LMFDB - Embedded newform 690.2.q.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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([11, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, 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:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	690.11
Dual form			690.2.q.a.251.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 - 0.841254i) q^{2} +(1.50109 + 0.864143i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.0845842 - 1.72998i) q^{6} +(0.920755 - 0.797839i) q^{7} +(0.989821 - 0.142315i) q^{8} +(1.50651 + 2.59431i) q^{9} +O(q^{10})$	\(q+(-0.540641 - 0.841254i) q^{2} +(1.50109 + 0.864143i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.0845842 - 1.72998i) q^{6} +(0.920755 - 0.797839i) q^{7} +(0.989821 - 0.142315i) q^{8} +(1.50651 + 2.59431i) q^{9} +(0.755750 + 0.654861i) q^{10} +(-0.473766 - 0.304471i) q^{11} +(-1.40963 + 1.00646i) q^{12} +(1.86571 - 2.15315i) q^{13} +(-1.16898 - 0.343244i) q^{14} +(-1.68374 - 0.406235i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.73289 + 3.79449i) q^{17} +(1.36799 - 2.66995i) q^{18} +(6.59342 + 3.01111i) q^{19} +(0.142315 - 0.989821i) q^{20} +(2.07158 - 0.401960i) q^{21} +0.563167i q^{22} +(-4.34822 - 2.02311i) q^{23} +(1.60879 + 0.641721i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-2.82002 - 0.405458i) q^{26} +(0.0195518 + 5.19612i) q^{27} +(0.343244 + 1.16898i) q^{28} +(3.46489 - 1.58236i) q^{29} +(0.568551 + 1.63608i) q^{30} +(0.639871 + 4.45040i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(-0.448056 - 0.866438i) q^{33} +(2.25526 - 3.50925i) q^{34} +(-0.658681 + 1.02493i) q^{35} +(-2.98569 + 0.292659i) q^{36} +(0.307684 - 1.04788i) q^{37} +(-1.03156 - 7.17466i) q^{38} +(4.66122 - 1.61981i) q^{39} +(-0.909632 + 0.415415i) q^{40} +(-0.199823 - 0.680536i) q^{41} +(-1.45813 - 1.52541i) q^{42} +(12.6134 + 1.81353i) q^{43} +(0.473766 - 0.304471i) q^{44} +(-2.17639 - 2.06478i) q^{45} +(0.648883 + 4.75173i) q^{46} +3.93452i q^{47} +(-0.329926 - 1.70034i) q^{48} +(-0.784961 + 5.45952i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(-0.677775 + 7.19332i) q^{51} +(1.18353 + 2.59156i) q^{52} +(-0.983002 - 1.13444i) q^{53} +(4.36068 - 2.82568i) q^{54} +(0.540354 + 0.158662i) q^{55} +(0.797839 - 0.920755i) q^{56} +(7.29524 + 10.2176i) q^{57} +(-3.20443 - 2.05936i) q^{58} +(-3.68301 - 3.19135i) q^{59} +(1.06897 - 1.36283i) q^{60} +(-4.64058 + 0.667214i) q^{61} +(3.39798 - 2.94436i) q^{62} +(3.45697 + 1.18677i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-1.18353 + 2.59156i) q^{65} +(-0.486657 + 0.845361i) q^{66} +(-4.57140 - 7.11324i) q^{67} -4.17146 q^{68} +(-4.77880 - 6.79434i) q^{69} +1.21833 q^{70} +(-4.36783 - 6.79648i) q^{71} +(1.86039 + 2.35350i) q^{72} +(0.204923 - 0.448718i) q^{73} +(-1.04788 + 0.307684i) q^{74} +(1.72998 - 0.0845842i) q^{75} +(-5.47801 + 4.74672i) q^{76} +(-0.679141 + 0.0976457i) q^{77} +(-3.88272 - 3.04553i) q^{78} +(-3.10719 - 2.69240i) q^{79} +(0.841254 + 0.540641i) q^{80} +(-4.46084 + 7.81671i) q^{81} +(-0.464471 + 0.536028i) q^{82} +(4.05006 + 1.18921i) q^{83} +(-0.494930 + 2.05135i) q^{84} +(-2.73172 - 3.15258i) q^{85} +(-5.29367 - 11.5915i) q^{86} +(6.56848 + 0.618901i) q^{87} +(-0.512274 - 0.233948i) q^{88} +(-0.605041 + 4.20815i) q^{89} +(-0.560362 + 2.94720i) q^{90} -3.47106i q^{91} +(3.64660 - 3.11485i) q^{92} +(-2.88529 + 7.23337i) q^{93} +(3.30993 - 2.12716i) q^{94} +(-7.17466 - 1.03156i) q^{95} +(-1.25204 + 1.19682i) q^{96} +(-3.38569 - 11.5306i) q^{97} +(5.01722 - 2.29129i) q^{98} +(0.0761561 - 1.68778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$3$	1.50109	+	0.864143i	0.866652	+	0.498913i
$3$	1.50109	+	0.864143i	0.866652	+	0.498913i
$4$	−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
$6$	−0.0845842	−	1.72998i	−0.0345314	−	0.706263i
$7$	0.920755	−	0.797839i	0.348013	−	0.301555i	−0.463260	−	0.886222i	$-0.653320\pi$
$7$	0.920755	−	0.797839i	0.348013	−	0.301555i	0.811273	+	0.584668i	$0.198775\pi$
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	1.50651	+	2.59431i	0.502171	+	0.864768i
$10$	0.755750	+	0.654861i	0.238989	+	0.207085i
$11$	−0.473766	−	0.304471i	−0.142846	−	0.0918014i	0.467266	−	0.884117i	$-0.345239\pi$
$11$	−0.473766	−	0.304471i	−0.142846	−	0.0918014i	−0.610112	+	0.792315i	$0.708875\pi$
$12$	−1.40963	+	1.00646i	−0.406924	+	0.290539i
$13$	1.86571	−	2.15315i	0.517456	−	0.597176i	−0.435536	−	0.900171i	$-0.643441\pi$
$13$	1.86571	−	2.15315i	0.517456	−	0.597176i	0.952992	+	0.302996i	$0.0979867\pi$
$14$	−1.16898	−	0.343244i	−0.312424	−	0.0917359i
$15$	−1.68374	−	0.406235i	−0.434739	−	0.104889i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	1.73289	+	3.79449i	0.420287	+	0.920299i	0.994804	+	0.101807i	$0.0324624\pi$
$17$	1.73289	+	3.79449i	0.420287	+	0.920299i	−0.574518	+	0.818492i	$0.694810\pi$
$18$	1.36799	−	2.66995i	0.322437	−	0.629312i
$19$	6.59342	+	3.01111i	1.51263	+	0.690796i	0.987119	−	0.159988i	$-0.0511457\pi$
$19$	6.59342	+	3.01111i	1.51263	+	0.690796i	0.525514	+	0.850785i	$0.323873\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	2.07158	−	0.401960i	0.452056	−	0.0877148i
$22$			0.563167i			0.120068i
$23$	−4.34822	−	2.02311i	−0.906667	−	0.421847i
$23$	−4.34822	−	2.02311i	−0.906667	−	0.421847i
$24$	1.60879	+	0.641721i	0.328392	+	0.130991i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−2.82002	−	0.405458i	−0.553052	−	0.0795169i
$27$	0.0195518	+	5.19612i	0.00376275	+	0.999993i
$28$	0.343244	+	1.16898i	0.0648671	+	0.220917i
$29$	3.46489	−	1.58236i	0.643414	−	0.293837i	−0.0668603	−	0.997762i	$-0.521298\pi$
$29$	3.46489	−	1.58236i	0.643414	−	0.293837i	0.710274	+	0.703925i	$0.248571\pi$
$30$	0.568551	+	1.63608i	0.103803	+	0.298706i
$31$	0.639871	+	4.45040i	0.114924	+	0.799316i	0.963012	+	0.269460i	$0.0868451\pi$
$31$	0.639871	+	4.45040i	0.114924	+	0.799316i	−0.848087	+	0.529856i	$0.822246\pi$
$32$	−0.281733	+	0.959493i	−0.0498038	+	0.169616i
$33$	−0.448056	−	0.866438i	−0.0779966	−	0.150828i
$34$	2.25526	−	3.50925i	0.386774	−	0.601832i
$35$	−0.658681	+	1.02493i	−0.111337	+	0.173244i
$36$	−2.98569	+	0.292659i	−0.497615	+	0.0487764i
$37$	0.307684	−	1.04788i	0.0505830	−	0.172270i	−0.930327	−	0.366730i	$-0.880477\pi$
$37$	0.307684	−	1.04788i	0.0505830	−	0.172270i	0.980910	+	0.194460i	$0.0622955\pi$
$38$	−1.03156	−	7.17466i	−0.167341	−	1.16388i
$39$	4.66122	−	1.61981i	0.746393	−	0.259378i
$40$	−0.909632	+	0.415415i	−0.143825	+	0.0656829i
$41$	−0.199823	−	0.680536i	−0.0312072	−	0.106282i	0.942417	−	0.334441i	$-0.108548\pi$
$41$	−0.199823	−	0.680536i	−0.0312072	−	0.106282i	−0.973624	+	0.228159i	$0.926729\pi$
$42$	−1.45813	−	1.52541i	−0.224994	−	0.235375i
$43$	12.6134	+	1.81353i	1.92352	+	0.276561i	0.995407	−	0.0957329i	$-0.0305195\pi$
$43$	12.6134	+	1.81353i	1.92352	+	0.276561i	0.928115	+	0.372294i	$0.121429\pi$
$44$	0.473766	−	0.304471i	0.0714229	−	0.0459007i
$45$	−2.17639	−	2.06478i	−0.324437	−	0.307800i
$46$	0.648883	+	4.75173i	0.0956725	+	0.700605i
$47$			3.93452i			0.573909i	0.957944	+	0.286954i	$0.0926428\pi$
$47$			3.93452i			0.573909i	−0.957944	+	0.286954i	$0.907357\pi$
$48$	−0.329926	−	1.70034i	−0.0476207	−	0.245423i
$49$	−0.784961	+	5.45952i	−0.112137	+	0.779932i
$50$	−0.909632	−	0.415415i	−0.128641	−	0.0587486i
$51$	−0.677775	+	7.19332i	−0.0949075	+	1.00727i
$52$	1.18353	+	2.59156i	0.164126	+	0.359385i
$53$	−0.983002	−	1.13444i	−0.135026	−	0.155828i	0.684210	−	0.729285i	$-0.260147\pi$
$53$	−0.983002	−	1.13444i	−0.135026	−	0.155828i	−0.819235	+	0.573457i	$0.805602\pi$
$54$	4.36068	−	2.82568i	0.593413	−	0.384526i
$55$	0.540354	+	0.158662i	0.0728614	+	0.0213940i
$56$	0.797839	−	0.920755i	0.106616	−	0.123041i
$57$	7.29524	+	10.2176i	0.966279	+	1.35335i
$58$	−3.20443	−	2.05936i	−0.420762	−	0.270407i
$59$	−3.68301	−	3.19135i	−0.479488	−	0.415478i	0.381293	−	0.924454i	$-0.375479\pi$
$59$	−3.68301	−	3.19135i	−0.479488	−	0.415478i	−0.860781	+	0.508976i	$0.830024\pi$
$60$	1.06897	−	1.36283i	0.138004	−	0.175940i
$61$	−4.64058	+	0.667214i	−0.594165	+	0.0854280i	−0.432836	−	0.901473i	$-0.642487\pi$
$61$	−4.64058	+	0.667214i	−0.594165	+	0.0854280i	−0.161329	+	0.986901i	$0.551578\pi$
$62$	3.39798	−	2.94436i	0.431543	−	0.373935i
$63$	3.45697	+	1.18677i	0.435537	+	0.149518i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−1.18353	+	2.59156i	−0.146798	+	0.321444i
$66$	−0.486657	+	0.845361i	−0.0599033	+	0.104057i
$67$	−4.57140	−	7.11324i	−0.558485	−	0.869020i	0.441110	−	0.897453i	$-0.354585\pi$
$67$	−4.57140	−	7.11324i	−0.558485	−	0.869020i	−0.999596	+	0.0284325i	$0.990948\pi$
$68$	−4.17146			−0.505864
$69$	−4.77880	−	6.79434i	−0.575300	−	0.817943i
$70$	1.21833			0.145619
$71$	−4.36783	−	6.79648i	−0.518366	−	0.806594i	0.479098	−	0.877761i	$-0.340964\pi$
$71$	−4.36783	−	6.79648i	−0.518366	−	0.806594i	−0.997464	+	0.0711677i	$0.977327\pi$
$72$	1.86039	+	2.35350i	0.219249	+	0.277363i
$73$	0.204923	−	0.448718i	0.0239844	−	0.0525185i	−0.897261	−	0.441501i	$-0.854446\pi$
$73$	0.204923	−	0.448718i	0.0239844	−	0.0525185i	0.921245	+	0.388983i	$0.127173\pi$
$74$	−1.04788	+	0.307684i	−0.121813	+	0.0357676i
$75$	1.72998	−	0.0845842i	0.199761	−	0.00976694i
$76$	−5.47801	+	4.74672i	−0.628371	+	0.544486i
$77$	−0.679141	+	0.0976457i	−0.0773953	+	0.0111278i
$78$	−3.88272	−	3.04553i	−0.439631	−	0.344838i
$79$	−3.10719	−	2.69240i	−0.349586	−	0.302918i	0.462312	−	0.886717i	$-0.347020\pi$
$79$	−3.10719	−	2.69240i	−0.349586	−	0.302918i	−0.811898	+	0.583799i	$0.801566\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	−4.46084	+	7.81671i	−0.495649	+	0.868523i
$82$	−0.464471	+	0.536028i	−0.0512922	+	0.0591943i
$83$	4.05006	+	1.18921i	0.444552	+	0.130532i	0.496344	−	0.868126i	$-0.334675\pi$
$83$	4.05006	+	1.18921i	0.444552	+	0.130532i	−0.0517926	+	0.998658i	$0.516493\pi$
$84$	−0.494930	+	2.05135i	−0.0540012	+	0.223821i
$85$	−2.73172	−	3.15258i	−0.296297	−	0.341945i
$86$	−5.29367	−	11.5915i	−0.570831	−	1.24995i
$87$	6.56848	+	0.618901i	0.704215	+	0.0663532i
$88$	−0.512274	−	0.233948i	−0.0546086	−	0.0249389i
$89$	−0.605041	+	4.20815i	−0.0641342	+	0.446063i	0.932300	+	0.361687i	$0.117799\pi$
$89$	−0.605041	+	4.20815i	−0.0641342	+	0.446063i	−0.996434	+	0.0843765i	$0.973110\pi$
$90$	−0.560362	+	2.94720i	−0.0590674	+	0.310662i
$91$		−	3.47106i		−	0.363866i
$92$	3.64660	−	3.11485i	0.380184	−	0.324746i
$93$	−2.88529	+	7.23337i	−0.299190	+	0.750066i
$94$	3.30993	−	2.12716i	0.341393	−	0.219400i
$95$	−7.17466	−	1.03156i	−0.736105	−	0.105836i
$96$	−1.25204	+	1.19682i	−0.127786	+	0.122150i
$97$	−3.38569	−	11.5306i	−0.343765	−	1.17076i	−0.932119	−	0.362152i	$-0.882042\pi$
$97$	−3.38569	−	11.5306i	−0.343765	−	1.17076i	0.588354	−	0.808604i	$-0.299776\pi$
$98$	5.01722	−	2.29129i	0.506816	−	0.231455i
$99$	0.0761561	−	1.68778i	0.00765397	−	0.169629i
$100$	0.142315	+	0.989821i	0.0142315	+	0.0989821i
$101$	−1.23983	+	4.22248i	−0.123368	+	0.420153i	−0.997897	−	0.0648205i	$-0.979353\pi$
$101$	−1.23983	+	4.22248i	−0.123368	+	0.420153i	0.874529	+	0.484973i	$0.161171\pi$
$102$	6.41784	−	3.31882i	0.635460	−	0.328612i
$103$	6.27083	−	9.75760i	0.617883	−	0.961445i	−0.381431	−	0.924397i	$-0.624568\pi$
$103$	6.27083	−	9.75760i	0.617883	−	0.961445i	0.999314	−	0.0370471i	$-0.0117952\pi$
$104$	1.54030	−	2.39675i	0.151039	−	0.235021i
$105$	−1.87442	+	0.969308i	−0.182925	+	0.0945948i
$106$	−0.422905	+	1.44028i	−0.0410761	+	0.139892i
$107$	−0.865885	−	6.02237i	−0.0837083	−	0.582204i	−0.987902	−	0.155081i	$-0.950436\pi$
$107$	−0.865885	−	6.02237i	−0.0837083	−	0.582204i	0.904193	−	0.427123i	$-0.140473\pi$
$108$	−4.73468	−	2.14076i	−0.455594	−	0.205995i
$109$	10.1682	−	4.64367i	0.973939	−	0.444783i	0.136097	−	0.990696i	$-0.456544\pi$
$109$	10.1682	−	4.64367i	0.973939	−	0.444783i	0.837842	+	0.545912i	$0.183817\pi$
$110$	−0.158662	−	0.540354i	−0.0151279	−	0.0515208i
$111$	1.36737	−	1.30707i	0.129785	−	0.124061i
$112$	−1.20593	−	0.173387i	−0.113950	−	0.0163835i
$113$	11.3026	−	7.26373i	1.06326	−	0.683314i	0.112627	−	0.993637i	$-0.464074\pi$
$113$	11.3026	−	7.26373i	1.06326	−	0.683314i	0.950631	+	0.310323i	$0.100437\pi$
$114$	4.65148	−	11.6612i	0.435651	−	1.09217i
$115$	4.74206	+	0.716119i	0.442200	+	0.0667784i
$116$			3.80911i			0.353667i
$117$	8.39664	+	1.59648i	0.776270	+	0.147595i
$118$	−0.693547	+	4.82372i	−0.0638461	+	0.444060i
$119$	4.62296	+	2.11123i	0.423786	+	0.193536i
$120$	−1.72441	−	0.162479i	−0.157417	−	0.0148323i
$121$	−4.43781	−	9.71746i	−0.403438	−	0.883405i
$122$	3.07018	+	3.54318i	0.277961	+	0.320784i
$123$	0.288129	−	1.19422i	0.0259797	−	0.107679i
$124$	−4.31404	−	1.26672i	−0.387412	−	0.113755i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−0.870606	−	3.54980i	−0.0775598	−	0.316241i
$127$	−17.2310	−	11.0737i	−1.52901	−	0.982633i	−0.990115	−	0.140259i	$-0.955207\pi$
$127$	−17.2310	−	11.0737i	−1.52901	−	0.982633i	−0.538892	−	0.842375i	$-0.681157\pi$
$128$	−0.755750	−	0.654861i	−0.0667995	−	0.0578821i
$129$	17.3666	+	13.6220i	1.52904	+	1.19935i
$130$	2.82002	−	0.405458i	0.247332	−	0.0355610i
$131$	−14.2773	+	12.3713i	−1.24741	+	1.08089i	−0.253893	+	0.967232i	$0.581711\pi$
$131$	−14.2773	+	12.3713i	−1.24741	+	1.08089i	−0.993520	+	0.113658i	$0.963743\pi$
$132$	0.974269	−	0.0476350i	0.0847993	−	0.00414609i
$133$	8.47330	−	2.48799i	0.734728	−	0.215736i
$134$	−3.51255	+	7.69141i	−0.303438	+	0.664437i
$135$	−1.48267	−	4.98013i	−0.127608	−	0.428621i
$136$	2.25526	+	3.50925i	0.193387	+	0.300916i
$137$	−5.82234			−0.497436			−0.248718	−	0.968576i	$-0.580009\pi$
$137$	−5.82234			−0.497436			−0.248718	+	0.968576i	$0.580009\pi$
$138$	−3.13215	+	7.69348i	−0.266626	+	0.654913i
$139$	−14.0348			−1.19042			−0.595209	−	0.803571i	$-0.702931\pi$
$139$	−14.0348			−1.19042			−0.595209	+	0.803571i	$0.702931\pi$
$140$	−0.658681	−	1.02493i	−0.0556687	−	0.0866222i
$141$	−3.39999	+	5.90605i	−0.286331	+	0.497379i
$142$	−3.35613	+	7.34891i	−0.281640	+	0.616707i
$143$	−1.53948	+	0.452032i	−0.128738	+	0.0378009i
$144$	0.974089	−	2.83745i	0.0811741	−	0.236455i
$145$	−2.87874	+	2.49444i	−0.239066	+	0.207152i
$146$	−0.488275	+	0.0702034i	−0.0404099	+	0.00581007i
$147$	−5.89610	+	7.51689i	−0.486302	+	0.619982i
$148$	0.825365	+	0.715183i	0.0678446	+	0.0587877i
$149$	−14.0581	−	9.03458i	−1.15168	−	0.740141i	−0.181709	−	0.983352i	$-0.558163\pi$
$149$	−14.0581	−	9.03458i	−1.15168	−	0.740141i	−0.969973	+	0.243211i	$0.921799\pi$
$150$	−1.00646	−	1.40963i	−0.0821769	−	0.115095i
$151$	−10.8338	+	12.5028i	−0.881640	+	1.01747i	0.118061	+	0.993006i	$0.462332\pi$
$151$	−10.8338	+	12.5028i	−0.881640	+	1.01747i	−0.999701	+	0.0244605i	$0.992213\pi$
$152$	6.95483	+	2.04212i	0.564111	+	0.165638i
$153$	−7.23345	+	10.2121i	−0.584790	+	0.825598i
$154$	0.449316	+	0.518538i	0.0362069	+	0.0417850i
$155$	−1.86778	−	4.08986i	−0.150023	−	0.328505i
$156$	−0.462907	+	4.91289i	−0.0370622	+	0.393346i
$157$	−1.69219	−	0.772798i	−0.135052	−	0.0616760i	0.346743	−	0.937960i	$-0.387288\pi$
$157$	−1.69219	−	0.772798i	−0.135052	−	0.0616760i	−0.481795	+	0.876284i	$0.660015\pi$
$158$	−0.585114	+	4.06955i	−0.0465491	+	0.323756i
$159$	−0.495247	−	2.55235i	−0.0392756	−	0.202415i
$160$		−	1.00000i		−	0.0790569i
$161$	−5.61776	+	1.60640i	−0.442742	+	0.126602i
$162$	8.98754	−	0.473334i	0.706128	−	0.0371886i
$163$	−2.80126	+	1.80026i	−0.219412	+	0.141008i	−0.645730	−	0.763566i	$-0.723447\pi$
$163$	−2.80126	+	1.80026i	−0.219412	+	0.141008i	0.426318	+	0.904573i	$0.359810\pi$
$164$	0.702047	+	0.100939i	0.0548206	+	0.00788202i
$165$	0.674011	+	0.705109i	0.0524717	+	0.0548927i
$166$	−1.18921	−	4.05006i	−0.0923002	−	0.314346i
$167$	18.0731	−	8.25372i	1.39854	−	0.638692i	0.433586	−	0.901112i	$-0.357248\pi$
$167$	18.0731	−	8.25372i	1.39854	−	0.638692i	0.964954	+	0.262421i	$0.0845208\pi$
$168$	1.99329	−	0.692685i	0.153786	−	0.0534418i
$169$	0.694934	+	4.83337i	0.0534565	+	0.371798i
$170$	−1.17524	+	4.00248i	−0.0901364	+	0.306977i
$171$	2.12132	+	21.6416i	0.162221	+	1.65498i
$172$	−6.88943	+	10.7202i	−0.525314	+	0.817405i
$173$	−8.44349	+	13.1383i	−0.641946	+	0.998888i	0.355978	+	0.934494i	$0.384148\pi$
$173$	−8.44349	+	13.1383i	−0.641946	+	0.998888i	−0.997925	+	0.0643939i	$0.979489\pi$
$174$	−3.03054	−	5.86036i	−0.229744	−	0.444273i
$175$	0.343244	−	1.16898i	0.0259468	−	0.0883668i
$176$	0.0801470	+	0.557434i	0.00604130	+	0.0420182i
$177$	−2.77073	−	7.97314i	−0.208261	−	0.599298i
$178$	3.86723	−	1.76611i	0.289861	−	0.132375i
$179$	1.68055	+	5.72342i	0.125610	+	0.427788i	0.998153	−	0.0607488i	$-0.0193489\pi$
$179$	1.68055	+	5.72342i	0.125610	+	0.427788i	−0.872543	+	0.488537i	$0.837531\pi$
$180$	2.78230	−	1.12197i	0.207380	−	0.0836267i
$181$	−7.73686	−	1.11239i	−0.575076	−	0.0826835i	−0.151360	−	0.988479i	$-0.548365\pi$
$181$	−7.73686	−	1.11239i	−0.575076	−	0.0826835i	−0.423716	+	0.905795i	$0.639274\pi$
$182$	−2.92004	+	1.87660i	−0.216448	+	0.139103i
$183$	−7.54247	−	3.00858i	−0.557555	−	0.222400i
$184$	−4.59188	−	1.38370i	−0.338518	−	0.102007i
$185$			1.09211i			0.0802938i
$186$	7.64500	−	1.48340i	0.560559	−	0.108768i
$187$	0.334330	−	2.32531i	0.0244486	−	0.170044i
$188$	−3.57896	−	1.63446i	−0.261023	−	0.119205i
$189$	4.16366	+	4.76875i	0.302862	+	0.346876i
$190$	3.01111	+	6.59342i	0.218449	+	0.478337i
$191$	−16.2061	−	18.7029i	−1.17263	−	1.35329i	−0.922929	−	0.384971i	$-0.874212\pi$
$191$	−16.2061	−	18.7029i	−1.17263	−	1.35329i	−0.249706	−	0.968322i	$-0.580334\pi$
$192$	1.68374	+	0.406235i	0.121513	+	0.0293175i
$193$	−4.81827	−	1.41477i	−0.346826	−	0.101837i	0.103680	−	0.994611i	$-0.466938\pi$
$193$	−4.81827	−	1.41477i	−0.346826	−	0.101837i	−0.450506	+	0.892773i	$0.648756\pi$
$194$	−7.86972	+	9.08214i	−0.565013	+	0.652060i
$195$	−4.01605	+	2.86742i	−0.287596	+	0.205340i
$196$	−4.64007	−	2.98199i	−0.331434	−	0.212999i
$197$	8.19024	+	7.09688i	0.583530	+	0.505632i	0.895857	−	0.444343i	$-0.146563\pi$
$197$	8.19024	+	7.09688i	0.583530	+	0.505632i	−0.312326	+	0.949975i	$0.601108\pi$
$198$	−1.46103	+	0.848417i	−0.103831	+	0.0602944i
$199$	−16.4424	+	2.36405i	−1.16557	+	0.167583i	−0.697816	−	0.716277i	$-0.745845\pi$
$199$	−16.4424	+	2.36405i	−1.16557	+	0.167583i	−0.467752	+	0.883860i	$0.654936\pi$
$200$	0.755750	−	0.654861i	0.0534396	−	0.0463056i
$201$	−0.715204	−	14.6279i	−0.0504466	−	1.03177i
$202$	4.22248	−	1.23983i	0.297093	−	0.0872344i
$203$	1.92785	−	4.22139i	0.135308	−	0.296284i
$204$	−6.26171	−	3.60474i	−0.438408	−	0.252382i
$205$	0.383458	+	0.596673i	0.0267819	+	0.0416734i
$206$	−11.5989			−0.808132
$207$	−1.30210	−	14.3285i	−0.0905023	−	0.995896i
$208$	−2.84902			−0.197544
$209$	−2.20694	−	3.43406i	−0.152657	−	0.237539i
$210$	1.82882	+	1.05281i	0.126201	+	0.0726511i
$211$	−6.63734	+	14.5337i	−0.456933	+	1.00054i	0.531243	+	0.847220i	$0.321725\pi$
$211$	−6.63734	+	14.5337i	−0.456933	+	1.00054i	−0.988176	+	0.153325i	$0.951002\pi$
$212$	1.44028	−	0.422905i	0.0989189	−	0.0290452i
$213$	−0.683355	−	13.9765i	−0.0468227	−	0.957656i
$214$	−4.59820	+	3.98437i	−0.314327	+	0.272366i
$215$	−12.6134	+	1.81353i	−0.860225	+	0.123682i
$216$	0.758837	+	5.14044i	0.0516323	+	0.349763i
$217$	4.13987	+	3.58722i	0.281033	+	0.243516i
$218$	−9.40386	−	6.04349i	−0.636910	−	0.409317i
$219$	0.695363	−	0.496481i	0.0469883	−	0.0335491i
$220$	−0.368796	+	0.425613i	−0.0248642	+	0.0286948i
$221$	11.4032	+	3.34827i	0.767060	+	0.225229i
$222$	−1.83883	−	0.443655i	−0.123414	−	0.0297762i
$223$	10.3452	+	11.9390i	0.692766	+	0.799494i	0.987756	−	0.156006i	$-0.0498619\pi$
$223$	10.3452	+	11.9390i	0.692766	+	0.799494i	−0.294990	+	0.955500i	$0.595316\pi$
$224$	0.506114	+	1.10824i	0.0338162	+	0.0740471i
$225$	2.66995	+	1.36799i	0.177996	+	0.0911991i
$226$	−12.2213	−	5.58127i	−0.812947	−	0.371261i
$227$	1.22901	−	8.54794i	0.0815722	−	0.567347i	−0.907515	−	0.420019i	$-0.862024\pi$
$227$	1.22901	−	8.54794i	0.0815722	−	0.567347i	0.989088	−	0.147328i	$-0.0470674\pi$
$228$	−12.3248	+	2.39145i	−0.816230	+	0.158377i
$229$			12.7466i			0.842322i	0.906986	+	0.421161i	$0.138377\pi$
$229$			12.7466i			0.842322i	−0.906986	+	0.421161i	$0.861623\pi$
$230$	−1.96132	−	4.37644i	−0.129325	−	0.288574i
$231$	−1.10383	−	0.440301i	−0.0726266	−	0.0289696i
$232$	3.20443	−	2.05936i	0.210381	−	0.135204i
$233$	14.3276	+	2.06000i	0.938633	+	0.134955i	0.594617	−	0.804009i	$-0.297304\pi$
$233$	14.3276	+	2.06000i	0.938633	+	0.134955i	0.344016	+	0.938964i	$0.388213\pi$
$234$	−3.19652	−	7.92683i	−0.208963	−	0.518193i
$235$	−1.10848	−	3.77514i	−0.0723094	−	0.246263i
$236$	4.43293	−	2.02445i	0.288559	−	0.131781i
$237$	−2.33754	−	6.72657i	−0.151840	−	0.436938i
$238$	−0.723276	−	5.03050i	−0.0468830	−	0.326079i
$239$	1.25937	−	4.28902i	0.0814619	−	0.277434i	−0.908682	−	0.417490i	$-0.862910\pi$
$239$	1.25937	−	4.28902i	0.0814619	−	0.277434i	0.990144	+	0.140056i	$0.0447282\pi$
$240$	0.795602	+	1.53851i	0.0513559	+	0.0993105i
$241$	11.6120	−	18.0686i	0.747994	−	1.16390i	−0.233491	−	0.972359i	$-0.575015\pi$
$241$	11.6120	−	18.0686i	0.747994	−	1.16390i	0.981484	−	0.191542i	$-0.0613488\pi$
$242$	−5.77558	+	8.98698i	−0.371268	+	0.577705i
$243$	−13.4509	+	7.87874i	−0.862873	+	0.505421i
$244$	1.32085	−	4.49839i	0.0845585	−	0.287980i
$245$	−0.784961	−	5.45952i	−0.0501493	−	0.348796i
$246$	−1.16041	+	0.403254i	−0.0739853	+	0.0257105i
$247$	18.7848	−	8.57872i	1.19525	−	0.545851i
$248$	1.26672	+	4.31404i	0.0804366	+	0.273942i
$249$	5.05184	+	5.28493i	0.320147	+	0.334919i
$250$	0.989821	+	0.142315i	0.0626018	+	0.00900078i
$251$	−14.0110	+	9.00435i	−0.884369	+	0.568349i	−0.902116	−	0.431493i	$-0.857987\pi$
$251$	−14.0110	+	9.00435i	−0.884369	+	0.568349i	0.0177473	+	0.999843i	$0.494351\pi$
$252$	−2.51560	+	2.65157i	−0.158468	+	0.167033i
$253$	1.44406	+	2.28239i	0.0907875	+	0.143492i
$254$			20.4826i			1.28519i
$255$	−1.37627	−	7.09289i	−0.0861854	−	0.444174i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	6.47300	+	2.95612i	0.403775	+	0.184398i	0.606942	−	0.794746i	$-0.292396\pi$
$257$	6.47300	+	2.95612i	0.403775	+	0.184398i	−0.203167	+	0.979144i	$0.565123\pi$
$258$	2.07049	−	21.9743i	0.128903	−	1.36806i
$259$	−0.552734	−	1.21032i	−0.0343452	−	0.0752056i
$260$	−1.86571	−	2.15315i	−0.115707	−	0.133533i
$261$	9.32503	+	6.60514i	0.577205	+	0.408848i
$262$	18.1263	+	5.32237i	1.11985	+	0.328817i
$263$	13.7197	−	15.8334i	0.845994	−	0.976329i	−0.153937	−	0.988081i	$-0.549195\pi$
$263$	13.7197	−	15.8334i	0.845994	−	0.976329i	0.999931	+	0.0117515i	$0.00374070\pi$
$264$	−0.566803	−	0.793854i	−0.0348843	−	0.0488583i
$265$	1.26279	+	0.811548i	0.0775728	+	0.0498530i
$266$	−6.67404	−	5.78309i	−0.409212	−	0.354584i
$267$	−4.54466	+	5.79395i	−0.278129	+	0.354584i
$268$	8.36946	−	1.20335i	0.511246	−	0.0735061i
$269$	4.13264	−	3.58095i	0.251971	−	0.218334i	−0.519712	−	0.854342i	$-0.673961\pi$
$269$	4.13264	−	3.58095i	0.251971	−	0.218334i	0.771683	+	0.636007i	$0.219415\pi$
$270$	−3.38796	+	3.93977i	−0.206184	+	0.239767i
$271$	−10.1206	+	2.97167i	−0.614781	+	0.180516i	−0.574274	−	0.818663i	$-0.694716\pi$
$271$	−10.1206	+	2.97167i	−0.614781	+	0.180516i	−0.0405072	+	0.999179i	$0.512897\pi$
$272$	1.73289	−	3.79449i	0.105072	−	0.230075i
$273$	2.99949	−	5.21035i	0.181538	−	0.315345i
$274$	3.14779	+	4.89806i	0.190165	+	0.295903i
$275$	−0.563167			−0.0339602
$276$	8.16554	−	1.52448i	0.491507	−	0.0917628i
$277$	21.1122			1.26851			0.634255	−	0.773124i	$-0.281307\pi$
$277$	21.1122			1.26851			0.634255	+	0.773124i	$0.281307\pi$
$278$	7.58780	+	11.8068i	0.455086	+	0.708127i
$279$	−10.5817	+	8.36461i	−0.633512	+	0.500776i
$280$	−0.506114	+	1.10824i	−0.0302461	+	0.0662297i
$281$	30.1367	−	8.84894i	1.79781	−	0.527883i	0.800374	−	0.599501i	$-0.204634\pi$
$281$	30.1367	−	8.84894i	1.79781	−	0.527883i	0.997432	+	0.0716177i	$0.0228162\pi$
$282$	6.80666	−	0.332798i	0.405331	−	0.0198178i
$283$	−16.2386	+	14.0708i	−0.965285	+	0.836424i	−0.986568	−	0.163349i	$-0.947770\pi$
$283$	−16.2386	+	14.0708i	−0.965285	+	0.836424i	0.0212831	+	0.999773i	$0.493225\pi$
$284$	7.99676	−	1.14976i	0.474520	−	0.0682257i
$285$	−9.87836	−	7.74840i	−0.585144	−	0.458976i
$286$	1.21258	+	1.05071i	0.0717014	+	0.0621296i
$287$	−0.726946	−	0.467180i	−0.0429103	−	0.0275768i
$288$	−2.91365	+	0.714588i	−0.171689	+	0.0421075i
$289$	−0.262637	+	0.303100i	−0.0154492	+	0.0178294i
$290$	3.65482	+	1.07315i	0.214618	+	0.0630176i
$291$	4.88189	−	20.2341i	0.286181	−	1.18615i
$292$	0.323040	+	0.372808i	0.0189045	+	0.0218170i
$293$	−1.93621	−	4.23971i	−0.113115	−	0.247687i	0.844605	−	0.535390i	$-0.179835\pi$
$293$	−1.93621	−	4.23971i	−0.113115	−	0.247687i	−0.957720	+	0.287704i	$0.907108\pi$
$294$	9.51128	+	0.896180i	0.554709	+	0.0522663i
$295$	4.43293	+	2.02445i	0.258095	+	0.117868i
$296$	0.155424	−	1.08100i	0.00903384	−	0.0628317i
$297$	1.57280	−	2.46769i	0.0912633	−	0.143190i
$298$			16.7109i			0.968034i
$299$	−12.4686	+	5.58783i	−0.721076	+	0.323153i
$300$	−0.641721	+	1.60879i	−0.0370498	+	0.0928833i
$301$	13.0607	−	8.39362i	0.752808	−	0.483800i
$302$	16.3752	+	2.35440i	0.942289	+	0.135481i
$303$	−5.50993	+	5.26691i	−0.316537	+	0.302576i
$304$	−2.04212	−	6.95483i	−0.117124	−	0.398887i
$305$	4.26462	−	1.94759i	0.244192	−	0.111519i
$306$	12.5017	+	0.564099i	0.714672	+	0.0322474i
$307$	−4.63928	−	32.2669i	−0.264778	−	1.84157i	−0.495573	−	0.868566i	$-0.665042\pi$
$307$	−4.63928	−	32.2669i	−0.264778	−	1.84157i	0.230795	−	0.973002i	$-0.425867\pi$
$308$	0.193304	−	0.658332i	0.0110145	−	0.0375119i
$309$	17.8450	−	9.22809i	1.01517	−	0.524968i
$310$	−2.43081	+	3.78242i	−0.138061	+	0.214827i
$311$	−5.74031	+	8.93210i	−0.325503	+	0.506493i	−0.964982	−	0.262316i	$-0.915514\pi$
$311$	−5.74031	+	8.93210i	−0.325503	+	0.506493i	0.639479	+	0.768809i	$0.279150\pi$
$312$	4.38325	−	2.26669i	0.248153	−	0.128326i
$313$	−4.10535	+	13.9815i	−0.232048	+	0.790282i	0.758327	+	0.651874i	$0.226017\pi$
$313$	−4.10535	+	13.9815i	−0.232048	+	0.790282i	−0.990375	+	0.138408i	$0.955801\pi$
$314$	0.264749	+	1.84137i	0.0149406	+	0.103914i
$315$	−3.65129	−	0.164753i	−0.205727	−	0.00928279i
$316$	3.73986	−	1.70794i	0.210384	−	0.0960790i
$317$	3.00389	+	10.2303i	0.168715	+	0.574592i	0.999829	+	0.0184893i	$0.00588567\pi$
$317$	3.00389	+	10.2303i	0.168715	+	0.574592i	−0.831114	+	0.556103i	$0.812296\pi$
$318$	−1.87943	+	1.79653i	−0.105393	+	0.100745i
$319$	−2.12333	−	0.305289i	−0.118884	−	0.0170929i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	3.90442	−	9.78833i	0.217923	−	0.546331i
$322$	4.38858	+	3.85748i	0.244566	+	0.214969i
$323$			30.2366i			1.68241i
$324$	−5.25723	−	7.30490i	−0.292068	−	0.405828i
$325$	0.405458	−	2.82002i	0.0224908	−	0.156427i
$326$	3.02896	+	1.38328i	0.167758	+	0.0766127i
$327$	19.2762	+	1.81626i	1.06597	+	0.100439i
$328$	−0.294640	−	0.645171i	−0.0162688	−	0.0356236i
$329$	3.13911	+	3.62273i	0.173065	+	0.199727i
$330$	0.228778	−	0.948225i	0.0125938	−	0.0521981i
$331$	−33.4474	−	9.82105i	−1.83844	−	0.539814i	−0.838451	−	0.544977i	$-0.816538\pi$
$331$	−33.4474	−	9.82105i	−1.83844	−	0.539814i	−0.999987	+	0.00516315i	$0.998357\pi$
$332$	−2.76419	+	3.19005i	−0.151705	+	0.175077i
$333$	3.18204	−	0.780412i	0.174375	−	0.0427663i
$334$	−16.7145	−	10.7418i	−0.914578	−	0.587764i
$335$	6.39026	+	5.53719i	0.349137	+	0.302529i
$336$	−1.66038	−	1.30237i	−0.0905809	−	0.0710500i
$337$	−22.2437	+	3.19817i	−1.21169	+	0.174215i	−0.718389	−	0.695641i	$-0.755120\pi$
$337$	−22.2437	+	3.19817i	−1.21169	+	0.174215i	−0.493305	+	0.869857i	$0.664211\pi$
$338$	3.69038	−	3.19773i	0.200730	−	0.173934i
$339$	23.2430	−	1.13642i	1.26239	−	0.0617220i
$340$	4.00248	−	1.17524i	0.217065	−	0.0637361i
$341$	1.05187	−	2.30327i	0.0569619	−	0.124729i
$342$	17.0592	−	13.4849i	0.922456	−	0.729180i
$343$	8.24383	+	12.8276i	0.445125	+	0.692628i
$344$	12.7431			0.687061
$345$	6.49941	+	5.17278i	0.349917	+	0.278493i
$346$	15.6176			0.839605
$347$	−18.8845	−	29.3849i	−1.01377	−	1.57746i	−0.799480	−	0.600692i	$-0.794892\pi$
$347$	−18.8845	−	29.3849i	−1.01377	−	1.57746i	−0.214293	−	0.976769i	$-0.568745\pi$
$348$	−3.29162	+	5.71780i	−0.176449	+	0.306506i
$349$	10.7656	−	23.5734i	0.576271	−	1.26186i	−0.367120	−	0.930174i	$-0.619656\pi$
$349$	10.7656	−	23.5734i	0.576271	−	1.26186i	0.943391	−	0.331684i	$-0.107617\pi$
$350$	−1.16898	+	0.343244i	−0.0624847	+	0.0183472i
$351$	11.2245	+	9.65236i	0.599118	+	0.515205i
$352$	0.425613	−	0.368796i	0.0226852	−	0.0196569i
$353$	10.0903	−	1.45076i	0.537050	−	0.0772162i	0.131547	−	0.991310i	$-0.458005\pi$
$353$	10.0903	−	1.45076i	0.537050	−	0.0772162i	0.405503	+	0.914094i	$0.367096\pi$
$354$	−5.20946	+	6.64149i	−0.276880	+	0.352991i
$355$	6.10569	+	5.29061i	0.324057	+	0.280797i
$356$	−3.57653	−	2.29849i	−0.189555	−	0.121820i
$357$	5.11504	+	7.16404i	0.270717	+	0.379161i
$358$	3.90627	−	4.50808i	0.206453	−	0.238259i
$359$	33.4629	+	9.82558i	1.76610	+	0.518574i	0.993248	−	0.116009i	$-0.0370103\pi$
$359$	33.4629	+	9.82558i	1.76610	+	0.518574i	0.772854	+	0.634584i	$0.218828\pi$
$360$	−2.44809	−	1.73404i	−0.129025	−	0.0913917i
$361$	21.9640	+	25.3478i	1.15600	+	1.33409i
$362$	3.24706	+	7.11007i	0.170662	+	0.373697i
$363$	1.73574	−	18.4216i	0.0911027	−	0.966885i
$364$	3.15739	+	1.44193i	0.165492	+	0.0755777i
$365$	−0.0702034	+	0.488275i	−0.00367461	+	0.0255575i
$366$	1.54679	+	7.97169i	0.0808520	+	0.416687i
$367$		−	5.68817i		−	0.296920i	−0.988918	−	0.148460i	$-0.952568\pi$
$367$		−	5.68817i		−	0.296920i	0.988918	−	0.148460i	$-0.0474316\pi$
$368$	1.31852	+	4.61102i	0.0687326	+	0.240366i
$369$	1.46448	−	1.54364i	0.0762379	−	0.0803586i
$370$	0.918745	−	0.590441i	0.0477633	−	0.0306956i
$371$	−1.81021	−	0.260269i	−0.0939813	−	0.0135125i
$372$	−5.38112	−	5.62940i	−0.278998	−	0.291871i
$373$	0.212425	+	0.723452i	0.0109989	+	0.0374589i	0.964810	−	0.262949i	$-0.0846952\pi$
$373$	0.212425	+	0.723452i	0.0109989	+	0.0374589i	−0.953811	+	0.300408i	$0.902877\pi$
$374$	−2.13693	+	0.975903i	−0.110498	+	0.0504628i
$375$	−1.63608	+	0.568551i	−0.0844867	+	0.0293598i
$376$	0.559941	+	3.89447i	0.0288767	+	0.200842i
$377$	3.05743	−	10.4127i	0.157466	−	0.536279i
$378$	1.76068	−	6.08088i	0.0905597	−	0.312767i
$379$	0.664670	−	1.03425i	0.0341418	−	0.0531257i	−0.823763	−	0.566934i	$-0.808129\pi$
$379$	0.664670	−	1.03425i	0.0341418	−	0.0531257i	0.857905	+	0.513808i	$0.171766\pi$
$380$	3.91880	−	6.09778i	0.201030	−	0.312809i
$381$	−16.2960	−	31.5127i	−0.834868	−	1.61444i
$382$	−6.97216	+	23.7450i	−0.356727	+	1.21490i
$383$	−2.58249	−	17.9616i	−0.131959	−	0.917794i	−0.942997	−	0.332801i	$-0.892006\pi$
$383$	−2.58249	−	17.9616i	−0.131959	−	0.917794i	0.811038	−	0.584993i	$-0.198903\pi$
$384$	−0.568551	−	1.63608i	−0.0290137	−	0.0834907i
$385$	0.624121	−	0.285026i	0.0318081	−	0.0145263i
$386$	1.41477	+	4.81827i	0.0720099	+	0.245243i
$387$	14.2974	+	35.4551i	0.726776	+	1.80228i
$388$	11.8951	+	1.71025i	0.603881	+	0.0868250i
$389$	9.53793	−	6.12965i	0.483592	−	0.310786i	−0.276032	−	0.961149i	$-0.589019\pi$
$389$	9.53793	−	6.12965i	0.483592	−	0.310786i	0.759624	+	0.650363i	$0.225383\pi$
$390$	4.58347	+	1.82828i	0.232093	+	0.0925784i
$391$	0.141679	−	20.0051i	0.00716501	−	1.01170i
$392$			5.51566i			0.278583i
$393$	−32.1221	+	6.23281i	−1.62034	+	0.314404i
$394$	1.54230	−	10.7269i	0.0777000	−	0.540415i
$395$	3.73986	+	1.70794i	0.188173	+	0.0859357i
$396$	1.50362	+	0.770404i	0.0755600	+	0.0387143i
$397$	0.601762	+	1.31767i	0.0302015	+	0.0661322i	0.924132	−	0.382074i	$-0.124790\pi$
$397$	0.601762	+	1.31767i	0.0302015	+	0.0661322i	−0.893930	+	0.448207i	$0.852063\pi$
$398$	10.8782	+	12.5541i	0.545274	+	0.629280i
$399$	14.8691	+	3.58747i	0.744387	+	0.179598i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	24.8022	−	28.6232i	1.23856	−	1.42938i	0.373561	−	0.927605i	$-0.378137\pi$
$401$	24.8022	−	28.6232i	1.23856	−	1.42938i	0.865000	−	0.501771i	$-0.167318\pi$
$402$	−11.9191	+	8.51012i	−0.594472	+	0.424446i
$403$	10.7762	+	6.92544i	0.536800	+	0.344981i
$404$	−3.32586	−	2.88188i	−0.165468	−	0.143379i
$405$	2.07792	−	8.75684i	0.103253	−	0.435131i
$406$	−4.59353	+	0.660450i	−0.227973	+	0.0327776i
$407$	−0.464818	+	0.402767i	−0.0230402	+	0.0199644i
$408$	0.352839	+	7.21656i	0.0174682	+	0.357273i
$409$	22.1746	−	6.51105i	1.09646	−	0.321951i	0.317017	−	0.948420i	$-0.397319\pi$
$409$	22.1746	−	6.51105i	1.09646	−	0.321951i	0.779446	+	0.626469i	$0.215501\pi$
$410$	0.294640	−	0.645171i	0.0145512	−	0.0318627i
$411$	−8.73982	−	5.03133i	−0.431104	−	0.248177i
$412$	6.27083	+	9.75760i	0.308941	+	0.480722i
$413$	−5.93734			−0.292157
$414$	−11.3499	+	8.84194i	−0.557817	+	0.434558i
$415$	−4.22104			−0.207203
$416$	1.54030	+	2.39675i	0.0755193	+	0.117510i
$417$	−21.0675	−	12.1281i	−1.03168	−	0.593916i
$418$	−1.69576	+	3.71319i	−0.0829422	+	0.181618i
$419$	−2.63036	+	0.772344i	−0.128502	+	0.0377315i	−0.345351	−	0.938474i	$-0.612240\pi$
$419$	−2.63036	+	0.772344i	−0.128502	+	0.0377315i	0.216849	+	0.976205i	$0.430422\pi$
$420$	−0.103052	−	2.10770i	−0.00502841	−	0.102845i
$421$	6.39971	−	5.54538i	0.311903	−	0.270265i	−0.484815	−	0.874617i	$-0.661113\pi$
$421$	6.39971	−	5.54538i	0.311903	−	0.270265i	0.796718	+	0.604351i	$0.206568\pi$
$422$	15.8150	−	2.27385i	0.769861	−	0.110689i
$423$	−10.2073	+	5.92740i	−0.496298	+	0.288200i
$424$	−1.13444	−	0.983002i	−0.0550935	−	0.0477388i
$425$	3.50925	+	2.25526i	0.170224	+	0.109396i
$426$	−11.3884	+	8.13116i	−0.551767	+	0.393956i
$427$	−3.74050	+	4.31677i	−0.181016	+	0.208903i
$428$	5.83784	+	1.71414i	0.282183	+	0.0828563i
$429$	−2.70151	−	0.651793i	−0.130430	−	0.0314689i
$430$	8.34495	+	9.63058i	0.402429	+	0.464428i
$431$	5.80199	+	12.7046i	0.279472	+	0.611958i	0.996361	−	0.0852286i	$-0.0271621\pi$
$431$	5.80199	+	12.7046i	0.279472	+	0.611958i	−0.716889	+	0.697187i	$0.754435\pi$
$432$	3.91416	−	3.41751i	0.188320	−	0.164425i
$433$	11.7804	+	5.37991i	0.566128	+	0.258542i	0.677854	−	0.735197i	$-0.262910\pi$
$433$	11.7804	+	5.37991i	0.566128	+	0.258542i	−0.111725	+	0.993739i	$0.535638\pi$
$434$	0.779577	−	5.42208i	0.0374209	−	0.260268i
$435$	−6.47678	+	1.25672i	−0.310538	+	0.0602553i
$436$			11.1784i			0.535348i
$437$	−22.5778	−	26.4322i	−1.08004	−	1.26442i
$438$	−0.793608	−	0.316558i	−0.0379201	−	0.0151257i
$439$	−5.99600	+	3.85339i	−0.286173	+	0.183912i	−0.675850	−	0.737039i	$-0.736223\pi$
$439$	−5.99600	+	3.85339i	−0.286173	+	0.183912i	0.389676	+	0.920952i	$0.372587\pi$
$440$	0.557434	+	0.0801470i	0.0265746	+	0.00382086i
$441$	−15.3462	+	6.18841i	−0.730772	+	0.294686i
$442$	−3.34827	−	11.4032i	−0.159261	−	0.542393i
$443$	−4.55328	+	2.07941i	−0.216333	+	0.0987958i	−0.520634	−	0.853780i	$-0.674304\pi$
$443$	−4.55328	+	2.07941i	−0.216333	+	0.0987958i	0.304301	+	0.952576i	$0.401577\pi$
$444$	0.620922	+	1.78678i	0.0294677	+	0.0847970i
$445$	−0.605041	−	4.20815i	−0.0286817	−	0.199485i
$446$	4.45069	−	15.1576i	0.210746	−	0.717735i
$447$	−13.2952	−	25.7099i	−0.628841	−	1.21603i
$448$	0.658681	−	1.02493i	0.0311197	−	0.0484233i
$449$	−2.56158	+	3.98589i	−0.120888	+	0.188106i	−0.896424	−	0.443198i	$-0.853844\pi$
$449$	−2.56158	+	3.98589i	−0.120888	+	0.188106i	0.775535	+	0.631304i	$0.217480\pi$
$450$	−0.292659	−	2.98569i	−0.0137961	−	0.140747i
$451$	−0.112534	+	0.383255i	−0.00529901	+	0.0180468i
$452$	1.91206	+	13.2987i	0.0899357	+	0.625516i
$453$	−27.0667	+	9.40589i	−1.27170	+	0.441927i
$454$	−7.85544	+	3.58746i	−0.368674	+	0.168368i
$455$	0.977910	+	3.33046i	0.0458451	+	0.156134i
$456$	8.67510	+	9.07537i	0.406249	+	0.424993i
$457$	−6.84751	−	0.984523i	−0.320313	−	0.0460540i	−0.0197169	−	0.999806i	$-0.506276\pi$
$457$	−6.84751	−	0.984523i	−0.320313	−	0.0460540i	−0.300596	+	0.953752i	$0.597186\pi$
$458$	10.7232	−	6.89136i	0.501060	−	0.322012i
$459$	−19.6827	+	9.07847i	−0.918711	+	0.423746i
$460$	−2.62133	+	4.01605i	−0.122220	+	0.187249i
$461$			10.0040i			0.465934i	0.972485	+	0.232967i	$0.0748434\pi$
$461$			10.0040i			0.465934i	−0.972485	+	0.232967i	$0.925157\pi$
$462$	0.226370	+	1.16664i	0.0105317	+	0.0542772i
$463$	2.48353	−	17.2733i	0.115419	−	0.802760i	−0.847078	−	0.531469i	$-0.821640\pi$
$463$	2.48353	−	17.2733i	0.115419	−	0.802760i	0.962497	−	0.271291i	$-0.0874507\pi$
$464$	−3.46489	−	1.58236i	−0.160854	−	0.0734593i
$465$	0.730534	−	7.75325i	0.0338777	−	0.359548i
$466$	−6.01311	−	13.1669i	−0.278552	−	0.609944i
$467$	13.5764	+	15.6680i	0.628242	+	0.725030i	0.977250	−	0.212089i	$-0.0680268\pi$
$467$	13.5764	+	15.6680i	0.628242	+	0.725030i	−0.349008	+	0.937120i	$0.613481\pi$
$468$	−4.94030	+	6.97465i	−0.228366	+	0.322403i
$469$	−9.88436	−	2.90231i	−0.456417	−	0.134016i
$470$	−2.57656	+	2.97351i	−0.118848	+	0.137158i
$471$	−1.87231	−	2.62233i	−0.0862717	−	0.120831i
$472$	−4.09970	−	2.63472i	−0.188704	−	0.121273i
$473$	−5.42362	−	4.69959i	−0.249378	−	0.216088i
$474$	−4.39498	+	5.60312i	−0.201868	+	0.257360i
$475$	7.17466	−	1.03156i	0.329196	−	0.0473313i
$476$	−3.84089	+	3.32815i	−0.176047	+	0.152546i
$477$	1.46219	−	4.25926i	0.0669491	−	0.195018i
$478$	−4.28902	+	1.25937i	−0.196175	+	0.0576022i
$479$	−12.7635	+	27.9481i	−0.583177	+	1.27698i	0.356301	+	0.934371i	$0.384038\pi$
$479$	−12.7635	+	27.9481i	−0.583177	+	1.27698i	−0.939478	+	0.342609i	$0.888689\pi$
$480$	0.864143	−	1.50109i	0.0394426	−	0.0685148i
$481$	−1.68218	−	2.61752i	−0.0767008	−	0.119349i
$482$	−21.4782			−0.978305
$483$	−9.82089	−	2.44321i	−0.446866	−	0.111170i
$484$	10.6828			0.485584
$485$	6.49710	+	10.1097i	0.295018	+	0.459057i
$486$	13.9001	+	7.05601i	0.630521	+	0.320067i
$487$	−1.61871	+	3.54448i	−0.0733508	+	0.160616i	−0.942755	−	0.333485i	$-0.891775\pi$
$487$	−1.61871	+	3.54448i	−0.0733508	+	0.160616i	0.869405	+	0.494101i	$0.164503\pi$
$488$	−4.49839	+	1.32085i	−0.203632	+	0.0597919i
$489$	−5.76062	+	0.281654i	−0.260504	+	0.0127369i
$490$	−4.16846	+	3.61199i	−0.188312	+	0.163173i
$491$	−20.1205	+	2.89289i	−0.908024	+	0.130554i	−0.580473	−	0.814280i	$-0.697132\pi$
$491$	−20.1205	+	2.89289i	−0.908024	+	0.130554i	−0.327551	+	0.944834i	$0.606223\pi$
$492$	0.966606	+	0.758187i	0.0435780	+	0.0341817i
$493$	12.0085	+	10.4054i	0.540837	+	0.468638i
$494$	−17.3727	−	11.1648i	−0.781635	−	0.502326i
$495$	0.402432	+	1.64087i	0.0180880	+	0.0737517i
$496$	2.94436	−	3.39798i	0.132206	−	0.152574i
$497$	−9.44420	−	2.77307i	−0.423630	−	0.124389i
$498$	1.71473	−	7.10713i	0.0768391	−	0.318478i
$499$	19.5319	+	22.5410i	0.874367	+	1.00907i	0.999856	+	0.0169785i	$0.00540468\pi$
$499$	19.5319	+	22.5410i	0.874367	+	1.00907i	−0.125489	+	0.992095i	$0.540050\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	34.2617	+	3.22823i	1.53070	+	0.144227i
$502$	15.1499	+	6.91872i	0.676172	+	0.308798i
$503$	4.58698	−	31.9032i	0.204523	−	1.42249i	−0.586125	−	0.810221i	$-0.699347\pi$
$503$	4.58698	−	31.9032i	0.204523	−	1.42249i	0.790648	−	0.612271i	$-0.209744\pi$
$504$	3.59067	+	0.682708i	0.159941	+	0.0304102i
$505$		−	4.40075i		−	0.195831i
$506$	1.13935	−	2.44877i	0.0506501	−	0.108861i
$507$	−3.13357	+	7.85582i	−0.139167	+	0.348889i
$508$	17.2310	−	11.0737i	0.764504	−	0.491317i
$509$	−20.6038	−	2.96238i	−0.913249	−	0.131305i	−0.330358	−	0.943856i	$-0.607169\pi$
$509$	−20.6038	−	2.96238i	−0.913249	−	0.131305i	−0.582891	+	0.812550i	$0.698079\pi$
$510$	−5.22285	+	4.99250i	−0.231272	+	0.221071i
$511$	−0.169321	−	0.576654i	−0.00749032	−	0.0255097i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	−15.5172	+	34.3190i	−0.685100	+	1.51522i
$514$	−1.01272	−	7.04364i	−0.0446693	−	0.310681i
$515$	−3.26778	+	11.1290i	−0.143996	+	0.490404i
$516$	−19.6054	+	10.1384i	−0.863079	+	0.446319i
$517$	1.19795	−	1.86404i	0.0526856	−	0.0819804i
$518$	−0.719355	+	1.11934i	−0.0316066	+	0.0491809i
$519$	−24.0278	+	12.4254i	−1.05470	+	0.545413i
$520$	−0.802662	+	2.73362i	−0.0351991	+	0.119877i
$521$	4.17743	+	29.0547i	0.183017	+	1.27291i	0.849580	+	0.527460i	$0.176856\pi$
$521$	4.17743	+	29.0547i	0.183017	+	1.27291i	−0.666563	+	0.745448i	$0.732235\pi$
$522$	0.515100	−	11.4157i	0.0225453	−	0.499653i
$523$	19.9378	−	9.10528i	0.871818	−	0.398146i	0.0713004	−	0.997455i	$-0.477285\pi$
$523$	19.9378	−	9.10528i	0.871818	−	0.398146i	0.800518	+	0.599309i	$0.204558\pi$
$524$	−5.32237	−	18.1263i	−0.232509	−	0.791852i
$525$	1.52541	−	1.45813i	0.0665742	−	0.0636380i
$526$	−20.7373	−	2.98158i	−0.904191	−	0.130003i
$527$	−15.7782	+	10.1400i	−0.687309	+	0.441707i
$528$	−0.361396	+	0.906015i	−0.0157277	+	0.0394292i
$529$	14.8141	+	17.5938i	0.644091	+	0.764949i
$530$		−	1.50109i		−	0.0652030i
$531$	2.73083	−	14.3627i	0.118508	−	0.623287i
$532$	−1.25679	+	8.74113i	−0.0544885	+	0.378976i
$533$	−1.83811	−	0.839435i	−0.0796172	−	0.0363600i
$534$	7.33121	+	0.690768i	0.317253	+	0.0298924i
$535$	2.52751	+	5.53447i	0.109274	+	0.239276i
$536$	−5.53719	−	6.39026i	−0.239170	−	0.276017i
$537$	−2.42321	+	10.0436i	−0.104569	+	0.433412i
$538$	−5.24676	−	1.54059i	−0.226204	−	0.0664195i
$539$	2.03415	−	2.34754i	0.0876172	−	0.101116i
$540$	5.14601	+	0.720132i	0.221449	+	0.0309895i
$541$	5.02505	+	3.22940i	0.216044	+	0.138843i	0.644187	−	0.764868i	$-0.277196\pi$
$541$	5.02505	+	3.22940i	0.216044	+	0.138843i	−0.428143	+	0.903711i	$0.640832\pi$
$542$	7.97152	+	6.90736i	0.342406	+	0.296697i
$543$	−10.6524	−	8.35555i	−0.457139	−	0.358571i
$544$	−4.12900	+	0.593660i	−0.177029	+	0.0254530i
$545$	−8.44806	+	7.32029i	−0.361875	+	0.313567i
$546$	−6.00488	+	0.293597i	−0.256985	+	0.0125648i
$547$	−43.3465	+	12.7277i	−1.85336	+	0.544197i	−0.853635	+	0.520871i	$0.825607\pi$
$547$	−43.3465	+	12.7277i	−1.85336	+	0.544197i	−0.999728	+	0.0233251i	$0.992575\pi$
$548$	2.41869	−	5.29618i	0.103321	−	0.226242i
$549$	−8.72204	−	11.0339i	−0.372248	−	0.470916i
$550$	0.304471	+	0.473766i	0.0129827	+	0.0202014i
$551$	27.6101			1.17623
$552$	−5.69709	−	6.04509i	−0.242484	−	0.257296i
$553$	−5.00906			−0.213007
$554$	−11.4141	−	17.7607i	−0.484940	−	0.754581i
$555$	−0.943743	+	1.63936i	−0.0400597	+	0.0695868i
$556$	5.83028	−	12.7665i	0.247259	−	0.541421i
$557$	12.5222	−	3.67685i	0.530582	−	0.155793i	−0.00545847	−	0.999985i	$-0.501737\pi$
$557$	12.5222	−	3.67685i	0.530582	−	0.155793i	0.536041	+	0.844192i	$0.319919\pi$
$558$	12.7577	+	4.37967i	0.540075	+	0.185406i
$559$	27.4377	−	23.7749i	1.16049	−	1.00557i
$560$	1.20593	−	0.173387i	0.0509600	−	0.00732694i
$561$	2.51126	−	3.20158i	0.106026	−	0.135171i
$562$	−23.7373	−	20.5685i	−1.00130	−	0.867631i
$563$	3.64724	+	2.34394i	0.153713	+	0.0987853i	0.615236	−	0.788343i	$-0.289061\pi$
$563$	3.64724	+	2.34394i	0.153713	+	0.0987853i	−0.461523	+	0.887128i	$0.652697\pi$
$564$	−3.95992	−	5.54620i	−0.166743	−	0.233537i
$565$	−8.79832	+	10.1538i	−0.370148	+	0.427174i
$566$	20.6164	+	6.05352i	0.866572	+	0.254448i
$567$	2.12913	+	10.7563i	0.0894151	+	0.451722i
$568$	−5.29061	−	6.10569i	−0.221989	−	0.256189i
$569$	18.4639	+	40.4303i	0.774046	+	1.69492i	0.717535	+	0.696523i	$0.245271\pi$
$569$	18.4639	+	40.4303i	0.774046	+	1.69492i	0.0565116	+	0.998402i	$0.482002\pi$
$570$	−1.17772	+	12.4993i	−0.0493293	+	0.523538i
$571$	−18.6469	−	8.51574i	−0.780347	−	0.356373i	−0.0149147	−	0.999889i	$-0.504748\pi$
$571$	−18.6469	−	8.51574i	−0.780347	−	0.356373i	−0.765433	+	0.643516i	$0.777475\pi$
$572$	0.228340	−	1.58814i	0.00954739	−	0.0664036i
$573$	−8.16482	−	42.0790i	−0.341090	−	1.75788i
$574$			0.864123i			0.0360678i
$575$	−4.75173	+	0.648883i	−0.198161	+	0.0270603i
$576$	2.17639	+	2.06478i	0.0906829	+	0.0860327i
$577$	−4.89256	+	3.14426i	−0.203680	+	0.130897i	−0.638505	−	0.769618i	$-0.720447\pi$
$577$	−4.89256	+	3.14426i	−0.203680	+	0.130897i	0.434825	+	0.900515i	$0.356810\pi$
$578$	0.396976	+	0.0570765i	0.0165120	+	0.00237407i
$579$	−6.01006	−	6.28736i	−0.249770	−	0.261294i
$580$	−1.07315	−	3.65482i	−0.0445602	−	0.151758i
$581$	4.67791	−	2.13633i	0.194072	−	0.0886298i
$582$	−19.6614	+	6.83250i	−0.814991	+	0.283216i
$583$	0.120307	+	0.836757i	0.00498263	+	0.0346549i
$584$	0.138978	−	0.473314i	0.00575093	−	0.0195859i
$585$	−8.50630	+	0.833791i	−0.351692	+	0.0344730i
$586$	−2.51988	+	3.92101i	−0.104095	+	0.161975i
$587$	−16.9258	+	26.3370i	−0.698601	+	1.08704i	0.292798	+	0.956174i	$0.405414\pi$
$587$	−16.9258	+	26.3370i	−0.698601	+	1.08704i	−0.991399	+	0.130871i	$0.958223\pi$
$588$	−4.38827	−	8.48591i	−0.180969	−	0.349953i
$589$	−9.18172	+	31.2701i	−0.378326	+	1.28846i
$590$	−0.693547	−	4.82372i	−0.0285529	−	0.198590i
$591$	6.16152	+	17.7306i	0.253451	+	0.729338i
$592$	−0.993422	+	0.453681i	−0.0408294	+	0.0186462i
$593$	6.07647	+	20.6946i	0.249531	+	0.849824i	0.985042	+	0.172312i	$0.0551237\pi$
$593$	6.07647	+	20.6946i	0.249531	+	0.849824i	−0.735512	+	0.677512i	$0.763058\pi$
$594$	−2.92628	+	0.0110109i	−0.120067	+	0.000451784i
$595$	−5.03050	−	0.723276i	−0.206230	−	0.0296514i
$596$	14.0581	−	9.03458i	0.575841	−	0.370071i
$597$	−26.7243	−	10.6599i	−1.09375	−	0.436281i
$598$	11.4418	+	7.46822i	0.467890	+	0.305398i
$599$		−	24.8744i		−	1.01634i	−0.861257	−	0.508170i	$-0.830322\pi$
$599$		−	24.8744i		−	1.01634i	0.861257	−	0.508170i	$-0.169678\pi$
$600$	1.70034	−	0.329926i	0.0694160	−	0.0134692i
$601$	1.82768	−	12.7118i	0.0745526	−	0.518525i	−0.917988	−	0.396609i	$-0.870187\pi$
$601$	1.82768	−	12.7118i	0.0745526	−	0.518525i	0.992540	−	0.121916i	$-0.0389039\pi$
$602$	−14.1223	−	6.44945i	−0.575583	−	0.262860i
$603$	11.5670	−	22.5758i	0.471046	−	0.919357i
$604$	−6.87247	−	15.0486i	−0.279637	−	0.612319i
$605$	6.99577	+	8.07355i	0.284419	+	0.328237i
$606$	7.40970	+	1.78774i	0.300999	+	0.0726218i
$607$	−33.8299	−	9.93335i	−1.37311	−	0.403182i	−0.489747	−	0.871865i	$-0.662911\pi$
$607$	−33.8299	−	9.93335i	−1.37311	−	0.403182i	−0.883367	+	0.468682i	$0.844729\pi$
$608$	−4.74672	+	5.47801i	−0.192505	+	0.222163i
$609$	6.54175	−	4.67073i	0.265085	−	0.189268i
$610$	−3.94405	−	2.53468i	−0.159690	−	0.102626i
$611$	8.47160	+	7.34068i	0.342724	+	0.296972i
$612$	−6.28435	−	10.8220i	−0.254030	−	0.437455i
$613$	−2.30533	+	0.331457i	−0.0931116	+	0.0133874i	−0.188713	−	0.982032i	$-0.560432\pi$
$613$	−2.30533	+	0.331457i	−0.0931116	+	0.0133874i	0.0956015	+	0.995420i	$0.469523\pi$
$614$	−24.6365	+	21.3476i	−0.994246	+	0.861519i
$615$	0.0599927	+	1.22702i	0.00241914	+	0.0494782i
$616$	−0.658332	+	0.193304i	−0.0265249	+	0.00778843i
$617$	−6.19843	+	13.5727i	−0.249540	+	0.546415i	−0.992403	−	0.123027i	$-0.960740\pi$
$617$	−6.19843	+	13.5727i	−0.249540	+	0.546415i	0.742864	+	0.669443i	$0.233467\pi$
$618$	−17.4109	−	10.0231i	−0.700369	−	0.403188i
$619$	1.87484	+	2.91731i	0.0753563	+	0.117257i	0.876886	−	0.480698i	$-0.159617\pi$
$619$	1.87484	+	2.91731i	0.0753563	+	0.117257i	−0.801530	+	0.597955i	$0.795980\pi$
$620$	4.49617			0.180570
$621$	10.4273	−	22.6334i	0.418432	−	0.908248i
$622$	10.6176			0.425727
$623$	2.80033	+	4.35740i	0.112193	+	0.174576i
$624$	−4.27662	−	2.46196i	−0.171202	−	0.0985574i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	13.9815	−	4.10535i	0.558814	−	0.164083i
$627$	−0.345279	−	7.06193i	−0.0137891	−	0.282026i
$628$	1.40592	−	1.21824i	0.0561024	−	0.0486130i
$629$	4.50934	−	0.648345i	0.179799	−	0.0258512i
$630$	1.83543	+	3.16073i	0.0731255	+	0.125926i
$631$	−8.36594	−	7.24913i	−0.333043	−	0.288583i	0.472245	−	0.881467i	$-0.343444\pi$
$631$	−8.36594	−	7.24913i	−0.333043	−	0.288583i	−0.805288	+	0.592884i	$0.797989\pi$
$632$	−3.45873	−	2.22279i	−0.137581	−	0.0884179i
$633$	−22.5225	+	16.0808i	−0.895187	+	0.639154i
$634$	6.98226	−	8.05796i	0.277301	−	0.320023i
$635$	19.6529	+	5.77061i	0.779901	+	0.229000i
$636$	2.52743	+	0.609793i	0.100219	+	0.0241799i
$637$	10.2906	+	11.8760i	0.407730	+	0.470546i
$638$	0.891134	+	1.95131i	0.0352803	+	0.0772531i
$639$	11.0519	−	21.5705i	0.437208	−	0.853315i
$640$	0.909632	+	0.415415i	0.0359564	+	0.0164207i
$641$	−0.545196	+	3.79192i	−0.0215339	+	0.149772i	−0.997752	−	0.0670211i	$-0.978651\pi$
$641$	−0.545196	+	3.79192i	−0.0215339	+	0.149772i	0.976218	+	0.216793i	$0.0695596\pi$
$642$	−10.3454	+	2.00737i	−0.408299	+	0.0792244i
$643$			20.5051i			0.808643i	0.914617	+	0.404322i	$0.132492\pi$
$643$			20.5051i			0.808643i	−0.914617	+	0.404322i	$0.867508\pi$
$644$	0.872472	−	5.77742i	0.0343802	−	0.227662i
$645$	−20.5009	−	8.17750i	−0.807222	−	0.321989i
$646$	25.4366	−	16.3471i	1.00079	−	0.643169i
$647$	14.6619	+	2.10807i	0.576420	+	0.0828767i	0.424358	−	0.905494i	$-0.360500\pi$
$647$	14.6619	+	2.10807i	0.576420	+	0.0828767i	0.152062	+	0.988371i	$0.451409\pi$
$648$	−3.30300	+	8.37199i	−0.129754	+	0.328883i
$649$	0.773213	+	2.63332i	0.0303513	+	0.103367i
$650$	−2.59156	+	1.18353i	−0.101649	+	0.0464217i
$651$	3.11443	+	8.96216i	0.122064	+	0.351255i
$652$	−0.473890	−	3.29598i	−0.0185590	−	0.129080i
$653$	6.24943	−	21.2836i	0.244559	−	0.832892i	−0.742127	−	0.670259i	$-0.766183\pi$
$653$	6.24943	−	21.2836i	0.244559	−	0.832892i	0.986687	−	0.162633i	$-0.0519987\pi$
$654$	−8.89355	−	17.1981i	−0.347765	−	0.672498i
$655$	10.2136	−	15.8926i	0.399077	−	0.620975i
$656$	−0.383458	+	0.596673i	−0.0149715	+	0.0232962i
$657$	1.47283	−	0.144367i	0.0574606	−	0.00563231i
$658$	1.35050	−	4.59938i	0.0526480	−	0.179303i
$659$	−5.14004	−	35.7497i	−0.200227	−	1.39261i	−0.803608	−	0.595159i	$-0.797089\pi$
$659$	−5.14004	−	35.7497i	−0.200227	−	1.39261i	0.603381	−	0.797453i	$-0.293820\pi$
$660$	−0.921384	+	0.320189i	−0.0358648	+	0.0124633i
$661$	−19.0946	+	8.72019i	−0.742692	+	0.339176i	−0.750568	−	0.660793i	$-0.770220\pi$
$661$	−19.0946	+	8.72019i	−0.742692	+	0.339176i	0.00787622	+	0.999969i	$0.497493\pi$
$662$	9.82105	+	33.4474i	0.381706	+	1.29997i
$663$	14.2237	+	14.8800i	0.552404	+	0.577892i
$664$	4.17808	+	0.600717i	0.162141	+	0.0233123i
$665$	−7.42913	+	4.77441i	−0.288089	+	0.185144i
$666$	−2.37686	−	2.25498i	−0.0921016	−	0.0873787i
$667$	−18.2674	−	0.129372i	−0.707317	−	0.00500931i
$668$			19.8686i			0.768739i
$669$	5.21202	+	26.8612i	0.201508	+	1.03851i
$670$	1.20335	−	8.36946i	0.0464893	−	0.323340i
$671$	2.40169	+	1.09682i	0.0927163	+	0.0423421i
$672$	−0.197954	+	2.10091i	−0.00763623	+	0.0810444i
$673$	−0.130673	−	0.286134i	−0.00503707	−	0.0110296i	0.907097	−	0.420922i	$-0.138293\pi$
$673$	−0.130673	−	0.286134i	−0.00503707	−	0.0110296i	−0.912134	+	0.409893i	$0.865566\pi$
$674$	14.7163	+	16.9836i	0.566852	+	0.654183i
$675$	2.82568	+	4.36068i	0.108760	+	0.167843i
$676$	−4.68528	−	1.37572i	−0.180203	−	0.0529123i
$677$	−11.3998	+	13.1560i	−0.438129	+	0.505628i	−0.931274	−	0.364319i	$-0.881302\pi$
$677$	−11.3998	+	13.1560i	−0.438129	+	0.505628i	0.493145	+	0.869947i	$0.335847\pi$
$678$	−13.5222	−	18.9389i	−0.519315	−	0.727344i
$679$	−12.3170	−	7.91563i	−0.472682	−	0.303774i
$680$	−3.15258	−	2.73172i	−0.120896	−	0.104757i
$681$	9.23149	−	11.7692i	0.353752	−	0.450995i
$682$	−2.50632	+	0.360354i	−0.0959719	+	0.0137987i
$683$	−29.1743	+	25.2796i	−1.11632	+	0.967298i	−0.999665	−	0.0258739i	$-0.991763\pi$
$683$	−29.1743	+	25.2796i	−1.11632	+	0.967298i	−0.116657	+	0.993172i	$0.537218\pi$
$684$	−20.5671	−	7.06063i	−0.786404	−	0.269970i
$685$	5.58649	−	1.64034i	0.213449	−	0.0626742i
$686$	6.33435	−	13.8703i	0.241847	−	0.529570i
$687$	−11.0149	+	19.1338i	−0.420246	+	0.730000i
$688$	−6.88943	−	10.7202i	−0.262657	−	0.408702i
$689$	−4.27663			−0.162926
$690$	0.837771	−	8.26427i	0.0318934	−	0.314615i
$691$	19.2194			0.731141			0.365571	−	0.930784i	$-0.380874\pi$
$691$	19.2194			0.731141			0.365571	+	0.930784i	$0.380874\pi$
$692$	−8.44349	−	13.1383i	−0.320973	−	0.499444i
$693$	−1.27646	−	1.61479i	−0.0484886	−	0.0613410i
$694$	−14.5104	+	31.7733i	−0.550807	+	1.20610i
$695$	13.4663	−	3.95407i	0.510806	−	0.149986i
$696$	6.58970	−	0.322191i	0.249782	−	0.0122126i
$697$	2.23602	−	1.93752i	0.0846952	−	0.0733888i
$698$	−25.6516	+	3.68814i	−0.970927	+	0.139598i
$699$	19.7268	+	15.4733i	0.746137	+	0.585256i
$700$	0.920755	+	0.797839i	0.0348013	+	0.0301555i
$701$	22.3626	+	14.3716i	0.844624	+	0.542807i	0.889894	−	0.456168i	$-0.150778\pi$
$701$	22.3626	+	14.3716i	0.844624	+	0.542807i	−0.0452697	+	0.998975i	$0.514415\pi$
$702$	2.05167	−	14.6611i	0.0774353	−	0.553347i
$703$	5.18396	−	5.98261i	0.195517	−	0.225638i
$704$	−0.540354	−	0.158662i	−0.0203654	−	0.00597981i
$705$	1.59834	−	6.62470i	0.0601969	−	0.249501i
$706$	−6.67566	−	7.70413i	−0.251242	−	0.289949i
$707$	2.22728	+	4.87706i	0.0837654	+	0.183421i
$708$	8.40363	+	0.791814i	0.315828	+	0.0297582i
$709$	−8.06137	−	3.68150i	−0.302751	−	0.138262i	0.258247	−	0.966079i	$-0.416855\pi$
$709$	−8.06137	−	3.68150i	−0.302751	−	0.138262i	−0.560998	+	0.827817i	$0.689582\pi$
$710$	1.14976	−	7.99676i	0.0431497	−	0.300113i
$711$	2.30388	−	12.1171i	0.0864021	−	0.454428i
$712$			4.25142i			0.159329i
$713$	6.22133	−	20.6459i	0.232991	−	0.773194i
$714$	3.26137	−	8.17622i	0.122054	−	0.305987i
$715$	1.34977	−	0.867444i	0.0504785	−	0.0324406i
$716$	−5.90433	−	0.848914i	−0.220655	−	0.0317254i
$717$	5.59675	−	5.34991i	0.209014	−	0.199796i
$718$	−9.82558	−	33.4629i	−0.366687	−	1.24882i
$719$	31.1391	−	14.2208i	1.16129	−	0.530345i	0.260876	−	0.965372i	$-0.415988\pi$
$719$	31.1391	−	14.2208i	1.16129	−	0.530345i	0.900417	+	0.435027i	$0.143261\pi$
$720$	−0.135228	+	2.99695i	−0.00503966	+	0.111690i
$721$	−2.01109	−	13.9875i	−0.0748970	−	0.520920i
$722$	9.44929	−	32.1813i	0.351666	−	1.19766i
$723$	33.0444	−	17.0881i	1.22894	−	0.635513i
$724$	4.22588	−	6.57559i	0.157053	−	0.244380i
$725$	2.05936	−	3.20443i	0.0764828	−	0.119010i
$726$	−16.4357	+	8.49929i	−0.609985	+	0.315438i
$727$	−2.47429	+	8.42666i	−0.0917663	+	0.312527i	−0.992566	−	0.121707i	$-0.961163\pi$
$727$	−2.47429	+	8.42666i	−0.0917663	+	0.312527i	0.900800	+	0.434235i	$0.142981\pi$
$728$	−0.493983	−	3.43573i	−0.0183082	−	0.127337i
$729$	−26.9992	+	0.203187i	−0.999972	+	0.00752545i
$730$	0.448718	−	0.204923i	0.0166078	−	0.00758453i
$731$	14.9761	+	51.0040i	0.553912	+	1.88645i
$732$	5.86995	−	5.61106i	0.216960	−	0.207391i
$733$	31.5746	+	4.53974i	1.16624	+	0.167679i	0.698115	−	0.715986i	$-0.254022\pi$
$733$	31.5746	+	4.53974i	1.16624	+	0.167679i	0.468120	+	0.883665i	$0.344931\pi$
$734$	−4.78519	+	3.07526i	−0.176625	+	0.113510i
$735$	3.53952	−	8.87353i	0.130557	−	0.327305i
$736$	3.16619	−	3.60212i	0.116707	−	0.132776i
$737$			4.76187i			0.175406i
$738$	−2.09035	−	0.397446i	−0.0769468	−	0.0146302i
$739$	3.69974	−	25.7323i	0.136097	−	0.946577i	−0.801287	−	0.598280i	$-0.795851\pi$
$739$	3.69974	−	25.7323i	0.136097	−	0.946577i	0.937384	−	0.348297i	$-0.113240\pi$
$740$	−0.993422	−	0.453681i	−0.0365189	−	0.0166776i
$741$	35.6108	+	3.35535i	1.30820	+	0.123262i
$742$	0.759721	+	1.66356i	0.0278902	+	0.0610711i
$743$	−13.6407	−	15.7422i	−0.500429	−	0.577526i	0.448193	−	0.893937i	$-0.352068\pi$
$743$	−13.6407	−	15.7422i	−0.500429	−	0.577526i	−0.948622	+	0.316411i	$0.897522\pi$
$744$	−1.82650	+	7.57037i	−0.0669628	+	0.277543i
$745$	16.0340	+	4.70799i	0.587439	+	0.172488i
$746$	0.493761	−	0.569831i	0.0180779	−	0.0208630i
$747$	3.01631	+	12.2986i	0.110361	+	0.449984i
$748$	1.97629	+	1.27009i	0.0722605	+	0.0464390i
$749$	−5.60215	−	4.85429i	−0.204698	−	0.177372i
$750$	1.36283	+	1.06897i	0.0497634	+	0.0390334i
$751$	−41.3667	+	5.94764i	−1.50949	+	0.217032i	−0.846821	−	0.531877i	$-0.821487\pi$
$751$	−41.3667	+	5.94764i	−1.50949	+	0.217032i	−0.662672	+	0.748910i	$0.730578\pi$
$752$	2.97351	−	2.57656i	0.108433	−	0.0939576i
$753$	−28.8128	+	1.40875i	−1.05000	+	0.0513376i
$754$	−10.4127	+	3.05743i	−0.379206	+	0.111345i
$755$	6.87247	−	15.0486i	0.250115	−	0.547675i
$756$	−6.06746	+	1.80639i	−0.220671	+	0.0656979i
$757$	−17.4891	−	27.2135i	−0.635650	−	0.989091i	−0.998363	−	0.0571904i	$-0.981786\pi$
$757$	−17.4891	−	27.2135i	−0.635650	−	0.989091i	0.362713	−	0.931901i	$-0.381851\pi$
$758$	−1.22941			−0.0446542
$759$	0.195354	+	4.67393i	0.00709089	+	0.169653i
$760$	−7.24844			−0.262929
$761$	22.9033	+	35.6382i	0.830243	+	1.29188i	0.954071	+	0.299580i	$0.0968466\pi$
$761$	22.9033	+	35.6382i	0.830243	+	1.29188i	−0.123828	+	0.992304i	$0.539517\pi$
$762$	−17.6999	+	30.7461i	−0.641199	+	1.11381i
$763$	5.65754	−	12.3883i	0.204817	−	0.448486i
$764$	23.7450	−	6.97216i	0.859064	−	0.252244i
$765$	4.06337	−	11.8363i	0.146912	−	0.427943i
$766$	−13.7140	+	11.8833i	−0.495509	+	0.429361i
$767$	−13.7429	+	1.97593i	−0.496227	+	0.0713467i
$768$	−1.06897	+	1.36283i	−0.0385733	+	0.0491767i
$769$	6.66390	+	5.77430i	0.240306	+	0.208227i	0.766685	−	0.642024i	$-0.221905\pi$
$769$	6.66390	+	5.77430i	0.240306	+	0.208227i	−0.526378	+	0.850250i	$0.676450\pi$
$770$	−0.577205	−	0.370947i	−0.0208010	−	0.0133680i
$771$	7.16202	+	10.0310i	0.257934	+	0.361257i
$772$	3.28850	−	3.79513i	0.118356	−	0.136590i
$773$	22.5824	+	6.63079i	0.812232	+	0.238493i	0.661368	−	0.750062i	$-0.269976\pi$
$773$	22.5824	+	6.63079i	0.812232	+	0.238493i	0.150864	+	0.988554i	$0.451794\pi$
$774$	22.0970	−	31.1962i	0.794259	−	1.12132i
$775$	2.94436	+	3.39798i	0.105765	+	0.122059i
$776$	−4.99221	−	10.9314i	−0.179210	−	0.392415i
$777$	0.216188	−	2.29443i	0.00775571	−	0.0823124i
$778$	−10.3132	−	4.70987i	−0.369746	−	0.168857i
$779$	0.731651	−	5.08875i	0.0262141	−	0.182323i
$780$	−0.939965	−	4.84430i	−0.0336562	−	0.173454i
$781$			4.54982i			0.162805i
$782$	−16.9060	+	10.6964i	−0.604556	+	0.382502i
$783$	8.28988	+	17.9730i	0.296256	+	0.642304i
$784$	4.64007	−	2.98199i	0.165717	−	0.106500i
$785$	1.84137	+	0.264749i	0.0657212	+	0.00944929i
$786$	22.6099	+	23.6531i	0.806467	+	0.843677i
$787$	8.29258	+	28.2419i	0.295599	+	1.00672i	0.964658	+	0.263507i	$0.0848792\pi$
$787$	8.29258	+	28.2419i	0.295599	+	1.00672i	−0.669059	+	0.743209i	$0.733303\pi$
$788$	−9.85790	+	4.50195i	−0.351173	+	0.160375i
$789$	34.2768	−	11.9115i	1.22029	−	0.424060i
$790$	−0.585114	−	4.06955i	−0.0208174	−	0.144788i
$791$	4.61163	−	15.7058i	0.163971	−	0.558432i
$792$	−0.164816	−	1.68144i	−0.00585647	−	0.0597474i
$793$	−7.22137	+	11.2367i	−0.256438	+	0.399026i
$794$	0.783161	−	1.21862i	0.0277933	−	0.0432473i
$795$	1.19427	+	2.30944i	0.0423563	+	0.0819073i
$796$	4.67998	−	15.9386i	0.165878	−	0.564927i
$797$	−7.94451	−	55.2553i	−0.281409	−	1.95724i	−0.289187	−	0.957273i	$-0.593385\pi$
$797$	−7.94451	−	55.2553i	−0.281409	−	1.95724i	0.00777773	−	0.999970i	$-0.497524\pi$
$798$	−5.02088	−	14.4482i	−0.177737	−	0.511462i
$799$	−14.9295	+	6.81807i	−0.528168	+	0.241206i
$800$	0.281733	+	0.959493i	0.00996075	+	0.0339232i
$801$	−11.8287	+	4.76997i	−0.417948	+	0.168539i
$802$	−37.4885	−	5.39003i	−1.32376	−	0.190329i
$803$	−0.233707	+	0.150194i	−0.00824733	+	0.00530024i
$804$	13.6031	+	5.42609i	0.479745	+	0.191363i
$805$	4.93763	−	3.12403i	0.174028	−	0.110108i
$806$		−	12.8097i		−	0.451202i
$807$	9.29790	−	1.80412i	0.327302	−	0.0635081i
$808$	−0.626291	+	4.35595i	−0.0220329	+	0.153242i
$809$	−43.5891	−	19.9065i	−1.53251	−	0.699875i	−0.542396	−	0.840123i	$-0.682483\pi$
$809$	−43.5891	−	19.9065i	−1.53251	−	0.699875i	−0.990116	+	0.140248i	$0.955210\pi$
$810$	−8.49013	+	2.98624i	−0.298313	+	0.104926i
$811$	−18.5784	−	40.6810i	−0.652375	−	1.42850i	−0.889460	−	0.457013i	$-0.848919\pi$
$811$	−18.5784	−	40.6810i	−0.652375	−	1.42850i	0.237085	−	0.971489i	$-0.423808\pi$
$812$	3.03906	+	3.50726i	0.106650	+	0.123081i
$813$	−17.7598	−	4.28490i	−0.622863	−	0.150278i
$814$	0.590129	+	0.173277i	0.0206840	+	0.00607337i
$815$	2.18060	−	2.51655i	0.0763831	−	0.0881508i
$816$	5.88019	−	4.19839i	0.205848	−	0.146973i
$817$	77.7045	+	49.9376i	2.71854	+	1.74710i
$818$	−17.4659	−	15.1343i	−0.610682	−	0.529159i
$819$	9.00499	−	5.22919i	0.314660	−	0.182723i
$820$	−0.702047	+	0.100939i	−0.0245165	+	0.00352495i
$821$	−22.6062	+	19.5884i	−0.788963	+	0.683640i	−0.953053	−	0.302805i	$-0.902077\pi$
$821$	−22.6062	+	19.5884i	−0.788963	+	0.683640i	0.164089	+	0.986445i	$0.447531\pi$
$822$	0.492478	+	10.0725i	0.0171771	+	0.351321i
$823$	42.7618	−	12.5560i	1.49058	−	0.437674i	0.567854	−	0.823129i	$-0.307774\pi$
$823$	42.7618	−	12.5560i	1.49058	−	0.437674i	0.922727	+	0.385455i	$0.125955\pi$
$824$	4.81835	−	10.5507i	0.167855	−	0.367551i
$825$	−0.845361	−	0.486657i	−0.0294317	−	0.0169432i
$826$	3.20997	+	4.99481i	0.111689	+	0.173792i
$827$	−13.6697			−0.475343			−0.237671	−	0.971346i	$-0.576384\pi$
$827$	−13.6697			−0.475343			−0.237671	+	0.971346i	$0.576384\pi$
$828$	13.5745	+	4.76782i	0.471748	+	0.165693i
$829$	−16.3434			−0.567628			−0.283814	−	0.958879i	$-0.591600\pi$
$829$	−16.3434			−0.567628			−0.283814	+	0.958879i	$0.591600\pi$
$830$	2.28207	+	3.55097i	0.0792117	+	0.123256i
$831$	31.6912	+	18.2440i	1.09936	+	0.632877i
$832$	1.18353	−	2.59156i	0.0410314	−	0.0898462i
$833$	−22.0764	+	6.48220i	−0.764900	+	0.224595i
$834$	1.18712	+	24.2800i	0.0411068	+	0.840748i
$835$	−15.0157	+	13.0112i	−0.519639	+	0.450270i
$836$	4.04053	−	0.580941i	0.139745	−	0.0200922i
$837$	−23.1123	+	3.41186i	−0.798878	+	0.117931i
$838$	2.07182	+	1.79524i	0.0715698	+	0.0620155i
$839$	1.73142	+	1.11272i	0.0597754	+	0.0384153i	0.570187	−	0.821515i	$-0.306871\pi$
$839$	1.73142	+	1.11272i	0.0597754	+	0.0384153i	−0.510412	+	0.859930i	$0.670507\pi$
$840$	−1.71739	+	1.22620i	−0.0592557	+	0.0423079i
$841$	−9.48936	+	10.9513i	−0.327219	+	0.377631i
$842$	−8.12502	−	2.38572i	−0.280007	−	0.0822174i
$843$	52.8845	+	12.7594i	1.82144	+	0.439458i
$844$	−10.4631	−	12.0751i	−0.360155	−	0.415641i
$845$	−2.02850	−	4.44180i	−0.0697826	−	0.152803i
$846$	10.5050	+	5.38237i	0.361168	+	0.185050i
$847$	−11.8391	−	5.40674i	−0.406796	−	0.185778i
$848$	−0.213627	+	1.48581i	−0.00733597	+	0.0510228i
$849$	−36.5348	+	7.08903i	−1.25387	+	0.243295i
$850$		−	4.17146i		−	0.143080i
$851$	−3.45784	+	3.93392i	−0.118533	+	0.134853i
$852$	12.9974	+	5.18446i	0.445283	+	0.177617i
$853$	−36.6578	+	23.5585i	−1.25514	+	0.806628i	−0.987611	−	0.156922i	$-0.949843\pi$
$853$	−36.6578	+	23.5585i	−1.25514	+	0.806628i	−0.267527	+	0.963550i	$0.586206\pi$
$854$	5.65377	+	0.812889i	0.193468	+	0.0278165i
$855$	−8.13254	−	20.1673i	−0.278127	−	0.689708i
$856$	−1.71414	−	5.83784i	−0.0585882	−	0.199533i
$857$	−26.4128	+	12.0623i	−0.902245	+	0.412041i	−0.811851	−	0.583865i	$-0.801540\pi$
$857$	−26.4128	+	12.0623i	−0.902245	+	0.412041i	−0.0903938	+	0.995906i	$0.528813\pi$
$858$	0.912225	+	2.62504i	0.0311428	+	0.0896175i
$859$	−4.73700	−	32.9466i	−0.161625	−	1.12412i	−0.895572	−	0.444917i	$-0.853233\pi$
$859$	−4.73700	−	32.9466i	−0.161625	−	1.12412i	0.733947	−	0.679206i	$-0.237676\pi$
$860$	3.59014	−	12.2269i	0.122423	−	0.416934i
$861$	−0.687498	−	1.32946i	−0.0234299	−	0.0453080i
$862$	7.55098	−	11.7496i	0.257188	−	0.400192i
$863$	13.6654	−	21.2637i	0.465174	−	0.723825i	−0.526838	−	0.849966i	$-0.676623\pi$
$863$	13.6654	−	21.2637i	0.465174	−	0.723825i	0.992012	+	0.126140i	$0.0402590\pi$
$864$	−4.99114	−	1.44516i	−0.169802	−	0.0491652i
$865$	4.39997	−	14.9849i	0.149604	−	0.509503i
$866$	−1.84308	−	12.8189i	−0.0626303	−	0.435603i
$867$	−0.656162	+	0.228022i	−0.0222844	+	0.00774403i
$868$	−4.98281	+	2.27557i	−0.169128	+	0.0772380i
$869$	0.652325	+	2.22161i	0.0221286	+	0.0753631i
$870$	4.55883	+	4.76918i	0.154559	+	0.161690i
$871$	−23.8448	−	3.42836i	−0.807949	−	0.116166i
$872$	9.40386	−	6.04349i	0.318455	−	0.204659i
$873$	24.8133	−	26.1545i	0.839804	−	0.885197i
$874$	−10.0296	+	33.2840i	−0.339258	+	1.12585i
$875$			1.21833i			0.0411872i
$876$	0.162751	+	0.838770i	0.00549885	+	0.0283394i
$877$	−6.18895	+	43.0451i	−0.208986	+	1.45353i	0.567488	+	0.823382i	$0.307915\pi$
$877$	−6.18895	+	43.0451i	−0.208986	+	1.45353i	−0.776474	+	0.630149i	$0.782994\pi$
$878$	6.48336	+	2.96085i	0.218803	+	0.0999239i
$879$	0.757301	−	8.03734i	0.0255431	−	0.271093i
$880$	−0.233948	−	0.512274i	−0.00788638	−	0.0172688i
$881$	−14.3846	−	16.6007i	−0.484629	−	0.559291i	0.459794	−	0.888026i	$-0.347923\pi$
$881$	−14.3846	−	16.6007i	−0.484629	−	0.559291i	−0.944422	+	0.328734i	$0.893378\pi$
$882$	13.5028	+	9.56435i	0.454663	+	0.322049i
$883$	12.0168	+	3.52845i	0.404397	+	0.118742i	0.477604	−	0.878575i	$-0.341505\pi$
$883$	12.0168	+	3.52845i	0.404397	+	0.118742i	−0.0732070	+	0.997317i	$0.523323\pi$
$884$	−7.78274	+	8.98176i	−0.261762	+	0.302089i
$885$	4.90479	+	6.86957i	0.164873	+	0.230918i
$886$	4.21100	+	2.70624i	0.141471	+	0.0909181i
$887$	−38.1022	−	33.0157i	−1.27935	−	1.10856i	−0.988409	−	0.151817i	$-0.951487\pi$
$887$	−38.1022	−	33.0157i	−1.27935	−	1.10856i	−0.290937	−	0.956742i	$-0.593967\pi$
$888$	1.16744	−	1.48836i	0.0391768	−	0.0499461i
$889$	−24.7006	+	3.55141i	−0.828432	+	0.119110i
$890$	−3.21301	+	2.78409i	−0.107700	+	0.0933229i
$891$	4.49335	−	2.34509i	0.150533	−	0.0785636i
$892$	−15.1576	+	4.45069i	−0.507516	+	0.149020i
$893$	−11.8473	+	25.9419i	−0.396454	+	0.868113i
$894$	−14.4406	+	25.0844i	−0.482965	+	0.838949i
$895$	−3.22495	−	5.01811i	−0.107798	−	0.167737i
$896$	−1.21833			−0.0407017
$897$	−23.5451	−	2.38683i	−0.786147	−	0.0796939i
$898$	4.73804			0.158110
$899$	9.25924	+	14.4077i	0.308813	+	0.480522i
$900$	−2.35350	+	1.86039i	−0.0784500	+	0.0620129i
$901$	2.60121	−	5.69586i	0.0866589	−	0.189757i
$902$	0.383255	−	0.112534i	0.0127610	−	0.00374697i
$903$	26.8586	−	1.31320i	0.893797	−	0.0437005i
$904$	10.1538	−	8.79832i	0.337711	−	0.292628i
$905$	7.73686	−	1.11239i	0.257182	−	0.0369772i
$906$	22.5461	+	17.6847i	0.749044	+	0.587535i
$907$	24.3726	+	21.1190i	0.809279	+	0.701244i	0.957728	−	0.287676i	$-0.0928826\pi$
$907$	24.3726	+	21.1190i	0.809279	+	0.701244i	−0.148449	+	0.988920i	$0.547428\pi$
$908$	7.26493	+	4.66889i	0.241095	+	0.154943i
$909$	−12.8222	+	3.14472i	−0.425287	+	0.104304i
$910$	2.27306	−	2.62325i	0.0753512	−	0.0869599i
$911$	42.0979	+	12.3611i	1.39477	+	0.409540i	0.890883	−	0.454232i	$-0.150086\pi$
$911$	42.0979	+	12.3611i	1.39477	+	0.409540i	0.503882	+	0.863772i	$0.331905\pi$
$912$	2.94457	−	12.2045i	0.0975045	−	0.404131i
$913$	−1.55670	−	1.79653i	−0.0515193	−	0.0594565i
$914$	2.87381	+	6.29276i	0.0950571	+	0.208146i
$915$	8.08456	+	0.761750i	0.267267	+	0.0251827i
$916$	−11.5948	−	5.29515i	−0.383102	−	0.174957i
$917$	−3.27555	+	22.7820i	−0.108168	+	0.752327i
$918$	18.2786	+	11.6500i	0.603283	+	0.384507i
$919$			44.2330i			1.45911i	0.683921	+	0.729556i	$0.260273\pi$
$919$			44.2330i			1.45911i	−0.683921	+	0.729556i	$0.739727\pi$
$920$	4.79571	+	0.0339639i	0.158110	+	0.00111976i
$921$	20.9193	−	52.4444i	0.689313	−	1.72810i
$922$	8.41593	−	5.40859i	0.277164	−	0.178122i
$923$	−22.7829	−	3.27569i	−0.749910	−	0.107821i
$924$	0.859058	−	0.821170i	0.0282609	−	0.0270145i
$925$	−0.307684	−	1.04788i	−0.0101166	−	0.0344539i
$926$	−15.8740	+	7.24939i	−0.521651	+	0.238230i
$927$	34.7613	+	1.56850i	1.14171	+	0.0515162i
$928$	0.542093	+	3.77034i	0.0177951	+	0.123768i
$929$	2.83703	−	9.66203i	0.0930798	−	0.317001i	−0.899771	−	0.436362i	$-0.856267\pi$
$929$	2.83703	−	9.66203i	0.0930798	−	0.317001i	0.992851	+	0.119362i	$0.0380848\pi$
$930$	−6.91741	+	3.57716i	−0.226831	+	0.117300i
$931$	−21.6148	+	33.6333i	−0.708397	+	1.10229i
$932$	−7.82575	+	12.1771i	−0.256341	+	0.398874i
$933$	−16.3353	+	8.44739i	−0.534794	+	0.276555i
$934$	5.84082	−	19.8920i	0.191117	−	0.650886i
$935$	0.334330	+	2.32531i	0.0109337	+	0.0760459i
$936$	8.53838	+	0.385268i	0.279086	+	0.0125929i
$937$	30.3517	−	13.8612i	0.991547	−	0.452824i	0.147482	−	0.989065i	$-0.452883\pi$
$937$	30.3517	−	13.8612i	0.991547	−	0.452824i	0.844065	+	0.536240i	$0.180156\pi$
$938$	2.90231	+	9.88436i	0.0947638	+	0.322736i
$939$	−18.2445	+	17.4398i	−0.595387	+	0.569128i
$940$	3.89447	+	0.559941i	0.127024	+	0.0182632i
$941$	8.27762	−	5.31971i	0.269843	−	0.173417i	−0.398721	−	0.917072i	$-0.630546\pi$
$941$	8.27762	−	5.31971i	0.269843	−	0.173417i	0.668564	+	0.743655i	$0.266909\pi$
$942$	−1.19380	+	2.99283i	−0.0388960	+	0.0975117i
$943$	−0.507919	+	3.36339i	−0.0165401	+	0.109527i
$944$			4.87333i			0.158613i
$945$	−5.33852	−	3.40254i	−0.173662	−	0.110685i
$946$	−1.02132	+	7.10343i	−0.0332060	+	0.230952i
$947$	5.77636	+	2.63797i	0.187706	+	0.0857226i	0.507051	−	0.861916i	$-0.330736\pi$
$947$	5.77636	+	2.63797i	0.187706	+	0.0857226i	−0.319345	+	0.947639i	$0.603463\pi$
$948$	7.08976	+	0.668017i	0.230265	+	0.0216962i
$949$	−0.583829	−	1.27841i	−0.0189519	−	0.0414989i
$950$	−4.74672	−	5.47801i	−0.154004	−	0.177730i
$951$	−4.33136	+	17.9524i	−0.140454	+	0.582146i
$952$	4.87636	+	1.43183i	0.158044	+	0.0464058i
$953$	−5.72719	+	6.60953i	−0.185522	+	0.214104i	−0.840890	−	0.541206i	$-0.817968\pi$
$953$	−5.72719	+	6.60953i	−0.185522	+	0.214104i	0.655368	+	0.755310i	$0.272513\pi$
$954$	−4.37364	+	1.07266i	−0.141602	+	0.0347286i
$955$	20.8189	+	13.3795i	0.673683	+	0.432950i
$956$	3.37827	+	2.92729i	0.109261	+	0.0946752i
$957$	−2.92349	−	2.29313i	−0.0945029	−	0.0741262i
$958$	30.4119	−	4.37257i	0.982563	−	0.141271i
$959$	−5.36095	+	4.64529i	−0.173114	+	0.150004i
$960$	−1.72998	+	0.0845842i	−0.0558350	+	0.00272994i
$961$	10.3476	−	3.03834i	0.333794	−	0.0980109i
$962$	−1.29255	+	2.83028i	−0.0416734	+	0.0912519i
$963$	14.3194	−	11.3191i	0.461436	−	0.364754i
$964$	11.6120	+	18.0686i	0.373997	+	0.581950i
$965$	5.02168			0.161654
$966$	3.25422	+	9.58276i	0.104703	+	0.308320i
$967$	−5.54237			−0.178230			−0.0891152	−	0.996021i	$-0.528404\pi$
$967$	−5.54237			−0.178230			−0.0891152	+	0.996021i	$0.528404\pi$
$968$	−5.77558	−	8.98698i	−0.185634	−	0.288852i
$969$	−26.1287	+	45.3877i	−0.839376	+	1.45806i
$970$	4.99221	−	10.9314i	0.160290	−	0.350986i
$971$	26.9619	−	7.91673i	0.865248	−	0.254060i	0.181155	−	0.983455i	$-0.442016\pi$
$971$	26.9619	−	7.91673i	0.865248	−	0.254060i	0.684093	+	0.729395i	$0.260198\pi$
$972$	−1.57906	−	15.5083i	−0.0506485	−	0.497428i
$973$	−12.9226	+	11.1975i	−0.414281	+	0.358976i
$974$	3.85695	−	0.554546i	0.123585	−	0.0177688i
$975$	3.04553	−	3.88272i	0.0975351	−	0.124347i
$976$	3.54318	+	3.07018i	0.113414	+	0.0982741i
$977$	−38.2423	−	24.5768i	−1.22348	−	0.786282i	−0.240616	−	0.970621i	$-0.577349\pi$
$977$	−38.2423	−	24.5768i	−1.22348	−	0.786282i	−0.982863	+	0.184339i	$0.940986\pi$
$978$	3.35137	+	4.69387i	0.107165	+	0.150093i
$979$	1.56791	−	1.80946i	0.0501105	−	0.0578306i
$980$	5.29224	+	1.55394i	0.169054	+	0.0496389i
$981$	27.3657	+	19.3837i	0.873718	+	0.618875i
$982$	13.3116	+	15.3624i	0.424790	+	0.490234i
$983$	3.51610	+	7.69918i	0.112146	+	0.245566i	0.957380	−	0.288830i	$-0.0932663\pi$
$983$	3.51610	+	7.69918i	0.112146	+	0.245566i	−0.845234	+	0.534396i	$0.820539\pi$
$984$	0.115241	−	1.22307i	0.00367375	−	0.0389900i
$985$	−9.85790	−	4.50195i	−0.314099	−	0.143444i
$986$	2.26132	−	15.7278i	0.0720151	−	0.500876i
$987$	1.58152	+	8.15067i	0.0503403	+	0.259439i
$988$			20.6510i			0.656995i
$989$	−51.1768	−	33.4038i	−1.62733	−	1.06218i
$990$	1.16282	−	1.22567i	0.0369568	−	0.0389543i
$991$	6.02854	−	3.87430i	0.191503	−	0.123071i	−0.441376	−	0.897322i	$-0.645510\pi$
$991$	6.02854	−	3.87430i	0.191503	−	0.123071i	0.632879	+	0.774251i	$0.281873\pi$
$992$	−4.45040	−	0.639871i	−0.141300	−	0.0203159i
$993$	−41.7207	−	43.6456i	−1.32396	−	1.38505i
$994$	2.77307	+	9.44420i	0.0879563	+	0.299552i
$995$	15.1103	−	6.90064i	0.479029	−	0.218765i
$996$	−6.90595	+	2.39988i	−0.218823	+	0.0760430i
$997$	−3.06257	−	21.3006i	−0.0969924	−	0.674597i	−0.979075	−	0.203502i	$-0.934768\pi$
$997$	−3.06257	−	21.3006i	−0.0969924	−	0.674597i	0.882082	−	0.471096i	$-0.156141\pi$
$998$	8.40296	−	28.6178i	0.265991	−	0.905882i
$999$	5.45090	+	1.57827i	0.172459	+	0.0499344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.a.11.8	✓	160
3.2	odd	2		690.2.q.b.11.9	yes	160
23.21	odd	22		690.2.q.b.251.9	yes	160
69.44	even	22	inner	690.2.q.a.251.8	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.11.8	✓	160	1.1	even	1	trivial
690.2.q.a.251.8	yes	160	69.44	even	22	inner
690.2.q.b.11.9	yes	160	3.2	odd	2
690.2.q.b.251.9	yes	160	23.21	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 - 0.841254i) q^{2} +(1.50109 + 0.864143i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.0845842 - 1.72998i) q^{6} +(0.920755 - 0.797839i) q^{7} +(0.989821 - 0.142315i) q^{8} +(1.50651 + 2.59431i) q^{9} +O(q^{10})\)	\(q+(-0.540641 - 0.841254i) q^{2} +(1.50109 + 0.864143i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.0845842 - 1.72998i) q^{6} +(0.920755 - 0.797839i) q^{7} +(0.989821 - 0.142315i) q^{8} +(1.50651 + 2.59431i) q^{9} +(0.755750 + 0.654861i) q^{10} +(-0.473766 - 0.304471i) q^{11} +(-1.40963 + 1.00646i) q^{12} +(1.86571 - 2.15315i) q^{13} +(-1.16898 - 0.343244i) q^{14} +(-1.68374 - 0.406235i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.73289 + 3.79449i) q^{17} +(1.36799 - 2.66995i) q^{18} +(6.59342 + 3.01111i) q^{19} +(0.142315 - 0.989821i) q^{20} +(2.07158 - 0.401960i) q^{21} +0.563167i q^{22} +(-4.34822 - 2.02311i) q^{23} +(1.60879 + 0.641721i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-2.82002 - 0.405458i) q^{26} +(0.0195518 + 5.19612i) q^{27} +(0.343244 + 1.16898i) q^{28} +(3.46489 - 1.58236i) q^{29} +(0.568551 + 1.63608i) q^{30} +(0.639871 + 4.45040i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(-0.448056 - 0.866438i) q^{33} +(2.25526 - 3.50925i) q^{34} +(-0.658681 + 1.02493i) q^{35} +(-2.98569 + 0.292659i) q^{36} +(0.307684 - 1.04788i) q^{37} +(-1.03156 - 7.17466i) q^{38} +(4.66122 - 1.61981i) q^{39} +(-0.909632 + 0.415415i) q^{40} +(-0.199823 - 0.680536i) q^{41} +(-1.45813 - 1.52541i) q^{42} +(12.6134 + 1.81353i) q^{43} +(0.473766 - 0.304471i) q^{44} +(-2.17639 - 2.06478i) q^{45} +(0.648883 + 4.75173i) q^{46} +3.93452i q^{47} +(-0.329926 - 1.70034i) q^{48} +(-0.784961 + 5.45952i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(-0.677775 + 7.19332i) q^{51} +(1.18353 + 2.59156i) q^{52} +(-0.983002 - 1.13444i) q^{53} +(4.36068 - 2.82568i) q^{54} +(0.540354 + 0.158662i) q^{55} +(0.797839 - 0.920755i) q^{56} +(7.29524 + 10.2176i) q^{57} +(-3.20443 - 2.05936i) q^{58} +(-3.68301 - 3.19135i) q^{59} +(1.06897 - 1.36283i) q^{60} +(-4.64058 + 0.667214i) q^{61} +(3.39798 - 2.94436i) q^{62} +(3.45697 + 1.18677i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-1.18353 + 2.59156i) q^{65} +(-0.486657 + 0.845361i) q^{66} +(-4.57140 - 7.11324i) q^{67} -4.17146 q^{68} +(-4.77880 - 6.79434i) q^{69} +1.21833 q^{70} +(-4.36783 - 6.79648i) q^{71} +(1.86039 + 2.35350i) q^{72} +(0.204923 - 0.448718i) q^{73} +(-1.04788 + 0.307684i) q^{74} +(1.72998 - 0.0845842i) q^{75} +(-5.47801 + 4.74672i) q^{76} +(-0.679141 + 0.0976457i) q^{77} +(-3.88272 - 3.04553i) q^{78} +(-3.10719 - 2.69240i) q^{79} +(0.841254 + 0.540641i) q^{80} +(-4.46084 + 7.81671i) q^{81} +(-0.464471 + 0.536028i) q^{82} +(4.05006 + 1.18921i) q^{83} +(-0.494930 + 2.05135i) q^{84} +(-2.73172 - 3.15258i) q^{85} +(-5.29367 - 11.5915i) q^{86} +(6.56848 + 0.618901i) q^{87} +(-0.512274 - 0.233948i) q^{88} +(-0.605041 + 4.20815i) q^{89} +(-0.560362 + 2.94720i) q^{90} -3.47106i q^{91} +(3.64660 - 3.11485i) q^{92} +(-2.88529 + 7.23337i) q^{93} +(3.30993 - 2.12716i) q^{94} +(-7.17466 - 1.03156i) q^{95} +(-1.25204 + 1.19682i) q^{96} +(-3.38569 - 11.5306i) q^{97} +(5.01722 - 2.29129i) q^{98} +(0.0761561 - 1.68778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Introduction

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