LMFDB - Embedded newform 819.2.j.h.352.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(235,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("819.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.j (of order $3$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.1
Root			$1.50426 - 2.60546i$ of defining polynomial
Character	$\chi$	$=$	819.352
Dual form			819.2.j.h.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00426 + 1.73943i) q^{2} +(-1.01709 - 1.76164i) q^{4} +(0.452861 - 0.784378i) q^{5} +(0.237709 + 2.63505i) q^{7} +0.0686323 q^{8} +O(q^{10})$	\(q+(-1.00426 + 1.73943i) q^{2} +(-1.01709 - 1.76164i) q^{4} +(0.452861 - 0.784378i) q^{5} +(0.237709 + 2.63505i) q^{7} +0.0686323 q^{8} +(0.909582 + 1.57544i) q^{10} +(0.358181 + 0.620387i) q^{11} +1.00000 q^{13} +(-4.82222 - 2.23280i) q^{14} +(1.96525 - 3.40391i) q^{16} +(1.17614 + 2.03713i) q^{17} +(-3.31796 + 5.74687i) q^{19} -1.84239 q^{20} -1.43883 q^{22} +(1.87953 - 3.25544i) q^{23} +(2.08983 + 3.61970i) q^{25} +(-1.00426 + 1.73943i) q^{26} +(4.40025 - 3.09883i) q^{28} -3.25799 q^{29} +(-0.785250 - 1.36009i) q^{31} +(4.01588 + 6.95570i) q^{32} -4.72459 q^{34} +(2.17452 + 1.00686i) q^{35} +(-2.60441 + 4.51098i) q^{37} +(-6.66419 - 11.5427i) q^{38} +(0.0310809 - 0.0538337i) q^{40} -4.92168 q^{41} -9.43766 q^{43} +(0.728600 - 1.26197i) q^{44} +(3.77508 + 6.53863i) q^{46} +(-4.15993 + 7.20521i) q^{47} +(-6.88699 + 1.25275i) q^{49} -8.39497 q^{50} +(-1.01709 - 1.76164i) q^{52} +(7.04163 + 12.1965i) q^{53} +0.648824 q^{55} +(0.0163145 + 0.180850i) q^{56} +(3.27188 - 5.66706i) q^{58} +(0.358181 + 0.620387i) q^{59} +(5.82633 - 10.0915i) q^{61} +3.15439 q^{62} -8.27099 q^{64} +(0.452861 - 0.784378i) q^{65} +(-4.69587 - 8.13349i) q^{67} +(2.39246 - 4.14386i) q^{68} +(-3.93516 + 2.77129i) q^{70} -10.9914 q^{71} +(1.73650 + 3.00771i) q^{73} +(-5.23103 - 9.06041i) q^{74} +13.4986 q^{76} +(-1.54961 + 1.09130i) q^{77} +(-6.50408 + 11.2654i) q^{79} +(-1.77997 - 3.08299i) q^{80} +(4.94265 - 8.56093i) q^{82} -3.54083 q^{83} +2.13050 q^{85} +(9.47789 - 16.4162i) q^{86} +(0.0245828 + 0.0425786i) q^{88} +(6.02503 - 10.4357i) q^{89} +(0.237709 + 2.63505i) q^{91} -7.64656 q^{92} +(-8.35532 - 14.4718i) q^{94} +(3.00514 + 5.20506i) q^{95} +7.43766 q^{97} +(4.73727 - 13.2375i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8	$ 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8} + 5 q^{10} + 11 q^{11} + 10 q^{13} - 10 q^{14} - 10 q^{16} - 5 q^{17} - 9 q^{19} - 2 q^{20} + 16 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} + 37 q^{28} + 6 q^{29} + 6 q^{31} + 22 q^{32} - 44 q^{34} + 4 q^{35} - 4 q^{37} - 10 q^{38} - 28 q^{40} - 28 q^{41} + 4 q^{43} - 3 q^{46} + q^{47} - 11 q^{49} - 18 q^{50} - 8 q^{52} + 17 q^{53} + 21 q^{56} + 27 q^{58} + 11 q^{59} + 11 q^{61} + 46 q^{62} + 18 q^{64} + 2 q^{65} - 13 q^{67} - 32 q^{68} + 49 q^{70} - 30 q^{71} - 33 q^{74} + 16 q^{76} + 46 q^{77} - 2 q^{79} + 55 q^{80} - 34 q^{82} - 12 q^{83} - 44 q^{85} + 28 q^{86} + 3 q^{88} - 4 q^{89} + q^{91} - 42 q^{92} - 20 q^{94} - 12 q^{95} - 24 q^{97} + 7 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8 + 5 * q^10 + 11 * q^11 + 10 * q^13 - 10 * q^14 - 10 * q^16 - 5 * q^17 - 9 * q^19 - 2 * q^20 + 16 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 + 37 * q^28 + 6 * q^29 + 6 * q^31 + 22 * q^32 - 44 * q^34 + 4 * q^35 - 4 * q^37 - 10 * q^38 - 28 * q^40 - 28 * q^41 + 4 * q^43 - 3 * q^46 + q^47 - 11 * q^49 - 18 * q^50 - 8 * q^52 + 17 * q^53 + 21 * q^56 + 27 * q^58 + 11 * q^59 + 11 * q^61 + 46 * q^62 + 18 * q^64 + 2 * q^65 - 13 * q^67 - 32 * q^68 + 49 * q^70 - 30 * q^71 - 33 * q^74 + 16 * q^76 + 46 * q^77 - 2 * q^79 + 55 * q^80 - 34 * q^82 - 12 * q^83 - 44 * q^85 + 28 * q^86 + 3 * q^88 - 4 * q^89 + q^91 - 42 * q^92 - 20 * q^94 - 12 * q^95 - 24 * q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00426	+	1.73943i	−0.710121	+	1.22997i	0.254691	+	0.967023i	$0.418026\pi$
$2$	−1.00426	+	1.73943i	−0.710121	+	1.22997i	−0.964812	+	0.262942i	$0.915307\pi$
$3$		0			0
$3$		0			0
$4$	−1.01709	−	1.76164i	−0.508543	−	0.880822i
$5$	0.452861	−	0.784378i	0.202526	−	0.350784i	−0.746816	−	0.665031i	$-0.768418\pi$
$5$	0.452861	−	0.784378i	0.202526	−	0.350784i	0.949342	+	0.314246i	$0.101752\pi$
$6$		0			0
$7$	0.237709	+	2.63505i	0.0898454	+	0.995956i
$7$	0.237709	+	2.63505i	0.0898454	+	0.995956i
$8$	0.0686323			0.0242652
$9$		0			0
$10$	0.909582	+	1.57544i	0.287635	+	0.498199i
$11$	0.358181	+	0.620387i	0.107996	+	0.187054i	0.914958	−	0.403549i	$-0.132223\pi$
$11$	0.358181	+	0.620387i	0.107996	+	0.187054i	−0.806963	+	0.590603i	$0.798890\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−4.82222	−	2.23280i	−1.28879	−	0.596742i
$15$		0			0
$16$	1.96525	−	3.40391i	0.491311	−	0.850976i
$17$	1.17614	+	2.03713i	0.285255	+	0.494076i	0.972671	−	0.232188i	$-0.0745885\pi$
$17$	1.17614	+	2.03713i	0.285255	+	0.494076i	−0.687416	+	0.726264i	$0.741255\pi$
$18$		0			0
$19$	−3.31796	+	5.74687i	−0.761191	+	1.31842i	0.181046	+	0.983475i	$0.442052\pi$
$19$	−3.31796	+	5.74687i	−0.761191	+	1.31842i	−0.942237	+	0.334947i	$0.891282\pi$
$20$	−1.84239			−0.411971
$21$		0			0
$22$	−1.43883			−0.306759
$23$	1.87953	−	3.25544i	0.391909	−	0.678806i	−0.600793	−	0.799405i	$-0.705148\pi$
$23$	1.87953	−	3.25544i	0.391909	−	0.678806i	0.992701	+	0.120599i	$0.0384816\pi$
$24$		0			0
$25$	2.08983	+	3.61970i	0.417967	+	0.723940i
$26$	−1.00426	+	1.73943i	−0.196952	+	0.341131i
$27$		0			0
$28$	4.40025	−	3.09883i	0.831569	−	0.585624i
$29$	−3.25799			−0.604994			−0.302497	−	0.953150i	$-0.597820\pi$
$29$	−3.25799			−0.604994			−0.302497	+	0.953150i	$0.597820\pi$
$30$		0			0
$31$	−0.785250	−	1.36009i	−0.141035	−	0.244280i	0.786852	−	0.617142i	$-0.211710\pi$
$31$	−0.785250	−	1.36009i	−0.141035	−	0.244280i	−0.927887	+	0.372862i	$0.878376\pi$
$32$	4.01588	+	6.95570i	0.709913	+	1.22961i
$33$		0			0
$34$	−4.72459			−0.810261
$35$	2.17452	+	1.00686i	0.367562	+	0.170190i
$36$		0			0
$37$	−2.60441	+	4.51098i	−0.428163	+	0.741600i	−0.996710	−	0.0810508i	$-0.974172\pi$
$37$	−2.60441	+	4.51098i	−0.428163	+	0.741600i	0.568547	+	0.822651i	$0.307506\pi$
$38$	−6.66419	−	11.5427i	−1.08108	−	1.87248i
$39$		0			0
$40$	0.0310809	−	0.0538337i	0.00491432	−	0.00851185i
$41$	−4.92168			−0.768637			−0.384318	−	0.923201i	$-0.625563\pi$
$41$	−4.92168			−0.768637			−0.384318	+	0.923201i	$0.625563\pi$
$42$		0			0
$43$	−9.43766			−1.43923			−0.719615	−	0.694373i	$-0.755682\pi$
$43$	−9.43766			−1.43923			−0.719615	+	0.694373i	$0.755682\pi$
$44$	0.728600	−	1.26197i	0.109841	−	0.190250i
$45$		0			0
$46$	3.77508	+	6.53863i	0.556605	+	0.964068i
$47$	−4.15993	+	7.20521i	−0.606788	+	1.05099i	0.384978	+	0.922926i	$0.374209\pi$
$47$	−4.15993	+	7.20521i	−0.606788	+	1.05099i	−0.991766	+	0.128062i	$0.959124\pi$
$48$		0			0
$49$	−6.88699	+	1.25275i	−0.983856	+	0.178964i
$50$	−8.39497			−1.18723
$51$		0			0
$52$	−1.01709	−	1.76164i	−0.141044	−	0.244296i
$53$	7.04163	+	12.1965i	0.967243	+	1.67531i	0.703465	+	0.710729i	$0.251635\pi$
$53$	7.04163	+	12.1965i	0.967243	+	1.67531i	0.263777	+	0.964584i	$0.415032\pi$
$54$		0			0
$55$	0.648824			0.0874874
$56$	0.0163145	+	0.180850i	0.00218012	+	0.0241671i
$57$		0			0
$58$	3.27188	−	5.66706i	0.429619	−	0.744122i
$59$	0.358181	+	0.620387i	0.0466311	+	0.0807675i	0.888399	−	0.459072i	$-0.151818\pi$
$59$	0.358181	+	0.620387i	0.0466311	+	0.0807675i	−0.841768	+	0.539840i	$0.818485\pi$
$60$		0			0
$61$	5.82633	−	10.0915i	0.745986	−	1.29208i	−0.203747	−	0.979024i	$-0.565312\pi$
$61$	5.82633	−	10.0915i	0.745986	−	1.29208i	0.949733	−	0.313061i	$-0.101355\pi$
$62$	3.15439			0.400607
$63$		0			0
$64$	−8.27099			−1.03387
$65$	0.452861	−	0.784378i	0.0561705	−	0.0972901i
$66$		0			0
$67$	−4.69587	−	8.13349i	−0.573692	−	0.993664i	−0.996182	−	0.0872964i	$-0.972177\pi$
$67$	−4.69587	−	8.13349i	−0.573692	−	0.993664i	0.422490	−	0.906367i	$-0.361156\pi$
$68$	2.39246	−	4.14386i	0.290128	−	0.502517i
$69$		0			0
$70$	−3.93516	+	2.77129i	−0.470341	+	0.331233i
$71$	−10.9914			−1.30444			−0.652220	−	0.758030i	$-0.726162\pi$
$71$	−10.9914			−1.30444			−0.652220	+	0.758030i	$0.726162\pi$
$72$		0			0
$73$	1.73650	+	3.00771i	0.203242	+	0.352025i	0.949571	−	0.313552i	$-0.101519\pi$
$73$	1.73650	+	3.00771i	0.203242	+	0.352025i	−0.746329	+	0.665577i	$0.768186\pi$
$74$	−5.23103	−	9.06041i	−0.608095	−	1.05325i
$75$		0			0
$76$	13.4986			1.54839
$77$	−1.54961	+	1.09130i	−0.176594	+	0.124365i
$78$		0			0
$79$	−6.50408	+	11.2654i	−0.731766	+	1.26746i	0.224361	+	0.974506i	$0.427970\pi$
$79$	−6.50408	+	11.2654i	−0.731766	+	1.26746i	−0.956128	+	0.292950i	$0.905363\pi$
$80$	−1.77997	−	3.08299i	−0.199006	−	0.344689i
$81$		0			0
$82$	4.94265	−	8.56093i	0.545825	−	0.945396i
$83$	−3.54083			−0.388656			−0.194328	−	0.980937i	$-0.562253\pi$
$83$	−3.54083			−0.388656			−0.194328	+	0.980937i	$0.562253\pi$
$84$		0			0
$85$	2.13050			0.231085
$86$	9.47789	−	16.4162i	1.02203	−	1.77020i
$87$		0			0
$88$	0.0245828	+	0.0425786i	0.00262053	+	0.00453889i
$89$	6.02503	−	10.4357i	0.638651	−	1.10618i	−0.347077	−	0.937836i	$-0.612826\pi$
$89$	6.02503	−	10.4357i	0.638651	−	1.10618i	0.985729	−	0.168340i	$-0.0538408\pi$
$90$		0			0
$91$	0.237709	+	2.63505i	0.0249186	+	0.276228i
$92$	−7.64656			−0.797209
$93$		0			0
$94$	−8.35532	−	14.4718i	−0.861786	−	1.49266i
$95$	3.00514	+	5.20506i	0.308321	+	0.534028i
$96$		0			0
$97$	7.43766			0.755180			0.377590	−	0.925973i	$-0.376753\pi$
$97$	7.43766			0.755180			0.377590	+	0.925973i	$0.376753\pi$
$98$	4.73727	−	13.2375i	0.478537	−	1.33719i
$99$		0			0
$100$	4.25108	−	7.36309i	0.425108	−	0.736309i
$101$	−0.599526	−	1.03841i	−0.0596551	−	0.103326i	0.834656	−	0.550772i	$-0.185667\pi$
$101$	−0.599526	−	1.03841i	−0.0596551	−	0.103326i	−0.894311	+	0.447447i	$0.852333\pi$
$102$		0			0
$103$	7.20615	−	12.4814i	0.710043	−	1.22983i	−0.254797	−	0.966995i	$-0.582009\pi$
$103$	7.20615	−	12.4814i	0.710043	−	1.22983i	0.964840	−	0.262837i	$-0.0846580\pi$
$104$	0.0686323			0.00672995
$105$		0			0
$106$	−28.2866			−2.74744
$107$	6.79661	−	11.7721i	0.657053	−	1.13805i	−0.324322	−	0.945947i	$-0.605136\pi$
$107$	6.79661	−	11.7721i	0.657053	−	1.13805i	0.981375	−	0.192102i	$-0.0615305\pi$
$108$		0			0
$109$	6.86241	+	11.8860i	0.657299	+	1.13848i	0.981312	+	0.192423i	$0.0616346\pi$
$109$	6.86241	+	11.8860i	0.657299	+	1.13848i	−0.324013	+	0.946053i	$0.605032\pi$
$110$	−0.651589	+	1.12859i	−0.0621266	+	0.107606i
$111$		0			0
$112$	9.43662	+	4.36939i	0.891677	+	0.412868i
$113$	3.25799			0.306486			0.153243	−	0.988189i	$-0.451028\pi$
$113$	3.25799			0.306486			0.153243	+	0.988189i	$0.451028\pi$
$114$		0			0
$115$	−1.70233	−	2.94852i	−0.158743	−	0.274951i
$116$	3.31366	+	5.73942i	0.307665	+	0.532892i
$117$		0			0
$118$	−1.43883			−0.132455
$119$	−5.08836	+	3.58342i	−0.466449	+	0.328492i
$120$		0			0
$121$	5.24341	−	9.08186i	0.476674	−	0.825623i
$122$	11.7023	+	20.2690i	1.05948	+	1.83507i
$123$		0			0
$124$	−1.59733	+	2.76666i	−0.143445	+	0.248453i
$125$	8.31422			0.743647
$126$		0			0
$127$	−0.950834			−0.0843729			−0.0421865	−	0.999110i	$-0.513432\pi$
$127$	−0.950834			−0.0843729			−0.0421865	+	0.999110i	$0.513432\pi$
$128$	0.274489	−	0.475429i	0.0242617	−	0.0420224i
$129$		0			0
$130$	0.909582	+	1.57544i	0.0797756	+	0.138175i
$131$	−9.40980	+	16.2983i	−0.822138	+	1.42399i	0.0819487	+	0.996637i	$0.473886\pi$
$131$	−9.40980	+	16.2983i	−0.822138	+	1.42399i	−0.904087	+	0.427349i	$0.859448\pi$
$132$		0			0
$133$	−15.9320	−	7.37690i	−1.38148	−	0.639658i
$134$	18.8635			1.62956
$135$		0			0
$136$	0.0807209	+	0.139813i	0.00692176	+	0.0119888i
$137$	3.09090	+	5.35359i	0.264073	+	0.457388i	0.967320	−	0.253557i	$-0.0816006\pi$
$137$	3.09090	+	5.35359i	0.264073	+	0.457388i	−0.703247	+	0.710945i	$0.748267\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−0.437952	−	4.85480i	−0.0370137	−	0.410305i
$141$		0			0
$142$	11.0383	−	19.1188i	0.926309	−	1.60441i
$143$	0.358181	+	0.620387i	0.0299526	+	0.0518794i
$144$		0			0
$145$	−1.47542	+	2.55550i	−0.122527	+	0.212223i
$146$	−6.97560			−0.577305
$147$		0			0
$148$	10.5956			0.870956
$149$	−10.5385	+	18.2533i	−0.863351	+	1.49537i	0.00532425	+	0.999986i	$0.498305\pi$
$149$	−10.5385	+	18.2533i	−0.863351	+	1.49537i	−0.868675	+	0.495382i	$0.835028\pi$
$150$		0			0
$151$	7.86171	+	13.6169i	0.639777	+	1.10813i	0.985481	+	0.169783i	$0.0543067\pi$
$151$	7.86171	+	13.6169i	0.639777	+	1.10813i	−0.345704	+	0.938344i	$0.612360\pi$
$152$	−0.227719	+	0.394421i	−0.0184705	+	0.0319918i
$153$		0			0
$154$	−0.342022	−	3.79139i	−0.0275609	−	0.305519i
$155$	−1.42244			−0.114253
$156$		0			0
$157$	3.89250	+	6.74200i	0.310655	+	0.538070i	0.978504	−	0.206226i	$-0.0661183\pi$
$157$	3.89250	+	6.74200i	0.310655	+	0.538070i	−0.667849	+	0.744297i	$0.732785\pi$
$158$	−13.0636	−	22.6268i	−1.03928	−	1.80009i
$159$		0			0
$160$	7.27453			0.575102
$161$	9.02503	+	4.17881i	0.711272	+	0.329336i
$162$		0			0
$163$	−0.844956	+	1.46351i	−0.0661820	+	0.114631i	−0.897218	−	0.441588i	$-0.854415\pi$
$163$	−0.844956	+	1.46351i	−0.0661820	+	0.114631i	0.831036	+	0.556219i	$0.187748\pi$
$164$	5.00576	+	8.67024i	0.390884	+	0.677032i
$165$		0			0
$166$	3.55592	−	6.15903i	0.275993	−	0.478034i
$167$	21.8667			1.69210			0.846049	−	0.533105i	$-0.178975\pi$
$167$	21.8667			1.69210			0.846049	+	0.533105i	$0.178975\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−2.13958	+	3.70587i	−0.164099	+	0.284227i
$171$		0			0
$172$	9.59891	+	16.6258i	0.731910	+	1.26770i
$173$	2.92061	−	5.05865i	0.222050	−	0.384602i	−0.733380	−	0.679819i	$-0.762058\pi$
$173$	2.92061	−	5.05865i	0.222050	−	0.384602i	0.955430	+	0.295217i	$0.0953918\pi$
$174$		0			0
$175$	−9.04132	+	6.36725i	−0.683460	+	0.481319i
$176$	2.81565			0.212238
$177$		0			0
$178$	12.1014	+	20.9603i	0.907039	+	1.57104i
$179$	1.26714	+	2.19475i	0.0947103	+	0.164043i	0.909488	−	0.415731i	$-0.136474\pi$
$179$	1.26714	+	2.19475i	0.0947103	+	0.164043i	−0.814777	+	0.579774i	$0.803141\pi$
$180$		0			0
$181$	−10.7248			−0.797169			−0.398585	−	0.917132i	$-0.630498\pi$
$181$	−10.7248			−0.797169			−0.398585	+	0.917132i	$0.630498\pi$
$182$	−4.82222	−	2.23280i	−0.357447	−	0.165506i
$183$		0			0
$184$	0.128996	−	0.223428i	0.00950974	−	0.0164714i
$185$	2.35887	+	4.08569i	0.173428	+	0.300386i
$186$		0			0
$187$	−0.842538	+	1.45932i	−0.0616125	+	0.106716i
$188$	16.9240			1.23431
$189$		0			0
$190$	−12.0718			−0.875781
$191$	−0.839303	+	1.45371i	−0.0607298	+	0.105187i	−0.894792	−	0.446484i	$-0.852676\pi$
$191$	−0.839303	+	1.45371i	−0.0607298	+	0.105187i	0.834062	+	0.551671i	$0.186009\pi$
$192$		0			0
$193$	3.22408	+	5.58427i	0.232074	+	0.401964i	0.958418	−	0.285367i	$-0.0921154\pi$
$193$	3.22408	+	5.58427i	0.232074	+	0.401964i	−0.726344	+	0.687331i	$0.758782\pi$
$194$	−7.46936	+	12.9373i	−0.536269	+	0.928845i
$195$		0			0
$196$	9.21155	+	10.8583i	0.657968	+	0.775590i
$197$	−1.87251			−0.133411			−0.0667054	−	0.997773i	$-0.521249\pi$
$197$	−1.87251			−0.133411			−0.0667054	+	0.997773i	$0.521249\pi$
$198$		0			0
$199$	5.69833	+	9.86979i	0.403944	+	0.699651i	0.994198	−	0.107566i	$-0.0343058\pi$
$199$	5.69833	+	9.86979i	0.403944	+	0.699651i	−0.590254	+	0.807217i	$0.700972\pi$
$200$	0.143430	+	0.248428i	0.0101420	+	0.0175665i
$201$		0			0
$202$	2.40833			0.169449
$203$	−0.774453	−	8.58498i	−0.0543559	−	0.602547i
$204$		0			0
$205$	−2.22883	+	3.86045i	−0.155669	+	0.269626i
$206$	14.4737	+	25.0692i	1.00843	+	1.74666i
$207$		0			0
$208$	1.96525	−	3.40391i	0.136265	−	0.236018i
$209$	−4.75371			−0.328821
$210$		0			0
$211$	7.53599			0.518799			0.259400	−	0.965770i	$-0.416475\pi$
$211$	7.53599			0.518799			0.259400	+	0.965770i	$0.416475\pi$
$212$	14.3239	−	24.8097i	0.983768	−	1.70394i
$213$		0			0
$214$	13.6512	+	23.6445i	0.933174	+	1.61630i
$215$	−4.27395	+	7.40269i	−0.291481	+	0.504859i
$216$		0			0
$217$	3.39725	−	2.39248i	0.230621	−	0.162412i
$218$	−27.5666			−1.86705
$219$		0			0
$220$	−0.659909	−	1.14300i	−0.0444911	−	0.0770608i
$221$	1.17614	+	2.03713i	0.0791154	+	0.137032i
$222$		0			0
$223$	17.6349			1.18092			0.590459	−	0.807067i	$-0.298947\pi$
$223$	17.6349			1.18092			0.590459	+	0.807067i	$0.298947\pi$
$224$	−17.3740	+	12.2355i	−1.16085	+	0.817517i
$225$		0			0
$226$	−3.27188	+	5.66706i	−0.217642	+	0.376967i
$227$	−2.66452	−	4.61509i	−0.176851	−	0.306314i	0.763950	−	0.645276i	$-0.223258\pi$
$227$	−2.66452	−	4.61509i	−0.176851	−	0.306314i	−0.940800	+	0.338962i	$0.889924\pi$
$228$		0			0
$229$	4.25950	−	7.37767i	0.281476	−	0.487530i	−0.690273	−	0.723549i	$-0.742509\pi$
$229$	4.25950	−	7.37767i	0.281476	−	0.487530i	0.971748	+	0.236019i	$0.0758428\pi$
$230$	6.83834			0.450907
$231$		0			0
$232$	−0.223604			−0.0146803
$233$	2.37685	−	4.11683i	0.155713	−	0.269703i	−0.777605	−	0.628752i	$-0.783566\pi$
$233$	2.37685	−	4.11683i	0.155713	−	0.269703i	0.933318	+	0.359050i	$0.116899\pi$
$234$		0			0
$235$	3.76774	+	6.52592i	0.245780	+	0.425704i
$236$	0.728600	−	1.26197i	0.0474278	−	0.0821474i
$237$		0			0
$238$	−1.12308	−	12.4495i	−0.0727983	−	0.806984i
$239$	−14.8314			−0.959365			−0.479682	−	0.877442i	$-0.659248\pi$
$239$	−14.8314			−0.959365			−0.479682	+	0.877442i	$0.659248\pi$
$240$		0			0
$241$	3.06066	+	5.30121i	0.197154	+	0.341481i	0.947605	−	0.319446i	$-0.103497\pi$
$241$	3.06066	+	5.30121i	0.197154	+	0.341481i	−0.750450	+	0.660927i	$0.770163\pi$
$242$	10.5315	+	18.2411i	0.676992	+	1.17258i
$243$		0			0
$244$	−23.7035			−1.51746
$245$	−2.13622	+	5.96932i	−0.136478	+	0.381366i
$246$		0			0
$247$	−3.31796	+	5.74687i	−0.211116	+	0.365664i
$248$	−0.0538935	−	0.0933463i	−0.00342224	−	0.00592750i
$249$		0			0
$250$	−8.34966	+	14.4620i	−0.528079	+	0.914660i
$251$	13.9708			0.881832			0.440916	−	0.897548i	$-0.354654\pi$
$251$	13.9708			0.881832			0.440916	+	0.897548i	$0.354654\pi$
$252$		0			0
$253$	2.69284			0.169298
$254$	0.954887	−	1.65391i	0.0599149	−	0.103776i
$255$		0			0
$256$	−7.71967	−	13.3709i	−0.482479	−	0.835679i
$257$	8.63253	−	14.9520i	0.538482	−	0.932679i	−0.460504	−	0.887658i	$-0.652331\pi$
$257$	8.63253	−	14.9520i	0.538482	−	0.932679i	0.998986	−	0.0450210i	$-0.0143355\pi$
$258$		0			0
$259$	−12.5057	−	5.79047i	−0.777069	−	0.359802i
$260$	−1.84239			−0.114260
$261$		0			0
$262$	−18.8998	−	32.7354i	−1.16763	−	2.02240i
$263$	−1.30336	−	2.25749i	−0.0803687	−	0.139203i	0.823040	−	0.567984i	$-0.192276\pi$
$263$	−1.30336	−	2.25749i	−0.0803687	−	0.139203i	−0.903408	+	0.428781i	$0.858943\pi$
$264$		0			0
$265$	12.7555			0.783565
$266$	28.8315	−	20.3043i	1.76777	−	1.24494i
$267$		0			0
$268$	−9.55221	+	16.5449i	−0.583494	+	1.01064i
$269$	−7.24477	−	12.5483i	−0.441721	−	0.765084i	0.556096	−	0.831118i	$-0.312299\pi$
$269$	−7.24477	−	12.5483i	−0.441721	−	0.765084i	−0.997817	+	0.0660343i	$0.978965\pi$
$270$		0			0
$271$	4.31796	−	7.47892i	0.262297	−	0.454312i	−0.704555	−	0.709650i	$-0.748853\pi$
$271$	4.31796	−	7.47892i	0.262297	−	0.454312i	0.966852	+	0.255338i	$0.0821866\pi$
$272$	9.24558			0.560596
$273$		0			0
$274$	−12.4163			−0.750095
$275$	−1.49708	+	2.59301i	−0.0902771	+	0.156364i
$276$		0			0
$277$	−6.11349	−	10.5889i	−0.367324	−	0.636223i	0.621822	−	0.783158i	$-0.286393\pi$
$277$	−6.11349	−	10.5889i	−0.367324	−	0.636223i	−0.989146	+	0.146935i	$0.953059\pi$
$278$	4.01705	−	6.95773i	0.240927	−	0.417297i
$279$		0			0
$280$	0.149243	+	0.0691030i	0.00891896	+	0.00412970i
$281$	24.1822			1.44259			0.721293	−	0.692630i	$-0.243548\pi$
$281$	24.1822			1.44259			0.721293	+	0.692630i	$0.243548\pi$
$282$		0			0
$283$	15.3842	+	26.6461i	0.914493	+	1.58395i	0.807642	+	0.589674i	$0.200744\pi$
$283$	15.3842	+	26.6461i	0.914493	+	1.58395i	0.106851	+	0.994275i	$0.465923\pi$
$284$	11.1792	+	19.3629i	0.663363	+	1.14898i
$285$		0			0
$286$	−1.43883			−0.0850797
$287$	−1.16992	−	12.9689i	−0.0690585	−	0.765528i
$288$		0			0
$289$	5.73341	−	9.93056i	0.337259	−	0.584150i
$290$	−2.96341	−	5.13278i	−0.174018	−	0.301407i
$291$		0			0
$292$	3.53234	−	6.11819i	0.206714	−	0.358040i
$293$	31.8295			1.85950			0.929749	−	0.368193i	$-0.120024\pi$
$293$	31.8295			1.85950			0.929749	+	0.368193i	$0.120024\pi$
$294$		0			0
$295$	0.648824			0.0377760
$296$	−0.178747	+	0.309599i	−0.0103895	+	0.0179951i
$297$		0			0
$298$	−21.1669	−	36.6622i	−1.22617	−	2.12378i
$299$	1.87953	−	3.25544i	0.108696	−	0.188267i
$300$		0			0
$301$	−2.24341	−	24.8687i	−0.129308	−	1.43341i
$302$	−31.5809			−1.81728
$303$		0			0
$304$	13.0412	+	22.5880i	0.747964	+	1.29551i
$305$	−5.27704	−	9.14010i	−0.302162	−	0.523360i
$306$		0			0
$307$	28.7884			1.64304			0.821520	−	0.570179i	$-0.193126\pi$
$307$	28.7884			1.64304			0.821520	+	0.570179i	$0.193126\pi$
$308$	3.49856	+	1.61992i	0.199349	+	0.0923034i
$309$		0			0
$310$	1.42850	−	2.47423i	0.0811332	−	0.140527i
$311$	2.75931	+	4.77927i	0.156466	+	0.271007i	0.933592	−	0.358338i	$-0.116656\pi$
$311$	2.75931	+	4.77927i	0.156466	+	0.271007i	−0.777126	+	0.629345i	$0.783323\pi$
$312$		0			0
$313$	2.42399	−	4.19848i	0.137012	−	0.237312i	−0.789352	−	0.613941i	$-0.789583\pi$
$313$	2.42399	−	4.19848i	0.137012	−	0.237312i	0.926364	+	0.376629i	$0.122917\pi$
$314$	−15.6363			−0.882410
$315$		0			0
$316$	26.4608			1.48854
$317$	−3.82756	+	6.62952i	−0.214977	+	0.372351i	−0.953265	−	0.302134i	$-0.902301\pi$
$317$	−3.82756	+	6.62952i	−0.214977	+	0.372351i	0.738288	+	0.674485i	$0.235634\pi$
$318$		0			0
$319$	−1.16695	−	2.02122i	−0.0653366	−	0.113166i
$320$	−3.74561	+	6.48758i	−0.209386	+	0.362667i
$321$		0			0
$322$	−16.3322	+	11.5018i	−0.910161	+	0.640971i
$323$	−15.6095			−0.868534
$324$		0			0
$325$	2.08983	+	3.61970i	0.115923	+	0.200785i
$326$	−1.69711	−	2.93949i	−0.0939945	−	0.162803i
$327$		0			0
$328$	−0.337786			−0.0186511
$329$	−19.9750	−	9.24889i	−1.10125	−	0.509908i
$330$		0			0
$331$	−5.67159	+	9.82348i	−0.311739	+	0.539947i	−0.978739	−	0.205110i	$-0.934245\pi$
$331$	−5.67159	+	9.82348i	−0.311739	+	0.539947i	0.667000	+	0.745058i	$0.267578\pi$
$332$	3.60132	+	6.23768i	0.197648	+	0.342337i
$333$		0			0
$334$	−21.9599	+	38.0357i	−1.20159	+	2.08122i
$335$	−8.50631			−0.464749
$336$		0			0
$337$	1.74149			0.0948649			0.0474324	−	0.998874i	$-0.484896\pi$
$337$	1.74149			0.0948649			0.0474324	+	0.998874i	$0.484896\pi$
$338$	−1.00426	+	1.73943i	−0.0546247	+	0.0946127i
$339$		0			0
$340$	−2.16690	−	3.75319i	−0.117517	−	0.203545i
$341$	0.562522	−	0.974317i	0.0304623	−	0.0527622i
$342$		0			0
$343$	−4.93815	−	17.8498i	−0.266635	−	0.963798i
$344$	−0.647729			−0.0349232
$345$		0			0
$346$	5.86612	+	10.1604i	0.315365	+	0.546228i
$347$	10.5251	+	18.2301i	0.565019	+	0.978641i	0.997048	+	0.0767814i	$0.0244643\pi$
$347$	10.5251	+	18.2301i	0.565019	+	0.978641i	−0.432029	+	0.901860i	$0.642202\pi$
$348$		0			0
$349$	−8.35601			−0.447287			−0.223643	−	0.974671i	$-0.571795\pi$
$349$	−8.35601			−0.447287			−0.223643	+	0.974671i	$0.571795\pi$
$350$	−1.99556	−	22.1212i	−0.106667	−	1.18243i
$351$		0			0
$352$	−2.87682	+	4.98279i	−0.153335	+	0.265584i
$353$	−4.26677	−	7.39027i	−0.227097	−	0.393344i	0.729849	−	0.683608i	$-0.239590\pi$
$353$	−4.26677	−	7.39027i	−0.227097	−	0.393344i	−0.956947	+	0.290264i	$0.906257\pi$
$354$		0			0
$355$	−4.97758	+	8.62141i	−0.264182	+	0.457577i
$356$	−24.5119			−1.29913
$357$		0			0
$358$	−5.09015			−0.269023
$359$	−8.08565	+	14.0047i	−0.426744	+	0.739142i	−0.996582	−	0.0826150i	$-0.973673\pi$
$359$	−8.08565	+	14.0047i	−0.426744	+	0.739142i	0.569837	+	0.821757i	$0.307006\pi$
$360$		0			0
$361$	−12.5177	−	21.6812i	−0.658824	−	1.14112i
$362$	10.7705	−	18.6551i	0.566086	−	0.980490i
$363$		0			0
$364$	4.40025	−	3.09883i	0.230636	−	0.162423i
$365$	3.14557			0.164647
$366$		0			0
$367$	−14.0770	−	24.3821i	−0.734813	−	1.27273i	−0.954805	−	0.297232i	$-0.903936\pi$
$367$	−14.0770	−	24.3821i	−0.734813	−	1.27273i	0.219992	−	0.975502i	$-0.429397\pi$
$368$	−7.38747	−	12.7955i	−0.385098	−	0.667010i
$369$		0			0
$370$	−9.47571			−0.492619
$371$	−30.4644	+	21.4543i	−1.58164	+	1.11385i
$372$		0			0
$373$	14.2518	−	24.6849i	0.737932	−	1.27814i	−0.215493	−	0.976505i	$-0.569136\pi$
$373$	14.2518	−	24.6849i	0.737932	−	1.27814i	0.953425	−	0.301630i	$-0.0975308\pi$
$374$	−1.69226	−	2.93108i	−0.0875046	−	0.151562i
$375$		0			0
$376$	−0.285506	+	0.494511i	−0.0147238	+	0.0255024i
$377$	−3.25799			−0.167795
$378$		0			0
$379$	−7.26263			−0.373056			−0.186528	−	0.982450i	$-0.559724\pi$
$379$	−7.26263			−0.373056			−0.186528	+	0.982450i	$0.559724\pi$
$380$	6.11297	−	10.5880i	0.313589	−	0.543152i
$381$		0			0
$382$	−1.68576	−	2.91982i	−0.0862510	−	0.149391i
$383$	6.46627	−	11.1999i	0.330411	−	0.572289i	−0.652181	−	0.758063i	$-0.726146\pi$
$383$	6.46627	−	11.1999i	0.330411	−	0.572289i	0.982592	+	0.185774i	$0.0594793\pi$
$384$		0			0
$385$	0.154231	+	1.70968i	0.00786034	+	0.0871336i
$386$	−12.9513			−0.659203
$387$		0			0
$388$	−7.56474	−	13.1025i	−0.384041	−	0.665179i
$389$	−10.5679	−	18.3041i	−0.535811	−	0.928053i	−0.999124	−	0.0418574i	$-0.986672\pi$
$389$	−10.5679	−	18.3041i	−0.535811	−	0.928053i	0.463312	−	0.886195i	$-0.346661\pi$
$390$		0			0
$391$	8.84232			0.447175
$392$	−0.472670	+	0.0859791i	−0.0238734	+	0.00434260i
$393$		0			0
$394$	1.88049	−	3.25711i	0.0947378	−	0.164091i
$395$	5.89089	+	10.2033i	0.296403	+	0.513384i
$396$		0			0
$397$	−9.60366	+	16.6340i	−0.481994	+	0.834838i	−0.999786	−	0.0206683i	$-0.993421\pi$
$397$	−9.60366	+	16.6340i	−0.481994	+	0.834838i	0.517792	+	0.855506i	$0.326754\pi$
$398$	−22.8905			−1.14740
$399$		0			0
$400$	16.4282			0.821408
$401$	8.33460	−	14.4360i	0.416210	−	0.720897i	−0.579344	−	0.815083i	$-0.696691\pi$
$401$	8.33460	−	14.4360i	0.416210	−	0.720897i	0.995555	+	0.0941856i	$0.0300247\pi$
$402$		0			0
$403$	−0.785250	−	1.36009i	−0.0391161	−	0.0677510i
$404$	−1.21954	+	2.11230i	−0.0606743	+	0.105091i
$405$		0			0
$406$	15.7107	+	7.27446i	0.779711	+	0.361025i
$407$	−3.73140			−0.184959
$408$		0			0
$409$	−6.17416	−	10.6940i	−0.305293	−	0.528782i	0.672034	−	0.740520i	$-0.265421\pi$
$409$	−6.17416	−	10.6940i	−0.305293	−	0.528782i	−0.977326	+	0.211738i	$0.932088\pi$
$410$	−4.47667	−	7.75382i	−0.221087	−	0.382934i
$411$		0			0
$412$	−29.3171			−1.44435
$413$	−1.54961	+	1.09130i	−0.0762513	+	0.0536991i
$414$		0			0
$415$	−1.60350	+	2.77735i	−0.0787128	+	0.136335i
$416$	4.01588	+	6.95570i	0.196895	+	0.341031i
$417$		0			0
$418$	4.77397	−	8.26876i	0.233502	−	0.404438i
$419$	−4.35934			−0.212968			−0.106484	−	0.994314i	$-0.533959\pi$
$419$	−4.35934			−0.212968			−0.106484	+	0.994314i	$0.533959\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−7.56811	+	13.1084i	−0.368410	+	0.638105i
$423$		0			0
$424$	0.483284	+	0.837072i	0.0234703	+	0.0406518i
$425$	−4.91586	+	8.51451i	−0.238454	+	0.413015i
$426$		0			0
$427$	27.9766	+	12.9538i	1.35388	+	0.626881i
$428$	−27.6509			−1.33656
$429$		0			0
$430$	−8.58433	−	14.8685i	−0.413973	−	0.717022i
$431$	−11.6813	−	20.2326i	−0.562667	−	0.974569i	−0.997262	−	0.0739426i	$-0.976442\pi$
$431$	−11.6813	−	20.2326i	−0.562667	−	0.974569i	0.434595	−	0.900626i	$-0.356891\pi$
$432$		0			0
$433$	−2.71285			−0.130371			−0.0651856	−	0.997873i	$-0.520764\pi$
$433$	−2.71285			−0.130371			−0.0651856	+	0.997873i	$0.520764\pi$
$434$	0.749825	+	8.31197i	0.0359927	+	0.398987i
$435$		0			0
$436$	13.9593	−	24.1782i	0.668529	−	1.15793i
$437$	12.4724	+	21.6028i	0.596635	+	1.03340i
$438$		0			0
$439$	4.41760	−	7.65150i	0.210840	−	0.365186i	−0.741137	−	0.671353i	$-0.765713\pi$
$439$	4.41760	−	7.65150i	0.210840	−	0.365186i	0.951978	+	0.306167i	$0.0990467\pi$
$440$	0.0445303			0.00212290
$441$		0			0
$442$	−4.72459			−0.224726
$443$	−1.45279	+	2.51630i	−0.0690240	+	0.119553i	−0.898472	−	0.439031i	$-0.855322\pi$
$443$	−1.45279	+	2.51630i	−0.0690240	+	0.119553i	0.829448	+	0.558584i	$0.188655\pi$
$444$		0			0
$445$	−5.45700	−	9.45179i	−0.258686	−	0.448058i
$446$	−17.7100	+	30.6747i	−0.838595	+	1.45249i
$447$		0			0
$448$	−1.96609	−	21.7945i	−0.0928888	−	1.02969i
$449$	15.2777			0.720998			0.360499	−	0.932760i	$-0.382606\pi$
$449$	15.2777			0.720998			0.360499	+	0.932760i	$0.382606\pi$
$450$		0			0
$451$	−1.76285	−	3.05334i	−0.0830093	−	0.143776i
$452$	−3.31366	−	5.73942i	−0.155861	−	0.269960i
$453$		0			0
$454$	10.7035			0.502341
$455$	2.17452	+	1.00686i	0.101943	+	0.0472022i
$456$		0			0
$457$	−11.8300	+	20.4902i	−0.553384	+	0.958489i	0.444643	+	0.895708i	$0.353330\pi$
$457$	−11.8300	+	20.4902i	−0.553384	+	0.958489i	−0.998027	+	0.0627815i	$0.980003\pi$
$458$	8.55531	+	14.8182i	0.399763	+	0.692410i
$459$		0			0
$460$	−3.46283	+	5.99779i	−0.161455	+	0.279649i
$461$	26.6170			1.23968			0.619839	−	0.784729i	$-0.287198\pi$
$461$	26.6170			1.23968			0.619839	+	0.784729i	$0.287198\pi$
$462$		0			0
$463$	−1.44250			−0.0670385			−0.0335193	−	0.999438i	$-0.510672\pi$
$463$	−1.44250			−0.0670385			−0.0335193	+	0.999438i	$0.510672\pi$
$464$	−6.40276	+	11.0899i	−0.297240	+	0.514836i
$465$		0			0
$466$	4.77397	+	8.26876i	0.221150	+	0.383043i
$467$	−4.19480	+	7.26560i	−0.194112	+	0.336212i	−0.946609	−	0.322384i	$-0.895516\pi$
$467$	−4.19480	+	7.26560i	−0.194112	+	0.336212i	0.752497	+	0.658596i	$0.228849\pi$
$468$		0			0
$469$	20.3159	−	14.3073i	0.938102	−	0.660648i
$470$	−15.1352			−0.698135
$471$		0			0
$472$	0.0245828	+	0.0425786i	0.00113151	+	0.00195984i
$473$	−3.38039	−	5.85500i	−0.155430	−	0.269213i
$474$		0			0
$475$	−27.7359			−1.27261
$476$	11.4880	+	5.31922i	0.526552	+	0.243806i
$477$		0			0
$478$	14.8946	−	25.7983i	0.681265	−	1.17999i
$479$	6.30608	+	10.9225i	0.288132	+	0.499060i	0.973364	−	0.229265i	$-0.0736324\pi$
$479$	6.30608	+	10.9225i	0.288132	+	0.499060i	−0.685232	+	0.728325i	$0.740299\pi$
$480$		0			0
$481$	−2.60441	+	4.51098i	−0.118751	+	0.205683i
$482$	−12.2948			−0.560013
$483$		0			0
$484$	−21.3320			−0.969636
$485$	3.36823	−	5.83394i	0.152943	−	0.264905i
$486$		0			0
$487$	−10.7840	−	18.6785i	−0.488671	−	0.846403i	0.511244	−	0.859435i	$-0.329185\pi$
$487$	−10.7840	−	18.6785i	−0.488671	−	0.846403i	−0.999915	+	0.0130329i	$0.995851\pi$
$488$	0.399875	−	0.692604i	0.0181015	−	0.0313527i
$489$		0			0
$490$	−8.23791	−	9.71058i	−0.372151	−	0.438679i
$491$	−39.2347			−1.77064			−0.885318	−	0.464987i	$-0.846059\pi$
$491$	−39.2347			−1.77064			−0.885318	+	0.464987i	$0.846059\pi$
$492$		0			0
$493$	−3.83184	−	6.63694i	−0.172577	−	0.298913i
$494$	−6.66419	−	11.5427i	−0.299836	−	0.519332i
$495$		0			0
$496$	−6.17283			−0.277168
$497$	−2.61275	−	28.9629i	−0.117198	−	1.29916i
$498$		0			0
$499$	−4.58407	+	7.93984i	−0.205211	+	0.355436i	−0.950200	−	0.311641i	$-0.899121\pi$
$499$	−4.58407	+	7.93984i	−0.205211	+	0.355436i	0.744989	+	0.667077i	$0.232455\pi$
$500$	−8.45627	−	14.6467i	−0.378176	−	0.655020i
$501$		0			0
$502$	−14.0304	+	24.3013i	−0.626207	+	1.08462i
$503$	−24.9370			−1.11188			−0.555942	−	0.831221i	$-0.687642\pi$
$503$	−24.9370			−1.11188			−0.555942	+	0.831221i	$0.687642\pi$
$504$		0			0
$505$	−1.08601			−0.0483267
$506$	−2.70432	+	4.68402i	−0.120222	+	0.208230i
$507$		0			0
$508$	0.967080	+	1.67503i	0.0429072	+	0.0743175i
$509$	2.94904	−	5.10788i	0.130714	−	0.226403i	−0.793238	−	0.608912i	$-0.791606\pi$
$509$	2.94904	−	5.10788i	0.130714	−	0.226403i	0.923952	+	0.382509i	$0.124940\pi$
$510$		0			0
$511$	−7.51268	+	5.29072i	−0.332341	+	0.234048i
$512$	32.1083			1.41900
$513$		0			0
$514$	17.3386	+	30.0314i	0.764775	+	1.32463i
$515$	−6.52677	−	11.3047i	−0.287604	−	0.498144i
$516$		0			0
$517$	−5.96003			−0.262122
$518$	22.6312	−	15.9378i	0.994357	−	0.700265i
$519$		0			0
$520$	0.0310809	−	0.0538337i	0.00136299	−	0.00236076i
$521$	−18.5948	−	32.2071i	−0.814652	−	1.41102i	−0.909578	−	0.415534i	$-0.863595\pi$
$521$	−18.5948	−	32.2071i	−0.814652	−	1.41102i	0.0949259	−	0.995484i	$-0.469739\pi$
$522$		0			0
$523$	2.54540	−	4.40876i	0.111303	−	0.192782i	−0.804993	−	0.593284i	$-0.797831\pi$
$523$	2.54540	−	4.40876i	0.111303	−	0.192782i	0.916296	+	0.400502i	$0.131164\pi$
$524$	38.2823			1.67237
$525$		0			0
$526$	5.23567			0.228286
$527$	1.84712	−	3.19931i	0.0804618	−	0.139364i
$528$		0			0
$529$	4.43475	+	7.68121i	0.192815	+	0.333966i
$530$	−12.8099	+	22.1874i	−0.556426	+	0.963758i
$531$		0			0
$532$	3.20873	+	35.5694i	0.139116	+	1.54213i
$533$	−4.92168			−0.213181
$534$		0			0
$535$	−6.15583	−	10.6622i	−0.266140	−	0.460968i
$536$	−0.322289	−	0.558220i	−0.0139208	−	0.0241114i
$537$		0			0
$538$	29.1026			1.25470
$539$	−3.24397	−	3.82389i	−0.139728	−	0.164707i
$540$		0			0
$541$	0.383425	−	0.664111i	0.0164847	−	0.0285524i	−0.857665	−	0.514208i	$-0.828086\pi$
$541$	0.383425	−	0.664111i	0.0164847	−	0.0285524i	0.874150	+	0.485656i	$0.161419\pi$
$542$	8.67272	+	15.0216i	0.372525	+	0.645232i
$543$		0			0
$544$	−9.44643	+	16.3617i	−0.405012	+	0.701502i
$545$	12.4309			0.532480
$546$		0			0
$547$	14.1428			0.604702			0.302351	−	0.953197i	$-0.402229\pi$
$547$	14.1428			0.604702			0.302351	+	0.953197i	$0.402229\pi$
$548$	6.28741	−	10.8901i	0.268585	−	0.465203i
$549$		0			0
$550$	−3.00691	−	5.20813i	−0.128215	−	0.222075i
$551$	10.8099	−	18.7233i	0.460516	−	0.797637i
$552$		0			0
$553$	−31.2310	−	14.4607i	−1.32808	−	0.614932i
$554$	24.5582			1.04338
$555$		0			0
$556$	4.06834	+	7.04657i	0.172536	+	0.298841i
$557$	−12.4314	−	21.5317i	−0.526733	−	0.912329i	−0.999515	−	0.0311490i	$-0.990083\pi$
$557$	−12.4314	−	21.5317i	−0.526733	−	0.912329i	0.472782	−	0.881180i	$-0.343250\pi$
$558$		0			0
$559$	−9.43766			−0.399171
$560$	7.70072	−	5.42315i	0.325415	−	0.229170i
$561$		0			0
$562$	−24.2852	+	42.0633i	−1.02441	+	1.77433i
$563$	22.0047	+	38.1133i	0.927388	+	1.60628i	0.787675	+	0.616091i	$0.211285\pi$
$563$	22.0047	+	38.1133i	0.927388	+	1.60628i	0.139713	+	0.990192i	$0.455382\pi$
$564$		0			0
$565$	1.47542	−	2.55550i	0.0620713	−	0.107511i
$566$	−61.7989			−2.59760
$567$		0			0
$568$	−0.754366			−0.0316525
$569$	−16.6308	+	28.8054i	−0.697199	+	1.20758i	0.272235	+	0.962231i	$0.412237\pi$
$569$	−16.6308	+	28.8054i	−0.697199	+	1.20758i	−0.969434	+	0.245353i	$0.921096\pi$
$570$		0			0
$571$	6.17699	+	10.6989i	0.258499	+	0.447734i	0.965840	−	0.259139i	$-0.0834387\pi$
$571$	6.17699	+	10.6989i	0.258499	+	0.447734i	−0.707341	+	0.706873i	$0.750105\pi$
$572$	0.728600	−	1.26197i	0.0304643	−	0.0527657i
$573$		0			0
$574$	23.7334	+	10.9891i	0.990613	+	0.458678i
$575$	15.7116			0.655219
$576$		0			0
$577$	12.9829	+	22.4871i	0.540486	+	0.936150i	0.998876	+	0.0473984i	$0.0150930\pi$
$577$	12.9829	+	22.4871i	0.540486	+	0.936150i	−0.458390	+	0.888751i	$0.651574\pi$
$578$	11.5157	+	19.9458i	0.478990	+	0.829635i
$579$		0			0
$580$	6.00250			0.249240
$581$	−0.841685	−	9.33026i	−0.0349190	−	0.387085i
$582$		0			0
$583$	−5.04435	+	8.73707i	−0.208916	+	0.361853i
$584$	0.119180	+	0.206426i	0.00493171	+	0.00854196i
$585$		0			0
$586$	−31.9652	+	55.3653i	−1.32047	+	2.28712i
$587$	23.9747			0.989543			0.494771	−	0.869023i	$-0.335252\pi$
$587$	23.9747			0.989543			0.494771	+	0.869023i	$0.335252\pi$
$588$		0			0
$589$	10.4217			0.429418
$590$	−0.651589	+	1.12859i	−0.0268255	+	0.0464631i
$591$		0			0
$592$	10.2366	+	17.7304i	0.420723	+	0.728713i
$593$	23.5240	−	40.7448i	0.966015	−	1.67319i	0.259154	−	0.965836i	$-0.416556\pi$
$593$	23.5240	−	40.7448i	0.966015	−	1.67319i	0.706862	−	0.707352i	$-0.250110\pi$
$594$		0			0
$595$	0.506439	+	5.61398i	0.0207620	+	0.230151i
$596$	42.8744			1.75620
$597$		0			0
$598$	3.77508	+	6.53863i	0.154374	+	0.267384i
$599$	10.0868	+	17.4708i	0.412135	+	0.713840i	0.995123	−	0.0986415i	$-0.0314497\pi$
$599$	10.0868	+	17.4708i	0.412135	+	0.713840i	−0.582988	+	0.812481i	$0.698116\pi$
$600$		0			0
$601$	29.5773			1.20648			0.603242	−	0.797558i	$-0.293875\pi$
$601$	29.5773			1.20648			0.603242	+	0.797558i	$0.293875\pi$
$602$	45.5105	+	21.0724i	1.85487	+	0.858849i
$603$		0			0
$604$	15.9921	−	27.6991i	0.650708	−	1.12706i
$605$	−4.74907	−	8.22564i	−0.193077	−	0.334420i
$606$		0			0
$607$	7.72099	−	13.3732i	0.313385	−	0.542799i	−0.665708	−	0.746213i	$-0.731870\pi$
$607$	7.72099	−	13.3732i	0.313385	−	0.542799i	0.979093	+	0.203413i	$0.0652035\pi$
$608$	−53.2980			−2.16152
$609$		0			0
$610$	21.1981			0.858287
$611$	−4.15993	+	7.20521i	−0.168293	+	0.291492i
$612$		0			0
$613$	−0.997423	−	1.72759i	−0.0402855	−	0.0697766i	0.845180	−	0.534482i	$-0.179493\pi$
$613$	−0.997423	−	1.72759i	−0.0402855	−	0.0697766i	−0.885465	+	0.464706i	$0.846160\pi$
$614$	−28.9111	+	50.0755i	−1.16676	+	2.02088i
$615$		0			0
$616$	−0.106353	+	0.0748982i	−0.00428510	+	0.00301773i
$617$	2.85584			0.114972			0.0574858	−	0.998346i	$-0.481692\pi$
$617$	2.85584			0.114972			0.0574858	+	0.998346i	$0.481692\pi$
$618$		0			0
$619$	−15.9911	−	27.6975i	−0.642738	−	1.11326i	−0.984819	−	0.173585i	$-0.944465\pi$
$619$	−15.9911	−	27.6975i	−0.642738	−	1.11326i	0.342080	−	0.939671i	$-0.388868\pi$
$620$	1.44674	+	2.50582i	0.0581024	+	0.100636i
$621$		0			0
$622$	−11.0843			−0.444440
$623$	28.9307	+	13.3956i	1.15908	+	0.536684i
$624$		0			0
$625$	−6.68398	+	11.5770i	−0.267359	+	0.463080i
$626$	4.86865	+	8.43275i	0.194590	+	0.337040i
$627$		0			0
$628$	7.91800	−	13.7144i	0.315963	−	0.547263i
$629$	−12.2526			−0.488542
$630$		0			0
$631$	32.1115			1.27834			0.639169	−	0.769066i	$-0.279278\pi$
$631$	32.1115			1.27834			0.639169	+	0.769066i	$0.279278\pi$
$632$	−0.446390	+	0.773171i	−0.0177565	+	0.0307551i
$633$		0			0
$634$	−7.68774	−	13.3156i	−0.305319	−	0.528828i
$635$	−0.430596	+	0.745814i	−0.0170877	+	0.0295967i
$636$		0			0
$637$	−6.88699	+	1.25275i	−0.272872	+	0.0496357i
$638$	4.68769			0.185588
$639$		0			0
$640$	−0.248611	−	0.430607i	−0.00982721	−	0.0170212i
$641$	16.5124	+	28.6003i	0.652200	+	1.12964i	0.982588	+	0.185799i	$0.0594873\pi$
$641$	16.5124	+	28.6003i	0.652200	+	1.12964i	−0.330387	+	0.943845i	$0.607179\pi$
$642$		0			0
$643$	15.7942			0.622863			0.311432	−	0.950269i	$-0.399192\pi$
$643$	15.7942			0.622863			0.311432	+	0.950269i	$0.399192\pi$
$644$	−1.81765	−	20.1491i	−0.0716256	−	0.793985i
$645$		0			0
$646$	15.6760	−	27.1516i	0.616764	−	1.06827i
$647$	−2.32036	−	4.01898i	−0.0912227	−	0.158002i	0.816803	−	0.576916i	$-0.195744\pi$
$647$	−2.32036	−	4.01898i	−0.0912227	−	0.158002i	−0.908026	+	0.418914i	$0.862411\pi$
$648$		0			0
$649$	−0.256587	+	0.444421i	−0.0100719	+	0.0174451i
$650$	−8.39497			−0.329278
$651$		0			0
$652$	3.43757			0.134626
$653$	13.4143	−	23.2342i	0.524941	−	0.909225i	−0.474637	−	0.880182i	$-0.657421\pi$
$653$	13.4143	−	23.2342i	0.524941	−	0.909225i	0.999578	−	0.0290430i	$-0.00924599\pi$
$654$		0			0
$655$	8.52266	+	14.7617i	0.333008	+	0.576787i
$656$	−9.67230	+	16.7529i	−0.377640	+	0.654092i
$657$		0			0
$658$	36.1479	−	25.4568i	1.40919	−	0.992409i
$659$	42.9889			1.67461			0.837306	−	0.546735i	$-0.184129\pi$
$659$	42.9889			1.67461			0.837306	+	0.546735i	$0.184129\pi$
$660$		0			0
$661$	14.7349	+	25.5216i	0.573122	+	0.992676i	0.996243	+	0.0866030i	$0.0276012\pi$
$661$	14.7349	+	25.5216i	0.573122	+	0.992676i	−0.423121	+	0.906073i	$0.639066\pi$
$662$	−11.3915	−	19.7307i	−0.442744	−	0.766855i
$663$		0			0
$664$	−0.243015			−0.00943082
$665$	−13.0013	+	9.15599i	−0.504167	+	0.355054i
$666$		0			0
$667$	−6.12349	+	10.6062i	−0.237102	+	0.410673i
$668$	−22.2403	−	38.5214i	−0.860504	−	1.49044i
$669$		0			0
$670$	8.54256	−	14.7962i	0.330028	−	0.571625i
$671$	8.34752			0.322252
$672$		0			0
$673$	−20.1702			−0.777504			−0.388752	−	0.921342i	$-0.627094\pi$
$673$	−20.1702			−0.777504			−0.388752	+	0.921342i	$0.627094\pi$
$674$	−1.74891	+	3.02920i	−0.0673655	+	0.116680i
$675$		0			0
$676$	−1.01709	−	1.76164i	−0.0391187	−	0.0677555i
$677$	−3.10241	+	5.37353i	−0.119235	+	0.206521i	−0.919465	−	0.393172i	$-0.871378\pi$
$677$	−3.10241	+	5.37353i	−0.119235	+	0.206521i	0.800230	+	0.599694i	$0.204711\pi$
$678$		0			0
$679$	1.76800	+	19.5986i	0.0678495	+	0.752126i
$680$	0.146221			0.00560733
$681$		0			0
$682$	1.12984	+	1.95694i	0.0432638	+	0.0749351i
$683$	−0.884758	−	1.53245i	−0.0338543	−	0.0586374i	0.848602	−	0.529032i	$-0.177445\pi$
$683$	−0.884758	−	1.53245i	−0.0338543	−	0.0586374i	−0.882456	+	0.470395i	$0.844112\pi$
$684$		0			0
$685$	5.59899			0.213926
$686$	36.0077	+	9.33627i	1.37478	+	0.356460i
$687$		0			0
$688$	−18.5473	+	32.1249i	−0.707110	+	1.22475i
$689$	7.04163	+	12.1965i	0.268265	+	0.464648i
$690$		0			0
$691$	−22.4658	+	38.9120i	−0.854641	+	1.48028i	0.0223363	+	0.999751i	$0.492890\pi$
$691$	−22.4658	+	38.9120i	−0.854641	+	1.48028i	−0.876977	+	0.480531i	$0.840444\pi$
$692$	−11.8820			−0.451688
$693$		0			0
$694$	−42.2800			−1.60493
$695$	−1.81144	+	3.13751i	−0.0687120	+	0.119013i
$696$		0			0
$697$	−5.78856	−	10.0261i	−0.219257	−	0.379765i
$698$	8.39162	−	14.5347i	0.317628	−	0.550147i
$699$		0			0
$700$	20.4126	+	9.45154i	0.771525	+	0.357235i
$701$	−38.5707			−1.45679			−0.728397	−	0.685156i	$-0.759734\pi$
$701$	−38.5707			−1.45679			−0.728397	+	0.685156i	$0.759734\pi$
$702$		0			0
$703$	−17.2827	−	29.9344i	−0.651828	−	1.12900i
$704$	−2.96251	−	5.13121i	−0.111654	−	0.193390i
$705$		0			0
$706$	17.1398			0.645066
$707$	2.59375	−	1.82662i	0.0975480	−	0.0686972i
$708$		0			0
$709$	−4.38866	+	7.60137i	−0.164819	+	0.285476i	−0.936591	−	0.350424i	$-0.886037\pi$
$709$	−4.38866	+	7.60137i	−0.164819	+	0.285476i	0.771772	+	0.635900i	$0.219371\pi$
$710$	−9.99758	−	17.3163i	−0.375203	−	0.649870i
$711$		0			0
$712$	0.413512	−	0.716223i	0.0154970	−	0.0268416i
$713$	−5.90360			−0.221091
$714$		0			0
$715$	0.648824			0.0242646
$716$	2.57757	−	4.46449i	0.0963284	−	0.166846i
$717$		0			0
$718$	−16.2402	−	28.1289i	−0.606080	−	1.04976i
$719$	2.10218	−	3.64109i	0.0783982	−	0.135790i	−0.824161	−	0.566356i	$-0.808353\pi$
$719$	2.10218	−	3.64109i	0.0783982	−	0.135790i	0.902559	+	0.430566i	$0.141686\pi$
$720$		0			0
$721$	34.6022	+	16.0216i	1.28865	+	0.596677i
$722$	50.2840			1.87138
$723$		0			0
$724$	10.9080	+	18.8933i	0.405394	+	0.702164i
$725$	−6.80866	−	11.7930i	−0.252867	−	0.437979i
$726$		0			0
$727$	−28.9856			−1.07502			−0.537509	−	0.843258i	$-0.680634\pi$
$727$	−28.9856			−1.07502			−0.537509	+	0.843258i	$0.680634\pi$
$728$	0.0163145	+	0.180850i	0.000604656	+	0.00670274i
$729$		0			0
$730$	−3.15898	+	5.47151i	−0.116919	+	0.202510i
$731$	−11.1000	−	19.2257i	−0.410547	−	0.711089i
$732$		0			0
$733$	12.0172	−	20.8145i	0.443867	−	0.768800i	−0.554106	−	0.832446i	$-0.686940\pi$
$733$	12.0172	−	20.8145i	0.443867	−	0.768800i	0.997972	+	0.0636467i	$0.0202731\pi$
$734$	56.5480			2.08722
$735$		0			0
$736$	30.1918			1.11288
$737$	3.36394	−	5.82652i	0.123912	−	0.214622i
$738$		0			0
$739$	−5.90276	−	10.2239i	−0.217136	−	0.376091i	0.736795	−	0.676116i	$-0.236338\pi$
$739$	−5.90276	−	10.2239i	−0.217136	−	0.376091i	−0.953931	+	0.300025i	$0.903005\pi$
$740$	4.79835	−	8.31099i	0.176391	−	0.305518i
$741$		0			0
$742$	−6.72396	−	74.5366i	−0.246844	−	2.73632i
$743$	−47.2786			−1.73448			−0.867241	−	0.497888i	$-0.834109\pi$
$743$	−47.2786			−1.73448			−0.867241	+	0.497888i	$0.834109\pi$
$744$		0			0
$745$	9.54499	+	16.5324i	0.349701	+	0.605700i
$746$	28.6252	+	49.5802i	1.04804	+	1.81526i
$747$		0			0
$748$	3.42773			0.125330
$749$	32.6356	+	15.1111i	1.19248	+	0.552147i
$750$		0			0
$751$	−2.73850	+	4.74322i	−0.0999294	+	0.173083i	−0.911655	−	0.410956i	$-0.865195\pi$
$751$	−2.73850	+	4.74322i	−0.0999294	+	0.173083i	0.811726	+	0.584039i	$0.198528\pi$
$752$	16.3506	+	28.3200i	0.596244	+	1.03273i
$753$		0			0
$754$	3.27188	−	5.66706i	0.119155	−	0.206382i
$755$	14.2410			0.518285
$756$		0			0
$757$	10.7453			0.390546			0.195273	−	0.980749i	$-0.437441\pi$
$757$	10.7453			0.390546			0.195273	+	0.980749i	$0.437441\pi$
$758$	7.29358	−	12.6329i	0.264915	−	0.458846i
$759$		0			0
$760$	0.206250	+	0.357236i	0.00748148	+	0.0129583i
$761$	−16.5200	+	28.6134i	−0.598848	+	1.03724i	0.394143	+	0.919049i	$0.371041\pi$
$761$	−16.5200	+	28.6134i	−0.598848	+	1.03724i	−0.992991	+	0.118186i	$0.962292\pi$
$762$		0			0
$763$	−29.6891	+	20.9082i	−1.07482	+	0.756928i
$764$	3.41457			0.123535
$765$		0			0
$766$	12.9877	+	22.4953i	0.469263	+	0.812788i
$767$	0.358181	+	0.620387i	0.0129332	+	0.0224009i
$768$		0			0
$769$	2.98332			0.107581			0.0537907	−	0.998552i	$-0.482870\pi$
$769$	2.98332			0.107581			0.0537907	+	0.998552i	$0.482870\pi$
$770$	−3.12877	−	1.44870i	−0.112753	−	0.0522074i
$771$		0			0
$772$	6.55833	−	11.3594i	0.236039	−	0.408832i
$773$	−10.9543	−	18.9733i	−0.393998	−	0.682424i	0.598975	−	0.800768i	$-0.295575\pi$
$773$	−10.9543	−	18.9733i	−0.393998	−	0.682424i	−0.992973	+	0.118344i	$0.962242\pi$
$774$		0			0
$775$	3.28208	−	5.68473i	0.117896	−	0.204202i
$776$	0.510464			0.0183246
$777$		0			0
$778$	42.4516			1.52196
$779$	16.3299	−	28.2842i	0.585079	−	1.01339i
$780$		0			0
$781$	−3.93691	−	6.81892i	−0.140874	−	0.244000i
$782$	−8.88001	+	15.3806i	−0.317548	+	0.550010i
$783$		0			0
$784$	−9.27039	+	25.9046i	−0.331085	+	0.925165i
$785$	7.05104			0.251662
$786$		0			0
$787$	6.68161	+	11.5729i	0.238174	+	0.412529i	0.960190	−	0.279347i	$-0.0901179\pi$
$787$	6.68161	+	11.5729i	0.238174	+	0.412529i	−0.722017	+	0.691876i	$0.756785\pi$
$788$	1.90450	+	3.29869i	0.0678451	+	0.117511i
$789$		0			0
$790$	−23.6640			−0.841927
$791$	0.774453	+	8.58498i	0.0275364	+	0.305247i
$792$		0			0
$793$	5.82633	−	10.0915i	0.206899	−	0.358360i
$794$	−19.2892	−	33.4099i	−0.684548	−	1.18567i
$795$		0			0
$796$	11.5914	−	20.0768i	0.410845	−	0.711605i
$797$	−32.5388			−1.15258			−0.576292	−	0.817244i	$-0.695501\pi$
$797$	−32.5388			−1.15258			−0.576292	+	0.817244i	$0.695501\pi$
$798$		0			0
$799$	−19.5706			−0.692357
$800$	−16.7850	+	29.0725i	−0.593440	+	1.02787i
$801$		0			0
$802$	16.7403	+	28.9950i	0.591119	+	1.02385i
$803$	−1.24396	+	2.15460i	−0.0438984	+	0.0760343i
$804$		0			0
$805$	7.36484	−	5.18661i	0.259577	−	0.182804i
$806$	3.15439			0.111109
$807$		0			0
$808$	−0.0411469	−	0.0712685i	−0.00144754	−	0.00250722i
$809$	3.84413	+	6.65824i	0.135153	+	0.234091i	0.925656	−	0.378367i	$-0.123514\pi$
$809$	3.84413	+	6.65824i	0.135153	+	0.234091i	−0.790503	+	0.612458i	$0.790181\pi$
$810$		0			0
$811$	−48.3178			−1.69667			−0.848334	−	0.529461i	$-0.822394\pi$
$811$	−48.3178			−1.69667			−0.848334	+	0.529461i	$0.822394\pi$
$812$	−14.3360	+	10.0960i	−0.503094	+	0.354299i
$813$		0			0
$814$	3.74731	−	6.49052i	0.131343	−	0.227493i
$815$	0.765295	+	1.32553i	0.0268071	+	0.0464313i
$816$		0			0
$817$	31.3137	−	54.2370i	1.09553	−	1.89751i
$818$	24.8019			0.867178
$819$		0			0
$820$	9.06766			0.316656
$821$	−1.86721	+	3.23410i	−0.0651661	+	0.112871i	−0.896768	−	0.442502i	$-0.854091\pi$
$821$	−1.86721	+	3.23410i	−0.0651661	+	0.112871i	0.831602	+	0.555373i	$0.187424\pi$
$822$		0			0
$823$	−7.11590	−	12.3251i	−0.248045	−	0.429626i	0.714939	−	0.699187i	$-0.246455\pi$
$823$	−7.11590	−	12.3251i	−0.248045	−	0.429626i	−0.962983	+	0.269561i	$0.913121\pi$
$824$	0.494575	−	0.856629i	0.0172293	−	0.0298421i
$825$		0			0
$826$	−0.342022	−	3.79139i	−0.0119005	−	0.131919i
$827$	−48.3016			−1.67961			−0.839805	−	0.542888i	$-0.817331\pi$
$827$	−48.3016			−1.67961			−0.839805	+	0.542888i	$0.817331\pi$
$828$		0			0
$829$	−5.75506	−	9.96806i	−0.199882	−	0.346205i	0.748608	−	0.663013i	$-0.230722\pi$
$829$	−5.75506	−	9.96806i	−0.199882	−	0.346205i	−0.948490	+	0.316808i	$0.897389\pi$
$830$	−3.22067	−	5.57837i	−0.111791	−	0.193628i
$831$		0			0
$832$	−8.27099			−0.286745
$833$	−10.6520	−	12.5563i	−0.369071	−	0.435049i
$834$		0			0
$835$	9.90258	−	17.1518i	0.342693	−	0.593562i
$836$	4.83493	+	8.37434i	0.167219	+	0.289633i
$837$		0			0
$838$	4.37792	−	7.58278i	0.151233	−	0.261943i
$839$	−13.1103			−0.452616			−0.226308	−	0.974056i	$-0.572666\pi$
$839$	−13.1103			−0.452616			−0.226308	+	0.974056i	$0.572666\pi$
$840$		0			0
$841$	−18.3855			−0.633982
$842$	10.0426	−	17.3943i	0.346092	−	0.599448i
$843$		0			0
$844$	−7.66475	−	13.2757i	−0.263831	−	0.456969i
$845$	0.452861	−	0.784378i	0.0155789	−	0.0269834i
$846$		0			0
$847$	25.1776	+	11.6578i	0.865111	+	0.400568i
$848$	55.3541			1.90087
$849$		0			0
$850$	−9.87362	−	17.1016i	−0.338662	−	0.586580i
$851$	9.79014	+	16.9570i	0.335602	+	0.581279i
$852$		0			0
$853$	8.80346			0.301425			0.150712	−	0.988578i	$-0.451843\pi$
$853$	8.80346			0.301425			0.150712	+	0.988578i	$0.451843\pi$
$854$	−50.6282	+	35.6544i	−1.73246	+	1.22007i
$855$		0			0
$856$	0.466467	−	0.807945i	0.0159435	−	0.0276150i
$857$	8.48254	+	14.6922i	0.289758	+	0.501876i	0.973752	−	0.227612i	$-0.0730918\pi$
$857$	8.48254	+	14.6922i	0.289758	+	0.501876i	−0.683994	+	0.729488i	$0.739758\pi$
$858$		0			0
$859$	−7.27049	+	12.5929i	−0.248066	+	0.429663i	−0.962989	−	0.269540i	$-0.913128\pi$
$859$	−7.27049	+	12.5929i	−0.248066	+	0.429663i	0.714923	+	0.699203i	$0.246462\pi$
$860$	17.3879			0.592922
$861$		0			0
$862$	46.9243			1.59825
$863$	19.5222	−	33.8135i	0.664544	−	1.15102i	−0.314865	−	0.949136i	$-0.601959\pi$
$863$	19.5222	−	33.8135i	0.664544	−	1.15102i	0.979409	−	0.201887i	$-0.0647074\pi$
$864$		0			0
$865$	−2.64526	−	4.58173i	−0.0899416	−	0.155783i
$866$	2.72441	−	4.71882i	0.0925793	−	0.160352i
$867$		0			0
$868$	−7.66999	−	3.55139i	−0.260336	−	0.120542i
$869$	−9.31854			−0.316110
$870$		0			0
$871$	−4.69587	−	8.13349i	−0.159114	−	0.275593i
$872$	0.470983	+	0.815767i	0.0159495	+	0.0276253i
$873$		0			0
$874$	−50.1022			−1.69473
$875$	1.97636	+	21.9084i	0.0668133	+	0.740639i
$876$		0			0
$877$	−16.2971	+	28.2273i	−0.550312	+	0.953169i	0.447939	+	0.894064i	$0.352158\pi$
$877$	−16.2971	+	28.2273i	−0.550312	+	0.953169i	−0.998252	+	0.0591051i	$0.981175\pi$
$878$	8.87285	+	15.3682i	0.299444	+	0.518652i
$879$		0			0
$880$	1.27510	−	2.20853i	0.0429835	−	0.0744497i
$881$	43.4141			1.46266			0.731330	−	0.682024i	$-0.238900\pi$
$881$	43.4141			1.46266			0.731330	+	0.682024i	$0.238900\pi$
$882$		0			0
$883$	28.2902			0.952040			0.476020	−	0.879434i	$-0.342079\pi$
$883$	28.2902			0.952040			0.476020	+	0.879434i	$0.342079\pi$
$884$	2.39246	−	4.14386i	0.0804672	−	0.139373i
$885$		0			0
$886$	−2.91796	−	5.05406i	−0.0980308	−	0.169794i
$887$	−25.1325	+	43.5307i	−0.843866	+	1.46162i	0.0427364	+	0.999086i	$0.486392\pi$
$887$	−25.1325	+	43.5307i	−0.843866	+	1.46162i	−0.886602	+	0.462532i	$0.846941\pi$
$888$		0			0
$889$	−0.226022	−	2.50550i	−0.00758052	−	0.0840317i
$890$	21.9210			0.734794
$891$		0			0
$892$	−17.9362	−	31.0664i	−0.600548	−	1.04018i
$893$	−27.6049	−	47.8131i	−0.923764	−	1.60001i
$894$		0			0
$895$	2.29535			0.0767250
$896$	1.31803	+	0.610280i	0.0440323	+	0.0203880i
$897$		0			0
$898$	−15.3428	+	26.5745i	−0.511996	+	0.886803i
$899$	2.55834	+	4.43117i	0.0853253	+	0.147788i
$900$		0			0
$901$	−16.5638	+	28.6894i	−0.551821	+	0.955782i
$902$	7.08145			0.235786
$903$		0			0
$904$	0.223604			0.00743695
$905$	−4.85685	+	8.41231i	−0.161447	+	0.279635i
$906$		0			0
$907$	−13.4138	−	23.2334i	−0.445399	−	0.771453i	0.552681	−	0.833393i	$-0.313605\pi$
$907$	−13.4138	−	23.2334i	−0.445399	−	0.771453i	−0.998080	+	0.0619394i	$0.980271\pi$
$908$	−5.42009	+	9.38787i	−0.179872	+	0.311548i
$909$		0			0
$910$	−3.93516	+	2.77129i	−0.130449	+	0.0918674i
$911$	22.3560			0.740687			0.370344	−	0.928895i	$-0.379240\pi$
$911$	22.3560			0.740687			0.370344	+	0.928895i	$0.379240\pi$
$912$		0			0
$913$	−1.26826	−	2.19668i	−0.0419731	−	0.0726996i
$914$	−23.7608	−	41.1550i	−0.785939	−	1.36129i
$915$		0			0
$916$	−17.3291			−0.572569
$917$	−45.1835	−	20.9211i	−1.49209	−	0.690875i
$918$		0			0
$919$	4.31122	−	7.46725i	0.142214	−	0.246322i	−0.786116	−	0.618079i	$-0.787911\pi$
$919$	4.31122	−	7.46725i	0.142214	−	0.246322i	0.928330	+	0.371757i	$0.121245\pi$
$920$	−0.116835	−	0.202364i	−0.00385193	−	0.00667174i
$921$		0			0
$922$	−26.7305	+	46.2985i	−0.880321	+	1.52476i
$923$	−10.9914			−0.361786
$924$		0			0
$925$	−21.7712			−0.715832
$926$	1.44865	−	2.50913i	0.0476054	−	0.0824550i
$927$		0			0
$928$	−13.0837	−	22.6616i	−0.429493	−	0.743904i
$929$	20.6930	−	35.8414i	0.678916	−	1.17592i	−0.296391	−	0.955067i	$-0.595783\pi$
$929$	20.6930	−	35.8414i	0.678916	−	1.17592i	0.975308	−	0.220851i	$-0.0708834\pi$
$930$		0			0
$931$	15.6513	−	43.7352i	0.512952	−	1.43336i
$932$	−9.66985			−0.316747
$933$		0			0
$934$	−8.42535	−	14.5931i	−0.275686	−	0.477502i
$935$	0.763105	+	1.32174i	0.0249562	+	0.0432254i
$936$		0			0
$937$	21.3818			0.698514			0.349257	−	0.937027i	$-0.386434\pi$
$937$	21.3818			0.698514			0.349257	+	0.937027i	$0.386434\pi$
$938$	4.48403	+	49.7064i	0.146409	+	1.62297i
$939$		0			0
$940$	7.66423	−	13.2748i	0.249979	−	0.432977i
$941$	−26.5740	−	46.0275i	−0.866288	−	1.50046i	−0.865762	−	0.500455i	$-0.833166\pi$
$941$	−26.5740	−	46.0275i	−0.866288	−	1.50046i	−0.000525658	−	1.00000i	$-0.500167\pi$
$942$		0			0
$943$	−9.25043	+	16.0222i	−0.301235	+	0.521755i
$944$	2.81565			0.0916416
$945$		0			0
$946$	13.5792			0.441497
$947$	−4.43468	+	7.68109i	−0.144108	+	0.249602i	−0.929040	−	0.369980i	$-0.879365\pi$
$947$	−4.43468	+	7.68109i	−0.144108	+	0.249602i	0.784932	+	0.619582i	$0.212698\pi$
$948$		0			0
$949$	1.73650	+	3.00771i	0.0563692	+	0.0976343i
$950$	27.8541	−	48.2448i	0.903707	−	1.56527i
$951$		0			0
$952$	−0.349226	+	0.245939i	−0.0113185	+	0.00797091i
$953$	39.8167			1.28979			0.644894	−	0.764272i	$-0.276901\pi$
$953$	39.8167			1.28979			0.644894	+	0.764272i	$0.276901\pi$
$954$		0			0
$955$	0.760174	+	1.31666i	0.0245987	+	0.0426061i
$956$	15.0848	+	26.1277i	0.487878	+	0.845029i
$957$		0			0
$958$	−25.3319			−0.818435
$959$	−13.3723	+	9.41727i	−0.431813	+	0.304099i
$960$		0			0
$961$	14.2668	−	24.7108i	0.460218	−	0.797121i
$962$	−5.23103	−	9.06041i	−0.168655	−	0.292119i
$963$		0			0
$964$	6.22589	−	10.7836i	0.200523	−	0.347315i
$965$	5.84024			0.188004
$966$		0			0
$967$	−22.1611			−0.712652			−0.356326	−	0.934362i	$-0.615971\pi$
$967$	−22.1611			−0.712652			−0.356326	+	0.934362i	$0.615971\pi$
$968$	0.359868	−	0.623309i	0.0115666	−	0.0200339i
$969$		0			0
$970$	6.76516	+	11.7176i	0.217216	+	0.376230i
$971$	18.0212	−	31.2136i	0.578327	−	1.00169i	−0.417345	−	0.908748i	$-0.637039\pi$
$971$	18.0212	−	31.2136i	0.578327	−	1.00169i	0.995671	−	0.0929428i	$-0.0296274\pi$
$972$		0			0
$973$	−0.950834	−	10.5402i	−0.0304824	−	0.337903i
$974$	43.3199			1.38806
$975$		0			0
$976$	−22.9004	−	39.6646i	−0.733022	−	1.26963i
$977$	16.4708	+	28.5283i	0.526947	+	0.912700i	0.999507	+	0.0314009i	$0.00999687\pi$
$977$	16.4708	+	28.5283i	0.526947	+	0.912700i	−0.472559	+	0.881299i	$0.656670\pi$
$978$		0			0
$979$	8.63219			0.275886
$980$	12.6885	−	2.30805i	0.405320	−	0.0737281i
$981$		0			0
$982$	39.4019	−	68.2461i	1.25736	−	2.17782i
$983$	−2.09973	−	3.63683i	−0.0669709	−	0.115997i	0.830596	−	0.556876i	$-0.188000\pi$
$983$	−2.09973	−	3.63683i	−0.0669709	−	0.115997i	−0.897567	+	0.440879i	$0.854667\pi$
$984$		0			0
$985$	−0.847986	+	1.46876i	−0.0270191	+	0.0467984i
$986$	15.3927			0.490203
$987$		0			0
$988$	13.4986			0.429447
$989$	−17.7383	+	30.7237i	−0.564047	+	0.976958i
$990$		0			0
$991$	6.70693	+	11.6167i	0.213053	+	0.369018i	0.952668	−	0.304011i	$-0.0983261\pi$
$991$	6.70693	+	11.6167i	0.213053	+	0.369018i	−0.739616	+	0.673029i	$0.764993\pi$
$992$	6.30693	−	10.9239i	0.200245	−	0.346835i
$993$		0			0
$994$	53.0029	+	24.5416i	1.68115	+	0.778414i
$995$	10.3222			0.327236
$996$		0			0
$997$	23.9434	+	41.4712i	0.758295	+	1.31341i	0.943719	+	0.330747i	$0.107301\pi$
$997$	23.9434	+	41.4712i	0.758295	+	1.31341i	−0.185424	+	0.982659i	$0.559366\pi$
$998$	−9.20722	−	15.9474i	−0.291449	−	0.504805i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.j.h.352.1		10
3.2	odd	2		91.2.e.c.79.5	yes	10
7.2	even	3		5733.2.a.bl.1.5		5
7.4	even	3	inner	819.2.j.h.235.1		10
7.5	odd	6		5733.2.a.bm.1.5		5
12.11	even	2		1456.2.r.p.625.4		10
21.2	odd	6		637.2.a.l.1.1		5
21.5	even	6		637.2.a.k.1.1		5
21.11	odd	6		91.2.e.c.53.5	✓	10
21.17	even	6		637.2.e.m.508.5		10
21.20	even	2		637.2.e.m.79.5		10
39.38	odd	2		1183.2.e.f.170.1		10
84.11	even	6		1456.2.r.p.417.4		10
273.116	odd	6		1183.2.e.f.508.1		10
273.194	even	6		8281.2.a.bx.1.5		5
273.233	odd	6		8281.2.a.bw.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.5	✓	10	21.11	odd	6
91.2.e.c.79.5	yes	10	3.2	odd	2
637.2.a.k.1.1		5	21.5	even	6
637.2.a.l.1.1		5	21.2	odd	6
637.2.e.m.79.5		10	21.20	even	2
637.2.e.m.508.5		10	21.17	even	6
819.2.j.h.235.1		10	7.4	even	3	inner
819.2.j.h.352.1		10	1.1	even	1	trivial
1183.2.e.f.170.1		10	39.38	odd	2
1183.2.e.f.508.1		10	273.116	odd	6
1456.2.r.p.417.4		10	84.11	even	6
1456.2.r.p.625.4		10	12.11	even	2
5733.2.a.bl.1.5		5	7.2	even	3
5733.2.a.bm.1.5		5	7.5	odd	6
8281.2.a.bw.1.5		5	273.233	odd	6
8281.2.a.bx.1.5		5	273.194	even	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00426 + 1.73943i) q^{2} +(-1.01709 - 1.76164i) q^{4} +(0.452861 - 0.784378i) q^{5} +(0.237709 + 2.63505i) q^{7} +0.0686323 q^{8} +O(q^{10})\)	\(q+(-1.00426 + 1.73943i) q^{2} +(-1.01709 - 1.76164i) q^{4} +(0.452861 - 0.784378i) q^{5} +(0.237709 + 2.63505i) q^{7} +0.0686323 q^{8} +(0.909582 + 1.57544i) q^{10} +(0.358181 + 0.620387i) q^{11} +1.00000 q^{13} +(-4.82222 - 2.23280i) q^{14} +(1.96525 - 3.40391i) q^{16} +(1.17614 + 2.03713i) q^{17} +(-3.31796 + 5.74687i) q^{19} -1.84239 q^{20} -1.43883 q^{22} +(1.87953 - 3.25544i) q^{23} +(2.08983 + 3.61970i) q^{25} +(-1.00426 + 1.73943i) q^{26} +(4.40025 - 3.09883i) q^{28} -3.25799 q^{29} +(-0.785250 - 1.36009i) q^{31} +(4.01588 + 6.95570i) q^{32} -4.72459 q^{34} +(2.17452 + 1.00686i) q^{35} +(-2.60441 + 4.51098i) q^{37} +(-6.66419 - 11.5427i) q^{38} +(0.0310809 - 0.0538337i) q^{40} -4.92168 q^{41} -9.43766 q^{43} +(0.728600 - 1.26197i) q^{44} +(3.77508 + 6.53863i) q^{46} +(-4.15993 + 7.20521i) q^{47} +(-6.88699 + 1.25275i) q^{49} -8.39497 q^{50} +(-1.01709 - 1.76164i) q^{52} +(7.04163 + 12.1965i) q^{53} +0.648824 q^{55} +(0.0163145 + 0.180850i) q^{56} +(3.27188 - 5.66706i) q^{58} +(0.358181 + 0.620387i) q^{59} +(5.82633 - 10.0915i) q^{61} +3.15439 q^{62} -8.27099 q^{64} +(0.452861 - 0.784378i) q^{65} +(-4.69587 - 8.13349i) q^{67} +(2.39246 - 4.14386i) q^{68} +(-3.93516 + 2.77129i) q^{70} -10.9914 q^{71} +(1.73650 + 3.00771i) q^{73} +(-5.23103 - 9.06041i) q^{74} +13.4986 q^{76} +(-1.54961 + 1.09130i) q^{77} +(-6.50408 + 11.2654i) q^{79} +(-1.77997 - 3.08299i) q^{80} +(4.94265 - 8.56093i) q^{82} -3.54083 q^{83} +2.13050 q^{85} +(9.47789 - 16.4162i) q^{86} +(0.0245828 + 0.0425786i) q^{88} +(6.02503 - 10.4357i) q^{89} +(0.237709 + 2.63505i) q^{91} -7.64656 q^{92} +(-8.35532 - 14.4718i) q^{94} +(3.00514 + 5.20506i) q^{95} +7.43766 q^{97} +(4.73727 - 13.2375i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8	\( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8} + 5 q^{10} + 11 q^{11} + 10 q^{13} - 10 q^{14} - 10 q^{16} - 5 q^{17} - 9 q^{19} - 2 q^{20} + 16 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} + 37 q^{28} + 6 q^{29} + 6 q^{31} + 22 q^{32} - 44 q^{34} + 4 q^{35} - 4 q^{37} - 10 q^{38} - 28 q^{40} - 28 q^{41} + 4 q^{43} - 3 q^{46} + q^{47} - 11 q^{49} - 18 q^{50} - 8 q^{52} + 17 q^{53} + 21 q^{56} + 27 q^{58} + 11 q^{59} + 11 q^{61} + 46 q^{62} + 18 q^{64} + 2 q^{65} - 13 q^{67} - 32 q^{68} + 49 q^{70} - 30 q^{71} - 33 q^{74} + 16 q^{76} + 46 q^{77} - 2 q^{79} + 55 q^{80} - 34 q^{82} - 12 q^{83} - 44 q^{85} + 28 q^{86} + 3 q^{88} - 4 q^{89} + q^{91} - 42 q^{92} - 20 q^{94} - 12 q^{95} - 24 q^{97} + 7 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8 + 5 * q^10 + 11 * q^11 + 10 * q^13 - 10 * q^14 - 10 * q^16 - 5 * q^17 - 9 * q^19 - 2 * q^20 + 16 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 + 37 * q^28 + 6 * q^29 + 6 * q^31 + 22 * q^32 - 44 * q^34 + 4 * q^35 - 4 * q^37 - 10 * q^38 - 28 * q^40 - 28 * q^41 + 4 * q^43 - 3 * q^46 + q^47 - 11 * q^49 - 18 * q^50 - 8 * q^52 + 17 * q^53 + 21 * q^56 + 27 * q^58 + 11 * q^59 + 11 * q^61 + 46 * q^62 + 18 * q^64 + 2 * q^65 - 13 * q^67 - 32 * q^68 + 49 * q^70 - 30 * q^71 - 33 * q^74 + 16 * q^76 + 46 * q^77 - 2 * q^79 + 55 * q^80 - 34 * q^82 - 12 * q^83 - 44 * q^85 + 28 * q^86 + 3 * q^88 - 4 * q^89 + q^91 - 42 * q^92 - 20 * q^94 - 12 * q^95 - 24 * q^97 + 7 * q^98

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