LMFDB - Embedded newform 729.2.c.b.487.2

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			487.2
Root			$0.500000 - 2.22827i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.b.244.2

$q$-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	$0.435815\pi$
$2$	−1.05831	+	1.83305i	−0.748339	+	1.29616i	−0.948618	+	0.316423i	$0.897518\pi$
$3$		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	$-0.961850\pi$
$5$	−1.34155	−	2.32363i	−0.599959	−	1.03916i	0.392868	−	0.919595i	$-0.371483\pi$
$6$		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	−0.888924	−	0.458055i	$-0.848546\pi$
$11$	−0.158451	+	0.274445i	−0.0477748	+	0.0827484i	0.841149	+	0.540803i	$0.181880\pi$
$12$		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	$-0.545498\pi$
$17$	−1.17468			−0.284903			−0.142451	+	0.989802i	$0.545498\pi$
$18$		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	0.956464	−	0.291851i	$-0.0942712\pi$
$23$	1.08137	+	1.87299i	0.225481	+	0.390545i	−0.730982	+	0.682396i	$0.760938\pi$
$24$		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	−0.994776	−	0.102078i	$-0.967451\pi$
$29$	−2.20246	+	3.81476i	−0.408986	+	0.708384i	0.585791	+	0.810462i	$0.300784\pi$
$30$		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	0.998769	−	0.0495972i	$-0.0157937\pi$
$41$	2.92259	+	5.06208i	0.456432	+	0.790564i	−0.542337	+	0.840161i	$0.682460\pi$
$42$		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	−0.942080	−	0.335388i	$-0.891133\pi$
$47$	−1.23803	+	2.14434i	−0.180586	+	0.312784i	0.761494	+	0.648172i	$0.224466\pi$
$48$		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	$-0.230984\pi$
$53$	10.8920			1.49613			0.748063	+	0.663628i	$0.230984\pi$
$54$		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	0.804435	−	0.594040i	$-0.202468\pi$
$59$	−0.862105	−	1.49321i	−0.112237	−	0.194399i	−0.916672	+	0.399641i	$0.869135\pi$
$60$		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	$-0.307174\pi$
$71$	9.59577			1.13881			0.569404	+	0.822058i	$0.307174\pi$
$72$		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	−0.708350	−	0.705861i	$-0.750560\pi$
$83$	2.34247	−	4.05727i	0.257119	−	0.445343i	0.965469	+	0.260518i	$0.0838935\pi$
$84$		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	$-0.193153\pi$
$89$	15.4995			1.64295			0.821473	+	0.570248i	$0.193153\pi$
$90$		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	$0.334966\pi$
$101$	−5.06952	+	8.78067i	−0.504436	+	0.873709i	−0.999987	+	0.00513025i	$0.998367\pi$
$102$		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	$-0.580411\pi$
$107$	−5.17080			−0.499880			−0.249940	+	0.968261i	$0.580411\pi$
$108$		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	0.999905	−	0.0137681i	$-0.00438265\pi$
$113$	5.18782	+	8.98557i	0.488029	+	0.845291i	−0.511876	+	0.859059i	$0.671049\pi$
$114$		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	0.663624	−	0.748066i	$-0.269017\pi$
$131$	−3.61715	−	6.26509i	−0.316032	−	0.547383i	−0.979656	+	0.200683i	$0.935684\pi$
$132$		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	−0.519204	−	0.854650i	$-0.673771\pi$
$137$	5.62466	−	9.74220i	0.480547	−	0.832332i	0.999751	+	0.0223185i	$0.00710478\pi$
$138$		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	$0.118302\pi$
$149$	9.52562	+	16.4989i	0.780369	+	1.35164i	−0.151357	+	0.988479i	$0.548364\pi$
$150$		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	0.817382	−	0.576097i	$-0.195425\pi$
$167$	−1.16594	−	2.01947i	−0.0902234	−	0.156272i	−0.907605	+	0.419825i	$0.862091\pi$
$168$		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	−0.926047	−	0.377409i	$-0.876815\pi$
$173$	−1.79113	+	3.10234i	−0.136177	+	0.235866i	0.789869	+	0.613275i	$0.210148\pi$
$174$		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	$-0.231362\pi$
$179$	19.9957			1.49455			0.747275	+	0.664515i	$0.231362\pi$
$180$		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	$0.388731\pi$
$191$	−8.87826	+	15.3776i	−0.642409	+	1.11268i	−0.984894	+	0.173161i	$0.944602\pi$
$192$		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	$-0.668282\pi$
$197$	−14.1589			−1.00878			−0.504390	+	0.863476i	$0.668282\pi$
$198$		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	$0.342008\pi$
$227$	−7.88599	+	13.6589i	−0.523412	+	0.906576i	−0.999629	+	0.0272479i	$0.991326\pi$
$228$		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	$-0.349547\pi$
$233$	13.8984			0.910514			0.455257	+	0.890360i	$0.349547\pi$
$234$		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	$-0.945006\pi$
$239$	−9.91634	−	17.1756i	−0.641435	−	1.11100i	0.343678	−	0.939088i	$-0.388327\pi$
$240$		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	$-0.444715\pi$
$251$	5.47572			0.345625			0.172812	+	0.984955i	$0.444715\pi$
$252$		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	0.627370	−	0.778721i	$-0.284131\pi$
$257$	−5.78258	−	10.0157i	−0.360708	−	0.624764i	−0.988077	+	0.153957i	$0.950798\pi$
$258$		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	−0.748715	−	0.662892i	$-0.769329\pi$
$263$	3.23897	−	5.61006i	0.199723	−	0.345931i	0.948439	+	0.316961i	$0.102662\pi$
$264$		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	$-0.361371\pi$
$269$	13.8387			0.843758			0.421879	+	0.906652i	$0.361371\pi$
$270$		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	−0.683052	−	0.730370i	$-0.739348\pi$
$281$	4.87793	−	8.44883i	0.290993	−	0.504015i	0.974045	+	0.226355i	$0.0726810\pi$
$282$		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	0.987634	−	0.156777i	$-0.0501103\pi$
$293$	6.12873	+	10.6153i	0.358044	+	0.620151i	−0.629590	+	0.776928i	$0.716777\pi$
$294$		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	$-0.999747\pi$
$311$	−8.82974	−	15.2936i	−0.500689	−	0.867218i	0.499311	−	0.866423i	$-0.333587\pi$
$312$		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	−0.913411	−	0.407037i	$-0.866562\pi$
$317$	−1.85525	+	3.21338i	−0.104201	+	0.180481i	0.809211	+	0.587519i	$0.199895\pi$
$318$		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	0.794381	−	0.607420i	$-0.207796\pi$
$347$	−2.40023	−	4.15732i	−0.128851	−	0.223177i	−0.923232	+	0.384244i	$0.874462\pi$
$348$		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	$0.456877\pi$
$353$	−14.8533	+	25.7266i	−0.790560	+	1.36929i	−0.925620	+	0.378453i	$0.876456\pi$
$354$		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	$-0.615225\pi$
$359$	−13.4198			−0.708271			−0.354136	+	0.935194i	$0.615225\pi$
$360$		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	0.961075	−	0.276288i	$-0.0891045\pi$
$383$	4.72164	+	8.17812i	0.241265	+	0.417883i	−0.719810	+	0.694171i	$0.755771\pi$
$384$		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	−0.896511	−	0.443022i	$-0.853906\pi$
$389$	−1.27385	+	2.20638i	−0.0645869	+	0.111868i	0.831924	+	0.554890i	$0.187240\pi$
$390$		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	0.994112	−	0.108359i	$-0.0345595\pi$
$401$	8.07436	+	13.9852i	0.403214	+	0.698388i	−0.590897	+	0.806747i	$0.701226\pi$
$402$		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	0.768114	−	0.640313i	$-0.221195\pi$
$419$	−3.48944	−	6.04388i	−0.170470	−	0.295263i	−0.938584	+	0.345050i	$0.887862\pi$
$420$		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	$-0.734513\pi$
$431$	−27.8971			−1.34376			−0.671879	+	0.740661i	$0.734513\pi$
$432$		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	$-0.646093\pi$
$443$	11.6791	−	20.2288i	0.554892	−	0.961102i	0.997912	−	0.0645896i	$-0.0205738\pi$
$444$		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	$-0.536274\pi$
$449$	−4.81906			−0.227426			−0.113713	+	0.993514i	$0.536274\pi$
$450$		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	$-0.607338\pi$
$461$	13.9952	−	24.2404i	0.651823	−	1.12899i	0.982680	−	0.185309i	$-0.0593287\pi$
$462$		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	$-0.336418\pi$
$467$	21.2465			0.983170			0.491585	+	0.870830i	$0.336418\pi$
$468$		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	$0.567828\pi$
$479$	−20.8394	+	36.0949i	−0.952177	+	1.64922i	−0.740699	+	0.671837i	$0.765506\pi$
$480$		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	$-0.829828\pi$
$491$	−19.3107	−	33.4471i	−0.871479	−	1.50945i	−0.0110115	−	0.999939i	$-0.503505\pi$
$492$		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	$-0.475665\pi$
$503$	3.42594			0.152755			0.0763775	+	0.997079i	$0.475665\pi$
$504$		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	0.697535	−	0.716550i	$-0.254280\pi$
$509$	−6.13171	−	10.6204i	−0.271783	−	0.470742i	−0.969319	+	0.245808i	$0.920947\pi$
$510$		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	$-0.599820\pi$
$521$	−14.0823			−0.616959			−0.308479	+	0.951231i	$0.599820\pi$
$522$		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	$-0.766290\pi$
$557$	−35.0403			−1.48470			−0.742352	+	0.670010i	$0.766290\pi$
$558$		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	$-0.862299\pi$
$563$	−19.3856	−	33.5768i	−0.817005	−	1.41509i	0.0908735	−	0.995862i	$-0.471034\pi$
$564$		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	$0.418883\pi$
$569$	−16.9842	+	29.4174i	−0.712013	+	1.23324i	−0.964100	+	0.265539i	$0.914450\pi$
$570$		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	$-0.605911\pi$
$587$	15.8746	−	27.4956i	0.655215	−	1.13487i	0.981840	−	0.189711i	$-0.0607552\pi$
$588$		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	$-0.589339\pi$
$593$	−13.4906			−0.553993			−0.276996	+	0.960871i	$0.589339\pi$
$594$		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	$-0.832821\pi$
$599$	−21.2152	−	36.7458i	−0.866829	−	1.50139i	−0.00160947	−	0.999999i	$-0.500512\pi$
$600$		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	$0.285399\pi$
$617$	24.5584	+	42.5363i	0.988683	+	1.71245i	0.364419	+	0.931235i	$0.381268\pi$
$618$		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	$-0.562688\pi$
$641$	19.0252	−	32.9526i	0.751450	−	1.30155i	0.947120	−	0.320880i	$-0.103979\pi$
$642$		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	$-0.312725\pi$
$647$	28.2333			1.10997			0.554983	+	0.831862i	$0.312725\pi$
$648$		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	$0.0760919\pi$
$653$	17.6536	+	30.5769i	0.690839	+	1.19657i	−0.280725	+	0.959788i	$0.590575\pi$
$654$		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	$-0.531669\pi$
$659$	20.8469	−	36.1078i	0.812078	−	1.40656i	0.911407	−	0.411506i	$-0.134997\pi$
$660$		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	−0.639589	−	0.768717i	$-0.720895\pi$
$677$	9.00094	−	15.5901i	0.345934	−	0.599176i	0.985523	+	0.169541i	$0.0542286\pi$
$678$		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	$-0.775151\pi$
$683$	−39.7614			−1.52143			−0.760715	+	0.649087i	$0.775151\pi$
$684$		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	$-0.445823\pi$
$701$	8.96921			0.338762			0.169381	+	0.985551i	$0.445823\pi$
$702$		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	$-0.700367\pi$
$719$	−31.5720			−1.17744			−0.588718	+	0.808339i	$0.700367\pi$
$720$		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	$0.0650630\pi$
$743$	18.1369	+	31.4140i	0.665378	+	1.15247i	−0.313804	+	0.949488i	$0.601604\pi$
$744$		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	0.994110	−	0.108374i	$-0.0345644\pi$
$761$	11.1228	+	19.2652i	0.403200	+	0.698364i	−0.590910	+	0.806738i	$0.701231\pi$
$762$		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	$-0.378866\pi$
$773$	20.6540			0.742871			0.371436	+	0.928459i	$0.378866\pi$
$774$		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	$-0.984581\pi$
$797$	−15.2829	−	26.4707i	−0.541348	−	0.937642i	0.457479	−	0.889220i	$-0.348752\pi$
$798$		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	$-0.808124\pi$
$809$	−46.8599			−1.64751			−0.823753	+	0.566949i	$0.808124\pi$
$810$		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	$0.382757\pi$
$821$	−17.9917	+	31.1625i	−0.627913	+	1.08758i	−0.987970	+	0.154647i	$0.950576\pi$
$822$		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	$-0.412507\pi$
$827$	15.6107			0.542836			0.271418	+	0.962462i	$0.412507\pi$
$828$		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	−0.871795	−	0.489870i	$-0.837044\pi$
$839$	−0.337662	+	0.584848i	−0.0116574	+	0.0201912i	0.860138	+	0.510062i	$0.170377\pi$
$840$		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	$-0.644957\pi$
$857$	16.3311	−	28.2862i	0.557858	−	0.966239i	0.997675	−	0.0681513i	$-0.0217101\pi$
$858$		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	$-0.626148\pi$
$863$	−22.6796			−0.772024			−0.386012	+	0.922494i	$0.626148\pi$
$864$		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	$-0.541878\pi$
$881$	−7.78755			−0.262369			−0.131185	+	0.991358i	$0.541878\pi$
$882$		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	$-0.974289\pi$
$887$	−16.9238	−	29.3129i	−0.568247	−	0.984232i	0.428493	−	0.903545i	$-0.359045\pi$
$888$		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	−0.743208	−	0.669061i	$-0.766697\pi$
$911$	6.27258	−	10.8644i	0.207820	−	0.359955i	0.951028	+	0.309106i	$0.100030\pi$
$912$		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	−0.936507	−	0.350649i	$-0.885961\pi$
$929$	−5.01639	+	8.68864i	−0.164582	+	0.285065i	0.771925	+	0.635714i	$0.219294\pi$
$930$		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	0.522100	−	0.852884i	$-0.325149\pi$
$941$	−14.6498	−	25.3742i	−0.477569	−	0.827174i	−0.999669	+	0.0257102i	$0.991815\pi$
$942$		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	$-0.496228\pi$
$947$	26.8310	−	46.4726i	0.871889	−	1.51016i	0.860040	−	0.510226i	$-0.170438\pi$
$948$		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	$-0.474729\pi$
$953$	4.89656			0.158615			0.0793076	+	0.996850i	$0.474729\pi$
$954$		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	$-0.486288\pi$
$971$	2.68374			0.0861253			0.0430627	+	0.999072i	$0.486288\pi$
$972$		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	0.940455	−	0.339919i	$-0.110400\pi$
$977$	5.49652	+	9.52025i	0.175849	+	0.304580i	−0.764606	+	0.644498i	$0.777066\pi$
$978$		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	$0.442401\pi$
$983$	−23.8878	+	41.3749i	−0.761903	+	1.31965i	−0.941868	+	0.335982i	$0.890932\pi$
$984$		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.b.487.2		12
3.2	odd	2		729.2.c.e.487.5		12
9.2	odd	6		729.2.a.a.1.2		6
9.4	even	3	inner	729.2.c.b.244.2		12
9.5	odd	6		729.2.c.e.244.5		12
9.7	even	3		729.2.a.d.1.5		6
27.2	odd	18		27.2.e.a.22.1	yes	12
27.4	even	9		243.2.e.b.55.1		12
27.5	odd	18		27.2.e.a.16.1	✓	12
27.7	even	9		243.2.e.a.28.2		12
27.11	odd	18		243.2.e.c.190.2		12
27.13	even	9		243.2.e.a.217.2		12
27.14	odd	18		243.2.e.d.217.1		12
27.16	even	9		243.2.e.b.190.1		12
27.20	odd	18		243.2.e.d.28.1		12
27.22	even	9		81.2.e.a.46.2		12
27.23	odd	18		243.2.e.c.55.2		12
27.25	even	9		81.2.e.a.37.2		12
108.59	even	18		432.2.u.c.97.2		12
108.83	even	18		432.2.u.c.49.2		12
135.2	even	36		675.2.u.b.49.1		24
135.29	odd	18		675.2.l.c.76.2		12
135.32	even	36		675.2.u.b.124.4		24
135.59	odd	18		675.2.l.c.151.2		12
135.83	even	36		675.2.u.b.49.4		24
135.113	even	36		675.2.u.b.124.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.16.1	✓	12	27.5	odd	18
27.2.e.a.22.1	yes	12	27.2	odd	18
81.2.e.a.37.2		12	27.25	even	9
81.2.e.a.46.2		12	27.22	even	9
243.2.e.a.28.2		12	27.7	even	9
243.2.e.a.217.2		12	27.13	even	9
243.2.e.b.55.1		12	27.4	even	9
243.2.e.b.190.1		12	27.16	even	9
243.2.e.c.55.2		12	27.23	odd	18
243.2.e.c.190.2		12	27.11	odd	18
243.2.e.d.28.1		12	27.20	odd	18
243.2.e.d.217.1		12	27.14	odd	18
432.2.u.c.49.2		12	108.83	even	18
432.2.u.c.97.2		12	108.59	even	18
675.2.l.c.76.2		12	135.29	odd	18
675.2.l.c.151.2		12	135.59	odd	18
675.2.u.b.49.1		24	135.2	even	36
675.2.u.b.49.4		24	135.83	even	36
675.2.u.b.124.1		24	135.113	even	36
675.2.u.b.124.4		24	135.32	even	36
729.2.a.a.1.2		6	9.2	odd	6
729.2.a.d.1.5		6	9.7	even	3
729.2.c.b.244.2		12	9.4	even	3	inner
729.2.c.b.487.2		12	1.1	even	1	trivial
729.2.c.e.244.5		12	9.5	odd	6
729.2.c.e.487.5		12	3.2	odd	2

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