LMFDB - Embedded newform 507.2.m.a.40.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.13
Character	$\chi$	$=$	507.40
Dual form			507.2.m.a.469.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74042 + 0.428975i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.07413 + 0.563748i) q^{4} +(-1.82535 + 2.64447i) q^{5} +(-0.635632 + 1.67602i) q^{6} +(2.27352 + 2.01416i) q^{7} +(-1.05581 - 0.935370i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(1.74042 + 0.428975i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.07413 + 0.563748i) q^{4} +(-1.82535 + 2.64447i) q^{5} +(-0.635632 + 1.67602i) q^{6} +(2.27352 + 2.01416i) q^{7} +(-1.05581 - 0.935370i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-4.31129 + 3.81947i) q^{10} +(-1.90225 + 0.468862i) q^{11} +(-0.689110 + 0.998348i) q^{12} +(-3.56904 - 0.511806i) q^{13} +(3.09285 + 4.48077i) q^{14} +(-2.40517 - 2.13080i) q^{15} +(-2.81453 - 4.07755i) q^{16} +(4.02845 + 3.56889i) q^{17} +(-1.58719 - 0.833020i) q^{18} +1.72244 q^{19} +(-3.45148 + 1.81148i) q^{20} +(-2.27352 + 2.01416i) q^{21} -3.51184 q^{22} +4.27440 q^{23} +(1.05581 - 0.935370i) q^{24} +(-1.88832 - 4.97910i) q^{25} +(-5.99208 - 2.42179i) q^{26} +(0.354605 - 0.935016i) q^{27} +(1.30658 + 3.44517i) q^{28} +(8.90715 + 2.19542i) q^{29} +(-3.27195 - 4.74024i) q^{30} +(-2.20404 + 5.81157i) q^{31} +(-2.14892 - 5.66624i) q^{32} +(-0.236153 - 1.94489i) q^{33} +(5.48023 + 7.93948i) q^{34} +(-9.47636 + 2.33571i) q^{35} +(-0.908006 - 0.804423i) q^{36} +(3.65981 - 9.65013i) q^{37} +(2.99777 + 0.738883i) q^{38} +(0.938275 - 3.48133i) q^{39} +(4.40079 - 1.08470i) q^{40} +(-1.35948 + 11.1964i) q^{41} +(-4.82090 + 2.53020i) q^{42} +(-0.398891 - 1.05179i) q^{43} +(-2.30759 - 0.568769i) q^{44} +(2.40517 - 2.13080i) q^{45} +(7.43925 + 1.83361i) q^{46} +(-8.31684 + 4.36502i) q^{47} +(4.38708 - 2.30252i) q^{48} +(0.268281 + 2.20949i) q^{49} +(-1.15057 - 9.47576i) q^{50} +(-4.02845 + 3.56889i) q^{51} +(-3.54509 - 2.56179i) q^{52} +(4.81961 + 4.26980i) q^{53} +(1.01826 - 1.47520i) q^{54} +(2.23237 - 5.88628i) q^{55} +(-0.516427 - 4.25316i) q^{56} +(-0.207617 + 1.70988i) q^{57} +(14.5604 + 7.64190i) q^{58} +(6.07512 - 8.80133i) q^{59} +(-1.38224 - 3.64467i) q^{60} +(1.84176 - 1.63166i) q^{61} +(-6.32897 + 9.16910i) q^{62} +(-1.72543 - 2.49972i) q^{63} +(-0.114930 - 0.946532i) q^{64} +(7.86820 - 8.50401i) q^{65} +(0.423306 - 3.48624i) q^{66} +(4.40115 - 2.30990i) q^{67} +(2.31513 + 6.10449i) q^{68} +(-0.515222 + 4.24323i) q^{69} -17.4948 q^{70} +(0.594718 - 4.89795i) q^{71} +(0.801286 + 1.16086i) q^{72} +(4.60068 - 1.13397i) q^{73} +(10.5093 - 15.2253i) q^{74} +(5.17040 - 1.27439i) q^{75} +(1.85013 + 0.971021i) q^{76} +(-5.26916 - 2.76547i) q^{77} +(3.12640 - 5.65648i) q^{78} +(11.5080 - 6.03984i) q^{79} +15.9205 q^{80} +(0.885456 + 0.464723i) q^{81} +(-7.16903 + 18.9032i) q^{82} +(-0.790846 - 6.51320i) q^{83} +(-3.57754 + 0.881784i) q^{84} +(-16.7912 + 4.13865i) q^{85} +(-0.243047 - 2.00167i) q^{86} +(-3.25305 + 8.57758i) q^{87} +(2.44698 + 1.28427i) q^{88} -2.81396 q^{89} +(5.10007 - 2.67672i) q^{90} +(-7.08342 - 8.35222i) q^{91} +(4.59127 + 2.40968i) q^{92} +(-5.50353 - 2.88848i) q^{93} +(-16.3473 + 4.02924i) q^{94} +(-3.14405 + 4.55494i) q^{95} +(5.88395 - 1.45026i) q^{96} +(-4.56939 - 6.61991i) q^{97} +(-0.480896 + 3.96054i) q^{98} +1.95918 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) $ 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	1.74042	+	0.428975i	1.23066	+	0.303331i	0.800452	−	0.599397i	$-0.204593\pi$
$2$	1.74042	+	0.428975i	1.23066	+	0.303331i	0.430211	+	0.902728i	$0.358439\pi$
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$4$	1.07413	+	0.563748i	0.537066	+	0.281874i
$5$	−1.82535	+	2.64447i	−0.816321	+	1.18264i	0.164238	+	0.986421i	$0.447483\pi$
$5$	−1.82535	+	2.64447i	−0.816321	+	1.18264i	−0.980559	+	0.196224i	$0.937132\pi$
$6$	−0.635632	+	1.67602i	−0.259496	+	0.684234i
$7$	2.27352	+	2.01416i	0.859309	+	0.761281i	0.972650	−	0.232275i	$-0.0746169\pi$
$7$	2.27352	+	2.01416i	0.859309	+	0.761281i	−0.113341	+	0.993556i	$0.536155\pi$
$8$	−1.05581	−	0.935370i	−0.373287	−	0.330703i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	−4.31129	+	3.81947i	−1.36335	+	1.20782i
$11$	−1.90225	+	0.468862i	−0.573549	+	0.141367i	−0.515414	−	0.856942i	$-0.672362\pi$
$11$	−1.90225	+	0.468862i	−0.573549	+	0.141367i	−0.0581355	+	0.998309i	$0.518516\pi$
$12$	−0.689110	+	0.998348i	−0.198929	+	0.288198i
$13$	−3.56904	−	0.511806i	−0.989874	−	0.141949i
$13$	−3.56904	−	0.511806i	−0.989874	−	0.141949i
$14$	3.09285	+	4.48077i	0.826599	+	1.19754i
$15$	−2.40517	−	2.13080i	−0.621013	−	0.550169i
$16$	−2.81453	−	4.07755i	−0.703633	−	1.01939i
$17$	4.02845	+	3.56889i	0.977042	+	0.865584i	0.990938	−	0.134320i	$-0.0428850\pi$
$17$	4.02845	+	3.56889i	0.977042	+	0.865584i	−0.0138962	+	0.999903i	$0.504423\pi$
$18$	−1.58719	−	0.833020i	−0.374104	−	0.196345i
$19$	1.72244			0.395154			0.197577	−	0.980287i	$-0.436693\pi$
$19$	1.72244			0.395154			0.197577	+	0.980287i	$0.436693\pi$
$20$	−3.45148	+	1.81148i	−0.771775	+	0.405059i
$21$	−2.27352	+	2.01416i	−0.496122	+	0.439526i
$22$	−3.51184			−0.748727
$23$	4.27440			0.891273			0.445637	−	0.895214i	$-0.352977\pi$
$23$	4.27440			0.891273			0.445637	+	0.895214i	$0.352977\pi$
$24$	1.05581	−	0.935370i	0.215517	−	0.190932i
$25$	−1.88832	−	4.97910i	−0.377664	−	0.995819i
$26$	−5.99208	−	2.42179i	−1.17514	−	0.474952i
$27$	0.354605	−	0.935016i	0.0682437	−	0.179944i
$28$	1.30658	+	3.44517i	0.246920	+	0.651075i
$29$	8.90715	+	2.19542i	1.65402	+	0.407679i	0.952394	−	0.304870i	$-0.0986130\pi$
$29$	8.90715	+	2.19542i	1.65402	+	0.407679i	0.701623	+	0.712549i	$0.252459\pi$
$30$	−3.27195	−	4.74024i	−0.597374	−	0.865446i
$31$	−2.20404	+	5.81157i	−0.395857	+	1.04379i	0.577882	+	0.816121i	$0.303880\pi$
$31$	−2.20404	+	5.81157i	−0.395857	+	1.04379i	−0.973739	+	0.227669i	$0.926890\pi$
$32$	−2.14892	−	5.66624i	−0.379879	−	1.00166i
$33$	−0.236153	−	1.94489i	−0.0411089	−	0.338562i
$34$	5.48023	+	7.93948i	0.939851	+	1.36161i
$35$	−9.47636	+	2.33571i	−1.60180	+	0.394807i
$36$	−0.908006	−	0.804423i	−0.151334	−	0.134071i
$37$	3.65981	−	9.65013i	0.601669	−	1.58647i	−0.194173	−	0.980967i	$-0.562202\pi$
$37$	3.65981	−	9.65013i	0.601669	−	1.58647i	0.795842	−	0.605504i	$-0.207029\pi$
$38$	2.99777	+	0.738883i	0.486302	+	0.119863i
$39$	0.938275	−	3.48133i	0.150244	−	0.557459i
$40$	4.40079	−	1.08470i	0.695826	−	0.171506i
$41$	−1.35948	+	11.1964i	−0.212316	+	1.74858i	0.364045	+	0.931381i	$0.381395\pi$
$41$	−1.35948	+	11.1964i	−0.212316	+	1.74858i	−0.576361	+	0.817195i	$0.695528\pi$
$42$	−4.82090	+	2.53020i	−0.743881	+	0.390419i
$43$	−0.398891	−	1.05179i	−0.0608303	−	0.160396i	0.901155	−	0.433496i	$-0.142720\pi$
$43$	−0.398891	−	1.05179i	−0.0608303	−	0.160396i	−0.961986	+	0.273100i	$0.911951\pi$
$44$	−2.30759	−	0.568769i	−0.347882	−	0.0857451i
$45$	2.40517	−	2.13080i	0.358542	−	0.317640i
$46$	7.43925	+	1.83361i	1.09686	+	0.270351i
$47$	−8.31684	+	4.36502i	−1.21314	+	0.636703i	−0.945124	−	0.326712i	$-0.894059\pi$
$47$	−8.31684	+	4.36502i	−1.21314	+	0.636703i	−0.268012	+	0.963415i	$0.586367\pi$
$48$	4.38708	−	2.30252i	0.633220	−	0.332339i
$49$	0.268281	+	2.20949i	0.0383259	+	0.315642i
$50$	−1.15057	−	9.47576i	−0.162715	−	1.34008i
$51$	−4.02845	+	3.56889i	−0.564095	+	0.499745i
$52$	−3.54509	−	2.56179i	−0.491616	−	0.355256i
$53$	4.81961	+	4.26980i	0.662024	+	0.586502i	0.925769	−	0.378091i	$-0.123419\pi$
$53$	4.81961	+	4.26980i	0.662024	+	0.586502i	−0.263745	+	0.964593i	$0.584958\pi$
$54$	1.01826	−	1.47520i	0.138568	−	0.200750i
$55$	2.23237	−	5.88628i	0.301013	−	0.793706i
$56$	−0.516427	−	4.25316i	−0.0690105	−	0.568352i
$57$	−0.207617	+	1.70988i	−0.0274995	+	0.226479i
$58$	14.5604	+	7.64190i	1.91188	+	1.00343i
$59$	6.07512	−	8.80133i	0.790913	−	1.14584i	−0.195363	−	0.980731i	$-0.562588\pi$
$59$	6.07512	−	8.80133i	0.790913	−	1.14584i	0.986276	−	0.165105i	$-0.0527963\pi$
$60$	−1.38224	−	3.64467i	−0.178446	−	0.470525i
$61$	1.84176	−	1.63166i	0.235814	−	0.208913i	−0.536937	−	0.843622i	$-0.680419\pi$
$61$	1.84176	−	1.63166i	0.235814	−	0.208913i	0.772751	+	0.634710i	$0.218880\pi$
$62$	−6.32897	+	9.16910i	−0.803781	+	1.16448i
$63$	−1.72543	−	2.49972i	−0.217384	−	0.314935i
$64$	−0.114930	−	0.946532i	−0.0143662	−	0.118317i
$65$	7.86820	−	8.50401i	0.975930	−	1.05479i
$66$	0.423306	−	3.48624i	0.0521053	−	0.429126i
$67$	4.40115	−	2.30990i	0.537686	−	0.282199i	−0.173942	−	0.984756i	$-0.555651\pi$
$67$	4.40115	−	2.30990i	0.537686	−	0.282199i	0.711628	+	0.702557i	$0.247958\pi$
$68$	2.31513	+	6.10449i	0.280751	+	0.740278i
$69$	−0.515222	+	4.24323i	−0.0620254	+	0.510825i
$70$	−17.4948			−2.09103
$71$	0.594718	−	4.89795i	0.0705801	−	0.581279i	−0.913920	−	0.405895i	$-0.866960\pi$
$71$	0.594718	−	4.89795i	0.0705801	−	0.581279i	0.984500	−	0.175385i	$-0.0561169\pi$
$72$	0.801286	+	1.16086i	0.0944324	+	0.136809i
$73$	4.60068	−	1.13397i	0.538469	−	0.132721i	0.0393034	−	0.999227i	$-0.487486\pi$
$73$	4.60068	−	1.13397i	0.538469	−	0.132721i	0.499166	+	0.866507i	$0.333640\pi$
$74$	10.5093	−	15.2253i	1.22168	−	1.76991i
$75$	5.17040	−	1.27439i	0.597027	−	0.147154i
$76$	1.85013	+	0.971021i	0.212224	+	0.111384i
$77$	−5.26916	−	2.76547i	−0.600476	−	0.315154i
$78$	3.12640	−	5.65648i	0.353995	−	0.640470i
$79$	11.5080	−	6.03984i	1.29475	−	0.679535i	0.330315	−	0.943871i	$-0.392845\pi$
$79$	11.5080	−	6.03984i	1.29475	−	0.679535i	0.964431	+	0.264335i	$0.0851526\pi$
$80$	15.9205			1.77996
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	−7.16903	+	18.9032i	−0.791687	+	2.08751i
$83$	−0.790846	−	6.51320i	−0.0868066	−	0.714917i	−0.969521	−	0.245007i	$-0.921210\pi$
$83$	−0.790846	−	6.51320i	−0.0868066	−	0.714917i	0.882715	−	0.469909i	$-0.155713\pi$
$84$	−3.57754	+	0.881784i	−0.390341	+	0.0962105i
$85$	−16.7912	+	4.13865i	−1.82126	+	0.448900i
$86$	−0.243047	−	2.00167i	−0.0262084	−	0.215846i
$87$	−3.25305	+	8.57758i	−0.348763	+	0.919613i
$88$	2.44698	+	1.28427i	0.260849	+	0.136904i
$89$	−2.81396			−0.298280			−0.149140	−	0.988816i	$-0.547650\pi$
$89$	−2.81396			−0.298280			−0.149140	+	0.988816i	$0.547650\pi$
$90$	5.10007	−	2.67672i	0.537595	−	0.282151i
$91$	−7.08342	−	8.35222i	−0.742544	−	0.875551i
$92$	4.59127	+	2.40968i	0.478673	+	0.251227i
$93$	−5.50353	−	2.88848i	−0.570690	−	0.299521i
$94$	−16.3473	+	4.02924i	−1.68609	+	0.415585i
$95$	−3.14405	+	4.55494i	−0.322573	+	0.467327i
$96$	5.88395	−	1.45026i	0.600528	−	0.148017i
$97$	−4.56939	−	6.61991i	−0.463952	−	0.672150i	0.519261	−	0.854616i	$-0.326207\pi$
$97$	−4.56939	−	6.61991i	−0.463952	−	0.672150i	−0.983212	+	0.182466i	$0.941592\pi$
$98$	−0.480896	+	3.96054i	−0.0485778	+	0.400075i
$99$	1.95918			0.196905
$100$	0.778648	−	6.41275i	0.0778648	−	0.641275i
$101$	−2.60946	−	6.88058i	−0.259651	−	0.684643i	−0.999924	−	0.0123369i	$-0.996073\pi$
$101$	−2.60946	−	6.88058i	−0.259651	−	0.684643i	0.740273	−	0.672307i	$-0.234696\pi$
$102$	−8.54216	+	4.48327i	−0.845800	+	0.443910i
$103$	−0.219426	+	1.80714i	−0.0216207	+	0.178062i	−0.999519	−	0.0310198i	$-0.990125\pi$
$103$	−0.219426	+	1.80714i	−0.0216207	+	0.178062i	0.977898	+	0.209082i	$0.0670476\pi$
$104$	3.28952	+	3.87875i	0.322564	+	0.380342i
$105$	−1.17643	−	9.68880i	−0.114808	−	0.945530i
$106$	6.55650	+	9.49874i	0.636824	+	0.922599i
$107$	−6.93073	+	10.0409i	−0.670019	+	0.970689i	0.329628	+	0.944111i	$0.393077\pi$
$107$	−6.93073	+	10.0409i	−0.670019	+	0.970689i	−0.999647	+	0.0265786i	$0.991539\pi$
$108$	0.908006	−	0.804423i	0.0873729	−	0.0774057i
$109$	−6.90192	−	18.1989i	−0.661084	−	1.74314i	−0.669104	−	0.743169i	$-0.733322\pi$
$109$	−6.90192	−	18.1989i	−0.661084	−	1.74314i	0.00801988	−	0.999968i	$-0.497447\pi$
$110$	6.41033	−	9.28697i	0.611201	−	0.885478i
$111$	9.13863	+	4.79632i	0.867400	+	0.455247i
$112$	1.81396	−	14.9393i	0.171403	−	1.41163i
$113$	1.98395	+	16.3393i	0.186634	+	1.53707i	0.721668	+	0.692240i	$0.243376\pi$
$113$	1.98395	+	16.3393i	0.186634	+	1.53707i	−0.535034	+	0.844831i	$0.679701\pi$
$114$	−1.09484	+	2.88685i	−0.102541	+	0.270378i
$115$	−7.80227	+	11.3035i	−0.727565	+	1.05406i
$116$	8.32980	+	7.37956i	0.773403	+	0.685175i
$117$	3.34285	+	1.35106i	0.309046	+	0.124906i
$118$	14.3488	−	12.7119i	1.32092	−	1.17023i
$119$	1.97042	+	16.2279i	0.180628	+	1.48761i
$120$	0.546332	+	4.49945i	0.0498731	+	0.410742i
$121$	−6.34130	+	3.32817i	−0.576482	+	0.302561i
$122$	3.90538	−	2.04970i	0.353577	−	0.185571i
$123$	−10.9509	−	2.69914i	−0.987405	−	0.243373i
$124$	−5.64369	+	4.99988i	−0.506819	+	0.449002i
$125$	1.01442	+	0.250031i	0.0907322	+	0.0223635i
$126$	−1.93066	−	5.09073i	−0.171997	−	0.453519i
$127$	−1.32237	+	0.694034i	−0.117341	+	0.0615855i	−0.522373	−	0.852717i	$-0.674953\pi$
$127$	−1.32237	+	0.694034i	−0.117341	+	0.0615855i	0.405031	+	0.914303i	$0.367261\pi$
$128$	−1.25490	+	10.3351i	−0.110919	+	0.913498i
$129$	1.09220	−	0.269204i	0.0961630	−	0.0237021i
$130$	17.3420	−	11.4253i	1.52099	−	1.00206i
$131$	22.1150	+	5.45087i	1.93220	+	0.476244i	0.989971	+	0.141274i	$0.0451198\pi$
$131$	22.1150	+	5.45087i	1.93220	+	0.476244i	0.942229	+	0.334970i	$0.108726\pi$
$132$	0.842771	−	2.22220i	0.0733538	−	0.193418i
$133$	3.91599	+	3.46927i	0.339560	+	0.300824i
$134$	8.65074	−	2.13221i	0.747310	−	0.184195i
$135$	1.82535	+	2.64447i	0.157101	+	0.227600i
$136$	−0.915057	−	7.53618i	−0.0784655	−	0.646222i
$137$	−2.67491	−	7.05317i	−0.228533	−	0.602593i	0.770875	−	0.636986i	$-0.219819\pi$
$137$	−2.67491	−	7.05317i	−0.228533	−	0.602593i	−0.999408	+	0.0343935i	$0.989050\pi$
$138$	−2.71694	+	7.16399i	−0.231282	+	0.609839i
$139$	1.60757	+	2.32897i	0.136353	+	0.197541i	0.885212	−	0.465188i	$-0.154013\pi$
$139$	1.60757	+	2.32897i	0.136353	+	0.197541i	−0.748859	+	0.662729i	$0.769398\pi$
$140$	−11.4956	−	2.83341i	−0.971557	−	0.239467i
$141$	−3.33071	−	8.78235i	−0.280496	−	0.739607i
$142$	3.13616	−	8.26937i	0.263180	−	0.693950i
$143$	7.02917	−	0.699806i	0.587808	−	0.0585207i
$144$	1.75692	+	4.63263i	0.146410	+	0.386052i
$145$	−22.0644	+	19.5473i	−1.83235	+	1.62332i
$146$	8.49356			0.702932
$147$	−2.22572			−0.183575
$148$	9.37137	−	8.30231i	0.770322	−	0.682445i
$149$	−14.5832	+	7.65383i	−1.19470	+	0.627026i	−0.940390	−	0.340097i	$-0.889540\pi$
$149$	−14.5832	+	7.65383i	−1.19470	+	0.627026i	−0.254308	+	0.967123i	$0.581848\pi$
$150$	9.54536			0.779375
$151$	−12.7949	−	6.71527i	−1.04123	−	0.546481i	−0.144707	−	0.989474i	$-0.546224\pi$
$151$	−12.7949	−	6.71527i	−1.04123	−	0.546481i	−0.896525	+	0.442994i	$0.853916\pi$
$152$	−1.81857	−	1.61112i	−0.147506	−	0.130679i
$153$	−3.05730	−	4.42926i	−0.247168	−	0.358084i
$154$	−7.98423	−	7.07341i	−0.643388	−	0.569992i
$155$	−11.3454	−	16.4367i	−0.911286	−	1.32023i
$156$	2.97042	−	3.21046i	0.237824	−	0.257042i
$157$	6.15562	−	8.91795i	0.491272	−	0.711730i	−0.496430	−	0.868077i	$-0.665356\pi$
$157$	6.15562	−	8.91795i	0.491272	−	0.711730i	0.987702	+	0.156346i	$0.0499716\pi$
$158$	22.6196	−	5.57524i	1.79952	−	0.443542i
$159$	−4.81961	+	4.26980i	−0.382220	+	0.338617i
$160$	18.9068	+	4.66010i	1.49471	+	0.368413i
$161$	9.71791	+	8.60932i	0.765879	+	0.678510i
$162$	1.34171	+	1.18865i	0.105415	+	0.0933894i
$163$	−1.22142	+	3.22061i	−0.0956687	+	0.252258i	−0.974304	−	0.225235i	$-0.927685\pi$
$163$	−1.22142	+	3.22061i	−0.0956687	+	0.252258i	0.878636	+	0.477493i	$0.158454\pi$
$164$	−7.77219	+	11.2600i	−0.606906	+	0.879255i
$165$	5.57428	+	2.92561i	0.433957	+	0.227758i
$166$	1.41760	−	11.6750i	0.110027	−	0.906153i
$167$	5.53154	+	1.36340i	0.428043	+	0.105503i	0.447451	−	0.894308i	$-0.352332\pi$
$167$	5.53154	+	1.36340i	0.428043	+	0.105503i	−0.0194076	+	0.999812i	$0.506178\pi$
$168$	4.28440			0.330548
$169$	12.4761	+	3.65331i	0.959701	+	0.281024i
$170$	−30.9991			−2.37752
$171$	−1.67239	−	0.412206i	−0.127891	−	0.0315222i
$172$	0.164483	−	1.35464i	0.0125417	−	0.103290i
$173$	−18.8645	−	9.90085i	−1.43424	−	0.752747i	−0.444521	−	0.895769i	$-0.646626\pi$
$173$	−18.8645	−	9.90085i	−1.43424	−	0.752747i	−0.989720	+	0.143021i	$0.954318\pi$
$174$	−9.34124	+	13.5331i	−0.708158	+	1.02594i
$175$	5.73557	−	15.1234i	0.433568	−	1.14322i
$176$	7.26574	+	6.43689i	0.547676	+	0.485199i
$177$	8.00489	+	7.09171i	0.601684	+	0.533046i
$178$	−4.89748	−	1.20712i	−0.367082	−	0.0904775i
$179$	−7.50773	+	6.65127i	−0.561154	+	0.497139i	−0.895349	−	0.445365i	$-0.853074\pi$
$179$	−7.50773	+	6.65127i	−0.561154	+	0.497139i	0.334195	+	0.942504i	$0.391536\pi$
$180$	3.78471	−	0.932846i	0.282095	−	0.0695302i
$181$	−4.39286	+	6.36416i	−0.326519	+	0.473044i	−0.951523	−	0.307577i	$-0.900482\pi$
$181$	−4.39286	+	6.36416i	−0.326519	+	0.473044i	0.625004	+	0.780621i	$0.285097\pi$
$182$	−8.74523	−	17.5750i	−0.648240	−	1.30274i
$183$	1.39776	+	2.02501i	0.103326	+	0.149693i
$184$	−4.51297	−	3.99814i	−0.332701	−	0.294747i
$185$	18.8391	+	27.2931i	1.38508	+	2.00663i
$186$	−8.33938	−	7.38804i	−0.611473	−	0.541718i
$187$	−9.33642	−	4.90013i	−0.682747	−	0.358333i
$188$	−11.3942			−0.831004
$189$	2.68947	−	1.41154i	0.195630	−	0.102675i
$190$	−7.42593	+	6.57880i	−0.538733	+	0.477276i
$191$	−1.96389			−0.142102			−0.0710512	−	0.997473i	$-0.522635\pi$
$191$	−1.96389			−0.142102			−0.0710512	+	0.997473i	$0.522635\pi$
$192$	0.953484			0.0688118
$193$	−4.30855	+	3.81704i	−0.310136	+	0.274757i	−0.803804	−	0.594894i	$-0.797194\pi$
$193$	−4.30855	+	3.81704i	−0.310136	+	0.274757i	0.493668	+	0.869650i	$0.335656\pi$
$194$	−5.11289	−	13.4816i	−0.367084	−	0.967921i
$195$	7.49360	+	8.83588i	0.536628	+	0.632751i
$196$	−0.957429	+	2.52453i	−0.0683878	+	0.180324i
$197$	−3.32342	−	8.76313i	−0.236784	−	0.624347i	0.762973	−	0.646431i	$-0.223739\pi$
$197$	−3.32342	−	8.76313i	−0.236784	−	0.624347i	−0.999756	+	0.0220840i	$0.992970\pi$
$198$	3.40979	+	0.840439i	0.242323	+	0.0597274i
$199$	7.23492	+	10.4816i	0.512870	+	0.743020i	0.990794	−	0.135381i	$-0.0432259\pi$
$199$	7.23492	+	10.4816i	0.512870	+	0.743020i	−0.477924	+	0.878401i	$0.658611\pi$
$200$	−2.66358	+	7.02328i	−0.188343	+	0.496621i
$201$	1.76256	+	4.64748i	0.124321	+	0.327808i
$202$	−1.58996	−	13.0945i	−0.111869	−	0.921326i
$203$	15.8286	+	22.9318i	1.11095	+	1.60949i
$204$	−6.33904	+	1.56243i	−0.443822	+	0.109392i
$205$	−27.1269	−	24.0324i	−1.89463	−	1.67849i
$206$	−1.15711	+	3.05105i	−0.0806196	+	0.212577i
$207$	−4.15019	−	1.02293i	−0.288458	−	0.0710986i
$208$	7.95826	+	15.9934i	0.551806	+	1.10895i
$209$	−3.27650	+	0.807585i	−0.226640	+	0.0558619i
$210$	2.10877	−	17.3673i	0.145519	−	1.19845i
$211$	3.42933	−	1.79985i	0.236085	−	0.123907i	−0.342533	−	0.939506i	$-0.611285\pi$
$211$	3.42933	−	1.79985i	0.236085	−	0.123907i	0.578617	+	0.815599i	$0.303592\pi$
$212$	2.76980	+	7.30337i	0.190231	+	0.501598i
$213$	4.79055	+	1.18076i	0.328243	+	0.0809046i
$214$	−16.3697	+	14.5023i	−1.11901	+	0.991354i
$215$	3.50955	+	0.865025i	0.239349	+	0.0589942i
$216$	−1.24898	+	0.655517i	−0.0849825	+	0.0446023i
$217$	−16.7164	+	8.77342i	−1.13478	+	0.595579i
$218$	−4.20538	−	34.6345i	−0.284825	−	2.34574i
$219$	0.571147	+	4.70382i	0.0385946	+	0.317855i
$220$	5.71624	−	5.06415i	0.385389	−	0.341425i
$221$	−12.5511	−	14.7993i	−0.844279	−	0.995509i
$222$	13.8476	+	12.2679i	0.929387	+	0.823365i
$223$	0.555709	−	0.805083i	0.0372130	−	0.0539124i	−0.803936	−	0.594716i	$-0.797264\pi$
$223$	0.555709	−	0.805083i	0.0372130	−	0.0539124i	0.841149	+	0.540804i	$0.181880\pi$
$224$	6.52711	−	17.2106i	0.436111	−	1.14993i
$225$	0.641875	+	5.28632i	0.0427917	+	0.352421i
$226$	−3.55624	+	29.2883i	−0.236558	+	1.94823i
$227$	−0.717452	−	0.376548i	−0.0476189	−	0.0249923i	0.440746	−	0.897632i	$-0.354714\pi$
$227$	−0.717452	−	0.376548i	−0.0476189	−	0.0249923i	−0.488365	+	0.872640i	$0.662406\pi$
$228$	−1.18695	+	1.71959i	−0.0786076	+	0.113883i
$229$	2.15849	+	5.69147i	0.142637	+	0.376103i	0.987229	−	0.159307i	$-0.0509261\pi$
$229$	2.15849	+	5.69147i	0.142637	+	0.376103i	−0.844592	+	0.535411i	$0.820157\pi$
$230$	−18.4282	+	16.3259i	−1.21512	+	1.07650i
$231$	3.38043	−	4.89740i	0.222416	−	0.322225i
$232$	−7.35077	−	10.6494i	−0.482602	−	0.699170i
$233$	−0.567136	−	4.67078i	−0.0371543	−	0.305993i	−0.999425	−	0.0339001i	$-0.989207\pi$
$233$	−0.567136	−	4.67078i	−0.0371543	−	0.305993i	0.962271	−	0.272093i	$-0.0877159\pi$
$234$	5.23839	+	3.78541i	0.342444	+	0.247460i
$235$	3.63797	−	29.9614i	0.237315	−	1.95446i
$236$	11.4872	−	6.02896i	0.747754	−	0.392452i
$237$	4.60867	+	12.1521i	0.299365	+	0.789362i
$238$	−3.53199	+	29.0886i	−0.228945	+	1.88553i
$239$	26.4241			1.70923			0.854617	−	0.519259i	$-0.173792\pi$
$239$	26.4241			1.70923			0.854617	+	0.519259i	$0.173792\pi$
$240$	−1.91900	+	15.8044i	−0.123871	+	1.02017i
$241$	2.64666	+	3.83435i	0.170486	+	0.246992i	0.898908	−	0.438137i	$-0.144361\pi$
$241$	2.64666	+	3.83435i	0.170486	+	0.246992i	−0.728422	+	0.685129i	$0.759746\pi$
$242$	−12.4642	+	3.07216i	−0.801231	+	0.197486i
$243$	−0.568065	+	0.822984i	−0.0364414	+	0.0527944i
$244$	2.89814	−	0.714328i	0.185535	−	0.0457302i
$245$	−6.33266	−	3.32364i	−0.404579	−	0.212339i
$246$	−17.9012	−	9.39529i	−1.14134	−	0.599022i
$247$	−6.14745	−	0.881554i	−0.391153	−	0.0560919i
$248$	7.76302	−	4.07435i	0.492953	−	0.258721i
$249$	6.56104			0.415789
$250$	1.65825	+	0.870319i	0.104877	+	0.0550438i
$251$	7.01483	−	18.4966i	0.442772	−	1.16749i	−0.509021	−	0.860754i	$-0.669993\pi$
$251$	7.01483	−	18.4966i	0.442772	−	1.16749i	0.951793	−	0.306740i	$-0.0992382\pi$
$252$	−0.444130	−	3.65774i	−0.0279776	−	0.230416i
$253$	−8.13096	+	2.00410i	−0.511189	+	0.125997i
$254$	−2.59920	+	0.640646i	−0.163089	+	0.0401977i
$255$	−2.08452	−	17.1676i	−0.130538	−	1.07508i
$256$	−7.29376	+	19.2321i	−0.455860	+	1.20200i
$257$	19.1871	+	10.0702i	1.19686	+	0.628161i	0.940952	−	0.338541i	$-0.109933\pi$
$257$	19.1871	+	10.0702i	1.19686	+	0.628161i	0.255908	+	0.966701i	$0.417626\pi$
$258$	2.01637			0.125534
$259$	27.7576	−	14.5683i	1.72477	−	0.905229i
$260$	13.2456	−	4.69875i	0.821458	−	0.291404i
$261$	−8.12293	−	4.26324i	−0.502797	−	0.263888i
$262$	36.1512	+	18.9736i	2.23343	+	1.17219i
$263$	−6.05563	+	1.49258i	−0.373406	+	0.0920364i	−0.421553	−	0.906804i	$-0.638515\pi$
$263$	−6.05563	+	1.49258i	−0.373406	+	0.0920364i	0.0481465	+	0.998840i	$0.484669\pi$
$264$	−1.56986	+	2.27434i	−0.0966183	+	0.139976i
$265$	−20.0888	+	4.95145i	−1.23405	+	0.304165i
$266$	5.32724	+	7.71785i	0.326634	+	0.473211i
$267$	0.339186	−	2.79345i	0.0207578	−	0.170956i
$268$	6.02962			0.368317
$269$	1.82558	−	15.0350i	0.111308	−	0.916700i	−0.824906	−	0.565269i	$-0.808772\pi$
$269$	1.82558	−	15.0350i	0.111308	−	0.916700i	0.936214	−	0.351431i	$-0.114305\pi$
$270$	2.04246	+	5.38553i	0.124300	+	0.327753i
$271$	9.73328	−	5.10842i	0.591254	−	0.310314i	−0.142430	−	0.989805i	$-0.545491\pi$
$271$	9.73328	−	5.10842i	0.591254	−	0.310314i	0.733684	+	0.679491i	$0.237799\pi$
$272$	3.21416	−	26.4710i	0.194887	−	1.60504i
$273$	9.14514	−	6.02502i	0.553489	−	0.364651i
$274$	−1.62984	−	13.4230i	−0.0984623	−	0.810910i
$275$	5.92656	+	8.58611i	0.357385	+	0.517762i
$276$	−2.94553	+	4.26734i	−0.177300	+	0.256864i
$277$	8.16179	−	7.23072i	0.490394	−	0.434452i	−0.381337	−	0.924436i	$-0.624536\pi$
$277$	8.16179	−	7.23072i	0.490394	−	0.434452i	0.871731	+	0.489985i	$0.162998\pi$
$278$	1.79878	+	4.74300i	0.107884	+	0.284466i
$279$	3.53079	−	5.11524i	0.211383	−	0.306241i
$280$	12.1900	+	6.39782i	0.728494	+	0.382343i
$281$	3.05752	−	25.1810i	0.182396	−	1.50217i	−0.557911	−	0.829901i	$-0.688397\pi$
$281$	3.05752	−	25.1810i	0.182396	−	1.50217i	0.740307	−	0.672269i	$-0.234680\pi$
$282$	−2.02942	−	16.7138i	−0.120850	−	0.995290i
$283$	1.27193	−	3.35380i	0.0756084	−	0.199363i	−0.891883	−	0.452265i	$-0.850616\pi$
$283$	1.27193	−	3.35380i	0.0756084	−	0.199363i	0.967492	+	0.252903i	$0.0813852\pi$
$284$	3.40001	−	4.92577i	0.201754	−	0.292291i
$285$	−4.14276	−	3.67016i	−0.245396	−	0.217402i
$286$	12.5339	+	1.79738i	0.741145	+	0.106281i
$287$	−25.6421	+	22.7169i	−1.51360	+	1.34094i
$288$	0.730458	+	6.01586i	0.0430426	+	0.354488i
$289$	1.44227	+	11.8781i	0.0848392	+	0.698714i
$290$	−46.7866	+	24.5555i	−2.74741	+	1.44195i
$291$	7.12242	−	3.73814i	0.417524	−	0.219133i
$292$	5.58101	+	1.37560i	0.326604	+	0.0805007i
$293$	−18.9200	+	16.7617i	−1.10532	+	0.979227i	−0.999884	−	0.0151996i	$-0.995162\pi$
$293$	−18.9200	+	16.7617i	−1.10532	+	0.979227i	−0.105434	+	0.994426i	$0.533623\pi$
$294$	−3.87369	−	0.954780i	−0.225918	−	0.0556839i
$295$	12.1857	+	32.1310i	0.709478	+	1.87074i
$296$	−12.8905	+	6.76547i	−0.749246	+	0.393235i
$297$	−0.236153	+	1.94489i	−0.0137030	+	0.112854i
$298$	−28.6641	+	7.06507i	−1.66047	+	0.409269i
$299$	−15.2555	−	2.18766i	−0.882248	−	0.126516i
$300$	6.27213	+	1.54594i	0.362122	+	0.0892550i
$301$	1.21159	−	3.19469i	0.0698347	−	0.184139i
$302$	−19.3878	−	17.1761i	−1.11564	−	0.988372i
$303$	7.14495	−	1.76107i	0.410467	−	0.101171i
$304$	−4.84785	−	7.02333i	−0.278044	−	0.402816i
$305$	0.953022	+	7.84884i	0.0545699	+	0.449424i
$306$	−3.42094	−	9.02028i	−0.195562	−	0.515655i
$307$	−1.78754	+	4.71334i	−0.102020	+	0.269005i	−0.976302	−	0.216414i	$-0.930564\pi$
$307$	−1.78754	+	4.71334i	−0.102020	+	0.269005i	0.874282	+	0.485419i	$0.161333\pi$
$308$	−4.10074	−	5.94095i	−0.233662	−	0.338517i
$309$	−1.76751	−	0.435652i	−0.100550	−	0.0247834i
$310$	−12.6949	−	33.4736i	−0.721020	−	1.90117i
$311$	4.51359	−	11.9014i	0.255942	−	0.674864i	−0.744035	−	0.668140i	$-0.767091\pi$
$311$	4.51359	−	11.9014i	0.255942	−	0.674864i	0.999977	−	0.00672347i	$-0.00214016\pi$
$312$	−4.24697	+	2.79800i	−0.240437	+	0.158406i
$313$	8.09466	+	21.3439i	0.457537	+	1.20643i	0.943184	+	0.332271i	$0.107815\pi$
$313$	8.09466	+	21.3439i	0.457537	+	1.20643i	−0.485647	+	0.874155i	$0.661416\pi$
$314$	14.5389	−	12.8804i	0.820480	−	0.726882i
$315$	9.75996			0.549912
$316$	15.7660			0.886908
$317$	2.78742	−	2.46944i	0.156557	−	0.138697i	−0.581208	−	0.813755i	$-0.697420\pi$
$317$	2.78742	−	2.46944i	0.156557	−	0.138697i	0.737765	+	0.675058i	$0.235881\pi$
$318$	−10.2198	+	5.36375i	−0.573097	+	0.300784i
$319$	−17.9730			−1.00629
$320$	2.71287	+	1.42382i	0.151654	+	0.0795941i
$321$	−9.13227	−	8.09049i	−0.509714	−	0.451567i
$322$	13.2201	+	19.1526i	0.736726	+	1.06733i
$323$	6.93875	+	6.14720i	0.386082	+	0.342039i
$324$	0.689110	+	0.998348i	0.0382839	+	0.0554638i
$325$	4.19117	+	18.7371i	0.232484	+	1.03934i
$326$	−3.50734	+	5.08126i	−0.194254	+	0.281425i
$327$	18.8981	−	4.65797i	1.04507	−	0.257586i
$328$	11.9081	−	10.5496i	0.657514	−	0.582507i
$329$	−27.7003	−	6.82752i	−1.52717	−	0.376413i
$330$	8.44658	+	7.48302i	0.464969	+	0.411927i
$331$	26.1390	+	23.1571i	1.43673	+	1.27283i	0.904665	+	0.426124i	$0.140121\pi$
$331$	26.1390	+	23.1571i	1.43673	+	1.27283i	0.532062	+	0.846705i	$0.321417\pi$
$332$	2.82233	−	7.44188i	0.154896	−	0.408426i
$333$	−5.86289	+	8.49387i	−0.321284	+	0.465461i
$334$	9.04234	+	4.74579i	0.494775	+	0.259678i
$335$	−1.92516	+	15.8551i	−0.105183	+	0.866256i
$336$	14.6117	+	3.60147i	0.797135	+	0.196476i
$337$	−33.4239			−1.82072			−0.910358	−	0.413821i	$-0.864194\pi$
$337$	−33.4239			−1.82072			−0.910358	+	0.413821i	$0.864194\pi$
$338$	20.1465	+	11.7102i	1.09583	+	0.636953i
$339$	−16.4593			−0.893946
$340$	−20.3691	−	5.02053i	−1.10467	−	0.272276i
$341$	1.46780	−	12.0884i	0.0794859	−	0.654626i
$342$	−2.73383	−	1.43482i	−0.147829	−	0.0775864i
$343$	8.23769	−	11.9344i	0.444794	−	0.644395i
$344$	−0.562657	+	1.48361i	−0.0303364	+	0.0799906i
$345$	−10.2807	−	9.10787i	−0.553492	−	0.490351i
$346$	−28.5849	−	25.3240i	−1.53674	−	1.36143i
$347$	−5.07173	−	1.25007i	−0.272265	−	0.0671073i	0.100819	−	0.994905i	$-0.467854\pi$
$347$	−5.07173	−	1.25007i	−0.272265	−	0.0671073i	−0.373084	+	0.927797i	$0.621700\pi$
$348$	−8.32980	+	7.37956i	−0.446524	+	0.395586i
$349$	−7.19649	+	1.77378i	−0.385219	+	0.0949480i	−0.427169	−	0.904172i	$-0.640489\pi$
$349$	−7.19649	+	1.77378i	−0.385219	+	0.0949480i	0.0419500	+	0.999120i	$0.486643\pi$
$350$	16.4699	−	23.8607i	0.880352	−	1.27541i
$351$	−1.74415	+	3.15562i	−0.0930956	+	0.168435i
$352$	6.74446	+	9.77104i	0.359481	+	0.520798i
$353$	5.88553	+	5.21413i	0.313255	+	0.277520i	0.805070	−	0.593180i	$-0.202128\pi$
$353$	5.88553	+	5.21413i	0.313255	+	0.277520i	−0.491815	+	0.870700i	$0.663666\pi$
$354$	10.8897	+	15.7765i	0.578781	+	0.838509i
$355$	11.8669	+	10.5132i	0.629831	+	0.557981i
$356$	−3.02257	−	1.58637i	−0.160196	−	0.0840773i
$357$	−16.3471			−0.865178
$358$	−15.9198	+	8.35538i	−0.841390	+	0.441595i
$359$	5.76614	−	5.10835i	0.304325	−	0.269609i	−0.497113	−	0.867686i	$-0.665607\pi$
$359$	5.76614	−	5.10835i	0.304325	−	0.269609i	0.801439	+	0.598077i	$0.204068\pi$
$360$	−4.53250			−0.238884
$361$	−16.0332			−0.843853
$362$	−10.3755	+	9.19188i	−0.545324	+	0.483115i
$363$	−2.53955	−	6.69623i	−0.133292	−	0.351461i
$364$	−2.89998	−	12.9647i	−0.152000	−	0.679533i
$365$	−5.39910	+	14.2363i	−0.282602	+	0.745160i
$366$	1.56402	+	4.12397i	0.0817525	+	0.215564i
$367$	19.4338	+	4.79001i	1.01444	+	0.250036i	0.711283	−	0.702905i	$-0.248114\pi$
$367$	19.4338	+	4.79001i	1.01444	+	0.250036i	0.303154	+	0.952942i	$0.401960\pi$
$368$	−12.0304	−	17.4291i	−0.627129	−	0.908553i
$369$	3.99944	−	10.5457i	0.208203	−	0.548985i
$370$	21.0799	+	55.5830i	1.09589	+	2.88962i
$371$	2.35740	+	19.4149i	0.122390	+	1.00797i
$372$	−4.28315	−	6.20521i	−0.222071	−	0.321725i
$373$	8.87327	−	2.18707i	0.459441	−	0.113242i	−0.00280071	−	0.999996i	$-0.500891\pi$
$373$	8.87327	−	2.18707i	0.459441	−	0.113242i	0.462241	+	0.886754i	$0.347045\pi$
$374$	−14.1473	−	12.5334i	−0.731538	−	0.648086i
$375$	−0.370483	+	0.976883i	−0.0191316	+	0.0504460i
$376$	12.8639	+	3.17068i	0.663407	+	0.163515i
$377$	−30.6664	−	12.3943i	−1.57940	−	0.638337i
$378$	5.28633	−	1.30296i	0.271900	−	0.0670172i
$379$	−1.54887	+	12.7561i	−0.0795603	+	0.655238i	0.897309	+	0.441402i	$0.145519\pi$
$379$	−1.54887	+	12.7561i	−0.0795603	+	0.655238i	−0.976870	+	0.213836i	$0.931404\pi$
$380$	−5.94497	+	3.12016i	−0.304970	+	0.160061i
$381$	−0.529579	−	1.39639i	−0.0271312	−	0.0715390i
$382$	−3.41800	−	0.842462i	−0.174880	−	0.0431041i
$383$	−7.16177	+	6.34478i	−0.365949	+	0.324203i	−0.825979	−	0.563701i	$-0.809377\pi$
$383$	−7.16177	+	6.34478i	−0.365949	+	0.324203i	0.460030	+	0.887903i	$0.347839\pi$
$384$	−10.1084	−	2.49151i	−0.515844	−	0.127144i
$385$	16.9313	−	8.88621i	0.862896	−	0.452883i
$386$	−9.13611	+	4.79500i	−0.465016	+	0.244059i
$387$	0.135590	+	1.11669i	0.00689245	+	0.0567644i
$388$	−1.17617	−	9.68665i	−0.0597111	−	0.491765i
$389$	10.7936	−	9.56230i	0.547258	−	0.484828i	−0.343597	−	0.939117i	$-0.611645\pi$
$389$	10.7936	−	9.56230i	0.547258	−	0.484828i	0.890854	+	0.454289i	$0.150107\pi$
$390$	9.25165	+	18.5927i	0.468475	+	0.941479i
$391$	17.2192	+	15.2549i	0.870811	+	0.771472i
$392$	1.78344	−	2.58376i	0.0900773	−	0.130499i
$393$	−8.07679	+	21.2968i	−0.407420	+	1.07428i
$394$	−2.02498	−	16.6772i	−0.102017	−	0.840185i
$395$	−5.03383	+	41.4573i	−0.253279	+	2.08594i
$396$	2.10442	+	1.10448i	0.105751	+	0.0555023i
$397$	−10.2615	+	14.8663i	−0.515008	+	0.746118i	−0.991077	−	0.133290i	$-0.957446\pi$
$397$	−10.2615	+	14.8663i	−0.515008	+	0.746118i	0.476069	+	0.879408i	$0.342061\pi$
$398$	8.09546	+	21.3460i	0.405789	+	1.06998i
$399$	−3.91599	+	3.46927i	−0.196045	+	0.173681i
$400$	−14.9878	+	21.7135i	−0.749389	+	1.08568i
$401$	−4.18881	−	6.06853i	−0.209179	−	0.303048i	0.704325	−	0.709877i	$-0.251250\pi$
$401$	−4.18881	−	6.06853i	−0.209179	−	0.303048i	−0.913504	+	0.406829i	$0.866634\pi$
$402$	1.07394	+	8.84467i	0.0535631	+	0.441132i
$403$	10.8407	−	19.6137i	0.540014	−	0.977028i
$404$	1.07601	−	8.86173i	0.0535335	−	0.440888i
$405$	−2.84521	+	1.49328i	−0.141380	+	0.0742019i
$406$	17.7113	+	46.7010i	0.879000	+	2.31773i
$407$	−2.43729	+	20.0729i	−0.120812	+	0.994976i
$408$	7.59153			0.375837
$409$	4.13787	−	34.0784i	0.204605	−	1.68507i	−0.422679	−	0.906280i	$-0.638910\pi$
$409$	4.13787	−	34.0784i	0.204605	−	1.68507i	0.627283	−	0.778791i	$-0.284167\pi$
$410$	−36.9030	−	53.4632i	−1.82251	−	2.64036i
$411$	7.32417	−	1.80525i	0.361275	−	0.0890462i
$412$	−1.25446	+	1.81740i	−0.0618029	+	0.0895369i
$413$	31.5392	−	7.77371i	1.55194	−	0.382519i
$414$	−6.78427	−	3.56066i	−0.333428	−	0.174997i
$415$	18.6676	+	9.79749i	0.916355	+	0.480940i
$416$	4.76957	+	21.3229i	0.233848	+	1.04544i
$417$	−2.50576	+	1.31513i	−0.122708	+	0.0644020i
$418$	−6.04893			−0.295863
$419$	−7.13001	−	3.74212i	−0.348324	−	0.182815i	0.281483	−	0.959566i	$-0.409174\pi$
$419$	−7.13001	−	3.74212i	−0.348324	−	0.182815i	−0.629807	+	0.776752i	$0.716866\pi$
$420$	4.19840	−	11.0703i	0.204861	−	0.540174i
$421$	−1.72393	−	14.1979i	−0.0840194	−	0.691962i	−0.972476	−	0.233002i	$-0.925145\pi$
$421$	−1.72393	−	14.1979i	−0.0840194	−	0.691962i	0.888457	−	0.458960i	$-0.151778\pi$
$422$	6.74057	−	1.66140i	0.328126	−	0.0808757i
$423$	9.11979	−	2.24783i	0.443419	−	0.109293i
$424$	−1.09477	−	9.01623i	−0.0531667	−	0.437867i
$425$	10.1629	−	26.7972i	0.492971	−	1.29986i
$426$	7.83105	+	4.11005i	0.379416	+	0.199133i
$427$	7.47370			0.361678
$428$	−13.1050	+	6.87806i	−0.633456	+	0.332464i
$429$	−0.152569	+	7.06227i	−0.00736608	+	0.340969i
$430$	5.73701	+	3.01102i	0.276663	+	0.145204i
$431$	−8.69045	−	4.56110i	−0.418604	−	0.219700i	0.242251	−	0.970213i	$-0.422114\pi$
$431$	−8.69045	−	4.56110i	−0.418604	−	0.219700i	−0.660856	+	0.750513i	$0.729806\pi$
$432$	−4.81062	+	1.18571i	−0.231451	+	0.0570476i
$433$	18.3956	−	26.6507i	0.884037	−	1.28075i	−0.0749178	−	0.997190i	$-0.523869\pi$
$433$	18.3956	−	26.6507i	0.884037	−	1.28075i	0.958955	−	0.283559i	$-0.0915152\pi$
$434$	−32.8571	+	8.09854i	−1.57719	+	0.388742i
$435$	−16.7452	−	24.2597i	−0.802873	−	1.16316i
$436$	2.84600	−	23.4390i	0.136299	−	1.12252i
$437$	7.36238			0.352191
$438$	−1.02379	+	8.43164i	−0.0489184	+	0.402879i
$439$	−8.99219	−	23.7104i	−0.429174	−	1.13164i	−0.958969	−	0.283512i	$-0.908500\pi$
$439$	−8.99219	−	23.7104i	−0.429174	−	1.13164i	0.529795	−	0.848126i	$-0.322269\pi$
$440$	−7.86282	+	4.12673i	−0.374845	+	0.196734i
$441$	0.268281	−	2.20949i	0.0127753	−	0.105214i
$442$	−15.4957	−	31.1411i	−0.737054	−	1.48123i
$443$	−4.54767	−	37.4534i	−0.216066	−	1.77947i	−0.548312	−	0.836274i	$-0.684729\pi$
$443$	−4.54767	−	37.4534i	−0.216066	−	1.77947i	0.332245	−	0.943193i	$-0.392194\pi$
$444$	7.11218	+	10.3038i	0.337529	+	0.488995i
$445$	5.13646	−	7.44145i	0.243492	−	0.352759i
$446$	1.31253	−	1.16280i	0.0621500	−	0.0550601i
$447$	−5.84022	−	15.3994i	−0.276233	−	0.728366i
$448$	1.64517	−	2.38344i	0.0777271	−	0.112607i
$449$	8.00678	+	4.20228i	0.377863	+	0.198318i	0.642953	−	0.765906i	$-0.277709\pi$
$449$	8.00678	+	4.20228i	0.377863	+	0.198318i	−0.265089	+	0.964224i	$0.585401\pi$
$450$	−1.15057	+	9.47576i	−0.0542382	+	0.446692i
$451$	−2.66347	−	21.9356i	−0.125418	−	1.03291i
$452$	−7.08022	+	18.6690i	−0.333025	+	0.878116i
$453$	8.20856	−	11.8921i	0.385672	−	0.558742i
$454$	−1.08714	−	0.963120i	−0.0510219	−	0.0452015i
$455$	35.0169	−	3.48620i	1.64162	−	0.163436i
$456$	1.81857	−	1.61112i	0.0851626	−	0.0754474i
$457$	−0.568604	−	4.68288i	−0.0265982	−	0.219056i	0.973349	−	0.229329i	$-0.0736531\pi$
$457$	−0.568604	−	4.68288i	−0.0265982	−	0.219056i	−0.999947	+	0.0102729i	$0.996730\pi$
$458$	1.31518	+	10.8315i	0.0614544	+	0.506123i
$459$	4.76548	−	2.50112i	0.222434	−	0.116742i
$460$	−14.7530	+	7.74298i	−0.687863	+	0.361018i
$461$	−21.9899	−	5.42003i	−1.02417	−	0.252436i	−0.308762	−	0.951139i	$-0.599914\pi$
$461$	−21.9899	−	5.42003i	−1.02417	−	0.252436i	−0.715411	+	0.698704i	$0.753761\pi$
$462$	7.98423	−	7.07341i	0.371460	−	0.329085i
$463$	−10.2118	−	2.51698i	−0.474583	−	0.116974i	−0.00523280	−	0.999986i	$-0.501666\pi$
$463$	−10.2118	−	2.51698i	−0.474583	−	0.116974i	−0.469350	+	0.883012i	$0.655512\pi$
$464$	−16.1175	−	42.4984i	−0.748238	−	1.97294i
$465$	17.6844	−	9.28147i	0.820093	−	0.430418i
$466$	1.01660	−	8.37241i	0.0470929	−	0.387845i
$467$	26.5081	−	6.53367i	1.22665	−	0.302342i	0.427800	−	0.903873i	$-0.359289\pi$
$467$	26.5081	−	6.53367i	1.22665	−	0.302342i	0.798849	+	0.601531i	$0.205442\pi$
$468$	2.82900	+	3.33574i	0.130771	+	0.154195i
$469$	14.6586	+	3.61302i	0.676871	+	0.166834i
$470$	19.1843	−	50.5848i	0.884904	−	2.33330i
$471$	8.11095	+	7.18568i	0.373733	+	0.331099i
$472$	−14.6467	+	3.61009i	−0.674169	+	0.166168i
$473$	1.25193	+	1.81374i	0.0575640	+	0.0833958i
$474$	2.80809	+	23.1267i	0.128980	+	1.06225i
$475$	−3.25252	−	8.57618i	−0.149236	−	0.393502i
$476$	−7.03194	+	18.5417i	−0.322309	+	0.849858i
$477$	−3.65773	−	5.29913i	−0.167476	−	0.242631i
$478$	45.9891	+	11.3353i	2.10349	+	0.518464i
$479$	6.88498	+	18.1542i	0.314583	+	0.829486i	0.995291	+	0.0969317i	$0.0309028\pi$
$479$	6.88498	+	18.1542i	0.314583	+	0.829486i	−0.680708	+	0.732554i	$0.738328\pi$
$480$	−6.90508	+	18.2072i	−0.315172	+	0.831041i
$481$	−18.0010	+	32.5686i	−0.820776	+	1.48500i
$482$	2.96146	+	7.80873i	0.134891	+	0.355678i
$483$	−9.71791	+	8.60932i	−0.442180	+	0.391738i
$484$	−8.68765			−0.394893
$485$	25.8469			1.17365
$486$	−1.34171	+	1.18865i	−0.0608613	+	0.0539184i
$487$	15.5962	−	8.18554i	0.706733	−	0.370922i	−0.0727460	−	0.997351i	$-0.523176\pi$
$487$	15.5962	−	8.18554i	0.706733	−	0.370922i	0.779479	+	0.626428i	$0.215484\pi$
$488$	−3.47077			−0.157114
$489$	−3.04990	−	1.60071i	−0.137921	−	0.0723867i
$490$	−9.59573	−	8.50108i	−0.433491	−	0.384040i
$491$	−11.1676	−	16.1791i	−0.503989	−	0.730154i	0.485583	−	0.874190i	$-0.338607\pi$
$491$	−11.1676	−	16.1791i	−0.503989	−	0.730154i	−0.989572	+	0.144036i	$0.953992\pi$
$492$	−10.2410	−	9.07276i	−0.461701	−	0.409031i
$493$	28.0468	+	40.6328i	1.26316	+	1.83001i
$494$	−10.3210	−	4.17138i	−0.464363	−	0.187679i
$495$	−3.57618	+	5.18100i	−0.160737	+	0.232868i
$496$	29.9003	−	7.36977i	1.34256	−	0.330912i
$497$	11.2173	−	9.93770i	0.503167	−	0.445767i
$498$	11.4190	+	2.81452i	0.511696	+	0.126122i
$499$	24.0352	+	21.2933i	1.07596	+	0.953221i	0.999040	−	0.0438163i	$-0.0139516\pi$
$499$	24.0352	+	21.2933i	1.07596	+	0.953221i	0.0769241	+	0.997037i	$0.475490\pi$
$500$	0.948663	+	0.840442i	0.0424255	+	0.0375857i
$501$	−2.02022	+	5.32687i	−0.0902566	+	0.237987i
$502$	20.1433	−	29.1826i	0.899041	−	1.30249i
$503$	24.7958	+	13.0138i	1.10559	+	0.580259i	0.915828	−	0.401571i	$-0.131536\pi$
$503$	24.7958	+	13.0138i	1.10559	+	0.580259i	0.189763	+	0.981830i	$0.439228\pi$
$504$	−0.516427	+	4.25316i	−0.0230035	+	0.189451i
$505$	22.9587	+	5.65881i	1.02165	+	0.251814i
$506$	−15.0110			−0.667320
$507$	−5.13050	+	11.9448i	−0.227854	+	0.530487i
$508$	−1.81166			−0.0803795
$509$	−35.6442	−	8.78550i	−1.57990	−	0.389410i	−0.650803	−	0.759247i	$-0.725568\pi$
$509$	−35.6442	−	8.78550i	−1.57990	−	0.389410i	−0.929097	+	0.369836i	$0.879414\pi$
$510$	3.73653	−	30.7731i	0.165456	−	1.36265i
$511$	12.7437	+	6.68842i	0.563749	+	0.295878i
$512$	−9.11609	+	13.2069i	−0.402878	+	0.583670i
$513$	0.610785	−	1.61051i	0.0269668	−	0.0711056i
$514$	29.0738	+	25.7571i	1.28239	+	1.13610i
$515$	−4.37839	−	3.87892i	−0.192935	−	0.170926i
$516$	1.32493	+	0.326567i	0.0583269	+	0.0143763i
$517$	13.7741	−	12.2028i	0.605784	−	0.536678i
$518$	54.5593	−	13.4477i	2.39720	−	0.590856i
$519$	12.1025	−	17.5335i	0.531242	−	0.769636i
$520$	−16.2618	+	1.61898i	−0.713125	+	0.0709970i
$521$	−17.3171	−	25.0882i	−0.758677	−	1.09913i	−0.991939	−	0.126719i	$-0.959555\pi$
$521$	−17.3171	−	25.0882i	−0.758677	−	1.09913i	0.233262	−	0.972414i	$-0.425060\pi$
$522$	−12.3085	−	10.9044i	−0.538728	−	0.477271i
$523$	−12.2693	−	17.7751i	−0.536497	−	0.777250i	0.457198	−	0.889365i	$-0.348853\pi$
$523$	−12.2693	−	17.7751i	−0.536497	−	0.777250i	−0.993695	+	0.112115i	$0.964238\pi$
$524$	20.6816	+	18.3223i	0.903478	+	0.800412i
$525$	14.3218	+	7.51668i	0.625056	+	0.328055i
$526$	−11.1796			−0.487455
$527$	−29.6197	+	15.5456i	−1.29026	+	0.677178i
$528$	−7.26574	+	6.43689i	−0.316201	+	0.280130i
$529$	−4.72953			−0.205632
$530$	−37.0871			−1.61096
$531$	−8.00489	+	7.09171i	−0.347382	+	0.307754i
$532$	2.25050	+	5.93408i	0.0975716	+	0.257275i
$533$	10.5824	−	39.2644i	0.458375	−	1.70073i
$534$	1.78865	−	4.71627i	0.0774022	−	0.204093i
$535$	−13.9019	−	36.6563i	−0.601031	−	1.58479i
$536$	−6.80740	−	1.67787i	−0.294035	−	0.0724731i
$537$	−5.69782	−	8.25472i	−0.245879	−	0.356217i
$538$	9.62692	−	25.3841i	0.415046	−	1.09439i
$539$	−1.54629	−	4.07722i	−0.0666032	−	0.175618i
$540$	0.469849	+	3.86955i	0.0202191	+	0.166519i
$541$	3.26986	+	4.73721i	0.140582	+	0.203668i	0.886950	−	0.461865i	$-0.152820\pi$
$541$	3.26986	+	4.73721i	0.140582	+	0.203668i	−0.746368	+	0.665533i	$0.768204\pi$
$542$	19.1314	−	4.71546i	0.821763	−	0.202546i
$543$	−5.78825	−	5.12795i	−0.248398	−	0.220061i
$544$	11.5654	−	30.4954i	0.495862	−	1.30748i
$545$	60.7249	+	14.9673i	2.60117	+	0.641130i
$546$	18.5010	−	6.56304i	0.791768	−	0.280872i
$547$	20.2748	−	4.99730i	0.866889	−	0.213669i	0.219299	−	0.975658i	$-0.429623\pi$
$547$	20.2748	−	4.99730i	0.866889	−	0.213669i	0.647590	+	0.761989i	$0.275777\pi$
$548$	1.10300	−	9.08401i	0.0471178	−	0.388050i
$549$	−2.17873	+	1.14348i	−0.0929858	+	0.0488027i
$550$	6.63149	+	17.4858i	0.282768	+	0.745597i
$551$	15.3420	+	3.78147i	0.653592	+	0.161096i
$552$	4.51297	−	3.99814i	0.192085	−	0.170172i
$553$	38.3287	+	9.44719i	1.62990	+	0.401735i
$554$	17.3067	−	9.08328i	0.735293	−	0.385912i
$555$	−29.3649	+	15.4119i	−1.24647	+	0.654199i
$556$	0.413793	+	3.40789i	0.0175487	+	0.144527i
$557$	−1.30077	−	10.7128i	−0.0551155	−	0.453917i	−0.993974	−	0.109614i	$-0.965038\pi$
$557$	−1.30077	−	10.7128i	−0.0551155	−	0.453917i	0.938859	−	0.344303i	$-0.111885\pi$
$558$	8.33938	−	7.38804i	0.353034	−	0.312761i
$559$	0.885347	+	3.95804i	0.0374462	+	0.167407i
$560$	36.1955	+	32.0664i	1.52954	+	1.35505i
$561$	5.98979	−	8.67770i	0.252889	−	0.366373i
$562$	16.1234	−	42.5139i	0.680124	−	1.79334i
$563$	3.55643	+	29.2898i	0.149886	+	1.23442i	0.852454	+	0.522803i	$0.175113\pi$
$563$	3.55643	+	29.2898i	0.149886	+	1.23442i	−0.702568	+	0.711616i	$0.747963\pi$
$564$	1.37341	−	11.3111i	0.0578312	−	0.476283i
$565$	−46.8302	−	24.5784i	−1.97016	−	1.03402i
$566$	3.65239	−	5.29140i	0.153521	−	0.222414i
$567$	1.07707	+	2.84001i	0.0452328	+	0.119269i
$568$	−5.20930	+	4.61504i	−0.218577	+	0.193643i
$569$	−2.33413	+	3.38158i	−0.0978520	+	0.141763i	−0.868852	−	0.495072i	$-0.835142\pi$
$569$	−2.33413	+	3.38158i	−0.0978520	+	0.141763i	0.771000	+	0.636835i	$0.219757\pi$
$570$	−5.63573	−	8.16477i	−0.236055	−	0.341985i
$571$	−0.338407	−	2.78704i	−0.0141619	−	0.116634i	0.983914	−	0.178645i	$-0.0571715\pi$
$571$	−0.338407	−	2.78704i	−0.0141619	−	0.116634i	−0.998075	+	0.0620116i	$0.980248\pi$
$572$	7.94477	+	3.21099i	0.332187	+	0.134258i
$573$	0.236721	−	1.94958i	0.00988918	−	0.0814447i
$574$	−54.3729	+	28.5371i	−2.26948	+	1.19112i
$575$	−8.07144	−	21.2826i	−0.336602	−	0.887547i
$576$	−0.114930	+	0.946532i	−0.00478874	+	0.0394388i
$577$	4.58496			0.190874			0.0954372	−	0.995435i	$-0.469575\pi$
$577$	4.58496			0.190874			0.0954372	+	0.995435i	$0.469575\pi$
$578$	−2.58527	+	21.2917i	−0.107533	+	0.885616i
$579$	−3.26987	−	4.73723i	−0.135891	−	0.196873i
$580$	−34.7198	+	8.55767i	−1.44166	+	0.355338i
$581$	11.3206	−	16.4008i	0.469659	−	0.680418i
$582$	13.9996	−	3.45059i	0.580301	−	0.143031i
$583$	−11.1700	−	5.86248i	−0.462615	−	0.242799i
$584$	−5.91814	−	3.10608i	−0.244894	−	0.128531i
$585$	−9.67471	+	6.37392i	−0.400000	+	0.263529i
$586$	−40.1191	+	21.0561i	−1.65730	+	0.869821i
$587$	4.28516			0.176867			0.0884337	−	0.996082i	$-0.471814\pi$
$587$	4.28516			0.176867			0.0884337	+	0.996082i	$0.471814\pi$
$588$	−2.39072	−	1.25475i	−0.0985917	−	0.0517449i
$589$	−3.79632	+	10.0101i	−0.156425	+	0.412458i
$590$	7.42481	+	61.1488i	0.305675	+	2.51746i
$591$	9.09983	−	2.24291i	0.374317	−	0.0922608i
$592$	−49.6496	+	12.2375i	−2.04058	+	0.502959i
$593$	5.56924	+	45.8668i	0.228701	+	1.88352i	0.428285	+	0.903644i	$0.359118\pi$
$593$	5.56924	+	45.8668i	0.228701	+	1.88352i	−0.199583	+	0.979881i	$0.563959\pi$
$594$	−1.24532	+	3.28363i	−0.0510959	+	0.134729i
$595$	−46.5109	−	24.4108i	−1.90676	−	1.00075i
$596$	−19.9791			−0.818374
$597$	−11.2772	+	5.91875i	−0.461547	+	0.242238i
$598$	−25.6125	−	10.3517i	−1.04737	−	0.423312i
$599$	−0.398766	−	0.209289i	−0.0162931	−	0.00855130i	0.456557	−	0.889694i	$-0.349082\pi$
$599$	−0.398766	−	0.209289i	−0.0162931	−	0.00855130i	−0.472850	+	0.881143i	$0.656775\pi$
$600$	−6.65101	−	3.49072i	−0.271526	−	0.142508i
$601$	6.64740	−	1.63844i	0.271153	−	0.0668332i	−0.101395	−	0.994846i	$-0.532330\pi$
$601$	6.64740	−	1.63844i	0.271153	−	0.0668332i	0.372548	+	0.928013i	$0.378484\pi$
$602$	3.47911	−	5.04037i	0.141798	−	0.205430i
$603$	−4.82605	+	1.18952i	−0.196532	+	0.0484408i
$604$	−9.95767	−	14.4262i	−0.405172	−	0.586993i
$605$	2.77382	−	22.8445i	0.112772	−	0.928760i
$606$	13.1907			0.535835
$607$	3.34519	−	27.5501i	0.135777	−	1.11823i	−0.752394	−	0.658713i	$-0.771101\pi$
$607$	3.34519	−	27.5501i	0.135777	−	1.11823i	0.888171	−	0.459512i	$-0.151976\pi$
$608$	−3.70138	−	9.75974i	−0.150111	−	0.395810i
$609$	−24.6725	+	12.9491i	−0.999780	+	0.524725i
$610$	−1.70830	+	14.0691i	−0.0691670	+	0.569642i
$611$	31.9172	−	11.3223i	1.29123	−	0.458052i
$612$	−0.786955	−	6.48115i	−0.0318108	−	0.261985i
$613$	−4.62522	−	6.70079i	−0.186811	−	0.270642i	0.718377	−	0.695654i	$-0.244885\pi$
$613$	−4.62522	−	6.70079i	−0.186811	−	0.270642i	−0.905188	+	0.425012i	$0.860270\pi$
$614$	−5.13297	+	7.43639i	−0.207150	+	0.300108i
$615$	27.1269	−	24.0324i	1.09386	−	0.969079i
$616$	2.97652	+	7.84843i	0.119927	+	0.316222i
$617$	−20.7356	+	30.0408i	−0.834785	+	1.20940i	0.140857	+	0.990030i	$0.455014\pi$
$617$	−20.7356	+	30.0408i	−0.834785	+	1.20940i	−0.975643	+	0.219366i	$0.929601\pi$
$618$	−2.88933	−	1.51644i	−0.116226	−	0.0610000i
$619$	4.89495	−	40.3135i	0.196744	−	1.62034i	−0.475299	−	0.879825i	$-0.657660\pi$
$619$	4.89495	−	40.3135i	0.196744	−	1.62034i	0.672043	−	0.740512i	$-0.265417\pi$
$620$	−2.92033	−	24.0511i	−0.117283	−	0.965916i
$621$	1.51572	−	3.99663i	0.0608238	−	0.160379i
$622$	12.9609	−	18.7771i	0.519686	−	0.752895i
$623$	−6.39759	−	5.66777i	−0.256314	−	0.227075i
$624$	−16.8361	+	5.97244i	−0.673983	+	0.239089i
$625$	17.4168	−	15.4299i	0.696671	−	0.617196i
$626$	4.93212	+	40.6197i	0.197127	+	1.62349i
$627$	−0.406758	−	3.34996i	−0.0162444	−	0.133784i
$628$	11.6394	−	6.10884i	0.464464	−	0.243769i
$629$	49.1836	−	25.8136i	1.96108	−	1.02925i
$630$	16.9864	+	4.18678i	0.676756	+	0.166805i
$631$	−20.9535	+	18.5632i	−0.834147	+	0.738990i	−0.967714	−	0.252050i	$-0.918895\pi$
$631$	−20.9535	+	18.5632i	−0.834147	+	0.738990i	0.133567	+	0.991040i	$0.457357\pi$
$632$	−17.7997	−	4.38724i	−0.708036	−	0.174515i
$633$	1.37337	+	3.62127i	0.0545865	+	0.143933i
$634$	5.91061	−	3.10213i	0.234740	−	0.123201i
$635$	0.578433	−	4.76383i	0.0229544	−	0.189047i
$636$	−7.58399	+	1.86928i	−0.300725	+	0.0741220i
$637$	0.173325	−	8.02309i	0.00686740	−	0.317886i
$638$	−31.2805	−	7.70995i	−1.23841	−	0.305240i
$639$	−1.74959	+	4.61329i	−0.0692128	+	0.182499i
$640$	−25.0401	−	22.1836i	−0.989799	−	0.876885i
$641$	−0.348788	+	0.0859686i	−0.0137763	+	0.00339556i	−0.246198	−	0.969220i	$-0.579181\pi$
$641$	−0.348788	+	0.0859686i	−0.0137763	+	0.00339556i	0.232421	+	0.972615i	$0.425335\pi$
$642$	−12.4234	−	17.9984i	−0.490312	−	0.710339i
$643$	5.67529	+	46.7403i	0.223812	+	1.84326i	0.480787	+	0.876838i	$0.340351\pi$
$643$	5.67529	+	46.7403i	0.223812	+	1.84326i	−0.256975	+	0.966418i	$0.582726\pi$
$644$	5.58484	+	14.7260i	0.220073	+	0.580286i
$645$	−1.28175	+	3.37969i	−0.0504688	+	0.133075i
$646$	9.43935	+	13.6753i	0.371386	+	0.538046i
$647$	9.97640	+	2.45896i	0.392213	+	0.0966718i	0.430490	−	0.902595i	$-0.358341\pi$
$647$	9.97640	+	2.45896i	0.392213	+	0.0966718i	−0.0382771	+	0.999267i	$0.512187\pi$
$648$	−0.500189	−	1.31889i	−0.0196493	−	0.0518109i
$649$	−7.42978	+	19.5907i	−0.291644	+	0.769003i
$650$	−0.743333	+	34.4083i	−0.0291559	+	1.34960i
$651$	−6.69452	−	17.6520i	−0.262379	−	0.691836i
$652$	−3.12758	+	2.77079i	−0.122485	+	0.108513i
$653$	3.82618			0.149730			0.0748649	−	0.997194i	$-0.476147\pi$
$653$	3.82618			0.149730			0.0748649	+	0.997194i	$0.476147\pi$
$654$	34.8888			1.36426
$655$	−54.7823	+	48.5329i	−2.14052	+	1.89634i
$656$	49.4800	−	25.9691i	1.93187	−	1.01392i
$657$	−4.73837			−0.184861
$658$	−45.2814	−	23.7655i	−1.76525	−	0.926476i
$659$	9.10925	+	8.07009i	0.354846	+	0.314366i	0.821647	−	0.569996i	$-0.193055\pi$
$659$	9.10925	+	8.07009i	0.354846	+	0.314366i	−0.466802	+	0.884362i	$0.654594\pi$
$660$	4.33821	+	6.28498i	0.168865	+	0.244643i
$661$	−11.9570	−	10.5930i	−0.465073	−	0.412018i	0.397775	−	0.917483i	$-0.369783\pi$
$661$	−11.9570	−	10.5930i	−0.465073	−	0.412018i	−0.862847	+	0.505465i	$0.831321\pi$
$662$	35.5590	+	51.5160i	1.38204	+	2.00223i
$663$	16.2043	−	10.6757i	0.629322	−	0.414611i
$664$	−5.25727	+	7.61647i	−0.204022	+	0.295576i
$665$	−16.3224	+	4.02312i	−0.632957	+	0.156010i
$666$	−13.8476	+	12.2679i	−0.536582	+	0.475370i
$667$	38.0727	+	9.38408i	1.47418	+	0.363353i
$668$	5.17299	+	4.58287i	0.200149	+	0.177317i
$669$	0.732230	+	0.648699i	0.0283096	+	0.0250802i
$670$	−10.1520	+	26.7687i	−0.392207	+	1.03416i
$671$	−2.73847	+	3.96735i	−0.105717	+	0.153158i
$672$	16.2983	+	8.55402i	0.628721	+	0.329978i
$673$	−4.50917	+	37.1364i	−0.173816	+	1.43150i	0.600967	+	0.799274i	$0.294782\pi$
$673$	−4.50917	+	37.1364i	−0.173816	+	1.43150i	−0.774783	+	0.632227i	$0.782141\pi$
$674$	−58.1717	−	14.3380i	−2.24069	−	0.552280i
$675$	−5.32514			−0.204965
$676$	11.3414	+	10.9575i	0.436209	+	0.421443i
$677$	−9.82736			−0.377696			−0.188848	−	0.982006i	$-0.560475\pi$
$677$	−9.82736			−0.377696			−0.188848	+	0.982006i	$0.560475\pi$
$678$	−28.6461	−	7.06063i	−1.10015	−	0.271162i
$679$	2.94496	−	24.2540i	0.113017	−	0.930782i
$680$	21.5995	+	11.3363i	0.828304	+	0.434727i
$681$	0.460281	−	0.666833i	0.0176380	−	0.0255531i
$682$	7.74023	−	20.4093i	0.296389	−	0.781513i
$683$	4.26855	+	3.78161i	0.163332	+	0.144699i	0.740830	−	0.671693i	$-0.234433\pi$
$683$	4.26855	+	3.78161i	0.163332	+	0.144699i	−0.577498	+	0.816392i	$0.695971\pi$
$684$	−1.56398	−	1.38557i	−0.0598004	−	0.0529786i
$685$	23.5346	+	5.80075i	0.899210	+	0.221635i
$686$	19.4566	−	17.2370i	0.742856	−	0.658113i
$687$	−5.91015	+	1.45672i	−0.225486	+	0.0555774i
$688$	−3.16604	+	4.58679i	−0.120704	+	0.174870i
$689$	−15.0161	−	17.7058i	−0.572067	−	0.674537i
$690$	−13.9856	−	20.2617i	−0.532423	−	0.771349i
$691$	−2.93005	−	2.59580i	−0.111464	−	0.0987488i	0.605550	−	0.795807i	$-0.292953\pi$
$691$	−2.93005	−	2.59580i	−0.111464	−	0.0987488i	−0.717014	+	0.697059i	$0.754492\pi$
$692$	−14.6814	−	21.2696i	−0.558102	−	0.808550i
$693$	4.45422	+	3.94610i	0.169202	+	0.149900i
$694$	−8.29070	−	4.35130i	−0.314711	−	0.165173i
$695$	−9.09329			−0.344928
$696$	11.4578	−	6.01353i	0.434308	−	0.227942i
$697$	−45.4352	+	40.2521i	−1.72098	+	1.52466i
$698$	−13.2858			−0.502876
$699$	4.70509			0.177963
$700$	14.6866	−	13.0112i	0.555100	−	0.491776i
$701$	3.63408	+	9.58229i	0.137257	+	0.361918i	0.985967	−	0.166941i	$-0.0533890\pi$
$701$	3.63408	+	9.58229i	0.137257	+	0.361918i	−0.848709	+	0.528860i	$0.822620\pi$
$702$	−4.38923	+	4.74392i	−0.165661	+	0.179048i
$703$	6.30380	−	16.6217i	0.237752	−	0.626901i
$704$	0.662418	+	1.74665i	0.0249658	+	0.0658294i
$705$	29.3044	+	7.22288i	1.10367	+	0.272030i
$706$	8.00657	+	11.5995i	0.301331	+	0.436554i
$707$	7.92594	−	20.8990i	0.298086	−	0.785987i
$708$	4.60037	+	12.1302i	0.172892	+	0.455880i
$709$	4.11952	+	33.9273i	0.154712	+	1.27417i	0.838668	+	0.544643i	$0.183335\pi$
$709$	4.11952	+	33.9273i	0.154712	+	1.27417i	−0.683957	+	0.729523i	$0.739742\pi$
$710$	16.1435	+	23.3880i	0.605856	+	0.877735i
$711$	−12.6190	+	3.11030i	−0.473249	+	0.116645i
$712$	2.97102	+	2.63210i	0.111344	+	0.0986420i
$713$	−9.42094	+	24.8410i	−0.352817	+	0.930301i
$714$	−28.4508	−	7.01249i	−1.06474	−	0.262436i
$715$	−10.9801	+	19.8658i	−0.410631	+	0.742940i
$716$	−11.8139	+	2.91187i	−0.441508	+	0.108822i
$717$	−3.18507	+	26.2314i	−0.118949	+	0.979631i
$718$	12.2269	−	6.41715i	0.456303	−	0.239486i
$719$	−1.93327	−	5.09762i	−0.0720989	−	0.190109i	0.894123	−	0.447822i	$-0.147800\pi$
$719$	−1.93327	−	5.09762i	−0.0720989	−	0.190109i	−0.966221	+	0.257713i	$0.917031\pi$
$720$	−15.4579	−	3.81002i	−0.576081	−	0.141991i
$721$	−4.13873	+	3.66659i	−0.154134	+	0.136551i
$722$	−27.9045	−	6.87785i	−1.03850	−	0.255967i
$723$	−4.12541	+	2.16518i	−0.153426	+	0.0805240i
$724$	−8.30630	+	4.35948i	−0.308701	+	0.162019i
$725$	−5.88839	−	48.4952i	−0.218689	−	1.80107i
$726$	−1.54736	−	12.7437i	−0.0574280	−	0.472962i
$727$	9.53659	−	8.44868i	0.353693	−	0.313344i	−0.467503	−	0.883992i	$-0.654846\pi$
$727$	9.53659	−	8.44868i	0.353693	−	0.313344i	0.821195	+	0.570647i	$0.193308\pi$
$728$	−0.333642	+	15.4440i	−0.0123656	+	0.572393i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	−15.5037	+	22.4610i	−0.573818	+	0.831319i
$731$	2.14681	−	5.66068i	0.0794027	−	0.209368i
$732$	0.359787	+	2.96311i	0.0132981	+	0.109520i
$733$	−1.04102	+	8.57356i	−0.0384509	+	0.316672i	0.960775	+	0.277329i	$0.0894494\pi$
$733$	−1.04102	+	8.57356i	−0.0384509	+	0.316672i	−0.999226	+	0.0393423i	$0.987474\pi$
$734$	31.7682	+	16.6733i	1.17259	+	0.615421i
$735$	4.06272	−	5.88587i	0.149856	−	0.217103i
$736$	−9.18534	−	24.2198i	−0.338576	−	0.892752i
$737$	−7.28905	+	6.45753i	−0.268495	+	0.237866i
$738$	11.4845	−	16.6382i	0.422752	−	0.612462i
$739$	20.3601	+	29.4967i	0.748958	+	1.08505i	0.993323	+	0.115370i	$0.0368053\pi$
$739$	20.3601	+	29.4967i	0.748958	+	1.08505i	−0.244364	+	0.969683i	$0.578579\pi$
$740$	4.84922	+	39.9369i	0.178261	+	1.46811i
$741$	1.61612	−	5.99637i	0.0593696	−	0.220282i
$742$	−4.22565	+	34.8014i	−0.155129	+	1.27760i
$743$	11.5042	−	6.03786i	0.422048	−	0.221508i	−0.240309	−	0.970696i	$-0.577249\pi$
$743$	11.5042	−	6.03786i	0.422048	−	0.221508i	0.662357	+	0.749189i	$0.269556\pi$
$744$	3.10891	+	8.19753i	0.113978	+	0.300536i
$745$	6.37899	−	52.5357i	0.233708	−	1.92476i
$746$	16.3814			0.599767
$747$	−0.790846	+	6.51320i	−0.0289355	+	0.238306i
$748$	−7.26611	−	10.5268i	−0.265675	−	0.384897i
$749$	−35.9811	+	8.86854i	−1.31472	+	0.324049i
$750$	−1.06385	+	1.54126i	−0.0388465	+	0.0562788i
$751$	−11.5103	+	2.83703i	−0.420016	+	0.103525i	−0.443659	−	0.896196i	$-0.646320\pi$
$751$	−11.5103	+	2.83703i	−0.420016	+	0.103525i	0.0236425	+	0.999720i	$0.492474\pi$
$752$	41.2066	+	21.6269i	1.50265	+	0.788651i
$753$	17.5162	+	9.19320i	0.638325	+	0.335019i
$754$	−48.0556	−	34.7263i	−1.75008	−	1.26466i
$755$	41.1135	−	21.5780i	1.49627	−	0.785304i
$756$	3.68461			0.134008
$757$	13.6879	+	7.18398i	0.497496	+	0.261106i	0.694757	−	0.719245i	$-0.255512\pi$
$757$	13.6879	+	7.18398i	0.497496	+	0.261106i	−0.197260	+	0.980351i	$0.563204\pi$
$758$	−8.16775	+	21.5366i	−0.296666	+	0.782244i
$759$	−1.00941	−	8.31324i	−0.0366393	−	0.301752i
$760$	7.58009	−	1.86832i	0.274959	−	0.0677712i
$761$	−13.0177	+	3.20858i	−0.471891	+	0.116311i	−0.468088	−	0.883682i	$-0.655057\pi$
$761$	−13.0177	+	3.20858i	−0.471891	+	0.116311i	−0.00380358	+	0.999993i	$0.501211\pi$
$762$	−0.322676	−	2.65747i	−0.0116893	−	0.0962701i
$763$	20.9638	−	55.2770i	0.758941	−	2.00116i
$764$	−2.10948	−	1.10714i	−0.0763184	−	0.0400550i
$765$	17.2937			0.625255
$766$	−15.1862	+	7.97036i	−0.548701	+	0.287981i
$767$	−26.1869	+	28.3030i	−0.945555	+	1.02196i
$768$	−18.2127	−	9.55875i	−0.657193	−	0.344922i
$769$	−5.78555	−	3.03649i	−0.208632	−	0.109499i	0.357171	−	0.934039i	$-0.383741\pi$
$769$	−5.78555	−	3.03649i	−0.208632	−	0.109499i	−0.565803	+	0.824540i	$0.691434\pi$
$770$	33.2795	−	8.20265i	1.19931	−	0.295603i
$771$	−12.3095	+	17.8334i	−0.443316	+	0.642254i
$772$	−6.77981	+	1.67107i	−0.244011	+	0.0601432i
$773$	−14.4336	−	20.9107i	−0.519142	−	0.752107i	0.472472	−	0.881346i	$-0.343362\pi$
$773$	−14.4336	−	20.9107i	−0.519142	−	0.752107i	−0.991613	+	0.129239i	$0.958746\pi$
$774$	−0.243047	+	2.00167i	−0.00873614	+	0.0719486i
$775$	33.0983			1.18893
$776$	−1.36763	+	11.2635i	−0.0490951	+	0.404335i
$777$	11.1163	+	29.3112i	0.398794	+	1.05153i
$778$	22.8874	−	12.0122i	0.820553	−	0.430660i
$779$	−2.34163	+	19.2850i	−0.0838974	+	0.690958i
$780$	3.06791	+	13.7154i	0.109849	+	0.491090i
$781$	1.16516	+	9.59594i	0.0416927	+	0.343370i
$782$	23.4247	+	33.9365i	0.837664	+	1.21357i
$783$	5.21127	−	7.54983i	0.186236	−	0.269809i
$784$	8.25424	−	7.31262i	0.294794	−	0.261165i
$785$	12.3471	+	32.5568i	0.440689	+	1.16200i
$786$	−23.1928	+	33.6006i	−0.827260	+	1.19849i
$787$	−21.7306	−	11.4051i	−0.774612	−	0.406548i	0.0306026	−	0.999532i	$-0.490257\pi$
$787$	−21.7306	−	11.4051i	−0.774612	−	0.406548i	−0.805214	+	0.592984i	$0.797950\pi$
$788$	1.37041	−	11.2863i	0.0488188	−	0.402059i
$789$	−0.751771	−	6.19139i	−0.0267637	−	0.220419i
$790$	−26.5451	+	69.9938i	−0.944434	+	2.49027i
$791$	−28.3994	+	41.1436i	−1.00977	+	1.46290i
$792$	−2.06853	−	1.83256i	−0.0735019	−	0.0651170i
$793$	−7.40842	+	4.88084i	−0.263081	+	0.173324i
$794$	−24.2365	+	21.4717i	−0.860123	+	0.762002i
$795$	−2.49391	−	20.5392i	−0.0884499	−	0.728450i
$796$	1.86228	+	15.3373i	0.0660069	+	0.543616i
$797$	−42.1502	+	22.1221i	−1.49304	+	0.783606i	−0.996434	−	0.0843726i	$-0.973111\pi$
$797$	−42.1502	+	22.1221i	−1.49304	+	0.783606i	−0.496602	+	0.867978i	$0.665419\pi$
$798$	−8.30370	+	4.35812i	−0.293948	+	0.154276i
$799$	−49.0822	−	12.0977i	−1.73640	−	0.427985i
$800$	−24.1549	+	21.3994i	−0.854004	+	0.756582i
$801$	2.73219	+	0.673425i	0.0965374	+	0.0237943i
$802$	−4.68703	−	12.3587i	−0.165505	−	0.436401i
$803$	−8.21996	+	4.31417i	−0.290076	+	0.152244i
$804$	−0.726790	+	5.98565i	−0.0256319	+	0.211098i
$805$	−40.5057	+	9.98376i	−1.42764	+	0.351881i
$806$	27.2812	−	29.4857i	0.960938	−	1.03859i
$807$	14.7053	+	3.62454i	0.517652	+	0.127590i
$808$	−3.68078	+	9.70543i	−0.129489	+	0.341436i
$809$	−9.43168	−	8.35574i	−0.331600	−	0.293772i	0.480850	−	0.876803i	$-0.340328\pi$
$809$	−9.43168	−	8.35574i	−0.331600	−	0.293772i	−0.812450	+	0.583031i	$0.801867\pi$
$810$	−5.59245	+	1.37842i	−0.196499	+	0.0484326i
$811$	14.7225	+	21.3292i	0.516977	+	0.748971i	0.991335	−	0.131362i	$-0.0419349\pi$
$811$	14.7225	+	21.3292i	0.516977	+	0.748971i	−0.474357	+	0.880332i	$0.657320\pi$
$812$	4.07433	+	33.5551i	0.142981	+	1.17755i
$813$	3.89795	+	10.2781i	0.136707	+	0.360467i
$814$	−12.8527	+	33.8897i	−0.450486	+	1.18783i
$815$	−6.28731	−	9.10874i	−0.220235	−	0.319065i
$816$	25.8905	+	6.38144i	0.906350	+	0.223395i
$817$	−0.687065	−	1.81164i	−0.0240374	−	0.0633813i
$818$	21.8204	−	57.5358i	0.762934	−	2.01169i
$819$	4.87877	+	9.80469i	0.170478	+	0.342604i
$820$	−15.5897	−	41.1067i	−0.544416	−	1.43551i
$821$	36.6322	−	32.4533i	1.27847	−	1.13263i	0.294242	−	0.955731i	$-0.404933\pi$
$821$	36.6322	−	32.4533i	1.27847	−	1.13263i	0.984229	−	0.176896i	$-0.0566058\pi$
$822$	13.5215			0.471618
$823$	−22.1413			−0.771799			−0.385899	−	0.922541i	$-0.626109\pi$
$823$	−22.1413			−0.771799			−0.385899	+	0.922541i	$0.626109\pi$
$824$	1.92201	−	1.70275i	0.0669565	−	0.0593183i
$825$	−9.23788	+	4.84841i	−0.321622	+	0.168800i
$826$	58.2262			2.02595
$827$	6.37019	+	3.34334i	0.221513	+	0.116259i	0.571830	−	0.820372i	$-0.306234\pi$
$827$	6.37019	+	3.34334i	0.221513	+	0.116259i	−0.350317	+	0.936631i	$0.613926\pi$
$828$	−3.88118	−	3.43842i	−0.134880	−	0.119494i
$829$	−3.13686	−	4.54452i	−0.108947	−	0.157838i	0.764717	−	0.644366i	$-0.222879\pi$
$829$	−3.13686	−	4.54452i	−0.108947	−	0.157838i	−0.873665	+	0.486528i	$0.838263\pi$
$830$	28.2865	+	25.0597i	0.981840	+	0.869834i
$831$	6.19420	+	8.97385i	0.214874	+	0.311299i
$832$	−0.0742514	+	3.43703i	−0.00257420	+	0.119158i
$833$	−6.80469	+	9.85830i	−0.235769	+	0.341570i
$834$	−4.92524	+	1.21396i	−0.170547	+	0.0420361i
$835$	−13.7025	+	12.1393i	−0.474194	+	0.420099i
$836$	−3.97467	−	0.979669i	−0.137467	−	0.0338826i
$837$	4.65235	+	4.12162i	0.160809	+	0.142464i
$838$	−10.8039	−	9.57146i	−0.373216	−	0.330641i
$839$	−17.9800	+	47.4092i	−0.620737	+	1.63675i	0.141869	+	0.989885i	$0.454689\pi$
$839$	−17.9800	+	47.4092i	−0.620737	+	1.63675i	−0.762606	+	0.646863i	$0.776080\pi$
$840$	−7.82052	+	11.3300i	−0.269834	+	0.390921i
$841$	48.8393	+	25.6328i	1.68411	+	0.883891i
$842$	3.09016	−	25.4498i	0.106494	−	0.877058i
$843$	24.6288	+	6.07046i	0.848261	+	0.209078i
$844$	4.69822			0.161719
$845$	−32.4343	+	26.3242i	−1.11578	+	0.905579i
$846$	16.8365			0.578852
$847$	−21.1205	−	5.20574i	−0.725710	−	0.178871i
$848$	3.84539	−	31.6697i	0.132051	−	1.08754i
$849$	3.17604	+	1.66691i	0.109001	+	0.0572083i
$850$	29.1830	−	42.2789i	1.00097	−	1.45015i
$851$	15.6435	−	41.2485i	0.536252	−	1.41398i
$852$	4.48003	+	3.96896i	0.153483	+	0.135974i
$853$	−35.5484	−	31.4931i	−1.21715	−	1.07830i	−0.994643	−	0.103374i	$-0.967036\pi$
$853$	−35.5484	−	31.4931i	−1.21715	−	1.07830i	−0.222511	−	0.974930i	$-0.571425\pi$
$854$	13.0074	+	3.20603i	0.445104	+	0.109708i
$855$	4.14276	−	3.67016i	0.141679	−	0.125517i
$856$	16.7095	−	4.11852i	0.571119	−	0.140768i
$857$	−27.6629	+	40.0766i	−0.944946	+	1.36899i	−0.0155613	+	0.999879i	$0.504954\pi$
$857$	−27.6629	+	40.0766i	−0.944946	+	1.36899i	−0.929385	+	0.369112i	$0.879662\pi$
$858$	−3.29507	+	12.2259i	−0.112492	+	0.417384i
$859$	2.09780	+	3.03919i	0.0715759	+	0.103696i	0.857137	−	0.515088i	$-0.172241\pi$
$859$	2.09780	+	3.03919i	0.0715759	+	0.103696i	−0.785561	+	0.618784i	$0.787626\pi$
$860$	3.28206	+	2.90765i	0.111917	+	0.0991501i
$861$	−19.4604	−	28.1933i	−0.663210	−	0.960826i
$862$	−13.1684	−	11.6662i	−0.448519	−	0.397353i
$863$	25.0845	+	13.1653i	0.853885	+	0.448154i	0.834076	−	0.551650i	$-0.186002\pi$
$863$	25.0845	+	13.1653i	0.853885	+	0.448154i	0.0198097	+	0.999804i	$0.493694\pi$
$864$	−6.06004			−0.206167
$865$	60.6168	−	31.8142i	2.06103	−	1.08171i
$866$	43.4486	−	38.4921i	1.47644	−	1.30801i
$867$	−11.9654			−0.406366
$868$	−22.9016			−0.777330
$869$	−19.0591	+	16.8849i	−0.646537	+	0.572781i
$870$	−18.7370	−	49.4053i	−0.635243	−	1.67500i
$871$	−16.8901	+	5.99160i	−0.572299	+	0.203017i
$872$	−9.73553	+	25.6705i	−0.329687	+	0.869312i
$873$	2.85237	+	7.52107i	0.0965380	+	0.254550i
$874$	12.8136	+	3.15828i	0.433428	+	0.106830i
$875$	1.80269	+	2.61165i	0.0609421	+	0.0882898i
$876$	−2.03828	+	5.37451i	−0.0688672	+	0.181588i
$877$	−1.54586	−	4.07609i	−0.0521999	−	0.137640i	0.906380	−	0.422463i	$-0.138834\pi$
$877$	−1.54586	−	4.07609i	−0.0521999	−	0.137640i	−0.958580	+	0.284823i	$0.908065\pi$
$878$	−5.47899	−	45.1236i	−0.184907	−	1.52285i
$879$	−14.3589	−	20.8025i	−0.484314	−	0.701649i
$880$	−30.2847	+	7.46451i	−1.02090	+	0.251629i
$881$	−12.7987	−	11.3387i	−0.431199	−	0.382009i	0.419419	−	0.907793i	$-0.362234\pi$
$881$	−12.7987	−	11.3387i	−0.431199	−	0.382009i	−0.850618	+	0.525784i	$0.823772\pi$
$882$	1.41474	−	3.73036i	0.0476368	−	0.125608i
$883$	27.2622	+	6.71952i	0.917445	+	0.226130i	0.669645	−	0.742681i	$-0.266446\pi$
$883$	27.2622	+	6.71952i	0.917445	+	0.226130i	0.247800	+	0.968811i	$0.420292\pi$
$884$	−5.13847	−	22.9721i	−0.172826	−	0.772635i
$885$	−33.3656	+	8.22387i	−1.12157	+	0.276442i
$886$	8.15174	−	67.1356i	0.273863	−	2.25546i
$887$	−23.8093	+	12.4961i	−0.799438	+	0.419577i	−0.814395	−	0.580311i	$-0.802931\pi$
$887$	−23.8093	+	12.4961i	−0.799438	+	0.419577i	0.0149573	+	0.999888i	$0.495239\pi$
$888$	−5.16236	−	13.6120i	−0.173237	−	0.456790i
$889$	−4.40433	−	1.08557i	−0.147716	−	0.0364088i
$890$	12.1318	−	10.7478i	0.406659	−	0.360269i
$891$	−1.90225	−	0.468862i	−0.0637277	−	0.0157075i
$892$	1.05077	−	0.551486i	0.0351823	−	0.0184651i
$893$	−14.3252	+	7.51847i	−0.479376	+	0.251596i
$894$	−3.55848	−	29.3067i	−0.119013	−	0.980164i
$895$	−3.88488	−	31.9949i	−0.129857	−	1.06947i
$896$	−23.6695	+	20.9693i	−0.790742	+	0.700537i
$897$	4.01056	−	14.8806i	0.133909	−	0.496848i
$898$	12.1325	+	10.7485i	0.404867	+	0.358680i
$899$	−32.3905	+	46.9258i	−1.08028	+	1.56506i
$900$	−2.29069	+	6.04006i	−0.0763564	+	0.201335i
$901$	4.17708	+	34.4013i	0.139159	+	1.14607i
$902$	4.77429	−	39.3198i	0.158966	−	1.30921i
$903$	3.02536	+	1.58783i	0.100678	+	0.0528397i
$904$	13.1886	−	19.1070i	0.438646	−	0.635488i
$905$	−8.81135	−	23.2336i	−0.292899	−	0.772312i
$906$	19.3878	−	17.1761i	0.644116	−	0.570637i
$907$	27.5350	−	39.8913i	0.914285	−	1.32457i	−0.0314073	−	0.999507i	$-0.509999\pi$
$907$	27.5350	−	39.8913i	0.914285	−	1.32457i	0.945692	−	0.325064i	$-0.105386\pi$
$908$	−0.558360	−	0.808924i	−0.0185298	−	0.0268451i
$909$	0.887003	+	7.30513i	0.0294200	+	0.242296i
$910$	62.4397	+	8.95395i	2.06986	+	0.296820i
$911$	1.29700	−	10.6817i	0.0429715	−	0.353902i	−0.955325	−	0.295557i	$-0.904495\pi$
$911$	1.29700	−	10.6817i	0.0429715	−	0.353902i	0.998296	−	0.0583447i	$-0.0185823\pi$
$912$	7.55647	−	3.96594i	0.250220	−	0.131325i
$913$	4.55818	+	12.0189i	0.150854	+	0.397768i
$914$	1.01923	−	8.39409i	0.0337130	−	0.277652i
$915$	−7.90649			−0.261381
$916$	−0.890053	+	7.33024i	−0.0294082	+	0.242198i
$917$	39.3000	+	56.9359i	1.29780	+	1.88019i
$918$	9.36686	−	2.30872i	0.309152	−	0.0761992i
$919$	−19.3969	+	28.1012i	−0.639843	+	0.926973i	−0.999982	−	0.00592538i	$-0.998114\pi$
$919$	−19.3969	+	28.1012i	−0.639843	+	0.926973i	0.360139	+	0.932899i	$0.382729\pi$
$920$	18.8107	−	4.63643i	0.620171	−	0.152858i
$921$	−4.46351	−	2.34263i	−0.147078	−	0.0771924i
$922$	−35.9467	−	18.8663i	−1.18384	−	0.621327i
$923$	−4.62937	+	17.1766i	−0.152378	+	0.565374i
$924$	6.39193	−	3.35474i	0.210279	−	0.110363i
$925$	−54.9598			−1.80707
$926$	−16.6931	−	8.76123i	−0.548570	−	0.287912i
$927$	0.645526	−	1.70211i	0.0212018	−	0.0559047i
$928$	−6.70102	−	55.1878i	−0.219972	−	1.81163i
$929$	−18.5205	+	4.56490i	−0.607639	+	0.149770i	−0.531117	−	0.847298i	$-0.678228\pi$
$929$	−18.5205	+	4.56490i	−0.607639	+	0.149770i	−0.0765220	+	0.997068i	$0.524382\pi$
$930$	34.7598	−	8.56751i	1.13982	−	0.280940i
$931$	0.462098	+	3.80572i	0.0151446	+	0.124727i
$932$	2.02397	−	5.33676i	0.0662972	−	0.174811i
$933$	11.2705	+	5.91523i	0.368980	+	0.193656i
$934$	48.9381			1.60130
$935$	30.0005	−	15.7455i	0.981121	−	0.514932i
$936$	−2.26569	−	4.55327i	−0.0740562	−	0.148828i
$937$	52.7157	+	27.6673i	1.72215	+	0.903852i	0.969380	+	0.245564i	$0.0789732\pi$
$937$	52.7157	+	27.6673i	1.72215	+	0.903852i	0.752766	+	0.658288i	$0.228719\pi$
$938$	23.9622	+	12.5763i	0.782394	+	0.410632i
$939$	−22.1639	+	5.46292i	−0.723293	+	0.178276i
$940$	20.7983	−	30.1316i	0.678366	−	0.982783i
$941$	−15.8837	+	3.91498i	−0.517793	+	0.127625i	−0.489548	−	0.871976i	$-0.662838\pi$
$941$	−15.8837	+	3.91498i	−0.517793	+	0.127625i	−0.0282454	+	0.999601i	$0.508992\pi$
$942$	11.0340	+	15.9855i	0.359507	+	0.520836i
$943$	−5.81097	+	47.8576i	−0.189231	+	1.55846i
$944$	−52.9865			−1.72456
$945$	−1.17643	+	9.68880i	−0.0382694	+	0.315177i
$946$	1.40084	+	3.69372i	0.0455453	+	0.120093i
$947$	−41.2307	+	21.6395i	−1.33982	+	0.703190i	−0.973797	−	0.227417i	$-0.926972\pi$
$947$	−41.2307	+	21.6395i	−1.33982	+	0.703190i	−0.366019	+	0.930607i	$0.619280\pi$
$948$	−1.90038	+	15.6511i	−0.0617216	+	0.508323i
$949$	−17.0004	+	1.69252i	−0.551856	+	0.0549414i
$950$	−1.98178	−	16.3214i	−0.0642974	−	0.529537i
$951$	2.11545	+	3.06475i	0.0685981	+	0.0993815i
$952$	13.0987	−	18.9767i	0.424530	−	0.615038i
$953$	9.23178	−	8.17864i	0.299047	−	0.264932i	−0.500234	−	0.865890i	$-0.666753\pi$
$953$	9.23178	−	8.17864i	0.299047	−	0.264932i	0.799280	+	0.600958i	$0.205214\pi$
$954$	−4.09279	−	10.7918i	−0.132509	−	0.349397i
$955$	3.58479	−	5.19347i	0.116001	−	0.168057i
$956$	28.3830	+	14.8965i	0.917972	+	0.481789i
$957$	2.16640	−	17.8419i	0.0700298	−	0.576747i
$958$	4.19506	+	34.5494i	0.135536	+	1.11624i
$959$	8.12475	−	21.4232i	0.262362	−	0.691791i
$960$	−1.74044	+	2.52146i	−0.0561725	+	0.0813799i
$961$	−5.71275	−	5.06106i	−0.184282	−	0.163260i
$962$	−45.3005	+	48.9611i	−1.46055	+	1.57857i
$963$	9.13227	−	8.09049i	0.294283	−	0.260712i
$964$	0.681255	+	5.61064i	0.0219418	+	0.180707i
$965$	−2.22946	−	18.3613i	−0.0717690	−	0.591071i
$966$	−20.6064	+	10.8151i	−0.663001	+	0.347970i
$967$	−15.9786	+	8.38623i	−0.513838	+	0.269683i	−0.701650	−	0.712522i	$-0.747553\pi$
$967$	−15.9786	+	8.38623i	−0.513838	+	0.269683i	0.187812	+	0.982205i	$0.439861\pi$
$968$	9.80831	+	2.41753i	0.315251	+	0.0777024i
$969$	−6.93875	+	6.14720i	−0.222905	+	0.197476i
$970$	44.9845	+	11.0877i	1.44437	+	0.356004i
$971$	−21.4480	−	56.5537i	−0.688299	−	1.81490i	−0.569524	−	0.821974i	$-0.692873\pi$
$971$	−21.4480	−	56.5537i	−0.688299	−	1.81490i	−0.118775	−	0.992921i	$-0.537897\pi$
$972$	−1.07413	+	0.563748i	−0.0344528	+	0.0180822i
$973$	−1.03608	+	8.53287i	−0.0332151	+	0.273551i
$974$	30.6554	−	7.55588i	0.982263	−	0.242106i
$975$	−19.1056	+	1.90211i	−0.611870	+	0.0609162i
$976$	−11.8369	−	2.91753i	−0.378889	−	0.0933878i
$977$	0.597677	−	1.57594i	0.0191214	−	0.0504189i	−0.925116	−	0.379685i	$-0.876032\pi$
$977$	0.597677	−	1.57594i	0.0191214	−	0.0504189i	0.944237	+	0.329267i	$0.106801\pi$
$978$	−4.62145	−	4.09425i	−0.147778	−	0.130920i
$979$	5.35285	−	1.31936i	0.171078	−	0.0421669i
$980$	−4.92842	−	7.14005i	−0.157433	−	0.228081i
$981$	2.34609	+	19.3218i	0.0749049	+	0.616897i
$982$	−12.4960	−	32.9491i	−0.398762	−	1.05145i
$983$	18.7368	−	49.4049i	0.597611	−	1.57577i	−0.204675	−	0.978830i	$-0.565614\pi$
$983$	18.7368	−	49.4049i	0.597611	−	1.57577i	0.802286	−	0.596940i	$-0.203617\pi$
$984$	9.03737	+	13.0929i	0.288101	+	0.417386i
$985$	29.2403	+	7.20708i	0.931672	+	0.229637i
$986$	31.3828	+	82.7495i	0.999431	+	2.63528i
$987$	10.1166	−	26.6754i	0.322016	−	0.849087i
$988$	−6.10620	−	4.41252i	−0.194264	−	0.140381i
$989$	−1.70502	−	4.49577i	−0.0542165	−	0.142957i
$990$	−8.44658	+	7.48302i	−0.268450	+	0.237826i
$991$	−56.6451			−1.79939			−0.899696	−	0.436518i	$-0.856212\pi$
$991$	−56.6451			−1.79939			−0.899696	+	0.436518i	$0.856212\pi$
$992$	37.6661			1.19590
$993$	−26.1390	+	23.1571i	−0.829495	+	0.734868i
$994$	23.7859	−	12.4838i	0.754444	−	0.395963i
$995$	−40.9245			−1.29740
$996$	7.04742	+	3.69877i	0.223306	+	0.117200i
$997$	−26.4083	−	23.3957i	−0.836360	−	0.740950i	0.131802	−	0.991276i	$-0.457924\pi$
$997$	−26.4083	−	23.3957i	−0.836360	−	0.740950i	−0.968162	+	0.250326i	$0.919462\pi$
$998$	32.6971	+	47.3699i	1.03501	+	1.49947i
$999$	−7.72524	−	6.84397i	−0.244416	−	0.216534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.a.40.13	✓	180
169.131	even	13	inner	507.2.m.a.469.13	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.a.40.13	✓	180	1.1	even	1	trivial
507.2.m.a.469.13	yes	180	169.131	even	13	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74042 + 0.428975i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.07413 + 0.563748i) q^{4} +(-1.82535 + 2.64447i) q^{5} +(-0.635632 + 1.67602i) q^{6} +(2.27352 + 2.01416i) q^{7} +(-1.05581 - 0.935370i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(1.74042 + 0.428975i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.07413 + 0.563748i) q^{4} +(-1.82535 + 2.64447i) q^{5} +(-0.635632 + 1.67602i) q^{6} +(2.27352 + 2.01416i) q^{7} +(-1.05581 - 0.935370i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-4.31129 + 3.81947i) q^{10} +(-1.90225 + 0.468862i) q^{11} +(-0.689110 + 0.998348i) q^{12} +(-3.56904 - 0.511806i) q^{13} +(3.09285 + 4.48077i) q^{14} +(-2.40517 - 2.13080i) q^{15} +(-2.81453 - 4.07755i) q^{16} +(4.02845 + 3.56889i) q^{17} +(-1.58719 - 0.833020i) q^{18} +1.72244 q^{19} +(-3.45148 + 1.81148i) q^{20} +(-2.27352 + 2.01416i) q^{21} -3.51184 q^{22} +4.27440 q^{23} +(1.05581 - 0.935370i) q^{24} +(-1.88832 - 4.97910i) q^{25} +(-5.99208 - 2.42179i) q^{26} +(0.354605 - 0.935016i) q^{27} +(1.30658 + 3.44517i) q^{28} +(8.90715 + 2.19542i) q^{29} +(-3.27195 - 4.74024i) q^{30} +(-2.20404 + 5.81157i) q^{31} +(-2.14892 - 5.66624i) q^{32} +(-0.236153 - 1.94489i) q^{33} +(5.48023 + 7.93948i) q^{34} +(-9.47636 + 2.33571i) q^{35} +(-0.908006 - 0.804423i) q^{36} +(3.65981 - 9.65013i) q^{37} +(2.99777 + 0.738883i) q^{38} +(0.938275 - 3.48133i) q^{39} +(4.40079 - 1.08470i) q^{40} +(-1.35948 + 11.1964i) q^{41} +(-4.82090 + 2.53020i) q^{42} +(-0.398891 - 1.05179i) q^{43} +(-2.30759 - 0.568769i) q^{44} +(2.40517 - 2.13080i) q^{45} +(7.43925 + 1.83361i) q^{46} +(-8.31684 + 4.36502i) q^{47} +(4.38708 - 2.30252i) q^{48} +(0.268281 + 2.20949i) q^{49} +(-1.15057 - 9.47576i) q^{50} +(-4.02845 + 3.56889i) q^{51} +(-3.54509 - 2.56179i) q^{52} +(4.81961 + 4.26980i) q^{53} +(1.01826 - 1.47520i) q^{54} +(2.23237 - 5.88628i) q^{55} +(-0.516427 - 4.25316i) q^{56} +(-0.207617 + 1.70988i) q^{57} +(14.5604 + 7.64190i) q^{58} +(6.07512 - 8.80133i) q^{59} +(-1.38224 - 3.64467i) q^{60} +(1.84176 - 1.63166i) q^{61} +(-6.32897 + 9.16910i) q^{62} +(-1.72543 - 2.49972i) q^{63} +(-0.114930 - 0.946532i) q^{64} +(7.86820 - 8.50401i) q^{65} +(0.423306 - 3.48624i) q^{66} +(4.40115 - 2.30990i) q^{67} +(2.31513 + 6.10449i) q^{68} +(-0.515222 + 4.24323i) q^{69} -17.4948 q^{70} +(0.594718 - 4.89795i) q^{71} +(0.801286 + 1.16086i) q^{72} +(4.60068 - 1.13397i) q^{73} +(10.5093 - 15.2253i) q^{74} +(5.17040 - 1.27439i) q^{75} +(1.85013 + 0.971021i) q^{76} +(-5.26916 - 2.76547i) q^{77} +(3.12640 - 5.65648i) q^{78} +(11.5080 - 6.03984i) q^{79} +15.9205 q^{80} +(0.885456 + 0.464723i) q^{81} +(-7.16903 + 18.9032i) q^{82} +(-0.790846 - 6.51320i) q^{83} +(-3.57754 + 0.881784i) q^{84} +(-16.7912 + 4.13865i) q^{85} +(-0.243047 - 2.00167i) q^{86} +(-3.25305 + 8.57758i) q^{87} +(2.44698 + 1.28427i) q^{88} -2.81396 q^{89} +(5.10007 - 2.67672i) q^{90} +(-7.08342 - 8.35222i) q^{91} +(4.59127 + 2.40968i) q^{92} +(-5.50353 - 2.88848i) q^{93} +(-16.3473 + 4.02924i) q^{94} +(-3.14405 + 4.55494i) q^{95} +(5.88395 - 1.45026i) q^{96} +(-4.56939 - 6.61991i) q^{97} +(-0.480896 + 3.96054i) q^{98} +1.95918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Introduction

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