LMFDB - Embedded newform 672.2.ch.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(11,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 12, 16]))

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

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

chi := DirichletCharacter("672.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.ch (of order $24$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$124$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	672.11
Dual form			672.2.ch.a.611.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40759 - 0.136707i) q^{2} +(-1.57871 + 0.712503i) q^{3} +(1.96262 + 0.384854i) q^{4} +(-0.304006 - 2.30915i) q^{5} +(2.31959 - 0.787091i) q^{6} +(2.28276 - 1.33754i) q^{7} +(-2.70996 - 0.810020i) q^{8} +(1.98468 - 2.24968i) q^{9} +O(q^{10})$	\(q+(-1.40759 - 0.136707i) q^{2} +(-1.57871 + 0.712503i) q^{3} +(1.96262 + 0.384854i) q^{4} +(-0.304006 - 2.30915i) q^{5} +(2.31959 - 0.787091i) q^{6} +(2.28276 - 1.33754i) q^{7} +(-2.70996 - 0.810020i) q^{8} +(1.98468 - 2.24968i) q^{9} +(0.112239 + 3.29190i) q^{10} +(3.21659 - 2.46818i) q^{11} +(-3.37263 + 0.790800i) q^{12} +(1.98742 + 4.79806i) q^{13} +(-3.39604 + 1.57065i) q^{14} +(2.12522 + 3.42889i) q^{15} +(3.70378 + 1.51064i) q^{16} +(-0.963095 + 1.66813i) q^{17} +(-3.10116 + 2.89531i) q^{18} +(-6.74038 - 5.17208i) q^{19} +(0.292037 - 4.64899i) q^{20} +(-2.65082 + 3.73807i) q^{21} +(-4.86506 + 3.03446i) q^{22} +(-4.64570 - 1.24481i) q^{23} +(4.85539 - 0.652062i) q^{24} +(-0.410136 + 0.109896i) q^{25} +(-2.14155 - 7.02539i) q^{26} +(-1.53034 + 4.96569i) q^{27} +(4.99495 - 1.74657i) q^{28} +(-1.62618 - 3.92595i) q^{29} +(-2.52268 - 5.11700i) q^{30} +(4.36956 + 2.52277i) q^{31} +(-5.00688 - 2.63270i) q^{32} +(-3.31950 + 6.18838i) q^{33} +(1.58369 - 2.21638i) q^{34} +(-3.78256 - 4.86461i) q^{35} +(4.76097 - 3.65146i) q^{36} +(5.53795 - 0.729086i) q^{37} +(8.78064 + 8.20162i) q^{38} +(-6.55620 - 6.15872i) q^{39} +(-1.04662 + 6.50395i) q^{40} +(5.87710 + 5.87710i) q^{41} +(4.24229 - 4.89929i) q^{42} +(2.59792 - 6.27193i) q^{43} +(7.26285 - 3.60619i) q^{44} +(-5.79820 - 3.89901i) q^{45} +(6.36908 + 2.38728i) q^{46} +(5.42418 - 3.13165i) q^{47} +(-6.92354 + 0.254073i) q^{48} +(3.42196 - 6.10657i) q^{49} +(0.592327 - 0.0986198i) q^{50} +(0.331906 - 3.31971i) q^{51} +(2.05401 + 10.1816i) q^{52} +(-1.24418 - 1.62144i) q^{53} +(2.83294 - 6.78045i) q^{54} +(-6.67726 - 6.67726i) q^{55} +(-7.26961 + 1.77561i) q^{56} +(14.3263 + 3.36269i) q^{57} +(1.75229 + 5.74844i) q^{58} +(-4.61022 - 6.00815i) q^{59} +(2.85138 + 7.54751i) q^{60} +(-10.4494 - 8.01807i) q^{61} +(-5.80568 - 4.14837i) q^{62} +(1.52150 - 7.79006i) q^{63} +(6.68774 + 4.39024i) q^{64} +(10.4753 - 6.04789i) q^{65} +(5.51849 - 8.25691i) q^{66} +(-8.07953 - 1.06369i) q^{67} +(-2.53218 + 2.90326i) q^{68} +(8.22117 - 1.34487i) q^{69} +(4.65927 + 7.36448i) q^{70} +(-2.94218 - 2.94218i) q^{71} +(-7.20068 + 4.48890i) q^{72} +(-0.161699 - 0.603469i) q^{73} +(-7.89484 + 0.269180i) q^{74} +(0.569187 - 0.465717i) q^{75} +(-11.2383 - 12.7449i) q^{76} +(4.04140 - 9.93658i) q^{77} +(8.38651 + 9.56523i) q^{78} +(-7.54048 - 13.0605i) q^{79} +(2.36234 - 9.01183i) q^{80} +(-1.12209 - 8.92978i) q^{81} +(-7.46912 - 9.07599i) q^{82} +(3.14669 + 7.59679i) q^{83} +(-6.64117 + 6.31624i) q^{84} +(4.14475 + 1.71681i) q^{85} +(-4.51422 + 8.47315i) q^{86} +(5.36453 + 5.03929i) q^{87} +(-10.7161 + 4.08316i) q^{88} +(12.0453 + 3.22753i) q^{89} +(7.62847 + 6.28087i) q^{90} +(10.9544 + 8.29454i) q^{91} +(-8.63869 - 4.23101i) q^{92} +(-8.69577 - 0.869407i) q^{93} +(-8.06315 + 3.66657i) q^{94} +(-9.89400 + 17.1369i) q^{95} +(9.78025 + 0.588863i) q^{96} +2.65142 q^{97} +(-5.65152 + 8.12775i) q^{98} +(0.831305 - 12.1348i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9	$ 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} + 24 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 44 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} - 36 q^{30} - 8 q^{33} + 64 q^{36} - 8 q^{37} - 4 q^{39} - 72 q^{40} - 68 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 20 q^{51} + 16 q^{52} - 92 q^{54} - 32 q^{55} - 16 q^{57} + 24 q^{58} - 20 q^{60} - 8 q^{61} - 128 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 16 q^{75} - 32 q^{76} + 136 q^{78} - 16 q^{79} - 48 q^{82} + 124 q^{84} + 48 q^{85} - 4 q^{87} - 8 q^{88} + 128 q^{90} - 64 q^{91} - 28 q^{93} - 64 q^{94} - 72 q^{96} - 64 q^{97} - 16 q^{99}+O(q^{100}) $ 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 - 32 * q^13 - 32 * q^15 + 24 * q^16 - 4 * q^18 - 8 * q^19 - 8 * q^21 - 32 * q^22 - 44 * q^24 - 8 * q^25 - 16 * q^27 - 16 * q^28 - 36 * q^30 - 8 * q^33 + 64 * q^36 - 8 * q^37 - 4 * q^39 - 72 * q^40 - 68 * q^42 - 32 * q^43 - 4 * q^45 - 8 * q^46 - 16 * q^48 + 20 * q^51 + 16 * q^52 - 92 * q^54 - 32 * q^55 - 16 * q^57 + 24 * q^58 - 20 * q^60 - 8 * q^61 - 128 * q^64 - 20 * q^66 - 72 * q^67 - 16 * q^69 - 16 * q^70 - 4 * q^72 - 8 * q^73 + 16 * q^75 - 32 * q^76 + 136 * q^78 - 16 * q^79 - 48 * q^82 + 124 * q^84 + 48 * q^85 - 4 * q^87 - 8 * q^88 + 128 * q^90 - 64 * q^91 - 28 * q^93 - 64 * q^94 - 72 * q^96 - 64 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.40759	−	0.136707i	−0.995317	−	0.0966661i
$2$	−1.40759	−	0.136707i	−0.995317	−	0.0966661i
$3$	−1.57871	+	0.712503i	−0.911471	+	0.411364i
$3$	−1.57871	+	0.712503i	−0.911471	+	0.411364i
$4$	1.96262	+	0.384854i	0.981311	+	0.192427i
$5$	−0.304006	−	2.30915i	−0.135955	−	1.03268i	−0.914355	−	0.404915i	$-0.867301\pi$
$5$	−0.304006	−	2.30915i	−0.135955	−	1.03268i	0.778399	−	0.627770i	$-0.216032\pi$
$6$	2.31959	−	0.787091i	0.946968	−	0.321329i
$7$	2.28276	−	1.33754i	0.862801	−	0.505544i
$7$	2.28276	−	1.33754i	0.862801	−	0.505544i
$8$	−2.70996	−	0.810020i	−0.958115	−	0.286385i
$9$	1.98468	−	2.24968i	0.661560	−	0.749892i
$10$	0.112239	+	3.29190i	0.0354932	+	1.04099i
$11$	3.21659	−	2.46818i	0.969839	−	0.744184i	0.00311262	−	0.999995i	$-0.499009\pi$
$11$	3.21659	−	2.46818i	0.969839	−	0.744184i	0.966727	+	0.255811i	$0.0823426\pi$
$12$	−3.37263	+	0.790800i	−0.973595	+	0.228284i
$13$	1.98742	+	4.79806i	0.551211	+	1.33074i	0.916570	+	0.399875i	$0.130946\pi$
$13$	1.98742	+	4.79806i	0.551211	+	1.33074i	−0.365358	+	0.930867i	$0.619054\pi$
$14$	−3.39604	+	1.57065i	−0.907629	+	0.419773i
$15$	2.12522	+	3.42889i	0.548728	+	0.885335i
$16$	3.70378	+	1.51064i	0.925944	+	0.377661i
$17$	−0.963095	+	1.66813i	−0.233585	+	0.404581i	−0.958860	−	0.283878i	$-0.908379\pi$
$17$	−0.963095	+	1.66813i	−0.233585	+	0.404581i	0.725276	+	0.688459i	$0.241712\pi$
$18$	−3.10116	+	2.89531i	−0.730951	+	0.682430i
$19$	−6.74038	−	5.17208i	−1.54635	−	1.18656i	−0.909600	−	0.415486i	$-0.863611\pi$
$19$	−6.74038	−	5.17208i	−1.54635	−	1.18656i	−0.636750	−	0.771070i	$-0.719722\pi$
$20$	0.292037	−	4.64899i	0.0653015	−	1.03955i
$21$	−2.65082	+	3.73807i	−0.578456	+	0.815714i
$22$	−4.86506	+	3.03446i	−1.03723	+	0.646948i
$23$	−4.64570	−	1.24481i	−0.968696	−	0.259561i	−0.260419	−	0.965496i	$-0.583861\pi$
$23$	−4.64570	−	1.24481i	−0.968696	−	0.259561i	−0.708277	+	0.705934i	$0.750527\pi$
$24$	4.85539	−	0.652062i	0.991102	−	0.133102i
$25$	−0.410136	+	0.109896i	−0.0820272	+	0.0219791i
$26$	−2.14155	−	7.02539i	−0.419992	−	1.37779i
$27$	−1.53034	+	4.96569i	−0.294515	+	0.955647i
$28$	4.99495	−	1.74657i	0.943957	−	0.330070i
$29$	−1.62618	−	3.92595i	−0.301974	−	0.729030i	−0.999917	−	0.0128769i	$-0.995901\pi$
$29$	−1.62618	−	3.92595i	−0.301974	−	0.729030i	0.697943	−	0.716154i	$-0.254099\pi$
$30$	−2.52268	−	5.11700i	−0.460577	−	0.934232i
$31$	4.36956	+	2.52277i	0.784797	+	0.453103i	0.838128	−	0.545474i	$-0.183650\pi$
$31$	4.36956	+	2.52277i	0.784797	+	0.453103i	−0.0533308	+	0.998577i	$0.516984\pi$
$32$	−5.00688	−	2.63270i	−0.885101	−	0.465400i
$33$	−3.31950	+	6.18838i	−0.577851	+	1.07726i
$34$	1.58369	−	2.21638i	0.271600	−	0.380106i
$35$	−3.78256	−	4.86461i	−0.639370	−	0.822270i
$36$	4.76097	−	3.65146i	0.793496	−	0.608576i
$37$	5.53795	−	0.729086i	0.910434	−	0.119861i	0.339263	−	0.940692i	$-0.389822\pi$
$37$	5.53795	−	0.729086i	0.910434	−	0.119861i	0.571171	+	0.820831i	$0.306489\pi$
$38$	8.78064	+	8.20162i	1.42441	+	1.33048i
$39$	−6.55620	−	6.15872i	−1.04983	−	0.986185i
$40$	−1.04662	+	6.50395i	−0.165485	+	1.02837i
$41$	5.87710	+	5.87710i	0.917849	+	0.917849i	0.996873	−	0.0790236i	$-0.0251802\pi$
$41$	5.87710	+	5.87710i	0.917849	+	0.917849i	−0.0790236	+	0.996873i	$0.525180\pi$
$42$	4.24229	−	4.89929i	0.654599	−	0.755976i
$43$	2.59792	−	6.27193i	0.396179	−	0.956460i	−0.592385	−	0.805655i	$-0.701813\pi$
$43$	2.59792	−	6.27193i	0.396179	−	0.956460i	0.988564	−	0.150805i	$-0.0481865\pi$
$44$	7.26285	−	3.60619i	1.09492	−	0.543653i
$45$	−5.79820	−	3.89901i	−0.864345	−	0.581231i
$46$	6.36908	+	2.38728i	0.939069	+	0.351986i
$47$	5.42418	−	3.13165i	0.791199	−	0.456799i	−0.0491857	−	0.998790i	$-0.515663\pi$
$47$	5.42418	−	3.13165i	0.791199	−	0.456799i	0.840384	+	0.541991i	$0.182329\pi$
$48$	−6.92354	+	0.254073i	−0.999327	+	0.0366722i
$49$	3.42196	−	6.10657i	0.488851	−	0.872367i
$50$	0.592327	−	0.0986198i	0.0837677	−	0.0139469i
$51$	0.331906	−	3.31971i	0.0464761	−	0.464852i
$52$	2.05401	+	10.1816i	0.284840	+	1.41194i
$53$	−1.24418	−	1.62144i	−0.170901	−	0.222722i	0.700048	−	0.714096i	$-0.253162\pi$
$53$	−1.24418	−	1.62144i	−0.170901	−	0.222722i	−0.870949	+	0.491373i	$0.836495\pi$
$54$	2.83294	−	6.78045i	0.385514	−	0.922702i
$55$	−6.67726	−	6.67726i	−0.900362	−	0.900362i
$56$	−7.26961	+	1.77561i	−0.971442	+	0.237275i
$57$	14.3263	+	3.36269i	1.89756	+	0.445400i
$58$	1.75229	+	5.74844i	0.230088	+	0.754807i
$59$	−4.61022	−	6.00815i	−0.600199	−	0.782194i	0.390156	−	0.920749i	$-0.372421\pi$
$59$	−4.61022	−	6.00815i	−0.600199	−	0.782194i	−0.990355	+	0.138554i	$0.955754\pi$
$60$	2.85138	+	7.54751i	0.368111	+	0.974379i
$61$	−10.4494	−	8.01807i	−1.33790	−	1.02661i	−0.996227	−	0.0867908i	$-0.972339\pi$
$61$	−10.4494	−	8.01807i	−1.33790	−	1.02661i	−0.341676	−	0.939818i	$-0.610994\pi$
$62$	−5.80568	−	4.14837i	−0.737322	−	0.526844i
$63$	1.52150	−	7.79006i	0.191691	−	0.981455i
$64$	6.68774	+	4.39024i	0.835967	+	0.548780i
$65$	10.4753	−	6.04789i	1.29930	−	0.750149i
$66$	5.51849	−	8.25691i	0.679279	−	1.01636i
$67$	−8.07953	−	1.06369i	−0.987072	−	0.129950i	−0.380331	−	0.924850i	$-0.624190\pi$
$67$	−8.07953	−	1.06369i	−0.987072	−	0.129950i	−0.606741	+	0.794900i	$0.707523\pi$
$68$	−2.53218	+	2.90326i	−0.307072	+	0.352072i
$69$	8.22117	−	1.34487i	0.989713	−	0.161904i
$70$	4.65927	+	7.36448i	0.556890	+	0.880224i
$71$	−2.94218	−	2.94218i	−0.349172	−	0.349172i	0.510629	−	0.859801i	$-0.329413\pi$
$71$	−2.94218	−	2.94218i	−0.349172	−	0.349172i	−0.859801	+	0.510629i	$0.829413\pi$
$72$	−7.20068	+	4.48890i	−0.848608	+	0.529022i
$73$	−0.161699	−	0.603469i	−0.0189254	−	0.0706307i	0.955817	−	0.293961i	$-0.0949737\pi$
$73$	−0.161699	−	0.603469i	−0.0189254	−	0.0706307i	−0.974743	+	0.223331i	$0.928307\pi$
$74$	−7.89484	+	0.269180i	−0.917757	+	0.0312915i
$75$	0.569187	−	0.465717i	0.0657241	−	0.0537764i
$76$	−11.2383	−	12.7449i	−1.28913	−	1.46194i
$77$	4.04140	−	9.93658i	0.460561	−	1.13238i
$78$	8.38651	+	9.56523i	0.949585	+	1.08305i
$79$	−7.54048	−	13.0605i	−0.848371	−	1.46942i	−0.882662	−	0.470009i	$-0.844251\pi$
$79$	−7.54048	−	13.0605i	−0.848371	−	1.46942i	0.0342912	−	0.999412i	$-0.489083\pi$
$80$	2.36234	−	9.01183i	0.264118	−	1.00755i
$81$	−1.12209	−	8.92978i	−0.124677	−	0.992197i
$82$	−7.46912	−	9.07599i	−0.824826	−	1.00228i
$83$	3.14669	+	7.59679i	0.345394	+	0.833856i	0.997151	+	0.0754278i	$0.0240322\pi$
$83$	3.14669	+	7.59679i	0.345394	+	0.833856i	−0.651757	+	0.758428i	$0.725968\pi$
$84$	−6.64117	+	6.31624i	−0.724611	+	0.689159i
$85$	4.14475	+	1.71681i	0.449561	+	0.186214i
$86$	−4.51422	+	8.47315i	−0.486781	+	0.913684i
$87$	5.36453	+	5.03929i	0.575137	+	0.540269i
$88$	−10.7161	+	4.08316i	−1.14234	+	0.435266i
$89$	12.0453	+	3.22753i	1.27680	+	0.342117i	0.832632	−	0.553826i	$-0.186833\pi$
$89$	12.0453	+	3.22753i	1.27680	+	0.342117i	0.444167	+	0.895944i	$0.353500\pi$
$90$	7.62847	+	6.28087i	0.804111	+	0.662062i
$91$	10.9544	+	8.29454i	1.14833	+	0.869504i
$92$	−8.63869	−	4.23101i	−0.900646	−	0.441114i
$93$	−8.69577	−	0.869407i	−0.901710	−	0.0901533i
$94$	−8.06315	+	3.66657i	−0.831650	+	0.378177i
$95$	−9.89400	+	17.1369i	−1.01510	+	1.75821i
$96$	9.78025	+	0.588863i	0.998192	+	0.0601006i
$97$	2.65142			0.269211			0.134605	−	0.990899i	$-0.457023\pi$
$97$	2.65142			0.269211			0.134605	+	0.990899i	$0.457023\pi$
$98$	−5.65152	+	8.12775i	−0.570890	+	0.821027i
$99$	0.831305	−	12.1348i	0.0835492	−	1.21960i
$100$	−0.847236	+	0.0578413i	−0.0847236	+	0.00578413i
$101$	−3.12004	+	2.39409i	−0.310456	+	0.238221i	−0.752223	−	0.658909i	$-0.771018\pi$
$101$	−3.12004	+	2.39409i	−0.310456	+	0.238221i	0.441767	+	0.897130i	$0.354352\pi$
$102$	−0.921013	+	4.62741i	−0.0911938	+	0.458182i
$103$	3.20042	+	0.857549i	0.315346	+	0.0844968i	0.413021	−	0.910722i	$-0.364474\pi$
$103$	3.20042	+	0.857549i	0.315346	+	0.0844968i	−0.0976744	+	0.995218i	$0.531140\pi$
$104$	−1.49930	−	14.6124i	−0.147019	−	1.43286i
$105$	9.43764	+	4.98475i	0.921019	+	0.486462i
$106$	1.52963	+	2.45242i	0.148571	+	0.238200i
$107$	0.648625	+	4.92680i	0.0627049	+	0.476291i	0.993771	+	0.111441i	$0.0355466\pi$
$107$	0.648625	+	4.92680i	0.0627049	+	0.476291i	−0.931066	+	0.364850i	$0.881120\pi$
$108$	−4.91455	+	9.15681i	−0.472903	+	0.881115i
$109$	−3.44712	−	0.453822i	−0.330175	−	0.0434683i	−0.0363833	−	0.999338i	$-0.511584\pi$
$109$	−3.44712	−	0.453822i	−0.330175	−	0.0434683i	−0.293791	+	0.955870i	$0.594917\pi$
$110$	8.48603	+	10.3117i	0.809111	+	0.983180i
$111$	−8.22338	+	5.09683i	−0.780528	+	0.483769i
$112$	10.4754	−	1.50553i	0.989830	−	0.142259i
$113$	9.11136			0.857124			0.428562	−	0.903512i	$-0.359020\pi$
$113$	9.11136			0.857124			0.428562	+	0.903512i	$0.359020\pi$
$114$	−19.7058	−	6.69179i	−1.84562	−	0.626744i
$115$	−1.46214	+	11.1061i	−0.136345	+	1.03565i
$116$	−1.68066	−	8.33100i	−0.156046	−	0.773514i
$117$	14.7385	+	5.05156i	1.36257	+	0.467017i
$118$	5.66794	+	9.08726i	0.521776	+	0.836550i
$119$	0.0326836	+	5.09611i	0.00299610	+	0.467160i
$120$	−2.98178	−	11.0136i	−0.272198	−	1.00540i
$121$	1.40756	−	5.25307i	0.127960	−	0.477552i
$122$	13.6123	+	12.7147i	1.23240	+	1.15113i
$123$	−13.4657	−	5.09082i	−1.21416	−	0.459024i
$124$	7.60491	+	6.63289i	0.682941	+	0.595651i
$125$	−4.07805	−	9.84528i	−0.364752	−	0.880589i
$126$	−3.20660	+	10.7572i	−0.285667	+	0.958329i
$127$		−	9.98980i		−	0.886451i	−0.896410	−	0.443226i	$-0.853834\pi$
$127$		−	9.98980i		−	0.886451i	0.896410	−	0.443226i	$-0.146166\pi$
$128$	−8.81342	−	7.09391i	−0.779004	−	0.627019i
$129$	0.367394	+	11.7526i	0.0323473	+	1.03476i
$130$	−15.5717	+	7.08092i	−1.36573	+	0.621038i
$131$	−13.3769	−	10.2644i	−1.16874	−	0.896809i	−0.172639	−	0.984985i	$-0.555230\pi$
$131$	−13.3769	−	10.2644i	−1.16874	−	0.896809i	−0.996105	+	0.0881761i	$0.971896\pi$
$132$	−8.89655	+	10.8679i	−0.774345	+	0.945932i
$133$	−22.3045	−	2.79104i	−1.93405	−	0.242014i
$134$	11.2273	+	2.60176i	0.969887	+	0.224758i
$135$	11.9318	+	2.02420i	1.02692	+	0.174215i
$136$	3.96116	−	3.74043i	0.339667	−	0.320739i
$137$	−7.14460	+	1.91439i	−0.610405	+	0.163557i	−0.550762	−	0.834662i	$-0.685663\pi$
$137$	−7.14460	+	1.91439i	−0.610405	+	0.163557i	−0.0596426	+	0.998220i	$0.518996\pi$
$138$	−11.7559	+	0.769142i	−1.00073	+	0.0654737i
$139$	−1.05195	+	2.53963i	−0.0892251	+	0.215408i	−0.962193	−	0.272370i	$-0.912193\pi$
$139$	−1.05195	+	2.53963i	−0.0892251	+	0.215408i	0.872968	+	0.487778i	$0.162193\pi$
$140$	−5.55158	−	11.0031i	−0.469194	−	0.929934i
$141$	−6.33193	+	8.80873i	−0.533245	+	0.741829i
$142$	3.73917	+	4.54360i	0.313784	+	0.381290i
$143$	18.2352	+	10.5281i	1.52490	+	0.880403i
$144$	10.7493	−	5.33415i	0.895773	−	0.444513i
$145$	−8.57125	+	4.94861i	−0.711803	+	0.410960i
$146$	0.145108	+	0.871543i	0.0120092	+	0.0721294i
$147$	−1.05135	+	12.0787i	−0.0867135	+	0.996233i
$148$	11.1495	+	0.700382i	0.916484	+	0.0575710i
$149$	3.75336	−	0.494139i	0.307487	−	0.0404815i	0.0247964	−	0.999693i	$-0.492106\pi$
$149$	3.75336	−	0.494139i	0.307487	−	0.0404815i	0.282691	+	0.959211i	$0.408773\pi$
$150$	−0.864849	+	0.577727i	−0.0706146	+	0.0471712i
$151$	2.96067	−	0.793310i	0.240936	−	0.0645587i	−0.136330	−	0.990663i	$-0.543531\pi$
$151$	2.96067	−	0.793310i	0.240936	−	0.0645587i	0.377266	+	0.926105i	$0.376864\pi$
$152$	14.0767	+	19.4760i	1.14177	+	1.57971i
$153$	1.84132	+	5.47735i	0.148862	+	0.442818i
$154$	−7.04704	+	13.4342i	−0.567867	+	1.08256i
$155$	4.49709	−	10.8569i	0.361215	−	0.872049i
$156$	−10.4971	−	14.6104i	−0.840444	−	1.16977i
$157$	1.19354	−	9.06587i	0.0952552	−	0.723535i	−0.875458	−	0.483294i	$-0.839440\pi$
$157$	1.19354	−	9.06587i	0.0952552	−	0.723535i	0.970713	−	0.240241i	$-0.0772265\pi$
$158$	8.82846	+	19.4147i	0.702354	+	1.54455i
$159$	3.11948	+	1.67332i	0.247391	+	0.132703i
$160$	−4.55718	+	12.3620i	−0.360277	+	0.977303i
$161$	−12.2700	+	3.37223i	−0.967012	+	0.265769i
$162$	0.358684	+	12.7229i	0.0281809	+	0.999603i
$163$	−9.81213	+	12.7874i	−0.768546	+	1.00159i	0.231044	+	0.972943i	$0.425786\pi$
$163$	−9.81213	+	12.7874i	−0.768546	+	1.00159i	−0.999590	+	0.0286450i	$0.990881\pi$
$164$	9.27271	+	13.7964i	0.724077	+	1.07731i
$165$	15.2991	+	5.78393i	1.19103	+	0.450278i
$166$	−3.39072	−	11.1233i	−0.263171	−	0.863339i
$167$	−7.77483	−	7.77483i	−0.601634	−	0.601634i	0.339112	−	0.940746i	$-0.389873\pi$
$167$	−7.77483	−	7.77483i	−0.601634	−	0.601634i	−0.940746	+	0.339112i	$0.889873\pi$
$168$	10.2115	−	7.98279i	0.787835	−	0.615886i
$169$	−9.87913	+	9.87913i	−0.759933	+	0.759933i
$170$	−5.59941	−	2.98318i	−0.429455	−	0.228800i
$171$	−25.0130	+	4.89876i	−1.91279	+	0.374618i
$172$	7.51251	−	11.3096i	0.572823	−	0.862350i
$173$	14.0244	+	10.7613i	1.06625	+	0.818164i	0.983950	−	0.178443i	$-0.0571061\pi$
$173$	14.0244	+	10.7613i	1.06625	+	0.818164i	0.0823020	+	0.996607i	$0.473773\pi$
$174$	−6.86215	−	7.82663i	−0.520218	−	0.593335i
$175$	−0.789251	+	0.799440i	−0.0596618	+	0.0604320i
$176$	15.6421	−	4.28245i	1.17907	−	0.322802i
$177$	11.5590	+	6.20036i	0.868830	+	0.466048i
$178$	−16.5136	−	6.18971i	−1.23775	−	0.463938i
$179$	21.7470	+	2.86304i	1.62544	+	0.213994i	0.887480	−	0.460846i	$-0.152454\pi$
$179$	21.7470	+	2.86304i	1.62544	+	0.213994i	0.737964	+	0.674840i	$0.235787\pi$
$180$	−9.87913	−	9.88375i	−0.736347	−	0.736691i
$181$	2.70317	+	1.11969i	0.200925	+	0.0832257i	0.480877	−	0.876788i	$-0.340319\pi$
$181$	2.70317	+	1.11969i	0.200925	+	0.0832257i	−0.279952	+	0.960014i	$0.590319\pi$
$182$	−14.2854	−	13.1729i	−1.05890	−	0.976437i
$183$	22.2094	+	5.21305i	1.64177	+	0.385360i
$184$	11.5813	+	7.13650i	0.853788	+	0.526110i
$185$	−3.36714	−	12.5663i	−0.247557	−	0.923895i
$186$	12.1212	+	2.41254i	0.888772	+	0.176896i
$187$	1.01936	+	7.74278i	0.0745427	+	0.566208i
$188$	11.8509	−	4.05874i	0.864312	−	0.296014i
$189$	3.14842	+	13.3824i	0.229014	+	0.973423i
$190$	16.2694	−	22.7692i	1.18031	−	1.65185i
$191$	4.68074	+	8.10728i	0.338686	+	0.586622i	0.984186	−	0.177139i	$-0.0566841\pi$
$191$	4.68074	+	8.10728i	0.338686	+	0.586622i	−0.645500	+	0.763761i	$0.723351\pi$
$192$	−13.6861	−	2.16590i	−0.987708	−	0.156310i
$193$	2.52660	−	4.37620i	0.181869	−	0.315006i	−0.760648	−	0.649164i	$-0.775119\pi$
$193$	2.52660	−	4.37620i	0.181869	−	0.315006i	0.942517	+	0.334158i	$0.108452\pi$
$194$	−3.73211	−	0.362466i	−0.267950	−	0.0260235i
$195$	−12.2283	+	17.0115i	−0.875687	+	1.21822i
$196$	9.06615	−	10.6679i	0.647582	−	0.761996i
$197$	−2.20435	−	0.913070i	−0.157053	−	0.0650536i	0.302772	−	0.953063i	$-0.402088\pi$
$197$	−2.20435	−	0.913070i	−0.157053	−	0.0650536i	−0.459825	+	0.888009i	$0.652088\pi$
$198$	−2.82905	+	16.9672i	−0.201052	+	1.20581i
$199$	−0.0383869	−	0.143262i	−0.00272118	−	0.0101556i	0.964552	−	0.263893i	$-0.0850067\pi$
$199$	−0.0383869	−	0.143262i	−0.00272118	−	0.0101556i	−0.967273	+	0.253738i	$0.918340\pi$
$200$	1.20047	+	0.0344058i	0.0848860	+	0.00243286i
$201$	13.5132	−	4.07742i	0.953144	−	0.287599i
$202$	4.71903	−	2.94337i	0.332030	−	0.207095i
$203$	−8.96330	−	6.78690i	−0.629101	−	0.476347i
$204$	1.92901	−	6.38760i	0.135057	−	0.447221i
$205$	11.7845	−	15.3578i	0.823062	−	1.07264i
$206$	−4.38764	−	1.64460i	−0.305702	−	0.114584i
$207$	−12.0207	+	7.98078i	−0.835494	+	0.554702i
$208$	0.112799	+	20.7732i	0.00782121	+	1.44036i
$209$	−34.4467			−2.38273
$210$	−12.6029	−	8.30667i	−0.869681	−	0.573215i
$211$	13.4545	−	5.57303i	0.926245	−	0.383663i	0.131992	−	0.991251i	$-0.457863\pi$
$211$	13.4545	−	5.57303i	0.926245	−	0.383663i	0.794253	+	0.607587i	$0.207863\pi$
$212$	−1.81783	−	3.66111i	−0.124849	−	0.251446i
$213$	6.74117	+	2.54855i	0.461897	+	0.174624i
$214$	−0.239473	−	7.02358i	−0.0163701	−	0.480122i
$215$	−15.2726	−	4.09229i	−1.04158	−	0.279092i
$216$	8.16947	−	12.2172i	0.555862	−	0.831275i
$217$	13.3490	−	0.0856126i	0.906187	−	0.00581176i
$218$	4.79010	+	1.11004i	0.324426	+	0.0751814i
$219$	0.685250	+	0.837494i	0.0463049	+	0.0565926i
$220$	−10.5352	−	15.6747i	−0.710282	−	1.05679i
$221$	−9.91785	−	1.30571i	−0.667147	−	0.0878316i
$222$	12.2719	−	6.05005i	0.823637	−	0.406053i
$223$			18.0657i			1.20977i	0.796312	+	0.604886i	$0.206781\pi$
$223$			18.0657i			1.20977i	−0.796312	+	0.604886i	$0.793219\pi$
$224$	−14.9508	+	0.687112i	−0.998946	+	0.0459096i
$225$	−0.566759	+	1.14078i	−0.0377840	+	0.0760521i
$226$	−12.8251	−	1.24558i	−0.853110	−	0.0828549i
$227$	0.219713	−	1.66889i	0.0145829	−	0.110768i	−0.982605	−	0.185706i	$-0.940543\pi$
$227$	0.219713	−	1.66889i	0.0145829	−	0.110768i	0.997188	+	0.0749384i	$0.0238760\pi$
$228$	26.8229	+	12.1132i	1.77639	+	0.802217i
$229$	9.14214	−	1.20359i	0.604130	−	0.0795352i	0.177744	−	0.984077i	$-0.443120\pi$
$229$	9.14214	−	1.20359i	0.604130	−	0.0795352i	0.426385	+	0.904542i	$0.359787\pi$
$230$	3.57637	−	15.4329i	0.235819	−	1.01762i
$231$	0.699618	+	18.5665i	0.0460315	+	1.22159i
$232$	1.22679	+	11.9564i	0.0805425	+	0.784976i
$233$	−3.69711	+	13.7978i	−0.242206	+	0.903925i	0.732561	+	0.680701i	$0.238325\pi$
$233$	−3.69711	+	13.7978i	−0.242206	+	0.903925i	−0.974767	+	0.223224i	$0.928342\pi$
$234$	−20.0552	−	9.12537i	−1.31105	−	0.596544i
$235$	−8.88045	−	11.5732i	−0.579297	−	0.754954i
$236$	−6.73585	−	13.5660i	−0.438467	−	0.883071i
$237$	21.2099	+	15.2462i	1.37773	+	0.990346i
$238$	0.650667	−	7.17771i	0.0421765	−	0.465262i
$239$		−	1.93411i		−	0.125107i	−0.998042	−	0.0625536i	$-0.980076\pi$
$239$		−	1.93411i		−	0.125107i	0.998042	−	0.0625536i	$-0.0199244\pi$
$240$	2.69149	+	15.9103i	0.173735	+	1.02700i
$241$	6.82271	+	3.93909i	0.439489	+	0.253739i	0.703381	−	0.710813i	$-0.251673\pi$
$241$	6.82271	+	3.93909i	0.439489	+	0.253739i	−0.263892	+	0.964552i	$0.585006\pi$
$242$	−2.69939	+	7.20175i	−0.173523	+	0.462946i
$243$	8.13395	+	13.2981i	0.521793	+	0.853072i
$244$	−17.4224	−	19.7579i	−1.11535	−	1.26487i
$245$	−15.1413	−	6.04539i	−0.967342	−	0.386226i
$246$	18.2583	+	9.00664i	1.16410	+	0.574242i
$247$	11.4200	−	42.6198i	0.726634	−	2.71184i
$248$	−9.79784	−	10.3760i	−0.622163	−	0.658878i
$249$	−10.3805	−	9.75113i	−0.657835	−	0.617953i
$250$	4.39431	+	14.4156i	0.277920	+	0.911724i
$251$	−8.26134	+	19.9446i	−0.521451	+	1.25889i	0.415551	+	0.909570i	$0.363589\pi$
$251$	−8.26134	+	19.9446i	−0.521451	+	1.25889i	−0.937002	+	0.349325i	$0.886411\pi$
$252$	5.98417	−	14.7034i	0.376967	−	0.926227i
$253$	−18.0158	+	7.46237i	−1.13264	+	0.469155i
$254$	−1.36567	+	14.0615i	−0.0856898	+	0.882300i
$255$	−7.76661	+	0.242789i	−0.486364	+	0.0152041i
$256$	11.4359	+	11.1902i	0.714744	+	0.699386i
$257$	−25.6458	+	14.8066i	−1.59974	+	0.923610i	−0.608203	+	0.793781i	$0.708109\pi$
$257$	−25.6458	+	14.8066i	−1.59974	+	0.923610i	−0.991536	+	0.129829i	$0.958557\pi$
$258$	1.08952	−	16.5931i	0.0678304	−	1.03304i
$259$	11.6666	−	9.07158i	0.724928	−	0.563680i
$260$	22.8865	−	7.83829i	1.41936	−	0.486110i
$261$	−12.0596	−	4.13337i	−0.746468	−	0.255849i
$262$	17.4260	+	16.2768i	1.07658	+	1.00559i
$263$	26.7760	−	7.17461i	1.65108	−	0.442405i	0.691164	−	0.722698i	$-0.257098\pi$
$263$	26.7760	−	7.17461i	1.65108	−	0.442405i	0.959915	+	0.280292i	$0.0904314\pi$
$264$	14.0084	−	14.0814i	0.862158	−	0.866650i
$265$	−3.36592	+	3.36592i	−0.206767	+	0.206767i
$266$	31.0141	+	6.97782i	1.90160	+	0.427838i
$267$	−21.3157	+	3.48696i	−1.30450	+	0.213399i
$268$	−15.4477	−	5.19706i	−0.943619	−	0.317461i
$269$	−0.556033	+	4.22349i	−0.0339019	+	0.257511i	−1.00000		0.000665417i	$-0.999788\pi$
$269$	−0.556033	+	4.22349i	−0.0339019	+	0.257511i	0.966098	+	0.258176i	$0.0831215\pi$
$270$	−16.5183	−	4.48039i	−1.00527	−	0.272668i
$271$	−4.48661	−	7.77104i	−0.272542	−	0.472057i	0.696970	−	0.717100i	$-0.254531\pi$
$271$	−4.48661	−	7.77104i	−0.272542	−	0.472057i	−0.969512	+	0.245043i	$0.921198\pi$
$272$	−6.08704	+	4.72348i	−0.369081	+	0.286403i
$273$	−23.2038	−	5.28967i	−1.40436	−	0.320145i
$274$	10.3184	−	1.71796i	0.623356	−	0.103786i
$275$	−1.04800	+	1.36578i	−0.0631967	+	0.0823596i
$276$	16.6526	+	0.524471i	1.00237	+	0.0315695i
$277$	3.18858	−	2.44668i	0.191583	−	0.147007i	−0.508516	−	0.861053i	$-0.669806\pi$
$277$	3.18858	−	2.44668i	0.191583	−	0.147007i	0.700099	+	0.714046i	$0.253139\pi$
$278$	1.82790	−	3.43095i	0.109630	−	0.205775i
$279$	14.3476	−	4.82322i	0.858968	−	0.288758i
$280$	6.31015	+	16.2468i	0.377104	+	0.970934i
$281$	−3.96268	+	3.96268i	−0.236394	+	0.236394i	−0.815355	−	0.578961i	$-0.803458\pi$
$281$	−3.96268	+	3.96268i	−0.236394	+	0.236394i	0.578961	+	0.815355i	$0.303458\pi$
$282$	10.1170	−	11.5335i	0.602457	−	0.686808i
$283$	9.96534	−	7.64667i	0.592378	−	0.454547i	−0.268556	−	0.963264i	$-0.586547\pi$
$283$	9.96534	−	7.64667i	0.592378	−	0.454547i	0.860934	+	0.508717i	$0.169880\pi$
$284$	−4.64208	−	6.90669i	−0.275457	−	0.409837i
$285$	3.40971	−	34.1038i	0.201974	−	2.02013i
$286$	−24.2284	−	17.3121i	−1.43266	−	1.02369i
$287$	21.2769	+	5.55512i	1.25593	+	0.327908i
$288$	−15.8598	+	6.03880i	−0.934547	+	0.355840i
$289$	6.64490	+	11.5093i	0.390876	+	0.677018i
$290$	12.7413	−	5.79387i	0.748196	−	0.340228i
$291$	−4.18583	+	1.88914i	−0.245378	+	0.110743i
$292$	−0.0851070	−	1.24661i	−0.00498051	−	0.0729525i
$293$	−14.2837	−	5.91652i	−0.834465	−	0.345647i	−0.0757960	−	0.997123i	$-0.524150\pi$
$293$	−14.2837	−	5.91652i	−0.834465	−	0.345647i	−0.758669	+	0.651477i	$0.774150\pi$
$294$	3.13110	−	16.8581i	0.182609	−	0.983186i
$295$	−12.4722	+	12.4722i	−0.726160	+	0.726160i
$296$	−15.5982	−	2.51006i	−0.906627	−	0.145894i
$297$	7.33371	+	19.7498i	0.425545	+	1.14600i
$298$	−5.35075	+	0.182437i	−0.309961	+	0.0105683i
$299$	−3.26029	−	24.7643i	−0.188547	−	1.43216i
$300$	1.29633	−	0.694973i	0.0748438	−	0.0401243i
$301$	−2.45856	−	17.7921i	−0.141709	−	1.02552i
$302$	−4.27587	+	0.711912i	−0.246048	+	0.0409660i
$303$	3.21986	−	6.00262i	0.184976	−	0.344842i
$304$	−17.1517	−	29.3385i	−0.983717	−	1.68268i
$305$	−15.3383	+	26.5667i	−0.878267	+	1.52120i
$306$	−1.84303	−	7.96159i	−0.105359	−	0.455134i
$307$	−15.7818	+	6.53706i	−0.900718	+	0.373089i	−0.784496	−	0.620134i	$-0.787078\pi$
$307$	−15.7818	+	6.53706i	−0.900718	+	0.373089i	−0.116222	+	0.993223i	$0.537078\pi$
$308$	11.7559	−	17.9464i	0.669854	−	1.02259i
$309$	−5.66355	+	0.926480i	−0.322188	+	0.0527056i
$310$	−7.81427	+	14.6673i	−0.443821	+	0.833048i
$311$	−7.00359	−	26.1377i	−0.397137	−	1.48214i	−0.818110	−	0.575062i	$-0.804978\pi$
$311$	−7.00359	−	26.1377i	−0.397137	−	1.48214i	0.420973	−	0.907073i	$-0.361689\pi$
$312$	12.7783	+	22.0005i	0.723431	+	1.24553i
$313$	−3.50803	+	13.0922i	−0.198286	+	0.740013i	0.793106	+	0.609084i	$0.208463\pi$
$313$	−3.50803	+	13.0922i	−0.198286	+	0.740013i	−0.991392	+	0.130929i	$0.958204\pi$
$314$	−2.91938	+	12.5979i	−0.164750	+	0.710939i
$315$	−18.4510	−	1.14516i	−1.03959	−	0.0645224i
$316$	−9.77274	−	28.5348i	−0.549760	−	1.60521i
$317$	−1.86094	+	2.42522i	−0.104521	+	0.136214i	−0.842685	−	0.538407i	$-0.819026\pi$
$317$	−1.86094	+	2.42522i	−0.104521	+	0.136214i	0.738164	+	0.674621i	$0.235693\pi$
$318$	−4.16220	−	2.78180i	−0.233405	−	0.155996i
$319$	−14.9207	−	8.61448i	−0.835399	−	0.482318i
$320$	8.10462	−	16.7777i	0.453062	−	0.937900i
$321$	−4.53435	−	7.31586i	−0.253083	−	0.408331i
$322$	17.7321	−	3.06932i	0.988174	−	0.171047i
$323$	15.1193	−	6.26263i	0.841261	−	0.348462i
$324$	1.23442	−	17.9576i	0.0685788	−	0.997646i
$325$	−1.34240	−	1.74945i	−0.0744629	−	0.0970419i
$326$	15.5596	−	16.6581i	0.861766	−	0.922605i
$327$	5.76537	−	1.73963i	0.318826	−	0.0962017i
$328$	−11.1661	−	20.6873i	−0.616546	−	1.14226i
$329$	8.19337	−	14.4039i	0.451715	−	0.794112i
$330$	−20.7441	−	10.2329i	−1.14193	−	0.563302i
$331$	23.4571	−	3.08819i	1.28932	−	0.169742i	0.545493	−	0.838115i	$-0.316342\pi$
$331$	23.4571	−	3.08819i	1.28932	−	0.169742i	0.743826	+	0.668373i	$0.233009\pi$
$332$	3.25212	+	16.1206i	0.178483	+	0.884735i
$333$	9.35086	−	13.9056i	0.512424	−	0.762023i
$334$	9.88090	+	12.0066i	0.540659	+	0.656974i
$335$			18.9802i			1.03700i
$336$	−15.4649	+	9.84052i	−0.843681	+	0.536845i
$337$		−	6.00678i		−	0.327210i	−0.986526	−	0.163605i	$-0.947688\pi$
$337$		−	6.00678i		−	0.327210i	0.986526	−	0.163605i	$-0.0523123\pi$
$338$	15.2563	−	12.5552i	0.829834	−	0.682914i
$339$	−14.3842	+	6.49187i	−0.781244	+	0.352590i
$340$	7.47386	+	4.96457i	0.405327	+	0.269242i
$341$	20.2818	−	2.67014i	1.09832	−	0.144596i
$342$	35.8778	−	3.47601i	1.94005	−	0.187961i
$343$	−0.356308	−	18.5168i	−0.0192388	−	0.999815i
$344$	−12.1206	+	14.8923i	−0.653501	+	0.802939i
$345$	−5.60480	−	18.5751i	−0.301752	−	1.00005i
$346$	−18.2694	−	17.0647i	−0.982170	−	0.917403i
$347$	11.1041	+	14.4711i	0.596098	+	0.776851i	0.989812	−	0.142383i	$-0.0454764\pi$
$347$	11.1041	+	14.4711i	0.596098	+	0.776851i	−0.393713	+	0.919233i	$0.628810\pi$
$348$	8.58915	+	11.9548i	0.460427	+	0.640844i
$349$	31.4530	−	13.0283i	1.68364	−	0.697388i	0.684154	−	0.729338i	$-0.260172\pi$
$349$	31.4530	−	13.0283i	1.68364	−	0.697388i	0.999489	+	0.0319502i	$0.0101718\pi$
$350$	1.22023	−	1.01739i	0.0652241	−	0.0543817i
$351$	−26.8671	+	2.52623i	−1.43406	+	0.134840i
$352$	−22.6031	+	3.88956i	−1.20475	+	0.207314i
$353$	2.46023	+	1.42042i	0.130945	+	0.0756011i	0.564042	−	0.825746i	$-0.309246\pi$
$353$	2.46023	+	1.42042i	0.130945	+	0.0756011i	−0.433097	+	0.901348i	$0.642579\pi$
$354$	−15.4228	−	10.3078i	−0.819710	−	0.547852i
$355$	−5.89950	+	7.68838i	−0.313113	+	0.408057i
$356$	22.3983	+	10.9701i	1.18711	+	0.581414i
$357$	−3.68259	−	8.02202i	−0.194903	−	0.424570i
$358$	−30.2194	−	7.00294i	−1.59715	−	0.370117i
$359$	−4.66447	+	17.4080i	−0.246181	+	0.918762i	0.726604	+	0.687056i	$0.241097\pi$
$359$	−4.66447	+	17.4080i	−0.246181	+	0.918762i	−0.972786	+	0.231706i	$0.925569\pi$
$360$	12.5546	+	15.2628i	0.661685	+	0.804421i
$361$	13.7648	+	51.3710i	0.724464	+	2.70374i
$362$	−3.65188	−	1.94560i	−0.191939	−	0.102259i
$363$	1.52070	+	9.29599i	0.0798159	+	0.487913i
$364$	18.3072	+	20.4949i	0.959557	+	1.07422i
$365$	−1.34434	+	0.556846i	−0.0703662	+	0.0291466i
$366$	−30.5491	−	10.3740i	−1.59683	−	0.542259i
$367$	−8.65094	+	14.9839i	−0.451575	+	0.782151i	−0.998484	−	0.0550408i	$-0.982471\pi$
$367$	−8.65094	+	14.9839i	−0.451575	+	0.782151i	0.546909	+	0.837192i	$0.315804\pi$
$368$	−15.3262	−	11.6285i	−0.798932	−	0.606178i
$369$	24.8857	−	1.55741i	1.29550	−	0.0810756i
$370$	3.02165	+	18.1486i	0.157088	+	0.943499i
$371$	−5.00890	−	2.03722i	−0.260049	−	0.105767i
$372$	−16.7319	−	5.05292i	−0.867510	−	0.261982i
$373$	−0.160908	−	1.22221i	−0.00833147	−	0.0632838i	0.986774	−	0.162102i	$-0.0518272\pi$
$373$	−0.160908	−	1.22221i	−0.00833147	−	0.0632838i	−0.995106	+	0.0988178i	$0.968494\pi$
$374$	−0.376348	−	11.0380i	−0.0194605	−	0.570762i
$375$	13.4529	+	12.6373i	0.694703	+	0.652586i
$376$	−17.2360	+	4.09295i	−0.888879	+	0.211078i
$377$	15.6050	−	15.6050i	0.803700	−	0.803700i
$378$	−2.60223	−	19.2673i	−0.133844	−	0.991002i
$379$	17.0094	+	7.04553i	0.873715	+	0.361905i	0.774056	−	0.633117i	$-0.218225\pi$
$379$	17.0094	+	7.04553i	0.873715	+	0.361905i	0.0996590	+	0.995022i	$0.468225\pi$
$380$	−26.0134	+	29.8256i	−1.33446	+	1.53002i
$381$	7.11776	+	15.7710i	0.364654	+	0.807975i
$382$	−5.48025	−	12.0516i	−0.280394	−	0.616614i
$383$	5.69265	+	9.85996i	0.290881	+	0.503820i	0.974018	−	0.226469i	$-0.0727183\pi$
$383$	5.69265	+	9.85996i	0.290881	+	0.503820i	−0.683137	+	0.730290i	$0.739385\pi$
$384$	18.9683	+	4.91968i	0.967972	+	0.251056i
$385$	−24.1737	−	6.31144i	−1.23201	−	0.321661i
$386$	−4.15468	+	5.81450i	−0.211467	+	0.295950i
$387$	−8.95377	−	18.2922i	−0.455146	−	0.929847i
$388$	5.20373	+	1.02041i	0.264179	+	0.0518033i
$389$	27.7694	−	21.3082i	1.40796	−	1.08037i	0.423283	−	0.905998i	$-0.360878\pi$
$389$	27.7694	−	21.3082i	1.40796	−	1.08037i	0.984680	−	0.174370i	$-0.0557890\pi$
$390$	19.5380	−	22.2736i	0.989347	−	1.12787i
$391$	6.55076	−	6.55076i	0.331286	−	0.331286i
$392$	−14.2198	+	13.7767i	−0.718208	+	0.695828i
$393$	28.4317	+	6.67357i	1.43419	+	0.336637i
$394$	2.97799	+	1.58658i	0.150029	+	0.0799306i
$395$	−27.8663	+	21.3826i	−1.40211	+	1.07587i
$396$	6.30167	−	23.4962i	0.316671	−	1.18073i
$397$	−13.0978	+	17.0693i	−0.657358	+	0.856686i	−0.996460	−	0.0840637i	$-0.973210\pi$
$397$	−13.0978	+	17.0693i	−0.657358	+	0.856686i	0.339102	+	0.940750i	$0.389877\pi$
$398$	0.0344482	+	0.206902i	0.00172673	+	0.0103711i
$399$	37.2011	−	11.4858i	1.86239	−	0.575008i
$400$	−1.68507	−	0.212541i	−0.0842533	−	0.0106271i
$401$	9.68077	+	16.7676i	0.483434	+	0.837333i	0.999819	−	0.0190238i	$-0.00605583\pi$
$401$	9.68077	+	16.7676i	0.483434	+	0.837333i	−0.516385	+	0.856357i	$0.672722\pi$
$402$	−19.5784	+	3.89201i	−0.976482	+	0.194116i
$403$	−3.42023	+	25.9792i	−0.170374	+	1.29412i
$404$	−7.04484	+	3.49794i	−0.350494	+	0.174029i
$405$	−20.2791	+	5.30578i	−1.00768	+	0.263646i
$406$	11.6888	+	10.7785i	0.580108	+	0.534929i
$407$	16.0138	−	16.0138i	0.793776	−	0.793776i
$408$	−3.58848	+	8.72741i	−0.177656	+	0.432071i
$409$	−0.406974	+	0.109048i	−0.0201235	+	0.00539209i	−0.268867	−	0.963177i	$-0.586649\pi$
$409$	−0.406974	+	0.109048i	−0.0201235	+	0.00539209i	0.248743	+	0.968569i	$0.419982\pi$
$410$	−18.6872	+	20.0065i	−0.922895	+	0.988050i
$411$	9.91528	−	8.11282i	0.489085	−	0.400176i
$412$	5.95118	+	2.91474i	0.293193	+	0.143599i
$413$	−18.5602	−	7.54878i	−0.913286	−	0.371451i
$414$	18.0112	−	9.59037i	0.885202	−	0.471341i
$415$	16.5855	−	9.57566i	0.814152	−	0.470051i
$416$	2.68106	−	29.2556i	0.131450	−	1.43437i
$417$	−0.148765	−	4.75886i	−0.00728506	−	0.233043i
$418$	48.4868	+	4.70909i	2.37157	+	0.230329i
$419$	12.0426	−	4.98822i	0.588321	−	0.243690i	−0.0686072	−	0.997644i	$-0.521856\pi$
$419$	12.0426	−	4.98822i	0.588321	−	0.243690i	0.656928	+	0.753953i	$0.271856\pi$
$420$	16.6041	+	13.4153i	0.810198	+	0.654599i
$421$	−8.52111	+	20.5718i	−0.415293	+	1.00261i	0.568400	+	0.822752i	$0.307563\pi$
$421$	−8.52111	+	20.5718i	−0.415293	+	1.00261i	−0.983693	+	0.179854i	$0.942437\pi$
$422$	−19.7003	+	6.00523i	−0.958995	+	0.292330i
$423$	3.72006	−	18.4180i	0.180876	−	0.895513i
$424$	2.05827	+	5.40185i	0.0999582	+	0.262337i
$425$	0.211680	−	0.790000i	0.0102680	−	0.0383206i
$426$	−9.14041	−	4.50888i	−0.442854	−	0.218456i
$427$	−34.5778	−	4.32684i	−1.67334	−	0.209391i
$428$	−0.623089	+	9.91907i	−0.0301181	+	0.479456i
$429$	−36.2895	−	3.62823i	−1.75207	−	0.175173i
$430$	20.9382	+	7.84813i	1.00973	+	0.378470i
$431$	−1.41899	−	0.819256i	−0.0683505	−	0.0394622i	0.465435	−	0.885082i	$-0.345898\pi$
$431$	−1.41899	−	0.819256i	−0.0683505	−	0.0394622i	−0.533786	+	0.845620i	$0.679231\pi$
$432$	−13.1694	+	16.0800i	−0.633615	+	0.773649i
$433$		−	13.8761i		−	0.666841i	−0.942778	−	0.333421i	$-0.891797\pi$
$433$		−	13.8761i		−	0.666841i	0.942778	−	0.333421i	$-0.108203\pi$
$434$	−18.8016	−	1.70438i	−0.902505	−	0.0818130i
$435$	10.0057	−	13.9195i	0.479734	−	0.667388i
$436$	−6.59075	−	2.21732i	−0.315640	−	0.106190i
$437$	24.8756	+	32.4185i	1.18996	+	1.55079i
$438$	−0.850060	−	1.27253i	−0.0406175	−	0.0608037i
$439$	−3.02370	+	11.2846i	−0.144313	+	0.538585i	0.855472	+	0.517850i	$0.173267\pi$
$439$	−3.02370	+	11.2846i	−0.144313	+	0.538585i	−0.999785	+	0.0207352i	$0.993399\pi$
$440$	12.6864	+	23.5038i	0.604800	+	1.12050i
$441$	−6.94632	−	19.8179i	−0.330777	−	0.943709i
$442$	13.7818	+	3.19374i	0.655532	+	0.151911i
$443$	3.17216	−	0.417622i	0.150714	−	0.0198418i	−0.0547917	−	0.998498i	$-0.517449\pi$
$443$	3.17216	−	0.417622i	0.150714	−	0.0198418i	0.205505	+	0.978656i	$0.434116\pi$
$444$	−18.1009	+	6.83835i	−0.859031	+	0.324534i
$445$	3.79102	−	28.7956i	0.179711	−	1.36504i
$446$	2.46970	−	25.4292i	0.116944	−	1.20411i
$447$	−5.57341	+	3.45438i	−0.263613	+	0.163387i
$448$	21.1386	+	1.07671i	0.998705	+	0.0508696i
$449$		−	13.6220i		−	0.642861i	−0.946933	−	0.321430i	$-0.895836\pi$
$449$		−	13.6220i		−	0.642861i	0.946933	−	0.321430i	$-0.104164\pi$
$450$	0.953717	−	1.52827i	0.0449587	−	0.0720435i
$451$	33.4100	+	4.39851i	1.57321	+	0.207118i
$452$	17.8822	+	3.50654i	0.841106	+	0.164934i
$453$	−4.10882	+	3.36190i	−0.193049	+	0.157956i
$454$	−0.537414	+	2.31907i	−0.0252221	+	0.108840i
$455$	15.8232	−	27.8170i	0.741801	−	1.30408i
$456$	−36.0997	−	20.7173i	−1.69052	−	0.970177i
$457$	17.2635	+	4.62575i	0.807554	+	0.216383i	0.638898	−	0.769292i	$-0.279391\pi$
$457$	17.2635	+	4.62575i	0.807554	+	0.216383i	0.168656	+	0.985675i	$0.446057\pi$
$458$	−13.0329	+	0.444366i	−0.608989	+	0.0207638i
$459$	−6.80954	−	7.33524i	−0.317842	−	0.342379i
$460$	−7.14384	+	21.2343i	−0.333083	+	0.990055i
$461$	−20.9809	+	8.69058i	−0.977179	+	0.404761i	−0.813380	−	0.581733i	$-0.802375\pi$
$461$	−20.9809	+	8.69058i	−0.977179	+	0.404761i	−0.163799	+	0.986494i	$0.552375\pi$
$462$	1.55339	−	26.2297i	0.0722703	−	1.22032i
$463$	−20.9139			−0.971953			−0.485977	−	0.873972i	$-0.661536\pi$
$463$	−20.9139			−0.971953			−0.485977	+	0.873972i	$0.661536\pi$
$464$	−0.0922964	−	16.9974i	−0.00428475	−	0.789085i
$465$	0.635972	+	20.3442i	0.0294925	+	0.943438i
$466$	7.09027	−	18.9162i	0.328450	−	0.876278i
$467$	−7.35877	+	9.59013i	−0.340523	+	0.443778i	−0.931954	−	0.362578i	$-0.881897\pi$
$467$	−7.35877	+	9.59013i	−0.340523	+	0.443778i	0.591430	+	0.806356i	$0.298563\pi$
$468$	26.9820	+	15.5865i	1.24724	+	0.720484i
$469$	−19.8663	+	8.37857i	−0.917342	+	0.386887i
$470$	10.9179	+	17.5044i	0.503605	+	0.807417i
$471$	4.57519	+	15.1628i	0.210814	+	0.698666i
$472$	7.62677	+	20.0162i	0.351050	+	0.921320i
$473$	−7.12380	−	26.5864i	−0.327552	−	1.22244i
$474$	−27.7706	−	24.3599i	−1.27555	−	1.11889i
$475$	3.33286	+	1.38052i	0.152922	+	0.0633425i
$476$	−1.89711	+	10.0143i	−0.0869540	+	0.459006i
$477$	−6.11702	−	0.419050i	−0.280079	−	0.0191870i
$478$	−0.264406	+	2.72244i	−0.0120936	+	0.124521i
$479$	4.38696	−	7.59844i	0.200445	−	0.347181i	−0.748227	−	0.663443i	$-0.769094\pi$
$479$	4.38696	−	7.59844i	0.200445	−	0.347181i	0.948672	+	0.316262i	$0.102428\pi$
$480$	−1.61348	−	22.7631i	−0.0736448	−	1.03899i
$481$	14.5044	+	25.1224i	0.661346	+	1.14548i
$482$	−9.06508	−	6.47734i	−0.412903	−	0.295035i
$483$	16.9681	−	14.0662i	0.772076	−	0.640034i
$484$	4.78416	−	9.76809i	0.217462	−	0.444004i
$485$	−0.806046	−	6.12253i	−0.0366007	−	0.278010i
$486$	−9.63134	−	19.8302i	−0.436886	−	0.899517i
$487$	−2.20693	−	8.23639i	−0.100006	−	0.373227i	0.897725	−	0.440556i	$-0.145219\pi$
$487$	−2.20693	−	8.23639i	−0.100006	−	0.373227i	−0.997731	+	0.0673297i	$0.978552\pi$
$488$	21.8225	+	30.1928i	0.987858	+	1.36676i
$489$	6.37949	−	27.1789i	0.288490	−	1.22907i
$490$	20.4863	+	10.5793i	0.925477	+	0.477926i
$491$	31.7996	+	13.1718i	1.43509	+	0.594436i	0.958604	−	0.284744i	$-0.0919086\pi$
$491$	31.7996	+	13.1718i	1.43509	+	0.594436i	0.476491	+	0.879179i	$0.341909\pi$
$492$	−24.4689	−	15.1737i	−1.10314	−	0.684082i
$493$	8.11515	+	1.06838i	0.365488	+	0.0481174i
$494$	−21.9010	+	58.4301i	−0.985374	+	2.62889i
$495$	−28.2739	+	1.76945i	−1.27082	+	0.0795309i
$496$	12.3729	+	15.9446i	0.555559	+	0.715935i
$497$	−10.6516	−	2.78099i	−0.477788	−	0.124744i
$498$	13.2784	+	15.1447i	0.595019	+	0.678649i
$499$	−22.6275	−	17.3627i	−1.01295	−	0.777262i	−0.0379052	−	0.999281i	$-0.512068\pi$
$499$	−22.6275	−	17.3627i	−1.01295	−	0.777262i	−0.975042	+	0.222019i	$0.928735\pi$
$500$	−4.21468	−	20.8920i	−0.188486	−	0.934320i
$501$	17.8138	+	6.73465i	0.795863	+	0.300882i
$502$	14.3551	−	26.9445i	0.640702	−	1.20259i
$503$	9.77404	−	9.77404i	0.435803	−	0.435803i	−0.454794	−	0.890597i	$-0.650287\pi$
$503$	9.77404	−	9.77404i	0.435803	−	0.435803i	0.890597	+	0.454794i	$0.150287\pi$
$504$	−10.4333	+	19.8783i	−0.464736	+	0.885449i
$505$	6.47683	+	6.47683i	0.288215	+	0.288215i
$506$	26.3790	−	8.04110i	1.17269	−	0.357470i
$507$	8.55742	−	22.6352i	0.380048	−	1.00527i
$508$	3.84461	−	19.6062i	0.170577	−	0.869885i
$509$	−17.2247	+	22.4476i	−0.763471	+	0.994974i	0.236258	+	0.971690i	$0.424079\pi$
$509$	−17.2247	+	22.4476i	−0.763471	+	0.994974i	−0.999729	+	0.0232839i	$0.992588\pi$
$510$	10.9654	+	0.719998i	0.485556	+	0.0318821i
$511$	−1.17629	−	1.16129i	−0.0520358	−	0.0513726i
$512$	−14.5673	−	17.3146i	−0.643790	−	0.765202i
$513$	35.9980	−	25.5556i	1.58935	−	1.12831i
$514$	38.1229	−	17.3357i	1.68153	−	0.764644i
$515$	1.00727	−	7.65095i	0.0443855	−	0.337141i
$516$	−3.80198	+	23.2073i	−0.167373	+	1.02165i
$517$	9.71791	−	23.4611i	0.427393	−	1.03182i
$518$	−17.6620	+	11.1742i	−0.776022	+	0.490965i
$519$	−29.8079	−	6.99658i	−1.30842	−	0.307116i
$520$	−33.2864	+	7.90437i	−1.45971	+	0.346630i
$521$	9.48468	−	2.54141i	0.415531	−	0.111341i	−0.0449953	−	0.998987i	$-0.514327\pi$
$521$	9.48468	−	2.54141i	0.415531	−	0.111341i	0.460527	+	0.887646i	$0.347661\pi$
$522$	16.4099	+	7.46672i	0.718241	+	0.326809i
$523$	−33.9358	+	4.46773i	−1.48391	+	0.195360i	−0.828531	−	0.559943i	$-0.810823\pi$
$523$	−33.9358	+	4.46773i	−1.48391	+	0.195360i	−0.655376	+	0.755303i	$0.727490\pi$
$524$	−22.3035	−	25.2934i	−0.974332	−	1.10495i
$525$	0.676399	−	1.82443i	0.0295205	−	0.0796247i
$526$	−38.6705	+	6.43846i	−1.68611	+	0.280730i
$527$	−8.41661	+	4.85933i	−0.366633	+	0.211676i
$528$	−21.6431	+	17.9058i	−0.941896	+	0.779250i
$529$	0.114430	+	0.0660663i	0.00497522	+	0.00287245i
$530$	5.19798	−	4.27770i	0.225786	−	0.185811i
$531$	−22.6662	−	1.55276i	−0.983629	−	0.0673841i
$532$	−42.7012	−	14.0617i	−1.85133	−	0.609654i
$533$	−16.5184	+	39.8790i	−0.715491	+	1.72735i
$534$	30.4805	−	1.99422i	1.31902	−	0.0862982i
$535$	11.1795	−	2.99555i	0.483334	−	0.129509i
$536$	21.0336	+	9.42713i	0.908512	+	0.407190i
$537$	−36.3722	+	10.9748i	−1.56957	+	0.473599i
$538$	1.36005	−	5.86893i	0.0586357	−	0.253028i
$539$	−4.06507	−	28.0884i	−0.175095	−	1.20985i
$540$	22.6385	+	8.56472i	0.974207	+	0.368567i
$541$	21.1535	+	16.2317i	0.909462	+	0.697854i	0.953570	−	0.301172i	$-0.0973779\pi$
$541$	21.1535	+	16.2317i	0.909462	+	0.697854i	−0.0441081	+	0.999027i	$0.514045\pi$
$542$	5.25296	+	11.5518i	0.225634	+	0.496192i
$543$	−5.06531	+	0.158345i	−0.217373	+	0.00679523i
$544$	9.21379	−	5.81659i	0.395038	−	0.249384i
$545$			8.09790i			0.346876i
$546$	31.9383	+	10.6178i	1.36683	+	0.454399i
$547$	11.8482	+	28.6041i	0.506592	+	1.22302i	0.945833	+	0.324652i	$0.105247\pi$
$547$	11.8482	+	28.6041i	0.506592	+	1.22302i	−0.439241	+	0.898369i	$0.644753\pi$
$548$	−14.7589	+	1.00760i	−0.630470	+	0.0430426i
$549$	−38.7767	+	7.59436i	−1.65495	+	0.324119i
$550$	1.66186	−	1.77919i	0.0708621	−	0.0758649i
$551$	−9.34423	+	34.8731i	−0.398078	+	1.48565i
$552$	−23.3684	−	3.01477i	−0.994625	−	0.128317i
$553$	−34.6821	−	19.7282i	−1.47483	−	0.838929i
$554$	−4.82270	+	3.00803i	−0.204897	+	0.127799i
$555$	14.2693	+	17.4396i	0.605698	+	0.740268i
$556$	−3.04196	+	4.57948i	−0.129008	+	0.194213i
$557$	−0.888613	+	6.74969i	−0.0376517	+	0.285993i	0.962253	+	0.272158i	$0.0877374\pi$
$557$	−0.888613	+	6.74969i	−0.0376517	+	0.285993i	−0.999904	+	0.0138353i	$0.995596\pi$
$558$	−20.8549	+	4.82770i	−0.882859	+	0.204373i
$559$	35.2562			1.49118
$560$	−6.66106	−	23.7315i	−0.281481	−	1.00284i
$561$	−7.12602	−	11.4973i	−0.300861	−	0.485418i
$562$	6.11956	−	5.03611i	0.258138	−	0.212436i
$563$	27.7450	+	3.65270i	1.16931	+	0.153943i	0.690072	−	0.723740i	$-0.257579\pi$
$563$	27.7450	+	3.65270i	1.16931	+	0.153943i	0.479241	+	0.877683i	$0.340912\pi$
$564$	−15.8173	+	14.8514i	−0.666027	+	0.625355i
$565$	−2.76990	−	21.0395i	−0.116531	−	0.885139i
$566$	−15.0725	+	9.40106i	−0.633543	+	0.395156i
$567$	−14.5054	−	18.8837i	−0.609170	−	0.793039i
$568$	5.58996	+	10.3564i	0.234549	+	0.434545i
$569$	7.69125	+	2.06086i	0.322434	+	0.0863959i	0.416406	−	0.909179i	$-0.363290\pi$
$569$	7.69125	+	2.06086i	0.322434	+	0.0863959i	−0.0939717	+	0.995575i	$0.529956\pi$
$570$	−9.46169	+	47.5381i	−0.396306	+	1.99115i
$571$	−12.9328	+	9.92367i	−0.541220	+	0.415293i	−0.842863	−	0.538128i	$-0.819132\pi$
$571$	−12.9328	+	9.92367i	−0.541220	+	0.415293i	0.301643	+	0.953421i	$0.402465\pi$
$572$	31.7370	+	27.6805i	1.32699	+	1.15738i
$573$	−13.1660	−	9.46404i	−0.550018	−	0.395366i
$574$	−29.1897	−	10.7280i	−1.21835	−	0.447779i
$575$	2.04217			0.0851644
$576$	23.1496	−	6.33203i	0.964568	−	0.263835i
$577$	0.981543	−	1.70008i	0.0408622	−	0.0707754i	−0.844871	−	0.534970i	$-0.820323\pi$
$577$	0.981543	−	1.70008i	0.0408622	−	0.0707754i	0.885733	+	0.464195i	$0.153656\pi$
$578$	−7.77990	−	17.1088i	−0.323601	−	0.711632i
$579$	−0.870728	+	8.70899i	−0.0361862	+	0.361933i
$580$	−18.7266	+	6.41358i	−0.777580	+	0.266309i
$581$	17.3442	+	13.1328i	0.719557	+	0.544840i
$582$	6.15019	−	2.08691i	0.254934	−	0.0865051i
$583$	−8.00402	−	2.14467i	−0.331493	−	0.0888232i
$584$	−0.0506242	+	1.76635i	−0.00209485	+	0.0730923i
$585$	7.18423	−	35.5691i	0.297032	−	1.47060i
$586$	19.2968	+	10.2807i	0.797144	+	0.424692i
$587$	19.4412	+	8.05282i	0.802425	+	0.332375i	0.745927	−	0.666027i	$-0.232007\pi$
$587$	19.4412	+	8.05282i	0.802425	+	0.332375i	0.0564979	+	0.998403i	$0.482007\pi$
$588$	−6.71192	+	23.3013i	−0.276795	+	0.960929i
$589$	−16.4046	−	39.6042i	−0.675939	−	1.63186i
$590$	19.2608	−	15.8507i	0.792954	−	0.652564i
$591$	4.13060	−	0.129125i	0.169910	−	0.00531150i
$592$	21.6127	+	5.66551i	0.888278	+	0.232851i
$593$	−3.78526	−	6.55626i	−0.155442	−	0.269233i	0.777778	−	0.628539i	$-0.216347\pi$
$593$	−3.78526	−	6.55626i	−0.155442	−	0.269233i	−0.933220	+	0.359306i	$0.883013\pi$
$594$	−7.62294	−	28.8021i	−0.312773	−	1.18177i
$595$	11.7578	−	1.62472i	0.482021	−	0.0666070i
$596$	7.55660	+	0.474685i	0.309531	+	0.0194439i
$597$	0.162676	+	0.198819i	0.00665790	+	0.00813711i
$598$	1.20370	+	35.3037i	0.0492231	+	1.44368i
$599$	−2.56384	−	9.56839i	−0.104756	−	0.390954i	0.893562	−	0.448941i	$-0.148199\pi$
$599$	−2.56384	−	9.56839i	−0.104756	−	0.390954i	−0.998317	+	0.0579867i	$0.981532\pi$
$600$	−1.91971	+	0.801020i	−0.0783719	+	0.0327015i
$601$	11.5645	+	11.5645i	0.471724	+	0.471724i	0.902472	−	0.430748i	$-0.141750\pi$
$601$	11.5645	+	11.5645i	0.471724	+	0.471724i	−0.430748	+	0.902472i	$0.641750\pi$
$602$	1.02835	+	25.3801i	0.0419124	+	1.03442i
$603$	−18.4282	+	16.0652i	−0.750456	+	0.654227i
$604$	6.11599	−	0.417543i	0.248856	−	0.0169896i
$605$	−12.5580	−	1.65330i	−0.510557	−	0.0672161i
$606$	−5.35284	+	8.00906i	−0.217444	+	0.325346i
$607$	12.2655	−	7.08150i	0.497842	−	0.287429i	−0.229980	−	0.973195i	$-0.573866\pi$
$607$	12.2655	−	7.08150i	0.497842	−	0.287429i	0.727822	+	0.685766i	$0.240533\pi$
$608$	20.1318	+	43.6414i	0.816452	+	1.76989i
$609$	18.9862	+	4.32820i	0.769359	+	0.175388i
$610$	25.2219	−	35.2982i	1.02120	−	1.42918i
$611$	25.8060	+	19.8016i	1.04400	+	0.801088i
$612$	1.50583	+	11.4586i	0.0608695	+	0.463187i
$613$	−8.10293	−	10.5599i	−0.327274	−	0.426512i	0.600517	−	0.799612i	$-0.294962\pi$
$613$	−8.10293	−	10.5599i	−0.327274	−	0.426512i	−0.927791	+	0.373100i	$0.878295\pi$
$614$	23.1080	−	7.04402i	0.932565	−	0.284273i
$615$	−7.66182	+	32.6420i	−0.308954	+	1.31625i
$616$	−19.0009	+	23.6541i	−0.765566	+	0.953051i
$617$	−4.69949	−	4.69949i	−0.189194	−	0.189194i	0.606153	−	0.795348i	$-0.292712\pi$
$617$	−4.69949	−	4.69949i	−0.189194	−	0.189194i	−0.795348	+	0.606153i	$0.792712\pi$
$618$	8.09861	−	0.529860i	0.325774	−	0.0213141i
$619$	5.84614	+	7.61884i	0.234976	+	0.306227i	0.895926	−	0.444203i	$-0.146513\pi$
$619$	5.84614	+	7.61884i	0.234976	+	0.306227i	−0.660950	+	0.750430i	$0.729846\pi$
$620$	13.0044	−	19.5773i	0.522270	−	0.786244i
$621$	13.2909	−	21.1641i	0.533344	−	0.849287i
$622$	6.28498	+	37.7487i	0.252005	+	1.51358i
$623$	31.8135	−	8.74345i	1.27458	−	0.350299i
$624$	−14.9790	−	32.7146i	−0.599642	−	1.30963i
$625$	−23.3331	+	13.4714i	−0.933324	+	0.538855i
$626$	6.72766	−	17.9488i	0.268891	−	0.717379i
$627$	54.3815	−	24.5434i	2.17179	−	0.980167i
$628$	5.83151	−	17.3335i	0.232703	−	0.691684i
$629$	−4.11737	+	9.94020i	−0.164170	+	0.396342i
$630$	25.8149	+	4.13428i	1.02849	+	0.164714i
$631$	22.2368	+	22.2368i	0.885233	+	0.885233i	0.994061	−	0.108827i	$-0.0347096\pi$
$631$	22.2368	+	22.2368i	0.885233	+	0.885233i	−0.108827	+	0.994061i	$0.534710\pi$
$632$	9.85513	+	41.5013i	0.392016	+	1.65083i
$633$	−17.2700	+	18.3846i	−0.686421	+	0.730722i
$634$	2.95098	−	3.15932i	0.117199	−	0.125473i
$635$	−23.0680	+	3.03696i	−0.915424	+	0.120518i
$636$	5.47839	+	4.48463i	0.217232	+	0.177827i
$637$	36.1005	+	4.28242i	1.43036	+	0.169676i
$638$	19.8246	+	14.1654i	0.784863	+	0.560814i
$639$	−12.4582	+	0.779667i	−0.492840	+	0.0308432i
$640$	−13.7016	+	22.5081i	−0.541603	+	0.889712i
$641$	−34.5947	−	19.9733i	−1.36641	−	0.788896i	−0.375941	−	0.926644i	$-0.622681\pi$
$641$	−34.5947	−	19.9733i	−1.36641	−	0.788896i	−0.990467	+	0.137747i	$0.956014\pi$
$642$	5.38238	+	10.9176i	0.212426	+	0.430884i
$643$	10.0940	+	24.3691i	0.398068	+	0.961022i	0.988124	+	0.153659i	$0.0491058\pi$
$643$	10.0940	+	24.3691i	0.398068	+	0.961022i	−0.590056	+	0.807363i	$0.700894\pi$
$644$	−25.3792	+	1.89625i	−1.00008	+	0.0747228i
$645$	27.0269	−	4.42123i	1.06418	−	0.174086i
$646$	−22.1380	+	6.74831i	−0.871006	+	0.265509i
$647$	16.4999	−	4.42113i	0.648678	−	0.173813i	0.0805469	−	0.996751i	$-0.474333\pi$
$647$	16.4999	−	4.42113i	0.648678	−	0.173813i	0.568131	+	0.822938i	$0.307667\pi$
$648$	−4.19248	+	25.1082i	−0.164696	+	0.986344i
$649$	−29.6584	−	7.94694i	−1.16419	−	0.311945i
$650$	1.65039	+	2.64602i	0.0647335	+	0.103786i
$651$	−21.0132	+	9.64633i	−0.823572	+	0.378069i
$652$	−24.1788	+	21.3207i	−0.946915	+	0.834981i
$653$	−7.29221	−	5.59551i	−0.285366	−	0.218969i	0.456152	−	0.889902i	$-0.349227\pi$
$653$	−7.29221	−	5.59551i	−0.285366	−	0.218969i	−0.741518	+	0.670933i	$0.765894\pi$
$654$	−8.35310	+	1.66052i	−0.326632	+	0.0649315i
$655$	−19.6355	+	34.0097i	−0.767223	+	1.32887i
$656$	12.8893	+	30.6457i	0.503241	+	1.19651i
$657$	−1.67853	−	0.833922i	−0.0654857	−	0.0325344i
$658$	−13.5020	+	19.1547i	−0.526363	+	0.746727i
$659$	13.7459	+	33.1854i	0.535463	+	1.29272i	0.927861	+	0.372926i	$0.121645\pi$
$659$	13.7459	+	33.1854i	0.535463	+	1.29272i	−0.392399	+	0.919795i	$0.628355\pi$
$660$	27.8003	+	17.2396i	1.08213	+	0.671049i
$661$	−12.0894	+	9.27655i	−0.470224	+	0.360816i	−0.816527	−	0.577307i	$-0.804104\pi$
$661$	−12.0894	+	9.27655i	−0.470224	+	0.360816i	0.346303	+	0.938123i	$0.387437\pi$
$662$	−33.4402	+	1.14016i	−1.29969	+	0.0443137i
$663$	16.5878	−	5.00515i	0.644216	−	0.194384i
$664$	−2.37386	−	23.1359i	−0.0921235	−	0.897845i
$665$	0.335763	+	52.3531i	0.0130203	+	2.03016i
$666$	−15.0632	+	18.2951i	−0.583686	+	0.708920i
$667$	2.66769	+	20.2631i	0.103293	+	0.784590i
$668$	−12.2669	−	18.2512i	−0.474620	−	0.706161i
$669$	−12.8719	−	28.5206i	−0.497656	−	1.10267i
$670$	2.59472	−	26.7164i	0.100243	−	1.03214i
$671$	−53.4013			−2.06154
$672$	23.1136	−	11.7373i	0.891625	−	0.452775i
$673$	−8.61483			−0.332077			−0.166039	−	0.986119i	$-0.553098\pi$
$673$	−8.61483			−0.332077			−0.166039	+	0.986119i	$0.553098\pi$
$674$	−0.821166	+	8.45508i	−0.0316301	+	0.325678i
$675$	0.0819417	−	2.20479i	0.00315394	−	0.0848623i
$676$	−23.1910	+	15.5870i	−0.891962	+	0.599499i
$677$	−4.85352	−	36.8661i	−0.186536	−	1.41688i	−0.786864	−	0.617127i	$-0.788297\pi$
$677$	−4.85352	−	36.8661i	−0.186536	−	1.41688i	0.600328	−	0.799754i	$-0.295037\pi$
$678$	21.1346	−	7.17147i	0.811669	−	0.275419i
$679$	6.05254	−	3.54638i	0.232275	−	0.136098i
$680$	−9.84144	−	8.00981i	−0.377402	−	0.307162i
$681$	0.842222	+	2.79124i	0.0322740	+	0.106961i
$682$	−28.9134	+	0.985821i	−1.10715	+	0.0377491i
$683$	−26.3403	+	20.2116i	−1.00788	+	0.773377i	−0.974115	−	0.226052i	$-0.927418\pi$
$683$	−26.3403	+	20.2116i	−1.00788	+	0.773377i	−0.0337698	+	0.999430i	$0.510751\pi$
$684$	−50.9764	−	0.0119236i	−1.94913	−	0.000455910i
$685$	6.59262	+	15.9160i	0.251891	+	0.608119i
$686$	−2.02984	+	26.1128i	−0.0774995	+	0.996992i
$687$	−13.5753	+	8.41392i	−0.517929	+	0.321011i
$688$	19.0968	−	19.3053i	0.728057	−	0.736007i
$689$	5.30707	−	9.19212i	0.202183	−	0.350192i
$690$	5.34993	+	26.9123i	0.203668	+	1.02454i
$691$	30.0855	+	23.0854i	1.14451	+	0.878211i	0.993889	−	0.110381i	$-0.0352072\pi$
$691$	30.0855	+	23.0854i	1.14451	+	0.878211i	0.150617	+	0.988592i	$0.451874\pi$
$692$	23.3830	+	26.5176i	0.888889	+	1.00805i
$693$	−14.3332	−	28.8128i	−0.544473	−	1.09451i
$694$	−13.6517	−	21.8874i	−0.518212	−	0.830835i
$695$	6.18419	+	1.65705i	0.234580	+	0.0628554i
$696$	−10.4557	−	18.0016i	−0.396323	−	0.682351i
$697$	−15.4640	+	4.14356i	−0.585740	+	0.156948i
$698$	−46.0541	+	14.0386i	−1.74317	+	0.531371i
$699$	−3.99429	−	24.4170i	−0.151078	−	0.923536i
$700$	−1.85667	+	1.26525i	−0.0701755	+	0.0478221i
$701$	5.23280	+	12.6331i	0.197640	+	0.477145i	0.991365	−	0.131132i	$-0.0418610\pi$
$701$	5.23280	+	12.6331i	0.197640	+	0.477145i	−0.793725	+	0.608277i	$0.791861\pi$
$702$	38.1632	+	0.117003i	1.44038	+	0.00441598i
$703$	−41.0988	−	23.7284i	−1.55007	−	0.894934i
$704$	32.3476	−	2.38492i	1.21915	−	0.0898852i
$705$	22.2657	+	11.9435i	0.838573	+	0.449818i
$706$	−3.26882	−	2.33569i	−0.123024	−	0.0879050i
$707$	−3.92009	+	9.63832i	−0.147430	+	0.362486i
$708$	20.2998	+	16.6175i	0.762913	+	0.624524i
$709$	37.9134	−	4.99139i	1.42387	−	0.187456i	0.621092	−	0.783737i	$-0.286689\pi$
$709$	37.9134	−	4.99139i	1.42387	−	0.187456i	0.802775	+	0.596282i	$0.203356\pi$
$710$	9.35513	−	10.0156i	0.351092	−	0.375878i
$711$	−44.3473	−	8.95726i	−1.66316	−	0.335924i
$712$	−30.0279	−	18.5034i	−1.12534	−	0.693444i
$713$	−17.1593	−	17.1593i	−0.642622	−	0.642622i
$714$	4.08692	+	11.7952i	0.152949	+	0.441423i
$715$	18.7674	−	45.3084i	0.701860	−	1.69444i
$716$	41.5792	+	13.9885i	1.55389	+	0.522773i
$717$	1.37806	+	3.05341i	0.0514646	+	0.114032i
$718$	8.94546	−	23.8657i	0.333842	−	0.890662i
$719$	9.11545	−	5.26281i	0.339949	−	0.196270i	−0.320301	−	0.947316i	$-0.603784\pi$
$719$	9.11545	−	5.26281i	0.339949	−	0.196270i	0.660249	+	0.751046i	$0.270451\pi$
$720$	−15.5852	−	23.2001i	−0.580826	−	0.864616i
$721$	8.45278	−	2.32312i	0.314798	−	0.0865175i
$722$	−12.3525	−	74.1911i	−0.459712	−	2.76111i
$723$	−13.5777	−	1.35751i	−0.504961	−	0.0504862i
$724$	4.87438	+	3.23785i	0.181155	+	0.120334i
$725$	1.09840	+	1.43146i	0.0407936	+	0.0531632i
$726$	−0.869697	−	13.2928i	−0.0322775	−	0.493343i
$727$	−3.51919	−	3.51919i	−0.130520	−	0.130520i	0.638829	−	0.769349i	$-0.279419\pi$
$727$	−3.51919	−	3.51919i	−0.130520	−	0.130520i	−0.769349	+	0.638829i	$0.779419\pi$
$728$	−22.9672	−	31.3511i	−0.851222	−	1.16195i
$729$	−22.3161	−	15.1984i	−0.826522	−	0.562904i
$730$	1.96841	−	0.600030i	0.0728542	−	0.0222081i
$731$	7.96034	+	10.3741i	0.294424	+	0.383701i
$732$	41.5825	+	18.7786i	1.53693	+	0.694079i
$733$	1.97892	+	1.51848i	0.0730932	+	0.0560864i	0.644662	−	0.764468i	$-0.276998\pi$
$733$	1.97892	+	1.51848i	0.0730932	+	0.0560864i	−0.571569	+	0.820554i	$0.693665\pi$
$734$	14.2254	−	19.9085i	0.525068	−	0.734836i
$735$	28.2111	−	1.24427i	1.04058	−	0.0458957i
$736$	19.9833	+	18.4634i	0.736594	+	0.680569i
$737$	−28.6139	+	16.5203i	−1.05401	+	0.608532i
$738$	−35.2419	−	1.20985i	−1.29727	−	0.0445350i
$739$	−11.3380	−	1.49268i	−0.417076	−	0.0549091i	−0.0809317	−	0.996720i	$-0.525790\pi$
$739$	−11.3380	−	1.49268i	−0.417076	−	0.0549091i	−0.336144	+	0.941811i	$0.609123\pi$
$740$	−1.77222	−	25.9588i	−0.0651483	−	0.954266i
$741$	12.3379	+	75.4213i	0.453244	+	2.77067i
$742$	6.77198	+	3.55232i	0.248607	+	0.130410i
$743$	−3.10266	−	3.10266i	−0.113825	−	0.113825i	0.647900	−	0.761725i	$-0.275647\pi$
$743$	−3.10266	−	3.10266i	−0.113825	−	0.113825i	−0.761725	+	0.647900i	$0.775647\pi$
$744$	22.8609	+	9.39980i	0.838123	+	0.344613i
$745$	−2.28209	−	8.51686i	−0.0836092	−	0.312034i
$746$	0.0594073	+	1.74237i	0.00217506	+	0.0637928i
$747$	23.3355	+	7.99815i	0.853801	+	0.292637i
$748$	−0.979225	+	15.5885i	−0.0358040	+	0.569971i
$749$	8.07046	+	10.3791i	0.294888	+	0.379245i
$750$	−17.2085	−	19.6272i	−0.628366	−	0.716684i
$751$	16.3523	+	28.3231i	0.596705	+	1.03352i	0.993304	+	0.115531i	$0.0368571\pi$
$751$	16.3523	+	28.3231i	0.596705	+	1.03352i	−0.396599	+	0.917992i	$0.629810\pi$
$752$	24.8208	−	3.40493i	0.905121	−	0.124165i
$753$	−1.16831	−	37.3731i	−0.0425755	−	1.36195i
$754$	−24.0988	+	19.8322i	−0.877626	+	0.722245i
$755$	−2.73194	−	6.59547i	−0.0994253	−	0.240034i
$756$	1.02891	+	27.4762i	0.0374212	+	0.999300i
$757$	−29.4880	−	12.2143i	−1.07176	−	0.443937i	−0.224148	−	0.974555i	$-0.571960\pi$
$757$	−29.4880	−	12.2143i	−1.07176	−	0.443937i	−0.847611	+	0.530618i	$0.821960\pi$
$758$	−22.9791	−	12.2425i	−0.834639	−	0.444668i
$759$	23.1248	−	24.6172i	0.839377	−	0.893549i
$760$	40.6936	−	38.4260i	1.47611	−	1.39386i
$761$	9.26807	+	2.48337i	0.335967	+	0.0900222i	0.422859	−	0.906196i	$-0.361027\pi$
$761$	9.26807	+	2.48337i	0.335967	+	0.0900222i	−0.0868914	+	0.996218i	$0.527693\pi$
$762$	−7.86288	−	23.1722i	−0.284842	−	0.839441i
$763$	−8.47595	+	3.57471i	−0.306850	+	0.129413i
$764$	6.06641	+	17.7129i	0.219475	+	0.640831i
$765$	12.0883	−	5.91702i	0.437052	−	0.213930i
$766$	−6.66500	−	14.6570i	−0.240816	−	0.529579i
$767$	19.6650	−	34.0608i	0.710062	−	1.22986i
$768$	−26.0271	−	9.51799i	−0.939171	−	0.343451i
$769$	−21.3033			−0.768217			−0.384108	−	0.923288i	$-0.625491\pi$
$769$	−21.3033			−0.768217			−0.384108	+	0.923288i	$0.625491\pi$
$770$	33.1639	+	12.1886i	1.19514	+	0.439248i
$771$	29.9376	−	41.6481i	1.07818	−	1.49992i
$772$	6.64296	−	7.61646i	0.239085	−	0.274123i
$773$	29.1847	−	22.3942i	1.04970	−	0.805464i	0.0683446	−	0.997662i	$-0.478228\pi$
$773$	29.1847	−	22.3942i	1.04970	−	0.805464i	0.981356	+	0.192198i	$0.0615616\pi$
$774$	10.1026	+	26.9720i	0.363130	+	0.969490i
$775$	−2.06936	−	0.554483i	−0.0743335	−	0.0199176i
$776$	−7.18523	−	2.14770i	−0.257935	−	0.0770979i
$777$	−11.9547	+	22.6339i	−0.428874	+	0.811988i
$778$	−42.0009	+	26.1970i	−1.50580	+	0.939206i
$779$	−9.21709	−	70.0108i	−0.330237	−	2.50840i
$780$	−30.5465	+	28.6811i	−1.09374	+	1.02695i
$781$	−16.7256	−	2.20197i	−0.598490	−	0.0787926i
$782$	−10.1163	+	8.32526i	−0.361759	+	0.297711i
$783$	21.9837	−	2.06706i	0.785632	−	0.0738706i
$784$	21.8990	−	17.4480i	0.782108	−	0.623143i
$785$	−21.2973			−0.760134
$786$	−39.1079	−	13.2805i	−1.39493	−	0.473698i
$787$	−3.63281	+	27.5939i	−0.129496	+	0.983617i	0.796116	+	0.605144i	$0.206884\pi$
$787$	−3.63281	+	27.5939i	−0.129496	+	0.983617i	−0.925612	+	0.378474i	$0.876449\pi$
$788$	−3.97490	−	2.64036i	−0.141600	−	0.0940590i
$789$	−37.1597	+	30.4046i	−1.32292	+	1.08243i
$790$	42.1475	−	26.2884i	1.49954	−	0.935300i
$791$	20.7990	−	12.1868i	0.739528	−	0.433314i
$792$	−12.0823	+	32.2115i	−0.429324	+	1.14459i
$793$	17.7039	−	66.0719i	0.628684	−	2.34628i
$794$	20.7698	−	22.2361i	0.737092	−	0.789130i
$795$	2.91560	−	7.71206i	0.103406	−	0.273519i
$796$	−0.0202042	−	0.295942i	−0.000716118	−	0.0104894i
$797$	−1.34818	−	3.25479i	−0.0477549	−	0.115290i	0.898202	−	0.439583i	$-0.144874\pi$
$797$	−1.34818	−	3.25479i	−0.0477549	−	0.115290i	−0.945957	+	0.324293i	$0.894874\pi$
$798$	−53.9341	+	11.0816i	−1.90925	+	0.392286i
$799$			12.0643i			0.426805i
$800$	2.34283	+	0.529530i	0.0828314	+	0.0187217i
$801$	31.1670	−	20.6924i	1.10123	−	0.731131i
$802$	−11.3343	−	24.9253i	−0.400229	−	0.880143i
$803$	−2.00959	−	1.54201i	−0.0709169	−	0.0544164i
$804$	28.0904	−	2.80186i	0.990673	−	0.0988138i
$805$	11.5171	+	27.3081i	0.405926	+	0.962485i
$806$	8.36581	−	36.1005i	0.294673	−	1.27159i
$807$	−2.13143	−	7.06386i	−0.0750299	−	0.248660i
$808$	10.3944	−	3.96059i	0.365675	−	0.139333i
$809$	10.3376	−	2.76995i	0.363451	−	0.0973864i	−0.0724719	−	0.997370i	$-0.523089\pi$
$809$	10.3376	−	2.76995i	0.363451	−	0.0973864i	0.435923	+	0.899984i	$0.356422\pi$
$810$	29.2700	−	4.69608i	1.02844	−	0.165003i
$811$	−1.28613	+	3.10499i	−0.0451621	+	0.109031i	−0.944851	−	0.327501i	$-0.893793\pi$
$811$	−1.28613	+	3.10499i	−0.0451621	+	0.109031i	0.899689	+	0.436532i	$0.143793\pi$
$812$	−14.9796	−	16.7697i	−0.525682	−	0.588500i
$813$	12.6200	+	9.07153i	0.442602	+	0.318152i
$814$	−24.7301	+	20.3517i	−0.866790	+	0.713328i
$815$	32.5111	+	18.7703i	1.13881	+	0.657494i
$816$	6.24420	−	11.7941i	0.218591	−	0.412875i
$817$	−49.9499	+	28.8386i	−1.74752	+	1.00893i
$818$	0.587760	−	0.0978594i	0.0205505	−	0.00342157i
$819$	40.4010	−	8.18187i	1.41173	−	0.285898i
$820$	29.0389	−	25.6063i	1.01408	−	0.894210i
$821$	24.4292	−	3.21617i	0.852585	−	0.112245i	0.308448	−	0.951241i	$-0.400190\pi$
$821$	24.4292	−	3.21617i	0.852585	−	0.112245i	0.544137	+	0.838996i	$0.316857\pi$
$822$	−15.0657	+	10.0641i	−0.525478	+	0.351024i
$823$	−9.27901	+	2.48630i	−0.323446	+	0.0866671i	−0.416889	−	0.908958i	$-0.636879\pi$
$823$	−9.27901	+	2.48630i	−0.323446	+	0.0866671i	0.0934427	+	0.995625i	$0.470213\pi$
$824$	−7.97836	−	4.91632i	−0.277939	−	0.171268i
$825$	0.681371	−	2.90288i	0.0237223	−	0.101065i
$826$	25.0931	+	13.1629i	0.873102	+	0.457995i
$827$	16.2871	−	39.3205i	0.566358	−	1.36731i	−0.338247	−	0.941057i	$-0.609834\pi$
$827$	16.2871	−	39.3205i	0.566358	−	1.36731i	0.904605	−	0.426251i	$-0.140166\pi$
$828$	−26.6635	+	11.0371i	−0.926619	+	0.383564i
$829$	2.21877	−	16.8532i	0.0770610	−	0.585336i	−0.908733	−	0.417378i	$-0.862949\pi$
$829$	2.21877	−	16.8532i	0.0770610	−	0.585336i	0.985794	−	0.167959i	$-0.0537175\pi$
$830$	−24.6547	+	11.2113i	−0.855777	+	0.389148i
$831$	−3.29059	+	6.13449i	−0.114149	+	0.212803i
$832$	−7.77326	+	40.8134i	−0.269489	+	1.41495i
$833$	6.89088	+	11.5895i	0.238755	+	0.401551i
$834$	−0.441167	+	6.71887i	−0.0152764	+	0.232655i
$835$	−15.5897	+	20.3169i	−0.539503	+	0.703094i
$836$	−67.6058	−	13.2569i	−2.33820	−	0.458501i
$837$	−19.2142	+	17.8372i	−0.664140	+	0.616543i
$838$	−17.6330	+	5.37507i	−0.609122	+	0.185679i
$839$	3.44668	+	3.44668i	0.118993	+	0.118993i	0.764096	−	0.645103i	$-0.223186\pi$
$839$	3.44668	+	3.44668i	0.118993	+	0.118993i	−0.645103	+	0.764096i	$0.723186\pi$
$840$	−21.5378	−	21.1531i	−0.743126	−	0.729852i
$841$	7.73749	−	7.73749i	0.266810	−	0.266810i
$842$	14.8065	−	27.7917i	0.510267	−	0.957767i
$843$	3.43252	−	9.07937i	0.118222	−	0.312710i
$844$	28.5509	−	5.75975i	0.982762	−	0.198259i
$845$	25.8157	+	19.8091i	0.888088	+	0.681454i
$846$	−7.75418	+	25.4164i	−0.266594	+	0.873835i
$847$	−3.81310	−	13.8742i	−0.131020	−	0.476721i
$848$	−2.15873	−	7.88497i	−0.0741310	−	0.270771i
$849$	−10.2841	+	19.1722i	−0.352951	+	0.657990i
$850$	−0.405957	+	1.08306i	−0.0139242	+	0.0371486i
$851$	−26.6353	−	3.50660i	−0.913046	−	0.120205i
$852$	12.2496	+	7.59621i	0.419663	+	0.260242i
$853$	−1.04361	−	0.432278i	−0.0357326	−	0.0148009i	0.364746	−	0.931107i	$-0.381156\pi$
$853$	−1.04361	−	0.432278i	−0.0357326	−	0.0148009i	−0.400478	+	0.916306i	$0.631156\pi$
$854$	48.0799	+	10.8174i	1.64526	+	0.370165i
$855$	18.9161	+	56.2696i	0.646916	+	1.92438i
$856$	2.23306	−	13.8768i	0.0763243	−	0.474299i
$857$	−0.523305	−	1.95300i	−0.0178758	−	0.0667133i	0.956412	−	0.292021i	$-0.0943278\pi$
$857$	−0.523305	−	1.95300i	−0.0178758	−	0.0667133i	−0.974288	+	0.225308i	$0.927661\pi$
$858$	50.5847	+	10.0681i	1.72693	+	0.343718i
$859$	−2.80206	−	21.2838i	−0.0956052	−	0.726193i	−0.970366	−	0.241639i	$-0.922315\pi$
$859$	−2.80206	−	21.2838i	−0.0956052	−	0.726193i	0.874761	−	0.484555i	$-0.161018\pi$
$860$	−28.3995	−	13.9093i	−0.968413	−	0.474304i
$861$	−37.5481	+	6.38988i	−1.27964	+	0.217767i
$862$	1.88536	+	1.34716i	0.0642157	+	0.0458845i
$863$	26.9085	+	46.6069i	0.915977	+	1.58652i	0.805465	+	0.592644i	$0.201916\pi$
$863$	26.9085	+	46.6069i	0.915977	+	1.58652i	0.110512	+	0.993875i	$0.464751\pi$
$864$	20.7354	−	20.8337i	0.705433	−	0.708776i
$865$	20.5859	−	35.6559i	0.699942	−	1.21234i
$866$	−1.89695	+	19.5318i	−0.0644609	+	0.663718i
$867$	−18.6908	−	13.4354i	−0.634773	−	0.456290i
$868$	26.2319	+	4.96937i	0.890370	+	0.168671i
$869$	−56.4903	−	23.3991i	−1.91630	−	0.793758i
$870$	−15.9867	+	18.2251i	−0.542002	+	0.617888i
$871$	−10.9538	−	40.8800i	−0.371155	−	1.38517i
$872$	8.97395	+	4.02208i	0.303896	+	0.136205i
$873$	5.26221	−	5.96483i	0.178099	−	0.201879i
$874$	−30.5828	−	49.0326i	−1.03448	−	1.65855i
$875$	−22.4777	−	17.0198i	−0.759884	−	0.575375i
$876$	1.02257	+	1.90741i	0.0345496	+	0.0644453i
$877$	2.87298	−	3.74415i	0.0970138	−	0.126431i	−0.742324	−	0.670041i	$-0.766276\pi$
$877$	2.87298	−	3.74415i	0.0970138	−	0.126431i	0.839338	+	0.543610i	$0.182943\pi$
$878$	5.79881	−	15.4707i	0.195700	−	0.522112i
$879$	26.7655	−	0.836706i	0.902777	−	0.0282214i
$880$	−14.6441	−	34.8181i	−0.493653	−	1.17372i
$881$	34.2699			1.15458			0.577291	−	0.816538i	$-0.304110\pi$
$881$	34.2699			1.15458			0.577291	+	0.816538i	$0.304110\pi$
$882$	7.06834	+	28.8451i	0.238003	+	0.971264i
$883$	38.6114	−	15.9934i	1.29938	−	0.538220i	0.377611	−	0.925964i	$-0.376746\pi$
$883$	38.6114	−	15.9934i	1.29938	−	0.538220i	0.921767	+	0.387744i	$0.126746\pi$
$884$	−18.9625	−	6.37954i	−0.637778	−	0.214567i
$885$	10.8036	−	28.5765i	0.363158	−	0.960589i
$886$	−4.52219	+	0.154187i	−0.151926	+	0.00518001i
$887$	−46.6683	−	12.5047i	−1.56697	−	0.419868i	−0.632106	−	0.774882i	$-0.717809\pi$
$887$	−46.6683	−	12.5047i	−1.56697	−	0.419868i	−0.934861	+	0.355014i	$0.884476\pi$
$888$	26.4135	−	7.15108i	0.886380	−	0.239975i
$889$	−13.3618	−	22.8043i	−0.448140	−	0.764831i
$890$	−9.27275	+	40.0142i	−0.310823	+	1.34128i
$891$	−25.6496	−	25.9539i	−0.859294	−	0.869490i
$892$	−6.95266	+	35.4562i	−0.232792	+	1.18716i
$893$	−52.7582	−	6.94575i	−1.76549	−	0.232431i
$894$	8.31732	−	4.10044i	0.278173	−	0.137139i
$895$		−	51.0874i		−	1.70766i
$896$	−29.6073	−	4.40535i	−0.989111	−	0.147172i
$897$	22.7917	+	36.7728i	0.760993	+	1.22781i
$898$	−1.86221	+	19.1742i	−0.0621428	+	0.639850i
$899$	2.79856	−	21.2572i	0.0933372	−	0.708966i
$900$	−1.55137	+	2.02080i	−0.0517123	+	0.0673601i
$901$	3.90304	−	0.513844i	0.130029	−	0.0171186i
$902$	−46.4263	−	10.7587i	−1.54583	−	0.358224i
$903$	16.5583	+	26.3369i	0.551025	+	0.876438i
$904$	−24.6914	−	7.38038i	−0.821223	−	0.245468i
$905$	1.76375	−	6.58241i	0.0586291	−	0.218807i
$906$	6.24313	−	4.17047i	0.207414	−	0.138555i
$907$	24.8713	+	32.4129i	0.825838	+	1.07625i	0.995868	+	0.0908147i	$0.0289471\pi$
$907$	24.8713	+	32.4129i	0.825838	+	1.07625i	−0.170029	+	0.985439i	$0.554386\pi$
$908$	1.07349	−	3.19084i	0.0356251	−	0.105892i
$909$	−0.806351	+	11.7706i	−0.0267450	+	0.390406i
$910$	−26.0753	+	36.9918i	−0.864387	+	1.22627i
$911$		−	31.2528i		−	1.03545i	−0.855547	−	0.517726i	$-0.826779\pi$
$911$		−	31.2528i		−	1.03545i	0.855547	−	0.517726i	$-0.173221\pi$
$912$	47.9814	+	34.0966i	1.58882	+	1.12905i
$913$	28.8719	+	16.6692i	0.955519	+	0.551669i
$914$	−23.6676	−	8.87120i	−0.782855	−	0.293433i
$915$	5.28594	−	52.8698i	0.174748	−	1.74782i
$916$	18.4058	+	1.15620i	0.608144	+	0.0382020i
$917$	−44.2653	−	5.53907i	−1.46177	−	0.182916i
$918$	8.58227	+	11.2559i	0.283257	+	0.371501i
$919$	−9.73866	+	36.3452i	−0.321249	+	1.19892i	0.596780	+	0.802405i	$0.296446\pi$
$919$	−9.73866	+	36.3452i	−0.321249	+	1.19892i	−0.918029	+	0.396513i	$0.870220\pi$
$920$	12.9585	−	28.9126i	0.427228	−	0.953221i
$921$	20.2574	−	21.5648i	0.667503	−	0.710583i
$922$	30.7206	−	9.36456i	1.01173	−	0.308405i
$923$	8.26940	−	19.9641i	0.272191	−	0.657126i
$924$	−5.77231	+	36.7084i	−0.189895	+	1.20762i
$925$	−2.19119	+	0.907622i	−0.0720460	+	0.0298424i
$926$	29.4383	+	2.85907i	0.967402	+	0.0939549i
$927$	8.28101	−	5.49794i	0.271984	−	0.180576i
$928$	−2.19374	+	23.9380i	−0.0720131	+	0.785804i
$929$	28.5710	−	16.4955i	0.937383	−	0.541198i	0.0482438	−	0.998836i	$-0.484638\pi$
$929$	28.5710	−	16.4955i	0.937383	−	0.541198i	0.889139	+	0.457637i	$0.151304\pi$
$930$	1.88599	−	28.7232i	0.0618441	−	0.941871i
$931$	−54.6490	+	23.4620i	−1.79105	+	0.768936i
$932$	−12.5662	+	25.6570i	−0.411619	+	0.840425i
$933$	29.6799	+	36.2740i	0.971675	+	1.18756i
$934$	11.6692	−	12.4930i	0.381827	−	0.408783i
$935$	17.5694	−	4.70770i	0.574580	−	0.153958i
$936$	−35.8488	−	25.6280i	−1.17175	−	0.837676i
$937$	9.53147	−	9.53147i	0.311380	−	0.311380i	−0.534064	−	0.845444i	$-0.679336\pi$
$937$	9.53147	−	9.53147i	0.311380	−	0.311380i	0.845444	+	0.534064i	$0.179336\pi$
$938$	29.1091	−	9.07774i	0.950445	−	0.296399i
$939$	−3.79001	−	23.1683i	−0.123682	−	0.756068i
$940$	−12.9750	−	26.1316i	−0.423197	−	0.852317i
$941$	4.08417	−	31.0223i	0.133140	−	1.01130i	−0.786238	−	0.617924i	$-0.787974\pi$
$941$	4.08417	−	31.0223i	0.133140	−	1.01130i	0.919378	−	0.393375i	$-0.128693\pi$
$942$	−4.36714	−	21.9685i	−0.142289	−	0.715773i
$943$	−19.9874	−	34.6192i	−0.650879	−	1.12736i
$944$	−7.99902	−	29.2172i	−0.260346	−	0.950940i
$945$	29.9448	−	11.3385i	0.974103	−	0.368841i
$946$	6.39286	+	38.3966i	0.207850	+	1.24838i
$947$	−21.5692	+	28.1095i	−0.700905	+	0.913437i	−0.999157	−	0.0410500i	$-0.986930\pi$
$947$	−21.5692	+	28.1095i	−0.700905	+	0.913437i	0.298252	+	0.954487i	$0.403596\pi$
$948$	35.7595	+	38.0852i	1.16141	+	1.23695i
$949$	2.57412	−	1.97519i	0.0835593	−	0.0641173i
$950$	−4.50258	−	2.39883i	−0.146083	−	0.0778282i
$951$	1.20991	−	5.15466i	0.0392342	−	0.167151i
$952$	4.03938	−	13.8367i	0.130917	−	0.448451i
$953$	−34.3393	+	34.3393i	−1.11236	+	1.11236i	−0.119527	+	0.992831i	$0.538138\pi$
$953$	−34.3393	+	34.3393i	−1.11236	+	1.11236i	−0.992831	+	0.119527i	$0.961862\pi$
$954$	8.55297	+	1.42609i	0.276913	+	0.0461713i
$955$	17.2980	−	13.2732i	0.559749	−	0.429511i
$956$	0.744350	−	3.79593i	0.0240740	−	0.122769i
$957$	29.6934	+	2.96875i	0.959851	+	0.0959662i
$958$	−7.21380	+	10.0958i	−0.233067	+	0.326179i
$959$	−13.7488	+	13.9263i	−0.443972	+	0.449704i
$960$	−0.840750	+	32.2617i	−0.0271351	+	1.04124i
$961$	−2.77128	−	4.79999i	−0.0893960	−	0.154838i
$962$	−16.9819	−	37.3449i	−0.547519	−	1.20405i
$963$	12.3710	+	8.31892i	0.398650	+	0.268073i
$964$	11.8744	+	10.3567i	0.382449	+	0.333567i
$965$	−10.8734	−	4.50392i	−0.350028	−	0.144986i
$966$	−25.8071	+	17.4798i	−0.830330	+	0.562403i
$967$	−4.71937	+	4.71937i	−0.151765	+	0.151765i	−0.778906	−	0.627141i	$-0.784225\pi$
$967$	−4.71937	+	4.71937i	−0.151765	+	0.151765i	0.627141	+	0.778906i	$0.284225\pi$
$968$	−8.06951	+	13.0955i	−0.259364	+	0.420904i
$969$	−19.4070	+	20.6595i	−0.623441	+	0.663677i
$970$	0.297593	+	8.72820i	0.00955515	+	0.280246i
$971$	2.93745	+	22.3121i	0.0942671	+	0.716030i	0.971681	+	0.236296i	$0.0759335\pi$
$971$	2.93745	+	22.3121i	0.0942671	+	0.716030i	−0.877414	+	0.479734i	$0.840733\pi$
$972$	10.8461	+	29.2295i	0.347888	+	0.937536i
$973$	0.995520	+	7.20438i	0.0319149	+	0.230962i
$974$	1.98049	+	11.8952i	0.0634591	+	0.381146i
$975$	3.36575	+	1.80542i	0.107790	+	0.0578196i
$976$	−26.5896	−	45.4824i	−0.851112	−	1.45586i
$977$	1.63024	−	2.82367i	0.0521561	−	0.0903371i	−0.838769	−	0.544488i	$-0.816724\pi$
$977$	1.63024	−	2.82367i	0.0521561	−	0.0903371i	0.890925	+	0.454151i	$0.150057\pi$
$978$	−12.6952	+	37.3846i	−0.405949	+	1.19543i
$979$	46.7110	−	19.3483i	1.49289	−	0.618375i
$980$	−27.3901	−	17.6920i	−0.874944	−	0.565150i
$981$	−7.86239	+	6.85422i	−0.251027	+	0.218838i
$982$	−42.9601	−	22.8877i	−1.37091	−	0.730377i
$983$	−13.4600	−	50.2333i	−0.429307	−	1.60219i	−0.754335	−	0.656490i	$-0.772040\pi$
$983$	−13.4600	−	50.2333i	−0.429307	−	1.60219i	0.325028	−	0.945704i	$-0.394626\pi$
$984$	32.3679	+	24.7034i	1.03185	+	0.787515i
$985$	−1.43828	+	5.36775i	−0.0458275	+	0.171031i
$986$	−11.2768	−	2.61324i	−0.359125	−	0.0832224i
$987$	−2.67219	+	28.5774i	−0.0850567	+	0.909629i
$988$	38.8155	−	79.2517i	1.23488	−	2.52133i
$989$	−19.8765	+	25.9036i	−0.632037	+	0.823687i
$990$	40.0400	+	1.37456i	1.27255	+	0.0436865i
$991$	14.1126	+	8.14791i	0.448301	+	0.258827i	0.707112	−	0.707101i	$-0.249997\pi$
$991$	14.1126	+	8.14791i	0.448301	+	0.258827i	−0.258811	+	0.965928i	$0.583331\pi$
$992$	−15.2362	−	24.1350i	−0.483750	−	0.766286i
$993$	−34.8318	+	21.5886i	−1.10535	+	0.685094i
$994$	14.6129	+	5.37063i	0.463492	+	0.170346i
$995$	−0.319144	+	0.132194i	−0.0101175	+	0.00419082i
$996$	−16.6202	−	23.1328i	−0.526630	−	0.732989i
$997$	3.07870	+	4.01224i	0.0975034	+	0.127069i	0.839557	−	0.543272i	$-0.182815\pi$
$997$	3.07870	+	4.01224i	0.0975034	+	0.127069i	−0.742054	+	0.670341i	$0.766148\pi$
$998$	29.4767	+	27.5329i	0.933069	+	0.871540i
$999$	−4.85456	+	28.6155i	−0.153591	+	0.905354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.ch.a.11.6	✓	992
3.2	odd	2	inner	672.2.ch.a.11.119	yes	992
7.2	even	3	inner	672.2.ch.a.107.78	yes	992
21.2	odd	6	inner	672.2.ch.a.107.47	yes	992
32.3	odd	8	inner	672.2.ch.a.515.47	yes	992
96.35	even	8	inner	672.2.ch.a.515.78	yes	992
224.163	odd	24	inner	672.2.ch.a.611.119	yes	992
672.611	even	24	inner	672.2.ch.a.611.6	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.ch.a.11.6	✓	992	1.1	even	1	trivial
672.2.ch.a.11.119	yes	992	3.2	odd	2	inner
672.2.ch.a.107.47	yes	992	21.2	odd	6	inner
672.2.ch.a.107.78	yes	992	7.2	even	3	inner
672.2.ch.a.515.47	yes	992	32.3	odd	8	inner
672.2.ch.a.515.78	yes	992	96.35	even	8	inner
672.2.ch.a.611.6	yes	992	672.611	even	24	inner
672.2.ch.a.611.119	yes	992	224.163	odd	24	inner

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.ch (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40759 - 0.136707i) q^{2} +(-1.57871 + 0.712503i) q^{3} +(1.96262 + 0.384854i) q^{4} +(-0.304006 - 2.30915i) q^{5} +(2.31959 - 0.787091i) q^{6} +(2.28276 - 1.33754i) q^{7} +(-2.70996 - 0.810020i) q^{8} +(1.98468 - 2.24968i) q^{9} +O(q^{10})\)	\(q+(-1.40759 - 0.136707i) q^{2} +(-1.57871 + 0.712503i) q^{3} +(1.96262 + 0.384854i) q^{4} +(-0.304006 - 2.30915i) q^{5} +(2.31959 - 0.787091i) q^{6} +(2.28276 - 1.33754i) q^{7} +(-2.70996 - 0.810020i) q^{8} +(1.98468 - 2.24968i) q^{9} +(0.112239 + 3.29190i) q^{10} +(3.21659 - 2.46818i) q^{11} +(-3.37263 + 0.790800i) q^{12} +(1.98742 + 4.79806i) q^{13} +(-3.39604 + 1.57065i) q^{14} +(2.12522 + 3.42889i) q^{15} +(3.70378 + 1.51064i) q^{16} +(-0.963095 + 1.66813i) q^{17} +(-3.10116 + 2.89531i) q^{18} +(-6.74038 - 5.17208i) q^{19} +(0.292037 - 4.64899i) q^{20} +(-2.65082 + 3.73807i) q^{21} +(-4.86506 + 3.03446i) q^{22} +(-4.64570 - 1.24481i) q^{23} +(4.85539 - 0.652062i) q^{24} +(-0.410136 + 0.109896i) q^{25} +(-2.14155 - 7.02539i) q^{26} +(-1.53034 + 4.96569i) q^{27} +(4.99495 - 1.74657i) q^{28} +(-1.62618 - 3.92595i) q^{29} +(-2.52268 - 5.11700i) q^{30} +(4.36956 + 2.52277i) q^{31} +(-5.00688 - 2.63270i) q^{32} +(-3.31950 + 6.18838i) q^{33} +(1.58369 - 2.21638i) q^{34} +(-3.78256 - 4.86461i) q^{35} +(4.76097 - 3.65146i) q^{36} +(5.53795 - 0.729086i) q^{37} +(8.78064 + 8.20162i) q^{38} +(-6.55620 - 6.15872i) q^{39} +(-1.04662 + 6.50395i) q^{40} +(5.87710 + 5.87710i) q^{41} +(4.24229 - 4.89929i) q^{42} +(2.59792 - 6.27193i) q^{43} +(7.26285 - 3.60619i) q^{44} +(-5.79820 - 3.89901i) q^{45} +(6.36908 + 2.38728i) q^{46} +(5.42418 - 3.13165i) q^{47} +(-6.92354 + 0.254073i) q^{48} +(3.42196 - 6.10657i) q^{49} +(0.592327 - 0.0986198i) q^{50} +(0.331906 - 3.31971i) q^{51} +(2.05401 + 10.1816i) q^{52} +(-1.24418 - 1.62144i) q^{53} +(2.83294 - 6.78045i) q^{54} +(-6.67726 - 6.67726i) q^{55} +(-7.26961 + 1.77561i) q^{56} +(14.3263 + 3.36269i) q^{57} +(1.75229 + 5.74844i) q^{58} +(-4.61022 - 6.00815i) q^{59} +(2.85138 + 7.54751i) q^{60} +(-10.4494 - 8.01807i) q^{61} +(-5.80568 - 4.14837i) q^{62} +(1.52150 - 7.79006i) q^{63} +(6.68774 + 4.39024i) q^{64} +(10.4753 - 6.04789i) q^{65} +(5.51849 - 8.25691i) q^{66} +(-8.07953 - 1.06369i) q^{67} +(-2.53218 + 2.90326i) q^{68} +(8.22117 - 1.34487i) q^{69} +(4.65927 + 7.36448i) q^{70} +(-2.94218 - 2.94218i) q^{71} +(-7.20068 + 4.48890i) q^{72} +(-0.161699 - 0.603469i) q^{73} +(-7.89484 + 0.269180i) q^{74} +(0.569187 - 0.465717i) q^{75} +(-11.2383 - 12.7449i) q^{76} +(4.04140 - 9.93658i) q^{77} +(8.38651 + 9.56523i) q^{78} +(-7.54048 - 13.0605i) q^{79} +(2.36234 - 9.01183i) q^{80} +(-1.12209 - 8.92978i) q^{81} +(-7.46912 - 9.07599i) q^{82} +(3.14669 + 7.59679i) q^{83} +(-6.64117 + 6.31624i) q^{84} +(4.14475 + 1.71681i) q^{85} +(-4.51422 + 8.47315i) q^{86} +(5.36453 + 5.03929i) q^{87} +(-10.7161 + 4.08316i) q^{88} +(12.0453 + 3.22753i) q^{89} +(7.62847 + 6.28087i) q^{90} +(10.9544 + 8.29454i) q^{91} +(-8.63869 - 4.23101i) q^{92} +(-8.69577 - 0.869407i) q^{93} +(-8.06315 + 3.66657i) q^{94} +(-9.89400 + 17.1369i) q^{95} +(9.78025 + 0.588863i) q^{96} +2.65142 q^{97} +(-5.65152 + 8.12775i) q^{98} +(0.831305 - 12.1348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9	\( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} + 24 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 44 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} - 36 q^{30} - 8 q^{33} + 64 q^{36} - 8 q^{37} - 4 q^{39} - 72 q^{40} - 68 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 20 q^{51} + 16 q^{52} - 92 q^{54} - 32 q^{55} - 16 q^{57} + 24 q^{58} - 20 q^{60} - 8 q^{61} - 128 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 16 q^{75} - 32 q^{76} + 136 q^{78} - 16 q^{79} - 48 q^{82} + 124 q^{84} + 48 q^{85} - 4 q^{87} - 8 q^{88} + 128 q^{90} - 64 q^{91} - 28 q^{93} - 64 q^{94} - 72 q^{96} - 64 q^{97} - 16 q^{99}+O(q^{100}) \) 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 - 32 * q^13 - 32 * q^15 + 24 * q^16 - 4 * q^18 - 8 * q^19 - 8 * q^21 - 32 * q^22 - 44 * q^24 - 8 * q^25 - 16 * q^27 - 16 * q^28 - 36 * q^30 - 8 * q^33 + 64 * q^36 - 8 * q^37 - 4 * q^39 - 72 * q^40 - 68 * q^42 - 32 * q^43 - 4 * q^45 - 8 * q^46 - 16 * q^48 + 20 * q^51 + 16 * q^52 - 92 * q^54 - 32 * q^55 - 16 * q^57 + 24 * q^58 - 20 * q^60 - 8 * q^61 - 128 * q^64 - 20 * q^66 - 72 * q^67 - 16 * q^69 - 16 * q^70 - 4 * q^72 - 8 * q^73 + 16 * q^75 - 32 * q^76 + 136 * q^78 - 16 * q^79 - 48 * q^82 + 124 * q^84 + 48 * q^85 - 4 * q^87 - 8 * q^88 + 128 * q^90 - 64 * q^91 - 28 * q^93 - 64 * q^94 - 72 * q^96 - 64 * q^97 - 16 * q^99

Introduction

L-functions

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