0435622	−	0.0180441i	0.404358	+	0.914601i	$0.367495\pi$
$524$	−0.923144	−	3.84143i	−0.0403278	−	0.167814i
$525$	12.9608	−	5.36853i	0.565655	−	0.234302i
$526$	−8.80332	−	27.0836i	−0.383843	−	1.18090i
$527$	−16.8579	−	16.8579i	−0.734342	−	0.734342i
$528$	7.83377	−	3.99587i	0.340921	−	0.173898i
$529$		−	5.18351i		−	0.225370i
$530$	−27.4583	−	13.9869i	−1.19271	−	0.607551i
$531$	4.00463	−	1.65877i	0.173786	−	0.0719846i
$532$	−23.8407	−	14.6023i	−1.03363	−	0.633092i
$533$	0.0207631	−	0.108176i	0.000899352	−	0.00468560i
$534$	5.42281	+	6.34788i	0.234668	+	0.274700i
$535$		−	6.54653i		−	0.283031i
$536$	1.77595	+	2.89593i	0.0767094	+	0.125085i
$537$	−3.98813	−	3.98813i	−0.172100	−	0.172100i
$538$	29.2235	+	34.2087i	1.25992	+	1.47484i
$539$	−3.06610	−	1.27002i	−0.132066	−	0.0547036i
$540$	12.1102	+	16.6606i	0.521142	+	0.716957i
$541$	−25.5732	+	10.5928i	−1.09948	+	0.455418i	−0.857302	−	0.514815i	$-0.827861\pi$
$541$	−25.5732	+	10.5928i	−1.09948	+	0.455418i	−0.242175	+	0.970233i	$0.577861\pi$
$542$	4.57737	+	14.0824i	0.196615	+	0.604891i
$543$	3.61025			0.154931
$544$	−13.3214	+	13.3362i	−0.571152	+	0.571784i
$545$			43.2922i			1.85443i
$546$	3.02621	+	5.31819i	0.129510	+	0.227598i
$547$	−38.4895	−	15.9429i	−1.64569	−	0.681669i	−0.648839	−	0.760926i	$-0.724745\pi$
$547$	−38.4895	−	15.9429i	−1.64569	−	0.681669i	−0.996854	+	0.0792571i	$0.974745\pi$
$548$	−23.0983	+	16.7897i	−0.986712	+	0.717222i
$549$	4.04504	−	1.67551i	0.172638	−	0.0715091i
$550$	−6.56571	+	83.5433i	−0.279963	+	3.56230i
$551$	−12.9803			−0.552979
$552$	−4.41424	+	2.70707i	−0.187883	+	0.115220i
$553$		−	29.8344i		−	1.26869i
$554$	−11.5162	−	0.905064i	−0.489277	−	0.0384525i
$555$	15.5534	−	6.44245i	0.660207	−	0.273467i
$556$	3.23541	+	1.98168i	0.137212	+	0.0840419i
$557$	−1.12136	−	2.70721i	−0.0475136	−	0.114708i	0.898341	−	0.439299i	$-0.144773\pi$
$557$	−1.12136	−	2.70721i	−0.0475136	−	0.114708i	−0.945854	+	0.324591i	$0.894773\pi$
$558$	−12.9137	+	25.3515i	−0.546680	+	1.07321i
$559$	23.9992	−	4.94153i	1.01506	−	0.209004i
$560$	29.3479	−	34.3928i	1.24018	−	1.45336i
$561$	5.18018	+	5.18018i	0.218707	+	0.218707i
$562$	5.29852	+	2.69899i	0.223505	+	0.113850i
$563$	31.7116	+	13.1354i	1.33648	+	0.553589i	0.932498	−	0.361176i	$-0.117625\pi$
$563$	31.7116	+	13.1354i	1.33648	+	0.553589i	0.403985	+	0.914765i	$0.367625\pi$
$564$	−1.56708	+	2.55851i	−0.0659859	+	0.107733i
$565$	−39.4429	−	16.3378i	−1.65938	−	0.687336i
$566$	16.9380	+	1.33117i	0.711959	+	0.0559531i
$567$	20.3140			0.853108
$568$	−3.99075	−	25.1426i	−0.167448	−	1.05496i
$569$	−6.07877	−	6.07877i	−0.254835	−	0.254835i	0.568114	−	0.822950i	$-0.307673\pi$
$569$	−6.07877	−	6.07877i	−0.254835	−	0.254835i	−0.822950	+	0.568114i	$0.807673\pi$
$570$	−8.22376	−	9.62663i	−0.344456	−	0.403215i
$571$	−28.0933	+	11.6366i	−1.17567	+	0.486977i	−0.883062	−	0.469256i	$-0.844522\pi$
$571$	−28.0933	+	11.6366i	−1.17567	+	0.486977i	−0.292605	+	0.956233i	$0.594522\pi$
$572$	−36.5127	+	1.68836i	−1.52667	+	0.0705940i
$573$	2.30364	−	5.56147i	0.0962358	−	0.232334i
$574$	0.0542558	−	0.106512i	0.00226459	−	0.00444573i
$575$		−	49.3446i		−	2.05781i
$576$	20.0500	+	10.1992i	0.835415	+	0.424967i
$577$	−12.7075	+	12.7075i	−0.529020	+	0.529020i	−0.920280	−	0.391260i	$-0.872039\pi$
$577$	−12.7075	+	12.7075i	−0.529020	+	0.529020i	0.391260	+	0.920280i	$0.372039\pi$
$578$	7.43034	+	3.78491i	0.309061	+	0.157432i
$579$	0.213117	+	0.514509i	0.00885682	+	0.0213823i
$580$	3.27925	−	20.7340i	0.136163	−	0.860934i
$581$	4.55354	−	1.88614i	0.188913	−	0.0782501i
$582$	6.21079	+	0.488109i	0.257445	+	0.0202328i
$583$			27.0349i			1.11967i
$584$	−18.9807	+	3.01271i	−0.785429	+	0.124667i
$585$	−8.35313	−	40.5681i	−0.345359	−	1.67728i
$586$	−27.5464	−	32.2454i	−1.13793	−	1.33205i
$587$	3.40655	−	8.22415i	0.140603	−	0.339447i	−0.837854	−	0.545894i	$-0.816190\pi$
$587$	3.40655	−	8.22415i	0.140603	−	0.339447i	0.978458	+	0.206447i	$0.0661901\pi$
$588$	0.132710	+	0.552238i	0.00547286	+	0.0227739i
$589$	13.8333	−	33.3965i	0.569991	−	1.37608i
$590$	−2.75315	−	8.47013i	−0.113345	−	0.348710i
$591$	−5.28924	+	5.28924i	−0.217570	+	0.217570i
$592$	24.6681	−	28.9085i	1.01385	−	1.18813i
$593$	−18.3627	+	18.3627i	−0.754067	+	0.754067i	−0.975236	−	0.221169i	$-0.929013\pi$
$593$	−18.3627	+	18.3627i	−0.754067	+	0.754067i	0.221169	+	0.975236i	$0.429013\pi$
$594$	8.20185	−	16.1014i	0.336526	−	0.660650i
$595$	34.7973	+	14.4135i	1.42655	+	0.590896i
$596$	3.09337	+	12.8723i	0.126709	+	0.527269i
$597$	2.46042	−	1.01914i	0.100698	−	0.0417105i
$598$	21.3558	−	2.67559i	0.873303	−	0.109413i
$599$	11.8896	−	11.8896i	0.485794	−	0.485794i	−0.421182	−	0.906976i	$-0.638385\pi$
$599$	11.8896	−	11.8896i	0.485794	−	0.485794i	0.906976	+	0.421182i	$0.138385\pi$
$600$	12.2257	−	7.49749i	0.499112	−	0.306084i
$601$	−19.4345	+	19.4345i	−0.792750	+	0.792750i	−0.981940	−	0.189191i	$-0.939414\pi$
$601$	−19.4345	+	19.4345i	−0.792750	+	0.792750i	0.189191	+	0.981940i	$0.439414\pi$
$602$	26.5084	+	2.08331i	1.08040	+	0.0849093i
$603$	3.12016	+	1.29241i	0.127063	+	0.0526311i
$604$	−5.91947	−	8.14367i	−0.240860	−	0.331361i
$605$	55.4565	−	22.9708i	2.25463	−	0.933897i
$606$	0.666298	−	1.30804i	0.0270665	−	0.0531355i
$607$			15.6810i			0.636471i	0.948012	+	0.318235i	$0.103090\pi$
$607$			15.6810i			0.636471i	−0.948012	+	0.318235i	$0.896910\pi$
$608$	−26.4113	−	10.9228i	−1.07112	−	0.442978i
$609$	2.18001	+	2.18001i	0.0883384	+	0.0883384i
$610$	−2.78093	−	8.55560i	−0.112597	−	0.346406i
$611$	10.3220	−	6.99769i	0.417584	−	0.283096i
$612$	−2.92741	+	18.5094i	−0.118333	+	0.748199i
$613$	−8.26934	+	19.9639i	−0.333995	+	0.806336i	0.664272	+	0.747491i	$0.268742\pi$
$613$	−8.26934	+	19.9639i	−0.333995	+	0.806336i	−0.998267	+	0.0588449i	$0.981258\pi$
$614$	43.6939	+	3.43392i	1.76334	+	0.138582i
$615$	0.0382784	−	0.0382784i	0.00154354	−	0.00154354i
$616$	−38.5728	−	9.24699i	−1.55414	−	0.372572i
$617$	−18.4583			−0.743103			−0.371552	−	0.928412i	$-0.621174\pi$
$617$	−18.4583			−0.743103			−0.371552	+	0.928412i	$0.621174\pi$
$618$	−7.44618	−	0.585198i	−0.299529	−	0.0235401i
$619$	37.6771	+	15.6064i	1.51437	+	0.627273i	0.976454	−	0.215724i	$-0.0692111\pi$
$619$	37.6771	+	15.6064i	1.51437	+	0.627273i	0.537918	+	0.842997i	$0.319211\pi$
$620$	49.8511	+	30.5336i	2.00207	+	1.22626i
$621$	−4.07183	+	9.83027i	−0.163397	+	0.394475i
$622$	−1.35351	−	4.16412i	−0.0542710	−	0.166966i
$623$		−	37.6575i		−	1.50872i
$624$	3.90774	+	4.88461i	0.156435	+	0.195541i
$625$			53.2130i			2.12852i
$626$	18.0597	−	5.87017i	0.721812	−	0.234619i
$627$	−4.25076	+	10.2623i	−0.169759	+	0.409835i
$628$	−2.02564	+	0.486787i	−0.0808318	+	0.0194249i
$629$	29.2484	+	12.1151i	1.16621	+	0.483061i
$630$	3.52162	−	44.8097i	0.140305	−	1.78526i
$631$	26.6954			1.06273			0.531363	−	0.847144i	$-0.321680\pi$
$631$	26.6954			1.06273			0.531363	+	0.847144i	$0.321680\pi$
$632$	−4.78122	−	30.1227i	−0.190187	−	1.19822i
$633$	−2.10743	+	2.10743i	−0.0837628	+	0.0837628i
$634$	2.23905	−	28.4902i	0.0889242	−	1.13149i
$635$	31.1951	−	75.3116i	1.23794	−	2.98865i
$636$	3.74249	−	2.72034i	0.148399	−	0.107869i
$637$	0.444984	−	2.31836i	0.0176309	−	0.0918568i
$638$	−17.5145	+	5.69293i	−0.693404	+	0.225385i
$639$	−17.8957	−	17.8957i	−0.707944	−	0.707944i
$640$	24.1198	−	39.4284i	0.953420	−	1.55855i
$641$			10.7626i			0.425097i	0.977151	+	0.212548i	$0.0681763\pi$
$641$			10.7626i			0.425097i	−0.977151	+	0.212548i	$0.931824\pi$
$642$	0.875832	+	0.446137i	0.0345664	+	0.0176076i
$643$	−8.97502	+	3.71757i	−0.353940	+	0.146607i	−0.552567	−	0.833468i	$-0.686352\pi$
$643$	−8.97502	+	3.71757i	−0.353940	+	0.146607i	0.198627	+	0.980075i	$0.436352\pi$
$644$	23.0697	+	3.64865i	0.909072	+	0.143777i
$645$	11.1253	+	4.60825i	0.438058	+	0.181450i
$646$	1.86543	−	23.7361i	0.0733943	−	0.933883i
$647$	4.95783	−	4.95783i	0.194913	−	0.194913i	−0.602902	−	0.797815i	$-0.705989\pi$
$647$	4.95783	−	4.95783i	0.194913	−	0.194913i	0.797815	+	0.602902i	$0.205989\pi$
$648$	20.5103	−	3.25549i	0.805722	−	0.127888i
$649$	−5.52512	+	5.52512i	−0.216880	+	0.216880i
$650$	−59.1471	+	7.41031i	−2.31994	+	0.290656i
$651$	−7.93213	+	3.28560i	−0.310885	+	0.128773i
$652$	0.251924	−	0.411307i	0.00986611	−	0.0161080i
$653$	−16.9683	−	7.02851i	−0.664022	−	0.275047i	0.0251078	−	0.999685i	$-0.492007\pi$
$653$	−16.9683	−	7.02851i	−0.664022	−	0.275047i	−0.689130	+	0.724638i	$0.742007\pi$
$654$	−5.79188	−	2.95030i	−0.226480	−	0.115366i
$655$	−5.70654	+	5.70654i	−0.222973	+	0.222973i
$656$	0.0377107	−	0.116236i	0.00147235	−	0.00453827i
$657$	−13.5099	+	13.5099i	−0.527072	+	0.527072i
$658$	12.8701	−	4.18331i	0.501727	−	0.163082i
$659$	−9.45512	+	22.8267i	−0.368319	+	0.889201i	0.625707	+	0.780058i	$0.284811\pi$
$659$	−9.45512	+	22.8267i	−0.368319	+	0.889201i	−0.994026	+	0.109143i	$0.965189\pi$
$660$	−15.3185	−	9.38252i	−0.596271	−	0.365214i
$661$	11.2619	−	27.1886i	0.438037	−	1.05751i	−0.538589	−	0.842568i	$-0.681043\pi$
$661$	11.2619	−	27.1886i	0.438037	−	1.05751i	0.976626	−	0.214946i	$-0.0689574\pi$
$662$	9.25733	−	7.90828i	0.359797	−	0.307364i
$663$	−2.86594	+	4.35218i	−0.111304	+	0.169025i
$664$	4.29527	−	2.63411i	0.166689	−	0.102223i
$665$			57.1081i			2.21456i
$666$	2.96005	−	37.6643i	0.114700	−	1.45946i
$667$	10.0187	−	4.14989i	0.387926	−	0.160684i
$668$	−25.0876	+	18.2357i	−0.970668	+	0.705560i
$669$	−0.924592	−	2.23216i	−0.0357468	−	0.0863004i
$670$	3.14968	−	6.18328i	0.121683	−	0.238881i
$671$	−5.58088	+	5.58088i	−0.215447	+	0.215447i
$672$	2.60125	+	6.27016i	0.100345	+	0.241877i
$673$			35.5378i			1.36988i	0.728598	+	0.684941i	$0.240172\pi$
$673$			35.5378i			1.36988i	−0.728598	+	0.684941i	$0.759828\pi$
$674$	−16.3991	−	8.35349i	−0.631671	−	0.321764i
$675$	11.2773	−	27.2259i	0.434065	−	1.04793i
$676$	−6.41420	−	25.1964i	−0.246700	−	0.969092i
$677$	−42.4275	+	17.5741i	−1.63062	+	0.675426i	−0.995302	−	0.0968222i	$-0.969132\pi$
$677$	−42.4275	+	17.5741i	−1.63062	+	0.675426i	−0.635321	+	0.772248i	$0.719132\pi$
$678$	4.87374	−	4.16350i	0.187175	−	0.159898i
$679$	−19.8699	−	19.8699i	−0.762538	−	0.762538i
$680$	37.4434	+	8.97624i	1.43589	+	0.344223i
$681$	−3.38254			−0.129619
$682$	4.01828	−	51.1294i	0.153868	−	1.95784i
$683$	−37.7219	−	15.6249i	−1.44339	−	0.597871i	−0.482771	−	0.875747i	$-0.660370\pi$
$683$	−37.7219	−	15.6249i	−1.44339	−	0.597871i	−0.960617	+	0.277876i	$0.910370\pi$
$684$	−27.6270	+	6.63912i	−1.05635	+	0.253853i
$685$	53.8904	+	22.3221i	2.05905	+	0.852885i
$686$	−11.2689	+	22.1226i	−0.430249	+	0.844643i
$687$	−6.17248	−	6.17248i	−0.235495	−	0.235495i
$688$	27.0985	−	2.14476i	1.03312	−	0.0817681i
$689$	−18.8354	+	3.87829i	−0.717572	+	0.147751i
$690$	9.42512	+	4.80103i	0.358808	+	0.182772i
$691$	−13.7702	−	33.2442i	−0.523843	−	1.26467i	−0.935499	−	0.353330i	$-0.885049\pi$
$691$	−13.7702	−	33.2442i	−0.523843	−	1.26467i	0.411655	−	0.911340i	$-0.364951\pi$
$692$	36.3847	−	8.74371i	1.38314	−	0.332386i
$693$	−36.4319	+	15.0906i	−1.38393	+	0.573244i
$694$	−3.20784	+	40.8171i	−0.121768	+	1.54940i
$695$		−	7.75011i		−	0.293979i
$696$	2.55044	+	1.85171i	0.0966742	+	0.0701890i
$697$	0.101799			0.00385593
$698$	37.9580	+	2.98313i	1.43673	+	0.112913i
$699$	−5.44634	+	2.25595i	−0.205999	+	0.0853278i
$700$	−63.8938	−	10.1053i	−2.41496	−	0.381944i
$701$	−7.87216	−	3.26076i	−0.297328	−	0.123157i	0.229033	−	0.973419i	$-0.426444\pi$
$701$	−7.87216	−	3.26076i	−0.297328	−	0.123157i	−0.526360	+	0.850262i	$0.676444\pi$
$702$	12.3946	+	3.40445i	0.467803	+	0.128493i
$703$			48.0015i			1.81041i
$704$	−40.4275	−	3.15473i	−1.52367	−	0.118898i
$705$	6.12866			0.230819
$706$	−23.0461	+	7.49094i	−0.867350	+	0.281925i
$707$	−6.11728	+	2.53386i	−0.230064	+	0.0952957i
$708$	1.32081	+	0.208896i	0.0496389	+	0.00785078i
$709$	2.49025	+	1.03149i	0.0935232	+	0.0387386i	0.428955	−	0.903326i	$-0.358882\pi$
$709$	2.49025	+	1.03149i	0.0935232	+	0.0387386i	−0.335431	+	0.942065i	$0.608882\pi$
$710$	−39.5386	+	33.7767i	−1.48386	+	1.26762i
$711$	−21.4404	−	21.4404i	−0.804079	−	0.804079i
$712$	−6.03493	−	38.0214i	−0.226169	−	1.42491i
$713$			30.1994i			1.13098i
$714$	−4.29971	+	3.67312i	−0.160912	+	0.137463i
$715$	41.8970	+	61.8007i	1.56686	+	2.31121i
$716$	6.07682	+	25.2872i	0.227102	+	0.945025i
$717$	−11.4226	+	4.73139i	−0.426585	+	0.176697i
$718$	−1.96865	+	3.86475i	−0.0734694	+	0.144231i
$719$			38.3966i			1.43195i	0.698124	+	0.715976i	$0.254018\pi$
$719$			38.3966i			1.43195i	−0.698124	+	0.715976i	$0.745982\pi$
$720$	−3.62549	−	45.8071i	−0.135114	−	1.70713i
$721$	23.8223	+	23.8223i	0.887187	+	0.887187i
$722$	8.77839	−	2.85334i	0.326698	−	0.106191i
$723$	−8.70176	+	3.60439i	−0.323622	+	0.134049i
$724$	−14.1961	−	8.69508i	−0.527595	−	0.323150i
$725$	−27.7478	+	11.4935i	−1.03053	+	0.426859i
$726$	−0.706113	+	8.98472i	−0.0262063	+	0.333454i
$727$	11.9588	+	11.9588i	0.443527	+	0.443527i	0.893196	−	0.449668i	$-0.148458\pi$
$727$	11.9588	+	11.9588i	0.443527	+	0.443527i	−0.449668	+	0.893196i	$0.648458\pi$
$728$	0.908980	−	28.2005i	0.0336890	−	1.04518i
$729$	12.2793	−	12.2793i	0.454787	−	0.454787i
$730$	25.4988	+	29.8486i	0.943753	+	1.10475i
$731$	8.66587	+	20.9213i	0.320519	+	0.773801i
$732$	1.33413	+	0.211004i	0.0493110	+	0.00779892i
$733$	−9.86013	−	23.8045i	−0.364192	−	0.879238i	−0.994678	−	0.103037i	$-0.967144\pi$
$733$	−9.86013	−	23.8045i	−0.364192	−	0.879238i	0.630485	−	0.776201i	$-0.282856\pi$
$734$	39.4781	+	20.1096i	1.45716	+	0.742259i
$735$	0.820363	−	0.820363i	0.0302595	−	0.0302595i
$736$	23.8773	−	0.0132015i	0.880131	−	0.000486613i
$737$	−6.08795			−0.224253
$738$	−0.0375539	−	0.115535i	−0.00138238	−	0.00425292i
$739$	−5.96247	−	14.3947i	−0.219333	−	0.529517i	0.775464	−	0.631391i	$-0.217516\pi$
$739$	−5.96247	−	14.3947i	−0.219333	−	0.529517i	−0.994797	+	0.101875i	$0.967516\pi$
$740$	−76.6750	−	12.1267i	−2.81863	−	0.445788i
$741$	−7.75957	−	1.48937i	−0.285055	−	0.0547132i
$742$	−20.8048	−	1.63506i	−0.763767	−	0.0600248i
$743$	28.0260			1.02817			0.514087	−	0.857738i	$-0.328131\pi$
$743$	28.0260			1.02817			0.514087	+	0.857738i	$0.328131\pi$
$744$	−7.48225	+	4.58854i	−0.274312	+	0.168224i
$745$	19.1221	−	19.1221i	0.700579	−	0.700579i
$746$	−1.37587	+	17.5069i	−0.0503743	+	0.640973i
$747$	1.91692	−	4.62786i	0.0701365	−	0.169324i
$748$	−7.89318	−	32.8455i	−0.288603	−	1.20095i
$749$	−1.69661	−	4.09599i	−0.0619929	−	0.149664i
$750$	−14.9392	−	7.60981i	−0.545501	−	0.277871i
$751$			34.5873i			1.26211i	0.775739	+	0.631054i	$0.217377\pi$
$751$			34.5873i			1.26211i	−0.775739	+	0.631054i	$0.782623\pi$
$752$	12.3240	−	6.28628i	0.449411	−	0.229237i
$753$	−1.00416			−0.0365937
$754$	−6.47883	−	11.3858i	−0.235945	−	0.414645i
$755$	−7.87000	+	18.9999i	−0.286419	+	0.691476i
$756$	11.8948	+	7.28555i	0.432611	+	0.264973i
$757$	20.4386	+	49.3430i	0.742852	+	1.79340i	0.593866	+	0.804564i	$0.297601\pi$
$757$	20.4386	+	49.3430i	0.742852	+	1.79340i	0.148986	+	0.988839i	$0.452399\pi$
$758$	−15.8235	−	18.5227i	−0.574734	−	0.672776i
$759$		−	9.27981i		−	0.336836i
$760$	9.15205	+	57.6600i	0.331980	+	2.09155i
$761$	0.754180			0.0273390			0.0136695	−	0.999907i	$-0.495649\pi$
$761$	0.754180			0.0273390			0.0136695	+	0.999907i	$0.495649\pi$
$762$	7.94972	+	9.30584i	0.287988	+	0.337115i
$763$	11.2197	+	27.0868i	0.406181	+	0.980607i
$764$	−22.4528	+	16.3205i	−0.812312	+	0.590454i
$765$	35.3652	−	14.6487i	1.27863	−	0.529626i
$766$	2.08590	+	6.41734i	0.0753668	+	0.231868i
$767$	−4.64199	−	3.05678i	−0.167613	−	0.110374i
$768$	3.63123	+	5.91388i	0.131031	+	0.213399i
$769$	5.74698	−	5.74698i	0.207242	−	0.207242i	−0.595852	−

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)

\(f(q)\)	\(=\)	\(q+(-1.26014 - 0.641900i) q^{2} +(-0.400717 - 0.165982i) q^{3} +(1.17593 + 1.61777i) q^{4} +(1.56341 - 3.77440i) q^{5} +(0.398417 + 0.466382i) q^{6} -2.76672i q^{7} +(-0.443390 - 2.79346i) q^{8} +(-1.98830 - 1.98830i) q^{9} +O(q^{10})\)	\(q+(-1.26014 - 0.641900i) q^{2} +(-0.400717 - 0.165982i) q^{3} +(1.17593 + 1.61777i) q^{4} +(1.56341 - 3.77440i) q^{5} +(0.398417 + 0.466382i) q^{6} -2.76672i q^{7} +(-0.443390 - 2.79346i) q^{8} +(-1.98830 - 1.98830i) q^{9} +(-4.39291 + 3.75274i) q^{10} +(4.68296 + 1.93975i) q^{11} +(-0.202693 - 0.843453i) q^{12} +(-0.679641 + 3.54092i) q^{13} +(-1.77596 + 3.48647i) q^{14} +(-1.25297 + 1.25297i) q^{15} +(-1.23439 + 3.80477i) q^{16} -3.33220 q^{17} +(1.22925 + 3.78183i) q^{18} +(-1.93348 - 4.66783i) q^{19} +(7.94459 - 1.90919i) q^{20} +(-0.459227 + 1.10867i) q^{21} +(-4.65609 - 5.45036i) q^{22} +(2.98467 + 2.98467i) q^{23} +(-0.285991 + 1.19298i) q^{24} +(-8.26634 - 8.26634i) q^{25} +(3.12936 - 4.02580i) q^{26} +(0.964670 + 2.32892i) q^{27} +(4.47593 - 3.25346i) q^{28} +(0.983162 - 2.37356i) q^{29} +(2.38320 - 0.774642i) q^{30} +(5.05908 + 5.05908i) q^{31} +(3.99779 - 4.00221i) q^{32} +(-1.55458 - 1.55458i) q^{33} +(4.19906 + 2.13894i) q^{34} +(-10.4427 - 4.32551i) q^{35} +(0.878520 - 5.55471i) q^{36} +(-8.77750 - 3.63576i) q^{37} +(-0.559818 + 7.12323i) q^{38} +(0.860074 - 1.30610i) q^{39} +(-11.2368 - 2.69378i) q^{40} -0.0305502 q^{41} +(1.29035 - 1.10231i) q^{42} +(-2.60064 - 6.27850i) q^{43} +(2.36876 + 9.85698i) q^{44} +(-10.6132 + 4.39611i) q^{45} +(-1.84525 - 5.67697i) q^{46} +(-2.44565 - 2.44565i) q^{47} +(1.12616 - 1.31975i) q^{48} -0.654734 q^{49} +(5.11062 + 15.7230i) q^{50} +(1.33527 + 0.553088i) q^{51} +(-6.52761 + 3.06436i) q^{52} +(2.04108 + 4.92760i) q^{53} +(0.279310 - 3.55400i) q^{54} +(14.6428 - 14.6428i) q^{55} +(-7.72871 + 1.22674i) q^{56} +2.19140i q^{57} +(-2.76252 + 2.35994i) q^{58} +(-0.589917 + 1.42419i) q^{59} +(-3.50042 - 0.553619i) q^{60} +(-0.595870 + 1.43856i) q^{61} +(-3.12775 - 9.62260i) q^{62} +(-5.50106 + 5.50106i) q^{63} +(-7.60681 + 2.47718i) q^{64} +(12.3023 + 8.10114i) q^{65} +(0.961110 + 2.95688i) q^{66} +(-1.10964 + 0.459627i) q^{67} +(-3.91843 - 5.39075i) q^{68} +(-0.700605 - 1.69141i) q^{69} +(10.3828 + 12.1540i) q^{70} +9.00054 q^{71} +(-4.67263 + 6.43581i) q^{72} -6.79471i q^{73} +(8.72713 + 10.2159i) q^{74} +(1.94040 + 4.68453i) q^{75} +(5.27786 - 8.61696i) q^{76} +(5.36674 - 12.9564i) q^{77} +(-1.92220 + 1.09379i) q^{78} +10.7833 q^{79} +(12.4309 + 10.6075i) q^{80} +7.34227i q^{81} +(0.0384976 + 0.0196102i) q^{82} +(0.681723 + 1.64583i) q^{83} +(-2.33360 + 0.560793i) q^{84} +(-5.20960 + 12.5771i) q^{85} +(-0.752989 + 9.58117i) q^{86} +(-0.787940 + 0.787940i) q^{87} +(3.34222 - 13.9417i) q^{88} +13.6109 q^{89} +(16.1960 + 1.27285i) q^{90} +(9.79672 + 1.88038i) q^{91} +(-1.31876 + 8.33828i) q^{92} +(-1.18754 - 2.86698i) q^{93} +(1.51201 + 4.65174i) q^{94} -20.6411 q^{95} +(-2.26628 + 0.940192i) q^{96} +(7.18176 - 7.18176i) q^{97} +(0.825060 + 0.420274i) q^{98} +(-5.45433 - 13.1679i) 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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