LMFDB - Embedded newform 529.2.c.o.487.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,2,Mod(118,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("529.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	529.c (of order $11$, degree $10$, not 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:	$4.22408626693$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	20.0.54296067514572573056640625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 2 x^{18} - 3 x^{17} + 5 x^{16} - 8 x^{15} + 13 x^{14} - 21 x^{13} + 34 x^{12} + \cdots + 1 $ x^20 - x^19 + 2x^18 - 3x^17 + 5x^16 - 8x^15 + 13x^14 - 21x^13 + 34x^12 - 55x^11 + 89x^10 + 55x^9 + 34x^8 + 21x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			487.2
Root			$-0.0879554 + 0.611743i$ of defining polynomial
Character	$\chi$	$=$	529.487
Dual form			529.2.c.o.466.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.256741 + 0.562183i) q^{2} +(2.14549 - 0.629973i) q^{3} +(1.05959 - 1.22283i) q^{4} +(1.03985 + 0.668269i) q^{5} +(0.904995 + 1.04442i) q^{6} +(-0.460540 - 3.20313i) q^{7} +(2.14549 + 0.629973i) q^{8} +(1.68251 - 1.08128i) q^{9} +O(q^{10})$	\(q+(0.256741 + 0.562183i) q^{2} +(2.14549 - 0.629973i) q^{3} +(1.05959 - 1.22283i) q^{4} +(1.03985 + 0.668269i) q^{5} +(0.904995 + 1.04442i) q^{6} +(-0.460540 - 3.20313i) q^{7} +(2.14549 + 0.629973i) q^{8} +(1.68251 - 1.08128i) q^{9} +(-0.108719 + 0.756156i) q^{10} +(-2.17514 + 4.76289i) q^{11} +(1.50299 - 3.29108i) q^{12} +(-0.426945 + 2.96946i) q^{13} +(1.68251 - 1.08128i) q^{14} +(2.65197 + 0.778690i) q^{15} +(-0.263866 - 1.83523i) q^{16} +(-0.500269 - 0.577341i) q^{17} +(1.03985 + 0.668269i) q^{18} +(1.30972 - 1.51150i) q^{19} +(1.91899 - 0.563465i) q^{20} +(-3.00597 - 6.58216i) q^{21} -3.23607 q^{22} +5.00000 q^{24} +(-1.44238 - 3.15837i) q^{25} +(-1.77900 + 0.522361i) q^{26} +(-1.46431 + 1.68991i) q^{27} +(-4.40486 - 2.83083i) q^{28} +(1.96458 + 2.26725i) q^{29} +(0.243103 + 1.69082i) q^{30} +(-6.43647 - 1.88992i) q^{31} +(4.72619 - 3.03734i) q^{32} +(-1.66625 + 11.5890i) q^{33} +(0.196132 - 0.429470i) q^{34} +(1.66166 - 3.63853i) q^{35} +(0.460540 - 3.20313i) q^{36} +(-1.03985 + 0.668269i) q^{37} +(1.18600 + 0.348241i) q^{38} +(0.954677 + 6.63992i) q^{39} +(1.80999 + 2.08884i) q^{40} +(-2.92095 - 1.87718i) q^{41} +(2.92863 - 3.37981i) q^{42} +(3.51945 + 7.70653i) q^{44} +2.47214 q^{45} -2.23607 q^{47} +(-1.72227 - 3.77124i) q^{48} +(-3.33149 + 0.978214i) q^{49} +(1.40526 - 1.62176i) q^{50} +(-1.43703 - 0.923525i) q^{51} +(3.17876 + 3.66849i) q^{52} +(-0.0671920 - 0.467330i) q^{53} +(-1.32599 - 0.389345i) q^{54} +(-5.44471 + 3.49910i) q^{55} +(1.02980 - 7.16242i) q^{56} +(1.85779 - 4.06800i) q^{57} +(-0.770222 + 1.68655i) q^{58} +(-0.921081 + 6.40626i) q^{59} +(3.76220 - 2.41782i) q^{60} +(6.66298 + 1.95643i) q^{61} +(-0.590023 - 4.10370i) q^{62} +(-4.23835 - 4.89131i) q^{63} +(-0.198593 - 0.127628i) q^{64} +(-2.42836 + 2.80247i) q^{65} +(-6.94296 + 2.03864i) q^{66} +(-1.14818 - 2.51416i) q^{67} -1.23607 q^{68} +2.47214 q^{70} +(5.08305 + 11.1303i) q^{71} +(4.29098 - 1.25995i) q^{72} +(-4.27484 + 4.93343i) q^{73} +(-0.642661 - 0.413013i) q^{74} +(-5.08429 - 5.86759i) q^{75} +(-0.460540 - 3.20313i) q^{76} +(16.2579 + 4.77375i) q^{77} +(-3.48775 + 2.24144i) q^{78} +(1.55753 - 10.8329i) q^{79} +(0.952046 - 2.08469i) q^{80} +(-4.56957 + 10.0060i) q^{81} +(0.305393 - 2.12406i) q^{82} +(-7.37269 + 4.73814i) q^{83} +(-11.2339 - 3.29858i) q^{84} +(-0.134384 - 0.934661i) q^{85} +(5.64330 + 3.62673i) q^{87} +(-7.66724 + 8.84847i) q^{88} +(10.0479 - 2.95034i) q^{89} +(0.634698 + 1.38979i) q^{90} +9.70820 q^{91} -15.0000 q^{93} +(-0.574089 - 1.25708i) q^{94} +(2.37200 - 0.696481i) q^{95} +(8.22656 - 9.49396i) q^{96} +(14.8971 + 9.57378i) q^{97} +(-1.40526 - 1.62176i) q^{98} +(1.49034 + 10.3655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + q^{4} + 2 q^{5} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 20 * q + q^2 + q^4 + 2 * q^5 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 20 q + q^{2} + q^{4} + 2 q^{5} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{11} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 10 q^{15} + 3 q^{16} - 6 q^{17} + 2 q^{18} + 4 q^{19} + 4 q^{20} + 10 q^{21} - 20 q^{22} + 100 q^{24} - 2 q^{25} + 3 q^{26} + 6 q^{28} + 6 q^{29} - 10 q^{30} - 9 q^{32} - 10 q^{33} + 8 q^{34} - 8 q^{35} + 2 q^{36} - 2 q^{37} - 2 q^{38} + 10 q^{40} - 2 q^{41} - 8 q^{44} - 40 q^{45} + 15 q^{48} + 2 q^{49} + 11 q^{50} - 10 q^{51} + 3 q^{52} + 8 q^{53} - 5 q^{54} + 4 q^{55} + 10 q^{56} - 3 q^{58} - 4 q^{59} - 4 q^{61} - 15 q^{62} - 4 q^{63} - 4 q^{64} + 6 q^{65} - 10 q^{66} + 10 q^{67} + 20 q^{68} - 40 q^{70} - 20 q^{71} - 22 q^{73} + 6 q^{74} - 20 q^{75} - 2 q^{76} + 16 q^{77} + 15 q^{78} + 4 q^{79} - 18 q^{80} + 22 q^{81} + 11 q^{82} + 22 q^{83} - 10 q^{84} + 16 q^{85} - 10 q^{88} + 12 q^{89} - 12 q^{90} + 60 q^{91} - 300 q^{93} + 5 q^{94} - 4 q^{95} + 5 q^{96} - 22 q^{97} - 11 q^{98} + 12 q^{99}+O(q^{100}) $ 20 * q + q^2 + q^4 + 2 * q^5 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^11 - 5 * q^12 - 6 * q^13 - 4 * q^14 + 10 * q^15 + 3 * q^16 - 6 * q^17 + 2 * q^18 + 4 * q^19 + 4 * q^20 + 10 * q^21 - 20 * q^22 + 100 * q^24 - 2 * q^25 + 3 * q^26 + 6 * q^28 + 6 * q^29 - 10 * q^30 - 9 * q^32 - 10 * q^33 + 8 * q^34 - 8 * q^35 + 2 * q^36 - 2 * q^37 - 2 * q^38 + 10 * q^40 - 2 * q^41 - 8 * q^44 - 40 * q^45 + 15 * q^48 + 2 * q^49 + 11 * q^50 - 10 * q^51 + 3 * q^52 + 8 * q^53 - 5 * q^54 + 4 * q^55 + 10 * q^56 - 3 * q^58 - 4 * q^59 - 4 * q^61 - 15 * q^62 - 4 * q^63 - 4 * q^64 + 6 * q^65 - 10 * q^66 + 10 * q^67 + 20 * q^68 - 40 * q^70 - 20 * q^71 - 22 * q^73 + 6 * q^74 - 20 * q^75 - 2 * q^76 + 16 * q^77 + 15 * q^78 + 4 * q^79 - 18 * q^80 + 22 * q^81 + 11 * q^82 + 22 * q^83 - 10 * q^84 + 16 * q^85 - 10 * q^88 + 12 * q^89 - 12 * q^90 + 60 * q^91 - 300 * q^93 + 5 * q^94 - 4 * q^95 + 5 * q^96 - 22 * q^97 - 11 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/529\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{2}{11}\right)$

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 $

$2$	0.256741	+	0.562183i	0.181543	+	0.397524i	0.978422	−	0.206615i	$-0.0662447\pi$
$2$	0.256741	+	0.562183i	0.181543	+	0.397524i	−0.796879	+	0.604138i	$0.793517\pi$
$3$	2.14549	−	0.629973i	1.23870	−	0.363715i	0.404173	−	0.914682i	$-0.367559\pi$
$3$	2.14549	−	0.629973i	1.23870	−	0.363715i	0.834527	+	0.550967i	$0.185741\pi$
$4$	1.05959	−	1.22283i	0.529793	−	0.611414i
$5$	1.03985	+	0.668269i	0.465034	+	0.298859i	0.752097	−	0.659053i	$-0.229043\pi$
$5$	1.03985	+	0.668269i	0.465034	+	0.298859i	−0.287063	+	0.957912i	$0.592679\pi$
$6$	0.904995	+	1.04442i	0.369463	+	0.426383i
$7$	−0.460540	−	3.20313i	−0.174068	−	1.21067i	−0.870179	−	0.492735i	$-0.835997\pi$
$7$	−0.460540	−	3.20313i	−0.174068	−	1.21067i	0.696111	−	0.717934i	$-0.254912\pi$
$8$	2.14549	+	0.629973i	0.758546	+	0.222729i
$9$	1.68251	−	1.08128i	0.560836	−	0.360427i
$10$	−0.108719	+	0.756156i	−0.0343799	+	0.239118i
$11$	−2.17514	+	4.76289i	−0.655830	+	1.43607i	0.230528	+	0.973066i	$0.425955\pi$
$11$	−2.17514	+	4.76289i	−0.655830	+	1.43607i	−0.886358	+	0.463001i	$0.846773\pi$
$12$	1.50299	−	3.29108i	0.433875	−	0.950053i
$13$	−0.426945	+	2.96946i	−0.118413	+	0.823581i	0.840891	+	0.541205i	$0.182032\pi$
$13$	−0.426945	+	2.96946i	−0.118413	+	0.823581i	−0.959304	+	0.282376i	$0.908877\pi$
$14$	1.68251	−	1.08128i	0.449669	−	0.288985i
$15$	2.65197	+	0.778690i	0.684737	+	0.201057i
$16$	−0.263866	−	1.83523i	−0.0659666	−	0.458807i
$17$	−0.500269	−	0.577341i	−0.121333	−	0.140026i	0.691833	−	0.722058i	$-0.256803\pi$
$17$	−0.500269	−	0.577341i	−0.121333	−	0.140026i	−0.813166	+	0.582032i	$0.802258\pi$
$18$	1.03985	+	0.668269i	0.245094	+	0.157512i
$19$	1.30972	−	1.51150i	0.300471	−	0.346762i	−0.585357	−	0.810775i	$-0.699046\pi$
$19$	1.30972	−	1.51150i	0.300471	−	0.346762i	0.885828	+	0.464014i	$0.153591\pi$
$20$	1.91899	−	0.563465i	0.429098	−	0.125995i
$21$	−3.00597	−	6.58216i	−0.655957	−	1.43634i
$22$	−3.23607			−0.689932
$23$		0			0
$23$		0			0
$24$	5.00000			1.02062
$25$	−1.44238	−	3.15837i	−0.288475	−	0.631673i
$26$	−1.77900	+	0.522361i	−0.348890	+	0.102443i
$27$	−1.46431	+	1.68991i	−0.281807	+	0.325223i
$28$	−4.40486	−	2.83083i	−0.832440	−	0.534977i
$29$	1.96458	+	2.26725i	0.364814	+	0.421018i	0.908247	−	0.418435i	$-0.137421\pi$
$29$	1.96458	+	2.26725i	0.364814	+	0.421018i	−0.543433	+	0.839453i	$0.682876\pi$
$30$	0.243103	+	1.69082i	0.0443843	+	0.308700i
$31$	−6.43647	−	1.88992i	−1.15602	−	0.339440i	−0.353138	−	0.935571i	$-0.614885\pi$
$31$	−6.43647	−	1.88992i	−1.15602	−	0.339440i	−0.802887	+	0.596132i	$0.796704\pi$
$32$	4.72619	−	3.03734i	0.835480	−	0.536931i
$33$	−1.66625	+	11.5890i	−0.290057	+	2.01739i
$34$	0.196132	−	0.429470i	0.0336364	−	0.0736535i
$35$	1.66166	−	3.63853i	0.280872	−	0.615023i
$36$	0.460540	−	3.20313i	0.0767567	−	0.533855i
$37$	−1.03985	+	0.668269i	−0.170950	+	0.109863i	−0.623318	−	0.781969i	$-0.714216\pi$
$37$	−1.03985	+	0.668269i	−0.170950	+	0.109863i	0.452368	+	0.891831i	$0.350579\pi$
$38$	1.18600	+	0.348241i	0.192394	+	0.0564921i
$39$	0.954677	+	6.63992i	0.152871	+	1.06324i
$40$	1.80999	+	2.08884i	0.286185	+	0.330275i
$41$	−2.92095	−	1.87718i	−0.456175	−	0.293166i	0.292303	−	0.956326i	$-0.405579\pi$
$41$	−2.92095	−	1.87718i	−0.456175	−	0.293166i	−0.748478	+	0.663160i	$0.769215\pi$
$42$	2.92863	−	3.37981i	0.451897	−	0.521517i
$43$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$43$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$44$	3.51945	+	7.70653i	0.530577	+	1.16180i
$45$	2.47214			0.368524
$46$		0			0
$47$	−2.23607			−0.326164			−0.163082	−	0.986613i	$-0.552144\pi$
$47$	−2.23607			−0.326164			−0.163082	+	0.986613i	$0.552144\pi$
$48$	−1.72227	−	3.77124i	−0.248588	−	0.544332i
$49$	−3.33149	+	0.978214i	−0.475927	+	0.139745i
$50$	1.40526	−	1.62176i	0.198734	−	0.229352i
$51$	−1.43703	−	0.923525i	−0.201225	−	0.129319i
$52$	3.17876	+	3.66849i	0.440815	+	0.508727i
$53$	−0.0671920	−	0.467330i	−0.00922952	−	0.0641928i	0.984686	−	0.174336i	$-0.0557780\pi$
$53$	−0.0671920	−	0.467330i	−0.00922952	−	0.0641928i	−0.993916	+	0.110144i	$0.964869\pi$
$54$	−1.32599	−	0.389345i	−0.180444	−	0.0529831i
$55$	−5.44471	+	3.49910i	−0.734164	+	0.471819i
$56$	1.02980	−	7.16242i	0.137613	−	0.957118i
$57$	1.85779	−	4.06800i	0.246071	−	0.538819i
$58$	−0.770222	+	1.68655i	−0.101135	+	0.221455i
$59$	−0.921081	+	6.40626i	−0.119915	+	0.834024i	0.837733	+	0.546080i	$0.183881\pi$
$59$	−0.921081	+	6.40626i	−0.119915	+	0.834024i	−0.957647	+	0.287944i	$0.907028\pi$
$60$	3.76220	−	2.41782i	0.485698	−	0.312139i
$61$	6.66298	+	1.95643i	0.853107	+	0.250495i	0.678915	−	0.734217i	$-0.262450\pi$
$61$	6.66298	+	1.95643i	0.853107	+	0.250495i	0.174192	+	0.984712i	$0.444269\pi$
$62$	−0.590023	−	4.10370i	−0.0749330	−	0.521170i
$63$	−4.23835	−	4.89131i	−0.533982	−	0.616248i
$64$	−0.198593	−	0.127628i	−0.0248241	−	0.0159535i
$65$	−2.42836	+	2.80247i	−0.301201	+	0.347604i
$66$	−6.94296	+	2.03864i	−0.854619	+	0.250939i
$67$	−1.14818	−	2.51416i	−0.140272	−	0.307154i	0.826438	−	0.563028i	$-0.190364\pi$
$67$	−1.14818	−	2.51416i	−0.140272	−	0.307154i	−0.966710	+	0.255875i	$0.917637\pi$
$68$	−1.23607			−0.149895
$69$		0			0
$70$	2.47214			0.295477
$71$	5.08305	+	11.1303i	0.603247	+	1.32093i	0.927098	+	0.374818i	$0.122295\pi$
$71$	5.08305	+	11.1303i	0.603247	+	1.32093i	−0.323852	+	0.946108i	$0.604978\pi$
$72$	4.29098	−	1.25995i	0.505697	−	0.148486i
$73$	−4.27484	+	4.93343i	−0.500332	+	0.577414i	−0.948597	−	0.316487i	$-0.897497\pi$
$73$	−4.27484	+	4.93343i	−0.500332	+	0.577414i	0.448265	+	0.893901i	$0.352042\pi$
$74$	−0.642661	−	0.413013i	−0.0747078	−	0.0480118i
$75$	−5.08429	−	5.86759i	−0.587084	−	0.677531i
$76$	−0.460540	−	3.20313i	−0.0528276	−	0.367424i
$77$	16.2579	+	4.77375i	1.85276	+	0.544020i
$78$	−3.48775	+	2.24144i	−0.394910	+	0.253793i
$79$	1.55753	−	10.8329i	0.175236	−	1.21879i	−0.692370	−	0.721542i	$-0.743434\pi$
$79$	1.55753	−	10.8329i	0.175236	−	1.21879i	0.867606	−	0.497251i	$-0.165657\pi$
$80$	0.952046	−	2.08469i	0.106442	−	0.233076i
$81$	−4.56957	+	10.0060i	−0.507729	+	1.11177i
$82$	0.305393	−	2.12406i	0.0337250	−	0.234563i
$83$	−7.37269	+	4.73814i	−0.809258	+	0.520078i	−0.878625	−	0.477513i	$-0.841538\pi$
$83$	−7.37269	+	4.73814i	−0.809258	+	0.520078i	0.0693670	+	0.997591i	$0.477902\pi$
$84$	−11.2339	−	3.29858i	−1.22572	−	0.359905i
$85$	−0.134384	−	0.934661i	−0.0145760	−	0.101378i
$86$		0			0
$87$	5.64330	+	3.62673i	0.605025	+	0.388826i
$88$	−7.66724	+	8.84847i	−0.817331	+	0.943250i
$89$	10.0479	−	2.95034i	1.06508	−	0.312736i	0.298185	−	0.954508i	$-0.403619\pi$
$89$	10.0479	−	2.95034i	1.06508	−	0.312736i	0.766895	+	0.641773i	$0.221801\pi$
$90$	0.634698	+	1.38979i	0.0669030	+	0.146497i
$91$	9.70820			1.01770
$92$		0			0
$93$	−15.0000			−1.55543
$94$	−0.574089	−	1.25708i	−0.0592128	−	0.129658i
$95$	2.37200	−	0.696481i	0.243362	−	0.0714575i
$96$	8.22656	−	9.49396i	0.839620	−	0.968973i
$97$	14.8971	+	9.57378i	1.51257	+	0.972070i	0.993060	+	0.117605i	$0.0375218\pi$
$97$	14.8971	+	9.57378i	1.51257	+	0.972070i	0.519510	+	0.854464i	$0.326115\pi$
$98$	−1.40526	−	1.62176i	−0.141953	−	0.163823i
$99$	1.49034	+	10.3655i	0.149785	+	1.04178i
$100$	−5.39046	−	1.58278i	−0.539046	−	0.158278i
$101$	3.76220	−	2.41782i	0.374353	−	0.240582i	−0.339912	−	0.940457i	$-0.610397\pi$
$101$	3.76220	−	2.41782i	0.374353	−	0.240582i	0.714265	+	0.699875i	$0.246761\pi$
$102$	0.150246	−	1.04498i	0.0148765	−	0.103469i
$103$	−1.73658	+	3.80257i	−0.171110	+	0.374678i	−0.975687	−	0.219170i	$-0.929665\pi$
$103$	−1.73658	+	3.80257i	−0.171110	+	0.374678i	0.804577	+	0.593849i	$0.202392\pi$
$104$	−2.78669	+	6.10200i	−0.273257	+	0.598350i
$105$	1.27290	−	8.85323i	0.124223	−	0.863987i
$106$	0.245474	−	0.157757i	0.0238426	−	0.0153227i
$107$	−12.8729	−	3.77984i	−1.24447	−	0.365411i	−0.407780	−	0.913080i	$-0.633697\pi$
$107$	−12.8729	−	3.77984i	−1.24447	−	0.365411i	−0.836695	+	0.547669i	$0.815515\pi$
$108$	0.514900	+	3.58121i	0.0495463	+	0.344602i
$109$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$109$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$110$	−3.36501	−	2.16256i	−0.320842	−	0.206192i
$111$	−1.80999	+	2.08884i	−0.171797	+	0.198264i
$112$	−5.75696	+	1.69040i	−0.543981	+	0.159727i
$113$	3.64067	+	7.97195i	0.342485	+	0.749938i	0.999994	−	0.00350886i	$-0.00111691\pi$
$113$	3.64067	+	7.97195i	0.342485	+	0.749938i	−0.657509	+	0.753447i	$0.728390\pi$
$114$	2.76393			0.258866
$115$		0			0
$116$	4.85410			0.450692
$117$	2.49249	+	5.45779i	0.230431	+	0.504573i
$118$	−3.83797	+	1.12693i	−0.353314	+	0.103742i
$119$	−1.61890	+	1.86832i	−0.148405	+	0.171268i
$120$	5.19923	+	3.34134i	0.474623	+	0.305022i
$121$	−10.7505	−	12.4067i	−0.977315	−	1.12788i
$122$	0.610786	+	4.24811i	0.0552980	+	0.384606i
$123$	−7.44944	−	2.18735i	−0.671693	−	0.197227i
$124$	−9.13105	+	5.86817i	−0.819993	+	0.526977i
$125$	1.49034	−	10.3655i	0.133300	−	0.927123i
$126$	1.66166	−	3.63853i	0.148032	−	0.324146i
$127$	−3.02912	+	6.63285i	−0.268791	+	0.588570i	−0.995108	−	0.0987892i	$-0.968503\pi$
$127$	−3.02912	+	6.63285i	−0.268791	+	0.588570i	0.726317	+	0.687360i	$0.241230\pi$
$128$	1.61982	−	11.2661i	0.143173	−	0.995793i
$129$		0			0
$130$	−2.19896	−	0.645674i	−0.192862	−	0.0566293i
$131$	−2.66246	−	18.5178i	−0.232620	−	1.61791i	−0.686697	−	0.726944i	$-0.740940\pi$
$131$	−2.66246	−	18.5178i	−0.232620	−	1.61791i	0.454077	−	0.890962i	$-0.349969\pi$
$132$	12.4059	+	14.3171i	1.07979	+	1.24615i
$133$	−5.44471	−	3.49910i	−0.472116	−	0.303411i
$134$	1.11864	−	1.29097i	0.0966354	−	0.111523i
$135$	−2.65197	+	0.778690i	−0.228246	+	0.0670189i
$136$	−0.709614	−	1.55384i	−0.0608489	−	0.133240i
$137$	−21.8885			−1.87006			−0.935032	−	0.354563i	$-0.884630\pi$
$137$	−21.8885			−1.87006			−0.935032	+	0.354563i	$0.884630\pi$
$138$		0			0
$139$	−10.7082			−0.908258			−0.454129	−	0.890936i	$-0.650049\pi$
$139$	−10.7082			−0.908258			−0.454129	+	0.890936i	$0.650049\pi$
$140$	−2.68862	−	5.88726i	−0.227230	−	0.497564i
$141$	−4.79746	+	1.40866i	−0.404019	+	0.118631i
$142$	−4.95226	+	5.71521i	−0.415584	+	0.479610i
$143$	−13.2146	−	8.49250i	−1.10506	−	0.710178i
$144$	−2.42836	−	2.80247i	−0.202363	−	0.233539i
$145$	0.527732	+	3.67046i	0.0438258	+	0.304815i
$146$	−3.87102	−	1.13663i	−0.320368	−	0.0940685i
$147$	−6.53144	+	4.19750i	−0.538704	+	0.346204i
$148$	−0.284630	+	1.97964i	−0.0233964	+	0.162726i
$149$	9.92366	−	21.7298i	0.812978	−	1.78017i	0.218936	−	0.975739i	$-0.429741\pi$
$149$	9.92366	−	21.7298i	0.812978	−	1.78017i	0.594042	−	0.804434i	$-0.297531\pi$
$150$	1.99332	−	4.36475i	0.162754	−	0.356381i
$151$	−0.602855	+	4.19295i	−0.0490597	+	0.341218i	0.950477	+	0.310794i	$0.100595\pi$
$151$	−0.602855	+	4.19295i	−0.0490597	+	0.341218i	−0.999537	+	0.0304239i	$0.990314\pi$
$152$	3.76220	−	2.41782i	0.305155	−	0.196111i
$153$	−1.46597	−	0.430449i	−0.118517	−	0.0347997i
$154$	1.49034	+	10.3655i	0.120095	+	0.835279i
$155$	−5.42997	−	6.26652i	−0.436146	−	0.503339i
$156$	9.13105	+	5.86817i	0.731069	+	0.469830i
$157$	7.47616	−	8.62795i	0.596662	−	0.688585i	−0.374439	−	0.927251i	$-0.622165\pi$
$157$	7.47616	−	8.62795i	0.596662	−	0.688585i	0.971102	+	0.238666i	$0.0767102\pi$
$158$	6.48995	−	1.90562i	0.516312	−	0.151603i
$159$	−0.438565	−	0.960324i	−0.0347805	−	0.0761587i
$160$	6.94427			0.548993
$161$		0			0
$162$	−6.79837			−0.534131
$163$	−2.39442	−	5.24306i	−0.187546	−	0.410668i	0.792381	−	0.610027i	$-0.208841\pi$
$163$	−2.39442	−	5.24306i	−0.187546	−	0.410668i	−0.979927	+	0.199359i	$0.936114\pi$
$164$	−5.39046	+	1.58278i	−0.420925	+	0.123595i
$165$	−9.47723	+	10.9373i	−0.737802	+	0.851468i
$166$	−4.55657	−	2.92833i	−0.353659	−	0.227283i
$167$	−1.00054	−	1.15468i	−0.0774240	−	0.0893520i	0.715716	−	0.698392i	$-0.246101\pi$
$167$	−1.00054	−	1.15468i	−0.0774240	−	0.0893520i	−0.793140	+	0.609039i	$0.791555\pi$
$168$	−2.30270	−	16.0156i	−0.177657	−	1.23563i
$169$	3.83797	+	1.12693i	0.295229	+	0.0866869i
$170$	0.490949	−	0.315514i	0.0376541	−	0.0241988i
$171$	0.569259	−	3.95929i	0.0435324	−	0.302774i
$172$		0			0
$173$	9.53140	−	20.8708i	0.724659	−	1.58678i	−0.0825999	−	0.996583i	$-0.526322\pi$
$173$	9.53140	−	20.8708i	0.724659	−	1.58678i	0.807258	−	0.590198i	$-0.200950\pi$
$174$	−0.590023	+	4.10370i	−0.0447295	+	0.311101i
$175$	−9.45238	+	6.07468i	−0.714533	+	0.459202i
$176$	9.31495	+	2.73512i	0.702141	+	0.206167i
$177$	2.05960	+	14.3248i	0.154809	+	1.07672i
$178$	4.23835	+	4.89131i	0.317678	+	0.366619i
$179$	0.595779	+	0.382884i	0.0445306	+	0.0286181i	0.562717	−	0.826650i	$-0.309756\pi$
$179$	0.595779	+	0.382884i	0.0445306	+	0.0286181i	−0.518186	+	0.855268i	$0.673393\pi$
$180$	2.61944	−	3.02300i	0.195242	−	0.225321i
$181$	−15.9779	+	4.69154i	−1.18763	+	0.348720i	−0.815111	−	0.579305i	$-0.803324\pi$
$181$	−15.9779	+	4.69154i	−1.18763	+	0.348720i	−0.372519	+	0.928024i	$0.621506\pi$
$182$	2.49249	+	5.45779i	0.184756	+	0.404558i
$183$	15.5279			1.14785
$184$		0			0
$185$	−1.52786			−0.112331
$186$	−3.85111	−	8.43275i	−0.282377	−	0.618319i
$187$	3.83797	−	1.12693i	0.280660	−	0.0824093i
$188$	−2.36931	+	2.73433i	−0.172800	+	0.199421i
$189$	6.08737	+	3.91211i	0.442791	+	0.284564i
$190$	1.00054	+	1.15468i	0.0725867	+	0.0837695i
$191$	3.72585	+	25.9139i	0.269593	+	1.87506i	0.452260	+	0.891886i	$0.350618\pi$
$191$	3.72585	+	25.9139i	0.269593	+	1.87506i	−0.182667	+	0.983175i	$0.558473\pi$
$192$	−0.506482	−	0.148716i	−0.0365522	−	0.0107327i
$193$	8.36565	−	5.37628i	0.602173	−	0.386993i	−0.203742	−	0.979025i	$-0.565310\pi$
$193$	8.36565	−	5.37628i	0.602173	−	0.386993i	0.805915	+	0.592032i	$0.201674\pi$
$194$	−1.55753	+	10.8329i	−0.111824	+	0.777755i
$195$	−3.44454	+	7.54248i	−0.246668	+	0.540128i
$196$	−2.33382	+	5.11034i	−0.166701	+	0.365025i
$197$	0.209507	−	1.45715i	0.0149267	−	0.103818i	−0.980996	−	0.194028i	$-0.937845\pi$
$197$	0.209507	−	1.45715i	0.0149267	−	0.103818i	0.995923	+	0.0902101i	$0.0287539\pi$
$198$	−5.44471	+	3.49910i	−0.386938	+	0.248670i
$199$	11.7939	+	3.46300i	0.836047	+	0.245485i	0.671613	−	0.740903i	$-0.265602\pi$
$199$	11.7939	+	3.46300i	0.836047	+	0.245485i	0.164434	+	0.986388i	$0.447420\pi$
$200$	−1.10492	−	7.68491i	−0.0781298	−	0.543405i
$201$	−4.04726	−	4.67079i	−0.285472	−	0.329452i
$202$	2.32517	+	1.49429i	0.163598	+	0.105138i
$203$	6.35752	−	7.33697i	0.446211	−	0.514954i
$204$	−2.65197	+	0.778690i	−0.185675	+	0.0545192i
$205$	−1.78288	−	3.90396i	−0.124521	−	0.272664i
$206$	−2.58359			−0.180007
$207$		0			0
$208$	5.56231			0.385677
$209$	4.35028	+	9.52579i	0.300915	+	0.658913i
$210$	5.30395	−	1.55738i	0.366007	−	0.107469i
$211$	15.3345	−	17.6969i	1.05567	−	1.21831i	0.0805216	−	0.996753i	$-0.474341\pi$
$211$	15.3345	−	17.6969i	1.05567	−	1.21831i	0.975148	−	0.221555i	$-0.0711132\pi$
$212$	−0.642661	−	0.413013i	−0.0441381	−	0.0283658i
$213$	17.9174	+	20.6778i	1.22768	+	1.41682i
$214$	−1.18005	−	8.20740i	−0.0806663	−	0.561046i
$215$		0			0
$216$	−4.20627	+	2.70320i	−0.286200	+	0.183930i
$217$	−3.08940	+	21.4872i	−0.209722	+	1.45865i
$218$		0			0
$219$	−6.06371	+	13.2777i	−0.409747	+	0.897222i
$220$	−1.49034	+	10.3655i	−0.100479	+	0.698845i
$221$	1.92798	−	1.23904i	0.129690	−	0.0833467i
$222$	−1.63901	−	0.481257i	−0.110003	−	0.0322998i
$223$	−0.569259	−	3.95929i	−0.0381204	−	0.265133i	0.961844	−	0.273599i	$-0.0882142\pi$
$223$	−0.569259	−	3.95929i	−0.0381204	−	0.265133i	−0.999964	+	0.00846600i	$0.997305\pi$
$224$	−11.9056	−	13.7398i	−0.795476	−	0.918028i
$225$	−5.84189	−	3.75436i	−0.389460	−	0.250290i
$226$	−3.54699	+	4.09345i	−0.235942	+	0.272292i
$227$	11.6870	−	3.43160i	0.775690	−	0.227763i	0.130155	−	0.991494i	$-0.458453\pi$
$227$	11.6870	−	3.43160i	0.775690	−	0.227763i	0.645535	+	0.763730i	$0.276634\pi$
$228$	−3.00597	−	6.58216i	−0.199075	−	0.435914i
$229$	−12.0000			−0.792982			−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000			−0.792982			−0.396491	+	0.918039i	$0.629772\pi$
$230$		0			0
$231$	37.8885			2.49288
$232$	2.78669	+	6.10200i	0.182955	+	0.400616i
$233$	6.26344	−	1.83911i	0.410332	−	0.120484i	−0.0700507	−	0.997543i	$-0.522316\pi$
$233$	6.26344	−	1.83911i	0.410332	−	0.120484i	0.480382	+	0.877059i	$0.340498\pi$
$234$	−2.42836	+	2.80247i	−0.158747	+	0.183203i
$235$	−2.32517	−	1.49429i	−0.151677	−	0.0974770i
$236$	6.85779	+	7.91431i	0.446404	+	0.515178i
$237$	−3.48275	−	24.2230i	−0.226229	−	1.57346i
$238$	−1.46597	−	0.430449i	−0.0950250	−	0.0279019i
$239$	11.5790	−	7.44134i	0.748980	−	0.481340i	−0.109628	−	0.993973i	$-0.534966\pi$
$239$	11.5790	−	7.44134i	0.748980	−	0.481340i	0.858608	+	0.512632i	$0.171330\pi$
$240$	0.729308	−	5.07245i	0.0470766	−	0.327425i
$241$	−9.60631	+	21.0349i	−0.618797	+	1.35498i	0.297594	+	0.954692i	$0.403816\pi$
$241$	−9.60631	+	21.0349i	−0.618797	+	1.35498i	−0.916391	+	0.400284i	$0.868912\pi$
$242$	4.21476	−	9.22903i	0.270935	−	0.593265i
$243$	−2.54581	+	17.7065i	−0.163313	+	1.13587i
$244$	9.45238	−	6.07468i	0.605127	−	0.388891i
$245$	−4.11795	−	1.20914i	−0.263086	−	0.0772490i
$246$	−0.682880	−	4.74953i	−0.0435388	−	0.302819i
$247$	3.92916	+	4.53450i	0.250007	+	0.288523i
$248$	−12.6188	−	8.10961i	−0.801295	−	0.514961i
$249$	−12.8331	+	14.8102i	−0.813267	+	0.938560i
$250$	6.20997	−	1.82341i	0.392753	−	0.115323i
$251$	0.952046	+	2.08469i	0.0600926	+	0.131585i	0.937296	−	0.348535i	$-0.113321\pi$
$251$	0.952046	+	2.08469i	0.0600926	+	0.131585i	−0.877203	+	0.480119i	$0.840593\pi$
$252$	−10.4721			−0.659683
$253$		0			0
$254$	−4.50658			−0.282768
$255$	−0.877131	−	1.92065i	−0.0549280	−	0.120276i
$256$	6.29649	−	1.84882i	0.393530	−	0.115551i
$257$	4.89321	−	5.64706i	0.305230	−	0.352254i	−0.582325	−	0.812956i	$-0.697857\pi$
$257$	4.89321	−	5.64706i	0.305230	−	0.352254i	0.887555	+	0.460702i	$0.152402\pi$
$258$		0			0
$259$	2.61944	+	3.02300i	0.162764	+	0.187840i
$260$	0.853889	+	5.93893i	0.0529559	+	0.368317i
$261$	5.75696	+	1.69040i	0.356347	+	0.104633i
$262$	9.72683	−	6.25105i	0.600926	−	0.386191i
$263$	−0.419014	+	2.91430i	−0.0258375	+	0.179704i	−0.998654	−	0.0518754i	$-0.983480\pi$
$263$	−0.419014	+	2.91430i	−0.0258375	+	0.179704i	0.972816	+	0.231579i	$0.0743892\pi$
$264$	−10.8757	+	23.8145i	−0.669353	+	1.46568i
$265$	0.242433	−	0.530854i	0.0148925	−	0.0326101i
$266$	0.569259	−	3.95929i	0.0349035	−	0.242759i
$267$	19.6991	−	12.6599i	1.20557	−	0.774771i
$268$	−4.29098	−	1.25995i	−0.262114	−	0.0769635i
$269$	1.13059	+	7.86341i	0.0689332	+	0.479441i	0.994821	+	0.101642i	$0.0324097\pi$
$269$	1.13059	+	7.86341i	0.0689332	+	0.479441i	−0.925888	+	0.377798i	$0.876681\pi$
$270$	−1.11864	−	1.29097i	−0.0680780	−	0.0785662i
$271$	6.73003	+	4.32513i	0.408820	+	0.262733i	0.728848	−	0.684675i	$-0.240056\pi$
$271$	6.73003	+	4.32513i	0.408820	+	0.262733i	−0.320028	+	0.947408i	$0.603692\pi$
$272$	−0.927550	+	1.07045i	−0.0562410	+	0.0649055i
$273$	20.8289	−	6.11591i	1.26062	−	0.370152i
$274$	−5.61968	−	12.3054i	−0.339497	−	0.743395i
$275$	18.1803			1.09632
$276$		0			0
$277$	15.4721			0.929631			0.464815	−	0.885408i	$-0.346121\pi$
$277$	15.4721			0.929631			0.464815	+	0.885408i	$0.346121\pi$
$278$	−2.74923	−	6.01998i	−0.164888	−	0.361054i
$279$	−12.8729	+	3.77984i	−0.770683	+	0.226293i
$280$	5.85725	−	6.75963i	0.350038	−	0.403965i
$281$	−7.37269	−	4.73814i	−0.439818	−	0.282654i	0.301933	−	0.953329i	$-0.402368\pi$
$281$	−7.37269	−	4.73814i	−0.439818	−	0.282654i	−0.741751	+	0.670675i	$0.766004\pi$
$282$	−2.02363	−	2.33539i	−0.120505	−	0.139071i
$283$	−3.94329	−	27.4262i	−0.234404	−	1.63032i	−0.678685	−	0.734429i	$-0.737450\pi$
$283$	−3.94329	−	27.4262i	−0.234404	−	1.63032i	0.444281	−	0.895887i	$-0.353459\pi$
$284$	18.9964	+	5.57785i	1.12723	+	0.330984i
$285$	4.65034	−	2.98859i	0.275462	−	0.177029i
$286$	1.38162	−	9.60939i	0.0816970	−	0.568215i
$287$	−4.66763	+	10.2207i	−0.275522	+	0.603308i
$288$	4.66763	−	10.2207i	0.275043	−	0.602260i
$289$	2.33630	−	16.2493i	0.137429	−	0.955842i
$290$	−1.92798	+	1.23904i	−0.113215	+	0.0727588i
$291$	37.9928	+	11.1557i	2.22718	+	0.653958i
$292$	1.50317	+	10.4548i	0.0879665	+	0.611821i
$293$	1.00054	+	1.15468i	0.0584521	+	0.0674573i	0.784223	−	0.620480i	$-0.213062\pi$
$293$	1.00054	+	1.15468i	0.0584521	+	0.0674573i	−0.725771	+	0.687937i	$0.758517\pi$
$294$	−4.03665	−	2.59420i	−0.235422	−	0.151297i
$295$	−5.23889	+	6.04600i	−0.305020	+	0.352012i
$296$	−2.65197	+	0.778690i	−0.154143	+	0.0452604i
$297$	−4.86376	−	10.6502i	−0.282224	−	0.617985i
$298$	14.7639			0.855252
$299$		0			0
$300$	−12.5623			−0.725285
$301$		0			0
$302$	−2.51199	+	0.737585i	−0.144549	+	0.0424433i
$303$	6.54861	−	7.55750i	0.376208	−	0.434167i
$304$	−3.11954	−	2.00481i	−0.178918	−	0.114984i
$305$	5.62106	+	6.48705i	0.321861	+	0.371447i
$306$	−0.134384	−	0.934661i	−0.00768222	−	0.0534310i
$307$	−9.14192	−	2.68431i	−0.521757	−	0.153202i	0.0102406	−	0.999948i	$-0.496740\pi$
$307$	−9.14192	−	2.68431i	−0.521757	−	0.153202i	−0.531997	+	0.846746i	$0.678558\pi$
$308$	23.0641	−	14.8224i	1.31420	−	0.844586i
$309$	−1.33029	+	9.25238i	−0.0756776	+	0.526349i
$310$	2.12884	−	4.66151i	0.120910	−	0.264756i
$311$	5.47531	−	11.9893i	0.310476	−	0.679848i	−0.688493	−	0.725243i	$-0.741727\pi$
$311$	5.47531	−	11.9893i	0.310476	−	0.679848i	0.998969	+	0.0453948i	$0.0144546\pi$
$312$	−2.13472	+	14.8473i	−0.120855	+	0.840564i
$313$	20.4935	−	13.1704i	1.15836	−	0.744434i	0.187075	−	0.982346i	$-0.440099\pi$
$313$	20.4935	−	13.1704i	1.15836	−	0.744434i	0.971287	+	0.237912i	$0.0764630\pi$
$314$	6.76992	+	1.98783i	0.382049	+	0.112180i
$315$	−1.13852	−	7.91857i	−0.0641483	−	0.446161i
$316$	−11.5964	−	13.3830i	−0.652349	−	0.752851i
$317$	21.3816	+	13.7411i	1.20091	+	0.771780i	0.979114	−	0.203313i	$-0.0651708\pi$
$317$	21.3816	+	13.7411i	1.20091	+	0.771780i	0.221799	+	0.975092i	$0.428807\pi$
$318$	0.427281	−	0.493108i	0.0239607	−	0.0276521i
$319$	−15.0719	+	4.42551i	−0.843865	+	0.247781i
$320$	−0.121216	−	0.265427i	−0.00677621	−	0.0148378i
$321$	−30.0000			−1.67444
$322$		0			0
$323$	−1.52786			−0.0850126
$324$	7.39371	+	16.1900i	0.410762	+	0.899443i
$325$	9.99447	−	2.93464i	0.554393	−	0.162785i
$326$	2.33281	−	2.69221i	0.129203	−	0.149108i
$327$		0			0
$328$	−5.08429	−	5.86759i	−0.280733	−	0.323983i
$329$	1.02980	+	7.16242i	0.0567747	+	0.394877i
$330$	−8.58197	−	2.51989i	−0.472422	−	0.138716i
$331$	−16.5327	+	10.6249i	−0.908720	+	0.583999i	−0.909364	−	0.416001i	$-0.863431\pi$
$331$	−16.5327	+	10.6249i	−0.908720	+	0.583999i	0.000644066		1.00000i	$0.499795\pi$
$332$	−2.01807	+	14.0360i	−0.110756	+	0.770326i
$333$	−1.02696	+	2.24873i	−0.0562772	+	0.123230i
$334$	0.392265	−	0.858940i	0.0214638	−	0.0469991i
$335$	0.486206	−	3.38163i	0.0265642	−	0.184758i
$336$	−11.2866	+	7.25346i	−0.615735	+	0.395709i
$337$	−22.4679	−	6.59716i	−1.22390	−	0.359370i	−0.394958	−	0.918699i	$-0.629241\pi$
$337$	−22.4679	−	6.59716i	−1.22390	−	0.359370i	−0.828946	+	0.559329i	$0.811059\pi$
$338$	0.351822	+	2.44697i	0.0191366	+	0.133098i
$339$	12.8331	+	14.8102i	0.697001	+	0.804381i
$340$	−1.28532	−	0.826026i	−0.0697063	−	0.0447975i
$341$	23.0017	−	26.5454i	1.24561	−	1.43751i
$342$	2.37200	−	0.696481i	0.128263	−	0.0376614i
$343$	−4.74255	−	10.3847i	−0.256073	−	0.560723i
$344$		0			0
$345$		0			0
$346$	14.1803			0.762340
$347$	−4.10785	−	8.99494i	−0.220521	−	0.482873i	0.766745	−	0.641952i	$-0.221875\pi$
$347$	−4.10785	−	8.99494i	−0.220521	−	0.482873i	−0.987266	+	0.159078i	$0.949148\pi$
$348$	10.4144	−	3.05795i	0.558272	−	0.163924i
$349$	−15.9893	+	18.4527i	−0.855890	+	0.987750i	−0.999998	−	0.00181209i	$-0.999423\pi$
$349$	−15.9893	+	18.4527i	−0.855890	+	0.987750i	0.144108	+	0.989562i	$0.453969\pi$
$350$	−5.84189	−	3.75436i	−0.312262	−	0.200679i
$351$	−4.39294	−	5.06972i	−0.234478	−	0.270602i
$352$	4.18639	+	29.1170i	0.223135	+	1.55194i
$353$	−8.98151	−	2.63721i	−0.478037	−	0.140364i	0.0338324	−	0.999428i	$-0.489229\pi$
$353$	−8.98151	−	2.63721i	−0.478037	−	0.140364i	−0.511870	+	0.859063i	$0.671047\pi$
$354$	−7.52440	+	4.83564i	−0.399917	+	0.257011i
$355$	−2.15246	+	14.9707i	−0.114241	+	0.794560i
$356$	7.03890	−	15.4131i	0.373061	−	0.816890i
$357$	−2.29636	+	5.02832i	−0.121536	+	0.266127i
$358$	−0.0622904	+	0.433239i	−0.00329215	+	0.0228974i
$359$	−16.7313	+	10.7526i	−0.883045	+	0.567498i	−0.901717	−	0.432327i	$-0.857693\pi$
$359$	−16.7313	+	10.7526i	−0.883045	+	0.567498i	0.0186721	+	0.999826i	$0.494056\pi$
$360$	5.30395	+	1.55738i	0.279543	+	0.0820811i
$361$	2.13472	+	14.8473i	0.112354	+	0.781438i
$362$	−6.73969	−	7.77802i	−0.354230	−	0.408804i
$363$	−30.8809	−	19.8460i	−1.62083	−	1.04164i
$364$	10.2867	−	11.8715i	0.539169	−	0.622234i
$365$	−7.74204	+	2.27327i	−0.405237	+	0.118988i
$366$	3.98663	+	8.72951i	0.208385	+	0.456299i
$367$	−4.18034			−0.218212			−0.109106	−	0.994030i	$-0.534799\pi$
$367$	−4.18034			−0.218212			−0.109106	+	0.994030i	$0.534799\pi$
$368$		0			0
$369$	−6.94427			−0.361504
$370$	−0.392265	−	0.858940i	−0.0203929	−	0.0446542i
$371$	−1.46597	+	0.430449i	−0.0761096	+	0.0223478i
$372$	−15.8938	+	18.3424i	−0.824055	+	0.951011i
$373$	6.48455	+	4.16737i	0.335757	+	0.215778i	0.697645	−	0.716443i	$-0.254231\pi$
$373$	6.48455	+	4.16737i	0.335757	+	0.215778i	−0.361888	+	0.932222i	$0.617868\pi$
$374$	1.61890	+	1.86832i	0.0837116	+	0.0966083i
$375$	−3.33250	−	23.1781i	−0.172090	−	1.19691i
$376$	−4.79746	−	1.40866i	−0.247410	−	0.0726462i
$377$	−7.57128	+	4.86577i	−0.389941	+	0.250600i
$378$	−0.636451	+	4.42662i	−0.0327355	+	0.227681i
$379$	10.1198	−	22.1593i	0.519819	−	1.13824i	−0.449689	−	0.893185i	$-0.648465\pi$
$379$	10.1198	−	22.1593i	0.519819	−	1.13824i	0.969508	−	0.245059i	$-0.0788074\pi$
$380$	1.66166	−	3.63853i	0.0852414	−	0.186653i
$381$	−2.32044	+	16.1390i	−0.118880	+	0.826826i
$382$	−13.6118	+	8.74775i	−0.696439	+	0.447574i
$383$	−6.76992	−	1.98783i	−0.345927	−	0.101573i	0.104154	−	0.994561i	$-0.466787\pi$
$383$	−6.76992	−	1.98783i	−0.345927	−	0.101573i	−0.450081	+	0.892988i	$0.648605\pi$
$384$	−3.62203	−	25.1918i	−0.184836	−	1.28556i
$385$	13.7156	+	15.8286i	0.699011	+	0.806701i
$386$	5.17026	+	3.32272i	0.263159	+	0.169122i
$387$		0			0
$388$	27.4918	−	8.07234i	1.39569	−	0.409811i
$389$	10.6047	+	23.2210i	0.537678	+	1.17735i	0.962303	+	0.271980i	$0.0876786\pi$
$389$	10.6047	+	23.2210i	0.537678	+	1.17735i	−0.424625	+	0.905369i	$0.639594\pi$
$390$	−5.12461			−0.259495
$391$		0			0
$392$	−7.76393			−0.392138
$393$	−17.3780	−	38.0525i	−0.876603	−	1.91949i
$394$	0.872976	−	0.256329i	0.0439799	−	0.0129137i
$395$	8.85887	−	10.2237i	0.445738	−	0.514409i
$396$	14.2544	+	9.16077i	0.716312	+	0.460346i
$397$	15.9893	+	18.4527i	0.802482	+	0.926114i	0.998515	−	0.0544835i	$-0.0173512\pi$
$397$	15.9893	+	18.4527i	0.802482	+	0.926114i	−0.196032	+	0.980597i	$0.562806\pi$
$398$	1.08113	+	7.51942i	0.0541921	+	0.376915i
$399$	−13.8859	−	4.07727i	−0.695165	−	0.204119i
$400$	−5.41573	+	3.48048i	−0.270787	+	0.174024i
$401$	2.01807	−	14.0360i	0.100778	−	0.700925i	−0.875312	−	0.483558i	$-0.839344\pi$
$401$	2.01807	−	14.0360i	0.100778	−	0.700925i	0.976090	−	0.217367i	$-0.0697467\pi$
$402$	1.58674	−	3.47449i	0.0791396	−	0.173292i
$403$	8.36007	−	18.3060i	0.416445	−	0.911886i
$404$	1.02980	−	7.16242i	0.0512345	−	0.356343i
$405$	−11.4383	+	7.35096i	−0.568374	+	0.365272i
$406$	5.75696	+	1.69040i	0.285713	+	0.0838929i
$407$	−0.921081	−	6.40626i	−0.0456563	−	0.317546i
$408$	−2.50135	−	2.88671i	−0.123835	−	0.142913i
$409$	17.9697	+	11.5485i	0.888547	+	0.571034i	0.903373	−	0.428856i	$-0.141083\pi$
$409$	17.9697	+	11.5485i	0.888547	+	0.571034i	−0.0148262	+	0.999890i	$0.504719\pi$
$410$	1.73700	−	2.00461i	0.0857844	−	0.0990005i
$411$	−46.9617	+	13.7892i	−2.31645	+	0.680171i
$412$	2.80984	+	6.15269i	0.138431	+	0.303121i
$413$	20.9443			1.03060
$414$		0			0
$415$	−10.8328			−0.531762
$416$	7.00145	+	15.3310i	0.343274	+	0.751666i
$417$	−22.9744	+	6.74588i	−1.12506	+	0.330347i
$418$	−4.23835	+	4.89131i	−0.207304	+	0.239242i
$419$	−3.85596	−	2.47808i	−0.188376	−	0.121062i	0.443053	−	0.896495i	$-0.353895\pi$
$419$	−3.85596	−	2.47808i	−0.188376	−	0.121062i	−0.631430	+	0.775433i	$0.717532\pi$
$420$	−9.47723	−	10.9373i	−0.462442	−	0.533686i
$421$	1.46468	+	10.1870i	0.0713839	+	0.496486i	0.993879	+	0.110477i	$0.0352377\pi$
$421$	1.46468	+	10.1870i	0.0713839	+	0.496486i	−0.922495	+	0.386009i	$0.873853\pi$
$422$	13.8859	+	4.07727i	0.675956	+	0.198478i
$423$	−3.76220	+	2.41782i	−0.182924	+	0.117558i
$424$	0.150246	−	1.04498i	0.00729658	−	0.0507488i
$425$	−1.10188	+	2.41278i	−0.0534489	+	0.117037i
$426$	−7.02460	+	15.3817i	−0.340343	+	0.745247i
$427$	3.19812	−	22.2434i	0.154768	−	1.07643i
$428$	−18.2621	+	11.7363i	−0.882732	+	0.567297i
$429$	−33.7018	−	9.89575i	−1.62714	−	0.477771i
$430$		0			0
$431$	11.4783	+	13.2467i	0.552891	+	0.638070i	0.961554	−	0.274615i	$-0.0885505\pi$
$431$	11.4783	+	13.2467i	0.552891	+	0.638070i	−0.408663	+	0.912685i	$0.634005\pi$
$432$	3.48775	+	2.24144i	0.167805	+	0.107841i
$433$	−11.6694	+	13.4672i	−0.560795	+	0.647192i	−0.963364	−	0.268197i	$-0.913572\pi$
$433$	−11.6694	+	13.4672i	−0.560795	+	0.647192i	0.402569	+	0.915390i	$0.368117\pi$
$434$	−12.8729	+	3.77984i	−0.617921	+	0.181438i
$435$	3.44454	+	7.54248i	0.165153	+	0.361634i
$436$		0			0
$437$		0			0
$438$	−9.02129			−0.431054
$439$	−7.77167	−	17.0176i	−0.370922	−	0.812205i	−0.999409	−	0.0343849i	$-0.989053\pi$
$439$	−7.77167	−	17.0176i	−0.370922	−	0.812205i	0.628487	−	0.777820i	$-0.283674\pi$
$440$	−13.8859	+	4.07727i	−0.661985	+	0.194376i
$441$	−4.54753	+	5.24813i	−0.216549	+	0.249911i
$442$	1.19156	+	0.765768i	0.0566766	+	0.0364239i
$443$	−24.9663	−	28.8127i	−1.18619	−	1.36893i	−0.913506	−	0.406826i	$-0.866636\pi$
$443$	−24.9663	−	28.8127i	−1.18619	−	1.36893i	−0.272679	−	0.962105i	$-0.587910\pi$
$444$	0.636451	+	4.42662i	0.0302046	+	0.210078i
$445$	12.4199	+	3.64682i	0.588762	+	0.172876i
$446$	2.07969	−	1.33654i	0.0984763	−	0.0632869i
$447$	7.60195	−	52.8727i	0.359560	−	2.50079i
$448$	−0.317349	+	0.694897i	−0.0149933	+	0.0328308i
$449$	−6.20807	+	13.5938i	−0.292977	+	0.641531i	−0.997688	−	0.0679644i	$-0.978350\pi$
$449$	−6.20807	+	13.5938i	−0.292977	+	0.641531i	0.704711	+	0.709495i	$0.251077\pi$
$450$	0.610786	−	4.24811i	0.0287927	−	0.200258i
$451$	15.2943	−	9.82903i	0.720179	−	0.462831i
$452$	13.6059	+	3.99506i	0.639969	+	0.187912i
$453$	1.34803	+	9.37572i	0.0633358	+	0.440510i
$454$	4.92970	+	5.68918i	0.231362	+	0.267006i
$455$	10.0950	+	6.48769i	0.473263	+	0.304148i
$456$	6.54861	−	7.55750i	0.306667	−	0.353912i
$457$	4.91703	−	1.44377i	0.230009	−	0.0675367i	−0.164697	−	0.986344i	$-0.552665\pi$
$457$	4.91703	−	1.44377i	0.230009	−	0.0675367i	0.394706	+	0.918807i	$0.370846\pi$
$458$	−3.08089	−	6.74620i	−0.143960	−	0.315229i
$459$	1.70820			0.0797321
$460$		0			0
$461$	−1.47214			−0.0685642			−0.0342821	−	0.999412i	$-0.510914\pi$
$461$	−1.47214			−0.0685642			−0.0342821	+	0.999412i	$0.510914\pi$
$462$	9.72753	+	21.3003i	0.452566	+	0.990980i
$463$	19.1899	−	5.63465i	0.891828	−	0.261864i	0.196455	−	0.980513i	$-0.437057\pi$
$463$	19.1899	−	5.63465i	0.891828	−	0.261864i	0.695374	+	0.718648i	$0.255239\pi$
$464$	3.64254	−	4.20371i	0.169100	−	0.195152i
$465$	−15.5977	−	10.0240i	−0.723326	−	0.464853i
$466$	2.64200	+	3.04903i	0.122388	+	0.141243i
$467$	1.85802	+	12.9228i	0.0859791	+	0.597998i	0.986571	+	0.163332i	$0.0522243\pi$
$467$	1.85802	+	12.9228i	0.0859791	+	0.597998i	−0.900592	+	0.434665i	$0.856867\pi$
$468$	9.31495	+	2.73512i	0.430584	+	0.126431i
$469$	−7.52440	+	4.83564i	−0.347445	+	0.223289i
$470$	0.243103	−	1.69082i	0.0112135	−	0.0779916i
$471$	10.6047	−	23.2210i	0.488637	−	1.06997i
$472$	−6.01194	+	13.1643i	−0.276722	+	0.605937i
$473$		0			0
$474$	12.7236	−	8.17698i	0.584416	−	0.375581i
$475$	−6.66298	−	1.95643i	−0.305718	−	0.0897670i
$476$	0.569259	+	3.95929i	0.0260920	+	0.181474i
$477$	−0.618367	−	0.713633i	−0.0283131	−	0.0326750i
$478$	7.15619	+	4.59900i	0.327316	+	0.210354i
$479$	−20.6915	+	23.8792i	−0.945417	+	1.09107i	0.0503105	+	0.998734i	$0.483979\pi$
$479$	−20.6915	+	23.8792i	−0.945417	+	1.09107i	−0.995728	+	0.0923362i	$0.970567\pi$
$480$	14.8989	−	4.37470i	0.680038	−	0.199677i
$481$	−1.54044	−	3.37310i	−0.0702382	−	0.153800i
$482$	−14.2918			−0.650973
$483$		0			0
$484$	−26.5623			−1.20738
$485$	9.09283	+	19.9105i	0.412884	+	0.904090i
$486$	−10.6079	+	3.11476i	−0.481184	+	0.141288i
$487$	9.63183	−	11.1157i	0.436460	−	0.503701i	−0.494321	−	0.869279i	$-0.664583\pi$
$487$	9.63183	−	11.1157i	0.436460	−	0.503701i	0.930781	+	0.365578i	$0.119129\pi$
$488$	13.0629	+	8.39500i	0.591328	+	0.380024i
$489$	−8.44020	−	9.74051i	−0.381679	−	0.440481i
$490$	−0.377487	−	2.62548i	−0.0170531	−	0.118607i
$491$	−8.00939	−	2.35177i	−0.361459	−	0.106134i	0.0959602	−	0.995385i	$-0.469408\pi$
$491$	−8.00939	−	2.35177i	−0.361459	−	0.106134i	−0.457419	+	0.889251i	$0.651226\pi$
$492$	−10.5681	+	6.79170i	−0.476446	+	0.306193i
$493$	0.326157	−	2.26847i	0.0146894	−	0.102167i
$494$	−1.54044	+	3.37310i	−0.0693078	+	0.151763i
$495$	−5.37724	+	11.7745i	−0.241689	+	0.529225i
$496$	−1.77007	+	12.3111i	−0.0794784	+	0.552785i
$497$	33.3109	−	21.4076i	1.49420	−	0.960263i
$498$	−11.6209	−	3.41219i	−0.520743	−	0.152904i
$499$	−2.74551	−	19.0954i	−0.122906	−	0.854829i	−0.954237	−	0.299052i	$-0.903330\pi$
$499$	−2.74551	−	19.0954i	−0.122906	−	0.854829i	0.831331	−	0.555777i	$-0.187579\pi$
$500$	−11.0961	−	12.8056i	−0.496234	−	0.572685i
$501$	−2.87407	−	1.84705i	−0.128404	−	0.0825201i
$502$	−0.927550	+	1.07045i	−0.0413986	+	0.0477765i
$503$	25.8528	−	7.59108i	1.15272	−	0.338469i	0.351121	−	0.936330i	$-0.385801\pi$
$503$	25.8528	−	7.59108i	1.15272	−	0.338469i	0.801600	+	0.597861i	$0.203982\pi$
$504$	−6.01194	−	13.1643i	−0.267793	−	0.586385i
$505$	5.52786			0.245987
$506$		0			0
$507$	8.94427			0.397229
$508$	4.90122	+	10.7322i	0.217457	+	0.476163i
$509$	27.1584	−	7.97443i	1.20378	−	0.353460i	0.382480	−	0.923964i	$-0.375070\pi$
$509$	27.1584	−	7.97443i	1.20378	−	0.353460i	0.821295	+	0.570504i	$0.193252\pi$
$510$	0.854562	−	0.986217i	0.0378406	−	0.0436704i
$511$	17.7712	+	11.4208i	0.786150	+	0.505228i
$512$	−12.2513	−	14.1387i	−0.541435	−	0.624849i
$513$	0.636451	+	4.42662i	0.0281000	+	0.195440i
$514$	4.43097	+	1.30105i	0.195442	+	0.0573869i
$515$	−4.34691	+	2.79359i	−0.191548	+	0.123100i
$516$		0			0
$517$	4.86376	−	10.6502i	0.213908	−	0.468393i
$518$	−1.02696	+	2.24873i	−0.0451221	+	0.0988037i
$519$	7.30146	−	50.7827i	0.320498	−	2.22911i
$520$	−6.97550	+	4.48288i	−0.305896	+	0.196587i
$521$	−30.1438	−	8.85102i	−1.32062	−	0.387770i	−0.455907	−	0.890028i	$-0.650685\pi$
$521$	−30.1438	−	8.85102i	−1.32062	−	0.387770i	−0.864718	+	0.502257i	$0.832503\pi$
$522$	0.527732	+	3.67046i	0.0230982	+	0.160652i
$523$	−26.9309	−	31.0799i	−1.17761	−	1.35903i	−0.919585	−	0.392890i	$-0.871475\pi$
$523$	−26.9309	−	31.0799i	−1.17761	−	1.35903i	−0.258020	−	0.966140i	$-0.583070\pi$
$524$	−25.4652	−	16.3655i	−1.11245	−	0.714929i
$525$	−16.4531	+	18.9879i	−0.718073	+	0.828701i
$526$	−1.74595	+	0.512657i	−0.0761271	+	0.0223529i
$527$	2.12884	+	4.66151i	0.0927338	+	0.203059i
$528$	21.7082			0.944728
$529$		0			0
$530$	0.360680			0.0156669
$531$	5.37724	+	11.7745i	0.233353	+	0.510971i
$532$	−10.0479	+	2.95034i	−0.435633	+	0.127914i
$533$	6.82130	−	7.87220i	0.295463	−	0.340983i
$534$	12.1747	+	7.82423i	0.526852	+	0.338587i
$535$	−10.8599	−	12.5330i	−0.469516	−	0.541851i
$536$	−0.879554	−	6.11743i	−0.0379909	−	0.264233i
$537$	1.51945	+	0.446149i	0.0655689	+	0.0192528i
$538$	−4.13041	+	2.65445i	−0.178075	+	0.114442i
$539$	2.58733	−	17.9953i	0.111444	−	0.775112i
$540$	−1.85779	+	4.06800i	−0.0799467	+	0.175059i
$541$	−14.2971	+	31.3063i	−0.614680	+	1.34596i	0.304646	+	0.952466i	$0.401462\pi$
$541$	−14.2971	+	31.3063i	−0.614680	+	1.34596i	−0.919326	+	0.393496i	$0.871266\pi$
$542$	−0.703643	+	4.89395i	−0.0302241	+	0.210213i
$543$	−31.3250	+	20.1313i	−1.34428	+	0.863918i
$544$	−4.11795	−	1.20914i	−0.176556	−	0.0518414i
$545$		0			0
$546$	8.78588	+	10.1394i	0.376001	+	0.433928i
$547$	−24.8515	−	15.9711i	−1.06257	−	0.682874i	−0.112105	−	0.993696i	$-0.535759\pi$
$547$	−24.8515	−	15.9711i	−1.06257	−	0.682874i	−0.950468	+	0.310822i	$0.899396\pi$
$548$	−23.1928	+	26.7659i	−0.990748	+	1.14338i
$549$	13.3260	−	3.91285i	0.568738	−	0.166997i
$550$	4.66763	+	10.2207i	0.199028	+	0.435812i
$551$	6.00000			0.255609
$552$		0			0
$553$	−35.4164			−1.50606
$554$	3.97233	+	8.69818i	0.168768	+	0.369550i
$555$	−3.27802	+	0.962513i	−0.139144	+	0.0408564i
$556$	−11.3463	+	13.0943i	−0.481189	+	0.555322i
$557$	−6.23908	−	4.00961i	−0.264358	−	0.169893i	0.401747	−	0.915751i	$-0.368403\pi$
$557$	−6.23908	−	4.00961i	−0.264358	−	0.169893i	−0.666105	+	0.745858i	$0.732040\pi$
$558$	−5.42997	−	6.26652i	−0.229869	−	0.265283i
$559$		0			0
$560$	−7.11599	−	2.08944i	−0.300706	−	0.0882951i
$561$	7.52440	−	4.83564i	0.317680	−	0.204161i
$562$	0.770835	−	5.36128i	0.0325157	−	0.226152i
$563$	−13.6855	+	29.9672i	−0.576777	+	1.26297i	0.366333	+	0.930484i	$0.380613\pi$
$563$	−13.6855	+	29.9672i	−0.576777	+	1.26297i	−0.943110	+	0.332481i	$0.892114\pi$
$564$	−3.36078	+	7.35908i	−0.141514	+	0.309873i
$565$	−1.54167	+	10.7226i	−0.0648586	+	0.451101i
$566$	14.4061	−	9.25826i	0.605535	−	0.389154i
$567$	34.1548	+	10.0288i	1.43437	+	0.421168i
$568$	3.89383	+	27.0822i	0.163382	+	1.13634i
$569$	14.5250	+	16.7628i	0.608921	+	0.702732i	0.973564	−	0.228415i	$-0.0733543\pi$
$569$	14.5250	+	16.7628i	0.608921	+	0.702732i	−0.364643	+	0.931148i	$0.618809\pi$
$570$	2.87407	+	1.84705i	0.120381	+	0.0773644i
$571$	9.35914	−	10.8010i	0.391668	−	0.452009i	−0.525332	−	0.850898i	$-0.676059\pi$
$571$	9.35914	−	10.8010i	0.391668	−	0.452009i	0.916999	+	0.398889i	$0.130604\pi$
$572$	−24.3869	+	7.16063i	−1.01967	+	0.299401i
$573$	24.3188	+	53.2508i	1.01593	+	2.22458i
$574$	−6.94427			−0.289848
$575$		0			0
$576$	−0.472136			−0.0196723
$577$	9.50824	+	20.8202i	0.395833	+	0.866754i	0.997676	+	0.0681394i	$0.0217063\pi$
$577$	9.50824	+	20.8202i	0.395833	+	0.866754i	−0.601842	+	0.798615i	$0.705566\pi$
$578$	9.73492	−	2.85843i	0.404919	−	0.118895i
$579$	14.5615	−	16.8049i	0.605156	−	0.698388i
$580$	5.04752	+	3.24384i	0.209587	+	0.134693i
$581$	18.5723	+	21.4336i	0.770509	+	0.889214i
$582$	3.48275	+	24.2230i	0.144365	+	1.00408i
$583$	2.37200	+	0.696481i	0.0982381	+	0.0288453i
$584$	−12.2796	+	7.89160i	−0.508132	+	0.326557i
$585$	−1.05546	+	7.34092i	−0.0436381	+	0.303510i
$586$	−0.392265	+	0.858940i	−0.0162043	+	0.0354825i
$587$	−10.2642	+	22.4754i	−0.423647	+	0.927658i	0.570668	+	0.821181i	$0.306684\pi$
$587$	−10.2642	+	22.4754i	−0.423647	+	0.927658i	−0.994315	+	0.106477i	$0.966043\pi$
$588$	−1.78780	+	12.4344i	−0.0737277	+	0.512788i
$589$	−11.2866	+	7.25346i	−0.465056	+	0.298874i
$590$	−4.74399	−	1.39296i	−0.195307	−	0.0573474i
$591$	−0.468471	−	3.25829i	−0.0192703	−	0.134028i
$592$	1.50081	+	1.73202i	0.0616828	+	0.0711857i
$593$	−2.47688	−	1.59179i	−0.101713	−	0.0653671i	0.488795	−	0.872398i	$-0.337436\pi$
$593$	−2.47688	−	1.59179i	−0.101713	−	0.0653671i	−0.590509	+	0.807031i	$0.701073\pi$
$594$	4.73862	−	5.46866i	0.194428	−	0.224382i
$595$	−2.93195	+	0.860898i	−0.120198	+	0.0352934i
$596$	−16.0568	−	35.1595i	−0.657713	−	1.44019i
$597$	27.4853			1.12490
$598$		0			0
$599$	33.8885			1.38465			0.692324	−	0.721587i	$-0.256587\pi$
$599$	33.8885			1.38465			0.692324	+	0.721587i	$0.256587\pi$
$600$	−7.21189	−	15.7918i	−0.294424	−	0.644699i
$601$	−44.9892	+	13.2100i	−1.83515	+	0.538848i	−0.999939	−	0.0110823i	$-0.996472\pi$
$601$	−44.9892	+	13.2100i	−1.83515	+	0.538848i	−0.835210	+	0.549931i	$0.814654\pi$
$602$		0			0
$603$	−4.65034	−	2.98859i	−0.189376	−	0.121705i
$604$	4.48848	+	5.17998i	0.182634	+	0.210771i
$605$	−2.88782	−	20.0853i	−0.117407	−	0.816582i
$606$	5.92999	+	1.74120i	0.240889	+	0.0707315i
$607$	22.2698	−	14.3119i	0.903902	−	0.580903i	−0.00404274	−	0.999992i	$-0.501287\pi$
$607$	22.2698	−	14.3119i	0.903902	−	0.580903i	0.907945	+	0.419089i	$0.137650\pi$
$608$	1.59906	−	11.1217i	0.0648504	−	0.451045i
$609$	9.01791	−	19.7465i	0.365424	−	0.800168i
$610$	−2.20376	+	4.82555i	−0.0892275	+	0.195381i
$611$	0.954677	−	6.63992i	0.0386221	−	0.268623i
$612$	−2.07969	+	1.33654i	−0.0840666	+	0.0540263i
$613$	−5.47698	−	1.60819i	−0.221213	−	0.0649541i	0.169248	−	0.985574i	$-0.445866\pi$
$613$	−5.47698	−	1.60819i	−0.221213	−	0.0649541i	−0.390461	+	0.920619i	$0.627684\pi$
$614$	−0.838027	−	5.82861i	−0.0338200	−	0.235223i
$615$	−6.28453	−	7.25274i	−0.253417	−	0.292459i
$616$	31.8739	+	20.4841i	1.28423	+	0.825328i
$617$	4.92970	−	5.68918i	0.198462	−	0.229038i	−0.647791	−	0.761818i	$-0.724307\pi$
$617$	4.92970	−	5.68918i	0.198462	−	0.229038i	0.846254	+	0.532780i	$0.178853\pi$
$618$	−5.54307	+	1.62759i	−0.222975	+	0.0654714i
$619$	8.06587	+	17.6618i	0.324195	+	0.709887i	0.999621	−	0.0275406i	$-0.00876754\pi$
$619$	8.06587	+	17.6618i	0.324195	+	0.709887i	−0.675426	+	0.737428i	$0.736040\pi$
$620$	−13.4164			−0.538816
$621$		0			0
$622$	8.14590			0.326621
$623$	−14.0778	−	30.8261i	−0.564016	−	1.23502i
$624$	11.9339	−	3.50410i	0.477738	−	0.140276i
$625$	−2.89213	+	3.33770i	−0.115685	+	0.133508i
$626$	12.6657	+	8.13974i	0.506223	+	0.325329i
$627$	15.3345	+	17.6969i	0.612400	+	0.706748i
$628$	−2.62886	−	18.2841i	−0.104903	−	0.729616i
$629$	0.906022	+	0.266032i	0.0361255	+	0.0106074i
$630$	4.15939	−	2.67308i	0.165714	−	0.106498i
$631$	−1.75911	+	12.2349i	−0.0700290	+	0.487062i	0.924381	+	0.381471i	$0.124583\pi$
$631$	−1.75911	+	12.2349i	−0.0700290	+	0.487062i	−0.994410	+	0.105591i	$0.966327\pi$
$632$	10.1661	−	22.2606i	0.404385	−	0.885481i
$633$	21.7514	−	47.6289i	0.864541	−	1.89308i
$634$	−2.23551	+	15.5483i	−0.0887835	+	0.617503i
$635$	−7.58235	+	4.87288i	−0.300896	+	0.193374i
$636$	−1.63901	−	0.481257i	−0.0649910	−	0.0190831i
$637$	−1.48241	−	10.3104i	−0.0587352	−	0.408512i
$638$	−6.35752	−	7.33697i	−0.251697	−	0.290473i
$639$	20.5873	+	13.2306i	0.814420	+	0.523396i
$640$	9.21316	−	10.6326i	0.364182	−	0.420289i
$641$	16.6040	−	4.87537i	0.655818	−	0.192565i	0.0631394	−	0.998005i	$-0.479889\pi$
$641$	16.6040	−	4.87537i	0.655818	−	0.192565i	0.592678	+	0.805439i	$0.298071\pi$
$642$	−7.70222	−	16.8655i	−0.303982	−	0.665628i
$643$	−29.5967			−1.16718			−0.583591	−	0.812048i	$-0.698353\pi$
$643$	−29.5967			−1.16718			−0.583591	+	0.812048i	$0.698353\pi$
$644$		0			0
$645$		0			0
$646$	−0.392265	−	0.858940i	−0.0154334	−	0.0337945i
$647$	−6.43647	+	1.88992i	−0.253044	+	0.0743004i	−0.405794	−	0.913964i	$-0.633005\pi$
$647$	−6.43647	+	1.88992i	−0.253044	+	0.0743004i	0.152750	+	0.988265i	$0.451187\pi$
$648$	−16.1074	+	18.5890i	−0.632760	+	0.730244i
$649$	−28.5089	−	18.3215i	−1.11907	−	0.719183i
$650$	4.21579	+	4.86528i	0.165357	+	0.190832i
$651$	6.90811	+	48.0469i	0.270750	+	1.88311i
$652$	−8.94846	−	2.62750i	−0.350449	−	0.102901i
$653$	−32.2242	+	20.7092i	−1.26103	+	0.810414i	−0.988425	−	0.151712i	$-0.951521\pi$
$653$	−32.2242	+	20.7092i	−1.26103	+	0.810414i	−0.272605	+	0.962126i	$0.587885\pi$
$654$		0			0
$655$	9.60631	−	21.0349i	0.375350	−	0.821901i
$656$	−2.67431	+	5.85593i	−0.104414	+	0.228636i
$657$	−1.85802	+	12.9228i	−0.0724884	+	0.504168i
$658$	−3.76220	+	2.41782i	−0.146666	+	0.0942564i
$659$	10.2210	+	3.00115i	0.398153	+	0.116908i	0.474678	−	0.880159i	$-0.342564\pi$
$659$	10.2210	+	3.00115i	0.398153	+	0.116908i	−0.0765255	+	0.997068i	$0.524383\pi$
$660$	3.33250	+	23.1781i	0.129717	+	0.902205i
$661$	15.0253	+	17.3401i	0.584417	+	0.674453i	0.968548	−	0.248826i	$-0.0800446\pi$
$661$	15.0253	+	17.3401i	0.584417	+	0.674453i	−0.384132	+	0.923278i	$0.625499\pi$
$662$	−10.2178	−	6.56657i	−0.397125	−	0.255217i
$663$	3.35591	−	3.87292i	0.130333	−	0.150412i
$664$	−18.8029	+	5.52104i	−0.729696	+	0.214258i
$665$	−3.32332	−	7.27706i	−0.128873	−	0.282192i
$666$	−1.52786			−0.0592035
$667$		0			0
$668$	−2.47214			−0.0956498
$669$	−3.71558	−	8.13600i	−0.143653	−	0.314556i
$670$	2.02593	−	0.594866i	0.0782684	−	0.0229817i
$671$	−23.8112	+	27.4796i	−0.919220	+	1.06084i
$672$	−34.1990	−	21.9784i	−1.31926	−	0.847835i
$673$	−1.96458	−	2.26725i	−0.0757291	−	0.0873960i	0.716621	−	0.697463i	$-0.245688\pi$
$673$	−1.96458	−	2.26725i	−0.0757291	−	0.0873960i	−0.792350	+	0.610067i	$0.791142\pi$
$674$	−2.05960	−	14.3248i	−0.0793328	−	0.551772i
$675$	7.44944	+	2.18735i	0.286729	+	0.0841912i
$676$	5.44471	−	3.49910i	0.209412	−	0.134581i
$677$	−2.56167	+	17.8168i	−0.0984529	+	0.684755i	0.879495	+	0.475907i	$0.157880\pi$
$677$	−2.56167	+	17.8168i	−0.0984529	+	0.684755i	−0.977948	+	0.208847i	$0.933029\pi$
$678$	−5.03128	+	11.0170i	−0.193225	+	0.423104i
$679$	23.8053	−	52.1264i	0.913565	−	2.00043i
$680$	0.300492	−	2.08996i	0.0115233	−	0.0801465i
$681$	22.9124	−	14.7249i	0.878007	−	0.564261i
$682$	20.8289	+	6.11591i	0.797579	+	0.234190i
$683$	−3.78511	−	26.3260i	−0.144833	−	1.00734i	−0.924511	−	0.381156i	$-0.875526\pi$
$683$	−3.78511	−	26.3260i	−0.144833	−	1.00734i	0.779677	−	0.626181i	$-0.215383\pi$
$684$	−4.23835	−	4.89131i	−0.162057	−	0.187024i
$685$	−22.7607	−	14.6274i	−0.869643	−	0.558885i
$686$	4.62052	−	5.33236i	0.176412	−	0.203591i
$687$	−25.7459	+	7.55968i	−0.982267	+	0.288420i
$688$		0			0
$689$	1.41641			0.0539608
$690$		0			0
$691$	7.05573			0.268413			0.134206	−	0.990953i	$-0.457152\pi$
$691$	7.05573			0.268413			0.134206	+	0.990953i	$0.457152\pi$
$692$	−15.4221	−	33.7697i	−0.586261	−	1.28373i
$693$	32.5158	−	9.54751i	1.23517	−	0.362680i
$694$	4.00215	−	4.61873i	0.151920	−	0.175325i
$695$	−11.1349	−	7.15596i	−0.422370	−	0.271441i
$696$	9.82291	+	11.3362i	0.372336	+	0.429699i
$697$	0.377487	+	2.62548i	0.0142983	+	0.0994471i
$698$	−14.4789	−	4.25139i	−0.548035	−	0.160918i
$699$	12.2796	−	7.89160i	0.464456	−	0.298488i
$700$	−2.58733	+	17.9953i	−0.0977920	+	0.680158i
$701$	−1.58674	+	3.47449i	−0.0599305	+	0.131229i	−0.937228	−	0.348718i	$-0.886617\pi$
$701$	−1.58674	+	3.47449i	−0.0599305	+	0.131229i	0.877297	+	0.479948i	$0.159344\pi$
$702$	1.72227	−	3.77124i	0.0650028	−	0.142336i
$703$	−0.351822	+	2.44697i	−0.0132692	+	0.0922893i
$704$	1.03985	−	0.668269i	0.0391907	−	0.0251863i
$705$	−5.92999	−	1.74120i	−0.223336	−	0.0655775i
$706$	−0.823322	−	5.72633i	−0.0309861	−	0.215513i
$707$	−9.47723	−	10.9373i	−0.356428	−	0.411340i
$708$	19.6991	+	12.6599i	0.740339	+	0.475787i
$709$	27.5493	−	31.7935i	1.03463	−	1.19403i	0.0539278	−	0.998545i	$-0.482826\pi$
$709$	27.5493	−	31.7935i	1.03463	−	1.19403i	0.980706	−	0.195487i	$-0.0626286\pi$
$710$	−8.96888	+	2.63350i	−0.336596	+	0.0988336i
$711$	−9.09283	−	19.9105i	−0.341008	−	0.746703i
$712$	23.4164			0.877567
$713$		0			0
$714$	−3.41641			−0.127856
$715$	−8.06587	−	17.6618i	−0.301646	−	0.660513i
$716$	1.09948	−	0.322837i	0.0410895	−	0.0120650i
$717$	20.1547	−	23.2598i	0.752691	−	0.868652i
$718$	−10.3405	−	6.64545i	−0.385905	−	0.248006i
$719$	2.00108	+	2.30937i	0.0746276	+	0.0861248i	0.791836	−	0.610734i	$-0.209126\pi$
$719$	2.00108	+	2.30937i	0.0746276	+	0.0861248i	−0.717208	+	0.696859i	$0.754580\pi$
$720$	−0.652313	−	4.53694i	−0.0243103	−	0.169082i
$721$	12.9799	+	3.81124i	0.483396	+	0.141938i
$722$	−7.79885	+	5.01202i	−0.290243	+	0.186528i
$723$	−7.35884	+	51.1819i	−0.273678	+	1.90347i
$724$	−11.1931	+	24.5094i	−0.415987	+	0.910884i
$725$	4.32713	−	9.47510i	0.160706	−	0.351896i
$726$	3.22869	−	22.4560i	0.119828	−	0.833420i
$727$	−23.3096	+	14.9802i	−0.864506	+	0.555584i	−0.896068	−	0.443917i	$-0.853588\pi$
$727$	−23.3096	+	14.9802i	−0.864506	+	0.555584i	0.0315616	+	0.999502i	$0.489952\pi$
$728$	20.8289	+	6.11591i	0.771969	+	0.226671i
$729$	0.996204	+	6.92875i	0.0368964	+	0.256620i
$730$	−3.26569	−	3.76881i	−0.120869	−	0.139490i
$731$		0			0
$732$	16.4531	−	18.9879i	0.608125	−	0.701814i
$733$	29.9708	−	8.80022i	1.10700	−	0.325043i	0.323368	−	0.946273i	$-0.395185\pi$
$733$	29.9708	−	8.80022i	1.10700	−	0.325043i	0.783628	+	0.621230i	$0.213367\pi$
$734$	−1.07326	−	2.35012i	−0.0396149	−	0.0867444i
$735$	−9.59675			−0.353981
$736$		0			0
$737$	14.4721			0.533088
$738$	−1.78288	−	3.90396i	−0.0656286	−	0.143707i
$739$	−25.7333	+	7.55597i	−0.946614	+	0.277951i	−0.718376	−	0.695655i	$-0.755114\pi$
$739$	−25.7333	+	7.55597i	−0.946614	+	0.277951i	−0.228237	+	0.973606i	$0.573296\pi$
$740$	−1.61890	+	1.86832i	−0.0595121	+	0.0686807i
$741$	11.2866	+	7.25346i	0.414624	+	0.266462i
$742$	−0.618367	−	0.713633i	−0.0227010	−	0.0261983i
$743$	−5.85264	−	40.7060i	−0.214713	−	1.49336i	−0.757138	−	0.653255i	$-0.773403\pi$
$743$	−5.85264	−	40.7060i	−0.214713	−	1.49336i	0.542425	−	0.840104i	$-0.317506\pi$
$744$	−32.1824	−	9.44960i	−1.17986	−	0.346439i
$745$	24.8404	−	15.9640i	0.910083	−	0.584875i
$746$	−0.677978	+	4.71544i	−0.0248225	+	0.172645i
$747$	−7.28134	+	15.9439i	−0.266410	+	0.583357i
$748$	2.68862	−	5.88726i	0.0983058	−	0.215260i
$749$	−6.17880	+	42.9745i	−0.225768	+	1.57025i
$750$	12.1747	−	7.82423i	0.444558	−	0.285700i
$751$	−0.346070	−	0.101615i	−0.0126283	−	0.00370799i	0.275412	−	0.961326i	$-0.411186\pi$
$751$	−0.346070	−	0.101615i	−0.0126283	−	0.00370799i	−0.288041	+	0.957618i	$0.593004\pi$
$752$	0.590023	+	4.10370i	0.0215159	+	0.149646i
$753$	3.35591	+	3.87292i	0.122296	+	0.141137i
$754$	−4.67931	−	3.00721i	−0.170410	−	0.109516i
$755$	−3.42890	+	3.95716i	−0.124790	+	0.144016i
$756$	11.2339	−	3.29858i	0.408574	−	0.119968i
$757$	0.663313	+	1.45245i	0.0241085	+	0.0527903i	0.921303	−	0.388845i	$-0.127126\pi$
$757$	0.663313	+	1.45245i	0.0241085	+	0.0527903i	−0.897195	+	0.441635i	$0.854399\pi$
$758$	15.0557			0.546849
$759$		0			0
$760$	5.52786			0.200517
$761$	19.2358	+	42.1205i	0.697296	+	1.52687i	0.843219	+	0.537570i	$0.180658\pi$
$761$	19.2358	+	42.1205i	0.697296	+	1.52687i	−0.145923	+	0.989296i	$0.546615\pi$
$762$	−9.66882	+	2.83902i	−0.350265	+	0.102847i
$763$		0			0
$764$	35.6361	+	22.9019i	1.28927	+	0.828562i
$765$	−1.23673	−	1.42727i	−0.0447142	−	0.0516029i
$766$	−0.620589	−	4.31629i	−0.0224228	−	0.155954i
$767$	−18.6299	−	5.47023i	−0.672687	−	0.197519i
$768$	12.3444	−	7.93323i	0.445439	−	0.286266i
$769$	3.29098	−	22.8892i	0.118676	−	0.825407i	−0.840341	−	0.542058i	$-0.817645\pi$
$769$	3.29098	−	22.8892i	0.118676	−	0.825407i	0.959017	−	0.283349i	$-0.0914455\pi$
$770$	−5.37724	+	11.7745i	−0.193782	+	0.424324i
$771$	6.94084	−	15.1983i	0.249968	−	0.547354i
$772$	2.28987	−	15.9264i	0.0824142	−	0.573204i
$773$	−4.65034	+	2.98859i	−0.167261	+	0.107492i	−0.621593	−	0.783340i	$-0.713514\pi$
$773$	−4.65034	+	2.98859i	−0.167261	+	0.107492i	0.454332	+	0.890832i	$0.349878\pi$
$774$		0			0
$775$	3.31477	+	23.0547i	0.119070	+	0.828150i
$776$	25.9304	+	29.9252i	0.930846	+	1.07425i
$777$	7.52440	+	4.83564i	0.269936	+	0.173478i
$778$	−10.3318	+	11.9235i	−0.370413	+	0.427479i
$779$	−6.66298	+	1.95643i	−0.238726	+	0.0700963i
$780$	5.57338	+	12.2040i	0.199559	+	0.436973i
$781$	−64.0689			−2.29256
$782$		0			0
$783$	−6.70820			−0.239732
$784$	2.67431	+	5.85593i	0.0955112	+	0.209140i
$785$	13.5398	−	3.97566i	0.483258	−	0.141897i
$786$	16.9308	−	19.5392i	0.603903	−	0.696941i
$787$	20.6810	+	13.2909i	0.737199	+	0.473769i	0.854581	−	0.519318i	$-0.173814\pi$
$787$	20.6810	+	13.2909i	0.737199	+	0.473769i	−0.117382	+	0.993087i	$0.537450\pi$
$788$	−1.55986	−	1.80017i	−0.0555676	−	0.0641284i
$789$	0.936943	+	6.51658i	0.0333560	+	0.231996i
$790$	8.02201	+	2.35548i	0.285410	+	0.0838041i
$791$	23.8585	−	15.3329i	0.848311	−	0.545177i
$792$	−3.33250	+	23.1781i	−0.118415	+	0.823597i
$793$	−8.65426	+	18.9502i	−0.307322	+	0.672941i
$794$	−6.26868	+	13.7265i	−0.222467	+	0.487135i
$795$	0.185714	−	1.29167i	0.00658660	−	0.0458108i
$796$	16.7313	−	10.7526i	0.593025	−	0.381114i
$797$	32.9688	+	9.68052i	1.16782	+	0.342902i	0.807465	−	0.589915i	$-0.200839\pi$
$797$	32.9688	+	9.68052i	1.16782	+	0.342902i	0.360351	+	0.932817i	$0.382657\pi$
$798$	−1.27290	−	8.85323i	−0.0450603	−	0.313401i
$799$	1.11864	+	1.29097i	0.0395745	+	0.0456714i
$800$	−16.4100	−	10.5461i	−0.580180	−	0.372859i
$801$	13.7156	−	15.8286i	0.484616	−	0.559277i
$802$	8.40893	−	2.46908i	0.296930	−	0.0871864i
$803$	−14.1990	−	31.0915i	−0.501073	−	1.09720i
$804$	−10.0000			−0.352673
$805$		0			0
$806$	12.4377			0.438099
$807$	7.37940	+	16.1586i	0.259767	+	0.568811i
$808$	9.59493	−	2.81733i	0.337548	−	0.0991132i
$809$	−7.93132	+	9.15323i	−0.278850	+	0.321810i	−0.877847	−	0.478941i	$-0.841021\pi$
$809$	−7.93132	+	9.15323i	−0.278850	+	0.321810i	0.598997	+	0.800751i	$0.295566\pi$
$810$	−7.06927	−	4.54314i	−0.248389	−	0.159630i
$811$	15.9442	+	18.4006i	0.559878	+	0.646134i	0.963156	−	0.268944i	$-0.0866747\pi$
$811$	15.9442	+	18.4006i	0.559878	+	0.646134i	−0.403278	+	0.915078i	$0.632129\pi$
$812$	−2.23551	−	15.5483i	−0.0784510	−	0.545639i
$813$	17.1639	+	5.03979i	0.601965	+	0.176753i
$814$	3.36501	−	2.16256i	0.117944	−	0.0757978i
$815$	1.01394	−	7.05209i	0.0355167	−	0.247024i
$816$	−1.31570	+	2.88097i	−0.0460586	+	0.100854i
$817$		0			0
$818$	−1.87879	+	13.0673i	−0.0656903	+	0.456886i
$819$	16.3341	−	10.4973i	0.570760	−	0.366805i
$820$	−6.66298	−	1.95643i	−0.232681	−	0.0683214i
$821$	5.54235	+	38.5479i	0.193429	+	1.34533i	0.822847	+	0.568263i	$0.192384\pi$
$821$	5.54235	+	38.5479i	0.193429	+	1.34533i	−0.629418	+	0.777067i	$0.716707\pi$
$822$	−19.8090	−	22.8608i	−0.690919	−	0.797363i
$823$	−33.2640	−	21.3775i	−1.15951	−	0.745172i	−0.188000	−	0.982169i	$-0.560201\pi$
$823$	−33.2640	−	21.3775i	−1.15951	−	0.745172i	−0.971510	+	0.236997i	$0.923837\pi$
$824$	−6.12133	+	7.06439i	−0.213247	+	0.246100i
$825$	39.0058	−	11.4531i	1.35801	−	0.398747i
$826$	5.37724	+	11.7745i	0.187098	+	0.409688i
$827$	1.52786			0.0531290			0.0265645	−	0.999647i	$-0.491543\pi$
$827$	1.52786			0.0531290			0.0265645	+	0.999647i	$0.491543\pi$
$828$		0			0
$829$	40.2492			1.39791			0.698957	−	0.715164i	$-0.253648\pi$
$829$	40.2492			1.39791			0.698957	+	0.715164i	$0.253648\pi$
$830$	−2.78122	−	6.09003i	−0.0965377	−	0.211388i
$831$	33.1953	−	9.74703i	1.15153	−	0.338121i
$832$	0.463775	−	0.535225i	0.0160785	−	0.0185556i
$833$	2.23140	+	1.43404i	0.0773136	+	0.0496864i
$834$	−9.69087	−	11.1839i	−0.335568	−	0.387266i
$835$	−0.268768	−	1.86932i	−0.00930109	−	0.0646905i
$836$	16.2579	+	4.77375i	0.562292	+	0.165104i
$837$	12.6188	−	8.10961i	0.436170	−	0.280309i
$838$	0.403152	−	2.80398i	0.0139266	−	0.0968619i
$839$	−17.0838	+	37.4083i	−0.589798	+	1.29148i	0.345767	+	0.938320i	$0.387619\pi$
$839$	−17.0838	+	37.4083i	−0.589798	+	1.29148i	−0.935564	+	0.353156i	$0.885108\pi$
$840$	8.30830	−	18.1926i	0.286664	−	0.627706i
$841$	2.84630	−	19.7964i	0.0981482	−	0.682635i
$842$	−5.35094	+	3.43884i	−0.184406	+	0.118510i
$843$	−18.8029	−	5.52104i	−0.647608	−	0.190155i
$844$	−5.39210	−	37.5029i	−0.185604	−	1.29090i
$845$	3.23781	+	3.73663i	0.111384	+	0.128544i
$846$	−2.32517	−	1.49429i	−0.0799409	−	0.0513749i
$847$	−34.7892	+	40.1489i	−1.19537	+	1.37953i
$848$	−0.839929	+	0.246625i	−0.0288433	+	0.00846915i
$849$	−25.7380	−	56.3585i	−0.883327	−	1.93422i
$850$	−1.63932			−0.0562282
$851$		0			0
$852$	44.2705			1.51668
$853$	−4.39658	−	9.62717i	−0.150536	−	0.329628i	0.819308	−	0.573353i	$-0.194358\pi$
$853$	−4.39658	−	9.62717i	−0.150536	−	0.329628i	−0.969844	+	0.243725i	$0.921630\pi$
$854$	13.3260	−	3.91285i	0.456005	−	0.133895i
$855$	3.23781	−	3.73663i	0.110731	−	0.127790i
$856$	−25.2376	−	16.2192i	−0.862604	−	0.554362i
$857$	−0.964044	−	1.11257i	−0.0329311	−	0.0380045i	0.739045	−	0.673656i	$-0.235277\pi$
$857$	−0.964044	−	1.11257i	−0.0329311	−	0.0380045i	−0.771976	+	0.635651i	$0.780732\pi$
$858$	−3.08940	−	21.4872i	−0.105470	−	0.733562i
$859$	16.0314	+	4.70725i	0.546984	+	0.160609i	0.543537	−	0.839385i	$-0.317085\pi$
$859$	16.0314	+	4.70725i	0.546984	+	0.160609i	0.00344703	+	0.999994i	$0.498903\pi$
$860$		0			0
$861$	−3.57561	+	24.8689i	−0.121856	+	0.847529i
$862$	−4.50011	+	9.85388i	−0.153275	+	0.335624i
$863$	−8.94846	+	19.5944i	−0.304609	+	0.667001i	−0.998595	−	0.0529874i	$-0.983126\pi$
$863$	−8.94846	+	19.5944i	−0.304609	+	0.667001i	0.693986	+	0.719989i	$0.255853\pi$
$864$	−1.78780	+	12.4344i	−0.0608223	+	0.423028i
$865$	23.8585	−	15.3329i	0.811214	−	0.521336i
$866$	−10.5670	−	3.10276i	−0.359083	−	0.105436i
$867$	−5.22412	−	36.3346i	−0.177420	−	1.23399i
$868$	23.0017	+	26.5454i	0.780730	+	0.901010i
$869$	48.2080	+	30.9814i	1.63534	+	1.05097i
$870$	−3.35591	+	3.87292i	−0.113776	+	0.131304i
$871$	7.95592	−	2.33607i	0.269576	−	0.0791547i
$872$		0			0
$873$	35.4164			1.19866
$874$		0			0
$875$	−33.8885			−1.14564
$876$	9.81129	+	21.4837i	0.331493	+	0.725868i
$877$	34.9948	−	10.2754i	1.18169	−	0.346975i	0.368864	−	0.929483i	$-0.379747\pi$
$877$	34.9948	−	10.2754i	1.18169	−	0.346975i	0.812825	+	0.582508i	$0.197929\pi$
$878$	7.57170	−	8.73821i	0.255533	−	0.294900i
$879$	2.87407	+	1.84705i	0.0969398	+	0.0622994i
$880$	7.85833	+	9.06899i	0.264904	+	0.305716i
$881$	−6.28752	−	43.7306i	−0.211832	−	1.47332i	−0.767033	−	0.641607i	$-0.778268\pi$
$881$	−6.28752	−	43.7306i	−0.211832	−	1.47332i	0.555202	−	0.831716i	$-0.312641\pi$
$882$	−4.11795	−	1.20914i	−0.138659	−	0.0407138i
$883$	3.36501	−	2.16256i	0.113242	−	0.0727760i	−0.482794	−	0.875734i	$-0.660378\pi$
$883$	3.36501	−	2.16256i	0.113242	−	0.0727760i	0.596036	+	0.802958i	$0.296742\pi$
$884$	0.527732	−	3.67046i	0.0177496	−	0.123451i
$885$	−7.43117	+	16.2720i	−0.249796	+	0.546977i
$886$	9.78814	−	21.4330i	0.328839	−	0.720057i
$887$	−3.28304	+	22.8341i	−0.110234	+	0.766693i	0.857457	+	0.514555i	$0.172043\pi$
$887$	−3.28304	+	22.8341i	−0.110234	+	0.766693i	−0.967691	+	0.252138i	$0.918866\pi$
$888$	−5.19923	+	3.34134i	−0.174475	+	0.112128i
$889$	22.6409	+	6.64797i	0.759352	+	0.222966i
$890$	1.13852	+	7.91857i	0.0381632	+	0.265431i
$891$	−37.7178	−	43.5287i	−1.26360	−	1.45827i
$892$	−5.44471	−	3.49910i	−0.182302	−	0.117159i
$893$	−2.92863	+	3.37981i	−0.0980027	+	0.113101i
$894$	31.6759	−	9.30088i	1.05940	−	0.311068i
$895$	0.363649	+	0.796281i	0.0121555	+	0.0266167i
$896$	−36.8328			−1.23050
$897$		0			0
$898$	−9.23607			−0.308212
$899$	−8.36007	−	18.3060i	−0.278824	−	0.610539i
$900$	−10.7809	+	3.16557i	−0.359364	+	0.105519i
$901$	−0.236195	+	0.272584i	−0.00786880	+	0.00908108i
$902$	9.45238	+	6.07468i	0.314730	+	0.202265i
$903$		0			0
$904$	2.78891	+	19.3973i	0.0927577	+	0.645144i
$905$	−19.7498	−	5.79907i	−0.656506	−	0.192768i
$906$	−4.92478	+	3.16497i	−0.163615	+	0.105149i
$907$	5.72806	−	39.8395i	0.190197	−	1.32285i	−0.641287	−	0.767301i	$-0.721599\pi$
$907$	5.72806	−	39.8395i	0.190197	−	1.32285i	0.831484	−	0.555549i	$-0.187492\pi$
$908$	8.18708	−	17.9272i	0.271698	−	0.594935i
$909$	3.71558	−	8.13600i	0.123238	−	0.269854i
$910$	−1.05546	+	7.34092i	−0.0349883	+	0.243349i
$911$	26.3354	−	16.9247i	0.872531	−	0.560741i	−0.0259951	−	0.999662i	$-0.508275\pi$
$911$	26.3354	−	16.9247i	0.872531	−	0.560741i	0.898526	+	0.438921i	$0.144639\pi$
$912$	−7.95592	−	2.33607i	−0.263447	−	0.0773550i
$913$	−6.53062	−	45.4215i	−0.216132	−	1.50323i
$914$	2.07406	+	2.39360i	0.0686040	+	0.0791732i
$915$	16.1466	+	10.3768i	0.533790	+	0.343046i
$916$	−12.7150	+	14.6739i	−0.420117	+	0.484841i
$917$	−58.0887	+	17.0564i	−1.91826	+	0.563251i
$918$	0.438565	+	0.960324i	0.0144748	+	0.0316954i
$919$	41.1246			1.35658			0.678288	−	0.734796i	$-0.262722\pi$
$919$	41.1246			1.35658			0.678288	+	0.734796i	$0.262722\pi$
$920$		0			0
$921$	−21.3050			−0.702022
$922$	−0.377957	−	0.827611i	−0.0124474	−	0.0272559i
$923$	−35.2213	+	10.3419i	−1.15932	+	0.340408i
$924$	40.1462	−	46.3312i	1.32071	−	1.52418i
$925$	3.61049	+	2.32032i	0.118712	+	0.0762917i
$926$	8.09452	+	9.34158i	0.266003	+	0.306983i
$927$	1.18985	+	8.27558i	0.0390798	+	0.271806i
$928$	16.1714	+	4.74835i	0.530852	+	0.155872i
$929$	−20.2370	+	13.0055i	−0.663953	+	0.426697i	−0.828741	−	0.559632i	$-0.810942\pi$
$929$	−20.2370	+	13.0055i	−0.663953	+	0.426697i	0.164788	+	0.986329i	$0.447306\pi$
$930$	1.63078	−	11.3423i	0.0534755	−	0.371930i
$931$	−2.88475	+	6.31673i	−0.0945440	+	0.207023i
$932$	4.38774	−	9.60781i	0.143725	−	0.314714i
$933$	4.19432	−	29.1722i	0.137316	−	0.955053i
$934$	−6.78798	+	4.36237i	−0.222109	+	0.142741i
$935$	4.74399	+	1.39296i	0.155145	+	0.0455547i
$936$	1.90935	+	13.2798i	0.0624092	+	0.434065i
$937$	−22.3834	−	25.8318i	−0.731233	−	0.843887i	0.261377	−	0.965237i	$-0.415823\pi$
$937$	−22.3834	−	25.8318i	−0.731233	−	0.843887i	−0.992610	+	0.121349i	$0.961278\pi$
$938$	−4.65034	−	2.98859i	−0.151839	−	0.0975809i
$939$	35.6717	−	41.1673i	1.16410	−	1.34344i
$940$	−4.29098	+	1.25995i	−0.139956	+	0.0410949i
$941$	2.76354	+	6.05130i	0.0900888	+	0.197267i	0.949313	−	0.314332i	$-0.101781\pi$
$941$	2.76354	+	6.05130i	0.0900888	+	0.197267i	−0.859224	+	0.511599i	$0.829053\pi$
$942$	15.7771			0.514045
$943$		0			0
$944$	12.0000			0.390567
$945$	3.71558	+	8.13600i	0.120868	+	0.264664i
$946$		0			0
$947$	7.08537	−	8.17695i	0.230244	−	0.265715i	−0.628858	−	0.777520i	$-0.716477\pi$
$947$	7.08537	−	8.17695i	0.230244	−	0.265715i	0.859102	+	0.511805i	$0.171023\pi$
$948$	−33.3109	−	21.4076i	−1.08189	−	0.695287i
$949$	−12.8245	−	14.8003i	−0.416302	−	0.480438i
$950$	−0.610786	−	4.24811i	−0.0198165	−	0.137827i
$951$	54.5307	+	16.0117i	1.76828	+	0.519213i
$952$	−4.65034	+	2.98859i	−0.150718	+	0.0968607i
$953$	−2.91349	+	20.2638i	−0.0943772	+	0.656408i	0.886636	+	0.462468i	$0.153036\pi$
$953$	−2.91349	+	20.2638i	−0.0943772	+	0.656408i	−0.981013	+	0.193940i	$0.937873\pi$
$954$	0.242433	−	0.530854i	0.00784906	−	0.0171870i
$955$	−13.4431	+	29.4363i	−0.435009	+	0.952537i
$956$	3.16942	−	22.0438i	0.102506	−	0.712948i
$957$	−29.5487	+	18.9898i	−0.955174	+	0.613853i
$958$	−18.7368	−	5.50164i	−0.605360	−	0.177750i
$959$	10.0806	+	70.1118i	0.325518	+	2.26403i
$960$	−0.427281	−	0.493108i	−0.0137904	−	0.0159150i
$961$	11.7775	+	7.56897i	0.379921	+	0.244160i
$962$	1.50081	−	1.73202i	0.0483880	−	0.0558427i
$963$	−25.7459	+	7.55968i	−0.829650	+	0.243607i
$964$	15.5433	+	34.0352i	0.500617	+	1.09620i
$965$	12.2918			0.395687
$966$		0			0
$967$	27.5410			0.885659			0.442830	−	0.896606i	$-0.353975\pi$
$967$	27.5410			0.885659			0.442830	+	0.896606i	$0.353975\pi$
$968$	−15.2491	−	33.3910i	−0.490126	−	1.07323i
$969$	−3.27802	+	0.962513i	−0.105305	+	0.0309204i
$970$	−8.85887	+	10.2237i	−0.284441	+	0.328263i
$971$	13.8572	+	8.90551i	0.444700	+	0.285791i	0.743765	−	0.668441i	$-0.233038\pi$
$971$	13.8572	+	8.90551i	0.444700	+	0.285791i	−0.299065	+	0.954233i	$0.596675\pi$
$972$	18.9545	+	21.8746i	0.607965	+	0.701629i
$973$	4.93156	+	34.2998i	0.158099	+	1.09960i
$974$	8.72195	+	2.56100i	0.279469	+	0.0820596i
$975$	19.5943	−	12.5925i	0.627520	−	0.403283i
$976$	1.83236	−	12.7443i	0.0586524	−	0.407936i
$977$	−9.69891	+	21.2377i	−0.310296	+	0.679453i	−0.998958	−	0.0456290i	$-0.985471\pi$
$977$	−9.69891	+	21.2377i	−0.310296	+	0.679453i	0.688663	+	0.725082i	$0.258198\pi$
$978$	3.30901	−	7.24573i	0.105811	−	0.231693i
$979$	−7.80352	+	54.2747i	−0.249402	+	1.73463i
$980$	−5.84189	+	3.75436i	−0.186612	+	0.119929i
$981$		0			0
$982$	−0.734210	−	5.10654i	−0.0234296	−	0.162956i
$983$	26.5036	+	30.5868i	0.845334	+	0.975567i	0.999923	−	0.0124115i	$-0.00395079\pi$
$983$	26.5036	+	30.5868i	0.845334	+	0.975567i	−0.154589	+	0.987979i	$0.549405\pi$
$984$	−14.6047	−	9.38589i	−0.465582	−	0.299211i
$985$	1.19162	−	1.37521i	0.0379683	−	0.0438177i
$986$	1.35903	−	0.399048i	0.0432804	−	0.0127083i
$987$	6.72156	+	14.7182i	0.213949	+	0.468484i
$988$	9.70820			0.308859
$989$		0			0
$990$	−8.00000			−0.254257
$991$	9.96996	+	21.8312i	0.316706	+	0.693490i	0.999304	−	0.0373044i	$-0.0118771\pi$
$991$	9.96996	+	21.8312i	0.316706	+	0.693490i	−0.682598	+	0.730794i	$0.739150\pi$
$992$	−36.1603	+	10.6176i	−1.14809	+	0.337110i
$993$	−28.7774	+	33.2109i	−0.913222	+	1.05391i
$994$	20.5873	+	13.2306i	0.652989	+	0.419650i
$995$	9.94962	+	11.4825i	0.315424	+	0.364019i
$996$	4.51255	+	31.3855i	0.142986	+	0.994486i
$997$	−16.1510	−	4.74235i	−0.511506	−	0.150192i	0.0157866	−	0.999875i	$-0.494975\pi$
$997$	−16.1510	−	4.74235i	−0.511506	−	0.150192i	−0.527293	+	0.849684i	$0.676793\pi$
$998$	10.0303	−	6.44605i	0.317502	−	0.204046i
$999$	0.393349	−	2.73580i	0.0124450	−	0.0865569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.2.c.o.487.2		20
23.2	even	11	inner	529.2.c.o.177.1		20
23.3	even	11	inner	529.2.c.o.266.1		20
23.4	even	11	inner	529.2.c.o.501.1		20
23.5	odd	22		529.2.c.n.399.1		20
23.6	even	11	inner	529.2.c.o.466.2		20
23.7	odd	22		529.2.c.n.334.2		20
23.8	even	11	inner	529.2.c.o.118.1		20
23.9	even	11	inner	529.2.c.o.255.2		20
23.10	odd	22		529.2.c.n.170.1		20
23.11	odd	22		529.2.a.a.1.2		2
23.12	even	11		23.2.a.a.1.2	✓	2
23.13	even	11	inner	529.2.c.o.170.1		20
23.14	odd	22		529.2.c.n.255.2		20
23.15	odd	22		529.2.c.n.118.1		20
23.16	even	11	inner	529.2.c.o.334.2		20
23.17	odd	22		529.2.c.n.466.2		20
23.18	even	11	inner	529.2.c.o.399.1		20
23.19	odd	22		529.2.c.n.501.1		20
23.20	odd	22		529.2.c.n.266.1		20
23.21	odd	22		529.2.c.n.177.1		20
23.22	odd	2		529.2.c.n.487.2		20
69.11	even	22		4761.2.a.w.1.1		2
69.35	odd	22		207.2.a.d.1.1		2
92.11	even	22		8464.2.a.bb.1.2		2
92.35	odd	22		368.2.a.h.1.2		2
115.12	odd	44		575.2.b.d.24.3		4
115.58	odd	44		575.2.b.d.24.2		4
115.104	even	22		575.2.a.f.1.1		2
161.104	odd	22		1127.2.a.c.1.2		2
184.35	odd	22		1472.2.a.s.1.1		2
184.173	even	22		1472.2.a.t.1.2		2
253.219	odd	22		2783.2.a.c.1.1		2
276.35	even	22		3312.2.a.ba.1.1		2
299.12	even	22		3887.2.a.i.1.1		2
345.104	odd	22		5175.2.a.be.1.2		2
391.288	even	22		6647.2.a.b.1.2		2
437.265	odd	22		8303.2.a.e.1.1		2
460.219	odd	22		9200.2.a.bt.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.a.a.1.2	✓	2	23.12	even	11
207.2.a.d.1.1		2	69.35	odd	22
368.2.a.h.1.2		2	92.35	odd	22
529.2.a.a.1.2		2	23.11	odd	22
529.2.c.n.118.1		20	23.15	odd	22
529.2.c.n.170.1		20	23.10	odd	22
529.2.c.n.177.1		20	23.21	odd	22
529.2.c.n.255.2		20	23.14	odd	22
529.2.c.n.266.1		20	23.20	odd	22
529.2.c.n.334.2		20	23.7	odd	22
529.2.c.n.399.1		20	23.5	odd	22
529.2.c.n.466.2		20	23.17	odd	22
529.2.c.n.487.2		20	23.22	odd	2
529.2.c.n.501.1		20	23.19	odd	22
529.2.c.o.118.1		20	23.8	even	11	inner
529.2.c.o.170.1		20	23.13	even	11	inner
529.2.c.o.177.1		20	23.2	even	11	inner
529.2.c.o.255.2		20	23.9	even	11	inner
529.2.c.o.266.1		20	23.3	even	11	inner
529.2.c.o.334.2		20	23.16	even	11	inner
529.2.c.o.399.1		20	23.18	even	11	inner
529.2.c.o.466.2		20	23.6	even	11	inner
529.2.c.o.487.2		20	1.1	even	1	trivial
529.2.c.o.501.1		20	23.4	even	11	inner
575.2.a.f.1.1		2	115.104	even	22
575.2.b.d.24.2		4	115.58	odd	44
575.2.b.d.24.3		4	115.12	odd	44
1127.2.a.c.1.2		2	161.104	odd	22
1472.2.a.s.1.1		2	184.35	odd	22
1472.2.a.t.1.2		2	184.173	even	22
2783.2.a.c.1.1		2	253.219	odd	22
3312.2.a.ba.1.1		2	276.35	even	22
3887.2.a.i.1.1		2	299.12	even	22
4761.2.a.w.1.1		2	69.11	even	22
5175.2.a.be.1.2		2	345.104	odd	22
6647.2.a.b.1.2		2	391.288	even	22
8303.2.a.e.1.1		2	437.265	odd	22
8464.2.a.bb.1.2		2	92.11	even	22
9200.2.a.bt.1.1		2	460.219	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:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	529.c (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.256741 + 0.562183i) q^{2} +(2.14549 - 0.629973i) q^{3} +(1.05959 - 1.22283i) q^{4} +(1.03985 + 0.668269i) q^{5} +(0.904995 + 1.04442i) q^{6} +(-0.460540 - 3.20313i) q^{7} +(2.14549 + 0.629973i) q^{8} +(1.68251 - 1.08128i) q^{9} +O(q^{10})\)	\(q+(0.256741 + 0.562183i) q^{2} +(2.14549 - 0.629973i) q^{3} +(1.05959 - 1.22283i) q^{4} +(1.03985 + 0.668269i) q^{5} +(0.904995 + 1.04442i) q^{6} +(-0.460540 - 3.20313i) q^{7} +(2.14549 + 0.629973i) q^{8} +(1.68251 - 1.08128i) q^{9} +(-0.108719 + 0.756156i) q^{10} +(-2.17514 + 4.76289i) q^{11} +(1.50299 - 3.29108i) q^{12} +(-0.426945 + 2.96946i) q^{13} +(1.68251 - 1.08128i) q^{14} +(2.65197 + 0.778690i) q^{15} +(-0.263866 - 1.83523i) q^{16} +(-0.500269 - 0.577341i) q^{17} +(1.03985 + 0.668269i) q^{18} +(1.30972 - 1.51150i) q^{19} +(1.91899 - 0.563465i) q^{20} +(-3.00597 - 6.58216i) q^{21} -3.23607 q^{22} +5.00000 q^{24} +(-1.44238 - 3.15837i) q^{25} +(-1.77900 + 0.522361i) q^{26} +(-1.46431 + 1.68991i) q^{27} +(-4.40486 - 2.83083i) q^{28} +(1.96458 + 2.26725i) q^{29} +(0.243103 + 1.69082i) q^{30} +(-6.43647 - 1.88992i) q^{31} +(4.72619 - 3.03734i) q^{32} +(-1.66625 + 11.5890i) q^{33} +(0.196132 - 0.429470i) q^{34} +(1.66166 - 3.63853i) q^{35} +(0.460540 - 3.20313i) q^{36} +(-1.03985 + 0.668269i) q^{37} +(1.18600 + 0.348241i) q^{38} +(0.954677 + 6.63992i) q^{39} +(1.80999 + 2.08884i) q^{40} +(-2.92095 - 1.87718i) q^{41} +(2.92863 - 3.37981i) q^{42} +(3.51945 + 7.70653i) q^{44} +2.47214 q^{45} -2.23607 q^{47} +(-1.72227 - 3.77124i) q^{48} +(-3.33149 + 0.978214i) q^{49} +(1.40526 - 1.62176i) q^{50} +(-1.43703 - 0.923525i) q^{51} +(3.17876 + 3.66849i) q^{52} +(-0.0671920 - 0.467330i) q^{53} +(-1.32599 - 0.389345i) q^{54} +(-5.44471 + 3.49910i) q^{55} +(1.02980 - 7.16242i) q^{56} +(1.85779 - 4.06800i) q^{57} +(-0.770222 + 1.68655i) q^{58} +(-0.921081 + 6.40626i) q^{59} +(3.76220 - 2.41782i) q^{60} +(6.66298 + 1.95643i) q^{61} +(-0.590023 - 4.10370i) q^{62} +(-4.23835 - 4.89131i) q^{63} +(-0.198593 - 0.127628i) q^{64} +(-2.42836 + 2.80247i) q^{65} +(-6.94296 + 2.03864i) q^{66} +(-1.14818 - 2.51416i) q^{67} -1.23607 q^{68} +2.47214 q^{70} +(5.08305 + 11.1303i) q^{71} +(4.29098 - 1.25995i) q^{72} +(-4.27484 + 4.93343i) q^{73} +(-0.642661 - 0.413013i) q^{74} +(-5.08429 - 5.86759i) q^{75} +(-0.460540 - 3.20313i) q^{76} +(16.2579 + 4.77375i) q^{77} +(-3.48775 + 2.24144i) q^{78} +(1.55753 - 10.8329i) q^{79} +(0.952046 - 2.08469i) q^{80} +(-4.56957 + 10.0060i) q^{81} +(0.305393 - 2.12406i) q^{82} +(-7.37269 + 4.73814i) q^{83} +(-11.2339 - 3.29858i) q^{84} +(-0.134384 - 0.934661i) q^{85} +(5.64330 + 3.62673i) q^{87} +(-7.66724 + 8.84847i) q^{88} +(10.0479 - 2.95034i) q^{89} +(0.634698 + 1.38979i) q^{90} +9.70820 q^{91} -15.0000 q^{93} +(-0.574089 - 1.25708i) q^{94} +(2.37200 - 0.696481i) q^{95} +(8.22656 - 9.49396i) q^{96} +(14.8971 + 9.57378i) q^{97} +(-1.40526 - 1.62176i) q^{98} +(1.49034 + 10.3655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + q^{4} + 2 q^{5} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q + q^2 + q^4 + 2 * q^5 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 20 q + q^{2} + q^{4} + 2 q^{5} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{11} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 10 q^{15} + 3 q^{16} - 6 q^{17} + 2 q^{18} + 4 q^{19} + 4 q^{20} + 10 q^{21} - 20 q^{22} + 100 q^{24} - 2 q^{25} + 3 q^{26} + 6 q^{28} + 6 q^{29} - 10 q^{30} - 9 q^{32} - 10 q^{33} + 8 q^{34} - 8 q^{35} + 2 q^{36} - 2 q^{37} - 2 q^{38} + 10 q^{40} - 2 q^{41} - 8 q^{44} - 40 q^{45} + 15 q^{48} + 2 q^{49} + 11 q^{50} - 10 q^{51} + 3 q^{52} + 8 q^{53} - 5 q^{54} + 4 q^{55} + 10 q^{56} - 3 q^{58} - 4 q^{59} - 4 q^{61} - 15 q^{62} - 4 q^{63} - 4 q^{64} + 6 q^{65} - 10 q^{66} + 10 q^{67} + 20 q^{68} - 40 q^{70} - 20 q^{71} - 22 q^{73} + 6 q^{74} - 20 q^{75} - 2 q^{76} + 16 q^{77} + 15 q^{78} + 4 q^{79} - 18 q^{80} + 22 q^{81} + 11 q^{82} + 22 q^{83} - 10 q^{84} + 16 q^{85} - 10 q^{88} + 12 q^{89} - 12 q^{90} + 60 q^{91} - 300 q^{93} + 5 q^{94} - 4 q^{95} + 5 q^{96} - 22 q^{97} - 11 q^{98} + 12 q^{99}+O(q^{100}) \) 20 * q + q^2 + q^4 + 2 * q^5 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^11 - 5 * q^12 - 6 * q^13 - 4 * q^14 + 10 * q^15 + 3 * q^16 - 6 * q^17 + 2 * q^18 + 4 * q^19 + 4 * q^20 + 10 * q^21 - 20 * q^22 + 100 * q^24 - 2 * q^25 + 3 * q^26 + 6 * q^28 + 6 * q^29 - 10 * q^30 - 9 * q^32 - 10 * q^33 + 8 * q^34 - 8 * q^35 + 2 * q^36 - 2 * q^37 - 2 * q^38 + 10 * q^40 - 2 * q^41 - 8 * q^44 - 40 * q^45 + 15 * q^48 + 2 * q^49 + 11 * q^50 - 10 * q^51 + 3 * q^52 + 8 * q^53 - 5 * q^54 + 4 * q^55 + 10 * q^56 - 3 * q^58 - 4 * q^59 - 4 * q^61 - 15 * q^62 - 4 * q^63 - 4 * q^64 + 6 * q^65 - 10 * q^66 + 10 * q^67 + 20 * q^68 - 40 * q^70 - 20 * q^71 - 22 * q^73 + 6 * q^74 - 20 * q^75 - 2 * q^76 + 16 * q^77 + 15 * q^78 + 4 * q^79 - 18 * q^80 + 22 * q^81 + 11 * q^82 + 22 * q^83 - 10 * q^84 + 16 * q^85 - 10 * q^88 + 12 * q^89 - 12 * q^90 + 60 * q^91 - 300 * q^93 + 5 * q^94 - 4 * q^95 + 5 * q^96 - 22 * q^97 - 11 * q^98 + 12 * q^99

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