LMFDB - Embedded newform 966.2.y.c.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	966.25
Dual form			966.2.y.c.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.748398 - 3.08494i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.13670 + 1.56029i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.748398 - 3.08494i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.13670 + 1.56029i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-3.11705 + 0.600763i) q^{10} +(0.176110 + 3.69700i) q^{11} +(0.888835 + 0.458227i) q^{12} +(3.85692 + 4.45112i) q^{13} +(1.66019 - 2.06004i) q^{14} +(-0.451767 + 3.14211i) q^{15} +(0.981929 + 0.189251i) q^{16} +(1.43383 + 2.01353i) q^{17} +(0.723734 - 0.690079i) q^{18} +(-3.55923 + 4.99824i) q^{19} +(0.451767 + 3.14211i) q^{20} +(-1.40375 - 2.24265i) q^{21} +3.70120 q^{22} +(2.94970 + 3.78144i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.51256 + 2.32639i) q^{25} +(4.62960 - 3.64076i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-1.97871 - 1.75633i) q^{28} +(3.00663 - 6.58361i) q^{29} +(3.11705 + 0.600763i) q^{30} +(-7.92477 - 6.23211i) q^{31} +(0.235759 - 0.971812i) q^{32} +(1.21054 - 3.49763i) q^{33} +(2.07948 - 1.33640i) q^{34} +(3.21428 - 7.75931i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(6.38655 + 6.08956i) q^{37} +(4.82322 + 3.79302i) q^{38} +(-1.92633 - 5.56575i) q^{39} +(3.16004 - 0.301748i) q^{40} +(0.0901129 + 0.0264595i) q^{41} +(-2.30691 + 1.29545i) q^{42} +(1.32572 + 9.22057i) q^{43} +(0.176110 - 3.69700i) q^{44} +(1.58721 - 2.74913i) q^{45} +(3.91751 - 2.76643i) q^{46} +(-1.77855 - 3.08053i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(2.13101 + 6.66774i) q^{49} +(2.10904 + 4.61814i) q^{50} +(-0.582767 - 2.40220i) q^{51} +(-3.41635 - 4.79759i) q^{52} +(-1.19379 - 3.44924i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(11.2732 - 3.31012i) q^{55} +(-1.84849 + 1.89290i) q^{56} +(5.16193 - 3.31737i) q^{57} +(-6.43309 - 3.31649i) q^{58} +(-6.08330 + 1.17246i) q^{59} +(0.748398 - 3.08494i) q^{60} +(13.8032 - 5.52596i) q^{61} +(-6.60213 + 7.61926i) q^{62} +(0.469685 + 2.60373i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(10.8449 - 15.2296i) q^{65} +(-3.43607 - 1.37560i) q^{66} +(-9.90046 + 5.10404i) q^{67} +(-1.23594 - 2.14071i) q^{68} +(-1.33299 - 4.60686i) q^{69} +(-7.59758 - 3.57984i) q^{70} +(5.90094 + 3.79231i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(-0.966948 - 0.0923323i) q^{73} +(6.38655 - 6.08956i) q^{74} +(5.05395 - 0.482593i) q^{75} +(4.01822 - 4.63728i) q^{76} +(-5.39209 + 8.17419i) q^{77} +(-5.65111 + 1.65931i) q^{78} +(1.10358 - 3.18860i) q^{79} +(-0.151045 - 3.17082i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(0.0307173 - 0.0887519i) q^{82} +(15.2042 - 4.46434i) q^{83} +(1.18421 + 2.36593i) q^{84} +(5.13855 - 5.93020i) q^{85} +(9.27321 - 0.885484i) q^{86} +(-5.23814 + 4.99456i) q^{87} +(-3.68444 - 0.351821i) q^{88} +(-11.8488 + 9.31800i) q^{89} +(-2.67049 - 1.71622i) q^{90} +(1.29607 + 15.5286i) q^{91} +(-2.57690 - 4.04470i) q^{92} +(5.04086 + 8.73103i) q^{93} +(-3.16167 + 1.62995i) q^{94} +(18.0830 + 7.23933i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(-8.27516 - 2.42981i) q^{97} +(6.76159 - 1.81133i) q^{98} +(-2.42377 + 2.79718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.0475819	−	0.998867i	0.0336455	−	0.706306i
$2$	0.0475819	−	0.998867i	0.0336455	−	0.706306i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$4$	−0.995472	−	0.0950560i	−0.497736	−	0.0475280i
$5$	−0.748398	−	3.08494i	−0.334694	−	1.37963i	−0.851873	−	0.523749i	$-0.824533\pi$
$5$	−0.748398	−	3.08494i	−0.334694	−	1.37963i	0.517179	−	0.855877i	$-0.326982\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	2.13670	+	1.56029i	0.807598	+	0.589733i
$7$	2.13670	+	1.56029i	0.807598	+	0.589733i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	−3.11705	+	0.600763i	−0.985699	+	0.189978i
$11$	0.176110	+	3.69700i	0.0530992	+	1.11469i	0.855467	+	0.517858i	$0.173270\pi$
$11$	0.176110	+	3.69700i	0.0530992	+	1.11469i	−0.802367	+	0.596830i	$0.796426\pi$
$12$	0.888835	+	0.458227i	0.256585	+	0.132279i
$13$	3.85692	+	4.45112i	1.06972	+	1.23452i	0.970918	+	0.239412i	$0.0769547\pi$
$13$	3.85692	+	4.45112i	1.06972	+	1.23452i	0.0987994	+	0.995107i	$0.468500\pi$
$14$	1.66019	−	2.06004i	0.443704	−	0.550570i
$15$	−0.451767	+	3.14211i	−0.116646	+	0.811289i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	1.43383	+	2.01353i	0.347755	+	0.488353i	0.950995	−	0.309206i	$-0.100063\pi$
$17$	1.43383	+	2.01353i	0.347755	+	0.488353i	−0.603240	+	0.797560i	$0.706124\pi$
$18$	0.723734	−	0.690079i	0.170586	−	0.162653i
$19$	−3.55923	+	4.99824i	−0.816543	+	1.14667i	0.170364	+	0.985381i	$0.445506\pi$
$19$	−3.55923	+	4.99824i	−0.816543	+	1.14667i	−0.986907	+	0.161293i	$0.948434\pi$
$20$	0.451767	+	3.14211i	0.101018	+	0.702597i
$21$	−1.40375	−	2.24265i	−0.306323	−	0.489387i
$22$	3.70120			0.789098
$23$	2.94970	+	3.78144i	0.615055	+	0.788484i
$23$	2.94970	+	3.78144i	0.615055	+	0.788484i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−4.51256	+	2.32639i	−0.902512	+	0.465277i
$26$	4.62960	−	3.64076i	0.907940	−	0.714012i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	−1.97871	−	1.75633i	−0.373942	−	0.331915i
$29$	3.00663	−	6.58361i	0.558318	−	1.22255i	−0.394470	−	0.918909i	$-0.629072\pi$
$29$	3.00663	−	6.58361i	0.558318	−	1.22255i	0.952788	−	0.303636i	$-0.0982008\pi$
$30$	3.11705	+	0.600763i	0.569093	+	0.109684i
$31$	−7.92477	−	6.23211i	−1.42333	−	1.11932i	−0.974156	−	0.225876i	$-0.927476\pi$
$31$	−7.92477	−	6.23211i	−1.42333	−	1.11932i	−0.449175	−	0.893444i	$-0.648282\pi$
$32$	0.235759	−	0.971812i	0.0416767	−	0.171794i
$33$	1.21054	−	3.49763i	0.210728	−	0.608860i
$34$	2.07948	−	1.33640i	0.356627	−	0.229190i
$35$	3.21428	−	7.75931i	0.543313	−	1.31156i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	6.38655	+	6.08956i	1.04994	+	1.00112i	0.999997	+	0.00236605i	$0.000753139\pi$
$37$	6.38655	+	6.08956i	1.04994	+	1.00112i	0.0499452	+	0.998752i	$0.484095\pi$
$38$	4.82322	+	3.79302i	0.782430	+	0.615309i
$39$	−1.92633	−	5.56575i	−0.308459	−	0.891234i
$40$	3.16004	−	0.301748i	0.499647	−	0.0477105i
$41$	0.0901129	+	0.0264595i	0.0140733	+	0.00413229i	0.288762	−	0.957401i	$-0.406756\pi$
$41$	0.0901129	+	0.0264595i	0.0140733	+	0.00413229i	−0.274688	+	0.961533i	$0.588575\pi$
$42$	−2.30691	+	1.29545i	−0.355963	+	0.199892i
$43$	1.32572	+	9.22057i	0.202170	+	1.40612i	0.797828	+	0.602885i	$0.205982\pi$
$43$	1.32572	+	9.22057i	0.202170	+	1.40612i	−0.595658	+	0.803238i	$0.703108\pi$
$44$	0.176110	−	3.69700i	0.0265496	−	0.557344i
$45$	1.58721	−	2.74913i	0.236607	−	0.409816i
$46$	3.91751	−	2.76643i	0.577605	−	0.407888i
$47$	−1.77855	−	3.08053i	−0.259428	−	0.449342i	0.706661	−	0.707552i	$-0.250201\pi$
$47$	−1.77855	−	3.08053i	−0.259428	−	0.449342i	−0.966089	+	0.258210i	$0.916867\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	2.13101	+	6.66774i	0.304430	+	0.952535i
$50$	2.10904	+	4.61814i	0.298263	+	0.653104i
$51$	−0.582767	−	2.40220i	−0.0816037	−	0.336375i
$52$	−3.41635	−	4.79759i	−0.473763	−	0.665306i
$53$	−1.19379	−	3.44924i	−0.163980	−	0.473790i	0.832836	−	0.553520i	$-0.186716\pi$
$53$	−1.19379	−	3.44924i	−0.163980	−	0.473790i	−0.996817	+	0.0797294i	$0.974594\pi$
$54$	−0.928368	+	0.371662i	−0.126335	+	0.0505769i
$55$	11.2732	−	3.31012i	1.52008	−	0.446336i
$56$	−1.84849	+	1.89290i	−0.247015	+	0.252950i
$57$	5.16193	−	3.31737i	0.683714	−	0.439396i
$58$	−6.43309	−	3.31649i	−0.844706	−	0.435476i
$59$	−6.08330	+	1.17246i	−0.791978	+	0.152641i	−0.569169	−	0.822221i	$-0.692735\pi$
$59$	−6.08330	+	1.17246i	−0.791978	+	0.152641i	−0.222809	+	0.974862i	$0.571523\pi$
$60$	0.748398	−	3.08494i	0.0966177	−	0.398264i
$61$	13.8032	−	5.52596i	1.76732	−	0.707527i	0.769710	−	0.638394i	$-0.220401\pi$
$61$	13.8032	−	5.52596i	1.76732	−	0.707527i	0.997607	−	0.0691337i	$-0.0220235\pi$
$62$	−6.60213	+	7.61926i	−0.838471	+	0.967647i
$63$	0.469685	+	2.60373i	0.0591747	+	0.328039i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	10.8449	−	15.2296i	1.34515	−	1.88900i
$66$	−3.43607	−	1.37560i	−0.422951	−	0.169324i
$67$	−9.90046	+	5.10404i	−1.20953	+	0.623558i	−0.940573	−	0.339593i	$-0.889711\pi$
$67$	−9.90046	+	5.10404i	−1.20953	+	0.623558i	−0.268961	+	0.963151i	$0.586680\pi$
$68$	−1.23594	−	2.14071i	−0.149880	−	0.259599i
$69$	−1.33299	−	4.60686i	−0.160473	−	0.554601i
$70$	−7.59758	−	3.57984i	−0.908085	−	0.427873i
$71$	5.90094	+	3.79231i	0.700313	+	0.450064i	0.841739	−	0.539885i	$-0.181532\pi$
$71$	5.90094	+	3.79231i	0.700313	+	0.450064i	−0.141426	+	0.989949i	$0.545169\pi$
$72$	−0.786053	+	0.618159i	−0.0926372	+	0.0728507i
$73$	−0.966948	−	0.0923323i	−0.113173	−	0.0108067i	0.0383160	−	0.999266i	$-0.487801\pi$
$73$	−0.966948	−	0.0923323i	−0.113173	−	0.0108067i	−0.151489	+	0.988459i	$0.548407\pi$
$74$	6.38655	−	6.08956i	0.742421	−	0.707897i
$75$	5.05395	−	0.482593i	0.583579	−	0.0557251i
$76$	4.01822	−	4.63728i	0.460922	−	0.531932i
$77$	−5.39209	+	8.17419i	−0.614486	+	0.931535i
$78$	−5.65111	+	1.65931i	−0.639862	+	0.187880i
$79$	1.10358	−	3.18860i	0.124163	−	0.358745i	−0.865740	−	0.500495i	$-0.833151\pi$
$79$	1.10358	−	3.18860i	0.124163	−	0.358745i	0.989903	+	0.141749i	$0.0452727\pi$
$80$	−0.151045	−	3.17082i	−0.0168873	−	0.354509i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	0.0307173	−	0.0887519i	0.00339216	−	0.00980100i
$83$	15.2042	−	4.46434i	1.66887	−	0.490025i	0.695361	−	0.718661i	$-0.255245\pi$
$83$	15.2042	−	4.46434i	1.66887	−	0.490025i	0.973512	+	0.228636i	$0.0734265\pi$
$84$	1.18421	+	2.36593i	0.129208	+	0.258144i
$85$	5.13855	−	5.93020i	0.557353	−	0.643220i
$86$	9.27321	−	0.885484i	0.999956	−	0.0954842i
$87$	−5.23814	+	4.99456i	−0.561588	+	0.535473i
$88$	−3.68444	−	0.351821i	−0.392762	−	0.0375043i
$89$	−11.8488	+	9.31800i	−1.25597	+	0.987706i	−0.256192	+	0.966626i	$0.582468\pi$
$89$	−11.8488	+	9.31800i	−1.25597	+	0.987706i	−0.999778	+	0.0210796i	$0.993290\pi$
$90$	−2.67049	−	1.71622i	−0.281494	−	0.180906i
$91$	1.29607	+	15.5286i	0.135865	+	1.62784i
$92$	−2.57690	−	4.04470i	−0.268660	−	0.421689i
$93$	5.04086	+	8.73103i	0.522713	+	0.905366i
$94$	−3.16167	+	1.62995i	−0.326101	+	0.168117i
$95$	18.0830	+	7.23933i	1.85527	+	0.742739i
$96$	−0.580057	+	0.814576i	−0.0592018	+	0.0831373i
$97$	−8.27516	−	2.42981i	−0.840215	−	0.246709i	−0.166816	−	0.985988i	$-0.553348\pi$
$97$	−8.27516	−	2.42981i	−0.840215	−	0.246709i	−0.673400	+	0.739279i	$0.735167\pi$
$98$	6.76159	−	1.81133i	0.683023	−	0.182972i
$99$	−2.42377	+	2.79718i	−0.243598	+	0.281127i
$100$	4.71326	−	1.88691i	0.471326	−	0.188691i
$101$	0.742236	−	3.05954i	0.0738553	−	0.304436i	−0.922889	−	0.385067i	$-0.874178\pi$
$101$	0.742236	−	3.05954i	0.0738553	−	0.304436i	0.996744	+	0.0806312i	$0.0256936\pi$
$102$	−2.42721	+	0.467806i	−0.240329	+	0.0463197i
$103$	−8.46492	−	4.36397i	−0.834073	−	0.429995i	−0.0123791	−	0.999923i	$-0.503940\pi$
$103$	−8.46492	−	4.36397i	−0.834073	−	0.429995i	−0.821694	+	0.569929i	$0.806971\pi$
$104$	−4.95471	+	3.18420i	−0.485850	+	0.312237i
$105$	−5.86788	+	6.00887i	−0.572647	+	0.586406i
$106$	−3.50214	+	1.02832i	−0.340158	+	0.0998794i
$107$	1.79194	−	0.717386i	0.173234	−	0.0693523i	−0.283424	−	0.958995i	$-0.591471\pi$
$107$	1.79194	−	0.717386i	0.173234	−	0.0693523i	0.456658	+	0.889642i	$0.349046\pi$
$108$	0.327068	+	0.945001i	0.0314721	+	0.0909327i
$109$	3.31267	+	4.65200i	0.317297	+	0.445581i	0.942165	−	0.335149i	$-0.108787\pi$
$109$	3.31267	+	4.65200i	0.317297	+	0.445581i	−0.624868	+	0.780730i	$0.714847\pi$
$110$	−2.76997	−	11.4180i	−0.264106	−	1.08866i
$111$	−3.66581	−	8.02700i	−0.347943	−	0.761889i
$112$	1.80281	+	1.93646i	0.170349	+	0.182979i
$113$	3.81037	+	2.44878i	0.358449	+	0.230361i	0.707454	−	0.706760i	$-0.249844\pi$
$113$	3.81037	+	2.44878i	0.358449	+	0.230361i	−0.349004	+	0.937121i	$0.613480\pi$
$114$	−3.06800	−	5.31393i	−0.287344	−	0.497695i
$115$	9.45795	−	11.9297i	0.881958	−	1.11245i
$116$	−3.61883	+	6.26800i	−0.336000	+	0.581969i
$117$	−0.280242	+	5.88301i	−0.0259084	+	0.543884i
$118$	0.881676	+	6.13219i	0.0811649	+	0.564514i
$119$	−0.0780164	+	6.53951i	−0.00715175	+	0.599476i
$120$	−3.04583	−	0.894337i	−0.278045	−	0.0816414i
$121$	−2.68663	+	0.256542i	−0.244239	+	0.0233220i
$122$	−4.86292	−	14.0505i	−0.440268	−	1.27207i
$123$	−0.0738239	−	0.0580558i	−0.00665648	−	0.00523471i
$124$	7.29649	+	6.95719i	0.655244	+	0.624774i
$125$	0.159933	+	0.184572i	0.0143048	+	0.0165086i
$126$	2.62313	−	0.345263i	0.233687	−	0.0307584i
$127$	−4.74822	+	3.05150i	−0.421337	+	0.270777i	−0.734083	−	0.679060i	$-0.762388\pi$
$127$	−4.74822	+	3.05150i	−0.421337	+	0.270777i	0.312746	+	0.949837i	$0.398751\pi$
$128$	−0.327068	+	0.945001i	−0.0289090	+	0.0835271i
$129$	2.19619	−	9.05280i	0.193363	−	0.797055i
$130$	−14.6963	−	11.5573i	−1.28895	−	1.01364i
$131$	1.25003	+	0.240924i	0.109216	+	0.0210497i	0.243566	−	0.969884i	$-0.421683\pi$
$131$	1.25003	+	0.240924i	0.109216	+	0.0210497i	−0.134350	+	0.990934i	$0.542895\pi$
$132$	−1.53753	+	3.36673i	−0.133825	+	0.293036i
$133$	−15.4037	+	5.12634i	−1.33567	+	0.444510i
$134$	4.62718	+	10.1321i	0.399727	+	0.875281i
$135$	−2.49526	+	1.96230i	−0.214758	+	0.168888i
$136$	−2.19709	+	1.13268i	−0.188399	+	0.0971265i
$137$	5.87128	−	10.1694i	0.501618	−	0.868827i	−0.498381	−	0.866958i	$-0.666072\pi$
$137$	5.87128	−	10.1694i	0.501618	−	0.868827i	0.999998	−	0.00186874i	$-0.000594839\pi$
$138$	−4.66507	+	1.11228i	−0.397117	+	0.0946833i
$139$	12.8887			1.09320			0.546601	−	0.837393i	$-0.315922\pi$
$139$	12.8887			1.09320			0.546601	+	0.837393i	$0.315922\pi$
$140$	−3.93730	+	7.41864i	−0.332762	+	0.626990i
$141$	0.506227	+	3.52089i	0.0426320	+	0.296512i
$142$	4.06879	−	5.71381i	0.341445	−	0.479493i
$143$	−15.7766	+	15.0429i	−1.31930	+	1.25795i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	−22.5602	−	4.34812i	−1.87352	−	0.361091i
$146$	−0.138237	+	0.961460i	−0.0114406	+	0.0795710i
$147$	0.499786	−	6.98214i	0.0412216	−	0.575877i
$148$	−5.77878	−	6.66907i	−0.475013	−	0.548194i
$149$	−7.14014	−	3.68100i	−0.584943	−	0.301559i	0.140237	−	0.990118i	$-0.455213\pi$
$149$	−7.14014	−	3.68100i	−0.584943	−	0.301559i	−0.725181	+	0.688559i	$0.758244\pi$
$150$	−0.241570	−	5.07118i	−0.0197241	−	0.414060i
$151$	−14.1890	+	2.73471i	−1.15468	+	0.222547i	−0.730425	−	0.682993i	$-0.760678\pi$
$151$	−14.1890	+	2.73471i	−1.15468	+	0.222547i	−0.424260	+	0.905541i	$0.639466\pi$
$152$	−4.44083	−	4.23432i	−0.360199	−	0.343449i
$153$	−0.351785	+	2.44672i	−0.0284401	+	0.197805i
$154$	7.90836	+	5.77493i	0.637274	+	0.465357i
$155$	−13.2948	+	29.1115i	−1.06786	+	2.33829i
$156$	1.38854	+	5.72366i	0.111173	+	0.458260i
$157$	11.3213	+	1.08105i	0.903537	+	0.0862773i	0.536472	−	0.843918i	$-0.319757\pi$
$157$	11.3213	+	1.08105i	0.903537	+	0.0862773i	0.367065	+	0.930195i	$0.380363\pi$
$158$	−3.13248	−	1.25405i	−0.249206	−	0.0997672i
$159$	−0.173674	+	3.64586i	−0.0137732	+	0.289135i
$160$	−3.17442			−0.250960
$161$	0.402514	+	12.6822i	0.0317225	+	0.999497i
$162$	1.00000			0.0785674
$163$	0.100486	−	2.10946i	0.00787065	−	0.165225i	−0.991510	−	0.130032i	$-0.958492\pi$
$163$	0.100486	−	2.10946i	0.00787065	−	0.165225i	0.999381	−	0.0351938i	$-0.0112048\pi$
$164$	−0.0871898	−	0.0349055i	−0.00680838	−	0.00272566i
$165$	−11.6959	−	1.11683i	−0.910528	−	0.0869449i
$166$	−3.73584	−	15.3994i	−0.289958	−	1.19522i
$167$	8.40722	−	18.4093i	0.650570	−	1.42455i	−0.240483	−	0.970653i	$-0.577306\pi$
$167$	8.40722	−	18.4093i	0.650570	−	1.42455i	0.891054	−	0.453897i	$-0.149967\pi$
$168$	2.41960	−	1.07030i	0.186676	−	0.0825752i
$169$	−3.08657	+	21.4676i	−0.237429	+	1.65135i
$170$	−5.67898	−	5.41490i	−0.435558	−	0.415303i
$171$	−6.02511	+	1.16125i	−0.460752	+	0.0888026i
$172$	−0.443244	−	9.30484i	−0.0337970	−	0.709487i
$173$	5.75467	+	2.96674i	0.437519	+	0.225557i	0.662891	−	0.748716i	$-0.269329\pi$
$173$	5.75467	+	2.96674i	0.437519	+	0.225557i	−0.225372	+	0.974273i	$0.572360\pi$
$174$	4.73966	+	5.46986i	0.359313	+	0.414669i
$175$	−13.2718	−	2.07009i	−1.00326	−	0.156484i
$176$	−0.526735	+	3.66352i	−0.0397042	+	0.276148i
$177$	6.08330	+	1.17246i	0.457249	+	0.0881274i
$178$	8.74365	+	12.2787i	0.655365	+	0.920331i
$179$	−10.0490	+	9.58174i	−0.751101	+	0.716173i	−0.965451	−	0.260584i	$-0.916085\pi$
$179$	−10.0490	+	9.58174i	−0.751101	+	0.716173i	0.214351	+	0.976757i	$0.431236\pi$
$180$	−1.84134	+	2.58581i	−0.137246	+	0.192735i
$181$	−2.93992	−	20.4476i	−0.218523	−	1.51986i	−0.743495	−	0.668741i	$-0.766834\pi$
$181$	−2.93992	−	20.4476i	−0.218523	−	1.51986i	0.524973	−	0.851119i	$-0.324076\pi$
$182$	15.5727	−	0.555722i	1.15433	−	0.0411928i
$183$	−14.8682			−1.09909
$184$	−4.16273	+	2.38152i	−0.306881	+	0.175568i
$185$	14.0062	−	24.2595i	1.02976	−	1.78360i
$186$	8.96099	−	4.61971i	0.657052	−	0.338734i
$187$	−7.19152	+	5.65548i	−0.525896	+	0.413569i
$188$	1.47767	+	3.23565i	0.107770	+	0.235984i
$189$	0.531667	−	2.59178i	0.0386731	−	0.188524i
$190$	8.09155	−	17.7180i	0.587023	−	1.28540i
$191$	9.07067	+	1.74823i	0.656331	+	0.126497i	0.506535	−	0.862220i	$-0.330926\pi$
$191$	9.07067	+	1.74823i	0.656331	+	0.126497i	0.149796	+	0.988717i	$0.452138\pi$
$192$	0.786053	+	0.618159i	0.0567285	+	0.0446118i
$193$	1.37164	−	5.65397i	0.0987328	−	0.406982i	−0.900902	−	0.434023i	$-0.857093\pi$
$193$	1.37164	−	5.65397i	0.0987328	−	0.406982i	0.999634	+	0.0270415i	$0.00860863\pi$
$194$	−2.82080	+	8.15017i	−0.202522	+	0.585148i
$195$	−15.7283	+	10.1080i	−1.12633	+	0.723848i
$196$	−1.48755	−	6.84012i	−0.106254	−	0.488580i
$197$	−3.54063	−	4.08611i	−0.252260	−	0.291123i	0.615469	−	0.788161i	$-0.288966\pi$
$197$	−3.54063	−	4.08611i	−0.252260	−	0.291123i	−0.867729	+	0.497038i	$0.834421\pi$
$198$	2.67868	+	2.55412i	0.190366	+	0.181513i
$199$	4.51365	+	3.54957i	0.319964	+	0.251623i	0.765203	−	0.643789i	$-0.222639\pi$
$199$	4.51365	+	3.54957i	0.319964	+	0.251623i	−0.445239	+	0.895412i	$0.646881\pi$
$200$	−1.66050	−	4.79771i	−0.117415	−	0.339249i
$201$	11.0883	−	1.05880i	0.782105	−	0.0746820i
$202$	−3.02076	−	0.886974i	−0.212540	−	0.0624073i
$203$	16.6966	−	9.37601i	1.17187	−	0.658067i
$204$	0.351785	+	2.44672i	0.0246299	+	0.171305i
$205$	0.0141857	−	0.297795i	0.000990774	−	0.0207989i
$206$	−4.76180	+	8.24768i	−0.331771	+	0.574643i
$207$	−0.474692	+	4.77228i	−0.0329933	+	0.331696i
$208$	2.94484	+	5.10061i	0.204188	+	0.353664i
$209$	−19.1053	−	12.2782i	−1.32154	−	0.849304i
$210$	5.72286	+	6.14715i	0.394915	+	0.424194i
$211$	12.0152	+	26.3096i	0.827160	+	1.81123i	0.498989	+	0.866609i	$0.333705\pi$
$211$	12.0152	+	26.3096i	0.827160	+	1.81123i	0.328171	+	0.944618i	$0.393568\pi$
$212$	0.860518	+	3.54710i	0.0591006	+	0.243616i
$213$	−4.06879	−	5.71381i	−0.278789	−	0.391504i
$214$	−0.631309	−	1.82405i	−0.0431554	−	0.124689i
$215$	27.4527	−	10.9904i	1.87226	−	0.749540i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	−7.20902	−	25.6811i	−0.489380	−	1.74335i
$218$	4.80435	−	3.08757i	0.325392	−	0.209117i
$219$	0.863367	+	0.445097i	0.0583409	+	0.0300768i
$220$	−11.5368	+	2.22354i	−0.777813	+	0.149911i
$221$	−3.43231	+	14.1482i	−0.230882	+	0.951710i
$222$	−8.19233	+	3.27971i	−0.549833	+	0.220120i
$223$	6.33651	−	7.31273i	0.424324	−	0.489696i	−0.502825	−	0.864388i	$-0.667706\pi$
$223$	6.33651	−	7.31273i	0.424324	−	0.489696i	0.927149	+	0.374692i	$0.122251\pi$
$224$	2.02005	−	1.70862i	0.134970	−	0.114162i
$225$	−4.87128	−	1.43034i	−0.324752	−	0.0953559i
$226$	2.62731	−	3.68954i	0.174766	−	0.245424i
$227$	11.5180	+	4.61113i	0.764479	+	0.306051i	0.720937	−	0.693000i	$-0.243712\pi$
$227$	11.5180	+	4.61113i	0.764479	+	0.306051i	0.0435417	+	0.999052i	$0.486136\pi$
$228$	−5.45389	+	2.81168i	−0.361193	+	0.186208i
$229$	5.78093	+	10.0129i	0.382015	+	0.661669i	0.991350	−	0.131244i	$-0.0418970\pi$
$229$	5.78093	+	10.0129i	0.382015	+	0.661669i	−0.609335	+	0.792913i	$0.708564\pi$
$230$	−11.4661	−	10.0149i	−0.756054	−	0.660361i
$231$	8.04388	−	5.58462i	0.529249	−	0.367441i
$232$	6.08871	+	3.91297i	0.399743	+	0.256899i
$233$	−12.7481	+	10.0252i	−0.835154	+	0.656772i	−0.941297	−	0.337578i	$-0.890392\pi$
$233$	−12.7481	+	10.0252i	−0.835154	+	0.656772i	0.106143	+	0.994351i	$0.466150\pi$
$234$	5.86301	+	0.559850i	0.383277	+	0.0365985i
$235$	−8.17219	+	7.79217i	−0.533095	+	0.508305i
$236$	6.16720	−	0.588896i	0.401451	−	0.0383339i
$237$	−2.20962	+	2.55003i	−0.143530	+	0.165642i
$238$	6.52839	+	0.389090i	0.423173	+	0.0252210i
$239$	−9.10639	+	2.67388i	−0.589043	+	0.172959i	−0.562653	−	0.826693i	$-0.690219\pi$
$239$	−9.10639	+	2.67388i	−0.589043	+	0.172959i	−0.0263902	+	0.999652i	$0.508401\pi$
$240$	−1.03825	+	2.99983i	−0.0670188	+	0.193638i
$241$	−0.422853	−	8.87678i	−0.0272384	−	0.571804i	−0.970696	−	0.240311i	$-0.922751\pi$
$241$	−0.422853	−	8.87678i	−0.0272384	−	0.571804i	0.943458	−	0.331493i	$-0.107552\pi$
$242$	0.128417	+	2.69580i	0.00825493	+	0.173292i
$243$	0.327068	−	0.945001i	0.0209814	−	0.0606218i
$244$	−14.2660	+	4.18887i	−0.913285	+	0.268165i
$245$	18.9747	−	11.5642i	1.21225	−	0.738807i
$246$	−0.0615027	+	0.0709779i	−0.00392127	+	0.00452539i
$247$	−35.9754	+	3.43524i	−2.28906	+	0.218579i
$248$	7.29649	−	6.95719i	0.463327	−	0.441782i
$249$	−15.7743	−	1.50626i	−0.999654	−	0.0954554i
$250$	0.191973	−	0.150969i	0.0121414	−	0.00954813i
$251$	3.39478	+	2.18169i	0.214277	+	0.137707i	0.643377	−	0.765550i	$-0.277533\pi$
$251$	3.39478	+	2.18169i	0.214277	+	0.137707i	−0.429100	+	0.903257i	$0.641169\pi$
$252$	−0.220058	−	2.63658i	−0.0138624	−	0.166089i
$253$	−13.4605	+	11.5710i	−0.846255	+	0.727463i
$254$	2.82211	+	4.88804i	0.177075	+	0.306703i
$255$	−6.97449	+	3.59560i	−0.436760	+	0.225165i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	−5.18868	+	7.28648i	−0.323661	+	0.454518i	−0.944063	−	0.329766i	$-0.893030\pi$
$257$	−5.18868	+	7.28648i	−0.323661	+	0.454518i	0.620402	+	0.784284i	$0.286970\pi$
$258$	−8.93805	−	2.62445i	−0.556459	−	0.163391i
$259$	4.14471	+	22.9764i	0.257540	+	1.42769i
$260$	−12.2435	+	14.1297i	−0.759309	+	0.876289i
$261$	6.71921	−	2.68997i	0.415909	−	0.166505i
$262$	0.300131	−	1.23716i	0.0185421	−	0.0764317i
$263$	22.9400	−	4.42132i	1.41454	−	0.272631i	0.575992	−	0.817455i	$-0.304616\pi$
$263$	22.9400	−	4.42132i	1.41454	−	0.272631i	0.838550	+	0.544825i	$0.183404\pi$
$264$	3.28975	+	1.69599i	0.202470	+	0.104381i
$265$	−9.74727	+	6.26419i	−0.598770	+	0.384806i
$266$	4.38759	+	15.6302i	0.269021	+	0.958347i
$267$	14.4632	−	4.24678i	0.885133	−	0.259898i
$268$	10.3408	−	4.13983i	0.631665	−	0.252881i
$269$	9.45411	+	27.3159i	0.576427	+	1.66548i	0.734949	+	0.678122i	$0.237206\pi$
$269$	9.45411	+	27.3159i	0.576427	+	1.66548i	−0.158522	+	0.987355i	$0.550673\pi$
$270$	1.84134	+	2.58581i	0.112061	+	0.157367i
$271$	−6.19427	−	25.5331i	−0.376275	−	1.55103i	−0.773797	−	0.633434i	$-0.781645\pi$
$271$	−6.19427	−	25.5331i	−0.376275	−	1.55103i	0.397522	−	0.917593i	$-0.369870\pi$
$272$	1.02686	+	2.24850i	0.0622622	+	0.136335i
$273$	4.56818	−	14.8980i	0.276479	−	0.901667i
$274$	−9.87847	−	6.34851i	−0.596780	−	0.383528i
$275$	−9.39537	−	16.2733i	−0.566562	−	0.981314i
$276$	0.889044	+	4.71271i	0.0535141	+	0.283672i
$277$	−5.68541	+	9.84742i	−0.341603	+	0.591674i	−0.984731	−	0.174085i	$-0.944303\pi$
$277$	−5.68541	+	9.84742i	−0.341603	+	0.591674i	0.643127	+	0.765759i	$0.277637\pi$
$278$	0.613267	−	12.8741i	0.0367813	−	0.772134i
$279$	−1.43478	−	9.97911i	−0.0858980	−	0.597434i
$280$	7.22289	+	4.28583i	0.431651	+	0.256127i
$281$	−18.4025	−	5.40347i	−1.09780	−	0.322344i	−0.317824	−	0.948150i	$-0.602952\pi$
$281$	−18.4025	−	5.40347i	−1.09780	−	0.322344i	−0.779979	+	0.625806i	$0.784770\pi$
$282$	3.54099	−	0.338123i	0.210863	−	0.0201349i
$283$	4.69348	+	13.5609i	0.278999	+	0.806113i	0.994234	+	0.107230i	$0.0341981\pi$
$283$	4.69348	+	13.5609i	0.278999	+	0.806113i	−0.715236	+	0.698883i	$0.753681\pi$
$284$	−5.51374	−	4.33605i	−0.327180	−	0.257297i
$285$	−14.0971	−	13.4415i	−0.835037	−	0.796207i
$286$	14.2752	+	16.4745i	0.844111	+	0.974157i
$287$	0.151260	+	0.197138i	0.00892861	+	0.0116367i
$288$	0.841254	−	0.540641i	0.0495713	−	0.0318576i
$289$	3.56171	−	10.2909i	0.209512	−	0.605346i
$290$	−5.41665	+	22.3277i	−0.318076	+	1.31113i
$291$	6.77932	+	5.33132i	0.397411	+	0.312528i
$292$	0.953793	+	0.183829i	0.0558165	+	0.0107578i
$293$	−0.706331	+	1.54665i	−0.0412643	+	0.0903562i	−0.929142	−	0.369724i	$-0.879452\pi$
$293$	−0.706331	+	1.54665i	−0.0412643	+	0.0903562i	0.887877	+	0.460080i	$0.152179\pi$
$294$	−6.95045	−	0.831443i	−0.405358	−	0.0484907i
$295$	8.16969	+	17.8891i	0.475658	+	1.04154i
$296$	−6.93648	+	5.45491i	−0.403175	+	0.317060i
$297$	3.28975	−	1.69599i	0.190891	−	0.0984111i
$298$	−4.01657	+	6.95690i	−0.232674	+	0.403003i
$299$	−5.45488	+	27.7142i	−0.315464	+	1.60275i
$300$	−5.07694			−0.293117
$301$	−11.5541	+	21.7701i	−0.665965	+	1.25481i
$302$	2.05647	+	14.3031i	0.118336	+	0.823048i
$303$	−1.82618	+	2.56452i	−0.104912	+	0.147328i
$304$	−4.44083	+	4.23432i	−0.254699	+	0.242855i
$305$	−27.3775	−	38.4464i	−1.56763	−	2.20143i
$306$	2.42721	+	0.467806i	0.138754	+	0.0267427i
$307$	−0.961437	+	6.68694i	−0.0548721	+	0.381644i	0.943817	+	0.330467i	$0.107206\pi$
$307$	−0.961437	+	6.68694i	−0.0548721	+	0.381644i	−0.998690	+	0.0511768i	$0.983703\pi$
$308$	6.14468	−	7.62462i	0.350126	−	0.434453i
$309$	6.23664	+	7.19746i	0.354790	+	0.409449i
$310$	28.4459	+	14.6649i	1.61562	+	0.832911i
$311$	0.168829	+	3.54416i	0.00957343	+	0.200971i	0.998587	+	0.0531450i	$0.0169245\pi$
$311$	0.168829	+	3.54416i	0.00957343	+	0.200971i	−0.989013	+	0.147826i	$0.952772\pi$
$312$	5.78325	−	1.11463i	0.327412	−	0.0631035i
$313$	6.25490	+	5.96403i	0.353548	+	0.337107i	0.845952	−	0.533260i	$-0.179033\pi$
$313$	6.25490	+	5.96403i	0.353548	+	0.337107i	−0.492404	+	0.870367i	$0.663882\pi$
$314$	1.61852	−	11.2570i	0.0913381	−	0.635271i
$315$	7.68082	−	3.39757i	0.432765	−	0.191431i
$316$	−1.40168	+	3.06926i	−0.0788508	+	0.172659i
$317$	−3.04720	−	12.5607i	−0.171148	−	0.705480i	−0.991108	−	0.133060i	$-0.957520\pi$
$317$	−3.04720	−	12.5607i	−0.171148	−	0.705480i	0.819960	−	0.572420i	$-0.193995\pi$
$318$	3.63346	+	0.346954i	0.203754	+	0.0194562i
$319$	24.8691	+	9.95609i	1.39240	+	0.557434i
$320$	−0.151045	+	3.17082i	−0.00844367	+	0.177254i
$321$	−1.93021			−0.107734
$322$	12.6870	+	0.201385i	0.707018	+	0.0112227i
$323$	−15.1674			−0.843939
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	−27.7596	−	11.1133i	−1.53983	−	0.616454i
$326$	−2.10229	−	0.200744i	−0.116435	−	0.0111182i
$327$	−1.34641	−	5.54996i	−0.0744564	−	0.306914i
$328$	−0.0390146	+	0.0854301i	−0.00215422	+	0.00471709i
$329$	1.00629	−	9.35723i	0.0554783	−	0.515881i
$330$	−1.67208	+	11.6296i	−0.0920449	+	0.640186i
$331$	14.2569	+	13.5940i	0.783632	+	0.747191i	0.972019	−	0.234904i	$-0.0754774\pi$
$331$	14.2569	+	13.5940i	0.783632	+	0.747191i	−0.188387	+	0.982095i	$0.560326\pi$
$332$	−15.5597	+	2.99888i	−0.853948	+	0.164585i
$333$	0.419884	+	8.81445i	0.0230095	+	0.483029i
$334$	−17.9884	−	9.27365i	−0.984280	−	0.507431i
$335$	23.1551	+	26.7224i	1.26510	+	1.46000i
$336$	−0.953956	−	2.46779i	−0.0520425	−	0.134629i
$337$	0.312099	−	2.17070i	0.0170011	−	0.118245i	−0.979554	−	0.201183i	$-0.935521\pi$
$337$	0.312099	−	2.17070i	0.0170011	−	0.118245i	0.996555	+	0.0829380i	$0.0264303\pi$
$338$	21.2964	+	4.10455i	1.15837	+	0.223258i
$339$	−2.62731	−	3.68954i	−0.142696	−	0.200388i
$340$	−5.67898	+	5.41490i	−0.307986	+	0.293664i
$341$	21.6445	−	30.3954i	1.17212	−	1.64601i
$342$	0.873243	+	6.07354i	0.0472196	+	0.328420i
$343$	−5.85024	+	17.5720i	−0.315883	+	0.948798i
$344$	−9.31539			−0.502252
$345$	−13.2143	+	7.55995i	−0.711432	+	0.407014i
$346$	3.23720	−	5.60699i	0.174033	−	0.301434i
$347$	19.4451	−	10.0246i	1.04387	−	0.538151i	0.151029	−	0.988529i	$-0.451741\pi$
$347$	19.4451	−	10.0246i	1.04387	−	0.538151i	0.892838	+	0.450379i	$0.148711\pi$
$348$	5.68918	−	4.47402i	0.304972	−	0.239833i
$349$	−10.8036	−	23.6567i	−0.578306	−	1.26631i	−0.942256	−	0.334894i	$-0.891299\pi$
$349$	−10.8036	−	23.6567i	−0.578306	−	1.26631i	0.363950	−	0.931418i	$-0.381428\pi$
$350$	−2.69924	+	13.1583i	−0.144280	+	0.703341i
$351$	2.44666	−	5.35744i	0.130593	−	0.285959i
$352$	3.63431	+	0.700456i	0.193709	+	0.0373344i
$353$	−20.0370	−	15.7573i	−1.06646	−	0.838676i	−0.0790547	−	0.996870i	$-0.525190\pi$
$353$	−20.0370	−	15.7573i	−1.06646	−	0.838676i	−0.987408	+	0.158195i	$0.949433\pi$
$354$	1.46059	−	6.02062i	0.0776293	−	0.319992i
$355$	7.28277	−	21.0422i	0.386529	−	1.11680i
$356$	12.6809	−	8.14950i	0.672085	−	0.431923i
$357$	2.50292	−	6.04207i	0.132468	−	0.319780i
$358$	9.09274	+	10.4936i	0.480566	+	0.554603i
$359$	17.1142	+	16.3184i	0.903255	+	0.861252i	0.990859	−	0.134903i	$-0.0430724\pi$
$359$	17.1142	+	16.3184i	0.903255	+	0.861252i	−0.0876035	+	0.996155i	$0.527921\pi$
$360$	2.49526	+	1.96230i	0.131512	+	0.103422i
$361$	−6.09997	−	17.6247i	−0.321051	−	0.927616i
$362$	−20.5644	+	1.96366i	−1.08084	+	0.103208i
$363$	2.58953	+	0.760355i	0.135915	+	0.0399083i
$364$	0.185888	−	15.5815i	0.00974316	−	0.816694i
$365$	0.438822	+	3.05208i	0.0229690	+	0.159753i
$366$	−0.707459	+	14.8514i	−0.0369795	+	0.776295i
$367$	11.2052	−	19.4080i	0.584907	−	1.01309i	−0.409980	−	0.912095i	$-0.634464\pi$
$367$	11.2052	−	19.4080i	0.584907	−	1.01309i	0.994887	−	0.100995i	$-0.0322025\pi$
$368$	2.18075	+	4.27134i	0.113680	+	0.222659i
$369$	0.0469586	+	0.0813347i	0.00244457	+	0.00423412i
$370$	−23.5656	−	15.1447i	−1.22512	−	0.787335i
$371$	2.83102	−	9.23268i	0.146979	−	0.479337i
$372$	−4.18810	−	9.17066i	−0.217143	−	0.475477i
$373$	2.67203	+	11.0143i	0.138352	+	0.570296i	0.998212	+	0.0597664i	$0.0190356\pi$
$373$	2.67203	+	11.0143i	0.138352	+	0.570296i	−0.859860	+	0.510530i	$0.829449\pi$
$374$	5.30689	+	7.45248i	0.274413	+	0.385358i
$375$	−0.0798778	−	0.230792i	−0.00412487	−	0.0119180i
$376$	3.30229	−	1.32204i	0.170303	−	0.0681789i
$377$	40.9008	−	12.0096i	2.10650	−	0.618524i
$378$	−2.56355	−	0.654387i	−0.131855	−	0.0336580i
$379$	22.2500	−	14.2992i	1.14291	−	0.734501i	0.174692	−	0.984623i	$-0.444107\pi$
$379$	22.2500	−	14.2992i	1.14291	−	0.734501i	0.968214	+	0.250122i	$0.0804707\pi$
$380$	−17.3129	−	8.92544i	−0.888135	−	0.457865i
$381$	5.54223	−	1.06818i	0.283937	−	0.0547244i
$382$	2.17785	−	8.97721i	0.111428	−	0.459314i
$383$	−19.8546	+	7.94858i	−1.01452	+	0.406154i	−0.818537	−	0.574453i	$-0.805215\pi$
$383$	−19.8546	+	7.94858i	−1.01452	+	0.406154i	−0.195985	+	0.980607i	$0.562791\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	29.2523	+	10.5167i	1.49083	+	0.535981i
$386$	−5.58231	−	1.63911i	−0.284132	−	0.0834286i
$387$	−5.40346	+	7.58809i	−0.274673	+	0.385724i
$388$	8.00672	+	3.20541i	0.406480	+	0.162730i
$389$	9.11340	−	4.69828i	0.462068	−	0.238212i	−0.211442	−	0.977390i	$-0.567816\pi$
$389$	9.11340	−	4.69828i	0.462068	−	0.238212i	0.673510	+	0.739178i	$0.264786\pi$
$390$	9.34816	+	16.1915i	0.473362	+	0.819888i
$391$	−3.38468	+	11.3613i	−0.171170	+	0.574563i
$392$	−6.90315	+	1.16040i	−0.348662	+	0.0586092i
$393$	−1.07095	−	0.688257i	−0.0540223	−	0.0347180i
$394$	−4.24995	+	3.34220i	−0.214109	+	0.168377i
$395$	−10.6625	−	1.01815i	−0.536491	−	0.0512287i
$396$	2.67868	−	2.55412i	0.134609	−	0.128349i
$397$	−7.86528	+	0.751043i	−0.394747	+	0.0376938i	−0.290542	−	0.956862i	$-0.593836\pi$
$397$	−7.86528	+	0.751043i	−0.394747	+	0.0376938i	−0.104205	+	0.994556i	$0.533230\pi$
$398$	3.76032	−	4.33964i	0.188488	−	0.217527i
$399$	16.2056	+	0.965848i	0.811293	+	0.0483529i
$400$	−4.87128	+	1.43034i	−0.243564	+	0.0715169i
$401$	0.516990	−	1.49374i	0.0258173	−	0.0745941i	−0.931356	−	0.364110i	$-0.881373\pi$
$401$	0.516990	−	1.49374i	0.0258173	−	0.0745941i	0.957173	+	0.289516i	$0.0934944\pi$
$402$	−0.530000	−	11.1261i	−0.0264340	−	0.554918i
$403$	−2.82533	−	59.3109i	−0.140739	−	2.95449i
$404$	−1.02970	+	2.97513i	−0.0512296	+	0.148018i
$405$	3.04583	−	0.894337i	0.151349	−	0.0444400i
$406$	−8.57094	−	17.1238i	−0.425369	−	0.849841i
$407$	−21.3884	+	24.6835i	−1.06018	+	1.22352i
$408$	2.46068	−	0.234967i	0.121822	−	0.0116326i
$409$	4.95442	−	4.72403i	0.244980	−	0.233588i	−0.557633	−	0.830087i	$-0.688291\pi$
$409$	4.95442	−	4.72403i	0.244980	−	0.233588i	0.802614	+	0.596499i	$0.203442\pi$
$410$	−0.296783	−	0.0283393i	−0.0146571	−	0.00139958i
$411$	−9.23028	+	7.25877i	−0.455296	+	0.358049i
$412$	8.01177	+	5.14885i	0.394711	+	0.253666i
$413$	−14.8276	−	6.98649i	−0.729618	−	0.343783i
$414$	4.74429	+	0.701228i	0.233169	+	0.0344635i
$415$	−25.1510	−	43.5627i	−1.23461	−	2.13841i
$416$	5.23496	−	2.69881i	0.256665	−	0.132320i
$417$	−11.9654	−	4.79023i	−0.585949	−	0.234578i
$418$	−13.1734	+	18.4995i	−0.644332	+	0.904838i
$419$	−26.1053	−	7.66520i	−1.27533	−	0.374470i	−0.427149	−	0.904181i	$-0.640482\pi$
$419$	−26.1053	−	7.66520i	−1.27533	−	0.374470i	−0.848178	+	0.529712i	$0.822300\pi$
$420$	6.41249	−	5.42388i	0.312897	−	0.264658i
$421$	22.2111	−	25.6330i	1.08250	−	1.24928i	0.115828	−	0.993269i	$-0.463048\pi$
$421$	22.2111	−	25.6330i	1.08250	−	1.24928i	0.966675	−	0.256006i	$-0.0824068\pi$
$422$	26.8515	−	10.7497i	1.30711	−	0.523288i
$423$	0.838616	−	3.45682i	0.0407749	−	0.168077i
$424$	3.58403	−	0.690765i	0.174056	−	0.0335465i
$425$	−11.1545	−	5.75054i	−0.541073	−	0.278942i
$426$	−5.90094	+	3.79231i	−0.285902	+	0.183738i
$427$	38.1154	+	9.72958i	1.84453	+	0.470847i
$428$	−1.85202	+	0.543803i	−0.0895208	+	0.0262857i
$429$	20.2374	−	8.10182i	0.977069	−	0.391160i
$430$	−9.67171	−	27.9446i	−0.466411	−	1.34761i
$431$	−13.5995	−	19.0979i	−0.655067	−	0.919913i	0.344757	−	0.938692i	$-0.387961\pi$
$431$	−13.5995	−	19.0979i	−0.655067	−	0.919913i	−0.999824	+	0.0187791i	$0.994022\pi$
$432$	−0.235759	−	0.971812i	−0.0113430	−	0.0467563i
$433$	−7.57175	−	16.5798i	−0.363875	−	0.796775i	−0.999689	−	0.0249331i	$-0.992063\pi$
$433$	−7.57175	−	16.5798i	−0.363875	−	0.796775i	0.635814	−	0.771842i	$-0.280665\pi$
$434$	−25.9950	+	5.97890i	−1.24780	+	0.286996i
$435$	19.3281	+	12.4214i	0.926712	+	0.595561i
$436$	−2.85547	−	4.94582i	−0.136752	−	0.236862i
$437$	−29.3992	+	1.28430i	−1.40635	+	0.0614366i
$438$	0.485673	−	0.841211i	0.0232064	−	0.0401946i
$439$	−0.686977	+	14.4214i	−0.0327876	+	0.688297i	0.921315	+	0.388817i	$0.127116\pi$
$439$	−0.686977	+	14.4214i	−0.0327876	+	0.688297i	−0.954103	+	0.299480i	$0.903187\pi$
$440$	1.67208	+	11.6296i	0.0797132	+	0.554417i
$441$	−3.05898	+	6.29624i	−0.145666	+	0.299821i
$442$	13.9688	+	4.10162i	0.664430	+	0.195094i
$443$	−13.9767	+	1.33461i	−0.664052	+	0.0634093i	−0.421639	−	0.906764i	$-0.638545\pi$
$443$	−13.9767	+	1.33461i	−0.664052	+	0.0634093i	−0.242413	+	0.970173i	$0.577939\pi$
$444$	2.88619	+	8.33911i	0.136973	+	0.395756i
$445$	37.6130	+	29.5792i	1.78303	+	1.40219i
$446$	−7.00294	−	6.67729i	−0.331599	−	0.316179i
$447$	5.26059	+	6.07104i	0.248817	+	0.287150i
$448$	−1.61057	−	2.09906i	−0.0760923	−	0.0991714i
$449$	−18.0914	+	11.6266i	−0.853785	+	0.548694i	−0.892753	−	0.450546i	$-0.851229\pi$
$449$	−18.0914	+	11.6266i	−0.853785	+	0.548694i	0.0389681	+	0.999240i	$0.487593\pi$
$450$	−1.66050	+	4.79771i	−0.0782769	+	0.226166i
$451$	−0.0819512	+	0.337808i	−0.00385893	+	0.0159067i
$452$	−3.56035	−	2.79989i	−0.167465	−	0.131696i
$453$	14.1890	+	2.73471i	0.666657	+	0.128488i
$454$	5.15395	−	11.2856i	0.241887	−	0.529659i
$455$	46.9349	−	15.6199i	2.20034	−	0.732272i
$456$	2.54899	+	5.58150i	0.119367	+	0.261378i
$457$	10.4116	−	8.18780i	0.487036	−	0.383009i	−0.344229	−	0.938886i	$-0.611860\pi$
$457$	10.4116	−	8.18780i	0.487036	−	0.383009i	0.831265	+	0.555876i	$0.187617\pi$
$458$	10.2766	−	5.29795i	0.480194	−	0.247557i
$459$	1.23594	−	2.14071i	0.0576887	−	0.0999197i
$460$	−10.5491	+	10.9766i	−0.491855	+	0.511787i
$461$	20.4053			0.950369			0.475184	−	0.879886i	$-0.342381\pi$
$461$	20.4053			0.950369			0.475184	+	0.879886i	$0.342381\pi$
$462$	−5.19555	−	8.30050i	−0.241719	−	0.386174i
$463$	−2.67492	−	18.6045i	−0.124314	−	0.864623i	−0.952580	−	0.304288i	$-0.901582\pi$
$463$	−2.67492	−	18.6045i	−0.124314	−	0.864623i	0.828266	−	0.560335i	$-0.189328\pi$
$464$	4.19825	−	5.89562i	0.194899	−	0.273697i
$465$	23.1621	−	22.0850i	1.07412	−	1.02417i
$466$	9.40726	+	13.2107i	0.435783	+	0.611972i
$467$	−25.5565	−	4.92561i	−1.18261	−	0.227930i	−0.440217	−	0.897891i	$-0.645099\pi$
$467$	−25.5565	−	4.92561i	−1.18261	−	0.227930i	−0.742396	+	0.669961i	$0.766311\pi$
$468$	0.838189	−	5.82973i	0.0387453	−	0.269479i
$469$	−29.1181	−	4.54172i	−1.34455	−	0.209717i
$470$	7.39449	+	8.53370i	0.341082	+	0.393630i
$471$	−10.1085	−	5.21131i	−0.465777	−	0.240125i
$472$	−0.294782	−	6.18824i	−0.0135684	−	0.284837i
$473$	−33.8550	+	6.52502i	−1.55666	+	0.300021i
$474$	2.44201	+	2.32845i	0.112165	+	0.106949i
$475$	4.43340	−	30.8350i	0.203418	−	1.41481i
$476$	0.699283	−	6.50248i	0.0320516	−	0.298041i
$477$	1.51626	−	3.32015i	0.0694248	−	0.152019i
$478$	2.23755	+	9.22331i	0.102343	+	0.421864i
$479$	−30.9370	−	2.95413i	−1.41355	−	0.134978i	−0.639835	−	0.768512i	$-0.720997\pi$
$479$	−30.9370	−	2.95413i	−1.41355	−	0.134978i	−0.773714	+	0.633535i	$0.781603\pi$
$480$	2.94703	+	1.17981i	0.134513	+	0.0538508i
$481$	−2.47298	+	51.9143i	−0.112758	+	2.36709i
$482$	−8.88685			−0.404785
$483$	4.33981	−	11.9233i	0.197468	−	0.542531i
$484$	2.69885			0.122675
$485$	−1.30269	+	27.3468i	−0.0591521	+	1.24175i
$486$	−0.928368	−	0.371662i	−0.0421116	−	0.0168590i
$487$	22.6145	+	2.15942i	1.02476	+	0.0978527i	0.593878	−	0.804555i	$-0.297596\pi$
$487$	22.6145	+	2.15942i	1.02476	+	0.0978527i	0.430883	+	0.902408i	$0.358202\pi$
$488$	3.50532	+	14.4491i	0.158678	+	0.654081i
$489$	−0.877293	+	1.92100i	−0.0396726	+	0.0868708i
$490$	−10.6482	−	19.5035i	−0.481037	−	0.881077i
$491$	2.35124	−	16.3532i	0.106110	−	0.738010i	−0.865412	−	0.501061i	$-0.832943\pi$
$491$	2.35124	−	16.3532i	0.106110	−	0.738010i	0.971522	−	0.236950i	$-0.0761476\pi$
$492$	0.0679711	+	0.0648103i	0.00306437	+	0.00292187i
$493$	17.5673	−	3.38582i	0.791192	−	0.152490i
$494$	1.71957	+	36.0981i	0.0773669	+	1.62413i
$495$	10.4431	+	5.38377i	0.469381	+	0.241982i
$496$	−6.60213	−	7.61926i	−0.296444	−	0.342115i
$497$	6.69149	+	17.3102i	0.300154	+	0.776468i
$498$	−2.25512	+	15.6847i	−0.101055	+	0.702850i
$499$	−2.44823	−	0.471858i	−0.109598	−	0.0211233i	0.134157	−	0.990960i	$-0.457167\pi$
$499$	−2.44823	−	0.471858i	−0.109598	−	0.0211233i	−0.243755	+	0.969837i	$0.578379\pi$
$500$	−0.141664	−	0.198939i	−0.00633540	−	0.00889682i
$501$	−14.6470	+	13.9659i	−0.654381	+	0.623951i
$502$	2.34075	−	3.28712i	0.104473	−	0.146712i
$503$	−3.89281	−	27.0751i	−0.173572	−	1.20722i	−0.871262	−	0.490819i	$-0.836698\pi$
$503$	−3.89281	−	27.0751i	−0.173572	−	1.20722i	0.697690	−	0.716400i	$-0.254211\pi$
$504$	−2.64407	+	0.0943551i	−0.117776	+	0.00420291i
$505$	−9.99397			−0.444726
$506$	10.9174	+	13.9958i	0.485339	+	0.622191i
$507$	10.8442	−	18.7827i	0.481607	−	0.834167i
$508$	5.01679	−	2.58633i	0.222584	−	0.114750i
$509$	−4.16478	+	3.27522i	−0.184601	+	0.145172i	−0.706183	−	0.708029i	$-0.749584\pi$
$509$	−4.16478	+	3.27522i	−0.184601	+	0.145172i	0.521582	+	0.853201i	$0.325342\pi$
$510$	3.25967	+	7.13768i	0.144341	+	0.316062i
$511$	−1.92202	−	1.70600i	−0.0850250	−	0.0754691i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	6.02511	+	1.16125i	0.266015	+	0.0512702i
$514$	7.03134	+	5.52951i	0.310139	+	0.243896i
$515$	−7.12744	+	29.3797i	−0.314073	+	1.29463i
$516$	−3.04677	+	8.80305i	−0.134126	+	0.387533i
$517$	11.0755	−	7.11780i	0.487101	−	0.313041i
$518$	23.1476	−	3.04675i	1.01705	−	0.133866i
$519$	−4.23982	−	4.89302i	−0.186108	−	0.214780i
$520$	13.5312	+	12.9019i	0.593381	+	0.565787i
$521$	−23.9023	−	18.7970i	−1.04718	−	0.823511i	−0.0625279	−	0.998043i	$-0.519916\pi$
$521$	−23.9023	−	18.7970i	−1.04718	−	0.823511i	−0.984651	+	0.174532i	$0.944159\pi$
$522$	−2.36721	−	6.83959i	−0.103610	−	0.299361i
$523$	−11.9474	+	1.14083i	−0.522422	+	0.0498852i	−0.352936	−	0.935647i	$-0.614817\pi$
$523$	−11.9474	+	1.14083i	−0.522422	+	0.0498852i	−0.169486	+	0.985533i	$0.554211\pi$
$524$	−1.22147	−	0.358657i	−0.0533603	−	0.0156680i
$525$	11.5518	+	6.85444i	0.504161	+	0.299152i
$526$	−3.32479	−	23.1244i	−0.144968	−	1.00827i
$527$	1.18578	−	24.8926i	0.0516533	−	1.08434i
$528$	1.85060	−	3.20533i	0.0805369	−	0.139494i
$529$	−5.59853	+	22.3082i	−0.243414	+	0.969922i
$530$	5.79330	+	10.0343i	0.251645	+	0.435862i
$531$	−5.21178	−	3.34941i	−0.226172	−	0.145352i
$532$	15.8212	−	3.63891i	0.685938	−	0.157767i
$533$	0.229784	+	0.503156i	0.00995304	+	0.0217941i
$534$	−3.55378	−	14.6489i	−0.153787	−	0.633919i
$535$	−3.55418	−	4.99114i	−0.153660	−	0.215786i
$536$	−3.64311	−	10.5261i	−0.157358	−	0.454657i
$537$	12.8904	−	5.16053i	0.556261	−	0.222693i
$538$	27.7348	−	8.14366i	1.19573	−	0.351098i
$539$	−24.2754	+	9.05262i	−1.04561	+	0.389924i
$540$	2.67049	−	1.71622i	0.114920	−	0.0738544i
$541$	−3.26866	−	1.68511i	−0.140531	−	0.0724487i	0.386527	−	0.922278i	$-0.373675\pi$
$541$	−3.26866	−	1.68511i	−0.140531	−	0.0724487i	−0.527058	+	0.849829i	$0.676705\pi$
$542$	−25.7989	+	4.97234i	−1.10816	+	0.213580i
$543$	−4.87028	+	20.0756i	−0.209004	+	0.861526i
$544$	2.29481	−	0.918704i	0.0983893	−	0.0393891i
$545$	11.8719	−	13.7009i	0.508537	−	0.586883i
$546$	−14.6638	−	5.27188i	−0.627551	−	0.225616i
$547$	−9.01516	−	2.64709i	−0.385460	−	0.113181i	0.0832603	−	0.996528i	$-0.473467\pi$
$547$	−9.01516	−	2.64709i	−0.385460	−	0.113181i	−0.468721	+	0.883346i	$0.655285\pi$
$548$	−6.81136	+	9.56521i	−0.290967	+	0.408606i
$549$	13.8032	+	5.52596i	0.589106	+	0.235842i
$550$	−16.7019	+	8.61041i	−0.712170	+	0.367149i
$551$	22.2051	+	38.4604i	0.945970	+	1.63847i
$552$	4.74967	−	0.663797i	0.202159	−	0.0282531i
$553$	7.33316	−	5.09118i	0.311838	−	0.216499i
$554$	9.56574	+	6.14753i	0.406409	+	0.261183i
$555$	−22.0193	+	17.3162i	−0.934667	+	0.735030i
$556$	−12.8303	−	1.22514i	−0.544126	−	0.0519577i
$557$	16.8951	−	16.1094i	0.715867	−	0.682578i	−0.241842	−	0.970316i	$-0.577752\pi$
$557$	16.8951	−	16.1094i	0.715867	−	0.682578i	0.957709	+	0.287738i	$0.0929032\pi$
$558$	−10.0361	+	0.958329i	−0.424861	+	0.0405693i
$559$	−35.9287	+	41.4639i	−1.51962	+	1.75374i
$560$	4.62465	−	7.01079i	0.195427	−	0.296260i
$561$	8.77831	−	2.57754i	0.370621	−	0.108824i
$562$	−6.27298	+	18.1246i	−0.264609	+	0.764539i
$563$	−0.602097	−	12.6396i	−0.0253754	−	0.532695i	−0.975390	−	0.220488i	$-0.929235\pi$
$563$	−0.602097	−	12.6396i	−0.0253754	−	0.532695i	0.950014	−	0.312206i	$-0.101068\pi$
$564$	−0.169253	−	3.55306i	−0.00712685	−	0.149611i
$565$	4.70265	−	13.5874i	0.197842	−	0.571627i
$566$	13.7689	−	4.04291i	0.578750	−	0.169936i
$567$	−1.45685	+	2.20853i	−0.0611820	+	0.0927494i
$568$	−4.59350	+	5.30118i	−0.192739	+	0.222433i
$569$	−2.38031	+	0.227292i	−0.0997879	+	0.00952859i	−0.144831	−	0.989456i	$-0.546264\pi$
$569$	−2.38031	+	0.227292i	−0.0997879	+	0.00952859i	0.0450426	+	0.998985i	$0.485658\pi$
$570$	−14.0971	+	13.4415i	−0.590461	+	0.563003i
$571$	23.0537	+	2.20136i	0.964768	+	0.0921242i	0.565534	−	0.824725i	$-0.308670\pi$
$571$	23.0537	+	2.20136i	0.964768	+	0.0921242i	0.399234	+	0.916849i	$0.369276\pi$
$572$	17.1351	−	13.4752i	0.716453	−	0.563425i
$573$	−7.77117	−	4.99423i	−0.324645	−	0.208637i
$574$	0.204112	−	0.141709i	0.00851948	−	0.00591481i
$575$	−22.1078	−	10.2018i	−0.921958	−	0.425445i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	32.1520	−	16.5755i	1.33851	−	0.690047i	0.367706	−	0.929942i	$-0.380143\pi$
$577$	32.1520	−	16.5755i	1.33851	−	0.690047i	0.970799	+	0.239895i	$0.0771129\pi$
$578$	−10.1098	−	4.04734i	−0.420511	−	0.168347i
$579$	−3.37476	+	4.73918i	−0.140250	+	0.196954i
$580$	22.0447	+	6.47291i	0.915356	+	0.268773i
$581$	39.4524	+	14.1839i	1.63676	+	0.588445i
$582$	5.64785	−	6.51797i	0.234111	−	0.270179i
$583$	12.5416	−	5.02091i	0.519421	−	0.207945i
$584$	0.229004	−	0.943966i	0.00947624	−	0.0390616i
$585$	18.3584	−	3.53830i	0.759028	−	0.146291i
$586$	1.51129	+	0.779123i	0.0624308	+	0.0321853i
$587$	23.9746	−	15.4076i	0.989539	−	0.635938i	0.0575185	−	0.998344i	$-0.481681\pi$
$587$	23.9746	−	15.4076i	0.989539	−	0.635938i	0.932020	+	0.362407i	$0.118045\pi$
$588$	−1.16122	+	6.90301i	−0.0478878	+	0.284675i
$589$	59.3556	−	17.4284i	2.44571	−	0.718124i
$590$	18.2576	−	7.30924i	0.751653	−	0.300916i
$591$	1.76836	+	5.10933i	0.0727405	+	0.210170i
$592$	5.11868	+	7.18818i	0.210376	+	0.295432i
$593$	−0.290251	−	1.19643i	−0.0119192	−	0.0491316i	0.965541	−	0.260249i	$-0.0838048\pi$
$593$	−0.290251	−	1.19643i	−0.0119192	−	0.0491316i	−0.977461	+	0.211118i	$0.932290\pi$
$594$	−1.53753	−	3.36673i	−0.0630857	−	0.138138i
$595$	20.2324	−	4.65348i	0.829446	−	0.190774i
$596$	6.75791	+	4.34304i	0.276815	+	0.177898i
$597$	−2.87108	−	4.97286i	−0.117506	−	0.203526i
$598$	27.4232	+	6.76740i	1.12142	+	0.276739i
$599$	−5.59821	+	9.69638i	−0.228737	+	0.396183i	−0.957434	−	0.288652i	$-0.906793\pi$
$599$	−5.59821	+	9.69638i	−0.228737	+	0.396183i	0.728697	+	0.684836i	$0.240126\pi$
$600$	−0.241570	+	5.07118i	−0.00986207	+	0.207030i
$601$	1.73584	+	12.0731i	0.0708065	+	0.492470i	0.994108	+	0.108394i	$0.0345709\pi$
$601$	1.73584	+	12.0731i	0.0708065	+	0.492470i	−0.923301	+	0.384076i	$0.874520\pi$
$602$	21.1957	+	12.5768i	0.863873	+	0.512594i
$603$	−10.6875	−	3.13813i	−0.435228	−	0.127795i
$604$	14.3847	−	1.37357i	0.585305	−	0.0558899i
$605$	2.80209	+	8.09609i	0.113921	+	0.329153i
$606$	2.47472	+	1.94614i	0.100529	+	0.0790566i
$607$	5.81582	+	5.54537i	0.236057	+	0.225080i	0.798869	−	0.601505i	$-0.205432\pi$
$607$	5.81582	+	5.54537i	0.236057	+	0.225080i	−0.562812	+	0.826585i	$0.690281\pi$
$608$	4.01822	+	4.63728i	0.162960	+	0.188066i
$609$	−18.9853	+	2.49889i	−0.769323	+	0.101260i
$610$	−39.7055	+	25.5172i	−1.60763	+	1.03316i
$611$	6.85212	−	19.7979i	0.277207	−	0.800937i
$612$	0.582767	−	2.40220i	0.0235570	−	0.0971032i
$613$	8.97809	+	7.06045i	0.362622	+	0.285169i	0.782801	−	0.622272i	$-0.213790\pi$
$613$	8.97809	+	7.06045i	0.362622	+	0.285169i	−0.420179	+	0.907441i	$0.638033\pi$
$614$	6.63362	+	1.27853i	0.267711	+	0.0515971i
$615$	−0.123849	+	0.271191i	−0.00499406	+	0.0109355i
$616$	−7.32361	−	6.50051i	−0.295077	−	0.261913i
$617$	−13.2313	−	28.9725i	−0.532673	−	1.16639i	−0.964415	−	0.264394i	$-0.914828\pi$
$617$	−13.2313	−	28.9725i	−0.532673	−	1.16639i	0.431742	−	0.901997i	$-0.357899\pi$
$618$	7.48606	−	5.88710i	0.301133	−	0.236814i
$619$	−4.07224	+	2.09939i	−0.163677	+	0.0843815i	−0.538119	−	0.842869i	$-0.680865\pi$
$619$	−4.07224	+	2.09939i	−0.163677	+	0.0843815i	0.374441	+	0.927251i	$0.377834\pi$
$620$	16.0018	−	27.7159i	0.642648	−	1.11310i
$621$	2.21437	−	4.25401i	0.0888595	−	0.170707i
$622$	3.54818			0.142269
$623$	−39.8561	+	1.42229i	−1.59680	+	0.0569828i
$624$	−0.838189	−	5.82973i	−0.0335544	−	0.233376i
$625$	−14.2749	+	20.0462i	−0.570994	+	0.801849i
$626$	6.25490	−	5.96403i	0.249996	−	0.238371i
$627$	13.1734	+	18.4995i	0.526095	+	0.738797i
$628$	−11.1673	−	2.15231i	−0.445622	−	0.0858867i
$629$	−3.10431	+	21.5909i	−0.123777	+	0.860886i
$630$	−3.02825	−	7.83379i	−0.120649	−	0.312106i
$631$	−5.65031	−	6.52080i	−0.224935	−	0.259589i	0.632053	−	0.774925i	$-0.282213\pi$
$631$	−5.65031	−	6.52080i	−0.224935	−	0.259589i	−0.856988	+	0.515336i	$0.827667\pi$
$632$	2.99909	+	1.54614i	0.119297	+	0.0615020i
$633$	−1.37623	−	28.8906i	−0.0547001	−	1.14830i
$634$	−12.6915	+	2.44608i	−0.504043	+	0.0971464i
$635$	12.9672	+	12.3642i	0.514589	+	0.490660i
$636$	0.519448	−	3.61284i	0.0205974	−	0.143258i
$637$	−21.4598	+	35.2024i	−0.850268	+	1.39477i
$638$	11.1281	−	24.3672i	0.440567	−	0.964707i
$639$	1.65372	+	6.81674i	0.0654203	+	0.269666i
$640$	3.16004	+	0.301748i	0.124912	+	0.0119276i
$641$	1.99292	+	0.797843i	0.0787154	+	0.0315129i	0.410686	−	0.911777i	$-0.365289\pi$
$641$	1.99292	+	0.797843i	0.0787154	+	0.0315129i	−0.331971	+	0.943290i	$0.607713\pi$
$642$	−0.0918430	+	1.92802i	−0.00362475	+	0.0760930i
$643$	−47.7045			−1.88128			−0.940641	−	0.339403i	$-0.889775\pi$
$643$	−47.7045			−1.88128			−0.940641	+	0.339403i	$0.889775\pi$
$644$	0.804828	−	12.6630i	0.0317147	−	0.498993i
$645$	−29.5709			−1.16435
$646$	−0.721696	+	15.1503i	−0.0283947	+	0.596079i
$647$	−5.79554	−	2.32018i	−0.227846	−	0.0912158i	0.254930	−	0.966959i	$-0.417947\pi$
$647$	−5.79554	−	2.32018i	−0.227846	−	0.0912158i	−0.482777	+	0.875744i	$0.660372\pi$
$648$	−0.995472	−	0.0950560i	−0.0391058	−	0.00373415i
$649$	−5.40592	−	22.2835i	−0.212201	−	0.874703i
$650$	−12.4215	+	27.1994i	−0.487213	+	1.06685i
$651$	−2.85207	+	26.5208i	−0.111782	+	1.03943i
$652$	−0.300547	+	2.09035i	−0.0117703	+	0.0818645i
$653$	−13.6205	−	12.9871i	−0.533011	−	0.508225i	0.375083	−	0.926991i	$-0.377614\pi$
$653$	−13.6205	−	12.9871i	−0.533011	−	0.508225i	−0.908094	+	0.418766i	$0.862463\pi$
$654$	−5.60774	+	1.08080i	−0.219280	+	0.0422628i
$655$	−0.192286	−	4.03659i	−0.00751325	−	0.157722i
$656$	0.0834770	+	0.0430354i	0.00325923	+	0.00168025i
$657$	−0.636097	−	0.734095i	−0.0248165	−	0.0286398i
$658$	−9.29875	−	1.45038i	−0.362503	−	0.0565417i
$659$	2.88414	−	20.0597i	0.112350	−	0.781413i	−0.853272	−	0.521466i	$-0.825386\pi$
$659$	2.88414	−	20.0597i	0.112350	−	0.781413i	0.965623	−	0.259948i	$-0.0837054\pi$
$660$	11.5368	+	2.22354i	0.449070	+	0.0865512i
$661$	6.91426	+	9.70972i	0.268933	+	0.377664i	0.926853	−	0.375424i	$-0.122503\pi$
$661$	6.91426	+	9.70972i	0.268933	+	0.377664i	−0.657920	+	0.753088i	$0.728563\pi$
$662$	14.2569	−	13.5940i	0.554111	−	0.528344i
$663$	8.44480	−	11.8591i	0.327969	−	0.460568i
$664$	2.25512	+	15.6847i	0.0875158	+	0.608686i
$665$	27.3425	+	43.6829i	1.06030	+	1.69395i
$666$	8.82444			0.341940
$667$	33.7642	−	8.05028i	1.30735	−	0.311708i
$668$	−10.1191	+	17.5267i	−0.391518	+	0.678130i
$669$	−8.60048	+	4.43386i	−0.332514	+	0.171423i
$670$	27.7939	−	21.8574i	1.07377	−	0.844425i
$671$	22.8604	+	50.0573i	0.882516	+	1.93244i
$672$	−2.51038	+	0.835453i	−0.0968401	+	0.0322283i
$673$	−15.4584	+	33.8493i	−0.595879	+	1.30479i	0.335945	+	0.941882i	$0.390944\pi$
$673$	−15.4584	+	33.8493i	−0.595879	+	1.30479i	−0.931824	+	0.362911i	$0.881783\pi$
$674$	−2.15339	−	0.415032i	−0.0829455	−	0.0159864i
$675$	3.99074	+	3.13835i	0.153604	+	0.120795i
$676$	5.11322	−	21.0770i	0.196662	−	0.810653i
$677$	0.0619395	−	0.178962i	0.00238053	−	0.00687809i	−0.943804	−	0.330505i	$-0.892781\pi$
$677$	0.0619395	−	0.178962i	0.00238053	−	0.00687809i	0.946185	+	0.323627i	$0.104902\pi$
$678$	−3.81037	+	2.44878i	−0.146336	+	0.0940447i
$679$	−13.8904	−	18.1034i	−0.533064	−	0.694745i
$680$	5.13855	+	5.93020i	0.197054	+	0.227413i
$681$	−8.97919	−	8.56164i	−0.344083	−	0.328083i
$682$	−29.3311	−	23.0663i	−1.12315	−	0.883253i
$683$	0.173729	+	0.501958i	0.00664757	+	0.0192069i	0.948276	−	0.317448i	$-0.102826\pi$
$683$	0.173729	+	0.501958i	0.00664757	+	0.0192069i	−0.941628	+	0.336655i	$0.890705\pi$
$684$	6.10821	−	0.583264i	0.233553	−	0.0223016i
$685$	−35.7659	−	10.5018i	−1.36654	−	0.401254i
$686$	17.2737	+	6.67973i	0.659514	+	0.255033i
$687$	−1.64542	−	11.4442i	−0.0627769	−	0.436623i
$688$	−0.443244	+	9.30484i	−0.0168985	+	0.354744i
$689$	10.7486	−	18.6172i	0.409491	−	0.709258i
$690$	6.92263	+	13.5590i	0.263540	+	0.516183i
$691$	7.68251	+	13.3065i	0.292257	+	0.506203i	0.974343	−	0.225068i	$-0.0722605\pi$
$691$	7.68251	+	13.3065i	0.292257	+	0.506203i	−0.682086	+	0.731272i	$0.738927\pi$
$692$	−5.44660	−	3.50032i	−0.207049	−	0.133062i
$693$	−9.54327	+	2.19497i	−0.362519	+	0.0833800i
$694$	−9.08805	−	19.9001i	−0.344978	−	0.755396i
$695$	−9.64584	−	39.7607i	−0.365887	−	1.50821i
$696$	−4.19825	−	5.89562i	−0.159134	−	0.223473i
$697$	0.0759295	+	0.219384i	0.00287603	+	0.00830975i
$698$	−24.1439	+	9.66577i	−0.913861	+	0.365855i
$699$	15.5609	−	4.56909i	0.588567	−	0.172819i
$700$	13.0150	+	3.32228i	0.491919	+	0.125570i
$701$	19.8735	−	12.7719i	0.750610	−	0.482388i	−0.108552	−	0.994091i	$-0.534621\pi$
$701$	19.8735	−	12.7719i	0.750610	−	0.482388i	0.859163	+	0.511703i	$0.170985\pi$
$702$	−5.23496	−	2.69881i	−0.197581	−	0.101860i
$703$	−53.1683	+	10.2473i	−2.00528	+	0.386486i
$704$	0.872590	−	3.59687i	0.0328870	−	0.135562i
$705$	10.4829	−	4.19670i	0.394807	−	0.158057i
$706$	−16.6928	+	19.2646i	−0.628243	+	0.725031i
$707$	6.35970	−	5.37923i	0.239181	−	0.202307i
$708$	−5.94430	−	1.74540i	−0.223401	−	0.0655963i
$709$	−0.619208	+	0.869556i	−0.0232549	+	0.0326569i	−0.826040	−	0.563612i	$-0.809411\pi$
$709$	−0.619208	+	0.869556i	−0.0232549	+	0.0326569i	0.802785	+	0.596269i	$0.203351\pi$
$710$	−20.6718	−	8.27575i	−0.775800	−	0.310583i
$711$	2.99909	−	1.54614i	0.112475	−	0.0579847i
$712$	−7.53689	−	13.0543i	−0.282457	−	0.489230i
$713$	0.190625	−	48.3499i	0.00713895	−	1.81072i
$714$	−5.91614	−	2.78758i	−0.221406	−	0.104322i
$715$	58.2137	+	37.4117i	2.17707	+	1.39912i
$716$	10.9143	−	8.58313i	0.407888	−	0.320767i
$717$	9.44786	+	0.902161i	0.352837	+	0.0336918i
$718$	17.1142	−	16.3184i	0.638698	−	0.608997i
$719$	−49.2377	+	4.70163i	−1.83626	+	0.175341i	−0.954864	−	0.297045i	$-0.903999\pi$
$719$	−49.2377	+	4.70163i	−1.83626	+	0.175341i	−0.881392	+	0.472386i	$0.843393\pi$
$720$	2.07880	−	2.39907i	0.0774724	−	0.0894079i
$721$	−11.2780	−	22.5322i	−0.420014	−	0.839143i
$722$	−17.8950	+	5.25444i	−0.665982	+	0.195550i
$723$	−2.90660	+	8.39808i	−0.108098	+	0.312328i
$724$	0.982942	+	20.6345i	0.0365308	+	0.766875i
$725$	1.74840	+	36.7035i	0.0649341	+	1.36313i
$726$	0.882708	−	2.55042i	0.0327604	−	0.0946549i
$727$	49.7261	−	14.6009i	1.84424	−	0.541517i	0.844255	−	0.535942i	$-0.180043\pi$
$727$	49.7261	−	14.6009i	1.84424	−	0.541517i	0.999984	−	0.00557530i	$-0.00177468\pi$
$728$	−15.5550	−	0.927076i	−0.576508	−	0.0343597i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	3.06950	−	0.293102i	0.113607	−	0.0108482i
$731$	−16.6651	+	15.8901i	−0.616380	+	0.587717i
$732$	14.8009	+	1.41332i	0.547057	+	0.0522376i
$733$	−38.7153	+	30.4461i	−1.42998	+	1.12455i	−0.458153	+	0.888873i	$0.651489\pi$
$733$	−38.7153	+	30.4461i	−1.42998	+	1.12455i	−0.971831	+	0.235678i	$0.924269\pi$
$734$	−18.8528	−	12.1160i	−0.695871	−	0.447209i
$735$	−21.9135	+	3.68361i	−0.808291	+	0.135872i
$736$	4.37026	−	1.97505i	0.161090	−	0.0728011i
$737$	−20.6132	−	35.7032i	−0.759298	−	1.31514i
$738$	0.0834770	−	0.0430354i	0.00307283	−	0.00158415i
$739$	−45.7066	−	18.2982i	−1.68135	−	0.673109i	−0.682989	−	0.730428i	$-0.739321\pi$
$739$	−45.7066	−	18.2982i	−1.68135	−	0.673109i	−0.998356	+	0.0573191i	$0.981745\pi$
$740$	−16.2488	+	22.8183i	−0.597319	+	0.838817i
$741$	34.6752	+	10.1816i	1.27382	+	0.374029i
$742$	−9.08751	−	3.26712i	−0.333613	−	0.119940i
$743$	6.74575	−	7.78501i	0.247478	−	0.285604i	−0.618397	−	0.785866i	$-0.712217\pi$
$743$	6.74575	−	7.78501i	0.247478	−	0.285604i	0.865874	+	0.500262i	$0.166763\pi$
$744$	−9.35955	+	3.74700i	−0.343138	+	0.137372i
$745$	−6.01198	+	24.7817i	−0.220262	+	0.907933i
$746$	11.1289	−	2.14492i	0.407459	−	0.0785312i
$747$	14.0845	+	7.26107i	0.515325	+	0.265669i
$748$	7.69655	−	4.94627i	0.281414	−	0.180854i
$749$	4.94818	+	1.26310i	0.180803	+	0.0461528i
$750$	−0.234331	+	0.0688059i	−0.00855657	+	0.00251243i
$751$	38.5274	−	15.4240i	1.40589	−	0.562832i	0.460171	−	0.887830i	$-0.347788\pi$
$751$	38.5274	−	15.4240i	1.40589	−	0.562832i	0.945714	+	0.324999i	$0.105364\pi$
$752$	−1.16341	−	3.36146i	−0.0424252	−	0.122580i
$753$	−2.34075	−	3.28712i	−0.0853017	−	0.119789i
$754$	−10.0498	−	41.4259i	−0.365993	−	1.50864i
$755$	19.0554	+	41.7255i	0.693497	+	1.51855i
$756$	−0.775624	+	2.52951i	−0.0282092	+	0.0919973i
$757$	−19.1134	−	12.2834i	−0.694689	−	0.446449i	0.145061	−	0.989423i	$-0.453662\pi$
$757$	−19.1134	−	12.2834i	−0.694689	−	0.446449i	−0.839750	+	0.542973i	$0.817298\pi$
$758$	−13.2243	−	22.9052i	−0.480329	−	0.831954i
$759$	16.7968	−	5.73938i	0.609686	−	0.208326i
$760$	−9.73911	+	16.8686i	−0.353275	+	0.611890i
$761$	0.664028	−	13.9397i	0.0240710	−	0.505313i	−0.954350	−	0.298691i	$-0.903450\pi$
$761$	0.664028	−	13.9397i	0.0240710	−	0.505313i	0.978421	−	0.206622i	$-0.0662469\pi$
$762$	−0.803257	−	5.58678i	−0.0290989	−	0.202388i
$763$	−0.180247	+	15.1087i	−0.00652536	+	0.546970i
$764$	−8.86342	−	2.60253i	−0.320667	−	0.0941564i
$765$	7.81124	−	0.745883i	0.282416	−	0.0269675i
$766$	6.99486	+	20.2103i	0.252735	+	0.730229i
$767$	−28.6816	−	22.5554i	−1.03563	−	0.814429i
$768$	−0.723734	−	0.690079i	−0.0261155	−	0.0249011i
$769$	33.2537	+	38.3768i	1.19916	+	1.38390i	0.903487	+	0.428615i	$0.140998\pi$
$769$	33.2537	+	38.3768i	1.19916	+	1.38390i	0.295673	+	0.955289i	$0.404456\pi$
$770$	11.8967	−	28.7187i	0.428727	−	1.03495i
$771$	7.52512	−	4.83610i	0.271011	−	0.174168i
$772$	−1.90287	+	5.49799i	−0.0684859	+	0.197877i
$773$	−4.74183	+	19.5461i	−0.170552	+	0.703024i	0.820736	+	0.571308i	$0.193564\pi$
$773$	−4.74183	+	19.5461i	−0.170552	+	0.703024i	−0.991288	+	0.131716i	$0.957951\pi$
$774$	7.32239	+	5.75839i	0.263198	+	0.206981i
$775$	50.2593	+	9.68669i	1.80537	+	0.347956i
$776$	3.58275	−	7.84513i	0.128613	−	0.281624i
$777$	4.69167	−	22.8710i	0.168313	−	0.820494i
$778$	−4.25933	−	9.32663i	−0.152704	−	0.334376i
$779$	−0.452983	+	0.356230i	−0.0162298	+	0.0127633i
$780$	16.6179	−	8.56715i	0.595018	−	0.306753i
$781$	−12.9810	+	22.4837i	−0.464495	+	0.804529i
$782$	11.1873	+	3.92143i	0.400058	+	0.140230i
$783$	−7.23766			−0.258653
$784$	0.830624	+	6.95054i	0.0296651	+	0.248234i
$785$	−5.13785	−	35.7345i	−0.183378	−	1.27542i
$786$	−0.738436	+	1.03699i	−0.0263391	+	0.0369881i
$787$	27.5120	−	26.2326i	0.980696	−	0.935092i	−0.0172045	−	0.999852i	$-0.505477\pi$
$787$	27.5120	−	26.2326i	0.980696	−	0.935092i	0.997901	+	0.0647599i	$0.0206281\pi$
$788$	3.13619	+	4.40416i	0.111722	+	0.156892i
$789$	−22.9400	−	4.42132i	−0.816686	−	0.157403i
$790$	−1.52434	+	10.6020i	−0.0542336	+	0.377203i
$791$	4.32084	+	11.1776i	0.153631	+	0.397429i
$792$	−2.42377	−	2.79718i	−0.0861248	−	0.0993934i
$793$	77.8346	+	40.1265i	2.76399	+	1.42493i
$794$	0.375947	+	7.89211i	0.0133419	+	0.280080i
$795$	11.3772	−	2.19278i	0.403508	−	0.0777698i
$796$	−4.15580	−	3.96255i	−0.147299	−	0.140449i
$797$	−4.96307	+	34.5189i	−0.175801	+	1.22272i	0.690549	+	0.723285i	$0.257369\pi$
$797$	−4.96307	+	34.5189i	−0.175801	+	1.22272i	−0.866350	+	0.499437i	$0.833540\pi$
$798$	1.73585	−	16.1413i	0.0614483	−	0.571394i
$799$	3.65262	−	7.99812i	0.129220	−	0.282953i
$800$	1.19693	+	4.93382i	0.0423180	+	0.174437i
$801$	−15.0055	−	1.43285i	−0.530194	−	0.0506274i
$802$	−1.46745	−	0.587480i	−0.0518176	−	0.0207446i
$803$	0.171064	−	3.59107i	0.00603671	−	0.126726i
$804$	−11.1387			−0.392831
$805$	38.8225	−	10.7331i	1.36831	−	0.378290i
$806$	−59.3781			−2.09151
$807$	1.37539	−	28.8729i	0.0484159	−	1.01637i
$808$	2.92277	+	1.17010i	0.102823	+	0.0411639i
$809$	38.4332	+	3.66993i	1.35124	+	0.129028i	0.745431	−	0.666583i	$-0.232244\pi$
$809$	38.4332	+	3.66993i	1.35124	+	0.129028i	0.605809	+	0.795610i	$0.292850\pi$
$810$	−0.748398	−	3.08494i	−0.0262960	−	0.108394i
$811$	−11.2337	+	24.5984i	−0.394469	+	0.863767i	0.603332	+	0.797490i	$0.293839\pi$
$811$	−11.2337	+	24.5984i	−0.394469	+	0.863767i	−0.997801	+	0.0662768i	$0.978888\pi$
$812$	−17.5122	+	7.74645i	−0.614559	+	0.271847i
$813$	−3.73914	+	26.0063i	−0.131137	+	0.912081i
$814$	23.6379	+	22.5387i	0.828507	+	0.789980i
$815$	−6.58274	+	1.26872i	−0.230583	+	0.0444413i
$816$	−0.117617	−	2.46908i	−0.00411741	−	0.0864350i
$817$	−50.8051	−	26.1919i	−1.77745	−	0.916337i
$818$	−4.48294	−	5.17359i	−0.156742	−	0.180890i
$819$	−9.77798	+	12.1330i	−0.341670	+	0.423961i
$820$	−0.0424287	+	0.295098i	−0.00148167	+	0.0103053i
$821$	17.5591	+	3.38424i	0.612816	+	0.118111i	0.486209	−	0.873842i	$-0.338379\pi$
$821$	17.5591	+	3.38424i	0.612816	+	0.118111i	0.126607	+	0.991953i	$0.459591\pi$
$822$	6.81136	+	9.56521i	0.237573	+	0.333625i
$823$	4.13236	−	3.94020i	0.144045	−	0.137347i	−0.614631	−	0.788815i	$-0.710695\pi$
$823$	4.13236	−	3.94020i	0.144045	−	0.137347i	0.758676	+	0.651468i	$0.225847\pi$
$824$	5.52423	−	7.75770i	0.192446	−	0.270252i
$825$	2.67420	+	18.5995i	0.0931037	+	0.647550i
$826$	−7.68410	+	14.4784i	−0.267364	+	0.503766i
$827$	−24.7103			−0.859261			−0.429631	−	0.903005i	$-0.641356\pi$
$827$	−24.7103			−0.859261			−0.429631	+	0.903005i	$0.641356\pi$
$828$	0.926176	−	4.70555i	0.0321869	−	0.163529i
$829$	−7.65718	+	13.2626i	−0.265945	+	0.460630i	−0.967811	−	0.251679i	$-0.919017\pi$
$829$	−7.65718	+	13.2626i	−0.265945	+	0.460630i	0.701866	+	0.712309i	$0.252351\pi$
$830$	−44.7101	+	23.0497i	−1.55191	+	0.800066i
$831$	8.93807	−	7.02897i	0.310058	−	0.243832i
$832$	−2.44666	−	5.35744i	−0.0848227	−	0.185736i
$833$	−10.3702	+	13.8513i	−0.359306	+	0.479918i
$834$	−5.35414	+	11.7239i	−0.185399	+	0.405967i
$835$	−63.0833	−	12.1583i	−2.18309	−	0.420756i
$836$	17.8517	+	14.0387i	0.617413	+	0.485539i
$837$	−2.37686	+	9.79754i	−0.0821562	+	0.338652i
$838$	−8.89866	+	25.7110i	−0.307399	+	0.888171i
$839$	−21.7945	+	14.0065i	−0.752431	+	0.483558i	−0.859781	−	0.510663i	$-0.829400\pi$
$839$	−21.7945	+	14.0065i	−0.752431	+	0.483558i	0.107350	+	0.994221i	$0.465763\pi$
$840$	−5.11262	−	6.66331i	−0.176402	−	0.229906i
$841$	−15.3131	−	17.6722i	−0.528037	−	0.609387i
$842$	−24.5471	−	23.4056i	−0.845949	−	0.806611i
$843$	15.0760	+	11.8559i	0.519247	+	0.408340i
$844$	−9.45990	−	27.3326i	−0.325623	−	0.940826i
$845$	68.5361	−	6.54441i	2.35771	−	0.225134i
$846$	−3.41301	−	1.00215i	−0.117342	−	0.0344546i
$847$	−6.14082	−	3.64376i	−0.211001	−	0.125201i
$848$	−0.519448	−	3.61284i	−0.0178379	−	0.124065i
$849$	0.682809	−	14.3339i	0.0234339	−	0.491939i
$850$	−6.27478	+	10.8682i	−0.215223	+	0.372778i
$851$	−4.18889	+	42.1127i	−0.143593	+	1.44361i
$852$	3.50723	+	6.07470i	0.120156	+	0.208116i
$853$	−0.162621	−	0.104510i	−0.00556802	−	0.00357835i	0.537854	−	0.843038i	$-0.319235\pi$
$853$	−0.162621	−	0.104510i	−0.00556802	−	0.00357835i	−0.543422	+	0.839460i	$0.682872\pi$
$854$	11.5322	−	37.6093i	0.394623	−	1.28696i
$855$	8.09155	+	17.7180i	0.276725	+	0.605943i
$856$	0.455064	+	1.87580i	0.0155538	+	0.0641135i
$857$	−24.5637	−	34.4949i	−0.839081	−	1.17833i	−0.982054	−	0.188598i	$-0.939606\pi$
$857$	−24.5637	−	34.4949i	−0.839081	−	1.17833i	0.142973	−	0.989727i	$-0.454334\pi$
$858$	−7.12971	−	20.5999i	−0.243404	−	0.703270i
$859$	−0.575071	+	0.230224i	−0.0196212	+	0.00785513i	−0.381452	−	0.924389i	$-0.624576\pi$
$859$	−0.575071	+	0.230224i	−0.0196212	+	0.00785513i	0.361831	+	0.932244i	$0.382152\pi$
$860$	−28.3731	+	8.33110i	−0.967515	+	0.284088i
$861$	−0.0671563	−	0.239235i	−0.00228868	−	0.00815309i
$862$	−19.7234	+	12.6754i	−0.671780	+	0.431727i
$863$	−41.0570	−	21.1664i	−1.39760	−	0.720512i	−0.415625	−	0.909536i	$-0.636437\pi$
$863$	−41.0570	−	21.1664i	−1.39760	−	0.720512i	−0.981972	+	0.189024i	$0.939468\pi$
$864$	−0.981929	+	0.189251i	−0.0334059	+	0.00643846i
$865$	4.84542	−	19.9731i	0.164749	−	0.679105i
$866$	−16.9213	+	6.77428i	−0.575010	+	0.230199i
$867$	−7.13132	+	8.22998i	−0.242192	+	0.279505i
$868$	4.73523	+	26.2501i	0.160724	+	0.890985i
$869$	11.9826	+	3.51841i	0.406482	+	0.119354i
$870$	13.3270	−	18.7152i	0.451828	−	0.634504i
$871$	−60.9040	−	24.3823i	−2.06365	−	0.826162i
$872$	−5.07609	+	2.61691i	−0.171898	+	0.0886196i
$873$	−4.31226	−	7.46905i	−0.145948	−	0.252789i
$874$	−0.116019	+	29.4270i	−0.00392440	+	0.995382i
$875$	0.0537435	+	0.643917i	0.00181686	+	0.0217684i
$876$	−0.817149	−	0.525150i	−0.0276089	−	0.0177432i
$877$	2.69547	−	2.11974i	0.0910197	−	0.0715787i	−0.571612	−	0.820524i	$-0.693682\pi$
$877$	2.69547	−	2.11974i	0.0910197	−	0.0715787i	0.662632	+	0.748945i	$0.269439\pi$
$878$	14.3724	+	1.37240i	0.485045	+	0.0463162i
$879$	1.23057	−	1.17334i	0.0415060	−	0.0395759i
$880$	11.6959	−	1.11683i	0.394270	−	0.0376482i
$881$	−7.17006	+	8.27469i	−0.241565	+	0.278781i	−0.863566	−	0.504235i	$-0.831775\pi$
$881$	−7.17006	+	8.27469i	−0.241565	+	0.278781i	0.622001	+	0.783016i	$0.286320\pi$
$882$	6.14356	+	3.35511i	0.206864	+	0.112972i
$883$	−3.32837	+	0.977297i	−0.112008	+	0.0328886i	−0.337256	−	0.941413i	$-0.609499\pi$
$883$	−3.32837	+	0.977297i	−0.112008	+	0.0328886i	0.225248	+	0.974301i	$0.427681\pi$
$884$	4.76164	−	13.7579i	0.160151	−	0.462727i
$885$	−0.935762	−	19.6441i	−0.0314553	−	0.660328i
$886$	0.668063	+	14.0244i	0.0224440	+	0.471158i
$887$	−6.63703	+	19.1764i	−0.222850	+	0.643882i	0.777046	+	0.629444i	$0.216717\pi$
$887$	−6.63703	+	19.1764i	−0.222850	+	0.643882i	−0.999896	+	0.0144383i	$0.995404\pi$
$888$	8.46699	−	2.48613i	0.284134	−	0.0834292i
$889$	−14.9068	−	0.888439i	−0.499957	−	0.0297973i
$890$	31.3354	−	36.1630i	1.05037	−	1.21219i
$891$	−3.68444	+	0.351821i	−0.123433	+	0.0117864i
$892$	−7.00294	+	6.67729i	−0.234476	+	0.223572i
$893$	21.7275	+	2.07472i	0.727082	+	0.0694279i
$894$	6.31448	−	4.96576i	0.211188	−	0.166080i
$895$	37.0797	+	23.8297i	1.23944	+	0.796539i
$896$	−2.17332	+	1.50887i	−0.0726055	+	0.0504077i
$897$	15.3645	−	23.7016i	0.513004	−	0.791373i
$898$	10.7526	+	18.6241i	0.358820	+	0.621494i
$899$	−64.8566	+	33.4359i	−2.16309	+	1.11515i
$900$	4.71326	+	1.88691i	0.157109	+	0.0628969i
$901$	5.23347	−	7.34937i	0.174352	−	0.244843i
$902$	0.333526	+	0.0979320i	0.0111052	+	0.00326078i
$903$	18.8176	−	15.9165i	0.626209	−	0.529667i
$904$	−2.96612	+	3.42309i	−0.0986518	+	0.113850i
$905$	−60.8794	+	24.3724i	−2.02370	+	0.810167i
$906$	3.40675	−	14.0428i	0.113182	−	0.466541i
$907$	24.8389	−	4.78730i	0.824762	−	0.158960i	0.240628	−	0.970617i	$-0.422647\pi$
$907$	24.8389	−	4.78730i	0.824762	−	0.158960i	0.584134	+	0.811658i	$0.301434\pi$
$908$	−11.0276	−	5.68511i	−0.365963	−	0.188667i
$909$	2.64851	−	1.70209i	0.0878454	−	0.0564548i
$910$	−13.3690	−	47.6250i	−0.443176	−	1.57875i
$911$	−47.3056	+	13.8902i	−1.56730	+	0.460202i	−0.946215	−	0.323539i	$-0.895127\pi$
$911$	−47.3056	+	13.8902i	−1.56730	+	0.460202i	−0.621088	+	0.783741i	$0.713309\pi$
$912$	5.69646	−	2.28052i	0.188629	−	0.0755156i
$913$	19.1823	+	55.4236i	0.634841	+	1.83425i
$914$	−7.68312	−	10.7894i	−0.254135	−	0.356883i
$915$	11.1274	+	45.8676i	0.367859	+	1.51633i
$916$	−4.80297	−	10.5170i	−0.158695	−	0.347493i
$917$	2.29504	+	2.46520i	0.0757890	+	0.0814080i
$918$	−2.07948	−	1.33640i	−0.0686329	−	0.0441077i
$919$	5.67636	+	9.83175i	0.187246	+	0.324319i	0.944331	−	0.328997i	$-0.106711\pi$
$919$	5.67636	+	9.83175i	0.187246	+	0.324319i	−0.757085	+	0.653316i	$0.773377\pi$
$920$	10.4622	+	11.0594i	0.344929	+	0.364619i
$921$	3.37785	−	5.85061i	0.111304	−	0.192784i
$922$	0.970922	−	20.3822i	0.0319756	−	0.671251i
$923$	5.87945	+	40.8925i	0.193524	+	1.34599i
$924$	−8.53831	+	4.79471i	−0.280890	+	0.157734i
$925$	−42.9864	−	12.6219i	−1.41338	−	0.415007i
$926$	−18.7107	+	1.78665i	−0.614871	+	0.0587130i
$927$	−3.11487	−	8.99982i	−0.102306	−	0.295593i
$928$	−5.68918	−	4.47402i	−0.186757	−	0.146867i
$929$	12.6666	+	12.0775i	0.415576	+	0.396251i	0.868814	−	0.495139i	$-0.164883\pi$
$929$	12.6666	+	12.0775i	0.415576	+	0.396251i	−0.453238	+	0.891390i	$0.649731\pi$
$930$	−20.9579	−	24.1867i	−0.687237	−	0.793114i
$931$	−40.9117	−	13.0807i	−1.34083	−	0.428703i
$932$	13.6433	−	8.76802i	0.446901	−	0.287206i
$933$	1.16050	−	3.35303i	0.0379930	−	0.109773i
$934$	−6.13606	+	25.2932i	−0.200778	+	0.827618i
$935$	22.8289	+	17.9529i	0.746585	+	0.587121i
$936$	−5.78325	−	1.11463i	−0.189031	−	0.0364328i
$937$	−1.53829	+	3.36838i	−0.0502537	+	0.110040i	−0.933093	−	0.359634i	$-0.882901\pi$
$937$	−1.53829	+	3.36838i	−0.0502537	+	0.110040i	0.882840	+	0.469675i	$0.155629\pi$
$938$	−5.92208	+	28.8690i	−0.193363	+	0.942608i
$939$	−3.59024	−	7.86153i	−0.117163	−	0.256551i
$940$	8.87588	−	6.98007i	0.289499	−	0.227665i
$941$	18.6872	−	9.63392i	0.609185	−	0.314057i	−0.125888	−	0.992044i	$-0.540178\pi$
$941$	18.6872	−	9.63392i	0.609185	−	0.314057i	0.735073	+	0.677988i	$0.237148\pi$
$942$	−5.68639	+	9.84912i	−0.185273	+	0.320902i
$943$	0.165751	+	0.418804i	0.00539760	+	0.0136381i
$944$	−6.19525			−0.201638
$945$	−8.39338	+	0.299523i	−0.273037	+	0.00974347i
$946$	4.90674	+	34.1271i	0.159532	+	1.10957i
$947$	−1.20941	+	1.69838i	−0.0393005	+	0.0551898i	−0.833759	−	0.552129i	$-0.813816\pi$
$947$	−1.20941	+	1.69838i	−0.0393005	+	0.0551898i	0.794458	+	0.607319i	$0.207755\pi$
$948$	2.44201	−	2.32845i	0.0793127	−	0.0756245i
$949$	−3.31846	−	4.66012i	−0.107722	−	0.151274i
$950$	−30.5891	−	5.89557i	−0.992441	−	0.191277i
$951$	−1.83943	+	12.7935i	−0.0596475	+	0.414858i
$952$	−6.46184	−	1.00789i	−0.209430	−	0.0326659i
$953$	−1.14201	−	1.31795i	−0.0369933	−	0.0426926i	0.736951	−	0.675946i	$-0.236265\pi$
$953$	−1.14201	−	1.31795i	−0.0369933	−	0.0426926i	−0.773945	+	0.633253i	$0.781719\pi$
$954$	−3.24424	−	1.67252i	−0.105036	−	0.0541499i
$955$	−1.39529	−	29.2908i	−0.0451506	−	0.947829i
$956$	9.31933	−	1.79615i	0.301409	−	0.0580917i
$957$	−19.3874	−	18.4858i	−0.626705	−	0.597562i
$958$	−4.42283	+	30.7614i	−0.142895	+	0.993857i
$959$	28.4123	−	12.5680i	0.917481	−	0.405843i
$960$	1.31870	−	2.88755i	0.0425609	−	0.0931954i
$961$	16.6543	+	68.6499i	0.537235	+	2.21451i
$962$	51.7378	+	4.94036i	1.66809	+	0.159284i
$963$	1.79194	+	0.717386i	0.0577446	+	0.0231174i
$964$	−0.422853	+	8.87678i	−0.0136192	+	0.285902i
$965$	−18.4687			−0.594528
$966$	−11.7033	−	4.90223i	−0.376549	−	0.157727i
$967$	37.4788			1.20524			0.602619	−	0.798029i	$-0.294124\pi$
$967$	37.4788			1.20524			0.602619	+	0.798029i	$0.294124\pi$
$968$	0.128417	−	2.69580i	0.00412746	−	0.0866461i
$969$	14.0810	+	5.63717i	0.452346	+	0.181092i
$970$	27.2538	+	2.60243i	0.875068	+	0.0835589i
$971$	−3.58159	−	14.7635i	−0.114939	−	0.473784i	−0.999966	−	0.00824475i	$-0.997376\pi$
$971$	−3.58159	−	14.7635i	−0.114939	−	0.473784i	0.885027	−	0.465539i	$-0.154140\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	27.5392	+	20.1100i	0.882868	+	0.644697i
$974$	3.23302	−	22.4861i	0.103593	−	0.720502i
$975$	21.6408	+	20.6344i	0.693059	+	0.660830i
$976$	14.5995	−	2.81383i	0.467320	−	0.0900686i
$977$	2.51265	+	52.7470i	0.0803868	+	1.68753i	0.574795	+	0.818297i	$0.305082\pi$
$977$	2.51265	+	52.7470i	0.0803868	+	1.68753i	−0.494408	+	0.869230i	$0.664615\pi$
$978$	1.87709	+	0.967705i	0.0600226	+	0.0309438i
$979$	−36.5354	−	42.1640i	−1.16768	−	1.34757i
$980$	−19.9880	+	9.70814i	−0.638495	+	0.310115i
$981$	−0.812752	+	5.65282i	−0.0259492	+	0.180481i
$982$	−16.2228	−	3.12669i	−0.517691	−	0.0997768i
$983$	14.9979	+	21.0616i	0.478359	+	0.671761i	0.981283	−	0.192569i	$-0.0616821\pi$
$983$	14.9979	+	21.0616i	0.478359	+	0.671761i	−0.502925	+	0.864330i	$0.667743\pi$
$984$	0.0679711	−	0.0648103i	0.00216684	−	0.00206608i
$985$	−9.95558	+	13.9807i	−0.317211	+	0.445461i
$986$	−2.54610	−	17.7085i	−0.0810843	−	0.563954i
$987$	−4.41193	+	8.31295i	−0.140433	+	0.264604i
$988$	36.1391			1.14974
$989$	−30.9565	+	32.2110i	−0.984361	+	1.02425i
$990$	5.87457	−	10.1751i	0.186706	−	0.323385i
$991$	5.80185	−	2.99106i	0.184302	−	0.0950142i	−0.363606	−	0.931553i	$-0.618455\pi$
$991$	5.80185	−	2.99106i	0.184302	−	0.0950142i	0.547908	+	0.836539i	$0.315424\pi$
$992$	−7.92477	+	6.23211i	−0.251612	+	0.197870i
$993$	−8.18331	−	17.9190i	−0.259690	−	0.568641i
$994$	17.6090	−	5.86026i	0.558523	−	0.185876i
$995$	7.57220	−	16.5808i	0.240055	−	0.525647i
$996$	15.5597	+	2.99888i	0.493027	+	0.0950232i
$997$	19.2387	+	15.1295i	0.609296	+	0.479155i	0.874493	−	0.485039i	$-0.161195\pi$
$997$	19.2387	+	15.1295i	0.609296	+	0.479155i	−0.265197	+	0.964194i	$0.585437\pi$
$998$	−0.587815	+	2.42301i	−0.0186070	+	0.0766989i
$999$	2.88619	−	8.33911i	0.0913151	−	0.263838i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.c.25.2	✓	160
7.2	even	3	inner	966.2.y.c.163.2	yes	160
23.12	even	11	inner	966.2.y.c.403.2	yes	160
161.58	even	33	inner	966.2.y.c.541.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.c.25.2	✓	160	1.1	even	1	trivial
966.2.y.c.163.2	yes	160	7.2	even	3	inner
966.2.y.c.403.2	yes	160	23.12	even	11	inner
966.2.y.c.541.2	yes	160	161.58	even	33	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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.748398 - 3.08494i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.13670 + 1.56029i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.748398 - 3.08494i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.13670 + 1.56029i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-3.11705 + 0.600763i) q^{10} +(0.176110 + 3.69700i) q^{11} +(0.888835 + 0.458227i) q^{12} +(3.85692 + 4.45112i) q^{13} +(1.66019 - 2.06004i) q^{14} +(-0.451767 + 3.14211i) q^{15} +(0.981929 + 0.189251i) q^{16} +(1.43383 + 2.01353i) q^{17} +(0.723734 - 0.690079i) q^{18} +(-3.55923 + 4.99824i) q^{19} +(0.451767 + 3.14211i) q^{20} +(-1.40375 - 2.24265i) q^{21} +3.70120 q^{22} +(2.94970 + 3.78144i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.51256 + 2.32639i) q^{25} +(4.62960 - 3.64076i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-1.97871 - 1.75633i) q^{28} +(3.00663 - 6.58361i) q^{29} +(3.11705 + 0.600763i) q^{30} +(-7.92477 - 6.23211i) q^{31} +(0.235759 - 0.971812i) q^{32} +(1.21054 - 3.49763i) q^{33} +(2.07948 - 1.33640i) q^{34} +(3.21428 - 7.75931i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(6.38655 + 6.08956i) q^{37} +(4.82322 + 3.79302i) q^{38} +(-1.92633 - 5.56575i) q^{39} +(3.16004 - 0.301748i) q^{40} +(0.0901129 + 0.0264595i) q^{41} +(-2.30691 + 1.29545i) q^{42} +(1.32572 + 9.22057i) q^{43} +(0.176110 - 3.69700i) q^{44} +(1.58721 - 2.74913i) q^{45} +(3.91751 - 2.76643i) q^{46} +(-1.77855 - 3.08053i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(2.13101 + 6.66774i) q^{49} +(2.10904 + 4.61814i) q^{50} +(-0.582767 - 2.40220i) q^{51} +(-3.41635 - 4.79759i) q^{52} +(-1.19379 - 3.44924i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(11.2732 - 3.31012i) q^{55} +(-1.84849 + 1.89290i) q^{56} +(5.16193 - 3.31737i) q^{57} +(-6.43309 - 3.31649i) q^{58} +(-6.08330 + 1.17246i) q^{59} +(0.748398 - 3.08494i) q^{60} +(13.8032 - 5.52596i) q^{61} +(-6.60213 + 7.61926i) q^{62} +(0.469685 + 2.60373i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(10.8449 - 15.2296i) q^{65} +(-3.43607 - 1.37560i) q^{66} +(-9.90046 + 5.10404i) q^{67} +(-1.23594 - 2.14071i) q^{68} +(-1.33299 - 4.60686i) q^{69} +(-7.59758 - 3.57984i) q^{70} +(5.90094 + 3.79231i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(-0.966948 - 0.0923323i) q^{73} +(6.38655 - 6.08956i) q^{74} +(5.05395 - 0.482593i) q^{75} +(4.01822 - 4.63728i) q^{76} +(-5.39209 + 8.17419i) q^{77} +(-5.65111 + 1.65931i) q^{78} +(1.10358 - 3.18860i) q^{79} +(-0.151045 - 3.17082i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(0.0307173 - 0.0887519i) q^{82} +(15.2042 - 4.46434i) q^{83} +(1.18421 + 2.36593i) q^{84} +(5.13855 - 5.93020i) q^{85} +(9.27321 - 0.885484i) q^{86} +(-5.23814 + 4.99456i) q^{87} +(-3.68444 - 0.351821i) q^{88} +(-11.8488 + 9.31800i) q^{89} +(-2.67049 - 1.71622i) q^{90} +(1.29607 + 15.5286i) q^{91} +(-2.57690 - 4.04470i) q^{92} +(5.04086 + 8.73103i) q^{93} +(-3.16167 + 1.62995i) q^{94} +(18.0830 + 7.23933i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(-8.27516 - 2.42981i) q^{97} +(6.76159 - 1.81133i) q^{98} +(-2.42377 + 2.79718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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