LMFDB - Embedded newform 729.2.c.e.487.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.5
Root			$0.500000 - 2.22827i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.e.244.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05831 - 1.83305i) q^{2} +(-1.24005 - 2.14782i) q^{4} +(1.34155 + 2.32363i) q^{5} +(-0.486166 + 0.842065i) q^{7} -1.01617 q^{8} +O(q^{10})$	\(q+(1.05831 - 1.83305i) q^{2} +(-1.24005 - 2.14782i) q^{4} +(1.34155 + 2.32363i) q^{5} +(-0.486166 + 0.842065i) q^{7} -1.01617 q^{8} +5.67911 q^{10} +(0.158451 - 0.274445i) q^{11} +(0.757015 + 1.31119i) q^{13} +(1.02903 + 1.78233i) q^{14} +(1.40466 - 2.43295i) q^{16} +1.17468 q^{17} +6.22080 q^{19} +(3.32716 - 5.76282i) q^{20} +(-0.335381 - 0.580897i) q^{22} +(-1.08137 - 1.87299i) q^{23} +(-1.09951 + 1.90440i) q^{25} +3.20463 q^{26} +2.41147 q^{28} +(2.20246 - 3.81476i) q^{29} +(4.33661 + 7.51124i) q^{31} +(-3.98932 - 6.90970i) q^{32} +(1.24318 - 2.15325i) q^{34} -2.60886 q^{35} -4.46665 q^{37} +(6.58355 - 11.4030i) q^{38} +(-1.36325 - 2.36121i) q^{40} +(-2.92259 - 5.06208i) q^{41} +(-2.79550 + 4.84194i) q^{43} -0.785946 q^{44} -4.57771 q^{46} +(1.23803 - 2.14434i) q^{47} +(3.02728 + 5.24341i) q^{49} +(2.32724 + 4.03090i) q^{50} +(1.87747 - 3.25187i) q^{52} -10.8920 q^{53} +0.850279 q^{55} +(0.494029 - 0.855683i) q^{56} +(-4.66177 - 8.07442i) q^{58} +(0.862105 + 1.49321i) q^{59} +(-0.507389 + 0.878823i) q^{61} +18.3580 q^{62} -11.2691 q^{64} +(-2.03115 + 3.51805i) q^{65} +(-0.428276 - 0.741795i) q^{67} +(-1.45666 - 2.52301i) q^{68} +(-2.76099 + 4.78218i) q^{70} -9.59577 q^{71} -15.2418 q^{73} +(-4.72710 + 8.18758i) q^{74} +(-7.71408 - 13.3612i) q^{76} +(0.154067 + 0.266852i) q^{77} +(5.60688 - 9.71141i) q^{79} +7.53771 q^{80} -12.3721 q^{82} +(-2.34247 + 4.05727i) q^{83} +(1.57590 + 2.72953i) q^{85} +(5.91701 + 10.2486i) q^{86} +(-0.161014 + 0.278884i) q^{88} -15.4995 q^{89} -1.47214 q^{91} +(-2.68190 + 4.64519i) q^{92} +(-2.62045 - 4.53876i) q^{94} +(8.34551 + 14.4549i) q^{95} +(2.77474 - 4.80600i) q^{97} +12.8152 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8 + 6 * q^10 + 12 * q^11 + 6 * q^14 + 3 * q^16 - 18 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 15 * q^23 + 6 * q^25 - 30 * q^26 - 12 * q^28 + 12 * q^29 - 24 * q^35 + 6 * q^37 - 3 * q^38 - 6 * q^40 + 15 * q^41 - 6 * q^44 + 6 * q^46 + 21 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^52 - 18 * q^53 - 12 * q^55 - 6 * q^56 + 12 * q^58 + 24 * q^59 + 9 * q^61 + 24 * q^62 - 24 * q^64 - 6 * q^65 + 9 * q^67 - 9 * q^68 - 15 * q^70 - 54 * q^71 - 12 * q^73 - 12 * q^74 - 6 * q^76 - 12 * q^77 + 42 * q^80 - 12 * q^82 + 12 * q^83 - 21 * q^86 - 12 * q^88 - 18 * q^89 - 12 * q^91 + 6 * q^92 - 6 * q^94 + 12 * q^95 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.05831	−	1.83305i	0.748339	−	1.29616i	−0.200279	−	0.979739i	$-0.564185\pi$
$2$	1.05831	−	1.83305i	0.748339	−	1.29616i	0.948618	−	0.316423i	$-0.102482\pi$
$3$		0			0
$3$		0			0
$4$	−1.24005	−	2.14782i	−0.620023	−	1.07391i
$5$	1.34155	+	2.32363i	0.599959	+	1.03916i	0.992826	+	0.119564i	$0.0381498\pi$
$5$	1.34155	+	2.32363i	0.599959	+	1.03916i	−0.392868	+	0.919595i	$0.628517\pi$
$6$		0			0
$7$	−0.486166	+	0.842065i	−0.183754	+	0.318271i	−0.943156	−	0.332351i	$-0.892158\pi$
$7$	−0.486166	+	0.842065i	−0.183754	+	0.318271i	0.759402	+	0.650621i	$0.225492\pi$
$8$	−1.01617			−0.359271
$9$		0			0
$10$	5.67911			1.79589
$11$	0.158451	−	0.274445i	0.0477748	−	0.0827484i	−0.841149	−	0.540803i	$-0.818120\pi$
$11$	0.158451	−	0.274445i	0.0477748	−	0.0827484i	0.888924	+	0.458055i	$0.151454\pi$
$12$		0			0
$13$	0.757015	+	1.31119i	0.209958	+	0.363658i	0.951701	−	0.307026i	$-0.0993339\pi$
$13$	0.757015	+	1.31119i	0.209958	+	0.363658i	−0.741743	+	0.670684i	$0.766001\pi$
$14$	1.02903	+	1.78233i	0.275020	+	0.476349i
$15$		0			0
$16$	1.40466	−	2.43295i	0.351166	−	0.608238i
$17$	1.17468			0.284903			0.142451	−	0.989802i	$-0.454502\pi$
$17$	1.17468			0.284903			0.142451	+	0.989802i	$0.454502\pi$
$18$		0			0
$19$	6.22080			1.42715			0.713575	−	0.700579i	$-0.247075\pi$
$19$	6.22080			1.42715			0.713575	+	0.700579i	$0.247075\pi$
$20$	3.32716	−	5.76282i	0.743977	−	1.28861i
$21$		0			0
$22$	−0.335381	−	0.580897i	−0.0715035	−	0.123848i
$23$	−1.08137	−	1.87299i	−0.225481	−	0.390545i	0.730982	−	0.682396i	$-0.239062\pi$
$23$	−1.08137	−	1.87299i	−0.225481	−	0.390545i	−0.956464	+	0.291851i	$0.905729\pi$
$24$		0			0
$25$	−1.09951	+	1.90440i	−0.219901	+	0.380880i
$26$	3.20463			0.628480
$27$		0			0
$28$	2.41147			0.455726
$29$	2.20246	−	3.81476i	0.408986	−	0.708384i	−0.585791	−	0.810462i	$-0.699216\pi$
$29$	2.20246	−	3.81476i	0.408986	−	0.708384i	0.994776	+	0.102078i	$0.0325493\pi$
$30$		0			0
$31$	4.33661	+	7.51124i	0.778879	+	1.34906i	0.932588	+	0.360942i	$0.117545\pi$
$31$	4.33661	+	7.51124i	0.778879	+	1.34906i	−0.153710	+	0.988116i	$0.549122\pi$
$32$	−3.98932	−	6.90970i	−0.705218	−	1.22147i
$33$		0			0
$34$	1.24318	−	2.15325i	0.213204	−	0.369280i
$35$	−2.60886			−0.440978
$36$		0			0
$37$	−4.46665			−0.734312			−0.367156	−	0.930159i	$-0.619668\pi$
$37$	−4.46665			−0.734312			−0.367156	+	0.930159i	$0.619668\pi$
$38$	6.58355	−	11.4030i	1.06799	−	1.84982i
$39$		0			0
$40$	−1.36325	−	2.36121i	−0.215548	−	0.373340i
$41$	−2.92259	−	5.06208i	−0.456432	−	0.790564i	0.542337	−	0.840161i	$-0.317540\pi$
$41$	−2.92259	−	5.06208i	−0.456432	−	0.790564i	−0.998769	+	0.0495972i	$0.984206\pi$
$42$		0			0
$43$	−2.79550	+	4.84194i	−0.426309	+	0.738389i	−0.996542	−	0.0830943i	$-0.973520\pi$
$43$	−2.79550	+	4.84194i	−0.426309	+	0.738389i	0.570233	+	0.821483i	$0.306853\pi$
$44$	−0.785946			−0.118486
$45$		0			0
$46$	−4.57771			−0.674946
$47$	1.23803	−	2.14434i	0.180586	−	0.312784i	−0.761494	−	0.648172i	$-0.775534\pi$
$47$	1.23803	−	2.14434i	0.180586	−	0.312784i	0.942080	+	0.335388i	$0.108867\pi$
$48$		0			0
$49$	3.02728	+	5.24341i	0.432469	+	0.749059i
$50$	2.32724	+	4.03090i	0.329122	+	0.570055i
$51$		0			0
$52$	1.87747	−	3.25187i	0.260358	−	0.450953i
$53$	−10.8920			−1.49613			−0.748063	−	0.663628i	$-0.769016\pi$
$53$	−10.8920			−1.49613			−0.748063	+	0.663628i	$0.769016\pi$
$54$		0			0
$55$	0.850279			0.114652
$56$	0.494029	−	0.855683i	0.0660174	−	0.114345i
$57$		0			0
$58$	−4.66177	−	8.07442i	−0.612120	−	1.06022i
$59$	0.862105	+	1.49321i	0.112237	+	0.194399i	0.916672	−	0.399641i	$-0.130865\pi$
$59$	0.862105	+	1.49321i	0.112237	+	0.194399i	−0.804435	+	0.594040i	$0.797532\pi$
$60$		0			0
$61$	−0.507389	+	0.878823i	−0.0649645	+	0.112522i	−0.896678	−	0.442683i	$-0.854027\pi$
$61$	−0.507389	+	0.878823i	−0.0649645	+	0.112522i	0.831714	+	0.555205i	$0.187360\pi$
$62$	18.3580			2.33146
$63$		0			0
$64$	−11.2691			−1.40864
$65$	−2.03115	+	3.51805i	−0.251933	+	0.436360i
$66$		0			0
$67$	−0.428276	−	0.741795i	−0.0523222	−	0.0906247i	0.838678	−	0.544627i	$-0.183329\pi$
$67$	−0.428276	−	0.741795i	−0.0523222	−	0.0906247i	−0.891000	+	0.454003i	$0.849996\pi$
$68$	−1.45666	−	2.52301i	−0.176646	−	0.305960i
$69$		0			0
$70$	−2.76099	+	4.78218i	−0.330001	+	0.571579i
$71$	−9.59577			−1.13881			−0.569404	−	0.822058i	$-0.692826\pi$
$71$	−9.59577			−1.13881			−0.569404	+	0.822058i	$0.692826\pi$
$72$		0			0
$73$	−15.2418			−1.78392			−0.891960	−	0.452113i	$-0.850670\pi$
$73$	−15.2418			−1.78392			−0.891960	+	0.452113i	$0.850670\pi$
$74$	−4.72710	+	8.18758i	−0.549514	+	0.951787i
$75$		0			0
$76$	−7.71408	−	13.3612i	−0.884866	−	1.53263i
$77$	0.154067	+	0.266852i	0.0175576	+	0.0304106i
$78$		0			0
$79$	5.60688	−	9.71141i	0.630824	−	1.09262i	−0.356560	−	0.934272i	$-0.616050\pi$
$79$	5.60688	−	9.71141i	0.630824	−	1.09262i	0.987384	−	0.158346i	$-0.0506162\pi$
$80$	7.53771			0.842741
$81$		0			0
$82$	−12.3721			−1.36626
$83$	−2.34247	+	4.05727i	−0.257119	+	0.445343i	−0.965469	−	0.260518i	$-0.916107\pi$
$83$	−2.34247	+	4.05727i	−0.257119	+	0.445343i	0.708350	+	0.705861i	$0.249440\pi$
$84$		0			0
$85$	1.57590	+	2.72953i	0.170930	+	0.296059i
$86$	5.91701	+	10.2486i	0.638048	+	1.10513i
$87$		0			0
$88$	−0.161014	+	0.278884i	−0.0171641	+	0.0297291i
$89$	−15.4995			−1.64295			−0.821473	−	0.570248i	$-0.806847\pi$
$89$	−15.4995			−1.64295			−0.821473	+	0.570248i	$0.806847\pi$
$90$		0			0
$91$	−1.47214			−0.154322
$92$	−2.68190	+	4.64519i	−0.279607	+	0.484294i
$93$		0			0
$94$	−2.62045	−	4.53876i	−0.270279	−	0.468137i
$95$	8.34551	+	14.4549i	0.856231	+	1.48304i
$96$		0			0
$97$	2.77474	−	4.80600i	0.281732	−	0.487975i	−0.690079	−	0.723734i	$-0.742424\pi$
$97$	2.77474	−	4.80600i	0.281732	−	0.487975i	0.971812	+	0.235759i	$0.0757576\pi$
$98$	12.8152			1.29453
$99$		0			0
$100$	5.45376			0.545376
$101$	5.06952	−	8.78067i	0.504436	−	0.873709i	−0.495550	−	0.868579i	$-0.665034\pi$
$101$	5.06952	−	8.78067i	0.504436	−	0.873709i	0.999987	−	0.00513025i	$-0.00163302\pi$
$102$		0			0
$103$	4.92665	+	8.53320i	0.485437	+	0.840801i	0.999860	−	0.0167353i	$-0.00532726\pi$
$103$	4.92665	+	8.53320i	0.485437	+	0.840801i	−0.514423	+	0.857536i	$0.671994\pi$
$104$	−0.769258	−	1.33239i	−0.0754320	−	0.130652i
$105$		0			0
$106$	−11.5271	+	19.9655i	−1.11961	+	1.93922i
$107$	5.17080			0.499880			0.249940	−	0.968261i	$-0.419589\pi$
$107$	5.17080			0.499880			0.249940	+	0.968261i	$0.419589\pi$
$108$		0			0
$109$	−7.31065			−0.700234			−0.350117	−	0.936706i	$-0.613858\pi$
$109$	−7.31065			−0.700234			−0.350117	+	0.936706i	$0.613858\pi$
$110$	0.899860	−	1.55860i	0.0857983	−	0.148607i
$111$		0			0
$112$	1.36580	+	2.36564i	0.129056	+	0.223532i
$113$	−5.18782	−	8.98557i	−0.488029	−	0.845291i	0.511876	−	0.859059i	$-0.328951\pi$
$113$	−5.18782	−	8.98557i	−0.488029	−	0.845291i	−0.999905	+	0.0137681i	$0.995617\pi$
$114$		0			0
$115$	2.90142	−	5.02541i	0.270559	−	0.468622i
$116$	−10.9246			−1.01432
$117$		0			0
$118$	3.64950			0.335964
$119$	−0.571092	+	0.989160i	−0.0523519	+	0.0906762i
$120$		0			0
$121$	5.44979	+	9.43931i	0.495435	+	0.858119i
$122$	1.07395	+	1.86014i	0.0972310	+	0.168409i
$123$		0			0
$124$	10.7552	−	18.6286i	0.965845	−	1.67289i
$125$	7.51532			0.672191
$126$		0			0
$127$	5.22743			0.463860			0.231930	−	0.972733i	$-0.425496\pi$
$127$	5.22743			0.463860			0.231930	+	0.972733i	$0.425496\pi$
$128$	−3.94758	+	6.83741i	−0.348920	+	0.604348i
$129$		0			0
$130$	4.29917	+	7.44638i	0.377062	+	0.653091i
$131$	3.61715	+	6.26509i	0.316032	+	0.547383i	0.979656	−	0.200683i	$-0.0643160\pi$
$131$	3.61715	+	6.26509i	0.316032	+	0.547383i	−0.663624	+	0.748066i	$0.730983\pi$
$132$		0			0
$133$	−3.02435	+	5.23832i	−0.262244	+	0.454220i
$134$	−1.81300			−0.156619
$135$		0			0
$136$	−1.19368			−0.102357
$137$	−5.62466	+	9.74220i	−0.480547	+	0.832332i	−0.999751	−	0.0223185i	$-0.992895\pi$
$137$	−5.62466	+	9.74220i	−0.480547	+	0.832332i	0.519204	+	0.854650i	$0.326229\pi$
$138$		0			0
$139$	−4.69008	−	8.12346i	−0.397808	−	0.689023i	0.595648	−	0.803246i	$-0.296895\pi$
$139$	−4.69008	−	8.12346i	−0.397808	−	0.689023i	−0.993455	+	0.114223i	$0.963562\pi$
$140$	3.23511	+	5.60338i	0.273417	+	0.473572i
$141$		0			0
$142$	−10.1553	+	17.5895i	−0.852215	+	1.47608i
$143$	0.479799			0.0401228
$144$		0			0
$145$	11.8188			0.981498
$146$	−16.1306	+	27.9390i	−1.33498	+	2.31225i
$147$		0			0
$148$	5.53885	+	9.59356i	0.455290	+	0.788586i
$149$	−9.52562	−	16.4989i	−0.780369	−	1.35164i	−0.931727	−	0.363160i	$-0.881698\pi$
$149$	−9.52562	−	16.4989i	−0.780369	−	1.35164i	0.151357	−	0.988479i	$-0.451636\pi$
$150$		0			0
$151$	−2.00700	+	3.47623i	−0.163327	+	0.282891i	−0.936060	−	0.351840i	$-0.885556\pi$
$151$	−2.00700	+	3.47623i	−0.163327	+	0.282891i	0.772733	+	0.634732i	$0.218889\pi$
$152$	−6.32141			−0.512734
$153$		0			0
$154$	0.652204			0.0525561
$155$	−11.6356	+	20.1534i	−0.934591	+	1.61876i
$156$		0			0
$157$	−3.63796	−	6.30113i	−0.290341	−	0.502885i	0.683550	−	0.729904i	$-0.260435\pi$
$157$	−3.63796	−	6.30113i	−0.290341	−	0.502885i	−0.973890	+	0.227019i	$0.927102\pi$
$158$	−11.8677	−	20.5554i	−0.944140	−	1.63530i
$159$		0			0
$160$	10.7037	−	18.5394i	0.846204	−	1.46567i
$161$	2.10290			0.165732
$162$		0			0
$163$	12.4492			0.975094			0.487547	−	0.873097i	$-0.337892\pi$
$163$	12.4492			0.975094			0.487547	+	0.873097i	$0.337892\pi$
$164$	−7.24830	+	12.5544i	−0.565997	+	0.980335i
$165$		0			0
$166$	4.95811	+	8.58771i	0.384824	+	0.666535i
$167$	1.16594	+	2.01947i	0.0902234	+	0.156272i	0.907605	−	0.419825i	$-0.137909\pi$
$167$	1.16594	+	2.01947i	0.0902234	+	0.156272i	−0.817382	+	0.576097i	$0.804575\pi$
$168$		0			0
$169$	5.35386	−	9.27315i	0.411835	−	0.713319i
$170$	6.67116			0.511654
$171$		0			0
$172$	13.8662			1.05729
$173$	1.79113	−	3.10234i	0.136177	−	0.235866i	−0.789869	−	0.613275i	$-0.789852\pi$
$173$	1.79113	−	3.10234i	0.136177	−	0.235866i	0.926047	+	0.377409i	$0.123185\pi$
$174$		0			0
$175$	−1.06909	−	1.85171i	−0.0808154	−	0.139976i
$176$	−0.445141	−	0.771007i	−0.0335538	−	0.0581168i
$177$		0			0
$178$	−16.4033	+	28.4114i	−1.22948	+	2.12952i
$179$	−19.9957			−1.49455			−0.747275	−	0.664515i	$-0.768638\pi$
$179$	−19.9957			−1.49455			−0.747275	+	0.664515i	$0.768638\pi$
$180$		0			0
$181$	9.73232			0.723398			0.361699	−	0.932295i	$-0.382197\pi$
$181$	9.73232			0.723398			0.361699	+	0.932295i	$0.382197\pi$
$182$	−1.55798	+	2.69851i	−0.115485	+	0.200027i
$183$		0			0
$184$	1.09886	+	1.90328i	0.0810090	+	0.140312i
$185$	−5.99222	−	10.3788i	−0.440557	−	0.763067i
$186$		0			0
$187$	0.186130	−	0.322387i	0.0136112	−	0.0235752i
$188$	−6.14088			−0.447869
$189$		0			0
$190$	35.3286			2.56301
$191$	8.87826	−	15.3776i	0.642409	−	1.11268i	−0.342485	−	0.939523i	$-0.611269\pi$
$191$	8.87826	−	15.3776i	0.642409	−	1.11268i	0.984894	−	0.173161i	$-0.0553981\pi$
$192$		0			0
$193$	−5.29217	−	9.16630i	−0.380939	−	0.659805i	0.610258	−	0.792203i	$-0.291066\pi$
$193$	−5.29217	−	9.16630i	−0.380939	−	0.659805i	−0.991197	+	0.132398i	$0.957732\pi$
$194$	−5.87308	−	10.1725i	−0.421663	−	0.730341i
$195$		0			0
$196$	7.50794	−	13.0041i	0.536282	−	0.928867i
$197$	14.1589			1.00878			0.504390	−	0.863476i	$-0.331718\pi$
$197$	14.1589			1.00878			0.504390	+	0.863476i	$0.331718\pi$
$198$		0			0
$199$	7.54019			0.534510			0.267255	−	0.963626i	$-0.413883\pi$
$199$	7.54019			0.534510			0.267255	+	0.963626i	$0.413883\pi$
$200$	1.11729	−	1.93520i	0.0790043	−	0.136839i
$201$		0			0
$202$	−10.7303	−	18.5854i	−0.754979	−	1.30766i
$203$	2.14152	+	3.70922i	0.150305	+	0.260336i
$204$		0			0
$205$	7.84160	−	13.5821i	0.547681	−	0.948612i
$206$	20.8557			1.45309
$207$		0			0
$208$	4.25341			0.294921
$209$	0.985693	−	1.70727i	0.0681818	−	0.118094i
$210$		0			0
$211$	−2.60682	−	4.51514i	−0.179461	−	0.310835i	0.762235	−	0.647300i	$-0.224102\pi$
$211$	−2.60682	−	4.51514i	−0.179461	−	0.310835i	−0.941696	+	0.336465i	$0.890769\pi$
$212$	13.5065	+	23.3940i	0.927632	+	1.60671i
$213$		0			0
$214$	5.47232	−	9.47833i	0.374080	−	0.647925i
$215$	−15.0012			−1.02307
$216$		0			0
$217$	−8.43326			−0.572487
$218$	−7.73695	+	13.4008i	−0.524012	+	0.907616i
$219$		0			0
$220$	−1.05439	−	1.82625i	−0.0710866	−	0.123126i
$221$	0.889254	+	1.54023i	0.0598177	+	0.103607i
$222$		0			0
$223$	−8.84690	+	15.3233i	−0.592432	+	1.02612i	0.401471	+	0.915872i	$0.368499\pi$
$223$	−8.84690	+	15.3233i	−0.592432	+	1.02612i	−0.993904	+	0.110251i	$0.964834\pi$
$224$	7.75789			0.518346
$225$		0			0
$226$	−21.9613			−1.46085
$227$	7.88599	−	13.6589i	0.523412	−	0.906576i	−0.476217	−	0.879328i	$-0.657992\pi$
$227$	7.88599	−	13.6589i	0.523412	−	0.906576i	0.999629	−	0.0272479i	$-0.00867435\pi$
$228$		0			0
$229$	0.883432	+	1.53015i	0.0583788	+	0.101115i	0.893738	−	0.448590i	$-0.148074\pi$
$229$	0.883432	+	1.53015i	0.0583788	+	0.101115i	−0.835359	+	0.549705i	$0.814740\pi$
$230$	−6.14122	−	10.6369i	−0.404940	−	0.701377i
$231$		0			0
$232$	−2.23807	+	3.87646i	−0.146937	+	0.254502i
$233$	−13.8984			−0.910514			−0.455257	−	0.890360i	$-0.650453\pi$
$233$	−13.8984			−0.910514			−0.455257	+	0.890360i	$0.650453\pi$
$234$		0			0
$235$	6.64354			0.433376
$236$	2.13810	−	3.70330i	0.139178	−	0.241064i
$237$		0			0
$238$	1.20879	+	2.09368i	0.0783540	+	0.135713i
$239$	9.91634	+	17.1756i	0.641435	+	1.11100i	0.985113	+	0.171910i	$0.0549939\pi$
$239$	9.91634	+	17.1756i	0.641435	+	1.11100i	−0.343678	+	0.939088i	$0.611673\pi$
$240$		0			0
$241$	−9.68735	+	16.7790i	−0.624017	+	1.08083i	0.364713	+	0.931120i	$0.381167\pi$
$241$	−9.68735	+	16.7790i	−0.624017	+	1.08083i	−0.988730	+	0.149709i	$0.952166\pi$
$242$	23.0703			1.48301
$243$		0			0
$244$	2.51674			0.161118
$245$	−8.12250	+	14.0686i	−0.518928	+	0.898809i
$246$		0			0
$247$	4.70924	+	8.15665i	0.299642	+	0.518995i
$248$	−4.40675	−	7.63271i	−0.279829	−	0.484678i
$249$		0			0
$250$	7.95355	−	13.7759i	0.503026	−	0.871267i
$251$	−5.47572			−0.345625			−0.172812	−	0.984955i	$-0.555285\pi$
$251$	−5.47572			−0.345625			−0.172812	+	0.984955i	$0.555285\pi$
$252$		0			0
$253$	−0.685377			−0.0430893
$254$	5.53225	−	9.58214i	0.347124	−	0.601237i
$255$		0			0
$256$	−2.91356	−	5.04643i	−0.182097	−	0.315402i
$257$	5.78258	+	10.0157i	0.360708	+	0.624764i	0.988077	−	0.153957i	$-0.0492019\pi$
$257$	5.78258	+	10.0157i	0.360708	+	0.624764i	−0.627370	+	0.778721i	$0.715869\pi$
$258$		0			0
$259$	2.17153	−	3.76121i	0.134933	−	0.233710i
$260$	10.0749			0.624816
$261$		0			0
$262$	15.3123			0.945996
$263$	−3.23897	+	5.61006i	−0.199723	+	0.345931i	−0.948439	−	0.316961i	$-0.897338\pi$
$263$	−3.23897	+	5.61006i	−0.199723	+	0.345931i	0.748715	+	0.662892i	$0.230671\pi$
$264$		0			0
$265$	−14.6121	−	25.3089i	−0.897614	−	1.55471i
$266$	6.40140	+	11.0875i	0.392495	+	0.679821i
$267$		0			0
$268$	−1.06216	+	1.83972i	−0.0648819	+	0.112379i
$269$	−13.8387			−0.843758			−0.421879	−	0.906652i	$-0.638629\pi$
$269$	−13.8387			−0.843758			−0.421879	+	0.906652i	$0.638629\pi$
$270$		0			0
$271$	1.94536			0.118172			0.0590860	−	0.998253i	$-0.481181\pi$
$271$	1.94536			0.118172			0.0590860	+	0.998253i	$0.481181\pi$
$272$	1.65004	−	2.85795i	0.100048	−	0.173289i
$273$		0			0
$274$	11.9053	+	20.6206i	0.719224	+	1.24573i
$275$	0.348436	+	0.603509i	0.0210115	+	0.0363930i
$276$		0			0
$277$	−6.23634	+	10.8017i	−0.374706	+	0.649009i	−0.990283	−	0.139067i	$-0.955590\pi$
$277$	−6.23634	+	10.8017i	−0.374706	+	0.649009i	0.615577	+	0.788076i	$0.288923\pi$
$278$	−19.8543			−1.19078
$279$		0			0
$280$	2.65106			0.158431
$281$	−4.87793	+	8.44883i	−0.290993	+	0.504015i	−0.974045	−	0.226355i	$-0.927319\pi$
$281$	−4.87793	+	8.44883i	−0.290993	+	0.504015i	0.683052	+	0.730370i	$0.260652\pi$
$282$		0			0
$283$	−13.2856	−	23.0114i	−0.789748	−	1.36788i	−0.926121	−	0.377226i	$-0.876878\pi$
$283$	−13.2856	−	23.0114i	−0.789748	−	1.36788i	0.136373	−	0.990658i	$-0.456455\pi$
$284$	11.8992	+	20.6100i	0.706087	+	1.22298i
$285$		0			0
$286$	0.507777	−	0.879496i	0.0300255	−	0.0520057i
$287$	5.68346			0.335484
$288$		0			0
$289$	−15.6201			−0.918830
$290$	12.5080	−	21.6645i	0.734494	−	1.27218i
$291$		0			0
$292$	18.9006	+	32.7367i	1.10607	+	1.91577i
$293$	−6.12873	−	10.6153i	−0.358044	−	0.620151i	0.629590	−	0.776928i	$-0.283223\pi$
$293$	−6.12873	−	10.6153i	−0.358044	−	0.620151i	−0.987634	+	0.156777i	$0.949890\pi$
$294$		0			0
$295$	−2.31311	+	4.00643i	−0.134675	+	0.233263i
$296$	4.53888			0.263817
$297$		0			0
$298$	−40.3243			−2.33592
$299$	1.63723	−	2.83576i	0.0946834	−	0.163996i
$300$		0			0
$301$	−2.71815	−	4.70798i	−0.156672	−	0.271363i
$302$	4.24806	+	7.35786i	0.244449	+	0.423397i
$303$		0			0
$304$	8.73814	−	15.1349i	0.501167	−	0.868046i
$305$	−2.72275			−0.155904
$306$		0			0
$307$	−26.4740			−1.51095			−0.755475	−	0.655178i	$-0.772594\pi$
$307$	−26.4740			−1.51095			−0.755475	+	0.655178i	$0.772594\pi$
$308$	0.382101	−	0.661818i	0.0217722	−	0.0377106i
$309$		0			0
$310$	24.6281	+	42.6571i	1.39878	+	2.42276i
$311$	8.82974	+	15.2936i	0.500689	+	0.867218i	1.00000		0.000795555i	$0.000253233\pi$
$311$	8.82974	+	15.2936i	0.500689	+	0.867218i	−0.499311	+	0.866423i	$0.666413\pi$
$312$		0			0
$313$	−4.82360	+	8.35473i	−0.272646	+	0.472237i	−0.969539	−	0.244939i	$-0.921232\pi$
$313$	−4.82360	+	8.35473i	−0.272646	+	0.472237i	0.696892	+	0.717176i	$0.254566\pi$
$314$	−15.4004			−0.869093
$315$		0			0
$316$	−27.8112			−1.56450
$317$	1.85525	−	3.21338i	0.104201	−	0.180481i	−0.809211	−	0.587519i	$-0.800105\pi$
$317$	1.85525	−	3.21338i	0.104201	−	0.180481i	0.913411	+	0.407037i	$0.133438\pi$
$318$		0			0
$319$	−0.697963	−	1.20891i	−0.0390784	−	0.0676858i
$320$	−15.1181	−	26.1852i	−0.845125	−	1.46380i
$321$		0			0
$322$	2.22553	−	3.85473i	0.124024	−	0.214816i
$323$	7.30748			0.406599
$324$		0			0
$325$	−3.32937			−0.184680
$326$	13.1751	−	22.8199i	0.729701	−	1.26388i
$327$		0			0
$328$	2.96986	+	5.14394i	0.163983	+	0.284027i
$329$	1.20378	+	2.08501i	0.0663666	+	0.114950i
$330$		0			0
$331$	0.706398	−	1.22352i	0.0388271	−	0.0672506i	−0.845959	−	0.533248i	$-0.820971\pi$
$331$	0.706398	−	1.22352i	0.0388271	−	0.0672506i	0.884786	+	0.465998i	$0.154304\pi$
$332$	11.6191			0.637678
$333$		0			0
$334$	4.93573			0.270071
$335$	1.14911	−	1.99031i	0.0627823	−	0.108742i
$336$		0			0
$337$	6.49503	+	11.2497i	0.353807	+	0.612812i	0.986913	−	0.161253i	$-0.0515536\pi$
$337$	6.49503	+	11.2497i	0.353807	+	0.612812i	−0.633106	+	0.774065i	$0.718220\pi$
$338$	−11.3321	−	19.6278i	−0.616385	−	1.06761i
$339$		0			0
$340$	3.90837	−	6.76949i	0.211961	−	0.367127i
$341$	2.74856			0.148843
$342$		0			0
$343$	−12.6934			−0.685378
$344$	2.84071	−	4.92025i	0.153161	−	0.265282i
$345$		0			0
$346$	−3.79116	−	6.56648i	−0.203814	−	0.353016i
$347$	2.40023	+	4.15732i	0.128851	+	0.223177i	0.923232	−	0.384244i	$-0.125538\pi$
$347$	2.40023	+	4.15732i	0.128851	+	0.223177i	−0.794381	+	0.607420i	$0.792204\pi$
$348$		0			0
$349$	11.2888	−	19.5527i	0.604275	−	1.04663i	−0.387891	−	0.921705i	$-0.626796\pi$
$349$	11.2888	−	19.5527i	0.604275	−	1.04663i	0.992166	−	0.124929i	$-0.0398704\pi$
$350$	−4.52571			−0.241909
$351$		0			0
$352$	−2.52845			−0.134767
$353$	14.8533	−	25.7266i	0.790560	−	1.36929i	−0.135060	−	0.990837i	$-0.543123\pi$
$353$	14.8533	−	25.7266i	0.790560	−	1.36929i	0.925620	−	0.378453i	$-0.123544\pi$
$354$		0			0
$355$	−12.8732	−	22.2970i	−0.683238	−	1.18340i
$356$	19.2201	+	33.2902i	1.01866	+	1.76438i
$357$		0			0
$358$	−21.1617	+	36.6531i	−1.11843	+	1.93718i
$359$	13.4198			0.708271			0.354136	−	0.935194i	$-0.384775\pi$
$359$	13.4198			0.708271			0.354136	+	0.935194i	$0.384775\pi$
$360$		0			0
$361$	19.6984			1.03676
$362$	10.2998	−	17.8398i	0.541347	−	0.937640i
$363$		0			0
$364$	1.82552	+	3.16190i	0.0956834	+	0.165728i
$365$	−20.4477	−	35.4164i	−1.07028	−	1.85378i
$366$		0			0
$367$	3.97499	−	6.88488i	0.207493	−	0.359388i	−0.743431	−	0.668812i	$-0.766803\pi$
$367$	3.97499	−	6.88488i	0.207493	−	0.359388i	0.950924	+	0.309424i	$0.100136\pi$
$368$	−6.07585			−0.316726
$369$		0			0
$370$	−25.3666			−1.31874
$371$	5.29530	−	9.17174i	0.274918	−	0.476173i
$372$		0			0
$373$	5.71026	+	9.89045i	0.295666	+	0.512108i	0.975140	−	0.221592i	$-0.0711252\pi$
$373$	5.71026	+	9.89045i	0.295666	+	0.512108i	−0.679474	+	0.733700i	$0.737792\pi$
$374$	−0.393967	−	0.682371i	−0.0203715	−	0.0352845i
$375$		0			0
$376$	−1.25806	+	2.17902i	−0.0648793	+	0.112374i
$377$	6.66917			0.343480
$378$		0			0
$379$	−24.1705			−1.24155			−0.620777	−	0.783987i	$-0.713183\pi$
$379$	−24.1705			−1.24155			−0.620777	+	0.783987i	$0.713183\pi$
$380$	20.6976	−	35.8494i	1.06177	−	1.83903i
$381$		0			0
$382$	−18.7919	−	32.5486i	−0.961479	−	1.66533i
$383$	−4.72164	−	8.17812i	−0.241265	−	0.417883i	0.719810	−	0.694171i	$-0.244229\pi$
$383$	−4.72164	−	8.17812i	−0.241265	−	0.417883i	−0.961075	+	0.276288i	$0.910896\pi$
$384$		0			0
$385$	−0.413377	+	0.715990i	−0.0210677	+	0.0364902i
$386$	−22.4030			−1.14029
$387$		0			0
$388$	−13.7632			−0.698722
$389$	1.27385	−	2.20638i	0.0645869	−	0.111868i	−0.831924	−	0.554890i	$-0.812760\pi$
$389$	1.27385	−	2.20638i	0.0645869	−	0.111868i	0.896511	+	0.443022i	$0.146094\pi$
$390$		0			0
$391$	−1.27027	−	2.20017i	−0.0642403	−	0.111267i
$392$	−3.07624	−	5.32821i	−0.155374	−	0.269115i
$393$		0			0
$394$	14.9845	−	25.9539i	0.754909	−	1.30754i
$395$	30.0876			1.51387
$396$		0			0
$397$	3.67517			0.184452			0.0922258	−	0.995738i	$-0.470602\pi$
$397$	3.67517			0.184452			0.0922258	+	0.995738i	$0.470602\pi$
$398$	7.97987	−	13.8215i	0.399995	−	0.692811i
$399$		0			0
$400$	3.08888	+	5.35009i	0.154444	+	0.267505i
$401$	−8.07436	−	13.9852i	−0.403214	−	0.698388i	0.590897	−	0.806747i	$-0.298774\pi$
$401$	−8.07436	−	13.9852i	−0.403214	−	0.698388i	−0.994112	+	0.108359i	$0.965440\pi$
$402$		0			0
$403$	−6.56576	+	11.3722i	−0.327064	+	0.566492i
$404$	−25.1458			−1.25105
$405$		0			0
$406$	9.06558			0.449917
$407$	−0.707745	+	1.22585i	−0.0350816	+	0.0607631i
$408$		0			0
$409$	−4.59099	−	7.95182i	−0.227010	−	0.393192i	0.729911	−	0.683542i	$-0.239562\pi$
$409$	−4.59099	−	7.95182i	−0.227010	−	0.393192i	−0.956920	+	0.290350i	$0.906228\pi$
$410$	−16.5977	−	28.7481i	−0.819703	−	1.41977i
$411$		0			0
$412$	12.2185	−	21.1631i	0.601964	−	1.04263i
$413$	−1.67651			−0.0824955
$414$		0			0
$415$	−12.5701			−0.617043
$416$	6.03995	−	10.4615i	0.296133	−	0.512917i
$417$		0			0
$418$	−2.08634	−	3.61365i	−0.102046	−	0.176749i
$419$	3.48944	+	6.04388i	0.170470	+	0.295263i	0.938584	−	0.345050i	$-0.112138\pi$
$419$	3.48944	+	6.04388i	0.170470	+	0.295263i	−0.768114	+	0.640313i	$0.778805\pi$
$420$		0			0
$421$	−15.4053	+	26.6828i	−0.750809	+	1.30044i	0.196622	+	0.980479i	$0.437003\pi$
$421$	−15.4053	+	26.6828i	−0.750809	+	1.30044i	−0.947431	+	0.319960i	$0.896331\pi$
$422$	−11.0353			−0.537190
$423$		0			0
$424$	11.0681			0.537515
$425$	−1.29157	+	2.23707i	−0.0626505	+	0.108514i
$426$		0			0
$427$	−0.493351	−	0.854509i	−0.0238749	−	0.0413526i
$428$	−6.41203	−	11.1060i	−0.309937	−	0.536827i
$429$		0			0
$430$	−15.8759	+	27.4979i	−0.765605	+	1.32607i
$431$	27.8971			1.34376			0.671879	−	0.740661i	$-0.265487\pi$
$431$	27.8971			1.34376			0.671879	+	0.740661i	$0.265487\pi$
$432$		0			0
$433$	19.1706			0.921278			0.460639	−	0.887588i	$-0.347620\pi$
$433$	19.1706			0.921278			0.460639	+	0.887588i	$0.347620\pi$
$434$	−8.92502	+	15.4586i	−0.428415	+	0.742036i
$435$		0			0
$436$	9.06554	+	15.7020i	0.434161	+	0.751989i
$437$	−6.72700	−	11.6515i	−0.321796	−	0.557367i
$438$		0			0
$439$	11.8745	−	20.5672i	0.566739	−	0.981620i	−0.430147	−	0.902759i	$-0.641538\pi$
$439$	11.8745	−	20.5672i	0.566739	−	0.981620i	0.996886	−	0.0788611i	$-0.0251284\pi$
$440$	−0.864030			−0.0411910
$441$		0			0
$442$	3.76443			0.179056
$443$	−11.6791	+	20.2288i	−0.554892	+	0.961102i	0.443020	+	0.896512i	$0.353907\pi$
$443$	−11.6791	+	20.2288i	−0.554892	+	0.961102i	−0.997912	+	0.0645896i	$0.979426\pi$
$444$		0			0
$445$	−20.7934	−	36.0151i	−0.985700	−	1.70728i
$446$	18.7255	+	32.4336i	0.886680	+	1.53578i
$447$		0			0
$448$	5.47866	−	9.48931i	0.258842	−	0.448328i
$449$	4.81906			0.227426			0.113713	−	0.993514i	$-0.463726\pi$
$449$	4.81906			0.227426			0.113713	+	0.993514i	$0.463726\pi$
$450$		0			0
$451$	−1.85235			−0.0872238
$452$	−12.8663	+	22.2850i	−0.605178	+	1.04820i
$453$		0			0
$454$	−16.6917	−	28.9108i	−0.783379	−	1.35685i
$455$	−1.97495	−	3.42071i	−0.0925871	−	0.160366i
$456$		0			0
$457$	2.44680	−	4.23798i	0.114456	−	0.198244i	−0.803106	−	0.595836i	$-0.796821\pi$
$457$	2.44680	−	4.23798i	0.114456	−	0.198244i	0.917562	+	0.397592i	$0.130154\pi$
$458$	3.73978			0.174749
$459$		0			0
$460$	−14.3916			−0.671012
$461$	−13.9952	+	24.2404i	−0.651823	+	1.12899i	0.330857	+	0.943681i	$0.392662\pi$
$461$	−13.9952	+	24.2404i	−0.651823	+	1.12899i	−0.982680	+	0.185309i	$0.940671\pi$
$462$		0			0
$463$	13.7377	+	23.7943i	0.638444	+	1.10582i	0.985774	+	0.168074i	$0.0537548\pi$
$463$	13.7377	+	23.7943i	0.638444	+	1.10582i	−0.347331	+	0.937743i	$0.612912\pi$
$464$	−6.18742	−	10.7169i	−0.287244	−	0.497521i
$465$		0			0
$466$	−14.7088	+	25.4764i	−0.681373	+	1.18017i
$467$	−21.2465			−0.983170			−0.491585	−	0.870830i	$-0.663582\pi$
$467$	−21.2465			−0.983170			−0.491585	+	0.870830i	$0.663582\pi$
$468$		0			0
$469$	0.832853			0.0384576
$470$	7.03093	−	12.1779i	0.324313	−	0.561726i
$471$		0			0
$472$	−0.876048	−	1.51736i	−0.0403234	−	0.0698421i
$473$	0.885898	+	1.53442i	0.0407337	+	0.0705528i
$474$		0			0
$475$	−6.83982	+	11.8469i	−0.313832	+	0.543574i
$476$	2.83272			0.129838
$477$		0			0
$478$	41.9783			1.92004
$479$	20.8394	−	36.0949i	0.952177	−	1.64922i	0.211478	−	0.977383i	$-0.432172\pi$
$479$	20.8394	−	36.0949i	0.952177	−	1.64922i	0.740699	−	0.671837i	$-0.234494\pi$
$480$		0			0
$481$	−3.38132	−	5.85662i	−0.154175	−	0.267039i
$482$	20.5045	+	35.5148i	0.933953	+	1.61765i
$483$		0			0
$484$	13.5160	−	23.4103i	0.614362	−	1.06411i
$485$	14.8898			0.676112
$486$		0			0
$487$	4.02801			0.182527			0.0912634	−	0.995827i	$-0.470909\pi$
$487$	4.02801			0.182527			0.0912634	+	0.995827i	$0.470909\pi$
$488$	0.515595	−	0.893036i	0.0233399	−	0.0404258i
$489$		0			0
$490$	17.1923	+	29.7779i	0.776668	+	1.34523i
$491$	19.3107	+	33.4471i	0.871479	+	1.50945i	0.860467	+	0.509506i	$0.170172\pi$
$491$	19.3107	+	33.4471i	0.871479	+	1.50945i	0.0110115	+	0.999939i	$0.496495\pi$
$492$		0			0
$493$	2.58719	−	4.48114i	0.116521	−	0.201821i
$494$	19.9354			0.896935
$495$		0			0
$496$	24.3660			1.09406
$497$	4.66514	−	8.08026i	0.209260	−	0.362449i
$498$		0			0
$499$	2.03593	+	3.52633i	0.0911407	+	0.157860i	0.907991	−	0.418989i	$-0.137615\pi$
$499$	2.03593	+	3.52633i	0.0911407	+	0.157860i	−0.816851	+	0.576849i	$0.804282\pi$
$500$	−9.31934	−	16.1416i	−0.416774	−	0.721873i
$501$		0			0
$502$	−5.79502	+	10.0373i	−0.258644	+	0.447985i
$503$	−3.42594			−0.152755			−0.0763775	−	0.997079i	$-0.524335\pi$
$503$	−3.42594			−0.152755			−0.0763775	+	0.997079i	$0.524335\pi$
$504$		0			0
$505$	27.2041			1.21056
$506$	−0.725343	+	1.25633i	−0.0322454	+	0.0558507i
$507$		0			0
$508$	−6.48225	−	11.2276i	−0.287604	−	0.498144i
$509$	6.13171	+	10.6204i	0.271783	+	0.470742i	0.969319	−	0.245808i	$-0.0790533\pi$
$509$	6.13171	+	10.6204i	0.271783	+	0.470742i	−0.697535	+	0.716550i	$0.745720\pi$
$510$		0			0
$511$	7.41006	−	12.8346i	0.327802	−	0.567770i
$512$	−28.1241			−1.24292
$513$		0			0
$514$	24.4791			1.07973
$515$	−13.2187	+	22.8954i	−0.582484	+	1.00889i
$516$		0			0
$517$	−0.392336	−	0.679545i	−0.0172549	−	0.0298864i
$518$	−4.59632	−	7.96105i	−0.201951	−	0.349789i
$519$		0			0
$520$	2.06399	−	3.57494i	0.0905121	−	0.156772i
$521$	14.0823			0.616959			0.308479	−	0.951231i	$-0.400180\pi$
$521$	14.0823			0.616959			0.308479	+	0.951231i	$0.400180\pi$
$522$		0			0
$523$	9.77912			0.427611			0.213806	−	0.976876i	$-0.431414\pi$
$523$	9.77912			0.427611			0.213806	+	0.976876i	$0.431414\pi$
$524$	8.97086	−	15.5380i	0.391894	−	0.678780i
$525$		0			0
$526$	6.85567	+	11.8744i	0.298922	+	0.517747i
$527$	5.09415	+	8.82333i	0.221905	+	0.384350i
$528$		0			0
$529$	9.16127	−	15.8678i	0.398316	−	0.689904i
$530$	−61.8566			−2.68688
$531$		0			0
$532$	15.0013			0.650389
$533$	4.42489	−	7.66414i	0.191663	−	0.331971i
$534$		0			0
$535$	6.93688	+	12.0150i	0.299908	+	0.519455i
$536$	0.435202	+	0.753792i	0.0187979	+	0.0325588i
$537$		0			0
$538$	−14.6456	+	25.3669i	−0.631417	+	1.09365i
$539$	1.91871			0.0826445
$540$		0			0
$541$	40.9454			1.76038			0.880189	−	0.474623i	$-0.157416\pi$
$541$	40.9454			1.76038			0.880189	+	0.474623i	$0.157416\pi$
$542$	2.05879	−	3.56594i	0.0884328	−	0.153170i
$543$		0			0
$544$	−4.68619	−	8.11672i	−0.200919	−	0.348001i
$545$	−9.80760	−	16.9873i	−0.420111	−	0.727654i
$546$		0			0
$547$	−0.555138	+	0.961528i	−0.0237360	+	0.0411120i	−0.877649	−	0.479303i	$-0.840889\pi$
$547$	−0.555138	+	0.961528i	−0.0237360	+	0.0411120i	0.853913	+	0.520415i	$0.174223\pi$
$548$	27.8993			1.19180
$549$		0			0
$550$	1.47502			0.0628949
$551$	13.7010	−	23.7309i	0.583684	−	1.01097i
$552$		0			0
$553$	5.45176	+	9.44272i	0.231832	+	0.401545i
$554$	13.2000	+	22.8630i	0.560814	+	0.971358i
$555$		0			0
$556$	−11.6318	+	20.1469i	−0.493300	+	0.854420i
$557$	35.0403			1.48470			0.742352	−	0.670010i	$-0.233710\pi$
$557$	35.0403			1.48470			0.742352	+	0.670010i	$0.233710\pi$
$558$		0			0
$559$	−8.46493			−0.358028
$560$	−3.66458	+	6.34724i	−0.154857	+	0.268220i
$561$		0			0
$562$	10.3247	+	17.8830i	0.435523	+	0.754348i
$563$	19.3856	+	33.5768i	0.817005	+	1.41509i	0.907879	+	0.419232i	$0.137701\pi$
$563$	19.3856	+	33.5768i	0.817005	+	1.41509i	−0.0908735	+	0.995862i	$0.528966\pi$
$564$		0			0
$565$	13.9194	−	24.1092i	0.585595	−	1.01428i
$566$	−56.2413			−2.36400
$567$		0			0
$568$	9.75095			0.409141
$569$	16.9842	−	29.4174i	0.712013	−	1.23324i	−0.252087	−	0.967705i	$-0.581117\pi$
$569$	16.9842	−	29.4174i	0.712013	−	1.23324i	0.964100	−	0.265539i	$-0.0855498\pi$
$570$		0			0
$571$	−5.04443	−	8.73721i	−0.211103	−	0.365641i	0.740957	−	0.671552i	$-0.234372\pi$
$571$	−5.04443	−	8.73721i	−0.211103	−	0.365641i	−0.952060	+	0.305911i	$0.901039\pi$
$572$	−0.594973	−	1.03052i	−0.0248771	−	0.0430884i
$573$		0			0
$574$	6.01487	−	10.4181i	0.251056	−	0.434842i
$575$	4.75590			0.198335
$576$		0			0
$577$	−12.1323			−0.505074			−0.252537	−	0.967587i	$-0.581265\pi$
$577$	−12.1323			−0.505074			−0.252537	+	0.967587i	$0.581265\pi$
$578$	−16.5309	+	28.6324i	−0.687597	+	1.19095i
$579$		0			0
$580$	−14.6559	−	25.3847i	−0.608551	−	1.05404i
$581$	−2.27766	−	3.94501i	−0.0944931	−	0.163667i
$582$		0			0
$583$	−1.72584	+	2.98925i	−0.0714771	+	0.123802i
$584$	15.4883			0.640911
$585$		0			0
$586$	−25.9444			−1.07175
$587$	−15.8746	+	27.4956i	−0.655215	+	1.13487i	0.326625	+	0.945154i	$0.394089\pi$
$587$	−15.8746	+	27.4956i	−0.655215	+	1.13487i	−0.981840	+	0.189711i	$0.939245\pi$
$588$		0			0
$589$	26.9772	+	46.7259i	1.11158	+	1.92531i
$590$	4.89599	+	8.48010i	0.201565	+	0.349120i
$591$		0			0
$592$	−6.27414	+	10.8671i	−0.257866	+	0.446636i
$593$	13.4906			0.553993			0.276996	−	0.960871i	$-0.410661\pi$
$593$	13.4906			0.553993			0.276996	+	0.960871i	$0.410661\pi$
$594$		0			0
$595$	−3.06459			−0.125636
$596$	−23.6244	+	40.9187i	−0.967694	+	1.67609i
$597$		0			0
$598$	−3.46539	−	6.00224i	−0.141711	−	0.245450i
$599$	21.2152	+	36.7458i	0.866829	+	1.50139i	0.865220	+	0.501393i	$0.167179\pi$
$599$	21.2152	+	36.7458i	0.866829	+	1.50139i	0.00160947	+	0.999999i	$0.499488\pi$
$600$		0			0
$601$	9.90237	−	17.1514i	0.403926	−	0.699620i	−0.590270	−	0.807206i	$-0.700979\pi$
$601$	9.90237	−	17.1514i	0.403926	−	0.699620i	0.994196	+	0.107586i	$0.0343120\pi$
$602$	−11.5066			−0.468974
$603$		0			0
$604$	9.95509			0.405067
$605$	−14.6223	+	25.3266i	−0.594481	+	1.02967i
$606$		0			0
$607$	17.9995	+	31.1761i	0.730578	+	1.26540i	0.956637	+	0.291284i	$0.0940825\pi$
$607$	17.9995	+	31.1761i	0.730578	+	1.26540i	−0.226059	+	0.974114i	$0.572584\pi$
$608$	−24.8168	−	42.9839i	−1.00645	−	1.74323i
$609$		0			0
$610$	−2.88152	+	4.99093i	−0.116669	+	0.202077i
$611$	3.74884			0.151662
$612$		0			0
$613$	26.4628			1.06882			0.534411	−	0.845225i	$-0.320533\pi$
$613$	26.4628			1.06882			0.534411	+	0.845225i	$0.320533\pi$
$614$	−28.0177	+	48.5281i	−1.13070	+	1.95843i
$615$		0			0
$616$	−0.156559	−	0.271168i	−0.00630793	−	0.0109257i
$617$	−24.5584	−	42.5363i	−0.988683	−	1.71245i	−0.624264	−	0.781214i	$-0.714601\pi$
$617$	−24.5584	−	42.5363i	−0.988683	−	1.71245i	−0.364419	−	0.931235i	$-0.618732\pi$
$618$		0			0
$619$	12.1031	−	20.9632i	0.486465	−	0.842582i	−0.513414	−	0.858141i	$-0.671619\pi$
$619$	12.1031	−	20.9632i	0.486465	−	0.842582i	0.999879	+	0.0155592i	$0.00495283\pi$
$620$	57.7145			2.31787
$621$		0			0
$622$	37.3785			1.49874
$623$	7.53534	−	13.0516i	0.301897	−	0.522901i
$624$		0			0
$625$	15.5797	+	26.9848i	0.623188	+	1.07939i
$626$	10.2097	+	17.6838i	0.408064	+	0.706787i
$627$		0			0
$628$	−9.02247	+	15.6274i	−0.360036	+	0.623600i
$629$	−5.24690			−0.209208
$630$		0			0
$631$	17.6968			0.704500			0.352250	−	0.935906i	$-0.385417\pi$
$631$	17.6968			0.704500			0.352250	+	0.935906i	$0.385417\pi$
$632$	−5.69756	+	9.86846i	−0.226637	+	0.392546i
$633$		0			0
$634$	−3.92685	−	6.80151i	−0.155955	−	0.270123i
$635$	7.01286	+	12.1466i	0.278297	+	0.482024i
$636$		0			0
$637$	−4.58340	+	7.93868i	−0.181601	+	0.314542i
$638$	−2.95465			−0.116976
$639$		0			0
$640$	−21.1835			−0.837351
$641$	−19.0252	+	32.9526i	−0.751450	+	1.30155i	0.195669	+	0.980670i	$0.437312\pi$
$641$	−19.0252	+	32.9526i	−0.751450	+	1.30155i	−0.947120	+	0.320880i	$0.896021\pi$
$642$		0			0
$643$	−23.4712	−	40.6534i	−0.925616	−	1.60321i	−0.790568	−	0.612374i	$-0.790215\pi$
$643$	−23.4712	−	40.6534i	−0.925616	−	1.60321i	−0.135048	−	0.990839i	$-0.543119\pi$
$644$	−2.60770	−	4.51667i	−0.102758	−	0.177982i
$645$		0			0
$646$	7.73359	−	13.3950i	0.304274	−	0.527018i
$647$	−28.2333			−1.10997			−0.554983	−	0.831862i	$-0.687275\pi$
$647$	−28.2333			−1.10997			−0.554983	+	0.831862i	$0.687275\pi$
$648$		0			0
$649$	0.546406			0.0214483
$650$	−3.52351	+	6.10291i	−0.138204	+	0.239376i
$651$		0			0
$652$	−15.4375	−	26.7386i	−0.604580	−	1.04716i
$653$	−17.6536	−	30.5769i	−0.690839	−	1.19657i	−0.971563	−	0.236780i	$-0.923908\pi$
$653$	−17.6536	−	30.5769i	−0.690839	−	1.19657i	0.280725	−	0.959788i	$-0.409425\pi$
$654$		0			0
$655$	−9.70517	+	16.8098i	−0.379212	+	0.656815i
$656$	−16.4210			−0.641134
$657$		0			0
$658$	5.09590			0.198659
$659$	−20.8469	+	36.1078i	−0.812078	+	1.40656i	0.0993285	+	0.995055i	$0.468331\pi$
$659$	−20.8469	+	36.1078i	−0.812078	+	1.40656i	−0.911407	+	0.411506i	$0.865003\pi$
$660$		0			0
$661$	−0.636957	−	1.10324i	−0.0247747	−	0.0429111i	0.853372	−	0.521302i	$-0.174554\pi$
$661$	−0.636957	−	1.10324i	−0.0247747	−	0.0429111i	−0.878147	+	0.478391i	$0.841220\pi$
$662$	−1.49518	−	2.58972i	−0.0581117	−	0.100652i
$663$		0			0
$664$	2.38035	−	4.12288i	0.0923754	−	0.159999i
$665$	−16.2292			−0.629343
$666$		0			0
$667$	−9.52668			−0.368875
$668$	2.89165	−	5.00848i	0.111881	−	0.193784i
$669$		0			0
$670$	−2.43222	−	4.21273i	−0.0939649	−	0.162752i
$671$	0.160793	+	0.278501i	0.00620733	+	0.0107514i
$672$		0			0
$673$	−17.8164	+	30.8589i	−0.686771	+	1.18952i	0.286106	+	0.958198i	$0.407639\pi$
$673$	−17.8164	+	30.8589i	−0.686771	+	1.18952i	−0.972877	+	0.231324i	$0.925694\pi$
$674$	27.4951			1.05907
$675$		0			0
$676$	−26.5561			−1.02139
$677$	−9.00094	+	15.5901i	−0.345934	+	0.599176i	−0.985523	−	0.169541i	$-0.945771\pi$
$677$	−9.00094	+	15.5901i	−0.345934	+	0.599176i	0.639589	+	0.768717i	$0.279105\pi$
$678$		0			0
$679$	2.69797	+	4.67303i	0.103539	+	0.179334i
$680$	−1.60138	−	2.77368i	−0.0614102	−	0.106366i
$681$		0			0
$682$	2.90884	−	5.03825i	0.111385	−	0.192925i
$683$	39.7614			1.52143			0.760715	−	0.649087i	$-0.224849\pi$
$683$	39.7614			1.52143			0.760715	+	0.649087i	$0.224849\pi$
$684$		0			0
$685$	−30.1830			−1.15323
$686$	−13.4336	+	23.2676i	−0.512895	+	0.888361i
$687$		0			0
$688$	7.85347	+	13.6026i	0.299411	+	0.518594i
$689$	−8.24538	−	14.2814i	−0.314124	−	0.544079i
$690$		0			0
$691$	8.42035	−	14.5845i	0.320325	−	0.554820i	−0.660230	−	0.751064i	$-0.729541\pi$
$691$	8.42035	−	14.5845i	0.320325	−	0.554820i	0.980555	+	0.196244i	$0.0628744\pi$
$692$	−8.88436			−0.337733
$693$		0			0
$694$	10.1608			0.385697
$695$	12.5839	−	21.7960i	0.477336	−	0.826771i
$696$		0			0
$697$	−3.43312	−	5.94634i	−0.130039	−	0.225234i
$698$	−23.8941	−	41.3858i	−0.904405	−	1.56648i
$699$		0			0
$700$	−2.65143	+	4.59242i	−0.100215	+	0.173577i
$701$	−8.96921			−0.338762			−0.169381	−	0.985551i	$-0.554177\pi$
$701$	−8.96921			−0.338762			−0.169381	+	0.985551i	$0.554177\pi$
$702$		0			0
$703$	−27.7861			−1.04797
$704$	−1.78560	+	3.09275i	−0.0672974	+	0.116562i
$705$		0			0
$706$	−31.4388	−	54.4536i	−1.18321	−	2.04939i
$707$	4.92926	+	8.53773i	0.185384	+	0.321095i
$708$		0			0
$709$	−9.07082	+	15.7111i	−0.340662	+	0.590043i	−0.984556	−	0.175071i	$-0.943984\pi$
$709$	−9.07082	+	15.7111i	−0.340662	+	0.590043i	0.643894	+	0.765115i	$0.277318\pi$
$710$	−54.4954			−2.04518
$711$		0			0
$712$	15.7502			0.590263
$713$	9.37898	−	16.2449i	0.351245	−	0.608375i
$714$		0			0
$715$	0.643674	+	1.11488i	0.0240721	+	0.0416940i
$716$	24.7956	+	42.9472i	0.926655	+	1.60501i
$717$		0			0
$718$	14.2024	−	24.5992i	0.530027	−	0.918034i
$719$	31.5720			1.17744			0.588718	−	0.808339i	$-0.299633\pi$
$719$	31.5720			1.17744			0.588718	+	0.808339i	$0.299633\pi$
$720$		0			0
$721$	−9.58068			−0.356803
$722$	20.8470	−	36.1081i	0.775846	−	1.34381i
$723$		0			0
$724$	−12.0685	−	20.9033i	−0.448523	−	0.776865i
$725$	4.84323	+	8.38872i	0.179873	+	0.311549i
$726$		0			0
$727$	−19.2046	+	33.2634i	−0.712260	+	1.23367i	0.251746	+	0.967793i	$0.418995\pi$
$727$	−19.2046	+	33.2634i	−0.712260	+	1.23367i	−0.964007	+	0.265878i	$0.914338\pi$
$728$	1.49595			0.0554436
$729$		0			0
$730$	−86.5599			−3.20373
$731$	−3.28382	+	5.68775i	−0.121457	+	0.210369i
$732$		0			0
$733$	15.1651	+	26.2668i	0.560138	+	0.970187i	0.997484	+	0.0708936i	$0.0225851\pi$
$733$	15.1651	+	26.2668i	0.560138	+	0.970187i	−0.437346	+	0.899293i	$0.644082\pi$
$734$	−8.41355	−	14.5727i	−0.310550	−	0.537888i
$735$		0			0
$736$	−8.62786	+	14.9439i	−0.318027	+	0.550839i
$737$	−0.271443			−0.00999872
$738$		0			0
$739$	10.0025			0.367949			0.183975	−	0.982931i	$-0.441104\pi$
$739$	10.0025			0.367949			0.183975	+	0.982931i	$0.441104\pi$
$740$	−14.8613	+	25.7405i	−0.546311	+	0.946238i
$741$		0			0
$742$	−11.2082	−	19.4131i	−0.411465	−	0.712677i
$743$	−18.1369	−	31.4140i	−0.665378	−	1.15247i	−0.979183	−	0.202981i	$-0.934937\pi$
$743$	−18.1369	−	31.4140i	−0.665378	−	1.15247i	0.313804	−	0.949488i	$-0.398396\pi$
$744$		0			0
$745$	25.5582	−	44.2681i	0.936379	−	1.62186i
$746$	24.1729			0.885033
$747$		0			0
$748$	−0.923239			−0.0337569
$749$	−2.51387	+	4.35415i	−0.0918548	+	0.159097i
$750$		0			0
$751$	7.27718	+	12.6044i	0.265548	+	0.459943i	0.967707	−	0.252077i	$-0.0811138\pi$
$751$	7.27718	+	12.6044i	0.265548	+	0.459943i	−0.702159	+	0.712020i	$0.747780\pi$
$752$	−3.47805	−	6.02415i	−0.126831	−	0.219678i
$753$		0			0
$754$	7.05806	−	12.2249i	0.257039	−	0.445205i
$755$	−10.7700			−0.391959
$756$		0			0
$757$	−45.5754			−1.65646			−0.828232	−	0.560385i	$-0.810653\pi$
$757$	−45.5754			−1.65646			−0.828232	+	0.560385i	$0.810653\pi$
$758$	−25.5799	+	44.3057i	−0.929104	+	1.60925i
$759$		0			0
$760$	−8.48048	−	14.6886i	−0.307619	−	0.532812i
$761$	−11.1228	−	19.2652i	−0.403200	−	0.698364i	0.590910	−	0.806738i	$-0.298769\pi$
$761$	−11.1228	−	19.2652i	−0.403200	−	0.698364i	−0.994110	+	0.108374i	$0.965436\pi$
$762$		0			0
$763$	3.55419	−	6.15604i	0.128670	−	0.222864i
$764$	−44.0378			−1.59323
$765$		0			0
$766$	−19.9879			−0.722191
$767$	−1.30525	+	2.26077i	−0.0471300	+	0.0816315i
$768$		0			0
$769$	−6.83247	−	11.8342i	−0.246385	−	0.426752i	0.716135	−	0.697962i	$-0.245909\pi$
$769$	−6.83247	−	11.8342i	−0.246385	−	0.426752i	−0.962520	+	0.271210i	$0.912576\pi$
$770$	0.874964	+	1.51548i	0.0315315	+	0.0546142i
$771$		0			0
$772$	−13.1251	+	22.7333i	−0.472381	+	0.818188i
$773$	−20.6540			−0.742871			−0.371436	−	0.928459i	$-0.621134\pi$
$773$	−20.6540			−0.742871			−0.371436	+	0.928459i	$0.621134\pi$
$774$		0			0
$775$	−19.0726			−0.685106
$776$	−2.81962	+	4.88372i	−0.101218	+	0.175315i
$777$		0			0
$778$	−2.69627	−	4.67007i	−0.0966659	−	0.167430i
$779$	−18.1809	−	31.4902i	−0.651397	−	1.12825i
$780$		0			0
$781$	−1.52046	+	2.63351i	−0.0544063	+	0.0942345i
$782$	−5.37736			−0.192294
$783$		0			0
$784$	17.0093			0.607474
$785$	9.76100	−	16.9065i	0.348385	−	0.603421i
$786$		0			0
$787$	12.3517	+	21.3938i	0.440290	+	0.762605i	0.997711	−	0.0676252i	$-0.0215422\pi$
$787$	12.3517	+	21.3938i	0.440290	+	0.762605i	−0.557421	+	0.830230i	$0.688209\pi$
$788$	−17.5577	−	30.4108i	−0.625466	−	1.08334i
$789$		0			0
$790$	31.8421	−	55.1521i	1.13289	−	1.96222i
$791$	10.0886			0.358708
$792$		0			0
$793$	−1.53640			−0.0545593
$794$	3.88948	−	6.73677i	0.138032	−	0.239079i
$795$		0			0
$796$	−9.35018	−	16.1950i	−0.331408	−	0.574016i
$797$	15.2829	+	26.4707i	0.541348	+	0.937642i	0.998827	+	0.0484217i	$0.0154191\pi$
$797$	15.2829	+	26.4707i	0.541348	+	0.937642i	−0.457479	+	0.889220i	$0.651248\pi$
$798$		0			0
$799$	1.45430	−	2.51892i	0.0514494	−	0.0891130i
$800$	17.5451			0.620314
$801$		0			0
$802$	−34.1808			−1.20696
$803$	−2.41508	+	4.18305i	−0.0852264	+	0.147617i
$804$		0			0
$805$	2.82115	+	4.88637i	0.0994325	+	0.172222i
$806$	13.8972	+	24.0707i	0.489510	+	0.847856i
$807$		0			0
$808$	−5.15151	+	8.92268i	−0.181229	+	0.313899i
$809$	46.8599			1.64751			0.823753	−	0.566949i	$-0.191876\pi$
$809$	46.8599			1.64751			0.823753	+	0.566949i	$0.191876\pi$
$810$		0			0
$811$	10.9984			0.386206			0.193103	−	0.981178i	$-0.438145\pi$
$811$	10.9984			0.386206			0.193103	+	0.981178i	$0.438145\pi$
$812$	5.31116	−	9.19921i	0.186385	−	0.322829i
$813$		0			0
$814$	1.49803	+	2.59466i	0.0525059	+	0.0909428i
$815$	16.7012	+	28.9273i	0.585016	+	1.01328i
$816$		0			0
$817$	−17.3902	+	30.1208i	−0.608407	+	1.05379i
$818$	−19.4348			−0.679521
$819$		0			0
$820$	−38.8958			−1.35830
$821$	17.9917	−	31.1625i	0.627913	−	1.08758i	−0.360056	−	0.932931i	$-0.617243\pi$
$821$	17.9917	−	31.1625i	0.627913	−	1.08758i	0.987970	−	0.154647i	$-0.0494241\pi$
$822$		0			0
$823$	24.4933	+	42.4237i	0.853783	+	1.47880i	0.877769	+	0.479084i	$0.159031\pi$
$823$	24.4933	+	42.4237i	0.853783	+	1.47880i	−0.0239856	+	0.999712i	$0.507636\pi$
$824$	−5.00632	−	8.67120i	−0.174403	−	0.302076i
$825$		0			0
$826$	−1.77427	+	3.07312i	−0.0617346	+	0.106927i
$827$	−15.6107			−0.542836			−0.271418	−	0.962462i	$-0.587493\pi$
$827$	−15.6107			−0.542836			−0.271418	+	0.962462i	$0.587493\pi$
$828$		0			0
$829$	11.4708			0.398398			0.199199	−	0.979959i	$-0.436166\pi$
$829$	11.4708			0.398398			0.199199	+	0.979959i	$0.436166\pi$
$830$	−13.3031	+	23.0417i	−0.461758	+	0.799788i
$831$		0			0
$832$	−8.53088	−	14.7759i	−0.295755	−	0.512263i
$833$	3.55610	+	6.15935i	0.123212	+	0.213409i
$834$		0			0
$835$	−3.12834	+	5.41845i	−0.108261	+	0.187513i
$836$	−4.88922			−0.169097
$837$		0			0
$838$	14.7716			0.510278
$839$	0.337662	−	0.584848i	0.0116574	−	0.0201912i	−0.860138	−	0.510062i	$-0.829623\pi$
$839$	0.337662	−	0.584848i	0.0116574	−	0.0201912i	0.871795	+	0.489870i	$0.162956\pi$
$840$		0			0
$841$	4.79838	+	8.31104i	0.165461	+	0.286588i
$842$	32.6072	+	56.4774i	1.12372	+	1.94634i
$843$		0			0
$844$	−6.46515	+	11.1980i	−0.222540	+	0.385450i
$845$	28.7298			0.988337
$846$		0			0
$847$	−10.5980			−0.364152
$848$	−15.2995	+	26.4996i	−0.525389	+	0.910000i
$849$		0			0
$850$	2.73377	+	4.73504i	0.0937677	+	0.162410i
$851$	4.83010	+	8.36598i	0.165574	+	0.286782i
$852$		0			0
$853$	−19.6779	+	34.0831i	−0.673758	+	1.16698i	0.303073	+	0.952967i	$0.401987\pi$
$853$	−19.6779	+	34.0831i	−0.673758	+	1.16698i	−0.976830	+	0.214015i	$0.931346\pi$
$854$	−2.08848			−0.0714662
$855$		0			0
$856$	−5.25443			−0.179593
$857$	−16.3311	+	28.2862i	−0.557858	+	0.966239i	0.439817	+	0.898088i	$0.355043\pi$
$857$	−16.3311	+	28.2862i	−0.557858	+	0.966239i	−0.997675	+	0.0681513i	$0.978290\pi$
$858$		0			0
$859$	16.5983	+	28.7491i	0.566327	+	0.980908i	0.996925	+	0.0783636i	$0.0249695\pi$
$859$	16.5983	+	28.7491i	0.566327	+	0.980908i	−0.430598	+	0.902544i	$0.641697\pi$
$860$	18.6021	+	32.2199i	0.634328	+	1.09869i
$861$		0			0
$862$	29.5239	−	51.1368i	1.00559	−	1.74173i
$863$	22.6796			0.772024			0.386012	−	0.922494i	$-0.373852\pi$
$863$	22.6796			0.772024			0.386012	+	0.922494i	$0.373852\pi$
$864$		0			0
$865$	9.61158			0.326804
$866$	20.2884	−	35.1406i	0.689428	−	1.19413i
$867$		0			0
$868$	10.4576	+	18.1131i	0.354955	+	0.614800i
$869$	−1.77683	−	3.07757i	−0.0602749	−	0.104399i
$870$		0			0
$871$	0.648422	−	1.12310i	0.0219709	−	0.0380548i
$872$	7.42888			0.251574
$873$		0			0
$874$	−28.4770			−0.963250
$875$	−3.65370	+	6.32839i	−0.123517	+	0.213938i
$876$		0			0
$877$	−4.62188	−	8.00533i	−0.156070	−	0.270321i	0.777378	−	0.629033i	$-0.216549\pi$
$877$	−4.62188	−	8.00533i	−0.156070	−	0.270321i	−0.933448	+	0.358713i	$0.883216\pi$
$878$	−25.1338	−	43.5330i	−0.848225	−	1.46917i
$879$		0			0
$880$	1.19436	−	2.06869i	0.0402618	−	0.0697354i
$881$	7.78755			0.262369			0.131185	−	0.991358i	$-0.458122\pi$
$881$	7.78755			0.262369			0.131185	+	0.991358i	$0.458122\pi$
$882$		0			0
$883$	−32.4618			−1.09243			−0.546213	−	0.837647i	$-0.683931\pi$
$883$	−32.4618			−1.09243			−0.546213	+	0.837647i	$0.683931\pi$
$884$	2.20543	−	3.81992i	0.0741767	−	0.128478i
$885$		0			0
$886$	24.7203	+	42.8168i	0.830495	+	1.43846i
$887$	16.9238	+	29.3129i	0.568247	+	0.984232i	0.996739	+	0.0806869i	$0.0257114\pi$
$887$	16.9238	+	29.3129i	0.568247	+	0.984232i	−0.428493	+	0.903545i	$0.640955\pi$
$888$		0			0
$889$	−2.54140	+	4.40184i	−0.0852359	+	0.147633i
$890$	−88.0234			−2.95055
$891$		0			0
$892$	43.8822			1.46929
$893$	7.70157	−	13.3395i	0.257723	−	0.446390i
$894$		0			0
$895$	−26.8252	−	46.4626i	−0.896668	−	1.55307i
$896$	−3.83836	−	6.64824i	−0.128231	−	0.222102i
$897$		0			0
$898$	5.10007	−	8.83358i	0.170192	−	0.294780i
$899$	38.2048			1.27420
$900$		0			0
$901$	−12.7946			−0.426250
$902$	−1.96036	+	3.39545i	−0.0652730	+	0.113056i
$903$		0			0
$904$	5.27172	+	9.13089i	0.175335	+	0.303689i
$905$	13.0564	+	22.6143i	0.434009	+	0.751726i
$906$		0			0
$907$	5.52992	−	9.57811i	0.183618	−	0.318036i	−0.759492	−	0.650517i	$-0.774552\pi$
$907$	5.52992	−	9.57811i	0.183618	−	0.318036i	0.943110	+	0.332481i	$0.107886\pi$
$908$	−39.1160			−1.29811
$909$		0			0
$910$	−8.36045			−0.277146
$911$	−6.27258	+	10.8644i	−0.207820	+	0.359955i	−0.951028	−	0.309106i	$-0.899970\pi$
$911$	−6.27258	+	10.8644i	−0.207820	+	0.359955i	0.743208	+	0.669061i	$0.233303\pi$
$912$		0			0
$913$	0.742332	+	1.28576i	0.0245676	+	0.0425523i
$914$	−5.17895	−	8.97021i	−0.171305	−	0.296708i
$915$		0			0
$916$	2.19099	−	3.79491i	0.0723924	−	0.125387i
$917$	−7.03415			−0.232288
$918$		0			0
$919$	−5.92909			−0.195583			−0.0977913	−	0.995207i	$-0.531178\pi$
$919$	−5.92909			−0.195583			−0.0977913	+	0.995207i	$0.531178\pi$
$920$	−2.94835	+	5.10669i	−0.0972041	+	0.168362i
$921$		0			0
$922$	29.6226	+	51.3079i	0.975569	+	1.68973i
$923$	−7.26414	−	12.5819i	−0.239102	−	0.414137i
$924$		0			0
$925$	4.91111	−	8.50629i	0.161476	−	0.279685i
$926$	58.1549			1.91109
$927$		0			0
$928$	−35.1452			−1.15370
$929$	5.01639	−	8.68864i	0.164582	−	0.285065i	−0.771925	−	0.635714i	$-0.780706\pi$
$929$	5.01639	−	8.68864i	0.164582	−	0.285065i	0.936507	+	0.350649i	$0.114039\pi$
$930$		0			0
$931$	18.8321	+	32.6182i	0.617199	+	1.06902i
$932$	17.2346	+	29.8513i	0.564540	+	0.977811i
$933$		0			0
$934$	−22.4854	+	38.9458i	−0.735745	+	1.27435i
$935$	0.998810			0.0326646
$936$		0			0
$937$	−23.5341			−0.768826			−0.384413	−	0.923161i	$-0.625596\pi$
$937$	−23.5341			−0.768826			−0.384413	+	0.923161i	$0.625596\pi$
$938$	0.881417	−	1.52666i	0.0287793	−	0.0498472i
$939$		0			0
$940$	−8.23829	−	14.2691i	−0.268703	−	0.465408i
$941$	14.6498	+	25.3742i	0.477569	+	0.827174i	0.999669	−	0.0257102i	$-0.00818470\pi$
$941$	14.6498	+	25.3742i	0.477569	+	0.827174i	−0.522100	+	0.852884i	$0.674851\pi$
$942$		0			0
$943$	−6.32081	+	10.9480i	−0.205834	+	0.356515i
$944$	4.84388			0.157655
$945$		0			0
$946$	3.75023			0.121930
$947$	−26.8310	+	46.4726i	−0.871889	+	1.51016i	−0.0118485	+	0.999930i	$0.503772\pi$
$947$	−26.8310	+	46.4726i	−0.871889	+	1.51016i	−0.860040	+	0.510226i	$0.829562\pi$
$948$		0			0
$949$	−11.5383	−	19.9849i	−0.374549	−	0.648738i
$950$	14.4773	+	25.0754i	0.469706	+	0.813555i
$951$		0			0
$952$	0.580328	−	1.00516i	0.0188085	−	0.0325773i
$953$	−4.89656			−0.158615			−0.0793076	−	0.996850i	$-0.525271\pi$
$953$	−4.89656			−0.158615			−0.0793076	+	0.996850i	$0.525271\pi$
$954$		0			0
$955$	47.6425			1.54167
$956$	24.5934	−	42.5971i	0.795409	−	1.37769i
$957$		0			0
$958$	−44.1092	−	76.3994i	−1.42510	−	2.46835i
$959$	−5.46904	−	9.47266i	−0.176605	−	0.305888i
$960$		0			0
$961$	−22.1124	+	38.2999i	−0.713304	+	1.23548i
$962$	−14.3140			−0.461500
$963$		0			0
$964$	48.0510			1.54762
$965$	14.1994	−	24.5941i	0.457095	−	0.791712i
$966$		0			0
$967$	−8.49657	−	14.7165i	−0.273231	−	0.473250i	0.696456	−	0.717599i	$-0.254759\pi$
$967$	−8.49657	−	14.7165i	−0.273231	−	0.473250i	−0.969687	+	0.244349i	$0.921426\pi$
$968$	−5.53792	−	9.59196i	−0.177996	−	0.308297i
$969$		0			0
$970$	15.7581	−	27.2938i	0.505961	−	0.876350i
$971$	−2.68374			−0.0861253			−0.0430627	−	0.999072i	$-0.513712\pi$
$971$	−2.68374			−0.0861253			−0.0430627	+	0.999072i	$0.513712\pi$
$972$		0			0
$973$	9.12064			0.292394
$974$	4.26289	−	7.38355i	0.136592	−	0.236584i
$975$		0			0
$976$	1.42542	+	2.46890i	0.0456267	+	0.0790277i
$977$	−5.49652	−	9.52025i	−0.175849	−	0.304580i	0.764606	−	0.644498i	$-0.222934\pi$
$977$	−5.49652	−	9.52025i	−0.175849	−	0.304580i	−0.940455	+	0.339919i	$0.889600\pi$
$978$		0			0
$979$	−2.45591	+	4.25377i	−0.0784914	+	0.135951i
$980$	40.2891			1.28699
$981$		0			0
$982$	81.7468			2.60865
$983$	23.8878	−	41.3749i	0.761903	−	1.31965i	−0.179965	−	0.983673i	$-0.557599\pi$
$983$	23.8878	−	41.3749i	0.761903	−	1.31965i	0.941868	−	0.335982i	$-0.109068\pi$
$984$		0			0
$985$	18.9948	+	32.9000i	0.605226	+	1.04828i
$986$	−5.47610	−	9.48489i	−0.174395	−	0.302060i
$987$		0			0
$988$	11.6794	−	20.2292i	0.371570	−	0.643578i
$989$	12.0919			0.384499
$990$		0			0
$991$	55.5006			1.76303			0.881517	−	0.472152i	$-0.156523\pi$
$991$	55.5006			1.76303			0.881517	+	0.472152i	$0.156523\pi$
$992$	34.6003	−	59.9294i	1.09856	−	1.90276i
$993$		0			0
$994$	−9.87434	−	17.1029i	−0.313195	−	0.542470i
$995$	10.1155	+	17.5206i	0.320684	+	0.555441i
$996$		0			0
$997$	22.5234	−	39.0116i	0.713322	−	1.23551i	−0.250281	−	0.968173i	$-0.580523\pi$
$997$	22.5234	−	39.0116i	0.713322	−	1.23551i	0.963603	−	0.267337i	$-0.0861436\pi$
$998$	8.61859			0.272817
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.e.487.5		12
3.2	odd	2		729.2.c.b.487.2		12
9.2	odd	6		729.2.a.d.1.5		6
9.4	even	3	inner	729.2.c.e.244.5		12
9.5	odd	6		729.2.c.b.244.2		12
9.7	even	3		729.2.a.a.1.2		6
27.2	odd	18		81.2.e.a.37.2		12
27.4	even	9		243.2.e.c.55.2		12
27.5	odd	18		81.2.e.a.46.2		12
27.7	even	9		243.2.e.d.28.1		12
27.11	odd	18		243.2.e.b.190.1		12
27.13	even	9		243.2.e.d.217.1		12
27.14	odd	18		243.2.e.a.217.2		12
27.16	even	9		243.2.e.c.190.2		12
27.20	odd	18		243.2.e.a.28.2		12
27.22	even	9		27.2.e.a.16.1	✓	12
27.23	odd	18		243.2.e.b.55.1		12
27.25	even	9		27.2.e.a.22.1	yes	12
108.79	odd	18		432.2.u.c.49.2		12
108.103	odd	18		432.2.u.c.97.2		12
135.22	odd	36		675.2.u.b.124.4		24
135.49	even	18		675.2.l.c.151.2		12
135.52	odd	36		675.2.u.b.49.1		24
135.79	even	18		675.2.l.c.76.2		12
135.103	odd	36		675.2.u.b.124.1		24
135.133	odd	36		675.2.u.b.49.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.16.1	✓	12	27.22	even	9
27.2.e.a.22.1	yes	12	27.25	even	9
81.2.e.a.37.2		12	27.2	odd	18
81.2.e.a.46.2		12	27.5	odd	18
243.2.e.a.28.2		12	27.20	odd	18
243.2.e.a.217.2		12	27.14	odd	18
243.2.e.b.55.1		12	27.23	odd	18
243.2.e.b.190.1		12	27.11	odd	18
243.2.e.c.55.2		12	27.4	even	9
243.2.e.c.190.2		12	27.16	even	9
243.2.e.d.28.1		12	27.7	even	9
243.2.e.d.217.1		12	27.13	even	9
432.2.u.c.49.2		12	108.79	odd	18
432.2.u.c.97.2		12	108.103	odd	18
675.2.l.c.76.2		12	135.79	even	18
675.2.l.c.151.2		12	135.49	even	18
675.2.u.b.49.1		24	135.52	odd	36
675.2.u.b.49.4		24	135.133	odd	36
675.2.u.b.124.1		24	135.103	odd	36
675.2.u.b.124.4		24	135.22	odd	36
729.2.a.a.1.2		6	9.7	even	3
729.2.a.d.1.5		6	9.2	odd	6
729.2.c.b.244.2		12	9.5	odd	6
729.2.c.b.487.2		12	3.2	odd	2
729.2.c.e.244.5		12	9.4	even	3	inner
729.2.c.e.487.5		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.05831 - 1.83305i) q^{2} +(-1.24005 - 2.14782i) q^{4} +(1.34155 + 2.32363i) q^{5} +(-0.486166 + 0.842065i) q^{7} -1.01617 q^{8} +O(q^{10})\)	\(q+(1.05831 - 1.83305i) q^{2} +(-1.24005 - 2.14782i) q^{4} +(1.34155 + 2.32363i) q^{5} +(-0.486166 + 0.842065i) q^{7} -1.01617 q^{8} +5.67911 q^{10} +(0.158451 - 0.274445i) q^{11} +(0.757015 + 1.31119i) q^{13} +(1.02903 + 1.78233i) q^{14} +(1.40466 - 2.43295i) q^{16} +1.17468 q^{17} +6.22080 q^{19} +(3.32716 - 5.76282i) q^{20} +(-0.335381 - 0.580897i) q^{22} +(-1.08137 - 1.87299i) q^{23} +(-1.09951 + 1.90440i) q^{25} +3.20463 q^{26} +2.41147 q^{28} +(2.20246 - 3.81476i) q^{29} +(4.33661 + 7.51124i) q^{31} +(-3.98932 - 6.90970i) q^{32} +(1.24318 - 2.15325i) q^{34} -2.60886 q^{35} -4.46665 q^{37} +(6.58355 - 11.4030i) q^{38} +(-1.36325 - 2.36121i) q^{40} +(-2.92259 - 5.06208i) q^{41} +(-2.79550 + 4.84194i) q^{43} -0.785946 q^{44} -4.57771 q^{46} +(1.23803 - 2.14434i) q^{47} +(3.02728 + 5.24341i) q^{49} +(2.32724 + 4.03090i) q^{50} +(1.87747 - 3.25187i) q^{52} -10.8920 q^{53} +0.850279 q^{55} +(0.494029 - 0.855683i) q^{56} +(-4.66177 - 8.07442i) q^{58} +(0.862105 + 1.49321i) q^{59} +(-0.507389 + 0.878823i) q^{61} +18.3580 q^{62} -11.2691 q^{64} +(-2.03115 + 3.51805i) q^{65} +(-0.428276 - 0.741795i) q^{67} +(-1.45666 - 2.52301i) q^{68} +(-2.76099 + 4.78218i) q^{70} -9.59577 q^{71} -15.2418 q^{73} +(-4.72710 + 8.18758i) q^{74} +(-7.71408 - 13.3612i) q^{76} +(0.154067 + 0.266852i) q^{77} +(5.60688 - 9.71141i) q^{79} +7.53771 q^{80} -12.3721 q^{82} +(-2.34247 + 4.05727i) q^{83} +(1.57590 + 2.72953i) q^{85} +(5.91701 + 10.2486i) q^{86} +(-0.161014 + 0.278884i) q^{88} -15.4995 q^{89} -1.47214 q^{91} +(-2.68190 + 4.64519i) q^{92} +(-2.62045 - 4.53876i) q^{94} +(8.34551 + 14.4549i) q^{95} +(2.77474 - 4.80600i) q^{97} +12.8152 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8 + 6 * q^10 + 12 * q^11 + 6 * q^14 + 3 * q^16 - 18 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 15 * q^23 + 6 * q^25 - 30 * q^26 - 12 * q^28 + 12 * q^29 - 24 * q^35 + 6 * q^37 - 3 * q^38 - 6 * q^40 + 15 * q^41 - 6 * q^44 + 6 * q^46 + 21 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^52 - 18 * q^53 - 12 * q^55 - 6 * q^56 + 12 * q^58 + 24 * q^59 + 9 * q^61 + 24 * q^62 - 24 * q^64 - 6 * q^65 + 9 * q^67 - 9 * q^68 - 15 * q^70 - 54 * q^71 - 12 * q^73 - 12 * q^74 - 6 * q^76 - 12 * q^77 + 42 * q^80 - 12 * q^82 + 12 * q^83 - 21 * q^86 - 12 * q^88 - 18 * q^89 - 12 * q^91 + 6 * q^92 - 6 * q^94 + 12 * q^95 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more