LMFDB - Embedded newform 256.2.m.a.5.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	256.5
Dual form			256.2.m.a.205.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104160 - 1.41037i) q^{2} +(0.381661 - 2.57295i) q^{3} +(-1.97830 - 0.293808i) q^{4} +(2.12912 + 0.104597i) q^{5} +(-3.58906 - 0.806282i) q^{6} +(-1.14227 - 0.610554i) q^{7} +(-0.620438 + 2.75954i) q^{8} +(-3.60358 - 1.09313i) q^{9} +O(q^{10})$	\(q+(0.104160 - 1.41037i) q^{2} +(0.381661 - 2.57295i) q^{3} +(-1.97830 - 0.293808i) q^{4} +(2.12912 + 0.104597i) q^{5} +(-3.58906 - 0.806282i) q^{6} +(-1.14227 - 0.610554i) q^{7} +(-0.620438 + 2.75954i) q^{8} +(-3.60358 - 1.09313i) q^{9} +(0.369290 - 2.99196i) q^{10} +(-1.59142 - 2.65513i) q^{11} +(-1.51099 + 4.97793i) q^{12} +(2.15012 - 2.37229i) q^{13} +(-0.980087 + 1.54743i) q^{14} +(1.08173 - 5.43821i) q^{15} +(3.82735 + 1.16248i) q^{16} +(1.28594 + 6.46488i) q^{17} +(-1.91707 + 4.96853i) q^{18} +(2.66744 + 5.63984i) q^{19} +(-4.18132 - 0.832478i) q^{20} +(-2.00688 + 2.70597i) q^{21} +(-3.91048 + 1.96794i) q^{22} +(-4.38646 - 3.59988i) q^{23} +(6.86336 + 2.64956i) q^{24} +(-0.453693 - 0.0446849i) q^{25} +(-3.12186 - 3.27957i) q^{26} +(-0.851583 + 1.80052i) q^{27} +(2.08036 + 1.54347i) q^{28} +(5.67707 - 1.42203i) q^{29} +(-7.55723 - 2.09208i) q^{30} +(2.05173 + 0.849854i) q^{31} +(2.03819 - 5.27691i) q^{32} +(-7.43890 + 3.08129i) q^{33} +(9.25183 - 1.14028i) q^{34} +(-2.36817 - 1.41942i) q^{35} +(6.80780 + 3.22131i) q^{36} +(0.303269 + 0.847580i) q^{37} +(8.23211 - 3.17465i) q^{38} +(-5.28317 - 6.43756i) q^{39} +(-1.60963 + 5.81051i) q^{40} +(7.63154 - 0.751641i) q^{41} +(3.60739 + 3.11231i) q^{42} +(-2.87027 + 0.425765i) q^{43} +(2.36822 + 5.72022i) q^{44} +(-7.55813 - 2.70434i) q^{45} +(-5.53406 + 5.81159i) q^{46} +(4.68515 - 7.01182i) q^{47} +(4.45176 - 9.40391i) q^{48} +(-2.95699 - 4.42546i) q^{49} +(-0.110279 + 0.635222i) q^{50} +(17.1246 - 0.841277i) q^{51} +(-4.95058 + 4.06138i) q^{52} +(-12.1257 - 3.03732i) q^{53} +(2.45070 + 1.38859i) q^{54} +(-3.11062 - 5.81956i) q^{55} +(2.39355 - 2.77332i) q^{56} +(15.5291 - 4.71069i) q^{57} +(-1.41427 - 8.15491i) q^{58} +(8.03084 + 8.86067i) q^{59} +(-3.73777 + 10.4406i) q^{60} +(2.79314 + 3.76611i) q^{61} +(1.41232 - 2.80518i) q^{62} +(3.44883 + 3.44883i) q^{63} +(-7.23011 - 3.42425i) q^{64} +(4.82601 - 4.82601i) q^{65} +(3.57094 + 10.8126i) q^{66} +(0.947152 - 0.702456i) q^{67} +(-0.644553 - 13.1673i) q^{68} +(-10.9364 + 9.91222i) q^{69} +(-2.24858 + 3.19215i) q^{70} +(1.18254 + 3.89830i) q^{71} +(5.25235 - 9.26600i) q^{72} +(-7.15524 + 3.82456i) q^{73} +(1.22699 - 0.339438i) q^{74} +(-0.288129 + 1.15028i) q^{75} +(-3.61998 - 11.9410i) q^{76} +(0.196729 + 4.00452i) q^{77} +(-9.62965 + 6.78070i) q^{78} +(4.41411 - 2.94941i) q^{79} +(8.02732 + 2.87540i) q^{80} +(-5.08565 - 3.39812i) q^{81} +(-0.265195 - 10.8416i) q^{82} +(-1.92964 + 5.39298i) q^{83} +(4.76526 - 4.76359i) q^{84} +(2.06173 + 13.8990i) q^{85} +(0.301520 + 4.09250i) q^{86} +(-1.49210 - 15.1496i) q^{87} +(8.31431 - 2.74425i) q^{88} +(1.98911 - 1.63242i) q^{89} +(-4.60139 + 10.3781i) q^{90} +(-3.90442 + 1.39702i) q^{91} +(7.62008 + 8.41042i) q^{92} +(2.96970 - 4.95464i) q^{93} +(-9.40128 - 7.33816i) q^{94} +(5.08941 + 12.2869i) q^{95} +(-12.7993 - 7.25814i) q^{96} +(-5.27929 + 12.7453i) q^{97} +(-6.54954 + 3.70951i) q^{98} +(2.83241 + 11.3076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{64}\right)$	$1$

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 $

$2$	0.104160	−	1.41037i	0.0736520	−	0.997284i
$2$	0.104160	−	1.41037i	0.0736520	−	0.997284i
$3$	0.381661	−	2.57295i	0.220352	−	1.48549i	−0.543122	−	0.839654i	$-0.682758\pi$
$3$	0.381661	−	2.57295i	0.220352	−	1.48549i	0.763474	−	0.645839i	$-0.223492\pi$
$4$	−1.97830	−	0.293808i	−0.989151	−	0.146904i
$5$	2.12912	+	0.104597i	0.952173	+	0.0467773i	0.519221	−	0.854640i	$-0.326222\pi$
$5$	2.12912	+	0.104597i	0.952173	+	0.0467773i	0.432952	+	0.901417i	$0.357472\pi$
$6$	−3.58906	−	0.806282i	−1.46523	−	0.329163i
$7$	−1.14227	−	0.610554i	−0.431736	−	0.230768i	0.241189	−	0.970478i	$-0.422463\pi$
$7$	−1.14227	−	0.610554i	−0.431736	−	0.230768i	−0.672925	+	0.739710i	$0.734963\pi$
$8$	−0.620438	+	2.75954i	−0.219358	+	0.975644i
$9$	−3.60358	−	1.09313i	−1.20119	−	0.364378i
$10$	0.369290	−	2.99196i	0.116780	−	0.946142i
$11$	−1.59142	−	2.65513i	−0.479832	−	0.800551i	0.518686	−	0.854965i	$-0.326421\pi$
$11$	−1.59142	−	2.65513i	−0.479832	−	0.800551i	−0.998519	+	0.0544131i	$0.982671\pi$
$12$	−1.51099	+	4.97793i	−0.436186	+	1.43701i
$13$	2.15012	−	2.37229i	0.596336	−	0.657955i	−0.365747	−	0.930715i	$-0.619186\pi$
$13$	2.15012	−	2.37229i	0.596336	−	0.657955i	0.962082	+	0.272759i	$0.0879363\pi$
$14$	−0.980087	+	1.54743i	−0.261939	+	0.413567i
$15$	1.08173	−	5.43821i	0.279301	−	1.40414i
$16$	3.82735	+	1.16248i	0.956838	+	0.290620i
$17$	1.28594	+	6.46488i	0.311887	+	1.56796i	0.745276	+	0.666756i	$0.232318\pi$
$17$	1.28594	+	6.46488i	0.311887	+	1.56796i	−0.433389	+	0.901207i	$0.642682\pi$
$18$	−1.91707	+	4.96853i	−0.451859	+	1.17109i
$19$	2.66744	+	5.63984i	0.611954	+	1.29387i	0.937383	+	0.348301i	$0.113241\pi$
$19$	2.66744	+	5.63984i	0.611954	+	1.29387i	−0.325429	+	0.945566i	$0.605509\pi$
$20$	−4.18132	−	0.832478i	−0.934971	−	0.186148i
$21$	−2.00688	+	2.70597i	−0.437938	+	0.590491i
$22$	−3.91048	+	1.96794i	−0.833718	+	0.419567i
$23$	−4.38646	−	3.59988i	−0.914641	−	0.750627i	0.0541429	−	0.998533i	$-0.482757\pi$
$23$	−4.38646	−	3.59988i	−0.914641	−	0.750627i	−0.968784	+	0.247907i	$0.920257\pi$
$24$	6.86336	+	2.64956i	1.40098	+	0.540840i
$25$	−0.453693	−	0.0446849i	−0.0907387	−	0.00893698i
$26$	−3.12186	−	3.27957i	−0.612247	−	0.643176i
$27$	−0.851583	+	1.80052i	−0.163887	+	0.346510i
$28$	2.08036	+	1.54347i	0.393152	+	0.291688i
$29$	5.67707	−	1.42203i	1.05421	−	0.264065i	0.323126	−	0.946356i	$-0.395266\pi$
$29$	5.67707	−	1.42203i	1.05421	−	0.264065i	0.731080	+	0.682291i	$0.239016\pi$
$30$	−7.55723	−	2.09208i	−1.37975	−	0.381960i
$31$	2.05173	+	0.849854i	0.368501	+	0.152638i	0.559247	−	0.829001i	$-0.311090\pi$
$31$	2.05173	+	0.849854i	0.368501	+	0.152638i	−0.190745	+	0.981640i	$0.561090\pi$
$32$	2.03819	−	5.27691i	0.360304	−	0.932835i
$33$	−7.43890	+	3.08129i	−1.29495	+	0.536384i
$34$	9.25183	−	1.14028i	1.58668	−	0.195556i
$35$	−2.36817	−	1.41942i	−0.400293	−	0.239926i
$36$	6.80780	+	3.22131i	1.13463	+	0.536885i
$37$	0.303269	+	0.847580i	0.0498571	+	0.139341i	0.963891	−	0.266296i	$-0.0857998\pi$
$37$	0.303269	+	0.847580i	0.0498571	+	0.139341i	−0.914034	+	0.405637i	$0.867050\pi$
$38$	8.23211	−	3.17465i	1.33542	−	0.514996i
$39$	−5.28317	−	6.43756i	−0.845984	−	1.03083i
$40$	−1.60963	+	5.81051i	−0.254505	+	0.918722i
$41$	7.63154	−	0.751641i	1.19185	−	0.117387i	0.517422	−	0.855731i	$-0.326892\pi$
$41$	7.63154	−	0.751641i	1.19185	−	0.117387i	0.674424	+	0.738344i	$0.264392\pi$
$42$	3.60739	+	3.11231i	0.556632	+	0.480239i
$43$	−2.87027	+	0.425765i	−0.437713	+	0.0649285i	−0.361950	−	0.932197i	$-0.617889\pi$
$43$	−2.87027	+	0.425765i	−0.437713	+	0.0649285i	−0.0757623	+	0.997126i	$0.524139\pi$
$44$	2.36822	+	5.72022i	0.357022	+	0.862355i
$45$	−7.55813	−	2.70434i	−1.12670	−	0.403140i
$46$	−5.53406	+	5.81159i	−0.815953	+	0.856872i
$47$	4.68515	−	7.01182i	0.683399	−	1.02278i	−0.313909	−	0.949453i	$-0.601639\pi$
$47$	4.68515	−	7.01182i	0.683399	−	1.02278i	0.997308	−	0.0733262i	$-0.0233614\pi$
$48$	4.45176	−	9.40391i	0.642556	−	1.35734i
$49$	−2.95699	−	4.42546i	−0.422428	−	0.632208i
$50$	−0.110279	+	0.635222i	−0.0155958	+	0.0898340i
$51$	17.1246	−	0.841277i	2.39792	−	0.117802i
$52$	−4.95058	+	4.06138i	−0.686522	+	0.563213i
$53$	−12.1257	−	3.03732i	−1.66559	−	0.417209i	−0.708201	−	0.706011i	$-0.750493\pi$
$53$	−12.1257	−	3.03732i	−1.66559	−	0.417209i	−0.957389	+	0.288802i	$0.906743\pi$
$54$	2.45070	+	1.38859i	0.333499	+	0.188963i
$55$	−3.11062	−	5.81956i	−0.419436	−	0.784709i
$56$	2.39355	−	2.77332i	0.319852	−	0.370600i
$57$	15.5291	−	4.71069i	2.05688	−	0.623947i
$58$	−1.41427	−	8.15491i	−0.185703	−	1.07079i
$59$	8.03084	+	8.86067i	1.04553	+	1.15356i	0.987879	+	0.155224i	$0.0496098\pi$
$59$	8.03084	+	8.86067i	1.04553	+	1.15356i	0.0576471	+	0.998337i	$0.481640\pi$
$60$	−3.73777	+	10.4406i	−0.482544	+	1.34788i
$61$	2.79314	+	3.76611i	0.357624	+	0.482201i	0.944980	−	0.327128i	$-0.106081\pi$
$61$	2.79314	+	3.76611i	0.357624	+	0.482201i	−0.587355	+	0.809329i	$0.699831\pi$
$62$	1.41232	−	2.80518i	0.179365	−	0.356258i
$63$	3.44883	+	3.44883i	0.434512	+	0.434512i
$64$	−7.23011	−	3.42425i	−0.903764	−	0.428031i
$65$	4.82601	−	4.82601i	0.598592	−	0.598592i
$66$	3.57094	+	10.8126i	0.439552	+	1.33093i
$67$	0.947152	−	0.702456i	0.115713	−	0.0858186i	−0.536295	−	0.844030i	$-0.680177\pi$
$67$	0.947152	−	0.702456i	0.115713	−	0.0858186i	0.652008	+	0.758212i	$0.273927\pi$
$68$	−0.644553	−	13.1673i	−0.0781635	−	1.59677i
$69$	−10.9364	+	9.91222i	−1.31659	+	1.19329i
$70$	−2.24858	+	3.19215i	−0.268757	+	0.381535i
$71$	1.18254	+	3.89830i	0.140341	+	0.462643i	0.998731	−	0.0503544i	$-0.0160351\pi$
$71$	1.18254	+	3.89830i	0.140341	+	0.462643i	−0.858390	+	0.512997i	$0.828535\pi$
$72$	5.25235	−	9.26600i	0.618995	−	1.09201i
$73$	−7.15524	+	3.82456i	−0.837458	+	0.447630i	−0.833604	−	0.552362i	$-0.813727\pi$
$73$	−7.15524	+	3.82456i	−0.837458	+	0.447630i	−0.00385340	+	0.999993i	$0.501227\pi$
$74$	1.22699	−	0.339438i	0.142635	−	0.0394589i
$75$	−0.288129	+	1.15028i	−0.0332703	+	0.132822i
$76$	−3.61998	−	11.9410i	−0.415240	−	1.36973i
$77$	0.196729	+	4.00452i	0.0224194	+	0.456357i
$78$	−9.62965	+	6.78070i	−1.09034	+	0.767763i
$79$	4.41411	−	2.94941i	0.496626	−	0.331835i	−0.281904	−	0.959443i	$-0.590966\pi$
$79$	4.41411	−	2.94941i	0.496626	−	0.331835i	0.778530	+	0.627608i	$0.215966\pi$
$80$	8.02732	+	2.87540i	0.897482	+	0.321479i
$81$	−5.08565	−	3.39812i	−0.565072	−	0.377569i
$82$	−0.265195	−	10.8416i	−0.0292859	−	1.19725i
$83$	−1.92964	+	5.39298i	−0.211805	+	0.591956i	−0.999716	−	0.0238334i	$-0.992413\pi$
$83$	−1.92964	+	5.39298i	−0.211805	+	0.591956i	0.787911	+	0.615790i	$0.211163\pi$
$84$	4.76526	−	4.76359i	0.519932	−	0.519750i
$85$	2.06173	+	13.8990i	0.223626	+	1.50756i
$86$	0.301520	+	4.09250i	0.0325138	+	0.441306i
$87$	−1.49210	−	15.1496i	−0.159970	−	1.62420i
$88$	8.31431	−	2.74425i	0.886309	−	0.292538i
$89$	1.98911	−	1.63242i	0.210846	−	0.173036i	−0.523043	−	0.852306i	$-0.675203\pi$
$89$	1.98911	−	1.63242i	0.210846	−	0.173036i	0.733889	+	0.679270i	$0.237703\pi$
$90$	−4.60139	+	10.3781i	−0.485029	+	1.09395i
$91$	−3.90442	+	1.39702i	−0.409295	+	0.146448i
$92$	7.62008	+	8.41042i	0.794448	+	0.876847i
$93$	2.96970	−	4.95464i	0.307943	−	0.513772i
$94$	−9.40128	−	7.33816i	−0.969668	−	0.756873i
$95$	5.08941	+	12.2869i	0.522162	+	1.26061i
$96$	−12.7993	−	7.25814i	−1.30633	−	0.740781i
$97$	−5.27929	+	12.7453i	−0.536030	+	1.29409i	0.391443	+	0.920202i	$0.371976\pi$
$97$	−5.27929	+	12.7453i	−0.536030	+	1.29409i	−0.927473	+	0.373889i	$0.878024\pi$
$98$	−6.54954	+	3.70951i	−0.661604	+	0.374717i
$99$	2.83241	+	11.3076i	0.284668	+	1.13646i
$100$	0.884413	+	0.221699i	0.0884413	+	0.0221699i
$101$	8.78691	+	4.15590i	0.874330	+	0.413527i	0.811401	−	0.584490i	$-0.198706\pi$
$101$	8.78691	+	4.15590i	0.874330	+	0.413527i	0.0629298	+	0.998018i	$0.479956\pi$
$102$	0.597178	−	24.2397i	0.0591294	−	2.40009i
$103$	−0.991349	+	10.0653i	−0.0976806	+	0.991767i	0.813999	+	0.580866i	$0.197286\pi$
$103$	−0.991349	+	10.0653i	−0.0976806	+	0.991767i	−0.911680	+	0.410901i	$0.865214\pi$
$104$	5.21241	+	7.40520i	0.511119	+	0.726139i
$105$	−4.55594	+	5.55143i	−0.444614	+	0.541764i
$106$	−5.54677	+	16.7854i	−0.538749	+	1.63034i
$107$	5.65461	+	4.19375i	0.546652	+	0.405425i	0.833474	−	0.552559i	$-0.186349\pi$
$107$	5.65461	+	4.19375i	0.546652	+	0.405425i	−0.286822	+	0.957984i	$0.592599\pi$
$108$	2.21369	−	3.31177i	0.213013	−	0.318675i
$109$	−5.69986	+	2.69583i	−0.545947	+	0.258214i	−0.680570	−	0.732683i	$-0.738268\pi$
$109$	−5.69986	+	2.69583i	−0.545947	+	0.258214i	0.134623	+	0.990897i	$0.457018\pi$
$110$	−8.53175	+	3.78097i	−0.813470	+	0.360501i
$111$	2.29652	−	0.456807i	0.217977	−	0.0433582i
$112$	−3.66210	−	3.66467i	−0.346036	−	0.346279i
$113$	15.3041	+	3.04417i	1.43969	+	0.286372i	0.852351	−	0.522970i	$-0.175176\pi$
$113$	15.3041	+	3.04417i	1.43969	+	0.286372i	0.587338	+	0.809342i	$0.300176\pi$
$114$	−5.02633	−	22.3924i	−0.470759	−	2.09724i
$115$	−8.96279	−	8.12340i	−0.835785	−	0.757511i
$116$	−11.6488	+	1.14524i	−1.08156	+	0.106333i
$117$	−10.3414	+	6.19837i	−0.956059	+	0.573040i
$118$	13.3333	−	10.4036i	1.22743	−	0.957725i
$119$	2.47827	−	8.16975i	0.227182	−	0.748920i
$120$	14.3358	+	6.35914i	1.30867	+	0.580507i
$121$	0.668283	−	1.25027i	0.0607530	−	0.113661i
$122$	5.60255	−	3.54709i	0.507231	−	0.321138i
$123$	0.978726	−	19.9224i	0.0882488	−	1.79634i
$124$	−3.80924	−	2.28408i	−0.342080	−	0.205117i
$125$	−11.5044	−	1.70652i	−1.02898	−	0.152635i
$126$	5.22337	−	4.50491i	0.465335	−	0.401329i
$127$		−	15.3463i		−	1.36177i	−0.732392	−	0.680883i	$-0.761596\pi$
$127$		−	15.3463i		−	1.36177i	0.732392	−	0.680883i	$-0.238404\pi$
$128$	−5.58255	+	9.84049i	−0.493432	+	0.869784i
$129$			7.54757i			0.664526i
$130$	−6.30379	−	7.30914i	−0.552879	−	0.641054i
$131$	3.71127	+	0.550514i	0.324255	+	0.0480987i	0.306874	−	0.951750i	$-0.400717\pi$
$131$	3.71127	+	0.550514i	0.324255	+	0.0480987i	0.0173812	+	0.999849i	$0.494467\pi$
$132$	15.6217	−	3.91012i	1.35969	−	0.340332i
$133$	0.396494	−	8.07082i	0.0343804	−	0.699829i
$134$	−0.892069	−	1.40900i	−0.0770630	−	0.121719i
$135$	−2.00145	+	3.74446i	−0.172258	+	0.322272i
$136$	−18.6379	−	0.462442i	−1.59819	−	0.0396541i
$137$	1.26227	−	4.16114i	0.107843	−	0.355510i	−0.886365	−	0.462988i	$-0.846777\pi$
$137$	1.26227	−	4.16114i	0.107843	−	0.355510i	0.994208	+	0.107478i	$0.0342774\pi$
$138$	12.8408	+	16.4569i	1.09308	+	1.40091i
$139$	−19.3463	+	11.5957i	−1.64093	+	0.983535i	−0.670577	+	0.741840i	$0.733953\pi$
$139$	−19.3463	+	11.5957i	−1.64093	+	0.983535i	−0.970352	+	0.241695i	$0.922297\pi$
$140$	4.26791	+	3.50383i	0.360704	+	0.296128i
$141$	−16.2529	−	14.7308i	−1.36874	−	1.24056i
$142$	5.62123	−	1.26177i	0.471723	−	0.105885i
$143$	−9.72049	−	1.93352i	−0.812868	−	0.161689i
$144$	−12.5214	−	8.37291i	−1.04345	−	0.697742i
$145$	12.2359	−	2.43388i	1.01614	−	0.202123i
$146$	4.64876	+	10.4899i	0.384734	+	0.868152i
$147$	−12.5150	+	5.91917i	−1.03222	+	0.488205i
$148$	−0.350932	−	1.76587i	−0.0288464	−	0.145154i
$149$	−3.69931	−	2.74360i	−0.303060	−	0.224764i	0.433473	−	0.901167i	$-0.357288\pi$
$149$	−3.69931	−	2.74360i	−0.303060	−	0.224764i	−0.736532	+	0.676402i	$0.763538\pi$
$150$	1.59231	+	0.526182i	0.130011	+	0.0429625i
$151$	−13.6803	+	16.6695i	−1.11329	+	1.35655i	−0.185847	+	0.982579i	$0.559503\pi$
$151$	−13.6803	+	16.6695i	−1.11329	+	1.35655i	−0.927442	+	0.373968i	$0.877997\pi$
$152$	−17.2183	+	3.86175i	−1.39659	+	0.313229i
$153$	2.43298	−	24.7024i	0.196694	−	1.99707i
$154$	5.66835	+	0.139648i	0.456769	+	0.0112531i
$155$	4.27949	+	2.02405i	0.343737	+	0.162576i
$156$	8.56029	+	14.2877i	0.685372	+	1.14393i
$157$	2.78309	+	11.1107i	0.222114	+	0.886730i	0.973836	+	0.227250i	$0.0729735\pi$
$157$	2.78309	+	11.1107i	0.222114	+	0.886730i	−0.751722	+	0.659480i	$0.770776\pi$
$158$	−3.70000	−	6.53274i	−0.294356	−	0.519717i
$159$	−12.4428	+	30.0395i	−0.986777	+	2.38229i
$160$	4.89151	−	11.0220i	0.386707	−	0.871367i
$161$	2.81259	+	6.79020i	0.221663	+	0.535142i
$162$	−5.32233	+	6.81871i	−0.418162	+	0.535728i
$163$	−8.39115	+	13.9998i	−0.657246	+	1.09655i	0.330993	+	0.943633i	$0.392616\pi$
$163$	−8.39115	+	13.9998i	−0.657246	+	1.09655i	−0.988239	+	0.152916i	$0.951134\pi$
$164$	−15.3183	−	0.755234i	−1.19616	−	0.0589739i
$165$	−16.1606	+	5.78237i	−1.25810	+	0.450157i
$166$	7.40512	+	3.28324i	0.574749	+	0.254829i
$167$	1.78927	−	1.46841i	0.138458	−	0.113629i	−0.562615	−	0.826719i	$-0.690205\pi$
$167$	1.78927	−	1.46841i	0.138458	−	0.113629i	0.701073	+	0.713090i	$0.252705\pi$
$168$	−6.22208	−	7.21696i	−0.480044	−	0.556801i
$169$	0.269471	+	2.73599i	0.0207285	+	0.210460i
$170$	19.8176	−	1.46008i	1.51994	−	0.111983i
$171$	−3.44725	−	23.2395i	−0.263618	−	1.77717i
$172$	5.80336	+	0.00101786i	0.442502	+	7.76112e-5i
$173$	6.68365	−	18.6795i	0.508148	−	1.42018i	−0.364212	−	0.931316i	$-0.618662\pi$
$173$	6.68365	−	18.6795i	0.508148	−	1.42018i	0.872360	−	0.488864i	$-0.162588\pi$
$174$	−21.5219	+	0.526445i	−1.63157	+	0.0399097i
$175$	0.490956	+	0.328046i	0.0371128	+	0.0247980i
$176$	−3.00440	−	12.0121i	−0.226465	−	0.905447i
$177$	25.8631	−	17.2812i	1.94399	−	1.29893i
$178$	−2.09514	−	2.97542i	−0.157037	−	0.223017i
$179$	0.547804	+	11.1508i	0.0409448	+	0.833450i	0.928180	+	0.372132i	$0.121373\pi$
$179$	0.547804	+	11.1508i	0.0409448	+	0.833450i	−0.887235	+	0.461318i	$0.847377\pi$
$180$	14.1577	+	7.57065i	1.05525	+	0.564283i
$181$	0.306572	−	1.22390i	0.0227873	−	0.0909719i	−0.957571	−	0.288199i	$-0.906944\pi$
$181$	0.306572	−	1.22390i	0.0227873	−	0.0909719i	0.980358	+	0.197227i	$0.0631936\pi$
$182$	1.56364	+	5.65220i	0.115905	+	0.418969i
$183$	10.7560	−	5.74922i	0.795109	−	0.424995i
$184$	12.6555	−	9.87112i	0.932978	−	0.727709i
$185$	0.557043	+	1.83632i	0.0409546	+	0.135009i
$186$	−6.67856	−	4.70445i	−0.489696	−	0.344947i
$187$	15.1186	−	13.7027i	1.10558	−	1.00204i
$188$	−11.3288	+	12.4950i	−0.826235	+	0.911289i
$189$	2.07205	−	1.53674i	0.150719	−	0.111781i
$190$	17.8592	−	5.89816i	1.29565	−	0.427898i
$191$	−2.67332	+	2.67332i	−0.193435	+	0.193435i	−0.797179	−	0.603744i	$-0.793675\pi$
$191$	−2.67332	+	2.67332i	−0.193435	+	0.193435i	0.603744	+	0.797179i	$0.293675\pi$
$192$	−11.5699	+	17.2958i	−0.834983	+	1.24822i
$193$	−3.13725	−	3.13725i	−0.225824	−	0.225824i	0.585121	−	0.810946i	$-0.301047\pi$
$193$	−3.13725	−	3.13725i	−0.225824	−	0.225824i	−0.810946	+	0.585121i	$0.801047\pi$
$194$	17.4258	+	8.77331i	1.25110	+	0.629887i
$195$	−10.5752	−	14.2590i	−0.757304	−	1.02111i
$196$	4.54959	+	9.62367i	0.324971	+	0.687405i
$197$	12.6824	+	13.9929i	0.903583	+	0.996951i	0.999999	+	0.00160947i	$0.000512309\pi$
$197$	12.6824	+	13.9929i	0.903583	+	0.996951i	−0.0964153	+	0.995341i	$0.530738\pi$
$198$	16.2430	−	2.81696i	1.15434	−	0.200192i
$199$	−22.8088	+	6.91898i	−1.61687	+	0.490473i	−0.963756	−	0.266784i	$-0.914039\pi$
$199$	−22.8088	+	6.91898i	−1.61687	+	0.490473i	−0.653117	+	0.757257i	$0.726539\pi$
$200$	0.404798	−	1.22426i	0.0286236	−	0.0865683i
$201$	−1.44589	−	2.70507i	−0.101985	−	0.190801i
$202$	6.77661	−	11.9599i	0.476801	−	0.841499i
$203$	−7.35296	−	1.84182i	−0.516077	−	0.129270i
$204$	−34.1248	−	3.36704i	−2.38921	−	0.235740i
$205$	16.3271	−	0.802100i	1.14033	−	0.0560211i
$206$	14.0926	+	2.44657i	0.981879	+	0.170461i
$207$	11.8718	+	17.7675i	0.825149	+	1.23492i
$208$	10.9870	−	6.58012i	0.761812	−	0.456249i
$209$	10.7295	−	16.0578i	0.742172	−	1.11074i
$210$	7.35504	+	7.00381i	0.507546	+	0.483309i
$211$	2.17801	+	0.779303i	0.149940	+	0.0536494i	0.410790	−	0.911730i	$-0.365253\pi$
$211$	2.17801	+	0.779303i	0.149940	+	0.0536494i	−0.260850	+	0.965379i	$0.584003\pi$
$212$	23.0959	+	9.57136i	1.58623	+	0.657364i
$213$	10.4815	−	1.55478i	0.718177	−	0.106532i
$214$	6.50373	−	7.53829i	0.444586	−	0.515307i
$215$	−6.15570	+	0.606284i	−0.419816	+	0.0413482i
$216$	−4.44025	−	3.46709i	−0.302121	−	0.235905i
$217$	−1.82474	−	2.22345i	−0.123871	−	0.150938i
$218$	3.20843	+	8.31972i	0.217302	+	0.563482i
$219$	7.10951	+	19.8698i	0.480416	+	1.34267i
$220$	4.44391	+	12.4268i	0.299608	+	0.837812i
$221$	18.1015	+	10.8496i	1.21764	+	0.729825i
$222$	−0.405063	−	3.28654i	−0.0271861	−	0.220578i
$223$	7.65072	−	3.16903i	0.512330	−	0.212214i	−0.111514	−	0.993763i	$-0.535570\pi$
$223$	7.65072	−	3.16903i	0.512330	−	0.212214i	0.623844	+	0.781549i	$0.285570\pi$
$224$	−5.54999	+	4.78322i	−0.370825	+	0.319592i
$225$	1.58607	+	0.656973i	0.105738	+	0.0437982i
$226$	5.88749	−	21.2674i	0.391630	−	1.41469i
$227$	−7.24265	+	1.81419i	−0.480712	+	0.120412i	−0.475759	−	0.879576i	$-0.657826\pi$
$227$	−7.24265	+	1.81419i	−0.480712	+	0.120412i	−0.00495269	+	0.999988i	$0.501576\pi$
$228$	−32.1052	+	4.75661i	−2.12622	+	0.315014i
$229$	4.03442	−	8.53007i	0.266602	−	0.563683i	−0.725630	−	0.688085i	$-0.758451\pi$
$229$	4.03442	−	8.53007i	0.266602	−	0.563683i	0.992232	+	0.124403i	$0.0397015\pi$
$230$	−12.3906	+	11.7947i	−0.817011	+	0.777722i
$231$	10.3785	+	1.02219i	0.682855	+	0.0672554i
$232$	0.401884	+	16.5484i	0.0263850	+	1.08645i
$233$	−18.6283	−	15.2878i	−1.22038	−	1.00154i	−0.999657	−	0.0262019i	$-0.991659\pi$
$233$	−18.6283	−	15.2878i	−1.22038	−	1.00154i	−0.220722	−	0.975337i	$-0.570841\pi$
$234$	7.66486	+	15.2308i	0.501068	+	0.995668i
$235$	10.7087	−	14.4390i	0.698558	−	0.941896i
$236$	−13.2841	−	19.8886i	−0.864721	−	1.29464i
$237$	−5.90399	−	12.4829i	−0.383506	−	0.810855i
$238$	−11.2643	−	4.34624i	−0.730153	−	0.281725i
$239$	−4.50129	−	22.6295i	−0.291164	−	1.46378i	−0.798480	−	0.602022i	$-0.794362\pi$
$239$	−4.50129	−	22.6295i	−0.291164	−	1.46378i	0.507315	−	0.861761i	$-0.330638\pi$
$240$	10.4620	−	19.5565i	0.675317	−	1.26236i
$241$	−3.57456	+	17.9705i	−0.230258	+	1.15758i	0.676666	+	0.736290i	$0.263424\pi$
$241$	−3.57456	+	17.9705i	−0.230258	+	1.15758i	−0.906924	+	0.421294i	$0.861576\pi$
$242$	−1.69374	−	1.07275i	−0.108878	−	0.0689593i
$243$	−14.6969	+	16.2155i	−0.942808	+	1.04023i
$244$	−4.41915	−	8.27114i	−0.282907	−	0.529506i
$245$	−5.83292	−	9.73164i	−0.372652	−	0.621732i
$246$	−27.9961	−	3.45548i	−1.78497	−	0.220314i
$247$	19.1147	+	5.79837i	1.21624	+	0.368941i
$248$	−3.61818	+	5.13454i	−0.229754	+	0.326044i
$249$	13.1394	+	7.02315i	0.832675	+	0.445074i
$250$	−3.60512	+	16.0477i	−0.228008	+	1.01495i
$251$	23.2968	+	1.14450i	1.47048	+	0.0722400i	0.768450	−	0.639909i	$-0.221028\pi$
$251$	23.2968	+	1.14450i	1.47048	+	0.0722400i	0.702028	+	0.712149i	$0.252278\pi$
$252$	−5.80954	−	7.83613i	−0.365966	−	0.493630i
$253$	−2.57742	+	17.3756i	−0.162041	+	1.09239i
$254$	−21.6440	−	1.59847i	−1.35807	−	0.100297i
$255$	36.5484			2.28875
$256$	13.2973	+	8.89845i	0.831080	+	0.556153i
$257$	18.8466			1.17562			0.587810	−	0.808999i	$-0.299990\pi$
$257$	18.8466			1.17562			0.587810	+	0.808999i	$0.299990\pi$
$258$	10.6449	+	0.786152i	0.662721	+	0.0489437i
$259$	0.171079	−	1.15332i	0.0106304	−	0.0716641i
$260$	−10.9652	+	8.12938i	−0.680034	+	0.504163i
$261$	−22.0123	−	1.08139i	−1.36253	−	0.0669366i
$262$	1.16299	−	5.17693i	0.0718500	−	0.319832i
$263$	−25.3155	−	13.5314i	−1.56102	−	0.834384i	−0.999978	−	0.00659801i	$-0.997900\pi$
$263$	−25.3155	−	13.5314i	−1.56102	−	0.834384i	−0.561044	−	0.827786i	$-0.689600\pi$
$264$	−3.88757	−	22.4397i	−0.239263	−	1.38107i
$265$	−25.4994	−	7.73515i	−1.56641	−	0.475167i
$266$	−11.3416	−	1.39986i	−0.695396	−	0.0858308i
$267$	−3.44097	−	5.74092i	−0.210584	−	0.351339i
$268$	−2.08014	+	1.11139i	−0.127065	+	0.0678888i
$269$	9.57984	−	10.5697i	0.584093	−	0.644447i	−0.375172	−	0.926955i	$-0.622416\pi$
$269$	9.57984	−	10.5697i	0.584093	−	0.644447i	0.959265	+	0.282508i	$0.0911664\pi$
$270$	5.07261	+	3.21282i	0.308709	+	0.195526i
$271$	−0.488088	+	2.45378i	−0.0296492	+	0.149057i	−0.992774	−	0.119998i	$-0.961711\pi$
$271$	−0.488088	+	2.45378i	−0.0296492	+	0.149057i	0.963125	+	0.269055i	$0.0867112\pi$
$272$	−2.59354	+	26.2383i	−0.157256	+	1.59093i
$273$	2.10431	+	10.5791i	0.127359	+	0.640274i
$274$	−5.73728	−	2.21369i	−0.346602	−	0.133734i
$275$	0.603374	+	1.27573i	0.0363848	+	0.0769292i
$276$	24.5479	−	16.3961i	1.47761	−	0.986932i
$277$	11.6852	−	15.7557i	0.702098	−	0.946669i	−0.297871	−	0.954606i	$-0.596277\pi$
$277$	11.6852	−	15.7557i	0.702098	−	0.946669i	0.999968	+	0.00793721i	$0.00252652\pi$
$278$	14.3392	+	28.4933i	0.860006	+	1.70891i
$279$	−6.46457	−	5.30533i	−0.387023	−	0.317622i
$280$	5.38626	−	5.65438i	0.321890	−	0.337914i
$281$	−20.4346	−	2.01263i	−1.21902	−	0.120063i	−0.532030	−	0.846726i	$-0.678570\pi$
$281$	−20.4346	−	2.01263i	−1.21902	−	0.120063i	−0.686995	+	0.726662i	$0.741070\pi$
$282$	−22.4688	+	21.3883i	−1.33800	+	1.27366i
$283$	8.28299	−	17.5129i	0.492373	−	1.04103i	−0.492907	−	0.870082i	$-0.664066\pi$
$283$	8.28299	−	17.5129i	0.492373	−	1.04103i	0.985279	−	0.170952i	$-0.0546844\pi$
$284$	−1.19406	−	8.05945i	−0.0708545	−	0.478240i
$285$	33.5561	−	8.40535i	1.98769	−	0.497890i
$286$	−3.73947	+	13.5081i	−0.221120	+	0.798751i
$287$	−9.17617	−	3.80089i	−0.541652	−	0.224360i
$288$	−13.1131	+	16.7878i	−0.772700	+	0.989229i
$289$	−24.4350	+	10.1213i	−1.43735	+	0.595372i
$290$	−2.15818	−	17.5107i	−0.126733	−	1.02827i
$291$	30.7782	+	18.4477i	1.80425	+	1.08143i
$292$	15.2789	−	5.46386i	0.894131	−	0.319748i
$293$	−10.2776	−	28.7238i	−0.600421	−	1.67806i	−0.727446	−	0.686165i	$-0.759293\pi$
$293$	−10.2776	−	28.7238i	−0.600421	−	1.67806i	0.127025	−	0.991899i	$-0.459457\pi$
$294$	7.04468	+	18.2674i	0.410854	+	1.06538i
$295$	16.1719	+	19.7055i	0.941562	+	1.14730i
$296$	−2.52709	+	0.311012i	−0.146884	+	0.0180772i
$297$	6.13584	−	0.604328i	0.356038	−	0.0350666i
$298$	−4.25481	+	4.93164i	−0.246475	+	0.285682i
$299$	−17.9714	+	2.66580i	−1.03931	+	0.154167i
$300$	0.907966	−	2.19094i	0.0524214	−	0.126494i
$301$	3.53857	+	1.26612i	0.203960	+	0.0729780i
$302$	22.0853	+	21.0306i	1.27087	+	1.21018i
$303$	14.0465	−	21.0221i	0.806953	−	1.20769i
$304$	3.65305	+	24.6865i	0.209517	+	1.41587i
$305$	5.55301	+	8.31067i	0.317964	+	0.475867i
$306$	−34.5862	−	6.00440i	−1.97716	−	0.343249i
$307$	5.73728	−	0.281855i	0.327444	−	0.0160863i	0.115318	−	0.993329i	$-0.463211\pi$
$307$	5.73728	−	0.281855i	0.327444	−	0.0160863i	0.212126	+	0.977242i	$0.431961\pi$
$308$	0.787369	−	7.97994i	0.0448645	−	0.454699i
$309$	25.5192	+	6.39224i	1.45174	+	0.363642i
$310$	3.30041	−	5.82486i	0.187451	−	0.330830i
$311$	−1.47082	−	2.75170i	−0.0834023	−	0.156035i	0.836763	−	0.547566i	$-0.184445\pi$
$311$	−1.47082	−	2.75170i	−0.0834023	−	0.156035i	−0.920165	+	0.391531i	$0.871945\pi$
$312$	21.0426	−	10.5850i	1.19130	−	0.599258i
$313$	−10.9002	+	3.30653i	−0.616115	+	0.186896i	−0.582889	−	0.812552i	$-0.698078\pi$
$313$	−10.9002	+	3.30653i	−0.616115	+	0.186896i	−0.0332253	+	0.999448i	$0.510578\pi$
$314$	15.9601	−	2.76790i	0.900681	−	0.156202i
$315$	6.98226	+	7.70373i	0.393406	+	0.434056i
$316$	−9.59899	+	4.53793i	−0.539986	+	0.255278i
$317$	12.4990	+	16.8530i	0.702015	+	0.946558i	0.999968	−	0.00802249i	$-0.00255366\pi$
$317$	12.4990	+	16.8530i	0.702015	+	0.946558i	−0.297952	+	0.954581i	$0.596304\pi$
$318$	41.0709	+	20.6779i	2.30314	+	1.15956i
$319$	−12.8103	−	12.8103i	−0.717239	−	0.717239i
$320$	−15.0356	−	8.04689i	−0.840518	−	0.449835i
$321$	12.9484	−	12.9484i	0.722712	−	0.722712i
$322$	9.86967	−	3.25954i	0.550015	−	0.181647i
$323$	−33.0307	+	24.4972i	−1.83788	+	1.36306i
$324$	9.06255	+	8.21671i	0.503475	+	0.456484i
$325$	−1.08150	+	0.980215i	−0.0599908	+	0.0543725i
$326$	18.8709	+	13.2929i	1.04516	+	0.736224i
$327$	4.76082	+	15.6943i	0.263274	+	0.867898i
$328$	−2.66071	+	21.5259i	−0.146913	+	1.18857i
$329$	−9.63279	+	5.14883i	−0.531073	+	0.283864i
$330$	6.47200	+	23.3948i	0.356272	+	1.28784i
$331$	0.560108	−	2.23608i	0.0307863	−	0.122906i	−0.952690	−	0.303945i	$-0.901696\pi$
$331$	0.560108	−	2.23608i	0.0307863	−	0.122906i	0.983476	+	0.181039i	$0.0579461\pi$
$332$	5.40191	−	10.1020i	0.296468	−	0.554419i
$333$	−0.166335	−	3.38584i	−0.00911513	−	0.185543i
$334$	−1.88464	−	2.67648i	−0.103123	−	0.146451i
$335$	2.09008	−	1.39655i	0.114193	−	0.0763015i
$336$	−10.8267	+	8.02374i	−0.590645	+	0.437731i
$337$	−20.5396	−	13.7241i	−1.11886	−	0.747601i	−0.148419	−	0.988925i	$-0.547419\pi$
$337$	−20.5396	−	13.7241i	−1.11886	−	0.747601i	−0.970445	+	0.241323i	$0.922419\pi$
$338$	3.88683	−	0.0950752i	0.211415	−	0.00517141i
$339$	13.6735	−	38.2148i	0.742642	−	2.07554i
$340$	0.00492890	−	28.1022i	0.000267307	−	1.52406i
$341$	−1.00870	−	6.80008i	−0.0546240	−	0.368245i
$342$	−33.1354	+	2.44129i	−1.79176	+	0.132010i
$343$	1.56436	+	15.8832i	0.0844675	+	0.857613i
$344$	0.605912	−	8.18479i	0.0326686	−	0.441295i
$345$	−24.3218	+	19.9604i	−1.30944	+	1.07463i
$346$	−25.6490	−	11.3721i	−1.37890	−	0.611367i
$347$	−17.3901	+	6.22228i	−0.933550	+	0.334029i	−0.759351	−	0.650681i	$-0.774484\pi$
$347$	−17.3901	+	6.22228i	−0.933550	+	0.334029i	−0.174199	+	0.984711i	$0.555734\pi$
$348$	−1.49923	+	30.4088i	−0.0803674	+	1.63008i
$349$	1.07194	−	1.78843i	0.0573798	−	0.0957323i	−0.827702	−	0.561168i	$-0.810352\pi$
$349$	1.07194	−	1.78843i	0.0573798	−	0.0957323i	0.885082	+	0.465435i	$0.154102\pi$
$350$	0.513806	−	0.658262i	0.0274641	−	0.0351856i
$351$	2.44035	+	5.89153i	0.130256	+	0.314467i
$352$	−17.2545	+	2.98615i	−0.919668	+	0.159162i
$353$	8.73138	−	21.0794i	0.464724	−	1.12194i	−0.501711	−	0.865035i	$-0.667296\pi$
$353$	8.73138	−	21.0794i	0.464724	−	1.12194i	0.966436	−	0.256909i	$-0.0827040\pi$
$354$	−21.6790	−	38.2766i	−1.15223	−	2.03438i
$355$	2.11002	+	8.42365i	0.111988	+	0.447081i
$356$	−4.41468	+	2.64501i	−0.233978	+	0.140185i
$357$	−20.0745	−	9.49453i	−1.06246	−	0.502504i
$358$	15.7838	+	0.388857i	0.834202	+	0.0205517i
$359$	1.77750	−	18.0473i	0.0938130	−	0.952499i	−0.826924	−	0.562314i	$-0.809911\pi$
$359$	1.77750	−	18.0473i	0.0938130	−	0.952499i	0.920737	−	0.390185i	$-0.127589\pi$
$360$	12.1521	−	19.1791i	0.640472	−	1.01083i
$361$	−12.6390	+	15.4007i	−0.665212	+	0.810563i
$362$	−1.69423	−	0.559861i	−0.0890465	−	0.0294257i
$363$	−2.96182	−	2.19664i	−0.155455	−	0.115293i
$364$	8.13458	−	1.61659i	0.426368	−	0.0847321i
$365$	−15.6344	+	7.39454i	−0.818344	+	0.387048i
$366$	−6.98820	−	15.7689i	−0.365279	−	0.824251i
$367$	−25.0159	+	4.97598i	−1.30582	+	0.259744i	−0.798490	−	0.602008i	$-0.794368\pi$
$367$	−25.0159	+	4.97598i	−1.30582	+	0.259744i	−0.507330	+	0.861752i	$0.669368\pi$
$368$	−12.6038	−	18.8772i	−0.657016	−	0.984042i
$369$	−28.3225	−	5.63370i	−1.47441	−	0.293279i
$370$	2.64792	−	0.594367i	0.137659	−	0.0308997i
$371$	11.9963	+	10.8728i	0.622817	+	0.564489i
$372$	−7.33066	+	8.92925i	−0.380077	+	0.462960i
$373$	17.5557	−	10.5225i	0.908999	−	0.544833i	0.0185056	−	0.999829i	$-0.494109\pi$
$373$	17.5557	−	10.5225i	0.908999	−	0.544833i	0.890494	+	0.454996i	$0.150359\pi$
$374$	−17.7512	−	22.7501i	−0.917891	−	1.17638i
$375$	−8.78156	+	28.9489i	−0.453478	+	1.49492i
$376$	16.4426	+	17.2793i	0.847960	+	0.891110i
$377$	8.83291	−	16.5252i	0.454918	−	0.851092i
$378$	−1.95155	−	3.08243i	−0.100377	−	0.158543i
$379$	0.667824	−	13.5939i	0.0343038	−	0.698270i	−0.918635	−	0.395107i	$-0.870707\pi$
$379$	0.667824	−	13.5939i	0.0343038	−	0.698270i	0.952939	−	0.303163i	$-0.0980426\pi$
$380$	−6.45839	−	25.8025i	−0.331309	−	1.32364i
$381$	−39.4853	−	5.85709i	−2.02289	−	0.300068i
$382$	3.49193	+	4.04883i	0.178663	+	0.207156i
$383$		−	1.53950i		−	0.0786649i	−0.999226	−	0.0393324i	$-0.987477\pi$
$383$		−	1.53950i		−	0.0786649i	0.999226	−	0.0393324i	$-0.0125231\pi$
$384$	23.1884	+	18.1193i	1.18333	+	0.924649i
$385$			8.54669i			0.435580i
$386$	−4.75147	+	4.09792i	−0.241843	+	0.208578i
$387$	10.8087	+	1.60332i	0.549436	+	0.0815012i
$388$	14.1887	−	23.6630i	0.720322	−	1.20131i
$389$	−1.38411	+	28.1742i	−0.0701771	+	1.42849i	0.663086	+	0.748543i	$0.269246\pi$
$389$	−1.38411	+	28.1742i	−0.0701771	+	1.42849i	−0.733263	+	0.679945i	$0.762004\pi$
$390$	−21.2120	+	13.4297i	−1.07411	+	0.680040i
$391$	17.6320	−	32.9872i	0.891690	−	1.66823i
$392$	14.0468	−	5.41422i	0.709473	−	0.273460i
$393$	2.83289	−	9.33879i	0.142900	−	0.471080i
$394$	21.0562	−	16.4294i	1.06079	−	0.827702i
$395$	9.70668	−	5.81796i	0.488396	−	0.292733i
$396$	−2.28109	−	23.2021i	−0.114629	−	1.16595i
$397$	−4.98853	−	4.52134i	−0.250367	−	0.226919i	0.536722	−	0.843759i	$-0.319663\pi$
$397$	−4.98853	−	4.52134i	−0.250367	−	0.226919i	−0.787089	+	0.616840i	$0.788413\pi$
$398$	7.38258	+	32.8896i	0.370055	+	1.64861i
$399$	−20.6145	−	4.10047i	−1.03201	−	0.205280i
$400$	−1.68450	−	0.698435i	−0.0842250	−	0.0349217i
$401$	−31.9221	+	6.34970i	−1.59411	+	0.317089i	−0.910740	−	0.412979i	$-0.864488\pi$
$401$	−31.9221	+	6.34970i	−1.59411	+	0.317089i	−0.683374	+	0.730068i	$0.739488\pi$
$402$	−3.96576	+	1.75749i	−0.197794	+	0.0876555i
$403$	6.42756	−	3.04001i	0.320180	−	0.151434i
$404$	−16.1621	−	10.8033i	−0.804096	−	0.537484i
$405$	−10.4725	−	7.76696i	−0.520385	−	0.385944i
$406$	−3.36354	+	10.1786i	−0.166929	+	0.505154i
$407$	1.76780	−	2.15408i	0.0876268	−	0.106774i
$408$	−8.30321	+	47.7779i	−0.411070	+	2.36536i
$409$	2.07682	−	21.0863i	0.102692	−	1.04265i	−0.796363	−	0.604818i	$-0.793246\pi$
$409$	2.07682	−	21.0863i	0.102692	−	1.04265i	0.899056	−	0.437834i	$-0.144254\pi$
$410$	0.569368	−	23.1109i	0.0281191	−	1.14136i
$411$	−10.2246	−	4.83590i	−0.504344	−	0.238537i
$412$	4.91846	−	19.6210i	0.242315	−	0.966658i
$413$	−3.76344	−	15.0245i	−0.185187	−	0.739308i
$414$	26.2953	−	14.8931i	1.29234	−	0.731954i
$415$	−4.67253	+	11.2805i	−0.229366	+	0.553737i
$416$	−8.13602	−	16.1812i	−0.398901	−	0.793347i
$417$	22.4515	+	54.2026i	1.09945	+	2.65431i
$418$	−21.5299	−	16.8051i	−1.05306	−	0.821965i
$419$	−12.1306	+	20.2386i	−0.592617	+	0.988723i	0.404623	+	0.914484i	$0.367403\pi$
$419$	−12.1306	+	20.2386i	−0.592617	+	0.988723i	−0.997240	+	0.0742390i	$0.976347\pi$
$420$	10.6441	−	9.64383i	0.519378	−	0.470571i
$421$	4.73979	−	1.69593i	0.231003	−	0.0826544i	−0.218844	−	0.975760i	$-0.570228\pi$
$421$	4.73979	−	1.69593i	0.231003	−	0.0826544i	0.449847	+	0.893106i	$0.351478\pi$
$422$	1.32597	−	2.99063i	0.0645471	−	0.145582i
$423$	−24.5482	+	20.1462i	−1.19357	+	0.979541i
$424$	15.9048	−	31.5768i	0.772408	−	1.53351i
$425$	−0.294542	−	2.99053i	−0.0142874	−	0.145062i
$426$	−1.10107	−	14.9447i	−0.0533470	−	0.724073i
$427$	−0.891093	−	6.00726i	−0.0431230	−	0.290712i
$428$	−9.95437	−	9.95787i	−0.481163	−	0.481332i
$429$	−8.68479	+	24.2724i	−0.419306	+	1.17188i
$430$	0.213910	+	8.74499i	0.0103157	+	0.421721i
$431$	13.9018	+	9.28887i	0.669625	+	0.447429i	0.843350	−	0.537365i	$-0.180580\pi$
$431$	13.9018	+	9.28887i	0.669625	+	0.447429i	−0.173725	+	0.984794i	$0.555580\pi$
$432$	−5.35238	+	5.90128i	−0.257516	+	0.283925i
$433$	−20.5373	+	13.7226i	−0.986961	+	0.659466i	−0.940621	−	0.339459i	$-0.889756\pi$
$433$	−20.5373	+	13.7226i	−0.986961	+	0.659466i	−0.0463404	+	0.998926i	$0.514756\pi$
$434$	−3.32596	+	2.34197i	−0.159651	+	0.112418i
$435$	−1.59227	−	32.4114i	−0.0763434	−	1.55401i
$436$	12.0681	−	3.65850i	0.577957	−	0.175211i
$437$	8.60208	−	34.3414i	0.411493	−	1.64277i
$438$	28.7643	−	7.95743i	1.37441	−	0.380221i
$439$	23.9730	−	12.8139i	1.14417	−	0.611572i	0.213324	−	0.976982i	$-0.431571\pi$
$439$	23.9730	−	12.8139i	1.14417	−	0.611572i	0.930847	+	0.365410i	$0.119071\pi$
$440$	17.9892	−	4.97320i	0.857604	−	0.237088i
$441$	5.81815	+	19.1799i	0.277055	+	0.913328i
$442$	17.1875	−	24.3998i	0.817524	−	1.16058i
$443$	−3.27948	+	2.97235i	−0.155813	+	0.141221i	−0.745743	−	0.666234i	$-0.767905\pi$
$443$	−3.27948	+	2.97235i	−0.155813	+	0.141221i	0.589930	+	0.807454i	$0.299155\pi$
$444$	−4.67743	+	0.228965i	−0.221981	+	0.0108662i
$445$	4.40582	−	3.26758i	0.208856	−	0.154898i
$446$	−3.67262	−	11.1204i	−0.173904	−	0.526568i
$447$	−8.47102	+	8.47102i	−0.400666	+	0.400666i
$448$	6.16803	+	8.32578i	0.291412	+	0.393356i
$449$	7.57814	+	7.57814i	0.357634	+	0.357634i	0.862940	−	0.505306i	$-0.168620\pi$
$449$	7.57814	+	7.57814i	0.357634	+	0.357634i	−0.505306	+	0.862940i	$0.668620\pi$
$450$	1.09178	−	2.16853i	0.0514671	−	0.102225i
$451$	−14.1407	−	19.0665i	−0.665860	−	0.897808i
$452$	−29.3817	−	10.5188i	−1.38200	−	0.494761i
$453$	37.6686	+	41.5609i	1.76982	+	1.95270i
$454$	1.80429	+	10.4038i	0.0846796	+	0.488275i
$455$	−8.45913	+	2.56605i	−0.396570	+	0.120298i
$456$	3.36452	+	45.7758i	0.157558	+	2.14365i
$457$	3.87252	+	7.24498i	0.181149	+	0.338906i	0.956063	−	0.293161i	$-0.0947070\pi$
$457$	3.87252	+	7.24498i	0.181149	+	0.338906i	−0.774914	+	0.632066i	$0.782207\pi$
$458$	−11.6103	−	6.57853i	−0.542516	−	0.307394i
$459$	−12.7352	−	3.19001i	−0.594430	−	0.148897i
$460$	15.3444	+	18.7039i	0.715436	+	0.872073i
$461$	30.0099	−	1.47429i	1.39770	−	0.0686647i	0.663795	−	0.747915i	$-0.268945\pi$
$461$	30.0099	−	1.47429i	1.39770	−	0.0686647i	0.733907	+	0.679250i	$0.237695\pi$
$462$	2.52269	−	14.5311i	0.117366	−	0.676047i
$463$	−18.0949	−	27.0809i	−0.840939	−	1.25855i	−0.963932	−	0.266147i	$-0.914249\pi$
$463$	−18.0949	−	27.0809i	−0.840939	−	1.25855i	0.122993	−	0.992408i	$-0.460751\pi$
$464$	23.3813	+	1.15687i	1.08545	+	0.0537063i
$465$	6.84109	−	10.2384i	0.317248	−	0.474795i
$466$	−23.5018	+	24.6804i	−1.08870	+	1.14330i
$467$	−4.38013	−	1.56723i	−0.202688	−	0.0725230i	0.233589	−	0.972336i	$-0.424953\pi$
$467$	−4.38013	−	1.56723i	−0.202688	−	0.0725230i	−0.436277	+	0.899813i	$0.643703\pi$
$468$	22.2795	−	9.22388i	1.02987	−	0.426374i
$469$	−1.51079	+	0.224104i	−0.0697617	+	0.0103482i
$470$	−19.2489	−	16.6072i	−0.887887	−	0.766033i
$471$	29.6495	−	2.92022i	1.36618	−	0.134557i
$472$	−29.4340	+	16.6639i	−1.35481	+	0.767019i
$473$	5.69828	+	6.94337i	0.262007	+	0.319257i
$474$	−18.2206	+	7.02661i	−0.836898	+	0.322743i
$475$	−0.958186	−	2.67795i	−0.0439646	−	0.122873i
$476$	−7.30310	+	15.4341i	−0.334737	+	0.707421i
$477$	40.3757	+	24.2002i	1.84867	+	1.10805i
$478$	−32.3849	+	3.99142i	−1.48125	+	0.182563i
$479$	3.44962	−	1.42888i	0.157617	−	0.0652871i	−0.302480	−	0.953156i	$-0.597815\pi$
$479$	3.44962	−	1.42888i	0.157617	−	0.0652871i	0.460097	+	0.887869i	$0.347815\pi$
$480$	−26.4922	−	16.7923i	−1.20920	−	0.766459i
$481$	2.66277	+	1.10296i	0.121412	+	0.0502904i
$482$	24.9728	+	6.91327i	1.13748	+	0.314891i
$483$	18.5443	−	4.64510i	0.843794	−	0.211359i
$484$	−1.68940	+	2.27706i	−0.0767911	+	0.103503i
$485$	−12.5734	+	26.5842i	−0.570928	+	1.20713i
$486$	21.3391	+	22.4171i	0.967963	+	1.01686i
$487$	−10.1876	−	1.00339i	−0.461646	−	0.0454681i	−0.135479	−	0.990780i	$-0.543257\pi$
$487$	−10.1876	−	1.00339i	−0.461646	−	0.0454681i	−0.326167	+	0.945312i	$0.605757\pi$
$488$	−12.1257	+	5.37113i	−0.548904	+	0.243140i
$489$	32.8182	+	26.9332i	1.48409	+	1.21796i
$490$	−14.3328	+	7.21295i	−0.647490	+	0.325848i
$491$	−11.9965	+	16.1755i	−0.541396	+	0.729988i	−0.986185	−	0.165647i	$-0.947029\pi$
$491$	−11.9965	+	16.1755i	−0.541396	+	0.729988i	0.444789	+	0.895635i	$0.353279\pi$
$492$	−7.78958	+	39.1250i	−0.351182	+	1.76389i
$493$	16.4937	+	34.8729i	0.742837	+	1.57060i
$494$	10.1688	−	26.3548i	0.457518	−	1.18576i
$495$	4.84781	+	24.3716i	0.217893	+	1.09542i
$496$	6.86475	+	5.63779i	0.308236	+	0.253144i
$497$	1.02935	−	5.17490i	0.0461727	−	0.232126i
$498$	11.2739	−	17.7999i	0.505194	−	0.797633i
$499$	10.1199	−	11.1656i	0.453029	−	0.499841i	−0.471016	−	0.882125i	$-0.656112\pi$
$499$	10.1199	−	11.1656i	0.453029	−	0.499841i	0.924045	+	0.382284i	$0.124862\pi$
$500$	22.2578	+	6.75609i	0.995398	+	0.302141i
$501$	−3.09526	−	5.16413i	−0.138286	−	0.230716i
$502$	4.04075	−	32.7379i	0.180347	−	1.46116i
$503$	12.8083	+	3.88536i	0.571095	+	0.173240i	0.562608	−	0.826724i	$-0.309798\pi$
$503$	12.8083	+	3.88536i	0.571095	+	0.173240i	0.00848775	+	0.999964i	$0.497298\pi$
$504$	−11.6570	+	7.37740i	−0.519243	+	0.328616i
$505$	18.2737	+	9.76751i	0.813170	+	0.434649i
$506$	24.2375	+	5.44496i	1.07749	+	0.242058i
$507$	7.14240	+	0.350883i	0.317205	+	0.0155833i
$508$	−4.50887	+	30.3596i	−0.200049	+	1.34699i
$509$	2.81707	−	18.9911i	0.124864	−	0.841767i	−0.832737	−	0.553669i	$-0.813227\pi$
$509$	2.81707	−	18.9911i	0.124864	−	0.841767i	0.957601	−	0.288098i	$-0.0930228\pi$
$510$	3.80687	−	51.5468i	0.168571	−	2.28253i
$511$	10.5083			0.464860
$512$	13.9352	−	17.8273i	0.615854	−	0.787861i
$513$	−12.4262			−0.548630
$514$	1.96306	−	26.5808i	0.0865868	−	1.17243i
$515$	−3.16351	+	21.3267i	−0.139401	+	0.939765i
$516$	2.21753	−	14.9314i	0.0976215	−	0.657317i
$517$	−26.0733	−	1.28090i	−1.14670	−	0.0563340i
$518$	−1.60880	−	0.361416i	−0.0706865	−	0.0158797i
$519$	−45.5106	−	24.3259i	−1.99770	−	1.06779i
$520$	10.3233	+	16.3118i	0.452707	+	0.715319i
$521$	−16.1887	−	4.91079i	−0.709241	−	0.215146i	−0.0850034	−	0.996381i	$-0.527090\pi$
$521$	−16.1887	−	4.91079i	−0.709241	−	0.215146i	−0.624237	+	0.781235i	$0.714590\pi$
$522$	−3.81796	+	30.9329i	−0.167108	+	1.35389i
$523$	13.6246	+	22.7313i	0.595763	+	0.993970i	0.996955	+	0.0779761i	$0.0248458\pi$
$523$	13.6246	+	22.7313i	0.595763	+	0.993970i	−0.401193	+	0.915994i	$0.631404\pi$
$524$	−7.18026	−	2.17948i	−0.313671	−	0.0952111i
$525$	1.03143	−	1.13800i	0.0450151	−	0.0496665i
$526$	−21.7212	+	34.2949i	−0.947090	+	1.49533i
$527$	−2.85579	+	14.3570i	−0.124400	+	0.625402i
$528$	−32.0532	+	3.14562i	−1.39494	+	0.136895i
$529$	1.79487	+	9.02341i	0.0780378	+	0.392322i
$530$	−13.5655	+	35.1579i	−0.589246	+	1.52716i
$531$	−19.2539	−	40.7089i	−0.835548	−	1.76662i
$532$	−3.15565	+	15.8500i	−0.136815	+	0.687185i
$533$	14.6256	−	19.7203i	0.633505	−	0.854183i
$534$	−8.45524	+	4.25508i	−0.365894	+	0.184135i
$535$	11.6007	+	9.52047i	0.501543	+	0.411606i
$536$	1.35081	+	3.04953i	0.0583459	+	0.131720i
$537$	28.8995	+	2.84636i	1.24711	+	0.122829i
$538$	−13.9094	−	14.6121i	−0.599677	−	0.629971i
$539$	−7.04432	+	14.8940i	−0.303421	+	0.641529i
$540$	5.05963	−	6.81962i	0.217732	−	0.293470i
$541$	−20.6421	+	5.17057i	−0.887472	+	0.222300i	−0.659803	−	0.751438i	$-0.729360\pi$
$541$	−20.6421	+	5.17057i	−0.887472	+	0.222300i	−0.227669	+	0.973739i	$0.573110\pi$
$542$	3.40991	+	0.943971i	0.146468	+	0.0405470i
$543$	−3.03203	−	1.25591i	−0.130117	−	0.0538962i
$544$	36.7356	+	6.39082i	1.57502	+	0.274004i
$545$	−12.4177	+	5.14357i	−0.531915	+	0.220326i
$546$	15.1396	−	1.86595i	0.647916	−	0.0798551i
$547$	−0.370993	−	0.222364i	−0.0158625	−	0.00950762i	0.506150	−	0.862446i	$-0.331068\pi$
$547$	−0.370993	−	0.222364i	−0.0158625	−	0.00950762i	−0.522012	+	0.852938i	$0.674818\pi$
$548$	−3.71972	+	7.86113i	−0.158899	+	0.335811i
$549$	−5.94843	−	16.6248i	−0.253873	−	0.709527i
$550$	1.86210	−	0.718103i	0.0794001	−	0.0306200i
$551$	23.1633	+	28.2246i	0.986790	+	1.20241i
$552$	−20.5678	−	36.3295i	−0.875422	−	1.54628i
$553$	−6.84286	+	0.673963i	−0.290988	+	0.0286598i
$554$	−21.0043	−	18.1216i	−0.892387	−	0.769915i
$555$	4.93737	−	0.732389i	0.209580	−	0.0310882i
$556$	41.6797	−	17.2557i	1.76761	−	0.731806i
$557$	−21.8851	−	7.83061i	−0.927301	−	0.331794i	−0.170439	−	0.985368i	$-0.554519\pi$
$557$	−21.8851	−	7.83061i	−0.927301	−	0.331794i	−0.756862	+	0.653575i	$0.773269\pi$
$558$	−8.15584	+	8.56485i	−0.345264	+	0.362579i
$559$	−5.16139	+	7.72457i	−0.218304	+	0.326714i
$560$	−7.41375	−	8.18559i	−0.313288	−	0.345904i
$561$	−29.4862	−	44.1292i	−1.24491	−	1.86314i
$562$	−4.96702	+	28.6107i	−0.209521	+	1.20687i
$563$	7.52691	−	0.369774i	0.317222	−	0.0155841i	0.110166	−	0.993913i	$-0.464862\pi$
$563$	7.52691	−	0.369774i	0.317222	−	0.0155841i	0.207056	+	0.978329i	$0.433612\pi$
$564$	27.8252	+	33.9172i	1.17165	+	1.42817i
$565$	32.2659	+	8.08219i	1.35744	+	0.340020i
$566$	−23.8370	−	13.5062i	−1.00194	−	0.567710i
$567$	3.73443	+	6.98662i	0.156831	+	0.293411i
$568$	−11.4912	+	0.844602i	−0.482160	+	0.0354387i
$569$	−13.3068	+	4.03657i	−0.557850	+	0.169222i	−0.556605	−	0.830777i	$-0.687896\pi$
$569$	−13.3068	+	4.03657i	−0.557850	+	0.169222i	−0.00124486	+	0.999999i	$0.500396\pi$
$570$	−8.35949	−	48.2020i	−0.350141	−	2.01896i
$571$	10.8219	+	11.9402i	0.452883	+	0.499680i	0.924001	−	0.382391i	$-0.124899\pi$
$571$	10.8219	+	11.9402i	0.452883	+	0.499680i	−0.471117	+	0.882071i	$0.656149\pi$
$572$	18.6620	+	6.68105i	0.780296	+	0.279349i
$573$	5.85802	+	7.89863i	0.244722	+	0.329970i
$574$	−6.31646	+	12.5459i	−0.263644	+	0.523656i
$575$	1.82925	+	1.82925i	0.0762850	+	0.0762850i
$576$	22.3111	+	20.2430i	0.929631	+	0.843460i
$577$	1.95222	−	1.95222i	0.0812718	−	0.0812718i	−0.665302	−	0.746574i	$-0.731697\pi$
$577$	1.95222	−	1.95222i	0.0812718	−	0.0812718i	0.746574	+	0.665302i	$0.231697\pi$
$578$	11.7297	+	35.5167i	0.487891	+	1.47730i
$579$	−9.26935	+	6.87462i	−0.385221	+	0.285699i
$580$	−24.9215	+	1.21993i	−1.03481	+	0.0506549i
$581$	5.49687	−	4.98207i	0.228049	−	0.206691i
$582$	29.2240	−	41.4872i	1.21137	−	1.71970i
$583$	11.2326	+	37.0289i	0.465207	+	1.53358i
$584$	−6.11463	−	22.1181i	−0.253025	−	0.915252i
$585$	−22.6664	+	12.1154i	−0.937140	+	0.500912i
$586$	−41.5818	+	11.5033i	−1.71773	+	0.475197i
$587$	10.4033	−	41.5323i	0.429390	−	1.71422i	−0.239532	−	0.970888i	$-0.576994\pi$
$587$	10.4033	−	41.5323i	0.429390	−	1.71422i	0.668922	−	0.743333i	$-0.266756\pi$
$588$	26.4976	−	8.03289i	1.09274	−	0.331271i
$589$	0.679835	+	13.8384i	0.0280121	+	0.570199i
$590$	29.4765	−	20.7558i	1.21353	−	0.854504i
$591$	40.8433	−	27.2906i	1.68007	−	1.12259i
$592$	0.175422	+	3.59653i	0.00720978	+	0.147817i
$593$	26.2934	+	17.5687i	1.07974	+	0.721461i	0.962401	−	0.271631i	$-0.0875631\pi$
$593$	26.2934	+	17.5687i	1.07974	+	0.721461i	0.117341	+	0.993092i	$0.462563\pi$
$594$	−0.213220	−	8.71677i	−0.00874851	−	0.357653i
$595$	6.13107	−	17.1352i	0.251349	−	0.702475i
$596$	6.51227	+	6.51455i	0.266753	+	0.266846i
$597$	9.09694	+	61.3266i	0.372313	+	2.50993i
$598$	1.88788	+	25.6240i	0.0772012	+	1.04784i
$599$	−0.679419	−	6.89826i	−0.0277603	−	0.281855i	−0.999036	−	0.0438983i	$-0.986022\pi$
$599$	−0.679419	−	6.89826i	−0.0277603	−	0.281855i	0.971276	−	0.237957i	$-0.0764777\pi$
$600$	−2.99546	−	1.50878i	−0.122289	−	0.0615956i
$601$	−19.1397	+	15.7076i	−0.780727	+	0.640726i	−0.937924	−	0.346842i	$-0.887254\pi$
$601$	−19.1397	+	15.7076i	−0.780727	+	0.640726i	0.157197	+	0.987567i	$0.449754\pi$
$602$	2.15428	−	4.85882i	0.0878018	−	0.198031i
$603$	−4.18102	+	1.49599i	−0.170264	+	0.0609215i
$604$	31.9614	−	28.9580i	1.30049	−	1.17828i
$605$	1.55363	−	2.59208i	0.0631641	−	0.105383i
$606$	−28.1860	−	22.0005i	−1.14498	−	0.893710i
$607$	10.9210	+	26.3656i	0.443270	+	1.07015i	0.974794	+	0.223106i	$0.0716195\pi$
$607$	10.9210	+	26.3656i	0.443270	+	1.07015i	−0.531524	+	0.847043i	$0.678381\pi$
$608$	35.1977	−	2.58082i	1.42745	−	0.104666i
$609$	−7.54525	+	18.2158i	−0.305749	+	0.738143i
$610$	12.2995	−	6.96618i	0.497994	−	0.282052i
$611$	−6.56045	−	26.1908i	−0.265407	−	1.05957i
$612$	−12.0709	+	48.1540i	−0.487938	+	1.94651i
$613$	3.29421	+	1.55804i	0.133052	+	0.0629288i	0.492922	−	0.870074i	$-0.335929\pi$
$613$	3.29421	+	1.55804i	0.133052	+	0.0629288i	−0.359870	+	0.933002i	$0.617179\pi$
$614$	0.200074	−	8.12107i	0.00807431	−	0.327740i
$615$	4.16766	−	42.3150i	0.168056	−	1.70630i
$616$	−11.1727	−	1.94167i	−0.450160	−	0.0782322i
$617$	19.5439	−	23.8143i	0.786807	−	0.958727i	−0.213025	−	0.977047i	$-0.568332\pi$
$617$	19.5439	−	23.8143i	0.786807	−	0.958727i	0.999832	+	0.0183197i	$0.00583167\pi$
$618$	11.6735	−	35.3258i	0.469578	−	1.42101i
$619$	13.4623	+	9.98431i	0.541095	+	0.401303i	0.831437	−	0.555620i	$-0.187519\pi$
$619$	13.4623	+	9.98431i	0.541095	+	0.401303i	−0.290342	+	0.956923i	$0.593769\pi$
$620$	−7.87145	−	5.26153i	−0.316125	−	0.211308i
$621$	10.2171	−	4.83232i	0.409998	−	0.193914i
$622$	−4.03412	+	1.78778i	−0.161754	+	0.0716835i
$623$	−3.26878	+	0.650201i	−0.130961	+	0.0260497i
$624$	−12.7370	−	30.7804i	−0.509888	−	1.23220i
$625$	−22.0801	−	4.39201i	−0.883206	−	0.175681i
$626$	3.52809	+	15.7177i	0.141011	+	0.628207i
$627$	−37.2208	−	33.7350i	−1.48646	−	1.34725i
$628$	−2.24137	−	22.7980i	−0.0894404	−	0.909740i
$629$	−5.08951	+	3.05054i	−0.202932	+	0.121633i
$630$	11.5924	−	9.04517i	0.461852	−	0.360368i
$631$	−5.45589	+	17.9857i	−0.217196	+	0.715998i	0.778854	+	0.627205i	$0.215801\pi$
$631$	−5.45589	+	17.9857i	−0.217196	+	0.715998i	−0.996050	+	0.0887933i	$0.971699\pi$
$632$	5.40034	+	14.0108i	0.214814	+	0.557321i
$633$	2.83637	−	5.30647i	0.112735	−	0.210913i
$634$	25.0709	−	15.8729i	0.995692	−	0.630393i
$635$	1.60518	−	32.6742i	0.0636997	−	1.29664i
$636$	33.4414	−	55.7715i	1.32604	−	2.21148i
$637$	−16.8564	−	2.50040i	−0.667873	−	0.0990696i
$638$	−19.4016	+	16.7330i	−0.768117	+	0.662465i
$639$		−	15.3405i		−	0.606861i
$640$	−12.9152	+	20.3677i	−0.510519	+	0.805104i
$641$		−	4.56614i		−	0.180352i	−0.995926	−	0.0901759i	$-0.971257\pi$
$641$		−	4.56614i		−	0.180352i	0.995926	−	0.0901759i	$-0.0287429\pi$
$642$	−16.9134	−	19.6108i	−0.667520	−	0.773978i
$643$	0.624129	+	0.0925809i	0.0246133	+	0.00365103i	0.159026	−	0.987274i	$-0.449165\pi$
$643$	0.624129	+	0.0925809i	0.0246133	+	0.00365103i	−0.134412	+	0.990925i	$0.542915\pi$
$644$	−3.56914	−	14.2594i	−0.140644	−	0.561900i
$645$	−0.789454	+	16.0697i	−0.0310847	+	0.632744i
$646$	31.1097	+	49.1372i	1.22400	+	1.93328i
$647$	−12.6654	+	23.6953i	−0.497928	+	0.931558i	0.499925	+	0.866068i	$0.333361\pi$
$647$	−12.6654	+	23.6953i	−0.497928	+	0.931558i	−0.997853	+	0.0654891i	$0.979139\pi$
$648$	12.5326	−	11.9257i	0.492326	−	0.468486i
$649$	10.7457	−	35.4240i	0.421808	−	1.39051i
$650$	1.26982	+	1.62742i	0.0498064	+	0.0638326i
$651$	−6.41726	+	3.84636i	−0.251512	+	0.150751i
$652$	20.7135	−	25.2304i	0.811203	−	0.988100i
$653$	−15.7567	−	14.2810i	−0.616608	−	0.558861i	0.302360	−	0.953194i	$-0.402226\pi$
$653$	−15.7567	−	14.2810i	−0.616608	−	0.558861i	−0.918968	+	0.394333i	$0.870976\pi$
$654$	22.6307	−	5.07982i	0.884932	−	0.198637i
$655$	7.84416	+	1.56030i	0.306497	+	0.0609660i
$656$	30.0824	+	5.99472i	1.17452	+	0.234055i
$657$	29.9653	−	5.96046i	1.16906	−	0.232540i
$658$	6.25842	+	14.1221i	0.243979	+	0.550538i
$659$	16.9762	−	8.02916i	0.661300	−	0.312771i	−0.0672783	−	0.997734i	$-0.521432\pi$
$659$	16.9762	−	8.02916i	0.661300	−	0.312771i	0.728578	+	0.684963i	$0.240182\pi$
$660$	33.6695	−	6.69114i	1.31058	−	0.260452i
$661$	−14.2884	−	10.5970i	−0.555755	−	0.412176i	0.281037	−	0.959697i	$-0.409322\pi$
$661$	−14.2884	−	10.5970i	−0.555755	−	0.412176i	−0.836792	+	0.547521i	$0.815572\pi$
$662$	−3.09536	−	1.02287i	−0.120305	−	0.0397550i
$663$	34.8242	−	42.4334i	1.35246	−	1.64798i
$664$	−13.6849	−	8.67092i	−0.531078	−	0.336497i
$665$	1.68837	−	17.1423i	0.0654722	−	0.664750i
$666$	−4.79262	−	0.118073i	−0.185710	−	0.00457522i
$667$	−30.0214	−	14.1991i	−1.16243	−	0.549790i
$668$	−3.97114	+	2.37926i	−0.153648	+	0.0920565i
$669$	−5.23378	−	20.8944i	−0.202349	−	0.807824i
$670$	−1.75195	−	3.09325i	−0.0676837	−	0.119503i
$671$	5.55444	−	13.4096i	0.214427	−	0.517672i
$672$	10.1888	+	16.1054i	0.393040	+	0.621280i
$673$	−0.474168	−	1.14474i	−0.0182778	−	0.0441266i	0.914477	−	0.404638i	$-0.132602\pi$
$673$	−0.474168	−	1.14474i	−0.0182778	−	0.0441266i	−0.932755	+	0.360511i	$0.882602\pi$
$674$	−21.4955	+	27.5390i	−0.827977	+	1.06076i
$675$	0.466813	−	0.778831i	0.0179677	−	0.0299772i
$676$	0.270759	−	5.49178i	0.0104138	−	0.211222i
$677$	−20.1394	+	7.20598i	−0.774019	+	0.276948i	−0.694124	−	0.719855i	$-0.744208\pi$
$677$	−20.1394	+	7.20598i	−0.774019	+	0.276948i	−0.0798943	+	0.996803i	$0.525458\pi$
$678$	−52.4729	−	23.2652i	−2.01521	−	0.893493i
$679$	13.8121	−	11.3353i	0.530058	−	0.435008i
$680$	−39.6341	−	2.93407i	−1.51990	−	0.112516i
$681$	1.90358	+	19.3274i	0.0729454	+	0.740627i
$682$	−9.69571	+	0.714344i	−0.371268	+	0.0273536i
$683$	−6.71626	−	45.2774i	−0.256991	−	1.73249i	−0.606083	−	0.795401i	$-0.707260\pi$
$683$	−6.71626	−	45.2774i	−0.256991	−	1.73249i	0.349092	−	0.937088i	$-0.386490\pi$
$684$	−0.00824122	+	46.9875i	−0.000315111	+	1.79661i
$685$	3.12277	−	8.72756i	0.119315	−	0.333463i
$686$	22.5642	−	0.551940i	0.861505	−	0.0210732i
$687$	−20.4076	−	13.6360i	−0.778600	−	0.520244i
$688$	−11.4805	−	1.70709i	−0.437690	−	0.0650821i
$689$	−33.2771	+	22.2350i	−1.26776	+	0.847087i
$690$	25.6183	+	36.3819i	0.975271	+	1.38504i
$691$	−0.613008	−	12.4781i	−0.0233199	−	0.474688i	−0.981846	−	0.189682i	$-0.939254\pi$
$691$	−0.613008	−	12.4781i	−0.0233199	−	0.474688i	0.958526	−	0.285006i	$-0.0919956\pi$
$692$	−18.7105	+	34.9901i	−0.711265	+	1.33012i
$693$	3.66854	−	14.6456i	0.139356	−	0.556342i
$694$	6.96438	+	25.1746i	0.264364	+	0.955616i
$695$	−42.4035	+	22.6651i	−1.60846	+	0.859738i
$696$	42.7315	+	5.28185i	1.61974	+	0.200208i
$697$	14.6730	+	48.3704i	0.555779	+	1.83216i
$698$	−2.41070	−	1.69812i	−0.0912462	−	0.0642748i
$699$	−46.4445	+	42.0948i	−1.75669	+	1.59217i
$700$	−0.874877	−	0.793222i	−0.0330672	−	0.0299810i
$701$	−5.33989	+	3.96033i	−0.201685	+	0.149580i	−0.691828	−	0.722062i	$-0.743194\pi$
$701$	−5.33989	+	3.96033i	−0.201685	+	0.149580i	0.490143	+	0.871642i	$0.336944\pi$
$702$	8.56345	−	2.82815i	0.323206	−	0.106742i
$703$	−3.97126	+	3.97126i	−0.149779	+	0.149779i
$704$	2.41436	+	24.6463i	0.0909945	+	0.928893i
$705$	−33.0637	−	33.0637i	−1.24525	−	1.24525i
$706$	−28.8204	−	14.5101i	−1.08467	−	0.546096i
$707$	−7.49960	−	10.1120i	−0.282051	−	0.380302i
$708$	−56.2424	+	26.5886i	−2.11372	+	0.999260i
$709$	17.8179	+	19.6590i	0.669165	+	0.738310i	0.977026	−	0.213122i	$-0.0683630\pi$
$709$	17.8179	+	19.6590i	0.669165	+	0.738310i	−0.307861	+	0.951431i	$0.599613\pi$
$710$	12.1003	−	2.09850i	0.454115	−	0.0787554i
$711$	−19.1307	+	5.80323i	−0.717457	+	0.217638i
$712$	3.27061	+	6.50185i	0.122571	+	0.243667i
$713$	−5.94046	−	11.1138i	−0.222472	−	0.416216i
$714$	−15.4818	+	27.3236i	−0.579391	+	1.02256i
$715$	−20.4939	−	5.13345i	−0.766428	−	0.191980i
$716$	2.19247	−	22.2206i	0.0819366	−	0.830423i
$717$	−59.9426	+	2.94479i	−2.23860	+	0.109975i
$718$	−25.2682	−	4.38674i	−0.943003	−	0.163712i
$719$	29.3530	+	43.9299i	1.09468	+	1.63831i	0.689915	+	0.723890i	$0.257648\pi$
$719$	29.3530	+	43.9299i	1.09468	+	1.63831i	0.404768	+	0.914419i	$0.367352\pi$
$720$	−25.7839	−	19.1367i	−0.960909	−	0.713182i
$721$	7.27782	−	10.8920i	0.271040	−	0.405640i
$722$	20.4042	+	19.4299i	0.759368	+	0.723105i
$723$	44.8730	+	16.0558i	1.66884	+	0.597122i
$724$	−0.966083	+	2.33117i	−0.0359042	+	0.0866374i
$725$	−2.63919	+	0.391487i	−0.0980172	+	0.0145395i
$726$	−3.40658	+	3.94847i	−0.126430	+	0.146541i
$727$	16.0288	−	1.57870i	0.594476	−	0.0585508i	0.203695	−	0.979034i	$-0.434705\pi$
$727$	16.0288	−	1.57870i	0.594476	−	0.0585508i	0.390781	+	0.920484i	$0.372205\pi$
$728$	−1.43269	−	11.6412i	−0.0530991	−	0.431451i
$729$	24.4718	+	29.8190i	0.906364	+	1.10441i
$730$	8.80058	+	22.8206i	0.325724	+	0.844628i
$731$	−6.44353	−	18.0085i	−0.238323	−	0.666067i
$732$	−22.9678	+	8.21348i	−0.848916	+	0.303579i
$733$	−13.3498	−	8.00159i	−0.493088	−	0.295545i	0.245863	−	0.969305i	$-0.420929\pi$
$733$	−13.3498	−	8.00159i	−0.493088	−	0.295545i	−0.738951	+	0.673759i	$0.764679\pi$
$734$	4.41233	+	35.8001i	0.162862	+	1.32140i
$735$	−27.2652	+	11.2936i	−1.00569	+	0.416571i
$736$	−27.9367	+	15.8098i	−1.02976	+	0.582755i
$737$	−3.37243	−	1.39691i	−0.124225	−	0.0514557i
$738$	−10.8957	+	39.3585i	−0.401075	+	1.44881i
$739$	29.3055	−	7.34064i	1.07802	−	0.270030i	0.336994	−	0.941507i	$-0.390590\pi$
$739$	29.3055	−	7.34064i	1.07802	−	0.270030i	0.741025	+	0.671477i	$0.234340\pi$
$740$	−0.562472	−	3.79646i	−0.0206769	−	0.139561i
$741$	22.2142	−	46.9680i	0.816060	−	1.72541i
$742$	16.5843	−	15.7868i	0.608827	−	0.579550i
$743$	7.14571	+	0.703791i	0.262151	+	0.0258196i	0.228239	−	0.973605i	$-0.426703\pi$
$743$	7.14571	+	0.703791i	0.262151	+	0.0258196i	0.0339120	+	0.999425i	$0.489203\pi$
$744$	11.8300	+	11.2690i	0.433709	+	0.413143i
$745$	−7.58933	−	6.22840i	−0.278051	−	0.228191i
$746$	−13.0120	−	25.8561i	−0.476404	−	0.946659i
$747$	12.8489	−	17.3247i	0.470115	−	0.633877i
$748$	−33.9351	+	22.6661i	−1.24079	+	0.828755i
$749$	−3.89857	−	8.24283i	−0.142451	−	0.301186i
$750$	39.9141	+	15.4006i	1.45746	+	0.562350i
$751$	1.81453	+	9.12228i	0.0662133	+	0.332877i	0.999667	−	0.0258224i	$-0.00822045\pi$
$751$	1.81453	+	9.12228i	0.0662133	+	0.332877i	−0.933453	+	0.358699i	$0.883220\pi$
$752$	26.0828	−	21.3903i	0.951143	−	0.780025i
$753$	11.8362	−	59.5046i	0.431335	−	2.16847i
$754$	−22.3867	−	14.1790i	−0.815274	−	0.516367i
$755$	−30.8707	+	34.0606i	−1.12350	+	1.23959i
$756$	−4.55064	+	2.43134i	−0.165505	+	0.0884271i
$757$	0.395816	+	0.660379i	0.0143862	+	0.0240019i	0.864838	−	0.502051i	$-0.167421\pi$
$757$	0.395816	+	0.660379i	0.0143862	+	0.0240019i	−0.850452	+	0.526053i	$0.823671\pi$
$758$	−19.1029	−	2.35781i	−0.693847	−	0.0856397i
$759$	43.7227	+	13.2631i	1.58703	+	0.481422i
$760$	−37.0639	+	6.42115i	−1.34445	+	0.232920i
$761$	−1.22795	−	0.656351i	−0.0445130	−	0.0237927i	0.448990	−	0.893537i	$-0.351784\pi$
$761$	−1.22795	−	0.656351i	−0.0445130	−	0.0237927i	−0.493503	+	0.869744i	$0.664284\pi$
$762$	−12.3735	+	55.0789i	−0.448243	+	1.99530i
$763$	8.15671	+	0.400713i	0.295293	+	0.0145068i
$764$	6.07408	−	4.50320i	0.219753	−	0.162920i
$765$	7.76391	−	52.3400i	0.280705	−	1.89236i
$766$	−2.17127	−	0.160354i	−0.0784512	−	0.00579383i
$767$	38.2873			1.38248
$768$	27.9703	−	30.8170i	1.00929	−	1.11201i
$769$	8.10807			0.292385			0.146192	−	0.989256i	$-0.453298\pi$
$769$	8.10807			0.292385			0.146192	+	0.989256i	$0.453298\pi$
$770$	12.0540	+	0.890220i	0.434397	+	0.0320813i
$771$	7.19302	−	48.4914i	0.259050	−	1.74638i
$772$	5.28468	+	7.12817i	0.190200	+	0.256549i
$773$	−11.0020	−	0.540491i	−0.395713	−	0.0194401i	−0.149761	−	0.988722i	$-0.547850\pi$
$773$	−11.0020	−	0.540491i	−0.395713	−	0.0194401i	−0.245952	+	0.969282i	$0.579100\pi$
$774$	3.38710	−	15.0773i	0.121747	−	0.541941i
$775$	−0.892880	−	0.477254i	−0.0320732	−	0.0171435i
$776$	−31.8958	−	22.4761i	−1.14499	−	0.806844i
$777$	−2.90215	−	0.880358i	−0.104114	−	0.0315826i
$778$	39.5919	+	4.88673i	1.41944	+	0.175198i
$779$	24.5958	+	41.0357i	0.881237	+	1.47026i
$780$	16.7315	+	31.3156i	0.599083	+	1.12128i
$781$	8.46857	−	9.34363i	0.303029	−	0.334341i
$782$	−44.6877	−	28.3037i	−1.59803	−	1.01214i
$783$	−2.27410	+	11.4327i	−0.0812696	+	0.408570i
$784$	−6.17296	−	20.3752i	−0.220463	−	0.727687i
$785$	4.76339	+	23.9472i	0.170013	+	0.854711i
$786$	−12.8761	−	4.96816i	−0.459275	−	0.177208i
$787$	−6.23472	−	13.1822i	−0.222244	−	0.469895i	0.761802	−	0.647810i	$-0.224315\pi$
$787$	−6.23472	−	13.1822i	−0.222244	−	0.469895i	−0.984046	+	0.177915i	$0.943065\pi$
$788$	−20.9784	−	31.4083i	−0.747324	−	1.11887i
$789$	−44.4776	+	59.9712i	−1.58345	+	2.13503i
$790$	−7.19445	−	14.2960i	−0.255967	−	0.508630i
$791$	−15.6227	−	12.8212i	−0.555480	−	0.455871i
$792$	−32.9611	+	0.800474i	−1.17122	+	0.0284436i
$793$	14.9399	+	1.47145i	0.530531	+	0.0522527i
$794$	−6.89638	+	6.56474i	−0.244743	+	0.232974i
$795$	−29.6343	+	62.6564i	−1.05102	+	2.22219i
$796$	47.1556	−	6.98641i	1.67138	−	0.247627i
$797$	−39.5824	+	9.91487i	−1.40208	+	0.351203i	−0.868979	−	0.494849i	$-0.835223\pi$
$797$	−39.5824	+	9.91487i	−1.40208	+	0.351203i	−0.533101	+	0.846052i	$0.678973\pi$
$798$	−7.93039	+	28.6470i	−0.280733	+	1.01409i
$799$	51.3554	+	21.2721i	1.81682	+	0.752553i
$800$	−1.16051	+	2.30302i	−0.0410302	+	0.0814242i
$801$	−8.95239	+	3.70820i	−0.316317	+	0.131023i
$802$	5.63045	+	45.6835i	0.198818	+	1.61314i
$803$	21.5417	+	12.9116i	0.760190	+	0.455640i
$804$	2.06564	+	5.77627i	0.0728494	+	0.203713i
$805$	5.27812	+	14.7514i	0.186029	+	0.519917i
$806$	−3.61805	−	9.38190i	−0.127441	−	0.330463i
$807$	−23.5391	−	28.6825i	−0.828616	−	1.00967i
$808$	−16.9201	+	21.6694i	−0.595247	+	0.762325i
$809$	0.204154	−	0.0201075i	0.00717769	−	0.000706940i	−0.0944277	−	0.995532i	$-0.530102\pi$
$809$	0.204154	−	0.0201075i	0.00717769	−	0.000706940i	0.101605	+	0.994825i	$0.467602\pi$
$810$	−12.0451	+	13.9612i	−0.423223	+	0.490546i
$811$	19.7560	−	2.93052i	0.693726	−	0.102904i	0.209449	−	0.977820i	$-0.432833\pi$
$811$	19.7560	−	2.93052i	0.693726	−	0.102904i	0.484276	+	0.874915i	$0.339083\pi$
$812$	14.0052	+	5.80403i	0.491487	+	0.203682i
$813$	6.12718	+	2.19234i	0.214889	+	0.0768887i
$814$	−2.85391	−	2.71763i	−0.100030	−	0.0952529i
$815$	−19.3302	+	28.9296i	−0.677106	+	1.01336i
$816$	66.5198	+	16.6872i	2.32866	+	0.584167i
$817$	−10.0575	−	15.0522i	−0.351869	−	0.526609i
$818$	−29.5233	−	5.12544i	−1.03226	−	0.179207i
$819$	15.5970	−	0.766233i	0.545005	−	0.0267744i
$820$	−32.5356	−	3.21024i	−1.13619	−	0.112106i
$821$	34.1220	+	8.54711i	1.19087	+	0.298296i	0.787251	−	0.616633i	$-0.211504\pi$
$821$	34.1220	+	8.54711i	1.19087	+	0.298296i	0.403615	+	0.914929i	$0.367754\pi$
$822$	−7.88541	+	13.9169i	−0.275035	+	0.485406i
$823$	−14.8272	−	27.7398i	−0.516845	−	0.966949i	−0.996012	−	0.0892247i	$-0.971561\pi$
$823$	−14.8272	−	27.7398i	−0.516845	−	0.966949i	0.479167	−	0.877724i	$-0.340939\pi$
$824$	−27.1606	−	8.98059i	−0.946185	−	0.312854i
$825$	3.51266	−	1.06556i	0.122295	−	0.0370979i
$826$	−21.5822	+	3.74291i	−0.750939	+	0.130232i
$827$	23.6414	+	26.0843i	0.822093	+	0.907040i	0.996989	−	0.0775472i	$-0.0247089\pi$
$827$	23.6414	+	26.0843i	0.822093	+	0.907040i	−0.174896	+	0.984587i	$0.555959\pi$
$828$	−18.2658	−	38.6374i	−0.634782	−	1.34274i
$829$	−7.63200	−	10.2906i	−0.265070	−	0.357406i	0.650541	−	0.759471i	$-0.274542\pi$
$829$	−7.63200	−	10.2906i	−0.265070	−	0.357406i	−0.915611	+	0.402066i	$0.868292\pi$
$830$	15.4230	+	7.76498i	0.535340	+	0.269526i
$831$	−36.0788	−	36.0788i	−1.25156	−	1.25156i
$832$	−23.6689	+	9.78940i	−0.820572	+	0.339386i
$833$	24.8075	−	24.8075i	0.859529	−	0.859529i
$834$	78.7844	−	26.0192i	2.72808	−	0.900971i
$835$	3.96316	−	2.93928i	0.137151	−	0.101718i
$836$	−25.9440	+	28.6147i	−0.897292	+	0.989661i
$837$	−3.27740	+	2.97046i	−0.113283	+	0.102674i
$838$	27.2805	+	19.2167i	0.942390	+	0.663829i
$839$	−4.84592	−	15.9749i	−0.167300	−	0.551514i	0.832698	−	0.553728i	$-0.186795\pi$
$839$	−4.84592	−	15.9749i	−0.167300	−	0.551514i	−0.999998	+	0.00221425i	$0.999295\pi$
$840$	−12.4927	−	16.0166i	−0.431040	−	0.552626i
$841$	4.63126	−	2.47546i	0.159699	−	0.0853608i
$842$	−1.89819	−	6.86152i	−0.0654160	−	0.236464i
$843$	−12.9775	+	51.8090i	−0.446968	+	1.78440i
$844$	−4.07979	−	2.18161i	−0.140432	−	0.0750942i
$845$	0.287561	+	5.85344i	0.00989240	+	0.201364i
$846$	25.8567	+	36.7205i	0.888971	+	1.26248i
$847$	−1.52671	+	1.02012i	−0.0524585	+	0.0350517i
$848$	−42.8784	−	25.7208i	−1.47245	−	0.883255i
$849$	−41.8985	−	27.9957i	−1.43795	−	0.960810i
$850$	−4.24845	+	0.103921i	−0.145720	+	0.00356445i
$851$	1.72091	−	4.80961i	0.0589919	−	0.164871i
$852$	−21.1923	−	0.00371695i	−0.726036	−	0.000127341i
$853$	−2.62047	−	17.6658i	−0.0897232	−	0.604864i	−0.986671	−	0.162728i	$-0.947971\pi$
$853$	−2.62047	−	17.6658i	−0.0897232	−	0.604864i	0.896948	−	0.442136i	$-0.145779\pi$
$854$	−8.56529	+	0.631059i	−0.293098	+	0.0215944i
$855$	−4.90884	−	49.8403i	−0.167879	−	1.70450i
$856$	−15.0811	+	13.0022i	−0.515463	+	0.444405i
$857$	38.6829	−	31.7463i	1.32138	−	1.08443i	0.331365	−	0.943503i	$-0.392491\pi$
$857$	38.6829	−	31.7463i	1.32138	−	1.08443i	0.990020	−	0.140929i	$-0.0450090\pi$
$858$	33.3285	+	14.7770i	1.13782	+	0.504478i
$859$	23.0975	−	8.26442i	0.788077	−	0.281978i	0.0880697	−	0.996114i	$-0.471930\pi$
$859$	23.0975	−	8.26442i	0.788077	−	0.281978i	0.700007	+	0.714136i	$0.253180\pi$
$860$	12.3560	+	0.609182i	0.421335	+	0.0207729i
$861$	−13.2817	+	22.1592i	−0.452639	+	0.755182i
$862$	14.5488	−	18.6392i	0.495533	−	0.634852i
$863$	−3.14169	−	7.58470i	−0.106944	−	0.258186i	0.861344	−	0.508022i	$-0.169623\pi$
$863$	−3.14169	−	7.58470i	−0.106944	−	0.258186i	−0.968288	+	0.249836i	$0.919623\pi$
$864$	7.76550	+	8.16352i	0.264188	+	0.277729i
$865$	16.1841	−	39.0720i	0.550278	−	1.32849i
$866$	17.2148	+	30.3946i	0.584984	+	1.03285i
$867$	16.7157	+	66.7330i	0.567696	+	2.26637i
$868$	2.95662	+	4.93478i	0.100354	+	0.167497i
$869$	−14.8558	−	7.02626i	−0.503948	−	0.238350i
$870$	−45.8779	−	1.13027i	−1.55541	−	0.0383196i
$871$	0.370060	−	3.75728i	0.0125390	−	0.127311i
$872$	−3.90284	−	17.4016i	−0.132167	−	0.589291i
$873$	32.9567	−	40.1579i	1.11542	−	1.35914i
$874$	−47.5382	−	15.7091i	−1.60800	−	0.531369i
$875$	12.0992	+	8.97335i	0.409027	+	0.303355i
$876$	−8.22687	−	41.3972i	−0.277960	−	1.39868i
$877$	27.0256	−	12.7821i	0.912589	−	0.431622i	0.0872026	−	0.996191i	$-0.472207\pi$
$877$	27.0256	−	12.7821i	0.912589	−	0.431622i	0.825386	+	0.564568i	$0.190957\pi$
$878$	−15.5753	−	35.1456i	−0.525640	−	1.18611i
$879$	−77.8275	+	15.4809i	−2.62506	+	0.522156i
$880$	−5.14031	−	25.8895i	−0.173280	−	0.872736i
$881$	10.8505	+	2.15830i	0.365562	+	0.0727149i	0.374454	−	0.927246i	$-0.377830\pi$
$881$	10.8505	+	2.15830i	0.365562	+	0.0727149i	−0.00889135	+	0.999960i	$0.502830\pi$
$882$	27.6568	−	6.20799i	0.931253	−	0.209034i
$883$	0.705220	+	0.639174i	0.0237325	+	0.0215099i	0.683339	−	0.730101i	$-0.260527\pi$
$883$	0.705220	+	0.639174i	0.0237325	+	0.0215099i	−0.659607	+	0.751611i	$0.729277\pi$
$884$	−32.6225	−	26.7822i	−1.09721	−	0.900782i
$885$	56.8733	−	34.0886i	1.91178	−	1.14587i
$886$	3.85053	+	4.93489i	0.129361	+	0.165791i
$887$	−7.23284	+	23.8435i	−0.242855	+	0.800585i	0.747768	+	0.663960i	$0.231126\pi$
$887$	−7.23284	+	23.8435i	−0.242855	+	0.800585i	−0.990623	+	0.136625i	$0.956374\pi$
$888$	−0.164274	+	6.62077i	−0.00551266	+	0.222179i
$889$	−9.36976	+	17.5296i	−0.314252	+	0.587924i
$890$	−4.14959	−	6.55419i	−0.139095	−	0.219697i
$891$	−0.929033	+	18.9109i	−0.0311238	+	0.633539i
$892$	−16.0665	+	4.02146i	−0.537947	+	0.134648i
$893$	52.0429	+	7.71984i	1.74155	+	0.258334i
$894$	11.0650	+	12.8296i	0.370068	+	0.429087i
$895$			23.7988i			0.795504i
$896$	12.3849	−	7.83201i	0.413751	−	0.261649i
$897$			47.2569i			1.57786i
$898$	11.4773	−	9.89866i	0.383003	−	0.330322i
$899$	12.8563	+	1.90706i	0.428783	+	0.0636039i
$900$	−2.94471	−	1.76569i	−0.0981570	−	0.0588564i
$901$	4.04298	−	82.2968i	0.134691	−	2.74171i
$902$	−28.3638	+	17.9577i	−0.944412	+	0.597926i
$903$	4.60820	−	8.62133i	0.153351	−	0.286900i
$904$	−17.8958	+	40.3435i	−0.595204	+	1.34181i
$905$	0.780746	−	2.57377i	0.0259529	−	0.0855551i
$906$	62.5399	−	48.7978i	2.07775	−	1.62120i
$907$	−29.4244	+	17.6363i	−0.977022	+	0.585604i	−0.911085	−	0.412219i	$-0.864754\pi$
$907$	−29.4244	+	17.6363i	−0.977022	+	0.585604i	−0.0659374	+	0.997824i	$0.521004\pi$
$908$	14.8612	−	1.46107i	0.493185	−	0.0484872i
$909$	−27.1214	−	24.5814i	−0.899560	−	0.815314i
$910$	2.73798	+	12.1978i	0.0907633	+	0.404353i
$911$	−32.9160	−	6.54740i	−1.09056	−	0.216925i	−0.383117	−	0.923700i	$-0.625149\pi$
$911$	−32.9160	−	6.54740i	−1.09056	−	0.216925i	−0.707439	+	0.706775i	$0.750149\pi$
$912$	64.9114	+	0.0227698i	2.14943	+	0.000753984i
$913$	17.3899	−	3.45907i	0.575522	−	0.114479i
$914$	10.6215	−	4.70706i	0.351327	−	0.155696i
$915$	23.5023	−	11.1158i	0.776962	−	0.367476i
$916$	−10.4875	+	15.6897i	−0.346517	+	0.518402i
$917$	−3.90314	−	2.89476i	−0.128893	−	0.0955935i
$918$	−5.82560	+	17.6291i	−0.192273	+	0.581849i
$919$	0.714482	−	0.870599i	0.0235686	−	0.0287184i	−0.761093	−	0.648643i	$-0.775337\pi$
$919$	0.714482	−	0.870599i	0.0235686	−	0.0287184i	0.784661	+	0.619925i	$0.212837\pi$
$920$	27.9777	−	19.6931i	0.922397	−	0.649263i
$921$	1.46450	−	14.8693i	0.0482569	−	0.489961i
$922$	1.04652	−	42.4787i	0.0344654	−	1.39896i
$923$	11.7905	+	5.57649i	0.388089	+	0.183552i
$924$	−20.2315	−	5.07149i	−0.665567	−	0.166840i
$925$	−0.0997170	−	0.398093i	−0.00327868	−	0.0130892i
$926$	−40.0789	+	22.6998i	−1.31707	+	0.745960i
$927$	14.5752	−	35.1876i	0.478712	−	1.15571i
$928$	4.06700	−	32.8558i	0.133506	−	1.07854i
$929$	−1.19266	−	2.87933i	−0.0391299	−	0.0944679i	0.903106	−	0.429417i	$-0.141281\pi$
$929$	−1.19266	−	2.87933i	−0.0391299	−	0.0944679i	−0.942236	+	0.334949i	$0.891281\pi$
$930$	−13.7274	−	10.7149i	−0.450140	−	0.351356i
$931$	17.0712	−	28.4816i	0.559487	−	0.933448i
$932$	32.3606	+	35.7171i	1.06001	+	1.16995i
$933$	−7.64134	+	2.73412i	−0.250166	+	0.0895109i
$934$	−2.66662	+	6.01437i	−0.0872544	+	0.196796i
$935$	33.6226	−	27.5934i	1.09958	−	0.902400i
$936$	−10.6885	−	32.3831i	−0.349364	−	1.05847i
$937$	−4.39987	−	44.6726i	−0.143737	−	1.45939i	−0.748579	−	0.663045i	$-0.769264\pi$
$937$	−4.39987	−	44.6726i	−0.143737	−	1.45939i	0.604842	−	0.796346i	$-0.293236\pi$
$938$	0.158707	+	2.15412i	0.00518197	+	0.0703344i
$939$	4.34737	+	29.3076i	0.141871	+	0.956417i
$940$	−25.4273	+	25.4184i	−0.829347	+	0.829056i
$941$	−18.6134	+	52.0210i	−0.606780	+	1.69584i	0.105928	+	0.994374i	$0.466219\pi$
$941$	−18.6134	+	52.0210i	−0.606780	+	1.69584i	−0.712707	+	0.701461i	$0.752531\pi$
$942$	−1.03032	−	42.1210i	−0.0335695	−	1.37237i
$943$	−36.1813	−	24.1756i	−1.17822	−	0.787265i
$944$	20.4365	+	43.2486i	0.665152	+	1.40762i
$945$	4.57239	−	3.05517i	0.148740	−	0.0993848i
$946$	10.3863	−	7.31348i	0.337687	−	0.237782i
$947$	0.508049	+	10.3416i	0.0165094	+	0.336056i	0.992815	+	0.119660i	$0.0381803\pi$
$947$	0.508049	+	10.3416i	0.0165094	+	0.336056i	−0.976306	+	0.216396i	$0.930570\pi$
$948$	8.01229	+	26.4297i	0.260227	+	0.858396i
$949$	−6.31166	+	25.1976i	−0.204885	+	0.817948i
$950$	−3.87671	+	1.07246i	−0.125777	+	0.0347954i
$951$	48.1323	−	25.7272i	1.56080	−	0.834263i
$952$	21.0071	+	11.9077i	0.680845	+	0.385931i
$953$	14.9983	+	49.4427i	0.485842	+	1.60161i	0.766800	+	0.641887i	$0.221848\pi$
$953$	14.9983	+	49.4427i	0.485842	+	1.60161i	−0.280958	+	0.959720i	$0.590652\pi$
$954$	38.3369	−	54.4240i	1.24120	−	1.76204i
$955$	−5.97146	+	5.41221i	−0.193232	+	0.175135i
$956$	2.25618	+	46.0905i	0.0729701	+	1.49067i
$957$	−37.8495	+	28.0711i	−1.22350	+	0.907409i
$958$	−1.65594	−	5.01408i	−0.0535010	−	0.161998i
$959$	−3.98245	+	3.98245i	−0.128600	+	0.128600i
$960$	−26.4428	+	35.6148i	−0.853437	+	1.14946i
$961$	−18.4330	−	18.4330i	−0.594612	−	0.594612i
$962$	1.83293	−	3.64061i	0.0590961	−	0.117378i
$963$	−15.7925	−	21.2938i	−0.508907	−	0.686182i
$964$	12.3514	−	34.5009i	0.397813	−	1.11120i
$965$	−6.35145	−	7.00774i	−0.204460	−	0.225587i
$966$	−4.61976	−	26.6382i	−0.148638	−	0.857070i
$967$	−0.460827	+	0.139790i	−0.0148192	+	0.00449535i	−0.297686	−	0.954664i	$-0.596215\pi$
$967$	−0.460827	+	0.139790i	−0.0148192	+	0.00449535i	0.282866	+	0.959159i	$0.408715\pi$
$968$	3.03554	+	2.61987i	0.0975659	+	0.0842057i
$969$	50.4236	+	94.3359i	1.61984	+	3.03050i
$970$	36.1840	+	20.5022i	1.16180	+	0.658285i
$971$	30.2869	+	7.58646i	0.971952	+	0.243461i	0.696264	−	0.717786i	$-0.254844\pi$
$971$	30.2869	+	7.58646i	0.971952	+	0.243461i	0.275688	+	0.961247i	$0.411094\pi$
$972$	33.8392	−	27.7612i	1.08539	−	0.890440i
$973$	29.1784	−	1.43344i	0.935417	−	0.0459541i
$974$	−2.47630	+	14.2638i	−0.0793457	+	0.457043i
$975$	2.10928	+	3.15675i	0.0675509	+	0.101097i
$976$	6.31229	+	17.6612i	0.202051	+	0.565321i
$977$	28.9547	−	43.3338i	0.926344	−	1.38637i	0.00400448	−	0.999992i	$-0.498725\pi$
$977$	28.9547	−	43.3338i	0.926344	−	1.38637i	0.922340	−	0.386380i	$-0.126275\pi$
$978$	41.4042	−	43.4805i	1.32396	−	1.39035i
$979$	−7.49981	−	2.68348i	−0.239695	−	0.0857643i
$980$	8.68004	+	20.9659i	0.277274	+	0.669730i
$981$	23.4868	−	3.48394i	0.749876	−	0.111234i
$982$	21.5639	+	18.6044i	0.688131	+	0.593691i
$983$	−40.4423	+	3.98322i	−1.28991	+	0.127045i	−0.719602	−	0.694387i	$-0.755676\pi$
$983$	−40.4423	+	3.98322i	−1.28991	+	0.127045i	−0.570307	+	0.821432i	$0.693176\pi$
$984$	54.3695	+	15.0615i	1.73324	+	0.480142i
$985$	25.5388	+	31.1191i	0.813733	+	0.991537i
$986$	50.9018	−	19.6299i	1.62104	−	0.625142i
$987$	9.57123	+	26.7498i	0.304656	+	0.851455i
$988$	−36.1109	−	17.0870i	−1.14884	−	0.543609i
$989$	14.1231	+	8.46503i	0.449087	+	0.269172i
$990$	34.8779	−	4.29868i	1.10849	−	0.136621i
$991$	−23.4353	+	9.70721i	−0.744446	+	0.308360i	−0.722473	−	0.691399i	$-0.756995\pi$
$991$	−23.4353	+	9.70721i	−0.744446	+	0.308360i	−0.0219731	+	0.999759i	$0.506995\pi$
$992$	8.66641	−	9.09463i	0.275159	−	0.288755i
$993$	−5.53954	−	2.29455i	−0.175792	−	0.0728155i
$994$	−7.19132	−	1.99079i	−0.228095	−	0.0631439i
$995$	−49.2865	+	12.3456i	−1.56249	+	0.391383i
$996$	−23.9302	−	17.7544i	−0.758258	−	0.562569i
$997$	−20.8473	+	44.0780i	−0.660242	+	1.39596i	0.244351	+	0.969687i	$0.421425\pi$
$997$	−20.8473	+	44.0780i	−0.660242	+	1.39596i	−0.904592	+	0.426277i	$0.859825\pi$
$998$	−14.6936	−	15.4358i	−0.465117	−	0.488613i
$999$	−1.78434	−	0.175742i	−0.0564541	−	0.00556024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.5.18	✓	992
256.205	even	64	inner	256.2.m.a.205.18	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.5.18	✓	992	1.1	even	1	trivial
256.2.m.a.205.18	yes	992	256.205	even	64	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104160 - 1.41037i) q^{2} +(0.381661 - 2.57295i) q^{3} +(-1.97830 - 0.293808i) q^{4} +(2.12912 + 0.104597i) q^{5} +(-3.58906 - 0.806282i) q^{6} +(-1.14227 - 0.610554i) q^{7} +(-0.620438 + 2.75954i) q^{8} +(-3.60358 - 1.09313i) q^{9} +O(q^{10})\)	\(q+(0.104160 - 1.41037i) q^{2} +(0.381661 - 2.57295i) q^{3} +(-1.97830 - 0.293808i) q^{4} +(2.12912 + 0.104597i) q^{5} +(-3.58906 - 0.806282i) q^{6} +(-1.14227 - 0.610554i) q^{7} +(-0.620438 + 2.75954i) q^{8} +(-3.60358 - 1.09313i) q^{9} +(0.369290 - 2.99196i) q^{10} +(-1.59142 - 2.65513i) q^{11} +(-1.51099 + 4.97793i) q^{12} +(2.15012 - 2.37229i) q^{13} +(-0.980087 + 1.54743i) q^{14} +(1.08173 - 5.43821i) q^{15} +(3.82735 + 1.16248i) q^{16} +(1.28594 + 6.46488i) q^{17} +(-1.91707 + 4.96853i) q^{18} +(2.66744 + 5.63984i) q^{19} +(-4.18132 - 0.832478i) q^{20} +(-2.00688 + 2.70597i) q^{21} +(-3.91048 + 1.96794i) q^{22} +(-4.38646 - 3.59988i) q^{23} +(6.86336 + 2.64956i) q^{24} +(-0.453693 - 0.0446849i) q^{25} +(-3.12186 - 3.27957i) q^{26} +(-0.851583 + 1.80052i) q^{27} +(2.08036 + 1.54347i) q^{28} +(5.67707 - 1.42203i) q^{29} +(-7.55723 - 2.09208i) q^{30} +(2.05173 + 0.849854i) q^{31} +(2.03819 - 5.27691i) q^{32} +(-7.43890 + 3.08129i) q^{33} +(9.25183 - 1.14028i) q^{34} +(-2.36817 - 1.41942i) q^{35} +(6.80780 + 3.22131i) q^{36} +(0.303269 + 0.847580i) q^{37} +(8.23211 - 3.17465i) q^{38} +(-5.28317 - 6.43756i) q^{39} +(-1.60963 + 5.81051i) q^{40} +(7.63154 - 0.751641i) q^{41} +(3.60739 + 3.11231i) q^{42} +(-2.87027 + 0.425765i) q^{43} +(2.36822 + 5.72022i) q^{44} +(-7.55813 - 2.70434i) q^{45} +(-5.53406 + 5.81159i) q^{46} +(4.68515 - 7.01182i) q^{47} +(4.45176 - 9.40391i) q^{48} +(-2.95699 - 4.42546i) q^{49} +(-0.110279 + 0.635222i) q^{50} +(17.1246 - 0.841277i) q^{51} +(-4.95058 + 4.06138i) q^{52} +(-12.1257 - 3.03732i) q^{53} +(2.45070 + 1.38859i) q^{54} +(-3.11062 - 5.81956i) q^{55} +(2.39355 - 2.77332i) q^{56} +(15.5291 - 4.71069i) q^{57} +(-1.41427 - 8.15491i) q^{58} +(8.03084 + 8.86067i) q^{59} +(-3.73777 + 10.4406i) q^{60} +(2.79314 + 3.76611i) q^{61} +(1.41232 - 2.80518i) q^{62} +(3.44883 + 3.44883i) q^{63} +(-7.23011 - 3.42425i) q^{64} +(4.82601 - 4.82601i) q^{65} +(3.57094 + 10.8126i) q^{66} +(0.947152 - 0.702456i) q^{67} +(-0.644553 - 13.1673i) q^{68} +(-10.9364 + 9.91222i) q^{69} +(-2.24858 + 3.19215i) q^{70} +(1.18254 + 3.89830i) q^{71} +(5.25235 - 9.26600i) q^{72} +(-7.15524 + 3.82456i) q^{73} +(1.22699 - 0.339438i) q^{74} +(-0.288129 + 1.15028i) q^{75} +(-3.61998 - 11.9410i) q^{76} +(0.196729 + 4.00452i) q^{77} +(-9.62965 + 6.78070i) q^{78} +(4.41411 - 2.94941i) q^{79} +(8.02732 + 2.87540i) q^{80} +(-5.08565 - 3.39812i) q^{81} +(-0.265195 - 10.8416i) q^{82} +(-1.92964 + 5.39298i) q^{83} +(4.76526 - 4.76359i) q^{84} +(2.06173 + 13.8990i) q^{85} +(0.301520 + 4.09250i) q^{86} +(-1.49210 - 15.1496i) q^{87} +(8.31431 - 2.74425i) q^{88} +(1.98911 - 1.63242i) q^{89} +(-4.60139 + 10.3781i) q^{90} +(-3.90442 + 1.39702i) q^{91} +(7.62008 + 8.41042i) q^{92} +(2.96970 - 4.95464i) q^{93} +(-9.40128 - 7.33816i) q^{94} +(5.08941 + 12.2869i) q^{95} +(-12.7993 - 7.25814i) q^{96} +(-5.27929 + 12.7453i) q^{97} +(-6.54954 + 3.70951i) q^{98} +(2.83241 + 11.3076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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