LMFDB - Embedded newform 115.2.g.c.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	115.31
Dual form			115.2.g.c.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.362593 + 2.52189i) q^{2} +(0.804293 + 1.76116i) q^{3} +(-4.30948 - 1.26538i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(-4.73308 + 1.38976i) q^{6} +(0.564436 + 0.362741i) q^{7} +(2.63693 - 5.77406i) q^{8} +(-0.490203 + 0.565724i) q^{9} +O(q^{10})$	\(q+(-0.362593 + 2.52189i) q^{2} +(0.804293 + 1.76116i) q^{3} +(-4.30948 - 1.26538i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(-4.73308 + 1.38976i) q^{6} +(0.564436 + 0.362741i) q^{7} +(2.63693 - 5.77406i) q^{8} +(-0.490203 + 0.565724i) q^{9} +(2.14337 - 1.37746i) q^{10} +(0.677087 + 4.70925i) q^{11} +(-1.23756 - 8.60741i) q^{12} +(2.77319 - 1.78222i) q^{13} +(-1.11945 + 1.29192i) q^{14} +(0.804293 - 1.76116i) q^{15} +(6.04859 + 3.88719i) q^{16} +(3.87808 - 1.13871i) q^{17} +(-1.24895 - 1.44137i) q^{18} +(-7.66507 - 2.25067i) q^{19} +(1.86580 + 4.08553i) q^{20} +(-0.184872 + 1.28581i) q^{21} -12.1217 q^{22} +(-2.45039 + 4.12257i) q^{23} +12.2899 q^{24} +(-0.142315 + 0.989821i) q^{25} +(3.48903 + 7.63991i) q^{26} +(4.18248 + 1.22809i) q^{27} +(-1.97342 - 2.27745i) q^{28} +(6.35438 - 1.86581i) q^{29} +(4.14982 + 2.66692i) q^{30} +(2.31756 - 5.07476i) q^{31} +(-3.68256 + 4.24990i) q^{32} +(-7.74914 + 4.98007i) q^{33} +(1.46553 + 10.1930i) q^{34} +(-0.0954857 - 0.664117i) q^{35} +(2.82838 - 1.81769i) q^{36} +(-1.02232 + 1.17982i) q^{37} +(8.45525 - 18.5144i) q^{38} +(5.36923 + 3.45060i) q^{39} +(-6.09056 + 1.78835i) q^{40} +(-3.37652 - 3.89671i) q^{41} +(-3.17564 - 0.932453i) q^{42} +(0.646896 + 1.41651i) q^{43} +(3.04108 - 21.1512i) q^{44} +0.748561 q^{45} +(-9.50818 - 7.67444i) q^{46} +7.40147 q^{47} +(-1.98112 + 13.7790i) q^{48} +(-2.72090 - 5.95794i) q^{49} +(-2.44462 - 0.717805i) q^{50} +(5.12456 + 5.91406i) q^{51} +(-14.2062 + 4.17132i) q^{52} +(-1.43096 - 0.919621i) q^{53} +(-4.61365 + 10.1025i) q^{54} +(3.11561 - 3.59561i) q^{55} +(3.58287 - 2.30257i) q^{56} +(-2.20119 - 15.3096i) q^{57} +(2.40133 + 16.7016i) q^{58} +(-9.89375 + 6.35833i) q^{59} +(-5.69461 + 6.57194i) q^{60} +(0.248849 - 0.544904i) q^{61} +(11.9577 + 7.68472i) q^{62} +(-0.481900 + 0.141499i) q^{63} +(0.0343466 + 0.0396381i) q^{64} +(-3.16297 - 0.928731i) q^{65} +(-9.74942 - 21.3482i) q^{66} +(1.56057 - 10.8540i) q^{67} -18.1534 q^{68} +(-9.23133 - 0.999764i) q^{69} +1.70945 q^{70} +(1.66451 - 11.5769i) q^{71} +(1.97390 + 4.32223i) q^{72} +(-3.31786 - 0.974213i) q^{73} +(-2.60469 - 3.00597i) q^{74} +(-1.85769 + 0.545468i) q^{75} +(30.1845 + 19.3984i) q^{76} +(-1.32606 + 2.90368i) q^{77} +(-10.6489 + 12.2895i) q^{78} +(-0.900221 + 0.578537i) q^{79} +(-1.02324 - 7.11679i) q^{80} +(1.52068 + 10.5766i) q^{81} +(11.0514 - 7.10230i) q^{82} +(-0.985815 + 1.13769i) q^{83} +(2.42374 - 5.30724i) q^{84} +(-3.40018 - 2.18516i) q^{85} +(-3.80684 + 1.11779i) q^{86} +(8.39678 + 9.69040i) q^{87} +(28.9769 + 8.50839i) q^{88} +(-1.31463 - 2.87863i) q^{89} +(-0.271423 + 1.88779i) q^{90} +2.21177 q^{91} +(15.7765 - 14.6655i) q^{92} +10.8014 q^{93} +(-2.68372 + 18.6657i) q^{94} +(3.31861 + 7.26675i) q^{95} +(-10.4466 - 3.06740i) q^{96} +(-2.41873 - 2.79137i) q^{97} +(16.0119 - 4.70150i) q^{98} +(-2.99605 - 1.92544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.362593	+	2.52189i	−0.256392	+	1.78325i	0.301634	+	0.953424i	$0.402468\pi$
$2$	−0.362593	+	2.52189i	−0.256392	+	1.78325i	−0.558026	+	0.829823i	$0.688441\pi$
$3$	0.804293	+	1.76116i	0.464359	+	1.01680i	0.986472	+	0.163928i	$0.0524165\pi$
$3$	0.804293	+	1.76116i	0.464359	+	1.01680i	−0.522113	+	0.852876i	$0.674856\pi$
$4$	−4.30948	−	1.26538i	−2.15474	−	0.632689i
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$6$	−4.73308	+	1.38976i	−1.93227	+	0.567366i
$7$	0.564436	+	0.362741i	0.213337	+	0.137103i	0.642946	−	0.765912i	$-0.277712\pi$
$7$	0.564436	+	0.362741i	0.213337	+	0.137103i	−0.429609	+	0.903015i	$0.641349\pi$
$8$	2.63693	−	5.77406i	0.932294	−	2.04144i
$9$	−0.490203	+	0.565724i	−0.163401	+	0.188575i
$10$	2.14337	−	1.37746i	0.677792	−	0.435591i
$11$	0.677087	+	4.70925i	0.204150	+	1.41989i	0.791802	+	0.610778i	$0.209143\pi$
$11$	0.677087	+	4.70925i	0.204150	+	1.41989i	−0.587653	+	0.809113i	$0.699948\pi$
$12$	−1.23756	−	8.60741i	−0.357252	−	2.48474i
$13$	2.77319	−	1.78222i	0.769145	−	0.494299i	−0.0962701	−	0.995355i	$-0.530691\pi$
$13$	2.77319	−	1.78222i	0.769145	−	0.494299i	0.865415	+	0.501056i	$0.167055\pi$
$14$	−1.11945	+	1.29192i	−0.299187	+	0.345280i
$15$	0.804293	−	1.76116i	0.207668	−	0.454729i
$16$	6.04859	+	3.88719i	1.51215	+	0.971799i
$17$	3.87808	−	1.13871i	0.940573	−	0.276177i	0.224716	−	0.974424i	$-0.427854\pi$
$17$	3.87808	−	1.13871i	0.940573	−	0.276177i	0.715857	+	0.698247i	$0.246036\pi$
$18$	−1.24895	−	1.44137i	−0.294381	−	0.339733i
$19$	−7.66507	−	2.25067i	−1.75849	−	0.516339i	−0.766453	−	0.642300i	$-0.777980\pi$
$19$	−7.66507	−	2.25067i	−1.75849	−	0.516339i	−0.992035	+	0.125961i	$0.959798\pi$
$20$	1.86580	+	4.08553i	0.417206	+	0.913553i
$21$	−0.184872	+	1.28581i	−0.0403423	+	0.280587i
$22$	−12.1217			−2.58436
$23$	−2.45039	+	4.12257i	−0.510942	+	0.859615i
$23$	−2.45039	+	4.12257i	−0.510942	+	0.859615i
$24$	12.2899			2.50866
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	3.48903	+	7.63991i	0.684255	+	1.49831i
$27$	4.18248	+	1.22809i	0.804920	+	0.236346i
$28$	−1.97342	−	2.27745i	−0.372942	−	0.430398i
$29$	6.35438	−	1.86581i	1.17998	−	0.346473i	0.367813	−	0.929900i	$-0.380107\pi$
$29$	6.35438	−	1.86581i	1.17998	−	0.346473i	0.812166	+	0.583427i	$0.198288\pi$
$30$	4.14982	+	2.66692i	0.757649	+	0.486912i
$31$	2.31756	−	5.07476i	0.416247	−	0.911453i	−0.579115	−	0.815246i	$-0.696602\pi$
$31$	2.31756	−	5.07476i	0.416247	−	0.911453i	0.995361	−	0.0962072i	$-0.0306711\pi$
$32$	−3.68256	+	4.24990i	−0.650991	+	0.751283i
$33$	−7.74914	+	4.98007i	−1.34895	+	0.866919i
$34$	1.46553	+	10.1930i	0.251337	+	1.74808i
$35$	−0.0954857	−	0.664117i	−0.0161400	−	0.112256i
$36$	2.82838	−	1.81769i	0.471396	−	0.302948i
$37$	−1.02232	+	1.17982i	−0.168068	+	0.193961i	−0.833535	−	0.552466i	$-0.813687\pi$
$37$	−1.02232	+	1.17982i	−0.168068	+	0.193961i	0.665467	+	0.746427i	$0.268232\pi$
$38$	8.45525	−	18.5144i	1.37162	−	3.00343i
$39$	5.36923	+	3.45060i	0.859765	+	0.552537i
$40$	−6.09056	+	1.78835i	−0.963003	+	0.282763i
$41$	−3.37652	−	3.89671i	−0.527324	−	0.608564i	0.428125	−	0.903719i	$-0.359174\pi$
$41$	−3.37652	−	3.89671i	−0.527324	−	0.608564i	−0.955449	+	0.295155i	$0.904629\pi$
$42$	−3.17564	−	0.932453i	−0.490012	−	0.143881i
$43$	0.646896	+	1.41651i	0.0986508	+	0.216015i	0.952522	−	0.304469i	$-0.0984789\pi$
$43$	0.646896	+	1.41651i	0.0986508	+	0.216015i	−0.853872	+	0.520484i	$0.825752\pi$
$44$	3.04108	−	21.1512i	0.458460	−	3.18866i
$45$	0.748561			0.111589
$46$	−9.50818	−	7.67444i	−1.40191	−	1.13153i
$47$	7.40147			1.07961			0.539807	−	0.841789i	$-0.318497\pi$
$47$	7.40147			1.07961			0.539807	+	0.841789i	$0.318497\pi$
$48$	−1.98112	+	13.7790i	−0.285949	+	1.98882i
$49$	−2.72090	−	5.95794i	−0.388700	−	0.851134i
$50$	−2.44462	−	0.717805i	−0.345722	−	0.101513i
$51$	5.12456	+	5.91406i	0.717582	+	0.828134i
$52$	−14.2062	+	4.17132i	−1.97005	+	0.578457i
$53$	−1.43096	−	0.919621i	−0.196557	−	0.126320i	0.438660	−	0.898653i	$-0.355453\pi$
$53$	−1.43096	−	0.919621i	−0.196557	−	0.126320i	−0.635217	+	0.772333i	$0.719090\pi$
$54$	−4.61365	+	10.1025i	−0.627838	+	1.37477i
$55$	3.11561	−	3.59561i	0.420109	−	0.484832i
$56$	3.58287	−	2.30257i	0.478781	−	0.307694i
$57$	−2.20119	−	15.3096i	−0.291554	−	2.02780i
$58$	2.40133	+	16.7016i	0.315310	+	2.19303i
$59$	−9.89375	+	6.35833i	−1.28806	+	0.827784i	−0.991859	−	0.127343i	$-0.959355\pi$
$59$	−9.89375	+	6.35833i	−1.28806	+	0.827784i	−0.296198	+	0.955127i	$0.595719\pi$
$60$	−5.69461	+	6.57194i	−0.735172	+	0.848433i
$61$	0.248849	−	0.544904i	0.0318619	−	0.0697678i	−0.893032	−	0.449993i	$-0.851426\pi$
$61$	0.248849	−	0.544904i	0.0318619	−	0.0697678i	0.924894	+	0.380226i	$0.124154\pi$
$62$	11.9577	+	7.68472i	1.51862	+	0.975960i
$63$	−0.481900	+	0.141499i	−0.0607137	+	0.0178271i
$64$	0.0343466	+	0.0396381i	0.00429332	+	0.00495476i
$65$	−3.16297	−	0.928731i	−0.392318	−	0.115195i
$66$	−9.74942	−	21.3482i	−1.20007	−	2.62779i
$67$	1.56057	−	10.8540i	0.190654	−	1.32603i	−0.639627	−	0.768685i	$-0.720911\pi$
$67$	1.56057	−	10.8540i	0.190654	−	1.32603i	0.830282	−	0.557344i	$-0.188180\pi$
$68$	−18.1534			−2.20143
$69$	−9.23133	−	0.999764i	−1.11132	−	0.120357i
$70$	1.70945			0.204319
$71$	1.66451	−	11.5769i	0.197541	−	1.37393i	−0.613849	−	0.789423i	$-0.710380\pi$
$71$	1.66451	−	11.5769i	0.197541	−	1.37393i	0.811390	−	0.584505i	$-0.198711\pi$
$72$	1.97390	+	4.32223i	0.232626	+	0.509380i
$73$	−3.31786	−	0.974213i	−0.388327	−	0.114023i	0.0817405	−	0.996654i	$-0.473952\pi$
$73$	−3.31786	−	0.974213i	−0.388327	−	0.114023i	−0.470067	+	0.882631i	$0.655770\pi$
$74$	−2.60469	−	3.00597i	−0.302789	−	0.349437i
$75$	−1.85769	+	0.545468i	−0.214508	+	0.0629852i
$76$	30.1845	+	19.3984i	3.46240	+	2.22515i
$77$	−1.32606	+	2.90368i	−0.151119	+	0.330905i
$78$	−10.6489	+	12.2895i	−1.20575	+	1.39151i
$79$	−0.900221	+	0.578537i	−0.101283	+	0.0650905i	−0.590302	−	0.807183i	$-0.700991\pi$
$79$	−0.900221	+	0.578537i	−0.101283	+	0.0650905i	0.489019	+	0.872273i	$0.337355\pi$
$80$	−1.02324	−	7.11679i	−0.114402	−	0.795682i
$81$	1.52068	+	10.5766i	0.168965	+	1.17518i
$82$	11.0514	−	7.10230i	1.22042	−	0.784318i
$83$	−0.985815	+	1.13769i	−0.108207	+	0.124878i	−0.807269	−	0.590183i	$-0.799056\pi$
$83$	−0.985815	+	1.13769i	−0.108207	+	0.124878i	0.699062	+	0.715061i	$0.253601\pi$
$84$	2.42374	−	5.30724i	0.264451	−	0.579068i
$85$	−3.40018	−	2.18516i	−0.368802	−	0.237014i
$86$	−3.80684	+	1.11779i	−0.410502	+	0.120534i
$87$	8.39678	+	9.69040i	0.900229	+	1.03892i
$88$	28.9769	+	8.50839i	3.08895	+	0.906997i
$89$	−1.31463	−	2.87863i	−0.139350	−	0.305135i	0.827071	−	0.562098i	$-0.190005\pi$
$89$	−1.31463	−	2.87863i	−0.139350	−	0.305135i	−0.966421	+	0.256963i	$0.917278\pi$
$90$	−0.271423	+	1.88779i	−0.0286105	+	0.198990i
$91$	2.21177			0.231857
$92$	15.7765	−	14.6655i	1.64482	−	1.52898i
$93$	10.8014			1.12006
$94$	−2.68372	+	18.6657i	−0.276805	+	1.92522i
$95$	3.31861	+	7.26675i	0.340483	+	0.745553i
$96$	−10.4466	−	3.06740i	−1.06620	−	0.313065i
$97$	−2.41873	−	2.79137i	−0.245585	−	0.283420i	0.619552	−	0.784956i	$-0.287314\pi$
$97$	−2.41873	−	2.79137i	−0.245585	−	0.283420i	−0.865137	+	0.501535i	$0.832769\pi$
$98$	16.0119	−	4.70150i	1.61744	−	0.474924i
$99$	−2.99605	−	1.92544i	−0.301114	−	0.193514i
$100$	1.86580	−	4.08553i	0.186580	−	0.408553i
$101$	−1.89614	+	2.18826i	−0.188673	+	0.217740i	−0.842203	−	0.539160i	$-0.818742\pi$
$101$	−1.89614	+	2.18826i	−0.188673	+	0.217740i	0.653530	+	0.756900i	$0.273287\pi$
$102$	−16.7727	+	10.7792i	−1.66075	+	1.06730i
$103$	−0.407782	−	2.83619i	−0.0401800	−	0.279458i	0.959819	−	0.280619i	$-0.0905396\pi$
$103$	−0.407782	−	2.83619i	−0.0401800	−	0.279458i	−0.999999	+	0.00116068i	$0.999631\pi$
$104$	−2.97796	−	20.7122i	−0.292013	−	2.03099i
$105$	1.09282	−	0.702310i	0.106648	−	0.0685385i
$106$	2.83804	−	3.27527i	0.275655	−	0.318123i
$107$	−6.89574	+	15.0996i	−0.666636	+	1.45973i	0.209570	+	0.977794i	$0.432794\pi$
$107$	−6.89574	+	15.0996i	−0.666636	+	1.45973i	−0.876206	+	0.481937i	$0.839934\pi$
$108$	−16.4703	−	10.5848i	−1.58486	−	1.01853i
$109$	−5.86874	+	1.72322i	−0.562123	+	0.165054i	−0.550436	−	0.834878i	$-0.685538\pi$
$109$	−5.86874	+	1.72322i	−0.562123	+	0.165054i	−0.0116871	+	0.999932i	$0.503720\pi$
$110$	7.93804	+	9.16098i	0.756862	+	0.873465i
$111$	−2.90009	−	0.851544i	−0.275265	−	0.0808250i
$112$	2.00400	+	4.38815i	0.189360	+	0.414641i
$113$	−1.03509	+	7.19922i	−0.0973732	+	0.677246i	0.881411	+	0.472351i	$0.156594\pi$
$113$	−1.03509	+	7.19922i	−0.0973732	+	0.677246i	−0.978784	+	0.204895i	$0.934315\pi$
$114$	39.4073			3.69083
$115$	4.72030	−	0.847829i	0.440170	−	0.0790604i
$116$	−29.7450			−2.76176
$117$	−0.351180	+	2.44251i	−0.0324666	+	0.225810i
$118$	−12.4476	−	27.2565i	−1.14590	−	2.50916i
$119$	2.60199	+	0.764012i	0.238524	+	0.0700369i
$120$	−8.04817	−	9.28808i	−0.734694	−	0.847882i
$121$	−11.1641	+	3.27808i	−1.01492	+	0.298008i
$122$	1.28396	+	0.825150i	0.116244	+	0.0747056i
$123$	4.14701	−	9.08068i	0.373923	−	0.818777i
$124$	−16.4090	+	18.9370i	−1.47357	+	1.70059i
$125$	0.841254	−	0.540641i	0.0752440	−	0.0483564i
$126$	−0.182110	−	1.26661i	−0.0162237	−	0.112838i
$127$	0.865379	+	6.01884i	0.0767900	+	0.534086i	0.991513	+	0.130005i	$0.0414994\pi$
$127$	0.865379	+	6.01884i	0.0767900	+	0.534086i	−0.914723	+	0.404081i	$0.867591\pi$
$128$	−9.57387	+	6.15275i	−0.846218	+	0.543831i
$129$	−1.97439	+	2.27857i	−0.173836	+	0.200617i
$130$	3.48903	−	7.63991i	0.306008	−	0.670065i
$131$	−9.73145	−	6.25403i	−0.850241	−	0.546417i	0.0414089	−	0.999142i	$-0.486815\pi$
$131$	−9.73145	−	6.25403i	−0.850241	−	0.546417i	−0.891650	+	0.452726i	$0.850452\pi$
$132$	39.6965	−	11.6559i	3.45513	−	1.01452i
$133$	−3.51003	−	4.05080i	−0.304359	−	0.351249i
$134$	26.8068	+	7.87119i	2.31576	+	0.679967i
$135$	−1.81082	−	3.96514i	−0.155850	−	0.341265i
$136$	3.65125	−	25.3950i	0.313092	−	2.17760i
$137$	−13.3384			−1.13957			−0.569787	−	0.821792i	$-0.692974\pi$
$137$	−13.3384			−1.13957			−0.569787	+	0.821792i	$0.692974\pi$
$138$	5.86852	−	22.9179i	0.499561	−	1.95090i
$139$	13.3943			1.13609			0.568046	−	0.822997i	$-0.307700\pi$
$139$	13.3943			1.13609			0.568046	+	0.822997i	$0.307700\pi$
$140$	−0.428866	+	2.98283i	−0.0362458	+	0.252095i
$141$	5.95295	+	13.0351i	0.501329	+	1.09776i
$142$	28.5922	+	8.39543i	2.39941	+	0.704529i
$143$	10.2706	+	11.8529i	0.858872	+	0.991191i
$144$	−5.16412	+	1.51632i	−0.430343	+	0.126360i
$145$	−5.57132	−	3.58047i	−0.462673	−	0.297342i
$146$	3.65989	−	8.01405i	0.302895	−	0.663248i
$147$	8.30446	−	9.58386i	0.684940	−	0.790463i
$148$	5.89858	−	3.79079i	0.484861	−	0.311601i
$149$	0.425667	+	2.96058i	0.0348720	+	0.242540i	0.999801	−	0.0199726i	$-0.00635791\pi$
$149$	0.425667	+	2.96058i	0.0348720	+	0.242540i	−0.964929	+	0.262513i	$0.915449\pi$
$150$	−0.702024	−	4.88269i	−0.0573200	−	0.398670i
$151$	−7.66784	+	4.92782i	−0.624000	+	0.401021i	−0.814084	−	0.580747i	$-0.802760\pi$
$151$	−7.66784	+	4.92782i	−0.624000	+	0.401021i	0.190084	+	0.981768i	$0.439124\pi$
$152$	−33.2077	+	38.3238i	−2.69350	+	3.10847i
$153$	−1.25685	+	2.75212i	−0.101611	+	0.222496i
$154$	−6.84194	−	4.39705i	−0.551339	−	0.354324i
$155$	−5.35293	+	1.57176i	−0.429957	+	0.126247i
$156$	−18.7723	−	21.6644i	−1.50299	−	1.73454i
$157$	−14.0706	−	4.13151i	−1.12296	−	0.329730i	−0.333022	−	0.942919i	$-0.608068\pi$
$157$	−14.0706	−	4.13151i	−1.12296	−	0.329730i	−0.789936	+	0.613189i	$0.789886\pi$
$158$	−1.13259	−	2.48004i	−0.0901044	−	0.197301i
$159$	0.468687	−	3.25979i	0.0371693	−	0.258518i
$160$	5.62342			0.444571
$161$	−2.87851	+	1.43807i	−0.226859	+	0.113336i
$162$	−27.2244			−2.13895
$163$	−0.888601	+	6.18036i	−0.0696006	+	0.484083i	0.924972	+	0.380036i	$0.124088\pi$
$163$	−0.888601	+	6.18036i	−0.0696006	+	0.484083i	−0.994572	+	0.104047i	$0.966821\pi$
$164$	9.62024	+	21.0654i	0.751214	+	1.64493i
$165$	8.83830	+	2.59516i	0.688060	+	0.202033i
$166$	−2.51168	−	2.89864i	−0.194945	−	0.224978i
$167$	8.30745	−	2.43929i	0.642850	−	0.188758i	0.0559708	−	0.998432i	$-0.482175\pi$
$167$	8.30745	−	2.43929i	0.642850	−	0.188758i	0.586879	+	0.809675i	$0.300356\pi$
$168$	6.93686	+	4.45805i	0.535190	+	0.343946i
$169$	−0.886120	+	1.94033i	−0.0681631	+	0.149256i
$170$	6.74363	−	7.78257i	0.517213	−	0.596896i
$171$	5.03070	−	3.23303i	0.384707	−	0.247236i
$172$	−0.995373	−	6.92297i	−0.0758965	−	0.527872i
$173$	1.58909	+	11.0524i	0.120816	+	0.840295i	0.956635	+	0.291289i	$0.0940842\pi$
$173$	1.58909	+	11.0524i	0.120816	+	0.840295i	−0.835819	+	0.549005i	$0.815007\pi$
$174$	−27.4828	+	17.6621i	−2.08346	+	1.33896i
$175$	−0.439377	+	0.507068i	−0.0332137	+	0.0383307i
$176$	−14.2103	+	31.1163i	−1.07114	+	2.34548i
$177$	−19.1555	−	12.3105i	−1.43981	−	0.925313i
$178$	7.73628	−	2.27158i	0.579859	−	0.170262i
$179$	−12.7513	−	14.7158i	−0.953075	−	1.09991i	−0.994908	−	0.100782i	$-0.967865\pi$
$179$	−12.7513	−	14.7158i	−0.953075	−	1.09991i	0.0418337	−	0.999125i	$-0.486680\pi$
$180$	−3.22591	−	0.947212i	−0.240445	−	0.0706010i
$181$	7.02637	+	15.3856i	0.522266	+	1.14360i	0.968574	+	0.248724i	$0.0800112\pi$
$181$	7.02637	+	15.3856i	0.522266	+	1.14360i	−0.446308	+	0.894879i	$0.647262\pi$
$182$	−0.801975	+	5.57786i	−0.0594463	+	0.413458i
$183$	1.15981			0.0857356
$184$	17.3425	+	25.0196i	1.27850	+	1.84447i
$185$	1.56112			0.114776
$186$	−3.91653	+	27.2401i	−0.287174	+	1.99734i
$187$	7.98826	+	17.4918i	0.584159	+	1.27913i
$188$	−31.8965	−	9.36565i	−2.32629	−	0.683060i
$189$	1.91527	+	2.21034i	0.139315	+	0.160778i
$190$	−19.5293	+	5.73431i	−1.41680	+	0.416011i
$191$	−9.06831	−	5.82785i	−0.656160	−	0.421688i	0.169753	−	0.985487i	$-0.445703\pi$
$191$	−9.06831	−	5.82785i	−0.656160	−	0.421688i	−0.825912	+	0.563798i	$0.809340\pi$
$192$	−0.0421841	+	0.0923704i	−0.00304438	+	0.00666626i
$193$	11.7753	−	13.5894i	0.847601	−	0.978184i	−0.152347	−	0.988327i	$-0.548683\pi$
$193$	11.7753	−	13.5894i	0.847601	−	0.978184i	0.999949	+	0.0101431i	$0.00322869\pi$
$194$	7.91655	−	5.08765i	0.568375	−	0.365272i
$195$	−0.908313	−	6.31745i	−0.0650456	−	0.452402i
$196$	4.18662	+	29.1186i	0.299044	+	2.07990i
$197$	−5.52987	+	3.55383i	−0.393987	+	0.253200i	−0.722603	−	0.691264i	$-0.757054\pi$
$197$	−5.52987	+	3.55383i	−0.393987	+	0.253200i	0.328616	+	0.944464i	$0.393418\pi$
$198$	5.94210	−	6.85755i	0.422287	−	0.487345i
$199$	9.69194	−	21.2224i	0.687043	−	1.50442i	−0.167960	−	0.985794i	$-0.553718\pi$
$199$	9.69194	−	21.2224i	0.687043	−	1.50442i	0.855004	−	0.518622i	$-0.173555\pi$
$200$	5.34002	+	3.43182i	0.377596	+	0.242666i
$201$	20.3708	−	5.98140i	1.43684	−	0.421896i
$202$	−4.83104	−	5.57532i	−0.339911	−	0.392278i
$203$	4.26345	+	1.25186i	0.299235	+	0.0878635i
$204$	−14.6007	−	31.9710i	−1.02225	−	2.23842i
$205$	−0.733788	+	5.10361i	−0.0512500	+	0.356451i
$206$	7.30042			0.508645
$207$	−1.13105	−	3.40714i	−0.0786134	−	0.236813i
$208$	23.7017			1.64342
$209$	5.40903	−	37.6206i	0.374150	−	2.60227i
$210$	1.37490	+	3.01062i	0.0948773	+	0.207752i
$211$	3.15248	+	0.925652i	0.217026	+	0.0637245i	0.388438	−	0.921475i	$-0.373015\pi$
$211$	3.15248	+	0.925652i	0.217026	+	0.0637245i	−0.171412	+	0.985199i	$0.554833\pi$
$212$	5.00302	+	5.77379i	0.343609	+	0.396546i
$213$	21.7275	−	6.37978i	1.48875	−	0.437135i
$214$	−35.5791	−	22.8653i	−2.43214	−	1.56304i
$215$	0.646896	−	1.41651i	0.0441180	−	0.0966049i
$216$	18.1200	−	20.9115i	1.23291	−	1.42285i
$217$	3.14894	−	2.02370i	0.213764	−	0.137378i
$218$	−2.21780	−	15.4251i	−0.150208	−	1.04472i
$219$	−0.952794	−	6.62683i	−0.0643839	−	0.447800i
$220$	−17.9765	+	11.5528i	−1.21197	+	0.778888i
$221$	8.72524	−	10.0695i	0.586923	−	0.677345i
$222$	3.19906	−	7.00495i	0.214707	−	0.470142i
$223$	7.34270	+	4.71887i	0.491703	+	0.315999i	0.762890	−	0.646528i	$-0.223780\pi$
$223$	7.34270	+	4.71887i	0.491703	+	0.315999i	−0.271187	+	0.962527i	$0.587416\pi$
$224$	−3.62018	+	1.06298i	−0.241884	+	0.0710235i
$225$	−0.490203	−	0.565724i	−0.0326802	−	0.0377150i
$226$	−17.7803	−	5.22078i	−1.18273	−	0.347281i
$227$	9.81301	+	21.4875i	0.651312	+	1.42617i	0.890401	+	0.455177i	$0.150424\pi$
$227$	9.81301	+	21.4875i	0.651312	+	1.42617i	−0.239089	+	0.970998i	$0.576849\pi$
$228$	−9.88644	+	68.7617i	−0.654746	+	4.55386i
$229$	21.0966			1.39410			0.697051	−	0.717022i	$-0.254495\pi$
$229$	21.0966			1.39410			0.697051	+	0.717022i	$0.254495\pi$
$230$	0.426585	+	12.2115i	0.0281282	+	0.805202i
$231$	−6.18037			−0.406639
$232$	5.98270	−	41.6106i	0.392783	−	2.73187i
$233$	2.23822	+	4.90102i	0.146631	+	0.321076i	0.968669	−	0.248356i	$-0.0798903\pi$
$233$	2.23822	+	4.90102i	0.146631	+	0.321076i	−0.822038	+	0.569432i	$0.807163\pi$
$234$	−6.03242	−	1.77128i	−0.394351	−	0.115792i
$235$	−4.84693	−	5.59366i	−0.316179	−	0.364890i
$236$	50.6826	−	14.8818i	3.29916	−	0.968720i
$237$	−1.74294	−	1.12012i	−0.113216	−	0.0727594i
$238$	−2.87022	+	6.28490i	−0.186049	+	0.407390i
$239$	−8.03307	+	9.27066i	−0.519616	+	0.599669i	−0.953535	−	0.301283i	$-0.902585\pi$
$239$	−8.03307	+	9.27066i	−0.519616	+	0.599669i	0.433919	+	0.900952i	$0.357131\pi$
$240$	11.7108	−	7.52607i	0.755929	−	0.485806i
$241$	−1.53631	−	10.6853i	−0.0989626	−	0.688300i	−0.977548	−	0.210714i	$-0.932421\pi$
$241$	−1.53631	−	10.6853i	−0.0989626	−	0.688300i	0.878585	−	0.477586i	$-0.158488\pi$
$242$	−4.21893	−	29.3433i	−0.271203	−	1.88626i
$243$	−6.40272	+	4.11478i	−0.410735	+	0.263963i
$244$	−1.76192	+	2.03337i	−0.112795	+	0.130173i
$245$	−2.72090	+	5.95794i	−0.173832	+	0.380639i
$246$	21.3968	+	13.7509i	1.36421	+	0.876726i
$247$	−25.2679	+	7.41933i	−1.60776	+	0.472080i
$248$	−23.1907	−	26.7635i	−1.47261	−	1.69948i
$249$	−2.79654	−	0.821137i	−0.177223	−	0.0520375i
$250$	1.05840	+	2.31758i	0.0669394	+	0.146577i
$251$	−0.392601	+	2.73060i	−0.0247807	+	0.172354i	−0.998453	−	0.0555975i	$-0.982294\pi$
$251$	−0.392601	+	2.73060i	−0.0247807	+	0.172354i	0.973673	+	0.227951i	$0.0732027\pi$
$252$	2.25579			0.142101
$253$	−21.0733	−	8.74815i	−1.32487	−	0.549991i
$254$	−15.4927			−0.972096
$255$	1.11367	−	7.74577i	0.0697409	−	0.485059i
$256$	−12.0016	−	26.2798i	−0.750099	−	1.64249i
$257$	2.19567	+	0.644708i	0.136962	+	0.0402158i	0.349495	−	0.936938i	$-0.386353\pi$
$257$	2.19567	+	0.644708i	0.136962	+	0.0402158i	−0.212533	+	0.977154i	$0.568171\pi$
$258$	−5.03041	−	5.80540i	−0.313180	−	0.361429i
$259$	−1.00500	+	0.295096i	−0.0624479	+	0.0183363i
$260$	12.4556	+	8.00470i	0.772461	+	0.496430i
$261$	−2.05940	+	4.50945i	−0.127474	+	0.279128i
$262$	19.3005	−	22.2740i	1.19239	−	1.37609i
$263$	8.78218	−	5.64396i	0.541532	−	0.348022i	−0.241106	−	0.970499i	$-0.577510\pi$
$263$	8.78218	−	5.64396i	0.541532	−	0.348022i	0.782638	+	0.622477i	$0.213874\pi$
$264$	8.32133	+	57.8761i	0.512142	+	3.56203i
$265$	0.242075	+	1.68367i	0.0148706	+	0.103427i
$266$	11.4884	−	7.38314i	0.704398	−	0.452689i
$267$	4.01238	−	4.63053i	0.245554	−	0.283384i
$268$	−20.4597	+	44.8005i	−1.24977	+	2.73662i
$269$	24.9947	+	16.0631i	1.52395	+	0.979384i	0.991092	+	0.133181i	$0.0425192\pi$
$269$	24.9947	+	16.0631i	1.52395	+	0.979384i	0.532860	+	0.846203i	$0.321117\pi$
$270$	10.6562	−	3.12895i	0.648518	−	0.190422i
$271$	−3.64480	−	4.20632i	−0.221406	−	0.255516i	0.634170	−	0.773194i	$-0.281342\pi$
$271$	−3.64480	−	4.20632i	−0.221406	−	0.255516i	−0.855576	+	0.517678i	$0.826797\pi$
$272$	27.8833	+	8.18728i	1.69067	+	0.496427i
$273$	1.77892	+	3.89528i	0.107665	+	0.235753i
$274$	4.83641	−	33.6379i	0.292178	−	2.03214i
$275$	−4.75767			−0.286898
$276$	38.5171	+	15.9896i	2.31846	+	0.962459i
$277$	24.8346			1.49217			0.746085	−	0.665851i	$-0.231931\pi$
$277$	24.8346			1.49217			0.746085	+	0.665851i	$0.231931\pi$
$278$	−4.85669	+	33.7790i	−0.291285	+	2.02593i
$279$	1.73484	+	3.79876i	0.103862	+	0.227426i
$280$	−4.08644	−	1.19989i	−0.244212	−	0.0717070i
$281$	2.96290	+	3.41937i	0.176752	+	0.203983i	0.837212	−	0.546879i	$-0.184184\pi$
$281$	2.96290	+	3.41937i	0.176752	+	0.203983i	−0.660460	+	0.750861i	$0.729639\pi$
$282$	−35.0317	+	10.2862i	−2.08611	+	0.612537i
$283$	−4.40980	−	2.83401i	−0.262135	−	0.168464i	0.402971	−	0.915213i	$-0.367977\pi$
$283$	−4.40980	−	2.83401i	−0.262135	−	0.168464i	−0.665106	+	0.746749i	$0.731614\pi$
$284$	−21.8224	+	47.7843i	−1.29492	+	2.83548i
$285$	−10.1287	+	11.6892i	−0.599975	+	0.692408i
$286$	−33.6158	+	21.6036i	−1.98775	+	1.27745i
$287$	−0.492333	−	3.42425i	−0.0290615	−	0.202127i
$288$	−0.599071	−	4.16663i	−0.0353006	−	0.245521i
$289$	−0.558436	+	0.358885i	−0.0328492	+	0.0211109i
$290$	11.0497	−	12.7520i	0.648860	−	0.748824i
$291$	2.97066	−	6.50485i	0.174143	−	0.381321i
$292$	13.0655	+	8.39670i	0.764602	+	0.491380i
$293$	4.54530	−	1.33462i	0.265539	−	0.0779693i	−0.146253	−	0.989247i	$-0.546721\pi$
$293$	4.54530	−	1.33462i	0.265539	−	0.0779693i	0.411792	+	0.911278i	$0.364903\pi$
$294$	21.1583	+	24.4180i	1.23398	+	1.42409i
$295$	11.2843	+	3.31338i	0.656999	+	0.192912i
$296$	4.11657	+	9.01403i	0.239271	+	0.523930i
$297$	−2.95146	+	20.5279i	−0.171261	+	1.19115i
$298$	−7.62061			−0.441450
$299$	0.551936	+	15.7998i	0.0319193	+	0.913727i
$300$	8.69592			0.502059
$301$	−0.148693	+	1.03418i	−0.00857053	+	0.0596093i
$302$	−9.64713	−	21.1243i	−0.555130	−	1.21557i
$303$	−5.37893	−	1.57940i	−0.309012	−	0.0907340i
$304$	−37.6141	−	43.4090i	−2.15732	−	2.48968i
$305$	−0.574773	+	0.168769i	−0.0329114	+	0.00966366i
$306$	−6.48483	−	4.16755i	−0.370713	−	0.238243i
$307$	−3.56744	+	7.81159i	−0.203604	+	0.445831i	−0.983697	−	0.179832i	$-0.942444\pi$
$307$	−3.56744	+	7.81159i	−0.203604	+	0.445831i	0.780093	+	0.625664i	$0.215172\pi$
$308$	9.38890	−	10.8354i	0.534982	−	0.617402i
$309$	4.66700	−	2.99930i	0.265496	−	0.170624i
$310$	−2.02288	−	14.0694i	−0.114892	−	0.799089i
$311$	−2.77999	−	19.3352i	−0.157639	−	1.09640i	−0.902969	−	0.429705i	$-0.858617\pi$
$311$	−2.77999	−	19.3352i	−0.157639	−	1.09640i	0.745331	−	0.666695i	$-0.232292\pi$
$312$	34.0822	−	21.9033i	1.92953	−	1.24003i
$313$	4.37884	−	5.05345i	0.247507	−	0.285638i	−0.618379	−	0.785880i	$-0.712210\pi$
$313$	4.37884	−	5.05345i	0.247507	−	0.285638i	0.865886	+	0.500242i	$0.166756\pi$
$314$	15.5211	−	33.9865i	0.875908	−	1.91797i
$315$	0.422515	+	0.271534i	0.0238060	+	0.0152992i
$316$	4.61155	−	1.35407i	0.259420	−	0.0761727i
$317$	−19.5529	−	22.5652i	−1.09820	−	1.26739i	−0.960910	−	0.276860i	$-0.910706\pi$
$317$	−19.5529	−	22.5652i	−1.09820	−	1.26739i	−0.137290	−	0.990531i	$-0.543839\pi$
$318$	8.05089	+	2.36395i	0.451471	+	0.132564i
$319$	13.0890	+	28.6610i	0.732846	+	1.60471i
$320$	0.00746423	−	0.0519148i	0.000417263	−	0.00290213i
$321$	−32.1389			−1.79382
$322$	−2.58293	−	7.78074i	−0.143941	−	0.433604i
$323$	−32.2886			−1.79659
$324$	6.83001	−	47.5038i	0.379445	−	2.63910i
$325$	1.36942	+	2.99860i	0.0759615	+	0.166332i
$326$	−15.2640	−	4.48191i	−0.845395	−	0.248230i
$327$	−7.75504	−	8.94979i	−0.428855	−	0.494925i
$328$	−31.4035	+	9.22090i	−1.73397	+	0.509139i
$329$	4.17766	+	2.68482i	0.230322	+	0.148019i
$330$	−9.74942	+	21.3482i	−0.536688	+	1.17518i
$331$	5.83377	−	6.73253i	0.320653	−	0.370053i	−0.572423	−	0.819958i	$-0.693997\pi$
$331$	5.83377	−	6.73253i	0.320653	−	0.370053i	0.893077	+	0.449905i	$0.148542\pi$
$332$	5.68796	−	3.65543i	0.312167	−	0.200618i
$333$	−0.166309	−	1.15670i	−0.00911366	−	0.0633869i
$334$	3.13939	+	21.8350i	0.171780	+	1.19476i
$335$	−9.22488	+	5.92847i	−0.504009	+	0.323907i
$336$	−6.11641	+	7.05871i	−0.333678	+	0.385084i
$337$	−1.70905	+	3.74229i	−0.0930978	+	0.203856i	−0.950452	−	0.310871i	$-0.899379\pi$
$337$	−1.70905	+	3.74229i	−0.0930978	+	0.203856i	0.857354	+	0.514727i	$0.172107\pi$
$338$	−4.57201	−	2.93825i	−0.248684	−	0.159820i
$339$	−13.5115	+	3.96733i	−0.733842	+	0.215476i
$340$	11.8880	+	13.7194i	0.644715	+	0.744041i
$341$	25.4675	+	7.47793i	1.37914	+	0.404952i
$342$	6.32927	+	13.8592i	0.342247	+	0.749417i
$343$	1.29381	−	8.99868i	0.0698594	−	0.485883i
$344$	9.88481			0.532953
$345$	5.28966	+	7.63128i	0.284786	+	0.410854i
$346$	−28.4490			−1.52943
$347$	−3.37614	+	23.4815i	−0.181241	+	1.26056i	0.672594	+	0.740011i	$0.265180\pi$
$347$	−3.37614	+	23.4815i	−0.181241	+	1.26056i	−0.853835	+	0.520544i	$0.825729\pi$
$348$	−23.9237	−	52.3857i	−1.28245	−	2.80817i
$349$	−12.8172	−	3.76347i	−0.686088	−	0.201454i	−0.0799332	−	0.996800i	$-0.525471\pi$
$349$	−12.8172	−	3.76347i	−0.686088	−	0.201454i	−0.606155	+	0.795347i	$0.707289\pi$
$350$	−1.11945	−	1.29192i	−0.0598374	−	0.0690560i
$351$	13.7876	−	4.04839i	0.735925	−	0.216087i
$352$	−22.5072	−	14.4645i	−1.19964	−	0.770962i
$353$	−5.12082	+	11.2130i	−0.272554	+	0.596809i	−0.995570	−	0.0940214i	$-0.970028\pi$
$353$	−5.12082	+	11.2130i	−0.272554	+	0.596809i	0.723016	+	0.690831i	$0.242755\pi$
$354$	37.9914	−	43.8444i	2.01922	−	2.33030i
$355$	−9.83928	+	6.32332i	−0.522215	+	0.335607i
$356$	2.02281	+	14.0689i	0.107208	+	0.745651i
$357$	0.747215	+	5.19700i	0.0395468	+	0.275054i
$358$	41.7351	−	26.8215i	2.20577	−	1.41756i
$359$	−4.62411	+	5.33651i	−0.244051	+	0.281650i	−0.864539	−	0.502566i	$-0.832389\pi$
$359$	−4.62411	+	5.33651i	−0.244051	+	0.281650i	0.620487	+	0.784216i	$0.286935\pi$
$360$	1.97390	−	4.32223i	0.104034	−	0.227802i
$361$	37.7040	+	24.2309i	1.98442	+	1.27531i
$362$	−41.3486	+	12.1410i	−2.17323	+	0.638118i
$363$	−14.7524	−	17.0252i	−0.774303	−	0.893593i
$364$	−9.53160	−	2.79873i	−0.499592	−	0.146693i
$365$	1.43648	+	3.14545i	0.0751887	+	0.164640i
$366$	−0.420539	+	2.92491i	−0.0219819	+	0.152888i
$367$	−11.9140			−0.621905			−0.310953	−	0.950425i	$-0.600648\pi$
$367$	−11.9140			−0.621905			−0.310953	+	0.950425i	$0.600648\pi$
$368$	−30.8466	+	15.4106i	−1.60799	+	0.803334i
$369$	3.85965			0.200925
$370$	−0.566054	+	3.93699i	−0.0294277	+	0.204674i
$371$	−0.474100	−	1.03813i	−0.0246141	−	0.0538973i
$372$	−46.5486	−	13.6679i	−2.41343	−	0.708648i
$373$	19.1418	+	22.0909i	0.991127	+	1.14382i	0.989603	+	0.143823i	$0.0459395\pi$
$373$	19.1418	+	22.0909i	0.991127	+	1.14382i	0.00152365	+	0.999999i	$0.499515\pi$
$374$	−47.0090	+	13.8031i	−2.43078	+	0.713741i
$375$	1.62877	+	1.04675i	0.0841092	+	0.0540537i
$376$	19.5171	−	42.7365i	1.00652	−	2.20397i
$377$	14.2966	−	16.4992i	0.736313	−	0.849751i
$378$	−6.26869	+	4.02864i	−0.322427	+	0.207211i
$379$	−0.538139	−	3.74284i	−0.0276424	−	0.192257i	0.971321	−	0.237771i	$-0.0764166\pi$
$379$	−0.538139	−	3.74284i	−0.0276424	−	0.192257i	−0.998964	+	0.0455137i	$0.985508\pi$
$380$	−5.10632	−	35.5152i	−0.261949	−	1.82189i
$381$	−9.90411	+	6.36498i	−0.507403	+	0.326088i
$382$	17.9853	−	20.7562i	0.920209	−	1.06198i
$383$	5.49204	−	12.0259i	0.280630	−	0.614494i	−0.715857	−	0.698247i	$-0.753964\pi$
$383$	5.49204	−	12.0259i	0.280630	−	0.614494i	0.996486	+	0.0837536i	$0.0266909\pi$
$384$	−18.5362	−	11.9125i	−0.945919	−	0.607905i
$385$	3.06284	−	0.899331i	0.156097	−	0.0458341i
$386$	30.0013	+	34.6233i	1.52703	+	1.76228i
$387$	−1.11846	−	0.328410i	−0.0568546	−	0.0166940i
$388$	6.89135	+	15.0900i	0.349855	+	0.766076i
$389$	−0.979897	+	6.81533i	−0.0496827	+	0.345551i	0.949784	+	0.312905i	$0.101302\pi$
$389$	−0.979897	+	6.81533i	−0.0496827	+	0.345551i	−0.999467	+	0.0326455i	$0.989607\pi$
$390$	16.2613			0.823422
$391$	−4.80841	+	18.7780i	−0.243172	+	0.949642i
$392$	−41.5763			−2.09992
$393$	3.18738	−	22.1687i	0.160782	−	1.11826i
$394$	−6.95729	−	15.2343i	−0.350503	−	0.767495i
$395$	1.02675	+	0.301481i	0.0516613	+	0.0151691i
$396$	10.4750	+	12.0888i	0.526388	+	0.607484i
$397$	12.6596	−	3.71719i	0.635367	−	0.186561i	0.0518414	−	0.998655i	$-0.483491\pi$
$397$	12.6596	−	3.71719i	0.635367	−	0.186561i	0.583526	+	0.812095i	$0.301673\pi$
$398$	50.0063	+	32.1371i	2.50659	+	1.61089i
$399$	4.31099	−	9.43975i	0.215819	−	0.472579i
$400$	−4.70843	+	5.43382i	−0.235422	+	0.271691i
$401$	−22.0751	+	14.1868i	−1.10238	+	0.708456i	−0.959620	−	0.281301i	$-0.909234\pi$
$401$	−22.0751	+	14.1868i	−1.10238	+	0.708456i	−0.142760	+	0.989757i	$0.545598\pi$
$402$	7.69814	+	53.5417i	0.383948	+	2.67042i
$403$	−2.61730	−	18.2037i	−0.130377	−	0.906790i
$404$	10.9404	−	7.03095i	0.544304	−	0.349803i
$405$	6.99741	−	8.07544i	0.347704	−	0.401272i
$406$	−4.70296	+	10.2980i	−0.233404	+	0.511083i
$407$	−6.24826	−	4.01551i	−0.309715	−	0.199042i
$408$	47.6612	−	13.9946i	2.35958	−	0.692836i
$409$	5.14192	+	5.93409i	0.254251	+	0.293422i	0.868498	−	0.495692i	$-0.165086\pi$
$409$	5.14192	+	5.93409i	0.254251	+	0.293422i	−0.614247	+	0.789114i	$0.710540\pi$
$410$	−12.6047	−	3.70107i	−0.622501	−	0.182783i
$411$	−10.7280	−	23.4910i	−0.529171	−	1.15872i
$412$	−1.83152	+	12.7385i	−0.0902325	+	0.627581i
$413$	−7.89082			−0.388282
$414$	9.00255	−	1.61698i	0.442451	−	0.0794702i
$415$	1.50538			0.0738962
$416$	−2.63818	+	18.3489i	−0.129347	+	0.899630i
$417$	10.7730	+	23.5895i	0.527554	+	1.15518i
$418$	92.9138	+	27.2820i	4.54456	+	1.33440i
$419$	14.8785	+	17.1707i	0.726864	+	0.838845i	0.992115	−	0.125334i	$-0.0400003\pi$
$419$	14.8785	+	17.1707i	0.726864	+	0.838845i	−0.265251	+	0.964179i	$0.585455\pi$
$420$	−5.59816	+	1.64377i	−0.273162	+	0.0802076i
$421$	−26.6764	−	17.1439i	−1.30013	−	0.835540i	−0.306900	−	0.951742i	$-0.599292\pi$
$421$	−26.6764	−	17.1439i	−1.30013	−	0.835540i	−0.993226	+	0.116202i	$0.962928\pi$
$422$	−3.47746	+	7.61458i	−0.169280	+	0.370672i
$423$	−3.62822	+	4.18719i	−0.176410	+	0.203588i
$424$	−9.08328	+	5.83747i	−0.441123	+	0.283493i
$425$	0.575209	+	4.00067i	0.0279017	+	0.194061i
$426$	8.21086	+	57.1078i	0.397817	+	2.76688i
$427$	0.338119	−	0.217296i	0.0163627	−	0.0105157i
$428$	48.8237	−	56.3456i	2.35998	−	2.72357i
$429$	−12.6143	+	27.6214i	−0.609022	+	1.33357i
$430$	3.33771	+	2.14502i	0.160959	+	0.103442i
$431$	−18.9004	+	5.54965i	−0.910399	+	0.267317i	−0.703209	−	0.710983i	$-0.748250\pi$
$431$	−18.9004	+	5.54965i	−0.910399	+	0.267317i	−0.207190	+	0.978301i	$0.566432\pi$
$432$	20.5243	+	23.6863i	0.987477	+	1.13961i
$433$	−17.6924	−	5.19495i	−0.850242	−	0.249653i	−0.172551	−	0.985001i	$-0.555201\pi$
$433$	−17.6924	−	5.19495i	−0.850242	−	0.249653i	−0.677691	+	0.735347i	$0.737019\pi$
$434$	3.96177	+	8.67507i	0.190171	+	0.416417i
$435$	1.82479	−	12.6917i	0.0874922	−	0.608521i
$436$	27.4717			1.31566
$437$	28.0610	−	26.0848i	1.34234	−	1.24780i
$438$	17.0576			0.815045
$439$	−1.89506	+	13.1804i	−0.0904462	+	0.629067i	0.893294	+	0.449472i	$0.148388\pi$
$439$	−1.89506	+	13.1804i	−0.0904462	+	0.629067i	−0.983741	+	0.179595i	$0.942521\pi$
$440$	−12.5456	−	27.4711i	−0.598089	−	1.30963i
$441$	4.70434	+	1.38132i	0.224016	+	0.0657771i
$442$	22.2304	+	25.6552i	1.05739	+	1.22029i
$443$	−24.9201	+	7.31722i	−1.18399	+	0.347651i	−0.813712	−	0.581269i	$-0.802557\pi$
$443$	−24.9201	+	7.31722i	−1.18399	+	0.347651i	−0.370280	+	0.928920i	$0.620738\pi$
$444$	11.4204	+	7.33942i	0.541987	+	0.348314i
$445$	−1.31463	+	2.87863i	−0.0623194	+	0.136460i
$446$	−14.5629	+	16.8065i	−0.689573	+	0.795809i
$447$	−4.87168	+	3.13084i	−0.230423	+	0.148084i
$448$	0.00500810	+	0.0348321i	0.000236610	+	0.00164566i
$449$	−4.82620	−	33.5669i	−0.227762	−	1.58412i	−0.707502	−	0.706711i	$-0.750178\pi$
$449$	−4.82620	−	33.5669i	−0.227762	−	1.58412i	0.479740	−	0.877411i	$-0.340731\pi$
$450$	1.60444	−	1.03111i	0.0756340	−	0.0486070i
$451$	16.0644	−	18.5393i	0.756442	−	0.872981i
$452$	13.5704	−	29.7151i	0.638300	−	1.39768i
$453$	−14.8459	−	9.54086i	−0.697520	−	0.448269i
$454$	−57.7472	+	16.9561i	−2.71021	+	0.795790i
$455$	−1.44840	−	1.67155i	−0.0679022	−	0.0783634i
$456$	−94.2029	−	27.6605i	−4.41145	−	1.29532i
$457$	−13.1430	−	28.7791i	−0.614802	−	1.34623i	−0.919241	−	0.393696i	$-0.871196\pi$
$457$	−13.1430	−	28.7791i	−0.614802	−	1.34623i	0.304439	−	0.952532i	$-0.401531\pi$
$458$	−7.64948	+	53.2033i	−0.357437	+	2.48603i
$459$	17.6185			0.822359
$460$	−21.4148	−	2.31926i	−0.998472	−	0.108136i
$461$	12.3450			0.574964			0.287482	−	0.957786i	$-0.407182\pi$
$461$	12.3450			0.574964			0.287482	+	0.957786i	$0.407182\pi$
$462$	2.24096	−	15.5862i	0.104259	−	0.725137i
$463$	5.74917	+	12.5889i	0.267187	+	0.585057i	0.994905	−	0.100819i	$-0.0321464\pi$
$463$	5.74917	+	12.5889i	0.267187	+	0.585057i	−0.727718	+	0.685876i	$0.759419\pi$
$464$	45.6878	+	13.4152i	2.12100	+	0.622783i
$465$	−7.07344	−	8.16319i	−0.328023	−	0.378559i
$466$	−13.1714	+	3.86747i	−0.610153	+	0.179157i
$467$	−8.14946	−	5.23734i	−0.377112	−	0.242355i	0.338330	−	0.941028i	$-0.390138\pi$
$467$	−8.14946	−	5.23734i	−0.377112	−	0.242355i	−0.715442	+	0.698673i	$0.753774\pi$
$468$	4.60410	−	10.0816i	0.212825	−	0.466021i
$469$	4.81804	−	5.56032i	0.222477	−	0.256752i
$470$	15.8641	−	10.1952i	0.731755	−	0.470270i
$471$	−4.04068	−	28.1035i	−0.186185	−	1.29494i
$472$	10.6243	+	73.8936i	0.489023	+	3.40123i
$473$	−6.23267	+	4.00549i	−0.286578	+	0.184173i
$474$	3.45679	−	3.98935i	0.158776	−	0.183237i
$475$	3.31861	−	7.26675i	0.152268	−	0.333421i
$476$	−10.2464	−	6.58499i	−0.469645	−	0.301823i
$477$	1.22171	−	0.358727i	0.0559383	−	0.0164250i
$478$	−20.4669	−	23.6200i	−0.936132	−	1.08035i
$479$	−32.1827	−	9.44969i	−1.47046	−	0.431767i	−0.554215	−	0.832374i	$-0.686981\pi$
$479$	−32.1827	−	9.44969i	−1.47046	−	0.431767i	−0.916250	+	0.400606i	$0.868800\pi$
$480$	4.52288	+	9.90373i	0.206440	+	0.452041i
$481$	−0.732387	+	5.09387i	−0.0333940	+	0.232260i
$482$	27.5042			1.25278
$483$	−4.84784	−	3.91288i	−0.220584	−	0.178042i
$484$	52.2596			2.37544
$485$	−0.525641	+	3.65591i	−0.0238681	+	0.166007i
$486$	−8.05544	−	17.6390i	−0.365402	−	0.800119i
$487$	−3.73085	−	1.09548i	−0.169061	−	0.0496408i	0.196107	−	0.980583i	$-0.437170\pi$
$487$	−3.73085	−	1.09548i	−0.169061	−	0.0496408i	−0.365168	+	0.930942i	$0.618988\pi$
$488$	−2.49011	−	2.87374i	−0.112722	−	0.130088i
$489$	−11.5993	+	3.40585i	−0.524537	+	0.154018i
$490$	−14.0387	−	9.02212i	−0.634203	−	0.407578i
$491$	3.44647	−	7.54673i	0.155537	−	0.340579i	−0.815782	−	0.578360i	$-0.803693\pi$
$491$	3.44647	−	7.54673i	0.155537	−	0.340579i	0.971319	+	0.237781i	$0.0764201\pi$
$492$	−29.3619	+	33.8855i	−1.32374	+	1.52768i
$493$	22.5182	−	14.4716i	1.01417	−	0.651767i
$494$	−9.54877	−	66.4131i	−0.429619	−	2.98807i
$495$	0.506841	+	3.52516i	0.0227808	+	0.158444i
$496$	33.7446	−	21.6863i	1.51518	−	0.973744i
$497$	5.13894	−	5.93065i	0.230513	−	0.266026i
$498$	3.08483	−	6.75482i	0.138234	−	0.302691i
$499$	4.04184	+	2.59753i	0.180938	+	0.116282i	0.627974	−	0.778234i	$-0.283884\pi$
$499$	4.04184	+	2.59753i	0.180938	+	0.116282i	−0.447037	+	0.894516i	$0.647521\pi$
$500$	−4.30948	+	1.26538i	−0.192726	+	0.0565894i
$501$	10.9776	+	12.6688i	0.490443	+	0.566001i
$502$	−6.74392	−	1.98019i	−0.300996	−	0.0883804i
$503$	6.34858	+	13.9015i	0.283069	+	0.619835i	0.996743	−	0.0806430i	$-0.0256974\pi$
$503$	6.34858	+	13.9015i	0.283069	+	0.619835i	−0.713674	+	0.700478i	$0.752970\pi$
$504$	−0.453712	+	3.15564i	−0.0202100	+	0.140563i
$505$	2.89549			0.128848
$506$	29.7029	−	49.9726i	1.32046	−	2.22155i
$507$	−4.12993			−0.183417
$508$	3.88678	−	27.0331i	0.172448	−	1.19940i
$509$	7.40816	+	16.2216i	0.328361	+	0.719010i	0.999756	−	0.0220893i	$-0.00703182\pi$
$509$	7.40816	+	16.2216i	0.328361	+	0.719010i	−0.671395	+	0.741100i	$0.734305\pi$
$510$	19.1302	+	5.61713i	0.847099	+	0.248731i
$511$	−1.51934	−	1.75341i	−0.0672114	−	0.0775661i
$512$	48.7875	−	14.3253i	2.15612	−	0.633095i
$513$	−29.2950	−	18.8268i	−1.29341	−	0.831222i
$514$	−2.42202	+	5.30348i	−0.106831	+	0.233927i
$515$	−1.87641	+	2.16549i	−0.0826844	+	0.0954229i
$516$	11.3919	−	7.32111i	0.501499	−	0.322294i
$517$	5.01144	+	34.8553i	0.220403	+	1.53294i
$518$	−0.379792	−	2.64151i	−0.0166871	−	0.116061i
$519$	−18.1868	+	11.6880i	−0.798313	+	0.513045i
$520$	−13.7031	+	15.8142i	−0.600919	+	0.693497i
$521$	13.1431	−	28.7794i	0.575811	−	1.26085i	−0.367834	−	0.929891i	$-0.619901\pi$
$521$	13.1431	−	28.7794i	0.575811	−	1.26085i	0.943645	−	0.330959i	$-0.107372\pi$
$522$	−10.6256	−	6.82868i	−0.465071	−	0.298883i
$523$	39.4786	−	11.5920i	1.72628	−	0.506881i	0.740091	−	0.672507i	$-0.234783\pi$
$523$	39.4786	−	11.5920i	1.72628	−	0.506881i	0.986189	+	0.165626i	$0.0529645\pi$
$524$	34.0238	+	39.2656i	1.48634	+	1.71532i
$525$	−1.24641	−	0.365980i	−0.0543979	−	0.0159727i
$526$	11.0491	+	24.1942i	0.481764	+	1.05492i
$527$	3.20904	−	22.3194i	0.139788	−	0.972247i
$528$	−66.2299			−2.88229
$529$	−10.9912	−	20.2038i	−0.477877	−	0.878427i
$530$	−4.33381			−0.188249
$531$	1.25289	−	8.71401i	0.0543706	−	0.378156i
$532$	10.0006	+	21.8983i	0.433583	+	0.949414i
$533$	−16.3085	−	4.78862i	−0.706401	−	0.207418i
$534$	10.2228	+	11.7978i	0.442386	+	0.510540i
$535$	15.9272	−	4.67666i	0.688595	−	0.202190i
$536$	−58.5567	−	37.6321i	−2.52926	−	1.62546i
$537$	15.6610	−	34.2928i	0.675821	−	1.47984i
$538$	−49.5723	+	57.2095i	−2.13721	+	2.46648i
$539$	26.2151	−	16.8474i	1.12916	−	0.725670i
$540$	2.78629	+	19.3791i	0.119903	+	0.833942i
$541$	3.96747	+	27.5944i	0.170575	+	1.18637i	0.877674	+	0.479259i	$0.159095\pi$
$541$	3.96747	+	27.5944i	0.170575	+	1.18637i	−0.707099	+	0.707115i	$0.749996\pi$
$542$	11.9295	−	7.66661i	0.512415	−	0.329309i
$543$	−21.4452	+	24.7491i	−0.920302	+	1.06208i
$544$	−9.44188	+	20.6748i	−0.404817	+	0.886426i
$545$	5.14552	+	3.30683i	0.220410	+	0.141649i
$546$	−10.4685	+	3.07383i	−0.448011	+	0.131548i
$547$	−7.07852	−	8.16904i	−0.302655	−	0.349283i	0.583967	−	0.811778i	$-0.301500\pi$
$547$	−7.07852	−	8.16904i	−0.302655	−	0.349283i	−0.886622	+	0.462495i	$0.846954\pi$
$548$	57.4815	+	16.8781i	2.45549	+	0.720996i
$549$	0.186279	+	0.407894i	0.00795019	+	0.0174085i
$550$	1.72510	−	11.9983i	0.0735585	−	0.511611i
$551$	−52.9061			−2.25388
$552$	−30.1150	+	50.6659i	−1.28178	+	2.15649i
$553$	−0.717977			−0.0305315
$554$	−9.00488	+	62.6303i	−0.382581	+	2.66091i
$555$	1.25560	+	2.74939i	0.0532974	+	0.116705i
$556$	−57.7226	−	16.9489i	−2.44798	−	0.718793i
$557$	2.14334	+	2.47354i	0.0908162	+	0.104807i	0.799339	−	0.600881i	$-0.205183\pi$
$557$	2.14334	+	2.47354i	0.0908162	+	0.104807i	−0.708522	+	0.705688i	$0.750638\pi$
$558$	−10.2091	+	2.99767i	−0.432186	+	0.126901i
$559$	4.31850	+	2.77533i	0.182653	+	0.117384i
$560$	2.00400	−	4.38815i	0.0846844	−	0.185433i
$561$	−24.3810	+	28.1371i	−1.02937	+	1.18795i
$562$	−9.69761	+	6.23228i	−0.409069	+	0.262893i
$563$	−1.24556	−	8.66306i	−0.0524941	−	0.365104i	−0.999089	−	0.0426787i	$-0.986411\pi$
$563$	−1.24556	−	8.66306i	−0.0524941	−	0.365104i	0.946595	−	0.322426i	$-0.104498\pi$
$564$	−9.15975	−	63.7074i	−0.385695	−	2.68257i
$565$	6.11865	−	3.93222i	0.257413	−	0.165430i
$566$	8.74602	−	10.0934i	0.367623	−	0.424259i
$567$	−2.97823	+	6.52142i	−0.125074	+	0.273874i
$568$	−62.4567	−	40.1385i	−2.62062	−	1.68417i
$569$	22.3853	−	6.57290i	0.938439	−	0.275550i	0.223473	−	0.974710i	$-0.428261\pi$
$569$	22.3853	−	6.57290i	0.938439	−	0.275550i	0.714966	+	0.699160i	$0.246442\pi$
$570$	−25.8063	−	29.7820i	−1.08091	−	1.24743i
$571$	44.3129	+	13.0114i	1.85444	+	0.544512i	0.999675	+	0.0254912i	$0.00811498\pi$
$571$	44.3129	+	13.0114i	1.85444	+	0.544512i	0.854762	+	0.519021i	$0.173703\pi$
$572$	−29.2626	−	64.0761i	−1.22353	−	2.67916i
$573$	2.97017	−	20.6580i	0.124081	−	0.863001i
$574$	8.81410			0.367894
$575$	−3.73188	−	3.01215i	−0.155630	−	0.125615i
$576$	−0.0392610			−0.00163588
$577$	−4.28570	+	29.8077i	−0.178416	+	1.24091i	0.682013	+	0.731340i	$0.261105\pi$
$577$	−4.28570	+	29.8077i	−0.178416	+	1.24091i	−0.860429	+	0.509571i	$0.829804\pi$
$578$	−0.702584	−	1.53844i	−0.0292236	−	0.0639908i
$579$	33.4038	+	9.80823i	1.38821	+	0.407616i
$580$	19.4789	+	22.4798i	0.808815	+	0.933423i
$581$	−0.969117	+	0.284558i	−0.0402057	+	0.0118055i
$582$	15.3274	+	9.85031i	0.635340	+	0.408308i
$583$	3.36184	−	7.36140i	0.139233	−	0.304878i
$584$	−14.3741	+	16.5886i	−0.594805	+	0.686442i
$585$	2.07590	−	1.33410i	0.0858280	−	0.0551583i
$586$	1.71767	+	11.9467i	0.0709564	+	0.493512i
$587$	−0.977335	−	6.79751i	−0.0403389	−	0.280563i	0.959661	−	0.281160i	$-0.0907192\pi$
$587$	−0.977335	−	6.79751i	−0.0403389	−	0.280563i	−1.00000		0.000596630i	$0.999810\pi$
$588$	−47.9151	+	30.7932i	−1.97599	+	1.26989i
$589$	−29.1859	+	33.6823i	−1.20258	+	1.38786i
$590$	−12.4476	+	27.2565i	−0.512460	+	1.12213i
$591$	−10.7065	−	6.88065i	−0.440406	−	0.283032i
$592$	−10.7698	+	3.16229i	−0.442635	+	0.129969i
$593$	29.9592	+	34.5748i	1.23028	+	1.41982i	0.874346	+	0.485303i	$0.161291\pi$
$593$	29.9592	+	34.5748i	1.23028	+	1.41982i	0.355930	+	0.934512i	$0.384164\pi$
$594$	−50.6989	−	14.8865i	−2.08020	−	0.610802i
$595$	−1.12654	−	2.46677i	−0.0461835	−	0.101128i
$596$	1.91185	−	13.2972i	0.0783123	−	0.544674i
$597$	45.1711			1.84873
$598$	−40.0456	−	4.33699i	−1.63758	−	0.177353i
$599$	−38.2909			−1.56452			−0.782262	−	0.622949i	$-0.785934\pi$
$599$	−38.2909			−1.56452			−0.782262	+	0.622949i	$0.785934\pi$
$600$	−1.74903	+	12.1648i	−0.0714040	+	0.496626i
$601$	12.4541	+	27.2708i	0.508015	+	1.11240i	0.973780	+	0.227490i	$0.0730519\pi$
$601$	12.4541	+	27.2708i	0.508015	+	1.11240i	−0.465765	+	0.884908i	$0.654221\pi$
$602$	−2.55418	−	0.749976i	−0.104101	−	0.0305667i
$603$	5.37539	+	6.20353i	0.218903	+	0.252627i
$604$	39.2800	−	11.5336i	1.59828	−	0.469297i
$605$	9.78836	+	6.29060i	0.397953	+	0.255749i
$606$	5.93343	−	12.9924i	0.241029	−	0.527780i
$607$	−7.18844	+	8.29590i	−0.291770	+	0.336720i	−0.882643	−	0.470044i	$-0.844238\pi$
$607$	−7.18844	+	8.29590i	−0.291770	+	0.336720i	0.590873	+	0.806765i	$0.298783\pi$
$608$	37.7922	−	24.2876i	1.53268	−	0.984991i
$609$	1.22434	+	8.51547i	0.0496127	+	0.345064i
$610$	−0.217207	−	1.51071i	−0.00879446	−	0.0611668i
$611$	20.5257	−	13.1911i	0.830380	−	0.533653i
$612$	8.89886	−	10.2698i	0.359715	−	0.415133i
$613$	−15.4209	+	33.7671i	−0.622846	+	1.36384i	0.290586	+	0.956849i	$0.406150\pi$
$613$	−15.4209	+	33.7671i	−0.622846	+	1.36384i	−0.913431	+	0.406993i	$0.866577\pi$
$614$	−18.4065	−	11.8291i	−0.742825	−	0.477384i
$615$	−9.57843	+	2.81248i	−0.386240	+	0.113410i
$616$	13.2693	+	15.3136i	0.534634	+	0.617001i
$617$	−22.2454	−	6.53183i	−0.895564	−	0.262961i	−0.198611	−	0.980078i	$-0.563643\pi$
$617$	−22.2454	−	6.53183i	−0.895564	−	0.262961i	−0.696953	+	0.717117i	$0.745461\pi$
$618$	5.87168	+	12.8572i	0.236194	+	0.517192i
$619$	−3.19766	+	22.2402i	−0.128525	+	0.893910i	0.818901	+	0.573935i	$0.194584\pi$
$619$	−3.19766	+	22.2402i	−0.128525	+	0.893910i	−0.947426	+	0.319975i	$0.896325\pi$
$620$	25.0572			1.00632
$621$	−15.3116	+	14.2333i	−0.614433	+	0.571162i
$622$	49.7694			1.99557
$623$	0.302175	−	2.10168i	0.0121064	−	0.0842018i
$624$	19.0632	+	41.7425i	0.763137	+	1.67104i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	11.1565	+	12.8753i	0.445904	+	0.514601i
$627$	70.6062	−	20.7319i	2.81974	−	0.827951i
$628$	55.4092	+	35.6093i	2.21107	+	1.42097i
$629$	−2.62117	+	5.73956i	−0.104513	+	0.228851i
$630$	−0.837980	+	0.967080i	−0.0333859	+	0.0385294i
$631$	21.8748	−	14.0581i	0.870820	−	0.559642i	−0.0271831	−	0.999630i	$-0.508654\pi$
$631$	21.8748	−	14.0581i	0.870820	−	0.559642i	0.898004	+	0.439988i	$0.145017\pi$
$632$	0.966692	+	6.72349i	0.0384530	+	0.267446i
$633$	0.905302	+	6.29651i	0.0359825	+	0.250264i
$634$	63.9969	−	41.1283i	2.54164	−	1.63341i
$635$	3.98204	−	4.59551i	0.158022	−	0.182367i
$636$	−6.14466	+	13.4549i	−0.243652	+	0.533522i
$637$	−18.1639	−	11.6733i	−0.719681	−	0.462511i
$638$	−77.0260	+	22.6169i	−3.04949	+	0.895411i
$639$	5.73340	+	6.61670i	0.226810	+	0.261752i
$640$	10.9195	+	3.20625i	0.431631	+	0.126738i
$641$	−9.82873	−	21.5219i	−0.388212	−	0.850065i	−0.998331	−	0.0577551i	$-0.981606\pi$
$641$	−9.82873	−	21.5219i	−0.388212	−	0.850065i	0.610119	−	0.792310i	$-0.291122\pi$
$642$	11.6534	−	81.0509i	0.459921	−	3.19882i
$643$	−47.0284			−1.85462			−0.927309	−	0.374296i	$-0.877885\pi$
$643$	−47.0284			−1.85462			−0.927309	+	0.374296i	$0.877885\pi$
$644$	14.2246	−	2.55493i	0.560528	−	0.100678i
$645$	3.01498			0.118715
$646$	11.7076	−	81.4285i	0.460631	−	3.20376i
$647$	−15.4909	−	33.9203i	−0.609010	−	1.33355i	−0.923249	−	0.384202i	$-0.874477\pi$
$647$	−15.4909	−	33.9203i	−0.609010	−	1.33355i	0.314239	−	0.949344i	$-0.398251\pi$
$648$	65.0797	+	19.1091i	2.55657	+	0.750678i
$649$	−36.6419	−	42.2870i	−1.43832	−	1.65991i
$650$	−8.05869	+	2.36624i	−0.316088	+	0.0928117i
$651$	6.09673	+	3.91813i	0.238950	+	0.153564i
$652$	11.6499	−	25.5097i	0.456245	−	0.999038i
$653$	2.03233	−	2.34543i	0.0795312	−	0.0917839i	−0.714589	−	0.699544i	$-0.753386\pi$
$653$	2.03233	−	2.34543i	0.0795312	−	0.0917839i	0.794121	+	0.607760i	$0.207932\pi$
$654$	25.3823	−	16.3122i	0.992528	−	0.637859i
$655$	1.64627	+	11.4501i	0.0643251	+	0.447391i
$656$	−5.27592	−	36.6948i	−0.205990	−	1.43269i
$657$	2.17756	−	1.39943i	0.0849548	−	0.0545971i
$658$	−8.28561	+	9.56210i	−0.323007	+	0.372770i
$659$	−7.71735	+	16.8986i	−0.300625	+	0.658277i	−0.998309	−	0.0581284i	$-0.981487\pi$
$659$	−7.71735	+	16.8986i	−0.300625	+	0.658277i	0.697684	+	0.716406i	$0.254214\pi$
$660$	−34.8046	−	22.3676i	−1.35477	−	0.870656i
$661$	34.5376	−	10.1412i	1.34336	−	0.394445i	0.470491	−	0.882405i	$-0.344077\pi$
$661$	34.5376	−	10.1412i	1.34336	−	0.394445i	0.872866	+	0.487960i	$0.162259\pi$
$662$	14.8634	+	17.1533i	0.577684	+	0.666683i
$663$	24.7515	+	7.26771i	0.961270	+	0.282254i
$664$	3.96958	+	8.69216i	0.154049	+	0.337321i
$665$	−0.762803	+	5.30541i	−0.0295802	+	0.205735i
$666$	2.97738			0.115371
$667$	−7.87876	+	30.7684i	−0.305067	+	1.19136i
$668$	−38.8874			−1.50460
$669$	−2.40498	+	16.7270i	−0.0929819	+	0.646703i
$670$	−11.6061	−	25.4138i	−0.448382	−	0.981820i
$671$	2.73458	+	0.802945i	0.105567	+	0.0309974i
$672$	−4.78377	−	5.52076i	−0.184538	−	0.212968i
$673$	−21.9527	+	6.44589i	−0.846214	+	0.248471i	−0.675968	−	0.736931i	$-0.736274\pi$
$673$	−21.9527	+	6.44589i	−0.846214	+	0.248471i	−0.170246	+	0.985402i	$0.554456\pi$
$674$	−8.81797	−	5.66697i	−0.339656	−	0.218283i
$675$	−1.81082	+	3.96514i	−0.0696984	+	0.152618i
$676$	6.27397	−	7.24055i	0.241306	−	0.278483i
$677$	13.4418	−	8.63851i	0.516610	−	0.332005i	−0.256220	−	0.966619i	$-0.582477\pi$
$677$	13.4418	−	8.63851i	0.516610	−	0.332005i	0.772830	+	0.634614i	$0.218841\pi$
$678$	−5.10600	−	35.5130i	−0.196095	−	1.36387i
$679$	−0.352677	−	2.45292i	−0.0135345	−	0.0941345i
$680$	−21.5833	+	13.8707i	−0.827682	+	0.531919i
$681$	−29.9503	+	34.5645i	−1.14770	+	1.32451i
$682$	−28.0929	+	61.5148i	−1.07573	+	2.35552i
$683$	24.7182	+	15.8854i	0.945816	+	0.607839i	0.920038	−	0.391829i	$-0.128157\pi$
$683$	24.7182	+	15.8854i	0.945816	+	0.607839i	0.0257777	+	0.999668i	$0.491794\pi$
$684$	−25.7707	+	7.56696i	−0.985368	+	0.289330i
$685$	8.73478	+	10.0805i	0.333739	+	0.385155i
$686$	22.2246	+	6.52572i	0.848538	+	0.249153i
$687$	16.9678	+	37.1544i	0.647364	+	1.41753i
$688$	−1.59342	+	11.0825i	−0.0607486	+	0.422515i
$689$	−5.60729			−0.213621
$690$	−21.1633	+	10.5729i	−0.805671	+	0.402504i
$691$	−38.2850			−1.45643			−0.728215	−	0.685349i	$-0.759650\pi$
$691$	−38.2850			−1.45643			−0.728215	+	0.685349i	$0.759650\pi$
$692$	7.13725	−	49.6407i	0.271318	−	1.88706i
$693$	−0.992640	−	2.17358i	−0.0377073	−	0.0825674i
$694$	−57.9938	−	17.0285i	−2.20141	−	0.646393i
$695$	−8.77142	−	10.1228i	−0.332719	−	0.383978i
$696$	78.0946	−	22.9306i	2.96017	−	0.869184i
$697$	−17.5316	−	11.2669i	−0.664058	−	0.426764i
$698$	14.1385	−	30.9590i	0.535149	−	1.17181i
$699$	−6.83127	+	7.88371i	−0.258383	+	0.298189i
$700$	2.53512	−	1.62922i	0.0958184	−	0.0615788i
$701$	−0.449462	−	3.12608i	−0.0169760	−	0.118070i	0.979571	−	0.201097i	$-0.0644505\pi$
$701$	−0.449462	−	3.12608i	−0.0169760	−	0.118070i	−0.996547	+	0.0830263i	$0.973541\pi$
$702$	5.21033	+	36.2386i	0.196651	+	1.36774i
$703$	10.4915	−	6.74250i	0.395696	−	0.254298i
$704$	−0.163410	+	0.188585i	−0.00615874	+	0.00710756i
$705$	5.95295	−	13.0351i	0.224201	−	0.490932i
$706$	−26.4213	−	16.9799i	−0.994378	−	0.639048i
$707$	−1.86402	+	0.547327i	−0.0701039	+	0.0205844i
$708$	66.9728	+	77.2907i	2.51699	+	2.90476i
$709$	−13.3197	−	3.91103i	−0.500233	−	0.146882i	0.0218756	−	0.999761i	$-0.493036\pi$
$709$	−13.3197	−	3.91103i	−0.500233	−	0.146882i	−0.522109	+	0.852879i	$0.674854\pi$
$710$	−12.3791	−	27.1064i	−0.464578	−	1.01728i
$711$	0.113999	−	0.792878i	0.00427528	−	0.0297352i
$712$	−20.0880			−0.752829
$713$	15.2421	+	21.9895i	0.570822	+	0.823512i
$714$	−13.3772			−0.500629
$715$	2.23202	−	15.5240i	0.0834727	−	0.580566i
$716$	36.3304	+	79.5524i	1.35773	+	2.97301i
$717$	−22.7880	−	6.69117i	−0.851034	−	0.249886i
$718$	−11.7814	−	13.5965i	−0.439679	−	0.507417i
$719$	37.3629	−	10.9707i	1.39340	−	0.409139i	0.502988	−	0.864293i	$-0.332234\pi$
$719$	37.3629	−	10.9707i	1.39340	−	0.409139i	0.890413	+	0.455154i	$0.150416\pi$
$720$	4.52774	+	2.90980i	0.168739	+	0.108442i
$721$	0.798635	−	1.74877i	0.0297427	−	0.0651275i
$722$	−74.7789	+	86.2995i	−2.78298	+	3.21173i
$723$	17.5828	−	11.2998i	0.653912	−	0.420244i
$724$	−10.8114	−	75.1950i	−0.401803	−	2.79460i
$725$	0.942500	+	6.55523i	0.0350036	+	0.243455i
$726$	48.2849	−	31.0309i	1.79202	−	1.15166i
$727$	16.8897	−	19.4917i	0.626404	−	0.722908i	−0.350506	−	0.936560i	$-0.613990\pi$
$727$	16.8897	−	19.4917i	0.626404	−	0.722908i	0.976910	+	0.213652i	$0.0685359\pi$
$728$	5.83228	−	12.7709i	0.216159	−	0.473322i
$729$	14.5708	+	9.36409i	0.539659	+	0.346818i
$730$	−8.45334	+	2.48212i	−0.312872	+	0.0918675i
$731$	4.12170	+	4.75670i	0.152447	+	0.175933i
$732$	−4.99818	−	1.46760i	−0.184738	−	0.0542440i
$733$	−13.0982	−	28.6811i	−0.483794	−	1.05936i	−0.981403	−	0.191960i	$-0.938516\pi$
$733$	−13.0982	−	28.6811i	−0.483794	−	1.05936i	0.497608	−	0.867402i	$-0.334212\pi$
$734$	4.31993	−	30.0458i	0.159452	−	1.10901i
$735$	−12.6813			−0.467755
$736$	−8.49681	−	25.5955i	−0.313196	−	0.943464i
$737$	52.1709			1.92174
$738$	−1.39948	+	9.73361i	−0.0515156	+	0.358299i
$739$	2.83764	+	6.21356i	0.104384	+	0.228569i	0.954616	−	0.297839i	$-0.0962657\pi$
$739$	2.83764	+	6.21356i	0.104384	+	0.228569i	−0.850232	+	0.526408i	$0.823538\pi$
$740$	−6.72764	−	1.97541i	−0.247313	−	0.0726176i
$741$	−33.3894	−	38.5334i	−1.22659	−	1.41556i
$742$	2.78997	−	0.819209i	0.102423	−	0.0300741i
$743$	40.7347	+	26.1786i	1.49441	+	0.960400i	0.995602	+	0.0936883i	$0.0298657\pi$
$743$	40.7347	+	26.1786i	1.49441	+	0.960400i	0.498810	+	0.866712i	$0.333771\pi$
$744$	28.4826	−	62.3682i	1.04422	−	2.28653i
$745$	1.95870	−	2.26047i	0.0717614	−	0.0828170i
$746$	−62.6515	+	40.2637i	−2.29383	+	1.47416i
$747$	−0.160370	−	1.11540i	−0.00586764	−	0.0408103i
$748$	−12.2915	−	85.4889i	−0.449420	−	3.12578i
$749$	−9.36944	+	6.02137i	−0.342352	+	0.220016i
$750$	−3.23036	+	3.72803i	−0.117956	+	0.136129i
$751$	−3.59056	+	7.86222i	−0.131021	+	0.286896i	−0.963761	−	0.266769i	$-0.914044\pi$
$751$	−3.59056	+	7.86222i	−0.131021	+	0.286896i	0.832739	+	0.553665i	$0.186771\pi$
$752$	44.7685	+	28.7709i	1.63254	+	1.04917i
$753$	−5.12478	+	1.50477i	−0.186757	+	0.0548369i
$754$	36.4253	+	42.0370i	1.32653	+	1.53090i
$755$	8.74557	+	2.56793i	0.318284	+	0.0934566i
$756$	−5.45690	−	11.9489i	−0.198465	−	0.434579i
$757$	−2.22679	+	15.4877i	−0.0809342	+	0.562910i	0.908495	+	0.417895i	$0.137232\pi$
$757$	−2.22679	+	15.4877i	−0.0809342	+	0.562910i	−0.989430	+	0.145015i	$0.953677\pi$
$758$	9.63417			0.349929
$759$	−1.54228	−	44.1495i	−0.0559811	−	1.60253i
$760$	50.7096			1.83943
$761$	2.56345	−	17.8292i	0.0929250	−	0.646307i	−0.889122	−	0.457670i	$-0.848684\pi$
$761$	2.56345	−	17.8292i	0.0929250	−	0.646307i	0.982047	−	0.188637i	$-0.0604069\pi$
$762$	−12.4606	−	27.2850i	−0.451401	−	0.988431i
$763$	−3.93761	−	1.15619i	−0.142551	−	0.0418567i
$764$	31.7053	+	36.5898i	1.14706	+	1.32377i
$765$	2.90298	−	0.852392i	0.104957	−	0.0308183i
$766$	28.3366	+	18.2108i	1.02384	+	0.657984i
$767$	−16.1053	+	35.2657i	−0.581529	+	1.27337i
$768$	36.6300	−	42.2733i	1.32177	−	1.52541i
$769$	−29.1879	+	18.7579i	−1.05254	+	0.676427i	−0.948057	−	0.318100i	$-0.896955\pi$
$769$	−29.1879	+	18.7579i	−1.05254	+	0.676427i	−0.104484	+	0.994527i	$0.533319\pi$
$770$	1.15745	+	8.05024i	0.0417116	+	0.290111i
$771$	0.630534	+	4.38546i	0.0227081	+	0.157938i
$772$	−67.9409	+	43.6630i	−2.44525	+	1.57146i
$773$	10.9943	−	12.6880i	0.395436	−	0.456357i	−0.522762	−	0.852478i	$-0.675099\pi$
$773$	10.9943	−	12.6880i	0.395436	−	0.456357i	0.918198	+	0.396121i	$0.129644\pi$
$774$	1.23376	−	2.70156i	0.0443467	−	0.0971056i
$775$	4.69328	+	3.01619i	0.168588	+	0.108345i
$776$	−22.4955	+	6.60529i	−0.807543	+	0.237116i
$777$	−1.32803	−	1.53262i	−0.0476427	−	0.0549826i
$778$	−16.8322	−	4.94239i	−0.603464	−	0.177193i
$779$	17.1111	+	37.4680i	0.613068	+	1.34243i
$780$	−4.07961	+	28.3743i	−0.146073	+	1.01596i
$781$	55.6456			1.99116
$782$	−45.6125	−	18.9351i	−1.63110	−	0.677116i
$783$	28.8685			1.03168
$784$	6.70205	−	46.6138i	0.239359	−	1.66478i
$785$	6.09191	+	13.3394i	0.217430	+	0.476105i
$786$	54.7513	+	16.0764i	1.95291	+	0.573428i
$787$	−14.1085	−	16.2821i	−0.502913	−	0.580393i	0.446357	−	0.894855i	$-0.352721\pi$
$787$	−14.1085	−	16.2821i	−0.502913	−	0.580393i	−0.949270	+	0.314462i	$0.898176\pi$
$788$	28.3278	−	8.31780i	1.00914	−	0.296309i
$789$	17.0034	+	10.9274i	0.605335	+	0.389025i
$790$	−1.13259	+	2.48004i	−0.0402959	+	0.0882357i
$791$	−3.19570	+	3.68803i	−0.113626	+	0.131131i
$792$	−19.0180	+	12.2221i	−0.675774	+	0.434294i
$793$	−0.281033	−	1.95463i	−0.00997978	−	0.0694109i
$794$	4.78407	+	33.2740i	0.169780	+	1.18085i
$795$	−2.77051	+	1.78050i	−0.0982598	+	0.0631477i
$796$	−68.6216	+	79.1935i	−2.43223	+	2.80694i
$797$	9.08656	−	19.8968i	0.321862	−	0.704780i	−0.677670	−	0.735366i	$-0.737010\pi$
$797$	9.08656	−	19.8968i	0.321862	−	0.704780i	0.999532	+	0.0305862i	$0.00973740\pi$
$798$	22.2429	+	14.2946i	0.787390	+	0.506025i
$799$	28.7035	−	8.42811i	1.01546	−	0.298165i
$800$	−3.68256	−	4.24990i	−0.130198	−	0.150257i
$801$	2.27295	+	0.667398i	0.0803107	+	0.0235813i
$802$	−27.7733	−	60.8151i	−0.980711	−	2.14746i
$803$	2.34132	−	16.2843i	0.0826235	−	0.574659i
$804$	−95.3562			−3.36296
$805$	2.97185	+	1.23370i	0.104744	+	0.0434822i
$806$	46.8568			1.65046
$807$	−8.18659	+	56.9390i	−0.288182	+	2.00435i
$808$	7.63519	+	16.7187i	0.268605	+	0.588163i
$809$	13.8647	+	4.07104i	0.487456	+	0.143130i	0.516220	−	0.856456i	$-0.327339\pi$
$809$	13.8647	+	4.07104i	0.487456	+	0.143130i	−0.0287634	+	0.999586i	$0.509157\pi$
$810$	17.8282	+	20.5748i	0.626418	+	0.722925i
$811$	−37.4909	+	11.0083i	−1.31648	+	0.386554i	−0.863223	−	0.504823i	$-0.831558\pi$
$811$	−37.4909	+	11.0083i	−1.31648	+	0.386554i	−0.453261	+	0.891378i	$0.649739\pi$
$812$	−16.7892	−	10.7897i	−0.589185	−	0.378646i
$813$	4.47651	−	9.80218i	0.156998	−	0.343778i
$814$	12.3923	−	14.3014i	0.434349	−	0.501265i
$815$	5.25271	−	3.37571i	0.183995	−	0.118246i
$816$	8.00728	+	55.6919i	0.280311	+	1.94961i
$817$	−1.77042	−	12.3136i	−0.0619393	−	0.430797i
$818$	−16.8296	+	10.8157i	−0.588432	+	0.378162i
$819$	−1.08422	+	1.25125i	−0.0378857	+	0.0437224i
$820$	9.62024	−	21.0654i	0.335953	−	0.735635i
$821$	−34.0214	−	21.8642i	−1.18735	−	0.763067i	−0.210631	−	0.977566i	$-0.567552\pi$
$821$	−34.0214	−	21.8642i	−1.18735	−	0.763067i	−0.976724	+	0.214499i	$0.931188\pi$
$822$	63.1316	−	18.5371i	2.20197	−	0.646556i
$823$	−29.8160	−	34.4095i	−1.03932	−	1.19944i	−0.979545	−	0.201227i	$-0.935507\pi$
$823$	−29.8160	−	34.4095i	−1.03932	−	1.19944i	−0.0597755	−	0.998212i	$-0.519038\pi$
$824$	−17.4516	−	5.12426i	−0.607956	−	0.178512i
$825$	−3.82656	−	8.37901i	−0.133224	−	0.291720i
$826$	2.86116	−	19.8998i	0.0995524	−	0.692402i
$827$	−0.301411			−0.0104811			−0.00524055	−	0.999986i	$-0.501668\pi$
$827$	−0.301411			−0.0104811			−0.00524055	+	0.999986i	$0.501668\pi$
$828$	0.562919	+	16.1142i	0.0195628	+	0.560008i
$829$	2.34891			0.0815810			0.0407905	−	0.999168i	$-0.487012\pi$
$829$	2.34891			0.0815810			0.0407905	+	0.999168i	$0.487012\pi$
$830$	−0.545841	+	3.79641i	−0.0189464	+	0.131775i
$831$	19.9743	+	43.7377i	0.692902	+	1.51724i
$832$	0.165894	+	0.0487107i	0.00575132	+	0.00168874i
$833$	−17.3362	−	20.0071i	−0.600664	−	0.693204i
$834$	−63.3964	+	18.6149i	−2.19524	+	0.644580i
$835$	−7.28371	−	4.68096i	−0.252063	−	0.161991i
$836$	−70.9144	+	155.281i	−2.45263	+	5.37050i
$837$	15.9254	−	18.3789i	0.550463	−	0.635268i
$838$	−48.6976	+	31.2960i	−1.68223	+	1.08110i
$839$	3.18821	+	22.1745i	0.110069	+	0.765548i	0.967849	+	0.251531i	$0.0809340\pi$
$839$	3.18821	+	22.1745i	0.110069	+	0.765548i	−0.857780	+	0.514017i	$0.828157\pi$
$840$	−1.17351	−	8.16193i	−0.0404899	−	0.281613i
$841$	12.5005	−	8.03360i	0.431053	−	0.277021i
$842$	52.9076	−	61.0586i	1.82332	−	2.10422i
$843$	−3.63900	+	7.96831i	−0.125334	+	0.274443i
$844$	−12.4143	−	7.97816i	−0.427316	−	0.274620i
$845$	2.04669	−	0.600962i	0.0704083	−	0.0206737i
$846$	−9.24407	−	10.6682i	−0.317818	−	0.366781i
$847$	−7.49053	−	2.19942i	−0.257378	−	0.0755729i
$848$	−5.08054	−	11.1248i	−0.174466	−	0.382028i
$849$	1.44436	−	10.0457i	0.0495702	−	0.344768i
$850$	−10.2978			−0.353212
$851$	−2.35881	−	7.10560i	−0.0808589	−	0.243577i
$852$	−101.707			−3.48443
$853$	0.981765	−	6.82833i	0.0336150	−	0.233797i	−0.966087	−	0.258218i	$-0.916865\pi$
$853$	0.981765	−	6.82833i	0.0336150	−	0.233797i	0.999702	+	0.0244202i	$0.00777395\pi$
$854$	0.425397	+	0.931489i	0.0145568	+	0.0318749i
$855$	−5.73777	−	1.68476i	−0.196228	−	0.0576176i
$856$	69.0023	+	79.6329i	2.35845	+	2.72180i
$857$	−3.78816	+	1.11230i	−0.129401	+	0.0379956i	−0.345792	−	0.938311i	$-0.612390\pi$
$857$	−3.78816	+	1.11230i	−0.129401	+	0.0379956i	0.216391	+	0.976307i	$0.430571\pi$
$858$	−65.0843	−	41.8271i	−2.22194	−	1.42796i
$859$	9.74624	−	21.3413i	0.332538	−	0.728156i	−0.667324	−	0.744767i	$-0.732561\pi$
$859$	9.74624	−	21.3413i	0.332538	−	0.728156i	0.999862	+	0.0166114i	$0.00528782\pi$
$860$	−4.58020	+	5.28584i	−0.156184	+	0.180245i
$861$	5.63466	−	3.62117i	0.192029	−	0.123409i
$862$	−7.14247	−	49.6770i	−0.243274	−	1.69200i
$863$	3.09834	+	21.5494i	0.105469	+	0.733551i	0.972094	+	0.234592i	$0.0753753\pi$
$863$	3.09834	+	21.5494i	0.105469	+	0.733551i	−0.866625	+	0.498959i	$0.833716\pi$
$864$	−20.6215	+	13.2526i	−0.701558	+	0.450864i
$865$	7.31218	−	8.43870i	0.248622	−	0.286925i
$866$	19.5162	−	42.7346i	0.663189	−	1.45218i
$867$	−1.08120	−	0.694844i	−0.0367194	−	0.0235981i
$868$	−16.1310	+	4.73650i	−0.547523	+	0.160767i
$869$	−3.33400	−	3.84764i	−0.113098	−	0.130522i
$870$	31.3455	+	9.20387i	1.06271	+	0.312040i
$871$	−15.0165	−	32.8816i	−0.508815	−	1.11415i
$872$	−5.52546	+	38.4304i	−0.187116	+	1.30142i
$873$	2.76481			0.0935748
$874$	55.6083	+	80.2249i	1.88098	+	2.71365i
$875$	0.670947			0.0226821
$876$	−4.27939	+	29.7638i	−0.144587	+	1.00563i
$877$	−20.9962	−	45.9754i	−0.708993	−	1.55248i	−0.828715	−	0.559671i	$-0.810928\pi$
$877$	−20.9962	−	45.9754i	−0.708993	−	1.55248i	0.119722	−	0.992807i	$-0.461800\pi$
$878$	−32.5525	−	9.55826i	−1.09859	−	0.322576i
$879$	6.00622	+	6.93155i	0.202585	+	0.233795i
$880$	32.8219	−	9.63738i	1.10643	−	0.324876i
$881$	25.4163	+	16.3341i	0.856296	+	0.550308i	0.893533	−	0.448998i	$-0.148219\pi$
$881$	25.4163	+	16.3341i	0.856296	+	0.550308i	−0.0372364	+	0.999306i	$0.511855\pi$
$882$	−5.18930	+	11.3630i	−0.174733	+	0.382612i
$883$	12.6237	−	14.5685i	0.424820	−	0.490268i	−0.502479	−	0.864589i	$-0.667579\pi$
$883$	12.6237	−	14.5685i	0.424820	−	0.490268i	0.927299	+	0.374321i	$0.122124\pi$
$884$	−50.3429	+	32.3534i	−1.69322	+	1.08816i
$885$	3.24053	+	22.5384i	0.108929	+	0.757620i
$886$	−9.41735	−	65.4991i	−0.316382	−	2.20049i
$887$	1.81594	−	1.16703i	0.0609731	−	0.0391851i	−0.509799	−	0.860293i	$-0.670280\pi$
$887$	1.81594	−	1.16703i	0.0609731	−	0.0391851i	0.570772	+	0.821108i	$0.306644\pi$
$888$	−12.5642	+	14.4999i	−0.421627	+	0.486583i
$889$	−1.69483	+	3.71116i	−0.0568428	+	0.124468i
$890$	−6.78293	−	4.35913i	−0.227364	−	0.146118i
$891$	−48.7781	+	14.3225i	−1.63413	+	0.479823i
$892$	−25.6721	−	29.6271i	−0.859565	−	0.991990i
$893$	−56.7328	−	16.6582i	−1.89849	−	0.557447i
$894$	−6.12920	−	13.4211i	−0.204991	−	0.448868i
$895$	−2.77112	+	19.2735i	−0.0926282	+	0.644243i
$896$	−7.63569			−0.255091
$897$	−27.3820	+	13.6797i	−0.914259	+	0.456753i
$898$	86.4021			2.88328
$899$	5.25813	−	36.5711i	0.175368	−	1.21971i
$900$	1.39667	+	3.05827i	0.0465555	+	0.101942i
$901$	−6.59656	−	1.93692i	−0.219763	−	0.0645283i
$902$	40.9292	+	47.2348i	1.36279	+	1.57275i
$903$	−1.94095	+	0.569915i	−0.0645908	+	0.0189656i
$904$	38.8393	+	24.9605i	1.29178	+	0.830173i
$905$	7.02637	−	15.3856i	0.233564	−	0.511435i
$906$	29.4440	−	33.9802i	0.978212	−	1.12892i
$907$	0.121158	−	0.0778637i	0.00402300	−	0.00258542i	−0.538628	−	0.842544i	$-0.681057\pi$
$907$	0.121158	−	0.0778637i	0.00402300	−	0.00258542i	0.542651	+	0.839958i	$0.317421\pi$
$908$	−15.0992	−	105.017i	−0.501084	−	3.48511i
$909$	−0.308460	−	2.14539i	−0.0102310	−	0.0711580i
$910$	4.74065	−	3.04663i	0.157151	−	0.100995i
$911$	1.02577	−	1.18380i	0.0339853	−	0.0392211i	−0.738502	−	0.674251i	$-0.764467\pi$
$911$	1.02577	−	1.18380i	0.0339853	−	0.0392211i	0.772488	+	0.635030i	$0.219012\pi$
$912$	46.1973	−	101.158i	1.52974	−	3.34967i
$913$	−6.02515	−	3.87213i	−0.199403	−	0.128149i
$914$	77.3433	−	22.7100i	2.55829	−	0.751181i
$915$	−0.759514	−	0.876526i	−0.0251088	−	0.0289770i
$916$	−90.9153	−	26.6952i	−3.00393	−	0.882033i
$917$	−3.22419	−	7.06000i	−0.106472	−	0.233142i
$918$	−6.38834	+	44.4319i	−0.210846	+	1.46647i
$919$	−19.0323			−0.627818			−0.313909	−	0.949453i	$-0.601639\pi$
$919$	−19.0323			−0.627818			−0.313909	+	0.949453i	$0.601639\pi$
$920$	7.55165	−	29.4909i	0.248971	−	0.972287i
$921$	−16.6267			−0.547869
$922$	−4.47621	+	31.1327i	−0.147416	+	1.02530i
$923$	−16.0166	−	35.0715i	−0.527194	−	1.15439i
$924$	26.6342	+	7.82051i	0.876201	+	0.257276i
$925$	−1.02232	−	1.17982i	−0.0336137	−	0.0387922i
$926$	−33.8325	+	9.93413i	−1.11181	+	0.326456i
$927$	1.80440	+	1.15962i	0.0592642	+	0.0380868i
$928$	−15.4709	+	33.8765i	−0.507856	+	1.11205i
$929$	−1.31028	+	1.51214i	−0.0429888	+	0.0496117i	−0.776837	−	0.629702i	$-0.783177\pi$
$929$	−1.31028	+	1.51214i	−0.0429888	+	0.0496117i	0.733848	+	0.679314i	$0.237722\pi$
$930$	23.1515	−	14.8785i	0.759166	−	0.487887i
$931$	7.44654	+	51.7918i	0.244051	+	1.69741i
$932$	−3.44393	−	23.9530i	−0.112810	−	0.784608i
$933$	31.8164	−	20.4472i	1.04162	−	0.669411i
$934$	16.1629	−	18.6530i	0.528868	−	0.610346i
$935$	7.98826	−	17.4918i	0.261244	−	0.572044i
$936$	13.1772	+	8.46846i	0.430710	+	0.276800i
$937$	−7.04843	+	2.06960i	−0.230262	+	0.0676110i	−0.394828	−	0.918755i	$-0.629196\pi$
$937$	−7.04843	+	2.06960i	−0.230262	+	0.0676110i	0.164566	+	0.986366i	$0.447378\pi$
$938$	12.2755	+	14.1667i	0.400810	+	0.462560i
$939$	12.4218	+	3.64737i	0.405370	+	0.119027i
$940$	13.8097	+	30.2389i	0.450422	+	0.986286i
$941$	0.336626	−	2.34129i	0.0109737	−	0.0763237i	−0.983599	−	0.180371i	$-0.942270\pi$
$941$	0.336626	−	2.34129i	0.0109737	−	0.0763237i	0.994572	+	0.104047i	$0.0331793\pi$
$942$	72.3392			2.35694
$943$	24.3383	−	4.37148i	0.792563	−	0.142355i
$944$	−84.5593			−2.75217
$945$	0.416227	−	2.89493i	0.0135399	−	0.0941719i
$946$	−7.84150	−	17.1705i	−0.254949	−	0.558261i
$947$	−52.4391	−	15.3975i	−1.70404	−	0.500352i	−0.722464	−	0.691409i	$-0.756990\pi$
$947$	−52.4391	−	15.3975i	−1.70404	−	0.500352i	−0.981579	+	0.191057i	$0.938808\pi$
$948$	6.09378	+	7.03260i	0.197917	+	0.228408i
$949$	−10.9373	+	3.21149i	−0.355041	+	0.104249i
$950$	17.1227	+	11.0041i	0.555532	+	0.357019i
$951$	24.0147	−	52.5848i	0.778729	−	1.70518i
$952$	11.2727	−	13.0094i	0.365350	−	0.421637i
$953$	16.1508	−	10.3795i	0.523177	−	0.336225i	−0.252251	−	0.967662i	$-0.581171\pi$
$953$	16.1508	−	10.3795i	0.523177	−	0.336225i	0.775428	+	0.631436i	$0.217534\pi$
$954$	0.461686	+	3.21110i	0.0149476	+	0.103963i
$955$	1.53409	+	10.6698i	0.0496418	+	0.345267i
$956$	46.3492	−	29.7868i	1.49904	−	0.963376i
$957$	−39.9491	+	46.1037i	−1.29137	+	1.49032i
$958$	35.5003	−	77.7349i	1.14696	−	2.51150i
$959$	−7.52866	−	4.83838i	−0.243113	−	0.156239i
$960$	0.0974336	−	0.0286091i	0.00314466	−	0.000923354i
$961$	−0.0813785	−	0.0939158i	−0.00262511	−	0.00302954i
$962$	−12.5806	−	3.69400i	−0.405616	−	0.119099i
$963$	−5.16188	−	11.3029i	−0.166339	−	0.364232i
$964$	−6.90022	+	47.9921i	−0.222241	+	1.54572i
$965$	−17.9813			−0.578839
$966$	11.6257	−	10.8069i	0.374050	−	0.347708i
$967$	16.1740			0.520122			0.260061	−	0.965592i	$-0.416257\pi$
$967$	16.1740			0.520122			0.260061	+	0.965592i	$0.416257\pi$
$968$	−10.5111	+	73.1064i	−0.337840	+	2.34973i
$969$	−25.9695	−	56.8654i	−0.834262	−	1.82678i
$970$	−9.02923	−	2.65122i	−0.289911	−	0.0851256i
$971$	12.2771	+	14.1685i	0.393990	+	0.454688i	0.917739	−	0.397184i	$-0.130013\pi$
$971$	12.2771	+	14.1685i	0.393990	+	0.454688i	−0.523749	+	0.851872i	$0.675467\pi$
$972$	32.7991	−	9.63070i	1.05203	−	0.308905i
$973$	7.56024	+	4.85867i	0.242370	+	0.155762i
$974$	4.11545	−	9.01159i	0.131868	−	0.288750i
$975$	−4.17959	+	4.82351i	−0.133854	+	0.154476i
$976$	3.62334	−	2.32858i	0.115980	−	0.0745359i
$977$	7.78696	+	54.1595i	0.249127	+	1.73272i	0.603281	+	0.797529i	$0.293860\pi$
$977$	7.78696	+	54.1595i	0.249127	+	1.73272i	−0.354154	+	0.935187i	$0.615231\pi$
$978$	−4.38338	−	30.4871i	−0.140165	−	0.974869i
$979$	12.6661	−	8.14000i	0.404810	−	0.260155i
$980$	19.2647	−	22.2326i	0.615388	−	0.710196i
$981$	1.90201	−	4.16481i	0.0607264	−	0.132972i
$982$	17.7824	+	11.4280i	0.567458	+	0.364683i
$983$	−19.8769	+	5.83639i	−0.633975	+	0.186152i	−0.582901	−	0.812543i	$-0.698083\pi$
$983$	−19.8769	+	5.83639i	−0.633975	+	0.186152i	−0.0510740	+	0.998695i	$0.516264\pi$
$984$	−41.4971	−	47.8902i	−1.32288	−	1.52668i
$985$	6.30711	+	1.85193i	0.200961	+	0.0590075i
$986$	28.3308	+	62.0358i	0.902236	+	1.97562i
$987$	−1.36832	+	9.51689i	−0.0435542	+	0.302926i
$988$	118.280			3.76298
$989$	−7.42479	−	0.804115i	−0.236095	−	0.0255694i
$990$	−9.07384			−0.288386
$991$	4.81231	−	33.4704i	0.152868	−	1.06322i	−0.758513	−	0.651658i	$-0.774074\pi$
$991$	4.81231	−	33.4704i	0.152868	−	1.06322i	0.911381	−	0.411564i	$-0.135017\pi$
$992$	13.0326	+	28.5375i	0.413787	+	0.906067i
$993$	16.5491	+	4.85926i	0.525170	+	0.154204i
$994$	13.0931	+	15.1103i	0.415288	+	0.479268i
$995$	−22.3857	+	6.57303i	−0.709674	+	0.208379i
$996$	11.0126	+	7.07735i	0.348947	+	0.224254i
$997$	−8.82892	+	19.3326i	−0.279615	+	0.612270i	−0.996377	−	0.0850470i	$-0.972896\pi$
$997$	−8.82892	+	19.3326i	−0.279615	+	0.612270i	0.716762	+	0.697317i	$0.245623\pi$
$998$	−8.01625	+	9.25124i	−0.253750	+	0.292843i
$999$	−5.72476	+	3.67908i	−0.181123	+	0.116401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.c.31.1	yes	50
5.2	odd	4		575.2.p.d.399.2		100
5.3	odd	4		575.2.p.d.399.9		100
5.4	even	2		575.2.k.d.376.5		50
23.3	even	11	inner	115.2.g.c.26.1	✓	50
23.7	odd	22		2645.2.a.x.1.23		25
23.16	even	11		2645.2.a.y.1.23		25
115.3	odd	44		575.2.p.d.49.2		100
115.49	even	22		575.2.k.d.26.5		50
115.72	odd	44		575.2.p.d.49.9		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.26.1	✓	50	23.3	even	11	inner
115.2.g.c.31.1	yes	50	1.1	even	1	trivial
575.2.k.d.26.5		50	115.49	even	22
575.2.k.d.376.5		50	5.4	even	2
575.2.p.d.49.2		100	115.3	odd	44
575.2.p.d.49.9		100	115.72	odd	44
575.2.p.d.399.2		100	5.2	odd	4
575.2.p.d.399.9		100	5.3	odd	4
2645.2.a.x.1.23		25	23.7	odd	22
2645.2.a.y.1.23		25	23.16	even	11

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.362593 + 2.52189i) q^{2} +(0.804293 + 1.76116i) q^{3} +(-4.30948 - 1.26538i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(-4.73308 + 1.38976i) q^{6} +(0.564436 + 0.362741i) q^{7} +(2.63693 - 5.77406i) q^{8} +(-0.490203 + 0.565724i) q^{9} +O(q^{10})\)	\(q+(-0.362593 + 2.52189i) q^{2} +(0.804293 + 1.76116i) q^{3} +(-4.30948 - 1.26538i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(-4.73308 + 1.38976i) q^{6} +(0.564436 + 0.362741i) q^{7} +(2.63693 - 5.77406i) q^{8} +(-0.490203 + 0.565724i) q^{9} +(2.14337 - 1.37746i) q^{10} +(0.677087 + 4.70925i) q^{11} +(-1.23756 - 8.60741i) q^{12} +(2.77319 - 1.78222i) q^{13} +(-1.11945 + 1.29192i) q^{14} +(0.804293 - 1.76116i) q^{15} +(6.04859 + 3.88719i) q^{16} +(3.87808 - 1.13871i) q^{17} +(-1.24895 - 1.44137i) q^{18} +(-7.66507 - 2.25067i) q^{19} +(1.86580 + 4.08553i) q^{20} +(-0.184872 + 1.28581i) q^{21} -12.1217 q^{22} +(-2.45039 + 4.12257i) q^{23} +12.2899 q^{24} +(-0.142315 + 0.989821i) q^{25} +(3.48903 + 7.63991i) q^{26} +(4.18248 + 1.22809i) q^{27} +(-1.97342 - 2.27745i) q^{28} +(6.35438 - 1.86581i) q^{29} +(4.14982 + 2.66692i) q^{30} +(2.31756 - 5.07476i) q^{31} +(-3.68256 + 4.24990i) q^{32} +(-7.74914 + 4.98007i) q^{33} +(1.46553 + 10.1930i) q^{34} +(-0.0954857 - 0.664117i) q^{35} +(2.82838 - 1.81769i) q^{36} +(-1.02232 + 1.17982i) q^{37} +(8.45525 - 18.5144i) q^{38} +(5.36923 + 3.45060i) q^{39} +(-6.09056 + 1.78835i) q^{40} +(-3.37652 - 3.89671i) q^{41} +(-3.17564 - 0.932453i) q^{42} +(0.646896 + 1.41651i) q^{43} +(3.04108 - 21.1512i) q^{44} +0.748561 q^{45} +(-9.50818 - 7.67444i) q^{46} +7.40147 q^{47} +(-1.98112 + 13.7790i) q^{48} +(-2.72090 - 5.95794i) q^{49} +(-2.44462 - 0.717805i) q^{50} +(5.12456 + 5.91406i) q^{51} +(-14.2062 + 4.17132i) q^{52} +(-1.43096 - 0.919621i) q^{53} +(-4.61365 + 10.1025i) q^{54} +(3.11561 - 3.59561i) q^{55} +(3.58287 - 2.30257i) q^{56} +(-2.20119 - 15.3096i) q^{57} +(2.40133 + 16.7016i) q^{58} +(-9.89375 + 6.35833i) q^{59} +(-5.69461 + 6.57194i) q^{60} +(0.248849 - 0.544904i) q^{61} +(11.9577 + 7.68472i) q^{62} +(-0.481900 + 0.141499i) q^{63} +(0.0343466 + 0.0396381i) q^{64} +(-3.16297 - 0.928731i) q^{65} +(-9.74942 - 21.3482i) q^{66} +(1.56057 - 10.8540i) q^{67} -18.1534 q^{68} +(-9.23133 - 0.999764i) q^{69} +1.70945 q^{70} +(1.66451 - 11.5769i) q^{71} +(1.97390 + 4.32223i) q^{72} +(-3.31786 - 0.974213i) q^{73} +(-2.60469 - 3.00597i) q^{74} +(-1.85769 + 0.545468i) q^{75} +(30.1845 + 19.3984i) q^{76} +(-1.32606 + 2.90368i) q^{77} +(-10.6489 + 12.2895i) q^{78} +(-0.900221 + 0.578537i) q^{79} +(-1.02324 - 7.11679i) q^{80} +(1.52068 + 10.5766i) q^{81} +(11.0514 - 7.10230i) q^{82} +(-0.985815 + 1.13769i) q^{83} +(2.42374 - 5.30724i) q^{84} +(-3.40018 - 2.18516i) q^{85} +(-3.80684 + 1.11779i) q^{86} +(8.39678 + 9.69040i) q^{87} +(28.9769 + 8.50839i) q^{88} +(-1.31463 - 2.87863i) q^{89} +(-0.271423 + 1.88779i) q^{90} +2.21177 q^{91} +(15.7765 - 14.6655i) q^{92} +10.8014 q^{93} +(-2.68372 + 18.6657i) q^{94} +(3.31861 + 7.26675i) q^{95} +(-10.4466 - 3.06740i) q^{96} +(-2.41873 - 2.79137i) q^{97} +(16.0119 - 4.70150i) q^{98} +(-2.99605 - 1.92544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Introduction

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