LMFDB - Embedded newform 270.2.k.e.211.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(31,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("270.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.k (of order $9$, degree $6$, 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			211.4
Character	$\chi$	$=$	270.211
Dual form			270.2.k.e.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(1.16797 - 1.27900i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} +(-0.0725903 + 1.73053i) q^{6} +(0.781269 + 4.43080i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.271692 - 2.98767i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(1.16797 - 1.27900i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} +(-0.0725903 + 1.73053i) q^{6} +(0.781269 + 4.43080i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.271692 - 2.98767i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(0.978505 + 0.356147i) q^{11} +(-1.05676 - 1.37232i) q^{12} +(2.22799 + 1.86951i) q^{13} +(-3.44655 - 2.89200i) q^{14} +(0.660088 - 1.60134i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.16530 - 5.48247i) q^{17} +(2.12857 + 2.11405i) q^{18} +(-0.956131 - 1.65607i) q^{19} +(-0.173648 - 0.984808i) q^{20} +(6.57950 + 4.17580i) q^{21} +(-0.978505 + 0.356147i) q^{22} +(0.953104 - 5.40532i) q^{23} +(1.69163 + 0.371991i) q^{24} +(0.766044 - 0.642788i) q^{25} -2.90844 q^{26} +(-4.13857 - 3.14202i) q^{27} +4.49915 q^{28} +(-5.97572 + 5.01422i) q^{29} +(0.523663 + 1.65099i) q^{30} +(-1.09858 + 6.23038i) q^{31} +(0.939693 - 0.342020i) q^{32} +(1.59838 - 0.835541i) q^{33} +(1.09930 + 6.23443i) q^{34} +(2.24958 + 3.89638i) q^{35} +(-2.98946 - 0.251239i) q^{36} +(-1.09572 + 1.89784i) q^{37} +(1.79694 + 0.654032i) q^{38} +(4.99334 - 0.666079i) q^{39} +(0.766044 + 0.642788i) q^{40} +(-6.63474 - 5.56721i) q^{41} +(-7.72434 + 1.03038i) q^{42} +(7.48957 + 2.72598i) q^{43} +(0.520652 - 0.901795i) q^{44} +(-1.27715 - 2.71457i) q^{45} +(2.74435 + 4.75336i) q^{46} +(1.46717 + 8.32074i) q^{47} +(-1.53498 + 0.802399i) q^{48} +(-12.4437 + 4.52915i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(-3.31511 - 10.4518i) q^{51} +(2.22799 - 1.86951i) q^{52} -7.94437 q^{53} +(5.18998 - 0.253295i) q^{54} +1.04130 q^{55} +(-3.44655 + 2.89200i) q^{56} +(-3.23485 - 0.711344i) q^{57} +(1.35458 - 7.68223i) q^{58} +(-0.00700732 + 0.00255046i) q^{59} +(-1.46239 - 0.928130i) q^{60} +(-2.63861 - 14.9643i) q^{61} +(-3.16325 - 5.47890i) q^{62} +(13.0255 - 3.53799i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.73304 + 0.994745i) q^{65} +(-0.687352 + 1.66748i) q^{66} +(-8.46057 - 7.09926i) q^{67} +(-4.84953 - 4.06924i) q^{68} +(-5.80022 - 7.53228i) q^{69} +(-4.22782 - 1.53880i) q^{70} +(-3.83372 + 6.64020i) q^{71} +(2.45155 - 1.72913i) q^{72} +(4.26097 + 7.38021i) q^{73} +(-0.380538 - 2.15814i) q^{74} +(0.0725903 - 1.73053i) q^{75} +(-1.79694 + 0.654032i) q^{76} +(-0.813538 + 4.61381i) q^{77} +(-3.39697 + 3.71990i) q^{78} +(-2.91155 + 2.44308i) q^{79} -1.00000 q^{80} +(-8.85237 + 1.62345i) q^{81} +8.66104 q^{82} +(0.910253 - 0.763793i) q^{83} +(5.25487 - 5.75442i) q^{84} +(1.09930 - 6.23443i) q^{85} +(-7.48957 + 2.72598i) q^{86} +(-0.566259 + 13.4994i) q^{87} +(0.180820 + 1.02548i) q^{88} +(1.75776 + 3.04453i) q^{89} +(2.72325 + 1.25854i) q^{90} +(-6.54276 + 11.3324i) q^{91} +(-5.15770 - 1.87725i) q^{92} +(6.68555 + 8.68199i) q^{93} +(-6.47239 - 5.43098i) q^{94} +(-1.46488 - 1.22918i) q^{95} +(0.660088 - 1.60134i) q^{96} +(-2.30205 - 0.837879i) q^{97} +(6.62118 - 11.4682i) q^{98} +(0.798198 - 3.02021i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 3 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 + 3 * q^7 + 12 * q^8 + 9 * q^9	$ 24 q - 3 q^{3} + 3 q^{7} + 12 q^{8} + 9 q^{9} - 12 q^{10} + 9 q^{13} - 3 q^{14} + 15 q^{17} - 12 q^{18} - 9 q^{19} + 24 q^{21} - 12 q^{23} + 3 q^{24} - 12 q^{26} - 3 q^{27} + 6 q^{28} - 33 q^{29} + 6 q^{30} - 21 q^{31} + 6 q^{33} - 15 q^{34} + 3 q^{35} - 6 q^{36} - 12 q^{37} + 12 q^{38} - 36 q^{39} + 21 q^{41} + 15 q^{42} + 12 q^{43} + 9 q^{44} - 12 q^{45} - 15 q^{46} - 21 q^{47} + 27 q^{49} + 3 q^{51} + 9 q^{52} - 60 q^{53} + 36 q^{54} + 18 q^{55} - 3 q^{56} - 24 q^{57} - 21 q^{58} + 36 q^{59} + 33 q^{61} + 18 q^{62} + 39 q^{63} - 12 q^{64} - 9 q^{66} - 12 q^{67} - 3 q^{68} - 48 q^{69} - 6 q^{70} + 12 q^{71} + 6 q^{74} - 12 q^{76} - 60 q^{77} - 36 q^{78} - 15 q^{79} - 24 q^{80} - 15 q^{81} + 6 q^{82} - 27 q^{83} + 3 q^{84} - 15 q^{85} - 12 q^{86} + 78 q^{87} - 9 q^{88} + 30 q^{89} - 9 q^{90} - 9 q^{91} + 6 q^{92} - 30 q^{93} + 12 q^{94} - 15 q^{95} + 3 q^{97} + 27 q^{98} - 111 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 3 * q^7 + 12 * q^8 + 9 * q^9 - 12 * q^10 + 9 * q^13 - 3 * q^14 + 15 * q^17 - 12 * q^18 - 9 * q^19 + 24 * q^21 - 12 * q^23 + 3 * q^24 - 12 * q^26 - 3 * q^27 + 6 * q^28 - 33 * q^29 + 6 * q^30 - 21 * q^31 + 6 * q^33 - 15 * q^34 + 3 * q^35 - 6 * q^36 - 12 * q^37 + 12 * q^38 - 36 * q^39 + 21 * q^41 + 15 * q^42 + 12 * q^43 + 9 * q^44 - 12 * q^45 - 15 * q^46 - 21 * q^47 + 27 * q^49 + 3 * q^51 + 9 * q^52 - 60 * q^53 + 36 * q^54 + 18 * q^55 - 3 * q^56 - 24 * q^57 - 21 * q^58 + 36 * q^59 + 33 * q^61 + 18 * q^62 + 39 * q^63 - 12 * q^64 - 9 * q^66 - 12 * q^67 - 3 * q^68 - 48 * q^69 - 6 * q^70 + 12 * q^71 + 6 * q^74 - 12 * q^76 - 60 * q^77 - 36 * q^78 - 15 * q^79 - 24 * q^80 - 15 * q^81 + 6 * q^82 - 27 * q^83 + 3 * q^84 - 15 * q^85 - 12 * q^86 + 78 * q^87 - 9 * q^88 + 30 * q^89 - 9 * q^90 - 9 * q^91 + 6 * q^92 - 30 * q^93 + 12 * q^94 - 15 * q^95 + 3 * q^97 + 27 * q^98 - 111 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	1.16797	−	1.27900i	0.674328	−	0.738432i
$3$	1.16797	−	1.27900i	0.674328	−	0.738432i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$6$	−0.0725903	+	1.73053i	−0.0296349	+	0.706486i
$7$	0.781269	+	4.43080i	0.295292	+	1.67468i	0.666013	+	0.745940i	$0.268000\pi$
$7$	0.781269	+	4.43080i	0.295292	+	1.67468i	−0.370721	+	0.928744i	$0.620889\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.271692	−	2.98767i	−0.0905640	−	0.995891i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	0.978505	+	0.356147i	0.295030	+	0.107382i	0.485295	−	0.874351i	$-0.338712\pi$
$11$	0.978505	+	0.356147i	0.295030	+	0.107382i	−0.190264	+	0.981733i	$0.560935\pi$
$12$	−1.05676	−	1.37232i	−0.305059	−	0.396155i
$13$	2.22799	+	1.86951i	0.617935	+	0.518509i	0.897154	−	0.441719i	$-0.145631\pi$
$13$	2.22799	+	1.86951i	0.617935	+	0.518509i	−0.279219	+	0.960227i	$0.590076\pi$
$14$	−3.44655	−	2.89200i	−0.921129	−	0.772919i
$15$	0.660088	−	1.60134i	0.170434	−	0.413464i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.16530	−	5.48247i	0.767699	−	1.32969i	−0.171109	−	0.985252i	$-0.554735\pi$
$17$	3.16530	−	5.48247i	0.767699	−	1.32969i	0.938808	−	0.344441i	$-0.111932\pi$
$18$	2.12857	+	2.11405i	0.501708	+	0.498286i
$19$	−0.956131	−	1.65607i	−0.219351	−	0.379928i	0.735258	−	0.677787i	$-0.237061\pi$
$19$	−0.956131	−	1.65607i	−0.219351	−	0.379928i	−0.954610	+	0.297859i	$0.903727\pi$
$20$	−0.173648	−	0.984808i	−0.0388289	−	0.220210i
$21$	6.57950	+	4.17580i	1.43576	+	0.911233i
$22$	−0.978505	+	0.356147i	−0.208618	+	0.0759307i
$23$	0.953104	−	5.40532i	0.198736	−	1.12709i	−0.708261	−	0.705951i	$-0.750520\pi$
$23$	0.953104	−	5.40532i	0.198736	−	1.12709i	0.906997	−	0.421137i	$-0.138369\pi$
$24$	1.69163	+	0.371991i	0.345303	+	0.0759323i
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$	−2.90844			−0.570392
$27$	−4.13857	−	3.14202i	−0.796467	−	0.604681i
$28$	4.49915			0.850260
$29$	−5.97572	+	5.01422i	−1.10966	+	0.931117i	−0.998037	−	0.0626329i	$-0.980050\pi$
$29$	−5.97572	+	5.01422i	−1.10966	+	0.931117i	−0.111626	+	0.993750i	$0.535606\pi$
$30$	0.523663	+	1.65099i	0.0956074	+	0.301429i
$31$	−1.09858	+	6.23038i	−0.197312	+	1.11901i	0.711777	+	0.702406i	$0.247891\pi$
$31$	−1.09858	+	6.23038i	−0.197312	+	1.11901i	−0.909088	+	0.416604i	$0.863220\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	1.59838	−	0.835541i	0.278242	−	0.145449i
$34$	1.09930	+	6.23443i	0.188528	+	1.06920i
$35$	2.24958	+	3.89638i	0.380248	+	0.658608i
$36$	−2.98946	−	0.251239i	−0.498244	−	0.0418732i
$37$	−1.09572	+	1.89784i	−0.180135	+	0.312002i	−0.941926	−	0.335820i	$-0.890987\pi$
$37$	−1.09572	+	1.89784i	−0.180135	+	0.312002i	0.761792	+	0.647822i	$0.224320\pi$
$38$	1.79694	+	0.654032i	0.291502	+	0.106098i
$39$	4.99334	−	0.666079i	0.799574	−	0.106658i
$40$	0.766044	+	0.642788i	0.121122	+	0.101634i
$41$	−6.63474	−	5.56721i	−1.03617	−	0.869452i	−0.0446003	−	0.999005i	$-0.514201\pi$
$41$	−6.63474	−	5.56721i	−1.03617	−	0.869452i	−0.991573	+	0.129553i	$0.958646\pi$
$42$	−7.72434	+	1.03038i	−1.19189	+	0.158990i
$43$	7.48957	+	2.72598i	1.14215	+	0.415708i	0.842689	−	0.538401i	$-0.180971\pi$
$43$	7.48957	+	2.72598i	1.14215	+	0.415708i	0.299460	+	0.954109i	$0.403194\pi$
$44$	0.520652	−	0.901795i	0.0784912	−	0.135951i
$45$	−1.27715	−	2.71457i	−0.190386	−	0.404664i
$46$	2.74435	+	4.75336i	0.404633	+	0.700845i
$47$	1.46717	+	8.32074i	0.214009	+	1.21370i	0.882618	+	0.470091i	$0.155779\pi$
$47$	1.46717	+	8.32074i	0.214009	+	1.21370i	−0.668609	+	0.743614i	$0.733110\pi$
$48$	−1.53498	+	0.802399i	−0.221555	+	0.115816i
$49$	−12.4437	+	4.52915i	−1.77768	+	0.647022i
$50$	−0.173648	+	0.984808i	−0.0245576	+	0.139273i
$51$	−3.31511	−	10.4518i	−0.464208	−	1.46354i
$52$	2.22799	−	1.86951i	0.308967	−	0.259254i
$53$	−7.94437			−1.09124			−0.545622	−	0.838032i	$-0.683706\pi$
$53$	−7.94437			−1.09124			−0.545622	+	0.838032i	$0.683706\pi$
$54$	5.18998	−	0.253295i	0.706266	−	0.0344690i
$55$	1.04130			0.140409
$56$	−3.44655	+	2.89200i	−0.460565	+	0.386460i
$57$	−3.23485	−	0.711344i	−0.428466	−	0.0942198i
$58$	1.35458	−	7.68223i	0.177866	−	1.00873i
$59$	−0.00700732	+	0.00255046i	−0.000912275	+	0.000332041i	−0.342476	−	0.939526i	$-0.611266\pi$
$59$	−0.00700732	+	0.00255046i	−0.000912275	+	0.000332041i	0.341564	+	0.939859i	$0.389043\pi$
$60$	−1.46239	−	0.928130i	−0.188793	−	0.119821i
$61$	−2.63861	−	14.9643i	−0.337839	−	1.91598i	−0.397179	−	0.917741i	$-0.630011\pi$
$61$	−2.63861	−	14.9643i	−0.337839	−	1.91598i	0.0593401	−	0.998238i	$-0.481100\pi$
$62$	−3.16325	−	5.47890i	−0.401733	−	0.695822i
$63$	13.0255	−	3.53799i	1.64106	−	0.445745i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.73304	+	0.994745i	0.338992	+	0.123383i
$66$	−0.687352	+	1.66748i	−0.0846072	+	0.205252i
$67$	−8.46057	−	7.09926i	−1.03362	−	0.867313i	−0.0423456	−	0.999103i	$-0.513483\pi$
$67$	−8.46057	−	7.09926i	−1.03362	−	0.867313i	−0.991278	+	0.131790i	$0.957927\pi$
$68$	−4.84953	−	4.06924i	−0.588091	−	0.493467i
$69$	−5.80022	−	7.53228i	−0.698265	−	0.906780i
$70$	−4.22782	−	1.53880i	−0.505321	−	0.183922i
$71$	−3.83372	+	6.64020i	−0.454979	+	0.788047i	−0.998687	−	0.0512274i	$-0.983687\pi$
$71$	−3.83372	+	6.64020i	−0.454979	+	0.788047i	0.543708	+	0.839275i	$0.317020\pi$
$72$	2.45155	−	1.72913i	0.288918	−	0.203780i
$73$	4.26097	+	7.38021i	0.498708	+	0.863788i	0.999999	−	0.00149084i	$-0.000474548\pi$
$73$	4.26097	+	7.38021i	0.498708	+	0.863788i	−0.501291	+	0.865279i	$0.667141\pi$
$74$	−0.380538	−	2.15814i	−0.0442367	−	0.250879i
$75$	0.0725903	−	1.73053i	0.00838201	−	0.199824i
$76$	−1.79694	+	0.654032i	−0.206123	+	0.0750226i
$77$	−0.813538	+	4.61381i	−0.0927113	+	0.525792i
$78$	−3.39697	+	3.71990i	−0.384631	+	0.421196i
$79$	−2.91155	+	2.44308i	−0.327575	+	0.274868i	−0.791711	−	0.610896i	$-0.790809\pi$
$79$	−2.91155	+	2.44308i	−0.327575	+	0.274868i	0.464136	+	0.885764i	$0.346365\pi$
$80$	−1.00000			−0.111803
$81$	−8.85237	+	1.62345i	−0.983596	+	0.180384i
$82$	8.66104			0.956452
$83$	0.910253	−	0.763793i	0.0999132	−	0.0838372i	−0.591463	−	0.806332i	$-0.701449\pi$
$83$	0.910253	−	0.763793i	0.0999132	−	0.0838372i	0.691376	+	0.722495i	$0.257005\pi$
$84$	5.25487	−	5.75442i	0.573354	−	0.627859i
$85$	1.09930	−	6.23443i	0.119236	−	0.676219i
$86$	−7.48957	+	2.72598i	−0.807621	+	0.293950i
$87$	−0.566259	+	13.4994i	−0.0607093	+	1.44729i
$88$	0.180820	+	1.02548i	0.0192755	+	0.109317i
$89$	1.75776	+	3.04453i	0.186322	+	0.322720i	0.944021	−	0.329885i	$-0.107010\pi$
$89$	1.75776	+	3.04453i	0.186322	+	0.322720i	−0.757699	+	0.652604i	$0.773676\pi$
$90$	2.72325	+	1.25854i	0.287055	+	0.132662i
$91$	−6.54276	+	11.3324i	−0.685867	+	1.18796i
$92$	−5.15770	−	1.87725i	−0.537727	−	0.195717i
$93$	6.68555	+	8.68199i	0.693260	+	0.900280i
$94$	−6.47239	−	5.43098i	−0.667576	−	0.560162i
$95$	−1.46488	−	1.22918i	−0.150293	−	0.126111i
$96$	0.660088	−	1.60134i	0.0673700	−	0.163436i
$97$	−2.30205	−	0.837879i	−0.233738	−	0.0850738i	0.222496	−	0.974934i	$-0.428580\pi$
$97$	−2.30205	−	0.837879i	−0.233738	−	0.0850738i	−0.456234	+	0.889860i	$0.650802\pi$
$98$	6.62118	−	11.4682i	0.668840	−	1.15847i
$99$	0.798198	−	3.02021i	0.0802219	−	0.303543i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.10705	−	6.27840i	−0.110156	−	0.624724i	−0.989035	−	0.147680i	$-0.952819\pi$
$101$	−1.10705	−	6.27840i	−0.110156	−	0.624724i	0.878879	−	0.477044i	$-0.158292\pi$
$102$	9.25780	+	5.87562i	0.916658	+	0.581773i
$103$	−5.07667	+	1.84776i	−0.500219	+	0.182065i	−0.579792	−	0.814764i	$-0.696866\pi$
$103$	−5.07667	+	1.84776i	−0.500219	+	0.182065i	0.0795735	+	0.996829i	$0.474644\pi$
$104$	−0.505045	+	2.86426i	−0.0495238	+	0.280863i
$105$	7.61091	+	1.67364i	0.742749	+	0.163331i
$106$	6.08574	−	5.10654i	0.591100	−	0.495991i
$107$	6.10435			0.590130			0.295065	−	0.955477i	$-0.404659\pi$
$107$	6.10435			0.590130			0.295065	+	0.955477i	$0.404659\pi$
$108$	−3.81294	+	3.53009i	−0.366900	+	0.339683i
$109$	−1.48807			−0.142531			−0.0712654	−	0.997457i	$-0.522704\pi$
$109$	−1.48807			−0.142531			−0.0712654	+	0.997457i	$0.522704\pi$
$110$	−0.797685	+	0.669337i	−0.0760562	+	0.0638188i
$111$	1.14757	+	3.61804i	0.108923	+	0.343409i
$112$	0.781269	−	4.43080i	0.0738230	−	0.418671i
$113$	3.38041	−	1.23037i	0.318002	−	0.115743i	−0.178087	−	0.984015i	$-0.556991\pi$
$113$	3.38041	−	1.23037i	0.318002	−	0.115743i	0.496090	+	0.868271i	$0.334769\pi$
$114$	2.93528	−	1.53440i	0.274914	−	0.143710i
$115$	−0.953104	−	5.40532i	−0.0888774	−	0.504049i
$116$	3.90037	+	6.75564i	0.362140	+	0.627246i
$117$	4.98015	−	7.16445i	0.460415	−	0.662354i
$118$	0.00372852	−	0.00645798i	0.000343238	−	0.000594505i
$119$	26.7647	+	9.74154i	2.45351	+	0.893005i
$120$	1.71684	−	0.229016i	0.156726	−	0.0209062i
$121$	−7.59586	−	6.37368i	−0.690532	−	0.579426i
$122$	11.6401	+	9.76724i	1.05385	+	0.884284i
$123$	−14.8697	+	1.98351i	−1.34075	+	0.178847i
$124$	5.94496	+	2.16379i	0.533873	+	0.194314i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	−7.70394	+	11.0829i	−0.686322	+	0.987343i
$127$	−1.43709	−	2.48911i	−0.127521	−	0.220873i	0.795195	−	0.606354i	$-0.207369\pi$
$127$	−1.43709	−	2.48911i	−0.127521	−	0.220873i	−0.922715	+	0.385482i	$0.874035\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	12.2341	−	6.39531i	1.07715	−	0.563076i
$130$	−2.73304	+	0.994745i	−0.239703	+	0.0872449i
$131$	3.09405	−	17.5473i	0.270329	−	1.53311i	−0.483091	−	0.875570i	$-0.660486\pi$
$131$	3.09405	−	17.5473i	0.270329	−	1.53311i	0.753419	−	0.657540i	$-0.228403\pi$
$132$	−0.545292	−	1.71918i	−0.0474616	−	0.149636i
$133$	6.59071	−	5.53026i	0.571487	−	0.479534i
$134$	11.0445			0.954099
$135$	−4.96361	−	1.53706i	−0.427200	−	0.132289i
$136$	6.33061			0.542845
$137$	−13.3223	+	11.1787i	−1.13820	+	0.955064i	−0.999378	−	0.0352536i	$-0.988776\pi$
$137$	−13.3223	+	11.1787i	−1.13820	+	0.955064i	−0.138822	+	0.990317i	$0.544332\pi$
$138$	9.28488	+	2.04175i	0.790382	+	0.173805i
$139$	−3.09916	+	17.5762i	−0.262867	+	1.49079i	0.512173	+	0.858882i	$0.328841\pi$
$139$	−3.09916	+	17.5762i	−0.262867	+	1.49079i	−0.775040	+	0.631912i	$0.782270\pi$
$140$	4.22782	−	1.53880i	0.357316	−	0.130052i
$141$	12.3559	+	7.84186i	1.04055	+	0.660404i
$142$	−1.33144	−	7.55096i	−0.111732	−	0.633663i
$143$	1.51428	+	2.62282i	0.126631	+	0.219331i
$144$	−0.766537	+	2.90042i	−0.0638781	+	0.241701i
$145$	−3.90037	+	6.75564i	−0.323908	+	0.561025i
$146$	−8.00800	−	2.91467i	−0.662747	−	0.241220i
$147$	−8.74113	+	21.2055i	−0.720956	+	1.74900i
$148$	1.67873	+	1.40863i	0.137991	+	0.115788i
$149$	3.04070	+	2.55145i	0.249104	+	0.209023i	0.758786	−	0.651340i	$-0.225793\pi$
$149$	3.04070	+	2.55145i	0.249104	+	0.209023i	−0.509683	+	0.860363i	$0.670237\pi$
$150$	1.05676	+	1.37232i	0.0862837	+	0.112050i
$151$	11.1025	+	4.04096i	0.903505	+	0.328849i	0.751656	−	0.659555i	$-0.229255\pi$
$151$	11.1025	+	4.04096i	0.903505	+	0.328849i	0.151848	+	0.988404i	$0.451477\pi$
$152$	0.956131	−	1.65607i	0.0775525	−	0.134325i
$153$	−17.2398	−	7.96735i	−1.39376	−	0.644122i
$154$	−2.34249	−	4.05731i	−0.188763	−	0.326948i
$155$	1.09858	+	6.23038i	0.0882404	+	0.500436i
$156$	0.211125	−	5.03314i	0.0169035	−	0.402974i
$157$	17.8295	−	6.48942i	1.42295	−	0.517912i	0.488048	−	0.872817i	$-0.337709\pi$
$157$	17.8295	−	6.48942i	1.42295	−	0.517912i	0.934902	+	0.354905i	$0.115487\pi$
$158$	0.659995	−	3.74302i	0.0525064	−	0.297778i
$159$	−9.27879	+	10.1609i	−0.735856	+	0.805809i
$160$	0.766044	−	0.642788i	0.0605611	−	0.0508168i
$161$	24.6945			1.94620
$162$	5.73777	−	6.93383i	0.450802	−	0.544773i
$163$	12.7000			0.994741			0.497371	−	0.867538i	$-0.334299\pi$
$163$	12.7000			0.994741			0.497371	+	0.867538i	$0.334299\pi$
$164$	−6.63474	+	5.56721i	−0.518086	+	0.434726i
$165$	1.21621	−	1.33183i	0.0946819	−	0.103683i
$166$	−0.206338	+	1.17020i	−0.0160149	+	0.0908250i
$167$	−2.79174	+	1.01611i	−0.216032	+	0.0786291i	−0.447769	−	0.894149i	$-0.647781\pi$
$167$	−2.79174	+	1.01611i	−0.216032	+	0.0786291i	0.231737	+	0.972778i	$0.425559\pi$
$168$	−0.326595	+	7.78591i	−0.0251973	+	0.600696i
$169$	−0.788531	−	4.47198i	−0.0606563	−	0.343999i
$170$	3.16530	+	5.48247i	0.242768	+	0.420486i
$171$	−4.68801	+	3.30655i	−0.358501	+	0.252858i
$172$	3.98512	−	6.90243i	0.303862	−	0.526305i
$173$	2.45299	+	0.892817i	0.186498	+	0.0678796i	0.433581	−	0.901115i	$-0.357250\pi$
$173$	2.45299	+	0.892817i	0.186498	+	0.0678796i	−0.247083	+	0.968994i	$0.579472\pi$
$174$	−8.24347	−	10.7051i	−0.624936	−	0.811554i
$175$	3.44655	+	2.89200i	0.260535	+	0.218615i
$176$	−0.797685	−	0.669337i	−0.0601277	−	0.0504532i
$177$	−0.00492230	+	0.0119412i	−0.000369983	+	0.000897558i
$178$	−3.30351	−	1.20238i	−0.247609	−	0.0901221i
$179$	−6.62823	+	11.4804i	−0.495418	+	0.858088i	−0.999986	−	0.00528334i	$-0.998318\pi$
$179$	−6.62823	+	11.4804i	−0.495418	+	0.858088i	0.504569	+	0.863372i	$0.331652\pi$
$180$	−2.89510	+	0.786368i	−0.215788	+	0.0586124i
$181$	−8.00291	−	13.8615i	−0.594852	−	1.03031i	−0.993568	−	0.113239i	$-0.963877\pi$
$181$	−8.00291	−	13.8615i	−0.594852	−	1.03031i	0.398716	−	0.917074i	$-0.369456\pi$
$182$	−2.27228	−	12.8867i	−0.168432	−	0.955227i
$183$	−22.2211	−	14.1030i	−1.64263	−	1.04253i
$184$	5.15770	−	1.87725i	0.380231	−	0.138393i
$185$	−0.380538	+	2.15814i	−0.0279777	+	0.158670i
$186$	−10.7021	−	2.35340i	−0.784717	−	0.172559i
$187$	5.04983	−	4.23731i	0.369280	−	0.309863i
$188$	8.44910			0.616214
$189$	10.6883	−	20.7919i	0.777460	−	1.51239i
$190$	1.91226			0.138730
$191$	−1.61241	+	1.35297i	−0.116670	+	0.0978974i	−0.699256	−	0.714871i	$-0.746485\pi$
$191$	−1.61241	+	1.35297i	−0.116670	+	0.0978974i	0.582586	+	0.812769i	$0.302041\pi$
$192$	0.523663	+	1.65099i	0.0377921	+	0.119150i
$193$	1.72731	−	9.79605i	0.124334	−	0.705135i	−0.857367	−	0.514706i	$-0.827901\pi$
$193$	1.72731	−	9.79605i	0.124334	−	0.705135i	0.981701	−	0.190429i	$-0.0609879\pi$
$194$	2.30205	−	0.837879i	0.165278	−	0.0601562i
$195$	4.46439	−	2.33373i	0.319702	−	0.167122i
$196$	2.29951	+	13.0412i	0.164251	+	0.931513i
$197$	−4.11536	−	7.12801i	−0.293207	−	0.507850i	0.681359	−	0.731949i	$-0.261389\pi$
$197$	−4.11536	−	7.12801i	−0.293207	−	0.507850i	−0.974566	+	0.224100i	$0.928056\pi$
$198$	1.32990	+	2.82669i	0.0945120	+	0.200884i
$199$	−2.80269	+	4.85439i	−0.198677	+	0.344119i	−0.948100	−	0.317973i	$-0.896998\pi$
$199$	−2.80269	+	4.85439i	−0.198677	+	0.344119i	0.749423	+	0.662092i	$0.230331\pi$
$200$	0.939693	+	0.342020i	0.0664463	+	0.0241845i
$201$	−18.9617	+	2.52936i	−1.33745	+	0.178407i
$202$	4.88373	+	4.09794i	0.343618	+	0.288330i
$203$	−26.8856	−	22.5597i	−1.88700	−	1.58338i
$204$	−10.8687	+	1.44981i	−0.760959	+	0.101507i
$205$	−8.13872	−	2.96225i	−0.568433	−	0.206893i
$206$	2.70124	−	4.67868i	0.188204	−	0.325979i
$207$	−16.4083	−	1.37898i	−1.14045	−	0.0958457i
$208$	−1.45422	−	2.51878i	−0.100832	−	0.174646i
$209$	−0.345776	−	1.96099i	−0.0239178	−	0.135645i
$210$	−6.90609	+	3.61012i	−0.476566	+	0.249122i
$211$	10.6547	−	3.87798i	0.733497	−	0.266971i	0.0518525	−	0.998655i	$-0.483487\pi$
$211$	10.6547	−	3.87798i	0.733497	−	0.266971i	0.681644	+	0.731684i	$0.261265\pi$
$212$	−1.37953	+	7.82368i	−0.0947462	+	0.537332i
$213$	4.01516	+	12.6589i	0.275114	+	0.867373i
$214$	−4.67620	+	3.92380i	−0.319659	+	0.268225i
$215$	7.97023			0.543565
$216$	0.651783	−	5.15511i	0.0443482	−	0.350761i
$217$	−28.4639			−1.93225
$218$	1.13992	−	0.956510i	0.0772054	−	0.0647830i
$219$	14.4160	+	3.17008i	0.974142	+	0.214214i
$220$	0.180820	−	1.02548i	0.0121909	−	0.0691381i
$221$	17.3018	−	6.29734i	1.16385	−	0.423605i
$222$	−3.20472	−	2.03393i	−0.215087	−	0.136509i
$223$	−1.22919	−	6.97110i	−0.0823128	−	0.466819i	−0.997904	−	0.0647091i	$-0.979388\pi$
$223$	−1.22919	−	6.97110i	−0.0823128	−	0.466819i	0.915591	−	0.402110i	$-0.131723\pi$
$224$	2.24958	+	3.89638i	0.150306	+	0.260338i
$225$	−2.12857	−	2.11405i	−0.141904	−	0.140937i
$226$	−1.79868	+	3.11540i	−0.119646	+	0.207233i
$227$	12.4488	+	4.53101i	0.826259	+	0.300734i	0.720323	−	0.693639i	$-0.243994\pi$
$227$	12.4488	+	4.53101i	0.826259	+	0.300734i	0.105936	+	0.994373i	$0.466216\pi$
$228$	−1.26226	+	3.06218i	−0.0835953	+	0.202798i
$229$	−13.3335	−	11.1881i	−0.881101	−	0.739332i	0.0853038	−	0.996355i	$-0.472814\pi$
$229$	−13.3335	−	11.1881i	−0.881101	−	0.739332i	−0.966405	+	0.257023i	$0.917258\pi$
$230$	4.20459	+	3.52807i	0.277243	+	0.232634i
$231$	4.95088	+	6.42930i	0.325744	+	0.423017i
$232$	−7.33030	−	2.66801i	−0.481258	−	0.175164i
$233$	−10.8413	+	18.7776i	−0.710236	+	1.23016i	0.254532	+	0.967064i	$0.418078\pi$
$233$	−10.8413	+	18.7776i	−0.710236	+	1.23016i	−0.964768	+	0.263101i	$0.915255\pi$
$234$	0.790200	+	8.68947i	0.0516570	+	0.568048i
$235$	4.22455	+	7.31713i	0.275579	+	0.477317i
$236$	0.00129490	+	0.00734375i	8.42908e−5	+	0.000478037i
$237$	−0.275898	+	6.57732i	−0.0179215	+	0.427243i
$238$	−26.7647	+	9.74154i	−1.73490	+	0.631450i
$239$	1.66281	−	9.43027i	0.107558	−	0.609994i	−0.882609	−	0.470107i	$-0.844215\pi$
$239$	1.66281	−	9.43027i	0.107558	−	0.609994i	0.990168	−	0.139886i	$-0.0446737\pi$
$240$	−1.16797	+	1.27900i	−0.0753921	+	0.0825592i
$241$	12.8166	−	10.7544i	0.825590	−	0.692752i	−0.128684	−	0.991686i	$-0.541075\pi$
$241$	12.8166	−	10.7544i	0.825590	−	0.692752i	0.954274	+	0.298933i	$0.0966308\pi$
$242$	9.91569			0.637405
$243$	−8.26290	+	13.2183i	−0.530065	+	0.847957i
$244$	−15.1951			−0.972768
$245$	−10.1442	+	8.51203i	−0.648092	+	0.543813i
$246$	10.1158	−	11.0775i	0.644962	−	0.706275i
$247$	0.965779	−	5.47721i	0.0614511	−	0.348506i
$248$	−5.94496	+	2.16379i	−0.377505	+	0.137401i
$249$	0.0862555	−	2.05630i	0.00546622	−	0.130313i
$250$	0.173648	+	0.984808i	0.0109825	+	0.0622847i
$251$	−6.58047	−	11.3977i	−0.415355	−	0.719417i	0.580110	−	0.814538i	$-0.303009\pi$
$251$	−6.58047	−	11.3977i	−0.415355	−	0.719417i	−0.995466	+	0.0951213i	$0.969676\pi$
$252$	−1.22238	−	13.4420i	−0.0770029	−	0.846766i
$253$	2.85771	−	4.94969i	0.179662	−	0.311184i
$254$	2.70084	+	0.983025i	0.169466	+	0.0616805i
$255$	−6.68990	−	8.68763i	−0.418938	−	0.544041i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	5.71894	+	4.79876i	0.356737	+	0.299338i	0.803489	−	0.595320i	$-0.202975\pi$
$257$	5.71894	+	4.79876i	0.356737	+	0.299338i	−0.446751	+	0.894658i	$0.647419\pi$
$258$	−5.26106	+	12.7630i	−0.327539	+	0.794592i
$259$	−9.26498	−	3.37218i	−0.575698	−	0.209537i
$260$	1.45422	−	2.51878i	0.0901869	−	0.156208i
$261$	16.6044	+	16.4912i	1.02779	+	1.02078i
$262$	8.90897	+	15.4308i	0.550398	+	0.953318i
$263$	−2.42282	−	13.7405i	−0.149397	−	0.847274i	−0.963731	−	0.266877i	$-0.914008\pi$
$263$	−2.42282	−	13.7405i	−0.149397	−	0.847274i	0.814333	−	0.580397i	$-0.197103\pi$
$264$	1.52279	+	0.966464i	0.0937211	+	0.0594818i
$265$	−7.46527	+	2.71714i	−0.458588	+	0.166912i
$266$	−1.49399	+	8.47285i	−0.0916025	+	0.519504i
$267$	5.94697	+	1.30774i	0.363949	+	0.0800325i
$268$	−8.46057	+	7.09926i	−0.516812	+	0.433656i
$269$	−5.79747			−0.353478			−0.176739	−	0.984258i	$-0.556555\pi$
$269$	−5.79747			−0.353478			−0.176739	+	0.984258i	$0.556555\pi$
$270$	4.79035	−	2.01310i	0.291531	−	0.122513i
$271$	27.1766			1.65086			0.825431	−	0.564504i	$-0.190932\pi$
$271$	27.1766			1.65086			0.825431	+	0.564504i	$0.190932\pi$
$272$	−4.84953	+	4.06924i	−0.294046	+	0.246734i
$273$	6.85240	+	21.6041i	0.414726	+	1.30754i
$274$	3.01992	−	17.1268i	0.182440	−	1.03467i
$275$	0.978505	−	0.356147i	0.0590061	−	0.0214765i
$276$	−8.42504	+	4.40414i	−0.507128	+	0.265098i
$277$	−1.17705	−	6.67539i	−0.0707221	−	0.401085i	−0.999534	−	0.0305329i	$-0.990280\pi$
$277$	−1.17705	−	6.67539i	−0.0707221	−	0.401085i	0.928812	−	0.370552i	$-0.120832\pi$
$278$	−8.92367	−	15.4563i	−0.535206	−	0.927004i
$279$	18.9128	+	1.58946i	1.13228	+	0.0951587i
$280$	−2.24958	+	3.89638i	−0.134438	+	0.232853i
$281$	0.113162	+	0.0411874i	0.00675065	+	0.00245704i	0.345393	−	0.938458i	$-0.387746\pi$
$281$	0.113162	+	0.0411874i	0.00675065	+	0.00245704i	−0.338643	+	0.940915i	$0.609968\pi$
$282$	−14.5058	+	1.93498i	−0.863807	+	0.115226i
$283$	23.4636	+	19.6883i	1.39477	+	1.17035i	0.963367	+	0.268185i	$0.0864239\pi$
$283$	23.4636	+	19.6883i	1.39477	+	1.17035i	0.431398	+	0.902162i	$0.358021\pi$
$284$	5.87361	+	4.92854i	0.348534	+	0.292455i
$285$	−3.28305	+	0.437938i	−0.194471	+	0.0259412i
$286$	−2.84592	−	1.03583i	−0.168283	−	0.0612500i
$287$	19.4837	−	33.7467i	1.15008	−	1.99201i
$288$	−1.27715	−	2.71457i	−0.0752568	−	0.159958i
$289$	−11.5383	−	19.9849i	−0.678723	−	1.17558i
$290$	−1.35458	−	7.68223i	−0.0795440	−	0.451116i
$291$	−3.76038	+	1.96571i	−0.220437	+	0.115232i
$292$	8.00800	−	2.91467i	0.468633	−	0.170568i
$293$	−4.37636	+	24.8195i	−0.255669	+	1.44997i	0.538679	+	0.842511i	$0.318924\pi$
$293$	−4.37636	+	24.8195i	−0.255669	+	1.44997i	−0.794348	+	0.607462i	$0.792188\pi$
$294$	−6.93454	−	21.8630i	−0.404430	−	1.27508i
$295$	−0.00571242	+	0.00479329i	−0.000332590	+	0.000279076i
$296$	−2.19143			−0.127374
$297$	−2.93059	−	4.54842i	−0.170050	−	0.263926i
$298$	−3.96935			−0.229938
$299$	12.2288	−	10.2612i	0.707211	−	0.593420i
$300$	−1.69163	−	0.371991i	−0.0976665	−	0.0214769i
$301$	−6.22690	+	35.3145i	−0.358913	+	2.03549i
$302$	−11.1025	+	4.04096i	−0.638874	+	0.232531i
$303$	−9.32309	−	5.91706i	−0.535598	−	0.339926i
$304$	0.332061	+	1.88321i	0.0190450	+	0.108010i
$305$	−7.59756	−	13.1594i	−0.435035	−	0.753503i
$306$	18.3278	−	4.97819i	1.04773	−	0.284584i
$307$	−13.3766	+	23.1690i	−0.763445	+	1.32233i	0.177619	+	0.984099i	$0.443160\pi$
$307$	−13.3766	+	23.1690i	−0.763445	+	1.32233i	−0.941065	+	0.338227i	$0.890173\pi$
$308$	4.40244	+	1.60236i	0.250852	+	0.0913028i
$309$	−3.56611	+	8.65119i	−0.202869	+	0.492149i
$310$	−4.84638	−	4.06659i	−0.275256	−	0.230967i
$311$	21.4267	+	17.9791i	1.21500	+	1.01950i	0.999071	+	0.0430925i	$0.0137210\pi$
$311$	21.4267	+	17.9791i	1.21500	+	1.01950i	0.215925	+	0.976410i	$0.430723\pi$
$312$	3.07351	+	3.99132i	0.174003	+	0.225964i
$313$	29.3074	+	10.6670i	1.65655	+	0.602936i	0.989815	−	0.142357i	$-0.0454683\pi$
$313$	29.3074	+	10.6670i	1.65655	+	0.602936i	0.666737	+	0.745293i	$0.267690\pi$
$314$	−9.48689	+	16.4318i	−0.535376	+	0.927299i
$315$	11.0299	−	7.77961i	0.621465	−	0.438331i
$316$	1.90038	+	3.29155i	0.106905	+	0.185164i
$317$	−3.17333	−	17.9968i	−0.178232	−	1.01080i	−0.934347	−	0.356364i	$-0.884016\pi$
$317$	−3.17333	−	17.9968i	−0.178232	−	1.01080i	0.756115	−	0.654438i	$-0.227095\pi$
$318$	0.576685	−	13.7480i	0.0323389	−	0.770948i
$319$	−7.63307	+	2.77821i	−0.427370	+	0.155550i
$320$	−0.173648	+	0.984808i	−0.00970723	+	0.0550524i
$321$	7.12970	−	7.80747i	0.397941	−	0.435771i
$322$	−18.9171	+	15.8733i	−1.05421	+	0.884587i
$323$	−12.1058			−0.673583
$324$	0.0615918	+	8.99979i	0.00342177	+	0.499988i
$325$	2.90844			0.161331
$326$	−9.72877	+	8.16341i	−0.538827	+	0.452129i
$327$	−1.73802	+	1.90324i	−0.0961125	+	0.105249i
$328$	1.50397	−	8.52946i	0.0830431	−	0.470961i
$329$	−35.7213	+	13.0015i	−1.96938	+	0.716795i
$330$	−0.0755886	+	1.80201i	−0.00416101	+	0.0991971i
$331$	−0.544913	−	3.09036i	−0.0299511	−	0.169861i	0.966163	−	0.257932i	$-0.0830410\pi$
$331$	−0.544913	−	3.09036i	−0.0299511	−	0.169861i	−0.996114	+	0.0880705i	$0.971930\pi$
$332$	−0.594125	−	1.02906i	−0.0326069	−	0.0564767i
$333$	5.96781	+	2.75801i	0.327034	+	0.151138i
$334$	1.48546	−	2.57288i	0.0812805	−	0.140782i
$335$	−10.3784	−	3.77744i	−0.567034	−	0.206384i
$336$	−4.75450	−	6.17429i	−0.259379	−	0.336835i
$337$	22.3508	+	18.7546i	1.21753	+	1.02163i	0.998950	+	0.0458079i	$0.0145862\pi$
$337$	22.3508	+	18.7546i	1.21753	+	1.02163i	0.218578	+	0.975820i	$0.429858\pi$
$338$	3.47859	+	2.91888i	0.189210	+	0.158766i
$339$	2.37457	−	5.76058i	0.128969	−	0.312872i
$340$	−5.94882	−	2.16520i	−0.322620	−	0.117424i
$341$	−3.29390	+	5.70520i	−0.178375	+	0.308954i
$342$	1.46582	−	5.54636i	0.0792624	−	0.299913i
$343$	−14.0427	−	24.3226i	−0.758233	−	1.31330i
$344$	1.38402	+	7.84915i	0.0746212	+	0.423198i
$345$	−8.02662	−	5.09423i	−0.432138	−	0.274264i
$346$	−2.45299	+	0.892817i	−0.131874	+	0.0479981i
$347$	0.859502	−	4.87448i	0.0461405	−	0.261676i	−0.953007	−	0.302947i	$-0.902030\pi$
$347$	0.859502	−	4.87448i	0.0461405	−	0.261676i	0.999148	+	0.0412710i	$0.0131407\pi$
$348$	13.1960	+	2.90180i	0.707380	+	0.155553i
$349$	26.2542	−	22.0299i	1.40535	−	1.17923i	0.446689	−	0.894689i	$-0.352603\pi$
$349$	26.2542	−	22.0299i	1.40535	−	1.17923i	0.958664	−	0.284541i	$-0.0918413\pi$
$350$	−4.49915			−0.240490
$351$	−3.34667	−	14.7375i	−0.178632	−	0.786629i
$352$	1.04130			0.0555017
$353$	−12.0053	+	10.0736i	−0.638978	+	0.536166i	−0.903704	−	0.428158i	$-0.859163\pi$
$353$	−12.0053	+	10.0736i	−0.638978	+	0.536166i	0.264726	+	0.964324i	$0.414718\pi$
$354$	−0.00390497	−	0.0123115i	−0.000207547	−	0.000654349i
$355$	−1.33144	+	7.55096i	−0.0706654	+	0.400763i
$356$	3.30351	−	1.20238i	0.175086	−	0.0637260i
$357$	43.7198	−	22.8542i	2.31390	−	1.20957i
$358$	−2.30196	−	13.0551i	−0.121662	−	0.689982i
$359$	4.84257	+	8.38757i	0.255581	+	0.442679i	0.965053	−	0.262054i	$-0.0844000\pi$
$359$	4.84257	+	8.38757i	0.255581	+	0.442679i	−0.709472	+	0.704733i	$0.751067\pi$
$360$	1.71231	−	2.46333i	0.0902467	−	0.129829i
$361$	7.67163	−	13.2876i	0.403770	−	0.699350i
$362$	15.0406	+	5.47432i	0.790514	+	0.287724i
$363$	−17.0237	+	2.27085i	−0.893512	+	0.119189i
$364$	10.0241	+	8.41121i	0.525405	+	0.440867i
$365$	6.52818	+	5.47779i	0.341700	+	0.286721i
$366$	26.0876	−	3.47992i	1.36362	−	0.181898i
$367$	−18.8775	−	6.87086i	−0.985398	−	0.358656i	−0.201462	−	0.979496i	$-0.564569\pi$
$367$	−18.8775	−	6.87086i	−0.985398	−	0.358656i	−0.783937	+	0.620841i	$0.786791\pi$
$368$	−2.74435	+	4.75336i	−0.143059	+	0.247786i
$369$	−14.8304	+	21.3350i	−0.772039	+	1.11066i
$370$	−1.09572	−	1.89784i	−0.0569636	−	0.0986638i
$371$	−6.20669	−	35.1999i	−0.322236	−	1.82749i
$372$	9.71102	−	5.07637i	0.503493	−	0.263198i
$373$	20.7651	−	7.55789i	1.07518	−	0.391333i	0.257067	−	0.966394i	$-0.417244\pi$
$373$	20.7651	−	7.55789i	1.07518	−	0.391333i	0.818111	+	0.575061i	$0.195022\pi$
$374$	−1.14470	+	6.49193i	−0.0591912	+	0.335690i
$375$	−0.523663	−	1.65099i	−0.0270418	−	0.0852569i
$376$	−6.47239	+	5.43098i	−0.333788	+	0.280081i
$377$	−22.6880			−1.16849
$378$	5.17707	+	22.7978i	0.266280	+	1.17259i
$379$	−4.24995			−0.218305			−0.109153	−	0.994025i	$-0.534814\pi$
$379$	−4.24995			−0.218305			−0.109153	+	0.994025i	$0.534814\pi$
$380$	−1.46488	+	1.22918i	−0.0751466	+	0.0630555i
$381$	−4.86205	−	1.06917i	−0.249090	−	0.0547750i
$382$	0.365503	−	2.07287i	0.0187007	−	0.106057i
$383$	4.88582	−	1.77829i	0.249654	−	0.0908666i	−0.214162	−	0.976798i	$-0.568702\pi$
$383$	4.88582	−	1.77829i	0.249654	−	0.0908666i	0.463816	+	0.885932i	$0.346480\pi$
$384$	−1.46239	−	0.928130i	−0.0746271	−	0.0473634i
$385$	0.813538	+	4.61381i	0.0414618	+	0.235141i
$386$	4.97358	+	8.61450i	0.253149	+	0.438467i
$387$	6.10948	−	23.1170i	0.310562	−	1.17510i
$388$	−1.22490	+	2.12159i	−0.0621848	+	0.107707i
$389$	27.3531	+	9.95573i	1.38686	+	0.504776i	0.924250	−	0.381787i	$-0.124691\pi$
$389$	27.3531	+	9.95573i	1.38686	+	0.504776i	0.462609	+	0.886562i	$0.346913\pi$
$390$	−1.91983	+	4.65740i	−0.0972143	+	0.235836i
$391$	−26.6176	−	22.3348i	−1.34611	−	1.12952i
$392$	−10.1442	−	8.51203i	−0.512361	−	0.429922i
$393$	−18.8292	−	24.4520i	−0.949808	−	1.23344i
$394$	7.73435	+	2.81507i	0.389651	+	0.141821i
$395$	−1.90038	+	3.29155i	−0.0956185	+	0.165616i
$396$	−2.83572	−	1.31053i	−0.142501	−	0.0658564i
$397$	15.5080	+	26.8607i	0.778326	+	1.34810i	0.932906	+	0.360119i	$0.117264\pi$
$397$	15.5080	+	26.8607i	0.778326	+	1.34810i	−0.154581	+	0.987980i	$0.549403\pi$
$398$	−0.973363	−	5.52021i	−0.0487903	−	0.276703i
$399$	0.624535	−	14.8887i	0.0312659	−	0.745367i
$400$	−0.939693	+	0.342020i	−0.0469846	+	0.0171010i
$401$	2.70680	−	15.3510i	0.135171	−	0.766592i	−0.839570	−	0.543252i	$-0.817193\pi$
$401$	2.70680	−	15.3510i	0.135171	−	0.766592i	0.974741	−	0.223340i	$-0.0716961\pi$
$402$	12.8996	−	14.1259i	0.643375	−	0.704537i
$403$	−14.0954	+	11.8274i	−0.702142	+	0.589167i
$404$	−6.37526			−0.317181
$405$	−7.76325	+	4.55323i	−0.385759	+	0.226252i
$406$	35.0967			1.74182
$407$	−1.74807	+	1.46681i	−0.0866487	+	0.0727069i
$408$	7.39396	−	8.09686i	0.366056	−	0.400854i
$409$	−4.70504	+	26.6836i	−0.232649	+	1.31942i	0.614859	+	0.788637i	$0.289213\pi$
$409$	−4.70504	+	26.6836i	−0.232649	+	1.31942i	−0.847508	+	0.530783i	$0.821898\pi$
$410$	8.13872	−	2.96225i	0.401943	−	0.146295i
$411$	−1.26242	+	30.0957i	−0.0622706	+	1.48451i
$412$	0.938130	+	5.32040i	0.0462184	+	0.262117i
$413$	−0.0167752	−	0.0290554i	−0.000825452	−	0.00142972i
$414$	13.4559	−	9.49068i	0.661320	−	0.466442i
$415$	0.594125	−	1.02906i	0.0291645	−	0.0505143i
$416$	2.73304	+	0.994745i	0.133998	+	0.0487714i
$417$	18.8603	+	24.4923i	0.923592	+	1.19939i
$418$	1.52538	+	1.27995i	0.0746089	+	0.0626043i
$419$	−17.8678	−	14.9928i	−0.872897	−	0.732447i	0.0918092	−	0.995777i	$-0.470735\pi$
$419$	−17.8678	−	14.9928i	−0.872897	−	0.732447i	−0.964706	+	0.263329i	$0.915179\pi$
$420$	2.96984	−	7.20466i	0.144913	−	0.351551i
$421$	−1.57077	−	0.571715i	−0.0765548	−	0.0278637i	0.303459	−	0.952845i	$-0.401859\pi$
$421$	−1.57077	−	0.571715i	−0.0765548	−	0.0278637i	−0.380014	+	0.924981i	$0.624081\pi$
$422$	−5.66922	+	9.81938i	−0.275973	+	0.478000i
$423$	24.4610	−	6.64410i	1.18934	−	0.323047i
$424$	−3.97219	−	6.88003i	−0.192906	−	0.334124i
$425$	−1.09930	−	6.23443i	−0.0533238	−	0.302414i
$426$	−11.2128	−	7.11638i	−0.543261	−	0.344790i
$427$	64.2422	−	23.3823i	3.10890	−	1.13155i
$428$	1.06001	−	6.01161i	0.0512375	−	0.290582i
$429$	5.12323	+	1.12660i	0.247352	+	0.0543927i
$430$	−6.10555	+	5.12317i	−0.294436	+	0.247061i
$431$	−30.5125			−1.46974			−0.734868	−	0.678210i	$-0.762756\pi$
$431$	−30.5125			−1.46974			−0.734868	+	0.678210i	$0.762756\pi$
$432$	2.81435	+	4.36800i	0.135405	+	0.210156i
$433$	−20.6724			−0.993453			−0.496727	−	0.867907i	$-0.665465\pi$
$433$	−20.6724			−0.993453			−0.496727	+	0.867907i	$0.665465\pi$
$434$	21.8046	−	18.2962i	1.04665	−	0.878246i
$435$	4.08496	+	12.8790i	0.195859	+	0.617499i
$436$	−0.258400	+	1.46546i	−0.0123751	+	0.0701827i
$437$	−9.86287	+	3.58979i	−0.471805	+	0.171723i
$438$	−13.0810	+	6.83799i	−0.625033	+	0.326732i
$439$	5.59606	+	31.7368i	0.267085	+	1.51472i	0.763030	+	0.646363i	$0.223711\pi$
$439$	5.59606	+	31.7368i	0.267085	+	1.51472i	−0.495945	+	0.868354i	$0.665178\pi$
$440$	0.520652	+	0.901795i	0.0248211	+	0.0429914i
$441$	16.9125	+	35.9473i	0.805357	+	1.71178i
$442$	−9.20610	+	15.9454i	−0.437889	+	0.758447i
$443$	7.90098	+	2.87572i	0.375387	+	0.136630i	0.522822	−	0.852442i	$-0.324879\pi$
$443$	7.90098	+	2.87572i	0.375387	+	0.136630i	−0.147435	+	0.989072i	$0.547102\pi$
$444$	3.76235	−	0.501872i	0.178553	−	0.0238178i
$445$	2.69305	+	2.25973i	0.127663	+	0.107122i
$446$	5.42255	+	4.55006i	0.256765	+	0.215452i
$447$	6.81475	−	0.909043i	0.322327	−	0.0429963i
$448$	−4.22782	−	1.53880i	−0.199746	−	0.0727015i
$449$	−0.268245	+	0.464614i	−0.0126593	+	0.0219265i	−0.872286	−	0.488997i	$-0.837363\pi$
$449$	−0.268245	+	0.464614i	−0.0126593	+	0.0219265i	0.859626	+	0.510923i	$0.170696\pi$
$450$	2.98946	+	0.251239i	0.140925	+	0.0118435i
$451$	−4.50939	−	7.81049i	−0.212339	−	0.367781i
$452$	−0.624674	−	3.54270i	−0.0293822	−	0.166635i
$453$	18.1357	−	9.48034i	0.852091	−	0.445425i
$454$	−12.4488	+	4.53101i	−0.584253	+	0.212651i
$455$	−2.27228	+	12.8867i	−0.106526	+	0.604139i
$456$	−1.00138	−	3.15713i	−0.0468940	−	0.147846i
$457$	−13.3703	+	11.2190i	−0.625434	+	0.524802i	−0.899507	−	0.436907i	$-0.856074\pi$
$457$	−13.3703	+	11.2190i	−0.625434	+	0.524802i	0.274072	+	0.961709i	$0.411629\pi$
$458$	17.4056			0.813312
$459$	−30.3258	+	12.7441i	−1.41549	+	0.594844i
$460$	−5.48871			−0.255912
$461$	−25.3547	+	21.2751i	−1.18088	+	0.990879i	−0.180911	+	0.983499i	$0.557905\pi$
$461$	−25.3547	+	21.2751i	−1.18088	+	0.990879i	−0.999973	+	0.00737974i	$0.997651\pi$
$462$	−7.92527	−	1.74277i	−0.368717	−	0.0810810i
$463$	−0.530377	+	3.00792i	−0.0246487	+	0.139790i	−0.994649	−	0.103315i	$-0.967055\pi$
$463$	−0.530377	+	3.00792i	−0.0246487	+	0.139790i	0.970000	+	0.243105i	$0.0781660\pi$
$464$	7.33030	−	2.66801i	0.340301	−	0.123859i
$465$	9.25178	+	5.87181i	0.429041	+	0.272298i
$466$	−3.76514	−	21.3532i	−0.174417	−	0.989166i
$467$	2.05999	+	3.56800i	0.0953248	+	0.165107i	0.909744	−	0.415169i	$-0.136278\pi$
$467$	2.05999	+	3.56800i	0.0953248	+	0.165107i	−0.814419	+	0.580277i	$0.802944\pi$
$468$	−6.19081	−	6.14859i	−0.286170	−	0.284219i
$469$	24.8454	−	43.0335i	1.14725	−	1.98710i
$470$	−7.93956	−	2.88976i	−0.366224	−	0.133295i
$471$	12.5244	−	30.3834i	0.577093	−	1.39999i
$472$	−0.00571242	−	0.00479329i	−0.000262935	−	0.000220629i
$473$	6.35773	+	5.33477i	0.292329	+	0.245293i
$474$	−4.01647	−	5.21587i	−0.184483	−	0.239573i
$475$	−1.79694	−	0.654032i	−0.0824492	−	0.0300090i
$476$	14.2412	−	24.6664i	0.652743	−	1.13058i
$477$	2.15842	+	23.7352i	0.0988274	+	1.08676i
$478$	4.78787	+	8.29284i	0.218992	+	0.379306i
$479$	−0.869952	−	4.93374i	−0.0397491	−	0.225428i	0.958462	−	0.285221i	$-0.0920671\pi$
$479$	−0.869952	−	4.93374i	−0.0397491	−	0.225428i	−0.998211	+	0.0597929i	$0.980956\pi$
$480$	0.0725903	−	1.73053i	0.00331328	−	0.0789875i
$481$	−5.98927	+	2.17992i	−0.273087	+	0.0993957i
$482$	−2.90529	+	16.4767i	−0.132332	+	0.750493i
$483$	28.8425	−	31.5844i	1.31238	−	1.43714i
$484$	−7.59586	+	6.37368i	−0.345266	+	0.289713i
$485$	−2.44980			−0.111239
$486$	−2.16684	−	15.4371i	−0.0982897	−	0.700242i
$487$	−17.8452			−0.808642			−0.404321	−	0.914617i	$-0.632492\pi$
$487$	−17.8452			−0.808642			−0.404321	+	0.914617i	$0.632492\pi$
$488$	11.6401	−	9.76724i	0.526924	−	0.442142i
$489$	14.8332	−	16.2433i	0.670782	−	0.734549i
$490$	2.29951	−	13.0412i	0.103881	−	0.589140i
$491$	−8.81678	+	3.20904i	−0.397896	+	0.144822i	−0.533215	−	0.845980i	$-0.679016\pi$
$491$	−8.81678	+	3.20904i	−0.397896	+	0.144822i	0.135319	+	0.990802i	$0.456794\pi$
$492$	−0.628708	+	14.9882i	−0.0283443	+	0.675720i
$493$	8.57534	+	48.6332i	0.386214	+	2.19033i
$494$	2.78085	+	4.81657i	0.125116	+	0.216708i
$495$	−0.282914	−	3.11107i	−0.0127160	−	0.139832i
$496$	3.16325	−	5.47890i	0.142034	−	0.246010i
$497$	−32.4166	−	11.7987i	−1.45408	−	0.529243i
$498$	1.25569	+	1.63066i	0.0562688	+	0.0730718i
$499$	4.72528	+	3.96498i	0.211532	+	0.177497i	0.742398	−	0.669959i	$-0.233689\pi$
$499$	4.72528	+	3.96498i	0.211532	+	0.177497i	−0.530865	+	0.847456i	$0.678133\pi$
$500$	−0.766044	−	0.642788i	−0.0342585	−	0.0287463i
$501$	−1.96106	+	4.75743i	−0.0876139	+	0.212546i
$502$	12.3672	+	4.50130i	0.551977	+	0.200903i
$503$	−13.7665	+	23.8443i	−0.613818	+	1.06316i	0.376773	+	0.926306i	$0.377034\pi$
$503$	−13.7665	+	23.8443i	−0.613818	+	1.06316i	−0.990591	+	0.136858i	$0.956299\pi$
$504$	9.57674	+	9.51143i	0.426582	+	0.423673i
$505$	−3.18763	−	5.52113i	−0.141848	−	0.245687i
$506$	0.992471	+	5.62858i	0.0441207	+	0.250221i
$507$	−6.64066	−	4.21461i	−0.294922	−	0.187177i
$508$	−2.70084	+	0.983025i	−0.119830	+	0.0436147i
$509$	1.18154	−	6.70086i	0.0523710	−	0.297011i	−0.947361	−	0.320168i	$-0.896261\pi$
$509$	1.18154	−	6.70086i	0.0523710	−	0.297011i	0.999732	+	0.0231572i	$0.00737184\pi$
$510$	10.7091	+	2.35493i	0.474205	+	0.104278i
$511$	−29.3713	+	24.6454i	−1.29931	+	1.09025i
$512$	−1.00000			−0.0441942
$513$	−1.24638	+	9.85792i	−0.0550290	+	0.435238i
$514$	−7.46554			−0.329291
$515$	−4.13854	+	3.47265i	−0.182366	+	0.153023i
$516$	−4.17372	−	13.1588i	−0.183738	−	0.579284i
$517$	−1.52777	+	8.66441i	−0.0671912	+	0.381060i
$518$	9.26498	−	3.37218i	0.407080	−	0.148165i
$519$	4.00694	−	2.09460i	0.175885	−	0.0919428i
$520$	0.505045	+	2.86426i	0.0221477	+	0.125606i
$521$	6.67365	+	11.5591i	0.292378	+	0.506414i	0.974372	−	0.224945i	$-0.0722201\pi$
$521$	6.67365	+	11.5591i	0.292378	+	0.506414i	−0.681994	+	0.731358i	$0.738887\pi$
$522$	−23.3200	−	1.95985i	−1.02069	−	0.0857805i
$523$	−1.06763	+	1.84919i	−0.0466843	+	0.0808596i	−0.888423	−	0.459025i	$-0.848199\pi$
$523$	−1.06763	+	1.84919i	−0.0466843	+	0.0808596i	0.841739	+	0.539885i	$0.181532\pi$
$524$	−16.7434	−	6.09410i	−0.731439	−	0.266222i
$525$	7.72434	−	1.03038i	0.337118	−	0.0449693i
$526$	10.6882	+	8.96846i	0.466027	+	0.391043i
$527$	30.6805	+	25.7440i	1.33646	+	1.12143i
$528$	−1.78775	+	0.238475i	−0.0778020	+	0.0103783i
$529$	−6.69618	−	2.43721i	−0.291138	−	0.105966i
$530$	3.97219	−	6.88003i	0.172541	−	0.298849i
$531$	0.00952376	+	0.0202426i	0.000413296	+	0.000878456i
$532$	−4.30178	−	7.45090i	−0.186506	−	0.323037i
$533$	−4.37422	−	24.8074i	−0.189469	−	1.07453i
$534$	−5.39625	+	2.82085i	−0.233518	+	0.122070i
$535$	5.73621	−	2.08781i	0.247998	−	0.0902639i
$536$	1.91786	−	10.8767i	0.0828387	−	0.469802i
$537$	6.94192	+	21.8863i	0.299566	+	0.944465i
$538$	4.44112	−	3.72654i	0.191470	−	0.160663i
$539$	−13.7893			−0.593948
$540$	−2.37563	+	4.62130i	−0.102231	+	0.198869i
$541$	−15.8254			−0.680386			−0.340193	−	0.940356i	$-0.610492\pi$
$541$	−15.8254			−0.680386			−0.340193	+	0.940356i	$0.610492\pi$
$542$	−20.8185	+	17.4688i	−0.894231	+	0.750348i
$543$	−27.0760	−	5.95402i	−1.16194	−	0.255511i
$544$	1.09930	−	6.23443i	0.0471320	−	0.267299i
$545$	−1.39832	+	0.508948i	−0.0598976	+	0.0218009i
$546$	−19.1361	−	12.1451i	−0.818949	−	0.519760i
$547$	−2.23559	−	12.6787i	−0.0955870	−	0.542101i	−0.994566	−	0.104109i	$-0.966801\pi$
$547$	−2.23559	−	12.6787i	−0.0955870	−	0.542101i	0.898979	−	0.437992i	$-0.144310\pi$
$548$	8.69551	+	15.0611i	0.371454	+	0.643377i
$549$	−43.9915	+	11.9490i	−1.87751	+	0.509969i
$550$	−0.520652	+	0.901795i	−0.0222007	+	0.0384527i
$551$	14.0175	+	5.10194i	0.597164	+	0.217350i
$552$	3.62303	−	8.78928i	0.154207	−	0.374097i
$553$	−13.0995	−	10.9918i	−0.557048	−	0.467418i
$554$	5.19253	+	4.35705i	0.220609	+	0.185113i
$555$	2.31581	+	3.00735i	0.0983006	+	0.127655i
$556$	16.7710	+	6.10415i	0.711250	+	0.258874i
$557$	8.05089	−	13.9445i	0.341127	−	0.590849i	−0.643515	−	0.765433i	$-0.722525\pi$
$557$	8.05089	−	13.9445i	0.341127	−	0.590849i	0.984642	+	0.174584i	$0.0558580\pi$
$558$	−15.5097	+	10.9393i	−0.656580	+	0.463098i
$559$	11.5905	+	20.0753i	0.490225	+	0.849095i
$560$	−0.781269	−	4.43080i	−0.0330147	−	0.187235i
$561$	0.478522	−	11.4078i	0.0202032	−	0.481637i
$562$	−0.113162	+	0.0411874i	−0.00477343	+	0.00173739i
$563$	4.32216	−	24.5122i	0.182157	−	1.03307i	−0.747396	−	0.664379i	$-0.768696\pi$
$563$	4.32216	−	24.5122i	0.182157	−	1.03307i	0.929554	−	0.368687i	$-0.120193\pi$
$564$	9.86829	−	10.8064i	0.415530	−	0.455032i
$565$	2.75573	−	2.31234i	0.115935	−	0.0972807i
$566$	−30.6295			−1.28746
$567$	−14.1093	−	37.9547i	−0.592534	−	1.59395i
$568$	−7.66745			−0.321719
$569$	21.5829	−	18.1102i	0.904804	−	0.759220i	−0.0663197	−	0.997798i	$-0.521126\pi$
$569$	21.5829	−	18.1102i	0.904804	−	0.759220i	0.971123	+	0.238578i	$0.0766813\pi$
$570$	2.23346	−	2.44579i	0.0935495	−	0.102443i
$571$	3.70345	−	21.0033i	0.154985	−	0.878961i	−0.803815	−	0.594879i	$-0.797200\pi$
$571$	3.70345	−	21.0033i	0.154985	−	0.878961i	0.958800	−	0.284082i	$-0.0916888\pi$
$572$	2.84592	−	1.03583i	0.118994	−	0.0433103i
$573$	−0.152792	+	3.64250i	−0.00638296	+	0.152167i
$574$	6.76661	+	38.3753i	0.282433	+	1.60176i
$575$	−2.74435	−	4.75336i	−0.114447	−	0.198229i
$576$	2.72325	+	1.25854i	0.113469	+	0.0524393i
$577$	18.0221	−	31.2151i	0.750269	−	1.29950i	−0.197424	−	0.980318i	$-0.563257\pi$
$577$	18.0221	−	31.2151i	0.750269	−	1.29950i	0.947692	−	0.319185i	$-0.103409\pi$
$578$	21.6849	+	7.89266i	0.901973	+	0.328291i
$579$	−10.5117	−	13.6507i	−0.436852	−	0.567305i
$580$	5.97572	+	5.01422i	0.248128	+	0.208204i
$581$	4.09537	+	3.43642i	0.169904	+	0.142567i
$582$	1.61708	−	3.92295i	0.0670302	−	0.162612i
$583$	−7.77361	−	2.82936i	−0.321950	−	0.117180i
$584$	−4.26097	+	7.38021i	−0.176320	+	0.305395i
$585$	2.22943	−	8.43569i	0.0921755	−	0.348773i
$586$	−12.6012	−	21.8259i	−0.520551	−	0.901621i
$587$	−2.88975	−	16.3886i	−0.119273	−	0.676429i	−0.984546	−	0.175128i	$-0.943966\pi$
$587$	−2.88975	−	16.3886i	−0.119273	−	0.676429i	0.865273	−	0.501301i	$-0.167145\pi$
$588$	19.3655	+	12.2906i	0.798618	+	0.506857i
$589$	11.3683	−	4.13773i	0.468423	−	0.170492i
$590$	0.00129490	−	0.00734375i	5.33102e−5	−	0.000302337i
$591$	−13.9234	−	3.06175i	−0.572730	−	0.125944i
$592$	1.67873	−	1.40863i	0.0689956	−	0.0578942i
$593$	−17.9818			−0.738423			−0.369211	−	0.929345i	$-0.620372\pi$
$593$	−17.9818			−0.738423			−0.369211	+	0.929345i	$0.620372\pi$
$594$	5.16863	+	1.60054i	0.212071	+	0.0656711i
$595$	28.4824			1.16766
$596$	3.04070	−	2.55145i	0.124552	−	0.104511i
$597$	2.93533	+	9.25443i	0.120135	+	0.378759i
$598$	−2.77205	+	15.7211i	−0.113357	+	0.642882i
$599$	17.1440	−	6.23989i	0.700484	−	0.254955i	0.0328662	−	0.999460i	$-0.489536\pi$
$599$	17.1440	−	6.23989i	0.700484	−	0.254955i	0.667617	+	0.744505i	$0.267314\pi$
$600$	1.53498	−	0.802399i	0.0626652	−	0.0327578i
$601$	7.02934	+	39.8654i	0.286733	+	1.62614i	0.699030	+	0.715092i	$0.253615\pi$
$601$	7.02934	+	39.8654i	0.286733	+	1.62614i	−0.412297	+	0.911049i	$0.635273\pi$
$602$	−17.9296	−	31.0551i	−0.730758	−	1.26571i
$603$	−18.9116	+	27.2062i	−0.770140	+	1.10792i
$604$	5.90749	−	10.2321i	0.240372	−	0.416337i
$605$	−9.31770	−	3.39136i	−0.378818	−	0.137879i
$606$	10.9453	−	1.46003i	0.444623	−	0.0593098i
$607$	−12.7734	−	10.7182i	−0.518457	−	0.435037i	0.345637	−	0.938368i	$-0.387663\pi$
$607$	−12.7734	−	10.7182i	−0.518457	−	0.435037i	−0.864093	+	0.503332i	$0.832107\pi$
$608$	−1.46488	−	1.22918i	−0.0594086	−	0.0498498i
$609$	−60.2556	+	8.03770i	−2.44168	+	0.325704i
$610$	14.2787	+	5.19704i	0.578129	+	0.210422i
$611$	−12.2869	+	21.2815i	−0.497073	+	0.860955i
$612$	−10.8400	+	15.5944i	−0.438180	+	0.630365i
$613$	−7.23109	−	12.5246i	−0.292061	−	0.505864i	0.682236	−	0.731132i	$-0.261008\pi$
$613$	−7.23109	−	12.5246i	−0.292061	−	0.505864i	−0.974297	+	0.225268i	$0.927674\pi$
$614$	−4.64566	−	26.3468i	−0.187484	−	1.06327i
$615$	−13.2945	+	6.94962i	−0.536086	+	0.280236i
$616$	−4.40244	+	1.60236i	−0.177379	+	0.0645608i
$617$	−1.25002	+	7.08922i	−0.0503239	+	0.285401i	−0.999576	−	0.0291148i	$-0.990731\pi$
$617$	−1.25002	+	7.08922i	−0.0503239	+	0.285401i	0.949252	+	0.314516i	$0.101842\pi$
$618$	−2.82908	−	8.91945i	−0.113802	−	0.358793i
$619$	0.656586	−	0.550941i	0.0263904	−	0.0221442i	−0.629497	−	0.777003i	$-0.716739\pi$
$619$	0.656586	−	0.550941i	0.0263904	−	0.0221442i	0.655887	+	0.754859i	$0.272295\pi$
$620$	6.32649			0.254078
$621$	−20.9281	+	19.3756i	−0.839816	+	0.777517i
$622$	−27.9706			−1.12152
$623$	−12.1164	+	10.1669i	−0.485434	+	0.407328i
$624$	−4.92002	−	1.08191i	−0.196958	−	0.0433112i
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	−29.3074	+	10.6670i	−1.17136	+	0.426340i
$627$	−2.91197	−	1.84813i	−0.116293	−	0.0738073i
$628$	−3.29476	−	18.6855i	−0.131475	−	0.745634i
$629$	6.93655	+	12.0145i	0.276578	+	0.479048i
$630$	−3.44877	+	13.0494i	−0.137402	+	0.519901i
$631$	−20.8032	+	36.0322i	−0.828162	+	1.43442i	0.0713167	+	0.997454i	$0.477280\pi$
$631$	−20.8032	+	36.0322i	−0.828162	+	1.43442i	−0.899479	+	0.436965i	$0.856053\pi$
$632$	−3.57154	−	1.29994i	−0.142068	−	0.0517087i
$633$	7.48438	−	18.1567i	0.297477	−	0.721664i
$634$	13.9990	+	11.7466i	0.555973	+	0.466517i
$635$	−2.20174	−	1.84748i	−0.0873736	−	0.0733151i
$636$	8.39526	+	10.9022i	0.332894	+	0.432302i
$637$	−36.1919	−	13.1728i	−1.43398	−	0.521924i
$638$	4.06147	−	7.03467i	0.160795	−	0.278505i
$639$	20.8803	+	9.64982i	0.826014	+	0.381741i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	3.28567	+	18.6340i	0.129776	+	0.735998i	0.978356	+	0.206930i	$0.0663472\pi$
$641$	3.28567	+	18.6340i	0.129776	+	0.735998i	−0.848580	+	0.529068i	$0.822542\pi$
$642$	−0.443117	+	10.5638i	−0.0174884	+	0.416918i
$643$	−1.56943	+	0.571224i	−0.0618921	+	0.0225269i	−0.372781	−	0.927919i	$-0.621596\pi$
$643$	−1.56943	+	0.571224i	−0.0618921	+	0.0225269i	0.310889	+	0.950446i	$0.399373\pi$
$644$	4.28816	−	24.3194i	0.168977	−	0.958317i
$645$	9.30899	−	10.1939i	0.366541	−	0.401386i
$646$	9.27356	−	7.78144i	0.364863	−	0.306157i
$647$	−41.9906			−1.65082			−0.825410	−	0.564533i	$-0.809056\pi$
$647$	−41.9906			−1.65082			−0.825410	+	0.564533i	$0.809056\pi$
$648$	−5.83214	−	6.85465i	−0.229108	−	0.269276i
$649$	−0.00776504			−0.000304804
$650$	−2.22799	+	1.86951i	−0.0873892	+	0.0733282i
$651$	−33.2449	+	36.4053i	−1.30297	+	1.42684i
$652$	2.20533	−	12.5071i	0.0863675	−	0.489814i
$653$	44.3845	−	16.1546i	1.73690	−	0.632179i	0.737816	−	0.675002i	$-0.235857\pi$
$653$	44.3845	−	16.1546i	1.73690	−	0.632179i	0.999083	+	0.0428222i	$0.0136349\pi$
$654$	0.108019	−	2.57514i	0.00422388	−	0.100696i
$655$	−3.09405	−	17.5473i	−0.120895	−	0.685628i
$656$	4.33052	+	7.50068i	0.169078	+	0.292852i
$657$	20.8920	−	14.7355i	0.815074	−	0.574887i
$658$	19.0069	−	32.9209i	0.740966	−	1.28339i
$659$	27.5273	+	10.0191i	1.07231	+	0.390289i	0.817040	−	0.576581i	$-0.195613\pi$
$659$	27.5273	+	10.0191i	1.07231	+	0.390289i	0.255270	+	0.966870i	$0.417836\pi$
$660$	−1.10040	−	1.42900i	−0.0428331	−	0.0556239i
$661$	6.81275	+	5.71658i	0.264985	+	0.222349i	0.765593	−	0.643325i	$-0.222446\pi$
$661$	6.81275	+	5.71658i	0.264985	+	0.222349i	−0.500608	+	0.865674i	$0.666890\pi$
$662$	2.40387	+	2.01709i	0.0934291	+	0.0783963i
$663$	12.1537	−	29.4841i	0.472010	−	1.14507i
$664$	1.11659	+	0.406406i	0.0433321	+	0.0157716i
$665$	4.30178	−	7.45090i	0.166816	−	0.288933i
$666$	−6.34442	+	1.72327i	−0.245841	+	0.0667755i
$667$	21.4080	+	37.0797i	0.828921	+	1.43573i
$668$	0.515893	+	2.92578i	0.0199605	+	0.113202i
$669$	−10.3517	−	6.56989i	−0.400220	−	0.254007i
$670$	10.3784	−	3.77744i	0.400954	−	0.145935i
$671$	2.74759	−	15.5823i	0.106069	−	0.601550i
$672$	7.61091	+	1.67364i	0.293597	+	0.0645622i
$673$	19.3051	−	16.1989i	0.744157	−	0.624422i	−0.189794	−	0.981824i	$-0.560782\pi$
$673$	19.3051	−	16.1989i	0.744157	−	0.624422i	0.933951	+	0.357402i	$0.116338\pi$
$674$	−29.1770			−1.12385
$675$	−5.18998	+	0.253295i	−0.199762	+	0.00974932i
$676$	−4.54097			−0.174653
$677$	29.9879	−	25.1629i	1.15253	−	0.967088i	0.152754	−	0.988264i	$-0.451186\pi$
$677$	29.9879	−	25.1629i	1.15253	−	0.967088i	0.999776	+	0.0211766i	$0.00674123\pi$
$678$	1.88380	+	5.93921i	0.0723470	+	0.228094i
$679$	1.91395	−	10.8546i	0.0734507	−	0.416559i
$680$	5.94882	−	2.16520i	0.228127	−	0.0830314i
$681$	20.3350	−	10.6300i	0.779241	−	0.407343i
$682$	−1.14396	−	6.48772i	−0.0438045	−	0.248427i
$683$	4.97083	+	8.60974i	0.190204	+	0.329442i	0.945318	−	0.326151i	$-0.105752\pi$
$683$	4.97083	+	8.60974i	0.190204	+	0.329442i	−0.755114	+	0.655594i	$0.772418\pi$
$684$	2.44225	+	5.19097i	0.0933816	+	0.198482i
$685$	−8.69551	+	15.0611i	−0.332238	+	0.575454i
$686$	26.3916	+	9.60575i	1.00763	+	0.366749i
$687$	−29.8827	+	3.98616i	−1.14010	+	0.152082i
$688$	−6.10555	−	5.12317i	−0.232772	−	0.195319i
$689$	−17.7000	−	14.8521i	−0.674317	−	0.565819i
$690$	9.42325	−	1.25700i	0.358737	−	0.0478532i
$691$	−30.8004	−	11.2104i	−1.17170	−	0.426464i	−0.318437	−	0.947944i	$-0.603158\pi$
$691$	−30.8004	−	11.2104i	−1.17170	−	0.426464i	−0.853264	+	0.521480i	$0.825380\pi$
$692$	1.30521	−	2.26069i	0.0496167	−	0.0859386i
$693$	14.0056	+	1.17705i	0.532028	+	0.0447125i
$694$	2.47484	+	4.28655i	0.0939436	+	0.162715i
$695$	3.09916	+	17.5762i	0.117558	+	0.666703i
$696$	−11.9740	+	6.25931i	−0.453872	+	0.237259i
$697$	−51.5230	+	18.7528i	−1.95157	+	0.710315i
$698$	−5.95133	+	33.7517i	−0.225261	+	1.27752i
$699$	11.3544	+	35.7978i	0.429461	+	1.35400i
$700$	3.44655	−	2.89200i	0.130267	−	0.109307i
$701$	13.4334			0.507373			0.253687	−	0.967286i	$-0.418357\pi$
$701$	13.4334			0.507373			0.253687	+	0.967286i	$0.418357\pi$
$702$	12.0368	+	9.13837i	0.454299	+	0.344906i
$703$	4.19059			0.158051
$704$	−0.797685	+	0.669337i	−0.0300639	+	0.0252266i
$705$	14.2928	+	3.14299i	0.538297	+	0.118372i
$706$	2.72138	−	15.4337i	0.102421	−	0.580856i
$707$	26.9534	−	9.81025i	1.01369	−	0.368952i
$708$	0.0109051	+	0.00692109i	0.000409838	+	0.000260111i
$709$	−1.52552	−	8.65166i	−0.0572922	−	0.324920i	0.942669	−	0.333729i	$-0.108307\pi$
$709$	−1.52552	−	8.65166i	−0.0572922	−	0.324920i	−0.999961	+	0.00880904i	$0.997196\pi$
$710$	−3.83372	−	6.64020i	−0.143877	−	0.249202i
$711$	8.09017	+	8.03499i	0.303405	+	0.301336i
$712$	−1.75776	+	3.04453i	−0.0658749	+	0.114099i
$713$	32.6302	+	11.8764i	1.22201	+	0.444775i
$714$	−18.8009	+	45.6099i	−0.703605	+	1.70691i
$715$	2.32002	+	1.94673i	0.0867638	+	0.0728035i
$716$	10.1550	+	8.52109i	0.379512	+	0.318448i
$717$	−10.1192	−	13.1410i	−0.377909	−	0.490760i
$718$	−9.10105	−	3.31251i	−0.339648	−	0.123622i
$719$	13.7650	−	23.8417i	0.513349	−	0.889147i	−0.486531	−	0.873663i	$-0.661738\pi$
$719$	13.7650	−	23.8417i	0.513349	−	0.889147i	0.999880	−	0.0154833i	$-0.00492868\pi$
$720$	0.271692	+	2.98767i	0.0101254	+	0.111344i
$721$	−12.1533	−	21.0501i	−0.452612	−	0.783947i
$722$	2.66433	+	15.1102i	0.0991560	+	0.562342i
$723$	1.21450	−	28.9533i	0.0451678	−	1.07678i
$724$	−15.0406	+	5.47432i	−0.558978	+	0.203451i
$725$	−1.35458	+	7.68223i	−0.0503080	+	0.285311i
$726$	11.5812	−	12.6822i	0.429820	−	0.470680i
$727$	−30.1042	+	25.2604i	−1.11650	+	0.936856i	−0.998422	−	0.0561481i	$-0.982118\pi$
$727$	−30.1042	+	25.2604i	−1.11650	+	0.936856i	−0.118079	+	0.993004i	$0.537674\pi$
$728$	−13.0855			−0.484981
$729$	7.25546	+	26.0069i	0.268721	+	0.963218i
$730$	−8.52193			−0.315411
$731$	38.6519	−	32.4328i	1.42959	−	1.19957i
$732$	−17.7474	+	19.4346i	−0.655965	+	0.718323i
$733$	−3.37643	+	19.1487i	−0.124711	+	0.707273i	0.856768	+	0.515703i	$0.172469\pi$
$733$	−3.37643	+	19.1487i	−0.124711	+	0.707273i	−0.981479	+	0.191570i	$0.938642\pi$
$734$	18.8775	−	6.87086i	0.696782	−	0.253608i
$735$	−0.961268	+	22.9163i	−0.0354569	+	0.845280i
$736$	−0.953104	−	5.40532i	−0.0351319	−	0.199243i
$737$	−5.75033	−	9.95987i	−0.211816	−	0.366876i
$738$	−2.35314	−	25.8764i	−0.0866201	−	0.952522i
$739$	25.3396	−	43.8894i	0.932132	−	1.61450i	0.152461	−	0.988310i	$-0.451280\pi$
$739$	25.3396	−	43.8894i	0.932132	−	1.61450i	0.779671	−	0.626190i	$-0.215386\pi$
$740$	2.05927	+	0.749514i	0.0757004	+	0.0275527i
$741$	−5.87736	−	7.63245i	−0.215910	−	0.280385i
$742$	27.3807	+	22.9751i	1.00518	+	0.843443i
$743$	16.4209	+	13.7788i	0.602426	+	0.505495i	0.892224	−	0.451592i	$-0.149144\pi$
$743$	16.4209	+	13.7788i	0.602426	+	0.505495i	−0.289798	+	0.957088i	$0.593588\pi$
$744$	−4.17604	+	10.1309i	−0.153101	+	0.371415i
$745$	3.72997	+	1.35760i	0.136655	+	0.0497385i
$746$	−11.0489	+	19.1373i	−0.404529	+	0.700665i
$747$	−2.52927	−	2.51202i	−0.0925412	−	0.0919100i
$748$	−3.29604	−	5.70891i	−0.120515	−	0.208738i
$749$	4.76914	+	27.0471i	0.174261	+	0.988281i
$750$	1.46239	+	0.928130i	0.0533988	+	0.0338905i
$751$	0.0575145	−	0.0209336i	0.00209873	−	0.000763877i	−0.340971	−	0.940074i	$-0.610756\pi$
$751$	0.0575145	−	0.0209336i	0.00209873	−	0.000763877i	0.343069	+	0.939310i	$0.388533\pi$
$752$	1.46717	−	8.32074i	0.0535022	−	0.303426i
$753$	−22.2635	−	4.89574i	−0.811326	−	0.178411i
$754$	17.3800	−	14.5836i	0.632943	−	0.531102i
$755$	11.8150			0.429991
$756$	−18.6200	−	14.1364i	−0.677204	−	0.514136i
$757$	7.63063			0.277340			0.138670	−	0.990339i	$-0.455717\pi$
$757$	7.63063			0.277340			0.138670	+	0.990339i	$0.455717\pi$
$758$	3.25565	−	2.73182i	0.118251	−	0.0992241i
$759$	−2.99295	−	9.43610i	−0.108637	−	0.342509i
$760$	0.332061	−	1.88321i	0.0120451	−	0.0683112i
$761$	−25.0005	+	9.09944i	−0.906268	+	0.329854i	−0.752762	−	0.658293i	$-0.771279\pi$
$761$	−25.0005	+	9.09944i	−0.906268	+	0.329854i	−0.153506	+	0.988148i	$0.549056\pi$
$762$	4.41179	−	2.30624i	0.159822	−	0.0835461i
$763$	−1.16258	−	6.59332i	−0.0420882	−	0.238694i
$764$	1.05242	+	1.82285i	0.0380753	+	0.0659484i
$765$	−18.9251	−	1.59050i	−0.684239	−	0.0575046i
$766$	−2.59969	+	4.50280i	−0.0939307	+	0.162693i
$767$	−0.0203804	−	0.00741785i	−0.000735893	−	0.000267843i
$768$	1.71684	−	0.229016i	0.0619513	−	0.00826389i
$769$	−13.0099	−	10.9166i	−0.469150	−	0.393663i	0.377335	−	0.926077i	$-0.376841\pi$
$769$	−13.0099	−	10.9166i	−0.469150	−	0.393663i	−0.846484	+	0.532414i	$0.821285\pi$
$770$	−3.58890	−	3.01145i	−0.129335	−	0.108525i
$771$	12.8172	−	1.70973i	0.461599	−	0.0615743i
$772$	−9.34728	−	3.40213i	−0.336416	−	0.122445i
$773$	10.2787	−	17.8032i	0.369698	−	0.640335i	−0.619820	−	0.784744i	$-0.712795\pi$
$773$	10.2787	−	17.8032i	0.369698	−	0.640335i	0.989518	+	0.144408i	$0.0461279\pi$
$774$	10.1792	+	21.6358i	0.365883	+	0.777681i
$775$	3.16325	+	5.47890i	0.113627	+	0.196808i
$776$	−0.425403	−	2.41258i	−0.0152711	−	0.0866065i
$777$	−15.1342	+	7.91133i	−0.542938	+	0.283817i
$778$	−27.3531	+	9.95573i	−0.980658	+	0.356930i
$779$	−2.87599	+	16.3106i	−0.103043	+	0.584387i
$780$	−1.52304	−	4.80181i	−0.0545337	−	0.171933i
$781$	−6.11620	+	5.13211i	−0.218855	+	0.183641i
$782$	34.7469			1.24255
$783$	40.4857	−	1.97589i	1.44684	−	0.0706124i
$784$	13.2424			0.472941
$785$	14.5348	−	12.1961i	0.518768	−	0.435298i
$786$	30.1414	+	6.62811i	1.07511	+	0.236417i
$787$	8.44956	−	47.9199i	0.301194	−	1.70816i	−0.339704	−	0.940533i	$-0.610327\pi$
$787$	8.44956	−	47.9199i	0.301194	−	1.70816i	0.640898	−	0.767626i	$-0.278562\pi$
$788$	−7.73435	+	2.81507i	−0.275525	+	0.100283i
$789$	−20.4039	−	12.9497i	−0.726397	−	0.461021i
$790$	−0.659995	−	3.74302i	−0.0234816	−	0.133171i
$791$	8.09252	+	14.0167i	0.287737	+	0.498375i
$792$	3.01468	−	0.818848i	0.107122	−	0.0290965i
$793$	22.0971	−	38.2732i	0.784690	−	1.35912i
$794$	−29.1456	−	10.6081i	−1.03434	−	0.376468i
$795$	−5.24399	+	12.7216i	−0.185985	+	0.451190i
$796$	4.29396	+	3.60306i	0.152196	+	0.127707i
$797$	31.7229	+	26.6187i	1.12368	+	0.942882i	0.998785	−	0.0492878i	$-0.0156952\pi$
$797$	31.7229	+	26.6187i	1.12368	+	0.942882i	0.124898	+	0.992170i	$0.460140\pi$
$798$	9.09185	+	11.8069i	0.321848	+	0.417958i
$799$	50.2622	+	18.2939i	1.77815	+	0.647193i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	8.61849	−	6.07879i	0.304519	−	0.214783i
$802$	7.79391	+	13.4994i	0.275212	+	0.476682i
$803$	1.54094	+	8.73910i	0.0543786	+	0.308396i
$804$	−0.801723	+	19.1128i	−0.0282746	+	0.674057i
$805$	23.2053	−	8.44603i	0.817878	−	0.297683i
$806$	3.19517	−	18.1207i	0.112545	−	0.638274i
$807$	−6.77127	+	7.41497i	−0.238360	+	0.261019i
$808$	4.88373	−	4.09794i	0.171809	−	0.144165i
$809$	6.03595			0.212213			0.106106	−	0.994355i	$-0.466162\pi$
$809$	6.03595			0.212213			0.106106	+	0.994355i	$0.466162\pi$
$810$	3.02023	−	8.47810i	0.106120	−	0.297890i
$811$	−10.8481			−0.380927			−0.190463	−	0.981694i	$-0.560999\pi$
$811$	−10.8481			−0.380927			−0.190463	+	0.981694i	$0.560999\pi$
$812$	−26.8856	+	22.5597i	−0.943501	+	0.791692i
$813$	31.7415	−	34.7589i	1.11322	−	1.21905i
$814$	0.396256	−	2.24728i	0.0138888	−	0.0787671i
$815$	11.9341	−	4.34366i	0.418033	−	0.152152i
$816$	−0.459541	+	10.9553i	−0.0160872	+	0.383512i
$817$	−2.64660	−	15.0096i	−0.0925929	−	0.525120i
$818$	−13.5476	−	23.4652i	−0.473682	−	0.820441i
$819$	35.6351	+	16.4687i	1.24519	+	0.575463i
$820$	−4.33052	+	7.50068i	−0.151228	+	0.261935i
$821$	0.405758	+	0.147684i	0.0141611	+	0.00515420i	0.349091	−	0.937089i	$-0.386490\pi$
$821$	0.405758	+	0.147684i	0.0141611	+	0.00515420i	−0.334930	+	0.942243i	$0.608713\pi$
$822$	−18.3781	−	23.8661i	−0.641008	−	0.832425i
$823$	−27.4766	−	23.0556i	−0.957773	−	0.803667i	0.0228166	−	0.999740i	$-0.492737\pi$
$823$	−27.4766	−	23.0556i	−0.957773	−	0.803667i	−0.980589	+	0.196073i	$0.937181\pi$
$824$	−4.13854	−	3.47265i	−0.144173	−	0.120975i
$825$	0.687352	−	1.66748i	0.0239305	−	0.0580542i
$826$	0.0315270	+	0.0114749i	0.00109696	+	0.000399262i
$827$	−11.0212	+	19.0893i	−0.383245	+	0.663800i	−0.991524	−	0.129923i	$-0.958527\pi$
$827$	−11.0212	+	19.0893i	−0.383245	+	0.663800i	0.608279	+	0.793724i	$0.291860\pi$
$828$	−4.20730	+	15.9195i	−0.146214	+	0.553242i
$829$	−4.69740	−	8.13614i	−0.163148	−	0.282580i	0.772848	−	0.634591i	$-0.218831\pi$
$829$	−4.69740	−	8.13614i	−0.163148	−	0.282580i	−0.935996	+	0.352011i	$0.885498\pi$
$830$	0.206338	+	1.17020i	0.00716208	+	0.0406182i
$831$	−9.91259	−	6.29120i	−0.343864	−	0.218239i
$832$	−2.73304	+	0.994745i	−0.0947511	+	0.0344866i
$833$	−14.5573	+	82.5586i	−0.504381	+	2.86049i
$834$	−30.1912	−	6.63905i	−1.04543	−	0.229891i
$835$	−2.27585	+	1.90967i	−0.0787591	+	0.0660867i
$836$	−1.99124			−0.0688686
$837$	24.1225	−	22.3331i	0.833796	−	0.771944i
$838$	23.3247			0.805738
$839$	−32.3444	+	27.1401i	−1.11665	+	0.936982i	−0.998430	−	0.0560056i	$-0.982164\pi$
$839$	−32.3444	+	27.1401i	−1.11665	+	0.936982i	−0.118221	+	0.992987i	$0.537719\pi$
$840$	2.35604	+	7.42807i	0.0812911	+	0.256293i
$841$	5.53097	−	31.3677i	0.190723	−	1.08164i
$842$	1.57077	−	0.571715i	0.0541324	−	0.0197026i
$843$	0.184848	−	0.0966282i	0.00636651	−	0.00332805i
$844$	−1.96890	−	11.1662i	−0.0677724	−	0.384356i
$845$	−2.27049	−	3.93260i	−0.0781071	−	0.135285i
$846$	−14.4675	+	20.8129i	−0.497402	+	0.715563i
$847$	22.3061	−	38.6353i	0.766446	−	1.32752i
$848$	7.46527	+	2.71714i	0.256358	+	0.0933068i
$849$	52.5861	−	7.01464i	1.80475	−	0.240742i
$850$	4.84953	+	4.06924i	0.166337	+	0.139574i
$851$	9.21409	+	7.73154i	0.315855	+	0.265034i
$852$	13.1638	−	1.75597i	0.450985	−	0.0601584i
$853$	22.5933	+	8.22328i	0.773579	+	0.281560i	0.698493	−	0.715617i	$-0.253854\pi$
$853$	22.5933	+	8.22328i	0.773579	+	0.281560i	0.0750865	+	0.997177i	$0.476077\pi$
$854$	−34.1826	+	59.2060i	−1.16970	+	2.02599i
$855$	−3.27439	+	4.71053i	−0.111982	+	0.161097i
$856$	3.05217	+	5.28652i	0.104321	+	0.180690i
$857$	2.81752	+	15.9789i	0.0962446	+	0.545830i	0.994359	+	0.106068i	$0.0338262\pi$
$857$	2.81752	+	15.9789i	0.0962446	+	0.545830i	−0.898114	+	0.439762i	$0.855063\pi$
$858$	−4.64878	+	2.43012i	−0.158707	+	0.0829630i
$859$	−3.42952	+	1.24824i	−0.117014	+	0.0425895i	−0.399863	−	0.916575i	$-0.630942\pi$
$859$	−3.42952	+	1.24824i	−0.117014	+	0.0425895i	0.282850	+	0.959164i	$0.408720\pi$
$860$	1.38402	−	7.84915i	0.0471946	−	0.267654i
$861$	−20.4058	−	64.3348i	−0.695426	−	2.19252i
$862$	23.3739	−	19.6131i	0.796120	−	0.668024i
$863$	55.7759			1.89863			0.949317	−	0.314319i	$-0.101776\pi$
$863$	55.7759			1.89863			0.949317	+	0.314319i	$0.101776\pi$
$864$	−4.96361	−	1.53706i	−0.168866	−	0.0522917i
$865$	2.61042			0.0887570
$866$	15.8360	−	13.2880i	0.538129	−	0.451544i
$867$	−39.0371	−	8.58427i	−1.32577	−	0.291537i
$868$	−4.94270	+	28.0314i	−0.167766	+	0.951448i
$869$	−3.71906	+	1.35363i	−0.126161	+	0.0459187i
$870$	−11.4077	−	7.24010i	−0.386757	−	0.245462i
$871$	−5.57797	−	31.6342i	−0.189002	−	1.07189i
$872$	−0.744033	−	1.28870i	−0.0251961	−	0.0436410i
$873$	−1.87786	+	7.10543i	−0.0635559	+	0.240482i
$874$	5.24792	−	9.08967i	0.177514	−	0.307463i
$875$	4.22782	+	1.53880i	0.142926	+	0.0520209i
$876$	5.62523	−	13.6465i	0.190059	−	0.461072i
$877$	−12.4065	−	10.4103i	−0.418938	−	0.351531i	0.408821	−	0.912615i	$-0.365940\pi$
$877$	−12.4065	−	10.4103i	−0.418938	−	0.351531i	−0.827759	+	0.561084i	$0.810384\pi$
$878$	−24.6869	−	20.7147i	−0.833142	−	0.699089i
$879$	26.6328	+	34.5859i	0.898302	+	1.16655i
$880$	−0.978505	−	0.356147i	−0.0329854	−	0.0120057i
$881$	−8.24703	+	14.2843i	−0.277849	+	0.481249i	−0.970850	−	0.239688i	$-0.922955\pi$
$881$	−8.24703	+	14.2843i	−0.277849	+	0.481249i	0.693001	+	0.720937i	$0.256288\pi$
$882$	−36.0622	−	16.6661i	−1.21428	−	0.561176i
$883$	8.85612	+	15.3393i	0.298032	+	0.516207i	0.975686	−	0.219174i	$-0.0703363\pi$
$883$	8.85612	+	15.3393i	0.298032	+	0.516207i	−0.677653	+	0.735381i	$0.737003\pi$
$884$	−3.19724	−	18.1325i	−0.107535	−	0.609861i
$885$	−0.000541309		0.0129046i	−1.81959e−5		0.000433784i
$886$	−7.90098	+	2.87572i	−0.265439	+	0.0966118i
$887$	−5.54900	+	31.4699i	−0.186317	+	1.05666i	0.737934	+	0.674873i	$0.235801\pi$
$887$	−5.54900	+	31.4699i	−0.186317	+	1.05666i	−0.924251	+	0.381784i	$0.875310\pi$
$888$	−2.55953	+	2.80285i	−0.0858921	+	0.0940574i
$889$	9.90598	−	8.31211i	0.332236	−	0.278779i
$890$	−3.51552			−0.117841
$891$	−9.24027	−	1.56418i	−0.309561	−	0.0524021i
$892$	−7.07864			−0.237010
$893$	12.3769	−	10.3854i	0.414177	−	0.347536i
$894$	−4.63608	+	5.07680i	−0.155054	+	0.169794i
$895$	−2.30196	+	13.0551i	−0.0769461	+	0.436383i
$896$	4.22782	−	1.53880i	0.141242	−	0.0514077i
$897$	1.15880	−	27.6254i	0.0386913	−	0.922387i
$898$	−0.0931605	−	0.528340i	−0.00310881	−	0.0176309i
$899$	−24.6757	−	42.7395i	−0.822980	−	1.42544i
$900$	−2.45155	+	1.72913i	−0.0817185	+	0.0576376i
$901$	−25.1463	+	43.5548i	−0.837746	+	1.45102i
$902$	8.47487	+	3.08460i	0.282182	+	0.102706i
$903$	37.8945	+	49.2105i	1.26105	+	1.63762i
$904$	2.75573	+	2.31234i	0.0916544	+	0.0769071i
$905$	−12.2612	−	10.2883i	−0.407575	−	0.341996i
$906$	−7.79893	+	18.9198i	−0.259102	+	0.628568i
$907$	25.9562	+	9.44729i	0.861862	+	0.313692i	0.734867	−	0.678211i	$-0.237244\pi$
$907$	25.9562	+	9.44729i	0.861862	+	0.313692i	0.126995	+	0.991903i	$0.459467\pi$
$908$	6.62389	−	11.4729i	0.219822	−	0.380742i
$909$	−18.4570	+	5.01330i	−0.612181	+	0.166281i
$910$	−6.54276	−	11.3324i	−0.216890	−	0.375665i
$911$	0.673457	+	3.81936i	0.0223126	+	0.126541i	0.993929	−	0.110019i	$-0.0350911\pi$
$911$	0.673457	+	3.81936i	0.0223126	+	0.126541i	−0.971617	+	0.236560i	$0.923980\pi$
$912$	2.79647	+	1.77483i	0.0926003	+	0.0587704i
$913$	1.16271	−	0.423192i	0.0384801	−	0.0140056i
$914$	3.03079	−	17.1885i	0.100250	−	0.568544i
$915$	−25.7046	−	5.65244i	−0.849767	−	0.186864i
$916$	−13.3335	+	11.1881i	−0.440551	+	0.369666i
$917$	80.1656			2.64730
$918$	15.0392	−	29.2556i	0.496366	−	0.965579i
$919$	−1.19751			−0.0395023			−0.0197512	−	0.999805i	$-0.506287\pi$
$919$	−1.19751			−0.0395023			−0.0197512	+	0.999805i	$0.506287\pi$
$920$	4.20459	−	3.52807i	0.138621	−	0.116317i
$921$	14.0097	+	44.1695i	0.461636	+	1.45543i
$922$	5.74743	−	32.5953i	0.189282	−	1.07347i
$923$	−20.9554	+	7.62716i	−0.689757	+	0.251051i
$924$	7.19134	−	3.75923i	0.236578	−	0.123669i
$925$	0.380538	+	2.15814i	0.0125120	+	0.0709592i
$926$	−1.52716	−	2.64512i	−0.0501856	−	0.0869240i
$927$	6.89978	+	14.6654i	0.226618	+	0.481675i
$928$	−3.90037	+	6.75564i	−0.128036	+	0.221765i
$929$	−22.0336	−	8.01959i	−0.722900	−	0.263114i	−0.0457436	−	0.998953i	$-0.514566\pi$
$929$	−22.0336	−	8.01959i	−0.722900	−	0.263114i	−0.677156	+	0.735839i	$0.736788\pi$
$930$	−10.8616	+	1.44887i	−0.356166	+	0.0475102i
$931$	19.3984	+	16.2772i	0.635758	+	0.533464i
$932$	16.6098	+	13.9373i	0.544072	+	0.456531i
$933$	48.0211	−	6.40569i	1.57214	−	0.209713i
$934$	−3.87151	−	1.40911i	−0.126680	−	0.0461076i
$935$	3.29604	−	5.70891i	0.107792	−	0.186701i
$936$	8.69467	+	0.730715i	0.284194	+	0.0238842i
$937$	8.83997	+	15.3113i	0.288789	+	0.500198i	0.973521	−	0.228598i	$-0.0734140\pi$
$937$	8.83997	+	15.3113i	0.288789	+	0.500198i	−0.684732	+	0.728795i	$0.740081\pi$
$938$	8.62872	+	48.9359i	0.281738	+	1.59781i
$939$	47.8733	−	25.0255i	1.56229	−	0.816675i
$940$	7.93956	−	2.88976i	0.258960	−	0.0942536i
$941$	−3.32971	+	18.8837i	−0.108546	+	0.615592i	0.881199	+	0.472745i	$0.156737\pi$
$941$	−3.32971	+	18.8837i	−0.108546	+	0.615592i	−0.989745	+	0.142847i	$0.954374\pi$
$942$	9.93587	+	31.3256i	0.323728	+	1.02064i
$943$	−36.4162	+	30.5568i	−1.18587	+	0.995066i
$944$	0.00745704			0.000242706
$945$	2.93247	−	23.1936i	0.0953933	−	0.754489i
$946$	−8.29943			−0.269838
$947$	−34.1827	+	28.6827i	−1.11079	+	0.932063i	−0.998103	−	0.0615673i	$-0.980390\pi$
$947$	−34.1827	+	28.6827i	−1.11079	+	0.932063i	−0.112687	+	0.993631i	$0.535946\pi$
$948$	6.42949	+	1.41385i	0.208820	+	0.0459196i
$949$	−4.30396	+	24.4090i	−0.139713	+	0.792349i
$950$	1.79694	−	0.654032i	0.0583004	−	0.0212196i
$951$	−26.7243	−	16.9611i	−0.866596	−	0.550000i
$952$	4.94591	+	28.0496i	0.160298	+	0.909094i
$953$	23.9555	+	41.4921i	0.775994	+	1.34406i	0.934234	+	0.356661i	$0.116085\pi$
$953$	23.9555	+	41.4921i	0.775994	+	1.34406i	−0.158240	+	0.987401i	$0.550582\pi$
$954$	−16.9101	−	16.7948i	−0.547486	−	0.543752i
$955$	−1.05242	+	1.82285i	−0.0340556	+	0.0589860i
$956$	−8.99826	−	3.27510i	−0.291025	−	0.105924i
$957$	−5.36186	+	13.0076i	−0.173324	+	0.420475i
$958$	3.83777	+	3.22027i	0.123993	+	0.104042i
$959$	−59.9390	−	50.2948i	−1.93553	−	1.62410i
$960$	1.05676	+	1.37232i	0.0341066	+	0.0442915i
$961$	−8.48028	−	3.08657i	−0.273557	−	0.0995667i
$962$	3.18683	−	5.51974i	0.102747	−	0.177964i
$963$	−1.65850	−	18.2378i	−0.0534445	−	0.587705i
$964$	−8.36544	−	14.4894i	−0.269433	−	0.466671i
$965$	−1.72731	−	9.79605i	−0.0556040	−	0.315346i
$966$	−1.79258	+	42.7346i	−0.0576755	+	1.37496i
$967$	3.10518	−	1.13019i	0.0998559	−	0.0363446i	−0.291609	−	0.956538i	$-0.594191\pi$
$967$	3.10518	−	1.13019i	0.0998559	−	0.0363446i	0.391465	+	0.920193i	$0.371968\pi$
$968$	1.72184	−	9.76505i	0.0553421	−	0.313860i
$969$	−14.1392	+	15.4833i	−0.454216	+	0.497396i
$970$	1.87665	−	1.57470i	0.0602557	−	0.0505605i
$971$	24.3377			0.781034			0.390517	−	0.920596i	$-0.372296\pi$
$971$	24.3377			0.781034			0.390517	+	0.920596i	$0.372296\pi$
$972$	11.5827	+	10.4327i	0.371515	+	0.334629i
$973$	−80.2979			−2.57423
$974$	13.6702	−	11.4707i	0.438022	−	0.367544i
$975$	3.39697	−	3.71990i	0.108790	−	0.119132i
$976$	−2.63861	+	14.9643i	−0.0844597	+	0.478995i
$977$	39.7660	−	14.4737i	1.27223	−	0.463053i	0.384374	−	0.923177i	$-0.374417\pi$
$977$	39.7660	−	14.4737i	1.27223	−	0.463053i	0.887855	+	0.460124i	$0.152195\pi$
$978$	−0.921898	+	21.9777i	−0.0294790	+	0.702770i
$979$	0.635678	+	3.60511i	0.0203164	+	0.115220i
$980$	6.62118	+	11.4682i	0.211506	+	0.366339i
$981$	0.404295	+	4.44585i	0.0129082	+	0.141945i
$982$	4.69131	−	8.12559i	0.149706	−	0.259298i
$983$	−24.1406	−	8.78647i	−0.769967	−	0.280245i	−0.0729842	−	0.997333i	$-0.523252\pi$
$983$	−24.1406	−	8.78647i	−0.769967	−	0.280245i	−0.696982	+	0.717088i	$0.745474\pi$
$984$	−9.15260	−	11.8857i	−0.291774	−	0.378904i
$985$	−6.30510	−	5.29060i	−0.200897	−	0.168573i
$986$	−37.8299	−	31.7431i	−1.20475	−	1.01090i
$987$	−25.0924	+	60.8729i	−0.798701	+	1.93761i
$988$	−5.22629	−	1.90221i	−0.166270	−	0.0605175i
$989$	21.8731	−	37.8854i	0.695526	−	1.20469i
$990$	2.21648	+	2.20137i	0.0704445	+	0.0699640i
$991$	−21.6574	−	37.5118i	−0.687971	−	1.19160i	−0.972493	−	0.232931i	$-0.925168\pi$
$991$	−21.6574	−	37.5118i	−0.687971	−	1.19160i	0.284523	−	0.958669i	$-0.408165\pi$
$992$	1.09858	+	6.23038i	0.0348801	+	0.197815i
$993$	−4.58902	−	2.91250i	−0.145628	−	0.0924254i
$994$	32.4166	−	11.7987i	1.02819	−	0.374231i
$995$	−0.973363	+	5.52021i	−0.0308577	+	0.175003i
$996$	−2.01008	−	0.442018i	−0.0636920	−	0.0140059i
$997$	−20.6110	+	17.2947i	−0.652758	+	0.547729i	−0.907907	−	0.419173i	$-0.862320\pi$
$997$	−20.6110	+	17.2947i	−0.652758	+	0.547729i	0.255148	+	0.966902i	$0.417876\pi$
$998$	−6.16841			−0.195258
$999$	10.4977	−	4.41156i	0.332133	−	0.139576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.k.e.211.4	yes	24
3.2	odd	2		810.2.k.e.361.4		24
27.4	even	9		7290.2.a.s.1.12		12
27.11	odd	18		810.2.k.e.451.4		24
27.16	even	9	inner	270.2.k.e.151.4	✓	24
27.23	odd	18		7290.2.a.v.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.k.e.151.4	✓	24	27.16	even	9	inner
270.2.k.e.211.4	yes	24	1.1	even	1	trivial
810.2.k.e.361.4		24	3.2	odd	2
810.2.k.e.451.4		24	27.11	odd	18
7290.2.a.s.1.12		12	27.4	even	9
7290.2.a.v.1.12		12	27.23	odd	18

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.16797 - 1.27900i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} +(-0.0725903 + 1.73053i) q^{6} +(0.781269 + 4.43080i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.271692 - 2.98767i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.16797 - 1.27900i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} +(-0.0725903 + 1.73053i) q^{6} +(0.781269 + 4.43080i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.271692 - 2.98767i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(0.978505 + 0.356147i) q^{11} +(-1.05676 - 1.37232i) q^{12} +(2.22799 + 1.86951i) q^{13} +(-3.44655 - 2.89200i) q^{14} +(0.660088 - 1.60134i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.16530 - 5.48247i) q^{17} +(2.12857 + 2.11405i) q^{18} +(-0.956131 - 1.65607i) q^{19} +(-0.173648 - 0.984808i) q^{20} +(6.57950 + 4.17580i) q^{21} +(-0.978505 + 0.356147i) q^{22} +(0.953104 - 5.40532i) q^{23} +(1.69163 + 0.371991i) q^{24} +(0.766044 - 0.642788i) q^{25} -2.90844 q^{26} +(-4.13857 - 3.14202i) q^{27} +4.49915 q^{28} +(-5.97572 + 5.01422i) q^{29} +(0.523663 + 1.65099i) q^{30} +(-1.09858 + 6.23038i) q^{31} +(0.939693 - 0.342020i) q^{32} +(1.59838 - 0.835541i) q^{33} +(1.09930 + 6.23443i) q^{34} +(2.24958 + 3.89638i) q^{35} +(-2.98946 - 0.251239i) q^{36} +(-1.09572 + 1.89784i) q^{37} +(1.79694 + 0.654032i) q^{38} +(4.99334 - 0.666079i) q^{39} +(0.766044 + 0.642788i) q^{40} +(-6.63474 - 5.56721i) q^{41} +(-7.72434 + 1.03038i) q^{42} +(7.48957 + 2.72598i) q^{43} +(0.520652 - 0.901795i) q^{44} +(-1.27715 - 2.71457i) q^{45} +(2.74435 + 4.75336i) q^{46} +(1.46717 + 8.32074i) q^{47} +(-1.53498 + 0.802399i) q^{48} +(-12.4437 + 4.52915i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(-3.31511 - 10.4518i) q^{51} +(2.22799 - 1.86951i) q^{52} -7.94437 q^{53} +(5.18998 - 0.253295i) q^{54} +1.04130 q^{55} +(-3.44655 + 2.89200i) q^{56} +(-3.23485 - 0.711344i) q^{57} +(1.35458 - 7.68223i) q^{58} +(-0.00700732 + 0.00255046i) q^{59} +(-1.46239 - 0.928130i) q^{60} +(-2.63861 - 14.9643i) q^{61} +(-3.16325 - 5.47890i) q^{62} +(13.0255 - 3.53799i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.73304 + 0.994745i) q^{65} +(-0.687352 + 1.66748i) q^{66} +(-8.46057 - 7.09926i) q^{67} +(-4.84953 - 4.06924i) q^{68} +(-5.80022 - 7.53228i) q^{69} +(-4.22782 - 1.53880i) q^{70} +(-3.83372 + 6.64020i) q^{71} +(2.45155 - 1.72913i) q^{72} +(4.26097 + 7.38021i) q^{73} +(-0.380538 - 2.15814i) q^{74} +(0.0725903 - 1.73053i) q^{75} +(-1.79694 + 0.654032i) q^{76} +(-0.813538 + 4.61381i) q^{77} +(-3.39697 + 3.71990i) q^{78} +(-2.91155 + 2.44308i) q^{79} -1.00000 q^{80} +(-8.85237 + 1.62345i) q^{81} +8.66104 q^{82} +(0.910253 - 0.763793i) q^{83} +(5.25487 - 5.75442i) q^{84} +(1.09930 - 6.23443i) q^{85} +(-7.48957 + 2.72598i) q^{86} +(-0.566259 + 13.4994i) q^{87} +(0.180820 + 1.02548i) q^{88} +(1.75776 + 3.04453i) q^{89} +(2.72325 + 1.25854i) q^{90} +(-6.54276 + 11.3324i) q^{91} +(-5.15770 - 1.87725i) q^{92} +(6.68555 + 8.68199i) q^{93} +(-6.47239 - 5.43098i) q^{94} +(-1.46488 - 1.22918i) q^{95} +(0.660088 - 1.60134i) q^{96} +(-2.30205 - 0.837879i) q^{97} +(6.62118 - 11.4682i) q^{98} +(0.798198 - 3.02021i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 3 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 + 3 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - 3 q^{3} + 3 q^{7} + 12 q^{8} + 9 q^{9} - 12 q^{10} + 9 q^{13} - 3 q^{14} + 15 q^{17} - 12 q^{18} - 9 q^{19} + 24 q^{21} - 12 q^{23} + 3 q^{24} - 12 q^{26} - 3 q^{27} + 6 q^{28} - 33 q^{29} + 6 q^{30} - 21 q^{31} + 6 q^{33} - 15 q^{34} + 3 q^{35} - 6 q^{36} - 12 q^{37} + 12 q^{38} - 36 q^{39} + 21 q^{41} + 15 q^{42} + 12 q^{43} + 9 q^{44} - 12 q^{45} - 15 q^{46} - 21 q^{47} + 27 q^{49} + 3 q^{51} + 9 q^{52} - 60 q^{53} + 36 q^{54} + 18 q^{55} - 3 q^{56} - 24 q^{57} - 21 q^{58} + 36 q^{59} + 33 q^{61} + 18 q^{62} + 39 q^{63} - 12 q^{64} - 9 q^{66} - 12 q^{67} - 3 q^{68} - 48 q^{69} - 6 q^{70} + 12 q^{71} + 6 q^{74} - 12 q^{76} - 60 q^{77} - 36 q^{78} - 15 q^{79} - 24 q^{80} - 15 q^{81} + 6 q^{82} - 27 q^{83} + 3 q^{84} - 15 q^{85} - 12 q^{86} + 78 q^{87} - 9 q^{88} + 30 q^{89} - 9 q^{90} - 9 q^{91} + 6 q^{92} - 30 q^{93} + 12 q^{94} - 15 q^{95} + 3 q^{97} + 27 q^{98} - 111 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 3 * q^7 + 12 * q^8 + 9 * q^9 - 12 * q^10 + 9 * q^13 - 3 * q^14 + 15 * q^17 - 12 * q^18 - 9 * q^19 + 24 * q^21 - 12 * q^23 + 3 * q^24 - 12 * q^26 - 3 * q^27 + 6 * q^28 - 33 * q^29 + 6 * q^30 - 21 * q^31 + 6 * q^33 - 15 * q^34 + 3 * q^35 - 6 * q^36 - 12 * q^37 + 12 * q^38 - 36 * q^39 + 21 * q^41 + 15 * q^42 + 12 * q^43 + 9 * q^44 - 12 * q^45 - 15 * q^46 - 21 * q^47 + 27 * q^49 + 3 * q^51 + 9 * q^52 - 60 * q^53 + 36 * q^54 + 18 * q^55 - 3 * q^56 - 24 * q^57 - 21 * q^58 + 36 * q^59 + 33 * q^61 + 18 * q^62 + 39 * q^63 - 12 * q^64 - 9 * q^66 - 12 * q^67 - 3 * q^68 - 48 * q^69 - 6 * q^70 + 12 * q^71 + 6 * q^74 - 12 * q^76 - 60 * q^77 - 36 * q^78 - 15 * q^79 - 24 * q^80 - 15 * q^81 + 6 * q^82 - 27 * q^83 + 3 * q^84 - 15 * q^85 - 12 * q^86 + 78 * q^87 - 9 * q^88 + 30 * q^89 - 9 * q^90 - 9 * q^91 + 6 * q^92 - 30 * q^93 + 12 * q^94 - 15 * q^95 + 3 * q^97 + 27 * q^98 - 111 * q^99

Introduction

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