LMFDB - Embedded newform 1638.2.j.t.1171.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(235,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, 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("1638.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.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:	$13.0794958511$
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} + 14x^{8} + 63x^{6} + 110x^{4} + 73x^{2} + 12 $ x^10 + 14x^8 + 63x^6 + 110x^4 + 73x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.4
Root			$1.26571i$ of defining polynomial
Character	$\chi$	$=$	1638.1171
Dual form			1638.2.j.t.235.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.397140 - 0.687867i) q^{5} +(2.08474 + 1.62907i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.397140 - 0.687867i) q^{5} +(2.08474 + 1.62907i) q^{7} -1.00000 q^{8} +(-0.397140 - 0.687867i) q^{10} +(1.92668 + 3.33711i) q^{11} -1.00000 q^{13} +(2.45318 - 0.990902i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.05520 + 1.82765i) q^{17} +(-2.48188 + 4.29874i) q^{19} -0.794280 q^{20} +3.85336 q^{22} +(1.76559 - 3.05808i) q^{23} +(2.18456 + 3.78377i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(0.368446 - 2.61997i) q^{28} +5.70065 q^{29} +(0.0295415 + 0.0511674i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.11039 q^{34} +(1.94852 - 0.787053i) q^{35} +(-4.74280 + 8.21476i) q^{37} +(2.48188 + 4.29874i) q^{38} +(-0.397140 + 0.687867i) q^{40} -2.05739 q^{41} +3.47378 q^{43} +(1.92668 - 3.33711i) q^{44} +(-1.76559 - 3.05808i) q^{46} +(0.472154 - 0.817794i) q^{47} +(1.69227 + 6.79237i) q^{49} +4.36912 q^{50} +(0.500000 + 0.866025i) q^{52} +(1.92116 + 3.32755i) q^{53} +3.06065 q^{55} +(-2.08474 - 1.62907i) q^{56} +(2.85032 - 4.93691i) q^{58} +(-4.58170 - 7.93574i) q^{59} +(2.75788 - 4.77679i) q^{61} +0.0590831 q^{62} +1.00000 q^{64} +(-0.397140 + 0.687867i) q^{65} +(-6.59227 - 11.4181i) q^{67} +(1.05520 - 1.82765i) q^{68} +(0.292649 - 2.08099i) q^{70} +1.96983 q^{71} +(2.61895 + 4.53615i) q^{73} +(4.74280 + 8.21476i) q^{74} +4.96376 q^{76} +(-1.41976 + 10.0957i) q^{77} +(-2.76643 + 4.79160i) q^{79} +(0.397140 + 0.687867i) q^{80} +(-1.02869 + 1.78175i) q^{82} +16.8852 q^{83} +1.67624 q^{85} +(1.73689 - 3.00839i) q^{86} +(-1.92668 - 3.33711i) q^{88} +(6.93506 - 12.0119i) q^{89} +(-2.08474 - 1.62907i) q^{91} -3.53117 q^{92} +(-0.472154 - 0.817794i) q^{94} +(1.97131 + 3.41440i) q^{95} -4.74870 q^{97} +(6.72849 + 1.93064i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8}+O(q^{10}) $ 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8	$ 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8} + q^{10} + 9 q^{11} - 10 q^{13} - 6 q^{14} - 5 q^{16} - 8 q^{17} + 4 q^{19} + 2 q^{20} + 18 q^{22} + 6 q^{23} - 12 q^{25} - 5 q^{26} - 3 q^{28} - 14 q^{29} - 5 q^{31} + 5 q^{32} - 16 q^{34} - 8 q^{35} - 10 q^{37} - 4 q^{38} + q^{40} - 24 q^{41} + 8 q^{43} + 9 q^{44} - 6 q^{46} - 4 q^{47} - 5 q^{49} - 24 q^{50} + 5 q^{52} + 19 q^{53} - 2 q^{55} + 3 q^{56} - 7 q^{58} - 7 q^{59} + 4 q^{61} - 10 q^{62} + 10 q^{64} + q^{65} - 8 q^{68} + 11 q^{70} - 8 q^{71} - 6 q^{73} + 10 q^{74} - 8 q^{76} + 19 q^{77} - 9 q^{79} - q^{80} - 12 q^{82} - 34 q^{83} + 36 q^{85} + 4 q^{86} - 9 q^{88} + 10 q^{89} + 3 q^{91} - 12 q^{92} + 4 q^{94} + 18 q^{95} + 14 q^{97} + 5 q^{98}+O(q^{100}) $ 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8 + q^10 + 9 * q^11 - 10 * q^13 - 6 * q^14 - 5 * q^16 - 8 * q^17 + 4 * q^19 + 2 * q^20 + 18 * q^22 + 6 * q^23 - 12 * q^25 - 5 * q^26 - 3 * q^28 - 14 * q^29 - 5 * q^31 + 5 * q^32 - 16 * q^34 - 8 * q^35 - 10 * q^37 - 4 * q^38 + q^40 - 24 * q^41 + 8 * q^43 + 9 * q^44 - 6 * q^46 - 4 * q^47 - 5 * q^49 - 24 * q^50 + 5 * q^52 + 19 * q^53 - 2 * q^55 + 3 * q^56 - 7 * q^58 - 7 * q^59 + 4 * q^61 - 10 * q^62 + 10 * q^64 + q^65 - 8 * q^68 + 11 * q^70 - 8 * q^71 - 6 * q^73 + 10 * q^74 - 8 * q^76 + 19 * q^77 - 9 * q^79 - q^80 - 12 * q^82 - 34 * q^83 + 36 * q^85 + 4 * q^86 - 9 * q^88 + 10 * q^89 + 3 * q^91 - 12 * q^92 + 4 * q^94 + 18 * q^95 + 14 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.397140	−	0.687867i	0.177606	−	0.307623i	−0.763454	−	0.645862i	$-0.776498\pi$
$5$	0.397140	−	0.687867i	0.177606	−	0.307623i	0.941060	+	0.338239i	$0.109831\pi$
$6$		0			0
$7$	2.08474	+	1.62907i	0.787957	+	0.615730i
$7$	2.08474	+	1.62907i	0.787957	+	0.615730i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.397140	−	0.687867i	−0.125587	−	0.217523i
$11$	1.92668	+	3.33711i	0.580916	+	1.00618i	0.995371	+	0.0961067i	$0.0306390\pi$
$11$	1.92668	+	3.33711i	0.580916	+	1.00618i	−0.414455	+	0.910070i	$0.636028\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	2.45318	−	0.990902i	0.655641	−	0.264830i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.05520	+	1.82765i	0.255923	+	0.443271i	0.965146	−	0.261713i	$-0.0842874\pi$
$17$	1.05520	+	1.82765i	0.255923	+	0.443271i	−0.709223	+	0.704984i	$0.750954\pi$
$18$		0			0
$19$	−2.48188	+	4.29874i	−0.569382	+	0.986198i	0.427245	+	0.904136i	$0.359484\pi$
$19$	−2.48188	+	4.29874i	−0.569382	+	0.986198i	−0.996627	+	0.0820626i	$0.973849\pi$
$20$	−0.794280			−0.177606
$21$		0			0
$22$	3.85336			0.821540
$23$	1.76559	−	3.05808i	0.368150	−	0.637655i	−0.621126	−	0.783711i	$-0.713325\pi$
$23$	1.76559	−	3.05808i	0.368150	−	0.637655i	0.989276	+	0.146056i	$0.0466579\pi$
$24$		0			0
$25$	2.18456	+	3.78377i	0.436912	+	0.756754i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$		0			0
$28$	0.368446	−	2.61997i	0.0696298	−	0.495128i
$29$	5.70065			1.05858			0.529292	−	0.848440i	$-0.322458\pi$
$29$	5.70065			1.05858			0.529292	+	0.848440i	$0.322458\pi$
$30$		0			0
$31$	0.0295415	+	0.0511674i	0.00530582	+	0.00918994i	0.868666	−	0.495398i	$-0.164978\pi$
$31$	0.0295415	+	0.0511674i	0.00530582	+	0.00918994i	−0.863360	+	0.504588i	$0.831644\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	2.11039			0.361930
$35$	1.94852	−	0.787053i	0.329359	−	0.133036i
$36$		0			0
$37$	−4.74280	+	8.21476i	−0.779711	+	1.35050i	0.152398	+	0.988319i	$0.451301\pi$
$37$	−4.74280	+	8.21476i	−0.779711	+	1.35050i	−0.932108	+	0.362179i	$0.882033\pi$
$38$	2.48188	+	4.29874i	0.402614	+	0.697348i
$39$		0			0
$40$	−0.397140	+	0.687867i	−0.0627933	+	0.108761i
$41$	−2.05739			−0.321310			−0.160655	−	0.987011i	$-0.551361\pi$
$41$	−2.05739			−0.321310			−0.160655	+	0.987011i	$0.551361\pi$
$42$		0			0
$43$	3.47378			0.529747			0.264874	−	0.964283i	$-0.414670\pi$
$43$	3.47378			0.529747			0.264874	+	0.964283i	$0.414670\pi$
$44$	1.92668	−	3.33711i	0.290458	−	0.503088i
$45$		0			0
$46$	−1.76559	−	3.05808i	−0.260321	−	0.450890i
$47$	0.472154	−	0.817794i	0.0688707	−	0.119288i	−0.829534	−	0.558457i	$-0.811394\pi$
$47$	0.472154	−	0.817794i	0.0688707	−	0.119288i	0.898404	+	0.439169i	$0.144727\pi$
$48$		0			0
$49$	1.69227	+	6.79237i	0.241753	+	0.970338i
$50$	4.36912			0.617887
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	1.92116	+	3.32755i	0.263892	+	0.457075i	0.967273	−	0.253739i	$-0.0816603\pi$
$53$	1.92116	+	3.32755i	0.263892	+	0.457075i	−0.703381	+	0.710813i	$0.748327\pi$
$54$		0			0
$55$	3.06065			0.412698
$56$	−2.08474	−	1.62907i	−0.278585	−	0.217694i
$57$		0			0
$58$	2.85032	−	4.93691i	0.374266	−	0.648248i
$59$	−4.58170	−	7.93574i	−0.596486	−	1.03314i	−0.993335	−	0.115261i	$-0.963230\pi$
$59$	−4.58170	−	7.93574i	−0.596486	−	1.03314i	0.396849	−	0.917884i	$-0.370104\pi$
$60$		0			0
$61$	2.75788	−	4.77679i	0.353110	−	0.611605i	−0.633683	−	0.773593i	$-0.718457\pi$
$61$	2.75788	−	4.77679i	0.353110	−	0.611605i	0.986793	+	0.161989i	$0.0517908\pi$
$62$	0.0590831			0.00750356
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.397140	+	0.687867i	−0.0492592	+	0.0853194i
$66$		0			0
$67$	−6.59227	−	11.4181i	−0.805374	−	1.39495i	−0.916038	−	0.401091i	$-0.868631\pi$
$67$	−6.59227	−	11.4181i	−0.805374	−	1.39495i	0.110664	−	0.993858i	$-0.464702\pi$
$68$	1.05520	−	1.82765i	0.127961	−	0.221636i
$69$		0			0
$70$	0.292649	−	2.08099i	0.0349783	−	0.248726i
$71$	1.96983			0.233776			0.116888	−	0.993145i	$-0.462708\pi$
$71$	1.96983			0.233776			0.116888	+	0.993145i	$0.462708\pi$
$72$		0			0
$73$	2.61895	+	4.53615i	0.306525	+	0.530917i	0.977600	−	0.210473i	$-0.0675004\pi$
$73$	2.61895	+	4.53615i	0.306525	+	0.530917i	−0.671075	+	0.741390i	$0.734167\pi$
$74$	4.74280	+	8.21476i	0.551339	+	0.954947i
$75$		0			0
$76$	4.96376			0.569382
$77$	−1.41976	+	10.0957i	−0.161796	+	1.15051i
$78$		0			0
$79$	−2.76643	+	4.79160i	−0.311248	+	0.539098i	−0.978633	−	0.205616i	$-0.934080\pi$
$79$	−2.76643	+	4.79160i	−0.311248	+	0.539098i	0.667385	+	0.744713i	$0.267414\pi$
$80$	0.397140	+	0.687867i	0.0444016	+	0.0769058i
$81$		0			0
$82$	−1.02869	+	1.78175i	−0.113600	+	0.196761i
$83$	16.8852			1.85339			0.926695	−	0.375813i	$-0.122637\pi$
$83$	16.8852			1.85339			0.926695	+	0.375813i	$0.122637\pi$
$84$		0			0
$85$	1.67624			0.181814
$86$	1.73689	−	3.00839i	0.187294	−	0.324403i
$87$		0			0
$88$	−1.92668	−	3.33711i	−0.205385	−	0.355737i
$89$	6.93506	−	12.0119i	0.735115	−	1.27326i	−0.219558	−	0.975600i	$-0.570461\pi$
$89$	6.93506	−	12.0119i	0.735115	−	1.27326i	0.954673	−	0.297657i	$-0.0962053\pi$
$90$		0			0
$91$	−2.08474	−	1.62907i	−0.218540	−	0.170773i
$92$	−3.53117			−0.368150
$93$		0			0
$94$	−0.472154	−	0.817794i	−0.0486989	−	0.0843490i
$95$	1.97131	+	3.41440i	0.202252	+	0.350310i
$96$		0			0
$97$	−4.74870			−0.482157			−0.241079	−	0.970506i	$-0.577501\pi$
$97$	−4.74870			−0.482157			−0.241079	+	0.970506i	$0.577501\pi$
$98$	6.72849	+	1.93064i	0.679681	+	0.195024i
$99$		0			0
$100$	2.18456	−	3.78377i	0.218456	−	0.378377i
$101$	−0.0227910	−	0.0394751i	−0.00226779	−	0.00392792i	0.864889	−	0.501963i	$-0.167389\pi$
$101$	−0.0227910	−	0.0394751i	−0.00226779	−	0.00392792i	−0.867157	+	0.498035i	$0.834055\pi$
$102$		0			0
$103$	−2.05301	+	3.55591i	−0.202289	+	0.350374i	−0.949265	−	0.314476i	$-0.898171\pi$
$103$	−2.05301	+	3.55591i	−0.202289	+	0.350374i	0.746977	+	0.664850i	$0.231505\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	3.84233			0.373200
$107$	9.98722	−	17.2984i	0.965501	−	1.67230i	0.257238	−	0.966348i	$-0.417187\pi$
$107$	9.98722	−	17.2984i	0.965501	−	1.67230i	0.708263	−	0.705949i	$-0.249479\pi$
$108$		0			0
$109$	−0.794280	−	1.37573i	−0.0760782	−	0.131771i	0.825476	−	0.564437i	$-0.190907\pi$
$109$	−0.794280	−	1.37573i	−0.0760782	−	0.131771i	−0.901555	+	0.432665i	$0.857573\pi$
$110$	1.53032	−	2.65060i	0.145911	−	0.252725i
$111$		0			0
$112$	−2.45318	+	0.990902i	−0.231804	+	0.0936314i
$113$	10.2017			0.959691			0.479845	−	0.877353i	$-0.340693\pi$
$113$	10.2017			0.959691			0.479845	+	0.877353i	$0.340693\pi$
$114$		0			0
$115$	−1.40237	−	2.42898i	−0.130772	−	0.226503i
$116$	−2.85032	−	4.93691i	−0.264646	−	0.458380i
$117$		0			0
$118$	−9.16340			−0.843559
$119$	−0.777566	+	5.52917i	−0.0712794	+	0.506858i
$120$		0			0
$121$	−1.92420	+	3.33282i	−0.174928	+	0.302983i
$122$	−2.75788	−	4.77679i	−0.249687	−	0.432470i
$123$		0			0
$124$	0.0295415	−	0.0511674i	0.00265291	−	0.00459497i
$125$	7.44170			0.665606
$126$		0			0
$127$	−9.81443			−0.870890			−0.435445	−	0.900215i	$-0.643409\pi$
$127$	−9.81443			−0.870890			−0.435445	+	0.900215i	$0.643409\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	0.397140	+	0.687867i	0.0348315	+	0.0603299i
$131$	−0.454528	+	0.787265i	−0.0397123	+	0.0687837i	−0.885198	−	0.465214i	$-0.845977\pi$
$131$	−0.454528	+	0.787265i	−0.0397123	+	0.0687837i	0.845486	+	0.533997i	$0.179311\pi$
$132$		0			0
$133$	−12.1770	+	4.91860i	−1.05588	+	0.426496i
$134$	−13.1845			−1.13897
$135$		0			0
$136$	−1.05520	−	1.82765i	−0.0904824	−	0.156720i
$137$	0.912223	+	1.58002i	0.0779365	+	0.134990i	0.902359	−	0.430984i	$-0.141834\pi$
$137$	0.912223	+	1.58002i	0.0779365	+	0.134990i	−0.824423	+	0.565974i	$0.808500\pi$
$138$		0			0
$139$	4.44192			0.376759			0.188379	−	0.982096i	$-0.439677\pi$
$139$	4.44192			0.376759			0.188379	+	0.982096i	$0.439677\pi$
$140$	−1.65587	−	1.29394i	−0.139946	−	0.109358i
$141$		0			0
$142$	0.984917	−	1.70593i	0.0826524	−	0.143158i
$143$	−1.92668	−	3.33711i	−0.161117	−	0.279063i
$144$		0			0
$145$	2.26396	−	3.92129i	0.188011	−	0.325645i
$146$	5.23790			0.433492
$147$		0			0
$148$	9.48559			0.779711
$149$	3.63071	−	6.28857i	0.297439	−	0.515180i	−0.678110	−	0.734960i	$-0.737201\pi$
$149$	3.63071	−	6.28857i	0.297439	−	0.515180i	0.975549	+	0.219781i	$0.0705342\pi$
$150$		0			0
$151$	3.62936	+	6.28624i	0.295353	+	0.511567i	0.975067	−	0.221911i	$-0.0712293\pi$
$151$	3.62936	+	6.28624i	0.295353	+	0.511567i	−0.679714	+	0.733478i	$0.737896\pi$
$152$	2.48188	−	4.29874i	0.201307	−	0.348674i
$153$		0			0
$154$	8.03325	+	6.27739i	0.647338	+	0.505847i
$155$	0.0469285			0.00376939
$156$		0			0
$157$	−8.54648	−	14.8029i	−0.682083	−	1.18140i	−0.974344	−	0.225064i	$-0.927741\pi$
$157$	−8.54648	−	14.8029i	−0.682083	−	1.18140i	0.292261	−	0.956339i	$-0.405592\pi$
$158$	2.76643	+	4.79160i	0.220086	+	0.381200i
$159$		0			0
$160$	0.794280			0.0627933
$161$	8.66262	−	3.49904i	0.682710	−	0.275763i
$162$		0			0
$163$	−0.174835	+	0.302823i	−0.0136942	+	0.0237190i	−0.872791	−	0.488094i	$-0.837692\pi$
$163$	−0.174835	+	0.302823i	−0.0136942	+	0.0237190i	0.859097	+	0.511813i	$0.171026\pi$
$164$	1.02869	+	1.78175i	0.0803275	+	0.139131i
$165$		0			0
$166$	8.44260	−	14.6230i	0.655273	−	1.13497i
$167$	−21.1195			−1.63428			−0.817138	−	0.576441i	$-0.804441\pi$
$167$	−21.1195			−1.63428			−0.817138	+	0.576441i	$0.804441\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	0.838122	−	1.45167i	0.0642810	−	0.111338i
$171$		0			0
$172$	−1.73689	−	3.00839i	−0.132437	−	0.229387i
$173$	−11.3748	+	19.7017i	−0.864810	+	1.49789i	0.00242647	+	0.999997i	$0.499228\pi$
$173$	−11.3748	+	19.7017i	−0.864810	+	1.49789i	−0.867236	+	0.497897i	$0.834106\pi$
$174$		0			0
$175$	−1.60978	+	11.4470i	−0.121688	+	0.865309i
$176$	−3.85336			−0.290458
$177$		0			0
$178$	−6.93506	−	12.0119i	−0.519805	−	0.900329i
$179$	7.79428	+	13.5001i	0.582572	+	1.00904i	0.995173	+	0.0981324i	$0.0312869\pi$
$179$	7.79428	+	13.5001i	0.582572	+	1.00904i	−0.412602	+	0.910912i	$0.635380\pi$
$180$		0			0
$181$	4.27491			0.317752			0.158876	−	0.987299i	$-0.449213\pi$
$181$	4.27491			0.317752			0.158876	+	0.987299i	$0.449213\pi$
$182$	−2.45318	+	0.990902i	−0.181842	+	0.0734505i
$183$		0			0
$184$	−1.76559	+	3.05808i	−0.130161	+	0.225445i
$185$	3.76711	+	6.52482i	0.276963	+	0.479714i
$186$		0			0
$187$	−4.06606	+	7.04262i	−0.297339	+	0.515007i
$188$	−0.944308			−0.0688707
$189$		0			0
$190$	3.94261			0.286027
$191$	−0.689615	+	1.19445i	−0.0498988	+	0.0864272i	−0.889896	−	0.456164i	$-0.849223\pi$
$191$	−0.689615	+	1.19445i	−0.0498988	+	0.0864272i	0.839997	+	0.542591i	$0.182557\pi$
$192$		0			0
$193$	9.33980	+	16.1770i	0.672294	+	1.16445i	0.977252	+	0.212081i	$0.0680241\pi$
$193$	9.33980	+	16.1770i	0.672294	+	1.16445i	−0.304959	+	0.952366i	$0.598643\pi$
$194$	−2.37435	+	4.11249i	−0.170468	+	0.295260i
$195$		0			0
$196$	5.03623	−	4.86173i	0.359731	−	0.347266i
$197$	−11.0775			−0.789242			−0.394621	−	0.918844i	$-0.629124\pi$
$197$	−11.0775			−0.789242			−0.394621	+	0.918844i	$0.629124\pi$
$198$		0			0
$199$	−0.381051	−	0.660000i	−0.0270120	−	0.0467861i	0.852203	−	0.523211i	$-0.175266\pi$
$199$	−0.381051	−	0.660000i	−0.0270120	−	0.0467861i	−0.879215	+	0.476424i	$0.841933\pi$
$200$	−2.18456	−	3.78377i	−0.154472	−	0.267553i
$201$		0			0
$202$	−0.0455819			−0.00320713
$203$	11.8844	+	9.28675i	0.834119	+	0.651802i
$204$		0			0
$205$	−0.817071	+	1.41521i	−0.0570667	+	0.0988424i
$206$	2.05301	+	3.55591i	0.143040	+	0.247752i
$207$		0			0
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	−19.1272			−1.32305
$210$		0			0
$211$	−6.25127			−0.430355			−0.215178	−	0.976575i	$-0.569033\pi$
$211$	−6.25127			−0.430355			−0.215178	+	0.976575i	$0.569033\pi$
$212$	1.92116	−	3.32755i	0.131946	−	0.228537i
$213$		0			0
$214$	−9.98722	−	17.2984i	−0.682712	−	1.18249i
$215$	1.37958	−	2.38950i	0.0940865	−	0.162963i
$216$		0			0
$217$	−0.0217689	+	0.154796i	−0.00147777	+	0.0105082i
$218$	−1.58856			−0.107591
$219$		0			0
$220$	−1.53032	−	2.65060i	−0.103174	−	0.178703i
$221$	−1.05520	−	1.82765i	−0.0709802	−	0.122941i
$222$		0			0
$223$	−10.6600			−0.713848			−0.356924	−	0.934133i	$-0.616174\pi$
$223$	−10.6600			−0.713848			−0.356924	+	0.934133i	$0.616174\pi$
$224$	−0.368446	+	2.61997i	−0.0246178	+	0.175054i
$225$		0			0
$226$	5.10083	−	8.83489i	0.339302	−	0.587688i
$227$	−7.84497	−	13.5879i	−0.520689	−	0.901859i	−0.999711	−	0.0240563i	$-0.992342\pi$
$227$	−7.84497	−	13.5879i	−0.520689	−	0.901859i	0.479022	−	0.877803i	$-0.340991\pi$
$228$		0			0
$229$	10.1214	−	17.5308i	0.668843	−	1.15847i	−0.309385	−	0.950937i	$-0.600123\pi$
$229$	10.1214	−	17.5308i	0.668843	−	1.15847i	0.978228	−	0.207533i	$-0.0665434\pi$
$230$	−2.80474			−0.184939
$231$		0			0
$232$	−5.70065			−0.374266
$233$	3.01126	−	5.21566i	0.197274	−	0.341689i	−0.750369	−	0.661019i	$-0.770124\pi$
$233$	3.01126	−	5.21566i	0.197274	−	0.341689i	0.947644	+	0.319330i	$0.103458\pi$
$234$		0			0
$235$	−0.375022	−	0.649558i	−0.0244638	−	0.0423725i
$236$	−4.58170	+	7.93574i	−0.298243	+	0.516572i
$237$		0			0
$238$	4.39962	+	3.43798i	0.285185	+	0.222851i
$239$	−25.5919			−1.65540			−0.827702	−	0.561168i	$-0.810352\pi$
$239$	−25.5919			−1.65540			−0.827702	+	0.561168i	$0.810352\pi$
$240$		0			0
$241$	−0.654345	−	1.13336i	−0.0421501	−	0.0730060i	0.844181	−	0.536059i	$-0.180087\pi$
$241$	−0.654345	−	1.13336i	−0.0421501	−	0.0730060i	−0.886331	+	0.463053i	$0.846754\pi$
$242$	1.92420	+	3.33282i	0.123692	+	0.214242i
$243$		0			0
$244$	−5.51576			−0.353110
$245$	5.34431	+	1.53347i	0.341435	+	0.0979695i
$246$		0			0
$247$	2.48188	−	4.29874i	0.157918	−	0.273522i
$248$	−0.0295415	−	0.0511674i	−0.00187589	−	0.00324914i
$249$		0			0
$250$	3.72085	−	6.44470i	0.235327	−	0.407599i
$251$	−20.6188			−1.30145			−0.650724	−	0.759314i	$-0.725535\pi$
$251$	−20.6188			−1.30145			−0.650724	+	0.759314i	$0.725535\pi$
$252$		0			0
$253$	13.6069			0.855458
$254$	−4.90722	+	8.49955i	−0.307906	+	0.533309i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.59026	+	9.68261i	−0.348711	+	0.603984i	−0.986021	−	0.166623i	$-0.946714\pi$
$257$	−5.59026	+	9.68261i	−0.348711	+	0.603984i	0.637310	+	0.770607i	$0.280047\pi$
$258$		0			0
$259$	−23.2699	+	9.39929i	−1.44592	+	0.584043i
$260$	0.794280			0.0492592
$261$		0			0
$262$	0.454528	+	0.787265i	0.0280808	+	0.0486374i
$263$	8.52970	+	14.7739i	0.525964	+	0.910996i	0.999543	+	0.0302446i	$0.00962861\pi$
$263$	8.52970	+	14.7739i	0.525964	+	0.910996i	−0.473579	+	0.880752i	$0.657038\pi$
$264$		0			0
$265$	3.05189			0.187476
$266$	−1.82888	+	13.0049i	−0.112136	+	0.797381i
$267$		0			0
$268$	−6.59227	+	11.4181i	−0.402687	+	0.697475i
$269$	−12.9563	−	22.4410i	−0.789962	−	1.36825i	−0.925990	−	0.377549i	$-0.876767\pi$
$269$	−12.9563	−	22.4410i	−0.789962	−	1.36825i	0.136028	−	0.990705i	$-0.456566\pi$
$270$		0			0
$271$	−1.27701	+	2.21184i	−0.0775726	+	0.134360i	−0.902202	−	0.431314i	$-0.858050\pi$
$271$	−1.27701	+	2.21184i	−0.0775726	+	0.134360i	0.824630	+	0.565673i	$0.191384\pi$
$272$	−2.11039			−0.127961
$273$		0			0
$274$	1.82445			0.110219
$275$	−8.41790	+	14.5802i	−0.507619	+	0.879221i
$276$		0			0
$277$	9.84744	+	17.0563i	0.591676	+	1.02481i	0.994007	+	0.109318i	$0.0348667\pi$
$277$	9.84744	+	17.0563i	0.591676	+	1.02481i	−0.402331	+	0.915494i	$0.631800\pi$
$278$	2.22096	−	3.84682i	0.133204	−	0.230717i
$279$		0			0
$280$	−1.94852	+	0.787053i	−0.116446	+	0.0470354i
$281$	14.1517			0.844219			0.422110	−	0.906545i	$-0.361290\pi$
$281$	14.1517			0.844219			0.422110	+	0.906545i	$0.361290\pi$
$282$		0			0
$283$	−8.39044	−	14.5327i	−0.498760	−	0.863877i	0.501239	−	0.865309i	$-0.332878\pi$
$283$	−8.39044	−	14.5327i	−0.498760	−	0.863877i	−0.999999	+	0.00143150i	$0.999544\pi$
$284$	−0.984917	−	1.70593i	−0.0584441	−	0.101228i
$285$		0			0
$286$	−3.85336			−0.227854
$287$	−4.28912	−	3.35163i	−0.253178	−	0.197840i
$288$		0			0
$289$	6.27312	−	10.8654i	0.369007	−	0.639139i
$290$	−2.26396	−	3.92129i	−0.132944	−	0.230266i
$291$		0			0
$292$	2.61895	−	4.53615i	0.153262	−	0.265458i
$293$	−23.3574			−1.36455			−0.682277	−	0.731094i	$-0.739010\pi$
$293$	−23.3574			−1.36455			−0.682277	+	0.731094i	$0.739010\pi$
$294$		0			0
$295$	−7.27830			−0.423759
$296$	4.74280	−	8.21476i	0.275669	−	0.477473i
$297$		0			0
$298$	−3.63071	−	6.28857i	−0.210321	−	0.364287i
$299$	−1.76559	+	3.05808i	−0.102106	+	0.176854i
$300$		0			0
$301$	7.24193	+	5.65903i	0.417418	+	0.326181i
$302$	7.25873			0.417693
$303$		0			0
$304$	−2.48188	−	4.29874i	−0.142345	−	0.246550i
$305$	−2.19053	−	3.79410i	−0.125429	−	0.217250i
$306$		0			0
$307$	−30.8913			−1.76306			−0.881529	−	0.472130i	$-0.843485\pi$
$307$	−30.8913			−1.76306			−0.881529	+	0.472130i	$0.843485\pi$
$308$	9.45301	−	3.81830i	0.538635	−	0.217568i
$309$		0			0
$310$	0.0234642	−	0.0406413i	0.00133268	−	0.00230827i
$311$	1.87767	+	3.25223i	0.106473	+	0.184417i	0.914339	−	0.404949i	$-0.132711\pi$
$311$	1.87767	+	3.25223i	0.106473	+	0.184417i	−0.807866	+	0.589366i	$0.799378\pi$
$312$		0			0
$313$	1.25805	−	2.17901i	0.0711093	−	0.123165i	−0.828278	−	0.560317i	$-0.810679\pi$
$313$	1.25805	−	2.17901i	0.0711093	−	0.123165i	0.899388	+	0.437152i	$0.144013\pi$
$314$	−17.0930			−0.964611
$315$		0			0
$316$	5.53287			0.311248
$317$	12.0507	−	20.8724i	0.676834	−	1.17231i	−0.299095	−	0.954223i	$-0.596685\pi$
$317$	12.0507	−	20.8724i	0.676834	−	1.17231i	0.975929	−	0.218088i	$-0.0699818\pi$
$318$		0			0
$319$	10.9833	+	19.0237i	0.614949	+	1.06512i
$320$	0.397140	−	0.687867i	0.0222008	−	0.0384529i
$321$		0			0
$322$	1.30105	−	9.25157i	0.0725045	−	0.515570i
$323$	−10.4755			−0.582871
$324$		0			0
$325$	−2.18456	−	3.78377i	−0.121178	−	0.209886i
$326$	0.174835	+	0.302823i	0.00968323	+	0.0167718i
$327$		0			0
$328$	2.05739			0.113600
$329$	2.31656	−	0.935716i	0.127716	−	0.0515877i
$330$		0			0
$331$	−6.47044	+	11.2071i	−0.355648	+	0.616000i	−0.987229	−	0.159310i	$-0.949073\pi$
$331$	−6.47044	+	11.2071i	−0.355648	+	0.616000i	0.631581	+	0.775310i	$0.282406\pi$
$332$	−8.44260	−	14.6230i	−0.463348	−	0.802542i
$333$		0			0
$334$	−10.5598	+	18.2900i	−0.577804	+	1.00079i
$335$	−10.4722			−0.572158
$336$		0			0
$337$	30.5618			1.66480			0.832402	−	0.554172i	$-0.186965\pi$
$337$	30.5618			1.66480			0.832402	+	0.554172i	$0.186965\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$		0			0
$340$	−0.838122	−	1.45167i	−0.0454535	−	0.0787278i
$341$	−0.113834	+	0.197167i	−0.00616447	+	0.0106772i
$342$		0			0
$343$	−7.53730	+	16.9171i	−0.406976	+	0.913439i
$344$	−3.47378			−0.187294
$345$		0			0
$346$	11.3748	+	19.7017i	0.611513	+	1.05917i
$347$	5.94852	+	10.3031i	0.319333	+	0.553101i	0.980349	−	0.197271i	$-0.0632078\pi$
$347$	5.94852	+	10.3031i	0.319333	+	0.553101i	−0.661016	+	0.750372i	$0.729874\pi$
$348$		0			0
$349$	19.6258			1.05055			0.525273	−	0.850934i	$-0.323963\pi$
$349$	19.6258			1.05055			0.525273	+	0.850934i	$0.323963\pi$
$350$	9.10847	+	7.11760i	0.486868	+	0.380452i
$351$		0			0
$352$	−1.92668	+	3.33711i	−0.102692	+	0.177869i
$353$	−11.9695	−	20.7318i	−0.637071	−	1.10344i	−0.986072	−	0.166318i	$-0.946812\pi$
$353$	−11.9695	−	20.7318i	−0.637071	−	1.10344i	0.349001	−	0.937122i	$-0.386521\pi$
$354$		0			0
$355$	0.782300	−	1.35498i	0.0415202	−	0.0719150i
$356$	−13.8701			−0.735115
$357$		0			0
$358$	15.5886			0.823881
$359$	15.4738	−	26.8015i	0.816678	−	1.41453i	−0.0914393	−	0.995811i	$-0.529147\pi$
$359$	15.4738	−	26.8015i	0.816678	−	1.41453i	0.908117	−	0.418717i	$-0.137520\pi$
$360$		0			0
$361$	−2.81944	−	4.88341i	−0.148392	−	0.257022i
$362$	2.13746	−	3.70218i	0.112342	−	0.194582i
$363$		0			0
$364$	−0.368446	+	2.61997i	−0.0193118	+	0.137324i
$365$	4.16036			0.217763
$366$		0			0
$367$	−12.9779	−	22.4784i	−0.677440	−	1.17336i	−0.975749	−	0.218891i	$-0.929756\pi$
$367$	−12.9779	−	22.4784i	−0.677440	−	1.17336i	0.298309	−	0.954469i	$-0.403577\pi$
$368$	1.76559	+	3.05808i	0.0920375	+	0.159414i
$369$		0			0
$370$	7.53421			0.391685
$371$	−1.41569	+	10.0668i	−0.0734990	+	0.522642i
$372$		0			0
$373$	−16.6189	+	28.7848i	−0.860496	+	1.49042i	0.0109554	+	0.999940i	$0.496513\pi$
$373$	−16.6189	+	28.7848i	−0.860496	+	1.49042i	−0.871451	+	0.490482i	$0.836821\pi$
$374$	4.06606	+	7.04262i	0.210251	+	0.364165i
$375$		0			0
$376$	−0.472154	+	0.817794i	−0.0243495	+	0.0421745i
$377$	−5.70065			−0.293598
$378$		0			0
$379$	−20.9899			−1.07818			−0.539088	−	0.842249i	$-0.681231\pi$
$379$	−20.9899			−1.07818			−0.539088	+	0.842249i	$0.681231\pi$
$380$	1.97131	−	3.41440i	0.101126	−	0.175155i
$381$		0			0
$382$	0.689615	+	1.19445i	0.0352838	+	0.0611133i
$383$	−7.51941	+	13.0240i	−0.384224	+	0.665496i	−0.991661	−	0.128872i	$-0.958864\pi$
$383$	−7.51941	+	13.0240i	−0.384224	+	0.665496i	0.607437	+	0.794368i	$0.292198\pi$
$384$		0			0
$385$	6.38065	+	4.98601i	0.325188	+	0.254111i
$386$	18.6796			0.950767
$387$		0			0
$388$	2.37435	+	4.11249i	0.120539	+	0.208780i
$389$	3.96912	+	6.87471i	0.201242	+	0.348562i	0.948929	−	0.315490i	$-0.102169\pi$
$389$	3.96912	+	6.87471i	0.201242	+	0.348562i	−0.747687	+	0.664052i	$0.768836\pi$
$390$		0			0
$391$	7.45216			0.376872
$392$	−1.69227	−	6.79237i	−0.0854724	−	0.343066i
$393$		0			0
$394$	−5.53877	+	9.59343i	−0.279039	+	0.483310i
$395$	2.19732	+	3.80587i	0.110559	+	0.191494i
$396$		0			0
$397$	7.64747	−	13.2458i	0.383815	−	0.664788i	−0.607789	−	0.794099i	$-0.707943\pi$
$397$	7.64747	−	13.2458i	0.383815	−	0.664788i	0.991604	+	0.129311i	$0.0412765\pi$
$398$	−0.762102			−0.0382007
$399$		0			0
$400$	−4.36912			−0.218456
$401$	−5.69918	+	9.87126i	−0.284603	+	0.492947i	−0.972513	−	0.232849i	$-0.925195\pi$
$401$	−5.69918	+	9.87126i	−0.284603	+	0.492947i	0.687910	+	0.725796i	$0.258529\pi$
$402$		0			0
$403$	−0.0295415	−	0.0511674i	−0.00147157	−	0.00254883i
$404$	−0.0227910	+	0.0394751i	−0.00113389	+	0.00196396i
$405$		0			0
$406$	13.9847	−	5.64878i	0.694051	−	0.280344i
$407$	−36.5514			−1.81179
$408$		0			0
$409$	9.39888	+	16.2793i	0.464745	+	0.804962i	0.999190	−	0.0402414i	$-0.0128127\pi$
$409$	9.39888	+	16.2793i	0.464745	+	0.804962i	−0.534445	+	0.845203i	$0.679479\pi$
$410$	0.817071	+	1.41521i	0.0403523	+	0.0698922i
$411$		0			0
$412$	4.10601			0.202289
$413$	3.37622	−	24.0078i	0.166133	−	1.18135i
$414$		0			0
$415$	6.70578	−	11.6148i	0.329174	−	0.570146i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$		0			0
$418$	−9.56358	+	16.5646i	−0.467770	+	0.810201i
$419$	−5.76706			−0.281739			−0.140870	−	0.990028i	$-0.544990\pi$
$419$	−5.76706			−0.281739			−0.140870	+	0.990028i	$0.544990\pi$
$420$		0			0
$421$	−0.0721382			−0.00351580			−0.00175790	−	0.999998i	$-0.500560\pi$
$421$	−0.0721382			−0.00351580			−0.00175790	+	0.999998i	$0.500560\pi$
$422$	−3.12563	+	5.41376i	−0.152154	+	0.263538i
$423$		0			0
$424$	−1.92116	−	3.32755i	−0.0933000	−	0.161600i
$425$	−4.61028	+	7.98524i	−0.223631	+	0.387341i
$426$		0			0
$427$	13.5312	−	5.46557i	0.654819	−	0.264498i
$428$	−19.9744			−0.965501
$429$		0			0
$430$	−1.37958	−	2.38950i	−0.0665292	−	0.115232i
$431$	0.691262	+	1.19730i	0.0332969	+	0.0576719i	0.882194	−	0.470887i	$-0.156066\pi$
$431$	0.691262	+	1.19730i	0.0332969	+	0.0576719i	−0.848897	+	0.528559i	$0.822733\pi$
$432$		0			0
$433$	26.0215			1.25051			0.625257	−	0.780419i	$-0.284994\pi$
$433$	26.0215			1.25051			0.625257	+	0.780419i	$0.284994\pi$
$434$	0.123173	+	0.0962504i	0.00591248	+	0.00462017i
$435$		0			0
$436$	−0.794280	+	1.37573i	−0.0380391	+	0.0658857i
$437$	8.76394	+	15.1796i	0.419236	+	0.726138i
$438$		0			0
$439$	8.96291	−	15.5242i	0.427776	−	0.740930i	−0.568899	−	0.822407i	$-0.692630\pi$
$439$	8.96291	−	15.5242i	0.427776	−	0.740930i	0.996675	+	0.0814772i	$0.0259638\pi$
$440$	−3.06065			−0.145911
$441$		0			0
$442$	−2.11039			−0.100381
$443$	19.2065	−	33.2666i	0.912528	−	1.58054i	0.102047	−	0.994780i	$-0.467461\pi$
$443$	19.2065	−	33.2666i	0.912528	−	1.58054i	0.810481	−	0.585765i	$-0.199206\pi$
$444$		0			0
$445$	−5.50838	−	9.54080i	−0.261122	−	0.452277i
$446$	−5.33001	+	9.23185i	−0.252383	+	0.437141i
$447$		0			0
$448$	2.08474	+	1.62907i	0.0984946	+	0.0769663i
$449$	−36.3759			−1.71668			−0.858342	−	0.513079i	$-0.828505\pi$
$449$	−36.3759			−1.71668			−0.858342	+	0.513079i	$0.828505\pi$
$450$		0			0
$451$	−3.96393	−	6.86573i	−0.186654	−	0.323295i
$452$	−5.10083	−	8.83489i	−0.239923	−	0.415558i
$453$		0			0
$454$	−15.6899			−0.736365
$455$	−1.94852	+	0.787053i	−0.0913478	+	0.0368976i
$456$		0			0
$457$	9.93600	−	17.2097i	0.464787	−	0.805034i	−0.534405	−	0.845228i	$-0.679464\pi$
$457$	9.93600	−	17.2097i	0.464787	−	0.805034i	0.999192	+	0.0401943i	$0.0127977\pi$
$458$	−10.1214	−	17.5308i	−0.472943	−	0.819162i
$459$		0			0
$460$	−1.40237	+	2.42898i	−0.0653858	+	0.113252i
$461$	−38.3812			−1.78759			−0.893796	−	0.448473i	$-0.851968\pi$
$461$	−38.3812			−1.78759			−0.893796	+	0.448473i	$0.851968\pi$
$462$		0			0
$463$	20.3423			0.945389			0.472694	−	0.881226i	$-0.343281\pi$
$463$	20.3423			0.945389			0.472694	+	0.881226i	$0.343281\pi$
$464$	−2.85032	+	4.93691i	−0.132323	+	0.229190i
$465$		0			0
$466$	−3.01126	−	5.21566i	−0.139494	−	0.241611i
$467$	1.86096	−	3.22328i	0.0861150	−	0.149156i	−0.819751	−	0.572720i	$-0.805888\pi$
$467$	1.86096	−	3.22328i	0.0861150	−	0.149156i	0.905866	+	0.423565i	$0.139221\pi$
$468$		0			0
$469$	4.85779	−	34.5431i	0.224312	−	1.59505i
$470$	−0.750045			−0.0345970
$471$		0			0
$472$	4.58170	+	7.93574i	0.210890	+	0.365272i
$473$	6.69288	+	11.5924i	0.307739	+	0.533019i
$474$		0			0
$475$	−21.6872			−0.995079
$476$	5.17718	−	2.09119i	0.237296	−	0.0958497i
$477$		0			0
$478$	−12.7960	+	22.1633i	−0.585274	+	1.01372i
$479$	1.48391	+	2.57021i	0.0678016	+	0.117436i	0.897933	−	0.440131i	$-0.145068\pi$
$479$	1.48391	+	2.57021i	0.0678016	+	0.117436i	−0.830132	+	0.557567i	$0.811735\pi$
$480$		0			0
$481$	4.74280	−	8.21476i	0.216253	−	0.374561i
$482$	−1.30869			−0.0596092
$483$		0			0
$484$	3.84841			0.174928
$485$	−1.88590	+	3.26647i	−0.0856342	+	0.148323i
$486$		0			0
$487$	9.34346	+	16.1834i	0.423393	+	0.733338i	0.996269	−	0.0863042i	$-0.0275057\pi$
$487$	9.34346	+	16.1834i	0.423393	+	0.733338i	−0.572876	+	0.819642i	$0.694172\pi$
$488$	−2.75788	+	4.77679i	−0.124843	+	0.216235i
$489$		0			0
$490$	4.00017	−	3.86157i	0.180709	−	0.174448i
$491$	4.66770			0.210650			0.105325	−	0.994438i	$-0.466412\pi$
$491$	4.66770			0.210650			0.105325	+	0.994438i	$0.466412\pi$
$492$		0			0
$493$	6.01531	+	10.4188i	0.270916	+	0.469240i
$494$	−2.48188	−	4.29874i	−0.111665	−	0.193409i
$495$		0			0
$496$	−0.0590831			−0.00265291
$497$	4.10659	+	3.20900i	0.184206	+	0.143943i
$498$		0			0
$499$	−8.88358	+	15.3868i	−0.397684	+	0.688808i	−0.993440	−	0.114357i	$-0.963519\pi$
$499$	−8.88358	+	15.3868i	−0.397684	+	0.688808i	0.595756	+	0.803165i	$0.296852\pi$
$500$	−3.72085	−	6.44470i	−0.166402	−	0.288216i
$501$		0			0
$502$	−10.3094	+	17.8564i	−0.460132	+	0.796971i
$503$	44.5363			1.98578			0.992888	−	0.119050i	$-0.0379849\pi$
$503$	44.5363			1.98578			0.992888	+	0.119050i	$0.0379849\pi$
$504$		0			0
$505$	−0.0362048			−0.00161109
$506$	6.80344	−	11.7839i	0.302450	−	0.523859i
$507$		0			0
$508$	4.90722	+	8.49955i	0.217723	+	0.377106i
$509$	−17.5792	+	30.4480i	−0.779183	+	1.34958i	0.153230	+	0.988191i	$0.451032\pi$
$509$	−17.5792	+	30.4480i	−0.779183	+	1.34958i	−0.932413	+	0.361394i	$0.882301\pi$
$510$		0			0
$511$	−1.92988	+	13.7231i	−0.0853730	+	0.607076i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	5.59026	+	9.68261i	0.246576	+	0.427081i
$515$	1.63066	+	2.82439i	0.0718555	+	0.124457i
$516$		0			0
$517$	3.63876			0.160032
$518$	−3.49493	+	24.8520i	−0.153558	+	1.09193i
$519$		0			0
$520$	0.397140	−	0.687867i	0.0174157	−	0.0301649i
$521$	9.92751	+	17.1950i	0.434932	+	0.753325i	0.997290	−	0.0735692i	$-0.0234390\pi$
$521$	9.92751	+	17.1950i	0.434932	+	0.753325i	−0.562358	+	0.826894i	$0.690106\pi$
$522$		0			0
$523$	−14.8127	+	25.6564i	−0.647716	+	1.12188i	0.335951	+	0.941879i	$0.390942\pi$
$523$	−14.8127	+	25.6564i	−0.647716	+	1.12188i	−0.983667	+	0.179997i	$0.942391\pi$
$524$	0.909055			0.0397123
$525$		0			0
$526$	17.0594			0.743825
$527$	−0.0623443	+	0.107983i	−0.00271576	+	0.00470383i
$528$		0			0
$529$	5.26541	+	9.11996i	0.228931	+	0.396520i
$530$	1.52594	−	2.64301i	0.0662827	−	0.114805i
$531$		0			0
$532$	10.3481	+	8.08630i	0.448648	+	0.350586i
$533$	2.05739			0.0891154
$534$		0			0
$535$	−7.93265	−	13.7398i	−0.342958	−	0.594021i
$536$	6.59227	+	11.4181i	0.284743	+	0.493189i
$537$		0			0
$538$	−25.9127			−1.11717
$539$	−19.4064	+	18.7340i	−0.835893	+	0.806931i
$540$		0			0
$541$	17.2666	−	29.9067i	0.742351	−	1.28579i	−0.209071	−	0.977900i	$-0.567044\pi$
$541$	17.2666	−	29.9067i	0.742351	−	1.28579i	0.951422	−	0.307889i	$-0.0996226\pi$
$542$	1.27701	+	2.21184i	0.0548521	+	0.0950066i
$543$		0			0
$544$	−1.05520	+	1.82765i	−0.0452412	+	0.0783600i
$545$	−1.26176			−0.0540479
$546$		0			0
$547$	12.4500			0.532323			0.266162	−	0.963928i	$-0.414245\pi$
$547$	12.4500			0.532323			0.266162	+	0.963928i	$0.414245\pi$
$548$	0.912223	−	1.58002i	0.0389682	−	0.0674950i
$549$		0			0
$550$	8.41790	+	14.5802i	0.358941	+	0.621703i
$551$	−14.1483	+	24.5056i	−0.602739	+	1.04397i
$552$		0			0
$553$	−13.5731	+	5.48253i	−0.577189	+	0.233141i
$554$	19.6949			0.836756
$555$		0			0
$556$	−2.22096	−	3.84682i	−0.0941897	−	0.163141i
$557$	−6.92983	−	12.0028i	−0.293626	−	0.508576i	0.681038	−	0.732248i	$-0.261529\pi$
$557$	−6.92983	−	12.0028i	−0.293626	−	0.508576i	−0.974664	+	0.223672i	$0.928196\pi$
$558$		0			0
$559$	−3.47378			−0.146925
$560$	−0.292649	+	2.08099i	−0.0123667	+	0.0879379i
$561$		0			0
$562$	7.07585	−	12.2557i	0.298477	−	0.516977i
$563$	−7.29838	−	12.6412i	−0.307590	−	0.532761i	0.670245	−	0.742140i	$-0.266189\pi$
$563$	−7.29838	−	12.6412i	−0.307590	−	0.532761i	−0.977835	+	0.209379i	$0.932856\pi$
$564$		0			0
$565$	4.05148	−	7.01738i	0.170447	−	0.295223i
$566$	−16.7809			−0.705353
$567$		0			0
$568$	−1.96983			−0.0826524
$569$	6.44385	−	11.1611i	0.270140	−	0.467896i	−0.698757	−	0.715359i	$-0.746263\pi$
$569$	6.44385	−	11.1611i	0.270140	−	0.467896i	0.968898	+	0.247462i	$0.0795967\pi$
$570$		0			0
$571$	−14.9822	−	25.9500i	−0.626986	−	1.08597i	−0.988153	−	0.153471i	$-0.950955\pi$
$571$	−14.9822	−	25.9500i	−0.626986	−	1.08597i	0.361167	−	0.932501i	$-0.382378\pi$
$572$	−1.92668	+	3.33711i	−0.0805586	+	0.139532i
$573$		0			0
$574$	−5.04715	+	2.03867i	−0.210664	+	0.0850924i
$575$	15.4281			0.643397
$576$		0			0
$577$	16.7513	+	29.0142i	0.697367	+	1.20788i	0.969376	+	0.245581i	$0.0789786\pi$
$577$	16.7513	+	29.0142i	0.697367	+	1.20788i	−0.272009	+	0.962295i	$0.587688\pi$
$578$	−6.27312	−	10.8654i	−0.260927	−	0.451939i
$579$		0			0
$580$	−4.52791			−0.188011
$581$	35.2012	+	27.5071i	1.46039	+	1.14119i
$582$		0			0
$583$	−7.40294	+	12.8223i	−0.306599	+	0.531044i
$584$	−2.61895	−	4.53615i	−0.108373	−	0.187707i
$585$		0			0
$586$	−11.6787	+	20.2281i	−0.482443	+	0.835616i
$587$	−23.0030			−0.949437			−0.474719	−	0.880138i	$-0.657450\pi$
$587$	−23.0030			−0.949437			−0.474719	+	0.880138i	$0.657450\pi$
$588$		0			0
$589$	−0.293274			−0.0120841
$590$	−3.63915	+	6.30320i	−0.149822	+	0.259498i
$591$		0			0
$592$	−4.74280	−	8.21476i	−0.194928	−	0.337625i
$593$	19.3682	−	33.5467i	0.795358	−	1.37760i	−0.127254	−	0.991870i	$-0.540616\pi$
$593$	19.3682	−	33.5467i	0.795358	−	1.37760i	0.922612	−	0.385730i	$-0.126050\pi$
$594$		0			0
$595$	3.49453	+	2.73072i	0.143262	+	0.111948i
$596$	−7.26141			−0.297439
$597$		0			0
$598$	1.76559	+	3.05808i	0.0722002	+	0.125054i
$599$	−4.50821	−	7.80844i	−0.184200	−	0.319044i	0.759106	−	0.650967i	$-0.225636\pi$
$599$	−4.50821	−	7.80844i	−0.184200	−	0.319044i	−0.943307	+	0.331922i	$0.892303\pi$
$600$		0			0
$601$	2.14699			0.0875774			0.0437887	−	0.999041i	$-0.486057\pi$
$601$	2.14699			0.0875774			0.0437887	+	0.999041i	$0.486057\pi$
$602$	8.52183	−	3.44218i	0.347324	−	0.140293i
$603$		0			0
$604$	3.62936	−	6.28624i	0.147677	−	0.255784i
$605$	1.52836	+	2.64719i	0.0621365	+	0.107624i
$606$		0			0
$607$	10.9841	−	19.0249i	0.445829	−	0.772198i	−0.552281	−	0.833658i	$-0.686242\pi$
$607$	10.9841	−	19.0249i	0.445829	−	0.772198i	0.998110	+	0.0614599i	$0.0195756\pi$
$608$	−4.96376			−0.201307
$609$		0			0
$610$	−4.38105			−0.177384
$611$	−0.472154	+	0.817794i	−0.0191013	+	0.0330844i
$612$		0			0
$613$	−7.11378	−	12.3214i	−0.287323	−	0.497658i	0.685847	−	0.727746i	$-0.259432\pi$
$613$	−7.11378	−	12.3214i	−0.287323	−	0.497658i	−0.973170	+	0.230088i	$0.926099\pi$
$614$	−15.4456	+	26.7526i	−0.623335	+	1.07965i
$615$		0			0
$616$	1.41976	−	10.0957i	0.0572036	−	0.406767i
$617$	3.94556			0.158842			0.0794211	−	0.996841i	$-0.474693\pi$
$617$	3.94556			0.158842			0.0794211	+	0.996841i	$0.474693\pi$
$618$		0			0
$619$	18.7034	+	32.3952i	0.751752	+	1.30207i	0.946973	+	0.321314i	$0.104125\pi$
$619$	18.7034	+	32.3952i	0.751752	+	1.30207i	−0.195220	+	0.980759i	$0.562542\pi$
$620$	−0.0234642	−	0.0406413i	−0.000942347	−	0.00163219i
$621$		0			0
$622$	3.75535			0.150576
$623$	34.0260	−	13.7439i	1.36322	−	0.550639i
$624$		0			0
$625$	−7.96740	+	13.7999i	−0.318696	+	0.551998i
$626$	−1.25805	−	2.17901i	−0.0502819	−	0.0870908i
$627$		0			0
$628$	−8.54648	+	14.8029i	−0.341042	+	0.590701i
$629$	−20.0183			−0.798183
$630$		0			0
$631$	−29.6268			−1.17943			−0.589713	−	0.807613i	$-0.700759\pi$
$631$	−29.6268			−1.17943			−0.589713	+	0.807613i	$0.700759\pi$
$632$	2.76643	−	4.79160i	0.110043	−	0.190600i
$633$		0			0
$634$	−12.0507	−	20.8724i	−0.478594	−	0.828949i
$635$	−3.89770	+	6.75102i	−0.154676	+	0.267906i
$636$		0			0
$637$	−1.69227	−	6.79237i	−0.0670501	−	0.269123i
$638$	21.9667			0.869669
$639$		0			0
$640$	−0.397140	−	0.687867i	−0.0156983	−	0.0271903i
$641$	−9.14499	−	15.8396i	−0.361205	−	0.625626i	0.626954	−	0.779056i	$-0.284301\pi$
$641$	−9.14499	−	15.8396i	−0.361205	−	0.625626i	−0.988160	+	0.153430i	$0.950968\pi$
$642$		0			0
$643$	−16.8610			−0.664932			−0.332466	−	0.943115i	$-0.607881\pi$
$643$	−16.8610			−0.664932			−0.332466	+	0.943115i	$0.607881\pi$
$644$	−7.36157	−	5.75252i	−0.290086	−	0.226681i
$645$		0			0
$646$	−5.23774	+	9.07203i	−0.206076	+	0.356934i
$647$	−12.4644	−	21.5891i	−0.490028	−	0.848753i	0.509906	−	0.860230i	$-0.329680\pi$
$647$	−12.4644	−	21.5891i	−0.490028	−	0.848753i	−0.999934	+	0.0114767i	$0.996347\pi$
$648$		0			0
$649$	17.6550	−	30.5793i	0.693017	−	1.20034i
$650$	−4.36912			−0.171371
$651$		0			0
$652$	0.349670			0.0136942
$653$	−0.525194	+	0.909662i	−0.0205524	+	0.0355978i	−0.876119	−	0.482095i	$-0.839876\pi$
$653$	−0.525194	+	0.909662i	−0.0205524	+	0.0355978i	0.855566	+	0.517693i	$0.173209\pi$
$654$		0			0
$655$	0.361022	+	0.625309i	0.0141063	+	0.0244328i
$656$	1.02869	−	1.78175i	0.0401637	−	0.0695657i
$657$		0			0
$658$	0.347926	−	2.47406i	0.0135636	−	0.0964488i
$659$	23.4466			0.913351			0.456675	−	0.889633i	$-0.349040\pi$
$659$	23.4466			0.913351			0.456675	+	0.889633i	$0.349040\pi$
$660$		0			0
$661$	−5.57840	−	9.66208i	−0.216975	−	0.375811i	0.736907	−	0.675994i	$-0.236286\pi$
$661$	−5.57840	−	9.66208i	−0.216975	−	0.375811i	−0.953882	+	0.300183i	$0.902952\pi$
$662$	6.47044	+	11.2071i	0.251481	+	0.435578i
$663$		0			0
$664$	−16.8852			−0.655273
$665$	−1.45264	+	10.3295i	−0.0563310	+	0.400562i
$666$		0			0
$667$	10.0650	−	17.4331i	0.389718	−	0.675011i
$668$	10.5598	+	18.2900i	0.408569	+	0.707663i
$669$		0			0
$670$	−5.23611	+	9.06921i	−0.202289	+	0.350374i
$671$	21.2542			0.820510
$672$		0			0
$673$	−3.83437			−0.147804			−0.0739020	−	0.997266i	$-0.523545\pi$
$673$	−3.83437			−0.147804			−0.0739020	+	0.997266i	$0.523545\pi$
$674$	15.2809	−	26.4673i	0.588597	−	1.01948i
$675$		0			0
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−10.6765	+	18.4922i	−0.410330	+	0.710712i	−0.994926	−	0.100612i	$-0.967920\pi$
$677$	−10.6765	+	18.4922i	−0.410330	+	0.710712i	0.584596	+	0.811325i	$0.301253\pi$
$678$		0			0
$679$	−9.89979	−	7.73596i	−0.379919	−	0.296879i
$680$	−1.67624			−0.0642810
$681$		0			0
$682$	0.113834	+	0.197167i	0.00435894	+	0.00754990i
$683$	−14.4503	−	25.0286i	−0.552925	−	0.957694i	−0.998062	−	0.0622315i	$-0.980178\pi$
$683$	−14.4503	−	25.0286i	−0.552925	−	0.957694i	0.445137	−	0.895463i	$-0.353155\pi$
$684$		0			0
$685$	1.44912			0.0553681
$686$	10.8820	+	14.9861i	0.415477	+	0.572170i
$687$		0			0
$688$	−1.73689	+	3.00839i	−0.0662184	+	0.114694i
$689$	−1.92116	−	3.32755i	−0.0731905	−	0.126770i
$690$		0			0
$691$	9.91178	−	17.1677i	0.377062	−	0.653090i	−0.613572	−	0.789639i	$-0.710268\pi$
$691$	9.91178	−	17.1677i	0.377062	−	0.653090i	0.990633	+	0.136549i	$0.0436011\pi$
$692$	22.7496			0.864810
$693$		0			0
$694$	11.8970			0.451605
$695$	1.76407	−	3.05545i	0.0669148	−	0.115900i
$696$		0			0
$697$	−2.17095	−	3.76019i	−0.0822306	−	0.142427i
$698$	9.81291	−	16.9965i	0.371424	−	0.643326i
$699$		0			0
$700$	10.7183	−	4.32937i	0.405112	−	0.163635i
$701$	45.5093			1.71886			0.859431	−	0.511252i	$-0.170818\pi$
$701$	45.5093			1.71886			0.859431	+	0.511252i	$0.170818\pi$
$702$		0			0
$703$	−23.5421	−	40.7761i	−0.887906	−	1.53790i
$704$	1.92668	+	3.33711i	0.0726145	+	0.125772i
$705$		0			0
$706$	−23.9390			−0.900955
$707$	0.0167945	−	0.119423i	0.000631622	−	0.00449138i
$708$		0			0
$709$	7.38167	−	12.7854i	0.277225	−	0.480167i	−0.693469	−	0.720486i	$-0.743919\pi$
$709$	7.38167	−	12.7854i	0.277225	−	0.480167i	0.970694	+	0.240319i	$0.0772521\pi$
$710$	−0.782300	−	1.35498i	−0.0293592	−	0.0508516i
$711$		0			0
$712$	−6.93506	+	12.0119i	−0.259902	+	0.450164i
$713$	0.208632			0.00781335
$714$		0			0
$715$	−3.06065			−0.114462
$716$	7.79428	−	13.5001i	0.291286	−	0.504522i
$717$		0			0
$718$	−15.4738	−	26.8015i	−0.577478	−	1.00022i
$719$	17.5369	−	30.3748i	0.654016	−	1.13279i	−0.328123	−	0.944635i	$-0.606416\pi$
$719$	17.5369	−	30.3748i	0.654016	−	1.13279i	0.982140	−	0.188154i	$-0.0602505\pi$
$720$		0			0
$721$	−10.0728	+	4.06865i	−0.375131	+	0.151525i
$722$	−5.63888			−0.209857
$723$		0			0
$724$	−2.13746	−	3.70218i	−0.0794380	−	0.137591i
$725$	12.4534	+	21.5699i	0.462508	+	0.801087i
$726$		0			0
$727$	−9.40005			−0.348628			−0.174314	−	0.984690i	$-0.555771\pi$
$727$	−9.40005			−0.348628			−0.174314	+	0.984690i	$0.555771\pi$
$728$	2.08474	+	1.62907i	0.0772655	+	0.0603773i
$729$		0			0
$730$	2.08018	−	3.60298i	0.0769909	−	0.133352i
$731$	3.66553	+	6.34888i	0.135574	+	0.234822i
$732$		0			0
$733$	20.8625	−	36.1350i	0.770575	−	1.33468i	−0.166673	−	0.986012i	$-0.553302\pi$
$733$	20.8625	−	36.1350i	0.770575	−	1.33468i	0.937248	−	0.348663i	$-0.113364\pi$
$734$	−25.9558			−0.958045
$735$		0			0
$736$	3.53117			0.130161
$737$	25.4024	−	43.9983i	0.935710	−	1.62070i
$738$		0			0
$739$	9.60697	+	16.6398i	0.353398	+	0.612103i	0.986842	−	0.161685i	$-0.0516928\pi$
$739$	9.60697	+	16.6398i	0.353398	+	0.612103i	−0.633444	+	0.773788i	$0.718359\pi$
$740$	3.76711	−	6.52482i	0.138482	−	0.239857i
$741$		0			0
$742$	8.01025	+	6.25942i	0.294066	+	0.229791i
$743$	0.583287			0.0213987			0.0106994	−	0.999943i	$-0.496594\pi$
$743$	0.583287			0.0213987			0.0106994	+	0.999943i	$0.496594\pi$
$744$		0			0
$745$	−2.88380	−	4.99488i	−0.105654	−	0.182998i
$746$	16.6189	+	28.7848i	0.608462	+	1.05389i
$747$		0			0
$748$	8.13211			0.297339
$749$	49.0010	−	19.7927i	1.79046	−	0.723210i
$750$		0			0
$751$	9.14736	−	15.8437i	0.333792	−	0.578144i	−0.649460	−	0.760396i	$-0.725005\pi$
$751$	9.14736	−	15.8437i	0.333792	−	0.578144i	0.983252	+	0.182251i	$0.0583384\pi$
$752$	0.472154	+	0.817794i	0.0172177	+	0.0298219i
$753$		0			0
$754$	−2.85032	+	4.93691i	−0.103803	+	0.179792i
$755$	5.76546			0.209827
$756$		0			0
$757$	−7.13854			−0.259455			−0.129727	−	0.991550i	$-0.541410\pi$
$757$	−7.13854			−0.259455			−0.129727	+	0.991550i	$0.541410\pi$
$758$	−10.4949	+	18.1777i	−0.381193	+	0.660246i
$759$		0			0
$760$	−1.97131	−	3.41440i	−0.0715068	−	0.123853i
$761$	−12.8095	+	22.1867i	−0.464343	+	0.804266i	−0.999172	−	0.0406947i	$-0.987043\pi$
$761$	−12.8095	+	22.1867i	−0.464343	+	0.804266i	0.534828	+	0.844961i	$0.320376\pi$
$762$		0			0
$763$	0.585299	−	4.16198i	0.0211892	−	0.150674i
$764$	1.37923			0.0498988
$765$		0			0
$766$	7.51941	+	13.0240i	0.271688	+	0.470577i
$767$	4.58170	+	7.93574i	0.165436	+	0.286543i
$768$		0			0
$769$	42.4554			1.53098			0.765491	−	0.643447i	$-0.222496\pi$
$769$	42.4554			1.53098			0.765491	+	0.643447i	$0.222496\pi$
$770$	7.50834	−	3.03280i	0.270582	−	0.109295i
$771$		0			0
$772$	9.33980	−	16.1770i	0.336147	−	0.582223i
$773$	4.67285	+	8.09362i	0.168071	+	0.291107i	0.937742	−	0.347334i	$-0.112913\pi$
$773$	4.67285	+	8.09362i	0.168071	+	0.291107i	−0.769671	+	0.638441i	$0.779580\pi$
$774$		0			0
$775$	−0.129070	+	0.223557i	−0.00463635	+	0.00803039i
$776$	4.74870			0.170468
$777$		0			0
$778$	7.93823			0.284599
$779$	5.10619	−	8.84417i	0.182948	−	0.316875i
$780$		0			0
$781$	3.79524	+	6.57355i	0.135804	+	0.235220i
$782$	3.72608	−	6.45376i	0.133244	−	0.230786i
$783$		0			0
$784$	−6.72849	−	1.93064i	−0.240303	−	0.0689513i
$785$	−13.5766			−0.484569
$786$		0			0
$787$	−15.3940	−	26.6631i	−0.548736	−	0.950439i	−0.998362	−	0.0572214i	$-0.981776\pi$
$787$	−15.3940	−	26.6631i	−0.548736	−	0.950439i	0.449626	−	0.893217i	$-0.351557\pi$
$788$	5.53877	+	9.59343i	0.197311	+	0.341752i
$789$		0			0
$790$	4.39465			0.156354
$791$	21.2678	+	16.6192i	0.756195	+	0.590911i
$792$		0			0
$793$	−2.75788	+	4.77679i	−0.0979351	+	0.169629i
$794$	−7.64747	−	13.2458i	−0.271399	−	0.470076i
$795$		0			0
$796$	−0.381051	+	0.660000i	−0.0135060	+	0.0233931i
$797$	−39.6642			−1.40498			−0.702489	−	0.711695i	$-0.747928\pi$
$797$	−39.6642			−1.40498			−0.702489	+	0.711695i	$0.747928\pi$
$798$		0			0
$799$	1.99286			0.0705023
$800$	−2.18456	+	3.78377i	−0.0772358	+	0.133776i
$801$		0			0
$802$	5.69918	+	9.87126i	0.201245	+	0.348566i
$803$	−10.0918	+	17.4794i	−0.356131	+	0.616836i
$804$		0			0
$805$	1.03340	−	7.34834i	0.0364224	−	0.258995i
$806$	−0.0590831			−0.00208111
$807$		0			0
$808$	0.0227910	+	0.0394751i	0.000801783	+	0.00138873i
$809$	19.0958	+	33.0749i	0.671372	+	1.16285i	0.977515	+	0.210865i	$0.0676281\pi$
$809$	19.0958	+	33.0749i	0.671372	+	1.16285i	−0.306143	+	0.951986i	$0.599039\pi$
$810$		0			0
$811$	−9.53152			−0.334697			−0.167348	−	0.985898i	$-0.553520\pi$
$811$	−9.53152			−0.334697			−0.167348	+	0.985898i	$0.553520\pi$
$812$	2.10038	−	14.9355i	0.0737090	−	0.524134i
$813$		0			0
$814$	−18.2757	+	31.6545i	−0.640563	+	1.10949i
$815$	0.138868	+	0.240527i	0.00486434	+	0.00842528i
$816$		0			0
$817$	−8.62151	+	14.9329i	−0.301628	+	0.522436i
$818$	18.7978			0.657249
$819$		0			0
$820$	1.63414			0.0570667
$821$	25.7317	−	44.5686i	0.898043	−	1.55546i	0.0680501	−	0.997682i	$-0.478322\pi$
$821$	25.7317	−	44.5686i	0.898043	−	1.55546i	0.829993	−	0.557774i	$-0.188344\pi$
$822$		0			0
$823$	−5.62221	−	9.73795i	−0.195978	−	0.339444i	0.751243	−	0.660026i	$-0.229455\pi$
$823$	−5.62221	−	9.73795i	−0.195978	−	0.339444i	−0.947221	+	0.320582i	$0.896121\pi$
$824$	2.05301	−	3.55591i	0.0715198	−	0.123876i
$825$		0			0
$826$	−19.1033	−	14.9278i	−0.664688	−	0.519405i
$827$	47.8936			1.66542			0.832712	−	0.553706i	$-0.186787\pi$
$827$	47.8936			1.66542			0.832712	+	0.553706i	$0.186787\pi$
$828$		0			0
$829$	−23.5286	−	40.7528i	−0.817182	−	1.41540i	−0.907750	−	0.419511i	$-0.862201\pi$
$829$	−23.5286	−	40.7528i	−0.817182	−	1.41540i	0.0905677	−	0.995890i	$-0.471132\pi$
$830$	−6.70578	−	11.6148i	−0.232761	−	0.403154i
$831$		0			0
$832$	−1.00000			−0.0346688
$833$	−10.6284	+	10.2602i	−0.368253	+	0.355494i
$834$		0			0
$835$	−8.38740	+	14.5274i	−0.290258	+	0.502742i
$836$	9.56358	+	16.5646i	0.330763	+	0.572899i
$837$		0			0
$838$	−2.88353	+	4.99442i	−0.0996099	+	0.172529i
$839$	−20.3034			−0.700952			−0.350476	−	0.936572i	$-0.613980\pi$
$839$	−20.3034			−0.700952			−0.350476	+	0.936572i	$0.613980\pi$
$840$		0			0
$841$	3.49740			0.120600
$842$	−0.0360691	+	0.0624735i	−0.00124302	+	0.00215298i
$843$		0			0
$844$	3.12563	+	5.41376i	0.107589	+	0.186349i
$845$	0.397140	−	0.687867i	0.0136620	−	0.0236633i
$846$		0			0
$847$	−9.44085	+	3.81339i	−0.324391	+	0.131030i
$848$	−3.84233			−0.131946
$849$		0			0
$850$	4.61028	+	7.98524i	0.158131	+	0.273891i
$851$	16.7476	+	29.0077i	0.574101	+	0.994372i
$852$		0			0
$853$	48.4331			1.65832			0.829159	−	0.559013i	$-0.188820\pi$
$853$	48.4331			1.65832			0.829159	+	0.559013i	$0.188820\pi$
$854$	2.03226	−	14.4511i	0.0695425	−	0.494507i
$855$		0			0
$856$	−9.98722	+	17.2984i	−0.341356	+	0.591246i
$857$	0.498240	+	0.862978i	0.0170196	+	0.0294788i	0.874410	−	0.485188i	$-0.161249\pi$
$857$	0.498240	+	0.862978i	0.0170196	+	0.0294788i	−0.857390	+	0.514667i	$0.827916\pi$
$858$		0			0
$859$	20.0077	−	34.6544i	0.682655	−	1.18239i	−0.291512	−	0.956567i	$-0.594158\pi$
$859$	20.0077	−	34.6544i	0.682655	−	1.18239i	0.974168	−	0.225827i	$-0.0725083\pi$
$860$	−2.75916			−0.0940865
$861$		0			0
$862$	1.38252			0.0470889
$863$	−3.76242	+	6.51670i	−0.128074	+	0.221831i	−0.922930	−	0.384967i	$-0.874213\pi$
$863$	−3.76242	+	6.51670i	−0.128074	+	0.221831i	0.794856	+	0.606798i	$0.207546\pi$
$864$		0			0
$865$	9.03477	+	15.6487i	0.307191	+	0.532071i
$866$	13.0107	−	22.5353i	0.442123	−	0.765780i
$867$		0			0
$868$	0.144942	−	0.0585455i	0.00491964	−	0.00198716i
$869$	−21.3201			−0.723236
$870$		0			0
$871$	6.59227	+	11.4181i	0.223371	+	0.386889i
$872$	0.794280	+	1.37573i	0.0268977	+	0.0465882i
$873$		0			0
$874$	17.5279			0.592889
$875$	15.5140	+	12.1230i	0.524469	+	0.409834i
$876$		0			0
$877$	1.92273	−	3.33027i	0.0649260	−	0.112455i	−0.831735	−	0.555173i	$-0.812652\pi$
$877$	1.92273	−	3.33027i	0.0649260	−	0.112455i	0.896661	+	0.442717i	$0.145986\pi$
$878$	−8.96291	−	15.5242i	−0.302484	−	0.523917i
$879$		0			0
$880$	−1.53032	+	2.65060i	−0.0515872	+	0.0893517i
$881$	30.2732			1.01993			0.509966	−	0.860195i	$-0.329658\pi$
$881$	30.2732			1.01993			0.509966	+	0.860195i	$0.329658\pi$
$882$		0			0
$883$	−35.9878			−1.21108			−0.605542	−	0.795813i	$-0.707044\pi$
$883$	−35.9878			−1.21108			−0.605542	+	0.795813i	$0.707044\pi$
$884$	−1.05520	+	1.82765i	−0.0354901	+	0.0614707i
$885$		0			0
$886$	−19.2065	−	33.2666i	−0.645255	−	1.11761i
$887$	24.4728	−	42.3881i	0.821715	−	1.42325i	−0.0826894	−	0.996575i	$-0.526351\pi$
$887$	24.4728	−	42.3881i	0.821715	−	1.42325i	0.904404	−	0.426677i	$-0.140316\pi$
$888$		0			0
$889$	−20.4605	−	15.9884i	−0.686224	−	0.536233i
$890$	−11.0168			−0.369283
$891$		0			0
$892$	5.33001	+	9.23185i	0.178462	+	0.309105i
$893$	2.34366	+	4.05933i	0.0784275	+	0.135840i
$894$		0			0
$895$	12.3817			0.413874
$896$	2.45318	−	0.990902i	0.0819551	−	0.0331037i
$897$		0			0
$898$	−18.1879	+	31.5024i	−0.606939	+	1.05125i
$899$	0.168406	+	0.291688i	0.00561665	+	0.00972833i
$900$		0			0
$901$	−4.05441	+	7.02245i	−0.135072	+	0.233952i
$902$	−7.92786			−0.263969
$903$		0			0
$904$	−10.2017			−0.339302
$905$	1.69774	−	2.94057i	0.0564348	−	0.0977479i
$906$		0			0
$907$	17.5008	+	30.3123i	0.581106	+	1.00650i	0.995349	+	0.0963381i	$0.0307130\pi$
$907$	17.5008	+	30.3123i	0.581106	+	1.00650i	−0.414243	+	0.910166i	$0.635954\pi$
$908$	−7.84497	+	13.5879i	−0.260344	+	0.450930i
$909$		0			0
$910$	−0.292649	+	2.08099i	−0.00970123	+	0.0689842i
$911$	7.05428			0.233719			0.116859	−	0.993148i	$-0.462717\pi$
$911$	7.05428			0.233719			0.116859	+	0.993148i	$0.462717\pi$
$912$		0			0
$913$	32.5324	+	56.3477i	1.07666	+	1.86484i
$914$	−9.93600	−	17.2097i	−0.328654	−	0.569245i
$915$		0			0
$916$	−20.2429			−0.668843
$917$	−2.23008	+	0.900785i	−0.0736437	+	0.0297465i
$918$		0			0
$919$	21.0587	−	36.4748i	0.694664	−	1.20319i	−0.275630	−	0.961264i	$-0.588887\pi$
$919$	21.0587	−	36.4748i	0.694664	−	1.20319i	0.970294	−	0.241929i	$-0.0777801\pi$
$920$	1.40237	+	2.42898i	0.0462348	+	0.0800809i
$921$		0			0
$922$	−19.1906	+	33.2391i	−0.632009	+	1.09467i
$923$	−1.96983			−0.0648379
$924$		0			0
$925$	−41.4437			−1.36266
$926$	10.1712	−	17.6170i	0.334245	−	0.578930i
$927$		0			0
$928$	2.85032	+	4.93691i	0.0935665	+	0.162062i
$929$	1.71111	−	2.96373i	0.0561396	−	0.0972367i	−0.836590	−	0.547830i	$-0.815454\pi$
$929$	1.71111	−	2.96373i	0.0561396	−	0.0972367i	0.892729	+	0.450593i	$0.148787\pi$
$930$		0			0
$931$	−33.3986	−	9.58321i	−1.09460	−	0.314077i
$932$	−6.02252			−0.197274
$933$		0			0
$934$	−1.86096	−	3.22328i	−0.0608925	−	0.105469i
$935$	3.22959	+	5.59381i	0.105619	+	0.182937i
$936$		0			0
$937$	10.9128			0.356504			0.178252	−	0.983985i	$-0.442956\pi$
$937$	10.9128			0.356504			0.178252	+	0.983985i	$0.442956\pi$
$938$	−27.4863	−	21.4785i	−0.897460	−	0.701299i
$939$		0			0
$940$	−0.375022	+	0.649558i	−0.0122319	+	0.0211862i
$941$	−3.97484	−	6.88463i	−0.129576	−	0.224432i	0.793936	−	0.608001i	$-0.208028\pi$
$941$	−3.97484	−	6.88463i	−0.129576	−	0.224432i	−0.923512	+	0.383569i	$0.874695\pi$
$942$		0			0
$943$	−3.63250	+	6.29167i	−0.118290	+	0.204885i
$944$	9.16340			0.298243
$945$		0			0
$946$	13.3858			0.435208
$947$	−7.50411	+	12.9975i	−0.243851	+	0.422362i	−0.961808	−	0.273725i	$-0.911744\pi$
$947$	−7.50411	+	12.9975i	−0.243851	+	0.422362i	0.717957	+	0.696087i	$0.245077\pi$
$948$		0			0
$949$	−2.61895	−	4.53615i	−0.0850147	−	0.147250i
$950$	−10.8436	+	18.7817i	−0.351814	+	0.609359i
$951$		0			0
$952$	0.777566	−	5.52917i	0.0252011	−	0.179201i
$953$	−33.8775			−1.09740			−0.548699	−	0.836020i	$-0.684877\pi$
$953$	−33.8775			−1.09740			−0.548699	+	0.836020i	$0.684877\pi$
$954$		0			0
$955$	0.547747	+	0.948726i	0.0177247	+	0.0307001i
$956$	12.7960	+	22.1633i	0.413851	+	0.716811i
$957$		0			0
$958$	2.96782			0.0958860
$959$	−0.672210	+	4.78000i	−0.0217068	+	0.154354i
$960$		0			0
$961$	15.4983	−	26.8438i	0.499944	−	0.865928i
$962$	−4.74280	−	8.21476i	−0.152914	−	0.264855i
$963$		0			0
$964$	−0.654345	+	1.13336i	−0.0210750	+	0.0365030i
$965$	14.8368			0.477615
$966$		0			0
$967$	−43.7735			−1.40766			−0.703831	−	0.710368i	$-0.748529\pi$
$967$	−43.7735			−1.40766			−0.703831	+	0.710368i	$0.748529\pi$
$968$	1.92420	−	3.33282i	0.0618462	−	0.107121i
$969$		0			0
$970$	1.88590	+	3.26647i	0.0605525	+	0.104880i
$971$	2.40379	−	4.16349i	0.0771414	−	0.133613i	−0.824874	−	0.565316i	$-0.808754\pi$
$971$	2.40379	−	4.16349i	0.0771414	−	0.133613i	0.902015	+	0.431704i	$0.142087\pi$
$972$		0			0
$973$	9.26025	+	7.23620i	0.296870	+	0.231982i
$974$	18.6869			0.598768
$975$		0			0
$976$	2.75788	+	4.77679i	0.0882775	+	0.152901i
$977$	−9.77154	−	16.9248i	−0.312619	−	0.541472i	0.666309	−	0.745675i	$-0.267873\pi$
$977$	−9.77154	−	16.9248i	−0.312619	−	0.541472i	−0.978929	+	0.204203i	$0.934540\pi$
$978$		0			0
$979$	53.4466			1.70816
$980$	−1.34413	−	5.39504i	−0.0429368	−	0.172338i
$981$		0			0
$982$	2.33385	−	4.04235i	0.0744761	−	0.128996i
$983$	21.9695	+	38.0524i	0.700720	+	1.21368i	0.968214	+	0.250123i	$0.0804710\pi$
$983$	21.9695	+	38.0524i	0.700720	+	1.21368i	−0.267494	+	0.963559i	$0.586196\pi$
$984$		0			0
$985$	−4.39933	+	7.61987i	−0.140174	+	0.242789i
$986$	12.0306			0.383133
$987$		0			0
$988$	−4.96376			−0.157918
$989$	6.13327	−	10.6231i	0.195026	−	0.337796i
$990$		0			0
$991$	21.7197	+	37.6197i	0.689950	+	1.19503i	0.971854	+	0.235586i	$0.0757008\pi$
$991$	21.7197	+	37.6197i	0.689950	+	1.19503i	−0.281904	+	0.959443i	$0.590966\pi$
$992$	−0.0295415	+	0.0511674i	−0.000937945	+	0.00162457i
$993$		0			0
$994$	4.83237	−	1.95191i	0.153273	−	0.0619109i
$995$	−0.605322			−0.0191900
$996$		0			0
$997$	−12.7387	−	22.0640i	−0.403438	−	0.698774i	0.590701	−	0.806891i	$-0.298851\pi$
$997$	−12.7387	−	22.0640i	−0.403438	−	0.698774i	−0.994138	+	0.108116i	$0.965518\pi$
$998$	8.88358	+	15.3868i	0.281205	+	0.487061i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.j.t.1171.4	yes	10
3.2	odd	2		1638.2.j.s.1171.2	yes	10
7.4	even	3	inner	1638.2.j.t.235.4	yes	10
21.11	odd	6		1638.2.j.s.235.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.j.s.235.2	✓	10	21.11	odd	6
1638.2.j.s.1171.2	yes	10	3.2	odd	2
1638.2.j.t.235.4	yes	10	7.4	even	3	inner
1638.2.j.t.1171.4	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.397140 - 0.687867i) q^{5} +(2.08474 + 1.62907i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.397140 - 0.687867i) q^{5} +(2.08474 + 1.62907i) q^{7} -1.00000 q^{8} +(-0.397140 - 0.687867i) q^{10} +(1.92668 + 3.33711i) q^{11} -1.00000 q^{13} +(2.45318 - 0.990902i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.05520 + 1.82765i) q^{17} +(-2.48188 + 4.29874i) q^{19} -0.794280 q^{20} +3.85336 q^{22} +(1.76559 - 3.05808i) q^{23} +(2.18456 + 3.78377i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(0.368446 - 2.61997i) q^{28} +5.70065 q^{29} +(0.0295415 + 0.0511674i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.11039 q^{34} +(1.94852 - 0.787053i) q^{35} +(-4.74280 + 8.21476i) q^{37} +(2.48188 + 4.29874i) q^{38} +(-0.397140 + 0.687867i) q^{40} -2.05739 q^{41} +3.47378 q^{43} +(1.92668 - 3.33711i) q^{44} +(-1.76559 - 3.05808i) q^{46} +(0.472154 - 0.817794i) q^{47} +(1.69227 + 6.79237i) q^{49} +4.36912 q^{50} +(0.500000 + 0.866025i) q^{52} +(1.92116 + 3.32755i) q^{53} +3.06065 q^{55} +(-2.08474 - 1.62907i) q^{56} +(2.85032 - 4.93691i) q^{58} +(-4.58170 - 7.93574i) q^{59} +(2.75788 - 4.77679i) q^{61} +0.0590831 q^{62} +1.00000 q^{64} +(-0.397140 + 0.687867i) q^{65} +(-6.59227 - 11.4181i) q^{67} +(1.05520 - 1.82765i) q^{68} +(0.292649 - 2.08099i) q^{70} +1.96983 q^{71} +(2.61895 + 4.53615i) q^{73} +(4.74280 + 8.21476i) q^{74} +4.96376 q^{76} +(-1.41976 + 10.0957i) q^{77} +(-2.76643 + 4.79160i) q^{79} +(0.397140 + 0.687867i) q^{80} +(-1.02869 + 1.78175i) q^{82} +16.8852 q^{83} +1.67624 q^{85} +(1.73689 - 3.00839i) q^{86} +(-1.92668 - 3.33711i) q^{88} +(6.93506 - 12.0119i) q^{89} +(-2.08474 - 1.62907i) q^{91} -3.53117 q^{92} +(-0.472154 - 0.817794i) q^{94} +(1.97131 + 3.41440i) q^{95} -4.74870 q^{97} +(6.72849 + 1.93064i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8}+O(q^{10}) \) 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8	\( 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8} + q^{10} + 9 q^{11} - 10 q^{13} - 6 q^{14} - 5 q^{16} - 8 q^{17} + 4 q^{19} + 2 q^{20} + 18 q^{22} + 6 q^{23} - 12 q^{25} - 5 q^{26} - 3 q^{28} - 14 q^{29} - 5 q^{31} + 5 q^{32} - 16 q^{34} - 8 q^{35} - 10 q^{37} - 4 q^{38} + q^{40} - 24 q^{41} + 8 q^{43} + 9 q^{44} - 6 q^{46} - 4 q^{47} - 5 q^{49} - 24 q^{50} + 5 q^{52} + 19 q^{53} - 2 q^{55} + 3 q^{56} - 7 q^{58} - 7 q^{59} + 4 q^{61} - 10 q^{62} + 10 q^{64} + q^{65} - 8 q^{68} + 11 q^{70} - 8 q^{71} - 6 q^{73} + 10 q^{74} - 8 q^{76} + 19 q^{77} - 9 q^{79} - q^{80} - 12 q^{82} - 34 q^{83} + 36 q^{85} + 4 q^{86} - 9 q^{88} + 10 q^{89} + 3 q^{91} - 12 q^{92} + 4 q^{94} + 18 q^{95} + 14 q^{97} + 5 q^{98}+O(q^{100}) \) 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8 + q^10 + 9 * q^11 - 10 * q^13 - 6 * q^14 - 5 * q^16 - 8 * q^17 + 4 * q^19 + 2 * q^20 + 18 * q^22 + 6 * q^23 - 12 * q^25 - 5 * q^26 - 3 * q^28 - 14 * q^29 - 5 * q^31 + 5 * q^32 - 16 * q^34 - 8 * q^35 - 10 * q^37 - 4 * q^38 + q^40 - 24 * q^41 + 8 * q^43 + 9 * q^44 - 6 * q^46 - 4 * q^47 - 5 * q^49 - 24 * q^50 + 5 * q^52 + 19 * q^53 - 2 * q^55 + 3 * q^56 - 7 * q^58 - 7 * q^59 + 4 * q^61 - 10 * q^62 + 10 * q^64 + q^65 - 8 * q^68 + 11 * q^70 - 8 * q^71 - 6 * q^73 + 10 * q^74 - 8 * q^76 + 19 * q^77 - 9 * q^79 - q^80 - 12 * q^82 - 34 * q^83 + 36 * q^85 + 4 * q^86 - 9 * q^88 + 10 * q^89 + 3 * q^91 - 12 * q^92 + 4 * q^94 + 18 * q^95 + 14 * q^97 + 5 * q^98

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