LMFDB - Embedded newform 216.2.t.a.13.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.14
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.565401 + 1.29627i) q^{2} +(-1.67042 + 0.457945i) q^{3} +(-1.36064 - 1.46583i) q^{4} +(1.52309 - 1.81515i) q^{5} +(0.350834 - 2.42424i) q^{6} +(0.767101 + 0.279202i) q^{7} +(2.66942 - 0.934982i) q^{8} +(2.58057 - 1.52992i) q^{9} +O(q^{10})$	\(q+(-0.565401 + 1.29627i) q^{2} +(-1.67042 + 0.457945i) q^{3} +(-1.36064 - 1.46583i) q^{4} +(1.52309 - 1.81515i) q^{5} +(0.350834 - 2.42424i) q^{6} +(0.767101 + 0.279202i) q^{7} +(2.66942 - 0.934982i) q^{8} +(2.58057 - 1.52992i) q^{9} +(1.49177 + 3.00063i) q^{10} +(3.58256 + 4.26953i) q^{11} +(2.94411 + 1.82544i) q^{12} +(-2.36616 - 0.417219i) q^{13} +(-0.795642 + 0.836511i) q^{14} +(-1.71296 + 3.72954i) q^{15} +(-0.297302 + 3.98894i) q^{16} +(1.52854 - 2.64751i) q^{17} +(0.524128 + 4.21014i) q^{18} +(-0.631691 + 0.364707i) q^{19} +(-4.73308 + 0.237181i) q^{20} +(-1.40924 - 0.115093i) q^{21} +(-7.56006 + 2.22998i) q^{22} +(6.38462 - 2.32381i) q^{23} +(-4.03087 + 2.78426i) q^{24} +(-0.106720 - 0.605238i) q^{25} +(1.87866 - 2.83130i) q^{26} +(-3.61001 + 3.73735i) q^{27} +(-0.634489 - 1.50433i) q^{28} +(9.24326 - 1.62984i) q^{29} +(-3.86600 - 4.32915i) q^{30} +(1.92800 - 0.701734i) q^{31} +(-5.00265 - 2.64073i) q^{32} +(-7.93957 - 5.49127i) q^{33} +(2.56766 + 3.47831i) q^{34} +(1.67516 - 0.967153i) q^{35} +(-5.75383 - 1.70101i) q^{36} +(4.61364 + 2.66369i) q^{37} +(-0.115601 - 1.02505i) q^{38} +(4.14354 - 0.386644i) q^{39} +(2.36864 - 6.26946i) q^{40} +(-1.29167 + 7.32541i) q^{41} +(0.945976 - 1.76168i) q^{42} +(-4.42023 - 5.26782i) q^{43} +(1.38381 - 11.0607i) q^{44} +(1.15342 - 7.01433i) q^{45} +(-0.597580 + 9.59009i) q^{46} +(-10.2350 - 3.72522i) q^{47} +(-1.33009 - 6.79933i) q^{48} +(-4.85182 - 4.07116i) q^{49} +(0.844892 + 0.203864i) q^{50} +(-1.34089 + 5.12243i) q^{51} +(2.60793 + 4.03608i) q^{52} -2.99582i q^{53} +(-2.80352 - 6.79266i) q^{54} +13.2064 q^{55} +(2.30877 + 0.0280815i) q^{56} +(0.888170 - 0.898491i) q^{57} +(-3.11344 + 12.9033i) q^{58} +(0.837520 - 0.998118i) q^{59} +(7.79759 - 2.56368i) q^{60} +(-0.528763 + 1.45277i) q^{61} +(-0.180455 + 2.89597i) q^{62} +(2.40672 - 0.453099i) q^{63} +(6.25162 - 4.99172i) q^{64} +(-4.36120 + 3.65948i) q^{65} +(11.6072 - 7.18708i) q^{66} +(-4.70399 - 0.829441i) q^{67} +(-5.96060 + 1.36174i) q^{68} +(-9.60078 + 6.80553i) q^{69} +(0.306557 + 2.71829i) q^{70} +(-4.37210 + 7.57270i) q^{71} +(5.45819 - 6.49678i) q^{72} +(-2.62609 - 4.54853i) q^{73} +(-6.06142 + 4.47448i) q^{74} +(0.455432 + 0.962127i) q^{75} +(1.39410 + 0.429714i) q^{76} +(1.55613 + 4.27542i) q^{77} +(-1.84157 + 5.58977i) q^{78} +(-0.739506 - 4.19395i) q^{79} +(6.78770 + 6.61516i) q^{80} +(4.31872 - 7.89612i) q^{81} +(-8.76541 - 5.81615i) q^{82} +(-14.1745 + 2.49935i) q^{83} +(1.74876 + 2.22230i) q^{84} +(-2.47752 - 6.80694i) q^{85} +(9.32773 - 2.75138i) q^{86} +(-14.6937 + 6.95541i) q^{87} +(13.5553 + 8.04754i) q^{88} +(4.96560 + 8.60067i) q^{89} +(8.44033 + 5.46106i) q^{90} +(-1.69860 - 0.980687i) q^{91} +(-12.0935 - 6.19687i) q^{92} +(-2.89920 + 2.05510i) q^{93} +(10.6158 - 11.1611i) q^{94} +(-0.300125 + 1.70209i) q^{95} +(9.56582 + 2.12018i) q^{96} +(-11.8735 + 9.96305i) q^{97} +(8.02056 - 3.98744i) q^{98} +(15.7771 + 5.53682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.565401	+	1.29627i	−0.399799	+	0.916603i
$2$	−0.565401	+	1.29627i	−0.399799	+	0.916603i
$3$	−1.67042	+	0.457945i	−0.964415	+	0.264395i
$3$	−1.67042	+	0.457945i	−0.964415	+	0.264395i
$4$	−1.36064	−	1.46583i	−0.680321	−	0.732914i
$5$	1.52309	−	1.81515i	0.681147	−	0.811760i	−0.309108	−	0.951027i	$-0.600030\pi$
$5$	1.52309	−	1.81515i	0.681147	−	0.811760i	0.990255	+	0.139268i	$0.0444748\pi$
$6$	0.350834	−	2.42424i	0.143227	−	0.989690i
$7$	0.767101	+	0.279202i	0.289937	+	0.105528i	0.482894	−	0.875679i	$-0.339586\pi$
$7$	0.767101	+	0.279202i	0.289937	+	0.105528i	−0.192957	+	0.981207i	$0.561808\pi$
$8$	2.66942	−	0.934982i	0.943783	−	0.330566i
$9$	2.58057	−	1.52992i	0.860191	−	0.509972i
$10$	1.49177	+	3.00063i	0.471739	+	0.948882i
$11$	3.58256	+	4.26953i	1.08018	+	1.28731i	0.955460	+	0.295120i	$0.0953598\pi$
$11$	3.58256	+	4.26953i	1.08018	+	1.28731i	0.124723	+	0.992192i	$0.460196\pi$
$12$	2.94411	+	1.82544i	0.849890	+	0.526960i
$13$	−2.36616	−	0.417219i	−0.656256	−	0.115716i	−0.164402	−	0.986393i	$-0.552569\pi$
$13$	−2.36616	−	0.417219i	−0.656256	−	0.115716i	−0.491854	+	0.870678i	$0.663681\pi$
$14$	−0.795642	+	0.836511i	−0.212644	+	0.223567i
$15$	−1.71296	+	3.72954i	−0.442283	+	0.962964i
$16$	−0.297302	+	3.98894i	−0.0743256	+	0.997234i
$17$	1.52854	−	2.64751i	0.370726	−	0.642116i	−0.618951	−	0.785429i	$-0.712442\pi$
$17$	1.52854	−	2.64751i	0.370726	−	0.642116i	0.989677	+	0.143313i	$0.0457755\pi$
$18$	0.524128	+	4.21014i	0.123538	+	0.992340i
$19$	−0.631691	+	0.364707i	−0.144920	+	0.0836695i	−0.570707	−	0.821154i	$-0.693331\pi$
$19$	−0.631691	+	0.364707i	−0.144920	+	0.0836695i	0.425787	+	0.904823i	$0.359997\pi$
$20$	−4.73308	+	0.237181i	−1.05835	+	0.0530352i
$21$	−1.40924	−	0.115093i	−0.307521	−	0.0251154i
$22$	−7.56006	+	2.22998i	−1.61181	+	0.475433i
$23$	6.38462	−	2.32381i	1.33128	−	0.484548i	0.424228	−	0.905556i	$-0.360546\pi$
$23$	6.38462	−	2.32381i	1.33128	−	0.484548i	0.907057	+	0.421008i	$0.138323\pi$
$24$	−4.03087	+	2.78426i	−0.822798	+	0.568334i
$25$	−0.106720	−	0.605238i	−0.0213440	−	0.121048i
$26$	1.87866	−	2.83130i	0.368436	−	0.555263i
$27$	−3.61001	+	3.73735i	−0.694747	+	0.719254i
$28$	−0.634489	−	1.50433i	−0.119907	−	0.284292i
$29$	9.24326	−	1.62984i	1.71643	−	0.302653i	0.773045	−	0.634351i	$-0.218733\pi$
$29$	9.24326	−	1.62984i	1.71643	−	0.302653i	0.943385	+	0.331698i	$0.107622\pi$
$30$	−3.86600	−	4.32915i	−0.705831	−	0.790390i
$31$	1.92800	−	0.701734i	0.346279	−	0.126035i	−0.163025	−	0.986622i	$-0.552125\pi$
$31$	1.92800	−	0.701734i	0.346279	−	0.126035i	0.509304	+	0.860587i	$0.329903\pi$
$32$	−5.00265	−	2.64073i	−0.884352	−	0.466820i
$33$	−7.93957	−	5.49127i	−1.38210	−	0.955908i
$34$	2.56766	+	3.47831i	0.440350	+	0.596526i
$35$	1.67516	−	0.967153i	0.283154	−	0.163479i
$36$	−5.75383	−	1.70101i	−0.958972	−	0.283501i
$37$	4.61364	+	2.66369i	0.758478	+	0.437907i	0.828749	−	0.559621i	$-0.189053\pi$
$37$	4.61364	+	2.66369i	0.758478	+	0.437907i	−0.0702711	+	0.997528i	$0.522386\pi$
$38$	−0.115601	−	1.02505i	−0.0187529	−	0.166285i
$39$	4.14354	−	0.386644i	0.663497	−	0.0619126i
$40$	2.36864	−	6.26946i	0.374515	−	0.991289i
$41$	−1.29167	+	7.32541i	−0.201725	+	1.14404i	0.700787	+	0.713371i	$0.252832\pi$
$41$	−1.29167	+	7.32541i	−0.201725	+	1.14404i	−0.902511	+	0.430666i	$0.858279\pi$
$42$	0.945976	−	1.76168i	0.145967	−	0.271833i
$43$	−4.42023	−	5.26782i	−0.674078	−	0.803335i	0.315255	−	0.949007i	$-0.397910\pi$
$43$	−4.42023	−	5.26782i	−0.674078	−	0.803335i	−0.989333	+	0.145672i	$0.953466\pi$
$44$	1.38381	−	11.0607i	0.208617	−	1.66747i
$45$	1.15342	−	7.01433i	0.171942	−	1.04563i
$46$	−0.597580	+	9.59009i	−0.0881083	+	1.41398i
$47$	−10.2350	−	3.72522i	−1.49292	−	0.543380i	−0.538706	−	0.842494i	$-0.681087\pi$
$47$	−10.2350	−	3.72522i	−1.49292	−	0.543380i	−0.954217	+	0.299114i	$0.903309\pi$
$48$	−1.33009	−	6.79933i	−0.191983	−	0.981398i
$49$	−4.85182	−	4.07116i	−0.693117	−	0.581594i
$50$	0.844892	+	0.203864i	0.119486	+	0.0288308i
$51$	−1.34089	+	5.12243i	−0.187762	+	0.717284i
$52$	2.60793	+	4.03608i	0.361655	+	0.559703i
$53$		−	2.99582i		−	0.411507i	−0.978604	−	0.205754i	$-0.934035\pi$
$53$		−	2.99582i		−	0.411507i	0.978604	−	0.205754i	$-0.0659645\pi$
$54$	−2.80352	−	6.79266i	−0.381511	−	0.924364i
$55$	13.2064			1.78075
$56$	2.30877	+	0.0280815i	0.308522	+	0.00375255i
$57$	0.888170	−	0.898491i	0.117641	−	0.119008i
$58$	−3.11344	+	12.9033i	−0.408815	+	1.69429i
$59$	0.837520	−	0.998118i	0.109036	−	0.129944i	−0.708766	−	0.705443i	$-0.750748\pi$
$59$	0.837520	−	0.998118i	0.109036	−	0.129944i	0.817802	+	0.575500i	$0.195192\pi$
$60$	7.79759	−	2.56368i	1.00666	−	0.330970i
$61$	−0.528763	+	1.45277i	−0.0677012	+	0.186008i	−0.968929	−	0.247337i	$-0.920444\pi$
$61$	−0.528763	+	1.45277i	−0.0677012	+	0.186008i	0.901228	+	0.433345i	$0.142667\pi$
$62$	−0.180455	+	2.89597i	−0.0229177	+	0.367789i
$63$	2.40672	−	0.453099i	0.303218	−	0.0570851i
$64$	6.25162	−	4.99172i	0.781452	−	0.623965i
$65$	−4.36120	+	3.65948i	−0.540940	+	0.453903i
$66$	11.6072	−	7.18708i	1.42875	−	0.884668i
$67$	−4.70399	−	0.829441i	−0.574684	−	0.101332i	−0.121250	−	0.992622i	$-0.538690\pi$
$67$	−4.70399	−	0.829441i	−0.574684	−	0.101332i	−0.453434	+	0.891290i	$0.649801\pi$
$68$	−5.96060	+	1.36174i	−0.722829	+	0.165135i
$69$	−9.60078	+	6.80553i	−1.15580	+	0.819289i
$70$	0.306557	+	2.71829i	0.0366406	+	0.324898i
$71$	−4.37210	+	7.57270i	−0.518873	+	0.898714i	0.480887	+	0.876783i	$0.340315\pi$
$71$	−4.37210	+	7.57270i	−0.518873	+	0.898714i	−0.999759	+	0.0219314i	$0.993018\pi$
$72$	5.45819	−	6.49678i	0.643254	−	0.765653i
$73$	−2.62609	−	4.54853i	−0.307361	−	0.532365i	0.670423	−	0.741979i	$-0.266113\pi$
$73$	−2.62609	−	4.54853i	−0.307361	−	0.532365i	−0.977784	+	0.209614i	$0.932779\pi$
$74$	−6.06142	+	4.47448i	−0.704626	+	0.520148i
$75$	0.455432	+	0.962127i	0.0525887	+	0.111097i
$76$	1.39410	+	0.429714i	0.159915	+	0.0492916i
$77$	1.55613	+	4.27542i	0.177337	+	0.487230i
$78$	−1.84157	+	5.58977i	−0.208516	+	0.632916i
$79$	−0.739506	−	4.19395i	−0.0832010	−	0.471856i	−0.997730	−	0.0673365i	$-0.978550\pi$
$79$	−0.739506	−	4.19395i	−0.0832010	−	0.471856i	0.914529	−	0.404520i	$-0.132561\pi$
$80$	6.78770	+	6.61516i	0.758888	+	0.739598i
$81$	4.31872	−	7.89612i	0.479857	−	0.877347i
$82$	−8.76541	−	5.81615i	−0.967978	−	0.642286i
$83$	−14.1745	+	2.49935i	−1.55585	+	0.274339i	−0.884408	−	0.466716i	$-0.845437\pi$
$83$	−14.1745	+	2.49935i	−1.55585	+	0.274339i	−0.671445	+	0.741054i	$0.734326\pi$
$84$	1.74876	+	2.22230i	0.190805	+	0.242473i
$85$	−2.47752	−	6.80694i	−0.268725	−	0.738316i
$86$	9.32773	−	2.75138i	1.00584	−	0.296689i
$87$	−14.6937	+	6.95541i	−1.57533	+	0.745698i
$88$	13.5553	+	8.04754i	1.44500	+	0.857871i
$89$	4.96560	+	8.60067i	0.526352	+	0.911669i	0.999529	+	0.0307010i	$0.00977397\pi$
$89$	4.96560	+	8.60067i	0.526352	+	0.911669i	−0.473176	+	0.880968i	$0.656893\pi$
$90$	8.44033	+	5.46106i	0.889689	+	0.575646i
$91$	−1.69860	−	0.980687i	−0.178062	−	0.102804i
$92$	−12.0935	−	6.19687i	−1.26083	−	0.646069i
$93$	−2.89920	+	2.05510i	−0.300633	+	0.213104i
$94$	10.6158	−	11.1611i	1.09493	−	1.15118i
$95$	−0.300125	+	1.70209i	−0.0307922	+	0.174631i
$96$	9.56582	+	2.12018i	0.976307	+	0.216390i
$97$	−11.8735	+	9.96305i	−1.20557	+	1.01159i	−0.206119	+	0.978527i	$0.566083\pi$
$97$	−11.8735	+	9.96305i	−1.20557	+	1.01159i	−0.999453	+	0.0330678i	$0.989472\pi$
$98$	8.02056	−	3.98744i	0.810199	−	0.402792i
$99$	15.7771	+	5.53682i	1.58566	+	0.556471i
$100$	−0.741967	+	0.979945i	−0.0741967	+	0.0979945i
$101$	3.29440	−	9.05130i	0.327805	−	0.900638i	−0.660861	−	0.750508i	$-0.729809\pi$
$101$	3.29440	−	9.05130i	0.327805	−	0.900638i	0.988666	−	0.150129i	$-0.0479690\pi$
$102$	−5.88193	−	4.63438i	−0.582398	−	0.458872i
$103$	−0.566175	−	0.475077i	−0.0557869	−	0.0468108i	0.614468	−	0.788942i	$-0.289371\pi$
$103$	−0.566175	−	0.475077i	−0.0557869	−	0.0468108i	−0.670255	+	0.742131i	$0.733815\pi$
$104$	−6.70638	+	1.09859i	−0.657615	+	0.107726i
$105$	−2.35531	+	2.38268i	−0.229854	+	0.232526i
$106$	3.88339	+	1.69384i	0.377189	+	0.164520i
$107$		−	2.41557i		−	0.233522i	−0.993160	−	0.116761i	$-0.962749\pi$
$107$		−	2.41557i		−	0.233522i	0.993160	−	0.116761i	$-0.0372512\pi$
$108$	10.3903	+	0.206451i	0.999803	+	0.0198658i
$109$		−	5.27617i		−	0.505365i	−0.967549	−	0.252683i	$-0.918687\pi$
$109$		−	5.27617i		−	0.505365i	0.967549	−	0.252683i	$-0.0813129\pi$
$110$	−7.46692	+	17.1191i	−0.711943	+	1.63224i
$111$	−8.92652	−	2.33667i	−0.847267	−	0.221787i
$112$	−1.34178	+	2.97691i	−0.126786	+	0.281292i
$113$	10.7854	+	9.05004i	1.01461	+	0.851356i	0.988940	−	0.148315i	$-0.0473849\pi$
$113$	10.7854	+	9.05004i	1.01461	+	0.851356i	0.0256661	+	0.999671i	$0.491829\pi$
$114$	0.662517	+	1.65932i	0.0620504	+	0.155409i
$115$	5.50629	−	15.1284i	0.513464	−	1.41073i
$116$	−14.9658	−	11.3314i	−1.38954	−	1.05209i
$117$	−6.74437	+	2.54337i	−0.623517	+	0.235135i
$118$	0.820297	+	1.64999i	0.0755145	+	0.151894i
$119$	1.91174	−	1.60414i	0.175249	−	0.147051i
$120$	−1.08554	+	11.5573i	−0.0990961	+	1.05503i
$121$	−3.48402	+	19.7588i	−0.316729	+	1.79626i
$122$	−1.58422	−	1.50682i	−0.143428	−	0.136421i
$123$	−1.19701	−	12.8280i	−0.107931	−	1.15666i
$124$	−3.65194	−	1.87130i	−0.327954	−	0.168048i
$125$	8.99914	+	5.19565i	0.804907	+	0.464713i
$126$	−0.773421	+	3.37594i	−0.0689018	+	0.300753i
$127$	6.59181	+	11.4173i	0.584928	+	1.01313i	0.994884	+	0.101020i	$0.0322108\pi$
$127$	6.59181	+	11.4173i	0.584928	+	1.01313i	−0.409956	+	0.912105i	$0.634456\pi$
$128$	2.93596	+	10.9261i	0.259505	+	0.965742i
$129$	9.79598	+	6.77523i	0.862488	+	0.596526i
$130$	−2.27786	−	7.72238i	−0.199781	−	0.677297i
$131$	4.87820	+	13.4028i	0.426211	+	1.17100i	0.948095	+	0.317988i	$0.103007\pi$
$131$	4.87820	+	13.4028i	0.426211	+	1.17100i	−0.521884	+	0.853016i	$0.674771\pi$
$132$	2.75366	+	19.1097i	0.239676	+	1.66329i
$133$	−0.586398	+	0.103398i	−0.0508471	+	0.00896572i
$134$	3.73483	−	5.62869i	0.322640	−	0.486245i
$135$	1.28548	+	12.2450i	0.110636	+	1.05389i
$136$	1.60495	−	8.49649i	0.137623	−	0.728568i
$137$	−2.35896	−	13.3783i	−0.201539	−	1.14299i	−0.902793	−	0.430075i	$-0.858487\pi$
$137$	−2.35896	−	13.3783i	−0.201539	−	1.14299i	0.701254	−	0.712912i	$-0.252624\pi$
$138$	−3.39352	−	16.2931i	−0.288876	−	1.38696i
$139$	3.70358	+	10.1755i	0.314133	+	0.863074i	0.991811	+	0.127715i	$0.0407642\pi$
$139$	3.70358	+	10.1755i	0.314133	+	0.863074i	−0.677678	+	0.735359i	$0.737014\pi$
$140$	−3.69697	−	1.13954i	−0.312451	−	0.0963090i
$141$	18.8026	+	1.53562i	1.58346	+	0.129323i
$142$	−7.34429	−	9.94905i	−0.616319	−	0.834905i
$143$	−6.69560	−	11.5971i	−0.559915	−	0.969800i
$144$	5.33553	+	10.7486i	0.444627	+	0.895716i
$145$	11.1199	−	19.2603i	0.923460	−	1.59948i
$146$	7.38092	−	0.832388i	0.610850	−	0.0688890i
$147$	9.96892	+	4.57866i	0.822223	+	0.377642i
$148$	−2.37301	−	10.3871i	−0.195060	−	0.853817i
$149$	−10.8534	−	1.91374i	−0.889141	−	0.156780i	−0.289623	−	0.957141i	$-0.593530\pi$
$149$	−10.8534	−	1.91374i	−0.889141	−	0.156780i	−0.599518	+	0.800361i	$0.704641\pi$
$150$	−1.50468	+	0.0463759i	−0.122857	+	0.00378658i
$151$	−0.654630	+	0.549300i	−0.0532730	+	0.0447014i	−0.669035	−	0.743231i	$-0.733293\pi$
$151$	−0.654630	+	0.549300i	−0.0532730	+	0.0447014i	0.615762	+	0.787932i	$0.288848\pi$
$152$	−1.34525	+	1.56418i	−0.109115	+	0.126871i
$153$	−0.105956	−	9.17064i	−0.00856605	−	0.741403i
$154$	−6.42195	−	0.400166i	−0.517495	−	0.0322463i
$155$	1.66277	−	4.56841i	0.133557	−	0.366944i
$156$	−6.20463	−	5.54763i	−0.496768	−	0.444166i
$157$	−2.44013	+	2.90803i	−0.194743	+	0.232086i	−0.854576	−	0.519327i	$-0.826183\pi$
$157$	−2.44013	+	2.90803i	−0.194743	+	0.232086i	0.659832	+	0.751413i	$0.270627\pi$
$158$	5.85462	+	1.41266i	0.465768	+	0.112385i
$159$	1.37192	+	5.00426i	0.108800	+	0.396863i
$160$	−12.4128	+	5.05848i	−0.981320	+	0.399908i
$161$	5.54646			0.437122
$162$	7.79371	+	10.0627i	0.612332	+	0.790601i
$163$		−	15.6828i		−	1.22837i	−0.789162	−	0.614186i	$-0.789485\pi$
$163$		−	15.6828i		−	1.22837i	0.789162	−	0.614186i	$-0.210515\pi$
$164$	12.4953	−	8.07390i	0.975718	−	0.630466i
$165$	−22.0602	+	6.04780i	−1.71738	+	0.470821i
$166$	4.77444	−	19.7871i	0.370569	−	1.53578i
$167$	0.331925	+	0.278519i	0.0256852	+	0.0215524i	0.655540	−	0.755161i	$-0.272441\pi$
$167$	0.331925	+	0.278519i	0.0256852	+	0.0215524i	−0.629855	+	0.776713i	$0.716886\pi$
$168$	−3.86946	+	1.01038i	−0.298535	+	0.0779524i
$169$	−6.79134	−	2.47185i	−0.522411	−	0.190142i
$170$	10.2244	+	0.637108i	0.784179	+	0.0488639i
$171$	−1.07215	+	1.90759i	−0.0819896	+	0.145877i
$172$	−1.70737	+	13.6469i	−0.130186	+	1.04057i
$173$	4.07848	+	4.86054i	0.310081	+	0.369540i	0.898468	−	0.439039i	$-0.144681\pi$
$173$	4.07848	+	4.86054i	0.310081	+	0.369540i	−0.588387	+	0.808580i	$0.700237\pi$
$174$	−0.708258	−	22.9796i	−0.0536929	−	1.74208i
$175$	0.0871188	−	0.494075i	0.00658556	−	0.0373486i
$176$	−18.0960	+	13.0213i	−1.36404	+	0.981515i
$177$	−0.941924	+	2.05081i	−0.0707993	+	0.154148i
$178$	−13.9564	+	1.57394i	−1.04607	+	0.117972i
$179$	−22.8480	−	13.1913i	−1.70774	−	0.985966i	−0.937345	−	0.348402i	$-0.886724\pi$
$179$	−22.8480	−	13.1913i	−1.70774	−	0.985966i	−0.770398	−	0.637564i	$-0.779942\pi$
$180$	−11.8512	+	7.85327i	−0.883336	+	0.585349i
$181$	−10.1392	+	5.85386i	−0.753639	+	0.435114i	−0.827007	−	0.562191i	$-0.809959\pi$
$181$	−10.1392	+	5.85386i	−0.753639	+	0.435114i	0.0733680	+	0.997305i	$0.476625\pi$
$182$	2.23163	−	1.64737i	0.165419	−	0.122111i
$183$	0.217968	−	2.66887i	0.0161127	−	0.197288i
$184$	14.8705	−	12.1727i	1.09627	−	0.897386i
$185$	11.8620	−	4.31741i	0.872110	−	0.317422i
$186$	−1.02476	−	4.92011i	−0.0751391	−	0.360760i
$187$	16.7797	−	2.95872i	1.22706	−	0.216363i
$188$	8.46560	+	20.0714i	0.617417	+	1.46386i
$189$	−3.81272	+	1.85901i	−0.277335	+	0.135223i
$190$	−2.03669	−	1.35141i	−0.147757	−	0.0980416i
$191$	−3.61178	−	20.4834i	−0.261339	−	1.48213i	−0.779261	−	0.626700i	$-0.784405\pi$
$191$	−3.61178	−	20.4834i	−0.261339	−	1.48213i	0.517921	−	0.855428i	$-0.326706\pi$
$192$	−8.15686	+	11.2011i	−0.588671	+	0.808373i
$193$	−3.79638	+	1.38177i	−0.273270	+	0.0994620i	−0.475020	−	0.879975i	$-0.657559\pi$
$193$	−3.79638	+	1.38177i	−0.273270	+	0.0994620i	0.201750	+	0.979437i	$0.435337\pi$
$194$	−6.20153	−	21.0244i	−0.445244	−	1.50947i
$195$	5.60917	−	8.11004i	0.401681	−	0.580772i
$196$	0.633974	+	12.6513i	0.0452838	+	0.903666i
$197$	−15.7235	+	9.07798i	−1.12025	+	0.646779i	−0.941466	−	0.337108i	$-0.890551\pi$
$197$	−15.7235	+	9.07798i	−1.12025	+	0.646779i	−0.178788	+	0.983888i	$0.557218\pi$
$198$	−16.0976	+	17.3209i	−1.14401	+	1.23094i
$199$	8.84948	−	15.3277i	0.627323	−	1.08656i	−0.360764	−	0.932657i	$-0.617484\pi$
$199$	8.84948	−	15.3277i	0.627323	−	1.08656i	0.988087	−	0.153898i	$-0.0491827\pi$
$200$	−0.850767	−	1.51585i	−0.0601583	−	0.107187i
$201$	8.23746	−	0.768658i	0.581026	−	0.0542170i
$202$	9.87028	+	9.38806i	0.694471	+	0.660541i
$203$	7.54557	+	1.33049i	0.529595	+	0.0933819i
$204$	9.33307	−	5.00430i	0.653446	−	0.350371i
$205$	11.3294	+	13.5018i	0.791279	+	0.943009i
$206$	0.935946	−	0.465308i	0.0652104	−	0.0324195i
$207$	12.9207	−	15.7647i	0.898053	−	1.09572i
$208$	2.36773	−	9.31444i	0.164172	−	0.645840i
$209$	−3.82020	−	1.39044i	−0.264249	−	0.0961786i
$210$	−1.75690	−	4.40029i	−0.121238	−	0.303649i
$211$	2.99419	−	3.56833i	0.206128	−	0.245654i	−0.653069	−	0.757298i	$-0.726519\pi$
$211$	2.99419	−	3.56833i	0.206128	−	0.245654i	0.859197	+	0.511644i	$0.170963\pi$
$212$	−4.39135	+	4.07624i	−0.301599	+	0.279957i
$213$	3.83534	−	14.6517i	0.262793	−	1.00392i
$214$	3.13124	+	1.36577i	0.214047	+	0.0933619i
$215$	−16.2943			−1.11126
$216$	−6.14228	+	13.3519i	−0.417929	+	0.908480i
$217$	1.67490			0.113699
$218$	6.83935	+	2.98315i	0.463219	+	0.202045i
$219$	6.46964	+	6.39532i	0.437178	+	0.432156i
$220$	−17.9692	−	19.3583i	−1.21148	−	1.30514i
$221$	−4.72138	+	5.62672i	−0.317594	+	0.378494i
$222$	8.07602	−	10.2500i	0.542027	−	0.687937i
$223$	−23.9911	−	8.73206i	−1.60656	−	0.584742i	−0.625808	−	0.779977i	$-0.715231\pi$
$223$	−23.9911	−	8.73206i	−1.60656	−	0.584742i	−0.980756	+	0.195235i	$0.937453\pi$
$224$	−3.10024	−	3.42246i	−0.207144	−	0.228673i
$225$	−1.20136	−	1.39859i	−0.0800907	−	0.0932392i
$226$	−17.8294	+	8.86393i	−1.18599	+	0.589620i
$227$	5.61519	+	6.69192i	0.372693	+	0.444158i	0.919494	−	0.393104i	$-0.128599\pi$
$227$	5.61519	+	6.69192i	0.372693	+	0.444158i	−0.546801	+	0.837263i	$0.684154\pi$
$228$	−2.52552	−	0.0793789i	−0.167256	−	0.00525700i
$229$	−7.54563	−	1.33050i	−0.498629	−	0.0879218i	−0.0813232	−	0.996688i	$-0.525915\pi$
$229$	−7.54563	−	1.33050i	−0.498629	−	0.0879218i	−0.417306	+	0.908766i	$0.637026\pi$
$230$	16.4973	+	15.6913i	1.08780	+	1.03465i
$231$	−4.55728	−	6.42911i	−0.299847	−	0.423004i
$232$	23.1503	−	12.9930i	1.51989	−	0.853032i
$233$	−4.64693	+	8.04871i	−0.304430	+	0.527289i	−0.977134	−	0.212623i	$-0.931799\pi$
$233$	−4.64693	+	8.04871i	−0.304430	+	0.527289i	0.672704	+	0.739912i	$0.265133\pi$
$234$	0.516377	−	10.1806i	0.0337566	−	0.665524i
$235$	−22.3506	+	12.9041i	−1.45799	+	0.841773i
$236$	−2.60263	+	0.130421i	−0.169417	+	0.00848970i
$237$	3.15588	+	6.66698i	0.204996	+	0.433067i
$238$	0.998501	+	3.38512i	0.0647232	+	0.219424i
$239$	7.97388	−	2.90226i	0.515788	−	0.187731i	−0.0709937	−	0.997477i	$-0.522617\pi$
$239$	7.97388	−	2.90226i	0.515788	−	0.187731i	0.586781	+	0.809745i	$0.300395\pi$
$240$	−14.3676	−	7.94168i	−0.927428	−	0.512633i
$241$	0.538985	+	3.05674i	0.0347191	+	0.196902i	0.997234	−	0.0743274i	$-0.0236810\pi$
$241$	0.538985	+	3.05674i	0.0347191	+	0.196902i	−0.962515	+	0.271229i	$0.912570\pi$
$242$	−23.6430	−	15.6879i	−1.51983	−	1.00846i
$243$	−3.59806	+	15.1675i	−0.230816	+	0.972997i
$244$	2.84896	−	1.20162i	0.182386	−	0.0769258i
$245$	−14.7795	+	2.60603i	−0.944230	+	0.166493i
$246$	17.3054	+	5.70131i	1.10335	+	0.363502i
$247$	1.64685	−	0.599403i	0.104786	−	0.0381391i
$248$	4.49053	−	3.67587i	0.285149	−	0.233418i
$249$	22.5327	−	10.6661i	1.42795	−	0.675935i
$250$	−11.8231	+	8.72770i	−0.747759	+	0.551988i
$251$	7.67295	−	4.42998i	0.484312	−	0.279618i	−0.237899	−	0.971290i	$-0.576459\pi$
$251$	7.67295	−	4.42998i	0.484312	−	0.279618i	0.722212	+	0.691672i	$0.243126\pi$
$252$	−3.93885	−	2.91133i	−0.248124	−	0.183396i
$253$	32.7949	+	18.9341i	2.06180	+	1.19038i
$254$	−18.5270	+	2.08939i	−1.16249	+	0.131100i
$255$	7.25569	+	10.2358i	0.454369	+	0.640993i
$256$	−15.8232	−	2.37184i	−0.988951	−	0.148240i
$257$	−2.93606	+	16.6512i	−0.183146	+	1.03868i	0.745167	+	0.666878i	$0.232370\pi$
$257$	−2.93606	+	16.6512i	−0.183146	+	1.03868i	−0.928314	+	0.371798i	$0.878742\pi$
$258$	−14.3212	+	8.86754i	−0.891599	+	0.552069i
$259$	2.79542	+	3.33146i	0.173699	+	0.207007i
$260$	11.2982	+	1.41352i	0.700685	+	0.0876629i
$261$	21.3594	−	18.3473i	1.32211	−	1.13567i
$262$	−20.1318	−	1.25446i	−1.24374	−	0.0775005i
$263$	25.9536	+	9.44634i	1.60037	+	0.582487i	0.979503	−	0.201430i	$-0.0645590\pi$
$263$	25.9536	+	9.44634i	1.60037	+	0.582487i	0.620866	+	0.783917i	$0.286781\pi$
$264$	−26.3283	−	7.23516i	−1.62040	−	0.445293i
$265$	−5.43786	−	4.56290i	−0.334045	−	0.280297i
$266$	0.197518	−	0.818592i	0.0121106	−	0.0501911i
$267$	−12.2332	−	12.0927i	−0.748662	−	0.740062i
$268$	5.18464	+	8.02382i	0.316702	+	0.490133i
$269$		−	0.151914i		−	0.00926235i	−0.999989	−	0.00463118i	$-0.998526\pi$
$269$		−	0.151914i		−	0.00926235i	0.999989	−	0.00463118i	$-0.00147415\pi$
$270$	−16.5997	−	5.25703i	−1.01023	−	0.319933i
$271$	−15.3499			−0.932442			−0.466221	−	0.884668i	$-0.654385\pi$
$271$	−15.3499			−0.932442			−0.466221	+	0.884668i	$0.654385\pi$
$272$	10.1063	+	6.88437i	0.612786	+	0.417426i
$273$	3.28647	+	0.860290i	0.198906	+	0.0520671i
$274$	18.6757	+	4.50627i	1.12824	+	0.272233i
$275$	2.20175	−	2.62395i	0.132771	−	0.158230i
$276$	23.0390	+	4.81320i	1.38678	+	0.289721i
$277$	−7.89627	+	21.6948i	−0.474441	+	1.30351i	0.439710	+	0.898140i	$0.355081\pi$
$277$	−7.89627	+	21.6948i	−0.474441	+	1.30351i	−0.914150	+	0.405375i	$0.867141\pi$
$278$	−15.2842	−	0.952393i	−0.916686	−	0.0571208i
$279$	3.90175	−	4.76055i	0.233591	−	0.285007i
$280$	3.56743	−	4.14798i	0.213195	−	0.247889i
$281$	4.24157	−	3.55910i	0.253031	−	0.212318i	−0.507445	−	0.861684i	$-0.669410\pi$
$281$	4.24157	−	3.55910i	0.253031	−	0.212318i	0.760476	+	0.649366i	$0.224966\pi$
$282$	−12.6216	+	23.5050i	−0.751605	+	1.39970i
$283$	5.09313	+	0.898056i	0.302755	+	0.0533839i	0.322962	−	0.946412i	$-0.395321\pi$
$283$	5.09313	+	0.898056i	0.302755	+	0.0533839i	−0.0202070	+	0.999796i	$0.506433\pi$
$284$	17.0491	−	3.89499i	1.01168	−	0.231125i
$285$	−0.278132	−	2.98065i	−0.0164751	−	0.176558i
$286$	18.8187	−	2.12229i	1.11278	−	0.125494i
$287$	−3.03611	+	5.25870i	−0.179216	+	0.310411i
$288$	−16.9498	+	0.839027i	−0.998777	+	0.0494401i
$289$	3.82711	+	6.62876i	0.225124	+	0.389927i
$290$	18.6793	+	25.3042i	1.09689	+	1.48592i
$291$	15.2712	−	22.0798i	0.895211	−	1.29434i
$292$	−3.09418	+	10.0383i	−0.181073	+	0.587448i
$293$	−5.24603	−	14.4133i	−0.306476	−	0.842036i	−0.993337	−	0.115247i	$-0.963234\pi$
$293$	−5.24603	−	14.4133i	−0.306476	−	0.842036i	0.686861	−	0.726789i	$-0.258988\pi$
$294$	−11.5716	+	10.3337i	−0.674871	+	0.602671i
$295$	−0.536113	−	3.04045i	−0.0312137	−	0.177022i
$296$	14.8062	+	2.79683i	0.860596	+	0.162562i
$297$	−28.8898	−	2.02375i	−1.67636	−	0.117430i
$298$	8.61723	−	12.9869i	0.499182	−	0.752309i
$299$	−16.0766	+	2.83474i	−0.929733	+	0.163937i
$300$	0.790632	−	1.97670i	0.0456472	−	0.114125i
$301$	−1.91998	−	5.27509i	−0.110666	−	0.304051i
$302$	−0.341913	−	1.15915i	−0.0196749	−	0.0667018i
$303$	−1.35803	+	16.6281i	−0.0780165	+	0.955258i
$304$	−1.26699	−	2.62820i	−0.0726668	−	0.150738i
$305$	1.83163	+	3.17248i	0.104879	+	0.181656i
$306$	11.9476	+	5.04775i	0.682996	+	0.288560i
$307$	13.3505	+	7.70794i	0.761956	+	0.439916i	0.829998	−	0.557767i	$-0.188342\pi$
$307$	13.3505	+	7.70794i	0.761956	+	0.439916i	−0.0680415	+	0.997682i	$0.521675\pi$
$308$	4.14970	−	8.09833i	0.236451	−	0.461445i
$309$	1.16331	+	0.534300i	0.0661782	+	0.0303952i
$310$	4.98177	+	4.73838i	0.282946	+	0.269122i
$311$	3.82602	−	21.6984i	0.216954	−	1.23040i	−0.660531	−	0.750799i	$-0.729669\pi$
$311$	3.82602	−	21.6984i	0.216954	−	1.23040i	0.877484	−	0.479605i	$-0.159220\pi$
$312$	10.6993	−	4.90625i	0.605731	−	0.277762i
$313$	21.5889	−	18.1152i	1.22027	−	1.02393i	0.221465	−	0.975168i	$-0.428916\pi$
$313$	21.5889	−	18.1152i	1.22027	−	1.02393i	0.998810	−	0.0487638i	$-0.0155281\pi$
$314$	−2.38995	−	4.80728i	−0.134873	−	0.271290i
$315$	2.84321	−	5.05866i	0.160197	−	0.285023i
$316$	−5.14140	+	6.79045i	−0.289226	+	0.381993i
$317$	12.0843	−	33.2014i	0.678722	−	1.86477i	0.222416	−	0.974952i	$-0.428606\pi$
$317$	12.0843	−	33.2014i	0.678722	−	1.86477i	0.456307	−	0.889823i	$-0.349172\pi$
$318$	−7.26256	−	1.05103i	−0.407264	−	0.0589391i
$319$	40.0732	+	33.6254i	2.24367	+	1.88266i
$320$	0.461058	−	18.9505i	0.0257739	−	1.05936i
$321$	1.10620	+	4.03501i	0.0617420	+	0.225212i
$322$	−3.13598	+	7.18972i	−0.174761	+	0.400668i
$323$			2.22988i			0.124074i
$324$	−17.4506	+	4.41330i	−0.969477	+	0.245183i
$325$			1.47662i			0.0819080i
$326$	20.3292	+	8.86707i	1.12593	+	0.491102i
$327$	2.41619	+	8.81339i	0.133616	+	0.487382i
$328$	3.40113	+	20.7623i	0.187796	+	1.14641i
$329$	−6.81117	−	5.71525i	−0.375512	−	0.315092i
$330$	4.63325	−	32.0154i	0.255052	−	1.76239i
$331$	−2.25679	+	6.20048i	−0.124044	+	0.340809i	−0.986135	−	0.165945i	$-0.946933\pi$
$331$	−2.25679	+	6.20048i	−0.124044	+	0.340809i	0.862091	+	0.506754i	$0.169155\pi$
$332$	22.9500	+	17.3766i	1.25955	+	0.953667i
$333$	15.9811	−	0.184643i	0.875756	−	0.0101183i
$334$	−0.548707	+	0.272791i	−0.0300239	+	0.0149265i
$335$	−8.67017	+	7.27514i	−0.473702	+	0.397483i
$336$	0.878069	−	5.58714i	0.0479026	−	0.304803i
$337$	−3.49402	+	19.8156i	−0.190331	+	1.07942i	0.728581	+	0.684960i	$0.240180\pi$
$337$	−3.49402	+	19.8156i	−0.190331	+	1.07942i	−0.918912	+	0.394462i	$0.870931\pi$
$338$	7.04402	−	7.40584i	0.383144	−	0.402825i
$339$	−22.1605	−	10.1782i	−1.20359	−	0.552804i
$340$	−6.60678	+	12.8934i	−0.358303	+	0.699245i
$341$	9.90325	+	5.71764i	0.536291	+	0.309628i
$342$	−1.86655	−	2.46835i	−0.100932	−	0.133473i
$343$	−5.44232	−	9.42638i	−0.293858	−	0.508977i
$344$	−16.7248	−	9.92920i	−0.901739	−	0.535346i
$345$	−2.26982	+	27.7923i	−0.122203	+	1.49629i
$346$	−8.60656	+	2.53866i	−0.462692	+	0.136479i
$347$	1.25968	+	3.46095i	0.0676232	+	0.185793i	0.968901	−	0.247448i	$-0.0795920\pi$
$347$	1.25968	+	3.46095i	0.0676232	+	0.185793i	−0.901278	+	0.433241i	$0.857370\pi$
$348$	30.1883	+	12.0746i	1.61826	+	0.647268i
$349$	−25.7001	+	4.53163i	−1.37570	+	0.242572i	−0.812120	−	0.583491i	$-0.801686\pi$
$349$	−25.7001	+	4.53163i	−1.37570	+	0.242572i	−0.563577	+	0.826063i	$0.690575\pi$
$350$	0.591199	+	0.392280i	0.0316009	+	0.0209683i
$351$	10.1012	−	7.33703i	0.539161	−	0.391622i
$352$	−6.64761	−	30.8196i	−0.354319	−	1.64269i
$353$	−5.13961	−	29.1482i	−0.273554	−	1.55140i	−0.743519	−	0.668715i	$-0.766845\pi$
$353$	−5.13961	−	29.1482i	−0.273554	−	1.55140i	0.469965	−	0.882685i	$-0.344267\pi$
$354$	−2.12584	−	2.38052i	−0.112987	−	0.126523i
$355$	7.08647	+	19.4699i	0.376111	+	1.03336i
$356$	5.85069	−	18.9811i	0.310086	−	1.00600i
$357$	−2.45879	+	3.55505i	−0.130133	+	0.188153i
$358$	30.0179	−	22.1589i	1.58649	−	1.17113i
$359$	6.44307	+	11.1597i	0.340052	+	0.588988i	0.984442	−	0.175709i	$-0.0562219\pi$
$359$	6.44307	+	11.1597i	0.340052	+	0.588988i	−0.644390	+	0.764697i	$0.722889\pi$
$360$	−3.47930	−	19.8026i	−0.183375	−	1.04369i
$361$	−9.23398	+	15.9937i	−0.485999	+	0.841775i
$362$	−1.85549	−	16.4529i	−0.0975223	−	0.864746i
$363$	−3.22870	−	34.6009i	−0.169463	−	1.81608i
$364$	0.873669	+	3.82422i	0.0457927	+	0.200444i
$365$	−12.2560	−	2.16107i	−0.641510	−	0.113116i
$366$	3.33634	+	1.79153i	0.174393	+	0.0936446i
$367$	−7.76761	+	6.51780i	−0.405466	+	0.340226i	−0.822602	−	0.568618i	$-0.807478\pi$
$367$	−7.76761	+	6.51780i	−0.405466	+	0.340226i	0.417136	+	0.908844i	$0.363034\pi$
$368$	7.37137	+	26.1587i	0.384259	+	1.36362i
$369$	7.87402	+	20.8799i	0.409905	+	1.08696i
$370$	−1.11024	+	17.8174i	−0.0577188	+	0.926284i
$371$	0.836438	−	2.29810i	0.0434257	−	0.119311i
$372$	6.95721	+	1.45347i	0.360714	+	0.0753589i
$373$	−6.70393	+	7.98944i	−0.347117	+	0.413677i	−0.911150	−	0.412074i	$-0.864804\pi$
$373$	−6.70393	+	7.98944i	−0.347117	+	0.413677i	0.564034	+	0.825752i	$0.309249\pi$
$374$	−5.65198	+	23.4240i	−0.292257	+	1.21122i
$375$	−17.4116	−	4.55779i	−0.899132	−	0.235363i
$376$	−30.8045	−	0.374675i	−1.58862	−	0.0193224i
$377$	−22.5511			−1.16144
$378$	−0.254061	−	5.99341i	−0.0130675	−	0.308268i
$379$			14.1280i			0.725707i	0.931846	+	0.362853i	$0.118197\pi$
$379$			14.1280i			0.725707i	−0.931846	+	0.362853i	$0.881803\pi$
$380$	2.90334	−	1.87601i	0.148938	−	0.0962373i
$381$	−16.2396	−	16.0530i	−0.831978	−	0.822421i
$382$	28.5942	+	6.89950i	1.46301	+	0.353009i
$383$	−8.29387	−	6.95938i	−0.423797	−	0.355608i	0.405808	−	0.913958i	$-0.366990\pi$
$383$	−8.29387	−	6.95938i	−0.423797	−	0.355608i	−0.829605	+	0.558350i	$0.811434\pi$
$384$	−9.90783	−	16.9067i	−0.505607	−	0.862764i
$385$	10.1307	+	3.68726i	0.516306	+	0.187920i
$386$	0.355329	−	5.70240i	0.0180858	−	0.290245i
$387$	−19.4660	−	6.83142i	−0.989514	−	0.347261i
$388$	30.7597	+	3.84836i	1.56159	+	0.195371i
$389$	11.3791	+	13.5611i	0.576945	+	0.687577i	0.973041	−	0.230633i	$-0.0740796\pi$
$389$	11.3791	+	13.5611i	0.576945	+	0.687577i	−0.396096	+	0.918209i	$0.629635\pi$
$390$	7.34139	+	11.8564i	0.371745	+	0.600374i
$391$	3.60684	−	20.4554i	0.182406	−	1.03447i
$392$	−16.7580	−	6.33127i	−0.846408	−	0.319778i
$393$	−14.2863	−	20.1542i	−0.720651	−	1.01665i
$394$	−2.87743	−	25.5147i	−0.144963	−	1.28541i
$395$	−8.73898	−	5.04545i	−0.439706	−	0.253864i
$396$	−13.3510	−	30.6601i	−0.670911	−	1.54073i
$397$	29.7791	−	17.1929i	1.49457	−	0.862889i	0.494587	−	0.869128i	$-0.335319\pi$
$397$	29.7791	−	17.1929i	1.49457	−	0.862889i	0.999981	+	0.00623882i	$0.00198589\pi$
$398$	14.8654	+	20.1377i	0.745136	+	1.00941i
$399$	0.932177	−	0.441255i	0.0466672	−	0.0220904i
$400$	2.44598	−	0.245760i	0.122299	−	0.0122880i
$401$	−7.23952	+	2.63497i	−0.361525	+	0.131584i	−0.516395	−	0.856351i	$-0.672726\pi$
$401$	−7.23952	+	2.63497i	−0.361525	+	0.131584i	0.154870	+	0.987935i	$0.450504\pi$
$402$	−3.66108	+	11.1126i	−0.182598	+	0.554246i
$403$	−4.85474	+	0.856021i	−0.241832	+	0.0426415i
$404$	−17.7501	+	7.48655i	−0.883103	+	0.372470i
$405$	−7.75484	−	19.8656i	−0.385341	−	0.987131i
$406$	−5.99095	+	9.02885i	−0.297326	+	0.448094i
$407$	5.15596	+	29.2409i	0.255571	+	1.44942i
$408$	1.21000	+	14.9276i	0.0599038	+	0.739028i
$409$	0.988723	−	0.359866i	0.0488892	−	0.0177942i	−0.317460	−	0.948272i	$-0.602830\pi$
$409$	0.988723	−	0.359866i	0.0488892	−	0.0177942i	0.366349	+	0.930478i	$0.380608\pi$
$410$	−23.9077	+	7.05201i	−1.18072	+	0.348274i
$411$	10.0670	+	21.2671i	0.496567	+	1.04903i
$412$	0.0739805	+	1.47633i	0.00364476	+	0.0727334i
$413$	0.921140	−	0.531820i	0.0453263	−	0.0261692i
$414$	13.1299	+	25.6622i	0.645301	+	1.26123i
$415$	−17.0524	+	29.5356i	−0.837067	+	1.44984i
$416$	10.7353	+	8.33561i	0.526343	+	0.408687i
$417$	−10.8463	−	15.3013i	−0.531147	−	0.749306i
$418$	3.96233	−	4.16586i	0.193804	−	0.203759i
$419$	5.20073	+	0.917030i	0.254073	+	0.0447998i	0.299234	−	0.954180i	$-0.403269\pi$
$419$	5.20073	+	0.917030i	0.254073	+	0.0447998i	−0.0451611	+	0.998980i	$0.514380\pi$
$420$	6.69733	+	0.210502i	0.326796	+	0.0102715i
$421$	−20.0672	−	23.9151i	−0.978013	−	1.16555i	−0.986196	−	0.165585i	$-0.947049\pi$
$421$	−20.0672	−	23.9151i	−0.978013	−	1.16555i	0.00818210	−	0.999967i	$-0.497396\pi$
$422$	2.93261	+	5.89882i	0.142757	+	0.287150i
$423$	−32.1114	+	6.04543i	−1.56131	+	0.293939i
$424$	−2.80104	−	7.99710i	−0.136030	−	0.388373i
$425$	−1.76550	−	0.642590i	−0.0856394	−	0.0311702i
$426$	16.8241	+	13.2558i	0.815131	+	0.642244i
$427$	−0.811230	+	0.966786i	−0.0392582	+	0.0467861i
$428$	−3.54081	+	3.28673i	−0.171152	+	0.158870i
$429$	16.4953	+	16.3058i	0.796400	+	0.787251i
$430$	9.21281	−	21.1218i	0.444281	−	1.01859i
$431$	3.25058			0.156575			0.0782874	−	0.996931i	$-0.475055\pi$
$431$	3.25058			0.156575			0.0782874	+	0.996931i	$0.475055\pi$
$432$	−13.8348	−	15.5112i	−0.665627	−	0.746284i
$433$	−5.78000			−0.277769			−0.138885	−	0.990309i	$-0.544352\pi$
$433$	−5.78000			−0.277769			−0.138885	+	0.990309i	$0.544352\pi$
$434$	−0.946988	+	2.17112i	−0.0454569	+	0.104217i
$435$	−9.75475	+	37.2650i	−0.467705	+	1.78672i
$436$	−7.73396	+	7.17898i	−0.370389	+	0.343811i
$437$	−3.18559	+	3.79644i	−0.152388	+	0.181608i
$438$	−11.9480	+	4.77049i	−0.570898	+	0.227943i
$439$	−9.84846	−	3.58454i	−0.470041	−	0.171081i	0.0961299	−	0.995369i	$-0.469354\pi$
$439$	−9.84846	−	3.58454i	−0.470041	−	0.171081i	−0.566171	+	0.824288i	$0.691576\pi$
$440$	35.2535	−	12.3478i	1.68064	−	0.588656i
$441$	−18.7490	−	3.08305i	−0.892810	−	0.146812i
$442$	−4.62428	−	9.30154i	−0.219955	−	0.442429i
$443$	6.84059	+	8.15230i	0.325006	+	0.387327i	0.903663	−	0.428244i	$-0.140867\pi$
$443$	6.84059	+	8.15230i	0.325006	+	0.387327i	−0.578657	+	0.815571i	$0.696423\pi$
$444$	8.72064	+	16.2641i	0.413863	+	0.771860i
$445$	23.1745	+	4.08630i	1.09858	+	0.193709i
$446$	24.8837	−	26.1619i	1.17828	−	1.23880i
$447$	19.0060	−	1.77350i	0.898952	−	0.0838835i
$448$	6.18932	−	2.08369i	0.292418	−	0.0984453i
$449$	10.3809	−	17.9803i	0.489906	−	0.848542i	−0.510026	−	0.860159i	$-0.670364\pi$
$449$	10.3809	−	17.9803i	0.489906	−	0.848542i	0.999933	+	0.0116165i	$0.00369773\pi$
$450$	2.49220	−	0.766527i	0.117484	−	0.0361344i
$451$	−35.9035	+	20.7289i	−1.69063	+	0.976087i
$452$	−1.40930	−	28.1234i	−0.0662879	−	1.32281i
$453$	0.841955	−	1.21734i	0.0395585	−	0.0571958i
$454$	−11.8494	+	3.49519i	−0.556119	+	0.164037i
$455$	−4.36722	+	1.58954i	−0.204738	+	0.0745186i
$456$	1.53083	−	3.22887i	0.0716875	−	0.151206i
$457$	−2.42319	−	13.7426i	−0.113352	−	0.642851i	−0.987553	−	0.157287i	$-0.949725\pi$
$457$	−2.42319	−	13.7426i	−0.113352	−	0.642851i	0.874201	−	0.485564i	$-0.161386\pi$
$458$	5.99100	−	9.02893i	0.279941	−	0.421894i
$459$	4.37664	+	15.2703i	0.204284	+	0.712755i
$460$	−29.6677	+	12.5131i	−1.38327	+	0.583426i
$461$	−0.0322801	+	0.00569184i	−0.00150343	+	0.000265096i	−0.174400	−	0.984675i	$-0.555799\pi$
$461$	−0.0322801	+	0.00569184i	−0.00150343	+	0.000265096i	0.172896	+	0.984940i	$0.444687\pi$
$462$	10.9106	−	2.27245i	0.507606	−	0.105724i
$463$	−24.6873	+	8.98546i	−1.14732	+	0.417590i	−0.844551	−	0.535475i	$-0.820133\pi$
$463$	−24.6873	+	8.98546i	−1.14732	+	0.417590i	−0.302767	+	0.953065i	$0.597910\pi$
$464$	3.75327	+	37.3553i	0.174241	+	1.73418i
$465$	−0.685429	+	8.39260i	−0.0317860	+	0.389197i
$466$	−7.80594	−	10.5744i	−0.361603	−	0.489851i
$467$	6.99161	−	4.03661i	0.323533	−	0.186792i	−0.329433	−	0.944179i	$-0.606858\pi$
$467$	6.99161	−	4.03661i	0.323533	−	0.186792i	0.652966	+	0.757387i	$0.273524\pi$
$468$	12.9048	+	6.42547i	0.596526	+	0.297017i
$469$	−3.37686	−	1.94963i	−0.155929	−	0.0900255i
$470$	−4.09020	−	36.2685i	−0.188667	−	1.67294i
$471$	2.74431	−	5.97507i	0.126451	−	0.275316i
$472$	1.30247	−	3.44746i	0.0599511	−	0.158682i
$473$	6.65539	−	37.7446i	0.306015	−	1.73550i
$474$	−10.4266	+	0.321358i	−0.478908	+	0.0147605i
$475$	0.288148	+	0.343402i	0.0132211	+	0.0157564i
$476$	−4.95258	−	0.619619i	−0.227001	−	0.0284002i
$477$	−4.58335	−	7.73093i	−0.209857	−	0.353975i
$478$	−0.746330	+	11.9773i	−0.0341363	+	0.547827i
$479$	23.7888	+	8.65842i	1.08694	+	0.395613i	0.822486	−	0.568785i	$-0.192587\pi$
$479$	23.7888	+	8.65842i	1.08694	+	0.395613i	0.264453	+	0.964399i	$0.414809\pi$
$480$	18.4181	−	14.1341i	0.840666	−	0.645133i
$481$	−9.80529	−	8.22762i	−0.447083	−	0.375147i
$482$	−4.26711	−	1.02961i	−0.194361	−	0.0468975i
$483$	−9.26489	+	2.53997i	−0.421567	+	0.115573i
$484$	33.7035	−	21.7777i	1.53198	−	0.989898i
$485$			36.7268i			1.66768i
$486$	−17.6269	−	13.2398i	−0.799572	−	0.600570i
$487$	−11.9724			−0.542520			−0.271260	−	0.962506i	$-0.587440\pi$
$487$	−11.9724			−0.542520			−0.271260	+	0.962506i	$0.587440\pi$
$488$	−0.0531819	+	4.37243i	−0.00240743	+	0.197930i
$489$	7.18185	+	26.1968i	0.324775	+	1.18466i
$490$	4.97824	−	20.6317i	0.224894	−	0.932047i
$491$	−2.49167	+	2.96946i	−0.112448	+	0.134010i	−0.819332	−	0.573319i	$-0.805656\pi$
$491$	−2.49167	+	2.96946i	−0.112448	+	0.134010i	0.706885	+	0.707329i	$0.250100\pi$
$492$	−17.1749	+	19.2089i	−0.774305	+	0.866005i
$493$	9.81370	−	26.9629i	0.441987	−	1.21435i
$494$	−0.154140	+	2.47367i	−0.00693507	+	0.111295i
$495$	34.0801	−	20.2047i	1.53179	−	0.908133i
$496$	2.22597	+	7.89929i	0.0999492	+	0.354689i
$497$	−5.46816	+	4.58833i	−0.245280	+	0.205815i
$498$	1.08611	+	35.2392i	0.0486697	+	1.57910i
$499$	7.13635	+	1.25833i	0.319467	+	0.0563307i	0.331082	−	0.943602i	$-0.392586\pi$
$499$	7.13635	+	1.25833i	0.319467	+	0.0563307i	−0.0116153	+	0.999933i	$0.503697\pi$
$500$	−4.62868	−	20.2606i	−0.207001	−	0.906082i
$501$	−0.681999	−	0.313238i	−0.0304695	−	0.0139944i
$502$	1.40416	+	12.4510i	0.0626709	+	0.555713i
$503$	−14.1108	+	24.4406i	−0.629168	+	1.08975i	0.358551	+	0.933510i	$0.383271\pi$
$503$	−14.1108	+	24.4406i	−0.629168	+	1.08975i	−0.987719	+	0.156241i	$0.950062\pi$
$504$	6.00090	−	3.45975i	0.267301	−	0.154109i
$505$	−11.4118	−	19.7658i	−0.507818	−	0.879566i
$506$	−43.0860	+	31.8057i	−1.91541	+	1.41394i
$507$	12.4763	+	1.01895i	0.554093	+	0.0452531i
$508$	7.76677	−	25.1974i	0.344595	−	1.11795i
$509$	−4.18088	−	11.4869i	−0.185314	−	0.509147i	0.811895	−	0.583803i	$-0.198436\pi$
$509$	−4.18088	−	11.4869i	−0.185314	−	0.509147i	−0.997209	+	0.0746568i	$0.976214\pi$
$510$	−17.3708	+	3.61799i	−0.769193	+	0.160207i
$511$	−0.744521	−	4.22239i	−0.0329357	−	0.186788i
$512$	12.0210	−	19.1702i	0.531259	−	0.847209i
$513$	0.917372	−	3.67745i	0.0405030	−	0.162363i
$514$	−19.9245	−	13.2206i	−0.878831	−	0.583134i
$515$	−1.72467	+	0.304106i	−0.0759982	+	0.0134005i
$516$	−3.39752	−	23.5779i	−0.149567	−	1.03796i
$517$	−20.7624	−	57.0444i	−0.913131	−	2.50881i
$518$	−5.89901	+	1.74002i	−0.259188	+	0.0764521i
$519$	−9.03861	−	6.25140i	−0.396751	−	0.274406i
$520$	−8.22033	+	13.8463i	−0.360485	+	0.607202i
$521$	3.67878	+	6.37183i	0.161170	+	0.279155i	0.935289	−	0.353886i	$-0.115140\pi$
$521$	3.67878	+	6.37183i	0.161170	+	0.279155i	−0.774118	+	0.633041i	$0.781807\pi$
$522$	11.7065	+	38.0612i	0.512379	+	1.66589i
$523$	−15.4796	−	8.93716i	−0.676877	−	0.390795i	0.121801	−	0.992555i	$-0.461133\pi$
$523$	−15.4796	−	8.93716i	−0.676877	−	0.390795i	−0.798677	+	0.601760i	$0.794467\pi$
$524$	13.0086	−	25.3870i	0.568285	−	1.10903i
$525$	0.0807346	+	0.865206i	0.00352355	+	0.0377607i
$526$	−26.9192	+	28.3020i	−1.17373	+	1.23402i
$527$	1.08918	−	6.17703i	0.0474453	−	0.269076i
$528$	24.2648	−	30.0379i	1.05599	−	1.30723i
$529$	17.7442	−	14.8892i	0.771487	−	0.647355i
$530$	8.98933	−	4.46907i	0.390472	−	0.194124i
$531$	0.634246	−	3.85705i	0.0275239	−	0.167382i
$532$	0.949441	+	0.718871i	0.0411635	+	0.0311670i
$533$	6.11260	−	16.7942i	0.264766	−	0.727438i
$534$	22.5921	−	9.02037i	0.977657	−	0.390350i
$535$	−4.38462	−	3.67914i	−0.189564	−	0.159063i
$536$	−13.3325	+	2.18402i	−0.575874	+	0.0943355i
$537$	44.2066	+	11.5718i	1.90766	+	0.499362i
$538$	0.196922	+	0.0858923i	0.00848990	+	0.00370308i
$539$		−	35.3002i		−	1.52049i
$540$	16.2000	−	18.5454i	0.697139	−	0.798068i
$541$		−	16.9095i		−	0.726997i	−0.931595	−	0.363499i	$-0.881582\pi$
$541$		−	16.9095i		−	0.726997i	0.931595	−	0.363499i	$-0.118418\pi$
$542$	8.67888	−	19.8977i	0.372790	−	0.854679i
$543$	14.2559	−	14.4216i	0.611779	−	0.618888i
$544$	−14.6381	+	9.20811i	−0.627605	+	0.394795i
$545$	−9.57704	−	8.03609i	−0.410235	−	0.344228i
$546$	−2.97334	+	3.77375i	−0.127247	+	0.161501i
$547$	7.35226	−	20.2002i	0.314360	−	0.863696i	−0.677403	−	0.735612i	$-0.736895\pi$
$547$	7.35226	−	20.2002i	0.314360	−	0.863696i	0.991763	−	0.128085i	$-0.0408829\pi$
$548$	−16.4006	+	21.6609i	−0.700599	+	0.925309i
$549$	0.858096	+	4.55793i	0.0366226	+	0.194528i
$550$	2.15647	+	4.33765i	0.0919524	+	0.184958i
$551$	−5.24447	+	4.40063i	−0.223422	+	0.187473i
$552$	−19.2655	+	27.1434i	−0.819993	+	1.15530i
$553$	0.603683	−	3.42365i	0.0256712	−	0.145589i
$554$	−23.6578	−	22.5020i	−1.00512	−	0.956018i
$555$	−17.8373	+	12.6440i	−0.757151	+	0.536708i
$556$	9.87627	−	19.2740i	0.418847	−	0.817400i
$557$	−4.92698	−	2.84459i	−0.208763	−	0.120529i	0.391974	−	0.919976i	$-0.371792\pi$
$557$	−4.92698	−	2.84459i	−0.208763	−	0.120529i	−0.600736	+	0.799447i	$0.705126\pi$
$558$	3.96492	+	7.74935i	0.167848	+	0.328056i
$559$	8.26115	+	14.3087i	0.349409	+	0.605195i
$560$	3.35988	+	6.96964i	0.141981	+	0.294521i
$561$	−26.6742	+	12.6265i	−1.12619	+	0.533091i
$562$	2.21537	+	7.51056i	0.0934499	+	0.316814i
$563$	−2.37413	−	6.52288i	−0.100058	−	0.274907i	0.879556	−	0.475795i	$-0.157839\pi$
$563$	−2.37413	−	6.52288i	−0.100058	−	0.274907i	−0.979614	+	0.200888i	$0.935617\pi$
$564$	−23.3327	−	29.6508i	−0.982482	−	1.24852i
$565$	32.8543	−	5.79311i	1.38219	−	0.243718i
$566$	−4.04379	+	6.09432i	−0.169973	+	0.256163i
$567$	5.51751	−	4.85133i	0.231713	−	0.203737i
$568$	−4.59063	+	24.3026i	−0.192619	+	1.01971i
$569$	4.94312	+	28.0338i	0.207226	+	1.17524i	0.893898	+	0.448271i	$0.147960\pi$
$569$	4.94312	+	28.0338i	0.207226	+	1.17524i	−0.686671	+	0.726968i	$0.740929\pi$
$570$	4.02098	+	1.32473i	0.168420	+	0.0554867i
$571$	4.68351	+	12.8678i	0.195999	+	0.538503i	0.998292	−	0.0584282i	$-0.0186089\pi$
$571$	4.68351	+	12.8678i	0.195999	+	0.538503i	−0.802293	+	0.596931i	$0.796387\pi$
$572$	−7.88906	+	25.5941i	−0.329858	+	1.07015i
$573$	15.4134	+	32.5618i	0.643906	+	1.36029i
$574$	−5.10008	−	6.90890i	−0.212873	−	0.288372i
$575$	−2.08782	−	3.61622i	−0.0870682	−	0.150807i
$576$	8.49584	−	22.4460i	0.353993	−	0.935248i
$577$	5.00377	−	8.66678i	0.208309	−	0.360803i	−0.742873	−	0.669433i	$-0.766537\pi$
$577$	5.00377	−	8.66678i	0.208309	−	0.360803i	0.951182	+	0.308630i	$0.0998705\pi$
$578$	−10.7565	+	1.21307i	−0.447413	+	0.0504572i
$579$	5.70876	−	4.04667i	0.237248	−	0.168174i
$580$	−43.3625	+	9.90647i	−1.80053	+	0.411344i
$581$	−11.5711	−	2.04030i	−0.480050	−	0.0846457i
$582$	19.9872	+	32.2795i	0.828494	+	1.33803i
$583$	12.7907	−	10.7327i	0.529738	−	0.444503i
$584$	−11.2629	−	9.68658i	−0.466064	−	0.400834i
$585$	−5.65570	+	16.1158i	−0.233834	+	0.666307i
$586$	21.6497	+	1.34904i	0.894342	+	0.0557284i
$587$	−3.75574	+	10.3188i	−0.155016	+	0.425903i	−0.992753	−	0.120171i	$-0.961656\pi$
$587$	−3.75574	+	10.3188i	−0.155016	+	0.425903i	0.837737	+	0.546073i	$0.183878\pi$
$588$	−6.85261	−	20.8426i	−0.282597	−	0.859536i
$589$	−0.961972	+	1.14643i	−0.0396373	+	0.0472380i
$590$	4.24437	+	1.02413i	0.174738	+	0.0421626i
$591$	22.1076	−	22.3645i	0.909385	−	0.919952i
$592$	−11.9969	+	17.6116i	−0.493070	+	0.723832i
$593$	20.1534			0.827600			0.413800	−	0.910368i	$-0.364201\pi$
$593$	20.1534			0.827600			0.413800	+	0.910368i	$0.364201\pi$
$594$	18.9577	−	36.3049i	0.777843	−	1.48961i
$595$		−	5.91334i		−	0.242423i
$596$	11.9623	+	18.5131i	0.489996	+	0.758324i
$597$	−7.76304	+	29.6563i	−0.317720	+	1.21375i
$598$	5.41514	−	22.4424i	0.221441	−	0.917738i
$599$	19.4387	+	16.3110i	0.794245	+	0.666451i	0.946792	−	0.321845i	$-0.104303\pi$
$599$	19.4387	+	16.3110i	0.794245	+	0.666451i	−0.152547	+	0.988296i	$0.548748\pi$
$600$	2.11531	+	2.14250i	0.0863572	+	0.0874672i
$601$	33.1175	+	12.0538i	1.35089	+	0.491685i	0.913226	−	0.407453i	$-0.133583\pi$
$601$	33.1175	+	12.0538i	1.35089	+	0.491685i	0.437666	+	0.899137i	$0.355805\pi$
$602$	7.92351	+	0.493731i	0.322938	+	0.0201230i
$603$	−13.4080	+	5.05628i	−0.546015	+	0.205908i
$604$	1.69590	+	0.212174i	0.0690050	+	0.00863324i
$605$	30.5588	+	36.4185i	1.24239	+	1.48062i
$606$	−20.7867	−	11.1619i	−0.844401	−	0.453421i
$607$	6.30962	−	35.7836i	0.256099	−	1.45241i	−0.537135	−	0.843496i	$-0.680494\pi$
$607$	6.30962	−	35.7836i	0.256099	−	1.45241i	0.793235	−	0.608916i	$-0.208395\pi$
$608$	4.12322	−	0.156374i	0.167219	−	0.00634179i
$609$	−13.2135	+	1.23299i	−0.535439	+	0.0499632i
$610$	−5.14800	+	0.580569i	−0.208437	+	0.0235066i
$611$	22.6634	+	13.0847i	0.916863	+	0.529351i
$612$	−13.2984	+	12.6333i	−0.537557	+	0.510670i
$613$	−4.83669	+	2.79246i	−0.195352	+	0.112786i	−0.594486	−	0.804106i	$-0.702644\pi$
$613$	−4.83669	+	2.79246i	−0.195352	+	0.112786i	0.399134	+	0.916893i	$0.369311\pi$
$614$	−17.5400	+	12.9479i	−0.707857	+	0.522533i
$615$	−25.1079	−	17.3654i	−1.01245	−	0.700242i
$616$	8.15140	+	9.95795i	0.328429	+	0.401217i
$617$	−33.3230	+	12.1286i	−1.34154	+	0.488279i	−0.910296	−	0.413959i	$-0.864146\pi$
$617$	−33.3230	+	12.1286i	−1.34154	+	0.488279i	−0.431239	+	0.902238i	$0.641924\pi$
$618$	−1.35033	+	1.20587i	−0.0543184	+	0.0485072i
$619$	−3.57695	+	0.630714i	−0.143770	+	0.0253505i	−0.245070	−	0.969505i	$-0.578811\pi$
$619$	−3.57695	+	0.630714i	−0.143770	+	0.0253505i	0.101300	+	0.994856i	$0.467700\pi$
$620$	−8.95893	+	3.77865i	−0.359799	+	0.151754i
$621$	−14.3636	+	32.2506i	−0.576393	+	1.29417i
$622$	25.9638	+	17.2279i	1.04105	+	0.690775i
$623$	1.40779	+	7.98399i	0.0564020	+	0.319872i
$624$	0.310415	+	16.6433i	0.0124266	+	0.666264i
$625$	26.0249	−	9.47231i	1.04100	−	0.378892i
$626$	11.2759	+	38.2274i	0.450674	+	1.52787i
$627$	7.01806	+	0.573170i	0.280274	+	0.0228902i
$628$	7.58282	−	0.379985i	0.302587	−	0.0151630i
$629$	14.1043	−	8.14312i	0.562375	−	0.324687i
$630$	4.94985	+	6.54574i	0.197207	+	0.260789i
$631$	−7.14123	+	12.3690i	−0.284288	+	0.492401i	−0.972436	−	0.233169i	$-0.925090\pi$
$631$	−7.14123	+	12.3690i	−0.284288	+	0.492401i	0.688148	+	0.725570i	$0.258424\pi$
$632$	−5.89532	−	10.5040i	−0.234503	−	0.417826i
$633$	−3.36744	+	7.33177i	−0.133844	+	0.291412i
$634$	36.2055	+	34.4366i	1.43790	+	1.36765i
$635$	30.7641	+	5.42454i	1.22084	+	0.215266i
$636$	5.46869	−	8.82000i	0.216848	−	0.349736i
$637$	9.78164	+	11.6573i	0.387563	+	0.461879i
$638$	−66.2451	+	32.9339i	−2.62267	+	1.30387i
$639$	0.303067	+	26.2309i	0.0119891	+	1.03768i
$640$	24.3043	+	11.3123i	0.960711	+	0.447157i
$641$	−23.2736	−	8.47090i	−0.919252	−	0.334580i	−0.161311	−	0.986904i	$-0.551572\pi$
$641$	−23.2736	−	8.47090i	−0.919252	−	0.334580i	−0.757941	+	0.652323i	$0.773794\pi$
$642$	−5.85591	−	0.847464i	−0.231115	−	0.0334468i
$643$	0.0600848	−	0.0716063i	0.00236951	−	0.00282388i	−0.764858	−	0.644198i	$-0.777191\pi$
$643$	0.0600848	−	0.0716063i	0.00236951	−	0.00282388i	0.767228	+	0.641375i	$0.221636\pi$
$644$	−7.54675	−	8.13016i	−0.297384	−	0.320373i
$645$	27.2182	−	7.46188i	1.07172	−	0.293811i
$646$	−2.89053	−	1.26078i	−0.113726	−	0.0496046i
$647$	28.7206			1.12912			0.564562	−	0.825391i	$-0.309045\pi$
$647$	28.7206			1.12912			0.564562	+	0.825391i	$0.309045\pi$
$648$	4.14574	−	25.1160i	0.162860	−	0.986649i
$649$	7.26196			0.285057
$650$	−1.91410	−	0.834882i	−0.0750771	−	0.0327468i
$651$	−2.79777	+	0.767010i	−0.109653	+	0.0300615i
$652$	−22.9883	+	21.3387i	−0.900290	+	0.835687i
$653$	−15.4192	+	18.3759i	−0.603402	+	0.719106i	−0.978122	−	0.208032i	$-0.933294\pi$
$653$	−15.4192	+	18.3759i	−0.603402	+	0.719106i	0.374720	+	0.927138i	$0.377739\pi$
$654$	−12.7907	−	1.85106i	−0.500155	−	0.0723821i
$655$	31.7580	+	11.5590i	1.24089	+	0.451646i
$656$	−28.8366	−	7.33024i	−1.12588	−	0.286198i
$657$	−13.7357	−	7.72010i	−0.535880	−	0.301190i
$658$	11.2596	−	5.59772i	0.438943	−	0.218222i
$659$	0.657648	+	0.783755i	0.0256183	+	0.0305307i	0.778701	−	0.627395i	$-0.215879\pi$
$659$	0.657648	+	0.783755i	0.0256183	+	0.0305307i	−0.753083	+	0.657925i	$0.771434\pi$
$660$	38.8811	+	24.1075i	1.51344	+	0.938384i
$661$	−9.39844	−	1.65720i	−0.365557	−	0.0644575i	−0.0121473	−	0.999926i	$-0.503867\pi$
$661$	−9.39844	−	1.65720i	−0.365557	−	0.0644575i	−0.353410	+	0.935469i	$0.614978\pi$
$662$	−6.76152	−	6.43117i	−0.262794	−	0.249955i
$663$	5.30993	−	11.5611i	0.206221	−	0.448995i
$664$	−35.5008	+	19.9247i	−1.37770	+	0.773229i
$665$	−0.705455	+	1.22188i	−0.0273564	+	0.0473826i
$666$	−8.79636	+	20.8202i	−0.340852	+	0.806766i
$667$	55.2272	−	31.8855i	2.13841	−	1.23461i
$668$	−0.0433718	−	0.865510i	−0.00167810	−	0.0334876i
$669$	44.0739	+	3.59955i	1.70400	+	0.139167i
$670$	−4.52843	−	15.3523i	−0.174949	−	0.593110i
$671$	−8.09695	+	2.94705i	−0.312579	+	0.113770i
$672$	6.74599	+	4.29719i	0.260232	+	0.165768i
$673$	5.67344	+	32.1757i	0.218695	+	1.24028i	0.874378	+	0.485246i	$0.161270\pi$
$673$	5.67344	+	32.1757i	0.218695	+	1.24028i	−0.655683	+	0.755037i	$0.727619\pi$
$674$	−23.7108	−	15.7329i	−0.913307	−	0.606010i
$675$	2.64725	+	1.78607i	0.101893	+	0.0687457i
$676$	5.61729	+	13.3182i	0.216050	+	0.512240i
$677$	−42.8943	+	7.56342i	−1.64856	+	0.290686i	−0.919302	−	0.393553i	$-0.871246\pi$
$677$	−42.8943	+	7.56342i	−1.64856	+	0.290686i	−0.729258	+	0.684238i	$0.760135\pi$
$678$	25.7233	−	22.9713i	0.987898	−	0.882208i
$679$	−11.8899	+	4.32756i	−0.456292	+	0.166077i
$680$	−12.9779	−	15.8541i	−0.497680	−	0.607979i
$681$	−12.4442	−	8.60684i	−0.476864	−	0.329815i
$682$	−13.0109	+	9.60454i	−0.498214	+	0.367777i
$683$	−3.57110	+	2.06177i	−0.136644	+	0.0788916i	−0.566764	−	0.823880i	$-0.691805\pi$
$683$	−3.57110	+	2.06177i	−0.136644	+	0.0788916i	0.430119	+	0.902772i	$0.358471\pi$
$684$	4.25501	−	1.02395i	0.162694	−	0.0391517i
$685$	−27.8766	−	16.0945i	−1.06511	−	0.614941i
$686$	15.2963	−	1.72504i	0.584014	−	0.0658625i
$687$	13.2136	−	1.23300i	0.504131	−	0.0470418i
$688$	22.3271	−	16.0659i	0.851214	−	0.612505i
$689$	−1.24991	+	7.08860i	−0.0476178	+	0.270054i
$690$	−34.7430	−	18.6561i	−1.32264	−	0.710226i
$691$	−10.8896	−	12.9777i	−0.414260	−	0.493696i	0.518053	−	0.855349i	$-0.326657\pi$
$691$	−10.8896	−	12.9777i	−0.414260	−	0.493696i	−0.932313	+	0.361653i	$0.882213\pi$
$692$	1.57536	−	12.5918i	0.0598864	−	0.478669i
$693$	10.5567	+	8.65230i	0.401017	+	0.328674i
$694$	−5.19855	−	0.323933i	−0.197334	−	0.0122963i
$695$	24.1109	+	8.77566i	0.914579	+	0.332880i
$696$	−32.7205	+	32.3053i	−1.24027	+	1.22453i
$697$	17.4198	+	14.6169i	0.659820	+	0.553655i
$698$	8.65667	−	35.8766i	0.327660	−	1.35795i
$699$	4.07643	−	15.5727i	0.154185	−	0.589015i
$700$	−0.842767	+	0.544559i	−0.0318536	+	0.0205824i
$701$		−	8.56815i		−	0.323615i	−0.986822	−	0.161807i	$-0.948268\pi$
$701$		−	8.56815i		−	0.323615i	0.986822	−	0.161807i	$-0.0517323\pi$
$702$	3.79957	+	17.2422i	0.143406	+	0.650766i
$703$	−3.88586			−0.146558
$704$	43.7091	+	8.80831i	1.64735	+	0.331976i
$705$	31.4254	−	31.7906i	1.18355	−	1.19730i
$706$	40.6899	+	9.81808i	1.53138	+	0.369508i
$707$	5.05428	−	6.02346i	0.190086	−	0.226535i
$708$	4.28776	−	1.40972i	0.161144	−	0.0529805i
$709$	−14.2988	+	39.2856i	−0.537002	+	1.47540i	0.313582	+	0.949561i	$0.398471\pi$
$709$	−14.2988	+	39.2856i	−0.537002	+	1.47540i	−0.850584	+	0.525839i	$0.823751\pi$
$710$	−29.2450	−	1.82232i	−1.09755	−	0.0683906i
$711$	−8.32474	−	9.69141i	−0.312202	−	0.363456i
$712$	21.2967	+	18.3161i	0.798129	+	0.686423i
$713$	10.6788	−	8.96061i	0.399925	−	0.335577i
$714$	−3.21811	−	5.19729i	−0.120435	−	0.194504i
$715$	−31.2485	−	5.50996i	−1.16863	−	0.206061i
$716$	11.7518	+	51.4400i	0.439186	+	1.92240i
$717$	−11.9906	+	8.49957i	−0.447798	+	0.317422i
$718$	−18.1090	+	2.04225i	−0.675821	+	0.0762161i
$719$	15.6713	−	27.1435i	0.584441	−	1.01228i	−0.410504	−	0.911859i	$-0.634647\pi$
$719$	15.6713	−	27.1435i	0.584441	−	1.01228i	0.994945	−	0.100423i	$-0.0320195\pi$
$720$	27.6368	+	6.68631i	1.02996	+	0.249184i
$721$	−0.301671	−	0.522510i	−0.0112348	−	0.0194593i
$722$	−15.5113	−	21.0126i	−0.577271	−	0.782009i
$723$	−2.30015	−	4.85920i	−0.0855434	−	0.180715i
$724$	22.3766	+	6.89728i	0.831618	+	0.256335i
$725$	−1.97288	−	5.42043i	−0.0732708	−	0.201310i
$726$	46.6777	+	15.3781i	1.73237	+	0.570736i
$727$	−4.66774	−	26.4721i	−0.173117	−	0.981794i	−0.940295	−	0.340360i	$-0.889451\pi$
$727$	−4.66774	−	26.4721i	−0.173117	−	0.981794i	0.767178	−	0.641434i	$-0.221660\pi$
$728$	−5.45120	−	1.02971i	−0.202035	−	0.0381634i
$729$	−0.935632	−	26.9838i	−0.0346530	−	0.999399i
$730$	9.73091	−	14.6653i	0.360157	−	0.542786i
$731$	−20.7031	+	3.65052i	−0.765733	+	0.135019i
$732$	−4.20867	+	3.31187i	−0.155557	+	0.122410i
$733$	−0.226255	−	0.621630i	−0.00835691	−	0.0229604i	0.935444	−	0.353475i	$-0.115000\pi$
$733$	−0.226255	−	0.621630i	−0.00835691	−	0.0229604i	−0.943801	+	0.330514i	$0.892778\pi$
$734$	−4.05702	−	13.7541i	−0.149747	−	0.507673i
$735$	23.4945	−	11.1214i	0.866609	−	0.410218i
$736$	−38.0766	−	5.23486i	−1.40352	−	0.192960i
$737$	−13.3110	−	23.0554i	−0.490318	−	0.849255i
$738$	−31.5180	−	1.59865i	−1.16019	−	0.0588472i
$739$	−2.80715	−	1.62071i	−0.103263	−	0.0596186i	0.447479	−	0.894294i	$-0.352322\pi$
$739$	−2.80715	−	1.62071i	−0.103263	−	0.0596186i	−0.550742	+	0.834676i	$0.685655\pi$
$740$	−22.4685	−	11.5132i	−0.825959	−	0.423233i
$741$	−2.47642	+	1.75542i	−0.0909737	+	0.0644869i
$742$	2.50603	+	2.38360i	0.0919994	+	0.0875046i
$743$	−4.35112	+	24.6764i	−0.159627	+	0.905290i	0.794806	+	0.606864i	$0.207573\pi$
$743$	−4.35112	+	24.6764i	−0.159627	+	0.905290i	−0.954433	+	0.298426i	$0.903538\pi$
$744$	−5.81771	+	8.19664i	−0.213287	+	0.300503i
$745$	−20.0044	+	16.7857i	−0.732903	+	0.614979i
$746$	−6.56607	−	13.2074i	−0.240401	−	0.483556i
$747$	−32.7545	+	28.1355i	−1.19843	+	1.02942i
$748$	−27.1682	−	20.5704i	−0.993368	−	0.752130i
$749$	0.674433	−	1.85299i	0.0246432	−	0.0677067i
$750$	15.7527	−	19.9932i	0.575207	−	0.730049i
$751$	−13.0260	−	10.9301i	−0.475325	−	0.398845i	0.373408	−	0.927667i	$-0.378189\pi$
$751$	−13.0260	−	10.9301i	−0.475325	−	0.398845i	−0.848732	+	0.528823i	$0.822634\pi$
$752$	17.9026	−	39.7191i	0.652839	−	1.44841i
$753$	−10.7883	+	10.9137i	−0.393149	+	0.397717i
$754$	12.7504	−	29.2323i	0.464342	−	1.06458i
$755$			2.02488i			0.0736931i
$756$	7.91274	+	3.05935i	0.287783	+	0.111267i
$757$		−	11.7321i		−	0.426412i	−0.977007	−	0.213206i	$-0.931609\pi$
$757$		−	11.7321i		−	0.426412i	0.977007	−	0.213206i	$-0.0683906\pi$
$758$	−18.3137	−	7.98799i	−0.665185	−	0.290137i
$759$	−63.4518	−	16.6096i	−2.30316	−	0.602891i
$760$	0.790268	+	4.82422i	0.0286660	+	0.174993i
$761$	0.0993911	+	0.0833990i	0.00360292	+	0.00302321i	0.644587	−	0.764531i	$-0.277029\pi$
$761$	0.0993911	+	0.0833990i	0.00360292	+	0.00302321i	−0.640984	+	0.767554i	$0.721474\pi$
$762$	29.9910	−	11.9745i	1.08646	−	0.433790i
$763$	1.47312	−	4.04736i	0.0533304	−	0.146524i
$764$	−25.1108	+	33.1649i	−0.908478	+	1.19986i
$765$	−16.8075	−	13.7754i	−0.607675	−	0.498051i
$766$	13.7106	−	6.81627i	0.495385	−	0.246282i
$767$	−2.39814	+	2.01228i	−0.0865920	+	0.0726593i
$768$	27.5175	−	3.28420i	0.992953	−	0.118509i
$769$	1.99390	−	11.3080i	0.0719020	−	0.407776i	−0.927520	−	0.373774i	$-0.878064\pi$
$769$	1.99390	−	11.3080i	0.0719020	−	0.407776i	0.999422	−	0.0340023i	$-0.0108254\pi$
$770$	−10.5076	+	11.0473i	−0.378667	+	0.398117i
$771$	−2.72090	−	29.1590i	−0.0979909	−	1.05014i
$772$	7.19096	+	3.68475i	0.258808	+	0.132617i
$773$	13.9804	+	8.07158i	0.502839	+	0.290314i	0.729885	−	0.683570i	$-0.239573\pi$
$773$	13.9804	+	8.07158i	0.502839	+	0.290314i	−0.227046	+	0.973884i	$0.572907\pi$
$774$	19.8615	−	21.3708i	0.713907	−	0.768157i
$775$	−0.630472	−	1.09201i	−0.0226472	−	0.0392261i
$776$	−22.3801	+	37.6971i	−0.803399	+	1.35325i
$777$	−6.19514	−	4.28476i	−0.222249	−	0.153715i
$778$	−24.0127	+	7.08298i	−0.860897	+	0.253937i
$779$	−1.85569	−	5.09847i	−0.0664871	−	0.182672i
$780$	−19.5200	+	2.81279i	−0.698928	+	0.100714i
$781$	−47.9952	+	8.46285i	−1.71740	+	0.302825i
$782$	24.4765	+	16.2410i	0.875276	+	0.580775i
$783$	−27.2770	+	40.4291i	−0.974800	+	1.44482i
$784$	17.6821	−	18.1432i	0.631502	−	0.647973i
$785$	1.56197	+	8.85840i	0.0557493	+	0.316170i
$786$	34.2029	−	7.12377i	1.21998	−	0.254097i
$787$	10.3024	+	28.3055i	0.367240	+	1.00898i	0.976406	+	0.215941i	$0.0692818\pi$
$787$	10.3024	+	28.3055i	0.367240	+	1.00898i	−0.609167	+	0.793042i	$0.708496\pi$
$788$	34.7008	+	10.6961i	1.23617	+	0.381032i
$789$	−47.6792	−	3.89399i	−1.69743	−	0.138630i
$790$	11.4813	−	8.47539i	0.408487	−	0.301541i
$791$	5.74672	+	9.95360i	0.204330	+	0.353909i
$792$	47.2925	+	0.0288053i	1.68047	+	0.00102355i
$793$	1.85726	−	3.21687i	0.0659533	−	0.114234i
$794$	5.44962	+	48.3227i	0.193400	+	1.71491i
$795$	11.1730	+	5.13170i	0.396267	+	0.182003i
$796$	−34.5088	+	7.88378i	−1.22313	+	0.279433i
$797$	22.3243	+	3.93637i	0.790767	+	0.139434i	0.554422	−	0.832236i	$-0.312939\pi$
$797$	22.3243	+	3.93637i	0.790767	+	0.139434i	0.236345	+	0.971669i	$0.424051\pi$
$798$	0.0449323	+	1.45784i	0.00159059	+	0.0516070i
$799$	−25.5072	+	21.4031i	−0.902379	+	0.757186i
$800$	−1.06439	+	3.30961i	−0.0376319	+	0.117012i
$801$	25.9724	+	14.5977i	0.917689	+	0.515784i
$802$	0.677596	−	10.8742i	0.0239268	−	0.383982i
$803$	10.0119	−	27.5076i	0.353313	−	0.970721i
$804$	−12.3350	−	11.0288i	−0.435021	−	0.388957i
$805$	8.44777	−	10.0677i	0.297745	−	0.354838i
$806$	1.63524	−	6.77706i	0.0575988	−	0.238712i
$807$	0.0695682	+	0.253759i	0.00244892	+	0.00893275i
$808$	0.331344	−	27.2419i	0.0116566	−	0.958368i
$809$	41.9562			1.47510			0.737551	−	0.675292i	$-0.235982\pi$
$809$	41.9562			1.47510			0.737551	+	0.675292i	$0.235982\pi$
$810$	30.1359	+	1.17967i	1.05887	+	0.0414494i
$811$		−	14.6317i		−	0.513787i	−0.966440	−	0.256893i	$-0.917301\pi$
$811$		−	14.6317i		−	0.513787i	0.966440	−	0.256893i	$-0.0826989\pi$
$812$	−8.31656	−	12.8708i	−0.291854	−	0.451677i
$813$	25.6408	−	7.02942i	0.899261	−	0.246533i
$814$	−40.8194	−	9.84932i	−1.43072	−	0.345218i
$815$	−28.4666	−	23.8863i	−0.997142	−	0.836701i
$816$	−20.0344	−	6.87162i	−0.701345	−	0.240555i
$817$	4.71343	+	1.71555i	0.164902	+	0.0600194i
$818$	−0.0925414	+	1.48512i	−0.00323563	+	0.0519261i
$819$	−5.88373	+	0.0679797i	−0.205594	+	0.00237540i
$820$	4.37612	−	34.9781i	0.152821	−	1.22149i
$821$	−26.1627	−	31.1794i	−0.913083	−	1.08817i	−0.995796	−	0.0915963i	$-0.970803\pi$
$821$	−26.1627	−	31.1794i	−0.913083	−	1.08817i	0.0827134	−	0.996573i	$-0.473641\pi$
$822$	−33.2598	+	1.02510i	−1.16007	+	0.0357546i
$823$	9.20245	−	52.1897i	0.320777	−	1.81922i	−0.217048	−	0.976161i	$-0.569643\pi$
$823$	9.20245	−	52.1897i	0.320777	−	1.81922i	0.537825	−	0.843057i	$-0.319246\pi$
$824$	−1.95555	−	0.738818i	−0.0681248	−	0.0257379i
$825$	−2.47622	+	5.39136i	−0.0862108	+	0.187703i
$826$	0.168570	+	1.49474i	0.00586531	+	0.0520086i
$827$	33.8387	+	19.5368i	1.17669	+	0.679360i	0.955246	−	0.295813i	$-0.0955907\pi$
$827$	33.8387	+	19.5368i	1.17669	+	0.679360i	0.221441	+	0.975174i	$0.428924\pi$
$828$	−40.6888	+	2.51053i	−1.41403	+	0.0872471i
$829$	−12.8078	+	7.39457i	−0.444832	+	0.256824i	−0.705645	−	0.708565i	$-0.749343\pi$
$829$	−12.8078	+	7.39457i	−0.444832	+	0.256824i	0.260813	+	0.965389i	$0.416009\pi$
$830$	−28.6447	−	38.8039i	−0.994272	−	1.34690i
$831$	3.25502	−	39.8554i	0.112915	−	1.38257i
$832$	−16.8750	+	9.20295i	−0.585035	+	0.319055i
$833$	−18.1947	+	6.62232i	−0.630408	+	0.229450i
$834$	25.9671	−	5.40843i	0.899168	−	0.187279i
$835$	1.01111	−	0.178285i	0.0349907	−	0.00616981i
$836$	3.15978	+	7.49164i	0.109283	+	0.259104i
$837$	−4.33747	+	9.73888i	−0.149925	+	0.336625i
$838$	−4.12922	+	6.22308i	−0.142642	+	0.214973i
$839$	−1.90754	−	10.8182i	−0.0658556	−	0.373486i	−0.999868	−	0.0162452i	$-0.994829\pi$
$839$	−1.90754	−	10.8182i	−0.0658556	−	0.373486i	0.934012	−	0.357240i	$-0.116282\pi$
$840$	−4.05955	+	8.56254i	−0.140068	+	0.295436i
$841$	55.5304	−	20.2114i	1.91484	−	0.696945i
$842$	42.3465	−	12.4909i	1.45936	−	0.430464i
$843$	−5.45532	+	7.88759i	−0.187891	+	0.271663i
$844$	−9.30458	+	0.466264i	−0.320277	+	0.0160495i
$845$	−14.8306	+	8.56245i	−0.510188	+	0.294557i
$846$	10.3193	−	45.0432i	0.354784	−	1.54862i
$847$	−8.18930	+	14.1843i	−0.281388	+	0.487378i
$848$	11.9501	+	0.890663i	0.410369	+	0.0305855i
$849$	−8.91890	+	0.832245i	−0.306096	+	0.0285626i
$850$	1.83119	−	1.92525i	0.0628092	−	0.0660355i
$851$	35.6462	+	6.28539i	1.22194	+	0.215460i
$852$	−26.6955	+	14.3138i	−0.914571	+	0.490383i
$853$	18.0653	+	21.5293i	0.618543	+	0.737151i	0.980819	−	0.194920i	$-0.0624447\pi$
$853$	18.0653	+	21.5293i	0.618543	+	0.737151i	−0.362276	+	0.932071i	$0.618000\pi$
$854$	−0.794548	−	1.59820i	−0.0271889	−	0.0546892i
$855$	1.82957	+	4.85155i	0.0625699	+	0.165919i
$856$	−2.25852	−	6.44818i	−0.0771945	−	0.220394i
$857$	44.7520	+	16.2884i	1.52870	+	0.556401i	0.963303	−	0.268417i	$-0.0865006\pi$
$857$	44.7520	+	16.2884i	1.52870	+	0.556401i	0.565397	+	0.824819i	$0.308723\pi$
$858$	−30.4632	+	12.1631i	−1.04000	+	0.415240i
$859$	30.7024	−	36.5896i	1.04755	−	1.24842i	0.0797208	−	0.996817i	$-0.474597\pi$
$859$	30.7024	−	36.5896i	1.04755	−	1.24842i	0.967830	−	0.251605i	$-0.0809584\pi$
$860$	22.1707	+	23.8846i	0.756015	+	0.814459i
$861$	2.66337	−	10.1746i	0.0907674	−	0.346749i
$862$	−1.83788	+	4.21363i	−0.0625985	+	0.143517i
$863$	−51.9526			−1.76849			−0.884244	−	0.467026i	$-0.845325\pi$
$863$	−51.9526			−1.76849			−0.884244	+	0.467026i	$0.845325\pi$
$864$	27.9290	−	9.16360i	0.950164	−	0.311752i
$865$	15.0345			0.511189
$866$	3.26802	−	7.49245i	0.111052	−	0.254604i
$867$	−9.42847	−	9.32017i	−0.320208	−	0.316529i
$868$	−2.27893	−	2.45511i	−0.0773521	−	0.0833318i
$869$	15.2569	−	18.1824i	0.517554	−	0.616796i
$870$	−42.7902	−	33.7145i	−1.45072	−	1.14303i
$871$	10.7844	+	3.92519i	0.365414	+	0.133000i
$872$	−4.93313	−	14.0843i	−0.167057	−	0.476955i
$873$	−15.3978	+	43.8759i	−0.521137	+	1.48497i
$874$	−3.12008	−	6.27591i	−0.105538	−	0.212286i
$875$	5.45261	+	6.49817i	0.184332	+	0.219678i
$876$	0.571573	−	18.1851i	0.0193116	−	0.614418i
$877$	18.6056	+	3.28068i	0.628268	+	0.110781i	0.478711	−	0.877973i	$-0.341104\pi$
$877$	18.6056	+	3.28068i	0.628268	+	0.110781i	0.149557	+	0.988753i	$0.452215\pi$
$878$	10.2149	−	10.7396i	0.344735	−	0.362443i
$879$	15.3636	+	21.6739i	0.518200	+	0.731041i
$880$	−3.92630	+	52.6795i	−0.132355	+	1.77583i
$881$	7.13948	−	12.3659i	0.240535	−	0.416619i	−0.720332	−	0.693630i	$-0.756010\pi$
$881$	7.13948	−	12.3659i	0.240535	−	0.416619i	0.960867	+	0.277011i	$0.0893437\pi$
$882$	14.5972	−	22.5607i	0.491513	−	0.759657i
$883$	−8.00129	+	4.61954i	−0.269265	+	0.155460i	−0.628553	−	0.777766i	$-0.716353\pi$
$883$	−8.00129	+	4.61954i	−0.269265	+	0.155460i	0.359289	+	0.933226i	$0.383019\pi$
$884$	14.6719	−	0.735227i	0.493470	−	0.0247284i
$885$	2.28789	+	4.83330i	0.0769066	+	0.162470i
$886$	−14.4353	+	4.25795i	−0.484963	+	0.143049i
$887$	−14.3955	+	5.23952i	−0.483352	+	0.175926i	−0.572191	−	0.820120i	$-0.693907\pi$
$887$	−14.3955	+	5.23952i	−0.483352	+	0.175926i	0.0888391	+	0.996046i	$0.471684\pi$
$888$	−26.0134	+	2.10858i	−0.872952	+	0.0707593i
$889$	1.86884	+	10.5987i	0.0626788	+	0.355469i
$890$	−18.3999	+	27.7301i	−0.616765	+	0.929516i
$891$	49.1848	−	9.84944i	1.64775	−	0.329969i
$892$	19.8437	+	47.0481i	0.664415	+	1.57529i
$893$	7.82395	−	1.37957i	0.261818	−	0.0461657i
$894$	−8.44708	+	25.6397i	−0.282512	+	0.857519i
$895$	−58.7439	+	21.3810i	−1.96359	+	0.714689i
$896$	−0.798417	+	9.20117i	−0.0266732	+	0.307389i
$897$	25.5564	−	12.0974i	0.853304	−	0.403920i
$898$	17.4380	+	23.6226i	0.581912	+	0.788296i
$899$	16.6773	−	9.62863i	0.556218	−	0.321133i
$900$	−0.415466	+	3.66397i	−0.0138489	+	0.122132i
$901$	−7.93147	−	4.57923i	−0.264235	−	0.152556i
$902$	−6.57041	−	58.2609i	−0.218771	−	1.93988i
$903$	5.62285	+	7.93234i	0.187117	+	0.263972i
$904$	37.2524	+	14.0742i	1.23900	+	0.468100i
$905$	−4.81727	+	27.3201i	−0.160131	+	0.908151i
$906$	1.10197	+	1.77969i	0.0366103	+	0.0591262i
$907$	5.65685	+	6.74157i	0.187833	+	0.223850i	0.851740	−	0.523965i	$-0.175548\pi$
$907$	5.65685	+	6.74157i	0.187833	+	0.223850i	−0.663907	+	0.747815i	$0.731103\pi$
$908$	2.16894	−	17.3362i	0.0719788	−	0.575323i
$909$	−5.34627	−	28.3977i	−0.177325	−	0.941892i
$910$	0.408757	−	6.55983i	0.0135502	−	0.217456i
$911$	−30.8181	−	11.2169i	−1.02105	−	0.371632i	−0.223384	−	0.974731i	$-0.571710\pi$
$911$	−30.8181	−	11.2169i	−1.02105	−	0.371632i	−0.797667	+	0.603098i	$0.793933\pi$
$912$	3.31997	+	3.80998i	0.109935	+	0.126161i
$913$	−61.4520	−	51.5644i	−2.03377	−	1.70653i
$914$	19.1842	+	4.62896i	0.634557	+	0.153112i
$915$	−4.51240	−	4.46057i	−0.149176	−	0.147462i
$916$	8.31663	+	12.8709i	0.274789	+	0.425267i
$917$			11.6433i			0.384495i
$918$	−22.2690	−	2.96051i	−0.734986	−	0.0977114i
$919$	0.483799			0.0159591			0.00797953	−	0.999968i	$-0.497460\pi$
$919$	0.483799			0.0159591			0.00797953	+	0.999968i	$0.497460\pi$
$920$	0.553811	−	45.5324i	0.0182586	−	1.50116i
$921$	−25.8308	−	6.76165i	−0.851153	−	0.222804i
$922$	0.0108730	−	0.0450619i	0.000358083	−	0.00148403i
$923$	13.5046	−	16.0941i	0.444509	−	0.529745i
$924$	−3.22313	+	15.4279i	−0.106033	+	0.507541i
$925$	1.11980	−	3.07662i	0.0368187	−	0.101159i
$926$	2.31066	−	37.0819i	0.0759329	−	1.21859i
$927$	−2.18789	−	0.359772i	−0.0718596	−	0.0118165i
$928$	−50.5448	−	16.2555i	−1.65921	−	0.533613i
$929$	−36.5895	+	30.7023i	−1.20046	+	1.00731i	−0.200847	+	0.979623i	$0.564370\pi$
$929$	−36.5895	+	30.7023i	−1.20046	+	1.00731i	−0.999617	+	0.0276865i	$0.991186\pi$
$930$	−10.4915	−	5.63369i	−0.344031	−	0.184736i
$931$	4.54963	+	0.802223i	0.149108	+	0.0262918i
$932$	18.1208	−	4.13983i	0.593568	−	0.135605i
$933$	3.54564	+	37.9975i	0.116079	+	1.24398i
$934$	1.27948	+	11.3453i	0.0418658	+	0.371231i
$935$	20.1866	−	34.9641i	0.660171	−	1.14345i
$936$	−15.6256	+	13.0952i	−0.510737	+	0.428030i
$937$	4.51081	+	7.81296i	0.147362	+	0.255238i	0.930252	−	0.366922i	$-0.119588\pi$
$937$	4.51081	+	7.81296i	0.147362	+	0.255238i	−0.782890	+	0.622160i	$0.786255\pi$
$938$	4.43653	−	3.27500i	0.144858	−	0.106933i
$939$	−27.7666	+	40.1464i	−0.906129	+	1.31013i
$940$	49.3265	+	15.2042i	1.60885	+	0.495908i
$941$	11.2893	+	31.0172i	0.368022	+	1.01113i	0.976113	+	0.217264i	$0.0697132\pi$
$941$	11.2893	+	31.0172i	0.368022	+	1.01113i	−0.608091	+	0.793867i	$0.708065\pi$
$942$	6.19367	+	6.93568i	0.201801	+	0.225977i
$943$	8.77606	+	49.7715i	0.285788	+	1.62078i
$944$	3.73243	+	3.63756i	0.121480	+	0.118392i
$945$	−2.43275	+	9.75210i	−0.0791373	+	0.317236i
$946$	45.1643	+	29.9680i	1.46842	+	0.974345i
$947$	−5.66103	+	0.998192i	−0.183959	+	0.0324369i	−0.264868	−	0.964285i	$-0.585329\pi$
$947$	−5.66103	+	0.998192i	−0.183959	+	0.0324369i	0.0809098	+	0.996721i	$0.474217\pi$
$948$	5.47862	−	13.6974i	0.177937	−	0.444869i
$949$	4.31604	+	11.8582i	0.140105	+	0.384934i
$950$	−0.608061	+	0.179359i	−0.0197281	+	0.00581917i
$951$	−4.98142	+	60.9940i	−0.161534	+	1.97787i
$952$	3.60339	−	6.06956i	0.116787	−	0.196716i
$953$	−24.5955	−	42.6006i	−0.796726	−	1.37997i	−0.921738	−	0.387814i	$-0.873230\pi$
$953$	−24.5955	−	42.6006i	−0.796726	−	1.37997i	0.125012	−	0.992155i	$-0.460103\pi$
$954$	12.6128	−	1.57019i	0.408355	−	0.0508368i
$955$	−42.6815	−	24.6422i	−1.38114	−	0.797403i
$956$	−15.1038	−	7.73941i	−0.488492	−	0.250310i
$957$	−82.3374	−	37.8171i	−2.66159	−	1.22245i
$958$	−24.6739	+	25.9413i	−0.797177	+	0.838125i
$959$	1.92569	−	10.9211i	0.0621839	−	0.352662i
$960$	7.90811	+	31.8663i	0.255233	+	1.02848i
$961$	−20.5226	+	17.2205i	−0.662020	+	0.555501i
$962$	16.2092	−	8.05842i	0.522604	−	0.259814i
$963$	−3.69562	−	6.23356i	−0.119090	−	0.200874i
$964$	3.74728	−	4.94919i	0.120692	−	0.159403i
$965$	−3.27412	+	8.99557i	−0.105398	+	0.289578i
$966$	1.94589	−	13.4459i	0.0626079	−	0.432616i
$967$	18.4054	+	15.4439i	0.591876	+	0.496643i	0.888823	−	0.458251i	$-0.151524\pi$
$967$	18.4054	+	15.4439i	0.591876	+	0.496643i	−0.296947	+	0.954894i	$0.595968\pi$
$968$	9.17386	+	56.0021i	0.294859	+	1.79998i
$969$	−1.02116	−	3.72482i	−0.0328044	−	0.119659i
$970$	−47.6080	−	20.7654i	−1.52860	−	0.666737i
$971$			17.8707i			0.573497i	0.958006	+	0.286749i	$0.0925745\pi$
$971$			17.8707i			0.573497i	−0.958006	+	0.286749i	$0.907426\pi$
$972$	27.1287	−	15.3634i	0.870152	−	0.492783i
$973$			8.83968i			0.283387i
$974$	6.76920	−	15.5195i	0.216899	−	0.497276i
$975$	−0.676209	−	2.46656i	−0.0216560	−	0.0789933i
$976$	−5.63779	−	2.54111i	−0.180461	−	0.0813391i
$977$	13.5441	+	11.3648i	0.433313	+	0.363593i	0.833200	−	0.552972i	$-0.186506\pi$
$977$	13.5441	+	11.3648i	0.433313	+	0.363593i	−0.399887	+	0.916564i	$0.630951\pi$
$978$	−38.0188	−	5.50205i	−1.21571	−	0.175936i
$979$	−18.9313	+	52.0132i	−0.605045	+	1.66235i
$980$	23.9297	+	18.1184i	0.764405	+	0.578770i
$981$	−8.07209	−	13.6155i	−0.257722	−	0.434711i
$982$	−2.44043	−	4.90882i	−0.0778774	−	0.156647i
$983$	−21.1295	+	17.7297i	−0.673926	+	0.565491i	−0.914224	−	0.405208i	$-0.867199\pi$
$983$	−21.1295	+	17.7297i	−0.673926	+	0.565491i	0.240299	+	0.970699i	$0.422755\pi$
$984$	−15.1893	−	33.1241i	−0.484216	−	1.05596i
$985$	−7.47047	+	42.3671i	−0.238029	+	1.34993i
$986$	29.4026	+	27.9661i	0.936370	+	0.890622i
$987$	13.9947	+	6.42770i	0.445458	+	0.204596i
$988$	−3.11939	−	1.59842i	−0.0992411	−	0.0508525i
$989$	−40.4629	−	23.3612i	−1.28664	−	0.742844i
$990$	6.92184	+	55.6008i	0.219991	+	1.76711i
$991$	−10.5626	−	18.2950i	−0.335532	−	0.581159i	0.648054	−	0.761594i	$-0.275583\pi$
$991$	−10.5626	−	18.2950i	−0.335532	−	0.581159i	−0.983587	+	0.180435i	$0.942250\pi$
$992$	−11.4982	−	1.58080i	−0.365068	−	0.0501905i
$993$	0.930299	−	11.3909i	0.0295221	−	0.361478i
$994$	−2.85602	−	9.68247i	−0.0905874	−	0.307109i
$995$	−14.3436	−	39.4087i	−0.454722	−	1.24934i
$996$	−46.2936	−	18.5164i	−1.46687	−	0.586714i
$997$	56.4719	−	9.95752i	1.78848	−	0.315358i	0.821502	−	0.570206i	$-0.193136\pi$
$997$	56.4719	−	9.95752i	1.78848	−	0.315358i	0.966981	+	0.254848i	$0.0820254\pi$
$998$	−5.66604	+	8.53919i	−0.179355	+	0.270303i
$999$	−26.6104	+	7.62687i	−0.841917	+	0.241303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.14	✓	204
3.2	odd	2		648.2.t.a.253.21		204
4.3	odd	2		864.2.bf.a.337.32		204
8.3	odd	2		864.2.bf.a.337.3		204
8.5	even	2	inner	216.2.t.a.13.25	yes	204
24.5	odd	2		648.2.t.a.253.10		204
27.2	odd	18		648.2.t.a.397.10		204
27.25	even	9	inner	216.2.t.a.133.25	yes	204
108.79	odd	18		864.2.bf.a.241.3		204
216.29	odd	18		648.2.t.a.397.21		204
216.133	even	18	inner	216.2.t.a.133.14	yes	204
216.187	odd	18		864.2.bf.a.241.32		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.14	✓	204	1.1	even	1	trivial
216.2.t.a.13.25	yes	204	8.5	even	2	inner
216.2.t.a.133.14	yes	204	216.133	even	18	inner
216.2.t.a.133.25	yes	204	27.25	even	9	inner
648.2.t.a.253.10		204	24.5	odd	2
648.2.t.a.253.21		204	3.2	odd	2
648.2.t.a.397.10		204	27.2	odd	18
648.2.t.a.397.21		204	216.29	odd	18
864.2.bf.a.241.3		204	108.79	odd	18
864.2.bf.a.241.32		204	216.187	odd	18
864.2.bf.a.337.3		204	8.3	odd	2
864.2.bf.a.337.32		204	4.3	odd	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.565401 + 1.29627i) q^{2} +(-1.67042 + 0.457945i) q^{3} +(-1.36064 - 1.46583i) q^{4} +(1.52309 - 1.81515i) q^{5} +(0.350834 - 2.42424i) q^{6} +(0.767101 + 0.279202i) q^{7} +(2.66942 - 0.934982i) q^{8} +(2.58057 - 1.52992i) q^{9} +O(q^{10})\)	\(q+(-0.565401 + 1.29627i) q^{2} +(-1.67042 + 0.457945i) q^{3} +(-1.36064 - 1.46583i) q^{4} +(1.52309 - 1.81515i) q^{5} +(0.350834 - 2.42424i) q^{6} +(0.767101 + 0.279202i) q^{7} +(2.66942 - 0.934982i) q^{8} +(2.58057 - 1.52992i) q^{9} +(1.49177 + 3.00063i) q^{10} +(3.58256 + 4.26953i) q^{11} +(2.94411 + 1.82544i) q^{12} +(-2.36616 - 0.417219i) q^{13} +(-0.795642 + 0.836511i) q^{14} +(-1.71296 + 3.72954i) q^{15} +(-0.297302 + 3.98894i) q^{16} +(1.52854 - 2.64751i) q^{17} +(0.524128 + 4.21014i) q^{18} +(-0.631691 + 0.364707i) q^{19} +(-4.73308 + 0.237181i) q^{20} +(-1.40924 - 0.115093i) q^{21} +(-7.56006 + 2.22998i) q^{22} +(6.38462 - 2.32381i) q^{23} +(-4.03087 + 2.78426i) q^{24} +(-0.106720 - 0.605238i) q^{25} +(1.87866 - 2.83130i) q^{26} +(-3.61001 + 3.73735i) q^{27} +(-0.634489 - 1.50433i) q^{28} +(9.24326 - 1.62984i) q^{29} +(-3.86600 - 4.32915i) q^{30} +(1.92800 - 0.701734i) q^{31} +(-5.00265 - 2.64073i) q^{32} +(-7.93957 - 5.49127i) q^{33} +(2.56766 + 3.47831i) q^{34} +(1.67516 - 0.967153i) q^{35} +(-5.75383 - 1.70101i) q^{36} +(4.61364 + 2.66369i) q^{37} +(-0.115601 - 1.02505i) q^{38} +(4.14354 - 0.386644i) q^{39} +(2.36864 - 6.26946i) q^{40} +(-1.29167 + 7.32541i) q^{41} +(0.945976 - 1.76168i) q^{42} +(-4.42023 - 5.26782i) q^{43} +(1.38381 - 11.0607i) q^{44} +(1.15342 - 7.01433i) q^{45} +(-0.597580 + 9.59009i) q^{46} +(-10.2350 - 3.72522i) q^{47} +(-1.33009 - 6.79933i) q^{48} +(-4.85182 - 4.07116i) q^{49} +(0.844892 + 0.203864i) q^{50} +(-1.34089 + 5.12243i) q^{51} +(2.60793 + 4.03608i) q^{52} -2.99582i q^{53} +(-2.80352 - 6.79266i) q^{54} +13.2064 q^{55} +(2.30877 + 0.0280815i) q^{56} +(0.888170 - 0.898491i) q^{57} +(-3.11344 + 12.9033i) q^{58} +(0.837520 - 0.998118i) q^{59} +(7.79759 - 2.56368i) q^{60} +(-0.528763 + 1.45277i) q^{61} +(-0.180455 + 2.89597i) q^{62} +(2.40672 - 0.453099i) q^{63} +(6.25162 - 4.99172i) q^{64} +(-4.36120 + 3.65948i) q^{65} +(11.6072 - 7.18708i) q^{66} +(-4.70399 - 0.829441i) q^{67} +(-5.96060 + 1.36174i) q^{68} +(-9.60078 + 6.80553i) q^{69} +(0.306557 + 2.71829i) q^{70} +(-4.37210 + 7.57270i) q^{71} +(5.45819 - 6.49678i) q^{72} +(-2.62609 - 4.54853i) q^{73} +(-6.06142 + 4.47448i) q^{74} +(0.455432 + 0.962127i) q^{75} +(1.39410 + 0.429714i) q^{76} +(1.55613 + 4.27542i) q^{77} +(-1.84157 + 5.58977i) q^{78} +(-0.739506 - 4.19395i) q^{79} +(6.78770 + 6.61516i) q^{80} +(4.31872 - 7.89612i) q^{81} +(-8.76541 - 5.81615i) q^{82} +(-14.1745 + 2.49935i) q^{83} +(1.74876 + 2.22230i) q^{84} +(-2.47752 - 6.80694i) q^{85} +(9.32773 - 2.75138i) q^{86} +(-14.6937 + 6.95541i) q^{87} +(13.5553 + 8.04754i) q^{88} +(4.96560 + 8.60067i) q^{89} +(8.44033 + 5.46106i) q^{90} +(-1.69860 - 0.980687i) q^{91} +(-12.0935 - 6.19687i) q^{92} +(-2.89920 + 2.05510i) q^{93} +(10.6158 - 11.1611i) q^{94} +(-0.300125 + 1.70209i) q^{95} +(9.56582 + 2.12018i) q^{96} +(-11.8735 + 9.96305i) q^{97} +(8.02056 - 3.98744i) q^{98} +(15.7771 + 5.53682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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