LMFDB - Embedded newform 1560.2.dr.a.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1560,2,Mod(49,1560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 3, 5]))

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

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

chi := DirichletCharacter("1560.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1560.dr (of order $6$, 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:	$12.4566627153$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	1560.49
Dual form			1560.2.dr.a.1369.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{3} +(1.63725 - 1.52296i) q^{5} +(1.13279 - 1.96206i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{3} +(1.63725 - 1.52296i) q^{5} +(1.13279 - 1.96206i) q^{7} +(0.500000 - 0.866025i) q^{9} +(2.47690 - 1.43004i) q^{11} +(-1.36127 - 3.33870i) q^{13} +(-0.656421 + 2.13755i) q^{15} +(6.33380 + 3.65682i) q^{17} +(-6.64070 - 3.83401i) q^{19} +2.26559i q^{21} +(-0.617861 + 0.356722i) q^{23} +(0.361185 - 4.98694i) q^{25} +1.00000i q^{27} +(-3.35868 - 5.81741i) q^{29} +2.56170i q^{31} +(-1.43004 + 2.47690i) q^{33} +(-1.13347 - 4.93758i) q^{35} +(3.00272 + 5.20086i) q^{37} +(2.84825 + 2.21077i) q^{39} +(-4.15916 + 2.40130i) q^{41} +(1.62098 + 0.935871i) q^{43} +(-0.500296 - 2.17938i) q^{45} -9.49251 q^{47} +(0.933552 + 1.61696i) q^{49} -7.31364 q^{51} -8.14524i q^{53} +(1.87742 - 6.11356i) q^{55} +7.66802 q^{57} +(-8.96127 - 5.17379i) q^{59} +(0.359881 - 0.623333i) q^{61} +(-1.13279 - 1.96206i) q^{63} +(-7.31345 - 3.39314i) q^{65} +(2.93708 + 5.08717i) q^{67} +(0.356722 - 0.617861i) q^{69} +(-6.08342 - 3.51226i) q^{71} +13.2972 q^{73} +(2.18067 + 4.49941i) q^{75} -6.47977i q^{77} -9.81131 q^{79} +(-0.500000 - 0.866025i) q^{81} +17.6053 q^{83} +(15.9392 - 3.65899i) q^{85} +(5.81741 + 3.35868i) q^{87} +(13.0630 - 7.54192i) q^{89} +(-8.09277 - 1.11118i) q^{91} +(-1.28085 - 2.21850i) q^{93} +(-16.7115 + 3.83628i) q^{95} +(5.88598 - 10.1948i) q^{97} -2.86008i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{5} + 2 q^{7} + 22 q^{9}+O(q^{10}) $ 44 * q - 2 * q^5 + 2 * q^7 + 22 * q^9	$ 44 q - 2 q^{5} + 2 q^{7} + 22 q^{9} - 6 q^{11} - 4 q^{13} + 18 q^{17} - 6 q^{19} - 6 q^{23} + 2 q^{25} - 2 q^{29} - 6 q^{33} - 16 q^{37} - 2 q^{39} - 6 q^{41} - 36 q^{43} - 4 q^{45} - 48 q^{47} - 36 q^{49} + 24 q^{51} - 24 q^{55} + 24 q^{57} - 14 q^{61} - 2 q^{63} + 26 q^{65} - 4 q^{67} - 8 q^{69} + 44 q^{73} - 16 q^{75} + 28 q^{79} - 22 q^{81} - 56 q^{83} - 44 q^{85} - 6 q^{87} + 18 q^{89} + 30 q^{91} + 8 q^{93} - 34 q^{95} - 24 q^{97}+O(q^{100}) $ 44 * q - 2 * q^5 + 2 * q^7 + 22 * q^9 - 6 * q^11 - 4 * q^13 + 18 * q^17 - 6 * q^19 - 6 * q^23 + 2 * q^25 - 2 * q^29 - 6 * q^33 - 16 * q^37 - 2 * q^39 - 6 * q^41 - 36 * q^43 - 4 * q^45 - 48 * q^47 - 36 * q^49 + 24 * q^51 - 24 * q^55 + 24 * q^57 - 14 * q^61 - 2 * q^63 + 26 * q^65 - 4 * q^67 - 8 * q^69 + 44 * q^73 - 16 * q^75 + 28 * q^79 - 22 * q^81 - 56 * q^83 - 44 * q^85 - 6 * q^87 + 18 * q^89 + 30 * q^91 + 8 * q^93 - 34 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times$.

$n$	$391$	$521$	$781$	$937$	$1081$
$\chi(n)$	$1$	$1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$		0			0
$5$	1.63725	−	1.52296i	0.732201	−	0.681088i
$5$	1.63725	−	1.52296i	0.732201	−	0.681088i
$6$		0			0
$7$	1.13279	−	1.96206i	0.428156	−	0.741588i	−0.568553	−	0.822647i	$-0.692497\pi$
$7$	1.13279	−	1.96206i	0.428156	−	0.741588i	0.996709	+	0.0810582i	$0.0258300\pi$
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	2.47690	−	1.43004i	0.746814	−	0.431173i	−0.0777275	−	0.996975i	$-0.524766\pi$
$11$	2.47690	−	1.43004i	0.746814	−	0.431173i	0.824542	+	0.565801i	$0.191433\pi$
$12$		0			0
$13$	−1.36127	−	3.33870i	−0.377548	−	0.925990i
$13$	−1.36127	−	3.33870i	−0.377548	−	0.925990i
$14$		0			0
$15$	−0.656421	+	2.13755i	−0.169487	+	0.551912i
$16$		0			0
$17$	6.33380	+	3.65682i	1.53617	+	0.886910i	0.999058	+	0.0434002i	$0.0138191\pi$
$17$	6.33380	+	3.65682i	1.53617	+	0.886910i	0.537115	+	0.843509i	$0.319514\pi$
$18$		0			0
$19$	−6.64070	−	3.83401i	−1.52348	−	0.879583i	−0.999614	−	0.0277831i	$-0.991155\pi$
$19$	−6.64070	−	3.83401i	−1.52348	−	0.879583i	−0.523868	−	0.851800i	$-0.675511\pi$
$20$		0			0
$21$			2.26559i			0.494392i
$22$		0			0
$23$	−0.617861	+	0.356722i	−0.128833	+	0.0743817i	−0.563031	−	0.826436i	$-0.690365\pi$
$23$	−0.617861	+	0.356722i	−0.128833	+	0.0743817i	0.434198	+	0.900817i	$0.357032\pi$
$24$		0			0
$25$	0.361185	−	4.98694i	0.0722370	−	0.997387i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−3.35868	−	5.81741i	−0.623691	−	1.08027i	−0.988792	−	0.149297i	$-0.952299\pi$
$29$	−3.35868	−	5.81741i	−0.623691	−	1.08027i	0.365101	−	0.930968i	$-0.381034\pi$
$30$		0			0
$31$			2.56170i			0.460094i	0.973179	+	0.230047i	$0.0738881\pi$
$31$			2.56170i			0.460094i	−0.973179	+	0.230047i	$0.926112\pi$
$32$		0			0
$33$	−1.43004	+	2.47690i	−0.248938	+	0.431173i
$34$		0			0
$35$	−1.13347	−	4.93758i	−0.191591	−	0.834604i
$36$		0			0
$37$	3.00272	+	5.20086i	0.493644	+	0.855016i	0.999973	−	0.00732385i	$-0.00233127\pi$
$37$	3.00272	+	5.20086i	0.493644	+	0.855016i	−0.506329	+	0.862340i	$0.668998\pi$
$38$		0			0
$39$	2.84825	+	2.21077i	0.456084	+	0.354006i
$40$		0			0
$41$	−4.15916	+	2.40130i	−0.649552	+	0.375019i	−0.788285	−	0.615311i	$-0.789031\pi$
$41$	−4.15916	+	2.40130i	−0.649552	+	0.375019i	0.138732	+	0.990330i	$0.455697\pi$
$42$		0			0
$43$	1.62098	+	0.935871i	0.247196	+	0.142719i	0.618480	−	0.785801i	$-0.287749\pi$
$43$	1.62098	+	0.935871i	0.247196	+	0.142719i	−0.371283	+	0.928520i	$0.621082\pi$
$44$		0			0
$45$	−0.500296	−	2.17938i	−0.0745798	−	0.324883i
$46$		0			0
$47$	−9.49251			−1.38463			−0.692313	−	0.721598i	$-0.743408\pi$
$47$	−9.49251			−1.38463			−0.692313	+	0.721598i	$0.743408\pi$
$48$		0			0
$49$	0.933552	+	1.61696i	0.133365	+	0.230994i
$50$		0			0
$51$	−7.31364			−1.02411
$52$		0			0
$53$		−	8.14524i		−	1.11883i	−0.828886	−	0.559417i	$-0.811025\pi$
$53$		−	8.14524i		−	1.11883i	0.828886	−	0.559417i	$-0.188975\pi$
$54$		0			0
$55$	1.87742	−	6.11356i	0.253151	−	0.824352i
$56$		0			0
$57$	7.66802			1.01565
$58$		0			0
$59$	−8.96127	−	5.17379i	−1.16666	−	0.673570i	−0.213767	−	0.976885i	$-0.568573\pi$
$59$	−8.96127	−	5.17379i	−1.16666	−	0.673570i	−0.952890	+	0.303315i	$0.901907\pi$
$60$		0			0
$61$	0.359881	−	0.623333i	0.0460781	−	0.0798096i	−0.842067	−	0.539374i	$-0.818661\pi$
$61$	0.359881	−	0.623333i	0.0460781	−	0.0798096i	0.888145	+	0.459564i	$0.151994\pi$
$62$		0			0
$63$	−1.13279	−	1.96206i	−0.142719	−	0.247196i
$64$		0			0
$65$	−7.31345	−	3.39314i	−0.907122	−	0.420867i
$66$		0			0
$67$	2.93708	+	5.08717i	0.358822	+	0.621497i	0.987764	−	0.155954i	$-0.0498453\pi$
$67$	2.93708	+	5.08717i	0.358822	+	0.621497i	−0.628943	+	0.777452i	$0.716512\pi$
$68$		0			0
$69$	0.356722	−	0.617861i	0.0429443	−	0.0743817i
$70$		0			0
$71$	−6.08342	−	3.51226i	−0.721969	−	0.416829i	0.0935079	−	0.995619i	$-0.470192\pi$
$71$	−6.08342	−	3.51226i	−0.721969	−	0.416829i	−0.815477	+	0.578789i	$0.803525\pi$
$72$		0			0
$73$	13.2972			1.55631			0.778157	−	0.628070i	$-0.216155\pi$
$73$	13.2972			1.55631			0.778157	+	0.628070i	$0.216155\pi$
$74$		0			0
$75$	2.18067	+	4.49941i	0.251802	+	0.519547i
$76$		0			0
$77$		−	6.47977i		−	0.738438i
$78$		0			0
$79$	−9.81131			−1.10386			−0.551929	−	0.833891i	$-0.686108\pi$
$79$	−9.81131			−1.10386			−0.551929	+	0.833891i	$0.686108\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	17.6053			1.93244			0.966218	−	0.257726i	$-0.0829732\pi$
$83$	17.6053			1.93244			0.966218	+	0.257726i	$0.0829732\pi$
$84$		0			0
$85$	15.9392	−	3.65899i	1.72885	−	0.396873i
$86$		0			0
$87$	5.81741	+	3.35868i	0.623691	+	0.360088i
$88$		0			0
$89$	13.0630	−	7.54192i	1.38467	−	0.799442i	0.391965	−	0.919980i	$-0.371795\pi$
$89$	13.0630	−	7.54192i	1.38467	−	0.799442i	0.992709	+	0.120538i	$0.0384621\pi$
$90$		0			0
$91$	−8.09277	−	1.11118i	−0.848353	−	0.116483i
$92$		0			0
$93$	−1.28085	−	2.21850i	−0.132818	−	0.230047i
$94$		0			0
$95$	−16.7115	+	3.83628i	−1.71457	+	0.393594i
$96$		0			0
$97$	5.88598	−	10.1948i	0.597631	−	1.03513i	−0.395539	−	0.918449i	$-0.629442\pi$
$97$	5.88598	−	10.1948i	0.597631	−	1.03513i	0.993170	−	0.116678i	$-0.0372246\pi$
$98$		0			0
$99$		−	2.86008i		−	0.287449i
$100$		0			0
$101$	−0.0587229	−	0.101711i	−0.00584314	−	0.0101206i	0.863089	−	0.505052i	$-0.168527\pi$
$101$	−0.0587229	−	0.101711i	−0.00584314	−	0.0101206i	−0.868932	+	0.494931i	$0.835193\pi$
$102$		0			0
$103$			2.54791i			0.251053i	0.992090	+	0.125526i	$0.0400619\pi$
$103$			2.54791i			0.251053i	−0.992090	+	0.125526i	$0.959938\pi$
$104$		0			0
$105$	3.45040	+	3.70934i	0.336725	+	0.361995i
$106$		0			0
$107$	−0.333195	+	0.192370i	−0.0322112	+	0.0185971i	−0.516019	−	0.856577i	$-0.672587\pi$
$107$	−0.333195	+	0.192370i	−0.0322112	+	0.0185971i	0.483808	+	0.875174i	$0.339253\pi$
$108$		0			0
$109$		−	0.671974i		−	0.0643634i	−0.999482	−	0.0321817i	$-0.989754\pi$
$109$		−	0.671974i		−	0.0643634i	0.999482	−	0.0321817i	$-0.0102455\pi$
$110$		0			0
$111$	−5.20086	−	3.00272i	−0.493644	−	0.285005i
$112$		0			0
$113$	−6.51163	−	3.75949i	−0.612563	−	0.353663i	0.161405	−	0.986888i	$-0.448397\pi$
$113$	−6.51163	−	3.75949i	−0.612563	−	0.353663i	−0.773968	+	0.633225i	$0.781731\pi$
$114$		0			0
$115$	−0.468320	+	1.52502i	−0.0436711	+	0.142209i
$116$		0			0
$117$	−3.57204	−	0.490459i	−0.330235	−	0.0453429i
$118$		0			0
$119$	14.3498	−	8.28486i	1.31544	−	0.759472i
$120$		0			0
$121$	−1.40997	+	2.44214i	−0.128179	+	0.222013i
$122$		0			0
$123$	2.40130	−	4.15916i	0.216517	−	0.375019i
$124$		0			0
$125$	−7.00356	−	8.71494i	−0.626417	−	0.779488i
$126$		0			0
$127$	−2.91908	+	1.68533i	−0.259027	+	0.149549i	−0.623890	−	0.781512i	$-0.714449\pi$
$127$	−2.91908	+	1.68533i	−0.259027	+	0.149549i	0.364864	+	0.931061i	$0.381116\pi$
$128$		0			0
$129$	−1.87174			−0.164798
$130$		0			0
$131$	11.4928			1.00413			0.502064	−	0.864831i	$-0.332574\pi$
$131$	11.4928			1.00413			0.502064	+	0.864831i	$0.332574\pi$
$132$		0			0
$133$	−15.0451	+	8.68630i	−1.30458	+	0.753197i
$134$		0			0
$135$	1.52296	+	1.63725i	0.131076	+	0.140912i
$136$		0			0
$137$	5.60608	−	9.71001i	0.478960	−	0.829582i	−0.520749	−	0.853710i	$-0.674347\pi$
$137$	5.60608	−	9.71001i	0.478960	−	0.829582i	0.999709	+	0.0241272i	$0.00768068\pi$
$138$		0			0
$139$	8.62280	−	14.9351i	0.731376	−	1.26678i	−0.224919	−	0.974378i	$-0.572212\pi$
$139$	8.62280	−	14.9351i	0.731376	−	1.26678i	0.956295	−	0.292404i	$-0.0944551\pi$
$140$		0			0
$141$	8.22076	−	4.74626i	0.692313	−	0.399707i
$142$		0			0
$143$	−8.14621	−	6.32297i	−0.681220	−	0.528754i
$144$		0			0
$145$	−14.3587	−	4.40942i	−1.19242	−	0.366182i
$146$		0			0
$147$	−1.61696	−	0.933552i	−0.133365	−	0.0769981i
$148$		0			0
$149$	13.5775	+	7.83897i	1.11231	+	0.642193i	0.939427	−	0.342749i	$-0.111358\pi$
$149$	13.5775	+	7.83897i	1.11231	+	0.642193i	0.172884	+	0.984942i	$0.444691\pi$
$150$		0			0
$151$		−	5.72321i		−	0.465749i	−0.972507	−	0.232874i	$-0.925187\pi$
$151$		−	5.72321i		−	0.465749i	0.972507	−	0.232874i	$-0.0748131\pi$
$152$		0			0
$153$	6.33380	−	3.65682i	0.512057	−	0.295637i
$154$		0			0
$155$	3.90136	+	4.19414i	0.313365	+	0.336882i
$156$		0			0
$157$			15.1062i			1.20561i	0.797889	+	0.602804i	$0.205950\pi$
$157$			15.1062i			1.20561i	−0.797889	+	0.602804i	$0.794050\pi$
$158$		0			0
$159$	4.07262	+	7.05399i	0.322980	+	0.559417i
$160$		0			0
$161$			1.61637i			0.127388i
$162$		0			0
$163$	2.12355	−	3.67810i	0.166329	−	0.288091i	−0.770797	−	0.637081i	$-0.780142\pi$
$163$	2.12355	−	3.67810i	0.166329	−	0.288091i	0.937127	+	0.348990i	$0.113475\pi$
$164$		0			0
$165$	1.43089	+	6.23321i	0.111394	+	0.485254i
$166$		0			0
$167$	8.86529	+	15.3551i	0.686017	+	1.18822i	0.973116	+	0.230315i	$0.0739756\pi$
$167$	8.86529	+	15.3551i	0.686017	+	1.18822i	−0.287100	+	0.957901i	$0.592691\pi$
$168$		0			0
$169$	−9.29389	+	9.08975i	−0.714915	+	0.699211i
$170$		0			0
$171$	−6.64070	+	3.83401i	−0.507827	+	0.293194i
$172$		0			0
$173$	−20.6316	−	11.9117i	−1.56859	−	0.905628i	−0.996333	−	0.0855556i	$-0.972733\pi$
$173$	−20.6316	−	11.9117i	−1.56859	−	0.905628i	−0.572260	−	0.820072i	$-0.693933\pi$
$174$		0			0
$175$	−9.37551	−	6.35784i	−0.708722	−	0.480608i
$176$		0			0
$177$	10.3476			0.777772
$178$		0			0
$179$	−10.2909	−	17.8244i	−0.769180	−	1.33226i	−0.938008	−	0.346613i	$-0.887332\pi$
$179$	−10.2909	−	17.8244i	−0.769180	−	1.33226i	0.168829	−	0.985645i	$-0.446002\pi$
$180$		0			0
$181$	13.6966			1.01806			0.509030	−	0.860749i	$-0.330004\pi$
$181$	13.6966			1.01806			0.509030	+	0.860749i	$0.330004\pi$
$182$		0			0
$183$			0.719763i			0.0532064i
$184$		0			0
$185$	12.8369	+	3.94210i	0.943788	+	0.289829i
$186$		0			0
$187$	20.9176			1.52965
$188$		0			0
$189$	1.96206	+	1.13279i	0.142719	+	0.0823987i
$190$		0			0
$191$	−2.46888	+	4.27623i	−0.178642	+	0.309417i	−0.941416	−	0.337249i	$-0.890504\pi$
$191$	−2.46888	+	4.27623i	−0.178642	+	0.309417i	0.762774	+	0.646666i	$0.223837\pi$
$192$		0			0
$193$	−0.851415	−	1.47469i	−0.0612862	−	0.106151i	0.833754	−	0.552136i	$-0.186187\pi$
$193$	−0.851415	−	1.47469i	−0.0612862	−	0.106151i	−0.895041	+	0.445985i	$0.852854\pi$
$194$		0			0
$195$	8.03021	−	0.718180i	0.575055	−	0.0514300i
$196$		0			0
$197$	−1.41405	−	2.44921i	−0.100747	−	0.174499i	0.811245	−	0.584706i	$-0.198790\pi$
$197$	−1.41405	−	2.44921i	−0.100747	−	0.174499i	−0.911993	+	0.410206i	$0.865457\pi$
$198$		0			0
$199$	3.41843	−	5.92089i	0.242326	−	0.419721i	−0.719050	−	0.694958i	$-0.755423\pi$
$199$	3.41843	−	5.92089i	0.242326	−	0.419721i	0.961376	+	0.275237i	$0.0887563\pi$
$200$		0			0
$201$	−5.08717	−	2.93708i	−0.358822	−	0.207166i
$202$		0			0
$203$	−15.2188			−1.06815
$204$		0			0
$205$	−3.15252	+	10.2658i	−0.220182	+	0.716992i
$206$		0			0
$207$			0.713444i			0.0495878i
$208$		0			0
$209$	−21.9312			−1.51701
$210$		0			0
$211$	12.7265	+	22.0429i	0.876128	+	1.51750i	0.855556	+	0.517709i	$0.173215\pi$
$211$	12.7265	+	22.0429i	0.876128	+	1.51750i	0.0205713	+	0.999788i	$0.493451\pi$
$212$		0			0
$213$	7.02453			0.481313
$214$		0			0
$215$	4.07924	−	0.936425i	0.278202	−	0.0638637i
$216$		0			0
$217$	5.02620	+	2.90188i	0.341201	+	0.196992i
$218$		0			0
$219$	−11.5157	+	6.64858i	−0.778157	+	0.449269i
$220$		0			0
$221$	3.58704	−	26.1246i	0.241291	−	1.75733i
$222$		0			0
$223$	5.12347	+	8.87412i	0.343093	+	0.594255i	0.985005	−	0.172523i	$-0.0551920\pi$
$223$	5.12347	+	8.87412i	0.343093	+	0.594255i	−0.641912	+	0.766778i	$0.721859\pi$
$224$		0			0
$225$	−4.13822	−	2.80626i	−0.275881	−	0.187084i
$226$		0			0
$227$	−13.2387	+	22.9301i	−0.878684	+	1.52193i	−0.0258979	+	0.999665i	$0.508244\pi$
$227$	−13.2387	+	22.9301i	−0.878684	+	1.52193i	−0.852786	+	0.522261i	$0.825089\pi$
$228$		0			0
$229$			8.87771i			0.586656i	0.956012	+	0.293328i	$0.0947627\pi$
$229$			8.87771i			0.586656i	−0.956012	+	0.293328i	$0.905237\pi$
$230$		0			0
$231$	3.23988	+	5.61164i	0.213169	+	0.369219i
$232$		0			0
$233$		−	1.04430i		−	0.0684147i	−0.999415	−	0.0342073i	$-0.989109\pi$
$233$		−	1.04430i		−	0.0684147i	0.999415	−	0.0342073i	$-0.0108907\pi$
$234$		0			0
$235$	−15.5416	+	14.4567i	−1.01382	+	0.943052i
$236$		0			0
$237$	8.49684	−	4.90565i	0.551929	−	0.318656i
$238$		0			0
$239$		−	0.00808942i		−	0.000523261i	−1.00000		0.000261631i	$-0.999917\pi$
$239$		−	0.00808942i		−	0.000523261i	1.00000		0.000261631i	$-8.32796e-5\pi$
$240$		0			0
$241$	4.93946	+	2.85180i	0.318178	+	0.183700i	0.650580	−	0.759437i	$-0.274526\pi$
$241$	4.93946	+	2.85180i	0.318178	+	0.183700i	−0.332402	+	0.943138i	$0.607859\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$	3.99102	+	1.22561i	0.254977	+	0.0783011i
$246$		0			0
$247$	−3.76085	+	27.3905i	−0.239297	+	1.74281i
$248$		0			0
$249$	−15.2467	+	8.80267i	−0.966218	+	0.557846i
$250$		0			0
$251$	7.25050	−	12.5582i	0.457648	−	0.792669i	−0.541189	−	0.840901i	$-0.682025\pi$
$251$	7.25050	−	12.5582i	0.457648	−	0.792669i	0.998836	+	0.0482324i	$0.0153588\pi$
$252$		0			0
$253$	−1.02025	+	1.76713i	−0.0641428	+	0.111099i
$254$		0			0
$255$	−11.9743	+	11.1384i	−0.749858	+	0.697513i
$256$		0			0
$257$	−3.43691	+	1.98430i	−0.214388	+	0.123777i	−0.603349	−	0.797477i	$-0.706167\pi$
$257$	−3.43691	+	1.98430i	−0.214388	+	0.123777i	0.388961	+	0.921254i	$0.372834\pi$
$258$		0			0
$259$	13.6059			0.845427
$260$		0			0
$261$	−6.71736			−0.415794
$262$		0			0
$263$	−21.0422	+	12.1487i	−1.29752	+	0.749123i	−0.979975	−	0.199120i	$-0.936192\pi$
$263$	−21.0422	+	12.1487i	−1.29752	+	0.749123i	−0.317544	+	0.948243i	$0.602858\pi$
$264$		0			0
$265$	−12.4049	−	13.3358i	−0.762026	−	0.819212i
$266$		0			0
$267$	−7.54192	+	13.0630i	−0.461558	+	0.799442i
$268$		0			0
$269$	1.64721	−	2.85305i	0.100432	−	0.173954i	−0.811431	−	0.584449i	$-0.801311\pi$
$269$	1.64721	−	2.85305i	0.100432	−	0.173954i	0.911863	+	0.410495i	$0.134644\pi$
$270$		0			0
$271$	3.47040	−	2.00363i	0.210811	−	0.121712i	−0.390877	−	0.920443i	$-0.627828\pi$
$271$	3.47040	−	2.00363i	0.210811	−	0.121712i	0.601688	+	0.798731i	$0.294495\pi$
$272$		0			0
$273$	7.56413	−	3.08408i	0.457802	−	0.186657i
$274$		0			0
$275$	−6.23690	−	12.8687i	−0.376099	−	0.776010i
$276$		0			0
$277$	−14.4584	−	8.34757i	−0.868722	−	0.501557i	−0.00179860	−	0.999998i	$-0.500573\pi$
$277$	−14.4584	−	8.34757i	−0.868722	−	0.501557i	−0.866923	+	0.498442i	$0.833906\pi$
$278$		0			0
$279$	2.21850	+	1.28085i	0.132818	+	0.0766824i
$280$		0			0
$281$			6.08190i			0.362816i	0.983408	+	0.181408i	$0.0580654\pi$
$281$			6.08190i			0.362816i	−0.983408	+	0.181408i	$0.941935\pi$
$282$		0			0
$283$	1.21566	−	0.701863i	0.0722637	−	0.0417214i	−0.463433	−	0.886132i	$-0.653382\pi$
$283$	1.21566	−	0.701863i	0.0722637	−	0.0417214i	0.535696	+	0.844411i	$0.320049\pi$
$284$		0			0
$285$	12.5545	−	11.6781i	0.743663	−	0.691751i
$286$		0			0
$287$			10.8807i			0.642267i
$288$		0			0
$289$	18.2447	+	31.6007i	1.07322	+	1.85887i
$290$		0			0
$291$			11.7720i			0.690085i
$292$		0			0
$293$	1.30024	−	2.25209i	0.0759610	−	0.131568i	−0.825543	−	0.564340i	$-0.809131\pi$
$293$	1.30024	−	2.25209i	0.0759610	−	0.131568i	0.901504	+	0.432771i	$0.142464\pi$
$294$		0			0
$295$	−22.5513	+	5.17686i	−1.31299	+	0.301408i
$296$		0			0
$297$	1.43004	+	2.47690i	0.0829793	+	0.143724i
$298$		0			0
$299$	2.03206	+	1.57726i	0.117517	+	0.0912153i
$300$		0			0
$301$	3.67247	−	2.12030i	0.211677	−	0.122212i
$302$		0			0
$303$	0.101711	+	0.0587229i	0.00584314	+	0.00337354i
$304$		0			0
$305$	−0.360095	−	1.56864i	−0.0206190	−	0.0898199i
$306$		0			0
$307$	5.38032			0.307071			0.153535	−	0.988143i	$-0.450934\pi$
$307$	5.38032			0.307071			0.153535	+	0.988143i	$0.450934\pi$
$308$		0			0
$309$	−1.27395	−	2.20655i	−0.0724726	−	0.125526i
$310$		0			0
$311$	−7.02145			−0.398150			−0.199075	−	0.979984i	$-0.563794\pi$
$311$	−7.02145			−0.398150			−0.199075	+	0.979984i	$0.563794\pi$
$312$		0			0
$313$			22.1852i			1.25398i	0.779026	+	0.626991i	$0.215714\pi$
$313$			22.1852i			1.25398i	−0.779026	+	0.626991i	$0.784286\pi$
$314$		0			0
$315$	−4.84281	−	1.48718i	−0.272861	−	0.0837932i
$316$		0			0
$317$	20.6645			1.16063			0.580316	−	0.814392i	$-0.302929\pi$
$317$	20.6645			1.16063			0.580316	+	0.814392i	$0.302929\pi$
$318$		0			0
$319$	−16.6382	−	9.60609i	−0.931563	−	0.537838i
$320$		0			0
$321$	0.192370	−	0.333195i	0.0107371	−	0.0185971i
$322$		0			0
$323$	−28.0406	−	48.5677i	−1.56022	−	2.70238i
$324$		0			0
$325$	−17.1416	+	5.58267i	−0.950844	+	0.309671i
$326$		0			0
$327$	0.335987	+	0.581946i	0.0185801	+	0.0321817i
$328$		0			0
$329$	−10.7531	+	18.6249i	−0.592836	+	1.02682i
$330$		0			0
$331$	8.53482	+	4.92758i	0.469116	+	0.270844i	0.715870	−	0.698234i	$-0.246030\pi$
$331$	8.53482	+	4.92758i	0.469116	+	0.270844i	−0.246754	+	0.969078i	$0.579364\pi$
$332$		0			0
$333$	6.00544			0.329096
$334$		0			0
$335$	12.5563	+	3.85593i	0.686024	+	0.210672i
$336$		0			0
$337$			33.6610i			1.83363i	0.399310	+	0.916816i	$0.369250\pi$
$337$			33.6610i			1.83363i	−0.399310	+	0.916816i	$0.630750\pi$
$338$		0			0
$339$	7.51898			0.408375
$340$		0			0
$341$	3.66333	+	6.34507i	0.198380	+	0.343605i
$342$		0			0
$343$	20.0892			1.08472
$344$		0			0
$345$	−0.356934	−	1.55487i	−0.0192167	−	0.0837113i
$346$		0			0
$347$	2.37971	+	1.37393i	0.127749	+	0.0737562i	0.562513	−	0.826789i	$-0.309835\pi$
$347$	2.37971	+	1.37393i	0.127749	+	0.0737562i	−0.434763	+	0.900545i	$0.643168\pi$
$348$		0			0
$349$	−27.1320	+	15.6647i	−1.45234	+	0.838510i	−0.998614	−	0.0526301i	$-0.983240\pi$
$349$	−27.1320	+	15.6647i	−1.45234	+	0.838510i	−0.453728	+	0.891140i	$0.649906\pi$
$350$		0			0
$351$	3.33870	−	1.36127i	0.178207	−	0.0726592i
$352$		0			0
$353$	16.0120	+	27.7336i	0.852232	+	1.47611i	0.879189	+	0.476473i	$0.158085\pi$
$353$	16.0120	+	27.7336i	0.852232	+	1.47611i	−0.0269571	+	0.999637i	$0.508582\pi$
$354$		0			0
$355$	−15.3091	+	3.51435i	−0.812524	+	0.186522i
$356$		0			0
$357$	−8.28486	+	14.3498i	−0.438481	+	0.759472i
$358$		0			0
$359$			29.9749i			1.58201i	0.611807	+	0.791007i	$0.290443\pi$
$359$			29.9749i			1.58201i	−0.611807	+	0.791007i	$0.709557\pi$
$360$		0			0
$361$	19.8993	+	34.4666i	1.04733	+	1.81403i
$362$		0			0
$363$		−	2.81994i		−	0.148009i
$364$		0			0
$365$	21.7708	−	20.2510i	1.13953	−	1.05999i
$366$		0			0
$367$	19.7369	−	11.3951i	1.03026	−	0.594819i	0.113198	−	0.993572i	$-0.463890\pi$
$367$	19.7369	−	11.3951i	1.03026	−	0.594819i	0.917058	+	0.398753i	$0.130557\pi$
$368$		0			0
$369$			4.80259i			0.250013i
$370$		0			0
$371$	−15.9814	−	9.22689i	−0.829715	−	0.479036i
$372$		0			0
$373$	−17.4461	−	10.0725i	−0.903325	−	0.521535i	−0.0250474	−	0.999686i	$-0.507974\pi$
$373$	−17.4461	−	10.0725i	−0.903325	−	0.521535i	−0.878277	+	0.478151i	$0.841307\pi$
$374$		0			0
$375$	10.4227	+	4.04558i	0.538227	+	0.208913i
$376$		0			0
$377$	−14.8505	+	19.1327i	−0.764841	+	0.985384i
$378$		0			0
$379$	26.5235	−	15.3134i	1.36242	−	0.786594i	0.372475	−	0.928042i	$-0.378509\pi$
$379$	26.5235	−	15.3134i	1.36242	−	0.786594i	0.989946	+	0.141448i	$0.0451759\pi$
$380$		0			0
$381$	1.68533	−	2.91908i	0.0863422	−	0.149549i
$382$		0			0
$383$	1.49494	−	2.58932i	0.0763880	−	0.132308i	−0.825301	−	0.564693i	$-0.808995\pi$
$383$	1.49494	−	2.58932i	0.0763880	−	0.132308i	0.901689	+	0.432385i	$0.142328\pi$
$384$		0			0
$385$	−9.86843	−	10.6090i	−0.502942	−	0.540685i
$386$		0			0
$387$	1.62098	−	0.935871i	0.0823988	−	0.0475730i
$388$		0			0
$389$	26.7853			1.35807			0.679034	−	0.734107i	$-0.262399\pi$
$389$	26.7853			1.35807			0.679034	+	0.734107i	$0.262399\pi$
$390$		0			0
$391$	−5.21788			−0.263879
$392$		0			0
$393$	−9.95302	+	5.74638i	−0.502064	+	0.289867i
$394$		0			0
$395$	−16.0636	+	14.9422i	−0.808246	+	0.751825i
$396$		0			0
$397$	1.74986	−	3.03085i	0.0878231	−	0.152114i	−0.818768	−	0.574125i	$-0.805342\pi$
$397$	1.74986	−	3.03085i	0.0878231	−	0.152114i	0.906591	+	0.422011i	$0.138676\pi$
$398$		0			0
$399$	8.68630	−	15.0451i	0.434859	−	0.753197i
$400$		0			0
$401$	14.7527	−	8.51745i	0.736712	−	0.425341i	−0.0841605	−	0.996452i	$-0.526821\pi$
$401$	14.7527	−	8.51745i	0.736712	−	0.425341i	0.820873	+	0.571111i	$0.193487\pi$
$402$		0			0
$403$	8.55275	−	3.48716i	0.426043	−	0.173708i
$404$		0			0
$405$	−2.13755	−	0.656421i	−0.106216	−	0.0326178i
$406$		0			0
$407$	14.8749	+	8.58802i	0.737320	+	0.425692i
$408$		0			0
$409$	−18.0089	−	10.3974i	−0.890483	−	0.514121i	−0.0163826	−	0.999866i	$-0.505215\pi$
$409$	−18.0089	−	10.3974i	−0.890483	−	0.514121i	−0.874100	+	0.485745i	$0.838548\pi$
$410$		0			0
$411$			11.2122i			0.553055i
$412$		0			0
$413$	−20.3025	+	11.7217i	−0.999023	+	0.576786i
$414$		0			0
$415$	28.8244	−	26.8122i	1.41493	−	1.31616i
$416$		0			0
$417$			17.2456i			0.844521i
$418$		0			0
$419$	−0.608961	−	1.05475i	−0.0297497	−	0.0515280i	0.850767	−	0.525543i	$-0.176138\pi$
$419$	−0.608961	−	1.05475i	−0.0297497	−	0.0515280i	−0.880517	+	0.474015i	$0.842804\pi$
$420$		0			0
$421$		−	7.93509i		−	0.386733i	−0.981127	−	0.193366i	$-0.938059\pi$
$421$		−	7.93509i		−	0.386733i	0.981127	−	0.193366i	$-0.0619406\pi$
$422$		0			0
$423$	−4.74626	+	8.22076i	−0.230771	+	0.399707i
$424$		0			0
$425$	20.5240	−	30.2655i	0.995561	−	1.46809i
$426$		0			0
$427$	−0.815343	−	1.41222i	−0.0394572	−	0.0683419i
$428$		0			0
$429$	10.2163	+	1.40275i	0.493248	+	0.0677255i
$430$		0			0
$431$	−2.24775	+	1.29774i	−0.108270	+	0.0625098i	−0.553157	−	0.833077i	$-0.686577\pi$
$431$	−2.24775	+	1.29774i	−0.108270	+	0.0625098i	0.444887	+	0.895587i	$0.353244\pi$
$432$		0			0
$433$	−24.8423	−	14.3427i	−1.19384	−	0.689265i	−0.234667	−	0.972076i	$-0.575400\pi$
$433$	−24.8423	−	14.3427i	−1.19384	−	0.689265i	−0.959176	+	0.282811i	$0.908733\pi$
$434$		0			0
$435$	14.6397	−	3.36067i	0.701919	−	0.161132i
$436$		0			0
$437$	5.47071			0.261699
$438$		0			0
$439$	−6.07314	−	10.5190i	−0.289855	−	0.502044i	0.683920	−	0.729557i	$-0.260274\pi$
$439$	−6.07314	−	10.5190i	−0.289855	−	0.502044i	−0.973775	+	0.227514i	$0.926940\pi$
$440$		0			0
$441$	1.86710			0.0889097
$442$		0			0
$443$			24.7800i			1.17733i	0.808375	+	0.588667i	$0.200347\pi$
$443$			24.7800i			1.17733i	−0.808375	+	0.588667i	$0.799653\pi$
$444$		0			0
$445$	9.90135	−	32.2424i	0.469369	−	1.52844i
$446$		0			0
$447$	−15.6779			−0.741541
$448$		0			0
$449$	10.2512	+	5.91851i	0.483782	+	0.279312i	0.721991	−	0.691902i	$-0.243227\pi$
$449$	10.2512	+	5.91851i	0.483782	+	0.279312i	−0.238209	+	0.971214i	$0.576560\pi$
$450$		0			0
$451$	−6.86790	+	11.8955i	−0.323397	+	0.560139i
$452$		0			0
$453$	2.86161	+	4.95645i	0.134450	+	0.232874i
$454$		0			0
$455$	−14.9422	+	10.5057i	−0.700500	+	0.492514i
$456$		0			0
$457$	15.8258	+	27.4110i	0.740298	+	1.28223i	0.952360	+	0.304977i	$0.0986487\pi$
$457$	15.8258	+	27.4110i	0.740298	+	1.28223i	−0.212062	+	0.977256i	$0.568018\pi$
$458$		0			0
$459$	−3.65682	+	6.33380i	−0.170686	+	0.295637i
$460$		0			0
$461$	−27.7189	−	16.0035i	−1.29100	−	0.745357i	−0.312165	−	0.950028i	$-0.601054\pi$
$461$	−27.7189	−	16.0035i	−1.29100	−	0.745357i	−0.978831	+	0.204671i	$0.934388\pi$
$462$		0			0
$463$	2.99497			0.139188			0.0695941	−	0.997575i	$-0.477830\pi$
$463$	2.99497			0.139188			0.0695941	+	0.997575i	$0.477830\pi$
$464$		0			0
$465$	−5.47575	−	1.68155i	−0.253932	−	0.0779801i
$466$		0			0
$467$		−	10.6047i		−	0.490728i	−0.969431	−	0.245364i	$-0.921093\pi$
$467$		−	10.6047i		−	0.490728i	0.969431	−	0.245364i	$-0.0789074\pi$
$468$		0			0
$469$	13.3084			0.614527
$470$		0			0
$471$	−7.55311	−	13.0824i	−0.348029	−	0.602804i
$472$		0			0
$473$	5.35333			0.246146
$474$		0			0
$475$	−21.5185	+	31.7320i	−0.987336	+	1.45596i
$476$		0			0
$477$	−7.05399	−	4.07262i	−0.322980	−	0.186472i
$478$		0			0
$479$	34.2766	−	19.7896i	1.56614	−	0.904211i	0.569527	−	0.821973i	$-0.307126\pi$
$479$	34.2766	−	19.7896i	1.56614	−	0.904211i	0.996613	−	0.0822383i	$-0.0262068\pi$
$480$		0			0
$481$	13.2766	−	17.1050i	0.605362	−	0.779919i
$482$		0			0
$483$	−0.808186	−	1.39982i	−0.0367737	−	0.0636940i
$484$		0			0
$485$	−5.88947	−	25.6556i	−0.267427	−	1.16496i
$486$		0			0
$487$	16.9756	−	29.4026i	0.769238	−	1.33236i	−0.168739	−	0.985661i	$-0.553970\pi$
$487$	16.9756	−	29.4026i	0.769238	−	1.33236i	0.937977	−	0.346698i	$-0.112697\pi$
$488$		0			0
$489$			4.24710i			0.192061i
$490$		0			0
$491$	−17.6789	−	30.6208i	−0.797839	−	1.38190i	−0.921021	−	0.389513i	$-0.872643\pi$
$491$	−17.6789	−	30.6208i	−0.797839	−	1.38190i	0.123182	−	0.992384i	$-0.460690\pi$
$492$		0			0
$493$		−	49.1284i		−	2.21263i
$494$		0			0
$495$	−4.35579	−	4.68267i	−0.195778	−	0.210470i
$496$		0			0
$497$	−13.7825	+	7.95735i	−0.618231	+	0.356936i
$498$		0			0
$499$			39.5261i			1.76943i	0.466133	+	0.884715i	$0.345647\pi$
$499$			39.5261i			1.76943i	−0.466133	+	0.884715i	$0.654353\pi$
$500$		0			0
$501$	−15.3551	−	8.86529i	−0.686017	−	0.396072i
$502$		0			0
$503$	−8.34789	−	4.81966i	−0.372214	−	0.214898i	0.302211	−	0.953241i	$-0.402275\pi$
$503$	−8.34789	−	4.81966i	−0.372214	−	0.214898i	−0.674425	+	0.738343i	$0.735609\pi$
$504$		0			0
$505$	−0.251046	−	0.0770939i	−0.0111714	−	0.00343063i
$506$		0			0
$507$	3.50387	−	12.5189i	0.155613	−	0.555984i
$508$		0			0
$509$	2.93342	−	1.69361i	0.130022	−	0.0750681i	−0.433578	−	0.901116i	$-0.642749\pi$
$509$	2.93342	−	1.69361i	0.130022	−	0.0750681i	0.563600	+	0.826048i	$0.309416\pi$
$510$		0			0
$511$	15.0629	−	26.0898i	0.666345	−	1.15414i
$512$		0			0
$513$	3.83401	−	6.64070i	0.169276	−	0.293194i
$514$		0			0
$515$	3.88036	+	4.17156i	0.170989	+	0.183821i
$516$		0			0
$517$	−23.5120	+	13.5747i	−1.03406	+	0.597013i
$518$		0			0
$519$	23.8233			1.04573
$520$		0			0
$521$	−21.5610			−0.944604			−0.472302	−	0.881437i	$-0.656577\pi$
$521$	−21.5610			−0.944604			−0.472302	+	0.881437i	$0.656577\pi$
$522$		0			0
$523$	2.18487	−	1.26143i	0.0955375	−	0.0551586i	−0.451470	−	0.892286i	$-0.649100\pi$
$523$	2.18487	−	1.26143i	0.0955375	−	0.0551586i	0.547008	+	0.837128i	$0.315767\pi$
$524$		0			0
$525$	11.2984	+	0.818297i	0.493101	+	0.0357134i
$526$		0			0
$527$	−9.36767	+	16.2253i	−0.408062	+	0.706784i
$528$		0			0
$529$	−11.2455	+	19.4778i	−0.488935	+	0.846860i
$530$		0			0
$531$	−8.96127	+	5.17379i	−0.388886	+	0.224523i
$532$		0			0
$533$	13.6790	+	10.6174i	0.592501	+	0.459891i
$534$		0			0
$535$	−0.252552	+	0.822401i	−0.0109188	+	0.0355555i
$536$		0			0
$537$	17.8244	+	10.2909i	0.769180	+	0.444086i
$538$		0			0
$539$	4.62463	+	2.67003i	0.199197	+	0.115006i
$540$		0			0
$541$			39.9498i			1.71757i	0.512333	+	0.858787i	$0.328782\pi$
$541$			39.9498i			1.71757i	−0.512333	+	0.858787i	$0.671218\pi$
$542$		0			0
$543$	−11.8616	+	6.84830i	−0.509030	+	0.293889i
$544$		0			0
$545$	−1.02339	−	1.10019i	−0.0438372	−	0.0471270i
$546$		0			0
$547$		−	21.3909i		−	0.914608i	−0.889310	−	0.457304i	$-0.848815\pi$
$547$		−	21.3909i		−	0.914608i	0.889310	−	0.457304i	$-0.151185\pi$
$548$		0			0
$549$	−0.359881	−	0.623333i	−0.0153594	−	0.0266032i
$550$		0			0
$551$			51.5089i			2.19435i
$552$		0			0
$553$	−11.1142	+	19.2504i	−0.472624	+	0.818608i
$554$		0			0
$555$	−13.0881	+	3.00450i	−0.555561	+	0.127534i
$556$		0			0
$557$	−4.29134	−	7.43282i	−0.181830	−	0.314938i	0.760674	−	0.649134i	$-0.224869\pi$
$557$	−4.29134	−	7.43282i	−0.181830	−	0.314938i	−0.942504	+	0.334196i	$0.891535\pi$
$558$		0			0
$559$	0.918012	−	6.68593i	0.0388278	−	0.282785i
$560$		0			0
$561$	−18.1152	+	10.4588i	−0.764823	+	0.441571i
$562$		0			0
$563$	21.8485	+	12.6142i	0.920805	+	0.531627i	0.883892	−	0.467692i	$-0.154914\pi$
$563$	21.8485	+	12.6142i	0.920805	+	0.531627i	0.0369130	+	0.999318i	$0.488248\pi$
$564$		0			0
$565$	−16.3867	+	3.76172i	−0.689395	+	0.158257i
$566$		0			0
$567$	−2.26559			−0.0951458
$568$		0			0
$569$	−7.79198	−	13.4961i	−0.326657	−	0.565786i	0.655190	−	0.755464i	$-0.272589\pi$
$569$	−7.79198	−	13.4961i	−0.326657	−	0.565786i	−0.981846	+	0.189679i	$0.939255\pi$
$570$		0			0
$571$	7.91679			0.331308			0.165654	−	0.986184i	$-0.447027\pi$
$571$	7.91679			0.331308			0.165654	+	0.986184i	$0.447027\pi$
$572$		0			0
$573$		−	4.93776i		−	0.206278i
$574$		0			0
$575$	1.55579	+	3.21008i	0.0648809	+	0.133869i
$576$		0			0
$577$	37.4332			1.55836			0.779182	−	0.626798i	$-0.215635\pi$
$577$	37.4332			1.55836			0.779182	+	0.626798i	$0.215635\pi$
$578$		0			0
$579$	1.47469	+	0.851415i	0.0612862	+	0.0353836i
$580$		0			0
$581$	19.9432	−	34.5427i	0.827384	−	1.43307i
$582$		0			0
$583$	−11.6480	−	20.1750i	−0.482412	−	0.835562i
$584$		0			0
$585$	−6.59527	+	4.63707i	−0.272681	+	0.191719i
$586$		0			0
$587$	5.98997	+	10.3749i	0.247232	+	0.428219i	0.962757	−	0.270369i	$-0.0871456\pi$
$587$	5.98997	+	10.3749i	0.247232	+	0.428219i	−0.715525	+	0.698588i	$0.753812\pi$
$588$		0			0
$589$	9.82158	−	17.0115i	0.404691	−	0.700946i
$590$		0			0
$591$	2.44921	+	1.41405i	0.100747	+	0.0581664i
$592$		0			0
$593$	10.0990			0.414718			0.207359	−	0.978265i	$-0.433513\pi$
$593$	10.0990			0.414718			0.207359	+	0.978265i	$0.433513\pi$
$594$		0			0
$595$	10.8767	−	35.4186i	0.445902	−	1.45202i
$596$		0			0
$597$			6.83686i			0.279814i
$598$		0			0
$599$	−9.52616			−0.389228			−0.194614	−	0.980880i	$-0.562345\pi$
$599$	−9.52616			−0.389228			−0.194614	+	0.980880i	$0.562345\pi$
$600$		0			0
$601$	12.4296	+	21.5288i	0.507016	+	0.878177i	0.999967	+	0.00812002i	$0.00258471\pi$
$601$	12.4296	+	21.5288i	0.507016	+	0.878177i	−0.492951	+	0.870057i	$0.664082\pi$
$602$		0			0
$603$	5.87416			0.239214
$604$		0			0
$605$	1.41081	+	6.14573i	0.0573575	+	0.249859i
$606$		0			0
$607$	12.9708	+	7.48868i	0.526468	+	0.303956i	0.739577	−	0.673072i	$-0.235026\pi$
$607$	12.9708	+	7.48868i	0.526468	+	0.303956i	−0.213109	+	0.977028i	$0.568359\pi$
$608$		0			0
$609$	13.1799	−	7.60939i	0.534075	−	0.308348i
$610$		0			0
$611$	12.9219	+	31.6927i	0.522763	+	1.28215i
$612$		0			0
$613$	0.250193	+	0.433347i	0.0101052	+	0.0175027i	0.871034	−	0.491223i	$-0.163450\pi$
$613$	0.250193	+	0.433347i	0.0101052	+	0.0175027i	−0.860929	+	0.508726i	$0.830117\pi$
$614$		0			0
$615$	−2.40272	−	10.4667i	−0.0968870	−	0.422057i
$616$		0			0
$617$	−3.86365	+	6.69203i	−0.155545	+	0.269411i	−0.933257	−	0.359209i	$-0.883047\pi$
$617$	−3.86365	+	6.69203i	−0.155545	+	0.269411i	0.777713	+	0.628620i	$0.216380\pi$
$618$		0			0
$619$		−	37.1728i		−	1.49410i	−0.664766	−	0.747051i	$-0.731469\pi$
$619$		−	37.1728i		−	1.49410i	0.664766	−	0.747051i	$-0.268531\pi$
$620$		0			0
$621$	−0.356722	−	0.617861i	−0.0143148	−	0.0247939i
$622$		0			0
$623$		−	34.1738i		−	1.36914i
$624$		0			0
$625$	−24.7391	−	3.60241i	−0.989564	−	0.144097i
$626$		0			0
$627$	18.9929	−	10.9656i	0.758505	−	0.437923i
$628$		0			0
$629$			43.9216i			1.75127i
$630$		0			0
$631$	30.0923	+	17.3738i	1.19796	+	0.691640i	0.960099	−	0.279661i	$-0.0902220\pi$
$631$	30.0923	+	17.3738i	1.19796	+	0.691640i	0.237856	+	0.971300i	$0.423555\pi$
$632$		0			0
$633$	−22.0429	−	12.7265i	−0.876128	−	0.505833i
$634$		0			0
$635$	−2.21258	+	7.20496i	−0.0878034	+	0.285920i
$636$		0			0
$637$	4.12773	−	5.31797i	0.163547	−	0.210706i
$638$		0			0
$639$	−6.08342	+	3.51226i	−0.240656	+	0.138943i
$640$		0			0
$641$	−11.2338	+	19.4574i	−0.443707	+	0.768522i	−0.997961	−	0.0638248i	$-0.979670\pi$
$641$	−11.2338	+	19.4574i	−0.443707	+	0.768522i	0.554254	+	0.832347i	$0.313003\pi$
$642$		0			0
$643$	−12.8669	+	22.2862i	−0.507423	+	0.878882i	0.492540	+	0.870290i	$0.336068\pi$
$643$	−12.8669	+	22.2862i	−0.507423	+	0.878882i	−0.999963	+	0.00859230i	$0.997265\pi$
$644$		0			0
$645$	−3.06451	+	2.85059i	−0.120665	+	0.112242i
$646$		0			0
$647$	27.4018	−	15.8205i	1.07728	−	0.621966i	0.147116	−	0.989119i	$-0.453001\pi$
$647$	27.4018	−	15.8205i	1.07728	−	0.621966i	0.930161	+	0.367153i	$0.119667\pi$
$648$		0			0
$649$	−29.5949			−1.16170
$650$		0			0
$651$	−5.80376			−0.227467
$652$		0			0
$653$	13.5737	−	7.83676i	0.531178	−	0.306676i	−0.210318	−	0.977633i	$-0.567450\pi$
$653$	13.5737	−	7.83676i	0.531178	−	0.306676i	0.741496	+	0.670957i	$0.234117\pi$
$654$		0			0
$655$	18.8165	−	17.5030i	0.735223	−	0.683899i
$656$		0			0
$657$	6.64858	−	11.5157i	0.259386	−	0.449269i
$658$		0			0
$659$	−2.94682	+	5.10404i	−0.114792	+	0.198825i	−0.917697	−	0.397282i	$-0.869953\pi$
$659$	−2.94682	+	5.10404i	−0.114792	+	0.198825i	0.802905	+	0.596107i	$0.203287\pi$
$660$		0			0
$661$	38.9248	−	22.4733i	1.51400	−	0.874108i	0.514134	−	0.857710i	$-0.328113\pi$
$661$	38.9248	−	22.4733i	1.51400	−	0.874108i	0.999866	−	0.0163985i	$-0.00522004\pi$
$662$		0			0
$663$	9.95583	+	24.4181i	0.386653	+	0.948320i
$664$		0			0
$665$	−11.4037	+	37.1348i	−0.442218	+	1.44002i
$666$		0			0
$667$	4.15040	+	2.39623i	0.160704	+	0.0927825i
$668$		0			0
$669$	−8.87412	−	5.12347i	−0.343093	−	0.198085i
$670$		0			0
$671$		−	2.05858i		−	0.0794706i
$672$		0			0
$673$	−11.2756	+	6.50995i	−0.434641	+	0.250940i	−0.701322	−	0.712845i	$-0.747406\pi$
$673$	−11.2756	+	6.50995i	−0.434641	+	0.250940i	0.266681	+	0.963785i	$0.414073\pi$
$674$		0			0
$675$	4.98694	+	0.361185i	0.191947	+	0.0139020i
$676$		0			0
$677$		−	27.6353i		−	1.06211i	−0.847337	−	0.531056i	$-0.821795\pi$
$677$		−	27.6353i		−	1.06211i	0.847337	−	0.531056i	$-0.178205\pi$
$678$		0			0
$679$	−13.3352	−	23.0973i	−0.511759	−	0.886392i
$680$		0			0
$681$		−	26.4774i		−	1.01462i
$682$		0			0
$683$	15.0973	−	26.1492i	0.577681	−	1.00057i	−0.418064	−	0.908418i	$-0.637291\pi$
$683$	15.0973	−	26.1492i	0.577681	−	1.00057i	0.995745	−	0.0921547i	$-0.0293754\pi$
$684$		0			0
$685$	−5.60940	−	24.4356i	−0.214324	−	0.933635i
$686$		0			0
$687$	−4.43885	−	7.68832i	−0.169353	−	0.293328i
$688$		0			0
$689$	−27.1946	+	11.0879i	−1.03603	+	0.422414i
$690$		0			0
$691$	3.66648	−	2.11685i	0.139480	−	0.0805286i	−0.428636	−	0.903477i	$-0.641006\pi$
$691$	3.66648	−	2.11685i	0.139480	−	0.0805286i	0.568116	+	0.822949i	$0.307672\pi$
$692$		0			0
$693$	−5.61164	−	3.23988i	−0.213169	−	0.123073i
$694$		0			0
$695$	−8.62791	−	37.5847i	−0.327275	−	1.42567i
$696$		0			0
$697$	−35.1244			−1.33043
$698$		0			0
$699$	0.522152	+	0.904394i	0.0197496	+	0.0342073i
$700$		0			0
$701$	−52.5357			−1.98425			−0.992123	−	0.125271i	$-0.960020\pi$
$701$	−52.5357			−1.98425			−0.992123	+	0.125271i	$0.960020\pi$
$702$		0			0
$703$		−	46.0498i		−	1.73680i
$704$		0			0
$705$	6.23109	−	20.2907i	0.234676	−	0.764192i
$706$		0			0
$707$	−0.266084			−0.0100071
$708$		0			0
$709$	−5.19069	−	2.99685i	−0.194941	−	0.112549i	0.399353	−	0.916797i	$-0.369235\pi$
$709$	−5.19069	−	2.99685i	−0.194941	−	0.112549i	−0.594293	+	0.804248i	$0.702568\pi$
$710$		0			0
$711$	−4.90565	+	8.49684i	−0.183976	+	0.318656i
$712$		0			0
$713$	−0.913814	−	1.58277i	−0.0342226	−	0.0592753i
$714$		0			0
$715$	−22.9670	+	2.05405i	−0.858918	+	0.0768172i
$716$		0			0
$717$	0.00404471	+	0.00700565i	0.000151053	+	0.000261631i
$718$		0			0
$719$	1.22252	−	2.11747i	0.0455924	−	0.0789684i	−0.842329	−	0.538964i	$-0.818816\pi$
$719$	1.22252	−	2.11747i	0.0455924	−	0.0789684i	0.887921	+	0.459996i	$0.152149\pi$
$720$		0			0
$721$	4.99914	+	2.88625i	0.186178	+	0.107490i
$722$		0			0
$723$	−5.70359			−0.212119
$724$		0			0
$725$	−30.2241	+	14.6484i	−1.12250	+	0.544027i
$726$		0			0
$727$		−	3.41516i		−	0.126661i	−0.997993	−	0.0633306i	$-0.979828\pi$
$727$		−	3.41516i		−	0.126661i	0.997993	−	0.0633306i	$-0.0201723\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	6.84462	+	11.8552i	0.253158	+	0.438482i
$732$		0			0
$733$	−5.39830			−0.199391			−0.0996955	−	0.995018i	$-0.531787\pi$
$733$	−5.39830			−0.199391			−0.0996955	+	0.995018i	$0.531787\pi$
$734$		0			0
$735$	−4.06913	+	0.934105i	−0.150092	+	0.0344550i
$736$		0			0
$737$	14.5497	+	8.40029i	0.535946	+	0.309429i
$738$		0			0
$739$	2.19845	−	1.26928i	0.0808713	−	0.0466910i	−0.459019	−	0.888426i	$-0.651799\pi$
$739$	2.19845	−	1.26928i	0.0808713	−	0.0466910i	0.539890	+	0.841735i	$0.318466\pi$
$740$		0			0
$741$	−10.4382	−	25.6013i	−0.383458	−	0.940486i
$742$		0			0
$743$	13.7095	+	23.7455i	0.502953	+	0.871140i	0.999994	+	0.00341284i	$0.00108634\pi$
$743$	13.7095	+	23.7455i	0.502953	+	0.871140i	−0.497041	+	0.867727i	$0.665580\pi$
$744$		0			0
$745$	34.1682	−	7.84361i	1.25183	−	0.287368i
$746$		0			0
$747$	8.80267	−	15.2467i	0.322073	−	0.557846i
$748$		0			0
$749$			0.871663i			0.0318499i
$750$		0			0
$751$	−13.5522	−	23.4731i	−0.494526	−	0.856544i	0.505454	−	0.862853i	$-0.331325\pi$
$751$	−13.5522	−	23.4731i	−0.494526	−	0.856544i	−0.999980	+	0.00630941i	$0.997992\pi$
$752$		0			0
$753$			14.5010i			0.528446i
$754$		0			0
$755$	−8.71623	−	9.37034i	−0.317216	−	0.341022i
$756$		0			0
$757$	7.76622	−	4.48383i	0.282268	−	0.162968i	−0.352182	−	0.935932i	$-0.614560\pi$
$757$	7.76622	−	4.48383i	0.282268	−	0.162968i	0.634450	+	0.772964i	$0.281227\pi$
$758$		0			0
$759$		−	2.04051i		−	0.0740658i
$760$		0			0
$761$	−19.1749	−	11.0706i	−0.695091	−	0.401311i	0.110426	−	0.993884i	$-0.464779\pi$
$761$	−19.1749	−	11.0706i	−0.695091	−	0.401311i	−0.805516	+	0.592574i	$0.798112\pi$
$762$		0			0
$763$	−1.31845	−	0.761208i	−0.0477311	−	0.0275576i
$764$		0			0
$765$	4.80083	−	15.6333i	0.173574	−	0.565222i
$766$		0			0
$767$	−5.07506	+	36.9619i	−0.183250	+	1.33462i
$768$		0			0
$769$	−46.3751	+	26.7747i	−1.67233	+	0.965520i	−0.705999	+	0.708213i	$0.749502\pi$
$769$	−46.3751	+	26.7747i	−1.67233	+	0.965520i	−0.966330	+	0.257307i	$0.917165\pi$
$770$		0			0
$771$	1.98430	−	3.43691i	0.0714628	−	0.123777i
$772$		0			0
$773$	−2.99346	+	5.18483i	−0.107667	+	0.186485i	−0.914825	−	0.403851i	$-0.867672\pi$
$773$	−2.99346	+	5.18483i	−0.107667	+	0.186485i	0.807157	+	0.590336i	$0.201005\pi$
$774$		0			0
$775$	12.7750	+	0.925247i	0.458892	+	0.0332358i
$776$		0			0
$777$	−11.7830	+	6.80293i	−0.422713	+	0.244054i
$778$		0			0
$779$	36.8264			1.31944
$780$		0			0
$781$	−20.0907			−0.718902
$782$		0			0
$783$	5.81741	−	3.35868i	0.207897	−	0.120029i
$784$		0			0
$785$	23.0062	+	24.7327i	0.821126	+	0.882747i
$786$		0			0
$787$	−3.21479	+	5.56818i	−0.114595	+	0.198484i	−0.917618	−	0.397464i	$-0.869890\pi$
$787$	−3.21479	+	5.56818i	−0.114595	+	0.198484i	0.803023	+	0.595948i	$0.203224\pi$
$788$		0			0
$789$	12.1487	−	21.0422i	0.432506	−	0.749123i
$790$		0			0
$791$	−14.7527	+	8.51746i	−0.524545	+	0.302846i
$792$		0			0
$793$	−2.57102	−	0.353014i	−0.0912996	−	0.0125359i
$794$		0			0
$795$	17.4108	+	5.34671i	0.617499	+	0.189628i
$796$		0			0
$797$	14.0123	+	8.08999i	0.496340	+	0.286562i	0.727201	−	0.686425i	$-0.240821\pi$
$797$	14.0123	+	8.08999i	0.496340	+	0.286562i	−0.230861	+	0.972987i	$0.574154\pi$
$798$		0			0
$799$	−60.1237	−	34.7124i	−2.12702	−	1.22804i
$800$		0			0
$801$		−	15.0838i		−	0.532961i
$802$		0			0
$803$	32.9357	−	19.0155i	1.16228	−	0.671041i
$804$		0			0
$805$	2.46167	+	2.64641i	0.0867625	+	0.0932736i
$806$		0			0
$807$			3.29442i			0.115969i
$808$		0			0
$809$	−12.8802	−	22.3092i	−0.452844	−	0.784349i	0.545718	−	0.837969i	$-0.316257\pi$
$809$	−12.8802	−	22.3092i	−0.452844	−	0.784349i	−0.998561	+	0.0536206i	$0.982924\pi$
$810$		0			0
$811$			13.9104i			0.488460i	0.969717	+	0.244230i	$0.0785352\pi$
$811$			13.9104i			0.488460i	−0.969717	+	0.244230i	$0.921465\pi$
$812$		0			0
$813$	−2.00363	+	3.47040i	−0.0702705	+	0.121712i
$814$		0			0
$815$	−2.12481	−	9.25606i	−0.0744289	−	0.324226i
$816$		0			0
$817$	−7.17628	−	12.4297i	−0.251066	−	0.434859i
$818$		0			0
$819$	−5.00869	+	6.45296i	−0.175018	+	0.225485i
$820$		0			0
$821$	−3.26380	+	1.88436i	−0.113907	+	0.0657645i	−0.555871	−	0.831268i	$-0.687615\pi$
$821$	−3.26380	+	1.88436i	−0.113907	+	0.0657645i	0.441964	+	0.897033i	$0.354282\pi$
$822$		0			0
$823$	−6.06345	−	3.50074i	−0.211359	−	0.122028i	0.390584	−	0.920567i	$-0.372273\pi$
$823$	−6.06345	−	3.50074i	−0.211359	−	0.122028i	−0.601943	+	0.798539i	$0.705606\pi$
$824$		0			0
$825$	11.8356	+	8.02614i	0.412064	+	0.279434i
$826$		0			0
$827$	29.5086			1.02611			0.513057	−	0.858355i	$-0.328513\pi$
$827$	29.5086			1.02611			0.513057	+	0.858355i	$0.328513\pi$
$828$		0			0
$829$	15.9562	+	27.6370i	0.554183	+	0.959873i	0.997967	+	0.0637389i	$0.0203025\pi$
$829$	15.9562	+	27.6370i	0.554183	+	0.959873i	−0.443784	+	0.896134i	$0.646364\pi$
$830$		0			0
$831$	16.6951			0.579148
$832$		0			0
$833$			13.6553i			0.473129i
$834$		0			0
$835$	37.9000	+	11.6387i	1.31158	+	0.402775i
$836$		0			0
$837$	−2.56170			−0.0885452
$838$		0			0
$839$	26.3520	+	15.2143i	0.909772	+	0.525257i	0.880358	−	0.474310i	$-0.157302\pi$
$839$	26.3520	+	15.2143i	0.909772	+	0.525257i	0.0294143	+	0.999567i	$0.490636\pi$
$840$		0			0
$841$	−8.06147	+	13.9629i	−0.277982	+	0.481478i
$842$		0			0
$843$	−3.04095	−	5.26708i	−0.104736	−	0.181408i
$844$		0			0
$845$	−1.37312	+	29.0364i	−0.0472367	+	0.998884i
$846$		0			0
$847$	3.19442	+	5.53289i	0.109761	+	0.190112i
$848$		0			0
$849$	−0.701863	+	1.21566i	−0.0240879	+	0.0417214i
$850$		0			0
$851$	−3.71053	−	2.14227i	−0.127195	−	0.0734362i
$852$		0			0
$853$	46.9433			1.60731			0.803653	−	0.595098i	$-0.202887\pi$
$853$	46.9433			1.60731			0.803653	+	0.595098i	$0.202887\pi$
$854$		0			0
$855$	−5.03345	+	16.3908i	−0.172141	+	0.560552i
$856$		0			0
$857$		−	35.4976i		−	1.21258i	−0.795245	−	0.606288i	$-0.792658\pi$
$857$		−	35.4976i		−	1.21258i	0.795245	−	0.606288i	$-0.207342\pi$
$858$		0			0
$859$	15.8945			0.542313			0.271156	−	0.962535i	$-0.412594\pi$
$859$	15.8945			0.542313			0.271156	+	0.962535i	$0.412594\pi$
$860$		0			0
$861$	−5.44035	−	9.42296i	−0.185407	−	0.321134i
$862$		0			0
$863$	−11.0915			−0.377558			−0.188779	−	0.982020i	$-0.560453\pi$
$863$	−11.0915			−0.377558			−0.188779	+	0.982020i	$0.560453\pi$
$864$		0			0
$865$	−51.9202	+	11.9187i	−1.76534	+	0.405249i
$866$		0			0
$867$	−31.6007	−	18.2447i	−1.07322	−	0.619622i
$868$		0			0
$869$	−24.3016	+	14.0306i	−0.824377	+	0.475954i
$870$		0			0
$871$	12.9864	−	16.7311i	0.440028	−	0.566910i
$872$		0			0
$873$	−5.88598	−	10.1948i	−0.199210	−	0.345042i
$874$		0			0
$875$	−25.0328	+	3.86914i	−0.846264	+	0.130801i
$876$		0			0
$877$	−22.1902	+	38.4345i	−0.749309	+	1.29784i	0.198845	+	0.980031i	$0.436281\pi$
$877$	−22.1902	+	38.4345i	−0.749309	+	1.29784i	−0.948154	+	0.317810i	$0.897052\pi$
$878$		0			0
$879$			2.60049i			0.0877122i
$880$		0			0
$881$	−21.0268	−	36.4194i	−0.708410	−	1.22700i	−0.965447	−	0.260600i	$-0.916079\pi$
$881$	−21.0268	−	36.4194i	−0.708410	−	1.22700i	0.257037	−	0.966402i	$-0.417254\pi$
$882$		0			0
$883$			45.0797i			1.51705i	0.651642	+	0.758527i	$0.274081\pi$
$883$			45.0797i			1.51705i	−0.651642	+	0.758527i	$0.725919\pi$
$884$		0			0
$885$	16.9416	−	15.7589i	0.569485	−	0.529731i
$886$		0			0
$887$	34.6139	−	19.9843i	1.16222	−	0.671008i	0.210385	−	0.977619i	$-0.432528\pi$
$887$	34.6139	−	19.9843i	1.16222	−	0.671008i	0.951835	+	0.306611i	$0.0991950\pi$
$888$		0			0
$889$			7.63655i			0.256122i
$890$		0			0
$891$	−2.47690	−	1.43004i	−0.0829793	−	0.0479081i
$892$		0			0
$893$	63.0370	+	36.3944i	2.10945	+	1.21789i
$894$		0			0
$895$	−43.9947	−	13.5104i	−1.47058	−	0.451602i
$896$		0			0
$897$	−2.54845	−	0.349915i	−0.0850903	−	0.0116833i
$898$		0			0
$899$	14.9024	−	8.60392i	0.497024	−	0.286957i
$900$		0			0
$901$	29.7857	−	51.5903i	0.992305	−	1.71872i
$902$		0			0
$903$	−2.12030	+	3.67247i	−0.0705591	+	0.122212i
$904$		0			0
$905$	22.4248	−	20.8594i	0.745425	−	0.693389i
$906$		0			0
$907$	−45.7066	+	26.3887i	−1.51766	+	0.876224i	−0.517880	+	0.855454i	$0.673278\pi$
$907$	−45.7066	+	26.3887i	−1.51766	+	0.876224i	−0.999784	+	0.0207701i	$0.993388\pi$
$908$		0			0
$909$	−0.117446			−0.00389543
$910$		0			0
$911$	−1.85318			−0.0613985			−0.0306993	−	0.999529i	$-0.509773\pi$
$911$	−1.85318			−0.0613985			−0.0306993	+	0.999529i	$0.509773\pi$
$912$		0			0
$913$	43.6067	−	25.1763i	1.44317	−	0.833215i
$914$		0			0
$915$	1.09617	+	1.17843i	0.0362383	+	0.0389578i
$916$		0			0
$917$	13.0189	−	22.5495i	0.429923	−	0.744649i
$918$		0			0
$919$	−17.2199	+	29.8257i	−0.568032	+	0.983860i	0.428729	+	0.903433i	$0.358962\pi$
$919$	−17.2199	+	29.8257i	−0.568032	+	0.983860i	−0.996761	+	0.0804264i	$0.974372\pi$
$920$		0			0
$921$	−4.65949	+	2.69016i	−0.153535	+	0.0886437i
$922$		0			0
$923$	−3.44524	+	25.0919i	−0.113402	+	0.825909i
$924$		0			0
$925$	27.0209	−	13.0959i	0.888442	−	0.430590i
$926$		0			0
$927$	2.20655	+	1.27395i	0.0724726	+	0.0418421i
$928$		0			0
$929$	−13.3180	−	7.68917i	−0.436951	−	0.252274i	0.265353	−	0.964151i	$-0.414512\pi$
$929$	−13.3180	−	7.68917i	−0.436951	−	0.252274i	−0.702303	+	0.711878i	$0.747845\pi$
$930$		0			0
$931$		−	14.3170i		−	0.469221i
$932$		0			0
$933$	6.08076	−	3.51073i	0.199075	−	0.114936i
$934$		0			0
$935$	34.2474	−	31.8567i	1.12001	−	1.04182i
$936$		0			0
$937$		−	2.15544i		−	0.0704151i	−0.999380	−	0.0352075i	$-0.988791\pi$
$937$		−	2.15544i		−	0.0704151i	0.999380	−	0.0352075i	$-0.0112092\pi$
$938$		0			0
$939$	−11.0926	−	19.2130i	−0.361994	−	0.626991i
$940$		0			0
$941$		−	16.5015i		−	0.537934i	−0.963149	−	0.268967i	$-0.913318\pi$
$941$		−	16.5015i		−	0.537934i	0.963149	−	0.268967i	$-0.0866822\pi$
$942$		0			0
$943$	1.71319	−	2.96733i	0.0557892	−	0.0966297i
$944$		0			0
$945$	4.93758	−	1.13347i	0.160620	−	0.0368717i
$946$		0			0
$947$	−20.4847	−	35.4806i	−0.665664	−	1.15296i	−0.979105	−	0.203356i	$-0.934815\pi$
$947$	−20.4847	−	35.4806i	−0.665664	−	1.15296i	0.313441	−	0.949608i	$-0.398518\pi$
$948$		0			0
$949$	−18.1010	−	44.3953i	−0.587583	−	1.44113i
$950$		0			0
$951$	−17.8959	+	10.3322i	−0.580316	+	0.335045i
$952$		0			0
$953$	−9.49649	−	5.48280i	−0.307621	−	0.177605i	0.338240	−	0.941060i	$-0.390168\pi$
$953$	−9.49649	−	5.48280i	−0.307621	−	0.177605i	−0.645862	+	0.763454i	$0.723502\pi$
$954$		0			0
$955$	2.47035	+	10.7613i	0.0799385	+	0.348227i
$956$		0			0
$957$	19.2122			0.621042
$958$		0			0
$959$	−12.7011	−	21.9989i	−0.410139	−	0.710382i
$960$		0			0
$961$	24.4377			0.788313
$962$		0			0
$963$			0.384740i			0.0123981i
$964$		0			0
$965$	−3.63988	−	1.11777i	−0.117172	−	0.0359824i
$966$		0			0
$967$	9.50007			0.305502			0.152751	−	0.988265i	$-0.451187\pi$
$967$	9.50007			0.305502			0.152751	+	0.988265i	$0.451187\pi$
$968$		0			0
$969$	48.5677	+	28.0406i	1.56022	+	0.900794i
$970$		0			0
$971$	23.1602	−	40.1147i	0.743247	−	1.28734i	−0.207763	−	0.978179i	$-0.566618\pi$
$971$	23.1602	−	40.1147i	0.743247	−	1.28734i	0.951009	−	0.309162i	$-0.100048\pi$
$972$		0			0
$973$	−19.5357	−	33.8369i	−0.626287	−	1.08476i
$974$		0			0
$975$	12.0537	−	13.4055i	0.386028	−	0.429320i
$976$		0			0
$977$	0.457860	+	0.793037i	0.0146482	+	0.0253715i	0.873257	−	0.487261i	$-0.162004\pi$
$977$	0.457860	+	0.793037i	0.0146482	+	0.0253715i	−0.858608	+	0.512632i	$0.828670\pi$
$978$		0			0
$979$	21.5705	−	37.3612i	0.689396	−	1.19407i
$980$		0			0
$981$	−0.581946	−	0.335987i	−0.0185801	−	0.0107272i
$982$		0			0
$983$	14.9458			0.476696			0.238348	−	0.971180i	$-0.423394\pi$
$983$	14.9458			0.476696			0.238348	+	0.971180i	$0.423394\pi$
$984$		0			0
$985$	−6.04522	−	1.85643i	−0.192617	−	0.0591508i
$986$		0			0
$987$		−	21.5061i		−	0.684548i
$988$		0			0
$989$	−1.33538			−0.0424627
$990$		0			0
$991$	25.4508	+	44.0822i	0.808473	+	1.40032i	0.913921	+	0.405891i	$0.133039\pi$
$991$	25.4508	+	44.0822i	0.808473	+	1.40032i	−0.105448	+	0.994425i	$0.533628\pi$
$992$		0			0
$993$	−9.85516			−0.312744
$994$		0			0
$995$	−3.42045	−	14.9001i	−0.108436	−	0.472365i
$996$		0			0
$997$	9.75027	+	5.62932i	0.308794	+	0.178282i	0.646387	−	0.763010i	$-0.276279\pi$
$997$	9.75027	+	5.62932i	0.308794	+	0.178282i	−0.337593	+	0.941292i	$0.609613\pi$
$998$		0			0
$999$	−5.20086	+	3.00272i	−0.164548	+	0.0950018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1560.2.dr.a.49.5	✓	44
5.4	even	2		1560.2.dr.b.49.18	yes	44
13.4	even	6		1560.2.dr.b.1369.18	yes	44
65.4	even	6	inner	1560.2.dr.a.1369.5	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.dr.a.49.5	✓	44	1.1	even	1	trivial
1560.2.dr.a.1369.5	yes	44	65.4	even	6	inner
1560.2.dr.b.49.18	yes	44	5.4	even	2
1560.2.dr.b.1369.18	yes	44	13.4	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:	\( N \)	\(=\)	\( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1560.dr (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(1.63725 - 1.52296i) q^{5} +(1.13279 - 1.96206i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{3} +(1.63725 - 1.52296i) q^{5} +(1.13279 - 1.96206i) q^{7} +(0.500000 - 0.866025i) q^{9} +(2.47690 - 1.43004i) q^{11} +(-1.36127 - 3.33870i) q^{13} +(-0.656421 + 2.13755i) q^{15} +(6.33380 + 3.65682i) q^{17} +(-6.64070 - 3.83401i) q^{19} +2.26559i q^{21} +(-0.617861 + 0.356722i) q^{23} +(0.361185 - 4.98694i) q^{25} +1.00000i q^{27} +(-3.35868 - 5.81741i) q^{29} +2.56170i q^{31} +(-1.43004 + 2.47690i) q^{33} +(-1.13347 - 4.93758i) q^{35} +(3.00272 + 5.20086i) q^{37} +(2.84825 + 2.21077i) q^{39} +(-4.15916 + 2.40130i) q^{41} +(1.62098 + 0.935871i) q^{43} +(-0.500296 - 2.17938i) q^{45} -9.49251 q^{47} +(0.933552 + 1.61696i) q^{49} -7.31364 q^{51} -8.14524i q^{53} +(1.87742 - 6.11356i) q^{55} +7.66802 q^{57} +(-8.96127 - 5.17379i) q^{59} +(0.359881 - 0.623333i) q^{61} +(-1.13279 - 1.96206i) q^{63} +(-7.31345 - 3.39314i) q^{65} +(2.93708 + 5.08717i) q^{67} +(0.356722 - 0.617861i) q^{69} +(-6.08342 - 3.51226i) q^{71} +13.2972 q^{73} +(2.18067 + 4.49941i) q^{75} -6.47977i q^{77} -9.81131 q^{79} +(-0.500000 - 0.866025i) q^{81} +17.6053 q^{83} +(15.9392 - 3.65899i) q^{85} +(5.81741 + 3.35868i) q^{87} +(13.0630 - 7.54192i) q^{89} +(-8.09277 - 1.11118i) q^{91} +(-1.28085 - 2.21850i) q^{93} +(-16.7115 + 3.83628i) q^{95} +(5.88598 - 10.1948i) q^{97} -2.86008i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{5} + 2 q^{7} + 22 q^{9}+O(q^{10}) \) 44 * q - 2 * q^5 + 2 * q^7 + 22 * q^9	\( 44 q - 2 q^{5} + 2 q^{7} + 22 q^{9} - 6 q^{11} - 4 q^{13} + 18 q^{17} - 6 q^{19} - 6 q^{23} + 2 q^{25} - 2 q^{29} - 6 q^{33} - 16 q^{37} - 2 q^{39} - 6 q^{41} - 36 q^{43} - 4 q^{45} - 48 q^{47} - 36 q^{49} + 24 q^{51} - 24 q^{55} + 24 q^{57} - 14 q^{61} - 2 q^{63} + 26 q^{65} - 4 q^{67} - 8 q^{69} + 44 q^{73} - 16 q^{75} + 28 q^{79} - 22 q^{81} - 56 q^{83} - 44 q^{85} - 6 q^{87} + 18 q^{89} + 30 q^{91} + 8 q^{93} - 34 q^{95} - 24 q^{97}+O(q^{100}) \) 44 * q - 2 * q^5 + 2 * q^7 + 22 * q^9 - 6 * q^11 - 4 * q^13 + 18 * q^17 - 6 * q^19 - 6 * q^23 + 2 * q^25 - 2 * q^29 - 6 * q^33 - 16 * q^37 - 2 * q^39 - 6 * q^41 - 36 * q^43 - 4 * q^45 - 48 * q^47 - 36 * q^49 + 24 * q^51 - 24 * q^55 + 24 * q^57 - 14 * q^61 - 2 * q^63 + 26 * q^65 - 4 * q^67 - 8 * q^69 + 44 * q^73 - 16 * q^75 + 28 * q^79 - 22 * q^81 - 56 * q^83 - 44 * q^85 - 6 * q^87 + 18 * q^89 + 30 * q^91 + 8 * q^93 - 34 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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