LMFDB - Embedded newform 68.2.i.b.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [68,2,Mod(3,68)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(68, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 1]))

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

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

chi := DirichletCharacter("68.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 68 = 2^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	68.i (of order $16$, degree $8$, 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:	$0.542982733745$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			3.1
Character	$\chi$	$=$	68.3
Dual form			68.2.i.b.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17748 - 0.783289i) q^{2} +(0.418777 - 2.10534i) q^{3} +(0.772915 + 1.84461i) q^{4} +(-0.561585 - 0.840472i) q^{5} +(-2.14219 + 2.15097i) q^{6} +(-1.73093 - 1.15657i) q^{7} +(0.534775 - 2.77741i) q^{8} +(-1.48543 - 0.615285i) q^{9} +O(q^{10})$	\(q+(-1.17748 - 0.783289i) q^{2} +(0.418777 - 2.10534i) q^{3} +(0.772915 + 1.84461i) q^{4} +(-0.561585 - 0.840472i) q^{5} +(-2.14219 + 2.15097i) q^{6} +(-1.73093 - 1.15657i) q^{7} +(0.534775 - 2.77741i) q^{8} +(-1.48543 - 0.615285i) q^{9} +(0.00292235 + 1.42952i) q^{10} +(1.04891 - 0.208641i) q^{11} +(4.20721 - 0.854763i) q^{12} +(4.36539 + 4.36539i) q^{13} +(1.13221 + 2.71766i) q^{14} +(-2.00465 + 0.830355i) q^{15} +(-2.80520 + 2.85146i) q^{16} +(0.0297412 - 4.12300i) q^{17} +(1.26712 + 1.88801i) q^{18} +(2.55002 + 6.15628i) q^{19} +(1.11629 - 1.68552i) q^{20} +(-3.15985 + 3.15985i) q^{21} +(-1.39849 - 0.575928i) q^{22} +(0.773086 + 3.88657i) q^{23} +(-5.62343 - 2.28900i) q^{24} +(1.52240 - 3.67540i) q^{25} +(-1.72079 - 8.55953i) q^{26} +(1.66029 - 2.48480i) q^{27} +(0.795567 - 4.08684i) q^{28} +(-3.11609 + 2.08211i) q^{29} +(3.01085 + 0.592499i) q^{30} +(-5.38553 - 1.07125i) q^{31} +(5.53659 - 1.16025i) q^{32} -2.29568i q^{33} +(-3.26452 + 4.83145i) q^{34} +2.10432i q^{35} +(-0.0131473 - 3.21560i) q^{36} +(-5.03388 - 1.00130i) q^{37} +(1.81956 - 9.24630i) q^{38} +(11.0188 - 7.36249i) q^{39} +(-2.63466 + 1.11029i) q^{40} +(-4.02629 + 6.02577i) q^{41} +(6.19574 - 1.24558i) q^{42} +(0.733065 - 1.76977i) q^{43} +(1.19558 + 1.77357i) q^{44} +(0.317065 + 1.59399i) q^{45} +(2.13401 - 5.18190i) q^{46} +(-6.00982 + 6.00982i) q^{47} +(4.82853 + 7.10003i) q^{48} +(-1.02031 - 2.46325i) q^{49} +(-4.67150 + 3.13523i) q^{50} +(-8.66784 - 1.78923i) q^{51} +(-4.67839 + 11.4265i) q^{52} +(-1.43923 + 0.596147i) q^{53} +(-3.90127 + 1.62531i) q^{54} +(-0.764407 - 0.764407i) q^{55} +(-4.13794 + 4.18901i) q^{56} +(14.0289 - 2.79053i) q^{57} +(5.30003 - 0.0108348i) q^{58} +(4.31414 + 1.78698i) q^{59} +(-3.08111 - 3.05602i) q^{60} +(6.25751 + 4.18113i) q^{61} +(5.50225 + 5.47980i) q^{62} +(1.85956 + 2.78302i) q^{63} +(-7.42803 - 2.97058i) q^{64} +(1.21745 - 6.12053i) q^{65} +(-1.79818 + 2.70311i) q^{66} +0.616467 q^{67} +(7.62833 - 3.13187i) q^{68} +8.50628 q^{69} +(1.64829 - 2.47779i) q^{70} +(1.17044 - 5.88422i) q^{71} +(-2.50327 + 3.79661i) q^{72} +(0.112327 + 0.168110i) q^{73} +(5.14298 + 5.12199i) q^{74} +(-7.10042 - 4.74435i) q^{75} +(-9.38502 + 9.46208i) q^{76} +(-2.05690 - 0.851995i) q^{77} +(-18.7413 + 0.0383127i) q^{78} +(11.4809 - 2.28368i) q^{79} +(3.97193 + 0.756357i) q^{80} +(-7.94673 - 7.94673i) q^{81} +(9.46080 - 3.94147i) q^{82} +(-11.4667 + 4.74966i) q^{83} +(-8.27101 - 3.38641i) q^{84} +(-3.48197 + 2.29042i) q^{85} +(-2.24941 + 1.50967i) q^{86} +(3.07859 + 7.43237i) q^{87} +(-0.0185510 - 3.02482i) q^{88} +(1.64195 - 1.64195i) q^{89} +(0.875222 - 2.12525i) q^{90} +(-2.50731 - 12.6051i) q^{91} +(-6.57169 + 4.43003i) q^{92} +(-4.51067 + 10.8897i) q^{93} +(11.7839 - 2.36901i) q^{94} +(3.74213 - 5.60049i) q^{95} +(-0.124116 - 12.1423i) q^{96} +(-4.27885 + 2.85903i) q^{97} +(-0.728042 + 3.69963i) q^{98} +(-1.68645 - 0.335456i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 24 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} + 16 q^{25} - 16 q^{26} + 40 q^{28} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 48 q^{41} + 40 q^{42} + 24 q^{44} - 64 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} + 48 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 96 q^{65} - 96 q^{66} - 32 q^{68} + 32 q^{69} - 80 q^{70} - 64 q^{72} + 64 q^{73} - 16 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 40 q^{82} - 80 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 48 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 72 q^{98}+O(q^{100}) $ 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 24 * q^20 - 16 * q^21 - 8 * q^22 + 8 * q^24 + 16 * q^25 - 16 * q^26 + 40 * q^28 + 56 * q^30 + 32 * q^32 + 56 * q^34 + 56 * q^36 - 16 * q^37 + 32 * q^38 + 56 * q^40 - 48 * q^41 + 40 * q^42 + 24 * q^44 - 64 * q^45 + 8 * q^46 - 32 * q^48 - 16 * q^49 - 16 * q^52 + 48 * q^53 - 24 * q^54 - 48 * q^56 + 64 * q^57 - 64 * q^58 - 112 * q^60 + 16 * q^61 - 64 * q^62 - 56 * q^64 + 96 * q^65 - 96 * q^66 - 32 * q^68 + 32 * q^69 - 80 * q^70 - 64 * q^72 + 64 * q^73 - 16 * q^74 - 64 * q^76 + 16 * q^77 - 112 * q^78 - 24 * q^80 + 64 * q^81 - 40 * q^82 - 80 * q^85 + 64 * q^86 + 56 * q^88 - 16 * q^89 + 48 * q^90 + 104 * q^92 - 16 * q^93 + 88 * q^94 + 144 * q^96 - 16 * q^97 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/68\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{1}{16}\right)$

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 $

$2$	−1.17748	−	0.783289i	−0.832604	−	0.553869i
$2$	−1.17748	−	0.783289i	−0.832604	−	0.553869i
$3$	0.418777	−	2.10534i	0.241781	−	1.21552i	−0.648895	−	0.760878i	$-0.724768\pi$
$3$	0.418777	−	2.10534i	0.241781	−	1.21552i	0.890676	−	0.454638i	$-0.150232\pi$
$4$	0.772915	+	1.84461i	0.386458	+	0.922307i
$5$	−0.561585	−	0.840472i	−0.251149	−	0.375870i	0.684378	−	0.729128i	$-0.260074\pi$
$5$	−0.561585	−	0.840472i	−0.251149	−	0.375870i	−0.935526	+	0.353257i	$0.885074\pi$
$6$	−2.14219	+	2.15097i	−0.874545	+	0.878128i
$7$	−1.73093	−	1.15657i	−0.654232	−	0.437144i	0.183653	−	0.982991i	$-0.441208\pi$
$7$	−1.73093	−	1.15657i	−0.654232	−	0.437144i	−0.837885	+	0.545847i	$0.816208\pi$
$8$	0.534775	−	2.77741i	0.189072	−	0.981963i
$9$	−1.48543	−	0.615285i	−0.495143	−	0.205095i
$10$	0.00292235	+	1.42952i	0.000924130	+	0.452054i
$11$	1.04891	−	0.208641i	0.316257	−	0.0629075i	−0.0344093	−	0.999408i	$-0.510955\pi$
$11$	1.04891	−	0.208641i	0.316257	−	0.0629075i	0.350667	+	0.936500i	$0.385955\pi$
$12$	4.20721	−	0.854763i	1.21452	−	0.246749i
$13$	4.36539	+	4.36539i	1.21074	+	1.21074i	0.970783	+	0.239959i	$0.0771342\pi$
$13$	4.36539	+	4.36539i	1.21074	+	1.21074i	0.239959	+	0.970783i	$0.422866\pi$
$14$	1.13221	+	2.71766i	0.302595	+	0.726326i
$15$	−2.00465	+	0.830355i	−0.517600	+	0.214397i
$16$	−2.80520	+	2.85146i	−0.701301	+	0.712865i
$17$	0.0297412	−	4.12300i	0.00721330	−	0.999974i
$17$	0.0297412	−	4.12300i	0.00721330	−	0.999974i
$18$	1.26712	+	1.88801i	0.298662	+	0.445007i
$19$	2.55002	+	6.15628i	0.585014	+	1.41235i	0.888218	+	0.459423i	$0.151944\pi$
$19$	2.55002	+	6.15628i	0.585014	+	1.41235i	−0.303204	+	0.952926i	$0.598056\pi$
$20$	1.11629	−	1.68552i	0.249610	−	0.376894i
$21$	−3.15985	+	3.15985i	−0.689536	+	0.689536i
$22$	−1.39849	−	0.575928i	−0.298160	−	0.122788i
$23$	0.773086	+	3.88657i	0.161200	+	0.810405i	0.973769	+	0.227540i	$0.0730684\pi$
$23$	0.773086	+	3.88657i	0.161200	+	0.810405i	−0.812569	+	0.582865i	$0.801932\pi$
$24$	−5.62343	−	2.28900i	−1.14788	−	0.467240i
$25$	1.52240	−	3.67540i	0.304481	−	0.735081i
$26$	−1.72079	−	8.55953i	−0.337475	−	1.67866i
$27$	1.66029	−	2.48480i	0.319522	−	0.478199i
$28$	0.795567	−	4.08684i	0.150348	−	0.772340i
$29$	−3.11609	+	2.08211i	−0.578644	+	0.386638i	−0.810173	−	0.586190i	$-0.800627\pi$
$29$	−3.11609	+	2.08211i	−0.578644	+	0.386638i	0.231529	+	0.972828i	$0.425627\pi$
$30$	3.01085	+	0.592499i	0.549703	+	0.108175i
$31$	−5.38553	−	1.07125i	−0.967269	−	0.192402i	−0.313912	−	0.949452i	$-0.601640\pi$
$31$	−5.38553	−	1.07125i	−0.967269	−	0.192402i	−0.653357	+	0.757050i	$0.726640\pi$
$32$	5.53659	−	1.16025i	0.978740	−	0.205105i
$33$		−	2.29568i		−	0.399626i
$34$	−3.26452	+	4.83145i	−0.559861	+	0.828587i
$35$			2.10432i			0.355694i
$36$	−0.0131473	−	3.21560i	−0.00219122	−	0.535934i
$37$	−5.03388	−	1.00130i	−0.827564	−	0.164613i	−0.236904	−	0.971533i	$-0.576133\pi$
$37$	−5.03388	−	1.00130i	−0.827564	−	0.164613i	−0.590660	+	0.806920i	$0.701133\pi$
$38$	1.81956	−	9.24630i	0.295172	−	1.49995i
$39$	11.0188	−	7.36249i	1.76441	−	1.17894i
$40$	−2.63466	+	1.11029i	−0.416576	+	0.175552i
$41$	−4.02629	+	6.02577i	−0.628801	+	0.941067i	0.371121	+	0.928585i	$0.378974\pi$
$41$	−4.02629	+	6.02577i	−0.628801	+	0.941067i	−0.999922	+	0.0124828i	$0.996026\pi$
$42$	6.19574	−	1.24558i	0.956024	−	0.192197i
$43$	0.733065	−	1.76977i	0.111791	−	0.269888i	−0.858076	−	0.513523i	$-0.828340\pi$
$43$	0.733065	−	1.76977i	0.111791	−	0.269888i	0.969867	+	0.243635i	$0.0783400\pi$
$44$	1.19558	+	1.77357i	0.180240	+	0.267375i
$45$	0.317065	+	1.59399i	0.0472653	+	0.237619i
$46$	2.13401	−	5.18190i	0.314643	−	0.764030i
$47$	−6.00982	+	6.00982i	−0.876622	+	0.876622i	−0.993183	−	0.116561i	$-0.962813\pi$
$47$	−6.00982	+	6.00982i	−0.876622	+	0.876622i	0.116561	+	0.993183i	$0.462813\pi$
$48$	4.82853	+	7.10003i	0.696938	+	1.02480i
$49$	−1.02031	−	2.46325i	−0.145759	−	0.351893i
$50$	−4.67150	+	3.13523i	−0.660650	+	0.443389i
$51$	−8.66784	−	1.78923i	−1.21374	−	0.250543i
$52$	−4.67839	+	11.4265i	−0.648776	+	1.58458i
$53$	−1.43923	+	0.596147i	−0.197693	+	0.0818871i	−0.479333	−	0.877633i	$-0.659121\pi$
$53$	−1.43923	+	0.596147i	−0.197693	+	0.0818871i	0.281640	+	0.959520i	$0.409121\pi$
$54$	−3.90127	+	1.62531i	−0.530895	+	0.221177i
$55$	−0.764407	−	0.764407i	−0.103073	−	0.103073i
$56$	−4.13794	+	4.18901i	−0.552956	+	0.559780i
$57$	14.0289	−	2.79053i	1.85818	−	0.369615i
$58$	5.30003	−	0.0108348i	0.695928	−	0.00142268i
$59$	4.31414	+	1.78698i	0.561653	+	0.232644i	0.645403	−	0.763842i	$-0.276690\pi$
$59$	4.31414	+	1.78698i	0.561653	+	0.232644i	−0.0837494	+	0.996487i	$0.526690\pi$
$60$	−3.08111	−	3.05602i	−0.397770	−	0.394531i
$61$	6.25751	+	4.18113i	0.801192	+	0.535339i	0.887434	−	0.460935i	$-0.152486\pi$
$61$	6.25751	+	4.18113i	0.801192	+	0.535339i	−0.0862420	+	0.996274i	$0.527486\pi$
$62$	5.50225	+	5.47980i	0.698786	+	0.695935i
$63$	1.85956	+	2.78302i	0.234282	+	0.350628i
$64$	−7.42803	−	2.97058i	−0.928504	−	0.371323i
$65$	1.21745	−	6.12053i	0.151006	−	0.759158i
$66$	−1.79818	+	2.70311i	−0.221341	+	0.332730i
$67$	0.616467			0.0753134			0.0376567	−	0.999291i	$-0.488011\pi$
$67$	0.616467			0.0753134			0.0376567	+	0.999291i	$0.488011\pi$
$68$	7.62833	−	3.13187i	0.925071	−	0.379795i
$69$	8.50628			1.02404
$70$	1.64829	−	2.47779i	0.197008	−	0.296152i
$71$	1.17044	−	5.88422i	0.138906	−	0.698329i	−0.847075	−	0.531473i	$-0.821639\pi$
$71$	1.17044	−	5.88422i	0.138906	−	0.698329i	0.985981	−	0.166856i	$-0.0533613\pi$
$72$	−2.50327	+	3.79661i	−0.295013	+	0.447434i
$73$	0.112327	+	0.168110i	0.0131469	+	0.0196758i	0.837985	−	0.545693i	$-0.183734\pi$
$73$	0.112327	+	0.168110i	0.0131469	+	0.0196758i	−0.824838	+	0.565369i	$0.808734\pi$
$74$	5.14298	+	5.12199i	0.597859	+	0.595420i
$75$	−7.10042	−	4.74435i	−0.819885	−	0.547830i
$76$	−9.38502	+	9.46208i	−1.07654	+	1.08538i
$77$	−2.05690	−	0.851995i	−0.234405	−	0.0970939i
$78$	−18.7413	+	0.0383127i	−2.12204	+	0.00433805i
$79$	11.4809	−	2.28368i	1.29170	−	0.256935i	0.499028	−	0.866586i	$-0.333691\pi$
$79$	11.4809	−	2.28368i	1.29170	−	0.256935i	0.792670	+	0.609651i	$0.208691\pi$
$80$	3.97193	+	0.756357i	0.444076	+	0.0845632i
$81$	−7.94673	−	7.94673i	−0.882970	−	0.882970i
$82$	9.46080	−	3.94147i	1.04477	−	0.435262i
$83$	−11.4667	+	4.74966i	−1.25863	+	0.521343i	−0.909489	−	0.415727i	$-0.863527\pi$
$83$	−11.4667	+	4.74966i	−1.25863	+	0.521343i	−0.349143	+	0.937070i	$0.613527\pi$
$84$	−8.27101	−	3.38641i	−0.902441	−	0.369488i
$85$	−3.48197	+	2.29042i	−0.377672	+	0.248431i
$86$	−2.24941	+	1.50967i	−0.242561	+	0.162792i
$87$	3.07859	+	7.43237i	0.330059	+	0.796833i
$88$	−0.0185510	−	3.02482i	−0.00197755	−	0.322447i
$89$	1.64195	−	1.64195i	0.174046	−	0.174046i	−0.614708	−	0.788755i	$-0.710726\pi$
$89$	1.64195	−	1.64195i	0.174046	−	0.174046i	0.788755	+	0.614708i	$0.210726\pi$
$90$	0.875222	−	2.12525i	0.0922565	−	0.224021i
$91$	−2.50731	−	12.6051i	−0.262838	−	1.32137i
$92$	−6.57169	+	4.43003i	−0.685146	+	0.461863i
$93$	−4.51067	+	10.8897i	−0.467735	+	1.12921i
$94$	11.7839	−	2.36901i	1.21541	−	0.244345i
$95$	3.74213	−	5.60049i	0.383934	−	0.574599i
$96$	−0.124116	−	12.1423i	−0.0126675	−	1.23927i
$97$	−4.27885	+	2.85903i	−0.434451	+	0.290291i	−0.753501	−	0.657447i	$-0.771636\pi$
$97$	−4.27885	+	2.85903i	−0.434451	+	0.290291i	0.319050	+	0.947738i	$0.396636\pi$
$98$	−0.728042	+	3.69963i	−0.0735434	+	0.373719i
$99$	−1.68645	−	0.335456i	−0.169495	−	0.0337146i
$100$	7.95639	−	0.0325305i	0.795639	−	0.00325305i
$101$			4.66402i			0.464087i	0.972705	+	0.232044i	$0.0745412\pi$
$101$			4.66402i			0.464087i	−0.972705	+	0.232044i	$0.925459\pi$
$102$	8.80472	+	8.89622i	0.871797	+	0.880857i
$103$		−	8.53993i		−	0.841464i	−0.907185	−	0.420732i	$-0.861773\pi$
$103$		−	8.53993i		−	0.841464i	0.907185	−	0.420732i	$-0.138227\pi$
$104$	14.4590	−	9.78999i	1.41782	−	0.959987i
$105$	4.43029	+	0.881240i	0.432352	+	0.0860002i
$106$	2.16162	+	0.425380i	0.209955	+	0.0413166i
$107$	3.03293	−	2.02654i	0.293204	−	0.195913i	−0.400264	−	0.916400i	$-0.631082\pi$
$107$	3.03293	−	2.02654i	0.293204	−	0.195913i	0.693469	+	0.720487i	$0.256082\pi$
$108$	5.86675	+	1.14205i	0.564528	+	0.109894i
$109$	4.13331	−	6.18594i	0.395899	−	0.592505i	−0.578952	−	0.815362i	$-0.696538\pi$
$109$	4.13331	−	6.18594i	0.395899	−	0.592505i	0.974851	+	0.222856i	$0.0715381\pi$
$110$	0.301322	+	1.49883i	0.0287299	+	0.142907i
$111$	−4.21615	+	10.1787i	−0.400179	+	0.966118i
$112$	8.15355	−	1.69127i	0.770438	−	0.159810i
$113$	0.661577	+	3.32597i	0.0622359	+	0.312881i	0.999346	−	0.0361520i	$-0.0115100\pi$
$113$	0.661577	+	3.32597i	0.0622359	+	0.312881i	−0.937110	+	0.349033i	$0.886510\pi$
$114$	−18.7046	−	7.70293i	−1.75184	−	0.721445i
$115$	2.83240	−	2.83240i	0.264122	−	0.264122i
$116$	−6.24916	−	4.13870i	−0.580220	−	0.384269i
$117$	−3.79852	−	9.17044i	−0.351173	−	0.847807i
$118$	−3.68009	−	5.48335i	−0.338780	−	0.504783i
$119$	−4.82003	+	7.10224i	−0.441851	+	0.651061i
$120$	1.23420	+	6.01180i	0.112666	+	0.548800i
$121$	−9.10600	+	3.77183i	−0.827818	+	0.342893i
$122$	−4.09305	−	9.82464i	−0.370567	−	0.889481i
$123$	11.0002	+	11.0002i	0.991851	+	0.991851i
$124$	−2.18652	−	10.7622i	−0.196355	−	0.966474i
$125$	−8.90105	+	1.77053i	−0.796134	+	0.158361i
$126$	−0.00967669	−	4.73353i	−0.000862068	−	0.421696i
$127$	−3.23692	−	1.34078i	−0.287230	−	0.118975i	0.234416	−	0.972136i	$-0.424682\pi$
$127$	−3.23692	−	1.34078i	−0.287230	−	0.118975i	−0.521647	+	0.853162i	$0.674682\pi$
$128$	6.41953	+	9.31610i	0.567411	+	0.823435i
$129$	−3.41898	−	2.28449i	−0.301024	−	0.201138i
$130$	−6.22767	+	6.25318i	−0.546203	+	0.548440i
$131$	8.52460	+	12.7580i	0.744797	+	1.11467i	0.989424	+	0.145051i	$0.0463345\pi$
$131$	8.52460	+	12.7580i	0.744797	+	1.11467i	−0.244627	+	0.969617i	$0.578665\pi$
$132$	4.23464	−	1.77436i	0.368578	−	0.154439i
$133$	2.70628	−	13.6054i	0.234665	−	1.17974i
$134$	−0.725877	−	0.482872i	−0.0627062	−	0.0417138i
$135$	−3.02079			−0.259988
$136$	−11.4354	−	2.28748i	−0.980574	−	0.196150i
$137$	1.49452			0.127686			0.0638429	−	0.997960i	$-0.479664\pi$
$137$	1.49452			0.127686			0.0638429	+	0.997960i	$0.479664\pi$
$138$	−10.0160	−	6.66288i	−0.852616	−	0.567182i
$139$	−3.20590	+	16.1171i	−0.271921	+	1.36704i	0.567419	+	0.823429i	$0.307942\pi$
$139$	−3.20590	+	16.1171i	−0.271921	+	1.36704i	−0.839339	+	0.543608i	$0.817058\pi$
$140$	−3.88165	+	1.62646i	−0.328059	+	0.137461i
$141$	10.1359	+	15.1695i	0.853598	+	1.27750i
$142$	−5.98722	+	6.01175i	−0.502437	+	0.504495i
$143$	5.48969	+	3.66810i	0.459071	+	0.306742i
$144$	5.92139	−	2.50964i	0.493449	−	0.209137i
$145$	3.49990	+	1.44971i	0.290651	+	0.120392i
$146$	−0.000584525	−	0.285931i	−4.83756e−5	−	0.0236638i
$147$	−5.61326	+	1.11655i	−0.462973	+	0.0920912i
$148$	−2.04375	−	10.0595i	−0.167995	−	0.826884i
$149$	−4.60411	−	4.60411i	−0.377183	−	0.377183i	0.492902	−	0.870085i	$-0.335936\pi$
$149$	−4.60411	−	4.60411i	−0.377183	−	0.377183i	−0.870085	+	0.492902i	$0.835936\pi$
$150$	4.64440	+	11.1481i	0.379213	+	0.910235i
$151$	1.26412	−	0.523616i	0.102873	−	0.0426112i	−0.330654	−	0.943752i	$-0.607269\pi$
$151$	1.26412	−	0.523616i	0.102873	−	0.0426112i	0.433526	+	0.901141i	$0.357269\pi$
$152$	18.4622	−	3.79022i	1.49748	−	0.307427i
$153$	−2.58100	+	6.10612i	−0.208661	+	0.493650i
$154$	1.75460	+	2.61435i	0.141389	+	0.210671i
$155$	2.12408	+	5.12798i	0.170610	+	0.411889i
$156$	22.0975	+	14.6348i	1.76922	+	1.17172i
$157$	3.70126	−	3.70126i	0.295393	−	0.295393i	−0.543813	−	0.839206i	$-0.683020\pi$
$157$	3.70126	−	3.70126i	0.295393	−	0.295393i	0.839206	+	0.543813i	$0.183020\pi$
$158$	−15.3073	−	6.30384i	−1.21778	−	0.501507i
$159$	0.652375	+	3.27971i	0.0517367	+	0.260098i
$160$	−4.08442	−	4.00177i	−0.322902	−	0.316367i
$161$	3.15694	−	7.62153i	0.248802	−	0.600660i
$162$	3.13252	+	15.5817i	0.246114	+	1.22421i
$163$	4.61217	−	6.90260i	0.361253	−	0.540653i	−0.605672	−	0.795714i	$-0.707096\pi$
$163$	4.61217	−	6.90260i	0.361253	−	0.540653i	0.966925	+	0.255061i	$0.0820956\pi$
$164$	−14.2272	−	2.76955i	−1.11096	−	0.216265i
$165$	−1.92945	+	1.28922i	−0.150208	+	0.100365i
$166$	17.2221	+	3.38911i	1.33670	+	0.263046i
$167$	−20.1200	−	4.00211i	−1.55693	−	0.309693i	−0.659793	−	0.751447i	$-0.729356\pi$
$167$	−20.1200	−	4.00211i	−1.55693	−	0.309693i	−0.897136	+	0.441754i	$0.854356\pi$
$168$	7.08640	+	10.4660i	0.546728	+	0.807471i
$169$			25.1133i			1.93179i
$170$	5.89400	+	0.0304668i	0.452049	+	0.00233670i
$171$		−	10.7137i		−	0.819297i
$172$	3.83115	−	0.0156640i	0.292122	−	0.00119437i
$173$	8.78742	+	1.74793i	0.668095	+	0.132892i	0.517474	−	0.855699i	$-0.326873\pi$
$173$	8.78742	+	1.74793i	0.668095	+	0.132892i	0.150621	+	0.988592i	$0.451873\pi$
$174$	2.19672	−	11.1629i	0.166533	−	0.846256i
$175$	−6.88606	+	4.60111i	−0.520537	+	0.347812i
$176$	−2.34747	+	3.57620i	−0.176947	+	0.269566i
$177$	5.56885	−	8.33437i	0.418580	−	0.626450i
$178$	−3.21948	+	0.647240i	−0.241310	+	0.0485127i
$179$	8.09765	−	19.5495i	0.605247	−	1.46120i	−0.262868	−	0.964832i	$-0.584668\pi$
$179$	8.09765	−	19.5495i	0.605247	−	1.46120i	0.868115	−	0.496364i	$-0.165332\pi$
$180$	−2.69524	+	1.81689i	−0.200891	+	0.135423i
$181$	−4.60615	−	23.1567i	−0.342373	−	1.72122i	−0.641598	−	0.767041i	$-0.721728\pi$
$181$	−4.60615	−	23.1567i	−0.342373	−	1.72122i	0.299225	−	0.954182i	$-0.403272\pi$
$182$	−6.92114	+	16.8062i	−0.513029	+	1.24576i
$183$	11.4232	−	11.4232i	0.844427	−	0.844427i
$184$	11.2080	−	0.0687381i	0.826267	−	0.00506744i
$185$	1.98539	+	4.79315i	0.145968	+	0.352399i
$186$	13.8410	−	9.28927i	1.01487	−	0.681122i
$187$	−0.829029	−	4.33085i	−0.0606246	−	0.316703i
$188$	−15.7309	−	6.44072i	−1.14729	−	0.469738i
$189$	−5.74770	+	2.38077i	−0.418083	+	0.173176i
$190$	−8.79309	+	3.66329i	−0.637918	+	0.265763i
$191$	−7.02075	−	7.02075i	−0.508003	−	0.508003i	0.405910	−	0.913913i	$-0.366955\pi$
$191$	−7.02075	−	7.02075i	−0.508003	−	0.508003i	−0.913913	+	0.405910i	$0.866955\pi$
$192$	−9.36477	+	14.3945i	−0.675844	+	1.03883i
$193$	−17.6041	+	3.50168i	−1.26717	+	0.252057i	−0.782507	−	0.622642i	$-0.786059\pi$
$193$	−17.6041	+	3.50168i	−1.26717	+	0.252057i	−0.484667	+	0.874699i	$0.661059\pi$
$194$	7.27771	−	0.0148777i	0.522509	−	0.00106816i
$195$	−12.3759	−	5.12628i	−0.886259	−	0.367101i
$196$	3.75513	−	3.78597i	0.268224	−	0.270426i
$197$	1.75750	+	1.17432i	0.125217	+	0.0836670i	0.616601	−	0.787276i	$-0.288509\pi$
$197$	1.75750	+	1.17432i	0.125217	+	0.0836670i	−0.491385	+	0.870943i	$0.663509\pi$
$198$	1.72300	+	1.71597i	0.122448	+	0.121949i
$199$	−1.02043	−	1.52719i	−0.0723366	−	0.108259i	0.793537	−	0.608521i	$-0.208237\pi$
$199$	−1.02043	−	1.52719i	−0.0723366	−	0.108259i	−0.865874	+	0.500262i	$0.833237\pi$
$200$	−9.39397	−	6.19385i	−0.664254	−	0.437972i
$201$	0.258163	−	1.29787i	0.0182094	−	0.0915447i
$202$	3.65328	−	5.49179i	0.257044	−	0.386401i
$203$	7.80187			0.547584
$204$	−3.39906	−	17.3718i	−0.237982	−	1.21627i
$205$	7.32559			0.511642
$206$	−6.68923	+	10.0556i	−0.466061	+	0.700606i
$207$	1.24298	−	6.24889i	0.0863931	−	0.434328i
$208$	−24.6936	+	0.201927i	−1.71219	+	0.0140011i
$209$	3.95918	+	5.92534i	0.273862	+	0.409864i
$210$	−4.52631	−	4.50784i	−0.312345	−	0.311071i
$211$	20.1186	+	13.4428i	1.38502	+	0.925440i	0.999997	+	0.00253193i	$0.000805940\pi$
$211$	20.1186	+	13.4428i	1.38502	+	0.925440i	0.385021	+	0.922908i	$0.374194\pi$
$212$	−2.21206	−	2.19405i	−0.151925	−	0.150688i
$213$	−11.8981	−	4.92836i	−0.815245	−	0.337686i
$214$	−5.15858	+	0.0105456i	−0.352633	+	0.000720884i
$215$	−1.89912	+	0.377759i	−0.129519	+	0.0257630i
$216$	−6.01342	−	5.94011i	−0.409161	−	0.404173i
$217$	8.08302	+	8.08302i	0.548711	+	0.548711i
$218$	−9.71227	+	4.04623i	−0.657798	+	0.274046i
$219$	0.400968	−	0.166086i	0.0270949	−	0.0112231i
$220$	0.819215	−	2.00086i	0.0552315	−	0.134898i
$221$	18.1283	−	17.8687i	1.21944	−	1.20198i
$222$	12.9373	−	8.68272i	0.868294	−	0.582746i
$223$	−5.47542	−	13.2188i	−0.366661	−	0.885199i	−0.994293	−	0.106688i	$-0.965975\pi$
$223$	−5.47542	−	13.2188i	−0.366661	−	0.885199i	0.627631	−	0.778511i	$-0.284025\pi$
$224$	−10.9254	−	4.39516i	−0.729983	−	0.293664i
$225$	−4.52284	+	4.52284i	−0.301523	+	0.301523i
$226$	1.82621	−	4.43447i	0.121477	−	0.294977i
$227$	−4.02687	−	20.2445i	−0.267273	−	1.34367i	−0.848183	−	0.529704i	$-0.822303\pi$
$227$	−4.02687	−	20.2445i	−0.267273	−	1.34367i	0.580910	−	0.813968i	$-0.302697\pi$
$228$	15.9906	+	23.7211i	1.05901	+	1.57097i
$229$	0.275631	−	0.665433i	0.0182142	−	0.0439731i	−0.914511	−	0.404562i	$-0.867424\pi$
$229$	0.275631	−	0.665433i	0.0182142	−	0.0439731i	0.932725	+	0.360589i	$0.117424\pi$
$230$	−5.55367	+	1.11650i	−0.366198	+	0.0736199i
$231$	−2.65512	+	3.97367i	−0.174694	+	0.261448i
$232$	4.11646	+	9.76814i	0.270259	+	0.641310i
$233$	15.2485	−	10.1887i	0.998962	−	0.667485i	0.0553255	−	0.998468i	$-0.482380\pi$
$233$	15.2485	−	10.1887i	0.998962	−	0.667485i	0.943637	+	0.330983i	$0.107380\pi$
$234$	−2.71043	+	13.7733i	−0.177186	+	0.900392i
$235$	8.42611	+	1.67606i	0.549659	+	0.109334i
$236$	0.0381838	+	9.33911i	0.00248556	+	0.607924i
$237$		−	25.1274i		−	1.63220i
$238$	11.2386	−	4.58726i	0.728490	−	0.297348i
$239$		−	10.2504i		−	0.663044i	−0.943447	−	0.331522i	$-0.892438\pi$
$239$		−	10.2504i		−	0.663044i	0.943447	−	0.331522i	$-0.107562\pi$
$240$	3.25574	−	8.04551i	0.210157	−	0.519335i
$241$	10.6102	+	2.11050i	0.683462	+	0.135949i	0.524596	−	0.851351i	$-0.324216\pi$
$241$	10.6102	+	2.11050i	0.683462	+	0.135949i	0.158866	+	0.987300i	$0.449216\pi$
$242$	13.6766	+	2.69138i	0.879163	+	0.173009i
$243$	−12.6041	+	8.42177i	−0.808551	+	0.540257i
$244$	−2.87606	+	14.7744i	−0.184121	+	0.945831i
$245$	−1.49730	+	2.24087i	−0.0956590	+	0.143164i
$246$	−4.33615	−	21.5688i	−0.276463	−	1.37517i
$247$	−15.7428	+	38.0064i	−1.00169	+	2.41829i
$248$	−5.85534	+	14.3849i	−0.371815	+	0.913445i
$249$	5.19764	+	26.1303i	0.329387	+	1.65594i
$250$	11.8676	+	4.88734i	0.750575	+	0.309102i
$251$	−2.76475	+	2.76475i	−0.174509	+	0.174509i	−0.788957	−	0.614448i	$-0.789379\pi$
$251$	−2.76475	+	2.76475i	−0.174509	+	0.174509i	0.614448	+	0.788957i	$0.289379\pi$
$252$	−3.69633	+	5.58121i	−0.232847	+	0.351583i
$253$	1.62179	+	3.91535i	0.101961	+	0.246156i
$254$	2.76119	+	4.11418i	0.173253	+	0.258147i
$255$	3.36393	+	8.28988i	0.210658	+	0.519133i
$256$	−0.261657	−	15.9979i	−0.0163536	−	0.999866i
$257$	−13.2450	+	5.48626i	−0.826201	+	0.342224i	−0.755398	−	0.655266i	$-0.772556\pi$
$257$	−13.2450	+	5.48626i	−0.826201	+	0.342224i	−0.0708035	+	0.997490i	$0.522556\pi$
$258$	2.23636	+	5.36799i	0.139230	+	0.334197i
$259$	7.55523	+	7.55523i	0.469459	+	0.469459i
$260$	12.2310	−	2.48493i	0.758535	−	0.154109i
$261$	5.90982	−	1.17554i	0.365809	−	0.0727639i
$262$	−0.0443600	−	21.6995i	−0.00274057	−	1.34060i
$263$	16.6441	+	6.89422i	1.02632	+	0.425116i	0.831383	−	0.555700i	$-0.187550\pi$
$263$	16.6441	+	6.89422i	1.02632	+	0.425116i	0.194937	+	0.980816i	$0.437550\pi$
$264$	−6.37604	−	1.22767i	−0.392418	−	0.0755580i
$265$	1.30929	+	0.874842i	0.0804292	+	0.0537411i
$266$	−13.8436	+	13.9003i	−0.848803	+	0.852281i
$267$	−2.76924	−	4.14447i	−0.169475	−	0.253637i
$268$	0.476477	+	1.13714i	0.0291054	+	0.0694621i
$269$	−6.36128	+	31.9803i	−0.387854	+	1.94987i	−0.0869746	+	0.996211i	$0.527720\pi$
$269$	−6.36128	+	31.9803i	−0.387854	+	1.94987i	−0.300879	+	0.953662i	$0.597280\pi$
$270$	3.55692	+	2.36615i	0.216467	+	0.144000i
$271$	4.56417			0.277253			0.138627	−	0.990345i	$-0.455731\pi$
$271$	4.56417			0.277253			0.138627	+	0.990345i	$0.455731\pi$
$272$	11.6731	+	11.6507i	0.707788	+	0.706425i
$273$	−27.5880			−1.66970
$274$	−1.75977	−	1.17065i	−0.106312	−	0.0707213i
$275$	0.830020	−	4.17279i	0.0500521	−	0.251629i
$276$	6.57464	+	15.6908i	0.395747	+	0.944476i
$277$	−7.41492	−	11.0972i	−0.445519	−	0.666767i	0.538947	−	0.842340i	$-0.318822\pi$
$277$	−7.41492	−	11.0972i	−0.445519	−	0.666767i	−0.984466	+	0.175573i	$0.943822\pi$
$278$	16.3993	−	16.4664i	0.983562	−	0.987591i
$279$	7.34069	+	4.90489i	0.439476	+	0.293648i
$280$	5.84455	+	1.12534i	0.349279	+	0.0672517i
$281$	3.29326	+	1.36411i	0.196459	+	0.0813762i	0.478744	−	0.877955i	$-0.341092\pi$
$281$	3.29326	+	1.36411i	0.196459	+	0.0813762i	−0.282285	+	0.959331i	$0.591092\pi$
$282$	−0.0527449	−	25.8011i	−0.00314091	−	1.53643i
$283$	−32.5206	+	6.46874i	−1.93315	+	0.384527i	−0.933483	+	0.358621i	$0.883247\pi$
$283$	−32.5206	+	6.46874i	−1.93315	+	0.384527i	−0.999664	+	0.0259060i	$0.991753\pi$
$284$	11.7588	−	2.38899i	0.697755	−	0.141760i
$285$	−10.2238	−	10.2238i	−0.605606	−	0.605606i
$286$	−3.59082	−	8.61913i	−0.212330	−	0.509660i
$287$	13.9385	−	5.77351i	0.822763	−	0.340800i
$288$	−8.93809	−	1.68311i	−0.526682	−	0.0991783i
$289$	−16.9982	−	0.245246i	−0.999896	−	0.0144262i
$290$	−2.98552	−	4.44844i	−0.175316	−	0.261221i
$291$	4.22734	+	10.2057i	0.247811	+	0.598269i
$292$	−0.223278	+	0.337135i	−0.0130664	+	0.0197294i
$293$	8.72543	−	8.72543i	0.509745	−	0.509745i	−0.404703	−	0.914448i	$-0.632625\pi$
$293$	8.72543	−	8.72543i	0.509745	−	0.509745i	0.914448	+	0.404703i	$0.132625\pi$
$294$	7.48407	+	3.08209i	0.436480	+	0.179751i
$295$	−0.920855	−	4.62945i	−0.0536143	−	0.269537i
$296$	−5.47302	+	13.4457i	−0.318113	+	0.781514i
$297$	1.22306	−	2.95272i	0.0709690	−	0.171334i
$298$	1.81489	+	9.02759i	0.105134	+	0.522954i
$299$	−13.5916	+	20.3412i	−0.786021	+	1.17636i
$300$	3.26347	−	16.7645i	0.188417	−	0.967899i
$301$	−3.31576	+	2.21552i	−0.191117	+	0.127701i
$302$	−1.89862	−	0.373625i	−0.109253	−	0.0214997i
$303$	9.81933	+	1.95319i	0.564106	+	0.112208i
$304$	−24.7077	−	9.99836i	−1.41708	−	0.573445i
$305$		−	7.60732i		−	0.435594i
$306$	7.82193	−	5.16816i	0.447150	−	0.295444i
$307$		−	1.15950i		−	0.0661761i	−0.999452	−	0.0330881i	$-0.989466\pi$
$307$		−	1.15950i		−	0.0661761i	0.999452	−	0.0330881i	$-0.0105342\pi$
$308$	−0.0182053	−	4.45270i	−0.00103734	−	0.253716i
$309$	−17.9794	−	3.57633i	−1.02281	−	0.203450i
$310$	1.51563	−	7.70186i	0.0860822	−	0.437436i
$311$	6.43138	−	4.29731i	0.364690	−	0.243678i	−0.359701	−	0.933068i	$-0.617121\pi$
$311$	6.43138	−	4.29731i	0.364690	−	0.243678i	0.724391	+	0.689390i	$0.242121\pi$
$312$	−14.5561	−	34.5409i	−0.824078	−	1.95549i
$313$	−6.48916	+	9.71171i	−0.366789	+	0.548938i	−0.968256	−	0.249959i	$-0.919583\pi$
$313$	−6.48916	+	9.71171i	−0.366789	+	0.548938i	0.601468	+	0.798897i	$0.294583\pi$
$314$	−7.25732	+	1.45900i	−0.409554	+	0.0823361i
$315$	1.29475	−	3.12581i	0.0729511	−	0.176119i
$316$	13.0862	+	19.4127i	0.736159	+	1.09205i
$317$	2.37533	+	11.9416i	0.133412	+	0.670706i	0.988377	+	0.152021i	$0.0485782\pi$
$317$	2.37533	+	11.9416i	0.133412	+	0.670706i	−0.854965	+	0.518685i	$0.826422\pi$
$318$	1.80080	−	4.37279i	0.100984	−	0.245214i
$319$	−2.83408	+	2.83408i	−0.158678	+	0.158678i
$320$	1.67478	+	7.91128i	0.0936231	+	0.442254i
$321$	−2.99642	−	7.23401i	−0.167244	−	0.403763i
$322$	−9.68709	+	6.50139i	−0.539840	+	0.362308i
$323$	25.4582	−	10.3306i	1.41653	−	0.574811i
$324$	8.51651	−	20.8008i	0.473139	−	1.15560i
$325$	22.6905	−	9.39870i	1.25864	−	0.521346i
$326$	−10.8375	+	4.51500i	−0.600232	+	0.250063i
$327$	−11.2925	−	11.2925i	−0.624479	−	0.624479i
$328$	14.5829	+	14.4051i	0.805205	+	0.795389i
$329$	17.3534	−	3.45181i	0.956724	−	0.190304i
$330$	3.28172	−	0.00670878i	0.180653	−	0.000369306i
$331$	1.60439	+	0.664562i	0.0881855	+	0.0365276i	0.426340	−	0.904563i	$-0.359803\pi$
$331$	1.60439	+	0.664562i	0.0881855	+	0.0365276i	−0.338155	+	0.941091i	$0.609803\pi$
$332$	−17.6241	−	17.4805i	−0.967246	−	0.959369i
$333$	6.86138	+	4.58463i	0.376001	+	0.251236i
$334$	20.5560	+	20.4722i	1.12478	+	1.12019i
$335$	−0.346199	−	0.518123i	−0.0189149	−	0.0283081i
$336$	−0.146163	−	17.8742i	−0.00797387	−	0.975119i
$337$	1.90969	−	9.60067i	0.104028	−	0.522982i	−0.893270	−	0.449520i	$-0.851595\pi$
$337$	1.90969	−	9.60067i	0.104028	−	0.522982i	0.997298	−	0.0734621i	$-0.0234048\pi$
$338$	19.6710	−	29.5704i	1.06996	−	1.60842i
$339$	7.27934			0.395360
$340$	−6.91620	−	4.65258i	−0.375084	−	0.252322i
$341$	−5.87242			−0.318010
$342$	−8.39193	+	12.6152i	−0.453784	+	0.682150i
$343$	−3.92578	+	19.7362i	−0.211972	+	1.06566i
$344$	−4.52337	−	2.98245i	−0.243884	−	0.160803i
$345$	−4.77700	−	7.14929i	−0.257185	−	0.384905i
$346$	−8.97787	−	8.94124i	−0.482653	−	0.480684i
$347$	−23.9344	−	15.9925i	−1.28487	−	0.858520i	−0.289737	−	0.957106i	$-0.593568\pi$
$347$	−23.9344	−	15.9925i	−1.28487	−	0.858520i	−0.995129	+	0.0985862i	$0.968568\pi$
$348$	−11.3304	+	11.4234i	−0.607371	+	0.612358i
$349$	1.40518	+	0.582046i	0.0752178	+	0.0311562i	0.419975	−	0.907536i	$-0.362039\pi$
$349$	1.40518	+	0.582046i	0.0752178	+	0.0311562i	−0.344757	+	0.938692i	$0.612039\pi$
$350$	11.7122	−	0.0239431i	0.626043	−	0.00127981i
$351$	18.0949	−	3.59930i	0.965835	−	0.192117i
$352$	5.56529	−	2.37215i	0.296631	−	0.126436i
$353$	16.0913	+	16.0913i	0.856454	+	0.856454i	0.990918	−	0.134464i	$-0.0429313\pi$
$353$	16.0913	+	16.0913i	0.856454	+	0.856454i	−0.134464	+	0.990918i	$0.542931\pi$
$354$	−13.0854	+	5.45153i	−0.695483	+	0.289746i
$355$	−5.60283	+	2.32077i	−0.297367	+	0.123173i
$356$	4.29785	+	1.75968i	0.227786	+	0.0932626i
$357$	12.9341	+	13.1220i	0.684545	+	0.694492i
$358$	−24.8477	+	16.6763i	−1.31324	+	0.881369i
$359$	−11.2986	−	27.2772i	−0.596316	−	1.43963i	−0.877310	−	0.479924i	$-0.840664\pi$
$359$	−11.2986	−	27.2772i	−0.596316	−	1.43963i	0.280994	−	0.959710i	$-0.409336\pi$
$360$	4.59674	−	0.0281915i	0.242269	−	0.00148582i
$361$	−17.9622	+	17.9622i	−0.945380	+	0.945380i
$362$	−12.7147	+	30.8745i	−0.668272	+	1.62273i
$363$	4.12758	+	20.7507i	0.216642	+	1.08913i
$364$	21.3136	−	14.3677i	1.11714	−	0.753072i
$365$	0.0782101	−	0.188816i	0.00409370	−	0.00988308i
$366$	−22.3983	+	4.50291i	−1.17078	+	0.235371i
$367$	5.23108	−	7.82887i	0.273060	−	0.408664i	−0.669441	−	0.742865i	$-0.733467\pi$
$367$	5.23108	−	7.82887i	0.273060	−	0.408664i	0.942502	+	0.334201i	$0.108467\pi$
$368$	−13.2511	−	8.69819i	−0.690759	−	0.453425i
$369$	9.68833	−	6.47354i	0.504354	−	0.336999i
$370$	1.41667	−	7.19896i	0.0736492	−	0.374256i
$371$	3.18069	+	0.632680i	0.165133	+	0.0328471i
$372$	−23.5737	+	0.0963834i	−1.22224	+	0.00499724i
$373$		−	21.7371i		−	1.12550i	−0.826626	−	0.562751i	$-0.809743\pi$
$373$		−	21.7371i		−	1.12550i	0.826626	−	0.562751i	$-0.190257\pi$
$374$	−2.41614	+	5.74886i	−0.124936	+	0.297266i
$375$			19.4812i			1.00600i
$376$	13.4778	+	19.9056i	0.695066	+	1.02656i
$377$	−22.6922	−	4.51376i	−1.16871	−	0.232470i
$378$	8.63263	+	1.69880i	0.444015	+	0.0873768i
$379$	−3.46561	+	2.31565i	−0.178016	+	0.118947i	−0.641386	−	0.767218i	$-0.721640\pi$
$379$	−3.46561	+	2.31565i	−0.178016	+	0.118947i	0.463370	+	0.886165i	$0.346640\pi$
$380$	13.2231	+	2.57408i	0.678331	+	0.132048i
$381$	−4.17834	+	6.25332i	−0.214063	+	0.320367i
$382$	2.76751	+	13.7661i	0.141598	+	0.704333i
$383$	10.4436	−	25.2130i	0.533642	−	1.28833i	−0.395454	−	0.918486i	$-0.629413\pi$
$383$	10.4436	−	25.2130i	0.533642	−	1.28833i	0.929096	−	0.369839i	$-0.120587\pi$
$384$	22.3019	−	9.61389i	1.13809	−	0.490607i
$385$	0.439046	+	2.20723i	0.0223758	+	0.112491i
$386$	23.4713	+	9.66598i	1.19466	+	0.491985i
$387$	−2.17783	+	2.17783i	−0.110705	+	0.110705i
$388$	−8.58100	−	5.68303i	−0.435634	−	0.288512i
$389$	−0.852088	−	2.05712i	−0.0432026	−	0.104300i	0.900805	−	0.434223i	$-0.142977\pi$
$389$	−0.852088	−	2.05712i	−0.0432026	−	0.104300i	−0.944008	+	0.329923i	$0.892977\pi$
$390$	10.5570	+	15.7300i	0.534577	+	0.796521i
$391$	16.0473	−	3.07184i	0.811547	−	0.155350i
$392$	−7.38710	+	1.51654i	−0.373105	+	0.0765968i
$393$	30.4297	−	12.6044i	1.53498	−	0.635808i
$394$	−1.14958	−	2.75937i	−0.0579152	−	0.139015i
$395$	−8.36685	−	8.36685i	−0.420982	−	0.420982i
$396$	−0.684696	−	3.37013i	−0.0344073	−	0.169355i
$397$	−5.08689	+	1.01185i	−0.255304	+	0.0507831i	−0.321083	−	0.947051i	$-0.604047\pi$
$397$	−5.08689	+	1.01185i	−0.255304	+	0.0507831i	0.0657790	+	0.997834i	$0.479047\pi$
$398$	0.00531009	+	2.59753i	0.000266171	+	0.130202i
$399$	−27.5106	−	11.3953i	−1.37725	−	0.570477i
$400$	6.20962	+	14.6513i	0.310481	+	0.732567i
$401$	−11.0979	−	7.41540i	−0.554204	−	0.370307i	0.246708	−	0.969090i	$-0.420651\pi$
$401$	−11.0979	−	7.41540i	−0.554204	−	0.370307i	−0.800912	+	0.598783i	$0.795651\pi$
$402$	−1.32059	+	1.32600i	−0.0658650	+	0.0661349i
$403$	−18.8335	−	28.1864i	−0.938164	−	1.40406i
$404$	−8.60332	+	3.60489i	−0.428031	+	0.179350i
$405$	−2.21624	+	11.1418i	−0.110126	+	0.553639i
$406$	−9.18654	−	6.11112i	−0.455920	−	0.303290i
$407$	−5.48898			−0.272079
$408$	−9.60479	+	23.1173i	−0.475508	+	1.14448i
$409$	−0.0180838			−0.000894186			−0.000447093	−	1.00000i	$-0.500142\pi$
$409$	−0.0180838			−0.000894186			−0.000447093		1.00000i	$0.500142\pi$
$410$	−8.62574	−	5.73806i	−0.425995	−	0.283383i
$411$	0.625873	−	3.14648i	0.0308721	−	0.155204i
$412$	15.7529	−	6.60064i	0.776088	−	0.325190i
$413$	−5.40073	−	8.08276i	−0.265752	−	0.397727i
$414$	−6.35827	+	6.38432i	−0.312492	+	0.313772i
$415$	10.4315	+	6.97009i	0.512061	+	0.342148i
$416$	29.2343	+	19.1044i	1.43333	+	0.936673i
$417$	32.5894	+	13.4990i	1.59591	+	0.661048i
$418$	−0.0206026	−	10.0781i	−0.00100771	−	0.492938i
$419$	−2.09333	+	0.416388i	−0.102266	+	0.0203419i	−0.245958	−	0.969281i	$-0.579102\pi$
$419$	−2.09333	+	0.416388i	−0.102266	+	0.0203419i	0.143692	+	0.989622i	$0.454102\pi$
$420$	1.79869	+	8.85331i	0.0877672	+	0.431997i
$421$	12.0317	+	12.0317i	0.586391	+	0.586391i	0.936652	−	0.350261i	$-0.113907\pi$
$421$	12.0317	+	12.0317i	0.586391	+	0.586391i	−0.350261	+	0.936652i	$0.613907\pi$
$422$	−13.1596	−	31.5873i	−0.640599	−	1.53764i
$423$	12.6249	−	5.22941i	0.613844	−	0.254262i
$424$	0.886083	+	4.31613i	0.0430320	+	0.209610i
$425$	−15.1084	−	6.38617i	−0.732866	−	0.309775i
$426$	10.1494	+	15.1227i	0.491742	+	0.732697i
$427$	−5.99555	−	14.4745i	−0.290145	−	0.700472i
$428$	6.08238	+	4.02824i	0.294003	+	0.194713i
$429$	10.0215	−	10.0215i	0.483844	−	0.483844i
$430$	2.53207	+	1.04276i	0.122107	+	0.0502864i
$431$	7.00428	+	35.2129i	0.337385	+	1.69615i	0.661350	+	0.750078i	$0.269984\pi$
$431$	7.00428	+	35.2129i	0.337385	+	1.69615i	−0.323965	+	0.946069i	$0.605016\pi$
$432$	2.42785	+	11.7046i	0.116810	+	0.563138i
$433$	1.25174	−	3.02196i	0.0601546	−	0.145226i	−0.890944	−	0.454113i	$-0.849956\pi$
$433$	1.25174	−	3.02196i	0.0601546	−	0.145226i	0.951099	+	0.308887i	$0.0999563\pi$
$434$	−3.18624	−	15.8489i	−0.152945	−	0.760773i
$435$	4.51780	−	6.76137i	0.216612	−	0.324183i
$436$	14.6054	+	2.84316i	0.699470	+	0.136163i
$437$	−21.9554	+	14.6702i	−1.05027	+	0.701768i
$438$	−0.602225	−	0.118511i	−0.0287754	−	0.00566266i
$439$	1.05590	+	0.210032i	0.0503954	+	0.0100243i	0.220224	−	0.975449i	$-0.429321\pi$
$439$	1.05590	+	0.210032i	0.0503954	+	0.0100243i	−0.169828	+	0.985474i	$0.554321\pi$
$440$	−2.53186	+	1.71429i	−0.120702	+	0.0817255i
$441$			4.28676i			0.204132i
$442$	−35.3421	+	6.84026i	−1.68105	+	0.325358i
$443$			23.1842i			1.10152i	0.834665	+	0.550758i	$0.185661\pi$
$443$			23.1842i			1.10152i	−0.834665	+	0.550758i	$0.814339\pi$
$444$	−22.0345	+	0.0900900i	−1.04571	+	0.00427548i
$445$	−2.30211	−	0.457917i	−0.109130	−	0.0217074i
$446$	−3.90698	+	19.8537i	−0.185001	+	0.940102i
$447$	−11.6213	+	7.76510i	−0.549668	+	0.367277i
$448$	9.42174	+	13.7329i	0.445135	+	0.648821i
$449$	15.6952	−	23.4895i	0.740701	−	1.10854i	−0.249430	−	0.968393i	$-0.580243\pi$
$449$	15.6952	−	23.4895i	0.740701	−	1.10854i	0.990131	−	0.140145i	$-0.0447568\pi$
$450$	8.86824	−	1.78286i	0.418053	−	0.0840447i
$451$	−2.96599	+	7.16052i	−0.139663	+	0.337176i
$452$	−5.62379	+	3.79105i	−0.264521	+	0.178316i
$453$	−0.573002	−	2.88068i	−0.0269220	−	0.135346i
$454$	−11.1157	+	26.9916i	−0.521686	+	1.26678i
$455$	−9.18617	+	9.18617i	−0.430654	+	0.430654i
$456$	−0.248117	−	40.4564i	−0.0116191	−	1.89455i
$457$	8.21934	+	19.8432i	0.384485	+	0.928228i	0.991086	+	0.133222i	$0.0425323\pi$
$457$	8.21934	+	19.8432i	0.384485	+	0.928228i	−0.606602	+	0.795006i	$0.707468\pi$
$458$	−0.845777	+	0.567635i	−0.0395206	+	0.0265238i
$459$	−10.1954	−	6.91926i	−0.475882	−	0.322963i
$460$	7.41388	+	3.03548i	0.345674	+	0.141530i
$461$	6.76893	−	2.80378i	0.315260	−	0.130585i	−0.219442	−	0.975626i	$-0.570424\pi$
$461$	6.76893	−	2.80378i	0.315260	−	0.130585i	0.534702	+	0.845040i	$0.320424\pi$
$462$	6.23888	−	2.59918i	0.290259	−	0.120925i
$463$	−4.70840	−	4.70840i	−0.218818	−	0.218818i	0.589182	−	0.808000i	$-0.299450\pi$
$463$	−4.70840	−	4.70840i	−0.218818	−	0.218818i	−0.808000	+	0.589182i	$0.799450\pi$
$464$	2.80423	−	14.7262i	0.130183	−	0.683645i
$465$	11.6856	−	2.32442i	0.541908	−	0.107792i
$466$	−25.9355	+	0.0530197i	−1.20144	+	0.00245609i
$467$	25.4117	+	10.5259i	1.17591	+	0.487079i	0.883143	−	0.469104i	$-0.155423\pi$
$467$	25.4117	+	10.5259i	1.17591	+	0.487079i	0.292770	+	0.956183i	$0.405423\pi$
$468$	13.9800	−	14.0948i	0.646225	−	0.651531i
$469$	−1.06706	−	0.712989i	−0.0492724	−	0.0329228i
$470$	−8.60873	−	8.57360i	−0.397091	−	0.395471i
$471$	−6.24239	−	9.34240i	−0.287634	−	0.430475i
$472$	7.27026	−	11.0265i	0.334641	−	0.507537i
$473$	0.399670	−	2.00928i	0.0183769	−	0.0923867i
$474$	−19.6820	+	29.5870i	−0.904026	+	1.35898i
$475$	26.5090			1.21632
$476$	−16.8264	−	3.40167i	−0.771236	−	0.155915i
$477$	2.50467			0.114681
$478$	−8.02904	+	12.0696i	−0.367240	+	0.552053i
$479$	2.10832	−	10.5992i	0.0963315	−	0.484291i	−0.902258	−	0.431197i	$-0.858092\pi$
$479$	2.10832	−	10.5992i	0.0963315	−	0.484291i	0.998589	−	0.0530945i	$-0.0169085\pi$
$480$	−10.1355	+	6.92323i	−0.462622	+	0.316001i
$481$	−17.6038	−	26.3459i	−0.802664	−	1.20127i
$482$	−10.8401	−	10.7959i	−0.493755	−	0.491740i
$483$	−14.7238	−	9.83814i	−0.669957	−	0.447651i
$484$	−13.9957	−	13.8818i	−0.636170	−	0.630989i
$485$	4.80587	+	1.99066i	0.218224	+	0.0903911i
$486$	21.4377	−	0.0438249i	0.972435	−	0.00198794i
$487$	4.15661	−	0.826801i	0.188354	−	0.0374659i	−0.100012	−	0.994986i	$-0.531888\pi$
$487$	4.15661	−	0.826801i	0.188354	−	0.0374659i	0.288366	+	0.957520i	$0.406888\pi$
$488$	14.9591	−	15.1437i	0.677166	−	0.685524i
$489$	−12.6008	−	12.6008i	−0.569829	−	0.569829i
$490$	3.51829	−	1.46576i	0.158940	−	0.0662161i
$491$	2.21627	−	0.918009i	0.100019	−	0.0414292i	−0.332113	−	0.943240i	$-0.607762\pi$
$491$	2.21627	−	0.918009i	0.100019	−	0.0414292i	0.432132	+	0.901810i	$0.357762\pi$
$492$	−11.7889	+	28.7932i	−0.531483	+	1.29810i
$493$	8.49185	+	12.9096i	0.382454	+	0.581418i
$494$	48.3068	−	32.4206i	2.17343	−	1.45867i
$495$	0.665144	+	1.60580i	0.0298960	+	0.0721754i
$496$	18.1621	−	12.3515i	0.815503	−	0.554601i
$497$	−8.83150	+	8.83150i	−0.396147	+	0.396147i
$498$	14.3475	−	34.8391i	0.642925	−	1.56118i
$499$	−0.0192904	−	0.0969795i	−0.000863558	−	0.00434140i	0.980351	−	0.197261i	$-0.0632045\pi$
$499$	−0.0192904	−	0.0969795i	−0.000863558	−	0.00434140i	−0.981215	+	0.192919i	$0.938204\pi$
$500$	−10.1457	−	15.0505i	−0.453730	−	0.673081i
$501$	−16.8516	+	40.6833i	−0.752873	+	1.81760i
$502$	5.42103	−	1.08984i	0.241952	−	0.0486417i
$503$	−13.2387	+	19.8132i	−0.590286	+	0.883425i	−0.999580	−	0.0289774i	$-0.990775\pi$
$503$	−13.2387	+	19.8132i	−0.590286	+	0.883425i	0.409294	+	0.912402i	$0.365775\pi$
$504$	8.72405	−	3.67646i	0.388600	−	0.163763i
$505$	3.91998	−	2.61925i	0.174437	−	0.116555i
$506$	1.15723	−	5.88058i	0.0514451	−	0.261424i
$507$	52.8720	+	10.5169i	2.34813	+	0.467072i
$508$	−0.0286495	−	7.00718i	−0.00127112	−	0.310893i
$509$		−	4.80674i		−	0.213055i	−0.994310	−	0.106527i	$-0.966027\pi$
$509$		−	4.80674i		−	0.213055i	0.994310	−	0.106527i	$-0.0339732\pi$
$510$	2.53242	−	12.3961i	0.112137	−	0.548908i
$511$		−	0.420902i		−	0.0186196i
$512$	−12.2229	+	19.0421i	−0.540179	+	0.841550i
$513$	19.5309	+	3.88493i	0.862309	+	0.171524i
$514$	19.8931	+	3.91472i	0.877446	+	0.172671i
$515$	−7.17756	+	4.79590i	−0.316281	+	0.211332i
$516$	1.57142	−	8.07242i	0.0691779	−	0.355368i
$517$	−5.04985	+	7.55764i	−0.222092	+	0.332384i
$518$	−2.97820	−	14.8141i	−0.130854	−	0.650893i
$519$	7.35995	−	17.7685i	0.323066	−	0.779950i
$520$	−16.3482	−	6.65447i	−0.716915	−	0.291818i
$521$	−6.23757	−	31.3584i	−0.273273	−	1.37384i	−0.836696	−	0.547667i	$-0.815516\pi$
$521$	−6.23757	−	31.3584i	−0.273273	−	1.37384i	0.563423	−	0.826168i	$-0.309484\pi$
$522$	−7.87948	−	3.24493i	−0.344876	−	0.142027i
$523$	4.39174	−	4.39174i	0.192037	−	0.192037i	−0.604538	−	0.796576i	$-0.706642\pi$
$523$	4.39174	−	4.39174i	0.192037	−	0.192037i	0.796576	+	0.604538i	$0.206642\pi$
$524$	−16.9447	+	25.5854i	−0.740234	+	1.11770i
$525$	6.80317	+	16.4243i	0.296915	+	0.716815i
$526$	−14.1979	−	21.1550i	−0.619059	−	0.922400i
$527$	−4.57692	+	22.1727i	−0.199374	+	0.965856i
$528$	6.54603	+	6.43984i	0.284880	+	0.280258i
$529$	6.74148	−	2.79241i	0.293108	−	0.121409i
$530$	−0.856411	−	2.05566i	−0.0372001	−	0.0892923i
$531$	−5.30885	−	5.30885i	−0.230384	−	0.230384i
$532$	27.1885	−	5.52378i	1.17877	−	0.239486i
$533$	−43.8812	+	8.72852i	−1.90071	+	0.378074i
$534$	0.0144105	+	7.04914i	0.000623603	+	0.305046i
$535$	−3.40650	−	1.41102i	−0.147276	−	0.0610036i
$536$	0.329671	−	1.71218i	0.0142396	−	0.0739550i
$537$	−37.7671	−	25.2352i	−1.62977	−	1.08898i
$538$	32.5401	−	32.6734i	1.40290	−	1.40865i
$539$	−1.58415	−	2.37084i	−0.0682340	−	0.102119i
$540$	−2.33482	−	5.57220i	−0.100474	−	0.239789i
$541$	−3.65194	+	18.3596i	−0.157009	+	0.789339i	0.819368	+	0.573268i	$0.194324\pi$
$541$	−3.65194	+	18.3596i	−0.157009	+	0.789339i	−0.976378	+	0.216072i	$0.930676\pi$
$542$	−5.37421	−	3.57506i	−0.230842	−	0.153562i
$543$	−50.6816			−2.17495
$544$	−4.61904	−	22.8619i	−0.198040	−	0.980194i
$545$	−7.52031			−0.322135
$546$	32.4843	+	21.6094i	1.39020	+	0.924797i
$547$	3.86493	−	19.4303i	0.165253	−	0.830781i	−0.805850	−	0.592119i	$-0.798291\pi$
$547$	3.86493	−	19.4303i	0.165253	−	0.830781i	0.971103	−	0.238661i	$-0.0767086\pi$
$548$	1.15514	+	2.75682i	0.0493452	+	0.117766i
$549$	−6.72249	−	10.0609i	−0.286909	−	0.429390i
$550$	−4.24584	+	4.26323i	−0.181043	+	0.181785i
$551$	−20.7641	−	13.8742i	−0.884582	−	0.591059i
$552$	4.54895	−	23.6255i	0.193616	−	1.00557i
$553$	−22.5139	−	9.32555i	−0.957387	−	0.396563i
$554$	0.0385855	+	18.8748i	0.00163934	+	0.801912i
$555$	10.9226	−	2.17264i	0.463639	−	0.0922236i
$556$	−32.2078	+	6.54353i	−1.36591	+	0.277507i
$557$	2.93149	+	2.93149i	0.124211	+	0.124211i	0.766480	−	0.642269i	$-0.222007\pi$
$557$	2.93149	+	2.93149i	0.124211	+	0.124211i	−0.642269	+	0.766480i	$0.722007\pi$
$558$	−4.80156	−	11.5253i	−0.203266	−	0.487905i
$559$	10.9259	−	4.52565i	0.462116	−	0.191415i
$560$	−6.00037	−	5.90304i	−0.253562	−	0.249449i
$561$	−9.46507	−	0.0682761i	−0.399616	−	0.00288262i
$562$	−2.80925	−	4.18579i	−0.118501	−	0.176567i
$563$	10.2091	+	24.6470i	0.430264	+	1.03875i	0.979202	+	0.202886i	$0.0650322\pi$
$563$	10.2091	+	24.6470i	0.430264	+	1.03875i	−0.548938	+	0.835863i	$0.684968\pi$
$564$	−20.1476	+	30.4216i	−0.848368	+	1.28098i
$565$	2.42385	−	2.42385i	0.101972	−	0.101972i
$566$	43.3592	+	17.8562i	1.82252	+	0.750553i
$567$	4.56429	+	22.9463i	0.191682	+	0.963652i
$568$	−15.7170	−	6.39754i	−0.659470	−	0.268435i
$569$	12.5588	−	30.3197i	0.526494	−	1.27107i	−0.407312	−	0.913289i	$-0.633534\pi$
$569$	12.5588	−	30.3197i	0.526494	−	1.27107i	0.933806	−	0.357780i	$-0.116466\pi$
$570$	4.03012	+	20.0465i	0.168803	+	0.839656i
$571$	−5.97411	+	8.94088i	−0.250009	+	0.374164i	−0.935154	−	0.354242i	$-0.884739\pi$
$571$	−5.97411	+	8.94088i	−0.250009	+	0.374164i	0.685145	+	0.728407i	$0.259739\pi$
$572$	−2.52315	+	12.9615i	−0.105498	+	0.541947i
$573$	−17.7212	+	11.8409i	−0.740312	+	0.494661i
$574$	−20.9346	−	4.11968i	−0.873794	−	0.171952i
$575$	15.4617	+	3.07552i	0.644796	+	0.128258i
$576$	9.20605	+	8.98294i	0.383586	+	0.374289i
$577$			40.4944i			1.68581i	0.538066	+	0.842903i	$0.319155\pi$
$577$			40.4944i			1.68581i	−0.538066	+	0.842903i	$0.680845\pi$
$578$	19.8230	+	13.6033i	0.824527	+	0.565823i
$579$			38.5291i			1.60121i
$580$	0.0309771	+	7.57648i	0.00128626	+	0.314596i
$581$	25.3414	+	5.04072i	1.05134	+	0.209124i
$582$	3.01642	−	15.3282i	0.125034	−	0.635376i
$583$	−1.38523	+	0.925584i	−0.0573706	+	0.0383338i
$584$	0.526980	−	0.222078i	0.0218066	−	0.00918967i
$585$	−5.57430	+	8.34253i	−0.230469	+	0.344921i
$586$	−17.1085	+	3.43947i	−0.706747	+	0.142083i
$587$	3.22904	−	7.79559i	0.133277	−	0.321758i	−0.843126	−	0.537716i	$-0.819287\pi$
$587$	3.22904	−	7.79559i	0.133277	−	0.321758i	0.976403	+	0.215958i	$0.0692873\pi$
$588$	−6.39817	−	9.49130i	−0.263856	−	0.391414i
$589$	−7.13827	−	35.8865i	−0.294127	−	1.47868i
$590$	−2.54191	+	6.17238i	−0.104649	+	0.254113i
$591$	3.20834	−	3.20834i	0.131974	−	0.131974i
$592$	16.9762	−	11.5451i	0.697718	−	0.474499i
$593$	13.8864	+	33.5247i	0.570245	+	1.37669i	0.901347	+	0.433099i	$0.142580\pi$
$593$	13.8864	+	33.5247i	0.570245	+	1.37669i	−0.331101	+	0.943595i	$0.607420\pi$
$594$	−3.75296	+	2.51876i	−0.153986	+	0.103346i
$595$	8.67609	+	0.0625848i	0.355685	+	0.00256573i
$596$	4.93422	−	12.0514i	0.202113	−	0.493644i
$597$	−3.64258	+	1.50880i	−0.149081	+	0.0617513i
$598$	31.9369	−	13.3052i	1.30600	−	0.544092i
$599$	18.2511	+	18.2511i	0.745722	+	0.745722i	0.973673	−	0.227951i	$-0.0732026\pi$
$599$	18.2511	+	18.2511i	0.745722	+	0.745722i	−0.227951	+	0.973673i	$0.573203\pi$
$600$	−16.9741	+	17.1836i	−0.692966	+	0.701518i
$601$	29.1388	−	5.79607i	1.18860	−	0.236426i	0.439102	−	0.898437i	$-0.355297\pi$
$601$	29.1388	−	5.79607i	1.18860	−	0.236426i	0.749494	+	0.662011i	$0.230297\pi$
$602$	5.63964	−	0.0115290i	0.229854	−	0.000469889i
$603$	−0.915718	−	0.379303i	−0.0372909	−	0.0154464i
$604$	1.94293	+	1.92710i	0.0790566	+	0.0784127i
$605$	8.28391	+	5.53513i	0.336789	+	0.225035i
$606$	−10.0322	−	9.99122i	−0.407528	−	0.405865i
$607$	2.39265	+	3.58085i	0.0971145	+	0.145342i	0.876845	−	0.480773i	$-0.159644\pi$
$607$	2.39265	+	3.58085i	0.0971145	+	0.145342i	−0.779730	+	0.626115i	$0.784644\pi$
$608$	21.2612	+	31.1262i	0.862256	+	1.26233i
$609$	3.26725	−	16.4256i	0.132395	−	0.665597i
$610$	−5.95874	+	8.95746i	−0.241262	+	0.362677i
$611$	−52.4705			−2.12273
$612$	−13.2583	−	0.0414296i	−0.535936	−	0.00167469i
$613$	48.3994			1.95483			0.977417	−	0.211319i	$-0.0677760\pi$
$613$	48.3994			1.95483			0.977417	+	0.211319i	$0.0677760\pi$
$614$	−0.908224	+	1.36529i	−0.0366529	+	0.0550985i
$615$	3.06779	−	15.4228i	0.123705	−	0.621909i
$616$	−3.46632	+	5.25723i	−0.139662	+	0.211820i
$617$	18.1998	+	27.2379i	0.732697	+	1.09656i	0.991434	+	0.130611i	$0.0416938\pi$
$617$	18.1998	+	27.2379i	0.732697	+	1.09656i	−0.258737	+	0.965948i	$0.583306\pi$
$618$	18.3691	+	18.2941i	0.738913	+	0.735898i
$619$	7.40715	+	4.94930i	0.297718	+	0.198929i	0.695453	−	0.718571i	$-0.255204\pi$
$619$	7.40715	+	4.94930i	0.297718	+	0.198929i	−0.397735	+	0.917500i	$0.630204\pi$
$620$	−7.81741	+	7.88160i	−0.313955	+	0.316533i
$621$	10.9409	+	4.53186i	0.439042	+	0.181857i
$622$	−10.9389	+	0.0223622i	−0.438608	+	0.000896641i
$623$	−4.74114	+	0.943072i	−0.189950	+	0.0377834i
$624$	−9.91599	+	52.0728i	−0.396957	+	2.08458i
$625$	−7.57839	−	7.57839i	−0.303136	−	0.303136i
$626$	15.2479	−	6.35245i	0.609430	−	0.253895i
$627$	14.1328	−	5.85401i	0.564411	−	0.233787i
$628$	9.68816	+	3.96664i	0.386600	+	0.158286i
$629$	−4.27807	+	20.7249i	−0.170578	+	0.826355i
$630$	−3.97296	+	2.66641i	−0.158286	+	0.106232i
$631$	−12.8274	−	30.9682i	−0.510652	−	1.23282i	−0.943505	−	0.331359i	$-0.892493\pi$
$631$	−12.8274	−	30.9682i	−0.510652	−	1.23282i	0.432853	−	0.901465i	$-0.357507\pi$
$632$	−0.203051	−	33.1083i	−0.00807694	−	1.31698i
$633$	36.7268	−	36.7268i	1.45976	−	1.45976i
$634$	6.55682	−	15.9215i	0.260404	−	0.632325i
$635$	0.690922	+	3.47350i	0.0274184	+	0.137842i
$636$	−5.54557	+	3.73832i	−0.219896	+	0.148234i
$637$	6.29900	−	15.2071i	0.249575	−	0.602528i
$638$	5.55698	−	1.11717i	0.220003	−	0.0442290i
$639$	−5.35908	+	8.02043i	−0.212002	+	0.317283i
$640$	4.22481	−	10.6272i	0.167000	−	0.420077i
$641$	30.1359	−	20.1362i	1.19030	−	0.795331i	0.207179	−	0.978303i	$-0.433572\pi$
$641$	30.1359	−	20.1362i	1.19030	−	0.795331i	0.983118	+	0.182972i	$0.0585716\pi$
$642$	−2.13809	+	10.8650i	−0.0843839	+	0.428806i
$643$	11.5439	+	2.29622i	0.455246	+	0.0905540i	0.417387	−	0.908729i	$-0.362946\pi$
$643$	11.5439	+	2.29622i	0.455246	+	0.0905540i	0.0378593	+	0.999283i	$0.487946\pi$
$644$	16.4988	−	0.0674570i	0.650145	−	0.00265818i
$645$			4.15649i			0.163662i
$646$	−38.0684	−	7.77704i	−1.49778	−	0.305984i
$647$			24.9566i			0.981146i	0.871400	+	0.490573i	$0.163213\pi$
$647$			24.9566i			0.981146i	−0.871400	+	0.490573i	$0.836787\pi$
$648$	−26.3211	+	17.8216i	−1.03399	+	0.700100i
$649$	4.89797	+	0.974267i	0.192262	+	0.0382433i
$650$	−34.0795	−	6.70643i	−1.33671	−	0.263048i
$651$	20.4025	−	13.6325i	0.799635	−	0.534299i
$652$	16.2974	+	3.17255i	0.638257	+	0.124247i
$653$	−8.79462	+	13.1621i	−0.344160	+	0.515072i	−0.962660	−	0.270713i	$-0.912741\pi$
$653$	−8.79462	+	13.1621i	−0.344160	+	0.515072i	0.618500	+	0.785785i	$0.287741\pi$
$654$	4.45140	+	22.1421i	0.174064	+	0.865823i
$655$	5.93542	−	14.3294i	0.231916	−	0.559894i
$656$	−5.88768	−	28.3843i	−0.229875	−	1.10822i
$657$	−0.0634189	−	0.318828i	−0.00247421	−	0.0124387i
$658$	−23.1370	−	9.52831i	−0.901975	−	0.371452i
$659$	−14.1892	+	14.1892i	−0.552732	+	0.552732i	−0.927228	−	0.374496i	$-0.877816\pi$
$659$	−14.1892	+	14.1892i	−0.552732	+	0.552732i	0.374496	+	0.927228i	$0.377816\pi$
$660$	−3.86941	−	2.56264i	−0.150617	−	0.0997505i
$661$	−8.09850	−	19.5515i	−0.314995	−	0.760466i	−0.999505	−	0.0314620i	$-0.989984\pi$
$661$	−8.09850	−	19.5515i	−0.314995	−	0.760466i	0.684510	−	0.729004i	$-0.260016\pi$
$662$	−1.36860	−	2.03921i	−0.0531920	−	0.0792562i
$663$	−30.0278	−	45.6493i	−1.16618	−	1.77287i
$664$	7.05965	+	34.3877i	0.273968	+	1.33450i
$665$	−12.9548	+	5.36604i	−0.502364	+	0.208086i
$666$	−4.48804	−	10.7727i	−0.173908	−	0.417436i
$667$	−10.5013	−	10.5013i	−0.406611	−	0.406611i
$668$	−8.16868	−	40.2069i	−0.316056	−	1.55565i
$669$	−30.1231	+	5.99185i	−1.16463	+	0.231658i
$670$	0.00180154	+	0.881253i	6.95994e−5	+	0.0340458i
$671$	7.43590	+	3.08005i	0.287060	+	0.118904i
$672$	−13.8286	+	21.1610i	−0.533449	+	0.816304i
$673$	−30.4683	−	20.3583i	−1.17447	−	0.784753i	−0.193916	−	0.981018i	$-0.562119\pi$
$673$	−30.4683	−	20.3583i	−1.17447	−	0.784753i	−0.980551	+	0.196265i	$0.937119\pi$
$674$	−9.76872	+	9.80875i	−0.376277	+	0.377819i
$675$	−6.60500	−	9.88509i	−0.254227	−	0.380477i
$676$	−46.3244	+	19.4105i	−1.78171	+	0.746557i
$677$	−1.76369	+	8.86666i	−0.0677840	+	0.340773i	−0.999764	−	0.0217372i	$-0.993080\pi$
$677$	−1.76369	+	8.86666i	−0.0677840	+	0.340773i	0.931980	+	0.362510i	$0.118080\pi$
$678$	−8.57128	−	5.70183i	−0.329178	−	0.218978i
$679$	10.7131			0.411131
$680$	4.49936	+	10.8957i	0.172543	+	0.417831i
$681$	−44.3078			−1.69788
$682$	6.91466	+	4.59981i	0.264776	+	0.176136i
$683$	−0.887895	+	4.46375i	−0.0339744	+	0.170801i	−0.994047	−	0.108949i	$-0.965251\pi$
$683$	−0.887895	+	4.46375i	−0.0339744	+	0.170801i	0.960073	+	0.279750i	$0.0902515\pi$
$684$	19.7627	−	8.28078i	0.755644	−	0.316624i
$685$	−0.839303	−	1.25611i	−0.0320681	−	0.0479933i
$686$	20.0817	−	20.1640i	0.766723	−	0.769864i
$687$	−1.28553	−	0.858965i	−0.0490461	−	0.0327716i
$688$	2.99005	+	7.05489i	0.113994	+	0.268965i
$689$	−8.88521	−	3.68037i	−0.338499	−	0.140211i
$690$	0.0248584	+	12.1599i	0.000946342	+	0.462920i
$691$	10.1731	−	2.02356i	0.387003	−	0.0769797i	0.00224577	−	0.999997i	$-0.499285\pi$
$691$	10.1731	−	2.02356i	0.387003	−	0.0769797i	0.384757	+	0.923018i	$0.374285\pi$
$692$	3.56768	+	17.5604i	0.135623	+	0.667546i
$693$	2.53116	+	2.53116i	0.0961506	+	0.0961506i
$694$	15.6555	+	37.5784i	0.594276	+	1.42645i
$695$	15.3464	−	6.35667i	0.582121	−	0.241122i
$696$	22.2891	−	4.57586i	0.844866	−	0.173447i
$697$	24.7245	+	16.7796i	0.936507	+	0.635573i
$698$	−1.19866	−	1.78601i	−0.0453701	−	0.0676016i
$699$	−15.0650	−	36.3700i	−0.569809	−	1.37564i
$700$	−13.8096	−	9.14584i	−0.521955	−	0.345680i
$701$	−5.29204	+	5.29204i	−0.199878	+	0.199878i	−0.799948	−	0.600070i	$-0.795139\pi$
$701$	−5.29204	+	5.29204i	−0.199878	+	0.199878i	0.600070	+	0.799948i	$0.295139\pi$
$702$	−24.1257	−	9.93545i	−0.910565	−	0.374990i
$703$	−6.67218	−	33.5433i	−0.251646	−	1.26511i
$704$	−8.41110	−	1.56608i	−0.317005	−	0.0590238i
$705$	7.05733	−	17.0379i	0.265794	−	0.641684i
$706$	−6.34303	−	31.5514i	−0.238723	−	1.18745i
$707$	5.39428	−	8.07312i	0.202873	−	0.303621i
$708$	19.6780	+	3.83062i	0.739543	+	0.143963i
$709$	18.3393	−	12.2539i	0.688746	−	0.460205i	−0.161306	−	0.986904i	$-0.551571\pi$
$709$	18.3393	−	12.2539i	0.688746	−	0.460205i	0.850052	+	0.526699i	$0.176571\pi$
$710$	8.41504	+	1.65598i	0.315811	+	0.0621478i
$711$	−18.4591	−	3.67174i	−0.692270	−	0.137701i
$712$	−3.68229	−	5.43844i	−0.138000	−	0.203814i
$713$		−	21.7594i		−	0.814895i
$714$	−4.95126	−	25.5821i	−0.185296	−	0.957385i
$715$		−	6.67388i		−	0.249589i
$716$	42.3200	−	0.173029i	1.58157	−	0.00646641i
$717$	−21.5806	−	4.29264i	−0.805941	−	0.160312i
$718$	−8.06208	+	40.9684i	−0.300874	+	1.52893i
$719$	−1.76591	+	1.17995i	−0.0658575	+	0.0440046i	−0.588063	−	0.808815i	$-0.700109\pi$
$719$	−1.76591	+	1.17995i	−0.0658575	+	0.0440046i	0.522206	+	0.852820i	$0.325109\pi$
$720$	−5.43465	−	3.56738i	−0.202537	−	0.132948i
$721$	−9.87705	+	14.7821i	−0.367841	+	0.550512i
$722$	35.2198	−	7.08053i	1.31074	−	0.263510i
$723$	8.88661	−	21.4542i	0.330497	−	0.797889i
$724$	39.1550	−	26.3947i	1.45518	−	0.980953i
$725$	2.90864	+	14.6227i	0.108024	+	0.543074i
$726$	11.3937	−	27.6667i	0.422860	−	1.02681i
$727$	34.6182	−	34.6182i	1.28392	−	1.28392i	0.345497	−	0.938420i	$-0.387710\pi$
$727$	34.6182	−	34.6182i	1.28392	−	1.28392i	0.938420	−	0.345497i	$-0.112290\pi$
$728$	−36.3504	+	0.222935i	−1.34724	+	0.00826251i
$729$	−0.449861	−	1.08606i	−0.0166615	−	0.0402245i
$730$	−0.239988	+	0.161066i	−0.00888237	+	0.00596131i
$731$	−7.27498	−	3.07506i	−0.269075	−	0.113735i
$732$	29.9006	+	12.2422i	1.10516	+	0.452486i
$733$	−13.6215	+	5.64222i	−0.503122	+	0.208400i	−0.619785	−	0.784771i	$-0.712780\pi$
$733$	−13.6215	+	5.64222i	−0.503122	+	0.208400i	0.116663	+	0.993172i	$0.462780\pi$
$734$	−12.2918	+	5.12088i	−0.453697	+	0.189015i
$735$	4.09075	+	4.09075i	0.150889	+	0.150889i
$736$	8.78965	+	20.6214i	0.323991	+	0.760113i
$737$	0.646617	−	0.128620i	0.0238184	−	0.00473778i
$738$	−16.4785	+	0.0336867i	−0.606581	+	0.00124003i
$739$	−39.7609	−	16.4695i	−1.46263	−	0.605840i	−0.497463	−	0.867485i	$-0.665735\pi$
$739$	−39.7609	−	16.4695i	−1.46263	−	0.605840i	−0.965164	+	0.261646i	$0.915735\pi$
$740$	−7.30697	+	7.36697i	−0.268610	+	0.270815i
$741$	73.4236	+	49.0601i	2.69728	+	1.80227i
$742$	−3.24963	−	3.23637i	−0.119298	−	0.118811i
$743$	23.1475	+	34.6428i	0.849201	+	1.27092i	0.960821	+	0.277168i	$0.0893960\pi$
$743$	23.1475	+	34.6428i	0.849201	+	1.27092i	−0.111620	+	0.993751i	$0.535604\pi$
$744$	27.8331	+	18.3516i	1.02041	+	0.672801i
$745$	−1.28402	+	6.45522i	−0.0470430	+	0.236501i
$746$	−17.0264	+	25.5949i	−0.623381	+	0.937097i
$747$	19.9553			0.730127
$748$	7.34798	−	4.87662i	0.268669	−	0.178307i
$749$	−7.59364			−0.277466
$750$	15.2594	−	22.9387i	0.557194	−	0.837602i
$751$	−6.13003	+	30.8178i	−0.223688	+	1.12456i	0.691762	+	0.722125i	$0.256835\pi$
$751$	−6.13003	+	30.8178i	−0.223688	+	1.12456i	−0.915450	+	0.402431i	$0.868165\pi$
$752$	−0.277993	−	33.9955i	−0.0101373	−	1.23969i
$753$	4.66291	+	6.97854i	0.169926	+	0.254312i
$754$	23.1840	+	23.0894i	0.844312	+	0.840867i
$755$	−1.15000	−	0.768402i	−0.0418526	−	0.0279650i
$756$	−8.83409	−	8.76215i	−0.321293	−	0.318676i
$757$	−6.84851	−	2.83675i	−0.248913	−	0.103103i	0.254739	−	0.967010i	$-0.418011\pi$
$757$	−6.84851	−	2.83675i	−0.248913	−	0.103103i	−0.503652	+	0.863907i	$0.668011\pi$
$758$	5.89450	−	0.0120501i	0.214098	−	0.000437678i
$759$	8.92230	−	1.77476i	0.323859	−	0.0644196i
$760$	−13.5537	−	13.3884i	−0.491644	−	0.485650i
$761$	−20.6136	−	20.6136i	−0.747242	−	0.747242i	0.226718	−	0.973960i	$-0.427200\pi$
$761$	−20.6136	−	20.6136i	−0.747242	−	0.747242i	−0.973960	+	0.226718i	$0.927200\pi$
$762$	9.81807	−	4.09031i	0.355671	−	0.148176i
$763$	−14.3090	+	5.92697i	−0.518020	+	0.214571i
$764$	7.52413	−	18.3770i	0.272213	−	0.664857i
$765$	6.58147	−	1.25985i	0.237953	−	0.0455501i
$766$	−32.0462	+	21.5075i	−1.15788	+	0.777096i
$767$	11.0321	+	26.6338i	0.398345	+	0.961690i
$768$	−33.7905	−	6.14867i	−1.21931	−	0.221871i
$769$	2.07701	−	2.07701i	0.0748989	−	0.0748989i	−0.668665	−	0.743564i	$-0.733134\pi$
$769$	2.07701	−	2.07701i	0.0748989	−	0.0748989i	0.743564	+	0.668665i	$0.233134\pi$
$770$	1.21193	−	2.94287i	0.0436751	−	0.106054i
$771$	6.00372	+	30.1827i	0.216219	+	1.08700i
$772$	−20.0658	−	29.7663i	−0.722182	−	1.07131i
$773$	−12.4018	+	29.9406i	−0.446061	+	1.07689i	0.527724	+	0.849416i	$0.323046\pi$
$773$	−12.4018	+	29.9406i	−0.446061	+	1.07689i	−0.973785	+	0.227471i	$0.926954\pi$
$774$	4.27022	−	0.858479i	0.153490	−	0.0308574i
$775$	−12.1362	+	18.1631i	−0.435945	+	0.652438i
$776$	5.65249	+	13.4131i	0.202913	+	0.481501i
$777$	19.0703	−	12.7423i	0.684142	−	0.457129i
$778$	−0.608007	+	3.08965i	−0.0217981	+	0.110769i
$779$	−47.3635	−	9.42118i	−1.69697	−	0.337549i
$780$	−0.109538	−	26.7910i	−0.00392207	−	0.959272i
$781$		−	6.41621i		−	0.229590i
$782$	−21.3015	−	8.95265i	−0.761740	−	0.320146i
$783$			11.1998i			0.400247i
$784$	9.88605	+	4.00054i	0.353073	+	0.142877i
$785$	−5.18938	−	1.03223i	−0.185217	−	0.0368419i
$786$	−45.7032	−	8.99385i	−1.63018	−	0.320800i
$787$	−30.4237	+	20.3285i	−1.08449	+	0.724632i	−0.963416	−	0.268012i	$-0.913633\pi$
$787$	−30.4237	+	20.3285i	−1.08449	+	0.724632i	−0.121073	+	0.992644i	$0.538633\pi$
$788$	−0.807776	+	4.14956i	−0.0287758	+	0.147822i
$789$	21.4848	−	32.1543i	0.764880	−	1.14472i
$790$	3.29813	+	16.4055i	0.117342	+	0.583680i
$791$	2.70158	−	6.52220i	0.0960573	−	0.231903i
$792$	−1.83357	+	4.50457i	−0.0651531	+	0.160063i
$793$	9.06420	+	45.5688i	0.321879	+	1.61820i
$794$	6.78228	+	2.79308i	0.240694	+	0.0991227i
$795$	2.39014	−	2.39014i	0.0847695	−	0.0847695i
$796$	2.02836	−	3.06269i	0.0718934	−	0.108554i
$797$	−16.8463	−	40.6706i	−0.596727	−	1.44063i	−0.876898	−	0.480677i	$-0.840391\pi$
$797$	−16.8463	−	40.6706i	−0.596727	−	1.44063i	0.280171	−	0.959950i	$-0.409609\pi$
$798$	23.4674	+	34.9665i	0.830737	+	1.23780i
$799$	24.5997	+	24.9572i	0.870276	+	0.882923i
$800$	4.16453	−	22.1156i	0.147238	−	0.781904i
$801$	−3.44926	+	1.42873i	−0.121874	+	0.0504818i
$802$	7.25918	+	17.4244i	0.256330	+	0.615276i
$803$	0.152896	+	0.152896i	0.00539557	+	0.00539557i
$804$	2.59361	−	0.526934i	0.0914695	−	0.0185835i
$805$	−8.17857	+	1.62682i	−0.288257	+	0.0573378i
$806$	0.0980051	+	47.9410i	0.00345208	+	1.68865i
$807$	64.6653	+	26.7852i	2.27633	+	0.942885i
$808$	12.9539	+	2.49420i	0.455717	+	0.0877458i
$809$	−15.3649	−	10.2665i	−0.540202	−	0.360952i	0.255338	−	0.966852i	$-0.417813\pi$
$809$	−15.3649	−	10.2665i	−0.540202	−	0.360952i	−0.795541	+	0.605900i	$0.792813\pi$
$810$	11.3368	−	11.3832i	0.398335	−	0.399967i
$811$	12.0401	+	18.0192i	0.422784	+	0.632740i	0.980321	−	0.197412i	$-0.0632536\pi$
$811$	12.0401	+	18.0192i	0.422784	+	0.632740i	−0.557537	+	0.830152i	$0.688254\pi$
$812$	6.03018	+	14.3914i	0.211618	+	0.505040i
$813$	1.91137	−	9.60910i	0.0670347	−	0.337006i
$814$	6.46316	+	4.29946i	0.226534	+	0.150696i
$815$	−8.39156			−0.293944
$816$	29.4170	−	19.6968i	1.02980	−	0.689528i
$817$	12.7646			0.446576
$818$	0.0212933	+	0.0141648i	0.000744502	+	0.000495262i
$819$	−4.03130	+	20.2667i	−0.140865	+	0.708176i
$820$	5.66206	+	13.5129i	0.197728	+	0.471891i
$821$	−5.71100	−	8.54712i	−0.199315	−	0.298297i	0.718326	−	0.695707i	$-0.244909\pi$
$821$	−5.71100	−	8.54712i	−0.199315	−	0.298297i	−0.917641	+	0.397411i	$0.869909\pi$
$822$	−3.20156	+	3.21467i	−0.111667	+	0.112125i
$823$	6.33161	+	4.23065i	0.220706	+	0.147471i	0.661008	−	0.750378i	$-0.270129\pi$
$823$	6.33161	+	4.23065i	0.220706	+	0.147471i	−0.440302	+	0.897850i	$0.645129\pi$
$824$	−23.7189	−	4.56694i	−0.826287	−	0.159097i
$825$	−8.43754	−	3.49494i	−0.293758	−	0.121678i
$826$	0.0281041	+	13.7476i	0.000977866	+	0.478341i
$827$	15.4121	−	3.06566i	0.535932	−	0.106603i	0.0802981	−	0.996771i	$-0.474413\pi$
$827$	15.4121	−	3.06566i	0.535932	−	0.106603i	0.455634	+	0.890167i	$0.349413\pi$
$828$	12.4875	−	2.53704i	0.433971	−	0.0881682i
$829$	−10.2185	−	10.2185i	−0.354903	−	0.354903i	0.507027	−	0.861930i	$-0.330744\pi$
$829$	−10.2185	−	10.2185i	−0.354903	−	0.354903i	−0.861930	+	0.507027i	$0.830744\pi$
$830$	−6.82325	−	16.3780i	−0.236838	−	0.568488i
$831$	−26.4686	+	10.9636i	−0.918184	+	0.380324i
$832$	−19.4585	−	45.3940i	−0.674603	−	1.57376i
$833$	−10.1863	+	4.13348i	−0.352935	+	0.143217i
$834$	−27.7998	−	41.4217i	−0.962627	−	1.43432i
$835$	7.93541	+	19.1578i	0.274616	+	0.662982i
$836$	−7.86985	+	11.8829i	−0.272184	+	0.410980i
$837$	−11.6033	+	11.6033i	−0.401070	+	0.401070i
$838$	2.79100	+	1.14939i	0.0964135	+	0.0397051i
$839$	−4.47721	−	22.5084i	−0.154570	−	0.777077i	−0.977828	−	0.209410i	$-0.932846\pi$
$839$	−4.47721	−	22.5084i	−0.154570	−	0.777077i	0.823258	−	0.567668i	$-0.192154\pi$
$840$	4.81678	−	11.8335i	0.166195	−	0.408294i
$841$	−5.72295	+	13.8164i	−0.197343	+	0.476428i
$842$	−4.74279	−	23.5915i	−0.163447	−	0.813015i
$843$	4.25106	−	6.36216i	0.146414	−	0.219125i
$844$	−9.24682	+	47.5011i	−0.318289	+	1.63506i
$845$	21.1070	−	14.1033i	0.726104	−	0.485167i
$846$	−18.9617	−	3.73144i	−0.651917	−	0.128289i
$847$	20.1243	+	4.00297i	0.691479	+	0.137544i
$848$	2.33743	−	5.77621i	0.0802678	−	0.198356i
$849$			71.1757i			2.44274i
$850$	12.7876	+	19.3538i	0.438612	+	0.663831i
$851$		−	20.3386i		−	0.697198i
$852$	−0.105308	−	25.7566i	−0.00360781	−	0.882408i
$853$	−18.0315	−	3.58668i	−0.617386	−	0.122806i	−0.123517	−	0.992342i	$-0.539417\pi$
$853$	−18.0315	−	3.58668i	−0.617386	−	0.122806i	−0.493868	+	0.869537i	$0.664417\pi$
$854$	−4.27812	+	21.7397i	−0.146394	+	0.743918i
$855$	−9.00456	+	6.01666i	−0.307950	+	0.205765i
$856$	−4.00660	−	9.50744i	−0.136943	−	0.324958i
$857$	8.86432	−	13.2664i	0.302799	−	0.453171i	−0.648601	−	0.761129i	$-0.724645\pi$
$857$	8.86432	−	13.2664i	0.302799	−	0.453171i	0.951400	+	0.307958i	$0.0996455\pi$
$858$	−19.6499	+	3.95039i	−0.670837	+	0.134864i
$859$	−13.5362	+	32.6792i	−0.461848	+	1.11500i	0.505789	+	0.862657i	$0.331201\pi$
$859$	−13.5362	+	32.6792i	−0.461848	+	1.11500i	−0.967638	+	0.252343i	$0.918799\pi$
$860$	−2.16468	−	3.21118i	−0.0738150	−	0.109500i
$861$	−6.31806	−	31.7630i	−0.215319	−	1.08248i
$862$	19.3345	−	46.9489i	0.658536	−	1.59908i
$863$	−22.3530	+	22.3530i	−0.760906	+	0.760906i	−0.976486	−	0.215580i	$-0.930836\pi$
$863$	−22.3530	+	22.3530i	−0.760906	+	0.760906i	0.215580	+	0.976486i	$0.430836\pi$
$864$	6.30935	−	15.6836i	0.214648	−	0.533568i
$865$	−3.46580	−	8.36718i	−0.117841	−	0.284493i
$866$	−3.84096	+	2.57782i	−0.130521	+	0.0875980i
$867$	−7.63480	+	35.6843i	−0.259291	+	1.21190i
$868$	−8.66256	+	21.1575i	−0.294026	+	0.718133i
$869$	11.5659	−	4.79075i	0.392346	−	0.162515i
$870$	−10.6157	+	4.42263i	−0.359907	+	0.149941i
$871$	2.69112	+	2.69112i	0.0911852	+	0.0911852i
$872$	−14.9705	−	14.7880i	−0.506965	−	0.500785i
$873$	8.11504	−	1.61418i	0.274652	−	0.0546318i
$874$	37.3430	−	0.0763400i	1.26315	−	0.00258224i
$875$	17.4549	+	7.23005i	0.590083	+	0.244420i
$876$	0.616279	+	0.611260i	0.0208221	+	0.0206526i
$877$	1.36712	+	0.913483i	0.0461645	+	0.0308461i	0.578438	−	0.815726i	$-0.303662\pi$
$877$	1.36712	+	0.913483i	0.0461645	+	0.0308461i	−0.532274	+	0.846572i	$0.678662\pi$
$878$	−1.07879	−	1.07438i	−0.0364073	−	0.0362587i
$879$	−14.7159	−	22.0240i	−0.496357	−	0.742850i
$880$	4.32400	−	0.0353587i	0.145762	−	0.00119194i
$881$	−1.01383	+	5.09688i	−0.0341569	+	0.171718i	−0.994098	−	0.108482i	$-0.965401\pi$
$881$	−1.01383	+	5.09688i	−0.0341569	+	0.171718i	0.959941	+	0.280200i	$0.0904010\pi$
$882$	3.35778	−	5.04758i	0.113062	−	0.169961i
$883$	−13.1664			−0.443086			−0.221543	−	0.975151i	$-0.571109\pi$
$883$	−13.1664			−0.443086			−0.221543	+	0.975151i	$0.571109\pi$
$884$	46.9725	+	19.6288i	1.57986	+	0.660189i
$885$	−10.1322			−0.340590
$886$	18.1600	−	27.2990i	0.610096	−	0.917126i
$887$	8.37931	−	42.1257i	0.281350	−	1.41444i	−0.538868	−	0.842390i	$-0.681148\pi$
$887$	8.37931	−	42.1257i	0.281350	−	1.41444i	0.820218	−	0.572051i	$-0.193852\pi$
$888$	26.0157	+	17.1533i	0.873030	+	0.575627i
$889$	4.05219	+	6.06453i	0.135906	+	0.203398i
$890$	2.35200	+	2.34240i	0.0788392	+	0.0785176i
$891$	−9.99340	−	6.67737i	−0.334791	−	0.223700i
$892$	20.1516	−	20.3171i	0.674726	−	0.680266i
$893$	−52.3233	−	21.6730i	−1.75093	−	0.725260i
$894$	19.7662	−	0.0404077i	0.661079	−	0.00135144i
$895$	−20.9783	+	4.17284i	−0.701227	+	0.139483i
$896$	−0.337026	−	23.5502i	−0.0112593	−	0.786757i
$897$	37.1333	+	37.1333i	1.23984	+	1.23984i
$898$	−36.8798	+	15.3645i	−1.23070	+	0.512721i
$899$	19.0123	−	7.87514i	0.634094	−	0.262650i
$900$	−11.8387	−	4.84712i	−0.394622	−	0.161571i
$901$	2.41511	+	5.95166i	0.0804590	+	0.198279i
$902$	9.10115	−	6.10814i	0.303035	−	0.203379i
$903$	3.27585	+	7.90860i	0.109014	+	0.263182i
$904$	9.59139	−	0.0588234i	0.319005	−	0.00195644i
$905$	−16.8758	+	16.8758i	−0.560970	+	0.560970i
$906$	−1.58171	+	3.84076i	−0.0525487	+	0.127601i
$907$	−1.91211	−	9.61281i	−0.0634905	−	0.319188i	0.935968	−	0.352084i	$-0.114527\pi$
$907$	−1.91211	−	9.61281i	−0.0634905	−	0.319188i	−0.999459	+	0.0328961i	$0.989527\pi$
$908$	34.2308	−	23.0753i	1.13599	−	0.765780i
$909$	2.86970	−	6.92807i	0.0951819	−	0.229790i
$910$	18.0119	−	3.62109i	0.597090	−	0.120038i
$911$	26.4536	−	39.5905i	0.876445	−	1.31169i	−0.0728613	−	0.997342i	$-0.523213\pi$
$911$	26.4536	−	39.5905i	0.876445	−	1.31169i	0.949307	−	0.314351i	$-0.101787\pi$
$912$	−31.3970	+	47.8310i	−1.03966	+	1.58384i
$913$	−11.0365	+	7.37437i	−0.365256	+	0.244056i
$914$	5.86490	−	29.8031i	0.193994	−	0.985800i
$915$	−16.0160	−	3.18577i	−0.529472	−	0.105318i
$916$	1.44051	−	0.00588965i	0.0475957	−	0.000194599i
$917$		−	31.9425i		−	1.05483i
$918$	6.58512	+	16.1333i	0.217341	+	0.532477i
$919$		−	38.7851i		−	1.27940i	−0.768624	−	0.639701i	$-0.779058\pi$
$919$		−	38.7851i		−	1.27940i	0.768624	−	0.639701i	$-0.220942\pi$
$920$	−6.35203	−	9.38142i	−0.209420	−	0.309296i
$921$	−2.44114	−	0.485572i	−0.0804382	−	0.0160002i
$922$	−10.1664	−	2.00064i	−0.334814	−	0.0658874i
$923$	30.7964	−	20.5775i	1.01368	−	0.677316i
$924$	−9.38206	−	1.82636i	−0.308647	−	0.0600830i
$925$	−11.3438	+	16.9772i	−0.372981	+	0.558205i
$926$	1.85600	+	9.23208i	0.0609920	+	0.303385i
$927$	−5.25448	+	12.6854i	−0.172580	+	0.416645i
$928$	−14.8368	+	15.1432i	−0.487041	+	0.497101i
$929$	10.0100	+	50.3239i	0.328419	+	1.65107i	0.693765	+	0.720201i	$0.255950\pi$
$929$	10.0100	+	50.3239i	0.328419	+	1.65107i	−0.365347	+	0.930872i	$0.619050\pi$
$930$	−15.5803	−	6.41628i	−0.510898	−	0.210398i
$931$	12.5627	−	12.5627i	0.411725	−	0.411725i
$932$	30.5801	+	20.2526i	1.00168	+	0.663395i
$933$	−6.35397	−	15.3398i	−0.208020	−	0.502204i
$934$	−21.6769	−	32.2987i	−0.709291	−	1.05685i
$935$	−3.17438	+	3.12892i	−0.103813	+	0.102326i
$936$	−27.5014	+	5.64593i	−0.898913	+	0.184543i
$937$	−5.64323	+	2.33750i	−0.184356	+	0.0763629i	−0.472952	−	0.881088i	$-0.656812\pi$
$937$	−5.64323	+	2.33750i	−0.184356	+	0.0763629i	0.288596	+	0.957451i	$0.406812\pi$
$938$	0.697969	+	1.67535i	0.0227895	+	0.0547021i
$939$	17.7289	+	17.7289i	0.578561	+	0.578561i
$940$	3.42099	+	16.8384i	0.111580	+	0.549207i
$941$	20.8412	−	4.14557i	0.679403	−	0.135142i	0.156687	−	0.987648i	$-0.449919\pi$
$941$	20.8412	−	4.14557i	0.679403	−	0.135142i	0.522716	+	0.852507i	$0.324919\pi$
$942$	0.0324839	+	15.8901i	0.00105838	+	0.517727i
$943$	−26.5322	−	10.9900i	−0.864009	−	0.357884i
$944$	−17.1975	+	7.28877i	−0.559732	+	0.237229i
$945$	5.22879	+	3.49377i	0.170093	+	0.113652i
$946$	−2.04445	+	2.05283i	−0.0664708	+	0.0667431i
$947$	−3.28509	−	4.91648i	−0.106751	−	0.159764i	0.774248	−	0.632882i	$-0.218128\pi$
$947$	−3.28509	−	4.91648i	−0.106751	−	0.159764i	−0.880999	+	0.473118i	$0.843128\pi$
$948$	46.3504	−	19.4214i	1.50539	−	0.630777i
$949$	−0.243512	+	1.22422i	−0.00790474	+	0.0397398i
$950$	−31.2138	−	20.7642i	−1.01271	−	0.673680i
$951$	26.1358			0.847511
$952$	17.1482	+	17.1853i	0.555777	+	0.556979i
$953$	−24.7513			−0.801774			−0.400887	−	0.916127i	$-0.631298\pi$
$953$	−24.7513			−0.801774			−0.400887	+	0.916127i	$0.631298\pi$
$954$	−2.94919	−	1.96188i	−0.0954837	−	0.0635182i
$955$	−1.95799	+	9.84349i	−0.0633591	+	0.318528i
$956$	18.9081	−	7.92270i	0.611530	−	0.256238i
$957$	4.77985	+	7.15355i	0.154511	+	0.231241i
$958$	−10.7848	+	10.8289i	−0.348440	+	0.349867i
$959$	−2.58692	−	1.72853i	−0.0835361	−	0.0558171i
$960$	17.3573	−	0.212910i	0.560204	−	0.00687164i
$961$	−0.783955	−	0.324725i	−0.0252889	−	0.0104750i
$962$	0.0916059	+	44.8106i	0.00295349	+	1.44475i
$963$	−5.75210	+	1.14416i	−0.185359	+	0.0368702i
$964$	4.30772	+	21.2029i	0.138742	+	0.682900i
$965$	12.8293	+	12.8293i	0.412989	+	0.412989i
$966$	9.63088	+	23.1172i	0.309868	+	0.743784i
$967$	−41.5952	+	17.2293i	−1.33761	+	0.554056i	−0.932816	−	0.360352i	$-0.882657\pi$
$967$	−41.5952	+	17.2293i	−1.33761	+	0.554056i	−0.404794	+	0.914408i	$0.632657\pi$
$968$	5.60625	+	27.3082i	0.180192	+	0.877718i
$969$	−11.0881	−	57.9243i	−0.356201	−	1.86080i
$970$	−4.09956	−	6.10835i	−0.131629	−	0.196127i
$971$	−15.0873	−	36.4239i	−0.484174	−	1.16890i	−0.957609	−	0.288071i	$-0.906986\pi$
$971$	−15.0873	−	36.4239i	−0.484174	−	1.16890i	0.473435	−	0.880829i	$-0.343014\pi$
$972$	−25.2768	−	16.7403i	−0.810754	−	0.536946i
$973$	24.1898	−	24.1898i	0.775491	−	0.775491i
$974$	−5.54194	−	2.28229i	−0.177575	−	0.0731292i
$975$	−10.2852	−	51.7071i	−0.329389	−	1.65595i
$976$	−29.4759	+	6.11411i	−0.943502	+	0.195708i
$977$	6.19856	−	14.9646i	0.198309	−	0.478761i	−0.793174	−	0.608995i	$-0.791573\pi$
$977$	6.19856	−	14.9646i	0.198309	−	0.478761i	0.991483	+	0.130234i	$0.0415729\pi$
$978$	4.96711	+	24.7073i	0.158831	+	0.790052i
$979$	1.37968	−	2.06483i	0.0440946	−	0.0659923i
$980$	−5.29082	−	1.02994i	−0.169009	−	0.0329002i
$981$	−9.94585	+	6.64560i	−0.317546	+	0.212178i
$982$	−3.32868	−	0.655044i	−0.106222	−	0.0209033i
$983$	34.8034	+	6.92283i	1.11006	+	0.220804i	0.715875	−	0.698228i	$-0.246028\pi$
$983$	34.8034	+	6.92283i	1.11006	+	0.220804i	0.394182	+	0.919032i	$0.371028\pi$
$984$	36.4346	−	24.6693i	1.16149	−	0.786430i
$985$		−	2.13661i		−	0.0680780i
$986$	0.112957	−	21.8523i	0.00359729	−	0.695920i
$987$		−	37.9803i		−	1.20893i
$988$	−82.2750	+	0.336389i	−2.61752	+	0.0107020i
$989$	7.44507	+	1.48092i	0.236740	+	0.0470904i
$990$	0.474613	−	2.41180i	0.0150842	−	0.0766519i
$991$	−15.0339	+	10.0453i	−0.477568	+	0.319101i	−0.770951	−	0.636894i	$-0.780219\pi$
$991$	−15.0339	+	10.0453i	−0.477568	+	0.319101i	0.293383	+	0.955995i	$0.405219\pi$
$992$	−31.0604	+	0.317492i	−0.986167	+	0.0100804i
$993$	2.07101	−	3.09949i	0.0657215	−	0.0983592i
$994$	17.3165	−	3.48129i	0.549247	−	0.110420i
$995$	−0.710497	+	1.71529i	−0.0225243	+	0.0543784i
$996$	−44.1830	+	29.7841i	−1.39999	+	0.943746i
$997$	−2.81333	−	14.1436i	−0.0890991	−	0.447932i	−0.999421	−	0.0340301i	$-0.989166\pi$
$997$	−2.81333	−	14.1436i	−0.0890991	−	0.447932i	0.910322	−	0.413901i	$-0.135834\pi$
$998$	−0.0532489	+	0.129301i	−0.00168557	+	0.00409296i
$999$	−10.8457	+	10.8457i	−0.343143	+	0.343143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	68.2.i.b.3.1	✓	48
3.2	odd	2		612.2.bd.d.343.6		48
4.3	odd	2	inner	68.2.i.b.3.3	yes	48
12.11	even	2		612.2.bd.d.343.4		48
17.6	odd	16	inner	68.2.i.b.23.3	yes	48
51.23	even	16		612.2.bd.d.91.4		48
68.23	even	16	inner	68.2.i.b.23.1	yes	48
204.23	odd	16		612.2.bd.d.91.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.i.b.3.1	✓	48	1.1	even	1	trivial
68.2.i.b.3.3	yes	48	4.3	odd	2	inner
68.2.i.b.23.1	yes	48	68.23	even	16	inner
68.2.i.b.23.3	yes	48	17.6	odd	16	inner
612.2.bd.d.91.4		48	51.23	even	16
612.2.bd.d.91.6		48	204.23	odd	16
612.2.bd.d.343.4		48	12.11	even	2
612.2.bd.d.343.6		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	68.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17748 - 0.783289i) q^{2} +(0.418777 - 2.10534i) q^{3} +(0.772915 + 1.84461i) q^{4} +(-0.561585 - 0.840472i) q^{5} +(-2.14219 + 2.15097i) q^{6} +(-1.73093 - 1.15657i) q^{7} +(0.534775 - 2.77741i) q^{8} +(-1.48543 - 0.615285i) q^{9} +O(q^{10})\)	\(q+(-1.17748 - 0.783289i) q^{2} +(0.418777 - 2.10534i) q^{3} +(0.772915 + 1.84461i) q^{4} +(-0.561585 - 0.840472i) q^{5} +(-2.14219 + 2.15097i) q^{6} +(-1.73093 - 1.15657i) q^{7} +(0.534775 - 2.77741i) q^{8} +(-1.48543 - 0.615285i) q^{9} +(0.00292235 + 1.42952i) q^{10} +(1.04891 - 0.208641i) q^{11} +(4.20721 - 0.854763i) q^{12} +(4.36539 + 4.36539i) q^{13} +(1.13221 + 2.71766i) q^{14} +(-2.00465 + 0.830355i) q^{15} +(-2.80520 + 2.85146i) q^{16} +(0.0297412 - 4.12300i) q^{17} +(1.26712 + 1.88801i) q^{18} +(2.55002 + 6.15628i) q^{19} +(1.11629 - 1.68552i) q^{20} +(-3.15985 + 3.15985i) q^{21} +(-1.39849 - 0.575928i) q^{22} +(0.773086 + 3.88657i) q^{23} +(-5.62343 - 2.28900i) q^{24} +(1.52240 - 3.67540i) q^{25} +(-1.72079 - 8.55953i) q^{26} +(1.66029 - 2.48480i) q^{27} +(0.795567 - 4.08684i) q^{28} +(-3.11609 + 2.08211i) q^{29} +(3.01085 + 0.592499i) q^{30} +(-5.38553 - 1.07125i) q^{31} +(5.53659 - 1.16025i) q^{32} -2.29568i q^{33} +(-3.26452 + 4.83145i) q^{34} +2.10432i q^{35} +(-0.0131473 - 3.21560i) q^{36} +(-5.03388 - 1.00130i) q^{37} +(1.81956 - 9.24630i) q^{38} +(11.0188 - 7.36249i) q^{39} +(-2.63466 + 1.11029i) q^{40} +(-4.02629 + 6.02577i) q^{41} +(6.19574 - 1.24558i) q^{42} +(0.733065 - 1.76977i) q^{43} +(1.19558 + 1.77357i) q^{44} +(0.317065 + 1.59399i) q^{45} +(2.13401 - 5.18190i) q^{46} +(-6.00982 + 6.00982i) q^{47} +(4.82853 + 7.10003i) q^{48} +(-1.02031 - 2.46325i) q^{49} +(-4.67150 + 3.13523i) q^{50} +(-8.66784 - 1.78923i) q^{51} +(-4.67839 + 11.4265i) q^{52} +(-1.43923 + 0.596147i) q^{53} +(-3.90127 + 1.62531i) q^{54} +(-0.764407 - 0.764407i) q^{55} +(-4.13794 + 4.18901i) q^{56} +(14.0289 - 2.79053i) q^{57} +(5.30003 - 0.0108348i) q^{58} +(4.31414 + 1.78698i) q^{59} +(-3.08111 - 3.05602i) q^{60} +(6.25751 + 4.18113i) q^{61} +(5.50225 + 5.47980i) q^{62} +(1.85956 + 2.78302i) q^{63} +(-7.42803 - 2.97058i) q^{64} +(1.21745 - 6.12053i) q^{65} +(-1.79818 + 2.70311i) q^{66} +0.616467 q^{67} +(7.62833 - 3.13187i) q^{68} +8.50628 q^{69} +(1.64829 - 2.47779i) q^{70} +(1.17044 - 5.88422i) q^{71} +(-2.50327 + 3.79661i) q^{72} +(0.112327 + 0.168110i) q^{73} +(5.14298 + 5.12199i) q^{74} +(-7.10042 - 4.74435i) q^{75} +(-9.38502 + 9.46208i) q^{76} +(-2.05690 - 0.851995i) q^{77} +(-18.7413 + 0.0383127i) q^{78} +(11.4809 - 2.28368i) q^{79} +(3.97193 + 0.756357i) q^{80} +(-7.94673 - 7.94673i) q^{81} +(9.46080 - 3.94147i) q^{82} +(-11.4667 + 4.74966i) q^{83} +(-8.27101 - 3.38641i) q^{84} +(-3.48197 + 2.29042i) q^{85} +(-2.24941 + 1.50967i) q^{86} +(3.07859 + 7.43237i) q^{87} +(-0.0185510 - 3.02482i) q^{88} +(1.64195 - 1.64195i) q^{89} +(0.875222 - 2.12525i) q^{90} +(-2.50731 - 12.6051i) q^{91} +(-6.57169 + 4.43003i) q^{92} +(-4.51067 + 10.8897i) q^{93} +(11.7839 - 2.36901i) q^{94} +(3.74213 - 5.60049i) q^{95} +(-0.124116 - 12.1423i) q^{96} +(-4.27885 + 2.85903i) q^{97} +(-0.728042 + 3.69963i) q^{98} +(-1.68645 - 0.335456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 24 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} + 16 q^{25} - 16 q^{26} + 40 q^{28} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 48 q^{41} + 40 q^{42} + 24 q^{44} - 64 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} + 48 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 96 q^{65} - 96 q^{66} - 32 q^{68} + 32 q^{69} - 80 q^{70} - 64 q^{72} + 64 q^{73} - 16 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 40 q^{82} - 80 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 48 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 72 q^{98}+O(q^{100}) \) 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 24 * q^20 - 16 * q^21 - 8 * q^22 + 8 * q^24 + 16 * q^25 - 16 * q^26 + 40 * q^28 + 56 * q^30 + 32 * q^32 + 56 * q^34 + 56 * q^36 - 16 * q^37 + 32 * q^38 + 56 * q^40 - 48 * q^41 + 40 * q^42 + 24 * q^44 - 64 * q^45 + 8 * q^46 - 32 * q^48 - 16 * q^49 - 16 * q^52 + 48 * q^53 - 24 * q^54 - 48 * q^56 + 64 * q^57 - 64 * q^58 - 112 * q^60 + 16 * q^61 - 64 * q^62 - 56 * q^64 + 96 * q^65 - 96 * q^66 - 32 * q^68 + 32 * q^69 - 80 * q^70 - 64 * q^72 + 64 * q^73 - 16 * q^74 - 64 * q^76 + 16 * q^77 - 112 * q^78 - 24 * q^80 + 64 * q^81 - 40 * q^82 - 80 * q^85 + 64 * q^86 + 56 * q^88 - 16 * q^89 + 48 * q^90 + 104 * q^92 - 16 * q^93 + 88 * q^94 + 144 * q^96 - 16 * q^97 + 72 * q^98

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