LMFDB - Embedded newform 135.2.q.a.122.15

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			122.15
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.94894 + 1.36466i) q^{2} +(-0.583078 + 1.63096i) q^{3} +(1.25203 + 3.43992i) q^{4} +(0.278496 - 2.21866i) q^{5} +(-3.36209 + 2.38294i) q^{6} +(-1.02475 - 2.19758i) q^{7} +(-1.02263 + 3.81650i) q^{8} +(-2.32004 - 1.90195i) q^{9} +O(q^{10})$	\(q+(1.94894 + 1.36466i) q^{2} +(-0.583078 + 1.63096i) q^{3} +(1.25203 + 3.43992i) q^{4} +(0.278496 - 2.21866i) q^{5} +(-3.36209 + 2.38294i) q^{6} +(-1.02475 - 2.19758i) q^{7} +(-1.02263 + 3.81650i) q^{8} +(-2.32004 - 1.90195i) q^{9} +(3.57049 - 3.94398i) q^{10} +(0.00275056 + 0.00327799i) q^{11} +(-6.34039 + 0.0362633i) q^{12} +(0.792678 + 1.13206i) q^{13} +(1.00178 - 5.68139i) q^{14} +(3.45615 + 1.74787i) q^{15} +(-1.59279 + 1.33651i) q^{16} +(0.510074 + 1.90362i) q^{17} +(-1.92610 - 6.87287i) q^{18} +(-6.69182 + 3.86352i) q^{19} +(7.98068 - 1.81982i) q^{20} +(4.18166 - 0.389960i) q^{21} +(0.000887327 + 0.0101422i) q^{22} +(6.70002 + 3.12427i) q^{23} +(-5.62827 - 3.89318i) q^{24} +(-4.84488 - 1.23578i) q^{25} +3.28806i q^{26} +(4.45476 - 2.67490i) q^{27} +(6.27648 - 6.27648i) q^{28} +(-1.74110 - 9.87424i) q^{29} +(4.35059 + 8.12297i) q^{30} +(-5.62932 + 2.04890i) q^{31} +(2.94406 - 0.257571i) q^{32} +(-0.00695004 + 0.00257472i) q^{33} +(-1.60370 + 4.40613i) q^{34} +(-5.16106 + 1.66155i) q^{35} +(3.63779 - 10.3620i) q^{36} +(1.68417 - 0.451272i) q^{37} +(-18.3144 - 1.60230i) q^{38} +(-2.30854 + 0.632743i) q^{39} +(8.18270 + 3.33174i) q^{40} +(-2.95191 - 0.520501i) q^{41} +(8.68198 + 4.94656i) q^{42} +(-0.628957 + 7.18901i) q^{43} +(-0.00783223 + 0.0135658i) q^{44} +(-4.86590 + 4.61769i) q^{45} +(8.79437 + 15.2323i) q^{46} +(1.86865 - 0.871367i) q^{47} +(-1.25107 - 3.37706i) q^{48} +(0.720271 - 0.858385i) q^{49} +(-7.75597 - 9.02009i) q^{50} +(-3.40214 - 0.278051i) q^{51} +(-2.90174 + 4.14412i) 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} +(-2.39939 - 13.1668i) q^{57} +(10.0817 - 21.6203i) q^{58} +(0.763311 + 0.640494i) q^{59} +(-1.68532 + 14.0772i) q^{60} +(-6.39745 - 2.32848i) q^{61} +(-13.7673 - 3.68893i) q^{62} +(-1.80223 + 7.04749i) q^{63} +(9.69063 + 5.59489i) q^{64} +(2.73241 - 1.44340i) q^{65} +(-0.0170589 - 0.00446650i) q^{66} +(-7.45442 + 5.21964i) q^{67} +(-5.90968 + 4.13800i) q^{68} +(-9.00219 + 9.10575i) q^{69} +(-12.3261 - 3.80486i) q^{70} +(8.32564 + 4.80681i) q^{71} +(9.63132 - 6.90944i) q^{72} +(-2.77741 - 0.744204i) q^{73} +(3.89819 + 1.41882i) q^{74} +(4.84044 - 7.18124i) q^{75} +(-21.6685 - 18.1821i) q^{76} +(0.00438501 - 0.00940367i) q^{77} +(-5.36268 - 1.91719i) 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} +(5.84421 - 8.34640i) q^{83} +(6.57699 + 13.8963i) q^{84} +(4.36554 - 0.601528i) q^{85} +(-11.0364 + 13.1527i) q^{86} +(17.1197 + 2.91780i) q^{87} +(-0.0153232 + 0.00714534i) q^{88} +(3.03785 + 5.26171i) q^{89} +(-15.7849 + 2.35929i) q^{90} +(1.67550 - 2.90205i) q^{91} +(-2.35862 + 26.9592i) q^{92} +(-0.0593438 - 10.3758i) q^{93} +(4.83102 + 0.851839i) q^{94} +(6.70819 + 15.9228i) q^{95} +(-1.29653 + 4.95181i) q^{96} +(12.5529 + 1.09824i) q^{97} +(2.57517 - 0.690016i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.94894	+	1.36466i	1.37811	+	0.964963i	0.999219	+	0.0395221i	$0.0125835\pi$
$2$	1.94894	+	1.36466i	1.37811	+	0.964963i	0.378892	+	0.925441i	$0.376305\pi$
$3$	−0.583078	+	1.63096i	−0.336640	+	0.941633i
$3$	−0.583078	+	1.63096i	−0.336640	+	0.941633i
$4$	1.25203	+	3.43992i	0.626014	+	1.71996i
$5$	0.278496	−	2.21866i	0.124547	−	0.992214i
$5$	0.278496	−	2.21866i	0.124547	−	0.992214i
$6$	−3.36209	+	2.38294i	−1.37257	+	0.972829i
$7$	−1.02475	−	2.19758i	−0.387318	−	0.830607i	−0.999213	−	0.0396673i	$-0.987370\pi$
$7$	−1.02475	−	2.19758i	−0.387318	−	0.830607i	0.611895	−	0.790939i	$-0.290408\pi$
$8$	−1.02263	+	3.81650i	−0.361553	+	1.34934i
$9$	−2.32004	−	1.90195i	−0.773347	−	0.633983i
$10$	3.57049	−	3.94398i	1.12909	−	1.24720i
$11$	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	$0.777572\pi$
$12$	−6.34039	+	0.0362633i	−1.83031	+	0.0104683i
$13$	0.792678	+	1.13206i	0.219849	+	0.313977i	0.913893	−	0.405956i	$-0.133061\pi$
$13$	0.792678	+	1.13206i	0.219849	+	0.313977i	−0.694043	+	0.719933i	$0.744172\pi$
$14$	1.00178	−	5.68139i	0.267738	−	1.51842i
$15$	3.45615	+	1.74787i	0.892374	+	0.451297i
$16$	−1.59279	+	1.33651i	−0.398197	+	0.334127i
$17$	0.510074	+	1.90362i	0.123711	+	0.461696i	0.999790	−	0.0204707i	$-0.00651649\pi$
$17$	0.510074	+	1.90362i	0.123711	+	0.461696i	−0.876079	+	0.482167i	$0.839850\pi$
$18$	−1.92610	−	6.87287i	−0.453987	−	1.61995i
$19$	−6.69182	+	3.86352i	−1.53521	+	0.886353i	−0.536099	+	0.844155i	$0.680103\pi$
$19$	−6.69182	+	3.86352i	−1.53521	+	0.886353i	−0.999109	+	0.0421981i	$0.986564\pi$
$20$	7.98068	−	1.81982i	1.78453	−	0.406923i
$21$	4.18166	−	0.389960i	0.912514	−	0.0850962i
$22$	0.000887327		0.0101422i	0.000189179		0.00216232i
$23$	6.70002	+	3.12427i	1.39705	+	0.651456i	0.967798	−	0.251729i	$-0.0809990\pi$
$23$	6.70002	+	3.12427i	1.39705	+	0.651456i	0.429253	+	0.903184i	$0.358777\pi$
$24$	−5.62827	−	3.89318i	−1.14887	−	0.794691i
$25$	−4.84488	−	1.23578i	−0.968976	−	0.247155i
$26$			3.28806i			0.644842i
$27$	4.45476	−	2.67490i	0.857319	−	0.514785i
$28$	6.27648	−	6.27648i	1.18614	−	1.18614i
$29$	−1.74110	−	9.87424i	−0.323313	−	1.83360i	−0.521272	−	0.853391i	$-0.674542\pi$
$29$	−1.74110	−	9.87424i	−0.323313	−	1.83360i	0.197959	−	0.980210i	$-0.436569\pi$
$30$	4.35059	+	8.12297i	0.794305	+	1.48304i
$31$	−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	$0.569698\pi$
$32$	2.94406	−	0.257571i	0.520440	−	0.0455326i
$33$	−0.00695004	+	0.00257472i	−0.00120985	+	0.000448201i
$34$	−1.60370	+	4.40613i	−0.275032	+	0.755645i
$35$	−5.16106	+	1.66155i	−0.872379	+	0.280853i
$36$	3.63779	−	10.3620i	0.606299	−	1.72701i
$37$	1.68417	−	0.451272i	0.276876	−	0.0741887i	−0.117709	−	0.993048i	$-0.537555\pi$
$37$	1.68417	−	0.451272i	0.276876	−	0.0741887i	0.394585	+	0.918859i	$0.370888\pi$
$38$	−18.3144	−	1.60230i	−2.97098	−	0.259927i
$39$	−2.30854	+	0.632743i	−0.369661	+	0.101320i
$40$	8.18270	+	3.33174i	1.29380	+	0.526795i
$41$	−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	$0.630757\pi$
$42$	8.68198	+	4.94656i	1.33966	+	0.763270i
$43$	−0.628957	+	7.18901i	−0.0959151	+	1.09631i	0.783864	+	0.620932i	$0.213246\pi$
$43$	−0.628957	+	7.18901i	−0.0959151	+	1.09631i	−0.879779	+	0.475382i	$0.842310\pi$
$44$	−0.00783223	+	0.0135658i	−0.00118075	+	0.00204512i
$45$	−4.86590	+	4.61769i	−0.725365	+	0.688364i
$46$	8.79437	+	15.2323i	1.29666	+	2.24588i
$47$	1.86865	−	0.871367i	0.272571	−	0.127102i	−0.281527	−	0.959553i	$-0.590841\pi$
$47$	1.86865	−	0.871367i	0.272571	−	0.127102i	0.554098	+	0.832451i	$0.313063\pi$
$48$	−1.25107	−	3.37706i	−0.180576	−	0.487436i
$49$	0.720271	−	0.858385i	0.102896	−	0.122626i
$50$	−7.75597	−	9.02009i	−1.09686	−	1.27563i
$51$	−3.40214	−	0.278051i	−0.476395	−	0.0389350i
$52$	−2.90174	+	4.14412i	−0.402399	+	0.574686i
$53$	1.25315	+	1.25315i	0.172134	+	0.172134i	0.787916	−	0.615782i	$-0.211160\pi$
$53$	1.25315	+	1.25315i	0.172134	+	0.172134i	−0.615782	+	0.787916i	$0.711160\pi$
$54$	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
$57$	−2.39939	−	13.1668i	−0.317807	−	1.74399i
$58$	10.0817	−	21.6203i	1.32380	−	2.83889i
$59$	0.763311	+	0.640494i	0.0993747	+	0.0833853i	0.691121	−	0.722739i	$-0.257117\pi$
$59$	0.763311	+	0.640494i	0.0993747	+	0.0833853i	−0.591747	+	0.806124i	$0.701561\pi$
$60$	−1.68532	+	14.0772i	−0.217574	+	1.81736i
$61$	−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	$0.754659\pi$
$62$	−13.7673	−	3.68893i	−1.74845	−	0.468495i
$63$	−1.80223	+	7.04749i	−0.227059	+	0.887900i
$64$	9.69063	+	5.59489i	1.21133	+	0.699361i
$65$	2.73241	−	1.44340i	0.338914	−	0.179032i
$66$	−0.0170589	−	0.00446650i	−0.00209980	−	0.000549788i
$67$	−7.45442	+	5.21964i	−0.910702	+	0.637680i	−0.932143	−	0.362090i	$-0.882063\pi$
$67$	−7.45442	+	5.21964i	−0.910702	+	0.637680i	0.0214414	+	0.999770i	$0.493174\pi$
$68$	−5.90968	+	4.13800i	−0.716654	+	0.501806i
$69$	−9.00219	+	9.10575i	−1.08374	+	1.09620i
$70$	−12.3261	−	3.80486i	−1.47325	−	0.454767i
$71$	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	$0.473430\pi$
$72$	9.63132	−	6.90944i	1.13506	−	0.814286i
$73$	−2.77741	−	0.744204i	−0.325071	−	0.0871025i	0.0925931	−	0.995704i	$-0.470484\pi$
$73$	−2.77741	−	0.744204i	−0.325071	−	0.0871025i	−0.417664	+	0.908602i	$0.637151\pi$
$74$	3.89819	+	1.41882i	0.453155	+	0.164935i
$75$	4.84044	−	7.18124i	0.558926	−	0.829218i
$76$	−21.6685	−	18.1821i	−2.48555	−	2.08563i
$77$	0.00438501	−	0.00940367i	0.000499718	−	0.00107165i
$78$	−5.36268	−	1.91719i	−0.607204	−	0.217080i
$79$	6.95996	−	1.22723i	0.783057	−	0.138074i	0.232194	−	0.972670i	$-0.425410\pi$
$79$	6.95996	−	1.22723i	0.783057	−	0.138074i	0.550863	+	0.834595i	$0.314299\pi$
$80$	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
$83$	5.84421	−	8.34640i	0.641485	−	0.916136i	−0.358363	−	0.933582i	$-0.616665\pi$
$83$	5.84421	−	8.34640i	0.641485	−	0.916136i	0.999848	+	0.0174466i	$0.00555371\pi$
$84$	6.57699	+	13.8963i	0.717608	+	1.51621i
$85$	4.36554	−	0.601528i	0.473509	−	0.0652448i
$86$	−11.0364	+	13.1527i	−1.19008	+	1.41829i
$87$	17.1197	+	2.91780i	1.83542	+	0.312821i
$88$	−0.0153232	+	0.00714534i	−0.00163346	+	0.000761696i
$89$	3.03785	+	5.26171i	0.322012	+	0.557741i	0.980903	−	0.194498i	$-0.0623076\pi$
$89$	3.03785	+	5.26171i	0.322012	+	0.557741i	−0.658891	+	0.752238i	$0.728974\pi$
$90$	−15.7849	+	2.35929i	−1.66388	+	0.248691i
$91$	1.67550	−	2.90205i	0.175640	−	0.304217i
$92$	−2.35862	+	26.9592i	−0.245904	+	2.81069i
$93$	−0.0593438	−	10.3758i	−0.00615366	−	1.07593i
$94$	4.83102	+	0.851839i	0.498281	+	0.0878604i
$95$	6.70819	+	15.9228i	0.688245	+	1.63365i
$96$	−1.29653	+	4.95181i	−0.132326	+	0.505392i
$97$	12.5529	+	1.09824i	1.27456	+	0.111509i	0.704267	−	0.709935i	$-0.251276\pi$
$97$	12.5529	+	1.09824i	1.27456	+	0.111509i	0.570289	+	0.821444i	$0.306831\pi$
$98$	2.57517	−	0.690016i	0.260132	−	0.0697021i
$99$	−0.000146839	−	0.0128365i	−1.47579e−5	−	0.00129012i
$100$	−1.81496	−	18.2132i	−0.181496	−	1.82132i
$101$	−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	$0.189526\pi$
$102$	−6.25113	−	5.18468i	−0.618954	−	0.513360i
$103$	−11.5458	+	1.01013i	−1.13764	+	0.0995307i	−0.640371	−	0.768066i	$-0.721219\pi$
$103$	−11.5458	+	1.01013i	−1.13764	+	0.0995307i	−0.497269	+	0.867596i	$0.665664\pi$
$104$	−5.13112	+	1.86758i	−0.503148	+	0.183131i
$105$	0.299391	−	9.38628i	0.0292175	−	0.916007i
$106$	0.732191	+	4.15246i	0.0711167	+	0.403323i
$107$	−3.31844	+	3.31844i	−0.320806	+	0.320806i	−0.849076	−	0.528270i	$-0.822841\pi$
$107$	−3.31844	+	3.31844i	−0.320806	+	0.320806i	0.528270	+	0.849076i	$0.322841\pi$
$108$	14.7789	+	11.9750i	1.42210	+	1.15229i
$109$			11.2538i			1.07792i	0.842332	+	0.538960i	$0.181182\pi$
$109$			11.2538i			1.07792i	−0.842332	+	0.538960i	$0.818818\pi$
$110$	0.0227492		0.000855890i	0.00216905		8.16059e-5i
$111$	−0.245997	+	3.00994i	−0.0233490	+	0.285691i
$112$	4.56928	+	2.13069i	0.431757	+	0.201331i
$113$	−0.164272	−	1.87764i	−0.0154535	−	0.176634i	−0.999999	−	0.00150433i	$-0.999521\pi$
$113$	−0.164272	−	1.87764i	−0.0154535	−	0.176634i	0.984545	−	0.175129i	$-0.0560344\pi$
$114$	13.2920	−	28.9357i	1.24491	−	2.71008i
$115$	8.79762	−	13.9950i	0.820382	−	1.30504i
$116$	31.7867	−	18.3520i	2.95132	−	1.70394i
$117$	0.314079	−	4.13406i	0.0290366	−	0.382194i
$118$	0.613590	+	2.28995i	0.0564856	+	0.210807i
$119$	3.66066	−	3.07166i	0.335572	−	0.281579i
$120$	−10.2051	+	11.4030i	−0.931592	+	1.04094i
$121$	1.91013	−	10.8329i	0.173648	−	0.984806i
$122$	−9.29066	−	13.2684i	−0.841137	−	1.20127i
$123$	2.57011	−	4.51095i	0.231739	−	0.406738i
$124$	−14.0961	−	16.7991i	−1.26587	−	1.50860i
$125$	−4.09104	+	10.4050i	−0.365914	+	0.930649i
$126$	−13.1299	+	11.2757i	−1.16970	+	1.00452i
$127$	1.52603	−	5.69522i	0.135413	−	0.505369i	−0.864583	−	0.502491i	$-0.832417\pi$
$127$	1.52603	−	5.69522i	0.135413	−	0.505369i	0.999996	−	0.00287859i	$-0.000916284\pi$
$128$	8.75341	+	18.7718i	0.773700	+	1.65920i
$129$	−11.3582	−	5.21756i	−1.00004	−	0.459380i
$130$	7.29508	+	0.915713i	0.639821	+	0.0803133i
$131$	−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	$-0.347376\pi$
$132$	−0.0175585	−	0.0206840i	−0.00152827	−	0.00180031i
$133$	15.3478	+	10.7467i	1.33082	+	0.931854i
$134$	−21.6513			−1.87039
$135$	−4.69405	−	10.6285i	−0.404000	−	0.914759i
$136$	−7.78679			−0.667712
$137$	−3.20087	−	2.24127i	−0.273468	−	0.191485i	0.428795	−	0.903402i	$-0.358938\pi$
$137$	−3.20087	−	2.24127i	−0.273468	−	0.191485i	−0.702263	+	0.711917i	$0.747827\pi$
$138$	−29.9710	+	5.46163i	−2.55130	+	0.464924i
$139$	−1.85959	−	5.10917i	−0.157728	−	0.433354i	0.835506	−	0.549481i	$-0.185174\pi$
$139$	−1.85959	−	5.10917i	−0.157728	−	0.433354i	−0.993234	+	0.116126i	$0.962952\pi$
$140$	−12.1774	−	15.6733i	−1.02918	−	1.32464i
$141$	0.331592	+	3.55577i	0.0279251	+	0.299449i
$142$	9.66651	+	20.7299i	0.811196	+	1.73961i
$143$	−0.00153058	+	0.00571218i	−0.000127993	+	0.000477677i
$144$	6.23730	−	0.0713498i	0.519775	−	0.00594581i
$145$	−22.3924	+	1.11295i	−1.85959	+	0.0924257i
$146$	−4.39742	−	5.24064i	−0.363933	−	0.433718i
$147$	0.980015	+	1.67524i	0.0808303	+	0.138171i
$148$	3.66097	+	5.22840i	0.300930	+	0.429772i
$149$	1.59684	−	9.05612i	0.130818	−	0.741907i	−0.846863	−	0.531811i	$-0.821512\pi$
$149$	1.59684	−	9.05612i	0.130818	−	0.741907i	0.977681	−	0.210095i	$-0.0673774\pi$
$150$	19.2337	−	7.39024i	1.57043	−	0.603411i
$151$	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	$0.125072\pi$
$152$	−7.90189	−	29.4903i	−0.640928	−	2.39198i
$153$	2.43720	−	5.38662i	0.197036	−	0.435482i
$154$	0.0213790	−	0.0123432i	0.00172277	−	0.000994640i
$155$	2.97807	+	13.0601i	0.239204	+	1.04902i
$156$	−5.06693	−	7.14896i	−0.405679	−	0.572375i
$157$	−0.0766881	−	0.876549i	−0.00612037	−	0.0699562i	0.992520	−	0.122080i	$-0.0389565\pi$
$157$	−0.0766881	−	0.876549i	−0.00612037	−	0.0699562i	−0.998641	+	0.0521239i	$0.983401\pi$
$158$	15.2393	+	7.10621i	1.21238	+	0.565340i
$159$	−2.77453	+	1.31315i	−0.220034	+	0.104140i
$160$	0.248446	−	6.60358i	0.0196414	−	0.522059i
$161$		−	17.9254i		−	1.41272i
$162$	−8.60321	+	19.6087i	−0.675932	+	1.54060i
$163$	4.75545	−	4.75545i	0.372476	−	0.372476i	−0.495902	−	0.868378i	$-0.665163\pi$
$163$	4.75545	−	4.75545i	0.372476	−	0.372476i	0.868378	+	0.495902i	$0.165163\pi$
$164$	−1.90539	−	10.8060i	−0.148786	−	0.843808i
$165$	0.00377686	+	0.0161368i	0.000294028	+	0.00125625i
$166$	22.7800	−	8.29126i	1.76807	−	0.643527i
$167$	7.21152	−	0.630926i	0.558044	−	0.0488226i	0.195355	−	0.980733i	$-0.437414\pi$
$167$	7.21152	−	0.630926i	0.558044	−	0.0488226i	0.362689	+	0.931910i	$0.381859\pi$
$168$	−2.78800	+	16.3581i	−0.215099	+	1.26205i
$169$	3.79304	−	10.4213i	0.291772	−	0.801637i
$170$	9.32907	+	4.78515i	0.715507	+	0.367004i
$171$	22.8735	+	3.76397i	1.74918	+	0.287838i
$172$	−25.5171	+	6.83728i	−1.94566	+	0.521338i
$173$	2.37946	+	0.208175i	0.180907	+	0.0158273i	0.177249	−	0.984166i	$-0.443280\pi$
$173$	2.37946	+	0.208175i	0.180907	+	0.0158273i	0.00365760	+	0.999993i	$0.498836\pi$
$174$	29.3834	+	29.0492i	2.22755	+	2.20221i
$175$	2.24906	+	11.9134i	0.170013	+	0.900565i
$176$	−0.00876211	−	0.00154500i	−0.000660469	−	0.000116458i
$177$	−1.48969	+	0.871470i	−0.111972	+	0.0655037i
$178$	−1.25987	+	14.4004i	−0.0944315	+	1.07936i
$179$	−8.41245	+	14.5708i	−0.628776	+	1.08907i	0.359021	+	0.933329i	$0.383111\pi$
$179$	−8.41245	+	14.5708i	−0.628776	+	1.08907i	−0.987798	+	0.155743i	$0.950223\pi$
$180$	−21.9767	−	10.9568i	−1.63805	−	0.816672i
$181$	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	$0.748477\pi$
$182$	7.22577	−	3.36943i	0.535610	−	0.249759i
$183$	7.52786	−	9.07628i	0.556476	−	0.670938i
$184$	−18.7754	+	22.3757i	−1.38414	+	1.64955i
$185$	−0.532183	−	3.86228i	−0.0391269	−	0.283960i
$186$	14.0439	−	20.3029i	1.02975	−	1.48868i
$187$	−0.00483706	+	0.00690804i	−0.000353721	+	0.000505166i
$188$	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	$0.535951\pi$
$192$	−14.7754	+	12.5427i	−1.06632	+	0.905195i
$193$	−7.85219	+	16.8391i	−0.565213	+	1.21210i	0.391259	+	0.920280i	$0.372040\pi$
$193$	−7.85219	+	16.8391i	−0.565213	+	1.21210i	−0.956472	+	0.291823i	$0.905738\pi$
$194$	22.9662	+	19.2709i	1.64888	+	1.38357i
$195$	0.760922	+	5.29806i	0.0544907	+	0.379402i
$196$	3.85457	+	1.40295i	0.275327	+	0.100211i
$197$	−6.50660	−	1.74344i	−0.463576	−	0.124215i	0.0194688	−	0.999810i	$-0.493802\pi$
$197$	−6.50660	−	1.74344i	−0.463576	−	0.124215i	−0.483045	+	0.875596i	$0.660469\pi$
$198$	0.0172313	−	0.0252180i	0.00122458	−	0.00179216i
$199$	7.81601	+	4.51257i	0.554062	+	0.319888i	0.750759	−	0.660576i	$-0.229688\pi$
$199$	7.81601	+	4.51257i	0.554062	+	0.319888i	−0.196697	+	0.980464i	$0.563021\pi$
$200$	9.67084	−	17.2267i	0.683832	−	1.21811i
$201$	−4.16650	−	15.2013i	−0.293882	−	1.07222i
$202$	−9.55295	+	6.68904i	−0.672143	+	0.470640i
$203$	−19.9152	+	13.9448i	−1.39778	+	0.978733i
$204$	−3.30310	−	12.0512i	−0.231263	−	0.843753i
$205$	−1.97691	+	6.40432i	−0.138073	+	0.447297i
$206$	−23.8806	−	13.7874i	−1.66384	−	0.960617i
$207$	−9.60211	−	19.9915i	−0.667393	−	1.38951i
$208$	−2.77557	−	0.743713i	−0.192451	−	0.0515672i
$209$	−0.0310708	−	0.0113089i	−0.00214921	−	0.000782250i
$210$	13.3926	−	17.8847i	0.924178	−	1.23416i
$211$	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	$0.652010\pi$
$212$	−2.74176	+	5.87973i	−0.188305	+	0.403822i
$213$	−12.6942	+	10.7760i	−0.869792	+	0.738361i
$214$	−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
$218$	−15.3577	+	21.9330i	−1.04015	+	1.48549i
$219$	2.83321	−	4.09590i	0.191451	−	0.276775i
$220$	0.0279167	+	0.0211551i	0.00188214	+	0.00142627i
$221$	−1.75069	+	2.08639i	−0.117764	+	0.140346i
$222$	−4.58699	+	5.53049i	−0.307858	+	0.371182i
$223$	3.40610	−	1.58829i	0.228089	−	0.106360i	−0.305214	−	0.952284i	$-0.598728\pi$
$223$	3.40610	−	1.58829i	0.228089	−	0.106360i	0.533304	+	0.845924i	$0.320950\pi$
$224$	−3.58295	−	6.20585i	−0.239396	−	0.414646i
$225$	8.88993	+	12.0818i	0.592662	+	0.805451i
$226$	2.24219	−	3.88359i	0.149149	−	0.258333i
$227$	−0.568200	+	6.49455i	−0.0377127	+	0.431059i	0.953744	+	0.300621i	$0.0971938\pi$
$227$	−0.568200	+	6.49455i	−0.0377127	+	0.431059i	−0.991456	+	0.130438i	$0.958362\pi$
$228$	42.2886	−	24.7389i	2.80063	−	1.63837i
$229$	−4.26742	−	0.752462i	−0.281999	−	0.0497241i	0.0308595	−	0.999524i	$-0.490176\pi$
$229$	−4.26742	−	0.752462i	−0.281999	−	0.0497241i	−0.312859	+	0.949800i	$0.601287\pi$
$230$	36.2445	−	15.2696i	2.38989	−	1.00684i
$231$	0.0127802	+	0.0126348i	0.000840875	+	0.000831311i
$232$	39.4655	+	3.45279i	2.59104	+	0.226687i
$233$	25.2831	−	6.77460i	1.65635	−	0.443818i	0.694972	−	0.719037i	$-0.255417\pi$
$233$	25.2831	−	6.77460i	1.65635	−	0.443818i	0.961382	+	0.275219i	$0.0887503\pi$
$234$	6.25372	−	7.62843i	0.408819	−	0.498686i
$235$	−1.41285	−	4.38857i	−0.0921642	−	0.286279i
$236$	−1.24756	+	3.42764i	−0.0812093	+	0.223121i
$237$	−2.05664	+	12.0670i	−0.133593	+	0.783834i
$238$	11.3262	−	0.990915i	0.734169	−	0.0642314i
$239$	−17.2215	+	6.26813i	−1.11397	+	0.405452i	−0.832448	−	0.554103i	$-0.813061\pi$
$239$	−17.2215	+	6.26813i	−1.11397	+	0.405452i	−0.281521	+	0.959555i	$0.590839\pi$
$240$	−7.84095	+	1.83519i	−0.506131	+	0.118461i
$241$	−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
$243$	−15.4228	−	2.26685i	−0.989370	−	0.145419i
$244$		−	24.9220i		−	1.59547i
$245$	−1.70387	−	1.83709i	−0.108856	−	0.117367i
$246$	11.1649	−	5.28424i	0.711849	−	0.336911i
$247$	−9.67820	−	4.51302i	−0.615809	−	0.287156i
$248$	−2.06294	−	23.5795i	−0.130997	−	1.49730i
$249$	10.2050	+	14.3983i	0.646714	+	0.912452i
$250$	−22.1725	+	14.6958i	−1.40231	+	0.929443i
$251$	−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	$0.653146\pi$
$252$	−26.4992	+	2.62414i	−1.66929	+	0.165305i
$253$	0.00818747	+	0.0305561i	0.000514742	+	0.00192104i
$254$	10.7462	−	9.01714i	0.674277	−	0.565786i
$255$	−1.56438	+	7.47075i	−0.0979655	+	0.467836i
$256$	−4.67107	+	26.4910i	−0.291942	+	1.65569i
$257$	−2.24834	−	3.21096i	−0.140248	−	0.200294i	0.742883	−	0.669421i	$-0.233458\pi$
$257$	−2.24834	−	3.21096i	−0.140248	−	0.200294i	−0.883131	+	0.469127i	$0.844569\pi$
$258$	−15.0163	−	25.6689i	−0.934876	−	1.59808i
$259$	−2.71756	−	3.23866i	−0.168861	−	0.201240i
$260$	8.38625	+	7.59209i	0.520093	+	0.470841i
$261$	−14.7409	+	26.2201i	−0.912439	+	1.62298i
$262$	9.52815	−	35.5596i	0.588651	−	2.19688i
$263$	−13.0357	−	27.9551i	−0.803815	−	1.72379i	−0.682146	−	0.731216i	$-0.738953\pi$
$263$	−13.0357	−	27.9551i	−0.803815	−	1.72379i	−0.121669	−	0.992571i	$-0.538824\pi$
$264$	−0.00271910	−	0.0291578i	−0.000167349	−	0.00179454i
$265$	3.12932	−	2.43132i	0.192233	−	0.149355i
$266$	15.2464	+	41.8892i	0.934819	+	2.56839i
$267$	−10.3529	+	1.88662i	−0.633589	+	0.115459i
$268$	−27.2883	−	19.1074i	−1.66690	−	1.16717i
$269$	11.5179			0.702257			0.351128	−	0.936327i	$-0.385798\pi$
$269$	11.5179			0.702257			0.351128	+	0.936327i	$0.385798\pi$
$270$	5.35595	−	27.1202i	0.325952	−	1.65048i
$271$	−6.78072			−0.411899			−0.205950	−	0.978563i	$-0.566028\pi$
$271$	−6.78072			−0.411899			−0.205950	+	0.978563i	$0.566028\pi$
$272$	−3.35665	−	2.35035i	−0.203527	−	0.142511i
$273$	3.75617	+	4.42478i	0.227334	+	0.267800i
$274$	−3.17972	−	8.73621i	−0.192094	−	0.527774i
$275$	−0.00927526	−	0.0192805i	−0.000559319	−	0.00116266i
$276$	−42.5940	−	19.5661i	−2.56386	−	1.17774i
$277$	4.19864	+	9.00402i	0.252272	+	0.540999i	0.991135	−	0.132856i	$-0.0424149\pi$
$277$	4.19864	+	9.00402i	0.252272	+	0.540999i	−0.738863	+	0.673855i	$0.764637\pi$
$278$	3.34808	−	12.4952i	0.200804	−	0.749412i
$279$	16.9572	+	5.95314i	1.01520	+	0.356405i
$280$	−1.06344	−	21.3963i	−0.0635529	−	1.27867i
$281$	−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	$-0.505634\pi$
$282$	−4.20617	+	7.38249i	−0.250474	+	0.439621i
$283$	4.26583	+	6.09224i	0.253577	+	0.362146i	0.925677	−	0.378315i	$-0.123496\pi$
$283$	4.26583	+	6.09224i	0.253577	+	0.362146i	−0.672100	+	0.740461i	$0.734607\pi$
$284$	−6.11110	+	34.6578i	−0.362627	+	2.05656i
$285$	−29.8808	+	1.65651i	−1.76999	+	0.0981234i
$286$	−0.0107782	+	0.00904400i	−0.000637329	+	0.000534783i
$287$	1.88112	+	7.02044i	0.111039	+	0.414403i
$288$	−7.32021	−	5.00187i	−0.431348	−	0.294738i
$289$	11.3588	−	6.55802i	0.668166	−	0.385766i
$290$	−45.1604	−	28.3891i	−2.65191	−	1.66706i
$291$	−9.11051	+	19.8329i	−0.534068	+	1.16263i
$292$	−0.917390	−	10.4858i	−0.0536862	−	0.613636i
$293$	7.55448	+	3.52271i	0.441337	+	0.205799i	0.630568	−	0.776134i	$-0.282822\pi$
$293$	7.55448	+	3.52271i	0.441337	+	0.205799i	−0.189231	+	0.981933i	$0.560600\pi$
$294$	−0.376141	+	4.60233i	−0.0219370	+	0.268413i
$295$	1.63362	−	1.51515i	0.0951128	−	0.0882155i
$296$			6.88912i			0.400422i
$297$	0.0210214	+	0.00724518i	0.00121978	+	0.000420408i
$298$	15.4707	−	15.4707i	0.896194	−	0.896194i
$299$	1.77409	+	10.0614i	0.102598	+	0.581864i
$300$	30.7632	+	7.65961i	1.77612	+	0.442228i
$301$	16.4429	−	5.98474i	0.947755	−	0.344955i
$302$	26.8852	−	2.35215i	1.54707	−	0.135351i
$303$	−6.53469	−	5.41987i	−0.375408	−	0.311363i
$304$	5.49502	−	15.0974i	0.315161	−	0.865897i
$305$	−6.94777	+	13.5453i	−0.397828	+	0.775600i
$306$	12.1009	−	7.17224i	0.691762	−	0.410010i
$307$	−11.7737	+	3.15476i	−0.671962	+	0.180052i	−0.578638	−	0.815584i	$-0.696416\pi$
$307$	−11.7737	+	3.15476i	−0.671962	+	0.180052i	−0.0933234	+	0.995636i	$0.529749\pi$
$308$	0.0378380	+	0.00331040i	0.00215602	+	0.000188627i
$309$	5.08462	−	19.4197i	0.289254	−	1.10475i
$310$	−12.0186	+	29.5175i	−0.682611	+	1.67648i
$311$	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	$0.360958\pi$
$312$	−0.0540918	−	9.45758i	−0.00306235	−	0.535430i
$313$	0.631317	−	7.21599i	0.0356842	−	0.407872i	−0.957255	−	0.289246i	$-0.906596\pi$
$313$	0.631317	−	7.21599i	0.0356842	−	0.407872i	0.992939	−	0.118626i	$-0.0378489\pi$
$314$	1.04673	−	1.81300i	0.0590706	−	0.102313i
$315$	15.1340	+	5.96122i	0.852707	+	0.335877i
$316$	12.9356	+	22.4052i	0.727686	+	1.26039i
$317$	−4.44794	+	2.07411i	−0.249821	+	0.116493i	−0.543496	−	0.839412i	$-0.682900\pi$
$317$	−4.44794	+	2.07411i	−0.249821	+	0.116493i	0.293675	+	0.955905i	$0.405122\pi$
$318$	−7.19941	−	1.22704i	−0.403723	−	0.0688088i
$319$	0.0275787	−	0.0328670i	0.00154411	−	0.00184020i
$320$	15.1120	−	19.9420i	0.844784	−	1.11479i
$321$	−3.47733	−	7.34715i	−0.194085	−	0.410078i
$322$	24.4622	−	34.9356i	1.36322	−	1.94688i
$323$	−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
$327$	−18.3545	−	6.56185i	−1.01500	−	0.362871i
$328$	5.00520	−	10.7337i	0.276366	−	0.592668i
$329$	−3.82979	−	3.21358i	−0.211143	−	0.177170i
$330$	−0.0146605	+	0.0366039i	−0.000807031	+	0.00201498i
$331$	−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	$0.654688\pi$
$332$	36.0280	+	9.65368i	1.97729	+	0.529814i
$333$	−4.76564	−	2.15624i	−0.261156	−	0.118161i
$334$	14.9158	+	8.61167i	0.816159	+	0.471209i
$335$	9.50456	+	17.9924i	0.519290	+	0.983032i
$336$	−6.13932	+	6.20995i	−0.334927	+	0.338780i
$337$	17.9831	−	12.5919i	0.979602	−	0.685925i	0.0300546	−	0.999548i	$-0.490432\pi$
$337$	17.9831	−	12.5919i	0.979602	−	0.685925i	0.949547	+	0.313624i	$0.101543\pi$
$338$	21.6140	−	15.1343i	1.17564	−	0.823195i
$339$	3.15814	+	0.826891i	0.171527	+	0.0449105i
$340$	7.53498	+	14.2640i	0.408642	+	0.773572i
$341$	−0.0222000	−	0.0128172i	−0.00120220	−	0.000694090i
$342$	39.4426	+	38.5504i	2.13281	+	2.08457i
$343$	−19.0194	−	5.09624i	−1.02695	−	0.275171i
$344$	−26.7937	−	9.75210i	−1.44462	−	0.525798i
$345$	17.6955	+	22.5087i	0.952692	+	1.21183i
$346$	4.35333	+	3.65288i	0.234037	+	0.196380i
$347$	−6.59670	+	14.1467i	−0.354129	+	0.759433i	−0.999992	−	0.00402090i	$-0.998720\pi$
$347$	−6.59670	+	14.1467i	−0.354129	+	0.759433i	0.645863	+	0.763454i	$0.276498\pi$
$348$	11.3973	+	62.5434i	0.610959	+	3.35268i
$349$	−23.5190	+	4.14704i	−1.25895	+	0.221986i	−0.763017	−	0.646378i	$-0.776283\pi$
$349$	−23.5190	+	4.14704i	−1.25895	+	0.221986i	−0.495928	+	0.868364i	$0.665172\pi$
$350$	−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
$353$	0.184497	−	0.263489i	0.00981980	−	0.0140241i	−0.814212	−	0.580567i	$-0.802831\pi$
$353$	0.184497	−	0.263489i	0.00981980	−	0.0140241i	0.824032	+	0.566543i	$0.191720\pi$
$354$	−4.09258	−	0.334480i	−0.217518	−	0.0177774i
$355$	12.9833	−	17.1331i	0.689084	−	0.909329i
$356$	−14.2964	+	17.0378i	−0.757707	+	0.903000i
$357$	2.87529	+	7.76140i	0.152177	+	0.410777i
$358$	−36.2796	+	16.9175i	−1.91744	+	0.894116i
$359$	2.09252	+	3.62435i	0.110439	+	0.191286i	0.915947	−	0.401298i	$-0.131441\pi$
$359$	2.09252	+	3.62435i	0.110439	+	0.191286i	−0.805508	+	0.592585i	$0.798108\pi$
$360$	−12.6474	−	23.2929i	−0.666576	−	1.22764i
$361$	20.3536	−	35.2535i	1.07124	−	1.85545i
$362$	−1.46986	+	16.8006i	−0.0772543	+	0.883021i
$363$	16.5542	+	9.43174i	0.868869	+	0.495038i
$364$	12.0806	+	2.13013i	0.633194	+	0.111649i
$365$	−2.42463	+	5.95486i	−0.126911	+	0.311691i
$366$	27.0574	−	7.41614i	1.41431	−	0.387648i
$367$	−13.3335	−	1.16653i	−0.696004	−	0.0608924i	−0.266337	−	0.963880i	$-0.585813\pi$
$367$	−13.3335	−	1.16653i	−0.696004	−	0.0608924i	−0.429667	+	0.902988i	$0.641369\pi$
$368$	−14.8473	+	3.97833i	−0.773970	+	0.207385i
$369$	5.85858	+	6.82197i	0.304986	+	0.355138i
$370$	4.23351	−	8.25360i	0.220090	−	0.429084i
$371$	1.46974	−	4.03807i	0.0763050	−	0.209646i
$372$	35.6177	−	13.1950i	1.84669	−	0.684128i
$373$	−15.6366	+	1.36803i	−0.809634	+	0.0708338i	−0.484452	−	0.874818i	$-0.660981\pi$
$373$	−15.6366	+	1.36803i	−0.809634	+	0.0708338i	−0.325182	+	0.945652i	$0.605425\pi$
$374$	−0.0188543	+	0.00686241i	−0.000974933	+	0.000354847i
$375$	−14.5847	−	12.7392i	−0.753148	−	0.657851i
$376$	1.41463	+	8.02279i	0.0729542	+	0.413744i
$377$	9.79812	−	9.79812i	0.504629	−	0.504629i
$378$	−10.7345	−	27.9889i	−0.552121	−	1.43959i
$379$		−	26.4477i		−	1.35853i	−0.733894	−	0.679264i	$-0.762299\pi$
$379$		−	26.4477i		−	1.35853i	0.733894	−	0.679264i	$-0.237701\pi$
$380$	−46.3744	+	43.0114i	−2.37896	+	2.20644i
$381$	8.39887	+	5.80965i	0.430287	+	0.297637i
$382$	−16.8989	−	7.88010i	−0.864625	−	0.403181i
$383$	−1.62124	−	18.5309i	−0.0828415	−	0.946883i	−0.917923	−	0.396758i	$-0.870135\pi$
$383$	−1.62124	−	18.5309i	−0.0828415	−	0.946883i	0.835082	−	0.550126i	$-0.185420\pi$
$384$	−35.7198	+	3.33104i	−1.82282	+	0.169987i
$385$	−0.0196423	−	0.0123477i	−0.00100107	−	0.000629298i
$386$	−38.2831	+	22.1028i	−1.94856	+	1.12500i
$387$	15.1323	−	15.4826i	0.769220	−	0.787022i
$388$	11.9388	+	44.5560i	0.606098	+	2.26199i
$389$	25.4642	−	21.3670i	1.29108	−	1.08335i	0.299472	−	0.954105i	$-0.403190\pi$
$389$	25.4642	−	21.3670i	1.29108	−	1.08335i	0.991613	−	0.129243i	$-0.0412548\pi$
$390$	−5.74709	+	11.3640i	−0.291015	+	0.575440i
$391$	−2.52993	+	14.3479i	−0.127944	+	0.725606i
$392$	2.53946	+	3.62672i	0.128262	+	0.183177i
$393$	26.7998	−	0.153279i	1.35187	−	0.00773191i
$394$	−10.3018	−	12.2772i	−0.518996	−	0.618515i
$395$	−0.784477	−	15.7836i	−0.0394713	−	0.794157i
$396$	0.0439726	−	0.0165767i	0.00220971	−	0.000833013i
$397$	−8.84314	+	33.0030i	−0.443824	+	1.65637i	0.275198	+	0.961388i	$0.411257\pi$
$397$	−8.84314	+	33.0030i	−0.443824	+	1.65637i	−0.719022	+	0.694987i	$0.755410\pi$
$398$	9.07480	+	19.4610i	0.454879	+	0.975490i
$399$	−26.4763	+	18.7655i	−1.32547	+	0.939450i
$400$	9.36849	−	4.50689i	0.468424	−	0.225344i
$401$	−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	$0.972785\pi$
$402$	12.6244	−	35.3123i	0.629647	−	1.76122i
$403$	−6.78172	−	4.74861i	−0.337821	−	0.236545i
$404$	−17.9432			−0.892709
$405$	20.0717	−	1.45853i	0.997370	−	0.0724751i
$406$	−57.8436			−2.87073
$407$	0.00611167	+	0.00427944i	0.000302944	+	0.000212124i
$408$	4.54030	−	12.6999i	0.224779	−	0.628740i
$409$	13.0223	+	35.7785i	0.643911	+	1.76913i	0.639078	+	0.769142i	$0.279316\pi$
$409$	13.0223	+	35.7785i	0.643911	+	1.76913i	0.00483335	+	0.999988i	$0.498461\pi$
$410$	−12.5926	+	9.78383i	−0.621906	+	0.483189i
$411$	5.52177	−	3.91364i	0.272369	−	0.193046i
$412$	−17.9304	−	38.4519i	−0.883367	−	1.89439i
$413$	0.625335	−	2.33378i	0.0307707	−	0.114838i
$414$	8.56777	−	52.0660i	0.421083	−	2.55890i
$415$	−16.8902	−	15.2907i	−0.829107	−	0.750593i
$416$	2.62527	+	3.12868i	0.128715	+	0.153396i
$417$	9.41713	−	0.0538605i	0.461159	−	0.00263756i
$418$	−0.0451224	−	0.0644415i	−0.00220701	−	0.00315194i
$419$	4.45593	−	25.2708i	0.217686	−	1.23456i	−0.658497	−	0.752583i	$-0.728808\pi$
$419$	4.45593	−	25.2708i	0.217686	−	1.23456i	0.876184	−	0.481978i	$-0.160081\pi$
$420$	32.6629	−	10.7220i	1.59378	−	0.523180i
$421$	−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	$0.475747\pi$
$422$	3.91416	+	14.6078i	0.190538	+	0.711098i
$423$	−5.99264	−	1.53248i	−0.291372	−	0.0745115i
$424$	−6.06417	+	3.50115i	−0.294502	+	0.170031i
$425$	−0.118797	−	9.85316i	−0.00576248	−	0.477948i
$426$	−39.4459	+	3.67852i	−1.91116	+	0.178225i
$427$	1.43875	+	16.4450i	0.0696260	+	0.795829i
$428$	−15.5699	−	7.26039i	−0.752602	−	0.350944i
$429$	−0.00842388	−	0.00582695i	−0.000406709	−	0.000281328i
$430$	26.1076	+	28.1489i	1.25902	+	1.35746i
$431$		−	15.6671i		−	0.754660i	−0.926079	−	0.377330i	$-0.876842\pi$
$431$		−	15.6671i		−	0.754660i	0.926079	−	0.377330i	$-0.123158\pi$
$432$	−3.52046	+	10.2144i	−0.169378	+	0.491439i
$433$	10.5845	−	10.5845i	0.508657	−	0.508657i	−0.405457	−	0.914114i	$-0.632888\pi$
$433$	10.5845	−	10.5845i	0.508657	−	0.508657i	0.914114	+	0.405457i	$0.132888\pi$
$434$	6.00127	+	34.0349i	0.288070	+	1.63373i
$435$	11.2414	−	37.1701i	0.538982	−	1.78217i
$436$	−38.7122	+	14.0901i	−1.85398	+	0.674792i
$437$	−56.9060	+	4.97863i	−2.72218	+	0.238160i
$438$	11.1113	−	4.11630i	0.530918	−	0.196684i
$439$	7.09912	−	19.5047i	0.338823	−	0.930907i	−0.646907	−	0.762569i	$-0.723938\pi$
$439$	7.09912	−	19.5047i	0.338823	−	0.930907i	0.985729	−	0.168338i	$-0.0538401\pi$
$440$	0.0115856	+	0.0359869i	0.000552321	+	0.00171561i
$441$	−3.30366	+	0.621570i	−0.157317	+	0.0295986i
$442$	−6.25923	+	1.67715i	−0.297721	+	0.0797741i
$443$	−7.49047	−	0.655331i	−0.355883	−	0.0311357i	−0.0921874	−	0.995742i	$-0.529386\pi$
$443$	−7.49047	−	0.655331i	−0.355883	−	0.0311357i	−0.263696	+	0.964606i	$0.584941\pi$
$444$	−10.6619	+	2.92231i	−0.505993	+	0.138687i
$445$	12.5200	−	5.27458i	0.593504	−	0.250039i
$446$	8.80576	+	1.55269i	0.416965	+	0.0735222i
$447$	13.8391	+	7.88480i	0.654565	+	0.372938i
$448$	2.36476	−	27.0293i	0.111724	−	1.27701i
$449$	−2.66419	+	4.61452i	−0.125731	+	0.217773i	−0.922018	−	0.387146i	$-0.873461\pi$
$449$	−2.66419	+	4.61452i	−0.125731	+	0.217773i	0.796287	+	0.604918i	$0.206794\pi$
$450$	0.838413	+	35.6784i	0.0395232	+	1.68190i
$451$	−0.00641320	−	0.0111080i	−0.000301986	−	0.000523055i
$452$	6.25326	−	2.91594i	0.294129	−	0.137154i
$453$	6.82513	+	18.4233i	0.320672	+	0.865604i
$454$	−9.97027	+	11.8821i	−0.467928	+	0.557655i
$455$	−5.97203	−	4.52557i	−0.279973	−	0.212162i
$456$	52.7048	+	4.30747i	2.46813	+	0.201716i
$457$	−13.4866	+	19.2609i	−0.630879	+	0.900988i	−0.999592	−	0.0285551i	$-0.990909\pi$
$457$	−13.4866	+	19.2609i	−0.630879	+	0.900988i	0.368714	+	0.929543i	$0.379798\pi$
$458$	−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	$0.321993\pi$
$462$	0.00766555	+	0.0420652i	0.000356634	+	0.00195705i
$463$	−6.30838	+	13.5284i	−0.293175	+	0.628716i	−0.996630	−	0.0820233i	$-0.973862\pi$
$463$	−6.30838	+	13.5284i	−0.293175	+	0.628716i	0.703455	+	0.710740i	$0.251640\pi$
$464$	15.9702	+	13.4006i	0.741398	+	0.622106i
$465$	−23.0370	−	2.75797i	−1.06831	−	0.127898i
$466$	58.5204	+	21.2997i	2.71091	+	0.986689i
$467$	−6.07179	−	1.62693i	−0.280969	−	0.0752854i	0.115583	−	0.993298i	$-0.463127\pi$
$467$	−6.07179	−	1.62693i	−0.280969	−	0.0752854i	−0.396552	+	0.918012i	$0.629793\pi$
$468$	14.6141	−	4.09555i	0.675535	−	0.189317i
$469$	19.1095	+	11.0329i	0.882393	+	0.509450i
$470$	3.23536	−	10.4811i	0.149236	−	0.483459i
$471$	1.47433	+	0.386021i	0.0679335	+	0.0177869i
$472$	−3.22503	+	2.25819i	−0.148444	+	0.103942i
$473$	−0.0252955	+	0.0177121i	−0.00116309	+	0.000814402i
$474$	−20.4756	+	20.7112i	−0.940477	+	0.951297i
$475$	37.1955	−	10.4487i	1.70665	−	0.479420i
$476$	15.1495	+	8.74657i	0.694377	+	0.400899i
$477$	−0.523933	−	5.29081i	−0.0239892	−	0.242249i
$478$	−42.1177	−	11.2854i	−1.92642	−	0.516182i
$479$	6.42357	+	2.33799i	0.293501	+	0.106825i	0.484574	−	0.874750i	$-0.338975\pi$
$479$	6.42357	+	2.33799i	0.293501	+	0.106825i	−0.191073	+	0.981576i	$0.561197\pi$
$480$	10.6253	+	4.25561i	0.484976	+	0.194241i
$481$	1.84587	+	1.54887i	0.0841645	+	0.0706224i
$482$	6.36322	−	13.6460i	0.289837	−	0.621557i
$483$	29.2356	+	10.4519i	1.33026	+	0.475578i
$484$	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	0.389165	−	0.921168i	$-0.372763\pi$
$487$	−11.7403	−	11.7403i	−0.532002	−	0.532002i	−0.921168	+	0.389165i	$0.872763\pi$
$488$	15.4289	−	22.0347i	0.698431	−	0.997463i
$489$	4.98314	+	10.5287i	0.225345	+	0.476126i
$490$	−0.813732	−	5.90559i	−0.0367606	−	0.266788i
$491$	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	$0.0997121\pi$
$492$	18.7351	+	3.19313i	0.844645	+	0.143958i
$493$	17.9087	−	8.35099i	0.806569	−	0.376109i
$494$	−12.7035	−	22.0031i	−0.571557	−	0.989966i
$495$	−0.0285207	−	0.00324913i	−0.00128191	−	0.000146037i
$496$	6.22793	−	10.7871i	0.279642	−	0.484355i
$497$	2.03166	−	23.2220i	0.0911326	−	1.04165i
$498$	0.240145	+	41.9877i	0.0107612	+	1.88152i
$499$	−27.4365	−	4.83779i	−1.22823	−	0.216569i	−0.478363	−	0.878162i	$-0.658770\pi$
$499$	−27.4365	−	4.83779i	−1.22823	−	0.216569i	−0.749863	+	0.661593i	$0.769881\pi$
$500$	−40.9143	−	1.04555i	−1.82974	−	0.0467584i
$501$	−3.17587	+	12.1296i	−0.141887	+	0.541909i
$502$	−63.3862	−	5.54557i	−2.82906	−	0.247511i
$503$	−14.4253	+	3.86525i	−0.643192	+	0.172343i	−0.565649	−	0.824646i	$-0.691374\pi$
$503$	−14.4253	+	3.86525i	−0.643192	+	0.172343i	−0.0775431	+	0.996989i	$0.524708\pi$
$504$	−25.0537	−	14.0852i	−1.11598	−	0.627403i
$505$	9.75226	+	5.00222i	0.433970	+	0.222596i
$506$	−0.0257419	+	0.0707252i	−0.00114436	+	0.00314412i
$507$	14.7850	+	12.2627i	0.656626	+	0.544606i
$508$	21.5017	−	1.88116i	0.953985	−	0.0834629i
$509$	5.75433	−	2.09440i	0.255056	−	0.0928328i	−0.211328	−	0.977415i	$-0.567779\pi$
$509$	5.75433	−	2.09440i	0.255056	−	0.0928328i	0.466384	+	0.884582i	$0.345557\pi$
$510$	−13.2440	+	12.4252i	−0.586452	+	0.550197i
$511$	1.21069	+	6.86619i	0.0535580	+	0.303742i
$512$	−15.9632	+	15.9632i	−0.705482	+	0.705482i
$513$	−19.4759	+	35.1110i	−0.859883	+	1.55019i
$514$		−	9.32621i		−	0.411361i
$515$	−0.974338	+	25.8975i	−0.0429345	+	1.14118i
$516$	3.72713	−	45.6039i	0.164078	−	2.00760i
$517$	0.00799616	+	0.00372867i	0.000351671	+	0.000163987i
$518$	−0.876681	−	10.0205i	−0.0385191	−	0.440276i
$519$	−1.72693	+	3.75941i	−0.0758039	+	0.165020i
$520$	2.71451	+	11.9043i	0.119039	+	0.522039i
$521$	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	$0.170495\pi$
$522$	−64.5108	+	30.9851i	−2.82356	+	1.35618i
$523$	−0.878392	−	3.27820i	−0.0384094	−	0.143346i	0.944058	−	0.329778i	$-0.106974\pi$
$523$	−0.878392	−	3.27820i	−0.0384094	−	0.143346i	−0.982468	+	0.186433i	$0.940307\pi$
$524$	43.3905	−	36.4089i	1.89552	−	1.59053i
$525$	−20.7416	−	3.27829i	−0.905236	−	0.143076i
$526$	12.7435	−	72.2722i	0.555645	−	3.15122i
$527$	−6.77171	−	9.67101i	−0.294980	−	0.421276i
$528$	0.00762881	−	0.0133898i	0.000332001	−	0.000582715i
$529$	20.3451	+	24.2463i	0.884569	+	1.05419i
$530$	9.41680	−	0.468035i	0.409040	−	0.0203302i
$531$	−0.552725	−	2.93775i	−0.0239862	−	0.127488i
$532$	−17.7517	+	66.2503i	−0.769635	+	2.87232i
$533$	−1.75067	−	3.75433i	−0.0758301	−	0.162618i
$534$	−22.7519	−	10.4514i	−0.984570	−	0.452275i
$535$	6.43831	+	8.28666i	0.278353	+	0.358264i
$536$	−12.2976	−	33.7875i	−0.531178	−	1.45940i
$537$	−18.8592	−	22.2163i	−0.813836	−	0.958702i
$538$	22.4477	+	15.7180i	0.967787	+	0.677652i
$539$	0.00479492			0.000206532
$540$	30.6842	−	29.4544i	1.32044	−	1.26751i
$541$	−32.7244			−1.40693			−0.703466	−	0.710729i	$-0.748365\pi$
$541$	−32.7244			−1.40693			−0.703466	+	0.710729i	$0.748365\pi$
$542$	−13.2152	−	9.25340i	−0.567642	−	0.397467i
$543$	−12.0785	+	2.20107i	−0.518338	+	0.0944569i
$544$	1.99201	+	5.47299i	0.0854065	+	0.234653i
$545$	24.9683	+	3.13414i	1.06953	+	0.134252i
$546$	1.28221	+	13.7496i	0.0548736	+	0.588427i
$547$	12.0993	+	25.9469i	0.517327	+	1.10941i	0.975389	+	0.220491i	$0.0707658\pi$
$547$	12.0993	+	25.9469i	0.517327	+	1.10941i	−0.458063	+	0.888920i	$0.651456\pi$
$548$	3.70221	−	13.8168i	0.158151	−	0.590226i
$549$	10.4137	+	17.5698i	0.444445	+	0.749861i
$550$	0.00823449	−	0.0502342i	0.000351120	−	0.00214200i
$551$	49.8005	+	59.3499i	2.12157	+	2.52839i
$552$	−25.5462	−	43.6686i	−1.08732	−	1.85866i
$553$	−9.82914	−	14.0375i	−0.417977	−	0.596934i
$554$	−4.10455	+	23.2780i	−0.174385	+	0.988989i
$555$	6.60951	+	1.38404i	0.280558	+	0.0587492i
$556$	15.2469	−	12.7937i	0.646612	−	0.542572i
$557$	5.67171	+	21.1671i	0.240318	+	0.896879i	0.975679	+	0.219203i	$0.0703458\pi$
$557$	5.67171	+	21.1671i	0.240318	+	0.896879i	−0.735361	+	0.677675i	$0.762988\pi$
$558$	24.9245	+	34.7431i	1.05514	+	1.47079i
$559$	−8.63696	+	4.98655i	−0.365304	+	0.210909i
$560$	5.99980	−	9.54429i	0.253538	−	0.403320i
$561$	−0.00844633	−	0.0119170i	−0.000356604	−	0.000503135i
$562$	−5.40385	−	61.7663i	−0.227948	−	2.60545i
$563$	−9.80704	−	4.57310i	−0.413317	−	0.192733i	0.204826	−	0.978798i	$-0.434337\pi$
$563$	−9.80704	−	4.57310i	−0.413317	−	0.192733i	−0.618143	+	0.786065i	$0.712115\pi$
$564$	−11.8164	+	5.59256i	−0.497559	+	0.235489i
$565$	−4.21160	−	0.158452i	−0.177183	−	0.00666614i
$566$			17.6948i			0.743770i
$567$	17.5852	−	12.9227i	0.738509	−	0.542703i
$568$	−26.8592	+	26.8592i	−1.12699	+	1.12699i
$569$	2.29260	+	13.0020i	0.0961109	+	0.545072i	0.994401	+	0.105670i	$0.0336987\pi$
$569$	2.29260	+	13.0020i	0.0961109	+	0.545072i	−0.898290	+	0.439402i	$0.855190\pi$
$570$	−60.4966	−	37.5489i	−2.53392	−	1.57275i
$571$	−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	$0.441764\pi$
$572$	−0.0215658	+	0.00188676i	−0.000901710	+	7.88894e-5i
$573$	2.28062	−	13.3811i	0.0952742	−	0.559004i
$574$	−5.91434	+	16.2495i	−0.246860	+	0.678242i
$575$	−28.5999	−	23.4164i	−1.19270	−	0.976533i
$576$	−11.8415	−	31.4115i	−0.493394	−	1.30881i
$577$	25.1985	−	6.75192i	1.04903	−	0.281086i	0.307178	−	0.951652i	$-0.400615\pi$
$577$	25.1985	−	6.75192i	1.04903	−	0.281086i	0.741850	+	0.670566i	$0.233949\pi$
$578$	31.0872	+	2.71978i	1.29306	+	0.113128i
$579$	−22.8854	−	22.6251i	−0.951083	−	0.940266i
$580$	−31.8644	−	75.6347i	−1.32310	−	3.14056i
$581$	−24.3307	−	4.29016i	−1.00941	−	0.177986i
$582$	−44.8211	+	26.2204i	−1.85790	+	1.08687i
$583$	−0.000660950		0.00755470i	−2.73738e−5		0.000312884i
$584$	5.68051	−	9.83893i	0.235061	−	0.407138i
$585$	−9.08459	−	1.84815i	−0.375602	−	0.0764117i
$586$	9.91592	+	17.1749i	0.409623	+	0.709488i
$587$	13.7926	−	6.43160i	0.569282	−	0.265460i	−0.116593	−	0.993180i	$-0.537197\pi$
$587$	13.7926	−	6.43160i	0.569282	−	0.265460i	0.685875	+	0.727719i	$0.259420\pi$
$588$	−4.53567	+	5.46861i	−0.187048	+	0.225522i
$589$	29.7544	−	35.4599i	1.22601	−	1.46110i
$590$	5.25150	−	0.723604i	0.216201	−	0.0297903i
$591$	6.63732	−	9.59542i	0.273023	−	0.394703i
$592$	−2.07940	+	2.96969i	−0.0854627	+	0.122053i
$593$	30.1991	+	30.1991i	1.24013	+	1.24013i	0.959947	+	0.280181i	$0.0903946\pi$
$593$	30.1991	+	30.1991i	1.24013	+	1.24013i	0.280181	+	0.959947i	$0.409605\pi$
$594$	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
$597$	−11.9172	+	10.1164i	−0.487737	+	0.414036i
$598$	−10.2728	+	22.0301i	−0.420086	+	0.900876i
$599$	13.7064	+	11.5010i	0.560028	+	0.469920i	0.878320	−	0.478073i	$-0.158665\pi$
$599$	13.7064	+	11.5010i	0.560028	+	0.469920i	−0.318292	+	0.947993i	$0.603109\pi$
$600$	22.4572	+	25.8173i	0.916812	+	1.05399i
$601$	−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	$0.883121\pi$
$602$	40.2135	+	10.7752i	1.63898	+	0.439163i
$603$	27.2220	+	2.06815i	1.10857	+	0.0842216i
$604$	35.9606	+	20.7619i	1.46322	+	0.844788i
$605$	−23.5025	−	7.25483i	−0.955511	−	0.294951i
$606$	−5.33943	−	19.4807i	−0.216900	−	0.791348i
$607$	35.5036	−	24.8599i	1.44105	−	1.00903i	0.447663	−	0.894203i	$-0.352257\pi$
$607$	35.5036	−	24.8599i	1.44105	−	1.00903i	0.993385	−	0.114830i	$-0.0366323\pi$
$608$	−18.7059	+	13.0980i	−0.758626	+	0.531196i
$609$	−11.1312	−	40.6118i	−0.451060	−	1.64567i
$610$	−32.0255	+	16.9176i	−1.29668	+	0.684973i
$611$	2.46768	+	1.42471i	0.0998316	+	0.0576378i
$612$	21.5810	+	1.63958i	0.872359	+	0.0662761i
$613$	0.212147	+	0.0568446i	0.00856854	+	0.00229593i	0.263101	−	0.964768i	$-0.415255\pi$
$613$	0.212147	+	0.0568446i	0.00856854	+	0.00229593i	−0.254532	+	0.967064i	$0.581921\pi$
$614$	−27.2515	−	9.91873i	−1.09978	−	0.400287i
$615$	−9.29248	−	6.95847i	−0.374709	−	0.280593i
$616$	0.0314049	+	0.0263518i	0.00126534	+	0.00106175i
$617$	−11.5791	+	24.8316i	−0.466159	+	0.999681i	0.522932	+	0.852374i	$0.324838\pi$
$617$	−11.5791	+	24.8316i	−0.466159	+	0.999681i	−0.989091	+	0.147307i	$0.952940\pi$
$618$	36.4110	−	30.9090i	1.46466	−	1.24334i
$619$	−40.1687	+	7.08283i	−1.61452	+	0.284683i	−0.906720	−	0.421733i	$-0.861422\pi$
$619$	−40.1687	+	7.08283i	−1.61452	+	0.284683i	−0.707797	+	0.706416i	$0.750311\pi$
$620$	−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
$623$	8.45000	−	12.0678i	0.338542	−	0.483488i
$624$	2.83134	−	4.09320i	0.113344	−	0.163859i
$625$	21.9457	+	11.9744i	0.877829	+	0.478975i
$626$	11.0778	−	13.2020i	0.442758	−	0.527658i
$627$	0.0365609	−	0.0440812i	0.00146010	−	0.00176043i
$628$	2.91924	−	1.36126i	0.116490	−	0.0543203i
$629$	1.71810	+	2.97584i	0.0685053	+	0.118655i
$630$	21.3603	+	32.2710i	0.851015	+	1.28571i
$631$	−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	$0.850062\pi$
$632$	−2.43373	+	27.8177i	−0.0968087	+	1.10653i
$633$	−9.50288	+	5.55920i	−0.377706	+	0.220958i
$634$	−11.4992	−	2.02762i	−0.456693	−	0.0805272i
$635$	−12.2108	−	4.97184i	−0.484569	−	0.197301i
$636$	−7.99093	−	7.90004i	−0.316861	−	0.313257i
$637$	1.54269	+	0.134968i	0.0611235	+	0.00534761i
$638$	0.0986016	−	0.0264202i	0.00390367	−	0.00104599i
$639$	−10.1735	−	26.9869i	−0.402458	−	1.06759i
$640$	44.0859	−	14.1930i	1.74265	−	0.561026i
$641$	−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	$0.937708\pi$
$642$	3.24928	−	19.0645i	0.128239	−	0.752418i
$643$	−29.4868	+	2.57976i	−1.16284	+	0.101736i	−0.652194	−	0.758052i	$-0.726151\pi$
$643$	−29.4868	+	2.57976i	−1.16284	+	0.101736i	−0.510651	+	0.859788i	$0.670596\pi$
$644$	61.6619	−	22.4431i	2.42982	−	0.884382i
$645$	−14.7392	+	23.7470i	−0.580355	+	0.935036i
$646$	−6.29152	−	35.6810i	−0.247536	−	1.40385i
$647$	3.41329	−	3.41329i	0.134190	−	0.134190i	−0.636821	−	0.771012i	$-0.719751\pi$
$647$	3.41329	−	3.41329i	0.134190	−	0.134190i	0.771012	+	0.636821i	$0.219751\pi$
$648$	−35.4865	−	2.28810i	−1.39404	−	0.0898852i
$649$			0.00426384i			0.000167370i
$650$	4.06331	−	15.9303i	0.159376	−	0.624836i
$651$	−22.7409	+	10.7630i	−0.891287	+	0.421837i
$652$	22.3123	+	10.4044i	0.873818	+	0.407468i
$653$	3.91945	+	44.7996i	0.153380	+	1.75314i	0.550005	+	0.835161i	$0.314626\pi$
$653$	3.91945	+	44.7996i	0.153380	+	1.75314i	−0.396625	+	0.917981i	$0.629819\pi$
$654$	−26.8171	−	37.8364i	−1.04863	−	1.47952i
$655$	−33.7331	+	7.69207i	−1.31806	+	0.300554i
$656$	5.39742	−	3.11620i	0.210734	−	0.121667i
$657$	5.02826	+	7.00907i	0.196171	+	0.273450i
$658$	−3.07859	−	11.4895i	−0.120016	−	0.447906i
$659$	−31.0081	+	26.0189i	−1.20790	+	1.01355i	−0.208535	+	0.978015i	$0.566870\pi$
$659$	−31.0081	+	26.0189i	−1.20790	+	1.01355i	−0.999368	+	0.0355365i	$0.988686\pi$
$660$	−0.0507806	+	0.0331958i	−0.00197663	+	0.00129215i
$661$	−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	$0.947817\pi$
$662$	−6.77668	−	9.67810i	−0.263383	−	0.376150i
$663$	−2.38203	−	4.07183i	−0.0925103	−	0.158137i
$664$	25.8776	+	30.8397i	1.00424	+	1.19681i
$665$	28.1175	−	31.0586i	1.09035	−	1.20440i
$666$	−6.34542	−	10.7059i	−0.245880	−	0.414845i
$667$	19.1844	−	71.5973i	0.742824	−	2.77226i
$668$	11.1994	+	24.0171i	0.433316	+	0.929250i
$669$	0.604411	+	6.48129i	0.0233679	+	0.250581i
$670$	−6.02980	+	48.0368i	−0.232952	+	1.85582i
$671$	−0.00996382	−	0.0273754i	−0.000384649	−	0.00105681i
$672$	12.2106	−	2.22514i	0.471034	−	0.0858367i
$673$	25.0337	+	17.5288i	0.964978	+	0.675685i	0.946011	−	0.324135i	$-0.105073\pi$
$673$	25.0337	+	17.5288i	0.964978	+	0.675685i	0.0189672	+	0.999820i	$0.493962\pi$
$674$	52.2317			2.01189
$675$	−24.8884	+	7.45449i	−0.957954	+	0.286923i
$676$	40.5973			1.56144
$677$	17.6437	+	12.3542i	0.678102	+	0.474812i	0.861189	−	0.508284i	$-0.169720\pi$
$677$	17.6437	+	12.3542i	0.678102	+	0.474812i	−0.183087	+	0.983097i	$0.558609\pi$
$678$	5.02660	+	5.92136i	0.193045	+	0.227408i
$679$	−10.4501	−	28.7114i	−0.401038	−	1.10184i
$680$	−2.16859	+	17.2762i	−0.0831617	+	0.662513i
$681$	−10.2610	−	4.71354i	−0.393203	−	0.180623i
$682$	−0.0257754	−	0.0552756i	−0.000986992	−	0.00211661i
$683$	−2.39311	+	8.93120i	−0.0915697	+	0.341743i	−0.996477	−	0.0838658i	$-0.973273\pi$
$683$	−2.39311	+	8.93120i	−0.0915697	+	0.341743i	0.904907	+	0.425609i	$0.139940\pi$
$684$	15.6905	+	83.3956i	0.599942	+	3.18871i
$685$	−5.86404	+	6.47744i	−0.224053	+	0.247490i
$686$	−30.1131	−	35.8874i	−1.14972	−	1.37019i
$687$	3.71547	−	6.52124i	0.141754	−	0.248801i
$688$	−8.60637	−	12.2912i	−0.328115	−	0.468597i
$689$	−0.425300	+	2.41199i	−0.0162026	+	0.0918897i
$690$	3.77065	+	68.0165i	0.143546	+	2.58934i
$691$	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	$0.148579\pi$
$692$	2.26304	+	8.44577i	0.0860278	+	0.321060i
$693$	−0.0280587	+	0.0134768i	−0.00106586	+	0.000511943i
$694$	−32.1620	+	18.5688i	−1.22085	+	0.704860i
$695$	−11.8534	+	2.70290i	−0.449625	+	0.102527i
$696$	−28.6428	+	62.3533i	−1.08570	+	2.36350i
$697$	−0.514855	−	5.88482i	−0.0195015	−	0.222903i
$698$	−51.4966	−	24.0132i	−1.94917	−	0.908915i
$699$	−3.69296	+	45.1858i	−0.139681	+	1.70908i
$700$	−38.1651	+	22.6524i	−1.44250	+	0.856182i
$701$		−	5.94733i		−	0.224627i	−0.993673	−	0.112314i	$-0.964174\pi$
$701$		−	5.94733i		−	0.224627i	0.993673	−	0.112314i	$-0.0358262\pi$
$702$	8.79523	+	14.6475i	0.331955	+	0.552835i
$703$	−9.52667	+	9.52667i	−0.359305	+	0.359305i
$704$	0.00831467	+	0.0471548i	0.000313371	+	0.00177721i
$705$	7.98137	+	0.254579i	0.300596	+	0.00958799i
$706$	0.719149	−	0.261749i	0.0270655	−	0.00985105i
$707$	11.8400	−	1.03586i	0.445289	−	0.0389577i
$708$	−4.86292	−	4.03330i	−0.182760	−	0.151581i
$709$	0.0976022	−	0.268160i	0.00366553	−	0.0100710i	−0.937846	−	0.347051i	$-0.887183\pi$
$709$	0.0976022	−	0.268160i	0.00366553	−	0.0100710i	0.941512	+	0.336980i	$0.109405\pi$
$710$	48.6846	−	15.6735i	1.82710	−	0.588215i
$711$	−18.4815	−	10.3903i	−0.693111	−	0.389666i
$712$	−23.1879	+	6.21318i	−0.869004	+	0.232849i
$713$	−44.1179	−	3.85981i	−1.65223	−	0.144551i
$714$	−4.98792	+	19.0503i	−0.186668	+	0.712941i
$715$	0.0122471	+	0.00498664i	0.000458016	+	0.000186490i
$716$	−60.6550	−	10.6951i	−2.26678	−	0.399695i
$717$	−0.181548	−	31.7424i	−0.00678004	−	1.18544i
$718$	−0.867822	+	9.91925i	−0.0323868	+	0.370183i
$719$	13.3454	−	23.1148i	0.497698	−	0.862038i	−0.502299	−	0.864694i	$-0.667512\pi$
$719$	13.3454	−	23.1148i	0.497698	−	0.862038i	0.999996	+	0.00265626i	$0.000845516\pi$
$720$	1.57876	−	13.8583i	0.0588371	−	0.516468i
$721$	14.0514	+	24.3377i	0.523300	+	0.906382i
$722$	87.7772	−	40.9312i	3.26673	−	1.52330i
$723$	10.8053	+	1.84161i	0.401854	+	0.0684902i
$724$	−16.6792	+	19.8775i	−0.619879	+	0.738743i
$725$	−3.76695	+	49.9911i	−0.139901	+	1.85662i
$726$	19.3920	+	40.9728i	0.719705	+	1.52064i
$727$	−28.9346	+	41.3229i	−1.07313	+	1.53258i	−0.247067	+	0.968998i	$0.579467\pi$
$727$	−28.9346	+	41.3229i	−1.07313	+	1.53258i	−0.826059	+	0.563584i	$0.809422\pi$
$728$	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
$732$	40.6467	+	14.5315i	1.50235	+	0.537099i
$733$	16.9546	−	36.3592i	0.626231	−	1.34296i	−0.295580	−	0.955318i	$-0.595513\pi$
$733$	16.9546	−	36.3592i	0.626231	−	1.34296i	0.921811	−	0.387639i	$-0.126709\pi$
$734$	−24.3943	−	20.4693i	−0.900411	−	0.755535i
$735$	3.98970	−	1.70777i	0.147162	−	0.0629921i
$736$	20.5300	+	7.47229i	0.756744	+	0.275432i
$737$	−0.0376137	−	0.0100786i	−0.00138552	−	0.000371249i
$738$	2.10835	+	21.2906i	0.0776093	+	0.783719i
$739$	18.7080	+	10.8011i	0.688186	+	0.397324i	0.802932	−	0.596070i	$-0.203272\pi$
$739$	18.7080	+	10.8011i	0.688186	+	0.397324i	−0.114746	+	0.993395i	$0.536605\pi$
$740$	12.6196	−	6.66634i	0.463906	−	0.245060i
$741$	13.0037	−	13.1533i	0.477702	−	0.483198i
$742$	8.37505	−	5.86427i	0.307458	−	0.215284i
$743$	22.4982	−	15.7534i	0.825380	−	0.577937i	−0.0827765	−	0.996568i	$-0.526379\pi$
$743$	22.4982	−	15.7534i	0.825380	−	0.577937i	0.908156	+	0.418631i	$0.137490\pi$
$744$	39.6601	+	10.3841i	1.45401	+	0.380701i
$745$	−19.6477	−	6.06494i	−0.719837	−	0.222202i
$746$	−32.3418	−	18.6725i	−1.18412	−	0.683650i
$747$	−29.4332	+	8.24858i	−1.07691	+	0.301800i
$748$	−0.0298192	−	0.00799004i	−0.00109030	−	0.000292145i
$749$	10.6931	+	3.89197i	0.390717	+	0.142210i
$750$	−11.0399	−	44.7312i	−0.403120	−	1.63335i
$751$	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	$0.379383\pi$
$752$	−1.81178	+	3.88537i	−0.0660687	+	0.141685i
$753$	−8.30430	−	45.5704i	−0.302625	−	1.66068i
$754$	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	0.998052	−	0.0623799i	$-0.0198691\pi$
$757$	25.7438	+	25.7438i	0.935673	+	0.935673i	−0.0623799	+	0.998052i	$0.519869\pi$
$758$	36.0923	−	51.5451i	1.31093	−	1.87220i
$759$	−0.0546096	−	0.00446315i	−0.00198220	−	0.000162002i
$760$	−67.6294	+	9.31866i	−2.45318	+	0.338023i
$761$	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	$0.145801\pi$
$762$	8.44069	+	22.7843i	0.305774	+	0.825388i
$763$	24.7311	−	11.5323i	0.895327	−	0.417498i
$764$	−14.3444	−	24.8452i	−0.518961	−	0.898867i
$765$	−11.2723	−	6.90747i	−0.407551	−	0.249740i
$766$	22.1287	−	38.3280i	0.799543	−	1.38485i
$767$	−0.120019	+	1.37182i	−0.00433362	+	0.0495336i
$768$	−40.4820	−	23.0646i	−1.46077	−	0.832272i
$769$	−3.71767	−	0.655525i	−0.134062	−	0.0236388i	0.106214	−	0.994343i	$-0.466127\pi$
$769$	−3.71767	−	0.655525i	−0.134062	−	0.0236388i	−0.240277	+	0.970704i	$0.577238\pi$
$770$	−0.0214313	−	0.0508701i	−0.000772329	−	0.00183323i
$771$	6.54790	−	1.79470i	0.235817	−	0.0646347i
$772$	−67.7562	−	5.92790i	−2.43860	−	0.213350i
$773$	−22.9201	+	6.14142i	−0.824379	+	0.220892i	−0.646260	−	0.763117i	$-0.723668\pi$
$773$	−22.9201	+	6.14142i	−0.824379	+	0.220892i	−0.178119	+	0.984009i	$0.557001\pi$
$774$	50.6206	−	9.52404i	1.81952	−	0.342334i
$775$	29.8054	−	2.97012i	1.07064	−	0.106690i
$776$	−17.0284	+	46.7851i	−0.611284	+	1.67949i
$777$	6.86666	−	2.54383i	0.246340	−	0.0912593i
$778$	78.7869	−	6.89296i	2.82465	−	0.247125i
$779$	21.7646	−	7.92167i	0.779798	−	0.283823i
$780$	−17.2722	+	9.25083i	−0.618444	+	0.331233i
$781$	0.00714349	+	0.0405128i	0.000255614	+	0.00144966i
$782$	−24.5108	+	24.5108i	−0.876503	+	0.876503i
$783$	−34.1688	−	39.3301i	−1.22109	−	1.40554i
$784$			2.32987i			0.0832097i
$785$	−1.96612	−	0.0739711i	−0.0701738	−	0.00264014i
$786$	52.4404	+	36.2740i	1.87049	+	1.29385i
$787$	−2.14886	−	1.00203i	−0.0765987	−	0.0357185i	0.383941	−	0.923357i	$-0.374566\pi$
$787$	−2.14886	−	1.00203i	−0.0765987	−	0.0357185i	−0.460540	+	0.887639i	$0.652344\pi$
$788$	−2.14916	−	24.5650i	−0.0765606	−	0.875092i
$789$	53.1944	−	4.96063i	1.89377	−	0.176603i
$790$	20.0103	−	31.8318i	0.711936	−	1.13252i
$791$	−3.95793	+	2.28511i	−0.140728	+	0.0812492i
$792$	0.0491406	+	0.0125665i	0.00174613	+	0.000446532i
$793$	−2.43513	−	9.08804i	−0.0864741	−	0.322726i
$794$	−62.2728	+	52.2531i	−2.20998	+	1.85439i
$795$	2.14074	+	6.52144i	0.0759244	+	0.231291i
$796$	−5.73703	+	32.5363i	−0.203343	+	1.15322i
$797$	11.0535	+	15.7860i	0.391534	+	0.559169i	0.965730	−	0.259549i	$-0.0835740\pi$
$797$	11.0535	+	15.7860i	0.391534	+	0.559169i	−0.574196	+	0.818718i	$0.694685\pi$
$798$	−77.2094	+	0.441593i	−2.73318	+	0.0156322i
$799$	2.61190	+	3.11275i	0.0924025	+	0.110121i
$800$	−14.5819	−	2.39029i	−0.515548	−	0.0845095i
$801$	2.95958	−	17.9852i	0.104571	−	0.635477i
$802$	6.42520	−	23.9792i	0.226882	−	0.846734i
$803$	−0.00519993	−	0.0111513i	−0.000183501	−	0.000393520i
$804$	47.0746	−	33.3648i	1.66019	−	1.17669i
$805$	−39.7703	−	4.99216i	−1.40172	−	0.175951i
$806$	−6.73692	−	18.5095i	−0.237298	−	0.651971i
$807$	−6.71581	+	18.7851i	−0.236408	+	0.661268i
$808$	−15.8644	−	11.1084i	−0.558108	−	0.390792i
$809$	−48.9190			−1.71990			−0.859951	−	0.510377i	$-0.829506\pi$
$809$	−48.9190			−1.71990			−0.859951	+	0.510377i	$0.829506\pi$
$810$	41.1090	+	24.5485i	1.44442	+	0.862547i
$811$	11.0352			0.387500			0.193750	−	0.981051i	$-0.437935\pi$
$811$	11.0352			0.387500			0.193750	+	0.981051i	$0.437935\pi$
$812$	−72.9034	−	51.0475i	−2.55841	−	1.79142i
$813$	3.95368	−	11.0591i	0.138662	−	0.387858i
$814$	0.00607130	+	0.0166808i	0.000212799	+	0.000584660i
$815$	−9.22635	−	11.8751i	−0.323185	−	0.415967i
$816$	5.79050	−	4.10411i	0.202708	−	0.143673i
$817$	−23.5661	−	50.5376i	−0.824472	−	1.76809i
$818$	−23.4459	+	87.5012i	−0.819766	+	3.05941i
$819$	−9.40677	+	3.54616i	−0.328699	+	0.123913i
$820$	−24.5055	+	1.21798i	−0.855768	+	0.0425335i
$821$	−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	$0.847015\pi$
$822$	16.1024	−	0.0920964i	0.561636	−	0.00321223i
$823$	22.1538	+	31.6390i	0.772234	+	1.10286i	0.991867	+	0.127282i	$0.0406253\pi$
$823$	22.1538	+	31.6390i	0.772234	+	1.10286i	−0.219632	+	0.975583i	$0.570486\pi$
$824$	7.95190	−	45.0975i	0.277018	−	1.57104i
$825$	0.0368539	−	0.00388551i	0.00128309	−	0.000135276i
$826$	4.40357	−	3.69503i	0.153220	−	0.128567i
$827$	−4.58916	−	17.1270i	−0.159581	−	0.595563i	−0.998669	−	0.0515685i	$-0.983578\pi$
$827$	−4.58916	−	17.1270i	−0.159581	−	0.595563i	0.839089	−	0.543994i	$-0.183089\pi$
$828$	56.7471	−	58.0604i	1.97210	−	2.01774i
$829$	20.1611	−	11.6400i	0.700224	−	0.404275i	−0.107207	−	0.994237i	$-0.534191\pi$
$829$	20.1611	−	11.6400i	0.700224	−	0.404275i	0.807431	+	0.589962i	$0.200857\pi$
$830$	−12.0513	−	52.8502i	−0.418307	−	1.83446i
$831$	−17.1333	+	1.59776i	−0.594347	+	0.0554257i
$832$	1.34779	+	15.4053i	0.0467263	+	0.534084i
$833$	2.00143	+	0.933284i	0.0693455	+	0.0323364i
$834$	18.4269	+	12.7462i	0.638073	+	0.441366i
$835$	0.608573	−	16.1756i	0.0210605	−	0.559780i
$836$		−	0.121040i		−	0.00418626i
$837$	−19.5967	+	24.1853i	−0.677359	+	0.835965i
$838$	43.1705	−	43.1705i	1.49130	−	1.49130i
$839$	−0.280939	−	1.59329i	−0.00969910	−	0.0550063i	0.979574	−	0.201084i	$-0.0644463\pi$
$839$	−0.280939	−	1.59329i	−0.00969910	−	0.0550063i	−0.989273	+	0.146077i	$0.953335\pi$
$840$	35.5166	+	10.7413i	1.22544	+	0.370610i
$841$	−67.2182	+	24.4654i	−2.31787	+	0.843635i
$842$	−56.6667	+	4.95770i	−1.95286	+	0.170854i
$843$	42.3260	−	15.6801i	1.45778	−	0.540052i
$844$	−7.95832	+	21.8653i	−0.273937	+	0.752635i
$845$	−22.0649	−	11.3177i	−0.759056	−	0.389342i
$846$	−9.58800	−	11.1647i	−0.329642	−	0.383849i
$847$	−25.7635	+	6.90330i	−0.885243	+	0.237200i
$848$	−3.67086	−	0.321159i	−0.126058	−	0.0110286i
$849$	−12.4235	+	3.40514i	−0.426373	+	0.116864i
$850$	13.2147	−	19.3654i	0.453261	−	0.664226i
$851$	12.6939	+	2.23827i	0.435141	+	0.0767270i
$852$	−52.9621	−	30.1751i	−1.81445	−	1.03378i
$853$	−1.96923	+	22.5084i	−0.0674252	+	0.770674i	0.884938	+	0.465708i	$0.154200\pi$
$853$	−1.96923	+	22.5084i	−0.0674252	+	0.770674i	−0.952363	+	0.304965i	$0.901355\pi$
$854$	−19.6379	+	34.0138i	−0.671994	+	1.16393i
$855$	14.7212	−	49.7002i	0.503453	−	1.69971i
$856$	−9.27130	−	16.0584i	−0.316886	−	0.548863i
$857$	28.0044	−	13.0587i	0.956612	−	0.446076i	0.119335	−	0.992854i	$-0.461924\pi$
$857$	28.0044	−	13.0587i	0.956612	−	0.446076i	0.837277	+	0.546778i	$0.184146\pi$
$858$	−0.00846583	−	0.0228522i	−0.000289019	−	0.000780160i
$859$	17.7378	−	21.1391i	0.605205	−	0.721256i	−0.373246	−	0.927732i	$-0.621755\pi$
$859$	17.7378	−	21.1391i	0.605205	−	0.721256i	0.978452	+	0.206477i	$0.0661997\pi$
$860$	8.06317	+	58.5178i	0.274952	+	1.99544i
$861$	−12.5469	−	1.02543i	−0.427596	−	0.0349467i
$862$	21.3804	−	30.5344i	0.728219	−	1.04000i
$863$	15.5004	+	15.5004i	0.527641	+	0.527641i	0.919868	−	0.392228i	$-0.128295\pi$
$863$	15.5004	+	15.5004i	0.527641	+	0.527641i	−0.392228	+	0.919868i	$0.628295\pi$
$864$	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
$867$	4.07277	+	22.3496i	0.138319	+	0.759032i
$868$	−22.4724	+	48.1922i	−0.762762	+	1.63575i
$869$	0.0231666	+	0.0194391i	0.000785874	+	0.000659426i
$870$	72.6334	−	57.1016i	2.46250	−	1.93593i
$871$	−11.8179	−	4.30136i	−0.400434	−	0.145746i
$872$	−42.9501	−	11.5085i	−1.45448	−	0.389725i
$873$	−27.0345	−	26.4230i	−0.914979	−	0.894282i
$874$	−117.701	−	67.9545i	−3.98129	−	2.29860i
$875$	27.0580	−	1.67207i	0.914728	−	0.0565264i
$876$	17.6368	+	4.61782i	0.595893	+	0.156022i
$877$	2.23967	−	1.56824i	0.0756283	−	0.0529555i	−0.535151	−	0.844757i	$-0.679745\pi$
$877$	2.23967	−	1.56824i	0.0756283	−	0.0529555i	0.610779	+	0.791801i	$0.290856\pi$
$878$	40.4531	−	28.3256i	1.36523	−	0.955942i
$879$	−10.1502	+	10.2670i	−0.342359	+	0.346298i
$880$	−0.00586803	+	0.0190098i	−0.000197811	+	0.000640821i
$881$	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	$0.400994\pi$
$882$	−7.28688	−	3.29699i	−0.245362	−	0.111015i
$883$	−26.2915	−	7.04478i	−0.884779	−	0.237076i	−0.212311	−	0.977202i	$-0.568099\pi$
$883$	−26.2915	−	7.04478i	−0.884779	−	0.237076i	−0.672468	+	0.740126i	$0.734766\pi$
$884$	−9.36894	−	3.41001i	−0.315111	−	0.114691i
$885$	1.51862	+	3.54781i	0.0510479	+	0.119258i
$886$	−13.7042	−	11.4992i	−0.460401	−	0.386322i
$887$	22.6131	−	48.4940i	0.759274	−	1.62827i	−0.0185820	−	0.999827i	$-0.505915\pi$
$887$	22.6131	−	48.4940i	0.759274	−	1.62827i	0.777856	−	0.628442i	$-0.216307\pi$
$888$	−11.2359	−	4.01689i	−0.377051	−	0.134798i
$889$	−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
$893$	−9.13813	+	13.0506i	−0.305796	+	0.436722i
$894$	16.2114	+	34.2527i	0.542191	+	1.14558i
$895$	29.9848	+	22.7223i	1.00228	+	0.759522i
$896$	32.2824	−	38.4726i	1.07848	−	1.28528i
$897$	−17.4441	−	2.97310i	−0.582441	−	0.0992688i
$898$	−11.4896	+	5.35770i	−0.383414	+	0.178789i
$899$	30.0326	+	52.0179i	1.00164	+	1.73489i
$900$	−30.4298	+	45.7073i	−1.01433	+	1.52358i
$901$	−1.74633	+	3.02474i	−0.0581788	+	0.100769i
$902$	0.00265972	−	0.0304007i	8.85589e−5	−	0.00101223i
$903$	0.173340	+	30.3073i	0.00576839	+	1.00856i
$904$	7.33401	+	1.29318i	0.243926	+	0.0430107i
$905$	14.6067	−	6.15373i	0.485544	−	0.204557i
$906$	−11.8399	+	45.2200i	−0.393354	+	1.50234i
$907$	48.1046	+	4.20861i	1.59729	+	0.139745i	0.850740	−	0.525587i	$-0.176154\pi$
$907$	48.1046	+	4.20861i	1.59729	+	0.139745i	0.746548	+	0.665332i	$0.231710\pi$
$908$	−23.0521	+	6.17680i	−0.765011	+	0.204984i
$909$	12.6498	−	7.49759i	0.419568	−	0.248679i
$910$	−5.46326	−	16.9699i	−0.181105	−	0.562546i
$911$	−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	$0.861801\pi$
$912$	21.4192	+	17.7651i	0.709262	+	0.588262i
$913$	0.0434342	−	0.00380000i	0.00143746	−	0.000125762i
$914$	−52.5694	+	19.1337i	−1.73884	+	0.632886i
$915$	−18.0407	−	19.2295i	−0.596406	−	0.635706i
$916$	−2.75452	−	15.6217i	−0.0910121	−	0.516155i
$917$	−26.5297	+	26.5297i	−0.876087	+	0.876087i
$918$	4.64186	+	23.9180i	0.153204	+	0.789412i
$919$			29.7860i			0.982549i	0.871005	+	0.491274i	$0.163469\pi$
$919$			29.7860i			0.982549i	−0.871005	+	0.491274i	$0.836531\pi$
$920$	44.4150	+	47.8877i	1.46432	+	1.57881i
$921$	1.71972	−	21.0419i	0.0566667	−	0.693354i
$922$	34.7487	+	16.2036i	1.14439	+	0.533637i
$923$	1.15795	+	13.2354i	0.0381143	+	0.435648i
$924$	−0.0274616	+	0.0597819i	−0.000903421	+	0.00196668i
$925$	−8.71728	+	0.105102i	−0.286622	+	0.00345572i
$926$	−30.7563	+	17.7572i	−1.01072	+	0.583537i
$927$	28.7079	+	19.6160i	0.942892	+	0.644273i
$928$	−7.66920	−	28.6219i	−0.251754	−	0.939559i
$929$	−6.65219	+	5.58185i	−0.218251	+	0.183135i	−0.745358	−	0.666665i	$-0.767721\pi$
$929$	−6.65219	+	5.58185i	−0.218251	+	0.183135i	0.527106	+	0.849799i	$0.323277\pi$
$930$	−41.1340	−	36.8129i	−1.34884	−	1.20714i
$931$	−1.50353	+	8.52694i	−0.0492762	+	0.279459i
$932$	54.9592	+	78.4899i	1.80025	+	2.57102i
$933$	−17.3580	+	30.4660i	−0.568275	+	0.997412i
$934$	−9.61335	−	11.4567i	−0.314559	−	0.374876i
$935$	0.0139795	+	0.0126556i	0.000457178	+	0.000413884i
$936$	15.4564	+	5.42628i	0.505210	+	0.177364i
$937$	−8.64443	+	32.2615i	−0.282401	+	1.05394i	0.668316	+	0.743877i	$0.267015\pi$
$937$	−8.64443	+	32.2615i	−0.282401	+	1.05394i	−0.950717	+	0.310059i	$0.899651\pi$
$938$	22.1871	+	47.5804i	0.724434	+	1.55355i
$939$	11.4009	+	5.23713i	0.372053	+	0.170907i
$940$	13.3274	−	10.3547i	0.434692	−	0.337733i
$941$	−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	$0.928345\pi$
$942$	2.34659	+	2.76430i	0.0764561	+	0.0900656i
$943$	−18.1517	−	12.7099i	−0.591100	−	0.413893i
$944$	−2.07182			−0.0674319
$945$	−18.5468	+	21.2071i	−0.603328	+	0.689868i
$946$	−0.0734704			−0.00238873
$947$	−16.9682	−	11.8813i	−0.551393	−	0.386089i	0.264418	−	0.964408i	$-0.414820\pi$
$947$	−16.9682	−	11.8813i	−0.551393	−	0.386089i	−0.815811	+	0.578319i	$0.803709\pi$
$948$	−44.0844	+	8.03350i	−1.43179	+	0.260916i
$949$	−1.35910	−	3.73411i	−0.0441184	−	0.121214i
$950$	86.7509	+	30.3954i	2.81457	+	0.986158i
$951$	−0.789285	−	8.46376i	−0.0255943	−	0.274456i
$952$	7.97949	+	17.1121i	0.258617	+	0.554606i
$953$	8.62530	−	32.1900i	0.279401	−	1.04274i	−0.673434	−	0.739248i	$-0.735181\pi$
$953$	8.62530	−	32.1900i	0.279401	−	1.04274i	0.952835	−	0.303490i	$-0.0981520\pi$
$954$	6.19906	−	11.0265i	0.200702	−	0.356995i
$955$	0.869909	+	17.5024i	0.0281496	+	0.566366i
$956$	−43.1237	−	51.3928i	−1.39472	−	1.66216i
$957$	0.0375241	+	0.0641436i	0.00121298	+	0.00207347i
$958$	9.32860	+	13.3226i	0.301394	+	0.430435i
$959$	−1.64529	+	9.33089i	−0.0531291	+	0.301310i
$960$	23.7132	+	36.2747i	0.765339	+	1.17076i
$961$	3.74384	−	3.14145i	0.120769	−	0.101337i
$962$	1.48381	+	5.53765i	0.0478400	+	0.178541i
$963$	14.0104	−	1.38741i	0.451480	−	0.0447087i
$964$	20.0626	−	11.5831i	0.646173	−	0.373068i
$965$	35.1733	+	22.1109i	1.13227	+	0.711776i
$966$	42.7151	+	60.2669i	1.37434	+	1.93906i
$967$	−1.31002	−	14.9736i	−0.0421275	−	0.481519i	−0.987727	−	0.156188i	$-0.950080\pi$
$967$	−1.31002	−	14.9736i	−0.0421275	−	0.481519i	0.945600	−	0.325332i	$-0.105476\pi$
$968$	39.3903	+	18.3680i	1.26605	+	0.590369i
$969$	23.8408	−	11.2836i	0.765876	−	0.362481i
$970$	49.1516	−	45.5872i	1.57816	−	1.46372i
$971$			29.8876i			0.959139i	0.877504	+	0.479570i	$0.159207\pi$
$971$			29.8876i			0.959139i	−0.877504	+	0.479570i	$0.840793\pi$
$972$	−11.5119	−	55.8912i	−0.369245	−	1.79271i
$973$	−9.32220	+	9.32220i	−0.298856	+	0.298856i
$974$	−6.85958	−	38.9026i	−0.219795	−	1.24652i
$975$	11.9665	−	0.212733i	0.383235	−	0.00681290i
$976$	13.3018	−	4.84146i	0.425780	−	0.154971i
$977$	−38.8342	+	3.39755i	−1.24242	+	0.108697i	−0.689343	−	0.724435i	$-0.742101\pi$
$977$	−38.8342	+	3.39755i	−1.24242	+	0.108697i	−0.553074	+	0.833132i	$0.686545\pi$
$978$	−4.65634	+	27.3202i	−0.148893	+	0.873604i
$979$	−0.00889204	+	0.0244307i	−0.000284191	+	0.000780808i
$980$	4.18615	−	8.16126i	0.133722	−	0.260702i
$981$	21.4042	−	26.1093i	0.683383	−	0.833606i
$982$	38.2380	−	10.2458i	1.22022	−	0.326958i
$983$	−27.8303	−	2.43483i	−0.887648	−	0.0776592i	−0.365796	−	0.930695i	$-0.619203\pi$
$983$	−27.8303	−	2.43483i	−0.887648	−	0.0776592i	−0.521852	+	0.853036i	$0.674759\pi$
$984$	14.5878	+	14.4218i	0.465041	+	0.459751i
$985$	−5.68015	+	13.9504i	−0.180985	+	0.444496i
$986$	46.2994	+	8.16383i	1.47447	+	0.259989i
$987$	7.47427	−	4.37246i	0.237909	−	0.139177i
$988$	3.40704	−	38.9426i	0.108392	−	1.23893i
$989$	−26.6744	+	46.2015i	−0.848198	+	1.46912i
$990$	−0.0511511	−	0.0452535i	−0.00162569	−	0.00143825i
$991$	−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	$-0.374163\pi$
$992$	−16.0453	+	7.48204i	−0.509438	+	0.237555i
$993$	5.49088	−	6.62030i	0.174248	−	0.210089i
$994$	35.6498	−	42.4858i	1.13074	−	1.34757i
$995$	12.1886	−	16.0843i	0.386404	−	0.509907i
$996$	−36.7519	+	53.1313i	−1.16453	+	1.68353i
$997$	−4.38139	+	6.25727i	−0.138760	+	0.198170i	−0.882517	−	0.470280i	$-0.844153\pi$
$997$	−4.38139	+	6.25727i	−0.138760	+	0.198170i	0.743757	+	0.668450i	$0.233042\pi$
$998$	−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.122.15	yes	192
3.2	odd	2		405.2.r.a.152.2		192
5.2	odd	4		675.2.ba.b.68.2		192
5.3	odd	4	inner	135.2.q.a.68.15	yes	192
5.4	even	2		675.2.ba.b.257.2		192
15.8	even	4		405.2.r.a.233.2		192
27.2	odd	18	inner	135.2.q.a.2.15	✓	192
27.25	even	9		405.2.r.a.332.2		192
135.2	even	36		675.2.ba.b.218.2		192
135.29	odd	18		675.2.ba.b.407.2		192
135.83	even	36	inner	135.2.q.a.83.15	yes	192
135.133	odd	36		405.2.r.a.8.2		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.15	✓	192	27.2	odd	18	inner
135.2.q.a.68.15	yes	192	5.3	odd	4	inner
135.2.q.a.83.15	yes	192	135.83	even	36	inner
135.2.q.a.122.15	yes	192	1.1	even	1	trivial
405.2.r.a.8.2		192	135.133	odd	36
405.2.r.a.152.2		192	3.2	odd	2
405.2.r.a.233.2		192	15.8	even	4
405.2.r.a.332.2		192	27.25	even	9
675.2.ba.b.68.2		192	5.2	odd	4
675.2.ba.b.218.2		192	135.2	even	36
675.2.ba.b.257.2		192	5.4	even	2
675.2.ba.b.407.2		192	135.29	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.94894 + 1.36466i) q^{2} +(-0.583078 + 1.63096i) q^{3} +(1.25203 + 3.43992i) q^{4} +(0.278496 - 2.21866i) q^{5} +(-3.36209 + 2.38294i) q^{6} +(-1.02475 - 2.19758i) q^{7} +(-1.02263 + 3.81650i) q^{8} +(-2.32004 - 1.90195i) q^{9} +O(q^{10})\)	\(q+(1.94894 + 1.36466i) q^{2} +(-0.583078 + 1.63096i) q^{3} +(1.25203 + 3.43992i) q^{4} +(0.278496 - 2.21866i) q^{5} +(-3.36209 + 2.38294i) q^{6} +(-1.02475 - 2.19758i) q^{7} +(-1.02263 + 3.81650i) q^{8} +(-2.32004 - 1.90195i) q^{9} +(3.57049 - 3.94398i) q^{10} +(0.00275056 + 0.00327799i) q^{11} +(-6.34039 + 0.0362633i) q^{12} +(0.792678 + 1.13206i) q^{13} +(1.00178 - 5.68139i) q^{14} +(3.45615 + 1.74787i) q^{15} +(-1.59279 + 1.33651i) q^{16} +(0.510074 + 1.90362i) q^{17} +(-1.92610 - 6.87287i) q^{18} +(-6.69182 + 3.86352i) q^{19} +(7.98068 - 1.81982i) q^{20} +(4.18166 - 0.389960i) q^{21} +(0.000887327 + 0.0101422i) q^{22} +(6.70002 + 3.12427i) q^{23} +(-5.62827 - 3.89318i) q^{24} +(-4.84488 - 1.23578i) q^{25} +3.28806i q^{26} +(4.45476 - 2.67490i) q^{27} +(6.27648 - 6.27648i) q^{28} +(-1.74110 - 9.87424i) q^{29} +(4.35059 + 8.12297i) q^{30} +(-5.62932 + 2.04890i) q^{31} +(2.94406 - 0.257571i) q^{32} +(-0.00695004 + 0.00257472i) q^{33} +(-1.60370 + 4.40613i) q^{34} +(-5.16106 + 1.66155i) q^{35} +(3.63779 - 10.3620i) q^{36} +(1.68417 - 0.451272i) q^{37} +(-18.3144 - 1.60230i) q^{38} +(-2.30854 + 0.632743i) q^{39} +(8.18270 + 3.33174i) q^{40} +(-2.95191 - 0.520501i) q^{41} +(8.68198 + 4.94656i) q^{42} +(-0.628957 + 7.18901i) q^{43} +(-0.00783223 + 0.0135658i) q^{44} +(-4.86590 + 4.61769i) q^{45} +(8.79437 + 15.2323i) q^{46} +(1.86865 - 0.871367i) q^{47} +(-1.25107 - 3.37706i) q^{48} +(0.720271 - 0.858385i) q^{49} +(-7.75597 - 9.02009i) q^{50} +(-3.40214 - 0.278051i) q^{51} +(-2.90174 + 4.14412i) 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} +(-2.39939 - 13.1668i) q^{57} +(10.0817 - 21.6203i) q^{58} +(0.763311 + 0.640494i) q^{59} +(-1.68532 + 14.0772i) q^{60} +(-6.39745 - 2.32848i) q^{61} +(-13.7673 - 3.68893i) q^{62} +(-1.80223 + 7.04749i) q^{63} +(9.69063 + 5.59489i) q^{64} +(2.73241 - 1.44340i) q^{65} +(-0.0170589 - 0.00446650i) q^{66} +(-7.45442 + 5.21964i) q^{67} +(-5.90968 + 4.13800i) q^{68} +(-9.00219 + 9.10575i) q^{69} +(-12.3261 - 3.80486i) q^{70} +(8.32564 + 4.80681i) q^{71} +(9.63132 - 6.90944i) q^{72} +(-2.77741 - 0.744204i) q^{73} +(3.89819 + 1.41882i) q^{74} +(4.84044 - 7.18124i) q^{75} +(-21.6685 - 18.1821i) q^{76} +(0.00438501 - 0.00940367i) q^{77} +(-5.36268 - 1.91719i) 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} +(5.84421 - 8.34640i) q^{83} +(6.57699 + 13.8963i) q^{84} +(4.36554 - 0.601528i) q^{85} +(-11.0364 + 13.1527i) q^{86} +(17.1197 + 2.91780i) q^{87} +(-0.0153232 + 0.00714534i) q^{88} +(3.03785 + 5.26171i) q^{89} +(-15.7849 + 2.35929i) q^{90} +(1.67550 - 2.90205i) q^{91} +(-2.35862 + 26.9592i) q^{92} +(-0.0593438 - 10.3758i) q^{93} +(4.83102 + 0.851839i) q^{94} +(6.70819 + 15.9228i) q^{95} +(-1.29653 + 4.95181i) q^{96} +(12.5529 + 1.09824i) q^{97} +(2.57517 - 0.690016i) 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

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