LMFDB - Embedded newform 690.2.m.d.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 8 x^{18} - 32 x^{17} + 277 x^{16} - 1138 x^{15} + 2950 x^{14} - 6404 x^{13} + \cdots + 7921 $ x^20 - 5x^19 + 8x^18 - 32x^17 + 277x^16 - 1138x^15 + 2950x^14 - 6404x^13 + 24088x^12 - 93423x^11 + 318055x^10 - 798006x^9 + 1869818x^8 - 3381161x^7 + 6172602x^6 - 7296658x^5 + 10759748x^4 - 4308967x^3 + 7994447x^2 + 486652*x + 7921
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			361.1
Root			$1.01145 - 2.21477i$ of defining polynomial
Character	$\chi$	$=$	690.361
Dual form			690.2.m.d.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.783059 + 0.229927i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.783059 + 0.229927i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.959493 + 0.281733i) q^{10} +(1.71394 + 1.97799i) q^{11} +(0.654861 + 0.755750i) q^{12} +(-2.29152 - 0.672852i) q^{13} +(0.339028 - 0.742367i) q^{14} +(0.841254 + 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.649970 - 4.52064i) q^{17} +(0.415415 + 0.909632i) q^{18} +(1.10206 + 7.66498i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(0.534443 - 0.616781i) q^{21} -2.61725 q^{22} +(3.90203 - 2.78822i) q^{23} -1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(2.00914 - 1.29119i) q^{26} +(0.142315 + 0.989821i) q^{27} +(0.339028 + 0.742367i) q^{28} +(-1.15316 + 8.02038i) q^{29} +(-0.959493 + 0.281733i) q^{30} +(6.77416 + 4.35349i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-2.51123 - 0.737365i) q^{33} +(2.99083 + 3.45160i) q^{34} +(0.534443 + 0.616781i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-4.56855 + 10.0037i) q^{37} +(-6.51450 - 4.18662i) q^{38} +(2.29152 - 0.672852i) q^{39} +(0.142315 - 0.989821i) q^{40} +(1.04394 + 2.28592i) q^{41} +(0.116146 + 0.807811i) q^{42} +(-0.744407 + 0.478401i) q^{43} +(1.71394 - 1.97799i) q^{44} -1.00000 q^{45} +(-0.448084 + 4.77485i) q^{46} -2.60326 q^{47} +(0.654861 - 0.755750i) q^{48} +(-5.32846 + 3.42439i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(1.89725 + 4.15440i) q^{51} +(-0.339885 + 2.36395i) q^{52} +(0.800620 - 0.235083i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(1.08725 - 2.38074i) q^{55} +(-0.783059 - 0.229927i) q^{56} +(-5.07111 - 5.85238i) q^{57} +(-5.30624 - 6.12373i) q^{58} +(-1.85246 - 0.543931i) q^{59} +(0.415415 - 0.909632i) q^{60} +(4.71535 + 3.03037i) q^{61} +(-7.72628 + 2.26864i) q^{62} +(-0.116146 + 0.807811i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.339885 + 2.36395i) q^{65} +(2.20177 - 1.41499i) q^{66} +(3.11886 - 3.59935i) q^{67} -4.56713 q^{68} +(-1.77516 + 4.45520i) q^{69} -0.816118 q^{70} +(0.135277 - 0.156118i) q^{71} +(0.841254 - 0.540641i) q^{72} +(1.54798 + 10.7665i) q^{73} +(-4.56855 - 10.0037i) q^{74} +(0.142315 - 0.989821i) q^{75} +(7.43013 - 2.18168i) q^{76} +(-1.79691 - 1.15480i) q^{77} +(-0.992121 + 2.17244i) q^{78} +(-15.4803 - 4.54543i) q^{79} +(0.654861 + 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-2.41122 - 0.707998i) q^{82} +(0.283327 - 0.620399i) q^{83} +(-0.686562 - 0.441227i) q^{84} +(-4.38212 + 1.28671i) q^{85} +(0.125931 - 0.875872i) q^{86} +(-3.36605 - 7.37062i) q^{87} +(0.372474 + 2.59061i) q^{88} +(8.86906 - 5.69980i) q^{89} +(0.654861 - 0.755750i) q^{90} +1.94910 q^{91} +(-3.31516 - 3.46550i) q^{92} -8.05246 q^{93} +(1.70477 - 1.96741i) q^{94} +(6.51450 - 4.18662i) q^{95} +(0.142315 + 0.989821i) q^{96} +(5.54981 + 12.1524i) q^{97} +(0.901415 - 6.26948i) q^{98} +(2.51123 - 0.737365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	−0.783059	+	0.229927i	−0.295969	+	0.0869042i	−0.426346	−	0.904560i	$-0.640199\pi$
$7$	−0.783059	+	0.229927i	−0.295969	+	0.0869042i	0.130377	+	0.991464i	$0.458381\pi$
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	0.959493	+	0.281733i	0.303418	+	0.0890917i
$11$	1.71394	+	1.97799i	0.516771	+	0.596386i	0.952819	−	0.303538i	$-0.0981678\pi$
$11$	1.71394	+	1.97799i	0.516771	+	0.596386i	−0.436048	+	0.899923i	$0.643622\pi$
$12$	0.654861	+	0.755750i	0.189042	+	0.218166i
$13$	−2.29152	−	0.672852i	−0.635554	−	0.186615i	−0.0519445	−	0.998650i	$-0.516542\pi$
$13$	−2.29152	−	0.672852i	−0.635554	−	0.186615i	−0.583609	+	0.812035i	$0.698360\pi$
$14$	0.339028	−	0.742367i	0.0906089	−	0.198406i
$15$	0.841254	+	0.540641i	0.217211	+	0.139593i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.649970	−	4.52064i	0.157641	−	1.09642i	−0.745324	−	0.666702i	$-0.767705\pi$
$17$	0.649970	−	4.52064i	0.157641	−	1.09642i	0.902965	−	0.429714i	$-0.141386\pi$
$18$	0.415415	+	0.909632i	0.0979143	+	0.214402i
$19$	1.10206	+	7.66498i	0.252830	+	1.75847i	0.581051	+	0.813867i	$0.302642\pi$
$19$	1.10206	+	7.66498i	0.252830	+	1.75847i	−0.328221	+	0.944601i	$0.606449\pi$
$20$	−0.841254	+	0.540641i	−0.188110	+	0.120891i
$21$	0.534443	−	0.616781i	0.116625	−	0.134593i
$22$	−2.61725			−0.558000
$23$	3.90203	−	2.78822i	0.813629	−	0.581385i
$23$	3.90203	−	2.78822i	0.813629	−	0.581385i
$24$	−1.00000			−0.204124
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	2.00914	−	1.29119i	0.394024	−	0.253224i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	0.339028	+	0.742367i	0.0640702	+	0.140294i
$29$	−1.15316	+	8.02038i	−0.214136	+	1.48935i	0.545012	+	0.838428i	$0.316525\pi$
$29$	−1.15316	+	8.02038i	−0.214136	+	1.48935i	−0.759148	+	0.650919i	$0.774384\pi$
$30$	−0.959493	+	0.281733i	−0.175179	+	0.0514371i
$31$	6.77416	+	4.35349i	1.21668	+	0.781910i	0.981763	−	0.190107i	$-0.0608834\pi$
$31$	6.77416	+	4.35349i	1.21668	+	0.781910i	0.234912	+	0.972017i	$0.424520\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$	−2.51123	−	0.737365i	−0.437150	−	0.128359i
$34$	2.99083	+	3.45160i	0.512923	+	0.591945i
$35$	0.534443	+	0.616781i	0.0903374	+	0.104255i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	−4.56855	+	10.0037i	−0.751064	+	1.64460i	0.0133788	+	0.999910i	$0.495741\pi$
$37$	−4.56855	+	10.0037i	−0.751064	+	1.64460i	−0.764443	+	0.644691i	$0.776986\pi$
$38$	−6.51450	−	4.18662i	−1.05679	−	0.679159i
$39$	2.29152	−	0.672852i	0.366937	−	0.107742i
$40$	0.142315	−	0.989821i	0.0225020	−	0.156505i
$41$	1.04394	+	2.28592i	0.163037	+	0.357000i	0.973465	−	0.228838i	$-0.0734926\pi$
$41$	1.04394	+	2.28592i	0.163037	+	0.357000i	−0.810428	+	0.585838i	$0.800765\pi$
$42$	0.116146	+	0.807811i	0.0179217	+	0.124648i
$43$	−0.744407	+	0.478401i	−0.113521	+	0.0729555i	−0.596169	−	0.802859i	$-0.703311\pi$
$43$	−0.744407	+	0.478401i	−0.113521	+	0.0729555i	0.482648	+	0.875814i	$0.339675\pi$
$44$	1.71394	−	1.97799i	0.258386	−	0.298193i
$45$	−1.00000			−0.149071
$46$	−0.448084	+	4.77485i	−0.0660664	+	0.704014i
$47$	−2.60326			−0.379724			−0.189862	−	0.981811i	$-0.560804\pi$
$47$	−2.60326			−0.379724			−0.189862	+	0.981811i	$0.560804\pi$
$48$	0.654861	−	0.755750i	0.0945210	−	0.109083i
$49$	−5.32846	+	3.42439i	−0.761208	+	0.489199i
$50$	−0.142315	−	0.989821i	−0.0201264	−	0.139982i
$51$	1.89725	+	4.15440i	0.265668	+	0.581733i
$52$	−0.339885	+	2.36395i	−0.0471336	+	0.327822i
$53$	0.800620	−	0.235083i	0.109974	−	0.0322912i	−0.226283	−	0.974062i	$-0.572657\pi$
$53$	0.800620	−	0.235083i	0.109974	−	0.0322912i	0.336256	+	0.941770i	$0.390839\pi$
$54$	−0.841254	−	0.540641i	−0.114480	−	0.0735719i
$55$	1.08725	−	2.38074i	0.146604	−	0.321018i
$56$	−0.783059	−	0.229927i	−0.104641	−	0.0307253i
$57$	−5.07111	−	5.85238i	−0.671685	−	0.775166i
$58$	−5.30624	−	6.12373i	−0.696744	−	0.804085i
$59$	−1.85246	−	0.543931i	−0.241170	−	0.0708138i	0.158914	−	0.987292i	$-0.449201\pi$
$59$	−1.85246	−	0.543931i	−0.241170	−	0.0708138i	−0.400084	+	0.916479i	$0.631019\pi$
$60$	0.415415	−	0.909632i	0.0536298	−	0.117433i
$61$	4.71535	+	3.03037i	0.603739	+	0.387999i	0.806504	−	0.591228i	$-0.201357\pi$
$61$	4.71535	+	3.03037i	0.603739	+	0.387999i	−0.202766	+	0.979227i	$0.564993\pi$
$62$	−7.72628	+	2.26864i	−0.981239	+	0.288118i
$63$	−0.116146	+	0.807811i	−0.0146330	+	0.101775i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	0.339885	+	2.36395i	0.0421576	+	0.293212i
$66$	2.20177	−	1.41499i	0.271019	−	0.174174i
$67$	3.11886	−	3.59935i	0.381029	−	0.439731i	−0.532546	−	0.846401i	$-0.678765\pi$
$67$	3.11886	−	3.59935i	0.381029	−	0.439731i	0.913575	+	0.406670i	$0.133310\pi$
$68$	−4.56713			−0.553845
$69$	−1.77516	+	4.45520i	−0.213705	+	0.536343i
$70$	−0.816118			−0.0975447
$71$	0.135277	−	0.156118i	0.0160544	−	0.0185278i	−0.747666	−	0.664075i	$-0.768825\pi$
$71$	0.135277	−	0.156118i	0.0160544	−	0.0185278i	0.763720	+	0.645548i	$0.223371\pi$
$72$	0.841254	−	0.540641i	0.0991427	−	0.0637151i
$73$	1.54798	+	10.7665i	0.181178	+	1.26012i	0.853984	+	0.520299i	$0.174180\pi$
$73$	1.54798	+	10.7665i	0.181178	+	1.26012i	−0.672806	+	0.739819i	$0.734911\pi$
$74$	−4.56855	−	10.0037i	−0.531083	−	1.16291i
$75$	0.142315	−	0.989821i	0.0164331	−	0.114295i
$76$	7.43013	−	2.18168i	0.852294	−	0.250256i
$77$	−1.79691	−	1.15480i	−0.204776	−	0.131602i
$78$	−0.992121	+	2.17244i	−0.112336	+	0.245981i
$79$	−15.4803	−	4.54543i	−1.74167	−	0.511401i	−0.752555	−	0.658530i	$-0.771179\pi$
$79$	−15.4803	−	4.54543i	−1.74167	−	0.511401i	−0.989117	+	0.147129i	$0.952997\pi$
$80$	0.654861	+	0.755750i	0.0732157	+	0.0844954i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−2.41122	−	0.707998i	−0.266275	−	0.0781853i
$83$	0.283327	−	0.620399i	0.0310991	−	0.0680976i	−0.893445	−	0.449173i	$-0.851719\pi$
$83$	0.283327	−	0.620399i	0.0310991	−	0.0680976i	0.924544	+	0.381075i	$0.124446\pi$
$84$	−0.686562	−	0.441227i	−0.0749100	−	0.0481418i
$85$	−4.38212	+	1.28671i	−0.475308	+	0.139563i
$86$	0.125931	−	0.875872i	0.0135795	−	0.0944477i
$87$	−3.36605	−	7.37062i	−0.360878	−	0.790213i
$88$	0.372474	+	2.59061i	0.0397058	+	0.276160i
$89$	8.86906	−	5.69980i	0.940118	−	0.604177i	0.0216901	−	0.999765i	$-0.493095\pi$
$89$	8.86906	−	5.69980i	0.940118	−	0.604177i	0.918428	+	0.395587i	$0.129459\pi$
$90$	0.654861	−	0.755750i	0.0690284	−	0.0796630i
$91$	1.94910			0.204322
$92$	−3.31516	−	3.46550i	−0.345629	−	0.361304i
$93$	−8.05246			−0.835002
$94$	1.70477	−	1.96741i	0.175834	−	0.202923i
$95$	6.51450	−	4.18662i	0.668374	−	0.429538i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	5.54981	+	12.1524i	0.563498	+	1.23389i	0.950188	+	0.311678i	$0.100891\pi$
$97$	5.54981	+	12.1524i	0.563498	+	1.23389i	−0.386690	+	0.922210i	$0.626382\pi$
$98$	0.901415	−	6.26948i	0.0910567	−	0.633313i
$99$	2.51123	−	0.737365i	0.252389	−	0.0741080i
$100$	0.841254	+	0.540641i	0.0841254	+	0.0540641i
$101$	−0.447077	+	0.978962i	−0.0444858	+	0.0974104i	−0.930570	−	0.366114i	$-0.880688\pi$
$101$	−0.447077	+	0.978962i	−0.0444858	+	0.0974104i	0.886084	+	0.463524i	$0.153415\pi$
$102$	−4.38212	−	1.28671i	−0.433895	−	0.127403i
$103$	6.60318	+	7.62047i	0.650630	+	0.750867i	0.981217	−	0.192908i	$-0.0617920\pi$
$103$	6.60318	+	7.62047i	0.650630	+	0.750867i	−0.330587	+	0.943776i	$0.607247\pi$
$104$	−1.56398	−	1.80493i	−0.153361	−	0.176988i
$105$	−0.783059	−	0.229927i	−0.0764187	−	0.0224386i
$106$	−0.346631	+	0.759015i	−0.0336677	+	0.0737221i
$107$	13.8053	+	8.87214i	1.33461	+	0.857702i	0.996515	−	0.0834101i	$-0.0265811\pi$
$107$	13.8053	+	8.87214i	1.33461	+	0.857702i	0.338095	+	0.941112i	$0.390218\pi$
$108$	0.959493	−	0.281733i	0.0923273	−	0.0271097i
$109$	−1.39518	+	9.70367i	−0.133634	+	0.929443i	0.807129	+	0.590376i	$0.201020\pi$
$109$	−1.39518	+	9.70367i	−0.133634	+	0.929443i	−0.940762	+	0.339067i	$0.889889\pi$
$110$	1.08725	+	2.38074i	0.103665	+	0.226994i
$111$	−1.56511	−	10.8856i	−0.148554	−	1.03322i
$112$	0.686562	−	0.441227i	0.0648740	−	0.0416920i
$113$	6.38445	−	7.36805i	0.600598	−	0.693127i	−0.371304	−	0.928511i	$-0.621089\pi$
$113$	6.38445	−	7.36805i	0.600598	−	0.693127i	0.971902	+	0.235384i	$0.0756347\pi$
$114$	7.74381			0.725274
$115$	−4.15722	−	2.39114i	−0.387663	−	0.222975i
$116$	8.10285			0.752331
$117$	−1.56398	+	1.80493i	−0.144590	+	0.166866i
$118$	1.62418	−	1.04380i	0.149518	−	0.0960892i
$119$	0.530452	+	3.68937i	0.0486264	+	0.338204i
$120$	0.415415	+	0.909632i	0.0379220	+	0.0830377i
$121$	0.590605	−	4.10775i	0.0536914	−	0.373432i
$122$	−5.37810	+	1.57915i	−0.486910	+	0.142970i
$123$	−2.11408	−	1.35864i	−0.190620	−	0.122504i
$124$	3.34511	−	7.32478i	0.300400	−	0.657785i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	−0.534443	−	0.616781i	−0.0476120	−	0.0549472i
$127$	−13.5042	−	15.5847i	−1.19830	−	1.38292i	−0.904182	−	0.427148i	$-0.859518\pi$
$127$	−13.5042	−	15.5847i	−1.19830	−	1.38292i	−0.294122	−	0.955768i	$-0.595027\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$	0.367592	−	0.804914i	0.0323647	−	0.0708687i
$130$	−2.00914	−	1.29119i	−0.176213	−	0.113245i
$131$	13.4732	−	3.95608i	1.17716	−	0.345644i	0.366079	−	0.930584i	$-0.380700\pi$
$131$	13.4732	−	3.95608i	1.17716	−	0.345644i	0.811077	+	0.584940i	$0.198882\pi$
$132$	−0.372474	+	2.59061i	−0.0324197	+	0.225484i
$133$	−2.62536	−	5.74874i	−0.227648	−	0.498479i
$134$	0.677793	+	4.71415i	0.0585524	+	0.407241i
$135$	0.841254	−	0.540641i	0.0724036	−	0.0465310i
$136$	2.99083	−	3.45160i	0.256462	−	0.295973i
$137$	−11.7664			−1.00527			−0.502636	−	0.864498i	$-0.667637\pi$
$137$	−11.7664			−1.00527			−0.502636	+	0.864498i	$0.667637\pi$
$138$	−2.20453	−	4.25911i	−0.187662	−	0.362560i
$139$	14.8946			1.26335			0.631674	−	0.775234i	$-0.282368\pi$
$139$	14.8946			1.26335			0.631674	+	0.775234i	$0.282368\pi$
$140$	0.534443	−	0.616781i	0.0451687	−	0.0521275i
$141$	2.19000	−	1.40743i	0.184431	−	0.118527i
$142$	0.0293985	+	0.204471i	0.00246707	+	0.0171589i
$143$	−2.59663	−	5.68583i	−0.217141	−	0.475473i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	7.77463	−	2.28284i	0.645648	−	0.189579i
$146$	−9.15046	−	5.88064i	−0.757297	−	0.486685i
$147$	2.63122	−	5.76157i	0.217019	−	0.475206i
$148$	10.5521	+	3.09837i	0.867375	+	0.254684i
$149$	−12.4790	−	14.4016i	−1.02232	−	1.17982i	−0.983561	−	0.180574i	$-0.942204\pi$
$149$	−12.4790	−	14.4016i	−1.02232	−	1.17982i	−0.0387607	−	0.999249i	$-0.512341\pi$
$150$	0.654861	+	0.755750i	0.0534692	+	0.0617067i
$151$	21.2618	+	6.24301i	1.73026	+	0.508049i	0.986967	−	0.160920i	$-0.0514462\pi$
$151$	21.2618	+	6.24301i	1.73026	+	0.508049i	0.743290	+	0.668970i	$0.233264\pi$
$152$	−3.21689	+	7.04401i	−0.260924	+	0.571345i
$153$	−3.84211	−	2.46917i	−0.310616	−	0.199621i
$154$	2.04946	−	0.601777i	0.165150	−	0.0484925i
$155$	1.14599	−	7.97050i	0.0920477	−	0.640206i
$156$	−0.992121	−	2.17244i	−0.0794332	−	0.173934i
$157$	−0.586874	−	4.08180i	−0.0468376	−	0.325763i	−0.999747	−	0.0225067i	$-0.992835\pi$
$157$	−0.586874	−	4.08180i	−0.0468376	−	0.325763i	0.952909	−	0.303256i	$-0.0980738\pi$
$158$	13.5727	−	8.72262i	1.07978	−	0.693934i
$159$	−0.546429	+	0.630613i	−0.0433346	+	0.0500108i
$160$	−1.00000			−0.0790569
$161$	−2.41443	+	3.08053i	−0.190284	+	0.242779i
$162$	1.00000			0.0785674
$163$	4.05449	−	4.67913i	0.317572	−	0.366498i	−0.574411	−	0.818567i	$-0.694769\pi$
$163$	4.05449	−	4.67913i	0.317572	−	0.366498i	0.891983	+	0.452070i	$0.149314\pi$
$164$	2.11408	−	1.35864i	0.165082	−	0.106092i
$165$	0.372474	+	2.59061i	0.0289970	+	0.201679i
$166$	0.283327	+	0.620399i	0.0219904	+	0.0481523i
$167$	−2.99730	+	20.8467i	−0.231938	+	1.61316i	0.457767	+	0.889072i	$0.348649\pi$
$167$	−2.99730	+	20.8467i	−0.231938	+	1.61316i	−0.689705	+	0.724091i	$0.742260\pi$
$168$	0.783059	−	0.229927i	0.0604143	−	0.0177392i
$169$	−6.13795	−	3.94462i	−0.472150	−	0.303432i
$170$	1.89725	−	4.15440i	0.145513	−	0.318628i
$171$	7.43013	+	2.18168i	0.568196	+	0.166837i
$172$	0.579472	+	0.668747i	0.0441843	+	0.0509914i
$173$	−6.18555	−	7.13851i	−0.470279	−	0.542731i	0.470210	−	0.882554i	$-0.344178\pi$
$173$	−6.18555	−	7.13851i	−0.470279	−	0.542731i	−0.940489	+	0.339824i	$0.889633\pi$
$174$	7.77463	+	2.28284i	0.589393	+	0.173061i
$175$	0.339028	−	0.742367i	0.0256281	−	0.0561177i
$176$	−2.20177	−	1.41499i	−0.165965	−	0.106659i
$177$	1.85246	−	0.543931i	0.139239	−	0.0408844i
$178$	−1.50038	+	10.4354i	−0.112458	+	0.782163i
$179$	1.17018	+	2.56234i	0.0874636	+	0.191519i	0.948309	−	0.317347i	$-0.102792\pi$
$179$	1.17018	+	2.56234i	0.0874636	+	0.191519i	−0.860846	+	0.508866i	$0.830065\pi$
$180$	0.142315	+	0.989821i	0.0106075	+	0.0737769i
$181$	19.8838	−	12.7785i	1.47795	−	0.949820i	0.480608	−	0.876936i	$-0.340416\pi$
$181$	19.8838	−	12.7785i	1.47795	−	0.949820i	0.997340	−	0.0728840i	$-0.0232203\pi$
$182$	−1.27639	+	1.47303i	−0.0946125	+	0.109189i
$183$	−5.60515			−0.414344
$184$	4.79002	−	0.236009i	0.353125	−	0.0173988i
$185$	10.9975			0.808556
$186$	5.27324	−	6.08565i	0.386653	−	0.446221i
$187$	10.0558	−	6.46245i	0.735351	−	0.472581i
$188$	0.370482	+	2.57676i	0.0270202	+	0.187929i
$189$	−0.339028	−	0.742367i	−0.0246606	−	0.0539992i
$190$	−1.10206	+	7.66498i	−0.0799517	+	0.556076i
$191$	8.94892	−	2.62764i	0.647521	−	0.190129i	0.0585513	−	0.998284i	$-0.481352\pi$
$191$	8.94892	−	2.62764i	0.647521	−	0.190129i	0.588970	+	0.808155i	$0.299534\pi$
$192$	−0.841254	−	0.540641i	−0.0607122	−	0.0390174i
$193$	−3.94591	+	8.64035i	−0.284033	+	0.621946i	−0.996842	−	0.0794127i	$-0.974696\pi$
$193$	−3.94591	+	8.64035i	−0.284033	+	0.621946i	0.712809	+	0.701359i	$0.247423\pi$
$194$	−12.8185	−	3.76386i	−0.920316	−	0.270229i
$195$	−1.56398	−	1.80493i	−0.111999	−	0.129254i
$196$	4.14786	+	4.78688i	0.296275	+	0.341920i
$197$	−3.93143	−	1.15437i	−0.280103	−	0.0822456i	0.138664	−	0.990340i	$-0.455719\pi$
$197$	−3.93143	−	1.15437i	−0.280103	−	0.0822456i	−0.418767	+	0.908094i	$0.637537\pi$
$198$	−1.08725	+	2.38074i	−0.0772672	+	0.169192i
$199$	−9.30437	−	5.97955i	−0.659569	−	0.423879i	0.167583	−	0.985858i	$-0.446404\pi$
$199$	−9.30437	−	5.97955i	−0.659569	−	0.423879i	−0.827152	+	0.561979i	$0.810040\pi$
$200$	−0.959493	+	0.281733i	−0.0678464	+	0.0199215i
$201$	−0.677793	+	4.71415i	−0.0478078	+	0.332511i
$202$	−0.447077	−	0.978962i	−0.0314562	−	0.0688796i
$203$	−0.941111	−	6.54557i	−0.0660531	−	0.459409i
$204$	3.84211	−	2.46917i	0.269002	−	0.172877i
$205$	1.64567	−	1.89921i	0.114939	−	0.132647i
$206$	−10.0833			−0.702539
$207$	−0.915298	−	4.70768i	−0.0636176	−	0.327206i
$208$	2.38826			0.165596
$209$	−13.2724	+	15.3171i	−0.918070	+	1.05951i
$210$	0.686562	−	0.441227i	0.0473773	−	0.0304475i
$211$	−1.93113	−	13.4313i	−0.132944	−	0.924647i	−0.941688	−	0.336486i	$-0.890761\pi$
$211$	−1.93113	−	13.4313i	−0.132944	−	0.924647i	0.808744	−	0.588161i	$-0.200148\pi$
$212$	−0.346631	−	0.759015i	−0.0238067	−	0.0521294i
$213$	−0.0293985	+	0.204471i	−0.00201435	+	0.0140101i
$214$	−15.7457	+	4.62335i	−1.07635	+	0.316045i
$215$	0.744407	+	0.478401i	0.0507681	+	0.0326267i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	−6.30556	−	1.85148i	−0.428049	−	0.125687i
$218$	−6.41990	−	7.40896i	−0.434810	−	0.501798i
$219$	−7.12303	−	8.22041i	−0.481330	−	0.555484i
$220$	−2.51123	−	0.737365i	−0.169307	−	0.0497131i
$221$	−4.53114	+	9.92181i	−0.304797	+	0.667413i
$222$	9.25173	+	5.94572i	0.620935	+	0.399051i
$223$	−8.62122	+	2.53142i	−0.577320	+	0.169516i	−0.557341	−	0.830284i	$-0.688178\pi$
$223$	−8.62122	+	2.53142i	−0.577320	+	0.169516i	−0.0199793	+	0.999800i	$0.506360\pi$
$224$	−0.116146	+	0.807811i	−0.00776031	+	0.0539741i
$225$	0.415415	+	0.909632i	0.0276943	+	0.0606421i
$226$	1.38747	+	9.65009i	0.0922933	+	0.641914i
$227$	7.17000	−	4.60788i	0.475890	−	0.305836i	−0.280619	−	0.959819i	$-0.590540\pi$
$227$	7.17000	−	4.60788i	0.475890	−	0.305836i	0.756509	+	0.653983i	$0.226903\pi$
$228$	−5.07111	+	5.85238i	−0.335843	+	0.387583i
$229$	−24.6128			−1.62646			−0.813230	−	0.581942i	$-0.802293\pi$
$229$	−24.6128			−1.62646			−0.813230	+	0.581942i	$0.802293\pi$
$230$	4.52950	−	1.57595i	0.298666	−	0.103915i
$231$	2.13599			0.140538
$232$	−5.30624	+	6.12373i	−0.348372	+	0.402042i
$233$	4.06547	−	2.61272i	0.266338	−	0.171165i	−0.400655	−	0.916229i	$-0.631217\pi$
$233$	4.06547	−	2.61272i	0.266338	−	0.171165i	0.666993	+	0.745064i	$0.267581\pi$
$234$	−0.339885	−	2.36395i	−0.0222190	−	0.154537i
$235$	1.08143	+	2.36801i	0.0705448	+	0.154472i
$236$	−0.274762	+	1.91101i	−0.0178855	+	0.124396i
$237$	15.4803	−	4.54543i	1.00555	−	0.295258i
$238$	−3.13561	−	2.01514i	−0.203252	−	0.130622i
$239$	−4.04871	+	8.86543i	−0.261889	+	0.573457i	−0.994204	−	0.107509i	$-0.965713\pi$
$239$	−4.04871	+	8.86543i	−0.261889	+	0.573457i	0.732315	+	0.680966i	$0.238440\pi$
$240$	−0.959493	−	0.281733i	−0.0619350	−	0.0181858i
$241$	−6.60918	−	7.62740i	−0.425735	−	0.491324i	0.501841	−	0.864960i	$-0.332656\pi$
$241$	−6.60918	−	7.62740i	−0.425735	−	0.491324i	−0.927575	+	0.373636i	$0.878111\pi$
$242$	2.71767	+	3.13635i	0.174698	+	0.201613i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	2.32846	−	5.09862i	0.149065	−	0.326406i
$245$	5.32846	+	3.42439i	0.340423	+	0.218776i
$246$	2.41122	−	0.707998i	0.153734	−	0.0451403i
$247$	2.63201	−	18.3060i	0.167471	−	1.16478i
$248$	3.34511	+	7.32478i	0.212415	+	0.465124i
$249$	0.0970634	+	0.675091i	0.00615114	+	0.0427821i
$250$	−0.841254	+	0.540641i	−0.0532055	+	0.0341931i
$251$	−14.0280	+	16.1892i	−0.885439	+	1.02185i	0.114158	+	0.993463i	$0.463583\pi$
$251$	−14.0280	+	16.1892i	−0.885439	+	1.02185i	−0.999597	+	0.0283882i	$0.990963\pi$
$252$	0.816118			0.0514106
$253$	12.2029	+	2.93932i	0.767189	+	0.184793i
$254$	20.6215			1.29391
$255$	2.99083	−	3.45160i	0.187293	−	0.216148i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−2.19203	−	15.2459i	−0.136735	−	0.951013i	−0.936492	−	0.350689i	$-0.885947\pi$
$257$	−2.19203	−	15.2459i	−0.136735	−	0.951013i	0.799757	−	0.600324i	$-0.204962\pi$
$258$	0.367592	+	0.804914i	0.0228853	+	0.0501117i
$259$	1.27732	−	8.88394i	0.0793686	−	0.552021i
$260$	2.29152	−	0.672852i	0.142114	−	0.0417285i
$261$	6.81655	+	4.38073i	0.421934	+	0.271161i
$262$	−5.83324	+	12.7730i	−0.360379	+	0.789120i
$263$	−6.73400	−	1.97728i	−0.415236	−	0.121924i	0.0674399	−	0.997723i	$-0.478517\pi$
$263$	−6.73400	−	1.97728i	−0.415236	−	0.121924i	−0.482676	+	0.875799i	$0.660335\pi$
$264$	−1.71394	−	1.97799i	−0.105485	−	0.121737i
$265$	−0.546429	−	0.630613i	−0.0335669	−	0.0387382i
$266$	6.06386	+	1.78051i	0.371799	+	0.109170i
$267$	−4.37958	+	9.58995i	−0.268026	+	0.586896i
$268$	−4.00658	−	2.57487i	−0.244741	−	0.157285i
$269$	17.3480	−	5.09382i	1.05772	−	0.310576i	0.293790	−	0.955870i	$-0.405083\pi$
$269$	17.3480	−	5.09382i	1.05772	−	0.310576i	0.763934	+	0.645294i	$0.223265\pi$
$270$	−0.142315	+	0.989821i	−0.00866101	+	0.0602386i
$271$	−2.75426	−	6.03099i	−0.167309	−	0.366356i	0.807343	−	0.590083i	$-0.200905\pi$
$271$	−2.75426	−	6.03099i	−0.167309	−	0.366356i	−0.974652	+	0.223727i	$0.928178\pi$
$272$	0.649970	+	4.52064i	0.0394102	+	0.274104i
$273$	−1.63969	+	1.05377i	−0.0992386	+	0.0637768i
$274$	7.70536	−	8.89246i	0.465498	−	0.537213i
$275$	−2.61725			−0.157826
$276$	4.66248	+	1.12306i	0.280648	+	0.0676000i
$277$	−11.5655			−0.694904			−0.347452	−	0.937698i	$-0.612953\pi$
$277$	−11.5655			−0.694904			−0.347452	+	0.937698i	$0.612953\pi$
$278$	−9.75392	+	11.2566i	−0.585001	+	0.675127i
$279$	6.77416	−	4.35349i	0.405559	−	0.260637i
$280$	0.116146	+	0.807811i	0.00694103	+	0.0482759i
$281$	3.73018	+	8.16795i	0.222524	+	0.487259i	0.987661	−	0.156608i	$-0.0500560\pi$
$281$	3.73018	+	8.16795i	0.222524	+	0.487259i	−0.765137	+	0.643868i	$0.777329\pi$
$282$	−0.370482	+	2.57676i	−0.0220619	+	0.153444i
$283$	−25.8712	+	7.59646i	−1.53788	+	0.451563i	−0.937452	−	0.348114i	$-0.886822\pi$
$283$	−25.8712	+	7.59646i	−1.53788	+	0.451563i	−0.600430	+	0.799677i	$0.705004\pi$
$284$	−0.173781	−	0.111682i	−0.0103120	−	0.00662713i
$285$	−3.21689	+	7.04401i	−0.190552	+	0.417251i
$286$	5.99749	+	1.76102i	0.354639	+	0.104131i
$287$	−1.34306	−	1.54998i	−0.0792786	−	0.0914923i
$288$	−0.654861	−	0.755750i	−0.0385880	−	0.0445330i
$289$	−3.70233	−	1.08710i	−0.217784	−	0.0639473i
$290$	−3.36605	+	7.37062i	−0.197661	+	0.432817i
$291$	−11.2389	−	7.22279i	−0.658834	−	0.423407i
$292$	10.4366	−	3.06445i	0.610754	−	0.179333i
$293$	−3.47736	+	24.1856i	−0.203149	+	1.41294i	0.591714	+	0.806148i	$0.298451\pi$
$293$	−3.47736	+	24.1856i	−0.203149	+	1.41294i	−0.794864	+	0.606788i	$0.792458\pi$
$294$	2.63122	+	5.76157i	0.153456	+	0.336021i
$295$	0.274762	+	1.91101i	0.0159973	+	0.111263i
$296$	−9.25173	+	5.94572i	−0.537746	+	0.345588i
$297$	−1.71394	+	1.97799i	−0.0994526	+	0.114774i
$298$	19.0560			1.10388
$299$	−10.8176	+	3.76379i	−0.625600	+	0.217666i
$300$	−1.00000			−0.0577350
$301$	0.472917	−	0.545776i	0.0272585	−	0.0314580i
$302$	−18.6416	+	11.9803i	−1.07271	+	0.689386i
$303$	−0.153162	−	1.06526i	−0.00879892	−	0.0611978i
$304$	−3.21689	−	7.04401i	−0.184501	−	0.404002i
$305$	0.797696	−	5.54809i	0.0456759	−	0.317683i
$306$	4.38212	−	1.28671i	0.250509	−	0.0735562i
$307$	27.1963	+	17.4780i	1.55218	+	0.997524i	0.984725	+	0.174117i	$0.0557072\pi$
$307$	27.1963	+	17.4780i	1.55218	+	0.997524i	0.567452	+	0.823406i	$0.307929\pi$
$308$	−0.887320	+	1.94296i	−0.0505598	+	0.110710i
$309$	−9.67488	−	2.84080i	−0.550385	−	0.161608i
$310$	5.27324	+	6.08565i	0.299500	+	0.345641i
$311$	−10.0396	−	11.5863i	−0.569293	−	0.656999i	0.395975	−	0.918261i	$-0.370407\pi$
$311$	−10.0396	−	11.5863i	−0.569293	−	0.656999i	−0.965268	+	0.261263i	$0.915861\pi$
$312$	2.29152	+	0.672852i	0.129732	+	0.0380927i
$313$	−8.96140	+	19.6227i	−0.506529	+	1.10914i	0.467763	+	0.883854i	$0.345060\pi$
$313$	−8.96140	+	19.6227i	−0.506529	+	1.10914i	−0.974292	+	0.225289i	$0.927667\pi$
$314$	3.46914	+	2.22948i	0.195775	+	0.125817i
$315$	0.783059	−	0.229927i	0.0441204	−	0.0129549i
$316$	−2.29609	+	15.9696i	−0.129165	+	0.898362i
$317$	−11.9704	−	26.2114i	−0.672322	−	1.47218i	−0.870578	−	0.492030i	$-0.836255\pi$
$317$	−11.9704	−	26.2114i	−0.672322	−	1.47218i	0.198256	−	0.980150i	$-0.436472\pi$
$318$	−0.118750	−	0.825927i	−0.00665919	−	0.0463157i
$319$	−17.8406	+	11.4655i	−0.998884	+	0.641944i
$320$	0.654861	−	0.755750i	0.0366078	−	0.0422477i
$321$	−16.4104			−0.915940
$322$	−0.746991	−	3.84202i	−0.0416282	−	0.214107i
$323$	35.3669			1.96787
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	2.00914	−	1.29119i	0.111447	−	0.0716225i
$326$	0.881125	+	6.12836i	0.0488010	+	0.339418i
$327$	−4.07250	−	8.91753i	−0.225210	−	0.493141i
$328$	−0.357639	+	2.48744i	−0.0197473	+	0.137346i
$329$	2.03850	−	0.598559i	0.112386	−	0.0329996i
$330$	−2.20177	−	1.41499i	−0.121204	−	0.0778928i
$331$	11.4691	−	25.1138i	0.630398	−	1.38038i	−0.277311	−	0.960780i	$-0.589443\pi$
$331$	11.4691	−	25.1138i	0.630398	−	1.38038i	0.907709	−	0.419599i	$-0.137829\pi$
$332$	−0.654406	−	0.192151i	−0.0359152	−	0.0105456i
$333$	7.20186	+	8.31139i	0.394660	+	0.455461i
$334$	−13.7920	−	15.9169i	−0.754667	−	0.870932i
$335$	−4.56971	−	1.34179i	−0.249670	−	0.0733097i
$336$	−0.339028	+	0.742367i	−0.0184955	+	0.0404994i
$337$	−14.0192	−	9.00958i	−0.763674	−	0.490783i	0.0999053	−	0.994997i	$-0.468146\pi$
$337$	−14.0192	−	9.00958i	−0.763674	−	0.490783i	−0.863579	+	0.504214i	$0.831782\pi$
$338$	7.00065	−	2.05558i	0.380785	−	0.111809i
$339$	−1.38747	+	9.65009i	−0.0753572	+	0.524121i
$340$	1.89725	+	4.15440i	0.102893	+	0.225304i
$341$	2.99933	+	20.8608i	0.162423	+	1.12968i
$342$	−6.51450	+	4.18662i	−0.352264	+	0.226386i
$343$	7.12624	−	8.22412i	0.384781	−	0.444061i
$344$	−0.884878			−0.0477094
$345$	4.79002	−	0.236009i	0.257886	−	0.0127063i
$346$	9.44560			0.507799
$347$	−5.26549	+	6.07670i	−0.282667	+	0.326215i	−0.879272	−	0.476320i	$-0.841970\pi$
$347$	−5.26549	+	6.07670i	−0.282667	+	0.326215i	0.596605	+	0.802535i	$0.296516\pi$
$348$	−6.81655	+	4.38073i	−0.365406	+	0.234832i
$349$	4.01725	+	27.9406i	0.215039	+	1.49563i	0.755996	+	0.654576i	$0.227153\pi$
$349$	4.01725	+	27.9406i	0.215039	+	1.49563i	−0.540958	+	0.841050i	$0.681938\pi$
$350$	0.339028	+	0.742367i	0.0181218	+	0.0396812i
$351$	0.339885	−	2.36395i	0.0181417	−	0.126179i
$352$	2.51123	−	0.737365i	0.133849	−	0.0393017i
$353$	22.0142	+	14.1477i	1.17170	+	0.753004i	0.973842	−	0.227228i	$-0.0729662\pi$
$353$	22.0142	+	14.1477i	1.17170	+	0.753004i	0.197855	+	0.980231i	$0.436603\pi$
$354$	−0.802027	+	1.75619i	−0.0426272	+	0.0933406i
$355$	−0.198206	−	0.0581986i	−0.0105197	−	0.00308886i
$356$	−6.90398	−	7.96762i	−0.365910	−	0.422283i
$357$	−2.44087	−	2.81691i	−0.129185	−	0.149087i
$358$	−2.70280	−	0.793613i	−0.142847	−	0.0419437i
$359$	2.51179	−	5.50005i	0.132567	−	0.290282i	−0.831694	−	0.555234i	$-0.812629\pi$
$359$	2.51179	−	5.50005i	0.132567	−	0.290282i	0.964262	+	0.264952i	$0.0853561\pi$
$360$	−0.841254	−	0.540641i	−0.0443380	−	0.0284943i
$361$	−39.3071	+	11.5416i	−2.06879	+	0.607453i
$362$	−3.36374	+	23.3953i	−0.176794	+	1.22963i
$363$	1.72397	+	3.77497i	0.0904849	+	0.198134i
$364$	−0.277386	−	1.92927i	−0.0145390	−	0.101121i
$365$	9.15046	−	5.88064i	0.478957	−	0.307807i
$366$	3.67059	−	4.23609i	0.191865	−	0.221424i
$367$	8.51586			0.444524			0.222262	−	0.974987i	$-0.428656\pi$
$367$	8.51586			0.444524			0.222262	+	0.974987i	$0.428656\pi$
$368$	−2.95843	+	3.77461i	−0.154219	+	0.196765i
$369$	2.51301			0.130822
$370$	−7.20186	+	8.31139i	−0.374407	+	0.432089i
$371$	−0.572881	+	0.368168i	−0.0297425	+	0.0191143i
$372$	1.14599	+	7.97050i	0.0594166	+	0.413251i
$373$	−2.92770	−	6.41076i	−0.151590	−	0.331937i	0.818568	−	0.574410i	$-0.194769\pi$
$373$	−2.92770	−	6.41076i	−0.151590	−	0.331937i	−0.970158	+	0.242473i	$0.922041\pi$
$374$	−1.70113	+	11.8317i	−0.0879636	+	0.611800i
$375$	−0.959493	+	0.281733i	−0.0495480	+	0.0145486i
$376$	−2.19000	−	1.40743i	−0.112941	−	0.0725825i
$377$	8.03901	−	17.6030i	0.414030	−	0.906599i
$378$	0.783059	+	0.229927i	0.0402762	+	0.0118262i
$379$	6.36904	+	7.35027i	0.327156	+	0.377558i	0.895370	−	0.445323i	$-0.146911\pi$
$379$	6.36904	+	7.35027i	0.327156	+	0.377558i	−0.568214	+	0.822881i	$0.692366\pi$
$380$	−5.07111	−	5.85238i	−0.260143	−	0.300221i
$381$	19.7862	+	5.80974i	1.01368	+	0.297642i
$382$	−3.87446	+	8.48388i	−0.198235	+	0.434073i
$383$	−7.15086	−	4.59558i	−0.365392	−	0.234823i	0.345042	−	0.938587i	$-0.387865\pi$
$383$	−7.15086	−	4.59558i	−0.365392	−	0.234823i	−0.710434	+	0.703764i	$0.751501\pi$
$384$	0.959493	−	0.281733i	0.0489639	−	0.0143771i
$385$	−0.303982	+	2.11424i	−0.0154924	+	0.107752i
$386$	−3.94591	−	8.64035i	−0.200842	−	0.439782i
$387$	0.125931	+	0.875872i	0.00640145	+	0.0445231i
$388$	11.2389	−	7.22279i	0.570567	−	0.366681i
$389$	−8.64275	+	9.97427i	−0.438205	+	0.505715i	−0.931297	−	0.364262i	$-0.881321\pi$
$389$	−8.64275	+	9.97427i	−0.438205	+	0.505715i	0.493092	+	0.869977i	$0.335867\pi$
$390$	2.38826			0.120934
$391$	−10.0684	−	19.4519i	−0.509179	−	0.983725i
$392$	−6.33395			−0.319913
$393$	−9.19553	+	10.6122i	−0.463853	+	0.535315i
$394$	3.44696	−	2.21522i	0.173655	−	0.111601i
$395$	2.29609	+	15.9696i	0.115529	+	0.803519i
$396$	−1.08725	−	2.38074i	−0.0546362	−	0.119636i
$397$	0.456657	−	3.17612i	0.0229189	−	0.159405i	−0.975148	−	0.221555i	$-0.928887\pi$
$397$	0.456657	−	3.17612i	0.0229189	−	0.159405i	0.998067	+	0.0621504i	$0.0197958\pi$
$398$	10.6121	−	3.11600i	0.531937	−	0.156191i
$399$	5.31660	+	3.41677i	0.266163	+	0.171053i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	−15.3768	−	4.51505i	−0.767883	−	0.225471i	−0.125748	−	0.992062i	$-0.540133\pi$
$401$	−15.3768	−	4.51505i	−0.767883	−	0.225471i	−0.642135	+	0.766591i	$0.721951\pi$
$402$	−3.11886	−	3.59935i	−0.155555	−	0.179519i
$403$	−12.5939	−	14.5341i	−0.627346	−	0.723996i
$404$	1.03262	+	0.303206i	0.0513750	+	0.0150850i
$405$	−0.415415	+	0.909632i	−0.0206421	+	0.0452000i
$406$	5.56311	+	3.57519i	0.276093	+	0.177434i
$407$	−27.6174	+	8.10921i	−1.36894	+	0.401958i
$408$	−0.649970	+	4.52064i	−0.0321783	+	0.223805i
$409$	−6.32191	−	13.8430i	−0.312598	−	0.684495i	0.686492	−	0.727137i	$-0.259150\pi$
$409$	−6.32191	−	13.8430i	−0.312598	−	0.684495i	−0.999090	+	0.0426425i	$0.986422\pi$
$410$	0.357639	+	2.48744i	0.0176625	+	0.122846i
$411$	9.89854	−	6.36140i	0.488259	−	0.313785i
$412$	6.60318	−	7.62047i	0.325315	−	0.375434i
$413$	1.57565			0.0775326
$414$	4.15722	+	2.39114i	0.204316	+	0.117518i
$415$	−0.682033			−0.0334797
$416$	−1.56398	+	1.80493i	−0.0766804	+	0.0884939i
$417$	−12.5302	+	8.05265i	−0.613605	+	0.394340i
$418$	−2.88436	−	20.0612i	−0.141079	−	0.981225i
$419$	11.5379	+	25.2644i	0.563662	+	1.23425i	0.950104	+	0.311933i	$0.100976\pi$
$419$	11.5379	+	25.2644i	0.563662	+	1.23425i	−0.386443	+	0.922313i	$0.626296\pi$
$420$	−0.116146	+	0.807811i	−0.00566733	+	0.0394171i
$421$	−10.2935	+	3.02246i	−0.501676	+	0.147305i	−0.522773	−	0.852472i	$-0.675102\pi$
$421$	−10.2935	+	3.02246i	−0.501676	+	0.147305i	0.0210966	+	0.999777i	$0.493284\pi$
$422$	11.4153	+	7.33617i	0.555688	+	0.357119i
$423$	−1.08143	+	2.36801i	−0.0525810	+	0.115136i
$424$	0.800620	+	0.235083i	0.0388816	+	0.0114167i
$425$	2.99083	+	3.45160i	0.145077	+	0.167427i
$426$	−0.135277	−	0.156118i	−0.00655420	−	0.00756395i
$427$	−4.38916	−	1.28877i	−0.212406	−	0.0623682i
$428$	6.81713	−	14.9274i	0.329518	−	0.721545i
$429$	5.25841	+	3.37938i	0.253879	+	0.163158i
$430$	−0.849035	+	0.249299i	−0.0409441	+	0.0120223i
$431$	−3.72449	+	25.9044i	−0.179402	+	1.24777i	0.678748	+	0.734372i	$0.262523\pi$
$431$	−3.72449	+	25.9044i	−0.179402	+	1.24777i	−0.858150	+	0.513399i	$0.828386\pi$
$432$	−0.415415	−	0.909632i	−0.0199867	−	0.0437647i
$433$	−0.998097	−	6.94192i	−0.0479655	−	0.333607i	−0.999648	−	0.0265241i	$-0.991556\pi$
$433$	−0.998097	−	6.94192i	−0.0479655	−	0.333607i	0.951683	−	0.307083i	$-0.0993530\pi$
$434$	5.52851	−	3.55296i	0.265377	−	0.170548i
$435$	−5.30624	+	6.12373i	−0.254415	+	0.293610i
$436$	9.80345			0.469500
$437$	25.6720	+	26.8362i	1.22806	+	1.28375i
$438$	10.8772			0.519731
$439$	13.1793	−	15.2098i	0.629016	−	0.725923i	−0.348377	−	0.937355i	$-0.613267\pi$
$439$	13.1793	−	15.2098i	0.629016	−	0.725923i	0.977393	+	0.211431i	$0.0678125\pi$
$440$	2.20177	−	1.41499i	0.104965	−	0.0674572i
$441$	0.901415	+	6.26948i	0.0429245	+	0.298547i
$442$	−4.53114	−	9.92181i	−0.215524	−	0.471932i
$443$	0.869276	−	6.04595i	0.0413006	−	0.287252i	−0.958695	−	0.284435i	$-0.908194\pi$
$443$	0.869276	−	6.04595i	0.0413006	−	0.287252i	0.999996	−	0.00281722i	$-0.000896751\pi$
$444$	−10.5521	+	3.09837i	−0.500779	+	0.147042i
$445$	−8.86906	−	5.69980i	−0.420434	−	0.270196i
$446$	3.73258	−	8.17321i	0.176743	−	0.387013i
$447$	18.2841	+	5.36870i	0.864809	+	0.253931i
$448$	−0.534443	−	0.616781i	−0.0252501	−	0.0291401i
$449$	−2.95167	−	3.40641i	−0.139298	−	0.160759i	0.681814	−	0.731526i	$-0.261191\pi$
$449$	−2.95167	−	3.40641i	−0.139298	−	0.160759i	−0.821112	+	0.570767i	$0.806646\pi$
$450$	−0.959493	−	0.281733i	−0.0452309	−	0.0132810i
$451$	−2.73226	+	5.98282i	−0.128657	+	0.281720i
$452$	−8.20165	−	5.27088i	−0.385773	−	0.247921i
$453$	−21.2618	+	6.24301i	−0.998964	+	0.293322i
$454$	−1.21295	+	8.43624i	−0.0569265	+	0.395933i
$455$	−0.809687	−	1.77297i	−0.0379587	−	0.0831180i
$456$	−1.10206	−	7.66498i	−0.0516086	−	0.358946i
$457$	0.968615	−	0.622491i	0.0453099	−	0.0291189i	−0.517790	−	0.855508i	$-0.673245\pi$
$457$	0.968615	−	0.622491i	0.0453099	−	0.0291189i	0.563100	+	0.826389i	$0.309609\pi$
$458$	16.1180	−	18.6011i	0.753143	−	0.869173i
$459$	4.56713			0.213175
$460$	−1.77516	+	4.45520i	−0.0827675	+	0.207725i
$461$	−31.9504			−1.48808			−0.744039	−	0.668136i	$-0.767093\pi$
$461$	−31.9504			−1.48808			−0.744039	+	0.668136i	$0.767093\pi$
$462$	−1.39877	+	1.61427i	−0.0650768	+	0.0751026i
$463$	−1.62649	+	1.04528i	−0.0755893	+	0.0485783i	−0.577890	−	0.816115i	$-0.696124\pi$
$463$	−1.62649	+	1.04528i	−0.0755893	+	0.0485783i	0.502300	+	0.864693i	$0.332487\pi$
$464$	−1.15316	−	8.02038i	−0.0535339	−	0.372337i
$465$	3.34511	+	7.32478i	0.155126	+	0.339678i
$466$	−0.687755	+	4.78344i	−0.0318596	+	0.221589i
$467$	−3.41514	+	1.00277i	−0.158034	+	0.0464029i	−0.359792	−	0.933032i	$-0.617152\pi$
$467$	−3.41514	+	1.00277i	−0.158034	+	0.0464029i	0.201759	+	0.979435i	$0.435334\pi$
$468$	2.00914	+	1.29119i	0.0928723	+	0.0596854i
$469$	−1.61466	+	3.53562i	−0.0745582	+	0.163260i
$470$	−2.49781	−	0.733422i	−0.115215	−	0.0338302i
$471$	2.70050	+	3.11654i	0.124432	+	0.143603i
$472$	−1.26432	−	1.45910i	−0.0581949	−	0.0671605i
$473$	−2.22214	−	0.652478i	−0.102174	−	0.0300010i
$474$	−6.70224	+	14.6759i	−0.307844	+	0.674085i
$475$	−6.51450	−	4.18662i	−0.298906	−	0.192095i
$476$	3.57633	−	1.05011i	0.163921	−	0.0481315i
$477$	0.118750	−	0.825927i	0.00543721	−	0.0378166i
$478$	−4.04871	−	8.86543i	−0.185184	−	0.405495i
$479$	1.01598	+	7.06630i	0.0464213	+	0.322867i	0.999779	+	0.0210243i	$0.00669274\pi$
$479$	1.01598	+	7.06630i	0.0464213	+	0.322867i	−0.953358	+	0.301843i	$0.902398\pi$
$480$	0.841254	−	0.540641i	0.0383978	−	0.0246768i
$481$	17.1999	−	19.8498i	0.784250	−	0.905073i
$482$	10.0925			0.459701
$483$	0.365689	−	3.89684i	0.0166394	−	0.177312i
$484$	−4.14999			−0.188636
$485$	8.74873	−	10.0966i	0.397259	−	0.458462i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	3.85456	+	26.8090i	0.174667	+	1.21483i	0.868865	+	0.495049i	$0.164850\pi$
$487$	3.85456	+	26.8090i	0.174667	+	1.21483i	−0.694198	+	0.719784i	$0.744241\pi$
$488$	2.32846	+	5.09862i	0.105405	+	0.230804i
$489$	−0.881125	+	6.12836i	−0.0398458	+	0.277134i
$490$	−6.07738	+	1.78448i	−0.274548	+	0.0806146i
$491$	24.1905	+	15.5463i	1.09170	+	0.701594i	0.957231	−	0.289323i	$-0.0934303\pi$
$491$	24.1905	+	15.5463i	1.09170	+	0.701594i	0.134470	+	0.990918i	$0.457067\pi$
$492$	−1.04394	+	2.28592i	−0.0470646	+	0.103057i
$493$	35.5077	+	10.4260i	1.59919	+	0.469564i
$494$	12.1112	+	13.9770i	0.544907	+	0.628856i
$495$	−1.71394	−	1.97799i	−0.0770357	−	0.0889039i
$496$	−7.72628	−	2.26864i	−0.346920	−	0.101865i
$497$	−0.0700343	+	0.153354i	−0.00314147	+	0.00687885i
$498$	−0.573763	−	0.368735i	−0.0257109	−	0.0165234i
$499$	12.7909	−	3.75573i	0.572597	−	0.168130i	0.0174003	−	0.999849i	$-0.494461\pi$
$499$	12.7909	−	3.75573i	0.572597	−	0.168130i	0.555197	+	0.831719i	$0.312643\pi$
$500$	0.142315	−	0.989821i	0.00636451	−	0.0442662i
$501$	−8.74907	−	19.1578i	−0.390879	−	0.855907i
$502$	−3.04857	−	21.2033i	−0.136064	−	0.946349i
$503$	19.1789	−	12.3255i	0.855144	−	0.549568i	−0.0380312	−	0.999277i	$-0.512109\pi$
$503$	19.1789	−	12.3255i	0.855144	−	0.549568i	0.893175	+	0.449709i	$0.148472\pi$
$504$	−0.534443	+	0.616781i	−0.0238060	+	0.0274736i
$505$	1.07622			0.0478911
$506$	−10.2126	+	7.29749i	−0.454005	+	0.324413i
$507$	7.29620			0.324035
$508$	−13.5042	+	15.5847i	−0.599152	+	0.691458i
$509$	10.2266	−	6.57223i	0.453286	−	0.291309i	−0.294008	−	0.955803i	$-0.594989\pi$
$509$	10.2266	−	6.57223i	0.453286	−	0.291309i	0.747294	+	0.664494i	$0.231353\pi$
$510$	0.649970	+	4.52064i	0.0287811	+	0.200177i
$511$	−3.68766	−	8.07485i	−0.163132	−	0.357210i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	−7.43013	+	2.18168i	−0.328048	+	0.0963236i
$514$	12.9576	+	8.32732i	0.571533	+	0.367302i
$515$	4.18877	−	9.17212i	0.184579	−	0.404172i
$516$	−0.849035	−	0.249299i	−0.0373767	−	0.0109748i
$517$	−4.46181	−	5.14921i	−0.196230	−	0.226462i
$518$	5.87757	+	6.78307i	0.258245	+	0.298031i
$519$	9.06299	+	2.66113i	0.397821	+	0.116811i
$520$	−0.992121	+	2.17244i	−0.0435074	+	0.0952678i
$521$	−3.35044	−	2.15320i	−0.146785	−	0.0943333i	0.465187	−	0.885213i	$-0.345987\pi$
$521$	−3.35044	−	2.15320i	−0.146785	−	0.0943333i	−0.611972	+	0.790879i	$0.709624\pi$
$522$	−7.77463	+	2.28284i	−0.340286	+	0.0999171i
$523$	−2.26293	+	15.7390i	−0.0989511	+	0.688220i	0.878606	+	0.477548i	$0.158474\pi$
$523$	−2.26293	+	15.7390i	−0.0989511	+	0.688220i	−0.977557	+	0.210672i	$0.932435\pi$
$524$	−5.83324	−	12.7730i	−0.254826	−	0.557992i
$525$	0.116146	+	0.807811i	0.00506901	+	0.0352558i
$526$	5.90416	−	3.79437i	0.257433	−	0.165442i
$527$	24.0836	−	27.7939i	1.04910	−	1.21072i
$528$	2.61725			0.113901
$529$	7.45161	−	21.7594i	0.323983	−	0.946063i
$530$	0.834420			0.0362449
$531$	−1.26432	+	1.45910i	−0.0548666	+	0.0633195i
$532$	−5.31660	+	3.41677i	−0.230504	+	0.148136i
$533$	−0.854137	−	5.94065i	−0.0369968	−	0.257318i
$534$	−4.37958	−	9.58995i	−0.189523	−	0.414998i
$535$	2.33544	−	16.2434i	0.100970	−	0.702262i
$536$	4.56971	−	1.34179i	0.197381	−	0.0579564i
$537$	−2.36973	−	1.52293i	−0.102261	−	0.0657194i
$538$	−7.51085	+	16.4465i	−0.323816	+	0.709057i
$539$	−15.9060	−	4.67043i	−0.685122	−	0.201170i
$540$	−0.654861	−	0.755750i	−0.0281807	−	0.0325223i
$541$	−10.4360	−	12.0438i	−0.448680	−	0.517804i	0.485679	−	0.874137i	$-0.338572\pi$
$541$	−10.4360	−	12.0438i	−0.448680	−	0.517804i	−0.934359	+	0.356333i	$0.884027\pi$
$542$	6.36157	+	1.86793i	0.273253	+	0.0802343i
$543$	−9.81870	+	21.4999i	−0.421361	+	0.922651i
$544$	−3.84211	−	2.46917i	−0.164729	−	0.105865i
$545$	9.40634	−	2.76195i	0.402924	−	0.118309i
$546$	0.277386	−	1.92927i	0.0118710	−	0.0825649i
$547$	−3.29764	−	7.22082i	−0.140997	−	0.308740i	0.825939	−	0.563759i	$-0.190645\pi$
$547$	−3.29764	−	7.22082i	−0.140997	−	0.308740i	−0.966936	+	0.255019i	$0.917918\pi$
$548$	1.67454	+	11.6467i	0.0715326	+	0.497520i
$549$	4.71535	−	3.03037i	0.201246	−	0.129333i
$550$	1.71394	−	1.97799i	0.0730825	−	0.0843417i
$551$	−62.7469			−2.67311
$552$	−3.90203	+	2.78822i	−0.166081	+	0.118675i
$553$	13.1671			0.559923
$554$	7.57380	−	8.74063i	0.321780	−	0.371354i
$555$	−9.25173	+	5.94572i	−0.392714	+	0.252382i
$556$	−2.11973	−	14.7430i	−0.0898965	−	0.625244i
$557$	−5.36857	−	11.7555i	−0.227474	−	0.498098i	0.761137	−	0.648591i	$-0.224641\pi$
$557$	−5.36857	−	11.7555i	−0.227474	−	0.498098i	−0.988611	+	0.150493i	$0.951914\pi$
$558$	−1.14599	+	7.97050i	−0.0485134	+	0.337418i
$559$	2.02772	−	0.595392i	0.0857634	−	0.0251824i
$560$	−0.686562	−	0.441227i	−0.0290125	−	0.0186452i
$561$	−4.96559	+	10.8731i	−0.209647	+	0.459064i
$562$	−8.61567	−	2.52979i	−0.363430	−	0.106713i
$563$	−6.09842	−	7.03795i	−0.257018	−	0.296614i	0.612546	−	0.790435i	$-0.290145\pi$
$563$	−6.09842	−	7.03795i	−0.257018	−	0.296614i	−0.869564	+	0.493821i	$0.835600\pi$
$564$	−1.70477	−	1.96741i	−0.0717838	−	0.0828429i
$565$	−9.35441	−	2.74670i	−0.393543	−	0.115555i
$566$	11.2010	−	24.5268i	0.470813	−	1.03094i
$567$	0.686562	+	0.441227i	0.0288329	+	0.0185298i
$568$	0.198206	−	0.0581986i	0.00831655	−	0.00244196i
$569$	6.07546	−	42.2557i	0.254696	−	1.77145i	−0.314507	−	0.949255i	$-0.601839\pi$
$569$	6.07546	−	42.2557i	0.254696	−	1.77145i	0.569203	−	0.822197i	$-0.307252\pi$
$570$	−3.21689	−	7.04401i	−0.134741	−	0.295041i
$571$	−0.225406	−	1.56773i	−0.00943294	−	0.0656075i	0.984561	−	0.175040i	$-0.0560056\pi$
$571$	−0.225406	−	1.56773i	−0.00943294	−	0.0656075i	−0.993994	+	0.109433i	$0.965097\pi$
$572$	−5.25841	+	3.37938i	−0.219865	+	0.141299i
$573$	−6.10770	+	7.04866i	−0.255153	+	0.294462i
$574$	2.05092			0.0856036
$575$	−0.448084	+	4.77485i	−0.0186864	+	0.199125i
$576$	1.00000			0.0416667
$577$	17.3322	−	20.0025i	0.721551	−	0.832714i	−0.269942	−	0.962877i	$-0.587005\pi$
$577$	17.3322	−	20.0025i	0.721551	−	0.832714i	0.991493	+	0.130163i	$0.0415500\pi$
$578$	3.24609	−	2.08614i	0.135020	−	0.0867718i
$579$	−1.35181	−	9.40205i	−0.0561793	−	0.390736i
$580$	−3.36605	−	7.37062i	−0.139768	−	0.306048i
$581$	−0.0792152	+	0.550954i	−0.00328640	+	0.0228574i
$582$	12.8185	−	3.76386i	0.531345	−	0.156017i
$583$	1.83720	+	1.18070i	0.0760892	+	0.0488996i
$584$	−4.51854	+	9.89422i	−0.186978	+	0.409426i
$585$	2.29152	+	0.672852i	0.0947428	+	0.0278190i
$586$	−16.0010	−	18.4662i	−0.660997	−	0.762831i
$587$	−3.59824	−	4.15259i	−0.148515	−	0.171396i	0.676617	−	0.736335i	$-0.263445\pi$
$587$	−3.59824	−	4.15259i	−0.148515	−	0.171396i	−0.825133	+	0.564939i	$0.808900\pi$
$588$	−6.07738	−	1.78448i	−0.250627	−	0.0735907i
$589$	−25.9039	+	56.7217i	−1.06735	+	2.33718i
$590$	−1.62418	−	1.04380i	−0.0668663	−	0.0429724i
$591$	3.93143	−	1.15437i	0.161717	−	0.0474845i
$592$	1.56511	−	10.8856i	0.0643258	−	0.447396i
$593$	−3.93307	−	8.61222i	−0.161512	−	0.353661i	0.811523	−	0.584321i	$-0.198639\pi$
$593$	−3.93307	−	8.61222i	−0.161512	−	0.353661i	−0.973035	+	0.230659i	$0.925912\pi$
$594$	−0.372474	−	2.59061i	−0.0152828	−	0.106294i
$595$	3.13561	−	2.01514i	0.128548	−	0.0826126i
$596$	−12.4790	+	14.4016i	−0.511161	+	0.589911i
$597$	11.0601			0.452661
$598$	4.23956	−	10.6402i	0.173369	−	0.435110i
$599$	9.02446			0.368730			0.184365	−	0.982858i	$-0.440977\pi$
$599$	9.02446			0.368730			0.184365	+	0.982858i	$0.440977\pi$
$600$	0.654861	−	0.755750i	0.0267346	−	0.0308533i
$601$	28.7506	−	18.4769i	1.17276	−	0.753688i	0.198720	−	0.980056i	$-0.436322\pi$
$601$	28.7506	−	18.4769i	1.17276	−	0.753688i	0.974042	+	0.226368i	$0.0726851\pi$
$602$	0.102775	+	0.714814i	0.00418879	+	0.0291337i
$603$	−1.97847	−	4.33224i	−0.0805694	−	0.176422i
$604$	3.15361	−	21.9338i	0.128318	−	0.892474i
$605$	−3.98189	+	1.16919i	−0.161887	+	0.0475343i
$606$	0.905372	+	0.581847i	0.0367782	+	0.0236359i
$607$	3.07877	−	6.74156i	0.124963	−	0.273632i	−0.836802	−	0.547505i	$-0.815578\pi$
$607$	3.07877	−	6.74156i	0.124963	−	0.273632i	0.961766	+	0.273874i	$0.0883050\pi$
$608$	7.43013	+	2.18168i	0.301331	+	0.0884789i
$609$	4.33052	+	4.99768i	0.175481	+	0.202516i
$610$	3.67059	+	4.23609i	0.148618	+	0.171514i
$611$	5.96542	+	1.75161i	0.241335	+	0.0708624i
$612$	−1.89725	+	4.15440i	−0.0766919	+	0.167932i
$613$	36.9822	+	23.7670i	1.49370	+	0.959940i	0.995688	+	0.0927666i	$0.0295710\pi$
$613$	36.9822	+	23.7670i	1.49370	+	0.959940i	0.498007	+	0.867173i	$0.334065\pi$
$614$	−31.0188	+	9.10795i	−1.25182	+	0.367567i
$615$	−0.357639	+	2.48744i	−0.0144214	+	0.100303i
$616$	−0.887320	−	1.94296i	−0.0357512	−	0.0782841i
$617$	1.16292	+	8.08827i	0.0468173	+	0.325622i	0.999748	+	0.0224344i	$0.00714169\pi$
$617$	1.16292	+	8.08827i	0.0468173	+	0.325622i	−0.952931	+	0.303187i	$0.901949\pi$
$618$	8.48264	−	5.45146i	0.341222	−	0.219290i
$619$	11.5178	−	13.2923i	0.462940	−	0.534262i	−0.475494	−	0.879719i	$-0.657731\pi$
$619$	11.5178	−	13.2923i	0.462940	−	0.534262i	0.938434	+	0.345457i	$0.112276\pi$
$620$	−8.05246			−0.323395
$621$	3.31516	+	3.46550i	0.133033	+	0.139066i
$622$	15.3309			0.614712
$623$	−5.63446	+	6.50252i	−0.225740	+	0.260518i
$624$	−2.00914	+	1.29119i	−0.0804298	+	0.0516891i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	−8.96140	−	19.6227i	−0.358170	−	0.784282i
$627$	2.88436	−	20.0612i	0.115190	−	0.801167i
$628$	−3.95673	+	1.16180i	−0.157891	+	0.0463609i
$629$	42.2538	+	27.1549i	1.68477	+	1.08274i
$630$	−0.339028	+	0.742367i	−0.0135072	+	0.0295766i
$631$	11.6207	+	3.41214i	0.462613	+	0.135835i	0.504730	−	0.863277i	$-0.331592\pi$
$631$	11.6207	+	3.41214i	0.462613	+	0.135835i	−0.0421172	+	0.999113i	$0.513410\pi$
$632$	−10.5654	−	12.1932i	−0.420270	−	0.485018i
$633$	8.88606	+	10.2551i	0.353189	+	0.407602i
$634$	27.6482	+	8.11824i	1.09805	+	0.322417i
$635$	−8.56647	+	18.7580i	−0.339950	+	0.744387i
$636$	0.701959	+	0.451122i	0.0278345	+	0.0178881i
$637$	14.5144	−	4.26181i	0.575081	−	0.168859i
$638$	3.01810	−	20.9914i	0.119488	−	0.831056i
$639$	−0.0858139	−	0.187906i	−0.00339475	−	0.00743346i
$640$	0.142315	+	0.989821i	0.00562549	+	0.0391261i
$641$	−5.82437	+	3.74310i	−0.230049	+	0.147843i	−0.650588	−	0.759431i	$-0.725477\pi$
$641$	−5.82437	+	3.74310i	−0.230049	+	0.147843i	0.420539	+	0.907274i	$0.361841\pi$
$642$	10.7465	−	12.4022i	0.424132	−	0.489474i
$643$	−24.6438			−0.971855			−0.485928	−	0.873999i	$-0.661518\pi$
$643$	−24.6438			−0.971855			−0.485928	+	0.873999i	$0.661518\pi$
$644$	3.39278	+	1.95145i	0.133694	+	0.0768979i
$645$	−0.884878			−0.0348421
$646$	−23.1604	+	26.7285i	−0.911234	+	1.05162i
$647$	32.3568	−	20.7945i	1.27208	−	0.817514i	0.282188	−	0.959359i	$-0.408940\pi$
$647$	32.3568	−	20.7945i	1.27208	−	0.817514i	0.989889	+	0.141845i	$0.0453033\pi$
$648$	−0.142315	−	0.989821i	−0.00559065	−	0.0388839i
$649$	−2.09911	−	4.59640i	−0.0823971	−	0.180425i
$650$	−0.339885	+	2.36395i	−0.0133314	+	0.0927219i
$651$	6.30556	−	1.85148i	0.247134	−	0.0725651i
$652$	−5.20852	−	3.34731i	−0.203981	−	0.131091i
$653$	14.8535	−	32.5246i	0.581262	−	1.27279i	−0.359319	−	0.933215i	$-0.616991\pi$
$653$	14.8535	−	32.5246i	0.581262	−	1.27279i	0.940581	−	0.339570i	$-0.110282\pi$
$654$	9.40634	+	2.76195i	0.367817	+	0.108001i
$655$	−9.19553	−	10.6122i	−0.359299	−	0.414653i
$656$	−1.64567	−	1.89921i	−0.0642528	−	0.0741517i
$657$	10.4366	+	3.06445i	0.407169	+	0.119556i
$658$	−0.882576	+	1.93257i	−0.0344064	+	0.0753395i
$659$	28.2386	+	18.1478i	1.10002	+	0.706939i	0.959096	−	0.283082i	$-0.0913567\pi$
$659$	28.2386	+	18.1478i	1.10002	+	0.706939i	0.140923	+	0.990021i	$0.454993\pi$
$660$	2.51123	−	0.737365i	0.0977497	−	0.0287019i
$661$	−3.66823	+	25.5131i	−0.142678	+	0.992346i	0.785142	+	0.619316i	$0.212590\pi$
$661$	−3.66823	+	25.5131i	−0.142678	+	0.992346i	−0.927819	+	0.373030i	$0.878319\pi$
$662$	11.4691	+	25.1138i	0.445759	+	0.976076i
$663$	−1.55230	−	10.7965i	−0.0602863	−	0.419300i
$664$	0.573763	−	0.368735i	0.0222663	−	0.0143097i
$665$	−4.13863	+	4.77623i	−0.160489	+	0.185214i
$666$	−10.9975			−0.426146
$667$	17.8630	+	34.5110i	0.691657	+	1.33627i
$668$	21.0610			0.814876
$669$	5.88405	−	6.79055i	0.227490	−	0.262538i
$670$	4.00658	−	2.57487i	0.154788	−	0.0994759i
$671$	2.08777	+	14.5208i	0.0805975	+	0.560568i
$672$	−0.339028	−	0.742367i	−0.0130783	−	0.0286374i
$673$	2.96744	−	20.6390i	0.114386	−	0.795574i	−0.849180	−	0.528104i	$-0.822903\pi$
$673$	2.96744	−	20.6390i	0.114386	−	0.795574i	0.963566	−	0.267470i	$-0.0861876\pi$
$674$	15.9896	−	4.69497i	0.615896	−	0.180843i
$675$	−0.841254	−	0.540641i	−0.0323799	−	0.0208093i
$676$	−3.03095	+	6.63685i	−0.116575	+	0.255264i
$677$	−26.2845	−	7.71781i	−1.01019	−	0.296620i	−0.265561	−	0.964094i	$-0.585557\pi$
$677$	−26.2845	−	7.71781i	−1.01019	−	0.296620i	−0.744633	+	0.667474i	$0.767375\pi$
$678$	−6.38445	−	7.36805i	−0.245193	−	0.282968i
$679$	−7.13999	−	8.23999i	−0.274008	−	0.316222i
$680$	−4.38212	−	1.28671i	−0.168047	−	0.0493430i
$681$	−3.54058	+	7.75279i	−0.135675	+	0.297088i
$682$	−17.7297	−	11.3942i	−0.678905	−	0.436306i
$683$	5.59992	−	1.64428i	0.214275	−	0.0629168i	−0.172833	−	0.984951i	$-0.555292\pi$
$683$	5.59992	−	1.64428i	0.214275	−	0.0629168i	0.387108	+	0.922034i	$0.373474\pi$
$684$	1.10206	−	7.66498i	0.0421383	−	0.293078i
$685$	4.88795	+	10.7031i	0.186759	+	0.408945i
$686$	1.54868	+	10.7713i	0.0591289	+	0.411251i
$687$	20.7056	−	13.3067i	0.789969	−	0.507682i
$688$	0.579472	−	0.668747i	0.0220922	−	0.0254957i
$689$	−1.99282			−0.0759202
$690$	−2.95843	+	3.77461i	−0.112626	+	0.143697i
$691$	8.65111			0.329104			0.164552	−	0.986368i	$-0.447382\pi$
$691$	8.65111			0.329104			0.164552	+	0.986368i	$0.447382\pi$
$692$	−6.18555	+	7.13851i	−0.235139	+	0.271365i
$693$	−1.79691	+	1.15480i	−0.0682588	+	0.0438673i
$694$	−1.14430	−	7.95879i	−0.0434371	−	0.302112i
$695$	−6.18746	−	13.5486i	−0.234704	−	0.513929i
$696$	1.15316	−	8.02038i	0.0437103	−	0.304012i
$697$	11.0123	−	3.23352i	0.417122	−	0.122478i
$698$	−23.7468	−	15.2612i	−0.898831	−	0.577644i
$699$	−2.00755	+	4.39592i	−0.0759324	+	0.166269i
$700$	−0.783059	−	0.229927i	−0.0295969	−	0.00869042i
$701$	−28.0124	−	32.3280i	−1.05801	−	1.22101i	−0.974472	−	0.224507i	$-0.927923\pi$
$701$	−28.0124	−	32.3280i	−1.05801	−	1.22101i	−0.0835400	−	0.996504i	$-0.526623\pi$
$702$	1.56398	+	1.80493i	0.0590286	+	0.0681227i
$703$	−81.7132	−	23.9932i	−3.08187	−	0.904919i
$704$	−1.08725	+	2.38074i	−0.0409771	+	0.0897274i
$705$	−2.19000	−	1.40743i	−0.0824801	−	0.0530068i
$706$	−25.1083	+	7.37246i	−0.944963	+	0.277466i
$707$	0.124998	−	0.869381i	0.00470104	−	0.0326964i
$708$	−0.802027	−	1.75619i	−0.0301420	−	0.0660018i
$709$	−2.16229	−	15.0390i	−0.0812064	−	0.564803i	−0.989284	−	0.146002i	$-0.953360\pi$
$709$	−2.16229	−	15.0390i	−0.0812064	−	0.564803i	0.908078	−	0.418801i	$-0.137550\pi$
$710$	0.173781	−	0.111682i	0.00652189	−	0.00419136i
$711$	−10.5654	+	12.1932i	−0.396234	+	0.457279i
$712$	10.5427			0.395103
$713$	38.5715	−	1.90046i	1.44451	−	0.0711727i
$714$	3.72731			0.139491
$715$	−4.09333	+	4.72395i	−0.153082	+	0.176666i
$716$	2.36973	−	1.52293i	0.0885609	−	0.0569146i
$717$	−1.38703	−	9.64697i	−0.0517994	−	0.360273i
$718$	2.51179	+	5.50005i	0.0937392	+	0.205260i
$719$	1.00084	−	6.96101i	0.0373251	−	0.259602i	−0.962611	−	0.270887i	$-0.912683\pi$
$719$	1.00084	−	6.96101i	0.0373251	−	0.259602i	0.999936	+	0.0112849i	$0.00359218\pi$
$720$	0.959493	−	0.281733i	0.0357582	−	0.0104996i
$721$	−6.92283	−	4.44903i	−0.257820	−	0.165691i
$722$	17.0181	−	37.2645i	0.633348	−	1.38684i
$723$	9.68368	+	2.84338i	0.360140	+	0.105747i
$724$	−15.4782	−	17.8628i	−0.575243	−	0.663866i
$725$	−5.30624	−	6.12373i	−0.197069	−	0.227430i
$726$	−3.98189	−	1.16919i	−0.147782	−	0.0433926i
$727$	2.16740	−	4.74595i	0.0803845	−	0.176018i	−0.865172	−	0.501475i	$-0.832791\pi$
$727$	2.16740	−	4.74595i	0.0803845	−	0.176018i	0.945557	+	0.325457i	$0.105518\pi$
$728$	1.63969	+	1.05377i	0.0607710	+	0.0390551i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−1.54798	+	10.7665i	−0.0572934	+	0.398484i
$731$	1.67884	+	3.67614i	0.0620941	+	0.135967i
$732$	0.797696	+	5.54809i	0.0294837	+	0.205063i
$733$	12.1094	−	7.78221i	0.447269	−	0.287442i	−0.297553	−	0.954705i	$-0.596171\pi$
$733$	12.1094	−	7.78221i	0.447269	−	0.287442i	0.744822	+	0.667263i	$0.232534\pi$
$734$	−5.57670	+	6.43586i	−0.205840	+	0.237552i
$735$	−6.33395			−0.233631
$736$	−0.915298	−	4.70768i	−0.0337383	−	0.173527i
$737$	12.4650			0.459154
$738$	−1.64567	+	1.89921i	−0.0605781	+	0.0699109i
$739$	28.2985	−	18.1864i	1.04098	−	0.668997i	0.0957503	−	0.995405i	$-0.469475\pi$
$739$	28.2985	−	18.1864i	1.04098	−	0.668997i	0.945229	+	0.326409i	$0.105839\pi$
$740$	−1.56511	−	10.8856i	−0.0575347	−	0.400163i
$741$	7.68279	+	16.8230i	0.282234	+	0.618007i
$742$	0.0969143	−	0.674054i	0.00355784	−	0.0247453i
$743$	−23.1249	+	6.79008i	−0.848370	+	0.249104i	−0.676890	−	0.736084i	$-0.736673\pi$
$743$	−23.1249	+	6.79008i	−0.848370	+	0.249104i	−0.171480	+	0.985188i	$0.554855\pi$
$744$	−6.77416	−	4.35349i	−0.248353	−	0.159607i
$745$	−7.91615	+	17.3340i	−0.290025	+	0.635067i
$746$	6.76216	+	1.98555i	0.247580	+	0.0726962i
$747$	−0.446637	−	0.515446i	−0.0163416	−	0.0188592i
$748$	−7.82776	−	9.03372i	−0.286211	−	0.330305i
$749$	−12.8503	−	3.77320i	−0.469541	−	0.137870i
$750$	0.415415	−	0.909632i	0.0151688	−	0.0332151i
$751$	1.98338	+	1.27464i	0.0723747	+	0.0465124i	0.576328	−	0.817219i	$-0.304485\pi$
$751$	1.98338	+	1.27464i	0.0723747	+	0.0465124i	−0.503953	+	0.863731i	$0.668122\pi$
$752$	2.49781	−	0.733422i	0.0910856	−	0.0267452i
$753$	3.04857	−	21.2033i	0.111096	−	0.772691i
$754$	8.03901	+	17.6030i	0.292763	+	0.641062i
$755$	−3.15361	−	21.9338i	−0.114771	−	0.798253i
$756$	−0.686562	+	0.441227i	−0.0249700	+	0.0160473i
$757$	−0.536935	+	0.619656i	−0.0195152	+	0.0225218i	−0.765423	−	0.643527i	$-0.777470\pi$
$757$	−0.536935	+	0.619656i	−0.0195152	+	0.0225218i	0.745908	+	0.666049i	$0.232016\pi$
$758$	−9.72580			−0.353257
$759$	−11.8548	+	4.12467i	−0.430304	+	0.149716i
$760$	7.74381			0.280897
$761$	10.4755	−	12.0894i	0.379738	−	0.438241i	−0.533418	−	0.845852i	$-0.679093\pi$
$761$	10.4755	−	12.0894i	0.379738	−	0.438241i	0.913156	+	0.407611i	$0.133638\pi$
$762$	−17.3479	+	11.1488i	−0.628448	+	0.403879i
$763$	−1.13863	−	7.91933i	−0.0412211	−	0.286699i
$764$	−3.87446	−	8.48388i	−0.140173	−	0.306936i
$765$	−0.649970	+	4.52064i	−0.0234997	+	0.163444i
$766$	8.15592	−	2.39479i	0.294685	−	0.0865274i
$767$	3.87897	+	2.49286i	0.140061	+	0.0900119i
$768$	−0.415415	+	0.909632i	−0.0149900	+	0.0328235i
$769$	1.02577	+	0.301194i	0.0369903	+	0.0108613i	0.300175	−	0.953884i	$-0.402955\pi$
$769$	1.02577	+	0.301194i	0.0369903	+	0.0108613i	−0.263185	+	0.964745i	$0.584773\pi$
$770$	−1.39877	−	1.61427i	−0.0504083	−	0.0581743i
$771$	10.0866	+	11.6406i	0.363260	+	0.419225i
$772$	9.11396	+	2.67610i	0.328019	+	0.0963150i
$773$	10.8635	−	23.7878i	0.390733	−	0.855587i	−0.607393	−	0.794401i	$-0.707785\pi$
$773$	10.8635	−	23.7878i	0.390733	−	0.855587i	0.998126	−	0.0611852i	$-0.0194880\pi$
$774$	−0.744407	−	0.478401i	−0.0267572	−	0.0171958i
$775$	−7.72628	+	2.26864i	−0.277536	+	0.0814920i
$776$	−1.90128	+	13.2237i	−0.0682520	+	0.474703i
$777$	3.72847	+	8.16421i	0.133758	+	0.292890i
$778$	−1.87825	−	13.0635i	−0.0673385	−	0.468349i
$779$	−16.3710	+	10.5210i	−0.586553	+	0.376955i
$780$	−1.56398	+	1.80493i	−0.0559995	+	0.0646268i
$781$	0.540656			0.0193462
$782$	21.2941	+	5.12913i	0.761477	+	0.183417i
$783$	−8.10285			−0.289572
$784$	4.14786	−	4.78688i	0.148138	−	0.170960i
$785$	−3.46914	+	2.22948i	−0.123819	+	0.0795735i
$786$	−1.99838	−	13.8990i	−0.0712798	−	0.495762i
$787$	22.3150	+	48.8630i	0.795444	+	1.74178i	0.660367	+	0.750943i	$0.270401\pi$
$787$	22.3150	+	48.8630i	0.795444	+	1.74178i	0.135077	+	0.990835i	$0.456872\pi$
$788$	−0.583122	+	4.05570i	−0.0207728	+	0.144478i
$789$	6.73400	−	1.97728i	0.239737	−	0.0703930i
$790$	−13.5727	−	8.72262i	−0.482894	−	0.310337i
$791$	−3.30529	+	7.23757i	−0.117523	+	0.257338i
$792$	2.51123	+	0.737365i	0.0892328	+	0.0262011i
$793$	−8.76634	−	10.1169i	−0.311302	−	0.359261i
$794$	2.10130	+	2.42503i	0.0745724	+	0.0860612i
$795$	0.800620	+	0.235083i	0.0283951	+	0.00833755i
$796$	−4.59454	+	10.0606i	−0.162849	+	0.356590i
$797$	−21.5916	−	13.8761i	−0.764813	−	0.491515i	0.0991491	−	0.995073i	$-0.468388\pi$
$797$	−21.5916	−	13.8761i	−0.764813	−	0.491515i	−0.863962	+	0.503557i	$0.832024\pi$
$798$	−6.06386	+	1.78051i	−0.214658	+	0.0630293i
$799$	−1.69204	+	11.7684i	−0.0598600	+	0.416335i
$800$	0.415415	+	0.909632i	0.0146871	+	0.0321603i
$801$	−1.50038	−	10.4354i	−0.0530133	−	0.368715i
$802$	13.4819	−	8.66432i	0.476064	−	0.305948i
$803$	−18.6428	+	21.5149i	−0.657889	+	0.759244i
$804$	4.76263			0.167965
$805$	3.80513	+	0.916545i	0.134113	+	0.0323040i
$806$	19.2314			0.677397
$807$	−11.8401	+	13.6642i	−0.416792	+	0.481003i
$808$	−0.905372	+	0.581847i	−0.0318509	+	0.0204693i
$809$	3.71620	+	25.8468i	0.130655	+	0.908724i	0.944703	+	0.327927i	$0.106350\pi$
$809$	3.71620	+	25.8468i	0.130655	+	0.908724i	−0.814048	+	0.580797i	$0.802741\pi$
$810$	−0.415415	−	0.909632i	−0.0145962	−	0.0319612i
$811$	−1.02162	+	7.10553i	−0.0358739	+	0.249509i	−0.999865	−	0.0164255i	$-0.994771\pi$
$811$	−1.02162	+	7.10553i	−0.0358739	+	0.249509i	0.963991	+	0.265934i	$0.0856804\pi$
$812$	−6.34501	+	1.86306i	−0.222666	+	0.0653807i
$813$	5.57763	+	3.58452i	0.195616	+	0.125715i
$814$	11.9570	−	26.1823i	0.419094	−	0.917688i
$815$	−5.94058	−	1.74431i	−0.208089	−	0.0611006i
$816$	−2.99083	−	3.45160i	−0.104700	−	0.120830i
$817$	−4.48732	−	5.17864i	−0.156991	−	0.181178i
$818$	14.6018	+	4.28749i	0.510542	+	0.149909i
$819$	0.809687	−	1.77297i	0.0282928	−	0.0619525i
$820$	−2.11408	−	1.35864i	−0.0738270	−	0.0474457i
$821$	−25.1991	+	7.39911i	−0.879453	+	0.258231i	−0.690131	−	0.723684i	$-0.742447\pi$
$821$	−25.1991	+	7.39911i	−0.879453	+	0.258231i	−0.189322	+	0.981915i	$0.560629\pi$
$822$	−1.67454	+	11.6467i	−0.0584061	+	0.406224i
$823$	5.12442	+	11.2209i	0.178626	+	0.391136i	0.977673	−	0.210132i	$-0.0673895\pi$
$823$	5.12442	+	11.2209i	0.178626	+	0.391136i	−0.799047	+	0.601268i	$0.794662\pi$
$824$	1.43501	+	9.98069i	0.0499908	+	0.347694i
$825$	2.20177	−	1.41499i	0.0766559	−	0.0492637i
$826$	−1.03183	+	1.19080i	−0.0359020	+	0.0414331i
$827$	−17.5310			−0.609614			−0.304807	−	0.952414i	$-0.598592\pi$
$827$	−17.5310			−0.609614			−0.304807	+	0.952414i	$0.598592\pi$
$828$	−4.52950	+	1.57595i	−0.157411	+	0.0547682i
$829$	12.2677			0.426074			0.213037	−	0.977044i	$-0.431664\pi$
$829$	12.2677			0.426074			0.213037	+	0.977044i	$0.431664\pi$
$830$	0.446637	−	0.515446i	0.0155030	−	0.0178914i
$831$	9.72952	−	6.25279i	0.337513	−	0.216907i
$832$	−0.339885	−	2.36395i	−0.0117834	−	0.0819554i
$833$	12.0171	+	26.3138i	0.416368	+	0.911719i
$834$	2.11973	−	14.7430i	0.0734002	−	0.510510i
$835$	20.2079	−	5.93358i	0.699324	−	0.205340i
$836$	17.0501	+	10.9574i	0.589690	+	0.378971i
$837$	−3.34511	+	7.32478i	−0.115624	+	0.253181i
$838$	−26.6493	−	7.82493i	−0.920583	−	0.270308i
$839$	−27.8606	−	32.1528i	−0.961854	−	1.11004i	−0.993870	−	0.110551i	$-0.964738\pi$
$839$	−27.8606	−	32.1528i	−0.961854	−	1.11004i	0.0320163	−	0.999487i	$-0.489807\pi$
$840$	−0.534443	−	0.616781i	−0.0184400	−	0.0212810i
$841$	−35.1714	−	10.3273i	−1.21281	−	0.356112i
$842$	4.45661	−	9.75863i	0.153585	−	0.336304i
$843$	−7.55396	−	4.85463i	−0.260172	−	0.167202i
$844$	−13.0197	+	3.82294i	−0.448158	+	0.131591i
$845$	−1.03836	+	7.22193i	−0.0357206	+	0.248442i
$846$	−1.08143	−	2.36801i	−0.0371804	−	0.0814137i
$847$	0.482004	+	3.35241i	0.0165618	+	0.115190i
$848$	−0.701959	+	0.451122i	−0.0241054	+	0.0154916i
$849$	17.6573	−	20.3776i	0.605996	−	0.699356i
$850$	−4.56713			−0.156651
$851$	10.0660	+	51.7729i	0.345059	+	1.77475i
$852$	0.206574			0.00707711
$853$	−24.0365	+	27.7396i	−0.822995	+	0.949787i	−0.999404	−	0.0345303i	$-0.989006\pi$
$853$	−24.0365	+	27.7396i	−0.822995	+	0.949787i	0.176409	+	0.984317i	$0.443552\pi$
$854$	3.84828	−	2.47314i	0.131685	−	0.0846291i
$855$	−1.10206	−	7.66498i	−0.0376896	−	0.262137i
$856$	6.81713	+	14.9274i	0.233005	+	0.510209i
$857$	−4.10813	+	28.5727i	−0.140331	+	0.976024i	0.790991	+	0.611828i	$0.209565\pi$
$857$	−4.10813	+	28.5727i	−0.140331	+	0.976024i	−0.931322	+	0.364197i	$0.881344\pi$
$858$	−5.99749	+	1.76102i	−0.204751	+	0.0601203i
$859$	48.8160	+	31.3721i	1.66558	+	1.07040i	0.909288	+	0.416168i	$0.136627\pi$
$859$	48.8160	+	31.3721i	1.66558	+	1.07040i	0.756291	+	0.654235i	$0.227009\pi$
$860$	0.367592	−	0.804914i	0.0125348	−	0.0274473i
$861$	1.96784	+	0.577810i	0.0670638	+	0.0196917i
$862$	−17.1382	−	19.7786i	−0.583730	−	0.673660i
$863$	23.9324	+	27.6195i	0.814669	+	0.940178i	0.999089	−	0.0426693i	$-0.0135862\pi$
$863$	23.9324	+	27.6195i	0.814669	+	0.940178i	−0.184420	+	0.982847i	$0.559041\pi$
$864$	0.959493	+	0.281733i	0.0326426	+	0.00958474i
$865$	−3.92384	+	8.59202i	−0.133415	+	0.292137i
$866$	5.89996	+	3.79168i	0.200489	+	0.128846i
$867$	3.70233	−	1.08710i	0.125738	−	0.0369200i
$868$	−0.935259	+	6.50487i	−0.0317447	+	0.220790i
$869$	−17.5415	−	38.4104i	−0.595053	−	1.30299i
$870$	−1.15316	−	8.02038i	−0.0390957	−	0.271916i
$871$	−9.56876	+	6.14947i	−0.324225	+	0.208367i
$872$	−6.41990	+	7.40896i	−0.217405	+	0.250899i
$873$	13.3597			0.452156
$874$	−37.0930	+	1.82761i	−1.25469	+	0.0618199i
$875$	−0.816118			−0.0275898
$876$	−7.12303	+	8.22041i	−0.240665	+	0.277742i
$877$	−23.1171	+	14.8565i	−0.780610	+	0.501667i	−0.869236	−	0.494398i	$-0.835389\pi$
$877$	−23.1171	+	14.8565i	−0.780610	+	0.501667i	0.0886262	+	0.996065i	$0.471752\pi$
$878$	2.86415	+	19.9206i	0.0966603	+	0.672287i
$879$	−10.1504	−	22.2262i	−0.342363	−	0.749671i
$880$	−0.372474	+	2.59061i	−0.0125561	+	0.0873295i
$881$	−32.2133	+	9.45867i	−1.08529	+	0.318671i	−0.774994	−	0.631968i	$-0.782247\pi$
$881$	−32.2133	+	9.45867i	−1.08529	+	0.318671i	−0.310299	+	0.950639i	$0.600429\pi$
$882$	−5.32846	−	3.42439i	−0.179419	−	0.115305i
$883$	−18.4181	+	40.3300i	−0.619818	+	1.35721i	0.295833	+	0.955240i	$0.404403\pi$
$883$	−18.4181	+	40.3300i	−0.619818	+	1.35721i	−0.915651	+	0.401973i	$0.868325\pi$
$884$	10.4657	+	3.07300i	0.351999	+	0.103356i
$885$	−1.26432	−	1.45910i	−0.0424995	−	0.0490471i
$886$	3.99997	+	4.61621i	0.134382	+	0.155085i
$887$	−0.114557	−	0.0336369i	−0.00384644	−	0.00112942i	0.279809	−	0.960056i	$-0.409729\pi$
$887$	−0.114557	−	0.0336369i	−0.00384644	−	0.00112942i	−0.283655	+	0.958926i	$0.591547\pi$
$888$	4.56855	−	10.0037i	0.153310	−	0.335703i
$889$	14.1579	+	9.09874i	0.474841	+	0.305162i
$890$	10.1156	−	2.97021i	0.339076	−	0.0995618i
$891$	0.372474	−	2.59061i	0.0124783	−	0.0867888i
$892$	3.73258	+	8.17321i	0.124976	+	0.273659i
$893$	−2.86894	−	19.9539i	−0.0960054	−	0.667733i
$894$	−16.0309	+	10.3025i	−0.536155	+	0.344566i
$895$	1.84468	−	2.12887i	0.0616608	−	0.0711603i
$896$	0.816118			0.0272646
$897$	7.06552	−	9.01476i	0.235911	−	0.300994i
$898$	4.50733			0.150412
$899$	−42.7283	+	49.3111i	−1.42507	+	1.64462i
$900$	0.841254	−	0.540641i	0.0280418	−	0.0180214i
$901$	−0.542348	−	3.77211i	−0.0180682	−	0.125667i
$902$	−2.73226	−	5.98282i	−0.0909744	−	0.199206i
$903$	−0.102775	+	0.714814i	−0.00342013	+	0.0237875i
$904$	9.35441	−	2.74670i	0.311123	−	0.0913539i
$905$	−19.8838	−	12.7785i	−0.660959	−	0.424772i
$906$	9.20533	−	20.1569i	0.305827	−	0.669667i
$907$	22.2816	+	6.54247i	0.739849	+	0.217239i	0.629876	−	0.776695i	$-0.283106\pi$
$907$	22.2816	+	6.54247i	0.739849	+	0.217239i	0.109972	+	0.993935i	$0.464924\pi$
$908$	−5.58138	−	6.44125i	−0.185224	−	0.213760i
$909$	0.704773	+	0.813351i	0.0233758	+	0.0269772i
$910$	1.87015	+	0.549126i	0.0619949	+	0.0182034i
$911$	−8.20139	+	17.9585i	−0.271724	+	0.594993i	−0.995470	−	0.0950735i	$-0.969691\pi$
$911$	−8.20139	+	17.9585i	−0.271724	+	0.594993i	0.723746	+	0.690066i	$0.242419\pi$
$912$	6.51450	+	4.18662i	0.215717	+	0.138633i
$913$	1.71274	−	0.502907i	0.0566836	−	0.0166438i
$914$	−0.163861	+	1.13968i	−0.00542003	+	0.0376971i
$915$	2.32846	+	5.09862i	0.0769766	+	0.168555i
$916$	3.50277	+	24.3623i	0.115735	+	0.804953i
$917$	−9.64067	+	6.19568i	−0.318363	+	0.204600i
$918$	−2.99083	+	3.45160i	−0.0987121	+	0.113920i
$919$	13.0225			0.429573			0.214787	−	0.976661i	$-0.431094\pi$
$919$	13.0225			0.429573			0.214787	+	0.976661i	$0.431094\pi$
$920$	−2.20453	−	4.25911i	−0.0726811	−	0.140419i
$921$	−32.3284			−1.06526
$922$	20.9231	−	24.1465i	0.689065	−	0.795223i
$923$	−0.415035	+	0.266727i	−0.0136610	+	0.00877942i
$924$	−0.303982	−	2.11424i	−0.0100003	−	0.0695535i
$925$	−4.56855	−	10.0037i	−0.150213	−	0.328920i
$926$	0.275153	−	1.91373i	0.00904209	−	0.0628891i
$927$	9.67488	−	2.84080i	0.317765	−	0.0933042i
$928$	6.81655	+	4.38073i	0.223764	+	0.143805i
$929$	19.8504	−	43.4664i	0.651272	−	1.42609i	−0.239165	−	0.970979i	$-0.576874\pi$
$929$	19.8504	−	43.4664i	0.651272	−	1.42609i	0.890437	−	0.455107i	$-0.150399\pi$
$930$	−7.72628	−	2.26864i	−0.253355	−	0.0743917i
$931$	−32.1202	−	37.0687i	−1.05270	−	1.21488i
$932$	−3.16470	−	3.65226i	−0.103663	−	0.119634i
$933$	14.7099	+	4.31920i	0.481579	+	0.141404i
$934$	1.47859	−	3.23767i	0.0483810	−	0.105940i
$935$	−10.0558	−	6.46245i	−0.328859	−	0.211345i
$936$	−2.29152	+	0.672852i	−0.0749007	+	0.0219928i
$937$	−6.99498	+	48.6512i	−0.228516	+	1.58936i	0.475850	+	0.879527i	$0.342141\pi$
$937$	−6.99498	+	48.6512i	−0.228516	+	1.58936i	−0.704366	+	0.709837i	$0.748768\pi$
$938$	−1.61466	−	3.53562i	−0.0527206	−	0.115442i
$939$	−3.07004	−	21.3526i	−0.100187	−	0.696816i
$940$	2.19000	−	1.40743i	0.0714299	−	0.0459052i
$941$	0.601062	−	0.693662i	0.0195940	−	0.0226127i	−0.745868	−	0.666094i	$-0.767965\pi$
$941$	0.601062	−	0.693662i	0.0195940	−	0.0226127i	0.765462	+	0.643481i	$0.222510\pi$
$942$	−4.12377			−0.134360
$943$	10.4471	+	6.00896i	0.340206	+	0.195679i
$944$	1.93066			0.0628378
$945$	−0.534443	+	0.616781i	−0.0173854	+	0.0200639i
$946$	1.94830	−	1.25210i	0.0633447	−	0.0407092i
$947$	−1.75699	−	12.2201i	−0.0570944	−	0.397100i	−0.998250	−	0.0591278i	$-0.981168\pi$
$947$	−1.75699	−	12.2201i	−0.0570944	−	0.397100i	0.941156	−	0.337972i	$-0.109741\pi$
$948$	−6.70224	−	14.6759i	−0.217679	−	0.476650i
$949$	3.69699	−	25.7131i	0.120009	−	0.834683i
$950$	7.43013	−	2.18168i	0.241065	−	0.0707831i
$951$	24.2411	+	15.5788i	0.786071	+	0.505177i
$952$	−1.54838	+	3.39048i	−0.0501833	+	0.109886i
$953$	−7.51160	−	2.20560i	−0.243325	−	0.0714465i	0.157796	−	0.987472i	$-0.449561\pi$
$953$	−7.51160	−	2.20560i	−0.243325	−	0.0714465i	−0.401121	+	0.916025i	$0.631379\pi$
$954$	0.546429	+	0.630613i	0.0176913	+	0.0204168i
$955$	−6.10770	−	7.04866i	−0.197641	−	0.228089i
$956$	9.35139	+	2.74581i	0.302445	+	0.0888060i
$957$	8.80979	−	19.2908i	0.284780	−	0.623582i
$958$	−6.00568	−	3.85961i	−0.194035	−	0.124698i
$959$	9.21380	−	2.70542i	0.297529	−	0.0873624i
$960$	−0.142315	+	0.989821i	−0.00459319	+	0.0319463i
$961$	14.0585	+	30.7839i	0.453501	+	0.993030i
$962$	3.73791	+	25.9977i	0.120515	+	0.838200i
$963$	13.8053	−	8.87214i	0.444870	−	0.285901i
$964$	−6.60918	+	7.62740i	−0.212867	+	0.245662i
$965$	9.49873			0.305775
$966$	2.70556	+	2.82826i	0.0870500	+	0.0909977i
$967$	32.8462			1.05626			0.528131	−	0.849163i	$-0.322893\pi$
$967$	32.8462			1.05626			0.528131	+	0.849163i	$0.322893\pi$
$968$	2.71767	−	3.13635i	0.0873491	−	0.100806i
$969$	−29.7526	+	19.1208i	−0.955790	+	0.614249i
$970$	1.90128	+	13.2237i	0.0610464	+	0.424587i
$971$	24.7066	+	54.0999i	0.792872	+	1.73615i	0.668242	+	0.743944i	$0.267047\pi$
$971$	24.7066	+	54.0999i	0.792872	+	1.73615i	0.124630	+	0.992203i	$0.460226\pi$
$972$	0.142315	−	0.989821i	0.00456475	−	0.0317485i
$973$	−11.6634	+	3.42468i	−0.373911	+	0.109790i
$974$	−22.7851	−	14.6431i	−0.730082	−	0.469195i
$975$	−0.992121	+	2.17244i	−0.0317733	+	0.0695738i
$976$	−5.37810	−	1.57915i	−0.172149	−	0.0505474i
$977$	25.6908	+	29.6488i	0.821923	+	0.948549i	0.999367	−	0.0355816i	$-0.0113284\pi$
$977$	25.6908	+	29.6488i	0.821923	+	0.948549i	−0.177444	+	0.984131i	$0.556783\pi$
$978$	−4.05449	−	4.67913i	−0.129648	−	0.149622i
$979$	26.4751	+	7.77380i	0.846149	+	0.248452i
$980$	2.63122	−	5.76157i	0.0840512	−	0.184046i
$981$	8.24719	+	5.30015i	0.263312	+	0.169221i
$982$	−27.5905	+	8.10130i	−0.880448	+	0.258523i
$983$	8.23739	−	57.2923i	0.262732	−	1.82734i	−0.249362	−	0.968410i	$-0.580221\pi$
$983$	8.23739	−	57.2923i	0.262732	−	1.82734i	0.512094	−	0.858929i	$-0.328870\pi$
$984$	−1.04394	−	2.28592i	−0.0332797	−	0.0728724i
$985$	0.583122	+	4.05570i	0.0185798	+	0.129225i
$986$	−31.1321	+	20.0074i	−0.991447	+	0.637164i
$987$	−1.39129	+	1.60564i	−0.0442854	+	0.0511080i
$988$	−18.4942			−0.588380
$989$	−1.57081	+	3.94231i	−0.0499487	+	0.125358i
$990$	2.61725			0.0831817
$991$	19.6120	−	22.6335i	0.622996	−	0.718976i	−0.353277	−	0.935519i	$-0.614933\pi$
$991$	19.6120	−	22.6335i	0.622996	−	0.718976i	0.976273	+	0.216543i	$0.0694781\pi$
$992$	6.77416	−	4.35349i	0.215080	−	0.138223i
$993$	3.92914	+	27.3277i	0.124687	+	0.867220i
$994$	−0.0700343	−	0.153354i	−0.00222135	−	0.00486408i
$995$	−1.57402	+	10.9475i	−0.0498998	+	0.347061i
$996$	0.654406	−	0.192151i	0.0207356	−	0.00608853i
$997$	2.34876	+	1.50946i	0.0743861	+	0.0478050i	0.577305	−	0.816528i	$-0.304104\pi$
$997$	2.34876	+	1.50946i	0.0743861	+	0.0478050i	−0.502919	+	0.864333i	$0.667741\pi$
$998$	−5.53783	+	12.1262i	−0.175297	+	0.383847i
$999$	−10.5521	−	3.09837i	−0.333853	−	0.0980280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.d.361.1	yes	20
23.13	even	11	inner	690.2.m.d.151.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.d.151.1	✓	20	23.13	even	11	inner
690.2.m.d.361.1	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.783059 + 0.229927i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.783059 + 0.229927i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.959493 + 0.281733i) q^{10} +(1.71394 + 1.97799i) q^{11} +(0.654861 + 0.755750i) q^{12} +(-2.29152 - 0.672852i) q^{13} +(0.339028 - 0.742367i) q^{14} +(0.841254 + 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.649970 - 4.52064i) q^{17} +(0.415415 + 0.909632i) q^{18} +(1.10206 + 7.66498i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(0.534443 - 0.616781i) q^{21} -2.61725 q^{22} +(3.90203 - 2.78822i) q^{23} -1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(2.00914 - 1.29119i) q^{26} +(0.142315 + 0.989821i) q^{27} +(0.339028 + 0.742367i) q^{28} +(-1.15316 + 8.02038i) q^{29} +(-0.959493 + 0.281733i) q^{30} +(6.77416 + 4.35349i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-2.51123 - 0.737365i) q^{33} +(2.99083 + 3.45160i) q^{34} +(0.534443 + 0.616781i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-4.56855 + 10.0037i) q^{37} +(-6.51450 - 4.18662i) q^{38} +(2.29152 - 0.672852i) q^{39} +(0.142315 - 0.989821i) q^{40} +(1.04394 + 2.28592i) q^{41} +(0.116146 + 0.807811i) q^{42} +(-0.744407 + 0.478401i) q^{43} +(1.71394 - 1.97799i) q^{44} -1.00000 q^{45} +(-0.448084 + 4.77485i) q^{46} -2.60326 q^{47} +(0.654861 - 0.755750i) q^{48} +(-5.32846 + 3.42439i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(1.89725 + 4.15440i) q^{51} +(-0.339885 + 2.36395i) q^{52} +(0.800620 - 0.235083i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(1.08725 - 2.38074i) q^{55} +(-0.783059 - 0.229927i) q^{56} +(-5.07111 - 5.85238i) q^{57} +(-5.30624 - 6.12373i) q^{58} +(-1.85246 - 0.543931i) q^{59} +(0.415415 - 0.909632i) q^{60} +(4.71535 + 3.03037i) q^{61} +(-7.72628 + 2.26864i) q^{62} +(-0.116146 + 0.807811i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.339885 + 2.36395i) q^{65} +(2.20177 - 1.41499i) q^{66} +(3.11886 - 3.59935i) q^{67} -4.56713 q^{68} +(-1.77516 + 4.45520i) q^{69} -0.816118 q^{70} +(0.135277 - 0.156118i) q^{71} +(0.841254 - 0.540641i) q^{72} +(1.54798 + 10.7665i) q^{73} +(-4.56855 - 10.0037i) q^{74} +(0.142315 - 0.989821i) q^{75} +(7.43013 - 2.18168i) q^{76} +(-1.79691 - 1.15480i) q^{77} +(-0.992121 + 2.17244i) q^{78} +(-15.4803 - 4.54543i) q^{79} +(0.654861 + 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-2.41122 - 0.707998i) q^{82} +(0.283327 - 0.620399i) q^{83} +(-0.686562 - 0.441227i) q^{84} +(-4.38212 + 1.28671i) q^{85} +(0.125931 - 0.875872i) q^{86} +(-3.36605 - 7.37062i) q^{87} +(0.372474 + 2.59061i) q^{88} +(8.86906 - 5.69980i) q^{89} +(0.654861 - 0.755750i) q^{90} +1.94910 q^{91} +(-3.31516 - 3.46550i) q^{92} -8.05246 q^{93} +(1.70477 - 1.96741i) q^{94} +(6.51450 - 4.18662i) q^{95} +(0.142315 + 0.989821i) q^{96} +(5.54981 + 12.1524i) q^{97} +(0.901415 - 6.26948i) q^{98} +(2.51123 - 0.737365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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