LMFDB - Embedded newform 1890.2.bf.e.629.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(629,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 3]))

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

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

chi := DirichletCharacter("1890.629");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bf (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			629.1
Character	$\chi$	$=$	1890.629
Dual form			1890.2.bf.e.1259.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.23546 - 0.0519524i) q^{5} +(2.59656 - 0.507832i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.23546 - 0.0519524i) q^{5} +(2.59656 - 0.507832i) q^{7} +1.00000 q^{8} +(1.16272 - 1.90999i) q^{10} +(-4.30527 - 2.48565i) q^{11} +(1.15117 + 1.99388i) q^{13} +(-0.858483 + 2.50260i) q^{14} +(-0.500000 + 0.866025i) q^{16} +4.05745i q^{17} +1.63818i q^{19} +(1.07274 + 1.96195i) q^{20} +(4.30527 - 2.48565i) q^{22} +(-3.70342 - 6.41451i) q^{23} +(4.99460 + 0.232276i) q^{25} -2.30233 q^{26} +(-1.73807 - 1.99477i) q^{28} +(6.86211 + 3.96184i) q^{29} +(-6.00511 + 3.46705i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.51386 - 2.02873i) q^{34} +(-5.83089 + 1.00034i) q^{35} -10.4902i q^{37} +(-1.41871 - 0.819090i) q^{38} +(-2.23546 - 0.0519524i) q^{40} +(2.40962 + 4.17358i) q^{41} +(2.31707 + 1.33776i) q^{43} +4.97130i q^{44} +7.40684 q^{46} +(9.03708 + 5.21756i) q^{47} +(6.48421 - 2.63723i) q^{49} +(-2.69846 + 4.20931i) q^{50} +(1.15117 - 1.99388i) q^{52} +12.4295 q^{53} +(9.49514 + 5.78025i) q^{55} +(2.59656 - 0.507832i) q^{56} +(-6.86211 + 3.96184i) q^{58} +(-5.82902 - 10.0962i) q^{59} +(3.89175 + 2.24690i) q^{61} -6.93411i q^{62} +1.00000 q^{64} +(-2.46981 - 4.51705i) q^{65} +(0.266411 - 0.153812i) q^{67} +(3.51386 - 2.02873i) q^{68} +(2.04912 - 5.54987i) q^{70} +7.38341i q^{71} +3.95051 q^{73} +(9.08477 + 5.24509i) q^{74} +(1.41871 - 0.819090i) q^{76} +(-12.4412 - 4.26777i) q^{77} +(-1.42332 + 2.46526i) q^{79} +(1.16272 - 1.90999i) q^{80} -4.81924 q^{82} +(9.60784 + 5.54709i) q^{83} +(0.210795 - 9.07029i) q^{85} +(-2.31707 + 1.33776i) q^{86} +(-4.30527 - 2.48565i) q^{88} -5.77755 q^{89} +(4.00163 + 4.59262i) q^{91} +(-3.70342 + 6.41451i) q^{92} +(-9.03708 + 5.21756i) q^{94} +(0.0851075 - 3.66209i) q^{95} +(-4.81542 + 8.34056i) q^{97} +(-0.958199 + 6.93411i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 24 q^{11} - 16 q^{16} - 24 q^{22} - 24 q^{23} + 50 q^{25} + 36 q^{29} - 16 q^{32} - 48 q^{35} + 54 q^{43} + 48 q^{46} + 32 q^{49} - 58 q^{50} - 24 q^{53} - 36 q^{58} + 32 q^{64} + 66 q^{65} + 66 q^{67} + 12 q^{70} - 12 q^{74} + 18 q^{77} + 34 q^{79} - 32 q^{85} - 54 q^{86} + 24 q^{88} + 16 q^{91} - 24 q^{92} + 24 q^{95} - 64 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 24 * q^11 - 16 * q^16 - 24 * q^22 - 24 * q^23 + 50 * q^25 + 36 * q^29 - 16 * q^32 - 48 * q^35 + 54 * q^43 + 48 * q^46 + 32 * q^49 - 58 * q^50 - 24 * q^53 - 36 * q^58 + 32 * q^64 + 66 * q^65 + 66 * q^67 + 12 * q^70 - 12 * q^74 + 18 * q^77 + 34 * q^79 - 32 * q^85 - 54 * q^86 + 24 * q^88 + 16 * q^91 - 24 * q^92 + 24 * q^95 - 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	+	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
$5$	−2.23546	−	0.0519524i	−0.999730	−	0.0232338i
$5$	−2.23546	−	0.0519524i	−0.999730	−	0.0232338i
$6$		0			0
$7$	2.59656	−	0.507832i	0.981406	−	0.191943i
$7$	2.59656	−	0.507832i	0.981406	−	0.191943i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.16272	−	1.90999i	0.367686	−	0.603993i
$11$	−4.30527	−	2.48565i	−1.29809	−	0.749451i	−0.318014	−	0.948086i	$-0.603016\pi$
$11$	−4.30527	−	2.48565i	−1.29809	−	0.749451i	−0.980074	+	0.198635i	$0.936349\pi$
$12$		0			0
$13$	1.15117	+	1.99388i	0.319276	+	0.553003i	0.980337	−	0.197329i	$-0.0632269\pi$
$13$	1.15117	+	1.99388i	0.319276	+	0.553003i	−0.661061	+	0.750332i	$0.729894\pi$
$14$	−0.858483	+	2.50260i	−0.229439	+	0.668848i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			4.05745i			0.984077i	0.870574	+	0.492038i	$0.163748\pi$
$17$			4.05745i			0.984077i	−0.870574	+	0.492038i	$0.836252\pi$
$18$		0			0
$19$			1.63818i			0.375824i	0.982186	+	0.187912i	$0.0601720\pi$
$19$			1.63818i			0.375824i	−0.982186	+	0.187912i	$0.939828\pi$
$20$	1.07274	+	1.96195i	0.239872	+	0.438704i
$21$		0			0
$22$	4.30527	−	2.48565i	0.917887	−	0.529942i
$23$	−3.70342	−	6.41451i	−0.772216	−	1.33752i	−0.936346	−	0.351079i	$-0.885815\pi$
$23$	−3.70342	−	6.41451i	−0.772216	−	1.33752i	0.164130	−	0.986439i	$-0.447518\pi$
$24$		0			0
$25$	4.99460	+	0.232276i	0.998920	+	0.0464551i
$26$	−2.30233			−0.451525
$27$		0			0
$28$	−1.73807	−	1.99477i	−0.328465	−	0.376976i
$29$	6.86211	+	3.96184i	1.27426	+	0.735696i	0.975787	−	0.218721i	$-0.0701886\pi$
$29$	6.86211	+	3.96184i	1.27426	+	0.735696i	0.298475	+	0.954417i	$0.403522\pi$
$30$		0			0
$31$	−6.00511	+	3.46705i	−1.07855	+	0.622701i	−0.930505	−	0.366279i	$-0.880631\pi$
$31$	−6.00511	+	3.46705i	−1.07855	+	0.622701i	−0.148045	+	0.988981i	$0.547298\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−3.51386	−	2.02873i	−0.602621	−	0.347924i
$35$	−5.83089	+	1.00034i	−0.985601	+	0.169089i
$36$		0			0
$37$		−	10.4902i		−	1.72458i	−0.506419	−	0.862288i	$-0.669031\pi$
$37$		−	10.4902i		−	1.72458i	0.506419	−	0.862288i	$-0.330969\pi$
$38$	−1.41871	−	0.819090i	−0.230145	−	0.132874i
$39$		0			0
$40$	−2.23546	−	0.0519524i	−0.353458	−	0.00821440i
$41$	2.40962	+	4.17358i	0.376319	+	0.651804i	0.990524	−	0.137343i	$-0.0438562\pi$
$41$	2.40962	+	4.17358i	0.376319	+	0.651804i	−0.614204	+	0.789147i	$0.710523\pi$
$42$		0			0
$43$	2.31707	+	1.33776i	0.353350	+	0.204007i	0.666160	−	0.745809i	$-0.267937\pi$
$43$	2.31707	+	1.33776i	0.353350	+	0.204007i	−0.312810	+	0.949816i	$0.601270\pi$
$44$			4.97130i			0.749451i
$45$		0			0
$46$	7.40684			1.09208
$47$	9.03708	+	5.21756i	1.31819	+	0.761059i	0.983438	−	0.181246i	$-0.0580130\pi$
$47$	9.03708	+	5.21756i	1.31819	+	0.761059i	0.334755	+	0.942305i	$0.391346\pi$
$48$		0			0
$49$	6.48421	−	2.63723i	0.926316	−	0.376747i
$50$	−2.69846	+	4.20931i	−0.381620	+	0.595287i
$51$		0			0
$52$	1.15117	−	1.99388i	0.159638	−	0.276501i
$53$	12.4295			1.70733			0.853665	−	0.520823i	$-0.174375\pi$
$53$	12.4295			1.70733			0.853665	+	0.520823i	$0.174375\pi$
$54$		0			0
$55$	9.49514	+	5.78025i	1.28032	+	0.779409i
$56$	2.59656	−	0.507832i	0.346979	−	0.0678619i
$57$		0			0
$58$	−6.86211	+	3.96184i	−0.901040	+	0.520216i
$59$	−5.82902	−	10.0962i	−0.758874	−	1.31441i	−0.943425	−	0.331585i	$-0.892417\pi$
$59$	−5.82902	−	10.0962i	−0.758874	−	1.31441i	0.184552	−	0.982823i	$-0.440917\pi$
$60$		0			0
$61$	3.89175	+	2.24690i	0.498287	+	0.287686i	0.728006	−	0.685571i	$-0.240447\pi$
$61$	3.89175	+	2.24690i	0.498287	+	0.287686i	−0.229719	+	0.973257i	$0.573781\pi$
$62$		−	6.93411i		−	0.880633i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.46981	−	4.51705i	−0.306342	−	0.560271i
$66$		0			0
$67$	0.266411	−	0.153812i	0.0325472	−	0.0187912i	−0.483638	−	0.875268i	$-0.660685\pi$
$67$	0.266411	−	0.153812i	0.0325472	−	0.0187912i	0.516185	+	0.856477i	$0.327352\pi$
$68$	3.51386	−	2.02873i	0.426118	−	0.246019i
$69$		0			0
$70$	2.04912	−	5.54987i	0.244917	−	0.663337i
$71$			7.38341i			0.876249i	0.898914	+	0.438125i	$0.144357\pi$
$71$			7.38341i			0.876249i	−0.898914	+	0.438125i	$0.855643\pi$
$72$		0			0
$73$	3.95051			0.462372			0.231186	−	0.972910i	$-0.425739\pi$
$73$	3.95051			0.462372			0.231186	+	0.972910i	$0.425739\pi$
$74$	9.08477	+	5.24509i	1.05608	+	0.609730i
$75$		0			0
$76$	1.41871	−	0.819090i	0.162737	−	0.0939561i
$77$	−12.4412	−	4.26777i	−1.41780	−	0.486358i
$78$		0			0
$79$	−1.42332	+	2.46526i	−0.160136	+	0.277364i	−0.934917	−	0.354865i	$-0.884527\pi$
$79$	−1.42332	+	2.46526i	−0.160136	+	0.277364i	0.774781	+	0.632229i	$0.217860\pi$
$80$	1.16272	−	1.90999i	0.129997	−	0.213544i
$81$		0			0
$82$	−4.81924			−0.532196
$83$	9.60784	+	5.54709i	1.05460	+	0.608872i	0.923933	−	0.382554i	$-0.124956\pi$
$83$	9.60784	+	5.54709i	1.05460	+	0.608872i	0.130665	+	0.991427i	$0.458289\pi$
$84$		0			0
$85$	0.210795	−	9.07029i	0.0228639	−	0.983811i
$86$	−2.31707	+	1.33776i	−0.249856	+	0.144255i
$87$		0			0
$88$	−4.30527	−	2.48565i	−0.458943	−	0.264971i
$89$	−5.77755			−0.612419			−0.306209	−	0.951964i	$-0.599061\pi$
$89$	−5.77755			−0.612419			−0.306209	+	0.951964i	$0.599061\pi$
$90$		0			0
$91$	4.00163	+	4.59262i	0.419484	+	0.481438i
$92$	−3.70342	+	6.41451i	−0.386108	+	0.668759i
$93$		0			0
$94$	−9.03708	+	5.21756i	−0.932103	+	0.538150i
$95$	0.0851075	−	3.66209i	0.00873184	−	0.375723i
$96$		0			0
$97$	−4.81542	+	8.34056i	−0.488932	+	0.846855i	−0.999919	−	0.0127332i	$-0.995947\pi$
$97$	−4.81542	+	8.34056i	−0.488932	+	0.846855i	0.510987	+	0.859589i	$0.329280\pi$
$98$	−0.958199	+	6.93411i	−0.0967927	+	0.700451i
$99$		0			0
$100$	−2.29614	−	4.44159i	−0.229614	−	0.444159i
$101$	6.69877	−	11.6026i	0.666552	−	1.15450i	−0.312310	−	0.949980i	$-0.601103\pi$
$101$	6.69877	−	11.6026i	0.666552	−	1.15450i	0.978862	−	0.204522i	$-0.0655639\pi$
$102$		0			0
$103$	5.36750	+	9.29678i	0.528875	+	0.916039i	0.999433	+	0.0336694i	$0.0107193\pi$
$103$	5.36750	+	9.29678i	0.528875	+	0.916039i	−0.470558	+	0.882369i	$0.655947\pi$
$104$	1.15117	+	1.99388i	0.112881	+	0.195516i
$105$		0			0
$106$	−6.21477	+	10.7643i	−0.603632	+	1.04552i
$107$	8.66456			0.837634			0.418817	−	0.908071i	$-0.362445\pi$
$107$	8.66456			0.837634			0.418817	+	0.908071i	$0.362445\pi$
$108$		0			0
$109$	12.6662			1.21320			0.606600	−	0.795007i	$-0.292533\pi$
$109$	12.6662			1.21320			0.606600	+	0.795007i	$0.292533\pi$
$110$	−9.75341	+	5.33291i	−0.929952	+	0.508473i
$111$		0			0
$112$	−0.858483	+	2.50260i	−0.0811190	+	0.236473i
$113$	7.96108	+	13.7890i	0.748916	+	1.29716i	0.948343	+	0.317247i	$0.102759\pi$
$113$	7.96108	+	13.7890i	0.748916	+	1.29716i	−0.199427	+	0.979913i	$0.563908\pi$
$114$		0			0
$115$	7.94561	+	14.5318i	0.740932	+	1.35510i
$116$		−	7.92369i		−	0.735696i
$117$		0			0
$118$	11.6580			1.07321
$119$	2.06050	+	10.5354i	0.188886	+	0.965779i
$120$		0			0
$121$	6.85690	+	11.8765i	0.623355	+	1.07968i
$122$	−3.89175	+	2.24690i	−0.352342	+	0.203425i
$123$		0			0
$124$	6.00511	+	3.46705i	0.539275	+	0.311351i
$125$	−11.1532	−	0.778726i	−0.997571	−	0.0696513i
$126$		0			0
$127$			0.0958062i			0.00850143i	0.999991	+	0.00425071i	$0.00135305\pi$
$127$			0.0958062i			0.00850143i	−0.999991	+	0.00425071i	$0.998647\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	5.14679	+	0.119612i	0.451403	+	0.0104907i
$131$	5.51174	+	9.54661i	0.481563	+	0.834091i	0.999776	−	0.0211601i	$-0.00673597\pi$
$131$	5.51174	+	9.54661i	0.481563	+	0.834091i	−0.518213	+	0.855251i	$0.673403\pi$
$132$		0			0
$133$	0.831921	+	4.25363i	0.0721367	+	0.368836i
$134$			0.307624i			0.0265747i
$135$		0			0
$136$			4.05745i			0.347924i
$137$	0.646384	−	1.11957i	0.0552243	−	0.0956513i	−0.837092	−	0.547063i	$-0.815746\pi$
$137$	0.646384	−	1.11957i	0.0552243	−	0.0956513i	0.892316	+	0.451411i	$0.149079\pi$
$138$		0			0
$139$	−6.11640	+	3.53131i	−0.518787	+	0.299522i	−0.736438	−	0.676505i	$-0.763494\pi$
$139$	−6.11640	+	3.53131i	−0.518787	+	0.299522i	0.217651	+	0.976027i	$0.430160\pi$
$140$	3.78177	+	4.54953i	0.319618	+	0.384505i
$141$		0			0
$142$	−6.39422	−	3.69170i	−0.536591	−	0.309801i
$143$		−	11.4456i		−	0.957128i
$144$		0			0
$145$	−15.1342	−	9.21306i	−1.25683	−	0.765103i
$146$	−1.97525	+	3.42124i	−0.163473	+	0.283144i
$147$		0			0
$148$	−9.08477	+	5.24509i	−0.746763	+	0.431144i
$149$	−7.16878	+	4.13890i	−0.587289	+	0.339072i	−0.764025	−	0.645187i	$-0.776780\pi$
$149$	−7.16878	+	4.13890i	−0.587289	+	0.339072i	0.176736	+	0.984258i	$0.443446\pi$
$150$		0			0
$151$	0.0473069	−	0.0819379i	0.00384978	−	0.00666801i	−0.864094	−	0.503330i	$-0.832108\pi$
$151$	0.0473069	−	0.0819379i	0.00384978	−	0.00666801i	0.867944	+	0.496662i	$0.165441\pi$
$152$			1.63818i			0.132874i
$153$		0			0
$154$	9.91659	−	8.64048i	0.799101	−	0.696270i
$155$	13.6043	−	7.43850i	1.09273	−	0.597474i
$156$		0			0
$157$	−0.938382	−	1.62532i	−0.0748910	−	0.129715i	0.826148	−	0.563453i	$-0.190528\pi$
$157$	−0.938382	−	1.62532i	−0.0748910	−	0.129715i	−0.901039	+	0.433738i	$0.857194\pi$
$158$	−1.42332	−	2.46526i	−0.113233	−	0.196126i
$159$		0			0
$160$	1.07274	+	1.96195i	0.0848075	+	0.155105i
$161$	−12.8736	−	14.7749i	−1.01458	−	1.16443i
$162$		0			0
$163$			2.36790i			0.185468i	0.995691	+	0.0927341i	$0.0295606\pi$
$163$			2.36790i			0.185468i	−0.995691	+	0.0927341i	$0.970439\pi$
$164$	2.40962	−	4.17358i	0.188160	−	0.325902i
$165$		0			0
$166$	−9.60784	+	5.54709i	−0.745713	+	0.430538i
$167$	−6.32518	+	3.65184i	−0.489457	+	0.282588i	−0.724349	−	0.689433i	$-0.757860\pi$
$167$	−6.32518	+	3.65184i	−0.489457	+	0.282588i	0.234892	+	0.972021i	$0.424526\pi$
$168$		0			0
$169$	3.84963	−	6.66775i	0.296125	−	0.512904i
$170$	7.74970	+	4.71770i	0.594375	+	0.361831i
$171$		0			0
$172$		−	2.67552i		−	0.204007i
$173$	16.4983	+	9.52529i	1.25434	+	0.724194i	0.971969	−	0.235111i	$-0.0755453\pi$
$173$	16.4983	+	9.52529i	1.25434	+	0.724194i	0.282372	+	0.959305i	$0.408879\pi$
$174$		0			0
$175$	13.0867	−	1.93330i	0.989263	−	0.146144i
$176$	4.30527	−	2.48565i	0.324522	−	0.187363i
$177$		0			0
$178$	2.88877	−	5.00350i	0.216523	−	0.375028i
$179$		−	8.19441i		−	0.612479i	−0.951955	−	0.306239i	$-0.900929\pi$
$179$		−	8.19441i		−	0.612479i	0.951955	−	0.306239i	$-0.0990708\pi$
$180$		0			0
$181$			6.03316i			0.448441i	0.974538	+	0.224221i	$0.0719837\pi$
$181$			6.03316i			0.448441i	−0.974538	+	0.224221i	$0.928016\pi$
$182$	−5.97814	+	1.16920i	−0.443129	+	0.0866668i
$183$		0			0
$184$	−3.70342	−	6.41451i	−0.273020	−	0.472884i
$185$	−0.544991	+	23.4504i	−0.0400685	+	1.72411i
$186$		0			0
$187$	10.0854	−	17.4684i	0.737518	−	1.27742i
$188$		−	10.4351i		−	0.761059i
$189$		0			0
$190$	3.12891	+	1.90475i	0.226995	+	0.138185i
$191$	−1.19518	−	0.690038i	−0.0864803	−	0.0499294i	0.456136	−	0.889910i	$-0.349233\pi$
$191$	−1.19518	−	0.690038i	−0.0864803	−	0.0499294i	−0.542617	+	0.839981i	$0.682566\pi$
$192$		0			0
$193$	5.06489	−	2.92422i	0.364579	−	0.210490i	−0.306509	−	0.951868i	$-0.599161\pi$
$193$	5.06489	−	2.92422i	0.364579	−	0.210490i	0.671088	+	0.741378i	$0.265827\pi$
$194$	−4.81542	−	8.34056i	−0.345727	−	0.598817i
$195$		0			0
$196$	−5.52601	−	4.29688i	−0.394715	−	0.306920i
$197$	12.3268			0.878249			0.439124	−	0.898426i	$-0.355289\pi$
$197$	12.3268			0.878249			0.439124	+	0.898426i	$0.355289\pi$
$198$		0			0
$199$			4.62044i			0.327534i	0.986499	+	0.163767i	$0.0523646\pi$
$199$			4.62044i			0.327534i	−0.986499	+	0.163767i	$0.947635\pi$
$200$	4.99460	+	0.232276i	0.353172	+	0.0164244i
$201$		0			0
$202$	6.69877	+	11.6026i	0.471323	+	0.816356i
$203$	19.8298	+	6.80235i	1.39178	+	0.477431i
$204$		0			0
$205$	−5.16979	−	9.45508i	−0.361074	−	0.660372i
$206$	−10.7350			−0.747942
$207$		0			0
$208$	−2.30233			−0.159638
$209$	4.07194	−	7.05281i	0.281662	−	0.487853i
$210$		0			0
$211$	−1.35443	−	2.34594i	−0.0932428	−	0.161501i	0.815631	−	0.578572i	$-0.196390\pi$
$211$	−1.35443	−	2.34594i	−0.0932428	−	0.161501i	−0.908874	+	0.417071i	$0.863057\pi$
$212$	−6.21477	−	10.7643i	−0.426832	−	0.739295i
$213$		0			0
$214$	−4.33228	+	7.50373i	−0.296148	+	0.512944i
$215$	−5.11023	−	3.11090i	−0.348515	−	0.212161i
$216$		0			0
$217$	−13.8319	+	12.0520i	−0.938973	+	0.818143i
$218$	−6.33309	+	10.9692i	−0.428931	+	0.742930i
$219$		0			0
$220$	0.258271	−	11.1132i	0.0174126	−	0.749249i
$221$	−8.09007	+	4.67081i	−0.544197	+	0.314192i
$222$		0			0
$223$	2.64289	−	4.57762i	0.176981	−	0.306540i	−0.763864	−	0.645377i	$-0.776700\pi$
$223$	2.64289	−	4.57762i	0.176981	−	0.306540i	0.940845	+	0.338837i	$0.110034\pi$
$224$	−1.73807	−	1.99477i	−0.116130	−	0.133281i
$225$		0			0
$226$	−15.9222			−1.05913
$227$	−16.0790	−	9.28322i	−1.06720	−	0.616149i	−0.139786	−	0.990182i	$-0.544641\pi$
$227$	−16.0790	−	9.28322i	−1.06720	−	0.616149i	−0.927416	+	0.374033i	$0.877975\pi$
$228$		0			0
$229$	7.82193	−	4.51600i	0.516888	−	0.298425i	−0.218773	−	0.975776i	$-0.570205\pi$
$229$	7.82193	−	4.51600i	0.516888	−	0.298425i	0.735660	+	0.677351i	$0.236872\pi$
$230$	−16.5577	−	0.384803i	−1.09178	−	0.0253732i
$231$		0			0
$232$	6.86211	+	3.96184i	0.450520	+	0.260108i
$233$	2.62042			0.171669			0.0858346	−	0.996309i	$-0.472644\pi$
$233$	2.62042			0.171669			0.0858346	+	0.996309i	$0.472644\pi$
$234$		0			0
$235$	−19.9310	−	12.1332i	−1.30015	−	0.791480i
$236$	−5.82902	+	10.0962i	−0.379437	+	0.657204i
$237$		0			0
$238$	−10.1542	−	3.48325i	−0.658198	−	0.225786i
$239$	−4.21909	+	2.43589i	−0.272910	+	0.157565i	−0.630210	−	0.776425i	$-0.717031\pi$
$239$	−4.21909	+	2.43589i	−0.272910	+	0.157565i	0.357299	+	0.933990i	$0.383698\pi$
$240$		0			0
$241$	−12.6051	−	7.27755i	−0.811965	−	0.468788i	0.0356728	−	0.999364i	$-0.488643\pi$
$241$	−12.6051	−	7.27755i	−0.811965	−	0.468788i	−0.847638	+	0.530575i	$0.821976\pi$
$242$	−13.7138			−0.881557
$243$		0			0
$244$		−	4.49380i		−	0.287686i
$245$	−14.6322	+	5.55856i	−0.934819	+	0.355124i
$246$		0			0
$247$	−3.26634	+	1.88582i	−0.207832	+	0.119992i
$248$	−6.00511	+	3.46705i	−0.381325	+	0.220158i
$249$		0			0
$250$	6.25099	−	9.26958i	0.395347	−	0.586260i
$251$	20.6043			1.30053			0.650265	−	0.759707i	$-0.274658\pi$
$251$	20.6043			1.30053			0.650265	+	0.759707i	$0.274658\pi$
$252$		0			0
$253$			36.8216i			2.31495i
$254$	−0.0829706	−	0.0479031i	−0.00520604	−	0.00300571i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.274796	−	0.158654i	0.0171413	−	0.00989654i	−0.491405	−	0.870931i	$-0.663516\pi$
$257$	0.274796	−	0.158654i	0.0171413	−	0.00989654i	0.508546	+	0.861035i	$0.330183\pi$
$258$		0			0
$259$	−5.32725	−	27.2384i	−0.331019	−	1.69251i
$260$	−2.67698	+	4.39744i	−0.166019	+	0.272718i
$261$		0			0
$262$	−11.0235			−0.681033
$263$	−13.8308	+	23.9556i	−0.852841	+	1.47716i	0.0257917	+	0.999667i	$0.491789\pi$
$263$	−13.8308	+	23.9556i	−0.852841	+	1.47716i	−0.878633	+	0.477497i	$0.841544\pi$
$264$		0			0
$265$	−27.7858	−	0.645745i	−1.70687	−	0.0396678i
$266$	−4.09971	−	1.40635i	−0.251369	−	0.0862288i
$267$		0			0
$268$	−0.266411	−	0.153812i	−0.0162736	−	0.00939558i
$269$	15.6998			0.957235			0.478618	−	0.878023i	$-0.341138\pi$
$269$	15.6998			0.957235			0.478618	+	0.878023i	$0.341138\pi$
$270$		0			0
$271$		−	13.2951i		−	0.807622i	−0.914842	−	0.403811i	$-0.867685\pi$
$271$		−	13.2951i		−	0.807622i	0.914842	−	0.403811i	$-0.132315\pi$
$272$	−3.51386	−	2.02873i	−0.213059	−	0.123010i
$273$		0			0
$274$	0.646384	+	1.11957i	0.0390495	+	0.0676357i
$275$	−20.9258	−	13.4148i	−1.26187	−	0.808945i
$276$		0			0
$277$	−15.3861	−	8.88318i	−0.924462	−	0.533739i	−0.0394064	−	0.999223i	$-0.512547\pi$
$277$	−15.3861	−	8.88318i	−0.924462	−	0.533739i	−0.885056	+	0.465485i	$0.845880\pi$
$278$		−	7.06261i		−	0.423587i
$279$		0			0
$280$	−5.83089	+	1.00034i	−0.348463	+	0.0597819i
$281$	−5.91512	−	3.41510i	−0.352867	−	0.203728i	0.313080	−	0.949727i	$-0.398639\pi$
$281$	−5.91512	−	3.41510i	−0.352867	−	0.203728i	−0.665947	+	0.745999i	$0.731972\pi$
$282$		0			0
$283$	11.4981	+	19.9152i	0.683488	+	1.18384i	0.973909	+	0.226937i	$0.0728713\pi$
$283$	11.4981	+	19.9152i	0.683488	+	1.18384i	−0.290421	+	0.956899i	$0.593795\pi$
$284$	6.39422	−	3.69170i	0.379427	−	0.219062i
$285$		0			0
$286$	9.91217	+	5.72279i	0.586119	+	0.338396i
$287$	8.37619	+	9.61327i	0.494431	+	0.567453i
$288$		0			0
$289$	0.537081			0.0315930
$290$	15.5458	−	8.50006i	0.912883	−	0.499141i
$291$		0			0
$292$	−1.97525	−	3.42124i	−0.115593	−	0.200213i
$293$	12.6365	−	7.29571i	0.738235	−	0.426220i	−0.0831923	−	0.996534i	$-0.526512\pi$
$293$	12.6365	−	7.29571i	0.738235	−	0.426220i	0.821427	+	0.570313i	$0.193178\pi$
$294$		0			0
$295$	12.5060	+	22.8724i	0.728130	+	1.33168i
$296$		−	10.4902i		−	0.609730i
$297$		0			0
$298$		−	8.27779i		−	0.479520i
$299$	8.52651	−	14.7683i	0.493101	−	0.854075i
$300$		0			0
$301$	6.69576	+	2.29689i	0.385937	+	0.132391i
$302$	0.0473069	+	0.0819379i	0.00272220	+	0.00471499i
$303$		0			0
$304$	−1.41871	−	0.819090i	−0.0813684	−	0.0469781i
$305$	−8.58313	−	5.22505i	−0.491469	−	0.299186i
$306$		0			0
$307$	−8.23143			−0.469792			−0.234896	−	0.972020i	$-0.575475\pi$
$307$	−8.23143			−0.469792			−0.234896	+	0.972020i	$0.575475\pi$
$308$	2.52458	+	12.9083i	0.143852	+	0.735516i
$309$		0			0
$310$	−0.360244	+	15.5010i	−0.0204605	+	0.880395i
$311$	−5.27741	−	9.14075i	−0.299255	−	0.518324i	0.676711	−	0.736249i	$-0.263405\pi$
$311$	−5.27741	−	9.14075i	−0.299255	−	0.518324i	−0.975966	+	0.217924i	$0.930071\pi$
$312$		0			0
$313$	−9.20310	+	15.9402i	−0.520190	+	0.900996i	0.479534	+	0.877523i	$0.340806\pi$
$313$	−9.20310	+	15.9402i	−0.520190	+	0.900996i	−0.999724	+	0.0234725i	$0.992528\pi$
$314$	1.87676			0.105912
$315$		0			0
$316$	2.84664			0.160136
$317$	13.6314	−	23.6102i	0.765613	−	1.32608i	−0.174309	−	0.984691i	$-0.555769\pi$
$317$	13.6314	−	23.6102i	0.765613	−	1.32608i	0.939922	−	0.341390i	$-0.110898\pi$
$318$		0			0
$319$	−19.6955	−	34.1136i	−1.10274	−	1.91000i
$320$	−2.23546	−	0.0519524i	−0.124966	−	0.00290423i
$321$		0			0
$322$	19.2323	−	3.76143i	1.07177	−	0.209616i
$323$	−6.64684			−0.369840
$324$		0			0
$325$	5.28649	+	10.2260i	0.293242	+	0.567238i
$326$	−2.05066	−	1.18395i	−0.113576	−	0.0655729i
$327$		0			0
$328$	2.40962	+	4.17358i	0.133049	+	0.230448i
$329$	26.1149	+	8.95837i	1.43976	+	0.493891i
$330$		0			0
$331$	−9.19875	+	15.9327i	−0.505609	+	0.875740i	0.494370	+	0.869252i	$0.335399\pi$
$331$	−9.19875	+	15.9327i	−0.505609	+	0.875740i	−0.999979	+	0.00648873i	$0.997935\pi$
$332$		−	11.0942i		−	0.608872i
$333$		0			0
$334$		−	7.30368i		−	0.399640i
$335$	−0.603542	+	0.330001i	−0.0329750	+	0.0180299i
$336$		0			0
$337$	12.5155	−	7.22584i	0.681764	−	0.393617i	−0.118755	−	0.992924i	$-0.537890\pi$
$337$	12.5155	−	7.22584i	0.681764	−	0.393617i	0.800519	+	0.599307i	$0.204557\pi$
$338$	3.84963	+	6.66775i	0.209392	+	0.362678i
$339$		0			0
$340$	−7.96050	+	4.35259i	−0.431719	+	0.236052i
$341$	34.4715			1.86674
$342$		0			0
$343$	15.4974	−	10.1406i	0.836779	−	0.547541i
$344$	2.31707	+	1.33776i	0.124928	+	0.0721273i
$345$		0			0
$346$	−16.4983	+	9.52529i	−0.886953	+	0.512083i
$347$	−9.03284	−	15.6453i	−0.484908	−	0.839886i	0.514941	−	0.857225i	$-0.327814\pi$
$347$	−9.03284	−	15.6453i	−0.484908	−	0.839886i	−0.999850	+	0.0173396i	$0.994480\pi$
$348$		0			0
$349$	−7.58926	−	4.38166i	−0.406244	−	0.234545i	0.282931	−	0.959140i	$-0.408693\pi$
$349$	−7.58926	−	4.38166i	−0.406244	−	0.234545i	−0.689175	+	0.724595i	$0.742027\pi$
$350$	−4.86907	+	12.3001i	−0.260263	+	0.657467i
$351$		0			0
$352$			4.97130i			0.264971i
$353$	9.23289	+	5.33061i	0.491417	+	0.283720i	0.725162	−	0.688578i	$-0.241765\pi$
$353$	9.23289	+	5.33061i	0.491417	+	0.283720i	−0.233745	+	0.972298i	$0.575098\pi$
$354$		0			0
$355$	0.383586	−	16.5053i	0.0203586	−	0.876012i
$356$	2.88877	+	5.00350i	0.153105	+	0.265185i
$357$		0			0
$358$	7.09657	+	4.09720i	0.375065	+	0.216544i
$359$		−	16.4960i		−	0.870628i	−0.900279	−	0.435314i	$-0.856637\pi$
$359$		−	16.4960i		−	0.870628i	0.900279	−	0.435314i	$-0.143363\pi$
$360$		0			0
$361$	16.3164			0.858756
$362$	−5.22487	−	3.01658i	−0.274613	−	0.158548i
$363$		0			0
$364$	1.97651	−	5.76182i	0.103597	−	0.302002i
$365$	−8.83122	−	0.205239i	−0.462247	−	0.0107427i
$366$		0			0
$367$	0.205646	−	0.356189i	0.0107346	−	0.0185929i	−0.860608	−	0.509268i	$-0.829916\pi$
$367$	0.205646	−	0.356189i	0.0107346	−	0.0185929i	0.871343	+	0.490675i	$0.163250\pi$
$368$	7.40684			0.386108
$369$		0			0
$370$	−20.0362	−	12.1972i	−1.04163	−	0.634102i
$371$	32.2740	−	6.31212i	1.67558	−	0.327709i
$372$		0			0
$373$	−9.38126	+	5.41627i	−0.485743	+	0.280444i	−0.722807	−	0.691050i	$-0.757148\pi$
$373$	−9.38126	+	5.41627i	−0.485743	+	0.280444i	0.237064	+	0.971494i	$0.423815\pi$
$374$	10.0854	+	17.4684i	0.521504	+	0.903271i
$375$		0			0
$376$	9.03708	+	5.21756i	0.466052	+	0.269075i
$377$			18.2430i			0.939561i
$378$		0			0
$379$	−20.7547			−1.06610			−0.533049	−	0.846084i	$-0.678954\pi$
$379$	−20.7547			−1.06610			−0.533049	+	0.846084i	$0.678954\pi$
$380$	−3.21402	+	1.75734i	−0.164876	+	0.0901497i
$381$		0			0
$382$	1.19518	−	0.690038i	0.0611508	−	0.0353054i
$383$	−29.5240	+	17.0457i	−1.50860	+	0.870993i	−0.508655	+	0.860971i	$0.669857\pi$
$383$	−29.5240	+	17.0457i	−1.50860	+	0.870993i	−0.999950	+	0.0100224i	$0.996810\pi$
$384$		0			0
$385$	27.5901	+	10.1868i	1.40612	+	0.519168i
$386$			5.84844i			0.297678i
$387$		0			0
$388$	9.63085			0.488932
$389$	−15.5200	−	8.96050i	−0.786897	−	0.454315i	0.0519719	−	0.998649i	$-0.483449\pi$
$389$	−15.5200	−	8.96050i	−0.786897	−	0.454315i	−0.838869	+	0.544333i	$0.816783\pi$
$390$		0			0
$391$	26.0266	−	15.0264i	1.31622	−	0.759920i
$392$	6.48421	−	2.63723i	0.327502	−	0.133200i
$393$		0			0
$394$	−6.16341	+	10.6753i	−0.310508	+	0.537815i
$395$	3.30986	−	5.43707i	0.166537	−	0.273568i
$396$		0			0
$397$	−1.13391			−0.0569091			−0.0284546	−	0.999595i	$-0.509059\pi$
$397$	−1.13391			−0.0569091			−0.0284546	+	0.999595i	$0.509059\pi$
$398$	−4.00142	−	2.31022i	−0.200573	−	0.115801i
$399$		0			0
$400$	−2.69846	+	4.20931i	−0.134923	+	0.210466i
$401$	7.01673	−	4.05111i	0.350399	−	0.202303i	−0.314462	−	0.949270i	$-0.601824\pi$
$401$	7.01673	−	4.05111i	0.350399	−	0.202303i	0.664861	+	0.746967i	$0.268491\pi$
$402$		0			0
$403$	−13.8258	−	7.98232i	−0.688711	−	0.397628i
$404$	−13.3975			−0.666552
$405$		0			0
$406$	−15.8059	+	13.7720i	−0.784435	+	0.683491i
$407$	−26.0749	+	45.1631i	−1.29249	+	2.23865i
$408$		0			0
$409$	12.6764	−	7.31875i	0.626810	−	0.361889i	−0.152706	−	0.988272i	$-0.548799\pi$
$409$	12.6764	−	7.31875i	0.626810	−	0.361889i	0.779516	+	0.626383i	$0.215465\pi$
$410$	10.7732	+	0.250371i	0.532052	+	0.0123650i
$411$		0			0
$412$	5.36750	−	9.29678i	0.264438	−	0.458019i
$413$	−20.2625	−	23.2551i	−0.997054	−	1.14431i
$414$		0			0
$415$	−21.1898	−	12.8995i	−1.04017	−	0.633210i
$416$	1.15117	−	1.99388i	0.0564406	−	0.0977580i
$417$		0			0
$418$	4.07194	+	7.05281i	0.199165	+	0.344964i
$419$	−5.84160	−	10.1179i	−0.285381	−	0.494294i	0.687321	−	0.726354i	$-0.258787\pi$
$419$	−5.84160	−	10.1179i	−0.285381	−	0.494294i	−0.972701	+	0.232060i	$0.925453\pi$
$420$		0			0
$421$	12.5853	−	21.7984i	0.613370	−	1.06239i	−0.377298	−	0.926092i	$-0.623147\pi$
$421$	12.5853	−	21.7984i	0.613370	−	1.06239i	0.990668	−	0.136296i	$-0.0435199\pi$
$422$	2.70886			0.131865
$423$		0			0
$424$	12.4295			0.603632
$425$	−0.942447	+	20.2654i	−0.0457154	+	0.983014i
$426$		0			0
$427$	11.2462	+	3.85785i	0.544241	+	0.186695i
$428$	−4.33228	−	7.50373i	−0.209409	−	0.362706i
$429$		0			0
$430$	5.24923	−	2.87014i	0.253140	−	0.138410i
$431$			0.681468i			0.0328252i	0.999865	+	0.0164126i	$0.00522452\pi$
$431$			0.681468i			0.0328252i	−0.999865	+	0.0164126i	$0.994775\pi$
$432$		0			0
$433$	−1.64024			−0.0788247			−0.0394124	−	0.999223i	$-0.512549\pi$
$433$	−1.64024			−0.0788247			−0.0394124	+	0.999223i	$0.512549\pi$
$434$	−3.52136	−	18.0048i	−0.169031	−	0.864258i
$435$		0			0
$436$	−6.33309	−	10.9692i	−0.303300	−	0.525331i
$437$	10.5081	−	6.06687i	0.502672	−	0.290218i
$438$		0			0
$439$	−14.2849	−	8.24739i	−0.681781	−	0.393627i	0.118744	−	0.992925i	$-0.462113\pi$
$439$	−14.2849	−	8.24739i	−0.681781	−	0.393627i	−0.800526	+	0.599298i	$0.795446\pi$
$440$	9.49514	+	5.78025i	0.452663	+	0.275563i
$441$		0			0
$442$		−	9.34161i		−	0.444335i
$443$	11.5504	−	20.0059i	0.548775	−	0.950507i	−0.449583	−	0.893238i	$-0.648428\pi$
$443$	11.5504	−	20.0059i	0.548775	−	0.950507i	0.998359	−	0.0572684i	$-0.0182391\pi$
$444$		0			0
$445$	12.9155	+	0.300158i	0.612253	+	0.0142288i
$446$	2.64289	+	4.57762i	0.125144	+	0.216757i
$447$		0			0
$448$	2.59656	−	0.507832i	0.122676	−	0.0239928i
$449$			16.0497i			0.757430i	0.925513	+	0.378715i	$0.123634\pi$
$449$			16.0497i			0.757430i	−0.925513	+	0.378715i	$0.876366\pi$
$450$		0			0
$451$		−	23.9579i		−	1.12813i
$452$	7.96108	−	13.7890i	0.374458	−	0.648580i
$453$		0			0
$454$	16.0790	−	9.28322i	0.754625	−	0.435683i
$455$	−8.70690	−	10.4745i	−0.408186	−	0.491054i
$456$		0			0
$457$	−0.692830	−	0.400006i	−0.0324092	−	0.0187115i	0.483708	−	0.875230i	$-0.339290\pi$
$457$	−0.692830	−	0.400006i	−0.0324092	−	0.0187115i	−0.516117	+	0.856518i	$0.672623\pi$
$458$			9.03199i			0.422037i
$459$		0			0
$460$	8.61211	−	14.1470i	0.401542	−	0.659608i
$461$	−3.10910	+	5.38511i	−0.144805	+	0.250810i	−0.929300	−	0.369325i	$-0.879589\pi$
$461$	−3.10910	+	5.38511i	−0.144805	+	0.250810i	0.784495	+	0.620135i	$0.212922\pi$
$462$		0			0
$463$	−11.7010	+	6.75560i	−0.543793	+	0.313959i	−0.746615	−	0.665256i	$-0.768322\pi$
$463$	−11.7010	+	6.75560i	−0.543793	+	0.313959i	0.202822	+	0.979216i	$0.434989\pi$
$464$	−6.86211	+	3.96184i	−0.318566	+	0.183924i
$465$		0			0
$466$	−1.31021	+	2.26935i	−0.0606942	+	0.105125i
$467$		−	14.0650i		−	0.650853i	−0.945567	−	0.325426i	$-0.894492\pi$
$467$		−	14.0650i		−	0.650853i	0.945567	−	0.325426i	$-0.105508\pi$
$468$		0			0
$469$	0.613639	−	0.534674i	0.0283352	−	0.0246890i
$470$	20.4731	−	11.1942i	0.944355	−	0.516348i
$471$		0			0
$472$	−5.82902	−	10.0962i	−0.268302	−	0.464713i
$473$	−6.65041	−	11.5188i	−0.305786	−	0.529637i
$474$		0			0
$475$	−0.380509	+	8.18206i	−0.0174590	+	0.375419i
$476$	8.09368	−	7.05215i	0.370973	−	0.323235i
$477$		0			0
$478$		−	4.87179i		−	0.222830i
$479$	−2.52248	+	4.36907i	−0.115255	+	0.199628i	−0.917882	−	0.396854i	$-0.870102\pi$
$479$	−2.52248	+	4.36907i	−0.115255	+	0.199628i	0.802627	+	0.596482i	$0.203435\pi$
$480$		0			0
$481$	20.9162	−	12.0760i	0.953695	−	0.550616i
$482$	12.6051	−	7.27755i	0.574146	−	0.331483i
$483$		0			0
$484$	6.85690	−	11.8765i	0.311677	−	0.539841i
$485$	11.1980	−	18.3948i	0.508476	−	0.835267i
$486$		0			0
$487$			27.6648i			1.25361i	0.779176	+	0.626806i	$0.215638\pi$
$487$			27.6648i			1.25361i	−0.779176	+	0.626806i	$0.784362\pi$
$488$	3.89175	+	2.24690i	0.176171	+	0.101712i
$489$		0			0
$490$	2.50226	−	15.4512i	0.113041	−	0.698013i
$491$	−13.4050	+	7.73941i	−0.604961	+	0.349275i	−0.770991	−	0.636846i	$-0.780239\pi$
$491$	−13.4050	+	7.73941i	−0.604961	+	0.349275i	0.166030	+	0.986121i	$0.446905\pi$
$492$		0			0
$493$	−16.0750	+	27.8427i	−0.723981	+	1.25397i
$494$		−	3.77164i		−	0.169694i
$495$		0			0
$496$		−	6.93411i		−	0.311351i
$497$	3.74953	+	19.1714i	0.168189	+	0.859956i
$498$		0			0
$499$	7.72566	+	13.3812i	0.345848	+	0.599026i	0.985507	−	0.169632i	$-0.0542580\pi$
$499$	7.72566	+	13.3812i	0.345848	+	0.599026i	−0.639660	+	0.768658i	$0.720925\pi$
$500$	4.90220	+	10.0483i	0.219233	+	0.449374i
$501$		0			0
$502$	−10.3021	+	17.8438i	−0.459807	+	0.796409i
$503$		−	25.7705i		−	1.14905i	−0.818487	−	0.574524i	$-0.805187\pi$
$503$		−	25.7705i		−	1.14905i	0.818487	−	0.574524i	$-0.194813\pi$
$504$		0			0
$505$	−15.5776	+	25.5892i	−0.693196	+	1.13870i
$506$	−31.8884	−	18.4108i	−1.41761	−	0.818460i
$507$		0			0
$508$	0.0829706	−	0.0479031i	0.00368123	−	0.00212536i
$509$	−10.0008	−	17.3218i	−0.443276	−	0.767777i	0.554654	−	0.832081i	$-0.312851\pi$
$509$	−10.0008	−	17.3218i	−0.443276	−	0.767777i	−0.997930	+	0.0643043i	$0.979517\pi$
$510$		0			0
$511$	10.2577	−	2.00619i	0.453775	−	0.0887488i
$512$	1.00000			0.0441942
$513$		0			0
$514$			0.317307i			0.0139958i
$515$	−11.5159	−	21.0615i	−0.507449	−	0.928079i
$516$		0			0
$517$	−25.9380	−	44.9260i	−1.14075	−	1.97584i
$518$	26.2527	+	9.00564i	1.15348	+	0.395685i
$519$		0			0
$520$	−2.46981	−	4.51705i	−0.108308	−	0.198086i
$521$	−38.6845			−1.69480			−0.847400	−	0.530956i	$-0.821833\pi$
$521$	−38.6845			−1.69480			−0.847400	+	0.530956i	$0.821833\pi$
$522$		0			0
$523$	24.2102			1.05864			0.529318	−	0.848423i	$-0.322448\pi$
$523$	24.2102			1.05864			0.529318	+	0.848423i	$0.322448\pi$
$524$	5.51174	−	9.54661i	0.240781	−	0.417046i
$525$		0			0
$526$	−13.8308	−	23.9556i	−0.603050	−	1.04451i
$527$	−14.0674	−	24.3655i	−0.612786	−	1.06138i
$528$		0			0
$529$	−15.9306	+	27.5926i	−0.692636	+	1.19968i
$530$	14.4521	−	23.7403i	0.627761	−	1.03121i
$531$		0			0
$532$	3.26779	−	2.84728i	0.141677	−	0.123445i
$533$	−5.54775	+	9.60899i	−0.240300	+	0.416211i
$534$		0			0
$535$	−19.3693	−	0.450145i	−0.837408	−	0.0194615i
$536$	0.266411	−	0.153812i	0.0115072	−	0.00664368i
$537$		0			0
$538$	−7.84991	+	13.5964i	−0.338434	+	0.586185i
$539$	−34.4715	−	4.76349i	−1.48479	−	0.205178i
$540$		0			0
$541$	−44.0407			−1.89346			−0.946729	−	0.322030i	$-0.895635\pi$
$541$	−44.0407			−1.89346			−0.946729	+	0.322030i	$0.895635\pi$
$542$	11.5139	+	6.64757i	0.494566	+	0.285538i
$543$		0			0
$544$	3.51386	−	2.02873i	0.150655	−	0.0869809i
$545$	−28.3148	−	0.658039i	−1.21287	−	0.0281873i
$546$		0			0
$547$	6.01282	+	3.47150i	0.257089	+	0.148431i	0.623006	−	0.782217i	$-0.285911\pi$
$547$	6.01282	+	3.47150i	0.257089	+	0.148431i	−0.365917	+	0.930648i	$0.619244\pi$
$548$	−1.29277			−0.0552243
$549$		0			0
$550$	22.0805	−	11.4148i	0.941514	−	0.486729i
$551$	−6.49022	+	11.2414i	−0.276492	+	0.478899i
$552$		0			0
$553$	−2.44379	+	7.12401i	−0.103921	+	0.302944i
$554$	15.3861	−	8.88318i	0.653694	−	0.377410i
$555$		0			0
$556$	6.11640	+	3.53131i	0.259393	+	0.149761i
$557$	23.0000			0.974542			0.487271	−	0.873251i	$-0.337992\pi$
$557$	23.0000			0.974542			0.487271	+	0.873251i	$0.337992\pi$
$558$		0			0
$559$			6.15995i			0.260538i
$560$	2.04912	−	5.54987i	0.0865913	−	0.234525i
$561$		0			0
$562$	5.91512	−	3.41510i	0.249514	−	0.144057i
$563$	34.1966	−	19.7434i	1.44121	−	0.832085i	0.443283	−	0.896382i	$-0.353814\pi$
$563$	34.1966	−	19.7434i	1.44121	−	0.832085i	0.997931	+	0.0642966i	$0.0204804\pi$
$564$		0			0
$565$	−17.0803	−	31.2384i	−0.718575	−	1.31421i
$566$	−22.9961			−0.966598
$567$		0			0
$568$			7.38341i			0.309801i
$569$	−18.2142	−	10.5160i	−0.763579	−	0.440853i	0.0670000	−	0.997753i	$-0.478657\pi$
$569$	−18.2142	−	10.5160i	−0.763579	−	0.440853i	−0.830579	+	0.556900i	$0.811991\pi$
$570$		0			0
$571$	−0.697417	−	1.20796i	−0.0291860	−	0.0505516i	0.851063	−	0.525063i	$-0.175958\pi$
$571$	−0.697417	−	1.20796i	−0.0291860	−	0.0505516i	−0.880249	+	0.474511i	$0.842625\pi$
$572$	−9.91217	+	5.72279i	−0.414449	+	0.239282i
$573$		0			0
$574$	−12.5134	+	2.44736i	−0.522300	+	0.102151i
$575$	−17.0072	−	32.8981i	−0.709248	−	1.37195i
$576$		0			0
$577$	32.0089			1.33255			0.666273	−	0.745708i	$-0.267889\pi$
$577$	32.0089			1.33255			0.666273	+	0.745708i	$0.267889\pi$
$578$	−0.268541	+	0.465126i	−0.0111698	+	0.0193467i
$579$		0			0
$580$	−0.411655	+	17.7131i	−0.0170930	+	0.735497i
$581$	27.7643	+	9.52416i	1.15186	+	0.395129i
$582$		0			0
$583$	−53.5126	−	30.8955i	−2.21626	−	1.27956i
$584$	3.95051			0.163473
$585$		0			0
$586$			14.5914i			0.602766i
$587$	−8.54969	−	4.93616i	−0.352883	−	0.203737i	0.313071	−	0.949730i	$-0.398642\pi$
$587$	−8.54969	−	4.93616i	−0.352883	−	0.203737i	−0.665954	+	0.745992i	$0.731975\pi$
$588$		0			0
$589$	−5.67966	−	9.83746i	−0.234026	−	0.405346i
$590$	−26.0611	−	0.605663i	−1.07292	−	0.0249348i
$591$		0			0
$592$	9.08477	+	5.24509i	0.373382	+	0.215572i
$593$		−	6.53202i		−	0.268238i	−0.990965	−	0.134119i	$-0.957180\pi$
$593$		−	6.53202i		−	0.268238i	0.990965	−	0.134119i	$-0.0428204\pi$
$594$		0			0
$595$	−4.05884	−	23.6586i	−0.166396	−	0.969907i
$596$	7.16878	+	4.13890i	0.293645	+	0.169536i
$597$		0			0
$598$	8.52651	+	14.7683i	0.348675	+	0.603923i
$599$	3.97020	−	2.29220i	0.162218	−	0.0936565i	−0.416693	−	0.909047i	$-0.636811\pi$
$599$	3.97020	−	2.29220i	0.162218	−	0.0936565i	0.578911	+	0.815391i	$0.303478\pi$
$600$		0			0
$601$	−13.3073	−	7.68298i	−0.542816	−	0.313395i	0.203403	−	0.979095i	$-0.434800\pi$
$601$	−13.3073	−	7.68298i	−0.542816	−	0.313395i	−0.746220	+	0.665700i	$0.768133\pi$
$602$	−5.33705	+	4.65026i	−0.217522	+	0.189530i
$603$		0			0
$604$	−0.0946137			−0.00384978
$605$	−14.7113	−	26.9057i	−0.598101	−	1.09387i
$606$		0			0
$607$	−0.113970	−	0.197402i	−0.00462591	−	0.00801230i	0.863703	−	0.504001i	$-0.168139\pi$
$607$	−0.113970	−	0.197402i	−0.00462591	−	0.00801230i	−0.868329	+	0.495988i	$0.834806\pi$
$608$	1.41871	−	0.819090i	0.0575361	−	0.0332185i
$609$		0			0
$610$	8.81659	−	4.82068i	0.356973	−	0.195184i
$611$			24.0251i			0.971953i
$612$		0			0
$613$			26.7256i			1.07944i	0.841845	+	0.539719i	$0.181469\pi$
$613$			26.7256i			1.07944i	−0.841845	+	0.539719i	$0.818531\pi$
$614$	4.11571	−	7.12863i	0.166097	−	0.287688i
$615$		0			0
$616$	−12.4412	−	4.26777i	−0.501269	−	0.171954i
$617$	18.8600	+	32.6665i	0.759276	+	1.31510i	0.943220	+	0.332167i	$0.107780\pi$
$617$	18.8600	+	32.6665i	0.759276	+	1.31510i	−0.183945	+	0.982937i	$0.558887\pi$
$618$		0			0
$619$	−8.46555	−	4.88759i	−0.340259	−	0.196449i	0.320127	−	0.947374i	$-0.396274\pi$
$619$	−8.46555	−	4.88759i	−0.340259	−	0.196449i	−0.660387	+	0.750926i	$0.729608\pi$
$620$	−13.2441	−	8.06246i	−0.531896	−	0.323796i
$621$		0			0
$622$	10.5548			0.423210
$623$	−15.0017	+	2.93402i	−0.601031	+	0.117549i
$624$		0			0
$625$	24.8921	+	2.32025i	0.995684	+	0.0928099i
$626$	−9.20310	−	15.9402i	−0.367830	−	0.637100i
$627$		0			0
$628$	−0.938382	+	1.62532i	−0.0374455	+	0.0648575i
$629$	42.5634			1.69711
$630$		0			0
$631$	5.47839			0.218091			0.109046	−	0.994037i	$-0.465221\pi$
$631$	5.47839			0.218091			0.109046	+	0.994037i	$0.465221\pi$
$632$	−1.42332	+	2.46526i	−0.0566167	+	0.0980630i
$633$		0			0
$634$	13.6314	+	23.6102i	0.541370	+	0.937681i
$635$	0.00497737	−	0.214171i	0.000197521	−	0.00849913i
$636$		0			0
$637$	12.7227	+	9.89285i	0.504093	+	0.391969i
$638$	39.3910			1.55951
$639$		0			0
$640$	1.16272	−	1.90999i	0.0459607	−	0.0754991i
$641$	5.91036	+	3.41235i	0.233445	+	0.134780i	0.612160	−	0.790734i	$-0.290301\pi$
$641$	5.91036	+	3.41235i	0.233445	+	0.134780i	−0.378715	+	0.925513i	$0.623634\pi$
$642$		0			0
$643$	−9.33848	−	16.1747i	−0.368274	−	0.637869i	0.621022	−	0.783793i	$-0.286718\pi$
$643$	−9.33848	−	16.1747i	−0.368274	−	0.637869i	−0.989296	+	0.145924i	$0.953384\pi$
$644$	−6.35864	+	18.5364i	−0.250566	+	0.730435i
$645$		0			0
$646$	3.32342	−	5.75633i	0.130758	−	0.226480i
$647$		−	6.15085i		−	0.241815i	−0.992664	−	0.120907i	$-0.961420\pi$
$647$		−	6.15085i		−	0.241815i	0.992664	−	0.120907i	$-0.0385804\pi$
$648$		0			0
$649$			57.9556i			2.27496i
$650$	−11.4992	−	0.534776i	−0.451037	−	0.0209756i
$651$		0			0
$652$	2.05066	−	1.18395i	0.0803100	−	0.0463670i
$653$	4.62276	+	8.00685i	0.180902	+	0.313332i	0.942188	−	0.335084i	$-0.108765\pi$
$653$	4.62276	+	8.00685i	0.180902	+	0.313332i	−0.761286	+	0.648417i	$0.775432\pi$
$654$		0			0
$655$	−11.8253	−	21.6275i	−0.462054	−	0.845055i
$656$	−4.81924			−0.188160
$657$		0			0
$658$	−20.8156	+	18.1370i	−0.811478	+	0.707054i
$659$	11.1622	+	6.44447i	0.434816	+	0.251041i	0.701396	−	0.712772i	$-0.252560\pi$
$659$	11.1622	+	6.44447i	0.434816	+	0.251041i	−0.266580	+	0.963813i	$0.585894\pi$
$660$		0			0
$661$	29.4904	−	17.0263i	1.14704	−	0.662245i	0.198878	−	0.980024i	$-0.436270\pi$
$661$	29.4904	−	17.0263i	1.14704	−	0.662245i	0.948165	+	0.317779i	$0.102937\pi$
$662$	−9.19875	−	15.9327i	−0.357519	−	0.619242i
$663$		0			0
$664$	9.60784	+	5.54709i	0.372857	+	0.215269i
$665$	−1.63874	−	9.55206i	−0.0635477	−	0.370413i
$666$		0			0
$667$		−	58.6895i		−	2.27247i
$668$	6.32518	+	3.65184i	0.244728	+	0.141294i
$669$		0			0
$670$	0.0159818	−	0.687684i	0.000617432	−	0.0265675i
$671$	−11.1700	−	19.3470i	−0.431214	−	0.746884i
$672$		0			0
$673$	21.9800	+	12.6901i	0.847265	+	0.489169i	0.859727	−	0.510753i	$-0.170633\pi$
$673$	21.9800	+	12.6901i	0.847265	+	0.489169i	−0.0124618	+	0.999922i	$0.503967\pi$
$674$			14.4517i			0.556658i
$675$		0			0
$676$	−7.69926			−0.296125
$677$	−28.8703	−	16.6683i	−1.10958	−	0.640613i	−0.170856	−	0.985296i	$-0.554653\pi$
$677$	−28.8703	−	16.6683i	−1.10958	−	0.640613i	−0.938719	+	0.344683i	$0.887987\pi$
$678$		0			0
$679$	−8.26792	+	24.1022i	−0.317294	+	0.924956i
$680$	0.210795	−	9.07029i	0.00808360	−	0.347830i
$681$		0			0
$682$	−17.2358	+	29.8532i	−0.659991	+	1.14314i
$683$	−4.53570			−0.173554			−0.0867769	−	0.996228i	$-0.527657\pi$
$683$	−4.53570			−0.173554			−0.0867769	+	0.996228i	$0.527657\pi$
$684$		0			0
$685$	−1.50313	+	2.46918i	−0.0574317	+	0.0943424i
$686$	1.03335	+	18.4914i	0.0394533	+	0.706005i
$687$		0			0
$688$	−2.31707	+	1.33776i	−0.0883375	+	0.0510017i
$689$	14.3085	+	24.7830i	0.545110	+	0.944158i
$690$		0			0
$691$	−8.08693	−	4.66899i	−0.307641	−	0.177617i	0.338229	−	0.941064i	$-0.390172\pi$
$691$	−8.08693	−	4.66899i	−0.307641	−	0.177617i	−0.645871	+	0.763447i	$0.723505\pi$
$692$		−	19.0506i		−	0.724194i
$693$		0			0
$694$	18.0657			0.685764
$695$	13.8565	−	7.57635i	0.525606	−	0.287387i
$696$		0			0
$697$	−16.9341	+	9.77692i	−0.641425	+	0.370327i
$698$	7.58926	−	4.38166i	0.287258	−	0.165848i
$699$		0			0
$700$	−8.21765	−	10.3668i	−0.310598	−	0.391828i
$701$			5.36231i			0.202532i	0.994859	+	0.101266i	$0.0322892\pi$
$701$			5.36231i			0.202532i	−0.994859	+	0.101266i	$0.967711\pi$
$702$		0			0
$703$	17.1848			0.648138
$704$	−4.30527	−	2.48565i	−0.162261	−	0.0936814i
$705$		0			0
$706$	−9.23289	+	5.33061i	−0.347484	+	0.200620i
$707$	11.5015	−	33.5287i	0.432560	−	1.26098i
$708$		0			0
$709$	−16.7421	+	28.9982i	−0.628764	+	1.08905i	0.359036	+	0.933324i	$0.383106\pi$
$709$	−16.7421	+	28.9982i	−0.628764	+	1.08905i	−0.987800	+	0.155728i	$0.950228\pi$
$710$	14.1023	+	8.58487i	0.529248	+	0.322184i
$711$		0			0
$712$	−5.77755			−0.216523
$713$	44.4789	+	25.6799i	1.66575	+	0.961720i
$714$		0			0
$715$	−0.594626	+	25.5862i	−0.0222378	+	0.956870i
$716$	−7.09657	+	4.09720i	−0.265211	+	0.153120i
$717$		0			0
$718$	14.2860	+	8.24802i	0.533149	+	0.307813i
$719$	−2.15051			−0.0802004			−0.0401002	−	0.999196i	$-0.512768\pi$
$719$	−2.15051			−0.0802004			−0.0401002	+	0.999196i	$0.512768\pi$
$720$		0			0
$721$	18.6582	+	21.4138i	0.694868	+	0.797492i
$722$	−8.15818	+	14.1304i	−0.303616	+	0.525879i
$723$		0			0
$724$	5.22487	−	3.01658i	0.194181	−	0.112110i
$725$	33.3533	+	21.3817i	1.23871	+	0.794098i
$726$		0			0
$727$	−5.44298	+	9.42752i	−0.201869	+	0.349647i	−0.949131	−	0.314883i	$-0.898035\pi$
$727$	−5.44298	+	9.42752i	−0.201869	+	0.349647i	0.747262	+	0.664530i	$0.231368\pi$
$728$	4.00163	+	4.59262i	0.148310	+	0.170214i
$729$		0			0
$730$	4.59335	−	7.54544i	0.170008	−	0.279269i
$731$	−5.42790	+	9.40140i	−0.200758	+	0.347723i
$732$		0			0
$733$	18.0386	+	31.2438i	0.666271	+	1.15402i	0.978939	+	0.204153i	$0.0654441\pi$
$733$	18.0386	+	31.2438i	0.666271	+	1.15402i	−0.312668	+	0.949863i	$0.601223\pi$
$734$	0.205646	+	0.356189i	0.00759053	+	0.0131472i
$735$		0			0
$736$	−3.70342	+	6.41451i	−0.136510	+	0.236442i
$737$	−1.52929			−0.0563322
$738$		0			0
$739$	−8.61728			−0.316992			−0.158496	−	0.987360i	$-0.550664\pi$
$739$	−8.61728			−0.316992			−0.158496	+	0.987360i	$0.550664\pi$
$740$	20.5812	−	11.2532i	0.756579	−	0.413677i
$741$		0			0
$742$	−10.6706	+	31.1062i	−0.391728	+	1.14194i
$743$	15.2682	+	26.4453i	0.560135	+	0.970183i	0.997484	+	0.0708907i	$0.0225842\pi$
$743$	15.2682	+	26.4453i	0.560135	+	0.970183i	−0.437349	+	0.899292i	$0.644083\pi$
$744$		0			0
$745$	16.2406	−	8.87992i	0.595009	−	0.325335i
$746$		−	10.8325i		−	0.396608i
$747$		0			0
$748$	−20.1708			−0.737518
$749$	22.4980	−	4.40014i	0.822060	−	0.160778i
$750$		0			0
$751$	3.78106	+	6.54899i	0.137973	+	0.238976i	0.926729	−	0.375730i	$-0.122608\pi$
$751$	3.78106	+	6.54899i	0.137973	+	0.238976i	−0.788756	+	0.614706i	$0.789275\pi$
$752$	−9.03708	+	5.21756i	−0.329548	+	0.190265i
$753$		0			0
$754$	−15.7989	−	9.12149i	−0.575361	−	0.332185i
$755$	−0.110010	+	0.180711i	−0.00400366	+	0.00657676i
$756$		0			0
$757$		−	16.4905i		−	0.599358i	−0.954040	−	0.299679i	$-0.903121\pi$
$757$		−	16.4905i		−	0.599358i	0.954040	−	0.299679i	$-0.0968795\pi$
$758$	10.3774	−	17.9741i	0.376923	−	0.652850i
$759$		0			0
$760$	0.0851075	−	3.66209i	0.00308717	−	0.132838i
$761$	−7.56857	−	13.1092i	−0.274361	−	0.475206i	0.695613	−	0.718417i	$-0.255133\pi$
$761$	−7.56857	−	13.1092i	−0.274361	−	0.475206i	−0.969974	+	0.243210i	$0.921800\pi$
$762$		0			0
$763$	32.8885	−	6.43229i	1.19064	−	0.232865i
$764$			1.38008i			0.0499294i
$765$		0			0
$766$		−	34.0913i		−	1.23177i
$767$	13.4203	−	23.2447i	0.484581	−	0.839318i
$768$		0			0
$769$	23.8050	−	13.7438i	0.858430	−	0.495615i	−0.00505613	−	0.999987i	$-0.501609\pi$
$769$	23.8050	−	13.7438i	0.858430	−	0.495615i	0.863486	+	0.504372i	$0.168276\pi$
$770$	−22.6171	+	18.8003i	−0.815063	+	0.677516i
$771$		0			0
$772$	−5.06489	−	2.92422i	−0.182290	−	0.105245i
$773$			40.9642i			1.47338i	0.676230	+	0.736691i	$0.263613\pi$
$773$			40.9642i			1.47338i	−0.676230	+	0.736691i	$0.736387\pi$
$774$		0			0
$775$	−30.7985	+	15.9217i	−1.10631	+	0.571925i
$776$	−4.81542	+	8.34056i	−0.172864	+	0.299409i
$777$		0			0
$778$	15.5200	−	8.96050i	0.556420	−	0.321249i
$779$	−6.83708	+	3.94739i	−0.244964	+	0.141430i
$780$		0			0
$781$	18.3526	−	31.7876i	0.656706	−	1.13745i
$782$			30.0529i			1.07469i
$783$		0			0
$784$	−0.958199	+	6.93411i	−0.0342214	+	0.247647i
$785$	2.01328	+	3.68211i	0.0718570	+	0.131420i
$786$		0			0
$787$	−16.9398	−	29.3406i	−0.603839	−	1.04588i	−0.992234	−	0.124387i	$-0.960304\pi$
$787$	−16.9398	−	29.3406i	−0.603839	−	1.04588i	0.388395	−	0.921493i	$-0.373030\pi$
$788$	−6.16341	−	10.6753i	−0.219562	−	0.380293i
$789$		0			0
$790$	3.05371	+	5.58496i	0.108646	+	0.198704i
$791$	27.6739	+	31.7610i	0.983971	+	1.12929i
$792$		0			0
$793$			10.3462i			0.367406i
$794$	0.566953	−	0.981991i	0.0201204	−	0.0348496i
$795$		0			0
$796$	4.00142	−	2.31022i	0.141827	−	0.0818836i
$797$	−44.1099	+	25.4669i	−1.56245	+	0.902083i	−0.565445	+	0.824786i	$0.691295\pi$
$797$	−44.1099	+	25.4669i	−1.56245	+	0.902083i	−0.997008	+	0.0772962i	$0.975371\pi$
$798$		0			0
$799$	−21.1700	+	36.6675i	−0.748941	+	1.29720i
$800$	−2.29614	−	4.44159i	−0.0811810	−	0.157034i
$801$		0			0
$802$			8.10222i			0.286099i
$803$	−17.0080	−	9.81958i	−0.600199	−	0.346525i
$804$		0			0
$805$	28.0109	+	33.6976i	0.987256	+	1.18769i
$806$	13.8258	−	7.98232i	0.486992	−	0.281165i
$807$		0			0
$808$	6.69877	−	11.6026i	0.235662	−	0.408178i
$809$			3.46980i			0.121992i	0.998138	+	0.0609959i	$0.0194277\pi$
$809$			3.46980i			0.121992i	−0.998138	+	0.0609959i	$0.980572\pi$
$810$		0			0
$811$		−	38.8069i		−	1.36270i	−0.731960	−	0.681348i	$-0.761394\pi$
$811$		−	38.8069i		−	1.36270i	0.731960	−	0.681348i	$-0.238606\pi$
$812$	−4.02390	−	20.5743i	−0.141211	−	0.722017i
$813$		0			0
$814$	−26.0749	−	45.1631i	−0.913925	−	1.58297i
$815$	0.123018	−	5.29335i	0.00430914	−	0.185418i
$816$		0			0
$817$	−2.19149	+	3.79578i	−0.0766707	+	0.132798i
$818$			14.6375i			0.511788i
$819$		0			0
$820$	−5.60345	+	9.20471i	−0.195681	+	0.321443i
$821$	35.8129	+	20.6766i	1.24988	+	0.721617i	0.971085	−	0.238735i	$-0.0767326\pi$
$821$	35.8129	+	20.6766i	1.24988	+	0.721617i	0.278792	+	0.960351i	$0.410066\pi$
$822$		0			0
$823$	−46.7302	+	26.9797i	−1.62891	+	0.940453i	−0.644494	+	0.764609i	$0.722932\pi$
$823$	−46.7302	+	26.9797i	−1.62891	+	0.940453i	−0.984418	+	0.175844i	$0.943735\pi$
$824$	5.36750	+	9.29678i	0.186986	+	0.323869i
$825$		0			0
$826$	30.2708	−	5.92033i	1.05325	−	0.205994i
$827$	−20.1603			−0.701044			−0.350522	−	0.936555i	$-0.613996\pi$
$827$	−20.1603			−0.701044			−0.350522	+	0.936555i	$0.613996\pi$
$828$		0			0
$829$			34.6201i			1.20241i	0.799097	+	0.601203i	$0.205311\pi$
$829$			34.6201i			1.20241i	−0.799097	+	0.601203i	$0.794689\pi$
$830$	21.7662	−	11.9012i	0.755515	−	0.413096i
$831$		0			0
$832$	1.15117	+	1.99388i	0.0399095	+	0.0691253i
$833$	10.7004	+	26.3094i	0.370748	+	0.911566i
$834$		0			0
$835$	14.3294	−	7.83495i	0.495890	−	0.271140i
$836$	−8.14388			−0.281662
$837$		0			0
$838$	11.6832			0.403590
$839$	−18.3497	+	31.7826i	−0.633501	+	1.09726i	0.353329	+	0.935499i	$0.385050\pi$
$839$	−18.3497	+	31.7826i	−0.633501	+	1.09726i	−0.986831	+	0.161758i	$0.948284\pi$
$840$		0			0
$841$	16.8924	+	29.2585i	0.582497	+	1.00891i
$842$	12.5853	+	21.7984i	0.433718	+	0.751222i
$843$		0			0
$844$	−1.35443	+	2.34594i	−0.0466214	+	0.0807506i
$845$	−8.95211	+	14.7055i	−0.307962	+	0.505885i
$846$		0			0
$847$	23.8356	+	27.3559i	0.819001	+	0.939958i
$848$	−6.21477	+	10.7643i	−0.213416	+	0.369648i
$849$		0			0
$850$	−17.0791	−	10.9489i	−0.585808	−	0.375543i
$851$	−67.2894	+	38.8495i	−2.30665	+	1.33175i
$852$		0			0
$853$	12.5798	−	21.7888i	0.430723	−	0.746034i	−0.566213	−	0.824259i	$-0.691592\pi$
$853$	12.5798	−	21.7888i	0.430723	−	0.746034i	0.996936	+	0.0782251i	$0.0249253\pi$
$854$	−8.96409	+	7.81056i	−0.306745	+	0.267272i
$855$		0			0
$856$	8.66456			0.296148
$857$	−15.3574	−	8.86660i	−0.524599	−	0.302877i	0.214215	−	0.976786i	$-0.431281\pi$
$857$	−15.3574	−	8.86660i	−0.524599	−	0.302877i	−0.738814	+	0.673909i	$0.764614\pi$
$858$		0			0
$859$	26.6331	−	15.3766i	0.908710	−	0.524644i	0.0286940	−	0.999588i	$-0.490865\pi$
$859$	26.6331	−	15.3766i	0.908710	−	0.524644i	0.880016	+	0.474944i	$0.157532\pi$
$860$	−0.139000	+	5.98104i	−0.00473986	+	0.203952i
$861$		0			0
$862$	−0.590169	−	0.340734i	−0.0201012	−	0.0116054i
$863$	−20.1050			−0.684381			−0.342190	−	0.939631i	$-0.611169\pi$
$863$	−20.1050			−0.684381			−0.342190	+	0.939631i	$0.611169\pi$
$864$		0			0
$865$	−36.3865	−	22.1506i	−1.23718	−	0.753142i
$866$	0.820118	−	1.42049i	0.0278687	−	0.0482701i
$867$		0			0
$868$	17.3533	+	5.95281i	0.589009	+	0.202052i
$869$	12.2556	−	7.07575i	0.415742	−	0.240029i
$870$		0			0
$871$	0.613366	+	0.354127i	0.0207831	+	0.0119991i
$872$	12.6662			0.428931
$873$		0			0
$874$			12.1337i			0.410430i
$875$	−29.3553	+	3.64194i	−0.992392	+	0.123120i
$876$		0			0
$877$	−20.1511	+	11.6342i	−0.680454	+	0.392860i	−0.800026	−	0.599965i	$-0.795181\pi$
$877$	−20.1511	+	11.6342i	−0.680454	+	0.392860i	0.119572	+	0.992825i	$0.461848\pi$
$878$	14.2849	−	8.24739i	0.482092	−	0.278336i
$879$		0			0
$880$	−9.75341	+	5.33291i	−0.328788	+	0.179772i
$881$	−14.6821			−0.494653			−0.247326	−	0.968932i	$-0.579552\pi$
$881$	−14.6821			−0.494653			−0.247326	+	0.968932i	$0.579552\pi$
$882$		0			0
$883$		−	25.8044i		−	0.868386i	−0.900820	−	0.434193i	$-0.857034\pi$
$883$		−	25.8044i		−	0.868386i	0.900820	−	0.434193i	$-0.142966\pi$
$884$	8.09007	+	4.67081i	0.272099	+	0.157096i
$885$		0			0
$886$	11.5504	+	20.0059i	0.388043	+	0.672110i
$887$	11.3367	−	6.54525i	0.380649	−	0.219768i	−0.297451	−	0.954737i	$-0.596137\pi$
$887$	11.3367	−	6.54525i	0.380649	−	0.219768i	0.678101	+	0.734969i	$0.262803\pi$
$888$		0			0
$889$	0.0486535	+	0.248766i	0.00163179	+	0.00834335i
$890$	−6.71769	+	11.0351i	−0.225178	+	0.369896i
$891$		0			0
$892$	−5.28578			−0.176981
$893$	−8.54730	+	14.8044i	−0.286025	+	0.495409i
$894$		0			0
$895$	−0.425719	+	18.3183i	−0.0142302	+	0.612314i
$896$	−0.858483	+	2.50260i	−0.0286799	+	0.0836060i
$897$		0			0
$898$	−13.8994	−	8.02483i	−0.463829	−	0.267792i
$899$	−54.9437			−1.83248
$900$		0			0
$901$			50.4323i			1.68014i
$902$	20.7481	+	11.9789i	0.690837	+	0.398855i
$903$		0			0
$904$	7.96108	+	13.7890i	0.264782	+	0.458615i
$905$	0.313438	−	13.4869i	0.0104190	−	0.448320i
$906$		0			0
$907$	−10.9875	−	6.34364i	−0.364834	−	0.210637i	0.306365	−	0.951914i	$-0.400887\pi$
$907$	−10.9875	−	6.34364i	−0.364834	−	0.210637i	−0.671199	+	0.741277i	$0.734220\pi$
$908$			18.5664i			0.616149i
$909$		0			0
$910$	13.4247	−	2.30312i	0.445023	−	0.0763478i
$911$	43.7132	+	25.2378i	1.44828	+	0.836167i	0.998379	−	0.0569104i	$-0.0181249\pi$
$911$	43.7132	+	25.2378i	1.44828	+	0.836167i	0.449904	+	0.893077i	$0.351458\pi$
$912$		0			0
$913$	−27.5762	−	47.7635i	−0.912640	−	1.58074i
$914$	0.692830	−	0.400006i	0.0229168	−	0.0132310i
$915$		0			0
$916$	−7.82193	−	4.51600i	−0.258444	−	0.149213i
$917$	19.1596	+	21.9893i	0.632706	+	0.726150i
$918$		0			0
$919$	38.5621			1.27205			0.636024	−	0.771670i	$-0.280578\pi$
$919$	38.5621			1.27205			0.636024	+	0.771670i	$0.280578\pi$
$920$	7.94561	+	14.5318i	0.261959	+	0.479100i
$921$		0			0
$922$	−3.10910	−	5.38511i	−0.102393	−	0.177349i
$923$	−14.7216	+	8.49953i	−0.484568	+	0.279766i
$924$		0			0
$925$	2.43661	−	52.3943i	0.0801154	−	1.72271i
$926$		−	13.5112i		−	0.444005i
$927$		0			0
$928$		−	7.92369i		−	0.260108i
$929$	−20.4721	+	35.4587i	−0.671667	+	1.16336i	0.305764	+	0.952107i	$0.401088\pi$
$929$	−20.4721	+	35.4587i	−0.671667	+	1.16336i	−0.977431	+	0.211254i	$0.932245\pi$
$930$		0			0
$931$	4.32026	+	10.6223i	0.141591	+	0.348132i
$932$	−1.31021	−	2.26935i	−0.0429173	−	0.0743350i
$933$		0			0
$934$	12.1807	+	7.03252i	0.398564	+	0.230111i
$935$	−23.4531	+	38.5261i	−0.766998	+	1.25994i
$936$		0			0
$937$	21.5005			0.702390			0.351195	−	0.936302i	$-0.385775\pi$
$937$	21.5005			0.702390			0.351195	+	0.936302i	$0.385775\pi$
$938$	0.156222	+	0.798764i	0.00510082	+	0.0260806i
$939$		0			0
$940$	−0.542130	+	23.3273i	−0.0176823	+	0.760854i
$941$	19.3545	+	33.5229i	0.630937	+	1.09282i	0.987360	+	0.158491i	$0.0506627\pi$
$941$	19.3545	+	33.5229i	0.630937	+	1.09282i	−0.356423	+	0.934325i	$0.616004\pi$
$942$		0			0
$943$	17.8477	−	30.9131i	0.581200	−	1.00667i
$944$	11.6580			0.379437
$945$		0			0
$946$	13.3008			0.432447
$947$	−12.9866	+	22.4934i	−0.422007	+	0.730937i	−0.996136	−	0.0878280i	$-0.972007\pi$
$947$	−12.9866	+	22.4934i	−0.422007	+	0.730937i	0.574129	+	0.818765i	$0.305341\pi$
$948$		0			0
$949$	4.54769	+	7.87684i	0.147624	+	0.255693i
$950$	−6.89562	−	4.42056i	−0.223723	−	0.143422i
$951$		0			0
$952$	2.06050	+	10.5354i	0.0667813	+	0.341454i
$953$	−9.34565			−0.302735			−0.151368	−	0.988478i	$-0.548368\pi$
$953$	−9.34565			−0.302735			−0.151368	+	0.988478i	$0.548368\pi$
$954$		0			0
$955$	2.63594	+	1.60465i	0.0852969	+	0.0519252i
$956$	4.21909	+	2.43589i	0.136455	+	0.0787825i
$957$		0			0
$958$	−2.52248	−	4.36907i	−0.0814977	−	0.141158i
$959$	1.10982	−	3.23528i	0.0358379	−	0.104473i
$960$		0			0
$961$	8.54093	−	14.7933i	0.275514	−	0.477204i
$962$			24.1519i			0.778689i
$963$		0			0
$964$			14.5551i			0.468788i
$965$	−11.4743	+	6.27385i	−0.369371	+	0.201962i
$966$		0			0
$967$	52.6756	−	30.4123i	1.69393	−	0.977993i	0.742647	−	0.669683i	$-0.233570\pi$
$967$	52.6756	−	30.4123i	1.69393	−	0.977993i	0.951286	−	0.308310i	$-0.0997635\pi$
$968$	6.85690	+	11.8765i	0.220389	+	0.381725i
$969$		0			0
$970$	10.3314	+	18.8952i	0.331721	+	0.606688i
$971$	23.3430			0.749111			0.374556	−	0.927204i	$-0.377795\pi$
$971$	23.3430			0.749111			0.374556	+	0.927204i	$0.377795\pi$
$972$		0			0
$973$	−14.0883	+	12.2753i	−0.451649	+	0.393530i
$974$	−23.9584	−	13.8324i	−0.767677	−	0.443219i
$975$		0			0
$976$	−3.89175	+	2.24690i	−0.124572	+	0.0719216i
$977$	−10.2509	−	17.7551i	−0.327955	−	0.568035i	0.654151	−	0.756364i	$-0.273026\pi$
$977$	−10.2509	−	17.7551i	−0.327955	−	0.568035i	−0.982106	+	0.188329i	$0.939693\pi$
$978$		0			0
$979$	24.8739	+	14.3610i	0.794973	+	0.458978i
$980$	12.1300	+	9.89261i	0.387478	+	0.316008i
$981$		0			0
$982$		−	15.4788i		−	0.493949i
$983$	18.5257	+	10.6958i	0.590877	+	0.341143i	0.765444	−	0.643502i	$-0.222519\pi$
$983$	18.5257	+	10.6958i	0.590877	+	0.341143i	−0.174567	+	0.984645i	$0.555853\pi$
$984$		0			0
$985$	−27.5561	−	0.640408i	−0.878012	−	0.0204051i
$986$	−16.0750	−	27.8427i	−0.511932	−	0.886692i
$987$		0			0
$988$	3.26634	+	1.88582i	0.103916	+	0.0599959i
$989$		−	19.8172i		−	0.630149i
$990$		0			0
$991$	−8.23001			−0.261435			−0.130717	−	0.991420i	$-0.541728\pi$
$991$	−8.23001			−0.261435			−0.130717	+	0.991420i	$0.541728\pi$
$992$	6.00511	+	3.46705i	0.190663	+	0.110079i
$993$		0			0
$994$	−18.4777	−	6.33853i	−0.586077	−	0.201046i
$995$	0.240043	−	10.3288i	0.00760988	−	0.327446i
$996$		0			0
$997$	0.0357929	−	0.0619952i	0.00113357	−	0.00196341i	−0.865458	−	0.500981i	$-0.832973\pi$
$997$	0.0357929	−	0.0619952i	0.00113357	−	0.00196341i	0.866592	+	0.499018i	$0.166306\pi$
$998$	−15.4513			−0.489103
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bf.e.629.1		32
3.2	odd	2		630.2.bf.f.209.3	yes	32
5.4	even	2		1890.2.bf.f.629.12		32
7.6	odd	2	inner	1890.2.bf.e.629.16		32
9.4	even	3		630.2.bf.e.419.3	yes	32
9.5	odd	6		1890.2.bf.f.1259.5		32
15.14	odd	2		630.2.bf.e.209.14	yes	32
21.20	even	2		630.2.bf.f.209.14	yes	32
35.34	odd	2		1890.2.bf.f.629.5		32
45.4	even	6		630.2.bf.f.419.14	yes	32
45.14	odd	6	inner	1890.2.bf.e.1259.16		32
63.13	odd	6		630.2.bf.e.419.14	yes	32
63.41	even	6		1890.2.bf.f.1259.12		32
105.104	even	2		630.2.bf.e.209.3	✓	32
315.104	even	6	inner	1890.2.bf.e.1259.1		32
315.139	odd	6		630.2.bf.f.419.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.3	✓	32	105.104	even	2
630.2.bf.e.209.14	yes	32	15.14	odd	2
630.2.bf.e.419.3	yes	32	9.4	even	3
630.2.bf.e.419.14	yes	32	63.13	odd	6
630.2.bf.f.209.3	yes	32	3.2	odd	2
630.2.bf.f.209.14	yes	32	21.20	even	2
630.2.bf.f.419.3	yes	32	315.139	odd	6
630.2.bf.f.419.14	yes	32	45.4	even	6
1890.2.bf.e.629.1		32	1.1	even	1	trivial
1890.2.bf.e.629.16		32	7.6	odd	2	inner
1890.2.bf.e.1259.1		32	315.104	even	6	inner
1890.2.bf.e.1259.16		32	45.14	odd	6	inner
1890.2.bf.f.629.5		32	35.34	odd	2
1890.2.bf.f.629.12		32	5.4	even	2
1890.2.bf.f.1259.5		32	9.5	odd	6
1890.2.bf.f.1259.12		32	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.23546 - 0.0519524i) q^{5} +(2.59656 - 0.507832i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.23546 - 0.0519524i) q^{5} +(2.59656 - 0.507832i) q^{7} +1.00000 q^{8} +(1.16272 - 1.90999i) q^{10} +(-4.30527 - 2.48565i) q^{11} +(1.15117 + 1.99388i) q^{13} +(-0.858483 + 2.50260i) q^{14} +(-0.500000 + 0.866025i) q^{16} +4.05745i q^{17} +1.63818i q^{19} +(1.07274 + 1.96195i) q^{20} +(4.30527 - 2.48565i) q^{22} +(-3.70342 - 6.41451i) q^{23} +(4.99460 + 0.232276i) q^{25} -2.30233 q^{26} +(-1.73807 - 1.99477i) q^{28} +(6.86211 + 3.96184i) q^{29} +(-6.00511 + 3.46705i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.51386 - 2.02873i) q^{34} +(-5.83089 + 1.00034i) q^{35} -10.4902i q^{37} +(-1.41871 - 0.819090i) q^{38} +(-2.23546 - 0.0519524i) q^{40} +(2.40962 + 4.17358i) q^{41} +(2.31707 + 1.33776i) q^{43} +4.97130i q^{44} +7.40684 q^{46} +(9.03708 + 5.21756i) q^{47} +(6.48421 - 2.63723i) q^{49} +(-2.69846 + 4.20931i) q^{50} +(1.15117 - 1.99388i) q^{52} +12.4295 q^{53} +(9.49514 + 5.78025i) q^{55} +(2.59656 - 0.507832i) q^{56} +(-6.86211 + 3.96184i) q^{58} +(-5.82902 - 10.0962i) q^{59} +(3.89175 + 2.24690i) q^{61} -6.93411i q^{62} +1.00000 q^{64} +(-2.46981 - 4.51705i) q^{65} +(0.266411 - 0.153812i) q^{67} +(3.51386 - 2.02873i) q^{68} +(2.04912 - 5.54987i) q^{70} +7.38341i q^{71} +3.95051 q^{73} +(9.08477 + 5.24509i) q^{74} +(1.41871 - 0.819090i) q^{76} +(-12.4412 - 4.26777i) q^{77} +(-1.42332 + 2.46526i) q^{79} +(1.16272 - 1.90999i) q^{80} -4.81924 q^{82} +(9.60784 + 5.54709i) q^{83} +(0.210795 - 9.07029i) q^{85} +(-2.31707 + 1.33776i) q^{86} +(-4.30527 - 2.48565i) q^{88} -5.77755 q^{89} +(4.00163 + 4.59262i) q^{91} +(-3.70342 + 6.41451i) q^{92} +(-9.03708 + 5.21756i) q^{94} +(0.0851075 - 3.66209i) q^{95} +(-4.81542 + 8.34056i) q^{97} +(-0.958199 + 6.93411i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 24 q^{11} - 16 q^{16} - 24 q^{22} - 24 q^{23} + 50 q^{25} + 36 q^{29} - 16 q^{32} - 48 q^{35} + 54 q^{43} + 48 q^{46} + 32 q^{49} - 58 q^{50} - 24 q^{53} - 36 q^{58} + 32 q^{64} + 66 q^{65} + 66 q^{67} + 12 q^{70} - 12 q^{74} + 18 q^{77} + 34 q^{79} - 32 q^{85} - 54 q^{86} + 24 q^{88} + 16 q^{91} - 24 q^{92} + 24 q^{95} - 64 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 24 * q^11 - 16 * q^16 - 24 * q^22 - 24 * q^23 + 50 * q^25 + 36 * q^29 - 16 * q^32 - 48 * q^35 + 54 * q^43 + 48 * q^46 + 32 * q^49 - 58 * q^50 - 24 * q^53 - 36 * q^58 + 32 * q^64 + 66 * q^65 + 66 * q^67 + 12 * q^70 - 12 * q^74 + 18 * q^77 + 34 * q^79 - 32 * q^85 - 54 * q^86 + 24 * q^88 + 16 * q^91 - 24 * q^92 + 24 * q^95 - 64 * q^98

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