LMFDB - Embedded newform 770.2.bv.a.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			157.3
Character	$\chi$	$=$	770.157
Dual form			770.2.bv.a.103.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.358368 - 0.933580i) q^{2} +(-1.59018 - 2.44866i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(-1.02331 - 1.98817i) q^{5} +(-1.71615 + 2.36208i) q^{6} +(1.81969 - 1.92060i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.24705 + 5.04696i) q^{9} +O(q^{10})$	\(q+(-0.358368 - 0.933580i) q^{2} +(-1.59018 - 2.44866i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(-1.02331 - 1.98817i) q^{5} +(-1.71615 + 2.36208i) q^{6} +(1.81969 - 1.92060i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.24705 + 5.04696i) q^{9} +(-1.48940 + 1.66784i) q^{10} +(0.393609 + 3.29319i) q^{11} +(2.82020 + 0.755671i) q^{12} +(-4.47689 - 0.709069i) q^{13} +(-2.44516 - 1.01055i) q^{14} +(-3.24110 + 5.66729i) q^{15} +(0.104528 - 0.994522i) q^{16} +(0.807961 - 2.10481i) q^{17} +(5.51701 + 0.289134i) q^{18} +(-4.51411 + 5.01343i) q^{19} +(2.09082 + 0.792769i) q^{20} +(-7.59653 - 1.40170i) q^{21} +(2.93340 - 1.54764i) q^{22} +(-7.51078 - 2.01251i) q^{23} +(-0.305191 - 2.90369i) q^{24} +(-2.90566 + 4.06905i) q^{25} +(0.942399 + 4.43364i) q^{26} +(7.28026 - 1.15308i) q^{27} +(-0.0671596 + 2.64490i) q^{28} +(3.24139 + 1.05319i) q^{29} +(6.45238 + 0.994854i) q^{30} +(8.33577 - 0.876124i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(7.43798 - 6.20056i) q^{33} -2.25456 q^{34} +(-5.68061 - 1.65248i) q^{35} +(-1.70719 - 5.25419i) q^{36} +(3.54622 + 2.30294i) q^{37} +(6.29816 + 2.41764i) q^{38} +(5.38277 + 12.0899i) q^{39} +(-0.00916828 - 2.23605i) q^{40} +(0.464558 - 0.150944i) q^{41} +(1.41375 + 7.59430i) q^{42} +(0.127467 - 0.127467i) q^{43} +(-2.49608 - 2.18394i) q^{44} +(12.3337 - 0.697100i) q^{45} +(0.812786 + 7.73314i) q^{46} +(-0.353706 - 6.74911i) q^{47} +(-2.60146 + 1.32551i) q^{48} +(-0.377442 - 6.98982i) q^{49} +(4.84008 + 1.25445i) q^{50} +(-6.43876 + 1.36860i) q^{51} +(3.80143 - 2.46868i) q^{52} +(5.87175 + 4.75485i) q^{53} +(-3.68550 - 6.38348i) q^{54} +(6.14463 - 4.15253i) q^{55} +(2.49329 - 0.885148i) q^{56} +(19.4544 + 3.08128i) q^{57} +(-0.178371 - 3.40353i) q^{58} +(-5.40046 - 5.99781i) q^{59} +(-1.38355 - 6.38034i) q^{60} +(-7.24930 - 0.761932i) q^{61} +(-3.80520 - 7.46813i) q^{62} +(5.60427 + 13.4996i) q^{63} +(0.587785 + 0.809017i) q^{64} +(3.17151 + 9.62642i) q^{65} +(-8.45425 - 4.72187i) q^{66} +(-14.5861 + 3.90833i) q^{67} +(0.807961 + 2.10481i) q^{68} +(7.01553 + 21.5916i) q^{69} +(0.493025 + 5.89550i) q^{70} +(-5.22971 - 3.79961i) q^{71} +(-4.29341 + 3.47673i) q^{72} +(-0.497643 + 9.49559i) q^{73} +(0.879130 - 4.13598i) q^{74} +(14.5842 + 0.644450i) q^{75} -6.74624i q^{76} +(7.04115 + 5.23662i) q^{77} +(9.35789 - 9.35789i) q^{78} +(2.00922 - 4.51279i) q^{79} +(-2.08425 + 0.809888i) q^{80} +(-3.31038 - 3.67655i) q^{81} +(-0.307401 - 0.379609i) q^{82} +(0.126872 + 0.801041i) q^{83} +(6.58325 - 4.04141i) q^{84} +(-5.01153 + 0.547517i) q^{85} +(-0.164681 - 0.0733207i) q^{86} +(-2.57548 - 9.61181i) q^{87} +(-1.14437 + 3.11294i) q^{88} +(-6.87367 - 11.9056i) q^{89} +(-5.07079 - 11.2646i) q^{90} +(-9.50839 + 7.30804i) q^{91} +(6.92823 - 3.53011i) q^{92} +(-15.4007 - 19.0182i) q^{93} +(-6.17408 + 2.74888i) q^{94} +(14.5869 + 3.84452i) q^{95} +(2.16975 + 1.95365i) q^{96} +(-1.62753 + 10.2758i) q^{97} +(-6.39029 + 2.85730i) q^{98} +(-17.5050 - 5.41343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.358368	−	0.933580i	−0.253404	−	0.660141i
$2$	−0.358368	−	0.933580i	−0.253404	−	0.660141i
$3$	−1.59018	−	2.44866i	−0.918089	−	1.41373i	−0.910385	−	0.413763i	$-0.864214\pi$
$3$	−1.59018	−	2.44866i	−0.918089	−	1.41373i	−0.00770421	−	0.999970i	$-0.502452\pi$
$4$	−0.743145	+	0.669131i	−0.371572	+	0.334565i
$5$	−1.02331	−	1.98817i	−0.457640	−	0.889138i
$5$	−1.02331	−	1.98817i	−0.457640	−	0.889138i
$6$	−1.71615	+	2.36208i	−0.700615	+	0.964314i
$7$	1.81969	−	1.92060i	0.687779	−	0.725920i
$7$	1.81969	−	1.92060i	0.687779	−	0.725920i
$8$	0.891007	+	0.453990i	0.315018	+	0.160510i
$9$	−2.24705	+	5.04696i	−0.749017	+	1.68232i
$10$	−1.48940	+	1.66784i	−0.470988	+	0.527418i
$11$	0.393609	+	3.29319i	0.118678	+	0.992933i
$11$	0.393609	+	3.29319i	0.118678	+	0.992933i
$12$	2.82020	+	0.755671i	0.814123	+	0.218143i
$13$	−4.47689	−	0.709069i	−1.24166	−	0.196660i	−0.499165	−	0.866507i	$-0.666360\pi$
$13$	−4.47689	−	0.709069i	−1.24166	−	0.196660i	−0.742500	+	0.669847i	$0.766360\pi$
$14$	−2.44516	−	1.01055i	−0.653496	−	0.270080i
$15$	−3.24110	+	5.66729i	−0.836849	+	1.46329i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	0.807961	−	2.10481i	0.195959	−	0.510492i	−0.800030	−	0.599960i	$-0.795183\pi$
$17$	0.807961	−	2.10481i	0.195959	−	0.510492i	0.995990	+	0.0894678i	$0.0285166\pi$
$18$	5.51701	+	0.289134i	1.30037	+	0.0681496i
$19$	−4.51411	+	5.01343i	−1.03561	+	1.15016i	−0.0471165	+	0.998889i	$0.515003\pi$
$19$	−4.51411	+	5.01343i	−1.03561	+	1.15016i	−0.988492	+	0.151271i	$0.951663\pi$
$20$	2.09082	+	0.792769i	0.467521	+	0.177269i
$21$	−7.59653	−	1.40170i	−1.65770	−	0.305876i
$22$	2.93340	−	1.54764i	0.625402	−	0.329957i
$23$	−7.51078	−	2.01251i	−1.56611	−	0.419637i	−0.631516	−	0.775363i	$-0.717567\pi$
$23$	−7.51078	−	2.01251i	−1.56611	−	0.419637i	−0.934590	+	0.355726i	$0.884234\pi$
$24$	−0.305191	−	2.90369i	−0.0622968	−	0.592714i
$25$	−2.90566	+	4.06905i	−0.581131	+	0.813810i
$26$	0.942399	+	4.43364i	0.184820	+	0.869508i
$27$	7.28026	−	1.15308i	1.40109	−	0.221910i
$28$	−0.0671596	+	2.64490i	−0.0126920	+	0.499839i
$29$	3.24139	+	1.05319i	0.601911	+	0.195573i	0.594092	−	0.804397i	$-0.297511\pi$
$29$	3.24139	+	1.05319i	0.601911	+	0.195573i	0.00781827	+	0.999969i	$0.497511\pi$
$30$	6.45238	+	0.994854i	1.17804	+	0.181635i
$31$	8.33577	−	0.876124i	1.49715	−	0.157357i	0.679756	−	0.733439i	$-0.262086\pi$
$31$	8.33577	−	0.876124i	1.49715	−	0.157357i	0.817392	+	0.576082i	$0.195419\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	7.43798	−	6.20056i	1.29479	−	1.07938i
$34$	−2.25456			−0.386654
$35$	−5.68061	−	1.65248i	−0.960198	−	0.279320i
$36$	−1.70719	−	5.25419i	−0.284532	−	0.875699i
$37$	3.54622	+	2.30294i	0.582995	+	0.378601i	0.802180	−	0.597082i	$-0.203673\pi$
$37$	3.54622	+	2.30294i	0.582995	+	0.378601i	−0.219185	+	0.975683i	$0.570340\pi$
$38$	6.29816	+	2.41764i	1.02170	+	0.392192i
$39$	5.38277	+	12.0899i	0.861933	+	1.93593i
$40$	−0.00916828	−	2.23605i	−0.00144963	−	0.353550i
$41$	0.464558	−	0.150944i	0.0725518	−	0.0235735i	−0.272516	−	0.962151i	$-0.587856\pi$
$41$	0.464558	−	0.150944i	0.0725518	−	0.0235735i	0.345068	+	0.938578i	$0.387856\pi$
$42$	1.41375	+	7.59430i	0.218147	+	1.17183i
$43$	0.127467	−	0.127467i	0.0194386	−	0.0194386i	−0.697321	−	0.716759i	$-0.745625\pi$
$43$	0.127467	−	0.127467i	0.0194386	−	0.0194386i	0.716759	+	0.697321i	$0.245625\pi$
$44$	−2.49608	−	2.18394i	−0.376298	−	0.329241i
$45$	12.3337	−	0.697100i	1.83859	−	0.103918i
$46$	0.812786	+	7.73314i	0.119839	+	1.14019i
$47$	−0.353706	−	6.74911i	−0.0515933	−	0.984460i	−0.894687	−	0.446693i	$-0.852602\pi$
$47$	−0.353706	−	6.74911i	−0.0515933	−	0.984460i	0.843094	−	0.537766i	$-0.180732\pi$
$48$	−2.60146	+	1.32551i	−0.375489	+	0.191321i
$49$	−0.377442	−	6.98982i	−0.0539203	−	0.998545i
$50$	4.84008	+	1.25445i	0.684490	+	0.177406i
$51$	−6.43876	+	1.36860i	−0.901607	+	0.191643i
$52$	3.80143	−	2.46868i	0.527164	−	0.342344i
$53$	5.87175	+	4.75485i	0.806547	+	0.653129i	0.941232	−	0.337760i	$-0.109669\pi$
$53$	5.87175	+	4.75485i	0.806547	+	0.653129i	−0.134686	+	0.990888i	$0.543002\pi$
$54$	−3.68550	−	6.38348i	−0.501533	−	0.868681i
$55$	6.14463	−	4.15253i	0.828542	−	0.559926i
$56$	2.49329	−	0.885148i	0.333180	−	0.118283i
$57$	19.4544	+	3.08128i	2.57680	+	0.408125i
$58$	−0.178371	−	3.40353i	−0.0234213	−	0.446905i
$59$	−5.40046	−	5.99781i	−0.703079	−	0.780849i	0.280784	−	0.959771i	$-0.409406\pi$
$59$	−5.40046	−	5.99781i	−0.703079	−	0.780849i	−0.983863	+	0.178922i	$0.942739\pi$
$60$	−1.38355	−	6.38034i	−0.178615	−	0.823698i
$61$	−7.24930	−	0.761932i	−0.928178	−	0.0975554i	−0.371639	−	0.928377i	$-0.621204\pi$
$61$	−7.24930	−	0.761932i	−0.928178	−	0.0975554i	−0.556539	+	0.830822i	$0.687871\pi$
$62$	−3.80520	−	7.46813i	−0.483261	−	0.948454i
$63$	5.60427	+	13.4996i	0.706072	+	1.70079i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	3.17151	+	9.62642i	0.393377	+	1.19401i
$66$	−8.45425	−	4.72187i	−1.04065	−	0.581222i
$67$	−14.5861	+	3.90833i	−1.78197	+	0.477478i	−0.990941	−	0.134296i	$-0.957123\pi$
$67$	−14.5861	+	3.90833i	−1.78197	+	0.477478i	−0.791032	+	0.611775i	$0.790456\pi$
$68$	0.807961	+	2.10481i	0.0979797	+	0.255246i
$69$	7.01553	+	21.5916i	0.844570	+	2.59932i
$70$	0.493025	+	5.89550i	0.0589278	+	0.704647i
$71$	−5.22971	−	3.79961i	−0.620653	−	0.450930i	0.232497	−	0.972597i	$-0.425310\pi$
$71$	−5.22971	−	3.79961i	−0.620653	−	0.450930i	−0.853149	+	0.521667i	$0.825310\pi$
$72$	−4.29341	+	3.47673i	−0.505983	+	0.409737i
$73$	−0.497643	+	9.49559i	−0.0582447	+	1.11137i	0.800620	+	0.599172i	$0.204504\pi$
$73$	−0.497643	+	9.49559i	−0.0582447	+	1.11137i	−0.858865	+	0.512202i	$0.828830\pi$
$74$	0.879130	−	4.13598i	0.102197	−	0.480798i
$75$	14.5842	+	0.644450i	1.68404	+	0.0744147i
$76$		−	6.74624i		−	0.773847i
$77$	7.04115	+	5.23662i	0.802414	+	0.596768i
$78$	9.35789	−	9.35789i	1.05957	−	1.05957i
$79$	2.00922	−	4.51279i	0.226055	−	0.507728i	−0.764536	−	0.644581i	$-0.777032\pi$
$79$	2.00922	−	4.51279i	0.226055	−	0.507728i	0.990591	+	0.136853i	$0.0436986\pi$
$80$	−2.08425	+	0.809888i	−0.233026	+	0.0905482i
$81$	−3.31038	−	3.67655i	−0.367820	−	0.408506i
$82$	−0.307401	−	0.379609i	−0.0339468	−	0.0419208i
$83$	0.126872	+	0.801041i	0.0139261	+	0.0879256i	0.993672	−	0.112317i	$-0.0358271\pi$
$83$	0.126872	+	0.801041i	0.0139261	+	0.0879256i	−0.979746	+	0.200242i	$0.935827\pi$
$84$	6.58325	−	4.04141i	0.718291	−	0.440954i
$85$	−5.01153	+	0.547517i	−0.543576	+	0.0593865i
$86$	−0.164681	−	0.0733207i	−0.0177580	−	0.00790638i
$87$	−2.57548	−	9.61181i	−0.276120	−	1.03049i
$88$	−1.14437	+	3.11294i	−0.121990	+	0.331841i
$89$	−6.87367	−	11.9056i	−0.728608	−	1.26199i	−0.957472	−	0.288527i	$-0.906834\pi$
$89$	−6.87367	−	11.9056i	−0.728608	−	1.26199i	0.228864	−	0.973458i	$-0.426499\pi$
$90$	−5.07079	−	11.2646i	−0.534508	−	1.18740i
$91$	−9.50839	+	7.30804i	−0.996751	+	0.766091i
$92$	6.92823	−	3.53011i	0.722318	−	0.368039i
$93$	−15.4007	−	19.0182i	−1.59697	−	1.97210i
$94$	−6.17408	+	2.74888i	−0.636808	+	0.283525i
$95$	14.5869	+	3.84452i	1.49659	+	0.394440i
$96$	2.16975	+	1.95365i	0.221449	+	0.199394i
$97$	−1.62753	+	10.2758i	−0.165251	+	1.04335i	0.756054	+	0.654510i	$0.227125\pi$
$97$	−1.62753	+	10.2758i	−0.165251	+	1.04335i	−0.921304	+	0.388842i	$0.872875\pi$
$98$	−6.39029	+	2.85730i	−0.645517	+	0.288631i
$99$	−17.5050	−	5.41343i	−1.75932	−	0.544070i
$100$	−0.563402	−	4.96816i	−0.0563402	−	0.496816i
$101$	17.3443	−	1.82296i	1.72582	−	0.181391i	0.810946	−	0.585121i	$-0.198953\pi$
$101$	17.3443	−	1.82296i	1.72582	−	0.181391i	0.914878	+	0.403730i	$0.132287\pi$
$102$	3.58515	+	5.52064i	0.354982	+	0.546625i
$103$	−4.67362	−	3.03509i	−0.460506	−	0.299056i	0.293458	−	0.955972i	$-0.405194\pi$
$103$	−4.67362	−	3.03509i	−0.460506	−	0.299056i	−0.753964	+	0.656916i	$0.771861\pi$
$104$	−3.66702	−	2.66425i	−0.359581	−	0.261251i
$105$	4.98682	+	16.5376i	0.486663	+	1.61390i
$106$	2.33479	−	7.18573i	0.226775	−	0.697940i
$107$	−5.39562	+	0.282773i	−0.521615	+	0.0273367i	−0.311327	−	0.950303i	$-0.600773\pi$
$107$	−5.39562	+	0.282773i	−0.521615	+	0.0273367i	−0.210288	+	0.977640i	$0.567440\pi$
$108$	−4.63872	+	5.72835i	−0.446361	+	0.551210i
$109$	5.20184	+	3.00328i	0.498246	+	0.287662i	0.727989	−	0.685589i	$-0.240455\pi$
$109$	5.20184	+	3.00328i	0.498246	+	0.287662i	−0.229743	+	0.973251i	$0.573789\pi$
$110$	−6.07876	−	4.24838i	−0.579587	−	0.405067i
$111$		−	12.3456i		−	1.17179i
$112$	−1.71987	−	2.01048i	−0.162513	−	0.189973i
$113$	−11.9109	−	6.06889i	−1.12048	−	0.570913i	−0.207221	−	0.978294i	$-0.566442\pi$
$113$	−11.9109	−	6.06889i	−1.12048	−	0.570913i	−0.913258	+	0.407381i	$0.866442\pi$
$114$	−4.09522	−	19.2665i	−0.383552	−	1.80447i
$115$	3.68468	+	16.9922i	0.343598	+	1.58453i
$116$	−3.11354	+	1.38624i	−0.289085	+	0.128709i
$117$	13.6384	−	21.0013i	1.26087	−	1.94158i
$118$	−3.66409	+	7.19118i	−0.337307	+	0.662002i
$119$	−2.57227	−	5.38188i	−0.235800	−	0.493356i
$120$	−5.46074	+	3.57816i	−0.498495	+	0.326640i
$121$	−10.6901	+	2.59245i	−0.971831	+	0.235678i
$122$	1.88659	+	7.04086i	0.170804	+	0.637449i
$123$	−1.10834	−	0.897516i	−0.0999357	−	0.0809263i
$124$	−5.60844	+	6.22880i	−0.503653	+	0.559363i
$125$	11.0634	+	1.61303i	0.989538	+	0.144274i
$126$	10.5946	−	10.0699i	0.943840	−	0.897095i
$127$	0.330173	+	2.08463i	0.0292982	+	0.184981i	0.997997	−	0.0632564i	$-0.0201486\pi$
$127$	0.330173	+	2.08463i	0.0292982	+	0.184981i	−0.968699	+	0.248238i	$0.920149\pi$
$128$	0.544639	−	0.838671i	0.0481397	−	0.0741287i
$129$	−0.514819	−	0.109428i	−0.0453273	−	0.00963461i
$130$	7.85047	−	6.41066i	0.688532	−	0.562252i
$131$	−6.41746	+	3.70512i	−0.560696	+	0.323718i	−0.753425	−	0.657534i	$-0.771600\pi$
$131$	−6.41746	+	3.70512i	−0.560696	+	0.323718i	0.192729	+	0.981252i	$0.438266\pi$
$132$	−1.37851	+	9.58489i	−0.119984	+	0.834258i
$133$	1.41452	+	17.7927i	0.122655	+	1.54283i
$134$	8.87592	+	12.2167i	0.766763	+	1.05536i
$135$	−9.74251	−	13.2944i	−0.838502	−	1.14420i
$136$	1.67546	−	1.50859i	0.143670	−	0.129361i
$137$	18.2842	+	7.01866i	1.56213	+	0.599645i	0.977365	−	0.211560i	$-0.0678543\pi$
$137$	18.2842	+	7.01866i	1.56213	+	0.599645i	0.584763	+	0.811204i	$0.301188\pi$
$138$	17.6433	−	14.2873i	1.50190	−	1.21621i
$139$	−1.62666	+	5.00633i	−0.137971	+	0.424631i	−0.996040	−	0.0889026i	$-0.971664\pi$
$139$	−1.62666	+	5.00633i	−0.137971	+	0.424631i	0.858069	+	0.513534i	$0.171664\pi$
$140$	5.32724	−	2.57304i	0.450234	−	0.217461i
$141$	−15.9638	+	11.5984i	−1.34440	+	0.976761i
$142$	−1.67308	+	6.24401i	−0.140402	+	0.523986i
$143$	0.572954	−	15.0223i	0.0479128	−	1.25623i
$144$	4.78443	+	2.76229i	0.398703	+	0.230191i
$145$	−1.22303	−	7.52218i	−0.101567	−	0.624683i
$146$	9.04323	−	2.93832i	0.748423	−	0.243177i
$147$	−16.5155	+	12.0393i	−1.36217	+	0.992982i
$148$	−4.17632	+	0.661465i	−0.343292	+	0.0543721i
$149$	−6.47599	−	0.680654i	−0.530534	−	0.0557614i	−0.164525	−	0.986373i	$-0.552609\pi$
$149$	−6.47599	−	0.680654i	−0.530534	−	0.0557614i	−0.366009	+	0.930611i	$0.619276\pi$
$150$	−4.62487	−	13.8465i	−0.377619	−	1.13056i
$151$	−6.80258	−	1.44593i	−0.553586	−	0.117668i	−0.0773793	−	0.997002i	$-0.524655\pi$
$151$	−6.80258	−	1.44593i	−0.553586	−	0.117668i	−0.476207	+	0.879333i	$0.657989\pi$
$152$	−6.29816	+	2.41764i	−0.510848	+	0.196096i
$153$	8.80737	+	8.80737i	0.712034	+	0.712034i
$154$	2.36548	−	8.45012i	0.190616	−	0.680930i
$155$	−10.2720	−	15.6764i	−0.825066	−	1.25916i
$156$	−12.0899	−	5.38277i	−0.967967	−	0.430967i
$157$	−13.1870	+	8.56372i	−1.05243	+	0.683459i	−0.950308	−	0.311312i	$-0.899232\pi$
$157$	−13.1870	+	8.56372i	−1.05243	+	0.683459i	−0.102127	+	0.994771i	$0.532565\pi$
$158$	−4.93309	−	0.258532i	−0.392456	−	0.0205677i
$159$	2.30588	−	21.9389i	0.182868	−	1.73987i
$160$	1.50302	+	1.65557i	0.118824	+	0.130885i
$161$	−17.5325	+	10.7631i	−1.38176	+	0.848251i
$162$	−2.24602	+	4.40807i	−0.176464	+	0.346330i
$163$	−3.04551	+	1.16906i	−0.238542	+	0.0915678i	−0.474703	−	0.880146i	$-0.657444\pi$
$163$	−3.04551	+	1.16906i	−0.238542	+	0.0915678i	0.236160	+	0.971714i	$0.424111\pi$
$164$	−0.244233	+	0.423024i	−0.0190714	+	0.0330326i
$165$	−19.9392	−	8.44285i	−1.55226	−	0.657275i
$166$	0.702369	−	0.405513i	0.0545144	−	0.0314739i
$167$	0.232207	−	1.46609i	0.0179687	−	0.113450i	−0.977074	−	0.212901i	$-0.931709\pi$
$167$	0.232207	−	1.46609i	0.0179687	−	0.113450i	0.995042	+	0.0994514i	$0.0317088\pi$
$168$	−6.13220	−	4.69768i	−0.473110	−	0.362434i
$169$	7.17599	+	2.33162i	0.551999	+	0.179355i
$170$	2.30712	+	4.48245i	0.176948	+	0.343788i
$171$	−15.1591	−	34.0480i	−1.15925	−	2.60372i
$172$	−0.00943439	+	0.180019i	−0.000719365	+	0.0137263i
$173$	−15.6574	+	0.820568i	−1.19041	+	0.0623867i	−0.637228	−	0.770675i	$-0.719919\pi$
$173$	−15.6574	+	0.820568i	−1.19041	+	0.0623867i	−0.553180	+	0.833062i	$0.686586\pi$
$174$	−8.05043	+	5.84898i	−0.610301	+	0.443410i
$175$	2.52763	+	12.9850i	0.191071	+	0.981576i
$176$	3.31629	−	0.0472211i	0.249975	−	0.00355942i
$177$	−6.09891	+	22.7615i	−0.458422	+	1.71086i
$178$	−8.65149	+	10.6837i	−0.648456	+	0.800777i
$179$	1.70715	−	8.03151i	0.127598	−	0.600303i	−0.867158	−	0.498033i	$-0.834056\pi$
$179$	1.70715	−	8.03151i	0.127598	−	0.600303i	0.994757	−	0.102271i	$-0.0326108\pi$
$180$	−8.69925	+	8.77088i	−0.648404	+	0.653743i
$181$	−12.6061	+	17.3508i	−0.937006	+	1.28968i	0.0200571	+	0.999799i	$0.493615\pi$
$181$	−12.6061	+	17.3508i	−0.937006	+	1.28968i	−0.957063	+	0.289879i	$0.906385\pi$
$182$	10.2301	+	6.25788i	0.758309	+	0.463865i
$183$	9.66196	+	18.9627i	0.714233	+	1.40176i
$184$	−5.77850	−	5.20298i	−0.425996	−	0.383569i
$185$	0.949748	−	9.40713i	0.0698269	−	0.691626i
$186$	−12.2360	+	21.1933i	−0.897184	+	1.55397i
$187$	7.24956	+	1.83229i	0.530140	+	0.133991i
$188$	4.77889	+	4.77889i	0.348537	+	0.348537i
$189$	11.0332	−	16.0807i	0.802548	−	1.16970i
$190$	−1.63832	−	14.9958i	−0.118856	−	1.08791i
$191$	−0.910974	+	0.193634i	−0.0659158	+	0.0140108i	−0.240752	−	0.970587i	$-0.577394\pi$
$191$	−0.910974	+	0.193634i	−0.0659158	+	0.0140108i	0.174836	+	0.984598i	$0.444061\pi$
$192$	1.04632	−	2.72576i	0.0755119	−	0.196715i
$193$	5.96297	−	15.5341i	0.429224	−	1.11817i	−0.533049	−	0.846084i	$-0.678954\pi$
$193$	5.96297	−	15.5341i	0.429224	−	1.11817i	0.962274	−	0.272083i	$-0.0877127\pi$
$194$	10.1766	−	2.16310i	0.730635	−	0.155301i
$195$	18.5285	−	23.0736i	1.32686	−	1.65234i
$196$	4.95759	+	4.94189i	0.354114	+	0.352992i
$197$	−1.67203	−	1.67203i	−0.119127	−	0.119127i	0.645030	−	0.764157i	$-0.276845\pi$
$197$	−1.67203	−	1.67203i	−0.119127	−	0.119127i	−0.764157	+	0.645030i	$0.776845\pi$
$198$	1.21937	+	18.2824i	0.0866571	+	1.29927i
$199$	−3.23567	+	5.60435i	−0.229371	+	0.397282i	−0.957622	−	0.288029i	$-0.907000\pi$
$199$	−3.23567	+	5.60435i	−0.229371	+	0.397282i	0.728251	+	0.685310i	$0.240333\pi$
$200$	−4.43627	+	2.30641i	−0.313692	+	0.163088i
$201$	32.7646	+	29.5014i	2.31104	+	2.08087i
$202$	−7.91753	−	15.5390i	−0.557075	−	1.09332i
$203$	7.92109	−	4.30894i	0.555952	−	0.302428i
$204$	3.86916	−	5.32544i	0.270895	−	0.372856i
$205$	−0.775492	−	0.769159i	−0.0541627	−	0.0537204i
$206$	−1.15862	+	5.45088i	−0.0807249	+	0.379781i
$207$	27.0342	−	33.3844i	1.87900	−	2.32038i
$208$	−1.17315	+	4.37824i	−0.0813431	+	0.303577i
$209$	−18.2870	−	12.8925i	−1.26494	−	0.891792i
$210$	13.6521	−	10.5821i	0.942082	−	0.730237i
$211$	−10.9810	+	7.97817i	−0.755964	+	0.549240i	−0.897670	−	0.440669i	$-0.854741\pi$
$211$	−10.9810	+	7.97817i	−0.755964	+	0.549240i	0.141706	+	0.989909i	$0.454741\pi$
$212$	−7.54517	+	0.395426i	−0.518205	+	0.0271580i
$213$	−0.987772	+	18.8478i	−0.0676810	+	1.29143i
$214$	2.19761	+	4.93591i	0.150226	+	0.337412i
$215$	−0.383866	−	0.122988i	−0.0261794	−	0.00838770i
$216$	7.01024	+	2.27777i	0.476987	+	0.154982i
$217$	13.4858	−	17.6040i	0.915478	−	1.19504i
$218$	0.939634	−	5.93262i	0.0636401	−	0.401807i
$219$	24.0428	−	13.8811i	1.62466	−	0.937998i
$220$	−1.78777	+	7.19749i	−0.120532	+	0.485255i
$221$	−5.10961	+	8.85010i	−0.343709	+	0.595322i
$222$	−11.5256	+	4.42425i	−0.773546	+	0.296936i
$223$	−3.03014	+	5.94699i	−0.202913	+	0.398240i	−0.969929	−	0.243389i	$-0.921741\pi$
$223$	−3.03014	+	5.94699i	−0.202913	+	0.398240i	0.767015	+	0.641629i	$0.221741\pi$
$224$	−1.26060	+	2.32613i	−0.0842273	+	0.155421i
$225$	−14.0072	−	23.8081i	−0.933811	−	1.58721i
$226$	−1.39732	+	13.2946i	−0.0929485	+	0.884346i
$227$	−6.63507	−	0.347729i	−0.440385	−	0.0230796i	−0.169145	−	0.985591i	$-0.554100\pi$
$227$	−6.63507	−	0.347729i	−0.440385	−	0.0230796i	−0.271240	+	0.962512i	$0.587434\pi$
$228$	−16.5192	+	10.7277i	−1.09401	+	0.710460i
$229$	−3.92802	−	1.74887i	−0.259571	−	0.115568i	0.272826	−	0.962064i	$-0.412042\pi$
$229$	−3.92802	−	1.74887i	−0.259571	−	0.115568i	−0.532397	+	0.846495i	$0.678708\pi$
$230$	14.5431	−	9.52939i	0.958942	−	0.628349i
$231$	1.62600	−	25.5685i	0.106983	−	1.68229i
$232$	2.40996	+	2.40996i	0.158222	+	0.158222i
$233$	−5.14862	+	1.97637i	−0.337297	+	0.129476i	−0.521121	−	0.853483i	$-0.674486\pi$
$233$	−5.14862	+	1.97637i	−0.337297	+	0.129476i	0.183823	+	0.982959i	$0.441153\pi$
$234$	−24.4940	−	5.20637i	−1.60122	−	0.340351i
$235$	−13.0564	+	7.60969i	−0.851709	+	0.496402i
$236$	8.02664	+	0.843634i	0.522490	+	0.0549159i
$237$	−14.2453	+	2.25623i	−0.925331	+	0.146558i
$238$	−4.10260	+	4.33011i	−0.265932	+	0.280680i
$239$	6.11099	−	1.98558i	0.395287	−	0.128437i	−0.104627	−	0.994512i	$-0.533365\pi$
$239$	6.11099	−	1.98558i	0.395287	−	0.128437i	0.499914	+	0.866075i	$0.333365\pi$
$240$	5.29746	+	3.81574i	0.341949	+	0.246305i
$241$	12.6854	+	7.32389i	0.817135	+	0.471773i	0.849428	−	0.527705i	$-0.176947\pi$
$241$	12.6854	+	7.32389i	0.817135	+	0.471773i	−0.0322923	+	0.999478i	$0.510281\pi$
$242$	6.25127	+	9.05106i	0.401847	+	0.581824i
$243$	1.98475	−	7.40718i	0.127322	−	0.475171i
$244$	5.89711	−	4.28450i	0.377524	−	0.274287i
$245$	−13.5107	+	7.90320i	−0.863168	+	0.504917i
$246$	−0.440710	+	1.35637i	−0.0280986	+	0.0864787i
$247$	23.7640	−	19.2437i	1.51207	−	1.22445i
$248$	7.82497	+	3.00373i	0.496886	+	0.190737i
$249$	1.75972	−	1.58446i	0.111518	−	0.100411i
$250$	−2.45886	−	10.9066i	−0.155512	−	0.689794i
$251$	−10.0767	−	13.8694i	−0.636035	−	0.875427i	0.362361	−	0.932038i	$-0.381971\pi$
$251$	−10.0767	−	13.8694i	−0.636035	−	0.875427i	−0.998396	+	0.0566107i	$0.981971\pi$
$252$	−13.1978	−	6.28218i	−0.831382	−	0.395740i
$253$	3.67125	−	25.5265i	0.230810	−	1.60484i
$254$	1.82785	−	1.05531i	0.114689	−	0.0662160i
$255$	9.30989	+	11.4009i	0.583008	+	0.713950i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	0.0356960	−	0.0549670i	0.00222665	−	0.00342875i	−0.837555	−	0.546352i	$-0.816016\pi$
$257$	0.0356960	−	0.0549670i	0.00222665	−	0.00342875i	0.839782	+	0.542924i	$0.182683\pi$
$258$	0.0823346	+	0.519840i	0.00512593	+	0.0323639i
$259$	10.8761	−	2.62024i	0.675806	−	0.162814i
$260$	−8.79822	−	5.03167i	−0.545643	−	0.312051i
$261$	−12.5990	+	13.9926i	−0.779857	+	0.866119i
$262$	5.75885	+	4.66342i	0.355783	+	0.288107i
$263$	−4.73588	−	17.6746i	−0.292027	−	1.08986i	−0.943550	−	0.331231i	$-0.892536\pi$
$263$	−4.73588	−	17.6746i	−0.292027	−	1.08986i	0.651523	−	0.758629i	$-0.274130\pi$
$264$	9.44228	−	2.14797i	0.581132	−	0.132198i
$265$	3.44481	−	16.5397i	0.211613	−	1.01603i
$266$	16.1040	−	7.69691i	0.987401	−	0.471928i
$267$	−18.2223	+	35.7632i	−1.11518	+	2.18867i
$268$	8.22439	−	12.6644i	0.502384	−	0.773604i
$269$	9.04716	−	4.02805i	0.551615	−	0.245595i	−0.111949	−	0.993714i	$-0.535709\pi$
$269$	9.04716	−	4.02805i	0.551615	−	0.245595i	0.663565	+	0.748119i	$0.269043\pi$
$270$	−8.92003	+	13.8597i	−0.542855	+	0.843475i
$271$	1.82499	+	8.58592i	0.110860	+	0.521557i	0.998175	+	0.0603922i	$0.0192351\pi$
$271$	1.82499	+	8.58592i	0.110860	+	0.521557i	−0.887314	+	0.461165i	$0.847432\pi$
$272$	−2.00883	−	1.02355i	−0.121803	−	0.0620617i
$273$	33.0149	+	11.6617i	1.99815	+	0.705800i
$274$		−	19.5851i		−	1.18318i
$275$	−14.5438	−	7.96725i	−0.877026	−	0.480443i
$276$	−19.6611	−	11.3514i	−1.18346	−	0.683272i
$277$	−8.10817	+	10.0128i	−0.487173	+	0.601608i	−0.960156	−	0.279463i	$-0.909844\pi$
$277$	−8.10817	+	10.0128i	−0.487173	+	0.601608i	0.472984	+	0.881071i	$0.343177\pi$
$278$	5.25675	−	0.275495i	0.315279	−	0.0165231i
$279$	−14.3091	+	44.0390i	−0.856665	+	2.63654i
$280$	−4.31125	−	4.05131i	−0.257646	−	0.242112i
$281$	16.7911	+	12.1994i	1.00167	+	0.727757i	0.962446	−	0.271474i	$-0.0875110\pi$
$281$	16.7911	+	12.1994i	1.00167	+	0.727757i	0.0392252	+	0.999230i	$0.487511\pi$
$282$	16.5490	+	10.7470i	0.985476	+	0.639975i
$283$	−8.82085	−	13.5829i	−0.524345	−	0.807421i	0.472937	−	0.881096i	$-0.343194\pi$
$283$	−8.82085	−	13.5829i	−0.524345	−	0.807421i	−0.997282	+	0.0736755i	$0.976527\pi$
$284$	6.42887	−	0.675701i	0.381483	−	0.0400955i
$285$	−13.7819	−	41.8318i	−0.816368	−	2.47790i
$286$	−14.2299	+	4.84862i	−0.841430	+	0.286705i
$287$	0.555449	−	1.16690i	0.0327871	−	0.0688802i
$288$	0.864236	−	5.45657i	0.0509256	−	0.321531i
$289$	8.85603	+	7.97401i	0.520943	+	0.469059i
$290$	−6.58427	+	3.83751i	−0.386641	+	0.225346i
$291$	27.7500	−	12.3551i	1.62674	−	0.724270i
$292$	−5.98397	−	7.38958i	−0.350185	−	0.432443i
$293$	23.8794	−	12.1671i	1.39505	−	0.710812i	0.415046	−	0.909801i	$-0.363766\pi$
$293$	23.8794	−	12.1671i	1.39505	−	0.710812i	0.980002	+	0.198988i	$0.0637656\pi$
$294$	17.1582	+	11.1040i	1.00069	+	0.647600i
$295$	−6.39832	+	16.8747i	−0.372525	+	0.982482i
$296$	2.11419	+	3.66189i	0.122885	+	0.212843i
$297$	6.66288	+	23.5214i	0.386619	+	1.36485i
$298$	1.68534	+	6.28979i	0.0976293	+	0.364358i
$299$	32.1979	+	14.3354i	1.86205	+	0.829039i
$300$	−11.2694	+	9.27982i	−0.650639	+	0.535771i
$301$	−0.0128630	−	0.476765i	−0.000741411	−	0.0274803i
$302$	1.08793	+	6.86893i	0.0626034	+	0.395262i
$303$	−32.0443	−	39.5715i	−1.84090	−	2.27332i
$304$	4.51411	+	5.01343i	0.258902	+	0.287540i
$305$	5.90346	+	15.1926i	0.338031	+	0.869923i
$306$	5.06611	−	11.3787i	0.289610	−	0.650475i
$307$	−7.08616	+	7.08616i	−0.404428	+	0.404428i	−0.879790	−	0.475362i	$-0.842317\pi$
$307$	−7.08616	+	7.08616i	−0.404428	+	0.404428i	0.475362	+	0.879790i	$0.342317\pi$
$308$	−8.73658	+	0.819887i	−0.497813	+	0.0467174i
$309$			16.2704i			0.925592i
$310$	−10.9540	+	15.2076i	−0.622146	+	0.863736i
$311$	−0.951138	+	4.47475i	−0.0539341	+	0.253740i	−0.996852	−	0.0792855i	$-0.974736\pi$
$311$	−0.951138	+	4.47475i	−0.0539341	+	0.253740i	0.942918	+	0.333025i	$0.108069\pi$
$312$	−0.692617	+	13.2159i	−0.0392117	+	0.748204i
$313$	0.629374	−	0.509657i	0.0355743	−	0.0288075i	−0.611368	−	0.791346i	$-0.709381\pi$
$313$	0.629374	−	0.509657i	0.0355743	−	0.0288075i	0.646943	+	0.762539i	$0.276047\pi$
$314$	12.7207	+	9.24214i	0.717871	+	0.521564i
$315$	21.1046	−	24.9566i	1.18911	−	1.40614i
$316$	1.52650	+	4.69809i	0.0858724	+	0.264288i
$317$	−4.02309	−	10.4805i	−0.225959	−	0.588644i	0.772993	−	0.634415i	$-0.218759\pi$
$317$	−4.02309	−	10.4805i	−0.225959	−	0.588644i	−0.998952	+	0.0457711i	$0.985426\pi$
$318$	−21.3081	+	5.70950i	−1.19490	+	0.320173i
$319$	−2.19251	+	11.0890i	−0.122757	+	0.620867i
$320$	1.00698	−	1.99650i	0.0562917	−	0.111608i
$321$	9.27241	+	12.7624i	0.517535	+	0.712326i
$322$	16.3313	+	12.5109i	0.910109	+	0.697205i
$323$	6.90510	+	13.5520i	0.384210	+	0.754055i
$324$	4.92019	+	0.517132i	0.273344	+	0.0287296i
$325$	15.8935	−	16.1564i	0.881614	−	0.896193i
$326$	2.18282	+	2.42427i	0.120895	+	0.134268i
$327$	−0.917832	−	17.5133i	−0.0507562	−	0.968486i
$328$	0.482452	+	0.0764129i	0.0266389	+	0.00421919i
$329$	−13.6060	−	11.6020i	−0.750124	−	0.639638i
$330$	−0.736525	+	21.6405i	−0.0405444	+	1.19127i
$331$	1.76117	+	3.05044i	0.0968029	+	0.167667i	0.910360	−	0.413818i	$-0.135805\pi$
$331$	1.76117	+	3.05044i	0.0968029	+	0.167667i	−0.813557	+	0.581486i	$0.802472\pi$
$332$	−0.630285	−	0.510395i	−0.0345914	−	0.0280116i
$333$	−19.5914	+	12.7228i	−1.07360	+	0.697205i
$334$	−1.45193	+	0.308618i	−0.0794462	+	0.0168868i
$335$	22.6966	+	25.0002i	1.24005	+	1.36591i
$336$	−2.18808	+	7.40840i	−0.119369	+	0.404161i
$337$	18.3900	−	9.37015i	1.00176	−	0.510425i	0.125417	−	0.992104i	$-0.459973\pi$
$337$	18.3900	−	9.37015i	1.00176	−	0.510425i	0.876347	+	0.481679i	$0.159973\pi$
$338$	−0.394890	−	7.53494i	−0.0214792	−	0.409847i
$339$	4.07975	+	38.8162i	0.221582	+	2.10821i
$340$	3.35793	−	3.76025i	0.182109	−	0.203928i
$341$	6.16627	+	27.1064i	0.333922	+	1.46789i
$342$	−26.3540	+	26.3540i	−1.42506	+	1.42506i
$343$	−14.1115	−	11.9944i	−0.761949	−	0.647637i
$344$	0.171443	−	0.0557052i	0.00924359	−	0.00300342i
$345$	35.7487	−	36.0430i	1.92464	−	1.94049i
$346$	6.37717	+	14.3234i	0.342839	+	0.770028i
$347$	−27.6175	−	10.6014i	−1.48258	−	0.569111i	−0.523448	−	0.852058i	$-0.675355\pi$
$347$	−27.6175	−	10.6014i	−1.48258	−	0.569111i	−0.959136	+	0.282947i	$0.908688\pi$
$348$	8.34551	+	5.41964i	0.447366	+	0.290523i
$349$	−10.4464	−	32.1507i	−0.559183	−	1.72099i	−0.684634	−	0.728887i	$-0.740038\pi$
$349$	−10.4464	−	32.1507i	−0.559183	−	1.72099i	0.125451	−	0.992100i	$-0.459962\pi$
$350$	11.2167	−	7.01317i	0.599560	−	0.374870i
$351$	−33.4105			−1.78332
$352$	−1.23254	−	3.07910i	−0.0656944	−	0.164117i
$353$	−26.8873	+	7.20443i	−1.43107	+	0.383453i	−0.889396	−	0.457138i	$-0.848874\pi$
$353$	−26.8873	+	7.20443i	−1.43107	+	0.383453i	−0.541670	+	0.840591i	$0.682208\pi$
$354$	23.4353	−	2.46315i	1.24557	−	0.130915i
$355$	−2.20264	+	14.2858i	−0.116904	+	0.758209i
$356$	13.0745	+	4.24816i	0.692947	+	0.225152i
$357$	−9.08803	+	14.8568i	−0.480989	+	0.786303i
$358$	−8.10985	+	1.28447i	−0.428619	+	0.0678866i
$359$	0.954558	+	4.49084i	0.0503796	+	0.237018i	0.996132	−	0.0878713i	$-0.0280064\pi$
$359$	0.954558	+	4.49084i	0.0503796	+	0.237018i	−0.945752	+	0.324889i	$0.894673\pi$
$360$	11.3059	+	4.97825i	0.595871	+	0.262377i
$361$	−2.77123	−	26.3665i	−0.145854	−	1.38771i
$362$	20.7160	+	5.55085i	1.08881	+	0.291746i
$363$	23.3473	+	22.0540i	1.22541	+	1.15754i
$364$	2.17608	−	11.7933i	0.114058	−	0.618136i
$365$	19.3881	−	8.72757i	1.01482	−	0.456822i
$366$	14.2406	−	15.8158i	0.744370	−	0.826707i
$367$	−8.57580	−	0.449439i	−0.447653	−	0.0234605i	−0.172822	−	0.984953i	$-0.555289\pi$
$367$	−8.57580	−	0.449439i	−0.447653	−	0.0234605i	−0.274831	+	0.961493i	$0.588622\pi$
$368$	−2.78657	+	7.25927i	−0.145260	+	0.378416i
$369$	−0.282077	+	2.68379i	−0.0146844	+	0.139712i
$370$	−9.12267	+	2.48455i	−0.474265	+	0.129165i
$371$	19.8170	−	2.62495i	1.02885	−	0.136280i
$372$	24.1706	+	3.82825i	1.25319	+	0.198485i
$373$	−6.28611	−	1.68436i	−0.325483	−	0.0872128i	0.0923778	−	0.995724i	$-0.470553\pi$
$373$	−6.28611	−	1.68436i	−0.325483	−	0.0872128i	−0.417860	+	0.908511i	$0.637220\pi$
$374$	−0.887414	−	7.42468i	−0.0458871	−	0.383921i
$375$	−13.6430	−	29.6554i	−0.704519	−	1.53140i
$376$	2.74888	−	6.17408i	0.141763	−	0.318404i
$377$	−13.7645	−	7.01338i	−0.708910	−	0.361208i
$378$	−18.9666	−	4.53757i	−0.975537	−	0.233387i
$379$	−8.00845	+	11.0227i	−0.411366	+	0.566197i	−0.963551	−	0.267525i	$-0.913794\pi$
$379$	−8.00845	+	11.0227i	−0.411366	+	0.566197i	0.552185	+	0.833722i	$0.313794\pi$
$380$	−13.4127	+	6.90352i	−0.688056	+	0.354143i
$381$	4.57952	−	4.12342i	0.234616	−	0.211249i
$382$	0.507236	+	0.781076i	0.0259525	+	0.0399633i
$383$	9.83117	+	25.6111i	0.502349	+	1.30866i	0.917074	+	0.398717i	$0.130545\pi$
$383$	9.83117	+	25.6111i	0.502349	+	1.30866i	−0.414725	+	0.909947i	$0.636122\pi$
$384$	−2.91969			−0.148995
$385$	3.20598	−	19.3577i	0.163392	−	0.986561i
$386$	−16.6393			−0.846916
$387$	0.356897	+	0.929747i	0.0181421	+	0.0472617i
$388$	−5.66638	−	8.72546i	−0.287667	−	0.442968i
$389$	−9.99223	+	8.99705i	−0.506626	+	0.456168i	−0.882371	−	0.470555i	$-0.844054\pi$
$389$	−9.99223	+	8.99705i	−0.506626	+	0.456168i	0.375744	+	0.926723i	$0.377387\pi$
$390$	−28.1811	−	9.02903i	−1.42701	−	0.457203i
$391$	−10.3044	+	14.1828i	−0.521115	+	0.717253i
$392$	2.83701	−	6.39933i	0.143291	−	0.323215i
$393$	19.2775	+	9.82237i	0.972420	+	0.495473i
$394$	−0.961773	+	2.16018i	−0.0484534	+	0.108828i
$395$	−11.0283	+	0.623319i	−0.554892	+	0.0313626i
$396$	16.6311	−	7.69019i	0.835743	−	0.386447i
$397$	22.6276	+	6.06304i	1.13564	+	0.304295i	0.777199	−	0.629255i	$-0.216640\pi$
$397$	22.6276	+	6.06304i	1.13564	+	0.304295i	0.358446	+	0.933550i	$0.383307\pi$
$398$	6.39167	+	1.01234i	0.320385	+	0.0507441i
$399$	41.3190	−	31.7573i	2.06854	−	1.58985i
$400$	3.74303	+	3.31507i	0.187152	+	0.165754i
$401$	3.07481	−	29.2549i	0.153549	−	1.46092i	−0.598135	−	0.801395i	$-0.704091\pi$
$401$	3.07481	−	29.2549i	0.153549	−	1.46092i	0.751684	−	0.659524i	$-0.229242\pi$
$402$	15.8001	−	41.1607i	0.788039	−	2.05291i
$403$	−37.9395	−	1.98832i	−1.88990	−	0.0990455i
$404$	−11.6695	+	12.9603i	−0.580581	+	0.644801i
$405$	−3.92206	+	10.3439i	−0.194889	+	0.513991i
$406$	−6.86141	−	5.85079i	−0.340526	−	0.290370i
$407$	−6.18819	+	12.5848i	−0.306737	+	0.623806i
$408$	−6.35831	−	1.70370i	−0.314783	−	0.0843460i
$409$	−1.31673	−	12.5278i	−0.0651079	−	0.619460i	−0.977615	−	0.210400i	$-0.932523\pi$
$409$	−1.31673	−	12.5278i	−0.0651079	−	0.619460i	0.912507	−	0.409060i	$-0.134143\pi$
$410$	−0.440160	+	0.999626i	−0.0217380	+	0.0493680i
$411$	−11.8889	−	55.9327i	−0.586435	−	2.75896i
$412$	5.50405	−	0.871755i	0.271165	−	0.0429483i
$413$	−21.3466	−	0.542035i	−1.05040	−	0.0266718i
$414$	−40.8552	−	13.2747i	−2.00792	−	0.652414i
$415$	1.46278	−	1.07196i	0.0718049	−	0.0526205i
$416$	4.50786	−	0.473795i	0.221016	−	0.0232297i
$417$	14.8455	−	3.97783i	0.726985	−	0.194795i
$418$	−5.48271	+	21.6926i	−0.268168	+	1.06102i
$419$	1.40941			0.0688544			0.0344272	−	0.999407i	$-0.489039\pi$
$419$	1.40941			0.0688544			0.0344272	+	0.999407i	$0.489039\pi$
$420$	−14.7717	−	8.95300i	−0.720787	−	0.436862i
$421$	1.43255	+	4.40894i	0.0698182	+	0.214878i	0.979878	−	0.199600i	$-0.0639642\pi$
$421$	1.43255	+	4.40894i	0.0698182	+	0.214878i	−0.910059	+	0.414478i	$0.863964\pi$
$422$	11.3835	+	7.39253i	0.554140	+	0.359863i
$423$	34.8573	+	13.3805i	1.69482	+	0.650581i
$424$	3.07311	+	6.90232i	0.149243	+	0.335206i
$425$	6.21692	+	9.40349i	0.301565	+	0.456136i
$426$	17.9499	−	5.83229i	0.869677	−	0.282575i
$427$	−14.6549	+	12.5366i	−0.709199	+	0.606687i
$428$	3.82052	−	3.82052i	0.184672	−	0.184672i
$429$	−37.6956	+	22.4852i	−1.81996	+	1.08559i
$430$	0.0227462	+	0.402444i	0.00109692	+	0.0194076i
$431$	−0.164187	−	1.56213i	−0.00790859	−	0.0752452i	0.989856	−	0.142076i	$-0.0453778\pi$
$431$	−0.164187	−	1.56213i	−0.00790859	−	0.0752452i	−0.997764	+	0.0668310i	$0.978711\pi$
$432$	−0.385769	−	7.36090i	−0.0185603	−	0.354152i
$433$	26.4932	−	13.4990i	1.27318	−	0.648718i	0.318945	−	0.947773i	$-0.396671\pi$
$433$	26.4932	−	13.4990i	1.27318	−	0.648718i	0.954236	+	0.299055i	$0.0966714\pi$
$434$	−21.2676	−	6.28141i	−1.02088	−	0.301517i
$435$	−16.4744	+	14.9564i	−0.789887	+	0.717104i
$436$	−5.87531	+	1.24884i	−0.281376	+	0.0598084i
$437$	43.9941	−	28.5701i	2.10452	−	1.36669i
$438$	−21.5753	−	17.4713i	−1.03091	−	0.834812i
$439$	−14.0813	−	24.3896i	−0.672065	−	1.16405i	−0.977317	−	0.211780i	$-0.932074\pi$
$439$	−14.0813	−	24.3896i	−0.672065	−	1.16405i	0.305252	−	0.952272i	$-0.401259\pi$
$440$	7.36012	−	0.910322i	0.350880	−	0.0433979i
$441$	36.1255	+	13.8015i	1.72026	+	0.657216i
$442$	10.0934	+	1.59864i	0.480094	+	0.0760394i
$443$	1.50951	+	28.8031i	0.0717189	+	1.36848i	0.763237	+	0.646118i	$0.223609\pi$
$443$	1.50951	+	28.8031i	0.0717189	+	1.36848i	−0.691518	+	0.722359i	$0.743058\pi$
$444$	8.26079	+	9.17454i	0.392040	+	0.435404i
$445$	−16.6364	+	25.8492i	−0.788639	+	1.22537i
$446$	6.63790	+	0.697672i	0.314314	+	0.0330357i
$447$	8.63129	+	16.9399i	0.408246	+	0.801228i
$448$	2.62339	+	0.343259i	0.123944	+	0.0162175i
$449$	−0.789759	−	1.08701i	−0.0372710	−	0.0512992i	0.789975	−	0.613139i	$-0.210094\pi$
$449$	−0.789759	−	1.08701i	−0.0372710	−	0.0512992i	−0.827246	+	0.561840i	$0.810094\pi$
$450$	−17.2071	+	21.6089i	−0.811148	+	1.01865i
$451$	0.679942	+	1.47046i	0.0320172	+	0.0692414i
$452$	12.9124	−	3.45986i	0.607347	−	0.162738i
$453$	7.27671	+	18.9565i	0.341890	+	0.890653i
$454$	2.05316	+	6.31898i	0.0963597	+	0.296565i
$455$	24.2597	+	11.4259i	1.13731	+	0.535655i
$456$	15.9351	+	11.5776i	0.746231	+	0.542169i
$457$	−10.8498	+	8.78596i	−0.507530	+	0.410990i	−0.848589	−	0.529052i	$-0.822548\pi$
$457$	−10.8498	+	8.78596i	−0.507530	+	0.410990i	0.341059	+	0.940042i	$0.389214\pi$
$458$	−0.225032	+	4.29386i	−0.0105150	+	0.200639i
$459$	3.45515	−	16.2552i	0.161273	−	0.758728i
$460$	−14.1082	−	10.1621i	−0.657799	−	0.473810i
$461$		−	4.61152i		−	0.214780i	−0.994217	−	0.107390i	$-0.965751\pi$
$461$		−	4.61152i		−	0.214780i	0.994217	−	0.107390i	$-0.0342494\pi$
$462$	−24.4530	+	7.64493i	−1.13766	+	0.355675i
$463$	−23.1045	+	23.1045i	−1.07376	+	1.07376i	−0.0767055	+	0.997054i	$0.524440\pi$
$463$	−23.1045	+	23.1045i	−1.07376	+	1.07376i	−0.997054	+	0.0767055i	$0.975560\pi$
$464$	1.38624	−	3.11354i	0.0643545	−	0.144543i
$465$	−22.0518	+	50.0808i	−1.02263	+	2.32244i
$466$	3.69020	+	4.09838i	0.170945	+	0.189854i
$467$	−13.9321	−	17.2047i	−0.644699	−	0.796137i	0.345106	−	0.938564i	$-0.387843\pi$
$467$	−13.9321	−	17.2047i	−0.644699	−	0.796137i	−0.989805	+	0.142427i	$0.954510\pi$
$468$	3.91731	+	24.7329i	0.181078	+	1.14328i
$469$	−19.0358	+	35.1260i	−0.878993	+	1.62197i
$470$	11.7833	+	9.46218i	0.543522	+	0.436458i
$471$	41.9392	+	18.6725i	1.93246	+	0.860386i
$472$	−2.08889	−	7.79585i	−0.0961490	−	0.358833i
$473$	0.469945	+	0.369601i	0.0216081	+	0.0169943i
$474$	7.21143	+	12.4906i	0.331232	+	0.573710i
$475$	−7.28343	−	32.9355i	−0.334187	−	1.51118i
$476$	5.51275	+	2.27833i	0.252677	+	0.104427i
$477$	−37.1916	+	18.9501i	−1.70289	+	0.867665i
$478$	−4.04368	−	4.99353i	−0.184954	−	0.228399i
$479$	−8.03352	+	3.57675i	−0.367061	+	0.163426i	−0.581975	−	0.813207i	$-0.697720\pi$
$479$	−8.03352	+	3.57675i	−0.367061	+	0.163426i	0.214914	+	0.976633i	$0.431053\pi$
$480$	1.66386	−	6.31304i	0.0759445	−	0.288150i
$481$	−14.2431	−	12.8245i	−0.649428	−	0.584748i
$482$	2.29142	−	14.4674i	0.104371	−	0.658974i
$483$	54.2350	+	25.8160i	2.46778	+	1.17467i
$484$	6.20963	−	9.07967i	0.282256	−	0.412712i
$485$	22.0956	−	7.27959i	1.00331	−	0.330549i
$486$	−7.62646	+	0.801574i	−0.345943	+	0.0363601i
$487$	−9.40420	−	14.4812i	−0.426145	−	0.656206i	0.558754	−	0.829333i	$-0.311279\pi$
$487$	−9.40420	−	14.4812i	−0.426145	−	0.656206i	−0.984899	+	0.173127i	$0.944613\pi$
$488$	−6.11327	−	3.97000i	−0.276735	−	0.179713i
$489$	7.70552	+	5.59839i	0.348456	+	0.253168i
$490$	12.2201	+	9.78109i	0.552047	+	0.441865i
$491$	10.5302	−	32.4087i	0.475222	−	1.46258i	−0.370436	−	0.928858i	$-0.620792\pi$
$491$	10.5302	−	32.4087i	0.475222	−	1.46258i	0.845658	−	0.533725i	$-0.179208\pi$
$492$	1.42421	−	0.0746399i	0.0642085	−	0.00336502i
$493$	4.83568	−	5.97157i	0.217788	−	0.268946i
$494$	−26.4819	−	15.2893i	−1.19147	−	0.687898i
$495$	7.15032	+	40.3427i	0.321383	+	1.81327i
$496$		−	8.38168i		−	0.376349i
$497$	−16.8140	+	3.13009i	−0.754211	+	0.140404i
$498$	−2.10985	−	1.07502i	−0.0945447	−	0.0481730i
$499$	0.121620	+	0.572177i	0.00544446	+	0.0256142i	0.980786	−	0.195087i	$-0.0624989\pi$
$499$	0.121620	+	0.572177i	0.00544446	+	0.0256142i	−0.975342	+	0.220701i	$0.929166\pi$
$500$	−9.30101	+	6.20412i	−0.415954	+	0.277457i
$501$	−3.95921	+	1.76275i	−0.176885	+	0.0787541i
$502$	−9.33701	+	14.3777i	−0.416731	+	0.641710i
$503$	0.0117885	−	0.0231363i	0.000525625	−	0.00103160i	−0.890744	−	0.454506i	$-0.849816\pi$
$503$	0.0117885	−	0.0231363i	0.000525625	−	0.00103160i	0.891269	+	0.453475i	$0.149816\pi$
$504$	−1.13525	+	14.5725i	−0.0505681	+	0.649112i
$505$	−21.3730	−	32.6180i	−0.951088	−	1.45148i
$506$	−25.1467	+	5.72049i	−1.11791	+	0.254307i
$507$	−5.70175	−	21.2792i	−0.253224	−	0.945044i
$508$	−1.64026	−	1.32826i	−0.0727747	−	0.0589318i
$509$	−23.2155	+	25.7834i	−1.02901	+	1.14283i	−0.0393742	+	0.999225i	$0.512536\pi$
$509$	−23.2155	+	25.7834i	−1.02901	+	1.14283i	−0.989635	+	0.143606i	$0.954130\pi$
$510$	7.30725	−	12.7772i	0.323571	−	0.565786i
$511$	17.3317	+	18.2348i	0.766710	+	0.806661i
$512$	0.156434	+	0.987688i	0.00691349	+	0.0436501i
$513$	−27.0830	+	41.7042i	−1.19574	+	1.84129i
$514$	−0.0641084	−	0.0136267i	−0.00282770	−	0.000601046i
$515$	−1.25169	+	12.3978i	−0.0551560	+	0.546313i
$516$	0.455807	−	0.263160i	0.0200658	−	0.0115850i
$517$	22.0869	−	3.82133i	0.971379	−	0.168062i
$518$	−6.34384	−	9.21467i	−0.278732	−	0.404870i
$519$	26.9073	+	37.0347i	1.18110	+	1.62564i
$520$	−1.54447	+	10.0170i	−0.0677294	+	0.439276i
$521$	−9.90091	+	8.91482i	−0.433767	+	0.390566i	−0.856884	−	0.515510i	$-0.827603\pi$
$521$	−9.90091	+	8.91482i	−0.433767	+	0.390566i	0.423117	+	0.906075i	$0.360936\pi$
$522$	17.5783	+	6.74767i	0.769380	+	0.295337i
$523$	15.4878	−	12.5418i	0.677236	−	0.548415i	−0.227822	−	0.973703i	$-0.573160\pi$
$523$	15.4878	−	12.5418i	0.677236	−	0.548415i	0.905058	+	0.425288i	$0.139827\pi$
$524$	2.28989	−	7.04757i	0.100034	−	0.307874i
$525$	27.7765	−	26.8378i	1.21227	−	1.17130i
$526$	−14.8034	+	10.7553i	−0.645460	+	0.468954i
$527$	4.89090	−	18.2531i	0.213051	−	0.795117i
$528$	−5.38911	−	8.04536i	−0.234531	−	0.350130i
$529$	32.4431	+	18.7310i	1.41057	+	0.814392i
$530$	−16.6757	+	2.71131i	−0.724346	+	0.117772i
$531$	42.4058	−	13.7785i	1.84026	−	0.597935i
$532$	−12.9569	−	12.2761i	−0.561751	−	0.532235i
$533$	−2.18680	+	0.346356i	−0.0947210	+	0.0150023i
$534$	39.9181	+	4.19556i	1.72743	+	0.181560i
$535$	6.08362	+	10.4381i	0.263018	+	0.451277i
$536$	−14.7706	−	3.13960i	−0.637994	−	0.135610i
$537$	−22.3811	+	8.59130i	−0.965816	+	0.370742i
$538$	−7.00272	−	7.00272i	−0.301909	−	0.301909i
$539$	22.8702	−	3.99424i	0.985089	−	0.172044i
$540$	16.1358	+	3.36068i	0.694375	+	0.144621i
$541$	6.91385	+	3.07824i	0.297249	+	0.132344i	0.549943	−	0.835203i	$-0.314650\pi$
$541$	6.91385	+	3.07824i	0.297249	+	0.132344i	−0.252693	+	0.967546i	$0.581316\pi$
$542$	7.36163	−	4.78070i	0.316209	−	0.205349i
$543$	62.5322	+	3.27718i	2.68352	+	0.140637i
$544$	−0.235666	+	2.24221i	−0.0101041	+	0.0961339i
$545$	0.647929	−	13.4155i	0.0277542	−	0.574655i
$546$	−0.944325	−	35.0013i	−0.0404134	−	1.49792i
$547$	9.51780	−	18.6797i	0.406952	−	0.798688i	−0.593027	−	0.805182i	$-0.702067\pi$
$547$	9.51780	−	18.6797i	0.406952	−	0.798688i	0.999979	+	0.00649473i	$0.00206735\pi$
$548$	−18.2842	+	7.01866i	−0.781064	+	0.299822i
$549$	20.1350	−	34.8748i	0.859341	−	1.48842i
$550$	−2.22603	+	16.4330i	−0.0949182	+	0.700707i
$551$	−19.9121	+	11.4963i	−0.848284	+	0.489757i
$552$	−3.55149	+	22.4232i	−0.151161	+	0.954396i
$553$	−5.01111	−	12.0708i	−0.213094	−	0.513303i
$554$	12.2534	+	3.98138i	0.520598	+	0.169153i
$555$	−24.5451	+	12.6334i	−1.04188	+	0.536257i
$556$	−2.14105	−	4.80887i	−0.0908007	−	0.203942i
$557$	1.30032	−	24.8116i	0.0550964	−	1.05130i	−0.821541	−	0.570150i	$-0.806885\pi$
$557$	1.30032	−	24.8116i	0.0550964	−	1.05130i	0.876637	−	0.481152i	$-0.159781\pi$
$558$	46.2419	−	2.42343i	1.95757	−	0.102592i
$559$	−0.661039	+	0.480273i	−0.0279590	+	0.0203134i
$560$	−2.23721	+	5.47676i	−0.0945395	+	0.231435i
$561$	−7.04141	−	20.6654i	−0.297289	−	0.872492i
$562$	5.37176	−	20.0477i	0.226594	−	0.845661i
$563$	15.2090	−	18.7815i	0.640983	−	0.791548i	−0.348328	−	0.937373i	$-0.613250\pi$
$563$	15.2090	−	18.7815i	0.640983	−	0.791548i	0.989310	+	0.145825i	$0.0465837\pi$
$564$	4.10259	−	19.3012i	0.172750	−	0.812726i
$565$	0.122560	+	29.8912i	0.00515616	+	1.25753i
$566$	−9.51964	+	13.1027i	−0.400140	+	0.550746i
$567$	−13.0851	−	0.332258i	−0.549521	−	0.0139535i
$568$	−2.93472	−	5.75971i	−0.123138	−	0.241672i
$569$	2.90141	+	2.61244i	0.121634	+	0.109519i	0.727703	−	0.685892i	$-0.240588\pi$
$569$	2.90141	+	2.61244i	0.121634	+	0.109519i	−0.606069	+	0.795412i	$0.707255\pi$
$570$	−34.1144	+	27.8577i	−1.42890	+	1.16683i
$571$	22.9621	−	39.7716i	0.960936	−	1.66439i	0.240776	−	0.970581i	$-0.422598\pi$
$571$	22.9621	−	39.7716i	0.960936	−	1.66439i	0.720160	−	0.693809i	$-0.244069\pi$
$572$	9.62610	+	11.5471i	0.402488	+	0.482810i
$573$	1.92275	+	1.92275i	0.0803241	+	0.0803241i
$574$	−1.28845	−	0.100375i	−0.0537791	−	0.00418958i
$575$	30.0127	−	24.7141i	1.25162	−	1.03065i
$576$	−5.40386	+	1.14863i	−0.225161	+	0.0478594i
$577$	−5.40982	+	14.0931i	−0.225214	+	0.586702i	−0.998901	−	0.0468653i	$-0.985077\pi$
$577$	−5.40982	+	14.0931i	−0.225214	+	0.586702i	0.773687	+	0.633568i	$0.218410\pi$
$578$	4.27066	−	11.1254i	0.177636	−	0.462758i
$579$	−47.5198	+	10.1007i	−1.97486	+	0.419769i
$580$	5.94221	+	4.77170i	0.246737	+	0.198134i
$581$	1.76935	+	1.21398i	0.0734050	+	0.0503642i
$582$	−21.4792	−	21.4792i	−0.890342	−	0.890342i
$583$	−13.3474	+	21.2083i	−0.552794	+	0.878358i
$584$	−4.75431	+	8.23470i	−0.196735	+	0.340755i
$585$	−55.7107	−	5.62458i	−2.30335	−	0.232548i
$586$	−19.9166	−	17.9330i	−0.822748	−	0.740805i
$587$	−9.41226	−	18.4726i	−0.388486	−	0.762446i	0.611090	−	0.791561i	$-0.290731\pi$
$587$	−9.41226	−	18.4726i	−0.388486	−	0.762446i	−0.999576	+	0.0291148i	$0.990731\pi$
$588$	4.21754	−	19.9979i	0.173928	−	0.824701i
$589$	−33.2362	+	45.7457i	−1.36947	+	1.88492i
$590$	18.0468	−	0.0739959i	0.742976	−	0.00304636i
$591$	−1.43541	+	6.75306i	−0.0590447	+	0.277784i
$592$	2.66101	−	3.28607i	0.109367	−	0.135057i
$593$	9.80934	−	36.6089i	0.402821	−	1.50335i	−0.405218	−	0.914220i	$-0.632804\pi$
$593$	9.80934	−	36.6089i	0.402821	−	1.50335i	0.808039	−	0.589129i	$-0.200529\pi$
$594$	19.5713	−	14.6496i	0.803021	−	0.601082i
$595$	−8.06787	+	10.6215i	−0.330750	+	0.435438i
$596$	5.26805	−	3.82746i	0.215788	−	0.156779i
$597$	18.8684	−	0.988852i	0.772233	−	0.0404710i
$598$	1.84458	−	35.1967i	0.0754305	−	1.43930i
$599$	−4.76051	−	10.6923i	−0.194509	−	0.436875i	0.789791	−	0.613376i	$-0.210189\pi$
$599$	−4.76051	−	10.6923i	−0.194509	−	0.436875i	−0.984300	+	0.176501i	$0.943522\pi$
$600$	12.7021	+	7.19530i	0.518559	+	0.293747i
$601$	−23.7170	−	7.70612i	−0.967436	−	0.314339i	−0.217656	−	0.976026i	$-0.569841\pi$
$601$	−23.7170	−	7.70612i	−0.967436	−	0.314339i	−0.749781	+	0.661686i	$0.769841\pi$
$602$	−0.440489	+	0.182866i	−0.0179530	+	0.00745306i
$603$	13.0505	−	82.3976i	0.531457	−	3.35549i
$604$	6.02282	−	3.47728i	0.245065	−	0.141488i
$605$	16.0936	+	18.6010i	0.654299	+	0.756236i
$606$	−25.4595	+	44.0971i	−1.03422	+	1.79132i
$607$	−10.8217	+	4.15408i	−0.439241	+	0.168609i	−0.567931	−	0.823076i	$-0.692256\pi$
$607$	−10.8217	+	4.15408i	−0.439241	+	0.168609i	0.128690	+	0.991685i	$0.458923\pi$
$608$	3.06273	−	6.01094i	0.124210	−	0.243776i
$609$	−23.1471	−	12.5441i	−0.937966	−	0.508311i
$610$	12.0679	−	10.9559i	0.488613	−	0.443591i
$611$	−3.20209	+	30.4658i	−0.129543	+	1.23252i
$612$	−12.4384	−	0.651871i	−0.502794	−	0.0263503i
$613$	5.45936	−	3.54535i	0.220502	−	0.143195i	−0.429662	−	0.902990i	$-0.641367\pi$
$613$	5.45936	−	3.54535i	0.220502	−	0.143195i	0.650163	+	0.759795i	$0.274700\pi$
$614$	9.15495	+	4.07605i	0.369464	+	0.164496i
$615$	−0.650237	+	3.12201i	−0.0262201	+	0.125892i
$616$	3.89634	+	7.86248i	0.156988	+	0.316788i
$617$	12.1089	+	12.1089i	0.487488	+	0.487488i	0.907513	−	0.420025i	$-0.137979\pi$
$617$	12.1089	+	12.1089i	0.487488	+	0.487488i	−0.420025	+	0.907513i	$0.637979\pi$
$618$	15.1897	−	5.83080i	0.611021	−	0.234549i
$619$	−18.9333	−	4.02439i	−0.760992	−	0.161754i	−0.188960	−	0.981985i	$-0.560511\pi$
$619$	−18.9333	−	4.02439i	−0.760992	−	0.161754i	−0.572032	+	0.820231i	$0.693845\pi$
$620$	18.1231	+	4.77652i	0.727842	+	0.191830i
$621$	−57.0010	−	5.99105i	−2.28737	−	0.240412i
$622$	4.51840	−	0.715644i	0.181171	−	0.0286947i
$623$	−35.3738	−	8.46283i	−1.41722	−	0.339056i
$624$	12.5863	−	4.08955i	0.503856	−	0.163713i
$625$	−8.11432	−	23.6465i	−0.324573	−	0.945861i
$626$	−0.701353	−	0.404926i	−0.0280317	−	0.0161841i
$627$	−2.48978	+	65.2798i	−0.0994324	+	2.60703i
$628$	4.06958	−	15.1879i	0.162394	−	0.606063i
$629$	7.71247	−	5.60344i	0.307516	−	0.223424i
$630$	−30.8622	−	10.7592i	−1.22958	−	0.428657i
$631$	7.88141	−	24.2565i	0.313754	−	0.965636i	−0.662510	−	0.749053i	$-0.730509\pi$
$631$	7.88141	−	24.2565i	0.313754	−	0.965636i	0.976264	−	0.216583i	$-0.0694912\pi$
$632$	3.83899	−	3.10875i	0.152707	−	0.123660i
$633$	36.9975	+	14.2020i	1.47052	+	0.564480i
$634$	−8.34265	+	7.51175i	−0.331329	+	0.298330i
$635$	3.80674	−	2.78968i	0.151066	−	0.110705i
$636$	12.9664	+	17.8467i	0.514152	+	0.707670i
$637$	−3.26650	+	31.5602i	−0.129423	+	1.25046i
$638$	11.1382	−	1.92707i	0.440967	−	0.0762934i
$639$	30.9279	−	17.8562i	1.22349	−	0.706381i
$640$	−2.22476	−	0.224613i	−0.0879413	−	0.00887860i
$641$	38.7160	+	8.22935i	1.52919	+	0.325040i	0.894267	−	0.447534i	$-0.147698\pi$
$641$	38.7160	+	8.22935i	1.52919	+	0.325040i	0.634925	+	0.772574i	$0.281031\pi$
$642$	8.59177	−	13.2302i	0.339090	−	0.522153i
$643$	1.46555	+	9.25315i	0.0577958	+	0.364909i	0.999588	+	0.0287121i	$0.00914061\pi$
$643$	1.46555	+	9.25315i	0.0577958	+	0.364909i	−0.941792	+	0.336196i	$0.890859\pi$
$644$	5.82730	−	19.7301i	0.229628	−	0.777475i
$645$	0.309259	+	1.13553i	0.0121771	+	0.0447114i
$646$	10.1773	−	11.3031i	0.400422	−	0.444714i
$647$	−17.6407	−	14.2852i	−0.693528	−	0.561608i	0.216435	−	0.976297i	$-0.430557\pi$
$647$	−17.6407	−	14.2852i	−0.693528	−	0.561608i	−0.909963	+	0.414689i	$0.863890\pi$
$648$	−1.28045	−	4.77871i	−0.0503009	−	0.187726i
$649$	17.6262	−	20.1455i	0.691891	−	0.790780i
$650$	−20.7790	−	9.04797i	−0.815019	−	0.354890i
$651$	−64.5510	−	5.02875i	−2.52995	−	0.197092i
$652$	1.48100	−	2.90662i	0.0580004	−	0.113832i
$653$	−14.3878	+	22.1552i	−0.563037	+	0.867001i	−0.999464	−	0.0327389i	$-0.989577\pi$
$653$	−14.3878	+	22.1552i	−0.563037	+	0.867001i	0.436427	+	0.899740i	$0.356244\pi$
$654$	−16.0211	+	7.13307i	−0.626476	+	0.278925i
$655$	13.9335	+	8.96752i	0.544427	+	0.350390i
$656$	−0.101558	−	0.477791i	−0.00396516	−	0.0186546i
$657$	−46.8056	−	23.8487i	−1.82606	−	0.930425i
$658$	−5.95542	+	16.8601i	−0.232167	+	0.657275i
$659$			33.5782i			1.30802i	0.756486	+	0.654010i	$0.226914\pi$
$659$			33.5782i			1.30802i	−0.756486	+	0.654010i	$0.773086\pi$
$660$	20.4671	−	7.06764i	0.796679	−	0.275108i
$661$	−28.9514	−	16.7151i	−1.12608	−	0.650141i	−0.183132	−	0.983088i	$-0.558624\pi$
$661$	−28.9514	−	16.7151i	−1.12608	−	0.650141i	−0.942945	+	0.332947i	$0.891957\pi$
$662$	2.21669	−	2.73738i	0.0861539	−	0.106391i
$663$	29.7960	−	1.56154i	1.15718	−	0.0606454i
$664$	−0.250621	+	0.771331i	−0.00972597	+	0.0299335i
$665$	33.9275	−	21.0199i	1.31565	−	0.815115i
$666$	18.8987	+	13.7307i	0.732309	+	0.532054i
$667$	−22.2258	−	14.4336i	−0.860587	−	0.558872i
$668$	0.808445	+	1.24490i	0.0312797	+	0.0481665i
$669$	19.3806	−	2.03698i	0.749298	−	0.0787544i
$670$	15.2060	−	30.1483i	0.587458	−	1.16473i
$671$	−0.344206	−	24.1732i	−0.0132879	−	0.933196i
$672$	7.70048	−	0.612187i	0.297052	−	0.0236156i
$673$	2.13734	−	13.4946i	0.0823882	−	0.520179i	−0.911634	−	0.411003i	$-0.865179\pi$
$673$	2.13734	−	13.4946i	0.0823882	−	0.520179i	0.994022	−	0.109176i	$-0.0348213\pi$
$674$	−15.3382	−	13.8105i	−0.590804	−	0.531962i
$675$	−16.4620	+	32.9742i	−0.633622	+	1.26918i
$676$	−6.89296	+	3.06894i	−0.265114	+	0.118036i
$677$	0.383482	+	0.473560i	0.0147384	+	0.0182004i	0.784462	−	0.620177i	$-0.212939\pi$
$677$	0.383482	+	0.473560i	0.0147384	+	0.0182004i	−0.769723	+	0.638377i	$0.779606\pi$
$678$	34.7760	−	17.7193i	1.33556	−	0.680504i
$679$	16.7742	+	21.8247i	0.643734	+	0.837554i
$680$	−4.71387	−	1.78734i	−0.180769	−	0.0685415i
$681$	9.69946	+	16.8000i	0.371684	+	0.643776i
$682$	23.0962	−	15.4708i	0.884399	−	0.592406i
$683$	−3.13992	−	11.7183i	−0.120146	−	0.448390i	0.879475	−	0.475946i	$-0.157894\pi$
$683$	−3.13992	−	11.7183i	−0.120146	−	0.448390i	−0.999620	+	0.0275560i	$0.991228\pi$
$684$	34.0480	+	15.1591i	1.30186	+	0.579624i
$685$	−4.75621	−	43.5345i	−0.181725	−	1.66337i
$686$	−6.14063	+	17.4726i	−0.234450	+	0.667108i
$687$	1.96387	+	12.3994i	0.0749263	+	0.473066i
$688$	−0.113445	−	0.140093i	−0.00432505	−	0.00534099i
$689$	−22.9156	−	25.4504i	−0.873016	−	0.969583i
$690$	−46.4603	−	20.4576i	−1.76871	−	0.778807i
$691$	9.30777	−	20.9056i	0.354084	−	0.795286i	−0.645421	−	0.763827i	$-0.723318\pi$
$691$	9.30777	−	20.9056i	0.354084	−	0.795286i	0.999505	−	0.0314589i	$-0.0100153\pi$
$692$	11.0866	−	11.0866i	0.421450	−	0.421450i
$693$	−42.2508	+	23.7695i	−1.60498	+	0.902928i
$694$			29.5823i			1.12293i
$695$	11.6180	−	1.88898i	0.440697	−	0.0716530i
$696$	2.06890	−	9.73343i	0.0784216	−	0.368945i
$697$	0.0576362	−	1.09976i	0.00218313	−	0.0416566i
$698$	−26.2716	+	21.2743i	−0.994395	+	0.805245i
$699$	13.0267	+	9.46443i	0.492714	+	0.357978i
$700$	−10.5671	−	7.95844i	−0.399398	−	0.300801i
$701$	−5.17364	−	15.9228i	−0.195406	−	0.601397i	−0.999972	−	0.00753340i	$-0.997602\pi$
$701$	−5.17364	−	15.9228i	−0.195406	−	0.601397i	0.804566	−	0.593863i	$-0.202398\pi$
$702$	11.9732	+	31.1914i	0.451901	+	1.17724i
$703$	−27.5537	+	7.38299i	−1.03921	+	0.278455i
$704$	−2.43289	+	2.25412i	−0.0916928	+	0.0849554i
$705$	39.3956	+	19.8700i	1.48372	+	0.748348i
$706$	16.3615	+	22.5196i	0.615771	+	0.847537i
$707$	28.0601	−	36.6288i	1.05531	−	1.37757i
$708$	−10.6980	−	20.9960i	−0.402056	−	0.789079i
$709$	−30.5006	−	3.20574i	−1.14547	−	0.120394i	−0.487282	−	0.873245i	$-0.662012\pi$
$709$	−30.5006	−	3.20574i	−1.14547	−	0.120394i	−0.658191	+	0.752851i	$0.728678\pi$
$710$	14.1263	−	3.06322i	0.530149	−	0.114961i
$711$	18.2610	+	20.2809i	0.684842	+	0.760594i
$712$	−0.719481	−	13.7285i	−0.0269637	−	0.514498i
$713$	−64.3713	−	10.1954i	−2.41073	−	0.381821i
$714$	17.1268	+	3.16022i	0.640955	+	0.118268i
$715$	−30.4533	+	14.2334i	−1.13889	+	0.532299i
$716$	4.10547	+	7.11088i	0.153429	+	0.265746i
$717$	−14.5796	−	11.8063i	−0.544484	−	0.440914i
$718$	3.85048	−	2.50053i	0.143699	−	0.0933190i
$719$	−14.3872	+	3.05810i	−0.536553	+	0.114048i	−0.468216	−	0.883614i	$-0.655103\pi$
$719$	−14.3872	+	3.05810i	−0.536553	+	0.114048i	−0.0683379	+	0.997662i	$0.521770\pi$
$720$	0.595937	−	12.3390i	0.0222093	−	0.459846i
$721$	−14.3338	+	3.45326i	−0.533817	+	0.128606i
$722$	−23.6221	+	12.0361i	−0.879124	+	0.447936i
$723$	−2.23825	−	42.7084i	−0.0832414	−	1.58834i
$724$	−2.24180	−	21.3293i	−0.0833160	−	0.792699i
$725$	−13.7038	+	10.1292i	−0.508948	+	0.376187i
$726$	12.2223	−	29.7000i	0.453613	−	1.10227i
$727$	−2.77428	+	2.77428i	−0.102892	+	0.102892i	−0.756679	−	0.653787i	$-0.773179\pi$
$727$	−2.77428	+	2.77428i	−0.102892	+	0.102892i	0.653787	+	0.756679i	$0.273179\pi$
$728$	−11.7898	+	2.19479i	−0.436960	+	0.0813443i
$729$	−35.4092	+	11.5051i	−1.31145	+	0.426116i
$730$	−15.0960	−	14.9727i	−0.558727	−	0.554164i
$731$	−0.165306	−	0.371283i	−0.00611406	−	0.0137324i
$732$	−19.8687	−	7.62689i	−0.734370	−	0.281898i
$733$	36.8743	+	23.9464i	1.36198	+	0.884481i	0.998882	−	0.0472690i	$-0.0150518\pi$
$733$	36.8743	+	23.9464i	1.36198	+	0.884481i	0.363100	+	0.931750i	$0.381718\pi$
$734$	2.65370	+	8.16726i	0.0979500	+	0.301459i
$735$	40.8367	+	20.5156i	1.50628	+	0.756731i
$736$	7.77573			0.286617
$737$	−18.6121	−	46.4963i	−0.685584	−	1.71271i
$738$	2.60662	−	0.698441i	0.0959509	−	0.0257100i
$739$	3.99171	−	0.419545i	0.146837	−	0.0154332i	−0.0308246	−	0.999525i	$-0.509813\pi$
$739$	3.99171	−	0.419545i	0.146837	−	0.0154332i	0.177662	+	0.984092i	$0.443147\pi$
$740$	5.58880	+	7.62636i	0.205448	+	0.280351i
$741$	−84.9104	−	27.5891i	−3.11926	−	1.01351i
$742$	−9.55236	−	17.5600i	−0.350678	−	0.644649i
$743$	31.1279	−	4.93017i	1.14197	−	0.180870i	0.443341	−	0.896353i	$-0.353793\pi$
$743$	31.1279	−	4.93017i	1.14197	−	0.180870i	0.698630	+	0.715483i	$0.253793\pi$
$744$	−5.08799	−	23.9371i	−0.186535	−	0.877578i
$745$	5.27372	+	13.5719i	0.193214	+	0.497236i
$746$	0.680257	+	6.47221i	0.0249060	+	0.236965i
$747$	−4.32791	−	1.15966i	−0.158350	−	0.0424297i
$748$	−6.61351	+	3.48924i	−0.241814	+	0.127579i
$749$	−9.27528	+	10.8774i	−0.338911	+	0.397452i
$750$	−22.7965	+	23.3643i	−0.832411	+	0.853145i
$751$	10.6333	−	11.8095i	0.388016	−	0.430936i	−0.517215	−	0.855856i	$-0.673031\pi$
$751$	10.6333	−	11.8095i	0.388016	−	0.430936i	0.905231	+	0.424920i	$0.139698\pi$
$752$	−6.74911	−	0.353706i	−0.246115	−	0.0128983i
$753$	−17.9376	+	46.7291i	−0.653683	+	1.70290i
$754$	−1.61479	+	15.3637i	−0.0588071	+	0.559512i
$755$	4.08641	+	15.0043i	0.148720	+	0.546064i
$756$	2.56084	+	19.3330i	0.0931368	+	0.703134i
$757$	7.13517	+	1.13010i	0.259332	+	0.0410742i	0.284747	−	0.958603i	$-0.408091\pi$
$757$	7.13517	+	1.13010i	0.259332	+	0.0410742i	−0.0254145	+	0.999677i	$0.508091\pi$
$758$	13.1605	+	3.52635i	0.478012	+	0.128083i
$759$	−68.3437	+	31.6021i	−2.48072	+	1.14708i
$760$	11.2517	+	10.0478i	0.408141	+	0.364473i
$761$	−14.2981	+	32.1139i	−0.518304	+	1.16413i	0.444954	+	0.895553i	$0.353220\pi$
$761$	−14.2981	+	32.1139i	−0.518304	+	1.16413i	−0.963258	+	0.268576i	$0.913447\pi$
$762$	−5.49069	−	2.79765i	−0.198907	−	0.101348i
$763$	15.2339	−	4.52562i	0.551503	−	0.163839i
$764$	0.547420	−	0.753458i	0.0198049	−	0.0272592i
$765$	8.49786	−	26.5233i	0.307241	−	0.958951i
$766$	20.3868	−	18.3564i	0.736605	−	0.663243i
$767$	19.9244	+	30.6808i	0.719427	+	1.10782i
$768$	1.04632	+	2.72576i	0.0377559	+	0.0983576i
$769$	12.2868			0.443072			0.221536	−	0.975152i	$-0.428893\pi$
$769$	12.2868			0.443072			0.221536	+	0.975152i	$0.428893\pi$
$770$	−19.2209	+	3.94415i	−0.692674	+	0.142137i
$771$	−0.191358			−0.00689160
$772$	5.96297	+	15.5341i	0.214612	+	0.559084i
$773$	−11.2158	−	17.2709i	−0.403405	−	0.621189i	0.577335	−	0.816508i	$-0.304093\pi$
$773$	−11.2158	−	17.2709i	−0.403405	−	0.621189i	−0.980740	+	0.195318i	$0.937426\pi$
$774$	0.740094	−	0.666383i	0.0266021	−	0.0239527i
$775$	−20.6559	+	36.4644i	−0.741981	+	1.30984i
$776$	−6.11527	+	8.41694i	−0.219525	+	0.302151i
$777$	−23.7109	−	22.4651i	−0.850625	−	0.805932i
$778$	11.9804	+	6.10430i	0.429517	+	0.218850i
$779$	−1.34032	+	3.01041i	−0.0480220	+	0.107859i
$780$	1.66989	+	29.5451i	0.0597917	+	1.05788i
$781$	10.4544	−	18.7180i	0.374086	−	0.669782i
$782$	16.9335	+	4.53732i	0.605541	+	0.162254i
$783$	24.8125	+	3.92992i	0.886728	+	0.140444i
$784$	−6.99098	−	0.355261i	−0.249678	−	0.0126879i
$785$	30.5206	+	17.4546i	1.08933	+	0.622981i
$786$	2.26154	−	21.5171i	0.0806664	−	0.767490i
$787$	−14.1596	+	36.8871i	−0.504737	+	1.31488i	0.410460	+	0.911878i	$0.365368\pi$
$787$	−14.1596	+	36.8871i	−0.504737	+	1.31488i	−0.915197	+	0.403006i	$0.867965\pi$
$788$	2.36137	+	0.123754i	0.0841203	+	0.00440856i
$789$	−35.7480	+	39.7022i	−1.27266	+	1.41344i
$790$	4.53409	+	10.0724i	0.161316	+	0.358360i
$791$	−33.3300	+	11.8325i	−1.18508	+	0.420717i
$792$	−13.1395	−	12.7705i	−0.466890	−	0.453781i
$793$	31.9140	+	8.55134i	1.13330	+	0.303667i
$794$	−2.44866	−	23.2974i	−0.0868997	−	0.826795i
$795$	−45.9780	+	17.8660i	−1.63067	+	0.633640i
$796$	−1.34547	−	6.32993i	−0.0476888	−	0.224358i
$797$	−33.8251	+	5.35736i	−1.19815	+	0.189768i	−0.723446	−	0.690381i	$-0.757443\pi$
$797$	−33.8251	+	5.35736i	−1.19815	+	0.189768i	−0.474699	+	0.880148i	$0.657443\pi$
$798$	−44.4554	−	27.1938i	−1.57370	−	0.962650i
$799$	−14.4914	−	4.70854i	−0.512669	−	0.166576i
$800$	1.75350	−	4.68244i	0.0619956	−	0.165549i
$801$	75.5323	−	7.93877i	2.66880	−	0.280503i
$802$	−28.4137	+	7.61343i	−1.00332	+	0.268839i
$803$	−31.4666	+	2.09872i	−1.11043	+	0.0740622i
$804$	−44.0891			−1.55490
$805$	39.3402	+	23.8437i	1.38656	+	0.840379i
$806$	11.7400	+	36.1321i	0.413525	+	1.27270i
$807$	−24.2499	−	15.7481i	−0.853637	−	0.554358i
$808$	16.2815	+	6.24988i	0.572781	+	0.219870i
$809$	−15.2735	−	34.3048i	−0.536987	−	1.20609i	−0.954715	−	0.297521i	$-0.903840\pi$
$809$	−15.2735	−	34.3048i	−0.536987	−	1.20609i	0.417728	−	0.908572i	$-0.362826\pi$
$810$	11.0624	−	0.0453581i	0.388692	−	0.00159372i
$811$	−21.1835	+	6.88293i	−0.743852	+	0.241692i	−0.656334	−	0.754471i	$-0.727894\pi$
$811$	−21.1835	+	6.88293i	−0.743852	+	0.241692i	−0.0875185	+	0.996163i	$0.527894\pi$
$812$	−3.00327	+	8.50241i	−0.105394	+	0.298376i
$813$	18.1219	−	18.1219i	0.635563	−	0.635563i
$814$	13.9666	+	1.26718i	0.489529	+	0.0444146i
$815$	5.44080	+	4.85867i	0.190583	+	0.170192i
$816$	0.688070	+	6.54655i	0.0240873	+	0.229175i
$817$	0.0636466	+	1.21445i	0.00222671	+	0.0424882i
$818$	−11.2238	+	5.71884i	−0.392433	+	0.199954i
$819$	−15.5175	−	64.4100i	−0.542226	−	2.25067i
$820$	1.09097	+	0.0526908i	0.0380983	+	0.00184004i
$821$	−0.0931584	+	0.0198014i	−0.00325125	+	0.000691075i	−0.209537	−	0.977801i	$-0.567196\pi$
$821$	−0.0931584	+	0.0198014i	−0.00325125	+	0.000691075i	0.206286	+	0.978492i	$0.433862\pi$
$822$	−47.9571	+	31.1437i	−1.67270	+	1.08626i
$823$	−13.2377	−	10.7197i	−0.461438	−	0.373665i	0.370229	−	0.928941i	$-0.379279\pi$
$823$	−13.2377	−	10.7197i	−0.461438	−	0.373665i	−0.831666	+	0.555276i	$0.812613\pi$
$824$	−2.78633	−	4.82606i	−0.0970663	−	0.168124i
$825$	3.61818	+	48.2822i	0.125969	+	1.68097i
$826$	7.14390	+	20.1230i	0.248568	+	0.700169i
$827$	16.8310	+	2.66577i	0.585272	+	0.0926979i	0.442046	−	0.896992i	$-0.354253\pi$
$827$	16.8310	+	2.66577i	0.585272	+	0.0926979i	0.143225	+	0.989690i	$0.454253\pi$
$828$	2.24823	+	42.8988i	0.0781315	+	1.49084i
$829$	3.48668	+	3.87235i	0.121098	+	0.134492i	0.800645	−	0.599139i	$-0.204490\pi$
$829$	3.48668	+	3.87235i	0.121098	+	0.134492i	−0.679547	+	0.733632i	$0.737824\pi$
$830$	−1.52497	−	0.981463i	−0.0529326	−	0.0340671i
$831$	37.4112	+	3.93208i	1.29778	+	0.136402i
$832$	−2.05780	−	4.03866i	−0.0713413	−	0.140015i
$833$	−15.0172	−	4.85306i	−0.520315	−	0.168149i
$834$	−9.03376	−	12.4339i	−0.312814	−	0.430551i
$835$	−3.15247	+	1.03861i	−0.109096	+	0.0359425i
$836$	22.2166	−	2.65538i	0.768378	−	0.0918382i
$837$	59.6763	−	15.9902i	2.06271	−	0.552702i
$838$	−0.505089	−	1.31580i	−0.0174480	−	0.0454536i
$839$	−9.45686	−	29.1052i	−0.326487	−	1.00482i	−0.970765	−	0.240033i	$-0.922842\pi$
$839$	−9.45686	−	29.1052i	−0.326487	−	1.00482i	0.644278	−	0.764792i	$-0.277158\pi$
$840$	−3.06463	+	16.9991i	−0.105740	+	0.586524i
$841$	−14.0641	−	10.2182i	−0.484969	−	0.352351i
$842$	3.60272	−	2.91742i	0.124158	−	0.100541i
$843$	3.17145	−	60.5148i	0.109230	−	2.08424i
$844$	2.82204	−	13.2767i	0.0971387	−	0.457001i
$845$	−2.70763	−	16.6531i	−0.0931453	−	0.572884i
$846$		−	37.3372i		−	1.28368i
$847$	−14.4737	+	25.2490i	−0.497322	+	0.867566i
$848$	5.34257	−	5.34257i	0.183464	−	0.183464i
$849$	−19.2332	+	43.1985i	−0.660082	+	1.48257i
$850$	6.55097	−	9.17391i	0.224696	−	0.314662i
$851$	−22.0002	−	24.4337i	−0.754157	−	0.837576i
$852$	−11.8776	−	14.6676i	−0.406920	−	0.502504i
$853$	−8.12488	−	51.2985i	−0.278191	−	1.75643i	−0.591057	−	0.806630i	$-0.701289\pi$
$853$	−8.12488	−	51.2985i	−0.278191	−	1.75643i	0.312867	−	0.949797i	$-0.398711\pi$
$854$	16.9557	+	9.18880i	0.580213	+	0.314434i
$855$	−52.1807	+	64.9808i	−1.78454	+	2.22230i
$856$	−4.93591	−	2.19761i	−0.168706	−	0.0751128i
$857$	−5.57523	−	20.8071i	−0.190446	−	0.710756i	−0.993399	−	0.114712i	$-0.963405\pi$
$857$	−5.57523	−	20.8071i	−0.190446	−	0.710756i	0.802952	−	0.596043i	$-0.203261\pi$
$858$	34.5006	+	27.1339i	1.17783	+	0.926336i
$859$	−6.88850	−	11.9312i	−0.235033	−	0.407088i	0.724250	−	0.689538i	$-0.242186\pi$
$859$	−6.88850	−	11.9312i	−0.235033	−	0.407088i	−0.959282	+	0.282450i	$0.908853\pi$
$860$	0.367563	−	0.165459i	0.0125338	−	0.00564209i
$861$	−3.74061	+	0.495480i	−0.127480	+	0.0168859i
$862$	−1.39954	+	0.713099i	−0.0476684	+	0.0242882i
$863$	8.06335	+	9.95741i	0.274480	+	0.338954i	0.895681	−	0.444697i	$-0.146689\pi$
$863$	8.06335	+	9.95741i	0.274480	+	0.338954i	−0.621202	+	0.783651i	$0.713355\pi$
$864$	−6.73375	+	2.99806i	−0.229087	+	0.101996i
$865$	17.6538	+	30.2899i	0.600249	+	1.02989i
$866$	−22.0967	−	19.8959i	−0.750875	−	0.676091i
$867$	5.44296	−	34.3655i	0.184852	−	1.16711i
$868$	1.75743	+	22.1061i	0.0596512	+	0.750330i
$869$	15.6523	+	4.84047i	0.530968	+	0.164202i
$870$	19.8669	+	10.0203i	0.673551	+	0.339720i
$871$	68.0715	−	7.15460i	2.30651	−	0.242424i
$872$	3.27141	+	5.03753i	0.110784	+	0.170592i
$873$	−48.2045	−	31.3044i	−1.63148	−	1.05949i
$874$	−42.4386	−	30.8334i	−1.43551	−	1.04296i
$875$	23.2299	−	18.3131i	0.785315	−	0.619097i
$876$	−8.57899	+	26.4034i	−0.289857	+	0.892089i
$877$	36.2739	−	1.90103i	1.22488	−	0.0641933i	0.571102	−	0.820879i	$-0.306516\pi$
$877$	36.2739	−	1.90103i	1.22488	−	0.0641933i	0.653779	+	0.756686i	$0.273183\pi$
$878$	−17.7233	+	21.8865i	−0.598134	+	0.738634i
$879$	−67.7656	−	39.1245i	−2.28568	−	1.31964i
$880$	−3.48749	−	6.54503i	−0.117563	−	0.220633i
$881$		−	3.79667i		−	0.127913i	−0.997953	−	0.0639566i	$-0.979628\pi$
$881$		−	3.79667i		−	0.127913i	0.997953	−	0.0639566i	$-0.0203719\pi$
$882$	−0.0613549	−	38.6720i	−0.00206593	−	1.30216i
$883$	−1.66669	−	0.849223i	−0.0560887	−	0.0285786i	0.425721	−	0.904854i	$-0.360020\pi$
$883$	−1.66669	−	0.849223i	−0.0560887	−	0.0285786i	−0.481810	+	0.876276i	$0.660020\pi$
$884$	−2.12469	−	9.99590i	−0.0714612	−	0.336199i
$885$	51.4948	−	11.1664i	1.73098	−	0.375355i
$886$	26.3491	−	11.7314i	0.885214	−	0.394123i
$887$	3.24542	−	4.99750i	0.108970	−	0.167800i	−0.779978	−	0.625807i	$-0.784770\pi$
$887$	3.24542	−	4.99750i	0.108970	−	0.167800i	0.888949	+	0.458007i	$0.151437\pi$
$888$	5.60477	−	11.0000i	0.188084	−	0.369135i
$889$	4.60457	+	3.15926i	0.154432	+	0.105958i
$890$	30.0942	+	6.26787i	1.00876	+	0.210099i
$891$	10.8046	−	12.3488i	0.361967	−	0.413701i
$892$	−1.72748	−	6.44704i	−0.0578403	−	0.215863i
$893$	35.4329	+	28.6930i	1.18572	+	0.960174i
$894$	12.7215	−	14.1287i	0.425472	−	0.472534i
$895$	−17.7150	+	4.82465i	−0.592147	+	0.161270i
$896$	−0.619679	−	2.57216i	−0.0207020	−	0.0859298i
$897$	−16.0978	−	101.638i	−0.537490	−	3.39358i
$898$	−0.731787	+	1.12685i	−0.0244201	+	0.0376036i
$899$	27.9422	+	5.93929i	0.931924	+	0.198087i
$900$	26.3401	+	8.32024i	0.878003	+	0.277341i
$901$	14.7522	−	8.51719i	0.491467	−	0.283749i
$902$	1.12913	−	1.16175i	0.0375958	−	0.0386820i
$903$	−1.14698	+	0.789638i	−0.0381691	+	0.0262775i
$904$	−7.85744	−	10.8148i	−0.261334	−	0.359696i
$905$	47.3965	+	7.30779i	1.57551	+	0.242919i
$906$	15.0897	−	13.5868i	0.501320	−	0.451391i
$907$	25.5124	+	9.79328i	0.847124	+	0.325181i	0.742924	−	0.669376i	$-0.233438\pi$
$907$	25.5124	+	9.79328i	0.847124	+	0.325181i	0.104200	+	0.994556i	$0.466772\pi$
$908$	5.16349	−	4.18131i	0.171357	−	0.138762i
$909$	−29.7732	+	91.6323i	−0.987513	+	3.03925i
$910$	1.97310	−	26.7431i	0.0654076	−	0.886524i
$911$	4.20036	−	3.05174i	0.139164	−	0.101109i	−0.516025	−	0.856573i	$-0.672589\pi$
$911$	4.20036	−	3.05174i	0.139164	−	0.101109i	0.655189	+	0.755465i	$0.272589\pi$
$912$	5.09794	−	19.0258i	0.168810	−	0.630006i
$913$	−2.58804	+	0.733111i	−0.0856515	+	0.0242624i
$914$	12.0906	+	6.98052i	0.399922	+	0.230895i
$915$	27.8138	−	38.6144i	0.919497	−	1.27655i
$916$	4.08931	−	1.32870i	0.135115	−	0.0439014i
$917$	−4.56173	+	19.0676i	−0.150642	+	0.629667i
$918$	−16.4138	+	2.59968i	−0.541735	+	0.0858024i
$919$	33.6706	+	3.53892i	1.11069	+	0.116738i	0.642058	−	0.766656i	$-0.278081\pi$
$919$	33.6706	+	3.53892i	1.11069	+	0.116738i	0.468631	+	0.883394i	$0.344747\pi$
$920$	−4.43121	+	16.8129i	−0.146093	+	0.554306i
$921$	28.6198	+	6.08333i	0.943055	+	0.200453i
$922$	−4.30523	+	1.65262i	−0.141785	+	0.0544262i
$923$	20.7186	+	20.7186i	0.681962	+	0.681962i
$924$	15.9003	+	20.0891i	0.523082	+	0.660884i
$925$	−19.6749	+	7.73818i	−0.646906	+	0.254430i
$926$	29.8499	+	13.2900i	0.980928	+	0.436737i
$927$	25.8198	−	16.7676i	0.848034	−	0.550720i
$928$	−3.40353	−	0.178371i	−0.111726	−	0.00585532i
$929$	0.663396	−	6.31179i	0.0217653	−	0.207083i	−0.978235	−	0.207502i	$-0.933467\pi$
$929$	0.663396	−	6.31179i	0.0217653	−	0.207083i	1.00000		0.000418866i	$0.000133329\pi$
$930$	54.6571	+	2.63979i	1.79228	+	0.0865620i
$931$	36.7468	+	29.6606i	1.20433	+	0.972085i
$932$	2.50372	−	4.91383i	0.0820121	−	0.160958i
$933$	12.4696	−	4.78663i	0.408237	−	0.156707i
$934$	−11.0691	+	19.1723i	−0.362193	+	0.627337i
$935$	−3.77566	−	16.2884i	−0.123477	−	0.532687i
$936$	21.6863	−	12.5206i	0.708840	−	0.409249i
$937$	9.26358	−	58.4879i	0.302628	−	1.91072i	−0.0993208	−	0.995055i	$-0.531667\pi$
$937$	9.26358	−	58.4879i	0.302628	−	1.91072i	0.401949	−	0.915662i	$-0.368333\pi$
$938$	39.6148	+	5.18342i	1.29347	+	0.169245i
$939$	−2.24879	−	0.730676i	−0.0733865	−	0.0238447i
$940$	4.61095	−	14.3916i	0.150393	−	0.469401i
$941$	15.3591	+	34.4972i	0.500694	+	1.12458i	0.970345	+	0.241724i	$0.0777129\pi$
$941$	15.3591	+	34.4972i	0.500694	+	1.12458i	−0.469651	+	0.882852i	$0.655620\pi$
$942$	2.40265	−	45.8453i	0.0782826	−	1.49372i
$943$	−3.79297	+	0.198781i	−0.123516	+	0.00647321i
$944$	−6.52946	+	4.74393i	−0.212516	+	0.154402i
$945$	−43.2617	−	5.48028i	−1.40730	−	0.178274i
$946$	0.176639	−	0.571185i	0.00574302	−	0.0185708i
$947$	−2.45484	+	9.16159i	−0.0797716	+	0.297712i	−0.994273	−	0.106871i	$-0.965917\pi$
$947$	−2.45484	+	9.16159i	−0.0797716	+	0.297712i	0.914501	+	0.404583i	$0.132583\pi$
$948$	9.07660	−	11.2087i	0.294794	−	0.364040i
$949$	8.96092	−	42.1578i	0.290884	−	1.36850i
$950$	−28.1378	+	18.6027i	−0.912909	+	0.603551i
$951$	−19.2657	+	26.5170i	−0.624734	+	0.859873i
$952$	0.151415	−	5.96308i	0.00490740	−	0.193264i
$953$	13.0625	+	25.6365i	0.423135	+	0.830448i	0.999908	+	0.0135444i	$0.00431144\pi$
$953$	13.0625	+	25.6365i	0.423135	+	0.830448i	−0.576774	+	0.816904i	$0.695689\pi$
$954$	31.0197	+	27.9303i	1.00430	+	0.904277i
$955$	1.31719	+	1.61303i	0.0426233	+	0.0521963i
$956$	−3.21274	+	5.56462i	−0.103907	+	0.179973i
$957$	30.6397	−	12.2648i	0.990442	−	0.396465i
$958$	6.21814	+	6.21814i	0.200899	+	0.200899i
$959$	46.7517	−	22.3450i	1.50969	−	0.721557i
$960$	−6.49001	+	0.709043i	−0.209464	+	0.0228843i
$961$	38.3948	−	8.16107i	1.23854	−	0.263260i
$962$	−6.86846	+	17.8930i	−0.221448	+	0.576892i
$963$	10.6971	−	27.8669i	0.344709	−	0.897999i
$964$	−14.3277	+	3.04545i	−0.461464	+	0.0980872i
$965$	−36.9864	+	4.04082i	−1.19063	+	0.130079i
$966$	4.66520	−	59.8843i	0.150100	−	1.92675i
$967$	3.29881	+	3.29881i	0.106083	+	0.106083i	0.758156	−	0.652073i	$-0.226101\pi$
$967$	3.29881	+	3.29881i	0.106083	+	0.106083i	−0.652073	+	0.758156i	$0.726101\pi$
$968$	−10.7019	−	2.54333i	−0.343973	−	0.0817457i
$969$	22.2039	−	38.4583i	0.713293	−	1.23546i
$970$	−14.7144	−	18.0192i	−0.472452	−	0.578563i
$971$	−21.7213	−	19.5579i	−0.697069	−	0.627644i	0.242440	−	0.970166i	$-0.422052\pi$
$971$	−21.7213	−	19.5579i	−0.697069	−	0.627644i	−0.939510	+	0.342522i	$0.888719\pi$
$972$	3.48141	+	6.83266i	0.111666	+	0.219158i
$973$	6.65517	+	12.2341i	0.213355	+	0.392209i
$974$	−10.1492	+	13.9692i	−0.325201	+	0.447601i
$975$	−64.8349	−	13.2263i	−2.07638	−	0.423582i
$976$	−1.51552	+	7.12995i	−0.0485105	+	0.228224i
$977$	−35.5769	+	43.9338i	−1.13821	+	1.40557i	−0.237362	+	0.971421i	$0.576283\pi$
$977$	−35.5769	+	43.9338i	−1.13821	+	1.40557i	−0.900843	+	0.434145i	$0.857051\pi$
$978$	2.46513	−	9.20000i	0.0788263	−	0.294184i
$979$	36.5017	−	27.3224i	1.16660	−	0.873228i
$980$	4.75215	−	14.9137i	0.151802	−	0.476399i
$981$	−26.8463	+	19.5049i	−0.857135	+	0.622745i
$982$	−34.0298	+	1.78343i	−1.08593	+	0.0569114i
$983$	−1.75635	+	33.5131i	−0.0560188	+	1.06890i	0.815568	+	0.578661i	$0.196424\pi$
$983$	−1.75635	+	33.5131i	−0.0560188	+	1.06890i	−0.871587	+	0.490241i	$0.836909\pi$
$984$	−0.580075	−	1.30287i	−0.0184921	−	0.0415339i
$985$	−1.61327	+	5.03530i	−0.0514031	+	0.160438i
$986$	−7.30790	−	2.37448i	−0.232731	−	0.0756189i
$987$	−6.77331	+	51.7657i	−0.215597	+	1.64772i
$988$	−4.78355	+	30.2021i	−0.152185	+	0.960858i
$989$	−1.21391	+	0.700850i	−0.0386000	+	0.0222857i
$990$	35.1007	−	21.1329i	1.11557	−	0.671648i
$991$	−21.4667	+	37.1815i	−0.681913	+	1.18111i	0.292483	+	0.956271i	$0.405519\pi$
$991$	−21.4667	+	37.1815i	−0.681913	+	1.18111i	−0.974396	+	0.224838i	$0.927815\pi$
$992$	−7.82497	+	3.00373i	−0.248443	+	0.0953684i
$993$	4.66891	−	9.16325i	0.148163	−	0.290787i
$994$	8.94779	+	14.5755i	0.283807	+	0.462307i
$995$	14.4535	+	0.698064i	0.458207	+	0.0221301i
$996$	−0.247517	+	2.35497i	−0.00784289	+	0.0746201i
$997$	48.9727	+	2.56655i	1.55098	+	0.0812834i	0.808464	−	0.588545i	$-0.200299\pi$
$997$	48.9727	+	2.56655i	1.55098	+	0.0812834i	0.742516	+	0.669829i	$0.233632\pi$
$998$	0.490589	−	0.318592i	0.0155293	−	0.0100849i
$999$	28.4729	+	12.6769i	0.900841	+	0.401080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.157.3	yes	768
5.3	odd	4	inner	770.2.bv.a.3.22	✓	768
7.5	odd	6	inner	770.2.bv.a.47.3	yes	768
11.4	even	5	inner	770.2.bv.a.367.27	yes	768
35.33	even	12	inner	770.2.bv.a.663.27	yes	768
55.48	odd	20	inner	770.2.bv.a.213.3	yes	768
77.26	odd	30	inner	770.2.bv.a.257.22	yes	768
385.103	even	60	inner	770.2.bv.a.103.3	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.22	✓	768	5.3	odd	4	inner
770.2.bv.a.47.3	yes	768	7.5	odd	6	inner
770.2.bv.a.103.3	yes	768	385.103	even	60	inner
770.2.bv.a.157.3	yes	768	1.1	even	1	trivial
770.2.bv.a.213.3	yes	768	55.48	odd	20	inner
770.2.bv.a.257.22	yes	768	77.26	odd	30	inner
770.2.bv.a.367.27	yes	768	11.4	even	5	inner
770.2.bv.a.663.27	yes	768	35.33	even	12	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.358368 - 0.933580i) q^{2} +(-1.59018 - 2.44866i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(-1.02331 - 1.98817i) q^{5} +(-1.71615 + 2.36208i) q^{6} +(1.81969 - 1.92060i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.24705 + 5.04696i) q^{9} +O(q^{10})\)	\(q+(-0.358368 - 0.933580i) q^{2} +(-1.59018 - 2.44866i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(-1.02331 - 1.98817i) q^{5} +(-1.71615 + 2.36208i) q^{6} +(1.81969 - 1.92060i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.24705 + 5.04696i) q^{9} +(-1.48940 + 1.66784i) q^{10} +(0.393609 + 3.29319i) q^{11} +(2.82020 + 0.755671i) q^{12} +(-4.47689 - 0.709069i) q^{13} +(-2.44516 - 1.01055i) q^{14} +(-3.24110 + 5.66729i) q^{15} +(0.104528 - 0.994522i) q^{16} +(0.807961 - 2.10481i) q^{17} +(5.51701 + 0.289134i) q^{18} +(-4.51411 + 5.01343i) q^{19} +(2.09082 + 0.792769i) q^{20} +(-7.59653 - 1.40170i) q^{21} +(2.93340 - 1.54764i) q^{22} +(-7.51078 - 2.01251i) q^{23} +(-0.305191 - 2.90369i) q^{24} +(-2.90566 + 4.06905i) q^{25} +(0.942399 + 4.43364i) q^{26} +(7.28026 - 1.15308i) q^{27} +(-0.0671596 + 2.64490i) q^{28} +(3.24139 + 1.05319i) q^{29} +(6.45238 + 0.994854i) q^{30} +(8.33577 - 0.876124i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(7.43798 - 6.20056i) q^{33} -2.25456 q^{34} +(-5.68061 - 1.65248i) q^{35} +(-1.70719 - 5.25419i) q^{36} +(3.54622 + 2.30294i) q^{37} +(6.29816 + 2.41764i) q^{38} +(5.38277 + 12.0899i) q^{39} +(-0.00916828 - 2.23605i) q^{40} +(0.464558 - 0.150944i) q^{41} +(1.41375 + 7.59430i) q^{42} +(0.127467 - 0.127467i) q^{43} +(-2.49608 - 2.18394i) q^{44} +(12.3337 - 0.697100i) q^{45} +(0.812786 + 7.73314i) q^{46} +(-0.353706 - 6.74911i) q^{47} +(-2.60146 + 1.32551i) q^{48} +(-0.377442 - 6.98982i) q^{49} +(4.84008 + 1.25445i) q^{50} +(-6.43876 + 1.36860i) q^{51} +(3.80143 - 2.46868i) q^{52} +(5.87175 + 4.75485i) q^{53} +(-3.68550 - 6.38348i) q^{54} +(6.14463 - 4.15253i) q^{55} +(2.49329 - 0.885148i) q^{56} +(19.4544 + 3.08128i) q^{57} +(-0.178371 - 3.40353i) q^{58} +(-5.40046 - 5.99781i) q^{59} +(-1.38355 - 6.38034i) q^{60} +(-7.24930 - 0.761932i) q^{61} +(-3.80520 - 7.46813i) q^{62} +(5.60427 + 13.4996i) q^{63} +(0.587785 + 0.809017i) q^{64} +(3.17151 + 9.62642i) q^{65} +(-8.45425 - 4.72187i) q^{66} +(-14.5861 + 3.90833i) q^{67} +(0.807961 + 2.10481i) q^{68} +(7.01553 + 21.5916i) q^{69} +(0.493025 + 5.89550i) q^{70} +(-5.22971 - 3.79961i) q^{71} +(-4.29341 + 3.47673i) q^{72} +(-0.497643 + 9.49559i) q^{73} +(0.879130 - 4.13598i) q^{74} +(14.5842 + 0.644450i) q^{75} -6.74624i q^{76} +(7.04115 + 5.23662i) q^{77} +(9.35789 - 9.35789i) q^{78} +(2.00922 - 4.51279i) q^{79} +(-2.08425 + 0.809888i) q^{80} +(-3.31038 - 3.67655i) q^{81} +(-0.307401 - 0.379609i) q^{82} +(0.126872 + 0.801041i) q^{83} +(6.58325 - 4.04141i) q^{84} +(-5.01153 + 0.547517i) q^{85} +(-0.164681 - 0.0733207i) q^{86} +(-2.57548 - 9.61181i) q^{87} +(-1.14437 + 3.11294i) q^{88} +(-6.87367 - 11.9056i) q^{89} +(-5.07079 - 11.2646i) q^{90} +(-9.50839 + 7.30804i) q^{91} +(6.92823 - 3.53011i) q^{92} +(-15.4007 - 19.0182i) q^{93} +(-6.17408 + 2.74888i) q^{94} +(14.5869 + 3.84452i) q^{95} +(2.16975 + 1.95365i) q^{96} +(-1.62753 + 10.2758i) q^{97} +(-6.39029 + 2.85730i) q^{98} +(-17.5050 - 5.41343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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