LMFDB - Embedded newform 4020.2.q.l.3781.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.3
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.l.841.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} -1.00000 q^{5} +(-1.49766 - 2.59403i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} -1.00000 q^{5} +(-1.49766 - 2.59403i) q^{7} +1.00000 q^{9} +(-1.46984 - 2.54583i) q^{11} +(-3.57330 + 6.18914i) q^{13} +1.00000 q^{15} +(-3.28325 + 5.68676i) q^{17} +(3.84692 - 6.66305i) q^{19} +(1.49766 + 2.59403i) q^{21} +(-0.513819 + 0.889960i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(3.12686 + 5.41587i) q^{29} +(4.31459 + 7.47308i) q^{31} +(1.46984 + 2.54583i) q^{33} +(1.49766 + 2.59403i) q^{35} +(-3.14067 + 5.43981i) q^{37} +(3.57330 - 6.18914i) q^{39} +(1.49016 + 2.58104i) q^{41} +0.784978 q^{43} -1.00000 q^{45} +(-5.99272 - 10.3797i) q^{47} +(-0.985982 + 1.70777i) q^{49} +(3.28325 - 5.68676i) q^{51} +7.58069 q^{53} +(1.46984 + 2.54583i) q^{55} +(-3.84692 + 6.66305i) q^{57} -5.51489 q^{59} +(4.82170 - 8.35143i) q^{61} +(-1.49766 - 2.59403i) q^{63} +(3.57330 - 6.18914i) q^{65} +(-1.44798 - 8.05626i) q^{67} +(0.513819 - 0.889960i) q^{69} +(-0.651030 - 1.12762i) q^{71} +(2.78113 - 4.81706i) q^{73} -1.00000 q^{75} +(-4.40264 + 7.62559i) q^{77} +(-3.71649 - 6.43715i) q^{79} +1.00000 q^{81} +(-1.94862 + 3.37511i) q^{83} +(3.28325 - 5.68676i) q^{85} +(-3.12686 - 5.41587i) q^{87} +5.15537 q^{89} +21.4064 q^{91} +(-4.31459 - 7.47308i) q^{93} +(-3.84692 + 6.66305i) q^{95} +(-4.15807 + 7.20200i) q^{97} +(-1.46984 - 2.54583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−1.49766	−	2.59403i	−0.566063	−	0.980450i	−0.996950	−	0.0780439i	$-0.975133\pi$
$7$	−1.49766	−	2.59403i	−0.566063	−	0.980450i	0.430887	−	0.902406i	$-0.358201\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−1.46984	−	2.54583i	−0.443173	−	0.767598i	0.554750	−	0.832017i	$-0.312814\pi$
$11$	−1.46984	−	2.54583i	−0.443173	−	0.767598i	−0.997923	+	0.0644194i	$0.979480\pi$
$12$		0			0
$13$	−3.57330	+	6.18914i	−0.991055	+	1.71656i	−0.379952	+	0.925006i	$0.624060\pi$
$13$	−3.57330	+	6.18914i	−0.991055	+	1.71656i	−0.611103	+	0.791551i	$0.709274\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−3.28325	+	5.68676i	−0.796305	+	1.37924i	0.125701	+	0.992068i	$0.459882\pi$
$17$	−3.28325	+	5.68676i	−0.796305	+	1.37924i	−0.922007	+	0.387173i	$0.873451\pi$
$18$		0			0
$19$	3.84692	−	6.66305i	0.882543	−	1.52861i	0.0340391	−	0.999421i	$-0.489163\pi$
$19$	3.84692	−	6.66305i	0.882543	−	1.52861i	0.848504	−	0.529189i	$-0.177504\pi$
$20$		0			0
$21$	1.49766	+	2.59403i	0.326817	+	0.566063i
$22$		0			0
$23$	−0.513819	+	0.889960i	−0.107139	+	0.185570i	−0.914610	−	0.404337i	$-0.867502\pi$
$23$	−0.513819	+	0.889960i	−0.107139	+	0.185570i	0.807471	+	0.589907i	$0.200836\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.12686	+	5.41587i	0.580643	+	1.00570i	0.995403	+	0.0957719i	$0.0305319\pi$
$29$	3.12686	+	5.41587i	0.580643	+	1.00570i	−0.414761	+	0.909930i	$0.636135\pi$
$30$		0			0
$31$	4.31459	+	7.47308i	0.774923	+	1.34221i	0.934838	+	0.355075i	$0.115545\pi$
$31$	4.31459	+	7.47308i	0.774923	+	1.34221i	−0.159915	+	0.987131i	$0.551122\pi$
$32$		0			0
$33$	1.46984	+	2.54583i	0.255866	+	0.443173i
$34$		0			0
$35$	1.49766	+	2.59403i	0.253151	+	0.438470i
$36$		0			0
$37$	−3.14067	+	5.43981i	−0.516324	+	0.894299i	0.483497	+	0.875346i	$0.339367\pi$
$37$	−3.14067	+	5.43981i	−0.516324	+	0.894299i	−0.999820	+	0.0189527i	$0.993967\pi$
$38$		0			0
$39$	3.57330	−	6.18914i	0.572186	−	0.991055i
$40$		0			0
$41$	1.49016	+	2.58104i	0.232724	+	0.403090i	0.958609	−	0.284726i	$-0.0919027\pi$
$41$	1.49016	+	2.58104i	0.232724	+	0.403090i	−0.725885	+	0.687816i	$0.758569\pi$
$42$		0			0
$43$	0.784978			0.119708			0.0598540	−	0.998207i	$-0.480936\pi$
$43$	0.784978			0.119708			0.0598540	+	0.998207i	$0.480936\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−5.99272	−	10.3797i	−0.874127	−	1.51403i	−0.857689	−	0.514168i	$-0.828101\pi$
$47$	−5.99272	−	10.3797i	−0.874127	−	1.51403i	−0.0164379	−	0.999865i	$-0.505233\pi$
$48$		0			0
$49$	−0.985982	+	1.70777i	−0.140855	+	0.243967i
$50$		0			0
$51$	3.28325	−	5.68676i	0.459747	−	0.796305i
$52$		0			0
$53$	7.58069			1.04129			0.520644	−	0.853774i	$-0.325692\pi$
$53$	7.58069			1.04129			0.520644	+	0.853774i	$0.325692\pi$
$54$		0			0
$55$	1.46984	+	2.54583i	0.198193	+	0.343280i
$56$		0			0
$57$	−3.84692	+	6.66305i	−0.509536	+	0.882543i
$58$		0			0
$59$	−5.51489			−0.717978			−0.358989	−	0.933342i	$-0.616878\pi$
$59$	−5.51489			−0.717978			−0.358989	+	0.933342i	$0.616878\pi$
$60$		0			0
$61$	4.82170	−	8.35143i	0.617355	−	1.06929i	−0.372611	−	0.927988i	$-0.621537\pi$
$61$	4.82170	−	8.35143i	0.617355	−	1.06929i	0.989966	−	0.141303i	$-0.0451293\pi$
$62$		0			0
$63$	−1.49766	−	2.59403i	−0.188688	−	0.326817i
$64$		0			0
$65$	3.57330	−	6.18914i	0.443213	−	0.767668i
$66$		0			0
$67$	−1.44798	−	8.05626i	−0.176899	−	0.984229i
$67$	−1.44798	−	8.05626i	−0.176899	−	0.984229i
$68$		0			0
$69$	0.513819	−	0.889960i	0.0618565	−	0.107139i
$70$		0			0
$71$	−0.651030	−	1.12762i	−0.0772630	−	0.133823i	0.824805	−	0.565417i	$-0.191285\pi$
$71$	−0.651030	−	1.12762i	−0.0772630	−	0.133823i	−0.902068	+	0.431594i	$0.857951\pi$
$72$		0			0
$73$	2.78113	−	4.81706i	0.325507	−	0.563794i	−0.656108	−	0.754667i	$-0.727798\pi$
$73$	2.78113	−	4.81706i	0.325507	−	0.563794i	0.981615	+	0.190873i	$0.0611318\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−4.40264	+	7.62559i	−0.501727	+	0.869017i
$78$		0			0
$79$	−3.71649	−	6.43715i	−0.418138	−	0.724236i	0.577614	−	0.816310i	$-0.303984\pi$
$79$	−3.71649	−	6.43715i	−0.418138	−	0.724236i	−0.995752	+	0.0920738i	$0.970650\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−1.94862	+	3.37511i	−0.213889	+	0.370466i	−0.952928	−	0.303196i	$-0.901946\pi$
$83$	−1.94862	+	3.37511i	−0.213889	+	0.370466i	0.739040	+	0.673662i	$0.235280\pi$
$84$		0			0
$85$	3.28325	−	5.68676i	0.356119	−	0.616816i
$86$		0			0
$87$	−3.12686	−	5.41587i	−0.335234	−	0.580643i
$88$		0			0
$89$	5.15537			0.546468			0.273234	−	0.961948i	$-0.411907\pi$
$89$	5.15537			0.546468			0.273234	+	0.961948i	$0.411907\pi$
$90$		0			0
$91$	21.4064			2.24400
$92$		0			0
$93$	−4.31459	−	7.47308i	−0.447402	−	0.774923i
$94$		0			0
$95$	−3.84692	+	6.66305i	−0.394685	+	0.683615i
$96$		0			0
$97$	−4.15807	+	7.20200i	−0.422188	+	0.731252i	−0.996153	−	0.0876281i	$-0.972071\pi$
$97$	−4.15807	+	7.20200i	−0.422188	+	0.731252i	0.573965	+	0.818880i	$0.305405\pi$
$98$		0			0
$99$	−1.46984	−	2.54583i	−0.147724	−	0.255866i
$100$		0			0
$101$	−5.45906	−	9.45537i	−0.543197	−	0.940845i	−0.998718	−	0.0506198i	$-0.983880\pi$
$101$	−5.45906	−	9.45537i	−0.543197	−	0.940845i	0.455521	−	0.890225i	$-0.349453\pi$
$102$		0			0
$103$	2.81898	+	4.88262i	0.277763	+	0.481099i	0.970828	−	0.239775i	$-0.0770737\pi$
$103$	2.81898	+	4.88262i	0.277763	+	0.481099i	−0.693066	+	0.720874i	$0.743740\pi$
$104$		0			0
$105$	−1.49766	−	2.59403i	−0.146157	−	0.253151i
$106$		0			0
$107$	10.0622			0.972753			0.486376	−	0.873749i	$-0.338318\pi$
$107$	10.0622			0.972753			0.486376	+	0.873749i	$0.338318\pi$
$108$		0			0
$109$	0.219189			0.0209945			0.0104973	−	0.999945i	$-0.496659\pi$
$109$	0.219189			0.0209945			0.0104973	+	0.999945i	$0.496659\pi$
$110$		0			0
$111$	3.14067	−	5.43981i	0.298100	−	0.516324i
$112$		0			0
$113$	−7.08973	−	12.2798i	−0.666946	−	1.15518i	−0.978754	−	0.205039i	$-0.934268\pi$
$113$	−7.08973	−	12.2798i	−0.666946	−	1.15518i	0.311808	−	0.950145i	$-0.399066\pi$
$114$		0			0
$115$	0.513819	−	0.889960i	0.0479139	−	0.0829892i
$116$		0			0
$117$	−3.57330	+	6.18914i	−0.330352	+	0.572186i
$118$		0			0
$119$	19.6688			1.80304
$120$		0			0
$121$	1.17916	−	2.04236i	0.107196	−	0.185669i
$122$		0			0
$123$	−1.49016	−	2.58104i	−0.134363	−	0.232724i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	0.454280	+	0.786835i	0.0403108	+	0.0698203i	0.885477	−	0.464683i	$-0.153832\pi$
$127$	0.454280	+	0.786835i	0.0403108	+	0.0698203i	−0.845166	+	0.534504i	$0.820499\pi$
$128$		0			0
$129$	−0.784978			−0.0691134
$130$		0			0
$131$	1.83813			0.160598			0.0802991	−	0.996771i	$-0.474412\pi$
$131$	1.83813			0.160598			0.0802991	+	0.996771i	$0.474412\pi$
$132$		0			0
$133$	−23.0455			−1.99830
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	6.21469			0.530957			0.265478	−	0.964117i	$-0.414470\pi$
$137$	6.21469			0.530957			0.265478	+	0.964117i	$0.414470\pi$
$138$		0			0
$139$	−11.7136			−0.993531			−0.496765	−	0.867885i	$-0.665479\pi$
$139$	−11.7136			−0.993531			−0.496765	+	0.867885i	$0.665479\pi$
$140$		0			0
$141$	5.99272	+	10.3797i	0.504678	+	0.874127i
$142$		0			0
$143$	21.0087			1.75683
$144$		0			0
$145$	−3.12686	−	5.41587i	−0.259671	−	0.449764i
$146$		0			0
$147$	0.985982	−	1.70777i	0.0813224	−	0.140855i
$148$		0			0
$149$	−16.3964			−1.34324			−0.671622	−	0.740894i	$-0.734402\pi$
$149$	−16.3964			−1.34324			−0.671622	+	0.740894i	$0.734402\pi$
$150$		0			0
$151$	1.65858	−	2.87275i	0.134974	−	0.233781i	−0.790614	−	0.612315i	$-0.790238\pi$
$151$	1.65858	−	2.87275i	0.134974	−	0.233781i	0.925587	+	0.378534i	$0.123572\pi$
$152$		0			0
$153$	−3.28325	+	5.68676i	−0.265435	+	0.459747i
$154$		0			0
$155$	−4.31459	−	7.47308i	−0.346556	−	0.600253i
$156$		0			0
$157$	10.1802	−	17.6326i	0.812467	−	1.40723i	−0.0986660	−	0.995121i	$-0.531458\pi$
$157$	10.1802	−	17.6326i	0.812467	−	1.40723i	0.911133	−	0.412113i	$-0.135209\pi$
$158$		0			0
$159$	−7.58069			−0.601188
$160$		0			0
$161$	3.07811			0.242589
$162$		0			0
$163$	−2.61015	−	4.52091i	−0.204442	−	0.354105i	0.745512	−	0.666492i	$-0.232205\pi$
$163$	−2.61015	−	4.52091i	−0.204442	−	0.354105i	−0.949955	+	0.312387i	$0.898871\pi$
$164$		0			0
$165$	−1.46984	−	2.54583i	−0.114427	−	0.198193i
$166$		0			0
$167$	−4.48971	−	7.77641i	−0.347424	−	0.601757i	0.638367	−	0.769732i	$-0.279610\pi$
$167$	−4.48971	−	7.77641i	−0.347424	−	0.601757i	−0.985791	+	0.167976i	$0.946277\pi$
$168$		0			0
$169$	−19.0369	−	32.9729i	−1.46438	−	2.53638i
$170$		0			0
$171$	3.84692	−	6.66305i	0.294181	−	0.509536i
$172$		0			0
$173$	−7.78383	+	13.4820i	−0.591793	+	1.02502i	0.402197	+	0.915553i	$0.368247\pi$
$173$	−7.78383	+	13.4820i	−0.591793	+	1.02502i	−0.993991	+	0.109463i	$0.965087\pi$
$174$		0			0
$175$	−1.49766	−	2.59403i	−0.113213	−	0.196090i
$176$		0			0
$177$	5.51489			0.414525
$178$		0			0
$179$	14.0210			1.04798			0.523991	−	0.851724i	$-0.324443\pi$
$179$	14.0210			1.04798			0.523991	+	0.851724i	$0.324443\pi$
$180$		0			0
$181$	4.45563	+	7.71738i	0.331184	+	0.573628i	0.982744	−	0.184969i	$-0.0592184\pi$
$181$	4.45563	+	7.71738i	0.331184	+	0.573628i	−0.651560	+	0.758597i	$0.725885\pi$
$182$		0			0
$183$	−4.82170	+	8.35143i	−0.356430	+	0.617355i
$184$		0			0
$185$	3.14067	−	5.43981i	0.230907	−	0.399943i
$186$		0			0
$187$	19.3034			1.41160
$188$		0			0
$189$	1.49766	+	2.59403i	0.108939	+	0.188688i
$190$		0			0
$191$	−8.18155	+	14.1709i	−0.591996	+	1.02537i	0.401967	+	0.915654i	$0.368327\pi$
$191$	−8.18155	+	14.1709i	−0.591996	+	1.02537i	−0.993963	+	0.109713i	$0.965007\pi$
$192$		0			0
$193$	20.7375			1.49272			0.746360	−	0.665542i	$-0.231800\pi$
$193$	20.7375			1.49272			0.746360	+	0.665542i	$0.231800\pi$
$194$		0			0
$195$	−3.57330	+	6.18914i	−0.255889	+	0.443213i
$196$		0			0
$197$	−5.61403	−	9.72378i	−0.399983	−	0.692791i	0.593740	−	0.804657i	$-0.297651\pi$
$197$	−5.61403	−	9.72378i	−0.399983	−	0.692791i	−0.993723	+	0.111866i	$0.964317\pi$
$198$		0			0
$199$	−3.11350	+	5.39274i	−0.220710	+	0.382281i	−0.955024	−	0.296529i	$-0.904171\pi$
$199$	−3.11350	+	5.39274i	−0.220710	+	0.382281i	0.734314	+	0.678810i	$0.237504\pi$
$200$		0			0
$201$	1.44798	+	8.05626i	0.102133	+	0.568245i
$202$		0			0
$203$	9.36594	−	16.2223i	0.657360	−	1.13858i
$204$		0			0
$205$	−1.49016	−	2.58104i	−0.104077	−	0.180267i
$206$		0			0
$207$	−0.513819	+	0.889960i	−0.0357129	+	0.0618565i
$208$		0			0
$209$	−22.6174			−1.56448
$210$		0			0
$211$	11.2090	−	19.4145i	0.771657	−	1.33655i	−0.164998	−	0.986294i	$-0.552762\pi$
$211$	11.2090	−	19.4145i	0.771657	−	1.33655i	0.936655	−	0.350255i	$-0.113905\pi$
$212$		0			0
$213$	0.651030	+	1.12762i	0.0446078	+	0.0772630i
$214$		0			0
$215$	−0.784978			−0.0535350
$216$		0			0
$217$	12.9236	−	22.3843i	0.877310	−	1.51955i
$218$		0			0
$219$	−2.78113	+	4.81706i	−0.187931	+	0.325507i
$220$		0			0
$221$	−23.4641	−	40.6410i	−1.57836	−	2.73381i
$222$		0			0
$223$	−14.3687			−0.962198			−0.481099	−	0.876666i	$-0.659762\pi$
$223$	−14.3687			−0.962198			−0.481099	+	0.876666i	$0.659762\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−6.12489	−	10.6086i	−0.406524	−	0.704119i	0.587974	−	0.808880i	$-0.299926\pi$
$227$	−6.12489	−	10.6086i	−0.406524	−	0.704119i	−0.994497	+	0.104760i	$0.966592\pi$
$228$		0			0
$229$	11.8067	−	20.4497i	0.780206	−	1.35136i	−0.151616	−	0.988439i	$-0.548448\pi$
$229$	11.8067	−	20.4497i	0.780206	−	1.35136i	0.931822	−	0.362916i	$-0.118219\pi$
$230$		0			0
$231$	4.40264	−	7.62559i	0.289672	−	0.501727i
$232$		0			0
$233$	8.78786	+	15.2210i	0.575712	+	0.997162i	0.995964	+	0.0897546i	$0.0286083\pi$
$233$	8.78786	+	15.2210i	0.575712	+	0.997162i	−0.420252	+	0.907407i	$0.638058\pi$
$234$		0			0
$235$	5.99272	+	10.3797i	0.390922	+	0.677096i
$236$		0			0
$237$	3.71649	+	6.43715i	0.241412	+	0.418138i
$238$		0			0
$239$	4.95526	+	8.58276i	0.320529	+	0.555173i	0.980597	−	0.196033i	$-0.0628060\pi$
$239$	4.95526	+	8.58276i	0.320529	+	0.555173i	−0.660068	+	0.751206i	$0.729473\pi$
$240$		0			0
$241$	30.3488			1.95494			0.977469	−	0.211077i	$-0.0676970\pi$
$241$	30.3488			1.95494			0.977469	+	0.211077i	$0.0676970\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	0.985982	−	1.70777i	0.0629921	−	0.109105i
$246$		0			0
$247$	27.4924	+	47.6182i	1.74930	+	3.02987i
$248$		0			0
$249$	1.94862	−	3.37511i	0.123489	−	0.213889i
$250$		0			0
$251$	−3.75551	+	6.50474i	−0.237046	+	0.410575i	−0.959865	−	0.280462i	$-0.909512\pi$
$251$	−3.75551	+	6.50474i	−0.237046	+	0.410575i	0.722819	+	0.691037i	$0.242846\pi$
$252$		0			0
$253$	3.02092			0.189924
$254$		0			0
$255$	−3.28325	+	5.68676i	−0.205605	+	0.356119i
$256$		0			0
$257$	10.0928	+	17.4812i	0.629569	+	1.09045i	0.987638	+	0.156751i	$0.0501019\pi$
$257$	10.0928	+	17.4812i	0.629569	+	1.09045i	−0.358069	+	0.933695i	$0.616565\pi$
$258$		0			0
$259$	18.8147			1.16909
$260$		0			0
$261$	3.12686	+	5.41587i	0.193548	+	0.335234i
$262$		0			0
$263$	19.2765			1.18864			0.594321	−	0.804228i	$-0.297421\pi$
$263$	19.2765			1.18864			0.594321	+	0.804228i	$0.297421\pi$
$264$		0			0
$265$	−7.58069			−0.465678
$266$		0			0
$267$	−5.15537			−0.315503
$268$		0			0
$269$	19.4709			1.18716			0.593580	−	0.804775i	$-0.297714\pi$
$269$	19.4709			1.18716			0.593580	+	0.804775i	$0.297714\pi$
$270$		0			0
$271$	−0.675765			−0.0410498			−0.0205249	−	0.999789i	$-0.506534\pi$
$271$	−0.675765			−0.0410498			−0.0205249	+	0.999789i	$0.506534\pi$
$272$		0			0
$273$	−21.4064			−1.29557
$274$		0			0
$275$	−1.46984	−	2.54583i	−0.0886345	−	0.153520i
$276$		0			0
$277$	18.6094			1.11813			0.559065	−	0.829124i	$-0.311160\pi$
$277$	18.6094			1.11813			0.559065	+	0.829124i	$0.311160\pi$
$278$		0			0
$279$	4.31459	+	7.47308i	0.258308	+	0.447402i
$280$		0			0
$281$	2.44393	−	4.23302i	0.145793	−	0.252521i	−0.783876	−	0.620918i	$-0.786760\pi$
$281$	2.44393	−	4.23302i	0.145793	−	0.252521i	0.929668	+	0.368397i	$0.120093\pi$
$282$		0			0
$283$	25.5043			1.51607			0.758036	−	0.652213i	$-0.226159\pi$
$283$	25.5043			1.51607			0.758036	+	0.652213i	$0.226159\pi$
$284$		0			0
$285$	3.84692	−	6.66305i	0.227872	−	0.394685i
$286$		0			0
$287$	4.46352	−	7.73104i	0.263473	−	0.456349i
$288$		0			0
$289$	−13.0595	−	22.6197i	−0.768205	−	1.33057i
$290$		0			0
$291$	4.15807	−	7.20200i	0.243751	−	0.422188i
$292$		0			0
$293$	−24.2818			−1.41856			−0.709280	−	0.704927i	$-0.750980\pi$
$293$	−24.2818			−1.41856			−0.709280	+	0.704927i	$0.750980\pi$
$294$		0			0
$295$	5.51489			0.321089
$296$		0			0
$297$	1.46984	+	2.54583i	0.0852886	+	0.147724i
$298$		0			0
$299$	−3.67206	−	6.36019i	−0.212361	−	0.367819i
$300$		0			0
$301$	−1.17563	−	2.03625i	−0.0677622	−	0.117368i
$302$		0			0
$303$	5.45906	+	9.45537i	0.313615	+	0.543197i
$304$		0			0
$305$	−4.82170	+	8.35143i	−0.276090	+	0.478201i
$306$		0			0
$307$	−2.90950	+	5.03940i	−0.166054	+	0.287614i	−0.937029	−	0.349251i	$-0.886436\pi$
$307$	−2.90950	+	5.03940i	−0.166054	+	0.287614i	0.770975	+	0.636865i	$0.219769\pi$
$308$		0			0
$309$	−2.81898	−	4.88262i	−0.160366	−	0.277763i
$310$		0			0
$311$	5.11660			0.290136			0.145068	−	0.989422i	$-0.453660\pi$
$311$	5.11660			0.290136			0.145068	+	0.989422i	$0.453660\pi$
$312$		0			0
$313$	27.6070			1.56044			0.780221	−	0.625504i	$-0.215107\pi$
$313$	27.6070			1.56044			0.780221	+	0.625504i	$0.215107\pi$
$314$		0			0
$315$	1.49766	+	2.59403i	0.0843837	+	0.146157i
$316$		0			0
$317$	9.58430	−	16.6005i	0.538308	−	0.932377i	−0.460687	−	0.887562i	$-0.652397\pi$
$317$	9.58430	−	16.6005i	0.538308	−	0.932377i	0.998995	−	0.0448142i	$-0.0142696\pi$
$318$		0			0
$319$	9.19194	−	15.9209i	0.514650	−	0.891400i
$320$		0			0
$321$	−10.0622			−0.561619
$322$		0			0
$323$	25.2608	+	43.7530i	1.40555	+	2.43448i
$324$		0			0
$325$	−3.57330	+	6.18914i	−0.198211	+	0.343311i
$326$		0			0
$327$	−0.219189			−0.0121212
$328$		0			0
$329$	−17.9501	+	31.0905i	−0.989622	+	1.71408i
$330$		0			0
$331$	−9.39051	−	16.2648i	−0.516149	−	0.893996i	−0.999824	−	0.0187487i	$-0.994032\pi$
$331$	−9.39051	−	16.2648i	−0.516149	−	0.893996i	0.483675	−	0.875248i	$-0.339302\pi$
$332$		0			0
$333$	−3.14067	+	5.43981i	−0.172108	+	0.298100i
$334$		0			0
$335$	1.44798	+	8.05626i	0.0791115	+	0.440161i
$336$		0			0
$337$	15.5934	−	27.0086i	0.849427	−	1.47125i	−0.0322936	−	0.999478i	$-0.510281\pi$
$337$	15.5934	−	27.0086i	0.849427	−	1.47125i	0.881721	−	0.471772i	$-0.156385\pi$
$338$		0			0
$339$	7.08973	+	12.2798i	0.385062	+	0.666946i
$340$		0			0
$341$	12.6835	−	21.9684i	0.686849	−	1.18966i
$342$		0			0
$343$	−15.0606			−0.813196
$344$		0			0
$345$	−0.513819	+	0.889960i	−0.0276631	+	0.0479139i
$346$		0			0
$347$	−11.3209	−	19.6084i	−0.607740	−	1.05264i	−0.991612	−	0.129250i	$-0.958743\pi$
$347$	−11.3209	−	19.6084i	−0.607740	−	1.05264i	0.383872	−	0.923386i	$-0.374590\pi$
$348$		0			0
$349$	−12.5308			−0.670760			−0.335380	−	0.942083i	$-0.608865\pi$
$349$	−12.5308			−0.670760			−0.335380	+	0.942083i	$0.608865\pi$
$350$		0			0
$351$	3.57330	−	6.18914i	0.190729	−	0.330352i
$352$		0			0
$353$	8.07528	−	13.9868i	0.429804	−	0.744442i	−0.567052	−	0.823682i	$-0.691916\pi$
$353$	8.07528	−	13.9868i	0.429804	−	0.744442i	0.996856	+	0.0792404i	$0.0252495\pi$
$354$		0			0
$355$	0.651030	+	1.12762i	0.0345531	+	0.0598477i
$356$		0			0
$357$	−19.6688			−1.04098
$358$		0			0
$359$	2.78308			0.146886			0.0734428	−	0.997299i	$-0.476601\pi$
$359$	2.78308			0.146886			0.0734428	+	0.997299i	$0.476601\pi$
$360$		0			0
$361$	−20.0975	−	34.8099i	−1.05776	−	1.83210i
$362$		0			0
$363$	−1.17916	+	2.04236i	−0.0618896	+	0.107196i
$364$		0			0
$365$	−2.78113	+	4.81706i	−0.145571	+	0.252136i
$366$		0			0
$367$	4.64383	+	8.04335i	0.242406	+	0.419860i	0.961399	−	0.275158i	$-0.0887300\pi$
$367$	4.64383	+	8.04335i	0.242406	+	0.419860i	−0.718993	+	0.695017i	$0.755397\pi$
$368$		0			0
$369$	1.49016	+	2.58104i	0.0775747	+	0.134363i
$370$		0			0
$371$	−11.3533	−	19.6645i	−0.589434	−	1.02093i
$372$		0			0
$373$	4.11600	+	7.12912i	0.213118	+	0.369132i	0.952689	−	0.303947i	$-0.0983046\pi$
$373$	4.11600	+	7.12912i	0.213118	+	0.369132i	−0.739570	+	0.673079i	$0.764971\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−44.6928			−2.30179
$378$		0			0
$379$	17.6893	−	30.6387i	0.908636	−	1.57380i	0.0926759	−	0.995696i	$-0.470458\pi$
$379$	17.6893	−	30.6387i	0.908636	−	1.57380i	0.815960	−	0.578108i	$-0.196209\pi$
$380$		0			0
$381$	−0.454280	−	0.786835i	−0.0232734	−	0.0403108i
$382$		0			0
$383$	−6.09946	+	10.5646i	−0.311668	+	0.539825i	−0.978724	−	0.205183i	$-0.934221\pi$
$383$	−6.09946	+	10.5646i	−0.311668	+	0.539825i	0.667056	+	0.745008i	$0.267554\pi$
$384$		0			0
$385$	4.40264	−	7.62559i	0.224379	−	0.388636i
$386$		0			0
$387$	0.784978			0.0399027
$388$		0			0
$389$	−6.48532	+	11.2329i	−0.328819	+	0.569531i	−0.982278	−	0.187431i	$-0.939984\pi$
$389$	−6.48532	+	11.2329i	−0.328819	+	0.569531i	0.653459	+	0.756962i	$0.273317\pi$
$390$		0			0
$391$	−3.37399	−	5.84393i	−0.170630	−	0.295540i
$392$		0			0
$393$	−1.83813			−0.0927214
$394$		0			0
$395$	3.71649	+	6.43715i	0.186997	+	0.323888i
$396$		0			0
$397$	5.55284			0.278689			0.139344	−	0.990244i	$-0.455500\pi$
$397$	5.55284			0.278689			0.139344	+	0.990244i	$0.455500\pi$
$398$		0			0
$399$	23.0455			1.15372
$400$		0			0
$401$	−23.3495			−1.16602			−0.583008	−	0.812466i	$-0.698125\pi$
$401$	−23.3495			−1.16602			−0.583008	+	0.812466i	$0.698125\pi$
$402$		0			0
$403$	−61.6692			−3.07196
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	18.4651			0.915282
$408$		0			0
$409$	3.85045	+	6.66917i	0.190392	+	0.329769i	0.945380	−	0.325969i	$-0.105691\pi$
$409$	3.85045	+	6.66917i	0.190392	+	0.329769i	−0.754988	+	0.655739i	$0.772357\pi$
$410$		0			0
$411$	−6.21469			−0.306548
$412$		0			0
$413$	8.25944	+	14.3058i	0.406421	+	0.703941i
$414$		0			0
$415$	1.94862	−	3.37511i	0.0956539	−	0.165677i
$416$		0			0
$417$	11.7136			0.573615
$418$		0			0
$419$	−17.6945	+	30.6478i	−0.864434	+	1.49724i	0.00317339	+	0.999995i	$0.498990\pi$
$419$	−17.6945	+	30.6478i	−0.864434	+	1.49724i	−0.867608	+	0.497249i	$0.834343\pi$
$420$		0			0
$421$	1.68108	−	2.91171i	0.0819306	−	0.141908i	−0.822149	−	0.569273i	$-0.807225\pi$
$421$	1.68108	−	2.91171i	0.0819306	−	0.141908i	0.904079	+	0.427365i	$0.140558\pi$
$422$		0			0
$423$	−5.99272	−	10.3797i	−0.291376	−	0.504678i
$424$		0			0
$425$	−3.28325	+	5.68676i	−0.159261	+	0.275848i
$426$		0			0
$427$	−28.8851			−1.39785
$428$		0			0
$429$	−21.0087			−1.01431
$430$		0			0
$431$	6.73959	+	11.6733i	0.324635	+	0.562284i	0.981438	−	0.191778i	$-0.0614253\pi$
$431$	6.73959	+	11.6733i	0.324635	+	0.562284i	−0.656804	+	0.754062i	$0.728092\pi$
$432$		0			0
$433$	14.7647	+	25.5732i	0.709546	+	1.22897i	0.965026	+	0.262155i	$0.0844331\pi$
$433$	14.7647	+	25.5732i	0.709546	+	1.22897i	−0.255480	+	0.966814i	$0.582234\pi$
$434$		0			0
$435$	3.12686	+	5.41587i	0.149921	+	0.259671i
$436$		0			0
$437$	3.95324	+	6.84721i	0.189109	+	0.327546i
$438$		0			0
$439$	−2.40684	+	4.16877i	−0.114872	+	0.198965i	−0.917729	−	0.397208i	$-0.869979\pi$
$439$	−2.40684	+	4.16877i	−0.114872	+	0.198965i	0.802856	+	0.596172i	$0.203313\pi$
$440$		0			0
$441$	−0.985982	+	1.70777i	−0.0469515	+	0.0813224i
$442$		0			0
$443$	−8.61872	−	14.9281i	−0.409488	−	0.709254i	0.585345	−	0.810785i	$-0.300959\pi$
$443$	−8.61872	−	14.9281i	−0.409488	−	0.709254i	−0.994832	+	0.101531i	$0.967626\pi$
$444$		0			0
$445$	−5.15537			−0.244388
$446$		0			0
$447$	16.3964			0.775522
$448$		0			0
$449$	−0.844831	−	1.46329i	−0.0398701	−	0.0690570i	0.845402	−	0.534131i	$-0.179361\pi$
$449$	−0.844831	−	1.46329i	−0.0398701	−	0.0690570i	−0.885272	+	0.465074i	$0.846028\pi$
$450$		0			0
$451$	4.38059	−	7.58740i	0.206274	−	0.357277i
$452$		0			0
$453$	−1.65858	+	2.87275i	−0.0779271	+	0.134974i
$454$		0			0
$455$	−21.4064			−1.00355
$456$		0			0
$457$	3.07653	+	5.32871i	0.143914	+	0.249267i	0.928967	−	0.370162i	$-0.120698\pi$
$457$	3.07653	+	5.32871i	0.143914	+	0.249267i	−0.785053	+	0.619428i	$0.787364\pi$
$458$		0			0
$459$	3.28325	−	5.68676i	0.153249	−	0.265435i
$460$		0			0
$461$	32.3487			1.50663			0.753315	−	0.657660i	$-0.228454\pi$
$461$	32.3487			1.50663			0.753315	+	0.657660i	$0.228454\pi$
$462$		0			0
$463$	−3.48275	+	6.03229i	−0.161857	+	0.280344i	−0.935535	−	0.353235i	$-0.885082\pi$
$463$	−3.48275	+	6.03229i	−0.161857	+	0.280344i	0.773678	+	0.633579i	$0.218415\pi$
$464$		0			0
$465$	4.31459	+	7.47308i	0.200084	+	0.346556i
$466$		0			0
$467$	9.88909	−	17.1284i	0.457612	−	0.792608i	−0.541222	−	0.840880i	$-0.682038\pi$
$467$	9.88909	−	17.1284i	0.457612	−	0.792608i	0.998834	+	0.0482720i	$0.0153714\pi$
$468$		0			0
$469$	−18.7296	+	15.8216i	−0.864851	+	0.730576i
$470$		0			0
$471$	−10.1802	+	17.6326i	−0.469078	+	0.812467i
$472$		0			0
$473$	−1.15379	−	1.99842i	−0.0530513	−	0.0918875i
$474$		0			0
$475$	3.84692	−	6.66305i	0.176509	−	0.305722i
$476$		0			0
$477$	7.58069			0.347096
$478$		0			0
$479$	1.70297	−	2.94964i	0.0778109	−	0.134772i	−0.824494	−	0.565870i	$-0.808540\pi$
$479$	1.70297	−	2.94964i	0.0778109	−	0.134772i	0.902305	+	0.431098i	$0.141874\pi$
$480$		0			0
$481$	−22.4451	−	38.8761i	−1.02341	−	1.77260i
$482$		0			0
$483$	−3.07811			−0.140059
$484$		0			0
$485$	4.15807	−	7.20200i	0.188808	−	0.327026i
$486$		0			0
$487$	10.8300	−	18.7581i	0.490754	−	0.850011i	−0.509189	−	0.860655i	$-0.670055\pi$
$487$	10.8300	−	18.7581i	0.490754	−	0.850011i	0.999943	+	0.0106436i	$0.00338803\pi$
$488$		0			0
$489$	2.61015	+	4.52091i	0.118035	+	0.204442i
$490$		0			0
$491$	6.64727			0.299987			0.149993	−	0.988687i	$-0.452075\pi$
$491$	6.64727			0.299987			0.149993	+	0.988687i	$0.452075\pi$
$492$		0			0
$493$	−41.0650			−1.84948
$494$		0			0
$495$	1.46984	+	2.54583i	0.0660643	+	0.114427i
$496$		0			0
$497$	−1.95004	+	3.37758i	−0.0874714	+	0.151505i
$498$		0			0
$499$	−8.04499	+	13.9343i	−0.360143	+	0.623786i	−0.987984	−	0.154555i	$-0.950606\pi$
$499$	−8.04499	+	13.9343i	−0.360143	+	0.623786i	0.627841	+	0.778342i	$0.283939\pi$
$500$		0			0
$501$	4.48971	+	7.77641i	0.200586	+	0.347424i
$502$		0			0
$503$	13.0840	+	22.6621i	0.583385	+	1.01045i	0.995075	+	0.0991285i	$0.0316055\pi$
$503$	13.0840	+	22.6621i	0.583385	+	1.01045i	−0.411690	+	0.911324i	$0.635061\pi$
$504$		0			0
$505$	5.45906	+	9.45537i	0.242925	+	0.420759i
$506$		0			0
$507$	19.0369	+	32.9729i	0.845460	+	1.46438i
$508$		0			0
$509$	37.1020			1.64452			0.822258	−	0.569116i	$-0.192714\pi$
$509$	37.1020			1.64452			0.822258	+	0.569116i	$0.192714\pi$
$510$		0			0
$511$	−16.6608			−0.737029
$512$		0			0
$513$	−3.84692	+	6.66305i	−0.169845	+	0.294181i
$514$		0			0
$515$	−2.81898	−	4.88262i	−0.124219	−	0.215154i
$516$		0			0
$517$	−17.6166	+	30.5129i	−0.774779	+	1.34196i
$518$		0			0
$519$	7.78383	−	13.4820i	0.341672	−	0.591793i
$520$		0			0
$521$	−34.8102			−1.52506			−0.762532	−	0.646950i	$-0.776044\pi$
$521$	−34.8102			−1.52506			−0.762532	+	0.646950i	$0.776044\pi$
$522$		0			0
$523$	17.7718	−	30.7816i	0.777106	−	1.34599i	−0.156498	−	0.987678i	$-0.550020\pi$
$523$	17.7718	−	30.7816i	0.777106	−	1.34599i	0.933603	−	0.358308i	$-0.116646\pi$
$524$		0			0
$525$	1.49766	+	2.59403i	0.0653633	+	0.113213i
$526$		0			0
$527$	−56.6635			−2.46830
$528$		0			0
$529$	10.9720	+	19.0040i	0.477043	+	0.826262i
$530$		0			0
$531$	−5.51489			−0.239326
$532$		0			0
$533$	−21.2992			−0.922570
$534$		0			0
$535$	−10.0622			−0.435028
$536$		0			0
$537$	−14.0210			−0.605053
$538$		0			0
$539$	5.79693			0.249691
$540$		0			0
$541$	9.68682			0.416469			0.208234	−	0.978079i	$-0.433228\pi$
$541$	9.68682			0.416469			0.208234	+	0.978079i	$0.433228\pi$
$542$		0			0
$543$	−4.45563	−	7.71738i	−0.191209	−	0.331184i
$544$		0			0
$545$	−0.219189			−0.00938903
$546$		0			0
$547$	−14.6787	−	25.4243i	−0.627617	−	1.08706i	−0.988029	−	0.154271i	$-0.950697\pi$
$547$	−14.6787	−	25.4243i	−0.627617	−	1.08706i	0.360411	−	0.932793i	$-0.382636\pi$
$548$		0			0
$549$	4.82170	−	8.35143i	0.205785	−	0.356430i
$550$		0			0
$551$	48.1150			2.04977
$552$		0			0
$553$	−11.1321	+	19.2813i	−0.473385	+	0.819926i
$554$		0			0
$555$	−3.14067	+	5.43981i	−0.133314	+	0.230907i
$556$		0			0
$557$	11.7583	+	20.3660i	0.498216	+	0.862935i	0.999998	−	0.00205914i	$-0.000655446\pi$
$557$	11.7583	+	20.3660i	0.498216	+	0.862935i	−0.501782	+	0.864994i	$0.667322\pi$
$558$		0			0
$559$	−2.80496	+	4.85833i	−0.118637	+	0.205486i
$560$		0			0
$561$	−19.3034			−0.814990
$562$		0			0
$563$	−12.3840			−0.521924			−0.260962	−	0.965349i	$-0.584040\pi$
$563$	−12.3840			−0.521924			−0.260962	+	0.965349i	$0.584040\pi$
$564$		0			0
$565$	7.08973	+	12.2798i	0.298267	+	0.516614i
$566$		0			0
$567$	−1.49766	−	2.59403i	−0.0628959	−	0.108939i
$568$		0			0
$569$	12.7848	+	22.1440i	0.535968	+	0.928324i	0.999116	+	0.0420426i	$0.0133865\pi$
$569$	12.7848	+	22.1440i	0.535968	+	0.928324i	−0.463148	+	0.886281i	$0.653280\pi$
$570$		0			0
$571$	−15.5816	−	26.9881i	−0.652070	−	1.12942i	−0.982620	−	0.185630i	$-0.940567\pi$
$571$	−15.5816	−	26.9881i	−0.652070	−	1.12942i	0.330550	−	0.943789i	$-0.392766\pi$
$572$		0			0
$573$	8.18155	−	14.1709i	0.341789	−	0.591996i
$574$		0			0
$575$	−0.513819	+	0.889960i	−0.0214277	+	0.0371139i
$576$		0			0
$577$	−11.8309	−	20.4917i	−0.492527	−	0.853083i	0.507436	−	0.861690i	$-0.330594\pi$
$577$	−11.8309	−	20.4917i	−0.492527	−	0.853083i	−0.999963	+	0.00860718i	$0.997260\pi$
$578$		0			0
$579$	−20.7375			−0.861822
$580$		0			0
$581$	11.6735			0.484298
$582$		0			0
$583$	−11.1424	−	19.2992i	−0.461470	−	0.799290i
$584$		0			0
$585$	3.57330	−	6.18914i	0.147738	−	0.255889i
$586$		0			0
$587$	−1.09705	+	1.90014i	−0.0452800	+	0.0784273i	−0.887777	−	0.460273i	$-0.847751\pi$
$587$	−1.09705	+	1.90014i	−0.0452800	+	0.0784273i	0.842497	+	0.538701i	$0.181085\pi$
$588$		0			0
$589$	66.3914			2.73561
$590$		0			0
$591$	5.61403	+	9.72378i	0.230930	+	0.399983i
$592$		0			0
$593$	−18.8865	+	32.7124i	−0.775575	+	1.34334i	0.158895	+	0.987295i	$0.449207\pi$
$593$	−18.8865	+	32.7124i	−0.775575	+	1.34334i	−0.934471	+	0.356040i	$0.884127\pi$
$594$		0			0
$595$	−19.6688			−0.806342
$596$		0			0
$597$	3.11350	−	5.39274i	0.127427	−	0.220710i
$598$		0			0
$599$	8.79157	+	15.2274i	0.359214	+	0.622176i	0.987830	−	0.155539i	$-0.0497116\pi$
$599$	8.79157	+	15.2274i	0.359214	+	0.622176i	−0.628616	+	0.777716i	$0.716378\pi$
$600$		0			0
$601$	9.20498	−	15.9435i	0.375479	−	0.650348i	−0.614920	−	0.788590i	$-0.710812\pi$
$601$	9.20498	−	15.9435i	0.375479	−	0.650348i	0.990399	+	0.138241i	$0.0441450\pi$
$602$		0			0
$603$	−1.44798	−	8.05626i	−0.0589662	−	0.328076i
$604$		0			0
$605$	−1.17916	+	2.04236i	−0.0479395	+	0.0830337i
$606$		0			0
$607$	−11.0393	−	19.1207i	−0.448073	−	0.776085i	0.550188	−	0.835041i	$-0.314556\pi$
$607$	−11.0393	−	19.1207i	−0.448073	−	0.776085i	−0.998261	+	0.0589561i	$0.981223\pi$
$608$		0			0
$609$	−9.36594	+	16.2223i	−0.379527	+	0.657360i
$610$		0			0
$611$	85.6551			3.46523
$612$		0			0
$613$	−7.55978	+	13.0939i	−0.305337	+	0.528859i	−0.977336	−	0.211693i	$-0.932102\pi$
$613$	−7.55978	+	13.0939i	−0.305337	+	0.528859i	0.671999	+	0.740552i	$0.265436\pi$
$614$		0			0
$615$	1.49016	+	2.58104i	0.0600891	+	0.104077i
$616$		0			0
$617$	25.7286			1.03579			0.517897	−	0.855443i	$-0.326715\pi$
$617$	25.7286			1.03579			0.517897	+	0.855443i	$0.326715\pi$
$618$		0			0
$619$	−6.27297	+	10.8651i	−0.252132	+	0.436706i	−0.964113	−	0.265494i	$-0.914465\pi$
$619$	−6.27297	+	10.8651i	−0.252132	+	0.436706i	0.711980	+	0.702199i	$0.247798\pi$
$620$		0			0
$621$	0.513819	−	0.889960i	0.0206188	−	0.0357129i
$622$		0			0
$623$	−7.72100	−	13.3732i	−0.309335	−	0.535784i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	22.6174			0.903251
$628$		0			0
$629$	−20.6232	−	35.7205i	−0.822303	−	1.42427i
$630$		0			0
$631$	4.61594	−	7.99505i	0.183758	−	0.318278i	−0.759399	−	0.650625i	$-0.774507\pi$
$631$	4.61594	−	7.99505i	0.183758	−	0.318278i	0.943157	+	0.332347i	$0.107840\pi$
$632$		0			0
$633$	−11.2090	+	19.4145i	−0.445516	+	0.771657i
$634$		0			0
$635$	−0.454280	−	0.786835i	−0.0180275	−	0.0312246i
$636$		0			0
$637$	−7.04641	−	12.2047i	−0.279189	−	0.483570i
$638$		0			0
$639$	−0.651030	−	1.12762i	−0.0257543	−	0.0446078i
$640$		0			0
$641$	14.2844	+	24.7413i	0.564199	+	0.977222i	0.997124	+	0.0757916i	$0.0241484\pi$
$641$	14.2844	+	24.7413i	0.564199	+	0.977222i	−0.432924	+	0.901430i	$0.642518\pi$
$642$		0			0
$643$	1.45267			0.0572876			0.0286438	−	0.999590i	$-0.490881\pi$
$643$	1.45267			0.0572876			0.0286438	+	0.999590i	$0.490881\pi$
$644$		0			0
$645$	0.784978			0.0309085
$646$		0			0
$647$	12.1601	−	21.0619i	0.478062	−	0.828027i	−0.521622	−	0.853177i	$-0.674673\pi$
$647$	12.1601	−	21.0619i	0.478062	−	0.828027i	0.999684	+	0.0251497i	$0.00800623\pi$
$648$		0			0
$649$	8.10599	+	14.0400i	0.318188	+	0.551118i
$650$		0			0
$651$	−12.9236	+	22.3843i	−0.506515	+	0.877310i
$652$		0			0
$653$	−13.9142	+	24.1001i	−0.544505	+	0.943111i	0.454133	+	0.890934i	$0.349949\pi$
$653$	−13.9142	+	24.1001i	−0.544505	+	0.943111i	−0.998638	+	0.0521766i	$0.983384\pi$
$654$		0			0
$655$	−1.83813			−0.0718217
$656$		0			0
$657$	2.78113	−	4.81706i	0.108502	−	0.187931i
$658$		0			0
$659$	1.80079	+	3.11906i	0.0701487	+	0.121501i	0.898966	−	0.438018i	$-0.144319\pi$
$659$	1.80079	+	3.11906i	0.0701487	+	0.121501i	−0.828818	+	0.559519i	$0.810986\pi$
$660$		0			0
$661$	22.3328			0.868647			0.434323	−	0.900757i	$-0.356988\pi$
$661$	22.3328			0.868647			0.434323	+	0.900757i	$0.356988\pi$
$662$		0			0
$663$	23.4641	+	40.6410i	0.911269	+	1.57836i
$664$		0			0
$665$	23.0455			0.893667
$666$		0			0
$667$	−6.42655			−0.248837
$668$		0			0
$669$	14.3687			0.555525
$670$		0			0
$671$	−28.3485			−1.09438
$672$		0			0
$673$	−39.5053			−1.52282			−0.761408	−	0.648273i	$-0.775492\pi$
$673$	−39.5053			−1.52282			−0.761408	+	0.648273i	$0.775492\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−22.4510	−	38.8864i	−0.862864	−	1.49452i	−0.869153	−	0.494544i	$-0.835335\pi$
$677$	−22.4510	−	38.8864i	−0.862864	−	1.49452i	0.00628870	−	0.999980i	$-0.497998\pi$
$678$		0			0
$679$	24.9096			0.955941
$680$		0			0
$681$	6.12489	+	10.6086i	0.234706	+	0.406524i
$682$		0			0
$683$	19.4858	−	33.7504i	0.745604	−	1.29142i	−0.204307	−	0.978907i	$-0.565494\pi$
$683$	19.4858	−	33.7504i	0.745604	−	1.29142i	0.949912	−	0.312518i	$-0.101172\pi$
$684$		0			0
$685$	−6.21469			−0.237451
$686$		0			0
$687$	−11.8067	+	20.4497i	−0.450452	+	0.780206i
$688$		0			0
$689$	−27.0881	+	46.9179i	−1.03197	+	1.78743i
$690$		0			0
$691$	13.2741	+	22.9915i	0.504972	+	0.874638i	0.999983	+	0.00575104i	$0.00183062\pi$
$691$	13.2741	+	22.9915i	0.504972	+	0.874638i	−0.495011	+	0.868887i	$0.664836\pi$
$692$		0			0
$693$	−4.40264	+	7.62559i	−0.167242	+	0.289672i
$694$		0			0
$695$	11.7136			0.444321
$696$		0			0
$697$	−19.5703			−0.741278
$698$		0			0
$699$	−8.78786	−	15.2210i	−0.332387	−	0.575712i
$700$		0			0
$701$	0.0181189	+	0.0313829i	0.000684343	+	0.00118532i	0.866367	−	0.499407i	$-0.166449\pi$
$701$	0.0181189	+	0.0313829i	0.000684343	+	0.00118532i	−0.865683	+	0.500593i	$0.833116\pi$
$702$		0			0
$703$	24.1638	+	41.8530i	0.911356	+	1.57851i
$704$		0			0
$705$	−5.99272	−	10.3797i	−0.225699	−	0.390922i
$706$		0			0
$707$	−16.3517	+	28.3219i	−0.614967	+	1.06515i
$708$		0			0
$709$	5.41203	−	9.37391i	0.203253	−	0.352044i	−0.746322	−	0.665585i	$-0.768182\pi$
$709$	5.41203	−	9.37391i	0.203253	−	0.352044i	0.949575	+	0.313541i	$0.101515\pi$
$710$		0			0
$711$	−3.71649	−	6.43715i	−0.139379	−	0.241412i
$712$		0			0
$713$	−8.86766			−0.332097
$714$		0			0
$715$	−21.0087			−0.785680
$716$		0			0
$717$	−4.95526	−	8.58276i	−0.185058	−	0.320529i
$718$		0			0
$719$	−16.5267	+	28.6250i	−0.616340	+	1.06753i	0.373808	+	0.927506i	$0.378052\pi$
$719$	−16.5267	+	28.6250i	−0.616340	+	1.06753i	−0.990148	+	0.140026i	$0.955281\pi$
$720$		0			0
$721$	8.44377	−	14.6250i	0.314462	−	0.544665i
$722$		0			0
$723$	−30.3488			−1.12868
$724$		0			0
$725$	3.12686	+	5.41587i	0.116129	+	0.201140i
$726$		0			0
$727$	0.307750	−	0.533039i	0.0114138	−	0.0197693i	−0.860262	−	0.509852i	$-0.829700\pi$
$727$	0.307750	−	0.533039i	0.0114138	−	0.0197693i	0.871676	+	0.490083i	$0.163033\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.57728	+	4.46398i	−0.0953241	+	0.165106i
$732$		0			0
$733$	−10.0022	−	17.3243i	−0.369440	−	0.639889i	0.620038	−	0.784572i	$-0.287117\pi$
$733$	−10.0022	−	17.3243i	−0.369440	−	0.639889i	−0.989478	+	0.144683i	$0.953784\pi$
$734$		0			0
$735$	−0.985982	+	1.70777i	−0.0363685	+	0.0629921i
$736$		0			0
$737$	−18.3816	+	15.5277i	−0.677095	+	0.571970i
$738$		0			0
$739$	5.54969	−	9.61235i	0.204149	−	0.353596i	−0.745712	−	0.666268i	$-0.767891\pi$
$739$	5.54969	−	9.61235i	0.204149	−	0.353596i	0.949861	+	0.312672i	$0.101224\pi$
$740$		0			0
$741$	−27.4924	−	47.6182i	−1.00996	−	1.74930i
$742$		0			0
$743$	−11.1827	+	19.3689i	−0.410252	+	0.710577i	−0.994917	−	0.100698i	$-0.967892\pi$
$743$	−11.1827	+	19.3689i	−0.410252	+	0.710577i	0.584665	+	0.811275i	$0.301226\pi$
$744$		0			0
$745$	16.3964			0.600717
$746$		0			0
$747$	−1.94862	+	3.37511i	−0.0712962	+	0.123489i
$748$		0			0
$749$	−15.0698	−	26.1017i	−0.550639	−	0.953735i
$750$		0			0
$751$	0.272198			0.00993265			0.00496633	−	0.999988i	$-0.498419\pi$
$751$	0.272198			0.00993265			0.00496633	+	0.999988i	$0.498419\pi$
$752$		0			0
$753$	3.75551	−	6.50474i	0.136858	−	0.237046i
$754$		0			0
$755$	−1.65858	+	2.87275i	−0.0603620	+	0.104550i
$756$		0			0
$757$	−0.495378	−	0.858021i	−0.0180048	−	0.0311853i	0.856883	−	0.515512i	$-0.172398\pi$
$757$	−0.495378	−	0.858021i	−0.0180048	−	0.0311853i	−0.874887	+	0.484326i	$0.839065\pi$
$758$		0			0
$759$	−3.02092			−0.109652
$760$		0			0
$761$	13.2758			0.481249			0.240624	−	0.970618i	$-0.422648\pi$
$761$	13.2758			0.481249			0.240624	+	0.970618i	$0.422648\pi$
$762$		0			0
$763$	−0.328271	−	0.568582i	−0.0118842	−	0.0205841i
$764$		0			0
$765$	3.28325	−	5.68676i	0.118706	−	0.205605i
$766$		0			0
$767$	19.7064	−	34.1324i	0.711555	−	1.23245i
$768$		0			0
$769$	10.8793	+	18.8435i	0.392317	+	0.679514i	0.992755	−	0.120158i	$-0.0383401\pi$
$769$	10.8793	+	18.8435i	0.392317	+	0.679514i	−0.600437	+	0.799672i	$0.705007\pi$
$770$		0			0
$771$	−10.0928	−	17.4812i	−0.363482	−	0.629569i
$772$		0			0
$773$	−19.3814	−	33.5696i	−0.697101	−	1.20741i	−0.969467	−	0.245221i	$-0.921140\pi$
$773$	−19.3814	−	33.5696i	−0.697101	−	1.20741i	0.272366	−	0.962194i	$-0.412194\pi$
$774$		0			0
$775$	4.31459	+	7.47308i	0.154985	+	0.268441i
$776$		0			0
$777$	−18.8147			−0.674973
$778$		0			0
$779$	22.9301			0.821556
$780$		0			0
$781$	−1.91382	+	3.31482i	−0.0684817	+	0.118614i
$782$		0			0
$783$	−3.12686	−	5.41587i	−0.111745	−	0.193548i
$784$		0			0
$785$	−10.1802	+	17.6326i	−0.363346	+	0.629334i
$786$		0			0
$787$	−24.1420	+	41.8151i	−0.860568	+	1.49055i	0.0108134	+	0.999942i	$0.496558\pi$
$787$	−24.1420	+	41.8151i	−0.860568	+	1.49055i	−0.871381	+	0.490606i	$0.836775\pi$
$788$		0			0
$789$	−19.2765			−0.686263
$790$		0			0
$791$	−21.2360	+	36.7819i	−0.755067	+	1.30781i
$792$		0			0
$793$	34.4588	+	59.6843i	1.22367	+	2.11945i
$794$		0			0
$795$	7.58069			0.268859
$796$		0			0
$797$	18.2274	+	31.5708i	0.645648	+	1.11829i	0.984151	+	0.177330i	$0.0567459\pi$
$797$	18.2274	+	31.5708i	0.645648	+	1.11829i	−0.338504	+	0.940965i	$0.609921\pi$
$798$		0			0
$799$	78.7024			2.78429
$800$		0			0
$801$	5.15537			0.182156
$802$		0			0
$803$	−16.3512			−0.577023
$804$		0			0
$805$	−3.07811			−0.108489
$806$		0			0
$807$	−19.4709			−0.685407
$808$		0			0
$809$	−53.6700			−1.88694			−0.943468	−	0.331465i	$-0.892457\pi$
$809$	−53.6700			−1.88694			−0.943468	+	0.331465i	$0.892457\pi$
$810$		0			0
$811$	5.95999	+	10.3230i	0.209283	+	0.362489i	0.951489	−	0.307683i	$-0.0995536\pi$
$811$	5.95999	+	10.3230i	0.209283	+	0.362489i	−0.742206	+	0.670172i	$0.766220\pi$
$812$		0			0
$813$	0.675765			0.0237001
$814$		0			0
$815$	2.61015	+	4.52091i	0.0914295	+	0.158360i
$816$		0			0
$817$	3.01974	−	5.23035i	0.105647	−	0.182987i
$818$		0			0
$819$	21.4064			0.747999
$820$		0			0
$821$	25.1564	−	43.5722i	0.877966	−	1.52068i	0.0243963	−	0.999702i	$-0.492234\pi$
$821$	25.1564	−	43.5722i	0.877966	−	1.52068i	0.853569	−	0.520979i	$-0.174433\pi$
$822$		0			0
$823$	0.619901	−	1.07370i	0.0216084	−	0.0374268i	−0.855019	−	0.518597i	$-0.826455\pi$
$823$	0.619901	−	1.07370i	0.0216084	−	0.0374268i	0.876627	+	0.481170i	$0.159788\pi$
$824$		0			0
$825$	1.46984	+	2.54583i	0.0511732	+	0.0886345i
$826$		0			0
$827$	−6.89375	+	11.9403i	−0.239719	+	0.415206i	−0.960634	−	0.277818i	$-0.910389\pi$
$827$	−6.89375	+	11.9403i	−0.239719	+	0.415206i	0.720915	+	0.693024i	$0.243722\pi$
$828$		0			0
$829$	−18.2611			−0.634236			−0.317118	−	0.948386i	$-0.602715\pi$
$829$	−18.2611			−0.634236			−0.317118	+	0.948386i	$0.602715\pi$
$830$		0			0
$831$	−18.6094			−0.645552
$832$		0			0
$833$	−6.47445	−	11.2141i	−0.224326	−	0.388545i
$834$		0			0
$835$	4.48971	+	7.77641i	0.155373	+	0.269114i
$836$		0			0
$837$	−4.31459	−	7.47308i	−0.149134	−	0.258308i
$838$		0			0
$839$	12.9048	+	22.3518i	0.445524	+	0.771670i	0.998089	−	0.0618000i	$-0.0196841\pi$
$839$	12.9048	+	22.3518i	0.445524	+	0.771670i	−0.552565	+	0.833470i	$0.686351\pi$
$840$		0			0
$841$	−5.05445	+	8.75457i	−0.174291	+	0.301882i
$842$		0			0
$843$	−2.44393	+	4.23302i	−0.0841736	+	0.145793i
$844$		0			0
$845$	19.0369	+	32.9729i	0.654890	+	1.13430i
$846$		0			0
$847$	−7.06391			−0.242719
$848$		0			0
$849$	−25.5043			−0.875305
$850$		0			0
$851$	−3.22748	−	5.59015i	−0.110636	−	0.191628i
$852$		0			0
$853$	8.24224	−	14.2760i	0.282209	−	0.488800i	−0.689720	−	0.724077i	$-0.742266\pi$
$853$	8.24224	−	14.2760i	0.282209	−	0.488800i	0.971929	+	0.235276i	$0.0755995\pi$
$854$		0			0
$855$	−3.84692	+	6.66305i	−0.131562	+	0.227872i
$856$		0			0
$857$	−38.0063			−1.29827			−0.649135	−	0.760674i	$-0.724869\pi$
$857$	−38.0063			−1.29827			−0.649135	+	0.760674i	$0.724869\pi$
$858$		0			0
$859$	0.913297	+	1.58188i	0.0311613	+	0.0539729i	0.881185	−	0.472771i	$-0.156746\pi$
$859$	0.913297	+	1.58188i	0.0311613	+	0.0539729i	−0.850024	+	0.526744i	$0.823413\pi$
$860$		0			0
$861$	−4.46352	+	7.73104i	−0.152116	+	0.263473i
$862$		0			0
$863$	12.3933			0.421874			0.210937	−	0.977500i	$-0.432349\pi$
$863$	12.3933			0.421874			0.210937	+	0.977500i	$0.432349\pi$
$864$		0			0
$865$	7.78383	−	13.4820i	0.264658	−	0.458401i
$866$		0			0
$867$	13.0595	+	22.6197i	0.443523	+	0.768205i
$868$		0			0
$869$	−10.9253	+	18.9231i	−0.370614	+	0.641923i
$870$		0			0
$871$	55.0354	+	19.8257i	1.86480	+	0.671768i
$872$		0			0
$873$	−4.15807	+	7.20200i	−0.140729	+	0.243751i
$874$		0			0
$875$	1.49766	+	2.59403i	0.0506302	+	0.0876941i
$876$		0			0
$877$	2.10281	−	3.64217i	0.0710067	−	0.122987i	−0.828336	−	0.560232i	$-0.810712\pi$
$877$	2.10281	−	3.64217i	0.0710067	−	0.122987i	0.899343	+	0.437244i	$0.144045\pi$
$878$		0			0
$879$	24.2818			0.819006
$880$		0			0
$881$	8.21922	−	14.2361i	0.276913	−	0.479627i	−0.693703	−	0.720261i	$-0.744022\pi$
$881$	8.21922	−	14.2361i	0.276913	−	0.479627i	0.970616	+	0.240634i	$0.0773554\pi$
$882$		0			0
$883$	−7.85350	−	13.6027i	−0.264291	−	0.457766i	0.703086	−	0.711104i	$-0.251805\pi$
$883$	−7.85350	−	13.6027i	−0.264291	−	0.457766i	−0.967378	+	0.253339i	$0.918471\pi$
$884$		0			0
$885$	−5.51489			−0.185381
$886$		0			0
$887$	−20.8069	+	36.0387i	−0.698629	+	1.21006i	0.270313	+	0.962772i	$0.412873\pi$
$887$	−20.8069	+	36.0387i	−0.698629	+	1.21006i	−0.968942	+	0.247288i	$0.920461\pi$
$888$		0			0
$889$	1.36071	−	2.35683i	0.0456369	−	0.0790454i
$890$		0			0
$891$	−1.46984	−	2.54583i	−0.0492414	−	0.0852886i
$892$		0			0
$893$	−92.2139			−3.08582
$894$		0			0
$895$	−14.0210			−0.468672
$896$		0			0
$897$	3.67206	+	6.36019i	0.122606	+	0.212361i
$898$		0			0
$899$	−26.9822	+	46.7345i	−0.899906	+	1.55868i
$900$		0			0
$901$	−24.8893	+	43.1095i	−0.829183	+	1.43619i
$902$		0			0
$903$	1.17563	+	2.03625i	0.0391226	+	0.0677622i
$904$		0			0
$905$	−4.45563	−	7.71738i	−0.148110	−	0.256534i
$906$		0			0
$907$	−19.7799	−	34.2599i	−0.656782	−	1.13758i	−0.981444	−	0.191750i	$-0.938584\pi$
$907$	−19.7799	−	34.2599i	−0.656782	−	1.13758i	0.324662	−	0.945830i	$-0.394750\pi$
$908$		0			0
$909$	−5.45906	−	9.45537i	−0.181066	−	0.313615i
$910$		0			0
$911$	28.2435			0.935750			0.467875	−	0.883795i	$-0.345020\pi$
$911$	28.2435			0.935750			0.467875	+	0.883795i	$0.345020\pi$
$912$		0			0
$913$	11.4566			0.379158
$914$		0			0
$915$	4.82170	−	8.35143i	0.159400	−	0.276090i
$916$		0			0
$917$	−2.75290	−	4.76816i	−0.0909087	−	0.157459i
$918$		0			0
$919$	−6.82354	+	11.8187i	−0.225088	+	0.389864i	−0.956346	−	0.292237i	$-0.905600\pi$
$919$	−6.82354	+	11.8187i	−0.225088	+	0.389864i	0.731258	+	0.682101i	$0.238934\pi$
$920$		0			0
$921$	2.90950	−	5.03940i	0.0958713	−	0.166054i
$922$		0			0
$923$	9.30529			0.306287
$924$		0			0
$925$	−3.14067	+	5.43981i	−0.103265	+	0.178860i
$926$		0			0
$927$	2.81898	+	4.88262i	0.0925876	+	0.160366i
$928$		0			0
$929$	−46.8240			−1.53625			−0.768123	−	0.640302i	$-0.778809\pi$
$929$	−46.8240			−1.53625			−0.768123	+	0.640302i	$0.778809\pi$
$930$		0			0
$931$	7.58598	+	13.1393i	0.248620	+	0.430623i
$932$		0			0
$933$	−5.11660			−0.167510
$934$		0			0
$935$	−19.3034			−0.631288
$936$		0			0
$937$	−6.44329			−0.210493			−0.105247	−	0.994446i	$-0.533563\pi$
$937$	−6.44329			−0.210493			−0.105247	+	0.994446i	$0.533563\pi$
$938$		0			0
$939$	−27.6070			−0.900922
$940$		0			0
$941$	55.8275			1.81993			0.909963	−	0.414689i	$-0.136110\pi$
$941$	55.8275			1.81993			0.909963	+	0.414689i	$0.136110\pi$
$942$		0			0
$943$	−3.06269			−0.0997350
$944$		0			0
$945$	−1.49766	−	2.59403i	−0.0487189	−	0.0843837i
$946$		0			0
$947$	37.9181			1.23217			0.616087	−	0.787678i	$-0.288717\pi$
$947$	37.9181			1.23217			0.616087	+	0.787678i	$0.288717\pi$
$948$		0			0
$949$	19.8756	+	34.4256i	0.645190	+	1.11750i
$950$		0			0
$951$	−9.58430	+	16.6005i	−0.310792	+	0.538308i
$952$		0			0
$953$	−50.7587			−1.64424			−0.822118	−	0.569317i	$-0.807208\pi$
$953$	−50.7587			−1.64424			−0.822118	+	0.569317i	$0.807208\pi$
$954$		0			0
$955$	8.18155	−	14.1709i	0.264749	−	0.458558i
$956$		0			0
$957$	−9.19194	+	15.9209i	−0.297133	+	0.514650i
$958$		0			0
$959$	−9.30750	−	16.1211i	−0.300555	−	0.520576i
$960$		0			0
$961$	−21.7313	+	37.6398i	−0.701010	+	1.21419i
$962$		0			0
$963$	10.0622			0.324251
$964$		0			0
$965$	−20.7375			−0.667565
$966$		0			0
$967$	25.2831	+	43.7916i	0.813049	+	1.40824i	0.910721	+	0.413023i	$0.135527\pi$
$967$	25.2831	+	43.7916i	0.813049	+	1.40824i	−0.0976719	+	0.995219i	$0.531140\pi$
$968$		0			0
$969$	−25.2608	−	43.7530i	−0.811493	−	1.40555i
$970$		0			0
$971$	−18.7337	−	32.4478i	−0.601194	−	1.04130i	−0.992641	−	0.121098i	$-0.961358\pi$
$971$	−18.7337	−	32.4478i	−0.601194	−	1.04130i	0.391446	−	0.920201i	$-0.371975\pi$
$972$		0			0
$973$	17.5429	+	30.3853i	0.562401	+	0.974107i
$974$		0			0
$975$	3.57330	−	6.18914i	0.114437	−	0.198211i
$976$		0			0
$977$	24.8594	−	43.0578i	0.795324	−	1.37754i	−0.127310	−	0.991863i	$-0.540634\pi$
$977$	24.8594	−	43.0578i	0.795324	−	1.37754i	0.922633	−	0.385678i	$-0.126032\pi$
$978$		0			0
$979$	−7.57755	−	13.1247i	−0.242180	−	0.419467i
$980$		0			0
$981$	0.219189			0.00699817
$982$		0			0
$983$	−51.4084			−1.63967			−0.819837	−	0.572597i	$-0.805936\pi$
$983$	−51.4084			−1.63967			−0.819837	+	0.572597i	$0.805936\pi$
$984$		0			0
$985$	5.61403	+	9.72378i	0.178878	+	0.309825i
$986$		0			0
$987$	17.9501	−	31.0905i	0.571359	−	0.989622i
$988$		0			0
$989$	−0.403336	+	0.698599i	−0.0128253	+	0.0222142i
$990$		0			0
$991$	51.0468			1.62156			0.810778	−	0.585354i	$-0.199045\pi$
$991$	51.0468			1.62156			0.810778	+	0.585354i	$0.199045\pi$
$992$		0			0
$993$	9.39051	+	16.2648i	0.297999	+	0.516149i
$994$		0			0
$995$	3.11350	−	5.39274i	0.0987045	−	0.170961i
$996$		0			0
$997$	34.9737			1.10763			0.553815	−	0.832640i	$-0.313172\pi$
$997$	34.9737			1.10763			0.553815	+	0.832640i	$0.313172\pi$
$998$		0			0
$999$	3.14067	−	5.43981i	0.0993665	−	0.172108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.l.3781.3	yes	22
67.37	even	3	inner	4020.2.q.l.841.3	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.l.841.3	✓	22	67.37	even	3	inner
4020.2.q.l.3781.3	yes	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(-1.49766 - 2.59403i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(-1.49766 - 2.59403i) q^{7} +1.00000 q^{9} +(-1.46984 - 2.54583i) q^{11} +(-3.57330 + 6.18914i) q^{13} +1.00000 q^{15} +(-3.28325 + 5.68676i) q^{17} +(3.84692 - 6.66305i) q^{19} +(1.49766 + 2.59403i) q^{21} +(-0.513819 + 0.889960i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(3.12686 + 5.41587i) q^{29} +(4.31459 + 7.47308i) q^{31} +(1.46984 + 2.54583i) q^{33} +(1.49766 + 2.59403i) q^{35} +(-3.14067 + 5.43981i) q^{37} +(3.57330 - 6.18914i) q^{39} +(1.49016 + 2.58104i) q^{41} +0.784978 q^{43} -1.00000 q^{45} +(-5.99272 - 10.3797i) q^{47} +(-0.985982 + 1.70777i) q^{49} +(3.28325 - 5.68676i) q^{51} +7.58069 q^{53} +(1.46984 + 2.54583i) q^{55} +(-3.84692 + 6.66305i) q^{57} -5.51489 q^{59} +(4.82170 - 8.35143i) q^{61} +(-1.49766 - 2.59403i) q^{63} +(3.57330 - 6.18914i) q^{65} +(-1.44798 - 8.05626i) q^{67} +(0.513819 - 0.889960i) q^{69} +(-0.651030 - 1.12762i) q^{71} +(2.78113 - 4.81706i) q^{73} -1.00000 q^{75} +(-4.40264 + 7.62559i) q^{77} +(-3.71649 - 6.43715i) q^{79} +1.00000 q^{81} +(-1.94862 + 3.37511i) q^{83} +(3.28325 - 5.68676i) q^{85} +(-3.12686 - 5.41587i) q^{87} +5.15537 q^{89} +21.4064 q^{91} +(-4.31459 - 7.47308i) q^{93} +(-3.84692 + 6.66305i) q^{95} +(-4.15807 + 7.20200i) q^{97} +(-1.46984 - 2.54583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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