LMFDB - Embedded newform 69.2.e.c.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (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:	$0.550967773947$
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} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			64.2
Root			$-1.30051 - 1.50087i$ of defining polynomial
Character	$\chi$	$=$	69.64
Dual form			69.2.e.c.55.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.54781 + 0.454477i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.506650 + 0.325604i) q^{4} +(0.0749695 - 0.521424i) q^{5} +(-1.35707 + 0.872135i) q^{6} +(0.200934 + 0.439985i) q^{7} +(-1.47656 - 1.70404i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(1.54781 + 0.454477i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.506650 + 0.325604i) q^{4} +(0.0749695 - 0.521424i) q^{5} +(-1.35707 + 0.872135i) q^{6} +(0.200934 + 0.439985i) q^{7} +(-1.47656 - 1.70404i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.353014 - 0.772992i) q^{10} +(-3.21327 + 0.943501i) q^{11} +(-0.577861 + 0.169675i) q^{12} +(0.853105 - 1.86804i) q^{13} +(0.111045 + 0.772332i) q^{14} +(0.344971 + 0.398118i) q^{15} +(-2.01136 - 4.40426i) q^{16} +(-0.919522 + 0.590941i) q^{17} +(0.229575 - 1.59673i) q^{18} +(6.19469 + 3.98109i) q^{19} +(0.207761 - 0.239769i) q^{20} +(-0.464102 - 0.136273i) q^{21} -5.40232 q^{22} +(-1.81662 + 4.43846i) q^{23} +2.25477 q^{24} +(4.53120 + 1.33048i) q^{25} +(2.16942 - 2.50365i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.0414575 + 0.288343i) q^{28} +(-3.03219 + 1.94867i) q^{29} +(0.353014 + 0.772992i) q^{30} +(-3.65525 - 4.21838i) q^{31} +(-0.469783 - 3.26741i) q^{32} +(1.39119 - 3.04629i) q^{33} +(-1.69181 + 0.496761i) q^{34} +(0.244483 - 0.0717866i) q^{35} +(0.250186 - 0.547831i) q^{36} +(0.491920 + 3.42138i) q^{37} +(7.77887 + 8.97730i) q^{38} +(0.853105 + 1.86804i) q^{39} +(-0.999226 + 0.642164i) q^{40} +(1.47926 - 10.2885i) q^{41} +(-0.656408 - 0.421848i) q^{42} +(-5.05496 + 5.83373i) q^{43} +(-1.93521 - 0.568229i) q^{44} -0.526786 q^{45} +(-4.82895 + 6.04426i) q^{46} +10.7974 q^{47} +(4.64567 + 1.36409i) q^{48} +(4.43081 - 5.11343i) q^{49} +(6.40875 + 4.11866i) q^{50} +(0.155555 - 1.08191i) q^{51} +(1.04047 - 0.668668i) q^{52} +(-3.06811 - 6.71822i) q^{53} +(1.05639 + 1.21914i) q^{54} +(0.251067 + 1.74621i) q^{55} +(0.453061 - 0.992066i) q^{56} +(-7.06537 + 2.07458i) q^{57} +(-5.57887 + 1.63811i) q^{58} +(-0.390317 + 0.854675i) q^{59} +(0.0451508 + 0.314031i) q^{60} +(-3.75616 - 4.33483i) q^{61} +(-3.74046 - 8.19046i) q^{62} +(0.406911 - 0.261506i) q^{63} +(-0.620289 + 4.31421i) q^{64} +(-0.910084 - 0.584876i) q^{65} +(3.53777 - 4.08280i) q^{66} +(-12.3567 - 3.62825i) q^{67} -0.658289 q^{68} +(-2.16473 - 4.27948i) q^{69} +0.411037 q^{70} +(-5.99541 - 1.76041i) q^{71} +(-1.47656 + 1.70404i) q^{72} +(-0.00713288 - 0.00458402i) q^{73} +(-0.793542 + 5.51920i) q^{74} +(-3.97282 + 2.55317i) q^{75} +(1.84228 + 4.03404i) q^{76} +(-1.06078 - 1.22421i) q^{77} +(0.471461 + 3.27908i) q^{78} +(4.29440 - 9.40343i) q^{79} +(-2.44728 + 0.718585i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(6.96548 - 15.2523i) q^{82} +(0.861534 + 5.99210i) q^{83} +(-0.190767 - 0.220156i) q^{84} +(0.239195 + 0.523763i) q^{85} +(-10.4754 + 6.73213i) q^{86} +(0.512956 - 3.56769i) q^{87} +(6.35236 + 4.08241i) q^{88} +(-1.84618 + 2.13061i) q^{89} +(-0.815363 - 0.239412i) q^{90} +0.993327 q^{91} +(-2.36557 + 1.65724i) q^{92} +5.58172 q^{93} +(16.7123 + 4.90718i) q^{94} +(2.54025 - 2.93160i) q^{95} +(2.77699 + 1.78466i) q^{96} +(-2.61142 + 18.1628i) q^{97} +(9.18198 - 5.90090i) q^{98} +(1.39119 + 3.04629i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.54781	+	0.454477i	1.09446	+	0.321364i	0.778651	−	0.627457i	$-0.215904\pi$
$2$	1.54781	+	0.454477i	1.09446	+	0.321364i	0.315814	+	0.948821i	$0.397722\pi$
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$	0.506650	+	0.325604i	0.253325	+	0.162802i
$5$	0.0749695	−	0.521424i	0.0335274	−	0.233188i	−0.966167	−	0.257918i	$-0.916964\pi$
$5$	0.0749695	−	0.521424i	0.0335274	−	0.233188i	0.999694	+	0.0247301i	$0.00787264\pi$
$6$	−1.35707	+	0.872135i	−0.554021	+	0.356048i
$7$	0.200934	+	0.439985i	0.0759460	+	0.166299i	0.943797	−	0.330526i	$-0.107226\pi$
$7$	0.200934	+	0.439985i	0.0759460	+	0.166299i	−0.867851	+	0.496825i	$0.834499\pi$
$8$	−1.47656	−	1.70404i	−0.522043	−	0.602470i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	0.353014	−	0.772992i	0.111633	−	0.244441i
$11$	−3.21327	+	0.943501i	−0.968837	+	0.284476i	−0.727609	−	0.685992i	$-0.759368\pi$
$11$	−3.21327	+	0.943501i	−0.968837	+	0.284476i	−0.241228	+	0.970468i	$0.577550\pi$
$12$	−0.577861	+	0.169675i	−0.166814	+	0.0489810i
$13$	0.853105	−	1.86804i	0.236609	−	0.518101i	−0.753661	−	0.657264i	$-0.771714\pi$
$13$	0.853105	−	1.86804i	0.236609	−	0.518101i	0.990270	+	0.139163i	$0.0444411\pi$
$14$	0.111045	+	0.772332i	0.0296779	+	0.206414i
$15$	0.344971	+	0.398118i	0.0890712	+	0.102794i
$16$	−2.01136	−	4.40426i	−0.502839	−	1.10106i
$17$	−0.919522	+	0.590941i	−0.223017	+	0.143324i	−0.647379	−	0.762168i	$-0.724135\pi$
$17$	−0.919522	+	0.590941i	−0.223017	+	0.143324i	0.424362	+	0.905493i	$0.360498\pi$
$18$	0.229575	−	1.59673i	0.0541114	−	0.376353i
$19$	6.19469	+	3.98109i	1.42116	+	0.913324i	0.999980	+	0.00634685i	$0.00202028\pi$
$19$	6.19469	+	3.98109i	1.42116	+	0.913324i	0.421180	+	0.906977i	$0.361616\pi$
$20$	0.207761	−	0.239769i	0.0464568	−	0.0536140i
$21$	−0.464102	−	0.136273i	−0.101275	−	0.0297372i
$22$	−5.40232			−1.15178
$23$	−1.81662	+	4.43846i	−0.378791	+	0.925482i
$23$	−1.81662	+	4.43846i	−0.378791	+	0.925482i
$24$	2.25477			0.460253
$25$	4.53120	+	1.33048i	0.906240	+	0.266096i
$26$	2.16942	−	2.50365i	0.425459	−	0.491006i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	−0.0414575	+	0.288343i	−0.00783474	+	0.0544918i
$29$	−3.03219	+	1.94867i	−0.563064	+	0.361859i	−0.790999	−	0.611817i	$-0.790439\pi$
$29$	−3.03219	+	1.94867i	−0.563064	+	0.361859i	0.227935	+	0.973676i	$0.426802\pi$
$30$	0.353014	+	0.772992i	0.0644512	+	0.141128i
$31$	−3.65525	−	4.21838i	−0.656502	−	0.757643i	0.325700	−	0.945473i	$-0.394400\pi$
$31$	−3.65525	−	4.21838i	−0.656502	−	0.757643i	−0.982202	+	0.187830i	$0.939855\pi$
$32$	−0.469783	−	3.26741i	−0.0830466	−	0.577602i
$33$	1.39119	−	3.04629i	0.242176	−	0.530291i
$34$	−1.69181	+	0.496761i	−0.290143	+	0.0851938i
$35$	0.244483	−	0.0717866i	0.0413251	−	0.0121341i
$36$	0.250186	−	0.547831i	0.0416977	−	0.0913052i
$37$	0.491920	+	3.42138i	0.0808712	+	0.562471i	0.989463	+	0.144786i	$0.0462494\pi$
$37$	0.491920	+	3.42138i	0.0808712	+	0.562471i	−0.908592	+	0.417685i	$0.862841\pi$
$38$	7.77887	+	8.97730i	1.26190	+	1.45631i
$39$	0.853105	+	1.86804i	0.136606	+	0.299126i
$40$	−0.999226	+	0.642164i	−0.157991	+	0.101535i
$41$	1.47926	−	10.2885i	0.231021	−	1.60679i	−0.462680	−	0.886525i	$-0.653112\pi$
$41$	1.47926	−	10.2885i	0.231021	−	1.60679i	0.693701	−	0.720263i	$-0.255979\pi$
$42$	−0.656408	−	0.421848i	−0.101286	−	0.0650925i
$43$	−5.05496	+	5.83373i	−0.770874	+	0.889636i	−0.996415	−	0.0845976i	$-0.973040\pi$
$43$	−5.05496	+	5.83373i	−0.770874	+	0.889636i	0.225541	+	0.974234i	$0.427585\pi$
$44$	−1.93521	−	0.568229i	−0.291744	−	0.0856638i
$45$	−0.526786			−0.0785286
$46$	−4.82895	+	6.04426i	−0.711990	+	0.891178i
$47$	10.7974			1.57497			0.787483	−	0.616336i	$-0.211384\pi$
$47$	10.7974			1.57497			0.787483	+	0.616336i	$0.211384\pi$
$48$	4.64567	+	1.36409i	0.670545	+	0.196890i
$49$	4.43081	−	5.11343i	0.632973	−	0.730490i
$50$	6.40875	+	4.11866i	0.906335	+	0.582466i
$51$	0.155555	−	1.08191i	0.0217821	−	0.151498i
$52$	1.04047	−	0.668668i	0.144287	−	0.0927276i
$53$	−3.06811	−	6.71822i	−0.421437	−	0.922819i	−0.994639	−	0.103405i	$-0.967026\pi$
$53$	−3.06811	−	6.71822i	−0.421437	−	0.922819i	0.573202	−	0.819414i	$-0.305701\pi$
$54$	1.05639	+	1.21914i	0.143756	+	0.165904i
$55$	0.251067	+	1.74621i	0.0338539	+	0.235459i
$56$	0.453061	−	0.992066i	0.0605428	−	0.132570i
$57$	−7.06537	+	2.07458i	−0.935830	+	0.274785i
$58$	−5.57887	+	1.63811i	−0.732542	+	0.215094i
$59$	−0.390317	+	0.854675i	−0.0508149	+	0.111269i	−0.933337	−	0.359003i	$-0.883117\pi$
$59$	−0.390317	+	0.854675i	−0.0508149	+	0.111269i	0.882522	+	0.470272i	$0.155844\pi$
$60$	0.0451508	+	0.314031i	0.00582895	+	0.0405412i
$61$	−3.75616	−	4.33483i	−0.480926	−	0.555019i	0.462492	−	0.886623i	$-0.346955\pi$
$61$	−3.75616	−	4.33483i	−0.480926	−	0.555019i	−0.943418	+	0.331605i	$0.892410\pi$
$62$	−3.74046	−	8.19046i	−0.475039	−	1.04019i
$63$	0.406911	−	0.261506i	0.0512659	−	0.0329466i
$64$	−0.620289	+	4.31421i	−0.0775362	+	0.539276i
$65$	−0.910084	−	0.584876i	−0.112882	−	0.0725449i
$66$	3.53777	−	4.08280i	0.435469	−	0.502558i
$67$	−12.3567	−	3.62825i	−1.50961	−	0.443262i	−0.580872	−	0.813995i	$-0.697288\pi$
$67$	−12.3567	−	3.62825i	−1.50961	−	0.443262i	−0.928739	+	0.370733i	$0.879106\pi$
$68$	−0.658289			−0.0798292
$69$	−2.16473	−	4.27948i	−0.260603	−	0.515189i
$70$	0.411037			0.0491284
$71$	−5.99541	−	1.76041i	−0.711525	−	0.208923i	−0.0941117	−	0.995562i	$-0.530001\pi$
$71$	−5.99541	−	1.76041i	−0.711525	−	0.208923i	−0.617413	+	0.786639i	$0.711819\pi$
$72$	−1.47656	+	1.70404i	−0.174014	+	0.200823i
$73$	−0.00713288	−	0.00458402i	−0.000834840	−	0.000536519i	0.540223	−	0.841522i	$-0.318340\pi$
$73$	−0.00713288	−	0.00458402i	−0.000834840	−	0.000536519i	−0.541058	+	0.840985i	$0.681976\pi$
$74$	−0.793542	+	5.51920i	−0.0922473	+	0.641594i
$75$	−3.97282	+	2.55317i	−0.458741	+	0.294815i
$76$	1.84228	+	4.03404i	0.211324	+	0.462736i
$77$	−1.06078	−	1.22421i	−0.120887	−	0.139512i
$78$	0.471461	+	3.27908i	0.0533824	+	0.371283i
$79$	4.29440	−	9.40343i	0.483158	−	1.05797i	−0.498425	−	0.866933i	$-0.666088\pi$
$79$	4.29440	−	9.40343i	0.483158	−	1.05797i	0.981583	−	0.191036i	$-0.0611846\pi$
$80$	−2.44728	+	0.718585i	−0.273614	+	0.0803402i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	6.96548	−	15.2523i	0.769208	−	1.68433i
$83$	0.861534	+	5.99210i	0.0945656	+	0.657719i	0.980877	+	0.194629i	$0.0623502\pi$
$83$	0.861534	+	5.99210i	0.0945656	+	0.657719i	−0.886311	+	0.463090i	$0.846741\pi$
$84$	−0.190767	−	0.220156i	−0.0208143	−	0.0240210i
$85$	0.239195	+	0.523763i	0.0259443	+	0.0568101i
$86$	−10.4754	+	6.73213i	−1.12959	+	0.725944i
$87$	0.512956	−	3.56769i	0.0549946	−	0.382496i
$88$	6.35236	+	4.08241i	0.677164	+	0.435187i
$89$	−1.84618	+	2.13061i	−0.195695	+	0.225844i	−0.845113	−	0.534588i	$-0.820467\pi$
$89$	−1.84618	+	2.13061i	−0.195695	+	0.225844i	0.649418	+	0.760431i	$0.275012\pi$
$90$	−0.815363	−	0.239412i	−0.0859468	−	0.0252363i
$91$	0.993327			0.104129
$92$	−2.36557	+	1.65724i	−0.246628	+	0.172780i
$93$	5.58172			0.578797
$94$	16.7123	+	4.90718i	1.72375	+	0.506137i
$95$	2.54025	−	2.93160i	0.260624	−	0.300776i
$96$	2.77699	+	1.78466i	0.283425	+	0.182146i
$97$	−2.61142	+	18.1628i	−0.265150	+	1.84416i	0.227311	+	0.973822i	$0.427007\pi$
$97$	−2.61142	+	18.1628i	−0.265150	+	1.84416i	−0.492461	+	0.870335i	$0.663903\pi$
$98$	9.18198	−	5.90090i	0.927520	−	0.596081i
$99$	1.39119	+	3.04629i	0.139820	+	0.306164i
$100$	1.86252	+	2.14947i	0.186252	+	0.214947i
$101$	0.923803	+	6.42519i	0.0919219	+	0.639331i	0.982743	+	0.184976i	$0.0592209\pi$
$101$	0.923803	+	6.42519i	0.0919219	+	0.639331i	−0.890821	+	0.454354i	$0.849870\pi$
$102$	0.732474	−	1.60389i	0.0725258	−	0.158809i
$103$	13.1354	−	3.85690i	1.29427	−	0.380032i	0.439127	−	0.898425i	$-0.355288\pi$
$103$	13.1354	−	3.85690i	1.29427	−	0.380032i	0.855142	+	0.518394i	$0.173470\pi$
$104$	−4.44288	+	1.30455i	−0.435660	+	0.127921i
$105$	−0.105849	+	0.231778i	−0.0103298	+	0.0226192i
$106$	−1.69556	−	11.7929i	−0.164688	−	1.14543i
$107$	7.86436	+	9.07596i	0.760277	+	0.877406i	0.995522	−	0.0945299i	$-0.0301348\pi$
$107$	7.86436	+	9.07596i	0.760277	+	0.877406i	−0.235245	+	0.971936i	$0.575589\pi$
$108$	0.250186	+	0.547831i	0.0240742	+	0.0527151i
$109$	10.5081	−	6.75317i	1.00650	−	0.646837i	0.0700133	−	0.997546i	$-0.477696\pi$
$109$	10.5081	−	6.75317i	1.00650	−	0.646837i	0.936484	+	0.350709i	$0.114059\pi$
$110$	−0.405009	+	2.81690i	−0.0386161	+	0.268581i
$111$	−2.90785	−	1.86876i	−0.276001	−	0.177375i
$112$	1.53366	−	1.76993i	0.144917	−	0.167243i
$113$	−2.99845	−	0.880423i	−0.282070	−	0.0828233i	0.137637	−	0.990483i	$-0.456049\pi$
$113$	−2.99845	−	0.880423i	−0.282070	−	0.0828233i	−0.419707	+	0.907659i	$0.637867\pi$
$114$	−11.8787			−1.11254
$115$	2.17813	+	1.27998i	0.203111	+	0.119359i
$116$	−2.17076			−0.201550
$117$	−1.97044	−	0.578572i	−0.182167	−	0.0534890i
$118$	−0.992565	+	1.14548i	−0.0913731	+	0.105450i
$119$	−0.444769	−	0.285835i	−0.0407719	−	0.0262025i
$120$	0.169039	−	1.17569i	0.0154311	−	0.107326i
$121$	0.181123	−	0.116401i	0.0164657	−	0.0105819i
$122$	−3.84372	−	8.41657i	−0.347994	−	0.762001i
$123$	6.80679	+	7.85546i	0.613748	+	0.708303i
$124$	−0.478409	−	3.32741i	−0.0429624	−	0.298810i
$125$	2.12762	−	4.65884i	0.190300	−	0.416699i
$126$	0.748667	−	0.219829i	0.0666966	−	0.0195839i
$127$	−10.4847	+	3.07860i	−0.930370	+	0.273181i	−0.711592	−	0.702593i	$-0.752025\pi$
$127$	−10.4847	+	3.07860i	−0.930370	+	0.273181i	−0.218779	+	0.975775i	$0.570207\pi$
$128$	−5.66338	+	12.4011i	−0.500576	+	1.09611i
$129$	−1.09855	−	7.64057i	−0.0967217	−	0.672714i
$130$	−1.14282	−	1.31889i	−0.100232	−	0.115674i
$131$	−0.244434	−	0.535236i	−0.0213563	−	0.0467638i	0.898653	−	0.438660i	$-0.144547\pi$
$131$	−0.244434	−	0.535236i	−0.0213563	−	0.0467638i	−0.920010	+	0.391896i	$0.871819\pi$
$132$	1.69673	−	1.09042i	0.147682	−	0.0949093i
$133$	−0.506892	+	3.52551i	−0.0439531	+	0.305700i
$134$	−17.4768	−	11.2317i	−1.50977	−	0.970269i
$135$	0.344971	−	0.398118i	0.0296904	−	0.0342646i
$136$	2.36472	+	0.694344i	0.202773	+	0.0595395i
$137$	17.9223			1.53121			0.765603	−	0.643314i	$-0.222441\pi$
$137$	17.9223			1.53121			0.765603	+	0.643314i	$0.222441\pi$
$138$	−1.40566	−	7.60763i	−0.119657	−	0.647604i
$139$	−13.3492			−1.13227			−0.566133	−	0.824314i	$-0.691561\pi$
$139$	−13.3492			−1.13227			−0.566133	+	0.824314i	$0.691561\pi$
$140$	0.147241	+	0.0432339i	0.0124441	+	0.00365393i
$141$	−7.07081	+	8.16015i	−0.595470	+	0.687209i
$142$	−8.47968	−	5.44956i	−0.711599	−	0.457317i
$143$	−0.978760	+	6.80742i	−0.0818480	+	0.569265i
$144$	−4.07318	+	2.61767i	−0.339432	+	0.218140i
$145$	0.788762	+	1.72715i	0.0655031	+	0.143432i
$146$	−0.00895698	−	0.0103369i	−0.000741285	−	0.000855489i
$147$	0.962908	+	6.69717i	0.0794193	+	0.552373i
$148$	−0.864785	+	1.89361i	−0.0710849	+	0.155654i
$149$	−7.76039	+	2.27866i	−0.635756	+	0.186675i	−0.583700	−	0.811969i	$-0.698396\pi$
$149$	−7.76039	+	2.27866i	−0.635756	+	0.186675i	−0.0520557	+	0.998644i	$0.516577\pi$
$150$	−7.30951	+	2.14627i	−0.596819	+	0.175242i
$151$	1.87350	−	4.10240i	0.152464	−	0.333849i	−0.817953	−	0.575285i	$-0.804891\pi$
$151$	1.87350	−	4.10240i	0.152464	−	0.333849i	0.970417	+	0.241436i	$0.0776185\pi$
$152$	−2.36290	−	16.4343i	−0.191657	−	1.33300i
$153$	0.715787	+	0.826063i	0.0578680	+	0.0667832i
$154$	−1.08551	−	2.37694i	−0.0874731	−	0.191539i
$155$	−2.47360	+	1.58968i	−0.198684	+	0.127686i
$156$	−0.176016	+	1.22422i	−0.0140925	+	0.0980158i
$157$	1.74744	+	1.12301i	0.139461	+	0.0896263i	0.608511	−	0.793545i	$-0.291767\pi$
$157$	1.74744	+	1.12301i	0.139461	+	0.0896263i	−0.469050	+	0.883172i	$0.655404\pi$
$158$	10.9205	−	12.6030i	0.868792	−	1.00264i
$159$	7.08648	+	2.08078i	0.561994	+	0.165016i
$160$	−1.73893			−0.137474
$161$	−2.31787	+	0.0925529i	−0.182674	+	0.00729419i
$162$	−1.61315			−0.126741
$163$	−16.6050	−	4.87566i	−1.30060	−	0.381891i	−0.443147	−	0.896449i	$-0.646138\pi$
$163$	−16.6050	−	4.87566i	−1.30060	−	0.381891i	−0.857456	+	0.514558i	$0.827956\pi$
$164$	4.09943	−	4.73100i	0.320112	−	0.369429i
$165$	−1.48411	−	0.953781i	−0.115538	−	0.0742517i
$166$	−1.38978	+	9.66616i	−0.107868	+	0.750240i
$167$	14.4834	−	9.30794i	1.12076	−	0.720270i	0.157150	−	0.987575i	$-0.449769\pi$
$167$	14.4834	−	9.30794i	1.12076	−	0.720270i	0.963612	+	0.267305i	$0.0861331\pi$
$168$	0.453061	+	0.992066i	0.0349544	+	0.0765395i
$169$	5.75140	+	6.63747i	0.442416	+	0.510575i
$170$	0.132189	+	0.919393i	0.0101384	+	0.0705142i
$171$	3.05897	−	6.69821i	0.233925	−	0.512225i
$172$	−4.46058	+	1.30975i	−0.340116	+	0.0998672i
$173$	11.8788	−	3.48793i	0.903129	−	0.265183i	0.202983	−	0.979182i	$-0.434936\pi$
$173$	11.8788	−	3.48793i	0.903129	−	0.265183i	0.700146	+	0.714000i	$0.253118\pi$
$174$	2.41539	−	5.28896i	0.183110	−	0.400955i
$175$	0.325083	+	2.26100i	0.0245739	+	0.170916i
$176$	10.6185	+	12.2543i	0.800396	+	0.923706i
$177$	−0.390317	−	0.854675i	−0.0293380	−	0.0642413i
$178$	−3.82584	+	2.45872i	−0.286759	+	0.184289i
$179$	0.511848	−	3.55998i	0.0382573	−	0.266085i	−0.961711	−	0.274066i	$-0.911631\pi$
$179$	0.511848	−	3.55998i	0.0382573	−	0.266085i	0.999968	+	0.00798071i	$0.00254037\pi$
$180$	−0.266896	−	0.171524i	−0.0198933	−	0.0127846i
$181$	−6.81072	+	7.85999i	−0.506237	+	0.584229i	−0.950131	−	0.311851i	$-0.899051\pi$
$181$	−6.81072	+	7.85999i	−0.506237	+	0.584229i	0.443894	+	0.896079i	$0.353597\pi$
$182$	1.53748	+	0.451445i	0.113966	+	0.0334633i
$183$	5.73581			0.424003
$184$	10.2457	−	3.45805i	0.755321	−	0.254931i
$185$	1.82087			0.133873
$186$	8.63942	+	2.53676i	0.633473	+	0.186004i
$187$	2.39712	−	2.76642i	0.175295	−	0.202301i
$188$	5.47052	+	3.51569i	0.398979	+	0.256408i
$189$	−0.0688370	+	0.478772i	−0.00500716	+	0.0348255i
$190$	5.26416	−	3.38307i	0.381902	−	0.245434i
$191$	−2.78682	−	6.10229i	−0.201647	−	0.441546i	0.781610	−	0.623767i	$-0.214399\pi$
$191$	−2.78682	−	6.10229i	−0.201647	−	0.441546i	−0.983258	+	0.182221i	$0.941671\pi$
$192$	−2.85426	−	3.29399i	−0.205988	−	0.237723i
$193$	1.89436	+	13.1756i	0.136359	+	0.948398i	0.937019	+	0.349279i	$0.113573\pi$
$193$	1.89436	+	13.1756i	0.136359	+	0.948398i	−0.800660	+	0.599119i	$0.795517\pi$
$194$	−12.2966	+	26.9257i	−0.882842	+	1.93316i
$195$	1.03800	−	0.304784i	0.0743326	−	0.0218260i
$196$	3.90983	−	1.14803i	0.279273	−	0.0820021i
$197$	−7.95982	+	17.4296i	−0.567114	+	1.24181i	0.381206	+	0.924490i	$0.375509\pi$
$197$	−7.95982	+	17.4296i	−0.567114	+	1.24181i	−0.948320	+	0.317316i	$0.897219\pi$
$198$	0.768831	+	5.34733i	0.0546384	+	0.380019i
$199$	−15.2770	−	17.6306i	−1.08296	−	1.24980i	−0.966518	−	0.256600i	$-0.917398\pi$
$199$	−15.2770	−	17.6306i	−1.08296	−	1.24980i	−0.116438	−	0.993198i	$-0.537148\pi$
$200$	−4.42340	−	9.68590i	−0.312782	−	0.684897i
$201$	10.8340	−	6.96257i	0.764169	−	0.491102i
$202$	−1.49023	+	10.3648i	−0.104853	+	0.729265i
$203$	−1.46666	−	0.942563i	−0.102939	−	0.0661550i
$204$	0.431087	−	0.497501i	0.0301822	−	0.0348321i
$205$	−5.25375	−	1.54264i	−0.366938	−	0.107743i
$206$	22.0839			1.53866
$207$	4.65181	+	1.16647i	0.323323	+	0.0810754i
$208$	−9.94323			−0.689439
$209$	−23.6614	−	6.94761i	−1.63669	−	0.480576i
$210$	−0.269172	+	0.310641i	−0.0185746	+	0.0214363i
$211$	−1.72239	−	1.10691i	−0.118574	−	0.0762030i	0.480009	−	0.877263i	$-0.340633\pi$
$211$	−1.72239	−	1.10691i	−0.118574	−	0.0762030i	−0.598584	+	0.801060i	$0.704270\pi$
$212$	0.633024	−	4.40278i	0.0434763	−	0.302384i
$213$	5.25659	−	3.37821i	0.360176	−	0.231471i
$214$	8.04770	+	17.6220i	0.550130	+	1.20462i
$215$	2.66288	+	3.07313i	0.181607	+	0.209586i
$216$	−0.320887	−	2.23182i	−0.0218336	−	0.151856i
$217$	1.12156	−	2.45587i	0.0761363	−	0.166715i
$218$	19.3337	−	5.67690i	1.30945	−	0.384488i
$219$	0.00813541	−	0.00238877i	0.000549740	−	0.000161418i
$220$	−0.441370	+	0.966466i	−0.0297572	+	0.0651591i
$221$	0.319452	+	2.22184i	0.0214887	+	0.149457i
$222$	−3.65148	−	4.21403i	−0.245071	−	0.282827i
$223$	0.267566	+	0.585889i	0.0179176	+	0.0392340i	0.918379	−	0.395701i	$-0.129498\pi$
$223$	0.267566	+	0.585889i	0.0179176	+	0.0392340i	−0.900462	+	0.434935i	$0.856771\pi$
$224$	1.34322	−	0.863232i	0.0897474	−	0.0576771i
$225$	0.672081	−	4.67443i	0.0448054	−	0.311629i
$226$	−4.24088	−	2.72545i	−0.282099	−	0.181294i
$227$	−16.3006	+	18.8119i	−1.08191	+	1.24859i	−0.115030	+	0.993362i	$0.536697\pi$
$227$	−16.3006	+	18.8119i	−1.08191	+	1.24859i	−0.966880	+	0.255230i	$0.917849\pi$
$228$	−4.25516	−	1.24943i	−0.281805	−	0.0827454i
$229$	2.91045			0.192328			0.0961640	−	0.995366i	$-0.469343\pi$
$229$	2.91045			0.192328			0.0961640	+	0.995366i	$0.469343\pi$
$230$	2.78960	+	2.97107i	0.183941	+	0.195906i
$231$	1.61986			0.106579
$232$	7.79784	+	2.28965i	0.511953	+	0.150323i
$233$	−3.99921	+	4.61533i	−0.261997	+	0.302360i	−0.871472	−	0.490444i	$-0.836834\pi$
$233$	−3.99921	+	4.61533i	−0.261997	+	0.302360i	0.609476	+	0.792805i	$0.291380\pi$
$234$	−2.78691	−	1.79104i	−0.182186	−	0.117084i
$235$	0.809477	−	5.63004i	0.0528045	−	0.367263i
$236$	−0.476040	+	0.305932i	−0.0309876	+	0.0199145i
$237$	4.29440	+	9.40343i	0.278951	+	0.610818i
$238$	−0.558510	−	0.644555i	−0.0362028	−	0.0417803i
$239$	−4.26924	−	29.6932i	−0.276154	−	1.92069i	−0.377828	−	0.925876i	$-0.623329\pi$
$239$	−4.26924	−	29.6932i	−0.276154	−	1.92069i	0.101674	−	0.994818i	$-0.467580\pi$
$240$	1.05955	−	2.32010i	0.0683939	−	0.149762i
$241$	−2.92074	+	0.857606i	−0.188141	+	0.0552433i	−0.374446	−	0.927249i	$-0.622167\pi$
$241$	−2.92074	+	0.857606i	−0.188141	+	0.0552433i	0.186305	+	0.982492i	$0.440349\pi$
$242$	0.333245	−	0.0978496i	0.0214218	−	0.00629001i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	−0.491616	−	3.41926i	−0.0314725	−	0.218896i
$245$	−2.33409	−	2.69368i	−0.149120	−	0.172093i
$246$	6.96548	+	15.2523i	0.444103	+	0.972449i
$247$	12.7216	−	8.17565i	0.809453	−	0.520204i
$248$	−1.79110	+	12.4574i	−0.113735	+	0.791045i
$249$	−5.09271	−	3.27289i	−0.322738	−	0.207411i
$250$	5.41048	−	6.24403i	0.342189	−	0.394907i
$251$	3.39713	+	0.997487i	0.214425	+	0.0629608i	0.387181	−	0.922004i	$-0.373449\pi$
$251$	3.39713	+	0.997487i	0.214425	+	0.0629608i	−0.172756	+	0.984965i	$0.555267\pi$
$252$	0.291309			0.0183507
$253$	1.64960	−	15.9759i	0.103710	−	1.00440i
$254$	−17.6275			−1.10605
$255$	−0.552473	−	0.162221i	−0.0345972	−	0.0101587i
$256$	−8.69330	+	10.0326i	−0.543331	+	0.627038i
$257$	7.38840	+	4.74824i	0.460876	+	0.296187i	0.750400	−	0.660984i	$-0.229861\pi$
$257$	7.38840	+	4.74824i	0.460876	+	0.296187i	−0.289524	+	0.957171i	$0.593497\pi$
$258$	1.77212	−	12.3254i	0.110328	−	0.767345i
$259$	−1.40651	+	0.903910i	−0.0873964	+	0.0561663i
$260$	−0.270656	−	0.592655i	−0.0167854	−	0.0367549i
$261$	2.36036	+	2.72400i	0.146103	+	0.168612i
$262$	−0.135084	−	0.939532i	−0.00834553	−	0.0580445i
$263$	3.85133	−	8.43323i	0.237483	−	0.520015i	−0.752939	−	0.658091i	$-0.771364\pi$
$263$	3.85133	−	8.43323i	0.237483	−	0.520015i	0.990422	+	0.138076i	$0.0440917\pi$
$264$	−7.24519	+	2.12738i	−0.445911	+	0.130931i
$265$	−3.73306	+	1.09612i	−0.229320	+	0.0673344i
$266$	−2.38683	+	5.22644i	−0.146346	+	0.320453i
$267$	−0.401213	−	2.79050i	−0.0245539	−	0.170776i
$268$	−5.07915	−	5.86165i	−0.310258	−	0.358057i
$269$	5.27658	+	11.5541i	0.321719	+	0.704466i	0.999526	−	0.0307732i	$-0.00979696\pi$
$269$	5.27658	+	11.5541i	0.321719	+	0.704466i	−0.677807	+	0.735239i	$0.737070\pi$
$270$	0.714885	−	0.459429i	0.0435065	−	0.0279599i
$271$	0.696557	−	4.84466i	0.0423129	−	0.294292i	−0.957667	−	0.287880i	$-0.907050\pi$
$271$	0.696557	−	4.84466i	0.0423129	−	0.294292i	0.999979	−	0.00641267i	$-0.00204123\pi$
$272$	4.45214	+	2.86122i	0.269951	+	0.173487i
$273$	−0.650491	+	0.750707i	−0.0393695	+	0.0454348i
$274$	27.7403	+	8.14528i	1.67585	+	0.492074i
$275$	−15.8153			−0.953698
$276$	0.296657	−	2.87304i	0.0178567	−	0.172937i
$277$	3.82724			0.229957			0.114978	−	0.993368i	$-0.463320\pi$
$277$	3.82724			0.229957			0.114978	+	0.993368i	$0.463320\pi$
$278$	−20.6620	−	6.06691i	−1.23922	−	0.363869i
$279$	−3.65525	+	4.21838i	−0.218834	+	0.252548i
$280$	−0.483321	−	0.310612i	−0.0288840	−	0.0185626i
$281$	2.81648	−	19.5891i	0.168017	−	1.16859i	−0.714958	−	0.699167i	$-0.753554\pi$
$281$	2.81648	−	19.5891i	0.168017	−	1.16859i	0.882976	−	0.469419i	$-0.155537\pi$
$282$	−14.6529	+	9.41682i	−0.872565	+	0.560763i
$283$	−4.06513	−	8.90139i	−0.241647	−	0.529133i	0.749484	−	0.662023i	$-0.230302\pi$
$283$	−4.06513	−	8.90139i	−0.241647	−	0.529133i	−0.991131	+	0.132890i	$0.957574\pi$
$284$	−2.46438	−	2.84405i	−0.146234	−	0.168763i
$285$	0.552048	+	3.83958i	0.0327005	+	0.227437i
$286$	−4.60875	+	10.0918i	−0.272521	+	0.596738i
$287$	4.82400	−	1.41645i	0.284752	−	0.0836107i
$288$	−3.16730	+	0.930002i	−0.186635	+	0.0548009i
$289$	−6.56575	+	14.3770i	−0.386220	+	0.845705i
$290$	0.435902	+	3.03177i	0.0255971	+	0.178031i
$291$	−12.0164	−	13.8677i	−0.704416	−	0.812940i
$292$	−0.00212130	−	0.00464499i	−0.000124139	−	0.000271827i
$293$	−7.48457	+	4.81004i	−0.437253	+	0.281006i	−0.740691	−	0.671846i	$-0.765502\pi$
$293$	−7.48457	+	4.81004i	−0.437253	+	0.281006i	0.303438	+	0.952851i	$0.401866\pi$
$294$	−1.55332	+	10.8035i	−0.0905912	+	0.630076i
$295$	0.416386	+	0.267595i	0.0242429	+	0.0155800i
$296$	5.10383	−	5.89013i	0.296654	−	0.342357i
$297$	−3.21327	−	0.943501i	−0.186453	−	0.0547475i
$298$	−13.0472			−0.755803
$299$	6.74144	+	7.17999i	0.389868	+	0.415230i
$300$	−2.84415			−0.164207
$301$	−3.58247	−	1.05191i	−0.206490	−	0.0606310i
$302$	4.76427	−	5.49826i	0.274153	−	0.316389i
$303$	−5.46080	−	3.50944i	−0.313715	−	0.201612i
$304$	5.07399	−	35.2904i	0.291013	−	2.02404i
$305$	−2.54188	+	1.63357i	−0.145548	+	0.0935379i
$306$	0.732474	+	1.60389i	0.0418728	+	0.0916886i
$307$	8.53152	+	9.84590i	0.486920	+	0.561935i	0.945040	−	0.326955i	$-0.106023\pi$
$307$	8.53152	+	9.84590i	0.486920	+	0.561935i	−0.458120	+	0.888890i	$0.651477\pi$
$308$	−0.138838	−	0.965641i	−0.00791104	−	0.0550225i
$309$	−5.68700	+	12.4528i	−0.323522	+	0.708415i
$310$	−4.55112	+	1.33633i	−0.258486	+	0.0758985i
$311$	26.8983	−	7.89805i	1.52526	−	0.447857i	0.591666	−	0.806183i	$-0.298471\pi$
$311$	26.8983	−	7.89805i	1.52526	−	0.447857i	0.933597	+	0.358326i	$0.116652\pi$
$312$	1.92356	−	4.21200i	0.108900	−	0.238458i
$313$	2.09112	+	14.5440i	0.118197	+	0.822077i	0.959539	+	0.281575i	$0.0908568\pi$
$313$	2.09112	+	14.5440i	0.118197	+	0.822077i	−0.841342	+	0.540502i	$0.818234\pi$
$314$	2.19432	+	2.53238i	0.123833	+	0.142911i
$315$	−0.105849	−	0.231778i	−0.00596394	−	0.0130592i
$316$	5.23756	−	3.36597i	0.294636	−	0.189351i
$317$	1.75470	−	12.2042i	0.0985540	−	0.685458i	−0.879315	−	0.476241i	$-0.841999\pi$
$317$	1.75470	−	12.2042i	0.0985540	−	0.685458i	0.977869	−	0.209218i	$-0.0670917\pi$
$318$	10.0228	+	6.44129i	0.562053	+	0.361209i
$319$	7.90468	−	9.12248i	0.442577	−	0.510761i
$320$	2.20303	+	0.646868i	0.123153	+	0.0361610i
$321$	−12.0092			−0.670289
$322$	−3.62969	−	0.910167i	−0.202275	−	0.0507216i
$323$	−8.04874			−0.447844
$324$	−0.577861	−	0.169675i	−0.0321034	−	0.00942640i
$325$	6.35098	−	7.32943i	0.352289	−	0.406563i
$326$	−23.4854	−	15.0932i	−1.30074	−	0.835933i
$327$	−1.77766	+	12.3639i	−0.0983050	+	0.683726i
$328$	−19.7162	+	12.6708i	−1.08864	+	0.699630i
$329$	2.16957	+	4.75071i	0.119613	+	0.261915i
$330$	−1.86365	−	2.15076i	−0.102590	−	0.118396i
$331$	0.479124	+	3.33238i	0.0263350	+	0.183164i	0.998743	−	0.0501223i	$-0.0159611\pi$
$331$	0.479124	+	3.33238i	0.0263350	+	0.183164i	−0.972408	+	0.233286i	$0.925052\pi$
$332$	−1.51456	+	3.31642i	−0.0831221	+	0.182012i
$333$	3.31655	−	0.973826i	0.181746	−	0.0533654i
$334$	26.6478	−	7.82450i	1.45810	−	0.428138i
$335$	−2.81823	+	6.17107i	−0.153977	+	0.337162i
$336$	0.333295	+	2.31812i	0.0181827	+	0.126464i
$337$	1.48464	+	1.71336i	0.0808732	+	0.0933327i	0.794744	−	0.606945i	$-0.207605\pi$
$337$	1.48464	+	1.71336i	0.0808732	+	0.0933327i	−0.713871	+	0.700277i	$0.753060\pi$
$338$	5.88548	+	12.8874i	0.320128	+	0.700983i
$339$	2.62894	−	1.68952i	0.142785	−	0.0917621i
$340$	−0.0493515	+	0.343248i	−0.00267646	+	0.0186152i
$341$	15.7253	+	10.1061i	0.851575	+	0.547274i
$342$	7.77887	−	8.97730i	0.420633	−	0.485437i
$343$	6.38885	+	1.87594i	0.344966	+	0.101291i
$344$	17.4049			0.938409
$345$	−2.39371	+	0.807911i	−0.128873	+	0.0434965i
$346$	19.9713			1.07366
$347$	12.9692	+	3.80810i	0.696224	+	0.204430i	0.610648	−	0.791902i	$-0.290909\pi$
$347$	12.9692	+	3.80810i	0.696224	+	0.204430i	0.0855754	+	0.996332i	$0.472727\pi$
$348$	1.42154	−	1.64055i	0.0762027	−	0.0879426i
$349$	17.9744	+	11.5514i	0.962145	+	0.618333i	0.924591	−	0.380961i	$-0.124407\pi$
$349$	17.9744	+	11.5514i	0.962145	+	0.618333i	0.0375543	+	0.999295i	$0.488043\pi$
$350$	−0.524407	+	3.64733i	−0.0280308	+	0.194958i
$351$	1.72762	−	1.11027i	0.0922133	−	0.0592619i
$352$	4.59235	+	10.0558i	0.244773	+	0.535978i
$353$	−19.1742	−	22.1282i	−1.02054	−	1.17777i	−0.983952	−	0.178436i	$-0.942896\pi$
$353$	−19.1742	−	22.1282i	−1.02054	−	1.17777i	−0.0365884	−	0.999330i	$-0.511649\pi$
$354$	−0.215705	−	1.50026i	−0.0114646	−	0.0797380i
$355$	−1.36739	+	2.99418i	−0.0725738	+	0.158914i
$356$	−1.62910	+	0.478347i	−0.0863422	+	0.0253524i
$357$	0.507281	−	0.148951i	0.0268482	−	0.00788334i
$358$	2.41017	−	5.27754i	0.127382	−	0.278927i
$359$	4.14017	+	28.7955i	0.218510	+	1.51977i	0.743544	+	0.668687i	$0.233143\pi$
$359$	4.14017	+	28.7955i	0.218510	+	1.51977i	−0.525035	+	0.851081i	$0.675948\pi$
$360$	0.777832	+	0.897666i	0.0409953	+	0.0473111i
$361$	14.6323	+	32.0402i	0.770120	+	1.68633i
$362$	−14.1139	+	9.07043i	−0.741808	+	0.476731i
$363$	−0.0306406	+	0.213110i	−0.00160821	+	0.0111854i
$364$	0.503270	+	0.323432i	0.0263785	+	0.0169524i
$365$	−0.00292497	+	0.00337559i	−0.000153100	+	0.000176687i
$366$	8.87792	+	2.60679i	0.464057	+	0.136259i
$367$	−14.9673			−0.781284			−0.390642	−	0.920543i	$-0.627747\pi$
$367$	−14.9673			−0.781284			−0.390642	+	0.920543i	$0.627747\pi$
$368$	23.2020	−	0.926456i	1.20949	−	0.0482949i
$369$	−10.3943			−0.541104
$370$	2.81835	+	0.827543i	0.146519	+	0.0430219i
$371$	2.33943	−	2.69984i	0.121457	−	0.140169i
$372$	2.82798	+	1.81743i	0.146624	+	0.0942294i
$373$	4.71393	−	32.7861i	0.244078	−	1.69760i	−0.387160	−	0.922012i	$-0.626544\pi$
$373$	4.71393	−	32.7861i	0.244078	−	1.69760i	0.631238	−	0.775589i	$-0.282547\pi$
$374$	4.96755	−	3.19245i	0.256866	−	0.165078i
$375$	2.12762	+	4.65884i	0.109870	+	0.240581i
$376$	−15.9431	−	18.3993i	−0.822201	−	0.948871i
$377$	1.05342	+	7.32668i	0.0542537	+	0.377343i
$378$	−0.324137	+	0.709762i	−0.0166718	+	0.0365062i
$379$	18.0864	−	5.31066i	0.929038	−	0.272790i	0.218004	−	0.975948i	$-0.430045\pi$
$379$	18.0864	−	5.31066i	0.929038	−	0.272790i	0.711034	+	0.703158i	$0.248227\pi$
$380$	2.24156	−	0.658181i	0.114990	−	0.0337640i
$381$	4.53940	−	9.93989i	0.232560	−	0.509236i
$382$	−1.54011	−	10.7117i	−0.0787990	−	0.548059i
$383$	−12.0320	−	13.8856i	−0.614805	−	0.709523i	0.359907	−	0.932988i	$-0.382808\pi$
$383$	−12.0320	−	13.8856i	−0.614805	−	0.709523i	−0.974712	+	0.223466i	$0.928263\pi$
$384$	−5.66338	−	12.4011i	−0.289008	−	0.632839i
$385$	−0.717858	+	0.461339i	−0.0365854	+	0.0235120i
$386$	−3.05589	+	21.2542i	−0.155541	+	1.08181i
$387$	6.49375	+	4.17328i	0.330096	+	0.212140i
$388$	−7.23697	+	8.35191i	−0.367402	+	0.424004i
$389$	4.28212	+	1.25735i	0.217112	+	0.0637499i	0.388480	−	0.921457i	$-0.373000\pi$
$389$	4.28212	+	1.25735i	0.217112	+	0.0637499i	−0.171367	+	0.985207i	$0.554819\pi$
$390$	1.74514			0.0883685
$391$	−0.952443	−	5.15477i	−0.0481671	−	0.260688i
$392$	−15.2559			−0.770538
$393$	0.564575	+	0.165774i	0.0284790	+	0.00836220i
$394$	−20.2416	+	23.3601i	−1.01976	+	1.17686i
$395$	−4.58122	−	2.94417i	−0.230506	−	0.148137i
$396$	−0.287036	+	1.99638i	−0.0144241	+	0.100322i
$397$	−11.9955	+	7.70906i	−0.602039	+	0.386907i	−0.805864	−	0.592100i	$-0.798299\pi$
$397$	−11.9955	+	7.70906i	−0.602039	+	0.386907i	0.203825	+	0.979007i	$0.434663\pi$
$398$	−15.6331	−	34.2317i	−0.783617	−	1.71588i
$399$	−2.33246	−	2.69180i	−0.116769	−	0.134759i
$400$	−3.25408	−	22.6326i	−0.162704	−	1.13163i
$401$	−14.9051	+	32.6376i	−0.744324	+	1.62984i	0.0319840	+	0.999488i	$0.489817\pi$
$401$	−14.9051	+	32.6376i	−0.744324	+	1.62984i	−0.776308	+	0.630354i	$0.782910\pi$
$402$	19.9332	−	5.85292i	0.994179	−	0.291917i
$403$	−10.9984	+	3.22942i	−0.547870	+	0.160869i
$404$	−1.62403	+	3.55612i	−0.0807983	+	0.176924i
$405$	0.0749695	+	0.521424i	0.00372526	+	0.0259098i
$406$	−1.84173	−	2.12547i	−0.0914035	−	0.105485i
$407$	−4.80875	−	10.5297i	−0.238361	−	0.521937i
$408$	−2.07331	+	1.33244i	−0.102644	+	0.0659654i
$409$	−1.67097	+	11.6218i	−0.0826241	+	0.574663i	0.905887	+	0.423518i	$0.139205\pi$
$409$	−1.67097	+	11.6218i	−0.0826241	+	0.574663i	−0.988512	+	0.151145i	$0.951704\pi$
$410$	−7.43070	−	4.77542i	−0.366976	−	0.235841i
$411$	−11.7366	+	13.5448i	−0.578924	+	0.668114i
$412$	7.91087	+	2.32284i	0.389741	+	0.114438i
$413$	−0.454472			−0.0223631
$414$	6.66997	+	3.91961i	0.327811	+	0.192639i
$415$	3.18901			0.156543
$416$	−6.50443	−	1.90987i	−0.318906	−	0.0936392i
$417$	8.74188	−	10.0887i	0.428091	−	0.494044i
$418$	−33.4657	−	21.5071i	−1.63686	−	1.05195i
$419$	4.58075	−	31.8598i	0.223784	−	1.55645i	−0.499752	−	0.866169i	$-0.666576\pi$
$419$	4.58075	−	31.8598i	0.223784	−	1.55645i	0.723536	−	0.690286i	$-0.242515\pi$
$420$	−0.129096	+	0.0829653i	−0.00629926	+	0.00404829i
$421$	−10.6956	−	23.4201i	−0.521271	−	1.14142i	−0.968956	−	0.247233i	$-0.920479\pi$
$421$	−10.6956	−	23.4201i	−0.521271	−	1.14142i	0.447685	−	0.894191i	$-0.352249\pi$
$422$	−2.16286	−	2.49607i	−0.105286	−	0.121507i
$423$	−1.53663	−	10.6875i	−0.0747137	−	0.519645i
$424$	−6.91789	+	15.1481i	−0.335962	+	0.735655i
$425$	−4.95277	+	1.45427i	−0.240245	+	0.0705423i
$426$	9.67151	−	2.83981i	0.468586	−	0.137589i
$427$	1.15252	−	2.52367i	0.0557744	−	0.122129i
$428$	1.02931	+	7.15901i	0.0497536	+	0.346044i
$429$	−4.50376	−	5.19761i	−0.217443	−	0.250943i
$430$	2.72496	+	5.96683i	0.131409	+	0.287746i
$431$	−5.05580	+	3.24916i	−0.243529	+	0.156507i	−0.656712	−	0.754141i	$-0.728053\pi$
$431$	−5.05580	+	3.24916i	−0.243529	+	0.156507i	0.413183	+	0.910648i	$0.364417\pi$
$432$	0.689060	−	4.79252i	0.0331524	−	0.230580i
$433$	−24.9572	−	16.0390i	−1.19937	−	0.770787i	−0.220521	−	0.975382i	$-0.570776\pi$
$433$	−24.9572	−	16.0390i	−1.19937	−	0.770787i	−0.978847	+	0.204595i	$0.934412\pi$
$434$	2.85209	−	3.29149i	0.136905	−	0.157997i
$435$	−1.82182	−	0.534935i	−0.0873496	−	0.0256482i
$436$	7.52281			0.360277
$437$	−28.9233	+	20.2627i	−1.38359	+	0.969299i
$438$	0.0136777			0.000653545
$439$	−3.60675	−	1.05904i	−0.172141	−	0.0505451i	0.194526	−	0.980897i	$-0.437683\pi$
$439$	−3.60675	−	1.05904i	−0.172141	−	0.0505451i	−0.366667	+	0.930352i	$0.619501\pi$
$440$	2.60490	−	3.00622i	0.124184	−	0.143316i
$441$	−5.69195	−	3.65800i	−0.271045	−	0.174190i
$442$	−0.515325	+	3.58416i	−0.0245115	+	0.170481i
$443$	−9.98016	+	6.41386i	−0.474172	+	0.304732i	−0.755812	−	0.654788i	$-0.772758\pi$
$443$	−9.98016	+	6.41386i	−0.474172	+	0.304732i	0.281641	+	0.959520i	$0.409121\pi$
$444$	−0.864785	−	1.89361i	−0.0410409	−	0.0898669i
$445$	0.972542	+	1.12237i	0.0461029	+	0.0532056i
$446$	0.147868	+	1.02845i	0.00700176	+	0.0486983i
$447$	3.35988	−	7.35711i	0.158917	−	0.347979i
$448$	−2.02282	+	0.593955i	−0.0955694	+	0.0280617i
$449$	28.3526	−	8.32507i	1.33804	−	0.392885i	0.467071	−	0.884220i	$-0.345309\pi$
$449$	28.3526	−	8.32507i	1.33804	−	0.392885i	0.870971	+	0.491335i	$0.163491\pi$
$450$	3.16467	−	6.92967i	0.149184	−	0.326668i
$451$	4.95392	+	34.4553i	0.233271	+	1.62244i
$452$	−1.23249	−	1.42237i	−0.0579716	−	0.0669028i
$453$	1.87350	+	4.10240i	0.0880249	+	0.192748i
$454$	−33.7798	+	21.7090i	−1.58537	+	1.01885i
$455$	0.0744692	−	0.517945i	0.00349117	−	0.0242816i
$456$	13.9676	+	8.97644i	0.654094	+	0.420360i
$457$	17.3259	−	19.9951i	0.810470	−	0.935332i	−0.188436	−	0.982085i	$-0.560342\pi$
$457$	17.3259	−	19.9951i	0.810470	−	0.935332i	0.998906	+	0.0467529i	$0.0148874\pi$
$458$	4.50482	+	1.32273i	0.210496	+	0.0618073i
$459$	−1.09304			−0.0510186
$460$	0.686782	+	1.35771i	0.0320214	+	0.0633035i
$461$	39.8046			1.85388			0.926942	−	0.375205i	$-0.122428\pi$
$461$	39.8046			1.85388			0.926942	+	0.375205i	$0.122428\pi$
$462$	2.50723	+	0.736189i	0.116647	+	0.0342506i
$463$	−19.4034	+	22.3927i	−0.901752	+	1.04068i	0.0972160	+	0.995263i	$0.469006\pi$
$463$	−19.4034	+	22.3927i	−0.901752	+	1.04068i	−0.998968	+	0.0454143i	$0.985539\pi$
$464$	14.6813	+	9.43508i	0.681561	+	0.438012i
$465$	0.418458	−	2.91044i	0.0194055	−	0.134968i
$466$	−8.28756	+	5.32609i	−0.383914	+	0.246726i
$467$	1.73407	+	3.79709i	0.0802432	+	0.175708i	0.945501	−	0.325619i	$-0.105573\pi$
$467$	1.73407	+	3.79709i	0.0802432	+	0.175708i	−0.865258	+	0.501327i	$0.832845\pi$
$468$	−0.809936	−	0.934716i	−0.0374393	−	0.0432073i
$469$	−0.886508	−	6.16580i	−0.0409352	−	0.284710i
$470$	3.81164	−	8.34633i	0.175818	−	0.384987i
$471$	−1.99305	+	0.585212i	−0.0918349	+	0.0269652i
$472$	2.03273	−	0.596863i	0.0935640	−	0.0274729i
$473$	10.7388	−	23.5147i	0.493771	−	1.08121i
$474$	2.37326	+	16.5064i	0.109008	+	0.758164i
$475$	22.7726	+	26.2810i	1.04488	+	1.20586i
$476$	−0.132273	−	0.289637i	−0.00606271	−	0.0132755i
$477$	−6.21320	+	3.99298i	−0.284483	+	0.182826i
$478$	6.88693	−	47.8996i	0.315001	−	2.19088i
$479$	13.8273	+	8.88625i	0.631784	+	0.406023i	0.816970	−	0.576681i	$-0.195652\pi$
$479$	13.8273	+	8.88625i	0.631784	+	0.406023i	−0.185186	+	0.982704i	$0.559289\pi$
$480$	1.13875	−	1.31419i	0.0519768	−	0.0599844i
$481$	6.81093	+	1.99987i	0.310552	+	0.0911863i
$482$	−4.91050			−0.223667
$483$	1.44794	−	1.81234i	0.0658835	−	0.0824644i
$484$	0.129667			0.00589394
$485$	9.27476	+	2.72332i	0.421145	+	0.123659i
$486$	1.05639	−	1.21914i	0.0479188	−	0.0553012i
$487$	18.8374	+	12.1061i	0.853603	+	0.548578i	0.892697	−	0.450658i	$-0.148811\pi$
$487$	18.8374	+	12.1061i	0.853603	+	0.548578i	−0.0390933	+	0.999236i	$0.512447\pi$
$488$	−1.84055	+	12.8013i	−0.0833177	+	0.579488i
$489$	14.5587	−	9.35633i	0.658368	−	0.423108i
$490$	−2.38850	−	5.23009i	−0.107902	−	0.236272i
$491$	7.83692	+	9.04429i	0.353675	+	0.408163i	0.904511	−	0.426451i	$-0.140236\pi$
$491$	7.83692	+	9.04429i	0.353675	+	0.408163i	−0.550835	+	0.834614i	$0.685691\pi$
$492$	0.890892	+	6.19629i	0.0401645	+	0.279350i
$493$	1.63662	−	3.58369i	0.0737095	−	0.161401i
$494$	23.4062	−	6.87267i	1.05309	−	0.309216i
$495$	1.69271	−	0.497023i	0.0760815	−	0.0223395i
$496$	−11.2268	+	24.5833i	−0.504099	+	1.10382i
$497$	−0.430130	−	2.99162i	−0.0192940	−	0.134192i
$498$	−6.39508	−	7.38032i	−0.286571	−	0.330720i
$499$	4.66181	+	10.2079i	0.208691	+	0.456970i	0.984814	−	0.173611i	$-0.0555436\pi$
$499$	4.66181	+	10.2079i	0.208691	+	0.456970i	−0.776123	+	0.630582i	$0.782816\pi$
$500$	2.59490	−	1.66764i	0.116047	−	0.0745791i
$501$	−2.45016	+	17.0413i	−0.109465	+	0.761347i
$502$	4.80477	+	3.08784i	0.214447	+	0.137817i
$503$	−9.14150	+	10.5499i	−0.407599	+	0.470395i	−0.922019	−	0.387144i	$-0.873462\pi$
$503$	−9.14150	+	10.5499i	−0.407599	+	0.470395i	0.514420	+	0.857538i	$0.328007\pi$
$504$	−1.04645	−	0.307264i	−0.0466124	−	0.0136866i
$505$	3.41951			0.152166
$506$	9.81397	−	23.9780i	0.436284	−	1.06595i
$507$	−8.78264			−0.390051
$508$	−6.31450	−	1.85410i	−0.280161	−	0.0822626i
$509$	16.8921	−	19.4945i	0.748730	−	0.864080i	−0.245715	−	0.969342i	$-0.579023\pi$
$509$	16.8921	−	19.4945i	0.748730	−	0.864080i	0.994445	+	0.105262i	$0.0335681\pi$
$510$	−0.781396	−	0.502173i	−0.0346008	−	0.0222366i
$511$	0.000583660	−	0.00405944i	2.58196e−5	−	0.000179579i
$512$	4.92257	−	3.16355i	0.217549	−	0.139810i
$513$	3.05897	+	6.69821i	0.135057	+	0.295733i
$514$	9.27785	+	10.7072i	0.409229	+	0.472275i
$515$	−1.02633	−	7.13826i	−0.0452254	−	0.314549i
$516$	1.93122	−	4.22879i	0.0850173	−	0.186162i
$517$	−34.6951	+	10.1874i	−1.52589	+	0.448041i
$518$	−2.58782	+	0.759851i	−0.113702	+	0.0333859i
$519$	−5.14296	+	11.2615i	−0.225751	+	0.494325i
$520$	0.347142	+	2.41443i	0.0152232	+	0.105880i
$521$	−15.2342	−	17.5812i	−0.667421	−	0.770245i	0.316549	−	0.948576i	$-0.397476\pi$
$521$	−15.2342	−	17.5812i	−0.667421	−	0.770245i	−0.983971	+	0.178331i	$0.942930\pi$
$522$	2.41539	+	5.28896i	0.105719	+	0.231492i
$523$	9.64326	−	6.19735i	0.421670	−	0.270991i	−0.312551	−	0.949901i	$-0.601184\pi$
$523$	9.64326	−	6.19735i	0.421670	−	0.270991i	0.734222	+	0.678910i	$0.237547\pi$
$524$	0.0504326	−	0.350766i	0.00220316	−	0.0153233i
$525$	−1.92163	−	1.23496i	−0.0838670	−	0.0538980i
$526$	9.79382	−	11.3027i	0.427031	−	0.492820i
$527$	5.85389	+	1.71886i	0.255000	+	0.0748746i
$528$	−16.2148			−0.705660
$529$	−16.3998	−	16.1260i	−0.713034	−	0.701129i
$530$	−6.27622			−0.272621
$531$	0.901523	+	0.264711i	0.0391228	+	0.0114875i
$532$	−1.40474	+	1.62115i	−0.0609031	+	0.0702859i
$533$	−17.9573	−	11.5405i	−0.777817	−	0.499873i
$534$	0.647218	−	4.50150i	0.0280079	−	0.194799i
$535$	5.32201	−	3.42025i	0.230091	−	0.147870i
$536$	12.0627	+	26.4137i	0.521030	+	1.14090i
$537$	2.35526	+	2.71812i	0.101637	+	0.117296i
$538$	2.91606	+	20.2816i	0.125720	+	0.874402i
$539$	−9.41287	+	20.6113i	−0.405441	+	0.887792i
$540$	0.304409	−	0.0893825i	0.0130997	−	0.00384641i
$541$	22.5066	−	6.60855i	0.967636	−	0.284124i	0.240525	−	0.970643i	$-0.422680\pi$
$541$	22.5066	−	6.60855i	0.967636	−	0.284124i	0.727112	+	0.686519i	$0.240862\pi$
$542$	3.27993	−	7.18203i	0.140885	−	0.308495i
$543$	−1.48011	−	10.2944i	−0.0635177	−	0.441775i
$544$	2.36282	+	2.72684i	0.101305	+	0.116912i
$545$	−2.73348	−	5.98548i	−0.117089	−	0.256390i
$546$	−1.34801	+	0.866316i	−0.0576897	+	0.0370749i
$547$	2.11351	−	14.6998i	0.0903670	−	0.628516i	−0.893426	−	0.449210i	$-0.851706\pi$
$547$	2.11351	−	14.6998i	0.0903670	−	0.628516i	0.983793	−	0.179306i	$-0.0573853\pi$
$548$	9.08033	+	5.83558i	0.387893	+	0.249283i
$549$	−3.75616	+	4.33483i	−0.160309	+	0.185006i
$550$	−24.4790	−	7.18769i	−1.04379	−	0.306484i
$551$	−26.5413			−1.13070
$552$	−4.09606	+	10.0077i	−0.174340	+	0.425956i
$553$	5.00026			0.212633
$554$	5.92383	+	1.73939i	0.251680	+	0.0738998i
$555$	−1.19242	+	1.37612i	−0.0506152	+	0.0584131i
$556$	−6.76338	−	4.34656i	−0.286831	−	0.184335i
$557$	−3.28296	+	22.8335i	−0.139103	+	0.967485i	0.794011	+	0.607904i	$0.207989\pi$
$557$	−3.28296	+	22.8335i	−0.139103	+	0.967485i	−0.933114	+	0.359581i	$0.882920\pi$
$558$	−7.57477	+	4.86801i	−0.320666	+	0.206079i
$559$	6.58524	+	14.4197i	0.278526	+	0.609886i
$560$	−0.807908	−	0.932376i	−0.0341404	−	0.0394001i
$561$	0.520944	+	3.62324i	0.0219943	+	0.152973i
$562$	13.2622	−	29.0401i	0.559430	−	1.22498i
$563$	26.0066	−	7.63624i	1.09605	−	0.321829i	0.316768	−	0.948503i	$-0.397402\pi$
$563$	26.0066	−	7.63624i	1.09605	−	0.321829i	0.779281	+	0.626674i	$0.215584\pi$
$564$	−6.23941	+	1.83206i	−0.262726	+	0.0771435i
$565$	−0.683866	+	1.49746i	−0.0287704	+	0.0629985i
$566$	−2.24656	−	15.6251i	−0.0944298	−	0.656774i
$567$	−0.316753	−	0.365553i	−0.0133024	−	0.0153518i
$568$	5.85278	+	12.8158i	0.245577	+	0.537739i
$569$	14.0899	−	9.05501i	0.590678	−	0.379606i	−0.210890	−	0.977510i	$-0.567636\pi$
$569$	14.0899	−	9.05501i	0.590678	−	0.379606i	0.801568	+	0.597904i	$0.204000\pi$
$570$	−0.890537	+	6.19382i	−0.0373005	+	0.259431i
$571$	−6.90227	−	4.43582i	−0.288851	−	0.185633i	0.388188	−	0.921580i	$-0.373101\pi$
$571$	−6.90227	−	4.43582i	−0.288851	−	0.185633i	−0.677039	+	0.735947i	$0.736737\pi$
$572$	−2.71241	+	3.13029i	−0.113412	+	0.130884i
$573$	6.43678	+	1.89001i	0.268900	+	0.0789563i
$574$	8.11037			0.338520
$575$	−14.1368	+	17.6946i	−0.589543	+	0.737914i
$576$	4.35857			0.181607
$577$	−0.910674	−	0.267398i	−0.0379119	−	0.0111319i	0.262722	−	0.964872i	$-0.415380\pi$
$577$	−0.910674	−	0.267398i	−0.0379119	−	0.0111319i	−0.300633	+	0.953740i	$0.597198\pi$
$578$	−16.6965	+	19.2688i	−0.694484	+	0.801477i
$579$	−11.1980	−	7.19650i	−0.465372	−	0.299076i
$580$	−0.162740	+	1.13188i	−0.00675743	+	0.0469989i
$581$	−2.46332	+	1.58308i	−0.102196	+	0.0656773i
$582$	−12.2966	−	26.9257i	−0.509709	−	1.11611i
$583$	16.1973	+	18.6927i	0.670824	+	0.774173i
$584$	0.00272076	+	0.0189233i	0.000112586	+	0.000783052i
$585$	−0.449404	+	0.984057i	−0.0185806	+	0.0406858i
$586$	−13.7707	+	4.04345i	−0.568864	+	0.167033i
$587$	−27.0571	+	7.94468i	−1.11677	+	0.327912i	−0.787494	−	0.616323i	$-0.788622\pi$
$587$	−27.0571	+	7.94468i	−1.11677	+	0.327912i	−0.329272	+	0.944235i	$0.606803\pi$
$588$	−1.69277	+	3.70665i	−0.0698087	+	0.152860i
$589$	−5.84939	−	40.6834i	−0.241020	−	1.67633i
$590$	0.522870	+	0.603424i	0.0215262	+	0.0248426i
$591$	−7.95982	−	17.4296i	−0.327423	−	0.716957i
$592$	14.0792	−	9.04816i	0.578652	−	0.371877i
$593$	−0.686106	+	4.77197i	−0.0281750	+	0.195961i	−0.999048	−	0.0436352i	$-0.986106\pi$
$593$	−0.686106	+	4.77197i	−0.0281750	+	0.195961i	0.970873	+	0.239597i	$0.0770152\pi$
$594$	−4.54472	−	2.92072i	−0.186472	−	0.119838i
$595$	−0.182385	+	0.210484i	−0.00747708	+	0.00862901i
$596$	−4.67374	−	1.37233i	−0.191444	−	0.0562130i
$597$	23.3286			0.954775
$598$	7.17131	+	14.1771i	0.293257	+	0.579744i
$599$	−48.1882			−1.96892			−0.984458	−	0.175619i	$-0.943807\pi$
$599$	−48.1882			−1.96892			−0.984458	+	0.175619i	$0.943807\pi$
$600$	10.2168	+	2.99993i	0.417100	+	0.122472i
$601$	20.4011	−	23.5441i	0.832177	−	0.960383i	−0.167498	−	0.985872i	$-0.553569\pi$
$601$	20.4011	−	23.5441i	0.832177	−	0.960383i	0.999675	+	0.0254891i	$0.00811432\pi$
$602$	−5.06690	−	3.25630i	−0.206512	−	0.132717i
$603$	−1.83278	+	12.7473i	−0.0746367	+	0.519109i
$604$	2.28497	−	1.46846i	0.0929741	−	0.0597508i
$605$	−0.0471155	−	0.103168i	−0.00191552	−	0.00419440i
$606$	−6.85730	−	7.91375i	−0.278559	−	0.321474i
$607$	1.14997	+	7.99823i	0.0466759	+	0.324638i	0.999759	+	0.0219309i	$0.00698137\pi$
$607$	1.14997	+	7.99823i	0.0466759	+	0.324638i	−0.953084	+	0.302707i	$0.902110\pi$
$608$	10.0977	−	22.1109i	0.409515	−	0.896713i
$609$	1.67280	−	0.491178i	0.0677852	−	0.0199035i
$610$	−4.67677	+	1.37322i	−0.189357	+	0.0556001i
$611$	9.21134	−	20.1700i	0.372651	−	0.815992i
$612$	0.0936842	+	0.651588i	0.00378696	+	0.0263389i
$613$	−8.27956	−	9.55512i	−0.334408	−	0.385928i	0.563496	−	0.826119i	$-0.309456\pi$
$613$	−8.27956	−	9.55512i	−0.334408	−	0.385928i	−0.897904	+	0.440191i	$0.854911\pi$
$614$	8.73041	+	19.1169i	0.352331	+	0.771497i
$615$	4.60633	−	2.96031i	0.185745	−	0.119371i
$616$	−0.519793	+	3.61524i	−0.0209430	+	0.145662i
$617$	−21.9713	−	14.1201i	−0.884531	−	0.568454i	0.0176341	−	0.999845i	$-0.494387\pi$
$617$	−21.9713	−	14.1201i	−0.884531	−	0.568454i	−0.902165	+	0.431391i	$0.858023\pi$
$618$	−14.4619	+	16.6899i	−0.581743	+	0.671367i
$619$	−16.2418	−	4.76902i	−0.652812	−	0.191683i	−0.0614767	−	0.998109i	$-0.519581\pi$
$619$	−16.2418	−	4.76902i	−0.652812	−	0.191683i	−0.591336	+	0.806426i	$0.701399\pi$
$620$	−1.77086			−0.0711193
$621$	−3.92785	+	2.75173i	−0.157619	+	0.110423i
$622$	45.2228			1.81327
$623$	−1.30840	−	0.384180i	−0.0524198	−	0.0153918i
$624$	6.51143	−	7.51459i	0.260666	−	0.300824i
$625$	17.5944	+	11.3072i	0.703774	+	0.452288i
$626$	−3.37329	+	23.4617i	−0.134824	+	0.937719i
$627$	20.7456	−	13.3324i	0.828498	−	0.532443i
$628$	0.519685	+	1.13795i	0.0207377	+	0.0454092i
$629$	−2.47416	−	2.85534i	−0.0986514	−	0.113850i
$630$	−0.0584967	−	0.406854i	−0.00233056	−	0.0162094i
$631$	3.87646	−	8.48826i	0.154319	−	0.337912i	−0.816643	−	0.577142i	$-0.804168\pi$
$631$	3.87646	−	8.48826i	0.154319	−	0.337912i	0.970963	+	0.239230i	$0.0768950\pi$
$632$	−22.3648	+	6.56690i	−0.889624	+	0.261217i
$633$	1.96447	−	0.576822i	0.0780809	−	0.0229266i
$634$	8.26249	−	18.0923i	0.328145	−	0.718538i
$635$	0.819220	+	5.69780i	0.0325097	+	0.226110i
$636$	2.91286	+	3.36161i	0.115502	+	0.133297i
$637$	−5.77214	−	12.6392i	−0.228701	−	0.500785i
$638$	16.3809	−	10.5273i	0.648525	−	0.416782i
$639$	−0.889258	+	6.18492i	−0.0351785	+	0.244672i
$640$	6.04163	+	3.88272i	0.238816	+	0.153478i
$641$	−16.4777	+	19.0163i	−0.650830	+	0.751097i	−0.981251	−	0.192736i	$-0.938264\pi$
$641$	−16.4777	+	19.0163i	−0.650830	+	0.751097i	0.330421	+	0.943834i	$0.392809\pi$
$642$	−18.5879	−	5.45791i	−0.733608	−	0.215407i
$643$	15.1602			0.597859			0.298930	−	0.954275i	$-0.403370\pi$
$643$	15.1602			0.597859			0.298930	+	0.954275i	$0.403370\pi$
$644$	−1.20449	−	0.707818i	−0.0474634	−	0.0278919i
$645$	−4.06633			−0.160112
$646$	−12.4579	−	3.65797i	−0.490149	−	0.143921i
$647$	−2.75310	+	3.17725i	−0.108236	+	0.124910i	−0.807282	−	0.590166i	$-0.799062\pi$
$647$	−2.75310	+	3.17725i	−0.108236	+	0.124910i	0.699047	+	0.715076i	$0.253608\pi$
$648$	1.89683	+	1.21902i	0.0745147	+	0.0478877i
$649$	0.447807	−	3.11457i	0.0175780	−	0.122257i
$650$	13.1612	−	8.45816i	0.516223	−	0.331756i
$651$	1.12156	+	2.45587i	0.0439573	+	0.0962532i
$652$	−6.82538	−	7.87691i	−0.267302	−	0.308483i
$653$	−1.36644	−	9.50381i	−0.0534730	−	0.371913i	−0.998933	−	0.0461756i	$-0.985297\pi$
$653$	−1.36644	−	9.50381i	−0.0534730	−	0.371913i	0.945460	−	0.325737i	$-0.105612\pi$
$654$	−8.37059	+	18.3290i	−0.327316	+	0.716722i
$655$	−0.297410	+	0.0873274i	−0.0116208	+	0.00341217i
$656$	−48.2883	+	14.1787i	−1.88534	+	0.553587i
$657$	−0.00352225	+	0.00771265i	−0.000137416	+	0.000300899i
$658$	1.19900	+	8.33920i	0.0467417	+	0.325096i
$659$	0.317667	+	0.366608i	0.0123746	+	0.0142810i	0.761903	−	0.647691i	$-0.224265\pi$
$659$	0.317667	+	0.366608i	0.0123746	+	0.0142810i	−0.749529	+	0.661972i	$0.769720\pi$
$660$	−0.441370	−	0.966466i	−0.0171803	−	0.0376196i
$661$	−16.0121	+	10.2903i	−0.622797	+	0.400247i	−0.813636	−	0.581374i	$-0.802515\pi$
$661$	−16.0121	+	10.2903i	−0.622797	+	0.400247i	0.190840	+	0.981621i	$0.438879\pi$
$662$	−0.772899	+	5.37563i	−0.0300396	+	0.208930i
$663$	−1.88835	−	1.21357i	−0.0733374	−	0.0471311i
$664$	8.93869	−	10.3158i	0.346888	−	0.400331i
$665$	1.80028	+	0.528611i	0.0698120	+	0.0204986i
$666$	5.57596			0.216064
$667$	−3.14075	−	16.9982i	−0.121610	−	0.658175i
$668$	10.3687			0.401179
$669$	−0.618004	−	0.181462i	−0.0238934	−	0.00701574i
$670$	−7.16669	+	8.27081i	−0.276874	+	0.319529i
$671$	16.1595	+	10.3851i	0.623829	+	0.400911i
$672$	−0.227232	+	1.58043i	−0.00876566	+	0.0609665i
$673$	1.05038	−	0.675039i	0.0404892	−	0.0260208i	−0.520240	−	0.854020i	$-0.674157\pi$
$673$	1.05038	−	0.675039i	0.0404892	−	0.0260208i	0.560729	+	0.827999i	$0.310521\pi$
$674$	1.51925	+	3.32668i	0.0585192	+	0.128139i
$675$	3.09258	+	3.56902i	0.119033	+	0.137372i
$676$	0.752760	+	5.23556i	0.0289523	+	0.201368i
$677$	12.5543	−	27.4900i	0.482499	−	1.05653i	−0.499270	−	0.866447i	$-0.666398\pi$
$677$	12.5543	−	27.4900i	0.482499	−	1.05653i	0.981769	−	0.190079i	$-0.0608744\pi$
$678$	4.83695	−	1.42026i	0.185762	−	0.0545446i
$679$	−8.51610	+	2.50055i	−0.326818	+	0.0959624i
$680$	0.539329	−	1.18097i	0.0206823	−	0.0452880i
$681$	−3.54247	−	24.6384i	−0.135748	−	0.944145i
$682$	19.7468	+	22.7890i	0.756145	+	0.872638i
$683$	−6.59875	−	14.4493i	−0.252494	−	0.552885i	0.740361	−	0.672209i	$-0.234655\pi$
$683$	−6.59875	−	14.4493i	−0.252494	−	0.552885i	−0.992855	+	0.119324i	$0.961927\pi$
$684$	3.73079	−	2.39763i	0.142650	−	0.0916758i
$685$	1.34362	−	9.34512i	0.0513373	−	0.357059i
$686$	9.03614	+	5.80717i	0.345001	+	0.221719i
$687$	−1.90594	+	2.19957i	−0.0727161	+	0.0839189i
$688$	35.8606	+	10.5296i	1.36717	+	0.401438i
$689$	−15.1673			−0.577829
$690$	−4.07218	+	0.162602i	−0.155025	+	0.00619017i
$691$	−17.1403			−0.652047			−0.326024	−	0.945362i	$-0.605709\pi$
$691$	−17.1403			−0.652047			−0.326024	+	0.945362i	$0.605709\pi$
$692$	7.15408	+	2.10063i	0.271957	+	0.0798539i
$693$	−1.06078	+	1.22421i	−0.0402958	+	0.0465038i
$694$	18.3431	+	11.7884i	0.696296	+	0.447482i
$695$	−1.00078	+	6.96060i	−0.0379619	+	0.264031i
$696$	−6.83690	+	4.39381i	−0.259152	+	0.166547i
$697$	4.71966	+	10.3346i	0.178770	+	0.391452i
$698$	22.5710	+	26.0483i	0.854324	+	0.985943i
$699$	−0.869110	−	6.04480i	−0.0328728	−	0.228635i
$700$	−0.571488	+	1.25138i	−0.0216002	+	0.0472979i
$701$	−24.0907	+	7.07366i	−0.909892	+	0.267168i	−0.702995	−	0.711194i	$-0.748155\pi$
$701$	−24.0907	+	7.07366i	−0.909892	+	0.267168i	−0.206897	+	0.978363i	$0.566336\pi$
$702$	3.17861	−	0.933324i	0.119969	−	0.0352260i
$703$	−10.5735	+	23.1528i	−0.398788	+	0.873223i
$704$	−2.07730	−	14.4480i	−0.0782913	−	0.544528i
$705$	3.72480	+	4.29865i	0.140284	+	0.161897i
$706$	−19.6212	−	42.9644i	−0.738454	−	1.61699i
$707$	−2.64136	+	1.69750i	−0.0993387	+	0.0638411i
$708$	0.0805317	−	0.560110i	0.00302656	−	0.0210502i
$709$	−36.0468	−	23.1659i	−1.35377	−	0.870013i	−0.355851	−	0.934543i	$-0.615809\pi$
$709$	−36.0468	−	23.1659i	−1.35377	−	0.870013i	−0.997916	+	0.0645293i	$0.979445\pi$
$710$	−3.47725	+	4.01296i	−0.130499	+	0.150604i
$711$	−9.91887	−	2.91244i	−0.371987	−	0.109225i
$712$	6.35664			0.238225
$713$	25.3633	−	8.56046i	0.949862	−	0.320592i
$714$	0.852869			0.0319178
$715$	3.47618	+	1.02070i	0.130002	+	0.0381719i
$716$	1.41847	−	1.63700i	0.0530108	−	0.0611777i
$717$	25.2364	+	16.2184i	0.942470	+	0.605689i
$718$	−6.67871	+	46.4515i	−0.249247	+	1.73355i
$719$	12.1284	−	7.79448i	0.452315	−	0.290685i	−0.294581	−	0.955627i	$-0.595180\pi$
$719$	12.1284	−	7.79448i	0.452315	−	0.290685i	0.746895	+	0.664942i	$0.231544\pi$
$720$	1.05955	+	2.32010i	0.0394873	+	0.0864650i
$721$	4.33633	+	5.00439i	0.161493	+	0.186373i
$722$	8.08639	+	56.2421i	0.300944	+	2.09311i
$723$	1.26454	−	2.76896i	0.0470288	−	0.102979i
$724$	−6.00990	+	1.76467i	−0.223356	+	0.0655833i
$725$	−16.3321	+	4.79555i	−0.606561	+	0.178102i
$726$	−0.144279	+	0.315928i	−0.00535471	+	0.0117252i
$727$	−2.80380	−	19.5008i	−0.103987	−	0.723246i	−0.973392	−	0.229146i	$-0.926407\pi$
$727$	−2.80380	−	19.5008i	−0.103987	−	0.723246i	0.869405	−	0.494100i	$-0.164502\pi$
$728$	−1.46671	−	1.69267i	−0.0543599	−	0.0627346i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−0.00606141	+	0.00389543i	−0.000224343	+	0.000144176i
$731$	1.20075	−	8.35143i	0.0444115	−	0.308889i
$732$	2.90605	+	1.86760i	0.107411	+	0.0690286i
$733$	15.3498	−	17.7146i	0.566956	−	0.654302i	−0.397793	−	0.917475i	$-0.630224\pi$
$733$	15.3498	−	17.7146i	0.566956	−	0.654302i	0.964749	+	0.263173i	$0.0847691\pi$
$734$	−23.1664	−	6.80228i	−0.855088	−	0.251077i
$735$	3.56425			0.131469
$736$	15.3557	+	3.85053i	0.566018	+	0.141933i
$737$	43.1287			1.58867
$738$	−16.0883	−	4.72395i	−0.592219	−	0.173891i
$739$	1.33631	−	1.54218i	0.0491570	−	0.0567302i	−0.730639	−	0.682764i	$-0.760778\pi$
$739$	1.33631	−	1.54218i	0.0491570	−	0.0567302i	0.779796	+	0.626034i	$0.215323\pi$
$740$	0.922543	+	0.592883i	0.0339134	+	0.0217948i
$741$	−2.15210	+	14.9682i	−0.0790595	+	0.549871i
$742$	4.84800	−	3.11562i	0.177976	−	0.114378i
$743$	18.5746	+	40.6727i	0.681436	+	1.49214i	0.861114	+	0.508412i	$0.169767\pi$
$743$	18.5746	+	40.6727i	0.681436	+	1.49214i	−0.179678	+	0.983726i	$0.557505\pi$
$744$	−8.24175	−	9.51148i	−0.302157	−	0.348708i
$745$	0.606354	+	4.21728i	0.0222151	+	0.154509i
$746$	22.1968	−	48.6042i	0.812683	−	1.77953i
$747$	5.80850	−	1.70553i	0.212522	−	0.0624021i
$748$	2.11526	−	0.621096i	0.0773416	−	0.0227095i
$749$	−2.41306	+	5.28387i	−0.0881714	+	0.193069i
$750$	1.17581	+	8.17794i	0.0429345	+	0.298616i
$751$	35.7344	+	41.2397i	1.30397	+	1.50486i	0.722742	+	0.691118i	$0.242882\pi$
$751$	35.7344	+	41.2397i	1.30397	+	1.50486i	0.581227	+	0.813742i	$0.302573\pi$
$752$	−21.7175	−	47.5546i	−0.791955	−	1.73414i
$753$	−2.97850	+	1.91416i	−0.108542	+	0.0697560i
$754$	−1.69932	+	11.8190i	−0.0618856	+	0.430424i
$755$	−1.99864	−	1.28444i	−0.0727378	−	0.0467457i
$756$	−0.190767	+	0.220156i	−0.00693811	+	0.00800701i
$757$	−46.5029	−	13.6545i	−1.69018	−	0.496281i	−0.711673	−	0.702511i	$-0.752062\pi$
$757$	−46.5029	−	13.6545i	−1.69018	−	0.496281i	−0.978504	+	0.206230i	$0.933880\pi$
$758$	30.4079			1.10446
$759$	10.9936	+	11.7087i	0.399041	+	0.424999i
$760$	−8.74641			−0.317265
$761$	41.4432	+	12.1688i	1.50232	+	0.441120i	0.926448	−	0.376423i	$-0.122846\pi$
$761$	41.4432	+	12.1688i	1.50232	+	0.441120i	0.575868	+	0.817542i	$0.304664\pi$
$762$	11.5436	−	13.3220i	0.418179	−	0.482605i
$763$	5.08274	+	3.26648i	0.184008	+	0.118255i
$764$	0.574988	−	3.99913i	0.0208023	−	0.144683i
$765$	0.484391	−	0.311299i	0.0175132	−	0.0112551i
$766$	−12.3125	−	26.9605i	−0.444867	−	0.974124i
$767$	1.26359	+	1.45826i	0.0456254	+	0.0526545i
$768$	−1.88923	−	13.1399i	−0.0681719	−	0.474146i
$769$	−20.6411	+	45.1977i	−0.744337	+	1.62987i	0.0319500	+	0.999489i	$0.489828\pi$
$769$	−20.6411	+	45.1977i	−0.744337	+	1.62987i	−0.776287	+	0.630380i	$0.782899\pi$
$770$	−1.32077	+	0.387814i	−0.0475974	+	0.0139759i
$771$	−8.42685	+	2.47435i	−0.303486	+	0.0891114i
$772$	−3.33024	+	7.29222i	−0.119858	+	0.262453i
$773$	−1.52790	−	10.6267i	−0.0549546	−	0.382217i	−0.998674	−	0.0514717i	$-0.983609\pi$
$773$	−1.52790	−	10.6267i	−0.0549546	−	0.382217i	0.943720	−	0.330746i	$-0.107300\pi$
$774$	8.15441	+	9.41069i	0.293104	+	0.338260i
$775$	−10.9502	−	23.9776i	−0.393342	−	0.861300i
$776$	34.8062	−	22.3686i	1.24947	−	0.802985i
$777$	0.237940	−	1.65491i	0.00853603	−	0.0593694i
$778$	6.05647	+	3.89226i	0.217135	+	0.139544i
$779$	50.1228	−	57.8448i	1.79584	−	2.07251i
$780$	0.625141	+	0.183558i	0.0223836	+	0.00657242i
$781$	20.9258			0.748785
$782$	0.868529	−	8.41146i	0.0310585	−	0.300793i
$783$	−3.60437			−0.128810
$784$	−31.4328	−	9.22950i	−1.12260	−	0.329625i
$785$	0.716571	−	0.826968i	0.0255755	−	0.0295157i
$786$	0.798512	+	0.513173i	0.0284820	+	0.0183043i
$787$	−5.48677	+	38.1613i	−0.195582	+	1.36030i	0.621334	+	0.783546i	$0.286591\pi$
$787$	−5.48677	+	38.1613i	−0.195582	+	1.36030i	−0.816916	+	0.576757i	$0.804318\pi$
$788$	−9.70799	+	6.23894i	−0.345833	+	0.222253i
$789$	3.85133	+	8.43323i	0.137111	+	0.300231i
$790$	−5.75279	−	6.63908i	−0.204675	−	0.236208i
$791$	−0.215118	−	1.49618i	−0.00764871	−	0.0531980i
$792$	3.13682	−	6.86869i	0.111462	−	0.244068i
$793$	−11.3020	+	3.31858i	−0.401347	+	0.117846i
$794$	−22.0704	+	6.48045i	−0.783248	+	0.229982i
$795$	1.61624	−	3.53907i	0.0573220	−	0.125518i
$796$	−1.99949	−	13.9068i	−0.0708701	−	0.492913i
$797$	20.0127	+	23.0959i	0.708886	+	0.818098i	0.989924	−	0.141598i	$-0.0452242\pi$
$797$	20.0127	+	23.0959i	0.708886	+	0.818098i	−0.281038	+	0.959697i	$0.590679\pi$
$798$	−2.38683	−	5.22644i	−0.0844930	−	0.185014i
$799$	−9.92847	+	6.38064i	−0.351244	+	0.225731i
$800$	2.21855	−	15.4303i	0.0784375	−	0.545545i
$801$	2.37166	+	1.52417i	0.0837984	+	0.0538540i
$802$	−37.9032	+	43.7426i	−1.33841	+	1.54461i
$803$	0.0272449	+	0.00799982i	0.000961451	+	0.000282308i
$804$	7.75607			0.273536
$805$	−0.125511	+	1.21553i	−0.00442366	+	0.0428420i
$806$	−18.4911			−0.651322
$807$	−12.1874	−	3.57855i	−0.429018	−	0.125971i
$808$	9.58475	−	11.0614i	0.337190	−	0.389138i
$809$	−3.73925	−	2.40307i	−0.131465	−	0.0844874i	0.473255	−	0.880925i	$-0.343079\pi$
$809$	−3.73925	−	2.40307i	−0.131465	−	0.0844874i	−0.604720	+	0.796438i	$0.706715\pi$
$810$	−0.120937	+	0.841136i	−0.00424930	+	0.0295545i
$811$	27.3210	−	17.5582i	0.959371	−	0.616551i	0.0355474	−	0.999368i	$-0.488683\pi$
$811$	27.3210	−	17.5582i	0.959371	−	0.616551i	0.923824	+	0.382817i	$0.125046\pi$
$812$	−0.436179	−	0.955100i	−0.0153069	−	0.0335174i
$813$	3.20520	+	3.69900i	0.112411	+	0.129730i
$814$	−2.65751	−	18.4834i	−0.0931457	−	0.647843i
$815$	−3.78715	+	8.29271i	−0.132658	+	0.290481i
$816$	−5.07790	+	1.49100i	−0.177762	+	0.0521956i
$817$	−54.5385	+	16.0140i	−1.90806	+	0.560257i
$818$	−7.86820	+	17.2290i	−0.275105	+	0.602396i
$819$	−0.141365	−	0.983217i	−0.00493970	−	0.0343564i
$820$	−2.15952	−	2.49222i	−0.0754138	−	0.0870322i
$821$	14.0204	+	30.7003i	0.489314	+	1.07145i	0.979796	+	0.199997i	$0.0640934\pi$
$821$	14.0204	+	30.7003i	0.489314	+	1.07145i	−0.490482	+	0.871451i	$0.663179\pi$
$822$	−24.3218	+	15.6307i	−0.848320	+	0.545182i
$823$	−2.52621	+	17.5702i	−0.0880581	+	0.612458i	0.897231	+	0.441562i	$0.145575\pi$
$823$	−2.52621	+	17.5702i	−0.0880581	+	0.612458i	−0.985289	+	0.170896i	$0.945334\pi$
$824$	−25.9675	−	16.6883i	−0.904622	−	0.581365i
$825$	10.3568	−	11.9524i	0.360578	−	0.416129i
$826$	−0.703435	−	0.206547i	−0.0244756	−	0.00718670i
$827$	−17.7946			−0.618778			−0.309389	−	0.950936i	$-0.600125\pi$
$827$	−17.7946			−0.618778			−0.309389	+	0.950936i	$0.600125\pi$
$828$	1.97703	+	2.10564i	0.0687066	+	0.0731761i
$829$	−47.4537			−1.64814			−0.824068	−	0.566491i	$-0.808301\pi$
$829$	−47.4537			−1.64814			−0.824068	+	0.566491i	$0.808301\pi$
$830$	4.93598	+	1.44933i	0.171330	+	0.0503071i
$831$	−2.50631	+	2.89244i	−0.0869430	+	0.100338i
$832$	7.52994	+	4.83920i	0.261054	+	0.167769i
$833$	−1.05249	+	7.32026i	−0.0364668	+	0.253632i
$834$	18.1158	−	11.6423i	0.627299	−	0.403141i
$835$	−3.76757	−	8.24982i	−0.130382	−	0.285497i
$836$	−9.72587	−	11.2243i	−0.336376	−	0.388199i
$837$	−0.794361	−	5.52490i	−0.0274571	−	0.190969i
$838$	21.5697	−	47.2310i	0.745113	−	1.63157i
$839$	−1.56477	+	0.459459i	−0.0540220	+	0.0158623i	−0.308632	−	0.951182i	$-0.599871\pi$
$839$	−1.56477	+	0.459459i	−0.0540220	+	0.0158623i	0.254610	+	0.967044i	$0.418053\pi$
$840$	0.551253	−	0.161862i	0.0190200	−	0.00558478i
$841$	−6.65017	+	14.5618i	−0.229316	+	0.502132i
$842$	−5.91082	−	41.1107i	−0.203700	−	1.41677i
$843$	12.9600	+	14.9567i	0.446367	+	0.515135i
$844$	−0.512234	−	1.12164i	−0.0176318	−	0.0386083i
$845$	3.89212	−	2.50131i	0.133893	−	0.0860478i
$846$	2.47882	−	17.2406i	0.0852237	−	0.592744i
$847$	0.0876085	+	0.0563025i	0.00301026	+	0.00193458i
$848$	−23.4177	+	27.0255i	−0.804168	+	0.928059i
$849$	9.38932	+	2.75695i	0.322241	+	0.0946184i
$850$	−8.32687			−0.285609
$851$	−16.0793	−	4.03198i	−0.551191	−	0.138215i
$852$	3.76321			0.128926
$853$	21.2486	+	6.23916i	0.727539	+	0.213625i	0.624469	−	0.781049i	$-0.285315\pi$
$853$	21.2486	+	6.23916i	0.727539	+	0.213625i	0.103070	+	0.994674i	$0.467133\pi$
$854$	2.93083	−	3.38236i	0.100291	−	0.115742i
$855$	−3.26328	−	2.09718i	−0.111602	−	0.0717221i
$856$	3.85361	−	26.8024i	0.131714	−	0.916088i
$857$	−19.0420	+	12.2376i	−0.650463	+	0.418027i	−0.823835	−	0.566829i	$-0.808170\pi$
$857$	−19.0420	+	12.2376i	−0.650463	+	0.418027i	0.173372	+	0.984856i	$0.444534\pi$
$858$	−4.60875	−	10.0918i	−0.157340	−	0.344527i
$859$	−0.824575	−	0.951611i	−0.0281341	−	0.0324685i	0.741508	−	0.670944i	$-0.234111\pi$
$859$	−0.824575	−	0.951611i	−0.0281341	−	0.0324685i	−0.769642	+	0.638475i	$0.779565\pi$
$860$	0.348525	+	2.42405i	0.0118846	+	0.0826593i
$861$	−2.08856	+	4.57332i	−0.0711781	+	0.155858i
$862$	−9.30207	+	2.73133i	−0.316830	+	0.0930296i
$863$	−7.61520	+	2.23603i	−0.259225	+	0.0761152i	−0.408763	−	0.912641i	$-0.634040\pi$
$863$	−7.61520	+	2.23603i	−0.259225	+	0.0761152i	0.149538	+	0.988756i	$0.452221\pi$
$864$	1.37129	−	3.00270i	0.0466522	−	0.102154i
$865$	−0.928144	−	6.45538i	−0.0315578	−	0.219490i
$866$	−31.3396	−	36.1678i	−1.06496	−	1.22903i
$867$	−6.56575	−	14.3770i	−0.222984	−	0.488268i
$868$	1.36788	−	0.879083i	0.0464289	−	0.0298380i
$869$	−4.92693	+	34.2675i	−0.167135	+	1.16245i
$870$	−2.57671	−	1.65595i	−0.0873587	−	0.0561420i
$871$	−17.3193	+	19.9875i	−0.586842	+	0.677251i
$872$	−27.0236	−	7.93485i	−0.915135	−	0.268708i
$873$	18.3496			0.621040
$874$	−53.9766	+	18.2178i	−1.82579	+	0.616228i
$875$	2.47733			0.0837491
$876$	0.00489960	+	0.00143865i	0.000165542	+	4.86076e-5i
$877$	9.70823	−	11.2039i	0.327824	−	0.378329i	−0.567781	−	0.823180i	$-0.692198\pi$
$877$	9.70823	−	11.2039i	0.327824	−	0.378329i	0.895605	+	0.444851i	$0.146743\pi$
$878$	−5.10125	−	3.27837i	−0.172159	−	0.110640i
$879$	1.26616	−	8.80637i	0.0427067	−	0.297032i
$880$	7.18577	−	4.61801i	0.242232	−	0.155673i
$881$	−10.8447	−	23.7466i	−0.365368	−	0.800043i	−0.999637	−	0.0269316i	$-0.991426\pi$
$881$	−10.8447	−	23.7466i	−0.365368	−	0.800043i	0.634270	−	0.773112i	$-0.281301\pi$
$882$	−7.14757	−	8.24874i	−0.240671	−	0.277749i
$883$	−1.30435	−	9.07195i	−0.0438949	−	0.305296i	−0.999928	−	0.0120354i	$-0.996169\pi$
$883$	−1.30435	−	9.07195i	−0.0438949	−	0.305296i	0.956033	−	0.293260i	$-0.0947402\pi$
$884$	−0.561590	+	1.22971i	−0.0188883	+	0.0413596i
$885$	−0.474910	+	0.139446i	−0.0159639	+	0.00468743i
$886$	−18.3623	+	5.39166i	−0.616894	+	0.181136i
$887$	21.1375	−	46.2846i	0.709727	−	1.55408i	−0.118038	−	0.993009i	$-0.537660\pi$
$887$	21.1375	−	46.2846i	0.709727	−	1.55408i	0.827765	−	0.561075i	$-0.189612\pi$
$888$	1.10917	+	7.71443i	0.0372212	+	0.258879i
$889$	−3.46128	−	3.99453i	−0.116088	−	0.133972i
$890$	0.995214	+	2.17922i	0.0333597	+	0.0730475i
$891$	2.81730	−	1.81057i	0.0943829	−	0.0606562i
$892$	−0.0552053	+	0.383961i	−0.00184841	+	0.0128560i
$893$	66.8867	+	42.9855i	2.23828	+	1.43845i
$894$	8.54408	−	9.86040i	0.285757	−	0.329781i
$895$	−1.81789	−	0.533780i	−0.0607652	−	0.0178423i
$896$	−6.59425			−0.220298
$897$	−9.84098	+	0.392951i	−0.328581	+	0.0131203i
$898$	47.6679			1.59070
$899$	19.3036	+	5.66806i	0.643812	+	0.189040i
$900$	1.86252	−	2.14947i	0.0620841	−	0.0716489i
$901$	6.79127	+	4.36448i	0.226250	+	0.145402i
$902$	−7.99143	+	55.5816i	−0.266085	+	1.85066i
$903$	3.14100	−	2.01860i	0.104526	−	0.0671747i
$904$	2.92711	+	6.40948i	0.0973543	+	0.213176i
$905$	3.58779	+	4.14053i	0.119262	+	0.137636i
$906$	1.03537	+	7.20119i	0.0343980	+	0.239244i
$907$	15.9556	−	34.9378i	0.529795	−	1.16009i	−0.435801	−	0.900043i	$-0.643535\pi$
$907$	15.9556	−	34.9378i	0.529795	−	1.16009i	0.965596	−	0.260047i	$-0.0837380\pi$
$908$	−14.3840	+	4.22351i	−0.477349	+	0.140162i
$909$	6.22832	−	1.82880i	0.206580	−	0.0606575i
$910$	0.350658	−	0.767834i	0.0116242	−	0.0254535i
$911$	−0.0791753	−	0.550676i	−0.00262319	−	0.0182447i	0.988468	−	0.151431i	$-0.0483882\pi$
$911$	−0.0791753	−	0.550676i	−0.00262319	−	0.0182447i	−0.991091	+	0.133186i	$0.957479\pi$
$912$	23.3479	+	26.9450i	0.773128	+	0.892237i
$913$	−8.42190	−	18.4414i	−0.278724	−	0.610321i
$914$	35.9044	−	23.0744i	1.18761	−	0.763233i
$915$	0.430010	−	2.99079i	0.0142157	−	0.0988724i
$916$	1.47458	+	0.947655i	0.0487215	+	0.0313114i
$917$	0.186381	−	0.215095i	0.00615483	−	0.00710305i
$918$	−1.69181	−	0.496761i	−0.0558381	−	0.0163955i
$919$	−25.5118			−0.841555			−0.420778	−	0.907164i	$-0.638243\pi$
$919$	−25.5118			−0.841555			−0.420778	+	0.907164i	$0.638243\pi$
$920$	−1.03500	−	5.60159i	−0.0341230	−	0.184679i
$921$	−13.0280			−0.429287
$922$	61.6098	+	18.0903i	2.02901	+	0.595771i
$923$	−8.40324	+	9.69786i	−0.276596	+	0.319209i
$924$	0.820702	+	0.527433i	0.0269991	+	0.0173513i
$925$	−2.32309	+	16.1575i	−0.0763828	+	0.531254i
$926$	−40.2097	+	25.8412i	−1.32137	+	0.849194i
$927$	−5.68700	−	12.4528i	−0.186786	−	0.409004i
$928$	7.79158	+	8.99196i	0.255771	+	0.295176i
$929$	3.40247	+	23.6647i	0.111631	+	0.776413i	0.966333	+	0.257294i	$0.0828308\pi$
$929$	3.40247	+	23.6647i	0.111631	+	0.776413i	−0.854702	+	0.519119i	$0.826260\pi$
$930$	1.97042	−	4.31462i	0.0646127	−	0.141482i
$931$	47.8045	−	14.0367i	1.56673	−	0.460034i
$932$	−3.52897	+	1.03620i	−0.115595	+	0.0339418i
$933$	−11.6457	+	25.5005i	−0.381263	+	0.834849i
$934$	0.958319	+	6.66525i	0.0313571	+	0.218094i
$935$	−1.26277	−	1.45731i	−0.0412969	−	0.0476592i
$936$	1.92356	+	4.21200i	0.0628735	+	0.137674i
$937$	32.0799	−	20.6165i	1.04800	−	0.673511i	0.101050	−	0.994881i	$-0.467780\pi$
$937$	32.0799	−	20.6165i	1.04800	−	0.673511i	0.946954	+	0.321370i	$0.104143\pi$
$938$	1.43007	−	9.94637i	0.0466935	−	0.324760i
$939$	−12.3610	−	7.94396i	−0.403387	−	0.259241i
$940$	2.24329	−	2.58889i	0.0731679	−	0.0844403i
$941$	−13.5602	−	3.98163i	−0.442050	−	0.129797i	0.0531310	−	0.998588i	$-0.483080\pi$
$941$	−13.5602	−	3.98163i	−0.442050	−	0.129797i	−0.495181	+	0.868790i	$0.664898\pi$
$942$	−3.35082			−0.109176
$943$	42.9776	+	25.2558i	1.39954	+	0.822444i
$944$	4.54927			0.148066
$945$	0.244483	+	0.0717866i	0.00795302	+	0.00233522i
$946$	27.3085	−	31.5157i	0.887876	−	1.02466i
$947$	16.2633	+	10.4518i	0.528487	+	0.339638i	0.777521	−	0.628857i	$-0.216477\pi$
$947$	16.2633	+	10.4518i	0.528487	+	0.339638i	−0.249034	+	0.968495i	$0.580113\pi$
$948$	−0.886037	+	6.16252i	−0.0287771	+	0.200149i
$949$	−0.0146482	+	0.00941384i	−0.000475502	+	0.000305586i
$950$	23.3035	+	51.0276i	0.756066	+	1.65555i
$951$	8.07426	+	9.31819i	0.261826	+	0.302163i
$952$	0.169652	+	1.17996i	0.00549847	+	0.0382427i
$953$	5.19078	−	11.3662i	0.168146	−	0.368188i	−0.806735	−	0.590913i	$-0.798768\pi$
$953$	5.19078	−	11.3662i	0.168146	−	0.368188i	0.974881	+	0.222724i	$0.0714950\pi$
$954$	−11.4316	+	3.35661i	−0.370110	+	0.108674i
$955$	−3.39081	+	0.995631i	−0.109724	+	0.0322179i
$956$	7.50522	−	16.4341i	0.242736	−	0.531518i
$957$	1.71785	+	11.9479i	0.0555302	+	0.386221i
$958$	17.3633	+	20.0384i	0.560984	+	0.647410i
$959$	3.60121	+	7.88554i	0.116289	+	0.254637i
$960$	−1.93155	+	1.24133i	−0.0623404	+	0.0400637i
$961$	−0.0221369	+	0.153966i	−0.000714095	+	0.00496664i
$962$	9.63312	+	6.19083i	0.310584	+	0.199600i
$963$	7.86436	−	9.07596i	0.253426	−	0.292469i
$964$	−1.75903	−	0.516499i	−0.0566546	−	0.0166353i
$965$	7.01208			0.225727
$966$	3.06480	−	2.14710i	0.0986082	−	0.0690818i
$967$	9.35247			0.300755			0.150378	−	0.988629i	$-0.451951\pi$
$967$	9.35247			0.300755			0.150378	+	0.988629i	$0.451951\pi$
$968$	−0.465792	−	0.136769i	−0.0149711	−	0.00439591i
$969$	5.27080	−	6.08283i	0.169323	−	0.195409i
$970$	13.1179	+	8.43034i	0.421189	+	0.270682i
$971$	3.37468	−	23.4714i	0.108299	−	0.753233i	−0.861223	−	0.508227i	$-0.830301\pi$
$971$	3.37468	−	23.4714i	0.108299	−	0.753233i	0.969522	−	0.245006i	$-0.0787899\pi$
$972$	0.506650	−	0.325604i	0.0162508	−	0.0104438i
$973$	−2.68232	−	5.87345i	−0.0859911	−	0.188294i
$974$	23.6547	+	27.2990i	0.757946	+	0.874716i
$975$	1.38020	+	9.59951i	0.0442018	+	0.307430i
$976$	−11.5368	+	25.2620i	−0.369283	+	0.808616i
$977$	−46.3820	+	13.6190i	−1.48389	+	0.435710i	−0.920587	−	0.390538i	$-0.872289\pi$
$977$	−46.3820	+	13.6190i	−1.48389	+	0.435710i	−0.563306	+	0.826248i	$0.690471\pi$
$978$	26.7863	−	7.86518i	0.856533	−	0.251501i
$979$	3.92205	−	8.58809i	0.125349	−	0.274476i
$980$	−0.305492	−	2.12474i	−0.00975859	−	0.0678725i
$981$	−8.17990	−	9.44011i	−0.261164	−	0.301399i
$982$	8.01962	+	17.5605i	0.255916	+	0.560379i
$983$	−30.2232	+	19.4233i	−0.963972	+	0.619507i	−0.925094	−	0.379737i	$-0.876014\pi$
$983$	−30.2232	+	19.4233i	−0.963972	+	0.619507i	−0.0388772	+	0.999244i	$0.512378\pi$
$984$	3.33539	−	23.1981i	0.106328	−	0.739530i
$985$	8.49146	+	5.45713i	0.270560	+	0.173879i
$986$	4.16187	−	4.80306i	0.132541	−	0.152961i
$987$	−5.01111	−	1.47140i	−0.159505	−	0.0468350i
$988$	9.10740			0.289745
$989$	−16.7098	−	33.0339i	−0.531342	−	1.05042i
$990$	2.84587			0.0904476
$991$	−24.8432	−	7.29461i	−0.789169	−	0.231721i	−0.137778	−	0.990463i	$-0.543996\pi$
$991$	−24.8432	−	7.29461i	−0.789169	−	0.231721i	−0.651391	+	0.758742i	$0.725814\pi$
$992$	−12.0660	+	13.9249i	−0.383096	+	0.442116i
$993$	−2.83220	−	1.82015i	−0.0898772	−	0.0577606i
$994$	0.693864	−	4.82593i	0.0220080	−	0.153069i
$995$	−10.3383	+	6.64403i	−0.327746	+	0.210630i
$996$	−1.51456	−	3.31642i	−0.0479906	−	0.105085i
$997$	−20.0725	−	23.1648i	−0.635701	−	0.733638i	0.342908	−	0.939369i	$-0.388588\pi$
$997$	−20.0725	−	23.1648i	−0.635701	−	0.733638i	−0.978609	+	0.205731i	$0.934043\pi$
$998$	2.57631	+	17.9186i	0.0815516	+	0.567204i
$999$	−1.43591	+	3.14420i	−0.0454301	+	0.0994781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.c.64.2	yes	20
3.2	odd	2		207.2.i.d.64.1		20
23.3	even	11		1587.2.a.u.1.3		10
23.9	even	11	inner	69.2.e.c.55.2	✓	20
23.20	odd	22		1587.2.a.t.1.3		10
69.20	even	22		4761.2.a.bu.1.8		10
69.26	odd	22		4761.2.a.bt.1.8		10
69.32	odd	22		207.2.i.d.55.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.55.2	✓	20	23.9	even	11	inner
69.2.e.c.64.2	yes	20	1.1	even	1	trivial
207.2.i.d.55.1		20	69.32	odd	22
207.2.i.d.64.1		20	3.2	odd	2
1587.2.a.t.1.3		10	23.20	odd	22
1587.2.a.u.1.3		10	23.3	even	11
4761.2.a.bt.1.8		10	69.26	odd	22
4761.2.a.bu.1.8		10	69.20	even	22

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.54781 + 0.454477i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.506650 + 0.325604i) q^{4} +(0.0749695 - 0.521424i) q^{5} +(-1.35707 + 0.872135i) q^{6} +(0.200934 + 0.439985i) q^{7} +(-1.47656 - 1.70404i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(1.54781 + 0.454477i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.506650 + 0.325604i) q^{4} +(0.0749695 - 0.521424i) q^{5} +(-1.35707 + 0.872135i) q^{6} +(0.200934 + 0.439985i) q^{7} +(-1.47656 - 1.70404i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.353014 - 0.772992i) q^{10} +(-3.21327 + 0.943501i) q^{11} +(-0.577861 + 0.169675i) q^{12} +(0.853105 - 1.86804i) q^{13} +(0.111045 + 0.772332i) q^{14} +(0.344971 + 0.398118i) q^{15} +(-2.01136 - 4.40426i) q^{16} +(-0.919522 + 0.590941i) q^{17} +(0.229575 - 1.59673i) q^{18} +(6.19469 + 3.98109i) q^{19} +(0.207761 - 0.239769i) q^{20} +(-0.464102 - 0.136273i) q^{21} -5.40232 q^{22} +(-1.81662 + 4.43846i) q^{23} +2.25477 q^{24} +(4.53120 + 1.33048i) q^{25} +(2.16942 - 2.50365i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.0414575 + 0.288343i) q^{28} +(-3.03219 + 1.94867i) q^{29} +(0.353014 + 0.772992i) q^{30} +(-3.65525 - 4.21838i) q^{31} +(-0.469783 - 3.26741i) q^{32} +(1.39119 - 3.04629i) q^{33} +(-1.69181 + 0.496761i) q^{34} +(0.244483 - 0.0717866i) q^{35} +(0.250186 - 0.547831i) q^{36} +(0.491920 + 3.42138i) q^{37} +(7.77887 + 8.97730i) q^{38} +(0.853105 + 1.86804i) q^{39} +(-0.999226 + 0.642164i) q^{40} +(1.47926 - 10.2885i) q^{41} +(-0.656408 - 0.421848i) q^{42} +(-5.05496 + 5.83373i) q^{43} +(-1.93521 - 0.568229i) q^{44} -0.526786 q^{45} +(-4.82895 + 6.04426i) q^{46} +10.7974 q^{47} +(4.64567 + 1.36409i) q^{48} +(4.43081 - 5.11343i) q^{49} +(6.40875 + 4.11866i) q^{50} +(0.155555 - 1.08191i) q^{51} +(1.04047 - 0.668668i) q^{52} +(-3.06811 - 6.71822i) q^{53} +(1.05639 + 1.21914i) q^{54} +(0.251067 + 1.74621i) q^{55} +(0.453061 - 0.992066i) q^{56} +(-7.06537 + 2.07458i) q^{57} +(-5.57887 + 1.63811i) q^{58} +(-0.390317 + 0.854675i) q^{59} +(0.0451508 + 0.314031i) q^{60} +(-3.75616 - 4.33483i) q^{61} +(-3.74046 - 8.19046i) q^{62} +(0.406911 - 0.261506i) q^{63} +(-0.620289 + 4.31421i) q^{64} +(-0.910084 - 0.584876i) q^{65} +(3.53777 - 4.08280i) q^{66} +(-12.3567 - 3.62825i) q^{67} -0.658289 q^{68} +(-2.16473 - 4.27948i) q^{69} +0.411037 q^{70} +(-5.99541 - 1.76041i) q^{71} +(-1.47656 + 1.70404i) q^{72} +(-0.00713288 - 0.00458402i) q^{73} +(-0.793542 + 5.51920i) q^{74} +(-3.97282 + 2.55317i) q^{75} +(1.84228 + 4.03404i) q^{76} +(-1.06078 - 1.22421i) q^{77} +(0.471461 + 3.27908i) q^{78} +(4.29440 - 9.40343i) q^{79} +(-2.44728 + 0.718585i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(6.96548 - 15.2523i) q^{82} +(0.861534 + 5.99210i) q^{83} +(-0.190767 - 0.220156i) q^{84} +(0.239195 + 0.523763i) q^{85} +(-10.4754 + 6.73213i) q^{86} +(0.512956 - 3.56769i) q^{87} +(6.35236 + 4.08241i) q^{88} +(-1.84618 + 2.13061i) q^{89} +(-0.815363 - 0.239412i) q^{90} +0.993327 q^{91} +(-2.36557 + 1.65724i) q^{92} +5.58172 q^{93} +(16.7123 + 4.90718i) q^{94} +(2.54025 - 2.93160i) q^{95} +(2.77699 + 1.78466i) q^{96} +(-2.61142 + 18.1628i) q^{97} +(9.18198 - 5.90090i) q^{98} +(1.39119 + 3.04629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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