LMFDB - Embedded newform 1755.2.i.f.1171.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1755,2,Mod(586,1755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1755, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("1755.586");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1755 = 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1755.i (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:	$14.0137455547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 585)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.8
Root			$-0.724143 + 0.165319i$ of defining polynomial
Character	$\chi$	$=$	1755.1171
Dual form			1755.2.i.f.586.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22414 + 2.12028i) q^{2} +(-1.99705 + 3.45900i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.96726 + 3.40740i) q^{7} -4.88214 q^{8} +O(q^{10})$	\(q+(1.22414 + 2.12028i) q^{2} +(-1.99705 + 3.45900i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.96726 + 3.40740i) q^{7} -4.88214 q^{8} -2.44829 q^{10} +(2.33643 + 4.04682i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-4.81642 + 8.34228i) q^{14} +(-1.98233 - 3.43350i) q^{16} +7.96946 q^{17} -0.120966 q^{19} +(-1.99705 - 3.45900i) q^{20} +(-5.72025 + 9.90777i) q^{22} +(0.164078 - 0.284192i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.44829 q^{26} -15.7149 q^{28} +(-0.136463 - 0.236360i) q^{29} +(3.28806 - 5.69509i) q^{31} +(-0.0288185 + 0.0499151i) q^{32} +(9.75576 + 16.8975i) q^{34} -3.93452 q^{35} -7.43198 q^{37} +(-0.148079 - 0.256481i) q^{38} +(2.44107 - 4.22806i) q^{40} +(0.0455066 - 0.0788197i) q^{41} +(-3.89835 - 6.75213i) q^{43} -18.6639 q^{44} +0.803421 q^{46} +(-5.78798 - 10.0251i) q^{47} +(-4.24023 + 7.34429i) q^{49} +(1.22414 - 2.12028i) q^{50} +(1.99705 + 3.45900i) q^{52} +11.1782 q^{53} -4.67286 q^{55} +(-9.60445 - 16.6354i) q^{56} +(0.334099 - 0.578677i) q^{58} +(2.77780 - 4.81129i) q^{59} +(-6.63270 - 11.4882i) q^{61} +16.1002 q^{62} -8.07045 q^{64} +(0.500000 + 0.866025i) q^{65} +(-3.41069 + 5.90749i) q^{67} +(-15.9154 + 27.5663i) q^{68} +(-4.81642 - 8.34228i) q^{70} +6.32442 q^{71} -7.37048 q^{73} +(-9.09780 - 15.7579i) q^{74} +(0.241575 - 0.418420i) q^{76} +(-9.19274 + 15.9223i) q^{77} +(5.95876 + 10.3209i) q^{79} +3.96467 q^{80} +0.222826 q^{82} +(0.774276 + 1.34108i) q^{83} +(-3.98473 + 6.90175i) q^{85} +(9.54427 - 16.5312i) q^{86} +(-11.4068 - 19.7571i) q^{88} +3.59499 q^{89} +3.93452 q^{91} +(0.655346 + 1.13509i) q^{92} +(14.1706 - 24.5442i) q^{94} +(0.0604829 - 0.104759i) q^{95} +(-2.63979 - 4.57224i) q^{97} -20.7626 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.22414	+	2.12028i	0.865600	+	1.49926i	0.866450	+	0.499263i	$0.166396\pi$
$2$	1.22414	+	2.12028i	0.865600	+	1.49926i	−0.000850327		1.00000i	$0.500271\pi$
$3$		0			0
$3$		0			0
$4$	−1.99705	+	3.45900i	−0.998526	+	1.72950i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	1.96726	+	3.40740i	0.743555	+	1.28787i	0.950867	+	0.309600i	$0.100195\pi$
$7$	1.96726	+	3.40740i	0.743555	+	1.28787i	−0.207312	+	0.978275i	$0.566472\pi$
$8$	−4.88214			−1.72610
$9$		0			0
$10$	−2.44829			−0.774216
$11$	2.33643	+	4.04682i	0.704461	+	1.22016i	0.966886	+	0.255209i	$0.0821444\pi$
$11$	2.33643	+	4.04682i	0.704461	+	1.22016i	−0.262425	+	0.964952i	$0.584522\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−4.81642	+	8.34228i	−1.28724	+	2.22957i
$15$		0			0
$16$	−1.98233	−	3.43350i	−0.495584	−	0.858376i
$17$	7.96946			1.93288			0.966439	−	0.256897i	$-0.0827001\pi$
$17$	7.96946			1.93288			0.966439	+	0.256897i	$0.0827001\pi$
$18$		0			0
$19$	−0.120966			−0.0277515			−0.0138757	−	0.999904i	$-0.504417\pi$
$19$	−0.120966			−0.0277515			−0.0138757	+	0.999904i	$0.504417\pi$
$20$	−1.99705	−	3.45900i	−0.446555	−	0.773455i
$21$		0			0
$22$	−5.72025	+	9.90777i	−1.21956	+	2.11234i
$23$	0.164078	−	0.284192i	0.0342127	−	0.0592581i	−0.848412	−	0.529336i	$-0.822441\pi$
$23$	0.164078	−	0.284192i	0.0342127	−	0.0592581i	0.882625	+	0.470078i	$0.155774\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.44829			0.480148
$27$		0			0
$28$	−15.7149			−2.96984
$29$	−0.136463	−	0.236360i	−0.0253405	−	0.0438910i	0.853077	−	0.521785i	$-0.174734\pi$
$29$	−0.136463	−	0.236360i	−0.0253405	−	0.0438910i	−0.878418	+	0.477894i	$0.841400\pi$
$30$		0			0
$31$	3.28806	−	5.69509i	0.590553	−	1.02287i	−0.403605	−	0.914933i	$-0.632243\pi$
$31$	3.28806	−	5.69509i	0.590553	−	1.02287i	0.994158	−	0.107934i	$-0.0344237\pi$
$32$	−0.0288185	+	0.0499151i	−0.00509444	+	0.00882383i
$33$		0			0
$34$	9.75576	+	16.8975i	1.67310	+	2.89789i
$35$	−3.93452			−0.665055
$36$		0			0
$37$	−7.43198			−1.22181			−0.610905	−	0.791704i	$-0.709194\pi$
$37$	−7.43198			−1.22181			−0.610905	+	0.791704i	$0.709194\pi$
$38$	−0.148079	−	0.256481i	−0.0240217	−	0.0416067i
$39$		0			0
$40$	2.44107	−	4.22806i	0.385967	−	0.668515i
$41$	0.0455066	−	0.0788197i	0.00710694	−	0.0123096i	−0.862450	−	0.506142i	$-0.831071\pi$
$41$	0.0455066	−	0.0788197i	0.00710694	−	0.0123096i	0.869557	+	0.493833i	$0.164404\pi$
$42$		0			0
$43$	−3.89835	−	6.75213i	−0.594492	−	1.02969i	−0.993618	−	0.112795i	$-0.964020\pi$
$43$	−3.89835	−	6.75213i	−0.594492	−	1.02969i	0.399126	−	0.916896i	$-0.369314\pi$
$44$	−18.6639			−2.81369
$45$		0			0
$46$	0.803421			0.118458
$47$	−5.78798	−	10.0251i	−0.844263	−	1.46231i	−0.886260	−	0.463189i	$-0.846705\pi$
$47$	−5.78798	−	10.0251i	−0.844263	−	1.46231i	0.0419967	−	0.999118i	$-0.486628\pi$
$48$		0			0
$49$	−4.24023	+	7.34429i	−0.605747	+	1.04918i
$50$	1.22414	−	2.12028i	0.173120	−	0.299853i
$51$		0			0
$52$	1.99705	+	3.45900i	0.276941	+	0.479677i
$53$	11.1782			1.53544			0.767721	−	0.640784i	$-0.221391\pi$
$53$	11.1782			1.53544			0.767721	+	0.640784i	$0.221391\pi$
$54$		0			0
$55$	−4.67286			−0.630089
$56$	−9.60445	−	16.6354i	−1.28345	−	2.22300i
$57$		0			0
$58$	0.334099	−	0.578677i	0.0438694	−	0.0759840i
$59$	2.77780	−	4.81129i	0.361639	−	0.626376i	−0.626592	−	0.779347i	$-0.715551\pi$
$59$	2.77780	−	4.81129i	0.361639	−	0.626376i	0.988231	+	0.152971i	$0.0488841\pi$
$60$		0			0
$61$	−6.63270	−	11.4882i	−0.849230	−	1.47091i	−0.881897	−	0.471443i	$-0.843733\pi$
$61$	−6.63270	−	11.4882i	−0.849230	−	1.47091i	0.0326669	−	0.999466i	$-0.489600\pi$
$62$	16.1002			2.04473
$63$		0			0
$64$	−8.07045			−1.00881
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$		0			0
$67$	−3.41069	+	5.90749i	−0.416682	+	0.721715i	−0.995603	−	0.0936686i	$-0.970141\pi$
$67$	−3.41069	+	5.90749i	−0.416682	+	0.721715i	0.578921	+	0.815384i	$0.303474\pi$
$68$	−15.9154	+	27.5663i	−1.93003	+	3.34291i
$69$		0			0
$70$	−4.81642	−	8.34228i	−0.575672	−	0.997093i
$71$	6.32442			0.750570			0.375285	−	0.926909i	$-0.377545\pi$
$71$	6.32442			0.750570			0.375285	+	0.926909i	$0.377545\pi$
$72$		0			0
$73$	−7.37048			−0.862649			−0.431324	−	0.902197i	$-0.641954\pi$
$73$	−7.37048			−0.862649			−0.431324	+	0.902197i	$0.641954\pi$
$74$	−9.09780	−	15.7579i	−1.05760	−	1.83181i
$75$		0			0
$76$	0.241575	−	0.418420i	0.0277106	−	0.0479961i
$77$	−9.19274	+	15.9223i	−1.04761	+	1.81451i
$78$		0			0
$79$	5.95876	+	10.3209i	0.670413	+	1.16119i	0.977787	+	0.209601i	$0.0672166\pi$
$79$	5.95876	+	10.3209i	0.670413	+	1.16119i	−0.307374	+	0.951589i	$0.599450\pi$
$80$	3.96467			0.443264
$81$		0			0
$82$	0.222826			0.0246071
$83$	0.774276	+	1.34108i	0.0849878	+	0.147203i	0.905386	−	0.424589i	$-0.139582\pi$
$83$	0.774276	+	1.34108i	0.0849878	+	0.147203i	−0.820398	+	0.571793i	$0.806248\pi$
$84$		0			0
$85$	−3.98473	+	6.90175i	−0.432205	+	0.748600i
$86$	9.54427	−	16.5312i	1.02918	−	1.78260i
$87$		0			0
$88$	−11.4068	−	19.7571i	−1.21597	−	2.10612i
$89$	3.59499			0.381068			0.190534	−	0.981681i	$-0.438978\pi$
$89$	3.59499			0.381068			0.190534	+	0.981681i	$0.438978\pi$
$90$		0			0
$91$	3.93452			0.412450
$92$	0.655346	+	1.13509i	0.0683245	+	0.118342i
$93$		0			0
$94$	14.1706	−	24.5442i	1.46159	−	2.53154i
$95$	0.0604829	−	0.104759i	0.00620542	−	0.0107481i
$96$		0			0
$97$	−2.63979	−	4.57224i	−0.268030	−	0.464241i	0.700323	−	0.713826i	$-0.253039\pi$
$97$	−2.63979	−	4.57224i	−0.268030	−	0.464241i	−0.968353	+	0.249585i	$0.919706\pi$
$98$	−20.7626			−2.09734
$99$		0			0
$100$	3.99411			0.399411
$101$	−0.178545	−	0.309250i	−0.0177659	−	0.0307715i	0.857006	−	0.515307i	$-0.172322\pi$
$101$	−0.178545	−	0.309250i	−0.0177659	−	0.0307715i	−0.874772	+	0.484535i	$0.838989\pi$
$102$		0			0
$103$	2.30623	−	3.99450i	0.227239	−	0.393590i	−0.729750	−	0.683714i	$-0.760363\pi$
$103$	2.30623	−	3.99450i	0.227239	−	0.393590i	0.956989	+	0.290125i	$0.0936968\pi$
$104$	−2.44107	+	4.22806i	−0.239367	+	0.414595i
$105$		0			0
$106$	13.6837	+	23.7009i	1.32908	+	2.30203i
$107$	−1.48003			−0.143080			−0.0715399	−	0.997438i	$-0.522791\pi$
$107$	−1.48003			−0.143080			−0.0715399	+	0.997438i	$0.522791\pi$
$108$		0			0
$109$	−14.6820			−1.40628			−0.703140	−	0.711051i	$-0.748219\pi$
$109$	−14.6820			−1.40628			−0.703140	+	0.711051i	$0.748219\pi$
$110$	−5.72025	−	9.90777i	−0.545405	−	0.944669i
$111$		0			0
$112$	7.79954	−	13.5092i	0.736987	−	1.27650i
$113$	3.53690	−	6.12609i	0.332724	−	0.576294i	−0.650321	−	0.759659i	$-0.725366\pi$
$113$	3.53690	−	6.12609i	0.332724	−	0.576294i	0.983045	+	0.183365i	$0.0586991\pi$
$114$		0			0
$115$	0.164078	+	0.284192i	0.0153004	+	0.0265010i
$116$	1.09009			0.101212
$117$		0			0
$118$	13.6017			1.25214
$119$	15.6780	+	27.1551i	1.43720	+	2.48930i
$120$		0			0
$121$	−5.41783	+	9.38396i	−0.492530	+	0.853087i
$122$	16.2387	−	28.1263i	1.47019	−	2.54644i
$123$		0			0
$124$	13.1329	+	22.7468i	1.17937	+	2.04272i
$125$	1.00000			0.0894427
$126$		0			0
$127$	1.23715			0.109779			0.0548896	−	0.998492i	$-0.482519\pi$
$127$	1.23715			0.109779			0.0548896	+	0.998492i	$0.482519\pi$
$128$	−9.82175	−	17.0118i	−0.868128	−	1.50364i
$129$		0			0
$130$	−1.22414	+	2.12028i	−0.107364	+	0.185961i
$131$	6.37638	−	11.0442i	0.557107	−	0.964938i	−0.440629	−	0.897689i	$-0.645245\pi$
$131$	6.37638	−	11.0442i	0.557107	−	0.964938i	0.997736	−	0.0672484i	$-0.0214220\pi$
$132$		0			0
$133$	−0.237971	−	0.412178i	−0.0206347	−	0.0357404i
$134$	−16.7007			−1.44272
$135$		0			0
$136$	−38.9080			−3.33634
$137$	3.66450	+	6.34709i	0.313079	+	0.542269i	0.979027	−	0.203729i	$-0.0653062\pi$
$137$	3.66450	+	6.34709i	0.313079	+	0.542269i	−0.665948	+	0.745998i	$0.731973\pi$
$138$		0			0
$139$	8.42736	−	14.5966i	0.714799	−	1.23807i	−0.248237	−	0.968699i	$-0.579851\pi$
$139$	8.42736	−	14.5966i	0.714799	−	1.23807i	0.963037	−	0.269370i	$-0.0868154\pi$
$140$	7.85745	−	13.6095i	0.664075	−	1.15021i
$141$		0			0
$142$	7.74199	+	13.4095i	0.649694	+	1.12530i
$143$	4.67286			0.390765
$144$		0			0
$145$	0.272925			0.0226652
$146$	−9.02252	−	15.6275i	−0.746709	−	1.29334i
$147$		0			0
$148$	14.8421	−	25.7072i	1.22001	−	2.11312i
$149$	−4.11039	+	7.11941i	−0.336737	+	0.583245i	−0.983817	−	0.179177i	$-0.942657\pi$
$149$	−4.11039	+	7.11941i	−0.336737	+	0.583245i	0.647080	+	0.762422i	$0.275990\pi$
$150$		0			0
$151$	−7.70059	−	13.3378i	−0.626665	−	1.08542i	−0.988216	−	0.153063i	$-0.951086\pi$
$151$	−7.70059	−	13.3378i	−0.626665	−	1.08542i	0.361551	−	0.932352i	$-0.382247\pi$
$152$	0.590572			0.0479017
$153$		0			0
$154$	−45.0129			−3.62725
$155$	3.28806	+	5.69509i	0.264103	+	0.457440i
$156$		0			0
$157$	10.0899	−	17.4763i	0.805264	−	1.39476i	−0.110848	−	0.993837i	$-0.535357\pi$
$157$	10.0899	−	17.4763i	0.805264	−	1.39476i	0.916112	−	0.400921i	$-0.131310\pi$
$158$	−14.5888	+	25.2685i	−1.16062	+	2.01025i
$159$		0			0
$160$	−0.0288185	−	0.0499151i	−0.00227830	−	0.00394614i
$161$	1.29114			0.101756
$162$		0			0
$163$	8.27259			0.647959			0.323980	−	0.946064i	$-0.394979\pi$
$163$	8.27259			0.647959			0.323980	+	0.946064i	$0.394979\pi$
$164$	0.181758	+	0.314814i	0.0141929	+	0.0245829i
$165$		0			0
$166$	−1.89565	+	3.28336i	−0.147131	+	0.254838i
$167$	−6.81626	+	11.8061i	−0.527458	+	0.913584i	0.472030	+	0.881583i	$0.343521\pi$
$167$	−6.81626	+	11.8061i	−0.527458	+	0.913584i	−0.999488	+	0.0320015i	$0.989812\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−19.5115			−1.49646
$171$		0			0
$172$	31.1408			2.37446
$173$	1.73239	+	3.00059i	0.131711	+	0.228130i	0.924336	−	0.381579i	$-0.124620\pi$
$173$	1.73239	+	3.00059i	0.131711	+	0.228130i	−0.792625	+	0.609709i	$0.791286\pi$
$174$		0			0
$175$	1.96726	−	3.40740i	0.148711	−	0.257575i
$176$	9.26318	−	16.0443i	0.698239	−	1.20938i
$177$		0			0
$178$	4.40078	+	7.62237i	0.329852	+	0.571321i
$179$	6.80739			0.508808			0.254404	−	0.967098i	$-0.418121\pi$
$179$	6.80739			0.508808			0.254404	+	0.967098i	$0.418121\pi$
$180$		0			0
$181$	−8.23721			−0.612267			−0.306133	−	0.951989i	$-0.599035\pi$
$181$	−8.23721			−0.612267			−0.306133	+	0.951989i	$0.599035\pi$
$182$	4.81642	+	8.34228i	0.357017	+	0.618371i
$183$		0			0
$184$	−0.801054	+	1.38747i	−0.0590544	+	0.102285i
$185$	3.71599	−	6.43628i	0.273205	−	0.473205i
$186$		0			0
$187$	18.6201	+	32.2510i	1.36164	+	2.35842i
$188$	46.2356			3.37208
$189$		0			0
$190$	0.296159			0.0214856
$191$	8.86345	+	15.3519i	0.641337	+	1.11083i	0.985135	+	0.171784i	$0.0549531\pi$
$191$	8.86345	+	15.3519i	0.641337	+	1.11083i	−0.343798	+	0.939044i	$0.611714\pi$
$192$		0			0
$193$	−5.80167	+	10.0488i	−0.417613	+	0.723328i	−0.995699	−	0.0926485i	$-0.970467\pi$
$193$	−5.80167	+	10.0488i	−0.417613	+	0.723328i	0.578085	+	0.815976i	$0.303800\pi$
$194$	6.46295	−	11.1942i	0.464013	−	0.803694i
$195$		0			0
$196$	−16.9359	−	29.3339i	−1.20971	−	2.09528i
$197$	−2.00369			−0.142757			−0.0713783	−	0.997449i	$-0.522740\pi$
$197$	−2.00369			−0.142757			−0.0713783	+	0.997449i	$0.522740\pi$
$198$		0			0
$199$	11.2572			0.798004			0.399002	−	0.916950i	$-0.369357\pi$
$199$	11.2572			0.798004			0.399002	+	0.916950i	$0.369357\pi$
$200$	2.44107	+	4.22806i	0.172610	+	0.298969i
$201$		0			0
$202$	0.437130	−	0.757132i	0.0307564	−	0.0532716i
$203$	0.536915	−	0.929964i	0.0376840	−	0.0652707i
$204$		0			0
$205$	0.0455066	+	0.0788197i	0.00317832	+	0.00550501i
$206$	11.2926			0.786793
$207$		0			0
$208$	−3.96467			−0.274900
$209$	−0.282628	−	0.489527i	−0.0195498	−	0.0338613i
$210$		0			0
$211$	2.43205	−	4.21244i	0.167429	−	0.289996i	−0.770086	−	0.637940i	$-0.779787\pi$
$211$	2.43205	−	4.21244i	0.167429	−	0.289996i	0.937515	+	0.347944i	$0.113120\pi$
$212$	−22.3234	+	38.6653i	−1.53318	+	2.65555i
$213$		0			0
$214$	−1.81177	−	3.13807i	−0.123850	−	0.214514i
$215$	7.79669			0.531730
$216$		0			0
$217$	25.8739			1.75643
$218$	−17.9729	−	31.1299i	−1.21728	−	2.10838i
$219$		0			0
$220$	9.33196	−	16.1634i	0.629160	−	1.08974i
$221$	3.98473	−	6.90175i	0.268042	−	0.464262i
$222$		0			0
$223$	7.04118	+	12.1957i	0.471513	+	0.816684i	0.999469	−	0.0325878i	$-0.0103749\pi$
$223$	7.04118	+	12.1957i	0.471513	+	0.816684i	−0.527956	+	0.849272i	$0.677042\pi$
$224$	−0.226774			−0.0151520
$225$		0			0
$226$	17.3187			1.15202
$227$	−3.98166	−	6.89644i	−0.264272	−	0.457733i	0.703101	−	0.711090i	$-0.251798\pi$
$227$	−3.98166	−	6.89644i	−0.264272	−	0.457733i	−0.967373	+	0.253358i	$0.918465\pi$
$228$		0			0
$229$	−6.81425	+	11.8026i	−0.450298	+	0.779940i	−0.998404	−	0.0564691i	$-0.982016\pi$
$229$	−6.81425	+	11.8026i	−0.450298	+	0.779940i	0.548106	+	0.836409i	$0.315349\pi$
$230$	−0.401711	+	0.695783i	−0.0264880	+	0.0458786i
$231$		0			0
$232$	0.666230	+	1.15394i	0.0437401	+	0.0757601i
$233$	−6.76769			−0.443366			−0.221683	−	0.975119i	$-0.571155\pi$
$233$	−6.76769			−0.443366			−0.221683	+	0.975119i	$0.571155\pi$
$234$		0			0
$235$	11.5760			0.755132
$236$	11.0948	+	19.2168i	0.722211	+	1.25091i
$237$		0			0
$238$	−38.3842	+	66.4834i	−2.48808	+	4.30948i
$239$	12.7338	−	22.0556i	0.823681	−	1.42666i	−0.0792425	−	0.996855i	$-0.525250\pi$
$239$	12.7338	−	22.0556i	0.823681	−	1.42666i	0.902923	−	0.429802i	$-0.141417\pi$
$240$		0			0
$241$	10.0813	+	17.4613i	0.649392	+	1.12478i	0.983268	+	0.182163i	$0.0583098\pi$
$241$	10.0813	+	17.4613i	0.649392	+	1.12478i	−0.333877	+	0.942617i	$0.608357\pi$
$242$	−26.5288			−1.70534
$243$		0			0
$244$	52.9834			3.39191
$245$	−4.24023	−	7.34429i	−0.270898	−	0.469210i
$246$		0			0
$247$	−0.0604829	+	0.104759i	−0.00384844	+	0.00666569i
$248$	−16.0528	+	27.8042i	−1.01935	+	1.76557i
$249$		0			0
$250$	1.22414	+	2.12028i	0.0774216	+	0.134098i
$251$	−22.3167			−1.40862			−0.704308	−	0.709894i	$-0.748743\pi$
$251$	−22.3167			−1.40862			−0.704308	+	0.709894i	$0.748743\pi$
$252$		0			0
$253$	1.53343			0.0964060
$254$	1.51445	+	2.62310i	0.0950249	+	0.164588i
$255$		0			0
$256$	15.9760	−	27.6713i	0.998500	−	1.72945i
$257$	−1.72736	+	2.99187i	−0.107750	+	0.186628i	−0.914858	−	0.403775i	$-0.867698\pi$
$257$	−1.72736	+	2.99187i	−0.107750	+	0.186628i	0.807109	+	0.590403i	$0.201031\pi$
$258$		0			0
$259$	−14.6206	−	25.3237i	−0.908482	−	1.57354i
$260$	−3.99411			−0.247704
$261$		0			0
$262$	31.2224			1.92893
$263$	7.48718	+	12.9682i	0.461680	+	0.799652i	0.999045	−	0.0436971i	$-0.0139137\pi$
$263$	7.48718	+	12.9682i	0.461680	+	0.799652i	−0.537365	+	0.843350i	$0.680580\pi$
$264$		0			0
$265$	−5.58909	+	9.68059i	−0.343335	+	0.594674i
$266$	0.582622	−	1.00913i	0.0357228	−	0.0618738i
$267$		0			0
$268$	−13.6227	−	23.5951i	−0.832137	−	1.44130i
$269$	−10.5996			−0.646269			−0.323135	−	0.946353i	$-0.604737\pi$
$269$	−10.5996			−0.646269			−0.323135	+	0.946353i	$0.604737\pi$
$270$		0			0
$271$	−9.73751			−0.591512			−0.295756	−	0.955264i	$-0.595571\pi$
$271$	−9.73751			−0.591512			−0.295756	+	0.955264i	$0.595571\pi$
$272$	−15.7981	−	27.3632i	−0.957903	−	1.65914i
$273$		0			0
$274$	−8.97173	+	15.5395i	−0.542002	+	0.938776i
$275$	2.33643	−	4.04682i	0.140892	−	0.244032i
$276$		0			0
$277$	5.52080	+	9.56230i	0.331713	+	0.574543i	0.982848	−	0.184419i	$-0.0590403\pi$
$277$	5.52080	+	9.56230i	0.331713	+	0.574543i	−0.651135	+	0.758962i	$0.725707\pi$
$278$	41.2652			2.47492
$279$		0			0
$280$	19.2089			1.14795
$281$	−10.6532	−	18.4519i	−0.635519	−	1.10075i	−0.986405	−	0.164333i	$-0.947453\pi$
$281$	−10.6532	−	18.4519i	−0.635519	−	1.10075i	0.350886	−	0.936418i	$-0.385880\pi$
$282$		0			0
$283$	1.63526	−	2.83235i	0.0972060	−	0.168366i	−0.813321	−	0.581815i	$-0.802343\pi$
$283$	1.63526	−	2.83235i	0.0972060	−	0.168366i	0.910527	+	0.413449i	$0.135676\pi$
$284$	−12.6302	+	21.8761i	−0.749464	+	1.29811i
$285$		0			0
$286$	5.72025	+	9.90777i	0.338246	+	0.585859i
$287$	0.358093			0.0211376
$288$		0			0
$289$	46.5123			2.73602
$290$	0.334099	+	0.578677i	0.0196190	+	0.0339811i
$291$		0			0
$292$	14.7192	−	25.4945i	0.861378	−	1.49195i
$293$	−14.4984	+	25.1119i	−0.847004	+	1.46705i	0.0368649	+	0.999320i	$0.488263\pi$
$293$	−14.4984	+	25.1119i	−0.847004	+	1.46705i	−0.883869	+	0.467734i	$0.845070\pi$
$294$		0			0
$295$	2.77780	+	4.81129i	0.161730	+	0.280124i
$296$	36.2840			2.10896
$297$		0			0
$298$	−20.1268			−1.16592
$299$	−0.164078	−	0.284192i	−0.00948889	−	0.0164352i
$300$		0			0
$301$	15.3381	−	26.5664i	0.884075	−	1.53126i
$302$	18.8532	−	32.6548i	1.08488	−	1.87907i
$303$		0			0
$304$	0.239795	+	0.415337i	0.0137532	+	0.0238212i
$305$	13.2654			0.759574
$306$		0			0
$307$	7.67485			0.438027			0.219013	−	0.975722i	$-0.429716\pi$
$307$	7.67485			0.438027			0.219013	+	0.975722i	$0.429716\pi$
$308$	−36.7168	−	63.5953i	−2.09213	−	3.62368i
$309$		0			0
$310$	−8.05011	+	13.9432i	−0.457216	+	0.791921i
$311$	−3.29475	+	5.70667i	−0.186828	+	0.323596i	−0.944191	−	0.329399i	$-0.893154\pi$
$311$	−3.29475	+	5.70667i	−0.186828	+	0.323596i	0.757363	+	0.652994i	$0.226487\pi$
$312$		0			0
$313$	4.06651	+	7.04341i	0.229853	+	0.398117i	0.957764	−	0.287554i	$-0.0928422\pi$
$313$	4.06651	+	7.04341i	0.229853	+	0.398117i	−0.727911	+	0.685671i	$0.759509\pi$
$314$	49.4061			2.78815
$315$		0			0
$316$	−47.5999			−2.67770
$317$	11.6731	+	20.2183i	0.655624	+	1.13557i	0.981737	+	0.190243i	$0.0609277\pi$
$317$	11.6731	+	20.2183i	0.655624	+	1.13557i	−0.326113	+	0.945331i	$0.605739\pi$
$318$		0			0
$319$	0.637671	−	1.10448i	0.0357027	−	0.0618389i
$320$	4.03523	−	6.98922i	0.225576	−	0.390709i
$321$		0			0
$322$	1.58054	+	2.73757i	0.0880800	+	0.152559i
$323$	−0.964032			−0.0536402
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	10.1268	+	17.5402i	0.560874	+	0.971462i
$327$		0			0
$328$	−0.222170	+	0.384809i	−0.0122673	+	0.0212475i
$329$	22.7729	−	39.4438i	1.25551	−	2.17461i
$330$		0			0
$331$	2.24022	+	3.88018i	0.123134	+	0.213274i	0.921002	−	0.389558i	$-0.127372\pi$
$331$	2.24022	+	3.88018i	0.123134	+	0.213274i	−0.797868	+	0.602832i	$0.794039\pi$
$332$	−6.18508			−0.339450
$333$		0			0
$334$	−33.3763			−1.82627
$335$	−3.41069	−	5.90749i	−0.186346	−	0.322761i
$336$		0			0
$337$	2.32337	−	4.02420i	0.126562	−	0.219212i	−0.795780	−	0.605585i	$-0.792939\pi$
$337$	2.32337	−	4.02420i	0.126562	−	0.219212i	0.922342	+	0.386373i	$0.126272\pi$
$338$	1.22414	−	2.12028i	0.0665846	−	0.115328i
$339$		0			0
$340$	−15.9154	−	27.5663i	−0.863135	−	1.49499i
$341$	30.7293			1.66409
$342$		0			0
$343$	−5.82489			−0.314514
$344$	19.0323	+	32.9649i	1.02615	+	1.77735i
$345$		0			0
$346$	−4.24139	+	7.34630i	−0.228018	+	0.394939i
$347$	−2.21262	+	3.83236i	−0.118779	+	0.205732i	−0.919284	−	0.393594i	$-0.871231\pi$
$347$	−2.21262	+	3.83236i	−0.118779	+	0.205732i	0.800505	+	0.599326i	$0.204565\pi$
$348$		0			0
$349$	0.00675754	+	0.0117044i	0.000361723	+	0.000626522i	0.866206	−	0.499687i	$-0.166552\pi$
$349$	0.00675754	+	0.0117044i	0.000361723	+	0.000626522i	−0.865844	+	0.500313i	$0.833218\pi$
$350$	9.63283			0.514897
$351$		0			0
$352$	−0.269330			−0.0143553
$353$	14.8536	+	25.7272i	0.790578	+	1.36932i	0.925609	+	0.378481i	$0.123553\pi$
$353$	14.8536	+	25.7272i	0.790578	+	1.36932i	−0.135031	+	0.990841i	$0.543113\pi$
$354$		0			0
$355$	−3.16221	+	5.47711i	−0.167833	+	0.290695i
$356$	−7.17938	+	12.4351i	−0.380506	+	0.659056i
$357$		0			0
$358$	8.33322	+	14.4336i	0.440425	+	0.762838i
$359$	−35.9145			−1.89550			−0.947748	−	0.319020i	$-0.896646\pi$
$359$	−35.9145			−1.89550			−0.947748	+	0.319020i	$0.896646\pi$
$360$		0			0
$361$	−18.9854			−0.999230
$362$	−10.0835	−	17.4652i	−0.529978	−	0.917949i
$363$		0			0
$364$	−7.85745	+	13.6095i	−0.411842	+	0.713331i
$365$	3.68524	−	6.38302i	0.192894	−	0.334103i
$366$		0			0
$367$	−1.47986	−	2.56319i	−0.0772481	−	0.133798i	0.824814	−	0.565405i	$-0.191280\pi$
$367$	−1.47986	−	2.56319i	−0.0772481	−	0.133798i	−0.902062	+	0.431607i	$0.857947\pi$
$368$	−1.30103			−0.0678210
$369$		0			0
$370$	18.1956			0.945945
$371$	21.9904	+	38.0885i	1.14169	+	1.97746i
$372$		0			0
$373$	−2.28220	+	3.95289i	−0.118168	+	0.204673i	−0.919042	−	0.394160i	$-0.871035\pi$
$373$	−2.28220	+	3.95289i	−0.118168	+	0.204673i	0.800874	+	0.598833i	$0.204369\pi$
$374$	−45.5873	+	78.9596i	−2.35726	+	4.08290i
$375$		0			0
$376$	28.2577	+	48.9438i	1.45728	+	2.52408i
$377$	−0.272925			−0.0140564
$378$		0			0
$379$	−22.9852			−1.18067			−0.590336	−	0.807158i	$-0.701005\pi$
$379$	−22.9852			−1.18067			−0.590336	+	0.807158i	$0.701005\pi$
$380$	0.241575	+	0.418420i	0.0123925	+	0.0214645i
$381$		0			0
$382$	−21.7003	+	37.5860i	−1.11028	+	1.92306i
$383$	4.60271	−	7.97213i	0.235187	−	0.407357i	−0.724140	−	0.689653i	$-0.757763\pi$
$383$	4.60271	−	7.97213i	0.235187	−	0.407357i	0.959327	+	0.282297i	$0.0910963\pi$
$384$		0			0
$385$	−9.19274	−	15.9223i	−0.468505	−	0.811475i
$386$	−28.4083			−1.44594
$387$		0			0
$388$	21.0872			1.07054
$389$	−13.0121	−	22.5376i	−0.659738	−	1.14270i	−0.980683	−	0.195603i	$-0.937334\pi$
$389$	−13.0121	−	22.5376i	−0.659738	−	1.14270i	0.320945	−	0.947098i	$-0.396000\pi$
$390$		0			0
$391$	1.30762	−	2.26486i	0.0661289	−	0.114539i
$392$	20.7014	−	35.8559i	1.04558	−	1.81100i
$393$		0			0
$394$	−2.45280	−	4.24837i	−0.123570	−	0.214030i
$395$	−11.9175			−0.599636
$396$		0			0
$397$	−32.0420			−1.60814			−0.804071	−	0.594533i	$-0.797337\pi$
$397$	−32.0420			−1.60814			−0.804071	+	0.594533i	$0.797337\pi$
$398$	13.7805	+	23.8685i	0.690752	+	1.19642i
$399$		0			0
$400$	−1.98233	+	3.43350i	−0.0991167	+	0.171675i
$401$	0.412295	−	0.714116i	0.0205890	−	0.0356612i	−0.855547	−	0.517725i	$-0.826779\pi$
$401$	0.412295	−	0.714116i	0.0205890	−	0.0356612i	0.876136	+	0.482063i	$0.160113\pi$
$402$		0			0
$403$	−3.28806	−	5.69509i	−0.163790	−	0.283692i
$404$	1.42626			0.0709590
$405$		0			0
$406$	2.62904			0.130477
$407$	−17.3643	−	30.0759i	−0.860717	−	1.49081i
$408$		0			0
$409$	−14.1096	+	24.4385i	−0.697675	+	1.20841i	0.271596	+	0.962411i	$0.412449\pi$
$409$	−14.1096	+	24.4385i	−0.697675	+	1.20841i	−0.969271	+	0.245997i	$0.920885\pi$
$410$	−0.111413	+	0.192973i	−0.00550231	+	0.00953027i
$411$		0			0
$412$	9.21131	+	15.9545i	0.453809	+	0.786019i
$413$	21.8586			1.07559
$414$		0			0
$415$	−1.54855			−0.0760154
$416$	0.0288185	+	0.0499151i	0.00141294	+	0.00244729i
$417$		0			0
$418$	0.691955	−	1.19850i	0.0338446	−	0.0586206i
$419$	12.4112	−	21.4968i	0.606327	−	1.05019i	−0.385514	−	0.922702i	$-0.625976\pi$
$419$	12.4112	−	21.4968i	0.606327	−	1.05019i	0.991840	−	0.127486i	$-0.0406909\pi$
$420$		0			0
$421$	−16.4032	−	28.4112i	−0.799444	−	1.38468i	−0.919978	−	0.391969i	$-0.871794\pi$
$421$	−16.4032	−	28.4112i	−0.799444	−	1.38468i	0.120534	−	0.992709i	$-0.461539\pi$
$422$	11.9087			0.579707
$423$		0			0
$424$	−54.5735			−2.65032
$425$	−3.98473	−	6.90175i	−0.193288	−	0.334784i
$426$		0			0
$427$	26.0965	−	45.2004i	1.26290	−	2.18740i
$428$	2.95570	−	5.11942i	0.142869	−	0.247456i
$429$		0			0
$430$	9.54427	+	16.5312i	0.460265	+	0.797203i
$431$	−4.17377			−0.201043			−0.100522	−	0.994935i	$-0.532051\pi$
$431$	−4.17377			−0.201043			−0.100522	+	0.994935i	$0.532051\pi$
$432$		0			0
$433$	20.3832			0.979555			0.489777	−	0.871848i	$-0.337078\pi$
$433$	20.3832			0.979555			0.489777	+	0.871848i	$0.337078\pi$
$434$	31.6733	+	54.8598i	1.52037	+	2.63336i
$435$		0			0
$436$	29.3207	−	50.7850i	1.40421	−	2.43216i
$437$	−0.0198479	+	0.0343775i	−0.000949452	+	0.00164450i
$438$		0			0
$439$	−9.11140	−	15.7814i	−0.434864	−	0.753206i	0.562421	−	0.826851i	$-0.309870\pi$
$439$	−9.11140	−	15.7814i	−0.434864	−	0.753206i	−0.997284	+	0.0736453i	$0.976537\pi$
$440$	22.8136			1.08760
$441$		0			0
$442$	19.5115			0.928068
$443$	3.47615	+	6.02087i	0.165157	+	0.286060i	0.936711	−	0.350104i	$-0.113854\pi$
$443$	3.47615	+	6.02087i	0.165157	+	0.286060i	−0.771554	+	0.636164i	$0.780520\pi$
$444$		0			0
$445$	−1.79749	+	3.11335i	−0.0852094	+	0.147587i
$446$	−17.2388	+	29.8585i	−0.816282	+	1.41384i
$447$		0			0
$448$	−15.8767	−	27.4992i	−0.750103	−	1.29922i
$449$	−13.6819			−0.645687			−0.322843	−	0.946452i	$-0.604639\pi$
$449$	−13.6819			−0.645687			−0.322843	+	0.946452i	$0.604639\pi$
$450$		0			0
$451$	0.425292			0.0200262
$452$	14.1268	+	24.4683i	0.664466	+	1.15089i
$453$		0			0
$454$	9.74825	−	16.8845i	0.457508	−	0.792427i
$455$	−1.96726	+	3.40740i	−0.0922266	+	0.159741i
$456$		0			0
$457$	−8.41934	−	14.5827i	−0.393840	−	0.682151i	0.599112	−	0.800665i	$-0.295520\pi$
$457$	−8.41934	−	14.5827i	−0.393840	−	0.682151i	−0.992952	+	0.118514i	$0.962187\pi$
$458$	−33.3665			−1.55911
$459$		0			0
$460$	−1.31069			−0.0611113
$461$	−19.6855	−	34.0962i	−0.916844	−	1.58802i	−0.804180	−	0.594386i	$-0.797395\pi$
$461$	−19.6855	−	34.0962i	−0.916844	−	1.58802i	−0.112664	−	0.993633i	$-0.535938\pi$
$462$		0			0
$463$	1.44170	−	2.49710i	0.0670016	−	0.116050i	−0.830579	−	0.556902i	$-0.811990\pi$
$463$	1.44170	−	2.49710i	0.0670016	−	0.116050i	0.897580	+	0.440851i	$0.145323\pi$
$464$	−0.541029	+	0.937090i	−0.0251166	+	0.0435033i
$465$		0			0
$466$	−8.28462	−	14.3494i	−0.383778	−	0.664723i
$467$	−25.1278			−1.16278			−0.581388	−	0.813626i	$-0.697490\pi$
$467$	−25.1278			−1.16278			−0.581388	+	0.813626i	$0.697490\pi$
$468$		0			0
$469$	−26.8389			−1.23930
$470$	14.1706	+	24.5442i	0.653642	+	1.13214i
$471$		0			0
$472$	−13.5616	+	23.4894i	−0.624224	+	1.08119i
$473$	18.2164	−	31.5518i	0.837593	−	1.45075i
$474$		0			0
$475$	0.0604829	+	0.104759i	0.00277515	+	0.00480669i
$476$	−125.239			−5.74033
$477$		0			0
$478$	62.3520			2.85191
$479$	10.7329	+	18.5899i	0.490399	+	0.849396i	0.999939	−	0.0110508i	$-0.00351765\pi$
$479$	10.7329	+	18.5899i	0.490399	+	0.849396i	−0.509540	+	0.860447i	$0.670184\pi$
$480$		0			0
$481$	−3.71599	+	6.43628i	−0.169434	+	0.293469i
$482$	−24.6818	+	42.7502i	−1.12423	+	1.94722i
$483$		0			0
$484$	−21.6394	−	37.4805i	−0.983608	−	1.70366i
$485$	5.27957			0.239733
$486$		0			0
$487$	−32.0627			−1.45290			−0.726450	−	0.687220i	$-0.758831\pi$
$487$	−32.0627			−1.45290			−0.726450	+	0.687220i	$0.758831\pi$
$488$	32.3818	+	56.0869i	1.46585	+	2.53893i
$489$		0			0
$490$	10.3813	−	17.9809i	0.468979	−	0.812295i
$491$	−4.87000	+	8.43508i	−0.219780	+	0.380670i	−0.954741	−	0.297440i	$-0.903867\pi$
$491$	−4.87000	+	8.43508i	−0.219780	+	0.380670i	0.734961	+	0.678110i	$0.237201\pi$
$492$		0			0
$493$	−1.08753	−	1.88366i	−0.0489800	−	0.0848359i
$494$	−0.296159			−0.0133248
$495$		0			0
$496$	−26.0721			−1.17067
$497$	12.4418	+	21.5498i	0.558090	+	0.966640i
$498$		0			0
$499$	−15.8859	+	27.5151i	−0.711149	+	1.23175i	0.253277	+	0.967394i	$0.418491\pi$
$499$	−15.8859	+	27.5151i	−0.711149	+	1.23175i	−0.964426	+	0.264352i	$0.914842\pi$
$500$	−1.99705	+	3.45900i	−0.0893109	+	0.154691i
$501$		0			0
$502$	−27.3188	−	47.3176i	−1.21930	−	2.11189i
$503$	7.30099			0.325535			0.162768	−	0.986664i	$-0.447958\pi$
$503$	7.30099			0.325535			0.162768	+	0.986664i	$0.447958\pi$
$504$		0			0
$505$	0.357091			0.0158903
$506$	1.87714	+	3.25130i	0.0834490	+	0.144538i
$507$		0			0
$508$	−2.47065	+	4.27930i	−0.109617	+	0.189863i
$509$	−5.39561	+	9.34547i	−0.239156	+	0.414231i	−0.960472	−	0.278375i	$-0.910204\pi$
$509$	−5.39561	+	9.34547i	−0.239156	+	0.414231i	0.721316	+	0.692606i	$0.243537\pi$
$510$		0			0
$511$	−14.4996	−	25.1141i	−0.641427	−	1.11098i
$512$	38.9407			1.72095
$513$		0			0
$514$	−8.45813			−0.373072
$515$	2.30623	+	3.99450i	0.101624	+	0.176019i
$516$		0			0
$517$	27.0464	−	46.8458i	1.18950	−	2.06027i
$518$	35.7955	−	61.9996i	1.57276	−	2.72411i
$519$		0			0
$520$	−2.44107	−	4.22806i	−0.107048	−	0.185413i
$521$	3.58465			0.157046			0.0785231	−	0.996912i	$-0.474980\pi$
$521$	3.58465			0.157046			0.0785231	+	0.996912i	$0.474980\pi$
$522$		0			0
$523$	4.70071			0.205548			0.102774	−	0.994705i	$-0.467228\pi$
$523$	4.70071			0.205548			0.102774	+	0.994705i	$0.467228\pi$
$524$	25.4679	+	44.1118i	1.11257	+	1.92703i
$525$		0			0
$526$	−18.3308	+	31.7498i	−0.799260	+	1.38436i
$527$	26.2041	−	45.3868i	1.14147	−	1.97708i
$528$		0			0
$529$	11.4462	+	19.8253i	0.497659	+	0.861971i
$530$	−27.3674			−1.18876
$531$		0			0
$532$	1.90097			0.0824173
$533$	−0.0455066	−	0.0788197i	−0.00197111	−	0.00341406i
$534$		0			0
$535$	0.740014	−	1.28174i	0.0319936	−	0.0554146i
$536$	16.6515	−	28.8412i	0.719235	−	1.24575i
$537$		0			0
$538$	−12.9754	−	22.4741i	−0.559410	−	0.968927i
$539$	−39.6280			−1.70690
$540$		0			0
$541$	31.2736			1.34456			0.672278	−	0.740299i	$-0.265316\pi$
$541$	31.2736			1.34456			0.672278	+	0.740299i	$0.265316\pi$
$542$	−11.9201	−	20.6462i	−0.512013	−	0.886832i
$543$		0			0
$544$	−0.229668	+	0.397796i	−0.00984693	+	0.0170554i
$545$	7.34100	−	12.7150i	0.314454	−	0.544650i
$546$		0			0
$547$	1.72662	+	2.99059i	0.0738249	+	0.127868i	0.900575	−	0.434701i	$-0.143146\pi$
$547$	1.72662	+	2.99059i	0.0738249	+	0.127868i	−0.826750	+	0.562570i	$0.809813\pi$
$548$	−29.2728			−1.25047
$549$		0			0
$550$	11.4405			0.487825
$551$	0.0165073	+	0.0285915i	0.000703235	+	0.00121804i
$552$		0			0
$553$	−23.4449	+	40.6077i	−0.996978	+	1.72682i
$554$	−13.5165	+	23.4113i	−0.574261	+	0.994649i
$555$		0			0
$556$	33.6598	+	58.3004i	1.42749	+	2.47249i
$557$	−12.5254			−0.530720			−0.265360	−	0.964149i	$-0.585491\pi$
$557$	−12.5254			−0.530720			−0.265360	+	0.964149i	$0.585491\pi$
$558$		0			0
$559$	−7.79669			−0.329765
$560$	7.79954	+	13.5092i	0.329591	+	0.570868i
$561$		0			0
$562$	26.0822	−	45.1756i	1.10021	−	1.90562i
$563$	−13.2158	+	22.8905i	−0.556981	+	0.964719i	0.440766	+	0.897622i	$0.354707\pi$
$563$	−13.2158	+	22.8905i	−0.556981	+	0.964719i	−0.997746	+	0.0670966i	$0.978626\pi$
$564$		0			0
$565$	3.53690	+	6.12609i	0.148798	+	0.257727i
$566$	8.00716			0.336566
$567$		0			0
$568$	−30.8767			−1.29556
$569$	11.1862	+	19.3750i	0.468949	+	0.812244i	0.999370	−	0.0354904i	$-0.0112993\pi$
$569$	11.1862	+	19.3750i	0.468949	+	0.812244i	−0.530421	+	0.847735i	$0.677966\pi$
$570$		0			0
$571$	7.47062	−	12.9395i	0.312636	−	0.541501i	−0.666297	−	0.745687i	$-0.732121\pi$
$571$	7.47062	−	12.9395i	0.312636	−	0.541501i	0.978932	+	0.204186i	$0.0654548\pi$
$572$	−9.33196	+	16.1634i	−0.390189	+	0.675827i
$573$		0			0
$574$	0.438358	+	0.759258i	0.0182967	+	0.0316908i
$575$	−0.328157			−0.0136851
$576$		0			0
$577$	−2.65841			−0.110671			−0.0553355	−	0.998468i	$-0.517623\pi$
$577$	−2.65841			−0.110671			−0.0553355	+	0.998468i	$0.517623\pi$
$578$	56.9377	+	98.6190i	2.36830	+	4.10201i
$579$		0			0
$580$	−0.545046	+	0.944047i	−0.0226318	+	0.0391994i
$581$	−3.04640	+	5.27653i	−0.126386	+	0.218907i
$582$		0			0
$583$	26.1171	+	45.2361i	1.08166	+	1.87349i
$584$	35.9837			1.48902
$585$		0			0
$586$	−70.9924			−2.93267
$587$	−5.74909	−	9.95772i	−0.237291	−	0.410999i	0.722645	−	0.691219i	$-0.242926\pi$
$587$	−5.74909	−	9.95772i	−0.237291	−	0.410999i	−0.959936	+	0.280220i	$0.909593\pi$
$588$		0			0
$589$	−0.397743	+	0.688911i	−0.0163887	+	0.0283861i
$590$	−6.80085	+	11.7794i	−0.279986	+	0.484951i
$591$		0			0
$592$	14.7327	+	25.5177i	0.605509	+	1.04877i
$593$	22.0373			0.904964			0.452482	−	0.891774i	$-0.350539\pi$
$593$	22.0373			0.904964			0.452482	+	0.891774i	$0.350539\pi$
$594$		0			0
$595$	−31.3560			−1.28547
$596$	−16.4174	−	28.4357i	−0.672481	−	1.16477i
$597$		0			0
$598$	0.401711	−	0.695783i	0.0164272	−	0.0284527i
$599$	12.0613	−	20.8909i	0.492813	−	0.853577i	−0.507153	−	0.861856i	$-0.669302\pi$
$599$	12.0613	−	20.8909i	0.492813	−	0.853577i	0.999966	+	0.00827908i	$0.00263534\pi$
$600$		0			0
$601$	−0.171419	−	0.296906i	−0.00699232	−	0.0121111i	0.862508	−	0.506043i	$-0.168892\pi$
$601$	−0.171419	−	0.296906i	−0.00699232	−	0.0121111i	−0.869500	+	0.493932i	$0.835559\pi$
$602$	75.1042			3.06102
$603$		0			0
$604$	61.5139			2.50297
$605$	−5.41783	−	9.38396i	−0.220266	−	0.381512i
$606$		0			0
$607$	18.5443	−	32.1196i	0.752688	−	1.30369i	−0.193827	−	0.981036i	$-0.562090\pi$
$607$	18.5443	−	32.1196i	0.752688	−	1.30369i	0.946515	−	0.322659i	$-0.104577\pi$
$608$	0.00348605	−	0.00603802i	0.000141378	−	0.000244874i
$609$		0			0
$610$	16.2387	+	28.1263i	0.657487	+	1.13880i
$611$	−11.5760			−0.468313
$612$		0			0
$613$	38.1878			1.54239			0.771194	−	0.636600i	$-0.219660\pi$
$613$	38.1878			1.54239			0.771194	+	0.636600i	$0.219660\pi$
$614$	9.39511	+	16.2728i	0.379156	+	0.656717i
$615$		0			0
$616$	44.8803	−	77.7349i	1.80828	−	3.13203i
$617$	−6.45863	+	11.1867i	−0.260015	+	0.450359i	−0.966246	−	0.257623i	$-0.917061\pi$
$617$	−6.45863	+	11.1867i	−0.260015	+	0.450359i	0.706231	+	0.707982i	$0.250394\pi$
$618$		0			0
$619$	3.24865	+	5.62683i	0.130574	+	0.226161i	0.923898	−	0.382639i	$-0.124985\pi$
$619$	3.24865	+	5.62683i	0.130574	+	0.226161i	−0.793324	+	0.608800i	$0.791651\pi$
$620$	−26.2657			−1.05486
$621$		0			0
$622$	−16.1330			−0.646873
$623$	7.07228	+	12.2495i	0.283345	+	0.490768i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−9.95599	+	17.2443i	−0.397921	+	0.689220i
$627$		0			0
$628$	40.3003	+	69.8021i	1.60816	+	2.78541i
$629$	−59.2288			−2.36161
$630$		0			0
$631$	−37.1832			−1.48024			−0.740119	−	0.672476i	$-0.765231\pi$
$631$	−37.1832			−1.48024			−0.740119	+	0.672476i	$0.765231\pi$
$632$	−29.0915	−	50.3880i	−1.15720	−	2.00433i
$633$		0			0
$634$	−28.5790	+	49.5002i	−1.13502	+	1.96591i
$635$	−0.618575	+	1.07140i	−0.0245474	+	0.0425173i
$636$		0			0
$637$	4.24023	+	7.34429i	0.168004	+	0.290991i
$638$	3.12240			0.123617
$639$		0			0
$640$	19.6435			0.776478
$641$	20.7912	+	36.0114i	0.821203	+	1.42237i	0.904787	+	0.425865i	$0.140030\pi$
$641$	20.7912	+	36.0114i	0.821203	+	1.42237i	−0.0835833	+	0.996501i	$0.526636\pi$
$642$		0			0
$643$	7.24965	−	12.5568i	0.285898	−	0.495190i	−0.686928	−	0.726725i	$-0.741041\pi$
$643$	7.24965	−	12.5568i	0.285898	−	0.495190i	0.972827	+	0.231535i	$0.0743748\pi$
$644$	−2.57847	+	4.46605i	−0.101606	+	0.175987i
$645$		0			0
$646$	−1.18011	−	2.04402i	−0.0464309	−	0.0804207i
$647$	4.64226			0.182506			0.0912531	−	0.995828i	$-0.470913\pi$
$647$	4.64226			0.182506			0.0912531	+	0.995828i	$0.470913\pi$
$648$		0			0
$649$	25.9606			1.01904
$650$	−1.22414	−	2.12028i	−0.0480148	−	0.0831642i
$651$		0			0
$652$	−16.5208	+	28.6149i	−0.647005	+	1.12065i
$653$	5.28711	−	9.15755i	0.206901	−	0.358362i	−0.743836	−	0.668362i	$-0.766996\pi$
$653$	5.28711	−	9.15755i	0.206901	−	0.358362i	0.950737	+	0.310000i	$0.100329\pi$
$654$		0			0
$655$	6.37638	+	11.0442i	0.249146	+	0.431533i
$656$	−0.360837			−0.0140883
$657$		0			0
$658$	111.509			4.34708
$659$	−15.6513	−	27.1089i	−0.609690	−	1.05601i	−0.991291	−	0.131687i	$-0.957961\pi$
$659$	−15.6513	−	27.1089i	−0.609690	−	1.05601i	0.381602	−	0.924327i	$-0.375373\pi$
$660$		0			0
$661$	6.52034	−	11.2936i	0.253612	−	0.439269i	−0.710906	−	0.703287i	$-0.751715\pi$
$661$	6.52034	−	11.2936i	0.253612	−	0.439269i	0.964518	+	0.264019i	$0.0850480\pi$
$662$	−5.48471	+	9.49979i	−0.213169	+	0.369220i
$663$		0			0
$664$	−3.78012	−	6.54737i	−0.146697	−	0.254087i
$665$	0.475943			0.0184563
$666$		0			0
$667$	−0.0895622			−0.00346786
$668$	−27.2249	−	47.1548i	−1.05336	−	1.82448i
$669$		0			0
$670$	8.35035	−	14.4632i	0.322602	−	0.558763i
$671$	30.9937	−	53.6826i	1.19650	−	2.07240i
$672$		0			0
$673$	6.13953	+	10.6340i	0.236661	+	0.409910i	0.959754	−	0.280841i	$-0.0906134\pi$
$673$	6.13953	+	10.6340i	0.236661	+	0.409910i	−0.723093	+	0.690751i	$0.757280\pi$
$674$	11.3766			0.438209
$675$		0			0
$676$	3.99411			0.153619
$677$	18.1421	+	31.4231i	0.697258	+	1.20769i	0.969413	+	0.245434i	$0.0789303\pi$
$677$	18.1421	+	31.4231i	0.697258	+	1.20769i	−0.272155	+	0.962253i	$0.587736\pi$
$678$		0			0
$679$	10.3863	−	17.9896i	0.398589	−	0.690377i
$680$	19.4540	−	33.6953i	0.746027	−	1.29216i
$681$		0			0
$682$	37.6171	+	65.1547i	1.44043	+	2.49490i
$683$	25.2755			0.967141			0.483571	−	0.875305i	$-0.339340\pi$
$683$	25.2755			0.967141			0.483571	+	0.875305i	$0.339340\pi$
$684$		0			0
$685$	−7.32899			−0.280026
$686$	−7.13050	−	12.3504i	−0.272244	−	0.471540i
$687$		0			0
$688$	−15.4557	+	26.7700i	−0.589241	+	1.02060i
$689$	5.58909	−	9.68059i	0.212928	−	0.368801i
$690$		0			0
$691$	24.3378	+	42.1543i	0.925854	+	1.60363i	0.790181	+	0.612873i	$0.209986\pi$
$691$	24.3378	+	42.1543i	0.925854	+	1.60363i	0.135673	+	0.990754i	$0.456680\pi$
$692$	−13.8387			−0.526068
$693$		0			0
$694$	−10.8342			−0.411262
$695$	8.42736	+	14.5966i	0.319668	+	0.553681i
$696$		0			0
$697$	0.362663	−	0.628151i	0.0137368	−	0.0237929i
$698$	−0.0165444	+	0.0286557i	−0.000626215	+	0.00108464i
$699$		0			0
$700$	7.85745	+	13.6095i	0.296984	+	0.514391i
$701$	−22.9449			−0.866615			−0.433308	−	0.901246i	$-0.642654\pi$
$701$	−22.9449			−0.866615			−0.433308	+	0.901246i	$0.642654\pi$
$702$		0			0
$703$	0.899015			0.0339070
$704$	−18.8561	−	32.6597i	−0.710665	−	1.23091i
$705$		0			0
$706$	−36.3659	+	62.9876i	−1.36865	+	2.37057i
$707$	0.702490	−	1.21675i	0.0264199	−	0.0457606i
$708$		0			0
$709$	11.0072	+	19.0649i	0.413382	+	0.715999i	0.995257	−	0.0972792i	$-0.0310140\pi$
$709$	11.0072	+	19.0649i	0.413382	+	0.715999i	−0.581875	+	0.813278i	$0.697681\pi$
$710$	−15.4840			−0.581104
$711$		0			0
$712$	−17.5512			−0.657761
$713$	−1.07900	−	1.86888i	−0.0404088	−	0.0699901i
$714$		0			0
$715$	−2.33643	+	4.04682i	−0.0873776	+	0.151342i
$716$	−13.5947	+	23.5468i	−0.508059	+	0.879984i
$717$		0			0
$718$	−43.9645	−	76.1488i	−1.64074	−	2.84185i
$719$	−35.7966			−1.33499			−0.667494	−	0.744615i	$-0.732633\pi$
$719$	−35.7966			−1.33499			−0.667494	+	0.744615i	$0.732633\pi$
$720$		0			0
$721$	18.1478			0.675859
$722$	−23.2408	−	40.2543i	−0.864933	−	1.49811i
$723$		0			0
$724$	16.4501	−	28.4925i	0.611364	−	1.05891i
$725$	−0.136463	+	0.236360i	−0.00506809	+	0.00877819i
$726$		0			0
$727$	15.5687	+	26.9657i	0.577410	+	1.00010i	0.995775	+	0.0918250i	$0.0292700\pi$
$727$	15.5687	+	26.9657i	0.577410	+	1.00010i	−0.418365	+	0.908279i	$0.637397\pi$
$728$	−19.2089			−0.711929
$729$		0			0
$730$	18.0450			0.667877
$731$	−31.0677	−	53.8108i	−1.14908	−	1.99027i
$732$		0			0
$733$	11.6605	−	20.1967i	0.430692	−	0.745980i	−0.566241	−	0.824240i	$-0.691603\pi$
$733$	11.6605	−	20.1967i	0.430692	−	0.745980i	0.996933	+	0.0782593i	$0.0249362\pi$
$734$	3.62312	−	6.27543i	0.133732	−	0.231630i
$735$		0			0
$736$	0.00945698	+	0.0163800i	0.000348589	+	0.000603774i
$737$	−31.8754			−1.17415
$738$		0			0
$739$	−23.4244			−0.861682			−0.430841	−	0.902428i	$-0.641783\pi$
$739$	−23.4244			−0.861682			−0.430841	+	0.902428i	$0.641783\pi$
$740$	14.8421	+	25.7072i	0.545605	+	0.945015i
$741$		0			0
$742$	−53.8388	+	93.2516i	−1.97649	+	3.42337i
$743$	19.8360	−	34.3570i	0.727713	−	1.26044i	−0.230135	−	0.973159i	$-0.573917\pi$
$743$	19.8360	−	34.3570i	0.727713	−	1.26044i	0.957848	−	0.287276i	$-0.0927498\pi$
$744$		0			0
$745$	−4.11039	−	7.11941i	−0.150593	−	0.260835i
$746$	−11.1750			−0.409145
$747$		0			0
$748$	−148.741			−5.43852
$749$	−2.91160	−	5.04304i	−0.106388	−	0.184269i
$750$		0			0
$751$	10.5836	−	18.3314i	0.386203	−	0.668922i	−0.605733	−	0.795668i	$-0.707120\pi$
$751$	10.5836	−	18.3314i	0.386203	−	0.668922i	0.991935	+	0.126746i	$0.0404533\pi$
$752$	−22.9474	+	39.7461i	−0.836806	+	1.44939i
$753$		0			0
$754$	−0.334099	−	0.578677i	−0.0121672	−	0.0210742i
$755$	15.4012			0.560506
$756$		0			0
$757$	−6.75801			−0.245624			−0.122812	−	0.992430i	$-0.539191\pi$
$757$	−6.75801			−0.245624			−0.122812	+	0.992430i	$0.539191\pi$
$758$	−28.1372	−	48.7351i	−1.02199	−	1.77014i
$759$		0			0
$760$	−0.295286	+	0.511451i	−0.0107112	+	0.0185523i
$761$	−19.1813	+	33.2229i	−0.695320	+	1.20433i	0.274752	+	0.961515i	$0.411404\pi$
$761$	−19.1813	+	33.2229i	−0.695320	+	1.20433i	−0.970073	+	0.242815i	$0.921929\pi$
$762$		0			0
$763$	−28.8833	−	50.0274i	−1.04565	−	1.81111i
$764$	−70.8031			−2.56157
$765$		0			0
$766$	22.5375			0.814313
$767$	−2.77780	−	4.81129i	−0.100301	−	0.173726i
$768$		0			0
$769$	8.50812	−	14.7365i	0.306811	−	0.531412i	−0.670852	−	0.741591i	$-0.734072\pi$
$769$	8.50812	−	14.7365i	0.306811	−	0.531412i	0.977663	+	0.210180i	$0.0674049\pi$
$770$	22.5065	−	38.9823i	0.811077	−	1.40483i
$771$		0			0
$772$	−23.1725	−	40.1359i	−0.833996	−	1.44452i
$773$	−21.8081			−0.784382			−0.392191	−	0.919884i	$-0.628283\pi$
$773$	−21.8081			−0.784382			−0.392191	+	0.919884i	$0.628283\pi$
$774$		0			0
$775$	−6.57612			−0.236221
$776$	12.8878	+	22.3223i	0.462645	+	0.801325i
$777$		0			0
$778$	31.8573	−	55.1784i	1.14214	−	1.97824i
$779$	−0.00550474	+	0.00953450i	−0.000197228	+	0.000341609i
$780$		0			0
$781$	14.7766	+	25.5938i	0.528747	+	0.915817i
$782$	6.40283			0.228965
$783$		0			0
$784$	33.6222			1.20079
$785$	10.0899	+	17.4763i	0.360125	+	0.623755i
$786$		0			0
$787$	2.41300	−	4.17944i	0.0860141	−	0.148981i	−0.819809	−	0.572637i	$-0.805920\pi$
$787$	2.41300	−	4.17944i	0.0860141	−	0.148981i	0.905823	+	0.423657i	$0.139254\pi$
$788$	4.00147	−	6.93074i	0.142546	−	0.246897i
$789$		0			0
$790$	−14.5888	−	25.2685i	−0.519045	−	0.899012i
$791$	27.8320			0.989592
$792$		0			0
$793$	−13.2654			−0.471068
$794$	−39.2240	−	67.9380i	−1.39201	−	2.41103i
$795$		0			0
$796$	−22.4813	+	38.9387i	−0.796828	+	1.38015i
$797$	12.5729	−	21.7770i	0.445357	−	0.771380i	−0.552720	−	0.833367i	$-0.686410\pi$
$797$	12.5729	−	21.7770i	0.445357	−	0.771380i	0.998077	+	0.0619864i	$0.0197436\pi$
$798$		0			0
$799$	−46.1270	−	79.8944i	−1.63186	−	2.82646i
$800$	0.0576370			0.00203778
$801$		0			0
$802$	2.01883			0.0712874
$803$	−17.2206	−	29.8270i	−0.607702	−	1.05257i
$804$		0			0
$805$	−0.645569	+	1.11816i	−0.0227533	+	0.0394099i
$806$	8.05011	−	13.9432i	0.283553	−	0.491128i
$807$		0			0
$808$	0.871684	+	1.50980i	0.0306657	+	0.0531146i
$809$	51.2155			1.80064			0.900320	−	0.435228i	$-0.143332\pi$
$809$	51.2155			1.80064			0.900320	+	0.435228i	$0.143332\pi$
$810$		0			0
$811$	25.7297			0.903491			0.451745	−	0.892147i	$-0.350802\pi$
$811$	25.7297			0.903491			0.451745	+	0.892147i	$0.350802\pi$
$812$	2.14449	+	3.71437i	0.0752570	+	0.130349i
$813$		0			0
$814$	42.5128	−	73.6343i	1.49007	−	2.58088i
$815$	−4.13630	+	7.16428i	−0.144888	+	0.250954i
$816$		0			0
$817$	0.471567	+	0.816777i	0.0164980	+	0.0285754i
$818$	−69.0887			−2.41563
$819$		0			0
$820$	−0.363516			−0.0126945
$821$	10.6298	+	18.4114i	0.370983	+	0.642561i	0.989717	−	0.143039i	$-0.0456876\pi$
$821$	10.6298	+	18.4114i	0.370983	+	0.642561i	−0.618734	+	0.785600i	$0.712354\pi$
$822$		0			0
$823$	6.19775	−	10.7348i	0.216040	−	0.374192i	−0.737554	−	0.675288i	$-0.764019\pi$
$823$	6.19775	−	10.7348i	0.216040	−	0.374192i	0.953594	+	0.301096i	$0.0973525\pi$
$824$	−11.2593	+	19.5017i	−0.392237	+	0.679374i
$825$		0			0
$826$	26.7581	+	46.3463i	0.931033	+	1.61260i
$827$	41.1108			1.42956			0.714781	−	0.699349i	$-0.246527\pi$
$827$	41.1108			1.42956			0.714781	+	0.699349i	$0.246527\pi$
$828$		0			0
$829$	−28.6599			−0.995400			−0.497700	−	0.867349i	$-0.665822\pi$
$829$	−28.6599			−0.995400			−0.497700	+	0.867349i	$0.665822\pi$
$830$	−1.89565	−	3.28336i	−0.0657989	−	0.113967i
$831$		0			0
$832$	−4.03523	+	6.98922i	−0.139896	+	0.242307i
$833$	−33.7923	+	58.5300i	−1.17083	+	2.02795i
$834$		0			0
$835$	−6.81626	−	11.8061i	−0.235886	−	0.408567i
$836$	2.25770			0.0780840
$837$		0			0
$838$	60.7723			2.09934
$839$	−17.2695	−	29.9116i	−0.596209	−	1.03266i	−0.993375	−	0.114917i	$-0.963340\pi$
$839$	−17.2695	−	29.9116i	−0.596209	−	1.03266i	0.397166	−	0.917747i	$-0.369994\pi$
$840$		0			0
$841$	14.4628	−	25.0502i	0.498716	−	0.863801i
$842$	40.1598	−	69.5588i	1.38400	−	2.39716i
$843$		0			0
$844$	9.71387	+	16.8249i	0.334365	+	0.579137i
$845$	1.00000			0.0344010
$846$		0			0
$847$	−42.6331			−1.46489
$848$	−22.1589	−	38.3804i	−0.760940	−	1.31799i
$849$		0			0
$850$	9.75576	−	16.8975i	0.334620	−	0.579578i
$851$	−1.21943	+	2.11211i	−0.0418014	+	0.0724021i
$852$		0			0
$853$	14.2168	+	24.6243i	0.486775	+	0.843119i	0.999884	−	0.0152040i	$-0.00483976\pi$
$853$	14.2168	+	24.6243i	0.486775	+	0.843119i	−0.513109	+	0.858323i	$0.671506\pi$
$854$	127.783			4.37266
$855$		0			0
$856$	7.22571			0.246970
$857$	10.8757	+	18.8373i	0.371507	+	0.643468i	0.989798	−	0.142481i	$-0.0455080\pi$
$857$	10.8757	+	18.8373i	0.371507	+	0.643468i	−0.618291	+	0.785949i	$0.712175\pi$
$858$		0			0
$859$	1.93271	−	3.34755i	0.0659431	−	0.114217i	−0.831169	−	0.556020i	$-0.812328\pi$
$859$	1.93271	−	3.34755i	0.0659431	−	0.114217i	0.897112	+	0.441803i	$0.145661\pi$
$860$	−15.5704	+	26.9687i	−0.530946	+	0.919626i
$861$		0			0
$862$	−5.10929	−	8.84956i	−0.174023	−	0.301417i
$863$	−10.1359			−0.345030			−0.172515	−	0.985007i	$-0.555189\pi$
$863$	−10.1359			−0.345030			−0.172515	+	0.985007i	$0.555189\pi$
$864$		0			0
$865$	−3.46478			−0.117806
$866$	24.9520	+	43.2181i	0.847902	+	1.46861i
$867$		0			0
$868$	−51.6715	+	89.4977i	−1.75385	+	3.03775i
$869$	−27.8445	+	48.2281i	−0.944560	+	1.63603i
$870$		0			0
$871$	3.41069	+	5.90749i	0.115567	+	0.200168i
$872$	71.6796			2.42738
$873$		0			0
$874$	−0.0971865			−0.00328738
$875$	1.96726	+	3.40740i	0.0665055	+	0.115191i
$876$		0			0
$877$	−9.94057	+	17.2176i	−0.335669	+	0.581396i	−0.983613	−	0.180292i	$-0.942296\pi$
$877$	−9.94057	+	17.2176i	−0.335669	+	0.581396i	0.647944	+	0.761688i	$0.275629\pi$
$878$	22.3073	−	38.6374i	0.752836	−	1.30395i
$879$		0			0
$880$	9.26318	+	16.0443i	0.312262	+	0.540853i
$881$	21.4750			0.723511			0.361755	−	0.932273i	$-0.382178\pi$
$881$	21.4750			0.723511			0.361755	+	0.932273i	$0.382178\pi$
$882$		0			0
$883$	−32.0639			−1.07904			−0.539519	−	0.841974i	$-0.681394\pi$
$883$	−32.0639			−1.07904			−0.539519	+	0.841974i	$0.681394\pi$
$884$	15.9154	+	27.5663i	0.535294	+	0.927156i
$885$		0			0
$886$	−8.51061	+	14.7408i	−0.285920	+	0.495227i
$887$	−3.77758	+	6.54296i	−0.126839	+	0.219691i	−0.922450	−	0.386116i	$-0.873816\pi$
$887$	−3.77758	+	6.54296i	−0.126839	+	0.219691i	0.795611	+	0.605807i	$0.207150\pi$
$888$		0			0
$889$	2.43379	+	4.21546i	0.0816269	+	0.141382i
$890$	−8.80156			−0.295029
$891$		0			0
$892$	−56.2465			−1.88327
$893$	0.700147	+	1.21269i	0.0234295	+	0.0405811i
$894$		0			0
$895$	−3.40370	+	5.89538i	−0.113773	+	0.197061i
$896$	38.6439	−	66.9332i	1.29100	−	2.23608i
$897$		0			0
$898$	−16.7485	−	29.0093i	−0.558906	−	0.968054i
$899$	−1.79479			−0.0598595
$900$		0			0
$901$	89.0841			2.96782
$902$	0.520619	+	0.901738i	0.0173347	+	0.0300246i
$903$		0			0
$904$	−17.2676	+	29.9084i	−0.574313	+	0.994740i
$905$	4.11860	−	7.13363i	0.136907	−	0.237130i
$906$		0			0
$907$	−19.5449	−	33.8527i	−0.648977	−	1.12406i	−0.983368	−	0.181627i	$-0.941864\pi$
$907$	−19.5449	−	33.8527i	−0.648977	−	1.12406i	0.334391	−	0.942435i	$-0.391470\pi$
$908$	31.8064			1.05553
$909$		0			0
$910$	−9.63283			−0.319325
$911$	−17.9251	−	31.0473i	−0.593887	−	1.02864i	−0.993703	−	0.112046i	$-0.964259\pi$
$911$	−17.9251	−	31.0473i	−0.593887	−	1.02864i	0.399816	−	0.916595i	$-0.369074\pi$
$912$		0			0
$913$	−3.61809	+	6.26671i	−0.119741	+	0.207398i
$914$	20.6130	−	35.7027i	0.681816	−	1.18094i
$915$		0			0
$916$	−27.2168	−	47.1410i	−0.899270	−	1.55758i
$917$	50.1760			1.65696
$918$		0			0
$919$	−20.3071			−0.669869			−0.334934	−	0.942241i	$-0.608714\pi$
$919$	−20.3071			−0.669869			−0.334934	+	0.942241i	$0.608714\pi$
$920$	−0.801054	−	1.38747i	−0.0264100	−	0.0457434i
$921$		0			0
$922$	48.1957	−	83.4773i	1.58724	−	2.74918i
$923$	3.16221	−	5.47711i	0.104085	−	0.180281i
$924$		0			0
$925$	3.71599	+	6.43628i	0.122181	+	0.211624i
$926$	7.05940			0.231986
$927$		0			0
$928$	0.0157306			0.000516382
$929$	−1.90606	−	3.30140i	−0.0625359	−	0.108315i	0.833062	−	0.553179i	$-0.186585\pi$
$929$	−1.90606	−	3.30140i	−0.0625359	−	0.108315i	−0.895598	+	0.444864i	$0.853252\pi$
$930$		0			0
$931$	0.512923	−	0.888408i	0.0168104	−	0.0291164i
$932$	13.5154	−	23.4094i	0.442713	−	0.766801i
$933$		0			0
$934$	−30.7600	−	53.2779i	−1.00650	−	1.74331i
$935$	−37.2402			−1.21788
$936$		0			0
$937$	−0.408946			−0.0133597			−0.00667983	−	0.999978i	$-0.502126\pi$
$937$	−0.408946			−0.0133597			−0.00667983	+	0.999978i	$0.502126\pi$
$938$	−32.8546	−	56.9059i	−1.07274	−	1.85804i
$939$		0			0
$940$	−23.1178	+	40.0412i	−0.754019	+	1.30600i
$941$	−6.29373	+	10.9011i	−0.205170	+	0.355365i	−0.950187	−	0.311681i	$-0.899108\pi$
$941$	−6.29373	+	10.9011i	−0.205170	+	0.355365i	0.745017	+	0.667045i	$0.232441\pi$
$942$		0			0
$943$	−0.0149333	−	0.0258652i	−0.000486295	−	0.000842287i
$944$	−22.0261			−0.716889
$945$		0			0
$946$	89.1981			2.90008
$947$	−17.9147	−	31.0292i	−0.582149	−	1.00831i	−0.995224	−	0.0976150i	$-0.968879\pi$
$947$	−17.9147	−	31.0292i	−0.582149	−	1.00831i	0.413075	−	0.910697i	$-0.364455\pi$
$948$		0			0
$949$	−3.68524	+	6.38302i	−0.119628	+	0.207202i
$950$	−0.148079	+	0.256481i	−0.00480433	+	0.00832135i
$951$		0			0
$952$	−76.5422	−	132.575i	−2.48075	−	4.29678i
$953$	−6.87652			−0.222752			−0.111376	−	0.993778i	$-0.535526\pi$
$953$	−6.87652			−0.222752			−0.111376	+	0.993778i	$0.535526\pi$
$954$		0			0
$955$	−17.7269			−0.573629
$956$	50.8601	+	88.0923i	1.64493	+	2.84911i
$957$		0			0
$958$	−26.2772	+	45.5135i	−0.848979	+	1.47047i
$959$	−14.4180	+	24.9728i	−0.465583	+	0.806413i
$960$		0			0
$961$	−6.12267	−	10.6048i	−0.197506	−	0.342090i
$962$	−18.1956			−0.586650
$963$		0			0
$964$	−80.5313			−2.59374
$965$	−5.80167	−	10.0488i	−0.186762	−	0.323482i
$966$		0			0
$967$	8.02651	−	13.9023i	0.258115	−	0.447068i	−0.707622	−	0.706591i	$-0.750232\pi$
$967$	8.02651	−	13.9023i	0.258115	−	0.447068i	0.965737	+	0.259523i	$0.0835653\pi$
$968$	26.4506	−	45.8138i	0.850155	−	1.47251i
$969$		0			0
$970$	6.46295	+	11.1942i	0.207513	+	0.359423i
$971$	29.7306			0.954100			0.477050	−	0.878876i	$-0.341706\pi$
$971$	29.7306			0.954100			0.477050	+	0.878876i	$0.341706\pi$
$972$		0			0
$973$	66.3153			2.12597
$974$	−39.2493	−	67.9818i	−1.25763	−	2.17828i
$975$		0			0
$976$	−26.2965	+	45.5468i	−0.841729	+	1.45792i
$977$	12.6498	−	21.9102i	0.404704	−	0.700968i	−0.589583	−	0.807708i	$-0.700708\pi$
$977$	12.6498	−	21.9102i	0.404704	−	0.700968i	0.994287	+	0.106740i	$0.0340412\pi$
$978$		0			0
$979$	8.39944	+	14.5483i	0.268447	+	0.464965i
$980$	33.8718			1.08200
$981$		0			0
$982$	−23.8463			−0.760966
$983$	−13.1804	−	22.8291i	−0.420389	−	0.728135i	0.575588	−	0.817740i	$-0.304773\pi$
$983$	−13.1804	−	22.8291i	−0.420389	−	0.728135i	−0.995977	+	0.0896044i	$0.971440\pi$
$984$		0			0
$985$	1.00184	−	1.73524i	0.0319214	−	0.0552894i
$986$	2.66259	−	4.61174i	0.0847942	−	0.146868i
$987$		0			0
$988$	−0.241575	−	0.418420i	−0.00768553	−	0.0133117i
$989$	−2.55854			−0.0813567
$990$		0			0
$991$	−47.5111			−1.50924			−0.754621	−	0.656161i	$-0.772179\pi$
$991$	−47.5111			−1.50924			−0.754621	+	0.656161i	$0.772179\pi$
$992$	0.189514	+	0.328248i	0.00601707	+	0.0104219i
$993$		0			0
$994$	−30.4610	+	52.7601i	−0.966165	+	1.67345i
$995$	−5.62862	+	9.74905i	−0.178439	+	0.309066i
$996$		0			0
$997$	19.3542	+	33.5224i	0.612953	+	1.06167i	0.990740	+	0.135773i	$0.0433518\pi$
$997$	19.3542	+	33.5224i	0.612953	+	1.06167i	−0.377787	+	0.925892i	$0.623315\pi$
$998$	−77.7863			−2.46228
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1755.2.i.f.1171.8		16
3.2	odd	2		585.2.i.e.391.1	yes	16
9.2	odd	6		585.2.i.e.196.1	✓	16
9.4	even	3		5265.2.a.ba.1.1		8
9.5	odd	6		5265.2.a.bf.1.8		8
9.7	even	3	inner	1755.2.i.f.586.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.1	✓	16	9.2	odd	6
585.2.i.e.391.1	yes	16	3.2	odd	2
1755.2.i.f.586.8		16	9.7	even	3	inner
1755.2.i.f.1171.8		16	1.1	even	1	trivial
5265.2.a.ba.1.1		8	9.4	even	3
5265.2.a.bf.1.8		8	9.5	odd	6

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:	\( N \)	\(=\)	\( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1755.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22414 + 2.12028i) q^{2} +(-1.99705 + 3.45900i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.96726 + 3.40740i) q^{7} -4.88214 q^{8} +O(q^{10})\)	\(q+(1.22414 + 2.12028i) q^{2} +(-1.99705 + 3.45900i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.96726 + 3.40740i) q^{7} -4.88214 q^{8} -2.44829 q^{10} +(2.33643 + 4.04682i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-4.81642 + 8.34228i) q^{14} +(-1.98233 - 3.43350i) q^{16} +7.96946 q^{17} -0.120966 q^{19} +(-1.99705 - 3.45900i) q^{20} +(-5.72025 + 9.90777i) q^{22} +(0.164078 - 0.284192i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.44829 q^{26} -15.7149 q^{28} +(-0.136463 - 0.236360i) q^{29} +(3.28806 - 5.69509i) q^{31} +(-0.0288185 + 0.0499151i) q^{32} +(9.75576 + 16.8975i) q^{34} -3.93452 q^{35} -7.43198 q^{37} +(-0.148079 - 0.256481i) q^{38} +(2.44107 - 4.22806i) q^{40} +(0.0455066 - 0.0788197i) q^{41} +(-3.89835 - 6.75213i) q^{43} -18.6639 q^{44} +0.803421 q^{46} +(-5.78798 - 10.0251i) q^{47} +(-4.24023 + 7.34429i) q^{49} +(1.22414 - 2.12028i) q^{50} +(1.99705 + 3.45900i) q^{52} +11.1782 q^{53} -4.67286 q^{55} +(-9.60445 - 16.6354i) q^{56} +(0.334099 - 0.578677i) q^{58} +(2.77780 - 4.81129i) q^{59} +(-6.63270 - 11.4882i) q^{61} +16.1002 q^{62} -8.07045 q^{64} +(0.500000 + 0.866025i) q^{65} +(-3.41069 + 5.90749i) q^{67} +(-15.9154 + 27.5663i) q^{68} +(-4.81642 - 8.34228i) q^{70} +6.32442 q^{71} -7.37048 q^{73} +(-9.09780 - 15.7579i) q^{74} +(0.241575 - 0.418420i) q^{76} +(-9.19274 + 15.9223i) q^{77} +(5.95876 + 10.3209i) q^{79} +3.96467 q^{80} +0.222826 q^{82} +(0.774276 + 1.34108i) q^{83} +(-3.98473 + 6.90175i) q^{85} +(9.54427 - 16.5312i) q^{86} +(-11.4068 - 19.7571i) q^{88} +3.59499 q^{89} +3.93452 q^{91} +(0.655346 + 1.13509i) q^{92} +(14.1706 - 24.5442i) q^{94} +(0.0604829 - 0.104759i) q^{95} +(-2.63979 - 4.57224i) q^{97} -20.7626 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

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