LMFDB - Embedded newform 966.2.q.d.883.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (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:	$7.71354883526$
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} - 6 x^{19} + 10 x^{18} - 14 x^{17} + 77 x^{16} + 12 x^{15} - 226 x^{14} - 793 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 10x^18 - 14x^17 + 77x^16 + 12x^15 - 226x^14 - 793x^13 + 690x^12 + 6105x^11 + 13883x^10 + 24365x^9 + 36461x^8 + 41912x^7 + 45709x^6 + 33023x^5 + 25949x^4 + 12217x^3 + 2895x^2 - 172*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			883.1
Root			$0.150891 - 1.04947i$ of defining polynomial
Character	$\chi$	$=$	966.883
Dual form			966.2.q.d.547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.110384 - 0.767734i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.110384 - 0.767734i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.322208 + 0.705537i) q^{10} +(-1.03013 - 0.302473i) q^{11} +(0.959493 + 0.281733i) q^{12} +(-1.81011 - 3.96358i) q^{13} +(-0.142315 + 0.989821i) q^{14} +(0.507929 - 0.586181i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-4.59279 - 2.95161i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(0.993842 - 0.638704i) q^{19} +(-0.507929 - 0.586181i) q^{20} +(0.959493 - 0.281733i) q^{21} +1.07362 q^{22} +(-3.31669 - 3.46404i) q^{23} -1.00000 q^{24} +(4.22023 - 1.23917i) q^{25} +(2.85345 + 3.29306i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-0.142315 - 0.989821i) q^{28} +(2.11815 + 1.36125i) q^{29} +(-0.322208 + 0.705537i) q^{30} +(-3.19814 + 3.69085i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-0.445997 - 0.976598i) q^{33} +(5.23831 + 1.53811i) q^{34} +(-0.744211 - 0.218520i) q^{35} +(0.415415 + 0.909632i) q^{36} +(0.536989 - 3.73484i) q^{37} +(-0.773641 + 0.892829i) q^{38} +(1.81011 - 3.96358i) q^{39} +(0.652501 + 0.419337i) q^{40} +(-0.392815 - 2.73209i) q^{41} +(-0.841254 + 0.540641i) q^{42} +(-7.23161 - 8.34572i) q^{43} +(-1.03013 + 0.302473i) q^{44} +0.775629 q^{45} +(4.15827 + 2.38930i) q^{46} -8.68382 q^{47} +(0.959493 - 0.281733i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(-3.70017 + 2.37795i) q^{50} +(-0.776962 - 5.40389i) q^{51} +(-3.66563 - 2.35576i) q^{52} +(-1.43740 + 3.14748i) q^{53} +(0.654861 - 0.755750i) q^{54} +(-0.118510 + 0.824254i) q^{55} +(0.415415 + 0.909632i) q^{56} +(1.13353 + 0.332834i) q^{57} +(-2.41586 - 0.709361i) q^{58} +(2.35950 + 5.16658i) q^{59} +(0.110384 - 0.767734i) q^{60} +(-1.16601 + 1.34565i) q^{61} +(2.02876 - 4.44236i) q^{62} +(0.841254 + 0.540641i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-2.84317 + 1.82719i) q^{65} +(0.703071 + 0.811387i) q^{66} +(13.0559 - 3.83355i) q^{67} -5.45946 q^{68} +(0.445974 - 4.77505i) q^{69} +0.775629 q^{70} +(2.97654 - 0.873991i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(12.3622 - 7.94471i) q^{73} +(0.536989 + 3.73484i) q^{74} +(3.70017 + 2.37795i) q^{75} +(0.490764 - 1.07462i) q^{76} +(-0.703071 + 0.811387i) q^{77} +(-0.620114 + 4.31299i) q^{78} +(-2.51910 - 5.51607i) q^{79} +(-0.744211 - 0.218520i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(1.14662 + 2.51075i) q^{82} +(-0.124557 + 0.866311i) q^{83} +(0.654861 - 0.755750i) q^{84} +(-1.75908 + 3.85185i) q^{85} +(9.28994 + 5.97028i) q^{86} +(0.358328 + 2.49222i) q^{87} +(0.903185 - 0.580442i) q^{88} +(-4.75182 - 5.48389i) q^{89} +(-0.744211 + 0.218520i) q^{90} -4.35734 q^{91} +(-4.66298 - 1.12100i) q^{92} -4.88369 q^{93} +(8.33206 - 2.44651i) q^{94} +(-0.600059 - 0.692504i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(-1.00635 - 6.99932i) q^{97} +(0.841254 + 0.540641i) q^{98} +(0.445997 - 0.976598i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 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 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.110384	−	0.767734i	−0.0493650	−	0.343341i	−0.999503	−	0.0315125i	$-0.989968\pi$
$5$	−0.110384	−	0.767734i	−0.0493650	−	0.343341i	0.950138	−	0.311829i	$-0.100942\pi$
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	0.415415	−	0.909632i	0.157012	−	0.343809i
$7$	0.415415	−	0.909632i	0.157012	−	0.343809i
$8$	−0.654861	+	0.755750i	−0.231528	+	0.267198i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	0.322208	+	0.705537i	0.101891	+	0.223110i
$11$	−1.03013	−	0.302473i	−0.310596	−	0.0911991i	0.122720	−	0.992441i	$-0.460838\pi$
$11$	−1.03013	−	0.302473i	−0.310596	−	0.0911991i	−0.433316	+	0.901242i	$0.642656\pi$
$12$	0.959493	+	0.281733i	0.276982	+	0.0813292i
$13$	−1.81011	−	3.96358i	−0.502033	−	1.09930i	−0.975803	−	0.218650i	$-0.929835\pi$
$13$	−1.81011	−	3.96358i	−0.502033	−	1.09930i	0.473770	−	0.880648i	$-0.342893\pi$
$14$	−0.142315	+	0.989821i	−0.0380352	+	0.264541i
$15$	0.507929	−	0.586181i	0.131147	−	0.151351i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	−4.59279	−	2.95161i	−1.11391	−	0.715869i	−0.151772	−	0.988416i	$-0.548498\pi$
$17$	−4.59279	−	2.95161i	−1.11391	−	0.715869i	−0.962143	+	0.272546i	$0.912134\pi$
$18$	−0.142315	−	0.989821i	−0.0335439	−	0.233303i
$19$	0.993842	−	0.638704i	0.228003	−	0.146529i	−0.421652	−	0.906758i	$-0.638550\pi$
$19$	0.993842	−	0.638704i	0.228003	−	0.146529i	0.649655	+	0.760229i	$0.274913\pi$
$20$	−0.507929	−	0.586181i	−0.113576	−	0.131074i
$21$	0.959493	−	0.281733i	0.209379	−	0.0614791i
$22$	1.07362			0.228896
$23$	−3.31669	−	3.46404i	−0.691578	−	0.722302i
$23$	−3.31669	−	3.46404i	−0.691578	−	0.722302i
$24$	−1.00000			−0.204124
$25$	4.22023	−	1.23917i	0.844047	−	0.247834i
$26$	2.85345	+	3.29306i	0.559608	+	0.645822i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	−0.142315	−	0.989821i	−0.0268950	−	0.187059i
$29$	2.11815	+	1.36125i	0.393331	+	0.252778i	0.722325	−	0.691554i	$-0.243073\pi$
$29$	2.11815	+	1.36125i	0.393331	+	0.252778i	−0.328994	+	0.944332i	$0.606710\pi$
$30$	−0.322208	+	0.705537i	−0.0588269	+	0.128813i
$31$	−3.19814	+	3.69085i	−0.574403	+	0.662896i	−0.966392	−	0.257074i	$-0.917242\pi$
$31$	−3.19814	+	3.69085i	−0.574403	+	0.662896i	0.391989	+	0.919970i	$0.371787\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$	−0.445997	−	0.976598i	−0.0776382	−	0.170004i
$34$	5.23831	+	1.53811i	0.898363	+	0.263783i
$35$	−0.744211	−	0.218520i	−0.125795	−	0.0369366i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	0.536989	−	3.73484i	0.0882805	−	0.614004i	−0.896868	−	0.442299i	$-0.854163\pi$
$37$	0.536989	−	3.73484i	0.0882805	−	0.614004i	0.985148	−	0.171706i	$-0.0549278\pi$
$38$	−0.773641	+	0.892829i	−0.125501	+	0.144836i
$39$	1.81011	−	3.96358i	0.289849	−	0.634680i
$40$	0.652501	+	0.419337i	0.103169	+	0.0663030i
$41$	−0.392815	−	2.73209i	−0.0613475	−	0.426681i	−0.997231	−	0.0743706i	$-0.976305\pi$
$41$	−0.392815	−	2.73209i	−0.0613475	−	0.426681i	0.935883	−	0.352310i	$-0.114604\pi$
$42$	−0.841254	+	0.540641i	−0.129808	+	0.0834227i
$43$	−7.23161	−	8.34572i	−1.10281	−	1.27271i	−0.959093	−	0.283092i	$-0.908640\pi$
$43$	−7.23161	−	8.34572i	−1.10281	−	1.27271i	−0.143717	−	0.989619i	$-0.545905\pi$
$44$	−1.03013	+	0.302473i	−0.155298	+	0.0455996i
$45$	0.775629			0.115624
$46$	4.15827	+	2.38930i	0.613104	+	0.352283i
$47$	−8.68382			−1.26666			−0.633332	−	0.773880i	$-0.718313\pi$
$47$	−8.68382			−1.26666			−0.633332	+	0.773880i	$0.718313\pi$
$48$	0.959493	−	0.281733i	0.138491	−	0.0406646i
$49$	−0.654861	−	0.755750i	−0.0935515	−	0.107964i
$50$	−3.70017	+	2.37795i	−0.523283	+	0.336294i
$51$	−0.776962	−	5.40389i	−0.108796	−	0.756696i
$52$	−3.66563	−	2.35576i	−0.508331	−	0.326685i
$53$	−1.43740	+	3.14748i	−0.197443	+	0.432339i	−0.982294	−	0.187345i	$-0.940012\pi$
$53$	−1.43740	+	3.14748i	−0.197443	+	0.432339i	0.784852	+	0.619684i	$0.212739\pi$
$54$	0.654861	−	0.755750i	0.0891153	−	0.102844i
$55$	−0.118510	+	0.824254i	−0.0159799	+	0.111142i
$56$	0.415415	+	0.909632i	0.0555122	+	0.121555i
$57$	1.13353	+	0.332834i	0.150139	+	0.0440849i
$58$	−2.41586	−	0.709361i	−0.317218	−	0.0931436i
$59$	2.35950	+	5.16658i	0.307180	+	0.672631i	0.998766	−	0.0496635i	$-0.0158149\pi$
$59$	2.35950	+	5.16658i	0.307180	+	0.672631i	−0.691586	+	0.722294i	$0.743088\pi$
$60$	0.110384	−	0.767734i	0.0142505	−	0.0991141i
$61$	−1.16601	+	1.34565i	−0.149293	+	0.172293i	−0.825470	−	0.564446i	$-0.809090\pi$
$61$	−1.16601	+	1.34565i	−0.149293	+	0.172293i	0.676177	+	0.736739i	$0.263635\pi$
$62$	2.02876	−	4.44236i	0.257653	−	0.564181i
$63$	0.841254	+	0.540641i	0.105988	+	0.0681143i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−2.84317	+	1.82719i	−0.352652	+	0.226635i
$66$	0.703071	+	0.811387i	0.0865420	+	0.0998748i
$67$	13.0559	−	3.83355i	1.59503	−	0.468342i	0.640870	−	0.767649i	$-0.278574\pi$
$67$	13.0559	−	3.83355i	1.59503	−	0.468342i	0.954157	+	0.299307i	$0.0967555\pi$
$68$	−5.45946			−0.662056
$69$	0.445974	−	4.77505i	0.0536890	−	0.574849i
$70$	0.775629			0.0927054
$71$	2.97654	−	0.873991i	0.353250	−	0.103724i	−0.100293	−	0.994958i	$-0.531978\pi$
$71$	2.97654	−	0.873991i	0.353250	−	0.103724i	0.453543	+	0.891234i	$0.350160\pi$
$72$	−0.654861	−	0.755750i	−0.0771761	−	0.0890659i
$73$	12.3622	−	7.94471i	1.44689	−	0.929858i	0.447520	−	0.894274i	$-0.352307\pi$
$73$	12.3622	−	7.94471i	1.44689	−	0.929858i	0.999367	−	0.0355840i	$-0.0113291\pi$
$74$	0.536989	+	3.73484i	0.0624238	+	0.434167i
$75$	3.70017	+	2.37795i	0.427259	+	0.274583i
$76$	0.490764	−	1.07462i	0.0562945	−	0.123268i
$77$	−0.703071	+	0.811387i	−0.0801223	+	0.0924661i
$78$	−0.620114	+	4.31299i	−0.0702141	+	0.488350i
$79$	−2.51910	−	5.51607i	−0.283421	−	0.620606i	0.713358	−	0.700800i	$-0.247173\pi$
$79$	−2.51910	−	5.51607i	−0.283421	−	0.620606i	−0.996779	+	0.0801938i	$0.974446\pi$
$80$	−0.744211	−	0.218520i	−0.0832053	−	0.0244313i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	1.14662	+	2.51075i	0.126623	+	0.277266i
$83$	−0.124557	+	0.866311i	−0.0136719	+	0.0950900i	−0.995515	−	0.0946056i	$-0.969841\pi$
$83$	−0.124557	+	0.866311i	−0.0136719	+	0.0950900i	0.981843	+	0.189696i	$0.0607501\pi$
$84$	0.654861	−	0.755750i	0.0714512	−	0.0824590i
$85$	−1.75908	+	3.85185i	−0.190799	+	0.417792i
$86$	9.28994	+	5.97028i	1.00176	+	0.643792i
$87$	0.358328	+	2.49222i	0.0384167	+	0.267194i
$88$	0.903185	−	0.580442i	0.0962799	−	0.0618753i
$89$	−4.75182	−	5.48389i	−0.503692	−	0.581292i	0.445780	−	0.895142i	$-0.352926\pi$
$89$	−4.75182	−	5.48389i	−0.503692	−	0.581292i	−0.949472	+	0.313851i	$0.898381\pi$
$90$	−0.744211	+	0.218520i	−0.0784467	+	0.0230340i
$91$	−4.35734			−0.456774
$92$	−4.66298	−	1.12100i	−0.486149	−	0.116872i
$93$	−4.88369			−0.506415
$94$	8.33206	−	2.44651i	0.859386	−	0.252339i
$95$	−0.600059	−	0.692504i	−0.0615647	−	0.0710495i
$96$	−0.841254	+	0.540641i	−0.0858601	+	0.0551789i
$97$	−1.00635	−	6.99932i	−0.102179	−	0.710674i	−0.974931	−	0.222508i	$-0.928575\pi$
$97$	−1.00635	−	6.99932i	−0.102179	−	0.710674i	0.872751	−	0.488165i	$-0.162334\pi$
$98$	0.841254	+	0.540641i	0.0849794	+	0.0546130i
$99$	0.445997	−	0.976598i	0.0448244	−	0.0981518i
$100$	2.88034	−	3.32409i	0.288034	−	0.332409i
$101$	0.587180	−	4.08393i	0.0584266	−	0.406366i	−0.939530	−	0.342467i	$-0.888737\pi$
$101$	0.587180	−	4.08393i	0.0584266	−	0.406366i	0.997956	−	0.0638987i	$-0.0203534\pi$
$102$	2.26794	+	4.96610i	0.224560	+	0.491717i
$103$	14.6940	+	4.31456i	1.44785	+	0.425126i	0.908829	−	0.417169i	$-0.136978\pi$
$103$	14.6940	+	4.31456i	1.44785	+	0.425126i	0.539017	+	0.842295i	$0.318796\pi$
$104$	4.18084	+	1.22761i	0.409965	+	0.120377i
$105$	−0.322208	−	0.705537i	−0.0314443	−	0.0688534i
$106$	0.492433	−	3.42495i	0.0478293	−	0.332660i
$107$	2.56679	−	2.96223i	0.248141	−	0.286370i	−0.617991	−	0.786185i	$-0.712053\pi$
$107$	2.56679	−	2.96223i	0.248141	−	0.286370i	0.866132	+	0.499815i	$0.166599\pi$
$108$	−0.415415	+	0.909632i	−0.0399733	+	0.0875294i
$109$	5.30659	+	3.41034i	0.508279	+	0.326651i	0.769520	−	0.638623i	$-0.220495\pi$
$109$	5.30659	+	3.41034i	0.508279	+	0.326651i	−0.261241	+	0.965274i	$0.584132\pi$
$110$	−0.118510	−	0.824254i	−0.0112995	−	0.0785895i
$111$	3.17426	−	2.03997i	0.301287	−	0.193626i
$112$	−0.654861	−	0.755750i	−0.0618785	−	0.0714116i
$113$	−8.81659	+	2.58878i	−0.829395	+	0.243532i	−0.668757	−	0.743481i	$-0.733173\pi$
$113$	−8.81659	+	2.58878i	−0.829395	+	0.243532i	−0.160638	+	0.987013i	$0.551355\pi$
$114$	−1.18138			−0.110647
$115$	−2.29335	+	2.92871i	−0.213856	+	0.273104i
$116$	2.51785			0.233777
$117$	4.18084	−	1.22761i	0.386519	−	0.113492i
$118$	−3.71951	−	4.29255i	−0.342409	−	0.395161i
$119$	−4.59279	+	2.95161i	−0.421020	+	0.270573i
$120$	0.110384	+	0.767734i	0.0100766	+	0.0700842i
$121$	−8.28411	−	5.32388i	−0.753101	−	0.483989i
$122$	0.739669	−	1.61965i	0.0669665	−	0.146636i
$123$	1.80754	−	2.08601i	0.162980	−	0.188089i
$124$	−0.695022	+	4.83398i	−0.0624148	+	0.434105i
$125$	−3.02824	−	6.63092i	−0.270854	−	0.593087i
$126$	−0.959493	−	0.281733i	−0.0854784	−	0.0250987i
$127$	13.4197	+	3.94038i	1.19081	+	0.349652i	0.816331	−	0.577585i	$-0.196005\pi$
$127$	13.4197	+	3.94038i	1.19081	+	0.349652i	0.374475	+	0.927237i	$0.377823\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$	1.57158	−	10.9306i	0.138370	−	0.962383i
$130$	2.21322	−	2.55419i	0.194112	−	0.224018i
$131$	4.56656	−	9.99937i	0.398982	−	0.873649i	−0.598390	−	0.801205i	$-0.704193\pi$
$131$	4.56656	−	9.99937i	0.398982	−	0.873649i	0.997372	−	0.0724443i	$-0.0230800\pi$
$132$	−0.903185	−	0.580442i	−0.0786122	−	0.0505210i
$133$	−0.168128	−	1.16936i	−0.0145786	−	0.101396i
$134$	−11.4470	+	7.35652i	−0.988868	+	0.635507i
$135$	0.507929	+	0.586181i	0.0437156	+	0.0504505i
$136$	5.23831	−	1.53811i	0.449181	−	0.131892i
$137$	14.8007			1.26451			0.632257	−	0.774759i	$-0.282129\pi$
$137$	14.8007			1.26451			0.632257	+	0.774759i	$0.282129\pi$
$138$	0.917378	+	4.70727i	0.0780924	+	0.400710i
$139$	−19.6018			−1.66261			−0.831304	−	0.555819i	$-0.812405\pi$
$139$	−19.6018			−1.66261			−0.831304	+	0.555819i	$0.812405\pi$
$140$	−0.744211	+	0.218520i	−0.0628973	+	0.0184683i
$141$	−5.68669	−	6.56279i	−0.478906	−	0.552687i
$142$	−2.60974	+	1.67718i	−0.219004	+	0.140746i
$143$	0.665766	+	4.63051i	0.0556742	+	0.387222i
$144$	0.841254	+	0.540641i	0.0701045	+	0.0450534i
$145$	0.811272	−	1.77644i	0.0673724	−	0.147525i
$146$	−9.62317	+	11.1057i	−0.796419	+	0.919117i
$147$	0.142315	−	0.989821i	0.0117379	−	0.0816391i
$148$	−1.56746	−	3.43227i	−0.128845	−	0.282131i
$149$	−9.79673	−	2.87658i	−0.802580	−	0.235659i	−0.145381	−	0.989376i	$-0.546441\pi$
$149$	−9.79673	−	2.87658i	−0.802580	−	0.235659i	−0.657199	+	0.753717i	$0.728259\pi$
$150$	−4.22023	−	1.23917i	−0.344581	−	0.101178i
$151$	9.43932	+	20.6692i	0.768161	+	1.68204i	0.730661	+	0.682741i	$0.239212\pi$
$151$	9.43932	+	20.6692i	0.768161	+	1.68204i	0.0375001	+	0.999297i	$0.488061\pi$
$152$	−0.168128	+	1.16936i	−0.0136370	+	0.0948474i
$153$	3.57518	−	4.12598i	0.289036	−	0.333566i
$154$	0.445997	−	0.976598i	0.0359395	−	0.0786965i
$155$	3.18661	+	2.04791i	0.255955	+	0.164492i
$156$	−0.620114	−	4.31299i	−0.0496489	−	0.345316i
$157$	−14.5449	+	9.34744i	−1.16081	+	0.746007i	−0.971763	−	0.235961i	$-0.924176\pi$
$157$	−14.5449	+	9.34744i	−1.16081	+	0.746007i	−0.189047	+	0.981968i	$0.560540\pi$
$158$	3.97112	+	4.58291i	0.315925	+	0.364597i
$159$	−3.32000	+	0.974841i	−0.263294	+	0.0773100i
$160$	0.775629			0.0613189
$161$	−4.52880	+	1.57796i	−0.356920	+	0.124360i
$162$	1.00000			0.0785674
$163$	−3.69150	+	1.08392i	−0.289141	+	0.0848994i	−0.423087	−	0.906089i	$-0.639053\pi$
$163$	−3.69150	+	1.08392i	−0.289141	+	0.0848994i	0.133946	+	0.990989i	$0.457235\pi$
$164$	−1.80754	−	2.08601i	−0.141145	−	0.162890i
$165$	−0.700537	+	0.450208i	−0.0545367	+	0.0350486i
$166$	−0.124557	−	0.866311i	−0.00966748	−	0.0672388i
$167$	−14.6608	−	9.42195i	−1.13449	−	0.729092i	−0.167997	−	0.985788i	$-0.553730\pi$
$167$	−14.6608	−	9.42195i	−1.13449	−	0.729092i	−0.966492	+	0.256695i	$0.917366\pi$
$168$	−0.415415	+	0.909632i	−0.0320500	+	0.0701796i
$169$	−3.92028	+	4.52424i	−0.301560	+	0.348019i
$170$	0.602634	−	4.19141i	0.0462199	−	0.321467i
$171$	0.490764	+	1.07462i	0.0375297	+	0.0821785i
$172$	−10.5957	−	3.11116i	−0.807911	−	0.237224i
$173$	14.7435	+	4.32907i	1.12092	+	0.329133i	0.789135	−	0.614220i	$-0.210529\pi$
$173$	14.7435	+	4.32907i	1.12092	+	0.329133i	0.331790	+	0.943353i	$0.392347\pi$
$174$	−1.04595	−	2.29032i	−0.0792935	−	0.173629i
$175$	0.625958	−	4.35363i	0.0473179	−	0.329104i
$176$	−0.703071	+	0.811387i	−0.0529959	+	0.0611606i
$177$	−2.35950	+	5.16658i	−0.177351	+	0.388344i
$178$	6.10433	+	3.92302i	0.457539	+	0.294042i
$179$	1.88062	+	13.0800i	0.140564	+	0.977644i	0.930979	+	0.365072i	$0.118956\pi$
$179$	1.88062	+	13.0800i	0.140564	+	0.977644i	−0.790415	+	0.612572i	$0.790135\pi$
$180$	0.652501	−	0.419337i	0.0486345	−	0.0312555i
$181$	1.96443	+	2.26708i	0.146015	+	0.168511i	0.824046	−	0.566523i	$-0.191712\pi$
$181$	1.96443	+	2.26708i	0.146015	+	0.168511i	−0.678031	+	0.735034i	$0.737166\pi$
$182$	4.18084	−	1.22761i	0.309904	−	0.0909962i
$183$	−1.78055			−0.131622
$184$	4.78992	−	0.238126i	0.353117	−	0.0175549i
$185$	−2.92664			−0.215171
$186$	4.68587	−	1.37590i	0.343585	−	0.100886i
$187$	3.83838	+	4.42973i	0.280690	+	0.323934i
$188$	−7.30529	+	4.69483i	−0.532793	+	0.342405i
$189$	0.142315	+	0.989821i	0.0103519	+	0.0719989i
$190$	0.770853	+	0.495397i	0.0559236	+	0.0359399i
$191$	−8.40696	+	18.4087i	−0.608306	+	1.33201i	0.315420	+	0.948952i	$0.397855\pi$
$191$	−8.40696	+	18.4087i	−0.608306	+	1.33201i	−0.923726	+	0.383053i	$0.874873\pi$
$192$	0.654861	−	0.755750i	0.0472605	−	0.0545415i
$193$	1.40243	−	9.75410i	0.100949	−	0.702115i	−0.875001	−	0.484121i	$-0.839139\pi$
$193$	1.40243	−	9.75410i	0.100949	−	0.702115i	0.975950	−	0.217994i	$-0.0699514\pi$
$194$	2.93752	+	6.43228i	0.210902	+	0.461811i
$195$	−3.24278	−	0.952166i	−0.232220	−	0.0681860i
$196$	−0.959493	−	0.281733i	−0.0685352	−	0.0201238i
$197$	−2.45307	−	5.37147i	−0.174774	−	0.382702i	0.801891	−	0.597470i	$-0.203827\pi$
$197$	−2.45307	−	5.37147i	−0.174774	−	0.382702i	−0.976665	+	0.214769i	$0.931100\pi$
$198$	−0.152792	+	1.06269i	−0.0108584	+	0.0755221i
$199$	4.98774	−	5.75615i	0.353571	−	0.408043i	−0.550904	−	0.834568i	$-0.685717\pi$
$199$	4.98774	−	5.75615i	0.353571	−	0.408043i	0.904476	+	0.426525i	$0.140263\pi$
$200$	−1.82716	+	4.00092i	−0.129200	+	0.282908i
$201$	11.4470	+	7.35652i	0.807407	+	0.518889i
$202$	0.587180	+	4.08393i	0.0413138	+	0.287344i
$203$	2.11815	−	1.36125i	0.148665	−	0.0955412i
$204$	−3.57518	−	4.12598i	−0.250313	−	0.288877i
$205$	−2.05416	+	0.603156i	−0.143469	+	0.0421262i
$206$	−15.3144			−1.06700
$207$	3.90079	−	2.78995i	0.271124	−	0.193915i
$208$	−4.35734			−0.302127
$209$	−1.21698	+	0.357337i	−0.0841801	+	0.0247175i
$210$	0.507929	+	0.586181i	0.0350504	+	0.0404504i
$211$	9.99551	−	6.42372i	0.688119	−	0.442227i	−0.149298	−	0.988792i	$-0.547701\pi$
$211$	9.99551	−	6.42372i	0.688119	−	0.442227i	0.837417	+	0.546565i	$0.184065\pi$
$212$	0.492433	+	3.42495i	0.0338204	+	0.235226i
$213$	2.60974	+	1.67718i	0.178816	+	0.114918i
$214$	−1.62826	+	3.56539i	−0.111306	+	0.243725i
$215$	−5.60905	+	6.47318i	−0.382534	+	0.441467i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	2.02876	+	4.44236i	0.137721	+	0.301567i
$218$	−6.05243	−	1.77716i	−0.409923	−	0.120364i
$219$	14.0997	+	4.14006i	0.952772	+	0.279759i
$220$	0.345928	+	0.757478i	0.0233225	+	0.0510691i
$221$	−3.38549	+	23.5466i	−0.227733	+	1.58391i
$222$	−2.47095	+	2.85163i	−0.165840	+	0.191389i
$223$	−9.12588	+	19.9829i	−0.611114	+	1.33815i	0.310696	+	0.950509i	$0.399438\pi$
$223$	−9.12588	+	19.9829i	−0.611114	+	1.33815i	−0.921809	+	0.387643i	$0.873289\pi$
$224$	0.841254	+	0.540641i	0.0562086	+	0.0361231i
$225$	0.625958	+	4.35363i	0.0417305	+	0.290242i
$226$	7.73011	−	4.96784i	0.514199	−	0.330456i
$227$	5.40913	+	6.24247i	0.359016	+	0.414327i	0.906310	−	0.422614i	$-0.138887\pi$
$227$	5.40913	+	6.24247i	0.359016	+	0.414327i	−0.547293	+	0.836941i	$0.684342\pi$
$228$	1.13353	−	0.332834i	0.0750697	−	0.0220425i
$229$	−18.2054			−1.20305			−0.601524	−	0.798855i	$-0.705439\pi$
$229$	−18.2054			−1.20305			−0.601524	+	0.798855i	$0.705439\pi$
$230$	1.37534	−	3.45619i	0.0906874	−	0.227894i
$231$	−1.07362			−0.0706389
$232$	−2.41586	+	0.709361i	−0.158609	+	0.0465718i
$233$	12.6534	+	14.6028i	0.828953	+	0.956662i	0.999589	−	0.0286719i	$-0.00912779\pi$
$233$	12.6534	+	14.6028i	0.828953	+	0.956662i	−0.170636	+	0.985334i	$0.554582\pi$
$234$	−3.66563	+	2.35576i	−0.239630	+	0.154001i
$235$	0.958550	+	6.66686i	0.0625289	+	0.434898i
$236$	4.77820	+	3.07076i	0.311034	+	0.199889i
$237$	2.51910	−	5.51607i	0.163633	−	0.358307i
$238$	3.57518	−	4.12598i	0.231745	−	0.267448i
$239$	−0.0798705	+	0.555511i	−0.00516639	+	0.0359330i	−0.992242	−	0.124325i	$-0.960324\pi$
$239$	−0.0798705	+	0.555511i	−0.00516639	+	0.0359330i	0.987075	+	0.160258i	$0.0512326\pi$
$240$	−0.322208	−	0.705537i	−0.0207984	−	0.0455422i
$241$	−6.95381	−	2.04182i	−0.447934	−	0.131525i	0.0499828	−	0.998750i	$-0.484083\pi$
$241$	−6.95381	−	2.04182i	−0.447934	−	0.131525i	−0.497917	+	0.867225i	$0.665902\pi$
$242$	9.44846	+	2.77432i	0.607370	+	0.178340i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	−0.253399	+	1.76243i	−0.0162222	+	0.112828i
$245$	−0.507929	+	0.586181i	−0.0324504	+	0.0374498i
$246$	−1.14662	+	2.51075i	−0.0731060	+	0.160080i
$247$	−4.33051	−	2.78305i	−0.275544	−	0.177081i
$248$	−0.695022	−	4.83398i	−0.0441339	−	0.306958i
$249$	−0.736282	+	0.473179i	−0.0466599	+	0.0299865i
$250$	4.77372	+	5.50917i	0.301917	+	0.348430i
$251$	13.4987	−	3.96358i	0.852031	−	0.250179i	0.173576	−	0.984821i	$-0.444468\pi$
$251$	13.4987	−	3.96358i	0.852031	−	0.250179i	0.678455	+	0.734642i	$0.262650\pi$
$252$	1.00000			0.0629941
$253$	2.36884	+	4.57162i	0.148928	+	0.287415i
$254$	−13.9862			−0.877575
$255$	−4.06299	+	1.19300i	−0.254434	+	0.0747086i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	13.0263	−	8.37150i	0.812559	−	0.522200i	−0.0671331	−	0.997744i	$-0.521385\pi$
$257$	13.0263	−	8.37150i	0.812559	−	0.522200i	0.879692	+	0.475544i	$0.157749\pi$
$258$	1.57158	+	10.9306i	0.0978422	+	0.680507i
$259$	−3.17426	−	2.03997i	−0.197239	−	0.126758i
$260$	−1.40397	+	3.07427i	−0.0870706	+	0.190658i
$261$	−1.64884	+	1.90286i	−0.102061	+	0.117784i
$262$	−1.56443	+	10.8809i	−0.0966510	+	0.672223i
$263$	6.98429	+	15.2935i	0.430670	+	0.943035i	0.993218	+	0.116270i	$0.0370939\pi$
$263$	6.98429	+	15.2935i	0.430670	+	0.943035i	−0.562548	+	0.826765i	$0.690179\pi$
$264$	1.03013	+	0.302473i	0.0634001	+	0.0186159i
$265$	2.57509	+	0.756115i	0.158187	+	0.0464478i
$266$	0.490764	+	1.07462i	0.0300907	+	0.0658894i
$267$	1.03267	−	7.18237i	0.0631984	−	0.439554i
$268$	8.91072	−	10.2835i	0.544309	−	0.628166i
$269$	−4.86117	+	10.6445i	−0.296391	+	0.649005i	−0.997977	−	0.0635799i	$-0.979748\pi$
$269$	−4.86117	+	10.6445i	−0.296391	+	0.649005i	0.701586	+	0.712585i	$0.252476\pi$
$270$	−0.652501	−	0.419337i	−0.0397099	−	0.0255200i
$271$	3.73830	+	26.0004i	0.227085	+	1.57941i	0.710292	+	0.703907i	$0.248563\pi$
$271$	3.73830	+	26.0004i	0.227085	+	1.57941i	−0.483206	+	0.875507i	$0.660528\pi$
$272$	−4.59279	+	2.95161i	−0.278479	+	0.178967i
$273$	−2.85345	−	3.29306i	−0.172699	−	0.199305i
$274$	−14.2012	+	4.16985i	−0.857927	+	0.251910i
$275$	−4.72220			−0.284760
$276$	−2.20641	−	4.25814i	−0.132810	−	0.256310i
$277$	−0.482531			−0.0289925			−0.0144962	−	0.999895i	$-0.504614\pi$
$277$	−0.482531			−0.0289925			−0.0144962	+	0.999895i	$0.504614\pi$
$278$	18.8078	−	5.52248i	1.12802	−	0.331216i
$279$	−3.19814	−	3.69085i	−0.191468	−	0.220965i
$280$	0.652501	−	0.419337i	0.0389944	−	0.0250602i
$281$	−1.53578	−	10.6816i	−0.0916170	−	0.637210i	−0.982952	−	0.183864i	$-0.941139\pi$
$281$	−1.53578	−	10.6816i	−0.0916170	−	0.637210i	0.891335	−	0.453346i	$-0.149770\pi$
$282$	7.30529	+	4.69483i	0.435024	+	0.279573i
$283$	−8.55988	+	18.7435i	−0.508832	+	1.11419i	0.464665	+	0.885487i	$0.346175\pi$
$283$	−8.55988	+	18.7435i	−0.508832	+	1.11419i	−0.973497	+	0.228700i	$0.926552\pi$
$284$	2.03151	−	2.34449i	0.120548	−	0.139120i
$285$	0.130405	−	0.906988i	0.00772454	−	0.0537253i
$286$	−1.94336	−	4.25537i	−0.114913	−	0.251625i
$287$	−2.64838	−	0.777634i	−0.156329	−	0.0459023i
$288$	−0.959493	−	0.281733i	−0.0565387	−	0.0166013i
$289$	5.31967	+	11.6484i	0.312922	+	0.685203i
$290$	−0.277929	+	1.93304i	−0.0163206	+	0.113512i
$291$	4.63072	−	5.34413i	0.271457	−	0.313278i
$292$	6.10452	−	13.3670i	0.357240	−	0.782246i
$293$	−17.7560	−	11.4111i	−1.03732	−	0.666642i	−0.0929940	−	0.995667i	$-0.529644\pi$
$293$	−17.7560	−	11.4111i	−1.03732	−	0.666642i	−0.944321	+	0.329025i	$0.893280\pi$
$294$	0.142315	+	0.989821i	0.00829997	+	0.0577276i
$295$	3.70611	−	2.38177i	0.215778	−	0.138672i
$296$	2.47095	+	2.85163i	0.143621	+	0.165748i
$297$	1.03013	−	0.302473i	0.0597742	−	0.0175513i
$298$	10.2103			0.591468
$299$	−7.72642	+	19.4162i	−0.446831	+	1.12287i
$300$	4.39840			0.253942
$301$	−10.5957	+	3.11116i	−0.610723	+	0.179325i
$302$	−14.8802	−	17.1726i	−0.856256	−	0.988173i
$303$	3.47095	−	2.23064i	0.199401	−	0.128147i
$304$	−0.168128	−	1.16936i	−0.00964282	−	0.0670673i
$305$	1.16181	+	0.746652i	0.0665252	+	0.0427531i
$306$	−2.26794	+	4.96610i	−0.129650	+	0.283893i
$307$	−5.48311	+	6.32785i	−0.312938	+	0.361149i	−0.890329	−	0.455318i	$-0.849525\pi$
$307$	−5.48311	+	6.32785i	−0.312938	+	0.361149i	0.577391	+	0.816468i	$0.304071\pi$
$308$	−0.152792	+	1.06269i	−0.00870612	+	0.0605524i
$309$	6.36182	+	13.9304i	0.361911	+	0.792475i
$310$	−3.63450	−	1.06718i	−0.206426	−	0.0606120i
$311$	5.59141	+	1.64179i	0.317060	+	0.0930971i	0.436390	−	0.899757i	$-0.356257\pi$
$311$	5.59141	+	1.64179i	0.317060	+	0.0930971i	−0.119331	+	0.992855i	$0.538075\pi$
$312$	1.81011	+	3.96358i	0.102477	+	0.224393i
$313$	0.282601	−	1.96553i	0.0159736	−	0.111099i	−0.980275	−	0.197640i	$-0.936672\pi$
$313$	0.282601	−	1.96553i	0.0159736	−	0.111099i	0.996248	+	0.0865413i	$0.0275814\pi$
$314$	11.3223	−	13.0666i	0.638952	−	0.737390i
$315$	0.322208	−	0.705537i	0.0181544	−	0.0397525i
$316$	−5.10141	−	3.27848i	−0.286977	−	0.184429i
$317$	1.17576	+	8.17758i	0.0660371	+	0.459298i	0.995831	+	0.0912177i	$0.0290759\pi$
$317$	1.17576	+	8.17758i	0.0660371	+	0.459298i	−0.929794	+	0.368081i	$0.880015\pi$
$318$	2.91088	−	1.87071i	0.163234	−	0.104904i
$319$	−1.77023	−	2.04295i	−0.0991137	−	0.114383i
$320$	−0.744211	+	0.218520i	−0.0416026	+	0.0122156i
$321$	3.91960			0.218771
$322$	3.90079	−	2.78995i	0.217383	−	0.155478i
$323$	−6.44971			−0.358871
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	−12.5506	−	14.4842i	−0.696183	−	0.803438i
$326$	3.23659	−	2.08003i	0.179258	−	0.115202i
$327$	0.897715	+	6.24375i	0.0496438	+	0.345280i
$328$	2.32202	+	1.49227i	0.128212	+	0.0823968i
$329$	−3.60739	+	7.89908i	−0.198882	+	0.435490i
$330$	0.545322	−	0.629335i	0.0300190	−	0.0346438i
$331$	−3.48028	+	24.2059i	−0.191293	+	1.33047i	0.637297	+	0.770618i	$0.280053\pi$
$331$	−3.48028	+	24.2059i	−0.191293	+	1.33047i	−0.828590	+	0.559856i	$0.810857\pi$
$332$	0.363579	+	0.796128i	0.0199540	+	0.0436932i
$333$	3.62041	+	1.06305i	0.198397	+	0.0582546i
$334$	16.7214	+	4.90986i	0.914956	+	0.268655i
$335$	−4.38430	−	9.60027i	−0.239540	−	0.524519i
$336$	0.142315	−	0.989821i	0.00776391	−	0.0539992i
$337$	3.38281	−	3.90397i	0.184274	−	0.212663i	−0.656095	−	0.754678i	$-0.727793\pi$
$337$	3.38281	−	3.90397i	0.184274	−	0.212663i	0.840369	+	0.542015i	$0.182338\pi$
$338$	2.48685	−	5.44545i	0.135267	−	0.296194i
$339$	−7.73011	−	4.96784i	−0.419842	−	0.269816i
$340$	0.602634	+	4.19141i	0.0326824	+	0.227311i
$341$	4.41088	−	2.83470i	0.238863	−	0.153508i
$342$	−0.773641	−	0.892829i	−0.0418337	−	0.0482787i
$343$	−0.959493	+	0.281733i	−0.0518078	+	0.0152121i
$344$	11.0430			0.595397
$345$	−3.71520	+	0.184697i	−0.200020	+	0.00994376i
$346$	−15.3659			−0.826076
$347$	11.3718	−	3.33905i	0.610468	−	0.179250i	0.0381372	−	0.999273i	$-0.487858\pi$
$347$	11.3718	−	3.33905i	0.610468	−	0.179250i	0.572331	+	0.820023i	$0.306039\pi$
$348$	1.64884	+	1.90286i	0.0883872	+	0.102004i
$349$	−5.48789	+	3.52685i	−0.293760	+	0.188788i	−0.679217	−	0.733938i	$-0.737680\pi$
$349$	−5.48789	+	3.52685i	−0.293760	+	0.188788i	0.385457	+	0.922726i	$0.374044\pi$
$350$	0.625958	+	4.35363i	0.0334588	+	0.232711i
$351$	3.66563	+	2.35576i	0.195657	+	0.125741i
$352$	0.445997	−	0.976598i	0.0237717	−	0.0520528i
$353$	15.9540	−	18.4119i	0.849145	−	0.979965i	−0.150818	−	0.988561i	$-0.548191\pi$
$353$	15.9540	−	18.4119i	0.849145	−	0.979965i	0.999963	+	0.00859625i	$0.00273631\pi$
$354$	0.808327	−	5.62204i	0.0429621	−	0.298808i
$355$	−0.999554	−	2.18872i	−0.0530508	−	0.116165i
$356$	−6.96230	−	2.04432i	−0.369001	−	0.108349i
$357$	−5.23831	−	1.53811i	−0.277241	−	0.0814052i
$358$	−5.48950	−	12.0203i	−0.290129	−	0.635294i
$359$	4.29771	−	29.8912i	0.226824	−	1.57760i	−0.484537	−	0.874771i	$-0.661012\pi$
$359$	4.29771	−	29.8912i	0.226824	−	1.57760i	0.711361	−	0.702827i	$-0.248079\pi$
$360$	−0.507929	+	0.586181i	−0.0267702	+	0.0308945i
$361$	−7.31311	+	16.0135i	−0.384900	+	0.842814i
$362$	−2.52357	−	1.62180i	−0.132636	−	0.0852399i
$363$	−1.40142	−	9.74711i	−0.0735556	−	0.511591i
$364$	−3.66563	+	2.35576i	−0.192131	+	0.123475i
$365$	−7.46401	−	8.61393i	−0.390684	−	0.450873i
$366$	1.70843	−	0.501640i	0.0893010	−	0.0262211i
$367$	0.720164			0.0375922			0.0187961	−	0.999823i	$-0.494017\pi$
$367$	0.720164			0.0375922			0.0187961	+	0.999823i	$0.494017\pi$
$368$	−4.52880	+	1.57796i	−0.236080	+	0.0822566i
$369$	2.76019			0.143690
$370$	2.80809	−	0.824530i	0.145986	−	0.0428653i
$371$	2.26593	+	2.61502i	0.117641	+	0.135765i
$372$	−4.10842	+	2.64032i	−0.213012	+	0.136894i
$373$	−3.64048	−	25.3201i	−0.188497	−	1.31103i	−0.835902	−	0.548879i	$-0.815055\pi$
$373$	−3.64048	−	25.3201i	−0.188497	−	1.31103i	0.647405	−	0.762146i	$-0.275854\pi$
$374$	−4.93090	−	3.16890i	−0.254971	−	0.163860i
$375$	3.02824	−	6.63092i	0.156378	−	0.342419i
$376$	5.68669	−	6.56279i	0.293269	−	0.338450i
$377$	1.56136	−	10.8595i	0.0804139	−	0.559291i
$378$	−0.415415	−	0.909632i	−0.0213666	−	0.0467864i
$379$	−19.3186	−	5.67246i	−0.992332	−	0.291375i	−0.255026	−	0.966934i	$-0.582084\pi$
$379$	−19.3186	−	5.67246i	−0.992332	−	0.291375i	−0.737306	+	0.675559i	$0.763902\pi$
$380$	−0.879197	−	0.258156i	−0.0451019	−	0.0132431i
$381$	5.81009	+	12.7223i	0.297660	+	0.651785i
$382$	2.88010	−	20.0315i	0.147359	−	1.02490i
$383$	15.3593	−	17.7255i	0.784822	−	0.905733i	−0.212626	−	0.977134i	$-0.568202\pi$
$383$	15.3593	−	17.7255i	0.784822	−	0.905733i	0.997448	+	0.0714011i	$0.0227470\pi$
$384$	−0.415415	+	0.909632i	−0.0211991	+	0.0464195i
$385$	0.700537	+	0.450208i	0.0357027	+	0.0229447i
$386$	1.40243	+	9.75410i	0.0713817	+	0.496470i
$387$	9.28994	−	5.97028i	0.472234	−	0.303486i
$388$	−4.63072	−	5.34413i	−0.235089	−	0.271307i
$389$	15.3214	−	4.49877i	0.776826	−	0.228097i	0.130797	−	0.991409i	$-0.458246\pi$
$389$	15.3214	−	4.49877i	0.776826	−	0.228097i	0.646029	+	0.763312i	$0.276428\pi$
$390$	3.37968			0.171137
$391$	5.00839	+	25.6992i	0.253285	+	1.29966i
$392$	1.00000			0.0505076
$393$	10.5475	−	3.09702i	0.532050	−	0.156224i
$394$	3.86702	+	4.46278i	0.194818	+	0.224832i
$395$	−3.95681	+	2.54288i	−0.199088	+	0.127946i
$396$	−0.152792	−	1.06269i	−0.00767808	−	0.0534022i
$397$	−15.2109	−	9.77546i	−0.763414	−	0.490616i	0.100078	−	0.994980i	$-0.468091\pi$
$397$	−15.2109	−	9.77546i	−0.763414	−	0.490616i	−0.863492	+	0.504363i	$0.831727\pi$
$398$	−3.16400	+	6.92820i	−0.158597	+	0.347279i
$399$	0.773641	−	0.892829i	0.0387305	−	0.0446974i
$400$	0.625958	−	4.35363i	0.0312979	−	0.217682i
$401$	1.84493	+	4.03983i	0.0921312	+	0.201739i	0.950088	−	0.311983i	$-0.100993\pi$
$401$	1.84493	+	4.03983i	0.0921312	+	0.201739i	−0.857956	+	0.513723i	$0.828266\pi$
$402$	−13.0559	−	3.83355i	−0.651167	−	0.191200i
$403$	20.4179	+	5.99525i	1.01709	+	0.298645i
$404$	−1.71397	−	3.75307i	−0.0852732	−	0.186722i
$405$	−0.110384	+	0.767734i	−0.00548500	+	0.0381490i
$406$	−1.64884	+	1.90286i	−0.0818306	+	0.0944376i
$407$	−1.68286	+	3.68495i	−0.0834162	+	0.182656i
$408$	4.59279	+	2.95161i	0.227377	+	0.146126i
$409$	−1.87614	−	13.0488i	−0.0927692	−	0.645224i	−0.982156	−	0.188068i	$-0.939777\pi$
$409$	−1.87614	−	13.0488i	−0.0927692	−	0.645224i	0.889387	−	0.457156i	$-0.151132\pi$
$410$	1.80102	−	1.15745i	0.0889462	−	0.0571623i
$411$	9.69243	+	11.1857i	0.478092	+	0.551748i
$412$	14.6940	−	4.31456i	0.723923	−	0.212563i
$413$	5.67985			0.279487
$414$	−2.95676	+	3.77592i	−0.145317	+	0.185576i
$415$	0.678846			0.0333232
$416$	4.18084	−	1.22761i	0.204983	−	0.0601883i
$417$	−12.8365	−	14.8141i	−0.628605	−	0.725449i
$418$	1.06701	−	0.685724i	0.0521890	−	0.0335399i
$419$	0.136545	+	0.949692i	0.00667066	+	0.0463955i	0.992885	−	0.119078i	$-0.0379939\pi$
$419$	0.136545	+	0.949692i	0.00667066	+	0.0463955i	−0.986214	+	0.165473i	$0.947085\pi$
$420$	−0.652501	−	0.419337i	−0.0318388	−	0.0204615i
$421$	9.09661	−	19.9188i	0.443342	−	0.970783i	−0.547631	−	0.836720i	$-0.684470\pi$
$421$	9.09661	−	19.9188i	0.443342	−	0.970783i	0.990973	−	0.134063i	$-0.0428025\pi$
$422$	−7.78085	+	8.97958i	−0.378766	+	0.437119i
$423$	1.23584	−	8.59543i	0.0600884	−	0.417924i
$424$	−1.43740	−	3.14748i	−0.0698066	−	0.152855i
$425$	−23.0402	−	6.76521i	−1.11761	−	0.328161i
$426$	−2.97654	−	0.873991i	−0.144214	−	0.0423450i
$427$	0.739669	+	1.61965i	0.0357951	+	0.0783803i
$428$	0.557817	−	3.87970i	0.0269631	−	0.187532i
$429$	−3.06352	+	3.53549i	−0.147908	+	0.170695i
$430$	3.55813	−	7.79122i	0.171588	−	0.375726i
$431$	20.3957	+	13.1075i	0.982424	+	0.631366i	0.930116	−	0.367265i	$-0.119706\pi$
$431$	20.3957	+	13.1075i	0.982424	+	0.631366i	0.0523080	+	0.998631i	$0.483342\pi$
$432$	0.142315	+	0.989821i	0.00684713	+	0.0476228i
$433$	−8.85646	+	5.69170i	−0.425614	+	0.273526i	−0.735864	−	0.677130i	$-0.763224\pi$
$433$	−8.85646	+	5.69170i	−0.425614	+	0.273526i	0.310250	+	0.950655i	$0.399587\pi$
$434$	−3.19814	−	3.69085i	−0.153516	−	0.177166i
$435$	1.87381	−	0.550201i	0.0898424	−	0.0263801i
$436$	6.30795			0.302096
$437$	−5.50876	−	1.32432i	−0.263520	−	0.0633510i
$438$	−14.6950			−0.702154
$439$	21.9032	−	6.43135i	1.04538	−	0.306951i	0.286431	−	0.958101i	$-0.407531\pi$
$439$	21.9032	−	6.43135i	1.04538	−	0.306951i	0.758950	+	0.651149i	$0.225713\pi$
$440$	−0.545322	−	0.629335i	−0.0259972	−	0.0300024i
$441$	0.841254	−	0.540641i	0.0400597	−	0.0257448i
$442$	−3.38549	−	23.5466i	−0.161031	−	1.12000i
$443$	22.3772	+	14.3810i	1.06317	+	0.683261i	0.950611	−	0.310384i	$-0.100458\pi$
$443$	22.3772	+	14.3810i	1.06317	+	0.683261i	0.112563	+	0.993645i	$0.464094\pi$
$444$	1.56746	−	3.43227i	0.0743886	−	0.162888i
$445$	−3.68565	+	4.25347i	−0.174717	+	0.201634i
$446$	3.12639	−	21.7445i	0.148039	−	1.02963i
$447$	−4.24152	−	9.28764i	−0.200617	−	0.439290i
$448$	−0.959493	−	0.281733i	−0.0453318	−	0.0133106i
$449$	7.00087	+	2.05564i	0.330391	+	0.0970117i	0.442721	−	0.896659i	$-0.354013\pi$
$449$	7.00087	+	2.05564i	0.330391	+	0.0970117i	−0.112330	+	0.993671i	$0.535831\pi$
$450$	−1.82716	−	4.00092i	−0.0861332	−	0.188605i
$451$	−0.421734	+	2.93322i	−0.0198587	+	0.138120i
$452$	−6.01739	+	6.94443i	−0.283034	+	0.326639i
$453$	−9.43932	+	20.6692i	−0.443498	+	0.971125i
$454$	−6.94873	−	4.46568i	−0.326120	−	0.209585i
$455$	0.480979	+	3.34528i	0.0225486	+	0.156829i
$456$	−0.993842	+	0.638704i	−0.0465409	+	0.0299100i
$457$	−23.6805	−	27.3288i	−1.10773	−	1.27839i	−0.957087	−	0.289799i	$-0.906412\pi$
$457$	−23.6805	−	27.3288i	−1.10773	−	1.27839i	−0.150642	−	0.988588i	$-0.548134\pi$
$458$	17.4680	−	5.12906i	0.816224	−	0.239665i
$459$	5.45946			0.254826
$460$	−0.345911	+	3.70367i	−0.0161282	+	0.172684i
$461$	−39.7520			−1.85144			−0.925718	−	0.378214i	$-0.876538\pi$
$461$	−39.7520			−1.85144			−0.925718	+	0.378214i	$0.876538\pi$
$462$	1.03013	−	0.302473i	0.0479260	−	0.0140723i
$463$	17.3524	+	20.0258i	0.806435	+	0.930676i	0.998716	−	0.0506643i	$-0.0161338\pi$
$463$	17.3524	+	20.0258i	0.806435	+	0.930676i	−0.192281	+	0.981340i	$0.561588\pi$
$464$	2.11815	−	1.36125i	0.0983327	−	0.0631946i
$465$	0.539079	+	3.74938i	0.0249992	+	0.173873i
$466$	−16.2549	−	10.4464i	−0.752996	−	0.483921i
$467$	16.7990	−	36.7847i	0.777366	−	1.70219i	0.0676473	−	0.997709i	$-0.478451\pi$
$467$	16.7990	−	36.7847i	0.777366	−	1.70219i	0.709719	−	0.704485i	$-0.248822\pi$
$468$	2.85345	−	3.29306i	0.131901	−	0.152222i
$469$	1.93648	−	13.4685i	0.0894185	−	0.621919i
$470$	−2.79799	−	6.12675i	−0.129062	−	0.282606i
$471$	−16.5892	−	4.87103i	−0.764391	−	0.224445i
$472$	−5.44978	−	1.60020i	−0.250846	−	0.0736551i
$473$	4.92513	+	10.7845i	0.226458	+	0.495874i
$474$	−0.863006	+	6.00234i	−0.0396392	+	0.275697i
$475$	3.40278	−	3.92702i	0.156130	−	0.180184i
$476$	−2.26794	+	4.96610i	−0.103951	+	0.227621i
$477$	−2.91088	−	1.87071i	−0.133280	−	0.0856538i
$478$	−0.0798705	−	0.555511i	−0.00365319	−	0.0254085i
$479$	21.4544	−	13.7879i	0.980276	−	0.629985i	0.0507384	−	0.998712i	$-0.483843\pi$
$479$	21.4544	−	13.7879i	0.980276	−	0.629985i	0.929538	+	0.368727i	$0.120206\pi$
$480$	0.507929	+	0.586181i	0.0231837	+	0.0267554i
$481$	−15.7754	+	4.63206i	−0.719294	+	0.211204i
$482$	7.24737			0.330109
$483$	−4.15827	−	2.38930i	−0.189208	−	0.108717i
$484$	−9.84734			−0.447607
$485$	−5.26254	+	1.54522i	−0.238959	+	0.0701648i
$486$	0.654861	+	0.755750i	0.0297051	+	0.0342815i
$487$	−20.0945	+	12.9140i	−0.910570	+	0.585188i	−0.909907	−	0.414812i	$-0.863847\pi$
$487$	−20.0945	+	12.9140i	−0.910570	+	0.585188i	−0.000662751		1.00000i	$0.500211\pi$
$488$	−0.253399	−	1.76243i	−0.0114708	−	0.0797815i
$489$	−3.23659	−	2.08003i	−0.146364	−	0.0940623i
$490$	0.322208	−	0.705537i	0.0145559	−	0.0318729i
$491$	18.1259	−	20.9185i	0.818013	−	0.944037i	−0.181211	−	0.983444i	$-0.558002\pi$
$491$	18.1259	−	20.9185i	0.818013	−	0.944037i	0.999223	+	0.0394075i	$0.0125470\pi$
$492$	0.392815	−	2.73209i	0.0177095	−	0.123172i
$493$	−5.71034	−	12.5039i	−0.257181	−	0.563147i
$494$	4.93917	+	1.45027i	0.222224	+	0.0652508i
$495$	−0.798998	−	0.234607i	−0.0359123	−	0.0105448i
$496$	2.02876	+	4.44236i	0.0910940	+	0.199468i
$497$	0.441489	−	3.07063i	0.0198035	−	0.137736i
$498$	0.573147	−	0.661447i	0.0256833	−	0.0296401i
$499$	9.53374	−	20.8760i	0.426789	−	0.934537i	−0.567048	−	0.823685i	$-0.691915\pi$
$499$	9.53374	−	20.8760i	0.426789	−	0.934537i	0.993837	−	0.110852i	$-0.0353580\pi$
$500$	−6.13246	−	3.94109i	−0.274252	−	0.176251i
$501$	−2.48017	−	17.2500i	−0.110806	−	0.770672i
$502$	−11.8352	+	7.60605i	−0.528233	+	0.339475i
$503$	0.775226	+	0.894659i	0.0345656	+	0.0398909i	0.772769	−	0.634687i	$-0.218871\pi$
$503$	0.775226	+	0.894659i	0.0345656	+	0.0398909i	−0.738204	+	0.674578i	$0.764326\pi$
$504$	−0.959493	+	0.281733i	−0.0427392	+	0.0125494i
$505$	−3.20018			−0.142406
$506$	−3.56086	−	3.71906i	−0.158300	−	0.165332i
$507$	−5.98643			−0.265867
$508$	13.4197	−	3.94038i	0.595403	−	0.174826i
$509$	−22.9992	−	26.5425i	−1.01942	−	1.17648i	−0.984194	−	0.177096i	$-0.943330\pi$
$509$	−22.9992	−	26.5425i	−1.01942	−	1.17648i	−0.0352284	−	0.999379i	$-0.511216\pi$
$510$	3.56230	−	2.28935i	0.157741	−	0.101374i
$511$	−2.09131	−	14.5454i	−0.0925143	−	0.643451i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	−0.490764	+	1.07462i	−0.0216678	+	0.0474458i
$514$	−10.1401	+	11.7023i	−0.447262	+	0.516168i
$515$	1.69045	−	11.7574i	0.0744903	−	0.518092i
$516$	−4.58742	−	10.0450i	−0.201950	−	0.442208i
$517$	8.94545	+	2.62662i	0.393421	+	0.115519i
$518$	3.62041	+	1.06305i	0.159072	+	0.0467076i
$519$	6.38322	+	13.9773i	0.280192	+	0.613536i
$520$	0.480979	−	3.34528i	0.0210923	−	0.146700i
$521$	−4.67522	+	5.39549i	−0.204825	+	0.236381i	−0.848863	−	0.528613i	$-0.822712\pi$
$521$	−4.67522	+	5.39549i	−0.204825	+	0.236381i	0.644038	+	0.764994i	$0.277258\pi$
$522$	1.04595	−	2.29032i	0.0457801	−	0.100244i
$523$	14.8487	+	9.54270i	0.649290	+	0.417273i	0.823407	−	0.567452i	$-0.192071\pi$
$523$	14.8487	+	9.54270i	0.649290	+	0.417273i	−0.174117	+	0.984725i	$0.555707\pi$
$524$	−1.56443	−	10.8809i	−0.0683426	−	0.475333i
$525$	3.70017	−	2.37795i	0.161489	−	0.103782i
$526$	−11.0100	−	12.7063i	−0.480061	−	0.554019i
$527$	25.5823	−	7.51164i	1.11438	−	0.327212i
$528$	−1.07362			−0.0467232
$529$	−0.999117	+	22.9783i	−0.0434399	+	0.999056i
$530$	−2.68381			−0.116577
$531$	−5.44978	+	1.60020i	−0.236500	+	0.0694427i
$532$	−0.773641	−	0.892829i	−0.0335416	−	0.0387091i
$533$	−10.1178	+	6.50233i	−0.438251	+	0.281647i
$534$	1.03267	+	7.18237i	0.0446880	+	0.310812i
$535$	−2.55754	−	1.64363i	−0.110572	−	0.0710604i
$536$	−5.65257	+	12.3774i	−0.244154	+	0.534622i
$537$	−8.65365	+	9.98684i	−0.373433	+	0.430964i
$538$	1.66536	−	11.5828i	0.0717988	−	0.499372i
$539$	0.445997	+	0.976598i	0.0192105	+	0.0420650i
$540$	0.744211	+	0.218520i	0.0320257	+	0.00940360i
$541$	13.9630	+	4.09992i	0.600318	+	0.176269i	0.567751	−	0.823200i	$-0.307814\pi$
$541$	13.9630	+	4.09992i	0.600318	+	0.176269i	0.0325670	+	0.999470i	$0.489632\pi$
$542$	−10.9120	−	23.8940i	−0.468712	−	1.02634i
$543$	−0.426912	+	2.96924i	−0.0183206	+	0.127422i
$544$	3.57518	−	4.12598i	0.153285	−	0.176900i
$545$	2.03247	−	4.45049i	0.0870615	−	0.190638i
$546$	3.66563	+	2.35576i	0.156874	+	0.100817i
$547$	1.94664	+	13.5392i	0.0832323	+	0.578893i	0.988172	+	0.153352i	$0.0490070\pi$
$547$	1.94664	+	13.5392i	0.0832323	+	0.578893i	−0.904939	+	0.425541i	$0.860084\pi$
$548$	12.4512	−	8.00189i	0.531888	−	0.341824i
$549$	−1.16601	−	1.34565i	−0.0497643	−	0.0574311i
$550$	4.53092	−	1.33040i	0.193199	−	0.0567284i
$551$	2.97454			0.126720
$552$	3.31669	+	3.46404i	0.141168	+	0.147439i
$553$	−6.06406			−0.257870
$554$	0.462985	−	0.135945i	0.0196703	−	0.00577573i
$555$	−1.91654	−	2.21181i	−0.0813527	−	0.0938860i
$556$	−16.4901	+	10.5976i	−0.699337	+	0.449437i
$557$	−3.55747	−	24.7428i	−0.150735	−	1.04838i	−0.914992	−	0.403473i	$-0.867803\pi$
$557$	−3.55747	−	24.7428i	−0.150735	−	1.04838i	0.764257	−	0.644912i	$-0.223106\pi$
$558$	4.10842	+	2.64032i	0.173923	+	0.111774i
$559$	−19.9889	+	43.7697i	−0.845442	+	1.85126i
$560$	−0.507929	+	0.586181i	−0.0214639	+	0.0247707i
$561$	−0.834160	+	5.80171i	−0.0352183	+	0.244949i
$562$	4.48292	+	9.81623i	0.189101	+	0.414073i
$563$	−11.1022	−	3.25991i	−0.467904	−	0.137389i	0.0392776	−	0.999228i	$-0.487494\pi$
$563$	−11.1022	−	3.25991i	−0.467904	−	0.137389i	−0.507181	+	0.861839i	$0.669313\pi$
$564$	−8.33206	−	2.44651i	−0.350843	−	0.103017i
$565$	2.96071	+	6.48304i	0.124558	+	0.272744i
$566$	2.93248	−	20.3959i	0.123262	−	0.857303i
$567$	−0.654861	+	0.755750i	−0.0275016	+	0.0317385i
$568$	−1.28870	+	2.82186i	−0.0540727	+	0.118403i
$569$	31.7333	+	20.3938i	1.33033	+	0.854951i	0.996159	−	0.0875613i	$-0.0279074\pi$
$569$	31.7333	+	20.3938i	1.33033	+	0.854951i	0.334171	+	0.942513i	$0.391544\pi$
$570$	0.130405	+	0.906988i	0.00546207	+	0.0379895i
$571$	32.2086	−	20.6992i	1.34789	−	0.866236i	0.350369	−	0.936612i	$-0.386056\pi$
$571$	32.2086	−	20.6992i	1.34789	−	0.866236i	0.997521	+	0.0703755i	$0.0224198\pi$
$572$	3.06352	+	3.53549i	0.128092	+	0.147826i
$573$	−19.4177	+	5.70156i	−0.811188	+	0.238186i
$574$	2.76019			0.115208
$575$	−18.2898	−	10.5091i	−0.762735	−	0.438260i
$576$	1.00000			0.0416667
$577$	12.9168	−	3.79272i	0.537734	−	0.157893i	−0.00157820	−	0.999999i	$-0.500502\pi$
$577$	12.9168	−	3.79272i	0.537734	−	0.157893i	0.539312	+	0.842106i	$0.318684\pi$
$578$	−8.38593	−	9.67788i	−0.348809	−	0.402547i
$579$	8.29005	−	5.32769i	0.344523	−	0.221411i
$580$	−0.277929	−	1.93304i	−0.0115404	−	0.0802651i
$581$	0.736282	+	0.473179i	0.0305461	+	0.0196308i
$582$	−2.93752	+	6.43228i	−0.121764	+	0.266627i
$583$	2.43274	−	2.80753i	0.100754	−	0.116276i
$584$	−2.09131	+	14.5454i	−0.0865392	+	0.601893i
$585$	−1.40397	−	3.07427i	−0.0580470	−	0.127105i
$586$	20.2516	+	5.94641i	0.836586	+	0.245644i
$587$	−12.7570	−	3.74580i	−0.526539	−	0.154606i	0.00765023	−	0.999971i	$-0.497565\pi$
$587$	−12.7570	−	3.74580i	−0.526539	−	0.154606i	−0.534189	+	0.845365i	$0.679383\pi$
$588$	−0.415415	−	0.909632i	−0.0171314	−	0.0375126i
$589$	−0.821087	+	5.71078i	−0.0338323	+	0.235309i
$590$	−2.88496	+	3.32942i	−0.118772	+	0.137070i
$591$	2.45307	−	5.37147i	0.100906	−	0.220953i
$592$	−3.17426	−	2.03997i	−0.130461	−	0.0838424i
$593$	4.09511	+	28.4821i	0.168166	+	1.16962i	0.882672	+	0.469990i	$0.155743\pi$
$593$	4.09511	+	28.4821i	0.168166	+	1.16962i	−0.714506	+	0.699630i	$0.753348\pi$
$594$	−0.903185	+	0.580442i	−0.0370581	+	0.0238158i
$595$	2.77302	+	3.20023i	0.113683	+	0.131197i
$596$	−9.79673	+	2.87658i	−0.401290	+	0.117829i
$597$	7.61648			0.311722
$598$	1.94326	−	20.8065i	0.0794659	−	0.850842i
$599$	−5.24513			−0.214310			−0.107155	−	0.994242i	$-0.534174\pi$
$599$	−5.24513			−0.214310			−0.107155	+	0.994242i	$0.534174\pi$
$600$	−4.22023	+	1.23917i	−0.172290	+	0.0505890i
$601$	−1.84227	−	2.12609i	−0.0751477	−	0.0867251i	0.716931	−	0.697144i	$-0.245546\pi$
$601$	−1.84227	−	2.12609i	−0.0751477	−	0.0867251i	−0.792078	+	0.610419i	$0.791001\pi$
$602$	9.28994	−	5.97028i	0.378630	−	0.243330i
$603$	1.93648	+	13.4685i	0.0788597	+	0.548481i
$604$	19.1155	+	12.2848i	0.777798	+	0.499860i
$605$	−3.17289	+	6.94767i	−0.128996	+	0.282463i
$606$	−2.70190	+	3.11816i	−0.109757	+	0.126667i
$607$	2.47162	−	17.1905i	0.100320	−	0.697739i	−0.876143	−	0.482052i	$-0.839892\pi$
$607$	2.47162	−	17.1905i	0.100320	−	0.697739i	0.976462	−	0.215687i	$-0.0691992\pi$
$608$	0.490764	+	1.07462i	0.0199031	+	0.0435817i
$609$	2.41586	+	0.709361i	0.0978956	+	0.0287447i
$610$	−1.32511	−	0.389087i	−0.0536520	−	0.0157537i
$611$	15.7186	+	34.4190i	0.635907	+	1.39244i
$612$	0.776962	−	5.40389i	0.0314068	−	0.218439i
$613$	−4.54611	+	5.24649i	−0.183616	+	0.211904i	−0.840094	−	0.542442i	$-0.817500\pi$
$613$	−4.54611	+	5.24649i	−0.183616	+	0.211904i	0.656478	+	0.754345i	$0.272045\pi$
$614$	3.47825	−	7.61630i	0.140371	−	0.307369i
$615$	−1.80102	−	1.15745i	−0.0726243	−	0.0466728i
$616$	−0.152792	−	1.06269i	−0.00615616	−	0.0428170i
$617$	34.3500	−	22.0754i	1.38288	−	0.888723i	0.383486	−	0.923547i	$-0.374723\pi$
$617$	34.3500	−	22.0754i	1.38288	−	0.888723i	0.999393	+	0.0348237i	$0.0110870\pi$
$618$	−10.0288	−	11.5738i	−0.403417	−	0.465568i
$619$	4.10361	−	1.20493i	0.164938	−	0.0484301i	−0.198221	−	0.980157i	$-0.563516\pi$
$619$	4.10361	−	1.20493i	0.164938	−	0.0484301i	0.363159	+	0.931727i	$0.381698\pi$
$620$	3.78793			0.152127
$621$	4.66298	+	1.12100i	0.187119	+	0.0449840i
$622$	−5.82746			−0.233660
$623$	−6.96230	+	2.04432i	−0.278939	+	0.0819038i
$624$	−2.85345	−	3.29306i	−0.114230	−	0.131828i
$625$	13.7443	−	8.83294i	0.549773	−	0.353318i
$626$	0.282601	+	1.96553i	0.0112950	+	0.0785586i
$627$	−1.06701	−	0.685724i	−0.0426122	−	0.0273852i
$628$	−7.18234	+	15.7271i	−0.286607	+	0.627581i
$629$	−13.4901	+	15.5684i	−0.537884	+	0.620751i
$630$	−0.110384	+	0.767734i	−0.00439779	+	0.0305873i
$631$	7.64051	+	16.7304i	0.304164	+	0.666026i	0.998564	−	0.0535625i	$-0.0170576\pi$
$631$	7.64051	+	16.7304i	0.304164	+	0.666026i	−0.694401	+	0.719589i	$0.744330\pi$
$632$	5.81843	+	1.70844i	0.231445	+	0.0679583i
$633$	11.4004	+	3.34746i	0.453125	+	0.133049i
$634$	−3.43202	−	7.51508i	−0.136303	−	0.298462i
$635$	1.54385	−	10.7377i	0.0612658	−	0.426113i
$636$	−2.26593	+	2.61502i	−0.0898498	+	0.103692i
$637$	−1.81011	+	3.96358i	−0.0717190	+	0.157043i
$638$	2.27409	+	1.46147i	0.0900319	+	0.0578600i
$639$	0.441489	+	3.07063i	0.0174651	+	0.121472i
$640$	0.652501	−	0.419337i	0.0257924	−	0.0165757i
$641$	9.88729	+	11.4105i	0.390524	+	0.450689i	0.916634	−	0.399728i	$-0.130895\pi$
$641$	9.88729	+	11.4105i	0.390524	+	0.450689i	−0.526110	+	0.850417i	$0.676350\pi$
$642$	−3.76083	+	1.10428i	−0.148428	+	0.0435824i
$643$	−22.5010			−0.887352			−0.443676	−	0.896187i	$-0.646326\pi$
$643$	−22.5010			−0.887352			−0.443676	+	0.896187i	$0.646326\pi$
$644$	−2.95676	+	3.77592i	−0.116513	+	0.148792i
$645$	−8.56525			−0.337256
$646$	6.18845	−	1.81709i	0.243481	−	0.0714925i
$647$	−31.6683	−	36.5471i	−1.24501	−	1.43682i	−0.857126	−	0.515106i	$-0.827753\pi$
$647$	−31.6683	−	36.5471i	−1.24501	−	1.43682i	−0.387881	−	0.921709i	$-0.626793\pi$
$648$	0.841254	−	0.540641i	0.0330476	−	0.0212384i
$649$	−0.867835	−	6.03593i	−0.0340655	−	0.236931i
$650$	16.1229	+	10.3616i	0.632392	+	0.406414i
$651$	−2.02876	+	4.44236i	−0.0795134	+	0.174110i
$652$	−2.51948	+	2.90763i	−0.0986703	+	0.113872i
$653$	1.11804	−	7.77612i	0.0437522	−	0.304303i	−0.956181	−	0.292775i	$-0.905421\pi$
$653$	1.11804	−	7.77612i	0.0437522	−	0.304303i	0.999934	−	0.0115281i	$-0.00366960\pi$
$654$	−2.62042	−	5.73791i	−0.102466	−	0.224370i
$655$	−8.18093	−	2.40214i	−0.319655	−	0.0938593i
$656$	−2.64838	−	0.777634i	−0.103402	−	0.0303615i
$657$	6.10452	+	13.3670i	0.238160	+	0.521497i
$658$	1.23584	−	8.59543i	0.0481779	−	0.335085i
$659$	26.3135	−	30.3674i	1.02503	−	1.18295i	0.0420700	−	0.999115i	$-0.486605\pi$
$659$	26.3135	−	30.3674i	1.02503	−	1.18295i	0.982958	−	0.183831i	$-0.0588498\pi$
$660$	−0.345928	+	0.757478i	−0.0134652	+	0.0294848i
$661$	−9.55937	−	6.14343i	−0.371816	−	0.238952i	0.341366	−	0.939930i	$-0.389110\pi$
$661$	−9.55937	−	6.14343i	−0.371816	−	0.238952i	−0.713182	+	0.700979i	$0.752747\pi$
$662$	−3.48028	−	24.2059i	−0.135265	−	0.940787i
$663$	−20.0123	+	12.8612i	−0.777215	+	0.499486i
$664$	−0.573147	−	0.661447i	−0.0222424	−	0.0256691i
$665$	−0.879197	+	0.258156i	−0.0340938	+	0.0100108i
$666$	−3.77325			−0.146210
$667$	−2.30982	−	11.8522i	−0.0894366	−	0.458919i
$668$	−17.4274			−0.674285
$669$	−21.0782	+	6.18913i	−0.814932	+	0.239285i
$670$	6.91141	+	7.97619i	0.267011	+	0.308147i
$671$	1.60817	−	1.03351i	0.0620827	−	0.0398981i
$672$	0.142315	+	0.989821i	0.00548991	+	0.0381832i
$673$	22.3762	+	14.3803i	0.862538	+	0.554320i	0.895462	−	0.445138i	$-0.146845\pi$
$673$	22.3762	+	14.3803i	0.862538	+	0.554320i	−0.0329236	+	0.999458i	$0.510482\pi$
$674$	−2.14591	+	4.69888i	−0.0826573	+	0.180994i
$675$	−2.88034	+	3.32409i	−0.110864	+	0.127944i
$676$	−0.851958	+	5.92550i	−0.0327676	+	0.227904i
$677$	−15.4931	−	33.9252i	−0.595449	−	1.30385i	−0.932093	−	0.362220i	$-0.882019\pi$
$677$	−15.4931	−	33.9252i	−0.595449	−	1.30385i	0.336643	−	0.941632i	$-0.390708\pi$
$678$	8.81659	+	2.58878i	0.338599	+	0.0994217i
$679$	−6.78486	−	1.99221i	−0.260379	−	0.0764542i
$680$	−1.75908	−	3.85185i	−0.0674577	−	0.147712i
$681$	−1.17552	+	8.17589i	−0.0450459	+	0.313301i
$682$	−3.43358	+	3.96256i	−0.131479	+	0.151734i
$683$	8.50398	−	18.6211i	0.325396	−	0.712517i	−0.674267	−	0.738488i	$-0.735540\pi$
$683$	8.50398	−	18.6211i	0.325396	−	0.712517i	0.999663	+	0.0259706i	$0.00826762\pi$
$684$	0.993842	+	0.638704i	0.0380005	+	0.0244214i
$685$	−1.63376	−	11.3630i	−0.0624227	−	0.434160i
$686$	0.841254	−	0.540641i	0.0321192	−	0.0206418i
$687$	−11.9220	−	13.7587i	−0.454853	−	0.524928i
$688$	−10.5957	+	3.11116i	−0.403955	+	0.118612i
$689$	15.0771			0.574393
$690$	3.51267	−	1.22391i	0.133725	−	0.0465934i
$691$	−14.0707			−0.535275			−0.267638	−	0.963520i	$-0.586243\pi$
$691$	−14.0707			−0.535275			−0.267638	+	0.963520i	$0.586243\pi$
$692$	14.7435	−	4.32907i	0.560462	−	0.164567i
$693$	−0.703071	−	0.811387i	−0.0267074	−	0.0308220i
$694$	−9.97040	+	6.40759i	−0.378471	+	0.243229i
$695$	2.16372	+	15.0490i	0.0820746	+	0.570842i
$696$	−2.11815	−	1.36125i	−0.0802883	−	0.0515982i
$697$	−6.25994	+	13.7074i	−0.237112	+	0.519203i
$698$	4.27196	−	4.93011i	0.161696	−	0.186607i
$699$	−2.74985	+	19.1256i	−0.104009	+	0.723397i
$700$	−1.82716	−	4.00092i	−0.0690602	−	0.151221i
$701$	29.1382	+	8.55575i	1.10054	+	0.323146i	0.781065	−	0.624450i	$-0.214677\pi$
$701$	29.1382	+	8.55575i	1.10054	+	0.323146i	0.319470	+	0.947596i	$0.396495\pi$
$702$	−4.18084	−	1.22761i	−0.157796	−	0.0463330i
$703$	−1.85178	−	4.05482i	−0.0698410	−	0.152931i
$704$	−0.152792	+	1.06269i	−0.00575856	+	0.0400517i
$705$	−4.41076	+	5.09029i	−0.166119	+	0.191711i
$706$	−10.1205	+	22.1608i	−0.380890	+	0.834033i
$707$	−3.47095	−	2.23064i	−0.130538	−	0.0838919i
$708$	0.808327	+	5.62204i	0.0303788	+	0.211289i
$709$	−3.93563	+	2.52928i	−0.147806	+	0.0949891i	−0.612454	−	0.790507i	$-0.709817\pi$
$709$	−3.93563	+	2.52928i	−0.147806	+	0.0949891i	0.464648	+	0.885496i	$0.346181\pi$
$710$	1.57570	+	1.81845i	0.0591349	+	0.0682453i
$711$	5.81843	−	1.70844i	0.218208	−	0.0640717i
$712$	7.25623			0.271939
$713$	23.3925	−	1.16293i	0.876055	−	0.0435522i
$714$	5.45946			0.204315
$715$	3.48151	−	1.02226i	0.130201	−	0.0382305i
$716$	8.65365	+	9.98684i	0.323402	+	0.373226i
$717$	−0.472132	+	0.303421i	−0.0176321	+	0.0113314i
$718$	4.29771	+	29.8912i	0.160389	+	1.11553i
$719$	−12.1090	−	7.78199i	−0.451590	−	0.290219i	0.295008	−	0.955495i	$-0.404678\pi$
$719$	−12.1090	−	7.78199i	−0.451590	−	0.290219i	−0.746598	+	0.665276i	$0.768314\pi$
$720$	0.322208	−	0.705537i	0.0120080	−	0.0262938i
$721$	10.0288	−	11.5738i	0.373491	−	0.431032i
$722$	2.50536	−	17.4251i	0.0932398	−	0.648497i
$723$	−3.01067	−	6.59244i	−0.111968	−	0.245176i
$724$	2.87826	+	0.845134i	0.106970	+	0.0314092i
$725$	10.6259	+	3.12005i	0.394637	+	0.115876i
$726$	4.09073	+	8.95746i	0.151821	+	0.332442i
$727$	−2.16969	+	15.0905i	−0.0804694	+	0.559677i	0.909206	+	0.416347i	$0.136690\pi$
$727$	−2.16969	+	15.0905i	−0.0804694	+	0.559677i	−0.989675	+	0.143329i	$0.954219\pi$
$728$	2.85345	−	3.29306i	0.105756	−	0.122049i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	9.58849	+	6.16215i	0.354886	+	0.228071i
$731$	8.57996	+	59.6750i	0.317341	+	2.20716i
$732$	−1.49790	+	0.962640i	−0.0553639	+	0.0355802i
$733$	−4.54949	−	5.25039i	−0.168039	−	0.193928i	0.665484	−	0.746412i	$-0.268225\pi$
$733$	−4.54949	−	5.25039i	−0.168039	−	0.193928i	−0.833523	+	0.552485i	$0.813680\pi$
$734$	−0.690992	+	0.202894i	−0.0255050	+	0.00748894i
$735$	−0.775629			−0.0286095
$736$	3.90079	−	2.78995i	0.143785	−	0.102839i
$737$	−14.6088			−0.538121
$738$	−2.64838	+	0.777634i	−0.0974882	+	0.0286251i
$739$	12.8577	+	14.8385i	0.472977	+	0.545845i	0.941237	−	0.337746i	$-0.109665\pi$
$739$	12.8577	+	14.8385i	0.472977	+	0.545845i	−0.468260	+	0.883591i	$0.655119\pi$
$740$	−2.46205	+	1.58226i	−0.0905067	+	0.0581651i
$741$	−0.732592	−	5.09529i	−0.0269125	−	0.187180i
$742$	−2.91088	−	1.87071i	−0.106862	−	0.0686758i
$743$	−6.18355	+	13.5401i	−0.226852	+	0.496737i	−0.988494	−	0.151261i	$-0.951667\pi$
$743$	−6.18355	+	13.5401i	−0.226852	+	0.496737i	0.761641	+	0.647999i	$0.224394\pi$
$744$	3.19814	−	3.69085i	0.117249	−	0.135313i
$745$	−1.12705	+	7.83882i	−0.0412920	+	0.287192i
$746$	10.6265	+	23.2688i	0.389064	+	0.851932i
$747$	−0.839767	−	0.246578i	−0.0307255	−	0.00902181i
$748$	5.62395	+	1.65134i	0.205632	+	0.0603790i
$749$	−1.62826	−	3.56539i	−0.0594953	−	0.130277i
$750$	−1.03743	+	7.21547i	−0.0378815	+	0.263472i
$751$	−23.2591	+	26.8424i	−0.848736	+	0.979493i	−0.999959	−	0.00900621i	$-0.997133\pi$
$751$	−23.2591	+	26.8424i	−0.848736	+	0.979493i	0.151224	+	0.988500i	$0.451679\pi$
$752$	−3.60739	+	7.89908i	−0.131548	+	0.288050i
$753$	11.8352	+	7.60605i	0.431300	+	0.277180i
$754$	1.56136	+	10.8595i	0.0568612	+	0.395478i
$755$	14.8265	−	9.52843i	0.539593	−	0.346775i
$756$	0.654861	+	0.755750i	0.0238171	+	0.0274863i
$757$	33.5427	−	9.84904i	1.21913	−	0.357969i	0.391993	−	0.919968i	$-0.371786\pi$
$757$	33.5427	−	9.84904i	1.21913	−	0.357969i	0.827138	+	0.561999i	$0.189967\pi$
$758$	20.1342			0.731307
$759$	−1.90374	+	4.78402i	−0.0691012	+	0.173649i
$760$	0.916315			0.0332382
$761$	−11.6027	+	3.40686i	−0.420597	+	0.123498i	−0.485181	−	0.874414i	$-0.661246\pi$
$761$	−11.6027	+	3.40686i	−0.420597	+	0.123498i	0.0645838	+	0.997912i	$0.479428\pi$
$762$	−9.15904	−	10.5701i	−0.331797	−	0.382914i
$763$	5.30659	−	3.41034i	0.192111	−	0.123462i
$764$	2.88010	+	20.0315i	0.104198	+	0.724715i
$765$	−3.56230	−	2.28935i	−0.128795	−	0.0827717i
$766$	−9.74325	+	21.3347i	−0.352038	+	0.770855i
$767$	16.2072	−	18.7041i	0.585208	−	0.675366i
$768$	0.142315	−	0.989821i	0.00513534	−	0.0357171i
$769$	−14.8047	−	32.4177i	−0.533870	−	1.16901i	−0.963916	−	0.266206i	$-0.914230\pi$
$769$	−14.8047	−	32.4177i	−0.533870	−	1.16901i	0.430046	−	0.902807i	$-0.358497\pi$
$770$	−0.798998	−	0.234607i	−0.0287939	−	0.00845465i
$771$	14.8572	+	4.36246i	0.535068	+	0.157110i
$772$	−4.09367	−	8.96388i	−0.147334	−	0.322617i
$773$	−3.46874	+	24.1256i	−0.124762	+	0.867739i	0.827284	+	0.561784i	$0.189885\pi$
$773$	−3.46874	+	24.1256i	−0.124762	+	0.867739i	−0.952046	+	0.305955i	$0.901024\pi$
$774$	−7.23161	+	8.34572i	−0.259935	+	0.299981i
$775$	−8.92329	+	19.5393i	−0.320534	+	0.701872i
$776$	5.94875	+	3.82303i	0.213548	+	0.137239i
$777$	−0.536989	−	3.73484i	−0.0192644	−	0.133987i
$778$	−13.4333	+	8.63308i	−0.481608	+	0.309511i
$779$	−2.13539	−	2.46438i	−0.0765084	−	0.0882954i
$780$	−3.24278	+	0.952166i	−0.116110	+	0.0340930i
$781$	−3.33058			−0.119178
$782$	−12.0458	−	23.2471i	−0.430757	−	0.831316i
$783$	−2.51785			−0.0899806
$784$	−0.959493	+	0.281733i	−0.0342676	+	0.0100619i
$785$	8.78187	+	10.1348i	0.313438	+	0.361727i
$786$	−9.24770	+	5.94314i	−0.329855	+	0.211985i
$787$	−3.51302	−	24.4336i	−0.125226	−	0.870964i	−0.951490	−	0.307681i	$-0.900447\pi$
$787$	−3.51302	−	24.4336i	−0.125226	−	0.870964i	0.826264	−	0.563283i	$-0.190462\pi$
$788$	−4.96769	−	3.19254i	−0.176967	−	0.113730i
$789$	−6.98429	+	15.2935i	−0.248647	+	0.544462i
$790$	3.08011	−	3.55464i	0.109586	−	0.126468i
$791$	−1.30770	+	9.09527i	−0.0464966	+	0.323391i
$792$	0.445997	+	0.976598i	0.0158478	+	0.0347019i
$793$	7.44421	+	2.18582i	0.264352	+	0.0776206i
$794$	17.3488	+	5.09408i	0.615687	+	0.180782i
$795$	1.11489	+	2.44128i	0.0395412	+	0.0865831i
$796$	1.08394	−	7.53896i	0.0384192	−	0.267211i
$797$	33.8584	−	39.0747i	1.19933	−	1.38410i	0.295974	−	0.955196i	$-0.404356\pi$
$797$	33.8584	−	39.0747i	1.19933	−	1.38410i	0.903352	−	0.428900i	$-0.141099\pi$
$798$	−0.490764	+	1.07462i	−0.0173729	+	0.0380413i
$799$	39.8829	+	25.6312i	1.41096	+	0.906767i
$800$	0.625958	+	4.35363i	0.0221309	+	0.153924i
$801$	6.10433	−	3.92302i	0.215686	−	0.138613i
$802$	−2.90834	−	3.35641i	−0.102697	−	0.118519i
$803$	−15.1377	+	4.44484i	−0.534199	+	0.156855i
$804$	13.6070			0.479883
$805$	1.71136	+	3.30274i	0.0603174	+	0.116406i
$806$	−21.2799			−0.749553
$807$	−11.2279	+	3.29682i	−0.395242	+	0.116054i
$808$	2.70190	+	3.11816i	0.0950526	+	0.109697i
$809$	−32.3691	+	20.8024i	−1.13804	+	0.731372i	−0.967222	−	0.253931i	$-0.918277\pi$
$809$	−32.3691	+	20.8024i	−1.13804	+	0.731372i	−0.170815	+	0.985303i	$0.554640\pi$
$810$	−0.110384	−	0.767734i	−0.00387848	−	0.0269754i
$811$	12.5810	+	8.08535i	0.441780	+	0.283915i	0.742561	−	0.669778i	$-0.233611\pi$
$811$	12.5810	+	8.08535i	0.441780	+	0.283915i	−0.300781	+	0.953693i	$0.597247\pi$
$812$	1.04595	−	2.29032i	0.0367058	−	0.0803744i
$813$	−17.2018	+	19.8519i	−0.603292	+	0.696236i
$814$	0.576522	−	4.00980i	0.0202071	−	0.140543i
$815$	1.23965	+	2.71444i	0.0434229	+	0.0950828i
$816$	−5.23831	−	1.53811i	−0.183378	−	0.0538445i
$817$	−12.5175	−	3.67548i	−0.437933	−	0.128589i
$818$	5.47643	+	11.9917i	0.191479	+	0.419280i
$819$	0.620114	−	4.31299i	0.0216686	−	0.150708i
$820$	−1.40198	+	1.61797i	−0.0489592	+	0.0565019i
$821$	−12.2282	+	26.7761i	−0.426768	+	0.934493i	0.567072	+	0.823669i	$0.308076\pi$
$821$	−12.2282	+	26.7761i	−0.426768	+	0.934493i	−0.993840	+	0.110824i	$0.964651\pi$
$822$	−12.4512	−	8.00189i	−0.434285	−	0.279098i
$823$	0.296469	+	2.06199i	0.0103343	+	0.0718763i	0.994336	−	0.106283i	$-0.0338949\pi$
$823$	0.296469	+	2.06199i	0.0103343	+	0.0718763i	−0.984002	+	0.178159i	$0.942986\pi$
$824$	−12.8833	+	8.27958i	−0.448810	+	0.288433i
$825$	−3.09239	−	3.56880i	−0.107663	−	0.124250i
$826$	−5.44978	+	1.60020i	−0.189622	+	0.0556781i
$827$	−13.2852			−0.461972			−0.230986	−	0.972957i	$-0.574195\pi$
$827$	−13.2852			−0.461972			−0.230986	+	0.972957i	$0.574195\pi$
$828$	1.77320	−	4.45598i	0.0616228	−	0.154856i
$829$	0.877644			0.0304818			0.0152409	−	0.999884i	$-0.495148\pi$
$829$	0.877644			0.0304818			0.0152409	+	0.999884i	$0.495148\pi$
$830$	−0.651348	+	0.191253i	−0.0226086	+	0.00663849i
$831$	−0.315990	−	0.364672i	−0.0109616	−	0.0126503i
$832$	−3.66563	+	2.35576i	−0.127083	+	0.0816712i
$833$	0.776962	+	5.40389i	0.0269201	+	0.187234i
$834$	16.4901	+	10.5976i	0.571006	+	0.366963i
$835$	−5.61524	+	12.2957i	−0.194323	+	0.425509i
$836$	−0.830595	+	0.958558i	−0.0287267	+	0.0331524i
$837$	0.695022	−	4.83398i	0.0240235	−	0.167087i
$838$	−0.398573	−	0.872753i	−0.0137685	−	0.0301488i
$839$	21.8842	+	6.42577i	0.755526	+	0.221842i	0.636741	−	0.771078i	$-0.280282\pi$
$839$	21.8842	+	6.42577i	0.755526	+	0.221842i	0.118785	+	0.992920i	$0.462100\pi$
$840$	0.744211	+	0.218520i	0.0256777	+	0.00753966i
$841$	−9.41348	−	20.6126i	−0.324603	−	0.710781i
$842$	−3.11636	+	21.6748i	−0.107397	+	0.746962i
$843$	7.06689	−	8.15562i	0.243397	−	0.280895i
$844$	4.93583	−	10.8080i	0.169898	−	0.372025i
$845$	3.90615	+	2.51033i	0.134376	+	0.0863580i
$846$	1.23584	+	8.59543i	0.0424889	+	0.295517i
$847$	−8.28411	+	5.32388i	−0.284645	+	0.182931i
$848$	2.26593	+	2.61502i	0.0778122	+	0.0898001i
$849$	−19.7709	+	5.80527i	−0.678537	+	0.199236i
$850$	24.0129			0.823635
$851$	−14.7187	+	10.5272i	−0.504549	+	0.360867i
$852$	3.10220			0.106280
$853$	28.4595	−	8.35648i	0.974436	−	0.286120i	0.244510	−	0.969647i	$-0.421373\pi$
$853$	28.4595	−	8.35648i	0.974436	−	0.286120i	0.729926	+	0.683526i	$0.239555\pi$
$854$	−1.16601	−	1.34565i	−0.0399002	−	0.0460473i
$855$	0.770853	−	0.495397i	0.0263626	−	0.0169422i
$856$	0.557817	+	3.87970i	0.0190658	+	0.132605i
$857$	15.8811	+	10.2062i	0.542489	+	0.348637i	0.783012	−	0.622007i	$-0.213682\pi$
$857$	15.8811	+	10.2062i	0.542489	+	0.348637i	−0.240523	+	0.970644i	$0.577319\pi$
$858$	1.94336	−	4.25537i	0.0663453	−	0.145276i
$859$	1.25862	−	1.45253i	0.0429437	−	0.0495596i	−0.733871	−	0.679288i	$-0.762289\pi$
$859$	1.25862	−	1.45253i	0.0429437	−	0.0495596i	0.776815	+	0.629729i	$0.216834\pi$
$860$	−1.21896	+	8.47807i	−0.0415663	+	0.289100i
$861$	−1.14662	−	2.51075i	−0.0390768	−	0.0855662i
$862$	−23.2623	−	6.83043i	−0.792317	−	0.232645i
$863$	−28.8916	−	8.48334i	−0.983482	−	0.288776i	−0.249821	−	0.968292i	$-0.580372\pi$
$863$	−28.8916	−	8.48334i	−0.983482	−	0.288776i	−0.733661	+	0.679516i	$0.762190\pi$
$864$	−0.415415	−	0.909632i	−0.0141327	−	0.0309463i
$865$	1.69614	−	11.7969i	0.0576705	−	0.401107i
$866$	6.89417	−	7.95630i	0.234273	−	0.270366i
$867$	−5.31967	+	11.6484i	−0.180665	+	0.395602i
$868$	4.10842	+	2.64032i	0.139449	+	0.0896184i
$869$	0.926539	+	6.44422i	0.0314307	+	0.218605i
$870$	−1.64290	+	1.05583i	−0.0556995	+	0.0357959i
$871$	−38.8270	−	44.8088i	−1.31560	−	1.51829i
$872$	−6.05243	+	1.77716i	−0.204961	+	0.0601821i
$873$	7.07130			0.239327
$874$	5.65872	−	0.281318i	0.191409	−	0.00951571i
$875$	−7.28967			−0.246436
$876$	14.0997	−	4.14006i	0.476386	−	0.139880i
$877$	−20.0316	−	23.1177i	−0.676418	−	0.780628i	0.308948	−	0.951079i	$-0.400023\pi$
$877$	−20.0316	−	23.1177i	−0.676418	−	0.780628i	−0.985366	+	0.170451i	$0.945478\pi$
$878$	−19.2040	+	12.3417i	−0.648104	+	0.416511i
$879$	−3.00378	−	20.8917i	−0.101315	−	0.704661i
$880$	0.700537	+	0.450208i	0.0236151	+	0.0151765i
$881$	−6.96807	+	15.2579i	−0.234760	+	0.514053i	−0.989944	−	0.141460i	$-0.954820\pi$
$881$	−6.96807	+	15.2579i	−0.234760	+	0.514053i	0.755184	+	0.655513i	$0.227548\pi$
$882$	−0.654861	+	0.755750i	−0.0220503	+	0.0254474i
$883$	−6.44678	+	44.8383i	−0.216951	+	1.50893i	0.532249	+	0.846588i	$0.321347\pi$
$883$	−6.44678	+	44.8383i	−0.216951	+	1.50893i	−0.749201	+	0.662343i	$0.769562\pi$
$884$	9.88219	+	21.6390i	0.332374	+	0.727798i
$885$	4.22701	+	1.24116i	0.142089	+	0.0417212i
$886$	−25.5224	−	7.49405i	−0.857442	−	0.251768i
$887$	−2.32666	−	5.09466i	−0.0781214	−	0.171062i	0.866541	−	0.499106i	$-0.166338\pi$
$887$	−2.32666	−	5.09466i	−0.0781214	−	0.171062i	−0.944663	+	0.328043i	$0.893611\pi$
$888$	−0.536989	+	3.73484i	−0.0180202	+	0.125333i
$889$	9.15904	−	10.5701i	0.307184	−	0.354510i
$890$	2.33802	−	5.11954i	0.0783705	−	0.171607i
$891$	0.903185	+	0.580442i	0.0302578	+	0.0194455i
$892$	3.12639	+	21.7445i	0.104679	+	0.728059i
$893$	−8.63034	+	5.54638i	−0.288803	+	0.185603i
$894$	6.68634	+	7.71645i	0.223625	+	0.258077i
$895$	9.83436	−	2.88763i	0.328727	−	0.0965228i
$896$	1.00000			0.0334077
$897$	−19.7335	+	6.87569i	−0.658884	+	0.229573i
$898$	−7.29642			−0.243485
$899$	−11.7983	+	3.46430i	−0.393496	+	0.115541i
$900$	2.88034	+	3.32409i	0.0960113	+	0.110803i
$901$	15.8918	−	10.2130i	0.529433	−	0.340246i
$902$	−0.421734	−	2.93322i	−0.0140422	−	0.0976657i
$903$	−9.28994	−	5.97028i	−0.309150	−	0.198678i
$904$	3.81717	−	8.35843i	0.126957	−	0.277997i
$905$	1.52367	−	1.75841i	0.0506486	−	0.0584516i
$906$	3.23377	−	22.4913i	0.107435	−	0.747225i
$907$	−8.51861	−	18.6531i	−0.282856	−	0.619368i	0.713865	−	0.700283i	$-0.246943\pi$
$907$	−8.51861	−	18.6531i	−0.282856	−	0.619368i	−0.996721	+	0.0809155i	$0.974216\pi$
$908$	7.92538	+	2.32710i	0.263013	+	0.0772276i
$909$	3.95879	+	1.16241i	0.131305	+	0.0385546i
$910$	−1.40397	−	3.07427i	−0.0465412	−	0.101911i
$911$	−6.78694	+	47.2042i	−0.224861	+	1.56394i	0.494419	+	0.869224i	$0.335381\pi$
$911$	−6.78694	+	47.2042i	−0.224861	+	1.56394i	−0.719280	+	0.694720i	$0.755528\pi$
$912$	0.773641	−	0.892829i	0.0256178	−	0.0295645i
$913$	0.390345	−	0.854737i	0.0129186	−	0.0282877i
$914$	30.4207	+	19.5502i	1.00623	+	0.646664i
$915$	0.196544	+	1.36699i	0.00649754	+	0.0451914i
$916$	−15.3154	+	9.84259i	−0.506034	+	0.325208i
$917$	−7.19873	−	8.30778i	−0.237723	−	0.274347i
$918$	−5.23831	+	1.53811i	−0.172890	+	0.0507651i
$919$	20.1657			0.665206			0.332603	−	0.943067i	$-0.392073\pi$
$919$	20.1657			0.665206			0.332603	+	0.943067i	$0.392073\pi$
$920$	−0.711545	−	3.65110i	−0.0234589	−	0.120373i
$921$	−8.37295			−0.275898
$922$	38.1418	−	11.1994i	1.25613	−	0.368834i
$923$	−8.85199	−	10.2157i	−0.291367	−	0.336255i
$924$	−0.903185	+	0.580442i	−0.0297126	+	0.0190951i
$925$	−2.36189	−	16.4273i	−0.0776586	−	0.540127i
$926$	−22.2914	−	14.3258i	−0.732542	−	0.470776i
$927$	−6.36182	+	13.9304i	−0.208950	+	0.457536i
$928$	−1.64884	+	1.90286i	−0.0541259	+	0.0624646i
$929$	−2.22556	+	15.4791i	−0.0730183	+	0.507853i	0.920187	+	0.391479i	$0.128036\pi$
$929$	−2.22556	+	15.4791i	−0.0730183	+	0.507853i	−0.993205	+	0.116375i	$0.962873\pi$
$930$	−1.57356	−	3.44563i	−0.0515992	−	0.112987i
$931$	−1.13353	−	0.332834i	−0.0371499	−	0.0109082i
$932$	18.5396	+	5.44372i	0.607285	+	0.178315i
$933$	2.42081	+	5.30084i	0.0792539	+	0.173542i
$934$	−5.75509	+	40.0275i	−0.188312	+	1.30974i
$935$	2.97716	−	3.43583i	0.0973636	−	0.112364i
$936$	−1.81011	+	3.96358i	−0.0591651	+	0.129554i
$937$	40.1023	+	25.7722i	1.31008	+	0.841940i	0.994272	−	0.106881i	$-0.0340864\pi$
$937$	40.1023	+	25.7722i	1.31008	+	0.841940i	0.315813	+	0.948821i	$0.397723\pi$
$938$	1.93648	+	13.4685i	0.0632284	+	0.439763i
$939$	1.67052	−	1.07358i	0.0545152	−	0.0350348i
$940$	4.41076	+	5.09029i	0.143863	+	0.166027i
$941$	17.1652	−	5.04014i	0.559568	−	0.164304i	0.0102951	−	0.999947i	$-0.496723\pi$
$941$	17.1652	−	5.04014i	0.559568	−	0.164304i	0.549273	+	0.835643i	$0.314905\pi$
$942$	17.2896			0.563324
$943$	−8.16122	+	10.4222i	−0.265766	+	0.339395i
$944$	5.67985			0.184863
$945$	0.744211	−	0.218520i	0.0242092	−	0.00710846i
$946$	−7.76399	−	8.96012i	−0.252429	−	0.291319i
$947$	3.35729	−	2.15760i	0.109097	−	0.0701126i	−0.484954	−	0.874539i	$-0.661164\pi$
$947$	3.35729	−	2.15760i	0.109097	−	0.0701126i	0.594052	+	0.804427i	$0.297527\pi$
$948$	−0.863006	−	6.00234i	−0.0280291	−	0.194947i
$949$	−53.8664	−	34.6178i	−1.74858	−	1.12374i
$950$	−2.15858	+	4.72662i	−0.0700335	+	0.153352i
$951$	−5.41024	+	6.24375i	−0.175439	+	0.202468i
$952$	0.776962	−	5.40389i	0.0251815	−	0.175141i
$953$	−18.7666	−	41.0931i	−0.607910	−	1.33114i	−0.923994	−	0.382406i	$-0.875096\pi$
$953$	−18.7666	−	41.0931i	−0.607910	−	1.33114i	0.316084	−	0.948731i	$-0.397632\pi$
$954$	3.32000	+	0.974841i	0.107489	+	0.0315617i
$955$	15.0610	+	4.42230i	0.487361	+	0.143102i
$956$	0.233141	+	0.510507i	0.00754031	+	0.0165110i
$957$	0.384707	−	2.67570i	0.0124358	−	0.0864930i
$958$	−16.7008	+	19.2738i	−0.539580	+	0.622708i
$959$	6.14845	−	13.4632i	0.198544	−	0.434751i
$960$	−0.652501	−	0.419337i	−0.0210594	−	0.0135340i
$961$	1.01749	+	7.07677i	0.0328221	+	0.228283i
$962$	13.8313	−	8.88886i	0.445940	−	0.286588i
$963$	2.56679	+	2.96223i	0.0827137	+	0.0954567i
$964$	−6.95381	+	2.04182i	−0.223967	+	0.0657626i
$965$	−7.64336			−0.246048
$966$	4.66298	+	1.12100i	0.150029	+	0.0360674i
$967$	−59.3581			−1.90883			−0.954414	−	0.298485i	$-0.903519\pi$
$967$	−59.3581			−1.90883			−0.954414	+	0.298485i	$0.903519\pi$
$968$	9.44846	−	2.77432i	0.303685	−	0.0891699i
$969$	−4.22366	−	4.87436i	−0.135684	−	0.156587i
$970$	4.61403	−	2.96526i	0.148147	−	0.0952086i
$971$	−5.79077	−	40.2757i	−0.185835	−	1.29251i	−0.842652	−	0.538458i	$-0.819007\pi$
$971$	−5.79077	−	40.2757i	−0.185835	−	1.29251i	0.656817	−	0.754050i	$-0.271902\pi$
$972$	−0.841254	−	0.540641i	−0.0269832	−	0.0173411i
$973$	−8.14290	+	17.8305i	−0.261049	+	0.571619i
$974$	15.6423	−	18.0521i	0.501211	−	0.578428i
$975$	2.72751	−	18.9703i	0.0873503	−	0.607534i
$976$	0.739669	+	1.61965i	0.0236762	+	0.0518437i
$977$	−2.53203	−	0.743472i	−0.0810069	−	0.0237858i	0.240978	−	0.970531i	$-0.422532\pi$
$977$	−2.53203	−	0.743472i	−0.0810069	−	0.0237858i	−0.321985	+	0.946745i	$0.604350\pi$
$978$	3.69150	+	1.08392i	0.118041	+	0.0346600i
$979$	3.23626	+	7.08642i	0.103431	+	0.226483i
$980$	−0.110384	+	0.767734i	−0.00352607	+	0.0245244i
$981$	−4.13083	+	4.76723i	−0.131887	+	0.152206i
$982$	−11.4983	+	25.1778i	−0.366926	+	0.803455i
$983$	24.6706	+	15.8548i	0.786870	+	0.505691i	0.871307	−	0.490738i	$-0.163273\pi$
$983$	24.6706	+	15.8548i	0.786870	+	0.505691i	−0.0844371	+	0.996429i	$0.526909\pi$
$984$	0.392815	+	2.73209i	0.0125225	+	0.0870959i
$985$	−3.85308	+	2.47623i	−0.122769	+	0.0788992i
$986$	9.00178	+	10.3886i	0.286675	+	0.330841i
$987$	−8.33206	+	2.44651i	−0.265212	+	0.0778734i
$988$	−5.14769			−0.163770
$989$	−4.92488	+	52.7307i	−0.156602	+	1.67674i
$990$	0.832730			0.0264659
$991$	46.9373	−	13.7820i	1.49101	−	0.437800i	0.568148	−	0.822927i	$-0.307660\pi$
$991$	46.9373	−	13.7820i	1.49101	−	0.437800i	0.922864	+	0.385126i	$0.125842\pi$
$992$	−3.19814	−	3.69085i	−0.101541	−	0.117185i
$993$	−20.5727	+	13.2212i	−0.652854	+	0.419564i
$994$	0.441489	+	3.07063i	0.0140032	+	0.0973944i
$995$	−4.96976	−	3.19387i	−0.157552	−	0.101253i
$996$	−0.363579	+	0.796128i	−0.0115205	+	0.0252263i
$997$	24.4519	−	28.2190i	0.774400	−	0.893706i	−0.222291	−	0.974980i	$-0.571354\pi$
$997$	24.4519	−	28.2190i	0.774400	−	0.893706i	0.996692	+	0.0812745i	$0.0258990\pi$
$998$	−3.26611	+	22.7163i	−0.103387	+	0.719072i
$999$	1.56746	+	3.43227i	0.0495924	+	0.108592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.d.883.1	yes	20
23.18	even	11	inner	966.2.q.d.547.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.d.547.1	✓	20	23.18	even	11	inner
966.2.q.d.883.1	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.110384 - 0.767734i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.110384 - 0.767734i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.322208 + 0.705537i) q^{10} +(-1.03013 - 0.302473i) q^{11} +(0.959493 + 0.281733i) q^{12} +(-1.81011 - 3.96358i) q^{13} +(-0.142315 + 0.989821i) q^{14} +(0.507929 - 0.586181i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-4.59279 - 2.95161i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(0.993842 - 0.638704i) q^{19} +(-0.507929 - 0.586181i) q^{20} +(0.959493 - 0.281733i) q^{21} +1.07362 q^{22} +(-3.31669 - 3.46404i) q^{23} -1.00000 q^{24} +(4.22023 - 1.23917i) q^{25} +(2.85345 + 3.29306i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-0.142315 - 0.989821i) q^{28} +(2.11815 + 1.36125i) q^{29} +(-0.322208 + 0.705537i) q^{30} +(-3.19814 + 3.69085i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-0.445997 - 0.976598i) q^{33} +(5.23831 + 1.53811i) q^{34} +(-0.744211 - 0.218520i) q^{35} +(0.415415 + 0.909632i) q^{36} +(0.536989 - 3.73484i) q^{37} +(-0.773641 + 0.892829i) q^{38} +(1.81011 - 3.96358i) q^{39} +(0.652501 + 0.419337i) q^{40} +(-0.392815 - 2.73209i) q^{41} +(-0.841254 + 0.540641i) q^{42} +(-7.23161 - 8.34572i) q^{43} +(-1.03013 + 0.302473i) q^{44} +0.775629 q^{45} +(4.15827 + 2.38930i) q^{46} -8.68382 q^{47} +(0.959493 - 0.281733i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(-3.70017 + 2.37795i) q^{50} +(-0.776962 - 5.40389i) q^{51} +(-3.66563 - 2.35576i) q^{52} +(-1.43740 + 3.14748i) q^{53} +(0.654861 - 0.755750i) q^{54} +(-0.118510 + 0.824254i) q^{55} +(0.415415 + 0.909632i) q^{56} +(1.13353 + 0.332834i) q^{57} +(-2.41586 - 0.709361i) q^{58} +(2.35950 + 5.16658i) q^{59} +(0.110384 - 0.767734i) q^{60} +(-1.16601 + 1.34565i) q^{61} +(2.02876 - 4.44236i) q^{62} +(0.841254 + 0.540641i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-2.84317 + 1.82719i) q^{65} +(0.703071 + 0.811387i) q^{66} +(13.0559 - 3.83355i) q^{67} -5.45946 q^{68} +(0.445974 - 4.77505i) q^{69} +0.775629 q^{70} +(2.97654 - 0.873991i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(12.3622 - 7.94471i) q^{73} +(0.536989 + 3.73484i) q^{74} +(3.70017 + 2.37795i) q^{75} +(0.490764 - 1.07462i) q^{76} +(-0.703071 + 0.811387i) q^{77} +(-0.620114 + 4.31299i) q^{78} +(-2.51910 - 5.51607i) q^{79} +(-0.744211 - 0.218520i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(1.14662 + 2.51075i) q^{82} +(-0.124557 + 0.866311i) q^{83} +(0.654861 - 0.755750i) q^{84} +(-1.75908 + 3.85185i) q^{85} +(9.28994 + 5.97028i) q^{86} +(0.358328 + 2.49222i) q^{87} +(0.903185 - 0.580442i) q^{88} +(-4.75182 - 5.48389i) q^{89} +(-0.744211 + 0.218520i) q^{90} -4.35734 q^{91} +(-4.66298 - 1.12100i) q^{92} -4.88369 q^{93} +(8.33206 - 2.44651i) q^{94} +(-0.600059 - 0.692504i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(-1.00635 - 6.99932i) q^{97} +(0.841254 + 0.540641i) q^{98} +(0.445997 - 0.976598i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Introduction

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