LMFDB - Embedded newform 361.2.e.d.62.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(28,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("361.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			62.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	361.62
Dual form			361.2.e.d.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347296 + 1.96962i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.29813 + 1.92836i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.347296 + 1.96962i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.29813 + 1.92836i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-2.00000 - 3.46410i) q^{12} +(-0.694593 - 3.93923i) q^{13} +(-4.59627 + 3.85673i) q^{15} +(0.694593 - 3.93923i) q^{16} +(2.81908 - 1.02606i) q^{17} -6.00000 q^{20} +(-1.87939 + 0.684040i) q^{21} +(0.694593 + 3.93923i) q^{25} +(-2.00000 + 3.46410i) q^{27} +(-1.87939 - 0.684040i) q^{28} +(-5.63816 - 2.05212i) q^{29} +(2.00000 + 3.46410i) q^{31} +(-4.59627 - 3.85673i) q^{33} +(-0.520945 + 2.95442i) q^{35} +(1.87939 - 0.684040i) q^{36} +2.00000 q^{37} +8.00000 q^{39} +(-1.04189 + 5.90885i) q^{41} +(-0.766044 - 0.642788i) q^{43} +(-1.04189 - 5.90885i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(2.81908 + 1.02606i) q^{47} +(7.51754 + 2.73616i) q^{48} +(3.00000 - 5.19615i) q^{49} +(1.04189 + 5.90885i) q^{51} +(6.12836 + 5.14230i) q^{52} +(9.19253 - 7.71345i) q^{53} +(-8.45723 + 3.07818i) q^{55} +(5.63816 - 2.05212i) q^{59} +(2.08378 - 11.8177i) q^{60} +(-0.766044 + 0.642788i) q^{61} +(-0.173648 - 0.984808i) q^{63} +(4.00000 + 6.92820i) q^{64} +(6.00000 - 10.3923i) q^{65} +(3.75877 + 1.36808i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(4.59627 + 3.85673i) q^{71} +(-1.21554 + 6.89365i) q^{73} -8.00000 q^{75} -3.00000 q^{77} +(1.38919 - 7.87846i) q^{79} +(9.19253 - 7.71345i) q^{80} +(-8.42649 - 7.07066i) q^{81} +(-6.00000 - 10.3923i) q^{83} +(2.00000 - 3.46410i) q^{84} +(8.45723 + 3.07818i) q^{85} +(6.00000 - 10.3923i) q^{87} +(2.08378 + 11.8177i) q^{89} +(3.06418 - 2.57115i) q^{91} +(-7.51754 + 2.73616i) q^{93} +(-7.51754 + 2.73616i) q^{97} +(2.29813 - 1.92836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7}+O(q^{10}) $ 6 * q + 3 * q^7	$ 6 q + 3 q^{7} - 9 q^{11} - 12 q^{12} - 36 q^{20} - 12 q^{27} + 12 q^{31} + 12 q^{37} + 48 q^{39} - 9 q^{45} + 18 q^{49} + 24 q^{64} + 36 q^{65} - 18 q^{68} - 48 q^{75} - 18 q^{77} - 36 q^{83} + 12 q^{84} + 36 q^{87}+O(q^{100}) $ 6 * q + 3 * q^7 - 9 * q^11 - 12 * q^12 - 36 * q^20 - 12 * q^27 + 12 * q^31 + 12 * q^37 + 48 * q^39 - 9 * q^45 + 18 * q^49 + 24 * q^64 + 36 * q^65 - 18 * q^68 - 48 * q^75 - 18 * q^77 - 36 * q^83 + 12 * q^84 + 36 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$2$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$3$	−0.347296	+	1.96962i	−0.200512	+	1.13716i	0.703836	+	0.710362i	$0.251469\pi$
$3$	−0.347296	+	1.96962i	−0.200512	+	1.13716i	−0.904348	+	0.426796i	$0.859642\pi$
$4$	−1.53209	+	1.28558i	−0.766044	+	0.642788i
$5$	2.29813	+	1.92836i	1.02776	+	0.862390i	0.990582	−	0.136919i	$-0.0437199\pi$
$5$	2.29813	+	1.92836i	1.02776	+	0.862390i	0.0371742	+	0.999309i	$0.488164\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$		0			0
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	−2.00000	−	3.46410i	−0.577350	−	1.00000i
$13$	−0.694593	−	3.93923i	−0.192645	−	1.09255i	−0.915732	−	0.401789i	$-0.868389\pi$
$13$	−0.694593	−	3.93923i	−0.192645	−	1.09255i	0.723087	−	0.690757i	$-0.242723\pi$
$14$		0			0
$15$	−4.59627	+	3.85673i	−1.18675	+	0.995802i
$16$	0.694593	−	3.93923i	0.173648	−	0.984808i
$17$	2.81908	−	1.02606i	0.683727	−	0.248856i	0.0232799	−	0.999729i	$-0.492589\pi$
$17$	2.81908	−	1.02606i	0.683727	−	0.248856i	0.660447	+	0.750873i	$0.270367\pi$
$18$		0			0
$19$		0			0
$19$		0			0
$20$	−6.00000			−1.34164
$21$	−1.87939	+	0.684040i	−0.410115	+	0.149270i
$22$		0			0
$23$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$23$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$24$		0			0
$25$	0.694593	+	3.93923i	0.138919	+	0.787846i
$26$		0			0
$27$	−2.00000	+	3.46410i	−0.384900	+	0.666667i
$28$	−1.87939	−	0.684040i	−0.355170	−	0.129271i
$29$	−5.63816	−	2.05212i	−1.04698	−	0.381069i	−0.239457	−	0.970907i	$-0.576970\pi$
$29$	−5.63816	−	2.05212i	−1.04698	−	0.381069i	−0.807522	+	0.589838i	$0.799192\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$	−4.59627	−	3.85673i	−0.800107	−	0.671370i
$34$		0			0
$35$	−0.520945	+	2.95442i	−0.0880557	+	0.499389i
$36$	1.87939	−	0.684040i	0.313231	−	0.114007i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	8.00000			1.28103
$40$		0			0
$41$	−1.04189	+	5.90885i	−0.162716	+	0.922807i	0.788673	+	0.614813i	$0.210769\pi$
$41$	−1.04189	+	5.90885i	−0.162716	+	0.922807i	−0.951388	+	0.307994i	$0.900342\pi$
$42$		0			0
$43$	−0.766044	−	0.642788i	−0.116821	−	0.0980242i	0.582506	−	0.812826i	$-0.302072\pi$
$43$	−0.766044	−	0.642788i	−0.116821	−	0.0980242i	−0.699327	+	0.714802i	$0.746517\pi$
$44$	−1.04189	−	5.90885i	−0.157071	−	0.890792i
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$		0			0
$47$	2.81908	+	1.02606i	0.411205	+	0.149666i	0.539335	−	0.842091i	$-0.318675\pi$
$47$	2.81908	+	1.02606i	0.411205	+	0.149666i	−0.128131	+	0.991757i	$0.540898\pi$
$48$	7.51754	+	2.73616i	1.08506	+	0.394931i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$	1.04189	+	5.90885i	0.145894	+	0.827404i
$52$	6.12836	+	5.14230i	0.849850	+	0.713109i
$53$	9.19253	−	7.71345i	1.26269	−	1.05952i	0.267302	−	0.963613i	$-0.413868\pi$
$53$	9.19253	−	7.71345i	1.26269	−	1.05952i	0.995390	−	0.0959111i	$-0.0305765\pi$
$54$		0			0
$55$	−8.45723	+	3.07818i	−1.14037	+	0.415062i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.63816	−	2.05212i	0.734025	−	0.267163i	0.0521576	−	0.998639i	$-0.483390\pi$
$59$	5.63816	−	2.05212i	0.734025	−	0.267163i	0.681868	+	0.731475i	$0.261168\pi$
$60$	2.08378	−	11.8177i	0.269015	−	1.52566i
$61$	−0.766044	+	0.642788i	−0.0980819	+	0.0823005i	−0.690510	−	0.723323i	$-0.742614\pi$
$61$	−0.766044	+	0.642788i	−0.0980819	+	0.0823005i	0.592428	+	0.805623i	$0.298169\pi$
$62$		0			0
$63$	−0.173648	−	0.984808i	−0.0218776	−	0.124074i
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	6.00000	−	10.3923i	0.744208	−	1.28901i
$66$		0			0
$67$	3.75877	+	1.36808i	0.459207	+	0.167138i	0.561257	−	0.827642i	$-0.310318\pi$
$67$	3.75877	+	1.36808i	0.459207	+	0.167138i	−0.102050	+	0.994779i	$0.532540\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$	4.59627	+	3.85673i	0.545476	+	0.457709i	0.873406	−	0.486993i	$-0.161906\pi$
$71$	4.59627	+	3.85673i	0.545476	+	0.457709i	−0.327929	+	0.944702i	$0.606351\pi$
$72$		0			0
$73$	−1.21554	+	6.89365i	−0.142268	+	0.806841i	0.827252	+	0.561830i	$0.189903\pi$
$73$	−1.21554	+	6.89365i	−0.142268	+	0.806841i	−0.969520	+	0.245011i	$0.921208\pi$
$74$		0			0
$75$	−8.00000			−0.923760
$76$		0			0
$77$	−3.00000			−0.341882
$78$		0			0
$79$	1.38919	−	7.87846i	0.156296	−	0.886396i	−0.801296	−	0.598268i	$-0.795856\pi$
$79$	1.38919	−	7.87846i	0.156296	−	0.886396i	0.957592	−	0.288128i	$-0.0930330\pi$
$80$	9.19253	−	7.71345i	1.02776	−	0.862390i
$81$	−8.42649	−	7.07066i	−0.936277	−	0.785629i
$82$		0			0
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$	2.00000	−	3.46410i	0.218218	−	0.377964i
$85$	8.45723	+	3.07818i	0.917316	+	0.333876i
$86$		0			0
$87$	6.00000	−	10.3923i	0.643268	−	1.11417i
$88$		0			0
$89$	2.08378	+	11.8177i	0.220880	+	1.25267i	0.870406	+	0.492334i	$0.163856\pi$
$89$	2.08378	+	11.8177i	0.220880	+	1.25267i	−0.649526	+	0.760339i	$0.725033\pi$
$90$		0			0
$91$	3.06418	−	2.57115i	0.321213	−	0.269530i
$92$		0			0
$93$	−7.51754	+	2.73616i	−0.779533	+	0.283727i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.51754	+	2.73616i	−0.763291	+	0.277815i	−0.694187	−	0.719794i	$-0.744236\pi$
$97$	−7.51754	+	2.73616i	−0.763291	+	0.277815i	−0.0691034	+	0.997610i	$0.522014\pi$
$98$		0			0
$99$	2.29813	−	1.92836i	0.230971	−	0.193808i
$100$	−6.12836	−	5.14230i	−0.612836	−	0.514230i
$101$	1.04189	+	5.90885i	0.103672	+	0.587952i	0.991742	+	0.128245i	$0.0409345\pi$
$101$	1.04189	+	5.90885i	0.103672	+	0.587952i	−0.888071	+	0.459707i	$0.847954\pi$
$102$		0			0
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$		0			0
$105$	−5.63816	−	2.05212i	−0.550228	−	0.200266i
$106$		0			0
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.861931	+	0.507026i	$0.169255\pi$
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.00813215	+	0.999967i	$0.497411\pi$
$108$	−1.38919	−	7.87846i	−0.133674	−	0.758105i
$109$	−12.2567	−	10.2846i	−1.17398	−	0.985086i	−1.00000		0.000337014i	$-0.999893\pi$
$109$	−12.2567	−	10.2846i	−1.17398	−	0.985086i	−0.173980	−	0.984749i	$-0.555663\pi$
$110$		0			0
$111$	−0.694593	+	3.93923i	−0.0659278	+	0.373895i
$112$	3.75877	−	1.36808i	0.355170	−	0.129271i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$		0			0
$116$	11.2763	−	4.10424i	1.04698	−	0.381069i
$117$	−0.694593	+	3.93923i	−0.0642151	+	0.364182i
$118$		0			0
$119$	2.29813	+	1.92836i	0.210670	+	0.176773i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	−11.2763	−	4.10424i	−1.01675	−	0.370067i
$124$	−7.51754	−	2.73616i	−0.675095	−	0.245715i
$125$	1.50000	−	2.59808i	0.134164	−	0.232379i
$126$		0			0
$127$	0.347296	+	1.96962i	0.0308176	+	0.174775i	0.996332	−	0.0855756i	$-0.0272729\pi$
$127$	0.347296	+	1.96962i	0.0308176	+	0.174775i	−0.965514	+	0.260351i	$0.916162\pi$
$128$		0			0
$129$	1.53209	−	1.28558i	0.134893	−	0.113189i
$130$		0			0
$131$	14.0954	−	5.13030i	1.23152	−	0.448237i	0.357402	−	0.933951i	$-0.383663\pi$
$131$	14.0954	−	5.13030i	1.23152	−	0.448237i	0.874118	+	0.485714i	$0.161440\pi$
$132$	12.0000			1.04447
$133$		0			0
$134$		0			0
$135$	−11.2763	+	4.10424i	−0.970510	+	0.353237i
$136$		0			0
$137$	−2.29813	+	1.92836i	−0.196343	+	0.164751i	−0.735659	−	0.677352i	$-0.763127\pi$
$137$	−2.29813	+	1.92836i	−0.196343	+	0.164751i	0.539316	+	0.842103i	$0.318683\pi$
$138$		0			0
$139$	−2.25743	−	12.8025i	−0.191472	−	1.08589i	−0.917353	−	0.398074i	$-0.869679\pi$
$139$	−2.25743	−	12.8025i	−0.191472	−	1.08589i	0.725881	−	0.687820i	$-0.241432\pi$
$140$	−3.00000	−	5.19615i	−0.253546	−	0.439155i
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$		0			0
$143$	11.2763	+	4.10424i	0.942973	+	0.343214i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	−9.00000	−	15.5885i	−0.747409	−	1.29455i
$146$		0			0
$147$	9.19253	+	7.71345i	0.758187	+	0.636195i
$148$	−3.06418	+	2.57115i	−0.251874	+	0.211347i
$149$	3.64661	−	20.6810i	0.298742	−	1.69425i	−0.352849	−	0.935680i	$-0.614787\pi$
$149$	3.64661	−	20.6810i	0.298742	−	1.69425i	0.651591	−	0.758570i	$-0.274102\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$		0			0
$153$	−3.00000			−0.242536
$154$		0			0
$155$	−2.08378	+	11.8177i	−0.167373	+	0.949220i
$156$	−12.2567	+	10.2846i	−0.981322	+	0.823427i
$157$	10.7246	+	8.99903i	0.855918	+	0.718201i	0.961085	−	0.276254i	$-0.0890931\pi$
$157$	10.7246	+	8.99903i	0.855918	+	0.718201i	−0.105167	+	0.994455i	$0.533538\pi$
$158$		0			0
$159$	12.0000	+	20.7846i	0.951662	+	1.64833i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	−6.00000	−	10.3923i	−0.468521	−	0.811503i
$165$	−3.12567	−	17.7265i	−0.243333	−	1.38001i
$166$		0			0
$167$	−13.7888	+	11.5702i	−1.06701	+	0.895327i	−0.994778	−	0.102061i	$-0.967456\pi$
$167$	−13.7888	+	11.5702i	−1.06701	+	0.895327i	−0.0722312	+	0.997388i	$0.523012\pi$
$168$		0			0
$169$	−2.81908	+	1.02606i	−0.216852	+	0.0789277i
$170$		0			0
$171$		0			0
$172$	2.00000			0.152499
$173$	16.9145	−	6.15636i	1.28598	−	0.468060i	0.393577	−	0.919292i	$-0.371238\pi$
$173$	16.9145	−	6.15636i	1.28598	−	0.468060i	0.892407	+	0.451232i	$0.149015\pi$
$174$		0			0
$175$	−3.06418	+	2.57115i	−0.231630	+	0.194361i
$176$	9.19253	+	7.71345i	0.692913	+	0.581423i
$177$	2.08378	+	11.8177i	0.156626	+	0.888272i
$178$		0			0
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	−0.304446	−	0.952529i	$-0.598471\pi$
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	0.977138	−	0.212607i	$-0.0681952\pi$
$180$	5.63816	+	2.05212i	0.420243	+	0.152956i
$181$	−1.87939	−	0.684040i	−0.139694	−	0.0508443i	0.271227	−	0.962515i	$-0.412571\pi$
$181$	−1.87939	−	0.684040i	−0.139694	−	0.0508443i	−0.410921	+	0.911671i	$0.634793\pi$
$182$		0			0
$183$	−1.00000	−	1.73205i	−0.0739221	−	0.128037i
$184$		0			0
$185$	4.59627	+	3.85673i	0.337924	+	0.283552i
$186$		0			0
$187$	−1.56283	+	8.86327i	−0.114286	+	0.648146i
$188$	−5.63816	+	2.05212i	−0.411205	+	0.149666i
$189$	−4.00000			−0.290957
$190$		0			0
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	−15.0351	+	5.47232i	−1.08506	+	0.394931i
$193$	−0.694593	+	3.93923i	−0.0499979	+	0.283552i	−0.999548	−	0.0300633i	$-0.990429\pi$
$193$	−0.694593	+	3.93923i	−0.0499979	+	0.283552i	0.949550	+	0.313615i	$0.101540\pi$
$194$		0			0
$195$	18.3851	+	15.4269i	1.31658	+	1.10474i
$196$	2.08378	+	11.8177i	0.148841	+	0.844121i
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	−0.985160	−	0.171639i	$-0.945094\pi$
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	0.343937	−	0.938993i	$-0.388239\pi$
$198$		0			0
$199$	−10.3366	−	3.76222i	−0.732743	−	0.266697i	−0.0514178	−	0.998677i	$-0.516374\pi$
$199$	−10.3366	−	3.76222i	−0.732743	−	0.266697i	−0.681326	+	0.731980i	$0.738596\pi$
$200$		0			0
$201$	−4.00000	+	6.92820i	−0.282138	+	0.488678i
$202$		0			0
$203$	−1.04189	−	5.90885i	−0.0731263	−	0.414720i
$204$	−9.19253	−	7.71345i	−0.643606	−	0.540050i
$205$	−13.7888	+	11.5702i	−0.963052	+	0.808096i
$206$		0			0
$207$		0			0
$208$	−16.0000			−1.10940
$209$		0			0
$210$		0			0
$211$	−13.1557	+	4.78828i	−0.905676	+	0.329639i	−0.752525	−	0.658564i	$-0.771164\pi$
$211$	−13.1557	+	4.78828i	−0.905676	+	0.329639i	−0.153151	+	0.988203i	$0.548942\pi$
$212$	−4.16756	+	23.6354i	−0.286229	+	1.62328i
$213$	−9.19253	+	7.71345i	−0.629862	+	0.528517i
$214$		0			0
$215$	−0.520945	−	2.95442i	−0.0355281	−	0.201490i
$216$		0			0
$217$	−2.00000	+	3.46410i	−0.135769	+	0.235159i
$218$		0			0
$219$	−13.1557	−	4.78828i	−0.888980	−	0.323562i
$220$	9.00000	−	15.5885i	0.606780	−	1.05097i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$		0			0
$223$	−7.66044	−	6.42788i	−0.512981	−	0.430442i	0.349196	−	0.937050i	$-0.386455\pi$
$223$	−7.66044	−	6.42788i	−0.512981	−	0.430442i	−0.862177	+	0.506607i	$0.830899\pi$
$224$		0			0
$225$	0.694593	−	3.93923i	0.0463062	−	0.262615i
$226$		0			0
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$		0			0
$229$	5.00000			0.330409			0.165205	−	0.986259i	$-0.447172\pi$
$229$	5.00000			0.330409			0.165205	+	0.986259i	$0.447172\pi$
$230$		0			0
$231$	1.04189	−	5.90885i	0.0685513	−	0.388774i
$232$		0			0
$233$	−16.0869	−	13.4985i	−1.05389	−	0.884319i	−0.0603928	−	0.998175i	$-0.519235\pi$
$233$	−16.0869	−	13.4985i	−1.05389	−	0.884319i	−0.993497	+	0.113856i	$0.963680\pi$
$234$		0			0
$235$	4.50000	+	7.79423i	0.293548	+	0.508439i
$236$	−6.00000	+	10.3923i	−0.390567	+	0.676481i
$237$	15.0351	+	5.47232i	0.976634	+	0.355466i
$238$		0			0
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	−0.999854	−	0.0170808i	$-0.994563\pi$
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	0.514719	+	0.857359i	$0.327896\pi$
$240$	12.0000	+	20.7846i	0.774597	+	1.34164i
$241$	−1.73648	−	9.84808i	−0.111857	−	0.634370i	−0.988259	−	0.152790i	$-0.951174\pi$
$241$	−1.73648	−	9.84808i	−0.111857	−	0.634370i	0.876402	−	0.481580i	$-0.159937\pi$
$242$		0			0
$243$	7.66044	−	6.42788i	0.491418	−	0.412348i
$244$	0.347296	−	1.96962i	0.0222334	−	0.126092i
$245$	16.9145	−	6.15636i	1.08063	−	0.393316i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	22.5526	−	8.20848i	1.42921	−	0.520192i
$250$		0			0
$251$	16.0869	−	13.4985i	1.01540	−	0.852020i	0.0263559	−	0.999653i	$-0.491610\pi$
$251$	16.0869	−	13.4985i	1.01540	−	0.852020i	0.989042	+	0.147632i	$0.0471652\pi$
$252$	1.53209	+	1.28558i	0.0965125	+	0.0809836i
$253$		0			0
$254$		0			0
$255$	−9.00000	+	15.5885i	−0.563602	+	0.976187i
$256$	−15.0351	−	5.47232i	−0.939693	−	0.342020i
$257$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$257$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$258$		0			0
$259$	1.00000	+	1.73205i	0.0621370	+	0.107624i
$260$	4.16756	+	23.6354i	0.258461	+	1.46580i
$261$	4.59627	+	3.85673i	0.284502	+	0.238725i
$262$		0			0
$263$	1.56283	−	8.86327i	0.0963684	−	0.546533i	−0.897951	−	0.440095i	$-0.854945\pi$
$263$	1.56283	−	8.86327i	0.0963684	−	0.546533i	0.994319	−	0.106437i	$-0.0339443\pi$
$264$		0			0
$265$	36.0000			2.21146
$266$		0			0
$267$	−24.0000			−1.46878
$268$	−7.51754	+	2.73616i	−0.459207	+	0.167138i
$269$	4.16756	−	23.6354i	0.254100	−	1.44107i	−0.544271	−	0.838909i	$-0.683194\pi$
$269$	4.16756	−	23.6354i	0.254100	−	1.44107i	0.798371	−	0.602165i	$-0.205695\pi$
$270$		0			0
$271$	−12.2567	−	10.2846i	−0.744542	−	0.624745i	0.189511	−	0.981879i	$-0.439310\pi$
$271$	−12.2567	−	10.2846i	−0.744542	−	0.624745i	−0.934053	+	0.357133i	$0.883754\pi$
$272$	−2.08378	−	11.8177i	−0.126348	−	0.716553i
$273$	4.00000	+	6.92820i	0.242091	+	0.419314i
$274$		0			0
$275$	−11.2763	−	4.10424i	−0.679987	−	0.247495i
$276$		0			0
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	−0.425684	−	0.904872i	$-0.639967\pi$
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	0.996484	−	0.0837823i	$-0.0267000\pi$
$278$		0			0
$279$	−0.694593	−	3.93923i	−0.0415842	−	0.235836i
$280$		0			0
$281$	4.59627	−	3.85673i	0.274190	−	0.230073i	−0.495315	−	0.868713i	$-0.664947\pi$
$281$	4.59627	−	3.85673i	0.274190	−	0.230073i	0.769505	+	0.638641i	$0.220503\pi$
$282$		0			0
$283$	12.2160	−	4.44626i	0.726166	−	0.264303i	0.0476250	−	0.998865i	$-0.484835\pi$
$283$	12.2160	−	4.44626i	0.726166	−	0.264303i	0.678541	+	0.734562i	$0.262613\pi$
$284$	−12.0000			−0.712069
$285$		0			0
$286$		0			0
$287$	−5.63816	+	2.05212i	−0.332810	+	0.121133i
$288$		0			0
$289$	−6.12836	+	5.14230i	−0.360492	+	0.302488i
$290$		0			0
$291$	−2.77837	−	15.7569i	−0.162871	−	0.923687i
$292$	−7.00000	−	12.1244i	−0.409644	−	0.709524i
$293$	6.00000	−	10.3923i	0.350524	−	0.607125i	−0.635818	−	0.771839i	$-0.719337\pi$
$293$	6.00000	−	10.3923i	0.350524	−	0.607125i	0.986341	+	0.164714i	$0.0526703\pi$
$294$		0			0
$295$	16.9145	+	6.15636i	0.984798	+	0.358437i
$296$		0			0
$297$	−6.00000	−	10.3923i	−0.348155	−	0.603023i
$298$		0			0
$299$		0			0
$300$	12.2567	−	10.2846i	0.707642	−	0.593782i
$301$	0.173648	−	0.984808i	0.0100089	−	0.0567634i
$302$		0			0
$303$	−12.0000			−0.689382
$304$		0			0
$305$	−3.00000			−0.171780
$306$		0			0
$307$	3.47296	−	19.6962i	0.198212	−	1.12412i	−0.709557	−	0.704649i	$-0.751105\pi$
$307$	3.47296	−	19.6962i	0.198212	−	1.12412i	0.907769	−	0.419470i	$-0.137784\pi$
$308$	4.59627	−	3.85673i	0.261897	−	0.219757i
$309$	−21.4492	−	17.9981i	−1.22020	−	1.02387i
$310$		0			0
$311$	1.50000	+	2.59808i	0.0850572	+	0.147323i	0.905416	−	0.424526i	$-0.139559\pi$
$311$	1.50000	+	2.59808i	0.0850572	+	0.147323i	−0.820358	+	0.571850i	$0.806226\pi$
$312$		0			0
$313$	9.39693	+	3.42020i	0.531146	+	0.193321i	0.593650	−	0.804723i	$-0.297686\pi$
$313$	9.39693	+	3.42020i	0.531146	+	0.193321i	−0.0625041	+	0.998045i	$0.519909\pi$
$314$		0			0
$315$	1.50000	−	2.59808i	0.0845154	−	0.146385i
$316$	8.00000	+	13.8564i	0.450035	+	0.779484i
$317$	1.04189	+	5.90885i	0.0585183	+	0.331874i	0.999986	−	0.00522845i	$-0.00166427\pi$
$317$	1.04189	+	5.90885i	0.0585183	+	0.331874i	−0.941468	+	0.337102i	$0.890553\pi$
$318$		0			0
$319$	13.7888	−	11.5702i	0.772025	−	0.647806i
$320$	−4.16756	+	23.6354i	−0.232973	+	1.32126i
$321$	−33.8289	+	12.3127i	−1.88815	+	0.687229i
$322$		0			0
$323$		0			0
$324$	22.0000			1.22222
$325$	15.0351	−	5.47232i	0.833996	−	0.303550i
$326$		0			0
$327$	24.5134	−	20.5692i	1.35560	−	1.13748i
$328$		0			0
$329$	0.520945	+	2.95442i	0.0287206	+	0.162883i
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	22.5526	+	8.20848i	1.23774	+	0.450499i
$333$	−1.87939	−	0.684040i	−0.102990	−	0.0374852i
$334$		0			0
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$	1.38919	+	7.87846i	0.0757863	+	0.429805i
$337$	24.5134	+	20.5692i	1.33533	+	1.12048i	0.982799	+	0.184676i	$0.0591236\pi$
$337$	24.5134	+	20.5692i	1.33533	+	1.12048i	0.352532	+	0.935800i	$0.385321\pi$
$338$		0			0
$339$	−2.08378	+	11.8177i	−0.113175	+	0.641849i
$340$	−16.9145	+	6.15636i	−0.917316	+	0.333876i
$341$	−12.0000			−0.649836
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16.0869	+	13.4985i	0.863592	+	0.724640i	0.962739	−	0.270433i	$-0.0871669\pi$
$347$	16.0869	+	13.4985i	0.863592	+	0.724640i	−0.0991469	+	0.995073i	$0.531611\pi$
$348$	4.16756	+	23.6354i	0.223404	+	1.26699i
$349$	−8.50000	−	14.7224i	−0.454995	−	0.788074i	0.543693	−	0.839284i	$-0.317025\pi$
$349$	−8.50000	−	14.7224i	−0.454995	−	0.788074i	−0.998688	+	0.0512103i	$0.983692\pi$
$350$		0			0
$351$	15.0351	+	5.47232i	0.802513	+	0.292091i
$352$		0			0
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		0			0
$355$	3.12567	+	17.7265i	0.165893	+	0.940827i
$356$	−18.3851	−	15.4269i	−0.974407	−	0.817624i
$357$	−4.59627	+	3.85673i	−0.243260	+	0.204120i
$358$		0			0
$359$	−14.0954	+	5.13030i	−0.743926	+	0.270767i	−0.686048	−	0.727557i	$-0.740656\pi$
$359$	−14.0954	+	5.13030i	−0.743926	+	0.270767i	−0.0578786	+	0.998324i	$0.518434\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$	−3.75877	+	1.36808i	−0.197284	+	0.0718056i
$364$	−1.38919	+	7.87846i	−0.0728131	+	0.412944i
$365$	−16.0869	+	13.4985i	−0.842029	+	0.706546i
$366$		0			0
$367$	1.38919	+	7.87846i	0.0725149	+	0.411252i	0.999359	+	0.0358054i	$0.0113997\pi$
$367$	1.38919	+	7.87846i	0.0725149	+	0.411252i	−0.926844	+	0.375447i	$0.877489\pi$
$368$		0			0
$369$	3.00000	−	5.19615i	0.156174	−	0.270501i
$370$		0			0
$371$	11.2763	+	4.10424i	0.585437	+	0.213082i
$372$	8.00000	−	13.8564i	0.414781	−	0.718421i
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	4.59627	+	3.85673i	0.237350	+	0.199160i
$376$		0			0
$377$	−4.16756	+	23.6354i	−0.214640	+	1.21728i
$378$		0			0
$379$	−34.0000			−1.74646			−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000			−1.74646			−0.873231	+	0.487306i	$0.837980\pi$
$380$		0			0
$381$	−4.00000			−0.204926
$382$		0			0
$383$	2.08378	−	11.8177i	0.106476	−	0.603856i	−0.884144	−	0.467214i	$-0.845258\pi$
$383$	2.08378	−	11.8177i	0.106476	−	0.603856i	0.990620	−	0.136642i	$-0.0436310\pi$
$384$		0			0
$385$	−6.89440	−	5.78509i	−0.351371	−	0.294835i
$386$		0			0
$387$	0.500000	+	0.866025i	0.0254164	+	0.0440225i
$388$	8.00000	−	13.8564i	0.406138	−	0.703452i
$389$	−14.0954	−	5.13030i	−0.714665	−	0.260117i	−0.0410056	−	0.999159i	$-0.513056\pi$
$389$	−14.0954	−	5.13030i	−0.714665	−	0.260117i	−0.673659	+	0.739042i	$0.735278\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	5.20945	+	29.5442i	0.262782	+	1.49031i
$394$		0			0
$395$	18.3851	−	15.4269i	0.925053	−	0.776212i
$396$	−1.04189	+	5.90885i	−0.0523569	+	0.296931i
$397$	6.57785	−	2.39414i	0.330133	−	0.120158i	−0.171636	−	0.985160i	$-0.554905\pi$
$397$	6.57785	−	2.39414i	0.330133	−	0.120158i	0.501768	+	0.865002i	$0.332683\pi$
$398$		0			0
$399$		0			0
$400$	16.0000			0.800000
$401$	−11.2763	+	4.10424i	−0.563112	+	0.204956i	−0.607863	−	0.794042i	$-0.707973\pi$
$401$	−11.2763	+	4.10424i	−0.563112	+	0.204956i	0.0447506	+	0.998998i	$0.485751\pi$
$402$		0			0
$403$	12.2567	−	10.2846i	0.610550	−	0.512313i
$404$	−9.19253	−	7.71345i	−0.457346	−	0.383759i
$405$	−5.73039	−	32.4987i	−0.284745	−	1.61487i
$406$		0			0
$407$	−3.00000	+	5.19615i	−0.148704	+	0.257564i
$408$		0			0
$409$	3.75877	+	1.36808i	0.185859	+	0.0676472i	0.433273	−	0.901263i	$-0.357359\pi$
$409$	3.75877	+	1.36808i	0.185859	+	0.0676472i	−0.247414	+	0.968910i	$0.579581\pi$
$410$		0			0
$411$	−3.00000	−	5.19615i	−0.147979	−	0.256307i
$412$	−4.86215	−	27.5746i	−0.239541	−	1.35850i
$413$	4.59627	+	3.85673i	0.226167	+	0.189777i
$414$		0			0
$415$	6.25133	−	35.4531i	0.306866	−	1.74032i
$416$		0			0
$417$	26.0000			1.27323
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$	11.2763	−	4.10424i	0.550228	−	0.200266i
$421$	1.38919	−	7.87846i	0.0677048	−	0.383973i	−0.932060	−	0.362303i	$-0.881991\pi$
$421$	1.38919	−	7.87846i	0.0677048	−	0.383973i	0.999765	−	0.0216699i	$-0.00689828\pi$
$422$		0			0
$423$	−2.29813	−	1.92836i	−0.111739	−	0.0937602i
$424$		0			0
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$		0			0
$427$	−0.939693	−	0.342020i	−0.0454749	−	0.0165515i
$428$	−33.8289	−	12.3127i	−1.63518	−	0.595158i
$429$	−12.0000	+	20.7846i	−0.579365	+	1.00349i
$430$		0			0
$431$	−4.16756	−	23.6354i	−0.200744	−	1.13848i	−0.903998	−	0.427537i	$-0.859381\pi$
$431$	−4.16756	−	23.6354i	−0.200744	−	1.13848i	0.703254	−	0.710939i	$-0.251730\pi$
$432$	12.2567	+	10.2846i	0.589701	+	0.494818i
$433$	1.53209	−	1.28558i	0.0736275	−	0.0617808i	−0.605231	−	0.796050i	$-0.706919\pi$
$433$	1.53209	−	1.28558i	0.0736275	−	0.0617808i	0.678859	+	0.734269i	$0.262475\pi$
$434$		0			0
$435$	33.8289	−	12.3127i	1.62197	−	0.590350i
$436$	32.0000			1.53252
$437$		0			0
$438$		0			0
$439$	9.39693	−	3.42020i	0.448491	−	0.163237i	−0.107893	−	0.994162i	$-0.534411\pi$
$439$	9.39693	−	3.42020i	0.448491	−	0.163237i	0.556384	+	0.830925i	$0.312188\pi$
$440$		0			0
$441$	−4.59627	+	3.85673i	−0.218870	+	0.183654i
$442$		0			0
$443$	−0.520945	−	2.95442i	−0.0247508	−	0.140369i	0.969928	−	0.243391i	$-0.0782598\pi$
$443$	−0.520945	−	2.95442i	−0.0247508	−	0.140369i	−0.994679	+	0.103022i	$0.967149\pi$
$444$	−4.00000	−	6.92820i	−0.189832	−	0.328798i
$445$	−18.0000	+	31.1769i	−0.853282	+	1.47793i
$446$		0			0
$447$	39.4671	+	14.3648i	1.86673	+	0.679434i
$448$	−4.00000	+	6.92820i	−0.188982	+	0.327327i
$449$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$449$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$450$		0			0
$451$	−13.7888	−	11.5702i	−0.649289	−	0.544818i
$452$	−9.19253	+	7.71345i	−0.432380	+	0.362810i
$453$	3.47296	−	19.6962i	0.163174	−	0.925406i
$454$		0			0
$455$	12.0000			0.562569
$456$		0			0
$457$	−37.0000			−1.73079			−0.865393	−	0.501093i	$-0.832931\pi$
$457$	−37.0000			−1.73079			−0.865393	+	0.501093i	$0.832931\pi$
$458$		0			0
$459$	−2.08378	+	11.8177i	−0.0972624	+	0.551603i
$460$		0			0
$461$	6.89440	+	5.78509i	0.321104	+	0.269438i	0.789064	−	0.614312i	$-0.210566\pi$
$461$	6.89440	+	5.78509i	0.321104	+	0.269438i	−0.467959	+	0.883750i	$0.655011\pi$
$462$		0			0
$463$	15.5000	+	26.8468i	0.720346	+	1.24768i	0.960861	+	0.277031i	$0.0893503\pi$
$463$	15.5000	+	26.8468i	0.720346	+	1.24768i	−0.240515	+	0.970645i	$0.577316\pi$
$464$	−12.0000	+	20.7846i	−0.557086	+	0.964901i
$465$	−22.5526	−	8.20848i	−1.04585	−	0.380659i
$466$		0			0
$467$	13.5000	−	23.3827i	0.624705	−	1.08202i	−0.363892	−	0.931441i	$-0.618552\pi$
$467$	13.5000	−	23.3827i	0.624705	−	1.08202i	0.988598	−	0.150581i	$-0.0481143\pi$
$468$	−4.00000	−	6.92820i	−0.184900	−	0.320256i
$469$	0.694593	+	3.93923i	0.0320733	+	0.181897i
$470$		0			0
$471$	−21.4492	+	17.9981i	−0.988329	+	0.829307i
$472$		0			0
$473$	2.81908	−	1.02606i	0.129621	−	0.0471783i
$474$		0			0
$475$		0			0
$476$	−6.00000			−0.275010
$477$	−11.2763	+	4.10424i	−0.516307	+	0.187920i
$478$		0			0
$479$	−9.19253	+	7.71345i	−0.420018	+	0.352437i	−0.828170	−	0.560477i	$-0.810618\pi$
$479$	−9.19253	+	7.71345i	−0.420018	+	0.352437i	0.408152	+	0.912914i	$0.366173\pi$
$480$		0			0
$481$	−1.38919	−	7.87846i	−0.0633414	−	0.359227i
$482$		0			0
$483$		0			0
$484$	−3.75877	−	1.36808i	−0.170853	−	0.0621855i
$485$	−22.5526	−	8.20848i	−1.02406	−	0.372728i
$486$		0			0
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$		0			0
$489$	−30.6418	−	25.7115i	−1.38567	−	1.16271i
$490$		0			0
$491$	2.08378	−	11.8177i	0.0940396	−	0.533325i	−0.900998	−	0.433824i	$-0.857164\pi$
$491$	2.08378	−	11.8177i	0.0940396	−	0.533325i	0.995037	−	0.0995014i	$-0.0317248\pi$
$492$	22.5526	−	8.20848i	1.01675	−	0.370067i
$493$	−18.0000			−0.810679
$494$		0			0
$495$	9.00000			0.404520
$496$	15.0351	−	5.47232i	0.675095	−	0.245715i
$497$	−1.04189	+	5.90885i	−0.0467351	+	0.265048i
$498$		0			0
$499$	3.83022	+	3.21394i	0.171464	+	0.143876i	0.724482	−	0.689294i	$-0.242079\pi$
$499$	3.83022	+	3.21394i	0.171464	+	0.143876i	−0.553017	+	0.833170i	$0.686524\pi$
$500$	1.04189	+	5.90885i	0.0465947	+	0.264252i
$501$	−18.0000	−	31.1769i	−0.804181	−	1.39288i
$502$		0			0
$503$	−11.2763	−	4.10424i	−0.502786	−	0.182999i	0.0781607	−	0.996941i	$-0.475095\pi$
$503$	−11.2763	−	4.10424i	−0.502786	−	0.182999i	−0.580947	+	0.813942i	$0.697317\pi$
$504$		0			0
$505$	−9.00000	+	15.5885i	−0.400495	+	0.693677i
$506$		0			0
$507$	−1.04189	−	5.90885i	−0.0462719	−	0.262421i
$508$	−3.06418	−	2.57115i	−0.135951	−	0.114076i
$509$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$509$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$510$		0			0
$511$	−6.57785	+	2.39414i	−0.290987	+	0.105911i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−39.4671	+	14.3648i	−1.73913	+	0.632991i
$516$	−0.694593	+	3.93923i	−0.0305777	+	0.173415i
$517$	−6.89440	+	5.78509i	−0.303215	+	0.254428i
$518$		0			0
$519$	6.25133	+	35.4531i	0.274403	+	1.55622i
$520$		0			0
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$		0			0
$523$	−35.7083	−	12.9968i	−1.56142	−	0.568309i	−0.590356	−	0.807143i	$-0.701012\pi$
$523$	−35.7083	−	12.9968i	−1.56142	−	0.568309i	−0.971060	+	0.238834i	$0.923235\pi$
$524$	−15.0000	+	25.9808i	−0.655278	+	1.13497i
$525$	−4.00000	−	6.92820i	−0.174574	−	0.302372i
$526$		0			0
$527$	9.19253	+	7.71345i	0.400433	+	0.336003i
$528$	−18.3851	+	15.4269i	−0.800107	+	0.671370i
$529$	−3.99391	+	22.6506i	−0.173648	+	0.984808i
$530$		0			0
$531$	−6.00000			−0.260378
$532$		0			0
$533$	24.0000			1.03956
$534$		0			0
$535$	−9.37700	+	53.1796i	−0.405403	+	2.29916i
$536$		0			0
$537$	27.5776	+	23.1404i	1.19006	+	0.998580i
$538$		0			0
$539$	9.00000	+	15.5885i	0.387657	+	0.671442i
$540$	12.0000	−	20.7846i	0.516398	−	0.894427i
$541$	23.4923	+	8.55050i	1.01001	+	0.367615i	0.793438	−	0.608651i	$-0.208289\pi$
$541$	23.4923	+	8.55050i	1.01001	+	0.367615i	0.216575	+	0.976266i	$0.430511\pi$
$542$		0			0
$543$	2.00000	−	3.46410i	0.0858282	−	0.148659i
$544$		0			0
$545$	−8.33511	−	47.2708i	−0.357037	−	2.02486i
$546$		0			0
$547$	−21.4492	+	17.9981i	−0.917103	+	0.769541i	−0.973457	−	0.228870i	$-0.926497\pi$
$547$	−21.4492	+	17.9981i	−0.917103	+	0.769541i	0.0563536	+	0.998411i	$0.482053\pi$
$548$	1.04189	−	5.90885i	0.0445073	−	0.252413i
$549$	0.939693	−	0.342020i	0.0401051	−	0.0145971i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	7.51754	−	2.73616i	0.319678	−	0.116353i
$554$		0			0
$555$	−9.19253	+	7.71345i	−0.390201	+	0.327418i
$556$	19.9172	+	16.7125i	0.844676	+	0.708767i
$557$	3.64661	+	20.6810i	0.154512	+	0.876281i	0.959231	+	0.282624i	$0.0912050\pi$
$557$	3.64661	+	20.6810i	0.154512	+	0.876281i	−0.804719	+	0.593656i	$0.797684\pi$
$558$		0			0
$559$	−2.00000	+	3.46410i	−0.0845910	+	0.146516i
$560$	11.2763	+	4.10424i	0.476511	+	0.173436i
$561$	−16.9145	−	6.15636i	−0.714129	−	0.259922i
$562$		0			0
$563$	−3.00000	−	5.19615i	−0.126435	−	0.218992i	0.795858	−	0.605483i	$-0.207020\pi$
$563$	−3.00000	−	5.19615i	−0.126435	−	0.218992i	−0.922293	+	0.386492i	$0.873687\pi$
$564$	−2.08378	−	11.8177i	−0.0877429	−	0.497615i
$565$	13.7888	+	11.5702i	0.580099	+	0.486761i
$566$		0			0
$567$	1.91013	−	10.8329i	0.0802179	−	0.454938i
$568$		0			0
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−22.5526	+	8.20848i	−0.942973	+	0.343214i
$573$	−1.04189	+	5.90885i	−0.0435255	+	0.246846i
$574$		0			0
$575$		0			0
$576$	−1.38919	−	7.87846i	−0.0578827	−	0.328269i
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$		0			0
$579$	−7.51754	−	2.73616i	−0.312418	−	0.113711i
$580$	33.8289	+	12.3127i	1.40467	+	0.511258i
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$		0			0
$583$	6.25133	+	35.4531i	0.258904	+	1.46832i
$584$		0			0
$585$	−9.19253	+	7.71345i	−0.380064	+	0.318912i
$586$		0			0
$587$	−42.2862	+	15.3909i	−1.74534	+	0.635251i	−0.999522	−	0.0309029i	$-0.990162\pi$
$587$	−42.2862	+	15.3909i	−1.74534	+	0.635251i	−0.745815	+	0.666154i	$0.767940\pi$
$588$	−24.0000			−0.989743
$589$		0			0
$590$		0			0
$591$	33.8289	−	12.3127i	1.39154	−	0.506478i
$592$	1.38919	−	7.87846i	0.0570952	−	0.323803i
$593$	−32.1739	+	26.9971i	−1.32122	+	1.10864i	−0.335178	+	0.942155i	$0.608796\pi$
$593$	−32.1739	+	26.9971i	−1.32122	+	1.10864i	−0.986044	+	0.166482i	$0.946759\pi$
$594$		0			0
$595$	1.56283	+	8.86327i	0.0640699	+	0.363359i
$596$	21.0000	+	36.3731i	0.860194	+	1.48990i
$597$	11.0000	−	19.0526i	0.450200	−	0.779769i
$598$		0			0
$599$	33.8289	+	12.3127i	1.38221	+	0.503084i	0.922848	−	0.385164i	$-0.125855\pi$
$599$	33.8289	+	12.3127i	1.38221	+	0.503084i	0.459364	+	0.888248i	$0.348077\pi$
$600$		0			0
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$		0			0
$603$	−3.06418	−	2.57115i	−0.124783	−	0.104705i
$604$	15.3209	−	12.8558i	0.623398	−	0.523093i
$605$	−1.04189	+	5.90885i	−0.0423588	+	0.240229i
$606$		0			0
$607$	32.0000			1.29884			0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000			1.29884			0.649420	+	0.760430i	$0.275012\pi$
$608$		0			0
$609$	12.0000			0.486265
$610$		0			0
$611$	2.08378	−	11.8177i	0.0843006	−	0.478093i
$612$	4.59627	−	3.85673i	0.185793	−	0.155899i
$613$	22.2153	+	18.6408i	0.897267	+	0.752896i	0.969654	−	0.244480i	$-0.0786173\pi$
$613$	22.2153	+	18.6408i	0.897267	+	0.752896i	−0.0723872	+	0.997377i	$0.523062\pi$
$614$		0			0
$615$	−18.0000	−	31.1769i	−0.725830	−	1.25717i
$616$		0			0
$617$	−8.45723	−	3.07818i	−0.340475	−	0.123923i	0.166123	−	0.986105i	$-0.446875\pi$
$617$	−8.45723	−	3.07818i	−0.340475	−	0.123923i	−0.506598	+	0.862182i	$0.669097\pi$
$618$		0			0
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.0376891	+	0.999290i	$0.512000\pi$
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.846566	+	0.532284i	$0.821334\pi$
$620$	−12.0000	−	20.7846i	−0.481932	−	0.834730i
$621$		0			0
$622$		0			0
$623$	−9.19253	+	7.71345i	−0.368291	+	0.309033i
$624$	5.55674	−	31.5138i	0.222448	−	1.26156i
$625$	27.2511	−	9.91858i	1.09004	−	0.396743i
$626$		0			0
$627$		0			0
$628$	−28.0000			−1.11732
$629$	5.63816	−	2.05212i	0.224808	−	0.0818234i
$630$		0			0
$631$	8.42649	−	7.07066i	0.335453	−	0.281479i	−0.459464	−	0.888196i	$-0.651959\pi$
$631$	8.42649	−	7.07066i	0.335453	−	0.281479i	0.794917	+	0.606718i	$0.207514\pi$
$632$		0			0
$633$	−4.86215	−	27.5746i	−0.193253	−	1.09599i
$634$		0			0
$635$	−3.00000	+	5.19615i	−0.119051	+	0.206203i
$636$	−45.1052	−	16.4170i	−1.78854	−	0.650975i
$637$	−22.5526	−	8.20848i	−0.893567	−	0.325232i
$638$		0			0
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$		0			0
$641$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$641$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$642$		0			0
$643$	−2.25743	+	12.8025i	−0.0890242	+	0.504881i	0.907391	+	0.420287i	$0.138071\pi$
$643$	−2.25743	+	12.8025i	−0.0890242	+	0.504881i	−0.996415	+	0.0845944i	$0.973041\pi$
$644$		0			0
$645$	6.00000			0.236250
$646$		0			0
$647$	27.0000			1.06148			0.530740	−	0.847535i	$-0.321914\pi$
$647$	27.0000			1.06148			0.530740	+	0.847535i	$0.321914\pi$
$648$		0			0
$649$	−3.12567	+	17.7265i	−0.122693	+	0.695828i
$650$		0			0
$651$	−6.12836	−	5.14230i	−0.240189	−	0.201543i
$652$	−6.94593	−	39.3923i	−0.272023	−	1.54272i
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	0.941248	+	0.337715i	$0.109654\pi$
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	−0.178154	+	0.984003i	$0.557013\pi$
$654$		0			0
$655$	42.2862	+	15.3909i	1.65226	+	0.601372i
$656$	22.5526	+	8.20848i	0.880532	+	0.320487i
$657$	3.50000	−	6.06218i	0.136548	−	0.236508i
$658$		0			0
$659$	−5.20945	−	29.5442i	−0.202931	−	1.15088i	−0.900662	−	0.434520i	$-0.856918\pi$
$659$	−5.20945	−	29.5442i	−0.202931	−	1.15088i	0.697731	−	0.716360i	$-0.254193\pi$
$660$	27.5776	+	23.1404i	1.07346	+	0.900737i
$661$	24.5134	−	20.5692i	0.953462	−	0.800049i	−0.0264155	−	0.999651i	$-0.508409\pi$
$661$	24.5134	−	20.5692i	0.953462	−	0.800049i	0.979877	+	0.199602i	$0.0639648\pi$
$662$		0			0
$663$	22.5526	−	8.20848i	0.875871	−	0.318791i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	6.25133	−	35.4531i	0.241871	−	1.37172i
$669$	15.3209	−	12.8558i	0.592340	−	0.497032i
$670$		0			0
$671$	−0.520945	−	2.95442i	−0.0201108	−	0.114054i
$672$		0			0
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	−0.753420	−	0.657539i	$-0.771597\pi$
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	0.946156	+	0.323711i	$0.104931\pi$
$674$		0			0
$675$	−15.0351	−	5.47232i	−0.578701	−	0.210630i
$676$	3.00000	−	5.19615i	0.115385	−	0.199852i
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	0.914867	+	0.403755i	$0.132295\pi$
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	−0.107772	+	0.994176i	$0.534372\pi$
$678$		0			0
$679$	−6.12836	−	5.14230i	−0.235185	−	0.197343i
$680$		0			0
$681$	−4.16756	+	23.6354i	−0.159701	+	0.905710i
$682$		0			0
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$	−1.73648	+	9.84808i	−0.0662509	+	0.375728i
$688$	−3.06418	+	2.57115i	−0.116821	+	0.0980242i
$689$	−36.7701	−	30.8538i	−1.40083	−	1.17544i
$690$		0			0
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	0.657823	−	0.753173i	$-0.271478\pi$
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	−0.981178	+	0.193105i	$0.938144\pi$
$692$	−18.0000	+	31.1769i	−0.684257	+	1.18517i
$693$	2.81908	+	1.02606i	0.107088	+	0.0389768i
$694$		0			0
$695$	19.5000	−	33.7750i	0.739677	−	1.28116i
$696$		0			0
$697$	3.12567	+	17.7265i	0.118393	+	0.671441i
$698$		0			0
$699$	32.1739	−	26.9971i	1.21693	−	1.02112i
$700$	1.38919	−	7.87846i	0.0525063	−	0.297778i
$701$	−5.63816	+	2.05212i	−0.212950	+	0.0775075i	−0.446293	−	0.894887i	$-0.647256\pi$
$701$	−5.63816	+	2.05212i	−0.212950	+	0.0775075i	0.233342	+	0.972395i	$0.425034\pi$
$702$		0			0
$703$		0			0
$704$	−24.0000			−0.904534
$705$	−16.9145	+	6.15636i	−0.637036	+	0.231862i
$706$		0			0
$707$	−4.59627	+	3.85673i	−0.172860	+	0.145047i
$708$	−18.3851	−	15.4269i	−0.690953	−	0.579779i
$709$	4.51485	+	25.6050i	0.169559	+	0.961616i	0.944239	+	0.329262i	$0.106800\pi$
$709$	4.51485	+	25.6050i	0.169559	+	0.961616i	−0.774680	+	0.632354i	$0.782089\pi$
$710$		0			0
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	18.0000	+	31.1769i	0.673162	+	1.16595i
$716$	6.25133	+	35.4531i	0.233623	+	1.32494i
$717$	−22.9813	−	19.2836i	−0.858254	−	0.720160i
$718$		0			0
$719$	2.60472	−	14.7721i	0.0971398	−	0.550907i	−0.896931	−	0.442171i	$-0.854209\pi$
$719$	2.60472	−	14.7721i	0.0971398	−	0.550907i	0.994071	−	0.108736i	$-0.0346804\pi$
$720$	−11.2763	+	4.10424i	−0.420243	+	0.152956i
$721$	−14.0000			−0.521387
$722$		0			0
$723$	20.0000			0.743808
$724$	3.75877	−	1.36808i	0.139694	−	0.0508443i
$725$	4.16756	−	23.6354i	0.154779	−	0.877796i
$726$		0			0
$727$	−14.5548	−	12.2130i	−0.539809	−	0.452954i	0.331663	−	0.943398i	$-0.392390\pi$
$727$	−14.5548	−	12.2130i	−0.539809	−	0.452954i	−0.871473	+	0.490444i	$0.836835\pi$
$728$		0			0
$729$	−6.50000	−	11.2583i	−0.240741	−	0.416975i
$730$		0			0
$731$	−2.81908	−	1.02606i	−0.104267	−	0.0379502i
$732$	3.75877	+	1.36808i	0.138928	+	0.0505657i
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$		0			0
$735$	6.25133	+	35.4531i	0.230584	+	1.30771i
$736$		0			0
$737$	−9.19253	+	7.71345i	−0.338611	+	0.284129i
$738$		0			0
$739$	−10.3366	+	3.76222i	−0.380239	+	0.138396i	−0.525066	−	0.851061i	$-0.675959\pi$
$739$	−10.3366	+	3.76222i	−0.380239	+	0.138396i	0.144828	+	0.989457i	$0.453737\pi$
$740$	−12.0000			−0.441129
$741$		0			0
$742$		0			0
$743$	22.5526	−	8.20848i	0.827375	−	0.301140i	0.106594	−	0.994303i	$-0.466005\pi$
$743$	22.5526	−	8.20848i	0.827375	−	0.301140i	0.720781	+	0.693163i	$0.243783\pi$
$744$		0			0
$745$	48.2608	−	40.4956i	1.76814	−	1.48364i
$746$		0			0
$747$	2.08378	+	11.8177i	0.0762415	+	0.432387i
$748$	−9.00000	−	15.5885i	−0.329073	−	0.569970i
$749$	−9.00000	+	15.5885i	−0.328853	+	0.569590i
$750$		0			0
$751$	−30.0702	−	10.9446i	−1.09728	−	0.399376i	−0.270965	−	0.962589i	$-0.587343\pi$
$751$	−30.0702	−	10.9446i	−1.09728	−	0.399376i	−0.826311	+	0.563214i	$0.809565\pi$
$752$	6.00000	−	10.3923i	0.218797	−	0.378968i
$753$	21.0000	+	36.3731i	0.765283	+	1.32551i
$754$		0			0
$755$	−22.9813	−	19.2836i	−0.836376	−	0.701803i
$756$	6.12836	−	5.14230i	0.222886	−	0.187024i
$757$	−4.34120	+	24.6202i	−0.157784	+	0.894836i	0.798413	+	0.602111i	$0.205673\pi$
$757$	−4.34120	+	24.6202i	−0.157784	+	0.894836i	−0.956196	+	0.292726i	$0.905438\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	33.0000			1.19625			0.598125	−	0.801403i	$-0.295913\pi$
$761$	33.0000			1.19625			0.598125	+	0.801403i	$0.295913\pi$
$762$		0			0
$763$	2.77837	−	15.7569i	0.100584	−	0.570439i
$764$	−4.59627	+	3.85673i	−0.166287	+	0.139531i
$765$	−6.89440	−	5.78509i	−0.249268	−	0.209160i
$766$		0			0
$767$	−12.0000	−	20.7846i	−0.433295	−	0.750489i
$768$	16.0000	−	27.7128i	0.577350	−	1.00000i
$769$	−21.6129	−	7.86646i	−0.779382	−	0.283672i	−0.0784672	−	0.996917i	$-0.525003\pi$
$769$	−21.6129	−	7.86646i	−0.779382	−	0.283672i	−0.700915	+	0.713245i	$0.747225\pi$
$770$		0			0
$771$		0			0
$772$	−4.00000	−	6.92820i	−0.143963	−	0.249351i
$773$	−1.04189	−	5.90885i	−0.0374741	−	0.212526i	0.960321	−	0.278898i	$-0.0899690\pi$
$773$	−1.04189	−	5.90885i	−0.0374741	−	0.212526i	−0.997795	+	0.0663711i	$0.978858\pi$
$774$		0			0
$775$	−12.2567	+	10.2846i	−0.440274	+	0.369434i
$776$		0			0
$777$	−3.75877	+	1.36808i	−0.134845	+	0.0490796i
$778$		0			0
$779$		0			0
$780$	−48.0000			−1.71868
$781$	−16.9145	+	6.15636i	−0.605247	+	0.220292i
$782$		0			0
$783$	18.3851	−	15.4269i	0.657029	−	0.551313i
$784$	−18.3851	−	15.4269i	−0.656610	−	0.550961i
$785$	7.29322	+	41.3619i	0.260306	+	1.47627i
$786$		0			0
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	−0.828176	−	0.560469i	$-0.810621\pi$
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	0.899468	+	0.436987i	$0.143954\pi$
$788$	33.8289	+	12.3127i	1.20511	+	0.438623i
$789$	16.9145	+	6.15636i	0.602171	+	0.219172i
$790$		0			0
$791$	3.00000	+	5.19615i	0.106668	+	0.184754i
$792$		0			0
$793$	3.06418	+	2.57115i	0.108812	+	0.0913042i
$794$		0			0
$795$	−12.5027	+	70.9062i	−0.443424	+	2.51478i
$796$	20.6732	−	7.52444i	0.732743	−	0.266697i
$797$	−12.0000			−0.425062			−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000			−0.425062			−0.212531	+	0.977154i	$0.568171\pi$
$798$		0			0
$799$	9.00000			0.318397
$800$		0			0
$801$	2.08378	−	11.8177i	0.0736267	−	0.417558i
$802$		0			0
$803$	−16.0869	−	13.4985i	−0.567696	−	0.476353i
$804$	−2.77837	−	15.7569i	−0.0979856	−	0.555704i
$805$		0			0
$806$		0			0
$807$	45.1052	+	16.4170i	1.58778	+	0.577905i
$808$		0			0
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$		0			0
$811$	−2.77837	−	15.7569i	−0.0975618	−	0.553300i	−0.993932	−	0.109995i	$-0.964917\pi$
$811$	−2.77837	−	15.7569i	−0.0975618	−	0.553300i	0.896370	−	0.443306i	$-0.146194\pi$
$812$	9.19253	+	7.71345i	0.322595	+	0.270689i
$813$	24.5134	−	20.5692i	0.859723	−	0.721393i
$814$		0			0
$815$	−56.3816	+	20.5212i	−1.97496	+	0.718827i
$816$	24.0000			0.840168
$817$		0			0
$818$		0			0
$819$	−3.75877	+	1.36808i	−0.131342	+	0.0478046i
$820$	6.25133	−	35.4531i	0.218306	−	1.23808i
$821$	25.2795	−	21.2120i	0.882259	−	0.740304i	−0.0843829	−	0.996433i	$-0.526892\pi$
$821$	25.2795	−	21.2120i	0.882259	−	0.740304i	0.966642	+	0.256130i	$0.0824475\pi$
$822$		0			0
$823$	−8.50876	−	48.2556i	−0.296597	−	1.68208i	−0.660641	−	0.750702i	$-0.729715\pi$
$823$	−8.50876	−	48.2556i	−0.296597	−	1.68208i	0.364044	−	0.931382i	$-0.381396\pi$
$824$		0			0
$825$	12.0000	−	20.7846i	0.417786	−	0.723627i
$826$		0			0
$827$	−11.2763	−	4.10424i	−0.392116	−	0.142718i	0.138435	−	0.990371i	$-0.455793\pi$
$827$	−11.2763	−	4.10424i	−0.392116	−	0.142718i	−0.530551	+	0.847653i	$0.678015\pi$
$828$		0			0
$829$	8.00000	+	13.8564i	0.277851	+	0.481253i	0.970851	−	0.239686i	$-0.0770444\pi$
$829$	8.00000	+	13.8564i	0.277851	+	0.481253i	−0.692999	+	0.720938i	$0.743711\pi$
$830$		0			0
$831$	29.1097	+	24.4259i	1.00980	+	0.847326i
$832$	24.5134	−	20.5692i	0.849850	−	0.713109i
$833$	3.12567	−	17.7265i	0.108298	−	0.614188i
$834$		0			0
$835$	−54.0000			−1.86875
$836$		0			0
$837$	−16.0000			−0.553041
$838$		0			0
$839$	3.12567	−	17.7265i	0.107910	−	0.611988i	−0.882108	−	0.471047i	$-0.843876\pi$
$839$	3.12567	−	17.7265i	0.107910	−	0.611988i	0.990018	−	0.140941i	$-0.0450128\pi$
$840$		0			0
$841$	5.36231	+	4.49951i	0.184907	+	0.155156i
$842$		0			0
$843$	6.00000	+	10.3923i	0.206651	+	0.357930i
$844$	14.0000	−	24.2487i	0.481900	−	0.834675i
$845$	−8.45723	−	3.07818i	−0.290938	−	0.105893i
$846$		0			0
$847$	−1.00000	+	1.73205i	−0.0343604	+	0.0595140i
$848$	−24.0000	−	41.5692i	−0.824163	−	1.42749i
$849$	4.51485	+	25.6050i	0.154949	+	0.878761i
$850$		0			0
$851$		0			0
$852$	4.16756	−	23.6354i	0.142778	−	0.809735i
$853$	−24.4320	+	8.89252i	−0.836536	+	0.304474i	−0.724539	−	0.689234i	$-0.757947\pi$
$853$	−24.4320	+	8.89252i	−0.836536	+	0.304474i	−0.111997	+	0.993708i	$0.535725\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.9145	+	6.15636i	−0.577787	+	0.210297i	−0.614349	−	0.789034i	$-0.710581\pi$
$857$	−16.9145	+	6.15636i	−0.577787	+	0.210297i	0.0365623	+	0.999331i	$0.488359\pi$
$858$		0			0
$859$	−37.5362	+	31.4966i	−1.28072	+	1.07465i	−0.287573	+	0.957759i	$0.592848\pi$
$859$	−37.5362	+	31.4966i	−1.28072	+	1.07465i	−0.993145	+	0.116891i	$0.962707\pi$
$860$	4.59627	+	3.85673i	0.156731	+	0.131513i
$861$	−2.08378	−	11.8177i	−0.0710150	−	0.402746i
$862$		0			0
$863$	−9.00000	+	15.5885i	−0.306364	+	0.530637i	−0.977564	−	0.210639i	$-0.932446\pi$
$863$	−9.00000	+	15.5885i	−0.306364	+	0.530637i	0.671200	+	0.741276i	$0.265779\pi$
$864$		0			0
$865$	50.7434	+	18.4691i	1.72533	+	0.627968i
$866$		0			0
$867$	−8.00000	−	13.8564i	−0.271694	−	0.470588i
$868$	−1.38919	−	7.87846i	−0.0471520	−	0.267412i
$869$	18.3851	+	15.4269i	0.623671	+	0.523322i
$870$		0			0
$871$	2.77837	−	15.7569i	0.0941415	−	0.533903i
$872$		0			0
$873$	8.00000			0.270759
$874$		0			0
$875$	3.00000			0.101419
$876$	26.3114	−	9.57656i	0.888980	−	0.323562i
$877$	−3.82026	+	21.6658i	−0.129001	+	0.731601i	0.849850	+	0.527025i	$0.176693\pi$
$877$	−3.82026	+	21.6658i	−0.129001	+	0.731601i	−0.978851	+	0.204576i	$0.934418\pi$
$878$		0			0
$879$	18.3851	+	15.4269i	0.620113	+	0.520337i
$880$	6.25133	+	35.4531i	0.210732	+	1.19512i
$881$	13.5000	+	23.3827i	0.454827	+	0.787783i	0.998678	−	0.0513987i	$-0.0163679\pi$
$881$	13.5000	+	23.3827i	0.454827	+	0.787783i	−0.543852	+	0.839181i	$0.683035\pi$
$882$		0			0
$883$	−44.1656	−	16.0749i	−1.48629	−	0.540965i	−0.533820	−	0.845598i	$-0.679244\pi$
$883$	−44.1656	−	16.0749i	−1.48629	−	0.540965i	−0.952470	+	0.304633i	$0.901466\pi$
$884$	22.5526	+	8.20848i	0.758527	+	0.276081i
$885$	−18.0000	+	31.1769i	−0.605063	+	1.04800i
$886$		0			0
$887$	3.12567	+	17.7265i	0.104950	+	0.595199i	0.991240	+	0.132070i	$0.0421623\pi$
$887$	3.12567	+	17.7265i	0.104950	+	0.595199i	−0.886291	+	0.463129i	$0.846727\pi$
$888$		0			0
$889$	−1.53209	+	1.28558i	−0.0513846	+	0.0431168i
$890$		0			0
$891$	31.0099	−	11.2867i	1.03887	−	0.378117i
$892$	20.0000			0.669650
$893$		0			0
$894$		0			0
$895$	50.7434	−	18.4691i	1.69616	−	0.617354i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.16756	−	23.6354i	−0.138996	−	0.788284i
$900$	4.00000	+	6.92820i	0.133333	+	0.230940i
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$		0			0
$903$	1.87939	+	0.684040i	0.0625420	+	0.0227634i
$904$		0			0
$905$	−3.00000	−	5.19615i	−0.0997234	−	0.172726i
$906$		0			0
$907$	6.12836	+	5.14230i	0.203489	+	0.170747i	0.738837	−	0.673884i	$-0.235375\pi$
$907$	6.12836	+	5.14230i	0.203489	+	0.170747i	−0.535348	+	0.844631i	$0.679820\pi$
$908$	−18.3851	+	15.4269i	−0.610130	+	0.511960i
$909$	1.04189	−	5.90885i	0.0345573	−	0.195984i
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		0			0
$913$	36.0000			1.19143
$914$		0			0
$915$	1.04189	−	5.90885i	0.0344438	−	0.195340i
$916$	−7.66044	+	6.42788i	−0.253108	+	0.212383i
$917$	11.4907	+	9.64181i	0.379455	+	0.318401i
$918$		0			0
$919$	−10.0000	−	17.3205i	−0.329870	−	0.571351i	0.652616	−	0.757689i	$-0.273671\pi$
$919$	−10.0000	−	17.3205i	−0.329870	−	0.571351i	−0.982486	+	0.186338i	$0.940338\pi$
$920$		0			0
$921$	37.5877	+	13.6808i	1.23856	+	0.450798i
$922$		0			0
$923$	12.0000	−	20.7846i	0.394985	−	0.684134i
$924$	6.00000	+	10.3923i	0.197386	+	0.341882i
$925$	1.38919	+	7.87846i	0.0456761	+	0.259042i
$926$		0			0
$927$	10.7246	−	8.99903i	0.352243	−	0.295567i
$928$		0			0
$929$	16.9145	−	6.15636i	0.554946	−	0.201984i	−0.0492968	−	0.998784i	$-0.515698\pi$
$929$	16.9145	−	6.15636i	0.554946	−	0.201984i	0.604243	+	0.796800i	$0.293476\pi$
$930$		0			0
$931$		0			0
$932$	42.0000			1.37576
$933$	−5.63816	+	2.05212i	−0.184585	+	0.0671834i
$934$		0			0
$935$	−20.6832	+	17.3553i	−0.676413	+	0.567578i
$936$		0			0
$937$	−1.21554	−	6.89365i	−0.0397099	−	0.225206i	0.958494	−	0.285112i	$-0.0920309\pi$
$937$	−1.21554	−	6.89365i	−0.0397099	−	0.225206i	−0.998204	+	0.0599064i	$0.980920\pi$
$938$		0			0
$939$	−10.0000	+	17.3205i	−0.326338	+	0.565233i
$940$	−16.9145	−	6.15636i	−0.551689	−	0.200798i
$941$	16.9145	+	6.15636i	0.551396	+	0.200692i	0.602667	−	0.797993i	$-0.294105\pi$
$941$	16.9145	+	6.15636i	0.551396	+	0.200692i	−0.0512707	+	0.998685i	$0.516327\pi$
$942$		0			0
$943$		0			0
$944$	−4.16756	−	23.6354i	−0.135642	−	0.769266i
$945$	−9.19253	−	7.71345i	−0.299033	−	0.250919i
$946$		0			0
$947$	−6.25133	+	35.4531i	−0.203141	+	1.15207i	0.697197	+	0.716879i	$0.254430\pi$
$947$	−6.25133	+	35.4531i	−0.203141	+	1.15207i	−0.900338	+	0.435191i	$0.856681\pi$
$948$	−30.0702	+	10.9446i	−0.976634	+	0.355466i
$949$	28.0000			0.908918
$950$		0			0
$951$	−12.0000			−0.389127
$952$		0			0
$953$	−8.33511	+	47.2708i	−0.270001	+	1.53125i	0.484406	+	0.874843i	$0.339036\pi$
$953$	−8.33511	+	47.2708i	−0.270001	+	1.53125i	−0.754407	+	0.656407i	$0.772075\pi$
$954$		0			0
$955$	6.89440	+	5.78509i	0.223098	+	0.187201i
$956$	−5.20945	−	29.5442i	−0.168486	−	0.955529i
$957$	18.0000	+	31.1769i	0.581857	+	1.00781i
$958$		0			0
$959$	−2.81908	−	1.02606i	−0.0910328	−	0.0331332i
$960$	−45.1052	−	16.4170i	−1.45577	−	0.529855i
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−3.12567	−	17.7265i	−0.100723	−	0.571230i
$964$	15.3209	+	12.8558i	0.493453	+	0.414056i
$965$	−9.19253	+	7.71345i	−0.295918	+	0.248305i
$966$		0			0
$967$	37.5877	−	13.6808i	1.20874	−	0.439945i	0.342473	−	0.939528i	$-0.388736\pi$
$967$	37.5877	−	13.6808i	1.20874	−	0.439945i	0.866266	+	0.499583i	$0.166513\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−56.3816	+	20.5212i	−1.80937	+	0.658557i	−0.812200	+	0.583379i	$0.801730\pi$
$971$	−56.3816	+	20.5212i	−1.80937	+	0.658557i	−0.997170	+	0.0751780i	$0.976047\pi$
$972$	−3.47296	+	19.6962i	−0.111395	+	0.631754i
$973$	9.95858	−	8.35624i	0.319257	−	0.267889i
$974$		0			0
$975$	5.55674	+	31.5138i	0.177958	+	1.00925i
$976$	2.00000	+	3.46410i	0.0640184	+	0.110883i
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	−0.991618	−	0.129205i	$-0.958757\pi$
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	0.607704	+	0.794164i	$0.292091\pi$
$978$		0			0
$979$	−33.8289	−	12.3127i	−1.08118	−	0.393516i
$980$	−18.0000	+	31.1769i	−0.574989	+	0.995910i
$981$	8.00000	+	13.8564i	0.255420	+	0.442401i
$982$		0			0
$983$	−27.5776	−	23.1404i	−0.879589	−	0.738063i	0.0865057	−	0.996251i	$-0.472430\pi$
$983$	−27.5776	−	23.1404i	−0.879589	−	0.738063i	−0.966095	+	0.258189i	$0.916874\pi$
$984$		0			0
$985$	9.37700	−	53.1796i	0.298776	−	1.69444i
$986$		0			0
$987$	−6.00000			−0.190982
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−5.90404	+	33.4835i	−0.187548	+	1.06364i	0.735090	+	0.677970i	$0.237140\pi$
$991$	−5.90404	+	33.4835i	−0.187548	+	1.06364i	−0.922638	+	0.385668i	$0.873971\pi$
$992$		0			0
$993$	42.8985	+	35.9961i	1.36134	+	1.14230i
$994$		0			0
$995$	−16.5000	−	28.5788i	−0.523085	−	0.906010i
$996$	−24.0000	+	41.5692i	−0.760469	+	1.31717i
$997$	−15.9748	−	5.81434i	−0.505926	−	0.184142i	0.0764314	−	0.997075i	$-0.475647\pi$
$997$	−15.9748	−	5.81434i	−0.505926	−	0.184142i	−0.582358	+	0.812933i	$0.697870\pi$
$998$		0			0
$999$	−4.00000	+	6.92820i	−0.126554	+	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.d.62.1		6
19.2	odd	18		361.2.a.b.1.1		1
19.3	odd	18		361.2.c.a.292.1		2
19.4	even	9	inner	361.2.e.d.99.1		6
19.5	even	9		361.2.c.c.68.1		2
19.6	even	9	inner	361.2.e.d.28.1		6
19.7	even	3	inner	361.2.e.d.245.1		6
19.8	odd	6		361.2.e.e.54.1		6
19.9	even	9	inner	361.2.e.d.234.1		6
19.10	odd	18		361.2.e.e.234.1		6
19.11	even	3	inner	361.2.e.d.54.1		6
19.12	odd	6		361.2.e.e.245.1		6
19.13	odd	18		361.2.e.e.28.1		6
19.14	odd	18		361.2.c.a.68.1		2
19.15	odd	18		361.2.e.e.99.1		6
19.16	even	9		361.2.c.c.292.1		2
19.17	even	9		19.2.a.a.1.1	✓	1
19.18	odd	2		361.2.e.e.62.1		6
57.2	even	18		3249.2.a.d.1.1		1
57.17	odd	18		171.2.a.b.1.1		1
76.55	odd	18		304.2.a.f.1.1		1
76.59	even	18		5776.2.a.c.1.1		1
95.17	odd	36		475.2.b.a.324.2		2
95.59	odd	18		9025.2.a.d.1.1		1
95.74	even	18		475.2.a.b.1.1		1
95.93	odd	36		475.2.b.a.324.1		2
133.17	odd	18		931.2.f.b.324.1		2
133.55	odd	18		931.2.a.a.1.1		1
133.74	even	9		931.2.f.c.324.1		2
133.93	even	9		931.2.f.c.704.1		2
133.131	odd	18		931.2.f.b.704.1		2
152.93	even	18		1216.2.a.o.1.1		1
152.131	odd	18		1216.2.a.b.1.1		1
209.131	odd	18		2299.2.a.b.1.1		1
228.131	even	18		2736.2.a.c.1.1		1
247.207	even	18		3211.2.a.a.1.1		1
285.74	odd	18		4275.2.a.i.1.1		1
323.169	even	18		5491.2.a.b.1.1		1
380.359	odd	18		7600.2.a.c.1.1		1
399.188	even	18		8379.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.a.a.1.1	✓	1	19.17	even	9
171.2.a.b.1.1		1	57.17	odd	18
304.2.a.f.1.1		1	76.55	odd	18
361.2.a.b.1.1		1	19.2	odd	18
361.2.c.a.68.1		2	19.14	odd	18
361.2.c.a.292.1		2	19.3	odd	18
361.2.c.c.68.1		2	19.5	even	9
361.2.c.c.292.1		2	19.16	even	9
361.2.e.d.28.1		6	19.6	even	9	inner
361.2.e.d.54.1		6	19.11	even	3	inner
361.2.e.d.62.1		6	1.1	even	1	trivial
361.2.e.d.99.1		6	19.4	even	9	inner
361.2.e.d.234.1		6	19.9	even	9	inner
361.2.e.d.245.1		6	19.7	even	3	inner
361.2.e.e.28.1		6	19.13	odd	18
361.2.e.e.54.1		6	19.8	odd	6
361.2.e.e.62.1		6	19.18	odd	2
361.2.e.e.99.1		6	19.15	odd	18
361.2.e.e.234.1		6	19.10	odd	18
361.2.e.e.245.1		6	19.12	odd	6
475.2.a.b.1.1		1	95.74	even	18
475.2.b.a.324.1		2	95.93	odd	36
475.2.b.a.324.2		2	95.17	odd	36
931.2.a.a.1.1		1	133.55	odd	18
931.2.f.b.324.1		2	133.17	odd	18
931.2.f.b.704.1		2	133.131	odd	18
931.2.f.c.324.1		2	133.74	even	9
931.2.f.c.704.1		2	133.93	even	9
1216.2.a.b.1.1		1	152.131	odd	18
1216.2.a.o.1.1		1	152.93	even	18
2299.2.a.b.1.1		1	209.131	odd	18
2736.2.a.c.1.1		1	228.131	even	18
3211.2.a.a.1.1		1	247.207	even	18
3249.2.a.d.1.1		1	57.2	even	18
4275.2.a.i.1.1		1	285.74	odd	18
5491.2.a.b.1.1		1	323.169	even	18
5776.2.a.c.1.1		1	76.59	even	18
7600.2.a.c.1.1		1	380.359	odd	18
8379.2.a.j.1.1		1	399.188	even	18
9025.2.a.d.1.1		1	95.59	odd	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.347296 + 1.96962i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.29813 + 1.92836i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.347296 + 1.96962i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.29813 + 1.92836i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-2.00000 - 3.46410i) q^{12} +(-0.694593 - 3.93923i) q^{13} +(-4.59627 + 3.85673i) q^{15} +(0.694593 - 3.93923i) q^{16} +(2.81908 - 1.02606i) q^{17} -6.00000 q^{20} +(-1.87939 + 0.684040i) q^{21} +(0.694593 + 3.93923i) q^{25} +(-2.00000 + 3.46410i) q^{27} +(-1.87939 - 0.684040i) q^{28} +(-5.63816 - 2.05212i) q^{29} +(2.00000 + 3.46410i) q^{31} +(-4.59627 - 3.85673i) q^{33} +(-0.520945 + 2.95442i) q^{35} +(1.87939 - 0.684040i) q^{36} +2.00000 q^{37} +8.00000 q^{39} +(-1.04189 + 5.90885i) q^{41} +(-0.766044 - 0.642788i) q^{43} +(-1.04189 - 5.90885i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(2.81908 + 1.02606i) q^{47} +(7.51754 + 2.73616i) q^{48} +(3.00000 - 5.19615i) q^{49} +(1.04189 + 5.90885i) q^{51} +(6.12836 + 5.14230i) q^{52} +(9.19253 - 7.71345i) q^{53} +(-8.45723 + 3.07818i) q^{55} +(5.63816 - 2.05212i) q^{59} +(2.08378 - 11.8177i) q^{60} +(-0.766044 + 0.642788i) q^{61} +(-0.173648 - 0.984808i) q^{63} +(4.00000 + 6.92820i) q^{64} +(6.00000 - 10.3923i) q^{65} +(3.75877 + 1.36808i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(4.59627 + 3.85673i) q^{71} +(-1.21554 + 6.89365i) q^{73} -8.00000 q^{75} -3.00000 q^{77} +(1.38919 - 7.87846i) q^{79} +(9.19253 - 7.71345i) q^{80} +(-8.42649 - 7.07066i) q^{81} +(-6.00000 - 10.3923i) q^{83} +(2.00000 - 3.46410i) q^{84} +(8.45723 + 3.07818i) q^{85} +(6.00000 - 10.3923i) q^{87} +(2.08378 + 11.8177i) q^{89} +(3.06418 - 2.57115i) q^{91} +(-7.51754 + 2.73616i) q^{93} +(-7.51754 + 2.73616i) q^{97} +(2.29813 - 1.92836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7}+O(q^{10}) \) 6 * q + 3 * q^7	\( 6 q + 3 q^{7} - 9 q^{11} - 12 q^{12} - 36 q^{20} - 12 q^{27} + 12 q^{31} + 12 q^{37} + 48 q^{39} - 9 q^{45} + 18 q^{49} + 24 q^{64} + 36 q^{65} - 18 q^{68} - 48 q^{75} - 18 q^{77} - 36 q^{83} + 12 q^{84} + 36 q^{87}+O(q^{100}) \) 6 * q + 3 * q^7 - 9 * q^11 - 12 * q^12 - 36 * q^20 - 12 * q^27 + 12 * q^31 + 12 * q^37 + 48 * q^39 - 9 * q^45 + 18 * q^49 + 24 * q^64 + 36 * q^65 - 18 * q^68 - 48 * q^75 - 18 * q^77 - 36 * q^83 + 12 * q^84 + 36 * q^87

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