LMFDB - Embedded newform 135.2.q.a.68.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

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("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			68.15
Character	$\chi$	$=$	135.68
Dual form			135.2.q.a.2.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36466 - 1.94894i) q^{2} +(-1.63096 - 0.583078i) q^{3} +(-1.25203 - 3.43992i) q^{4} +(2.13659 - 0.659531i) q^{5} +(-3.36209 + 2.38294i) q^{6} +(-2.19758 + 1.02475i) q^{7} +(-3.81650 - 1.02263i) q^{8} +(2.32004 + 1.90195i) q^{9} +O(q^{10})$	\(q+(1.36466 - 1.94894i) q^{2} +(-1.63096 - 0.583078i) q^{3} +(-1.25203 - 3.43992i) q^{4} +(2.13659 - 0.659531i) q^{5} +(-3.36209 + 2.38294i) q^{6} +(-2.19758 + 1.02475i) q^{7} +(-3.81650 - 1.02263i) q^{8} +(2.32004 + 1.90195i) q^{9} +(1.63034 - 5.06413i) q^{10} +(0.00275056 + 0.00327799i) q^{11} +(0.0362633 + 6.34039i) q^{12} +(-1.13206 + 0.792678i) q^{13} +(-1.00178 + 5.68139i) q^{14} +(-3.86924 - 0.170132i) q^{15} +(-1.59279 + 1.33651i) q^{16} +(1.90362 - 0.510074i) q^{17} +(6.87287 - 1.92610i) q^{18} +(6.69182 - 3.86352i) q^{19} +(-4.94380 - 6.52394i) q^{20} +(4.18166 - 0.389960i) q^{21} +(0.0101422 - 0.000887327i) q^{22} +(-3.12427 + 6.70002i) q^{23} +(5.62827 + 3.89318i) q^{24} +(4.13004 - 2.81830i) q^{25} +3.28806i q^{26} +(-2.67490 - 4.45476i) q^{27} +(6.27648 + 6.27648i) q^{28} +(1.74110 + 9.87424i) q^{29} +(-5.61180 + 7.30876i) q^{30} +(-5.62932 + 2.04890i) q^{31} +(-0.257571 - 2.94406i) q^{32} +(-0.00257472 - 0.00695004i) q^{33} +(1.60370 - 4.40613i) q^{34} +(-4.01947 + 3.63884i) q^{35} +(3.63779 - 10.3620i) q^{36} +(-0.451272 - 1.68417i) q^{37} +(1.60230 - 18.3144i) q^{38} +(2.30854 - 0.632743i) q^{39} +(-8.82875 + 0.332163i) q^{40} +(-2.95191 - 0.520501i) q^{41} +(4.94656 - 8.68198i) q^{42} +(-7.18901 - 0.628957i) q^{43} +(0.00783223 - 0.0135658i) q^{44} +(6.21137 + 2.53355i) q^{45} +(8.79437 + 15.2323i) q^{46} +(-0.871367 - 1.86865i) q^{47} +(3.37706 - 1.25107i) q^{48} +(-0.720271 + 0.858385i) q^{49} +(0.143417 - 11.8952i) q^{50} +(-3.40214 - 0.278051i) q^{51} +(4.14412 + 2.90174i) q^{52} +(-1.25315 + 1.25315i) q^{53} +(-12.3324 - 0.866025i) q^{54} +(0.00803875 + 0.00518964i) q^{55} +(9.43499 - 1.66364i) q^{56} +(-13.1668 + 2.39939i) q^{57} +(21.6203 + 10.0817i) q^{58} +(-0.763311 - 0.640494i) q^{59} +(4.25916 + 13.5229i) q^{60} +(-6.39745 - 2.32848i) q^{61} +(-3.68893 + 13.7673i) q^{62} +(-7.04749 - 1.80223i) q^{63} +(-9.69063 - 5.59489i) q^{64} +(-1.89595 + 2.44026i) q^{65} +(-0.0170589 - 0.00446650i) q^{66} +(5.21964 + 7.45442i) q^{67} +(-4.13800 - 5.90968i) q^{68} +(9.00219 - 9.10575i) q^{69} +(1.60665 + 12.7995i) q^{70} +(8.32564 + 4.80681i) q^{71} +(-6.90944 - 9.63132i) q^{72} +(0.744204 - 2.77741i) q^{73} +(-3.89819 - 1.41882i) q^{74} +(-8.37920 + 2.18839i) q^{75} +(-21.6685 - 18.1821i) q^{76} +(-0.00940367 - 0.00438501i) q^{77} +(1.91719 - 5.36268i) q^{78} +(-6.95996 + 1.22723i) q^{79} +(-2.52167 + 3.90606i) q^{80} +(1.76518 + 8.82520i) q^{81} +(-5.04279 + 5.04279i) q^{82} +(8.34640 + 5.84421i) q^{83} +(-6.57699 - 13.8963i) q^{84} +(3.73085 - 2.34532i) q^{85} +(-11.0364 + 13.1527i) q^{86} +(2.91780 - 17.1197i) q^{87} +(-0.00714534 - 0.0153232i) q^{88} +(-3.03785 - 5.26171i) q^{89} +(13.4142 - 8.64816i) q^{90} +(1.67550 - 2.90205i) q^{91} +(26.9592 + 2.35862i) q^{92} +(10.3758 - 0.0593438i) q^{93} +(-4.83102 - 0.851839i) q^{94} +(11.7496 - 12.6682i) q^{95} +(-1.29653 + 4.95181i) q^{96} +(1.09824 - 12.5529i) q^{97} +(0.690016 + 2.57517i) q^{98} +(0.000146839 + 0.0128365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.36466	−	1.94894i	0.964963	−	1.37811i	0.0395221	−	0.999219i	$-0.487416\pi$
$2$	1.36466	−	1.94894i	0.964963	−	1.37811i	0.925441	−	0.378892i	$-0.123695\pi$
$3$	−1.63096	−	0.583078i	−0.941633	−	0.336640i
$3$	−1.63096	−	0.583078i	−0.941633	−	0.336640i
$4$	−1.25203	−	3.43992i	−0.626014	−	1.71996i
$5$	2.13659	−	0.659531i	0.955512	−	0.294951i
$5$	2.13659	−	0.659531i	0.955512	−	0.294951i
$6$	−3.36209	+	2.38294i	−1.37257	+	0.972829i
$7$	−2.19758	+	1.02475i	−0.830607	+	0.387318i	−0.790939	−	0.611895i	$-0.790408\pi$
$7$	−2.19758	+	1.02475i	−0.830607	+	0.387318i	−0.0396673	+	0.999213i	$0.512630\pi$
$8$	−3.81650	−	1.02263i	−1.34934	−	0.361553i
$9$	2.32004	+	1.90195i	0.773347	+	0.633983i
$10$	1.63034	−	5.06413i	0.515559	−	1.60142i
$11$	0.00275056	+	0.00327799i	0.000829324	+	0.000988350i	0.766459	−	0.642293i	$-0.222017\pi$
$11$	0.00275056	+	0.00327799i	0.000829324	+	0.000988350i	−0.765630	+	0.643282i	$0.777572\pi$
$12$	0.0362633	+	6.34039i	0.0104683	+	1.83031i
$13$	−1.13206	+	0.792678i	−0.313977	+	0.219849i	−0.719933	−	0.694043i	$-0.755828\pi$
$13$	−1.13206	+	0.792678i	−0.313977	+	0.219849i	0.405956	+	0.913893i	$0.366939\pi$
$14$	−1.00178	+	5.68139i	−0.267738	+	1.51842i
$15$	−3.86924	−	0.170132i	−0.999035	−	0.0439278i
$16$	−1.59279	+	1.33651i	−0.398197	+	0.334127i
$17$	1.90362	−	0.510074i	0.461696	−	0.123711i	−0.0204707	−	0.999790i	$-0.506516\pi$
$17$	1.90362	−	0.510074i	0.461696	−	0.123711i	0.482167	+	0.876079i	$0.339850\pi$
$18$	6.87287	−	1.92610i	1.61995	−	0.453987i
$19$	6.69182	−	3.86352i	1.53521	−	0.886353i	0.536099	−	0.844155i	$-0.319897\pi$
$19$	6.69182	−	3.86352i	1.53521	−	0.886353i	0.999109	−	0.0421981i	$-0.0134361\pi$
$20$	−4.94380	−	6.52394i	−1.10547	−	1.45880i
$21$	4.18166	−	0.389960i	0.912514	−	0.0850962i
$22$	0.0101422		0.000887327i	0.00216232		0.000189179i
$23$	−3.12427	+	6.70002i	−0.651456	+	1.39705i	0.251729	+	0.967798i	$0.419001\pi$
$23$	−3.12427	+	6.70002i	−0.651456	+	1.39705i	−0.903184	+	0.429253i	$0.858777\pi$
$24$	5.62827	+	3.89318i	1.14887	+	0.794691i
$25$	4.13004	−	2.81830i	0.826007	−	0.563659i
$26$			3.28806i			0.644842i
$27$	−2.67490	−	4.45476i	−0.514785	−	0.857319i
$28$	6.27648	+	6.27648i	1.18614	+	1.18614i
$29$	1.74110	+	9.87424i	0.323313	+	1.83360i	0.521272	+	0.853391i	$0.325458\pi$
$29$	1.74110	+	9.87424i	0.323313	+	1.83360i	−0.197959	+	0.980210i	$0.563431\pi$
$30$	−5.61180	+	7.30876i	−1.02457	+	1.33439i
$31$	−5.62932	+	2.04890i	−1.01106	+	0.367994i	−0.793838	−	0.608129i	$-0.791920\pi$
$31$	−5.62932	+	2.04890i	−1.01106	+	0.367994i	−0.217217	+	0.976123i	$0.569698\pi$
$32$	−0.257571	−	2.94406i	−0.0455326	−	0.520440i
$33$	−0.00257472	−	0.00695004i	−0.000448201	−	0.00120985i
$34$	1.60370	−	4.40613i	0.275032	−	0.755645i
$35$	−4.01947	+	3.63884i	−0.679415	+	0.615076i
$36$	3.63779	−	10.3620i	0.606299	−	1.72701i
$37$	−0.451272	−	1.68417i	−0.0741887	−	0.276876i	0.918859	−	0.394585i	$-0.129112\pi$
$37$	−0.451272	−	1.68417i	−0.0741887	−	0.276876i	−0.993048	+	0.117709i	$0.962445\pi$
$38$	1.60230	−	18.3144i	0.259927	−	2.97098i
$39$	2.30854	−	0.632743i	0.369661	−	0.101320i
$40$	−8.82875	+	0.332163i	−1.39595	+	0.0525196i
$41$	−2.95191	−	0.520501i	−0.461011	−	0.0812887i	−0.0616809	−	0.998096i	$-0.519646\pi$
$41$	−2.95191	−	0.520501i	−0.461011	−	0.0812887i	−0.399330	+	0.916807i	$0.630757\pi$
$42$	4.94656	−	8.68198i	0.763270	−	1.33966i
$43$	−7.18901	−	0.628957i	−1.09631	−	0.0959151i	−0.475382	−	0.879779i	$-0.657690\pi$
$43$	−7.18901	−	0.628957i	−1.09631	−	0.0959151i	−0.620932	+	0.783864i	$0.713246\pi$
$44$	0.00783223	−	0.0135658i	0.00118075	−	0.00204512i
$45$	6.21137	+	2.53355i	0.925937	+	0.377679i
$46$	8.79437	+	15.2323i	1.29666	+	2.24588i
$47$	−0.871367	−	1.86865i	−0.127102	−	0.272571i	0.832451	−	0.554098i	$-0.186937\pi$
$47$	−0.871367	−	1.86865i	−0.127102	−	0.272571i	−0.959553	+	0.281527i	$0.909159\pi$
$48$	3.37706	−	1.25107i	0.487436	−	0.180576i
$49$	−0.720271	+	0.858385i	−0.102896	+	0.122626i
$50$	0.143417	−	11.8952i	0.0202823	−	1.68224i
$51$	−3.40214	−	0.278051i	−0.476395	−	0.0389350i
$52$	4.14412	+	2.90174i	0.574686	+	0.402399i
$53$	−1.25315	+	1.25315i	−0.172134	+	0.172134i	−0.787916	−	0.615782i	$-0.788840\pi$
$53$	−1.25315	+	1.25315i	−0.172134	+	0.172134i	0.615782	+	0.787916i	$0.288840\pi$
$54$	−12.3324	−	0.866025i	−1.67823	−	0.117851i
$55$	0.00803875	+	0.00518964i	0.00108394	+	0.000699770i
$56$	9.43499	−	1.66364i	1.26080	−	0.222314i
$57$	−13.1668	+	2.39939i	−1.74399	+	0.317807i
$58$	21.6203	+	10.0817i	2.83889	+	1.32380i
$59$	−0.763311	−	0.640494i	−0.0993747	−	0.0833853i	0.591747	−	0.806124i	$-0.298439\pi$
$59$	−0.763311	−	0.640494i	−0.0993747	−	0.0833853i	−0.691121	+	0.722739i	$0.742883\pi$
$60$	4.25916	+	13.5229i	0.549855	+	1.74580i
$61$	−6.39745	−	2.32848i	−0.819109	−	0.298131i	−0.101728	−	0.994812i	$-0.532437\pi$
$61$	−6.39745	−	2.32848i	−0.819109	−	0.298131i	−0.717381	+	0.696681i	$0.754659\pi$
$62$	−3.68893	+	13.7673i	−0.468495	+	1.74845i
$63$	−7.04749	−	1.80223i	−0.887900	−	0.227059i
$64$	−9.69063	−	5.59489i	−1.21133	−	0.699361i
$65$	−1.89595	+	2.44026i	−0.235164	+	0.302677i
$66$	−0.0170589	−	0.00446650i	−0.00209980	−	0.000549788i
$67$	5.21964	+	7.45442i	0.637680	+	0.910702i	0.999770	−	0.0214414i	$-0.00682552\pi$
$67$	5.21964	+	7.45442i	0.637680	+	0.910702i	−0.362090	+	0.932143i	$0.617937\pi$
$68$	−4.13800	−	5.90968i	−0.501806	−	0.716654i
$69$	9.00219	−	9.10575i	1.08374	−	1.09620i
$70$	1.60665	+	12.7995i	0.192032	+	1.52983i
$71$	8.32564	+	4.80681i	0.988072	+	0.570464i	0.904697	−	0.426055i	$-0.140097\pi$
$71$	8.32564	+	4.80681i	0.988072	+	0.570464i	0.0833745	+	0.996518i	$0.473430\pi$
$72$	−6.90944	−	9.63132i	−0.814286	−	1.13506i
$73$	0.744204	−	2.77741i	0.0871025	−	0.325071i	−0.908602	−	0.417664i	$-0.862849\pi$
$73$	0.744204	−	2.77741i	0.0871025	−	0.325071i	0.995704	+	0.0925931i	$0.0295156\pi$
$74$	−3.89819	−	1.41882i	−0.453155	−	0.164935i
$75$	−8.37920	+	2.18839i	−0.967546	+	0.252693i
$76$	−21.6685	−	18.1821i	−2.48555	−	2.08563i
$77$	−0.00940367	−	0.00438501i	−0.00107165	−	0.000499718i
$78$	1.91719	−	5.36268i	0.217080	−	0.607204i
$79$	−6.95996	+	1.22723i	−0.783057	+	0.138074i	−0.550863	−	0.834595i	$-0.685701\pi$
$79$	−6.95996	+	1.22723i	−0.783057	+	0.138074i	−0.232194	+	0.972670i	$0.574590\pi$
$80$	−2.52167	+	3.90606i	−0.281931	+	0.436711i
$81$	1.76518	+	8.82520i	0.196131	+	0.980578i
$82$	−5.04279	+	5.04279i	−0.556883	+	0.556883i
$83$	8.34640	+	5.84421i	0.916136	+	0.641485i	0.933582	−	0.358363i	$-0.116665\pi$
$83$	8.34640	+	5.84421i	0.916136	+	0.641485i	−0.0174466	+	0.999848i	$0.505554\pi$
$84$	−6.57699	−	13.8963i	−0.717608	−	1.51621i
$85$	3.73085	−	2.34532i	0.404668	−	0.254385i
$86$	−11.0364	+	13.1527i	−1.19008	+	1.41829i
$87$	2.91780	−	17.1197i	0.312821	−	1.83542i
$88$	−0.00714534	−	0.0153232i	−0.000761696	−	0.00163346i
$89$	−3.03785	−	5.26171i	−0.322012	−	0.557741i	0.658891	−	0.752238i	$-0.271026\pi$
$89$	−3.03785	−	5.26171i	−0.322012	−	0.557741i	−0.980903	+	0.194498i	$0.937692\pi$
$90$	13.4142	−	8.64816i	1.41398	−	0.911596i
$91$	1.67550	−	2.90205i	0.175640	−	0.304217i
$92$	26.9592	+	2.35862i	2.81069	+	0.245904i
$93$	10.3758	−	0.0593438i	1.07593	−	0.00615366i
$94$	−4.83102	−	0.851839i	−0.498281	−	0.0878604i
$95$	11.7496	−	12.6682i	1.20548	−	1.29973i
$96$	−1.29653	+	4.95181i	−0.132326	+	0.505392i
$97$	1.09824	−	12.5529i	0.111509	−	1.27456i	−0.709935	−	0.704267i	$-0.751276\pi$
$97$	1.09824	−	12.5529i	0.111509	−	1.27456i	0.821444	−	0.570289i	$-0.193169\pi$
$98$	0.690016	+	2.57517i	0.0697021	+	0.260132i
$99$	0.000146839		0.0128365i	1.47579e−5		0.00129012i
$100$	−14.8656	−	10.6784i	−1.48656	−	1.06784i
$101$	−1.67645	+	4.60600i	−0.166813	+	0.458314i	−0.994729	−	0.102537i	$-0.967304\pi$
$101$	−1.67645	+	4.60600i	−0.166813	+	0.458314i	0.827916	+	0.560852i	$0.189526\pi$
$102$	−5.18468	+	6.25113i	−0.513360	+	0.618954i
$103$	−1.01013	−	11.5458i	−0.0995307	−	1.13764i	−0.867596	−	0.497269i	$-0.834336\pi$
$103$	−1.01013	−	11.5458i	−0.0995307	−	1.13764i	0.768066	−	0.640371i	$-0.221219\pi$
$104$	5.13112	−	1.86758i	0.503148	−	0.183131i
$105$	8.67731	−	3.59112i	0.846819	−	0.350458i
$106$	0.732191	+	4.15246i	0.0711167	+	0.403323i
$107$	3.31844	+	3.31844i	0.320806	+	0.320806i	0.849076	−	0.528270i	$-0.177159\pi$
$107$	3.31844	+	3.31844i	0.320806	+	0.320806i	−0.528270	+	0.849076i	$0.677159\pi$
$108$	−11.9750	+	14.7789i	−1.15229	+	1.42210i
$109$		−	11.2538i		−	1.07792i	−0.842332	−	0.538960i	$-0.818818\pi$
$109$		−	11.2538i		−	1.07792i	0.842332	−	0.538960i	$-0.181182\pi$
$110$	0.0210845	−	0.00858495i	0.00201033	−	0.000818543i
$111$	−0.245997	+	3.00994i	−0.0233490	+	0.285691i
$112$	2.13069	−	4.56928i	0.201331	−	0.431757i
$113$	1.87764	−	0.164272i	0.176634	−	0.0154535i	0.00150433	−	0.999999i	$-0.499521\pi$
$113$	1.87764	−	0.164272i	0.176634	−	0.0154535i	0.175129	+	0.984545i	$0.443966\pi$
$114$	−13.2920	+	28.9357i	−1.24491	+	2.71008i
$115$	−2.25642	+	16.3758i	−0.210412	+	1.52705i
$116$	31.7867	−	18.3520i	2.95132	−	1.70394i
$117$	−4.13406	−	0.314079i	−0.382194	−	0.0290366i
$118$	−2.28995	+	0.613590i	−0.210807	+	0.0564856i
$119$	−3.66066	+	3.07166i	−0.335572	+	0.281579i
$120$	14.5930	+	4.60610i	1.33215	+	0.420478i
$121$	1.91013	−	10.8329i	0.173648	−	0.984806i
$122$	−13.2684	+	9.29066i	−1.20127	+	0.841137i
$123$	4.51095	+	2.57011i	0.406738	+	0.231739i
$124$	14.0961	+	16.7991i	1.26587	+	1.50860i
$125$	6.96544	−	8.74543i	0.623008	−	0.782215i
$126$	−13.1299	+	11.2757i	−1.16970	+	1.00452i
$127$	−5.69522	−	1.52603i	−0.505369	−	0.135413i	−0.00287859	−	0.999996i	$-0.500916\pi$
$127$	−5.69522	−	1.52603i	−0.505369	−	0.135413i	−0.502491	+	0.864583i	$0.667583\pi$
$128$	−18.7718	+	8.75341i	−1.65920	+	0.773700i
$129$	11.3582	+	5.21756i	1.00004	+	0.459380i
$130$	2.16858	+	7.02524i	0.190197	+	0.616154i
$131$	−5.29212	−	14.5400i	−0.462375	−	1.27036i	−0.923694	−	0.383130i	$-0.874846\pi$
$131$	−5.29212	−	14.5400i	−0.462375	−	1.27036i	0.461320	−	0.887234i	$-0.347376\pi$
$132$	−0.0206840	+	0.0175585i	−0.00180031	+	0.00152827i
$133$	−10.7467	+	15.3478i	−0.931854	+	1.33082i
$134$	21.6513			1.87039
$135$	−8.65322	−	7.75382i	−0.744751	−	0.667343i
$136$	−7.78679			−0.667712
$137$	−2.24127	+	3.20087i	−0.191485	+	0.273468i	−0.903402	−	0.428795i	$-0.858938\pi$
$137$	−2.24127	+	3.20087i	−0.191485	+	0.273468i	0.711917	+	0.702263i	$0.247827\pi$
$138$	−5.46163	−	29.9710i	−0.464924	−	2.55130i
$139$	1.85959	+	5.10917i	0.157728	+	0.433354i	0.993234	−	0.116126i	$-0.0370478\pi$
$139$	1.85959	+	5.10917i	0.157728	+	0.433354i	−0.835506	+	0.549481i	$0.814826\pi$
$140$	17.5498	+	9.27073i	1.48323	+	0.783519i
$141$	0.331592	+	3.55577i	0.0279251	+	0.299449i
$142$	20.7299	−	9.66651i	1.73961	−	0.811196i
$143$	−0.00571218	−	0.00153058i	−0.000477677	−	0.000127993i
$144$	−6.23730	+	0.0713498i	−0.519775	+	0.00594581i
$145$	10.2324	+	19.9489i	0.849753	+	1.65667i
$146$	−4.39742	−	5.24064i	−0.363933	−	0.433718i
$147$	1.67524	−	0.980015i	0.138171	−	0.0808303i
$148$	−5.22840	+	3.66097i	−0.429772	+	0.300930i
$149$	−1.59684	+	9.05612i	−0.130818	+	0.741907i	0.846863	+	0.531811i	$0.178488\pi$
$149$	−1.59684	+	9.05612i	−0.130818	+	0.741907i	−0.977681	+	0.210095i	$0.932623\pi$
$150$	−7.16975	+	19.3170i	−0.585408	+	1.57723i
$151$	8.68937	−	7.29124i	0.707131	−	0.593353i	−0.216662	−	0.976247i	$-0.569517\pi$
$151$	8.68937	−	7.29124i	0.707131	−	0.593353i	0.923792	+	0.382894i	$0.125072\pi$
$152$	−29.4903	+	7.90189i	−2.39198	+	0.640928i
$153$	5.38662	+	2.43720i	0.435482	+	0.197036i
$154$	−0.0213790	+	0.0123432i	−0.00172277	+	0.000994640i
$155$	−10.6762	+	8.09038i	−0.857536	+	0.649835i
$156$	−5.06693	−	7.14896i	−0.405679	−	0.572375i
$157$	−0.876549	+	0.0766881i	−0.0699562	+	0.00612037i	−0.122080	−	0.992520i	$-0.538956\pi$
$157$	−0.876549	+	0.0766881i	−0.0699562	+	0.00612037i	0.0521239	+	0.998641i	$0.483401\pi$
$158$	−7.10621	+	15.2393i	−0.565340	+	1.21238i
$159$	2.77453	−	1.31315i	0.220034	−	0.104140i
$160$	−2.49202	−	6.12036i	−0.197012	−	0.483857i
$161$		−	17.9254i		−	1.41272i
$162$	19.6087	+	8.60321i	1.54060	+	0.675932i
$163$	4.75545	+	4.75545i	0.372476	+	0.372476i	0.868378	−	0.495902i	$-0.165163\pi$
$163$	4.75545	+	4.75545i	0.372476	+	0.372476i	−0.495902	+	0.868378i	$0.665163\pi$
$164$	1.90539	+	10.8060i	0.148786	+	0.843808i
$165$	−0.0100849	−	0.0131513i	−0.000785108	−	0.00102383i
$166$	22.7800	−	8.29126i	1.76807	−	0.643527i
$167$	−0.630926	−	7.21152i	−0.0488226	−	0.558044i	−0.980733	−	0.195355i	$-0.937414\pi$
$167$	−0.630926	−	7.21152i	−0.0488226	−	0.558044i	0.931910	−	0.362689i	$-0.118141\pi$
$168$	−16.3581	−	2.78800i	−1.26205	−	0.215099i
$169$	−3.79304	+	10.4213i	−0.291772	+	0.801637i
$170$	0.520470	−	10.4718i	0.0399183	−	0.803149i
$171$	22.8735	+	3.76397i	1.74918	+	0.287838i
$172$	6.83728	+	25.5171i	0.521338	+	1.94566i
$173$	−0.208175	+	2.37946i	−0.0158273	+	0.180907i	0.984166	+	0.177249i	$0.0567198\pi$
$173$	−0.208175	+	2.37946i	−0.0158273	+	0.180907i	−0.999993	+	0.00365760i	$0.998836\pi$
$174$	−29.3834	−	29.0492i	−2.22755	−	2.20221i
$175$	−6.18804	+	10.4257i	−0.467772	+	0.788107i
$176$	−0.00876211	−	0.00154500i	−0.000660469	−	0.000116458i
$177$	0.871470	+	1.48969i	0.0655037	+	0.111972i
$178$	−14.4004	−	1.25987i	−1.07936	−	0.0944315i
$179$	8.41245	−	14.5708i	0.628776	−	1.08907i	−0.359021	−	0.933329i	$-0.616889\pi$
$179$	8.41245	−	14.5708i	0.628776	−	1.08907i	0.987798	−	0.155743i	$-0.0497772\pi$
$180$	0.938389	−	24.5387i	0.0699434	−	1.82900i
$181$	3.54419	+	6.13871i	0.263437	+	0.456287i	0.967153	−	0.254195i	$-0.0818105\pi$
$181$	3.54419	+	6.13871i	0.263437	+	0.456287i	−0.703716	+	0.710482i	$0.748477\pi$
$182$	−3.36943	−	7.22577i	−0.249759	−	0.535610i
$183$	9.07628	+	7.52786i	0.670938	+	0.556476i
$184$	18.7754	−	22.3757i	1.38414	−	1.64955i
$185$	−2.07495	−	3.30076i	−0.152553	−	0.242676i
$186$	14.0439	−	20.3029i	1.02975	−	1.48868i
$187$	0.00690804	+	0.00483706i	0.000505166	+	0.000353721i
$188$	−5.33703	+	5.33703i	−0.389243	+	0.389243i
$189$	10.4433	+	7.04859i	0.759639	+	0.512709i
$190$	−8.65544	−	40.1871i	−0.627932	−	2.91548i
$191$	−7.71793	+	1.36088i	−0.558450	+	0.0984697i	−0.445747	−	0.895159i	$-0.647062\pi$
$191$	−7.71793	+	1.36088i	−0.558450	+	0.0984697i	−0.112703	+	0.993629i	$0.535951\pi$
$192$	12.5427	+	14.7754i	0.905195	+	1.06632i
$193$	−16.8391	−	7.85219i	−1.21210	−	0.565213i	−0.291823	−	0.956472i	$-0.594262\pi$
$193$	−16.8391	−	7.85219i	−1.21210	−	0.565213i	−0.920280	+	0.391259i	$0.872040\pi$
$194$	−22.9662	−	19.2709i	−1.64888	−	1.38357i
$195$	4.51508	−	2.87446i	0.323332	−	0.205845i
$196$	3.85457	+	1.40295i	0.275327	+	0.100211i
$197$	−1.74344	+	6.50660i	−0.124215	+	0.463576i	−0.999810	−	0.0194688i	$-0.993802\pi$
$197$	−1.74344	+	6.50660i	−0.124215	+	0.463576i	0.875596	+	0.483045i	$0.160469\pi$
$198$	0.0252180	+	0.0172313i	0.00179216	+	0.00122458i
$199$	−7.81601	−	4.51257i	−0.554062	−	0.319888i	0.196697	−	0.980464i	$-0.436979\pi$
$199$	−7.81601	−	4.51257i	−0.554062	−	0.319888i	−0.750759	+	0.660576i	$0.770312\pi$
$200$	−18.6443	+	6.53253i	−1.31835	+	0.461920i
$201$	−4.16650	−	15.2013i	−0.293882	−	1.07222i
$202$	6.68904	+	9.55295i	0.470640	+	0.672143i
$203$	−13.9448	−	19.9152i	−0.978733	−	1.39778i
$204$	3.30310	+	12.0512i	0.231263	+	0.843753i
$205$	−6.65031	+	0.834779i	−0.464478	+	0.0583035i
$206$	−23.8806	−	13.7874i	−1.66384	−	0.960617i
$207$	−19.9915	+	9.60211i	−1.38951	+	0.667393i
$208$	0.743713	−	2.77557i	0.0515672	−	0.192451i
$209$	0.0310708	+	0.0113089i	0.00214921	+	0.000782250i
$210$	4.84272	−	21.8123i	0.334180	−	1.50519i
$211$	4.86924	+	4.08578i	0.335213	+	0.281277i	0.794820	−	0.606846i	$-0.207565\pi$
$211$	4.86924	+	4.08578i	0.335213	+	0.281277i	−0.459607	+	0.888122i	$0.652010\pi$
$212$	5.87973	+	2.74176i	0.403822	+	0.188305i
$213$	−10.7760	−	12.6942i	−0.738361	−	0.869792i
$214$	10.9960	−	1.93889i	0.751672	−	0.132540i
$215$	−15.7748	+	3.39755i	−1.07583	+	0.231711i
$216$	5.65319	+	19.7370i	0.384651	+	1.34293i
$217$	10.2713	−	10.2713i	0.697258	−	0.697258i
$218$	−21.9330	−	15.3577i	−1.48549	−	1.04015i
$219$	−2.83321	+	4.09590i	−0.191451	+	0.276775i
$220$	0.00778719	−	0.0341502i	0.000525012	−	0.00230241i
$221$	−1.75069	+	2.08639i	−0.117764	+	0.140346i
$222$	5.53049	+	4.58699i	0.371182	+	0.307858i
$223$	1.58829	+	3.40610i	0.106360	+	0.228089i	0.952284	−	0.305214i	$-0.0987281\pi$
$223$	1.58829	+	3.40610i	0.106360	+	0.228089i	−0.845924	+	0.533304i	$0.820950\pi$
$224$	3.58295	+	6.20585i	0.239396	+	0.414646i
$225$	14.9421	+	1.31656i	0.996141	+	0.0877708i
$226$	2.24219	−	3.88359i	0.149149	−	0.258333i
$227$	6.49455	+	0.568200i	0.431059	+	0.0377127i	0.300621	−	0.953744i	$-0.402806\pi$
$227$	6.49455	+	0.568200i	0.431059	+	0.0377127i	0.130438	+	0.991456i	$0.458362\pi$
$228$	24.7389	+	42.2886i	1.63837	+	2.80063i
$229$	4.26742	+	0.752462i	0.281999	+	0.0497241i	0.312859	−	0.949800i	$-0.398713\pi$
$229$	4.26742	+	0.752462i	0.281999	+	0.0497241i	−0.0308595	+	0.999524i	$0.509824\pi$
$230$	28.8362	+	26.7450i	1.90140	+	1.76351i
$231$	0.0127802	+	0.0126348i	0.000840875	+	0.000831311i
$232$	3.45279	−	39.4655i	0.226687	−	2.59104i
$233$	6.77460	+	25.2831i	0.443818	+	1.65635i	0.719037	+	0.694972i	$0.244583\pi$
$233$	6.77460	+	25.2831i	0.443818	+	1.65635i	−0.275219	+	0.961382i	$0.588750\pi$
$234$	−6.25372	+	7.62843i	−0.408819	+	0.498686i
$235$	−3.09419	−	3.41785i	−0.201843	−	0.222956i
$236$	−1.24756	+	3.42764i	−0.0812093	+	0.223121i
$237$	12.0670	+	2.05664i	0.783834	+	0.133593i
$238$	0.990915	+	11.3262i	0.0642314	+	0.734169i
$239$	17.2215	−	6.26813i	1.11397	−	0.405452i	0.281521	−	0.959555i	$-0.409161\pi$
$239$	17.2215	−	6.26813i	1.11397	−	0.405452i	0.832448	+	0.554103i	$0.186939\pi$
$240$	6.39027	−	4.90029i	0.412490	−	0.316312i
$241$	−1.09892	−	6.23226i	−0.0707874	−	0.401455i	−0.999528	−	0.0307248i	$-0.990218\pi$
$241$	−1.09892	−	6.23226i	−0.0707874	−	0.401455i	0.928740	−	0.370731i	$-0.120893\pi$
$242$	−18.5060	−	18.5060i	−1.18961	−	1.18961i
$243$	2.26685	−	15.4228i	0.145419	−	0.989370i
$244$			24.9220i			1.59547i
$245$	−0.972792	+	2.30906i	−0.0621494	+	0.147520i
$246$	11.1649	−	5.28424i	0.711849	−	0.336911i
$247$	−4.51302	+	9.67820i	−0.287156	+	0.615809i
$248$	23.5795	−	2.06294i	1.49730	−	0.130997i
$249$	−10.2050	−	14.3983i	−0.646714	−	0.912452i
$250$	−7.53885	−	25.5098i	−0.476799	−	1.61338i
$251$	−23.1604	+	13.3717i	−1.46187	+	0.844013i	−0.999098	−	0.0424628i	$-0.986480\pi$
$251$	−23.1604	+	13.3717i	−1.46187	+	0.844013i	−0.462775	+	0.886476i	$0.653146\pi$
$252$	2.62414	+	26.4992i	0.165305	+	1.66929i
$253$	−0.0305561	+	0.00818747i	−0.00192104	+	0.000514742i
$254$	−10.7462	+	9.01714i	−0.674277	+	0.565786i
$255$	−7.45236	+	1.64974i	−0.466685	+	0.103310i
$256$	−4.67107	+	26.4910i	−0.291942	+	1.65569i
$257$	−3.21096	+	2.24834i	−0.200294	+	0.140248i	−0.669421	−	0.742883i	$-0.733458\pi$
$257$	−3.21096	+	2.24834i	−0.200294	+	0.140248i	0.469127	+	0.883131i	$0.344569\pi$
$258$	25.6689	−	15.0163i	1.59808	−	0.934876i
$259$	2.71756	+	3.23866i	0.168861	+	0.201240i
$260$	10.7681	+	3.46666i	0.667807	+	0.214993i
$261$	−14.7409	+	26.2201i	−0.912439	+	1.62298i
$262$	−35.5596	−	9.52815i	−2.19688	−	0.588651i
$263$	27.9551	−	13.0357i	1.72379	−	0.803815i	0.731216	−	0.682146i	$-0.238953\pi$
$263$	27.9551	−	13.0357i	1.72379	−	0.803815i	0.992571	−	0.121669i	$-0.0388245\pi$
$264$	0.00271910	+	0.0291578i	0.000167349	+	0.00179454i
$265$	−1.85098	+	3.50397i	−0.113705	+	0.215247i
$266$	15.2464	+	41.8892i	0.934819	+	2.56839i
$267$	1.88662	+	10.3529i	0.115459	+	0.633589i
$268$	19.1074	−	27.2883i	1.16717	−	1.66690i
$269$	−11.5179			−0.702257			−0.351128	−	0.936327i	$-0.614202\pi$
$269$	−11.5179			−0.702257			−0.351128	+	0.936327i	$0.614202\pi$
$270$	−26.9205	+	6.28327i	−1.63833	+	0.382388i
$271$	−6.78072			−0.411899			−0.205950	−	0.978563i	$-0.566028\pi$
$271$	−6.78072			−0.411899			−0.205950	+	0.978563i	$0.566028\pi$
$272$	−2.35035	+	3.35665i	−0.142511	+	0.203527i
$273$	−4.42478	+	3.75617i	−0.267800	+	0.227334i
$274$	3.17972	+	8.73621i	0.192094	+	0.527774i
$275$	0.0205982	+	0.00578632i	0.00124212	+	0.000348928i
$276$	−42.5940	−	19.5661i	−2.56386	−	1.17774i
$277$	9.00402	−	4.19864i	0.540999	−	0.252272i	−0.132856	−	0.991135i	$-0.542415\pi$
$277$	9.00402	−	4.19864i	0.540999	−	0.252272i	0.673855	+	0.738863i	$0.264637\pi$
$278$	12.4952	+	3.34808i	0.749412	+	0.200804i
$279$	−16.9572	−	5.95314i	−1.01520	−	0.356405i
$280$	19.0615	−	9.77719i	1.13914	−	0.584299i
$281$	−16.7510	−	19.9630i	−0.999280	−	1.19090i	−0.981580	−	0.191052i	$-0.938810\pi$
$281$	−16.7510	−	19.9630i	−0.999280	−	1.19090i	−0.0177003	−	0.999843i	$-0.505634\pi$
$282$	7.38249	+	4.20617i	0.439621	+	0.250474i
$283$	−6.09224	+	4.26583i	−0.362146	+	0.253577i	−0.740461	−	0.672100i	$-0.765393\pi$
$283$	−6.09224	+	4.26583i	−0.362146	+	0.253577i	0.378315	+	0.925677i	$0.376504\pi$
$284$	6.11110	−	34.6578i	0.362627	−	2.05656i
$285$	−26.5496	+	13.8104i	−1.57266	+	0.818059i
$286$	−0.0107782	+	0.00904400i	−0.000637329	+	0.000534783i
$287$	7.02044	−	1.88112i	0.414403	−	0.111039i
$288$	5.00187	−	7.32021i	0.294738	−	0.431348i
$289$	−11.3588	+	6.55802i	−0.668166	+	0.385766i
$290$	52.8430	+	7.28124i	3.10305	+	0.427569i
$291$	−9.11051	+	19.8329i	−0.534068	+	1.16263i
$292$	−10.4858	+	0.917390i	−0.613636	+	0.0536862i
$293$	−3.52271	+	7.55448i	−0.205799	+	0.441337i	−0.981933	−	0.189231i	$-0.939400\pi$
$293$	−3.52271	+	7.55448i	−0.205799	+	0.441337i	0.776134	+	0.630568i	$0.217178\pi$
$294$	0.376141	−	4.60233i	0.0219370	−	0.268413i
$295$	−2.05331	−	0.865046i	−0.119548	−	0.0503649i
$296$			6.88912i			0.400422i
$297$	0.00724518	−	0.0210214i	0.000420408	−	0.00121978i
$298$	15.4707	+	15.4707i	0.896194	+	0.896194i
$299$	−1.77409	−	10.0614i	−0.102598	−	0.581864i
$300$	18.0189	+	26.0838i	1.04032	+	1.50595i
$301$	16.4429	−	5.98474i	0.947755	−	0.344955i
$302$	−2.35215	−	26.8852i	−0.135351	−	1.54707i
$303$	5.41987	−	6.53469i	0.311363	−	0.375408i
$304$	−5.49502	+	15.0974i	−0.315161	+	0.865897i
$305$	−15.2044	−	0.755693i	−0.870603	−	0.0432709i
$306$	12.1009	−	7.17224i	0.691762	−	0.410010i
$307$	3.15476	+	11.7737i	0.180052	+	0.671962i	0.995636	+	0.0933234i	$0.0297491\pi$
$307$	3.15476	+	11.7737i	0.180052	+	0.671962i	−0.815584	+	0.578638i	$0.803584\pi$
$308$	−0.00331040	+	0.0378380i	−0.000188627	+	0.00215602i
$309$	−5.08462	+	19.4197i	−0.289254	+	1.10475i
$310$	1.19821	+	31.8480i	0.0680540	+	1.80885i
$311$	19.9366	+	3.51536i	1.13050	+	0.199338i	0.707447	−	0.706767i	$-0.249847\pi$
$311$	19.9366	+	3.51536i	1.13050	+	0.199338i	0.423054	+	0.906104i	$0.360958\pi$
$312$	−9.45758	+	0.0540918i	−0.535430	+	0.00306235i
$313$	7.21599	+	0.631317i	0.407872	+	0.0356842i	0.289246	−	0.957255i	$-0.406596\pi$
$313$	7.21599	+	0.631317i	0.407872	+	0.0356842i	0.118626	+	0.992939i	$0.462151\pi$
$314$	−1.04673	+	1.81300i	−0.0590706	+	0.102313i
$315$	−16.2462	+	0.797417i	−0.915371	+	0.0449294i
$316$	12.9356	+	22.4052i	0.727686	+	1.26039i
$317$	2.07411	+	4.44794i	0.116493	+	0.249821i	0.955905	−	0.293675i	$-0.0948782\pi$
$317$	2.07411	+	4.44794i	0.116493	+	0.249821i	−0.839412	+	0.543496i	$0.817100\pi$
$318$	1.22704	−	7.19941i	0.0688088	−	0.403723i
$319$	−0.0275787	+	0.0328670i	−0.00154411	+	0.00184020i
$320$	−24.3949	−	5.56271i	−1.36372	−	0.310965i
$321$	−3.47733	−	7.34715i	−0.194085	−	0.410078i
$322$	−34.9356	−	24.4622i	−1.94688	−	1.36322i
$323$	10.7680	−	10.7680i	0.599148	−	0.599148i
$324$	28.1479	−	17.1215i	1.56377	−	0.951192i
$325$	−2.44145	+	6.46427i	−0.135427	+	0.358573i
$326$	15.7577	−	2.77851i	0.872739	−	0.153887i
$327$	−6.56185	+	18.3545i	−0.362871	+	1.01500i
$328$	10.7337	+	5.00520i	0.592668	+	0.276366i
$329$	3.82979	+	3.21358i	0.211143	+	0.177170i
$330$	−0.0393936	+	0.00170778i	−0.00216855	+	9.40100e-5i
$331$	−4.66635	−	1.69841i	−0.256486	−	0.0933531i	0.210577	−	0.977577i	$-0.432466\pi$
$331$	−4.66635	−	1.69841i	−0.256486	−	0.0933531i	−0.467063	+	0.884224i	$0.654688\pi$
$332$	9.65368	−	36.0280i	0.529814	−	1.97729i
$333$	2.15624	−	4.76564i	0.118161	−	0.261156i
$334$	−14.9158	−	8.61167i	−0.816159	−	0.471209i
$335$	16.0686	+	12.4845i	0.877924	+	0.682102i
$336$	−6.13932	+	6.20995i	−0.334927	+	0.338780i
$337$	−12.5919	−	17.9831i	−0.685925	−	0.979602i	−0.999548	−	0.0300546i	$-0.990432\pi$
$337$	−12.5919	−	17.9831i	−0.685925	−	0.979602i	0.313624	−	0.949547i	$-0.398457\pi$
$338$	15.1343	+	21.6140i	0.823195	+	1.17564i
$339$	−3.15814	−	0.826891i	−0.171527	−	0.0449105i
$340$	−12.7388	−	9.89742i	−0.690860	−	0.536763i
$341$	−0.0222000	−	0.0128172i	−0.00120220	−	0.000694090i
$342$	38.5504	−	39.4426i	2.08457	−	2.13281i
$343$	5.09624	−	19.0194i	0.275171	−	1.02695i
$344$	26.7937	+	9.75210i	1.44462	+	0.525798i
$345$	13.2285	−	25.3925i	0.712196	−	1.36709i
$346$	4.35333	+	3.65288i	0.234037	+	0.196380i
$347$	14.1467	+	6.59670i	0.759433	+	0.354129i	0.763454	−	0.645863i	$-0.223502\pi$
$347$	14.1467	+	6.59670i	0.759433	+	0.354129i	−0.00402090	+	0.999992i	$0.501280\pi$
$348$	−62.5434	+	11.3973i	−3.35268	+	0.610959i
$349$	23.5190	−	4.14704i	1.25895	−	0.221986i	0.495928	−	0.868364i	$-0.334828\pi$
$349$	23.5190	−	4.14704i	1.25895	−	0.221986i	0.763017	+	0.646378i	$0.223717\pi$
$350$	11.8744	+	26.2877i	0.634715	+	1.40513i
$351$	6.55934	+	2.92273i	0.350112	+	0.156004i
$352$	0.00894211	−	0.00894211i	0.000476616	−	0.000476616i
$353$	0.263489	+	0.184497i	0.0140241	+	0.00981980i	0.580567	−	0.814212i	$-0.302831\pi$
$353$	0.263489	+	0.184497i	0.0140241	+	0.00981980i	−0.566543	+	0.824032i	$0.691720\pi$
$354$	4.09258	+	0.334480i	0.217518	+	0.0177774i
$355$	20.9587	+	4.77917i	1.11237	+	0.253652i
$356$	−14.2964	+	17.0378i	−0.757707	+	0.903000i
$357$	7.76140	−	2.87529i	0.410777	−	0.152177i
$358$	−16.9175	−	36.2796i	−0.894116	−	1.91744i
$359$	−2.09252	−	3.62435i	−0.110439	−	0.191286i	0.805508	−	0.592585i	$-0.201892\pi$
$359$	−2.09252	−	3.62435i	−0.110439	−	0.191286i	−0.915947	+	0.401298i	$0.868559\pi$
$360$	−21.1148	−	16.0212i	−1.11285	−	0.844391i
$361$	20.3536	−	35.2535i	1.07124	−	1.85545i
$362$	16.8006	+	1.46986i	0.883021	+	0.0772543i
$363$	−9.43174	+	16.5542i	−0.495038	+	0.868869i
$364$	−12.0806	−	2.13013i	−0.633194	−	0.111649i
$365$	−0.241727	−	6.42501i	−0.0126526	−	0.336300i
$366$	27.0574	−	7.41614i	1.41431	−	0.387648i
$367$	−1.16653	+	13.3335i	−0.0608924	+	0.696004i	0.902988	+	0.429667i	$0.141369\pi$
$367$	−1.16653	+	13.3335i	−0.0608924	+	0.696004i	−0.963880	+	0.266337i	$0.914187\pi$
$368$	−3.97833	−	14.8473i	−0.207385	−	0.773970i
$369$	−5.85858	−	6.82197i	−0.304986	−	0.355138i
$370$	−9.26459	−	0.460470i	−0.481643	−	0.0239387i
$371$	1.46974	−	4.03807i	0.0763050	−	0.209646i
$372$	−13.1950	−	35.6177i	−0.684128	−	1.84669i
$373$	−1.36803	−	15.6366i	−0.0708338	−	0.809634i	−0.945652	−	0.325182i	$-0.894575\pi$
$373$	−1.36803	−	15.6366i	−0.0708338	−	0.809634i	0.874818	−	0.484452i	$-0.160981\pi$
$374$	0.0188543	−	0.00686241i	0.000974933	−	0.000354847i
$375$	−16.4596	+	10.2020i	−0.849970	+	0.526830i
$376$	1.41463	+	8.02279i	0.0729542	+	0.413744i
$377$	−9.79812	−	9.79812i	−0.504629	−	0.504629i
$378$	27.9889	−	10.7345i	1.43959	−	0.552121i
$379$			26.4477i			1.35853i	0.733894	+	0.679264i	$0.237701\pi$
$379$			26.4477i			1.35853i	−0.733894	+	0.679264i	$0.762299\pi$
$380$	−58.2884	−	24.5565i	−2.99013	−	1.25972i
$381$	8.39887	+	5.80965i	0.430287	+	0.297637i
$382$	−7.88010	+	16.8989i	−0.403181	+	0.864625i
$383$	18.5309	−	1.62124i	0.946883	−	0.0828415i	0.396758	−	0.917923i	$-0.370135\pi$
$383$	18.5309	−	1.62124i	0.946883	−	0.0828415i	0.550126	+	0.835082i	$0.314580\pi$
$384$	35.7198	−	3.33104i	1.82282	−	0.169987i
$385$	−0.0229838	−	0.00316694i	−0.00117137	−	0.000161402i
$386$	−38.2831	+	22.1028i	−1.94856	+	1.12500i
$387$	−15.4826	−	15.1323i	−0.787022	−	0.769220i
$388$	−44.5560	+	11.9388i	−2.26199	+	0.606098i
$389$	−25.4642	+	21.3670i	−1.29108	+	1.08335i	−0.299472	+	0.954105i	$0.596810\pi$
$389$	−25.4642	+	21.3670i	−1.29108	+	1.08335i	−0.991613	+	0.129243i	$0.958745\pi$
$390$	0.559403	−	12.7223i	0.0283265	−	0.644219i
$391$	−2.52993	+	14.3479i	−0.127944	+	0.725606i
$392$	3.62672	−	2.53946i	0.183177	−	0.128262i
$393$	0.153279	+	26.7998i	0.00773191	+	1.35187i
$394$	10.3018	+	12.2772i	0.518996	+	0.618515i
$395$	−14.0612	+	7.21240i	−0.707496	+	0.362895i
$396$	0.0439726	−	0.0165767i	0.00220971	−	0.000833013i
$397$	33.0030	+	8.84314i	1.65637	+	0.443824i	0.961388	−	0.275198i	$-0.0887434\pi$
$397$	33.0030	+	8.84314i	1.65637	+	0.443824i	0.694987	+	0.719022i	$0.255410\pi$
$398$	−19.4610	+	9.07480i	−0.975490	+	0.454879i
$399$	26.4763	−	18.7655i	1.32547	−	0.939450i
$400$	−2.81160	+	10.0088i	−0.140580	+	0.500439i
$401$	−3.56868	−	9.80487i	−0.178211	−	0.489632i	0.818136	−	0.575025i	$-0.195008\pi$
$401$	−3.56868	−	9.80487i	−0.178211	−	0.489632i	−0.996347	+	0.0853930i	$0.972785\pi$
$402$	−35.3123	−	12.6244i	−1.76122	−	0.629647i
$403$	4.74861	−	6.78172i	0.236545	−	0.337821i
$404$	17.9432			0.892709
$405$	9.59195	+	17.6916i	0.476628	+	0.879105i
$406$	−57.8436			−2.87073
$407$	0.00427944	−	0.00611167i	0.000212124	−	0.000302944i
$408$	12.6999	+	4.54030i	0.628740	+	0.224779i
$409$	−13.0223	−	35.7785i	−0.643911	−	1.76913i	−0.639078	−	0.769142i	$-0.720684\pi$
$409$	−13.0223	−	35.7785i	−0.643911	−	1.76913i	−0.00483335	−	0.999988i	$-0.501539\pi$
$410$	−7.44850	+	14.1003i	−0.367855	+	0.696362i
$411$	5.52177	−	3.91364i	0.272369	−	0.193046i
$412$	−38.4519	+	17.9304i	−1.89439	+	0.883367i
$413$	2.33378	+	0.625335i	0.114838	+	0.0307707i
$414$	−8.56777	+	52.0660i	−0.421083	+	2.55890i
$415$	21.6873	+	6.98197i	1.06459	+	0.342732i
$416$	2.62527	+	3.12868i	0.128715	+	0.153396i
$417$	−0.0538605	−	9.41713i	−0.00263756	−	0.461159i
$418$	0.0644415	−	0.0451224i	0.00315194	−	0.00220701i
$419$	−4.45593	+	25.2708i	−0.217686	+	1.23456i	0.658497	+	0.752583i	$0.271192\pi$
$419$	−4.45593	+	25.2708i	−0.217686	+	1.23456i	−0.876184	+	0.481978i	$0.839919\pi$
$420$	−23.2174	−	25.3530i	−1.13289	−	1.23710i
$421$	−18.3149	+	15.3680i	−0.892611	+	0.748990i	−0.968732	−	0.248109i	$-0.920191\pi$
$421$	−18.3149	+	15.3680i	−0.892611	+	0.748990i	0.0761208	+	0.997099i	$0.475747\pi$
$422$	14.6078	−	3.91416i	0.711098	−	0.190538i
$423$	1.53248	−	5.99264i	0.0745115	−	0.291372i
$424$	6.06417	−	3.50115i	0.294502	−	0.170031i
$425$	6.42449	−	7.47160i	0.311634	−	0.362426i
$426$	−39.4459	+	3.67852i	−1.91116	+	0.178225i
$427$	16.4450	−	1.43875i	0.795829	−	0.0696260i
$428$	7.26039	−	15.5699i	0.350944	−	0.752602i
$429$	0.00842388	+	0.00582695i	0.000406709	+	0.000281328i
$430$	−14.9057	+	35.3807i	−0.718814	+	1.70621i
$431$		−	15.6671i		−	0.754660i	−0.926079	−	0.377330i	$-0.876842\pi$
$431$		−	15.6671i		−	0.754660i	0.926079	−	0.377330i	$-0.123158\pi$
$432$	10.2144	+	3.52046i	0.491439	+	0.169378i
$433$	10.5845	+	10.5845i	0.508657	+	0.508657i	0.914114	−	0.405457i	$-0.132888\pi$
$433$	10.5845	+	10.5845i	0.508657	+	0.508657i	−0.405457	+	0.914114i	$0.632888\pi$
$434$	−6.00127	−	34.0349i	−0.288070	−	1.63373i
$435$	−5.05680	−	38.5021i	−0.242455	−	1.84603i
$436$	−38.7122	+	14.0901i	−1.85398	+	0.674792i
$437$	4.97863	+	56.9060i	0.238160	+	2.72218i
$438$	4.11630	+	11.1113i	0.196684	+	0.530918i
$439$	−7.09912	+	19.5047i	−0.338823	+	0.930907i	0.646907	+	0.762569i	$0.276062\pi$
$439$	−7.09912	+	19.5047i	−0.338823	+	0.930907i	−0.985729	+	0.168338i	$0.946160\pi$
$440$	−0.0253728	−	0.0280269i	−0.00120960	−	0.00133613i
$441$	−3.30366	+	0.621570i	−0.157317	+	0.0295986i
$442$	1.67715	+	6.25923i	0.0797741	+	0.297721i
$443$	0.655331	−	7.49047i	0.0311357	−	0.355883i	−0.964606	−	0.263696i	$-0.915059\pi$
$443$	0.655331	−	7.49047i	0.0311357	−	0.355883i	0.995742	−	0.0921874i	$-0.0293859\pi$
$444$	10.6619	−	2.92231i	0.505993	−	0.138687i
$445$	−9.96091	−	9.23857i	−0.472192	−	0.437950i
$446$	8.80576	+	1.55269i	0.416965	+	0.0735222i
$447$	7.88480	−	13.8391i	0.372938	−	0.654565i
$448$	27.0293	+	2.36476i	1.27701	+	0.111724i
$449$	2.66419	−	4.61452i	0.125731	−	0.217773i	−0.796287	−	0.604918i	$-0.793206\pi$
$449$	2.66419	−	4.61452i	0.125731	−	0.217773i	0.922018	+	0.387146i	$0.126539\pi$
$450$	22.9569	−	27.3246i	1.08220	−	1.28810i
$451$	−0.00641320	−	0.0111080i	−0.000301986	−	0.000523055i
$452$	−2.91594	−	6.25326i	−0.137154	−	0.294129i
$453$	−18.4233	+	6.82513i	−0.865604	+	0.320672i
$454$	9.97027	−	11.8821i	0.467928	−	0.557655i
$455$	1.66586	−	7.30553i	0.0780968	−	0.342489i
$456$	52.7048	+	4.30747i	2.46813	+	0.201716i
$457$	19.2609	+	13.4866i	0.900988	+	0.630879i	0.929543	−	0.368714i	$-0.120202\pi$
$457$	19.2609	+	13.4866i	0.900988	+	0.630879i	−0.0285551	+	0.999592i	$0.509091\pi$
$458$	7.29010	−	7.29010i	0.340644	−	0.340644i
$459$	−7.36426	−	7.11579i	−0.343734	−	0.332137i
$460$	59.1563	−	12.7410i	2.75818	−	0.594053i
$461$	15.8701	−	2.79833i	0.739145	−	0.130331i	0.208615	−	0.977998i	$-0.433104\pi$
$461$	15.8701	−	2.79833i	0.739145	−	0.130331i	0.530529	+	0.847667i	$0.321993\pi$
$462$	0.0420652	−	0.00766555i	0.00195705	−	0.000356634i
$463$	−13.5284	−	6.30838i	−0.628716	−	0.293175i	0.0820233	−	0.996630i	$-0.473862\pi$
$463$	−13.5284	−	6.30838i	−0.628716	−	0.293175i	−0.710740	+	0.703455i	$0.751640\pi$
$464$	−15.9702	−	13.4006i	−0.741398	−	0.622106i
$465$	22.1298	−	6.96999i	1.02624	−	0.323225i
$466$	58.5204	+	21.2997i	2.71091	+	0.986689i
$467$	−1.62693	+	6.07179i	−0.0752854	+	0.280969i	−0.993298	−	0.115583i	$-0.963127\pi$
$467$	−1.62693	+	6.07179i	−0.0752854	+	0.280969i	0.918012	+	0.396552i	$0.129793\pi$
$468$	4.09555	+	14.6141i	0.189317	+	0.675535i
$469$	−19.1095	−	11.0329i	−0.882393	−	0.509450i
$470$	−10.8837	+	1.36618i	−0.502029	+	0.0630170i
$471$	1.47433	+	0.386021i	0.0679335	+	0.0177869i
$472$	2.25819	+	3.22503i	0.103942	+	0.148444i
$473$	−0.0177121	−	0.0252955i	−0.000814402	−	0.00116309i
$474$	20.4756	−	20.7112i	0.940477	−	0.951297i
$475$	16.7489	−	34.8160i	0.768493	−	1.59747i
$476$	15.1495	+	8.74657i	0.694377	+	0.400899i
$477$	−5.29081	+	0.523933i	−0.242249	+	0.0239892i
$478$	11.2854	−	42.1177i	0.516182	−	1.92642i
$479$	−6.42357	−	2.33799i	−0.293501	−	0.106825i	0.191073	−	0.981576i	$-0.438803\pi$
$479$	−6.42357	−	2.33799i	−0.293501	−	0.106825i	−0.484574	+	0.874750i	$0.661025\pi$
$480$	0.495730	+	11.4351i	0.0226269	+	0.521938i
$481$	1.84587	+	1.54887i	0.0841645	+	0.0706224i
$482$	−13.6460	−	6.36322i	−0.621557	−	0.289837i
$483$	−10.4519	+	29.2356i	−0.475578	+	1.33026i
$484$	−39.6557	+	6.99237i	−1.80253	+	0.317835i
$485$	−5.93256	−	27.5448i	−0.269384	−	1.25074i
$486$	−26.9646	−	25.4648i	−1.22314	−	1.15511i
$487$	−11.7403	+	11.7403i	−0.532002	+	0.532002i	−0.921168	−	0.389165i	$-0.872763\pi$
$487$	−11.7403	+	11.7403i	−0.532002	+	0.532002i	0.389165	+	0.921168i	$0.372763\pi$
$488$	22.0347	+	15.4289i	0.997463	+	0.698431i
$489$	−4.98314	−	10.5287i	−0.225345	−	0.476126i
$490$	3.17269	+	5.04700i	0.143327	+	0.228000i
$491$	10.6951	−	12.7459i	0.482663	−	0.575215i	−0.468673	−	0.883372i	$-0.655268\pi$
$491$	10.6951	−	12.7459i	0.482663	−	0.575215i	0.951336	+	0.308157i	$0.0997121\pi$
$492$	3.19313	−	18.7351i	0.143958	−	0.844645i
$493$	8.35099	+	17.9087i	0.376109	+	0.806569i
$494$	12.7035	+	22.0031i	0.571557	+	0.989966i
$495$	0.00877980	+	0.0273295i	0.000394622	+	0.00122837i
$496$	6.22793	−	10.7871i	0.279642	−	0.484355i
$497$	−23.2220	−	2.03166i	−1.04165	−	0.0911326i
$498$	−41.9877	+	0.240145i	−1.88152	+	0.0107612i
$499$	27.4365	+	4.83779i	1.22823	+	0.216569i	0.749863	−	0.661593i	$-0.230119\pi$
$499$	27.4365	+	4.83779i	1.22823	+	0.216569i	0.478363	+	0.878162i	$0.341230\pi$
$500$	−38.8045	−	13.0110i	−1.73539	−	0.581871i
$501$	−3.17587	+	12.1296i	−0.141887	+	0.541909i
$502$	−5.54557	+	63.3862i	−0.247511	+	2.82906i
$503$	−3.86525	−	14.4253i	−0.172343	−	0.643192i	−0.996989	−	0.0775431i	$-0.975292\pi$
$503$	−3.86525	−	14.4253i	−0.172343	−	0.643192i	0.824646	−	0.565649i	$-0.191374\pi$
$504$	25.0537	+	14.0852i	1.11598	+	0.627403i
$505$	−0.544080	+	10.9468i	−0.0242112	+	0.487127i
$506$	−0.0257419	+	0.0707252i	−0.00114436	+	0.00314412i
$507$	12.2627	−	14.7850i	0.544606	−	0.656626i
$508$	1.88116	+	21.5017i	0.0834629	+	0.953985i
$509$	−5.75433	+	2.09440i	−0.255056	+	0.0928328i	−0.466384	−	0.884582i	$-0.654443\pi$
$509$	−5.75433	+	2.09440i	−0.255056	+	0.0928328i	0.211328	+	0.977415i	$0.432221\pi$
$510$	−6.95473	+	16.7756i	−0.307961	+	0.742834i
$511$	1.21069	+	6.86619i	0.0535580	+	0.303742i
$512$	15.9632	+	15.9632i	0.705482	+	0.705482i
$513$	−35.1110	−	19.4759i	−1.55019	−	0.859883i
$514$			9.32621i			0.411361i
$515$	−9.77303	−	24.0024i	−0.430651	−	1.05767i
$516$	3.72713	−	45.6039i	0.164078	−	2.00760i
$517$	0.00372867	−	0.00799616i	0.000163987	−	0.000351671i
$518$	10.0205	−	0.876681i	0.440276	−	0.0385191i
$519$	1.72693	−	3.75941i	0.0758039	−	0.165020i
$520$	9.73138	−	7.37438i	0.426749	−	0.323388i
$521$	19.3541	−	11.1741i	0.847920	−	0.489547i	−0.0120282	−	0.999928i	$-0.503829\pi$
$521$	19.3541	−	11.1741i	0.847920	−	0.489547i	0.859949	+	0.510381i	$0.170495\pi$
$522$	30.9851	+	64.5108i	1.35618	+	2.82356i
$523$	3.27820	−	0.878392i	0.143346	−	0.0384094i	−0.186433	−	0.982468i	$-0.559693\pi$
$523$	3.27820	−	0.878392i	0.143346	−	0.0384094i	0.329778	+	0.944058i	$0.393026\pi$
$524$	−43.3905	+	36.4089i	−1.89552	+	1.59053i
$525$	16.1714	−	13.3957i	0.705778	−	0.584637i
$526$	12.7435	−	72.2722i	0.555645	−	3.15122i
$527$	−9.67101	+	6.77171i	−0.421276	+	0.294980i
$528$	0.0133898	+	0.00762881i	0.000582715	+	0.000332001i
$529$	−20.3451	−	24.2463i	−0.884569	−	1.05419i
$530$	4.30307	+	8.38921i	0.186913	+	0.364404i
$531$	−0.552725	−	2.93775i	−0.0239862	−	0.127488i
$532$	66.2503	+	17.7517i	2.87232	+	0.769635i
$533$	3.75433	−	1.75067i	0.162618	−	0.0758301i
$534$	22.7519	+	10.4514i	0.984570	+	0.452275i
$535$	9.27877	+	4.90154i	0.401156	+	0.211912i
$536$	−12.2976	−	33.7875i	−0.531178	−	1.45940i
$537$	−22.2163	+	18.8592i	−0.958702	+	0.813836i
$538$	−15.7180	+	22.4477i	−0.677652	+	0.967787i
$539$	−0.00479492			−0.000206532
$540$	−15.8384	+	39.4744i	−0.681577	+	1.69871i
$541$	−32.7244			−1.40693			−0.703466	−	0.710729i	$-0.748365\pi$
$541$	−32.7244			−1.40693			−0.703466	+	0.710729i	$0.748365\pi$
$542$	−9.25340	+	13.2152i	−0.397467	+	0.567642i
$543$	−2.20107	−	12.0785i	−0.0944569	−	0.518338i
$544$	−1.99201	−	5.47299i	−0.0854065	−	0.234653i
$545$	−7.42224	−	24.0448i	−0.317934	−	1.02997i
$546$	1.28221	+	13.7496i	0.0548736	+	0.588427i
$547$	25.9469	−	12.0993i	1.10941	−	0.517327i	0.220491	−	0.975389i	$-0.429234\pi$
$547$	25.9469	−	12.0993i	1.10941	−	0.517327i	0.888920	+	0.458063i	$0.151456\pi$
$548$	13.8168	+	3.70221i	0.590226	+	0.158151i
$549$	−10.4137	−	17.5698i	−0.444445	−	0.749861i
$550$	0.0393869	−	0.0322484i	0.00167946	−	0.00137508i
$551$	49.8005	+	59.3499i	2.12157	+	2.52839i
$552$	−43.6686	+	25.5462i	−1.85866	+	1.08732i
$553$	14.0375	−	9.82914i	0.596934	−	0.417977i
$554$	4.10455	−	23.2780i	0.174385	−	0.988989i
$555$	1.45955	+	6.59325i	0.0619545	+	0.279868i
$556$	15.2469	−	12.7937i	0.646612	−	0.542572i
$557$	21.1671	−	5.67171i	0.896879	−	0.240318i	0.219203	−	0.975679i	$-0.429654\pi$
$557$	21.1671	−	5.67171i	0.896879	−	0.240318i	0.677675	+	0.735361i	$0.262988\pi$
$558$	−34.7431	+	24.9245i	−1.47079	+	1.05514i
$559$	8.63696	−	4.98655i	0.365304	−	0.210909i
$560$	1.53883	−	11.1679i	0.0650275	−	0.471932i
$561$	−0.00844633	−	0.0119170i	−0.000356604	−	0.000503135i
$562$	−61.7663	+	5.40385i	−2.60545	+	0.227948i
$563$	4.57310	−	9.80704i	0.192733	−	0.413317i	−0.786065	−	0.618143i	$-0.787885\pi$
$563$	4.57310	−	9.80704i	0.192733	−	0.413317i	0.978798	+	0.204826i	$0.0656629\pi$
$564$	11.8164	−	5.59256i	0.497559	−	0.235489i
$565$	3.90341	−	1.58935i	0.164218	−	0.0668643i
$566$			17.6948i			0.743770i
$567$	−12.9227	−	17.5852i	−0.542703	−	0.738509i
$568$	−26.8592	−	26.8592i	−1.12699	−	1.12699i
$569$	−2.29260	−	13.0020i	−0.0961109	−	0.545072i	−0.994401	−	0.105670i	$-0.966301\pi$
$569$	−2.29260	−	13.0020i	−0.0961109	−	0.545072i	0.898290	−	0.439402i	$-0.144810\pi$
$570$	−9.31555	+	70.5902i	−0.390185	+	2.95670i
$571$	−7.42564	+	2.70271i	−0.310753	+	0.113105i	−0.492689	−	0.870206i	$-0.663986\pi$
$571$	−7.42564	+	2.70271i	−0.310753	+	0.113105i	0.181936	+	0.983310i	$0.441764\pi$
$572$	0.00188676	+	0.0215658i	7.88894e−5	+	0.000901710i
$573$	13.3811	+	2.28062i	0.559004	+	0.0952742i
$574$	5.91434	−	16.2495i	0.246860	−	0.678242i
$575$	5.97929	+	36.4765i	0.249353	+	1.52117i
$576$	−11.8415	−	31.4115i	−0.493394	−	1.30881i
$577$	−6.75192	−	25.1985i	−0.281086	−	1.04903i	−0.951652	−	0.307178i	$-0.900615\pi$
$577$	−6.75192	−	25.1985i	−0.281086	−	1.04903i	0.670566	−	0.741850i	$-0.266051\pi$
$578$	−2.71978	+	31.0872i	−0.113128	+	1.29306i
$579$	22.8854	+	22.6251i	0.951083	+	0.940266i
$580$	55.8114	−	60.1751i	2.31744	−	2.49864i
$581$	−24.3307	−	4.29016i	−1.00941	−	0.177986i
$582$	26.2204	+	44.8211i	1.08687	+	1.85790i
$583$	−0.00755470		0.000660950i	−0.000312884		2.73738e-5i
$584$	−5.68051	+	9.83893i	−0.235061	+	0.407138i
$585$	−9.03994	+	2.05548i	−0.373755	+	0.0849838i
$586$	9.91592	+	17.1749i	0.409623	+	0.709488i
$587$	−6.43160	−	13.7926i	−0.265460	−	0.569282i	0.727719	−	0.685875i	$-0.240580\pi$
$587$	−6.43160	−	13.7926i	−0.265460	−	0.569282i	−0.993180	+	0.116593i	$0.962803\pi$
$588$	−5.46861	−	4.53567i	−0.225522	−	0.187048i
$589$	−29.7544	+	35.4599i	−1.22601	+	1.46110i
$590$	−4.48800	+	2.82128i	−0.184768	+	0.116150i
$591$	6.63732	−	9.59542i	0.273023	−	0.394703i
$592$	2.96969	+	2.07940i	0.122053	+	0.0854627i
$593$	−30.1991	+	30.1991i	−1.24013	+	1.24013i	−0.280181	+	0.959947i	$0.590395\pi$
$593$	−30.1991	+	30.1991i	−1.24013	+	1.24013i	−0.959947	+	0.280181i	$0.909605\pi$
$594$	−0.0310822	−	0.0428075i	−0.00127532	−	0.00175641i
$595$	−5.79548	+	8.97720i	−0.237592	+	0.368029i
$596$	33.1516	−	5.84552i	1.35794	−	0.239442i
$597$	10.1164	+	11.9172i	0.414036	+	0.487737i
$598$	−22.0301	−	10.2728i	−0.900876	−	0.420086i
$599$	−13.7064	−	11.5010i	−0.560028	−	0.469920i	0.318292	−	0.947993i	$-0.396891\pi$
$599$	−13.7064	−	11.5010i	−0.560028	−	0.469920i	−0.878320	+	0.478073i	$0.841335\pi$
$600$	34.2171	+	0.216829i	1.39691	+	0.00885200i
$601$	−34.7520	−	12.6487i	−1.41757	−	0.515952i	−0.484225	−	0.874944i	$-0.660898\pi$
$601$	−34.7520	−	12.6487i	−1.41757	−	0.515952i	−0.933341	+	0.358992i	$0.883121\pi$
$602$	10.7752	−	40.2135i	0.439163	−	1.63898i
$603$	−2.06815	+	27.2220i	−0.0842216	+	1.10857i
$604$	−35.9606	−	20.7619i	−1.46322	−	0.844788i
$605$	−3.06346	−	24.4052i	−0.124547	−	0.992212i
$606$	−5.33943	−	19.4807i	−0.216900	−	0.791348i
$607$	−24.8599	−	35.5036i	−1.00903	−	1.44105i	−0.894203	−	0.447663i	$-0.852257\pi$
$607$	−24.8599	−	35.5036i	−1.00903	−	1.44105i	−0.114830	−	0.993385i	$-0.536632\pi$
$608$	−13.0980	−	18.7059i	−0.531196	−	0.758626i
$609$	11.1312	+	40.6118i	0.451060	+	1.64567i
$610$	−22.2217	+	28.6013i	−0.899732	+	1.15803i
$611$	2.46768	+	1.42471i	0.0998316	+	0.0576378i
$612$	1.63958	−	21.5810i	0.0662761	−	0.872359i
$613$	−0.0568446	+	0.212147i	−0.00229593	+	0.00856854i	−0.967064	−	0.254532i	$-0.918079\pi$
$613$	−0.0568446	+	0.212147i	−0.00229593	+	0.00856854i	0.964768	+	0.263101i	$0.0847452\pi$
$614$	27.2515	+	9.91873i	1.09978	+	0.400287i
$615$	11.3331	+	2.51616i	0.456995	+	0.101461i
$616$	0.0314049	+	0.0263518i	0.00126534	+	0.00106175i
$617$	24.8316	+	11.5791i	0.999681	+	0.466159i	0.852374	−	0.522932i	$-0.175162\pi$
$617$	24.8316	+	11.5791i	0.999681	+	0.466159i	0.147307	+	0.989091i	$0.452940\pi$
$618$	30.9090	+	36.4110i	1.24334	+	1.46466i
$619$	40.1687	−	7.08283i	1.61452	−	0.284683i	0.707797	−	0.706416i	$-0.249689\pi$
$619$	40.1687	−	7.08283i	1.61452	−	0.284683i	0.906720	+	0.421733i	$0.138578\pi$
$620$	41.1972	+	26.5960i	1.65452	+	1.06812i
$621$	38.2041	−	4.00401i	1.53308	−	0.160675i
$622$	34.0580	−	34.0580i	1.36560	−	1.36560i
$623$	12.0678	+	8.45000i	0.483488	+	0.338542i
$624$	−2.83134	+	4.09320i	−0.113344	+	0.163859i
$625$	9.11442	−	23.2793i	0.364577	−	0.931173i
$626$	11.0778	−	13.2020i	0.442758	−	0.527658i
$627$	−0.0440812	−	0.0365609i	−0.00176043	−	0.00146010i
$628$	1.36126	+	2.91924i	0.0543203	+	0.116490i
$629$	−1.71810	−	2.97584i	−0.0685053	−	0.118655i
$630$	−20.6165	+	32.7512i	−0.821382	+	1.30484i
$631$	−21.0645	+	36.4848i	−0.838565	+	1.45244i	0.0525304	+	0.998619i	$0.483271\pi$
$631$	−21.0645	+	36.4848i	−0.838565	+	1.45244i	−0.891095	+	0.453817i	$0.850062\pi$
$632$	27.8177	+	2.43373i	1.10653	+	0.0968087i
$633$	−5.55920	−	9.50288i	−0.220958	−	0.377706i
$634$	11.4992	+	2.02762i	0.456693	+	0.0805272i
$635$	−13.1748	+	0.495675i	−0.522827	+	0.0196703i
$636$	−7.99093	−	7.90004i	−0.316861	−	0.313257i
$637$	0.134968	−	1.54269i	0.00534761	−	0.0611235i
$638$	0.0264202	+	0.0986016i	0.00104599	+	0.00390367i
$639$	10.1735	+	26.9869i	0.402458	+	1.06759i
$640$	−34.3344	+	31.0830i	−1.35719	+	1.22866i
$641$	−8.97472	+	24.6578i	−0.354480	+	0.973926i	0.626432	+	0.779476i	$0.284514\pi$
$641$	−8.97472	+	24.6578i	−0.354480	+	0.973926i	−0.980912	+	0.194450i	$0.937708\pi$
$642$	−19.0645	−	3.24928i	−0.752418	−	0.128239i
$643$	−2.57976	−	29.4868i	−0.101736	−	1.16284i	−0.859788	−	0.510651i	$-0.829404\pi$
$643$	−2.57976	−	29.4868i	−0.101736	−	1.16284i	0.758052	−	0.652194i	$-0.226151\pi$
$644$	−61.6619	+	22.4431i	−2.42982	+	0.884382i
$645$	27.7090	+	3.65667i	1.09104	+	0.143981i
$646$	−6.29152	−	35.6810i	−0.247536	−	1.40385i
$647$	−3.41329	−	3.41329i	−0.134190	−	0.134190i	0.636821	−	0.771012i	$-0.280249\pi$
$647$	−3.41329	−	3.41329i	−0.134190	−	0.134190i	−0.771012	+	0.636821i	$0.780249\pi$
$648$	2.28810	−	35.4865i	0.0898852	−	1.39404i
$649$		−	0.00426384i		−	0.000167370i
$650$	9.26673	+	13.5798i	0.363471	+	0.532644i
$651$	−22.7409	+	10.7630i	−0.891287	+	0.421837i
$652$	10.4044	−	22.3123i	0.407468	−	0.873818i
$653$	−44.7996	+	3.91945i	−1.75314	+	0.153380i	−0.917981	−	0.396625i	$-0.870181\pi$
$653$	−44.7996	+	3.91945i	−1.75314	+	0.153380i	−0.835161	+	0.550005i	$0.814626\pi$
$654$	26.8171	+	37.8364i	1.04863	+	1.47952i
$655$	−20.8967	−	27.5757i	−0.816500	−	1.07747i
$656$	5.39742	−	3.11620i	0.210734	−	0.121667i
$657$	7.00907	−	5.02826i	0.273450	−	0.196171i
$658$	11.4895	−	3.07859i	0.447906	−	0.120016i
$659$	31.0081	−	26.0189i	1.20790	−	1.01355i	0.208535	−	0.978015i	$-0.433130\pi$
$659$	31.0081	−	26.0189i	1.20790	−	1.01355i	0.999368	−	0.0355365i	$-0.0113140\pi$
$660$	−0.0326128	+	0.0511570i	−0.00126945	+	0.00199128i
$661$	−2.96480	+	16.8142i	−0.115318	+	0.653998i	0.871275	+	0.490795i	$0.163294\pi$
$661$	−2.96480	+	16.8142i	−0.115318	+	0.653998i	−0.986593	+	0.163203i	$0.947817\pi$
$662$	−9.67810	+	6.77668i	−0.376150	+	0.263383i
$663$	4.07183	−	2.38203i	0.158137	−	0.0925103i
$664$	−25.8776	−	30.8397i	−1.00424	−	1.19681i
$665$	−12.8388	+	39.8798i	−0.497869	+	1.54647i
$666$	−6.34542	−	10.7059i	−0.245880	−	0.414845i
$667$	−71.5973	−	19.1844i	−2.77226	−	0.742824i
$668$	−24.0171	+	11.1994i	−0.929250	+	0.433316i
$669$	−0.604411	−	6.48129i	−0.0233679	−	0.250581i
$670$	46.2599	−	14.2797i	1.78718	−	0.551673i
$671$	−0.00996382	−	0.0273754i	−0.000384649	−	0.00105681i
$672$	−2.22514	−	12.2106i	−0.0858367	−	0.471034i
$673$	−17.5288	+	25.0337i	−0.675685	+	0.964978i	0.324135	+	0.946011i	$0.394927\pi$
$673$	−17.5288	+	25.0337i	−0.675685	+	0.964978i	−0.999820	+	0.0189672i	$0.993962\pi$
$674$	−52.2317			−2.01189
$675$	−23.6023	−	10.8597i	−0.908452	−	0.417989i
$676$	40.5973			1.56144
$677$	12.3542	−	17.6437i	0.474812	−	0.678102i	−0.508284	−	0.861189i	$-0.669720\pi$
$677$	12.3542	−	17.6437i	0.474812	−	0.678102i	0.983097	+	0.183087i	$0.0586090\pi$
$678$	−5.92136	+	5.02660i	−0.227408	+	0.193045i
$679$	10.4501	+	28.7114i	0.401038	+	1.10184i
$680$	−16.6372	+	5.13563i	−0.638007	+	0.196942i
$681$	−10.2610	−	4.71354i	−0.393203	−	0.180623i
$682$	−0.0552756	+	0.0257754i	−0.00211661	+	0.000986992i
$683$	−8.93120	−	2.39311i	−0.341743	−	0.0915697i	0.0838658	−	0.996477i	$-0.473273\pi$
$683$	−8.93120	−	2.39311i	−0.341743	−	0.0915697i	−0.425609	+	0.904907i	$0.639940\pi$
$684$	−15.6905	−	83.3956i	−0.599942	−	3.18871i
$685$	−2.67761	+	8.31713i	−0.102306	+	0.317781i
$686$	−30.1131	−	35.8874i	−1.14972	−	1.37019i
$687$	−6.52124	−	3.71547i	−0.248801	−	0.141754i
$688$	12.2912	−	8.60637i	0.468597	−	0.328115i
$689$	0.425300	−	2.41199i	0.0162026	−	0.0918897i
$690$	−31.4361	−	60.4337i	−1.19675	−	2.30067i
$691$	15.9016	−	13.3430i	0.604925	−	0.507592i	−0.288099	−	0.957601i	$-0.593023\pi$
$691$	15.9016	−	13.3430i	0.604925	−	0.507592i	0.893024	+	0.450008i	$0.148579\pi$
$692$	8.44577	−	2.26304i	0.321060	−	0.0860278i
$693$	−0.0134768	−	0.0280587i	−0.000511943	−	0.00106586i
$694$	32.1620	−	18.5688i	1.22085	−	0.704860i
$695$	7.34284	+	9.68976i	0.278530	+	0.367553i
$696$	−28.6428	+	62.3533i	−1.08570	+	2.36350i
$697$	−5.88482	+	0.514855i	−0.222903	+	0.0195015i
$698$	24.0132	−	51.4966i	0.908915	−	1.94917i
$699$	3.69296	−	45.1858i	0.139681	−	1.70908i
$700$	43.6110	+	8.23311i	1.64834	+	0.311182i
$701$		−	5.94733i		−	0.224627i	−0.993673	−	0.112314i	$-0.964174\pi$
$701$		−	5.94733i		−	0.224627i	0.993673	−	0.112314i	$-0.0358262\pi$
$702$	14.6475	−	8.79523i	0.552835	−	0.331955i
$703$	−9.52667	−	9.52667i	−0.359305	−	0.359305i
$704$	−0.00831467	−	0.0471548i	−0.000313371	−	0.00177721i
$705$	3.05361	+	7.37852i	0.115006	+	0.277891i
$706$	0.719149	−	0.261749i	0.0270655	−	0.00985105i
$707$	−1.03586	−	11.8400i	−0.0389577	−	0.445289i
$708$	4.03330	−	4.86292i	0.151581	−	0.182760i
$709$	−0.0976022	+	0.268160i	−0.00366553	+	0.0100710i	−0.941512	−	0.336980i	$-0.890595\pi$
$709$	−0.0976022	+	0.268160i	−0.00366553	+	0.0100710i	0.937846	+	0.347051i	$0.112817\pi$
$710$	37.9159	−	34.3254i	1.42296	−	1.28821i
$711$	−18.4815	−	10.3903i	−0.693111	−	0.389666i
$712$	6.21318	+	23.1879i	0.232849	+	0.869004i
$713$	3.85981	−	44.1179i	0.144551	−	1.65223i
$714$	4.98792	−	19.0503i	0.186668	−	0.712941i
$715$	−0.0132141		0.000497151i	−0.000494178		1.85924e-5i
$716$	−60.6550	−	10.6951i	−2.26678	−	0.399695i
$717$	−31.7424	+	0.181548i	−1.18544	+	0.00678004i
$718$	−9.91925	−	0.867822i	−0.370183	−	0.0323868i
$719$	−13.3454	+	23.1148i	−0.497698	+	0.862038i	−0.999996	−	0.00265626i	$-0.999154\pi$
$719$	−13.3454	+	23.1148i	−0.497698	+	0.862038i	0.502299	+	0.864694i	$0.332488\pi$
$720$	−13.2795	+	4.26614i	−0.494898	+	0.158990i
$721$	14.0514	+	24.3377i	0.523300	+	0.906382i
$722$	−40.9312	−	87.7772i	−1.52330	−	3.26673i
$723$	−1.84161	+	10.8053i	−0.0684902	+	0.401854i
$724$	16.6792	−	19.8775i	0.619879	−	0.738743i
$725$	35.0193	+	35.8741i	1.30059	+	1.33233i
$726$	19.3920	+	40.9728i	0.719705	+	1.52064i
$727$	41.3229	+	28.9346i	1.53258	+	1.07313i	0.968998	+	0.247067i	$0.0794668\pi$
$727$	41.3229	+	28.9346i	1.53258	+	1.07313i	0.563584	+	0.826059i	$0.309422\pi$
$728$	−9.36225	+	9.36225i	−0.346988	+	0.346988i
$729$	−12.6898	+	23.8321i	−0.469993	+	0.882670i
$730$	−12.8518	−	8.29686i	−0.475668	−	0.307081i
$731$	−14.0060	+	2.46963i	−0.518030	+	0.0913427i
$732$	14.5315	−	40.6467i	0.537099	−	1.50235i
$733$	36.3592	+	16.9546i	1.34296	+	0.626231i	0.955318	−	0.295580i	$-0.0955128\pi$
$733$	36.3592	+	16.9546i	1.34296	+	0.626231i	0.387639	+	0.921811i	$0.373291\pi$
$734$	24.3943	+	20.4693i	0.900411	+	0.755535i
$735$	2.93294	−	3.19876i	0.108183	−	0.117988i
$736$	20.5300	+	7.47229i	0.756744	+	0.275432i
$737$	−0.0100786	+	0.0376137i	−0.000371249	+	0.00138552i
$738$	−21.2906	+	2.10835i	−0.783719	+	0.0776093i
$739$	−18.7080	−	10.8011i	−0.688186	−	0.397324i	0.114746	−	0.993395i	$-0.463395\pi$
$739$	−18.7080	−	10.8011i	−0.688186	−	0.397324i	−0.802932	+	0.596070i	$0.796728\pi$
$740$	−8.75643	+	11.2703i	−0.321893	+	0.414304i
$741$	13.0037	−	13.1533i	0.477702	−	0.483198i
$742$	−5.86427	−	8.37505i	−0.215284	−	0.307458i
$743$	15.7534	+	22.4982i	0.577937	+	0.825380i	0.996568	−	0.0827765i	$-0.0263788\pi$
$743$	15.7534	+	22.4982i	0.577937	+	0.825380i	−0.418631	+	0.908156i	$0.637490\pi$
$744$	−39.6601	−	10.3841i	−1.45401	−	0.380701i
$745$	2.56101	+	20.4024i	0.0938280	+	0.747486i
$746$	−32.3418	−	18.6725i	−1.18412	−	0.683650i
$747$	8.24858	+	29.4332i	0.301800	+	1.07691i
$748$	0.00799004	−	0.0298192i	0.000292145	−	0.00109030i
$749$	−10.6931	−	3.89197i	−0.390717	−	0.142210i
$750$	−2.57867	+	46.0012i	−0.0941598	+	1.67972i
$751$	36.9715	+	31.0228i	1.34911	+	1.13204i	0.979184	+	0.202976i	$0.0650615\pi$
$751$	36.9715	+	31.0228i	1.34911	+	1.13204i	0.369926	+	0.929061i	$0.379383\pi$
$752$	3.88537	+	1.81178i	0.141685	+	0.0660687i
$753$	45.5704	−	8.30430i	1.66068	−	0.302625i
$754$	−32.4671	+	5.72483i	−1.18238	+	0.208486i
$755$	13.7568	−	21.3093i	0.500662	−	0.775525i
$756$	11.1713	−	44.7492i	0.406294	−	1.62751i
$757$	25.7438	−	25.7438i	0.935673	−	0.935673i	−0.0623799	−	0.998052i	$-0.519869\pi$
$757$	25.7438	−	25.7438i	0.935673	−	0.935673i	0.998052	+	0.0623799i	$0.0198691\pi$
$758$	51.5451	+	36.0923i	1.87220	+	1.31093i
$759$	0.0546096	+	0.00446315i	0.00198220	+	0.000162002i
$760$	−57.7971	+	36.3329i	−2.09652	+	1.31793i
$761$	8.43284	−	10.0499i	0.305690	−	0.364308i	−0.591227	−	0.806505i	$-0.701356\pi$
$761$	8.43284	−	10.0499i	0.305690	−	0.364308i	0.896918	+	0.442197i	$0.145801\pi$
$762$	22.7843	−	8.44069i	0.825388	−	0.305774i
$763$	11.5323	+	24.7311i	0.417498	+	0.895327i
$764$	14.3444	+	24.8452i	0.518961	+	0.898867i
$765$	13.1164	+	1.65466i	0.474225	+	0.0598244i
$766$	22.1287	−	38.3280i	0.799543	−	1.38485i
$767$	1.37182	+	0.120019i	0.0495336	+	0.00433362i
$768$	23.0646	−	40.4820i	0.832272	−	1.46077i
$769$	3.71767	+	0.655525i	0.134062	+	0.0236388i	0.240277	−	0.970704i	$-0.422762\pi$
$769$	3.71767	+	0.655525i	0.134062	+	0.0236388i	−0.106214	+	0.994343i	$0.533873\pi$
$770$	−0.0375374	+	0.0404724i	−0.00135275	+	0.00145852i
$771$	6.54790	−	1.79470i	0.235817	−	0.0646347i
$772$	−5.92790	+	67.7562i	−0.213350	+	2.43860i
$773$	−6.14142	−	22.9201i	−0.220892	−	0.824379i	−0.984009	−	0.178119i	$-0.942999\pi$
$773$	−6.14142	−	22.9201i	−0.220892	−	0.824379i	0.763117	−	0.646260i	$-0.223668\pi$
$774$	−50.6206	+	9.52404i	−1.81952	+	0.342334i
$775$	−17.4749	+	24.3271i	−0.627716	+	0.873857i
$776$	−17.0284	+	46.7851i	−0.611284	+	1.67949i
$777$	−2.54383	−	6.86666i	−0.0912593	−	0.246340i
$778$	6.89296	+	78.7869i	0.247125	+	2.82465i
$779$	−21.7646	+	7.92167i	−0.779798	+	0.283823i
$780$	−15.5409	−	11.9326i	−0.556454	−	0.427255i
$781$	0.00714349	+	0.0405128i	0.000255614	+	0.00144966i
$782$	24.5108	+	24.5108i	0.876503	+	0.876503i
$783$	39.3301	−	34.1688i	1.40554	−	1.22109i
$784$		−	2.32987i		−	0.0832097i
$785$	−1.82225	+	0.741962i	−0.0650388	+	0.0264818i
$786$	52.4404	+	36.2740i	1.87049	+	1.29385i
$787$	−1.00203	+	2.14886i	−0.0357185	+	0.0765987i	−0.923357	−	0.383941i	$-0.874566\pi$
$787$	−1.00203	+	2.14886i	−0.0357185	+	0.0765987i	0.887639	+	0.460540i	$0.152344\pi$
$788$	24.5650	−	2.14916i	0.875092	−	0.0765606i
$789$	−53.1944	+	4.96063i	−1.89377	+	0.176603i
$790$	−5.13226	+	37.2470i	−0.182598	+	1.32519i
$791$	−3.95793	+	2.28511i	−0.140728	+	0.0812492i
$792$	0.0125665	−	0.0491406i	0.000446532	−	0.00174613i
$793$	9.08804	−	2.43513i	0.322726	−	0.0864741i
$794$	62.2728	−	52.2531i	2.20998	−	1.85439i
$795$	5.06196	−	4.63556i	0.179529	−	0.164406i
$796$	−5.73703	+	32.5363i	−0.203343	+	1.15322i
$797$	15.7860	−	11.0535i	0.559169	−	0.391534i	−0.259549	−	0.965730i	$-0.583574\pi$
$797$	15.7860	−	11.0535i	0.559169	−	0.391534i	0.818718	+	0.574196i	$0.194685\pi$
$798$	−0.441593	−	77.2094i	−0.0156322	−	2.73318i
$799$	−2.61190	−	3.11275i	−0.0924025	−	0.110121i
$800$	−9.36100	−	11.4331i	−0.330961	−	0.404223i
$801$	2.95958	−	17.9852i	0.104571	−	0.635477i
$802$	−23.9792	−	6.42520i	−0.846734	−	0.226882i
$803$	0.0111513	−	0.00519993i	0.000393520	−	0.000183501i
$804$	−47.0746	+	33.3648i	−1.66019	+	1.17669i
$805$	−11.8224	−	38.2993i	−0.416684	−	1.34987i
$806$	−6.73692	−	18.5095i	−0.237298	−	0.651971i
$807$	18.7851	+	6.71581i	0.661268	+	0.236408i
$808$	11.1084	−	15.8644i	0.390792	−	0.558108i
$809$	48.9190			1.71990			0.859951	−	0.510377i	$-0.170494\pi$
$809$	48.9190			1.71990			0.859951	+	0.510377i	$0.170494\pi$
$810$	47.5698	+	5.44900i	1.67143	+	0.191458i
$811$	11.0352			0.387500			0.193750	−	0.981051i	$-0.437935\pi$
$811$	11.0352			0.387500			0.193750	+	0.981051i	$0.437935\pi$
$812$	−51.0475	+	72.9034i	−1.79142	+	2.55841i
$813$	11.0591	+	3.95368i	0.387858	+	0.138662i
$814$	−0.00607130	−	0.0166808i	−0.000212799	−	0.000584660i
$815$	13.2968	+	7.02409i	0.465768	+	0.246043i
$816$	5.79050	−	4.10411i	0.202708	−	0.143673i
$817$	−50.5376	+	23.5661i	−1.76809	+	0.824472i
$818$	−87.5012	−	23.4459i	−3.05941	−	0.819766i
$819$	9.40677	−	3.54616i	0.328699	−	0.123913i
$820$	11.1979	+	21.8314i	0.391049	+	0.762384i
$821$	−7.94924	−	9.47354i	−0.277431	−	0.330629i	0.609279	−	0.792956i	$-0.291459\pi$
$821$	−7.94924	−	9.47354i	−0.277431	−	0.330629i	−0.886709	+	0.462327i	$0.847015\pi$
$822$	−0.0920964	−	16.1024i	−0.00321223	−	0.561636i
$823$	−31.6390	+	22.1538i	−1.10286	+	0.772234i	−0.975583	−	0.219632i	$-0.929514\pi$
$823$	−31.6390	+	22.1538i	−1.10286	+	0.772234i	−0.127282	+	0.991867i	$0.540625\pi$
$824$	−7.95190	+	45.0975i	−0.277018	+	1.57104i
$825$	−0.0302210	−	0.0214476i	−0.00105216	−	0.000746710i
$826$	4.40357	−	3.69503i	0.153220	−	0.128567i
$827$	−17.1270	+	4.58916i	−0.595563	+	0.159581i	−0.543994	−	0.839089i	$-0.683089\pi$
$827$	−17.1270	+	4.58916i	−0.595563	+	0.159581i	−0.0515685	+	0.998669i	$0.516422\pi$
$828$	58.0604	+	56.7471i	2.01774	+	1.97210i
$829$	−20.1611	+	11.6400i	−0.700224	+	0.404275i	−0.807431	−	0.589962i	$-0.799143\pi$
$829$	−20.1611	+	11.6400i	−0.700224	+	0.404275i	0.107207	+	0.994237i	$0.465809\pi$
$830$	43.2033	−	32.7392i	1.49961	−	1.13639i
$831$	−17.1333	+	1.59776i	−0.594347	+	0.0554257i
$832$	15.4053	−	1.34779i	0.534084	−	0.0467263i
$833$	−0.933284	+	2.00143i	−0.0323364	+	0.0693455i
$834$	−18.4269	−	12.7462i	−0.638073	−	0.441366i
$835$	−6.10426	−	14.9920i	−0.211246	−	0.518818i
$836$		−	0.121040i		−	0.00418626i
$837$	24.1853	+	19.5967i	0.835965	+	0.677359i
$838$	43.1705	+	43.1705i	1.49130	+	1.49130i
$839$	0.280939	+	1.59329i	0.00969910	+	0.0550063i	0.989273	−	0.146077i	$-0.0466648\pi$
$839$	0.280939	+	1.59329i	0.00969910	+	0.0550063i	−0.979574	+	0.201084i	$0.935554\pi$
$840$	−36.7893	+	4.83185i	−1.26935	+	0.166715i
$841$	−67.2182	+	24.4654i	−2.31787	+	0.843635i
$842$	4.95770	+	56.6667i	0.170854	+	1.95286i
$843$	15.6801	+	42.3260i	0.540052	+	1.45778i
$844$	7.95832	−	21.8653i	0.273937	−	0.752635i
$845$	−1.23101	+	24.7676i	−0.0423479	+	0.852033i
$846$	−9.58800	−	11.1647i	−0.329642	−	0.383849i
$847$	6.90330	+	25.7635i	0.237200	+	0.885243i
$848$	0.321159	−	3.67086i	0.0110286	−	0.126058i
$849$	12.4235	−	3.40514i	0.426373	−	0.116864i
$850$	−5.79444	−	22.7172i	−0.198748	−	0.779193i
$851$	12.6939	+	2.23827i	0.435141	+	0.0767270i
$852$	−30.1751	+	52.9621i	−1.03378	+	1.81445i
$853$	−22.5084	−	1.96923i	−0.770674	−	0.0674252i	−0.304965	−	0.952363i	$-0.598645\pi$
$853$	−22.5084	−	1.96923i	−0.770674	−	0.0674252i	−0.465708	+	0.884938i	$0.654200\pi$
$854$	19.6379	−	34.0138i	0.671994	−	1.16393i
$855$	51.3538	−	7.04373i	1.75626	−	0.240891i
$856$	−9.27130	−	16.0584i	−0.316886	−	0.548863i
$857$	−13.0587	−	28.0044i	−0.446076	−	0.956612i	−0.992854	−	0.119335i	$-0.961924\pi$
$857$	−13.0587	−	28.0044i	−0.446076	−	0.956612i	0.546778	−	0.837277i	$-0.315854\pi$
$858$	0.0228522	−	0.00846583i	0.000780160	−	0.000289019i
$859$	−17.7378	+	21.1391i	−0.605205	+	0.721256i	−0.978452	−	0.206477i	$-0.933800\pi$
$859$	−17.7378	+	21.1391i	−0.605205	+	0.721256i	0.373246	+	0.927732i	$0.378245\pi$
$860$	31.4378	+	50.0101i	1.07202	+	1.70533i
$861$	−12.5469	−	1.02543i	−0.427596	−	0.0349467i
$862$	−30.5344	−	21.3804i	−1.04000	−	0.728219i
$863$	−15.5004	+	15.5004i	−0.527641	+	0.527641i	−0.919868	−	0.392228i	$-0.871705\pi$
$863$	−15.5004	+	15.5004i	−0.527641	+	0.527641i	0.392228	+	0.919868i	$0.371705\pi$
$864$	−12.4261	+	9.02248i	−0.422744	+	0.306951i
$865$	1.12454	+	5.22122i	0.0382355	+	0.177527i
$866$	35.0727	−	6.18427i	1.19182	−	0.210150i
$867$	22.3496	−	4.07277i	0.759032	−	0.138319i
$868$	−48.1922	−	22.4724i	−1.63575	−	0.762762i
$869$	−0.0231666	−	0.0194391i	−0.000785874	−	0.000659426i
$870$	−81.9392	−	42.6870i	−2.77800	−	1.44722i
$871$	−11.8179	−	4.30136i	−0.400434	−	0.145746i
$872$	−11.5085	+	42.9501i	−0.389725	+	1.45448i
$873$	26.4230	−	27.0345i	0.894282	−	0.914979i
$874$	117.701	+	67.9545i	3.98129	+	2.29860i
$875$	−6.34525	+	26.3566i	−0.214509	+	0.891016i
$876$	17.6368	+	4.61782i	0.595893	+	0.156022i
$877$	−1.56824	−	2.23967i	−0.0529555	−	0.0756283i	0.791801	−	0.610779i	$-0.209144\pi$
$877$	−1.56824	−	2.23967i	−0.0529555	−	0.0756283i	−0.844757	+	0.535151i	$0.820255\pi$
$878$	28.3256	+	40.4531i	0.955942	+	1.36523i
$879$	10.1502	−	10.2670i	0.342359	−	0.346298i
$880$	−0.0197400	+	0.00247786i	−0.000665435	+	8.35286e-5i
$881$	38.0975	+	21.9956i	1.28354	+	0.741051i	0.977493	−	0.210966i	$-0.0676609\pi$
$881$	38.0975	+	21.9956i	1.28354	+	0.741051i	0.306045	+	0.952017i	$0.400994\pi$
$882$	−3.29699	+	7.28688i	−0.111015	+	0.245362i
$883$	7.04478	−	26.2915i	0.237076	−	0.884779i	−0.740126	−	0.672468i	$-0.765234\pi$
$883$	7.04478	−	26.2915i	0.237076	−	0.884779i	0.977202	−	0.212311i	$-0.0680989\pi$
$884$	9.36894	+	3.41001i	0.315111	+	0.114691i
$885$	2.84447	+	2.60809i	0.0956158	+	0.0876701i
$886$	−13.7042	−	11.4992i	−0.460401	−	0.386322i
$887$	−48.4940	−	22.6131i	−1.62827	−	0.759274i	−0.628442	−	0.777856i	$-0.716307\pi$
$887$	−48.4940	−	22.6131i	−1.62827	−	0.759274i	−0.999827	+	0.0185820i	$0.994085\pi$
$888$	4.01689	−	11.2359i	0.134798	−	0.377051i
$889$	14.0795	−	2.48260i	0.472211	−	0.0832636i
$890$	−31.5987	+	6.80569i	−1.05919	+	0.228127i
$891$	−0.0240737	+	0.0300604i	−0.000806498	+	0.00100706i
$892$	9.72811	−	9.72811i	0.325721	−	0.325721i
$893$	−13.0506	−	9.13813i	−0.436722	−	0.305796i
$894$	−16.2114	−	34.2527i	−0.542191	−	1.14558i
$895$	8.36407	−	36.6801i	0.279580	−	1.22608i
$896$	32.2824	−	38.4726i	1.07848	−	1.28528i
$897$	−2.97310	+	17.4441i	−0.0992688	+	0.582441i
$898$	−5.35770	−	11.4896i	−0.178789	−	0.383414i
$899$	−30.0326	−	52.0179i	−1.00164	−	1.73489i
$900$	−14.1791	−	53.0480i	−0.472636	−	1.76827i
$901$	−1.74633	+	3.02474i	−0.0581788	+	0.100769i
$902$	−0.0304007	−	0.00265972i	−0.00101223	−	8.85589e-5i
$903$	−30.3073	+	0.173340i	−1.00856	+	0.00576839i
$904$	−7.33401	−	1.29318i	−0.243926	−	0.0430107i
$905$	11.6211	+	10.7784i	0.386300	+	0.358286i
$906$	−11.8399	+	45.2200i	−0.393354	+	1.50234i
$907$	4.20861	−	48.1046i	0.139745	−	1.59729i	−0.525587	−	0.850740i	$-0.676154\pi$
$907$	4.20861	−	48.1046i	0.139745	−	1.59729i	0.665332	−	0.746548i	$-0.268290\pi$
$908$	−6.17680	−	23.0521i	−0.204984	−	0.765011i
$909$	−12.6498	+	7.49759i	−0.419568	+	0.248679i
$910$	−11.9647	−	13.2163i	−0.396626	−	0.438115i
$911$	−14.5674	+	40.0237i	−0.482640	+	1.32604i	0.424581	+	0.905390i	$0.360421\pi$
$911$	−14.5674	+	40.0237i	−0.482640	+	1.32604i	−0.907221	+	0.420653i	$0.861801\pi$
$912$	17.7651	−	21.4192i	0.588262	−	0.709262i
$913$	0.00380000	+	0.0434342i	0.000125762	+	0.00143746i
$914$	52.5694	−	19.1337i	1.73884	−	0.632886i
$915$	24.3571	+	10.0979i	0.805222	+	0.333825i
$916$	−2.75452	−	15.6217i	−0.0910121	−	0.516155i
$917$	26.5297	+	26.5297i	0.876087	+	0.876087i
$918$	−23.9180	+	4.64186i	−0.789412	+	0.153204i
$919$		−	29.7860i		−	0.982549i	−0.871005	−	0.491274i	$-0.836531\pi$
$919$		−	29.7860i		−	0.982549i	0.871005	−	0.491274i	$-0.163469\pi$
$920$	25.3579	−	60.1906i	0.836025	−	1.98442i
$921$	1.71972	−	21.0419i	0.0566667	−	0.693354i
$922$	16.2036	−	34.7487i	0.533637	−	1.14439i
$923$	−13.2354	+	1.15795i	−0.435648	+	0.0381143i
$924$	0.0274616	−	0.0597819i	0.000903421	−	0.00196668i
$925$	−6.61026	−	5.68387i	−0.217344	−	0.186884i
$926$	−30.7563	+	17.7572i	−1.01072	+	0.583537i
$927$	19.6160	−	28.7079i	0.644273	−	0.942892i
$928$	28.6219	−	7.66920i	0.939559	−	0.251754i
$929$	6.65219	−	5.58185i	0.218251	−	0.183135i	−0.527106	−	0.849799i	$-0.676723\pi$
$929$	6.65219	−	5.58185i	0.218251	−	0.183135i	0.745358	+	0.666665i	$0.232279\pi$
$930$	16.6156	−	52.6414i	0.544848	−	1.72618i
$931$	−1.50353	+	8.52694i	−0.0492762	+	0.279459i
$932$	78.4899	−	54.9592i	2.57102	−	1.80025i
$933$	−30.4660	−	17.3580i	−0.997412	−	0.568275i
$934$	9.61335	+	11.4567i	0.314559	+	0.374876i
$935$	0.0179498	+	0.00577875i	0.000587023	+	0.000188985i
$936$	15.4564	+	5.42628i	0.505210	+	0.177364i
$937$	32.2615	+	8.64443i	1.05394	+	0.282401i	0.743877	−	0.668316i	$-0.232985\pi$
$937$	32.2615	+	8.64443i	1.05394	+	0.282401i	0.310059	+	0.950717i	$0.399651\pi$
$938$	−47.5804	+	22.1871i	−1.55355	+	0.724434i
$939$	−11.4009	−	5.23713i	−0.372053	−	0.170907i
$940$	−7.88311	+	14.9230i	−0.257119	+	0.486734i
$941$	−2.59435	−	7.12792i	−0.0845735	−	0.232364i	0.890196	−	0.455578i	$-0.150567\pi$
$941$	−2.59435	−	7.12792i	−0.0845735	−	0.232364i	−0.974769	+	0.223214i	$0.928345\pi$
$942$	2.76430	−	2.34659i	0.0900656	−	0.0764561i
$943$	12.7099	−	18.1517i	0.413893	−	0.591100i
$944$	2.07182			0.0674319
$945$	26.9618	+	8.17226i	0.877069	+	0.265844i
$946$	−0.0734704			−0.00238873
$947$	−11.8813	+	16.9682i	−0.386089	+	0.551393i	−0.964408	−	0.264418i	$-0.914820\pi$
$947$	−11.8813	+	16.9682i	−0.386089	+	0.551393i	0.578319	+	0.815811i	$0.303709\pi$
$948$	−8.03350	−	44.0844i	−0.260916	−	1.43179i
$949$	1.35910	+	3.73411i	0.0441184	+	0.121214i
$950$	−44.9978	−	80.1548i	−1.45992	−	2.60057i
$951$	−0.789285	−	8.46376i	−0.0255943	−	0.274456i
$952$	17.1121	−	7.97949i	0.554606	−	0.258617i
$953$	32.1900	+	8.62530i	1.04274	+	0.279401i	0.739248	−	0.673434i	$-0.235181\pi$
$953$	32.1900	+	8.62530i	1.04274	+	0.279401i	0.303490	+	0.952835i	$0.401848\pi$
$954$	−6.19906	+	11.0265i	−0.200702	+	0.356995i
$955$	−15.5925	+	7.99785i	−0.504562	+	0.258804i
$956$	−43.1237	−	51.3928i	−1.39472	−	1.66216i
$957$	0.0641436	−	0.0375241i	0.00207347	−	0.00121298i
$958$	−13.3226	+	9.32860i	−0.430435	+	0.301394i
$959$	1.64529	−	9.33089i	0.0531291	−	0.301310i
$960$	36.5436	+	23.2967i	1.17944	+	0.751897i
$961$	3.74384	−	3.14145i	0.120769	−	0.101337i
$962$	5.53765	−	1.48381i	0.178541	−	0.0478400i
$963$	1.38741	+	14.0104i	0.0447087	+	0.451480i
$964$	−20.0626	+	11.5831i	−0.646173	+	0.373068i
$965$	−41.1570	−	5.67102i	−1.32489	−	0.182557i
$966$	42.7151	+	60.2669i	1.37434	+	1.93906i
$967$	−14.9736	+	1.31002i	−0.481519	+	0.0421275i	−0.325332	−	0.945600i	$-0.605476\pi$
$967$	−14.9736	+	1.31002i	−0.481519	+	0.0421275i	−0.156188	+	0.987727i	$0.549920\pi$
$968$	−18.3680	+	39.3903i	−0.590369	+	1.26605i
$969$	−23.8408	+	11.2836i	−0.765876	+	0.362481i
$970$	−61.7791	−	26.0272i	−1.98361	−	0.835682i
$971$			29.8876i			0.959139i	0.877504	+	0.479570i	$0.159207\pi$
$971$			29.8876i			0.959139i	−0.877504	+	0.479570i	$0.840793\pi$
$972$	−55.8912	+	11.5119i	−1.79271	+	0.369245i
$973$	−9.32220	−	9.32220i	−0.298856	−	0.298856i
$974$	6.85958	+	38.9026i	0.219795	+	1.24652i
$975$	7.75108	−	9.11939i	0.248233	−	0.292054i
$976$	13.3018	−	4.84146i	0.425780	−	0.154971i
$977$	3.39755	+	38.8342i	0.108697	+	1.24242i	0.833132	+	0.553074i	$0.186545\pi$
$977$	3.39755	+	38.8342i	0.108697	+	1.24242i	−0.724435	+	0.689343i	$0.757899\pi$
$978$	−27.3202	−	4.65634i	−0.873604	−	0.148893i
$979$	0.00889204	−	0.0244307i	0.000284191	−	0.000780808i
$980$	9.16093	+	0.455318i	0.292635	+	0.0145446i
$981$	21.4042	−	26.1093i	0.683383	−	0.833606i
$982$	−10.2458	−	38.2380i	−0.326958	−	1.22022i
$983$	2.43483	−	27.8303i	0.0776592	−	0.887648i	−0.853036	−	0.521852i	$-0.825241\pi$
$983$	2.43483	−	27.8303i	0.0776592	−	0.887648i	0.930695	−	0.365796i	$-0.119203\pi$
$984$	−14.5878	−	14.4218i	−0.465041	−	0.459751i
$985$	0.566292	+	15.0518i	0.0180436	+	0.479590i
$986$	46.2994	+	8.16383i	1.47447	+	0.259989i
$987$	−4.37246	−	7.47427i	−0.139177	−	0.237909i
$988$	38.9426	+	3.40704i	1.23893	+	0.108392i
$989$	26.6744	−	46.2015i	0.848198	−	1.46912i
$990$	0.0652450	+	0.0201842i	0.00207362	+	0.000641497i
$991$	−19.0981	−	33.0789i	−0.606672	−	1.05079i	−0.991785	−	0.127917i	$-0.959171\pi$
$991$	−19.0981	−	33.0789i	−0.606672	−	1.05079i	0.385113	−	0.922870i	$-0.374163\pi$
$992$	7.48204	+	16.0453i	0.237555	+	0.509438i
$993$	6.62030	+	5.49088i	0.210089	+	0.174248i
$994$	−35.6498	+	42.4858i	−1.13074	+	1.34757i
$995$	−19.6758	−	4.48662i	−0.623765	−	0.142235i
$996$	−36.7519	+	53.1313i	−1.16453	+	1.68353i
$997$	6.25727	+	4.38139i	0.198170	+	0.138760i	0.668450	−	0.743757i	$-0.266958\pi$
$997$	6.25727	+	4.38139i	0.198170	+	0.138760i	−0.470280	+	0.882517i	$0.655847\pi$
$998$	46.8702	−	46.8702i	1.48365	−	1.48365i
$999$	−6.29547	+	6.51530i	−0.199180	+	0.206135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.68.15	yes	192
3.2	odd	2		405.2.r.a.233.2		192
5.2	odd	4	inner	135.2.q.a.122.15	yes	192
5.3	odd	4		675.2.ba.b.257.2		192
5.4	even	2		675.2.ba.b.68.2		192
15.2	even	4		405.2.r.a.152.2		192
27.2	odd	18	inner	135.2.q.a.83.15	yes	192
27.25	even	9		405.2.r.a.8.2		192
135.2	even	36	inner	135.2.q.a.2.15	✓	192
135.29	odd	18		675.2.ba.b.218.2		192
135.52	odd	36		405.2.r.a.332.2		192
135.83	even	36		675.2.ba.b.407.2		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.15	✓	192	135.2	even	36	inner
135.2.q.a.68.15	yes	192	1.1	even	1	trivial
135.2.q.a.83.15	yes	192	27.2	odd	18	inner
135.2.q.a.122.15	yes	192	5.2	odd	4	inner
405.2.r.a.8.2		192	27.25	even	9
405.2.r.a.152.2		192	15.2	even	4
405.2.r.a.233.2		192	3.2	odd	2
405.2.r.a.332.2		192	135.52	odd	36
675.2.ba.b.68.2		192	5.4	even	2
675.2.ba.b.218.2		192	135.29	odd	18
675.2.ba.b.257.2		192	5.3	odd	4
675.2.ba.b.407.2		192	135.83	even	36

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.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36466 - 1.94894i) q^{2} +(-1.63096 - 0.583078i) q^{3} +(-1.25203 - 3.43992i) q^{4} +(2.13659 - 0.659531i) q^{5} +(-3.36209 + 2.38294i) q^{6} +(-2.19758 + 1.02475i) q^{7} +(-3.81650 - 1.02263i) q^{8} +(2.32004 + 1.90195i) q^{9} +O(q^{10})\)	\(q+(1.36466 - 1.94894i) q^{2} +(-1.63096 - 0.583078i) q^{3} +(-1.25203 - 3.43992i) q^{4} +(2.13659 - 0.659531i) q^{5} +(-3.36209 + 2.38294i) q^{6} +(-2.19758 + 1.02475i) q^{7} +(-3.81650 - 1.02263i) q^{8} +(2.32004 + 1.90195i) q^{9} +(1.63034 - 5.06413i) q^{10} +(0.00275056 + 0.00327799i) q^{11} +(0.0362633 + 6.34039i) q^{12} +(-1.13206 + 0.792678i) q^{13} +(-1.00178 + 5.68139i) q^{14} +(-3.86924 - 0.170132i) q^{15} +(-1.59279 + 1.33651i) q^{16} +(1.90362 - 0.510074i) q^{17} +(6.87287 - 1.92610i) q^{18} +(6.69182 - 3.86352i) q^{19} +(-4.94380 - 6.52394i) q^{20} +(4.18166 - 0.389960i) q^{21} +(0.0101422 - 0.000887327i) q^{22} +(-3.12427 + 6.70002i) q^{23} +(5.62827 + 3.89318i) q^{24} +(4.13004 - 2.81830i) q^{25} +3.28806i q^{26} +(-2.67490 - 4.45476i) q^{27} +(6.27648 + 6.27648i) q^{28} +(1.74110 + 9.87424i) q^{29} +(-5.61180 + 7.30876i) q^{30} +(-5.62932 + 2.04890i) q^{31} +(-0.257571 - 2.94406i) q^{32} +(-0.00257472 - 0.00695004i) q^{33} +(1.60370 - 4.40613i) q^{34} +(-4.01947 + 3.63884i) q^{35} +(3.63779 - 10.3620i) q^{36} +(-0.451272 - 1.68417i) q^{37} +(1.60230 - 18.3144i) q^{38} +(2.30854 - 0.632743i) q^{39} +(-8.82875 + 0.332163i) q^{40} +(-2.95191 - 0.520501i) q^{41} +(4.94656 - 8.68198i) q^{42} +(-7.18901 - 0.628957i) q^{43} +(0.00783223 - 0.0135658i) q^{44} +(6.21137 + 2.53355i) q^{45} +(8.79437 + 15.2323i) q^{46} +(-0.871367 - 1.86865i) q^{47} +(3.37706 - 1.25107i) q^{48} +(-0.720271 + 0.858385i) q^{49} +(0.143417 - 11.8952i) q^{50} +(-3.40214 - 0.278051i) q^{51} +(4.14412 + 2.90174i) q^{52} +(-1.25315 + 1.25315i) q^{53} +(-12.3324 - 0.866025i) q^{54} +(0.00803875 + 0.00518964i) q^{55} +(9.43499 - 1.66364i) q^{56} +(-13.1668 + 2.39939i) q^{57} +(21.6203 + 10.0817i) q^{58} +(-0.763311 - 0.640494i) q^{59} +(4.25916 + 13.5229i) q^{60} +(-6.39745 - 2.32848i) q^{61} +(-3.68893 + 13.7673i) q^{62} +(-7.04749 - 1.80223i) q^{63} +(-9.69063 - 5.59489i) q^{64} +(-1.89595 + 2.44026i) q^{65} +(-0.0170589 - 0.00446650i) q^{66} +(5.21964 + 7.45442i) q^{67} +(-4.13800 - 5.90968i) q^{68} +(9.00219 - 9.10575i) q^{69} +(1.60665 + 12.7995i) q^{70} +(8.32564 + 4.80681i) q^{71} +(-6.90944 - 9.63132i) q^{72} +(0.744204 - 2.77741i) q^{73} +(-3.89819 - 1.41882i) q^{74} +(-8.37920 + 2.18839i) q^{75} +(-21.6685 - 18.1821i) q^{76} +(-0.00940367 - 0.00438501i) q^{77} +(1.91719 - 5.36268i) q^{78} +(-6.95996 + 1.22723i) q^{79} +(-2.52167 + 3.90606i) q^{80} +(1.76518 + 8.82520i) q^{81} +(-5.04279 + 5.04279i) q^{82} +(8.34640 + 5.84421i) q^{83} +(-6.57699 - 13.8963i) q^{84} +(3.73085 - 2.34532i) q^{85} +(-11.0364 + 13.1527i) q^{86} +(2.91780 - 17.1197i) q^{87} +(-0.00714534 - 0.0153232i) q^{88} +(-3.03785 - 5.26171i) q^{89} +(13.4142 - 8.64816i) q^{90} +(1.67550 - 2.90205i) q^{91} +(26.9592 + 2.35862i) q^{92} +(10.3758 - 0.0593438i) q^{93} +(-4.83102 - 0.851839i) q^{94} +(11.7496 - 12.6682i) q^{95} +(-1.29653 + 4.95181i) q^{96} +(1.09824 - 12.5529i) q^{97} +(0.690016 + 2.57517i) q^{98} +(0.000146839 + 0.0128365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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