LMFDB - Embedded newform 1710.2.l.l.1531.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1261,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1710.1261");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 19x^{2} + 18x + 324 $ x^4 - x^3 + 19x^2 + 18x + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1531.1
Root			$-1.88600 - 3.26665i$ of defining polynomial
Character	$\chi$	$=$	1710.1531
Dual form			1710.2.l.l.1261.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} -3.77200 q^{11} +(2.38600 + 4.13267i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.88600 + 3.26665i) q^{19} -1.00000 q^{20} +(1.88600 - 3.26665i) q^{22} +(-1.88600 - 3.26665i) q^{23} +(-0.500000 - 0.866025i) q^{25} -4.77200 q^{26} +(0.500000 + 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} +2.77200 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{35} -1.00000 q^{37} +(-4.27200 + 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-1.88600 + 3.26665i) q^{41} +(-4.38600 + 7.59678i) q^{43} +(1.88600 + 3.26665i) q^{44} +3.77200 q^{46} -6.00000 q^{49} +1.00000 q^{50} +(2.38600 - 4.13267i) q^{52} +(4.88600 + 8.46280i) q^{53} +(-1.88600 + 3.26665i) q^{55} -1.00000 q^{56} +6.00000 q^{58} +(-6.77200 + 11.7295i) q^{59} +(-1.38600 - 2.40062i) q^{61} +(-1.38600 + 2.40062i) q^{62} +1.00000 q^{64} +4.77200 q^{65} +(5.38600 + 9.32883i) q^{67} +(-0.500000 - 0.866025i) q^{70} +(-3.77200 + 6.53330i) q^{71} +(1.61400 - 2.79553i) q^{73} +(0.500000 - 0.866025i) q^{74} +(1.38600 - 4.13267i) q^{76} +3.77200 q^{77} +(-5.15800 + 8.93392i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-1.88600 - 3.26665i) q^{82} -6.00000 q^{83} +(-4.38600 - 7.59678i) q^{86} -3.77200 q^{88} +(8.65800 + 14.9961i) q^{89} +(-2.38600 - 4.13267i) q^{91} +(-1.88600 + 3.26665i) q^{92} +(4.27200 - 0.866025i) q^{95} +(5.00000 - 8.66025i) q^{97} +(3.00000 - 5.19615i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 4 q^{8} + 2 q^{10} + 2 q^{11} + q^{13} + 2 q^{14} - 2 q^{16} + 3 q^{19} - 4 q^{20} - q^{22} + q^{23} - 2 q^{25} - 2 q^{26} + 2 q^{28} - 12 q^{29} - 6 q^{31} - 2 q^{32} - 2 q^{35} - 4 q^{37} + 2 q^{40} + q^{41} - 9 q^{43} - q^{44} - 2 q^{46} - 24 q^{49} + 4 q^{50} + q^{52} + 11 q^{53} + q^{55} - 4 q^{56} + 24 q^{58} - 10 q^{59} + 3 q^{61} + 3 q^{62} + 4 q^{64} + 2 q^{65} + 13 q^{67} - 2 q^{70} + 2 q^{71} + 15 q^{73} + 2 q^{74} - 3 q^{76} - 2 q^{77} + 5 q^{79} + 2 q^{80} + q^{82} - 24 q^{83} - 9 q^{86} + 2 q^{88} + 9 q^{89} - q^{91} + q^{92} + 20 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 4 * q^8 + 2 * q^10 + 2 * q^11 + q^13 + 2 * q^14 - 2 * q^16 + 3 * q^19 - 4 * q^20 - q^22 + q^23 - 2 * q^25 - 2 * q^26 + 2 * q^28 - 12 * q^29 - 6 * q^31 - 2 * q^32 - 2 * q^35 - 4 * q^37 + 2 * q^40 + q^41 - 9 * q^43 - q^44 - 2 * q^46 - 24 * q^49 + 4 * q^50 + q^52 + 11 * q^53 + q^55 - 4 * q^56 + 24 * q^58 - 10 * q^59 + 3 * q^61 + 3 * q^62 + 4 * q^64 + 2 * q^65 + 13 * q^67 - 2 * q^70 + 2 * q^71 + 15 * q^73 + 2 * q^74 - 3 * q^76 - 2 * q^77 + 5 * q^79 + 2 * q^80 + q^82 - 24 * q^83 - 9 * q^86 + 2 * q^88 + 9 * q^89 - q^91 + q^92 + 20 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−3.77200			−1.13730			−0.568651	−	0.822579i	$-0.692534\pi$
$11$	−3.77200			−1.13730			−0.568651	+	0.822579i	$0.692534\pi$
$12$		0			0
$13$	2.38600	+	4.13267i	0.661758	+	1.14620i	0.980154	+	0.198240i	$0.0635225\pi$
$13$	2.38600	+	4.13267i	0.661758	+	1.14620i	−0.318396	+	0.947958i	$0.603144\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	2.88600	+	3.26665i	0.662094	+	0.749421i
$19$	2.88600	+	3.26665i	0.662094	+	0.749421i
$20$	−1.00000			−0.223607
$21$		0			0
$22$	1.88600	−	3.26665i	0.402097	−	0.696452i
$23$	−1.88600	−	3.26665i	−0.393258	−	0.681143i	0.599619	−	0.800286i	$-0.295319\pi$
$23$	−1.88600	−	3.26665i	−0.393258	−	0.681143i	−0.992877	+	0.119142i	$0.961986\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−4.77200			−0.935867
$27$		0			0
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	2.77200			0.497866			0.248933	−	0.968521i	$-0.419920\pi$
$31$	2.77200			0.497866			0.248933	+	0.968521i	$0.419920\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−4.27200	+	0.866025i	−0.693010	+	0.140488i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−1.88600	+	3.26665i	−0.294544	+	0.510165i	−0.974879	−	0.222737i	$-0.928501\pi$
$41$	−1.88600	+	3.26665i	−0.294544	+	0.510165i	0.680335	+	0.732901i	$0.261834\pi$
$42$		0			0
$43$	−4.38600	+	7.59678i	−0.668859	+	1.15850i	0.309365	+	0.950943i	$0.399884\pi$
$43$	−4.38600	+	7.59678i	−0.668859	+	1.15850i	−0.978224	+	0.207554i	$0.933450\pi$
$44$	1.88600	+	3.26665i	0.284325	+	0.492466i
$45$		0			0
$46$	3.77200			0.556151
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−6.00000			−0.857143
$50$	1.00000			0.141421
$51$		0			0
$52$	2.38600	−	4.13267i	0.330879	−	0.573099i
$53$	4.88600	+	8.46280i	0.671144	+	1.16246i	0.977580	+	0.210564i	$0.0675300\pi$
$53$	4.88600	+	8.46280i	0.671144	+	1.16246i	−0.306436	+	0.951891i	$0.599137\pi$
$54$		0			0
$55$	−1.88600	+	3.26665i	−0.254308	+	0.440475i
$56$	−1.00000			−0.133631
$57$		0			0
$58$	6.00000			0.787839
$59$	−6.77200	+	11.7295i	−0.881640	+	1.52704i	−0.0321221	+	0.999484i	$0.510227\pi$
$59$	−6.77200	+	11.7295i	−0.881640	+	1.52704i	−0.849517	+	0.527561i	$0.823107\pi$
$60$		0			0
$61$	−1.38600	−	2.40062i	−0.177459	−	0.307368i	0.763550	−	0.645748i	$-0.223454\pi$
$61$	−1.38600	−	2.40062i	−0.177459	−	0.307368i	−0.941010	+	0.338380i	$0.890121\pi$
$62$	−1.38600	+	2.40062i	−0.176022	+	0.304880i
$63$		0			0
$64$	1.00000			0.125000
$65$	4.77200			0.591894
$66$		0			0
$67$	5.38600	+	9.32883i	0.658005	+	1.13970i	0.981131	+	0.193342i	$0.0619327\pi$
$67$	5.38600	+	9.32883i	0.658005	+	1.13970i	−0.323127	+	0.946356i	$0.604734\pi$
$68$		0			0
$69$		0			0
$70$	−0.500000	−	0.866025i	−0.0597614	−	0.103510i
$71$	−3.77200	+	6.53330i	−0.447654	+	0.775360i	−0.998233	−	0.0594234i	$-0.981074\pi$
$71$	−3.77200	+	6.53330i	−0.447654	+	0.775360i	0.550579	+	0.834783i	$0.314407\pi$
$72$		0			0
$73$	1.61400	−	2.79553i	0.188904	−	0.327192i	−0.755981	−	0.654594i	$-0.772840\pi$
$73$	1.61400	−	2.79553i	0.188904	−	0.327192i	0.944885	+	0.327402i	$0.106173\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$		0			0
$76$	1.38600	−	4.13267i	0.158985	−	0.474050i
$77$	3.77200			0.429860
$78$		0			0
$79$	−5.15800	+	8.93392i	−0.580321	+	1.00514i	0.415120	+	0.909766i	$0.363739\pi$
$79$	−5.15800	+	8.93392i	−0.580321	+	1.00514i	−0.995441	+	0.0953784i	$0.969594\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	−1.88600	−	3.26665i	−0.208274	−	0.360741i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$		0			0
$86$	−4.38600	−	7.59678i	−0.472955	−	0.819181i
$87$		0			0
$88$	−3.77200			−0.402097
$89$	8.65800	+	14.9961i	0.917746	+	1.58958i	0.802830	+	0.596208i	$0.203327\pi$
$89$	8.65800	+	14.9961i	0.917746	+	1.58958i	0.114917	+	0.993375i	$0.463340\pi$
$90$		0			0
$91$	−2.38600	−	4.13267i	−0.250121	−	0.433222i
$92$	−1.88600	+	3.26665i	−0.196629	+	0.340572i
$93$		0			0
$94$		0			0
$95$	4.27200	−	0.866025i	0.438298	−	0.0888523i
$96$		0			0
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	−0.492287	−	0.870433i	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	3.00000	−	5.19615i	0.303046	−	0.524891i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−13.0000			−1.28093			−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000			−1.28093			−0.640464	+	0.767988i	$0.721258\pi$
$104$	2.38600	+	4.13267i	0.233967	+	0.405242i
$105$		0			0
$106$	−9.77200			−0.949141
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	−4.77200	+	8.26535i	−0.457075	+	0.791677i	−0.998805	−	0.0488756i	$-0.984436\pi$
$109$	−4.77200	+	8.26535i	−0.457075	+	0.791677i	0.541730	+	0.840553i	$0.317770\pi$
$110$	−1.88600	−	3.26665i	−0.179823	−	0.311463i
$111$		0			0
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	13.5440			1.27411			0.637056	−	0.770817i	$-0.280152\pi$
$113$	13.5440			1.27411			0.637056	+	0.770817i	$0.280152\pi$
$114$		0			0
$115$	−3.77200			−0.351741
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$		0			0
$118$	−6.77200	−	11.7295i	−0.623413	−	1.07978i
$119$		0			0
$120$		0			0
$121$	3.22800			0.293454
$122$	2.77200			0.250965
$123$		0			0
$124$	−1.38600	−	2.40062i	−0.124467	−	0.215582i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	4.65800	+	8.06790i	0.413331	+	0.715910i	0.995252	−	0.0973354i	$-0.0310319\pi$
$127$	4.65800	+	8.06790i	0.413331	+	0.715910i	−0.581921	+	0.813246i	$0.697699\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−2.38600	+	4.13267i	−0.209266	+	0.362460i
$131$	−5.65800	+	9.79995i	−0.494342	+	0.856225i	−0.999979	−	0.00652102i	$-0.997924\pi$
$131$	−5.65800	+	9.79995i	−0.494342	+	0.856225i	0.505637	+	0.862746i	$0.331258\pi$
$132$		0			0
$133$	−2.88600	−	3.26665i	−0.250248	−	0.283254i
$134$	−10.7720			−0.930559
$135$		0			0
$136$		0			0
$137$	−0.772002	−	1.33715i	−0.0659566	−	0.114240i	0.831161	−	0.556031i	$-0.187677\pi$
$137$	−0.772002	−	1.33715i	−0.0659566	−	0.114240i	−0.897118	+	0.441791i	$0.854343\pi$
$138$		0			0
$139$	5.38600	+	9.32883i	0.456835	+	0.791261i	0.998792	−	0.0491454i	$-0.0156498\pi$
$139$	5.38600	+	9.32883i	0.456835	+	0.791261i	−0.541957	+	0.840406i	$0.682316\pi$
$140$	1.00000			0.0845154
$141$		0			0
$142$	−3.77200	−	6.53330i	−0.316539	−	0.548262i
$143$	−9.00000	−	15.5885i	−0.752618	−	1.30357i
$144$		0			0
$145$	−6.00000			−0.498273
$146$	1.61400	+	2.79553i	0.133576	+	0.231360i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	−6.77200	+	11.7295i	−0.554784	+	0.960914i	0.443136	+	0.896454i	$0.353866\pi$
$149$	−6.77200	+	11.7295i	−0.554784	+	0.960914i	−0.997920	+	0.0644598i	$0.979468\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	2.88600	+	3.26665i	0.234086	+	0.264960i
$153$		0			0
$154$	−1.88600	+	3.26665i	−0.151978	+	0.263234i
$155$	1.38600	−	2.40062i	0.111326	−	0.192823i
$156$		0			0
$157$	−1.72800	+	2.99298i	−0.137909	+	0.238866i	−0.926705	−	0.375790i	$-0.877372\pi$
$157$	−1.72800	+	2.99298i	−0.137909	+	0.238866i	0.788796	+	0.614655i	$0.210705\pi$
$158$	−5.15800	−	8.93392i	−0.410349	−	0.710745i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	1.88600	+	3.26665i	0.148638	+	0.257448i
$162$		0			0
$163$	−18.3160			−1.43462			−0.717310	−	0.696754i	$-0.754627\pi$
$163$	−18.3160			−1.43462			−0.717310	+	0.696754i	$0.754627\pi$
$164$	3.77200			0.294544
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	−5.65800	−	9.79995i	−0.437829	−	0.758343i	0.559692	−	0.828700i	$-0.310919\pi$
$167$	−5.65800	−	9.79995i	−0.437829	−	0.758343i	−0.997522	+	0.0703577i	$0.977586\pi$
$168$		0			0
$169$	−4.88600	+	8.46280i	−0.375846	+	0.650985i
$170$		0			0
$171$		0			0
$172$	8.77200			0.668859
$173$	5.65800	−	9.79995i	0.430170	−	0.745076i	−0.566718	−	0.823912i	$-0.691787\pi$
$173$	5.65800	−	9.79995i	0.430170	−	0.745076i	0.996888	+	0.0788358i	$0.0251203\pi$
$174$		0			0
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	1.88600	−	3.26665i	0.142163	−	0.246233i
$177$		0			0
$178$	−17.3160			−1.29789
$179$	0.683994			0.0511241			0.0255621	−	0.999673i	$-0.491862\pi$
$179$	0.683994			0.0511241			0.0255621	+	0.999673i	$0.491862\pi$
$180$		0			0
$181$	−8.54400	−	14.7986i	−0.635071	−	1.09997i	−0.986500	−	0.163760i	$-0.947638\pi$
$181$	−8.54400	−	14.7986i	−0.635071	−	1.09997i	0.351429	−	0.936214i	$-0.385696\pi$
$182$	4.77200			0.353724
$183$		0			0
$184$	−1.88600	−	3.26665i	−0.139038	−	0.240821i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−1.38600	+	4.13267i	−0.100551	+	0.299816i
$191$	−7.54400			−0.545865			−0.272932	−	0.962033i	$-0.587994\pi$
$191$	−7.54400			−0.545865			−0.272932	+	0.962033i	$0.587994\pi$
$192$		0			0
$193$	−1.38600	+	2.40062i	−0.0997665	+	0.172801i	−0.911588	−	0.411105i	$-0.865143\pi$
$193$	−1.38600	+	2.40062i	−0.0997665	+	0.172801i	0.811821	+	0.583906i	$0.198476\pi$
$194$	5.00000	+	8.66025i	0.358979	+	0.621770i
$195$		0			0
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	11.3160			0.806232			0.403116	−	0.915149i	$-0.367927\pi$
$197$	11.3160			0.806232			0.403116	+	0.915149i	$0.367927\pi$
$198$		0			0
$199$	0.158003	+	0.273669i	0.0112005	+	0.0193999i	0.871571	−	0.490269i	$-0.163101\pi$
$199$	0.158003	+	0.273669i	0.0112005	+	0.0193999i	−0.860371	+	0.509669i	$0.829768\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	6.00000			0.422159
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$		0			0
$205$	1.88600	+	3.26665i	0.131724	+	0.228153i
$206$	6.50000	−	11.2583i	0.452876	−	0.784405i
$207$		0			0
$208$	−4.77200			−0.330879
$209$	−10.8860	−	12.3218i	−0.753000	−	0.852317i
$210$		0			0
$211$	10.2720	−	17.7916i	0.707154	−	1.22483i	−0.258755	−	0.965943i	$-0.583312\pi$
$211$	10.2720	−	17.7916i	0.707154	−	1.22483i	0.965909	−	0.258883i	$-0.0833545\pi$
$212$	4.88600	−	8.46280i	0.335572	−	0.581228i
$213$		0			0
$214$		0			0
$215$	4.38600	+	7.59678i	0.299123	+	0.518096i
$216$		0			0
$217$	−2.77200			−0.188176
$218$	−4.77200	−	8.26535i	−0.323201	−	0.559800i
$219$		0			0
$220$	3.77200			0.254308
$221$		0			0
$222$		0			0
$223$	12.5000	−	21.6506i	0.837062	−	1.44983i	−0.0552786	−	0.998471i	$-0.517605\pi$
$223$	12.5000	−	21.6506i	0.837062	−	1.44983i	0.892341	−	0.451363i	$-0.149062\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$	−6.77200	+	11.7295i	−0.450467	+	0.780231i
$227$	−9.08801			−0.603192			−0.301596	−	0.953436i	$-0.597519\pi$
$227$	−9.08801			−0.603192			−0.301596	+	0.953436i	$0.597519\pi$
$228$		0			0
$229$	23.8600			1.57671			0.788357	−	0.615218i	$-0.210932\pi$
$229$	23.8600			1.57671			0.788357	+	0.615218i	$0.210932\pi$
$230$	1.88600	−	3.26665i	0.124359	−	0.215396i
$231$		0			0
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	−2.22800	+	3.85901i	−0.145961	+	0.252812i	−0.929731	−	0.368239i	$-0.879961\pi$
$233$	−2.22800	+	3.85901i	−0.145961	+	0.252812i	0.783770	+	0.621051i	$0.213294\pi$
$234$		0			0
$235$		0			0
$236$	13.5440			0.881640
$237$		0			0
$238$		0			0
$239$	−13.5440			−0.876089			−0.438044	−	0.898953i	$-0.644329\pi$
$239$	−13.5440			−0.876089			−0.438044	+	0.898953i	$0.644329\pi$
$240$		0			0
$241$	−11.1580	−	19.3262i	−0.718750	−	1.24491i	−0.961495	−	0.274822i	$-0.911381\pi$
$241$	−11.1580	−	19.3262i	−0.718750	−	1.24491i	0.242745	−	0.970090i	$-0.421952\pi$
$242$	−1.61400	+	2.79553i	−0.103752	+	0.179703i
$243$		0			0
$244$	−1.38600	+	2.40062i	−0.0887296	+	0.153684i
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$		0			0
$247$	−6.61400	+	19.7211i	−0.420839	+	1.25483i
$248$	2.77200			0.176022
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	0.772002	+	1.33715i	0.0487283	+	0.0843999i	0.889361	−	0.457206i	$-0.151150\pi$
$251$	0.772002	+	1.33715i	0.0487283	+	0.0843999i	−0.840632	+	0.541606i	$0.817816\pi$
$252$		0			0
$253$	7.11400	+	12.3218i	0.447253	+	0.774665i
$254$	−9.31601			−0.584538
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.773427	−	0.633885i	$-0.781459\pi$
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.162247	−	0.986750i	$-0.551874\pi$
$258$		0			0
$259$	1.00000			0.0621370
$260$	−2.38600	−	4.13267i	−0.147973	−	0.256298i
$261$		0			0
$262$	−5.65800	−	9.79995i	−0.349553	−	0.605443i
$263$	7.88600	−	13.6590i	0.486272	−	0.842247i	−0.513604	−	0.858027i	$-0.671690\pi$
$263$	7.88600	−	13.6590i	0.486272	−	0.842247i	0.999875	+	0.0157802i	$0.00502322\pi$
$264$		0			0
$265$	9.77200			0.600289
$266$	4.27200	−	0.866025i	0.261933	−	0.0530994i
$267$		0			0
$268$	5.38600	−	9.32883i	0.329002	−	0.569849i
$269$	−12.7720	+	22.1218i	−0.778723	+	1.34879i	0.153956	+	0.988078i	$0.450799\pi$
$269$	−12.7720	+	22.1218i	−0.778723	+	1.34879i	−0.932678	+	0.360709i	$0.882535\pi$
$270$		0			0
$271$	−6.22800	+	10.7872i	−0.378324	+	0.655276i	−0.990819	−	0.135198i	$-0.956833\pi$
$271$	−6.22800	+	10.7872i	−0.378324	+	0.655276i	0.612495	+	0.790475i	$0.290166\pi$
$272$		0			0
$273$		0			0
$274$	1.54400			0.0932767
$275$	1.88600	+	3.26665i	0.113730	+	0.196986i
$276$		0			0
$277$	5.08801			0.305709			0.152854	−	0.988249i	$-0.451153\pi$
$277$	5.08801			0.305709			0.152854	+	0.988249i	$0.451153\pi$
$278$	−10.7720			−0.646062
$279$		0			0
$280$	−0.500000	+	0.866025i	−0.0298807	+	0.0517549i
$281$	13.8860	+	24.0513i	0.828369	+	1.43478i	0.899317	+	0.437298i	$0.144064\pi$
$281$	13.8860	+	24.0513i	0.828369	+	1.43478i	−0.0709474	+	0.997480i	$0.522602\pi$
$282$		0			0
$283$	13.3160	−	23.0640i	0.791554	−	1.37101i	−0.133450	−	0.991056i	$-0.542606\pi$
$283$	13.3160	−	23.0640i	0.791554	−	1.37101i	0.925004	−	0.379957i	$-0.124061\pi$
$284$	7.54400			0.447654
$285$		0			0
$286$	18.0000			1.06436
$287$	1.88600	−	3.26665i	0.111327	−	0.192824i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	3.00000	−	5.19615i	0.176166	−	0.305129i
$291$		0			0
$292$	−3.22800			−0.188904
$293$	20.2280			1.18173			0.590866	−	0.806770i	$-0.298786\pi$
$293$	20.2280			1.18173			0.590866	+	0.806770i	$0.298786\pi$
$294$		0			0
$295$	6.77200	+	11.7295i	0.394281	+	0.682915i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$	−6.77200	−	11.7295i	−0.392292	−	0.679469i
$299$	9.00000	−	15.5885i	0.520483	−	0.901504i
$300$		0			0
$301$	4.38600	−	7.59678i	0.252805	−	0.437871i
$302$	−4.00000	+	6.92820i	−0.230174	+	0.398673i
$303$		0			0
$304$	−4.27200	+	0.866025i	−0.245016	+	0.0496700i
$305$	−2.77200			−0.158724
$306$		0			0
$307$	11.7720	−	20.3897i	0.671864	−	1.16370i	−0.305511	−	0.952188i	$-0.598827\pi$
$307$	11.7720	−	20.3897i	0.671864	−	1.16370i	0.977375	−	0.211514i	$-0.0678392\pi$
$308$	−1.88600	−	3.26665i	−0.107465	−	0.186135i
$309$		0			0
$310$	1.38600	+	2.40062i	0.0787196	+	0.136346i
$311$	−25.5440			−1.44847			−0.724234	−	0.689555i	$-0.757806\pi$
$311$	−25.5440			−1.44847			−0.724234	+	0.689555i	$0.757806\pi$
$312$		0			0
$313$	1.22800	+	2.12696i	0.0694106	+	0.120223i	0.898642	−	0.438683i	$-0.144555\pi$
$313$	1.22800	+	2.12696i	0.0694106	+	0.120223i	−0.829231	+	0.558905i	$0.811221\pi$
$314$	−1.72800	−	2.99298i	−0.0975166	−	0.168904i
$315$		0			0
$316$	10.3160			0.580321
$317$	10.1140	+	17.5180i	0.568059	+	0.983907i	0.996758	+	0.0804593i	$0.0256387\pi$
$317$	10.1140	+	17.5180i	0.568059	+	0.983907i	−0.428699	+	0.903447i	$0.641028\pi$
$318$		0			0
$319$	11.3160	+	19.5999i	0.633575	+	1.09738i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	−3.77200			−0.210205
$323$		0			0
$324$		0			0
$325$	2.38600	−	4.13267i	0.132352	−	0.229240i
$326$	9.15800	−	15.8621i	0.507215	−	0.878522i
$327$		0			0
$328$	−1.88600	+	3.26665i	−0.104137	+	0.180371i
$329$		0			0
$330$		0			0
$331$	−26.5440			−1.45899			−0.729495	−	0.683986i	$-0.760245\pi$
$331$	−26.5440			−1.45899			−0.729495	+	0.683986i	$0.760245\pi$
$332$	3.00000	+	5.19615i	0.164646	+	0.285176i
$333$		0			0
$334$	11.3160			0.619184
$335$	10.7720			0.588537
$336$		0			0
$337$	15.1580	−	26.2544i	0.825709	−	1.43017i	−0.0756672	−	0.997133i	$-0.524109\pi$
$337$	15.1580	−	26.2544i	0.825709	−	1.43017i	0.901376	−	0.433037i	$-0.142558\pi$
$338$	−4.88600	−	8.46280i	−0.265763	−	0.460316i
$339$		0			0
$340$		0			0
$341$	−10.4560			−0.566224
$342$		0			0
$343$	13.0000			0.701934
$344$	−4.38600	+	7.59678i	−0.236477	+	0.409591i
$345$		0			0
$346$	5.65800	+	9.79995i	0.304176	+	0.526848i
$347$	−3.77200	+	6.53330i	−0.202492	+	0.350726i	−0.949331	−	0.314279i	$-0.898237\pi$
$347$	−3.77200	+	6.53330i	−0.202492	+	0.350726i	0.746839	+	0.665005i	$0.231571\pi$
$348$		0			0
$349$	−9.22800			−0.493963			−0.246982	−	0.969020i	$-0.579439\pi$
$349$	−9.22800			−0.493963			−0.246982	+	0.969020i	$0.579439\pi$
$350$	−1.00000			−0.0534522
$351$		0			0
$352$	1.88600	+	3.26665i	0.100524	+	0.174113i
$353$	13.5440			0.720875			0.360437	−	0.932783i	$-0.382627\pi$
$353$	13.5440			0.720875			0.360437	+	0.932783i	$0.382627\pi$
$354$		0			0
$355$	3.77200	+	6.53330i	0.200197	+	0.346752i
$356$	8.65800	−	14.9961i	0.458873	−	0.794792i
$357$		0			0
$358$	−0.341997	+	0.592357i	−0.0180751	+	0.0313070i
$359$	10.5440	−	18.2628i	0.556491	−	0.963871i	−0.441295	−	0.897362i	$-0.645481\pi$
$359$	10.5440	−	18.2628i	0.556491	−	0.963871i	0.997786	−	0.0665088i	$-0.0211860\pi$
$360$		0			0
$361$	−2.34200	+	18.8551i	−0.123263	+	0.992374i
$362$	17.0880			0.898126
$363$		0			0
$364$	−2.38600	+	4.13267i	−0.125060	+	0.216611i
$365$	−1.61400	−	2.79553i	−0.0844806	−	0.146325i
$366$		0			0
$367$	4.61400	+	7.99168i	0.240849	+	0.417162i	0.960956	−	0.276700i	$-0.0892409\pi$
$367$	4.61400	+	7.99168i	0.240849	+	0.417162i	−0.720108	+	0.693862i	$0.755908\pi$
$368$	3.77200			0.196629
$369$		0			0
$370$	−0.500000	−	0.866025i	−0.0259938	−	0.0450225i
$371$	−4.88600	−	8.46280i	−0.253669	−	0.439367i
$372$		0			0
$373$	−0.227998			−0.0118053			−0.00590265	−	0.999983i	$-0.501879\pi$
$373$	−0.227998			−0.0118053			−0.00590265	+	0.999983i	$0.501879\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.3160	−	24.7960i	0.737312	−	1.27706i
$378$		0			0
$379$	−9.22800			−0.474010			−0.237005	−	0.971508i	$-0.576166\pi$
$379$	−9.22800			−0.474010			−0.237005	+	0.971508i	$0.576166\pi$
$380$	−2.88600	−	3.26665i	−0.148049	−	0.167576i
$381$		0			0
$382$	3.77200	−	6.53330i	0.192992	−	0.334273i
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	0.377531	+	0.925997i	$0.376773\pi$
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	−0.990702	+	0.136047i	$0.956560\pi$
$384$		0			0
$385$	1.88600	−	3.26665i	0.0961195	−	0.166484i
$386$	−1.38600	−	2.40062i	−0.0705456	−	0.122189i
$387$		0			0
$388$	−10.0000			−0.507673
$389$	−4.54400	−	7.87045i	−0.230390	−	0.399047i	0.727533	−	0.686073i	$-0.240667\pi$
$389$	−4.54400	−	7.87045i	−0.230390	−	0.399047i	−0.957923	+	0.287025i	$0.907334\pi$
$390$		0			0
$391$		0			0
$392$	−6.00000			−0.303046
$393$		0			0
$394$	−5.65800	+	9.79995i	−0.285046	+	0.493714i
$395$	5.15800	+	8.93392i	0.259527	+	0.449514i
$396$		0			0
$397$	−1.04400	+	1.80827i	−0.0523970	+	0.0907543i	−0.891034	−	0.453936i	$-0.850019\pi$
$397$	−1.04400	+	1.80827i	−0.0523970	+	0.0907543i	0.838637	+	0.544690i	$0.183353\pi$
$398$	−0.316006			−0.0158399
$399$		0			0
$400$	1.00000			0.0500000
$401$	4.54400	−	7.87045i	0.226917	−	0.393031i	−0.729976	−	0.683473i	$-0.760469\pi$
$401$	4.54400	−	7.87045i	0.226917	−	0.393031i	0.956893	+	0.290441i	$0.0938021\pi$
$402$		0			0
$403$	6.61400	+	11.4558i	0.329467	+	0.570653i
$404$	−3.00000	+	5.19615i	−0.149256	+	0.258518i
$405$		0			0
$406$	−6.00000			−0.297775
$407$	3.77200			0.186971
$408$		0			0
$409$	15.2020	+	26.3306i	0.751691	+	1.30197i	0.947003	+	0.321226i	$0.104095\pi$
$409$	15.2020	+	26.3306i	0.751691	+	1.30197i	−0.195312	+	0.980741i	$0.562572\pi$
$410$	−3.77200			−0.186286
$411$		0			0
$412$	6.50000	+	11.2583i	0.320232	+	0.554658i
$413$	6.77200	−	11.7295i	0.333228	−	0.577169i
$414$		0			0
$415$	−3.00000	+	5.19615i	−0.147264	+	0.255069i
$416$	2.38600	−	4.13267i	0.116983	−	0.202621i
$417$		0			0
$418$	16.1140	−	3.26665i	0.788161	−	0.159777i
$419$	24.8600			1.21449			0.607245	−	0.794514i	$-0.292274\pi$
$419$	24.8600			1.21449			0.607245	+	0.794514i	$0.292274\pi$
$420$		0			0
$421$	8.77200	−	15.1936i	0.427521	−	0.740488i	−0.569131	−	0.822247i	$-0.692720\pi$
$421$	8.77200	−	15.1936i	0.427521	−	0.740488i	0.996652	+	0.0817584i	$0.0260536\pi$
$422$	10.2720	+	17.7916i	0.500033	+	0.866083i
$423$		0			0
$424$	4.88600	+	8.46280i	0.237285	+	0.410990i
$425$		0			0
$426$		0			0
$427$	1.38600	+	2.40062i	0.0670733	+	0.116174i
$428$		0			0
$429$		0			0
$430$	−8.77200			−0.423023
$431$	−1.54400	−	2.67429i	−0.0743720	−	0.128816i	0.826441	−	0.563023i	$-0.190362\pi$
$431$	−1.54400	−	2.67429i	−0.0743720	−	0.128816i	−0.900813	+	0.434207i	$0.857029\pi$
$432$		0			0
$433$	−5.15800	−	8.93392i	−0.247878	−	0.429337i	0.715059	−	0.699064i	$-0.246400\pi$
$433$	−5.15800	−	8.93392i	−0.247878	−	0.429337i	−0.962937	+	0.269727i	$0.913066\pi$
$434$	1.38600	−	2.40062i	0.0665302	−	0.115234i
$435$		0			0
$436$	9.54400			0.457075
$437$	5.22800	−	15.5885i	0.250089	−	0.745697i
$438$		0			0
$439$	−2.15800	+	3.73777i	−0.102996	+	0.178394i	−0.912918	−	0.408144i	$-0.866176\pi$
$439$	−2.15800	+	3.73777i	−0.102996	+	0.178394i	0.809922	+	0.586538i	$0.199510\pi$
$440$	−1.88600	+	3.26665i	−0.0899116	+	0.155731i
$441$		0			0
$442$		0			0
$443$	19.5440	+	33.8512i	0.928564	+	1.60832i	0.785727	+	0.618573i	$0.212289\pi$
$443$	19.5440	+	33.8512i	0.928564	+	1.60832i	0.142836	+	0.989746i	$0.454378\pi$
$444$		0			0
$445$	17.3160			0.820857
$446$	12.5000	+	21.6506i	0.591892	+	1.02519i
$447$		0			0
$448$	−1.00000			−0.0472456
$449$	−2.22800			−0.105146			−0.0525729	−	0.998617i	$-0.516742\pi$
$449$	−2.22800			−0.105146			−0.0525729	+	0.998617i	$0.516742\pi$
$450$		0			0
$451$	7.11400	−	12.3218i	0.334985	−	0.580211i
$452$	−6.77200	−	11.7295i	−0.318528	−	0.551707i
$453$		0			0
$454$	4.54400	−	7.87045i	0.213261	−	0.369378i
$455$	−4.77200			−0.223715
$456$		0			0
$457$	−25.8600			−1.20968			−0.604840	−	0.796347i	$-0.706763\pi$
$457$	−25.8600			−1.20968			−0.604840	+	0.796347i	$0.706763\pi$
$458$	−11.9300	+	20.6634i	−0.557453	+	0.965536i
$459$		0			0
$460$	1.88600	+	3.26665i	0.0879352	+	0.152308i
$461$	17.3160	−	29.9922i	0.806487	−	1.39688i	−0.108796	−	0.994064i	$-0.534700\pi$
$461$	17.3160	−	29.9922i	0.806487	−	1.39688i	0.915283	−	0.402812i	$-0.131967\pi$
$462$		0			0
$463$	27.6320			1.28417			0.642084	−	0.766634i	$-0.278070\pi$
$463$	27.6320			1.28417			0.642084	+	0.766634i	$0.278070\pi$
$464$	6.00000			0.278543
$465$		0			0
$466$	−2.22800	−	3.85901i	−0.103210	−	0.178765i
$467$	9.08801			0.420543			0.210271	−	0.977643i	$-0.432565\pi$
$467$	9.08801			0.420543			0.210271	+	0.977643i	$0.432565\pi$
$468$		0			0
$469$	−5.38600	−	9.32883i	−0.248702	−	0.430765i
$470$		0			0
$471$		0			0
$472$	−6.77200	+	11.7295i	−0.311707	+	0.539892i
$473$	16.5440	−	28.6551i	0.760694	−	1.31756i
$474$		0			0
$475$	1.38600	−	4.13267i	0.0635941	−	0.189620i
$476$		0			0
$477$		0			0
$478$	6.77200	−	11.7295i	0.309744	−	0.536493i
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$		0			0
$481$	−2.38600	−	4.13267i	−0.108792	−	0.188434i
$482$	22.3160			1.01647
$483$		0			0
$484$	−1.61400	−	2.79553i	−0.0733636	−	0.127069i
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$		0			0
$487$	−9.31601			−0.422149			−0.211074	−	0.977470i	$-0.567696\pi$
$487$	−9.31601			−0.422149			−0.211074	+	0.977470i	$0.567696\pi$
$488$	−1.38600	−	2.40062i	−0.0627413	−	0.108671i
$489$		0			0
$490$	−3.00000	−	5.19615i	−0.135526	−	0.234738i
$491$	3.34200	−	5.78851i	0.150822	−	0.261232i	−0.780708	−	0.624896i	$-0.785141\pi$
$491$	3.34200	−	5.78851i	0.150822	−	0.261232i	0.931530	+	0.363665i	$0.118475\pi$
$492$		0			0
$493$		0			0
$494$	−13.7720	−	15.5885i	−0.619632	−	0.701358i
$495$		0			0
$496$	−1.38600	+	2.40062i	−0.0622333	+	0.107791i
$497$	3.77200	−	6.53330i	0.169197	−	0.293059i
$498$		0			0
$499$	−10.8160	+	18.7339i	−0.484191	+	0.838643i	−0.999835	−	0.0181596i	$-0.994219\pi$
$499$	−10.8160	+	18.7339i	−0.484191	+	0.838643i	0.515644	+	0.856803i	$0.327553\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−1.54400			−0.0689123
$503$	8.65800	+	14.9961i	0.386041	+	0.668643i	0.991913	−	0.126919i	$-0.0405089\pi$
$503$	8.65800	+	14.9961i	0.386041	+	0.668643i	−0.605872	+	0.795562i	$0.707176\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$	−14.2280			−0.632512
$507$		0			0
$508$	4.65800	−	8.06790i	0.206665	−	0.357955i
$509$	17.3160	+	29.9922i	0.767518	+	1.32938i	0.938905	+	0.344177i	$0.111842\pi$
$509$	17.3160	+	29.9922i	0.767518	+	1.32938i	−0.171386	+	0.985204i	$0.554825\pi$
$510$		0			0
$511$	−1.61400	+	2.79553i	−0.0713991	+	0.123667i
$512$	1.00000			0.0441942
$513$		0			0
$514$	30.0000			1.32324
$515$	−6.50000	+	11.2583i	−0.286424	+	0.496101i
$516$		0			0
$517$		0			0
$518$	−0.500000	+	0.866025i	−0.0219687	+	0.0380510i
$519$		0			0
$520$	4.77200			0.209266
$521$	16.4560			0.720950			0.360475	−	0.932769i	$-0.382615\pi$
$521$	16.4560			0.720950			0.360475	+	0.932769i	$0.382615\pi$
$522$		0			0
$523$	−11.1580	−	19.3262i	−0.487905	−	0.845077i	0.511998	−	0.858987i	$-0.328906\pi$
$523$	−11.1580	−	19.3262i	−0.487905	−	0.845077i	−0.999903	+	0.0139098i	$0.995572\pi$
$524$	11.3160			0.494342
$525$		0			0
$526$	7.88600	+	13.6590i	0.343846	+	0.595559i
$527$		0			0
$528$		0			0
$529$	4.38600	−	7.59678i	0.190696	−	0.330295i
$530$	−4.88600	+	8.46280i	−0.212234	+	0.367601i
$531$		0			0
$532$	−1.38600	+	4.13267i	−0.0600908	+	0.179174i
$533$	−18.0000			−0.779667
$534$		0			0
$535$		0			0
$536$	5.38600	+	9.32883i	0.232640	+	0.402944i
$537$		0			0
$538$	−12.7720	−	22.1218i	−0.550640	−	0.953737i
$539$	22.6320			0.974830
$540$		0			0
$541$	−8.15800	−	14.1301i	−0.350740	−	0.607499i	0.635639	−	0.771986i	$-0.280737\pi$
$541$	−8.15800	−	14.1301i	−0.350740	−	0.607499i	−0.986379	+	0.164487i	$0.947403\pi$
$542$	−6.22800	−	10.7872i	−0.267515	−	0.463350i
$543$		0			0
$544$		0			0
$545$	4.77200	+	8.26535i	0.204410	+	0.354049i
$546$		0			0
$547$	−5.93000	−	10.2711i	−0.253549	−	0.439159i	0.710952	−	0.703241i	$-0.248264\pi$
$547$	−5.93000	−	10.2711i	−0.253549	−	0.439159i	−0.964500	+	0.264082i	$0.914931\pi$
$548$	−0.772002	+	1.33715i	−0.0329783	+	0.0571201i
$549$		0			0
$550$	−3.77200			−0.160839
$551$	8.31601	−	24.7960i	0.354274	−	1.05635i
$552$		0			0
$553$	5.15800	−	8.93392i	0.219341	−	0.379909i
$554$	−2.54400	+	4.40634i	−0.108084	+	0.187208i
$555$		0			0
$556$	5.38600	−	9.32883i	0.228417	−	0.395630i
$557$	1.11400	+	1.92950i	0.0472017	+	0.0817557i	0.888661	−	0.458565i	$-0.151636\pi$
$557$	1.11400	+	1.92950i	0.0472017	+	0.0817557i	−0.841459	+	0.540321i	$0.818303\pi$
$558$		0			0
$559$	−41.8600			−1.77049
$560$	−0.500000	−	0.866025i	−0.0211289	−	0.0365963i
$561$		0			0
$562$	−27.7720			−1.17149
$563$	−37.5440			−1.58229			−0.791146	−	0.611628i	$-0.790515\pi$
$563$	−37.5440			−1.58229			−0.791146	+	0.611628i	$0.790515\pi$
$564$		0			0
$565$	6.77200	−	11.7295i	0.284900	−	0.493462i
$566$	13.3160	+	23.0640i	0.559713	+	0.969452i
$567$		0			0
$568$	−3.77200	+	6.53330i	−0.158270	+	0.274131i
$569$	−2.22800			−0.0934025			−0.0467013	−	0.998909i	$-0.514871\pi$
$569$	−2.22800			−0.0934025			−0.0467013	+	0.998909i	$0.514871\pi$
$570$		0			0
$571$	−1.86001			−0.0778390			−0.0389195	−	0.999242i	$-0.512392\pi$
$571$	−1.86001			−0.0778390			−0.0389195	+	0.999242i	$0.512392\pi$
$572$	−9.00000	+	15.5885i	−0.376309	+	0.651786i
$573$		0			0
$574$	1.88600	+	3.26665i	0.0787202	+	0.136347i
$575$	−1.88600	+	3.26665i	−0.0786517	+	0.136229i
$576$		0			0
$577$	9.54400			0.397322			0.198661	−	0.980068i	$-0.436341\pi$
$577$	9.54400			0.397322			0.198661	+	0.980068i	$0.436341\pi$
$578$	−17.0000			−0.707107
$579$		0			0
$580$	3.00000	+	5.19615i	0.124568	+	0.215758i
$581$	6.00000			0.248922
$582$		0			0
$583$	−18.4300	−	31.9217i	−0.763293	−	1.32206i
$584$	1.61400	−	2.79553i	0.0667878	−	0.115680i
$585$		0			0
$586$	−10.1140	+	17.5180i	−0.417805	+	0.723660i
$587$	−12.7720	+	22.1218i	−0.527157	+	0.913063i	0.472342	+	0.881415i	$0.343409\pi$
$587$	−12.7720	+	22.1218i	−0.527157	+	0.913063i	−0.999499	+	0.0316473i	$0.989925\pi$
$588$		0			0
$589$	8.00000	+	9.05516i	0.329634	+	0.373111i
$590$	−13.5440			−0.557598
$591$		0			0
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	3.77200	+	6.53330i	0.154898	+	0.268290i	0.933022	−	0.359820i	$-0.117162\pi$
$593$	3.77200	+	6.53330i	0.154898	+	0.268290i	−0.778124	+	0.628110i	$0.783829\pi$
$594$		0			0
$595$		0			0
$596$	13.5440			0.554784
$597$		0			0
$598$	9.00000	+	15.5885i	0.368037	+	0.637459i
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		0			0
$601$	−35.6320			−1.45346			−0.726730	−	0.686923i	$-0.758961\pi$
$601$	−35.6320			−1.45346			−0.726730	+	0.686923i	$0.758961\pi$
$602$	4.38600	+	7.59678i	0.178760	+	0.309621i
$603$		0			0
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	1.61400	−	2.79553i	0.0656184	−	0.113654i
$606$		0			0
$607$	−40.0880			−1.62712			−0.813561	−	0.581480i	$-0.802474\pi$
$607$	−40.0880			−1.62712			−0.813561	+	0.581480i	$0.802474\pi$
$608$	1.38600	−	4.13267i	0.0562098	−	0.167602i
$609$		0			0
$610$	1.38600	−	2.40062i	0.0561175	−	0.0971984i
$611$		0			0
$612$		0			0
$613$	17.4300	−	30.1897i	0.703991	−	1.21935i	−0.263063	−	0.964779i	$-0.584733\pi$
$613$	17.4300	−	30.1897i	0.703991	−	1.21935i	0.967054	−	0.254570i	$-0.0819339\pi$
$614$	11.7720	+	20.3897i	0.475079	+	0.822862i
$615$		0			0
$616$	3.77200			0.151978
$617$	−1.54400	−	2.67429i	−0.0621593	−	0.107663i	0.833271	−	0.552865i	$-0.186465\pi$
$617$	−1.54400	−	2.67429i	−0.0621593	−	0.107663i	−0.895430	+	0.445202i	$0.853132\pi$
$618$		0			0
$619$	−31.1760			−1.25307			−0.626535	−	0.779393i	$-0.715527\pi$
$619$	−31.1760			−1.25307			−0.626535	+	0.779393i	$0.715527\pi$
$620$	−2.77200			−0.111326
$621$		0			0
$622$	12.7720	−	22.1218i	0.512111	−	0.887002i
$623$	−8.65800	−	14.9961i	−0.346876	−	0.600806i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.45600			−0.0981614
$627$		0			0
$628$	3.45600			0.137909
$629$		0			0
$630$		0			0
$631$	21.9300	+	37.9839i	0.873020	+	1.51211i	0.858857	+	0.512215i	$0.171175\pi$
$631$	21.9300	+	37.9839i	0.873020	+	1.51211i	0.0141623	+	0.999900i	$0.495492\pi$
$632$	−5.15800	+	8.93392i	−0.205174	+	0.355372i
$633$		0			0
$634$	−20.2280			−0.803356
$635$	9.31601			0.369694
$636$		0			0
$637$	−14.3160	−	24.7960i	−0.567221	−	0.982455i
$638$	−22.6320			−0.896010
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	9.77200	−	16.9256i	0.385971	−	0.668521i	−0.605933	−	0.795516i	$-0.707200\pi$
$641$	9.77200	−	16.9256i	0.385971	−	0.668521i	0.991903	+	0.126995i	$0.0405332\pi$
$642$		0			0
$643$	0.158003	−	0.273669i	0.00623102	−	0.0107924i	−0.862893	−	0.505387i	$-0.831350\pi$
$643$	0.158003	−	0.273669i	0.00623102	−	0.0107924i	0.869124	+	0.494594i	$0.164683\pi$
$644$	1.88600	−	3.26665i	0.0743188	−	0.128724i
$645$		0			0
$646$		0			0
$647$	12.6840			0.498659			0.249330	−	0.968419i	$-0.419790\pi$
$647$	12.6840			0.498659			0.249330	+	0.968419i	$0.419790\pi$
$648$		0			0
$649$	25.5440	−	44.2435i	1.00269	−	1.73671i
$650$	2.38600	+	4.13267i	0.0935867	+	0.162097i
$651$		0			0
$652$	9.15800	+	15.8621i	0.358655	+	0.621209i
$653$	−29.3160			−1.14722			−0.573612	−	0.819127i	$-0.694458\pi$
$653$	−29.3160			−1.14722			−0.573612	+	0.819127i	$0.694458\pi$
$654$		0			0
$655$	5.65800	+	9.79995i	0.221076	+	0.382916i
$656$	−1.88600	−	3.26665i	−0.0736360	−	0.127541i
$657$		0			0
$658$		0			0
$659$	6.34200	+	10.9847i	0.247049	+	0.427902i	0.962706	−	0.270551i	$-0.0872058\pi$
$659$	6.34200	+	10.9847i	0.247049	+	0.427902i	−0.715657	+	0.698452i	$0.753872\pi$
$660$		0			0
$661$	22.3160	+	38.6525i	0.867992	+	1.50341i	0.864045	+	0.503414i	$0.167923\pi$
$661$	22.3160	+	38.6525i	0.867992	+	1.50341i	0.00394672	+	0.999992i	$0.498744\pi$
$662$	13.2720	−	22.9878i	0.515831	−	0.893446i
$663$		0			0
$664$	−6.00000			−0.232845
$665$	−4.27200	+	0.866025i	−0.165661	+	0.0335830i
$666$		0			0
$667$	−11.3160	+	19.5999i	−0.438157	+	0.758911i
$668$	−5.65800	+	9.79995i	−0.218915	+	0.379171i
$669$		0			0
$670$	−5.38600	+	9.32883i	−0.208079	+	0.360404i
$671$	5.22800	+	9.05516i	0.201825	+	0.349571i
$672$		0			0
$673$	−21.2280			−0.818279			−0.409140	−	0.912472i	$-0.634171\pi$
$673$	−21.2280			−0.818279			−0.409140	+	0.912472i	$0.634171\pi$
$674$	15.1580	+	26.2544i	0.583864	+	1.01128i
$675$		0			0
$676$	9.77200			0.375846
$677$	−17.3160			−0.665508			−0.332754	−	0.943014i	$-0.607978\pi$
$677$	−17.3160			−0.665508			−0.332754	+	0.943014i	$0.607978\pi$
$678$		0			0
$679$	−5.00000	+	8.66025i	−0.191882	+	0.332350i
$680$		0			0
$681$		0			0
$682$	5.22800	−	9.05516i	0.200190	−	0.346740i
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$		0			0
$685$	−1.54400			−0.0589934
$686$	−6.50000	+	11.2583i	−0.248171	+	0.429845i
$687$		0			0
$688$	−4.38600	−	7.59678i	−0.167215	−	0.289624i
$689$	−23.3160	+	40.3845i	−0.888269	+	1.53853i
$690$		0			0
$691$	7.13999			0.271618			0.135809	−	0.990735i	$-0.456637\pi$
$691$	7.13999			0.271618			0.135809	+	0.990735i	$0.456637\pi$
$692$	−11.3160			−0.430170
$693$		0			0
$694$	−3.77200	−	6.53330i	−0.143183	−	0.248001i
$695$	10.7720			0.408605
$696$		0			0
$697$		0			0
$698$	4.61400	−	7.99168i	0.174642	−	0.302490i
$699$		0			0
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	17.3160	−	29.9922i	0.654017	−	1.13279i	−0.328123	−	0.944635i	$-0.606416\pi$
$701$	17.3160	−	29.9922i	0.654017	−	1.13279i	0.982139	−	0.188155i	$-0.0602507\pi$
$702$		0			0
$703$	−2.88600	−	3.26665i	−0.108848	−	0.123204i
$704$	−3.77200			−0.142163
$705$		0			0
$706$	−6.77200	+	11.7295i	−0.254868	+	0.441444i
$707$	3.00000	+	5.19615i	0.112827	+	0.195421i
$708$		0			0
$709$	17.3860	+	30.1134i	0.652945	+	1.13093i	0.982405	+	0.186764i	$0.0598001\pi$
$709$	17.3860	+	30.1134i	0.652945	+	1.13093i	−0.329460	+	0.944170i	$0.606867\pi$
$710$	−7.54400			−0.283121
$711$		0			0
$712$	8.65800	+	14.9961i	0.324472	+	0.562003i
$713$	−5.22800	−	9.05516i	−0.195790	−	0.339118i
$714$		0			0
$715$	−18.0000			−0.673162
$716$	−0.341997	−	0.592357i	−0.0127810	−	0.0221374i
$717$		0			0
$718$	10.5440	+	18.2628i	0.393499	+	0.681560i
$719$	14.3160	−	24.7960i	0.533897	−	0.924737i	−0.465319	−	0.885143i	$-0.654060\pi$
$719$	14.3160	−	24.7960i	0.533897	−	0.924737i	0.999216	−	0.0395935i	$-0.0126063\pi$
$720$		0			0
$721$	13.0000			0.484145
$722$	−15.1580	−	11.4558i	−0.564122	−	0.426340i
$723$		0			0
$724$	−8.54400	+	14.7986i	−0.317535	+	0.549987i
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		0			0
$727$	−21.7020	+	37.5890i	−0.804883	+	1.39410i	0.111487	+	0.993766i	$0.464439\pi$
$727$	−21.7020	+	37.5890i	−0.804883	+	1.39410i	−0.916370	+	0.400332i	$0.868895\pi$
$728$	−2.38600	−	4.13267i	−0.0884311	−	0.153167i
$729$		0			0
$730$	3.22800			0.119474
$731$		0			0
$732$		0			0
$733$	22.4040			0.827511			0.413756	−	0.910388i	$-0.364217\pi$
$733$	22.4040			0.827511			0.413756	+	0.910388i	$0.364217\pi$
$734$	−9.22800			−0.340612
$735$		0			0
$736$	−1.88600	+	3.26665i	−0.0695189	+	0.120410i
$737$	−20.3160	−	35.1884i	−0.748350	−	1.29618i
$738$		0			0
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	−0.908337	−	0.418238i	$-0.862648\pi$
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	0.816373	+	0.577524i	$0.195981\pi$
$740$	1.00000			0.0367607
$741$		0			0
$742$	9.77200			0.358741
$743$	10.1140	−	17.5180i	0.371047	−	0.642672i	−0.618680	−	0.785643i	$-0.712332\pi$
$743$	10.1140	−	17.5180i	0.371047	−	0.642672i	0.989727	+	0.142971i	$0.0456657\pi$
$744$		0			0
$745$	6.77200	+	11.7295i	0.248107	+	0.429734i
$746$	0.113999	−	0.197452i	0.00417380	−	0.00722924i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−25.3860	−	43.9698i	−0.926348	−	1.60448i	−0.789378	−	0.613907i	$-0.789597\pi$
$751$	−25.3860	−	43.9698i	−0.926348	−	1.60448i	−0.136970	−	0.990575i	$-0.543736\pi$
$752$		0			0
$753$		0			0
$754$	14.3160	+	24.7960i	0.521358	+	0.903019i
$755$	4.00000	−	6.92820i	0.145575	−	0.252143i
$756$		0			0
$757$	14.8160	−	25.6621i	0.538497	−	0.932704i	−0.460488	−	0.887666i	$-0.652326\pi$
$757$	14.8160	−	25.6621i	0.538497	−	0.932704i	0.998985	−	0.0450382i	$-0.0143410\pi$
$758$	4.61400	−	7.99168i	0.167588	−	0.290271i
$759$		0			0
$760$	4.27200	−	0.866025i	0.154962	−	0.0314140i
$761$	−21.9480			−0.795615			−0.397807	−	0.917469i	$-0.630229\pi$
$761$	−21.9480			−0.795615			−0.397807	+	0.917469i	$0.630229\pi$
$762$		0			0
$763$	4.77200	−	8.26535i	0.172758	−	0.299226i
$764$	3.77200	+	6.53330i	0.136466	+	0.236366i
$765$		0			0
$766$	−12.0000	−	20.7846i	−0.433578	−	0.750978i
$767$	−64.6320			−2.33373
$768$		0			0
$769$	−17.9300	−	31.0557i	−0.646573	−	1.11990i	−0.983936	−	0.178522i	$-0.942868\pi$
$769$	−17.9300	−	31.0557i	−0.646573	−	1.11990i	0.337363	−	0.941374i	$-0.390465\pi$
$770$	1.88600	+	3.26665i	0.0679668	+	0.117722i
$771$		0			0
$772$	2.77200			0.0997665
$773$	−1.88600	−	3.26665i	−0.0678347	−	0.117493i	0.830113	−	0.557595i	$-0.188276\pi$
$773$	−1.88600	−	3.26665i	−0.0678347	−	0.117493i	−0.897948	+	0.440102i	$0.854942\pi$
$774$		0			0
$775$	−1.38600	−	2.40062i	−0.0497866	−	0.0862330i
$776$	5.00000	−	8.66025i	0.179490	−	0.310885i
$777$		0			0
$778$	9.08801			0.325821
$779$	−16.1140	+	3.26665i	−0.577344	+	0.117040i
$780$		0			0
$781$	14.2280	−	24.6436i	0.509118	−	0.881818i
$782$		0			0
$783$		0			0
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	1.72800	+	2.99298i	0.0616749	+	0.106824i
$786$		0			0
$787$	34.3160			1.22323			0.611617	−	0.791154i	$-0.290519\pi$
$787$	34.3160			1.22323			0.611617	+	0.791154i	$0.290519\pi$
$788$	−5.65800	−	9.79995i	−0.201558	−	0.349109i
$789$		0			0
$790$	−10.3160			−0.367027
$791$	−13.5440			−0.481569
$792$		0			0
$793$	6.61400	−	11.4558i	0.234870	−	0.406807i
$794$	−1.04400	−	1.80827i	−0.0370503	−	0.0641730i
$795$		0			0
$796$	0.158003	−	0.273669i	0.00560026	−	0.00969994i
$797$	15.7720			0.558673			0.279336	−	0.960193i	$-0.409886\pi$
$797$	15.7720			0.558673			0.279336	+	0.960193i	$0.409886\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	4.54400	+	7.87045i	0.160454	+	0.277915i
$803$	−6.08801	+	10.5447i	−0.214841	+	0.372116i
$804$		0			0
$805$	3.77200			0.132946
$806$	−13.2280			−0.465936
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	18.0000			0.632846			0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000			0.632846			0.316423	+	0.948618i	$0.397518\pi$
$810$		0			0
$811$	−20.8860	−	36.1756i	−0.733407	−	1.27030i	−0.955419	−	0.295254i	$-0.904596\pi$
$811$	−20.8860	−	36.1756i	−0.733407	−	1.27030i	0.222012	−	0.975044i	$-0.428738\pi$
$812$	3.00000	−	5.19615i	0.105279	−	0.182349i
$813$		0			0
$814$	−1.88600	+	3.26665i	−0.0661043	+	0.114496i
$815$	−9.15800	+	15.8621i	−0.320791	+	0.555626i
$816$		0			0
$817$	−37.4740	+	7.59678i	−1.31105	+	0.265778i
$818$	−30.4040			−1.06305
$819$		0			0
$820$	1.88600	−	3.26665i	0.0658620	−	0.114076i
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$		0			0
$823$	20.4300	+	35.3858i	0.712145	+	1.23347i	0.964050	+	0.265720i	$0.0856096\pi$
$823$	20.4300	+	35.3858i	0.712145	+	1.23347i	−0.251905	+	0.967752i	$0.581057\pi$
$824$	−13.0000			−0.452876
$825$		0			0
$826$	6.77200	+	11.7295i	0.235628	+	0.408120i
$827$	−21.0000	−	36.3731i	−0.730242	−	1.26482i	−0.956780	−	0.290813i	$-0.906074\pi$
$827$	−21.0000	−	36.3731i	−0.730242	−	1.26482i	0.226538	−	0.974002i	$-0.427259\pi$
$828$		0			0
$829$	31.4040			1.09071			0.545353	−	0.838206i	$-0.316396\pi$
$829$	31.4040			1.09071			0.545353	+	0.838206i	$0.316396\pi$
$830$	−3.00000	−	5.19615i	−0.104132	−	0.180361i
$831$		0			0
$832$	2.38600	+	4.13267i	0.0827197	+	0.143275i
$833$		0			0
$834$		0			0
$835$	−11.3160			−0.391607
$836$	−5.22800	+	15.5885i	−0.180814	+	0.539138i
$837$		0			0
$838$	−12.4300	+	21.5294i	−0.429387	+	0.743721i
$839$	−0.683994	+	1.18471i	−0.0236141	+	0.0409008i	−0.877591	−	0.479410i	$-0.840851\pi$
$839$	−0.683994	+	1.18471i	−0.0236141	+	0.0409008i	0.853977	+	0.520311i	$0.174184\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	8.77200	+	15.1936i	0.302303	+	0.523604i
$843$		0			0
$844$	−20.5440			−0.707154
$845$	4.88600	+	8.46280i	0.168084	+	0.291129i
$846$		0			0
$847$	−3.22800			−0.110915
$848$	−9.77200			−0.335572
$849$		0			0
$850$		0			0
$851$	1.88600	+	3.26665i	0.0646513	+	0.111979i
$852$		0			0
$853$	3.15800	−	5.46982i	0.108128	−	0.187283i	−0.806884	−	0.590710i	$-0.798848\pi$
$853$	3.15800	−	5.46982i	0.108128	−	0.187283i	0.915012	+	0.403427i	$0.132181\pi$
$854$	−2.77200			−0.0948560
$855$		0			0
$856$		0			0
$857$	−22.6320	+	39.1998i	−0.773095	+	1.33904i	0.162764	+	0.986665i	$0.447959\pi$
$857$	−22.6320	+	39.1998i	−0.773095	+	1.33904i	−0.935859	+	0.352374i	$0.885374\pi$
$858$		0			0
$859$	25.2720	+	43.7724i	0.862270	+	1.49349i	0.869733	+	0.493523i	$0.164291\pi$
$859$	25.2720	+	43.7724i	0.862270	+	1.49349i	−0.00746341	+	0.999972i	$0.502376\pi$
$860$	4.38600	−	7.59678i	0.149561	−	0.259048i
$861$		0			0
$862$	3.08801			0.105178
$863$	24.6840			0.840253			0.420126	−	0.907466i	$-0.361986\pi$
$863$	24.6840			0.840253			0.420126	+	0.907466i	$0.361986\pi$
$864$		0			0
$865$	−5.65800	−	9.79995i	−0.192378	−	0.333208i
$866$	10.3160			0.350552
$867$		0			0
$868$	1.38600	+	2.40062i	0.0470439	+	0.0814825i
$869$	19.4560	−	33.6988i	0.659999	−	1.14315i
$870$		0			0
$871$	−25.7020	+	44.5172i	−0.870879	+	1.50841i
$872$	−4.77200	+	8.26535i	−0.161600	+	0.279900i
$873$		0			0
$874$	10.8860	+	12.3218i	0.368224	+	0.416791i
$875$	1.00000			0.0338062
$876$		0			0
$877$	−3.27200	+	5.66727i	−0.110488	+	0.191370i	−0.915967	−	0.401254i	$-0.868575\pi$
$877$	−3.27200	+	5.66727i	−0.110488	+	0.191370i	0.805479	+	0.592624i	$0.201908\pi$
$878$	−2.15800	−	3.73777i	−0.0728291	−	0.126144i
$879$		0			0
$880$	−1.88600	−	3.26665i	−0.0635771	−	0.110119i
$881$	−42.8600			−1.44399			−0.721995	−	0.691898i	$-0.756775\pi$
$881$	−42.8600			−1.44399			−0.721995	+	0.691898i	$0.756775\pi$
$882$		0			0
$883$	3.84200	+	6.65453i	0.129293	+	0.223943i	0.923403	−	0.383832i	$-0.125396\pi$
$883$	3.84200	+	6.65453i	0.129293	+	0.223943i	−0.794110	+	0.607775i	$0.792062\pi$
$884$		0			0
$885$		0			0
$886$	−39.0880			−1.31319
$887$	27.0880	+	46.9178i	0.909526	+	1.57535i	0.814724	+	0.579850i	$0.196889\pi$
$887$	27.0880	+	46.9178i	0.909526	+	1.57535i	0.0948028	+	0.995496i	$0.469778\pi$
$888$		0			0
$889$	−4.65800	−	8.06790i	−0.156224	−	0.270589i
$890$	−8.65800	+	14.9961i	−0.290217	+	0.502670i
$891$		0			0
$892$	−25.0000			−0.837062
$893$		0			0
$894$		0			0
$895$	0.341997	−	0.592357i	0.0114317	−	0.0198003i
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$		0			0
$898$	1.11400	−	1.92950i	0.0371746	−	0.0643883i
$899$	−8.31601	−	14.4037i	−0.277354	−	0.480392i
$900$		0			0
$901$		0			0
$902$	7.11400	+	12.3218i	0.236870	+	0.410271i
$903$		0			0
$904$	13.5440			0.450467
$905$	−17.0880			−0.568025
$906$		0			0
$907$	10.2280	−	17.7154i	0.339615	−	0.588231i	−0.644745	−	0.764398i	$-0.723037\pi$
$907$	10.2280	−	17.7154i	0.339615	−	0.588231i	0.984360	+	0.176167i	$0.0563699\pi$
$908$	4.54400	+	7.87045i	0.150798	+	0.261190i
$909$		0			0
$910$	2.38600	−	4.13267i	0.0790952	−	0.136997i
$911$	−36.1760			−1.19856			−0.599282	−	0.800538i	$-0.704547\pi$
$911$	−36.1760			−1.19856			−0.599282	+	0.800538i	$0.704547\pi$
$912$		0			0
$913$	22.6320			0.749010
$914$	12.9300	−	22.3954i	0.427687	−	0.740775i
$915$		0			0
$916$	−11.9300	−	20.6634i	−0.394178	−	0.682737i
$917$	5.65800	−	9.79995i	0.186844	−	0.323623i
$918$		0			0
$919$	−33.4040			−1.10190			−0.550948	−	0.834539i	$-0.685734\pi$
$919$	−33.4040			−1.10190			−0.550948	+	0.834539i	$0.685734\pi$
$920$	−3.77200			−0.124359
$921$		0			0
$922$	17.3160	+	29.9922i	0.570272	+	0.987741i
$923$	−36.0000			−1.18495
$924$		0			0
$925$	0.500000	+	0.866025i	0.0164399	+	0.0284747i
$926$	−13.8160	+	23.9300i	−0.454022	+	0.786389i
$927$		0			0
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	−27.5180	+	47.6626i	−0.902837	+	1.56376i	−0.0790416	+	0.996871i	$0.525186\pi$
$929$	−27.5180	+	47.6626i	−0.902837	+	1.56376i	−0.823795	+	0.566888i	$0.808147\pi$
$930$		0			0
$931$	−17.3160	−	19.5999i	−0.567509	−	0.642361i
$932$	4.45600			0.145961
$933$		0			0
$934$	−4.54400	+	7.87045i	−0.148684	+	0.257529i
$935$		0			0
$936$		0			0
$937$	26.3860	+	45.7019i	0.861993	+	1.49302i	0.870002	+	0.493048i	$0.164117\pi$
$937$	26.3860	+	45.7019i	0.861993	+	1.49302i	−0.00800910	+	0.999968i	$0.502549\pi$
$938$	10.7720			0.351718
$939$		0			0
$940$		0			0
$941$	−4.54400	−	7.87045i	−0.148130	−	0.256569i	0.782406	−	0.622769i	$-0.213992\pi$
$941$	−4.54400	−	7.87045i	−0.148130	−	0.256569i	−0.930536	+	0.366199i	$0.880659\pi$
$942$		0			0
$943$	14.2280			0.463327
$944$	−6.77200	−	11.7295i	−0.220410	−	0.381761i
$945$		0			0
$946$	16.5440	+	28.6551i	0.537892	+	0.931656i
$947$	−2.31601	+	4.01144i	−0.0752601	+	0.130354i	−0.901199	−	0.433405i	$-0.857312\pi$
$947$	−2.31601	+	4.01144i	−0.0752601	+	0.130354i	0.825939	+	0.563759i	$0.190645\pi$
$948$		0			0
$949$	15.4040			0.500035
$950$	2.88600	+	3.26665i	0.0936342	+	0.105984i
$951$		0			0
$952$		0			0
$953$	−30.0000	+	51.9615i	−0.971795	+	1.68320i	−0.281666	+	0.959512i	$0.590887\pi$
$953$	−30.0000	+	51.9615i	−0.971795	+	1.68320i	−0.690129	+	0.723686i	$0.742446\pi$
$954$		0			0
$955$	−3.77200	+	6.53330i	−0.122059	+	0.211413i
$956$	6.77200	+	11.7295i	0.219022	+	0.379358i
$957$		0			0
$958$	18.0000			0.581554
$959$	0.772002	+	1.33715i	0.0249292	+	0.0431787i
$960$		0			0
$961$	−23.3160			−0.752129
$962$	4.77200			0.153856
$963$		0			0
$964$	−11.1580	+	19.3262i	−0.359375	+	0.622456i
$965$	1.38600	+	2.40062i	0.0446169	+	0.0772788i
$966$		0			0
$967$	22.6140	−	39.1686i	0.727217	−	1.25958i	−0.230838	−	0.972992i	$-0.574147\pi$
$967$	22.6140	−	39.1686i	0.727217	−	1.25958i	0.958055	−	0.286585i	$-0.0925200\pi$
$968$	3.22800			0.103752
$969$		0			0
$970$	10.0000			0.321081
$971$	−19.5440	+	33.8512i	−0.627197	+	1.08634i	0.360915	+	0.932599i	$0.382465\pi$
$971$	−19.5440	+	33.8512i	−0.627197	+	1.08634i	−0.988112	+	0.153738i	$0.950869\pi$
$972$		0			0
$973$	−5.38600	−	9.32883i	−0.172667	−	0.299068i
$974$	4.65800	−	8.06790i	0.149252	−	0.258512i
$975$		0			0
$976$	2.77200			0.0887296
$977$	−60.1760			−1.92520			−0.962601	−	0.270924i	$-0.912671\pi$
$977$	−60.1760			−1.92520			−0.962601	+	0.270924i	$0.912671\pi$
$978$		0			0
$979$	−32.6580	−	56.5653i	−1.04375	−	1.80784i
$980$	6.00000			0.191663
$981$		0			0
$982$	3.34200	+	5.78851i	0.106647	+	0.184719i
$983$	−2.65800	+	4.60380i	−0.0847771	+	0.146838i	−0.905296	−	0.424781i	$-0.860351\pi$
$983$	−2.65800	+	4.60380i	−0.0847771	+	0.146838i	0.820519	+	0.571619i	$0.193684\pi$
$984$		0			0
$985$	5.65800	−	9.79995i	0.180279	−	0.312252i
$986$		0			0
$987$		0			0
$988$	20.3860	−	4.13267i	0.648565	−	0.131478i
$989$	33.0880			1.05214
$990$		0			0
$991$	−16.3860	+	28.3814i	−0.520518	+	0.901564i	0.479197	+	0.877707i	$0.340928\pi$
$991$	−16.3860	+	28.3814i	−0.520518	+	0.901564i	−0.999715	+	0.0238570i	$0.992405\pi$
$992$	−1.38600	−	2.40062i	−0.0440056	−	0.0762199i
$993$		0			0
$994$	3.77200	+	6.53330i	0.119641	+	0.207224i
$995$	0.316006			0.0100181
$996$		0			0
$997$	10.2720	+	17.7916i	0.325318	+	0.563467i	0.981577	−	0.191069i	$-0.0611955\pi$
$997$	10.2720	+	17.7916i	0.325318	+	0.563467i	−0.656259	+	0.754536i	$0.727862\pi$
$998$	−10.8160	−	18.7339i	−0.342375	−	0.593010i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.l.1531.1		4
3.2	odd	2		570.2.i.g.391.2	yes	4
19.7	even	3	inner	1710.2.l.l.1261.1		4
57.26	odd	6		570.2.i.g.121.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.g.121.2	✓	4	57.26	odd	6
570.2.i.g.391.2	yes	4	3.2	odd	2
1710.2.l.l.1261.1		4	19.7	even	3	inner
1710.2.l.l.1531.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} -3.77200 q^{11} +(2.38600 + 4.13267i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.88600 + 3.26665i) q^{19} -1.00000 q^{20} +(1.88600 - 3.26665i) q^{22} +(-1.88600 - 3.26665i) q^{23} +(-0.500000 - 0.866025i) q^{25} -4.77200 q^{26} +(0.500000 + 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} +2.77200 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{35} -1.00000 q^{37} +(-4.27200 + 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-1.88600 + 3.26665i) q^{41} +(-4.38600 + 7.59678i) q^{43} +(1.88600 + 3.26665i) q^{44} +3.77200 q^{46} -6.00000 q^{49} +1.00000 q^{50} +(2.38600 - 4.13267i) q^{52} +(4.88600 + 8.46280i) q^{53} +(-1.88600 + 3.26665i) q^{55} -1.00000 q^{56} +6.00000 q^{58} +(-6.77200 + 11.7295i) q^{59} +(-1.38600 - 2.40062i) q^{61} +(-1.38600 + 2.40062i) q^{62} +1.00000 q^{64} +4.77200 q^{65} +(5.38600 + 9.32883i) q^{67} +(-0.500000 - 0.866025i) q^{70} +(-3.77200 + 6.53330i) q^{71} +(1.61400 - 2.79553i) q^{73} +(0.500000 - 0.866025i) q^{74} +(1.38600 - 4.13267i) q^{76} +3.77200 q^{77} +(-5.15800 + 8.93392i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-1.88600 - 3.26665i) q^{82} -6.00000 q^{83} +(-4.38600 - 7.59678i) q^{86} -3.77200 q^{88} +(8.65800 + 14.9961i) q^{89} +(-2.38600 - 4.13267i) q^{91} +(-1.88600 + 3.26665i) q^{92} +(4.27200 - 0.866025i) q^{95} +(5.00000 - 8.66025i) q^{97} +(3.00000 - 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 4 q^{8} + 2 q^{10} + 2 q^{11} + q^{13} + 2 q^{14} - 2 q^{16} + 3 q^{19} - 4 q^{20} - q^{22} + q^{23} - 2 q^{25} - 2 q^{26} + 2 q^{28} - 12 q^{29} - 6 q^{31} - 2 q^{32} - 2 q^{35} - 4 q^{37} + 2 q^{40} + q^{41} - 9 q^{43} - q^{44} - 2 q^{46} - 24 q^{49} + 4 q^{50} + q^{52} + 11 q^{53} + q^{55} - 4 q^{56} + 24 q^{58} - 10 q^{59} + 3 q^{61} + 3 q^{62} + 4 q^{64} + 2 q^{65} + 13 q^{67} - 2 q^{70} + 2 q^{71} + 15 q^{73} + 2 q^{74} - 3 q^{76} - 2 q^{77} + 5 q^{79} + 2 q^{80} + q^{82} - 24 q^{83} - 9 q^{86} + 2 q^{88} + 9 q^{89} - q^{91} + q^{92} + 20 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 4 * q^8 + 2 * q^10 + 2 * q^11 + q^13 + 2 * q^14 - 2 * q^16 + 3 * q^19 - 4 * q^20 - q^22 + q^23 - 2 * q^25 - 2 * q^26 + 2 * q^28 - 12 * q^29 - 6 * q^31 - 2 * q^32 - 2 * q^35 - 4 * q^37 + 2 * q^40 + q^41 - 9 * q^43 - q^44 - 2 * q^46 - 24 * q^49 + 4 * q^50 + q^52 + 11 * q^53 + q^55 - 4 * q^56 + 24 * q^58 - 10 * q^59 + 3 * q^61 + 3 * q^62 + 4 * q^64 + 2 * q^65 + 13 * q^67 - 2 * q^70 + 2 * q^71 + 15 * q^73 + 2 * q^74 - 3 * q^76 - 2 * q^77 + 5 * q^79 + 2 * q^80 + q^82 - 24 * q^83 - 9 * q^86 + 2 * q^88 + 9 * q^89 - q^91 + q^92 + 20 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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