LMFDB - Embedded newform 69.2.e.a.52.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			52.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	69.52
Dual form			69.2.e.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.662317 + 1.45027i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.354905 - 0.409583i) q^{4} +(-0.438384 + 0.281733i) q^{5} +(-1.04408 + 1.20493i) q^{6} +(0.188515 - 1.31115i) q^{7} +(-2.23047 + 0.654925i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.662317 + 1.45027i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.354905 - 0.409583i) q^{4} +(-0.438384 + 0.281733i) q^{5} +(-1.04408 + 1.20493i) q^{6} +(0.188515 - 1.31115i) q^{7} +(-2.23047 + 0.654925i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.118239 - 0.822373i) q^{10} +(0.0950085 + 0.208040i) q^{11} +(-0.225136 - 0.492980i) q^{12} +(-0.382075 - 2.65739i) q^{13} +(1.77667 + 1.14180i) q^{14} +(-0.500000 + 0.146813i) q^{15} +(0.681716 - 4.74144i) q^{16} +(3.83307 - 4.42360i) q^{17} +(-1.34125 + 0.861971i) q^{18} +(1.30463 + 1.50563i) q^{19} +(0.270978 + 0.0795663i) q^{20} +(0.550273 - 1.20493i) q^{21} -0.364640 q^{22} +(-0.745229 - 4.73758i) q^{23} -2.32463 q^{24} +(-1.96427 + 4.30115i) q^{25} +(4.10700 + 1.20592i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-0.603930 + 0.388122i) q^{28} +(-4.19353 + 4.83960i) q^{29} +(0.118239 - 0.822373i) q^{30} +(-9.52067 + 2.79552i) q^{31} +(2.51365 + 1.61543i) q^{32} +(0.0325485 + 0.226380i) q^{33} +(3.87672 + 8.48882i) q^{34} +(0.286752 + 0.627899i) q^{35} +(-0.0771283 - 0.536439i) q^{36} +(7.40250 + 4.75730i) q^{37} +(-3.04765 + 0.894870i) q^{38} +(0.382075 - 2.65739i) q^{39} +(0.793290 - 0.915505i) q^{40} +(0.614669 - 0.395023i) q^{41} +(1.38302 + 1.59609i) q^{42} +(-9.98718 - 2.93250i) q^{43} +(0.0514904 - 0.112748i) q^{44} -0.521109 q^{45} +(7.36436 + 2.05699i) q^{46} -2.04380 q^{47} +(1.98992 - 4.35731i) q^{48} +(5.03287 + 1.47778i) q^{49} +(-4.93687 - 5.69745i) q^{50} +(4.92408 - 3.16451i) q^{51} +(-0.952821 + 1.09961i) q^{52} +(0.955435 - 6.64520i) q^{53} +(-1.52977 + 0.449181i) q^{54} +(-0.100262 - 0.0644343i) q^{55} +(0.438229 + 3.04795i) q^{56} +(0.827602 + 1.81219i) q^{57} +(-4.24128 - 9.28712i) q^{58} +(0.928393 + 6.45712i) q^{59} +(0.237585 + 0.152687i) q^{60} +(2.99298 - 0.878817i) q^{61} +(2.25144 - 15.6591i) q^{62} +(0.867451 - 1.00109i) q^{63} +(4.05189 - 2.60399i) q^{64} +(0.916170 + 1.05732i) q^{65} +(-0.349869 - 0.102731i) q^{66} +(-4.63685 + 10.1533i) q^{67} -3.17221 q^{68} +(0.619688 - 4.75563i) q^{69} -1.10055 q^{70} +(-2.37142 + 5.19268i) q^{71} +(-2.23047 - 0.654925i) q^{72} +(-1.53321 - 1.76941i) q^{73} +(-11.8022 + 7.58480i) q^{74} +(-3.09647 + 3.57352i) q^{75} +(0.153657 - 1.06871i) q^{76} +(0.290682 - 0.0853519i) q^{77} +(3.60089 + 2.31415i) q^{78} +(-1.38723 - 9.64839i) q^{79} +(1.03696 + 2.27063i) q^{80} +(0.415415 + 0.909632i) q^{81} +(0.165786 + 1.15307i) q^{82} +(-0.303301 - 0.194920i) q^{83} +(-0.688813 + 0.202254i) q^{84} +(-0.434086 + 3.01914i) q^{85} +(10.8676 - 12.5419i) q^{86} +(-5.38714 + 3.46210i) q^{87} +(-0.348164 - 0.401803i) q^{88} +(14.2049 + 4.17094i) q^{89} +(0.345139 - 0.755750i) q^{90} -3.55627 q^{91} +(-1.67594 + 1.98662i) q^{92} -9.92260 q^{93} +(1.35364 - 2.96407i) q^{94} +(-0.996114 - 0.292486i) q^{95} +(1.95671 + 2.25817i) q^{96} +(4.02823 - 2.58879i) q^{97} +(-5.47655 + 6.32027i) q^{98} +(-0.0325485 + 0.226380i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9 - 2 * q^10 + 7 * q^11 + 14 * q^12 - 30 * q^13 + q^14 - 5 * q^15 + 12 * q^16 - 2 * q^17 - 4 * q^18 + 10 * q^19 + 4 * q^20 - 3 * q^21 + 6 * q^22 - q^23 - 18 * q^24 + 24 * q^25 + q^26 + q^27 + 9 * q^28 - 14 * q^29 + 2 * q^30 - 28 * q^31 + 23 * q^32 - 7 * q^33 - 8 * q^34 - 4 * q^35 - 3 * q^36 + 19 * q^37 - 15 * q^38 + 30 * q^39 - 13 * q^40 + 19 * q^41 + 21 * q^42 - 24 * q^43 + 54 * q^44 - 6 * q^45 + 18 * q^46 + 26 * q^47 + 10 * q^48 - 13 * q^49 - 36 * q^50 + 24 * q^51 - 57 * q^52 - q^53 + 4 * q^54 - 24 * q^55 - 10 * q^56 + q^57 + 10 * q^58 + 2 * q^59 + 7 * q^60 + 30 * q^61 - 24 * q^62 - 8 * q^63 + 13 * q^64 - 4 * q^65 - 28 * q^66 + 4 * q^67 - 50 * q^68 + q^69 + 6 * q^70 - 14 * q^71 - 15 * q^72 - 26 * q^73 - 12 * q^74 - 13 * q^75 + 19 * q^76 - 43 * q^77 + 10 * q^78 + 20 * q^79 - 5 * q^80 - q^81 + 10 * q^82 + 18 * q^83 - 42 * q^84 + 21 * q^85 + 14 * q^86 - 8 * q^87 - 38 * q^88 - 5 * q^89 + 9 * q^90 + 46 * q^91 + 52 * q^92 - 16 * q^93 - 6 * q^94 + 5 * q^95 - q^96 + 15 * q^97 + 58 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$

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 $

$2$	−0.662317	+	1.45027i	−0.468329	+	1.02550i	0.517180	+	0.855877i	$0.326982\pi$
$2$	−0.662317	+	1.45027i	−0.468329	+	1.02550i	−0.985509	+	0.169621i	$0.945746\pi$
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$4$	−0.354905	−	0.409583i	−0.177453	−	0.204791i
$5$	−0.438384	+	0.281733i	−0.196051	+	0.125995i	−0.634984	−	0.772526i	$-0.718993\pi$
$5$	−0.438384	+	0.281733i	−0.196051	+	0.125995i	0.438932	+	0.898520i	$0.355357\pi$
$6$	−1.04408	+	1.20493i	−0.426243	+	0.491911i
$7$	0.188515	−	1.31115i	0.0712520	−	0.495569i	−0.922679	−	0.385568i	$-0.874006\pi$
$7$	0.188515	−	1.31115i	0.0712520	−	0.495569i	0.993931	−	0.110001i	$-0.0350854\pi$
$8$	−2.23047	+	0.654925i	−0.788590	+	0.231551i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.118239	−	0.822373i	−0.0373906	−	0.260057i
$11$	0.0950085	+	0.208040i	0.0286461	+	0.0627263i	0.923414	−	0.383805i	$-0.125386\pi$
$11$	0.0950085	+	0.208040i	0.0286461	+	0.0627263i	−0.894768	+	0.446531i	$0.852659\pi$
$12$	−0.225136	−	0.492980i	−0.0649913	−	0.142311i
$13$	−0.382075	−	2.65739i	−0.105969	−	0.737028i	−0.971649	−	0.236430i	$-0.924023\pi$
$13$	−0.382075	−	2.65739i	−0.105969	−	0.737028i	0.865680	−	0.500598i	$-0.166887\pi$
$14$	1.77667	+	1.14180i	0.474835	+	0.305158i
$15$	−0.500000	+	0.146813i	−0.129099	+	0.0379070i
$16$	0.681716	−	4.74144i	0.170429	−	1.18536i
$17$	3.83307	−	4.42360i	0.929656	−	1.07288i	−0.0675154	−	0.997718i	$-0.521507\pi$
$17$	3.83307	−	4.42360i	0.929656	−	1.07288i	0.997171	−	0.0751620i	$-0.0239474\pi$
$18$	−1.34125	+	0.861971i	−0.316136	+	0.203169i
$19$	1.30463	+	1.50563i	0.299303	+	0.345414i	0.885403	−	0.464825i	$-0.153883\pi$
$19$	1.30463	+	1.50563i	0.299303	+	0.345414i	−0.586100	+	0.810239i	$0.699337\pi$
$20$	0.270978	+	0.0795663i	0.0605925	+	0.0177916i
$21$	0.550273	−	1.20493i	0.120079	−	0.262937i
$22$	−0.364640			−0.0777415
$23$	−0.745229	−	4.73758i	−0.155391	−	0.987853i
$23$	−0.745229	−	4.73758i	−0.155391	−	0.987853i
$24$	−2.32463			−0.474514
$25$	−1.96427	+	4.30115i	−0.392853	+	0.860229i
$26$	4.10700	+	1.20592i	0.805449	+	0.236501i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	−0.603930	+	0.388122i	−0.114132	+	0.0733482i
$29$	−4.19353	+	4.83960i	−0.778720	+	0.898691i	−0.997016	−	0.0771919i	$-0.975405\pi$
$29$	−4.19353	+	4.83960i	−0.778720	+	0.898691i	0.218296	+	0.975883i	$0.429950\pi$
$30$	0.118239	−	0.822373i	0.0215875	−	0.150144i
$31$	−9.52067	+	2.79552i	−1.70996	+	0.502090i	−0.982847	−	0.184425i	$-0.940958\pi$
$31$	−9.52067	+	2.79552i	−1.70996	+	0.502090i	−0.727116	+	0.686515i	$0.759140\pi$
$32$	2.51365	+	1.61543i	0.444355	+	0.285570i
$33$	0.0325485	+	0.226380i	0.00566596	+	0.0394076i
$34$	3.87672	+	8.48882i	0.664851	+	1.45582i
$35$	0.286752	+	0.627899i	0.0484699	+	0.106134i
$36$	−0.0771283	−	0.536439i	−0.0128547	−	0.0894065i
$37$	7.40250	+	4.75730i	1.21696	+	0.782095i	0.981811	−	0.189863i	$-0.0608045\pi$
$37$	7.40250	+	4.75730i	1.21696	+	0.782095i	0.235153	+	0.971958i	$0.424441\pi$
$38$	−3.04765	+	0.894870i	−0.494394	+	0.145167i
$39$	0.382075	−	2.65739i	0.0611810	−	0.425523i
$40$	0.793290	−	0.915505i	0.125430	−	0.144754i
$41$	0.614669	−	0.395023i	0.0959951	−	0.0616923i	−0.491763	−	0.870729i	$-0.663647\pi$
$41$	0.614669	−	0.395023i	0.0959951	−	0.0616923i	0.587758	+	0.809037i	$0.300011\pi$
$42$	1.38302	+	1.59609i	0.213405	+	0.246282i
$43$	−9.98718	−	2.93250i	−1.52303	−	0.447202i	−0.590122	−	0.807314i	$-0.700920\pi$
$43$	−9.98718	−	2.93250i	−1.52303	−	0.447202i	−0.932909	+	0.360112i	$0.882739\pi$
$44$	0.0514904	−	0.112748i	0.00776247	−	0.0169974i
$45$	−0.521109			−0.0776823
$46$	7.36436	+	2.05699i	1.08582	+	0.303287i
$47$	−2.04380			−0.298119			−0.149059	−	0.988828i	$-0.547625\pi$
$47$	−2.04380			−0.298119			−0.149059	+	0.988828i	$0.547625\pi$
$48$	1.98992	−	4.35731i	0.287220	−	0.628924i
$49$	5.03287	+	1.47778i	0.718981	+	0.211112i
$50$	−4.93687	−	5.69745i	−0.698178	−	0.805741i
$51$	4.92408	−	3.16451i	0.689508	−	0.443120i
$52$	−0.952821	+	1.09961i	−0.132133	+	0.152489i
$53$	0.955435	−	6.64520i	0.131239	−	0.912788i	−0.812703	−	0.582678i	$-0.802005\pi$
$53$	0.955435	−	6.64520i	0.131239	−	0.912788i	0.943942	−	0.330110i	$-0.107086\pi$
$54$	−1.52977	+	0.449181i	−0.208175	+	0.0611257i
$55$	−0.100262	−	0.0644343i	−0.0135193	−	0.00868832i
$56$	0.438229	+	3.04795i	0.0585608	+	0.407299i
$57$	0.827602	+	1.81219i	0.109619	+	0.240031i
$58$	−4.24128	−	9.28712i	−0.556908	−	1.21946i
$59$	0.928393	+	6.45712i	0.120866	+	0.840645i	0.956578	+	0.291476i	$0.0941464\pi$
$59$	0.928393	+	6.45712i	0.120866	+	0.840645i	−0.835712	+	0.549169i	$0.814944\pi$
$60$	0.237585	+	0.152687i	0.0306721	+	0.0197117i
$61$	2.99298	−	0.878817i	0.383211	−	0.112521i	−0.0844523	−	0.996428i	$-0.526914\pi$
$61$	2.99298	−	0.878817i	0.383211	−	0.112521i	0.467664	+	0.883907i	$0.345096\pi$
$62$	2.25144	−	15.6591i	0.285933	−	1.98871i
$63$	0.867451	−	1.00109i	0.109289	−	0.126126i
$64$	4.05189	−	2.60399i	0.506487	−	0.325499i
$65$	0.916170	+	1.05732i	0.113637	+	0.131144i
$66$	−0.349869	−	0.102731i	−0.0430660	−	0.0126453i
$67$	−4.63685	+	10.1533i	−0.566482	+	1.24042i	0.382168	+	0.924093i	$0.375178\pi$
$67$	−4.63685	+	10.1533i	−0.566482	+	1.24042i	−0.948650	+	0.316329i	$0.897550\pi$
$68$	−3.17221			−0.384687
$69$	0.619688	−	4.75563i	0.0746017	−	0.572510i
$70$	−1.10055			−0.131540
$71$	−2.37142	+	5.19268i	−0.281436	+	0.616258i	−0.996572	−	0.0827267i	$-0.973637\pi$
$71$	−2.37142	+	5.19268i	−0.281436	+	0.616258i	0.715137	+	0.698985i	$0.246364\pi$
$72$	−2.23047	−	0.654925i	−0.262863	−	0.0771837i
$73$	−1.53321	−	1.76941i	−0.179448	−	0.207094i	0.658898	−	0.752232i	$-0.271023\pi$
$73$	−1.53321	−	1.76941i	−0.179448	−	0.207094i	−0.838346	+	0.545138i	$0.816477\pi$
$74$	−11.8022	+	7.58480i	−1.37198	+	0.881716i
$75$	−3.09647	+	3.57352i	−0.357550	+	0.412635i
$76$	0.153657	−	1.06871i	0.0176257	−	0.122589i
$77$	0.290682	−	0.0853519i	0.0331263	−	0.00972676i
$78$	3.60089	+	2.31415i	0.407720	+	0.262026i
$79$	−1.38723	−	9.64839i	−0.156075	−	1.08553i	−0.905778	−	0.423753i	$-0.860712\pi$
$79$	−1.38723	−	9.64839i	−0.156075	−	1.08553i	0.749702	−	0.661775i	$-0.230197\pi$
$80$	1.03696	+	2.27063i	0.115936	+	0.253865i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	0.165786	+	1.15307i	0.0183080	+	0.127335i
$83$	−0.303301	−	0.194920i	−0.0332916	−	0.0213952i	0.523889	−	0.851786i	$-0.324481\pi$
$83$	−0.303301	−	0.194920i	−0.0332916	−	0.0213952i	−0.557181	+	0.830391i	$0.688117\pi$
$84$	−0.688813	+	0.202254i	−0.0751557	+	0.0220677i
$85$	−0.434086	+	3.01914i	−0.0470833	+	0.327471i
$86$	10.8676	−	12.5419i	1.17188	−	1.35243i
$87$	−5.38714	+	3.46210i	−0.577562	+	0.371177i
$88$	−0.348164	−	0.401803i	−0.0371144	−	0.0428323i
$89$	14.2049	+	4.17094i	1.50572	+	0.442119i	0.927519	−	0.373776i	$-0.121937\pi$
$89$	14.2049	+	4.17094i	1.50572	+	0.442119i	0.578200	+	0.815895i	$0.303755\pi$
$90$	0.345139	−	0.755750i	0.0363809	−	0.0796630i
$91$	−3.55627			−0.372799
$92$	−1.67594	+	1.98662i	−0.174729	+	0.207120i
$93$	−9.92260			−1.02893
$94$	1.35364	−	2.96407i	0.139618	−	0.305720i
$95$	−0.996114	−	0.292486i	−0.102199	−	0.0300084i
$96$	1.95671	+	2.25817i	0.199706	+	0.230473i
$97$	4.02823	−	2.58879i	0.409005	−	0.262851i	−0.319921	−	0.947444i	$-0.603656\pi$
$97$	4.02823	−	2.58879i	0.409005	−	0.262851i	0.728926	+	0.684593i	$0.240020\pi$
$98$	−5.47655	+	6.32027i	−0.553215	+	0.638444i
$99$	−0.0325485	+	0.226380i	−0.00327124	+	0.0227520i
$100$	2.45880	−	0.721970i	0.245880	−	0.0721970i
$101$	4.55331	+	2.92624i	0.453072	+	0.291172i	0.747206	−	0.664593i	$-0.231395\pi$
$101$	4.55331	+	2.92624i	0.453072	+	0.291172i	−0.294134	+	0.955764i	$0.595031\pi$
$102$	1.32810	+	9.23716i	0.131502	+	0.914615i
$103$	−2.00457	−	4.38940i	−0.197516	−	0.432500i	0.784795	−	0.619755i	$-0.212768\pi$
$103$	−2.00457	−	4.38940i	−0.197516	−	0.432500i	−0.982311	+	0.187255i	$0.940041\pi$
$104$	2.59260	+	5.67701i	0.254225	+	0.556676i
$105$	0.0982369	+	0.683252i	0.00958694	+	0.0666786i
$106$	9.00455	+	5.78687i	0.874599	+	0.562071i
$107$	13.7226	−	4.02932i	1.32662	−	0.389530i	0.459740	−	0.888054i	$-0.347943\pi$
$107$	13.7226	−	4.02932i	1.32662	−	0.389530i	0.866876	+	0.498524i	$0.166124\pi$
$108$	0.0771283	−	0.536439i	0.00742168	−	0.0516189i
$109$	−1.81718	+	2.09714i	−0.174054	+	0.200869i	−0.836073	−	0.548618i	$-0.815154\pi$
$109$	−1.81718	+	2.09714i	−0.174054	+	0.200869i	0.662019	+	0.749487i	$0.269700\pi$
$110$	0.159852	−	0.102731i	0.0152413	−	0.00979501i
$111$	5.76236	+	6.65012i	0.546939	+	0.631201i
$112$	−6.08823	−	1.78767i	−0.575284	−	0.168919i
$113$	−4.69007	+	10.2698i	−0.441205	+	0.966103i	0.550171	+	0.835052i	$0.314563\pi$
$113$	−4.69007	+	10.2698i	−0.441205	+	0.966103i	−0.991376	+	0.131051i	$0.958165\pi$
$114$	−3.17631			−0.297489
$115$	1.66143	+	1.86692i	0.154929	+	0.174092i
$116$	3.47052			0.322230
$117$	1.11527	−	2.44211i	0.103107	−	0.225773i
$118$	−9.97947	−	2.93024i	−0.918685	−	0.269750i
$119$	−5.07742	−	5.85965i	−0.465446	−	0.537153i
$120$	1.01908	−	0.654925i	0.0930292	−	0.0597862i
$121$	7.16921	−	8.27371i	0.651747	−	0.752156i
$122$	−0.707775	+	4.92269i	−0.0640790	+	0.445679i
$123$	0.701061	−	0.205850i	0.0632125	−	0.0185609i
$124$	4.52393	+	2.90735i	0.406261	+	0.261088i
$125$	−0.721476	−	5.01798i	−0.0645308	−	0.448821i
$126$	0.877329	+	1.92108i	0.0781587	+	0.171144i
$127$	−6.47276	−	14.1734i	−0.574364	−	1.25768i	−0.944441	−	0.328681i	$-0.893396\pi$
$127$	−6.47276	−	14.1734i	−0.574364	−	1.25768i	0.370077	−	0.929001i	$-0.379331\pi$
$128$	1.94333	+	13.5162i	0.171768	+	1.19467i
$129$	−8.75645	−	5.62743i	−0.770963	−	0.495468i
$130$	−2.14019	+	0.628417i	−0.187707	+	0.0551158i
$131$	−1.60034	+	11.1306i	−0.139823	+	0.972488i	0.792245	+	0.610203i	$0.208912\pi$
$131$	−1.60034	+	11.1306i	−0.139823	+	0.972488i	−0.932067	+	0.362285i	$0.881997\pi$
$132$	0.0811695	−	0.0936746i	0.00706490	−	0.00815333i
$133$	2.22005	−	1.42674i	0.192503	−	0.123714i
$134$	−11.6540	−	13.4494i	−1.00675	−	1.16185i
$135$	−0.500000	−	0.146813i	−0.0430331	−	0.0126357i
$136$	−5.65242	+	12.3771i	−0.484691	+	1.06133i
$137$	−20.3976			−1.74269			−0.871343	−	0.490674i	$-0.836751\pi$
$137$	−20.3976			−1.74269			−0.871343	+	0.490674i	$0.836751\pi$
$138$	6.48653	+	4.04845i	0.552170	+	0.344627i
$139$	12.3293			1.04576			0.522879	−	0.852407i	$-0.324858\pi$
$139$	12.3293			1.04576			0.522879	+	0.852407i	$0.324858\pi$
$140$	0.155407	−	0.340294i	0.0131343	−	0.0287601i
$141$	−1.96101	−	0.575805i	−0.165147	−	0.0484915i
$142$	−5.96017	−	6.87841i	−0.500167	−	0.577223i
$143$	0.516542	−	0.331962i	0.0431954	−	0.0277600i
$144$	3.13691	−	3.62019i	0.261409	−	0.301682i
$145$	0.474908	−	3.30306i	0.0394390	−	0.274304i
$146$	3.58160	−	1.05165i	0.296415	−	0.0870354i
$147$	4.41266	+	2.83585i	0.363950	+	0.233897i
$148$	−0.678681	−	4.72033i	−0.0557872	−	0.388009i
$149$	−9.77633	−	21.4072i	−0.800909	−	1.75375i	−0.642373	−	0.766392i	$-0.722050\pi$
$149$	−9.77633	−	21.4072i	−0.800909	−	1.75375i	−0.158535	−	0.987353i	$-0.550677\pi$
$150$	−3.13173	−	6.85754i	−0.255705	−	0.559916i
$151$	−1.25356	−	8.71872i	−0.102014	−	0.709520i	−0.975070	−	0.221900i	$-0.928774\pi$
$151$	−1.25356	−	8.71872i	−0.102014	−	0.709520i	0.873056	−	0.487620i	$-0.162135\pi$
$152$	−3.89602	−	2.50382i	−0.316009	−	0.203086i
$153$	5.61616	−	1.64905i	0.454040	−	0.133318i
$154$	−0.0687402	+	0.478098i	−0.00553924	+	0.0385263i
$155$	3.38612	−	3.90779i	0.271980	−	0.313882i
$156$	−1.22402	+	0.786632i	−0.0980002	+	0.0629809i
$157$	15.4110	+	17.7853i	1.22993	+	1.41942i	0.874715	+	0.484637i	$0.161048\pi$
$157$	15.4110	+	17.7853i	1.22993	+	1.41942i	0.355219	+	0.934783i	$0.384406\pi$
$158$	14.9116	+	4.37843i	1.18630	+	0.348330i
$159$	2.78890	−	6.10684i	0.221174	−	0.484304i
$160$	−1.55706			−0.123097
$161$	−6.35217	+	0.0840028i	−0.500621	+	0.00662035i
$162$	−1.59435			−0.125264
$163$	2.07548	−	4.54466i	0.162564	−	0.355965i	−0.810768	−	0.585368i	$-0.800950\pi$
$163$	2.07548	−	4.54466i	0.162564	−	0.355965i	0.973332	+	0.229403i	$0.0736773\pi$
$164$	−0.379944	−	0.111562i	−0.0296686	−	0.00871150i
$165$	−0.0780472	−	0.0900713i	−0.00607597	−	0.00701204i
$166$	0.483568	−	0.310771i	0.0375322	−	0.0241205i
$167$	8.65299	−	9.98608i	0.669588	−	0.772746i	−0.314724	−	0.949183i	$-0.601912\pi$
$167$	8.65299	−	9.98608i	0.669588	−	0.772746i	0.984312	+	0.176437i	$0.0564573\pi$
$168$	−0.438229	+	3.04795i	−0.0338101	+	0.235154i
$169$	5.55766	−	1.63187i	0.427512	−	0.125529i
$170$	−4.09107	−	2.62917i	−0.313771	−	0.201648i
$171$	0.283524	+	1.97195i	0.0216816	+	0.150799i
$172$	2.34340	+	5.13134i	0.178683	+	0.391261i
$173$	2.89069	+	6.32973i	0.219775	+	0.481240i	0.987117	−	0.159997i	$-0.0511486\pi$
$173$	2.89069	+	6.32973i	0.219775	+	0.481240i	−0.767342	+	0.641238i	$0.778421\pi$
$174$	−1.45300	−	10.1058i	−0.110152	−	0.766121i
$175$	5.26916	+	3.38628i	0.398311	+	0.255979i
$176$	1.05118	−	0.308653i	0.0792353	−	0.0232656i
$177$	−0.928393	+	6.45712i	−0.0697823	+	0.485347i
$178$	−15.4572	+	17.8385i	−1.15856	+	1.33705i
$179$	−2.02703	+	1.30269i	−0.151507	+	0.0973677i	−0.614198	−	0.789152i	$-0.710520\pi$
$179$	−2.02703	+	1.30269i	−0.151507	+	0.0973677i	0.462691	+	0.886520i	$0.346884\pi$
$180$	0.184944	+	0.213437i	0.0137849	+	0.0159087i
$181$	−6.13613	−	1.80173i	−0.456095	−	0.133921i	0.0456121	−	0.998959i	$-0.485476\pi$
$181$	−6.13613	−	1.80173i	−0.456095	−	0.133921i	−0.501707	+	0.865038i	$0.667294\pi$
$182$	2.35538	−	5.15757i	0.174592	−	0.382304i
$183$	3.11933			0.230588
$184$	4.76497	+	10.0790i	0.351278	+	0.743031i
$185$	−4.58543			−0.337127
$186$	6.57191	−	14.3905i	0.481876	−	1.05516i
$187$	1.28446	+	0.377151i	0.0939289	+	0.0275800i
$188$	0.725356	+	0.837105i	0.0529020	+	0.0610521i
$189$	1.11435	−	0.716152i	0.0810573	−	0.0520924i
$190$	1.08393	−	1.25092i	0.0786364	−	0.0907512i
$191$	−1.55320	+	10.8027i	−0.112385	+	0.781658i	0.853202	+	0.521580i	$0.174657\pi$
$191$	−1.55320	+	10.8027i	−0.112385	+	0.781658i	−0.965588	+	0.260078i	$0.916252\pi$
$192$	4.62139	−	1.35696i	0.333520	−	0.0979304i
$193$	−4.51508	−	2.90167i	−0.325003	−	0.208866i	0.367957	−	0.929843i	$-0.380057\pi$
$193$	−4.51508	−	2.90167i	−0.325003	−	0.208866i	−0.692960	+	0.720976i	$0.743694\pi$
$194$	1.08648	+	7.55663i	0.0780047	+	0.542535i
$195$	0.581178	+	1.27260i	0.0416190	+	0.0911330i
$196$	−1.18092	−	2.58585i	−0.0843513	−	0.184704i
$197$	0.737421	+	5.12887i	0.0525391	+	0.365417i	0.999082	+	0.0428393i	$0.0136403\pi$
$197$	0.737421	+	5.12887i	0.0525391	+	0.365417i	−0.946543	+	0.322578i	$0.895451\pi$
$198$	−0.306755	−	0.197139i	−0.0218001	−	0.0140101i
$199$	−6.33466	+	1.86002i	−0.449052	+	0.131854i	−0.498436	−	0.866926i	$-0.666092\pi$
$199$	−6.33466	+	1.86002i	−0.449052	+	0.131854i	0.0493843	+	0.998780i	$0.484274\pi$
$200$	1.56431	−	10.8800i	0.110614	−	0.769334i
$201$	−7.30954	+	8.43566i	−0.515575	+	0.595006i
$202$	−7.25958	+	4.66545i	−0.510782	+	0.328260i
$203$	5.55490	+	6.41070i	0.389878	+	0.449943i
$204$	−3.04371	−	0.893714i	−0.213102	−	0.0625725i
$205$	−0.158170	+	0.346344i	−0.0110471	+	0.0241897i
$206$	7.69349			0.536031
$207$	1.93440	−	4.38840i	0.134450	−	0.305015i
$208$	−12.8603			−0.891703
$209$	−0.189279	+	0.414462i	−0.0130927	+	0.0286690i
$210$	−1.05597	−	0.310060i	−0.0728686	−	0.0213962i
$211$	12.2818	+	14.1740i	0.845516	+	0.975778i	0.999925	−	0.0122294i	$-0.00389284\pi$
$211$	12.2818	+	14.1740i	0.845516	+	0.975778i	−0.154409	+	0.988007i	$0.549347\pi$
$212$	−3.06085	+	1.96709i	−0.210220	+	0.135100i
$213$	−3.73831	+	4.31424i	−0.256145	+	0.295607i
$214$	−3.24511	+	22.5702i	−0.221831	+	1.54287i
$215$	5.20441	−	1.52815i	0.354938	−	0.104219i
$216$	−1.95561	−	1.25679i	−0.133062	−	0.0855139i
$217$	1.87056	+	13.0100i	0.126982	+	0.883179i
$218$	−1.83787	−	4.02437i	−0.124476	−	0.272565i
$219$	−0.972599	−	2.12969i	−0.0657221	−	0.143911i
$220$	0.00919226	+	0.0639336i	0.000619742	+	0.00431040i
$221$	−13.2198	−	8.49582i	−0.889257	−	0.571491i
$222$	−13.4610	+	3.95251i	−0.903443	+	0.265275i
$223$	−2.79952	+	19.4711i	−0.187470	+	1.30388i	0.651061	+	0.759025i	$0.274324\pi$
$223$	−2.79952	+	19.4711i	−0.187470	+	1.30388i	−0.838531	+	0.544854i	$0.816585\pi$
$224$	2.59193	−	2.99125i	0.173181	−	0.199861i
$225$	−3.97782	+	2.55639i	−0.265188	+	0.170426i
$226$	−11.7877	−	13.6038i	−0.784108	−	0.904909i
$227$	20.6819	+	6.07274i	1.37270	+	0.403062i	0.883223	−	0.468953i	$-0.155369\pi$
$227$	20.6819	+	6.07274i	1.37270	+	0.403062i	0.489480	+	0.872015i	$0.337187\pi$
$228$	0.448523	−	0.982129i	0.0297042	−	0.0650431i
$229$	−2.58372			−0.170737			−0.0853686	−	0.996349i	$-0.527207\pi$
$229$	−2.58372			−0.170737			−0.0853686	+	0.996349i	$0.527207\pi$
$230$	−3.80794	+	1.17302i	−0.251088	+	0.0773470i
$231$	0.302954			0.0199329
$232$	6.18398	−	13.5410i	0.405998	−	0.889012i
$233$	6.10079	+	1.79135i	0.399676	+	0.117355i	0.475392	−	0.879774i	$-0.342306\pi$
$233$	6.10079	+	1.79135i	0.399676	+	0.117355i	−0.0757164	+	0.997129i	$0.524124\pi$
$234$	2.80306	+	3.23490i	0.183242	+	0.211472i
$235$	0.895970	−	0.575805i	0.0584466	−	0.0375614i
$236$	2.31523	−	2.67192i	0.150709	−	0.173927i
$237$	1.38723	−	9.64839i	0.0901102	−	0.626730i
$238$	11.8610	−	3.48269i	0.768832	−	0.225749i
$239$	−15.3037	−	9.83506i	−0.989911	−	0.636177i	−0.0577920	−	0.998329i	$-0.518406\pi$
$239$	−15.3037	−	9.83506i	−0.989911	−	0.636177i	−0.932119	+	0.362151i	$0.882042\pi$
$240$	0.355248	+	2.47080i	0.0229312	+	0.159490i
$241$	−5.03218	−	11.0189i	−0.324151	−	0.709792i	0.675468	−	0.737389i	$-0.263942\pi$
$241$	−5.03218	−	11.0189i	−0.324151	−	0.709792i	−0.999619	+	0.0275972i	$0.991214\pi$
$242$	7.25085	+	15.8771i	0.466102	+	1.02062i
$243$	0.142315	+	0.989821i	0.00912950	+	0.0634971i
$244$	−1.42217	−	0.913974i	−0.0910452	−	0.0585112i
$245$	−2.62267	+	0.770086i	−0.167556	+	0.0491990i
$246$	−0.165786	+	1.15307i	−0.0105701	+	0.0735169i
$247$	3.50257	−	4.04218i	0.222863	−	0.257198i
$248$	19.4047	−	12.4707i	1.23220	−	0.791887i
$249$	−0.236100	−	0.272474i	−0.0149622	−	0.0172673i
$250$	7.75528	+	2.27716i	0.490487	+	0.144020i
$251$	1.31055	−	2.86971i	0.0827213	−	0.181134i	−0.863751	−	0.503918i	$-0.831891\pi$
$251$	1.31055	−	2.86971i	0.0827213	−	0.181134i	0.946473	+	0.322784i	$0.104619\pi$
$252$	−0.717893			−0.0452230
$253$	0.914800	−	0.605147i	0.0575130	−	0.0380453i
$254$	24.8423			1.55874
$255$	−1.26709	+	2.77454i	−0.0793484	+	0.173749i
$256$	−11.6464	−	3.41970i	−0.727902	−	0.213731i
$257$	−11.0307	−	12.7301i	−0.688078	−	0.794084i	0.299013	−	0.954249i	$-0.403343\pi$
$257$	−11.0307	−	12.7301i	−0.688078	−	0.794084i	−0.987090	+	0.160165i	$0.948797\pi$
$258$	13.9609	−	8.97210i	0.869165	−	0.558578i
$259$	7.63303	−	8.80898i	0.474293	−	0.547363i
$260$	0.107905	−	0.750495i	0.00669197	−	0.0465437i
$261$	−6.14431	+	1.80413i	−0.380323	+	0.111673i
$262$	−15.0825	−	9.69295i	−0.931802	−	0.598832i
$263$	−2.15669	−	15.0001i	−0.132987	−	0.924944i	−0.941631	−	0.336646i	$-0.890707\pi$
$263$	−2.15669	−	15.0001i	−0.132987	−	0.924944i	0.808644	−	0.588298i	$-0.200202\pi$
$264$	−0.220860	−	0.483616i	−0.0135930	−	0.0297645i
$265$	1.45332	+	3.18233i	0.0892768	+	0.195489i
$266$	0.598783	+	4.16463i	0.0367137	+	0.255350i
$267$	12.4544	+	8.00398i	0.762199	+	0.489836i
$268$	5.80426	−	1.70428i	0.354551	−	0.104106i
$269$	−1.62693	+	11.3156i	−0.0991959	+	0.689922i	0.878167	+	0.478354i	$0.158766\pi$
$269$	−1.62693	+	11.3156i	−0.0991959	+	0.689922i	−0.977363	+	0.211569i	$0.932143\pi$
$270$	0.544078	−	0.627899i	0.0331115	−	0.0382127i
$271$	−2.97406	+	1.91131i	−0.180662	+	0.116104i	−0.627846	−	0.778338i	$-0.716063\pi$
$271$	−2.97406	+	1.91131i	−0.180662	+	0.116104i	0.447184	+	0.894442i	$0.352427\pi$
$272$	−18.3612	−	21.1899i	−1.11331	−	1.28483i
$273$	−3.41222	−	1.00192i	−0.206517	−	0.0606388i
$274$	13.5097	−	29.5821i	0.816151	−	1.78712i
$275$	−1.08143			−0.0652127
$276$	−2.16775	+	1.43398i	−0.130483	+	0.0863157i
$277$	3.41155			0.204980			0.102490	−	0.994734i	$-0.467319\pi$
$277$	3.41155			0.204980			0.102490	+	0.994734i	$0.467319\pi$
$278$	−8.16592	+	17.8809i	−0.489759	+	1.07242i
$279$	−9.52067	−	2.79552i	−0.569987	−	0.167363i
$280$	−1.05082	−	1.21271i	−0.0627985	−	0.0724733i
$281$	−10.4812	+	6.73587i	−0.625257	+	0.401828i	−0.814551	−	0.580092i	$-0.803017\pi$
$281$	−10.4812	+	6.73587i	−0.625257	+	0.401828i	0.189294	+	0.981921i	$0.439380\pi$
$282$	2.13389	−	2.46264i	0.127071	−	0.146648i
$283$	1.25709	−	8.74322i	0.0747260	−	0.519731i	−0.917737	−	0.397188i	$-0.869986\pi$
$283$	1.25709	−	8.74322i	0.0747260	−	0.519731i	0.992463	−	0.122543i	$-0.0391048\pi$
$284$	2.96846	−	0.871619i	0.176146	−	0.0517211i
$285$	−0.873362	−	0.561276i	−0.0517335	−	0.0332471i
$286$	0.139320	+	0.968991i	0.00823816	+	0.0572977i
$287$	−0.402061	−	0.880392i	−0.0237329	−	0.0519679i
$288$	1.24125	+	2.71797i	0.0731416	+	0.160158i
$289$	−2.45645	−	17.0850i	−0.144497	−	1.00500i
$290$	4.47580	+	2.87642i	0.262828	+	0.168909i
$291$	4.59440	−	1.34904i	0.269329	−	0.0790821i
$292$	−0.180578	+	1.25595i	−0.0105675	+	0.0734989i
$293$	−12.5601	+	14.4952i	−0.733770	+	0.846816i	−0.992891	−	0.119029i	$-0.962022\pi$
$293$	−12.5601	+	14.4952i	−0.733770	+	0.846816i	0.259121	+	0.965845i	$0.416567\pi$
$294$	−7.03533	+	4.52133i	−0.410309	+	0.263690i
$295$	−2.22617	−	2.56914i	−0.129613	−	0.149581i
$296$	−19.6267	−	5.76293i	−1.14078	−	0.334964i
$297$	−0.0950085	+	0.208040i	−0.00551295	+	0.0120717i
$298$	37.5213			2.17355
$299$	−12.3049	+	3.79048i	−0.711609	+	0.219209i
$300$	2.56261			0.147952
$301$	−5.72769	+	12.5419i	−0.330139	+	0.722903i
$302$	13.4748	+	3.95655i	0.775387	+	0.227674i
$303$	3.54446	+	4.09052i	0.203624	+	0.234994i
$304$	8.02822	−	5.15942i	0.460450	−	0.295913i
$305$	−1.06448	+	1.22848i	−0.0609521	+	0.0703425i
$306$	−1.32810	+	9.23716i	−0.0759226	+	0.528053i
$307$	−17.0089	+	4.99426i	−0.970748	+	0.285037i	−0.728400	−	0.685152i	$-0.759736\pi$
$307$	−17.0089	+	4.99426i	−0.970748	+	0.285037i	−0.242348	+	0.970189i	$0.577918\pi$
$308$	−0.138123	−	0.0887665i	−0.00787031	−	0.00505794i
$309$	−0.686735	−	4.77635i	−0.0390670	−	0.271717i
$310$	3.42468	+	7.49900i	0.194509	+	0.425915i
$311$	7.63724	+	16.7232i	0.433068	+	0.948286i	0.992819	+	0.119626i	$0.0381694\pi$
$311$	7.63724	+	16.7232i	0.433068	+	0.948286i	−0.559751	+	0.828661i	$0.689103\pi$
$312$	0.888186	+	6.17747i	0.0502836	+	0.349730i
$313$	−28.9503	−	18.6052i	−1.63637	−	1.05163i	−0.943928	−	0.330153i	$-0.892900\pi$
$313$	−28.9503	−	18.6052i	−1.63637	−	1.05163i	−0.692439	−	0.721476i	$-0.743464\pi$
$314$	−36.0005	+	10.5707i	−2.03163	+	0.596539i
$315$	−0.0982369	+	0.683252i	−0.00553502	+	0.0384969i
$316$	−3.45948	+	3.99245i	−0.194611	+	0.224593i
$317$	0.405588	−	0.260655i	0.0227801	−	0.0146399i	−0.529201	−	0.848496i	$-0.677508\pi$
$317$	0.405588	−	0.260655i	0.0227801	−	0.0146399i	0.551981	+	0.833856i	$0.313872\pi$
$318$	7.00945	+	8.08934i	0.393071	+	0.453628i
$319$	−1.40525	−	0.412618i	−0.0786788	−	0.0231022i
$320$	−1.04266	+	2.28310i	−0.0582863	+	0.127629i
$321$	14.3020			0.798257
$322$	4.08533	−	9.26802i	0.227666	−	0.516486i
$323$	11.6610			0.648837
$324$	0.225136	−	0.492980i	0.0125076	−	0.0273878i
$325$	12.1803	+	3.57647i	0.675643	+	0.198387i
$326$	5.21637	+	6.02002i	0.288908	+	0.333418i
$327$	−2.33440	+	1.50023i	−0.129093	+	0.0829628i
$328$	−1.11229	+	1.28365i	−0.0614159	+	0.0708777i
$329$	−0.385287	+	2.67973i	−0.0212416	+	0.147738i
$330$	0.182320	−	0.0535340i	0.0100364	−	0.00294695i
$331$	−3.49551	−	2.24643i	−0.192131	−	0.123475i	0.441039	−	0.897488i	$-0.354610\pi$
$331$	−3.49551	−	2.24643i	−0.192131	−	0.123475i	−0.633170	+	0.774013i	$0.718246\pi$
$332$	0.0278074	+	0.193405i	0.00152613	+	0.0106145i
$333$	3.65539	+	8.00419i	0.200314	+	0.438627i
$334$	8.75151	+	19.1631i	0.478862	+	1.04856i
$335$	−0.827789	−	5.75740i	−0.0452269	−	0.314560i
$336$	−5.33797	−	3.43051i	−0.291210	−	0.187149i
$337$	3.88633	−	1.14113i	0.211702	−	0.0621613i	−0.174162	−	0.984717i	$-0.555722\pi$
$337$	3.88633	−	1.14113i	0.211702	−	0.0621613i	0.385864	+	0.922556i	$0.373903\pi$
$338$	−1.31427	+	9.14094i	−0.0714868	+	0.497201i
$339$	−7.39343	+	8.53248i	−0.401556	+	0.463420i
$340$	1.39065	−	0.893714i	0.0754184	−	0.0484684i
$341$	−1.48612	−	1.71508i	−0.0804781	−	0.0928766i
$342$	−3.04765	−	0.894870i	−0.164798	−	0.0483891i
$343$	6.73828	−	14.7548i	0.363833	−	0.796683i
$344$	24.1967			1.30460
$345$	1.06815	+	2.25938i	0.0575074	+	0.121641i
$346$	−11.0944			−0.596438
$347$	−10.2350	+	22.4115i	−0.549442	+	1.20311i	0.407599	+	0.913161i	$0.366366\pi$
$347$	−10.2350	+	22.4115i	−0.549442	+	1.20311i	−0.957042	+	0.289950i	$0.906361\pi$
$348$	3.32994	+	0.977759i	0.178504	+	0.0524134i
$349$	21.3981	+	24.6947i	1.14541	+	1.32188i	0.939200	+	0.343371i	$0.111569\pi$
$349$	21.3981	+	24.6947i	1.14541	+	1.32188i	0.206213	+	0.978507i	$0.433886\pi$
$350$	−8.40089	+	5.39893i	−0.449047	+	0.288585i
$351$	1.75812	−	2.02898i	0.0938413	−	0.108299i
$352$	−0.0972543	+	0.676418i	−0.00518367	+	0.0360532i
$353$	26.4957	−	7.77983i	1.41022	−	0.414078i	0.514040	−	0.857766i	$-0.328148\pi$
$353$	26.4957	−	7.77983i	1.41022	−	0.414078i	0.896181	+	0.443688i	$0.146330\pi$
$354$	−8.74969	−	5.62308i	−0.465041	−	0.298864i
$355$	−0.423355	−	2.94450i	−0.0224693	−	0.156278i
$356$	−3.33306	−	7.29838i	−0.176652	−	0.386814i
$357$	−3.22089	−	7.05277i	−0.170468	−	0.373272i
$358$	−0.546722	−	3.80254i	−0.0288952	−	0.200970i
$359$	2.82013	+	1.81239i	0.148841	+	0.0956542i	0.612942	−	0.790128i	$-0.289986\pi$
$359$	2.82013	+	1.81239i	0.148841	+	0.0956542i	−0.464101	+	0.885782i	$0.653622\pi$
$360$	1.16232	−	0.341287i	0.0612595	−	0.0179874i
$361$	2.13914	−	14.8780i	0.112586	−	0.783054i
$362$	6.67706	−	7.70574i	0.350939	−	0.405005i
$363$	9.20979	−	5.91877i	0.483388	−	0.310655i
$364$	1.26214	+	1.45659i	0.0661541	+	0.0763459i
$365$	1.17064	+	0.343729i	0.0612738	+	0.0179916i
$366$	−2.06599	+	4.52388i	−0.107991	+	0.236467i
$367$	−2.87657			−0.150156			−0.0750780	−	0.997178i	$-0.523921\pi$
$367$	−2.87657			−0.150156			−0.0750780	+	0.997178i	$0.523921\pi$
$368$	−22.9710	+	0.303774i	−1.19744	+	0.0158353i
$369$	0.730658			0.0380365
$370$	3.03701	−	6.65012i	0.157887	−	0.345723i
$371$	−8.53275	−	2.50544i	−0.442998	−	0.130076i
$372$	3.52158	+	4.06413i	0.182586	+	0.210715i
$373$	−2.99686	+	1.92596i	−0.155171	+	0.0997226i	−0.615922	−	0.787807i	$-0.711217\pi$
$373$	−2.99686	+	1.92596i	−0.155171	+	0.0997226i	0.460751	+	0.887529i	$0.347580\pi$
$374$	−1.39769	+	1.61302i	−0.0722728	+	0.0834073i
$375$	0.721476	−	5.01798i	0.0372569	−	0.259127i
$376$	4.55864	−	1.33854i	0.235094	−	0.0690297i
$377$	14.4630	+	9.29478i	0.744880	+	0.478705i
$378$	0.300559	+	2.09044i	0.0154591	+	0.107520i
$379$	7.53052	+	16.4895i	0.386817	+	0.847011i	0.998439	+	0.0558607i	$0.0177903\pi$
$379$	7.53052	+	16.4895i	0.386817	+	0.847011i	−0.611622	+	0.791150i	$0.709482\pi$
$380$	0.233729	+	0.511796i	0.0119901	+	0.0262546i
$381$	−2.21747	−	15.4228i	−0.113604	−	0.790135i
$382$	−14.6382	−	9.40740i	−0.748955	−	0.481324i
$383$	27.8674	−	8.18260i	1.42396	−	0.418112i	0.523116	−	0.852261i	$-0.324769\pi$
$383$	27.8674	−	8.18260i	1.42396	−	0.418112i	0.900841	+	0.434150i	$0.142951\pi$
$384$	−1.94333	+	13.5162i	−0.0991702	+	0.689744i
$385$	−0.103384	+	0.119312i	−0.00526894	+	0.00608068i
$386$	7.19862	−	4.62627i	0.366400	−	0.235471i
$387$	−6.81632	−	7.86646i	−0.346493	−	0.399874i
$388$	−2.48996	−	0.731119i	−0.126409	−	0.0371169i
$389$	15.9890	−	35.0111i	0.810676	−	1.77513i	0.206200	−	0.978510i	$-0.433890\pi$
$389$	15.9890	−	35.0111i	0.810676	−	1.77513i	0.604476	−	0.796623i	$-0.293382\pi$
$390$	−2.23055			−0.112948
$391$	−23.8137	−	14.8629i	−1.20431	−	0.751648i
$392$	−12.1935			−0.615865
$393$	−4.67138	+	10.2289i	−0.235640	+	0.515980i
$394$	−7.92667	−	2.32748i	−0.399340	−	0.117257i
$395$	3.32640	+	3.83888i	0.167370	+	0.193155i
$396$	0.104273	−	0.0670120i	0.00523990	−	0.00336748i
$397$	−17.3043	+	19.9703i	−0.868480	+	1.00228i	0.131460	+	0.991321i	$0.458034\pi$
$397$	−17.3043	+	19.9703i	−0.868480	+	1.00228i	−0.999940	+	0.0109578i	$0.996512\pi$
$398$	1.49801	−	10.4189i	0.0750886	−	0.522253i
$399$	2.53208	−	0.743485i	0.126762	−	0.0372208i
$400$	19.0545	+	12.2456i	0.952727	+	0.612281i
$401$	−2.04576	−	14.2286i	−0.102161	−	0.710542i	−0.974947	−	0.222439i	$-0.928598\pi$
$401$	−2.04576	−	14.2286i	−0.102161	−	0.710542i	0.872786	−	0.488103i	$-0.162311\pi$
$402$	−7.39277	−	16.1879i	−0.368718	−	0.807380i
$403$	11.0664	+	24.2320i	0.551257	+	1.20708i
$404$	−0.417460	−	2.90350i	−0.0207694	−	0.144454i
$405$	−0.438384	−	0.281733i	−0.0217835	−	0.0139994i
$406$	−12.9764	+	3.81021i	−0.644006	+	0.189097i
$407$	−0.286406	+	1.99200i	−0.0141966	+	0.0987396i
$408$	−8.91049	+	10.2833i	−0.441135	+	0.509097i
$409$	−22.4998	+	14.4597i	−1.11254	+	0.714987i	−0.961846	−	0.273593i	$-0.911788\pi$
$409$	−22.4998	+	14.4597i	−1.11254	+	0.714987i	−0.150697	+	0.988580i	$0.548152\pi$
$410$	−0.397535	−	0.458780i	−0.0196328	−	0.0226575i
$411$	−19.5714	−	5.74667i	−0.965385	−	0.283463i
$412$	−1.08639	+	2.37886i	−0.0535225	+	0.117198i
$413$	8.64128			0.425209
$414$	5.08320	+	5.71193i	0.249825	+	0.280726i
$415$	0.187878			0.00922255
$416$	3.33242	−	7.29697i	0.163385	−	0.357764i
$417$	11.8299	+	3.47357i	0.579312	+	0.170101i
$418$	−0.475721	−	0.549011i	−0.0232683	−	0.0268530i
$419$	7.58526	−	4.87475i	0.370564	−	0.238147i	−0.342083	−	0.939670i	$-0.611132\pi$
$419$	7.58526	−	4.87475i	0.370564	−	0.238147i	0.712647	+	0.701523i	$0.247496\pi$
$420$	0.244984	−	0.282726i	0.0119540	−	0.0137956i
$421$	4.45679	−	30.9977i	0.217211	−	1.51073i	−0.531056	−	0.847337i	$-0.678205\pi$
$421$	4.45679	−	30.9977i	0.217211	−	1.51073i	0.748267	−	0.663398i	$-0.230886\pi$
$422$	−28.6906	+	8.42433i	−1.39664	+	0.410090i
$423$	−1.71935	−	1.10496i	−0.0835978	−	0.0537251i
$424$	2.22104	+	15.4477i	0.107863	+	0.750205i
$425$	11.4974	+	25.1757i	0.557704	+	1.22120i
$426$	−3.78087	−	8.27896i	−0.183184	−	0.401117i
$427$	−0.588041	−	4.08992i	−0.0284573	−	0.197925i
$428$	−6.52057	−	4.19052i	−0.315184	−	0.202556i
$429$	0.589143	−	0.172988i	0.0284441	−	0.00835194i
$430$	−1.23073	+	8.55993i	−0.0593512	+	0.412797i
$431$	0.647659	−	0.747439i	0.0311967	−	0.0360029i	−0.739937	−	0.672676i	$-0.765145\pi$
$431$	0.647659	−	0.747439i	0.0311967	−	0.0360029i	0.771133	+	0.636674i	$0.219690\pi$
$432$	4.02977	−	2.58978i	0.193882	−	0.124601i
$433$	3.51011	+	4.05088i	0.168685	+	0.194673i	0.833798	−	0.552070i	$-0.186162\pi$
$433$	3.51011	+	4.05088i	0.168685	+	0.194673i	−0.665113	+	0.746743i	$0.731616\pi$
$434$	−20.1070	−	5.90395i	−0.965167	−	0.283399i
$435$	1.38625	−	3.03546i	0.0664656	−	0.145539i
$436$	1.50388			0.0720226
$437$	6.16077	−	7.30283i	0.294710	−	0.349342i
$438$	3.73281			0.178360
$439$	2.16852	−	4.74839i	0.103498	−	0.226628i	−0.850798	−	0.525493i	$-0.823881\pi$
$439$	2.16852	−	4.74839i	0.103498	−	0.226628i	0.954295	+	0.298865i	$0.0966081\pi$
$440$	0.265831	+	0.0780549i	0.0126730	+	0.00372112i
$441$	3.43497	+	3.96417i	0.163570	+	0.188770i
$442$	21.0769	−	13.5453i	1.00253	−	0.644285i
$443$	18.3025	−	21.1222i	0.869577	−	1.00354i	−0.130350	−	0.991468i	$-0.541610\pi$
$443$	18.3025	−	21.1222i	0.869577	−	1.00354i	0.999927	−	0.0120769i	$-0.00384430\pi$
$444$	0.678681	−	4.72033i	0.0322088	−	0.224017i
$445$	−7.40231	+	2.17351i	−0.350903	+	0.103034i
$446$	−26.3842	−	16.9561i	−1.24933	−	0.802894i
$447$	−3.34922	−	23.2944i	−0.158413	−	1.10179i
$448$	−2.65039	−	5.80354i	−0.125219	−	0.274192i
$449$	−3.81135	−	8.34570i	−0.179869	−	0.393858i	0.798125	−	0.602492i	$-0.205825\pi$
$449$	−3.81135	−	8.34570i	−0.179869	−	0.393858i	−0.977994	+	0.208634i	$0.933098\pi$
$450$	−1.07288	−	7.46207i	−0.0505762	−	0.351765i
$451$	0.140579	+	0.0903448i	0.00661962	+	0.00425417i
$452$	5.87087	−	1.72384i	0.276143	−	0.0810828i
$453$	1.25356	−	8.71872i	0.0588975	−	0.409641i
$454$	−22.5051	+	25.9722i	−1.05622	+	1.21894i
$455$	1.55901	−	1.00192i	0.0730877	−	0.0469706i
$456$	−3.03279	−	3.50003i	−0.142024	−	0.163904i
$457$	−7.75658	−	2.27754i	−0.362837	−	0.106539i	0.0952320	−	0.995455i	$-0.469641\pi$
$457$	−7.75658	−	2.27754i	−0.362837	−	0.106539i	−0.458069	+	0.888916i	$0.651459\pi$
$458$	1.71124	−	3.74710i	0.0799612	−	0.175091i
$459$	5.85326			0.273207
$460$	0.175011	−	1.34307i	0.00815992	−	0.0626211i
$461$	20.4511			0.952505			0.476252	−	0.879309i	$-0.341995\pi$
$461$	20.4511			0.952505			0.476252	+	0.879309i	$0.341995\pi$
$462$	−0.200652	+	0.439366i	−0.00933516	+	0.0204411i
$463$	−1.53573	−	0.450930i	−0.0713713	−	0.0209565i	0.245852	−	0.969307i	$-0.420932\pi$
$463$	−1.53573	−	0.450930i	−0.0713713	−	0.0209565i	−0.317223	+	0.948351i	$0.602750\pi$
$464$	20.0879	+	23.1826i	0.932555	+	1.07623i
$465$	4.34991	−	2.79552i	0.201722	−	0.129639i
$466$	−6.63861	+	7.66136i	−0.307528	+	0.354906i
$467$	−1.35158	+	9.40047i	−0.0625438	+	0.435002i	0.934357	+	0.356337i	$0.115975\pi$
$467$	−1.35158	+	9.40047i	−0.0625438	+	0.435002i	−0.996901	+	0.0786643i	$0.974934\pi$
$468$	−1.39606	+	0.409920i	−0.0645329	+	0.0189486i
$469$	12.4384	+	7.99367i	0.574352	+	0.369113i
$470$	0.241658	+	1.68077i	0.0111468	+	0.0775280i
$471$	9.77609	+	21.4066i	0.450458	+	0.986366i
$472$	−6.29968	−	13.7944i	−0.289966	−	0.634938i
$473$	−0.338791	−	2.35634i	−0.0155776	−	0.108345i
$474$	13.0740	+	8.40215i	0.600509	+	0.385924i
$475$	−9.03856	+	2.65396i	−0.414718	+	0.121772i
$476$	−0.598009	+	4.15924i	−0.0274097	+	0.190639i
$477$	4.39643	−	5.07375i	0.201299	−	0.232311i
$478$	24.3994	−	15.6805i	1.11600	−	0.717211i
$479$	−20.0205	−	23.1049i	−0.914760	−	1.05569i	−0.998247	−	0.0591805i	$-0.981151\pi$
$479$	−20.0205	−	23.1049i	−0.914760	−	1.05569i	0.0834873	−	0.996509i	$-0.473394\pi$
$480$	−1.49399	−	0.438676i	−0.0681911	−	0.0200227i
$481$	9.81370	−	21.4890i	0.447466	−	0.979814i
$482$	19.3134			0.879700
$483$	−6.11853	−	1.70901i	−0.278403	−	0.0777628i
$484$	−5.93316			−0.269689
$485$	−1.03657	+	2.26977i	−0.0470681	+	0.103065i
$486$	−1.52977	−	0.449181i	−0.0693917	−	0.0203752i
$487$	7.68423	+	8.86807i	0.348206	+	0.401851i	0.902654	−	0.430368i	$-0.141616\pi$
$487$	7.68423	+	8.86807i	0.348206	+	0.401851i	−0.554448	+	0.832218i	$0.687071\pi$
$488$	−6.10018	+	3.92035i	−0.276142	+	0.177466i
$489$	3.27179	−	3.77584i	0.147955	−	0.170749i
$490$	0.620206	−	4.31363i	0.0280181	−	0.194870i
$491$	−24.6102	+	7.22621i	−1.11064	+	0.326114i	−0.785073	−	0.619404i	$-0.787374\pi$
$491$	−24.6102	+	7.22621i	−1.11064	+	0.326114i	−0.325570	+	0.945518i	$0.605556\pi$
$492$	−0.333123	−	0.214085i	−0.0150183	−	0.00965170i
$493$	5.33432	+	37.1010i	0.240246	+	1.67095i
$494$	3.54245	+	7.75689i	0.159383	+	0.348999i
$495$	−0.0495097	−	0.108411i	−0.00222530	−	0.00487272i
$496$	6.76439	+	47.0474i	0.303730	+	2.11249i
$497$	6.36135	+	4.08819i	0.285345	+	0.183380i
$498$	0.551535	−	0.161945i	0.0247149	−	0.00725694i
$499$	−0.437925	+	3.04583i	−0.0196042	+	0.136350i	−0.997273	−	0.0738018i	$-0.976487\pi$
$499$	−0.437925	+	3.04583i	−0.0196042	+	0.136350i	0.977669	+	0.210152i	$0.0673959\pi$
$500$	−1.79922	+	2.07641i	−0.0804636	+	0.0928599i
$501$	11.1159	−	7.14374i	0.496621	−	0.319159i
$502$	3.29386	+	3.80132i	0.147012	+	0.169661i
$503$	−17.5937	−	5.16598i	−0.784465	−	0.230340i	−0.135116	−	0.990830i	$-0.543141\pi$
$503$	−17.5937	−	5.16598i	−0.784465	−	0.230340i	−0.649350	+	0.760490i	$0.724959\pi$
$504$	−1.27918	+	2.80102i	−0.0569794	+	0.124767i
$505$	−2.82052			−0.125511
$506$	0.271740	+	1.72751i	0.0120803	+	0.0767972i
$507$	5.79228			0.257244
$508$	−3.50795	+	7.68133i	−0.155640	+	0.340804i
$509$	−10.2437	−	3.00783i	−0.454045	−	0.133320i	0.0467102	−	0.998908i	$-0.485126\pi$
$509$	−10.2437	−	3.00783i	−0.454045	−	0.133320i	−0.500756	+	0.865589i	$0.666944\pi$
$510$	−3.18463	−	3.67526i	−0.141018	−	0.162743i
$511$	−2.60900	+	1.67670i	−0.115415	+	0.0741730i
$512$	−5.21131	+	6.01417i	−0.230309	+	0.265791i
$513$	−0.283524	+	1.97195i	−0.0125179	+	0.0870637i
$514$	25.7680	−	7.56617i	1.13658	−	0.333729i
$515$	2.11541	+	1.35949i	0.0932161	+	0.0599063i
$516$	0.802814	+	5.58370i	0.0353419	+	0.245809i
$517$	−0.194178	−	0.425191i	−0.00853995	−	0.0186999i
$518$	7.71994	+	16.9043i	0.339195	+	0.742733i
$519$	0.990306	+	6.88773i	0.0434696	+	0.302338i
$520$	−2.73595	−	1.75829i	−0.119979	−	0.0771061i
$521$	2.47812	−	0.727641i	0.108568	−	0.0318785i	−0.226997	−	0.973895i	$-0.572891\pi$
$521$	2.47812	−	0.727641i	0.108568	−	0.0318785i	0.335565	+	0.942017i	$0.391073\pi$
$522$	1.45300	−	10.1058i	0.0635961	−	0.442320i
$523$	21.2117	−	24.4796i	0.927522	−	1.07042i	−0.0698208	−	0.997560i	$-0.522243\pi$
$523$	21.2117	−	24.4796i	0.927522	−	1.07042i	0.997342	−	0.0728574i	$-0.0232118\pi$
$524$	5.12689	−	3.29485i	0.223969	−	0.143936i
$525$	4.10170	+	4.73361i	0.179013	+	0.206592i
$526$	23.1826	+	6.80703i	1.01081	+	0.296801i
$527$	−24.1271	+	52.8310i	−1.05099	+	2.30136i
$528$	1.09555			0.0476778
$529$	−21.8893	+	7.06116i	−0.951707	+	0.307007i
$530$	−5.57780			−0.242284
$531$	−2.70997	+	5.93400i	−0.117603	+	0.257514i
$532$	−1.37227	−	0.402936i	−0.0594956	−	0.0174695i
$533$	−1.28458	−	1.48249i	−0.0556414	−	0.0642136i
$534$	−19.8567	+	12.7612i	−0.859285	+	0.552229i
$535$	−4.88059	+	5.63250i	−0.211006	+	0.243514i
$536$	3.69272	−	25.6834i	0.159501	−	1.10935i
$537$	−2.31193	+	0.678844i	−0.0997671	+	0.0292943i
$538$	−15.3331	−	9.85399i	−0.661057	−	0.424836i
$539$	0.170728	+	1.18744i	0.00735377	+	0.0511466i
$540$	0.117321	+	0.256896i	0.00504867	+	0.0110551i
$541$	4.76219	+	10.4277i	0.204743	+	0.448324i	0.983950	−	0.178442i	$-0.0571057\pi$
$541$	4.76219	+	10.4277i	0.204743	+	0.448324i	−0.779208	+	0.626766i	$0.784378\pi$
$542$	−0.802154	−	5.57910i	−0.0344554	−	0.239643i
$543$	−5.37996	−	3.45749i	−0.230876	−	0.148375i
$544$	16.7810	−	4.92735i	0.719479	−	0.211258i
$545$	0.205791	−	1.43131i	0.00881513	−	0.0613106i
$546$	3.71303	−	4.28506i	0.158903	−	0.183384i
$547$	−23.0671	+	14.8243i	−0.986276	+	0.633841i	−0.931149	−	0.364638i	$-0.881193\pi$
$547$	−23.0671	+	14.8243i	−0.986276	+	0.633841i	−0.0551267	+	0.998479i	$0.517556\pi$
$548$	7.23923	+	8.35451i	0.309244	+	0.356887i
$549$	2.99298	+	0.878817i	0.127737	+	0.0375070i
$550$	0.716250	−	1.56837i	0.0305410	−	0.0668755i
$551$	−12.7576			−0.543494
$552$	1.73238	+	11.0131i	0.0737352	+	0.468750i
$553$	−12.9120			−0.549075
$554$	−2.25953	+	4.94768i	−0.0959982	+	0.210207i
$555$	−4.39968	−	1.29186i	−0.186756	−	0.0548366i
$556$	−4.37574	−	5.04987i	−0.185573	−	0.214162i
$557$	−26.6453	+	17.1239i	−1.12900	+	0.725564i	−0.965351	−	0.260955i	$-0.915963\pi$
$557$	−26.6453	+	17.1239i	−1.12900	+	0.725564i	−0.163648	+	0.986519i	$0.552326\pi$
$558$	10.3600	−	11.9560i	0.438572	−	0.506140i
$559$	−3.97695	+	27.6603i	−0.168207	+	1.16991i
$560$	3.17263	−	0.931568i	0.134068	−	0.0393659i
$561$	1.12617	+	0.723747i	0.0475470	+	0.0305566i
$562$	−2.82696	−	19.6619i	−0.119248	−	0.829388i
$563$	−15.8643	−	34.7380i	−0.668601	−	1.46403i	−0.874285	−	0.485413i	$-0.838669\pi$
$563$	−15.8643	−	34.7380i	−0.668601	−	1.46403i	0.205684	−	0.978619i	$-0.434058\pi$
$564$	0.460134	+	1.00755i	0.0193751	+	0.0424256i
$565$	−0.837289	−	5.82347i	−0.0352250	−	0.244995i
$566$	11.8475	+	7.61391i	0.497986	+	0.320036i
$567$	1.27098	−	0.373193i	0.0533760	−	0.0156726i
$568$	1.88856	−	13.1352i	0.0792422	−	0.551142i
$569$	−17.2036	+	19.8541i	−0.721214	+	0.832325i	−0.991452	−	0.130468i	$-0.958352\pi$
$569$	−17.2036	+	19.8541i	−0.721214	+	0.832325i	0.270239	+	0.962793i	$0.412897\pi$
$570$	1.39245	−	0.894870i	0.0583231	−	0.0374820i
$571$	−14.0796	−	16.2488i	−0.589214	−	0.679989i	0.380346	−	0.924844i	$-0.375805\pi$
$571$	−14.0796	−	16.2488i	−0.589214	−	0.679989i	−0.969560	+	0.244855i	$0.921260\pi$
$572$	−0.319289	−	0.0937518i	−0.0133502	−	0.00391996i
$573$	−4.53376	+	9.92756i	−0.189401	+	0.414730i
$574$	1.54310			0.0644078
$575$	21.8408	+	6.10053i	0.910826	+	0.254410i
$576$	4.81650			0.200687
$577$	17.3688	−	38.0323i	0.723072	−	1.58331i	−0.0864777	−	0.996254i	$-0.527561\pi$
$577$	17.3688	−	38.0323i	0.723072	−	1.58331i	0.809549	−	0.587052i	$-0.199712\pi$
$578$	26.4048	+	7.75315i	1.09829	+	0.322488i
$579$	−3.51469	−	4.05617i	−0.146066	−	0.168569i
$580$	−1.52142	+	0.977759i	−0.0631737	+	0.0405993i
$581$	−0.312746	+	0.360928i	−0.0129749	+	0.0149738i
$582$	−1.08648	+	7.55663i	−0.0450360	+	0.313232i
$583$	1.47324	−	0.432582i	0.0610153	−	0.0179157i
$584$	4.57860	+	2.94249i	0.189464	+	0.121761i
$585$	0.199103	+	1.38479i	0.00823189	+	0.0572540i
$586$	−12.7031	−	27.8160i	−0.524762	−	1.14907i
$587$	−16.9713	−	37.1620i	−0.700481	−	1.53384i	−0.839388	−	0.543533i	$-0.817086\pi$
$587$	−16.9713	−	37.1620i	−0.700481	−	1.53384i	0.138907	−	0.990305i	$-0.455641\pi$
$588$	−0.404564	−	2.81381i	−0.0166840	−	0.116039i
$589$	−16.6300	−	10.6874i	−0.685226	−	0.440368i
$590$	5.20039	−	1.52697i	0.214097	−	0.0628644i
$591$	−0.737421	+	5.12887i	−0.0303334	+	0.210974i
$592$	27.6028	−	31.8554i	1.13447	−	1.30925i
$593$	5.24865	−	3.37310i	0.215536	−	0.138517i	−0.428418	−	0.903581i	$-0.640929\pi$
$593$	5.24865	−	3.37310i	0.215536	−	0.138517i	0.643954	+	0.765064i	$0.277293\pi$
$594$	−0.238788	−	0.275576i	−0.00979761	−	0.0113070i
$595$	3.87672	+	1.13831i	0.158930	+	0.0466660i
$596$	−5.29834	+	11.6017i	−0.217028	+	0.475226i
$597$	−6.60209			−0.270206
$598$	2.65250	−	20.3559i	0.108469	−	0.832415i
$599$	4.84725			0.198053			0.0990267	−	0.995085i	$-0.468427\pi$
$599$	4.84725			0.198053			0.0990267	+	0.995085i	$0.468427\pi$
$600$	4.56620	−	9.99859i	0.186415	−	0.408191i
$601$	19.7564	+	5.80099i	0.805878	+	0.236627i	0.658625	−	0.752472i	$-0.271138\pi$
$601$	19.7564	+	5.80099i	0.805878	+	0.236627i	0.147254	+	0.989099i	$0.452957\pi$
$602$	−14.3956	−	16.6134i	−0.586722	−	0.677113i
$603$	−9.39005	+	6.03462i	−0.382393	+	0.245749i
$604$	−3.12614	+	3.60776i	−0.127201	+	0.146798i
$605$	−0.811897	+	5.64687i	−0.0330083	+	0.229578i
$606$	−8.27993	+	2.43121i	−0.336349	+	0.0987610i
$607$	32.3481	+	20.7889i	1.31297	+	0.843794i	0.994561	−	0.104159i	$-0.0332151\pi$
$607$	32.3481	+	20.7889i	1.31297	+	0.843794i	0.318409	+	0.947953i	$0.396851\pi$
$608$	0.847164	+	5.89216i	0.0343570	+	0.238958i
$609$	3.52379	+	7.71602i	0.142791	+	0.312669i
$610$	−1.07660	−	2.35743i	−0.0435904	−	0.0954497i
$611$	0.780885	+	5.43118i	0.0315912	+	0.219722i
$612$	−2.66863	−	1.71502i	−0.107873	−	0.0693258i
$613$	−18.8808	+	5.54391i	−0.762589	+	0.223916i	−0.639826	−	0.768520i	$-0.720994\pi$
$613$	−18.8808	+	5.54391i	−0.762589	+	0.223916i	−0.122763	+	0.992436i	$0.539175\pi$
$614$	4.02224	−	27.9753i	0.162324	−	1.12899i
$615$	−0.249340	+	0.287753i	−0.0100543	+	0.0116033i
$616$	−0.592459	+	0.380750i	−0.0238708	+	0.0153409i
$617$	24.9030	+	28.7396i	1.00256	+	1.15701i	0.987578	+	0.157127i	$0.0502231\pi$
$617$	24.9030	+	28.7396i	1.00256	+	1.15701i	0.0149804	+	0.999888i	$0.495231\pi$
$618$	7.38185	+	2.16751i	0.296941	+	0.0871899i
$619$	15.4088	−	33.7407i	0.619334	−	1.35615i	−0.296669	−	0.954980i	$-0.595876\pi$
$619$	15.4088	−	33.7407i	0.619334	−	1.35615i	0.916003	−	0.401171i	$-0.131397\pi$
$620$	−2.80232			−0.112544
$621$	3.09240	−	3.66566i	0.124094	−	0.147098i
$622$	−29.3115			−1.17528
$623$	8.14658	−	17.8385i	0.326386	−	0.714686i
$624$	−12.3394	−	3.62317i	−0.493971	−	0.145043i
$625$	−13.7524	−	15.8711i	−0.550094	−	0.634843i
$626$	46.1569	−	29.6632i	1.84480	−	1.18558i
$627$	−0.298379	+	0.344348i	−0.0119161	+	0.0137519i
$628$	1.81508	−	12.6242i	0.0724297	−	0.503760i
$629$	49.4187	−	14.5106i	1.97045	−	0.578577i
$630$	−0.925839	−	0.595000i	−0.0368863	−	0.0237054i
$631$	2.22892	+	15.5025i	0.0887318	+	0.617143i	0.984860	+	0.173349i	$0.0554588\pi$
$631$	2.22892	+	15.5025i	0.0887318	+	0.617143i	−0.896129	+	0.443794i	$0.853632\pi$
$632$	9.41315	+	20.6119i	0.374435	+	0.819898i
$633$	7.79106	+	17.0600i	0.309667	+	0.678075i
$634$	0.109394	+	0.760849i	0.00434458	+	0.0302172i
$635$	6.83065	+	4.38979i	0.271066	+	0.174204i
$636$	−3.49105	+	1.02507i	−0.138429	+	0.0406465i
$637$	2.00412	−	13.9389i	0.0794060	−	0.552281i
$638$	1.52913	−	1.76471i	0.0605388	−	0.0698656i
$639$	−4.80234	+	3.08628i	−0.189978	+	0.122091i
$640$	−4.65987	−	5.37778i	−0.184197	−	0.212575i
$641$	21.4890	+	6.30974i	0.848764	+	0.249220i	0.677059	−	0.735929i	$-0.263254\pi$
$641$	21.4890	+	6.30974i	0.848764	+	0.249220i	0.171705	+	0.985148i	$0.445072\pi$
$642$	−9.47243	+	20.7417i	−0.373847	+	0.818611i
$643$	−24.9262			−0.982993			−0.491496	−	0.870880i	$-0.663550\pi$
$643$	−24.9262			−0.982993			−0.491496	+	0.870880i	$0.663550\pi$
$644$	2.28883	+	2.57193i	0.0901924	+	0.101348i
$645$	5.42412			0.213575
$646$	−7.72330	+	16.9117i	−0.303869	+	0.665381i
$647$	−37.3390	−	10.9637i	−1.46795	−	0.431029i	−0.552517	−	0.833501i	$-0.686333\pi$
$647$	−37.3390	−	10.9637i	−1.46795	−	0.431029i	−0.915432	+	0.402473i	$0.868151\pi$
$648$	−1.52231	−	1.75684i	−0.0598021	−	0.0690153i
$649$	−1.25513	+	0.806623i	−0.0492682	+	0.0316627i
$650$	−13.2541	+	15.2960i	−0.519869	+	0.599960i
$651$	−1.87056	+	13.0100i	−0.0733131	+	0.509904i
$652$	−2.59801	+	0.762846i	−0.101746	+	0.0298753i
$653$	−20.1875	−	12.9737i	−0.789996	−	0.507700i	0.0823412	−	0.996604i	$-0.473760\pi$
$653$	−20.1875	−	12.9737i	−0.789996	−	0.507700i	−0.872337	+	0.488905i	$0.837397\pi$
$654$	−0.629626	−	4.37915i	−0.0246203	−	0.171238i
$655$	−2.43430	−	5.33037i	−0.0951159	−	0.208275i
$656$	−1.45395	−	3.18371i	−0.0567672	−	0.124303i
$657$	−0.333197	−	2.31744i	−0.0129993	−	0.0904119i
$658$	−3.63116	−	2.33360i	−0.141557	−	0.0909734i
$659$	−19.7438	+	5.79731i	−0.769110	+	0.225831i	−0.642670	−	0.766143i	$-0.722173\pi$
$659$	−19.7438	+	5.79731i	−0.769110	+	0.225831i	−0.126440	+	0.991974i	$0.540355\pi$
$660$	−0.00919226	+	0.0639336i	−0.000357808	+	0.00248861i
$661$	15.2015	−	17.5435i	0.591269	−	0.682361i	−0.378719	−	0.925512i	$-0.623635\pi$
$661$	15.2015	−	17.5435i	0.591269	−	0.682361i	0.969989	+	0.243150i	$0.0781808\pi$
$662$	5.57307	−	3.58160i	0.216604	−	0.139203i
$663$	−10.2907	−	11.8761i	−0.399658	−	0.461230i
$664$	0.804162	+	0.236123i	0.0312075	+	0.00916336i
$665$	−0.571276	+	1.25092i	−0.0221531	+	0.0485086i
$666$	−14.0293			−0.543624
$667$	26.0531	+	16.2606i	1.00878	+	0.629612i
$668$	−7.16112			−0.277072
$669$	−8.17175	+	17.8936i	−0.315938	+	0.691808i
$670$	8.89806	+	2.61270i	0.343762	+	0.100938i
$671$	0.467187	+	0.539162i	0.0180355	+	0.0208141i
$672$	3.32967	−	2.13985i	0.128445	−	0.0825465i
$673$	−8.66871	+	10.0042i	−0.334154	+	0.385635i	−0.897816	−	0.440371i	$-0.854847\pi$
$673$	−8.66871	+	10.0042i	−0.334154	+	0.385635i	0.563661	+	0.826006i	$0.309392\pi$
$674$	−0.919036	+	6.39203i	−0.0353999	+	0.246212i
$675$	−4.53691	+	1.33216i	−0.174626	+	0.0512748i
$676$	−2.64083	−	1.69716i	−0.101570	−	0.0652753i
$677$	0.0951453	+	0.661750i	0.00365673	+	0.0254331i	0.991568	−	0.129587i	$-0.0413650\pi$
$677$	0.0951453	+	0.661750i	0.00365673	+	0.0254331i	−0.987911	+	0.155020i	$0.950456\pi$
$678$	−7.47762	−	16.3737i	−0.287176	−	0.628828i
$679$	−2.63491	−	5.76965i	−0.101119	−	0.221419i
$680$	−1.00909	−	7.01839i	−0.0386969	−	0.269143i
$681$	18.1332	+	11.6535i	0.694866	+	0.446563i
$682$	3.47161	−	1.01936i	0.132935	−	0.0390332i
$683$	−2.14468	+	14.9166i	−0.0820638	+	0.570766i	0.906757	+	0.421654i	$0.138550\pi$
$683$	−2.14468	+	14.9166i	−0.0820638	+	0.570766i	−0.988820	+	0.149112i	$0.952359\pi$
$684$	0.707053	−	0.815982i	0.0270348	−	0.0311999i
$685$	8.94200	−	5.74667i	0.341656	−	0.219569i
$686$	16.9356	+	19.5447i	0.646603	+	0.746220i
$687$	−2.47906	−	0.727919i	−0.0945822	−	0.0277718i
$688$	−20.7127	+	45.3545i	−0.789664	+	1.72912i
$689$	−18.0239			−0.686658
$690$	−3.98417	+	0.0526878i	−0.151675	+	0.00200579i
$691$	21.5100			0.818279			0.409140	−	0.912472i	$-0.365829\pi$
$691$	21.5100			0.818279			0.409140	+	0.912472i	$0.365829\pi$
$692$	1.56662	−	3.43043i	0.0595541	−	0.130405i
$693$	0.290682	+	0.0853519i	0.0110421	+	0.00324225i
$694$	−25.7240	−	29.6870i	−0.976468	−	1.12690i
$695$	−5.40498	+	3.47357i	−0.205022	+	0.131760i
$696$	9.74844	−	11.2503i	0.369514	−	0.426441i
$697$	0.608642	−	4.23320i	0.0230540	−	0.160344i
$698$	−49.9864	+	14.6773i	−1.89201	+	0.555545i
$699$	5.34898	+	3.43758i	0.202317	+	0.130021i
$700$	−0.483090	−	3.35997i	−0.0182591	−	0.126995i
$701$	3.79994	+	8.32070i	0.143522	+	0.314269i	0.967718	−	0.252036i	$-0.0811000\pi$
$701$	3.79994	+	8.32070i	0.143522	+	0.314269i	−0.824196	+	0.566304i	$0.808373\pi$
$702$	1.77814	+	3.89358i	0.0671114	+	0.146954i
$703$	2.49483	+	17.3519i	0.0940943	+	0.654440i
$704$	0.926698	+	0.595553i	0.0349262	+	0.0224457i
$705$	1.02190	−	0.300057i	0.0384870	−	0.0113008i
$706$	−6.26566	+	43.5786i	−0.235811	+	1.64010i
$707$	4.69511	−	5.41845i	0.176578	−	0.203782i
$708$	2.97421	−	1.91141i	0.111778	−	0.0718352i
$709$	3.51871	+	4.06081i	0.132148	+	0.152507i	0.817967	−	0.575265i	$-0.195101\pi$
$709$	3.51871	+	4.06081i	0.132148	+	0.152507i	−0.685819	+	0.727772i	$0.740556\pi$
$710$	4.55072	+	1.33621i	0.170785	+	0.0501471i
$711$	4.04930	−	8.86673i	0.151861	−	0.332528i
$712$	−34.4153			−1.28977
$713$	20.3391	+	43.0216i	0.761704	+	1.61117i
$714$	12.3617			0.462625
$715$	−0.132920	+	0.291054i	−0.00497092	+	0.0108848i
$716$	1.25296	+	0.367903i	0.0468254	+	0.0137492i
$717$	−11.9129	−	13.7482i	−0.444895	−	0.513436i
$718$	−4.49628	+	2.88958i	−0.167800	+	0.107838i
$719$	16.4159	−	18.9449i	0.612209	−	0.706527i	−0.361999	−	0.932179i	$-0.617906\pi$
$719$	16.4159	−	18.9449i	0.612209	−	0.706527i	0.974208	+	0.225651i	$0.0724510\pi$
$720$	−0.355248	+	2.47080i	−0.0132393	+	0.0920814i
$721$	−6.13306	+	1.80083i	−0.228407	+	0.0670664i
$722$	20.1604	+	12.9563i	0.750293	+	0.482184i
$723$	−1.72395	−	11.9903i	−0.0641143	−	0.445925i
$724$	1.43979	+	3.15269i	0.0535093	+	0.117169i
$725$	−12.5786	−	27.5433i	−0.467157	−	1.02293i
$726$	2.48403	+	17.2768i	0.0921910	+	0.641202i
$727$	35.5083	+	22.8198i	1.31693	+	0.846339i	0.994946	−	0.100406i	$-0.0320143\pi$
$727$	35.5083	+	22.8198i	1.31693	+	0.846339i	0.321983	+	0.946746i	$0.395651\pi$
$728$	7.93216	−	2.32909i	0.293985	−	0.0863219i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−1.27383	+	1.47008i	−0.0471467	+	0.0544102i
$731$	−51.2538	+	32.9388i	−1.89569	+	1.21829i
$732$	−1.10707	−	1.27762i	−0.0409184	−	0.0472223i
$733$	35.2846	+	10.3605i	1.30327	+	0.382673i	0.858426	−	0.512937i	$-0.171442\pi$
$733$	35.2846	+	10.3605i	1.30327	+	0.382673i	0.444840	+	0.895610i	$0.353261\pi$
$734$	1.90520	−	4.17182i	0.0703224	−	0.153985i
$735$	−2.73339			−0.100823
$736$	5.77996	−	13.1125i	0.213052	−	0.483332i
$737$	−2.55283			−0.0940346
$738$	−0.483927	+	1.05965i	−0.0178136	+	0.0390064i
$739$	−17.2494	−	5.06487i	−0.634528	−	0.186314i	−0.0513789	−	0.998679i	$-0.516362\pi$
$739$	−17.2494	−	5.06487i	−0.634528	−	0.186314i	−0.583149	+	0.812365i	$0.698180\pi$
$740$	1.62739	+	1.87811i	0.0598242	+	0.0690408i
$741$	4.49951	−	2.89166i	0.165294	−	0.106228i
$742$	9.28496	−	10.7154i	0.340862	−	0.393375i
$743$	−1.99098	+	13.8476i	−0.0730419	+	0.508018i	0.920154	+	0.391558i	$0.128064\pi$
$743$	−1.99098	+	13.8476i	−0.0730419	+	0.508018i	−0.993195	+	0.116460i	$0.962845\pi$
$744$	22.1321	−	6.49856i	0.811401	−	0.238249i
$745$	10.3169	+	6.63027i	0.377982	+	0.242914i
$746$	−0.808302	−	5.62186i	−0.0295940	−	0.205831i
$747$	−0.149772	−	0.327954i	−0.00547985	−	0.0119992i
$748$	−0.301387	−	0.659945i	−0.0110198	−	0.0241300i
$749$	−2.69613	−	18.7520i	−0.0985146	−	0.685184i
$750$	6.79959	+	4.36983i	0.248286	+	0.159564i
$751$	24.3508	−	7.15004i	0.888574	−	0.260909i	0.194577	−	0.980887i	$-0.437666\pi$
$751$	24.3508	−	7.15004i	0.888574	−	0.260909i	0.693997	+	0.719978i	$0.255848\pi$
$752$	−1.39329	+	9.69055i	−0.0508081	+	0.353378i
$753$	2.06596	−	2.38424i	0.0752876	−	0.0868866i
$754$	−23.0590	+	14.8191i	−0.839760	+	0.539681i
$755$	3.00589	+	3.46898i	0.109396	+	0.126249i
$756$	−0.688813	−	0.202254i	−0.0250519	−	0.00735590i
$757$	−16.8002	+	36.7873i	−0.610614	+	1.33706i	0.311539	+	0.950233i	$0.399155\pi$
$757$	−16.8002	+	36.7873i	−0.610614	+	1.33706i	−0.922153	+	0.386825i	$0.873572\pi$
$758$	−28.9019			−1.04977
$759$	1.04823	−	0.322905i	0.0380485	−	0.0117207i
$760$	2.41336			0.0875418
$761$	10.7849	−	23.6157i	0.390953	−	0.856069i	−0.607155	−	0.794584i	$-0.707689\pi$
$761$	10.7849	−	23.6157i	0.390953	−	0.856069i	0.998108	−	0.0614849i	$-0.0195836\pi$
$762$	23.8360	+	6.99887i	0.863486	+	0.253542i
$763$	2.40710	+	2.77794i	0.0871428	+	0.100568i
$764$	4.97585	−	3.19778i	0.180020	−	0.115692i
$765$	−1.99745	+	2.30517i	−0.0722178	+	0.0833438i
$766$	−6.59005	+	45.8348i	−0.238108	+	1.65608i
$767$	16.8044	−	4.93421i	0.606771	−	0.178164i
$768$	−10.2112	−	6.56236i	−0.368466	−	0.236799i
$769$	−4.65743	−	32.3932i	−0.167951	−	1.16813i	−0.883110	−	0.469165i	$-0.844555\pi$
$769$	−4.65743	−	32.3932i	−0.167951	−	1.16813i	0.715159	−	0.698962i	$-0.246354\pi$
$770$	−0.104561	−	0.228957i	−0.00376813	−	0.00825104i
$771$	−6.99741	−	15.3222i	−0.252005	−	0.551815i
$772$	0.413954	+	2.87912i	0.0148985	+	0.103622i
$773$	−10.4237	−	6.69888i	−0.374913	−	0.240942i	0.339591	−	0.940573i	$-0.389711\pi$
$773$	−10.4237	−	6.69888i	−0.374913	−	0.240942i	−0.714504	+	0.699631i	$0.753348\pi$
$774$	15.9231	−	4.67544i	0.572343	−	0.168055i
$775$	6.67720	−	46.4409i	0.239852	−	1.66821i
$776$	−7.28939	+	8.41240i	−0.261674	+	0.301988i
$777$	9.80561	−	6.30168i	0.351774	−	0.226072i
$778$	40.1858	+	46.3769i	1.44073	+	1.66269i
$779$	1.39667	+	0.410100i	0.0500410	+	0.0146934i
$780$	0.314973	−	0.689694i	0.0112778	−	0.0246950i
$781$	−1.30559			−0.0467176
$782$	37.3274	−	24.6924i	1.33483	−	0.882997i
$783$	−6.40370			−0.228850
$784$	10.4378	−	22.8556i	0.372779	−	0.816272i
$785$	−11.7666	−	3.45500i	−0.419970	−	0.123314i
$786$	−11.7408	−	13.5496i	−0.418779	−	0.483297i
$787$	1.44894	−	0.931176i	0.0516491	−	0.0331929i	−0.514561	−	0.857453i	$-0.672045\pi$
$787$	1.44894	−	0.931176i	0.0516491	−	0.0331929i	0.566211	+	0.824261i	$0.308409\pi$
$788$	1.83898	−	2.12230i	0.0655111	−	0.0756038i
$789$	2.15669	−	15.0001i	0.0767800	−	0.534017i
$790$	−7.77055	+	2.28164i	−0.276464	+	0.0811771i
$791$	12.5811	+	8.08541i	0.447334	+	0.287484i
$792$	−0.0756633	−	0.526250i	−0.00268858	−	0.0186995i
$793$	−3.47890	−	7.61774i	−0.123539	−	0.270514i
$794$	−17.5014	−	38.3227i	−0.621101	−	1.36002i
$795$	0.497886	+	3.46287i	0.0176582	+	0.122815i
$796$	3.01004	+	1.93443i	0.106688	+	0.0685642i
$797$	14.3695	−	4.21926i	0.508993	−	0.149454i	−0.0171452	−	0.999853i	$-0.505458\pi$
$797$	14.3695	−	4.21926i	0.508993	−	0.149454i	0.526138	+	0.850399i	$0.323640\pi$
$798$	−0.598783	+	4.16463i	−0.0211967	+	0.147426i
$799$	−7.83403	+	9.04095i	−0.277148	+	0.319846i
$800$	−11.8857	+	7.63845i	−0.420222	+	0.270060i
$801$	9.69496	+	11.1886i	0.342555	+	0.395329i
$802$	21.9903	+	6.45693i	0.776504	+	0.228002i
$803$	0.222441	−	0.487077i	0.00784976	−	0.0171886i
$804$	6.04930			0.213342
$805$	2.76103	−	1.82644i	0.0973134	−	0.0643735i
$806$	−42.4726			−1.49603
$807$	−4.74899	+	10.3988i	−0.167173	+	0.366057i
$808$	−12.0725	−	3.54481i	−0.424709	−	0.124706i
$809$	−8.87852	−	10.2464i	−0.312152	−	0.360243i	0.577895	−	0.816111i	$-0.303874\pi$
$809$	−8.87852	−	10.2464i	−0.312152	−	0.360243i	−0.890047	+	0.455868i	$0.849329\pi$
$810$	0.698939	−	0.449181i	0.0245582	−	0.0157826i
$811$	6.62459	−	7.64519i	0.232621	−	0.268459i	−0.627423	−	0.778678i	$-0.715890\pi$
$811$	6.62459	−	7.64519i	0.232621	−	0.268459i	0.860044	+	0.510220i	$0.170436\pi$
$812$	0.654246	−	4.55038i	0.0229595	−	0.159687i
$813$	−3.39207	+	0.996002i	−0.118965	+	0.0349313i
$814$	−2.69925	−	1.73470i	−0.0946086	−	0.0608012i
$815$	0.370522	+	2.57704i	0.0129788	+	0.0902697i
$816$	−11.6475	−	25.5045i	−0.407744	−	0.892836i
$817$	−8.61435	−	18.8628i	−0.301378	−	0.659926i
$818$	−6.06856	−	42.2077i	−0.212182	−	1.47576i
$819$	−2.99173	−	1.92267i	−0.104539	−	0.0671834i
$820$	0.197992	−	0.0581357i	0.00691418	−	0.00203019i
$821$	1.31610	−	9.15365i	0.0459321	−	0.319465i	−0.953882	−	0.300182i	$-0.902953\pi$
$821$	1.31610	−	9.15365i	0.0459321	−	0.319465i	0.999814	−	0.0192828i	$-0.00613828\pi$
$822$	21.2967	−	24.5777i	0.742808	−	0.857246i
$823$	−9.36483	+	6.01841i	−0.326438	+	0.209789i	−0.693586	−	0.720374i	$-0.743970\pi$
$823$	−9.36483	+	6.01841i	−0.326438	+	0.209789i	0.367149	+	0.930162i	$0.380334\pi$
$824$	7.34586	+	8.47758i	0.255905	+	0.295330i
$825$	−1.03763	−	0.304674i	−0.0361255	−	0.0106074i
$826$	−5.72327	+	12.5322i	−0.199138	+	0.436051i
$827$	−28.2453			−0.982186			−0.491093	−	0.871107i	$-0.663402\pi$
$827$	−28.2453			−0.982186			−0.491093	+	0.871107i	$0.663402\pi$
$828$	−2.48394	+	0.765171i	−0.0863230	+	0.0265915i
$829$	−13.3377			−0.463237			−0.231618	−	0.972807i	$-0.574402\pi$
$829$	−13.3377			−0.463237			−0.231618	+	0.972807i	$0.574402\pi$
$830$	−0.124435	+	0.272474i	−0.00431919	+	0.00945771i
$831$	3.27336	+	0.961145i	0.113552	+	0.0333417i
$832$	−8.46796	−	9.77255i	−0.293574	−	0.338802i
$833$	25.8285	−	16.5989i	0.894903	−	0.575119i
$834$	−12.8728	+	14.8560i	−0.445747	+	0.514420i
$835$	−0.979931	+	6.81557i	−0.0339119	+	0.235862i
$836$	0.236933	−	0.0695697i	0.00819449	−	0.00240612i
$837$	−8.34742	−	5.36456i	−0.288529	−	0.185426i
$838$	2.04587	+	14.2293i	0.0706734	+	0.491544i
$839$	11.4734	+	25.1233i	0.396106	+	0.867352i	0.997650	+	0.0685123i	$0.0218252\pi$
$839$	11.4734	+	25.1233i	0.396106	+	0.867352i	−0.601544	+	0.798840i	$0.705447\pi$
$840$	−0.666594	−	1.45964i	−0.0229997	−	0.0503623i
$841$	−1.70884	−	11.8852i	−0.0589254	−	0.409835i
$842$	42.0033	+	26.9939i	1.44753	+	0.930270i
$843$	−11.9544	+	3.51012i	−0.411730	+	0.120895i
$844$	1.44653	−	10.0609i	0.0497917	−	0.346309i
$845$	−1.97664	+	2.28116i	−0.0679984	+	0.0784743i
$846$	2.74125	−	1.76170i	0.0942462	−	0.0605684i
$847$	−9.49659	−	10.9596i	−0.326307	−	0.376578i
$848$	−30.8565	−	9.06027i	−1.05962	−	0.311131i
$849$	3.66942	−	8.03490i	0.125934	−	0.275757i
$850$	−44.1266			−1.51353
$851$	17.0215	−	38.6152i	0.583490	−	1.32371i
$852$	3.09378			0.105991
$853$	−8.35407	+	18.2929i	−0.286038	+	0.626336i	−0.997043	−	0.0768517i	$-0.975513\pi$
$853$	−8.35407	+	18.2929i	−0.286038	+	0.626336i	0.711005	+	0.703187i	$0.248240\pi$
$854$	6.32096	+	1.85600i	0.216299	+	0.0635111i
$855$	−0.679855	−	0.784595i	−0.0232506	−	0.0268326i
$856$	−27.9690	+	17.9746i	−0.955961	+	0.614359i
$857$	−24.2865	+	28.0281i	−0.829612	+	0.957423i	−0.999607	−	0.0280216i	$-0.991079\pi$
$857$	−24.2865	+	28.0281i	−0.829612	+	0.957423i	0.169995	+	0.985445i	$0.445625\pi$
$858$	−0.139320	+	0.968991i	−0.00475630	+	0.0330808i
$859$	14.0208	−	4.11689i	0.478385	−	0.140467i	−0.0336454	−	0.999434i	$-0.510712\pi$
$859$	14.0208	−	4.11689i	0.478385	−	0.140467i	0.512030	+	0.858967i	$0.328894\pi$
$860$	−2.47298	−	1.58929i	−0.0843278	−	0.0541942i
$861$	−0.137740	−	0.958003i	−0.00469417	−	0.0326487i
$862$	0.655034	+	1.43432i	0.0223106	+	0.0488533i
$863$	−9.64304	−	21.1153i	−0.328253	−	0.718774i	0.671500	−	0.741005i	$-0.265650\pi$
$863$	−9.64304	−	21.1153i	−0.328253	−	0.718774i	−0.999753	+	0.0222308i	$0.992923\pi$
$864$	0.425234	+	2.95757i	0.0144668	+	0.100619i
$865$	−3.05052	−	1.96045i	−0.103721	−	0.0666574i
$866$	−8.19970	+	2.40765i	−0.278637	+	0.0818152i
$867$	2.45645	−	17.0850i	0.0834253	−	0.580236i
$868$	4.66481	−	5.38348i	0.158334	−	0.182727i
$869$	1.87545	−	1.20528i	0.0636202	−	0.0408862i
$870$	3.48411	+	4.02088i	0.118123	+	0.136321i
$871$	28.7529	+	8.44262i	0.974255	+	0.286067i
$872$	2.67970	−	5.86772i	0.0907459	−	0.198706i
$873$	4.78837			0.162062
$874$	6.51071	+	13.7716i	0.220228	+	0.465831i
$875$	−6.71534			−0.227020
$876$	−0.527105	+	1.15420i	−0.0178092	+	0.0389968i
$877$	17.5582	+	5.15556i	0.592899	+	0.174091i	0.564398	−	0.825503i	$-0.309108\pi$
$877$	17.5582	+	5.15556i	0.592899	+	0.174091i	0.0285011	+	0.999594i	$0.490927\pi$
$878$	5.45021	+	6.28988i	0.183936	+	0.212273i
$879$	−16.1351	+	10.3694i	−0.544223	+	0.349751i
$880$	−0.373861	+	0.431459i	−0.0126029	+	0.0145445i
$881$	−1.81333	+	12.6120i	−0.0610927	+	0.424909i	0.936206	+	0.351452i	$0.114312\pi$
$881$	−1.81333	+	12.6120i	−0.0610927	+	0.424909i	−0.997298	+	0.0734564i	$0.976597\pi$
$882$	−8.02416	+	2.35611i	−0.270188	+	0.0793342i
$883$	−28.7691	−	18.4888i	−0.968158	−	0.622197i	−0.0419134	−	0.999121i	$-0.513345\pi$
$883$	−28.7691	−	18.4888i	−0.968158	−	0.622197i	−0.926244	+	0.376924i	$0.876982\pi$
$884$	1.21202	+	8.42980i	0.0407647	+	0.283525i
$885$	−1.41219	−	3.09226i	−0.0474701	−	0.103945i
$886$	18.5109	+	40.5332i	0.621885	+	1.36174i
$887$	6.56176	+	45.6380i	0.220322	+	1.53237i	0.736822	+	0.676087i	$0.236326\pi$
$887$	6.56176	+	45.6380i	0.220322	+	1.53237i	−0.516499	+	0.856288i	$0.672765\pi$
$888$	−17.2081	−	11.0590i	−0.577466	−	0.371115i
$889$	−19.8036	+	5.81487i	−0.664193	+	0.195025i
$890$	1.75049	−	12.1749i	0.0586766	−	0.408104i
$891$	−0.149772	+	0.172846i	−0.00501753	+	0.00579054i
$892$	8.96858	−	5.76376i	0.300290	−	0.192985i
$893$	−2.66641	−	3.07720i	−0.0892279	−	0.102974i
$894$	36.0014	+	10.5710i	1.20407	+	0.353546i
$895$	0.521607	−	1.14216i	0.0174354	−	0.0381782i
$896$	18.0881			0.604281
$897$	−12.8743	+	0.170254i	−0.429862	+	0.00568460i
$898$	14.6279			0.488138
$899$	26.3961	−	57.7993i	0.880358	−	1.92771i
$900$	2.45880	+	0.721970i	0.0819601	+	0.0240657i
$901$	−25.7334	−	29.6980i	−0.857305	−	0.989383i
$902$	−0.224133	+	0.144041i	−0.00746280	+	0.00479605i
$903$	−9.02914	+	10.4202i	−0.300471	+	0.346762i
$904$	3.73510	−	25.9782i	0.124228	−	0.864021i
$905$	3.19759	−	0.938896i	0.106291	−	0.0312100i
$906$	11.8143	+	7.59257i	0.392503	+	0.252246i
$907$	0.00337689	+	0.0234868i	0.000112128	+	0.000779866i	0.989877	−	0.141925i	$-0.0453291\pi$
$907$	0.00337689	+	0.0234868i	0.000112128	+	0.000779866i	−0.989765	+	0.142705i	$0.954420\pi$
$908$	−4.85281	−	10.6262i	−0.161046	−	0.352642i
$909$	2.24845	+	4.92342i	0.0745763	+	0.163299i
$910$	0.420492	+	2.92458i	0.0139392	+	0.0969490i
$911$	22.8632	+	14.6933i	0.757491	+	0.486810i	0.861494	−	0.507767i	$-0.169529\pi$
$911$	22.8632	+	14.6933i	0.757491	+	0.486810i	−0.104004	+	0.994577i	$0.533165\pi$
$912$	9.15660	−	2.68862i	0.303205	−	0.0890291i
$913$	0.0117348	−	0.0816177i	0.000388367	−	0.00270115i
$914$	8.44037	−	9.74070i	0.279183	−	0.322194i
$915$	−1.36747	+	0.878817i	−0.0452070	+	0.0290528i
$916$	0.916977	+	1.05825i	0.0302978	+	0.0349655i
$917$	14.2923	+	4.19659i	0.471972	+	0.138584i
$918$	−3.87672	+	8.48882i	−0.127951	+	0.280173i
$919$	30.8038			1.01612			0.508061	−	0.861321i	$-0.330362\pi$
$919$	30.8038			1.01612			0.508061	+	0.861321i	$0.330362\pi$
$920$	−4.92846	−	3.07601i	−0.162486	−	0.101413i
$921$	−17.7269			−0.584123
$922$	−13.5452	+	29.6597i	−0.446086	+	0.976792i
$923$	14.7051	+	4.31779i	0.484023	+	0.142122i
$924$	−0.107520	−	0.124085i	−0.00353715	−	0.00408208i
$925$	−35.0023	+	22.4946i	−1.15087	+	0.739619i
$926$	1.67111	−	1.92857i	0.0549161	−	0.0633766i
$927$	0.686735	−	4.77635i	0.0225553	−	0.156876i
$928$	−18.3591	+	5.39072i	−0.602667	+	0.176959i
$929$	44.1267	+	28.3585i	1.44775	+	0.930413i	0.999330	+	0.0365911i	$0.0116499\pi$
$929$	44.1267	+	28.3585i	1.44775	+	0.930413i	0.448421	+	0.893822i	$0.351986\pi$
$930$	1.17324	+	8.16008i	0.0384721	+	0.267580i
$931$	4.34105	+	9.50558i	0.142272	+	0.311533i
$932$	−1.43150	−	3.13454i	−0.0468902	−	0.102675i
$933$	2.61640	+	18.1975i	0.0856571	+	0.595758i
$934$	−12.7381	−	8.18626i	−0.416802	−	0.267863i
$935$	−0.669342	+	0.196537i	−0.0218898	+	0.00642743i
$936$	−0.888186	+	6.17747i	−0.0290313	+	0.201917i
$937$	−2.51957	+	2.90774i	−0.0823109	+	0.0949918i	−0.795411	−	0.606070i	$-0.792745\pi$
$937$	−2.51957	+	2.90774i	−0.0823109	+	0.0949918i	0.713100	+	0.701062i	$0.247290\pi$
$938$	−19.8312	+	12.7447i	−0.647510	+	0.416130i
$939$	−22.5359	−	26.0078i	−0.735431	−	0.848733i
$940$	−0.553824	−	0.162617i	−0.0180638	−	0.00530400i
$941$	−3.04443	+	6.66638i	−0.0992457	+	0.217318i	−0.952742	−	0.303782i	$-0.901751\pi$
$941$	−3.04443	+	6.66638i	−0.0992457	+	0.217318i	0.853496	+	0.521099i	$0.174478\pi$
$942$	−37.5203			−1.22248
$943$	−2.32952	−	2.61766i	−0.0758597	−	0.0852426i
$944$	31.2489			1.01707
$945$	−0.286752	+	0.627899i	−0.00932805	+	0.0204256i
$946$	3.64173	+	1.06931i	0.118403	+	0.0347662i
$947$	−25.3043	−	29.2028i	−0.822280	−	0.948962i	0.177099	−	0.984193i	$-0.443329\pi$
$947$	−25.3043	−	29.2028i	−0.822280	−	0.948962i	−0.999379	+	0.0352310i	$0.988783\pi$
$948$	−4.44415	+	2.85608i	−0.144339	+	0.0927612i
$949$	−4.11623	+	4.75038i	−0.133618	+	0.154204i
$950$	2.13743	−	14.8661i	0.0693474	−	0.482321i
$951$	0.462594	−	0.135830i	0.0150006	−	0.00440458i
$952$	15.1627	+	9.74445i	0.491425	+	0.315820i
$953$	2.28805	+	15.9137i	0.0741172	+	0.515496i	0.992732	+	0.120343i	$0.0383994\pi$
$953$	2.28805	+	15.9137i	0.0741172	+	0.515496i	−0.918615	+	0.395153i	$0.870691\pi$
$954$	4.44649	+	9.73645i	0.143960	+	0.315229i
$955$	−2.36258	−	5.17333i	−0.0764514	−	0.167405i
$956$	1.40308	+	9.75863i	0.0453788	+	0.315617i
$957$	−1.23208	−	0.791809i	−0.0398274	−	0.0255955i
$958$	46.7683	−	13.7324i	1.51102	−	0.443674i
$959$	−3.84526	+	26.7444i	−0.124170	+	0.863621i
$960$	−1.64365	+	1.89687i	−0.0530484	+	0.0612212i
$961$	56.7493	−	36.4706i	1.83062	−	1.17647i
$962$	24.6651	+	28.4651i	0.795236	+	0.917751i
$963$	13.7226	+	4.02932i	0.442205	+	0.129843i
$964$	−2.72722	+	5.97177i	−0.0878378	+	0.192338i
$965$	2.79683			0.0900333
$966$	6.53094	−	7.74163i	0.210130	−	0.249083i
$967$	24.1742			0.777391			0.388695	−	0.921366i	$-0.372926\pi$
$967$	24.1742			0.777391			0.388695	+	0.921366i	$0.372926\pi$
$968$	−10.5721	+	23.1496i	−0.339799	+	0.744056i
$969$	11.1887	+	3.28529i	0.359432	+	0.105539i
$970$	−2.60524	−	3.00661i	−0.0836494	−	0.0965365i
$971$	39.8288	−	25.5964i	1.27817	−	0.821428i	0.287507	−	0.957779i	$-0.407174\pi$
$971$	39.8288	−	25.5964i	1.27817	−	0.821428i	0.990661	+	0.136351i	$0.0435373\pi$
$972$	0.354905	−	0.409583i	0.0113836	−	0.0131374i
$973$	2.32426	−	16.1656i	0.0745124	−	0.518245i
$974$	−17.9505	+	5.27075i	−0.575172	+	0.168886i
$975$	10.6793	+	6.86319i	0.342012	+	0.219798i
$976$	−2.12650	−	14.7901i	−0.0680675	−	0.473420i
$977$	−3.76210	−	8.23785i	−0.120360	−	0.263552i	0.839856	−	0.542809i	$-0.182639\pi$
$977$	−3.76210	−	8.23785i	−0.120360	−	0.263552i	−0.960216	+	0.279257i	$0.909912\pi$
$978$	3.30904	+	7.24579i	0.105811	+	0.231695i
$979$	0.481868	+	3.35146i	0.0154006	+	0.107113i
$980$	1.24621	+	0.800893i	0.0398088	+	0.0255836i
$981$	−2.66250	+	0.781782i	−0.0850072	+	0.0249604i
$982$	5.81979	−	40.4776i	0.185717	−	1.29169i
$983$	−6.60707	+	7.62497i	−0.210733	+	0.243199i	−0.851269	−	0.524729i	$-0.824167\pi$
$983$	−6.60707	+	7.62497i	−0.210733	+	0.243199i	0.640536	+	0.767928i	$0.278712\pi$
$984$	−1.42888	+	0.918285i	−0.0455510	+	0.0292739i
$985$	−1.76824	−	2.04066i	−0.0563410	−	0.0650209i
$986$	−57.3396	−	16.8364i	−1.82607	−	0.536181i
$987$	−1.12465	+	2.46264i	−0.0357979	+	0.0783866i
$988$	−2.89869			−0.0922196
$989$	−6.45022	+	49.5004i	−0.205105	+	1.57402i
$990$	0.190017			0.00603914
$991$	−12.8272	+	28.0878i	−0.407471	+	0.892237i	0.588987	+	0.808143i	$0.299527\pi$
$991$	−12.8272	+	28.0878i	−0.407471	+	0.892237i	−0.996458	+	0.0840943i	$0.973200\pi$
$992$	−28.4476	−	8.35297i	−0.903212	−	0.265207i
$993$	−2.72103	−	3.14023i	−0.0863491	−	0.0996522i
$994$	−10.1422	+	6.51801i	−0.321692	+	0.206739i
$995$	2.25299	−	2.60009i	0.0714245	−	0.0824283i
$996$	−0.0278074	+	0.193405i	−0.000881112	+	0.00612827i
$997$	−9.94975	+	2.92151i	−0.315112	+	0.0925251i	−0.435464	−	0.900206i	$-0.643416\pi$
$997$	−9.94975	+	2.92151i	−0.315112	+	0.0925251i	0.120352	+	0.992731i	$0.461598\pi$
$998$	−4.12724	−	2.65242i	−0.130646	−	0.0839608i
$999$	1.25228	+	8.70981i	0.0396204	+	0.275566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.a.52.1	yes	10
3.2	odd	2		207.2.i.b.190.1		10
23.2	even	11		1587.2.a.o.1.2		5
23.4	even	11	inner	69.2.e.a.4.1	✓	10
23.21	odd	22		1587.2.a.p.1.2		5
69.2	odd	22		4761.2.a.br.1.4		5
69.44	even	22		4761.2.a.bq.1.4		5
69.50	odd	22		207.2.i.b.73.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.a.4.1	✓	10	23.4	even	11	inner
69.2.e.a.52.1	yes	10	1.1	even	1	trivial
207.2.i.b.73.1		10	69.50	odd	22
207.2.i.b.190.1		10	3.2	odd	2
1587.2.a.o.1.2		5	23.2	even	11
1587.2.a.p.1.2		5	23.21	odd	22
4761.2.a.bq.1.4		5	69.44	even	22
4761.2.a.br.1.4		5	69.2	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.662317 + 1.45027i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.354905 - 0.409583i) q^{4} +(-0.438384 + 0.281733i) q^{5} +(-1.04408 + 1.20493i) q^{6} +(0.188515 - 1.31115i) q^{7} +(-2.23047 + 0.654925i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.662317 + 1.45027i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.354905 - 0.409583i) q^{4} +(-0.438384 + 0.281733i) q^{5} +(-1.04408 + 1.20493i) q^{6} +(0.188515 - 1.31115i) q^{7} +(-2.23047 + 0.654925i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.118239 - 0.822373i) q^{10} +(0.0950085 + 0.208040i) q^{11} +(-0.225136 - 0.492980i) q^{12} +(-0.382075 - 2.65739i) q^{13} +(1.77667 + 1.14180i) q^{14} +(-0.500000 + 0.146813i) q^{15} +(0.681716 - 4.74144i) q^{16} +(3.83307 - 4.42360i) q^{17} +(-1.34125 + 0.861971i) q^{18} +(1.30463 + 1.50563i) q^{19} +(0.270978 + 0.0795663i) q^{20} +(0.550273 - 1.20493i) q^{21} -0.364640 q^{22} +(-0.745229 - 4.73758i) q^{23} -2.32463 q^{24} +(-1.96427 + 4.30115i) q^{25} +(4.10700 + 1.20592i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-0.603930 + 0.388122i) q^{28} +(-4.19353 + 4.83960i) q^{29} +(0.118239 - 0.822373i) q^{30} +(-9.52067 + 2.79552i) q^{31} +(2.51365 + 1.61543i) q^{32} +(0.0325485 + 0.226380i) q^{33} +(3.87672 + 8.48882i) q^{34} +(0.286752 + 0.627899i) q^{35} +(-0.0771283 - 0.536439i) q^{36} +(7.40250 + 4.75730i) q^{37} +(-3.04765 + 0.894870i) q^{38} +(0.382075 - 2.65739i) q^{39} +(0.793290 - 0.915505i) q^{40} +(0.614669 - 0.395023i) q^{41} +(1.38302 + 1.59609i) q^{42} +(-9.98718 - 2.93250i) q^{43} +(0.0514904 - 0.112748i) q^{44} -0.521109 q^{45} +(7.36436 + 2.05699i) q^{46} -2.04380 q^{47} +(1.98992 - 4.35731i) q^{48} +(5.03287 + 1.47778i) q^{49} +(-4.93687 - 5.69745i) q^{50} +(4.92408 - 3.16451i) q^{51} +(-0.952821 + 1.09961i) q^{52} +(0.955435 - 6.64520i) q^{53} +(-1.52977 + 0.449181i) q^{54} +(-0.100262 - 0.0644343i) q^{55} +(0.438229 + 3.04795i) q^{56} +(0.827602 + 1.81219i) q^{57} +(-4.24128 - 9.28712i) q^{58} +(0.928393 + 6.45712i) q^{59} +(0.237585 + 0.152687i) q^{60} +(2.99298 - 0.878817i) q^{61} +(2.25144 - 15.6591i) q^{62} +(0.867451 - 1.00109i) q^{63} +(4.05189 - 2.60399i) q^{64} +(0.916170 + 1.05732i) q^{65} +(-0.349869 - 0.102731i) q^{66} +(-4.63685 + 10.1533i) q^{67} -3.17221 q^{68} +(0.619688 - 4.75563i) q^{69} -1.10055 q^{70} +(-2.37142 + 5.19268i) q^{71} +(-2.23047 - 0.654925i) q^{72} +(-1.53321 - 1.76941i) q^{73} +(-11.8022 + 7.58480i) q^{74} +(-3.09647 + 3.57352i) q^{75} +(0.153657 - 1.06871i) q^{76} +(0.290682 - 0.0853519i) q^{77} +(3.60089 + 2.31415i) q^{78} +(-1.38723 - 9.64839i) q^{79} +(1.03696 + 2.27063i) q^{80} +(0.415415 + 0.909632i) q^{81} +(0.165786 + 1.15307i) q^{82} +(-0.303301 - 0.194920i) q^{83} +(-0.688813 + 0.202254i) q^{84} +(-0.434086 + 3.01914i) q^{85} +(10.8676 - 12.5419i) q^{86} +(-5.38714 + 3.46210i) q^{87} +(-0.348164 - 0.401803i) q^{88} +(14.2049 + 4.17094i) q^{89} +(0.345139 - 0.755750i) q^{90} -3.55627 q^{91} +(-1.67594 + 1.98662i) q^{92} -9.92260 q^{93} +(1.35364 - 2.96407i) q^{94} +(-0.996114 - 0.292486i) q^{95} +(1.95671 + 2.25817i) q^{96} +(4.02823 - 2.58879i) q^{97} +(-5.47655 + 6.32027i) q^{98} +(-0.0325485 + 0.226380i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9 - 2 * q^10 + 7 * q^11 + 14 * q^12 - 30 * q^13 + q^14 - 5 * q^15 + 12 * q^16 - 2 * q^17 - 4 * q^18 + 10 * q^19 + 4 * q^20 - 3 * q^21 + 6 * q^22 - q^23 - 18 * q^24 + 24 * q^25 + q^26 + q^27 + 9 * q^28 - 14 * q^29 + 2 * q^30 - 28 * q^31 + 23 * q^32 - 7 * q^33 - 8 * q^34 - 4 * q^35 - 3 * q^36 + 19 * q^37 - 15 * q^38 + 30 * q^39 - 13 * q^40 + 19 * q^41 + 21 * q^42 - 24 * q^43 + 54 * q^44 - 6 * q^45 + 18 * q^46 + 26 * q^47 + 10 * q^48 - 13 * q^49 - 36 * q^50 + 24 * q^51 - 57 * q^52 - q^53 + 4 * q^54 - 24 * q^55 - 10 * q^56 + q^57 + 10 * q^58 + 2 * q^59 + 7 * q^60 + 30 * q^61 - 24 * q^62 - 8 * q^63 + 13 * q^64 - 4 * q^65 - 28 * q^66 + 4 * q^67 - 50 * q^68 + q^69 + 6 * q^70 - 14 * q^71 - 15 * q^72 - 26 * q^73 - 12 * q^74 - 13 * q^75 + 19 * q^76 - 43 * q^77 + 10 * q^78 + 20 * q^79 - 5 * q^80 - q^81 + 10 * q^82 + 18 * q^83 - 42 * q^84 + 21 * q^85 + 14 * q^86 - 8 * q^87 - 38 * q^88 - 5 * q^89 + 9 * q^90 + 46 * q^91 + 52 * q^92 - 16 * q^93 - 6 * q^94 + 5 * q^95 - q^96 + 15 * q^97 + 58 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more