LMFDB - Embedded newform 690.2.m.h.271.2

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:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			271.2
Character	$\chi$	$=$	690.271
Dual form			690.2.m.h.331.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.0700250 + 0.153333i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.0700250 + 0.153333i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.415415 - 0.909632i) q^{10} +(5.28134 - 1.55074i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(1.37637 - 3.01382i) q^{13} +(0.0239895 + 0.166851i) q^{14} +(0.654861 + 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-3.71636 + 2.38836i) q^{17} +(0.142315 - 0.989821i) q^{18} +(3.75657 + 2.41420i) q^{19} +(0.654861 - 0.755750i) q^{20} +(-0.161738 - 0.0474906i) q^{21} +5.50431 q^{22} +(3.07972 + 3.67632i) q^{23} -1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(2.16971 - 2.50398i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.0239895 + 0.166851i) q^{28} +(3.33941 - 2.14611i) q^{29} +(0.415415 + 0.909632i) q^{30} +(-2.47511 - 2.85642i) q^{31} +(0.142315 + 0.989821i) q^{32} +(-2.28657 + 5.00689i) q^{33} +(-4.23870 + 1.24459i) q^{34} +(0.161738 - 0.0474906i) q^{35} +(0.415415 - 0.909632i) q^{36} +(1.34691 + 9.36797i) q^{37} +(2.92424 + 3.37475i) q^{38} +(1.37637 + 3.01382i) q^{39} +(0.841254 - 0.540641i) q^{40} +(-1.37080 + 9.53411i) q^{41} +(-0.141807 - 0.0911338i) q^{42} +(7.12162 - 8.21879i) q^{43} +(5.28134 + 1.55074i) q^{44} -1.00000 q^{45} +(1.91923 + 4.39506i) q^{46} -8.61654 q^{47} +(-0.959493 - 0.281733i) q^{48} +(4.56542 - 5.26877i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(0.628696 - 4.37268i) q^{51} +(2.78727 - 1.79127i) q^{52} +(-4.59171 - 10.0544i) q^{53} +(0.654861 + 0.755750i) q^{54} +(-0.783344 - 5.44828i) q^{55} +(-0.0700250 + 0.153333i) q^{56} +(-4.28456 + 1.25806i) q^{57} +(3.80877 - 1.11836i) q^{58} +(-1.51648 + 3.32062i) q^{59} +(0.142315 + 0.989821i) q^{60} +(3.28638 + 3.79268i) q^{61} +(-1.57010 - 3.43804i) q^{62} +(0.141807 - 0.0911338i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-2.78727 - 1.79127i) q^{65} +(-3.60455 + 4.15988i) q^{66} +(-13.1092 - 3.84922i) q^{67} -4.41764 q^{68} +(-4.79516 - 0.0799796i) q^{69} +0.168566 q^{70} +(-9.05657 - 2.65925i) q^{71} +(0.654861 - 0.755750i) q^{72} +(8.80047 + 5.65572i) q^{73} +(-1.34691 + 9.36797i) q^{74} +(0.841254 - 0.540641i) q^{75} +(1.85501 + 4.06191i) q^{76} +(0.607606 + 0.701215i) q^{77} +(0.471522 + 3.27951i) q^{78} +(5.83069 - 12.7674i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-4.00134 + 8.76171i) q^{82} +(-1.07299 - 7.46280i) q^{83} +(-0.110387 - 0.127394i) q^{84} +(1.83516 + 4.01843i) q^{85} +(9.14864 - 5.87948i) q^{86} +(-0.564928 + 3.92916i) q^{87} +(4.63052 + 2.97585i) q^{88} +(-0.489361 + 0.564752i) q^{89} +(-0.959493 - 0.281733i) q^{90} +0.558500 q^{91} +(0.603258 + 4.75774i) q^{92} +3.77959 q^{93} +(-8.26751 - 2.42756i) q^{94} +(2.92424 - 3.37475i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(-1.17604 + 8.17956i) q^{97} +(5.86487 - 3.76912i) q^{98} +(-2.28657 - 5.00689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$6$	−0.841254	+	0.540641i	−0.343440	+	0.220716i
$7$	0.0700250	+	0.153333i	0.0264670	+	0.0579546i	0.922404	−	0.386227i	$-0.126222\pi$
$7$	0.0700250	+	0.153333i	0.0264670	+	0.0579546i	−0.895937	+	0.444181i	$0.853495\pi$
$8$	0.654861	+	0.755750i	0.231528	+	0.267198i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	0.415415	−	0.909632i	0.131366	−	0.287651i
$11$	5.28134	−	1.55074i	1.59238	−	0.467566i	0.638971	−	0.769231i	$-0.279360\pi$
$11$	5.28134	−	1.55074i	1.59238	−	0.467566i	0.953414	+	0.301665i	$0.0975423\pi$
$12$	−0.959493	+	0.281733i	−0.276982	+	0.0813292i
$13$	1.37637	−	3.01382i	0.381736	−	0.835884i	−0.617065	−	0.786913i	$-0.711678\pi$
$13$	1.37637	−	3.01382i	0.381736	−	0.835884i	0.998800	−	0.0489718i	$-0.0155945\pi$
$14$	0.0239895	+	0.166851i	0.00641146	+	0.0445927i
$15$	0.654861	+	0.755750i	0.169084	+	0.195134i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−3.71636	+	2.38836i	−0.901349	+	0.579262i	−0.907190	−	0.420721i	$-0.861777\pi$
$17$	−3.71636	+	2.38836i	−0.901349	+	0.579262i	0.00584071	+	0.999983i	$0.498141\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	3.75657	+	2.41420i	0.861815	+	0.553855i	0.895239	−	0.445586i	$-0.147005\pi$
$19$	3.75657	+	2.41420i	0.861815	+	0.553855i	−0.0334237	+	0.999441i	$0.510641\pi$
$20$	0.654861	−	0.755750i	0.146431	−	0.168991i
$21$	−0.161738	−	0.0474906i	−0.0352942	−	0.0103633i
$22$	5.50431			1.17352
$23$	3.07972	+	3.67632i	0.642166	+	0.766566i
$23$	3.07972	+	3.67632i	0.642166	+	0.766566i
$24$	−1.00000			−0.204124
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	2.16971	−	2.50398i	0.425515	−	0.491070i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	−0.0239895	+	0.166851i	−0.00453359	+	0.0315318i
$29$	3.33941	−	2.14611i	0.620113	−	0.398523i	−0.192524	−	0.981292i	$-0.561667\pi$
$29$	3.33941	−	2.14611i	0.620113	−	0.398523i	0.812637	+	0.582770i	$0.198031\pi$
$30$	0.415415	+	0.909632i	0.0758441	+	0.166075i
$31$	−2.47511	−	2.85642i	−0.444542	−	0.513029i	0.488614	−	0.872500i	$-0.337503\pi$
$31$	−2.47511	−	2.85642i	−0.444542	−	0.513029i	−0.933156	+	0.359471i	$0.882957\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$	−2.28657	+	5.00689i	−0.398041	+	0.871588i
$34$	−4.23870	+	1.24459i	−0.726931	+	0.213446i
$35$	0.161738	−	0.0474906i	0.0273387	−	0.00802738i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	1.34691	+	9.36797i	0.221431	+	1.54008i	0.732633	+	0.680624i	$0.238291\pi$
$37$	1.34691	+	9.36797i	0.221431	+	1.54008i	−0.511202	+	0.859461i	$0.670800\pi$
$38$	2.92424	+	3.37475i	0.474374	+	0.547457i
$39$	1.37637	+	3.01382i	0.220395	+	0.482598i
$40$	0.841254	−	0.540641i	0.133014	−	0.0854828i
$41$	−1.37080	+	9.53411i	−0.214083	+	1.48898i	0.545249	+	0.838274i	$0.316435\pi$
$41$	−1.37080	+	9.53411i	−0.214083	+	1.48898i	−0.759332	+	0.650703i	$0.774474\pi$
$42$	−0.141807	−	0.0911338i	−0.0218813	−	0.0140623i
$43$	7.12162	−	8.21879i	1.08604	−	1.25335i	0.120604	−	0.992701i	$-0.461517\pi$
$43$	7.12162	−	8.21879i	1.08604	−	1.25335i	0.965433	−	0.260652i	$-0.0839376\pi$
$44$	5.28134	+	1.55074i	0.796192	+	0.233783i
$45$	−1.00000			−0.149071
$46$	1.91923	+	4.39506i	0.282975	+	0.648016i
$47$	−8.61654			−1.25685			−0.628426	−	0.777870i	$-0.716300\pi$
$47$	−8.61654			−1.25685			−0.628426	+	0.777870i	$0.716300\pi$
$48$	−0.959493	−	0.281733i	−0.138491	−	0.0406646i
$49$	4.56542	−	5.26877i	0.652203	−	0.752682i
$50$	−0.841254	−	0.540641i	−0.118971	−	0.0764582i
$51$	0.628696	−	4.37268i	0.0880351	−	0.612298i
$52$	2.78727	−	1.79127i	0.386525	−	0.248404i
$53$	−4.59171	−	10.0544i	−0.630720	−	1.38108i	−0.907459	−	0.420140i	$-0.861981\pi$
$53$	−4.59171	−	10.0544i	−0.630720	−	1.38108i	0.276739	−	0.960945i	$-0.410746\pi$
$54$	0.654861	+	0.755750i	0.0891153	+	0.102844i
$55$	−0.783344	−	5.44828i	−0.105626	−	0.734646i
$56$	−0.0700250	+	0.153333i	−0.00935748	+	0.0204900i
$57$	−4.28456	+	1.25806i	−0.567503	+	0.166634i
$58$	3.80877	−	1.11836i	0.500116	−	0.146847i
$59$	−1.51648	+	3.32062i	−0.197429	+	0.432308i	−0.982291	−	0.187362i	$-0.940006\pi$
$59$	−1.51648	+	3.32062i	−0.197429	+	0.432308i	0.784862	+	0.619670i	$0.212734\pi$
$60$	0.142315	+	0.989821i	0.0183728	+	0.127785i
$61$	3.28638	+	3.79268i	0.420778	+	0.485604i	0.926074	−	0.377343i	$-0.123162\pi$
$61$	3.28638	+	3.79268i	0.420778	+	0.485604i	−0.505296	+	0.862946i	$0.668617\pi$
$62$	−1.57010	−	3.43804i	−0.199403	−	0.436631i
$63$	0.141807	−	0.0911338i	0.0178660	−	0.0114818i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−2.78727	−	1.79127i	−0.345718	−	0.222180i
$66$	−3.60455	+	4.15988i	−0.443690	+	0.512045i
$67$	−13.1092	−	3.84922i	−1.60155	−	0.470257i	−0.645572	−	0.763699i	$-0.723381\pi$
$67$	−13.1092	−	3.84922i	−1.60155	−	0.470257i	−0.955977	+	0.293442i	$0.905199\pi$
$68$	−4.41764			−0.535718
$69$	−4.79516	−	0.0799796i	−0.577270	−	0.00962841i
$70$	0.168566			0.0201475
$71$	−9.05657	−	2.65925i	−1.07482	−	0.315595i	−0.304014	−	0.952668i	$-0.598327\pi$
$71$	−9.05657	−	2.65925i	−1.07482	−	0.315595i	−0.770804	+	0.637073i	$0.780145\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	8.80047	+	5.65572i	1.03002	+	0.661952i	0.942498	−	0.334211i	$-0.108470\pi$
$73$	8.80047	+	5.65572i	1.03002	+	0.661952i	0.0875189	+	0.996163i	$0.472106\pi$
$74$	−1.34691	+	9.36797i	−0.156575	+	1.08900i
$75$	0.841254	−	0.540641i	0.0971396	−	0.0624278i
$76$	1.85501	+	4.06191i	0.212784	+	0.465933i
$77$	0.607606	+	0.701215i	0.0692432	+	0.0799109i
$78$	0.471522	+	3.27951i	0.0533894	+	0.371331i
$79$	5.83069	−	12.7674i	0.656004	−	1.43645i	−0.230196	−	0.973144i	$-0.573937\pi$
$79$	5.83069	−	12.7674i	0.656004	−	1.43645i	0.886200	−	0.463303i	$-0.153336\pi$
$80$	0.959493	−	0.281733i	0.107275	−	0.0314987i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−4.00134	+	8.76171i	−0.441874	+	0.967569i
$83$	−1.07299	−	7.46280i	−0.117776	−	0.819149i	−0.959996	−	0.280015i	$-0.909661\pi$
$83$	−1.07299	−	7.46280i	−0.117776	−	0.819149i	0.842220	−	0.539134i	$-0.181248\pi$
$84$	−0.110387	−	0.127394i	−0.0120443	−	0.0138998i
$85$	1.83516	+	4.01843i	0.199051	+	0.435860i
$86$	9.14864	−	5.87948i	0.986523	−	0.634000i
$87$	−0.564928	+	3.92916i	−0.0605667	+	0.421250i
$88$	4.63052	+	2.97585i	0.493615	+	0.317227i
$89$	−0.489361	+	0.564752i	−0.0518721	+	0.0598636i	−0.781093	−	0.624415i	$-0.785337\pi$
$89$	−0.489361	+	0.564752i	−0.0518721	+	0.0598636i	0.729221	+	0.684279i	$0.239883\pi$
$90$	−0.959493	−	0.281733i	−0.101139	−	0.0296972i
$91$	0.558500			0.0585467
$92$	0.603258	+	4.75774i	0.0628939	+	0.496029i
$93$	3.77959			0.391925
$94$	−8.26751	−	2.42756i	−0.852728	−	0.250384i
$95$	2.92424	−	3.37475i	0.300021	−	0.346242i
$96$	−0.841254	−	0.540641i	−0.0858601	−	0.0551789i
$97$	−1.17604	+	8.17956i	−0.119409	+	0.830508i	0.838800	+	0.544440i	$0.183258\pi$
$97$	−1.17604	+	8.17956i	−0.119409	+	0.830508i	−0.958209	+	0.286069i	$0.907651\pi$
$98$	5.86487	−	3.76912i	0.592441	−	0.380739i
$99$	−2.28657	−	5.00689i	−0.229809	−	0.503212i
$100$	−0.654861	−	0.755750i	−0.0654861	−	0.0755750i
$101$	0.221197	+	1.53846i	0.0220099	+	0.153082i	0.997863	−	0.0653476i	$-0.0208156\pi$
$101$	0.221197	+	1.53846i	0.0220099	+	0.153082i	−0.975853	+	0.218430i	$0.929907\pi$
$102$	1.83516	−	4.01843i	0.181708	−	0.397884i
$103$	−18.3613	+	5.39137i	−1.80919	+	0.531227i	−0.998526	−	0.0542799i	$-0.982714\pi$
$103$	−18.3613	+	5.39137i	−1.80919	+	0.531227i	−0.810667	+	0.585507i	$0.800896\pi$
$104$	3.17902	−	0.933446i	0.311729	−	0.0915319i
$105$	−0.0700250	+	0.153333i	−0.00683374	+	0.0149638i
$106$	−1.57305	−	10.9408i	−0.152788	−	1.06267i
$107$	5.87647	+	6.78181i	0.568100	+	0.655622i	0.965003	−	0.262238i	$-0.0844607\pi$
$107$	5.87647	+	6.78181i	0.568100	+	0.655622i	−0.396903	+	0.917860i	$0.629915\pi$
$108$	0.415415	+	0.909632i	0.0399733	+	0.0875294i
$109$	−7.58587	+	4.87514i	−0.726595	+	0.466954i	−0.850925	−	0.525287i	$-0.823958\pi$
$109$	−7.58587	+	4.87514i	−0.726595	+	0.466954i	0.124331	+	0.992241i	$0.460322\pi$
$110$	0.783344	−	5.44828i	0.0746890	−	0.519473i
$111$	−7.96188	−	5.11679i	−0.755708	−	0.485664i
$112$	−0.110387	+	0.127394i	−0.0104306	+	0.0120376i
$113$	−13.1368	−	3.85731i	−1.23580	−	0.362865i	−0.402367	−	0.915478i	$-0.631812\pi$
$113$	−13.1368	−	3.85731i	−1.23580	−	0.362865i	−0.833438	+	0.552613i	$0.813631\pi$
$114$	−4.46544			−0.418227
$115$	4.07719	−	2.52518i	0.380200	−	0.235474i
$116$	3.96957			0.368565
$117$	−3.17902	−	0.933446i	−0.293901	−	0.0862971i
$118$	−2.39058	+	2.75887i	−0.220071	+	0.253975i
$119$	−0.626453	−	0.402597i	−0.0574269	−	0.0369060i
$120$	−0.142315	+	0.989821i	−0.0129915	+	0.0903579i
$121$	16.2340	−	10.4330i	1.47582	−	0.948450i
$122$	2.08474	+	4.56493i	0.188743	+	0.413290i
$123$	−6.30772	−	7.27949i	−0.568748	−	0.656370i
$124$	−0.537892	−	3.74112i	−0.0483041	−	0.335962i
$125$	−0.415415	+	0.909632i	−0.0371558	+	0.0813600i
$126$	0.161738	−	0.0474906i	0.0144088	−	0.00423080i
$127$	18.6711	−	5.48233i	1.65679	−	0.486478i	0.686241	−	0.727374i	$-0.259259\pi$
$127$	18.6711	−	5.48233i	1.65679	−	0.486478i	0.970551	+	0.240896i	$0.0774412\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$	1.54768	+	10.7643i	0.136265	+	0.947745i
$130$	−2.16971	−	2.50398i	−0.190296	−	0.219613i
$131$	−6.66381	−	14.5917i	−0.582220	−	1.27488i	−0.940031	−	0.341089i	$-0.889204\pi$
$131$	−6.66381	−	14.5917i	−0.582220	−	1.27488i	0.357811	−	0.933794i	$-0.383523\pi$
$132$	−4.63052	+	2.97585i	−0.403035	+	0.259015i
$133$	−0.107124	+	0.745061i	−0.00928879	+	0.0646050i
$134$	−11.4938	−	7.38660i	−0.992911	−	0.638105i
$135$	0.654861	−	0.755750i	0.0563614	−	0.0650446i
$136$	−4.23870	−	1.24459i	−0.363465	−	0.106723i
$137$	−18.9859			−1.62207			−0.811037	−	0.584995i	$-0.801096\pi$
$137$	−18.9859			−1.62207			−0.811037	+	0.584995i	$0.801096\pi$
$138$	−4.57839	−	1.42769i	−0.389739	−	0.121533i
$139$	−0.127658			−0.0108278			−0.00541391	−	0.999985i	$-0.501723\pi$
$139$	−0.127658			−0.0108278			−0.00541391	+	0.999985i	$0.501723\pi$
$140$	0.161738	+	0.0474906i	0.0136694	+	0.00401369i
$141$	5.64263	−	6.51194i	0.475195	−	0.548405i
$142$	−7.94052	−	5.10306i	−0.666354	−	0.428239i
$143$	2.59540	−	18.0514i	0.217039	−	1.50954i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	−1.64902	−	3.61084i	−0.136943	−	0.299864i
$146$	6.85059	+	7.90600i	0.566959	+	0.654305i
$147$	0.992160	+	6.90062i	0.0818320	+	0.569154i
$148$	−3.93161	+	8.60903i	−0.323177	+	0.707658i
$149$	−13.3751	+	3.92729i	−1.09573	+	0.321736i	−0.779155	−	0.626831i	$-0.784352\pi$
$149$	−13.3751	+	3.92729i	−1.09573	+	0.321736i	−0.316576	+	0.948567i	$0.602533\pi$
$150$	0.959493	−	0.281733i	0.0783423	−	0.0230034i
$151$	6.15329	−	13.4738i	0.500748	−	1.09649i	−0.475478	−	0.879728i	$-0.657725\pi$
$151$	6.15329	−	13.4738i	0.500748	−	1.09649i	0.976226	−	0.216757i	$-0.0695480\pi$
$152$	0.635498	+	4.41999i	0.0515457	+	0.358508i
$153$	2.89294	+	3.33863i	0.233880	+	0.269912i
$154$	0.385439	+	0.843994i	0.0310596	+	0.0680109i
$155$	−3.17959	+	2.04340i	−0.255391	+	0.164130i
$156$	−0.471522	+	3.27951i	−0.0377520	+	0.262571i
$157$	−9.37886	−	6.02743i	−0.748514	−	0.481041i	0.109935	−	0.993939i	$-0.464936\pi$
$157$	−9.37886	−	6.02743i	−0.748514	−	0.481041i	−0.858450	+	0.512898i	$0.828572\pi$
$158$	9.19150	−	10.6076i	0.731237	−	0.843892i
$159$	10.6056	+	3.11408i	0.841077	+	0.246962i
$160$	1.00000			0.0790569
$161$	−0.348045	+	0.729658i	−0.0274298	+	0.0575051i
$162$	−1.00000			−0.0785674
$163$	8.58113	+	2.51965i	0.672126	+	0.197354i	0.599949	−	0.800038i	$-0.295187\pi$
$163$	8.58113	+	2.51965i	0.672126	+	0.197354i	0.0721765	+	0.997392i	$0.477006\pi$
$164$	−6.30772	+	7.27949i	−0.492550	+	0.568433i
$165$	4.63052	+	2.97585i	0.360485	+	0.231670i
$166$	1.07299	−	7.46280i	0.0832801	−	0.579226i
$167$	−12.0549	+	7.74720i	−0.932835	+	0.599496i	−0.916355	−	0.400368i	$-0.868882\pi$
$167$	−12.0549	+	7.74720i	−0.932835	+	0.599496i	−0.0164800	+	0.999864i	$0.505246\pi$
$168$	−0.0700250	−	0.153333i	−0.00540254	−	0.0118299i
$169$	1.32444	+	1.52849i	0.101880	+	0.117576i
$170$	0.628696	+	4.37268i	0.0482188	+	0.335369i
$171$	1.85501	−	4.06191i	0.141856	−	0.310622i
$172$	10.4345	−	3.06384i	0.795623	−	0.233616i
$173$	−9.59146	+	2.81631i	−0.729225	+	0.214120i	−0.625211	−	0.780456i	$-0.714987\pi$
$173$	−9.59146	+	2.81631i	−0.729225	+	0.214120i	−0.104014	+	0.994576i	$0.533169\pi$
$174$	−1.64902	+	3.61084i	−0.125012	+	0.273737i
$175$	−0.0239895	−	0.166851i	−0.00181344	−	0.0126127i
$176$	3.60455	+	4.15988i	0.271703	+	0.313563i
$177$	−1.51648	−	3.32062i	−0.113985	−	0.249593i
$178$	−0.628647	+	0.404007i	−0.0471191	+	0.0302816i
$179$	−2.56683	+	17.8527i	−0.191854	+	1.33438i	0.635241	+	0.772314i	$0.280901\pi$
$179$	−2.56683	+	17.8527i	−0.191854	+	1.33438i	−0.827095	+	0.562062i	$0.810008\pi$
$180$	−0.841254	−	0.540641i	−0.0627033	−	0.0402970i
$181$	7.10140	−	8.19546i	0.527843	−	0.609163i	−0.427734	−	0.903905i	$-0.640688\pi$
$181$	7.10140	−	8.19546i	0.527843	−	0.609163i	0.955577	+	0.294741i	$0.0952335\pi$
$182$	0.535877	+	0.157348i	0.0397218	+	0.0116634i
$183$	−5.01844			−0.370974
$184$	−0.761589	+	4.73497i	−0.0561451	+	0.349067i
$185$	9.46430			0.695829
$186$	3.62649	+	1.06483i	0.265907	+	0.0780774i
$187$	−15.9236	+	18.3769i	−1.16445	+	1.34385i
$188$	−7.24869	−	4.65845i	−0.528665	−	0.339753i
$189$	−0.0239895	+	0.166851i	−0.00174498	+	0.0121366i
$190$	3.75657	−	2.41420i	0.272530	−	0.175144i
$191$	0.307867	+	0.674135i	0.0222765	+	0.0487787i	0.920443	−	0.390876i	$-0.127828\pi$
$191$	0.307867	+	0.674135i	0.0222765	+	0.0487787i	−0.898167	+	0.439655i	$0.855101\pi$
$192$	−0.654861	−	0.755750i	−0.0472605	−	0.0545415i
$193$	−0.240286	−	1.67123i	−0.0172962	−	0.120298i	0.979344	−	0.202201i	$-0.0648093\pi$
$193$	−0.240286	−	1.67123i	−0.0172962	−	0.120298i	−0.996640	+	0.0819030i	$0.973900\pi$
$194$	−3.43285	+	7.51690i	−0.246464	+	0.539682i
$195$	3.17902	−	0.933446i	0.227655	−	0.0668455i
$196$	6.68919	−	1.96412i	0.477799	−	0.140294i
$197$	−5.46447	+	11.9655i	−0.389327	+	0.852508i	0.608915	+	0.793236i	$0.291605\pi$
$197$	−5.46447	+	11.9655i	−0.389327	+	0.852508i	−0.998242	+	0.0592721i	$0.981122\pi$
$198$	−0.783344	−	5.44828i	−0.0556699	−	0.387192i
$199$	−14.9137	−	17.2113i	−1.05720	−	1.22008i	−0.974707	−	0.223488i	$-0.928256\pi$
$199$	−14.9137	−	17.2113i	−1.05720	−	1.22008i	−0.0824980	−	0.996591i	$-0.526290\pi$
$200$	−0.415415	−	0.909632i	−0.0293743	−	0.0643207i
$201$	11.4938	−	7.38660i	0.810708	−	0.521011i
$202$	−0.221197	+	1.53846i	−0.0155633	+	0.108245i
$203$	0.562912	+	0.361762i	0.0395087	+	0.0253907i
$204$	2.89294	−	3.33863i	0.202546	−	0.233751i
$205$	9.24198	+	2.71369i	0.645488	+	0.189532i
$206$	−19.1365			−1.33330
$207$	3.20061	−	3.57157i	0.222458	−	0.248241i
$208$	3.31323			0.229731
$209$	23.5835	+	6.92474i	1.63131	+	0.478995i
$210$	−0.110387	+	0.127394i	−0.00761746	+	0.00879102i
$211$	−4.37492	−	2.81159i	−0.301182	−	0.193558i	0.381317	−	0.924444i	$-0.375471\pi$
$211$	−4.37492	−	2.81159i	−0.301182	−	0.193558i	−0.682499	+	0.730886i	$0.739107\pi$
$212$	1.57305	−	10.9408i	0.108038	−	0.751418i
$213$	7.94052	−	5.10306i	0.544075	−	0.349656i
$214$	3.72778	+	8.16269i	0.254825	+	0.557990i
$215$	−7.12162	−	8.21879i	−0.485690	−	0.560517i
$216$	0.142315	+	0.989821i	0.00968330	+	0.0673488i
$217$	0.264666	−	0.579537i	0.0179667	−	0.0393415i
$218$	−8.65208	+	2.54048i	−0.585992	+	0.172063i
$219$	−10.0374	+	2.94724i	−0.678264	+	0.199156i
$220$	2.28657	−	5.00689i	0.154161	−	0.337565i
$221$	2.08302	+	14.4877i	0.140119	+	0.974549i
$222$	−6.19780	−	7.15264i	−0.415969	−	0.480054i
$223$	10.6000	+	23.2108i	0.709831	+	1.55431i	0.827629	+	0.561275i	$0.189689\pi$
$223$	10.6000	+	23.2108i	0.709831	+	1.55431i	−0.117799	+	0.993037i	$0.537584\pi$
$224$	−0.141807	+	0.0911338i	−0.00947488	+	0.00608914i
$225$	−0.142315	+	0.989821i	−0.00948766	+	0.0659881i
$226$	−11.5179	−	7.40212i	−0.766161	−	0.492382i
$227$	−1.99314	+	2.30021i	−0.132289	+	0.152670i	−0.818029	−	0.575177i	$-0.804933\pi$
$227$	−1.99314	+	2.30021i	−0.132289	+	0.152670i	0.685740	+	0.727847i	$0.259479\pi$
$228$	−4.28456	−	1.25806i	−0.283752	−	0.0833170i
$229$	−0.678727			−0.0448515			−0.0224258	−	0.999749i	$-0.507139\pi$
$229$	−0.678727			−0.0448515			−0.0224258	+	0.999749i	$0.507139\pi$
$230$	4.62346	−	1.27421i	0.304862	−	0.0840192i
$231$	−0.927841			−0.0610474
$232$	3.80877	+	1.11836i	0.250058	+	0.0734237i
$233$	−3.69191	+	4.26069i	−0.241865	+	0.279127i	−0.863684	−	0.504034i	$-0.831849\pi$
$233$	−3.69191	+	4.26069i	−0.241865	+	0.279127i	0.621819	+	0.783161i	$0.286394\pi$
$234$	−2.78727	−	1.79127i	−0.182210	−	0.117099i
$235$	−1.22626	+	8.52883i	−0.0799925	+	0.556360i
$236$	−3.07101	+	1.97362i	−0.199906	+	0.128472i
$237$	5.83069	+	12.7674i	0.378744	+	0.829333i
$238$	−0.487653	−	0.562781i	−0.0316098	−	0.0364797i
$239$	0.365022	+	2.53878i	0.0236113	+	0.164220i	0.998216	−	0.0597143i	$-0.0190190\pi$
$239$	0.365022	+	2.53878i	0.0236113	+	0.164220i	−0.974604	+	0.223934i	$0.928110\pi$
$240$	−0.415415	+	0.909632i	−0.0268149	+	0.0587165i
$241$	−5.53022	+	1.62382i	−0.356233	+	0.104599i	−0.454952	−	0.890516i	$-0.650344\pi$
$241$	−5.53022	+	1.62382i	−0.356233	+	0.104599i	0.0987193	+	0.995115i	$0.468525\pi$
$242$	18.5157	−	5.43670i	1.19023	−	0.349484i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	0.714199	+	4.96736i	0.0457219	+	0.318003i
$245$	−4.56542	−	5.26877i	−0.291674	−	0.336610i
$246$	−4.00134	−	8.76171i	−0.255116	−	0.558626i
$247$	12.4464	−	7.99881i	0.791944	−	0.508952i
$248$	0.537892	−	3.74112i	0.0341562	−	0.237561i
$249$	6.34267	+	4.07618i	0.401950	+	0.258318i
$250$	−0.654861	+	0.755750i	−0.0414170	+	0.0477978i
$251$	15.7585	+	4.62710i	0.994665	+	0.292060i	0.738265	−	0.674511i	$-0.235645\pi$
$251$	15.7585	+	4.62710i	0.994665	+	0.292060i	0.256400	+	0.966571i	$0.417464\pi$
$252$	0.168566			0.0106187
$253$	21.9661	+	14.6400i	1.38100	+	0.920412i
$254$	19.4593			1.22099
$255$	−4.23870	−	1.24459i	−0.265438	−	0.0779395i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	8.95790	+	5.75689i	0.558779	+	0.359105i	0.789344	−	0.613952i	$-0.210421\pi$
$257$	8.95790	+	5.75689i	0.558779	+	0.359105i	−0.230565	+	0.973057i	$0.574057\pi$
$258$	−1.54768	+	10.7643i	−0.0963541	+	0.670157i
$259$	−1.34210	+	0.862518i	−0.0833943	+	0.0535943i
$260$	−1.37637	−	3.01382i	−0.0853587	−	0.186909i
$261$	−2.59951	−	3.00000i	−0.160906	−	0.185695i
$262$	−2.28292	−	15.8781i	−0.141039	−	0.980949i
$263$	3.85944	−	8.45099i	0.237983	−	0.521111i	−0.752525	−	0.658564i	$-0.771164\pi$
$263$	3.85944	−	8.45099i	0.237983	−	0.521111i	0.990508	+	0.137453i	$0.0438916\pi$
$264$	−5.28134	+	1.55074i	−0.325044	+	0.0954416i
$265$	−10.6056	+	3.11408i	−0.651495	+	0.191296i
$266$	−0.312692	+	0.684701i	−0.0191724	+	0.0419817i
$267$	−0.106348	−	0.739668i	−0.00650840	−	0.0452669i
$268$	−8.94715	−	10.3256i	−0.546534	−	0.630734i
$269$	0.944494	+	2.06815i	0.0575868	+	0.126097i	0.936238	−	0.351367i	$-0.114283\pi$
$269$	0.944494	+	2.06815i	0.0575868	+	0.126097i	−0.878651	+	0.477465i	$0.841556\pi$
$270$	0.841254	−	0.540641i	0.0511971	−	0.0329024i
$271$	−0.390663	+	2.71712i	−0.0237311	+	0.165053i	−0.998241	−	0.0592926i	$-0.981116\pi$
$271$	−0.390663	+	2.71712i	−0.0237311	+	0.165053i	0.974510	+	0.224346i	$0.0720246\pi$
$272$	−3.71636	−	2.38836i	−0.225337	−	0.144816i
$273$	−0.365740	+	0.422086i	−0.0221356	+	0.0255458i
$274$	−18.2168	−	5.34894i	−1.10052	−	0.323141i
$275$	−5.50431			−0.331922
$276$	−3.99071	−	2.65974i	−0.240212	−	0.160098i
$277$	4.22724			0.253990			0.126995	−	0.991903i	$-0.459467\pi$
$277$	4.22724			0.253990			0.126995	+	0.991903i	$0.459467\pi$
$278$	−0.122487	−	0.0359655i	−0.00734629	−	0.00215706i
$279$	−2.47511	+	2.85642i	−0.148181	+	0.171010i
$280$	0.141807	+	0.0911338i	0.00847459	+	0.00544629i
$281$	−2.80471	+	19.5072i	−0.167315	+	1.16370i	0.717090	+	0.696981i	$0.245474\pi$
$281$	−2.80471	+	19.5072i	−0.167315	+	1.16370i	−0.884405	+	0.466721i	$0.845435\pi$
$282$	7.24869	−	4.65845i	0.431653	−	0.277407i
$283$	6.54941	+	14.3412i	0.389322	+	0.852496i	0.998242	+	0.0592645i	$0.0188755\pi$
$283$	6.54941	+	14.3412i	0.389322	+	0.852496i	−0.608921	+	0.793231i	$0.708397\pi$
$284$	−6.18117	−	7.13346i	−0.366785	−	0.423293i
$285$	0.635498	+	4.41999i	0.0376437	+	0.261817i
$286$	7.57595	−	16.5890i	0.447975	−	0.980929i
$287$	−1.55789	+	0.457437i	−0.0919591	+	0.0270016i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	1.04501	−	2.28825i	0.0614712	−	0.134603i
$290$	−0.564928	−	3.92916i	−0.0331737	−	0.230728i
$291$	−5.41155	−	6.24526i	−0.317231	−	0.366104i
$292$	4.34571	+	9.51579i	0.254314	+	0.556869i
$293$	−2.47458	+	1.59031i	−0.144566	+	0.0929072i	−0.610925	−	0.791689i	$-0.709202\pi$
$293$	−2.47458	+	1.59031i	−0.144566	+	0.0929072i	0.466358	+	0.884596i	$0.345566\pi$
$294$	−0.992160	+	6.90062i	−0.0578639	+	0.402453i
$295$	3.07101	+	1.97362i	0.178801	+	0.114908i
$296$	−6.19780	+	7.15264i	−0.360240	+	0.415739i
$297$	5.28134	+	1.55074i	0.306455	+	0.0899832i
$298$	−13.9398			−0.807509
$299$	15.3186	−	4.22177i	0.885898	−	0.244151i
$300$	1.00000			0.0577350
$301$	1.75890	+	0.516461i	0.101382	+	0.0297683i
$302$	9.70006	−	11.1945i	0.558176	−	0.644169i
$303$	−1.30754	−	0.840306i	−0.0751163	−	0.0482743i
$304$	−0.635498	+	4.41999i	−0.0364483	+	0.253504i
$305$	4.22178	−	2.71317i	0.241739	−	0.155356i
$306$	1.83516	+	4.01843i	0.104909	+	0.229718i
$307$	−6.50468	−	7.50681i	−0.371242	−	0.428436i	0.539133	−	0.842221i	$-0.318752\pi$
$307$	−6.50468	−	7.50681i	−0.371242	−	0.428436i	−0.910375	+	0.413785i	$0.864207\pi$
$308$	0.132045	+	0.918397i	0.00752399	+	0.0523305i
$309$	7.94958	−	17.4071i	0.452236	−	0.990258i
$310$	−3.62649	+	1.06483i	−0.205971	+	0.0604785i
$311$	29.6211	−	8.69754i	1.67966	−	0.493192i	0.703582	−	0.710615i	$-0.251583\pi$
$311$	29.6211	−	8.69754i	1.67966	−	0.493192i	0.976078	+	0.217422i	$0.0697648\pi$
$312$	−1.37637	+	3.01382i	−0.0779215	+	0.170624i
$313$	−2.73006	−	18.9880i	−0.154312	−	1.07327i	−0.908884	−	0.417049i	$-0.863064\pi$
$313$	−2.73006	−	18.9880i	−0.154312	−	1.07327i	0.754572	−	0.656217i	$-0.227845\pi$
$314$	−7.30083	−	8.42560i	−0.412010	−	0.475484i
$315$	−0.0700250	−	0.153333i	−0.00394546	−	0.00863935i
$316$	11.8077	−	7.58833i	0.664234	−	0.426877i
$317$	−3.00316	+	20.8874i	−0.168674	+	1.17315i	0.712955	+	0.701210i	$0.247357\pi$
$317$	−3.00316	+	20.8874i	−0.168674	+	1.17315i	−0.881629	+	0.471944i	$0.843553\pi$
$318$	9.29864	+	5.97587i	0.521442	+	0.335110i
$319$	14.3085	−	16.5129i	0.801123	−	0.924545i
$320$	0.959493	+	0.281733i	0.0536373	+	0.0157493i
$321$	−8.97362			−0.500858
$322$	−0.539515	+	0.602046i	−0.0300660	+	0.0335507i
$323$	−19.7267			−1.09762
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−2.16971	+	2.50398i	−0.120354	+	0.138896i
$326$	7.52367	+	4.83517i	0.416697	+	0.267795i
$327$	1.28330	−	8.92556i	0.0709667	−	0.493584i
$328$	−8.10308	+	5.20753i	−0.447418	+	0.287538i
$329$	−0.603373	−	1.32120i	−0.0332650	−	0.0728402i
$330$	3.60455	+	4.15988i	0.198424	+	0.228994i
$331$	1.64610	+	11.4489i	0.0904780	+	0.629288i	0.983719	+	0.179711i	$0.0575162\pi$
$331$	1.64610	+	11.4489i	0.0904780	+	0.629288i	−0.893241	+	0.449577i	$0.851575\pi$
$332$	3.13204	−	6.85821i	0.171893	−	0.376393i
$333$	9.08093	−	2.66640i	0.497632	−	0.146118i
$334$	−13.7492	+	4.03713i	−0.752323	+	0.220902i
$335$	−5.67568	+	12.4280i	−0.310096	+	0.679015i
$336$	−0.0239895	−	0.166851i	−0.00130873	−	0.00910244i
$337$	1.95253	+	2.25334i	0.106361	+	0.122747i	0.806434	−	0.591324i	$-0.201395\pi$
$337$	1.95253	+	2.25334i	0.106361	+	0.122747i	−0.700073	+	0.714071i	$0.746849\pi$
$338$	0.840168	+	1.83971i	0.0456991	+	0.100067i
$339$	11.5179	−	7.40212i	0.625568	−	0.402028i
$340$	−0.628696	+	4.37268i	−0.0340958	+	0.237142i
$341$	−17.5015	−	11.2475i	−0.947757	−	0.609086i
$342$	2.92424	−	3.37475i	0.158125	−	0.182486i
$343$	2.25974	+	0.663519i	0.122014	+	0.0358267i
$344$	10.8750			0.586341
$345$	−0.761589	+	4.73497i	−0.0410026	+	0.254922i
$346$	−9.99638			−0.537409
$347$	0.417172	+	0.122493i	0.0223950	+	0.00657576i	0.292911	−	0.956140i	$-0.405376\pi$
$347$	0.417172	+	0.122493i	0.0223950	+	0.00657576i	−0.270516	+	0.962716i	$0.587194\pi$
$348$	−2.59951	+	3.00000i	−0.139349	+	0.160817i
$349$	−4.06580	−	2.61293i	−0.217637	−	0.139867i	0.427280	−	0.904119i	$-0.359472\pi$
$349$	−4.06580	−	2.61293i	−0.217637	−	0.139867i	−0.644917	+	0.764252i	$0.723108\pi$
$350$	0.0239895	−	0.166851i	0.00128229	−	0.00891854i
$351$	2.78727	−	1.79127i	0.148773	−	0.0956109i
$352$	2.28657	+	5.00689i	0.121875	+	0.266868i
$353$	10.6987	+	12.3469i	0.569433	+	0.657161i	0.965299	−	0.261147i	$-0.0841008\pi$
$353$	10.6987	+	12.3469i	0.569433	+	0.657161i	−0.395866	+	0.918308i	$0.629555\pi$
$354$	−0.519522	−	3.61336i	−0.0276123	−	0.192048i
$355$	−3.92107	+	8.58594i	−0.208109	+	0.455694i
$356$	−0.717004	+	0.210531i	−0.0380012	+	0.0111581i
$357$	0.714502	−	0.209797i	0.0378155	−	0.0111036i
$358$	−7.49256	+	16.4064i	−0.395994	+	0.867106i
$359$	−1.00707	−	7.00432i	−0.0531511	−	0.369674i	−0.998986	−	0.0450254i	$-0.985663\pi$
$359$	−1.00707	−	7.00432i	−0.0531511	−	0.369674i	0.945835	−	0.324648i	$-0.105246\pi$
$360$	−0.654861	−	0.755750i	−0.0345142	−	0.0398315i
$361$	0.390550	+	0.855186i	0.0205553	+	0.0450098i
$362$	9.12267	−	5.86279i	0.479477	−	0.308141i
$363$	−2.74630	+	19.1010i	−0.144144	+	1.00254i
$364$	0.469840	+	0.301948i	0.0246263	+	0.0158264i
$365$	6.85059	−	7.90600i	0.358576	−	0.413819i
$366$	−4.81516	−	1.41386i	−0.251692	−	0.0739036i
$367$	−6.72497			−0.351041			−0.175520	−	0.984476i	$-0.556161\pi$
$367$	−6.72497			−0.351041			−0.175520	+	0.984476i	$0.556161\pi$
$368$	−2.06474	+	4.32861i	−0.107632	+	0.225644i
$369$	9.63215			0.501430
$370$	9.08093	+	2.66640i	0.472095	+	0.138620i
$371$	1.22015	−	1.40813i	0.0633469	−	0.0731062i
$372$	3.17959	+	2.04340i	0.164854	+	0.105945i
$373$	−2.32023	+	16.1375i	−0.120137	+	0.835570i	0.837262	+	0.546802i	$0.184155\pi$
$373$	−2.32023	+	16.1375i	−0.120137	+	0.835570i	−0.957399	+	0.288768i	$0.906754\pi$
$374$	−20.4560	+	13.1463i	−1.05775	+	0.679777i
$375$	−0.415415	−	0.909632i	−0.0214519	−	0.0469732i
$376$	−5.64263	−	6.51194i	−0.290997	−	0.335828i
$377$	−1.87174	−	13.0182i	−0.0963995	−	0.670473i
$378$	−0.0700250	+	0.153333i	−0.00360170	+	0.00788662i
$379$	9.17404	−	2.69374i	0.471239	−	0.138368i	−0.0374865	−	0.999297i	$-0.511935\pi$
$379$	9.17404	−	2.69374i	0.471239	−	0.138368i	0.508725	+	0.860929i	$0.330117\pi$
$380$	4.28456	−	1.25806i	0.219793	−	0.0645371i
$381$	−8.08370	+	17.7008i	−0.414141	+	0.906841i
$382$	0.105471	+	0.733564i	0.00539634	+	0.0375324i
$383$	−12.7585	−	14.7241i	−0.651930	−	0.752367i	0.329507	−	0.944153i	$-0.393117\pi$
$383$	−12.7585	−	14.7241i	−0.651930	−	0.752367i	−0.981437	+	0.191786i	$0.938572\pi$
$384$	−0.415415	−	0.909632i	−0.0211991	−	0.0464195i
$385$	0.780549	−	0.501629i	0.0397805	−	0.0255654i
$386$	0.240286	−	1.67123i	0.0122303	−	0.0850633i
$387$	−9.14864	−	5.87948i	−0.465052	−	0.298871i
$388$	−5.41155	+	6.24526i	−0.274730	+	0.317055i
$389$	−27.9536	−	8.20790i	−1.41730	−	0.416157i	−0.518712	−	0.854949i	$-0.673588\pi$
$389$	−27.9536	−	8.20790i	−1.41730	−	0.416157i	−0.898589	+	0.438792i	$0.855407\pi$
$390$	3.31323			0.167772
$391$	−20.2257	−	6.30704i	−1.02286	−	0.318961i
$392$	6.97159			0.352118
$393$	15.3915	+	4.51936i	0.776401	+	0.227972i
$394$	−8.61420	+	9.94131i	−0.433977	+	0.500836i
$395$	−11.8077	−	7.58833i	−0.594109	−	0.381811i
$396$	0.783344	−	5.44828i	0.0393645	−	0.273786i
$397$	12.5173	−	8.04439i	0.628226	−	0.403736i	−0.187426	−	0.982279i	$-0.560015\pi$
$397$	12.5173	−	8.04439i	0.628226	−	0.403736i	0.815652	+	0.578542i	$0.196378\pi$
$398$	−9.46060	−	20.7158i	−0.474217	−	1.03839i
$399$	−0.492929	−	0.568870i	−0.0246773	−	0.0284791i
$400$	−0.142315	−	0.989821i	−0.00711574	−	0.0494911i
$401$	12.2707	−	26.8692i	0.612771	−	1.34178i	−0.307891	−	0.951422i	$-0.599623\pi$
$401$	12.2707	−	26.8692i	0.612771	−	1.34178i	0.920662	−	0.390360i	$-0.127650\pi$
$402$	13.1092	−	3.84922i	0.653830	−	0.191982i
$403$	−12.0154	+	3.52804i	−0.598530	+	0.175744i
$404$	−0.645670	+	1.41382i	−0.0321233	+	0.0703402i
$405$	0.142315	+	0.989821i	0.00707168	+	0.0491846i
$406$	0.438190	+	0.505699i	0.0217470	+	0.0250974i
$407$	21.6408	+	47.3868i	1.07269	+	2.34887i
$408$	3.71636	−	2.38836i	0.183987	−	0.118241i
$409$	−0.749719	+	5.21441i	−0.0370712	+	0.257836i	−0.999926	−	0.0121846i	$-0.996121\pi$
$409$	−0.749719	+	5.21441i	−0.0370712	+	0.257836i	0.962855	+	0.270021i	$0.0870305\pi$
$410$	8.10308	+	5.20753i	0.400183	+	0.257182i
$411$	12.4331	−	14.3486i	0.613280	−	0.707763i
$412$	−18.3613	−	5.39137i	−0.904597	−	0.265614i
$413$	−0.615354			−0.0302796
$414$	4.07719	−	2.52518i	0.200383	−	0.124106i
$415$	−7.53954			−0.370102
$416$	3.17902	+	0.933446i	0.155865	+	0.0457660i
$417$	0.0835983	−	0.0964776i	0.00409383	−	0.00472453i
$418$	20.6773	+	13.2885i	1.01136	+	0.649961i
$419$	−3.02422	+	21.0339i	−0.147743	+	1.02757i	0.772160	+	0.635428i	$0.219176\pi$
$419$	−3.02422	+	21.0339i	−0.147743	+	1.02757i	−0.919903	+	0.392146i	$0.871733\pi$
$420$	−0.141807	+	0.0911338i	−0.00691947	+	0.00444688i
$421$	4.26668	+	9.34272i	0.207945	+	0.455336i	0.984653	−	0.174525i	$-0.0558390\pi$
$421$	4.26668	+	9.34272i	0.207945	+	0.455336i	−0.776708	+	0.629861i	$0.783112\pi$
$422$	−3.40559	−	3.93026i	−0.165781	−	0.191322i
$423$	1.22626	+	8.52883i	0.0596229	+	0.414686i
$424$	4.59171	−	10.0544i	0.222993	−	0.488287i
$425$	4.23870	−	1.24459i	0.205607	−	0.0603717i
$426$	9.05657	−	2.65925i	0.438792	−	0.128841i
$427$	−0.351416	+	0.769494i	−0.0170062	+	0.0372384i
$428$	1.27708	+	8.88228i	0.0617299	+	0.429341i
$429$	11.9427	+	13.7826i	0.576600	+	0.665432i
$430$	−4.51764	−	9.89226i	−0.217860	−	0.477047i
$431$	26.8094	−	17.2293i	1.29136	−	0.829908i	0.299118	−	0.954216i	$-0.403307\pi$
$431$	26.8094	−	17.2293i	1.29136	−	0.829908i	0.992244	+	0.124308i	$0.0396711\pi$
$432$	−0.142315	+	0.989821i	−0.00684713	+	0.0476228i
$433$	10.3243	+	6.63500i	0.496152	+	0.318858i	0.764676	−	0.644415i	$-0.222899\pi$
$433$	10.3243	+	6.63500i	0.496152	+	0.318858i	−0.268523	+	0.963273i	$0.586536\pi$
$434$	0.417219	−	0.481497i	0.0200272	−	0.0231126i
$435$	3.80877	+	1.11836i	0.182617	+	0.0536211i
$436$	−9.01734			−0.431852
$437$	2.69381	+	21.2454i	0.128862	+	1.01630i
$438$	−10.4611			−0.499853
$439$	−19.2078	−	5.63993i	−0.916740	−	0.269179i	−0.210865	−	0.977515i	$-0.567628\pi$
$439$	−19.2078	−	5.63993i	−0.916740	−	0.269179i	−0.705875	+	0.708336i	$0.749446\pi$
$440$	3.60455	−	4.15988i	0.171840	−	0.198314i
$441$	−5.86487	−	3.76912i	−0.279280	−	0.179482i
$442$	−2.08302	+	14.4877i	−0.0990791	+	0.689110i
$443$	25.4998	−	16.3877i	1.21153	−	0.778605i	0.230619	−	0.973044i	$-0.425925\pi$
$443$	25.4998	−	16.3877i	1.21153	−	0.778605i	0.980915	+	0.194439i	$0.0622886\pi$
$444$	−3.93161	−	8.60903i	−0.186586	−	0.408567i
$445$	0.489361	+	0.564752i	0.0231979	+	0.0267718i
$446$	3.63141	+	25.2570i	0.171952	+	1.19595i
$447$	5.79079	−	12.6801i	0.273895	−	0.599746i
$448$	−0.161738	+	0.0474906i	−0.00764141	+	0.00224372i
$449$	31.0567	−	9.11907i	1.46566	−	0.430356i	0.550972	−	0.834524i	$-0.314257\pi$
$449$	31.0567	−	9.11907i	1.46566	−	0.430356i	0.914685	+	0.404168i	$0.132439\pi$
$450$	−0.415415	+	0.909632i	−0.0195829	+	0.0428805i
$451$	7.54529	+	52.4786i	0.355294	+	2.47112i
$452$	−8.96595	−	10.3473i	−0.421723	−	0.486694i
$453$	6.15329	+	13.4738i	0.289107	+	0.633056i
$454$	−2.56045	+	1.64550i	−0.120168	+	0.0772272i
$455$	0.0794828	−	0.552815i	0.00372621	−	0.0259164i
$456$	−3.75657	−	2.41420i	−0.175917	−	0.113055i
$457$	4.84487	−	5.59127i	0.226633	−	0.261549i	−0.631032	−	0.775757i	$-0.717368\pi$
$457$	4.84487	−	5.59127i	0.226633	−	0.261549i	0.857666	+	0.514208i	$0.171914\pi$
$458$	−0.651234	−	0.191220i	−0.0304302	−	0.00893510i
$459$	−4.41764			−0.206198
$460$	4.79516	+	0.0799796i	0.223576	+	0.00372907i
$461$	−15.8277			−0.737168			−0.368584	−	0.929594i	$-0.620157\pi$
$461$	−15.8277			−0.737168			−0.368584	+	0.929594i	$0.620157\pi$
$462$	−0.890257	−	0.261403i	−0.0414185	−	0.0121616i
$463$	0.194377	−	0.224323i	0.00903345	−	0.0104252i	−0.751215	−	0.660058i	$-0.770532\pi$
$463$	0.194377	−	0.224323i	0.00903345	−	0.0104252i	0.760248	+	0.649633i	$0.225077\pi$
$464$	3.33941	+	2.14611i	0.155028	+	0.0996306i
$465$	0.537892	−	3.74112i	0.0249441	−	0.173490i
$466$	−4.74274	+	3.04797i	−0.219703	+	0.141195i
$467$	−5.44610	−	11.9253i	−0.252015	−	0.551837i	0.740768	−	0.671761i	$-0.234462\pi$
$467$	−5.44610	−	11.9253i	−0.252015	−	0.551837i	−0.992783	+	0.119925i	$0.961735\pi$
$468$	−2.16971	−	2.50398i	−0.100295	−	0.115746i
$469$	−0.327761	−	2.27963i	−0.0151346	−	0.105263i
$470$	−3.57944	+	7.83788i	−0.165107	+	0.361534i
$471$	10.6971	−	3.14094i	0.492895	−	0.144727i
$472$	−3.50264	+	1.02847i	−0.161222	+	0.0473391i
$473$	24.8665	−	54.4500i	1.14336	−	2.50361i
$474$	1.99750	+	13.8930i	0.0917484	+	0.638124i
$475$	−2.92424	−	3.37475i	−0.134173	−	0.154844i
$476$	−0.309345	−	0.677372i	−0.0141788	−	0.0310473i
$477$	−9.29864	+	5.97587i	−0.425755	+	0.273616i
$478$	−0.365022	+	2.53878i	−0.0166957	+	0.116121i
$479$	1.99506	+	1.28215i	0.0911568	+	0.0585829i	0.585425	−	0.810726i	$-0.300928\pi$
$479$	1.99506	+	1.28215i	0.0911568	+	0.0585829i	−0.494268	+	0.869309i	$0.664564\pi$
$480$	−0.654861	+	0.755750i	−0.0298902	+	0.0344951i
$481$	30.0873	+	8.83442i	1.37186	+	0.402815i
$482$	−5.76369			−0.262529
$483$	−0.323518	−	0.740859i	−0.0147206	−	0.0337103i
$484$	19.2974			0.877154
$485$	7.92893	+	2.32814i	0.360034	+	0.105716i
$486$	0.654861	−	0.755750i	0.0297051	−	0.0342815i
$487$	−7.08794	−	4.55515i	−0.321185	−	0.206413i	0.370106	−	0.928990i	$-0.379321\pi$
$487$	−7.08794	−	4.55515i	−0.321185	−	0.206413i	−0.691291	+	0.722576i	$0.742958\pi$
$488$	−0.714199	+	4.96736i	−0.0323303	+	0.224862i
$489$	−7.52367	+	4.83517i	−0.340232	+	0.218654i
$490$	−2.89610	−	6.34158i	−0.130833	−	0.286483i
$491$	5.65835	+	6.53009i	0.255358	+	0.294699i	0.868925	−	0.494944i	$-0.164811\pi$
$491$	5.65835	+	6.53009i	0.255358	+	0.294699i	−0.613567	+	0.789643i	$0.710266\pi$
$492$	−1.37080	−	9.53411i	−0.0618003	−	0.429831i
$493$	−7.28477	+	15.9514i	−0.328090	+	0.718416i
$494$	14.1957	−	4.16825i	0.638697	−	0.187538i
$495$	−5.28134	+	1.55074i	−0.237379	+	0.0697007i
$496$	1.57010	−	3.43804i	0.0704995	−	0.154372i
$497$	−0.226435	−	1.57489i	−0.0101570	−	0.0706434i
$498$	4.93735	+	5.69801i	0.221248	+	0.255334i
$499$	−0.656467	−	1.43746i	−0.0293875	−	0.0643496i	0.894369	−	0.447330i	$-0.147625\pi$
$499$	−0.656467	−	1.43746i	−0.0293875	−	0.0643496i	−0.923757	+	0.382980i	$0.874898\pi$
$500$	−0.841254	+	0.540641i	−0.0376220	+	0.0241782i
$501$	2.03932	−	14.1838i	0.0911103	−	0.633686i
$502$	13.8165	+	8.87934i	0.616661	+	0.396304i
$503$	6.02675	−	6.95524i	0.268719	−	0.310119i	−0.605312	−	0.795988i	$-0.706952\pi$
$503$	6.02675	−	6.95524i	0.268719	−	0.310119i	0.874031	+	0.485870i	$0.161497\pi$
$504$	0.161738	+	0.0474906i	0.00720439	+	0.00211540i
$505$	1.55428			0.0691644
$506$	16.9517	+	20.2356i	0.753596	+	0.899581i
$507$	−2.02248			−0.0898214
$508$	18.6711	+	5.48233i	0.828396	+	0.243239i
$509$	0.525344	−	0.606279i	0.0232855	−	0.0268728i	−0.743987	−	0.668194i	$-0.767068\pi$
$509$	0.525344	−	0.606279i	0.0232855	−	0.0268728i	0.767273	+	0.641321i	$0.221613\pi$
$510$	−3.71636	−	2.38836i	−0.164563	−	0.105758i
$511$	−0.250957	+	1.74545i	−0.0111017	+	0.0772140i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$	1.85501	+	4.06191i	0.0819007	+	0.179338i
$514$	6.97314	+	8.04743i	0.307572	+	0.354957i
$515$	2.72340	+	18.9417i	0.120007	+	0.834670i
$516$	−4.51764	+	9.89226i	−0.198878	+	0.435482i
$517$	−45.5069	+	13.3620i	−2.00139	+	0.587661i
$518$	−1.53074	+	0.449466i	−0.0672568	+	0.0197484i
$519$	4.15265	−	9.09303i	0.182281	−	0.399140i
$520$	−0.471522	−	3.27951i	−0.0206776	−	0.143816i
$521$	−5.59267	−	6.45429i	−0.245019	−	0.282768i	0.619897	−	0.784683i	$-0.287174\pi$
$521$	−5.59267	−	6.45429i	−0.245019	−	0.282768i	−0.864917	+	0.501915i	$0.832629\pi$
$522$	−1.64902	−	3.61084i	−0.0721755	−	0.158042i
$523$	−16.2789	+	10.4618i	−0.711826	+	0.457463i	−0.845785	−	0.533524i	$-0.820867\pi$
$523$	−16.2789	+	10.4618i	−0.711826	+	0.457463i	0.133959	+	0.990987i	$0.457231\pi$
$524$	2.28292	−	15.8781i	0.0997298	−	0.693636i
$525$	0.141807	+	0.0911338i	0.00618897	+	0.00397741i
$526$	6.08403	−	7.02134i	0.265276	−	0.306145i
$527$	16.0205	+	4.70406i	0.697866	+	0.204912i
$528$	−5.50431			−0.239544
$529$	−4.03064	+	22.6441i	−0.175245	+	0.984525i
$530$	−11.0533			−0.480125
$531$	3.50264	+	1.02847i	0.152002	+	0.0446317i
$532$	−0.492929	+	0.568870i	−0.0213712	+	0.0246636i
$533$	26.8474	+	17.2538i	1.16289	+	0.747344i
$534$	0.106348	−	0.739668i	0.00460214	−	0.0320086i
$535$	7.54909	−	4.85150i	0.326375	−	0.209749i
$536$	−5.67568	−	12.4280i	−0.245152	−	0.536808i
$537$	−11.8113	−	13.6309i	−0.509694	−	0.588218i
$538$	0.323569	+	2.25047i	0.0139501	+	0.0970248i
$539$	15.9410	−	34.9060i	0.686629	−	1.50351i
$540$	0.959493	−	0.281733i	0.0412900	−	0.0121238i
$541$	−29.2785	+	8.59695i	−1.25878	+	0.369612i	−0.842041	−	0.539413i	$-0.818646\pi$
$541$	−29.2785	+	8.59695i	−1.25878	+	0.369612i	−0.416741	+	0.909025i	$0.636828\pi$
$542$	−1.14034	+	2.49700i	−0.0489818	+	0.107255i
$543$	1.54328	+	10.7338i	0.0662286	+	0.460630i
$544$	−2.89294	−	3.33863i	−0.124034	−	0.143143i
$545$	3.74594	+	8.20246i	0.160458	+	0.351355i
$546$	−0.469840	+	0.301948i	−0.0201073	+	0.0129222i
$547$	4.23158	−	29.4313i	0.180929	−	1.25839i	−0.673643	−	0.739057i	$-0.735271\pi$
$547$	4.23158	−	29.4313i	0.180929	−	1.25839i	0.854572	−	0.519333i	$-0.173820\pi$
$548$	−15.9719	−	10.2645i	−0.682287	−	0.438479i
$549$	3.28638	−	3.79268i	0.140259	−	0.161868i
$550$	−5.28134	−	1.55074i	−0.225197	−	0.0661239i
$551$	17.7259			0.755147
$552$	−3.07972	−	3.67632i	−0.131082	−	0.156475i
$553$	2.36597			0.100611
$554$	4.05601	+	1.19095i	0.172323	+	0.0505987i
$555$	−6.19780	+	7.15264i	−0.263082	+	0.303613i
$556$	−0.107393	−	0.0690172i	−0.00455447	−	0.00292698i
$557$	0.715827	−	4.97869i	0.0303306	−	0.210954i	−0.969020	−	0.246981i	$-0.920561\pi$
$557$	0.715827	−	4.97869i	0.0303306	−	0.210954i	0.999351	+	0.0360277i	$0.0114704\pi$
$558$	−3.17959	+	2.04340i	−0.134603	+	0.0865040i
$559$	−14.9680	−	32.7754i	−0.633079	−	1.38625i
$560$	0.110387	+	0.127394i	0.00466472	+	0.00538338i
$561$	−3.46054	−	24.0686i	−0.146104	−	1.01618i
$562$	−8.18691	+	17.9268i	−0.345344	+	0.756198i
$563$	−43.1916	+	12.6822i	−1.82031	+	0.534491i	−0.999335	−	0.0364713i	$-0.988388\pi$
$563$	−43.1916	+	12.6822i	−1.82031	+	0.534491i	−0.820976	+	0.570963i	$0.806570\pi$
$564$	8.26751	−	2.42756i	0.348125	−	0.102219i
$565$	−5.68761	+	12.4541i	−0.239279	+	0.523949i
$566$	2.24373	+	15.6055i	0.0943108	+	0.655946i
$567$	−0.110387	−	0.127394i	−0.00463584	−	0.00535004i
$568$	−3.92107	−	8.58594i	−0.164524	−	0.360258i
$569$	12.2803	−	7.89207i	0.514817	−	0.330853i	−0.257302	−	0.966331i	$-0.582833\pi$
$569$	12.2803	−	7.89207i	0.514817	−	0.330853i	0.772119	+	0.635478i	$0.219197\pi$
$570$	−0.635498	+	4.41999i	−0.0266181	+	0.185133i
$571$	−28.6702	−	18.4252i	−1.19981	−	0.771071i	−0.220886	−	0.975300i	$-0.570895\pi$
$571$	−28.6702	−	18.4252i	−1.19981	−	0.771071i	−0.978923	+	0.204229i	$0.934531\pi$
$572$	11.9427	−	13.7826i	0.499351	−	0.576281i
$573$	−0.711087	−	0.208794i	−0.0297061	−	0.00872249i
$574$	−1.62366			−0.0677701
$575$	−1.91923	−	4.39506i	−0.0800375	−	0.183287i
$576$	1.00000			0.0416667
$577$	−30.0429	−	8.82139i	−1.25070	−	0.367239i	−0.411676	−	0.911330i	$-0.635056\pi$
$577$	−30.0429	−	8.82139i	−1.25070	−	0.367239i	−0.839026	+	0.544091i	$0.816875\pi$
$578$	1.64736	−	1.90115i	0.0685210	−	0.0790774i
$579$	1.42038	+	0.912826i	0.0590292	+	0.0379357i
$580$	0.564928	−	3.92916i	0.0234574	−	0.163150i
$581$	1.06916	−	0.687108i	0.0443562	−	0.0285060i
$582$	−3.43285	−	7.51690i	−0.142296	−	0.311585i
$583$	−39.8423	−	45.9804i	−1.65010	−	1.90431i
$584$	1.48878	+	10.3547i	0.0616060	+	0.428479i
$585$	−1.37637	+	3.01382i	−0.0569058	+	0.124606i
$586$	−2.82238	+	0.828726i	−0.116592	+	0.0342344i
$587$	23.4584	−	6.88800i	0.968231	−	0.284298i	0.240873	−	0.970557i	$-0.422566\pi$
$587$	23.4584	−	6.88800i	0.968231	−	0.284298i	0.727358	+	0.686258i	$0.240748\pi$
$588$	−2.89610	+	6.34158i	−0.119433	+	0.261522i
$589$	−2.40192	−	16.7057i	−0.0989695	−	0.688348i
$590$	2.39058	+	2.75887i	0.0984185	+	0.113581i
$591$	−5.46447	−	11.9655i	−0.224778	−	0.492196i
$592$	−7.96188	+	5.11679i	−0.327231	+	0.210299i
$593$	−5.60505	+	38.9840i	−0.230172	+	1.60088i	0.467188	+	0.884158i	$0.345267\pi$
$593$	−5.60505	+	38.9840i	−0.230172	+	1.60088i	−0.697359	+	0.716722i	$0.745642\pi$
$594$	4.63052	+	2.97585i	0.189992	+	0.122101i
$595$	−0.487653	+	0.562781i	−0.0199918	+	0.0230718i
$596$	−13.3751	−	3.92729i	−0.547866	−	0.160868i
$597$	22.7739			0.932072
$598$	15.8875	+	0.264991i	0.649688	+	0.0108363i
$599$	−1.52695			−0.0623895			−0.0311947	−	0.999513i	$-0.509931\pi$
$599$	−1.52695			−0.0623895			−0.0311947	+	0.999513i	$0.509931\pi$
$600$	0.959493	+	0.281733i	0.0391711	+	0.0115017i
$601$	−29.3034	+	33.8180i	−1.19531	+	1.37946i	−0.288742	+	0.957407i	$0.593237\pi$
$601$	−29.3034	+	33.8180i	−1.19531	+	1.37946i	−0.906570	+	0.422056i	$0.861309\pi$
$602$	1.54215	+	0.991082i	0.0628535	+	0.0403935i
$603$	−1.94440	+	13.5236i	−0.0791822	+	0.550724i
$604$	12.4610	−	8.00819i	0.507030	−	0.325849i
$605$	−8.01642	−	17.5535i	−0.325914	−	0.713652i
$606$	−1.01784	−	1.17464i	−0.0413467	−	0.0477167i
$607$	−1.80190	−	12.5325i	−0.0731367	−	0.508677i	−0.993155	−	0.116802i	$-0.962736\pi$
$607$	−1.80190	−	12.5325i	−0.0731367	−	0.508677i	0.920019	−	0.391875i	$-0.128173\pi$
$608$	−1.85501	+	4.06191i	−0.0752306	+	0.164732i
$609$	−0.642031	+	0.188517i	−0.0260164	+	0.00763910i
$610$	4.81516	−	1.41386i	0.194960	−	0.0572454i
$611$	−11.8595	+	25.9687i	−0.479785	+	1.05058i
$612$	0.628696	+	4.37268i	0.0254135	+	0.176755i
$613$	7.64781	+	8.82604i	0.308892	+	0.356480i	0.888876	−	0.458147i	$-0.151487\pi$
$613$	7.64781	+	8.82604i	0.308892	+	0.356480i	−0.579984	+	0.814628i	$0.696941\pi$
$614$	−4.12629	−	9.03531i	−0.166523	−	0.364635i
$615$	−8.10308	+	5.20753i	−0.326748	+	0.209988i
$616$	−0.132045	+	0.918397i	−0.00532026	+	0.0370033i
$617$	−6.78990	−	4.36360i	−0.273351	−	0.175672i	0.396782	−	0.917913i	$-0.370127\pi$
$617$	−6.78990	−	4.36360i	−0.273351	−	0.175672i	−0.670133	+	0.742241i	$0.733763\pi$
$618$	12.5317	−	14.4624i	0.504100	−	0.581762i
$619$	24.2458	+	7.11921i	0.974521	+	0.286145i	0.729961	−	0.683489i	$-0.239538\pi$
$619$	24.2458	+	7.11921i	0.974521	+	0.286145i	0.244560	+	0.969634i	$0.421357\pi$
$620$	−3.77959			−0.151792
$621$	0.603258	+	4.75774i	0.0242079	+	0.190921i
$622$	30.8716			1.23784
$623$	−0.120863	−	0.0354885i	−0.00484227	−	0.00142182i
$624$	−2.16971	+	2.50398i	−0.0868578	+	0.100239i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	2.73006	−	18.9880i	0.109115	−	0.758914i
$627$	−20.6773	+	13.2885i	−0.825771	+	0.530691i
$628$	−4.63133	−	10.1412i	−0.184810	−	0.404677i
$629$	−27.3797	−	31.5978i	−1.09170	−	1.25989i
$630$	−0.0239895	−	0.166851i	−0.000955764	−	0.00664749i
$631$	6.34707	−	13.8982i	0.252673	−	0.553277i	−0.740209	−	0.672377i	$-0.765274\pi$
$631$	6.34707	−	13.8982i	0.252673	−	0.553277i	0.992882	+	0.119100i	$0.0380009\pi$
$632$	13.4673	−	3.95435i	0.535699	−	0.157295i
$633$	4.98982	−	1.46514i	0.198327	−	0.0582342i
$634$	−8.76617	+	19.1952i	−0.348149	+	0.762340i
$635$	−2.76935	−	19.2613i	−0.109898	−	0.764360i
$636$	7.23838	+	8.35354i	0.287020	+	0.331239i
$637$	−9.59546	−	21.0111i	−0.380186	−	0.832491i
$638$	18.3811	−	11.8128i	0.727716	−	0.467675i
$639$	−1.34330	+	9.34284i	−0.0531400	+	0.369597i
$640$	0.841254	+	0.540641i	0.0332535	+	0.0213707i
$641$	−27.0138	+	31.1756i	−1.06698	+	1.23136i	−0.0952029	+	0.995458i	$0.530350\pi$
$641$	−27.0138	+	31.1756i	−1.06698	+	1.23136i	−0.971777	+	0.235902i	$0.924195\pi$
$642$	−8.61012	−	2.52816i	−0.339814	−	0.0997785i
$643$	−17.0899			−0.673959			−0.336979	−	0.941512i	$-0.609405\pi$
$643$	−17.0899			−0.673959			−0.336979	+	0.941512i	$0.609405\pi$
$644$	−0.687277	+	0.425660i	−0.0270825	+	0.0167734i
$645$	10.8750			0.428203
$646$	−18.9277	−	5.55766i	−0.744698	−	0.218663i
$647$	2.47593	−	2.85737i	0.0973388	−	0.112335i	−0.704990	−	0.709217i	$-0.749049\pi$
$647$	2.47593	−	2.85737i	0.0973388	−	0.112335i	0.802329	+	0.596882i	$0.203594\pi$
$648$	−0.841254	−	0.540641i	−0.0330476	−	0.0212384i
$649$	−2.85961	+	19.8890i	−0.112249	+	0.780712i
$650$	−2.78727	+	1.79127i	−0.109326	+	0.0702594i
$651$	0.264666	+	0.579537i	0.0103731	+	0.0227139i
$652$	5.85668	+	6.75897i	0.229365	+	0.264702i
$653$	−5.55630	−	38.6449i	−0.217435	−	1.51229i	−0.747458	−	0.664309i	$-0.768726\pi$
$653$	−5.55630	−	38.6449i	−0.217435	−	1.51229i	0.530023	−	0.847983i	$-0.322183\pi$
$654$	3.74594	−	8.20246i	0.146478	−	0.320742i
$655$	−15.3915	+	4.51936i	−0.601397	+	0.176586i
$656$	−9.24198	+	2.71369i	−0.360839	+	0.105952i
$657$	4.34571	−	9.51579i	0.169542	−	0.371246i
$658$	−0.206706	−	1.43767i	−0.00805825	−	0.0560464i
$659$	23.9926	+	27.6890i	0.934620	+	1.07861i	0.996751	+	0.0805414i	$0.0256649\pi$
$659$	23.9926	+	27.6890i	0.934620	+	1.07861i	−0.0621309	+	0.998068i	$0.519790\pi$
$660$	2.28657	+	5.00689i	0.0890047	+	0.194893i
$661$	−19.1101	+	12.2813i	−0.743297	+	0.477688i	−0.856670	−	0.515864i	$-0.827471\pi$
$661$	−19.1101	+	12.2813i	−0.743297	+	0.477688i	0.113373	+	0.993552i	$0.463834\pi$
$662$	−1.64610	+	11.4489i	−0.0639776	+	0.444974i
$663$	−12.3132	−	7.91319i	−0.478204	−	0.307323i
$664$	4.93735	−	5.69801i	0.191606	−	0.221126i
$665$	0.722232	+	0.212066i	0.0280070	+	0.00822359i
$666$	9.46430			0.366734
$667$	18.1742	+	5.66733i	0.703709	+	0.219440i
$668$	−14.3297			−0.554431
$669$	−24.4831	−	7.18889i	−0.946572	−	0.277939i
$670$	−8.94715	+	10.3256i	−0.345659	+	0.398911i
$671$	23.2380	+	14.9341i	0.897092	+	0.576526i
$672$	0.0239895	−	0.166851i	0.000925415	−	0.00643640i
$673$	23.7399	−	15.2567i	0.915107	−	0.588104i	0.00387301	−	0.999992i	$-0.498767\pi$
$673$	23.7399	−	15.2567i	0.915107	−	0.588104i	0.911234	+	0.411889i	$0.135131\pi$
$674$	1.23860	+	2.71215i	0.0477090	+	0.104468i
$675$	−0.654861	−	0.755750i	−0.0252056	−	0.0290888i
$676$	0.287829	+	2.00189i	0.0110703	+	0.0769959i
$677$	19.1308	−	41.8907i	0.735258	−	1.60999i	−0.0559435	−	0.998434i	$-0.517817\pi$
$677$	19.1308	−	41.8907i	0.735258	−	1.60999i	0.791201	−	0.611556i	$-0.209456\pi$
$678$	13.1368	−	3.85731i	0.504515	−	0.148139i
$679$	−1.33655	+	0.392447i	−0.0512921	+	0.0150607i
$680$	−1.83516	+	4.01843i	−0.0703750	+	0.154100i
$681$	−0.433151	−	3.01263i	−0.0165984	−	0.115444i
$682$	−13.6237	−	15.7226i	−0.521680	−	0.602051i
$683$	−11.4163	−	24.9981i	−0.436831	−	0.956526i	−0.992169	−	0.124902i	$-0.960139\pi$
$683$	−11.4163	−	24.9981i	−0.436831	−	0.956526i	0.555338	−	0.831624i	$-0.312589\pi$
$684$	3.75657	−	2.41420i	0.143636	−	0.0923092i
$685$	−2.70197	+	18.7926i	−0.103237	+	0.718029i
$686$	1.98127	+	1.27328i	0.0756452	+	0.0486142i
$687$	0.444472	−	0.512948i	0.0169577	−	0.0195702i
$688$	10.4345	+	3.06384i	0.397811	+	0.116808i
$689$	−36.6222			−1.39520
$690$	−2.06474	+	4.32861i	−0.0786031	+	0.164787i
$691$	12.8509			0.488872			0.244436	−	0.969665i	$-0.421397\pi$
$691$	12.8509			0.488872			0.244436	+	0.969665i	$0.421397\pi$
$692$	−9.59146	−	2.81631i	−0.364613	−	0.107060i
$693$	0.607606	−	0.701215i	0.0230811	−	0.0266370i
$694$	0.365764	+	0.235062i	0.0138842	+	0.00892283i
$695$	−0.0181676	+	0.126359i	−0.000689138	+	0.00479306i
$696$	−3.33941	+	2.14611i	−0.126580	+	0.0813481i
$697$	−17.6765	−	38.7061i	−0.669545	−	1.46610i
$698$	−3.16496	−	3.65255i	−0.119795	−	0.138251i
$699$	−0.802329	−	5.58032i	−0.0303469	−	0.211067i
$700$	0.0700250	−	0.153333i	0.00264670	−	0.00579546i
$701$	−26.4991	+	7.78085i	−1.00086	+	0.293879i	−0.740808	−	0.671716i	$-0.765557\pi$
$701$	−26.4991	+	7.78085i	−1.00086	+	0.293879i	−0.260050	+	0.965595i	$0.583739\pi$
$702$	3.17902	−	0.933446i	0.119985	−	0.0352306i
$703$	−17.5564	+	38.4431i	−0.662151	+	1.44991i
$704$	0.783344	+	5.44828i	0.0295234	+	0.205340i
$705$	−5.64263	−	6.51194i	−0.212514	−	0.245254i
$706$	6.78678	+	14.8610i	0.255424	+	0.559300i
$707$	−0.220407	+	0.141647i	−0.00828927	+	0.00532719i
$708$	0.519522	−	3.61336i	0.0195248	−	0.135798i
$709$	16.1549	+	10.3821i	0.606710	+	0.389909i	0.807622	−	0.589700i	$-0.200754\pi$
$709$	16.1549	+	10.3821i	0.606710	+	0.389909i	−0.200912	+	0.979609i	$0.564390\pi$
$710$	−6.18117	+	7.13346i	−0.231975	+	0.267714i
$711$	−13.4673	−	3.95435i	−0.505062	−	0.148300i
$712$	−0.747274			−0.0280053
$713$	2.87849	−	17.8963i	0.107800	−	0.670220i
$714$	0.744666			0.0278684
$715$	−17.4983	−	5.13797i	−0.654400	−	0.192149i
$716$	−11.8113	+	13.6309i	−0.441408	+	0.509412i
$717$	−2.15772	−	1.38668i	−0.0805816	−	0.0517866i
$718$	1.00707	−	7.00432i	0.0375835	−	0.261399i
$719$	9.37823	−	6.02702i	0.349749	−	0.224770i	−0.353957	−	0.935262i	$-0.615164\pi$
$719$	9.37823	−	6.02702i	0.349749	−	0.224770i	0.703705	+	0.710492i	$0.251528\pi$
$720$	−0.415415	−	0.909632i	−0.0154816	−	0.0339000i
$721$	−2.11243	−	2.43787i	−0.0786709	−	0.0907910i
$722$	0.133797	+	0.930576i	0.00497939	+	0.0346325i
$723$	2.39432	−	5.24284i	0.0890458	−	0.194983i
$724$	10.4049	−	3.05515i	0.386694	−	0.113544i
$725$	−3.80877	+	1.11836i	−0.141454	+	0.0415347i
$726$	−8.01642	+	17.5535i	−0.297517	+	0.651472i
$727$	1.80290	+	12.5394i	0.0668659	+	0.465062i	0.995553	+	0.0941992i	$0.0300291\pi$
$727$	1.80290	+	12.5394i	0.0668659	+	0.465062i	−0.928687	+	0.370863i	$0.879062\pi$
$728$	0.365740	+	0.422086i	0.0135552	+	0.0156435i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	8.80047	−	5.65572i	0.325720	−	0.209328i
$731$	−6.83708	+	47.5529i	−0.252879	+	1.75881i
$732$	−4.22178	−	2.71317i	−0.156042	−	0.100282i
$733$	30.7624	−	35.5017i	1.13623	−	1.31128i	0.192231	−	0.981350i	$-0.438428\pi$
$733$	30.7624	−	35.5017i	1.13623	−	1.31128i	0.944004	−	0.329935i	$-0.107027\pi$
$734$	−6.45256	−	1.89464i	−0.238168	−	0.0699325i
$735$	6.97159			0.257151
$736$	−3.20061	+	3.57157i	−0.117976	+	0.131650i
$737$	−75.2036			−2.77016
$738$	9.24198	+	2.71369i	0.340202	+	0.0998923i
$739$	−22.2944	+	25.7291i	−0.820111	+	0.946459i	−0.999302	−	0.0373553i	$-0.988107\pi$
$739$	−22.2944	+	25.7291i	−0.820111	+	0.946459i	0.179191	+	0.983814i	$0.442652\pi$
$740$	7.96188	+	5.11679i	0.292684	+	0.188097i
$741$	−2.10555	+	14.6445i	−0.0773495	+	0.537977i
$742$	1.56744	−	1.00733i	0.0575424	−	0.0369803i
$743$	−10.5493	−	23.0998i	−0.387017	−	0.847449i	−0.998423	−	0.0561323i	$-0.982123\pi$
$743$	−10.5493	−	23.0998i	−0.387017	−	0.847449i	0.611406	−	0.791317i	$-0.290604\pi$
$744$	2.47511	+	2.85642i	0.0907418	+	0.104722i
$745$	1.98384	+	13.7979i	0.0726821	+	0.505515i
$746$	−6.77271	+	14.8302i	−0.247967	+	0.542971i
$747$	−7.23414	+	2.12413i	−0.264683	+	0.0777180i
$748$	−23.3311	+	6.85063i	−0.853069	+	0.250484i
$749$	−0.628377	+	1.37595i	−0.0229604	+	0.0502763i
$750$	−0.142315	−	0.989821i	−0.00519660	−	0.0361432i
$751$	−27.9995	−	32.3131i	−1.02171	−	1.17912i	−0.983695	−	0.179845i	$-0.942441\pi$
$751$	−27.9995	−	32.3131i	−1.02171	−	1.17912i	−0.0380196	−	0.999277i	$-0.512105\pi$
$752$	−3.57944	−	7.83788i	−0.130529	−	0.285818i
$753$	−13.8165	+	8.87934i	−0.503502	+	0.323581i
$754$	1.87174	−	13.0182i	0.0681647	−	0.474096i
$755$	−12.4610	−	8.00819i	−0.453502	−	0.291448i
$756$	−0.110387	+	0.127394i	−0.00401475	+	0.00463327i
$757$	26.0228	+	7.64097i	0.945813	+	0.277716i	0.718043	−	0.695999i	$-0.245038\pi$
$757$	26.0228	+	7.64097i	0.945813	+	0.277716i	0.227771	+	0.973715i	$0.426856\pi$
$758$	9.56134			0.347283
$759$	−25.4489	+	7.01366i	−0.923738	+	0.254580i
$760$	4.46544			0.161978
$761$	−9.45785	−	2.77708i	−0.342847	−	0.100669i	0.105776	−	0.994390i	$-0.466267\pi$
$761$	−9.45785	−	2.77708i	−0.342847	−	0.100669i	−0.448623	+	0.893721i	$0.648085\pi$
$762$	−12.7432	+	14.7064i	−0.461636	+	0.532756i
$763$	−1.27872	−	0.821785i	−0.0462929	−	0.0297506i
$764$	−0.105471	+	0.733564i	−0.00381579	+	0.0265394i
$765$	3.71636	−	2.38836i	0.134365	−	0.0863513i
$766$	−8.09344	−	17.7222i	−0.292428	−	0.640328i
$767$	7.92055	+	9.14080i	0.285994	+	0.330055i
$768$	−0.142315	−	0.989821i	−0.00513534	−	0.0357171i
$769$	16.4501	−	36.0207i	0.593207	−	1.29894i	−0.340278	−	0.940325i	$-0.610521\pi$
$769$	16.4501	−	36.0207i	0.593207	−	1.29894i	0.933485	−	0.358617i	$-0.116751\pi$
$770$	0.890257	−	0.261403i	0.0320826	−	0.00942031i
$771$	−10.2169	+	2.99997i	−0.367954	+	0.108041i
$772$	0.701393	−	1.53584i	0.0252437	−	0.0552759i
$773$	−6.89427	−	47.9507i	−0.247970	−	1.72467i	−0.609915	−	0.792467i	$-0.708796\pi$
$773$	−6.89427	−	47.9507i	−0.247970	−	1.72467i	0.361945	−	0.932199i	$-0.382113\pi$
$774$	−7.12162	−	8.21879i	−0.255981	−	0.295418i
$775$	1.57010	+	3.43804i	0.0563996	+	0.123498i
$776$	−6.95184	+	4.46768i	−0.249557	+	0.160380i
$777$	0.227044	−	1.57912i	0.00814515	−	0.0566508i
$778$	−24.5088	−	15.7509i	−0.878683	−	0.564695i
$779$	−28.1667	+	32.5061i	−1.00918	+	1.16465i
$780$	3.17902	+	0.933446i	0.113827	+	0.0334227i
$781$	−51.9547			−1.85908
$782$	−17.6295	−	11.7498i	−0.630431	−	0.420172i
$783$	3.96957			0.141861
$784$	6.68919	+	1.96412i	0.238900	+	0.0701472i
$785$	−7.30083	+	8.42560i	−0.260578	+	0.300723i
$786$	13.4948	+	8.67260i	0.481344	+	0.309341i
$787$	3.14965	−	21.9063i	0.112273	−	0.780875i	−0.853427	−	0.521213i	$-0.825480\pi$
$787$	3.14965	−	21.9063i	0.112273	−	0.780875i	0.965700	−	0.259662i	$-0.0836111\pi$
$788$	−11.0661	+	7.11172i	−0.394212	+	0.253345i
$789$	3.85944	+	8.45099i	0.137400	+	0.300863i
$790$	−9.19150	−	10.6076i	−0.327019	−	0.377400i
$791$	−0.328449	−	2.28442i	−0.0116783	−	0.0812244i
$792$	2.28657	−	5.00689i	0.0812498	−	0.177912i
$793$	15.9537	−	4.68444i	0.566534	−	0.166349i
$794$	14.2766	−	4.19200i	0.506659	−	0.148769i
$795$	4.59171	−	10.0544i	0.162851	−	0.356595i
$796$	−3.24106	−	22.5421i	−0.114876	−	0.798982i
$797$	11.9566	+	13.7986i	0.423523	+	0.488772i	0.926907	−	0.375291i	$-0.122457\pi$
$797$	11.9566	+	13.7986i	0.423523	+	0.488772i	−0.503384	+	0.864063i	$0.667912\pi$
$798$	−0.312692	−	0.684701i	−0.0110692	−	0.0242381i
$799$	32.0221	−	20.5794i	1.13286	−	0.728046i
$800$	0.142315	−	0.989821i	0.00503159	−	0.0349955i
$801$	0.628647	+	0.404007i	0.0222122	+	0.0142749i
$802$	19.3436	−	22.3237i	0.683046	−	0.788277i
$803$	55.2489	+	16.2225i	1.94969	+	0.572481i
$804$	13.6627			0.481845
$805$	0.672699	+	0.448343i	0.0237095	+	0.0158020i
$806$	−12.5227			−0.441092
$807$	−2.18152	−	0.640551i	−0.0767930	−	0.0225485i
$808$	−1.01784	+	1.17464i	−0.0358073	+	0.0413238i
$809$	−8.25960	−	5.30812i	−0.290392	−	0.186624i	0.387331	−	0.921941i	$-0.373397\pi$
$809$	−8.25960	−	5.30812i	−0.290392	−	0.186624i	−0.677723	+	0.735317i	$0.737033\pi$
$810$	−0.142315	+	0.989821i	−0.00500043	+	0.0347788i
$811$	30.4715	−	19.5828i	1.07000	−	0.687646i	0.117772	−	0.993041i	$-0.462425\pi$
$811$	30.4715	−	19.5828i	1.07000	−	0.687646i	0.952226	+	0.305395i	$0.0987885\pi$
$812$	0.277969	+	0.608667i	0.00975479	+	0.0213600i
$813$	−1.79763	−	2.07458i	−0.0630458	−	0.0727587i
$814$	7.41381	+	51.5642i	0.259854	+	1.80732i
$815$	3.71522	−	8.13520i	0.130139	−	0.284964i
$816$	4.23870	−	1.24459i	0.148384	−	0.0435695i
$817$	46.5946	−	13.6814i	1.63014	−	0.478652i
$818$	−2.18842	+	4.79197i	−0.0765163	+	0.167547i
$819$	−0.0794828	−	0.552815i	−0.00277735	−	0.0193169i
$820$	6.30772	+	7.27949i	0.220275	+	0.254211i
$821$	11.9451	+	26.1562i	0.416888	+	0.912856i	0.995275	+	0.0970943i	$0.0309548\pi$
$821$	11.9451	+	26.1562i	0.416888	+	0.912856i	−0.578388	+	0.815762i	$0.696318\pi$
$822$	15.9719	−	10.2645i	0.557085	−	0.358017i
$823$	1.72107	−	11.9703i	0.0599927	−	0.417259i	−0.937588	−	0.347747i	$-0.886947\pi$
$823$	1.72107	−	11.9703i	0.0599927	−	0.417259i	0.997581	−	0.0695117i	$-0.0221441\pi$
$824$	−16.0986	−	10.3460i	−0.560822	−	0.360418i
$825$	3.60455	−	4.15988i	0.125494	−	0.144828i
$826$	−0.590428	−	0.173365i	−0.0205436	−	0.00603215i
$827$	47.9166			1.66622			0.833111	−	0.553105i	$-0.186557\pi$
$827$	47.9166			1.66622			0.833111	+	0.553105i	$0.186557\pi$
$828$	4.62346	−	1.27421i	0.160676	−	0.0442820i
$829$	−23.8806			−0.829406			−0.414703	−	0.909957i	$-0.636115\pi$
$829$	−23.8806			−0.829406			−0.414703	+	0.909957i	$0.636115\pi$
$830$	−7.23414	−	2.12413i	−0.251101	−	0.0737298i
$831$	−2.76826	+	3.19474i	−0.0960297	+	0.110824i
$832$	2.78727	+	1.79127i	0.0966312	+	0.0621011i
$833$	−4.38301	+	30.4845i	−0.151862	+	1.05623i
$834$	0.107393	−	0.0690172i	0.00371871	−	0.00238987i
$835$	5.95276	+	13.0347i	0.206004	+	0.451085i
$836$	16.0959	+	18.5757i	0.556689	+	0.642453i
$837$	−0.537892	−	3.74112i	−0.0185923	−	0.129312i
$838$	−8.82766	+	19.3299i	−0.304946	+	0.667740i
$839$	5.07898	−	1.49132i	0.175346	−	0.0514862i	−0.192881	−	0.981222i	$-0.561783\pi$
$839$	5.07898	−	1.49132i	0.175346	−	0.0514862i	0.368227	+	0.929736i	$0.379965\pi$
$840$	−0.161738	+	0.0474906i	−0.00558050	+	0.00163858i
$841$	−5.50115	+	12.0458i	−0.189695	+	0.415374i
$842$	1.46170	+	10.1663i	0.0503735	+	0.350355i
$843$	−12.9059	−	14.8942i	−0.444501	−	0.512982i
$844$	−2.16035	−	4.73052i	−0.0743625	−	0.162831i
$845$	1.70142	−	1.09343i	0.0585305	−	0.0376153i
$846$	−1.22626	+	8.52883i	−0.0421597	+	0.293227i
$847$	2.73650	+	1.75864i	0.0940274	+	0.0604277i
$848$	7.23838	−	8.35354i	0.248567	−	0.286862i
$849$	−15.1273	−	4.44178i	−0.519168	−	0.152441i
$850$	4.41764			0.151524
$851$	−30.2915	+	33.8024i	−1.03838	+	1.15873i
$852$	9.43891			0.323372
$853$	42.2432	+	12.4037i	1.44638	+	0.424696i	0.908343	−	0.418225i	$-0.137348\pi$
$853$	42.2432	+	12.4037i	1.44638	+	0.424696i	0.538037	+	0.842921i	$0.319166\pi$
$854$	−0.553973	+	0.639319i	−0.0189566	+	0.0218770i
$855$	−3.75657	−	2.41420i	−0.128472	−	0.0825638i
$856$	−1.27708	+	8.88228i	−0.0436497	+	0.303590i
$857$	−2.25498	+	1.44919i	−0.0770286	+	0.0495033i	−0.578588	−	0.815620i	$-0.696396\pi$
$857$	−2.25498	+	1.44919i	−0.0770286	+	0.0495033i	0.501560	+	0.865123i	$0.332760\pi$
$858$	7.57595	+	16.5890i	0.258639	+	0.566339i
$859$	−16.9859	−	19.6028i	−0.579552	−	0.668838i	0.387957	−	0.921678i	$-0.373181\pi$
$859$	−16.9859	−	19.6028i	−0.579552	−	0.668838i	−0.967508	+	0.252839i	$0.918636\pi$
$860$	−1.54768	−	10.7643i	−0.0527753	−	0.367060i
$861$	0.674491	−	1.47693i	0.0229866	−	0.0503336i
$862$	30.5775	−	8.97835i	1.04147	−	0.305804i
$863$	49.4183	−	14.5105i	1.68222	−	0.493943i	0.705542	−	0.708668i	$-0.250703\pi$
$863$	49.4183	−	14.5105i	1.68222	−	0.493943i	0.976675	+	0.214724i	$0.0688853\pi$
$864$	−0.415415	+	0.909632i	−0.0141327	+	0.0309463i
$865$	1.42263	+	9.89463i	0.0483710	+	0.336428i
$866$	8.03676	+	9.27492i	0.273100	+	0.315175i
$867$	1.04501	+	2.28825i	0.0354904	+	0.0777132i
$868$	0.535972	−	0.344449i	0.0181921	−	0.0116913i
$869$	10.9949	−	76.4711i	0.372976	−	2.59410i
$870$	3.33941	+	2.14611i	0.113217	+	0.0727599i
$871$	−29.6440	+	34.2110i	−1.00445	+	1.15920i
$872$	−8.65208	−	2.54048i	−0.292996	−	0.0860315i
$873$	8.26367			0.279683
$874$	−3.40083	+	21.1437i	−0.115035	+	0.715198i
$875$	−0.168566			−0.00569858
$876$	−10.0374	−	2.94724i	−0.339132	−	0.0995781i
$877$	0.193710	−	0.223554i	0.00654113	−	0.00754887i	−0.752470	−	0.658627i	$-0.771138\pi$
$877$	0.193710	−	0.223554i	0.00654113	−	0.00754887i	0.759011	+	0.651078i	$0.225683\pi$
$878$	−16.8408	−	10.8229i	−0.568351	−	0.365257i
$879$	0.418624	−	2.91160i	0.0141198	−	0.0982057i
$880$	4.63052	−	2.97585i	0.156095	−	0.100316i
$881$	−0.520854	−	1.14051i	−0.0175480	−	0.0384248i	0.900655	−	0.434535i	$-0.143087\pi$
$881$	−0.520854	−	1.14051i	−0.0175480	−	0.0384248i	−0.918203	+	0.396110i	$0.870360\pi$
$882$	−4.56542	−	5.26877i	−0.153726	−	0.177409i
$883$	−0.0270432	−	0.188090i	−0.000910078	−	0.00632973i	0.989361	−	0.145479i	$-0.0464723\pi$
$883$	−0.0270432	−	0.188090i	−0.000910078	−	0.00632973i	−0.990271	+	0.139149i	$0.955563\pi$
$884$	−6.08030	+	13.3140i	−0.204503	+	0.447798i
$885$	−3.50264	+	1.02847i	−0.117740	+	0.0345716i
$886$	29.0839	−	8.53980i	0.977092	−	0.286900i
$887$	11.3170	−	24.7808i	0.379988	−	0.832058i	−0.618925	−	0.785450i	$-0.712432\pi$
$887$	11.3170	−	24.7808i	0.379988	−	0.832058i	0.998913	−	0.0466082i	$-0.0148412\pi$
$888$	−1.34691	−	9.36797i	−0.0451994	−	0.314369i
$889$	2.14807	+	2.47900i	0.0720439	+	0.0831431i
$890$	0.310429	+	0.679745i	0.0104056	+	0.0227851i
$891$	−4.63052	+	2.97585i	−0.155128	+	0.0996948i
$892$	−3.63141	+	25.2570i	−0.121589	+	0.845667i
$893$	−32.3686	−	20.8020i	−1.08317	−	0.696113i
$894$	9.12860	−	10.5350i	0.305306	−	0.352342i
$895$	17.3057	+	5.08142i	0.578466	+	0.169853i
$896$	−0.168566			−0.00563141
$897$	−6.84095	+	14.3417i	−0.228413	+	0.478855i
$898$	32.3678			1.08013
$899$	−14.3956	−	4.22693i	−0.480120	−	0.140976i
$900$	−0.654861	+	0.755750i	−0.0218287	+	0.0251917i
$901$	41.0781	+	26.3993i	1.36851	+	0.879488i
$902$	−7.54529	+	52.4786i	−0.251231	+	1.74735i
$903$	−1.54215	+	0.991082i	−0.0513196	+	0.0329811i
$904$	−5.68761	−	12.4541i	−0.189167	−	0.414218i
$905$	−7.10140	−	8.19546i	−0.236059	−	0.272426i
$906$	2.10802	+	14.6616i	0.0700344	+	0.487100i
$907$	−19.9171	+	43.6124i	−0.661337	+	1.44813i	0.219935	+	0.975515i	$0.429416\pi$
$907$	−19.9171	+	43.6124i	−0.661337	+	1.44813i	−0.881271	+	0.472610i	$0.843312\pi$
$908$	−2.92032	+	0.857484i	−0.0969144	+	0.0284566i
$909$	1.49132	−	0.437890i	0.0494639	−	0.0145239i
$910$	0.232009	−	0.508029i	0.00769103	−	0.0168410i
$911$	−1.16221	−	8.08334i	−0.0385057	−	0.267813i	0.961469	−	0.274913i	$-0.0886491\pi$
$911$	−1.16221	−	8.08334i	−0.0385057	−	0.267813i	−0.999975	+	0.00709994i	$0.997740\pi$
$912$	−2.92424	−	3.37475i	−0.0968313	−	0.111749i
$913$	−17.2397	−	37.7497i	−0.570551	−	1.24933i
$914$	6.22386	−	3.99983i	0.205867	−	0.132303i
$915$	−0.714199	+	4.96736i	−0.0236107	+	0.164216i
$916$	−0.570982	−	0.366948i	−0.0188658	−	0.0121243i
$917$	1.77076	−	2.04357i	0.0584757	−	0.0674846i
$918$	−4.23870	−	1.24459i	−0.139898	−	0.0410777i
$919$	38.1727			1.25920			0.629601	−	0.776918i	$-0.283218\pi$
$919$	38.1727			1.25920			0.629601	+	0.776918i	$0.283218\pi$
$920$	4.57839	+	1.42769i	0.150945	+	0.0470697i
$921$	9.93293			0.327301
$922$	−15.1865	−	4.45917i	−0.500142	−	0.146855i
$923$	−20.4797	+	23.6348i	−0.674097	+	0.777949i
$924$	−0.780549	−	0.501629i	−0.0256782	−	0.0165024i
$925$	1.34691	−	9.36797i	0.0442862	−	0.308017i
$926$	0.249702	−	0.160474i	0.00820572	−	0.00527349i
$927$	7.94958	+	17.4071i	0.261098	+	0.571726i
$928$	2.59951	+	3.00000i	0.0853332	+	0.0984798i
$929$	7.22886	+	50.2779i	0.237171	+	1.64956i	0.665835	+	0.746099i	$0.268075\pi$
$929$	7.22886	+	50.2779i	0.237171	+	1.64956i	−0.428664	+	0.903464i	$0.641016\pi$
$930$	1.57010	−	3.43804i	0.0514856	−	0.112738i
$931$	29.8702	−	8.77067i	0.978955	−	0.287447i
$932$	−5.40934	+	1.58833i	−0.177189	+	0.0520273i
$933$	−12.8245	+	28.0818i	−0.419857	+	0.919358i
$934$	−1.86575	−	12.9766i	−0.0610492	−	0.424607i
$935$	15.9236	+	18.3769i	0.520759	+	0.600987i
$936$	−1.37637	−	3.01382i	−0.0449880	−	0.0985099i
$937$	24.3336	−	15.6382i	0.794943	−	0.510879i	−0.0790191	−	0.996873i	$-0.525179\pi$
$937$	24.3336	−	15.6382i	0.794943	−	0.510879i	0.873962	+	0.485994i	$0.161542\pi$
$938$	0.327761	−	2.27963i	0.0107018	−	0.0744324i
$939$	16.1380	+	10.3713i	0.526644	+	0.338453i
$940$	−5.64263	+	6.51194i	−0.184042	+	0.212396i
$941$	−4.11152	−	1.20725i	−0.134032	−	0.0393552i	0.214029	−	0.976827i	$-0.431341\pi$
$941$	−4.11152	−	1.20725i	−0.134032	−	0.0393552i	−0.348060	+	0.937472i	$0.613160\pi$
$942$	11.1487			0.363243
$943$	−39.2721	+	24.3229i	−1.27888	+	0.792062i
$944$	−3.65051			−0.118814
$945$	0.161738	+	0.0474906i	0.00526134	+	0.00154487i
$946$	39.1996	−	45.2387i	1.27449	−	1.47084i
$947$	21.5480	+	13.8480i	0.700214	+	0.450000i	0.841704	−	0.539939i	$-0.181553\pi$
$947$	21.5480	+	13.8480i	0.700214	+	0.450000i	−0.141490	+	0.989940i	$0.545189\pi$
$948$	−1.99750	+	13.8930i	−0.0648759	+	0.451222i
$949$	29.1580	−	18.7387i	0.946509	−	0.608285i
$950$	−1.85501	−	4.06191i	−0.0601845	−	0.131786i
$951$	−13.8190	−	15.9480i	−0.448112	−	0.517149i
$952$	−0.105977	−	0.737086i	−0.00343474	−	0.0238891i
$953$	11.1220	−	24.3537i	0.360276	−	0.788895i	−0.639521	−	0.768774i	$-0.720867\pi$
$953$	11.1220	−	24.3537i	0.360276	−	0.788895i	0.999798	−	0.0201218i	$-0.00640539\pi$
$954$	−10.6056	+	3.11408i	−0.343368	+	0.100822i
$955$	0.711087	−	0.208794i	0.0230102	−	0.00675642i
$956$	−1.06549	+	2.33310i	−0.0344605	+	0.0754580i
$957$	3.10954	+	21.6273i	0.100517	+	0.699112i
$958$	1.55303	+	1.79229i	0.0501760	+	0.0579062i
$959$	−1.32949	−	2.91117i	−0.0429313	−	0.0940065i
$960$	−0.841254	+	0.540641i	−0.0271513	+	0.0174491i
$961$	2.37875	−	16.5446i	0.0767339	−	0.533696i
$962$	26.3796	+	16.9531i	0.850511	+	0.546591i
$963$	5.87647	−	6.78181i	0.189367	−	0.218541i
$964$	−5.53022	−	1.62382i	−0.178116	−	0.0522997i
$965$	−1.68841			−0.0543520
$966$	−0.101689	−	0.801995i	−0.00327179	−	0.0258038i
$967$	−3.72445			−0.119770			−0.0598852	−	0.998205i	$-0.519073\pi$
$967$	−3.72445			−0.119770			−0.0598852	+	0.998205i	$0.519073\pi$
$968$	18.5157	+	5.43670i	0.595117	+	0.174742i
$969$	12.9183	−	14.9085i	0.414994	−	0.478929i
$970$	6.95184	+	4.46768i	0.223210	+	0.143448i
$971$	0.386672	−	2.68936i	0.0124089	−	0.0863057i	−0.982676	−	0.185332i	$-0.940664\pi$
$971$	0.386672	−	2.68936i	0.0124089	−	0.0863057i	0.995085	+	0.0990267i	$0.0315729\pi$
$972$	0.841254	−	0.540641i	0.0269832	−	0.0173411i
$973$	−0.00893926	−	0.0195742i	−0.000286580	−	0.000627522i
$974$	−5.51750	−	6.36754i	−0.176792	−	0.204029i
$975$	−0.471522	−	3.27951i	−0.0151008	−	0.105028i
$976$	−2.08474	+	4.56493i	−0.0667308	+	0.146120i
$977$	−2.50344	+	0.735075i	−0.0800920	+	0.0235171i	−0.321533	−	0.946898i	$-0.604198\pi$
$977$	−2.50344	+	0.735075i	−0.0800920	+	0.0235171i	0.241441	+	0.970415i	$0.422380\pi$
$978$	−8.58113	+	2.51965i	−0.274394	+	0.0805694i
$979$	−1.70870	+	3.74152i	−0.0546102	+	0.119580i
$980$	−0.992160	−	6.90062i	−0.0316934	−	0.220432i
$981$	5.90510	+	6.81485i	0.188535	+	0.217581i
$982$	3.58941	+	7.85972i	0.114543	+	0.250814i
$983$	−44.8067	+	28.7955i	−1.42911	+	0.918434i	−0.429227	+	0.903197i	$0.641214\pi$
$983$	−44.8067	+	28.7955i	−1.42911	+	0.918434i	−0.999884	+	0.0152368i	$0.995150\pi$
$984$	1.37080	−	9.53411i	0.0436994	−	0.303936i
$985$	11.0661	+	7.11172i	0.352594	+	0.226598i
$986$	−11.4837	+	13.2529i	−0.365716	+	0.422059i
$987$	1.39362	+	0.409205i	0.0443595	+	0.0130251i
$988$	14.7950			0.470693
$989$	52.1475	+	0.869779i	1.65819	+	0.0276574i
$990$	−5.50431			−0.174938
$991$	49.1929	+	14.4443i	1.56266	+	0.458839i	0.944855	−	0.327490i	$-0.106203\pi$
$991$	49.1929	+	14.4443i	1.56266	+	0.458839i	0.617808	+	0.786329i	$0.288021\pi$
$992$	2.47511	−	2.85642i	0.0785847	−	0.0906915i
$993$	−9.73046	−	6.25339i	−0.308787	−	0.198445i
$994$	0.226435	−	1.57489i	0.00718207	−	0.0499524i
$995$	−19.1586	+	12.3125i	−0.607368	+	0.390332i
$996$	3.13204	+	6.85821i	0.0992425	+	0.217311i
$997$	−14.6065	−	16.8568i	−0.462593	−	0.533861i	0.475744	−	0.879584i	$-0.342179\pi$
$997$	−14.6065	−	16.8568i	−0.462593	−	0.533861i	−0.938336	+	0.345723i	$0.887634\pi$
$998$	−0.224895	−	1.56418i	−0.00711894	−	0.0495133i
$999$	−3.93161	+	8.60903i	−0.124391	+	0.272378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.271.2	✓	30
23.9	even	11	inner	690.2.m.h.331.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.271.2	✓	30	1.1	even	1	trivial
690.2.m.h.331.2	yes	30	23.9	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.0700250 + 0.153333i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.0700250 + 0.153333i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.415415 - 0.909632i) q^{10} +(5.28134 - 1.55074i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(1.37637 - 3.01382i) q^{13} +(0.0239895 + 0.166851i) q^{14} +(0.654861 + 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-3.71636 + 2.38836i) q^{17} +(0.142315 - 0.989821i) q^{18} +(3.75657 + 2.41420i) q^{19} +(0.654861 - 0.755750i) q^{20} +(-0.161738 - 0.0474906i) q^{21} +5.50431 q^{22} +(3.07972 + 3.67632i) q^{23} -1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(2.16971 - 2.50398i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.0239895 + 0.166851i) q^{28} +(3.33941 - 2.14611i) q^{29} +(0.415415 + 0.909632i) q^{30} +(-2.47511 - 2.85642i) q^{31} +(0.142315 + 0.989821i) q^{32} +(-2.28657 + 5.00689i) q^{33} +(-4.23870 + 1.24459i) q^{34} +(0.161738 - 0.0474906i) q^{35} +(0.415415 - 0.909632i) q^{36} +(1.34691 + 9.36797i) q^{37} +(2.92424 + 3.37475i) q^{38} +(1.37637 + 3.01382i) q^{39} +(0.841254 - 0.540641i) q^{40} +(-1.37080 + 9.53411i) q^{41} +(-0.141807 - 0.0911338i) q^{42} +(7.12162 - 8.21879i) q^{43} +(5.28134 + 1.55074i) q^{44} -1.00000 q^{45} +(1.91923 + 4.39506i) q^{46} -8.61654 q^{47} +(-0.959493 - 0.281733i) q^{48} +(4.56542 - 5.26877i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(0.628696 - 4.37268i) q^{51} +(2.78727 - 1.79127i) q^{52} +(-4.59171 - 10.0544i) q^{53} +(0.654861 + 0.755750i) q^{54} +(-0.783344 - 5.44828i) q^{55} +(-0.0700250 + 0.153333i) q^{56} +(-4.28456 + 1.25806i) q^{57} +(3.80877 - 1.11836i) q^{58} +(-1.51648 + 3.32062i) q^{59} +(0.142315 + 0.989821i) q^{60} +(3.28638 + 3.79268i) q^{61} +(-1.57010 - 3.43804i) q^{62} +(0.141807 - 0.0911338i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-2.78727 - 1.79127i) q^{65} +(-3.60455 + 4.15988i) q^{66} +(-13.1092 - 3.84922i) q^{67} -4.41764 q^{68} +(-4.79516 - 0.0799796i) q^{69} +0.168566 q^{70} +(-9.05657 - 2.65925i) q^{71} +(0.654861 - 0.755750i) q^{72} +(8.80047 + 5.65572i) q^{73} +(-1.34691 + 9.36797i) q^{74} +(0.841254 - 0.540641i) q^{75} +(1.85501 + 4.06191i) q^{76} +(0.607606 + 0.701215i) q^{77} +(0.471522 + 3.27951i) q^{78} +(5.83069 - 12.7674i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-4.00134 + 8.76171i) q^{82} +(-1.07299 - 7.46280i) q^{83} +(-0.110387 - 0.127394i) q^{84} +(1.83516 + 4.01843i) q^{85} +(9.14864 - 5.87948i) q^{86} +(-0.564928 + 3.92916i) q^{87} +(4.63052 + 2.97585i) q^{88} +(-0.489361 + 0.564752i) q^{89} +(-0.959493 - 0.281733i) q^{90} +0.558500 q^{91} +(0.603258 + 4.75774i) q^{92} +3.77959 q^{93} +(-8.26751 - 2.42756i) q^{94} +(2.92424 - 3.37475i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(-1.17604 + 8.17956i) q^{97} +(5.86487 - 3.76912i) q^{98} +(-2.28657 - 5.00689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

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