LMFDB - Embedded newform 138.2.e.d.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			55.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	138.55
Dual form			138.2.e.d.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.0651865 - 0.453382i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.134858 + 0.295298i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.0651865 - 0.453382i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.134858 + 0.295298i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.190279 - 0.416652i) q^{10} +(-2.38745 - 0.701020i) q^{11} +(0.959493 + 0.281733i) q^{12} +(0.564582 + 1.23626i) q^{13} +(-0.0462003 + 0.321330i) q^{14} +(0.299955 - 0.346167i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-2.26811 - 1.45762i) q^{17} +(0.142315 + 0.989821i) q^{18} +(-2.43450 + 1.56456i) q^{19} +(-0.299955 - 0.346167i) q^{20} +(-0.311485 + 0.0914602i) q^{21} -2.48825 q^{22} +(-4.35491 - 2.00868i) q^{23} +1.00000 q^{24} +(4.59616 - 1.34955i) q^{25} +(0.890008 + 1.02712i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.0462003 + 0.321330i) q^{28} +(-1.83493 - 1.17924i) q^{29} +(0.190279 - 0.416652i) q^{30} +(-1.61291 + 1.86139i) q^{31} +(0.142315 - 0.989821i) q^{32} +(-1.03365 - 2.26339i) q^{33} +(-2.58689 - 0.759581i) q^{34} +(0.142674 + 0.0418928i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-0.0683786 + 0.475583i) q^{37} +(-1.89510 + 2.18706i) q^{38} +(-0.564582 + 1.23626i) q^{39} +(-0.385331 - 0.247638i) q^{40} +(-0.120602 - 0.838807i) q^{41} +(-0.273100 + 0.175511i) q^{42} +(5.76770 + 6.65628i) q^{43} +(-2.38745 + 0.701020i) q^{44} +0.458044 q^{45} +(-4.74441 - 0.700397i) q^{46} -2.71406 q^{47} +(0.959493 - 0.281733i) q^{48} +(4.51501 + 5.21060i) q^{49} +(4.02977 - 2.58978i) q^{50} +(-0.383696 - 2.66866i) q^{51} +(1.14333 + 0.734774i) q^{52} +(3.62496 - 7.93756i) q^{53} +(-0.654861 + 0.755750i) q^{54} +(-0.162200 + 1.12813i) q^{55} +(0.134858 + 0.295298i) q^{56} +(-2.77667 - 0.815304i) q^{57} +(-2.09283 - 0.614511i) q^{58} +(4.52108 + 9.89978i) q^{59} +(0.0651865 - 0.453382i) q^{60} +(7.89921 - 9.11618i) q^{61} +(-1.02316 + 2.24040i) q^{62} +(-0.273100 - 0.175511i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(0.523697 - 0.336559i) q^{65} +(-1.62945 - 1.88049i) q^{66} +(-10.1378 + 2.97673i) q^{67} -2.69611 q^{68} +(-1.33380 - 4.60662i) q^{69} +0.148697 q^{70} +(15.7422 - 4.62233i) q^{71} +(0.654861 + 0.755750i) q^{72} +(9.89520 - 6.35926i) q^{73} +(0.0683786 + 0.475583i) q^{74} +(4.02977 + 2.58978i) q^{75} +(-1.20217 + 2.63238i) q^{76} +(0.528978 - 0.610473i) q^{77} +(-0.193417 + 1.34525i) q^{78} +(-4.45637 - 9.75808i) q^{79} +(-0.439490 - 0.129046i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.352036 - 0.770851i) q^{82} +(-1.15039 + 8.00114i) q^{83} +(-0.212591 + 0.245343i) q^{84} +(-0.513011 + 1.12334i) q^{85} +(7.40935 + 4.76170i) q^{86} +(-0.310415 - 2.15898i) q^{87} +(-2.09325 + 1.34525i) q^{88} +(6.74394 + 7.78292i) q^{89} +(0.439490 - 0.129046i) q^{90} -0.441205 q^{91} +(-4.74955 + 0.664630i) q^{92} -2.46297 q^{93} +(-2.60412 + 0.764638i) q^{94} +(0.868039 + 1.00177i) q^{95} +(0.841254 - 0.540641i) q^{96} +(0.0319166 + 0.221985i) q^{97} +(5.80012 + 3.72751i) q^{98} +(1.03365 - 2.26339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9} - 13 q^{10} - 5 q^{11} + q^{12} + 13 q^{13} + 9 q^{14} + 9 q^{15} - q^{16} + q^{18} - 9 q^{20} - 13 q^{21} - 6 q^{22} - 32 q^{23} + 10 q^{24} + q^{25} - 13 q^{26} + q^{27} - 9 q^{28} + 27 q^{29} + 13 q^{30} - 8 q^{31} + q^{32} - 6 q^{33} - 11 q^{34} - 26 q^{35} - q^{36} - 11 q^{37} + 11 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} + 2 q^{42} + 34 q^{43} - 5 q^{44} + 2 q^{45} - q^{46} + 8 q^{47} + q^{48} + 25 q^{49} + 21 q^{50} - 11 q^{51} + 2 q^{52} + 9 q^{53} - q^{54} - 23 q^{55} - 2 q^{56} - 11 q^{57} - 5 q^{58} - 21 q^{59} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} + 29 q^{65} + 6 q^{66} - 32 q^{67} + 22 q^{68} - q^{69} - 18 q^{70} + 22 q^{71} + q^{72} + 43 q^{73} + 11 q^{74} + 21 q^{75} + 10 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} - q^{81} + 32 q^{82} - 3 q^{83} + 9 q^{84} + 33 q^{85} + 32 q^{86} + 6 q^{87} - 6 q^{88} - 11 q^{89} - 2 q^{90} - 70 q^{91} - 21 q^{92} + 8 q^{93} + 3 q^{94} - q^{96} + 39 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9 - 13 * q^10 - 5 * q^11 + q^12 + 13 * q^13 + 9 * q^14 + 9 * q^15 - q^16 + q^18 - 9 * q^20 - 13 * q^21 - 6 * q^22 - 32 * q^23 + 10 * q^24 + q^25 - 13 * q^26 + q^27 - 9 * q^28 + 27 * q^29 + 13 * q^30 - 8 * q^31 + q^32 - 6 * q^33 - 11 * q^34 - 26 * q^35 - q^36 - 11 * q^37 + 11 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 + 2 * q^42 + 34 * q^43 - 5 * q^44 + 2 * q^45 - q^46 + 8 * q^47 + q^48 + 25 * q^49 + 21 * q^50 - 11 * q^51 + 2 * q^52 + 9 * q^53 - q^54 - 23 * q^55 - 2 * q^56 - 11 * q^57 - 5 * q^58 - 21 * q^59 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^63 - q^64 + 29 * q^65 + 6 * q^66 - 32 * q^67 + 22 * q^68 - q^69 - 18 * q^70 + 22 * q^71 + q^72 + 43 * q^73 + 11 * q^74 + 21 * q^75 + 10 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - q^81 + 32 * q^82 - 3 * q^83 + 9 * q^84 + 33 * q^85 + 32 * q^86 + 6 * q^87 - 6 * q^88 - 11 * q^89 - 2 * q^90 - 70 * q^91 - 21 * q^92 + 8 * q^93 + 3 * q^94 - q^96 + 39 * q^97 - 14 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$

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
$5$	−0.0651865	−	0.453382i	−0.0291523	−	0.202759i	0.970040	−	0.242946i	$-0.0781137\pi$
$5$	−0.0651865	−	0.453382i	−0.0291523	−	0.202759i	−0.999192	+	0.0401871i	$0.987205\pi$
$6$	0.841254	+	0.540641i	0.343440	+	0.220716i
$7$	−0.134858	+	0.295298i	−0.0509716	+	0.111612i	−0.933404	−	0.358826i	$-0.883177\pi$
$7$	−0.134858	+	0.295298i	−0.0509716	+	0.111612i	0.882433	+	0.470439i	$0.155904\pi$
$8$	0.654861	−	0.755750i	0.231528	−	0.267198i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	−0.190279	−	0.416652i	−0.0601714	−	0.131757i
$11$	−2.38745	−	0.701020i	−0.719844	−	0.211365i	−0.0987625	−	0.995111i	$-0.531488\pi$
$11$	−2.38745	−	0.701020i	−0.719844	−	0.211365i	−0.621082	+	0.783746i	$0.713307\pi$
$12$	0.959493	+	0.281733i	0.276982	+	0.0813292i
$13$	0.564582	+	1.23626i	0.156587	+	0.342878i	0.971624	−	0.236531i	$-0.0760106\pi$
$13$	0.564582	+	1.23626i	0.156587	+	0.342878i	−0.815037	+	0.579409i	$0.803283\pi$
$14$	−0.0462003	+	0.321330i	−0.0123476	+	0.0858792i
$15$	0.299955	−	0.346167i	0.0774481	−	0.0893799i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	−2.26811	−	1.45762i	−0.550097	−	0.353526i	0.235879	−	0.971782i	$-0.424203\pi$
$17$	−2.26811	−	1.45762i	−0.550097	−	0.353526i	−0.785976	+	0.618256i	$0.787839\pi$
$18$	0.142315	+	0.989821i	0.0335439	+	0.233303i
$19$	−2.43450	+	1.56456i	−0.558512	+	0.358934i	−0.789241	−	0.614084i	$-0.789526\pi$
$19$	−2.43450	+	1.56456i	−0.558512	+	0.358934i	0.230728	+	0.973018i	$0.425889\pi$
$20$	−0.299955	−	0.346167i	−0.0670720	−	0.0774053i
$21$	−0.311485	+	0.0914602i	−0.0679716	+	0.0199583i
$22$	−2.48825			−0.530496
$23$	−4.35491	−	2.00868i	−0.908061	−	0.418839i
$23$	−4.35491	−	2.00868i	−0.908061	−	0.418839i
$24$	1.00000			0.204124
$25$	4.59616	−	1.34955i	0.919232	−	0.269911i
$26$	0.890008	+	1.02712i	0.174545	+	0.201436i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	0.0462003	+	0.321330i	0.00873105	+	0.0607258i
$29$	−1.83493	−	1.17924i	−0.340738	−	0.218979i	0.359069	−	0.933311i	$-0.383094\pi$
$29$	−1.83493	−	1.17924i	−0.340738	−	0.218979i	−0.699807	+	0.714332i	$0.746731\pi$
$30$	0.190279	−	0.416652i	0.0347399	−	0.0760699i
$31$	−1.61291	+	1.86139i	−0.289686	+	0.334316i	−0.881875	−	0.471484i	$-0.843719\pi$
$31$	−1.61291	+	1.86139i	−0.289686	+	0.334316i	0.592188	+	0.805799i	$0.298264\pi$
$32$	0.142315	−	0.989821i	0.0251579	−	0.174977i
$33$	−1.03365	−	2.26339i	−0.179936	−	0.394005i
$34$	−2.58689	−	0.759581i	−0.443649	−	0.130267i
$35$	0.142674	+	0.0418928i	0.0241163	+	0.00708118i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−0.0683786	+	0.475583i	−0.0112414	+	0.0781854i	−0.994670	−	0.103111i	$-0.967120\pi$
$37$	−0.0683786	+	0.475583i	−0.0112414	+	0.0781854i	0.983428	+	0.181297i	$0.0580294\pi$
$38$	−1.89510	+	2.18706i	−0.307425	+	0.354788i
$39$	−0.564582	+	1.23626i	−0.0904055	+	0.197961i
$40$	−0.385331	−	0.247638i	−0.0609263	−	0.0391549i
$41$	−0.120602	−	0.838807i	−0.0188349	−	0.131000i	0.978234	−	0.207503i	$-0.0665336\pi$
$41$	−0.120602	−	0.838807i	−0.0188349	−	0.131000i	−0.997069	+	0.0765031i	$0.975624\pi$
$42$	−0.273100	+	0.175511i	−0.0421403	+	0.0270819i
$43$	5.76770	+	6.65628i	0.879565	+	1.01507i	0.999751	+	0.0223211i	$0.00710563\pi$
$43$	5.76770	+	6.65628i	0.879565	+	1.01507i	−0.120185	+	0.992751i	$0.538349\pi$
$44$	−2.38745	+	0.701020i	−0.359922	+	0.105683i
$45$	0.458044			0.0682812
$46$	−4.74441	−	0.700397i	−0.699525	−	0.103268i
$47$	−2.71406			−0.395886			−0.197943	−	0.980214i	$-0.563426\pi$
$47$	−2.71406			−0.395886			−0.197943	+	0.980214i	$0.563426\pi$
$48$	0.959493	−	0.281733i	0.138491	−	0.0406646i
$49$	4.51501	+	5.21060i	0.645002	+	0.744371i
$50$	4.02977	−	2.58978i	0.569895	−	0.366250i
$51$	−0.383696	−	2.66866i	−0.0537282	−	0.373688i
$52$	1.14333	+	0.734774i	0.158552	+	0.101895i
$53$	3.62496	−	7.93756i	0.497927	−	1.09031i	−0.479210	−	0.877700i	$-0.659077\pi$
$53$	3.62496	−	7.93756i	0.497927	−	1.09031i	0.977138	−	0.212608i	$-0.0681958\pi$
$54$	−0.654861	+	0.755750i	−0.0891153	+	0.102844i
$55$	−0.162200	+	1.12813i	−0.0218711	+	0.152116i
$56$	0.134858	+	0.295298i	0.0180212	+	0.0394609i
$57$	−2.77667	−	0.815304i	−0.367779	−	0.107990i
$58$	−2.09283	−	0.614511i	−0.274802	−	0.0806893i
$59$	4.52108	+	9.89978i	0.588594	+	1.28884i	0.936288	+	0.351233i	$0.114238\pi$
$59$	4.52108	+	9.89978i	0.588594	+	1.28884i	−0.347694	+	0.937608i	$0.613035\pi$
$60$	0.0651865	−	0.453382i	0.00841554	−	0.0585314i
$61$	7.89921	−	9.11618i	1.01139	−	1.16721i	0.0255243	−	0.999674i	$-0.491874\pi$
$61$	7.89921	−	9.11618i	1.01139	−	1.16721i	0.985866	−	0.167533i	$-0.0535801\pi$
$62$	−1.02316	+	2.24040i	−0.129941	+	0.284531i
$63$	−0.273100	−	0.175511i	−0.0344074	−	0.0221123i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	0.523697	−	0.336559i	0.0649566	−	0.0417450i
$66$	−1.62945	−	1.88049i	−0.200572	−	0.231472i
$67$	−10.1378	+	2.97673i	−1.23853	+	0.363665i	−0.834463	−	0.551065i	$-0.814222\pi$
$67$	−10.1378	+	2.97673i	−1.23853	+	0.363665i	−0.404067	+	0.914730i	$0.632404\pi$
$68$	−2.69611			−0.326951
$69$	−1.33380	−	4.60662i	−0.160570	−	0.554572i
$70$	0.148697			0.0177727
$71$	15.7422	−	4.62233i	1.86826	−	0.548570i	0.869777	−	0.493446i	$-0.164263\pi$
$71$	15.7422	−	4.62233i	1.86826	−	0.548570i	0.998480	−	0.0551238i	$-0.0175554\pi$
$72$	0.654861	+	0.755750i	0.0771761	+	0.0890659i
$73$	9.89520	−	6.35926i	1.15814	−	0.744295i	0.186900	−	0.982379i	$-0.440156\pi$
$73$	9.89520	−	6.35926i	1.15814	−	0.744295i	0.971245	+	0.238084i	$0.0765194\pi$
$74$	0.0683786	+	0.475583i	0.00794885	+	0.0552854i
$75$	4.02977	+	2.58978i	0.465318	+	0.299041i
$76$	−1.20217	+	2.63238i	−0.137898	+	0.301955i
$77$	0.528978	−	0.610473i	0.0602826	−	0.0695698i
$78$	−0.193417	+	1.34525i	−0.0219002	+	0.152319i
$79$	−4.45637	−	9.75808i	−0.501380	−	1.09787i	−0.976018	−	0.217689i	$-0.930148\pi$
$79$	−4.45637	−	9.75808i	−0.501380	−	1.09787i	0.474638	−	0.880181i	$-0.342579\pi$
$80$	−0.439490	−	0.129046i	−0.0491365	−	0.0144278i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−0.352036	−	0.770851i	−0.0388759	−	0.0851263i
$83$	−1.15039	+	8.00114i	−0.126272	+	0.878240i	0.823949	+	0.566663i	$0.191766\pi$
$83$	−1.15039	+	8.00114i	−0.126272	+	0.878240i	−0.950221	+	0.311576i	$0.899143\pi$
$84$	−0.212591	+	0.245343i	−0.0231955	+	0.0267691i
$85$	−0.513011	+	1.12334i	−0.0556439	+	0.121843i
$86$	7.40935	+	4.76170i	0.798971	+	0.513468i
$87$	−0.310415	−	2.15898i	−0.0332800	−	0.231467i
$88$	−2.09325	+	1.34525i	−0.223141	+	0.143404i
$89$	6.74394	+	7.78292i	0.714856	+	0.824988i	0.990679	−	0.136220i	$-0.0434955\pi$
$89$	6.74394	+	7.78292i	0.714856	+	0.824988i	−0.275822	+	0.961209i	$0.588950\pi$
$90$	0.439490	−	0.129046i	0.0463264	−	0.0136026i
$91$	−0.441205			−0.0462508
$92$	−4.74955	+	0.664630i	−0.495175	+	0.0692924i
$93$	−2.46297			−0.255399
$94$	−2.60412	+	0.764638i	−0.268594	+	0.0788664i
$95$	0.868039	+	1.00177i	0.0890589	+	0.102779i
$96$	0.841254	−	0.540641i	0.0858601	−	0.0551789i
$97$	0.0319166	+	0.221985i	0.00324064	+	0.0225392i	0.991378	−	0.131036i	$-0.0418304\pi$
$97$	0.0319166	+	0.221985i	0.00324064	+	0.0225392i	−0.988137	+	0.153575i	$0.950921\pi$
$98$	5.80012	+	3.72751i	0.585900	+	0.376535i
$99$	1.03365	−	2.26339i	0.103886	−	0.227479i
$100$	3.13691	−	3.62019i	0.313691	−	0.362019i
$101$	−1.52215	+	10.5868i	−0.151460	+	1.05342i	0.762316	+	0.647205i	$0.224062\pi$
$101$	−1.52215	+	10.5868i	−0.151460	+	1.05342i	−0.913775	+	0.406220i	$0.866847\pi$
$102$	−1.12000	−	2.45246i	−0.110897	−	0.242830i
$103$	−1.94475	−	0.571031i	−0.191622	−	0.0562653i	0.184513	−	0.982830i	$-0.440929\pi$
$103$	−1.94475	−	0.571031i	−0.191622	−	0.0562653i	−0.376135	+	0.926565i	$0.622747\pi$
$104$	1.30403	+	0.382897i	0.127870	+	0.0375462i
$105$	0.0617710	+	0.135260i	0.00602824	+	0.0132000i
$106$	1.24186	−	8.63731i	0.120620	−	0.838930i
$107$	−1.41996	+	1.63873i	−0.137273	+	0.158422i	−0.820224	−	0.572043i	$-0.806151\pi$
$107$	−1.41996	+	1.63873i	−0.137273	+	0.158422i	0.682950	+	0.730465i	$0.260696\pi$
$108$	−0.415415	+	0.909632i	−0.0399733	+	0.0875294i
$109$	−7.08241	−	4.55159i	−0.678372	−	0.435963i	0.155563	−	0.987826i	$-0.450281\pi$
$109$	−7.08241	−	4.55159i	−0.678372	−	0.435963i	−0.833935	+	0.551863i	$0.813917\pi$
$110$	0.162200	+	1.12813i	0.0154652	+	0.107563i
$111$	−0.404200	+	0.259764i	−0.0383650	+	0.0246557i
$112$	0.212591	+	0.245343i	0.0200879	+	0.0231827i
$113$	−0.186034	+	0.0546244i	−0.0175006	+	0.00513863i	−0.290471	−	0.956884i	$-0.593812\pi$
$113$	−0.186034	+	0.0546244i	−0.0175006	+	0.00513863i	0.272971	+	0.962022i	$0.411994\pi$
$114$	−2.89389			−0.271038
$115$	−0.626819	+	2.10538i	−0.0584512	+	0.196327i
$116$	−2.18119			−0.202518
$117$	−1.30403	+	0.382897i	−0.120557	+	0.0353989i
$118$	7.12703	+	8.22504i	0.656097	+	0.757176i
$119$	0.736307	−	0.473196i	0.0674971	−	0.0433778i
$120$	−0.0651865	−	0.453382i	−0.00595069	−	0.0413879i
$121$	−4.04528	−	2.59974i	−0.367753	−	0.236340i
$122$	5.01092	−	10.9724i	0.453667	−	0.993392i
$123$	0.554950	−	0.640447i	0.0500382	−	0.0577471i
$124$	−0.350518	+	2.43790i	−0.0314774	+	0.218930i
$125$	−1.86286	−	4.07910i	−0.166620	−	0.364846i
$126$	−0.311485	−	0.0914602i	−0.0277493	−	0.00814792i
$127$	−12.4055	−	3.64259i	−1.10081	−	0.323228i	−0.319638	−	0.947540i	$-0.603561\pi$
$127$	−12.4055	−	3.64259i	−1.10081	−	0.323228i	−0.781175	+	0.624312i	$0.785379\pi$
$128$	−0.415415	−	0.909632i	−0.0367178	−	0.0804009i
$129$	−1.25344	+	8.71787i	−0.110359	+	0.767565i
$130$	0.407663	−	0.470469i	0.0357544	−	0.0412628i
$131$	−2.44775	+	5.35982i	−0.213861	+	0.468289i	−0.985911	−	0.167272i	$-0.946504\pi$
$131$	−2.44775	+	5.35982i	−0.213861	+	0.468289i	0.772050	+	0.635562i	$0.219231\pi$
$132$	−2.09325	−	1.34525i	−0.182194	−	0.117089i
$133$	−0.133699	−	0.929896i	−0.0115932	−	0.0806322i
$134$	−8.88851	+	5.71230i	−0.767850	+	0.493467i
$135$	0.299955	+	0.346167i	0.0258160	+	0.0297933i
$136$	−2.58689	+	0.759581i	−0.221824	+	0.0651335i
$137$	−16.2119			−1.38508			−0.692538	−	0.721381i	$-0.743508\pi$
$137$	−16.2119			−1.38508			−0.692538	+	0.721381i	$0.743508\pi$
$138$	−2.57760	−	4.04425i	−0.219420	−	0.344269i
$139$	−19.6328			−1.66524			−0.832618	−	0.553848i	$-0.813159\pi$
$139$	−19.6328			−1.66524			−0.832618	+	0.553848i	$0.813159\pi$
$140$	0.142674	−	0.0418928i	0.0120581	−	0.00354059i
$141$	−1.77733	−	2.05115i	−0.149678	−	0.172738i
$142$	13.8023	−	8.87018i	1.15826	−	0.744369i
$143$	−0.481270	−	3.34730i	−0.0402458	−	0.279916i
$144$	0.841254	+	0.540641i	0.0701045	+	0.0450534i
$145$	−0.415033	+	0.908795i	−0.0344666	+	0.0754713i
$146$	7.70276	−	8.88946i	0.637485	−	0.735697i
$147$	−0.981206	+	6.82444i	−0.0809285	+	0.562870i
$148$	0.199596	+	0.437054i	0.0164067	+	0.0359256i
$149$	−3.05112	−	0.895889i	−0.249957	−	0.0733941i	0.154354	−	0.988016i	$-0.450670\pi$
$149$	−3.05112	−	0.895889i	−0.249957	−	0.0733941i	−0.404311	+	0.914622i	$0.632489\pi$
$150$	4.59616	+	1.34955i	0.375275	+	0.110191i
$151$	−0.529537	−	1.15953i	−0.0430931	−	0.0943608i	0.886861	−	0.462036i	$-0.152881\pi$
$151$	−0.529537	−	1.15953i	−0.0430931	−	0.0943608i	−0.929954	+	0.367675i	$0.880154\pi$
$152$	−0.411844	+	2.86444i	−0.0334050	+	0.232337i
$153$	1.76557	−	2.03758i	0.142738	−	0.164729i
$154$	0.335560	−	0.734774i	0.0270402	−	0.0592098i
$155$	0.949062	+	0.609925i	0.0762305	+	0.0489903i
$156$	0.193417	+	1.34525i	0.0154858	+	0.107706i
$157$	−14.5837	+	9.37238i	−1.16391	+	0.747998i	−0.972360	−	0.233486i	$-0.924987\pi$
$157$	−14.5837	+	9.37238i	−1.16391	+	0.747998i	−0.191547	+	0.981483i	$0.561350\pi$
$158$	−7.02502	−	8.10731i	−0.558881	−	0.644983i
$159$	8.37266	−	2.45843i	0.663995	−	0.194967i
$160$	−0.458044			−0.0362116
$161$	1.18045	−	1.01511i	0.0930328	−	0.0800018i
$162$	−1.00000			−0.0785674
$163$	5.05886	−	1.48542i	0.396241	−	0.116347i	−0.0775408	−	0.996989i	$-0.524707\pi$
$163$	5.05886	−	1.48542i	0.396241	−	0.116347i	0.473782	+	0.880642i	$0.342889\pi$
$164$	−0.554950	−	0.640447i	−0.0433343	−	0.0500105i
$165$	−0.958799	+	0.616183i	−0.0746424	+	0.0479698i
$166$	1.15039	+	8.00114i	0.0892876	+	0.621009i
$167$	−2.48840	−	1.59920i	−0.192558	−	0.123749i	0.440810	−	0.897601i	$-0.354691\pi$
$167$	−2.48840	−	1.59920i	−0.192558	−	0.123749i	−0.633367	+	0.773851i	$0.718328\pi$
$168$	−0.134858	+	0.295298i	−0.0104045	+	0.0227828i
$169$	7.30360	−	8.42880i	0.561815	−	0.648369i
$170$	−0.175750	+	1.22237i	−0.0134794	+	0.0937512i
$171$	−1.20217	−	2.63238i	−0.0919320	−	0.201303i
$172$	8.45075	+	2.48136i	0.644364	+	0.189202i
$173$	−3.96538	−	1.16434i	−0.301482	−	0.0885232i	0.127493	−	0.991840i	$-0.459307\pi$
$173$	−3.96538	−	1.16434i	−0.301482	−	0.0885232i	−0.428975	+	0.903316i	$0.641125\pi$
$174$	−0.906098	−	1.98408i	−0.0686911	−	0.150412i
$175$	−0.221309	+	1.53924i	−0.0167294	+	0.116355i
$176$	−1.62945	+	1.88049i	−0.122825	+	0.141747i
$177$	−4.52108	+	9.89978i	−0.339825	+	0.744113i
$178$	8.66347	+	5.56767i	0.649354	+	0.417315i
$179$	−1.44265	−	10.0338i	−0.107829	−	0.749965i	−0.969957	−	0.243275i	$-0.921778\pi$
$179$	−1.44265	−	10.0338i	−0.107829	−	0.749965i	0.862129	−	0.506689i	$-0.169131\pi$
$180$	0.385331	−	0.247638i	0.0287209	−	0.0184578i
$181$	17.4442	+	20.1316i	1.29661	+	1.49637i	0.754959	+	0.655772i	$0.227657\pi$
$181$	17.4442	+	20.1316i	1.29661	+	1.49637i	0.541655	+	0.840601i	$0.317798\pi$
$182$	−0.423333	+	0.124302i	−0.0313795	+	0.00921386i
$183$	12.0624			0.891681
$184$	−4.36992	+	1.97581i	−0.322155	+	0.145659i
$185$	0.220078			0.0161805
$186$	−2.36321	+	0.693900i	−0.173279	+	0.0508792i
$187$	4.39318	+	5.07000i	0.321261	+	0.370755i
$188$	−2.28321	+	1.46733i	−0.166520	+	0.107016i
$189$	−0.0462003	−	0.321330i	−0.00336058	−	0.0233734i
$190$	1.11511	+	0.716637i	0.0808985	+	0.0519903i
$191$	9.71754	−	21.2784i	0.703136	−	1.53965i	−0.132991	−	0.991117i	$-0.542458\pi$
$191$	9.71754	−	21.2784i	0.703136	−	1.53965i	0.836127	−	0.548536i	$-0.184815\pi$
$192$	0.654861	−	0.755750i	0.0472605	−	0.0545415i
$193$	−0.856252	+	5.95536i	−0.0616344	+	0.428676i	0.935519	+	0.353276i	$0.114932\pi$
$193$	−0.856252	+	5.95536i	−0.0616344	+	0.428676i	−0.997153	+	0.0754000i	$0.975977\pi$
$194$	0.0931641	+	0.204001i	0.00668880	+	0.0146464i
$195$	0.597303	+	0.175384i	0.0427737	+	0.0125595i
$196$	6.61533	+	1.94244i	0.472524	+	0.138745i
$197$	6.42396	+	14.0665i	0.457688	+	1.00220i	0.988008	+	0.154400i	$0.0493445\pi$
$197$	6.42396	+	14.0665i	0.457688	+	1.00220i	−0.530320	+	0.847797i	$0.677928\pi$
$198$	0.354114	−	2.46292i	0.0251658	−	0.175032i
$199$	7.66908	−	8.85059i	0.543647	−	0.627402i	−0.415744	−	0.909482i	$-0.636479\pi$
$199$	7.66908	−	8.85059i	0.543647	−	0.627402i	0.959391	+	0.282080i	$0.0910243\pi$
$200$	1.98992	−	4.35731i	0.140709	−	0.308109i
$201$	−8.88851	−	5.71230i	−0.626947	−	0.402914i
$202$	1.52215	+	10.5868i	0.107098	+	0.744884i
$203$	0.595682	−	0.382822i	0.0418087	−	0.0268688i
$204$	−1.76557	−	2.03758i	−0.123615	−	0.142659i
$205$	−0.372438	+	0.109358i	−0.0260122	+	0.00763788i
$206$	−2.02685			−0.141218
$207$	2.60800	−	4.02471i	0.181269	−	0.279737i
$208$	1.35908			0.0942353
$209$	6.90904	−	2.02868i	0.477908	−	0.140327i
$210$	0.0973759	+	0.112378i	0.00671958	+	0.00775481i
$211$	8.98039	−	5.77135i	0.618236	−	0.397316i	−0.193702	−	0.981060i	$-0.562049\pi$
$211$	8.98039	−	5.77135i	0.618236	−	0.397316i	0.811937	+	0.583745i	$0.198413\pi$
$212$	−1.24186	−	8.63731i	−0.0852911	−	0.593213i
$213$	13.8023	+	8.87018i	0.945716	+	0.607775i
$214$	−0.900763	+	1.97240i	−0.0615749	+	0.134830i
$215$	2.64186	−	3.04887i	0.180173	−	0.207931i
$216$	−0.142315	+	0.989821i	−0.00968330	+	0.0673488i
$217$	−0.332152	−	0.727312i	−0.0225480	−	0.0493731i
$218$	−8.07785	−	2.37187i	−0.547101	−	0.160643i
$219$	11.2860	+	3.31386i	0.762636	+	0.223930i
$220$	0.473460	+	1.03673i	0.0319206	+	0.0698965i
$221$	0.521474	−	3.62693i	0.0350781	−	0.243974i
$222$	−0.314643	+	0.363118i	−0.0211175	+	0.0243709i
$223$	3.14540	−	6.88747i	0.210632	−	0.461219i	−0.774599	−	0.632453i	$-0.782048\pi$
$223$	3.14540	−	6.88747i	0.210632	−	0.461219i	0.985230	+	0.171234i	$0.0547754\pi$
$224$	0.273100	+	0.175511i	0.0182473	+	0.0117268i
$225$	0.681716	+	4.74144i	0.0454477	+	0.316096i
$226$	−0.163109	+	0.104824i	−0.0108498	+	0.00697276i
$227$	8.28049	+	9.55620i	0.549596	+	0.634267i	0.960789	−	0.277281i	$-0.0894333\pi$
$227$	8.28049	+	9.55620i	0.549596	+	0.634267i	−0.411193	+	0.911548i	$0.634888\pi$
$228$	−2.77667	+	0.815304i	−0.183890	+	0.0539948i
$229$	−8.39479			−0.554743			−0.277372	−	0.960763i	$-0.589463\pi$
$229$	−8.39479			−0.554743			−0.277372	+	0.960763i	$0.589463\pi$
$230$	−0.00827561	+	2.19669i	−0.000545678	+	0.144845i
$231$	0.807771			0.0531474
$232$	−2.09283	+	0.614511i	−0.137401	+	0.0403446i
$233$	−17.2108	−	19.8623i	−1.12752	−	1.30122i	−0.948286	−	0.317417i	$-0.897184\pi$
$233$	−17.2108	−	19.8623i	−1.12752	−	1.30122i	−0.179231	−	0.983807i	$-0.557361\pi$
$234$	−1.14333	+	0.734774i	−0.0747419	+	0.0480337i
$235$	0.176920	+	1.23050i	0.0115410	+	0.0802693i
$236$	9.15560	+	5.88395i	0.595979	+	0.383012i
$237$	4.45637	−	9.75808i	0.289472	−	0.633856i
$238$	0.573167	−	0.661470i	0.0371529	−	0.0428767i
$239$	−1.11770	+	7.77380i	−0.0722983	+	0.502846i	0.921208	+	0.389070i	$0.127204\pi$
$239$	−1.11770	+	7.77380i	−0.0722983	+	0.502846i	−0.993506	+	0.113776i	$0.963706\pi$
$240$	−0.190279	−	0.416652i	−0.0122824	−	0.0268948i
$241$	25.4306	+	7.46711i	1.63813	+	0.480999i	0.965808	−	0.259258i	$-0.0834781\pi$
$241$	25.4306	+	7.46711i	1.63813	+	0.480999i	0.672324	+	0.740257i	$0.265296\pi$
$242$	−4.61385	−	1.35475i	−0.296590	−	0.0870866i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	1.71666	−	11.9397i	0.109898	−	0.764358i
$245$	2.06808	−	2.38669i	0.132125	−	0.152480i
$246$	0.352036	−	0.770851i	0.0224450	−	0.0491477i
$247$	−3.30868	−	2.12636i	−0.210526	−	0.135297i
$248$	0.350518	+	2.43790i	0.0222579	+	0.154807i
$249$	−6.80021	+	4.37023i	−0.430946	+	0.276952i
$250$	−2.93662	−	3.38904i	−0.185728	−	0.214342i
$251$	17.3220	−	5.08620i	1.09336	−	0.321038i	0.315147	−	0.949043i	$-0.397946\pi$
$251$	17.3220	−	5.08620i	1.09336	−	0.321038i	0.778210	+	0.628005i	$0.216128\pi$
$252$	−0.324635			−0.0204501
$253$	8.98901	+	7.84851i	0.565134	+	0.493431i
$254$	−12.9293			−0.811253
$255$	−1.18491	+	0.347922i	−0.0742021	+	0.0217877i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−19.2275	+	12.3568i	−1.19938	+	0.770794i	−0.978849	−	0.204586i	$-0.934415\pi$
$257$	−19.2275	+	12.3568i	−1.19938	+	0.770794i	−0.220531	+	0.975380i	$0.570779\pi$
$258$	1.25344	+	8.71787i	0.0780358	+	0.542751i
$259$	−0.131217	−	0.0843284i	−0.00815346	−	0.00523991i
$260$	0.258604	−	0.566263i	0.0160379	−	0.0351182i
$261$	1.42837	−	1.64843i	0.0884141	−	0.102035i
$262$	−0.838560	+	5.83232i	−0.0518064	+	0.360322i
$263$	−7.73481	−	16.9369i	−0.476949	−	1.04437i	−0.983291	−	0.182039i	$-0.941730\pi$
$263$	−7.73481	−	16.9369i	−0.476949	−	1.04437i	0.506343	−	0.862332i	$-0.330997\pi$
$264$	−2.38745	−	0.701020i	−0.146938	−	0.0431448i
$265$	−3.83505	−	1.12607i	−0.235585	−	0.0691741i
$266$	−0.390265	−	0.854562i	−0.0239287	−	0.0523965i
$267$	−1.46560	+	10.1935i	−0.0896932	+	0.623830i
$268$	−6.91912	+	7.98509i	−0.422653	+	0.487767i
$269$	0.327653	−	0.717460i	0.0199774	−	0.0437443i	−0.899380	−	0.437167i	$-0.855982\pi$
$269$	0.327653	−	0.717460i	0.0199774	−	0.0437443i	0.919358	+	0.393423i	$0.128709\pi$
$270$	0.385331	+	0.247638i	0.0234505	+	0.0150707i
$271$	−4.17271	−	29.0218i	−0.253474	−	1.76295i	−0.577013	−	0.816735i	$-0.695782\pi$
$271$	−4.17271	−	29.0218i	−0.253474	−	1.76295i	0.323540	−	0.946215i	$-0.395127\pi$
$272$	−2.26811	+	1.45762i	−0.137524	+	0.0883815i
$273$	−0.288928	−	0.333440i	−0.0174867	−	0.0201807i
$274$	−15.5552	+	4.56742i	−0.939725	+	0.275928i
$275$	−11.9192			−0.718754
$276$	−3.61259	−	3.15423i	−0.217452	−	0.189863i
$277$	−25.4356			−1.52828			−0.764138	−	0.645053i	$-0.776835\pi$
$277$	−25.4356			−1.52828			−0.764138	+	0.645053i	$0.776835\pi$
$278$	−18.8376	+	5.53121i	−1.12980	+	0.331740i
$279$	−1.61291	−	1.86139i	−0.0965621	−	0.111439i
$280$	0.125092	−	0.0803918i	0.00747568	−	0.00480433i
$281$	3.35608	+	23.3420i	0.200207	+	1.39247i	0.803669	+	0.595077i	$0.202878\pi$
$281$	3.35608	+	23.3420i	0.200207	+	1.39247i	−0.603462	+	0.797391i	$0.706213\pi$
$282$	−2.28321	−	1.46733i	−0.135963	−	0.0873782i
$283$	−11.0626	+	24.2237i	−0.657602	+	1.43995i	0.227138	+	0.973863i	$0.427063\pi$
$283$	−11.0626	+	24.2237i	−0.657602	+	1.43995i	−0.884740	+	0.466085i	$0.845664\pi$
$284$	10.7442	−	12.3994i	0.637549	−	0.735771i
$285$	−0.188643	+	1.31204i	−0.0111742	+	0.0777185i
$286$	−1.40482	−	3.07613i	−0.0830687	−	0.181895i
$287$	0.263962	+	0.0775063i	0.0155812	+	0.00457505i
$288$	0.959493	+	0.281733i	0.0565387	+	0.0166013i
$289$	−4.04241	−	8.85164i	−0.237789	−	0.520685i
$290$	−0.142184	+	0.988911i	−0.00834933	+	0.0580709i
$291$	−0.146864	+	0.169490i	−0.00860932	+	0.00993569i
$292$	4.88629	−	10.6995i	0.285949	−	0.626140i
$293$	−5.54585	−	3.56410i	−0.323992	−	0.208217i	0.368526	−	0.929617i	$-0.379862\pi$
$293$	−5.54585	−	3.56410i	−0.323992	−	0.208217i	−0.692518	+	0.721400i	$0.743499\pi$
$294$	0.981206	+	6.82444i	0.0572251	+	0.398009i
$295$	4.19367	−	2.69511i	0.244165	−	0.156915i
$296$	0.314643	+	0.363118i	0.0182883	+	0.0211058i
$297$	2.38745	−	0.701020i	0.138534	−	0.0406773i
$298$	−3.17993			−0.184208
$299$	0.0245549	−	6.51787i	0.00142005	−	0.376938i
$300$	4.79020			0.276562
$301$	−2.74341	+	0.805537i	−0.158127	+	0.0464304i
$302$	−0.834763	−	0.963368i	−0.0480352	−	0.0554356i
$303$	−8.99776	+	5.78251i	−0.516908	+	0.332196i
$304$	0.411844	+	2.86444i	0.0236209	+	0.164287i
$305$	−4.64804	−	2.98711i	−0.266146	−	0.171041i
$306$	1.12000	−	2.45246i	0.0640263	−	0.140198i
$307$	−14.6003	+	16.8497i	−0.833285	+	0.961662i	−0.999702	−	0.0243932i	$-0.992235\pi$
$307$	−14.6003	+	16.8497i	−0.833285	+	0.961662i	0.166417	+	0.986055i	$0.446780\pi$
$308$	0.114958	−	0.799549i	0.00655033	−	0.0455585i
$309$	−0.841985	−	1.84369i	−0.0478989	−	0.104884i
$310$	1.08245	+	0.317837i	0.0614792	+	0.0180519i
$311$	12.3837	+	3.63618i	0.702214	+	0.206189i	0.613299	−	0.789851i	$-0.289842\pi$
$311$	12.3837	+	3.63618i	0.702214	+	0.206189i	0.0889146	+	0.996039i	$0.471660\pi$
$312$	0.564582	+	1.23626i	0.0319632	+	0.0699896i
$313$	2.73568	−	19.0271i	0.154630	−	1.07547i	−0.753700	−	0.657219i	$-0.771733\pi$
$313$	2.73568	−	19.0271i	0.154630	−	1.07547i	0.908330	−	0.418255i	$-0.137358\pi$
$314$	−11.3525	+	13.1014i	−0.640657	+	0.739357i
$315$	−0.0617710	+	0.135260i	−0.00348040	+	0.00762102i
$316$	−9.02455	−	5.79973i	−0.507671	−	0.326260i
$317$	1.52863	+	10.6319i	0.0858564	+	0.597144i	0.986645	+	0.162886i	$0.0520803\pi$
$317$	1.52863	+	10.6319i	0.0858564	+	0.597144i	−0.900788	+	0.434258i	$0.857011\pi$
$318$	7.34089	−	4.71770i	0.411656	−	0.264556i
$319$	3.55414	+	4.10170i	0.198994	+	0.229651i
$320$	−0.439490	+	0.129046i	−0.0245683	+	0.00721389i
$321$	−2.16835			−0.121025
$322$	0.846649	−	1.30656i	0.0471819	−	0.0728119i
$323$	7.80224			0.434128
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	4.26331	+	4.92013i	0.236486	+	0.272920i
$326$	4.43545	−	2.85049i	0.245657	−	0.157874i
$327$	−1.19813	−	8.33318i	−0.0662568	−	0.460826i
$328$	−0.712905	−	0.458156i	−0.0393636	−	0.0252975i
$329$	0.366013	−	0.801456i	0.0201789	−	0.0441857i
$330$	−0.746362	+	0.861348i	−0.0410859	+	0.0474157i
$331$	2.49561	−	17.3573i	0.137171	−	0.954045i	−0.798707	−	0.601720i	$-0.794482\pi$
$331$	2.49561	−	17.3573i	0.137171	−	0.954045i	0.935878	−	0.352324i	$-0.114609\pi$
$332$	3.35797	+	7.35294i	0.184293	+	0.403545i
$333$	−0.461011	−	0.135365i	−0.0252633	−	0.00741796i
$334$	−2.83814	−	0.833354i	−0.155296	−	0.0455991i
$335$	2.01044	+	4.40226i	0.109842	+	0.240521i
$336$	−0.0462003	+	0.321330i	−0.00252044	+	0.0175300i
$337$	8.65628	−	9.98988i	0.471538	−	0.544184i	−0.469301	−	0.883038i	$-0.655494\pi$
$337$	8.65628	−	9.98988i	0.471538	−	0.544184i	0.940839	+	0.338855i	$0.110040\pi$
$338$	4.63308	−	10.1450i	0.252006	−	0.551817i
$339$	−0.163109	−	0.104824i	−0.00885884	−	0.00569323i
$340$	0.175750	+	1.22237i	0.00953137	+	0.0662921i
$341$	5.15561	−	3.31331i	0.279192	−	0.179426i
$342$	−1.89510	−	2.18706i	−0.102475	−	0.118263i
$343$	−4.32796	+	1.27080i	−0.233688	+	0.0686170i
$344$	8.80752			0.474869
$345$	−2.00162	+	0.905010i	−0.107763	+	0.0487241i
$346$	−4.13279			−0.222180
$347$	15.3250	−	4.49983i	0.822690	−	0.241564i	0.156816	−	0.987628i	$-0.449877\pi$
$347$	15.3250	−	4.49983i	0.822690	−	0.241564i	0.665874	+	0.746064i	$0.268059\pi$
$348$	−1.42837	−	1.64843i	−0.0765688	−	0.0883652i
$349$	2.41073	−	1.54928i	0.129043	−	0.0829311i	−0.474527	−	0.880241i	$-0.657381\pi$
$349$	2.41073	−	1.54928i	0.129043	−	0.0829311i	0.603570	+	0.797310i	$0.293744\pi$
$350$	0.221309	+	1.53924i	0.0118294	+	0.0822756i
$351$	−1.14333	−	0.734774i	−0.0610265	−	0.0392194i
$352$	−1.03365	+	2.26339i	−0.0550940	+	0.120639i
$353$	−5.27311	+	6.08549i	−0.280659	+	0.323898i	−0.878523	−	0.477700i	$-0.841471\pi$
$353$	−5.27311	+	6.08549i	−0.280659	+	0.323898i	0.597864	+	0.801597i	$0.296016\pi$
$354$	−1.54885	+	10.7725i	−0.0823206	+	0.572552i
$355$	−3.12186	−	6.83592i	−0.165691	−	0.362813i
$356$	9.88113	+	2.90136i	0.523699	+	0.153772i
$357$	0.839796	+	0.246586i	0.0444467	+	0.0130507i
$358$	−4.21107	−	9.22096i	−0.222562	−	0.487343i
$359$	−1.11880	+	7.78141i	−0.0590479	+	0.410687i	0.938763	+	0.344562i	$0.111973\pi$
$359$	−1.11880	+	7.78141i	−0.0590479	+	0.410687i	−0.997811	+	0.0661249i	$0.978936\pi$
$360$	0.299955	−	0.346167i	0.0158090	−	0.0182446i
$361$	−4.41394	+	9.66518i	−0.232313	+	0.508694i
$362$	22.4093	+	14.4016i	1.17781	+	0.756930i
$363$	−0.684340	−	4.75969i	−0.0359185	−	0.249819i
$364$	−0.371165	+	0.238533i	−0.0194543	+	0.0125025i
$365$	−3.52821	−	4.07177i	−0.184675	−	0.213126i
$366$	11.5738	−	3.39838i	0.604973	−	0.177636i
$367$	13.9011			0.725631			0.362816	−	0.931861i	$-0.381816\pi$
$367$	13.9011			0.725631			0.362816	+	0.931861i	$0.381816\pi$
$368$	−3.63625	+	3.12693i	−0.189553	+	0.163002i
$369$	0.847432			0.0441156
$370$	0.211164	−	0.0620032i	0.0109779	−	0.00322339i
$371$	1.85509	+	2.14089i	0.0963116	+	0.111150i
$372$	−2.07199	+	1.33158i	−0.107427	+	0.0690394i
$373$	1.37506	+	9.56372i	0.0711977	+	0.495191i	0.993953	+	0.109805i	$0.0350226\pi$
$373$	1.37506	+	9.56372i	0.0711977	+	0.495191i	−0.922755	+	0.385386i	$0.874068\pi$
$374$	5.64361	+	3.62693i	0.291824	+	0.187544i
$375$	1.86286	−	4.07910i	0.0961979	−	0.210644i
$376$	−1.77733	+	2.05115i	−0.0916587	+	0.105780i
$377$	0.421879	−	2.93423i	0.0217279	−	0.151121i
$378$	−0.134858	−	0.295298i	−0.00693636	−	0.0151885i
$379$	19.1257	+	5.61580i	0.982419	+	0.288464i	0.733223	−	0.679989i	$-0.238015\pi$
$379$	19.1257	+	5.61580i	0.982419	+	0.288464i	0.249197	+	0.968453i	$0.419833\pi$
$380$	1.27184	+	0.373446i	0.0652440	+	0.0191574i
$381$	−5.37101	−	11.7609i	−0.275165	−	0.602527i
$382$	3.32908	−	23.1543i	0.170331	−	1.18467i
$383$	−18.3187	+	21.1409i	−0.936043	+	1.08025i	0.0605823	+	0.998163i	$0.480704\pi$
$383$	−18.3187	+	21.1409i	−0.936043	+	1.08025i	−0.996625	+	0.0820878i	$0.973841\pi$
$384$	0.415415	−	0.909632i	0.0211991	−	0.0464195i
$385$	−0.311260	−	0.200034i	−0.0158633	−	0.0101947i
$386$	0.856252	+	5.95536i	0.0435821	+	0.303120i
$387$	−7.40935	+	4.76170i	−0.376639	+	0.242051i
$388$	0.146864	+	0.169490i	0.00745589	+	0.00860456i
$389$	25.4067	−	7.46007i	1.28817	−	0.378240i	0.435262	−	0.900304i	$-0.356656\pi$
$389$	25.4067	−	7.46007i	1.28817	−	0.378240i	0.852907	+	0.522064i	$0.174838\pi$
$390$	0.622519			0.0315225
$391$	6.94949	+	10.9037i	0.351451	+	0.551425i
$392$	6.89461			0.348231
$393$	−5.65361	+	1.66005i	−0.285187	+	0.0837385i
$394$	10.1267	+	11.6869i	0.510178	+	0.588777i
$395$	−4.13365	+	2.65653i	−0.207986	+	0.133665i
$396$	−0.354114	−	2.46292i	−0.0177949	−	0.123766i
$397$	−13.8368	−	8.89236i	−0.694448	−	0.446295i	0.145216	−	0.989400i	$-0.453612\pi$
$397$	−13.8368	−	8.89236i	−0.694448	−	0.446295i	−0.839665	+	0.543105i	$0.817248\pi$
$398$	4.86493	−	10.6527i	0.243857	−	0.533972i
$399$	0.615215	−	0.709996i	0.0307993	−	0.0355442i
$400$	0.681716	−	4.74144i	0.0340858	−	0.237072i
$401$	8.40890	+	18.4129i	0.419920	+	0.919497i	0.994856	+	0.101298i	$0.0322997\pi$
$401$	8.40890	+	18.4129i	0.419920	+	0.919497i	−0.574936	+	0.818198i	$0.694973\pi$
$402$	−10.1378	−	2.97673i	−0.505627	−	0.148466i
$403$	−3.21179	−	0.943066i	−0.159991	−	0.0469775i
$404$	4.44314	+	9.72911i	0.221054	+	0.484041i
$405$	−0.0651865	+	0.453382i	−0.00323914	+	0.0225287i
$406$	0.463700	−	0.535138i	0.0230130	−	0.0265584i
$407$	0.496644	−	1.08750i	0.0246177	−	0.0539053i
$408$	−2.26811	−	1.45762i	−0.112288	−	0.0721632i
$409$	−2.48089	−	17.2550i	−0.122672	−	0.853204i	−0.954509	−	0.298183i	$-0.903619\pi$
$409$	−2.48089	−	17.2550i	−0.122672	−	0.853204i	0.831836	−	0.555021i	$-0.187290\pi$
$410$	−0.326542	+	0.209856i	−0.0161268	+	0.0103641i
$411$	−10.6165	−	12.2521i	−0.523675	−	0.604354i
$412$	−1.94475	+	0.571031i	−0.0958110	+	0.0281327i
$413$	−3.53309			−0.173852
$414$	1.36847	−	4.59644i	0.0672565	−	0.225903i
$415$	3.70257			0.181752
$416$	1.30403	−	0.382897i	0.0639352	−	0.0187731i
$417$	−12.8568	−	14.8375i	−0.629599	−	0.726596i
$418$	6.05763	−	3.89300i	0.296288	−	0.190413i
$419$	2.34268	+	16.2937i	0.114447	+	0.795998i	0.963503	+	0.267696i	$0.0862622\pi$
$419$	2.34268	+	16.2937i	0.114447	+	0.795998i	−0.849056	+	0.528303i	$0.822829\pi$
$420$	0.125092	+	0.0803918i	0.00610387	+	0.00392272i
$421$	−12.8684	+	28.1779i	−0.627169	+	1.37331i	0.283020	+	0.959114i	$0.408664\pi$
$421$	−12.8684	+	28.1779i	−0.627169	+	1.37331i	−0.910189	+	0.414194i	$0.864064\pi$
$422$	6.99065	−	8.06764i	0.340299	−	0.392726i
$423$	0.386250	−	2.68643i	0.0187801	−	0.130619i
$424$	−3.62496	−	7.93756i	−0.176044	−	0.385482i
$425$	−12.3917	−	3.63854i	−0.601087	−	0.176495i
$426$	15.7422	+	4.62233i	0.762712	+	0.223953i
$427$	1.62672	+	3.56202i	0.0787224	+	0.172378i
$428$	−0.308588	+	2.14627i	−0.0149162	+	0.103744i
$429$	2.21456	−	2.55574i	0.106920	−	0.123392i
$430$	1.67588	−	3.66967i	0.0808182	−	0.176967i
$431$	−15.4083	−	9.90232i	−0.742192	−	0.476978i	0.114100	−	0.993469i	$-0.463601\pi$
$431$	−15.4083	−	9.90232i	−0.742192	−	0.476978i	−0.856292	+	0.516491i	$0.827238\pi$
$432$	0.142315	+	0.989821i	0.00684713	+	0.0476228i
$433$	12.7448	−	8.19061i	0.612478	−	0.393616i	−0.197308	−	0.980342i	$-0.563220\pi$
$433$	12.7448	−	8.19061i	0.612478	−	0.393616i	0.809785	+	0.586726i	$0.199583\pi$
$434$	−0.523605	−	0.604273i	−0.0251339	−	0.0290060i
$435$	−0.958610	+	0.281473i	−0.0459619	+	0.0134956i
$436$	−8.41887			−0.403191
$437$	13.7447	−	1.92337i	0.657499	−	0.0920072i
$438$	11.7624			0.562031
$439$	−5.59553	+	1.64300i	−0.267060	+	0.0784159i	−0.412521	−	0.910948i	$-0.635352\pi$
$439$	−5.59553	+	1.64300i	−0.267060	+	0.0784159i	0.145461	+	0.989364i	$0.453533\pi$
$440$	0.746362	+	0.861348i	0.0355814	+	0.0410632i
$441$	−5.80012	+	3.72751i	−0.276196	+	0.177500i
$442$	−0.521474	−	3.62693i	−0.0248040	−	0.172515i
$443$	−14.5928	−	9.37820i	−0.693323	−	0.445572i	0.145943	−	0.989293i	$-0.453378\pi$
$443$	−14.5928	−	9.37820i	−0.693323	−	0.445572i	−0.839266	+	0.543721i	$0.817015\pi$
$444$	−0.199596	+	0.437054i	−0.00947241	+	0.0207417i
$445$	3.08902	−	3.56492i	0.146434	−	0.168994i
$446$	1.07757	−	7.49464i	0.0510242	−	0.354881i
$447$	−1.32099	−	2.89256i	−0.0624807	−	0.136814i
$448$	0.311485	+	0.0914602i	0.0147163	+	0.00432109i
$449$	17.7555	+	5.21348i	0.837932	+	0.246039i	0.672421	−	0.740169i	$-0.265254\pi$
$449$	17.7555	+	5.21348i	0.837932	+	0.246039i	0.165511	+	0.986208i	$0.447073\pi$
$450$	1.98992	+	4.35731i	0.0938057	+	0.205406i
$451$	−0.300088	+	2.08716i	−0.0141306	+	0.0982804i
$452$	−0.126969	+	0.146530i	−0.00597214	+	0.00689221i
$453$	0.529537	−	1.15953i	0.0248798	−	0.0544792i
$454$	10.6374	+	6.83622i	0.499236	+	0.320840i
$455$	0.0287606	+	0.200034i	0.00134832	+	0.00937776i
$456$	−2.43450	+	1.56456i	−0.114006	+	0.0732671i
$457$	3.77320	+	4.35450i	0.176503	+	0.203695i	0.837107	−	0.547039i	$-0.184245\pi$
$457$	3.77320	+	4.35450i	0.176503	+	0.203695i	−0.660604	+	0.750734i	$0.729700\pi$
$458$	−8.05474	+	2.36508i	−0.376373	+	0.110513i
$459$	2.69611			0.125843
$460$	0.610938	+	2.11004i	0.0284851	+	0.0983811i
$461$	22.5329			1.04946			0.524730	−	0.851269i	$-0.324166\pi$
$461$	22.5329			1.04946			0.524730	+	0.851269i	$0.324166\pi$
$462$	0.775051	−	0.227575i	0.0360586	−	0.0105878i
$463$	19.6456	+	22.6722i	0.913009	+	1.05367i	0.998356	+	0.0573171i	$0.0182546\pi$
$463$	19.6456	+	22.6722i	0.913009	+	1.05367i	−0.0853472	+	0.996351i	$0.527200\pi$
$464$	−1.83493	+	1.17924i	−0.0851845	+	0.0547448i
$465$	0.160553	+	1.11667i	0.00744545	+	0.0517843i
$466$	−22.1095	−	14.2089i	−1.02420	−	0.658215i
$467$	−4.83680	+	10.5911i	−0.223821	+	0.490099i	−0.987913	−	0.155008i	$-0.950460\pi$
$467$	−4.83680	+	10.5911i	−0.223821	+	0.490099i	0.764093	+	0.645107i	$0.223187\pi$
$468$	−0.890008	+	1.02712i	−0.0411407	+	0.0474788i
$469$	0.488143	−	3.39511i	0.0225404	−	0.156772i
$470$	0.516427	+	1.13082i	0.0238210	+	0.0521607i
$471$	−16.6335	−	4.88403i	−0.766430	−	0.225044i
$472$	10.4424	+	3.06617i	0.480652	+	0.141132i
$473$	−9.10393	−	19.9348i	−0.418599	−	0.916604i
$474$	1.52668	−	10.6183i	0.0701229	−	0.487715i
$475$	−9.07789	+	10.4764i	−0.416522	+	0.480692i
$476$	0.363592	−	0.796155i	0.0166652	−	0.0364917i
$477$	7.34089	+	4.71770i	0.336116	+	0.216009i
$478$	1.11770	+	7.77380i	0.0511226	+	0.355565i
$479$	11.2218	−	7.21182i	0.512738	−	0.329517i	−0.258556	−	0.965996i	$-0.583246\pi$
$479$	11.2218	−	7.21182i	0.512738	−	0.329517i	0.771293	+	0.636480i	$0.219610\pi$
$480$	−0.299955	−	0.346167i	−0.0136910	−	0.0158003i
$481$	−0.626551	+	0.183972i	−0.0285683	+	0.00838841i
$482$	26.5043			1.20724
$483$	1.54020	+	0.227373i	0.0700816	+	0.0103458i
$484$	−4.80864			−0.218574
$485$	0.0985635	−	0.0289408i	0.00447554	−	0.00131414i
$486$	−0.654861	−	0.755750i	−0.0297051	−	0.0342815i
$487$	−11.3740	+	7.30962i	−0.515405	+	0.331231i	−0.772352	−	0.635195i	$-0.780920\pi$
$487$	−11.3740	+	7.30962i	−0.515405	+	0.331231i	0.256947	+	0.966425i	$0.417283\pi$
$488$	−1.71666	−	11.9397i	−0.0777097	−	0.540483i
$489$	4.43545	+	2.85049i	0.200578	+	0.128904i
$490$	1.31190	−	2.87265i	0.0592655	−	0.129773i
$491$	−26.8145	+	30.9455i	−1.21012	+	1.39655i	−0.315979	+	0.948766i	$0.602333\pi$
$491$	−26.8145	+	30.9455i	−1.21012	+	1.39655i	−0.894140	+	0.447787i	$0.852212\pi$
$492$	0.120602	−	0.838807i	0.00543717	−	0.0378163i
$493$	2.44293	+	5.34928i	0.110024	+	0.240919i
$494$	−3.77372	−	1.10806i	−0.169788	−	0.0498542i
$495$	−1.09356	−	0.321098i	−0.0491519	−	0.0144323i
$496$	1.02316	+	2.24040i	0.0459411	+	0.100597i
$497$	−0.758000	+	5.27200i	−0.0340009	+	0.236482i
$498$	−5.29352	+	6.10904i	−0.237208	+	0.273753i
$499$	8.88711	−	19.4601i	0.397842	−	0.871152i	−0.599643	−	0.800268i	$-0.704691\pi$
$499$	8.88711	−	19.4601i	0.397842	−	0.871152i	0.997485	−	0.0708840i	$-0.0225820\pi$
$500$	−3.77247	−	2.42442i	−0.168710	−	0.108423i
$501$	−0.420962	−	2.92785i	−0.0188072	−	0.130807i
$502$	15.1874	−	9.76036i	0.677847	−	0.435626i
$503$	−14.2265	−	16.4183i	−0.634330	−	0.732055i	0.344032	−	0.938958i	$-0.388207\pi$
$503$	−14.2265	−	16.4183i	−0.634330	−	0.732055i	−0.978362	+	0.206903i	$0.933662\pi$
$504$	−0.311485	+	0.0914602i	−0.0138746	+	0.00407396i
$505$	4.89909			0.218006
$506$	10.8361	+	4.99809i	0.481722	+	0.222192i
$507$	11.1529			0.495318
$508$	−12.4055	+	3.64259i	−0.550406	+	0.161614i
$509$	−20.5288	−	23.6915i	−0.909924	−	1.05011i	−0.998539	−	0.0540428i	$-0.982789\pi$
$509$	−20.5288	−	23.6915i	−0.909924	−	1.05011i	0.0886141	−	0.996066i	$-0.471756\pi$
$510$	−1.03889	+	0.667657i	−0.0460030	+	0.0295643i
$511$	0.543429	+	3.77963i	0.0240399	+	0.167201i
$512$	−0.841254	−	0.540641i	−0.0371785	−	0.0238932i
$513$	1.20217	−	2.63238i	0.0530770	−	0.116222i
$514$	−14.9674	+	17.2732i	−0.660182	+	0.761890i
$515$	−0.132124	+	0.918939i	−0.00582206	+	0.0404933i
$516$	3.65877	+	8.01160i	0.161069	+	0.352691i
$517$	6.47968	+	1.90261i	0.284976	+	0.0836765i
$518$	−0.149660	−	0.0439442i	−0.00657570	−	0.00193080i
$519$	−1.71682	−	3.75932i	−0.0753602	−	0.165016i
$520$	0.0885937	−	0.616183i	0.00388509	−	0.0270214i
$521$	5.97938	−	6.90057i	0.261961	−	0.302319i	−0.609498	−	0.792788i	$-0.708629\pi$
$521$	5.97938	−	6.90057i	0.261961	−	0.302319i	0.871459	+	0.490468i	$0.163174\pi$
$522$	0.906098	−	1.98408i	0.0396588	−	0.0868407i
$523$	14.5013	+	9.31942i	0.634098	+	0.407510i	0.817825	−	0.575468i	$-0.195180\pi$
$523$	14.5013	+	9.31942i	0.634098	+	0.407510i	−0.183727	+	0.982977i	$0.558816\pi$
$524$	0.838560	+	5.83232i	0.0366327	+	0.254786i
$525$	−1.30820	+	0.840731i	−0.0570947	+	0.0366925i
$526$	−12.1932	−	14.0717i	−0.531647	−	0.613553i
$527$	6.37145	−	1.87083i	0.277545	−	0.0814945i
$528$	−2.48825			−0.108287
$529$	14.9304	+	17.4952i	0.649148	+	0.760662i
$530$	−3.99695			−0.173617
$531$	−10.4424	+	3.06617i	−0.453163	+	0.133061i
$532$	−0.615215	−	0.709996i	−0.0266729	−	0.0307822i
$533$	0.968896	−	0.622672i	0.0419675	−	0.0269709i
$534$	1.46560	+	10.1935i	0.0634227	+	0.441114i
$535$	0.835532	+	0.536964i	0.0361232	+	0.0232150i
$536$	−4.38919	+	9.61098i	−0.189584	+	0.415131i
$537$	6.63834	−	7.66105i	0.286465	−	0.330599i
$538$	0.112249	−	0.780708i	0.00483939	−	0.0336587i
$539$	−7.12665	−	15.6052i	−0.306966	−	0.672163i
$540$	0.439490	+	0.129046i	0.0189127	+	0.00555326i
$541$	−41.0532	−	12.0543i	−1.76501	−	0.518255i	−0.771935	−	0.635701i	$-0.780711\pi$
$541$	−41.0532	−	12.0543i	−1.76501	−	0.518255i	−0.993079	+	0.117446i	$0.962529\pi$
$542$	−12.1801	−	26.6706i	−0.523179	−	1.14560i
$543$	−3.79098	+	26.3668i	−0.162686	+	1.13151i
$544$	−1.76557	+	2.03758i	−0.0756984	+	0.0873606i
$545$	−1.60193	+	3.50774i	−0.0686192	+	0.150255i
$546$	−0.371165	−	0.238533i	−0.0158844	−	0.0102083i
$547$	−2.55493	−	17.7699i	−0.109241	−	0.759786i	−0.968638	−	0.248477i	$-0.920070\pi$
$547$	−2.55493	−	17.7699i	−0.109241	−	0.759786i	0.859397	−	0.511309i	$-0.170839\pi$
$548$	−13.6383	+	8.76482i	−0.582600	+	0.374414i
$549$	7.89921	+	9.11618i	0.337130	+	0.389069i
$550$	−11.4364	+	3.35802i	−0.487648	+	0.143187i
$551$	6.31212			0.268905
$552$	−4.35491	−	2.00868i	−0.185357	−	0.0854951i
$553$	3.48252			0.148092
$554$	−24.4053	+	7.16603i	−1.03688	+	0.304455i
$555$	0.144121	+	0.166324i	0.00611758	+	0.00706007i
$556$	−16.5162	+	10.6143i	−0.700443	+	0.450147i
$557$	−2.00861	−	13.9702i	−0.0851075	−	0.591936i	−0.987090	−	0.160164i	$-0.948798\pi$
$557$	−2.00861	−	13.9702i	−0.0851075	−	0.591936i	0.901983	−	0.431772i	$-0.142111\pi$
$558$	−2.07199	−	1.33158i	−0.0877142	−	0.0563705i
$559$	−4.97257	+	10.8884i	−0.210317	+	0.460531i
$560$	0.0973759	−	0.112378i	0.00411488	−	0.00474883i
$561$	−0.954729	+	6.64029i	−0.0403087	+	0.280353i
$562$	9.79634	+	21.4510i	0.413234	+	0.904855i
$563$	−21.3328	−	6.26389i	−0.899072	−	0.263991i	−0.200638	−	0.979665i	$-0.564301\pi$
$563$	−21.3328	−	6.26389i	−0.899072	−	0.263991i	−0.698434	+	0.715674i	$0.746120\pi$
$564$	−2.60412	−	0.764638i	−0.109653	−	0.0321971i
$565$	0.0368926	+	0.0807836i	0.00155209	+	0.00339859i
$566$	−3.78987	+	26.3591i	−0.159300	+	1.10796i
$567$	0.212591	−	0.245343i	0.00892797	−	0.0103034i
$568$	6.81563	−	14.9241i	0.285977	−	0.626203i
$569$	−11.0733	−	7.11640i	−0.464218	−	0.298335i	0.287546	−	0.957767i	$-0.407161\pi$
$569$	−11.0733	−	7.11640i	−0.464218	−	0.298335i	−0.751764	+	0.659432i	$0.770797\pi$
$570$	0.188643	+	1.31204i	0.00790138	+	0.0549553i
$571$	17.6085	−	11.3163i	0.736893	−	0.473573i	−0.117583	−	0.993063i	$-0.537515\pi$
$571$	17.6085	−	11.3163i	0.736893	−	0.473573i	0.854476	+	0.519490i	$0.173878\pi$
$572$	−2.21456	−	2.55574i	−0.0925954	−	0.106861i
$573$	22.4448	−	6.59039i	0.937645	−	0.275317i
$574$	0.275106			0.0114827
$575$	−22.7267	−	3.35504i	−0.947767	−	0.139915i
$576$	1.00000			0.0416667
$577$	0.990929	−	0.290963i	0.0412529	−	0.0121129i	−0.261041	−	0.965328i	$-0.584066\pi$
$577$	0.990929	−	0.290963i	0.0412529	−	0.0121129i	0.302294	+	0.953215i	$0.402248\pi$
$578$	−6.37246	−	7.35421i	−0.265059	−	0.305895i
$579$	−5.06149	+	3.25282i	−0.210348	+	0.135183i
$580$	0.142184	+	0.988911i	0.00590387	+	0.0410623i
$581$	−2.20758	−	1.41873i	−0.0915860	−	0.0588588i
$582$	−0.0931641	+	0.204001i	−0.00386178	+	0.00845611i
$583$	−14.2188	+	16.4094i	−0.588884	+	0.679608i
$584$	1.67397	−	11.6427i	0.0692694	−	0.481779i
$585$	0.258604	+	0.566263i	0.0106920	+	0.0234121i
$586$	−6.32533	−	1.85728i	−0.261297	−	0.0767237i
$587$	4.49531	+	1.31994i	0.185541	+	0.0544798i	0.373183	−	0.927758i	$-0.378266\pi$
$587$	4.49531	+	1.31994i	0.185541	+	0.0544798i	−0.187642	+	0.982237i	$0.560084\pi$
$588$	2.86413	+	6.27156i	0.118115	+	0.258635i
$589$	1.01436	−	7.05504i	0.0417960	−	0.290698i
$590$	3.26450	−	3.76743i	0.134397	−	0.155103i
$591$	−6.42396	+	14.0665i	−0.264246	+	0.578619i
$592$	0.404200	+	0.259764i	0.0166125	+	0.0106762i
$593$	4.46279	+	31.0394i	0.183265	+	1.27463i	0.848979	+	0.528427i	$0.177218\pi$
$593$	4.46279	+	31.0394i	0.183265	+	1.27463i	−0.665714	+	0.746207i	$0.731873\pi$
$594$	2.09325	−	1.34525i	0.0858869	−	0.0551962i
$595$	−0.262536	−	0.302982i	−0.0107629	−	0.0124211i
$596$	−3.05112	+	0.895889i	−0.124979	+	0.0366970i
$597$	11.7110			0.479300
$598$	−1.81274	−	6.26077i	−0.0741283	−	0.256022i
$599$	27.2585			1.11375			0.556875	−	0.830596i	$-0.312000\pi$
$599$	27.2585			1.11375			0.556875	+	0.830596i	$0.312000\pi$
$600$	4.59616	−	1.34955i	0.187637	−	0.0550953i
$601$	−11.3031	−	13.0444i	−0.461062	−	0.532094i	0.476842	−	0.878989i	$-0.341781\pi$
$601$	−11.3031	−	13.0444i	−0.461062	−	0.532094i	−0.937904	+	0.346895i	$0.887236\pi$
$602$	−2.40533	+	1.54581i	−0.0980341	+	0.0630027i
$603$	−1.50367	−	10.4582i	−0.0612341	−	0.425893i
$604$	−1.07236	−	0.689165i	−0.0436338	−	0.0280417i
$605$	−0.914980	+	2.00353i	−0.0371992	+	0.0814550i
$606$	−7.00416	+	8.08324i	−0.284525	+	0.328359i
$607$	6.49805	−	45.1949i	0.263748	−	1.83441i	−0.240263	−	0.970708i	$-0.577234\pi$
$607$	6.49805	−	45.1949i	0.263748	−	1.83441i	0.504011	−	0.863697i	$-0.331857\pi$
$608$	1.20217	+	2.63238i	0.0487543	+	0.106757i
$609$	0.679406	+	0.199492i	0.0275309	+	0.00808381i
$610$	−5.30132	−	1.55661i	−0.214644	−	0.0630253i
$611$	−1.53231	−	3.35529i	−0.0619906	−	0.135740i
$612$	0.383696	−	2.66866i	0.0155100	−	0.107874i
$613$	1.32116	−	1.52470i	0.0533611	−	0.0615820i	−0.728441	−	0.685108i	$-0.759755\pi$
$613$	1.32116	−	1.52470i	0.0533611	−	0.0615820i	0.781803	+	0.623526i	$0.214300\pi$
$614$	−9.26181	+	20.2805i	−0.373776	+	0.818456i
$615$	−0.326542	−	0.209856i	−0.0131675	−	0.00846221i
$616$	−0.114958	−	0.799549i	−0.00463178	−	0.0322148i
$617$	31.5453	−	20.2730i	1.26997	−	0.816159i	0.280352	−	0.959897i	$-0.409549\pi$
$617$	31.5453	−	20.2730i	1.26997	−	0.816159i	0.989616	+	0.143739i	$0.0459125\pi$
$618$	−1.32731	−	1.53179i	−0.0533921	−	0.0616178i
$619$	−25.2336	+	7.40924i	−1.01422	+	0.297803i	−0.746280	−	0.665632i	$-0.768162\pi$
$619$	−25.2336	+	7.40924i	−1.01422	+	0.297803i	−0.267943	+	0.963435i	$0.586344\pi$
$620$	1.12815			0.0453077
$621$	4.74955	−	0.664630i	0.190593	−	0.0266707i
$622$	12.9065			0.517503
$623$	−3.20776	+	0.941883i	−0.128516	+	0.0377357i
$624$	0.890008	+	1.02712i	0.0356289	+	0.0411179i
$625$	18.4209	−	11.8384i	0.736835	−	0.473535i
$626$	−2.73568	−	19.0271i	−0.109340	−	0.760474i
$627$	6.05763	+	3.89300i	0.241918	+	0.155472i
$628$	−7.20151	+	15.7691i	−0.287371	+	0.629256i
$629$	0.848312	−	0.979004i	0.0338244	−	0.0390355i
$630$	−0.0211618	+	0.147184i	−0.000843107	+	0.00586394i
$631$	8.49601	+	18.6037i	0.338221	+	0.740600i	0.999958	−	0.00913542i	$-0.00290794\pi$
$631$	8.49601	+	18.6037i	0.338221	+	0.740600i	−0.661737	+	0.749736i	$0.730181\pi$
$632$	−10.2930	−	3.02229i	−0.409432	−	0.120220i
$633$	10.2426	+	3.00750i	0.407107	+	0.119537i
$634$	4.46205	+	9.77052i	0.177211	+	0.388037i
$635$	−0.842813	+	5.86189i	−0.0334460	+	0.232622i
$636$	5.71440	−	6.59477i	0.226591	−	0.261500i
$637$	−3.89258	+	8.52355i	−0.154230	+	0.337716i
$638$	4.56576	+	2.93423i	0.180760	+	0.116167i
$639$	2.33493	+	16.2398i	0.0923684	+	0.642437i
$640$	−0.385331	+	0.247638i	−0.0152316	+	0.00978873i
$641$	−18.6345	−	21.5053i	−0.736018	−	0.849410i	0.257117	−	0.966380i	$-0.417227\pi$
$641$	−18.6345	−	21.5053i	−0.736018	−	0.849410i	−0.993135	+	0.116970i	$0.962682\pi$
$642$	−2.08051	+	0.610893i	−0.0821113	+	0.0241100i
$643$	35.1379			1.38570			0.692851	−	0.721080i	$-0.256354\pi$
$643$	35.1379			1.38570			0.692851	+	0.721080i	$0.256354\pi$
$644$	0.444252	−	1.49217i	0.0175060	−	0.0587996i
$645$	4.03423			0.158848
$646$	7.48620	−	2.19815i	0.294541	−	0.0864849i
$647$	8.02115	+	9.25690i	0.315344	+	0.363926i	0.891189	−	0.453633i	$-0.149872\pi$
$647$	8.02115	+	9.25690i	0.315344	+	0.363926i	−0.575845	+	0.817559i	$0.695327\pi$
$648$	−0.841254	+	0.540641i	−0.0330476	+	0.0212384i
$649$	−3.85392	−	26.8046i	−0.151280	−	1.05217i
$650$	5.47678	+	3.51971i	0.214817	+	0.138054i
$651$	0.332152	−	0.727312i	0.0130181	−	0.0285056i
$652$	3.45271	−	3.98464i	0.135219	−	0.156051i
$653$	3.40835	−	23.7056i	0.133379	−	0.927671i	−0.807726	−	0.589558i	$-0.799302\pi$
$653$	3.40835	−	23.7056i	0.133379	−	0.927671i	0.941105	−	0.338113i	$-0.109789\pi$
$654$	−3.49733	−	7.65808i	−0.136756	−	0.299454i
$655$	2.58961	+	0.760377i	0.101184	+	0.0297104i
$656$	−0.813105	−	0.238749i	−0.0317464	−	0.00932159i
$657$	4.88629	+	10.6995i	0.190633	+	0.417427i
$658$	0.125390	−	0.872109i	0.00488822	−	0.0339983i
$659$	6.13650	−	7.08190i	0.239044	−	0.275872i	−0.623533	−	0.781797i	$-0.714303\pi$
$659$	6.13650	−	7.08190i	0.239044	−	0.275872i	0.862577	+	0.505925i	$0.168849\pi$
$660$	−0.473460	+	1.03673i	−0.0184294	+	0.0403547i
$661$	17.3162	+	11.1284i	0.673520	+	0.432845i	0.832193	−	0.554486i	$-0.187085\pi$
$661$	17.3162	+	11.1284i	0.673520	+	0.432845i	−0.158673	+	0.987331i	$0.550721\pi$
$662$	−2.49561	−	17.3573i	−0.0969945	−	0.674611i
$663$	3.08254	−	1.98103i	0.119716	−	0.0769368i
$664$	5.29352	+	6.10904i	0.205428	+	0.237077i
$665$	−0.412883	+	0.121233i	−0.0160109	+	0.00470123i
$666$	−0.480474			−0.0186180
$667$	5.62224	+	8.82126i	0.217694	+	0.341561i
$668$	−2.95796			−0.114447
$669$	7.26500	−	2.13320i	0.280881	−	0.0824741i
$670$	3.16926	+	3.65753i	0.122439	+	0.141303i
$671$	−25.2496	+	16.2270i	−0.974751	+	0.626435i
$672$	0.0462003	+	0.321330i	0.00178222	+	0.0123956i
$673$	−4.24556	−	2.72845i	−0.163654	−	0.105174i	0.456250	−	0.889852i	$-0.349192\pi$
$673$	−4.24556	−	2.72845i	−0.163654	−	0.105174i	−0.619904	+	0.784677i	$0.712829\pi$
$674$	5.49117	−	12.0240i	0.211512	−	0.463146i
$675$	−3.13691	+	3.62019i	−0.120740	+	0.139341i
$676$	1.58722	−	11.0394i	0.0610470	−	0.424592i
$677$	14.9029	+	32.6328i	0.572765	+	1.25418i	0.945312	+	0.326168i	$0.105757\pi$
$677$	14.9029	+	32.6328i	0.572765	+	1.25418i	−0.372547	+	0.928013i	$0.621515\pi$
$678$	−0.186034	−	0.0546244i	−0.00714458	−	0.00209784i
$679$	−0.0698560	−	0.0205116i	−0.00268083	−	0.000787161i
$680$	0.513011	+	1.12334i	0.0196731	+	0.0430780i
$681$	−1.79952	+	12.5160i	−0.0689579	+	0.479613i
$682$	4.01330	−	4.63160i	0.153677	−	0.177353i
$683$	9.19582	−	20.1360i	0.351868	−	0.770484i	−0.648092	−	0.761562i	$-0.724433\pi$
$683$	9.19582	−	20.1360i	0.351868	−	0.770484i	0.999960	−	0.00892206i	$-0.00284002\pi$
$684$	−2.43450	−	1.56456i	−0.0930854	−	0.0598223i
$685$	1.05680	+	7.35019i	0.0403782	+	0.280836i
$686$	−3.79462	+	2.43865i	−0.144879	+	0.0931083i
$687$	−5.49742	−	6.34436i	−0.209739	−	0.242052i
$688$	8.45075	−	2.48136i	0.322182	−	0.0946011i
$689$	11.8595			0.451811
$690$	−1.66557	+	1.43227i	−0.0634070	+	0.0545256i
$691$	19.2304			0.731560			0.365780	−	0.930701i	$-0.380802\pi$
$691$	19.2304			0.731560			0.365780	+	0.930701i	$0.380802\pi$
$692$	−3.96538	+	1.16434i	−0.150741	+	0.0442616i
$693$	0.528978	+	0.610473i	0.0200942	+	0.0231899i
$694$	13.4365	−	8.63512i	0.510043	−	0.327784i
$695$	1.27980	+	8.90118i	0.0485455	+	0.337641i
$696$	−1.83493	−	1.17924i	−0.0695529	−	0.0446989i
$697$	−0.949126	+	2.07830i	−0.0359507	+	0.0787211i
$698$	1.87659	−	2.16570i	0.0710301	−	0.0819731i
$699$	3.74026	−	26.0141i	0.141470	−	0.983944i
$700$	0.645997	+	1.41454i	0.0244164	+	0.0534644i
$701$	22.7658	+	6.68465i	0.859853	+	0.252476i	0.681794	−	0.731544i	$-0.261200\pi$
$701$	22.7658	+	6.68465i	0.859853	+	0.252476i	0.178059	+	0.984020i	$0.443018\pi$
$702$	−1.30403	−	0.382897i	−0.0492174	−	0.0144515i
$703$	−0.577610	−	1.26479i	−0.0217850	−	0.0477024i
$704$	−0.354114	+	2.46292i	−0.0133462	+	0.0928247i
$705$	−0.814095	+	0.939516i	−0.0306606	+	0.0353842i
$706$	−3.34503	+	7.32459i	−0.125892	+	0.275665i
$707$	−2.92099	−	1.87720i	−0.109855	−	0.0705995i
$708$	1.54885	+	10.7725i	0.0582094	+	0.404856i
$709$	−17.6711	+	11.3565i	−0.663653	+	0.426504i	−0.828632	−	0.559793i	$-0.810881\pi$
$709$	−17.6711	+	11.3565i	−0.663653	+	0.426504i	0.164980	+	0.986297i	$0.447244\pi$
$710$	−4.92131	−	5.67949i	−0.184693	−	0.213147i
$711$	10.2930	−	3.02229i	0.386016	−	0.113345i
$712$	10.2983			0.385945
$713$	10.7630	−	4.86637i	0.403077	−	0.182247i
$714$	0.875250			0.0327554
$715$	−1.48624	+	0.436398i	−0.0555821	+	0.0163204i
$716$	−6.63834	−	7.66105i	−0.248086	−	0.286307i
$717$	−6.60699	+	4.24605i	−0.246743	+	0.158572i
$718$	1.11880	+	7.78141i	0.0417532	+	0.290400i
$719$	10.3821	+	6.67218i	0.387187	+	0.248830i	0.719724	−	0.694260i	$-0.244268\pi$
$719$	10.3821	+	6.67218i	0.387187	+	0.248830i	−0.332537	+	0.943090i	$0.607905\pi$
$720$	0.190279	−	0.416652i	0.00709126	−	0.0155277i
$721$	0.430890	−	0.497274i	0.0160472	−	0.0185194i
$722$	−1.51215	+	10.5172i	−0.0562763	+	0.391411i
$723$	11.0103	+	24.1091i	0.409476	+	0.896628i
$724$	25.5589	+	7.50478i	0.949891	+	0.278913i
$725$	−10.0251	−	2.94363i	−0.372322	−	0.109324i
$726$	−1.99758	−	4.37409i	−0.0741371	−	0.162338i
$727$	−1.68354	+	11.7093i	−0.0624390	+	0.434273i	0.934492	+	0.355985i	$0.115855\pi$
$727$	−1.68354	+	11.7093i	−0.0624390	+	0.434273i	−0.996931	+	0.0782882i	$0.975055\pi$
$728$	−0.288928	+	0.333440i	−0.0107084	+	0.0123581i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−4.53244	−	2.91282i	−0.167753	−	0.107808i
$731$	−3.37941	−	23.5043i	−0.124992	−	0.869338i
$732$	10.1476	−	6.52144i	0.375065	−	0.241040i
$733$	−29.9830	−	34.6022i	−1.10745	−	1.27806i	−0.957204	−	0.289413i	$-0.906540\pi$
$733$	−29.9830	−	34.6022i	−1.10745	−	1.27806i	−0.150242	−	0.988649i	$-0.548005\pi$
$734$	13.3380	−	3.91639i	0.492315	−	0.144557i
$735$	3.15804			0.116486
$736$	−2.60800	+	4.02471i	−0.0961323	+	0.148353i
$737$	26.2903			0.968415
$738$	0.813105	−	0.238749i	0.0299308	−	0.00878848i
$739$	5.80020	+	6.69379i	0.213364	+	0.246235i	0.852336	−	0.522995i	$-0.175185\pi$
$739$	5.80020	+	6.69379i	0.213364	+	0.246235i	−0.638972	+	0.769230i	$0.720640\pi$
$740$	0.185142	−	0.118983i	0.00680594	−	0.00437391i
$741$	−0.559729	−	3.89300i	−0.0205622	−	0.143013i
$742$	2.38311	+	1.53153i	0.0874866	+	0.0562242i
$743$	−14.6652	+	32.1123i	−0.538014	+	1.17809i	0.424144	+	0.905595i	$0.360575\pi$
$743$	−14.6652	+	32.1123i	−0.538014	+	1.17809i	−0.962158	+	0.272492i	$0.912152\pi$
$744$	−1.61291	+	1.86139i	−0.0591320	+	0.0682419i
$745$	−0.207288	+	1.44172i	−0.00759446	+	0.0528206i
$746$	4.01377	+	8.78893i	0.146954	+	0.321785i
$747$	−7.75599	−	2.27736i	−0.283777	−	0.0833244i
$748$	6.43683	+	1.89002i	0.235354	+	0.0691061i
$749$	−0.292419	−	0.640308i	−0.0106848	−	0.0233964i
$750$	0.638189	−	4.43870i	0.0233034	−	0.162078i
$751$	−11.6294	+	13.4211i	−0.424364	+	0.489742i	−0.927161	−	0.374662i	$-0.877759\pi$
$751$	−11.6294	+	13.4211i	−0.424364	+	0.489742i	0.502798	+	0.864404i	$0.332304\pi$
$752$	−1.12746	+	2.46879i	−0.0411142	+	0.0900276i
$753$	15.1874	+	9.76036i	0.553460	+	0.355687i
$754$	−0.421879	−	2.93423i	−0.0153639	−	0.106859i
$755$	−0.491189	+	0.315668i	−0.0178762	+	0.0114883i
$756$	−0.212591	−	0.245343i	−0.00773184	−	0.00892302i
$757$	−7.70494	+	2.26237i	−0.280041	+	0.0822274i	−0.418737	−	0.908108i	$-0.637527\pi$
$757$	−7.70494	+	2.26237i	−0.280041	+	0.0822274i	0.138696	+	0.990335i	$0.455709\pi$
$758$	19.9331			0.724002
$759$	−0.0449558	+	11.9331i	−0.00163179	+	0.433145i
$760$	1.32553			0.0480821
$761$	−19.9673	+	5.86292i	−0.723813	+	0.212531i	−0.622830	−	0.782358i	$-0.714017\pi$
$761$	−19.9673	+	5.86292i	−0.723813	+	0.212531i	−0.100983	+	0.994888i	$0.532199\pi$
$762$	−8.46686	−	9.77128i	−0.306722	−	0.353976i
$763$	2.29920	−	1.47760i	0.0832365	−	0.0534928i
$764$	−3.32908	−	23.1543i	−0.120442	−	0.837692i
$765$	−1.03889	−	0.667657i	−0.0375613	−	0.0241392i
$766$	−11.6206	+	25.4456i	−0.419869	+	0.919385i
$767$	−9.68621	+	11.1785i	−0.349749	+	0.403632i
$768$	0.142315	−	0.989821i	0.00513534	−	0.0357171i
$769$	12.1816	+	26.6740i	0.439279	+	0.961888i	0.991730	+	0.128342i	$0.0409656\pi$
$769$	12.1816	+	26.6740i	0.439279	+	0.961888i	−0.552450	+	0.833546i	$0.686307\pi$
$770$	−0.355008	−	0.104240i	−0.0127936	−	0.00375654i
$771$	−21.9300	−	6.43922i	−0.789788	−	0.231903i
$772$	2.49939	+	5.47289i	0.0899549	+	0.196974i
$773$	5.93473	−	41.2770i	0.213457	−	1.48463i	−0.548035	−	0.836455i	$-0.684624\pi$
$773$	5.93473	−	41.2770i	0.213457	−	1.48463i	0.761493	−	0.648174i	$-0.224467\pi$
$774$	−5.76770	+	6.65628i	−0.207316	+	0.239255i
$775$	−4.90112	+	10.7320i	−0.176053	+	0.385503i
$776$	0.188666	+	0.121248i	0.00677271	+	0.00435256i
$777$	−0.0221981	−	0.154391i	−0.000796351	−	0.00553874i
$778$	22.2758	−	14.3158i	0.798625	−	0.513245i
$779$	1.60597	+	1.85338i	0.0575397	+	0.0664044i
$780$	0.597303	−	0.175384i	0.0213869	−	0.00627975i
$781$	−40.8241			−1.46080
$782$	9.73993	+	8.50415i	0.348299	+	0.304108i
$783$	2.18119			0.0779492
$784$	6.61533	−	1.94244i	0.236262	−	0.0693727i
$785$	5.19993	+	6.00104i	0.185594	+	0.214186i
$786$	−4.95691	+	3.18561i	−0.176807	+	0.113627i
$787$	−6.28618	−	43.7214i	−0.224078	−	1.55850i	−0.722381	−	0.691495i	$-0.756952\pi$
$787$	−6.28618	−	43.7214i	−0.224078	−	1.55850i	0.498303	−	0.867003i	$-0.333957\pi$
$788$	13.0091	+	8.36045i	0.463430	+	0.297829i
$789$	7.73481	−	16.9369i	0.275366	−	0.602968i
$790$	−3.21777	+	3.71351i	−0.114483	+	0.132121i
$791$	0.00895767	−	0.0623020i	0.000318498	−	0.00221520i
$792$	−1.03365	−	2.26339i	−0.0367293	−	0.0804260i
$793$	15.7298	+	4.61867i	0.558580	+	0.164014i
$794$	−15.7816	−	4.63388i	−0.560067	−	0.164450i
$795$	−1.66039	−	3.63576i	−0.0588881	−	0.128947i
$796$	1.66665	−	11.5918i	0.0590729	−	0.410861i
$797$	20.2917	−	23.4179i	0.718769	−	0.829504i	−0.272389	−	0.962187i	$-0.587814\pi$
$797$	20.2917	−	23.4179i	0.718769	−	0.829504i	0.991158	+	0.132683i	$0.0423593\pi$
$798$	0.390265	−	0.854562i	0.0138152	−	0.0302512i
$799$	6.15577	+	3.95607i	0.217776	+	0.139956i
$800$	−0.681716	−	4.74144i	−0.0241023	−	0.167635i
$801$	−8.66347	+	5.56767i	−0.306109	+	0.196724i
$802$	13.2558	+	15.2980i	0.468078	+	0.540191i
$803$	−28.0823	+	8.24570i	−0.991002	+	0.290985i
$804$	−10.5658			−0.372627
$805$	−0.537182	−	0.469026i	−0.0189332	−	0.0165310i
$806$	−3.34738			−0.117906
$807$	0.756787	−	0.222213i	0.0266402	−	0.00782226i
$808$	7.00416	+	8.08324i	0.246406	+	0.284367i
$809$	−21.4348	+	13.7753i	−0.753609	+	0.484315i	−0.860180	−	0.509990i	$-0.829649\pi$
$809$	−21.4348	+	13.7753i	−0.753609	+	0.484315i	0.106571	+	0.994305i	$0.466013\pi$
$810$	0.0651865	+	0.453382i	0.00229042	+	0.0159302i
$811$	−18.1906	−	11.6904i	−0.638758	−	0.410505i	0.180785	−	0.983523i	$-0.442136\pi$
$811$	−18.1906	−	11.6904i	−0.638758	−	0.410505i	−0.819543	+	0.573018i	$0.805772\pi$
$812$	0.294151	−	0.644100i	0.0103227	−	0.0226035i
$813$	19.2007	−	22.1588i	0.673397	−	0.777142i
$814$	0.170143	−	1.18337i	0.00596350	−	0.0414770i
$815$	−1.00323	−	2.19677i	−0.0351417	−	0.0769495i
$816$	−2.58689	−	0.759581i	−0.0905594	−	0.0265906i
$817$	−24.4556	−	7.18080i	−0.855592	−	0.251225i
$818$	−7.24169	−	15.8571i	−0.253200	−	0.554430i
$819$	0.0627900	−	0.436714i	0.00219406	−	0.0152600i
$820$	−0.254192	+	0.293353i	−0.00887676	+	0.0102443i
$821$	−19.8677	+	43.5042i	−0.693387	+	1.51831i	0.154422	+	0.988005i	$0.450649\pi$
$821$	−19.8677	+	43.5042i	−0.693387	+	1.51831i	−0.847809	+	0.530301i	$0.822079\pi$
$822$	−13.6383	−	8.76482i	−0.475691	−	0.305708i
$823$	3.03301	+	21.0951i	0.105724	+	0.735327i	0.971867	+	0.235531i	$0.0756829\pi$
$823$	3.03301	+	21.0951i	0.105724	+	0.735327i	−0.866143	+	0.499797i	$0.833408\pi$
$824$	−1.70510	+	1.09580i	−0.0593999	+	0.0381740i
$825$	−7.80540	−	9.00792i	−0.271749	−	0.313615i
$826$	−3.38998	+	0.995387i	−0.117952	+	0.0346339i
$827$	8.52696			0.296512			0.148256	−	0.988949i	$-0.452634\pi$
$827$	8.52696			0.296512			0.148256	+	0.988949i	$0.452634\pi$
$828$	0.0180673	−	4.79580i	0.000627881	−	0.166665i
$829$	−28.0337			−0.973651			−0.486826	−	0.873499i	$-0.661845\pi$
$829$	−28.0337			−0.973651			−0.486826	+	0.873499i	$0.661845\pi$
$830$	3.55259	−	1.04313i	0.123312	−	0.0362077i
$831$	−16.6568	−	19.2229i	−0.577817	−	0.666836i
$832$	1.14333	−	0.734774i	0.0396379	−	0.0254737i
$833$	−2.64543	−	18.3994i	−0.0916589	−	0.637501i
$834$	−16.5162	−	10.6143i	−0.571909	−	0.367544i
$835$	−0.562837	+	1.23244i	−0.0194778	+	0.0426504i
$836$	4.71547	−	5.44194i	0.163088	−	0.188213i
$837$	0.350518	−	2.43790i	0.0121157	−	0.0842663i
$838$	6.83824	+	14.9737i	0.236223	+	0.517257i
$839$	−37.8397	−	11.1107i	−1.30637	−	0.383585i	−0.446815	−	0.894626i	$-0.647442\pi$
$839$	−37.8397	−	11.1107i	−1.30637	−	0.383585i	−0.859556	+	0.511041i	$0.829260\pi$
$840$	0.142674	+	0.0418928i	0.00492272	+	0.00144544i
$841$	−10.0707	−	22.0517i	−0.347264	−	0.760403i
$842$	−4.40853	+	30.6620i	−0.151928	+	1.05668i
$843$	−15.4430	+	17.8221i	−0.531884	+	0.613827i
$844$	4.43456	−	9.71033i	0.152644	−	0.334243i
$845$	−4.29756	−	2.76188i	−0.147841	−	0.0950114i
$846$	−0.386250	−	2.68643i	−0.0132796	−	0.0923614i
$847$	1.31324	−	0.843968i	0.0451234	−	0.0289991i
$848$	−5.71440	−	6.59477i	−0.196233	−	0.226465i
$849$	−25.5515	+	7.50259i	−0.876924	+	0.257488i
$850$	−12.9149			−0.442976
$851$	1.25308	−	1.93377i	0.0429549	−	0.0662888i
$852$	16.4068			0.562088
$853$	−44.2335	+	12.9881i	−1.51453	+	0.444705i	−0.930273	−	0.366867i	$-0.880430\pi$
$853$	−44.2335	+	12.9881i	−1.51453	+	0.444705i	−0.584252	+	0.811572i	$0.698612\pi$
$854$	2.56436	+	2.95943i	0.0877506	+	0.101270i
$855$	−1.11511	+	0.716637i	−0.0381359	+	0.0245085i
$856$	0.308588	+	2.14627i	0.0105473	+	0.0733582i
$857$	−10.5582	−	6.78534i	−0.360661	−	0.231783i	0.347743	−	0.937590i	$-0.386948\pi$
$857$	−10.5582	−	6.78534i	−0.360661	−	0.231783i	−0.708404	+	0.705807i	$0.750584\pi$
$858$	1.40482	−	3.07613i	0.0479597	−	0.105017i
$859$	3.21092	−	3.70559i	0.109555	−	0.126433i	−0.698323	−	0.715782i	$-0.746070\pi$
$859$	3.21092	−	3.70559i	0.109555	−	0.126433i	0.807878	+	0.589349i	$0.200616\pi$
$860$	0.574131	−	3.99317i	0.0195777	−	0.136166i
$861$	0.114283	+	0.250245i	0.00389476	+	0.00852833i
$862$	−17.5740	−	5.16018i	−0.598572	−	0.175757i
$863$	38.1184	+	11.1926i	1.29757	+	0.381000i	0.856348	−	0.516400i	$-0.172728\pi$
$863$	38.1184	+	11.1926i	1.29757	+	0.381000i	0.441219	+	0.897400i	$0.354546\pi$
$864$	0.415415	+	0.909632i	0.0141327	+	0.0309463i
$865$	−0.269402	+	1.87373i	−0.00915995	+	0.0637088i
$866$	9.92102	−	11.4495i	0.337130	−	0.389069i
$867$	4.04241	−	8.85164i	0.137287	−	0.300618i
$868$	−0.672639	−	0.432279i	−0.0228308	−	0.0146725i
$869$	3.79876	+	26.4210i	0.128864	+	0.896270i
$870$	−0.840480	+	0.540144i	−0.0284949	+	0.0183126i
$871$	−9.40364	−	10.8524i	−0.318630	−	0.367719i
$872$	−8.07785	+	2.37187i	−0.273551	+	0.0803217i
$873$	−0.224268			−0.00759031
$874$	12.6461	−	5.71779i	0.427760	−	0.193407i
$875$	1.45577			0.0492142
$876$	11.2860	−	3.31386i	0.381318	−	0.111965i
$877$	−1.42882	−	1.64894i	−0.0482478	−	0.0556809i	0.731113	−	0.682257i	$-0.239001\pi$
$877$	−1.42882	−	1.64894i	−0.0482478	−	0.0556809i	−0.779360	+	0.626576i	$0.784456\pi$
$878$	−4.90599	+	3.15289i	−0.165569	+	0.106405i
$879$	−0.938191	−	6.52526i	−0.0316444	−	0.220092i
$880$	0.958799	+	0.616183i	0.0323211	+	0.0207715i
$881$	−21.0662	+	46.1285i	−0.709738	+	1.55411i	0.118013	+	0.993012i	$0.462348\pi$
$881$	−21.0662	+	46.1285i	−0.709738	+	1.55411i	−0.827751	+	0.561096i	$0.810380\pi$
$882$	−4.51501	+	5.21060i	−0.152028	+	0.175450i
$883$	5.44954	−	37.9024i	0.183392	−	1.27552i	−0.665279	−	0.746595i	$-0.731687\pi$
$883$	5.44954	−	37.9024i	0.183392	−	1.27552i	0.848670	−	0.528922i	$-0.177404\pi$
$884$	−1.52217	−	3.33310i	−0.0511962	−	0.112104i
$885$	4.78310	+	1.40444i	0.160782	+	0.0472099i
$886$	−16.6438	−	4.88706i	−0.559159	−	0.164184i
$887$	8.95322	+	19.6048i	0.300620	+	0.658266i	0.998309	−	0.0581352i	$-0.0185155\pi$
$887$	8.95322	+	19.6048i	0.300620	+	0.658266i	−0.697689	+	0.716401i	$0.745788\pi$
$888$	−0.0683786	+	0.475583i	−0.00229463	+	0.0159595i
$889$	2.74864	−	3.17210i	0.0921863	−	0.106389i
$890$	1.95954	−	4.29080i	0.0656840	−	0.143828i
$891$	2.09325	+	1.34525i	0.0701264	+	0.0450675i
$892$	−1.07757	−	7.49464i	−0.0360796	−	0.250939i
$893$	6.60736	−	4.24630i	0.221107	−	0.142097i
$894$	−2.08241	−	2.40323i	−0.0696462	−	0.0803760i
$895$	−4.45513	+	1.30814i	−0.148918	+	0.0437264i
$896$	0.324635			0.0108453
$897$	4.94196	−	4.24974i	0.165007	−	0.141895i
$898$	18.5051			0.617522
$899$	5.15459	−	1.51353i	0.171915	−	0.0504789i
$900$	3.13691	+	3.62019i	0.104564	+	0.120673i
$901$	−19.7918	+	12.7194i	−0.659361	+	0.423745i
$902$	0.300088	+	2.08716i	0.00999183	+	0.0694947i
$903$	−2.40533	−	1.54581i	−0.0800445	−	0.0514415i
$904$	−0.0805438	+	0.176366i	−0.00267885	+	0.00586586i
$905$	7.99020	−	9.22118i	0.265603	−	0.306523i
$906$	0.181411	−	1.26174i	0.00602699	−	0.0419186i
$907$	11.9325	+	26.1286i	0.396214	+	0.867587i	0.997640	+	0.0686589i	$0.0218720\pi$
$907$	11.9325	+	26.1286i	0.396214	+	0.867587i	−0.601426	+	0.798928i	$0.705401\pi$
$908$	12.1325	+	3.56241i	0.402630	+	0.118223i
$909$	−10.2624	−	3.01331i	−0.340383	−	0.0999453i
$910$	0.0839518	+	0.183829i	0.00278298	+	0.00609387i
$911$	0.517595	−	3.59995i	0.0171487	−	0.119272i	−0.979449	−	0.201692i	$-0.935356\pi$
$911$	0.517595	−	3.59995i	0.0171487	−	0.119272i	0.996598	+	0.0824204i	$0.0262650\pi$
$912$	−1.89510	+	2.18706i	−0.0627530	+	0.0724208i
$913$	8.35546	−	18.2959i	0.276526	−	0.605506i
$914$	4.84716	+	3.11508i	0.160330	+	0.103038i
$915$	−0.786308	−	5.46889i	−0.0259945	−	0.180796i
$916$	−7.06214	+	4.53856i	−0.233340	+	0.149958i
$917$	−1.25265	−	1.44563i	−0.0413660	−	0.0477389i
$918$	2.58689	−	0.759581i	0.0853802	−	0.0250699i
$919$	14.2577			0.470318			0.235159	−	0.971957i	$-0.424439\pi$
$919$	14.2577			0.470318			0.235159	+	0.971957i	$0.424439\pi$
$920$	1.18066	+	1.85245i	0.0389251	+	0.0610733i
$921$	−22.2953			−0.734656
$922$	21.6201	−	6.34824i	0.712021	−	0.209068i
$923$	14.6022	+	16.8518i	0.480637	+	0.554684i
$924$	0.679540	−	0.436714i	0.0223552	−	0.0143668i
$925$	0.327547	+	2.27814i	0.0107697	+	0.0749047i
$926$	25.2373	+	16.2190i	0.829350	+	0.532991i
$927$	0.841985	−	1.84369i	0.0276544	−	0.0605547i
$928$	−1.42837	+	1.64843i	−0.0468886	+	0.0541124i
$929$	−7.42433	+	51.6373i	−0.243584	+	1.69417i	0.390260	+	0.920705i	$0.372385\pi$
$929$	−7.42433	+	51.6373i	−0.243584	+	1.69417i	−0.633844	+	0.773461i	$0.718524\pi$
$930$	0.468651	+	1.02620i	0.0153677	+	0.0336505i
$931$	−19.1441	−	5.62121i	−0.627422	−	0.184228i
$932$	−25.2170	−	7.40439i	−0.826011	−	0.242539i
$933$	5.36155	+	11.7401i	0.175529	+	0.384355i
$934$	−1.65702	+	11.5248i	−0.0542192	+	0.377103i
$935$	2.01227	−	2.32229i	0.0658083	−	0.0759469i
$936$	−0.564582	+	1.23626i	−0.0184540	+	0.0404085i
$937$	−30.9751	−	19.9065i	−1.01191	−	0.650317i	−0.0740256	−	0.997256i	$-0.523585\pi$
$937$	−30.9751	−	19.9065i	−1.01191	−	0.650317i	−0.937888	+	0.346939i	$0.887221\pi$
$938$	−0.488143	−	3.39511i	−0.0159384	−	0.110854i
$939$	16.1712	−	10.3926i	0.527727	−	0.339149i
$940$	0.814095	+	0.939516i	0.0265529	+	0.0306436i
$941$	15.8211	−	4.64550i	0.515754	−	0.151439i	−0.0134897	−	0.999909i	$-0.504294\pi$
$941$	15.8211	−	4.64550i	0.515754	−	0.151439i	0.529243	+	0.848470i	$0.322476\pi$
$942$	−17.3357			−0.564827
$943$	−1.15968	+	3.89517i	−0.0377645	+	0.126844i
$944$	10.8833			0.354221
$945$	−0.142674	+	0.0418928i	−0.00464118	+	0.00136277i
$946$	−14.3514	−	16.5624i	−0.466606	−	0.538492i
$947$	40.8392	−	26.2458i	1.32710	−	0.852874i	0.331217	−	0.943555i	$-0.392541\pi$
$947$	40.8392	−	26.2458i	1.32710	−	0.852874i	0.995880	+	0.0906811i	$0.0289044\pi$
$948$	−1.52668	−	10.6183i	−0.0495844	−	0.344867i
$949$	13.4484	+	8.64274i	0.436552	+	0.280555i
$950$	−5.75862	+	12.6096i	−0.186834	+	0.409110i
$951$	−7.03398	+	8.11764i	−0.228092	+	0.263233i
$952$	0.124561	−	0.866341i	0.00403705	−	0.0280783i
$953$	23.5811	+	51.6354i	0.763867	+	1.67264i	0.739708	+	0.672928i	$0.234963\pi$
$953$	23.5811	+	51.6354i	0.763867	+	1.67264i	0.0241587	+	0.999708i	$0.492309\pi$
$954$	8.37266	+	2.45843i	0.271075	+	0.0795947i
$955$	−10.2807	−	3.01869i	−0.332676	−	0.0976825i
$956$	3.26256	+	7.14402i	0.105519	+	0.231054i
$957$	−0.772389	+	5.37208i	−0.0249678	+	0.173655i
$958$	8.73545	−	10.0812i	0.282230	−	0.325710i
$959$	2.18631	−	4.78735i	0.0705996	−	0.154591i
$960$	−0.385331	−	0.247638i	−0.0124365	−	0.00799247i
$961$	3.54844	+	24.6800i	0.114466	+	0.796128i
$962$	−0.549341	+	0.353040i	−0.0177115	+	0.0113825i
$963$	−1.41996	−	1.63873i	−0.0457577	−	0.0528072i
$964$	25.4306	−	7.46711i	0.819066	−	0.240499i
$965$	2.75587			0.0887146
$966$	1.54187	−	0.215762i	0.0496089	−	0.00694203i
$967$	26.3683			0.847948			0.423974	−	0.905674i	$-0.360635\pi$
$967$	26.3683			0.847948			0.423974	+	0.905674i	$0.360635\pi$
$968$	−4.61385	+	1.35475i	−0.148295	+	0.0435433i
$969$	5.10938	+	5.89654i	0.164137	+	0.189424i
$970$	0.0864174	−	0.0555371i	0.00277469	−	0.00178319i
$971$	−0.832978	−	5.79349i	−0.0267315	−	0.185922i	0.972081	−	0.234647i	$-0.0753933\pi$
$971$	−0.832978	−	5.79349i	−0.0267315	−	0.185922i	−0.998812	+	0.0487249i	$0.984484\pi$
$972$	−0.841254	−	0.540641i	−0.0269832	−	0.0173411i
$973$	2.64765	−	5.79754i	0.0848797	−	0.185861i
$974$	−8.85391	+	10.2180i	−0.283697	+	0.327404i
$975$	−0.926507	+	6.44400i	−0.0296720	+	0.206373i
$976$	−5.01092	−	10.9724i	−0.160396	−	0.351217i
$977$	30.4209	+	8.93237i	0.973249	+	0.285772i	0.729435	−	0.684050i	$-0.239783\pi$
$977$	30.4209	+	8.93237i	0.973249	+	0.285772i	0.243814	+	0.969822i	$0.421601\pi$
$978$	5.05886	+	1.48542i	0.161765	+	0.0474984i
$979$	−10.6449	−	23.3090i	−0.340211	−	0.744959i
$980$	0.449436	−	3.12589i	0.0143567	−	0.0998530i
$981$	5.51319	−	6.36256i	0.176023	−	0.203141i
$982$	−17.0099	+	37.2465i	−0.542808	+	1.18858i
$983$	21.8073	+	14.0147i	0.695543	+	0.446999i	0.840053	−	0.542505i	$-0.182524\pi$
$983$	21.8073	+	14.0147i	0.695543	+	0.446999i	−0.144509	+	0.989503i	$0.546160\pi$
$984$	−0.120602	−	0.838807i	−0.00384466	−	0.0267402i
$985$	5.95875	−	3.82946i	0.189862	−	0.122017i
$986$	3.85105	+	4.44434i	0.122642	+	0.141537i
$987$	0.845387	−	0.248228i	0.0269090	−	0.00790119i
$988$	−3.93303			−0.125127
$989$	−11.7474	−	40.5729i	−0.373547	−	1.29014i
$990$	−1.13973			−0.0362229
$991$	37.8199	−	11.1049i	1.20139	−	0.352760i	0.381006	−	0.924573i	$-0.375578\pi$
$991$	37.8199	−	11.1049i	1.20139	−	0.352760i	0.820384	+	0.571813i	$0.193760\pi$
$992$	1.61291	+	1.86139i	0.0512098	+	0.0590992i
$993$	14.7521	−	9.48057i	0.468143	−	0.300857i
$994$	0.758000	+	5.27200i	0.0240423	+	0.167218i
$995$	−4.51262	−	2.90009i	−0.143060	−	0.0919389i
$996$	−3.35797	+	7.35294i	−0.106401	+	0.232987i
$997$	19.4890	−	22.4915i	0.617223	−	0.712314i	−0.357954	−	0.933739i	$-0.616526\pi$
$997$	19.4890	−	22.4915i	0.617223	−	0.712314i	0.975177	+	0.221426i	$0.0710710\pi$
$998$	3.04459	−	21.1756i	0.0963747	−	0.670301i
$999$	−0.199596	−	0.437054i	−0.00631494	−	0.0138278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.d.55.1	✓	10
3.2	odd	2		414.2.i.a.55.1		10
23.8	even	11		3174.2.a.x.1.3		5
23.15	odd	22		3174.2.a.w.1.3		5
23.18	even	11	inner	138.2.e.d.133.1	yes	10
69.8	odd	22		9522.2.a.bx.1.3		5
69.38	even	22		9522.2.a.by.1.3		5
69.41	odd	22		414.2.i.a.271.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.d.55.1	✓	10	1.1	even	1	trivial
138.2.e.d.133.1	yes	10	23.18	even	11	inner
414.2.i.a.55.1		10	3.2	odd	2
414.2.i.a.271.1		10	69.41	odd	22
3174.2.a.w.1.3		5	23.15	odd	22
3174.2.a.x.1.3		5	23.8	even	11
9522.2.a.bx.1.3		5	69.8	odd	22
9522.2.a.by.1.3		5	69.38	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.0651865 - 0.453382i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.134858 + 0.295298i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.0651865 - 0.453382i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.134858 + 0.295298i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.190279 - 0.416652i) q^{10} +(-2.38745 - 0.701020i) q^{11} +(0.959493 + 0.281733i) q^{12} +(0.564582 + 1.23626i) q^{13} +(-0.0462003 + 0.321330i) q^{14} +(0.299955 - 0.346167i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-2.26811 - 1.45762i) q^{17} +(0.142315 + 0.989821i) q^{18} +(-2.43450 + 1.56456i) q^{19} +(-0.299955 - 0.346167i) q^{20} +(-0.311485 + 0.0914602i) q^{21} -2.48825 q^{22} +(-4.35491 - 2.00868i) q^{23} +1.00000 q^{24} +(4.59616 - 1.34955i) q^{25} +(0.890008 + 1.02712i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.0462003 + 0.321330i) q^{28} +(-1.83493 - 1.17924i) q^{29} +(0.190279 - 0.416652i) q^{30} +(-1.61291 + 1.86139i) q^{31} +(0.142315 - 0.989821i) q^{32} +(-1.03365 - 2.26339i) q^{33} +(-2.58689 - 0.759581i) q^{34} +(0.142674 + 0.0418928i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-0.0683786 + 0.475583i) q^{37} +(-1.89510 + 2.18706i) q^{38} +(-0.564582 + 1.23626i) q^{39} +(-0.385331 - 0.247638i) q^{40} +(-0.120602 - 0.838807i) q^{41} +(-0.273100 + 0.175511i) q^{42} +(5.76770 + 6.65628i) q^{43} +(-2.38745 + 0.701020i) q^{44} +0.458044 q^{45} +(-4.74441 - 0.700397i) q^{46} -2.71406 q^{47} +(0.959493 - 0.281733i) q^{48} +(4.51501 + 5.21060i) q^{49} +(4.02977 - 2.58978i) q^{50} +(-0.383696 - 2.66866i) q^{51} +(1.14333 + 0.734774i) q^{52} +(3.62496 - 7.93756i) q^{53} +(-0.654861 + 0.755750i) q^{54} +(-0.162200 + 1.12813i) q^{55} +(0.134858 + 0.295298i) q^{56} +(-2.77667 - 0.815304i) q^{57} +(-2.09283 - 0.614511i) q^{58} +(4.52108 + 9.89978i) q^{59} +(0.0651865 - 0.453382i) q^{60} +(7.89921 - 9.11618i) q^{61} +(-1.02316 + 2.24040i) q^{62} +(-0.273100 - 0.175511i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(0.523697 - 0.336559i) q^{65} +(-1.62945 - 1.88049i) q^{66} +(-10.1378 + 2.97673i) q^{67} -2.69611 q^{68} +(-1.33380 - 4.60662i) q^{69} +0.148697 q^{70} +(15.7422 - 4.62233i) q^{71} +(0.654861 + 0.755750i) q^{72} +(9.89520 - 6.35926i) q^{73} +(0.0683786 + 0.475583i) q^{74} +(4.02977 + 2.58978i) q^{75} +(-1.20217 + 2.63238i) q^{76} +(0.528978 - 0.610473i) q^{77} +(-0.193417 + 1.34525i) q^{78} +(-4.45637 - 9.75808i) q^{79} +(-0.439490 - 0.129046i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.352036 - 0.770851i) q^{82} +(-1.15039 + 8.00114i) q^{83} +(-0.212591 + 0.245343i) q^{84} +(-0.513011 + 1.12334i) q^{85} +(7.40935 + 4.76170i) q^{86} +(-0.310415 - 2.15898i) q^{87} +(-2.09325 + 1.34525i) q^{88} +(6.74394 + 7.78292i) q^{89} +(0.439490 - 0.129046i) q^{90} -0.441205 q^{91} +(-4.74955 + 0.664630i) q^{92} -2.46297 q^{93} +(-2.60412 + 0.764638i) q^{94} +(0.868039 + 1.00177i) q^{95} +(0.841254 - 0.540641i) q^{96} +(0.0319166 + 0.221985i) q^{97} +(5.80012 + 3.72751i) q^{98} +(1.03365 - 2.26339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9} - 13 q^{10} - 5 q^{11} + q^{12} + 13 q^{13} + 9 q^{14} + 9 q^{15} - q^{16} + q^{18} - 9 q^{20} - 13 q^{21} - 6 q^{22} - 32 q^{23} + 10 q^{24} + q^{25} - 13 q^{26} + q^{27} - 9 q^{28} + 27 q^{29} + 13 q^{30} - 8 q^{31} + q^{32} - 6 q^{33} - 11 q^{34} - 26 q^{35} - q^{36} - 11 q^{37} + 11 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} + 2 q^{42} + 34 q^{43} - 5 q^{44} + 2 q^{45} - q^{46} + 8 q^{47} + q^{48} + 25 q^{49} + 21 q^{50} - 11 q^{51} + 2 q^{52} + 9 q^{53} - q^{54} - 23 q^{55} - 2 q^{56} - 11 q^{57} - 5 q^{58} - 21 q^{59} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} + 29 q^{65} + 6 q^{66} - 32 q^{67} + 22 q^{68} - q^{69} - 18 q^{70} + 22 q^{71} + q^{72} + 43 q^{73} + 11 q^{74} + 21 q^{75} + 10 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} - q^{81} + 32 q^{82} - 3 q^{83} + 9 q^{84} + 33 q^{85} + 32 q^{86} + 6 q^{87} - 6 q^{88} - 11 q^{89} - 2 q^{90} - 70 q^{91} - 21 q^{92} + 8 q^{93} + 3 q^{94} - q^{96} + 39 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9 - 13 * q^10 - 5 * q^11 + q^12 + 13 * q^13 + 9 * q^14 + 9 * q^15 - q^16 + q^18 - 9 * q^20 - 13 * q^21 - 6 * q^22 - 32 * q^23 + 10 * q^24 + q^25 - 13 * q^26 + q^27 - 9 * q^28 + 27 * q^29 + 13 * q^30 - 8 * q^31 + q^32 - 6 * q^33 - 11 * q^34 - 26 * q^35 - q^36 - 11 * q^37 + 11 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 + 2 * q^42 + 34 * q^43 - 5 * q^44 + 2 * q^45 - q^46 + 8 * q^47 + q^48 + 25 * q^49 + 21 * q^50 - 11 * q^51 + 2 * q^52 + 9 * q^53 - q^54 - 23 * q^55 - 2 * q^56 - 11 * q^57 - 5 * q^58 - 21 * q^59 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^63 - q^64 + 29 * q^65 + 6 * q^66 - 32 * q^67 + 22 * q^68 - q^69 - 18 * q^70 + 22 * q^71 + q^72 + 43 * q^73 + 11 * q^74 + 21 * q^75 + 10 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - q^81 + 32 * q^82 - 3 * q^83 + 9 * q^84 + 33 * q^85 + 32 * q^86 + 6 * q^87 - 6 * q^88 - 11 * q^89 - 2 * q^90 - 70 * q^91 - 21 * q^92 + 8 * q^93 + 3 * q^94 - q^96 + 39 * q^97 - 14 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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