LMFDB - Embedded newform 690.2.m.c.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 3 x^{18} + 66 x^{17} - 163 x^{16} - 52 x^{15} + 1567 x^{14} - 6182 x^{13} + \cdots + 529 $ x^20 - 4x^19 - 3x^18 + 66x^17 - 163x^16 - 52x^15 + 1567x^14 - 6182x^13 + 17043x^12 - 35832x^11 + 60906x^10 - 87666x^9 + 106197x^8 - 102542x^7 + 92618x^6 - 8374x^5 + 38352x^4 + 60038x^3 + 32919x^2 + 5681*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			541.2
Root			$-0.359204 + 0.230846i$ of defining polynomial
Character	$\chi$	$=$	690.541
Dual form			690.2.m.c.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(1.54913 + 1.78779i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(1.54913 + 1.78779i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-0.654861 + 0.755750i) q^{10} +(-1.62678 - 1.04547i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(3.97412 - 4.58638i) q^{13} +(2.26976 + 0.666461i) q^{14} +(0.142315 + 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-2.45190 - 5.36891i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(3.60485 - 7.89352i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(1.99005 - 1.27893i) q^{21} -1.93376 q^{22} +(2.20490 + 4.25892i) q^{23} -1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.863659 - 6.00688i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(2.26976 - 0.666461i) q^{28} +(2.26162 + 4.95225i) q^{29} +(0.654861 + 0.755750i) q^{30} +(-0.123935 - 0.861987i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-1.26634 + 1.46144i) q^{33} +(-4.96532 - 3.19102i) q^{34} +(-1.99005 - 1.27893i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-5.29079 - 1.55352i) q^{37} +(-1.23497 - 8.58938i) q^{38} +(-3.97412 - 4.58638i) q^{39} +(0.415415 + 0.909632i) q^{40} +(-4.21153 + 1.23662i) q^{41} +(0.982698 - 2.15181i) q^{42} +(-1.59352 + 11.0832i) q^{43} +(-1.62678 + 1.04547i) q^{44} +1.00000 q^{45} +(4.15743 + 2.39077i) q^{46} -0.306240 q^{47} +(-0.841254 + 0.540641i) q^{48} +(0.199814 - 1.38973i) q^{49} +(0.415415 - 0.909632i) q^{50} +(-5.66321 + 1.66287i) q^{51} +(-2.52101 - 5.52024i) q^{52} +(4.65460 + 5.37169i) q^{53} +(0.142315 + 0.989821i) q^{54} +(1.85543 + 0.544803i) q^{55} +(1.54913 - 1.78779i) q^{56} +(-7.30015 - 4.69152i) q^{57} +(4.57999 + 2.94338i) q^{58} +(2.26729 - 2.61659i) q^{59} +(0.959493 + 0.281733i) q^{60} +(1.80512 + 12.5549i) q^{61} +(-0.570286 - 0.658145i) q^{62} +(-0.982698 - 2.15181i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-2.52101 + 5.52024i) q^{65} +(-0.275203 + 1.91408i) q^{66} +(8.25507 - 5.30521i) q^{67} -5.90229 q^{68} +(4.52936 - 1.57635i) q^{69} -2.36558 q^{70} +(3.04921 - 1.95961i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(1.63456 - 3.57920i) q^{73} +(-5.29079 + 1.55352i) q^{74} +(-0.415415 - 0.909632i) q^{75} +(-5.68269 - 6.55818i) q^{76} +(-0.651014 - 4.52790i) q^{77} +(-5.82283 - 1.70974i) q^{78} +(-3.55823 + 4.10642i) q^{79} +(0.841254 + 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-2.87440 + 3.31723i) q^{82} +(-3.72729 - 1.09443i) q^{83} +(-0.336657 - 2.34150i) q^{84} +(3.86518 + 4.46066i) q^{85} +(4.65146 + 10.1853i) q^{86} +(5.22371 - 1.53382i) q^{87} +(-0.803313 + 1.75901i) q^{88} +(-1.50084 + 10.4386i) q^{89} +(0.841254 - 0.540641i) q^{90} +14.3559 q^{91} +(4.79000 - 0.236428i) q^{92} -0.870851 q^{93} +(-0.257626 + 0.165566i) q^{94} +(-1.23497 + 8.58938i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(4.16125 - 1.22185i) q^{97} +(-0.583253 - 1.27715i) q^{98} +(1.26634 + 1.46144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−0.415415	−	0.909632i	−0.169592	−	0.371356i
$7$	1.54913	+	1.78779i	0.585515	+	0.675720i	0.968781	−	0.247918i	$-0.0797463\pi$
$7$	1.54913	+	1.78779i	0.585515	+	0.675720i	−0.383266	+	0.923638i	$0.625201\pi$
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	−0.654861	+	0.755750i	−0.207085	+	0.238989i
$11$	−1.62678	−	1.04547i	−0.490493	−	0.315221i	0.271910	−	0.962323i	$-0.412345\pi$
$11$	−1.62678	−	1.04547i	−0.490493	−	0.315221i	−0.762404	+	0.647102i	$0.775981\pi$
$12$	−0.841254	−	0.540641i	−0.242849	−	0.156070i
$13$	3.97412	−	4.58638i	1.10222	−	1.27203i	0.142895	−	0.989738i	$-0.454359\pi$
$13$	3.97412	−	4.58638i	1.10222	−	1.27203i	0.959328	−	0.282295i	$-0.0910955\pi$
$14$	2.26976	+	0.666461i	0.606618	+	0.178119i
$15$	0.142315	+	0.989821i	0.0367455	+	0.255571i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−2.45190	−	5.36891i	−0.594673	−	1.30215i	−0.932577	−	0.360972i	$-0.882445\pi$
$17$	−2.45190	−	5.36891i	−0.594673	−	1.30215i	0.337903	−	0.941181i	$-0.390282\pi$
$18$	−0.959493	+	0.281733i	−0.226155	+	0.0664050i
$19$	3.60485	−	7.89352i	0.827010	−	1.81090i	0.326372	−	0.945241i	$-0.394174\pi$
$19$	3.60485	−	7.89352i	0.827010	−	1.81090i	0.500638	−	0.865657i	$-0.333099\pi$
$20$	−0.142315	+	0.989821i	−0.0318226	+	0.221331i
$21$	1.99005	−	1.27893i	0.434265	−	0.279085i
$22$	−1.93376			−0.412279
$23$	2.20490	+	4.25892i	0.459754	+	0.888047i
$23$	2.20490	+	4.25892i	0.459754	+	0.888047i
$24$	−1.00000			−0.204124
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	0.863659	−	6.00688i	0.169377	−	1.17805i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	2.26976	−	0.666461i	0.428944	−	0.125949i
$29$	2.26162	+	4.95225i	0.419972	+	0.919611i	0.994849	+	0.101370i	$0.0323227\pi$
$29$	2.26162	+	4.95225i	0.419972	+	0.919611i	−0.574877	+	0.818240i	$0.694950\pi$
$30$	0.654861	+	0.755750i	0.119561	+	0.137980i
$31$	−0.123935	−	0.861987i	−0.0222594	−	0.154817i	0.975660	−	0.219288i	$-0.0703733\pi$
$31$	−0.123935	−	0.861987i	−0.0222594	−	0.154817i	−0.997920	+	0.0644702i	$0.979464\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	−1.26634	+	1.46144i	−0.220442	+	0.254404i
$34$	−4.96532	−	3.19102i	−0.851546	−	0.547255i
$35$	−1.99005	−	1.27893i	−0.336380	−	0.216179i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	−5.29079	−	1.55352i	−0.869801	−	0.255396i	−0.183770	−	0.982969i	$-0.558830\pi$
$37$	−5.29079	−	1.55352i	−0.869801	−	0.255396i	−0.686031	+	0.727573i	$0.740648\pi$
$38$	−1.23497	−	8.58938i	−0.200338	−	1.39338i
$39$	−3.97412	−	4.58638i	−0.636368	−	0.734408i
$40$	0.415415	+	0.909632i	0.0656829	+	0.143825i
$41$	−4.21153	+	1.23662i	−0.657731	+	0.193127i	−0.593533	−	0.804810i	$-0.702267\pi$
$41$	−4.21153	+	1.23662i	−0.657731	+	0.193127i	−0.0641982	+	0.997937i	$0.520449\pi$
$42$	0.982698	−	2.15181i	0.151634	−	0.332031i
$43$	−1.59352	+	11.0832i	−0.243010	+	1.69017i	0.393839	+	0.919180i	$0.371147\pi$
$43$	−1.59352	+	11.0832i	−0.243010	+	1.69017i	−0.636848	+	0.770989i	$0.719762\pi$
$44$	−1.62678	+	1.04547i	−0.245247	+	0.157610i
$45$	1.00000			0.149071
$46$	4.15743	+	2.39077i	0.612979	+	0.352500i
$47$	−0.306240			−0.0446697			−0.0223349	−	0.999751i	$-0.507110\pi$
$47$	−0.306240			−0.0446697			−0.0223349	+	0.999751i	$0.507110\pi$
$48$	−0.841254	+	0.540641i	−0.121424	+	0.0780348i
$49$	0.199814	−	1.38973i	0.0285448	−	0.198534i
$50$	0.415415	−	0.909632i	0.0587486	−	0.128641i
$51$	−5.66321	+	1.66287i	−0.793008	+	0.232848i
$52$	−2.52101	−	5.52024i	−0.349601	−	0.765519i
$53$	4.65460	+	5.37169i	0.639358	+	0.737858i	0.979261	−	0.202602i	$-0.0649398\pi$
$53$	4.65460	+	5.37169i	0.639358	+	0.737858i	−0.339903	+	0.940460i	$0.610394\pi$
$54$	0.142315	+	0.989821i	0.0193666	+	0.134698i
$55$	1.85543	+	0.544803i	0.250186	+	0.0734612i
$56$	1.54913	−	1.78779i	0.207011	−	0.238903i
$57$	−7.30015	−	4.69152i	−0.966929	−	0.621408i
$58$	4.57999	+	2.94338i	0.601382	+	0.386484i
$59$	2.26729	−	2.61659i	0.295176	−	0.340652i	−0.588718	−	0.808339i	$-0.700367\pi$
$59$	2.26729	−	2.61659i	0.295176	−	0.340652i	0.883894	+	0.467687i	$0.154913\pi$
$60$	0.959493	+	0.281733i	0.123870	+	0.0363715i
$61$	1.80512	+	12.5549i	0.231122	+	1.60749i	0.693264	+	0.720684i	$0.256172\pi$
$61$	1.80512	+	12.5549i	0.231122	+	1.60749i	−0.462142	+	0.886806i	$0.652919\pi$
$62$	−0.570286	−	0.658145i	−0.0724264	−	0.0835846i
$63$	−0.982698	−	2.15181i	−0.123808	−	0.271102i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−2.52101	+	5.52024i	−0.312692	+	0.684701i
$66$	−0.275203	+	1.91408i	−0.0338751	+	0.235607i
$67$	8.25507	−	5.30521i	1.00852	−	0.648135i	0.0715087	−	0.997440i	$-0.477219\pi$
$67$	8.25507	−	5.30521i	1.00852	−	0.648135i	0.937009	+	0.349305i	$0.113582\pi$
$68$	−5.90229			−0.715758
$69$	4.52936	−	1.57635i	0.545271	−	0.189770i
$70$	−2.36558			−0.282741
$71$	3.04921	−	1.95961i	0.361875	−	0.232563i	−0.347050	−	0.937847i	$-0.612817\pi$
$71$	3.04921	−	1.95961i	0.361875	−	0.232563i	0.708925	+	0.705284i	$0.249180\pi$
$72$	−0.142315	+	0.989821i	−0.0167720	+	0.116652i
$73$	1.63456	−	3.57920i	0.191311	−	0.418913i	−0.789533	−	0.613709i	$-0.789677\pi$
$73$	1.63456	−	3.57920i	0.191311	−	0.418913i	0.980844	+	0.194795i	$0.0624042\pi$
$74$	−5.29079	+	1.55352i	−0.615042	+	0.180593i
$75$	−0.415415	−	0.909632i	−0.0479680	−	0.105035i
$76$	−5.68269	−	6.55818i	−0.651849	−	0.752274i
$77$	−0.651014	−	4.52790i	−0.0741900	−	0.516003i
$78$	−5.82283	−	1.70974i	−0.659305	−	0.193589i
$79$	−3.55823	+	4.10642i	−0.400333	+	0.462008i	−0.919746	−	0.392515i	$-0.871605\pi$
$79$	−3.55823	+	4.10642i	−0.400333	+	0.462008i	0.519413	+	0.854523i	$0.326151\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−2.87440	+	3.31723i	−0.317424	+	0.366327i
$83$	−3.72729	−	1.09443i	−0.409124	−	0.120130i	0.0706935	−	0.997498i	$-0.477479\pi$
$83$	−3.72729	−	1.09443i	−0.409124	−	0.120130i	−0.479817	+	0.877369i	$0.659297\pi$
$84$	−0.336657	−	2.34150i	−0.0367323	−	0.255479i
$85$	3.86518	+	4.46066i	0.419238	+	0.483826i
$86$	4.65146	+	10.1853i	0.501580	+	1.09831i
$87$	5.22371	−	1.53382i	0.560040	−	0.164443i
$88$	−0.803313	+	1.75901i	−0.0856334	+	0.187511i
$89$	−1.50084	+	10.4386i	−0.159089	+	1.10649i	0.741228	+	0.671253i	$0.234244\pi$
$89$	−1.50084	+	10.4386i	−0.159089	+	1.10649i	−0.900317	+	0.435234i	$0.856666\pi$
$90$	0.841254	−	0.540641i	0.0886759	−	0.0569885i
$91$	14.3559			1.50491
$92$	4.79000	−	0.236428i	0.499392	−	0.0246493i
$93$	−0.870851			−0.0903031
$94$	−0.257626	+	0.165566i	−0.0265721	+	0.0170768i
$95$	−1.23497	+	8.58938i	−0.126705	+	0.881252i
$96$	−0.415415	+	0.909632i	−0.0423981	+	0.0928389i
$97$	4.16125	−	1.22185i	0.422511	−	0.124061i	−0.0635633	−	0.997978i	$-0.520246\pi$
$97$	4.16125	−	1.22185i	0.422511	−	0.124061i	0.486075	+	0.873917i	$0.338428\pi$
$98$	−0.583253	−	1.27715i	−0.0589175	−	0.129011i
$99$	1.26634	+	1.46144i	0.127272	+	0.146880i
$100$	−0.142315	−	0.989821i	−0.0142315	−	0.0989821i
$101$	14.8735	+	4.36724i	1.47996	+	0.434557i	0.919324	−	0.393503i	$-0.128737\pi$
$101$	14.8735	+	4.36724i	1.47996	+	0.434557i	0.560641	+	0.828059i	$0.310555\pi$
$102$	−3.86518	+	4.46066i	−0.382710	+	0.441671i
$103$	−0.959972	−	0.616937i	−0.0945888	−	0.0607886i	0.492491	−	0.870317i	$-0.336086\pi$
$103$	−0.959972	−	0.616937i	−0.0945888	−	0.0607886i	−0.587080	+	0.809529i	$0.699723\pi$
$104$	−5.10527	−	3.28096i	−0.500613	−	0.321724i
$105$	−1.54913	+	1.78779i	−0.151179	+	0.174470i
$106$	6.81985	+	2.00249i	0.662403	+	0.194499i
$107$	−1.20688	−	8.39401i	−0.116673	−	0.811480i	−0.961177	−	0.275931i	$-0.911014\pi$
$107$	−1.20688	−	8.39401i	−0.116673	−	0.811480i	0.844504	−	0.535549i	$-0.179895\pi$
$108$	0.654861	+	0.755750i	0.0630140	+	0.0727220i
$109$	4.98441	+	10.9143i	0.477420	+	1.04540i	0.983165	+	0.182720i	$0.0584903\pi$
$109$	4.98441	+	10.9143i	0.477420	+	1.04540i	−0.505745	+	0.862683i	$0.668782\pi$
$110$	1.85543	−	0.544803i	0.176908	−	0.0519449i
$111$	−2.29066	+	5.01585i	−0.217420	+	0.476083i
$112$	0.336657	−	2.34150i	0.0318111	−	0.221251i
$113$	−15.2523	+	9.80207i	−1.43482	+	0.922101i	−0.435053	+	0.900405i	$0.643270\pi$
$113$	−15.2523	+	9.80207i	−1.43482	+	0.922101i	−0.999765	+	0.0216960i	$0.993093\pi$
$114$	−8.67771			−0.812742
$115$	−3.31546	−	3.46521i	−0.309169	−	0.323133i
$116$	5.44424			0.505485
$117$	−5.10527	+	3.28096i	−0.471983	+	0.303325i
$118$	0.492730	−	3.42701i	0.0453594	−	0.315482i
$119$	5.80017	−	12.7006i	0.531701	−	1.16426i
$120$	0.959493	−	0.281733i	0.0875893	−	0.0257185i
$121$	−3.01615	−	6.60445i	−0.274196	−	0.600405i
$122$	8.30625	+	9.58593i	0.752013	+	0.867869i
$123$	0.624667	+	4.34465i	0.0563243	+	0.391744i
$124$	−0.835576	−	0.245347i	−0.0750369	−	0.0220328i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−1.99005	−	1.27893i	−0.177288	−	0.113936i
$127$	−2.59811	−	1.66970i	−0.230545	−	0.148162i	0.420269	−	0.907400i	$-0.361936\pi$
$127$	−2.59811	−	1.66970i	−0.230545	−	0.148162i	−0.650814	+	0.759237i	$0.725572\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	10.7436	+	3.15460i	0.945920	+	0.277747i
$130$	0.863659	+	6.00688i	0.0757479	+	0.526838i
$131$	9.84731	+	11.3644i	0.860363	+	0.992912i	0.999996	+	0.00270877i	$0.000862229\pi$
$131$	9.84731	+	11.3644i	0.860363	+	0.992912i	−0.139633	+	0.990203i	$0.544592\pi$
$132$	0.803313	+	1.75901i	0.0699194	+	0.153102i
$133$	19.6963	−	5.78336i	1.70789	−	0.501481i
$134$	4.07640	−	8.92606i	0.352147	−	0.771094i
$135$	0.142315	−	0.989821i	0.0122485	−	0.0851903i
$136$	−4.96532	+	3.19102i	−0.425773	+	0.273628i
$137$	−19.4446			−1.66127			−0.830633	−	0.556821i	$-0.812021\pi$
$137$	−19.4446			−1.66127			−0.830633	+	0.556821i	$0.812021\pi$
$138$	2.95810	−	3.77487i	0.251810	−	0.321338i
$139$	2.62788			0.222894			0.111447	−	0.993770i	$-0.464452\pi$
$139$	2.62788			0.222894			0.111447	+	0.993770i	$0.464452\pi$
$140$	−1.99005	+	1.27893i	−0.168190	+	0.108089i
$141$	−0.0435825	+	0.303123i	−0.00367031	+	0.0255276i
$142$	1.50572	−	3.29706i	0.126357	−	0.276683i
$143$	−11.2599	+	3.30622i	−0.941604	+	0.276480i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	−3.56522	−	4.11448i	−0.296075	−	0.341689i
$146$	−0.559977	−	3.89472i	−0.0463440	−	0.322330i
$147$	−1.34715	−	0.395560i	−0.111111	−	0.0326252i
$148$	−3.61100	+	4.16732i	−0.296823	+	0.342551i
$149$	−0.874541	−	0.562033i	−0.0716452	−	0.0460436i	0.504328	−	0.863512i	$-0.331740\pi$
$149$	−0.874541	−	0.562033i	−0.0716452	−	0.0460436i	−0.575973	+	0.817469i	$0.695377\pi$
$150$	−0.841254	−	0.540641i	−0.0686881	−	0.0441431i
$151$	12.3623	−	14.2669i	1.00603	−	1.16102i	0.0191118	−	0.999817i	$-0.493916\pi$
$151$	12.3623	−	14.2669i	1.00603	−	1.16102i	0.986921	−	0.161206i	$-0.0515384\pi$
$152$	−8.32620	−	2.44479i	−0.675344	−	0.198299i
$153$	0.839984	+	5.84222i	0.0679087	+	0.472315i
$154$	−2.99564	−	3.45715i	−0.241395	−	0.278585i
$155$	0.361765	+	0.792154i	0.0290576	+	0.0636273i
$156$	−5.82283	+	1.70974i	−0.466199	+	0.136888i
$157$	−3.25537	+	7.12827i	−0.259807	+	0.568898i	−0.993917	−	0.110133i	$-0.964872\pi$
$157$	−3.25537	+	7.12827i	−0.259807	+	0.568898i	0.734110	+	0.679031i	$0.237600\pi$
$158$	−0.773278	+	5.37827i	−0.0615187	+	0.427872i
$159$	5.97943	−	3.84275i	0.474200	−	0.304750i
$160$	1.00000			0.0790569
$161$	−4.19838	+	10.5395i	−0.330878	+	0.830629i
$162$	1.00000			0.0785674
$163$	1.39755	−	0.898152i	0.109465	−	0.0703487i	−0.484763	−	0.874646i	$-0.661094\pi$
$163$	1.39755	−	0.898152i	0.109465	−	0.0703487i	0.594228	+	0.804297i	$0.297458\pi$
$164$	−0.624667	+	4.34465i	−0.0487783	+	0.339260i
$165$	0.803313	−	1.75901i	0.0625378	−	0.136939i
$166$	−3.72729	+	1.09443i	−0.289294	+	0.0849444i
$167$	−5.01459	−	10.9804i	−0.388041	−	0.849691i	−0.998344	−	0.0575233i	$-0.981680\pi$
$167$	−5.01459	−	10.9804i	−0.388041	−	0.849691i	0.610303	−	0.792168i	$-0.291048\pi$
$168$	−1.54913	−	1.78779i	−0.119518	−	0.137931i
$169$	−3.39115	−	23.5859i	−0.260857	−	1.81430i
$170$	5.66321	+	1.66287i	0.434348	+	0.127536i
$171$	−5.68269	+	6.55818i	−0.434566	+	0.501516i
$172$	9.41964	+	6.05363i	0.718241	+	0.461585i
$173$	−18.8182	−	12.0937i	−1.43072	−	0.919470i	−0.999855	−	0.0170557i	$-0.994571\pi$
$173$	−18.8182	−	12.0937i	−1.43072	−	0.919470i	−0.430869	−	0.902414i	$-0.641793\pi$
$174$	3.56522	−	4.11448i	0.270279	−	0.311918i
$175$	2.26976	+	0.666461i	0.171578	+	0.0503797i
$176$	0.275203	+	1.91408i	0.0207442	+	0.144279i
$177$	−2.26729	−	2.61659i	−0.170420	−	0.196675i
$178$	4.38093	+	9.59291i	0.328365	+	0.719019i
$179$	10.5210	−	3.08926i	0.786379	−	0.230902i	0.136199	−	0.990682i	$-0.456511\pi$
$179$	10.5210	−	3.08926i	0.786379	−	0.230902i	0.650181	+	0.759780i	$0.274693\pi$
$180$	0.415415	−	0.909632i	0.0309632	−	0.0678000i
$181$	−2.90131	+	20.1791i	−0.215653	+	1.49990i	0.538179	+	0.842830i	$0.319112\pi$
$181$	−2.90131	+	20.1791i	−0.215653	+	1.49990i	−0.753832	+	0.657067i	$0.771797\pi$
$182$	12.0769	−	7.76137i	0.895202	−	0.575311i
$183$	12.6840			0.937628
$184$	3.90178	−	2.78857i	0.287643	−	0.205576i
$185$	5.51415			0.405409
$186$	−0.732607	+	0.470818i	−0.0537173	+	0.0345220i
$187$	−1.62433	+	11.2974i	−0.118783	+	0.826151i
$188$	−0.127217	+	0.278566i	−0.00927824	+	0.0203165i
$189$	−2.26976	+	0.666461i	−0.165101	+	0.0484779i
$190$	3.60485	+	7.89352i	0.261523	+	0.572656i
$191$	12.6019	+	14.5434i	0.911841	+	1.05232i	0.998426	+	0.0560762i	$0.0178590\pi$
$191$	12.6019	+	14.5434i	0.911841	+	1.05232i	−0.0865855	+	0.996244i	$0.527596\pi$
$192$	0.142315	+	0.989821i	0.0102707	+	0.0714342i
$193$	4.83087	+	1.41847i	0.347733	+	0.102104i	0.450935	−	0.892557i	$-0.351091\pi$
$193$	4.83087	+	1.41847i	0.347733	+	0.102104i	−0.103202	+	0.994660i	$0.532909\pi$
$194$	2.84009	−	3.27763i	0.203906	−	0.235320i
$195$	5.10527	+	3.28096i	0.365596	+	0.234954i
$196$	−1.18114	−	0.759074i	−0.0843673	−	0.0542195i
$197$	−10.0796	+	11.6325i	−0.718141	+	0.828779i	−0.991082	−	0.133252i	$-0.957458\pi$
$197$	−10.0796	+	11.6325i	−0.718141	+	0.828779i	0.272941	+	0.962031i	$0.412004\pi$
$198$	1.85543	+	0.544803i	0.131860	+	0.0387175i
$199$	2.28126	+	15.8665i	0.161714	+	1.12475i	0.895402	+	0.445259i	$0.146888\pi$
$199$	2.28126	+	15.8665i	0.161714	+	1.12475i	−0.733688	+	0.679487i	$0.762202\pi$
$200$	−0.654861	−	0.755750i	−0.0463056	−	0.0534396i
$201$	−4.07640	−	8.92606i	−0.287527	−	0.629596i
$202$	14.8735	−	4.36724i	1.04649	−	0.307278i
$203$	−5.35004	+	11.7150i	−0.375499	+	0.822229i
$204$	−0.839984	+	5.84222i	−0.0588106	+	0.409037i
$205$	3.69254	−	2.37305i	0.257898	−	0.165741i
$206$	−1.14112			−0.0795057
$207$	−0.915710	−	4.70760i	−0.0636462	−	0.327201i
$208$	−6.06865			−0.420785
$209$	−14.1167	+	9.07228i	−0.976476	+	0.627543i
$210$	−0.336657	+	2.34150i	−0.0232316	+	0.161579i
$211$	−8.23589	+	18.0341i	−0.566982	+	1.24152i	0.381406	+	0.924407i	$0.375440\pi$
$211$	−8.23589	+	18.0341i	−0.566982	+	1.24152i	−0.948389	+	0.317110i	$0.897287\pi$
$212$	6.81985	−	2.00249i	0.468389	−	0.137532i
$213$	−1.50572	−	3.29706i	−0.103170	−	0.225911i
$214$	−5.55344	−	6.40901i	−0.379625	−	0.438111i
$215$	−1.59352	−	11.0832i	−0.108677	−	0.755866i
$216$	0.959493	+	0.281733i	0.0652852	+	0.0191695i
$217$	1.34906	−	1.55690i	0.0915801	−	0.105689i
$218$	10.0939	+	6.48695i	0.683644	+	0.439351i
$219$	−3.31014	−	2.12730i	−0.223679	−	0.143750i
$220$	1.26634	−	1.46144i	0.0853768	−	0.0985301i
$221$	−34.3680	−	10.0914i	−2.31184	−	0.678818i
$222$	0.784746	+	5.45803i	0.0526687	+	0.366319i
$223$	13.5527	+	15.6406i	0.907555	+	1.04737i	0.998671	+	0.0515342i	$0.0164111\pi$
$223$	13.5527	+	15.6406i	0.907555	+	1.04737i	−0.0911161	+	0.995840i	$0.529043\pi$
$224$	−0.982698	−	2.15181i	−0.0656593	−	0.143774i
$225$	−0.959493	+	0.281733i	−0.0639662	+	0.0187822i
$226$	−7.53167	+	16.4920i	−0.500999	+	1.09703i
$227$	3.84330	−	26.7308i	0.255089	−	1.77418i	−0.311562	−	0.950226i	$-0.600852\pi$
$227$	3.84330	−	26.7308i	0.255089	−	1.77418i	0.566651	−	0.823958i	$-0.308239\pi$
$228$	−7.30015	+	4.69152i	−0.483465	+	0.310704i
$229$	−24.1932			−1.59873			−0.799366	−	0.600844i	$-0.794831\pi$
$229$	−24.1932			−1.59873			−0.799366	+	0.600844i	$0.794831\pi$
$230$	−4.66258	−	1.12265i	−0.307441	−	0.0740252i
$231$	−4.57447			−0.300978
$232$	4.57999	−	2.94338i	0.300691	−	0.193242i
$233$	−0.441041	+	3.06751i	−0.0288936	+	0.200959i	−0.999155	−	0.0411001i	$-0.986914\pi$
$233$	−0.441041	+	3.06751i	−0.0288936	+	0.200959i	0.970261	+	0.242059i	$0.0778228\pi$
$234$	−2.52101	+	5.52024i	−0.164803	+	0.360869i
$235$	0.293835	−	0.0862778i	0.0191677	−	0.00562815i
$236$	−1.43827	−	3.14937i	−0.0936235	−	0.205007i
$237$	3.55823	+	4.10642i	0.231132	+	0.266741i
$238$	−1.98705	−	13.8202i	−0.128801	−	0.895833i
$239$	−1.19283	−	0.350247i	−0.0771579	−	0.0226556i	0.242926	−	0.970045i	$-0.421893\pi$
$239$	−1.19283	−	0.350247i	−0.0771579	−	0.0226556i	−0.320084	+	0.947389i	$0.603711\pi$
$240$	0.654861	−	0.755750i	0.0422711	−	0.0487834i
$241$	20.5486	+	13.2058i	1.32365	+	0.850661i	0.995573	−	0.0939892i	$-0.0299619\pi$
$241$	20.5486	+	13.2058i	1.32365	+	0.850661i	0.328081	+	0.944650i	$0.393598\pi$
$242$	−6.10798	−	3.92536i	−0.392636	−	0.252332i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	12.1702	+	3.57350i	0.779118	+	0.228770i
$245$	0.199814	+	1.38973i	0.0127656	+	0.0887869i
$246$	2.87440	+	3.31723i	0.183265	+	0.211499i
$247$	−21.8766	−	47.9030i	−1.39197	−	3.04800i
$248$	−0.835576	+	0.245347i	−0.0530591	+	0.0155796i
$249$	−1.61374	+	3.53360i	−0.102267	+	0.223933i
$250$	−0.142315	+	0.989821i	−0.00900078	+	0.0626018i
$251$	5.94552	−	3.82095i	0.375278	−	0.241176i	−0.339382	−	0.940649i	$-0.610218\pi$
$251$	5.94552	−	3.82095i	0.375278	−	0.241176i	0.714660	+	0.699472i	$0.246582\pi$
$252$	−2.36558			−0.149018
$253$	0.865680	−	9.23349i	0.0544248	−	0.580505i
$254$	−3.08838			−0.193782
$255$	4.96532	−	3.19102i	0.310941	−	0.199829i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	0.104424	−	0.228658i	0.00651382	−	0.0142633i	−0.906347	−	0.422534i	$-0.861141\pi$
$257$	0.104424	−	0.228658i	0.00651382	−	0.0142633i	0.912861	+	0.408271i	$0.133868\pi$
$258$	10.7436	−	3.15460i	0.668866	−	0.196397i
$259$	−5.41875	−	11.8654i	−0.336704	−	0.737280i
$260$	3.97412	+	4.58638i	0.246464	+	0.284435i
$261$	−0.774796	−	5.38882i	−0.0479587	−	0.333560i
$262$	14.4281	+	4.23648i	0.891373	+	0.261731i
$263$	8.46439	−	9.76843i	0.521937	−	0.602347i	−0.432178	−	0.901788i	$-0.642255\pi$
$263$	8.46439	−	9.76843i	0.521937	−	0.602347i	0.954115	+	0.299441i	$0.0968003\pi$
$264$	1.62678	+	1.04547i	0.100122	+	0.0643442i
$265$	−5.97943	−	3.84275i	−0.367314	−	0.236058i
$266$	13.4429	−	15.5139i	0.824235	−	0.951218i
$267$	10.1187	+	2.97113i	0.619257	+	0.181830i
$268$	−1.39651	−	9.71295i	−0.0853055	−	0.593313i
$269$	−6.79047	−	7.83662i	−0.414022	−	0.477807i	0.509984	−	0.860184i	$-0.329651\pi$
$269$	−6.79047	−	7.83662i	−0.414022	−	0.477807i	−0.924007	+	0.382377i	$0.875106\pi$
$270$	−0.415415	−	0.909632i	−0.0252814	−	0.0553584i
$271$	19.0546	−	5.59494i	1.15749	−	0.339868i	0.354031	−	0.935234i	$-0.384811\pi$
$271$	19.0546	−	5.59494i	1.15749	−	0.339868i	0.803455	+	0.595365i	$0.202993\pi$
$272$	−2.45190	+	5.36891i	−0.148668	+	0.325538i
$273$	2.04305	−	14.2098i	0.123651	−	0.860014i
$274$	−16.3578	+	10.5126i	−0.988214	+	0.635086i
$275$	−1.93376			−0.116610
$276$	0.447667	−	4.77489i	0.0269464	−	0.287415i
$277$	−11.6528			−0.700148			−0.350074	−	0.936722i	$-0.613843\pi$
$277$	−11.6528			−0.700148			−0.350074	+	0.936722i	$0.613843\pi$
$278$	2.21071	−	1.42074i	0.132590	−	0.0852102i
$279$	−0.123935	+	0.861987i	−0.00741980	+	0.0516058i
$280$	−0.982698	+	2.15181i	−0.0587274	+	0.128595i
$281$	21.2257	−	6.23243i	1.26622	−	0.371796i	0.421414	−	0.906869i	$-0.361534\pi$
$281$	21.2257	−	6.23243i	1.26622	−	0.371796i	0.844806	+	0.535073i	$0.179716\pi$
$282$	0.127217	+	0.278566i	0.00757565	+	0.0165884i
$283$	13.4840	+	15.5614i	0.801541	+	0.925028i	0.998465	−	0.0553907i	$-0.0176404\pi$
$283$	13.4840	+	15.5614i	0.801541	+	0.925028i	−0.196923	+	0.980419i	$0.563095\pi$
$284$	−0.515835	−	3.58771i	−0.0306092	−	0.212892i
$285$	8.32620	+	2.44479i	0.493202	+	0.144817i
$286$	−7.68499	+	8.86895i	−0.454423	+	0.524432i
$287$	−8.73500	−	5.61365i	−0.515611	−	0.331363i
$288$	0.841254	+	0.540641i	0.0495713	+	0.0318576i
$289$	−11.6808	+	13.4803i	−0.687105	+	0.792962i
$290$	−5.22371	−	1.53382i	−0.306747	−	0.0900690i
$291$	−0.617210	−	4.29279i	−0.0361815	−	0.251648i
$292$	−2.57673	−	2.97370i	−0.150792	−	0.174023i
$293$	−0.139397	−	0.305236i	−0.00814364	−	0.0178321i	0.905516	−	0.424311i	$-0.139484\pi$
$293$	−0.139397	−	0.305236i	−0.00814364	−	0.0178321i	−0.913660	+	0.406479i	$0.866756\pi$
$294$	−1.34715	+	0.395560i	−0.0785675	+	0.0230695i
$295$	−1.43827	+	3.14937i	−0.0837394	+	0.183364i
$296$	−0.784746	+	5.45803i	−0.0456124	+	0.317241i
$297$	1.62678	−	1.04547i	0.0943955	−	0.0606643i
$298$	−1.03957			−0.0602206
$299$	28.2956	+	6.81296i	1.63637	+	0.394003i
$300$	−1.00000			−0.0577350
$301$	−22.2829	+	14.3204i	−1.28437	+	0.825412i
$302$	2.68659	−	18.6857i	0.154596	−	1.07524i
$303$	6.43950	−	14.1005i	0.369940	−	0.810055i
$304$	−8.32620	+	2.44479i	−0.477540	+	0.140219i
$305$	−5.26912	−	11.5378i	−0.301709	−	0.660651i
$306$	3.86518	+	4.46066i	0.220958	+	0.254999i
$307$	3.03982	+	21.1424i	0.173492	+	1.20666i	0.871436	+	0.490510i	$0.163189\pi$
$307$	3.03982	+	21.1424i	0.173492	+	1.20666i	−0.697944	+	0.716152i	$0.745902\pi$
$308$	−4.38917	−	1.28878i	−0.250096	−	0.0734348i
$309$	−0.747275	+	0.862402i	−0.0425110	+	0.0490603i
$310$	0.732607	+	0.470818i	0.0416093	+	0.0267406i
$311$	3.54403	+	2.27761i	0.200963	+	0.129151i	0.637252	−	0.770655i	$-0.280071\pi$
$311$	3.54403	+	2.27761i	0.200963	+	0.129151i	−0.436289	+	0.899807i	$0.643707\pi$
$312$	−3.97412	+	4.58638i	−0.224990	+	0.259653i
$313$	−11.3826	−	3.34224i	−0.643383	−	0.188914i	−0.0562655	−	0.998416i	$-0.517919\pi$
$313$	−11.3826	−	3.34224i	−0.643383	−	0.188914i	−0.587118	+	0.809501i	$0.699738\pi$
$314$	1.11524	+	7.75667i	0.0629367	+	0.437734i
$315$	1.54913	+	1.78779i	0.0872834	+	0.100730i
$316$	2.25719	+	4.94255i	0.126977	+	0.278040i
$317$	3.67684	−	1.07962i	0.206512	−	0.0606373i	−0.176841	−	0.984240i	$-0.556588\pi$
$317$	3.67684	−	1.07962i	0.206512	−	0.0606373i	0.383352	+	0.923602i	$0.374770\pi$
$318$	2.95267	−	6.46545i	0.165578	−	0.362564i
$319$	1.49827	−	10.4207i	0.0838870	−	0.583447i
$320$	0.841254	−	0.540641i	0.0470275	−	0.0302227i
$321$	−8.48033			−0.473326
$322$	2.16619	+	11.1362i	0.120717	+	0.620596i
$323$	−51.2184			−2.84987
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	0.863659	−	6.00688i	0.0479072	−	0.333202i
$326$	0.690118	−	1.51115i	0.0382221	−	0.0836947i
$327$	11.5126	−	3.38040i	0.636648	−	0.186937i
$328$	1.82339	+	3.99268i	0.100680	+	0.220459i
$329$	−0.474405	−	0.547492i	−0.0261548	−	0.0301842i
$330$	−0.275203	−	1.91408i	−0.0151494	−	0.105366i
$331$	1.61311	+	0.473650i	0.0886643	+	0.0260342i	0.325764	−	0.945451i	$-0.394379\pi$
$331$	1.61311	+	0.473650i	0.0886643	+	0.0260342i	−0.237100	+	0.971485i	$0.576197\pi$
$332$	−2.54390	+	2.93582i	−0.139615	+	0.161124i
$333$	4.63880	+	2.98118i	0.254205	+	0.163367i
$334$	−10.1550	−	6.52623i	−0.555658	−	0.357099i
$335$	−6.42603	+	7.41604i	−0.351092	+	0.405181i
$336$	−2.26976	−	0.666461i	−0.123825	−	0.0363584i
$337$	−1.88162	−	13.0870i	−0.102499	−	0.712893i	−0.974663	−	0.223680i	$-0.928193\pi$
$337$	−1.88162	−	13.0870i	−0.102499	−	0.712893i	0.872164	−	0.489213i	$-0.162716\pi$
$338$	−15.6043	−	18.0084i	−0.848764	−	0.979526i
$339$	7.53167	+	16.4920i	0.409064	+	0.895725i
$340$	5.66321	−	1.66287i	0.307131	−	0.0901817i
$341$	−0.699566	+	1.53184i	−0.0378836	+	0.0829536i
$342$	−1.23497	+	8.58938i	−0.0667794	+	0.464461i
$343$	16.7245	−	10.7482i	0.903036	−	0.580346i
$344$	11.1971			0.603710
$345$	−3.90178	+	2.78857i	−0.210065	+	0.150131i
$346$	−22.3693			−1.20258
$347$	0.259569	−	0.166815i	0.0139344	−	0.00895511i	−0.533655	−	0.845702i	$-0.679182\pi$
$347$	0.259569	−	0.166815i	0.0139344	−	0.00895511i	0.547589	+	0.836747i	$0.315546\pi$
$348$	0.774796	−	5.38882i	0.0415334	−	0.288871i
$349$	9.36546	−	20.5075i	0.501322	−	1.09774i	−0.474716	−	0.880139i	$-0.657449\pi$
$349$	9.36546	−	20.5075i	0.501322	−	1.09774i	0.976038	−	0.217602i	$-0.0698236\pi$
$350$	2.26976	−	0.666461i	0.121324	−	0.0356239i
$351$	2.52101	+	5.52024i	0.134561	+	0.294648i
$352$	1.26634	+	1.46144i	0.0674963	+	0.0778949i
$353$	3.32812	+	23.1476i	0.177138	+	1.23202i	0.863345	+	0.504614i	$0.168365\pi$
$353$	3.32812	+	23.1476i	0.177138	+	1.23202i	−0.686207	+	0.727406i	$0.740726\pi$
$354$	−3.32201	−	0.975429i	−0.176563	−	0.0518435i
$355$	−2.37361	+	2.73930i	−0.125978	+	0.145387i
$356$	8.87180	+	5.70156i	0.470204	+	0.302182i
$357$	−11.7459	−	7.54862i	−0.621658	−	0.399515i
$358$	7.18068	−	8.28695i	0.379511	−	0.437979i
$359$	0.321376	+	0.0943646i	0.0169616	+	0.00498037i	0.290202	−	0.956965i	$-0.406277\pi$
$359$	0.321376	+	0.0943646i	0.0169616	+	0.00498037i	−0.273241	+	0.961946i	$0.588096\pi$
$360$	−0.142315	−	0.989821i	−0.00750065	−	0.0521682i
$361$	−36.8704	−	42.5507i	−1.94055	−	2.23951i
$362$	8.46889	+	18.5443i	0.445115	+	0.974665i
$363$	−6.96647	+	2.04554i	−0.365645	+	0.107363i
$364$	5.96365	−	13.0586i	0.312580	−	0.684455i
$365$	−0.559977	+	3.89472i	−0.0293105	+	0.203859i
$366$	10.6705	−	6.85749i	0.557754	−	0.358447i
$367$	−30.2098			−1.57694			−0.788469	−	0.615074i	$-0.789126\pi$
$367$	−30.2098			−1.57694			−0.788469	+	0.615074i	$0.789126\pi$
$368$	1.77478	−	4.45535i	0.0925166	−	0.232251i
$369$	4.38933			0.228499
$370$	4.63880	−	2.98118i	0.241160	−	0.154984i
$371$	−2.39288	+	16.6429i	−0.124232	+	0.864054i
$372$	−0.361765	+	0.792154i	−0.0187566	+	0.0410713i
$373$	−7.27287	+	2.13551i	−0.376575	+	0.110572i	−0.464542	−	0.885551i	$-0.653781\pi$
$373$	−7.27287	+	2.13551i	−0.376575	+	0.110572i	0.0879673	+	0.996123i	$0.471963\pi$
$374$	4.74139	+	10.3822i	0.245171	+	0.536850i
$375$	0.654861	+	0.755750i	0.0338169	+	0.0390267i
$376$	0.0435825	+	0.303123i	0.00224760	+	0.0156324i
$377$	31.7009	+	9.30821i	1.63268	+	0.479397i
$378$	−1.54913	+	1.78779i	−0.0796785	+	0.0919538i
$379$	6.75705	+	4.34250i	0.347087	+	0.223059i	0.702555	−	0.711629i	$-0.252042\pi$
$379$	6.75705	+	4.34250i	0.347087	+	0.223059i	−0.355469	+	0.934688i	$0.615679\pi$
$380$	7.30015	+	4.69152i	0.374490	+	0.240670i
$381$	−2.02246	+	2.33404i	−0.103614	+	0.119577i
$382$	18.4641	+	5.42156i	0.944707	+	0.277391i
$383$	−4.37378	−	30.4203i	−0.223490	−	1.55441i	−0.724691	−	0.689074i	$-0.758017\pi$
$383$	−4.37378	−	30.4203i	−0.223490	−	1.55441i	0.501201	−	0.865331i	$-0.332892\pi$
$384$	0.654861	+	0.755750i	0.0334182	+	0.0385667i
$385$	1.90030	+	4.16108i	0.0968483	+	0.212068i
$386$	4.83087	−	1.41847i	0.245885	−	0.0721982i
$387$	4.65146	−	10.1853i	0.236447	−	0.517747i
$388$	0.617210	−	4.29279i	0.0313341	−	0.217933i
$389$	24.1072	−	15.4927i	1.22228	−	0.785513i	0.239610	−	0.970869i	$-0.422980\pi$
$389$	24.1072	−	15.4927i	1.22228	−	0.785513i	0.982671	+	0.185356i	$0.0593439\pi$
$390$	6.06865			0.307298
$391$	17.4596	−	22.2804i	0.882969	−	1.12677i
$392$	−1.40403			−0.0709140
$393$	12.6501	−	8.12975i	0.638115	−	0.410092i
$394$	−2.19051	+	15.2353i	−0.110356	+	0.767543i
$395$	2.25719	−	4.94255i	0.113571	−	0.248687i
$396$	1.85543	−	0.544803i	0.0932388	−	0.0273774i
$397$	−9.61110	−	21.0454i	−0.482367	−	1.05624i	−0.981806	−	0.189887i	$-0.939188\pi$
$397$	−9.61110	−	21.0454i	−0.482367	−	1.05624i	0.499439	−	0.866349i	$-0.333540\pi$
$398$	10.4972	+	12.1144i	0.526177	+	0.607240i
$399$	−2.92141	−	20.3189i	−0.146254	−	1.01722i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	−11.6482	+	13.4427i	−0.581681	+	0.671296i	−0.967965	−	0.251084i	$-0.919213\pi$
$401$	−11.6482	+	13.4427i	−0.581681	+	0.671296i	0.386284	+	0.922380i	$0.373758\pi$
$402$	−8.25507	−	5.30521i	−0.411726	−	0.264600i
$403$	−4.44593	−	2.85723i	−0.221468	−	0.142329i
$404$	10.1512	−	11.7152i	0.505043	−	0.582851i
$405$	−0.959493	−	0.281733i	−0.0476776	−	0.0139994i
$406$	1.83284	+	12.7477i	0.0909625	+	0.632658i
$407$	6.98281	+	8.05859i	0.346125	+	0.399450i
$408$	2.45190	+	5.36891i	0.121387	+	0.265801i
$409$	−9.99152	+	2.93378i	−0.494049	+	0.145066i	−0.519260	−	0.854616i	$-0.673792\pi$
$409$	−9.99152	+	2.93378i	−0.494049	+	0.145066i	0.0252110	+	0.999682i	$0.491974\pi$
$410$	1.82339	−	3.99268i	0.0900510	−	0.197184i
$411$	−2.76726	+	19.2467i	−0.136499	+	0.949369i
$412$	−0.959972	+	0.616937i	−0.0472944	+	0.0303943i
$413$	8.19023			0.403015
$414$	−3.31546	−	3.46521i	−0.162946	−	0.170306i
$415$	3.88465			0.190690
$416$	−5.10527	+	3.28096i	−0.250307	+	0.160862i
$417$	0.373986	−	2.60113i	0.0183142	−	0.127378i
$418$	−6.97092	+	15.2642i	−0.340959	+	0.746595i
$419$	−15.6250	+	4.58791i	−0.763331	+	0.224134i	−0.640150	−	0.768250i	$-0.721128\pi$
$419$	−15.6250	+	4.58791i	−0.763331	+	0.224134i	−0.123181	+	0.992384i	$0.539310\pi$
$420$	0.982698	+	2.15181i	0.0479507	+	0.104997i
$421$	−11.1382	−	12.8541i	−0.542841	−	0.626472i	0.416359	−	0.909200i	$-0.363306\pi$
$421$	−11.1382	−	12.8541i	−0.542841	−	0.626472i	−0.959200	+	0.282729i	$0.908760\pi$
$422$	2.82149	+	19.6239i	0.137348	+	0.955277i
$423$	0.293835	+	0.0862778i	0.0142868	+	0.00419497i
$424$	4.65460	−	5.37169i	0.226047	−	0.260872i
$425$	−4.96532	−	3.19102i	−0.240854	−	0.154787i
$426$	−3.04921	−	1.95961i	−0.147735	−	0.0949434i
$427$	−19.6491	+	22.6763i	−0.950887	+	1.09738i
$428$	−8.13682	−	2.38919i	−0.393308	−	0.115486i
$429$	1.67011	+	11.6159i	0.0806336	+	0.560819i
$430$	−7.33257	−	8.46224i	−0.353608	−	0.408085i
$431$	−10.8650	−	23.7910i	−0.523348	−	1.14597i	−0.968156	−	0.250347i	$-0.919455\pi$
$431$	−10.8650	−	23.7910i	−0.523348	−	1.14597i	0.444808	−	0.895626i	$-0.353272\pi$
$432$	0.959493	−	0.281733i	0.0461636	−	0.0135549i
$433$	11.8861	−	26.0268i	0.571207	−	1.25077i	−0.374945	−	0.927047i	$-0.622338\pi$
$433$	11.8861	−	26.0268i	0.571207	−	1.25077i	0.946152	−	0.323722i	$-0.104934\pi$
$434$	0.293178	−	2.03910i	0.0140730	−	0.0978800i
$435$	−4.57999	+	2.94338i	−0.219593	+	0.141124i
$436$	11.9986			0.574630
$437$	41.5662	−	2.05165i	1.98838	−	0.0981439i
$438$	−3.93477			−0.188011
$439$	−30.2628	+	19.4487i	−1.44437	+	0.928237i	−0.444899	+	0.895581i	$0.646760\pi$
$439$	−30.2628	+	19.4487i	−1.44437	+	0.928237i	−0.999467	+	0.0326563i	$0.989603\pi$
$440$	0.275203	−	1.91408i	0.0131198	−	0.0912500i
$441$	−0.583253	+	1.27715i	−0.0277740	+	0.0608165i
$442$	−34.3680	+	10.0914i	−1.63472	+	0.479997i
$443$	−4.31352	−	9.44530i	−0.204942	−	0.448760i	0.779053	−	0.626958i	$-0.215700\pi$
$443$	−4.31352	−	9.44530i	−0.204942	−	0.448760i	−0.983995	+	0.178198i	$0.942973\pi$
$444$	3.61100	+	4.16732i	0.171371	+	0.197772i
$445$	−1.50084	−	10.4386i	−0.0711467	−	0.494836i
$446$	19.8572	+	5.83060i	0.940266	+	0.276087i
$447$	−0.680773	+	0.785653i	−0.0321994	+	0.0371601i
$448$	−1.99005	−	1.27893i	−0.0940212	−	0.0604238i
$449$	0.216291	+	0.139002i	0.0102074	+	0.00655991i	0.545735	−	0.837958i	$-0.316251\pi$
$449$	0.216291	+	0.139002i	0.0102074	+	0.00655991i	−0.535527	+	0.844518i	$0.679887\pi$
$450$	−0.654861	+	0.755750i	−0.0308704	+	0.0356264i
$451$	8.14409	+	2.39132i	0.383490	+	0.112603i
$452$	2.58023	+	17.9459i	0.121364	+	0.844105i
$453$	−12.3623	−	14.2669i	−0.580833	−	0.670317i
$454$	−11.2186	−	24.5652i	−0.526513	−	1.15290i
$455$	−13.7744	+	4.04452i	−0.645752	+	0.189610i
$456$	−3.60485	+	7.89352i	−0.168813	+	0.369648i
$457$	−4.60490	+	32.0278i	−0.215408	+	1.49820i	0.539289	+	0.842121i	$0.318693\pi$
$457$	−4.60490	+	32.0278i	−0.215408	+	1.49820i	−0.754696	+	0.656074i	$0.772216\pi$
$458$	−20.3526	+	13.0798i	−0.951016	+	0.611181i
$459$	5.90229			0.275495
$460$	−4.52936	+	1.57635i	−0.211183	+	0.0734977i
$461$	28.8459			1.34349			0.671744	−	0.740783i	$-0.265545\pi$
$461$	28.8459			1.34349			0.671744	+	0.740783i	$0.265545\pi$
$462$	−3.84829	+	2.47314i	−0.179038	+	0.115061i
$463$	3.44072	−	23.9307i	0.159904	−	1.11216i	−0.738903	−	0.673811i	$-0.764656\pi$
$463$	3.44072	−	23.9307i	0.159904	−	1.11216i	0.898807	−	0.438344i	$-0.144435\pi$
$464$	2.26162	−	4.95225i	0.104993	−	0.229903i
$465$	0.835576	−	0.245347i	0.0387489	−	0.0113777i
$466$	1.28739	+	2.81900i	0.0596373	+	0.130587i
$467$	−1.44299	−	1.66530i	−0.0667738	−	0.0770611i	0.721380	−	0.692540i	$-0.243508\pi$
$467$	−1.44299	−	1.66530i	−0.0667738	−	0.0770611i	−0.788154	+	0.615479i	$0.788963\pi$
$468$	0.863659	+	6.00688i	0.0399226	+	0.277668i
$469$	22.2727	+	6.53987i	1.02846	+	0.301983i
$470$	0.200545	−	0.231441i	0.00925044	−	0.0106756i
$471$	6.59243	+	4.23670i	0.303763	+	0.195217i
$472$	−2.91263	−	1.87183i	−0.134065	−	0.0861581i
$473$	14.1794	−	16.3639i	0.651971	−	0.752415i
$474$	5.21347	+	1.53081i	0.239463	+	0.0703126i
$475$	−1.23497	−	8.58938i	−0.0566642	−	0.394108i
$476$	−9.14340	−	10.5520i	−0.419087	−	0.483652i
$477$	−2.95267	−	6.46545i	−0.135194	−	0.296033i
$478$	−1.19283	+	0.350247i	−0.0545589	+	0.0160199i
$479$	−0.694918	+	1.52166i	−0.0317516	+	0.0695263i	−0.924843	−	0.380348i	$-0.875804\pi$
$479$	−0.694918	+	1.52166i	−0.0317516	+	0.0695263i	0.893092	+	0.449875i	$0.148531\pi$
$480$	0.142315	−	0.989821i	0.00649575	−	0.0451790i
$481$	−28.1512	+	18.0917i	−1.28359	+	0.824911i
$482$	24.4262			1.11258
$483$	9.83473	+	5.65557i	0.447496	+	0.257337i
$484$	−7.26057			−0.330026
$485$	−3.64846	+	2.34472i	−0.165668	+	0.106468i
$486$	0.142315	−	0.989821i	0.00645553	−	0.0448992i
$487$	5.48941	−	12.0201i	0.248749	−	0.544684i	−0.743531	−	0.668701i	$-0.766851\pi$
$487$	5.48941	−	12.0201i	0.248749	−	0.544684i	0.992280	+	0.124017i	$0.0395778\pi$
$488$	12.1702	−	3.57350i	0.550919	−	0.161765i
$489$	−0.690118	−	1.51115i	−0.0312082	−	0.0683364i
$490$	0.919441	+	1.06109i	0.0415361	+	0.0479352i
$491$	−3.75614	−	26.1245i	−0.169512	−	1.17898i	−0.879896	−	0.475167i	$-0.842388\pi$
$491$	−3.75614	−	26.1245i	−0.169512	−	1.17898i	0.710383	−	0.703815i	$-0.248522\pi$
$492$	4.21153	+	1.23662i	0.189871	+	0.0557510i
$493$	21.0430	−	24.2849i	0.947727	−	1.09374i
$494$	−44.3021	−	28.4712i	−1.99324	−	1.28098i
$495$	−1.62678	−	1.04547i	−0.0731184	−	0.0469904i
$496$	−0.570286	+	0.658145i	−0.0256066	+	0.0295516i
$497$	8.22698	+	2.41566i	0.369031	+	0.108357i
$498$	0.552843	+	3.84511i	0.0247735	+	0.172303i
$499$	−0.236157	−	0.272539i	−0.0105718	−	0.0122005i	0.750439	−	0.660940i	$-0.229842\pi$
$499$	−0.236157	−	0.272539i	−0.0105718	−	0.0122005i	−0.761011	+	0.648739i	$0.775297\pi$
$500$	0.415415	+	0.909632i	0.0185779	+	0.0406800i
$501$	−11.5823	+	3.40087i	−0.517460	+	0.151940i
$502$	2.93592	−	6.42878i	0.131037	−	0.286930i
$503$	0.884410	−	6.15121i	0.0394339	−	0.274269i	−0.960559	−	0.278077i	$-0.910303\pi$
$503$	0.884410	−	6.15121i	0.0394339	−	0.274269i	0.999993	+	0.00380803i	$0.00121214\pi$
$504$	−1.99005	+	1.27893i	−0.0886440	+	0.0569681i
$505$	−15.5014			−0.689802
$506$	−4.26375	−	8.23573i	−0.189547	−	0.366123i
$507$	−23.8285			−1.05826
$508$	−2.59811	+	1.66970i	−0.115272	+	0.0740811i
$509$	−3.37889	+	23.5007i	−0.149767	+	1.04165i	0.766834	+	0.641845i	$0.221831\pi$
$509$	−3.37889	+	23.5007i	−0.149767	+	1.04165i	−0.916601	+	0.399804i	$0.869078\pi$
$510$	2.45190	−	5.36891i	0.108572	−	0.237740i
$511$	8.93099	−	2.62237i	0.395084	−	0.116007i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	5.68269	+	6.55818i	0.250897	+	0.289551i
$514$	−0.0357742	−	0.248815i	−0.00157793	−	0.0109748i
$515$	1.09490	+	0.321491i	0.0482469	+	0.0141666i
$516$	7.33257	−	8.46224i	0.322798	−	0.372529i
$517$	0.498186	+	0.320165i	0.0219102	+	0.0140808i
$518$	−10.9735	−	7.05221i	−0.482146	−	0.309856i
$519$	−14.6488	+	16.9056i	−0.643009	+	0.742072i
$520$	5.82283	+	1.70974i	0.255348	+	0.0749769i
$521$	−2.97529	−	20.6936i	−0.130350	−	0.906603i	−0.945098	−	0.326788i	$-0.894034\pi$
$521$	−2.97529	−	20.6936i	−0.130350	−	0.906603i	0.814748	−	0.579816i	$-0.196875\pi$
$522$	−3.56522	−	4.11448i	−0.156045	−	0.180086i
$523$	2.13656	+	4.67841i	0.0934251	+	0.204573i	0.950575	−	0.310494i	$-0.100494\pi$
$523$	2.13656	+	4.67841i	0.0934251	+	0.204573i	−0.857150	+	0.515067i	$0.827767\pi$
$524$	14.4281	−	4.23648i	0.630296	−	0.185072i
$525$	0.982698	−	2.15181i	0.0428885	−	0.0939126i
$526$	1.83949	−	12.7939i	0.0802055	−	0.557841i
$527$	−4.32406	+	2.77890i	−0.188359	+	0.121051i
$528$	1.93376			0.0841561
$529$	−13.2768	+	18.7810i	−0.577253	+	0.816565i
$530$	−7.10777			−0.308742
$531$	−2.91263	+	1.87183i	−0.126397	+	0.0812307i
$532$	2.92141	−	20.3189i	0.126659	−	0.880935i
$533$	−11.0655	+	24.2301i	−0.479302	+	1.04952i
$534$	10.1187	−	2.97113i	0.437881	−	0.128573i
$535$	3.52286	+	7.71398i	0.152306	+	0.333504i
$536$	−6.42603	−	7.41604i	−0.277562	−	0.320324i
$537$	−1.56051	−	10.8536i	−0.0673411	−	0.468367i
$538$	−9.94930	−	2.92138i	−0.428945	−	0.125950i
$539$	−1.77798	+	2.05190i	−0.0765830	+	0.0883814i
$540$	−0.841254	−	0.540641i	−0.0362018	−	0.0232655i
$541$	9.69757	+	6.23225i	0.416931	+	0.267945i	0.732244	−	0.681042i	$-0.238473\pi$
$541$	9.69757	+	6.23225i	0.416931	+	0.267945i	−0.315313	+	0.948988i	$0.602109\pi$
$542$	13.0049	−	15.0085i	0.558609	−	0.644669i
$543$	19.5608	+	5.74356i	0.839433	+	0.246480i
$544$	0.839984	+	5.84222i	0.0360140	+	0.250483i
$545$	−7.85743	−	9.06795i	−0.336575	−	0.388428i
$546$	−5.96365	−	13.0586i	−0.255221	−	0.558855i
$547$	−19.5231	+	5.73249i	−0.834746	+	0.245104i	−0.671054	−	0.741408i	$-0.734158\pi$
$547$	−19.5231	+	5.73249i	−0.834746	+	0.245104i	−0.163691	+	0.986512i	$0.552340\pi$
$548$	−8.07758	+	17.6874i	−0.345057	+	0.755570i
$549$	1.80512	−	12.5549i	0.0770407	−	0.535830i
$550$	−1.62678	+	1.04547i	−0.0693662	+	0.0445790i
$551$	47.2435			2.01264
$552$	−2.20490	−	4.25892i	−0.0938468	−	0.181272i
$553$	−12.8536			−0.546589
$554$	−9.80294	+	6.29997i	−0.416487	+	0.267660i
$555$	0.784746	−	5.45803i	0.0333106	−	0.231680i
$556$	1.09166	−	2.39040i	0.0462967	−	0.101376i
$557$	−9.60939	+	2.82157i	−0.407163	+	0.119554i	−0.478899	−	0.877870i	$-0.658964\pi$
$557$	−9.60939	+	2.82157i	−0.407163	+	0.119554i	0.0717365	+	0.997424i	$0.477146\pi$
$558$	0.361765	+	0.792154i	0.0153147	+	0.0335346i
$559$	44.4988	+	51.3544i	1.88210	+	2.17206i
$560$	0.336657	+	2.34150i	0.0142264	+	0.0989466i
$561$	10.9513	+	3.21559i	0.462364	+	0.135762i
$562$	14.4867	−	16.7185i	0.611084	−	0.705229i
$563$	18.6985	+	12.0168i	0.788048	+	0.506448i	0.871696	−	0.490048i	$-0.163021\pi$
$563$	18.6985	+	12.0168i	0.788048	+	0.506448i	−0.0836477	+	0.996495i	$0.526657\pi$
$564$	0.257626	+	0.165566i	0.0108480	+	0.00697158i
$565$	11.8729	−	13.7021i	0.499498	−	0.576451i
$566$	19.7566	+	5.80106i	0.830432	+	0.243837i
$567$	0.336657	+	2.34150i	0.0141383	+	0.0983339i
$568$	−2.37361	−	2.73930i	−0.0995946	−	0.114938i
$569$	4.65768	+	10.1989i	0.195260	+	0.427560i	0.981784	−	0.190000i	$-0.0608487\pi$
$569$	4.65768	+	10.1989i	0.195260	+	0.427560i	−0.786524	+	0.617560i	$0.788121\pi$
$570$	8.32620	−	2.44479i	0.348746	−	0.102401i
$571$	−5.13293	+	11.2395i	−0.214806	+	0.470360i	−0.986107	−	0.166110i	$-0.946879\pi$
$571$	−5.13293	+	11.2395i	−0.214806	+	0.470360i	0.771301	+	0.636471i	$0.219606\pi$
$572$	−1.67011	+	11.6159i	−0.0698307	+	0.485683i
$573$	16.1888	−	10.4039i	0.676295	−	0.434629i
$574$	−10.3833			−0.433391
$575$	4.15743	+	2.39077i	0.173377	+	0.0997022i
$576$	1.00000			0.0416667
$577$	−27.2689	+	17.5246i	−1.13522	+	0.729560i	−0.966643	−	0.256129i	$-0.917553\pi$
$577$	−27.2689	+	17.5246i	−1.13522	+	0.729560i	−0.168575	+	0.985689i	$0.553916\pi$
$578$	−2.53848	+	17.6555i	−0.105587	+	0.734372i
$579$	2.09154	−	4.57983i	0.0869213	−	0.190331i
$580$	−5.22371	+	1.53382i	−0.216903	+	0.0636884i
$581$	−3.81744	−	8.35902i	−0.158374	−	0.346791i
$582$	−2.84009	−	3.27763i	−0.117725	−	0.135862i
$583$	−1.95608	−	13.6048i	−0.0810124	−	0.563454i
$584$	−3.77539	−	1.10855i	−0.156227	−	0.0458723i
$585$	3.97412	−	4.58638i	0.164310	−	0.189623i
$586$	−0.282291	−	0.181417i	−0.0116613	−	0.00749428i
$587$	34.1750	+	21.9629i	1.41055	+	0.906506i	0.999986	−	0.00532466i	$-0.00169490\pi$
$587$	34.1750	+	21.9629i	1.41055	+	0.906506i	0.410566	+	0.911831i	$0.365331\pi$
$588$	−0.919441	+	1.06109i	−0.0379171	+	0.0437587i
$589$	−7.25088	−	2.12905i	−0.298767	−	0.0877260i
$590$	0.492730	+	3.42701i	0.0202854	+	0.141088i
$591$	10.0796	+	11.6325i	0.414619	+	0.478496i
$592$	2.29066	+	5.01585i	0.0941456	+	0.206150i
$593$	−2.53889	+	0.745485i	−0.104260	+	0.0306134i	−0.333446	−	0.942769i	$-0.608212\pi$
$593$	−2.53889	+	0.745485i	−0.104260	+	0.0306134i	0.229187	+	0.973383i	$0.426393\pi$
$594$	0.803313	−	1.75901i	0.0329603	−	0.0721730i
$595$	−1.98705	+	13.8202i	−0.0814611	+	0.566574i
$596$	−0.874541	+	0.562033i	−0.0358226	+	0.0230218i
$597$	16.0297			0.656050
$598$	27.4871	−	9.56631i	1.12403	−	0.391196i
$599$	20.8962			0.853796			0.426898	−	0.904300i	$-0.359606\pi$
$599$	20.8962			0.853796			0.426898	+	0.904300i	$0.359606\pi$
$600$	−0.841254	+	0.540641i	−0.0343440	+	0.0220716i
$601$	4.26278	−	29.6483i	0.173883	−	1.20938i	−0.696702	−	0.717361i	$-0.745350\pi$
$601$	4.26278	−	29.6483i	0.173883	−	1.20938i	0.870585	−	0.492019i	$-0.163741\pi$
$602$	−11.0034	+	24.0941i	−0.448466	+	0.982003i
$603$	−9.41534	+	2.76459i	−0.383422	+	0.112583i
$604$	−7.84212	−	17.1719i	−0.319092	−	0.698713i
$605$	4.75466	+	5.48718i	0.193305	+	0.223085i
$606$	−2.20607	−	15.3436i	−0.0896157	−	0.623291i
$607$	21.4429	+	6.29622i	0.870342	+	0.255556i	0.686261	−	0.727355i	$-0.259251\pi$
$607$	21.4429	+	6.29622i	0.870342	+	0.255556i	0.184081	+	0.982911i	$0.441069\pi$
$608$	−5.68269	+	6.55818i	−0.230464	+	0.265969i
$609$	10.8343	+	6.96280i	0.439029	+	0.282147i
$610$	−10.6705	−	6.85749i	−0.432034	−	0.277652i
$611$	−1.21704	+	1.40453i	−0.0492360	+	0.0568213i
$612$	5.66321	+	1.66287i	0.228922	+	0.0672175i
$613$	3.67014	+	25.5264i	0.148236	+	1.03100i	0.919106	+	0.394010i	$0.128912\pi$
$613$	3.67014	+	25.5264i	0.148236	+	1.03100i	−0.770871	+	0.636992i	$0.780179\pi$
$614$	13.9877	+	16.1427i	0.564498	+	0.651466i
$615$	−1.82339	−	3.99268i	−0.0735263	−	0.161000i
$616$	−4.38917	+	1.28878i	−0.176845	+	0.0519263i
$617$	−8.39926	+	18.3918i	−0.338141	+	0.740426i	−0.999957	−	0.00924007i	$-0.997059\pi$
$617$	−8.39926	+	18.3918i	−0.338141	+	0.740426i	0.661816	+	0.749666i	$0.269786\pi$
$618$	−0.162398	+	1.12951i	−0.00653262	+	0.0454354i
$619$	4.95083	−	3.18170i	0.198991	−	0.127883i	−0.437351	−	0.899291i	$-0.644083\pi$
$619$	4.95083	−	3.18170i	0.198991	−	0.127883i	0.636342	+	0.771407i	$0.280447\pi$
$620$	0.870851			0.0349742
$621$	−4.79000	+	0.236428i	−0.192216	+	0.00948753i
$622$	4.21280			0.168918
$623$	−20.9870	+	13.4875i	−0.840824	+	0.540365i
$624$	−0.863659	+	6.00688i	−0.0345740	+	0.240468i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−11.3826	+	3.34224i	−0.454941	+	0.133583i
$627$	6.97092	+	15.2642i	0.278392	+	0.609592i
$628$	5.13177	+	5.92238i	0.204780	+	0.236329i
$629$	4.63180	+	32.2149i	0.184682	+	1.28449i
$630$	2.26976	+	0.666461i	0.0904293	+	0.0265525i
$631$	−6.47994	+	7.47826i	−0.257963	+	0.297705i	−0.869927	−	0.493181i	$-0.835834\pi$
$631$	−6.47994	+	7.47826i	−0.257963	+	0.297705i	0.611964	+	0.790885i	$0.290380\pi$
$632$	4.57101	+	2.93761i	0.181825	+	0.116852i
$633$	16.6784	+	10.7186i	0.662908	+	0.426025i
$634$	2.50947	−	2.89608i	0.0996636	−	0.115018i
$635$	2.96328	+	0.870097i	0.117594	+	0.0345287i
$636$	−1.01154	−	7.03542i	−0.0401102	−	0.278973i
$637$	−5.57977	−	6.43939i	−0.221078	−	0.255138i
$638$	−4.37343	−	9.57647i	−0.173146	−	0.379136i
$639$	−3.47778	+	1.02117i	−0.137579	+	0.0403969i
$640$	0.415415	−	0.909632i	0.0164207	−	0.0359564i
$641$	−4.40027	+	30.6046i	−0.173800	+	1.20881i	0.696964	+	0.717107i	$0.254534\pi$
$641$	−4.40027	+	30.6046i	−0.173800	+	1.20881i	−0.870764	+	0.491701i	$0.836375\pi$
$642$	−7.13411	+	4.58481i	−0.281561	+	0.180948i
$643$	−23.2892			−0.918437			−0.459218	−	0.888323i	$-0.651870\pi$
$643$	−23.2892			−0.918437			−0.459218	+	0.888323i	$0.651870\pi$
$644$	7.84300	+	8.19724i	0.309057	+	0.323017i
$645$	−11.1971			−0.440887
$646$	−43.0876	+	27.6907i	−1.69526	+	1.08948i
$647$	4.18814	−	29.1292i	0.164653	−	1.14519i	−0.725067	−	0.688679i	$-0.758191\pi$
$647$	4.18814	−	29.1292i	0.164653	−	1.14519i	0.889720	−	0.456508i	$-0.150900\pi$
$648$	0.415415	−	0.909632i	0.0163190	−	0.0357337i
$649$	−6.42396	+	1.88624i	−0.252162	+	0.0740416i
$650$	−2.52101	−	5.52024i	−0.0988820	−	0.216521i
$651$	−1.34906	−	1.55690i	−0.0528738	−	0.0610196i
$652$	−0.236424	−	1.64436i	−0.00925907	−	0.0643983i
$653$	18.3778	+	5.39620i	0.719177	+	0.211169i	0.620788	−	0.783979i	$-0.286813\pi$
$653$	18.3778	+	5.39620i	0.719177	+	0.211169i	0.0983892	+	0.995148i	$0.468631\pi$
$654$	7.85743	−	9.06795i	0.307250	−	0.354585i
$655$	−12.6501	−	8.12975i	−0.494282	−	0.317656i
$656$	3.69254	+	2.37305i	0.144169	+	0.0926521i
$657$	−2.57673	+	2.97370i	−0.100528	+	0.116015i
$658$	−0.695091	−	0.204097i	−0.0270975	−	0.00795654i
$659$	−4.34742	−	30.2370i	−0.169351	−	1.17786i	−0.880229	−	0.474549i	$-0.842611\pi$
$659$	−4.34742	−	30.2370i	−0.169351	−	1.17786i	0.710878	−	0.703316i	$-0.248298\pi$
$660$	−1.26634	−	1.46144i	−0.0492923	−	0.0568864i
$661$	−10.8862	−	23.8374i	−0.423422	−	0.927166i	−0.994349	−	0.106164i	$-0.966143\pi$
$661$	−10.8862	−	23.8374i	−0.423422	−	0.927166i	0.570926	−	0.821001i	$-0.306584\pi$
$662$	1.61311	−	0.473650i	0.0626951	−	0.0184089i
$663$	−14.8797	+	32.5820i	−0.577881	+	1.26538i
$664$	−0.552843	+	3.84511i	−0.0214545	+	0.149219i
$665$	−17.2691	+	11.0982i	−0.669667	+	0.430369i
$666$	5.51415			0.213669
$667$	−16.1046	+	20.5513i	−0.623573	+	0.795749i
$668$	−12.0713			−0.467052
$669$	17.4102	−	11.1888i	0.673117	−	0.432586i
$670$	−1.39651	+	9.71295i	−0.0539519	+	0.375244i
$671$	10.1892	−	22.3113i	0.393350	−	0.861317i
$672$	−2.26976	+	0.666461i	−0.0875578	+	0.0257093i
$673$	4.63491	+	10.1490i	0.178663	+	0.391217i	0.977683	−	0.210088i	$-0.0673750\pi$
$673$	4.63491	+	10.1490i	0.178663	+	0.391217i	−0.799020	+	0.601305i	$0.794648\pi$
$674$	−8.65828	−	9.99219i	−0.333504	−	0.384885i
$675$	0.142315	+	0.989821i	0.00547770	+	0.0380982i
$676$	−22.8633	−	6.71326i	−0.879356	−	0.258202i
$677$	−15.0740	+	17.3963i	−0.579339	+	0.668593i	−0.967463	−	0.253014i	$-0.918578\pi$
$677$	−15.0740	+	17.3963i	−0.579339	+	0.668593i	0.388123	+	0.921608i	$0.373124\pi$
$678$	15.2523	+	9.80207i	0.585762	+	0.376446i
$679$	8.63072	+	5.54663i	0.331217	+	0.212860i
$680$	3.86518	−	4.46066i	0.148223	−	0.171058i
$681$	−25.9117	−	7.60837i	−0.992940	−	0.291553i
$682$	0.239661	+	1.66688i	0.00917708	+	0.0638280i
$683$	10.1587	+	11.7238i	0.388713	+	0.448599i	0.916054	−	0.401055i	$-0.131356\pi$
$683$	10.1587	+	11.7238i	0.388713	+	0.448599i	−0.527341	+	0.849654i	$0.676811\pi$
$684$	3.60485	+	7.89352i	0.137835	+	0.301816i
$685$	18.6570	−	5.47818i	0.712846	−	0.209310i
$686$	8.25862	−	18.0839i	0.315316	−	0.690445i
$687$	−3.44305	+	23.9470i	−0.131361	+	0.913634i
$688$	9.41964	−	6.05363i	0.359120	−	0.230793i
$689$	43.1345			1.64329
$690$	−1.77478	+	4.45535i	−0.0675645	+	0.169612i
$691$	−19.4011			−0.738051			−0.369026	−	0.929419i	$-0.620309\pi$
$691$	−19.4011			−0.738051			−0.369026	+	0.929419i	$0.620309\pi$
$692$	−18.8182	+	12.0937i	−0.715362	+	0.459735i
$693$	−0.651014	+	4.52790i	−0.0247300	+	0.172001i
$694$	0.128177	−	0.280668i	0.00486552	−	0.0106540i
$695$	−2.52143	+	0.740358i	−0.0956433	+	0.0280834i
$696$	−2.26162	−	4.95225i	−0.0857264	−	0.187715i
$697$	16.9656	+	19.5793i	0.642616	+	0.741618i
$698$	−3.20846	−	22.3154i	−0.121442	−	0.844649i
$699$	2.97352	+	0.873104i	0.112469	+	0.0330238i
$700$	1.54913	−	1.78779i	0.0585515	−	0.0675720i
$701$	10.5902	+	6.80588i	0.399985	+	0.257055i	0.725134	−	0.688608i	$-0.241778\pi$
$701$	10.5902	+	6.80588i	0.399985	+	0.257055i	−0.325149	+	0.945663i	$0.605414\pi$
$702$	5.10527	+	3.28096i	0.192686	+	0.123832i
$703$	−31.3352	+	36.1628i	−1.18183	+	1.36391i
$704$	1.85543	+	0.544803i	0.0699291	+	0.0205330i
$705$	−0.0435825	−	0.303123i	−0.00164141	−	0.0114163i
$706$	15.3143	+	17.6737i	0.576362	+	0.665157i
$707$	15.2332	+	33.3560i	0.572902	+	1.25448i
$708$	−3.32201	+	0.975429i	−0.124849	+	0.0366589i
$709$	−4.33736	+	9.49750i	−0.162893	+	0.356686i	−0.973424	−	0.229010i	$-0.926451\pi$
$709$	−4.33736	+	9.49750i	−0.162893	+	0.356686i	0.810531	+	0.585696i	$0.199179\pi$
$710$	−0.515835	+	3.58771i	−0.0193590	+	0.134644i
$711$	4.57101	−	2.93761i	0.171426	−	0.110169i
$712$	10.5459			0.395225
$713$	3.39787	−	2.42843i	0.127251	−	0.0909453i
$714$	−13.9624			−0.522528
$715$	9.87237	−	6.34459i	0.369206	−	0.237274i
$716$	1.56051	−	10.8536i	0.0583191	−	0.405618i
$717$	−0.516440	+	1.13085i	−0.0192868	+	0.0422322i
$718$	0.321376	−	0.0943646i	0.0119937	−	0.00352166i
$719$	−20.6825	−	45.2883i	−0.771327	−	1.68897i	−0.723710	−	0.690105i	$-0.757565\pi$
$719$	−20.6825	−	45.2883i	−0.771327	−	1.68897i	−0.0476171	−	0.998866i	$-0.515163\pi$
$720$	−0.654861	−	0.755750i	−0.0244052	−	0.0281651i
$721$	−0.384167	−	2.67194i	−0.0143071	−	0.0995082i
$722$	−54.0220	−	15.8623i	−2.01049	−	0.590333i
$723$	15.9958	−	18.4601i	0.594889	−	0.686538i
$724$	17.1503	+	11.0218i	0.637385	+	0.409622i
$725$	4.57999	+	2.94338i	0.170096	+	0.109314i
$726$	−4.75466	+	5.48718i	−0.176462	+	0.203648i
$727$	11.9834	+	3.51866i	0.444441	+	0.130500i	0.496293	−	0.868155i	$-0.334694\pi$
$727$	11.9834	+	3.51866i	0.444441	+	0.130500i	−0.0518517	+	0.998655i	$0.516512\pi$
$728$	−2.04305	−	14.2098i	−0.0757206	−	0.526649i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	1.63456	+	3.57920i	0.0604979	+	0.132472i
$731$	63.4118	−	18.6194i	2.34537	−	0.688663i
$732$	5.26912	−	11.5378i	0.194752	−	0.426448i
$733$	−4.48168	+	31.1708i	−0.165535	+	1.15132i	0.722442	+	0.691431i	$0.243019\pi$
$733$	−4.48168	+	31.1708i	−0.165535	+	1.15132i	−0.887977	+	0.459888i	$0.847890\pi$
$734$	−25.4141	+	16.3326i	−0.938051	+	0.602849i
$735$	1.40403			0.0517883
$736$	−0.915710	−	4.70760i	−0.0337535	−	0.173524i
$737$	−18.9756			−0.698977
$738$	3.69254	−	2.37305i	0.135924	−	0.0873532i
$739$	−0.857963	+	5.96727i	−0.0315607	+	0.219509i	−0.999498	−	0.0316825i	$-0.989913\pi$
$739$	−0.857963	+	5.96727i	−0.0315607	+	0.219509i	0.967937	+	0.251192i	$0.0808225\pi$
$740$	2.29066	−	5.01585i	0.0842064	−	0.184386i
$741$	−50.5288	+	14.8366i	−1.85622	+	0.545036i
$742$	6.98479	+	15.2945i	0.256420	+	0.561481i
$743$	14.3783	+	16.5934i	0.527487	+	0.608753i	0.955490	−	0.295025i	$-0.0953279\pi$
$743$	14.3783	+	16.5934i	0.527487	+	0.608753i	−0.428002	+	0.903778i	$0.640782\pi$
$744$	0.123935	+	0.861987i	0.00454368	+	0.0316020i
$745$	0.997459	+	0.292880i	0.0365441	+	0.0107303i
$746$	−4.96379	+	5.72851i	−0.181737	+	0.209736i
$747$	3.26797	+	2.10020i	0.119569	+	0.0768423i
$748$	9.60174	+	6.17067i	0.351075	+	0.225622i
$749$	13.1371	−	15.1610i	0.480019	−	0.553972i
$750$	0.959493	+	0.281733i	0.0350357	+	0.0102874i
$751$	−2.00583	−	13.9509i	−0.0731938	−	0.509074i	−0.993131	−	0.117008i	$-0.962670\pi$
$751$	−2.00583	−	13.9509i	−0.0731938	−	0.509074i	0.919937	−	0.392066i	$-0.128239\pi$
$752$	0.200545	+	0.231441i	0.00731311	+	0.00843978i
$753$	−2.93592	−	6.42878i	−0.106991	−	0.234278i
$754$	31.7009	−	9.30821i	1.15448	−	0.338985i
$755$	−7.84212	+	17.1719i	−0.285404	+	0.624948i
$756$	−0.336657	+	2.34150i	−0.0122441	+	0.0851596i
$757$	−32.1908	+	20.6878i	−1.16999	+	0.751910i	−0.973521	−	0.228599i	$-0.926586\pi$
$757$	−32.1908	+	20.6878i	−1.16999	+	0.751910i	−0.196474	+	0.980509i	$0.562949\pi$
$758$	8.03213			0.291740
$759$	−9.01631	−	2.17093i	−0.327271	−	0.0787998i
$760$	8.67771			0.314774
$761$	−27.7911	+	17.8602i	−1.00743	+	0.647433i	−0.936725	−	0.350065i	$-0.886160\pi$
$761$	−27.7911	+	17.8602i	−1.00743	+	0.647433i	−0.0706996	+	0.997498i	$0.522523\pi$
$762$	−0.439522	+	3.05694i	−0.0159222	+	0.110741i
$763$	−11.7910	+	25.8187i	−0.426864	+	0.934701i
$764$	18.4641	−	5.42156i	0.668008	−	0.196145i
$765$	−2.45190	−	5.36891i	−0.0886487	−	0.194113i
$766$	−20.1259	−	23.2265i	−0.727179	−	0.839209i
$767$	−2.99020	−	20.7973i	−0.107970	−	0.750948i
$768$	0.959493	+	0.281733i	0.0346227	+	0.0101661i
$769$	−2.10266	+	2.42660i	−0.0758240	+	0.0875055i	−0.792394	−	0.610010i	$-0.791166\pi$
$769$	−2.10266	+	2.42660i	−0.0758240	+	0.0875055i	0.716570	+	0.697515i	$0.245711\pi$
$770$	3.84829	+	2.47314i	0.138683	+	0.0891259i
$771$	−0.211469	−	0.135903i	−0.00761587	−	0.00489442i
$772$	3.29710	−	3.80506i	0.118665	−	0.136947i
$773$	−0.133456	−	0.0391863i	−0.00480009	−	0.00140943i	0.279332	−	0.960195i	$-0.409887\pi$
$773$	−0.133456	−	0.0391863i	−0.00480009	−	0.00140943i	−0.284132	+	0.958785i	$0.591705\pi$
$774$	−1.59352	−	11.0832i	−0.0572779	−	0.398377i
$775$	−0.570286	−	0.658145i	−0.0204853	−	0.0236413i
$776$	−1.80163	−	3.94501i	−0.0646746	−	0.141618i
$777$	−12.5158	+	3.67497i	−0.449002	+	0.131839i
$778$	11.9042	−	26.0666i	0.426787	−	0.934534i
$779$	−5.42068	+	37.7016i	−0.194216	+	1.35080i
$780$	5.10527	−	3.28096i	0.182798	−	0.117477i
$781$	−7.00912			−0.250806
$782$	2.64226	−	28.1828i	0.0944870	−	1.00782i
$783$	−5.44424			−0.194561
$784$	−1.18114	+	0.759074i	−0.0421836	+	0.0271098i
$785$	1.11524	−	7.75667i	0.0398047	−	0.276847i
$786$	6.24670	−	13.6784i	0.222812	−	0.487891i
$787$	7.01098	−	2.05861i	0.249915	−	0.0733815i	−0.154376	−	0.988012i	$-0.549337\pi$
$787$	7.01098	−	2.05861i	0.249915	−	0.0733815i	0.404290	+	0.914631i	$0.367519\pi$
$788$	6.39405	+	14.0010i	0.227779	+	0.498766i
$789$	−8.46439	−	9.76843i	−0.301340	−	0.347765i
$790$	−0.773278	−	5.37827i	−0.0275120	−	0.191350i
$791$	−41.1518	−	12.0833i	−1.46319	−	0.429631i
$792$	1.26634	−	1.46144i	0.0449975	−	0.0519299i
$793$	64.7553	+	41.6157i	2.29953	+	1.47782i
$794$	−19.4634	−	12.5083i	−0.690728	−	0.443904i
$795$	−4.65460	+	5.37169i	−0.165082	+	0.190514i
$796$	15.3803	+	4.51608i	0.545142	+	0.160068i
$797$	−1.40784	−	9.79175i	−0.0498683	−	0.346842i	−0.999445	−	0.0333073i	$-0.989396\pi$
$797$	−1.40784	−	9.79175i	−0.0498683	−	0.346842i	0.949577	−	0.313534i	$-0.101513\pi$
$798$	−13.4429	−	15.5139i	−0.475872	−	0.549186i
$799$	0.750871	+	1.64418i	0.0265639	+	0.0581668i
$800$	−0.959493	+	0.281733i	−0.0339232	+	0.00996075i
$801$	4.38093	−	9.59291i	0.154793	−	0.338949i
$802$	−2.53139	+	17.6062i	−0.0893863	+	0.621696i
$803$	−6.40102	+	4.11369i	−0.225887	+	0.145169i
$804$	−9.81283			−0.346072
$805$	1.05899	−	11.2954i	0.0373246	−	0.398110i
$806$	−5.28489			−0.186152
$807$	−8.72324	+	5.60608i	−0.307073	+	0.197344i
$808$	2.20607	−	15.3436i	0.0776094	−	0.539786i
$809$	−10.2492	+	22.4426i	−0.360342	+	0.789040i	0.639453	+	0.768830i	$0.279161\pi$
$809$	−10.2492	+	22.4426i	−0.360342	+	0.789040i	−0.999796	+	0.0202098i	$0.993567\pi$
$810$	−0.959493	+	0.281733i	−0.0337131	+	0.00989907i
$811$	−12.2349	−	26.7907i	−0.429626	−	0.940750i	−0.993387	−	0.114812i	$-0.963373\pi$
$811$	−12.2349	−	26.7907i	−0.429626	−	0.940750i	0.563761	−	0.825938i	$-0.309354\pi$
$812$	8.43381	+	9.73314i	0.295969	+	0.341566i
$813$	−2.82624	−	19.6569i	−0.0991205	−	0.689398i
$814$	10.2311	+	3.00413i	0.358600	+	0.105295i
$815$	−1.08790	+	1.25551i	−0.0381076	+	0.0439785i
$816$	4.96532	+	3.19102i	0.173821	+	0.111708i
$817$	81.7409	+	52.5317i	2.85975	+	1.83785i
$818$	−6.81929	+	7.86988i	−0.238431	+	0.275164i
$819$	−13.7744	−	4.04452i	−0.481315	−	0.141327i
$820$	−0.624667	−	4.34465i	−0.0218143	−	0.151722i
$821$	7.84671	+	9.05559i	0.273852	+	0.316042i	0.875971	−	0.482365i	$-0.160222\pi$
$821$	7.84671	+	9.05559i	0.273852	+	0.316042i	−0.602118	+	0.798407i	$0.705676\pi$
$822$	8.07758	+	17.6874i	0.281738	+	0.616920i
$823$	−43.1008	+	12.6555i	−1.50240	+	0.441145i	−0.926475	−	0.376357i	$-0.877177\pi$
$823$	−43.1008	+	12.6555i	−1.50240	+	0.441145i	−0.575926	+	0.817502i	$0.695358\pi$
$824$	−0.474039	+	1.03800i	−0.0165139	+	0.0361604i
$825$	−0.275203	+	1.91408i	−0.00958133	+	0.0666396i
$826$	6.89006	−	4.42798i	0.239736	−	0.154069i
$827$	1.80316			0.0627020			0.0313510	−	0.999508i	$-0.490019\pi$
$827$	1.80316			0.0627020			0.0313510	+	0.999508i	$0.490019\pi$
$828$	−4.66258	−	1.12265i	−0.162036	−	0.0390147i
$829$	21.4460			0.744849			0.372425	−	0.928062i	$-0.378527\pi$
$829$	21.4460			0.744849			0.372425	+	0.928062i	$0.378527\pi$
$830$	3.26797	−	2.10020i	0.113433	−	0.0728990i
$831$	−1.65836	+	11.5342i	−0.0575280	+	0.400116i
$832$	−2.52101	+	5.52024i	−0.0874002	+	0.191380i
$833$	−7.95129	+	2.33471i	−0.275496	+	0.0808929i
$834$	−1.09166	−	2.39040i	−0.0378011	−	0.0827728i
$835$	7.90501	+	9.12287i	0.273564	+	0.315710i
$836$	2.38813	+	16.6098i	0.0825952	+	0.574462i
$837$	0.835576	+	0.245347i	0.0288817	+	0.00848044i
$838$	−10.6642	+	12.3071i	−0.368388	+	0.425142i
$839$	−14.4428	−	9.28182i	−0.498620	−	0.320444i	0.267044	−	0.963684i	$-0.413953\pi$
$839$	−14.4428	−	9.28182i	−0.498620	−	0.320444i	−0.765664	+	0.643241i	$0.777590\pi$
$840$	1.99005	+	1.27893i	0.0686634	+	0.0441273i
$841$	−0.418941	+	0.483484i	−0.0144463	+	0.0166719i
$842$	−16.3195	−	4.79183i	−0.562407	−	0.165137i
$843$	−3.14826	−	21.8966i	−0.108432	−	0.754160i
$844$	12.9831	+	14.9833i	0.446896	+	0.515745i
$845$	9.89871	+	21.6752i	0.340526	+	0.745648i
$846$	0.293835	−	0.0862778i	0.0101023	−	0.00296629i
$847$	7.13495	−	15.6234i	0.245160	−	0.536825i
$848$	1.01154	−	7.03542i	0.0347364	−	0.241597i
$849$	17.3220	−	11.1322i	0.594488	−	0.382054i
$850$	−5.90229			−0.202447
$851$	−5.04936	−	25.9584i	−0.173090	−	0.889843i
$852$	−3.62461			−0.124177
$853$	13.9173	−	8.94411i	0.476520	−	0.306241i	−0.280245	−	0.959929i	$-0.590416\pi$
$853$	13.9173	−	8.94411i	0.476520	−	0.306241i	0.756764	+	0.653688i	$0.226779\pi$
$854$	−4.27016	+	29.6996i	−0.146122	+	1.01630i
$855$	3.60485	−	7.89352i	0.123283	−	0.269953i
$856$	−8.13682	+	2.38919i	−0.278111	+	0.0816607i
$857$	−7.48590	−	16.3918i	−0.255714	−	0.559935i	0.737619	−	0.675217i	$-0.235950\pi$
$857$	−7.48590	−	16.3918i	−0.255714	−	0.559935i	−0.993333	+	0.115282i	$0.963223\pi$
$858$	7.68499	+	8.86895i	0.262361	+	0.302781i
$859$	−2.54478	−	17.6994i	−0.0868269	−	0.603894i	−0.986056	−	0.166416i	$-0.946781\pi$
$859$	−2.54478	−	17.6994i	−0.0868269	−	0.603894i	0.899229	−	0.437479i	$-0.144128\pi$
$860$	−10.7436	−	3.15460i	−0.366353	−	0.107571i
$861$	−6.79963	+	7.84719i	−0.231731	+	0.267431i
$862$	−22.0026	−	14.1402i	−0.749412	−	0.481618i
$863$	−24.0215	−	15.4377i	−0.817701	−	0.525505i	0.0636465	−	0.997973i	$-0.479727\pi$
$863$	−24.0215	−	15.4377i	−0.817701	−	0.525505i	−0.881348	+	0.472468i	$0.843363\pi$
$864$	0.654861	−	0.755750i	0.0222788	−	0.0257111i
$865$	21.4632	+	6.30215i	0.729769	+	0.214280i
$866$	−4.07198	−	28.3212i	−0.138372	−	0.962395i
$867$	11.6808	+	13.4803i	0.396700	+	0.457817i
$868$	−0.855784	−	1.87390i	−0.0290472	−	0.0636045i
$869$	10.0816	−	2.96023i	0.341995	−	0.100419i
$870$	−2.26162	+	4.95225i	−0.0766761	+	0.167897i
$871$	8.47493	−	58.9444i	0.287162	−	1.99726i
$872$	10.0939	−	6.48695i	0.341822	−	0.219676i
$873$	−4.33693			−0.146783
$874$	33.8585	−	24.1984i	1.14528	−	0.818522i
$875$	−2.36558			−0.0799712
$876$	−3.31014	+	2.12730i	−0.111839	+	0.0718748i
$877$	−5.11434	+	35.5710i	−0.172699	+	1.20115i	0.700452	+	0.713699i	$0.252982\pi$
$877$	−5.11434	+	35.5710i	−0.172699	+	1.20115i	−0.873151	+	0.487449i	$0.837927\pi$
$878$	−14.9439	+	32.7226i	−0.504333	+	1.10434i
$879$	−0.321967	+	0.0945382i	−0.0108597	+	0.00318869i
$880$	−0.803313	−	1.75901i	−0.0270797	−	0.0592962i
$881$	14.8268	+	17.1110i	0.499527	+	0.576485i	0.948386	−	0.317118i	$-0.102715\pi$
$881$	14.8268	+	17.1110i	0.499527	+	0.576485i	−0.448859	+	0.893602i	$0.648170\pi$
$882$	0.199814	+	1.38973i	0.00672808	+	0.0467948i
$883$	27.0218	+	7.93431i	0.909355	+	0.267011i	0.702769	−	0.711418i	$-0.251947\pi$
$883$	27.0218	+	7.93431i	0.909355	+	0.267011i	0.206586	+	0.978429i	$0.433765\pi$
$884$	−23.4564	+	27.0701i	−0.788925	+	0.910468i
$885$	2.91263	+	1.87183i	0.0979070	+	0.0629210i
$886$	−8.73528	−	5.61383i	−0.293468	−	0.188600i
$887$	26.1943	−	30.2299i	0.879519	−	1.01502i	−0.120233	−	0.992746i	$-0.538364\pi$
$887$	26.1943	−	30.2299i	0.879519	−	1.01502i	0.999752	−	0.0222734i	$-0.00709042\pi$
$888$	5.29079	+	1.55352i	0.177547	+	0.0521326i
$889$	−1.03973	−	7.23145i	−0.0348713	−	0.242535i
$890$	−6.90611	−	7.97008i	−0.231493	−	0.267158i
$891$	−0.803313	−	1.75901i	−0.0269120	−	0.0589290i
$892$	19.8572	−	5.83060i	0.664869	−	0.195223i
$893$	−1.10395	+	2.41731i	−0.0369423	+	0.0808923i
$894$	−0.147946	+	1.02899i	−0.00494806	+	0.0344145i
$895$	−9.22452	+	5.92824i	−0.308342	+	0.198159i
$896$	−2.36558			−0.0790285
$897$	10.7705	−	27.0380i	0.359616	−	0.902772i
$898$	0.257106			0.00857974
$899$	3.98849	−	2.56324i	0.133023	−	0.0854890i
$900$	−0.142315	+	0.989821i	−0.00474383	+	0.0329940i
$901$	17.4275	−	38.1610i	0.580595	−	1.27133i
$902$	8.14409	−	2.39132i	0.271169	−	0.0796223i
$903$	11.0034	+	24.0941i	0.366171	+	0.801802i
$904$	11.8729	+	13.7021i	0.394888	+	0.455725i
$905$	−2.90131	−	20.1791i	−0.0964428	−	0.670775i
$906$	−18.1131	−	5.31849i	−0.601768	−	0.176695i
$907$	17.6971	−	20.4236i	0.587623	−	0.678154i	−0.381602	−	0.924327i	$-0.624628\pi$
$907$	17.6971	−	20.4236i	0.587623	−	0.678154i	0.969226	+	0.246173i	$0.0791731\pi$
$908$	−22.7186	−	14.6004i	−0.753943	−	0.484530i
$909$	−13.0406	−	8.38067i	−0.432529	−	0.277969i
$910$	−9.40110	+	10.8494i	−0.311643	+	0.359656i
$911$	−33.0733	−	9.71120i	−1.09577	−	0.321747i	−0.316598	−	0.948560i	$-0.602541\pi$
$911$	−33.0733	−	9.71120i	−1.09577	−	0.321747i	−0.779170	+	0.626813i	$0.784359\pi$
$912$	1.23497	+	8.58938i	0.0408938	+	0.284423i
$913$	4.91930	+	5.67717i	0.162805	+	0.187887i
$914$	13.4416	+	29.4331i	0.444609	+	0.973559i
$915$	−12.1702	+	3.57350i	−0.402335	+	0.118136i
$916$	−10.0502	+	22.0069i	−0.332069	+	0.727129i
$917$	−5.06240	+	35.2098i	−0.167175	+	1.16273i
$918$	4.96532	−	3.19102i	0.163880	−	0.105319i
$919$	−7.51214			−0.247803			−0.123901	−	0.992295i	$-0.539541\pi$
$919$	−7.51214			−0.247803			−0.123901	+	0.992295i	$0.539541\pi$
$920$	−2.95810	+	3.77487i	−0.0975258	+	0.124454i
$921$	21.3598			0.703831
$922$	24.2667	−	15.5953i	0.799182	−	0.513603i
$923$	3.13042	−	21.7726i	0.103039	−	0.716653i
$924$	−1.90030	+	4.16108i	−0.0625153	+	0.136889i
$925$	−5.29079	+	1.55352i	−0.173960	+	0.0510793i
$926$	−10.0434	−	21.9920i	−0.330047	−	0.722702i
$927$	0.747275	+	0.862402i	0.0245437	+	0.0283250i
$928$	−0.774796	−	5.38882i	−0.0254339	−	0.176897i
$929$	37.4478	+	10.9957i	1.22862	+	0.360756i	0.830730	−	0.556676i	$-0.187923\pi$
$929$	37.4478	+	10.9957i	1.22862	+	0.360756i	0.397893	+	0.917432i	$0.369742\pi$
$930$	0.570286	−	0.658145i	0.0187004	−	0.0215814i
$931$	−10.2496	−	6.58702i	−0.335917	−	0.215881i
$932$	2.60709	+	1.67547i	0.0853980	+	0.0548820i
$933$	2.75879	−	3.18382i	0.0903189	−	0.104234i
$934$	−2.11425	−	0.620801i	−0.0691805	−	0.0203132i
$935$	−1.62433	−	11.2974i	−0.0531212	−	0.369466i
$936$	3.97412	+	4.58638i	0.129898	+	0.149910i
$937$	−17.9695	−	39.3477i	−0.587038	−	1.28543i	−0.937215	−	0.348751i	$-0.886606\pi$
$937$	−17.9695	−	39.3477i	−0.587038	−	1.28543i	0.350177	−	0.936684i	$-0.386121\pi$
$938$	22.2727	−	6.53987i	0.727231	−	0.213534i
$939$	−4.92813	+	10.7911i	−0.160824	+	0.352154i
$940$	0.0435825	−	0.303123i	0.00142151	−	0.00988679i
$941$	36.3392	−	23.3538i	1.18463	−	0.761312i	0.208394	−	0.978045i	$-0.433176\pi$
$941$	36.3392	−	23.3538i	1.18463	−	0.761312i	0.976231	+	0.216732i	$0.0695399\pi$
$942$	7.83644			0.255325
$943$	−14.5527	−	15.2100i	−0.473900	−	0.495305i
$944$	−3.46225			−0.112687
$945$	1.99005	−	1.27893i	0.0647364	−	0.0416036i
$946$	3.08149	−	21.4322i	0.100188	−	0.696821i
$947$	−8.61904	+	18.8731i	−0.280081	+	0.613292i	−0.996427	−	0.0844528i	$-0.973086\pi$
$947$	−8.61904	+	18.8731i	−0.280081	+	0.613292i	0.716346	+	0.697745i	$0.245813\pi$
$948$	5.21347	−	1.53081i	0.169326	−	0.0497185i
$949$	−9.91960	−	21.7209i	−0.322004	−	0.705090i
$950$	−5.68269	−	6.55818i	−0.184371	−	0.212775i
$951$	−0.545359	−	3.79306i	−0.0176845	−	0.122998i
$952$	−13.3968	−	3.93365i	−0.434192	−	0.127490i
$953$	18.7176	−	21.6013i	0.606323	−	0.699733i	−0.366727	−	0.930328i	$-0.619522\pi$
$953$	18.7176	−	21.6013i	0.606323	−	0.699733i	0.973050	+	0.230595i	$0.0740672\pi$
$954$	−5.97943	−	3.84275i	−0.193591	−	0.124414i
$955$	−16.1888	−	10.4039i	−0.523856	−	0.336662i
$956$	−0.814116	+	0.939540i	−0.0263304	+	0.0303869i
$957$	−10.1014	−	2.96604i	−0.326532	−	0.0958784i
$958$	0.238068	+	1.65580i	0.00769164	+	0.0534965i
$959$	−30.1222	−	34.7628i	−0.972695	−	1.12255i
$960$	−0.415415	−	0.909632i	−0.0134075	−	0.0293582i
$961$	29.0166	−	8.52005i	0.936020	−	0.274840i
$962$	−13.9012	+	30.4394i	−0.448193	+	0.981406i
$963$	−1.20688	+	8.39401i	−0.0388911	+	0.270493i
$964$	20.5486	−	13.2058i	0.661827	−	0.425330i
$965$	−5.03481			−0.162076
$966$	11.3311	−	0.559290i	0.364573	−	0.0179948i
$967$	18.6988			0.601313			0.300657	−	0.953732i	$-0.402794\pi$
$967$	18.6988			0.601313			0.300657	+	0.953732i	$0.402794\pi$
$968$	−6.10798	+	3.92536i	−0.196318	+	0.126166i
$969$	−7.28914	+	50.6971i	−0.234161	+	1.62862i
$970$	−1.80163	+	3.94501i	−0.0578467	+	0.126667i
$971$	−31.1000	+	9.13179i	−0.998047	+	0.293053i	−0.739654	−	0.672987i	$-0.765011\pi$
$971$	−31.1000	+	9.13179i	−0.998047	+	0.293053i	−0.258393	+	0.966040i	$0.583193\pi$
$972$	−0.415415	−	0.909632i	−0.0133244	−	0.0291765i
$973$	4.07091	+	4.69808i	0.130507	+	0.150614i
$974$	−1.88059	−	13.0798i	−0.0602579	−	0.419103i
$975$	−5.82283	−	1.70974i	−0.186480	−	0.0547554i
$976$	8.30625	−	9.58593i	0.265877	−	0.306838i
$977$	−18.8319	−	12.1025i	−0.602485	−	0.387194i	0.203547	−	0.979065i	$-0.434753\pi$
$977$	−18.8319	−	12.1025i	−0.602485	−	0.387194i	−0.806032	+	0.591872i	$0.798389\pi$
$978$	−1.39755	−	0.898152i	−0.0446888	−	0.0287197i
$979$	13.3548	−	15.4122i	0.426820	−	0.492576i
$980$	1.34715	+	0.395560i	0.0430332	+	0.0126357i
$981$	−1.70758	−	11.8765i	−0.0545189	−	0.379187i
$982$	−17.2838	−	19.9466i	−0.551549	−	0.636522i
$983$	1.40398	+	3.07429i	0.0447801	+	0.0980548i	0.930700	−	0.365784i	$-0.119199\pi$
$983$	1.40398	+	3.07429i	0.0447801	+	0.0980548i	−0.885920	+	0.463839i	$0.846472\pi$
$984$	4.21153	−	1.23662i	0.134259	−	0.0394219i
$985$	6.39405	−	14.0010i	0.203731	−	0.446110i
$986$	4.57307	−	31.8064i	0.145636	−	1.01292i
$987$	−0.609434	+	0.391660i	−0.0193985	+	0.0124667i
$988$	−52.6620			−1.67540
$989$	−50.7159	+	17.6506i	−1.61267	+	0.561257i
$990$	−1.93376			−0.0614589
$991$	−13.1525	+	8.45260i	−0.417803	+	0.268506i	−0.732608	−	0.680651i	$-0.761697\pi$
$991$	−13.1525	+	8.45260i	−0.417803	+	0.268506i	0.314805	+	0.949156i	$0.398061\pi$
$992$	−0.123935	+	0.861987i	−0.00393494	+	0.0273681i
$993$	0.698398	−	1.52928i	0.0221630	−	0.0485302i
$994$	8.22698	−	2.41566i	0.260944	−	0.0766201i
$995$	−6.65896	−	14.5811i	−0.211103	−	0.462252i
$996$	2.54390	+	2.93582i	0.0806067	+	0.0930251i
$997$	−4.40118	−	30.6109i	−0.139387	−	0.969456i	−0.932703	−	0.360646i	$-0.882556\pi$
$997$	−4.40118	−	30.6109i	−0.139387	−	0.969456i	0.793316	−	0.608810i	$-0.208353\pi$
$998$	−0.346013	−	0.101599i	−0.0109529	−	0.00321605i
$999$	3.61100	−	4.16732i	0.114247	−	0.131848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.c.541.2	yes	20
23.2	even	11	inner	690.2.m.c.301.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.c.301.2	✓	20	23.2	even	11	inner
690.2.m.c.541.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(1.54913 + 1.78779i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(1.54913 + 1.78779i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-0.654861 + 0.755750i) q^{10} +(-1.62678 - 1.04547i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(3.97412 - 4.58638i) q^{13} +(2.26976 + 0.666461i) q^{14} +(0.142315 + 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-2.45190 - 5.36891i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(3.60485 - 7.89352i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(1.99005 - 1.27893i) q^{21} -1.93376 q^{22} +(2.20490 + 4.25892i) q^{23} -1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.863659 - 6.00688i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(2.26976 - 0.666461i) q^{28} +(2.26162 + 4.95225i) q^{29} +(0.654861 + 0.755750i) q^{30} +(-0.123935 - 0.861987i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-1.26634 + 1.46144i) q^{33} +(-4.96532 - 3.19102i) q^{34} +(-1.99005 - 1.27893i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-5.29079 - 1.55352i) q^{37} +(-1.23497 - 8.58938i) q^{38} +(-3.97412 - 4.58638i) q^{39} +(0.415415 + 0.909632i) q^{40} +(-4.21153 + 1.23662i) q^{41} +(0.982698 - 2.15181i) q^{42} +(-1.59352 + 11.0832i) q^{43} +(-1.62678 + 1.04547i) q^{44} +1.00000 q^{45} +(4.15743 + 2.39077i) q^{46} -0.306240 q^{47} +(-0.841254 + 0.540641i) q^{48} +(0.199814 - 1.38973i) q^{49} +(0.415415 - 0.909632i) q^{50} +(-5.66321 + 1.66287i) q^{51} +(-2.52101 - 5.52024i) q^{52} +(4.65460 + 5.37169i) q^{53} +(0.142315 + 0.989821i) q^{54} +(1.85543 + 0.544803i) q^{55} +(1.54913 - 1.78779i) q^{56} +(-7.30015 - 4.69152i) q^{57} +(4.57999 + 2.94338i) q^{58} +(2.26729 - 2.61659i) q^{59} +(0.959493 + 0.281733i) q^{60} +(1.80512 + 12.5549i) q^{61} +(-0.570286 - 0.658145i) q^{62} +(-0.982698 - 2.15181i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-2.52101 + 5.52024i) q^{65} +(-0.275203 + 1.91408i) q^{66} +(8.25507 - 5.30521i) q^{67} -5.90229 q^{68} +(4.52936 - 1.57635i) q^{69} -2.36558 q^{70} +(3.04921 - 1.95961i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(1.63456 - 3.57920i) q^{73} +(-5.29079 + 1.55352i) q^{74} +(-0.415415 - 0.909632i) q^{75} +(-5.68269 - 6.55818i) q^{76} +(-0.651014 - 4.52790i) q^{77} +(-5.82283 - 1.70974i) q^{78} +(-3.55823 + 4.10642i) q^{79} +(0.841254 + 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-2.87440 + 3.31723i) q^{82} +(-3.72729 - 1.09443i) q^{83} +(-0.336657 - 2.34150i) q^{84} +(3.86518 + 4.46066i) q^{85} +(4.65146 + 10.1853i) q^{86} +(5.22371 - 1.53382i) q^{87} +(-0.803313 + 1.75901i) q^{88} +(-1.50084 + 10.4386i) q^{89} +(0.841254 - 0.540641i) q^{90} +14.3559 q^{91} +(4.79000 - 0.236428i) q^{92} -0.870851 q^{93} +(-0.257626 + 0.165566i) q^{94} +(-1.23497 + 8.58938i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(4.16125 - 1.22185i) q^{97} +(-0.583253 - 1.27715i) q^{98} +(1.26634 + 1.46144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Introduction

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