LMFDB - Embedded newform 135.2.p.a.124.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(4,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.p (of order $18$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.15
Character	$\chi$	$=$	135.124
Dual form			135.2.p.a.49.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44418 - 1.72110i) q^{2} +(-0.130598 + 1.72712i) q^{3} +(-0.529254 - 3.00155i) q^{4} +(-0.536643 - 2.17072i) q^{5} +(2.78395 + 2.71904i) q^{6} +(3.05233 + 0.538208i) q^{7} +(-2.03885 - 1.17713i) q^{8} +(-2.96589 - 0.451117i) q^{9} +O(q^{10})$	\(q+(1.44418 - 1.72110i) q^{2} +(-0.130598 + 1.72712i) q^{3} +(-0.529254 - 3.00155i) q^{4} +(-0.536643 - 2.17072i) q^{5} +(2.78395 + 2.71904i) q^{6} +(3.05233 + 0.538208i) q^{7} +(-2.03885 - 1.17713i) q^{8} +(-2.96589 - 0.451117i) q^{9} +(-4.51104 - 2.21129i) q^{10} +(-3.82718 + 1.39298i) q^{11} +(5.25316 - 0.522089i) q^{12} +(0.913372 + 1.08851i) q^{13} +(5.33442 - 4.47611i) q^{14} +(3.81917 - 0.643355i) q^{15} +(0.757669 - 0.275769i) q^{16} +(-5.52192 + 3.18808i) q^{17} +(-5.05969 + 4.45311i) q^{18} +(-1.59710 + 2.76626i) q^{19} +(-6.23150 + 2.75962i) q^{20} +(-1.32818 + 5.20145i) q^{21} +(-3.12967 + 8.59869i) q^{22} +(4.75493 - 0.838423i) q^{23} +(2.29931 - 3.36760i) q^{24} +(-4.42403 + 2.32980i) q^{25} +3.19252 q^{26} +(1.16647 - 5.06353i) q^{27} -9.44656i q^{28} +(-2.87901 - 2.41578i) q^{29} +(4.40829 - 7.50232i) q^{30} +(0.453633 + 2.57268i) q^{31} +(2.22999 - 6.12685i) q^{32} +(-1.90602 - 6.79192i) q^{33} +(-2.48762 + 14.1080i) q^{34} +(-0.469712 - 6.91457i) q^{35} +(0.215659 + 9.14102i) q^{36} +(0.545540 - 0.314968i) q^{37} +(2.45452 + 6.74374i) q^{38} +(-1.99928 + 1.43535i) q^{39} +(-1.46108 + 5.05746i) q^{40} +(4.50871 - 3.78325i) q^{41} +(7.03411 + 9.79775i) q^{42} +(-3.01843 - 8.29308i) q^{43} +(6.20665 + 10.7502i) q^{44} +(0.612374 + 6.68019i) q^{45} +(5.42396 - 9.39457i) q^{46} +(8.23568 + 1.45217i) q^{47} +(0.377336 + 1.34460i) q^{48} +(2.44919 + 0.891433i) q^{49} +(-2.37926 + 10.9789i) q^{50} +(-4.78505 - 9.95338i) q^{51} +(2.78382 - 3.31763i) q^{52} -0.0211636i q^{53} +(-7.03027 - 9.32026i) q^{54} +(5.07759 + 7.56019i) q^{55} +(-5.58969 - 4.69031i) q^{56} +(-4.56908 - 3.11965i) q^{57} +(-8.31562 + 1.46627i) q^{58} +(1.27341 + 0.463483i) q^{59} +(-3.95238 - 11.1229i) q^{60} +(0.492631 - 2.79385i) q^{61} +(5.08298 + 2.93466i) q^{62} +(-8.81007 - 2.97322i) q^{63} +(-6.51815 - 11.2898i) q^{64} +(1.87270 - 2.56682i) q^{65} +(-14.4422 - 6.52828i) q^{66} +(-0.983770 - 1.17241i) q^{67} +(12.4917 + 14.8870i) q^{68} +(0.827072 + 8.32183i) q^{69} +(-12.5790 - 9.17745i) q^{70} +(-7.47278 - 12.9432i) q^{71} +(5.51597 + 4.41099i) q^{72} +(6.31067 + 3.64347i) q^{73} +(0.245765 - 1.39380i) q^{74} +(-3.44607 - 7.94510i) q^{75} +(9.14833 + 3.32972i) q^{76} +(-12.4315 + 2.19201i) q^{77} +(-0.416937 + 5.51386i) q^{78} +(-0.125585 - 0.105378i) q^{79} +(-1.00521 - 1.49670i) q^{80} +(8.59299 + 2.67593i) q^{81} -13.2236i q^{82} +(-2.27365 + 2.70963i) q^{83} +(16.3154 + 1.23370i) q^{84} +(9.88373 + 10.2757i) q^{85} +(-18.6324 - 6.78165i) q^{86} +(4.54833 - 4.65691i) q^{87} +(9.44275 + 1.66501i) q^{88} +(-7.60870 + 13.1787i) q^{89} +(12.3817 + 8.59343i) q^{90} +(2.20206 + 3.81409i) q^{91} +(-5.03313 - 13.8284i) q^{92} +(-4.50257 + 0.447492i) q^{93} +(14.3931 - 12.0773i) q^{94} +(6.86183 + 1.98236i) q^{95} +(10.2906 + 4.65161i) q^{96} +(4.59453 + 12.6234i) q^{97} +(5.07132 - 2.92793i) q^{98} +(11.9794 - 2.40492i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

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 $

$2$	1.44418	−	1.72110i	1.02119	−	1.21700i	0.0452462	−	0.998976i	$-0.485593\pi$
$2$	1.44418	−	1.72110i	1.02119	−	1.21700i	0.975942	−	0.218029i	$-0.0699628\pi$
$3$	−0.130598	+	1.72712i	−0.0754008	+	0.997153i
$3$	−0.130598	+	1.72712i	−0.0754008	+	0.997153i
$4$	−0.529254	−	3.00155i	−0.264627	−	1.50078i
$5$	−0.536643	−	2.17072i	−0.239994	−	0.970774i
$5$	−0.536643	−	2.17072i	−0.239994	−	0.970774i
$6$	2.78395	+	2.71904i	1.13654	+	1.11004i
$7$	3.05233	+	0.538208i	1.15367	+	0.203423i	0.717578	−	0.696478i	$-0.245251\pi$
$7$	3.05233	+	0.538208i	1.15367	+	0.203423i	0.436093	+	0.899901i	$0.356362\pi$
$8$	−2.03885	−	1.17713i	−0.720841	−	0.416178i
$9$	−2.96589	−	0.451117i	−0.988629	−	0.150372i
$10$	−4.51104	−	2.21129i	−1.42652	−	0.699270i
$11$	−3.82718	+	1.39298i	−1.15394	+	0.419999i	−0.846928	−	0.531707i	$-0.821551\pi$
$11$	−3.82718	+	1.39298i	−1.15394	+	0.419999i	−0.307010	+	0.951706i	$0.599328\pi$
$12$	5.25316	−	0.522089i	1.51646	−	0.150714i
$13$	0.913372	+	1.08851i	0.253324	+	0.301900i	0.877687	−	0.479235i	$-0.159086\pi$
$13$	0.913372	+	1.08851i	0.253324	+	0.301900i	−0.624363	+	0.781134i	$0.714641\pi$
$14$	5.33442	−	4.47611i	1.42568	−	1.19629i
$15$	3.81917	−	0.643355i	0.986107	−	0.166113i
$16$	0.757669	−	0.275769i	0.189417	−	0.0689423i
$17$	−5.52192	+	3.18808i	−1.33926	+	0.773224i	−0.986698	−	0.162564i	$-0.948024\pi$
$17$	−5.52192	+	3.18808i	−1.33926	+	0.773224i	−0.352565	+	0.935787i	$0.614690\pi$
$18$	−5.05969	+	4.45311i	−1.19258	+	1.04961i
$19$	−1.59710	+	2.76626i	−0.366400	+	0.634623i	−0.989000	−	0.147917i	$-0.952743\pi$
$19$	−1.59710	+	2.76626i	−0.366400	+	0.634623i	0.622600	+	0.782540i	$0.286076\pi$
$20$	−6.23150	+	2.75962i	−1.39341	+	0.617070i
$21$	−1.32818	+	5.20145i	−0.289832	+	1.13505i
$22$	−3.12967	+	8.59869i	−0.667247	+	1.83325i
$23$	4.75493	−	0.838423i	0.991472	−	0.174823i	0.345693	−	0.938348i	$-0.387644\pi$
$23$	4.75493	−	0.838423i	0.991472	−	0.174823i	0.645779	+	0.763525i	$0.276533\pi$
$24$	2.29931	−	3.36760i	0.469345	−	0.687409i
$25$	−4.42403	+	2.32980i	−0.884806	+	0.465960i
$26$	3.19252			0.626105
$27$	1.16647	−	5.06353i	0.224488	−	0.974477i
$28$		−	9.44656i		−	1.78523i
$29$	−2.87901	−	2.41578i	−0.534619	−	0.448599i	0.335074	−	0.942192i	$-0.391239\pi$
$29$	−2.87901	−	2.41578i	−0.534619	−	0.448599i	−0.869693	+	0.493593i	$0.835683\pi$
$30$	4.40829	−	7.50232i	0.804840	−	1.36973i
$31$	0.453633	+	2.57268i	0.0814749	+	0.462067i	0.998062	+	0.0622314i	$0.0198217\pi$
$31$	0.453633	+	2.57268i	0.0814749	+	0.462067i	−0.916587	+	0.399836i	$0.869067\pi$
$32$	2.22999	−	6.12685i	0.394210	−	1.08308i
$33$	−1.90602	−	6.79192i	−0.331796	−	1.18232i
$34$	−2.48762	+	14.1080i	−0.426623	+	2.41950i
$35$	−0.469712	−	6.91457i	−0.0793958	−	1.16878i
$36$	0.215659	+	9.14102i	0.0359431	+	1.52350i
$37$	0.545540	−	0.314968i	0.0896863	−	0.0517804i	−0.454486	−	0.890754i	$-0.650177\pi$
$37$	0.545540	−	0.314968i	0.0896863	−	0.0517804i	0.544172	+	0.838973i	$0.316844\pi$
$38$	2.45452	+	6.74374i	0.398176	+	1.09398i
$39$	−1.99928	+	1.43535i	−0.320141	+	0.229839i
$40$	−1.46108	+	5.05746i	−0.231017	+	0.799655i
$41$	4.50871	−	3.78325i	0.704142	−	0.590845i	−0.218807	−	0.975768i	$-0.570217\pi$
$41$	4.50871	−	3.78325i	0.704142	−	0.590845i	0.922949	+	0.384923i	$0.125772\pi$
$42$	7.03411	+	9.79775i	1.08539	+	1.51183i
$43$	−3.01843	−	8.29308i	−0.460307	−	1.26468i	−0.925255	−	0.379345i	$-0.876149\pi$
$43$	−3.01843	−	8.29308i	−0.460307	−	1.26468i	0.464948	−	0.885338i	$-0.346073\pi$
$44$	6.20665	+	10.7502i	0.935687	+	1.62066i
$45$	0.612374	+	6.68019i	0.0912874	+	0.995825i
$46$	5.42396	−	9.39457i	0.799719	−	1.38515i
$47$	8.23568	+	1.45217i	1.20130	+	0.211821i	0.738259	−	0.674517i	$-0.235648\pi$
$47$	8.23568	+	1.45217i	1.20130	+	0.211821i	0.463038	+	0.886338i	$0.346759\pi$
$48$	0.377336	+	1.34460i	0.0544638	+	0.194076i
$49$	2.44919	+	0.891433i	0.349884	+	0.127348i
$50$	−2.37926	+	10.9789i	−0.336478	+	1.55265i
$51$	−4.78505	−	9.95338i	−0.670041	−	1.39375i
$52$	2.78382	−	3.31763i	0.386047	−	0.460073i
$53$		−	0.0211636i		−	0.00290705i	−0.999999	−	0.00145352i	$-0.999537\pi$
$53$		−	0.0211636i		−	0.00290705i	0.999999	−	0.00145352i	$-0.000462671\pi$
$54$	−7.03027	−	9.32026i	−0.956699	−	1.26833i
$55$	5.07759	+	7.56019i	0.684662	+	1.01942i
$56$	−5.58969	−	4.69031i	−0.746954	−	0.626769i
$57$	−4.56908	−	3.11965i	−0.605189	−	0.413208i
$58$	−8.31562	+	1.46627i	−1.09189	+	0.192530i
$59$	1.27341	+	0.463483i	0.165784	+	0.0603403i	0.423579	−	0.905859i	$-0.360774\pi$
$59$	1.27341	+	0.463483i	0.165784	+	0.0603403i	−0.257795	+	0.966200i	$0.582996\pi$
$60$	−3.95238	−	11.1229i	−0.510250	−	1.43597i
$61$	0.492631	−	2.79385i	0.0630749	−	0.357715i	−0.936892	−	0.349618i	$-0.886311\pi$
$61$	0.492631	−	2.79385i	0.0630749	−	0.357715i	0.999967	−	0.00809745i	$-0.00257753\pi$
$62$	5.08298	+	2.93466i	0.645539	+	0.372702i
$63$	−8.81007	−	2.97322i	−1.10996	−	0.374591i
$64$	−6.51815	−	11.2898i	−0.814768	−	1.41122i
$65$	1.87270	−	2.56682i	0.232280	−	0.318374i
$66$	−14.4422	−	6.52828i	−1.77772	−	0.803576i
$67$	−0.983770	−	1.17241i	−0.120187	−	0.143233i	0.702596	−	0.711589i	$-0.252024\pi$
$67$	−0.983770	−	1.17241i	−0.120187	−	0.143233i	−0.822783	+	0.568356i	$0.807580\pi$
$68$	12.4917	+	14.8870i	1.51484	+	1.80532i
$69$	0.827072	+	8.32183i	0.0995678	+	1.00183i
$70$	−12.5790	−	9.17745i	−1.50348	−	1.09691i
$71$	−7.47278	−	12.9432i	−0.886856	−	1.53608i	−0.843572	−	0.537016i	$-0.819551\pi$
$71$	−7.47278	−	12.9432i	−0.886856	−	1.53608i	−0.0432839	−	0.999063i	$-0.513782\pi$
$72$	5.51597	+	4.41099i	0.650063	+	0.519840i
$73$	6.31067	+	3.64347i	0.738609	+	0.426436i	0.821563	−	0.570117i	$-0.193102\pi$
$73$	6.31067	+	3.64347i	0.738609	+	0.426436i	−0.0829546	+	0.996553i	$0.526436\pi$
$74$	0.245765	−	1.39380i	0.0285696	−	0.162026i
$75$	−3.44607	−	7.94510i	−0.397918	−	0.917421i
$76$	9.14833	+	3.32972i	1.04939	+	0.381945i
$77$	−12.4315	+	2.19201i	−1.41670	+	0.249803i
$78$	−0.416937	+	5.51386i	−0.0472088	+	0.624322i
$79$	−0.125585	−	0.105378i	−0.0141294	−	0.0118560i	0.635696	−	0.771940i	$-0.280713\pi$
$79$	−0.125585	−	0.105378i	−0.0141294	−	0.0118560i	−0.649825	+	0.760084i	$0.725158\pi$
$80$	−1.00521	−	1.49670i	−0.112386	−	0.167336i
$81$	8.59299	+	2.67593i	0.954776	+	0.297325i
$82$		−	13.2236i		−	1.46031i
$83$	−2.27365	+	2.70963i	−0.249565	+	0.297420i	−0.876254	−	0.481849i	$-0.839965\pi$
$83$	−2.27365	+	2.70963i	−0.249565	+	0.297420i	0.626689	+	0.779270i	$0.284410\pi$
$84$	16.3154	+	1.23370i	1.78015	+	0.134608i
$85$	9.88373	+	10.2757i	1.07204	+	1.11455i
$86$	−18.6324	−	6.78165i	−2.00919	−	0.731284i
$87$	4.54833	−	4.65691i	0.487633	−	0.499273i
$88$	9.44275	+	1.66501i	1.00660	+	0.177491i
$89$	−7.60870	+	13.1787i	−0.806520	+	1.39693i	0.108739	+	0.994070i	$0.465319\pi$
$89$	−7.60870	+	13.1787i	−0.806520	+	1.39693i	−0.915260	+	0.402864i	$0.868015\pi$
$90$	12.3817	+	8.59343i	1.30515	+	0.905827i
$91$	2.20206	+	3.81409i	0.230839	+	0.399825i
$92$	−5.03313	−	13.8284i	−0.524741	−	1.44171i
$93$	−4.50257	+	0.447492i	−0.466895	+	0.0464027i
$94$	14.3931	−	12.0773i	1.48454	−	1.24568i
$95$	6.86183	+	1.98236i	0.704009	+	0.203386i
$96$	10.2906	+	4.65161i	1.05028	+	0.474753i
$97$	4.59453	+	12.6234i	0.466504	+	1.28171i	0.920513	+	0.390711i	$0.127771\pi$
$97$	4.59453	+	12.6234i	0.466504	+	1.28171i	−0.454010	+	0.890997i	$0.650007\pi$
$98$	5.07132	−	2.92793i	0.512280	−	0.295765i
$99$	11.9794	−	2.40492i	1.20397	−	0.241703i
$100$	9.33444	+	12.0459i	0.933444	+	1.20459i
$101$	0.0288119	−	0.163400i	0.00286689	−	0.0162590i	−0.983341	−	0.181772i	$-0.941817\pi$
$101$	0.0288119	−	0.163400i	0.00286689	−	0.0162590i	0.986208	+	0.165513i	$0.0529279\pi$
$102$	−24.0413	−	6.13888i	−2.38044	−	0.607840i
$103$	3.82931	−	10.5209i	0.377313	−	1.03666i	−0.595153	−	0.803612i	$-0.702909\pi$
$103$	3.82931	−	10.5209i	0.377313	−	1.03666i	0.972466	−	0.233046i	$-0.0748692\pi$
$104$	−0.580904	−	3.29447i	−0.0569623	−	0.323049i
$105$	12.0036	+	0.0917800i	1.17143	+	0.00895681i
$106$	−0.0364248	−	0.0305641i	−0.00353789	−	0.00296864i
$107$			14.7326i			1.42426i	0.702048	+	0.712130i	$0.252269\pi$
$107$			14.7326i			1.42426i	−0.702048	+	0.712130i	$0.747731\pi$
$108$	−15.8158	−	0.821330i	−1.52188	−	0.0790325i
$109$	−11.6642			−1.11723			−0.558614	−	0.829428i	$-0.688667\pi$
$109$	−11.6642			−1.11723			−0.558614	+	0.829428i	$0.688667\pi$
$110$	20.3448	+	2.17920i	1.93980	+	0.207779i
$111$	0.472741	+	0.983348i	0.0448706	+	0.0933352i
$112$	2.46108	−	0.433954i	0.232550	−	0.0410048i
$113$	3.19851	−	8.78785i	0.300891	−	0.826691i	−0.693455	−	0.720500i	$-0.743912\pi$
$113$	3.19851	−	8.78785i	0.300891	−	0.826691i	0.994346	−	0.106191i	$-0.0338655\pi$
$114$	−11.9678	+	3.35853i	−1.12089	+	0.314556i
$115$	−4.37168	−	9.87168i	−0.407661	−	0.920539i
$116$	−5.72735	+	9.92006i	−0.531771	+	0.921055i
$117$	−2.21791	−	3.64045i	−0.205046	−	0.336560i
$118$	2.63673	−	1.52232i	0.242731	−	0.140141i
$119$	−18.5706	+	6.75913i	−1.70236	+	0.619609i
$120$	−8.54403	−	3.18396i	−0.779959	−	0.290654i
$121$	4.28042	−	3.59170i	0.389129	−	0.326518i
$122$	−4.09706	−	4.88268i	−0.370930	−	0.442057i
$123$	5.94531	+	8.28116i	0.536070	+	0.746687i
$124$	7.48194	−	2.72320i	0.671898	−	0.244551i
$125$	7.43146	+	8.35305i	0.664690	+	0.747119i
$126$	−17.8405	+	10.8692i	−1.58936	+	0.968305i
$127$	10.0122	+	5.78057i	0.888442	+	0.512942i	0.873433	−	0.486945i	$-0.161889\pi$
$127$	10.0122	+	5.78057i	0.888442	+	0.512942i	0.0150095	+	0.999887i	$0.495222\pi$
$128$	−16.0022	−	2.82163i	−1.41441	−	0.249399i
$129$	14.7173	−	4.13014i	1.29579	−	0.363638i
$130$	−1.71324	−	6.93006i	−0.150261	−	0.607806i
$131$	0.712124	+	4.03865i	0.0622185	+	0.352859i	0.999984	+	0.00559058i	$0.00177955\pi$
$131$	0.712124	+	4.03865i	0.0622185	+	0.352859i	−0.937766	+	0.347268i	$0.887109\pi$
$132$	−19.3775	+	9.31567i	−1.68660	+	0.810825i
$133$	−6.36369	+	7.58395i	−0.551802	+	0.657612i
$134$	−3.43858			−0.297048
$135$	−11.6175	+	0.185224i	−0.999873	+	0.0159415i
$136$	15.0111			1.28719
$137$	−2.50031	+	2.97975i	−0.213616	+	0.254577i	−0.862203	−	0.506563i	$-0.830916\pi$
$137$	−2.50031	+	2.97975i	−0.213616	+	0.254577i	0.648587	+	0.761140i	$0.275360\pi$
$138$	15.5172	+	10.5947i	1.32091	+	0.901884i
$139$	−2.01943	−	11.4528i	−0.171286	−	0.971411i	−0.942344	−	0.334646i	$-0.891383\pi$
$139$	−2.01943	−	11.4528i	−0.171286	−	0.971411i	0.771058	−	0.636765i	$-0.219728\pi$
$140$	−20.5058	+	5.06943i	−1.73306	+	0.428445i
$141$	−3.58364	+	14.0344i	−0.301797	+	1.18191i
$142$	−33.0687	−	5.83090i	−2.77506	−	0.489318i
$143$	−5.01191	−	2.89363i	−0.419117	−	0.241978i
$144$	−2.37157	+	0.476103i	−0.197631	+	0.0396752i
$145$	−3.69897	+	7.54593i	−0.307183	+	0.626656i
$146$	15.3845	−	5.59951i	1.27323	−	0.463419i
$147$	−1.85947	+	4.11363i	−0.153367	+	0.339286i
$148$	−1.23412	−	1.47077i	−0.101444	−	0.120896i
$149$	11.8482	−	9.94186i	0.970646	−	0.814469i	−0.0120057	−	0.999928i	$-0.503822\pi$
$149$	11.8482	−	9.94186i	0.970646	−	0.814469i	0.982652	+	0.185459i	$0.0593772\pi$
$150$	−18.6511	−	5.54309i	−1.52286	−	0.452591i
$151$	1.76007	−	0.640613i	0.143232	−	0.0521324i	−0.269409	−	0.963026i	$-0.586828\pi$
$151$	1.76007	−	0.640613i	0.143232	−	0.0521324i	0.412642	+	0.910893i	$0.364606\pi$
$152$	6.51248	−	3.75998i	0.528232	−	0.304975i
$153$	17.8156	−	6.96447i	1.44031	−	0.563044i
$154$	−14.1806	+	24.5616i	−1.14271	+	1.97923i
$155$	5.34112	−	2.36532i	0.429009	−	0.189987i
$156$	5.36639	+	5.24127i	0.429655	+	0.419638i
$157$	4.56652	−	12.5464i	0.364448	−	1.00131i	−0.612990	−	0.790091i	$-0.710033\pi$
$157$	4.56652	−	12.5464i	0.364448	−	1.00131i	0.977438	−	0.211222i	$-0.0677443\pi$
$158$	−0.362734	+	0.0639599i	−0.0288576	+	0.00508837i
$159$	0.0365521	+	0.00276393i	0.00289877	+	0.000219194i
$160$	−14.4964	−	1.55275i	−1.14604	−	0.122756i
$161$	14.9649			1.17940
$162$	17.0154	−	10.9249i	1.33685	−	0.858343i
$163$		−	3.85821i		−	0.302199i	−0.988519	−	0.151099i	$-0.951719\pi$
$163$		−	3.85821i		−	0.302199i	0.988519	−	0.151099i	$-0.0482813\pi$
$164$	−13.7419	−	11.5308i	−1.07306	−	0.900404i
$165$	−13.7205	+	7.78226i	−1.06814	+	0.605848i
$166$	1.38000	+	7.82637i	0.107109	+	0.607444i
$167$	−3.90890	+	10.7396i	−0.302480	+	0.831056i	0.691588	+	0.722292i	$0.256911\pi$
$167$	−3.90890	+	10.7396i	−0.302480	+	0.831056i	−0.994068	+	0.108764i	$0.965311\pi$
$168$	8.83073	−	9.04152i	0.681305	−	0.697569i
$169$	1.90681	−	10.8141i	0.146678	−	0.831851i
$170$	31.9594	−	2.17103i	2.45117	−	0.166510i
$171$	5.98472	−	7.48393i	0.457663	−	0.572310i
$172$	−23.2946	+	13.4491i	−1.77619	+	1.02549i
$173$	−3.15219	−	8.66057i	−0.239657	−	0.658451i	−0.999961	−	0.00888346i	$-0.997172\pi$
$173$	−3.15219	−	8.66057i	−0.239657	−	0.658451i	0.760304	−	0.649567i	$-0.225050\pi$
$174$	−1.44642	−	14.5536i	−0.109653	−	1.10330i
$175$	−14.7575	+	4.73026i	−1.11556	+	0.357574i
$176$	−2.51560	+	2.11083i	−0.189620	+	0.159110i
$177$	−0.966795	+	2.13880i	−0.0726687	+	0.160762i
$178$	11.6935	+	32.1277i	0.876467	+	2.40807i
$179$	9.71972	+	16.8351i	0.726486	+	1.25831i	0.958359	+	0.285565i	$0.0921812\pi$
$179$	9.71972	+	16.8351i	0.726486	+	1.25831i	−0.231873	+	0.972746i	$0.574485\pi$
$180$	19.7268	−	5.37359i	1.47035	−	0.400524i
$181$	−11.4591	+	19.8477i	−0.851748	+	1.47527i	0.0278814	+	0.999611i	$0.491124\pi$
$181$	−11.4591	+	19.8477i	−0.851748	+	1.47527i	−0.879629	+	0.475660i	$0.842209\pi$
$182$	9.74462	+	1.71824i	0.722319	+	0.127364i
$183$	4.76097	+	1.21570i	0.351941	+	0.0898674i
$184$	−10.6815	−	3.88775i	−0.787451	−	0.286609i
$185$	−0.976466	−	1.01519i	−0.0717912	−	0.0746382i
$186$	−5.73234	+	8.39566i	−0.420315	+	0.615599i
$187$	16.6924	−	19.8933i	1.22067	−	1.45474i
$188$		−	25.4884i		−	1.85893i
$189$	6.28569	−	14.8278i	0.457217	−	1.07856i
$190$	13.3216	−	8.94705i	0.966447	−	0.649087i
$191$	17.8815	+	15.0043i	1.29386	+	1.08567i	0.991172	+	0.132584i	$0.0423273\pi$
$191$	17.8815	+	15.0043i	1.29386	+	1.08567i	0.302685	+	0.953091i	$0.402117\pi$
$192$	20.3500	−	9.78320i	1.46864	−	0.706042i
$193$	−13.2329	+	2.33332i	−0.952525	+	0.167956i	−0.628254	−	0.778008i	$-0.716230\pi$
$193$	−13.2329	+	2.33332i	−0.952525	+	0.167956i	−0.324271	+	0.945964i	$0.605119\pi$
$194$	28.3614	+	10.3227i	2.03623	+	0.741128i
$195$	4.18863	+	3.56960i	0.299954	+	0.255625i
$196$	1.37943	−	7.82316i	0.0985311	−	0.558797i
$197$	−7.47271	−	4.31437i	−0.532409	−	0.307386i	0.209588	−	0.977790i	$-0.432788\pi$
$197$	−7.47271	−	4.31437i	−0.532409	−	0.307386i	−0.741997	+	0.670403i	$0.766121\pi$
$198$	13.1613	−	24.0909i	0.935330	−	1.71207i
$199$	−2.82835	−	4.89885i	−0.200496	−	0.347270i	0.748192	−	0.663482i	$-0.230922\pi$
$199$	−2.82835	−	4.89885i	−0.200496	−	0.347270i	−0.948688	+	0.316212i	$0.897589\pi$
$200$	11.7624	+	0.457550i	0.831727	+	0.0323537i
$201$	2.15337	−	1.54597i	0.151887	−	0.109045i
$202$	−0.239620	−	0.285568i	−0.0168596	−	0.0200925i
$203$	−7.48750	−	8.92326i	−0.525520	−	0.626290i
$204$	−27.3431	+	19.6304i	−1.91440	+	1.37441i
$205$	−10.6319	−	7.75687i	−0.742567	−	0.541763i
$206$	−12.5774	−	21.7847i	−0.876311	−	1.51781i
$207$	−14.4808	+	0.341638i	−1.00649	+	0.0237455i
$208$	0.992212	+	0.572854i	0.0687975	+	0.0397203i
$209$	2.25904	−	12.8117i	0.156261	−	0.886202i
$210$	17.4934	−	20.5270i	1.20716	−	1.41650i
$211$	−8.36219	−	3.04359i	−0.575677	−	0.209529i	0.0377412	−	0.999288i	$-0.487984\pi$
$211$	−8.36219	−	3.04359i	−0.575677	−	0.209529i	−0.613418	+	0.789758i	$0.710206\pi$
$212$	−0.0635237	+	0.0112009i	−0.00436283	+	0.000769284i
$213$	23.3304	−	11.2160i	1.59858	−	0.768510i
$214$	25.3564	+	21.2766i	1.73333	+	1.45444i
$215$	−16.3821	+	11.0026i	−1.11725	+	0.750370i
$216$	−8.33869	+	8.95068i	−0.567376	+	0.609016i
$217$			8.09681i			0.549647i
$218$	−16.8452	+	20.0753i	−1.14090	+	1.35967i
$219$	−7.11687	+	10.4235i	−0.480914	+	0.704352i
$220$	20.0050	−	19.2419i	1.34873	−	1.29729i
$221$	−8.51384	−	3.09879i	−0.572703	−	0.208447i
$222$	2.37517	+	0.606493i	0.159411	+	0.0407052i
$223$	11.6752	+	2.05865i	0.781828	+	0.137857i	0.550296	−	0.834970i	$-0.314515\pi$
$223$	11.6752	+	2.05865i	0.781828	+	0.137857i	0.231532	+	0.972827i	$0.425626\pi$
$224$	10.1042	−	17.5009i	0.675114	−	1.16933i
$225$	14.1722	−	4.91417i	0.944813	−	0.327611i
$226$	−10.5056	−	18.1962i	−0.698821	−	1.21039i
$227$	−1.83504	−	5.04173i	−0.121796	−	0.334632i	0.863779	−	0.503871i	$-0.168091\pi$
$227$	−1.83504	−	5.04173i	−0.121796	−	0.334632i	−0.985575	+	0.169239i	$0.945869\pi$
$228$	−6.94558	+	15.3654i	−0.459982	+	1.01760i
$229$	−16.3024	+	13.6794i	−1.07729	+	0.903957i	−0.995693	−	0.0927078i	$-0.970448\pi$
$229$	−16.3024	+	13.6794i	−1.07729	+	0.903957i	−0.0816010	+	0.996665i	$0.526003\pi$
$230$	−23.3037	−	6.73235i	−1.53660	−	0.443918i
$231$	−2.16234	−	21.7570i	−0.142271	−	1.43151i
$232$	3.02618	+	8.31437i	0.198679	+	0.545865i
$233$	−11.8157	+	6.82178i	−0.774070	+	0.446910i	−0.834325	−	0.551273i	$-0.814142\pi$
$233$	−11.8157	+	6.82178i	−0.774070	+	0.446910i	0.0602544	+	0.998183i	$0.480809\pi$
$234$	−9.46866	−	1.44020i	−0.618985	−	0.0941488i
$235$	−1.26736	−	18.6566i	−0.0826734	−	1.21702i
$236$	0.717210	−	4.06750i	0.0466864	−	0.264772i
$237$	0.198402	−	0.203138i	0.0128876	−	0.0131952i
$238$	−15.1860	+	41.7233i	−0.984365	+	2.70452i
$239$	−0.995338	−	5.64484i	−0.0643831	−	0.365135i	−0.999929	−	0.0119291i	$-0.996203\pi$
$239$	−0.995338	−	5.64484i	−0.0643831	−	0.365135i	0.935546	−	0.353205i	$-0.114908\pi$
$240$	2.71625	−	1.54066i	0.175333	−	0.0994492i
$241$	0.0608128	+	0.0510280i	0.00391730	+	0.00328700i	0.644744	−	0.764398i	$-0.276964\pi$
$241$	0.0608128	+	0.0510280i	0.00391730	+	0.00328700i	−0.640827	+	0.767685i	$0.721408\pi$
$242$		−	12.5541i		−	0.807008i
$243$	−5.74387	+	14.4917i	−0.368470	+	0.929640i
$244$	−8.64660			−0.553542
$245$	0.620708	−	5.79488i	0.0396556	−	0.370221i
$246$	22.8388	+	1.72698i	1.45615	+	0.110108i
$247$	−4.46985	+	0.788156i	−0.284410	+	0.0501492i
$248$	2.10349	−	5.77929i	0.133572	−	0.366985i
$249$	−4.38292	−	4.28074i	−0.277756	−	0.271281i
$250$	25.1088	−	0.727023i	1.58802	−	0.0459810i
$251$	0.946229	−	1.63892i	0.0597255	−	0.103448i	−0.834617	−	0.550831i	$-0.814311\pi$
$251$	0.946229	−	1.63892i	0.0597255	−	0.103448i	0.894342	+	0.447384i	$0.147644\pi$
$252$	−4.26151	+	28.0175i	−0.268450	+	1.76493i
$253$	−17.0301	+	9.83231i	−1.07067	+	0.618152i
$254$	24.4084	−	8.88394i	1.53152	−	0.557428i
$255$	−19.0381	+	15.7284i	−1.19221	+	0.984951i
$256$	−7.99364	+	6.70746i	−0.499602	+	0.419216i
$257$	6.36138	+	7.58119i	0.396812	+	0.472902i	0.927045	−	0.374950i	$-0.122340\pi$
$257$	6.36138	+	7.58119i	0.396812	+	0.472902i	−0.530233	+	0.847852i	$0.677896\pi$
$258$	14.1461	−	31.2948i	0.880696	−	1.94833i
$259$	1.83469	−	0.667771i	0.114002	−	0.0414933i
$260$	−8.69556	−	4.26251i	−0.539276	−	0.264350i
$261$	7.44903	+	8.46370i	0.461083	+	0.523890i
$262$	7.97938	+	4.60690i	0.492968	+	0.284615i
$263$	12.3333	+	2.17469i	0.760503	+	0.134097i	0.540433	−	0.841387i	$-0.318260\pi$
$263$	12.3333	+	2.17469i	0.760503	+	0.134097i	0.220070	+	0.975484i	$0.429371\pi$
$264$	−4.10888	+	16.0913i	−0.252884	+	0.990352i
$265$	−0.0459403	+	0.0113573i	−0.00282209	+	0.000697674i
$266$	3.86247	+	21.9052i	0.236823	+	1.34309i
$267$	−21.7674	−	14.8622i	−1.33215	−	0.909554i
$268$	−2.99839	+	3.57334i	−0.183156	+	0.218276i
$269$	−12.2764			−0.748505			−0.374253	−	0.927327i	$-0.622101\pi$
$269$	−12.2764			−0.748505			−0.374253	+	0.927327i	$0.622101\pi$
$270$	−16.4589	+	20.2624i	−1.00166	+	1.23313i
$271$	22.6640			1.37674			0.688369	−	0.725360i	$-0.258327\pi$
$271$	22.6640			1.37674			0.688369	+	0.725360i	$0.258327\pi$
$272$	−3.30462	+	3.93829i	−0.200372	+	0.238794i
$273$	−6.87497	+	3.30512i	−0.416092	+	0.200035i
$274$	1.51757	+	8.60658i	0.0916799	+	0.519943i
$275$	13.6862	−	15.0791i	0.825308	−	0.909306i
$276$	24.5407	−	6.88686i	1.47717	−	0.414541i
$277$	−16.7823	−	2.95917i	−1.00835	−	0.177799i	−0.355008	−	0.934863i	$-0.615522\pi$
$277$	−16.7823	−	2.95917i	−1.00835	−	0.177799i	−0.653340	+	0.757064i	$0.726633\pi$
$278$	−22.6278	−	13.0642i	−1.35713	−	0.783538i
$279$	−0.184845	−	7.83492i	−0.0110664	−	0.469065i
$280$	−7.18167	+	14.6507i	−0.429187	+	0.875544i
$281$	−14.6357	+	5.32695i	−0.873092	+	0.317779i	−0.739419	−	0.673246i	$-0.764899\pi$
$281$	−14.6357	+	5.32695i	−0.873092	+	0.317779i	−0.133673	+	0.991025i	$0.542677\pi$
$282$	18.9792	+	26.4359i	1.13019	+	1.57424i
$283$	−0.444412	−	0.529629i	−0.0264175	−	0.0314832i	0.752674	−	0.658393i	$-0.228764\pi$
$283$	−0.444412	−	0.529629i	−0.0264175	−	0.0314832i	−0.779091	+	0.626910i	$0.784319\pi$
$284$	−34.8948	+	29.2802i	−2.07062	+	1.73746i
$285$	−4.31991	+	11.5923i	−0.255890	+	0.686669i
$286$	−12.2183	+	4.44711i	−0.722486	+	0.262963i
$287$	15.7982	−	9.12111i	0.932540	−	0.538402i
$288$	−9.37782	+	17.1656i	−0.552594	+	1.01149i
$289$	11.8278	−	20.4863i	0.695750	−	1.20507i
$290$	7.64537	+	17.2640i	0.448951	+	1.01378i
$291$	−22.4021	+	6.28671i	−1.31323	+	0.368534i
$292$	7.59611	−	20.8701i	0.444528	−	1.22133i
$293$	12.5882	−	2.21964i	0.735412	−	0.129673i	0.206616	−	0.978422i	$-0.433755\pi$
$293$	12.5882	−	2.21964i	0.735412	−	0.129673i	0.528796	+	0.848749i	$0.322644\pi$
$294$	4.39458	+	9.14116i	0.256297	+	0.533123i
$295$	0.322725	−	3.01293i	0.0187898	−	0.175420i
$296$	−1.48303			−0.0861994
$297$	2.58909	+	21.0039i	0.150234	+	1.21877i
$298$		−	34.7499i		−	2.01301i
$299$	5.25566	+	4.41002i	0.303942	+	0.255038i
$300$	−22.0238	+	14.5485i	−1.27154	+	0.839960i
$301$	−4.74985	−	26.9377i	−0.273777	−	1.55267i
$302$	1.43929	−	3.95443i	0.0828220	−	0.227552i
$303$	0.278449	+	0.0711014i	0.0159965	+	0.00408467i
$304$	−0.447225	+	2.53634i	−0.0256501	+	0.145469i
$305$	−6.32902	+	0.429935i	−0.362399	+	0.0246180i
$306$	13.7423	−	40.7205i	0.785597	−	2.32783i
$307$	9.19113	−	5.30650i	0.524565	−	0.302858i	−0.214235	−	0.976782i	$-0.568726\pi$
$307$	9.19113	−	5.30650i	0.524565	−	0.302858i	0.738801	+	0.673924i	$0.235393\pi$
$308$	13.1589	+	36.1537i	0.749796	+	2.06005i
$309$	17.6708	+	7.98768i	1.00526	+	0.454403i
$310$	3.64257	−	12.6086i	0.206884	−	0.716119i
$311$	−13.0581	+	10.9571i	−0.740459	+	0.621319i	−0.932961	−	0.359978i	$-0.882784\pi$
$311$	−13.0581	+	10.9571i	−0.740459	+	0.621319i	0.192502	+	0.981297i	$0.438340\pi$
$312$	5.76581	−	0.573040i	0.326425	−	0.0324420i
$313$	−0.206883	−	0.568405i	−0.0116937	−	0.0321282i	0.933708	−	0.358034i	$-0.116553\pi$
$313$	−0.206883	−	0.568405i	−0.0116937	−	0.0321282i	−0.945402	+	0.325906i	$0.894331\pi$
$314$	−14.9988	−	25.9787i	−0.846432	−	1.46606i
$315$	−1.72617	+	20.7197i	−0.0972584	+	1.16742i
$316$	−0.249832	+	0.432722i	−0.0140541	+	0.0243425i
$317$	−12.4805	−	2.20064i	−0.700972	−	0.123600i	−0.188207	−	0.982129i	$-0.560268\pi$
$317$	−12.4805	−	2.20064i	−0.700972	−	0.123600i	−0.512765	+	0.858529i	$0.671379\pi$
$318$	0.0575448	−	0.0589185i	0.00322695	−	0.00330398i
$319$	14.3836	+	5.23521i	0.805328	+	0.293116i
$320$	−21.0090	+	20.2076i	−1.17444	+	1.12964i
$321$	−25.4451	−	1.92406i	−1.42020	−	0.107390i
$322$	21.6119	−	25.7561i	1.20439	−	1.43533i
$323$		−	20.3667i		−	1.13324i
$324$	3.48405	−	27.2085i	0.193558	−	1.51158i
$325$	−6.57680	−	2.68765i	−0.364815	−	0.149084i
$326$	−6.64039	−	5.57195i	−0.367777	−	0.308602i
$327$	1.52332	−	20.1455i	0.0842399	−	1.11405i
$328$	−13.6459	+	2.40615i	−0.753471	+	0.132857i
$329$	24.3564	+	8.86501i	1.34281	+	0.488744i
$330$	−6.42074	+	34.8534i	−0.353450	+	1.91861i
$331$	0.660144	−	3.74386i	0.0362848	−	0.205781i	−0.961276	−	0.275588i	$-0.911127\pi$
$331$	0.660144	−	3.74386i	0.0362848	−	0.205781i	0.997560	+	0.0698073i	$0.0222384\pi$
$332$	9.33642	+	5.39039i	0.512403	+	0.295836i
$333$	−1.76010	+	0.688057i	−0.0964528	+	0.0377053i
$334$	12.8388	+	22.2375i	0.702510	+	1.21678i
$335$	−2.01704	+	2.76465i	−0.110203	+	0.151049i
$336$	0.428079	+	4.30725i	0.0233536	+	0.234980i
$337$	11.5608	+	13.7777i	0.629759	+	0.750517i	0.982715	−	0.185122i	$-0.0592681\pi$
$337$	11.5608	+	13.7777i	0.629759	+	0.750517i	−0.352957	+	0.935640i	$0.614824\pi$
$338$	−15.8584	−	18.8993i	−0.862581	−	1.02798i
$339$	14.7599	+	6.67189i	0.801650	+	0.362368i
$340$	25.6119	−	35.1049i	1.38900	−	1.90383i
$341$	−5.31982	−	9.21420i	−0.288085	−	0.498977i
$342$	−4.23762	−	21.1085i	−0.229144	−	1.14141i
$343$	−11.7932	−	6.80883i	−0.636776	−	0.367643i
$344$	−3.60790	+	20.4614i	−0.194525	+	1.10321i
$345$	17.6205	−	6.26119i	0.948656	−	0.337091i
$346$	−19.4581	−	7.08216i	−1.04607	−	0.380739i
$347$	24.7468	−	4.36354i	1.32848	−	0.234247i	0.536038	−	0.844194i	$-0.319920\pi$
$347$	24.7468	−	4.36354i	1.32848	−	0.234247i	0.792442	+	0.609947i	$0.208809\pi$
$348$	−16.3852	−	11.1874i	−0.878337	−	0.599706i
$349$	−7.80720	−	6.55102i	−0.417910	−	0.350668i	0.409458	−	0.912329i	$-0.365718\pi$
$349$	−7.80720	−	6.55102i	−0.417910	−	0.350668i	−0.827367	+	0.561661i	$0.810162\pi$
$350$	−13.1712	+	32.2306i	−0.704030	+	1.72280i
$351$	6.57715	−	3.35516i	0.351062	−	0.179085i
$352$			26.5549i			1.41538i
$353$	7.78298	−	9.27539i	0.414246	−	0.493679i	−0.518063	−	0.855343i	$-0.673347\pi$
$353$	7.78298	−	9.27539i	0.414246	−	0.493679i	0.932309	+	0.361663i	$0.117791\pi$
$354$	2.28487	+	4.75276i	0.121440	+	0.252606i
$355$	−24.0859	+	23.1672i	−1.27835	+	1.22959i
$356$	43.5833	+	15.8630i	2.30991	+	0.840739i
$357$	−9.24856	−	32.9563i	−0.489486	−	1.74423i
$358$	43.0119	+	7.58416i	2.27325	+	0.400835i
$359$	2.90522	−	5.03199i	0.153332	−	0.265578i	−0.779119	−	0.626876i	$-0.784333\pi$
$359$	2.90522	−	5.03199i	0.153332	−	0.265578i	0.932450	+	0.361298i	$0.117666\pi$
$360$	6.61491	−	14.3407i	0.348637	−	0.755823i
$361$	4.39855	+	7.61852i	0.231503	+	0.400975i
$362$	17.6111	+	48.3860i	0.925617	+	2.54311i
$363$	5.64428	+	7.86186i	0.296248	+	0.412641i
$364$	10.2827	−	8.62823i	0.538961	−	0.452242i
$365$	4.52237	−	15.6539i	0.236712	−	0.819364i
$366$	8.96805	−	6.43844i	0.468767	−	0.336543i
$367$	9.29149	+	25.5282i	0.485012	+	1.33256i	0.905147	+	0.425098i	$0.139760\pi$
$367$	9.29149	+	25.5282i	0.485012	+	1.33256i	−0.420135	+	0.907461i	$0.638017\pi$
$368$	3.37145	−	1.94651i	0.175749	−	0.101469i
$369$	−15.0790	+	9.18675i	−0.784982	+	0.478243i
$370$	−3.15744	+	0.214487i	−0.164147	+	0.0111507i
$371$	0.0113904	−	0.0645983i	0.000591362	−	0.00335378i
$372$	3.72617	+	13.2779i	0.193193	+	0.688425i
$373$	−1.43371	+	3.93908i	−0.0742346	+	0.203958i	−0.971260	−	0.238021i	$-0.923501\pi$
$373$	−1.43371	+	3.93908i	−0.0742346	+	0.203958i	0.897025	+	0.441979i	$0.145723\pi$
$374$	−10.1316	−	57.4589i	−0.523890	−	2.97113i
$375$	−15.3973	+	11.7441i	−0.795111	+	0.606464i
$376$	−15.0819	−	12.6552i	−0.777789	−	0.652643i
$377$		−	5.34035i		−	0.275042i
$378$	−16.4425	−	32.2323i	−0.845709	−	1.65785i
$379$	28.2695			1.45211			0.726053	−	0.687638i	$-0.241353\pi$
$379$	28.2695			1.45211			0.726053	+	0.687638i	$0.241353\pi$
$380$	2.31850	−	21.6453i	0.118936	−	1.11038i
$381$	−11.2913	+	16.5374i	−0.578471	+	0.847237i
$382$	51.6480	−	9.10694i	2.64254	−	0.465952i
$383$	−8.69809	+	23.8978i	−0.444452	+	1.22112i	0.492084	+	0.870548i	$0.336235\pi$
$383$	−8.69809	+	23.8978i	−0.444452	+	1.22112i	−0.936535	+	0.350573i	$0.885987\pi$
$384$	6.96315	−	27.2693i	0.355337	−	1.39158i
$385$	11.4295	+	25.8090i	0.582502	+	1.31535i
$386$	−15.0948	+	26.1449i	−0.768304	+	1.33074i
$387$	5.21119	+	25.9580i	0.264900	+	1.31952i
$388$	35.4580	−	20.4717i	1.80011	−	1.03929i
$389$	−13.3674	+	4.86533i	−0.677753	+	0.246682i	−0.657883	−	0.753121i	$-0.728548\pi$
$389$	−13.3674	+	4.86533i	−0.677753	+	0.246682i	−0.0198708	+	0.999803i	$0.506325\pi$
$390$	12.1928	−	2.05392i	0.617406	−	0.104004i
$391$	−23.5834	+	19.7888i	−1.19266	+	1.00076i
$392$	−3.94420	−	4.70051i	−0.199212	−	0.237412i
$393$	−7.06824	+	0.702483i	−0.356546	+	0.0354356i
$394$	−18.2174	+	6.63060i	−0.917780	+	0.334045i
$395$	−0.161352	+	0.329160i	−0.00811852	+	0.0165618i
$396$	−13.5586	−	34.6839i	−0.681346	−	1.74293i
$397$	−14.9271	−	8.61817i	−0.749170	−	0.432534i	0.0762236	−	0.997091i	$-0.475714\pi$
$397$	−14.9271	−	8.61817i	−0.749170	−	0.432534i	−0.825394	+	0.564557i	$0.809047\pi$
$398$	−12.5161	−	2.20692i	−0.627374	−	0.110623i
$399$	−12.2673	−	11.9813i	−0.614134	−	0.599816i
$400$	−2.70946	+	2.98523i	−0.135473	+	0.149261i
$401$	−4.14546	−	23.5101i	−0.207014	−	1.17404i	−0.894239	−	0.447591i	$-0.852282\pi$
$401$	−4.14546	−	23.5101i	−0.207014	−	1.17404i	0.687224	−	0.726445i	$-0.258829\pi$
$402$	0.449072	−	5.93884i	0.0223977	−	0.296203i
$403$	−2.38606	+	2.84360i	−0.118858	+	0.141650i
$404$	−0.505703			−0.0251597
$405$	1.19732	−	20.0890i	0.0594951	−	0.998229i
$406$	−26.1711			−1.29885
$407$	−1.64914	+	1.96536i	−0.0817447	+	0.0974195i
$408$	−1.96043	+	25.9260i	−0.0970555	+	1.28353i
$409$	−4.34439	−	24.6383i	−0.214816	−	1.21828i	−0.881225	−	0.472698i	$-0.843280\pi$
$409$	−4.34439	−	24.6383i	−0.214816	−	1.21828i	0.666408	−	0.745587i	$-0.267831\pi$
$410$	−28.7048	+	7.09637i	−1.41763	+	0.350465i
$411$	−4.81985	−	4.70748i	−0.237746	−	0.232203i
$412$	−33.6058	−	5.92561i	−1.65564	−	0.291934i
$413$	3.63741	+	2.10006i	0.178985	+	0.103337i
$414$	−20.3249	+	25.4164i	−0.998914	+	1.24915i
$415$	7.10197	+	3.48135i	0.348622	+	0.170893i
$416$	8.70597	−	3.16871i	0.426845	−	0.155359i
$417$	20.0440	−	1.99209i	0.981561	−	0.0975532i
$418$	−18.7878	−	22.3904i	−0.918940	−	1.09515i
$419$	−31.2600	+	26.2302i	−1.52715	+	1.28143i	−0.711996	+	0.702183i	$0.752209\pi$
$419$	−31.2600	+	26.2302i	−1.52715	+	1.28143i	−0.815152	+	0.579247i	$0.803347\pi$
$420$	−6.07749	−	36.0781i	−0.296551	−	1.76043i
$421$	31.2501	−	11.3741i	1.52304	−	0.554341i	0.561133	−	0.827725i	$-0.310365\pi$
$421$	31.2501	−	11.3741i	1.52304	−	0.554341i	0.961905	+	0.273385i	$0.0881433\pi$
$422$	−17.3148	+	9.99672i	−0.842873	+	0.486633i
$423$	−23.7710	−	8.02224i	−1.15579	−	0.390054i
$424$	−0.0249123	+	0.0431494i	−0.00120985	+	0.00209552i
$425$	17.0016	−	26.9691i	0.824697	−	1.30820i
$426$	14.3894	−	56.3521i	0.697167	−	2.73027i
$427$	3.00734	−	8.26260i	0.145535	−	0.399855i
$428$	44.2208	−	7.79732i	2.13749	−	0.376898i
$429$	5.65219	−	8.27828i	0.272890	−	0.399679i
$430$	−4.72209	+	44.0850i	−0.227719	+	2.12597i
$431$	30.6282			1.47531			0.737655	−	0.675178i	$-0.235933\pi$
$431$	30.6282			1.47531			0.737655	+	0.675178i	$0.235933\pi$
$432$	−0.512565	−	4.15816i	−0.0246608	−	0.200059i
$433$		−	18.8590i		−	0.906306i	−0.891433	−	0.453153i	$-0.850299\pi$
$433$		−	18.8590i		−	0.906306i	0.891433	−	0.453153i	$-0.149701\pi$
$434$	13.9355	+	11.6932i	0.668924	+	0.561294i
$435$	−12.5497	−	7.37405i	−0.601710	−	0.353559i
$436$	6.17333	+	35.0107i	0.295649	+	1.67671i
$437$	−5.27480	+	14.4924i	−0.252328	+	0.693265i
$438$	7.66184	+	27.3022i	0.366097	+	1.30455i
$439$	1.35713	−	7.69667i	0.0647723	−	0.367342i	−0.935142	−	0.354272i	$-0.884729\pi$
$439$	1.35713	−	7.69667i	0.0647723	−	0.367342i	0.999915	−	0.0130696i	$-0.00416029\pi$
$440$	−1.45311	−	21.3911i	−0.0692744	−	1.01978i
$441$	−6.86189	−	3.74876i	−0.326757	−	0.178512i
$442$	−17.6288	+	10.1780i	−0.838519	+	0.484119i
$443$	1.62187	+	4.45605i	0.0770574	+	0.211713i	0.972240	−	0.233986i	$-0.0751771\pi$
$443$	1.62187	+	4.45605i	0.0770574	+	0.211713i	−0.895183	+	0.445700i	$0.852955\pi$
$444$	2.70137	−	1.93940i	0.128201	−	0.0920397i
$445$	32.6903	+	9.44411i	1.54967	+	0.447694i
$446$	20.4042	−	17.1211i	0.966166	−	0.810710i
$447$	15.6234	+	21.7617i	0.738963	+	1.02929i
$448$	−13.8193	−	37.9682i	−0.652900	−	1.79383i
$449$	4.94736	+	8.56908i	0.233480	+	0.404400i	0.958830	−	0.283981i	$-0.0916552\pi$
$449$	4.94736	+	8.56908i	0.233480	+	0.404400i	−0.725350	+	0.688381i	$0.758322\pi$
$450$	12.0094	−	31.4888i	0.566127	−	1.48439i
$451$	−11.9856	+	20.7597i	−0.564381	+	0.977537i
$452$	−28.0700	−	4.94950i	−1.32030	−	0.232805i
$453$	0.876554	+	3.12352i	0.0411841	+	0.146756i
$454$	−11.3275	−	4.12287i	−0.531625	−	0.193496i
$455$	7.09758	−	6.82686i	0.332740	−	0.320048i
$456$	5.64342	+	11.7389i	0.264278	+	0.549724i
$457$	−9.38146	+	11.1804i	−0.438846	+	0.522997i	−0.939453	−	0.342678i	$-0.888666\pi$
$457$	−9.38146	+	11.1804i	−0.438846	+	0.522997i	0.500607	+	0.865675i	$0.333110\pi$
$458$			47.8136i			2.23418i
$459$	9.70179	+	31.6792i	0.452841	+	1.47866i
$460$	−27.3166	+	18.3464i	−1.27364	+	0.855407i
$461$	7.00917	+	5.88140i	0.326450	+	0.273924i	0.791251	−	0.611491i	$-0.209430\pi$
$461$	7.00917	+	5.88140i	0.326450	+	0.273924i	−0.464802	+	0.885415i	$0.653874\pi$
$462$	−40.5689	−	27.6994i	−1.88743	−	1.28869i
$463$	1.86266	−	0.328437i	0.0865650	−	0.0152637i	−0.130198	−	0.991488i	$-0.541561\pi$
$463$	1.86266	−	0.328437i	0.0865650	−	0.0152637i	0.216763	+	0.976224i	$0.430450\pi$
$464$	−2.84754	−	1.03642i	−0.132194	−	0.0481145i
$465$	3.38765	+	9.53367i	0.157098	+	0.442113i
$466$	−5.32294	+	30.1879i	−0.246580	+	1.39843i
$467$	29.8147	+	17.2135i	1.37966	+	0.796547i	0.992118	−	0.125306i	$-0.0399913\pi$
$467$	29.8147	+	17.2135i	1.37966	+	0.796547i	0.387541	+	0.921853i	$0.373325\pi$
$468$	−9.75315	+	8.58390i	−0.450840	+	0.396791i
$469$	−2.37179	−	4.10806i	−0.109519	−	0.189692i
$470$	−33.9403	−	24.7622i	−1.56555	−	1.14220i
$471$	21.0728	+	9.52547i	0.970982	+	0.438910i
$472$	−2.05071	−	2.44394i	−0.0943914	−	0.112491i
$473$	23.1042	+	27.5345i	1.06233	+	1.26604i
$474$	−0.0630940	−	0.634839i	−0.00289800	−	0.0291591i
$475$	0.620792	−	15.9589i	0.0284839	−	0.732245i
$476$	30.1164	+	52.1632i	1.38038	+	2.39090i
$477$	−0.00954727	+	0.0627690i	−0.000437140	+	0.00287399i
$478$	−11.1528	−	6.43908i	−0.510118	−	0.294517i
$479$	1.01845	−	5.77590i	0.0465340	−	0.263908i	−0.952660	−	0.304036i	$-0.901666\pi$
$479$	1.01845	−	5.77590i	0.0465340	−	0.263908i	0.999195	+	0.0401285i	$0.0127767\pi$
$480$	4.57498	−	24.8342i	0.208819	−	1.13352i
$481$	0.841128	+	0.306146i	0.0383521	+	0.0139590i
$482$	0.175649	−	0.0309717i	0.00800060	−	0.00141072i
$483$	−1.95438	+	25.8461i	−0.0889274	+	1.17604i
$484$	−13.0461	−	10.9470i	−0.593004	−	0.497589i
$485$	24.9361	−	16.7477i	1.13229	−	0.760472i
$486$	16.6465	+	30.8143i	0.755099	+	1.39777i
$487$		−	14.2308i		−	0.644861i	−0.946593	−	0.322430i	$-0.895500\pi$
$487$		−	14.2308i		−	0.644861i	0.946593	−	0.322430i	$-0.104500\pi$
$488$	−4.29312	+	5.11634i	−0.194340	+	0.231606i
$489$	6.66360	+	0.503875i	0.301338	+	0.0227860i
$490$	−9.07719	−	9.43715i	−0.410066	−	0.426327i
$491$	0.392986	+	0.143035i	0.0177352	+	0.00645508i	0.350873	−	0.936423i	$-0.385885\pi$
$491$	0.392986	+	0.143035i	0.0177352	+	0.00645508i	−0.333137	+	0.942878i	$0.608107\pi$
$492$	21.7097	−	22.2280i	0.978751	−	1.00211i
$493$	23.5994	+	4.16121i	1.06286	+	0.187411i
$494$	−5.09877	+	8.83133i	−0.229404	+	0.397340i
$495$	−11.6490	−	24.7133i	−0.523585	−	1.11078i
$496$	1.05317	+	1.82414i	0.0472887	+	0.0819064i
$497$	−15.8432	−	43.5289i	−0.710666	−	1.95254i
$498$	−13.6973	+	1.36132i	−0.613791	+	0.0610021i
$499$	6.02202	−	5.05307i	0.269582	−	0.226207i	−0.497967	−	0.867196i	$-0.665920\pi$
$499$	6.02202	−	5.05307i	0.269582	−	0.226207i	0.767550	+	0.640989i	$0.221476\pi$
$500$	21.1390	−	26.7268i	0.945363	−	1.19526i
$501$	−18.0381	−	8.15371i	−0.805883	−	0.364281i
$502$	−1.45422	−	3.99545i	−0.0649052	−	0.178326i
$503$	2.89014	−	1.66862i	0.128865	−	0.0744002i	−0.434182	−	0.900825i	$-0.642962\pi$
$503$	2.89014	−	1.66862i	0.128865	−	0.0744002i	0.563047	+	0.826425i	$0.309629\pi$
$504$	14.4625	+	16.4325i	0.644212	+	0.731963i
$505$	−0.370158	+	0.0251451i	−0.0164718	+	0.00111894i
$506$	−7.67201	+	43.5101i	−0.341063	+	1.93426i
$507$	18.4282	+	4.70559i	0.818423	+	0.208982i
$508$	12.0516	−	33.1116i	0.534705	−	1.46909i
$509$	0.111584	+	0.632826i	0.00494588	+	0.0280495i	0.987181	−	0.159606i	$-0.0510223\pi$
$509$	0.111584	+	0.632826i	0.00494588	+	0.0280495i	−0.982235	+	0.187655i	$0.939911\pi$
$510$	−0.424210	+	55.4812i	−0.0187843	+	2.45675i
$511$	17.3013	+	14.5175i	0.765365	+	0.642217i
$512$		−	9.05354i		−	0.400114i
$513$	12.1440	+	11.3137i	0.536173	+	0.499513i
$514$	22.2350			0.980743
$515$	−24.8929	−	2.66636i	−1.09691	−	0.117494i
$516$	−20.1860	−	41.9890i	−0.888641	−	1.84846i
$517$	−33.5423	+	5.91440i	−1.47519	+	0.260115i
$518$	1.50031	−	4.12207i	0.0659198	−	0.181113i
$519$	15.3695	−	4.31316i	0.674647	−	0.189327i
$520$	−6.83963	+	3.02893i	−0.299938	+	0.132827i
$521$	4.47458	−	7.75020i	0.196035	−	0.339542i	−0.751204	−	0.660070i	$-0.770527\pi$
$521$	4.47458	−	7.75020i	0.196035	−	0.339542i	0.947239	+	0.320527i	$0.103860\pi$
$522$	25.3246	−	0.597470i	1.10843	−	0.0261505i
$523$	−17.5015	+	10.1045i	−0.765286	+	0.441838i	−0.831190	−	0.555988i	$-0.812340\pi$
$523$	−17.5015	+	10.1045i	−0.765286	+	0.441838i	0.0659047	+	0.997826i	$0.479007\pi$
$524$	11.7453	−	4.27495i	0.513097	−	0.186752i
$525$	−6.24243	−	26.1057i	−0.272442	−	1.13935i
$526$	21.5543	−	18.0862i	0.939814	−	0.788598i
$527$	−10.7068	−	12.7599i	−0.466397	−	0.555831i
$528$	−3.31713	−	4.62041i	−0.144360	−	0.201077i
$529$	0.293486	−	0.106820i	0.0127603	−	0.00464436i
$530$	−0.0467988	+	0.0954700i	−0.00203281	+	0.00414695i
$531$	−3.56770	−	1.94909i	−0.154825	−	0.0845835i
$532$	26.1316	+	15.0871i	1.13295	+	0.654109i
$533$	8.23625	+	1.45227i	0.356752	+	0.0629049i
$534$	−57.0155	+	16.0003i	−2.46730	+	0.692401i
$535$	31.9804	−	7.90617i	1.38263	−	0.341813i
$536$	0.625677	+	3.54839i	0.0270251	+	0.153267i
$537$	−30.3455	+	14.5885i	−1.30951	+	0.629540i
$538$	−17.7293	+	21.1290i	−0.764365	+	0.910935i
$539$	−10.6152			−0.457231
$540$	6.70456	+	34.7724i	0.288518	+	1.49637i
$541$	−40.3613			−1.73527			−0.867635	−	0.497202i	$-0.834361\pi$
$541$	−40.3613			−1.73527			−0.867635	+	0.497202i	$0.834361\pi$
$542$	32.7308	−	39.0071i	1.40591	−	1.67550i
$543$	−32.7829	−	22.3833i	−1.40685	−	0.960560i
$544$	7.21907	+	40.9414i	0.309515	+	1.75535i
$545$	6.25951	+	25.3197i	0.268128	+	1.08458i
$546$	−4.24023	+	16.6057i	−0.181465	+	0.710659i
$547$	−12.6486	−	2.23029i	−0.540814	−	0.0953601i	−0.103433	−	0.994636i	$-0.532983\pi$
$547$	−12.6486	−	2.23029i	−0.540814	−	0.0953601i	−0.437381	+	0.899276i	$0.644094\pi$
$548$	10.2672	+	5.92775i	0.438592	+	0.253221i
$549$	−2.72144	+	8.06401i	−0.116148	+	0.344163i
$550$	−6.18747	−	45.3323i	−0.263835	−	1.93298i
$551$	11.2807	−	4.10585i	0.480575	−	0.174915i
$552$	8.10960	−	17.9405i	0.345167	−	0.763599i
$553$	−0.326611	−	0.389240i	−0.0138889	−	0.0165522i
$554$	−29.3296	+	24.6105i	−1.24610	+	1.04560i
$555$	1.88088	−	1.55389i	0.0798388	−	0.0659591i
$556$	−33.3073	+	12.1229i	−1.41254	+	0.514124i
$557$	2.97668	−	1.71859i	0.126126	−	0.0728190i	−0.435610	−	0.900136i	$-0.643467\pi$
$557$	2.97668	−	1.71859i	0.126126	−	0.0728190i	0.561736	+	0.827317i	$0.310134\pi$
$558$	−13.7517	−	10.9969i	−0.582155	−	0.465535i
$559$	6.27018	−	10.8603i	0.265200	−	0.459341i
$560$	−2.26271	−	5.10942i	−0.0956170	−	0.215913i
$561$	32.1781	+	31.4279i	1.35856	+	1.32689i
$562$	−11.9683	+	32.8826i	−0.504852	+	1.38707i
$563$	−9.46695	+	1.66928i	−0.398984	+	0.0703517i	−0.369540	−	0.929215i	$-0.620485\pi$
$563$	−9.46695	+	1.66928i	−0.398984	+	0.0703517i	−0.0294440	+	0.999566i	$0.509374\pi$
$564$	44.0215	+	3.32873i	1.85364	+	0.140165i
$565$	−20.7924	−	2.22714i	−0.874743	−	0.0936965i
$566$	−1.55336			−0.0652925
$567$	24.7884	+	12.7926i	1.04102	+	0.537239i
$568$			35.1857i			1.47636i
$569$	−1.07284	−	0.900223i	−0.0449760	−	0.0377393i	0.620023	−	0.784584i	$-0.287123\pi$
$569$	−1.07284	−	0.900223i	−0.0449760	−	0.0377393i	−0.664999	+	0.746845i	$0.731568\pi$
$570$	13.7129	+	24.1764i	0.574369	+	1.01264i
$571$	−1.48813	−	8.43959i	−0.0622762	−	0.353186i	−0.999983	−	0.00575942i	$-0.998167\pi$
$571$	−1.48813	−	8.43959i	−0.0622762	−	0.353186i	0.937707	−	0.347427i	$-0.112944\pi$
$572$	−6.03280	+	16.5750i	−0.252244	+	0.693035i
$573$	−28.2495	+	28.9239i	−1.18014	+	1.20831i
$574$	7.11707	−	40.3629i	0.297061	−	1.68472i
$575$	−19.0826	+	14.7872i	−0.795799	+	0.616670i
$576$	14.2391	+	36.4246i	0.593296	+	1.51769i
$577$	22.7988	−	13.1629i	0.949126	−	0.547978i	0.0563164	−	0.998413i	$-0.482064\pi$
$577$	22.7988	−	13.1629i	0.949126	−	0.547978i	0.892809	+	0.450435i	$0.148731\pi$
$578$	−18.1776	−	49.9426i	−0.756090	−	2.07734i
$579$	−2.30173	−	23.1595i	−0.0956566	−	0.962477i
$580$	24.6072	+	7.10893i	1.02176	+	0.295182i
$581$	−8.39826	+	7.04698i	−0.348419	+	0.292358i
$582$	−21.5325	+	47.6355i	−0.892552	+	1.97455i
$583$	0.0294805	+	0.0809970i	0.00122096	+	0.00335455i
$584$	−8.57767	−	14.8570i	−0.354946	−	0.614785i
$585$	−6.71216	+	6.76808i	−0.277514	+	0.279826i
$586$	14.3594	−	24.8712i	0.593182	−	1.02742i
$587$	−12.4206	−	2.19008i	−0.512652	−	0.0903944i	−0.0886631	−	0.996062i	$-0.528259\pi$
$587$	−12.4206	−	2.19008i	−0.512652	−	0.0903944i	−0.423989	+	0.905667i	$0.639371\pi$
$588$	13.3314	+	3.40414i	0.549777	+	0.140384i
$589$	−7.84119	−	2.85396i	−0.323091	−	0.117595i
$590$	−4.71950	−	4.90666i	−0.194299	−	0.202004i
$591$	8.42736	−	12.3428i	0.346655	−	0.507716i
$592$	0.326481	−	0.389085i	0.0134183	−	0.0159913i
$593$		−	18.5207i		−	0.760554i	−0.924873	−	0.380277i	$-0.875829\pi$
$593$		−	18.5207i		−	0.760554i	0.924873	−	0.380277i	$-0.124171\pi$
$594$	39.8890	+	25.8773i	1.63667	+	1.06176i
$595$	24.6379	+	36.6842i	1.01006	+	1.50391i
$596$	−36.1117	−	30.3013i	−1.47919	−	1.24119i
$597$	8.83027	−	4.24512i	0.361399	−	0.173741i
$598$	15.1802	−	2.67668i	0.620765	−	0.109458i
$599$	−27.8910	−	10.1515i	−1.13959	−	0.414778i	−0.297827	−	0.954620i	$-0.596262\pi$
$599$	−27.8910	−	10.1515i	−1.13959	−	0.414778i	−0.841766	+	0.539842i	$0.818484\pi$
$600$	−2.32639	+	20.2553i	−0.0949744	+	0.826920i
$601$	−4.51681	+	25.6161i	−0.184245	+	1.04490i	0.742677	+	0.669649i	$0.233556\pi$
$601$	−4.51681	+	25.6161i	−0.184245	+	1.04490i	−0.926922	+	0.375254i	$0.877556\pi$
$602$	−53.2223	−	30.7279i	−2.16918	−	1.25238i
$603$	2.38886	+	3.92104i	0.0972818	+	0.159677i
$604$	−2.85436	−	4.94389i	−0.116142	−	0.201164i
$605$	−10.0936	−	7.36412i	−0.410364	−	0.299394i
$606$	0.524504	−	0.376558i	0.0213065	−	0.0152966i
$607$	−11.6909	−	13.9327i	−0.474519	−	0.565510i	0.474691	−	0.880152i	$-0.342560\pi$
$607$	−11.6909	−	13.9327i	−0.474519	−	0.565510i	−0.949210	+	0.314643i	$0.898115\pi$
$608$	13.3869	+	15.9539i	0.542911	+	0.647016i
$609$	16.3894	−	11.7665i	0.664132	−	0.476801i
$610$	−8.40027	+	11.5138i	−0.340117	+	0.466181i
$611$	5.94153	+	10.2910i	0.240368	+	0.416330i
$612$	−30.3332	−	49.7885i	−1.22615	−	2.01258i
$613$	34.4670	+	19.8995i	1.39211	+	0.803733i	0.993548	−	0.113409i	$-0.0361771\pi$
$613$	34.4670	+	19.8995i	1.39211	+	0.803733i	0.398559	+	0.917143i	$0.369510\pi$
$614$	4.14059	−	23.4824i	0.167100	−	0.947674i
$615$	14.7856	−	17.3496i	0.596211	−	0.699603i
$616$	27.9262	+	10.1643i	1.12518	+	0.409532i
$617$	−33.3359	+	5.87802i	−1.34205	+	0.236640i	−0.798125	−	0.602492i	$-0.794175\pi$
$617$	−33.3359	+	5.87802i	−1.34205	+	0.236640i	−0.543928	+	0.839132i	$0.683064\pi$
$618$	39.2675	−	18.8777i	1.57957	−	0.759372i
$619$	−37.7797	−	31.7009i	−1.51849	−	1.27417i	−0.844689	−	0.535258i	$-0.820215\pi$
$619$	−37.7797	−	31.7009i	−1.51849	−	1.27417i	−0.673804	−	0.738910i	$-0.735341\pi$
$620$	−9.92643	−	14.7798i	−0.398655	−	0.593571i
$621$	1.30112	−	25.0547i	0.0522120	−	1.00541i
$622$			38.2984i			1.53563i
$623$	−30.3171	+	36.1305i	−1.21463	+	1.44754i
$624$	−1.11897	+	1.63886i	−0.0447946	+	0.0656068i
$625$	14.1441	−	20.6142i	0.565763	−	0.824568i
$626$	−1.27706	−	0.464812i	−0.0510416	−	0.0185776i
$627$	21.8323	+	5.57482i	0.871897	+	0.222637i
$628$	−40.0755	−	7.06640i	−1.59919	−	0.281980i
$629$	−2.00829	+	3.47846i	−0.0800757	+	0.138695i
$630$	33.1679	+	32.8939i	1.32144	+	1.31052i
$631$	−10.1511	−	17.5822i	−0.404108	−	0.699935i	0.590110	−	0.807323i	$-0.299085\pi$
$631$	−10.1511	−	17.5822i	−0.404108	−	0.699935i	−0.994217	+	0.107388i	$0.965751\pi$
$632$	0.132005	+	0.362680i	0.00525087	+	0.0144266i
$633$	6.34873	−	14.0450i	0.252339	−	0.558240i
$634$	−21.8115	+	18.3020i	−0.866247	+	0.726867i
$635$	7.17499	−	24.8358i	0.284731	−	0.985580i
$636$	−0.0110493	−	0.111176i	−0.000438133	−	0.00440841i
$637$	1.26669	+	3.48019i	0.0501879	+	0.137890i
$638$	29.7829	−	17.1951i	1.17912	−	0.680762i
$639$	16.3245	+	41.7593i	0.645788	+	1.65197i
$640$	2.46253	+	36.2505i	0.0973399	+	1.43293i
$641$	6.49217	−	36.8189i	0.256425	−	1.45426i	−0.535963	−	0.844242i	$-0.680051\pi$
$641$	6.49217	−	36.8189i	0.256425	−	1.45426i	0.792388	−	0.610018i	$-0.208838\pi$
$642$	−40.0587	+	41.0149i	−1.58099	+	1.61873i
$643$	−2.15929	+	5.93260i	−0.0851540	+	0.233959i	−0.974960	−	0.222380i	$-0.928617\pi$
$643$	−2.15929	+	5.93260i	−0.0851540	+	0.233959i	0.889806	+	0.456339i	$0.150840\pi$
$644$	−7.92021	−	44.9178i	−0.312100	−	1.77001i
$645$	−16.8633	−	29.7308i	−0.663993	−	1.17065i
$646$	−35.0533	−	29.4132i	−1.37915	−	1.15725i
$647$			1.79592i			0.0706050i	0.999377	+	0.0353025i	$0.0112395\pi$
$647$			1.79592i			0.0706050i	−0.999377	+	0.0353025i	$0.988761\pi$
$648$	−14.3699	−	15.5709i	−0.564502	−	0.611681i
$649$	−5.51918			−0.216647
$650$	−14.1238	+	7.43793i	−0.553981	+	0.291740i
$651$	−13.9842	−	1.05743i	−0.548083	−	0.0414439i
$652$	−11.5806	+	2.04198i	−0.453532	+	0.0799699i
$653$	8.31809	−	22.8538i	0.325512	−	0.894337i	−0.663720	−	0.747981i	$-0.731023\pi$
$653$	8.31809	−	22.8538i	0.325512	−	0.894337i	0.989232	−	0.146356i	$-0.0467544\pi$
$654$	−32.4725	−	31.7155i	−1.26978	−	1.24017i
$655$	8.38462	−	3.71313i	0.327614	−	0.145084i
$656$	2.37280	−	4.10982i	0.0926424	−	0.160461i
$657$	−17.0731	−	13.6530i	−0.666086	−	0.532653i
$658$	50.4326	−	29.1173i	1.96607	−	1.13511i
$659$	27.4347	−	9.98541i	1.06870	−	0.388976i	0.253012	−	0.967463i	$-0.418579\pi$
$659$	27.4347	−	9.98541i	1.06870	−	0.388976i	0.815692	+	0.578487i	$0.196357\pi$
$660$	30.6205	+	37.0639i	1.19190	+	1.44271i
$661$	32.2601	−	27.0694i	1.25477	−	1.05288i	0.258553	−	0.965997i	$-0.416754\pi$
$661$	32.2601	−	27.0694i	1.25477	−	1.05288i	0.996219	−	0.0868815i	$-0.0276902\pi$
$662$	−5.49021	−	6.54298i	−0.213383	−	0.254300i
$663$	6.46387	−	14.2997i	0.251036	−	0.555356i
$664$	7.82520	−	2.84814i	0.303677	−	0.110529i
$665$	19.8776	+	9.74390i	0.770822	+	0.377852i
$666$	−1.35768	+	4.02299i	−0.0526090	+	0.155888i
$667$	−15.7150	−	9.07303i	−0.608485	−	0.351309i
$668$	34.3043	+	6.04877i	1.32727	+	0.234034i
$669$	−5.08029	+	19.8956i	−0.196415	+	0.769208i
$670$	1.84529	+	7.46419i	0.0712897	+	0.288367i
$671$	2.00639	+	11.3788i	0.0774556	+	0.439273i
$672$	28.9067	+	19.7367i	1.11510	+	0.761360i
$673$	9.63581	−	11.4835i	0.371433	−	0.442657i	−0.547658	−	0.836702i	$-0.684480\pi$
$673$	9.63581	−	11.4835i	0.371433	−	0.442657i	0.919091	+	0.394046i	$0.128925\pi$
$674$	40.4087			1.55649
$675$	6.63650	+	25.1189i	0.255439	+	0.966825i
$676$	−33.4681			−1.28724
$677$	9.83400	−	11.7197i	0.377951	−	0.450425i	−0.543215	−	0.839593i	$-0.682793\pi$
$677$	9.83400	−	11.7197i	0.377951	−	0.450425i	0.921166	+	0.389169i	$0.127238\pi$
$678$	32.7990	−	15.7680i	1.25964	−	0.605567i
$679$	7.23001	+	41.0034i	0.277462	+	1.57357i
$680$	−8.05562	−	32.5850i	−0.308919	−	1.24958i
$681$	8.94733	−	2.51090i	0.342863	−	0.0962177i
$682$	−23.5414	−	4.15098i	−0.901446	−	0.158949i
$683$	35.9321	+	20.7454i	1.37490	+	0.793800i	0.991540	−	0.129798i	$-0.0414329\pi$
$683$	35.9321	+	20.7454i	1.37490	+	0.793800i	0.383362	+	0.923598i	$0.374766\pi$
$684$	−25.6308	−	14.0025i	−0.980019	−	0.535400i
$685$	7.80997	+	3.82840i	0.298404	+	0.146276i
$686$	−28.7503	+	10.4642i	−1.09769	+	0.399527i
$687$	−21.4968	−	29.9427i	−0.820155	−	1.14239i
$688$	−4.57395	−	5.45102i	−0.174380	−	0.207818i
$689$	0.0230369	−	0.0193303i	0.000877637	−	0.000736425i
$690$	14.6710	−	39.3690i	0.558515	−	1.49875i
$691$	−16.2121	+	5.90074i	−0.616739	+	0.224475i	−0.631449	−	0.775417i	$-0.717540\pi$
$691$	−16.2121	+	5.90074i	−0.616739	+	0.224475i	0.0147103	+	0.999892i	$0.495317\pi$
$692$	−24.3268	+	14.0451i	−0.924767	+	0.533914i
$693$	37.8593	−	0.893194i	1.43816	−	0.0339296i
$694$	28.2288	−	48.8936i	1.07155	−	1.85598i
$695$	−23.7770	+	10.5297i	−0.901914	+	0.399413i
$696$	−14.7551	+	4.14074i	−0.559292	+	0.156954i
$697$	−12.8354	+	35.2650i	−0.486175	+	1.33576i
$698$	−22.5500	+	3.97617i	−0.853529	+	0.150500i
$699$	−10.2389	−	21.2980i	−0.387272	−	0.805564i
$700$	22.0086	+	41.7919i	0.831847	+	1.57958i
$701$	−43.7894			−1.65390			−0.826952	−	0.562272i	$-0.809927\pi$
$701$	−43.7894			−1.65390			−0.826952	+	0.562272i	$0.809927\pi$
$702$	3.72399	−	16.1654i	0.140553	−	0.610124i
$703$			2.01214i			0.0758892i
$704$	40.6725	+	34.1283i	1.53290	+	1.28626i
$705$	32.3878	+	0.247637i	1.21979	+	0.00932656i
$706$	−4.72391	−	26.7906i	−0.177787	−	1.00828i
$707$	0.175887	−	0.483245i	0.00661490	−	0.0181743i
$708$	6.93139	+	1.76991i	0.260498	+	0.0665175i
$709$	−5.99387	+	33.9929i	−0.225105	+	1.27663i	0.637381	+	0.770549i	$0.280018\pi$
$709$	−5.99387	+	33.9929i	−0.225105	+	1.27663i	−0.862485	+	0.506082i	$0.831093\pi$
$710$	5.08882	+	74.9119i	0.190980	+	2.81139i
$711$	0.324933	+	0.369194i	0.0121859	+	0.0138459i
$712$	31.0259	−	17.9128i	1.16275	−	0.671312i
$713$	4.31399	+	11.8526i	0.161560	+	0.443883i
$714$	−70.0779	−	31.6771i	−2.62260	−	1.18549i
$715$	−3.59165	+	12.4323i	−0.134320	+	0.464942i
$716$	45.3870	−	38.0843i	1.69619	−	1.42328i
$717$	9.87931	−	0.981863i	0.368950	−	0.0366684i
$718$	−4.46492	−	12.2673i	−0.166629	−	0.457811i
$719$	−9.43611	−	16.3438i	−0.351908	−	0.609522i	0.634676	−	0.772778i	$-0.281134\pi$
$719$	−9.43611	−	16.3438i	−0.351908	−	0.609522i	−0.986584	+	0.163256i	$0.947800\pi$
$720$	2.30617	+	4.89250i	0.0859458	+	0.182333i
$721$	17.3507	−	30.0524i	0.646176	−	1.11921i
$722$	19.4646	+	3.43213i	0.724396	+	0.127731i
$723$	−0.0960736	+	0.0983669i	−0.00357301	+	0.00365830i
$724$	65.6388	+	23.8906i	2.43945	+	0.887885i
$725$	18.3651	+	3.97996i	0.682063	+	0.147812i
$726$	21.6824	+	1.63954i	0.804710	+	0.0608490i
$727$	22.8595	−	27.2429i	0.847812	−	1.01038i	−0.151946	−	0.988389i	$-0.548554\pi$
$727$	22.8595	−	27.2429i	0.847812	−	1.01038i	0.999758	−	0.0219941i	$-0.00700151\pi$
$728$		−	10.3685i		−	0.384280i
$729$	−24.2787	−	11.8129i	−0.899211	−	0.437516i
$730$	−20.4110	−	30.3905i	−0.755443	−	1.12480i
$731$	43.1066	+	36.1707i	1.59435	+	1.33782i
$732$	1.12923	−	14.9337i	0.0417375	−	0.551966i
$733$	7.83605	−	1.38171i	0.289431	−	0.0510345i	−0.0270475	−	0.999634i	$-0.508611\pi$
$733$	7.83605	−	1.38171i	0.289431	−	0.0510345i	0.316479	+	0.948600i	$0.397499\pi$
$734$	57.3552	+	20.8756i	2.11702	+	0.770532i
$735$	9.92740	+	1.82884i	0.366178	+	0.0674577i
$736$	5.46656	−	31.0024i	0.201500	−	1.14276i
$737$	5.39821	+	3.11666i	0.198846	+	0.114804i
$738$	−5.96541	+	39.2199i	−0.219590	+	1.44370i
$739$	9.25585	+	16.0316i	0.340482	+	0.589732i	0.984522	−	0.175260i	$-0.0560765\pi$
$739$	9.25585	+	16.0316i	0.340482	+	0.589732i	−0.644040	+	0.764992i	$0.722743\pi$
$740$	−2.53034	+	3.46821i	−0.0930172	+	0.127494i
$741$	−0.777486	−	7.82291i	−0.0285617	−	0.287382i
$742$	−0.0947307	−	0.112896i	−0.00347767	−	0.00414453i
$743$	5.74868	+	6.85101i	0.210899	+	0.251339i	0.861115	−	0.508410i	$-0.169766\pi$
$743$	5.74868	+	6.85101i	0.210899	+	0.251339i	−0.650217	+	0.759749i	$0.725322\pi$
$744$	9.70681	+	4.38774i	0.355869	+	0.160862i
$745$	−27.9392	−	20.3840i	−1.02361	−	0.746811i
$746$	4.70904	+	8.15629i	0.172410	+	0.298623i
$747$	7.96575	−	7.01077i	0.291451	−	0.256511i
$748$	−68.5452	−	39.5746i	−2.50626	−	1.44699i
$749$	−7.92923	+	44.9689i	−0.289728	+	1.64313i
$750$	−2.02351	+	43.4609i	−0.0738880	+	1.58697i
$751$	−5.82056	−	2.11851i	−0.212395	−	0.0773055i	0.233631	−	0.972325i	$-0.424939\pi$
$751$	−5.82056	−	2.11851i	−0.212395	−	0.0773055i	−0.446027	+	0.895020i	$0.647161\pi$
$752$	6.64038	−	1.17088i	0.242150	−	0.0426976i
$753$	2.70703	+	1.84829i	0.0986497	+	0.0673555i
$754$	−9.19130	−	7.71242i	−0.334728	−	0.280870i
$755$	−2.33512	−	3.47684i	−0.0849837	−	0.126535i
$756$	−47.8330	−	11.0192i	−1.73967	−	0.400763i
$757$		−	28.0679i		−	1.02015i	−0.860131	−	0.510073i	$-0.829619\pi$
$757$		−	28.0679i		−	1.02015i	0.860131	−	0.510073i	$-0.170381\pi$
$758$	40.8262	−	48.6548i	1.48287	−	1.76722i
$759$	−14.7575	−	30.6970i	−0.535663	−	1.11423i
$760$	−11.6567	−	12.1190i	−0.422834	−	0.439602i
$761$	−35.1059	−	12.7775i	−1.27259	−	0.463184i	−0.384614	−	0.923078i	$-0.625665\pi$
$761$	−35.1059	−	12.7775i	−1.27259	−	0.463184i	−0.887974	+	0.459894i	$0.847888\pi$
$762$	12.1559	+	43.3165i	0.440363	+	1.56919i
$763$	−35.6030	−	6.27777i	−1.28891	−	0.227270i
$764$	35.5724	−	61.6132i	1.28696	−	2.22909i
$765$	−24.6785	−	34.9352i	−0.892253	−	1.26309i
$766$	28.5690	+	49.4830i	1.03224	+	1.78789i
$767$	0.658588	+	1.80945i	0.0237802	+	0.0653356i
$768$	−10.5406	−	14.6820i	−0.380352	−	0.529789i
$769$	−29.9381	+	25.1210i	−1.07959	+	0.905887i	−0.995887	−	0.0906036i	$-0.971120\pi$
$769$	−29.9381	+	25.1210i	−1.07959	+	0.905887i	−0.0837068	+	0.996490i	$0.526676\pi$
$770$	60.9262	+	17.6014i	2.19563	+	0.634310i
$771$	−13.9244	+	9.99677i	−0.501476	+	0.360025i
$772$	14.0071	+	38.4843i	0.504128	+	1.38508i
$773$	−41.1533	+	23.7599i	−1.48018	+	0.854584i	−0.999748	−	0.0224466i	$-0.992854\pi$
$773$	−41.1533	+	23.7599i	−1.48018	+	0.854584i	−0.480435	+	0.877031i	$0.659521\pi$
$774$	52.2024	+	28.5190i	1.87637	+	1.02509i
$775$	−8.00071	−	10.3247i	−0.287394	−	0.370876i
$776$	5.49178	−	31.1455i	0.197144	−	1.11806i
$777$	0.913715	+	3.25593i	0.0327793	+	0.116806i
$778$	−10.9311	+	30.0331i	−0.391901	+	1.07674i
$779$	3.26460	+	18.5145i	0.116966	+	0.663349i
$780$	8.49750	−	14.4616i	0.304259	−	0.517808i
$781$	46.6293	+	39.1266i	1.66853	+	1.40006i
$782$			69.1681i			2.47345i
$783$	−15.5907	+	11.7600i	−0.557165	+	0.420269i
$784$	2.10151			0.0750538
$785$	−29.6853	−	3.17969i	−1.05951	−	0.113488i
$786$	−8.99876	+	13.1797i	−0.320975	+	0.470104i
$787$	−35.8812	+	6.32682i	−1.27903	+	0.225527i	−0.771567	−	0.636148i	$-0.780527\pi$
$787$	−35.8812	+	6.32682i	−1.27903	+	0.225527i	−0.507460	+	0.861675i	$0.669415\pi$
$788$	−8.99484	+	24.7131i	−0.320428	+	0.880369i
$789$	−5.36666	+	21.0171i	−0.191058	+	0.748227i
$790$	0.333498	+	0.753070i	0.0118653	+	0.0267930i
$791$	14.4926	−	25.1019i	0.515298	−	0.892522i
$792$	−27.2550	−	9.19802i	−0.968465	−	0.326837i
$793$	3.49110	−	2.01559i	0.123973	−	0.0715756i
$794$	−36.3902	+	13.2450i	−1.29144	+	0.470046i
$795$	−0.0136157	−	0.0808276i	−0.000482900	−	0.00286666i
$796$	−13.2072	+	11.0822i	−0.468117	+	0.392797i
$797$	5.79043	+	6.90076i	0.205107	+	0.244437i	0.858786	−	0.512335i	$-0.171219\pi$
$797$	5.79043	+	6.90076i	0.205107	+	0.244437i	−0.653678	+	0.756773i	$0.726775\pi$
$798$	−38.3373	+	3.81018i	−1.35712	+	0.134879i
$799$	−50.1064	+	18.2372i	−1.77264	+	0.645187i
$800$	4.40878	+	32.3008i	0.155874	+	1.14200i
$801$	28.5117	−	35.6540i	1.00741	−	1.25977i
$802$	−46.4500	−	26.8179i	−1.64021	−	0.946975i
$803$	−29.2274	−	5.15357i	−1.03141	−	0.181866i
$804$	−5.78000	−	5.64524i	−0.203845	−	0.199092i
$805$	−8.03078	−	32.4845i	−0.283048	−	1.14493i
$806$	1.44823	+	8.21333i	0.0510118	+	0.289302i
$807$	1.60327	−	21.2028i	0.0564379	−	0.746375i
$808$	−0.251086	+	0.299233i	−0.00883319	+	0.0105270i
$809$	15.8700			0.557959			0.278979	−	0.960297i	$-0.410004\pi$
$809$	15.8700			0.557959			0.278979	+	0.960297i	$0.410004\pi$
$810$	−32.8461	−	31.0728i	−1.15409	−	1.09179i
$811$	−42.6147			−1.49640			−0.748202	−	0.663471i	$-0.769083\pi$
$811$	−42.6147			−1.49640			−0.748202	+	0.663471i	$0.769083\pi$
$812$	−22.8208	+	27.1968i	−0.800853	+	0.954420i
$813$	−2.95987	+	39.1434i	−0.103807	+	1.37282i
$814$	1.00095	+	5.67667i	0.0350833	+	0.198967i
$815$	−8.37509	+	2.07048i	−0.293367	+	0.0725258i
$816$	−6.37032	−	6.22180i	−0.223006	−	0.217807i
$817$	27.7615	+	4.89510i	0.971253	+	0.171258i
$818$	−48.6791	−	28.1049i	−1.70203	−	0.982665i
$819$	−4.81048	−	12.3055i	−0.168092	−	0.429990i
$820$	−17.6556	+	36.0177i	−0.616562	+	1.25779i
$821$	−18.7036	+	6.80756i	−0.652761	+	0.237585i	−0.647108	−	0.762399i	$-0.724022\pi$
$821$	−18.7036	+	6.80756i	−0.652761	+	0.237585i	−0.00565293	+	0.999984i	$0.501799\pi$
$822$	−15.0628	+	1.49703i	−0.525375	+	0.0522149i
$823$	34.1358	+	40.6815i	1.18990	+	1.41807i	0.884942	+	0.465701i	$0.154198\pi$
$823$	34.1358	+	40.6815i	1.18990	+	1.41807i	0.304957	+	0.952366i	$0.401358\pi$
$824$	−20.1919	+	16.9430i	−0.703417	+	0.590237i
$825$	24.2561	+	25.6070i	0.844489	+	0.891521i
$826$	8.86749	−	3.22750i	0.308539	−	0.112299i
$827$	8.71066	−	5.02910i	0.302899	−	0.174879i	−0.340845	−	0.940119i	$-0.610713\pi$
$827$	8.71066	−	5.02910i	0.302899	−	0.174879i	0.643745	+	0.765240i	$0.277380\pi$
$828$	8.68948	+	43.2841i	0.301980	+	1.50423i
$829$	−12.6463	+	21.9040i	−0.439223	+	0.760756i	−0.997630	−	0.0688110i	$-0.978079\pi$
$829$	−12.6463	+	21.9040i	−0.439223	+	0.760756i	0.558407	+	0.829567i	$0.311413\pi$
$830$	16.2483	−	7.19556i	0.563986	−	0.249761i
$831$	7.30256	−	28.5985i	0.253323	−	0.992072i
$832$	6.33557	−	17.4068i	0.219647	−	0.603474i
$833$	−16.3662	+	2.88580i	−0.567055	+	0.0999872i
$834$	25.5186	−	37.3749i	0.883636	−	1.29419i
$835$	25.4103	+	2.72178i	0.879361	+	0.0941912i
$836$	−39.6505			−1.37134
$837$	13.5560	+	0.703976i	0.468564	+	0.0243330i
$838$			91.6828i			3.16713i
$839$	−11.4795	−	9.63246i	−0.396317	−	0.332549i	0.422751	−	0.906246i	$-0.361064\pi$
$839$	−11.4795	−	9.63246i	−0.396317	−	0.332549i	−0.819068	+	0.573696i	$0.805509\pi$
$840$	−24.3655	−	14.3170i	−0.840691	−	0.493982i
$841$	−2.58307	−	14.6493i	−0.0890713	−	0.505149i
$842$	25.5547	−	70.2110i	0.880674	−	2.41963i
$843$	−7.28890	−	25.9733i	−0.251043	−	0.894567i
$844$	−4.70976	+	26.7104i	−0.162117	+	0.919409i
$845$	−24.4976	+	1.66414i	−0.842742	+	0.0572481i
$846$	−48.1367	+	29.3269i	−1.65497	+	1.00828i
$847$	14.9983	−	8.65928i	0.515348	−	0.297536i
$848$	−0.00583627	−	0.0160350i	−0.000200419	−	0.000550645i
$849$	0.972773	−	0.698384i	0.0333855	−	0.0239685i
$850$	−21.8634	−	68.2097i	−0.749910	−	2.33957i
$851$	2.32993	−	1.95504i	0.0798690	−	0.0670180i
$852$	−46.0132	−	64.0914i	−1.57639	−	2.19573i
$853$	1.73467	+	4.76597i	0.0593941	+	0.163184i	0.965841	−	0.259137i	$-0.0834380\pi$
$853$	1.73467	+	4.76597i	0.0593941	+	0.163184i	−0.906447	+	0.422320i	$0.861216\pi$
$854$	−9.87767	−	17.1086i	−0.338007	−	0.585445i
$855$	−19.4571	−	8.97495i	−0.665420	−	0.306937i
$856$	17.3422	−	30.0376i	0.592745	−	1.02666i
$857$	28.1751	+	4.96803i	0.962442	+	0.169705i	0.632726	−	0.774376i	$-0.281936\pi$
$857$	28.1751	+	4.96803i	0.962442	+	0.169705i	0.329716	+	0.944080i	$0.393047\pi$
$858$	−6.08501	−	21.6833i	−0.207739	−	0.740257i
$859$	−24.0992	−	8.77140i	−0.822255	−	0.299276i	−0.103579	−	0.994621i	$-0.533029\pi$
$859$	−24.0992	−	8.77140i	−0.822255	−	0.299276i	−0.718676	+	0.695345i	$0.755252\pi$
$860$	41.6951	+	43.3486i	1.42179	+	1.47817i
$861$	13.6900	+	28.4766i	0.466555	+	0.970481i
$862$	44.2326	−	52.7144i	1.50657	−	1.79546i
$863$			10.3457i			0.352170i	0.984375	+	0.176085i	$0.0563434\pi$
$863$			10.3457i			0.352170i	−0.984375	+	0.176085i	$0.943657\pi$
$864$	−28.4223	−	18.4384i	−0.966945	−	0.627288i
$865$	−17.1080	+	11.4901i	−0.581691	+	0.390677i
$866$	−32.4583	−	27.2358i	−1.10298	−	0.925510i
$867$	33.8376	+	23.1034i	1.14918	+	0.784633i
$868$	24.3030	−	4.28527i	0.824897	−	0.145452i
$869$	0.627426	+	0.228364i	0.0212840	+	0.00774673i
$870$	−30.8155	+	10.9498i	−1.04474	+	0.371234i
$871$	0.377639	−	2.14169i	0.0127958	−	0.0725686i
$872$	23.7815	+	13.7303i	0.805344	+	0.464966i
$873$	−7.93224	−	39.5121i	−0.268466	−	1.33728i
$874$	17.3252	+	30.0081i	0.586033	+	1.01504i
$875$	18.1876	+	29.4959i	0.614852	+	0.997144i
$876$	35.0532	+	15.8450i	1.18434	+	0.535352i
$877$	−7.03414	−	8.38296i	−0.237526	−	0.283073i	0.634093	−	0.773257i	$-0.281374\pi$
$877$	−7.03414	−	8.38296i	−0.237526	−	0.283073i	−0.871619	+	0.490185i	$0.836929\pi$
$878$	−11.2868	−	13.4511i	−0.380912	−	0.453953i
$879$	2.18959	+	22.0313i	0.0738532	+	0.743096i
$880$	5.93200	+	4.32788i	0.199968	+	0.145893i
$881$	16.9910	+	29.4293i	0.572443	+	0.991500i	0.996314	+	0.0857776i	$0.0273375\pi$
$881$	16.9910	+	29.4293i	0.572443	+	0.991500i	−0.423872	+	0.905722i	$0.639329\pi$
$882$	−16.3618	+	6.39615i	−0.550930	+	0.215369i
$883$	26.7935	+	15.4692i	0.901672	+	0.520581i	0.877742	−	0.479133i	$-0.159049\pi$
$883$	26.7935	+	15.4692i	0.901672	+	0.520581i	0.0239300	+	0.999714i	$0.492382\pi$
$884$	−4.79517	+	27.1948i	−0.161279	+	0.914659i
$885$	5.16155	+	0.950868i	0.173504	+	0.0319631i
$886$	10.0116	+	3.64392i	0.336346	+	0.122420i
$887$	−20.0348	+	3.53267i	−0.672701	+	0.118615i	−0.499557	−	0.866281i	$-0.666504\pi$
$887$	−20.0348	+	3.53267i	−0.672701	+	0.118615i	−0.173144	+	0.984896i	$0.555393\pi$
$888$	0.193681	−	2.56137i	0.00649951	−	0.0859540i
$889$	27.4495	+	23.0328i	0.920626	+	0.772497i
$890$	63.4649	−	42.6244i	2.12735	−	1.42877i
$891$	−36.6144	+	1.72861i	−1.22663	+	0.0579105i
$892$		−	36.1332i		−	1.20983i
$893$	−17.1703	+	20.4627i	−0.574581	+	0.684759i
$894$	60.0173	+	4.53827i	2.00728	+	0.151782i
$895$	31.3281	−	30.1332i	1.04718	−	1.00724i
$896$	−47.3255	−	17.2251i	−1.58103	−	0.575449i
$897$	−8.30301	+	8.50121i	−0.277229	+	0.283847i
$898$	21.8932	+	3.86036i	0.730584	+	0.128822i
$899$	4.90901	−	8.50265i	0.163725	−	0.283579i
$900$	−22.2508	−	39.9377i	−0.741694	−	1.33126i
$901$	0.0674714	+	0.116864i	0.00224780	+	0.00389330i
$902$	18.4203	+	50.6093i	0.613328	+	1.68510i
$903$	47.1450	−	4.68555i	1.56889	−	0.155925i
$904$	−16.8657	+	14.1520i	−0.560945	+	0.470689i
$905$	49.2333	+	14.2233i	1.63657	+	0.472799i
$906$	6.64180	+	3.00227i	0.220659	+	0.0997438i
$907$	19.1116	+	52.5088i	0.634591	+	1.74353i	0.668084	+	0.744086i	$0.267115\pi$
$907$	19.1116	+	52.5088i	0.634591	+	1.74353i	−0.0334925	+	0.999439i	$0.510663\pi$
$908$	−14.1618	+	8.17633i	−0.469976	+	0.271341i
$909$	−0.159166	+	0.471630i	−0.00527919	+	0.0156430i
$910$	−1.49956	−	22.0749i	−0.0497101	−	0.731775i
$911$	−0.739941	+	4.19641i	−0.0245153	+	0.139033i	−0.994609	−	0.103698i	$-0.966932\pi$
$911$	−0.739941	+	4.19641i	−0.0245153	+	0.139033i	0.970093	+	0.242732i	$0.0780435\pi$
$912$	−4.32215	−	1.10365i	−0.143121	−	0.0365456i
$913$	4.92720	−	13.5374i	0.163067	−	0.448022i
$914$	5.69412	+	32.2930i	0.188345	+	1.06816i
$915$	0.0840077	−	10.9871i	0.00277721	−	0.363223i
$916$	49.6874	+	41.6927i	1.64172	+	1.37756i
$917$			12.7106i			0.419740i
$918$	68.5344	+	29.0527i	2.26197	+	0.958881i
$919$	14.8879			0.491107			0.245553	−	0.969383i	$-0.421030\pi$
$919$	14.8879			0.491107			0.245553	+	0.969383i	$0.421030\pi$
$920$	−2.70706	+	25.2729i	−0.0892491	+	0.833222i
$921$	7.96462	+	16.5672i	0.262443	+	0.545908i
$922$	20.2450	−	3.56974i	0.666734	−	0.117563i
$923$	7.26347	−	19.9562i	0.239080	−	0.656867i
$924$	−64.1603	+	18.0053i	−2.11072	+	0.592332i
$925$	−1.67967	+	2.66443i	−0.0552274	+	0.0876058i
$926$	2.12474	−	3.68015i	0.0698231	−	0.120937i
$927$	−16.1035	+	29.4764i	−0.528907	+	0.968133i
$928$	−21.2213	+	12.2521i	−0.696622	+	0.402195i
$929$	2.45476	−	0.893461i	0.0805382	−	0.0293135i	−0.301437	−	0.953486i	$-0.597466\pi$
$929$	2.45476	−	0.893461i	0.0805382	−	0.0293135i	0.381975	+	0.924173i	$0.375244\pi$
$930$	21.3008	+	7.93782i	0.698481	+	0.260291i
$931$	−6.37753	+	5.35138i	−0.209015	+	0.175385i
$932$	26.7294	+	31.8549i	0.875551	+	1.04344i
$933$	−17.2188	−	23.9839i	−0.563719	−	0.785199i
$934$	72.6840	−	26.4548i	2.37829	−	0.865628i
$935$	−52.1406	−	25.5590i	−1.70518	−	0.835869i
$936$	0.236705	+	10.0331i	0.00773694	+	0.327942i
$937$	−48.4632	−	27.9802i	−1.58322	−	0.914074i	−0.994385	−	0.105823i	$-0.966252\pi$
$937$	−48.4632	−	27.9802i	−1.58322	−	0.914074i	−0.588838	−	0.808251i	$-0.700414\pi$
$938$	−10.4957	−	1.85067i	−0.342696	−	0.0604266i
$939$	1.00872	−	0.283078i	0.0329184	−	0.00923791i
$940$	−55.3281	+	13.6781i	−1.80460	+	0.446132i
$941$	6.83296	+	38.7517i	0.222748	+	1.26327i	0.866943	+	0.498407i	$0.166081\pi$
$941$	6.83296	+	38.7517i	0.222748	+	1.26327i	−0.644195	+	0.764861i	$0.722807\pi$
$942$	46.8272	−	22.5120i	1.52571	−	0.733480i
$943$	18.2666	−	21.7693i	0.594843	−	0.708906i
$944$	1.09264			0.0355623
$945$	−35.5600	−	5.68725i	−1.15677	−	0.185006i
$946$	80.7563			2.62561
$947$	27.9256	−	33.2804i	0.907459	−	1.08147i	−0.0888851	−	0.996042i	$-0.528330\pi$
$947$	27.9256	−	33.2804i	0.907459	−	1.08147i	0.996345	−	0.0854261i	$-0.0272252\pi$
$948$	−0.714735	−	0.488003i	−0.0232135	−	0.0158496i
$949$	1.79802	+	10.1971i	0.0583663	+	0.331012i
$950$	−26.5704	−	24.1160i	−0.862059	−	0.782425i
$951$	5.43069	−	21.2678i	0.176102	−	0.689657i
$952$	45.8189	+	8.07911i	1.48500	+	0.261846i
$953$	−41.1272	−	23.7448i	−1.33224	−	0.769169i	−0.346598	−	0.938014i	$-0.612663\pi$
$953$	−41.1272	−	23.7448i	−1.33224	−	0.769169i	−0.985643	+	0.168845i	$0.945996\pi$
$954$	0.0942440	+	0.107081i	0.00305126	+	0.00346689i
$955$	22.9742	−	46.8675i	0.743427	−	1.51660i
$956$	−16.4165	+	5.97511i	−0.530947	+	0.193249i
$957$	−10.9203	+	24.1585i	−0.353004	+	0.780935i
$958$	−8.47011	−	10.0943i	−0.273657	−	0.326132i
$959$	−9.23549	+	7.74949i	−0.298229	+	0.250244i
$960$	−32.1573	−	38.9241i	−1.03787	−	1.25627i
$961$	22.7176	−	8.26852i	0.732825	−	0.266726i
$962$	1.74165	−	1.00554i	0.0561530	−	0.0324199i
$963$	6.64615	−	43.6954i	0.214169	−	1.40806i
$964$	0.120978	−	0.209540i	0.00389643	−	0.00674881i
$965$	12.1663	+	27.4727i	0.391647	+	0.884378i
$966$	41.6614	+	40.6901i	1.34043	+	1.30918i
$967$	1.59085	−	4.37082i	0.0511582	−	0.140556i	−0.911482	−	0.411340i	$-0.865061\pi$
$967$	1.59085	−	4.37082i	0.0511582	−	0.140556i	0.962640	+	0.270784i	$0.0872830\pi$
$968$	−12.9550	+	2.28432i	−0.416390	+	0.0734207i
$969$	35.1758	+	2.65986i	1.13001	+	0.0854469i
$970$	7.18776	−	67.1043i	0.230785	−	2.15459i
$971$	−14.2904			−0.458601			−0.229300	−	0.973356i	$-0.573644\pi$
$971$	−14.2904			−0.458601			−0.229300	+	0.973356i	$0.573644\pi$
$972$	46.5374	+	9.57075i	1.49269	+	0.306982i
$973$		−	36.0445i		−	1.15553i
$974$	−24.4928	−	20.5519i	−0.784799	−	0.658524i
$975$	5.50081	−	11.0079i	0.176167	−	0.352536i
$976$	−0.397206	−	2.25266i	−0.0127142	−	0.0721060i
$977$	8.99180	−	24.7048i	0.287673	−	0.790375i	−0.708718	−	0.705492i	$-0.750726\pi$
$977$	8.99180	−	24.7048i	0.287673	−	0.790375i	0.996391	−	0.0848833i	$-0.0270517\pi$
$978$	10.4906	−	10.7411i	0.335454	−	0.343461i
$979$	10.7623	−	61.0358i	0.343963	−	1.95071i
$980$	−17.7221	+	1.20388i	−0.566113	+	0.0384565i
$981$	34.5947	+	5.26192i	1.10452	+	0.168000i
$982$	0.813720	−	0.469801i	0.0259668	−	0.0149920i
$983$	−2.83783	−	7.79687i	−0.0905127	−	0.248682i	0.886173	−	0.463354i	$-0.153354\pi$
$983$	−2.83783	−	7.79687i	−0.0905127	−	0.248682i	−0.976686	+	0.214672i	$0.931132\pi$
$984$	−2.37357	−	23.8824i	−0.0756667	−	0.761344i
$985$	−5.35511	+	18.5364i	−0.170628	+	0.590620i
$986$	41.2436	−	34.6075i	1.31346	−	1.10213i
$987$	−18.4918	+	40.9087i	−0.588602	+	1.30214i
$988$	4.73138	+	12.9994i	0.150525	+	0.413565i
$989$	−21.3056	−	36.9023i	−0.677477	−	1.17342i
$990$	−59.3574	−	15.6412i	−1.88650	−	0.497109i
$991$	−15.2451	+	26.4053i	−0.484277	+	0.838792i	−0.999837	−	0.0180615i	$-0.994251\pi$
$991$	−15.2451	+	26.4053i	−0.484277	+	0.838792i	0.515560	+	0.856853i	$0.327584\pi$
$992$	16.7740	+	2.95771i	0.532575	+	0.0939074i
$993$	6.37988	+	1.62909i	0.202459	+	0.0516975i
$994$	−97.7983	−	35.5957i	−3.10197	−	1.12903i
$995$	−9.11620	+	8.76848i	−0.289003	+	0.277979i
$996$	−10.5292	+	15.4212i	−0.333629	+	0.488638i
$997$	−31.7490	+	37.8369i	−1.00550	+	1.19831i	−0.0254251	+	0.999677i	$0.508094\pi$
$997$	−31.7490	+	37.8369i	−1.00550	+	1.19831i	−0.980074	+	0.198631i	$0.936351\pi$
$998$		−	17.6621i		−	0.559083i
$999$	−0.958491	−	3.12976i	−0.0303253	−	0.0990213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.p.a.124.15	yes	96
3.2	odd	2		405.2.p.a.289.2		96
5.2	odd	4		675.2.l.h.151.15		96
5.3	odd	4		675.2.l.h.151.2		96
5.4	even	2	inner	135.2.p.a.124.2	yes	96
15.14	odd	2		405.2.p.a.289.15		96
27.5	odd	18		405.2.p.a.199.15		96
27.22	even	9	inner	135.2.p.a.49.2	✓	96
135.22	odd	36		675.2.l.h.76.15		96
135.49	even	18	inner	135.2.p.a.49.15	yes	96
135.59	odd	18		405.2.p.a.199.2		96
135.103	odd	36		675.2.l.h.76.2		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.2	✓	96	27.22	even	9	inner
135.2.p.a.49.15	yes	96	135.49	even	18	inner
135.2.p.a.124.2	yes	96	5.4	even	2	inner
135.2.p.a.124.15	yes	96	1.1	even	1	trivial
405.2.p.a.199.2		96	135.59	odd	18
405.2.p.a.199.15		96	27.5	odd	18
405.2.p.a.289.2		96	3.2	odd	2
405.2.p.a.289.15		96	15.14	odd	2
675.2.l.h.76.2		96	135.103	odd	36
675.2.l.h.76.15		96	135.22	odd	36
675.2.l.h.151.2		96	5.3	odd	4
675.2.l.h.151.15		96	5.2	odd	4

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.44418 - 1.72110i) q^{2} +(-0.130598 + 1.72712i) q^{3} +(-0.529254 - 3.00155i) q^{4} +(-0.536643 - 2.17072i) q^{5} +(2.78395 + 2.71904i) q^{6} +(3.05233 + 0.538208i) q^{7} +(-2.03885 - 1.17713i) q^{8} +(-2.96589 - 0.451117i) q^{9} +O(q^{10})\)	\(q+(1.44418 - 1.72110i) q^{2} +(-0.130598 + 1.72712i) q^{3} +(-0.529254 - 3.00155i) q^{4} +(-0.536643 - 2.17072i) q^{5} +(2.78395 + 2.71904i) q^{6} +(3.05233 + 0.538208i) q^{7} +(-2.03885 - 1.17713i) q^{8} +(-2.96589 - 0.451117i) q^{9} +(-4.51104 - 2.21129i) q^{10} +(-3.82718 + 1.39298i) q^{11} +(5.25316 - 0.522089i) q^{12} +(0.913372 + 1.08851i) q^{13} +(5.33442 - 4.47611i) q^{14} +(3.81917 - 0.643355i) q^{15} +(0.757669 - 0.275769i) q^{16} +(-5.52192 + 3.18808i) q^{17} +(-5.05969 + 4.45311i) q^{18} +(-1.59710 + 2.76626i) q^{19} +(-6.23150 + 2.75962i) q^{20} +(-1.32818 + 5.20145i) q^{21} +(-3.12967 + 8.59869i) q^{22} +(4.75493 - 0.838423i) q^{23} +(2.29931 - 3.36760i) q^{24} +(-4.42403 + 2.32980i) q^{25} +3.19252 q^{26} +(1.16647 - 5.06353i) q^{27} -9.44656i q^{28} +(-2.87901 - 2.41578i) q^{29} +(4.40829 - 7.50232i) q^{30} +(0.453633 + 2.57268i) q^{31} +(2.22999 - 6.12685i) q^{32} +(-1.90602 - 6.79192i) q^{33} +(-2.48762 + 14.1080i) q^{34} +(-0.469712 - 6.91457i) q^{35} +(0.215659 + 9.14102i) q^{36} +(0.545540 - 0.314968i) q^{37} +(2.45452 + 6.74374i) q^{38} +(-1.99928 + 1.43535i) q^{39} +(-1.46108 + 5.05746i) q^{40} +(4.50871 - 3.78325i) q^{41} +(7.03411 + 9.79775i) q^{42} +(-3.01843 - 8.29308i) q^{43} +(6.20665 + 10.7502i) q^{44} +(0.612374 + 6.68019i) q^{45} +(5.42396 - 9.39457i) q^{46} +(8.23568 + 1.45217i) q^{47} +(0.377336 + 1.34460i) q^{48} +(2.44919 + 0.891433i) q^{49} +(-2.37926 + 10.9789i) q^{50} +(-4.78505 - 9.95338i) q^{51} +(2.78382 - 3.31763i) q^{52} -0.0211636i q^{53} +(-7.03027 - 9.32026i) q^{54} +(5.07759 + 7.56019i) q^{55} +(-5.58969 - 4.69031i) q^{56} +(-4.56908 - 3.11965i) q^{57} +(-8.31562 + 1.46627i) q^{58} +(1.27341 + 0.463483i) q^{59} +(-3.95238 - 11.1229i) q^{60} +(0.492631 - 2.79385i) q^{61} +(5.08298 + 2.93466i) q^{62} +(-8.81007 - 2.97322i) q^{63} +(-6.51815 - 11.2898i) q^{64} +(1.87270 - 2.56682i) q^{65} +(-14.4422 - 6.52828i) q^{66} +(-0.983770 - 1.17241i) q^{67} +(12.4917 + 14.8870i) q^{68} +(0.827072 + 8.32183i) q^{69} +(-12.5790 - 9.17745i) q^{70} +(-7.47278 - 12.9432i) q^{71} +(5.51597 + 4.41099i) q^{72} +(6.31067 + 3.64347i) q^{73} +(0.245765 - 1.39380i) q^{74} +(-3.44607 - 7.94510i) q^{75} +(9.14833 + 3.32972i) q^{76} +(-12.4315 + 2.19201i) q^{77} +(-0.416937 + 5.51386i) q^{78} +(-0.125585 - 0.105378i) q^{79} +(-1.00521 - 1.49670i) q^{80} +(8.59299 + 2.67593i) q^{81} -13.2236i q^{82} +(-2.27365 + 2.70963i) q^{83} +(16.3154 + 1.23370i) q^{84} +(9.88373 + 10.2757i) q^{85} +(-18.6324 - 6.78165i) q^{86} +(4.54833 - 4.65691i) q^{87} +(9.44275 + 1.66501i) q^{88} +(-7.60870 + 13.1787i) q^{89} +(12.3817 + 8.59343i) q^{90} +(2.20206 + 3.81409i) q^{91} +(-5.03313 - 13.8284i) q^{92} +(-4.50257 + 0.447492i) q^{93} +(14.3931 - 12.0773i) q^{94} +(6.86183 + 1.98236i) q^{95} +(10.2906 + 4.65161i) q^{96} +(4.59453 + 12.6234i) q^{97} +(5.07132 - 2.92793i) q^{98} +(11.9794 - 2.40492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

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