LMFDB - Embedded newform 1560.2.dr.a.49.9

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			49.9
Character	$\chi$	$=$	1560.49
Dual form			1560.2.dr.a.1369.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{3} +(1.24679 - 1.85621i) q^{5} +(0.168505 - 0.291860i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{3} +(1.24679 - 1.85621i) q^{5} +(0.168505 - 0.291860i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-5.01714 + 2.89665i) q^{11} +(3.26826 - 1.52264i) q^{13} +(-0.151651 + 2.23092i) q^{15} +(-6.16737 - 3.56073i) q^{17} +(-0.477290 - 0.275564i) q^{19} +0.337011i q^{21} +(0.670195 - 0.386937i) q^{23} +(-1.89101 - 4.62861i) q^{25} +1.00000i q^{27} +(0.288472 + 0.499648i) q^{29} +3.63801i q^{31} +(2.89665 - 5.01714i) q^{33} +(-0.331661 - 0.676670i) q^{35} +(-3.52425 - 6.10418i) q^{37} +(-2.06908 + 2.95278i) q^{39} +(-8.34117 + 4.81578i) q^{41} +(-6.56102 - 3.78801i) q^{43} +(-0.984126 - 2.00786i) q^{45} +4.67938 q^{47} +(3.44321 + 5.96382i) q^{49} +7.12147 q^{51} +10.0057i q^{53} +(-0.878560 + 12.9244i) q^{55} +0.551127 q^{57} +(-8.79577 - 5.07824i) q^{59} +(4.09606 - 7.09458i) q^{61} +(-0.168505 - 0.291860i) q^{63} +(1.24851 - 7.96500i) q^{65} +(-2.73025 - 4.72894i) q^{67} +(-0.386937 + 0.670195i) q^{69} +(4.65795 + 2.68927i) q^{71} -9.73652 q^{73} +(3.95197 + 3.06299i) q^{75} +1.95240i q^{77} -13.5983 q^{79} +(-0.500000 - 0.866025i) q^{81} -0.916806 q^{83} +(-14.2989 + 7.00842i) q^{85} +(-0.499648 - 0.288472i) q^{87} +(-3.73426 + 2.15597i) q^{89} +(0.106321 - 1.21045i) q^{91} +(-1.81901 - 3.15061i) q^{93} +(-1.10659 + 0.542379i) q^{95} +(3.30366 - 5.72210i) q^{97} +5.79329i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.24679	−	1.85621i	0.557583	−	0.830121i
$5$	1.24679	−	1.85621i	0.557583	−	0.830121i
$6$		0			0
$7$	0.168505	−	0.291860i	0.0636891	−	0.110313i	−0.832423	−	0.554141i	$-0.813047\pi$
$7$	0.168505	−	0.291860i	0.0636891	−	0.110313i	0.896112	+	0.443829i	$0.146380\pi$
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−5.01714	+	2.89665i	−1.51272	+	0.873372i	−0.512835	+	0.858487i	$0.671405\pi$
$11$	−5.01714	+	2.89665i	−1.51272	+	0.873372i	−0.999889	+	0.0148845i	$0.995262\pi$
$12$		0			0
$13$	3.26826	−	1.52264i	0.906454	−	0.422306i
$13$	3.26826	−	1.52264i	0.906454	−	0.422306i
$14$		0			0
$15$	−0.151651	+	2.23092i	−0.0391562	+	0.576021i
$16$		0			0
$17$	−6.16737	−	3.56073i	−1.49581	−	0.863605i	−0.495819	−	0.868426i	$-0.665132\pi$
$17$	−6.16737	−	3.56073i	−1.49581	−	0.863605i	−0.999988	+	0.00482093i	$0.998465\pi$
$18$		0			0
$19$	−0.477290	−	0.275564i	−0.109498	−	0.0632186i	0.444251	−	0.895902i	$-0.353470\pi$
$19$	−0.477290	−	0.275564i	−0.109498	−	0.0632186i	−0.553749	+	0.832684i	$0.686803\pi$
$20$		0			0
$21$			0.337011i			0.0735418i
$22$		0			0
$23$	0.670195	−	0.386937i	0.139745	−	0.0806819i	−0.428497	−	0.903543i	$-0.640957\pi$
$23$	0.670195	−	0.386937i	0.139745	−	0.0806819i	0.568243	+	0.822861i	$0.307624\pi$
$24$		0			0
$25$	−1.89101	−	4.62861i	−0.378202	−	0.925723i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	0.288472	+	0.499648i	0.0535679	+	0.0927823i	0.891566	−	0.452891i	$-0.149607\pi$
$29$	0.288472	+	0.499648i	0.0535679	+	0.0927823i	−0.837998	+	0.545673i	$0.816274\pi$
$30$		0			0
$31$			3.63801i			0.653406i	0.945127	+	0.326703i	$0.105938\pi$
$31$			3.63801i			0.653406i	−0.945127	+	0.326703i	$0.894062\pi$
$32$		0			0
$33$	2.89665	−	5.01714i	0.504241	−	0.873372i
$34$		0			0
$35$	−0.331661	−	0.676670i	−0.0560610	−	0.114378i
$36$		0			0
$37$	−3.52425	−	6.10418i	−0.579383	−	1.00352i	−0.995550	−	0.0942328i	$-0.969960\pi$
$37$	−3.52425	−	6.10418i	−0.579383	−	1.00352i	0.416167	−	0.909288i	$-0.363373\pi$
$38$		0			0
$39$	−2.06908	+	2.95278i	−0.331318	+	0.472823i
$40$		0			0
$41$	−8.34117	+	4.81578i	−1.30267	+	0.752098i	−0.980862	−	0.194706i	$-0.937625\pi$
$41$	−8.34117	+	4.81578i	−1.30267	+	0.752098i	−0.321811	+	0.946804i	$0.604292\pi$
$42$		0			0
$43$	−6.56102	−	3.78801i	−1.00055	−	0.577665i	−0.0921361	−	0.995746i	$-0.529369\pi$
$43$	−6.56102	−	3.78801i	−1.00055	−	0.577665i	−0.908410	+	0.418081i	$0.862703\pi$
$44$		0			0
$45$	−0.984126	−	2.00786i	−0.146705	−	0.299314i
$46$		0			0
$47$	4.67938			0.682557			0.341279	−	0.939962i	$-0.389140\pi$
$47$	4.67938			0.682557			0.341279	+	0.939962i	$0.389140\pi$
$48$		0			0
$49$	3.44321	+	5.96382i	0.491887	+	0.851974i
$50$		0			0
$51$	7.12147			0.997205
$52$		0			0
$53$			10.0057i			1.37440i	0.726471	+	0.687198i	$0.241159\pi$
$53$			10.0057i			1.37440i	−0.726471	+	0.687198i	$0.758841\pi$
$54$		0			0
$55$	−0.878560	+	12.9244i	−0.118465	+	1.74272i
$56$		0			0
$57$	0.551127			0.0729986
$58$		0			0
$59$	−8.79577	−	5.07824i	−1.14511	−	0.661131i	−0.197421	−	0.980319i	$-0.563257\pi$
$59$	−8.79577	−	5.07824i	−1.14511	−	0.661131i	−0.947691	+	0.319188i	$0.896590\pi$
$60$		0			0
$61$	4.09606	−	7.09458i	0.524447	−	0.908368i	−0.475148	−	0.879906i	$-0.657606\pi$
$61$	4.09606	−	7.09458i	0.524447	−	0.908368i	0.999595	−	0.0284626i	$-0.00906115\pi$
$62$		0			0
$63$	−0.168505	−	0.291860i	−0.0212297	−	0.0367709i
$64$		0			0
$65$	1.24851	−	7.96500i	0.154858	−	0.987937i
$66$		0			0
$67$	−2.73025	−	4.72894i	−0.333553	−	0.577732i	0.649652	−	0.760231i	$-0.274914\pi$
$67$	−2.73025	−	4.72894i	−0.333553	−	0.577732i	−0.983206	+	0.182500i	$0.941581\pi$
$68$		0			0
$69$	−0.386937	+	0.670195i	−0.0465817	+	0.0806819i
$70$		0			0
$71$	4.65795	+	2.68927i	0.552797	+	0.319157i	0.750249	−	0.661155i	$-0.229933\pi$
$71$	4.65795	+	2.68927i	0.552797	+	0.319157i	−0.197453	+	0.980312i	$0.563267\pi$
$72$		0			0
$73$	−9.73652			−1.13957			−0.569787	−	0.821792i	$-0.692974\pi$
$73$	−9.73652			−1.13957			−0.569787	+	0.821792i	$0.692974\pi$
$74$		0			0
$75$	3.95197	+	3.06299i	0.456334	+	0.353684i
$76$		0			0
$77$			1.95240i			0.222497i
$78$		0			0
$79$	−13.5983			−1.52993			−0.764965	−	0.644072i	$-0.777244\pi$
$79$	−13.5983			−1.52993			−0.764965	+	0.644072i	$0.777244\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−0.916806			−0.100633			−0.0503163	−	0.998733i	$-0.516023\pi$
$83$	−0.916806			−0.100633			−0.0503163	+	0.998733i	$0.516023\pi$
$84$		0			0
$85$	−14.2989	+	7.00842i	−1.55093	+	0.760170i
$86$		0			0
$87$	−0.499648	−	0.288472i	−0.0535679	−	0.0309274i
$88$		0			0
$89$	−3.73426	+	2.15597i	−0.395830	+	0.228533i	−0.684683	−	0.728841i	$-0.740059\pi$
$89$	−3.73426	+	2.15597i	−0.395830	+	0.228533i	0.288853	+	0.957374i	$0.406726\pi$
$90$		0			0
$91$	0.106321	−	1.21045i	0.0111455	−	0.126890i
$92$		0			0
$93$	−1.81901	−	3.15061i	−0.188622	−	0.326703i
$94$		0			0
$95$	−1.10659	+	0.542379i	−0.113533	+	0.0556469i
$96$		0			0
$97$	3.30366	−	5.72210i	0.335436	−	0.580992i	−0.648133	−	0.761527i	$-0.724450\pi$
$97$	3.30366	−	5.72210i	0.335436	−	0.580992i	0.983568	+	0.180536i	$0.0577832\pi$
$98$		0			0
$99$			5.79329i			0.582248i
$100$		0			0
$101$	−1.32718	−	2.29875i	−0.132059	−	0.228734i	0.792411	−	0.609988i	$-0.208826\pi$
$101$	−1.32718	−	2.29875i	−0.132059	−	0.228734i	−0.924470	+	0.381254i	$0.875492\pi$
$102$		0			0
$103$		−	9.59286i		−	0.945212i	−0.881274	−	0.472606i	$-0.843313\pi$
$103$		−	9.59286i		−	0.945212i	0.881274	−	0.472606i	$-0.156687\pi$
$104$		0			0
$105$	0.625562	+	0.420183i	0.0610486	+	0.0410057i
$106$		0			0
$107$	−1.04706	+	0.604518i	−0.101223	+	0.0584410i	−0.549757	−	0.835325i	$-0.685280\pi$
$107$	−1.04706	+	0.604518i	−0.101223	+	0.0584410i	0.448534	+	0.893766i	$0.351946\pi$
$108$		0			0
$109$			0.388703i			0.0372310i	0.999827	+	0.0186155i	$0.00592584\pi$
$109$			0.388703i			0.0372310i	−0.999827	+	0.0186155i	$0.994074\pi$
$110$		0			0
$111$	6.10418	+	3.52425i	0.579383	+	0.334507i
$112$		0			0
$113$	−5.55167	−	3.20526i	−0.522257	−	0.301526i	0.215600	−	0.976482i	$-0.430829\pi$
$113$	−5.55167	−	3.20526i	−0.522257	−	0.301526i	−0.737858	+	0.674956i	$0.764163\pi$
$114$		0			0
$115$	0.117359	−	1.72645i	0.0109438	−	0.160992i
$116$		0			0
$117$	0.315484	−	3.59172i	0.0291665	−	0.332055i
$118$		0			0
$119$	−2.07847	+	1.20001i	−0.190533	+	0.110004i
$120$		0			0
$121$	11.2811	−	19.5395i	1.02556	−	1.77632i
$122$		0			0
$123$	4.81578	−	8.34117i	0.434224	−	0.752098i
$124$		0			0
$125$	−10.9494	−	2.26082i	−0.979341	−	0.202214i
$126$		0			0
$127$	17.5335	−	10.1230i	1.55585	−	0.898270i	0.558202	−	0.829705i	$-0.311491\pi$
$127$	17.5335	−	10.1230i	1.55585	−	0.898270i	0.997647	−	0.0685645i	$-0.0218419\pi$
$128$		0			0
$129$	7.57601			0.667031
$130$		0			0
$131$	−21.1011			−1.84361			−0.921804	−	0.387656i	$-0.873285\pi$
$131$	−21.1011			−1.84361			−0.921804	+	0.387656i	$0.873285\pi$
$132$		0			0
$133$	−0.160852	+	0.0928680i	−0.0139476	+	0.00805267i
$134$		0			0
$135$	1.85621	+	1.24679i	0.159757	+	0.107307i
$136$		0			0
$137$	9.50671	−	16.4661i	0.812213	−	1.40679i	−0.0990995	−	0.995078i	$-0.531596\pi$
$137$	9.50671	−	16.4661i	0.812213	−	1.40679i	0.911312	−	0.411716i	$-0.135070\pi$
$138$		0			0
$139$	−9.38938	+	16.2629i	−0.796397	+	1.37940i	0.125552	+	0.992087i	$0.459930\pi$
$139$	−9.38938	+	16.2629i	−0.796397	+	1.37940i	−0.921948	+	0.387313i	$0.873403\pi$
$140$		0			0
$141$	−4.05246	+	2.33969i	−0.341279	+	0.197037i
$142$		0			0
$143$	−11.9868	+	17.1063i	−1.00238	+	1.43050i
$144$		0			0
$145$	1.28711	+	0.0874942i	0.106889	+	0.00726600i
$146$		0			0
$147$	−5.96382	−	3.44321i	−0.491887	−	0.283991i
$148$		0			0
$149$	−14.8609	−	8.57996i	−1.21745	−	0.702898i	−0.253082	−	0.967445i	$-0.581444\pi$
$149$	−14.8609	−	8.57996i	−1.21745	−	0.702898i	−0.964373	+	0.264547i	$0.914777\pi$
$150$		0			0
$151$			6.83525i			0.556244i	0.960546	+	0.278122i	$0.0897120\pi$
$151$			6.83525i			0.556244i	−0.960546	+	0.278122i	$0.910288\pi$
$152$		0			0
$153$	−6.16737	+	3.56073i	−0.498603	+	0.287868i
$154$		0			0
$155$	6.75291	+	4.53585i	0.542407	+	0.364328i
$156$		0			0
$157$		−	2.46456i		−	0.196693i	−0.995152	−	0.0983466i	$-0.968645\pi$
$157$		−	2.46456i		−	0.196693i	0.995152	−	0.0983466i	$-0.0313554\pi$
$158$		0			0
$159$	−5.00287	−	8.66523i	−0.396754	−	0.687198i
$160$		0			0
$161$		−	0.260804i		−	0.0205542i
$162$		0			0
$163$	0.829324	−	1.43643i	0.0649576	−	0.112510i	−0.831718	−	0.555199i	$-0.812642\pi$
$163$	0.829324	−	1.43643i	0.0649576	−	0.112510i	0.896675	+	0.442689i	$0.145975\pi$
$164$		0			0
$165$	−5.70133	−	11.6321i	−0.443848	−	0.905559i
$166$		0			0
$167$	4.25839	+	7.37575i	0.329524	+	0.570753i	0.982417	−	0.186697i	$-0.0597783\pi$
$167$	4.25839	+	7.37575i	0.329524	+	0.570753i	−0.652893	+	0.757450i	$0.726445\pi$
$168$		0			0
$169$	8.36311	−	9.95281i	0.643316	−	0.765601i
$170$		0			0
$171$	−0.477290	+	0.275564i	−0.0364993	+	0.0210729i
$172$		0			0
$173$	−13.8132	−	7.97505i	−1.05020	−	0.606332i	−0.127493	−	0.991839i	$-0.540693\pi$
$173$	−13.8132	−	7.97505i	−1.05020	−	0.606332i	−0.922705	+	0.385508i	$0.874026\pi$
$174$		0			0
$175$	−1.66955	−	0.228036i	−0.126206	−	0.0172379i
$176$		0			0
$177$	10.1565			0.763408
$178$		0			0
$179$	−5.40705	−	9.36529i	−0.404142	−	0.699994i	0.590079	−	0.807345i	$-0.299096\pi$
$179$	−5.40705	−	9.36529i	−0.404142	−	0.699994i	−0.994221	+	0.107351i	$0.965763\pi$
$180$		0			0
$181$	0.0980822			0.00729039			0.00364520	−	0.999993i	$-0.498840\pi$
$181$	0.0980822			0.00729039			0.00364520	+	0.999993i	$0.498840\pi$
$182$		0			0
$183$			8.19212i			0.605579i
$184$		0			0
$185$	−15.7246	−	1.06891i	−1.15610	−	0.0785881i
$186$		0			0
$187$	41.2567			3.01699
$188$		0			0
$189$	0.291860	+	0.168505i	0.0212297	+	0.0122570i
$190$		0			0
$191$	9.02206	−	15.6267i	0.652814	−	1.13071i	−0.329624	−	0.944112i	$-0.606922\pi$
$191$	9.02206	−	15.6267i	0.652814	−	1.13071i	0.982437	−	0.186594i	$-0.0597449\pi$
$192$		0			0
$193$	11.0631	+	19.1618i	0.796339	+	1.37930i	0.921985	+	0.387225i	$0.126566\pi$
$193$	11.0631	+	19.1618i	0.796339	+	1.37930i	−0.125646	+	0.992075i	$0.540100\pi$
$194$		0			0
$195$	2.90126	+	7.52215i	0.207764	+	0.538672i
$196$		0			0
$197$	6.89945	+	11.9502i	0.491566	+	0.851417i	0.999953	−	0.00971183i	$-0.00309142\pi$
$197$	6.89945	+	11.9502i	0.491566	+	0.851417i	−0.508387	+	0.861129i	$0.669758\pi$
$198$		0			0
$199$	2.06748	−	3.58098i	0.146560	−	0.253849i	−0.783394	−	0.621525i	$-0.786513\pi$
$199$	2.06748	−	3.58098i	0.146560	−	0.253849i	0.929954	+	0.367677i	$0.119847\pi$
$200$		0			0
$201$	4.72894	+	2.73025i	0.333553	+	0.192577i
$202$		0			0
$203$	0.194436			0.0136468
$204$		0			0
$205$	−1.46064	+	21.4872i	−0.102015	+	1.50073i
$206$		0			0
$207$		−	0.773874i		−	0.0537880i
$208$		0			0
$209$	3.19284			0.220854
$210$		0			0
$211$	4.40507	+	7.62981i	0.303258	+	0.525258i	0.976872	−	0.213825i	$-0.0685923\pi$
$211$	4.40507	+	7.62981i	0.303258	+	0.525258i	−0.673614	+	0.739083i	$0.735259\pi$
$212$		0			0
$213$	−5.37854			−0.368531
$214$		0			0
$215$	−15.2116	+	7.45575i	−1.03742	+	0.508478i
$216$		0			0
$217$	1.06179	+	0.613025i	0.0720790	+	0.0416149i
$218$		0			0
$219$	8.43208	−	4.86826i	0.569787	−	0.328967i
$220$		0			0
$221$	−25.5783	−	2.24671i	−1.72059	−	0.151130i
$222$		0			0
$223$	−1.13779	−	1.97071i	−0.0761919	−	0.131968i	0.825412	−	0.564531i	$-0.190943\pi$
$223$	−1.13779	−	1.97071i	−0.0761919	−	0.131968i	−0.901604	+	0.432562i	$0.857609\pi$
$224$		0			0
$225$	−4.95400	−	0.676644i	−0.330267	−	0.0451096i
$226$		0			0
$227$	4.84980	−	8.40009i	0.321892	−	0.557534i	−0.658986	−	0.752155i	$-0.729014\pi$
$227$	4.84980	−	8.40009i	0.321892	−	0.557534i	0.980878	+	0.194621i	$0.0623478\pi$
$228$		0			0
$229$			0.594657i			0.0392960i	0.999807	+	0.0196480i	$0.00625456\pi$
$229$			0.594657i			0.0392960i	−0.999807	+	0.0196480i	$0.993745\pi$
$230$		0			0
$231$	−0.976201	−	1.69083i	−0.0642293	−	0.111248i
$232$		0			0
$233$			6.35421i			0.416278i	0.978099	+	0.208139i	$0.0667407\pi$
$233$			6.35421i			0.416278i	−0.978099	+	0.208139i	$0.933259\pi$
$234$		0			0
$235$	5.83422	−	8.68589i	0.380582	−	0.566605i
$236$		0			0
$237$	11.7765	−	6.79916i	0.764965	−	0.441653i
$238$		0			0
$239$			21.3435i			1.38060i	0.723524	+	0.690299i	$0.242521\pi$
$239$			21.3435i			1.38060i	−0.723524	+	0.690299i	$0.757479\pi$
$240$		0			0
$241$	26.2860	+	15.1762i	1.69323	+	0.977586i	0.951882	+	0.306464i	$0.0991460\pi$
$241$	26.2860	+	15.1762i	1.69323	+	0.977586i	0.741347	+	0.671122i	$0.234187\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$	15.3631	+	1.04434i	0.981510	+	0.0667201i
$246$		0			0
$247$	−1.97950	−	0.173872i	−0.125952	−	0.0110632i
$248$		0			0
$249$	0.793978	−	0.458403i	0.0503163	−	0.0290501i
$250$		0			0
$251$	−11.8652	+	20.5511i	−0.748924	+	1.29717i	0.199416	+	0.979915i	$0.436096\pi$
$251$	−11.8652	+	20.5511i	−0.748924	+	1.29717i	−0.948339	+	0.317259i	$0.897238\pi$
$252$		0			0
$253$	−2.24164	+	3.88263i	−0.140931	+	0.244099i
$254$		0			0
$255$	8.87900	−	13.2189i	0.556025	−	0.827801i
$256$		0			0
$257$	−7.59998	+	4.38785i	−0.474074	+	0.273706i	−0.717943	−	0.696101i	$-0.754916\pi$
$257$	−7.59998	+	4.38785i	−0.474074	+	0.273706i	0.243870	+	0.969808i	$0.421583\pi$
$258$		0			0
$259$	−2.37542			−0.147601
$260$		0			0
$261$	0.576944			0.0357119
$262$		0			0
$263$	13.8500	−	7.99631i	0.854028	−	0.493073i	−0.00797966	−	0.999968i	$-0.502540\pi$
$263$	13.8500	−	7.99631i	0.854028	−	0.493073i	0.862008	+	0.506895i	$0.169207\pi$
$264$		0			0
$265$	18.5727	+	12.4751i	1.14091	+	0.766339i
$266$		0			0
$267$	2.15597	−	3.73426i	0.131943	−	0.228533i
$268$		0			0
$269$	12.5224	−	21.6894i	0.763502	−	1.32242i	−0.177532	−	0.984115i	$-0.556811\pi$
$269$	12.5224	−	21.6894i	0.763502	−	1.32242i	0.941035	−	0.338310i	$-0.109855\pi$
$270$		0			0
$271$	13.5897	−	7.84600i	0.825514	−	0.476611i	−0.0268004	−	0.999641i	$-0.508532\pi$
$271$	13.5897	−	7.84600i	0.825514	−	0.476611i	0.852314	+	0.523030i	$0.175199\pi$
$272$		0			0
$273$	0.513148	+	1.10144i	0.0310571	+	0.0666622i
$274$		0			0
$275$	22.8949	+	17.7448i	1.38062	+	1.07005i
$276$		0			0
$277$	13.4250	+	7.75093i	0.806631	+	0.465708i	0.845784	−	0.533525i	$-0.179133\pi$
$277$	13.4250	+	7.75093i	0.806631	+	0.465708i	−0.0391538	+	0.999233i	$0.512466\pi$
$278$		0			0
$279$	3.15061	+	1.81901i	0.188622	+	0.108901i
$280$		0			0
$281$			18.5432i			1.10619i	0.833117	+	0.553097i	$0.186554\pi$
$281$			18.5432i			1.10619i	−0.833117	+	0.553097i	$0.813446\pi$
$282$		0			0
$283$	3.81627	−	2.20332i	0.226853	−	0.130974i	−0.382266	−	0.924052i	$-0.624856\pi$
$283$	3.81627	−	2.20332i	0.226853	−	0.130974i	0.609120	+	0.793078i	$0.291523\pi$
$284$		0			0
$285$	0.687142	−	1.02301i	0.0407028	−	0.0605977i
$286$		0			0
$287$			3.24594i			0.191602i
$288$		0			0
$289$	16.8577	+	29.1983i	0.991627	+	1.71755i
$290$		0			0
$291$			6.60732i			0.387328i
$292$		0			0
$293$	2.12215	−	3.67568i	0.123977	−	0.214735i	−0.797355	−	0.603510i	$-0.793768\pi$
$293$	2.12215	−	3.67568i	0.123977	−	0.214735i	0.921333	+	0.388775i	$0.127102\pi$
$294$		0			0
$295$	−20.3928	+	9.99526i	−1.18731	+	0.581947i
$296$		0			0
$297$	−2.89665	−	5.01714i	−0.168080	−	0.291124i
$298$		0			0
$299$	1.60121	−	2.28508i	0.0926001	−	0.132150i
$300$		0			0
$301$	−2.21113	+	1.27660i	−0.127448	+	0.0735819i
$302$		0			0
$303$	2.29875	+	1.32718i	0.132059	+	0.0762446i
$304$		0			0
$305$	−8.06208	−	16.4486i	−0.461633	−	0.941845i
$306$		0			0
$307$	−21.5951			−1.23250			−0.616249	−	0.787552i	$-0.711348\pi$
$307$	−21.5951			−1.23250			−0.616249	+	0.787552i	$0.711348\pi$
$308$		0			0
$309$	4.79643	+	8.30766i	0.272859	+	0.472606i
$310$		0			0
$311$	21.5592			1.22251			0.611256	−	0.791433i	$-0.290665\pi$
$311$	21.5592			1.22251			0.611256	+	0.791433i	$0.290665\pi$
$312$		0			0
$313$			17.3839i			0.982594i	0.870992	+	0.491297i	$0.163477\pi$
$313$			17.3839i			0.982594i	−0.870992	+	0.491297i	$0.836523\pi$
$314$		0			0
$315$	−0.751844	−	0.0511081i	−0.0423616	−	0.00287962i
$316$		0			0
$317$	13.0115			0.730797			0.365399	−	0.930851i	$-0.380933\pi$
$317$	13.0115			0.730797			0.365399	+	0.930851i	$0.380933\pi$
$318$		0			0
$319$	−2.89461	−	1.67120i	−0.162067	−	0.0935693i
$320$		0			0
$321$	0.604518	−	1.04706i	0.0337409	−	0.0584410i
$322$		0			0
$323$	1.96242	+	3.39901i	0.109192	+	0.189126i
$324$		0			0
$325$	−13.2281	−	12.2482i	−0.733761	−	0.679408i
$326$		0			0
$327$	−0.194351	−	0.336627i	−0.0107477	−	0.0186155i
$328$		0			0
$329$	0.788501	−	1.36572i	0.0434714	−	0.0752947i
$330$		0			0
$331$	−23.4180	−	13.5204i	−1.28717	−	0.743148i	−0.309021	−	0.951055i	$-0.600001\pi$
$331$	−23.4180	−	13.5204i	−1.28717	−	0.743148i	−0.978149	+	0.207907i	$0.933335\pi$
$332$		0			0
$333$	−7.04850			−0.386255
$334$		0			0
$335$	−12.1819	−	0.828093i	−0.665571	−	0.0452435i
$336$		0			0
$337$		−	14.5787i		−	0.794152i	−0.917786	−	0.397076i	$-0.870025\pi$
$337$		−	14.5787i		−	0.794152i	0.917786	−	0.397076i	$-0.129975\pi$
$338$		0			0
$339$	6.41052			0.348172
$340$		0			0
$341$	−10.5380	−	18.2524i	−0.570667	−	0.988424i
$342$		0			0
$343$	4.67988			0.252690
$344$		0			0
$345$	0.761589	+	1.55383i	0.0410026	+	0.0836554i
$346$		0			0
$347$	3.44585	+	1.98946i	0.184983	+	0.106800i	0.589632	−	0.807672i	$-0.299273\pi$
$347$	3.44585	+	1.98946i	0.184983	+	0.106800i	−0.404649	+	0.914472i	$0.632606\pi$
$348$		0			0
$349$	22.9274	−	13.2372i	1.22728	−	0.708569i	0.260818	−	0.965388i	$-0.416008\pi$
$349$	22.9274	−	13.2372i	1.22728	−	0.708569i	0.966460	+	0.256819i	$0.0826744\pi$
$350$		0			0
$351$	1.52264	+	3.26826i	0.0812727	+	0.174447i
$352$		0			0
$353$	−2.14538	−	3.71591i	−0.114187	−	0.197778i	0.803267	−	0.595619i	$-0.203093\pi$
$353$	−2.14538	−	3.71591i	−0.114187	−	0.197778i	−0.917455	+	0.397841i	$0.869760\pi$
$354$		0			0
$355$	10.7993	−	5.29316i	0.573169	−	0.280932i
$356$		0			0
$357$	1.20001	−	2.07847i	0.0635111	−	0.110004i
$358$		0			0
$359$		−	17.3553i		−	0.915978i	−0.888958	−	0.457989i	$-0.848570\pi$
$359$		−	17.3553i		−	0.915978i	0.888958	−	0.457989i	$-0.151430\pi$
$360$		0			0
$361$	−9.34813	−	16.1914i	−0.492007	−	0.852181i
$362$		0			0
$363$			22.5622i			1.18421i
$364$		0			0
$365$	−12.1394	+	18.0730i	−0.635407	+	0.945984i
$366$		0			0
$367$	−8.49188	+	4.90279i	−0.443272	+	0.255923i	−0.704985	−	0.709222i	$-0.749046\pi$
$367$	−8.49188	+	4.90279i	−0.443272	+	0.255923i	0.261712	+	0.965146i	$0.415713\pi$
$368$		0			0
$369$			9.63156i			0.501399i
$370$		0			0
$371$	2.92028	+	1.68602i	0.151613	+	0.0875340i
$372$		0			0
$373$	17.7762	+	10.2631i	0.920418	+	0.531404i	0.883768	−	0.467924i	$-0.154998\pi$
$373$	17.7762	+	10.2631i	0.920418	+	0.531404i	0.0366498	+	0.999328i	$0.488331\pi$
$374$		0			0
$375$	10.6128	−	3.51676i	0.548045	−	0.181605i
$376$		0			0
$377$	1.70359	+	1.19374i	0.0877392	+	0.0614808i
$378$		0			0
$379$	13.9766	−	8.06942i	0.717932	−	0.414498i	−0.0960589	−	0.995376i	$-0.530624\pi$
$379$	13.9766	−	8.06942i	0.717932	−	0.414498i	0.813991	+	0.580877i	$0.197290\pi$
$380$		0			0
$381$	−10.1230	+	17.5335i	−0.518616	+	0.898270i
$382$		0			0
$383$	−18.3494	+	31.7822i	−0.937613	+	1.62399i	−0.167705	+	0.985837i	$0.553636\pi$
$383$	−18.3494	+	31.7822i	−0.937613	+	1.62399i	−0.769907	+	0.638156i	$0.779698\pi$
$384$		0			0
$385$	3.62406	+	2.43424i	0.184699	+	0.124061i
$386$		0			0
$387$	−6.56102	+	3.78801i	−0.333515	+	0.192555i
$388$		0			0
$389$	1.13139			0.0573640			0.0286820	−	0.999589i	$-0.490869\pi$
$389$	1.13139			0.0573640			0.0286820	+	0.999589i	$0.490869\pi$
$390$		0			0
$391$	−5.51112			−0.278709
$392$		0			0
$393$	18.2741	−	10.5505i	0.921804	−	0.532204i
$394$		0			0
$395$	−16.9543	+	25.2413i	−0.853063	+	1.27003i
$396$		0			0
$397$	−3.02716	+	5.24319i	−0.151929	+	0.263148i	−0.931936	−	0.362622i	$-0.881882\pi$
$397$	−3.02716	+	5.24319i	−0.151929	+	0.263148i	0.780008	+	0.625770i	$0.215215\pi$
$398$		0			0
$399$	0.0928680	−	0.160852i	0.00464921	−	0.00805267i
$400$		0			0
$401$	32.9200	−	19.0063i	1.64394	−	0.949131i	0.664532	−	0.747260i	$-0.268631\pi$
$401$	32.9200	−	19.0063i	1.64394	−	0.949131i	0.979412	−	0.201872i	$-0.0647024\pi$
$402$		0			0
$403$	5.53940	+	11.8900i	0.275937	+	0.592283i
$404$		0			0
$405$	−2.23092	−	0.151651i	−0.110855	−	0.00753561i
$406$		0			0
$407$	35.3633	+	20.4170i	1.75289	+	1.01203i
$408$		0			0
$409$	5.89482	+	3.40337i	0.291480	+	0.168286i	0.638609	−	0.769531i	$-0.279510\pi$
$409$	5.89482	+	3.40337i	0.291480	+	0.168286i	−0.347129	+	0.937817i	$0.612843\pi$
$410$		0			0
$411$			19.0134i			0.937862i
$412$		0			0
$413$	−2.96427	+	1.71142i	−0.145862	+	0.0842136i
$414$		0			0
$415$	−1.14307	+	1.70178i	−0.0561110	+	0.0835372i
$416$		0			0
$417$		−	18.7788i		−	0.919600i
$418$		0			0
$419$	2.24708	+	3.89206i	0.109777	+	0.190139i	0.915680	−	0.401908i	$-0.131653\pi$
$419$	2.24708	+	3.89206i	0.109777	+	0.190139i	−0.805903	+	0.592048i	$0.798320\pi$
$420$		0			0
$421$		−	28.6014i		−	1.39395i	−0.717097	−	0.696973i	$-0.754530\pi$
$421$		−	28.6014i		−	1.39395i	0.717097	−	0.696973i	$-0.245470\pi$
$422$		0			0
$423$	2.33969	−	4.05246i	0.113760	−	0.197037i
$424$		0			0
$425$	−4.81870	+	35.2798i	−0.233741	+	1.71132i
$426$		0			0
$427$	−1.38042	−	2.39095i	−0.0668031	−	0.115706i
$428$		0			0
$429$	1.82769	−	20.8079i	0.0882416	−	1.00461i
$430$		0			0
$431$	10.3150	−	5.95536i	0.496855	−	0.286859i	−0.230559	−	0.973058i	$-0.574055\pi$
$431$	10.3150	−	5.95536i	0.496855	−	0.286859i	0.727414	+	0.686199i	$0.240722\pi$
$432$		0			0
$433$	−10.0134	−	5.78121i	−0.481211	−	0.277827i	0.239710	−	0.970845i	$-0.422948\pi$
$433$	−10.0134	−	5.78121i	−0.481211	−	0.277827i	−0.720921	+	0.693017i	$0.756281\pi$
$434$		0			0
$435$	−1.15842	+	0.567785i	−0.0555420	+	0.0272232i
$436$		0			0
$437$	−0.426503			−0.0204024
$438$		0			0
$439$	−13.5955	−	23.5480i	−0.648876	−	1.12389i	−0.983392	−	0.181495i	$-0.941906\pi$
$439$	−13.5955	−	23.5480i	−0.648876	−	1.12389i	0.334516	−	0.942390i	$-0.391427\pi$
$440$		0			0
$441$	6.88642			0.327925
$442$		0			0
$443$		−	10.9123i		−	0.518457i	−0.965816	−	0.259228i	$-0.916532\pi$
$443$		−	10.9123i		−	0.518457i	0.965816	−	0.259228i	$-0.0834682\pi$
$444$		0			0
$445$	−0.653913	+	9.61961i	−0.0309984	+	0.456013i
$446$		0			0
$447$	17.1599			0.811636
$448$		0			0
$449$	10.7187	+	6.18847i	0.505849	+	0.292052i	0.731126	−	0.682243i	$-0.238995\pi$
$449$	10.7187	+	6.18847i	0.505849	+	0.292052i	−0.225277	+	0.974295i	$0.572329\pi$
$450$		0			0
$451$	27.8992	−	48.3229i	1.31372	−	2.27543i
$452$		0			0
$453$	−3.41762	−	5.91950i	−0.160574	−	0.278122i
$454$		0			0
$455$	−2.11428	−	1.70654i	−0.0991192	−	0.0800036i
$456$		0			0
$457$	3.83111	+	6.63567i	0.179212	+	0.310404i	0.941611	−	0.336703i	$-0.109312\pi$
$457$	3.83111	+	6.63567i	0.179212	+	0.310404i	−0.762399	+	0.647107i	$0.775979\pi$
$458$		0			0
$459$	3.56073	−	6.16737i	0.166201	−	0.287868i
$460$		0			0
$461$	11.8266	+	6.82811i	0.550821	+	0.318017i	0.749453	−	0.662057i	$-0.230316\pi$
$461$	11.8266	+	6.82811i	0.550821	+	0.318017i	−0.198632	+	0.980074i	$0.563650\pi$
$462$		0			0
$463$	−15.1671			−0.704877			−0.352439	−	0.935835i	$-0.614647\pi$
$463$	−15.1671			−0.704877			−0.352439	+	0.935835i	$0.614647\pi$
$464$		0			0
$465$	−8.11612	−	0.551709i	−0.376376	−	0.0255849i
$466$		0			0
$467$		−	22.9820i		−	1.06348i	−0.846907	−	0.531740i	$-0.821538\pi$
$467$		−	22.9820i		−	1.06348i	0.846907	−	0.531740i	$-0.178462\pi$
$468$		0			0
$469$	−1.84025			−0.0849748
$470$		0			0
$471$	1.23228	+	2.13437i	0.0567804	+	0.0983466i
$472$		0			0
$473$	43.8900			2.01807
$474$		0			0
$475$	−0.372917	+	2.73029i	−0.0171106	+	0.125274i
$476$		0			0
$477$	8.66523	+	5.00287i	0.396754	+	0.229066i
$478$		0			0
$479$	−19.1306	+	11.0451i	−0.874101	+	0.504663i	−0.868709	−	0.495323i	$-0.835050\pi$
$479$	−19.1306	+	11.0451i	−0.874101	+	0.504663i	−0.00539230	+	0.999985i	$0.501716\pi$
$480$		0			0
$481$	−20.8127	−	14.5839i	−0.948976	−	0.664968i
$482$		0			0
$483$	0.130402	+	0.225863i	0.00593350	+	0.0102771i
$484$		0			0
$485$	−6.50243	−	13.2666i	−0.295260	−	0.602403i
$486$		0			0
$487$	11.6846	−	20.2384i	0.529481	−	0.917087i	−0.469928	−	0.882705i	$-0.655720\pi$
$487$	11.6846	−	20.2384i	0.529481	−	0.917087i	0.999409	−	0.0343826i	$-0.0109465\pi$
$488$		0			0
$489$			1.65865i			0.0750066i
$490$		0			0
$491$	−8.62920	−	14.9462i	−0.389430	−	0.674513i	0.602943	−	0.797785i	$-0.293995\pi$
$491$	−8.62920	−	14.9462i	−0.389430	−	0.674513i	−0.992373	+	0.123271i	$0.960661\pi$
$492$		0			0
$493$		−	4.10869i		−	0.185046i
$494$		0			0
$495$	10.7536	+	7.22304i	0.483336	+	0.324652i
$496$		0			0
$497$	1.56978	−	0.906313i	0.0704142	−	0.0406537i
$498$		0			0
$499$			24.1571i			1.08142i	0.841209	+	0.540710i	$0.181844\pi$
$499$			24.1571i			1.08142i	−0.841209	+	0.540710i	$0.818156\pi$
$500$		0			0
$501$	−7.37575	−	4.25839i	−0.329524	−	0.190251i
$502$		0			0
$503$	−1.64297	−	0.948571i	−0.0732566	−	0.0422947i	0.462924	−	0.886398i	$-0.346800\pi$
$503$	−1.64297	−	0.948571i	−0.0732566	−	0.0422947i	−0.536181	+	0.844103i	$0.680134\pi$
$504$		0			0
$505$	−5.92167	−	0.402538i	−0.263511	−	0.0179127i
$506$		0			0
$507$	−2.26626	+	12.8009i	−0.100648	+	0.568510i
$508$		0			0
$509$	−2.06807	+	1.19400i	−0.0916655	+	0.0529231i	−0.545132	−	0.838350i	$-0.683520\pi$
$509$	−2.06807	+	1.19400i	−0.0916655	+	0.0529231i	0.453467	+	0.891273i	$0.350187\pi$
$510$		0			0
$511$	−1.64066	+	2.84170i	−0.0725784	+	0.125709i
$512$		0			0
$513$	0.275564	−	0.477290i	0.0121664	−	0.0210729i
$514$		0			0
$515$	−17.8063	−	11.9603i	−0.784641	−	0.527034i
$516$		0			0
$517$	−23.4771	+	13.5545i	−1.03252	+	0.596126i
$518$		0			0
$519$	15.9501			0.700132
$520$		0			0
$521$	−11.1734			−0.489516			−0.244758	−	0.969584i	$-0.578709\pi$
$521$	−11.1734			−0.489516			−0.244758	+	0.969584i	$0.578709\pi$
$522$		0			0
$523$	−0.665993	+	0.384511i	−0.0291218	+	0.0168135i	−0.514490	−	0.857496i	$-0.672019\pi$
$523$	−0.665993	+	0.384511i	−0.0291218	+	0.0168135i	0.485368	+	0.874310i	$0.338685\pi$
$524$		0			0
$525$	1.55989	−	0.637291i	0.0680793	−	0.0278137i
$526$		0			0
$527$	12.9540	−	22.4370i	0.564285	−	0.977370i
$528$		0			0
$529$	−11.2006	+	19.3999i	−0.486981	+	0.843476i
$530$		0			0
$531$	−8.79577	+	5.07824i	−0.381704	+	0.220377i
$532$		0			0
$533$	−19.9284	+	28.4399i	−0.863197	+	1.23187i
$534$		0			0
$535$	−0.183352	+	2.69726i	−0.00792699	+	0.116613i
$536$		0			0
$537$	9.36529	+	5.40705i	0.404142	+	0.233331i
$538$		0			0
$539$	−34.5501	−	19.9475i	−1.48818	−	0.859201i
$540$		0			0
$541$			4.88326i			0.209948i	0.994475	+	0.104974i	$0.0334759\pi$
$541$			4.88326i			0.209948i	−0.994475	+	0.104974i	$0.966524\pi$
$542$		0			0
$543$	−0.0849417	+	0.0490411i	−0.00364520	+	0.00210455i
$544$		0			0
$545$	0.721513	+	0.484632i	0.0309062	+	0.0207594i
$546$		0			0
$547$		−	16.5458i		−	0.707448i	−0.935350	−	0.353724i	$-0.884915\pi$
$547$		−	16.5458i		−	0.707448i	0.935350	−	0.353724i	$-0.115085\pi$
$548$		0			0
$549$	−4.09606	−	7.09458i	−0.174816	−	0.302789i
$550$		0			0
$551$		−	0.317969i		−	0.0135460i
$552$		0			0
$553$	−2.29139	+	3.96881i	−0.0974399	+	0.168771i
$554$		0			0
$555$	14.1524	−	6.93661i	0.600735	−	0.294443i
$556$		0			0
$557$	−18.8925	−	32.7227i	−0.800500	−	1.38651i	−0.919288	−	0.393586i	$-0.871234\pi$
$557$	−18.8925	−	32.7227i	−0.800500	−	1.38651i	0.118788	−	0.992920i	$-0.462099\pi$
$558$		0			0
$559$	−27.2109	−	2.39011i	−1.15090	−	0.101091i
$560$		0			0
$561$	−35.7294	+	20.6284i	−1.50850	+	0.870931i
$562$		0			0
$563$	−38.5815	−	22.2750i	−1.62602	−	0.938780i	−0.985266	−	0.171030i	$-0.945290\pi$
$563$	−38.5815	−	22.2750i	−1.62602	−	0.938780i	−0.640749	−	0.767750i	$-0.721376\pi$
$564$		0			0
$565$	−12.8714	+	6.30876i	−0.541505	+	0.265411i
$566$		0			0
$567$	−0.337011			−0.0141531
$568$		0			0
$569$	−1.26829	−	2.19675i	−0.0531696	−	0.0920925i	0.838216	−	0.545339i	$-0.183599\pi$
$569$	−1.26829	−	2.19675i	−0.0531696	−	0.0920925i	−0.891385	+	0.453246i	$0.850266\pi$
$570$		0			0
$571$	13.9832			0.585178			0.292589	−	0.956238i	$-0.405483\pi$
$571$	13.9832			0.585178			0.292589	+	0.956238i	$0.405483\pi$
$572$		0			0
$573$			18.0441i			0.753804i
$574$		0			0
$575$	−3.05833	−	2.37037i	−0.127541	−	0.0988513i
$576$		0			0
$577$	24.8772			1.03565			0.517827	−	0.855486i	$-0.326741\pi$
$577$	24.8772			1.03565			0.517827	+	0.855486i	$0.326741\pi$
$578$		0			0
$579$	−19.1618	−	11.0631i	−0.796339	−	0.459767i
$580$		0			0
$581$	−0.154487	+	0.267579i	−0.00640920	+	0.0111011i
$582$		0			0
$583$	−28.9831	−	50.2002i	−1.20036	−	2.07908i
$584$		0			0
$585$	−6.27364	−	5.06374i	−0.259383	−	0.209360i
$586$		0			0
$587$	13.8011	+	23.9042i	0.569633	+	0.986633i	0.996602	+	0.0823670i	$0.0262480\pi$
$587$	13.8011	+	23.9042i	0.569633	+	0.986633i	−0.426969	+	0.904266i	$0.640419\pi$
$588$		0			0
$589$	1.00250	−	1.73639i	0.0413075	−	0.0715466i
$590$		0			0
$591$	−11.9502	−	6.89945i	−0.491566	−	0.283806i
$592$		0			0
$593$	40.5475			1.66508			0.832542	−	0.553962i	$-0.186885\pi$
$593$	40.5475			1.66508			0.832542	+	0.553962i	$0.186885\pi$
$594$		0			0
$595$	−0.363965	+	5.35423i	−0.0149211	+	0.219502i
$596$		0			0
$597$			4.13496i			0.169233i
$598$		0			0
$599$	29.1652			1.19166			0.595829	−	0.803111i	$-0.296824\pi$
$599$	29.1652			1.19166			0.595829	+	0.803111i	$0.296824\pi$
$600$		0			0
$601$	19.5770	+	33.9084i	0.798563	+	1.38315i	0.920552	+	0.390621i	$0.127740\pi$
$601$	19.5770	+	33.9084i	0.798563	+	1.38315i	−0.121989	+	0.992531i	$0.538927\pi$
$602$		0			0
$603$	−5.46051			−0.222369
$604$		0			0
$605$	−22.2041	−	45.3018i	−0.902724	−	1.84178i
$606$		0			0
$607$	−31.4072	−	18.1330i	−1.27478	−	0.735995i	−0.298897	−	0.954286i	$-0.596619\pi$
$607$	−31.4072	−	18.1330i	−1.27478	−	0.735995i	−0.975884	+	0.218291i	$0.929952\pi$
$608$		0			0
$609$	−0.168387	+	0.0972181i	−0.00682338	+	0.00393948i
$610$		0			0
$611$	15.2934	−	7.12503i	0.618706	−	0.288248i
$612$		0			0
$613$	−0.715152	−	1.23868i	−0.0288847	−	0.0500298i	0.851222	−	0.524806i	$-0.175862\pi$
$613$	−0.715152	−	1.23868i	−0.0288847	−	0.0500298i	−0.880106	+	0.474776i	$0.842529\pi$
$614$		0			0
$615$	−9.47867	−	19.3388i	−0.382217	−	0.779816i
$616$		0			0
$617$	−9.23581	+	15.9969i	−0.371820	+	0.644011i	−0.989846	−	0.142147i	$-0.954599\pi$
$617$	−9.23581	+	15.9969i	−0.371820	+	0.644011i	0.618026	+	0.786158i	$0.287933\pi$
$618$		0			0
$619$		−	7.48214i		−	0.300733i	−0.988630	−	0.150366i	$-0.951955\pi$
$619$		−	7.48214i		−	0.300733i	0.988630	−	0.150366i	$-0.0480453\pi$
$620$		0			0
$621$	0.386937	+	0.670195i	0.0155272	+	0.0268940i
$622$		0			0
$623$			1.45317i			0.0582202i
$624$		0			0
$625$	−17.8482	+	17.5055i	−0.713926	+	0.700221i
$626$		0			0
$627$	−2.76508	+	1.59642i	−0.110427	+	0.0637549i
$628$		0			0
$629$			50.1957i			2.00143i
$630$		0			0
$631$	25.0067	+	14.4376i	0.995501	+	0.574752i	0.906914	−	0.421316i	$-0.138432\pi$
$631$	25.0067	+	14.4376i	0.995501	+	0.574752i	0.0885866	+	0.996068i	$0.471765\pi$
$632$		0			0
$633$	−7.62981	−	4.40507i	−0.303258	−	0.175086i
$634$		0			0
$635$	3.07033	−	45.1671i	0.121842	−	1.79240i
$636$		0			0
$637$	20.3341	+	14.2485i	0.805666	+	0.564548i
$638$		0			0
$639$	4.65795	−	2.68927i	0.184266	−	0.106386i
$640$		0			0
$641$	−6.55720	+	11.3574i	−0.258994	+	0.448590i	−0.965973	−	0.258644i	$-0.916724\pi$
$641$	−6.55720	+	11.3574i	−0.258994	+	0.448590i	0.706979	+	0.707235i	$0.250058\pi$
$642$		0			0
$643$	1.55224	−	2.68855i	0.0612142	−	0.106026i	−0.833794	−	0.552075i	$-0.813836\pi$
$643$	1.55224	−	2.68855i	0.0612142	−	0.106026i	0.895008	+	0.446049i	$0.147169\pi$
$644$		0			0
$645$	9.44572	−	14.0626i	0.371925	−	0.553716i
$646$		0			0
$647$	31.2130	−	18.0208i	1.22711	−	0.708473i	0.260686	−	0.965424i	$-0.416051\pi$
$647$	31.2130	−	18.0208i	1.22711	−	0.708473i	0.966424	+	0.256951i	$0.0827179\pi$
$648$		0			0
$649$	58.8395			2.30965
$650$		0			0
$651$	−1.22605			−0.0480527
$652$		0			0
$653$	−18.6499	+	10.7676i	−0.729829	+	0.421367i	−0.818360	−	0.574707i	$-0.805116\pi$
$653$	−18.6499	+	10.7676i	−0.729829	+	0.421367i	0.0885308	+	0.996073i	$0.471783\pi$
$654$		0			0
$655$	−26.3087	+	39.1680i	−1.02796	+	1.53042i
$656$		0			0
$657$	−4.86826	+	8.43208i	−0.189929	+	0.328967i
$658$		0			0
$659$	22.8919	−	39.6499i	0.891742	−	1.54454i	0.0539553	−	0.998543i	$-0.482817\pi$
$659$	22.8919	−	39.6499i	0.891742	−	1.54454i	0.837786	−	0.545998i	$-0.183850\pi$
$660$		0			0
$661$	−29.6804	+	17.1360i	−1.15444	+	0.666513i	−0.949964	−	0.312359i	$-0.898881\pi$
$661$	−29.6804	+	17.1360i	−1.15444	+	0.666513i	−0.204471	+	0.978873i	$0.565547\pi$
$662$		0			0
$663$	23.2748	−	10.8435i	0.903920	−	0.421125i
$664$		0			0
$665$	−0.0281671	+	0.414362i	−0.00109227	+	0.0160683i
$666$		0			0
$667$	0.386664	+	0.223241i	0.0149717	+	0.00864392i
$668$		0			0
$669$	1.97071	+	1.13779i	0.0761919	+	0.0439894i
$670$		0			0
$671$			47.4594i			1.83215i
$672$		0			0
$673$	−28.5348	+	16.4746i	−1.09994	+	0.635049i	−0.936204	−	0.351456i	$-0.885687\pi$
$673$	−28.5348	+	16.4746i	−1.09994	+	0.635049i	−0.163733	+	0.986505i	$0.552353\pi$
$674$		0			0
$675$	4.62861	−	1.89101i	0.178155	−	0.0727851i
$676$		0			0
$677$		−	42.1914i		−	1.62155i	−0.585359	−	0.810774i	$-0.699046\pi$
$677$		−	42.1914i		−	1.62155i	0.585359	−	0.810774i	$-0.300954\pi$
$678$		0			0
$679$	−1.11337	−	1.92841i	−0.0427272	−	0.0740056i
$680$		0			0
$681$			9.69959i			0.371689i
$682$		0			0
$683$	−20.7328	+	35.9103i	−0.793319	+	1.37407i	0.130582	+	0.991438i	$0.458315\pi$
$683$	−20.7328	+	35.9103i	−0.793319	+	1.37407i	−0.923901	+	0.382631i	$0.875018\pi$
$684$		0			0
$685$	−18.7116	−	38.1762i	−0.714933	−	1.45864i
$686$		0			0
$687$	−0.297328	−	0.514988i	−0.0113438	−	0.0196480i
$688$		0			0
$689$	15.2352	+	32.7014i	0.580415	+	1.24583i
$690$		0			0
$691$	4.43680	−	2.56159i	0.168784	−	0.0974473i	−0.413229	−	0.910627i	$-0.635599\pi$
$691$	4.43680	−	2.56159i	0.168784	−	0.0974473i	0.582012	+	0.813180i	$0.302266\pi$
$692$		0			0
$693$	1.69083	+	0.976201i	0.0642293	+	0.0370828i
$694$		0			0
$695$	18.4807	+	37.7051i	0.701011	+	1.43024i
$696$		0			0
$697$	68.5908			2.59806
$698$		0			0
$699$	−3.17711	−	5.50291i	−0.120169	−	0.208139i
$700$		0			0
$701$	−26.7820			−1.01154			−0.505772	−	0.862667i	$-0.668792\pi$
$701$	−26.7820			−1.01154			−0.505772	+	0.862667i	$0.668792\pi$
$702$		0			0
$703$			3.88462i			0.146511i
$704$		0			0
$705$	−0.709634	+	10.4393i	−0.0267263	+	0.393167i
$706$		0			0
$707$	−0.894549			−0.0336430
$708$		0			0
$709$	6.46676	+	3.73359i	0.242864	+	0.140218i	0.616493	−	0.787361i	$-0.288553\pi$
$709$	6.46676	+	3.73359i	0.242864	+	0.140218i	−0.373628	+	0.927579i	$0.621886\pi$
$710$		0			0
$711$	−6.79916	+	11.7765i	−0.254988	+	0.441653i
$712$		0			0
$713$	1.40768	+	2.43818i	0.0527181	+	0.0913104i
$714$		0			0
$715$	16.8079	+	43.5780i	0.628578	+	1.62972i
$716$		0			0
$717$	−10.6718	−	18.4840i	−0.398544	−	0.690299i
$718$		0			0
$719$	9.53984	−	16.5235i	0.355776	−	0.616222i	−0.631474	−	0.775397i	$-0.717550\pi$
$719$	9.53984	−	16.5235i	0.355776	−	0.616222i	0.987250	+	0.159175i	$0.0508833\pi$
$720$		0			0
$721$	−2.79977	−	1.61645i	−0.104269	−	0.0601997i
$722$		0			0
$723$	−30.3524			−1.12882
$724$		0			0
$725$	1.76717	−	2.28006i	0.0656312	−	0.0846795i
$726$		0			0
$727$		−	5.24769i		−	0.194626i	−0.995254	−	0.0973131i	$-0.968975\pi$
$727$		−	5.24769i		−	0.194626i	0.995254	−	0.0973131i	$-0.0310248\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	26.9762	+	46.7241i	0.997749	+	1.72815i
$732$		0			0
$733$	−21.9269			−0.809888			−0.404944	−	0.914342i	$-0.632709\pi$
$733$	−21.9269			−0.809888			−0.404944	+	0.914342i	$0.632709\pi$
$734$		0			0
$735$	−13.8270	+	6.77711i	−0.510015	+	0.249977i
$736$		0			0
$737$	27.3961	+	15.8172i	1.00915	+	0.582632i
$738$		0			0
$739$	−18.7410	+	10.8201i	−0.689400	+	0.398025i	−0.803387	−	0.595457i	$-0.796971\pi$
$739$	−18.7410	+	10.8201i	−0.689400	+	0.398025i	0.113987	+	0.993482i	$0.463638\pi$
$740$		0			0
$741$	1.80123	−	0.839171i	0.0661698	−	0.0308277i
$742$		0			0
$743$	−0.501164	−	0.868041i	−0.0183859	−	0.0318453i	0.856686	−	0.515838i	$-0.172519\pi$
$743$	−0.501164	−	0.868041i	−0.0183859	−	0.0318453i	−0.875072	+	0.483993i	$0.839186\pi$
$744$		0			0
$745$	−34.4547	+	16.8875i	−1.26232	+	0.618711i
$746$		0			0
$747$	−0.458403	+	0.793978i	−0.0167721	+	0.0290501i
$748$		0			0
$749$			0.407458i			0.0148882i
$750$		0			0
$751$	−11.2441	−	19.4753i	−0.410302	−	0.710663i	0.584621	−	0.811307i	$-0.301243\pi$
$751$	−11.2441	−	19.4753i	−0.410302	−	0.710663i	−0.994923	+	0.100643i	$0.967910\pi$
$752$		0			0
$753$		−	23.7304i		−	0.864782i
$754$		0			0
$755$	12.6876	+	8.52214i	0.461750	+	0.310152i
$756$		0			0
$757$	21.9108	−	12.6502i	0.796361	−	0.459779i	−0.0458362	−	0.998949i	$-0.514595\pi$
$757$	21.9108	−	12.6502i	0.796361	−	0.459779i	0.842197	+	0.539170i	$0.181262\pi$
$758$		0			0
$759$		−	4.48328i		−	0.162733i
$760$		0			0
$761$	15.1027	+	8.71954i	0.547472	+	0.316083i	0.748102	−	0.663584i	$-0.230966\pi$
$761$	15.1027	+	8.71954i	0.547472	+	0.316083i	−0.200630	+	0.979667i	$0.564299\pi$
$762$		0			0
$763$	0.113447	+	0.0654985i	0.00410705	+	0.00237121i
$764$		0			0
$765$	−1.07998	+	15.8874i	−0.0390468	+	0.574411i
$766$		0			0
$767$	−36.4793	−	3.20420i	−1.31719	−	0.115697i
$768$		0			0
$769$	−37.3172	+	21.5451i	−1.34569	+	0.776936i	−0.987636	−	0.156765i	$-0.949894\pi$
$769$	−37.3172	+	21.5451i	−1.34569	+	0.776936i	−0.358056	+	0.933700i	$0.616560\pi$
$770$		0			0
$771$	4.38785	−	7.59998i	0.158025	−	0.273706i
$772$		0			0
$773$	3.19453	−	5.53308i	0.114899	−	0.199011i	−0.802840	−	0.596194i	$-0.796679\pi$
$773$	3.19453	−	5.53308i	0.114899	−	0.199011i	0.917739	+	0.397183i	$0.130012\pi$
$774$		0			0
$775$	16.8390	−	6.87952i	0.604873	−	0.247120i
$776$		0			0
$777$	2.05718	−	1.18771i	0.0738007	−	0.0426089i
$778$		0			0
$779$	5.30822			0.190187
$780$		0			0
$781$	−31.1594			−1.11497
$782$		0			0
$783$	−0.499648	+	0.288472i	−0.0178560	+	0.0103091i
$784$		0			0
$785$	−4.57473	−	3.07279i	−0.163279	−	0.109673i
$786$		0			0
$787$	7.37436	−	12.7728i	0.262868	−	0.455300i	−0.704135	−	0.710066i	$-0.748665\pi$
$787$	7.37436	−	12.7728i	0.262868	−	0.455300i	0.967003	+	0.254766i	$0.0819984\pi$
$788$		0			0
$789$	−7.99631	+	13.8500i	−0.284676	+	0.493073i
$790$		0			0
$791$	−1.87097	+	1.08021i	−0.0665242	+	0.0384078i
$792$		0			0
$793$	2.58448	−	29.4238i	0.0917776	−	1.04487i
$794$		0			0
$795$	−22.3220	−	1.51738i	−0.791680	−	0.0538161i
$796$		0			0
$797$	−34.5928	−	19.9722i	−1.22534	−	0.707450i	−0.259288	−	0.965800i	$-0.583488\pi$
$797$	−34.5928	−	19.9722i	−1.22534	−	0.707450i	−0.966051	+	0.258350i	$0.916821\pi$
$798$		0			0
$799$	−28.8595	−	16.6620i	−1.02097	−	0.589460i
$800$		0			0
$801$			4.31195i			0.152355i
$802$		0			0
$803$	48.8495	−	28.2033i	1.72386	−	0.995272i
$804$		0			0
$805$	−0.484106	−	0.325169i	−0.0170625	−	0.0114607i
$806$		0			0
$807$			25.0447i			0.881617i
$808$		0			0
$809$	23.6857	+	41.0249i	0.832746	+	1.44236i	0.895852	+	0.444352i	$0.146566\pi$
$809$	23.6857	+	41.0249i	0.832746	+	1.44236i	−0.0631064	+	0.998007i	$0.520101\pi$
$810$		0			0
$811$		−	32.9745i		−	1.15789i	−0.815367	−	0.578945i	$-0.803465\pi$
$811$		−	32.9745i		−	1.15789i	0.815367	−	0.578945i	$-0.196535\pi$
$812$		0			0
$813$	−7.84600	+	13.5897i	−0.275171	+	0.476611i
$814$		0			0
$815$	−1.63232	−	3.33033i	−0.0571776	−	0.116656i
$816$		0			0
$817$	2.08767	+	3.61596i	0.0730384	+	0.126506i
$818$		0			0
$819$	−0.995119	−	0.697302i	−0.0347723	−	0.0243657i
$820$		0			0
$821$	−43.7075	+	25.2345i	−1.52540	+	0.880692i	−0.525856	+	0.850573i	$0.676255\pi$
$821$	−43.7075	+	25.2345i	−1.52540	+	0.880692i	−0.999546	+	0.0301184i	$0.990412\pi$
$822$		0			0
$823$	17.6609	+	10.1965i	0.615621	+	0.355429i	0.775162	−	0.631763i	$-0.217668\pi$
$823$	17.6609	+	10.1965i	0.615621	+	0.355429i	−0.159541	+	0.987191i	$0.551002\pi$
$824$		0			0
$825$	−28.7000	−	3.91999i	−0.999206	−	0.136477i
$826$		0			0
$827$	−24.8598			−0.864460			−0.432230	−	0.901764i	$-0.642273\pi$
$827$	−24.8598			−0.864460			−0.432230	+	0.901764i	$0.642273\pi$
$828$		0			0
$829$	16.8859	+	29.2472i	0.586472	+	1.01580i	0.994690	+	0.102915i	$0.0328168\pi$
$829$	16.8859	+	29.2472i	0.586472	+	1.01580i	−0.408218	+	0.912884i	$0.633850\pi$
$830$		0			0
$831$	−15.5019			−0.537754
$832$		0			0
$833$		−	49.0414i		−	1.69919i
$834$		0			0
$835$	19.0003	+	1.29158i	0.657531	+	0.0446970i
$836$		0			0
$837$	−3.63801			−0.125748
$838$		0			0
$839$	−42.0087	−	24.2537i	−1.45030	−	0.837331i	−0.451802	−	0.892118i	$-0.649219\pi$
$839$	−42.0087	−	24.2537i	−1.45030	−	0.837331i	−0.998498	+	0.0547870i	$0.982552\pi$
$840$		0			0
$841$	14.3336	−	24.8265i	0.494261	−	0.856085i
$842$		0			0
$843$	−9.27159	−	16.0589i	−0.319331	−	0.553097i
$844$		0			0
$845$	−8.04741	−	27.9328i	−0.276839	−	0.960916i
$846$		0			0
$847$	−3.80186	−	6.58502i	−0.130633	−	0.226264i
$848$		0			0
$849$	−2.20332	+	3.81627i	−0.0756178	+	0.130974i
$850$		0			0
$851$	−4.72387	−	2.72732i	−0.161932	−	0.0934915i
$852$		0			0
$853$	16.6190			0.569022			0.284511	−	0.958673i	$-0.408169\pi$
$853$	16.6190			0.569022			0.284511	+	0.958673i	$0.408169\pi$
$854$		0			0
$855$	−0.0835792	+	1.22952i	−0.00285835	+	0.0420487i
$856$		0			0
$857$		−	16.7353i		−	0.571665i	−0.958280	−	0.285833i	$-0.907730\pi$
$857$		−	16.7353i		−	0.571665i	0.958280	−	0.285833i	$-0.0922702\pi$
$858$		0			0
$859$	−36.6227			−1.24955			−0.624775	−	0.780805i	$-0.714809\pi$
$859$	−36.6227			−1.24955			−0.624775	+	0.780805i	$0.714809\pi$
$860$		0			0
$861$	−1.62297	−	2.81107i	−0.0553107	−	0.0958009i
$862$		0			0
$863$	−33.2272			−1.13107			−0.565534	−	0.824725i	$-0.691330\pi$
$863$	−33.2272			−1.13107			−0.565534	+	0.824725i	$0.691330\pi$
$864$		0			0
$865$	−32.0255	+	15.6969i	−1.08890	+	0.533711i
$866$		0			0
$867$	−29.1983	−	16.8577i	−0.991627	−	0.572516i
$868$		0			0
$869$	68.2247	−	39.3895i	2.31436	−	1.33620i
$870$		0			0
$871$	−16.1237	−	11.2982i	−0.546330	−	0.382825i
$872$		0			0
$873$	−3.30366	−	5.72210i	−0.111812	−	0.193664i
$874$		0			0
$875$	−2.50487	+	2.81472i	−0.0846801	+	0.0951550i
$876$		0			0
$877$	−18.5928	+	32.2037i	−0.627834	+	1.08744i	0.360151	+	0.932894i	$0.382725\pi$
$877$	−18.5928	+	32.2037i	−0.627834	+	1.08744i	−0.987985	+	0.154547i	$0.950608\pi$
$878$		0			0
$879$			4.24431i			0.143157i
$880$		0			0
$881$	−10.4283	−	18.0624i	−0.351340	−	0.608539i	0.635145	−	0.772393i	$-0.280941\pi$
$881$	−10.4283	−	18.0624i	−0.351340	−	0.608539i	−0.986484	+	0.163855i	$0.947607\pi$
$882$		0			0
$883$		−	31.7568i		−	1.06870i	−0.845263	−	0.534350i	$-0.820556\pi$
$883$		−	31.7568i		−	1.06870i	0.845263	−	0.534350i	$-0.179444\pi$
$884$		0			0
$885$	12.6630	−	18.8525i	0.425663	−	0.633721i
$886$		0			0
$887$	45.0084	−	25.9856i	1.51123	−	0.872511i	0.511320	−	0.859390i	$-0.329157\pi$
$887$	45.0084	−	25.9856i	1.51123	−	0.872511i	0.999914	−	0.0131212i	$-0.00417672\pi$
$888$		0			0
$889$		−	6.82311i		−	0.228840i
$890$		0			0
$891$	5.01714	+	2.89665i	0.168080	+	0.0970413i
$892$		0			0
$893$	−2.23342	−	1.28947i	−0.0747386	−	0.0431503i
$894$		0			0
$895$	−24.1254	−	1.63997i	−0.806423	−	0.0548182i
$896$		0			0
$897$	−0.244145	+	2.77954i	−0.00815175	+	0.0928062i
$898$		0			0
$899$	−1.81773	+	1.04946i	−0.0606245	+	0.0350016i
$900$		0			0
$901$	35.6278	−	61.7092i	1.18693	−	2.05583i
$902$		0			0
$903$	1.27660	−	2.21113i	0.0424826	−	0.0735819i
$904$		0			0
$905$	0.122288	−	0.182061i	0.00406500	−	0.00605191i
$906$		0			0
$907$	−35.3569	+	20.4133i	−1.17401	+	0.677814i	−0.954621	−	0.297824i	$-0.903739\pi$
$907$	−35.3569	+	20.4133i	−1.17401	+	0.677814i	−0.219387	+	0.975638i	$0.570406\pi$
$908$		0			0
$909$	−2.65436			−0.0880396
$910$		0			0
$911$	−22.7514			−0.753786			−0.376893	−	0.926257i	$-0.623008\pi$
$911$	−22.7514			−0.753786			−0.376893	+	0.926257i	$0.623008\pi$
$912$		0			0
$913$	4.59974	−	2.65566i	0.152229	−	0.0878896i
$914$		0			0
$915$	15.2063	+	10.2139i	0.502704	+	0.337661i
$916$		0			0
$917$	−3.55564	+	6.15856i	−0.117418	+	0.203373i
$918$		0			0
$919$	−17.6957	+	30.6498i	−0.583727	+	1.01105i	0.411306	+	0.911497i	$0.365073\pi$
$919$	−17.6957	+	30.6498i	−0.583727	+	1.01105i	−0.995033	+	0.0995476i	$0.968260\pi$
$920$		0			0
$921$	18.7019	−	10.7975i	0.616249	−	0.355791i
$922$		0			0
$923$	19.3182	+	1.69684i	0.635866	+	0.0558522i
$924$		0			0
$925$	−21.5895	+	27.8555i	−0.709858	+	0.915882i
$926$		0			0
$927$	−8.30766	−	4.79643i	−0.272859	−	0.157535i
$928$		0			0
$929$	15.1053	+	8.72102i	0.495587	+	0.286128i	0.726889	−	0.686754i	$-0.240965\pi$
$929$	15.1053	+	8.72102i	0.495587	+	0.286128i	−0.231302	+	0.972882i	$0.574299\pi$
$930$		0			0
$931$		−	3.79530i		−	0.124386i
$932$		0			0
$933$	−18.6708	+	10.7796i	−0.611256	+	0.352909i
$934$		0			0
$935$	51.4387	−	76.5811i	1.68222	−	2.50447i
$936$		0			0
$937$		−	20.2722i		−	0.662264i	−0.943584	−	0.331132i	$-0.892569\pi$
$937$		−	20.2722i		−	0.662264i	0.943584	−	0.331132i	$-0.107431\pi$
$938$		0			0
$939$	−8.69193	−	15.0549i	−0.283650	−	0.491297i
$940$		0			0
$941$			52.5023i			1.71152i	0.517369	+	0.855762i	$0.326911\pi$
$941$			52.5023i			1.71152i	−0.517369	+	0.855762i	$0.673089\pi$
$942$		0			0
$943$	−3.72681	+	6.45502i	−0.121362	+	0.210204i
$944$		0			0
$945$	0.676670	−	0.331661i	0.0220121	−	0.0107889i
$946$		0			0
$947$	−3.72040	−	6.44392i	−0.120897	−	0.209399i	0.799225	−	0.601032i	$-0.205244\pi$
$947$	−3.72040	−	6.44392i	−0.120897	−	0.209399i	−0.920122	+	0.391633i	$0.871910\pi$
$948$		0			0
$949$	−31.8215	+	14.8253i	−1.03297	+	0.481248i
$950$		0			0
$951$	−11.2683	+	6.50574i	−0.365399	+	0.210963i
$952$		0			0
$953$	−33.9671	−	19.6109i	−1.10030	−	0.635260i	−0.164003	−	0.986460i	$-0.552441\pi$
$953$	−33.9671	−	19.6109i	−1.10030	−	0.635260i	−0.936301	+	0.351200i	$0.885774\pi$
$954$		0			0
$955$	−17.7577	−	36.2301i	−0.574625	−	1.17238i
$956$		0			0
$957$	3.34240			0.108045
$958$		0			0
$959$	−3.20386	−	5.54925i	−0.103458	−	0.179195i
$960$		0			0
$961$	17.7649			0.573060
$962$		0			0
$963$			1.20904i			0.0389606i
$964$		0			0
$965$	49.3617	+	3.35547i	1.58901	+	0.108016i
$966$		0			0
$967$	−42.4070			−1.36372			−0.681859	−	0.731484i	$-0.738828\pi$
$967$	−42.4070			−1.36372			−0.681859	+	0.731484i	$0.738828\pi$
$968$		0			0
$969$	−3.39901	−	1.96242i	−0.109192	−	0.0630419i
$970$		0			0
$971$	−13.5876	+	23.5344i	−0.436047	+	0.755255i	−0.997380	−	0.0723343i	$-0.976955\pi$
$971$	−13.5876	+	23.5344i	−0.436047	+	0.755255i	0.561334	+	0.827590i	$0.310288\pi$
$972$		0			0
$973$	3.16432	+	5.48077i	0.101444	+	0.175705i
$974$		0			0
$975$	17.5799	+	3.99322i	0.563009	+	0.127885i
$976$		0			0
$977$	−3.43578	−	5.95094i	−0.109920	−	0.190387i	0.805818	−	0.592164i	$-0.201726\pi$
$977$	−3.43578	−	5.95094i	−0.109920	−	0.190387i	−0.915738	+	0.401777i	$0.868393\pi$
$978$		0			0
$979$	12.4902	−	21.6336i	0.399188	−	0.691414i
$980$		0			0
$981$	0.336627	+	0.194351i	0.0107477	+	0.00620516i
$982$		0			0
$983$	11.6056			0.370162			0.185081	−	0.982723i	$-0.440745\pi$
$983$	11.6056			0.370162			0.185081	+	0.982723i	$0.440745\pi$
$984$		0			0
$985$	30.7843	+	2.09262i	0.980868	+	0.0666765i
$986$		0			0
$987$			1.57700i			0.0501965i
$988$		0			0
$989$	−5.86288			−0.186429
$990$		0			0
$991$	−21.3799	−	37.0310i	−0.679153	−	1.17633i	−0.975236	−	0.221166i	$-0.929014\pi$
$991$	−21.3799	−	37.0310i	−0.679153	−	1.17633i	0.296083	−	0.955162i	$-0.404320\pi$
$992$		0			0
$993$	27.0408			0.858113
$994$		0			0
$995$	−4.06932	−	8.30241i	−0.129006	−	0.263204i
$996$		0			0
$997$	7.40425	+	4.27484i	0.234495	+	0.135386i	0.612644	−	0.790359i	$-0.290106\pi$
$997$	7.40425	+	4.27484i	0.234495	+	0.135386i	−0.378149	+	0.925745i	$0.623439\pi$
$998$		0			0
$999$	6.10418	−	3.52425i	0.193128	−	0.111502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1560.2.dr.a.49.9	✓	44
5.4	even	2		1560.2.dr.b.49.14	yes	44
13.4	even	6		1560.2.dr.b.1369.14	yes	44
65.4	even	6	inner	1560.2.dr.a.1369.9	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.dr.a.49.9	✓	44	1.1	even	1	trivial
1560.2.dr.a.1369.9	yes	44	65.4	even	6	inner
1560.2.dr.b.49.14	yes	44	5.4	even	2
1560.2.dr.b.1369.14	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(1.24679 - 1.85621i) q^{5} +(0.168505 - 0.291860i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{3} +(1.24679 - 1.85621i) q^{5} +(0.168505 - 0.291860i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-5.01714 + 2.89665i) q^{11} +(3.26826 - 1.52264i) q^{13} +(-0.151651 + 2.23092i) q^{15} +(-6.16737 - 3.56073i) q^{17} +(-0.477290 - 0.275564i) q^{19} +0.337011i q^{21} +(0.670195 - 0.386937i) q^{23} +(-1.89101 - 4.62861i) q^{25} +1.00000i q^{27} +(0.288472 + 0.499648i) q^{29} +3.63801i q^{31} +(2.89665 - 5.01714i) q^{33} +(-0.331661 - 0.676670i) q^{35} +(-3.52425 - 6.10418i) q^{37} +(-2.06908 + 2.95278i) q^{39} +(-8.34117 + 4.81578i) q^{41} +(-6.56102 - 3.78801i) q^{43} +(-0.984126 - 2.00786i) q^{45} +4.67938 q^{47} +(3.44321 + 5.96382i) q^{49} +7.12147 q^{51} +10.0057i q^{53} +(-0.878560 + 12.9244i) q^{55} +0.551127 q^{57} +(-8.79577 - 5.07824i) q^{59} +(4.09606 - 7.09458i) q^{61} +(-0.168505 - 0.291860i) q^{63} +(1.24851 - 7.96500i) q^{65} +(-2.73025 - 4.72894i) q^{67} +(-0.386937 + 0.670195i) q^{69} +(4.65795 + 2.68927i) q^{71} -9.73652 q^{73} +(3.95197 + 3.06299i) q^{75} +1.95240i q^{77} -13.5983 q^{79} +(-0.500000 - 0.866025i) q^{81} -0.916806 q^{83} +(-14.2989 + 7.00842i) q^{85} +(-0.499648 - 0.288472i) q^{87} +(-3.73426 + 2.15597i) q^{89} +(0.106321 - 1.21045i) q^{91} +(-1.81901 - 3.15061i) q^{93} +(-1.10659 + 0.542379i) q^{95} +(3.30366 - 5.72210i) q^{97} +5.79329i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{5} + 2 q^{7} + 22 q^{9}+O(q^{10}) \) 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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