LMFDB - Embedded newform 57.2.j.b.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(2,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("57.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.j (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	57.29
Dual form			57.2.j.b.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.448036 + 2.54094i) q^{2} +(0.504201 - 1.65704i) q^{3} +(-4.37626 + 1.59283i) q^{4} +(-0.533860 + 1.46677i) q^{5} +(4.43634 + 0.538732i) q^{6} +(1.49687 - 2.59266i) q^{7} +(-3.42787 - 5.93724i) q^{8} +(-2.49156 - 1.67096i) q^{9} +O(q^{10})$	\(q+(0.448036 + 2.54094i) q^{2} +(0.504201 - 1.65704i) q^{3} +(-4.37626 + 1.59283i) q^{4} +(-0.533860 + 1.46677i) q^{5} +(4.43634 + 0.538732i) q^{6} +(1.49687 - 2.59266i) q^{7} +(-3.42787 - 5.93724i) q^{8} +(-2.49156 - 1.67096i) q^{9} +(-3.96616 - 0.699341i) q^{10} +(1.05900 - 0.611412i) q^{11} +(0.432864 + 8.05474i) q^{12} +(0.203530 - 0.242558i) q^{13} +(7.25845 + 2.64186i) q^{14} +(2.16132 + 1.62417i) q^{15} +(6.41525 - 5.38303i) q^{16} +(-5.00468 + 0.882460i) q^{17} +(3.12951 - 7.07956i) q^{18} +(-0.461268 + 4.33442i) q^{19} -7.26931i q^{20} +(-3.54142 - 3.78760i) q^{21} +(2.02803 + 2.41691i) q^{22} +(0.211619 + 0.581418i) q^{23} +(-11.5666 + 2.68655i) q^{24} +(1.96382 + 1.64784i) q^{25} +(0.707514 + 0.408483i) q^{26} +(-4.02510 + 3.28612i) q^{27} +(-2.42104 + 13.7304i) q^{28} +(0.204862 - 1.16183i) q^{29} +(-3.15858 + 6.21948i) q^{30} +(-4.50103 - 2.59867i) q^{31} +(6.04864 + 5.07541i) q^{32} +(-0.479186 - 2.06307i) q^{33} +(-4.48456 - 12.3212i) q^{34} +(3.00371 + 3.57969i) q^{35} +(13.5653 + 3.34394i) q^{36} -3.64847i q^{37} +(-11.2202 + 0.769925i) q^{38} +(-0.299308 - 0.459555i) q^{39} +(10.5386 - 1.85823i) q^{40} +(0.118123 - 0.0991172i) q^{41} +(8.03739 - 10.6955i) q^{42} +(8.99072 + 3.27235i) q^{43} +(-3.66057 + 4.36249i) q^{44} +(3.78106 - 2.76248i) q^{45} +(-1.38254 + 0.798207i) q^{46} +(8.03246 + 1.41634i) q^{47} +(-5.68532 - 13.3444i) q^{48} +(-0.981262 - 1.69960i) q^{49} +(-3.30720 + 5.72824i) q^{50} +(-1.06109 + 8.73789i) q^{51} +(-0.504348 + 1.38568i) q^{52} +(2.88328 - 1.04943i) q^{53} +(-10.1532 - 8.75525i) q^{54} +(0.331444 + 1.87971i) q^{55} -20.5243 q^{56} +(6.94974 + 2.94976i) q^{57} +3.04393 q^{58} +(-0.468861 - 2.65904i) q^{59} +(-12.0455 - 3.66519i) q^{60} +(-6.47830 + 2.35791i) q^{61} +(4.58645 - 12.6012i) q^{62} +(-8.06180 + 3.95856i) q^{63} +(-1.81179 + 3.13812i) q^{64} +(0.247119 + 0.428023i) q^{65} +(5.02745 - 2.14192i) q^{66} +(8.96745 + 1.58120i) q^{67} +(20.4962 - 11.8335i) q^{68} +(1.07013 - 0.0575091i) q^{69} +(-7.75000 + 9.23609i) q^{70} +(-12.9496 - 4.71326i) q^{71} +(-1.38017 + 20.5208i) q^{72} +(-0.335304 + 0.281354i) q^{73} +(9.27055 - 1.63465i) q^{74} +(3.72070 - 2.42328i) q^{75} +(-4.88536 - 19.7033i) q^{76} -3.66082i q^{77} +(1.03360 - 0.966421i) q^{78} +(-0.940136 - 1.12041i) q^{79} +(4.47082 + 12.2835i) q^{80} +(3.41576 + 8.32662i) q^{81} +(0.304774 + 0.255736i) q^{82} +(9.46265 + 5.46326i) q^{83} +(21.5312 + 10.9347i) q^{84} +(1.37743 - 7.81181i) q^{85} +(-4.28669 + 24.3110i) q^{86} +(-1.82191 - 0.925262i) q^{87} +(-7.26019 - 4.19167i) q^{88} +(-6.02351 - 5.05433i) q^{89} +(8.71336 + 8.36976i) q^{90} +(-0.324211 - 0.890763i) q^{91} +(-1.85220 - 2.20736i) q^{92} +(-6.57553 + 6.14814i) q^{93} +21.0446i q^{94} +(-6.11134 - 2.99055i) q^{95} +(11.4599 - 7.46380i) q^{96} +(-18.2890 + 3.22484i) q^{97} +(3.87893 - 3.25481i) q^{98} +(-3.66020 - 0.246173i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.448036	+	2.54094i	0.316810	+	1.79672i	0.561888	+	0.827213i	$0.310075\pi$
$2$	0.448036	+	2.54094i	0.316810	+	1.79672i	−0.245078	+	0.969503i	$0.578814\pi$
$3$	0.504201	−	1.65704i	0.291101	−	0.956692i
$3$	0.504201	−	1.65704i	0.291101	−	0.956692i
$4$	−4.37626	+	1.59283i	−2.18813	+	0.796414i
$5$	−0.533860	+	1.46677i	−0.238750	+	0.655959i	0.761223	+	0.648491i	$0.224599\pi$
$5$	−0.533860	+	1.46677i	−0.238750	+	0.655959i	−0.999972	+	0.00746821i	$0.997623\pi$
$6$	4.43634	+	0.538732i	1.81113	+	0.219936i
$7$	1.49687	−	2.59266i	0.565765	−	0.979934i	−0.431213	−	0.902250i	$-0.641914\pi$
$7$	1.49687	−	2.59266i	0.565765	−	0.979934i	0.996978	−	0.0776837i	$-0.0247524\pi$
$8$	−3.42787	−	5.93724i	−1.21193	−	2.09913i
$9$	−2.49156	−	1.67096i	−0.830521	−	0.556988i
$10$	−3.96616	−	0.699341i	−1.25421	−	0.221151i
$11$	1.05900	−	0.611412i	0.319299	−	0.184348i	−0.331781	−	0.943356i	$-0.607649\pi$
$11$	1.05900	−	0.611412i	0.319299	−	0.184348i	0.651080	+	0.759009i	$0.274316\pi$
$12$	0.432864	+	8.05474i	0.124957	+	2.32520i
$13$	0.203530	−	0.242558i	0.0564491	−	0.0672734i	−0.737081	−	0.675804i	$-0.763796\pi$
$13$	0.203530	−	0.242558i	0.0564491	−	0.0672734i	0.793530	+	0.608531i	$0.208241\pi$
$14$	7.25845	+	2.64186i	1.93990	+	0.706067i
$15$	2.16132	+	1.62417i	0.558051	+	0.419360i
$16$	6.41525	−	5.38303i	1.60381	−	1.34576i
$17$	−5.00468	+	0.882460i	−1.21381	+	0.214028i	−0.743660	−	0.668558i	$-0.766912\pi$
$17$	−5.00468	+	0.882460i	−1.21381	+	0.214028i	−0.470152	+	0.882585i	$0.655801\pi$
$18$	3.12951	−	7.07956i	0.737632	−	1.66867i
$19$	−0.461268	+	4.33442i	−0.105822	+	0.994385i
$19$	−0.461268	+	4.33442i	−0.105822	+	0.994385i
$20$		−	7.26931i		−	1.62547i
$21$	−3.54142	−	3.78760i	−0.772801	−	0.826523i
$22$	2.02803	+	2.41691i	0.432377	+	0.515287i
$23$	0.211619	+	0.581418i	0.0441256	+	0.121234i	0.959798	−	0.280691i	$-0.0905635\pi$
$23$	0.211619	+	0.581418i	0.0441256	+	0.121234i	−0.915673	+	0.401925i	$0.868341\pi$
$24$	−11.5666	+	2.68655i	−2.36102	+	0.548389i
$25$	1.96382	+	1.64784i	0.392764	+	0.329568i
$26$	0.707514	+	0.408483i	0.138755	+	0.0801102i
$27$	−4.02510	+	3.28612i	−0.774631	+	0.632413i
$28$	−2.42104	+	13.7304i	−0.457534	+	2.59481i
$29$	0.204862	−	1.16183i	0.0380420	−	0.215747i	−0.959861	−	0.280477i	$-0.909507\pi$
$29$	0.204862	−	1.16183i	0.0380420	−	0.215747i	0.997903	+	0.0647299i	$0.0206186\pi$
$30$	−3.15858	+	6.21948i	−0.576675	+	1.13552i
$31$	−4.50103	−	2.59867i	−0.808409	−	0.466735i	0.0379939	−	0.999278i	$-0.487903\pi$
$31$	−4.50103	−	2.59867i	−0.808409	−	0.466735i	−0.846403	+	0.532543i	$0.821237\pi$
$32$	6.04864	+	5.07541i	1.06926	+	0.897214i
$33$	−0.479186	−	2.06307i	−0.0834156	−	0.359135i
$34$	−4.48456	−	12.3212i	−0.769095	−	2.11307i
$35$	3.00371	+	3.57969i	0.507720	+	0.605077i
$36$	13.5653	+	3.34394i	2.26088	+	0.557323i
$37$		−	3.64847i		−	0.599805i	−0.953970	−	0.299902i	$-0.903046\pi$
$37$		−	3.64847i		−	0.599805i	0.953970	−	0.299902i	$-0.0969541\pi$
$38$	−11.2202	+	0.769925i	−1.82015	+	0.124898i
$39$	−0.299308	−	0.459555i	−0.0479276	−	0.0735878i
$40$	10.5386	−	1.85823i	1.66629	−	0.293812i
$41$	0.118123	−	0.0991172i	0.0184477	−	0.0154795i	−0.633517	−	0.773729i	$-0.718389\pi$
$41$	0.118123	−	0.0991172i	0.0184477	−	0.0154795i	0.651965	+	0.758249i	$0.273945\pi$
$42$	8.03739	−	10.6955i	1.24020	−	1.65035i
$43$	8.99072	+	3.27235i	1.37107	+	0.499029i	0.919460	−	0.393185i	$-0.128627\pi$
$43$	8.99072	+	3.27235i	1.37107	+	0.499029i	0.451613	+	0.892214i	$0.350849\pi$
$44$	−3.66057	+	4.36249i	−0.551851	+	0.657671i
$45$	3.78106	−	2.76248i	0.563647	−	0.411807i
$46$	−1.38254	+	0.798207i	−0.203844	+	0.117689i
$47$	8.03246	+	1.41634i	1.17165	+	0.206594i	0.725410	−	0.688317i	$-0.241650\pi$
$47$	8.03246	+	1.41634i	1.17165	+	0.206594i	0.446244	+	0.894911i	$0.352761\pi$
$48$	−5.68532	−	13.3444i	−0.820605	−	1.92611i
$49$	−0.981262	−	1.69960i	−0.140180	−	0.242799i
$50$	−3.30720	+	5.72824i	−0.467709	+	0.810095i
$51$	−1.06109	+	8.73789i	−0.148583	+	1.22355i
$52$	−0.504348	+	1.38568i	−0.0699404	+	0.192160i
$53$	2.88328	−	1.04943i	0.396048	−	0.144150i	−0.136315	−	0.990665i	$-0.543526\pi$
$53$	2.88328	−	1.04943i	0.396048	−	0.144150i	0.532364	+	0.846516i	$0.321304\pi$
$54$	−10.1532	−	8.75525i	−1.38168	−	1.19144i
$55$	0.331444	+	1.87971i	0.0446919	+	0.253460i
$56$	−20.5243			−2.74268
$57$	6.94974	+	2.94976i	0.920516	+	0.390705i
$58$	3.04393			0.399688
$59$	−0.468861	−	2.65904i	−0.0610405	−	0.346178i	−0.999998	−	0.00214403i	$-0.999318\pi$
$59$	−0.468861	−	2.65904i	−0.0610405	−	0.346178i	0.938957	−	0.344034i	$-0.111794\pi$
$60$	−12.0455	−	3.66519i	−1.55507	−	0.473175i
$61$	−6.47830	+	2.35791i	−0.829462	+	0.301899i	−0.721638	−	0.692271i	$-0.756610\pi$
$61$	−6.47830	+	2.35791i	−0.829462	+	0.301899i	−0.107824	+	0.994170i	$0.534388\pi$
$62$	4.58645	−	12.6012i	0.582479	−	1.60035i
$63$	−8.06180	+	3.95856i	−1.01569	+	0.498731i
$64$	−1.81179	+	3.13812i	−0.226474	+	0.392265i
$65$	0.247119	+	0.428023i	0.0306514	+	0.0530898i
$66$	5.02745	−	2.14192i	0.618837	−	0.263652i
$67$	8.96745	+	1.58120i	1.09555	+	0.193175i	0.692081	−	0.721820i	$-0.256694\pi$
$67$	8.96745	+	1.58120i	1.09555	+	0.193175i	0.403467	+	0.914994i	$0.367805\pi$
$68$	20.4962	−	11.8335i	2.48552	−	1.43502i
$69$	1.07013	−	0.0575091i	0.128829	−	0.00692329i
$70$	−7.75000	+	9.23609i	−0.926302	+	1.10392i
$71$	−12.9496	−	4.71326i	−1.53683	−	0.559360i	−0.571548	−	0.820569i	$-0.693657\pi$
$71$	−12.9496	−	4.71326i	−1.53683	−	0.559360i	−0.965282	+	0.261208i	$0.915879\pi$
$72$	−1.38017	+	20.5208i	−0.162654	+	2.41840i
$73$	−0.335304	+	0.281354i	−0.0392444	+	0.0329300i	−0.662199	−	0.749328i	$-0.730377\pi$
$73$	−0.335304	+	0.281354i	−0.0392444	+	0.0329300i	0.622954	+	0.782258i	$0.285932\pi$
$74$	9.27055	−	1.63465i	1.07768	−	0.190024i
$75$	3.72070	−	2.42328i	0.429629	−	0.279817i
$76$	−4.88536	−	19.7033i	−0.560390	−	2.26012i
$77$		−	3.66082i		−	0.417190i
$78$	1.03360	−	0.966421i	0.117032	−	0.109426i
$79$	−0.940136	−	1.12041i	−0.105774	−	0.126056i	0.710560	−	0.703636i	$-0.248442\pi$
$79$	−0.940136	−	1.12041i	−0.105774	−	0.126056i	−0.816334	+	0.577580i	$0.803997\pi$
$80$	4.47082	+	12.2835i	0.499852	+	1.37333i
$81$	3.41576	+	8.32662i	0.379529	+	0.925180i
$82$	0.304774	+	0.255736i	0.0336567	+	0.0282413i
$83$	9.46265	+	5.46326i	1.03866	+	0.599671i	0.919454	−	0.393198i	$-0.128631\pi$
$83$	9.46265	+	5.46326i	1.03866	+	0.599671i	0.119207	+	0.992869i	$0.461965\pi$
$84$	21.5312	+	10.9347i	2.34924	+	1.19307i
$85$	1.37743	−	7.81181i	0.149404	−	0.847310i
$86$	−4.28669	+	24.3110i	−0.462246	+	2.62153i
$87$	−1.82191	−	0.925262i	−0.195329	−	0.0991985i
$88$	−7.26019	−	4.19167i	−0.773939	−	0.446834i
$89$	−6.02351	−	5.05433i	−0.638491	−	0.535758i	0.265063	−	0.964231i	$-0.414607\pi$
$89$	−6.02351	−	5.05433i	−0.638491	−	0.535758i	−0.903554	+	0.428473i	$0.859052\pi$
$90$	8.71336	+	8.36976i	0.918469	+	0.882250i
$91$	−0.324211	−	0.890763i	−0.0339866	−	0.0933773i
$92$	−1.85220	−	2.20736i	−0.193105	−	0.230134i
$93$	−6.57553	+	6.14814i	−0.681851	+	0.637532i
$94$			21.0446i			2.17058i
$95$	−6.11134	−	2.99055i	−0.627011	−	0.306824i
$96$	11.4599	−	7.46380i	1.16962	−	0.761771i
$97$	−18.2890	+	3.22484i	−1.85697	+	0.327433i	−0.986367	−	0.164561i	$-0.947379\pi$
$97$	−18.2890	+	3.22484i	−1.85697	+	0.327433i	−0.870599	+	0.491994i	$0.836268\pi$
$98$	3.87893	−	3.25481i	0.391831	−	0.328786i
$99$	−3.66020	−	0.246173i	−0.367864	−	0.0247414i
$100$	−11.2189	−	4.08335i	−1.12189	−	0.408335i
$101$	9.92594	−	11.8293i	0.987668	−	1.17706i	0.00346803	−	0.999994i	$-0.498896\pi$
$101$	9.92594	−	11.8293i	0.987668	−	1.17706i	0.984200	−	0.177062i	$-0.0566595\pi$
$102$	−22.6779	+	1.21871i	−2.24544	+	0.120671i
$103$	6.42425	−	3.70904i	0.633000	−	0.365463i	−0.148913	−	0.988850i	$-0.547577\pi$
$103$	6.42425	−	3.70904i	0.633000	−	0.365463i	0.781913	+	0.623387i	$0.214244\pi$
$104$	−2.13780	−	0.376951i	−0.209628	−	0.0369631i
$105$	7.44616	−	3.17239i	0.726671	−	0.309594i
$106$	3.95834	+	6.85605i	0.384468	+	0.665919i
$107$	6.82023	−	11.8130i	0.659337	−	1.14200i	−0.321451	−	0.946926i	$-0.604171\pi$
$107$	6.82023	−	11.8130i	0.659337	−	1.14200i	0.980788	−	0.195078i	$-0.0624962\pi$
$108$	12.3807	−	20.7922i	1.19133	−	2.00073i
$109$	−0.443482	+	1.21846i	−0.0424778	+	0.116707i	−0.959118	−	0.283007i	$-0.908668\pi$
$109$	−0.443482	+	1.21846i	−0.0424778	+	0.116707i	0.916640	+	0.399714i	$0.130890\pi$
$110$	−4.62773	+	1.68436i	−0.441237	+	0.160597i
$111$	−6.04566	−	1.83956i	−0.573829	−	0.174604i
$112$	−4.35356	−	24.6903i	−0.411373	−	2.33301i
$113$	−6.86179			−0.645503			−0.322752	−	0.946484i	$-0.604608\pi$
$113$	−6.86179			−0.645503			−0.322752	+	0.946484i	$0.604608\pi$
$114$	−4.38143	+	18.9805i	−0.410359	+	1.77769i
$115$	−0.965781			−0.0900595
$116$	0.954068	+	5.41079i	0.0885830	+	0.502379i
$117$	−0.912413	+	0.264256i	−0.0843526	+	0.0244305i
$118$	6.54641	−	2.38270i	0.602646	−	0.219345i
$119$	−5.20345	+	14.2964i	−0.477000	+	1.31055i
$120$	2.23439	−	18.3997i	0.203971	−	1.67966i
$121$	−4.75235	+	8.23131i	−0.432032	+	0.748301i
$122$	−8.89382	−	15.4046i	−0.805209	−	1.39466i
$123$	−0.104683	−	0.245710i	−0.00943896	−	0.0221549i
$124$	23.8369	+	4.20309i	2.14062	+	0.377449i
$125$	−10.2243	+	5.90301i	−0.914490	+	0.527981i
$126$	−13.6704	−	18.7110i	−1.21786	−	1.66691i
$127$	−2.00315	+	2.38726i	−0.177751	+	0.211835i	−0.847562	−	0.530696i	$-0.821931\pi$
$127$	−2.00315	+	2.38726i	−0.177751	+	0.211835i	0.669811	+	0.742531i	$0.266375\pi$
$128$	6.05398	+	2.20347i	0.535101	+	0.194761i
$129$	9.95556	−	13.2481i	0.876538	−	1.16643i
$130$	−0.976864	+	0.819686i	−0.0856766	+	0.0718912i
$131$	−3.61069	+	0.636662i	−0.315467	+	0.0556254i	−0.329140	−	0.944281i	$-0.606759\pi$
$131$	−3.61069	+	0.636662i	−0.315467	+	0.0556254i	0.0136728	+	0.999907i	$0.495648\pi$
$132$	5.38316	+	8.26528i	0.468544	+	0.719400i
$133$	10.5472	+	7.68400i	0.914561	+	0.666287i
$134$			23.4942i			2.02959i
$135$	−2.67113	−	7.65822i	−0.229894	−	0.659115i
$136$	22.3947	+	26.6890i	1.92033	+	2.28856i
$137$	5.40504	+	14.8502i	0.461784	+	1.26874i	0.924143	+	0.382048i	$0.124781\pi$
$137$	5.40504	+	14.8502i	0.461784	+	1.26874i	−0.462359	+	0.886693i	$0.652997\pi$
$138$	0.625585	+	2.69337i	0.0532533	+	0.229275i
$139$	−5.59691	−	4.69637i	−0.474724	−	0.398341i	0.373790	−	0.927513i	$-0.378058\pi$
$139$	−5.59691	−	4.69637i	−0.474724	−	0.398341i	−0.848514	+	0.529173i	$0.822502\pi$
$140$	−18.8469	−	10.8812i	−1.59285	−	0.919632i
$141$	6.39691	−	12.5960i	0.538717	−	1.06077i
$142$	6.17423	−	35.0158i	0.518130	−	2.93846i
$143$	0.0672349	−	0.381308i	0.00562247	−	0.0318866i
$144$	−24.9788	+	2.69251i	−2.08157	+	0.224376i
$145$	1.59477	+	0.920741i	0.132439	+	0.0764634i
$146$	−0.865132	−	0.725932i	−0.0715988	−	0.0600786i
$147$	−3.31105	+	0.769052i	−0.273091	+	0.0634304i
$148$	5.81139	+	15.9667i	0.477693	+	1.31245i
$149$	−3.59311	−	4.28210i	−0.294359	−	0.350803i	0.598514	−	0.801113i	$-0.295758\pi$
$149$	−3.59311	−	4.28210i	−0.294359	−	0.350803i	−0.892873	+	0.450309i	$0.851314\pi$
$150$	7.82443	+	8.36835i	0.638862	+	0.683273i
$151$		−	19.1657i		−	1.55968i	−0.625980	−	0.779839i	$-0.715301\pi$
$151$		−	19.1657i		−	1.55968i	0.625980	−	0.779839i	$-0.284699\pi$
$152$	27.3157	−	12.1192i	2.21559	−	0.982994i
$153$	13.9440	+	6.16393i	1.12731	+	0.498324i
$154$	9.30194	−	1.64018i	0.749572	−	0.132170i
$155$	6.21457	−	5.21465i	0.499167	−	0.418850i
$156$	2.04184	+	1.53439i	0.163478	+	0.122849i
$157$	−13.5243	−	4.92243i	−1.07935	−	0.392853i	−0.259687	−	0.965693i	$-0.583619\pi$
$157$	−13.5243	−	4.92243i	−1.07935	−	0.392853i	−0.819667	+	0.572840i	$0.805842\pi$
$158$	2.42568	−	2.89081i	0.192977	−	0.229981i
$159$	−0.285190	−	5.30683i	−0.0226171	−	0.420859i
$160$	−10.6736	+	6.16239i	−0.843820	+	0.487180i
$161$	1.82419	+	0.321653i	0.143766	+	0.0253498i
$162$	−19.6271	+	12.4099i	−1.54205	+	0.975012i
$163$	−0.951823	−	1.64861i	−0.0745525	−	0.129129i	0.826339	−	0.563173i	$-0.190420\pi$
$163$	−0.951823	−	1.64861i	−0.0745525	−	0.129129i	−0.900892	+	0.434044i	$0.857086\pi$
$164$	−0.359061	+	0.621912i	−0.0280380	+	0.0485632i
$165$	3.28187	+	0.398537i	0.255493	+	0.0310261i
$166$	−9.64222	+	26.4918i	−0.748381	+	2.05616i
$167$	−12.4088	+	4.51642i	−0.960220	+	0.349491i	−0.774120	−	0.633039i	$-0.781807\pi$
$167$	−12.4088	+	4.51642i	−0.960220	+	0.349491i	−0.186100	+	0.982531i	$0.559585\pi$
$168$	−10.3484	+	34.0096i	−0.798396	+	2.62390i
$169$	2.24002	+	12.7038i	0.172309	+	0.977213i
$170$	20.4665			1.56971
$171$	8.39194	−	10.0287i	0.641748	−	0.766916i
$172$	−44.5580			−3.39752
$173$	2.37910	+	13.4925i	0.180880	+	1.02582i	0.931136	+	0.364672i	$0.118819\pi$
$173$	2.37910	+	13.4925i	0.180880	+	1.02582i	−0.750256	+	0.661147i	$0.770070\pi$
$174$	1.53475	−	5.04392i	0.116349	−	0.382378i
$175$	7.21188	−	2.62491i	0.545167	−	0.198424i
$176$	3.50247	−	9.62296i	0.264009	−	0.725358i
$177$	−4.64254	−	0.563772i	−0.348955	−	0.0423757i
$178$	10.1440	−	17.5699i	0.760325	−	1.31692i
$179$	9.56990	+	16.5756i	0.715288	+	1.23892i	0.962848	+	0.270043i	$0.0870379\pi$
$179$	9.56990	+	16.5756i	0.715288	+	1.23892i	−0.247560	+	0.968873i	$0.579629\pi$
$180$	−12.1467	+	18.1119i	−0.905365	+	1.34998i
$181$	6.05191	+	1.06712i	0.449835	+	0.0793181i	0.393976	−	0.919121i	$-0.371099\pi$
$181$	6.05191	+	1.06712i	0.449835	+	0.0793181i	0.0558589	+	0.998439i	$0.482210\pi$
$182$	2.11812	−	1.22290i	0.157005	−	0.0906471i
$183$	0.640781	+	11.9237i	0.0473679	+	0.881423i
$184$	2.72662	−	3.24946i	0.201009	−	0.239553i
$185$	5.35146	+	1.94777i	0.393447	+	0.143203i
$186$	−18.5681	−	13.9534i	−1.36148	−	1.02312i
$187$	−4.76039	+	3.99444i	−0.348114	+	0.292102i
$188$	−37.4081	+	6.59606i	−2.72827	+	0.481067i
$189$	2.49472	+	15.3546i	0.181464	+	1.11688i
$190$	4.86070	−	16.8684i	0.352633	−	1.22377i
$191$		−	26.3867i		−	1.90927i	−0.297773	−	0.954637i	$-0.596244\pi$
$191$		−	26.3867i		−	1.90927i	0.297773	−	0.954637i	$-0.403756\pi$
$192$	4.28648	+	4.58446i	0.309350	+	0.330855i
$193$	−5.01339	−	5.97472i	−0.360871	−	0.430070i	0.554809	−	0.831978i	$-0.312792\pi$
$193$	−5.01339	−	5.97472i	−0.360871	−	0.430070i	−0.915680	+	0.401908i	$0.868347\pi$
$194$	−16.3883	−	45.0264i	−1.17661	−	3.23271i
$195$	0.833850	−	0.193677i	0.0597132	−	0.0138695i
$196$	7.00142	+	5.87489i	0.500102	+	0.419635i
$197$	20.9467	+	12.0936i	1.49239	+	0.861630i	0.999962	−	0.00872425i	$-0.00277705\pi$
$197$	20.9467	+	12.0936i	1.49239	+	0.861630i	0.492426	+	0.870355i	$0.336110\pi$
$198$	−1.01439	−	9.41065i	−0.0720896	−	0.668786i
$199$	−0.711595	+	4.03566i	−0.0504437	+	0.286080i	−0.999586	−	0.0287666i	$-0.990842\pi$
$199$	−0.711595	+	4.03566i	−0.0504437	+	0.286080i	0.949142	+	0.314847i	$0.101953\pi$
$200$	3.05191	−	17.3082i	0.215803	−	1.22388i
$201$	7.14152	−	14.0622i	0.503724	−	0.991869i
$202$	34.5047	+	19.9213i	2.42774	+	1.40166i
$203$	−2.70558	−	2.27025i	−0.189895	−	0.159341i
$204$	−9.27433	−	39.9294i	−0.649333	−	2.79562i
$205$	0.0823207	+	0.226174i	0.00574952	+	0.0157967i
$206$	12.3028	+	14.6619i	0.857174	+	1.02154i
$207$	0.444267	−	1.80225i	0.0308787	−	0.125265i
$208$		−	2.65168i		−	0.183861i
$209$	2.16164	+	4.87216i	0.149524	+	0.337015i
$210$	11.3970	+	17.4989i	0.786468	+	1.20754i
$211$	9.83078	−	1.73343i	0.676779	−	0.119334i	0.175314	−	0.984512i	$-0.443906\pi$
$211$	9.83078	−	1.73343i	0.676779	−	0.119334i	0.501465	+	0.865178i	$0.332795\pi$
$212$	−10.9464	+	9.18513i	−0.751802	+	0.630837i
$213$	−14.3392	+	19.0815i	−0.982508	+	1.30744i
$214$	33.0718	+	12.0372i	2.26074	+	0.822843i
$215$	−9.59958	+	11.4403i	−0.654686	+	0.780224i
$216$	33.3080	+	12.6336i	2.26632	+	0.859609i
$217$	−13.4750	+	7.77977i	−0.914740	+	0.528125i
$218$	−3.29472	−	0.580948i	−0.223147	−	0.0393468i
$219$	0.297154	+	0.697472i	0.0200798	+	0.0471308i
$220$	−4.44454	−	7.69817i	−0.299651	−	0.519010i
$221$	−0.804555	+	1.39353i	−0.0541202	+	0.0937390i
$222$	1.96555	−	16.1859i	0.131919	−	1.08632i
$223$	3.65141	−	10.0322i	0.244516	−	0.671803i	−0.755348	−	0.655324i	$-0.772532\pi$
$223$	3.65141	−	10.0322i	0.244516	−	0.671803i	0.999864	−	0.0164789i	$-0.00524564\pi$
$224$	22.2129	−	8.08482i	1.48416	−	0.540190i
$225$	−2.13950	−	7.38716i	−0.142633	−	0.492478i
$226$	−3.07433	−	17.4354i	−0.204502	−	1.15979i
$227$	−0.519141			−0.0344566			−0.0172283	−	0.999852i	$-0.505484\pi$
$227$	−0.519141			−0.0344566			−0.0172283	+	0.999852i	$0.505484\pi$
$228$	−35.1123	−	1.83918i	−2.32537	−	0.121803i
$229$	−3.84464			−0.254061			−0.127030	−	0.991899i	$-0.540545\pi$
$229$	−3.84464			−0.254061			−0.127030	+	0.991899i	$0.540545\pi$
$230$	−0.432705	−	2.45399i	−0.0285317	−	0.161811i
$231$	−6.06613	−	1.84579i	−0.399122	−	0.121444i
$232$	−7.60031	+	2.76629i	−0.498985	+	0.181616i
$233$	6.29055	−	17.2831i	0.412107	−	1.13226i	−0.543960	−	0.839111i	$-0.683076\pi$
$233$	6.29055	−	17.2831i	0.412107	−	1.13226i	0.956068	−	0.293145i	$-0.0947019\pi$
$234$	−1.08025	−	2.19999i	−0.0706184	−	0.143818i
$235$	−6.36565	+	11.0256i	−0.415249	+	0.719233i
$236$	6.28726	+	10.8899i	0.409266	+	0.708869i
$237$	−2.33058	+	0.992930i	−0.151388	+	0.0644978i
$238$	−38.6576	−	6.81637i	−2.50580	−	0.441840i
$239$	−14.2757	+	8.24205i	−0.923415	+	0.533134i	−0.884723	−	0.466117i	$-0.845653\pi$
$239$	−14.2757	+	8.24205i	−0.923415	+	0.533134i	−0.0386922	+	0.999251i	$0.512319\pi$
$240$	22.6084	−	1.21498i	1.45937	−	0.0784267i
$241$	−7.68280	+	9.15600i	−0.494893	+	0.589790i	−0.954455	−	0.298356i	$-0.903562\pi$
$241$	−7.68280	+	9.15600i	−0.494893	+	0.589790i	0.459562	+	0.888146i	$0.348006\pi$
$242$	−23.0445	−	8.38752i	−1.48136	−	0.539170i
$243$	15.5198	−	1.46176i	0.995594	−	0.0937722i
$244$	24.5950	−	20.6376i	1.57453	−	1.32119i
$245$	3.01677	−	0.531938i	0.192734	−	0.0339843i
$246$	0.577432	−	0.376081i	0.0368157	−	0.0239780i
$247$	0.957466	+	0.994070i	0.0609221	+	0.0632511i
$248$			35.6316i			2.26261i
$249$	13.8239	−	12.9254i	0.876056	−	0.819114i
$250$	−19.5801	−	23.3346i	−1.23835	−	1.47581i
$251$	−3.07435	−	8.44670i	−0.194051	−	0.533151i	0.804063	−	0.594545i	$-0.202668\pi$
$251$	−3.07435	−	8.44670i	−0.194051	−	0.533151i	−0.998114	+	0.0613939i	$0.980445\pi$
$252$	28.9752	−	30.1647i	1.82527	−	1.90020i
$253$	0.579589	+	0.486333i	0.0364385	+	0.0305755i
$254$	−6.96338	−	4.02031i	−0.436921	−	0.252257i
$255$	−12.2500	−	6.22119i	−0.767124	−	0.389586i
$256$	−4.14494	+	23.5071i	−0.259059	+	1.46919i
$257$	2.19345	−	12.4397i	0.136824	−	0.775965i	−0.836749	−	0.547587i	$-0.815547\pi$
$257$	2.19345	−	12.4397i	0.136824	−	0.775965i	0.973572	−	0.228378i	$-0.0733423\pi$
$258$	38.1230	+	19.3609i	2.37343	+	1.20535i
$259$	−9.45925	−	5.46130i	−0.587769	−	0.339349i
$260$	−1.76323	−	1.47952i	−0.109351	−	0.0917561i
$261$	−2.45181	+	2.55246i	−0.151763	+	0.157993i
$262$	−3.23544	−	8.88930i	−0.199886	−	0.549183i
$263$	0.255221	+	0.304161i	0.0157376	+	0.0187553i	0.773856	−	0.633362i	$-0.218325\pi$
$263$	0.255221	+	0.304161i	0.0157376	+	0.0187553i	−0.758118	+	0.652117i	$0.773881\pi$
$264$	−10.6064	+	9.91698i	−0.652777	+	0.610348i
$265$			4.78935i			0.294207i
$266$	−14.7990	+	30.2426i	−0.907387	+	1.85429i
$267$	−11.4123	+	7.43280i	−0.698421	+	0.454880i
$268$	−41.7625	+	7.36385i	−2.55105	+	0.449819i
$269$	−14.7929	+	12.4127i	−0.901936	+	0.756814i	−0.970568	−	0.240828i	$-0.922581\pi$
$269$	−14.7929	+	12.4127i	−0.901936	+	0.756814i	0.0686317	+	0.997642i	$0.478137\pi$
$270$	18.2623	−	10.2183i	1.11141	−	0.621869i
$271$	−0.628030	−	0.228584i	−0.0381501	−	0.0138855i	0.322875	−	0.946442i	$-0.395351\pi$
$271$	−0.628030	−	0.228584i	−0.0381501	−	0.0138855i	−0.361025	+	0.932556i	$0.617573\pi$
$272$	−27.3559	+	32.6015i	−1.65870	+	1.97676i
$273$	−1.63950	+	0.0881070i	−0.0992269	+	0.00533248i
$274$	−35.3119	+	20.3873i	−2.13327	+	1.23164i
$275$	3.08718	+	0.544354i	0.186164	+	0.0328258i
$276$	−4.59157	+	1.95621i	−0.276380	+	0.117750i
$277$	9.43326	+	16.3389i	0.566790	+	0.981709i	0.996881	+	0.0789232i	$0.0251482\pi$
$277$	9.43326	+	16.3389i	0.566790	+	0.981709i	−0.430091	+	0.902786i	$0.641518\pi$
$278$	9.42557	−	16.3256i	0.565308	−	0.979143i
$279$	6.87232	+	13.9958i	0.411435	+	0.837907i
$280$	10.9571	−	30.1045i	0.654813	−	1.79909i
$281$	12.1777	−	4.43233i	0.726463	−	0.264411i	0.0477960	−	0.998857i	$-0.484780\pi$
$281$	12.1777	−	4.43233i	0.726463	−	0.264411i	0.678667	+	0.734446i	$0.262558\pi$
$282$	34.8717	+	10.6107i	2.07658	+	0.631858i
$283$	−2.29514	−	13.0164i	−0.136432	−	0.773742i	−0.973852	−	0.227183i	$-0.927048\pi$
$283$	−2.29514	−	13.0164i	−0.136432	−	0.773742i	0.837420	−	0.546559i	$-0.184063\pi$
$284$	64.1780			3.80827
$285$	−8.03681	+	8.61890i	−0.476059	+	0.510540i
$286$	0.999006			0.0590724
$287$	−0.0801617	−	0.454619i	−0.00473179	−	0.0268353i
$288$	−6.58973	−	22.7527i	−0.388304	−	1.34072i
$289$	8.29328	−	3.01851i	0.487840	−	0.177559i
$290$	−1.62503	+	4.46474i	−0.0954253	+	0.262179i
$291$	−3.87764	+	31.9316i	−0.227311	+	1.87186i
$292$	1.01923	−	1.76536i	0.0596460	−	0.103310i
$293$	2.19757	+	3.80631i	0.128384	+	0.222367i	0.923051	−	0.384679i	$-0.125688\pi$
$293$	2.19757	+	3.80631i	0.128384	+	0.222367i	−0.794667	+	0.607046i	$0.792354\pi$
$294$	−3.43759	−	8.06863i	−0.200484	−	0.470572i
$295$	4.15051	+	0.731847i	0.241652	+	0.0426098i
$296$	−21.6618	+	12.5065i	−1.25907	+	0.726924i
$297$	−2.25340	+	5.94098i	−0.130755	+	0.344730i
$298$	9.27072	−	11.0484i	0.537038	−	0.640017i
$299$	0.184098	+	0.0670063i	0.0106467	+	0.00387507i
$300$	−12.4229	+	16.5313i	−0.717234	+	0.954437i
$301$	21.9421	−	18.4116i	1.26472	−	1.06123i
$302$	48.6988	−	8.58691i	2.80230	−	0.494121i
$303$	−14.5969	−	22.4120i	−0.838570	−	1.28754i
$304$	20.3732	+	30.2894i	1.16848	+	1.73722i
$305$		−	10.7610i		−	0.616171i
$306$	−9.41475	+	38.1926i	−0.538205	+	2.18333i
$307$	15.1110	+	18.0086i	0.862431	+	1.02781i	0.999307	+	0.0372172i	$0.0118493\pi$
$307$	15.1110	+	18.0086i	0.862431	+	1.02781i	−0.136876	+	0.990588i	$0.543706\pi$
$308$	5.83106	+	16.0207i	0.332256	+	0.912865i
$309$	−2.90692	−	12.5153i	−0.165369	−	0.711973i
$310$	16.0345	+	13.4545i	0.910696	+	0.764165i
$311$	−8.52818	−	4.92375i	−0.483589	−	0.279200i	0.238322	−	0.971186i	$-0.423403\pi$
$311$	−8.52818	−	4.92375i	−0.483589	−	0.279200i	−0.721911	+	0.691986i	$0.756736\pi$
$312$	−1.70250	+	3.35236i	−0.0963853	+	0.189790i
$313$	−1.00653	+	5.70833i	−0.0568926	+	0.322654i	−0.999950	−	0.00997537i	$-0.996825\pi$
$313$	−1.00653	+	5.70833i	−0.0568926	+	0.322654i	0.943058	+	0.332629i	$0.107936\pi$
$314$	6.44824	−	36.5698i	0.363895	−	2.06375i
$315$	−1.50241	−	13.9381i	−0.0846514	−	0.785323i
$316$	5.89890	+	3.40573i	0.331839	+	0.191587i
$317$	−4.09664	−	3.43749i	−0.230090	−	0.193069i	0.520452	−	0.853891i	$-0.325763\pi$
$317$	−4.09664	−	3.43749i	−0.230090	−	0.193069i	−0.750543	+	0.660822i	$0.770208\pi$
$318$	13.3566	−	3.10230i	0.748998	−	0.173968i
$319$	−0.493409	−	1.35563i	−0.0276256	−	0.0759007i
$320$	−3.63565	−	4.33280i	−0.203239	−	0.242211i
$321$	−16.1358	−	17.2575i	−0.900614	−	0.963221i
$322$			4.77926i			0.266338i
$323$	−1.51646	−	22.0994i	−0.0843779	−	1.22965i
$324$	−28.2111	−	30.9987i	−1.56729	−	1.72215i
$325$	0.799392	−	0.140954i	0.0443423	−	0.00781875i
$326$	3.76256	−	3.15716i	0.208389	−	0.174859i
$327$	1.79543	+	1.34921i	0.0992873	+	0.0746117i
$328$	−0.993393	−	0.361565i	−0.0548509	−	0.0199641i
$329$	15.6957	−	18.7054i	0.865330	−	1.03126i
$330$	0.457738	+	8.51760i	0.0251976	+	0.468878i
$331$	−4.46270	+	2.57654i	−0.245292	+	0.141620i	−0.617607	−	0.786487i	$-0.711898\pi$
$331$	−4.46270	+	2.57654i	−0.245292	+	0.141620i	0.372314	+	0.928107i	$0.378564\pi$
$332$	−50.1130	−	8.83628i	−2.75031	−	0.484954i
$333$	−6.09646	+	9.09039i	−0.334084	+	0.498150i
$334$	−17.0355	−	29.5064i	−0.932144	−	1.61452i
$335$	−7.10662	+	12.3090i	−0.388276	+	0.672514i
$336$	−43.1078	−	5.23484i	−2.35173	−	0.285584i
$337$	10.8959	−	29.9364i	0.593540	−	1.63074i	−0.170344	−	0.985385i	$-0.554488\pi$
$337$	10.8959	−	29.9364i	0.593540	−	1.63074i	0.763884	−	0.645353i	$-0.223290\pi$
$338$	−31.2759	+	11.3835i	−1.70119	+	0.619181i
$339$	−3.45972	+	11.3703i	−0.187906	+	0.617548i
$340$	6.41487	+	36.3805i	0.347895	+	1.97301i
$341$	−6.35543			−0.344166
$342$	29.2423	+	16.8302i	1.58124	+	0.910073i
$343$	15.0809			0.814294
$344$	−11.3902	−	64.5973i	−0.614121	−	3.48285i
$345$	−0.486948	+	1.60034i	−0.0262164	+	0.0861592i
$346$	−33.2178	+	12.0903i	−1.78580	+	0.649979i
$347$	−4.16813	+	11.4518i	−0.223757	+	0.614767i	−0.999875	−	0.0158208i	$-0.994964\pi$
$347$	−4.16813	+	11.4518i	−0.223757	+	0.614767i	0.776118	+	0.630588i	$0.217186\pi$
$348$	9.44693	+	1.14720i	0.506409	+	0.0614963i
$349$	7.60525	−	13.1727i	0.407100	−	0.705117i	−0.587464	−	0.809250i	$-0.699874\pi$
$349$	7.60525	−	13.1727i	0.407100	−	0.705117i	0.994563	+	0.104133i	$0.0332069\pi$
$350$	9.90092	+	17.1489i	0.529227	+	0.916647i
$351$	−0.0221566	+	1.64514i	−0.00118263	+	0.0878112i
$352$	9.50864	+	1.67663i	0.506812	+	0.0893647i
$353$	−11.6828	+	6.74506i	−0.621812	+	0.359003i	−0.777574	−	0.628791i	$-0.783550\pi$
$353$	−11.6828	+	6.74506i	−0.621812	+	0.359003i	0.155762	+	0.987795i	$0.450217\pi$
$354$	−0.647517	−	12.0490i	−0.0344152	−	0.640398i
$355$	13.8265	−	16.4778i	0.733835	−	0.874550i
$356$	34.4111	+	12.5246i	1.82379	+	0.663804i
$357$	21.0661	+	15.8306i	1.11493	+	0.837843i
$358$	−37.8299	+	31.7430i	−1.99937	+	1.67767i
$359$	17.2391	−	3.03973i	0.909847	−	0.160431i	0.300913	−	0.953652i	$-0.402709\pi$
$359$	17.2391	−	3.03973i	0.909847	−	0.160431i	0.608934	+	0.793221i	$0.291597\pi$
$360$	−29.3625	−	12.9796i	−1.54754	−	0.684087i
$361$	−18.5745	−	3.99866i	−0.977603	−	0.210456i
$362$			15.8557i			0.833355i
$363$	11.2435	+	12.0251i	0.590129	+	0.631153i
$364$	2.83766	+	3.38180i	0.148734	+	0.177254i
$365$	−0.233675	−	0.642018i	−0.0122311	−	0.0336047i
$366$	−30.0102	+	6.97042i	−1.56866	+	0.364350i
$367$	−0.400474	−	0.336037i	−0.0209046	−	0.0175410i	0.632275	−	0.774744i	$-0.282121\pi$
$367$	−0.400474	−	0.336037i	−0.0209046	−	0.0175410i	−0.653180	+	0.757203i	$0.726566\pi$
$368$	4.48738	+	2.59079i	0.233921	+	0.135054i
$369$	−0.459932	+	0.0495770i	−0.0239431	+	0.00258087i
$370$	−2.55153	+	14.4704i	−0.132648	+	0.752281i
$371$	1.59509	−	9.04622i	0.0828131	−	0.469656i
$372$	18.9833	−	37.3795i	0.984238	−	1.93804i
$373$	2.06421	+	1.19177i	0.106881	+	0.0617078i	0.552488	−	0.833521i	$-0.313679\pi$
$373$	2.06421	+	1.19177i	0.106881	+	0.0617078i	−0.445607	+	0.895229i	$0.647012\pi$
$374$	−12.2825	−	10.3062i	−0.635111	−	0.532921i
$375$	4.62641	+	19.9184i	0.238907	+	1.02858i
$376$	−19.1251	−	52.5456i	−0.986299	−	2.70983i
$377$	−0.240116	−	0.286159i	−0.0123666	−	0.0147379i
$378$	−37.8975	+	13.2184i	−1.94924	+	0.679879i
$379$			18.6924i			0.960166i	0.877223	+	0.480083i	$0.159393\pi$
$379$			18.6924i			0.960166i	−0.877223	+	0.480083i	$0.840607\pi$
$380$	31.5083	+	3.35310i	1.61634	+	0.172010i
$381$	2.94580	+	4.52296i	0.150918	+	0.231718i
$382$	67.0470	−	11.8222i	3.43042	−	0.604876i
$383$	25.4328	−	21.3407i	1.29956	−	1.09046i	0.309334	−	0.950953i	$-0.399894\pi$
$383$	25.4328	−	21.3407i	1.29956	−	1.09046i	0.990222	−	0.139503i	$-0.0445506\pi$
$384$	6.70366	−	8.92069i	0.342095	−	0.455232i
$385$	5.36958	+	1.95437i	0.273659	+	0.0996038i
$386$	12.9352	−	15.4156i	0.658386	−	0.784634i
$387$	−16.9330	−	23.1764i	−0.860750	−	1.17812i
$388$	74.9007	−	43.2440i	3.80251	−	2.19538i
$389$	−20.5469	−	3.62298i	−1.04177	−	0.183692i	−0.373515	−	0.927624i	$-0.621847\pi$
$389$	−20.5469	−	3.62298i	−1.04177	−	0.183692i	−0.668255	+	0.743932i	$0.732959\pi$
$390$	0.865716	+	2.03199i	0.0438373	+	0.102894i
$391$	−1.57216	−	2.72306i	−0.0795076	−	0.137711i
$392$	−6.72727	+	11.6520i	−0.339779	+	0.588514i
$393$	−0.765540	+	6.30406i	−0.0386164	+	0.317998i
$394$	−21.3442	+	58.6426i	−1.07530	+	2.95437i
$395$	2.14528	−	0.780820i	0.107941	−	0.0392873i
$396$	16.4101	−	4.75275i	0.824638	−	0.238835i
$397$	−4.74235	−	26.8952i	−0.238012	−	1.34983i	−0.836177	−	0.548460i	$-0.815214\pi$
$397$	−4.74235	−	26.8952i	−0.238012	−	1.34983i	0.598165	−	0.801373i	$-0.295897\pi$
$398$	−10.5732			−0.529986
$399$	18.0506	−	13.6029i	0.903661	−	0.680997i
$400$	21.4688			1.07344
$401$	3.70169	+	20.9933i	0.184853	+	1.04836i	0.926144	+	0.377171i	$0.123103\pi$
$401$	3.70169	+	20.9933i	0.184853	+	1.04836i	−0.741290	+	0.671185i	$0.765786\pi$
$402$	38.9308	+	11.8458i	1.94169	+	0.590815i
$403$	−1.54642	+	0.562852i	−0.0770328	+	0.0280377i
$404$	−24.5965	+	67.5783i	−1.22372	+	3.36214i
$405$	−14.0368	+	0.564885i	−0.697492	+	0.0280694i
$406$	4.55638	−	7.89189i	0.226129	−	0.391668i
$407$	−2.23072	−	3.86372i	−0.110573	−	0.191517i
$408$	55.5162	−	23.6523i	2.74846	−	1.17097i
$409$	−27.5154	−	4.85171i	−1.36055	−	0.239902i	−0.554714	−	0.832041i	$-0.687172\pi$
$409$	−27.5154	−	4.85171i	−1.36055	−	0.239902i	−0.805836	+	0.592139i	$0.798283\pi$
$410$	−0.537812	+	0.310506i	−0.0265607	+	0.0153348i
$411$	27.3326	−	1.46886i	1.34822	−	0.0724537i
$412$	−22.2063	+	26.4645i	−1.09403	+	1.30381i
$413$	−7.59583	−	2.76466i	−0.373766	−	0.136040i
$414$	4.77845	+	0.321383i	0.234848	+	0.0157951i
$415$	−13.0651	+	10.9629i	−0.641339	+	0.538147i
$416$	2.46216	−	0.434145i	0.120717	−	0.0212857i
$417$	−10.6040	+	6.90639i	−0.519282	+	0.338208i
$418$	−11.4114	+	7.67550i	−0.558149	+	0.375421i
$419$			18.7147i			0.914272i	0.889397	+	0.457136i	$0.151125\pi$
$419$			18.7147i			0.914272i	−0.889397	+	0.457136i	$0.848875\pi$
$420$	−27.5332	+	25.7437i	−1.34348	+	1.25616i
$421$	7.28959	+	8.68740i	0.355273	+	0.423398i	0.913848	−	0.406056i	$-0.133096\pi$
$421$	7.28959	+	8.68740i	0.355273	+	0.423398i	−0.558575	+	0.829454i	$0.688652\pi$
$422$	8.80910	+	24.2028i	0.428820	+	1.17817i
$423$	−17.6467	−	16.9508i	−0.858013	−	0.824178i
$424$	−16.1142	−	13.5214i	−0.782574	−	0.656657i
$425$	−11.2824	−	6.51391i	−0.547278	−	0.315971i
$426$	−54.9095	−	27.8859i	−2.66037	−	1.35108i
$427$	−3.58394	+	20.3255i	−0.173439	+	0.983622i
$428$	−11.0310	+	62.5602i	−0.533206	+	3.02396i
$429$	−0.597943	−	0.303667i	−0.0288690	−	0.0146612i
$430$	−33.3702	−	19.2663i	−1.60925	−	0.929102i
$431$	−0.337025	−	0.282798i	−0.0162339	−	0.0136219i	0.634635	−	0.772812i	$-0.281151\pi$
$431$	−0.337025	−	0.282798i	−0.0162339	−	0.0136219i	−0.650868	+	0.759190i	$0.725595\pi$
$432$	−8.13276	+	42.7485i	−0.391287	+	2.05674i
$433$	11.3377	+	31.1501i	0.544856	+	1.49698i	0.840570	+	0.541704i	$0.182220\pi$
$433$	11.3377	+	31.1501i	0.544856	+	1.49698i	−0.295713	+	0.955277i	$0.595557\pi$
$434$	−25.8052	−	30.7534i	−1.23869	−	1.47621i
$435$	2.32979	−	2.17836i	0.111705	−	0.104444i
$436$		−	6.03867i		−	0.289200i
$437$	−2.61773	+	0.649056i	−0.125223	+	0.0310486i
$438$	−1.63910	+	1.06754i	−0.0783192	+	0.0510092i
$439$	5.42779	−	0.957066i	0.259054	−	0.0456783i	−0.0426125	−	0.999092i	$-0.513568\pi$
$439$	5.42779	−	0.957066i	0.259054	−	0.0456783i	0.301667	+	0.953413i	$0.402457\pi$
$440$	10.0241	−	8.41126i	0.477882	−	0.400991i
$441$	−0.395087	+	5.87430i	−0.0188137	+	0.279729i
$442$	−3.90135	−	1.41997i	−0.185568	−	0.0675413i
$443$	4.10597	−	4.89330i	0.195080	−	0.232488i	−0.659633	−	0.751588i	$-0.729288\pi$
$443$	4.10597	−	4.89330i	0.195080	−	0.232488i	0.854714	+	0.519100i	$0.173733\pi$
$444$	29.3875	−	1.57929i	1.39467	−	0.0749499i
$445$	10.6292	−	6.13680i	0.503875	−	0.290912i
$446$	27.1271	+	4.78324i	1.28450	+	0.226493i
$447$	−8.90726	+	3.79488i	−0.421299	+	0.179492i
$448$	5.42405	+	9.39473i	0.256262	+	0.443859i
$449$	−11.0074	+	19.0653i	−0.519470	+	0.899749i	0.480274	+	0.877119i	$0.340537\pi$
$449$	−11.0074	+	19.0653i	−0.519470	+	0.899749i	−0.999744	+	0.0226300i	$0.992796\pi$
$450$	17.8118	−	8.74605i	0.839655	−	0.412293i
$451$	0.0644906	−	0.177187i	0.00303675	−	0.00834339i
$452$	30.0290	−	10.9297i	1.41244	−	0.514088i
$453$	−31.7583	−	9.66335i	−1.49213	−	0.454024i
$454$	−0.232594	−	1.31911i	−0.0109162	−	0.0619087i
$455$	1.47963			0.0693660
$456$	−6.30935	−	51.3737i	−0.295462	−	2.40579i
$457$	6.66744			0.311890			0.155945	−	0.987766i	$-0.450158\pi$
$457$	6.66744			0.311890			0.155945	+	0.987766i	$0.450158\pi$
$458$	−1.72254	−	9.76899i	−0.0804889	−	0.456475i
$459$	17.2445	−	19.9979i	0.804903	−	0.933424i
$460$	4.22651	−	1.53832i	0.197062	−	0.0717247i
$461$	5.50703	−	15.1304i	0.256488	−	0.704695i	−0.742890	−	0.669414i	$-0.766545\pi$
$461$	5.50703	−	15.1304i	0.256488	−	0.704695i	0.999377	−	0.0352807i	$-0.0112325\pi$
$462$	1.97220	−	16.2407i	0.0917551	−	0.755584i
$463$	−19.1725	+	33.2078i	−0.891023	+	1.54330i	−0.0523713	+	0.998628i	$0.516678\pi$
$463$	−19.1725	+	33.2078i	−0.891023	+	1.54330i	−0.838651	+	0.544669i	$0.816655\pi$
$464$	−4.93994	−	8.55622i	−0.229331	−	0.397212i
$465$	−5.50748	−	12.9270i	−0.255403	−	0.599477i
$466$	46.7338	+	8.24043i	2.16490	+	0.381731i
$467$	−18.0289	+	10.4090i	−0.834277	+	0.481670i	−0.855315	−	0.518109i	$-0.826636\pi$
$467$	−18.0289	+	10.4090i	−0.834277	+	0.481670i	0.0210381	+	0.999779i	$0.493303\pi$
$468$	3.57204	−	2.60977i	0.165118	−	0.120637i
$469$	17.5227	−	20.8827i	0.809121	−	0.964273i
$470$	−30.8675	−	11.2349i	−1.42381	−	0.518225i
$471$	−14.9756	+	19.9284i	−0.690040	+	0.918250i
$472$	−14.1802	+	11.8986i	−0.652696	+	0.547677i
$473$	11.5219	−	2.03162i	0.529777	−	0.0934140i
$474$	−3.56716	−	5.47700i	−0.163845	−	0.251567i
$475$	−8.04828	+	7.75193i	−0.369280	+	0.355683i
$476$		−	70.8528i		−	3.24753i
$477$	−8.93741	−	2.20314i	−0.409216	−	0.100875i
$478$	−27.3386	−	32.5809i	−1.25044	−	1.49021i
$479$	2.82297	+	7.75604i	0.128985	+	0.354383i	0.987328	−	0.158693i	$-0.0507281\pi$
$479$	2.82297	+	7.75604i	0.128985	+	0.354383i	−0.858343	+	0.513076i	$0.828506\pi$
$480$	4.82970	+	20.7936i	0.220445	+	0.949095i
$481$	−0.884965	−	0.742574i	−0.0403509	−	0.0338584i
$482$	−26.7070	−	15.4193i	−1.21647	−	0.702331i
$483$	1.45275	−	2.86057i	0.0661024	−	0.130161i
$484$	7.68645	−	43.5920i	0.349384	−	1.98146i
$485$	5.03366	−	28.5473i	0.228567	−	1.29627i
$486$	10.6677	+	38.7799i	0.483896	+	1.75909i
$487$	−22.5542	−	13.0217i	−1.02203	−	0.590069i	−0.107338	−	0.994223i	$-0.534233\pi$
$487$	−22.5542	−	13.0217i	−1.02203	−	0.590069i	−0.914691	+	0.404154i	$0.867566\pi$
$488$	36.2062	+	30.3806i	1.63898	+	1.37527i
$489$	−3.21172	+	0.745979i	−0.145239	+	0.0337344i
$490$	2.70325	+	7.42711i	0.122120	+	0.335523i
$491$	24.6341	+	29.3577i	1.11172	+	1.32490i	0.940550	+	0.339654i	$0.110310\pi$
$491$	24.6341	+	29.3577i	1.11172	+	1.32490i	0.171169	+	0.985242i	$0.445245\pi$
$492$	0.849494	+	0.908548i	0.0382982	+	0.0409605i
$493$			5.99538i			0.270018i
$494$	−2.09689	+	2.87824i	−0.0943437	+	0.129498i
$495$	2.31511	−	5.23725i	0.104057	−	0.235397i
$496$	−42.8640	+	7.55807i	−1.92465	+	0.339368i
$497$	−31.6037	+	26.5187i	−1.41762	+	1.18953i
$498$	39.0363	+	29.3347i	1.74926	+	1.31452i
$499$	−22.9331	−	8.34698i	−1.02663	−	0.373662i	−0.226832	−	0.973934i	$-0.572837\pi$
$499$	−22.9331	−	8.34698i	−1.02663	−	0.373662i	−0.799796	+	0.600272i	$0.795059\pi$
$500$	35.3418	−	42.1187i	1.58053	−	1.88360i
$501$	1.22737	+	22.8390i	0.0548351	+	1.02037i
$502$	20.0851	−	11.5962i	0.896443	−	0.517562i
$503$	39.5690	+	6.97708i	1.76429	+	0.311093i	0.959342	−	0.282246i	$-0.0910794\pi$
$503$	39.5690	+	6.97708i	1.76429	+	0.311093i	0.804953	+	0.593339i	$0.202191\pi$
$504$	51.1377	+	34.2954i	2.27785	+	1.52764i
$505$	12.0517	+	20.8742i	0.536295	+	0.928891i
$506$	−0.976067	+	1.69060i	−0.0433915	+	0.0751562i
$507$	22.1801	+	2.69346i	0.985051	+	0.119621i
$508$	4.96381	−	13.6380i	0.220233	−	0.605086i
$509$	−33.9250	+	12.3477i	−1.50370	+	0.547302i	−0.957016	−	0.290036i	$-0.906333\pi$
$509$	−33.9250	+	12.3477i	−1.50370	+	0.547302i	−0.546685	+	0.837338i	$0.684111\pi$
$510$	10.3192	−	33.9138i	0.456943	−	1.50173i
$511$	0.227547	+	1.29048i	0.0100661	+	0.0570876i
$512$	−48.7022			−2.15236
$513$	−12.3868	−	18.9623i	−0.546889	−	0.837205i
$514$	32.5912			1.43754
$515$	2.01066	+	11.4030i	0.0886001	+	0.502476i
$516$	−22.4662	+	73.8344i	−0.989020	+	3.25038i
$517$	9.37231	−	3.41124i	0.412194	−	0.150026i
$518$	9.63875	−	26.4823i	0.423502	−	1.16356i
$519$	23.5572	+	2.86070i	1.03405	+	0.125571i
$520$	1.69418	−	2.93441i	0.0742949	−	0.128683i
$521$	8.36859	+	14.4948i	0.366635	+	0.635030i	0.989037	−	0.147668i	$-0.0471766\pi$
$521$	8.36859	+	14.4948i	0.366635	+	0.635030i	−0.622402	+	0.782697i	$0.713843\pi$
$522$	−7.58415	−	5.08630i	−0.331949	−	0.222621i
$523$	−3.12791	−	0.551534i	−0.136774	−	0.0241169i	0.104842	−	0.994489i	$-0.466566\pi$
$523$	−3.12791	−	0.551534i	−0.136774	−	0.0241169i	−0.241616	+	0.970372i	$0.577677\pi$
$524$	14.7872	−	8.53740i	0.645982	−	0.372958i
$525$	−0.713340	−	13.2739i	−0.0311327	−	0.579318i
$526$	−0.658506	+	0.784777i	−0.0287122	+	0.0342179i
$527$	24.8194	+	9.03354i	1.08115	+	0.393507i
$528$	−14.1797	−	10.6556i	−0.617092	−	0.463728i
$529$	17.3258	−	14.5380i	0.753294	−	0.632089i
$530$	−12.1694	+	2.14580i	−0.528607	+	0.0932077i
$531$	−3.27497	+	7.40862i	−0.142122	+	0.321507i
$532$	−58.3967	−	16.8272i	−2.53182	−	0.729553i
$533$		−	0.0488250i		−	0.00211485i
$534$	−23.9994	−	25.6678i	−1.03856	−	1.11075i
$535$	13.6859	+	16.3102i	0.591692	+	0.705151i
$536$	−21.3512	−	58.6620i	−0.922233	−	2.53381i
$537$	32.2915	−	7.50029i	1.39348	−	0.323662i
$538$	−38.1676	−	32.0264i	−1.64552	−	1.38076i
$539$	−2.07831	−	1.19991i	−0.0895190	−	0.0516838i
$540$	23.8878	+	29.2597i	1.02797	+	1.25914i
$541$	0.328535	−	1.86322i	0.0141248	−	0.0801059i	−0.976931	−	0.213557i	$-0.931495\pi$
$541$	0.328535	−	1.86322i	0.0141248	−	0.0801059i	0.991055	+	0.133452i	$0.0426061\pi$
$542$	0.299439	−	1.69820i	0.0128620	−	0.0729440i
$543$	4.81964	−	9.49022i	0.206830	−	0.407264i
$544$	−34.7503	−	20.0631i	−1.48991	−	0.860198i
$545$	−1.55044	−	1.30097i	−0.0664134	−	0.0557274i
$546$	−0.958429	−	4.12639i	−0.0410170	−	0.176593i
$547$	−9.41432	−	25.8656i	−0.402527	−	1.10593i	−0.961033	−	0.276434i	$-0.910847\pi$
$547$	−9.41432	−	25.8656i	−0.402527	−	1.10593i	0.558506	−	0.829501i	$-0.311375\pi$
$548$	−47.3077	−	56.3791i	−2.02089	−	2.40840i
$549$	20.0811	+	4.95013i	0.857039	+	0.211266i
$550$			8.08824i			0.344884i
$551$	4.94138	+	1.42388i	0.210510	+	0.0606592i
$552$	−4.00971	−	6.15649i	−0.170665	−	0.262038i
$553$	−4.31211	+	0.760341i	−0.183370	+	0.0323330i
$554$	−37.2897	+	31.2898i	−1.58429	+	1.32938i
$555$	5.92575	−	7.88552i	0.251534	−	0.334722i
$556$	31.9740	+	11.6376i	1.35600	+	0.493544i
$557$	−4.41474	+	5.26128i	−0.187058	+	0.222928i	−0.851421	−	0.524483i	$-0.824259\pi$
$557$	−4.41474	+	5.26128i	−0.187058	+	0.222928i	0.664363	+	0.747410i	$0.268703\pi$
$558$	−32.4835	+	23.7328i	−1.37514	+	1.00469i
$559$	2.62362	−	1.51475i	0.110967	−	0.0640669i
$560$	38.5391	+	6.79549i	1.62858	+	0.287162i
$561$	4.21875	+	9.90215i	0.178116	+	0.418069i
$562$	16.7184	+	28.9571i	0.705222	+	1.22148i
$563$	8.11401	−	14.0539i	0.341965	−	0.592301i	−0.642833	−	0.766007i	$-0.722241\pi$
$563$	8.11401	−	14.0539i	0.341965	−	0.592301i	0.984798	+	0.173706i	$0.0555742\pi$
$564$	−7.93128	+	65.3125i	−0.333967	+	2.75015i
$565$	3.66324	−	10.0647i	0.154114	−	0.423424i
$566$	32.0455	−	11.6636i	1.34697	−	0.490258i
$567$	26.7011	+	3.60798i	1.12134	+	0.151521i
$568$	16.4056	+	93.0411i	0.688366	+	3.90392i
$569$	23.4699			0.983911			0.491956	−	0.870620i	$-0.336282\pi$
$569$	23.4699			0.983911			0.491956	+	0.870620i	$0.336282\pi$
$570$	−25.5009	−	16.5595i	−1.06812	−	0.693600i
$571$	−12.3766			−0.517944			−0.258972	−	0.965885i	$-0.583384\pi$
$571$	−12.3766			−0.517944			−0.258972	+	0.965885i	$0.583384\pi$
$572$	0.313121	+	1.77580i	0.0130922	+	0.0742498i
$573$	−43.7238	−	13.3042i	−1.82659	−	0.555791i
$574$	1.11925	−	0.407372i	0.0467164	−	0.0170034i
$575$	−0.542503	+	1.49051i	−0.0226239	+	0.0621587i
$576$	9.75787	−	4.79137i	0.406578	−	0.199641i
$577$	−7.38649	+	12.7938i	−0.307504	+	0.532612i	−0.977816	−	0.209467i	$-0.932827\pi$
$577$	−7.38649	+	12.7938i	−0.307504	+	0.532612i	0.670312	+	0.742079i	$0.266160\pi$
$578$	11.3855	+	19.7203i	0.473576	+	0.820258i
$579$	−12.4281	+	5.29492i	−0.516494	+	0.220049i
$580$	−8.44571	−	1.48921i	−0.350689	−	0.0618360i
$581$	28.3288	−	16.3556i	1.17528	−	0.678546i
$582$	−82.8735	+	4.45364i	−3.43522	+	0.184610i
$583$	2.41175	−	2.87421i	0.0998843	−	0.119037i
$584$	2.81984	+	1.02634i	0.116686	+	0.0424702i
$585$	0.0994980	−	1.47937i	0.00411374	−	0.0611646i
$586$	−8.68702	+	7.28927i	−0.358857	+	0.301117i
$587$	−16.0113	+	2.82322i	−0.660857	+	0.116527i	−0.494010	−	0.869456i	$-0.664470\pi$
$587$	−16.0113	+	2.82322i	−0.660857	+	0.116527i	−0.166847	+	0.985983i	$0.553358\pi$
$588$	13.2651	−	8.63951i	0.547042	−	0.356287i
$589$	13.3399	−	18.3107i	0.549662	−	0.754479i
$590$			10.8741i			0.447679i
$591$	30.6008	−	28.6119i	1.25875	−	1.17693i
$592$	−19.6398	−	23.4058i	−0.807192	−	0.961974i
$593$	−1.06316	−	2.92101i	−0.0436587	−	0.119951i	0.915947	−	0.401299i	$-0.131441\pi$
$593$	−1.06316	−	2.92101i	−0.0436587	−	0.119951i	−0.959606	+	0.281347i	$0.909219\pi$
$594$	−16.1053	−	3.06397i	−0.660808	−	0.125716i
$595$	−18.1915	−	15.2645i	−0.745781	−	0.625784i
$596$	22.5450	+	13.0164i	0.923480	+	0.533171i
$597$	6.32846	+	3.21393i	0.259007	+	0.131537i
$598$	−0.0877763	+	0.497804i	−0.00358944	+	0.0203567i
$599$	−1.76308	+	9.99893i	−0.0720375	+	0.408545i	0.927371	+	0.374144i	$0.122063\pi$
$599$	−1.76308	+	9.99893i	−0.0720375	+	0.408545i	−0.999408	+	0.0344010i	$0.989048\pi$
$600$	−27.1417	−	13.7840i	−1.10805	−	0.562728i
$601$	8.56591	+	4.94553i	0.349411	+	0.201732i	0.664426	−	0.747354i	$-0.268676\pi$
$601$	8.56591	+	4.94553i	0.349411	+	0.201732i	−0.315015	+	0.949087i	$0.602010\pi$
$602$	56.6136	+	47.5045i	2.30740	+	1.93614i
$603$	−19.7008	−	18.9239i	−0.802280	−	0.770643i
$604$	30.5276	+	83.8739i	1.24215	+	3.41278i
$605$	−9.53634	−	11.3650i	−0.387707	−	0.462052i
$606$	50.4076	−	47.1313i	2.04767	−	1.91458i
$607$			16.5025i			0.669817i	0.942251	+	0.334908i	$0.108705\pi$
$607$			16.5025i			0.669817i	−0.942251	+	0.334908i	$0.891295\pi$
$608$	−24.7890	+	23.8762i	−1.00533	+	0.968309i
$609$	−5.12606	+	3.33860i	−0.207718	+	0.135287i
$610$	27.3430	−	4.82130i	1.10708	−	0.195209i
$611$	1.97839	−	1.66007i	0.0800371	−	0.0671591i
$612$	−70.8407	−	4.76452i	−2.86357	−	0.192594i
$613$	−13.2779	−	4.83276i	−0.536289	−	0.195193i	0.0596550	−	0.998219i	$-0.481000\pi$
$613$	−13.2779	−	4.83276i	−0.536289	−	0.195193i	−0.595944	+	0.803026i	$0.703222\pi$
$614$	−38.9885	+	46.4647i	−1.57345	+	1.87516i
$615$	0.416286	−	0.0223713i	0.0167863	−	0.000902098i
$616$	−21.7352	+	12.5488i	−0.875736	+	0.505606i
$617$	−10.3704	−	1.82858i	−0.417496	−	0.0736158i	−0.0390458	−	0.999237i	$-0.512432\pi$
$617$	−10.3704	−	1.82858i	−0.417496	−	0.0736158i	−0.378450	+	0.925622i	$0.623543\pi$
$618$	30.4983	−	12.9936i	1.22682	−	0.522681i
$619$	−7.21587	−	12.4983i	−0.290030	−	0.502347i	0.683786	−	0.729682i	$-0.260332\pi$
$619$	−7.21587	−	12.4983i	−0.290030	−	0.502347i	−0.973817	+	0.227335i	$0.926999\pi$
$620$	−18.8905	+	32.7194i	−0.758663	+	1.31404i
$621$	−2.76239	−	1.64486i	−0.110851	−	0.0660061i
$622$	8.69001	−	23.8756i	0.348438	−	0.957325i
$623$	−22.1206	+	8.05124i	−0.886243	+	0.322566i
$624$	−4.39393	−	1.33698i	−0.175898	−	0.0535220i
$625$	−0.974188	−	5.52490i	−0.0389675	−	0.220996i
$626$	−14.9555			−0.597742
$627$	9.16327	−	1.12537i	0.365946	−	0.0449428i
$628$	67.0263			2.67464
$629$	3.21963	+	18.2594i	0.128375	+	0.728051i
$630$	34.7428	−	10.0623i	1.38418	−	0.400893i
$631$	6.27530	−	2.28402i	0.249816	−	0.0909254i	−0.214077	−	0.976817i	$-0.568674\pi$
$631$	6.27530	−	2.28402i	0.249816	−	0.0909254i	0.463893	+	0.885891i	$0.346452\pi$
$632$	−3.42948	+	9.42243i	−0.136418	+	0.374804i
$633$	2.08433	−	17.1640i	0.0828446	−	0.682208i
$634$	6.89901	−	11.9494i	0.273995	−	0.474573i
$635$	−2.43216	−	4.21262i	−0.0965173	−	0.167173i
$636$	9.70093	+	22.7698i	0.384667	+	0.902881i
$637$	−0.611967	−	0.107906i	−0.0242470	−	0.00427540i
$638$	3.22351	−	1.86110i	0.127620	−	0.0736815i
$639$	24.3890	+	33.3816i	0.964812	+	1.32056i
$640$	−6.46396	+	7.70344i	−0.255510	+	0.304505i
$641$	−24.7334	−	9.00224i	−0.976912	−	0.355567i	−0.196273	−	0.980549i	$-0.562884\pi$
$641$	−24.7334	−	9.00224i	−0.976912	−	0.355567i	−0.780639	+	0.624982i	$0.785106\pi$
$642$	36.6209	−	48.7322i	1.44531	−	1.92331i
$643$	−3.88657	+	3.26122i	−0.153272	+	0.128610i	−0.716199	−	0.697896i	$-0.754120\pi$
$643$	−3.88657	+	3.26122i	−0.153272	+	0.128610i	0.562927	+	0.826506i	$0.309675\pi$
$644$	−8.49545	+	1.49798i	−0.334768	+	0.0590286i
$645$	14.1170	+	21.6751i	0.555855	+	0.853456i
$646$	55.4739	−	13.7546i	2.18259	−	0.541167i
$647$		−	15.3275i		−	0.602585i	−0.953532	−	0.301293i	$-0.902582\pi$
$647$		−	15.3275i		−	0.602585i	0.953532	−	0.301293i	$-0.0974181\pi$
$648$	37.7283	−	48.8227i	1.48211	−	1.91794i
$649$	−2.12229	−	2.52925i	−0.0833073	−	0.0992818i
$650$	0.716314	+	1.96806i	0.0280961	+	0.0771935i
$651$	6.09730	+	26.2511i	0.238972	+	1.02886i
$652$	6.79137	+	5.69864i	0.265971	+	0.223176i
$653$	6.35742	+	3.67046i	0.248785	+	0.143636i	0.619208	−	0.785227i	$-0.287454\pi$
$653$	6.35742	+	3.67046i	0.248785	+	0.143636i	−0.370423	+	0.928863i	$0.620787\pi$
$654$	−2.62386	+	5.16657i	−0.102601	+	0.202029i
$655$	0.993767	−	5.63593i	0.0388297	−	0.220214i
$656$	0.224239	−	1.27172i	0.00875506	−	0.0496524i
$657$	1.30556	−	0.140729i	0.0509349	−	0.00549037i
$658$	54.5615	+	31.5011i	2.12703	+	1.22804i
$659$	−17.2736	−	14.4942i	−0.672882	−	0.564615i	0.241035	−	0.970517i	$-0.422513\pi$
$659$	−17.2736	−	14.4942i	−0.672882	−	0.564615i	−0.913917	+	0.405901i	$0.866958\pi$
$660$	−14.9971	+	3.48335i	−0.583762	+	0.135589i
$661$	−4.78873	−	13.1569i	−0.186260	−	0.511746i	0.811055	−	0.584969i	$-0.198893\pi$
$661$	−4.78873	−	13.1569i	−0.186260	−	0.511746i	−0.997316	+	0.0732238i	$0.976671\pi$
$662$	−8.54630	−	10.1851i	−0.332161	−	0.395854i
$663$	1.90348	+	2.03580i	0.0739249	+	0.0790639i
$664$		−	74.9093i		−	2.90705i
$665$	−16.9014	+	11.3682i	−0.655408	+	0.440839i
$666$	−25.8296	−	11.4179i	−1.00088	−	0.442435i
$667$	0.718863	−	0.126755i	0.0278345	−	0.00490797i
$668$	47.1101	−	39.5301i	1.82274	−	1.52946i
$669$	−14.7826	−	11.1088i	−0.571530	−	0.429489i
$670$	−34.4605	−	12.5426i	−1.33133	−	0.484563i
$671$	−5.41884	+	6.45793i	−0.209192	+	0.249305i
$672$	−2.19712	−	40.8840i	−0.0847556	−	1.57713i
$673$	−29.2421	+	16.8829i	−1.12720	+	0.650789i	−0.943229	−	0.332143i	$-0.892228\pi$
$673$	−29.2421	+	16.8829i	−1.12720	+	0.650789i	−0.183970	+	0.982932i	$0.558895\pi$
$674$	80.9483	+	14.2734i	3.11801	+	0.549790i
$675$	−13.3196	−	0.179386i	−0.512670	−	0.00690458i
$676$	−30.0378	−	52.0270i	−1.15530	−	2.00104i
$677$	20.9506	−	36.2875i	0.805197	−	1.39464i	−0.110961	−	0.993825i	$-0.535393\pi$
$677$	20.9506	−	36.2875i	0.805197	−	1.39464i	0.916158	−	0.400817i	$-0.131274\pi$
$678$	−30.4413	−	3.69666i	−1.16909	−	0.141970i
$679$	−19.0154	+	52.2443i	−0.729743	+	2.00495i
$680$	−51.1023	+	18.5997i	−1.95968	+	0.713266i
$681$	−0.261751	+	0.860237i	−0.0100303	+	0.0329643i
$682$	−2.84747	−	16.1488i	−0.109035	−	0.618369i
$683$	−37.5667			−1.43745			−0.718725	−	0.695295i	$-0.755274\pi$
$683$	−37.5667			−1.43745			−0.718725	+	0.695295i	$0.755274\pi$
$684$	−20.7513	+	57.2552i	−0.793445	+	2.18921i
$685$	−24.6674			−0.942492
$686$	6.75681	+	38.3198i	0.257976	+	1.46305i
$687$	−1.93847	+	6.37071i	−0.0739573	+	0.243058i
$688$	75.2929	−	27.4044i	2.87051	−	1.04478i
$689$	0.332287	−	0.912951i	0.0126591	−	0.0347807i
$690$	−4.28453	−	0.520296i	−0.163109	−	0.0198073i
$691$	−2.67694	+	4.63659i	−0.101835	+	0.176384i	−0.912441	−	0.409209i	$-0.865805\pi$
$691$	−2.67694	+	4.63659i	−0.101835	+	0.176384i	0.810605	+	0.585593i	$0.199138\pi$
$692$	−31.9029	−	55.2574i	−1.21277	−	2.10057i
$693$	−6.11710	+	9.12117i	−0.232370	+	0.346485i
$694$	−30.9659	−	5.46013i	−1.17545	−	0.207264i
$695$	9.87645	−	5.70217i	0.374635	−	0.216296i
$696$	0.751761	+	13.9888i	0.0284954	+	0.530244i
$697$	−0.503702	+	0.600288i	−0.0190791	+	0.0227375i
$698$	36.8784	+	13.4226i	1.39587	+	0.508055i
$699$	−25.4671	−	19.1379i	−0.963256	−	0.723861i
$700$	−27.3800	+	22.9746i	−1.03487	+	0.868357i
$701$	23.4648	−	4.13747i	0.886251	−	0.156270i	0.288050	−	0.957616i	$-0.406993\pi$
$701$	23.4648	−	4.13747i	0.886251	−	0.156270i	0.598202	+	0.801345i	$0.295882\pi$
$702$	−4.19014	+	0.680785i	−0.158147	+	0.0256946i
$703$	15.8140	+	1.68292i	0.596437	+	0.0634726i
$704$			4.43100i			0.167000i
$705$	15.0603	+	16.1073i	0.567205	+	0.606635i
$706$	−22.3731	−	26.6632i	−0.842023	−	1.00348i
$707$	−15.8114	−	43.4415i	−0.594650	−	1.63379i
$708$	21.2150	−	4.92756i	0.797307	−	0.185189i
$709$	33.4374	+	28.0573i	1.25577	+	1.05371i	0.996120	+	0.0880094i	$0.0280505\pi$
$709$	33.4374	+	28.0573i	1.25577	+	1.05371i	0.259647	+	0.965704i	$0.416394\pi$
$710$	48.0639	+	27.7497i	1.80381	+	1.04143i
$711$	0.470242	+	4.36251i	0.0176355	+	0.163607i
$712$	−9.36095	+	53.0886i	−0.350817	+	1.98958i
$713$	0.558412	−	3.16691i	0.0209127	−	0.118602i
$714$	−30.7862	+	60.6203i	−1.15214	+	2.26866i
$715$	0.523397	+	0.302183i	0.0195739	+	0.0113010i
$716$	−68.2824	−	57.2957i	−2.55183	−	2.14124i
$717$	6.45961	+	27.8110i	0.241238	+	1.03862i
$718$	15.4475	+	42.4417i	0.576497	+	1.58391i
$719$	9.49121	+	11.3112i	0.353962	+	0.421836i	0.913417	−	0.407025i	$-0.133434\pi$
$719$	9.49121	+	11.3112i	0.353962	+	0.421836i	−0.559455	+	0.828861i	$0.688989\pi$
$720$	9.38591	−	38.0756i	0.349792	−	1.41899i
$721$		−	22.2079i		−	0.827065i
$722$	1.83833	−	48.9882i	0.0684154	−	1.82315i
$723$	11.2982	+	17.3472i	0.420184	+	0.645148i
$724$	−28.1845	+	4.96968i	−1.04747	+	0.184697i
$725$	2.31683	−	1.94405i	0.0860447	−	0.0722001i
$726$	−25.5175	+	33.9567i	−0.947044	+	1.26025i
$727$	−29.6234	−	10.7820i	−1.09867	−	0.399884i	−0.271845	−	0.962341i	$-0.587634\pi$
$727$	−29.6234	−	10.7820i	−1.09867	−	0.399884i	−0.826826	+	0.562457i	$0.809856\pi$
$728$	−4.17732	+	4.97834i	−0.154822	+	0.184509i
$729$	5.40289	−	26.4539i	0.200107	−	0.979774i
$730$	1.52663	−	0.881402i	0.0565033	−	0.0326222i
$731$	−47.8834	−	8.44313i	−1.77103	−	0.312280i
$732$	−21.7966	−	51.1604i	−0.805625	−	1.89094i
$733$	0.100159	+	0.173480i	0.00369944	+	0.00640762i	0.867869	−	0.496793i	$-0.165489\pi$
$733$	0.100159	+	0.173480i	0.00369944	+	0.00640762i	−0.864170	+	0.503200i	$0.832156\pi$
$734$	0.674424	−	1.16814i	0.0248934	−	0.0431167i
$735$	0.639617	−	5.26711i	0.0235926	−	0.194280i
$736$	−1.67093	+	4.59084i	−0.0615912	+	0.169221i
$737$	10.4633	−	3.80831i	0.385419	−	0.140281i
$738$	−0.332039	−	1.14645i	−0.0122225	−	0.0422014i
$739$	2.98492	+	16.9283i	0.109802	+	0.622719i	0.989193	+	0.146619i	$0.0468390\pi$
$739$	2.98492	+	16.9283i	0.109802	+	0.622719i	−0.879391	+	0.476100i	$0.842050\pi$
$740$	−26.5219			−0.974963
$741$	2.12997	−	1.08535i	0.0782464	−	0.0398713i
$742$	23.7006			0.870075
$743$	−7.10350	−	40.2860i	−0.260602	−	1.47795i	−0.781272	−	0.624191i	$-0.785429\pi$
$743$	−7.10350	−	40.2860i	−0.260602	−	1.47795i	0.520670	−	0.853758i	$-0.325682\pi$
$744$	59.0430	+	17.9655i	2.16462	+	0.658647i
$745$	8.19907	−	2.98422i	0.300391	−	0.109333i
$746$	−2.10339	+	5.77901i	−0.0770104	+	0.211584i
$747$	−14.4479	−	29.4238i	−0.528620	−	1.07656i
$748$	14.4702	−	25.0632i	0.529084	−	0.916400i
$749$	−20.4181	−	35.3651i	−0.746059	−	1.29221i
$750$	−48.5387	+	20.6796i	−1.77238	+	0.755112i
$751$	9.89135	+	1.74411i	0.360941	+	0.0636436i	0.351178	−	0.936309i	$-0.385781\pi$
$751$	9.89135	+	1.74411i	0.360941	+	0.0636436i	0.00976278	+	0.999952i	$0.496892\pi$
$752$	59.1544	−	34.1528i	2.15714	−	1.24542i
$753$	−15.5466	+	0.835478i	−0.566550	+	0.0304465i
$754$	0.619532	−	0.738329i	0.0225620	−	0.0268884i
$755$	28.1116	+	10.2318i	1.02309	+	0.372373i
$756$	−35.3748	−	63.2222i	−1.28657	−	2.29937i
$757$	30.7487	−	25.8012i	1.11758	−	0.937760i	0.119099	−	0.992882i	$-0.461999\pi$
$757$	30.7487	−	25.8012i	1.11758	−	0.937760i	0.998480	+	0.0551222i	$0.0175548\pi$
$758$	−47.4964	+	8.37489i	−1.72515	+	0.304190i
$759$	1.09810	−	0.715193i	0.0398586	−	0.0259599i
$760$	3.19327	+	46.5357i	0.115832	+	1.68803i
$761$			13.1199i			0.475596i	0.971315	+	0.237798i	$0.0764257\pi$
$761$			13.1199i			0.475596i	−0.971315	+	0.237798i	$0.923574\pi$
$762$	−10.1728	+	9.51155i	−0.368520	+	0.344567i
$763$	2.49521	+	2.97367i	0.0903326	+	0.107654i
$764$	42.0294	+	115.475i	1.52057	+	4.17774i
$765$	−16.4852	+	17.1620i	−0.596024	+	0.620493i
$766$	65.6202	+	55.0619i	2.37095	+	1.98947i
$767$	−0.740399	−	0.427470i	−0.0267343	−	0.0154350i
$768$	36.8623	+	18.7206i	1.33015	+	0.675523i
$769$	2.89735	−	16.4317i	0.104481	−	0.592541i	−0.886945	−	0.461874i	$-0.847177\pi$
$769$	2.89735	−	16.4317i	0.104481	−	0.592541i	0.991426	−	0.130667i	$-0.0417118\pi$
$770$	−2.56017	+	14.5194i	−0.0922620	+	0.523244i
$771$	−19.5071	−	9.90673i	−0.702530	−	0.356782i
$772$	31.4566	+	18.1615i	1.13215	+	0.653645i
$773$	24.3598	+	20.4403i	0.876161	+	0.735187i	0.965386	−	0.260825i	$-0.0839945\pi$
$773$	24.3598	+	20.4403i	0.876161	+	0.735187i	−0.0892248	+	0.996012i	$0.528439\pi$
$774$	51.3034	−	53.4095i	1.84406	−	1.91977i
$775$	−4.55702	−	12.5203i	−0.163693	−	0.449742i
$776$	81.8389	+	97.5318i	2.93784	+	3.50119i
$777$	−13.8190	+	12.9208i	−0.495752	+	0.463530i
$778$		−	53.8317i		−	1.92996i
$779$	0.375129	+	0.557716i	0.0134404	+	0.0199822i
$780$	−3.34065	+	2.17576i	−0.119614	+	0.0779047i
$781$	−16.5953	+	2.92619i	−0.593826	+	0.104707i
$782$	6.21476	−	5.21480i	0.222239	−	0.186481i
$783$	2.99332	+	5.34969i	0.106973	+	0.191182i
$784$	−15.4440	−	5.62116i	−0.551572	−	0.200756i
$785$	14.4401	−	17.2091i	0.515391	−	0.614219i
$786$	−16.3612	+	0.879257i	−0.583586	+	0.0313621i
$787$	35.4572	−	20.4712i	1.26391	−	0.729721i	0.290084	−	0.957001i	$-0.406317\pi$
$787$	35.4572	−	20.4712i	1.26391	−	0.729721i	0.973829	+	0.227280i	$0.0729833\pi$
$788$	−110.931	−	19.5601i	−3.95175	−	0.696800i
$789$	0.632689	−	0.269553i	0.0225243	−	0.00959635i
$790$	2.94518	+	5.10120i	0.104785	+	0.181493i
$791$	−10.2712	+	17.7903i	−0.365203	+	0.632550i
$792$	11.0851	+	22.5753i	0.393891	+	0.802180i
$793$	−0.746600	+	2.05127i	−0.0265126	+	0.0728427i
$794$	66.2144	−	24.1001i	2.34986	−	0.855280i
$795$	7.93614	+	2.41479i	0.281466	+	0.0856439i
$796$	−3.31398	−	18.7945i	−0.117461	−	0.666155i
$797$	33.9496			1.20256			0.601278	−	0.799040i	$-0.294658\pi$
$797$	33.9496			1.20256			0.601278	+	0.799040i	$0.294658\pi$
$798$	42.6515	+	39.7710i	1.50985	+	1.40788i
$799$	−41.4497			−1.46639
$800$	3.51497	+	19.9344i	0.124273	+	0.704786i
$801$	6.56236	+	22.6582i	0.231870	+	0.800590i
$802$	−51.6843	+	18.8115i	−1.82504	+	0.664259i
$803$	−0.183063	+	0.502962i	−0.00646016	+	0.0177491i
$804$	−8.85450	+	72.9149i	−0.312274	+	2.57151i
$805$	−1.44565	+	2.50394i	−0.0509525	+	0.0882524i
$806$	−2.12303	−	3.67719i	−0.0747805	−	0.129524i
$807$	13.1097	+	30.7708i	0.461484	+	1.08318i
$808$	−104.258	−	18.3835i	−3.66778	−	0.646729i
$809$	34.8389	−	20.1142i	1.22487	−	0.707179i	0.258918	−	0.965899i	$-0.416634\pi$
$809$	34.8389	−	20.1142i	1.22487	−	0.707179i	0.965952	+	0.258720i	$0.0833007\pi$
$810$	−7.72432	−	35.4135i	−0.271405	−	1.24430i
$811$	3.57962	−	4.26603i	0.125698	−	0.149801i	−0.699525	−	0.714608i	$-0.746605\pi$
$811$	3.57962	−	4.26603i	0.125698	−	0.149801i	0.825223	+	0.564807i	$0.191050\pi$
$812$	15.4565	+	5.62569i	0.542415	+	0.197423i
$813$	−0.695427	+	0.925419i	−0.0243897	+	0.0324558i
$814$	8.81803	−	7.39921i	0.309072	−	0.259342i
$815$	2.92626	−	0.515979i	0.102503	−	0.0180740i
$816$	40.2291	+	61.7676i	1.40830	+	2.16230i
$817$	−18.3309	+	37.4602i	−0.641317	+	1.31057i
$818$		−	72.0888i		−	2.52053i
$819$	−0.680640	+	2.76114i	−0.0237835	+	0.0964819i
$820$	−0.720513	−	0.858674i	−0.0251614	−	0.0299862i
$821$	14.7571	+	40.5449i	0.515027	+	1.41503i	0.875937	+	0.482425i	$0.160244\pi$
$821$	14.7571	+	40.5449i	0.515027	+	1.41503i	−0.360910	+	0.932600i	$0.617534\pi$
$822$	15.9783	+	68.7925i	0.557308	+	2.39942i
$823$	−12.3611	−	10.3722i	−0.430882	−	0.361553i	0.401402	−	0.915902i	$-0.368523\pi$
$823$	−12.3611	−	10.3722i	−0.430882	−	0.361553i	−0.832284	+	0.554349i	$0.812967\pi$
$824$	−44.0430	−	25.4282i	−1.53431	−	0.885834i
$825$	2.45858	−	4.84112i	0.0855967	−	0.168546i
$826$	3.62162	−	20.5392i	0.126012	−	0.714651i
$827$	−4.52142	+	25.6422i	−0.157225	+	0.891668i	0.799498	+	0.600668i	$0.205099\pi$
$827$	−4.52142	+	25.6422i	−0.157225	+	0.891668i	−0.956723	+	0.290999i	$0.906012\pi$
$828$	0.926443	+	8.59474i	0.0321961	+	0.298688i
$829$	2.64421	+	1.52664i	0.0918373	+	0.0530223i	0.545215	−	0.838296i	$-0.316448\pi$
$829$	2.64421	+	1.52664i	0.0918373	+	0.0530223i	−0.453378	+	0.891318i	$0.649781\pi$
$830$	−33.7097	−	28.2858i	−1.17008	−	0.981814i
$831$	31.8305	−	7.39320i	1.10419	−	0.256467i
$832$	0.392420	+	1.07817i	0.0136047	+	0.0373787i
$833$	6.41073	+	7.64001i	0.222119	+	0.264711i
$834$	−22.2997	−	23.8499i	−0.772177	−	0.825855i
$835$		−	20.6119i		−	0.713305i
$836$	−17.2204	−	17.8787i	−0.595580	−	0.618349i
$837$	26.6567	−	4.33099i	0.921389	−	0.149701i
$838$	−47.5529	+	8.38486i	−1.64269	+	0.289650i
$839$	15.6775	−	13.1550i	0.541248	−	0.454161i	−0.330717	−	0.943730i	$-0.607290\pi$
$839$	15.6775	−	13.1550i	0.541248	−	0.454161i	0.871964	+	0.489569i	$0.162846\pi$
$840$	−44.3597	−	33.3351i	−1.53055	−	1.15017i
$841$	25.9432	+	9.44255i	0.894593	+	0.325605i
$842$	−18.8082	+	22.4147i	−0.648172	+	0.772461i
$843$	−1.20452	−	22.4138i	−0.0414860	−	0.771972i
$844$	−40.2610	+	23.2447i	−1.38584	+	0.800116i
$845$	−19.8293	−	3.49645i	−0.682150	−	0.120281i
$846$	35.1647	−	52.4339i	1.20899	−	1.80271i
$847$	14.2273	+	24.6425i	0.488857	+	0.846726i
$848$	12.8478	−	22.2531i	0.441196	−	0.764174i
$849$	−22.7258	−	2.75974i	−0.779949	−	0.0947139i
$850$	11.4965	−	31.5865i	0.394328	−	1.08341i
$851$	2.12129	−	0.772085i	0.0727168	−	0.0264667i
$852$	32.3587	−	106.346i	1.10859	−	3.64334i
$853$	3.67736	+	20.8553i	0.125910	+	0.714074i	0.980763	+	0.195203i	$0.0625364\pi$
$853$	3.67736	+	20.8553i	0.125910	+	0.714074i	−0.854853	+	0.518871i	$0.826352\pi$
$854$	−53.2517			−1.82224
$855$	10.2297	+	17.6630i	0.349848	+	0.604061i
$856$	−93.5154			−3.19629
$857$	3.52925	+	20.0154i	0.120557	+	0.683713i	0.983848	+	0.179006i	$0.0572882\pi$
$857$	3.52925	+	20.0154i	0.120557	+	0.683713i	−0.863291	+	0.504707i	$0.831601\pi$
$858$	0.503700	−	1.65539i	0.0171960	−	0.0565142i
$859$	31.7891	−	11.5703i	1.08463	−	0.394774i	0.263002	−	0.964795i	$-0.415287\pi$
$859$	31.7891	−	11.5703i	1.08463	−	0.394774i	0.821630	+	0.570022i	$0.193065\pi$
$860$	23.7878	−	65.3563i	0.811156	−	2.22863i
$861$	−0.793740	−	0.0963886i	−0.0270506	−	0.00328492i
$862$	0.567573	−	0.983065i	0.0193316	−	0.0334833i
$863$	−14.5264	−	25.1605i	−0.494484	−	0.856472i	0.505495	−	0.862829i	$-0.331310\pi$
$863$	−14.5264	−	25.1605i	−0.494484	−	0.856472i	−0.999980	+	0.00635715i	$0.997976\pi$
$864$	−41.0247	−	0.552516i	−1.39569	−	0.0187970i
$865$	−21.0606	−	3.71354i	−0.716080	−	0.126264i
$866$	−74.0710	+	42.7649i	−2.51703	+	1.45321i
$867$	−0.820304	−	15.2642i	−0.0278590	−	0.518400i
$868$	46.5781	−	55.5096i	1.58096	−	1.88412i
$869$	−1.68063	−	0.611700i	−0.0570115	−	0.0207505i
$870$	6.57892	+	4.94388i	0.223046	+	0.167613i
$871$	2.20868	−	1.85330i	0.0748382	−	0.0627967i
$872$	8.75446	−	1.54365i	0.296463	−	0.0522745i
$873$	50.9567	+	22.5253i	1.72462	+	0.762367i
$874$	−2.82205	−	6.36068i	−0.0954573	−	0.215153i
$875$			35.3442i			1.19485i
$876$	−2.41137	−	2.57900i	−0.0814728	−	0.0871364i
$877$	−10.5631	−	12.5886i	−0.356690	−	0.425087i	0.557623	−	0.830094i	$-0.311713\pi$
$877$	−10.5631	−	12.5886i	−0.356690	−	0.425087i	−0.914313	+	0.405007i	$0.867269\pi$
$878$	4.86370	+	13.3629i	0.164142	+	0.450976i
$879$	7.41523	−	1.72232i	0.250109	−	0.0580925i
$880$	12.2448	+	10.2746i	0.412773	+	0.346358i
$881$	−11.4445	−	6.60751i	−0.385577	−	0.222613i	0.294665	−	0.955601i	$-0.404792\pi$
$881$	−11.4445	−	6.60751i	−0.385577	−	0.222613i	−0.680242	+	0.732988i	$0.738125\pi$
$882$	−15.1033	+	1.62801i	−0.508554	+	0.0548179i
$883$	3.37508	−	19.1410i	0.113580	−	0.644146i	−0.873863	−	0.486172i	$-0.838393\pi$
$883$	3.37508	−	19.1410i	0.113580	−	0.644146i	0.987443	−	0.157974i	$-0.0504962\pi$
$884$	1.30129	−	7.37997i	0.0437670	−	0.248215i
$885$	3.30539	−	6.50856i	0.111110	−	0.218783i
$886$	14.2732	+	8.24064i	0.479518	+	0.276850i
$887$	10.2659	+	8.61409i	0.344694	+	0.289233i	0.798655	−	0.601789i	$-0.205545\pi$
$887$	10.2659	+	8.61409i	0.344694	+	0.289233i	−0.453961	+	0.891022i	$0.649989\pi$
$888$	9.80179	+	42.2003i	0.328927	+	1.41615i
$889$	3.19090	+	8.76692i	0.107019	+	0.294033i
$890$	20.3555	+	24.2588i	0.682319	+	0.813156i
$891$	8.70827	+	6.72942i	0.291738	+	0.225444i
$892$			49.7194i			1.66473i
$893$	−9.84413	+	34.1628i	−0.329421	+	1.14321i
$894$	−13.6333	−	20.9326i	−0.455967	−	0.700090i
$895$	−29.4215	+	5.18780i	−0.983452	+	0.173409i
$896$	14.7749	−	12.3976i	0.493594	−	0.414175i
$897$	0.203855	−	0.271273i	0.00680651	−	0.00905756i
$898$	−53.3756	−	19.4271i	−1.78117	−	0.648292i
$899$	−3.94131	+	4.69707i	−0.131450	+	0.156656i
$900$	21.1295	+	28.9203i	0.704316	+	0.964010i
$901$	−13.5038	+	7.79642i	−0.449876	+	0.259736i
$902$	0.479115	+	0.0844809i	0.0159528	+	0.00281291i
$903$	−19.4455	−	45.6421i	−0.647106	−	1.51887i
$904$	23.5213	+	40.7401i	0.782307	+	1.35500i
$905$	−4.79609	+	8.30707i	−0.159427	+	0.276136i
$906$	10.3251	−	85.0254i	0.343030	−	2.82478i
$907$	3.51601	−	9.66017i	0.116747	−	0.320761i	−0.867531	−	0.497382i	$-0.834295\pi$
$907$	3.51601	−	9.66017i	0.116747	−	0.320761i	0.984279	+	0.176622i	$0.0565169\pi$
$908$	2.27189	−	0.826902i	0.0753954	−	0.0274417i
$909$	−44.4974	+	12.8875i	−1.47588	+	0.427451i
$910$	0.662927	+	3.75964i	0.0219758	+	0.124631i
$911$	19.5762			0.648589			0.324294	−	0.945956i	$-0.394873\pi$
$911$	19.5762			0.648589			0.324294	+	0.945956i	$0.394873\pi$
$912$	60.4630	−	18.4872i	2.00213	−	0.612173i
$913$	13.3612			0.442191
$914$	2.98726	+	16.9416i	0.0988097	+	0.560377i
$915$	−17.8313	−	5.42569i	−0.589486	−	0.179368i
$916$	16.8251	−	6.12384i	0.555918	−	0.202337i
$917$	−3.75410	+	10.3143i	−0.123971	+	0.340608i
$918$	58.5397	+	34.8574i	1.93210	+	1.15046i
$919$	23.2470	−	40.2651i	0.766849	−	1.32822i	−0.172414	−	0.985024i	$-0.555157\pi$
$919$	23.2470	−	40.2651i	0.766849	−	1.32822i	0.939263	−	0.343197i	$-0.111510\pi$
$920$	3.31057	+	5.73407i	0.109146	+	0.189047i
$921$	37.4600	−	15.9596i	1.23435	−	0.525886i
$922$	40.9129	+	7.21405i	1.34739	+	0.237582i
$923$	−3.77886	+	2.18173i	−0.124383	+	0.0718124i
$924$	29.4870	−	1.58464i	0.970051	−	0.0521308i
$925$	6.01209	−	7.16493i	0.197676	−	0.235582i
$926$	−92.9690	−	33.8379i	−3.05515	−	1.11198i
$927$	−22.2041	−	1.49338i	−0.729278	−	0.0490489i
$928$	7.13591	−	5.98774i	0.234248	−	0.196557i
$929$	−30.1221	+	5.31134i	−0.988274	+	0.174259i	−0.644344	−	0.764736i	$-0.722869\pi$
$929$	−30.1221	+	5.31134i	−0.988274	+	0.174259i	−0.343930	+	0.938995i	$0.611758\pi$
$930$	30.3793	−	19.7860i	0.996175	−	0.648807i
$931$	7.81940	−	3.46924i	0.256270	−	0.113700i
$932$			85.6552i			2.80573i
$933$	−12.4588	+	11.6490i	−0.407882	+	0.381370i
$934$	−34.5262	−	41.1467i	−1.12973	−	1.34636i
$935$	−3.31754	−	9.11486i	−0.108495	−	0.298088i
$936$	4.69658	+	4.51138i	0.153513	+	0.147459i
$937$	28.6832	+	24.0681i	0.937039	+	0.786269i	0.977068	−	0.212929i	$-0.0683004\pi$
$937$	28.6832	+	24.0681i	0.937039	+	0.786269i	−0.0400285	+	0.999199i	$0.512745\pi$
$938$	60.9125	+	35.1678i	1.98886	+	1.14827i
$939$	8.95144	+	4.54601i	0.292119	+	0.148354i
$940$	10.2958	−	58.3904i	0.335812	−	1.90448i
$941$	−10.4374	+	59.1934i	−0.340249	+	1.92965i	0.0272576	+	0.999628i	$0.491323\pi$
$941$	−10.4374	+	59.1934i	−0.340249	+	1.92965i	−0.367507	+	0.930021i	$0.619789\pi$
$942$	−57.3464	−	29.1235i	−1.86845	−	0.948896i
$943$	0.0826256	+	0.0477039i	0.00269066	+	0.00155345i
$944$	−17.3216	−	14.5345i	−0.563769	−	0.473059i
$945$	−23.8535	−	4.53805i	−0.775955	−	0.147623i
$946$	10.3245	+	28.3662i	0.335677	+	0.922265i
$947$	−9.17974	−	10.9400i	−0.298302	−	0.355502i	0.595986	−	0.802995i	$-0.296761\pi$
$947$	−9.17974	−	10.9400i	−0.298302	−	0.355502i	−0.894287	+	0.447493i	$0.852317\pi$
$948$	8.61767	−	8.05754i	0.279889	−	0.261697i
$949$			0.138595i			0.00449897i
$950$	−23.3031	−	16.9771i	−0.756053	−	0.550809i
$951$	−7.76159	+	5.05511i	−0.251687	+	0.163923i
$952$	102.718	−	18.1119i	3.32910	−	0.587010i
$953$	27.9483	−	23.4514i	0.905334	−	0.759665i	−0.0658917	−	0.997827i	$-0.520989\pi$
$953$	27.9483	−	23.4514i	0.905334	−	0.759665i	0.971226	+	0.238162i	$0.0765448\pi$
$954$	1.59375	−	23.6965i	0.0515997	−	0.767203i
$955$	38.7032	+	14.0868i	1.25240	+	0.455838i
$956$	49.3458	−	58.8080i	1.59596	−	1.90199i
$957$	−2.49511	+	0.134088i	−0.0806555	+	0.00433445i
$958$	−18.4429	+	10.6480i	−0.595861	+	0.344021i
$959$	46.5923	+	8.21548i	1.50454	+	0.265292i
$960$	−9.01272	+	3.83981i	−0.290884	+	0.123929i
$961$	−1.99380	−	3.45337i	−0.0643162	−	0.111399i
$962$	1.49034	−	2.58134i	0.0480505	−	0.0832258i
$963$	−36.7321	+	18.0364i	−1.18368	+	0.581216i
$964$	19.0380	−	52.3064i	0.613172	−	1.68468i
$965$	11.4400	−	4.16381i	0.368266	−	0.134038i
$966$	7.91943	+	2.40971i	0.254803	+	0.0775312i
$967$	2.87010	+	16.2772i	0.0922963	+	0.523438i	0.995542	+	0.0943153i	$0.0300662\pi$
$967$	2.87010	+	16.2772i	0.0922963	+	0.523438i	−0.903246	+	0.429123i	$0.858823\pi$
$968$	65.1617			2.09438
$969$	−37.3843	−	8.62974i	−1.20096	−	0.277227i
$970$	74.7923			2.40144
$971$	−8.86117	−	50.2542i	−0.284369	−	1.61273i	−0.707532	−	0.706681i	$-0.750192\pi$
$971$	−8.86117	−	50.2542i	−0.284369	−	1.61273i	0.423164	−	0.906053i	$-0.360919\pi$
$972$	−65.5902	+	31.1174i	−2.10381	+	0.998090i
$973$	−20.5540	+	7.48103i	−0.658930	+	0.239831i
$974$	22.9822	−	63.1431i	0.736398	−	2.02324i
$975$	0.169488	−	1.39569i	0.00542795	−	0.0446980i
$976$	−28.8672	+	49.9995i	−0.924017	+	1.60044i
$977$	3.79775	+	6.57789i	0.121501	+	0.210445i	0.920360	−	0.391073i	$-0.127896\pi$
$977$	3.79775	+	6.57789i	0.121501	+	0.210445i	−0.798859	+	0.601518i	$0.794563\pi$
$978$	−3.33446	−	7.82655i	−0.106624	−	0.250266i
$979$	−9.46915	−	1.66967i	−0.302635	−	0.0533628i
$980$	−12.3549	+	7.13310i	−0.394662	+	0.227858i
$981$	3.14096	−	2.29482i	0.100283	−	0.0732679i
$982$	−63.5593	+	75.7470i	−2.02826	+	2.41719i
$983$	−29.7553	−	10.8301i	−0.949048	−	0.345425i	−0.179315	−	0.983792i	$-0.557388\pi$
$983$	−29.7553	−	10.8301i	−0.949048	−	0.345425i	−0.769733	+	0.638366i	$0.779610\pi$
$984$	−1.10000	+	1.46379i	−0.0350667	+	0.0466639i
$985$	−28.9210	+	24.2676i	−0.921501	+	0.773231i
$986$	−15.2339	+	2.68615i	−0.485146	+	0.0855443i
$987$	−23.0818	−	35.4396i	−0.734700	−	1.12806i
$988$	−5.77350	−	2.82523i	−0.183680	−	0.0898825i
$989$			5.91986i			0.188241i
$990$	14.3448	+	3.53609i	0.455907	+	0.112384i
$991$	9.88741	+	11.7834i	0.314084	+	0.374311i	0.899872	−	0.436153i	$-0.143659\pi$
$991$	9.88741	+	11.7834i	0.314084	+	0.374311i	−0.585788	+	0.810464i	$0.699215\pi$
$992$	−14.0358	−	38.5630i	−0.445637	−	1.22438i
$993$	2.01933	+	8.69397i	0.0640816	+	0.275895i
$994$	−81.5420	−	68.4219i	−2.58636	−	2.17021i
$995$	−5.53948	−	3.19822i	−0.175613	−	0.101390i
$996$	−39.9091	+	78.5840i	−1.26457	+	2.49003i
$997$	−5.27918	+	29.9397i	−0.167193	+	0.948201i	0.779581	+	0.626302i	$0.215432\pi$
$997$	−5.27918	+	29.9397i	−0.167193	+	0.948201i	−0.946774	+	0.321899i	$0.895679\pi$
$998$	10.9343	−	62.0115i	0.346119	−	1.96294i
$999$	11.9893	+	14.6855i	0.379325	+	0.464628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.j.b.29.4	yes	24
3.2	odd	2	inner	57.2.j.b.29.1	yes	24
4.3	odd	2		912.2.cc.e.257.2		24
12.11	even	2		912.2.cc.e.257.4		24
19.2	odd	18	inner	57.2.j.b.2.1	✓	24
19.6	even	9		1083.2.d.d.1082.23		24
19.13	odd	18		1083.2.d.d.1082.1		24
57.2	even	18	inner	57.2.j.b.2.4	yes	24
57.32	even	18		1083.2.d.d.1082.24		24
57.44	odd	18		1083.2.d.d.1082.2		24
76.59	even	18		912.2.cc.e.401.4		24
228.59	odd	18		912.2.cc.e.401.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.j.b.2.1	✓	24	19.2	odd	18	inner
57.2.j.b.2.4	yes	24	57.2	even	18	inner
57.2.j.b.29.1	yes	24	3.2	odd	2	inner
57.2.j.b.29.4	yes	24	1.1	even	1	trivial
912.2.cc.e.257.2		24	4.3	odd	2
912.2.cc.e.257.4		24	12.11	even	2
912.2.cc.e.401.2		24	228.59	odd	18
912.2.cc.e.401.4		24	76.59	even	18
1083.2.d.d.1082.1		24	19.13	odd	18
1083.2.d.d.1082.2		24	57.44	odd	18
1083.2.d.d.1082.23		24	19.6	even	9
1083.2.d.d.1082.24		24	57.32	even	18

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.448036 + 2.54094i) q^{2} +(0.504201 - 1.65704i) q^{3} +(-4.37626 + 1.59283i) q^{4} +(-0.533860 + 1.46677i) q^{5} +(4.43634 + 0.538732i) q^{6} +(1.49687 - 2.59266i) q^{7} +(-3.42787 - 5.93724i) q^{8} +(-2.49156 - 1.67096i) q^{9} +O(q^{10})\)	\(q+(0.448036 + 2.54094i) q^{2} +(0.504201 - 1.65704i) q^{3} +(-4.37626 + 1.59283i) q^{4} +(-0.533860 + 1.46677i) q^{5} +(4.43634 + 0.538732i) q^{6} +(1.49687 - 2.59266i) q^{7} +(-3.42787 - 5.93724i) q^{8} +(-2.49156 - 1.67096i) q^{9} +(-3.96616 - 0.699341i) q^{10} +(1.05900 - 0.611412i) q^{11} +(0.432864 + 8.05474i) q^{12} +(0.203530 - 0.242558i) q^{13} +(7.25845 + 2.64186i) q^{14} +(2.16132 + 1.62417i) q^{15} +(6.41525 - 5.38303i) q^{16} +(-5.00468 + 0.882460i) q^{17} +(3.12951 - 7.07956i) q^{18} +(-0.461268 + 4.33442i) q^{19} -7.26931i q^{20} +(-3.54142 - 3.78760i) q^{21} +(2.02803 + 2.41691i) q^{22} +(0.211619 + 0.581418i) q^{23} +(-11.5666 + 2.68655i) q^{24} +(1.96382 + 1.64784i) q^{25} +(0.707514 + 0.408483i) q^{26} +(-4.02510 + 3.28612i) q^{27} +(-2.42104 + 13.7304i) q^{28} +(0.204862 - 1.16183i) q^{29} +(-3.15858 + 6.21948i) q^{30} +(-4.50103 - 2.59867i) q^{31} +(6.04864 + 5.07541i) q^{32} +(-0.479186 - 2.06307i) q^{33} +(-4.48456 - 12.3212i) q^{34} +(3.00371 + 3.57969i) q^{35} +(13.5653 + 3.34394i) q^{36} -3.64847i q^{37} +(-11.2202 + 0.769925i) q^{38} +(-0.299308 - 0.459555i) q^{39} +(10.5386 - 1.85823i) q^{40} +(0.118123 - 0.0991172i) q^{41} +(8.03739 - 10.6955i) q^{42} +(8.99072 + 3.27235i) q^{43} +(-3.66057 + 4.36249i) q^{44} +(3.78106 - 2.76248i) q^{45} +(-1.38254 + 0.798207i) q^{46} +(8.03246 + 1.41634i) q^{47} +(-5.68532 - 13.3444i) q^{48} +(-0.981262 - 1.69960i) q^{49} +(-3.30720 + 5.72824i) q^{50} +(-1.06109 + 8.73789i) q^{51} +(-0.504348 + 1.38568i) q^{52} +(2.88328 - 1.04943i) q^{53} +(-10.1532 - 8.75525i) q^{54} +(0.331444 + 1.87971i) q^{55} -20.5243 q^{56} +(6.94974 + 2.94976i) q^{57} +3.04393 q^{58} +(-0.468861 - 2.65904i) q^{59} +(-12.0455 - 3.66519i) q^{60} +(-6.47830 + 2.35791i) q^{61} +(4.58645 - 12.6012i) q^{62} +(-8.06180 + 3.95856i) q^{63} +(-1.81179 + 3.13812i) q^{64} +(0.247119 + 0.428023i) q^{65} +(5.02745 - 2.14192i) q^{66} +(8.96745 + 1.58120i) q^{67} +(20.4962 - 11.8335i) q^{68} +(1.07013 - 0.0575091i) q^{69} +(-7.75000 + 9.23609i) q^{70} +(-12.9496 - 4.71326i) q^{71} +(-1.38017 + 20.5208i) q^{72} +(-0.335304 + 0.281354i) q^{73} +(9.27055 - 1.63465i) q^{74} +(3.72070 - 2.42328i) q^{75} +(-4.88536 - 19.7033i) q^{76} -3.66082i q^{77} +(1.03360 - 0.966421i) q^{78} +(-0.940136 - 1.12041i) q^{79} +(4.47082 + 12.2835i) q^{80} +(3.41576 + 8.32662i) q^{81} +(0.304774 + 0.255736i) q^{82} +(9.46265 + 5.46326i) q^{83} +(21.5312 + 10.9347i) q^{84} +(1.37743 - 7.81181i) q^{85} +(-4.28669 + 24.3110i) q^{86} +(-1.82191 - 0.925262i) q^{87} +(-7.26019 - 4.19167i) q^{88} +(-6.02351 - 5.05433i) q^{89} +(8.71336 + 8.36976i) q^{90} +(-0.324211 - 0.890763i) q^{91} +(-1.85220 - 2.20736i) q^{92} +(-6.57553 + 6.14814i) q^{93} +21.0446i q^{94} +(-6.11134 - 2.99055i) q^{95} +(11.4599 - 7.46380i) q^{96} +(-18.2890 + 3.22484i) q^{97} +(3.87893 - 3.25481i) q^{98} +(-3.66020 - 0.246173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more