LMFDB - Embedded newform 416.2.bd.a.83.2

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			83.2
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41215 - 0.0764043i) q^{2} +(2.23541 + 0.925935i) q^{3} +(1.98832 + 0.215788i) q^{4} +(0.344928 - 0.832729i) q^{5} +(-3.08598 - 1.47835i) q^{6} +1.15405i q^{7} +(-2.79132 - 0.456642i) q^{8} +(2.01836 + 2.01836i) q^{9} +O(q^{10})$	\(q+(-1.41215 - 0.0764043i) q^{2} +(2.23541 + 0.925935i) q^{3} +(1.98832 + 0.215788i) q^{4} +(0.344928 - 0.832729i) q^{5} +(-3.08598 - 1.47835i) q^{6} +1.15405i q^{7} +(-2.79132 - 0.456642i) q^{8} +(2.01836 + 2.01836i) q^{9} +(-0.550713 + 1.14958i) q^{10} +(0.739707 + 0.306397i) q^{11} +(4.24491 + 2.32343i) q^{12} +(2.43191 + 2.66192i) q^{13} +(0.0881743 - 1.62969i) q^{14} +(1.54211 - 1.54211i) q^{15} +(3.90687 + 0.858114i) q^{16} +2.50924 q^{17} +(-2.69602 - 3.00444i) q^{18} +(0.0724507 + 0.174911i) q^{19} +(0.865521 - 1.58130i) q^{20} +(-1.06858 + 2.57977i) q^{21} +(-1.02117 - 0.489194i) q^{22} +(-2.04351 - 2.04351i) q^{23} +(-5.81692 - 3.60536i) q^{24} +(2.96107 + 2.96107i) q^{25} +(-3.23084 - 3.94483i) q^{26} +(-0.134820 - 0.325485i) q^{27} +(-0.249030 + 2.29462i) q^{28} +(0.0118475 - 0.0286024i) q^{29} +(-2.29551 + 2.05986i) q^{30} +(-1.77310 - 1.77310i) q^{31} +(-5.45152 - 1.51029i) q^{32} +(1.36984 + 1.36984i) q^{33} +(-3.54342 - 0.191717i) q^{34} +(0.961010 + 0.398063i) q^{35} +(3.57762 + 4.44870i) q^{36} +(-6.94820 - 2.87804i) q^{37} +(-0.0889471 - 0.252536i) q^{38} +(2.97155 + 8.20226i) q^{39} +(-1.34306 + 2.16691i) q^{40} +3.61632 q^{41} +(1.70609 - 3.56137i) q^{42} +(2.96855 + 7.16672i) q^{43} +(1.40466 + 0.768836i) q^{44} +(2.37694 - 0.984560i) q^{45} +(2.72960 + 3.04187i) q^{46} +(-4.85990 - 4.85990i) q^{47} +(7.93888 + 5.53574i) q^{48} +5.66817 q^{49} +(-3.95523 - 4.40771i) q^{50} +(5.60917 + 2.32339i) q^{51} +(4.26102 + 5.81753i) q^{52} +(-0.104594 - 0.252513i) q^{53} +(0.165518 + 0.469934i) q^{54} +(0.510291 - 0.510291i) q^{55} +(0.526987 - 3.22132i) q^{56} +0.458083i q^{57} +(-0.0189158 + 0.0394856i) q^{58} +(2.43293 - 5.87361i) q^{59} +(3.39898 - 2.73344i) q^{60} +(0.846815 - 2.04439i) q^{61} +(2.36840 + 2.63935i) q^{62} +(-2.32929 + 2.32929i) q^{63} +(7.58296 + 2.54927i) q^{64} +(3.05549 - 1.10696i) q^{65} +(-1.82976 - 2.03908i) q^{66} +(-5.88874 + 2.43919i) q^{67} +(4.98918 + 0.541465i) q^{68} +(-2.67591 - 6.46023i) q^{69} +(-1.32667 - 0.635550i) q^{70} -1.39449 q^{71} +(-4.71223 - 6.55557i) q^{72} +0.899564i q^{73} +(9.59200 + 4.59509i) q^{74} +(3.87744 + 9.36096i) q^{75} +(0.106312 + 0.363415i) q^{76} +(-0.353597 + 0.853659i) q^{77} +(-3.56958 - 11.8098i) q^{78} -13.2971 q^{79} +(2.06216 - 2.95738i) q^{80} -9.41561i q^{81} +(-5.10678 - 0.276302i) q^{82} +(2.03448 + 4.91167i) q^{83} +(-2.68136 + 4.89883i) q^{84} +(0.865506 - 2.08952i) q^{85} +(-3.64447 - 10.3473i) q^{86} +(0.0529680 - 0.0529680i) q^{87} +(-1.92485 - 1.19303i) q^{88} -16.4199 q^{89} +(-3.43181 + 1.20874i) q^{90} +(-3.07198 + 2.80655i) q^{91} +(-3.62219 - 4.50412i) q^{92} +(-2.32182 - 5.60537i) q^{93} +(6.49158 + 7.23422i) q^{94} +0.170644 q^{95} +(-10.7879 - 8.42386i) q^{96} +(5.50506 - 5.50506i) q^{97} +(-8.00430 - 0.433072i) q^{98} +(0.874577 + 2.11142i) 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 $

$2$	−1.41215	−	0.0764043i	−0.998540	−	0.0540260i
$2$	−1.41215	−	0.0764043i	−0.998540	−	0.0540260i
$3$	2.23541	+	0.925935i	1.29061	+	0.534589i	0.919168	−	0.393866i	$-0.128863\pi$
$3$	2.23541	+	0.925935i	1.29061	+	0.534589i	0.371444	+	0.928455i	$0.378863\pi$
$4$	1.98832	+	0.215788i	0.994162	+	0.107894i
$5$	0.344928	−	0.832729i	0.154256	−	0.372408i	−0.827793	−	0.561034i	$-0.810404\pi$
$5$	0.344928	−	0.832729i	0.154256	−	0.372408i	0.982049	+	0.188627i	$0.0604036\pi$
$6$	−3.08598	−	1.47835i	−1.25985	−	0.603535i
$7$			1.15405i			0.436190i	0.975928	+	0.218095i	$0.0699842\pi$
$7$			1.15405i			0.436190i	−0.975928	+	0.218095i	$0.930016\pi$
$8$	−2.79132	−	0.456642i	−0.986881	−	0.161447i
$9$	2.01836	+	2.01836i	0.672787	+	0.672787i
$10$	−0.550713	+	1.14958i	−0.174151	+	0.363530i
$11$	0.739707	+	0.306397i	0.223030	+	0.0923821i	0.491401	−	0.870934i	$-0.336485\pi$
$11$	0.739707	+	0.306397i	0.223030	+	0.0923821i	−0.268370	+	0.963316i	$0.586485\pi$
$12$	4.24491	+	2.32343i	1.22540	+	0.670718i
$13$	2.43191	+	2.66192i	0.674491	+	0.738283i
$13$	2.43191	+	2.66192i	0.674491	+	0.738283i
$14$	0.0881743	−	1.62969i	0.0235656	−	0.435553i
$15$	1.54211	−	1.54211i	0.398170	−	0.398170i
$16$	3.90687	+	0.858114i	0.976718	+	0.214529i
$17$	2.50924			0.608580			0.304290	−	0.952579i	$-0.401581\pi$
$17$	2.50924			0.608580			0.304290	+	0.952579i	$0.401581\pi$
$18$	−2.69602	−	3.00444i	−0.635457	−	0.708153i
$19$	0.0724507	+	0.174911i	0.0166213	+	0.0401274i	0.931972	−	0.362529i	$-0.118087\pi$
$19$	0.0724507	+	0.174911i	0.0166213	+	0.0401274i	−0.915351	+	0.402657i	$0.868087\pi$
$20$	0.865521	−	1.58130i	0.193536	−	0.353590i
$21$	−1.06858	+	2.57977i	−0.233182	+	0.562952i
$22$	−1.02117	−	0.489194i	−0.217713	−	0.104297i
$23$	−2.04351	−	2.04351i	−0.426101	−	0.426101i	0.461197	−	0.887298i	$-0.347420\pi$
$23$	−2.04351	−	2.04351i	−0.426101	−	0.426101i	−0.887298	+	0.461197i	$0.847420\pi$
$24$	−5.81692	−	3.60536i	−1.18737	−	0.735942i
$25$	2.96107	+	2.96107i	0.592214	+	0.592214i
$26$	−3.23084	−	3.94483i	−0.633620	−	0.773644i
$27$	−0.134820	−	0.325485i	−0.0259462	−	0.0626397i
$28$	−0.249030	+	2.29462i	−0.0470623	+	0.433643i
$29$	0.0118475	−	0.0286024i	0.00220003	−	0.00531133i	−0.922776	−	0.385338i	$-0.874085\pi$
$29$	0.0118475	−	0.0286024i	0.00220003	−	0.00531133i	0.924976	+	0.380026i	$0.124085\pi$
$30$	−2.29551	+	2.05986i	−0.419100	+	0.376077i
$31$	−1.77310	−	1.77310i	−0.318458	−	0.318458i	0.529717	−	0.848175i	$-0.322298\pi$
$31$	−1.77310	−	1.77310i	−0.318458	−	0.318458i	−0.848175	+	0.529717i	$0.822298\pi$
$32$	−5.45152	−	1.51029i	−0.963701	−	0.266983i
$33$	1.36984	+	1.36984i	0.238459	+	0.238459i
$34$	−3.54342	−	0.191717i	−0.607691	−	0.0328791i
$35$	0.961010	+	0.398063i	0.162440	+	0.0672850i
$36$	3.57762	+	4.44870i	0.596270	+	0.741450i
$37$	−6.94820	−	2.87804i	−1.14228	−	0.473147i	−0.270340	−	0.962765i	$-0.587136\pi$
$37$	−6.94820	−	2.87804i	−1.14228	−	0.473147i	−0.871937	+	0.489618i	$0.837136\pi$
$38$	−0.0889471	−	0.252536i	−0.0144291	−	0.0409668i
$39$	2.97155	+	8.20226i	0.475829	+	1.31341i
$40$	−1.34306	+	2.16691i	−0.212357	+	0.342618i
$41$	3.61632			0.564775			0.282387	−	0.959300i	$-0.408874\pi$
$41$	3.61632			0.564775			0.282387	+	0.959300i	$0.408874\pi$
$42$	1.70609	−	3.56137i	0.263256	−	0.549532i
$43$	2.96855	+	7.16672i	0.452700	+	1.09291i	0.971292	+	0.237892i	$0.0764565\pi$
$43$	2.96855	+	7.16672i	0.452700	+	1.09291i	−0.518592	+	0.855022i	$0.673543\pi$
$44$	1.40466	+	0.768836i	0.211761	+	0.115906i
$45$	2.37694	−	0.984560i	0.354333	−	0.146769i
$46$	2.72960	+	3.04187i	0.402458	+	0.448499i
$47$	−4.85990	−	4.85990i	−0.708890	−	0.708890i	0.257412	−	0.966302i	$-0.417130\pi$
$47$	−4.85990	−	4.85990i	−0.708890	−	0.708890i	−0.966302	+	0.257412i	$0.917130\pi$
$48$	7.93888	+	5.53574i	1.14588	+	0.799016i
$49$	5.66817			0.809739
$50$	−3.95523	−	4.40771i	−0.559354	−	0.623344i
$51$	5.60917	+	2.32339i	0.785441	+	0.325340i
$52$	4.26102	+	5.81753i	0.590898	+	0.806747i
$53$	−0.104594	−	0.252513i	−0.0143671	−	0.0346854i	0.916533	−	0.399959i	$-0.130976\pi$
$53$	−0.104594	−	0.252513i	−0.0143671	−	0.0346854i	−0.930900	+	0.365273i	$0.880976\pi$
$54$	0.165518	+	0.469934i	0.0225241	+	0.0639500i
$55$	0.510291	−	0.510291i	0.0688076	−	0.0688076i
$56$	0.526987	−	3.22132i	0.0704216	−	0.430467i
$57$			0.458083i			0.0606745i
$58$	−0.0189158	+	0.0394856i	−0.00248376	+	0.00518472i
$59$	2.43293	−	5.87361i	0.316740	−	0.764678i	−0.682683	−	0.730715i	$-0.739187\pi$
$59$	2.43293	−	5.87361i	0.316740	−	0.764678i	0.999423	−	0.0339637i	$-0.0108130\pi$
$60$	3.39898	−	2.73344i	0.438806	−	0.352886i
$61$	0.846815	−	2.04439i	0.108424	−	0.261757i	−0.860351	−	0.509703i	$-0.829755\pi$
$61$	0.846815	−	2.04439i	0.108424	−	0.261757i	0.968774	+	0.247945i	$0.0797553\pi$
$62$	2.36840	+	2.63935i	0.300788	+	0.335198i
$63$	−2.32929	+	2.32929i	−0.293463	+	0.293463i
$64$	7.58296	+	2.54927i	0.947870	+	0.318658i
$65$	3.05549	−	1.10696i	0.378987	−	0.137301i
$66$	−1.82976	−	2.03908i	−0.225228	−	0.250994i
$67$	−5.88874	+	2.43919i	−0.719424	+	0.297995i	−0.712198	−	0.701979i	$-0.752300\pi$
$67$	−5.88874	+	2.43919i	−0.719424	+	0.297995i	−0.00722588	+	0.999974i	$0.502300\pi$
$68$	4.98918	+	0.541465i	0.605027	+	0.0656622i
$69$	−2.67591	−	6.46023i	−0.322142	−	0.777720i
$70$	−1.32667	−	0.635550i	−0.158568	−	0.0759627i
$71$	−1.39449			−0.165496			−0.0827479	−	0.996571i	$-0.526370\pi$
$71$	−1.39449			−0.165496			−0.0827479	+	0.996571i	$0.526370\pi$
$72$	−4.71223	−	6.55557i	−0.555342	−	0.772581i
$73$			0.899564i			0.105286i	0.998613	+	0.0526430i	$0.0167645\pi$
$73$			0.899564i			0.105286i	−0.998613	+	0.0526430i	$0.983235\pi$
$74$	9.59200	+	4.59509i	1.11505	+	0.534168i
$75$	3.87744	+	9.36096i	0.447728	+	1.08091i
$76$	0.106312	+	0.363415i	0.0121948	+	0.0416865i
$77$	−0.353597	+	0.853659i	−0.0402961	+	0.0972834i
$78$	−3.56958	−	11.8098i	−0.404176	−	1.33720i
$79$	−13.2971			−1.49604			−0.748022	−	0.663674i	$-0.768996\pi$
$79$	−13.2971			−1.49604			−0.748022	+	0.663674i	$0.768996\pi$
$80$	2.06216	−	2.95738i	0.230557	−	0.330645i
$81$		−	9.41561i		−	1.04618i
$82$	−5.10678	−	0.276302i	−0.563950	−	0.0305125i
$83$	2.03448	+	4.91167i	0.223313	+	0.539126i	0.995336	−	0.0964690i	$-0.0307549\pi$
$83$	2.03448	+	4.91167i	0.223313	+	0.539126i	−0.772023	+	0.635595i	$0.780755\pi$
$84$	−2.68136	+	4.89883i	−0.292560	+	0.534506i
$85$	0.865506	−	2.08952i	0.0938773	−	0.226640i
$86$	−3.64447	−	10.3473i	−0.392993	−	1.11578i
$87$	0.0529680	−	0.0529680i	0.00567876	−	0.00567876i
$88$	−1.92485	−	1.19303i	−0.205189	−	0.127178i
$89$	−16.4199			−1.74050			−0.870252	−	0.492606i	$-0.836044\pi$
$89$	−16.4199			−1.74050			−0.870252	+	0.492606i	$0.836044\pi$
$90$	−3.43181	+	1.20874i	−0.361745	+	0.127412i
$91$	−3.07198	+	2.80655i	−0.322031	+	0.294206i
$92$	−3.62219	−	4.50412i	−0.377640	−	0.469587i
$93$	−2.32182	−	5.60537i	−0.240761	−	0.581250i
$94$	6.49158	+	7.23422i	0.669556	+	0.746153i
$95$	0.170644			0.0175077
$96$	−10.7879	−	8.42386i	−1.10104	−	0.859756i
$97$	5.50506	−	5.50506i	0.558954	−	0.558954i	−0.370056	−	0.929010i	$-0.620661\pi$
$97$	5.50506	−	5.50506i	0.558954	−	0.558954i	0.929010	+	0.370056i	$0.120661\pi$
$98$	−8.00430	−	0.433072i	−0.808556	−	0.0437469i
$99$	0.874577	+	2.11142i	0.0878983	+	0.212205i
$100$	5.24861	+	6.52654i	0.524861	+	0.652654i
$101$	−5.95906	−	14.3864i	−0.592949	−	1.43150i	−0.880642	−	0.473782i	$-0.842888\pi$
$101$	−5.95906	−	14.3864i	−0.592949	−	1.43150i	0.287693	−	0.957723i	$-0.407112\pi$
$102$	−7.74346	−	3.70954i	−0.766717	−	0.367299i
$103$	−10.5301	+	10.5301i	−1.03756	+	1.03756i	−0.0382983	+	0.999266i	$0.512194\pi$
$103$	−10.5301	+	10.5301i	−1.03756	+	1.03756i	−0.999266	+	0.0382983i	$0.987806\pi$
$104$	−5.57271	−	8.54078i	−0.546449	−	0.837492i
$105$	1.77967	+	1.77967i	0.173678	+	0.173678i
$106$	0.128410	+	0.364578i	0.0124723	+	0.0354109i
$107$	−4.87267	+	2.01833i	−0.471059	+	0.195119i	−0.605568	−	0.795793i	$-0.707054\pi$
$107$	−4.87267	+	2.01833i	−0.471059	+	0.195119i	0.134509	+	0.990912i	$0.457054\pi$
$108$	−0.197831	−	0.676263i	−0.0190363	−	0.0650735i
$109$	10.1441	−	4.20184i	0.971632	−	0.402463i	0.160313	−	0.987066i	$-0.448750\pi$
$109$	10.1441	−	4.20184i	0.971632	−	0.402463i	0.811319	+	0.584603i	$0.198750\pi$
$110$	−0.759595	+	0.681618i	−0.0724245	+	0.0649897i
$111$	−12.8672	−	12.8672i	−1.22130	−	1.22130i
$112$	−0.990306	+	4.50872i	−0.0935752	+	0.426034i
$113$		−	9.65800i		−	0.908549i	−0.890862	−	0.454274i	$-0.849899\pi$
$113$		−	9.65800i		−	0.908549i	0.890862	−	0.454274i	$-0.150101\pi$
$114$	0.0349995	−	0.646880i	0.00327800	−	0.0605859i
$115$	−2.40655	+	0.996826i	−0.224412	+	0.0929545i
$116$	0.0297288	−	0.0543143i	0.00276025	−	0.00504296i
$117$	−0.464228	+	10.2812i	−0.0429179	+	0.950497i
$118$	−3.88442	+	8.10852i	−0.357590	+	0.746449i
$119$			2.89579i			0.265456i
$120$	−5.00870	+	3.60033i	−0.457230	+	0.328663i
$121$	−7.32489	−	7.32489i	−0.665899	−	0.665899i
$122$	−1.35203	+	2.82228i	−0.122407	+	0.255518i
$123$	8.08395	+	3.34848i	0.728905	+	0.301922i
$124$	−3.14288	−	3.90811i	−0.282239	−	0.350958i
$125$	7.65077	−	3.16905i	0.684306	−	0.283449i
$126$	3.46727	−	3.11133i	0.308889	−	0.277180i
$127$	−8.84360			−0.784743			−0.392371	−	0.919807i	$-0.628345\pi$
$127$	−8.84360			−0.784743			−0.392371	+	0.919807i	$0.628345\pi$
$128$	−10.5135	−	4.17931i	−0.929269	−	0.369403i
$129$			18.7692i			1.65254i
$130$	−4.39938	+	1.32973i	−0.385851	+	0.116625i
$131$	−16.4921	−	6.83127i	−1.44092	−	0.596851i	−0.480902	−	0.876774i	$-0.659691\pi$
$131$	−16.4921	−	6.83127i	−1.44092	−	0.596851i	−0.960022	+	0.279924i	$0.909691\pi$
$132$	2.42810	+	3.01929i	0.211339	+	0.262795i
$133$	−0.201856	+	0.0836116i	−0.0175032	+	0.00725005i
$134$	8.50213	−	2.99458i	0.734472	−	0.258692i
$135$	−0.317544			−0.0273299
$136$	−7.00410	−	1.14582i	−0.600596	−	0.0982535i
$137$			1.66307i			0.142085i	0.997473	+	0.0710426i	$0.0226326\pi$
$137$			1.66307i			0.142085i	−0.997473	+	0.0710426i	$0.977367\pi$
$138$	3.28520	+	9.32725i	0.279655	+	0.793988i
$139$	11.0115	−	4.56110i	0.933980	−	0.386867i	0.136793	−	0.990600i	$-0.456320\pi$
$139$	11.0115	−	4.56110i	0.933980	−	0.386867i	0.797187	+	0.603733i	$0.206320\pi$
$140$	1.82490	+	0.998854i	0.154232	+	0.0844186i
$141$	−6.36390	−	15.3638i	−0.535937	−	1.29387i
$142$	1.96923	+	0.106545i	0.165254	+	0.00894107i
$143$	0.983302	+	2.71417i	0.0822278	+	0.226970i
$144$	6.15350	+	9.61747i	0.512791	+	0.801456i
$145$	−0.0197315	−	0.0197315i	−0.00163861	−	0.00163861i
$146$	0.0687305	−	1.27032i	0.00568818	−	0.105132i
$147$	12.6707	+	5.24836i	1.04506	+	0.432877i
$148$	−13.1942	−	7.22182i	−1.08456	−	0.593630i
$149$	13.4417	+	5.56771i	1.10118	+	0.456125i	0.857893	−	0.513829i	$-0.171773\pi$
$149$	13.4417	+	5.56771i	1.10118	+	0.456125i	0.243290	+	0.969954i	$0.421773\pi$
$150$	−4.76030	−	13.5153i	−0.388677	−	1.10352i
$151$	11.2165			0.912789			0.456395	−	0.889777i	$-0.349141\pi$
$151$	11.2165			0.912789			0.456395	+	0.889777i	$0.349141\pi$
$152$	−0.122361	−	0.521318i	−0.00992481	−	0.0422845i
$153$	5.06455	+	5.06455i	0.409445	+	0.409445i
$154$	0.564554	−	1.17848i	0.0454931	−	0.0949643i
$155$	−2.08810	+	0.864919i	−0.167720	+	0.0694720i
$156$	4.13846	+	16.9500i	0.331342	+	1.35708i
$157$	4.54481	−	10.9722i	0.362716	−	0.875673i	−0.632185	−	0.774817i	$-0.717842\pi$
$157$	4.54481	−	10.9722i	0.362716	−	0.875673i	0.994901	−	0.100856i	$-0.0321581\pi$
$158$	18.7775	+	1.01596i	1.49386	+	0.0808252i
$159$		−	0.661317i		−	0.0524459i
$160$	−3.13804	+	4.01870i	−0.248084	+	0.317706i
$161$	2.35831	−	2.35831i	0.185861	−	0.185861i
$162$	−0.719393	+	13.2962i	−0.0565209	+	1.04465i
$163$	−6.59364	−	15.9184i	−0.516453	−	1.24683i	−0.940068	−	0.340987i	$-0.889239\pi$
$163$	−6.59364	−	15.9184i	−0.516453	−	1.24683i	0.423615	−	0.905842i	$-0.360761\pi$
$164$	7.19042	+	0.780360i	0.561478	+	0.0609359i
$165$	1.61320	−	0.668211i	0.125588	−	0.0520201i
$166$	−2.49772	−	7.09145i	−0.193860	−	0.550403i
$167$			20.0072i			1.54820i	0.633061	+	0.774102i	$0.281798\pi$
$167$			20.0072i			1.54820i	−0.633061	+	0.774102i	$0.718202\pi$
$168$	4.16077	−	6.71301i	0.321010	−	0.517920i
$169$	−1.17159	+	12.9471i	−0.0901226	+	0.995931i
$170$	−1.38187	+	2.88458i	−0.105985	+	0.221237i
$171$	−0.206803	+	0.499266i	−0.0158146	+	0.0381798i
$172$	4.35595	+	14.8903i	0.332138	+	1.13538i
$173$	5.72993	−	13.8333i	0.435639	−	1.05172i	−0.541800	−	0.840507i	$-0.682257\pi$
$173$	5.72993	−	13.8333i	0.435639	−	1.05172i	0.977439	−	0.211218i	$-0.0677429\pi$
$174$	−0.0788456	+	0.0707516i	−0.00597727	+	0.00536367i
$175$	−3.41722	+	3.41722i	−0.258318	+	0.258318i
$176$	2.62702	+	1.83181i	0.198019	+	0.138078i
$177$	10.8772	−	10.8772i	0.817577	−	0.817577i
$178$	23.1873	+	1.25455i	1.73796	+	0.0940325i
$179$	3.93283	+	1.62903i	0.293953	+	0.121759i	0.524786	−	0.851234i	$-0.324145\pi$
$179$	3.93283	+	1.62903i	0.293953	+	0.121759i	−0.230833	+	0.972993i	$0.574145\pi$
$180$	4.93858	−	1.44471i	0.368100	−	0.107682i
$181$	−7.85386	+	3.25318i	−0.583773	+	0.241807i	−0.654969	−	0.755656i	$-0.727318\pi$
$181$	−7.85386	+	3.25318i	−0.583773	+	0.241807i	0.0711961	+	0.997462i	$0.477318\pi$
$182$	4.55253	−	3.72855i	0.337456	−	0.276378i
$183$	3.78595	−	3.78595i	0.279865	−	0.279865i
$184$	4.77094	+	6.63724i	0.351718	+	0.489304i
$185$	−4.79325	+	4.79325i	−0.352407	+	0.352407i
$186$	2.85048	+	8.09301i	0.209007	+	0.593408i
$187$	1.85610	+	0.768823i	0.135732	+	0.0562219i
$188$	−8.61435	−	10.7118i	−0.628266	−	0.781236i
$189$	0.375626	−	0.155589i	0.0273228	−	0.0113175i
$190$	−0.240975	−	0.0130379i	−0.0174821	−	0.000945871i
$191$		−	12.6823i		−	0.917658i	−0.888525	−	0.458829i	$-0.848269\pi$
$191$		−	12.6823i		−	0.917658i	0.888525	−	0.458829i	$-0.151731\pi$
$192$	14.5905	+	12.7200i	1.05298	+	0.917985i
$193$	8.05832	+	8.05832i	0.580050	+	0.580050i	0.934917	−	0.354867i	$-0.115474\pi$
$193$	8.05832	+	8.05832i	0.580050	+	0.580050i	−0.354867	+	0.934917i	$0.615474\pi$
$194$	−8.19457	+	7.35335i	−0.588336	+	0.527940i
$195$	7.85523	+	0.354688i	0.562524	+	0.0253998i
$196$	11.2702	+	1.22312i	0.805012	+	0.0873661i
$197$	−2.71958	+	6.56565i	−0.193762	+	0.467783i	−0.990664	−	0.136325i	$-0.956471\pi$
$197$	−2.71958	+	6.56565i	−0.193762	+	0.467783i	0.796902	+	0.604109i	$0.206471\pi$
$198$	−1.07371	−	3.04845i	−0.0763054	−	0.216644i
$199$	−6.83389	+	6.83389i	−0.484442	+	0.484442i	−0.906547	−	0.422105i	$-0.861291\pi$
$199$	−6.83389	+	6.83389i	−0.484442	+	0.484442i	0.422105	+	0.906547i	$0.361291\pi$
$200$	−6.91316	−	9.61745i	−0.488834	−	0.680057i
$201$	−15.4223			−1.08780
$202$	7.31589	+	20.7711i	0.514744	+	1.46145i
$203$	0.0330086	+	0.0136726i	0.00231675	+	0.000959629i
$204$	10.6515	+	5.83005i	0.745753	+	0.408185i
$205$	1.24737	−	3.01142i	0.0871200	−	0.210326i
$206$	15.6747	−	14.0656i	1.09210	−	0.979994i
$207$		−	8.24908i		−	0.573351i
$208$	7.21694	+	12.4866i	0.500405	+	0.865791i
$209$			0.151582i			0.0104851i
$210$	−2.37718	−	2.64913i	−0.164041	−	0.182807i
$211$	5.41126	−	13.0639i	0.372527	−	0.899359i	−0.620794	−	0.783974i	$-0.713190\pi$
$211$	5.41126	−	13.0639i	0.372527	−	0.899359i	0.993321	−	0.115385i	$-0.0368103\pi$
$212$	−0.153478	−	0.524649i	−0.0105409	−	0.0360330i
$213$	−3.11726	−	1.29121i	−0.213591	−	0.0884723i
$214$	7.03514	−	2.47788i	0.480912	−	0.169385i
$215$	6.99187			0.476841
$216$	0.227697	+	0.970099i	0.0154928	+	0.0660069i
$217$	2.04624	−	2.04624i	0.138908	−	0.138908i
$218$	−14.6461	+	5.15856i	−0.991956	+	0.349382i
$219$	−0.832938	+	2.01089i	−0.0562847	+	0.135883i
$220$	1.12474	−	0.904509i	0.0758299	−	0.0609820i
$221$	6.10225	+	6.67938i	0.410482	+	0.449304i
$222$	17.1872	+	19.1535i	1.15353	+	1.28550i
$223$	−3.49139	−	3.49139i	−0.233801	−	0.233801i	0.580476	−	0.814277i	$-0.302866\pi$
$223$	−3.49139	−	3.49139i	−0.233801	−	0.233801i	−0.814277	+	0.580476i	$0.802866\pi$
$224$	1.74294	−	6.29132i	0.116455	−	0.420356i
$225$			11.9530i			0.796869i
$226$	−0.737913	+	13.6385i	−0.0490852	+	0.907222i
$227$	6.00222	−	2.48620i	0.398381	−	0.165015i	−0.174493	−	0.984658i	$-0.555829\pi$
$227$	6.00222	−	2.48620i	0.398381	−	0.165015i	0.572874	+	0.819644i	$0.305829\pi$
$228$	−0.0988488	+	0.910817i	−0.00654642	+	0.0603203i
$229$	4.84857	+	2.00834i	0.320403	+	0.132715i	0.537088	−	0.843526i	$-0.319524\pi$
$229$	4.84857	+	2.00834i	0.320403	+	0.132715i	−0.216685	+	0.976242i	$0.569524\pi$
$230$	3.47457	−	1.22380i	0.229106	−	0.0806947i
$231$	−1.58087	+	1.58087i	−0.104013	+	0.104013i
$232$	−0.0461313	+	0.0744285i	−0.00302866	+	0.00488647i
$233$	−20.4774	+	20.4774i	−1.34152	+	1.34152i	−0.446965	+	0.894552i	$0.647495\pi$
$233$	−20.4774	+	20.4774i	−1.34152	+	1.34152i	−0.894552	+	0.446965i	$0.852505\pi$
$234$	1.44109	−	14.4831i	0.0942068	−	0.946790i
$235$	−5.72329	+	2.37067i	−0.373347	+	0.154645i
$236$	6.10491	−	11.1536i	0.397395	−	0.726040i
$237$	−29.7245	−	12.3123i	−1.93081	−	0.799769i
$238$	0.221250	−	4.08928i	0.0143415	−	0.265069i
$239$	−14.2617	+	14.2617i	−0.922511	+	0.922511i	−0.997206	−	0.0746955i	$-0.976202\pi$
$239$	−14.2617	+	14.2617i	−0.922511	+	0.922511i	0.0746955	+	0.997206i	$0.476202\pi$
$240$	7.34811	−	4.70151i	0.474319	−	0.303481i
$241$	−0.761200	+	0.761200i	−0.0490332	+	0.0490332i	−0.731198	−	0.682165i	$-0.761039\pi$
$241$	−0.761200	+	0.761200i	−0.0490332	+	0.0490332i	0.682165	+	0.731198i	$0.261039\pi$
$242$	9.78417	+	10.9035i	0.628950	+	0.700902i
$243$	8.31379	−	20.0713i	0.533330	−	1.28757i
$244$	2.12490	−	3.88218i	0.136033	−	0.248531i
$245$	1.95511	−	4.72005i	0.124907	−	0.301553i
$246$	−11.1599	−	5.34620i	−0.711529	−	0.340861i
$247$	−0.289406	+	0.618227i	−0.0184144	+	0.0393368i
$248$	4.13962	+	5.75896i	0.262866	+	0.365694i
$249$			12.8634i			0.815183i
$250$	−11.0461	+	3.89062i	−0.698620	+	0.246064i
$251$	15.4135	−	6.38447i	0.972890	−	0.402984i	0.161103	−	0.986938i	$-0.448495\pi$
$251$	15.4135	−	6.38447i	0.972890	−	0.402984i	0.811787	+	0.583953i	$0.198495\pi$
$252$	−5.13402	+	4.12875i	−0.323413	+	0.260087i
$253$	−0.885474	−	2.13772i	−0.0556692	−	0.134397i
$254$	12.4885	+	0.675689i	0.783596	+	0.0423965i
$255$	3.86951	−	3.86951i	0.242318	−	0.242318i
$256$	14.5273	+	6.70508i	0.907955	+	0.419068i
$257$			19.1035i			1.19164i	0.803116	+	0.595822i	$0.203174\pi$
$257$			19.1035i			1.19164i	−0.803116	+	0.595822i	$0.796826\pi$
$258$	1.43405	−	26.5049i	0.0892799	−	1.65012i
$259$	3.32140	−	8.01857i	0.206382	−	0.498250i
$260$	6.31417	−	1.54165i	0.391588	−	0.0956091i
$261$	0.0816426	−	0.0338175i	0.00505355	−	0.00209325i
$262$	22.7674	+	10.9068i	1.40657	+	0.673826i
$263$	13.0752	+	13.0752i	0.806250	+	0.806250i	0.984064	−	0.177814i	$-0.0569025\pi$
$263$	13.0752	+	13.0752i	0.806250	+	0.806250i	−0.177814	+	0.984064i	$0.556902\pi$
$264$	−3.19814	−	4.44920i	−0.196832	−	0.273829i
$265$	−0.246353			−0.0151333
$266$	0.291439	−	0.102649i	0.0178693	−	0.00629383i
$267$	−36.7051	−	15.2038i	−2.24632	−	0.930455i
$268$	−12.2351	+	3.57919i	−0.747376	+	0.218634i
$269$	−5.56032	−	2.30316i	−0.339019	−	0.140426i	0.206678	−	0.978409i	$-0.433735\pi$
$269$	−5.56032	−	2.30316i	−0.339019	−	0.140426i	−0.545696	+	0.837983i	$0.683735\pi$
$270$	0.448420	+	0.0242617i	0.0272900	+	0.00147652i
$271$	14.2980	+	14.2980i	0.868540	+	0.868540i	0.992311	−	0.123771i	$-0.0394989\pi$
$271$	14.2980	+	14.2980i	0.868540	+	0.868540i	−0.123771	+	0.992311i	$0.539499\pi$
$272$	9.80327	+	2.15321i	0.594411	+	0.130558i
$273$	−9.46581	+	3.42932i	−0.572897	+	0.207552i
$274$	0.127065	−	2.34849i	0.00767629	−	0.141878i
$275$	1.28306	+	3.09759i	0.0773716	+	0.186792i
$276$	−3.92654	−	13.4225i	−0.236350	−	0.807937i
$277$	24.5685	−	10.1766i	1.47618	−	0.611452i	0.507917	−	0.861406i	$-0.330416\pi$
$277$	24.5685	−	10.1766i	1.47618	−	0.611452i	0.968258	+	0.249954i	$0.0804155\pi$
$278$	−15.8983	+	5.59962i	−0.953517	+	0.335843i
$279$		−	7.15751i		−	0.428509i
$280$	−2.50072	−	1.54996i	−0.149446	−	0.0926278i
$281$	−16.8816			−1.00707			−0.503537	−	0.863974i	$-0.667968\pi$
$281$	−16.8816			−1.00707			−0.503537	+	0.863974i	$0.667968\pi$
$282$	7.81291	+	22.1822i	0.465252	+	1.32093i
$283$	−19.3706	+	8.02356i	−1.15146	+	0.476951i	−0.875024	−	0.484080i	$-0.839154\pi$
$283$	−19.3706	+	8.02356i	−1.15146	+	0.476951i	−0.276439	+	0.961032i	$0.589154\pi$
$284$	−2.77270	−	0.300915i	−0.164530	−	0.0178560i
$285$	0.381459	+	0.158005i	0.0225957	+	0.00935943i
$286$	−1.18119	−	3.90794i	−0.0698454	−	0.231081i
$287$			4.17341i			0.246349i
$288$	−7.95483	−	14.0514i	−0.468743	−	0.827989i
$289$	−10.7037			−0.629630
$290$	0.0263563	+	0.0293714i	0.00154769	+	0.00172475i
$291$	17.4034	−	7.20871i	1.02020	−	0.422582i
$292$	−0.194115	+	1.78863i	−0.0113597	+	0.104671i
$293$	9.40482	+	3.89560i	0.549435	+	0.227584i	0.640091	−	0.768299i	$-0.278896\pi$
$293$	9.40482	+	3.89560i	0.549435	+	0.227584i	−0.0906562	+	0.995882i	$0.528896\pi$
$294$	−17.4919	−	8.37955i	−1.02015	−	0.488705i
$295$	−4.05194	−	4.05194i	−0.235913	−	0.235913i
$296$	18.0804	+	11.2064i	1.05090	+	0.651357i
$297$		−	0.282072i		−	0.0163675i
$298$	−18.5562	−	8.88944i	−1.07493	−	0.514951i
$299$	0.470012	−	10.4093i	0.0271815	−	0.601984i
$300$	5.68962	+	19.4493i	0.328490	+	1.12291i
$301$	−8.27075	+	3.42586i	−0.476718	+	0.197463i
$302$	−15.8394	−	0.856992i	−0.911456	−	0.0493143i
$303$		−	37.6772i		−	2.16450i
$304$	0.132961	+	0.745527i	0.00762586	+	0.0427589i
$305$	−1.41033	−	1.41033i	−0.0807555	−	0.0807555i
$306$	−6.76495	−	7.53886i	−0.386726	−	0.430968i
$307$	−6.10788	+	2.52997i	−0.348595	+	0.144393i	−0.550109	−	0.835093i	$-0.685414\pi$
$307$	−6.10788	+	2.52997i	−0.348595	+	0.144393i	0.201514	+	0.979486i	$0.435414\pi$
$308$	−0.887275	+	1.62105i	−0.0505572	+	0.0923678i
$309$	−33.2893	+	13.7889i	−1.89376	+	0.784423i
$310$	3.01479	−	1.06185i	0.171229	−	0.0603093i
$311$	−19.1932	−	19.1932i	−1.08835	−	1.08835i	−0.995699	−	0.0926502i	$-0.970466\pi$
$311$	−19.1932	−	19.1932i	−1.08835	−	1.08835i	−0.0926502	−	0.995699i	$-0.529534\pi$
$312$	−4.54907	−	24.2521i	−0.257540	−	1.37300i
$313$	−0.135692	+	0.135692i	−0.00766979	+	0.00766979i	−0.710931	−	0.703261i	$-0.751726\pi$
$313$	−0.135692	+	0.135692i	−0.00766979	+	0.00766979i	0.703261	+	0.710931i	$0.251726\pi$
$314$	−7.25627	+	15.1471i	−0.409495	+	0.854798i
$315$	1.13623	+	2.74310i	0.0640193	+	0.154556i
$316$	−26.4390	−	2.86937i	−1.48731	−	0.161414i
$317$	10.8643	+	26.2286i	0.610198	+	1.47315i	0.862784	+	0.505573i	$0.168719\pi$
$317$	10.8643	+	26.2286i	0.610198	+	1.47315i	−0.252586	+	0.967574i	$0.581281\pi$
$318$	−0.0505275	+	0.933878i	−0.00283344	+	0.0523693i
$319$	0.0175274	−	0.0175274i	0.000981344	−	0.000981344i
$320$	4.73842	−	5.43523i	0.264886	−	0.303839i
$321$	−12.7612			−0.712263
$322$	−3.51047	+	3.15010i	−0.195631	+	0.175548i
$323$	0.181796	+	0.438895i	0.0101154	+	0.0244207i
$324$	2.03178	−	18.7213i	0.112877	−	1.04007i
$325$	−0.681054	+	15.0832i	−0.0377781	+	0.836665i
$326$	8.09495	+	22.9830i	0.448338	+	1.27291i
$327$	26.5669			1.46915
$328$	−10.0943	−	1.65136i	−0.557366	−	0.0911813i
$329$	5.60857	−	5.60857i	0.309210	−	0.309210i
$330$	−2.32914	+	0.820357i	−0.128215	+	0.0451592i
$331$	9.48962	−	22.9100i	0.521597	−	1.25925i	−0.415314	−	0.909678i	$-0.636328\pi$
$331$	9.48962	−	22.9100i	0.521597	−	1.25925i	0.936911	−	0.349568i	$-0.113672\pi$
$332$	2.98533	+	10.2050i	0.163841	+	0.560073i
$333$	−8.21506	−	19.8329i	−0.450183	−	1.08684i
$334$	1.52864	−	28.2531i	0.0836432	−	1.54594i
$335$			5.74507i			0.313886i
$336$	−6.38852	+	9.16186i	−0.348522	+	0.499821i
$337$	−2.93788			−0.160037			−0.0800183	−	0.996793i	$-0.525498\pi$
$337$	−2.93788			−0.160037			−0.0800183	+	0.996793i	$0.525498\pi$
$338$	2.64368	−	18.1937i	0.143797	−	0.989607i
$339$	8.94269	−	21.5896i	0.485700	−	1.17258i
$340$	2.17180	−	3.96787i	0.117782	−	0.215188i
$341$	−0.768302	−	1.85484i	−0.0416059	−	0.100445i
$342$	0.330182	−	0.689237i	0.0178542	−	0.0372697i
$343$			14.6197i			0.789389i
$344$	−5.01356	−	21.3602i	−0.270313	−	1.15166i
$345$	−6.30261			−0.339321
$346$	−9.14843	+	19.0968i	−0.491823	+	1.02665i
$347$	13.2968	+	32.1014i	0.713811	+	1.72329i	0.690250	+	0.723571i	$0.257501\pi$
$347$	13.2968	+	32.1014i	0.713811	+	1.72329i	0.0235615	+	0.999722i	$0.492499\pi$
$348$	0.116747	−	0.0938877i	0.00625832	−	0.00503291i
$349$	13.5377	−	5.60752i	0.724659	−	0.300164i	0.0103039	−	0.999947i	$-0.496720\pi$
$349$	13.5377	−	5.60752i	0.724659	−	0.300164i	0.714355	+	0.699783i	$0.246720\pi$
$350$	5.08672	−	4.56453i	0.271896	−	0.243985i
$351$	0.538543	−	1.15043i	0.0287453	−	0.0614056i
$352$	−3.56978	−	2.78750i	−0.190270	−	0.148574i
$353$	3.47632	−	3.47632i	0.185026	−	0.185026i	−0.608516	−	0.793542i	$-0.708235\pi$
$353$	3.47632	−	3.47632i	0.185026	−	0.185026i	0.793542	+	0.608516i	$0.208235\pi$
$354$	−16.1912	+	14.5291i	−0.860554	+	0.772213i
$355$	−0.480999	+	1.16123i	−0.0255288	+	0.0616319i
$356$	−32.6481	−	3.54322i	−1.73034	−	0.187790i
$357$	−2.68131	+	6.47326i	−0.141910	+	0.342601i
$358$	−5.42927	−	2.60092i	−0.286946	−	0.137463i
$359$		−	5.74379i		−	0.303146i	−0.988446	−	0.151573i	$-0.951566\pi$
$359$		−	5.74379i		−	0.303146i	0.988446	−	0.151573i	$-0.0484338\pi$
$360$	−7.08439	+	1.66281i	−0.373380	+	0.0876380i
$361$	13.4097	−	13.4097i	0.705773	−	0.705773i
$362$	11.3394	−	3.99390i	0.595984	−	0.209915i
$363$	−9.59172	−	23.1565i	−0.503435	−	1.21540i
$364$	−6.71372	+	4.91743i	−0.351894	+	0.257743i
$365$	0.749093	+	0.310284i	0.0392093	+	0.0162410i
$366$	−5.63558	+	5.05706i	−0.294577	+	0.264337i
$367$	7.53460			0.393303			0.196652	−	0.980473i	$-0.436993\pi$
$367$	7.53460			0.393303			0.196652	+	0.980473i	$0.436993\pi$
$368$	−6.23016	−	9.73729i	−0.324769	−	0.507591i
$369$	7.29905	+	7.29905i	0.379973	+	0.379973i
$370$	7.13501	−	6.40256i	0.370931	−	0.332853i
$371$	0.291413	−	0.120707i	0.0151294	−	0.00626680i
$372$	−3.40696	−	11.6463i	−0.176643	−	0.603833i
$373$	11.8176	+	28.5303i	0.611894	+	1.47724i	0.860918	+	0.508745i	$0.169890\pi$
$373$	11.8176	+	28.5303i	0.611894	+	1.47724i	−0.249024	+	0.968497i	$0.580110\pi$
$374$	−2.56235	−	1.22751i	−0.132496	−	0.0634728i
$375$	20.0369			1.03470
$376$	11.3463	+	15.7848i	0.585142	+	0.814038i
$377$	0.104949	−	0.0380215i	0.00540516	−	0.00195821i
$378$	−0.542328	+	0.191016i	−0.0278943	+	0.00982480i
$379$	−1.35929	−	0.563035i	−0.0698219	−	0.0289212i	0.347499	−	0.937680i	$-0.387031\pi$
$379$	−1.35929	−	0.563035i	−0.0698219	−	0.0289212i	−0.417321	+	0.908759i	$0.637031\pi$
$380$	0.339296	+	0.0368230i	0.0174055	+	0.00188898i
$381$	−19.7690	−	8.18860i	−1.01280	−	0.419515i
$382$	−0.968980	+	17.9093i	−0.0495774	+	0.916317i
$383$	9.52469	+	9.52469i	0.486689	+	0.486689i	0.907260	−	0.420571i	$-0.138170\pi$
$383$	9.52469	+	9.52469i	0.486689	+	0.486689i	−0.420571	+	0.907260i	$0.638170\pi$
$384$	−19.6321	−	19.0773i	−1.00185	−	0.973533i
$385$	0.588901	+	0.588901i	0.0300132	+	0.0300132i
$386$	−10.7638	−	11.9952i	−0.547866	−	0.610541i
$387$	−8.47342	+	20.4566i	−0.430728	+	1.03987i
$388$	12.1338	−	9.75792i	0.615999	−	0.495383i
$389$	9.24248	+	22.3133i	0.468613	+	1.13133i	0.964769	+	0.263098i	$0.0847441\pi$
$389$	9.24248	+	22.3133i	0.468613	+	1.13133i	−0.496157	+	0.868233i	$0.665256\pi$
$390$	−11.0656	−	1.10105i	−0.560331	−	0.0557536i
$391$	−5.12765	−	5.12765i	−0.259317	−	0.259317i
$392$	−15.8217	−	2.58832i	−0.799116	−	0.130730i
$393$	−30.5413	−	30.5413i	−1.54061	−	1.54061i
$394$	4.34210	−	9.06389i	0.218752	−	0.456632i
$395$	−4.58655	+	11.0729i	−0.230774	+	0.557138i
$396$	1.28333	+	4.38691i	0.0644895	+	0.220450i
$397$	6.83669	+	16.5052i	0.343124	+	0.828374i	0.997396	+	0.0721149i	$0.0229748\pi$
$397$	6.83669	+	16.5052i	0.343124	+	0.828374i	−0.654273	+	0.756259i	$0.727025\pi$
$398$	10.1726	−	9.12833i	0.509906	−	0.457562i
$399$	−0.528650			−0.0264656
$400$	9.02759	+	14.1095i	0.451379	+	0.705473i
$401$	−28.1013	+	28.1013i	−1.40331	+	1.40331i	−0.614021	+	0.789290i	$0.710449\pi$
$401$	−28.1013	+	28.1013i	−1.40331	+	1.40331i	−0.789290	+	0.614021i	$0.789551\pi$
$402$	21.7785	+	1.17833i	1.08621	+	0.0587696i
$403$	0.407817	−	9.03186i	0.0203148	−	0.449909i
$404$	−8.74412	−	29.8908i	−0.435036	−	1.48712i
$405$	−7.84065	−	3.24770i	−0.389605	−	0.161380i
$406$	−0.0455684	−	0.0218297i	−0.00226152	−	0.00108339i
$407$	−4.25781	−	4.25781i	−0.211052	−	0.211052i
$408$	−14.5960	−	9.04672i	−0.722612	−	0.447879i
$409$		−	14.0615i		−	0.695296i	−0.937625	−	0.347648i	$-0.886980\pi$
$409$		−	14.0615i		−	0.695296i	0.937625	−	0.347648i	$-0.113020\pi$
$410$	−1.99156	+	4.15726i	−0.0983559	+	0.205312i
$411$	−1.53989	+	3.71763i	−0.0759572	+	0.183377i
$412$	−23.2096	+	18.6650i	−1.14345	+	0.919561i
$413$	6.77843	+	2.80772i	0.333545	+	0.138159i
$414$	−0.630265	+	11.6489i	−0.0309758	+	0.572513i
$415$	4.79184			0.235222
$416$	−9.23736	−	18.1844i	−0.452899	−	0.891562i
$417$	28.8384			1.41222
$418$	0.0115815	−	0.214056i	0.000566470	−	0.0104698i
$419$	19.0430	+	7.88788i	0.930313	+	0.385348i	0.795797	−	0.605563i	$-0.207052\pi$
$419$	19.0430	+	7.88788i	0.930313	+	0.385348i	0.134516	+	0.990911i	$0.457052\pi$
$420$	3.15452	+	3.92259i	0.153925	+	0.191403i
$421$	5.91937	−	14.2906i	0.288492	−	0.696482i	−0.711488	−	0.702698i	$-0.751979\pi$
$421$	5.91937	−	14.2906i	0.288492	−	0.696482i	0.999981	+	0.00621572i	$0.00197854\pi$
$422$	−8.63965	+	18.0348i	−0.420571	+	0.877919i
$423$		−	19.6181i		−	0.953864i
$424$	0.176649	+	0.752608i	0.00857882	+	0.0365499i
$425$	7.43004	+	7.43004i	0.360410	+	0.360410i
$426$	4.30337	+	2.06155i	0.208499	+	0.0998825i
$427$	2.35933	+	0.977266i	0.114176	+	0.0472932i
$428$	−10.1240	+	2.96162i	−0.489361	+	0.143155i
$429$	−0.315067	+	6.97774i	−0.0152116	+	0.336889i
$430$	−9.87355	−	0.534209i	−0.476145	−	0.0257618i
$431$	23.4545	−	23.4545i	1.12976	−	1.12976i	0.139546	−	0.990216i	$-0.455436\pi$
$431$	23.4545	−	23.4545i	1.12976	−	1.12976i	0.990216	−	0.139546i	$-0.0445642\pi$
$432$	−0.247422	−	1.38732i	−0.0119041	−	0.0667475i
$433$	27.3029			1.31209			0.656047	−	0.754720i	$-0.272227\pi$
$433$	27.3029			1.31209			0.656047	+	0.754720i	$0.272227\pi$
$434$	−3.04594	+	2.73326i	−0.146210	+	0.131200i
$435$	−0.0258378	−	0.0623781i	−0.00123883	−	0.00299080i
$436$	21.0765	−	6.16563i	1.00938	−	0.295280i
$437$	0.209379	−	0.505486i	0.0100160	−	0.0241807i
$438$	1.32987	−	2.77604i	0.0635438	−	0.132644i
$439$	−5.07865	−	5.07865i	−0.242391	−	0.242391i	0.575448	−	0.817839i	$-0.304828\pi$
$439$	−5.07865	−	5.07865i	−0.242391	−	0.242391i	−0.817839	+	0.575448i	$0.804828\pi$
$440$	−1.65741	+	1.19137i	−0.0790137	+	0.0567961i
$441$	11.4404	+	11.4404i	0.544782	+	0.544782i
$442$	−8.10695	−	9.89852i	−0.385608	−	0.470825i
$443$	−0.504588	−	1.21818i	−0.0239737	−	0.0578776i	0.911439	−	0.411434i	$-0.134972\pi$
$443$	−0.504588	−	1.21818i	−0.0239737	−	0.0578776i	−0.935413	+	0.353557i	$0.884972\pi$
$444$	−22.8075	−	28.3607i	−1.08240	−	1.34594i
$445$	−5.66367	+	13.6733i	−0.268484	+	0.648177i
$446$	4.66361	+	5.19712i	0.220828	+	0.246091i
$447$	24.8922	+	24.8922i	1.17736	+	1.17736i
$448$	−2.94198	+	8.75111i	−0.138995	+	0.413451i
$449$	27.7117	+	27.7117i	1.30780	+	1.30780i	0.923003	+	0.384793i	$0.125727\pi$
$449$	27.7117	+	27.7117i	1.30780	+	1.30780i	0.384793	+	0.923003i	$0.374273\pi$
$450$	0.913263	−	16.8795i	0.0430516	−	0.795705i
$451$	2.67502	+	1.10803i	0.125962	+	0.0521751i
$452$	2.08408	−	19.2032i	0.0980271	−	0.903245i
$453$	25.0735	+	10.3858i	1.17806	+	0.487967i
$454$	−8.66597	+	3.05229i	−0.406714	+	0.143251i
$455$	1.27748	+	3.52618i	0.0598893	+	0.165310i
$456$	0.209180	−	1.27866i	0.00979573	−	0.0598785i
$457$	37.8177			1.76904			0.884519	−	0.466505i	$-0.154487\pi$
$457$	37.8177			1.76904			0.884519	+	0.466505i	$0.154487\pi$
$458$	−6.69346	−	3.20653i	−0.312765	−	0.149831i
$459$	−0.338297	−	0.816721i	−0.0157903	−	0.0381213i
$460$	−5.00011	+	1.46271i	−0.233131	+	0.0681991i
$461$	7.47061	−	3.09443i	0.347941	−	0.144122i	−0.201867	−	0.979413i	$-0.564701\pi$
$461$	7.47061	−	3.09443i	0.347941	−	0.144122i	0.549808	+	0.835291i	$0.314701\pi$
$462$	2.35320	−	2.11163i	0.109481	−	0.0982420i
$463$	2.17099	+	2.17099i	0.100894	+	0.100894i	0.755752	−	0.654858i	$-0.227271\pi$
$463$	2.17099	+	2.17099i	0.100894	+	0.100894i	−0.654858	+	0.755752i	$0.727271\pi$
$464$	0.0708308	−	0.101579i	0.00328824	−	0.00471571i
$465$	−5.46861			−0.253601
$466$	30.4816	−	27.3525i	1.41203	−	1.26708i
$467$	23.2918	+	9.64779i	1.07782	+	0.446447i	0.849743	−	0.527197i	$-0.176757\pi$
$467$	23.2918	+	9.64779i	1.07782	+	0.446447i	0.228075	+	0.973644i	$0.426757\pi$
$468$	−3.14160	+	20.3422i	−0.145220	+	0.940317i
$469$	−2.81495	−	6.79589i	−0.129982	−	0.313805i
$470$	8.26327	−	2.91045i	0.381156	−	0.134249i
$471$	20.3190	−	20.3190i	0.936251	−	0.936251i
$472$	−9.47322	+	15.2842i	−0.436040	+	0.703510i
$473$			6.21083i			0.285574i
$474$	41.0347	+	19.6578i	1.88478	+	0.902915i
$475$	−0.303394	+	0.732457i	−0.0139206	+	0.0336074i
$476$	−0.624877	+	5.75776i	−0.0286412	+	0.263907i
$477$	0.298554	−	0.720773i	0.0136698	−	0.0330019i
$478$	21.2292	−	19.0499i	0.971003	−	0.871324i
$479$	−19.5362	+	19.5362i	−0.892630	+	0.892630i	−0.994770	−	0.102140i	$-0.967431\pi$
$479$	−19.5362	+	19.5362i	−0.892630	+	0.892630i	0.102140	+	0.994770i	$0.467431\pi$
$480$	−10.7358	+	6.07780i	−0.490022	+	0.277412i
$481$	−9.23633	−	25.4947i	−0.421140	−	1.16246i
$482$	1.13309	−	1.01677i	0.0516107	−	0.0463125i
$483$	7.45542	−	3.08814i	0.339233	−	0.140515i
$484$	−12.9836	−	16.1449i	−0.590165	−	0.733858i
$485$	−2.68537	−	6.48307i	−0.121937	−	0.294381i
$486$	−13.2738	+	27.7084i	−0.602113	+	1.25688i
$487$	−22.1299			−1.00280			−0.501400	−	0.865215i	$-0.667182\pi$
$487$	−22.1299			−1.00280			−0.501400	+	0.865215i	$0.667182\pi$
$488$	−3.29729	+	5.31986i	−0.149261	+	0.240819i
$489$		−	41.6895i		−	1.88526i
$490$	−3.12153	+	6.51603i	−0.141017	+	0.294364i
$491$	9.95219	+	24.0267i	0.449136	+	1.08431i	0.972646	+	0.232291i	$0.0746221\pi$
$491$	9.95219	+	24.0267i	0.449136	+	1.08431i	−0.523511	+	0.852019i	$0.675378\pi$
$492$	15.3510	+	8.40229i	0.692074	+	0.378804i
$493$	0.0297282	−	0.0717703i	0.00133889	−	0.00323237i
$494$	0.455919	−	0.850916i	0.0205128	−	0.0382845i
$495$	2.05990			0.0925858
$496$	−5.40574	−	8.44879i	−0.242725	−	0.379362i
$497$		−	1.60931i		−	0.0721876i
$498$	0.982817	−	18.1650i	0.0440411	−	0.813993i
$499$	1.94745	+	4.70156i	0.0871798	+	0.210471i	0.961456	−	0.274957i	$-0.0886637\pi$
$499$	1.94745	+	4.70156i	0.0871798	+	0.210471i	−0.874277	+	0.485428i	$0.838664\pi$
$500$	15.8961	−	4.65016i	0.710893	−	0.207961i
$501$	−18.5254	+	44.7242i	−0.827653	+	1.99813i
$502$	−22.2539	+	7.83816i	−0.993241	+	0.349834i
$503$	−30.6073	+	30.6073i	−1.36471	+	1.36471i	−0.496908	+	0.867803i	$0.665531\pi$
$503$	−30.6073	+	30.6073i	−1.36471	+	1.36471i	−0.867803	+	0.496908i	$0.834469\pi$
$504$	7.56545	−	5.43815i	0.336992	−	0.242234i
$505$	−14.0355			−0.624569
$506$	1.08709	+	3.08643i	0.0483270	+	0.137209i
$507$	−14.6072	+	27.8572i	−0.648727	+	1.23718i
$508$	−17.5839	−	1.90835i	−0.780162	−	0.0846691i
$509$	−11.4306	−	27.5958i	−0.506651	−	1.22316i	−0.945800	−	0.324750i	$-0.894720\pi$
$509$	−11.4306	−	27.5958i	−0.506651	−	1.22316i	0.439149	−	0.898414i	$-0.355280\pi$
$510$	−5.75997	+	5.16868i	−0.255056	+	0.228873i
$511$	−1.03814			−0.0459247
$512$	−20.0024	−	10.5785i	−0.883988	−	0.467509i
$513$	0.0471633	−	0.0471633i	0.00208231	−	0.00208231i
$514$	1.45959	−	26.9770i	0.0643798	−	1.18990i
$515$	5.13661	+	12.4009i	0.226346	+	0.546448i
$516$	−4.05018	+	37.3193i	−0.178299	+	1.64289i
$517$	−2.10585	−	5.08396i	−0.0926150	−	0.223592i
$518$	−5.30296	+	11.0696i	−0.232999	+	0.486372i
$519$	25.6174	−	25.6174i	1.12448	−	1.12448i
$520$	−9.03433	+	1.69461i	−0.396182	+	0.0743135i
$521$	−1.53099	−	1.53099i	−0.0670740	−	0.0670740i	0.672774	−	0.739848i	$-0.265103\pi$
$521$	−1.53099	−	1.53099i	−0.0670740	−	0.0670740i	−0.739848	+	0.672774i	$0.765103\pi$
$522$	−0.117875	+	0.0415174i	−0.00515926	+	0.00181717i
$523$	−21.3702	+	8.85181i	−0.934452	+	0.387063i	−0.797366	−	0.603497i	$-0.793774\pi$
$523$	−21.3702	+	8.85181i	−0.934452	+	0.387063i	−0.137086	+	0.990559i	$0.543774\pi$
$524$	−31.3176	−	17.1416i	−1.36812	−	0.748834i
$525$	−10.8030	+	4.47475i	−0.471482	+	0.195294i
$526$	−17.4651	−	19.4631i	−0.761514	−	0.848631i
$527$	−4.44913	−	4.44913i	−0.193807	−	0.193807i
$528$	4.17632	+	6.52728i	0.181751	+	0.284063i
$529$		−	14.6481i		−	0.636876i
$530$	0.347886	+	0.0188224i	0.0151112	+	0.000817592i
$531$	16.7656	−	6.94454i	0.727565	−	0.301367i
$532$	−0.419398	+	0.122689i	−0.0181832	+	0.00531924i
$533$	8.79458	+	9.62635i	0.380936	+	0.416963i
$534$	50.6714	+	24.2744i	2.19277	+	1.05046i
$535$			4.75379i			0.205524i
$536$	17.5512	−	4.11954i	0.758096	−	0.177937i
$537$	7.28309	+	7.28309i	0.314288	+	0.314288i
$538$	7.67602	+	3.67723i	0.330937	+	0.158537i
$539$	4.19279	+	1.73671i	0.180596	+	0.0748054i
$540$	−0.631381	−	0.0685224i	−0.0271703	−	0.00294873i
$541$	−36.9284	+	15.2962i	−1.58767	+	0.657636i	−0.989606	−	0.143808i	$-0.954065\pi$
$541$	−36.9284	+	15.2962i	−1.58767	+	0.657636i	−0.598069	+	0.801445i	$0.704065\pi$
$542$	−19.0984	−	21.2833i	−0.820348	−	0.914195i
$543$	−20.5688			−0.882692
$544$	−13.6792	−	3.78967i	−0.586489	−	0.162481i
$545$		−	9.89664i		−	0.423926i
$546$	13.6291	−	4.11948i	0.583273	−	0.176297i
$547$	−38.8333	−	16.0853i	−1.66039	−	0.687757i	−0.662285	−	0.749252i	$-0.730413\pi$
$547$	−38.8333	−	16.0853i	−1.66039	−	0.687757i	−0.998107	+	0.0614950i	$0.980413\pi$
$548$	−0.358870	+	3.30671i	−0.0153302	+	0.141256i
$549$	5.83550	−	2.41714i	0.249053	−	0.103161i
$550$	−1.57521	−	4.47229i	−0.0671670	−	0.190699i
$551$	0.00586125			0.000249697
$552$	4.51933	+	19.2545i	0.192355	+	0.819526i
$553$		−	15.3455i		−	0.652559i
$554$	−35.4718	+	12.4937i	−1.50705	+	0.530807i
$555$	−15.1531	+	6.27662i	−0.643214	+	0.266428i
$556$	22.8786	−	6.69280i	0.970268	−	0.283838i
$557$	−5.59310	−	13.5029i	−0.236987	−	0.572138i	0.759981	−	0.649945i	$-0.225208\pi$
$557$	−5.59310	−	13.5029i	−0.236987	−	0.572138i	−0.996968	+	0.0778073i	$0.975208\pi$
$558$	−0.546864	+	10.1075i	−0.0231506	+	0.427883i
$559$	−11.8579	+	25.3309i	−0.501537	+	1.07138i
$560$	3.41296	+	2.37984i	0.144224	+	0.100567i
$561$	3.43726	+	3.43726i	0.145121	+	0.145121i
$562$	23.8394	+	1.28983i	1.00560	+	0.0544081i
$563$	5.89009	+	2.43975i	0.248238	+	0.102823i	0.503333	−	0.864093i	$-0.332107\pi$
$563$	5.89009	+	2.43975i	0.248238	+	0.102823i	−0.255095	+	0.966916i	$0.582107\pi$
$564$	−9.33817	−	31.9215i	−0.393208	−	1.34414i
$565$	−8.04250	−	3.33131i	−0.338350	−	0.140149i
$566$	27.9672	−	9.85046i	1.17555	−	0.414046i
$567$	10.8661			0.456333
$568$	3.89248	+	0.636783i	0.163325	+	0.0267188i
$569$	−8.64118	−	8.64118i	−0.362257	−	0.362257i	0.502386	−	0.864643i	$-0.332456\pi$
$569$	−8.64118	−	8.64118i	−0.362257	−	0.362257i	−0.864643	+	0.502386i	$0.832456\pi$
$570$	−0.526604	−	0.252272i	−0.0220570	−	0.0105665i
$571$	−0.579560	+	0.240062i	−0.0242538	+	0.0100463i	−0.394777	−	0.918777i	$-0.629178\pi$
$571$	−0.579560	+	0.240062i	−0.0242538	+	0.0100463i	0.370524	+	0.928823i	$0.379178\pi$
$572$	1.36944	+	5.60883i	0.0572590	+	0.234517i
$573$	11.7430	−	28.3500i	0.490570	−	1.18434i
$574$	0.318867	−	5.89348i	0.0133092	−	0.245989i
$575$		−	12.1019i		−	0.504686i
$576$	10.1598	+	20.4505i	0.423325	+	0.852104i
$577$	18.4191	−	18.4191i	0.766796	−	0.766796i	−0.210745	−	0.977541i	$-0.567589\pi$
$577$	18.4191	−	18.4191i	0.766796	−	0.766796i	0.977541	+	0.210745i	$0.0675891\pi$
$578$	15.1152	+	0.817810i	0.628711	+	0.0340164i
$579$	10.5521	+	25.4751i	0.438532	+	1.05871i
$580$	−0.0349748	−	0.0434905i	−0.00145225	−	0.00180584i
$581$	−5.66831	+	2.34789i	−0.235161	+	0.0974069i
$582$	−25.1269	+	8.85008i	−1.04154	+	0.366847i
$583$		−	0.218833i		−	0.00906315i
$584$	0.410778	−	2.51097i	0.0169981	−	0.103905i
$585$	8.40132	+	3.93284i	0.347352	+	0.162603i
$586$	−12.9834	−	6.21974i	−0.536337	−	0.256935i
$587$	−2.94384	+	7.10705i	−0.121505	+	0.293340i	−0.972916	−	0.231161i	$-0.925748\pi$
$587$	−2.94384	+	7.10705i	−0.121505	+	0.293340i	0.851410	+	0.524500i	$0.175748\pi$
$588$	24.0609	+	13.1696i	0.992253	+	0.543106i
$589$	0.181673	−	0.438597i	0.00748570	−	0.0180721i
$590$	5.41235	+	6.03152i	0.222823	+	0.248314i
$591$	−12.1587	+	12.1587i	−0.500144	+	0.500144i
$592$	−24.6760	−	17.2065i	−1.01418	−	0.707182i
$593$	11.0895	−	11.0895i	0.455393	−	0.455393i	−0.441747	−	0.897140i	$-0.645641\pi$
$593$	11.0895	−	11.0895i	0.455393	−	0.455393i	0.897140	+	0.441747i	$0.145641\pi$
$594$	−0.0215515	+	0.398328i	−0.000884270	+	0.0163436i
$595$	2.41140	+	0.998836i	0.0988580	+	0.0409483i
$596$	25.5249	+	13.9710i	1.04554	+	0.572273i
$597$	−21.6043	+	8.94878i	−0.884203	+	0.366249i
$598$	−1.45904	+	14.6635i	−0.0596646	+	0.599637i
$599$	−1.73973	+	1.73973i	−0.0710836	+	0.0710836i	−0.741755	−	0.670671i	$-0.766006\pi$
$599$	−1.73973	+	1.73973i	−0.0710836	+	0.0710836i	0.670671	+	0.741755i	$0.266006\pi$
$600$	−6.54857	−	27.9000i	−0.267344	−	1.13901i
$601$	−16.5353	+	16.5353i	−0.674488	+	0.674488i	−0.958747	−	0.284259i	$-0.908252\pi$
$601$	−16.5353	+	16.5353i	−0.674488	+	0.674488i	0.284259	+	0.958747i	$0.408252\pi$
$602$	11.9413	−	4.20590i	0.486690	−	0.171419i
$603$	−16.8088	−	6.96243i	−0.684507	−	0.283532i
$604$	22.3021	+	2.42040i	0.907461	+	0.0984846i
$605$	−8.62620	+	3.57309i	−0.350705	+	0.145267i
$606$	−2.87870	+	53.2059i	−0.116939	+	2.16134i
$607$		−	11.0822i		−	0.449812i	−0.974380	−	0.224906i	$-0.927792\pi$
$607$		−	11.0822i		−	0.449812i	0.974380	−	0.224906i	$-0.0722076\pi$
$608$	−0.130800	−	1.06295i	−0.00530463	−	0.0431085i
$609$	0.0611276	+	0.0611276i	0.00247702	+	0.00247702i
$610$	1.88384	+	2.09936i	0.0762746	+	0.0850004i
$611$	1.11779	−	24.7555i	0.0452209	−	1.00150i
$612$	8.97711	+	11.1629i	0.362878	+	0.451232i
$613$	5.65034	−	13.6411i	0.228215	−	0.550960i	−0.767745	−	0.640755i	$-0.778621\pi$
$613$	5.65034	−	13.6411i	0.228215	−	0.550960i	0.995960	+	0.0897955i	$0.0286213\pi$
$614$	8.81854	−	3.10602i	0.355887	−	0.125349i
$615$	5.57675	−	5.57675i	0.224876	−	0.224876i
$616$	1.37682	−	2.22137i	0.0554736	−	0.0895015i
$617$	−29.5338			−1.18899			−0.594493	−	0.804101i	$-0.702647\pi$
$617$	−29.5338			−1.18899			−0.594493	+	0.804101i	$0.702647\pi$
$618$	48.0630	−	16.9285i	1.93338	−	0.680965i
$619$	10.2945	+	4.26411i	0.413770	+	0.171389i	0.579850	−	0.814723i	$-0.303111\pi$
$619$	10.2945	+	4.26411i	0.413770	+	0.171389i	−0.166080	+	0.986112i	$0.553111\pi$
$620$	−4.33846	+	1.26915i	−0.174237	+	0.0509704i
$621$	−0.389625	+	0.940639i	−0.0156351	+	0.0377465i
$622$	25.6373	+	28.5701i	1.02796	+	1.14556i
$623$		−	18.9494i		−	0.759190i
$624$	4.57099	+	34.5951i	0.182986	+	1.38491i
$625$			13.4738i			0.538953i
$626$	0.201985	−	0.181250i	0.00807296	−	0.00724422i
$627$	−0.140355	+	0.338847i	−0.00560524	+	0.0135322i
$628$	11.4042	−	20.8355i	0.455078	−	0.831426i
$629$	−17.4347	−	7.22169i	−0.695167	−	0.287948i
$630$	−1.39494	−	3.96048i	−0.0555758	−	0.157789i
$631$	31.4475			1.25191			0.625953	−	0.779861i	$-0.284710\pi$
$631$	31.4475			1.25191			0.625953	+	0.779861i	$0.284710\pi$
$632$	37.1166	+	6.07202i	1.47642	+	0.241532i
$633$	24.1927	−	24.1927i	0.961575	−	0.961575i
$634$	−13.3380	−	37.8688i	−0.529718	−	1.50396i
$635$	−3.05040	+	7.36432i	−0.121051	+	0.292244i
$636$	0.142705	−	1.31491i	0.00565860	−	0.0521397i
$637$	13.7845	+	15.0882i	0.546162	+	0.597816i
$638$	−0.0260904	+	0.0234121i	−0.00103293	+	0.000926893i
$639$	−2.81459	−	2.81459i	−0.111344	−	0.111344i
$640$	−7.10662	+	7.31332i	−0.280914	+	0.289084i
$641$			11.4636i			0.452785i	0.974036	+	0.226392i	$0.0726931\pi$
$641$			11.4636i			0.452785i	−0.974036	+	0.226392i	$0.927307\pi$
$642$	18.0208	+	0.975013i	0.711222	+	0.0384807i
$643$	−23.5941	+	9.77301i	−0.930462	+	0.385410i	−0.795854	−	0.605489i	$-0.792978\pi$
$643$	−23.5941	+	9.77301i	−0.930462	+	0.385410i	−0.134608	+	0.990899i	$0.542978\pi$
$644$	5.19798	−	4.18019i	0.204829	−	0.164723i
$645$	15.6297	+	6.47402i	0.615417	+	0.254914i
$646$	−0.223190	−	0.633674i	−0.00878128	−	0.0249316i
$647$	−7.14355	+	7.14355i	−0.280842	+	0.280842i	−0.833445	−	0.552603i	$-0.813635\pi$
$647$	−7.14355	+	7.14355i	−0.280842	+	0.280842i	0.552603	+	0.833445i	$0.313635\pi$
$648$	−4.29956	+	26.2820i	−0.168903	+	1.03245i
$649$	3.59931	−	3.59931i	0.141285	−	0.141285i
$650$	2.11417	−	21.2477i	0.0829245	−	0.833402i
$651$	6.46887	−	2.67949i	0.253535	−	0.105018i
$652$	−9.67528	−	33.0739i	−0.378913	−	1.29527i
$653$	12.7020	+	5.26132i	0.497066	+	0.205892i	0.617110	−	0.786877i	$-0.288303\pi$
$653$	12.7020	+	5.26132i	0.497066	+	0.205892i	−0.120044	+	0.992769i	$0.538303\pi$
$654$	−37.5164	−	2.02982i	−1.46701	−	0.0793724i
$655$	−11.3772	+	11.3772i	−0.444543	+	0.444543i
$656$	14.1285	+	3.10322i	0.551625	+	0.121160i
$657$	−1.81565	+	1.81565i	−0.0708351	+	0.0708351i
$658$	−8.34865	+	7.49161i	−0.325464	+	0.292053i
$659$	8.05605	−	19.4490i	0.313819	−	0.757627i	−0.685737	−	0.727849i	$-0.740520\pi$
$659$	8.05605	−	19.4490i	0.313819	−	0.757627i	0.999557	−	0.0297777i	$-0.00947993\pi$
$660$	3.35176	−	0.980510i	0.130467	−	0.0381663i
$661$	9.19732	−	22.2043i	0.357734	−	0.863647i	−0.637883	−	0.770133i	$-0.720190\pi$
$661$	9.19732	−	22.2043i	0.357734	−	0.863647i	0.995618	−	0.0935144i	$-0.0298101\pi$
$662$	−15.1512	+	31.6272i	−0.588867	+	1.22923i
$663$	7.45633	+	20.5814i	0.289580	+	0.799316i
$664$	−3.43602	−	14.6391i	−0.133343	−	0.568107i
$665$			0.196932i			0.00763668i
$666$	10.0856	+	28.6347i	0.390808	+	1.10957i
$667$	−0.0826597	+	0.0342388i	−0.00320060	+	0.00132573i
$668$	−4.31732	+	39.7808i	−0.167042	+	1.53917i
$669$	−4.57188	−	11.0375i	−0.176759	−	0.426734i
$670$	0.438948	−	8.11288i	0.0169580	−	0.313428i
$671$	1.25279	−	1.25279i	0.0483634	−	0.0483634i
$672$	9.72154	−	12.4498i	0.375017	−	0.480261i
$673$		−	41.9454i		−	1.61688i	−0.588582	−	0.808438i	$-0.700314\pi$
$673$		−	41.9454i		−	1.61688i	0.588582	−	0.808438i	$-0.299686\pi$
$674$	4.14872	+	0.224467i	0.159803	+	0.00864613i
$675$	0.564572	−	1.36300i	0.0217304	−	0.0524618i
$676$	−5.12334	+	25.4902i	−0.197052	+	0.980393i
$677$	−5.29844	+	2.19469i	−0.203636	+	0.0843486i	−0.482170	−	0.876078i	$-0.660151\pi$
$677$	−5.29844	+	2.19469i	−0.203636	+	0.0843486i	0.278535	+	0.960426i	$0.410151\pi$
$678$	−14.2779	+	29.8044i	−0.548341	+	1.14463i
$679$	6.35311	+	6.35311i	0.243810	+	0.243810i
$680$	−3.37007	+	5.43729i	−0.129236	+	0.208510i
$681$	15.7194			0.602371
$682$	0.943238	+	2.67802i	0.0361184	+	0.102547i
$683$	−5.03273	−	2.08462i	−0.192572	−	0.0797659i	0.284314	−	0.958731i	$-0.408234\pi$
$683$	−5.03273	−	2.08462i	−0.192572	−	0.0797659i	−0.476885	+	0.878965i	$0.658234\pi$
$684$	−0.518927	+	0.948078i	−0.0198417	+	0.0362507i
$685$	1.38488	+	0.573637i	0.0529136	+	0.0219175i
$686$	1.11701	−	20.6452i	0.0426475	−	0.788236i
$687$	8.97893	+	8.97893i	0.342567	+	0.342567i
$688$	5.44788	+	30.5468i	0.207699	+	1.16459i
$689$	0.417805	−	0.892512i	0.0159171	−	0.0340020i
$690$	8.90022	+	0.481547i	0.338826	+	0.0183322i
$691$	−5.11955	−	12.3597i	−0.194757	−	0.470184i	0.796090	−	0.605179i	$-0.206898\pi$
$691$	−5.11955	−	12.3597i	−0.194757	−	0.470184i	−0.990846	+	0.134994i	$0.956898\pi$
$692$	14.3780	−	26.2686i	0.546571	−	0.998582i
$693$	−2.43668	+	1.00931i	−0.0925618	+	0.0383403i
$694$	−16.3244	−	46.3479i	−0.619666	−	1.75934i
$695$		−	10.7428i		−	0.407498i
$696$	−0.172038	+	0.123663i	−0.00652108	+	0.00468744i
$697$	9.07422			0.343711
$698$	−19.5457	+	6.88431i	−0.739817	+	0.260575i
$699$	−64.7359	+	26.8145i	−2.44854	+	1.01422i
$700$	−7.53195	+	6.05715i	−0.284681	+	0.228939i
$701$	9.30572	+	3.85455i	0.351472	+	0.145585i	0.551433	−	0.834219i	$-0.314081\pi$
$701$	9.30572	+	3.85455i	0.351472	+	0.145585i	−0.199961	+	0.979804i	$0.564081\pi$
$702$	−0.848401	+	1.58343i	−0.0320208	+	0.0597629i
$703$		−	1.42384i		−	0.0537010i
$704$	4.82808	+	4.20910i	0.181965	+	0.158637i
$705$	−14.9890			−0.564517
$706$	−5.17469	+	4.64347i	−0.194752	+	0.174759i
$707$	16.6027	−	6.87705i	0.624408	−	0.258638i
$708$	23.9745	−	19.2802i	0.901017	−	0.724593i
$709$	45.6245	+	18.8983i	1.71346	+	0.709740i	0.999959	+	0.00908884i	$0.00289311\pi$
$709$	45.6245	+	18.8983i	1.71346	+	0.709740i	0.713504	+	0.700651i	$0.247107\pi$
$710$	0.767965	−	1.60308i	0.0288212	−	0.0601627i
$711$	−26.8384	−	26.8384i	−1.00652	−	1.00652i
$712$	45.8332	+	7.49800i	1.71767	+	0.281000i
$713$			7.24668i			0.271390i
$714$	4.28099	−	8.93633i	0.160212	−	0.334434i
$715$	2.59933	+	0.117368i	0.0972096	+	0.00438932i
$716$	7.46821	+	4.08770i	0.279100	+	0.152764i
$717$	−45.0860	+	18.6752i	−1.68377	+	0.697439i
$718$	−0.438850	+	8.11108i	−0.0163777	+	0.302703i
$719$		−	15.6190i		−	0.582492i	−0.956648	−	0.291246i	$-0.905930\pi$
$719$		−	15.6190i		−	0.582492i	0.956648	−	0.291246i	$-0.0940698\pi$
$720$	10.1313	−	1.80686i	0.377569	−	0.0673378i
$721$	−12.1523	−	12.1523i	−0.452575	−	0.452575i
$722$	−19.9610	+	17.9119i	−0.742872	+	0.666612i
$723$	−2.40641	+	0.996769i	−0.0894955	+	0.0370702i
$724$	−16.3180	+	4.77360i	−0.606455	+	0.177409i
$725$	0.119775	−	0.0496125i	0.00444834	−	0.00184256i
$726$	11.7757	+	33.4332i	0.437036	+	1.24082i
$727$	−16.8338	−	16.8338i	−0.624331	−	0.624331i	0.322305	−	0.946636i	$-0.395542\pi$
$727$	−16.8338	−	16.8338i	−0.624331	−	0.624331i	−0.946636	+	0.322305i	$0.895542\pi$
$728$	9.85648	−	6.43118i	0.365305	−	0.238356i
$729$	17.1958	−	17.1958i	0.636883	−	0.636883i
$730$	−1.03412	−	0.495401i	−0.0382746	−	0.0183356i
$731$	7.44881	+	17.9830i	0.275504	+	0.665126i
$732$	8.34466	−	6.71073i	0.308427	−	0.248036i
$733$	12.9675	+	31.3063i	0.478966	+	1.15633i	0.960095	+	0.279676i	$0.0902269\pi$
$733$	12.9675	+	31.3063i	0.478966	+	1.15633i	−0.481129	+	0.876650i	$0.659773\pi$
$734$	−10.6400	−	0.575676i	−0.392729	−	0.0212486i
$735$	8.74092	−	8.74092i	0.322414	−	0.322414i
$736$	8.05394	+	14.2265i	0.296872	+	0.524396i
$737$	−5.10330			−0.187983
$738$	−9.74966	−	10.8650i	−0.358890	−	0.399947i
$739$	−7.00116	−	16.9023i	−0.257542	−	0.621761i	0.741233	−	0.671248i	$-0.234241\pi$
$739$	−7.00116	−	16.9023i	−0.257542	−	0.621761i	−0.998775	+	0.0494870i	$0.984241\pi$
$740$	−10.5649	+	8.49622i	−0.388372	+	0.312327i
$741$	−1.21938	+	1.11402i	−0.0447949	+	0.0409244i
$742$	−0.420741	+	0.148191i	−0.0154459	+	0.00544027i
$743$	40.7184			1.49381			0.746907	−	0.664929i	$-0.231538\pi$
$743$	40.7184			1.49381			0.746907	+	0.664929i	$0.231538\pi$
$744$	3.92130	+	16.7066i	0.143762	+	0.612495i
$745$	9.27279	−	9.27279i	0.339729	−	0.339729i
$746$	−14.5084	−	41.1919i	−0.531191	−	1.50814i
$747$	−5.80721	+	14.0199i	−0.212475	+	0.512960i
$748$	3.52463	+	1.92919i	0.128873	+	0.0705383i
$749$	−2.32925	−	5.62330i	−0.0851089	−	0.205471i
$750$	−28.2951	−	1.53091i	−1.03319	−	0.0559008i
$751$		−	13.0313i		−	0.475518i	−0.971324	−	0.237759i	$-0.923587\pi$
$751$		−	13.0313i		−	0.475518i	0.971324	−	0.237759i	$-0.0764129\pi$
$752$	−14.8167	−	23.1574i	−0.540308	−	0.844462i
$753$	40.3670			1.47105
$754$	−0.151109	+	0.0456734i	−0.00550306	+	0.00166333i
$755$	3.86889	−	9.34034i	0.140803	−	0.339930i
$756$	0.780441	−	0.228307i	0.0283844	−	0.00830343i
$757$	−5.33975	−	12.8913i	−0.194077	−	0.468542i	0.796645	−	0.604447i	$-0.206606\pi$
$757$	−5.33975	−	12.8913i	−0.194077	−	0.468542i	−0.990722	+	0.135905i	$0.956606\pi$
$758$	1.87650	+	0.898945i	0.0681575	+	0.0326511i
$759$		−	5.59857i		−	0.203215i
$760$	−0.476322	−	0.0779231i	−0.0172780	−	0.00282657i
$761$	−45.0922			−1.63459			−0.817295	−	0.576219i	$-0.804527\pi$
$761$	−45.0922			−1.63459			−0.817295	+	0.576219i	$0.804527\pi$
$762$	27.2912	+	13.0740i	0.988654	+	0.473620i
$763$	4.84913	+	11.7068i	0.175550	+	0.423816i
$764$	2.73669	−	25.2165i	0.0990099	−	0.912301i
$765$	5.96431	−	2.47050i	0.215640	−	0.0893210i
$766$	−12.7225	−	14.1780i	−0.459684	−	0.512272i
$767$	21.5517	−	7.80785i	0.778187	−	0.281925i
$768$	26.2659	+	28.4399i	0.947789	+	1.02624i
$769$	−26.3171	+	26.3171i

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)

\(f(q)\)	\(=\)	\(q+(-1.41215 - 0.0764043i) q^{2} +(2.23541 + 0.925935i) q^{3} +(1.98832 + 0.215788i) q^{4} +(0.344928 - 0.832729i) q^{5} +(-3.08598 - 1.47835i) q^{6} +1.15405i q^{7} +(-2.79132 - 0.456642i) q^{8} +(2.01836 + 2.01836i) q^{9} +O(q^{10})\)	\(q+(-1.41215 - 0.0764043i) q^{2} +(2.23541 + 0.925935i) q^{3} +(1.98832 + 0.215788i) q^{4} +(0.344928 - 0.832729i) q^{5} +(-3.08598 - 1.47835i) q^{6} +1.15405i q^{7} +(-2.79132 - 0.456642i) q^{8} +(2.01836 + 2.01836i) q^{9} +(-0.550713 + 1.14958i) q^{10} +(0.739707 + 0.306397i) q^{11} +(4.24491 + 2.32343i) q^{12} +(2.43191 + 2.66192i) q^{13} +(0.0881743 - 1.62969i) q^{14} +(1.54211 - 1.54211i) q^{15} +(3.90687 + 0.858114i) q^{16} +2.50924 q^{17} +(-2.69602 - 3.00444i) q^{18} +(0.0724507 + 0.174911i) q^{19} +(0.865521 - 1.58130i) q^{20} +(-1.06858 + 2.57977i) q^{21} +(-1.02117 - 0.489194i) q^{22} +(-2.04351 - 2.04351i) q^{23} +(-5.81692 - 3.60536i) q^{24} +(2.96107 + 2.96107i) q^{25} +(-3.23084 - 3.94483i) q^{26} +(-0.134820 - 0.325485i) q^{27} +(-0.249030 + 2.29462i) q^{28} +(0.0118475 - 0.0286024i) q^{29} +(-2.29551 + 2.05986i) q^{30} +(-1.77310 - 1.77310i) q^{31} +(-5.45152 - 1.51029i) q^{32} +(1.36984 + 1.36984i) q^{33} +(-3.54342 - 0.191717i) q^{34} +(0.961010 + 0.398063i) q^{35} +(3.57762 + 4.44870i) q^{36} +(-6.94820 - 2.87804i) q^{37} +(-0.0889471 - 0.252536i) q^{38} +(2.97155 + 8.20226i) q^{39} +(-1.34306 + 2.16691i) q^{40} +3.61632 q^{41} +(1.70609 - 3.56137i) q^{42} +(2.96855 + 7.16672i) q^{43} +(1.40466 + 0.768836i) q^{44} +(2.37694 - 0.984560i) q^{45} +(2.72960 + 3.04187i) q^{46} +(-4.85990 - 4.85990i) q^{47} +(7.93888 + 5.53574i) q^{48} +5.66817 q^{49} +(-3.95523 - 4.40771i) q^{50} +(5.60917 + 2.32339i) q^{51} +(4.26102 + 5.81753i) q^{52} +(-0.104594 - 0.252513i) q^{53} +(0.165518 + 0.469934i) q^{54} +(0.510291 - 0.510291i) q^{55} +(0.526987 - 3.22132i) q^{56} +0.458083i q^{57} +(-0.0189158 + 0.0394856i) q^{58} +(2.43293 - 5.87361i) q^{59} +(3.39898 - 2.73344i) q^{60} +(0.846815 - 2.04439i) q^{61} +(2.36840 + 2.63935i) q^{62} +(-2.32929 + 2.32929i) q^{63} +(7.58296 + 2.54927i) q^{64} +(3.05549 - 1.10696i) q^{65} +(-1.82976 - 2.03908i) q^{66} +(-5.88874 + 2.43919i) q^{67} +(4.98918 + 0.541465i) q^{68} +(-2.67591 - 6.46023i) q^{69} +(-1.32667 - 0.635550i) q^{70} -1.39449 q^{71} +(-4.71223 - 6.55557i) q^{72} +0.899564i q^{73} +(9.59200 + 4.59509i) q^{74} +(3.87744 + 9.36096i) q^{75} +(0.106312 + 0.363415i) q^{76} +(-0.353597 + 0.853659i) q^{77} +(-3.56958 - 11.8098i) q^{78} -13.2971 q^{79} +(2.06216 - 2.95738i) q^{80} -9.41561i q^{81} +(-5.10678 - 0.276302i) q^{82} +(2.03448 + 4.91167i) q^{83} +(-2.68136 + 4.89883i) q^{84} +(0.865506 - 2.08952i) q^{85} +(-3.64447 - 10.3473i) q^{86} +(0.0529680 - 0.0529680i) q^{87} +(-1.92485 - 1.19303i) q^{88} -16.4199 q^{89} +(-3.43181 + 1.20874i) q^{90} +(-3.07198 + 2.80655i) q^{91} +(-3.62219 - 4.50412i) q^{92} +(-2.32182 - 5.60537i) q^{93} +(6.49158 + 7.23422i) q^{94} +0.170644 q^{95} +(-10.7879 - 8.42386i) q^{96} +(5.50506 - 5.50506i) q^{97} +(-8.00430 - 0.433072i) q^{98} +(0.874577 + 2.11142i) 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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