LMFDB - Embedded newform 966.2.q.d.169.1

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			169.1
Root			$0.287778 - 0.332113i$ of defining polynomial
Character	$\chi$	$=$	966.169
Dual form			966.2.q.d.463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.569907 + 0.657708i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.569907 + 0.657708i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.732120 + 0.470505i) q^{10} +(-0.719724 - 5.00579i) q^{11} +(0.142315 + 0.989821i) q^{12} +(-1.66573 + 1.07050i) q^{13} +(-0.654861 + 0.755750i) q^{14} +(0.361524 - 0.791628i) q^{15} +(0.841254 + 0.540641i) q^{16} +(6.13014 - 1.79997i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(-1.70036 - 0.499271i) q^{19} +(-0.361524 - 0.791628i) q^{20} +(0.142315 - 0.989821i) q^{21} +5.05727 q^{22} +(-1.38927 + 4.59020i) q^{23} -1.00000 q^{24} +(0.603789 - 4.19944i) q^{25} +(-0.822545 - 1.80112i) q^{26} +(0.959493 + 0.281733i) q^{27} +(-0.654861 - 0.755750i) q^{28} +(0.574936 - 0.168816i) q^{29} +(0.732120 + 0.470505i) q^{30} +(3.10060 - 6.78936i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-4.25445 + 2.73417i) q^{33} +(0.909240 + 6.32391i) q^{34} +(0.123853 + 0.861414i) q^{35} +(0.841254 - 0.540641i) q^{36} +(3.99464 - 4.61006i) q^{37} +(0.736176 - 1.61200i) q^{38} +(1.66573 + 1.07050i) q^{39} +(0.835020 - 0.245184i) q^{40} +(-0.129622 - 0.149592i) q^{41} +(0.959493 + 0.281733i) q^{42} +(-2.24835 - 4.92319i) q^{43} +(-0.719724 + 5.00579i) q^{44} -0.870273 q^{45} +(-4.34577 - 2.02838i) q^{46} -1.50923 q^{47} +(0.142315 - 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(4.07077 + 1.19529i) q^{50} +(-4.18386 - 4.82844i) q^{51} +(1.89985 - 0.557846i) q^{52} +(10.8506 + 6.97329i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(2.88217 - 3.32621i) q^{55} +(0.841254 - 0.540641i) q^{56} +(0.252203 + 1.75411i) q^{57} +(0.0852762 + 0.593109i) q^{58} +(-3.92418 + 2.52192i) q^{59} +(-0.569907 + 0.657708i) q^{60} +(3.87084 - 8.47596i) q^{61} +(6.27899 + 4.03526i) q^{62} +(-0.959493 + 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-1.65339 - 0.485478i) q^{65} +(-2.10087 - 4.60025i) q^{66} +(2.06291 - 14.3478i) q^{67} -6.38894 q^{68} +(4.75252 - 0.643117i) q^{69} -0.870273 q^{70} +(-0.906318 + 6.30358i) q^{71} +(0.415415 + 0.909632i) q^{72} +(13.3755 + 3.92741i) q^{73} +(3.99464 + 4.61006i) q^{74} +(-4.07077 + 1.19529i) q^{75} +(1.49082 + 0.958094i) q^{76} +(2.10087 - 4.60025i) q^{77} +(-1.29666 + 1.49643i) q^{78} +(7.35998 - 4.72997i) q^{79} +(0.123853 + 0.861414i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(0.166517 - 0.107014i) q^{82} +(8.19165 - 9.45367i) q^{83} +(-0.415415 + 0.909632i) q^{84} +(4.67747 + 3.00603i) q^{85} +(5.19305 - 1.52482i) q^{86} +(-0.392398 - 0.452851i) q^{87} +(-4.85241 - 1.42480i) q^{88} +(-1.96958 - 4.31278i) q^{89} +(0.123853 - 0.861414i) q^{90} -1.98006 q^{91} +(2.62620 - 4.01286i) q^{92} -7.46385 q^{93} +(0.214786 - 1.49387i) q^{94} +(-0.640674 - 1.40288i) q^{95} +(0.959493 + 0.281733i) q^{96} +(1.94704 + 2.24701i) q^{97} +(-0.959493 + 0.281733i) q^{98} +(4.25445 + 2.73417i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	0.569907	+	0.657708i	0.254870	+	0.294136i	0.868737	−	0.495274i	$-0.164932\pi$
$5$	0.569907	+	0.657708i	0.254870	+	0.294136i	−0.613867	+	0.789410i	$0.710387\pi$
$6$	0.959493	−	0.281733i	0.391711	−	0.115017i
$7$	0.841254	+	0.540641i	0.317964	+	0.204343i
$7$	0.841254	+	0.540641i	0.317964	+	0.204343i
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	−0.732120	+	0.470505i	−0.231517	+	0.148787i
$11$	−0.719724	−	5.00579i	−0.217005	−	1.50930i	−0.749008	−	0.662561i	$-0.769470\pi$
$11$	−0.719724	−	5.00579i	−0.217005	−	1.50930i	0.532003	−	0.846743i	$-0.321440\pi$
$12$	0.142315	+	0.989821i	0.0410828	+	0.285737i
$13$	−1.66573	+	1.07050i	−0.461990	+	0.296903i	−0.750855	−	0.660467i	$-0.770358\pi$
$13$	−1.66573	+	1.07050i	−0.461990	+	0.296903i	0.288865	+	0.957370i	$0.406722\pi$
$14$	−0.654861	+	0.755750i	−0.175019	+	0.201983i
$15$	0.361524	−	0.791628i	0.0933452	−	0.204397i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	6.13014	−	1.79997i	1.48678	−	0.436557i	0.565266	−	0.824909i	$-0.308774\pi$
$17$	6.13014	−	1.79997i	1.48678	−	0.436557i	0.921511	+	0.388352i	$0.126955\pi$
$18$	−0.654861	−	0.755750i	−0.154352	−	0.178132i
$19$	−1.70036	−	0.499271i	−0.390090	−	0.114541i	0.0808054	−	0.996730i	$-0.474251\pi$
$19$	−1.70036	−	0.499271i	−0.390090	−	0.114541i	−0.470895	+	0.882189i	$0.656069\pi$
$20$	−0.361524	−	0.791628i	−0.0808393	−	0.177013i
$21$	0.142315	−	0.989821i	0.0310556	−	0.215997i
$22$	5.05727			1.07821
$23$	−1.38927	+	4.59020i	−0.289682	+	0.957123i
$23$	−1.38927	+	4.59020i	−0.289682	+	0.957123i
$24$	−1.00000			−0.204124
$25$	0.603789	−	4.19944i	0.120758	−	0.839888i
$26$	−0.822545	−	1.80112i	−0.161314	−	0.353229i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	−0.654861	−	0.755750i	−0.123757	−	0.142823i
$29$	0.574936	−	0.168816i	0.106763	−	0.0313484i	−0.227915	−	0.973681i	$-0.573191\pi$
$29$	0.574936	−	0.168816i	0.106763	−	0.0313484i	0.334678	+	0.942333i	$0.391373\pi$
$30$	0.732120	+	0.470505i	0.133666	+	0.0859020i
$31$	3.10060	−	6.78936i	0.556884	−	1.21941i	−0.396609	−	0.917988i	$-0.629813\pi$
$31$	3.10060	−	6.78936i	0.556884	−	1.21941i	0.953492	−	0.301417i	$-0.0974598\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	−4.25445	+	2.73417i	−0.740604	+	0.475957i
$34$	0.909240	+	6.32391i	0.155933	+	1.08454i
$35$	0.123853	+	0.861414i	0.0209349	+	0.145606i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	3.99464	−	4.61006i	0.656715	−	0.757890i	−0.325522	−	0.945535i	$-0.605540\pi$
$37$	3.99464	−	4.61006i	0.656715	−	0.757890i	0.982237	+	0.187645i	$0.0600854\pi$
$38$	0.736176	−	1.61200i	0.119424	−	0.261501i
$39$	1.66573	+	1.07050i	0.266730	+	0.171417i
$40$	0.835020	−	0.245184i	0.132028	−	0.0387670i
$41$	−0.129622	−	0.149592i	−0.0202436	−	0.0233624i	0.745537	−	0.666464i	$-0.232193\pi$
$41$	−0.129622	−	0.149592i	−0.0202436	−	0.0233624i	−0.765781	+	0.643101i	$0.777647\pi$
$42$	0.959493	+	0.281733i	0.148053	+	0.0434723i
$43$	−2.24835	−	4.92319i	−0.342870	−	0.750780i	0.657126	−	0.753781i	$-0.271772\pi$
$43$	−2.24835	−	4.92319i	−0.342870	−	0.750780i	−0.999995	+	0.00300123i	$0.999045\pi$
$44$	−0.719724	+	5.00579i	−0.108503	+	0.754652i
$45$	−0.870273			−0.129733
$46$	−4.34577	−	2.02838i	−0.640748	−	0.299068i
$47$	−1.50923			−0.220144			−0.110072	−	0.993924i	$-0.535108\pi$
$47$	−1.50923			−0.220144			−0.110072	+	0.993924i	$0.535108\pi$
$48$	0.142315	−	0.989821i	0.0205414	−	0.142868i
$49$	0.415415	+	0.909632i	0.0593450	+	0.129947i
$50$	4.07077	+	1.19529i	0.575694	+	0.169039i
$51$	−4.18386	−	4.82844i	−0.585858	−	0.676116i
$52$	1.89985	−	0.557846i	0.263462	−	0.0773593i
$53$	10.8506	+	6.97329i	1.49045	+	0.957855i	0.996066	+	0.0886118i	$0.0282430\pi$
$53$	10.8506	+	6.97329i	1.49045	+	0.957855i	0.494385	+	0.869243i	$0.335393\pi$
$54$	−0.415415	+	0.909632i	−0.0565308	+	0.123785i
$55$	2.88217	−	3.32621i	0.388632	−	0.448506i
$56$	0.841254	−	0.540641i	0.112417	−	0.0722462i
$57$	0.252203	+	1.75411i	0.0334051	+	0.232337i
$58$	0.0852762	+	0.593109i	0.0111973	+	0.0778790i
$59$	−3.92418	+	2.52192i	−0.510885	+	0.328326i	−0.770557	−	0.637371i	$-0.780022\pi$
$59$	−3.92418	+	2.52192i	−0.510885	+	0.328326i	0.259672	+	0.965697i	$0.416386\pi$
$60$	−0.569907	+	0.657708i	−0.0735747	+	0.0849098i
$61$	3.87084	−	8.47596i	0.495610	−	1.08524i	−0.482261	−	0.876028i	$-0.660184\pi$
$61$	3.87084	−	8.47596i	0.495610	−	1.08524i	0.977871	−	0.209208i	$-0.0670885\pi$
$62$	6.27899	+	4.03526i	0.797433	+	0.512479i
$63$	−0.959493	+	0.281733i	−0.120885	+	0.0354950i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−1.65339	−	0.485478i	−0.205077	−	0.0602162i
$66$	−2.10087	−	4.60025i	−0.258599	−	0.566252i
$67$	2.06291	−	14.3478i	0.252024	−	1.75287i	−0.333998	−	0.942574i	$-0.608398\pi$
$67$	2.06291	−	14.3478i	0.252024	−	1.75287i	0.586023	−	0.810295i	$-0.300693\pi$
$68$	−6.38894			−0.774772
$69$	4.75252	−	0.643117i	0.572136	−	0.0774222i
$70$	−0.870273			−0.104017
$71$	−0.906318	+	6.30358i	−0.107560	+	0.748098i	0.862644	+	0.505811i	$0.168807\pi$
$71$	−0.906318	+	6.30358i	−0.107560	+	0.748098i	−0.970205	+	0.242287i	$0.922102\pi$
$72$	0.415415	+	0.909632i	0.0489571	+	0.107201i
$73$	13.3755	+	3.92741i	1.56549	+	0.459669i	0.945684	−	0.325088i	$-0.105394\pi$
$73$	13.3755	+	3.92741i	1.56549	+	0.459669i	0.619804	+	0.784757i	$0.287212\pi$
$74$	3.99464	+	4.61006i	0.464368	+	0.535909i
$75$	−4.07077	+	1.19529i	−0.470052	+	0.138020i
$76$	1.49082	+	0.958094i	0.171009	+	0.109901i
$77$	2.10087	−	4.60025i	0.239416	−	0.524248i
$78$	−1.29666	+	1.49643i	−0.146818	+	0.169437i
$79$	7.35998	−	4.72997i	0.828063	−	0.532164i	−0.0565991	−	0.998397i	$-0.518026\pi$
$79$	7.35998	−	4.72997i	0.828063	−	0.532164i	0.884662	+	0.466233i	$0.154389\pi$
$80$	0.123853	+	0.861414i	0.0138472	+	0.0963091i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	0.166517	−	0.107014i	0.0183887	−	0.0118177i
$83$	8.19165	−	9.45367i	0.899150	−	1.03767i	−0.0999384	−	0.994994i	$-0.531865\pi$
$83$	8.19165	−	9.45367i	0.899150	−	1.03767i	0.999089	−	0.0426812i	$-0.0135900\pi$
$84$	−0.415415	+	0.909632i	−0.0453255	+	0.0992490i
$85$	4.67747	+	3.00603i	0.507343	+	0.326049i
$86$	5.19305	−	1.52482i	0.559981	−	0.164425i
$87$	−0.392398	−	0.452851i	−0.0420695	−	0.0485507i
$88$	−4.85241	−	1.42480i	−0.517269	−	0.151884i
$89$	−1.96958	−	4.31278i	−0.208775	−	0.457154i	0.776057	−	0.630663i	$-0.217217\pi$
$89$	−1.96958	−	4.31278i	−0.208775	−	0.457154i	−0.984832	+	0.173509i	$0.944490\pi$
$90$	0.123853	−	0.861414i	0.0130552	−	0.0908011i
$91$	−1.98006			−0.207566
$92$	2.62620	−	4.01286i	0.273800	−	0.418370i
$93$	−7.46385			−0.773966
$94$	0.214786	−	1.49387i	0.0221535	−	0.154081i
$95$	−0.640674	−	1.40288i	−0.0657317	−	0.143932i
$96$	0.959493	+	0.281733i	0.0979278	+	0.0287542i
$97$	1.94704	+	2.24701i	0.197692	+	0.228149i	0.845937	−	0.533283i	$-0.179042\pi$
$97$	1.94704	+	2.24701i	0.197692	+	0.228149i	−0.648244	+	0.761432i	$0.724496\pi$
$98$	−0.959493	+	0.281733i	−0.0969234	+	0.0284593i
$99$	4.25445	+	2.73417i	0.427588	+	0.274794i
$100$	−1.76245	+	3.85923i	−0.176245	+	0.385923i
$101$	3.10627	−	3.58483i	0.309085	−	0.356703i	−0.579861	−	0.814716i	$-0.696893\pi$
$101$	3.10627	−	3.58483i	0.309085	−	0.356703i	0.888946	+	0.458012i	$0.151438\pi$
$102$	5.37472	−	3.45412i	0.532176	−	0.342009i
$103$	0.167452	+	1.16466i	0.0164996	+	0.114757i	0.996407	−	0.0846970i	$-0.0269922\pi$
$103$	0.167452	+	1.16466i	0.0164996	+	0.114757i	−0.979907	+	0.199454i	$0.936083\pi$
$104$	0.281791	+	1.95990i	0.0276319	+	0.192184i
$105$	0.732120	−	0.470505i	0.0714476	−	0.0459166i
$106$	−8.44652	+	9.74780i	−0.820398	+	0.946790i
$107$	−6.77655	+	14.8386i	−0.655114	+	1.43450i	0.231892	+	0.972742i	$0.425508\pi$
$107$	−6.77655	+	14.8386i	−0.655114	+	1.43450i	−0.887006	+	0.461758i	$0.847219\pi$
$108$	−0.841254	−	0.540641i	−0.0809497	−	0.0520232i
$109$	−6.78524	+	1.99233i	−0.649908	+	0.190830i	−0.590038	−	0.807376i	$-0.700887\pi$
$109$	−6.78524	+	1.99233i	−0.649908	+	0.190830i	−0.0598709	+	0.998206i	$0.519069\pi$
$110$	2.88217	+	3.32621i	0.274805	+	0.317141i
$111$	−5.85289	−	1.71856i	−0.555532	−	0.163119i
$112$	0.415415	+	0.909632i	0.0392530	+	0.0859521i
$113$	−1.24483	+	8.65797i	−0.117104	+	0.814473i	0.843615	+	0.536949i	$0.180423\pi$
$113$	−1.24483	+	8.65797i	−0.117104	+	0.814473i	−0.960719	+	0.277525i	$0.910486\pi$
$114$	−1.77215			−0.165977
$115$	−3.81077	+	1.70226i	−0.355356	+	0.158736i
$116$	−0.599208			−0.0556351
$117$	0.281791	−	1.95990i	0.0260516	−	0.181193i
$118$	−1.93778	−	4.24315i	−0.178387	−	0.390613i
$119$	6.13014	+	1.79997i	0.561949	+	0.165003i
$120$	−0.569907	−	0.657708i	−0.0520252	−	0.0600403i
$121$	−13.9855	+	4.10653i	−1.27141	+	0.373320i
$122$	7.83881	+	5.03770i	0.709692	+	0.456092i
$123$	−0.0822268	+	0.180051i	−0.00741414	+	0.0162347i
$124$	−4.88779	+	5.64081i	−0.438936	+	0.506559i
$125$	6.76671	−	4.34870i	0.605233	−	0.388960i
$126$	−0.142315	−	0.989821i	−0.0126784	−	0.0881803i
$127$	−0.254375	−	1.76922i	−0.0225721	−	0.156993i	0.975418	−	0.220363i	$-0.0707242\pi$
$127$	−0.254375	−	1.76922i	−0.0225721	−	0.156993i	−0.997990	+	0.0633703i	$0.979815\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	−3.54430	+	4.09033i	−0.312058	+	0.360134i
$130$	0.715838	−	1.56747i	0.0627832	−	0.137476i
$131$	−11.3530	−	7.29616i	−0.991920	−	0.637468i	−0.0592669	−	0.998242i	$-0.518876\pi$
$131$	−11.3530	−	7.29616i	−0.991920	−	0.637468i	−0.932653	+	0.360774i	$0.882513\pi$
$132$	4.85241	−	1.42480i	0.422348	−	0.124013i
$133$	−1.16051	−	1.33930i	−0.100629	−	0.116132i
$134$	13.9082	+	4.08382i	1.20149	+	0.352789i
$135$	0.361524	+	0.791628i	0.0311151	+	0.0681325i
$136$	0.909240	−	6.32391i	0.0779667	−	0.542270i
$137$	−20.4747			−1.74927			−0.874634	−	0.484784i	$-0.838898\pi$
$137$	−20.4747			−1.74927			−0.874634	+	0.484784i	$0.838898\pi$
$138$	−0.0397827	+	4.79567i	−0.00338653	+	0.408234i
$139$	1.60396			0.136046			0.0680231	−	0.997684i	$-0.478331\pi$
$139$	1.60396			0.136046			0.0680231	+	0.997684i	$0.478331\pi$
$140$	0.123853	−	0.861414i	0.0104675	−	0.0728028i
$141$	0.626958	+	1.37285i	0.0527994	+	0.115615i
$142$	−6.11044	−	1.79419i	−0.512777	−	0.150565i
$143$	6.55756	+	7.56783i	0.548371	+	0.632854i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	0.438692	+	0.281930i	0.0364314	+	0.0234130i
$146$	−5.79097	+	12.6805i	−0.479264	+	1.04944i
$147$	0.654861	−	0.755750i	0.0540120	−	0.0623332i
$148$	−5.13164	+	3.29790i	−0.421818	+	0.271086i
$149$	1.92460	+	13.3859i	0.157669	+	1.09661i	0.902913	+	0.429822i	$0.141424\pi$
$149$	1.92460	+	13.3859i	0.157669	+	1.09661i	−0.745244	+	0.666792i	$0.767667\pi$
$150$	−0.603789	−	4.19944i	−0.0492991	−	0.342883i
$151$	−17.9826	+	11.5567i	−1.46340	+	0.940470i	−0.464920	+	0.885352i	$0.653917\pi$
$151$	−17.9826	+	11.5567i	−1.46340	+	0.940470i	−0.998480	+	0.0551178i	$0.982447\pi$
$152$	−1.16051	+	1.33930i	−0.0941297	+	0.108631i
$153$	−2.65406	+	5.81158i	−0.214568	+	0.469838i
$154$	4.25445	+	2.73417i	0.342833	+	0.220325i
$155$	6.23247	−	1.83002i	0.500604	−	0.146991i
$156$	−1.29666	−	1.49643i	−0.103816	−	0.119810i
$157$	−16.2306	−	4.76572i	−1.29534	−	0.380346i	−0.439806	−	0.898093i	$-0.644953\pi$
$157$	−16.2306	−	4.76572i	−1.29534	−	0.380346i	−0.855534	+	0.517747i	$0.826771\pi$
$158$	3.63439	+	7.95821i	0.289137	+	0.633121i
$159$	1.83560	−	12.7669i	0.145573	−	1.01248i
$160$	−0.870273			−0.0688011
$161$	−3.65038	+	3.11043i	−0.287690	+	0.245136i
$162$	1.00000			0.0785674
$163$	−1.09752	+	7.63345i	−0.0859647	+	0.597898i	0.900615	+	0.434618i	$0.143116\pi$
$163$	−1.09752	+	7.63345i	−0.0859647	+	0.597898i	−0.986580	+	0.163280i	$0.947793\pi$
$164$	0.0822268	+	0.180051i	0.00642083	+	0.0140597i
$165$	−4.22292	−	1.23996i	−0.328754	−	0.0965309i
$166$	8.19165	+	9.45367i	0.635795	+	0.733747i
$167$	12.8826	−	3.78268i	0.996888	−	0.292713i	0.257710	−	0.966222i	$-0.417032\pi$
$167$	12.8826	−	3.78268i	0.996888	−	0.292713i	0.739178	+	0.673510i	$0.235214\pi$
$168$	−0.841254	−	0.540641i	−0.0649041	−	0.0417113i
$169$	−3.77171	+	8.25889i	−0.290132	+	0.635300i
$170$	−3.64110	+	4.20206i	−0.279260	+	0.322283i
$171$	1.49082	−	0.958094i	0.114006	−	0.0732673i
$172$	0.770249	+	5.35720i	0.0587309	+	0.408483i
$173$	0.562972	+	3.91555i	0.0428019	+	0.297694i	0.999967	+	0.00815046i	$0.00259440\pi$
$173$	0.562972	+	3.91555i	0.0428019	+	0.297694i	−0.957165	+	0.289544i	$0.906497\pi$
$174$	0.504086	−	0.323956i	0.0382147	−	0.0245591i
$175$	2.77833	−	3.20636i	0.210022	−	0.242378i
$176$	2.10087	−	4.60025i	0.158359	−	0.346757i
$177$	3.92418	+	2.52192i	0.294960	+	0.189559i
$178$	4.54919	−	1.33576i	0.340976	−	0.100120i
$179$	−10.4944	−	12.1112i	−0.784387	−	0.905231i	0.213031	−	0.977045i	$-0.431667\pi$
$179$	−10.4944	−	12.1112i	−0.784387	−	0.905231i	−0.997418	+	0.0718144i	$0.977121\pi$
$180$	0.835020	+	0.245184i	0.0622387	+	0.0182749i
$181$	−1.70338	−	3.72988i	−0.126611	−	0.277240i	0.835702	−	0.549183i	$-0.185061\pi$
$181$	−1.70338	−	3.72988i	−0.126611	−	0.277240i	−0.962313	+	0.271943i	$0.912334\pi$
$182$	0.281791	−	1.95990i	0.0208878	−	0.145278i
$183$	−9.31801			−0.688807
$184$	3.59827	+	3.17056i	0.265268	+	0.233737i
$185$	5.30865			0.390300
$186$	1.06222	−	7.38788i	0.0778855	−	0.541706i
$187$	−13.4223	−	29.3907i	−0.981536	−	2.14926i
$188$	1.44810	+	0.425200i	0.105613	+	0.0310109i
$189$	0.654861	+	0.755750i	0.0476341	+	0.0549727i
$190$	1.47978	−	0.434502i	0.107354	−	0.0315221i
$191$	16.8853	+	10.8515i	1.22178	+	0.785188i	0.982590	−	0.185785i	$-0.0594828\pi$
$191$	16.8853	+	10.8515i	1.22178	+	0.785188i	0.239187	+	0.970974i	$0.423119\pi$
$192$	−0.415415	+	0.909632i	−0.0299800	+	0.0656470i
$193$	−7.88597	+	9.10089i	−0.567644	+	0.655097i	−0.964902	−	0.262611i	$-0.915417\pi$
$193$	−7.88597	+	9.10089i	−0.567644	+	0.655097i	0.397257	+	0.917707i	$0.369962\pi$
$194$	−2.50123	+	1.60744i	−0.179578	+	0.115408i
$195$	0.245235	+	1.70565i	0.0175617	+	0.122144i
$196$	−0.142315	−	0.989821i	−0.0101653	−	0.0707015i
$197$	−8.45193	+	5.43173i	−0.602175	+	0.386995i	−0.805916	−	0.592030i	$-0.798327\pi$
$197$	−8.45193	+	5.43173i	−0.602175	+	0.386995i	0.203740	+	0.979025i	$0.434690\pi$
$198$	−3.31181	+	3.82203i	−0.235360	+	0.271620i
$199$	8.26591	−	18.0998i	0.585954	−	1.28306i	−0.351902	−	0.936037i	$-0.614465\pi$
$199$	8.26591	−	18.0998i	0.585954	−	1.28306i	0.937856	−	0.347024i	$-0.112808\pi$
$200$	−3.56912	−	2.29374i	−0.252375	−	0.162192i
$201$	−13.9082	+	4.08382i	−0.981010	+	0.288051i
$202$	3.10627	+	3.58483i	0.218556	+	0.252227i
$203$	0.574936	+	0.168816i	0.0403526	+	0.0118486i
$204$	2.65406	+	5.81158i	0.185821	+	0.406892i
$205$	0.0245153	−	0.170507i	0.00171222	−	0.0119088i
$206$	−1.17663			−0.0819799
$207$	−2.55927	−	4.05588i	−0.177881	−	0.281903i
$208$	−1.98006			−0.137292
$209$	−1.27546	+	8.87100i	−0.0882252	+	0.613620i
$210$	0.361524	+	0.791628i	0.0249475	+	0.0546275i
$211$	−6.02993	−	1.77055i	−0.415117	−	0.121889i	0.0675030	−	0.997719i	$-0.478497\pi$
$211$	−6.02993	−	1.77055i	−0.415117	−	0.121889i	−0.482621	+	0.875830i	$0.660315\pi$
$212$	−8.44652	−	9.74780i	−0.580109	−	0.669482i
$213$	6.11044	−	1.79419i	0.418680	−	0.122936i
$214$	−13.7231	−	8.81933i	−0.938094	−	0.602877i
$215$	1.95667	−	4.28452i	0.133444	−	0.292202i
$216$	0.654861	−	0.755750i	0.0445576	−	0.0514222i
$217$	6.27899	−	4.03526i	0.426246	−	0.273932i
$218$	−1.00641	−	6.99972i	−0.0681625	−	0.474081i
$219$	−1.98390	−	13.7983i	−0.134059	−	0.932404i
$220$	−3.70253	+	2.37947i	−0.249624	+	0.160424i
$221$	−8.28428	+	9.56057i	−0.557261	+	0.643114i
$222$	2.53403	−	5.54874i	0.170073	−	0.372407i
$223$	−10.8917	−	6.99965i	−0.729360	−	0.468731i	0.122521	−	0.992466i	$-0.460902\pi$
$223$	−10.8917	−	6.99965i	−0.729360	−	0.468731i	−0.851882	+	0.523735i	$0.824538\pi$
$224$	−0.959493	+	0.281733i	−0.0641088	+	0.0188240i
$225$	2.77833	+	3.20636i	0.185222	+	0.213757i
$226$	−8.39269	−	2.46431i	−0.558273	−	0.163924i
$227$	7.50771	+	16.4396i	0.498304	+	1.09113i	0.977017	+	0.213163i	$0.0683764\pi$
$227$	7.50771	+	16.4396i	0.498304	+	1.09113i	−0.478712	+	0.877972i	$0.658896\pi$
$228$	0.252203	−	1.75411i	0.0167025	−	0.116169i
$229$	−4.43826			−0.293289			−0.146644	−	0.989189i	$-0.546847\pi$
$229$	−4.43826			−0.293289			−0.146644	+	0.989189i	$0.546847\pi$
$230$	−1.14260	−	4.01423i	−0.0753409	−	0.264691i
$231$	−5.05727			−0.332744
$232$	0.0852762	−	0.593109i	0.00559866	−	0.0389395i
$233$	−1.68955	−	3.69961i	−0.110686	−	0.242369i	0.846180	−	0.532897i	$-0.178897\pi$
$233$	−1.68955	−	3.69961i	−0.110686	−	0.242369i	−0.956867	+	0.290527i	$0.906169\pi$
$234$	1.89985	+	0.557846i	0.124197	+	0.0364675i
$235$	−0.860123	−	0.992635i	−0.0561082	−	0.0647524i
$236$	4.47573	−	1.31419i	0.291345	−	0.0855467i
$237$	−7.35998	−	4.72997i	−0.478082	−	0.307245i
$238$	−2.65406	+	5.81158i	−0.172037	+	0.376709i
$239$	−0.440960	+	0.508895i	−0.0285233	+	0.0329177i	−0.769832	−	0.638247i	$-0.779660\pi$
$239$	−0.440960	+	0.508895i	−0.0285233	+	0.0329177i	0.741309	+	0.671164i	$0.234205\pi$
$240$	0.732120	−	0.470505i	0.0472581	−	0.0303710i
$241$	3.31014	+	23.0225i	0.213225	+	1.48301i	0.762292	+	0.647233i	$0.224074\pi$
$241$	3.31014	+	23.0225i	0.213225	+	1.48301i	−0.549067	+	0.835778i	$0.685017\pi$
$242$	−2.07438	−	14.4276i	−0.133346	−	0.927442i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	−6.10200	+	7.04208i	−0.390640	+	0.450823i
$245$	−0.361524	+	0.791628i	−0.0230969	+	0.0505752i
$246$	−0.166517	−	0.107014i	−0.0106167	−	0.00682295i
$247$	3.36681	−	0.988585i	0.214225	−	0.0629021i
$248$	−4.88779	−	5.64081i	−0.310375	−	0.358191i
$249$	−12.0023	−	3.52419i	−0.760614	−	0.223337i
$250$	3.34143	+	7.31672i	0.211331	+	0.462750i
$251$	1.36394	−	9.48643i	0.0860913	−	0.598778i	−0.900412	−	0.435038i	$-0.856735\pi$
$251$	1.36394	−	9.48643i	0.0860913	−	0.598778i	0.986503	−	0.163740i	$-0.0523560\pi$
$252$	1.00000			0.0629941
$253$	23.9775	+	3.65070i	1.50745	+	0.229518i
$254$	1.78741			0.112152
$255$	0.791287	−	5.50352i	0.0495523	−	0.344644i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	6.83545	+	2.00707i	0.426383	+	0.125197i	0.487882	−	0.872910i	$-0.337770\pi$
$257$	6.83545	+	2.00707i	0.426383	+	0.125197i	−0.0614983	+	0.998107i	$0.519588\pi$
$258$	−3.54430	−	4.09033i	−0.220658	−	0.254653i
$259$	5.85289	−	1.71856i	0.363681	−	0.106786i
$260$	1.44964	+	0.931626i	0.0899027	+	0.0577770i
$261$	−0.248920	+	0.545059i	−0.0154078	+	0.0337383i
$262$	8.83760	−	10.1991i	0.545989	−	0.630105i
$263$	−1.89811	+	1.21984i	−0.117042	+	0.0752186i	−0.597852	−	0.801606i	$-0.703979\pi$
$263$	−1.89811	+	1.21984i	−0.117042	+	0.0752186i	0.480810	+	0.876825i	$0.340343\pi$
$264$	0.719724	+	5.00579i	0.0442960	+	0.308085i
$265$	1.59748	+	11.1107i	0.0981322	+	0.682524i
$266$	1.49082	−	0.958094i	0.0914083	−	0.0587445i
$267$	−3.10485	+	3.58319i	−0.190014	+	0.219288i
$268$	−6.02160	+	13.1855i	−0.367828	+	0.805431i
$269$	13.6096	+	8.74638i	0.829794	+	0.533276i	0.885212	−	0.465187i	$-0.154013\pi$
$269$	13.6096	+	8.74638i	0.829794	+	0.533276i	−0.0554184	+	0.998463i	$0.517649\pi$
$270$	−0.835020	+	0.245184i	−0.0508177	+	0.0149214i
$271$	20.2712	+	23.3943i	1.23139	+	1.42110i	0.873136	+	0.487476i	$0.162082\pi$
$271$	20.2712	+	23.3943i	1.23139	+	1.42110i	0.358254	+	0.933624i	$0.383372\pi$
$272$	6.13014	+	1.79997i	0.371694	+	0.109139i
$273$	0.822545	+	1.80112i	0.0497827	+	0.109009i
$274$	2.91385	−	20.2663i	0.176032	−	1.22433i
$275$	−21.4561			−1.29385
$276$	−4.74119	−	0.721872i	−0.285386	−	0.0434516i
$277$	−1.50175			−0.0902313			−0.0451156	−	0.998982i	$-0.514366\pi$
$277$	−1.50175			−0.0902313			−0.0451156	+	0.998982i	$0.514366\pi$
$278$	−0.228267	+	1.58764i	−0.0136906	+	0.0952200i
$279$	3.10060	+	6.78936i	0.185628	+	0.406468i
$280$	0.835020	+	0.245184i	0.0499020	+	0.0146526i
$281$	−8.57065	−	9.89106i	−0.511282	−	0.590051i	0.440144	−	0.897927i	$-0.354927\pi$
$281$	−8.57065	−	9.89106i	−0.511282	−	0.590051i	−0.951427	+	0.307876i	$0.900382\pi$
$282$	−1.44810	+	0.425200i	−0.0862330	+	0.0253203i
$283$	−19.5458	−	12.5613i	−1.16188	−	0.746693i	−0.189908	−	0.981802i	$-0.560819\pi$
$283$	−19.5458	−	12.5613i	−1.16188	−	0.746693i	−0.971969	+	0.235109i	$0.924455\pi$
$284$	2.64553	−	5.79290i	0.156983	−	0.343746i
$285$	−1.00996	+	1.16555i	−0.0598248	+	0.0690415i
$286$	−8.42404	+	5.41380i	−0.498124	+	0.320125i
$287$	−0.0281696	−	0.195924i	−0.00166280	−	0.0115650i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	20.0374	−	12.8773i	1.17867	−	0.757486i
$290$	−0.341493	+	0.394104i	−0.0200532	+	0.0231426i
$291$	1.23512	−	2.70454i	0.0724040	−	0.158543i
$292$	−11.7272	−	7.53665i	−0.686285	−	0.441049i
$293$	−16.9450	+	4.97551i	−0.989940	+	0.290673i	−0.736322	−	0.676632i	$-0.763439\pi$
$293$	−16.9450	+	4.97551i	−0.989940	+	0.290673i	−0.253618	+	0.967304i	$0.581621\pi$
$294$	0.654861	+	0.755750i	0.0381923	+	0.0440762i
$295$	−3.89511	−	1.14371i	−0.226782	−	0.0665892i
$296$	−2.53403	−	5.54874i	−0.147287	−	0.322514i
$297$	0.719724	−	5.00579i	0.0417626	−	0.290466i
$298$	−13.5235			−0.783397
$299$	−2.59966	−	9.13324i	−0.150342	−	0.528189i
$300$	4.24263			0.244948
$301$	0.770249	−	5.35720i	0.0443964	−	0.308784i
$302$	−8.87988	−	19.4442i	−0.510979	−	1.11889i
$303$	−4.55126	−	1.33637i	−0.261463	−	0.0767725i
$304$	−1.16051	−	1.33930i	−0.0665597	−	0.0768140i
$305$	7.78073	−	2.28463i	0.445523	−	0.130817i
$306$	−5.37472	−	3.45412i	−0.307252	−	0.197459i
$307$	5.25386	−	11.5044i	0.299854	−	0.656588i	−0.698397	−	0.715711i	$-0.746103\pi$
$307$	5.25386	−	11.5044i	0.299854	−	0.656588i	0.998251	+	0.0591225i	$0.0188303\pi$
$308$	−3.31181	+	3.82203i	−0.188708	+	0.217780i
$309$	0.989847	−	0.636136i	0.0563104	−	0.0361885i
$310$	0.924419	+	6.42947i	0.0525034	+	0.365170i
$311$	1.02319	+	7.11646i	0.0580199	+	0.403537i	0.998049	+	0.0624420i	$0.0198888\pi$
$311$	1.02319	+	7.11646i	0.0580199	+	0.403537i	−0.940029	+	0.341095i	$0.889202\pi$
$312$	1.66573	−	1.07050i	0.0943033	−	0.0606051i
$313$	−0.697522	+	0.804984i	−0.0394263	+	0.0455004i	−0.775120	−	0.631814i	$-0.782311\pi$
$313$	−0.697522	+	0.804984i	−0.0394263	+	0.0455004i	0.735694	+	0.677314i	$0.236856\pi$
$314$	7.02706	−	15.3871i	0.396560	−	0.868345i
$315$	−0.732120	−	0.470505i	−0.0412503	−	0.0265099i
$316$	−8.39444	+	2.46483i	−0.472224	+	0.138657i
$317$	12.6006	+	14.5418i	0.707719	+	0.816751i	0.989774	−	0.142647i	$-0.0455613\pi$
$317$	12.6006	+	14.5418i	0.707719	+	0.816751i	−0.282054	+	0.959398i	$0.591016\pi$
$318$	12.3757	+	3.63384i	0.693996	+	0.203776i
$319$	−1.25886	−	2.75651i	−0.0704824	−	0.154335i
$320$	0.123853	−	0.861414i	0.00692358	−	0.0481545i
$321$	16.3127			0.910488
$322$	−2.55927	−	4.05588i	−0.142622	−	0.226025i
$323$	−11.3221			−0.629980
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	3.48975	+	7.64149i	0.193576	+	0.423873i
$326$	−7.39956	−	2.17271i	−0.409823	−	0.120335i
$327$	4.63098	+	5.34443i	0.256094	+	0.295548i
$328$	−0.189921	+	0.0557658i	−0.0104866	+	0.00307915i
$329$	−1.26965	−	0.815953i	−0.0699980	−	0.0449850i
$330$	1.82833	−	4.00347i	0.100646	−	0.220384i
$331$	−4.41468	+	5.09481i	−0.242653	+	0.280036i	−0.863992	−	0.503505i	$-0.832043\pi$
$331$	−4.41468	+	5.09481i	−0.242653	+	0.280036i	0.621339	+	0.783542i	$0.286589\pi$
$332$	−10.5232	+	6.76287i	−0.577538	+	0.371161i
$333$	0.868119	+	6.03790i	0.0475726	+	0.330875i
$334$	1.91079	+	13.2898i	0.104554	+	0.727187i
$335$	10.6124	−	6.82015i	0.579815	−	0.372625i
$336$	0.654861	−	0.755750i	0.0357256	−	0.0412295i
$337$	9.46780	−	20.7316i	0.515744	−	1.12932i	−0.455282	−	0.890347i	$-0.650461\pi$
$337$	9.46780	−	20.7316i	0.515744	−	1.12932i	0.971026	−	0.238975i	$-0.0768113\pi$
$338$	−7.63806	−	4.90868i	−0.415456	−	0.266997i
$339$	8.39269	−	2.46431i	0.455828	−	0.133843i
$340$	−3.64110	−	4.20206i	−0.197466	−	0.227888i
$341$	−36.2177	−	10.6345i	−1.96130	−	0.575889i
$342$	0.736176	+	1.61200i	0.0398078	+	0.0871670i
$343$	−0.142315	+	0.989821i	−0.00768428	+	0.0534453i
$344$	−5.41229			−0.291811
$345$	3.13148	+	2.75925i	0.168593	+	0.148553i
$346$	−3.95582			−0.212666
$347$	3.27793	−	22.7985i	0.175969	−	1.22389i	−0.690007	−	0.723802i	$-0.742393\pi$
$347$	3.27793	−	22.7985i	0.175969	−	1.22389i	0.865976	−	0.500086i	$-0.166698\pi$
$348$	0.248920	+	0.545059i	0.0133435	+	0.0292182i
$349$	23.0508	+	6.76833i	1.23388	+	0.362300i	0.832714	−	0.553704i	$-0.186786\pi$
$349$	23.0508	+	6.76833i	1.23388	+	0.362300i	0.401168	+	0.916004i	$0.368604\pi$
$350$	2.77833	+	3.20636i	0.148508	+	0.171387i
$351$	−1.89985	+	0.557846i	−0.101406	+	0.0297756i
$352$	4.25445	+	2.73417i	0.226763	+	0.145732i
$353$	−0.748430	+	1.63883i	−0.0398349	+	0.0872262i	−0.928503	−	0.371324i	$-0.878904\pi$
$353$	−0.748430	+	1.63883i	−0.0398349	+	0.0872262i	0.888668	+	0.458550i	$0.151631\pi$
$354$	−3.05472	+	3.52533i	−0.162356	+	0.187369i
$355$	−4.66244	+	2.99637i	−0.247456	+	0.159031i
$356$	0.674749	+	4.69298i	0.0357616	+	0.248727i
$357$	−0.909240	−	6.32391i	−0.0481221	−	0.334697i
$358$	13.4814	−	8.66397i	0.712514	−	0.457905i
$359$	−17.2561	+	19.9146i	−0.910744	+	1.05105i	0.0877473	+	0.996143i	$0.472033\pi$
$359$	−17.2561	+	19.9146i	−0.910744	+	1.05105i	−0.998491	+	0.0549117i	$0.982512\pi$
$360$	−0.361524	+	0.791628i	−0.0190540	+	0.0417224i
$361$	−13.3419	−	8.57429i	−0.702203	−	0.451279i
$362$	3.93433	−	1.15522i	0.206784	−	0.0607172i
$363$	9.54523	+	11.0158i	0.500995	+	0.578179i
$364$	1.89985	+	0.557846i	0.0995792	+	0.0292391i
$365$	5.03972	+	11.0355i	0.263791	+	0.577622i
$366$	1.32609	−	9.22317i	0.0693159	−	0.482103i
$367$	−25.6914			−1.34108			−0.670540	−	0.741874i	$-0.733937\pi$
$367$	−25.6914			−1.34108			−0.670540	+	0.741874i	$0.733937\pi$
$368$	−3.65038	+	3.11043i	−0.190289	+	0.162142i
$369$	0.197939			0.0103043
$370$	−0.755500	+	5.25462i	−0.0392766	+	0.273175i
$371$	5.35810	+	11.7326i	0.278179	+	0.609127i
$372$	7.16152	+	2.10281i	0.371307	+	0.109026i
$373$	−16.3986	−	18.9250i	−0.849086	−	0.979898i	0.150876	−	0.988553i	$-0.451791\pi$
$373$	−16.3986	−	18.9250i	−0.849086	−	0.979898i	−0.999963	+	0.00865465i	$0.997245\pi$
$374$	31.0018	−	9.10294i	1.60306	−	0.470702i
$375$	−6.76671	−	4.34870i	−0.349431	−	0.224566i
$376$	−0.626958	+	1.37285i	−0.0323329	+	0.0707992i
$377$	−0.776969	+	0.896671i	−0.0400160	+	0.0461809i
$378$	−0.841254	+	0.540641i	−0.0432694	+	0.0278076i
$379$	2.25013	+	15.6500i	0.115581	+	0.803885i	0.962328	+	0.271889i	$0.0876485\pi$
$379$	2.25013	+	15.6500i	0.115581	+	0.803885i	−0.846747	+	0.531995i	$0.821442\pi$
$380$	0.219485	+	1.52655i	0.0112593	+	0.0783105i
$381$	−1.50367	+	0.966347i	−0.0770351	+	0.0495075i
$382$	−13.1441	+	15.1691i	−0.672510	+	0.776118i
$383$	16.0692	−	35.1867i	0.821100	−	1.79796i	0.271744	−	0.962370i	$-0.412400\pi$
$383$	16.0692	−	35.1867i	0.821100	−	1.79796i	0.549356	−	0.835589i	$-0.314873\pi$
$384$	−0.841254	−	0.540641i	−0.0429300	−	0.0275895i
$385$	4.22292	−	1.23996i	0.215220	−	0.0631943i
$386$	−7.88597	−	9.10089i	−0.401385	−	0.463223i
$387$	5.19305	+	1.52482i	0.263978	+	0.0775108i
$388$	−1.23512	−	2.70454i	−0.0627037	−	0.137302i
$389$	−5.49979	+	38.2519i	−0.278850	+	1.93945i	0.0590263	+	0.998256i	$0.481200\pi$
$389$	−5.49979	+	38.2519i	−0.278850	+	1.93945i	−0.337877	+	0.941190i	$0.609709\pi$
$390$	−1.72319			−0.0872570
$391$	−0.254169	+	30.6392i	−0.0128539	+	1.54949i
$392$	1.00000			0.0505076
$393$	−1.92059	+	13.3580i	−0.0968812	+	0.673823i
$394$	−4.17360	−	9.13892i	−0.210263	−	0.460412i
$395$	7.30545	+	2.14507i	0.367577	+	0.107930i
$396$	−3.31181	−	3.82203i	−0.166425	−	0.192064i
$397$	−5.77673	+	1.69620i	−0.289926	+	0.0851299i	−0.423461	−	0.905914i	$-0.639185\pi$
$397$	−5.77673	+	1.69620i	−0.289926	+	0.0851299i	0.133536	+	0.991044i	$0.457367\pi$
$398$	16.7392	+	10.7576i	0.839061	+	0.539232i
$399$	−0.736176	+	1.61200i	−0.0368549	+	0.0807010i
$400$	2.77833	−	3.20636i	0.138916	−	0.160318i
$401$	20.8415	−	13.3940i	1.04078	−	0.668866i	0.0955976	−	0.995420i	$-0.469524\pi$
$401$	20.8415	−	13.3940i	1.04078	−	0.668866i	0.945179	+	0.326554i	$0.105887\pi$
$402$	−2.06291	−	14.3478i	−0.102889	−	0.715605i
$403$	2.10325	+	14.6284i	0.104770	+	0.728693i
$404$	−3.99041	+	2.56448i	−0.198530	+	0.127588i
$405$	0.569907	−	0.657708i	0.0283189	−	0.0326818i
$406$	−0.248920	+	0.545059i	−0.0123537	+	0.0270508i
$407$	−25.9521	−	16.6784i	−1.28640	−	0.826716i
$408$	−6.13014	+	1.79997i	−0.303487	+	0.0891119i
$409$	9.50951	+	10.9746i	0.470215	+	0.542657i	0.940471	−	0.339873i	$-0.110384\pi$
$409$	9.50951	+	10.9746i	0.470215	+	0.542657i	−0.470256	+	0.882530i	$0.655839\pi$
$410$	0.165283	+	0.0485315i	0.00816274	+	0.00239680i
$411$	8.50548	+	18.6244i	0.419544	+	0.918674i
$412$	0.167452	−	1.16466i	0.00824979	−	0.0573785i
$413$	−4.66468			−0.229534
$414$	4.37882	−	1.95600i	0.215207	−	0.0961324i
$415$	10.8862			0.534384
$416$	0.281791	−	1.95990i	0.0138160	−	0.0960921i
$417$	−0.666310	−	1.45901i	−0.0326293	−	0.0714482i
$418$	−8.59919	−	2.52495i	−0.420600	−	0.123499i
$419$	21.9017	+	25.2759i	1.06997	+	1.23481i	0.970839	+	0.239732i	$0.0770597\pi$
$419$	21.9017	+	25.2759i	1.06997	+	1.23481i	0.0991274	+	0.995075i	$0.468395\pi$
$420$	−0.835020	+	0.245184i	−0.0407448	+	0.0119638i
$421$	33.4198	+	21.4776i	1.62878	+	1.04675i	0.949922	+	0.312486i	$0.101162\pi$
$421$	33.4198	+	21.4776i	1.62878	+	1.04675i	0.678859	+	0.734269i	$0.262475\pi$
$422$	2.61067	−	5.71658i	0.127086	−	0.278279i
$423$	0.988338	−	1.14060i	0.0480546	−	0.0554580i
$424$	10.8506	−	6.97329i	0.526954	−	0.338653i
$425$	−3.85757	−	26.8300i	−0.187119	−	1.30144i
$426$	0.906318	+	6.30358i	0.0439113	+	0.305410i
$427$	7.83881	−	5.03770i	0.379347	−	0.243791i
$428$	10.6826	−	12.3283i	0.516361	−	0.595913i
$429$	4.15983	−	9.10876i	0.200839	−	0.439775i
$430$	3.96244	+	2.54651i	0.191086	+	0.122804i
$431$	−14.5320	+	4.26697i	−0.699980	+	0.205533i	−0.612311	−	0.790617i	$-0.709760\pi$
$431$	−14.5320	+	4.26697i	−0.699980	+	0.205533i	−0.0876693	+	0.996150i	$0.527942\pi$
$432$	0.654861	+	0.755750i	0.0315070	+	0.0363610i
$433$	32.1230	+	9.43216i	1.54373	+	0.453281i	0.939220	−	0.343315i	$-0.111550\pi$
$433$	32.1230	+	9.43216i	1.54373	+	0.453281i	0.604513	+	0.796596i	$0.293368\pi$
$434$	3.10060	+	6.78936i	0.148833	+	0.325900i
$435$	0.0742135	−	0.516167i	0.00355827	−	0.0247483i
$436$	7.07170			0.338673
$437$	4.65401	−	7.11138i	0.222632	−	0.340183i
$438$	13.9402			0.666089
$439$	−1.38301	+	9.61902i	−0.0660073	+	0.459091i	0.929833	+	0.367981i	$0.119951\pi$
$439$	−1.38301	+	9.61902i	−0.0660073	+	0.459091i	−0.995841	+	0.0911104i	$0.970958\pi$
$440$	−1.82833	−	4.00347i	−0.0871620	−	0.190858i
$441$	−0.959493	−	0.281733i	−0.0456901	−	0.0134158i
$442$	−8.28428	−	9.56057i	−0.394043	−	0.454750i
$443$	19.0435	−	5.59166i	0.904782	−	0.265668i	0.203939	−	0.978984i	$-0.434626\pi$
$443$	19.0435	−	5.59166i	0.904782	−	0.265668i	0.700843	+	0.713316i	$0.252807\pi$
$444$	5.13164	+	3.29790i	0.243537	+	0.156512i
$445$	1.71407	−	3.75330i	0.0812549	−	0.177923i
$446$	8.47845	−	9.78465i	0.401466	−	0.463317i
$447$	11.3767	−	7.31137i	0.538100	−	0.345816i
$448$	−0.142315	−	0.989821i	−0.00672374	−	0.0467647i
$449$	4.40017	+	30.6038i	0.207657	+	1.44428i	0.780775	+	0.624812i	$0.214824\pi$
$449$	4.40017	+	30.6038i	0.207657	+	1.44428i	−0.573119	+	0.819472i	$0.694267\pi$
$450$	−3.56912	+	2.29374i	−0.168250	+	0.108128i
$451$	−0.655535	+	0.756528i	−0.0308679	+	0.0356235i
$452$	3.63364	−	7.95655i	0.170912	−	0.374245i
$453$	17.9826	+	11.5567i	0.844895	+	0.542981i
$454$	−17.3407	+	5.09170i	−0.813840	+	0.238965i
$455$	−1.12845	−	1.30230i	−0.0529025	−	0.0610527i
$456$	1.70036	+	0.499271i	0.0796267	+	0.0233805i
$457$	8.40581	+	18.4062i	0.393207	+	0.861004i	0.997914	+	0.0645556i	$0.0205630\pi$
$457$	8.40581	+	18.4062i	0.393207	+	0.861004i	−0.604707	+	0.796448i	$0.706710\pi$
$458$	0.631631	−	4.39309i	0.0295142	−	0.205276i
$459$	6.38894			0.298210
$460$	4.13598	−	0.559687i	0.192841	−	0.0260955i
$461$	0.864099			0.0402451			0.0201225	−	0.999798i	$-0.493594\pi$
$461$	0.864099			0.0402451			0.0201225	+	0.999798i	$0.493594\pi$
$462$	0.719724	−	5.00579i	0.0334846	−	0.232891i
$463$	7.04403	+	15.4243i	0.327364	+	0.716827i	0.999726	−	0.0233951i	$-0.00744757\pi$
$463$	7.04403	+	15.4243i	0.327364	+	0.716827i	−0.672362	+	0.740222i	$0.734720\pi$
$464$	0.574936	+	0.168816i	0.0266907	+	0.00783711i
$465$	−4.25371	−	4.90904i	−0.197261	−	0.227651i
$466$	3.90240	−	1.14585i	0.180775	−	0.0530804i
$467$	−5.79273	−	3.72276i	−0.268056	−	0.172269i	0.399707	−	0.916643i	$-0.369112\pi$
$467$	−5.79273	−	3.72276i	−0.268056	−	0.172269i	−0.667763	+	0.744374i	$0.732748\pi$
$468$	−0.822545	+	1.80112i	−0.0380221	+	0.0832569i
$469$	9.49246	−	10.9549i	0.438321	−	0.505849i
$470$	1.10494	−	0.710102i	0.0509671	−	0.0327545i
$471$	2.40736	+	16.7436i	0.110925	+	0.771504i
$472$	0.663854	+	4.61720i	0.0305563	+	0.212524i
$473$	−23.0263	+	14.7981i	−1.05875	+	0.680417i
$474$	5.72926	−	6.61192i	0.263154	−	0.303696i
$475$	−3.12332	+	6.83912i	−0.143308	+	0.313800i
$476$	−5.37472	−	3.45412i	−0.246350	−	0.158319i
$477$	−12.3757	+	3.63384i	−0.566645	+	0.166382i
$478$	−0.440960	−	0.508895i	−0.0201690	−	0.0232763i
$479$	24.1386	+	7.08772i	1.10292	+	0.323846i	0.782011	−	0.623264i	$-0.214194\pi$
$479$	24.1386	+	7.08772i	1.10292	+	0.323846i	0.320908	+	0.947110i	$0.396012\pi$
$480$	0.361524	+	0.791628i	0.0165013	+	0.0361327i
$481$	−1.71892	+	11.9554i	−0.0783761	+	0.545118i
$482$	−23.2593			−1.05943
$483$	4.34577	+	2.02838i	0.197739	+	0.0922945i
$484$	14.5760			0.662544
$485$	−0.368241	+	2.56117i	−0.0167210	+	0.116297i
$486$	−0.415415	−	0.909632i	−0.0188436	−	0.0412617i
$487$	12.5334	+	3.68012i	0.567941	+	0.166762i	0.553081	−	0.833127i	$-0.313452\pi$
$487$	12.5334	+	3.68012i	0.567941	+	0.166762i	0.0148591	+	0.999890i	$0.495270\pi$
$488$	−6.10200	−	7.04208i	−0.276225	−	0.318780i
$489$	7.39956	−	2.17271i	0.334619	−	0.0982531i
$490$	−0.732120	−	0.470505i	−0.0330738	−	0.0212552i
$491$	15.4981	−	33.9360i	0.699418	−	1.53151i	−0.141259	−	0.989973i	$-0.545115\pi$
$491$	15.4981	−	33.9360i	0.699418	−	1.53151i	0.840676	−	0.541538i	$-0.182158\pi$
$492$	0.129622	−	0.149592i	0.00584383	−	0.00674414i
$493$	3.22057	−	2.06974i	0.145047	−	0.0932162i
$494$	0.499375	+	3.47323i	0.0224680	+	0.156268i
$495$	0.626356	+	4.35640i	0.0281526	+	0.195806i
$496$	6.27899	−	4.03526i	0.281935	−	0.181189i
$497$	−4.17042	+	4.81292i	−0.187069	+	0.215889i
$498$	5.19642	−	11.3786i	0.232857	−	0.509886i
$499$	−20.7739	−	13.3506i	−0.929966	−	0.597653i	−0.0144332	−	0.999896i	$-0.504594\pi$
$499$	−20.7739	−	13.3506i	−0.929966	−	0.597653i	−0.915533	+	0.402243i	$0.868231\pi$
$500$	−7.71778	+	2.26615i	−0.345150	+	0.101345i
$501$	−8.79249	−	10.1471i	−0.392819	−	0.453338i
$502$	9.19577	+	2.70012i	0.410427	+	0.120512i
$503$	−9.46892	−	20.7340i	−0.422198	−	0.924485i	−0.994529	−	0.104462i	$-0.966688\pi$
$503$	−9.46892	−	20.7340i	−0.422198	−	0.924485i	0.572331	−	0.820023i	$-0.306039\pi$
$504$	−0.142315	+	0.989821i	−0.00633921	+	0.0440902i
$505$	4.12805			0.183696
$506$	−7.02590	+	23.2139i	−0.312339	+	1.03198i
$507$	9.07938			0.403229
$508$	−0.254375	+	1.76922i	−0.0112861	+	0.0784963i
$509$	−12.7088	−	27.8284i	−0.563308	−	1.23347i	−0.950284	−	0.311383i	$-0.899208\pi$
$509$	−12.7088	−	27.8284i	−0.563308	−	1.23347i	0.386976	−	0.922090i	$-0.373520\pi$
$510$	5.33489	+	1.56647i	0.236233	+	0.0693643i
$511$	9.12889	+	10.5353i	0.403839	+	0.466054i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−1.49082	−	0.958094i	−0.0658215	−	0.0423009i
$514$	−2.95942	+	6.48024i	−0.130535	+	0.285831i
$515$	−0.670572	+	0.773881i	−0.0295489	+	0.0341013i
$516$	4.55311	−	2.92610i	0.200439	−	0.128815i
$517$	1.08623	+	7.55491i	0.0477724	+	0.332265i
$518$	0.868119	+	6.03790i	0.0381429	+	0.265290i
$519$	3.32785	−	2.13868i	0.146076	−	0.0938775i
$520$	−1.12845	+	1.30230i	−0.0494857	+	0.0571096i
$521$	−1.67692	+	3.67194i	−0.0734672	+	0.160871i	−0.942802	−	0.333352i	$-0.891820\pi$
$521$	−1.67692	+	3.67194i	−0.0734672	+	0.160871i	0.869335	+	0.494223i	$0.164547\pi$
$522$	−0.504086	−	0.323956i	−0.0220632	−	0.0141792i
$523$	26.8539	−	7.88500i	1.17424	−	0.344787i	0.364287	−	0.931287i	$-0.381313\pi$
$523$	26.8539	−	7.88500i	1.17424	−	0.344787i	0.809950	+	0.586499i	$0.199494\pi$
$524$	8.83760	+	10.1991i	0.386072	+	0.445551i
$525$	−4.07077	−	1.19529i	−0.177663	−	0.0521665i
$526$	−0.937295	−	2.05239i	−0.0408680	−	0.0894884i
$527$	6.78644	−	47.2007i	0.295622	−	2.05610i
$528$	−5.05727			−0.220089
$529$	−19.1399	−	12.7540i	−0.832169	−	0.554523i
$530$	−11.2249			−0.487580
$531$	0.663854	−	4.61720i	0.0288088	−	0.200370i
$532$	0.736176	+	1.61200i	0.0319173	+	0.0698891i
$533$	0.376054	+	0.110419i	0.0162887	+	0.00478280i
$534$	−3.10485	−	3.58319i	−0.134360	−	0.155060i
$535$	−13.6215	+	3.99962i	−0.588907	+	0.172919i
$536$	−12.1943	−	7.83680i	−0.526713	−	0.338498i
$537$	−6.65718	+	14.5772i	−0.287278	+	0.629052i
$538$	−10.5942	+	12.2264i	−0.456749	+	0.527116i
$539$	4.25445	−	2.73417i	0.183252	−	0.117769i
$540$	−0.123853	−	0.861414i	−0.00532977	−	0.0370694i
$541$	−3.11400	−	21.6583i	−0.133881	−	0.931165i	−0.940428	−	0.339994i	$-0.889575\pi$
$541$	−3.11400	−	21.6583i	−0.133881	−	0.931165i	0.806546	−	0.591171i	$-0.201334\pi$
$542$	−26.0410	+	16.7356i	−1.11856	+	0.718854i
$543$	−2.68521	+	3.09889i	−0.115233	+	0.132986i
$544$	−2.65406	+	5.81158i	−0.113792	+	0.249169i
$545$	−5.17733	−	3.32727i	−0.221772	−	0.142525i
$546$	−1.89985	+	0.557846i	−0.0813060	+	0.0238736i
$547$	17.9896	+	20.7611i	0.769179	+	0.887680i	0.996279	−	0.0861912i	$-0.0274696\pi$
$547$	17.9896	+	20.7611i	0.769179	+	0.887680i	−0.227099	+	0.973872i	$0.572924\pi$
$548$	19.6453	+	5.76838i	0.839205	+	0.246413i
$549$	3.87084	+	8.47596i	0.165203	+	0.361745i
$550$	3.05352	−	21.2377i	0.130203	−	0.905579i
$551$	−1.06188			−0.0452378
$552$	1.38927	−	4.59020i	0.0591311	−	0.195372i
$553$	8.74883			0.372038
$554$	0.213721	−	1.48646i	0.00908013	−	0.0631537i
$555$	−2.20529	−	4.82892i	−0.0936095	−	0.204976i
$556$	−1.53899	−	0.451888i	−0.0652677	−	0.0191643i
$557$	22.5203	+	25.9898i	0.954217	+	1.10122i	0.994779	+	0.102048i	$0.0325395\pi$
$557$	22.5203	+	25.9898i	0.954217	+	1.10122i	−0.0405628	+	0.999177i	$0.512915\pi$
$558$	−7.16152	+	2.10281i	−0.303171	+	0.0890191i
$559$	9.01540	+	5.79385i	0.381311	+	0.245054i
$560$	−0.361524	+	0.791628i	−0.0152772	+	0.0334524i
$561$	−21.1589	+	24.4187i	−0.893330	+	1.03096i
$562$	11.0101	−	7.07577i	0.464434	−	0.298473i
$563$	2.72657	+	18.9637i	0.114911	+	0.799226i	0.963025	+	0.269412i	$0.0868293\pi$
$563$	2.72657	+	18.9637i	0.114911	+	0.799226i	−0.848114	+	0.529814i	$0.822262\pi$
$564$	−0.214786	−	1.49387i	−0.00904413	−	0.0629033i
$565$	−6.40385	+	4.11551i	−0.269412	+	0.173141i
$566$	15.2151	−	17.5592i	0.639539	−	0.738068i
$567$	0.415415	−	0.909632i	0.0174458	−	0.0382010i
$568$	5.35744	+	3.44302i	0.224793	+	0.144466i
$569$	−17.0460	+	5.00516i	−0.714606	+	0.209827i	−0.618773	−	0.785570i	$-0.712370\pi$
$569$	−17.0460	+	5.00516i	−0.714606	+	0.209827i	−0.0958334	+	0.995397i	$0.530552\pi$
$570$	−1.00996	−	1.16555i	−0.0423025	−	0.0488197i
$571$	12.7101	+	3.73204i	0.531903	+	0.156181i	0.536645	−	0.843808i	$-0.319691\pi$
$571$	12.7101	+	3.73204i	0.531903	+	0.156181i	−0.00474228	+	0.999989i	$0.501510\pi$
$572$	−4.15983	−	9.10876i	−0.173931	−	0.380856i
$573$	2.85648	−	19.8673i	0.119331	−	0.829968i
$574$	0.197939			0.00826181
$575$	18.4375	+	8.60565i	0.768895	+	0.358881i
$576$	1.00000			0.0416667
$577$	0.146566	−	1.01939i	0.00610164	−	0.0424379i	−0.986543	−	0.163501i	$-0.947721\pi$
$577$	0.146566	−	1.01939i	0.00610164	−	0.0424379i	0.992645	+	0.121063i	$0.0386304\pi$
$578$	9.89457	+	21.6661i	0.411560	+	0.901190i
$579$	11.5544	+	3.39268i	0.480185	+	0.140995i
$580$	−0.341493	−	0.394104i	−0.0141797	−	0.0163643i
$581$	12.0023	−	3.52419i	0.497939	−	0.146208i
$582$	2.50123	+	1.60744i	0.103679	+	0.0666307i
$583$	27.0974	−	59.3350i	1.12226	−	2.45740i
$584$	9.12889	−	10.5353i	0.377756	−	0.435954i
$585$	1.44964	−	0.931626i	0.0599352	−	0.0385180i
$586$	−2.51334	−	17.4807i	−0.103825	−	0.722119i
$587$	−6.13130	−	42.6442i	−0.253066	−	1.76011i	−0.579575	−	0.814919i	$-0.696782\pi$
$587$	−6.13130	−	42.6442i	−0.253066	−	1.76011i	0.326509	−	0.945194i	$-0.394128\pi$
$588$	−0.841254	+	0.540641i	−0.0346927	+	0.0222957i
$589$	−8.66187	+	9.99633i	−0.356906	+	0.411892i
$590$	1.68640	−	3.69269i	0.0694278	−	0.152026i
$591$	8.45193	+	5.43173i	0.347666	+	0.223431i
$592$	5.85289	−	1.71856i	0.240552	−	0.0706326i
$593$	5.74573	+	6.63093i	0.235949	+	0.272300i	0.861359	−	0.507997i	$-0.169614\pi$
$593$	5.74573	+	6.63093i	0.235949	+	0.272300i	−0.625410	+	0.780296i	$0.715068\pi$
$594$	4.85241	+	1.42480i	0.199097	+	0.0584601i
$595$	2.30976	+	5.05766i	0.0946908	+	0.207344i
$596$	1.92460	−	13.3859i	0.0788347	−	0.548307i
$597$	−19.8979			−0.814369
$598$	9.41024	−	1.27341i	0.384813	−	0.0520735i
$599$	−22.9465			−0.937567			−0.468784	−	0.883313i	$-0.655308\pi$
$599$	−22.9465			−0.937567			−0.468784	+	0.883313i	$0.655308\pi$
$600$	−0.603789	+	4.19944i	−0.0246496	+	0.171441i
$601$	−13.8798	−	30.3925i	−0.566169	−	1.23974i	−0.948812	−	0.315841i	$-0.897713\pi$
$601$	−13.8798	−	30.3925i	−0.566169	−	1.23974i	0.382643	−	0.923896i	$-0.375014\pi$
$602$	5.19305	+	1.52482i	0.211653	+	0.0621469i
$603$	9.49246	+	10.9549i	0.386563	+	0.446117i
$604$	20.5100	−	6.02229i	0.834542	−	0.245044i
$605$	−10.6714	−	6.85807i	−0.433852	−	0.278820i
$606$	1.97048	−	4.31475i	0.0800453	−	0.175275i
$607$	25.5451	−	29.4806i	1.03684	−	1.19658i	0.0566795	−	0.998392i	$-0.481949\pi$
$607$	25.5451	−	29.4806i	1.03684	−	1.19658i	0.980164	−	0.198189i	$-0.0635059\pi$
$608$	1.49082	−	0.958094i	0.0604609	−	0.0388559i
$609$	−0.0852762	−	0.593109i	−0.00345557	−	0.0240340i
$610$	1.15406	+	8.02667i	0.0467266	+	0.324990i
$611$	2.51397	−	1.61563i	0.101704	−	0.0653615i
$612$	4.18386	−	4.82844i	0.169123	−	0.195178i
$613$	1.53776	−	3.36723i	0.0621097	−	0.136001i	−0.876032	−	0.482253i	$-0.839819\pi$
$613$	1.53776	−	3.36723i	0.0621097	−	0.136001i	0.938142	+	0.346252i	$0.112546\pi$
$614$	10.6396	+	6.83762i	0.429377	+	0.275944i
$615$	−0.165283	+	0.0485315i	−0.00666485	+	0.00195698i
$616$	−3.31181	−	3.82203i	−0.133437	−	0.153994i
$617$	−8.07039	−	2.36968i	−0.324902	−	0.0953997i	0.115214	−	0.993341i	$-0.463244\pi$
$617$	−8.07039	−	2.36968i	−0.324902	−	0.0953997i	−0.440116	+	0.897941i	$0.645063\pi$
$618$	0.488791	+	1.07030i	0.0196621	+	0.0430539i
$619$	−1.67515	+	11.6509i	−0.0673300	+	0.468290i	0.928064	+	0.372421i	$0.121472\pi$
$619$	−1.67515	+	11.6509i	−0.0673300	+	0.468290i	−0.995394	+	0.0958694i	$0.969437\pi$
$620$	−6.49559			−0.260869
$621$	−2.62620	+	4.01286i	−0.105386	+	0.161031i
$622$	−7.18964			−0.288278
$623$	0.674749	−	4.69298i	0.0270332	−	0.188020i
$624$	0.822545	+	1.80112i	0.0329281	+	0.0721026i
$625$	−13.6373	−	4.00426i	−0.545491	−	0.160171i
$626$	−0.697522	−	0.804984i	−0.0278786	−	0.0321736i
$627$	8.59919	−	2.52495i	0.343418	−	0.100837i
$628$	14.2304	+	9.14535i	0.567857	+	0.364939i
$629$	16.1897	−	35.4506i	0.645527	−	1.41351i
$630$	0.569907	−	0.657708i	0.0227057	−	0.0262037i
$631$	−4.72071	+	3.03382i	−0.187928	+	0.120774i	−0.631222	−	0.775602i	$-0.717446\pi$
$631$	−4.72071	+	3.03382i	−0.187928	+	0.120774i	0.443294	+	0.896377i	$0.353810\pi$
$632$	−1.24509	−	8.65978i	−0.0495269	−	0.344467i
$633$	0.894377	+	6.22053i	0.0355483	+	0.247244i
$634$	−16.1871	+	10.4028i	−0.642871	+	0.413148i
$635$	1.01866	−	1.17559i	0.0404242	−	0.0466520i
$636$	−5.35810	+	11.7326i	−0.212463	+	0.465228i
$637$	−1.66573	−	1.07050i	−0.0659986	−	0.0424147i
$638$	2.90761	−	0.853750i	0.115113	−	0.0338003i
$639$	−4.17042	−	4.81292i	−0.164979	−	0.190396i
$640$	0.835020	+	0.245184i	0.0330071	+	0.00969175i
$641$	10.2724	+	22.4935i	0.405737	+	0.888439i	0.996656	+	0.0817089i	$0.0260378\pi$
$641$	10.2724	+	22.4935i	0.405737	+	0.888439i	−0.590920	+	0.806730i	$0.701235\pi$
$642$	−2.32154	+	16.1467i	−0.0916240	+	0.637259i
$643$	−28.3554			−1.11823			−0.559113	−	0.829091i	$-0.688858\pi$
$643$	−28.3554			−1.11823			−0.559113	+	0.829091i	$0.688858\pi$
$644$	4.37882	−	1.95600i	0.172550	−	0.0770774i
$645$	−4.71017			−0.185463
$646$	1.61131	−	11.2069i	0.0633960	−	0.440929i
$647$	16.4849	+	36.0970i	0.648090	+	1.41912i	0.893216	+	0.449628i	$0.148443\pi$
$647$	16.4849	+	36.0970i	0.648090	+	1.41912i	−0.245126	+	0.969491i	$0.578829\pi$
$648$	−0.959493	−	0.281733i	−0.0376924	−	0.0110675i
$649$	15.4485	+	17.8286i	0.606408	+	0.699832i
$650$	−8.06035	+	2.36673i	−0.316153	+	0.0928309i
$651$	−6.27899	−	4.03526i	−0.246093	−	0.158154i
$652$	3.20366	−	7.01503i	0.125465	−	0.274730i
$653$	0.295252	−	0.340739i	0.0115541	−	0.0133342i	−0.749943	−	0.661502i	$-0.769919\pi$
$653$	0.295252	−	0.340739i	0.0115541	−	0.0133342i	0.761497	+	0.648168i	$0.224465\pi$
$654$	−5.94909	+	3.82325i	−0.232628	+	0.149501i
$655$	−1.67144	−	11.6251i	−0.0653086	−	0.454231i
$656$	−0.0281696	−	0.195924i	−0.00109984	−	0.00764955i
$657$	−11.7272	+	7.53665i	−0.457524	+	0.294033i
$658$	0.988338	−	1.14060i	0.0385294	−	0.0444653i
$659$	−13.4247	+	29.3959i	−0.522951	+	1.14510i	0.445359	+	0.895352i	$0.353076\pi$
$659$	−13.4247	+	29.3959i	−0.522951	+	1.14510i	−0.968310	+	0.249751i	$0.919651\pi$
$660$	3.70253	+	2.37947i	0.144121	+	0.0926207i
$661$	−13.0599	+	3.83474i	−0.507972	+	0.149154i	−0.525669	−	0.850689i	$-0.676185\pi$
$661$	−13.0599	+	3.83474i	−0.507972	+	0.149154i	0.0176968	+	0.999843i	$0.494367\pi$
$662$	−4.41468	−	5.09481i	−0.171581	−	0.198016i
$663$	12.1380	+	3.56404i	0.471402	+	0.138416i
$664$	−5.19642	−	11.3786i	−0.201660	−	0.441575i
$665$	0.219485	−	1.52655i	0.00851127	−	0.0591972i
$666$	−6.09999			−0.236370
$667$	−0.0238381	+	2.87360i	−0.000923015	+	0.111266i
$668$	−13.4265			−0.519487
$669$	−1.84254	+	12.8152i	−0.0712369	+	0.495463i
$670$	5.24043	+	11.4750i	0.202456	+	0.443316i
$671$	−45.2148	−	13.2763i	−1.74550	−	0.512525i
$672$	0.654861	+	0.755750i	0.0252618	+	0.0291537i
$673$	4.76135	−	1.39806i	0.183537	−	0.0538912i	−0.188673	−	0.982040i	$-0.560419\pi$
$673$	4.76135	−	1.39806i	0.183537	−	0.0538912i	0.372209	+	0.928149i	$0.378600\pi$
$674$	19.1732	+	12.3218i	0.738523	+	0.474620i
$675$	1.76245	−	3.85923i	0.0678367	−	0.148542i
$676$	5.94573	−	6.86174i	0.228682	−	0.263913i
$677$	−6.03114	+	3.87598i	−0.231795	+	0.148966i	−0.651383	−	0.758749i	$-0.725811\pi$
$677$	−6.03114	+	3.87598i	−0.231795	+	0.148966i	0.419588	+	0.907715i	$0.362175\pi$
$678$	1.24483	+	8.65797i	0.0478073	+	0.332507i
$679$	0.423133	+	2.94296i	0.0162384	+	0.112940i
$680$	4.67747	−	3.00603i	0.179373	−	0.115276i
$681$	11.8352	−	13.6585i	0.453525	−	0.523395i
$682$	15.6806	−	34.3356i	0.600439	−	1.31478i
$683$	3.79834	+	2.44104i	0.145339	+	0.0934039i	0.611290	−	0.791407i	$-0.290651\pi$
$683$	3.79834	+	2.44104i	0.145339	+	0.0934039i	−0.465950	+	0.884811i	$0.654287\pi$
$684$	−1.70036	+	0.499271i	−0.0650149	+	0.0190901i
$685$	−11.6687	−	13.4663i	−0.445836	−	0.514523i
$686$	−0.959493	−	0.281733i	−0.0366336	−	0.0107566i
$687$	1.84372	+	4.03719i	0.0703424	+	0.154028i
$688$	0.770249	−	5.35720i	0.0293655	−	0.204241i
$689$	−25.5391			−0.972964
$690$	−3.17682	+	2.70692i	−0.120940	+	0.103051i
$691$	−42.1282			−1.60263			−0.801315	−	0.598242i	$-0.795866\pi$
$691$	−42.1282			−1.60263			−0.801315	+	0.598242i	$0.795866\pi$
$692$	0.562972	−	3.91555i	0.0214010	−	0.148847i
$693$	2.10087	+	4.60025i	0.0798053	+	0.174749i
$694$	22.1000	+	6.48913i	0.838903	+	0.246324i
$695$	0.914109	+	1.05494i	0.0346741	+	0.0400161i
$696$	−0.574936	+	0.168816i	−0.0217929	+	0.00639897i
$697$	−1.06386	−	0.683704i	−0.0402968	−	0.0258972i
$698$	−9.97991	+	21.8530i	−0.377745	+	0.827147i
$699$	−2.66342	+	3.07374i	−0.100740	+	0.116260i
$700$	−3.56912	+	2.29374i	−0.134900	+	0.0866951i
$701$	−2.68861	−	18.6997i	−0.101548	−	0.706279i	−0.975457	−	0.220190i	$-0.929332\pi$
$701$	−2.68861	−	18.6997i	−0.101548	−	0.706279i	0.873909	−	0.486089i	$-0.161577\pi$
$702$	−0.281791	−	1.95990i	−0.0106355	−	0.0739717i
$703$	−9.09401	+	5.84436i	−0.342987	+	0.220424i
$704$	−3.31181	+	3.82203i	−0.124818	+	0.144048i
$705$	−0.545625	+	1.19475i	−0.0205494	+	0.0449969i
$706$	−1.51564	−	0.974042i	−0.0570418	−	0.0366586i
$707$	4.55126	−	1.33637i	0.171168	−	0.0502594i
$708$	−3.05472	−	3.52533i	−0.114803	−	0.132490i
$709$	10.5554	+	3.09934i	0.396415	+	0.116398i	0.473863	−	0.880598i	$-0.342859\pi$
$709$	10.5554	+	3.09934i	0.396415	+	0.116398i	−0.0774482	+	0.996996i	$0.524677\pi$
$710$	−2.30233	−	5.04141i	−0.0864050	−	0.189201i
$711$	−1.24509	+	8.65978i	−0.0466944	+	0.324767i
$712$	−4.74124			−0.177685
$713$	26.8570	+	23.6646i	1.00580	+	0.886246i
$714$	6.38894			0.239100
$715$	−1.24022	+	8.62592i	−0.0463816	+	0.322591i
$716$	6.65718	+	14.5772i	0.248790	+	0.544775i
$717$	0.646088	+	0.189709i	0.0241286	+	0.00708480i
$718$	−17.2561	−	19.9146i	−0.643993	−	0.743208i
$719$	−0.998593	+	0.293214i	−0.0372413	+	0.0109350i	−0.300300	−	0.953845i	$-0.597087\pi$
$719$	−0.998593	+	0.293214i	−0.0372413	+	0.0109350i	0.263059	+	0.964780i	$0.415269\pi$
$720$	−0.732120	−	0.470505i	−0.0272845	−	0.0175347i
$721$	−0.488791	+	1.07030i	−0.0182035	+	0.0398602i
$722$	10.3858	−	11.9858i	0.386518	−	0.446066i
$723$	19.5669	−	12.5749i	0.727703	−	0.467666i
$724$	0.583551	+	4.05869i	0.0216875	+	0.150840i
$725$	−0.361795	−	2.51634i	−0.0134367	−	0.0934545i
$726$	−12.2621	+	7.88036i	−0.455089	+	0.292468i
$727$	−10.3758	+	11.9743i	−0.384816	+	0.444101i	−0.914800	−	0.403906i	$-0.867652\pi$
$727$	−10.3758	+	11.9743i	−0.384816	+	0.444101i	0.529985	+	0.848007i	$0.322198\pi$
$728$	−0.822545	+	1.80112i	−0.0304855	+	0.0667540i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−11.6404	+	3.41792i	−0.430829	+	0.126503i
$731$	−22.6443	−	26.1329i	−0.837529	−	0.966560i
$732$	8.94056	+	2.62519i	0.330453	+	0.0970297i
$733$	6.75106	+	14.7828i	0.249356	+	0.546014i	0.992375	−	0.123257i	$-0.0393339\pi$
$733$	6.75106	+	14.7828i	0.249356	+	0.546014i	−0.743019	+	0.669271i	$0.766607\pi$
$734$	3.65626	−	25.4299i	0.134955	−	0.938634i
$735$	0.870273			0.0321005
$736$	−2.55927	−	4.05588i	−0.0943358	−	0.149502i
$737$	−73.3071			−2.70030
$738$	−0.0281696	+	0.195924i	−0.00103694	+	0.00721207i
$739$	−14.5503	−	31.8608i	−0.535242	−	1.17202i	−0.963340	−	0.268284i	$-0.913543\pi$
$739$	−14.5503	−	31.8608i	−0.535242	−	1.17202i	0.428098	−	0.903733i	$-0.359184\pi$
$740$	−5.09361	−	1.49562i	−0.187245	−	0.0549801i
$741$	−2.29787	−	2.65189i	−0.0844144	−	0.0974194i
$742$	−12.3757	+	3.63384i	−0.454327	+	0.133402i
$743$	−12.3806	−	7.95651i	−0.454199	−	0.291896i	0.293469	−	0.955969i	$-0.405190\pi$
$743$	−12.3806	−	7.95651i	−0.454199	−	0.291896i	−0.747668	+	0.664073i	$0.768827\pi$
$744$	−3.10060	+	6.78936i	−0.113673	+	0.248910i
$745$	−7.70716	+	8.89454i	−0.282368	+	0.325871i
$746$	21.0661	−	13.5384i	0.771285	−	0.495675i
$747$	1.78022	+	12.3817i	0.0651347	+	0.453022i
$748$	4.59827	+	31.9817i	0.168130	+	1.16937i
$749$	−13.7231	+	8.81933i	−0.501433	+	0.322251i
$750$	5.26744	−	6.07895i	0.192340	−	0.221972i
$751$	1.94254	−	4.25356i	0.0708841	−	0.155215i	−0.870873	−	0.491508i	$-0.836446\pi$
$751$	1.94254	−	4.25356i	0.0708841	−	0.155215i	0.941757	+	0.336293i	$0.109173\pi$
$752$	−1.26965	−	0.815953i	−0.0462993	−	0.0297547i
$753$	−9.19577	+	2.70012i	−0.335112	+	0.0983979i
$754$	−0.776969	−	0.896671i	−0.0282956	−	0.0326548i
$755$	−17.8493	−	5.24104i	−0.649603	−	0.190741i
$756$	−0.415415	−	0.909632i	−0.0151085	−	0.0330830i
$757$	4.90151	−	34.0907i	0.178148	−	1.23905i	−0.682895	−	0.730517i	$-0.739279\pi$
$757$	4.90151	−	34.0907i	0.178148	−	1.23905i	0.861043	−	0.508532i	$-0.169812\pi$
$758$	−15.8109			−0.574278
$759$	−6.63981	−	23.3272i	−0.241010	−	0.846725i
$760$	−1.54225			−0.0559433
$761$	3.47199	−	24.1483i	0.125860	−	0.875373i	−0.824863	−	0.565332i	$-0.808748\pi$
$761$	3.47199	−	24.1483i	0.125860	−	0.875373i	0.950723	−	0.310041i	$-0.100343\pi$
$762$	−0.742517	−	1.62589i	−0.0268986	−	0.0588996i
$763$	−6.78524	−	1.99233i	−0.245642	−	0.0721271i
$764$	−13.1441	−	15.1691i	−0.475537	−	0.548799i
$765$	−5.33489	+	1.56647i	−0.192883	+	0.0566357i
$766$	32.5417	+	20.9133i	1.17578	+	0.755627i
$767$	3.83691	−	8.40166i	0.138543	−	0.303366i
$768$	0.654861	−	0.755750i	0.0236303	−	0.0272708i
$769$	13.4231	−	8.62648i	0.484048	−	0.311079i	−0.275760	−	0.961227i	$-0.588929\pi$
$769$	13.4231	−	8.62648i	0.484048	−	0.311079i	0.759808	+	0.650148i	$0.225293\pi$
$770$	0.626356	+	4.35640i	0.0225723	+	0.156994i
$771$	−1.01385	−	7.05151i	−0.0365130	−	0.253954i
$772$	10.1305	−	6.51051i	0.364606	−	0.234318i
$773$	7.35672	−	8.49010i	0.264603	−	0.305368i	−0.607864	−	0.794041i	$-0.707974\pi$
$773$	7.35672	−	8.49010i	0.264603	−	0.305368i	0.872467	+	0.488673i	$0.162519\pi$
$774$	−2.24835	+	4.92319i	−0.0808151	+	0.176960i
$775$	−26.6394	−	17.1201i	−0.956916	−	0.614973i
$776$	2.85278	−	0.837653i	0.102409	−	0.0300700i
$777$	−3.99464	−	4.61006i	−0.143307	−	0.165385i
$778$	−37.0798	−	10.8876i	−1.32938	−	0.390340i
$779$	0.145718	+	0.319078i	0.00522088	+	0.0114321i
$780$	0.245235	−	1.70565i	0.00878083	−	0.0610720i
$781$	32.2067			1.15245
$782$	−30.2912	−	4.61200i	−1.08321	−	0.164925i
$783$	0.599208			0.0214139
$784$	−0.142315	+	0.989821i	−0.00508267	+	0.0353508i
$785$	−6.11546	−	13.3910i	−0.218270	−	0.477945i
$786$	−12.9487	−	3.80209i	−0.461866	−	0.135616i
$787$	8.15714	+	9.41384i	0.290771	+	0.335567i	0.882275	−	0.470735i	$-0.156011\pi$
$787$	8.15714	+	9.41384i	0.290771	+	0.335567i	−0.591504	+	0.806302i	$0.701466\pi$
$788$	9.63986	−	2.83052i	0.343406	−	0.100833i
$789$	1.89811	+	1.21984i	0.0675744	+	0.0434275i
$790$	−3.16291	+	6.92581i	−0.112531	+	0.246409i
$791$	−5.72807	+	6.61054i	−0.203667	+	0.235044i
$792$	4.25445	−	2.73417i	0.151175	−	0.0971544i
$793$	2.62573	+	18.2624i	0.0932425	+	0.648516i
$794$	−0.856822	−	5.95933i	−0.0304075	−	0.211489i
$795$	9.44302	−	6.06866i	0.334909	−	0.215233i
$796$	−13.0304	+	15.0379i	−0.461850	+	0.533003i
$797$	−1.66859	+	3.65371i	−0.0591047	+	0.129421i	−0.936880	−	0.349652i	$-0.886300\pi$
$797$	−1.66859	+	3.65371i	−0.0591047	+	0.129421i	0.877775	+	0.479073i	$0.159027\pi$
$798$	−1.49082	−	0.958094i	−0.0527746	−	0.0339162i
$799$	−9.25181	+	2.71658i	−0.327306	+	0.0961056i
$800$	2.77833	+	3.20636i	0.0982288	+	0.113362i
$801$	4.54919	+	1.33576i	0.160738	+	0.0471968i
$802$	10.2916	+	22.5356i	0.363411	+	0.795758i
$803$	10.0331	−	69.7818i	0.354061	−	2.46255i
$804$	14.4954			0.511213
$805$	−4.12613	−	0.628226i	−0.145427	−	0.0221420i
$806$	−14.7788			−0.520563
$807$	2.30234	−	16.0131i	0.0810463	−	0.563689i
$808$	−1.97048	−	4.31475i	−0.0693213	−	0.151792i
$809$	7.75103	+	2.27591i	0.272512	+	0.0800166i	0.415133	−	0.909761i	$-0.363735\pi$
$809$	7.75103	+	2.27591i	0.272512	+	0.0800166i	−0.142622	+	0.989777i	$0.545553\pi$
$810$	0.569907	+	0.657708i	0.0200245	+	0.0231095i
$811$	−25.0701	+	7.36126i	−0.880332	+	0.258489i	−0.690504	−	0.723329i	$-0.742611\pi$
$811$	−25.0701	+	7.36126i	−0.880332	+	0.258489i	−0.189828	+	0.981817i	$0.560793\pi$
$812$	−0.504086	−	0.323956i	−0.0176899	−	0.0113686i
$813$	12.8592	−	28.1577i	0.450992	−	0.987534i
$814$	20.2020	−	23.3143i	0.708079	−	0.817167i
$815$	−5.64607	+	3.62851i	−0.197773	+	0.127101i
$816$	−0.909240	−	6.32391i	−0.0318298	−	0.221381i
$817$	1.36499	+	9.49374i	0.0477551	+	0.332144i
$818$	−12.2162	+	7.85087i	−0.427129	+	0.274499i
$819$	1.29666	−	1.49643i	0.0453090	−	0.0522894i
$820$	−0.0715597	+	0.156694i	−0.00249897	+	0.00547199i
$821$	−19.1666	−	12.3177i	−0.668920	−	0.429889i	0.161616	−	0.986854i	$-0.448329\pi$
$821$	−19.1666	−	12.3177i	−0.668920	−	0.429889i	−0.830536	+	0.556965i	$0.811966\pi$
$822$	−19.6453	+	5.76838i	−0.685208	+	0.201195i
$823$	11.8170	+	13.6375i	0.411914	+	0.475374i	0.923357	−	0.383943i	$-0.125434\pi$
$823$	11.8170	+	13.6375i	0.411914	+	0.475374i	−0.511443	+	0.859317i	$0.670889\pi$
$824$	1.12897	+	0.331496i	0.0393296	+	0.0115482i
$825$	8.91319	+	19.5172i	0.310317	+	0.679500i
$826$	0.663854	−	4.61720i	0.0230984	−	0.160653i
$827$	31.6258			1.09974			0.549869	−	0.835251i	$-0.314678\pi$
$827$	31.6258			1.09974			0.549869	+	0.835251i	$0.314678\pi$
$828$	1.31292	+	4.61262i	0.0456273	+	0.160300i
$829$	40.0268			1.39019			0.695094	−	0.718918i	$-0.255363\pi$
$829$	40.0268			1.39019			0.695094	+	0.718918i	$0.255363\pi$
$830$	−1.54927	+	10.7754i	−0.0537760	+	0.374021i
$831$	0.623849	+	1.36604i	0.0216411	+	0.0473873i
$832$	1.89985	+	0.557846i	0.0658654	+	0.0193398i
$833$	4.18386	+	4.82844i	0.144962	+	0.167295i
$834$	1.53899	−	0.451888i	0.0532908	−	0.0156476i
$835$	9.82981	+	6.31723i	0.340174	+	0.218617i
$836$	3.72304	−	8.15232i	0.128764	−	0.281954i
$837$	4.88779	−	5.64081i	0.168947	−	0.194975i
$838$	−28.1355	+	18.0816i	−0.971926	+	0.624619i
$839$	6.58954	+	45.8313i	0.227496	+	1.58227i	0.708602	+	0.705608i	$0.249326\pi$
$839$	6.58954	+	45.8313i	0.227496	+	1.58227i	−0.481106	+	0.876662i	$0.659765\pi$
$840$	−0.123853	−	0.861414i	−0.00427332	−	0.0297216i
$841$	−24.0943	+	15.4845i	−0.830838	+	0.533947i
$842$	−26.0151	+	30.0231i	−0.896540	+	1.03466i
$843$	−5.43685	+	11.9050i	−0.187255	+	0.410031i
$844$	5.28685	+	3.39766i	0.181981	+	0.116952i
$845$	−7.58147	+	2.22612i	−0.260810	+	0.0765809i
$846$	0.988338	+	1.14060i	0.0339797	+	0.0392147i
$847$	−13.9855	−	4.10653i	−0.480549	−	0.141102i
$848$	5.35810	+	11.7326i	0.183998	+	0.402899i
$849$	−3.30656	+	22.9976i	−0.113481	+	0.789277i
$850$	27.1059			0.929724
$851$	15.6115	+	24.7408i	0.535155	+	0.848104i
$852$	−6.36840			−0.218178
$853$	2.83238	−	19.6997i	0.0969789	−	0.674503i	−0.882106	−	0.471051i	$-0.843875\pi$
$853$	2.83238	−	19.6997i	0.0969789	−	0.674503i	0.979085	−	0.203452i	$-0.0652162\pi$
$854$	3.87084	+	8.47596i	0.132457	+	0.290041i
$855$	1.47978	+	0.434502i	0.0506073	+	0.0148597i
$856$	10.6826	+	12.3283i	0.365123	+	0.421374i
$857$	16.3432	−	4.79879i	0.558272	−	0.163923i	0.00958911	−	0.999954i	$-0.496948\pi$
$857$	16.3432	−	4.79879i	0.558272	−	0.163923i	0.548683	+	0.836031i	$0.315129\pi$
$858$	8.42404	+	5.41380i	0.287592	+	0.184824i
$859$	−19.0568	+	41.7286i	−0.650211	+	1.42376i	0.241159	+	0.970486i	$0.422472\pi$
$859$	−19.0568	+	41.7286i	−0.650211	+	1.42376i	−0.891370	+	0.453277i	$0.850255\pi$
$860$	−3.08450	+	3.55971i	−0.105181	+	0.121385i
$861$	−0.166517	+	0.107014i	−0.00567488	+	0.00364702i
$862$	−2.15543	−	14.9913i	−0.0734141	−	0.510606i
$863$	−0.278818	−	1.93922i	−0.00949109	−	0.0660120i	0.984525	−	0.175242i	$-0.0560707\pi$
$863$	−0.278818	−	1.93922i	−0.00949109	−	0.0660120i	−0.994017	+	0.109230i	$0.965162\pi$
$864$	−0.841254	+	0.540641i	−0.0286200	+	0.0183930i
$865$	−2.25445	+	2.60177i	−0.0766536	+	0.0884629i
$866$	−13.9077	+	30.4537i	−0.472604	+	1.03486i
$867$	−20.0374	−	12.8773i	−0.680506	−	0.437335i
$868$	−7.16152	+	2.10281i	−0.243078	+	0.0713741i
$869$	−28.9744	−	33.4383i	−0.982890	−	1.13432i
$870$	0.500351	+	0.146916i	0.0169635	+	0.00498093i
$871$	11.9231	+	26.1080i	0.403999	+	0.884634i
$872$	−1.00641	+	6.99972i	−0.0340813	+	0.237040i
$873$	−2.97322			−0.100628
$874$	6.37666	+	5.61869i	0.215694	+	0.190055i
$875$	8.04360			0.271923
$876$	−1.98390	+	13.7983i	−0.0670297	+	0.466202i
$877$	−16.9484	−	37.1119i	−0.572308	−	1.25318i	−0.945560	−	0.325449i	$-0.894485\pi$
$877$	−16.9484	−	37.1119i	−0.572308	−	1.25318i	0.373252	−	0.927730i	$-0.378243\pi$
$878$	−9.32429	−	2.73786i	−0.314680	−	0.0923983i
$879$	11.5651	+	13.3469i	0.390082	+	0.450178i
$880$	4.22292	−	1.23996i	0.142355	−	0.0417991i
$881$	22.6872	+	14.5802i	0.764350	+	0.491218i	0.863806	−	0.503824i	$-0.168074\pi$
$881$	22.6872	+	14.5802i	0.764350	+	0.491218i	−0.0994564	+	0.995042i	$0.531710\pi$
$882$	0.415415	−	0.909632i	0.0139878	−	0.0306289i
$883$	−6.56898	+	7.58101i	−0.221064	+	0.255121i	−0.855438	−	0.517904i	$-0.826712\pi$
$883$	−6.56898	+	7.58101i	−0.221064	+	0.255121i	0.634375	+	0.773026i	$0.281258\pi$
$884$	10.6422	−	6.83935i	0.357937	−	0.230032i
$885$	0.577734	+	4.01823i	0.0194203	+	0.135071i
$886$	2.82458	+	19.6454i	0.0948937	+	0.660000i
$887$	−22.4255	+	14.4120i	−0.752975	+	0.483908i	−0.859965	−	0.510352i	$-0.829515\pi$
$887$	−22.4255	+	14.4120i	−0.752975	+	0.483908i	0.106990	+	0.994260i	$0.465879\pi$
$888$	−3.99464	+	4.61006i	−0.134051	+	0.154704i
$889$	0.742517	−	1.62589i	0.0249032	−	0.0545305i
$890$	3.47116	+	2.23078i	0.116353	+	0.0747758i
$891$	−4.85241	+	1.42480i	−0.162562	+	0.0477325i
$892$	8.47845	+	9.78465i	0.283880	+	0.327614i
$893$	2.56624	+	0.753517i	0.0858760	+	0.0252155i
$894$	5.61788	+	12.3014i	0.187890	+	0.411422i
$895$	1.98479	−	13.8045i	0.0663441	−	0.461433i
$896$	1.00000			0.0334077
$897$	−7.22795	+	6.15882i	−0.241334	+	0.205637i
$898$	−30.9185			−1.03177
$899$	0.636489	−	4.42688i	0.0212281	−	0.147645i
$900$	−1.76245	−	3.85923i	−0.0587483	−	0.128641i
$901$	79.0677	+	23.2164i	2.63413	+	0.773450i
$902$	−0.655535	−	0.756528i	−0.0218269	−	0.0251896i
$903$	−5.19305	+	1.52482i	−0.172814	+	0.0507428i
$904$	7.35844	+	4.72899i	0.244738	+	0.157284i
$905$	1.48240	−	3.24601i	0.0492767	−	0.107901i
$906$	−13.9982	+	16.1548i	−0.465061	+	0.536709i
$907$	−0.748902	+	0.481290i	−0.0248669	+	0.0159810i	−0.553015	−	0.833171i	$-0.686523\pi$
$907$	−0.748902	+	0.481290i	−0.0248669	+	0.0159810i	0.528148	+	0.849152i	$0.322887\pi$
$908$	−2.57203	−	17.8888i	−0.0853557	−	0.593662i
$909$	0.675057	+	4.69512i	0.0223902	+	0.155727i
$910$	1.44964	−	0.931626i	0.0480550	−	0.0308831i
$911$	−11.8823	+	13.7129i	−0.393678	+	0.454328i	−0.917640	−	0.397413i	$-0.869908\pi$
$911$	−11.8823	+	13.7129i	−0.393678	+	0.454328i	0.523962	+	0.851742i	$0.324453\pi$
$912$	−0.736176	+	1.61200i	−0.0243772	+	0.0533787i
$913$	−53.2188	−	34.2017i	−1.76129	−	1.13191i
$914$	−19.4151	+	5.70078i	−0.642194	+	0.188565i
$915$	−5.31040	−	6.12853i	−0.175556	−	0.202603i
$916$	4.25848	+	1.25040i	0.140704	+	0.0413145i
$917$	−5.60619	−	12.2758i	−0.185133	−	0.405384i
$918$	−0.909240	+	6.32391i	−0.0300094	+	0.208720i
$919$	6.52007			0.215077			0.107539	−	0.994201i	$-0.465703\pi$
$919$	6.52007			0.215077			0.107539	+	0.994201i	$0.465703\pi$
$920$	−0.0346218	+	4.17354i	−0.00114145	+	0.137597i
$921$	−12.6473			−0.416741
$922$	−0.122974	+	0.855303i	−0.00404994	+	0.0281679i
$923$	−5.23830	−	11.4703i	−0.172421	−	0.377549i
$924$	4.85241	+	1.42480i	0.159633	+	0.0468724i
$925$	−16.9478	−	19.5588i	−0.557239	−	0.643088i
$926$	−16.2698	+	4.77723i	−0.534657	+	0.156990i
$927$	−0.989847	−	0.636136i	−0.0325108	−	0.0208934i
$928$	−0.248920	+	0.545059i	−0.00817120	+	0.0178924i
$929$	−27.0801	+	31.2521i	−0.888468	+	1.02535i	0.111035	+	0.993817i	$0.464583\pi$
$929$	−27.0801	+	31.2521i	−0.888468	+	1.02535i	−0.999503	+	0.0315301i	$0.989962\pi$
$930$	5.46444	−	3.51178i	0.179186	−	0.115156i
$931$	−0.252203	−	1.75411i	−0.00826561	−	0.0574886i
$932$	0.578815	+	4.02575i	0.0189597	+	0.131868i
$933$	6.04831	−	3.88701i	0.198013	−	0.127255i
$934$	4.50926	−	5.20397i	0.147548	−	0.170279i
$935$	11.6811	−	25.5779i	0.382011	−	0.836488i
$936$	−1.66573	−	1.07050i	−0.0544460	−	0.0349903i
$937$	33.1391	−	9.73053i	1.08261	−	0.317882i	0.308686	−	0.951164i	$-0.400111\pi$
$937$	33.1391	−	9.73053i	1.08261	−	0.317882i	0.773922	+	0.633281i	$0.218292\pi$
$938$	9.49246	+	10.9549i	0.309940	+	0.357690i
$939$	1.02200	+	0.300086i	0.0333517	+	0.00979295i
$940$	0.545625	+	1.19475i	0.0177963	+	0.0389685i
$941$	−0.100067	+	0.695984i	−0.00326210	+	0.0226884i	−0.991387	−	0.130961i	$-0.958194\pi$
$941$	−0.100067	+	0.695984i	−0.00326210	+	0.0226884i	0.988125	+	0.153650i	$0.0491027\pi$
$942$	−16.9158			−0.551145
$943$	0.866738	−	0.387169i	0.0282249	−	0.0126080i
$944$	−4.66468			−0.151823
$945$	−0.123853	+	0.861414i	−0.00402893	+	0.0280218i
$946$	−11.3705	−	24.8979i	−0.369687	−	0.809501i
$947$	15.9638	+	4.68740i	0.518755	+	0.152320i	0.530620	−	0.847610i	$-0.321959\pi$
$947$	15.9638	+	4.68740i	0.518755	+	0.152320i	−0.0118659	+	0.999930i	$0.503777\pi$
$948$	5.72926	+	6.61192i	0.186078	+	0.214745i
$949$	−26.4843	+	7.77649i	−0.859717	+	0.252436i
$950$	−6.32501	−	4.06484i	−0.205210	−	0.131881i
$951$	7.99326	−	17.5028i	0.259199	−	0.567567i
$952$	4.18386	−	4.82844i	0.135600	−	0.156491i
$953$	−26.9978	+	17.3504i	−0.874544	+	0.562035i	−0.899139	−	0.437662i	$-0.855807\pi$
$953$	−26.9978	+	17.3504i	−0.874544	+	0.562035i	0.0245958	+	0.999697i	$0.492170\pi$
$954$	−1.83560	−	12.7669i	−0.0594299	−	0.413344i
$955$	2.48592	+	17.2900i	0.0804425	+	0.559490i
$956$	0.566470	−	0.364048i	0.0183209	−	0.0117742i
$957$	−1.98446	+	2.29019i	−0.0641485	+	0.0740313i
$958$	−10.4509	+	22.8842i	−0.337652	+	0.739354i
$959$	−17.2244	−	11.0694i	−0.556204	−	0.357451i
$960$	−0.835020	+	0.245184i	−0.0269502	+	0.00791328i
$961$	−16.1810	−	18.6739i	−0.521969	−	0.602384i
$962$	−11.5891	−	3.40285i	−0.373646	−	0.109712i
$963$	−6.77655	−	14.8386i	−0.218371	−	0.478166i
$964$	3.31014	−	23.0225i	0.106612	−	0.741506i
$965$	−10.4800			−0.337363
$966$	−2.62620	+	4.01286i	−0.0844966	+	0.129112i
$967$	32.4231			1.04266			0.521329	−	0.853356i	$-0.325437\pi$
$967$	32.4231			1.04266			0.521329	+	0.853356i	$0.325437\pi$
$968$	−2.07438	+	14.4276i	−0.0666730	+	0.463721i
$969$	4.70338	+	10.2990i	0.151094	+	0.330851i
$970$	−2.48270	−	0.728986i	−0.0797147	−	0.0234063i
$971$	36.4455	+	42.0603i	1.16959	+	1.34978i	0.924914	+	0.380176i	$0.124137\pi$
$971$	36.4455	+	42.0603i	1.16959	+	1.34978i	0.244677	+	0.969605i	$0.421318\pi$
$972$	0.959493	−	0.281733i	0.0307758	−	0.00903658i
$973$	1.34934	+	0.867167i	0.0432578	+	0.0278001i
$974$	−5.42635	+	11.8820i	−0.173871	+	0.380725i
$975$	5.50125	−	6.34878i	0.176181	−	0.203324i
$976$	7.83881	−	5.03770i	0.250914	−	0.161253i
$977$	7.31408	+	50.8706i	0.233998	+	1.62749i	0.680526	+	0.732724i	$0.261751\pi$
$977$	7.31408	+	50.8706i	0.233998	+	1.62749i	−0.446528	+	0.894770i	$0.647340\pi$
$978$	1.09752	+	7.63345i	0.0350949	+	0.244091i
$979$	−20.1713	+	12.9633i	−0.644679	+	0.414310i
$980$	0.569907	−	0.657708i	0.0182050	−	0.0210097i
$981$	2.93769	−	6.43264i	0.0937932	−	0.205378i
$982$	31.3850	+	20.1699i	1.00154	+	0.643648i
$983$	−39.6231	+	11.6344i	−1.26378	+	0.371079i	−0.843900	−	0.536500i	$-0.819746\pi$
$983$	−39.6231	+	11.6344i	−1.26378	+	0.371079i	−0.419880	+	0.907580i	$0.637928\pi$
$984$	0.129622	+	0.149592i	0.00413221	+	0.00476882i
$985$	−8.38931	−	2.46332i	−0.267306	−	0.0784880i
$986$	1.59033	+	3.48235i	0.0506466	+	0.110900i
$987$	−0.214786	+	1.49387i	−0.00683672	+	0.0475505i
$988$	−3.50895			−0.111634
$989$	25.7220	−	3.48073i	0.817911	−	0.110681i
$990$	−4.40120			−0.139879
$991$	3.25028	−	22.6062i	0.103249	−	0.718110i	−0.870778	−	0.491677i	$-0.836384\pi$
$991$	3.25028	−	22.6062i	0.103249	−	0.718110i	0.974027	−	0.226434i	$-0.0727067\pi$
$992$	3.10060	+	6.78936i	0.0984441	+	0.215562i
$993$	6.46833	+	1.89927i	0.205266	+	0.0602716i
$994$	−4.17042	−	4.81292i	−0.132278	−	0.152657i
$995$	16.6152	−	4.87866i	0.526737	−	0.154664i
$996$	10.5232	+	6.76287i	0.333441	+	0.214290i
$997$	9.55033	−	20.9123i	0.302462	−	0.662300i	−0.695982	−	0.718059i	$-0.745031\pi$
$997$	9.55033	−	20.9123i	0.302462	−	0.662300i	0.998444	+	0.0557595i	$0.0177580\pi$
$998$	16.1711	−	18.6624i	0.511887	−	0.590749i
$999$	5.13164	−	3.29790i	0.162358	−	0.104341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.d.169.1	✓	20
23.3	even	11	inner	966.2.q.d.463.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.d.169.1	✓	20	1.1	even	1	trivial
966.2.q.d.463.1	yes	20	23.3	even	11	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.569907 + 0.657708i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.569907 + 0.657708i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.732120 + 0.470505i) q^{10} +(-0.719724 - 5.00579i) q^{11} +(0.142315 + 0.989821i) q^{12} +(-1.66573 + 1.07050i) q^{13} +(-0.654861 + 0.755750i) q^{14} +(0.361524 - 0.791628i) q^{15} +(0.841254 + 0.540641i) q^{16} +(6.13014 - 1.79997i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(-1.70036 - 0.499271i) q^{19} +(-0.361524 - 0.791628i) q^{20} +(0.142315 - 0.989821i) q^{21} +5.05727 q^{22} +(-1.38927 + 4.59020i) q^{23} -1.00000 q^{24} +(0.603789 - 4.19944i) q^{25} +(-0.822545 - 1.80112i) q^{26} +(0.959493 + 0.281733i) q^{27} +(-0.654861 - 0.755750i) q^{28} +(0.574936 - 0.168816i) q^{29} +(0.732120 + 0.470505i) q^{30} +(3.10060 - 6.78936i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-4.25445 + 2.73417i) q^{33} +(0.909240 + 6.32391i) q^{34} +(0.123853 + 0.861414i) q^{35} +(0.841254 - 0.540641i) q^{36} +(3.99464 - 4.61006i) q^{37} +(0.736176 - 1.61200i) q^{38} +(1.66573 + 1.07050i) q^{39} +(0.835020 - 0.245184i) q^{40} +(-0.129622 - 0.149592i) q^{41} +(0.959493 + 0.281733i) q^{42} +(-2.24835 - 4.92319i) q^{43} +(-0.719724 + 5.00579i) q^{44} -0.870273 q^{45} +(-4.34577 - 2.02838i) q^{46} -1.50923 q^{47} +(0.142315 - 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(4.07077 + 1.19529i) q^{50} +(-4.18386 - 4.82844i) q^{51} +(1.89985 - 0.557846i) q^{52} +(10.8506 + 6.97329i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(2.88217 - 3.32621i) q^{55} +(0.841254 - 0.540641i) q^{56} +(0.252203 + 1.75411i) q^{57} +(0.0852762 + 0.593109i) q^{58} +(-3.92418 + 2.52192i) q^{59} +(-0.569907 + 0.657708i) q^{60} +(3.87084 - 8.47596i) q^{61} +(6.27899 + 4.03526i) q^{62} +(-0.959493 + 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-1.65339 - 0.485478i) q^{65} +(-2.10087 - 4.60025i) q^{66} +(2.06291 - 14.3478i) q^{67} -6.38894 q^{68} +(4.75252 - 0.643117i) q^{69} -0.870273 q^{70} +(-0.906318 + 6.30358i) q^{71} +(0.415415 + 0.909632i) q^{72} +(13.3755 + 3.92741i) q^{73} +(3.99464 + 4.61006i) q^{74} +(-4.07077 + 1.19529i) q^{75} +(1.49082 + 0.958094i) q^{76} +(2.10087 - 4.60025i) q^{77} +(-1.29666 + 1.49643i) q^{78} +(7.35998 - 4.72997i) q^{79} +(0.123853 + 0.861414i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(0.166517 - 0.107014i) q^{82} +(8.19165 - 9.45367i) q^{83} +(-0.415415 + 0.909632i) q^{84} +(4.67747 + 3.00603i) q^{85} +(5.19305 - 1.52482i) q^{86} +(-0.392398 - 0.452851i) q^{87} +(-4.85241 - 1.42480i) q^{88} +(-1.96958 - 4.31278i) q^{89} +(0.123853 - 0.861414i) q^{90} -1.98006 q^{91} +(2.62620 - 4.01286i) q^{92} -7.46385 q^{93} +(0.214786 - 1.49387i) q^{94} +(-0.640674 - 1.40288i) q^{95} +(0.959493 + 0.281733i) q^{96} +(1.94704 + 2.24701i) q^{97} +(-0.959493 + 0.281733i) q^{98} +(4.25445 + 2.73417i) 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

L-functions

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