LMFDB - Embedded newform 162.2.g.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	162.43
Dual form			162.2.g.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.286803 + 0.957990i) q^{2} +(-1.47699 - 0.904708i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.423867 + 0.982634i) q^{5} +(0.443094 - 1.67442i) q^{6} +(-0.264903 + 4.54820i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(1.36301 + 2.67249i) q^{9} +O(q^{10})$	\(q+(0.286803 + 0.957990i) q^{2} +(-1.47699 - 0.904708i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.423867 + 0.982634i) q^{5} +(0.443094 - 1.67442i) q^{6} +(-0.264903 + 4.54820i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(1.36301 + 2.67249i) q^{9} +(-0.819786 + 0.687882i) q^{10} +(1.50212 + 2.01769i) q^{11} +(1.73115 - 0.0557480i) q^{12} +(0.0221543 + 0.0234822i) q^{13} +(-4.43310 + 1.05066i) q^{14} +(0.262948 - 1.83482i) q^{15} +(0.396080 - 0.918216i) q^{16} +(-1.28317 - 7.27724i) q^{17} +(-2.16930 + 2.07223i) q^{18} +(-1.22783 + 6.96338i) q^{19} +(-0.894102 - 0.588060i) q^{20} +(4.50605 - 6.47800i) q^{21} +(-1.50212 + 2.01769i) q^{22} +(-0.167912 - 2.88293i) q^{23} +(0.549906 + 1.64244i) q^{24} +(2.64530 - 2.80386i) q^{25} +(-0.0161418 + 0.0279584i) q^{26} +(0.404671 - 5.18037i) q^{27} +(-2.27795 - 3.94553i) q^{28} +(0.245417 + 0.0581649i) q^{29} +(1.83315 - 0.274330i) q^{30} +(-2.86918 - 1.44096i) q^{31} +(0.993238 + 0.116093i) q^{32} +(-0.393192 - 4.33909i) q^{33} +(6.60350 - 3.31640i) q^{34} +(-4.58150 + 1.66753i) q^{35} +(-2.60733 - 1.48385i) q^{36} +(10.7770 + 3.92249i) q^{37} +(-7.02299 + 0.820869i) q^{38} +(-0.0114772 - 0.0547262i) q^{39} +(0.306924 - 1.02520i) q^{40} +(-1.21748 + 4.06667i) q^{41} +(7.49820 + 2.45884i) q^{42} +(3.10495 - 0.362916i) q^{43} +(-2.36374 - 0.860332i) q^{44} +(-2.04835 + 2.47212i) q^{45} +(2.71366 - 0.987691i) q^{46} +(6.73190 - 3.38089i) q^{47} +(-1.41572 + 0.997861i) q^{48} +(-13.6633 - 1.59701i) q^{49} +(3.44475 + 1.73002i) q^{50} +(-4.68853 + 11.9093i) q^{51} +(-0.0314133 - 0.00744510i) q^{52} +(-0.516900 - 0.895297i) q^{53} +(5.07880 - 1.09808i) q^{54} +(-1.34596 + 2.33126i) q^{55} +(3.12645 - 3.31385i) q^{56} +(8.11332 - 9.17402i) q^{57} +(0.0146650 + 0.251789i) q^{58} +(0.314656 - 0.422657i) q^{59} +(0.788558 + 1.67746i) q^{60} +(4.82343 + 3.17242i) q^{61} +(0.557532 - 3.16192i) q^{62} +(-12.5161 + 5.49129i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-0.0136839 + 0.0317229i) q^{65} +(4.04404 - 1.62114i) q^{66} +(-1.10768 + 0.262525i) q^{67} +(5.07098 + 5.37493i) q^{68} +(-2.36020 + 4.40997i) q^{69} +(-2.91146 - 3.91078i) q^{70} +(4.41828 - 3.70738i) q^{71} +(0.673719 - 2.92337i) q^{72} +(-8.95122 - 7.51097i) q^{73} +(-0.666840 + 11.4492i) q^{74} +(-6.44376 + 1.74805i) q^{75} +(-2.80060 - 6.49252i) q^{76} +(-9.57479 + 6.29744i) q^{77} +(0.0491354 - 0.0266907i) q^{78} +(-0.614615 - 2.05296i) q^{79} +1.07016 q^{80} +(-5.28442 + 7.28526i) q^{81} -4.24500 q^{82} +(-2.70592 - 9.03840i) q^{83} +(-0.205034 + 7.88840i) q^{84} +(6.60696 - 4.34547i) q^{85} +(1.23818 + 2.87042i) q^{86} +(-0.309857 - 0.307940i) q^{87} +(0.146260 - 2.51119i) q^{88} +(0.755271 + 0.633748i) q^{89} +(-2.95574 - 1.25328i) q^{90} +(-0.112670 + 0.0945417i) q^{91} +(1.72448 + 2.31638i) q^{92} +(2.93412 + 4.72406i) q^{93} +(5.16958 + 5.47944i) q^{94} +(-7.36288 + 1.74504i) q^{95} +(-1.36197 - 1.07006i) q^{96} +(-0.903213 + 2.09388i) q^{97} +(-2.38876 - 13.5473i) q^{98} +(-3.34487 + 6.76453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{27}\right)$

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 $

$2$	0.286803	+	0.957990i	0.202801	+	0.677401i
$2$	0.286803	+	0.957990i	0.202801	+	0.677401i
$3$	−1.47699	−	0.904708i	−0.852741	−	0.522333i
$3$	−1.47699	−	0.904708i	−0.852741	−	0.522333i
$4$	−0.835488	+	0.549509i	−0.417744	+	0.274754i
$5$	0.423867	+	0.982634i	0.189559	+	0.439447i	0.986319	−	0.164849i	$-0.0527137\pi$
$5$	0.423867	+	0.982634i	0.189559	+	0.439447i	−0.796760	+	0.604296i	$0.793454\pi$
$6$	0.443094	−	1.67442i	0.180893	−	0.683577i
$7$	−0.264903	+	4.54820i	−0.100124	+	1.71906i	0.457706	+	0.889103i	$0.348671\pi$
$7$	−0.264903	+	4.54820i	−0.100124	+	1.71906i	−0.557830	+	0.829955i	$0.688366\pi$
$8$	−0.766044	−	0.642788i	−0.270838	−	0.227260i
$9$	1.36301	+	2.67249i	0.454336	+	0.890830i
$10$	−0.819786	+	0.687882i	−0.259239	+	0.217528i
$11$	1.50212	+	2.01769i	0.452905	+	0.608358i	0.968664	−	0.248377i	$-0.0798971\pi$
$11$	1.50212	+	2.01769i	0.452905	+	0.608358i	−0.515758	+	0.856734i	$0.672490\pi$
$12$	1.73115	−	0.0557480i	0.499741	−	0.0160931i
$13$	0.0221543	+	0.0234822i	0.00614450	+	0.00651279i	0.730439	−	0.682978i	$-0.239316\pi$
$13$	0.0221543	+	0.0234822i	0.00614450	+	0.00651279i	−0.724294	+	0.689491i	$0.757834\pi$
$14$	−4.43310	+	1.05066i	−1.18480	+	0.280802i
$15$	0.262948	−	1.83482i	0.0678930	−	0.473748i
$16$	0.396080	−	0.918216i	0.0990199	−	0.229554i
$17$	−1.28317	−	7.27724i	−0.311215	−	1.76499i	−0.592700	−	0.805423i	$-0.701938\pi$
$17$	−1.28317	−	7.27724i	−0.311215	−	1.76499i	0.281485	−	0.959566i	$-0.409173\pi$
$18$	−2.16930	+	2.07223i	−0.511310	+	0.488429i
$19$	−1.22783	+	6.96338i	−0.281684	+	1.59751i	0.435212	+	0.900328i	$0.356673\pi$
$19$	−1.22783	+	6.96338i	−0.281684	+	1.59751i	−0.716896	+	0.697180i	$0.754438\pi$
$20$	−0.894102	−	0.588060i	−0.199927	−	0.131494i
$21$	4.50605	−	6.47800i	0.983301	−	1.41361i
$22$	−1.50212	+	2.01769i	−0.320253	+	0.430174i
$23$	−0.167912	−	2.88293i	−0.0350120	−	0.601132i	−0.969493	−	0.245119i	$-0.921173\pi$
$23$	−0.167912	−	2.88293i	−0.0350120	−	0.601132i	0.934481	−	0.356013i	$-0.115864\pi$
$24$	0.549906	+	1.64244i	0.112249	+	0.335261i
$25$	2.64530	−	2.80386i	0.529060	−	0.560771i
$26$	−0.0161418	+	0.0279584i	−0.00316566	+	0.00548309i
$27$	0.404671	−	5.18037i	0.0778790	−	0.996963i
$28$	−2.27795	−	3.94553i	−0.430493	−	0.745636i
$29$	0.245417	+	0.0581649i	0.0455728	+	0.0108010i	0.253339	−	0.967378i	$-0.418471\pi$
$29$	0.245417	+	0.0581649i	0.0455728	+	0.0108010i	−0.207766	+	0.978179i	$0.566619\pi$
$30$	1.83315	−	0.274330i	0.334686	−	0.0500855i
$31$	−2.86918	−	1.44096i	−0.515321	−	0.258804i	0.172079	−	0.985083i	$-0.444952\pi$
$31$	−2.86918	−	1.44096i	−0.515321	−	0.258804i	−0.687400	+	0.726279i	$0.741248\pi$
$32$	0.993238	+	0.116093i	0.175581	+	0.0205225i
$33$	−0.393192	−	4.33909i	−0.0684459	−	0.755339i
$34$	6.60350	−	3.31640i	1.13249	−	0.568758i
$35$	−4.58150	+	1.66753i	−0.774415	+	0.281864i
$36$	−2.60733	−	1.48385i	−0.434556	−	0.247308i
$37$	10.7770	+	3.92249i	1.77172	+	0.644854i	0.999960	+	0.00894017i	$0.00284578\pi$
$37$	10.7770	+	3.92249i	1.77172	+	0.644854i	0.771760	+	0.635913i	$0.219376\pi$
$38$	−7.02299	+	0.820869i	−1.13928	+	0.133163i
$39$	−0.0114772	−	0.0547262i	−0.00183782	−	0.00876320i
$40$	0.306924	−	1.02520i	0.0485289	−	0.162098i
$41$	−1.21748	+	4.06667i	−0.190139	+	0.635107i	0.808758	+	0.588142i	$0.200140\pi$
$41$	−1.21748	+	4.06667i	−0.190139	+	0.635107i	−0.998897	+	0.0469653i	$0.985045\pi$
$42$	7.49820	+	2.45884i	1.15700	+	0.379407i
$43$	3.10495	−	0.362916i	0.473500	−	0.0553442i	0.124003	−	0.992282i	$-0.460427\pi$
$43$	3.10495	−	0.362916i	0.473500	−	0.0553442i	0.349497	+	0.936938i	$0.386353\pi$
$44$	−2.36374	−	0.860332i	−0.356348	−	0.129700i
$45$	−2.04835	+	2.47212i	−0.305349	+	0.368522i
$46$	2.71366	−	0.987691i	0.400107	−	0.145627i
$47$	6.73190	−	3.38089i	0.981948	−	0.493153i	0.115980	−	0.993252i	$-0.462999\pi$
$47$	6.73190	−	3.38089i	0.981948	−	0.493153i	0.865968	+	0.500099i	$0.166703\pi$
$48$	−1.41572	+	0.997861i	−0.204342	+	0.144029i
$49$	−13.6633	−	1.59701i	−1.95190	−	0.228144i
$50$	3.44475	+	1.73002i	0.487161	+	0.244661i
$51$	−4.68853	+	11.9093i	−0.656526	+	1.66764i
$52$	−0.0314133	−	0.00744510i	−0.00435624	−	0.00103245i
$53$	−0.516900	−	0.895297i	−0.0710017	−	0.122979i	0.828339	−	0.560227i	$-0.189286\pi$
$53$	−0.516900	−	0.895297i	−0.0710017	−	0.122979i	−0.899341	+	0.437249i	$0.855953\pi$
$54$	5.07880	−	1.09808i	0.691137	−	0.149429i
$55$	−1.34596	+	2.33126i	−0.181489	+	0.314348i
$56$	3.12645	−	3.31385i	0.417790	−	0.442832i
$57$	8.11332	−	9.17402i	1.07463	−	1.21513i
$58$	0.0146650	+	0.251789i	0.00192561	+	0.0330615i
$59$	0.314656	−	0.422657i	0.0409647	−	0.0550252i	−0.781169	−	0.624320i	$-0.785376\pi$
$59$	0.314656	−	0.422657i	0.0409647	−	0.0550252i	0.822134	+	0.569295i	$0.192784\pi$
$60$	0.788558	+	1.67746i	0.101802	+	0.216559i
$61$	4.82343	+	3.17242i	0.617577	+	0.406187i	0.819389	−	0.573237i	$-0.194313\pi$
$61$	4.82343	+	3.17242i	0.617577	+	0.406187i	−0.201812	+	0.979424i	$0.564683\pi$
$62$	0.557532	−	3.16192i	0.0708066	−	0.401564i
$63$	−12.5161	+	5.49129i	−1.57688	+	0.691837i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	−0.0136839	+	0.0317229i	−0.00169728	+	0.00393474i
$66$	4.04404	−	1.62114i	0.497787	−	0.199549i
$67$	−1.10768	+	0.262525i	−0.135324	+	0.0320725i	−0.297720	−	0.954653i	$-0.596226\pi$
$67$	−1.10768	+	0.262525i	−0.135324	+	0.0320725i	0.162395	+	0.986726i	$0.448078\pi$
$68$	5.07098	+	5.37493i	0.614947	+	0.651806i
$69$	−2.36020	+	4.40997i	−0.284135	+	0.530898i
$70$	−2.91146	−	3.91078i	−0.347987	−	0.467427i
$71$	4.41828	−	3.70738i	0.524353	−	0.439985i	−0.341793	−	0.939775i	$-0.611034\pi$
$71$	4.41828	−	3.70738i	0.524353	−	0.439985i	0.866146	+	0.499791i	$0.166590\pi$
$72$	0.673719	−	2.92337i	0.0793986	−	0.344523i
$73$	−8.95122	−	7.51097i	−1.04766	−	0.879092i	−0.0548158	−	0.998496i	$-0.517457\pi$
$73$	−8.95122	−	7.51097i	−1.04766	−	0.879092i	−0.992846	+	0.119404i	$0.961902\pi$
$74$	−0.666840	+	11.4492i	−0.0775185	+	1.33094i
$75$	−6.44376	+	1.74805i	−0.744061	+	0.201847i
$76$	−2.80060	−	6.49252i	−0.321251	−	0.744743i
$77$	−9.57479	+	6.29744i	−1.09115	+	0.717660i
$78$	0.0491354	−	0.0266907i	0.00556349	−	0.00302212i
$79$	−0.614615	−	2.05296i	−0.0691496	−	0.230976i	0.916428	−	0.400199i	$-0.131059\pi$
$79$	−0.614615	−	2.05296i	−0.0691496	−	0.230976i	−0.985578	+	0.169224i	$0.945874\pi$
$80$	1.07016			0.119647
$81$	−5.28442	+	7.28526i	−0.587157	+	0.809473i
$82$	−4.24500			−0.468782
$83$	−2.70592	−	9.03840i	−0.297013	−	0.992093i	−0.968068	−	0.250686i	$-0.919344\pi$
$83$	−2.70592	−	9.03840i	−0.297013	−	0.992093i	0.671055	−	0.741407i	$-0.265841\pi$
$84$	−0.205034	+	7.88840i	−0.0223710	+	0.860695i
$85$	6.60696	−	4.34547i	0.716626	−	0.471332i
$86$	1.23818	+	2.87042i	0.133516	+	0.309525i
$87$	−0.309857	−	0.307940i	−0.0332201	−	0.0330146i
$88$	0.146260	−	2.51119i	0.0155914	−	0.267693i
$89$	0.755271	+	0.633748i	0.0800586	+	0.0671771i	0.681939	−	0.731409i	$-0.261137\pi$
$89$	0.755271	+	0.633748i	0.0800586	+	0.0671771i	−0.601880	+	0.798586i	$0.705582\pi$
$90$	−2.95574	−	1.25328i	−0.311562	−	0.132108i
$91$	−0.112670	+	0.0945417i	−0.0118111	+	0.00991067i
$92$	1.72448	+	2.31638i	0.179790	+	0.241500i
$93$	2.93412	+	4.72406i	0.304254	+	0.489862i
$94$	5.16958	+	5.47944i	0.533202	+	0.565161i
$95$	−7.36288	+	1.74504i	−0.755416	+	0.179037i
$96$	−1.36197	−	1.07006i	−0.139006	−	0.109212i
$97$	−0.903213	+	2.09388i	−0.0917074	+	0.212602i	−0.957896	−	0.287116i	$-0.907304\pi$
$97$	−0.903213	+	2.09388i	−0.0917074	+	0.212602i	0.866188	+	0.499717i	$0.166563\pi$
$98$	−2.38876	−	13.5473i	−0.241301	−	1.36849i
$99$	−3.34487	+	6.76453i	−0.336172	+	0.679861i
$100$	−0.669373	+	3.79621i	−0.0669373	+	0.379621i
$101$	13.4519	+	8.84745i	1.33851	+	0.880354i	0.998201	−	0.0599584i	$-0.0190968\pi$
$101$	13.4519	+	8.84745i	1.33851	+	0.880354i	0.340312	+	0.940312i	$0.389467\pi$
$102$	−12.7537	−	1.07594i	−1.26280	−	0.106534i
$103$	0.874799	−	1.17506i	0.0861965	−	0.115782i	−0.756933	−	0.653492i	$-0.773303\pi$
$103$	0.874799	−	1.17506i	0.0861965	−	0.115782i	0.843130	+	0.537710i	$0.180711\pi$
$104$	−0.00187712	−	0.0322289i	−0.000184067	−	0.00316031i
$105$	8.27546	+	1.68199i	0.807602	+	0.164145i
$106$	0.709437	−	0.751959i	0.0689066	−	0.0730367i
$107$	−6.90525	+	11.9602i	−0.667556	+	1.15624i	0.311030	+	0.950400i	$0.399326\pi$
$107$	−6.90525	+	11.9602i	−0.667556	+	1.15624i	−0.978586	+	0.205841i	$0.934007\pi$
$108$	2.50856	+	4.55051i	0.241387	+	0.437873i
$109$	2.58166	+	4.47156i	0.247278	+	0.428298i	0.962770	−	0.270323i	$-0.0871306\pi$
$109$	2.58166	+	4.47156i	0.247278	+	0.428298i	−0.715492	+	0.698621i	$0.753797\pi$
$110$	−2.61935	−	0.620798i	−0.249745	−	0.0591907i
$111$	−12.3688	−	15.5435i	−1.17399	−	1.47532i
$112$	4.07131	+	2.04469i	0.384703	+	0.193205i
$113$	19.0662	+	2.22852i	1.79360	+	0.209642i	0.946702	−	0.322111i	$-0.104393\pi$
$113$	19.0662	+	2.22852i	1.79360	+	0.209642i	0.846899	+	0.531753i	$0.178467\pi$
$114$	11.1155	+	5.14133i	1.04107	+	0.481530i
$115$	2.76169	−	1.38697i	0.257529	−	0.129336i
$116$	−0.237005	+	0.0862628i	−0.0220054	+	0.00800930i
$117$	−0.0325594	+	0.0912136i	−0.00301012	+	0.00843270i
$118$	0.495145	+	0.180218i	0.0455818	+	0.0165904i
$119$	33.4382	−	3.90837i	3.06528	−	0.358280i
$120$	−1.38083	+	1.23653i	−0.126052	+	0.112879i
$121$	1.34010	−	4.47626i	0.121828	−	0.406932i
$122$	−1.65577	+	5.53066i	−0.149906	+	0.500722i
$123$	5.47735	−	4.90497i	0.493876	−	0.442266i
$124$	3.18899	−	0.372739i	0.286380	−	0.0334730i
$125$	8.90450	+	3.24097i	0.796443	+	0.289882i
$126$	−8.85025	−	10.4154i	−0.788443	−	0.927875i
$127$	1.03480	−	0.376635i	0.0918233	−	0.0334209i	−0.295700	−	0.955281i	$-0.595553\pi$
$127$	1.03480	−	0.376635i	0.0918233	−	0.0334209i	0.387523	+	0.921860i	$0.373331\pi$
$128$	−0.893633	+	0.448799i	−0.0789867	+	0.0396686i
$129$	−4.91431	−	2.27304i	−0.432681	−	0.200130i
$130$	−0.0343148	−	0.00401082i	−0.00300961	−	0.000351772i
$131$	−12.1950	−	6.12454i	−1.06548	−	0.535103i	−0.172410	−	0.985025i	$-0.555156\pi$
$131$	−12.1950	−	6.12454i	−1.06548	−	0.535103i	−0.893068	+	0.449922i	$0.851452\pi$
$132$	2.71288	+	3.40920i	0.236126	+	0.296733i
$133$	−31.3456	−	7.42904i	−2.71801	−	0.644179i
$134$	−0.569181	−	0.985851i	−0.0491698	−	0.0851646i
$135$	5.26193	−	1.79814i	0.452875	−	0.154760i
$136$	−3.69475	+	6.39949i	−0.316822	+	0.548752i
$137$	−6.69403	+	7.09526i	−0.571910	+	0.606189i	−0.947171	−	0.320730i	$-0.896072\pi$
$137$	−6.69403	+	7.09526i	−0.571910	+	0.606189i	0.375261	+	0.926919i	$0.377553\pi$
$138$	−4.90162	−	0.996256i	−0.417254	−	0.0848070i
$139$	−0.213011	−	3.65725i	−0.0180673	−	0.310204i	−0.995220	−	0.0976633i	$-0.968863\pi$
$139$	−0.213011	−	3.65725i	−0.0180673	−	0.310204i	0.977152	−	0.212541i	$-0.0681739\pi$
$140$	2.91146	−	3.91078i	0.246064	−	0.330521i
$141$	−13.0017	−	1.09686i	−1.09494	−	0.0923721i
$142$	4.81880	+	3.16938i	0.404385	+	0.265968i
$143$	−0.0141015	+	0.0799736i	−0.00117923	+	0.00668773i
$144$	2.99378	−	0.193017i	0.249482	−	0.0160847i
$145$	0.0468694	+	0.265809i	0.00389229	+	0.0220743i
$146$	4.62819	−	10.7293i	0.383032	−	0.887967i
$147$	18.7357	+	14.7201i	1.54530	+	1.21409i
$148$	−11.1595	+	2.64484i	−0.917302	+	0.217405i
$149$	−8.89366	−	9.42673i	−0.728597	−	0.772268i	0.252121	−	0.967696i	$-0.418872\pi$
$149$	−8.89366	−	9.42673i	−0.728597	−	0.772268i	−0.980718	+	0.195428i	$0.937390\pi$
$150$	−3.52270	−	5.67171i	−0.287627	−	0.463093i
$151$	5.77177	+	7.75283i	0.469700	+	0.630917i	0.972337	−	0.233581i	$-0.0750443\pi$
$151$	5.77177	+	7.75283i	0.469700	+	0.630917i	−0.502637	+	0.864497i	$0.667637\pi$
$152$	5.41655	−	4.54502i	0.439340	−	0.368650i
$153$	17.6994	−	13.3482i	1.43091	−	1.07914i
$154$	−8.77896	−	7.36643i	−0.707429	−	0.593604i
$155$	0.199782	−	3.43013i	0.0160469	−	0.275515i
$156$	0.0396616	+	0.0394162i	0.00317547	+	0.00315582i
$157$	−7.82301	−	18.1358i	−0.624344	−	1.44739i	−0.877313	−	0.479919i	$-0.840666\pi$
$157$	−7.82301	−	18.1358i	−0.624344	−	1.44739i	0.252969	−	0.967474i	$-0.418593\pi$
$158$	1.79044	−	1.17759i	0.142440	−	0.0936840i
$159$	−0.0465251	+	1.78999i	−0.00368968	+	0.141955i
$160$	0.306924	+	1.02520i	0.0242645	+	0.0810490i
$161$	13.1566			1.03689
$162$	−8.49479	−	2.97298i	−0.667413	−	0.233579i
$163$	8.92367			0.698956			0.349478	−	0.936945i	$-0.386359\pi$
$163$	8.92367			0.698956			0.349478	+	0.936945i	$0.386359\pi$
$164$	−1.21748	−	4.06667i	−0.0950693	−	0.317553i
$165$	4.09708	−	2.22556i	0.318957	−	0.173260i
$166$	7.88263	−	5.18449i	0.611810	−	0.402394i
$167$	−6.98198	−	16.1860i	−0.540281	−	1.25251i	−0.941649	−	0.336596i	$-0.890724\pi$
$167$	−6.98198	−	16.1860i	−0.540281	−	1.25251i	0.401368	−	0.915917i	$-0.368535\pi$
$168$	−7.61581	+	2.06600i	−0.587573	+	0.159395i
$169$	0.755822	−	12.9770i	0.0581402	−	0.998228i
$170$	6.05781	+	5.08311i	0.464613	+	0.389856i
$171$	−20.2831	+	6.20977i	−1.55109	+	0.474873i
$172$	−2.39472	+	2.00941i	−0.182596	+	0.153216i
$173$	−5.76130	−	7.73876i	−0.438023	−	0.588367i	0.527217	−	0.849730i	$-0.323235\pi$
$173$	−5.76130	−	7.73876i	−0.438023	−	0.588367i	−0.965241	+	0.261363i	$0.915828\pi$
$174$	0.206135	−	0.385158i	0.0156271	−	0.0291987i
$175$	12.0518	+	12.7741i	0.911027	+	0.965632i
$176$	2.44764	−	0.580101i	0.184498	−	0.0437267i
$177$	−0.847125	+	0.339588i	−0.0636738	+	0.0255250i
$178$	−0.390509	+	0.905303i	−0.0292699	+	0.0678553i
$179$	1.56746	+	8.88951i	0.117158	+	0.664433i	0.985659	+	0.168747i	$0.0539722\pi$
$179$	1.56746	+	8.88951i	0.117158	+	0.664433i	−0.868502	+	0.495686i	$0.834917\pi$
$180$	0.352917	−	3.19101i	0.0263049	−	0.237844i
$181$	−2.31477	+	13.1277i	−0.172056	+	0.975776i	0.769432	+	0.638729i	$0.220539\pi$
$181$	−2.31477	+	13.1277i	−0.172056	+	0.975776i	−0.941488	+	0.337047i	$0.890572\pi$
$182$	−0.122884	−	0.0808222i	−0.00910879	−	0.00599094i
$183$	−4.25406	−	9.04944i	−0.314469	−	0.668954i
$184$	−1.72448	+	2.31638i	−0.127131	+	0.170766i
$185$	0.713622	+	12.2524i	0.0524665	+	0.900815i
$186$	−3.68408	+	4.16573i	−0.270130	+	0.305446i
$187$	12.7558	−	13.5203i	0.932793	−	0.988703i
$188$	−3.76659	+	6.52393i	−0.274707	+	0.475806i
$189$	23.4542	+	3.21282i	1.70604	+	0.233698i
$190$	−3.78343	−	6.55308i	−0.274479	−	0.475411i
$191$	−19.1870	−	4.54739i	−1.38832	−	0.329038i	−0.532552	−	0.846398i	$-0.678767\pi$
$191$	−19.1870	−	4.54739i	−1.38832	−	0.329038i	−0.855768	+	0.517360i	$0.826915\pi$
$192$	0.634486	−	1.61165i	0.0457901	−	0.116311i
$193$	4.30474	+	2.16192i	0.309862	+	0.155618i	0.596934	−	0.802291i	$-0.296386\pi$
$193$	4.30474	+	2.16192i	0.309862	+	0.155618i	−0.287072	+	0.957909i	$0.592682\pi$
$194$	−2.26496	−	0.264736i	−0.162615	−	0.0190069i
$195$	0.0489110	−	0.0344745i	0.00350259	−	0.00246877i
$196$	12.2931	−	6.17382i	0.878078	−	0.440987i
$197$	−18.9041	+	6.88052i	−1.34686	+	0.490217i	−0.911966	−	0.410266i	$-0.865436\pi$
$197$	−18.9041	+	6.88052i	−1.34686	+	0.490217i	−0.434893	+	0.900482i	$0.643214\pi$
$198$	−7.43967	−	1.26426i	−0.528714	−	0.0898472i
$199$	14.7627	+	5.37320i	1.04650	+	0.380896i	0.807342	−	0.590084i	$-0.200905\pi$
$199$	14.7627	+	5.37320i	1.04650	+	0.380896i	0.239161	+	0.970980i	$0.423128\pi$
$200$	−3.82870	+	0.447511i	−0.270730	+	0.0316438i
$201$	1.87354	+	0.614378i	0.132149	+	0.0433349i
$202$	−4.61772	+	15.4242i	−0.324901	+	1.08525i
$203$	−0.329557	+	1.10080i	−0.0231304	+	0.0772609i
$204$	−2.62706	−	12.5265i	−0.183931	−	0.877029i
$205$	−4.51210	+	0.527388i	−0.315138	+	0.0368344i
$206$	1.37659	+	0.501038i	0.0959116	+	0.0349090i
$207$	7.47574	−	4.37820i	0.519600	−	0.304306i
$208$	0.0303366	−	0.0110416i	0.00210346	−	0.000765599i
$209$	−15.8943	+	7.98242i	−1.09943	+	0.552156i
$210$	0.762100	+	8.41021i	0.0525899	+	0.580359i
$211$	−12.2614	−	1.43315i	−0.844106	−	0.0986619i	−0.316963	−	0.948438i	$-0.602663\pi$
$211$	−12.2614	−	1.43315i	−0.844106	−	0.0986619i	−0.527144	+	0.849776i	$0.676737\pi$
$212$	0.923838	+	0.463969i	0.0634494	+	0.0318655i
$213$	−9.87985	+	1.47851i	−0.676956	+	0.101306i
$214$	−13.4382	−	3.18492i	−0.918619	−	0.217717i
$215$	1.67270	+	2.89720i	0.114077	+	0.197587i
$216$	−3.63987	+	3.70828i	−0.247662	+	0.252316i
$217$	7.31382	−	12.6679i	0.496495	−	0.859954i
$218$	−3.54328	+	3.75566i	−0.239981	+	0.254365i
$219$	6.42565	+	19.1919i	0.434205	+	1.29687i
$220$	−0.156521	−	2.68736i	−0.0105526	−	0.181182i
$221$	0.142458	−	0.191354i	0.00958274	−	0.0128718i
$222$	11.3431	−	16.3071i	0.761298	−	1.09446i
$223$	−7.54360	−	4.96150i	−0.505157	−	0.332247i	0.271218	−	0.962518i	$-0.412573\pi$
$223$	−7.54360	−	4.96150i	−0.505157	−	0.332247i	−0.776375	+	0.630271i	$0.782944\pi$
$224$	−0.791125	+	4.48669i	−0.0528593	+	0.299780i
$225$	11.0989	+	3.24787i	0.739923	+	0.216524i
$226$	3.33336	+	18.9044i	0.221732	+	1.25750i
$227$	−5.77394	+	13.3855i	−0.383230	+	0.888426i	0.611999	+	0.790858i	$0.290366\pi$
$227$	−5.77394	+	13.3855i	−0.383230	+	0.888426i	−0.995229	+	0.0975679i	$0.968894\pi$
$228$	−1.73737	+	12.1231i	−0.115060	+	0.802873i
$229$	20.5841	−	4.87851i	1.36023	−	0.322381i	0.515189	−	0.857077i	$-0.327722\pi$
$229$	20.5841	−	4.87851i	1.36023	−	0.322381i	0.845045	+	0.534696i	$0.179574\pi$
$230$	2.12077	+	2.24788i	0.139839	+	0.148221i
$231$	19.8392	−	0.638879i	1.30533	−	0.0420351i
$232$	−0.150613	−	0.202308i	−0.00988821	−	0.0132822i
$233$	−11.3123	+	9.49216i	−0.741095	+	0.621852i	−0.933131	−	0.359536i	$-0.882935\pi$
$233$	−11.3123	+	9.49216i	−0.741095	+	0.621852i	0.192037	+	0.981388i	$0.438491\pi$
$234$	−0.0967198	−	0.00503125i	−0.00632277	−	0.000328903i
$235$	6.17560	+	5.18194i	0.402852	+	0.338033i
$236$	−0.0306378	+	0.526031i	−0.00199435	+	0.0342417i
$237$	−0.949544	+	3.58825i	−0.0616795	+	0.233082i
$238$	13.3344	+	30.9126i	0.864339	+	2.00376i
$239$	20.6818	−	13.6027i	1.33780	−	0.879883i	0.339640	−	0.940556i	$-0.389695\pi$
$239$	20.6818	−	13.6027i	1.33780	−	0.879883i	0.998158	+	0.0606726i	$0.0193246\pi$
$240$	−1.58061	−	0.968177i	−0.102028	−	0.0624956i
$241$	4.61819	+	15.4258i	0.297484	+	0.993664i	0.967828	+	0.251614i	$0.0809613\pi$
$241$	4.61819	+	15.4258i	0.297484	+	0.993664i	−0.670344	+	0.742050i	$0.733853\pi$
$242$	4.67255			0.300363
$243$	14.3961	−	5.97941i	0.923508	−	0.383579i
$244$	−5.77320			−0.369591
$245$	−4.22214	−	14.1029i	−0.269743	−	0.901003i
$246$	6.26983	+	3.84049i	0.399750	+	0.244860i
$247$	−0.190717	+	0.125437i	−0.0121350	+	0.00798134i
$248$	1.27169	+	2.94811i	0.0807526	+	0.187205i
$249$	−4.18049	+	15.7977i	−0.264928	+	1.00114i
$250$	−0.550979	+	9.45994i	−0.0348470	+	0.598299i
$251$	−7.07975	−	5.94062i	−0.446870	−	0.374969i	0.391403	−	0.920219i	$-0.371990\pi$
$251$	−7.07975	−	5.94062i	−0.446870	−	0.374969i	−0.838273	+	0.545251i	$0.816434\pi$
$252$	7.43953	−	11.4656i	0.468646	−	0.722265i
$253$	5.56465	−	4.66929i	0.349846	−	0.293556i
$254$	0.657595	+	0.883304i	0.0412612	+	0.0554234i
$255$	−13.6898	+	0.440850i	−0.857289	+	0.0276071i
$256$	−0.686242	−	0.727374i	−0.0428901	−	0.0454609i
$257$	−20.7242	+	4.91172i	−1.29274	+	0.306385i	−0.818752	−	0.574147i	$-0.805334\pi$
$257$	−20.7242	+	4.91172i	−1.29274	+	0.306385i	−0.473987	+	0.880532i	$0.657186\pi$
$258$	0.768112	−	5.35977i	0.0478205	−	0.333685i
$259$	−20.6951	+	47.9767i	−1.28593	+	2.98113i
$260$	−0.00599926	−	0.0340235i	−0.000372059	−	0.00211005i
$261$	0.179060	+	0.735154i	0.0110836	+	0.0455049i
$262$	2.36969	−	13.4392i	0.146400	−	0.830275i
$263$	−0.359032	−	0.236139i	−0.0221389	−	0.0145610i	0.538391	−	0.842695i	$-0.319032\pi$
$263$	−0.359032	−	0.236139i	−0.0221389	−	0.0145610i	−0.560530	+	0.828134i	$0.689403\pi$
$264$	−2.48791	+	3.57668i	−0.153121	+	0.220129i
$265$	0.660652	−	0.887410i	0.0405836	−	0.0545132i
$266$	−1.87307	−	32.1594i	−0.114845	−	1.97182i
$267$	−0.542173	−	1.61934i	−0.0331804	−	0.0991020i
$268$	0.781192	−	0.828015i	0.0477189	−	0.0505791i
$269$	−0.283018	+	0.490201i	−0.0172559	+	0.0298881i	−0.874524	−	0.484982i	$-0.838826\pi$
$269$	−0.283018	+	0.490201i	−0.0172559	+	0.0298881i	0.857269	+	0.514870i	$0.172160\pi$
$270$	3.23174	+	4.52516i	0.196678	+	0.275393i
$271$	−11.7891	−	20.4193i	−0.716137	−	1.24039i	−0.962519	−	0.271213i	$-0.912575\pi$
$271$	−11.7891	−	20.4193i	−0.716137	−	1.24039i	0.246382	−	0.969173i	$-0.420758\pi$
$272$	−7.19031	−	1.70414i	−0.435977	−	0.103328i
$273$	0.251946	−	0.0377035i	0.0152485	−	0.00228192i
$274$	−8.71706	−	4.37787i	−0.526617	−	0.264477i
$275$	9.63088	+	1.12569i	0.580764	+	0.0678816i
$276$	−0.451398	−	4.98143i	−0.0271710	−	0.299847i
$277$	5.18178	−	2.60239i	0.311343	−	0.156362i	−0.286266	−	0.958150i	$-0.592414\pi$
$277$	5.18178	−	2.60239i	0.311343	−	0.156362i	0.597609	+	0.801788i	$0.296118\pi$
$278$	3.44252	−	1.25297i	0.206469	−	0.0751484i
$279$	−0.0597736	−	9.63191i	−0.00357855	−	0.576647i
$280$	4.58150	+	1.66753i	0.273797	+	0.0996539i
$281$	−14.3679	+	1.67936i	−0.857115	+	0.100182i	−0.533288	−	0.845934i	$-0.679044\pi$
$281$	−14.3679	+	1.67936i	−0.857115	+	0.100182i	−0.323827	+	0.946116i	$0.604970\pi$
$282$	−2.67814	−	12.7700i	−0.159481	−	0.760445i
$283$	1.39517	−	4.66020i	0.0829345	−	0.277020i	−0.906456	−	0.422300i	$-0.861223\pi$
$283$	1.39517	−	4.66020i	0.0829345	−	0.277020i	0.989391	+	0.145279i	$0.0464081\pi$
$284$	−1.65418	+	5.52535i	−0.0981576	+	0.327869i
$285$	12.4537	+	4.08385i	0.737692	+	0.241907i
$286$	−0.0806582	+	0.00942760i	−0.00476942	+	0.000557466i
$287$	−18.1735	−	6.61462i	−1.07275	−	0.390449i
$288$	1.04353	+	2.81266i	0.0614909	+	0.165737i
$289$	−35.3368	+	12.8616i	−2.07864	+	0.756562i
$290$	−0.241200	+	0.121135i	−0.0141638	+	0.00711331i
$291$	3.22839	−	2.27550i	0.189252	−	0.133392i
$292$	11.6060	+	1.35654i	0.679189	+	0.0793858i
$293$	−14.9003	−	7.48320i	−0.870483	−	0.437173i	−0.0432713	−	0.999063i	$-0.513778\pi$
$293$	−14.9003	−	7.48320i	−0.870483	−	0.437173i	−0.827212	+	0.561890i	$0.810074\pi$
$294$	−8.72819	+	22.1704i	−0.509038	+	1.29300i
$295$	0.548689	+	0.130042i	0.0319459	+	0.00757132i
$296$	−5.73430	−	9.93210i	−0.333299	−	0.577291i
$297$	11.0603	−	6.96502i	0.641782	−	0.404152i
$298$	6.47998	−	11.2237i	0.375375	−	0.650169i
$299$	0.0639775	−	0.0678122i	0.00369992	−	0.00392168i
$300$	4.42311	−	5.00138i	0.255369	−	0.288755i
$301$	0.828107	+	14.2181i	0.0477313	+	0.819515i
$302$	−5.77177	+	7.75283i	−0.332128	+	0.446125i
$303$	−11.8640	−	25.2376i	−0.681568	−	1.44986i
$304$	5.90757	+	3.88547i	0.338822	+	0.222847i
$305$	−1.07284	+	6.08435i	−0.0614304	+	0.348389i
$306$	17.8637	+	13.1275i	1.02120	+	0.750449i
$307$	−1.30010	−	7.37324i	−0.0742007	−	0.420813i	−0.999169	−	0.0407680i	$-0.987020\pi$
$307$	−1.30010	−	7.37324i	−0.0742007	−	0.420813i	0.924968	−	0.380045i	$-0.124092\pi$
$308$	4.53912	−	10.5229i	0.258641	−	0.599596i
$309$	−2.35516	+	0.944115i	−0.133980	+	0.0537088i
$310$	3.34333	−	0.792383i	0.189888	−	0.0450044i
$311$	−2.15732	−	2.28662i	−0.122330	−	0.129662i	0.663314	−	0.748342i	$-0.269150\pi$
$311$	−2.15732	−	2.28662i	−0.122330	−	0.129662i	−0.785644	+	0.618679i	$0.787668\pi$
$312$	−0.0263853	+	0.0493001i	−0.00149377	+	0.00279107i
$313$	−16.0848	−	21.6057i	−0.909169	−	1.22123i	−0.974732	−	0.223378i	$-0.928292\pi$
$313$	−16.0848	−	21.6057i	−0.909169	−	1.22123i	0.0655628	−	0.997848i	$-0.479116\pi$
$314$	15.1302	−	12.6958i	0.853848	−	0.716464i
$315$	−10.7011	−	9.97116i	−0.602938	−	0.561811i
$316$	1.64162	+	1.37748i	0.0923484	+	0.0774895i
$317$	−0.500100	+	8.58639i	−0.0280884	+	0.482260i	0.954705	+	0.297553i	$0.0961705\pi$
$317$	−0.500100	+	8.58639i	−0.0280884	+	0.482260i	−0.982794	+	0.184707i	$0.940867\pi$
$318$	−1.72814	+	0.468804i	−0.0969090	+	0.0262892i
$319$	0.251286	+	0.582547i	0.0140693	+	0.0326164i
$320$	−0.894102	+	0.588060i	−0.0499818	+	0.0328735i
$321$	21.0195	−	11.4180i	1.17320	−	0.637288i
$322$	3.77336	+	12.6039i	0.210281	+	0.702388i
$323$	52.2496			2.90725
$324$	0.411752	−	8.99058i	0.0228751	−	0.499476i
$325$	0.124446			0.00690300
$326$	2.55934	+	8.54878i	0.141749	+	0.473473i
$327$	0.232370	−	8.94011i	0.0128501	−	0.494389i
$328$	3.54665	−	2.33267i	0.195831	−	0.128800i
$329$	13.5936	+	31.5136i	0.749442	+	1.73740i
$330$	3.30712	+	3.28666i	0.182051	+	0.180925i
$331$	−1.96020	+	33.6553i	−0.107742	+	1.84986i	0.321792	+	0.946810i	$0.395715\pi$
$331$	−1.96020	+	33.6553i	−0.107742	+	1.84986i	−0.429534	+	0.903050i	$0.641322\pi$
$332$	7.22745	+	6.06455i	0.396658	+	0.332835i
$333$	4.20626	+	34.1477i	0.230502	+	1.87128i
$334$	13.5036	−	11.3309i	0.738884	−	0.619997i
$335$	−0.727474	−	0.977167i	−0.0397461	−	0.0533883i
$336$	−4.16344	−	6.70333i	−0.227135	−	0.365697i
$337$	11.2627	+	11.9377i	0.613516	+	0.650289i	0.957414	−	0.288718i	$-0.0932289\pi$
$337$	11.2627	+	11.9377i	0.613516	+	0.650289i	−0.343898	+	0.939007i	$0.611747\pi$
$338$	12.6486	−	2.99777i	0.687991	−	0.163057i
$339$	−26.1445	−	20.5409i	−1.41998	−	1.11563i
$340$	−3.13216	+	7.26117i	−0.169865	+	0.393792i
$341$	−1.40244	−	7.95363i	−0.0759463	−	0.430713i
$342$	−11.7662	−	17.6500i	−0.636241	−	0.954404i
$343$	5.34509	−	30.3135i	0.288608	−	1.63678i
$344$	−2.61180	−	1.71781i	−0.140819	−	0.0926181i
$345$	−5.33380	−	0.449975i	−0.287162	−	0.0242258i
$346$	5.76130	−	7.73876i	0.309729	−	0.416039i
$347$	−0.250752	−	4.30524i	−0.0134611	−	0.231117i	−0.998328	−	0.0578048i	$-0.981590\pi$
$347$	−0.250752	−	4.30524i	−0.0134611	−	0.231117i	0.984867	−	0.173313i	$-0.0554471\pi$
$348$	0.428097	+	0.0870109i	0.0229484	+	0.00466427i
$349$	7.09807	−	7.52352i	0.379951	−	0.402725i	−0.508971	−	0.860784i	$-0.669974\pi$
$349$	7.09807	−	7.52352i	0.379951	−	0.402725i	0.888922	+	0.458059i	$0.151455\pi$
$350$	−8.78099	+	15.2091i	−0.469363	+	0.812961i
$351$	0.130612	−	0.105265i	0.00697153	−	0.00561863i
$352$	1.25772	+	2.17844i	0.0670367	+	0.116111i
$353$	−2.91521	−	0.690918i	−0.155161	−	0.0367738i	0.152301	−	0.988334i	$-0.451332\pi$
$353$	−2.91521	−	0.690918i	−0.155161	−	0.0367738i	−0.307462	+	0.951560i	$0.599480\pi$
$354$	−0.568280	−	0.714142i	−0.0302038	−	0.0379562i
$355$	5.51576	+	2.77012i	0.292746	+	0.147023i
$356$	−0.979270	−	0.114460i	−0.0519012	−	0.00606638i
$357$	−52.9239	−	24.4792i	−2.80103	−	1.29558i
$358$	−8.06651	+	4.05115i	−0.426328	+	0.214110i
$359$	−21.4717	+	7.81504i	−1.13323	+	0.412462i	−0.839464	−	0.543415i	$-0.817131\pi$
$359$	−21.4717	+	7.81504i	−1.13323	+	0.412462i	−0.293766	+	0.955877i	$0.594909\pi$
$360$	3.15817	−	0.577101i	0.166450	−	0.0304159i
$361$	−29.1269	−	10.6013i	−1.53299	−	0.557964i
$362$	−13.2401	+	1.54755i	−0.695885	+	0.0813372i
$363$	−6.02902	+	5.39899i	−0.316442	+	0.283374i
$364$	0.0421833	−	0.140902i	0.00221100	−	0.00738527i
$365$	3.58640	−	11.9794i	0.187721	−	0.627032i
$366$	7.44919	−	6.67075i	0.389375	−	0.348686i
$367$	17.1121	−	2.00012i	0.893246	−	0.104405i	0.342929	−	0.939361i	$-0.388581\pi$
$367$	17.1121	−	2.00012i	0.893246	−	0.104405i	0.550317	+	0.834956i	$0.314507\pi$
$368$	−2.71366	−	0.987691i	−0.141459	−	0.0514870i
$369$	−12.5276	+	2.28920i	−0.652159	+	0.119171i
$370$	−11.5330	+	4.19767i	−0.599573	+	0.218227i
$371$	4.20892	−	2.11380i	0.218516	−	0.109743i
$372$	−5.04733	−	2.33457i	−0.261692	−	0.121042i
$373$	18.9281	+	2.21238i	0.980059	+	0.114552i	0.591010	−	0.806665i	$-0.298730\pi$
$373$	18.9281	+	2.21238i	0.980059	+	0.114552i	0.389049	+	0.921217i	$0.372804\pi$
$374$	16.6107	+	8.34221i	0.858919	+	0.431366i
$375$	−10.2197	−	12.8429i	−0.527745	−	0.663203i
$376$	−7.33012	−	1.73727i	−0.378022	−	0.0895929i
$377$	0.00407121	+	0.00705153i	0.000209678	+	0.000363173i
$378$	3.64889	+	23.3903i	0.187678	+	1.20307i
$379$	18.4500	−	31.9564i	0.947715	−	1.64149i	0.197493	−	0.980304i	$-0.436720\pi$
$379$	18.4500	−	31.9564i	0.947715	−	1.64149i	0.750222	−	0.661186i	$-0.229947\pi$
$380$	5.19269	−	5.50393i	0.266379	−	0.282346i
$381$	−1.86913	−	0.379901i	−0.0957584	−	0.0194629i
$382$	−1.14653	−	19.6851i	−0.0586614	−	1.00718i
$383$	14.2837	−	19.1864i	0.729865	−	0.980379i	−0.269981	−	0.962866i	$-0.587018\pi$
$383$	14.2837	−	19.1864i	0.729865	−	0.980379i	0.999847	−	0.0175136i	$-0.00557505\pi$
$384$	1.72592	+	0.145604i	0.0880755	+	0.00743030i
$385$	−10.2465	−	6.73924i	−0.522211	−	0.343463i
$386$	−0.836485	+	4.74394i	−0.0425760	+	0.241460i
$387$	5.20196	+	7.80328i	0.264430	+	0.396663i
$388$	−0.395984	−	2.24574i	−0.0201030	−	0.114010i
$389$	11.3226	−	26.2488i	0.574081	−	1.33087i	−0.345667	−	0.938357i	$-0.612347\pi$
$389$	11.3226	−	26.2488i	0.574081	−	1.33087i	0.919747	−	0.392511i	$-0.128394\pi$
$390$	0.0470540	+	0.0369688i	0.00238267	+	0.00187199i
$391$	−20.7643	+	4.92123i	−1.05010	+	0.248877i
$392$	9.44015	+	10.0060i	0.476800	+	0.505378i
$393$	12.4709	+	20.0788i	0.629075	+	1.01284i
$394$	−12.0132	−	16.1365i	−0.605217	−	0.812947i
$395$	1.75679	−	1.47412i	0.0883937	−	0.0741711i
$396$	−0.922571	−	7.48972i	−0.0463610	−	0.376373i
$397$	16.6874	+	14.0024i	0.837516	+	0.702759i	0.957003	−	0.290077i	$-0.0936808\pi$
$397$	16.6874	+	14.0024i	0.837516	+	0.702759i	−0.119488	+	0.992836i	$0.538125\pi$
$398$	−0.913466	+	15.6836i	−0.0457879	+	0.786148i
$399$	39.5761	+	39.3312i	1.98128	+	1.96902i
$400$	−1.52680	−	3.53951i	−0.0763398	−	0.176976i
$401$	13.3241	−	8.76342i	0.665376	−	0.437625i	−0.171377	−	0.985206i	$-0.554822\pi$
$401$	13.3241	−	8.76342i	0.665376	−	0.437625i	0.836753	+	0.547581i	$0.184451\pi$
$402$	−0.0512308	+	1.97104i	−0.00255516	+	0.0983064i
$403$	−0.0297279	−	0.0992982i	−0.00148085	−	0.00494639i
$404$	−16.1006			−0.801037
$405$	−9.39863	−	2.10467i	−0.467021	−	0.104582i
$406$	−1.14907			−0.0570275
$407$	8.27387	+	27.6366i	0.410120	+	1.36990i
$408$	11.2468	−	6.10933i	0.556799	−	0.302457i
$409$	−5.44128	+	3.57878i	−0.269054	+	0.176959i	−0.676866	−	0.736106i	$-0.736662\pi$
$409$	−5.44128	+	3.57878i	−0.269054	+	0.176959i	0.407812	+	0.913066i	$0.366292\pi$
$410$	−1.79932	−	4.17128i	−0.0888619	−	0.206005i
$411$	16.3062	−	4.42350i	0.804324	−	0.218195i
$412$	−0.0851785	+	1.46246i	−0.00419644	+	0.0720501i
$413$	1.83897	+	1.54308i	0.0904900	+	0.0759301i
$414$	6.33834	+	5.90600i	0.311512	+	0.290264i
$415$	7.73449	−	6.49001i	0.379671	−	0.318582i
$416$	0.0192784	+	0.0258954i	0.000945201	+	0.00126963i
$417$	−2.99413	+	5.59445i	−0.146623	+	0.273961i
$418$	−12.2056	−	12.9372i	−0.596996	−	0.632779i
$419$	24.1866	−	5.73232i	1.18159	−	0.280042i	0.407553	−	0.913182i	$-0.366382\pi$
$419$	24.1866	−	5.73232i	1.18159	−	0.280042i	0.774038	+	0.633139i	$0.218234\pi$
$420$	−7.83832	+	3.14216i	−0.382471	+	0.153322i
$421$	−1.35917	+	3.15091i	−0.0662420	+	0.153566i	−0.948121	−	0.317909i	$-0.897019\pi$
$421$	−1.35917	+	3.15091i	−0.0662420	+	0.153566i	0.881879	+	0.471476i	$0.156278\pi$
$422$	−2.14366	−	12.1573i	−0.104352	−	0.591807i
$423$	18.2110	+	13.3828i	0.885450	+	0.650692i
$424$	−0.179518	+	1.01809i	−0.00871814	+	0.0494430i
$425$	−23.7987	−	15.6527i	−1.15441	−	0.759265i
$426$	−4.24997	−	9.04075i	−0.205912	−	0.438026i
$427$	−15.7066	+	21.0976i	−0.760094	+	1.02098i
$428$	−0.803010	−	13.7871i	−0.0388149	−	0.666427i
$429$	0.0931806	−	0.105363i	0.00449880	−	0.00508696i
$430$	−2.29575	+	2.43335i	−0.110711	+	0.117347i
$431$	1.39780	−	2.42105i	0.0673294	−	0.116618i	−0.830396	−	0.557174i	$-0.811885\pi$
$431$	1.39780	−	2.42105i	0.0673294	−	0.116618i	0.897725	+	0.440556i	$0.145219\pi$
$432$	−4.59642	−	2.42342i	−0.221145	−	0.116597i
$433$	8.92781	+	15.4634i	0.429043	+	0.743125i	0.996788	−	0.0800795i	$-0.0255174\pi$
$433$	8.92781	+	15.4634i	0.429043	+	0.743125i	−0.567745	+	0.823204i	$0.692184\pi$
$434$	14.2334	+	3.37337i	0.683223	+	0.161927i
$435$	0.171254	−	0.435001i	0.00821100	−	0.0208567i
$436$	−4.61411	−	2.31729i	−0.220976	−	0.110978i
$437$	20.2811	+	2.37052i	0.970176	+	0.113397i
$438$	−16.5427	+	11.6600i	−0.790442	+	0.557136i
$439$	14.0812	−	7.07185i	0.672060	−	0.337521i	−0.0798315	−	0.996808i	$-0.525438\pi$
$439$	14.0812	−	7.07185i	0.672060	−	0.337521i	0.751891	+	0.659287i	$0.229142\pi$
$440$	2.52957	−	0.920688i	0.120593	−	0.0438921i
$441$	−14.3552	−	38.6918i	−0.683580	−	1.84247i
$442$	0.224172	+	0.0815920i	0.0106628	+	0.00388094i
$443$	−6.96874	+	0.814529i	−0.331095	+	0.0386994i	−0.280016	−	0.959995i	$-0.590340\pi$
$443$	−6.96874	+	0.814529i	−0.331095	+	0.0386994i	−0.0510784	+	0.998695i	$0.516266\pi$
$444$	18.8752	+	6.18964i	0.895779	+	0.293747i
$445$	−0.302608	+	1.01078i	−0.0143450	+	0.0479155i
$446$	2.58954	−	8.64967i	0.122618	−	0.409574i
$447$	4.60743	+	21.9694i	0.217924	+	1.03912i
$448$	−4.52510	+	0.528909i	−0.213791	+	0.0249886i
$449$	37.6554	+	13.7054i	1.77707	+	0.646799i	0.999846	+	0.0175707i	$0.00559321\pi$
$449$	37.6554	+	13.7054i	1.77707	+	0.646799i	0.777220	+	0.629228i	$0.216629\pi$
$450$	0.0717643	+	11.5641i	0.00338300	+	0.545136i
$451$	−10.0341	+	3.65211i	−0.472487	+	0.171971i
$452$	−17.1542	+	8.61517i	−0.806866	+	0.405223i
$453$	−1.51081	−	16.6726i	−0.0709840	−	0.783349i
$454$	−14.4791	−	1.69237i	−0.679540	−	0.0794268i
$455$	−0.140657	−	0.0706407i	−0.00659411	−	0.00331169i
$456$	−12.1121	+	1.81257i	−0.567201	+	0.0848813i
$457$	−19.8905	−	4.71414i	−0.930439	−	0.220518i	−0.262669	−	0.964886i	$-0.584603\pi$
$457$	−19.8905	−	4.71414i	−0.930439	−	0.220518i	−0.667770	+	0.744368i	$0.732751\pi$
$458$	10.5771	+	18.3201i	0.494237	+	0.856044i
$459$	−38.2180	+	3.70243i	−1.78387	+	0.172814i
$460$	−1.54521	+	2.67637i	−0.0720456	+	0.124787i
$461$	−11.0636	+	11.7267i	−0.515283	+	0.546168i	−0.931806	−	0.362957i	$-0.881767\pi$
$461$	−11.0636	+	11.7267i	−0.515283	+	0.546168i	0.416523	+	0.909125i	$0.363249\pi$
$462$	6.30200	+	18.8225i	0.293195	+	0.875704i
$463$	−0.219873	−	3.77507i	−0.0102184	−	0.175442i	−0.999556	−	0.0298013i	$-0.990513\pi$
$463$	−0.219873	−	3.77507i	−0.0102184	−	0.175442i	0.989337	−	0.145641i	$-0.0465245\pi$
$464$	0.150613	−	0.202308i	0.00699202	−	0.00939191i
$465$	−3.39834	+	4.88553i	−0.157594	+	0.226561i
$466$	−12.3378	−	8.11470i	−0.571538	−	0.375906i
$467$	0.861950	−	4.88836i	0.0398863	−	0.226206i	−0.958348	−	0.285602i	$-0.907806\pi$
$467$	0.861950	−	4.88836i	0.0398863	−	0.226206i	0.998234	+	0.0593960i	$0.0189175\pi$
$468$	−0.0229197	−	0.0940996i	−0.00105946	−	0.00434975i
$469$	−0.900588	−	5.10749i	−0.0415853	−	0.235842i
$470$	−3.19306	+	7.40236i	−0.147285	+	0.341445i
$471$	−4.85306	+	33.8639i	−0.223617	+	1.56037i
$472$	−0.512719	+	0.121517i	−0.0235998	+	0.00559326i
$473$	5.39625	+	5.71969i	0.248120	+	0.262992i
$474$	−3.70983	+	0.119467i	−0.170398	+	0.00548730i
$475$	16.2763	+	21.8629i	0.746809	+	1.00314i
$476$	−25.7896	+	21.6400i	−1.18206	+	0.991868i
$477$	1.68813	−	2.60171i	0.0772944	−	0.119124i
$478$	18.9628	+	15.9117i	0.867340	+	0.727784i
$479$	1.24077	−	21.3032i	0.0566924	−	0.973370i	−0.843294	−	0.537452i	$-0.819387\pi$
$479$	1.24077	−	21.3032i	0.0566924	−	0.973370i	0.899986	−	0.435918i	$-0.143576\pi$
$480$	0.474180	−	1.79188i	0.0216432	−	0.0817880i
$481$	0.146647	+	0.339967i	0.00668654	+	0.0155011i
$482$	−13.4533	+	8.84835i	−0.612779	+	0.403031i
$483$	−19.4322	−	11.9029i	−0.884197	−	0.541601i
$484$	1.34010	+	4.47626i	0.0609138	+	0.203466i
$485$	−2.44036			−0.110811
$486$	9.85705	+	12.0764i	0.447125	+	0.547795i
$487$	−4.81976			−0.218404			−0.109202	−	0.994020i	$-0.534830\pi$
$487$	−4.81976			−0.218404			−0.109202	+	0.994020i	$0.534830\pi$
$488$	−1.65577	−	5.53066i	−0.0749532	−	0.250361i
$489$	−13.1802	−	8.07331i	−0.596028	−	0.365088i
$490$	12.2995	−	8.08953i	0.555636	−	0.365448i
$491$	−2.56693	−	5.95081i	−0.115844	−	0.268556i	0.850423	−	0.526100i	$-0.176346\pi$
$491$	−2.56693	−	5.95081i	−0.115844	−	0.268556i	−0.966267	+	0.257544i	$0.917087\pi$
$492$	−1.88094	+	7.10790i	−0.0847992	+	0.320449i
$493$	0.108367	−	1.86059i	0.00488062	−	0.0837969i
$494$	−0.174865	−	0.146729i	−0.00786756	−	0.00660166i
$495$	−8.06483	−	0.419523i	−0.362487	−	0.0188561i
$496$	−2.45954	+	2.06380i	−0.110436	+	0.0926672i
$497$	15.6915	+	21.0773i	0.703859	+	0.945447i
$498$	−16.3330	+	0.525969i	−0.731900	+	0.0235692i
$499$	−12.1824	−	12.9126i	−0.545361	−	0.578049i	0.394805	−	0.918765i	$-0.370812\pi$
$499$	−12.1824	−	12.9126i	−0.545361	−	0.578049i	−0.940166	+	0.340716i	$0.889331\pi$
$500$	−9.22055	+	2.18531i	−0.412356	+	0.0977300i
$501$	−4.33131	+	30.2233i	−0.193509	+	1.35028i
$502$	3.66055	−	8.48612i	0.163379	−	0.378754i
$503$	4.35531	+	24.7002i	0.194194	+	1.10133i	0.913562	+	0.406699i	$0.133320\pi$
$503$	4.35531	+	24.7002i	0.194194	+	1.10133i	−0.719369	+	0.694629i	$0.755569\pi$
$504$	13.1176	+	3.83862i	0.584305	+	0.170986i
$505$	−2.99199	+	16.9684i	−0.133142	+	0.755085i
$506$	6.06909	+	3.99171i	0.269804	+	0.177453i
$507$	−12.8567	+	18.4831i	−0.570986	+	0.820862i
$508$	−0.657595	+	0.883304i	−0.0291761	+	0.0391903i
$509$	0.510855	+	8.77103i	0.0226432	+	0.388769i	0.990522	+	0.137353i	$0.0438594\pi$
$509$	0.510855	+	8.77103i	0.0226432	+	0.388769i	−0.967879	+	0.251417i	$0.919104\pi$
$510$	−4.34861	−	12.9883i	−0.192560	−	0.575129i
$511$	36.5326	−	38.7223i	1.61611	−	1.71297i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$	35.5760	+	9.17850i	1.57072	+	0.405241i
$514$	−10.6491	−	18.4449i	−0.469714	−	0.813568i
$515$	1.52545	+	0.361539i	0.0672194	+	0.0159313i
$516$	5.35491	−	0.801358i	0.235737	−	0.0352778i
$517$	16.9337	+	8.50442i	0.744743	+	0.374024i
$518$	−51.8966	−	6.06584i	−2.28021	−	0.266518i
$519$	1.50807	+	16.6424i	0.0661968	+	0.730519i
$520$	0.0308736	−	0.0155053i	0.00135390	−	0.000679952i
$521$	21.9439	−	7.98692i	0.961378	−	0.349913i	0.186805	−	0.982397i	$-0.440187\pi$
$521$	21.9439	−	7.98692i	0.961378	−	0.349913i	0.774574	+	0.632484i	$0.217965\pi$
$522$	−0.652915	+	0.382383i	−0.0285773	+	0.0167364i
$523$	−21.2216	−	7.72403i	−0.927956	−	0.337748i	−0.166557	−	0.986032i	$-0.553265\pi$
$523$	−21.2216	−	7.72403i	−0.927956	−	0.337748i	−0.761399	+	0.648283i	$0.775487\pi$
$524$	13.5542	−	1.58426i	0.592119	−	0.0692088i
$525$	−6.24350	−	29.7706i	−0.272489	−	1.29929i
$526$	0.123247	−	0.411675i	0.00537384	−	0.0179499i
$527$	−6.80454	+	22.7287i	−0.296410	+	0.990079i
$528$	−4.13996	−	1.35759i	−0.180169	−	0.0590816i
$529$	14.5614	−	1.70198i	0.633104	−	0.0739993i
$530$	1.03961	+	0.378386i	0.0451576	+	0.0164360i
$531$	1.55842	+	0.264831i	0.0676299	+	0.0114927i
$532$	30.2712	−	11.0178i	1.31242	−	0.477682i
$533$	−0.122467	+	0.0615051i	−0.00530462	+	0.00266408i
$534$	1.39581	−	0.983828i	0.0604028	−	0.0425744i
$535$	−14.6795	−	1.71578i	−0.634648	−	0.0741797i
$536$	1.01728	+	0.510896i	0.0439397	+	0.0220674i
$537$	5.72728	−	14.5478i	0.247150	−	0.627785i
$538$	−0.550778	−	0.130537i	−0.0237457	−	0.00562784i
$539$	−17.3016	−	29.9672i	−0.745233	−	1.29078i
$540$	−3.40819	+	4.39381i	−0.146665	+	0.189079i
$541$	−3.72706	+	6.45546i	−0.160239	+	0.277542i	−0.934954	−	0.354768i	$-0.884560\pi$
$541$	−3.72706	+	6.45546i	−0.160239	+	0.277542i	0.774715	+	0.632310i	$0.217893\pi$
$542$	16.1804	−	17.1502i	0.695006	−	0.736663i
$543$	15.2957	−	17.2953i	0.656399	−	0.742214i
$544$	−0.429661	−	7.37700i	−0.0184216	−	0.316286i
$545$	−3.29963	+	4.43217i	−0.141341	+	0.189853i
$546$	0.108379	+	0.230548i	0.00463817	+	0.00986655i
$547$	−32.8522	−	21.6072i	−1.40466	−	0.923858i	−0.999956	−	0.00940898i	$-0.997005\pi$
$547$	−32.8522	−	21.6072i	−1.40466	−	0.923858i	−0.404702	−	0.914449i	$-0.632625\pi$
$548$	1.69387	−	9.60644i	0.0723587	−	0.410367i
$549$	−1.90389	+	17.2146i	−0.0812560	+	0.734702i
$550$	1.68377	+	9.54913i	0.0717962	+	0.407176i
$551$	−0.706355	+	1.63751i	−0.0300917	+	0.0697605i
$552$	4.64270	−	1.86113i	0.197606	−	0.0792148i
$553$	9.50007	−	2.25156i	0.403984	−	0.0957460i
$554$	3.97921	+	4.21772i	0.169060	+	0.179194i
$555$	10.0308	−	18.7423i	0.425785	−	0.795568i
$556$	2.18766	+	2.93854i	0.0927775	+	0.124622i
$557$	−4.60236	+	3.86184i	−0.195008	+	0.163631i	−0.735064	−	0.677998i	$-0.762848\pi$
$557$	−4.60236	+	3.86184i	−0.195008	+	0.163631i	0.540055	+	0.841630i	$0.318403\pi$
$558$	9.21012	−	2.81973i	0.389896	−	0.119368i
$559$	0.0773100	+	0.0648708i	0.00326986	+	0.00274374i
$560$	−0.283487	+	4.86728i	−0.0119795	+	0.205680i
$561$	−31.0721	+	8.42916i	−1.31186	+	0.355879i
$562$	−5.72956	−	13.2826i	−0.241687	−	0.560293i
$563$	−21.6674	+	14.2509i	−0.913172	+	0.600603i	−0.916781	−	0.399391i	$-0.869222\pi$
$563$	−21.6674	+	14.2509i	−0.913172	+	0.600603i	0.00360876	+	0.999993i	$0.498851\pi$
$564$	11.4655	−	6.22812i	0.482783	−	0.262251i
$565$	5.89172	+	19.6797i	0.247867	+	0.827932i
$566$	4.86457			0.204473
$567$	−31.7350	−	25.9645i	−1.33274	−	1.09041i
$568$	−5.76765			−0.242005
$569$	1.82982	+	6.11203i	0.0767101	+	0.256230i	0.987739	−	0.156112i	$-0.0498961\pi$
$569$	1.82982	+	6.11203i	0.0767101	+	0.256230i	−0.911029	+	0.412342i	$0.864711\pi$
$570$	−0.340538	+	13.1017i	−0.0142636	+	0.548772i
$571$	10.6976	−	7.03590i	0.447679	−	0.294443i	−0.305581	−	0.952166i	$-0.598851\pi$
$571$	10.6976	−	7.03590i	0.447679	−	0.294443i	0.753260	+	0.657723i	$0.228480\pi$
$572$	−0.0321646	−	0.0745659i	−0.00134487	−	0.00311776i
$573$	24.2249	+	24.0750i	1.01201	+	1.00575i
$574$	1.12451	−	19.3071i	0.0469362	−	0.805864i
$575$	−8.52750	−	7.15542i	−0.355621	−	0.298402i
$576$	−2.39521	+	1.80637i	−0.0998002	+	0.0752656i
$577$	−11.4531	+	9.61033i	−0.476801	+	0.400083i	−0.849268	−	0.527962i	$-0.822956\pi$
$577$	−11.4531	+	9.61033i	−0.476801	+	0.400083i	0.372467	+	0.928045i	$0.378512\pi$
$578$	−22.4560	−	30.1636i	−0.934045	−	1.25464i
$579$	−4.40216	−	7.08767i	−0.182947	−	0.294554i
$580$	−0.185223	−	0.196325i	−0.00769098	−	0.00815196i
$581$	41.8253	−	9.91277i	1.73520	−	0.411251i
$582$	3.10582	+	2.44014i	0.128740	+	0.101147i
$583$	1.02999	−	2.38779i	0.0426579	−	0.0988921i
$584$	2.02908	+	11.5075i	0.0839638	+	0.476183i
$585$	−0.103430	+	0.00666841i	−0.00427632	+	0.000275705i
$586$	2.89538	−	16.4205i	0.119607	−	0.678325i
$587$	19.9375	+	13.1131i	0.822907	+	0.541235i	0.889707	−	0.456532i	$-0.150909\pi$
$587$	19.9375	+	13.1131i	0.822907	+	0.541235i	−0.0667999	+	0.997766i	$0.521279\pi$
$588$	−23.7423	−	2.00297i	−0.979115	−	0.0826010i
$589$	13.5568	−	18.2100i	0.558599	−	0.750328i
$590$	0.0327872	+	0.562935i	0.00134983	+	0.0231756i
$591$	34.1460	+	6.94019i	1.40458	+	0.285481i
$592$	7.87023	−	8.34195i	0.323464	−	0.342852i
$593$	9.43255	−	16.3377i	0.387349	−	0.670907i	−0.604743	−	0.796420i	$-0.706724\pi$
$593$	9.43255	−	16.3377i	0.387349	−	0.670907i	0.992092	+	0.125513i	$0.0400577\pi$
$594$	9.84454	+	8.59803i	0.403926	+	0.352781i
$595$	18.0139	+	31.2009i	0.738496	+	1.27911i
$596$	12.6106	+	2.98877i	0.516551	+	0.122425i
$597$	−16.9433	−	21.2921i	−0.693442	−	0.871429i
$598$	0.0833124	+	0.0418410i	0.00340690	+	0.00171101i
$599$	−29.1802	−	3.41067i	−1.19227	−	0.139356i	−0.503277	−	0.864125i	$-0.667872\pi$
$599$	−29.1802	−	3.41067i	−1.19227	−	0.139356i	−0.688992	+	0.724769i	$0.741947\pi$
$600$	6.05983	+	2.80289i	0.247392	+	0.114427i
$601$	−10.1068	+	5.07584i	−0.412266	+	0.207048i	−0.642829	−	0.766010i	$-0.722239\pi$
$601$	−10.1068	+	5.07584i	−0.412266	+	0.207048i	0.230563	+	0.973057i	$0.425943\pi$
$602$	−13.3832	+	4.87110i	−0.545460	+	0.198531i
$603$	−2.21137	−	2.60244i	−0.0900539	−	0.105979i
$604$	−9.08250	−	3.30576i	−0.369562	−	0.134509i
$605$	4.96655	−	0.580506i	0.201919	−	0.0236009i
$606$	20.7748	−	18.6038i	0.843917	−	0.755728i
$607$	−10.3296	+	34.5033i	−0.419266	+	1.40045i	0.444150	+	0.895952i	$0.353506\pi$
$607$	−10.3296	+	34.5033i	−0.419266	+	1.40045i	−0.863416	+	0.504493i	$0.831679\pi$
$608$	−2.02793	+	6.77375i	−0.0822433	+	0.274712i
$609$	1.48265	−	1.32772i	0.0600802	−	0.0538018i
$610$	−6.13644	+	0.717247i	−0.248457	+	0.0290405i
$611$	0.228531	+	0.0831785i	0.00924538	+	0.00336504i
$612$	−7.45265	+	20.8782i	−0.301256	+	0.843952i
$613$	15.2887	−	5.56462i	0.617503	−	0.224753i	−0.0142800	−	0.999898i	$-0.504546\pi$
$613$	15.2887	−	5.56462i	0.617503	−	0.224753i	0.631783	+	0.775145i	$0.282323\pi$
$614$	6.69062	−	3.36015i	0.270011	−	0.135605i
$615$	7.14146	+	3.30318i	0.287971	+	0.133197i
$616$	11.3826	+	1.33044i	0.458619	+	0.0536049i
$617$	−6.88001	−	3.45527i	−0.276979	−	0.139104i	0.304888	−	0.952388i	$-0.401381\pi$
$617$	−6.88001	−	3.45527i	−0.276979	−	0.139104i	−0.581866	+	0.813284i	$0.697677\pi$
$618$	−1.57992	−	1.98544i	−0.0635537	−	0.0798661i
$619$	−19.1219	−	4.53198i	−0.768576	−	0.182156i	−0.172419	−	0.985024i	$-0.555158\pi$
$619$	−19.1219	−	4.53198i	−0.768576	−	0.182156i	−0.596157	+	0.802868i	$0.703306\pi$
$620$	1.71797	+	2.97562i	0.0689954	+	0.119504i
$621$	−15.0026	−	0.296794i	−0.602033	−	0.0119099i
$622$	1.57183	−	2.72250i	0.0630248	−	0.109162i
$623$	−3.08249	+	3.26724i	−0.123497	+	0.130899i
$624$	−0.0547963	−	0.0111374i	−0.00219361	−	0.000445852i
$625$	−0.531041	−	9.11762i	−0.0212416	−	0.364705i
$626$	16.0848	−	21.6057i	0.642880	−	0.863537i
$627$	30.6975	+	2.58973i	1.22594	+	0.103424i
$628$	16.5018	+	10.8534i	0.658494	+	0.433098i
$629$	14.7162	−	83.4597i	0.586773	−	3.32776i
$630$	6.48316	−	13.1113i	0.258295	−	0.522366i
$631$	−1.95387	−	11.0810i	−0.0777824	−	0.441126i	−0.998682	−	0.0513258i	$-0.983655\pi$
$631$	−1.95387	−	11.0810i	−0.0777824	−	0.441126i	0.920900	−	0.389800i	$-0.127456\pi$
$632$	−0.848793	+	1.96772i	−0.0337632	+	0.0782718i
$633$	16.8133	+	13.2097i	0.668270	+	0.525038i
$634$	−8.36910	+	1.98351i	−0.332379	+	0.0787754i
$635$	0.808710	+	0.857182i	0.0320927	+	0.0340162i
$636$	−0.944744	−	1.52108i	−0.0374615	−	0.0603148i
$637$	−0.265199	−	0.356225i	−0.0105076	−	0.0141141i
$638$	−0.486004	+	0.407806i	−0.0192411	+	0.0161452i
$639$	15.9301	+	6.75463i	0.630184	+	0.267209i
$640$	−0.819786	−	0.687882i	−0.0324049	−	0.0271909i
$641$	−0.311539	+	5.34892i	−0.0123051	+	0.211270i	0.986551	+	0.163453i	$0.0522633\pi$
$641$	−0.311539	+	5.34892i	−0.0123051	+	0.211270i	−0.998856	+	0.0478165i	$0.984774\pi$
$642$	16.9667	+	16.8618i	0.669624	+	0.665481i
$643$	2.68773	+	6.23086i	0.105994	+	0.245721i	0.962956	−	0.269658i	$-0.0869105\pi$
$643$	2.68773	+	6.23086i	0.105994	+	0.245721i	−0.856963	+	0.515379i	$0.827651\pi$
$644$	−10.9922	+	7.22968i	−0.433153	+	0.284889i
$645$	0.150556	−	5.79244i	0.00592813	−	0.228077i
$646$	14.9854	+	50.0546i	0.589591	+	1.96937i
$647$	−36.3500			−1.42906			−0.714532	−	0.699602i	$-0.753361\pi$
$647$	−36.3500			−1.42906			−0.714532	+	0.699602i	$0.753361\pi$
$648$	8.73097	−	2.18407i	0.342985	−	0.0857985i
$649$	1.32544			0.0520282
$650$	0.0356914	+	0.119218i	0.00139993	+	0.00467610i
$651$	−22.2632	+	12.0935i	−0.872564	+	0.473983i
$652$	−7.45562	+	4.90364i	−0.291984	+	0.192041i
$653$	−6.20679	−	14.3889i	−0.242890	−	0.563083i	0.752543	−	0.658543i	$-0.228827\pi$
$653$	−6.20679	−	14.3889i	−0.242890	−	0.563083i	−0.995433	+	0.0954601i	$0.969568\pi$
$654$	8.63117	−	2.34144i	0.337506	−	0.0915577i
$655$	0.849140	−	14.5792i	0.0331786	−	0.569655i
$656$	3.25186	+	2.72864i	0.126964	+	0.106535i
$657$	7.87240	−	34.1596i	0.307132	−	1.33269i
$658$	−26.2910	+	22.0608i	−1.02493	+	0.860019i
$659$	13.8687	+	18.6289i	0.540247	+	0.725678i	0.985490	−	0.169732i	$-0.0542902\pi$
$659$	13.8687	+	18.6289i	0.540247	+	0.725678i	−0.445243	+	0.895410i	$0.646883\pi$
$660$	−2.20009	+	4.11081i	−0.0856385	+	0.160013i
$661$	−7.50061	−	7.95018i	−0.291740	−	0.309226i	0.564881	−	0.825172i	$-0.308922\pi$
$661$	−7.50061	−	7.95018i	−0.291740	−	0.309226i	−0.856621	+	0.515946i	$0.827440\pi$
$662$	−32.8036	+	7.77459i	−1.27495	+	0.302168i
$663$	−0.383528	+	0.153745i	−0.0148950	+	0.00597098i
$664$	−3.73692	+	8.66315i	−0.145021	+	0.336195i
$665$	−5.98633	−	33.9501i	−0.232140	−	1.31653i
$666$	−31.5068	+	13.8232i	−1.22086	+	0.535639i
$667$	0.126477	−	0.717287i	0.00489721	−	0.0277735i
$668$	14.7277	+	9.68658i	0.569833	+	0.374785i
$669$	6.65312	+	14.1529i	0.257225	+	0.547181i
$670$	0.727474	−	0.977167i	0.0281048	−	0.0377512i
$671$	0.844387	+	14.4976i	0.0325972	+	0.559672i
$672$	5.22763	−	5.91107i	0.201660	−	0.228025i
$673$	22.8015	−	24.1682i	0.878933	−	0.931615i	−0.119189	−	0.992872i	$-0.538029\pi$
$673$	22.8015	−	24.1682i	0.878933	−	0.931615i	0.998122	+	0.0612570i	$0.0195109\pi$
$674$	−8.20605	+	14.2133i	−0.316085	+	0.547475i
$675$	−13.4545	−	14.8383i	−0.517865	−	0.571126i
$676$	6.49948	+	11.2574i	0.249980	+	0.432978i
$677$	−5.32779	−	1.26271i	−0.204764	−	0.0485299i	0.126954	−	0.991909i	$-0.459480\pi$
$677$	−5.32779	−	1.26271i	−0.204764	−	0.0485299i	−0.331718	+	0.943379i	$0.607628\pi$
$678$	12.1796	−	30.9374i	0.467755	−	1.18814i
$679$	−9.28414	−	4.66267i	−0.356293	−	0.178937i
$680$	−7.85444	−	0.918052i	−0.301204	−	0.0352057i
$681$	20.6380	−	14.5465i	0.790850	−	0.557424i
$682$	7.21727	−	3.62465i	0.276363	−	0.138795i
$683$	−2.98508	+	1.08648i	−0.114221	+	0.0415730i	−0.398498	−	0.917169i	$-0.630469\pi$
$683$	−2.98508	+	1.08648i	−0.114221	+	0.0415730i	0.284277	+	0.958742i	$0.408246\pi$
$684$	13.5340	−	16.3339i	0.517484	−	0.624544i
$685$	−9.80942	−	3.57034i	−0.374799	−	0.136416i
$686$	30.5730	−	3.57347i	1.16728	−	0.136436i
$687$	−34.8161	−	11.4170i	−1.32832	−	0.435587i
$688$	0.896571	−	2.99475i	0.0341814	−	0.114174i
$689$	0.00957198	−	0.0319726i	0.000364663	−	0.00121806i
$690$	−1.09868	−	5.23878i	−0.0418260	−	0.199437i
$691$	37.7306	−	4.41008i	1.43534	−	0.167767i	0.637414	−	0.770521i	$-0.280004\pi$
$691$	37.7306	−	4.41008i	1.43534	−	0.167767i	0.797927	+	0.602754i	$0.205930\pi$
$692$	9.06601	+	3.29976i	0.344638	+	0.125438i
$693$	−29.8804	−	17.0051i	−1.13506	−	0.645970i
$694$	4.05246	−	1.47497i	0.153829	−	0.0559893i
$695$	3.50345	−	1.75950i	0.132894	−	0.0667416i
$696$	0.0394241	+	0.435068i	0.00149437	+	0.0164912i
$697$	31.1563	+	3.64165i	1.18013	+	0.137937i
$698$	9.24320	+	4.64211i	0.349860	+	0.175706i
$699$	25.2958	−	3.78550i	0.956776	−	0.143181i
$700$	−17.0886	−	4.05007i	−0.645888	−	0.153078i
$701$	8.54783	+	14.8053i	0.322847	+	0.559188i	0.981074	−	0.193632i	$-0.0620267\pi$
$701$	8.54783	+	14.8053i	0.322847	+	0.559188i	−0.658227	+	0.752819i	$0.728693\pi$
$702$	0.138303	+	0.0949343i	0.00521989	+	0.00358306i
$703$	−40.5461	+	70.2278i	−1.52922	+	2.64869i
$704$	−1.72620	+	1.82967i	−0.0650586	+	0.0689581i
$705$	−4.43316	−	13.2408i	−0.166963	−	0.498677i
$706$	−0.174200	−	2.99090i	−0.00655610	−	0.112564i
$707$	−43.8034	+	58.8382i	−1.64740	+	2.21284i
$708$	0.521156	−	0.749225i	0.0195862	−	0.0281576i
$709$	0.0964573	+	0.0634410i	0.00362253	+	0.00238258i	0.551319	−	0.834295i	$-0.314125\pi$
$709$	0.0964573	+	0.0634410i	0.00362253	+	0.00238258i	−0.547696	+	0.836677i	$0.684495\pi$
$710$	−1.07181	+	6.07851i	−0.0402242	+	0.228123i
$711$	4.64878	−	4.44075i	0.174343	−	0.166541i
$712$	−0.171206	−	0.970958i	−0.00641622	−	0.0363882i
$713$	−3.67241	+	8.51361i	−0.137533	+	0.318837i
$714$	8.27206	−	57.7213i	0.309574	−	2.16017i
$715$	−0.0845619	+	0.0200415i	−0.00316244	+	0.000749511i
$716$	−6.19446	−	6.56574i	−0.231498	−	0.245373i
$717$	−42.8533	+	1.38000i	−1.60039	+	0.0515370i
$718$	−13.6449	−	18.3282i	−0.509222	−	0.684004i
$719$	3.65249	−	3.06480i	0.136215	−	0.114298i	−0.572135	−	0.820160i	$-0.693885\pi$
$719$	3.65249	−	3.06480i	0.136215	−	0.114298i	0.708349	+	0.705862i	$0.249440\pi$
$720$	1.45863	+	2.85998i	0.0543599	+	0.106585i
$721$	5.11267	+	4.29004i	0.190406	+	0.159769i
$722$	1.80227	−	30.9437i	0.0670734	−	1.15161i
$723$	7.13483	−	26.9619i	0.265347	−	1.00272i
$724$	−5.27984	−	12.2400i	−0.196224	−	0.454898i
$725$	0.812289	−	0.534251i	0.0301676	−	0.0198416i
$726$	−6.90132	−	4.22729i	−0.256132	−	0.156890i
$727$	13.3708	+	44.6614i	0.495894	+	1.65640i	0.729432	+	0.684053i	$0.239784\pi$
$727$	13.3708	+	44.6614i	0.495894	+	1.65640i	−0.233538	+	0.972348i	$0.575030\pi$
$728$	0.147081			0.00545118
$729$	−26.6725	−	4.19269i	−0.987870	−	0.155285i
$730$	12.5048			0.462822
$731$	−6.62521	−	22.1297i	−0.245042	−	0.818498i
$732$	8.52696	+	5.22305i	0.315166	+	0.193050i
$733$	−34.5510	+	22.7246i	−1.27617	+	0.839351i	−0.992815	−	0.119663i	$-0.961818\pi$
$733$	−34.5510	+	22.7246i	−1.27617	+	0.839351i	−0.283357	+	0.959015i	$0.591448\pi$
$734$	6.82391	+	15.8196i	0.251875	+	0.583912i
$735$	−6.52296	+	24.6497i	−0.240603	+	0.909218i
$736$	0.167912	−	2.88293i	0.00618930	−	0.106266i
$737$	−2.19356	−	1.84061i	−0.0808007	−	0.0677999i
$738$	−5.78597	−	11.3447i	−0.212985	−	0.417605i
$739$	3.88648	−	3.26115i	0.142967	−	0.119963i	−0.568500	−	0.822684i	$-0.692476\pi$
$739$	3.88648	−	3.26115i	0.142967	−	0.119963i	0.711466	+	0.702720i	$0.248031\pi$
$740$	−7.32903	−	9.84460i	−0.269421	−	0.361895i
$741$	0.395171	−	0.0127256i	0.0145170	−	0.000467487i
$742$	3.23213	+	3.42586i	0.118655	+	0.125767i
$743$	6.88798	−	1.63248i	0.252696	−	0.0598900i	−0.102316	−	0.994752i	$-0.532625\pi$
$743$	6.88798	−	1.63248i	0.252696	−	0.0598900i	0.355011	+	0.934862i	$0.384477\pi$
$744$	0.788903	−	5.50485i	0.0289226	−	0.201818i
$745$	5.49330	−	12.7349i	0.201259	−	0.466570i
$746$	3.30920	+	18.7674i	0.121158	+	0.687124i
$747$	20.4669	−	19.5510i	0.748843	−	0.715332i
$748$	−3.22775	+	18.3055i	−0.118018	+	0.669314i
$749$	−52.5684	−	34.5748i	−1.92081	−	1.26334i
$750$	9.37227	−	13.4738i	0.342227	−	0.491993i
$751$	−4.27907	+	5.74779i	−0.156146	+	0.209740i	−0.873311	−	0.487163i	$-0.838032\pi$
$751$	−4.27907	+	5.74779i	−0.156146	+	0.209740i	0.717165	+	0.696903i	$0.245439\pi$
$752$	−0.438015	−	7.52044i	−0.0159728	−	0.274242i
$753$	5.08221	+	15.1794i	0.185206	+	0.553166i
$754$	−0.00558766	+	0.00592258i	−0.000203491	+	0.000215687i
$755$	−5.17173	+	8.95771i	−0.188219	+	0.326004i
$756$	−21.3611	+	10.2040i	−0.776897	+	0.371116i
$757$	5.07851	+	8.79623i	0.184581	+	0.319704i	0.943435	−	0.331556i	$-0.107574\pi$
$757$	5.07851	+	8.79623i	0.184581	+	0.319704i	−0.758854	+	0.651261i	$0.774240\pi$
$758$	35.9054	+	8.50974i	1.30414	+	0.309088i
$759$	−12.4433	+	1.86213i	−0.451663	+	0.0675910i
$760$	6.76198	+	3.39600i	0.245283	+	0.123186i
$761$	6.02575	+	0.704309i	0.218433	+	0.0255312i	0.224605	−	0.974450i	$-0.427891\pi$
$761$	6.02575	+	0.704309i	0.218433	+	0.0255312i	−0.00617237	+	0.999981i	$0.501965\pi$
$762$	−0.172131	−	1.89956i	−0.00623565	−	0.0688139i
$763$	−21.0215	+	10.5574i	−0.761028	+	0.382203i
$764$	18.5293	−	6.74411i	0.670367	−	0.243994i
$765$	20.6186	+	11.7341i	0.745466	+	0.424249i
$766$	22.4770	+	8.18096i	0.812127	+	0.295590i
$767$	0.0168959	−	0.00197485i	0.000610075	−	7.13076e-5i
$768$	0.355513	+	1.69517i	0.0128285	+	0.0611693i
$769$	−5.69257	+	19.0145i	−0.205279	+	0.685680i	0.791902	+	0.610648i	$0.209091\pi$
$769$	−5.69257	+	19.0145i	−0.205279	+	0.685680i	−0.997181	+	0.0750321i	$0.976094\pi$
$770$	3.51739	−	11.7489i	0.126758	−	0.423401i
$771$	35.0531	+	11.4948i	1.26241	+	0.413974i
$772$	−4.78455	+	0.559234i	−0.172200	+	0.0201273i
$773$	−20.1427	−	7.33134i	−0.724482	−	0.263690i	−0.0466549	−	0.998911i	$-0.514856\pi$
$773$	−20.1427	−	7.33134i	−0.724482	−	0.263690i	−0.677827	+	0.735221i	$0.737078\pi$
$774$	−5.98352	+	7.22143i	−0.215073	+	0.259569i
$775$	−11.6301	+	4.23301i	−0.417766	+	0.152054i
$776$	2.03782	−	1.02343i	0.0731536	−	0.0367391i
$777$	73.9714	−	52.1381i	2.65371	−	1.87044i
$778$	28.3935	+	3.31872i	1.01796	+	0.118982i
$779$	−26.8229	−	13.4710i	−0.961029	−	0.482647i
$780$	−0.0219205	+	0.0556800i	−0.000784879	+	0.00199367i
$781$	14.1171	+	3.34582i	0.505151	+	0.119723i
$782$	−10.6698	−	18.4806i	−0.381550	−	0.660863i
$783$	0.400629	−	1.24781i	0.0143173	−	0.0445932i
$784$	−6.87815	+	11.9133i	−0.245648	+	0.425475i
$785$	14.5049	−	15.3743i	0.517703	−	0.548733i
$786$	−15.6585	+	17.7057i	−0.558522	+	0.631541i
$787$	1.43064	+	24.5631i	0.0509967	+	0.875580i	0.922694	+	0.385534i	$0.125983\pi$
$787$	1.43064	+	24.5631i	0.0509967	+	0.875580i	−0.871697	+	0.490046i	$0.836980\pi$
$788$	12.0132	−	16.1365i	0.427953	−	0.574841i
$789$	0.316651	+	0.673595i	0.0112731	+	0.0239806i
$790$	1.91605	+	1.26020i	0.0681698	+	0.0448360i
$791$	−15.1865	+	86.1268i	−0.539969	+	3.06232i
$792$	6.91048	−	3.03189i	0.245553	−	0.107733i
$793$	0.0323644	+	0.183548i	0.00114929	+	0.00651797i
$794$	−8.62813	+	20.0023i	−0.306201	+	0.709854i
$795$	−1.77862	+	0.713000i	−0.0630813	+	0.0252875i
$796$	−15.2867	+	3.62302i	−0.541823	+	0.128414i
$797$	−19.4096	−	20.5730i	−0.687525	−	0.728734i	0.285768	−	0.958299i	$-0.407751\pi$
$797$	−19.4096	−	20.5730i	−0.687525	−	0.728734i	−0.973293	+	0.229565i	$0.926270\pi$
$798$	−26.3284	+	49.1938i	−0.932014	+	1.74144i
$799$	−33.2417	−	44.6513i	−1.17601	−	1.57965i
$800$	2.95292	−	2.47780i	0.104402	−	0.0876034i
$801$	−0.664244	+	2.88226i	−0.0234699	+	0.101840i
$802$	12.2167	+	10.2510i	0.431386	+	0.361976i
$803$	1.70905	−	29.3432i	0.0603109	−	1.03550i
$804$	−1.90293	+	0.516221i	−0.0671110	+	0.0182057i
$805$	5.57666	+	12.9281i	0.196551	+	0.455657i
$806$	0.0866006	−	0.0569581i	0.00305037	−	0.00200626i
$807$	0.861504	−	0.467975i	0.0303264	−	0.0164735i
$808$	−4.61772	−	15.4242i	−0.162451	−	0.542623i
$809$	−18.4006			−0.646932			−0.323466	−	0.946240i	$-0.604848\pi$
$809$	−18.4006			−0.646932			−0.323466	+	0.946240i	$0.604848\pi$
$810$	−0.679307	−	9.60741i	−0.0238684	−	0.337570i
$811$	4.70105			0.165076			0.0825380	−	0.996588i	$-0.473697\pi$
$811$	4.70105			0.165076			0.0825380	+	0.996588i	$0.473697\pi$
$812$	−0.329557	−	1.10080i	−0.0115652	−	0.0386305i
$813$	−1.06111	+	40.8249i	−0.0372149	+	1.43179i
$814$	−24.1026	+	15.8526i	−0.844797	+	0.555632i
$815$	3.78245	+	8.76870i	0.132493	+	0.307154i
$816$	9.07829	+	9.02213i	0.317804	+	0.315838i
$817$	−1.28523	+	22.0665i	−0.0449644	+	0.772009i
$818$	−4.98901	−	4.18628i	−0.174437	−	0.146370i
$819$	−0.406233	−	0.172250i	−0.0141949	−	0.00601889i
$820$	3.48000	−	2.92006i	0.121527	−	0.101973i
$821$	−14.7422	−	19.8022i	−0.514507	−	0.691103i	0.466622	−	0.884457i	$-0.345471\pi$
$821$	−14.7422	−	19.8022i	−0.514507	−	0.691103i	−0.981129	+	0.193354i	$0.938064\pi$
$822$	8.91433	+	14.3525i	0.310923	+	0.500600i
$823$	−22.8446	−	24.2138i	−0.796312	−	0.844042i	0.194272	−	0.980948i	$-0.437766\pi$
$823$	−22.8446	−	24.2138i	−0.796312	−	0.844042i	−0.990584	+	0.136906i	$0.956284\pi$
$824$	−1.42545	+	0.337838i	−0.0496579	+	0.0117691i
$825$	−13.2063	−	10.3758i	−0.459785	−	0.361238i
$826$	−0.950833	+	2.20428i	−0.0330837	+	0.0766967i
$827$	5.83783	+	33.1080i	0.203001	+	1.15128i	0.900554	+	0.434744i	$0.143161\pi$
$827$	5.83783	+	33.1080i	0.203001	+	1.15128i	−0.697553	+	0.716533i	$0.745728\pi$
$828$	−3.84003	+	7.76592i	−0.133450	+	0.269884i
$829$	−8.20429	+	46.5288i	−0.284947	+	1.61601i	0.420529	+	0.907279i	$0.361845\pi$
$829$	−8.20429	+	46.5288i	−0.284947	+	1.61601i	−0.705475	+	0.708734i	$0.749266\pi$
$830$	8.43563	+	5.54820i	0.292805	+	0.192581i
$831$	−10.0078	−	0.844290i	−0.347168	−	0.0292881i
$832$	−0.0192784	+	0.0258954i	−0.000668358	+	0.000897760i
$833$	5.91055	+	101.480i	0.204788	+	3.51608i
$834$	−6.21815	−	1.26384i	−0.215317	−	0.0437632i
$835$	12.9455	−	13.7214i	0.447998	−	0.474850i
$836$	8.89309	−	15.4033i	0.307574	−	0.532734i
$837$	−8.62578	+	14.2803i	−0.298150	+	0.493600i
$838$	12.4283	+	21.5264i	0.429328	+	0.743618i
$839$	38.2661	+	9.06924i	1.32109	+	0.313105i	0.829884	−	0.557936i	$-0.188407\pi$
$839$	38.2661	+	9.06924i	1.32109	+	0.313105i	0.491210	+	0.871041i	$0.336555\pi$
$840$	−5.25821	−	6.60784i	−0.181425	−	0.227992i
$841$	−25.8585	−	12.9866i	−0.891672	−	0.447815i
$842$	−3.40836	−	0.398380i	−0.117460	−	0.0137291i
$843$	22.7405	+	10.5183i	0.783226	+	0.362270i
$844$	11.0317	−	5.54035i	0.379728	−	0.190707i
$845$	13.0720	−	4.75781i	0.449689	−	0.163674i
$846$	−7.59756	+	21.2842i	−0.261210	+	0.731765i
$847$	20.0039	+	7.28083i	0.687343	+	0.250172i
$848$	−1.02681	+	0.120017i	−0.0352608	+	0.00412140i
$849$	−6.27678	+	5.62086i	−0.215419	+	0.192907i
$850$	8.16953	−	27.2881i	0.280213	−	0.935976i
$851$	9.49869	−	31.7278i	0.325611	−	1.08762i
$852$	7.44204	−	6.66435i	0.254960	−	0.228317i
$853$	25.5084	−	2.98150i	0.873390	−	0.102085i	0.332425	−	0.943130i	$-0.392133\pi$
$853$	25.5084	−	2.98150i	0.873390	−	0.102085i	0.540965	+	0.841045i	$0.318059\pi$
$854$	−24.7159	−	8.99587i	−0.845762	−	0.307832i
$855$	−14.6993	−	17.2987i	−0.502704	−	0.591605i
$856$	12.9776	−	4.72347i	0.443566	−	0.161445i
$857$	37.3756	−	18.7707i	1.27673	−	0.641196i	0.324297	−	0.945955i	$-0.394872\pi$
$857$	37.3756	−	18.7707i	1.27673	−	0.641196i	0.952429	+	0.304759i	$0.0985759\pi$
$858$	0.127661	+	0.0590476i	0.00435827	+	0.00201585i
$859$	−22.4579	−	2.62495i	−0.766252	−	0.0895620i	−0.276018	−	0.961153i	$-0.589015\pi$
$859$	−22.4579	−	2.62495i	−0.766252	−	0.0895620i	−0.490235	+	0.871591i	$0.663089\pi$
$860$	−2.98955	−	1.50141i	−0.101943	−	0.0511977i
$861$	20.8578	+	26.2115i	0.710833	+	0.893284i
$862$	2.72023	+	0.644707i	0.0926516	+	0.0219588i
$863$	−27.1694	−	47.0588i	−0.924857	−	1.60190i	−0.791792	−	0.610791i	$-0.790851\pi$
$863$	−27.1694	−	47.0588i	−0.924857	−	1.60190i	−0.133065	−	0.991107i	$-0.542482\pi$
$864$	1.00334	−	5.09836i	0.0341343	−	0.173450i
$865$	5.16235	−	8.94145i	0.175525	−	0.304018i
$866$	−12.2533	+	12.9877i	−0.416383	+	0.441340i
$867$	63.8282	+	12.9731i	2.16772	+	0.440589i
$868$	0.850522	+	14.6029i	0.0288686	+	0.495655i
$869$	3.21901	−	4.32389i	0.109198	−	0.146678i
$870$	0.465843	+	0.0392998i	0.0157935	+	0.00133239i
$871$	−0.0307045	−	0.0201947i	−0.00104038	−	0.000684270i
$872$	0.896601	−	5.08487i	0.0303627	−	0.172196i
$873$	−6.82697	+	0.440152i	−0.231058	+	0.0148969i
$874$	3.54575	+	20.1089i	0.119937	+	0.680195i
$875$	−17.0994	+	39.6409i	−0.578066	+	1.34011i
$876$	−15.9147	−	12.5036i	−0.537707	−	0.422458i
$877$	39.9652	−	9.47192i	1.34953	−	0.319844i	0.508606	−	0.861000i	$-0.330161\pi$
$877$	39.9652	−	9.47192i	1.34953	−	0.319844i	0.840922	+	0.541156i	$0.182013\pi$
$878$	10.8133	+	11.4614i	0.364931	+	0.386804i
$879$	15.2375	+	24.5330i	0.513947	+	0.827478i
$880$	1.60750	+	2.15925i	0.0541888	+	0.0727882i
$881$	−38.4069	+	32.2272i	−1.29396	+	1.08576i	−0.302806	+	0.953052i	$0.597924\pi$
$881$	−38.4069	+	32.2272i	−1.29396	+	1.08576i	−0.991155	+	0.132710i	$0.957632\pi$
$882$	32.9492	−	24.8490i	1.10946	−	0.836711i
$883$	−41.7762	−	35.0544i	−1.40588	−	1.17967i	−0.958416	−	0.285374i	$-0.907882\pi$
$883$	−41.7762	−	35.0544i	−1.40588	−	1.17967i	−0.447465	−	0.894301i	$-0.647673\pi$
$884$	−0.0138710	+	0.238156i	−0.000466532	+	0.00801004i
$885$	−0.692759	−	0.688473i	−0.0232868	−	0.0231428i
$886$	−2.77897	−	6.44237i	−0.0933612	−	0.216436i
$887$	33.9785	−	22.3480i	1.14089	−	0.750373i	0.168953	−	0.985624i	$-0.445962\pi$
$887$	33.9785	−	22.3480i	1.14089	−	0.750373i	0.971935	+	0.235251i	$0.0755911\pi$
$888$	−0.516132	+	19.8575i	−0.0173203	+	0.666374i
$889$	1.43889	+	4.80623i	0.0482589	+	0.161196i
$890$	−1.05510			−0.0353672
$891$	−22.6372	+	0.280975i	−0.758376	+	0.00941300i
$892$	9.02898			0.302313
$893$	15.2767	+	51.0279i	0.511217	+	1.70758i
$894$	−19.7250	+	10.7148i	−0.659703	+	0.358355i
$895$	−8.07074	+	5.30821i	−0.269775	+	0.177434i
$896$	−1.80450	−	4.18331i	−0.0602842	−	0.139755i
$897$	−0.155845	+	0.0422771i	−0.00520350	+	0.00141159i
$898$	−2.32998	+	40.0042i	−0.0777524	+	1.33496i
$899$	−0.620334	−	0.520522i	−0.0206893	−	0.0173604i
$900$	−11.0577	+	3.38537i	−0.368590	+	0.112846i
$901$	−5.85202	+	4.91042i	−0.194959	+	0.163590i
$902$	−6.37649	−	8.56512i	−0.212314	−	0.285187i
$903$	11.6401	−	21.7491i	0.387357	−	0.723766i
$904$	−13.1731	−	13.9627i	−0.438131	−	0.464392i
$905$	−13.8809	+	3.28983i	−0.461417	+	0.109358i
$906$	15.5389	−	6.22911i	0.516246	−	0.206948i
$907$	14.6960	−	34.0691i	0.487972	−	1.13125i	−0.479334	−	0.877632i	$-0.659122\pi$
$907$	14.6960	−	34.0691i	0.487972	−	1.13125i	0.967306	−	0.253613i	$-0.0816189\pi$
$908$	−2.53139	−	14.3562i	−0.0840072	−	0.476429i
$909$	−5.30969	+	48.0092i	−0.176111	+	1.59236i
$910$	0.0273321	−	0.155008i	0.000906050	−	0.00513847i
$911$	13.7973	+	9.07464i	0.457126	+	0.300656i	0.757109	−	0.653288i	$-0.226611\pi$
$911$	13.7973	+	9.07464i	0.457126	+	0.300656i	−0.299984	+	0.953944i	$0.596981\pi$
$912$	−5.21021	−	11.0834i	−0.172527	−	0.367009i
$913$	14.1721	−	19.0365i	0.469029	−	0.630015i
$914$	−1.18857	−	20.4069i	−0.0393144	−	0.675001i
$915$	7.08913	−	8.01594i	0.234359	−	0.264999i
$916$	−14.5169	+	15.3871i	−0.479653	+	0.508403i
$917$	31.0861	−	53.8427i	1.02655	−	1.77804i
$918$	−14.5079	−	35.5506i	−0.478833	−	1.17335i
$919$	−19.2468	−	33.3365i	−0.634895	−	1.09967i	−0.986537	−	0.163536i	$-0.947710\pi$
$919$	−19.2468	−	33.3365i	−0.634895	−	1.09967i	0.351642	−	0.936134i	$-0.385623\pi$
$920$	−3.00711	−	0.712698i	−0.0991414	−	0.0234969i
$921$	−4.75039	+	12.0664i	−0.156531	+	0.397602i
$922$	−14.4072	−	7.23555i	−0.474475	−	0.238290i
$923$	0.184941	+	0.0216165i	0.00608742	+	0.000711517i
$924$	−16.2244	+	11.4356i	−0.533743	+	0.376204i
$925$	39.5064	−	19.8409i	1.29896	−	0.652364i
$926$	3.55342	−	1.29334i	0.116773	−	0.0425017i
$927$	4.33269	+	0.736278i	0.142304	+	0.0241825i
$928$	0.237005	+	0.0862628i	0.00778008	+	0.00283172i
$929$	−38.7238	+	4.52616i	−1.27049	+	0.148498i	−0.724487	−	0.689288i	$-0.757923\pi$
$929$	−38.7238	+	4.52616i	−1.27049	+	0.148498i	−0.545998	+	0.837787i	$0.683849\pi$
$930$	−5.65494	−	1.85439i	−0.185433	−	0.0608079i
$931$	27.8968	−	93.1818i	0.914281	−	3.05391i
$932$	4.23528	−	14.1468i	0.138731	−	0.463394i
$933$	1.11761	+	5.32906i	0.0365891	+	0.174466i
$934$	4.93021	−	0.576259i	0.161321	−	0.0188558i
$935$	18.6923	+	6.80343i	0.611302	+	0.222496i
$936$	0.0835730	−	0.0489449i	0.00273167	−	0.00159981i
$937$	41.0334	−	14.9349i	1.34050	−	0.487903i	0.430531	−	0.902576i	$-0.358326\pi$
$937$	41.0334	−	14.9349i	1.34050	−	0.487903i	0.909971	+	0.414673i	$0.136104\pi$
$938$	4.63463	−	2.32760i	0.151326	−	0.0759988i
$939$	4.21034	+	46.4635i	0.137399	+	1.51628i
$940$	−8.00716	−	0.935903i	−0.261165	−	0.0305258i
$941$	31.5186	+	15.8293i	1.02748	+	0.516019i	0.880961	−	0.473189i	$-0.156897\pi$
$941$	31.5186	+	15.8293i	1.02748	+	0.516019i	0.146517	+	0.989208i	$0.453194\pi$
$942$	−33.8332	+	5.06311i	−1.10234	+	0.164965i
$943$	11.9283	+	2.82707i	0.388440	+	0.0920621i
$944$	−0.263461	−	0.456328i	−0.00857493	−	0.0148522i
$945$	6.78442	+	24.4087i	0.220697	+	0.794014i
$946$	−3.93174	+	6.80997i	−0.127832	+	0.221411i
$947$	−7.62372	+	8.08067i	−0.247738	+	0.262587i	−0.839295	−	0.543676i	$-0.817032\pi$
$947$	−7.62372	+	8.08067i	−0.247738	+	0.262587i	0.591557	+	0.806263i	$0.298513\pi$
$948$	−1.17844	−	3.51972i	−0.0382740	−	0.114315i
$949$	−0.0219341	−	0.376595i	−0.000712012	−	0.0122248i
$950$	−16.2763	+	21.8629i	−0.528074	+	0.709326i
$951$	8.50681	−	12.2296i	0.275852	−	0.396571i
$952$	−28.1274	−	18.4997i	−0.911615	−	0.599579i
$953$	4.54093	−	25.7529i	0.147095	−	0.834218i	−0.818566	−	0.574413i	$-0.805230\pi$
$953$	4.54093	−	25.7529i	0.147095	−	0.834218i	0.965661	−	0.259806i	$-0.0836585\pi$
$954$	2.97657	+	0.871037i	0.0963701	+	0.0282009i
$955$	−3.66429	−	20.7812i	−0.118574	−	0.672465i
$956$	−9.80464	+	22.7297i	−0.317105	+	0.735132i
$957$	0.155887	−	1.08776i	0.00503911	−	0.0351622i
$958$	20.7641	−	4.92119i	0.670859	−	0.158997i
$959$	−30.4974	−	32.3254i	−0.984813	−	1.04384i
$960$	1.85260	−	0.0596590i	0.0597925	−	0.00192549i
$961$	−12.3561	−	16.5971i	−0.398583	−	0.535389i
$962$	−0.283626	+	0.237990i	−0.00914445	+	0.00767311i
$963$	−41.3756	−	2.15231i	−1.33331	−	0.0693571i
$964$	−12.3351	−	10.3503i	−0.397286	−	0.333362i
$965$	−0.299741	+	5.14635i	−0.00964899	+	0.165667i
$966$	5.82963	−	22.0297i	0.187565	−	0.708793i
$967$	11.7699	+	27.2858i	0.378496	+	0.877452i	0.995871	+	0.0907829i	$0.0289369\pi$
$967$	11.7699	+	27.2858i	0.378496	+	0.877452i	−0.617375	+	0.786669i	$0.711804\pi$
$968$	−3.90386	+	2.56761i	−0.125475	+	0.0825261i
$969$	−77.1723	−	47.2707i	−2.47913	−	1.51855i
$970$	−0.699904	−	2.33784i	−0.0224726	−	0.0750636i
$971$	−16.7630			−0.537951			−0.268975	−	0.963147i	$-0.586685\pi$
$971$	−16.7630			−0.537951			−0.268975	+	0.963147i	$0.586685\pi$
$972$	−8.74200	+	12.9065i	−0.280400	+	0.413976i
$973$	16.6904			0.535068
$974$	−1.38232	−	4.61728i	−0.0442924	−	0.147947i
$975$	−0.183805	−	0.112587i	−0.00588647	−	0.00360566i
$976$	4.82343	−	3.17242i	0.154394	−	0.101547i
$977$	−16.8901	−	39.1557i	−0.540363	−	1.25270i	−0.941602	−	0.336729i	$-0.890679\pi$
$977$	−16.8901	−	39.1557i	−0.540363	−	1.25270i	0.401239	−	0.915974i	$-0.368580\pi$
$978$	3.95403	−	14.9419i	0.126436	−	0.477790i
$979$	−0.144203	+	2.47587i	−0.00460875	+	0.0791291i
$980$	11.2772	+	9.46272i	0.360238	+	0.302276i
$981$	−8.43139	+	12.9942i	−0.269194	+	0.414874i
$982$	4.96461	−	4.16580i	0.158427	−	0.132936i
$983$	23.0934	+	31.0198i	0.736566	+	0.989379i	0.999697	+	0.0246192i	$0.00783732\pi$
$983$	23.0934	+	31.0198i	0.736566	+	0.989379i	−0.263131	+	0.964760i	$0.584755\pi$
$984$	−7.34875	+	0.236650i	−0.234270	+	0.00754414i
$985$	−14.7738	−	15.6594i	−0.470734	−	0.498948i
$986$	1.81351	−	0.429810i	0.0577539	−	0.0136879i
$987$	8.43291	−	58.8436i	0.268422	−	1.87301i
$988$	0.0904133	−	0.209601i	0.00287643	−	0.00666831i
$989$	−1.56762	−	8.89040i	−0.0498473	−	0.282698i
$990$	−1.91112	−	7.84635i	−0.0607394	−	0.249373i
$991$	5.83166	−	33.0730i	0.185249	−	1.05060i	−0.740387	−	0.672181i	$-0.765358\pi$
$991$	5.83166	−	33.0730i	0.185249	−	1.05060i	0.925635	−	0.378416i	$-0.123531\pi$
$992$	−2.68250	−	1.76431i	−0.0851694	−	0.0560168i
$993$	33.3434	−	47.9351i	1.05812	−	1.52118i
$994$	−15.6915	+	21.0773i	−0.497704	+	0.668532i
$995$	0.977551	+	16.7839i	0.0309904	+	0.532085i
$996$	−5.18823	−	15.4960i	−0.164396	−	0.491010i
$997$	1.34392	−	1.42447i	0.0425624	−	0.0451135i	−0.705743	−	0.708468i	$-0.749386\pi$
$997$	1.34392	−	1.42447i	0.0425624	−	0.0451135i	0.748305	+	0.663355i	$0.230868\pi$
$998$	8.87620	−	15.3740i	0.280971	−	0.486657i
$999$	24.6811	−	54.2413i	0.780875	−	1.71612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.43.1	✓	72
3.2	odd	2		486.2.g.a.289.1		72
81.32	odd	54		486.2.g.a.37.1		72
81.49	even	27	inner	162.2.g.a.49.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.43.1	✓	72	1.1	even	1	trivial
162.2.g.a.49.1	yes	72	81.49	even	27	inner
486.2.g.a.37.1		72	81.32	odd	54
486.2.g.a.289.1		72	3.2	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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.286803 + 0.957990i) q^{2} +(-1.47699 - 0.904708i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.423867 + 0.982634i) q^{5} +(0.443094 - 1.67442i) q^{6} +(-0.264903 + 4.54820i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(1.36301 + 2.67249i) q^{9} +O(q^{10})\)	\(q+(0.286803 + 0.957990i) q^{2} +(-1.47699 - 0.904708i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.423867 + 0.982634i) q^{5} +(0.443094 - 1.67442i) q^{6} +(-0.264903 + 4.54820i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(1.36301 + 2.67249i) q^{9} +(-0.819786 + 0.687882i) q^{10} +(1.50212 + 2.01769i) q^{11} +(1.73115 - 0.0557480i) q^{12} +(0.0221543 + 0.0234822i) q^{13} +(-4.43310 + 1.05066i) q^{14} +(0.262948 - 1.83482i) q^{15} +(0.396080 - 0.918216i) q^{16} +(-1.28317 - 7.27724i) q^{17} +(-2.16930 + 2.07223i) q^{18} +(-1.22783 + 6.96338i) q^{19} +(-0.894102 - 0.588060i) q^{20} +(4.50605 - 6.47800i) q^{21} +(-1.50212 + 2.01769i) q^{22} +(-0.167912 - 2.88293i) q^{23} +(0.549906 + 1.64244i) q^{24} +(2.64530 - 2.80386i) q^{25} +(-0.0161418 + 0.0279584i) q^{26} +(0.404671 - 5.18037i) q^{27} +(-2.27795 - 3.94553i) q^{28} +(0.245417 + 0.0581649i) q^{29} +(1.83315 - 0.274330i) q^{30} +(-2.86918 - 1.44096i) q^{31} +(0.993238 + 0.116093i) q^{32} +(-0.393192 - 4.33909i) q^{33} +(6.60350 - 3.31640i) q^{34} +(-4.58150 + 1.66753i) q^{35} +(-2.60733 - 1.48385i) q^{36} +(10.7770 + 3.92249i) q^{37} +(-7.02299 + 0.820869i) q^{38} +(-0.0114772 - 0.0547262i) q^{39} +(0.306924 - 1.02520i) q^{40} +(-1.21748 + 4.06667i) q^{41} +(7.49820 + 2.45884i) q^{42} +(3.10495 - 0.362916i) q^{43} +(-2.36374 - 0.860332i) q^{44} +(-2.04835 + 2.47212i) q^{45} +(2.71366 - 0.987691i) q^{46} +(6.73190 - 3.38089i) q^{47} +(-1.41572 + 0.997861i) q^{48} +(-13.6633 - 1.59701i) q^{49} +(3.44475 + 1.73002i) q^{50} +(-4.68853 + 11.9093i) q^{51} +(-0.0314133 - 0.00744510i) q^{52} +(-0.516900 - 0.895297i) q^{53} +(5.07880 - 1.09808i) q^{54} +(-1.34596 + 2.33126i) q^{55} +(3.12645 - 3.31385i) q^{56} +(8.11332 - 9.17402i) q^{57} +(0.0146650 + 0.251789i) q^{58} +(0.314656 - 0.422657i) q^{59} +(0.788558 + 1.67746i) q^{60} +(4.82343 + 3.17242i) q^{61} +(0.557532 - 3.16192i) q^{62} +(-12.5161 + 5.49129i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-0.0136839 + 0.0317229i) q^{65} +(4.04404 - 1.62114i) q^{66} +(-1.10768 + 0.262525i) q^{67} +(5.07098 + 5.37493i) q^{68} +(-2.36020 + 4.40997i) q^{69} +(-2.91146 - 3.91078i) q^{70} +(4.41828 - 3.70738i) q^{71} +(0.673719 - 2.92337i) q^{72} +(-8.95122 - 7.51097i) q^{73} +(-0.666840 + 11.4492i) q^{74} +(-6.44376 + 1.74805i) q^{75} +(-2.80060 - 6.49252i) q^{76} +(-9.57479 + 6.29744i) q^{77} +(0.0491354 - 0.0266907i) q^{78} +(-0.614615 - 2.05296i) q^{79} +1.07016 q^{80} +(-5.28442 + 7.28526i) q^{81} -4.24500 q^{82} +(-2.70592 - 9.03840i) q^{83} +(-0.205034 + 7.88840i) q^{84} +(6.60696 - 4.34547i) q^{85} +(1.23818 + 2.87042i) q^{86} +(-0.309857 - 0.307940i) q^{87} +(0.146260 - 2.51119i) q^{88} +(0.755271 + 0.633748i) q^{89} +(-2.95574 - 1.25328i) q^{90} +(-0.112670 + 0.0945417i) q^{91} +(1.72448 + 2.31638i) q^{92} +(2.93412 + 4.72406i) q^{93} +(5.16958 + 5.47944i) q^{94} +(-7.36288 + 1.74504i) q^{95} +(-1.36197 - 1.07006i) q^{96} +(-0.903213 + 2.09388i) q^{97} +(-2.38876 - 13.5473i) q^{98} +(-3.34487 + 6.76453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

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