LMFDB - Embedded newform 1323.2.s.b.656.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			656.5
Root			$1.07065 + 1.85442i$ of defining polynomial
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.b.962.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24607 - 1.29677i) q^{2} +(2.36322 - 4.09323i) q^{4} +1.25299 q^{5} -7.07116i q^{8} +O(q^{10})$	\(q+(2.24607 - 1.29677i) q^{2} +(2.36322 - 4.09323i) q^{4} +1.25299 q^{5} -7.07116i q^{8} +(2.81429 - 1.62483i) q^{10} +0.616756i q^{11} +(1.06343 - 0.613974i) q^{13} +(-4.44321 - 7.69587i) q^{16} +(-2.21501 - 3.83652i) q^{17} +(1.64679 + 0.950775i) q^{19} +(2.96109 - 5.12875i) q^{20} +(0.799790 + 1.38528i) q^{22} -4.74890i q^{23} -3.43003 q^{25} +(1.59237 - 2.75806i) q^{26} +(5.07629 + 2.93080i) q^{29} +(2.14851 + 1.24044i) q^{31} +(-7.71195 - 4.45249i) q^{32} +(-9.95016 - 5.74473i) q^{34} +(1.33217 - 2.30738i) q^{37} +4.93175 q^{38} -8.86005i q^{40} +(2.09966 + 3.63671i) q^{41} +(-2.24637 + 3.89083i) q^{43} +(2.52452 + 1.45753i) q^{44} +(-6.15823 - 10.6664i) q^{46} +(3.80738 + 6.59458i) q^{47} +(-7.70409 + 4.44796i) q^{50} -5.80384i q^{52} +(-2.67782 + 1.54604i) q^{53} +0.772786i q^{55} +15.2023 q^{58} +(1.78229 - 3.08702i) q^{59} +(-12.5136 + 7.22473i) q^{61} +6.43428 q^{62} -5.32259 q^{64} +(1.33247 - 0.769301i) q^{65} +(-6.80644 + 11.7891i) q^{67} -20.9383 q^{68} -10.4095i q^{71} +(-9.95016 + 5.74473i) q^{73} -6.91006i q^{74} +(7.78348 - 4.49379i) q^{76} +(2.01592 + 3.49168i) q^{79} +(-5.56728 - 9.64281i) q^{80} +(9.43196 + 5.44554i) q^{82} +(4.36775 - 7.56516i) q^{83} +(-2.77538 - 4.80710i) q^{85} +11.6521i q^{86} +4.36118 q^{88} +(-0.811226 + 1.40508i) q^{89} +(-19.4383 - 11.2227i) q^{92} +(17.1033 + 9.87459i) q^{94} +(2.06341 + 1.19131i) q^{95} +(8.76527 + 5.06063i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4}+O(q^{10}) $ 10 * q + 4 * q^4	$ 10 q + 4 q^{4} + 15 q^{10} - 6 q^{13} - 6 q^{16} - 12 q^{17} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 14 q^{25} + 3 q^{26} + 15 q^{29} + 9 q^{31} - 48 q^{32} - 3 q^{34} + 6 q^{37} + 36 q^{38} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} + 15 q^{47} - 3 q^{50} + 9 q^{53} - 16 q^{58} - 18 q^{59} - 12 q^{61} + 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} - 54 q^{68} - 3 q^{73} - 9 q^{76} + 20 q^{79} - 30 q^{80} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 16 q^{88} + 24 q^{89} - 39 q^{92} + 3 q^{94} - 6 q^{97}+O(q^{100}) $ 10 * q + 4 * q^4 + 15 * q^10 - 6 * q^13 - 6 * q^16 - 12 * q^17 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 14 * q^25 + 3 * q^26 + 15 * q^29 + 9 * q^31 - 48 * q^32 - 3 * q^34 + 6 * q^37 + 36 * q^38 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 + 15 * q^47 - 3 * q^50 + 9 * q^53 - 16 * q^58 - 18 * q^59 - 12 * q^61 + 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 - 54 * q^68 - 3 * q^73 - 9 * q^76 + 20 * q^79 - 30 * q^80 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 16 * q^88 + 24 * q^89 - 39 * q^92 + 3 * q^94 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.24607	−	1.29677i	1.58821	−	0.916955i	0.594611	−	0.804014i	$-0.297306\pi$
$2$	2.24607	−	1.29677i	1.58821	−	0.916955i	0.993602	−	0.112941i	$-0.0360271\pi$
$3$		0			0
$3$		0			0
$4$	2.36322	−	4.09323i	1.18161	−	2.04661i
$5$	1.25299			0.560352			0.280176	−	0.959949i	$-0.409607\pi$
$5$	1.25299			0.560352			0.280176	+	0.959949i	$0.409607\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	7.07116i		−	2.50003i
$9$		0			0
$10$	2.81429	−	1.62483i	0.889958	−	0.513817i
$11$			0.616756i			0.185959i	0.995668	+	0.0929794i	$0.0296391\pi$
$11$			0.616756i			0.185959i	−0.995668	+	0.0929794i	$0.970361\pi$
$12$		0			0
$13$	1.06343	−	0.613974i	0.294944	−	0.170286i	−0.345226	−	0.938520i	$-0.612198\pi$
$13$	1.06343	−	0.613974i	0.294944	−	0.170286i	0.640169	+	0.768234i	$0.278864\pi$
$14$		0			0
$15$		0			0
$16$	−4.44321	−	7.69587i	−1.11080	−	1.92397i
$17$	−2.21501	−	3.83652i	−0.537220	−	0.930492i	−0.999052	−	0.0435249i	$-0.986141\pi$
$17$	−2.21501	−	3.83652i	−0.537220	−	0.930492i	0.461833	−	0.886967i	$-0.347192\pi$
$18$		0			0
$19$	1.64679	+	0.950775i	0.377800	+	0.218123i	0.676861	−	0.736111i	$-0.263340\pi$
$19$	1.64679	+	0.950775i	0.377800	+	0.218123i	−0.299061	+	0.954234i	$0.596673\pi$
$20$	2.96109	−	5.12875i	0.662119	−	1.14682i
$21$		0			0
$22$	0.799790	+	1.38528i	0.170516	+	0.295342i
$23$		−	4.74890i		−	0.990213i	−0.868832	−	0.495107i	$-0.835129\pi$
$23$		−	4.74890i		−	0.990213i	0.868832	−	0.495107i	$-0.164871\pi$
$24$		0			0
$25$	−3.43003			−0.686006
$26$	1.59237	−	2.75806i	0.312289	−	0.540900i
$27$		0			0
$28$		0			0
$29$	5.07629	+	2.93080i	0.942643	+	0.544235i	0.890788	−	0.454419i	$-0.150153\pi$
$29$	5.07629	+	2.93080i	0.942643	+	0.544235i	0.0518553	+	0.998655i	$0.483487\pi$
$30$		0			0
$31$	2.14851	+	1.24044i	0.385884	+	0.222790i	0.680375	−	0.732864i	$-0.261817\pi$
$31$	2.14851	+	1.24044i	0.385884	+	0.222790i	−0.294491	+	0.955654i	$0.595150\pi$
$32$	−7.71195	−	4.45249i	−1.36329	−	0.787097i
$33$		0			0
$34$	−9.95016	−	5.74473i	−1.70644	−	0.985213i
$35$		0			0
$36$		0			0
$37$	1.33217	−	2.30738i	0.219007	−	0.379331i	−0.735498	−	0.677527i	$-0.763052\pi$
$37$	1.33217	−	2.30738i	0.219007	−	0.379331i	0.954505	+	0.298196i	$0.0963849\pi$
$38$	4.93175			0.800035
$39$		0			0
$40$		−	8.86005i		−	1.40090i
$41$	2.09966	+	3.63671i	0.327911	+	0.567959i	0.982097	−	0.188375i	$-0.0603220\pi$
$41$	2.09966	+	3.63671i	0.327911	+	0.567959i	−0.654186	+	0.756334i	$0.726989\pi$
$42$		0			0
$43$	−2.24637	+	3.89083i	−0.342568	+	0.593346i	−0.984909	−	0.173073i	$-0.944630\pi$
$43$	−2.24637	+	3.89083i	−0.342568	+	0.593346i	0.642340	+	0.766419i	$0.277964\pi$
$44$	2.52452	+	1.45753i	0.380586	+	0.219731i
$45$		0			0
$46$	−6.15823	−	10.6664i	−0.907981	−	1.57267i
$47$	3.80738	+	6.59458i	0.555364	+	0.961918i	0.997875	+	0.0651551i	$0.0207542\pi$
$47$	3.80738	+	6.59458i	0.555364	+	0.961918i	−0.442512	+	0.896763i	$0.645912\pi$
$48$		0			0
$49$		0			0
$50$	−7.70409	+	4.44796i	−1.08952	+	0.629036i
$51$		0			0
$52$		−	5.80384i		−	0.804847i
$53$	−2.67782	+	1.54604i	−0.367827	+	0.212365i	−0.672509	−	0.740089i	$-0.734783\pi$
$53$	−2.67782	+	1.54604i	−0.367827	+	0.212365i	0.304682	+	0.952454i	$0.401450\pi$
$54$		0			0
$55$			0.772786i			0.104202i
$56$		0			0
$57$		0			0
$58$	15.2023			1.99616
$59$	1.78229	−	3.08702i	0.232035	−	0.401896i	−0.726372	−	0.687302i	$-0.758795\pi$
$59$	1.78229	−	3.08702i	0.232035	−	0.401896i	0.958407	+	0.285406i	$0.0921283\pi$
$60$		0			0
$61$	−12.5136	+	7.22473i	−1.60220	+	0.925032i	−0.611156	+	0.791510i	$0.709295\pi$
$61$	−12.5136	+	7.22473i	−1.60220	+	0.925032i	−0.991046	+	0.133521i	$0.957372\pi$
$62$	6.43428			0.817154
$63$		0			0
$64$	−5.32259			−0.665324
$65$	1.33247	−	0.769301i	0.165272	−	0.0954200i
$66$		0			0
$67$	−6.80644	+	11.7891i	−0.831539	+	1.44027i	0.0652791	+	0.997867i	$0.479206\pi$
$67$	−6.80644	+	11.7891i	−0.831539	+	1.44027i	−0.896818	+	0.442400i	$0.854127\pi$
$68$	−20.9383			−2.53914
$69$		0			0
$70$		0			0
$71$		−	10.4095i		−	1.23538i	−0.786420	−	0.617692i	$-0.788068\pi$
$71$		−	10.4095i		−	1.23538i	0.786420	−	0.617692i	$-0.211932\pi$
$72$		0			0
$73$	−9.95016	+	5.74473i	−1.16458	+	0.672369i	−0.952397	−	0.304861i	$-0.901390\pi$
$73$	−9.95016	+	5.74473i	−1.16458	+	0.672369i	−0.212181	+	0.977230i	$0.568057\pi$
$74$		−	6.91006i		−	0.803278i
$75$		0			0
$76$	7.78348	−	4.49379i	0.892826	−	0.515473i
$77$		0			0
$78$		0			0
$79$	2.01592	+	3.49168i	0.226809	+	0.392845i	0.956861	−	0.290547i	$-0.0938373\pi$
$79$	2.01592	+	3.49168i	0.226809	+	0.392845i	−0.730052	+	0.683392i	$0.760504\pi$
$80$	−5.56728	−	9.64281i	−0.622441	−	1.07810i
$81$		0			0
$82$	9.43196	+	5.44554i	1.04159	+	0.601360i
$83$	4.36775	−	7.56516i	0.479422	−	0.830384i	−0.520299	−	0.853984i	$-0.674180\pi$
$83$	4.36775	−	7.56516i	0.479422	−	0.830384i	0.999721	+	0.0236001i	$0.00751285\pi$
$84$		0			0
$85$	−2.77538	−	4.80710i	−0.301032	−	0.521403i
$86$			11.6521i			1.25648i
$87$		0			0
$88$	4.36118			0.464903
$89$	−0.811226	+	1.40508i	−0.0859897	+	0.148939i	−0.905813	−	0.423679i	$-0.860739\pi$
$89$	−0.811226	+	1.40508i	−0.0859897	+	0.148939i	0.819823	+	0.572617i	$0.194072\pi$
$90$		0			0
$91$		0			0
$92$	−19.4383	−	11.2227i	−2.02658	−	1.17005i
$93$		0			0
$94$	17.1033	+	9.87459i	1.76407	+	1.01849i
$95$	2.06341	+	1.19131i	0.211701	+	0.122226i
$96$		0			0
$97$	8.76527	+	5.06063i	0.889979	+	0.513829i	0.873936	−	0.486042i	$-0.161560\pi$
$97$	8.76527	+	5.06063i	0.889979	+	0.513829i	0.0160431	+	0.999871i	$0.494893\pi$
$98$		0			0
$99$		0			0
$100$	−8.10593	+	14.0399i	−0.810593	+	1.40399i
$101$	−1.71322			−0.170472			−0.0852360	−	0.996361i	$-0.527164\pi$
$101$	−1.71322			−0.170472			−0.0852360	+	0.996361i	$0.527164\pi$
$102$		0			0
$103$			7.40526i			0.729662i	0.931074	+	0.364831i	$0.118873\pi$
$103$			7.40526i			0.729662i	−0.931074	+	0.364831i	$0.881127\pi$
$104$	−4.34151	−	7.51971i	−0.425720	−	0.737368i
$105$		0			0
$106$	−4.00972	+	6.94503i	−0.389458	+	0.674561i
$107$	0.131657	+	0.0760123i	0.0127278	+	0.00734839i	0.506350	−	0.862328i	$-0.330994\pi$
$107$	0.131657	+	0.0760123i	0.0127278	+	0.00734839i	−0.493623	+	0.869676i	$0.664328\pi$
$108$		0			0
$109$	2.70051	+	4.67742i	0.258662	+	0.448016i	0.965884	−	0.258976i	$-0.0833851\pi$
$109$	2.70051	+	4.67742i	0.258662	+	0.448016i	−0.707222	+	0.706992i	$0.750052\pi$
$110$	1.00213	+	1.73573i	0.0955489	+	0.165496i
$111$		0			0
$112$		0			0
$113$	5.60391	−	3.23542i	0.527171	−	0.304362i	−0.212693	−	0.977119i	$-0.568223\pi$
$113$	5.60391	−	3.23542i	0.527171	−	0.304362i	0.739864	+	0.672757i	$0.234890\pi$
$114$		0			0
$115$		−	5.95030i		−	0.554868i
$116$	23.9928	−	13.8523i	2.22768	−	1.28615i
$117$		0			0
$118$		−	9.24490i		−	0.851062i
$119$		0			0
$120$		0			0
$121$	10.6196			0.965419
$122$	−18.7376	+	32.4545i	−1.69642	+	2.93829i
$123$		0			0
$124$	10.1548	−	5.86289i	0.911930	−	0.526503i
$125$	−10.5627			−0.944757
$126$		0			0
$127$	−2.93175			−0.260151			−0.130075	−	0.991504i	$-0.541522\pi$
$127$	−2.93175			−0.260151			−0.130075	+	0.991504i	$0.541522\pi$
$128$	3.46897	−	2.00281i	0.306617	−	0.177025i
$129$		0			0
$130$	1.99521	−	3.45581i	0.174992	−	0.303094i
$131$	16.2276			1.41782			0.708908	−	0.705301i	$-0.249188\pi$
$131$	16.2276			1.41782			0.708908	+	0.705301i	$0.249188\pi$
$132$		0			0
$133$		0			0
$134$			35.3055i			3.04993i
$135$		0			0
$136$	−27.1286	+	15.6627i	−2.32626	+	1.34307i
$137$			17.4026i			1.48680i	0.668845	+	0.743402i	$0.266789\pi$
$137$			17.4026i			1.48680i	−0.668845	+	0.743402i	$0.733211\pi$
$138$		0			0
$139$	−5.45273	+	3.14813i	−0.462494	+	0.267021i	−0.713092	−	0.701070i	$-0.752706\pi$
$139$	−5.45273	+	3.14813i	−0.462494	+	0.267021i	0.250598	+	0.968091i	$0.419373\pi$
$140$		0			0
$141$		0			0
$142$	−13.4988	−	23.3805i	−1.13279	−	1.96205i
$143$	0.378672	+	0.655879i	0.0316661	+	0.0548474i
$144$		0			0
$145$	6.36052	+	3.67225i	0.528212	+	0.304963i
$146$	−14.8992	+	25.8061i	−1.23306	+	2.13573i
$147$		0			0
$148$	−6.29642	−	10.9057i	−0.517563	−	0.896445i
$149$		−	10.6269i		−	0.870592i	−0.900287	−	0.435296i	$-0.856644\pi$
$149$		−	10.6269i		−	0.870592i	0.900287	−	0.435296i	$-0.143356\pi$
$150$		0			0
$151$	9.48930			0.772229			0.386114	−	0.922451i	$-0.373817\pi$
$151$	9.48930			0.772229			0.386114	+	0.922451i	$0.373817\pi$
$152$	6.72308	−	11.6447i	0.545314	−	0.944511i
$153$		0			0
$154$		0			0
$155$	2.69205	+	1.55426i	0.216231	+	0.124841i
$156$		0			0
$157$	−20.6214	−	11.9058i	−1.64577	−	0.950185i	−0.978728	−	0.205163i	$-0.934228\pi$
$157$	−20.6214	−	11.9058i	−1.64577	−	0.950185i	−0.667040	−	0.745022i	$-0.732439\pi$
$158$	9.05582	+	5.22838i	0.720442	+	0.415947i
$159$		0			0
$160$	−9.66295	−	5.57891i	−0.763924	−	0.441051i
$161$		0			0
$162$		0			0
$163$	−4.41101	+	7.64009i	−0.345497	+	0.598418i	−0.985444	−	0.170001i	$-0.945623\pi$
$163$	−4.41101	+	7.64009i	−0.345497	+	0.598418i	0.639947	+	0.768419i	$0.278956\pi$
$164$	19.8478			1.54986
$165$		0			0
$166$		−	22.6558i		−	1.75843i
$167$	−11.0335	−	19.1106i	−0.853800	−	1.47883i	−0.877754	−	0.479112i	$-0.840959\pi$
$167$	−11.0335	−	19.1106i	−0.853800	−	1.47883i	0.0239535	−	0.999713i	$-0.492375\pi$
$168$		0			0
$169$	−5.74607	+	9.95249i	−0.442005	+	0.765576i
$170$	−12.4674	−	7.19806i	−0.956206	−	0.552066i
$171$		0			0
$172$	10.6174	+	18.3898i	0.809566	+	1.40221i
$173$	2.03375	+	3.52256i	0.154623	+	0.267815i	0.932922	−	0.360079i	$-0.117250\pi$
$173$	2.03375	+	3.52256i	0.154623	+	0.267815i	−0.778299	+	0.627894i	$0.783917\pi$
$174$		0			0
$175$		0			0
$176$	4.74647	−	2.74038i	0.357779	−	0.206564i
$177$		0			0
$178$			4.20789i			0.315395i
$179$	−7.20787	+	4.16146i	−0.538741	+	0.311042i	−0.744569	−	0.667546i	$-0.767345\pi$
$179$	−7.20787	+	4.16146i	−0.538741	+	0.311042i	0.205827	+	0.978588i	$0.434011\pi$
$180$		0			0
$181$		−	12.6701i		−	0.941763i	−0.882196	−	0.470881i	$-0.843936\pi$
$181$		−	12.6701i		−	0.941763i	0.882196	−	0.470881i	$-0.156064\pi$
$182$		0			0
$183$		0			0
$184$	−33.5802			−2.47556
$185$	1.66919	−	2.89111i	0.122721	−	0.212559i
$186$		0			0
$187$	2.36619	−	1.36612i	0.173033	−	0.0999008i
$188$	35.9908			2.62490
$189$		0			0
$190$	6.17941			0.448301
$191$	3.29133	−	1.90025i	0.238152	−	0.137497i	−0.376175	−	0.926549i	$-0.622761\pi$
$191$	3.29133	−	1.90025i	0.238152	−	0.137497i	0.614327	+	0.789051i	$0.289427\pi$
$192$		0			0
$193$	−3.39448	+	5.87942i	−0.244340	+	0.423210i	−0.961946	−	0.273240i	$-0.911905\pi$
$193$	−3.39448	+	5.87942i	−0.244340	+	0.423210i	0.717606	+	0.696450i	$0.245238\pi$
$194$	26.2499			1.88463
$195$		0			0
$196$		0			0
$197$			6.41453i			0.457017i	0.973542	+	0.228508i	$0.0733848\pi$
$197$			6.41453i			0.457017i	−0.973542	+	0.228508i	$0.926615\pi$
$198$		0			0
$199$	13.8921	−	8.02063i	0.984788	−	0.568568i	0.0810756	−	0.996708i	$-0.474164\pi$
$199$	13.8921	−	8.02063i	0.984788	−	0.568568i	0.903712	+	0.428140i	$0.140831\pi$
$200$			24.2543i			1.71504i
$201$		0			0
$202$	−3.84802	+	2.22166i	−0.270746	+	0.156315i
$203$		0			0
$204$		0			0
$205$	2.63084	+	4.55675i	0.183746	+	0.318257i
$206$	9.60292	+	16.6327i	0.669067	+	1.15886i
$207$		0			0
$208$	−9.45013	−	5.45604i	−0.655249	−	0.378308i
$209$	−0.586396	+	1.01567i	−0.0405619	+	0.0702552i
$210$		0			0
$211$	−4.06070	−	7.03333i	−0.279550	−	0.484194i	0.691723	−	0.722163i	$-0.256852\pi$
$211$	−4.06070	−	7.03333i	−0.279550	−	0.484194i	−0.971273	+	0.237968i	$0.923519\pi$
$212$			14.6146i			1.00373i
$213$		0			0
$214$	0.394282			0.0269526
$215$	−2.81467	+	4.87515i	−0.191959	+	0.332483i
$216$		0			0
$217$		0			0
$218$	12.1311	+	7.00388i	0.821620	+	0.474363i
$219$		0			0
$220$	3.16319	+	1.82627i	0.213262	+	0.123127i
$221$	−4.71104	−	2.71992i	−0.316899	−	0.182962i
$222$		0			0
$223$	6.96205	+	4.01954i	0.466213	+	0.269168i	0.714653	−	0.699479i	$-0.246585\pi$
$223$	6.96205	+	4.01954i	0.466213	+	0.269168i	−0.248440	+	0.968647i	$0.579918\pi$
$224$		0			0
$225$		0			0
$226$	8.39118	−	14.5340i	0.558173	−	0.966784i
$227$	−20.8234			−1.38210			−0.691048	−	0.722809i	$-0.742851\pi$
$227$	−20.8234			−1.38210			−0.691048	+	0.722809i	$0.742851\pi$
$228$		0			0
$229$		−	6.01918i		−	0.397759i	−0.980024	−	0.198879i	$-0.936270\pi$
$229$		−	6.01918i		−	0.397759i	0.980024	−	0.198879i	$-0.0637302\pi$
$230$	−7.71617	−	13.3648i	−0.508789	−	0.881248i
$231$		0			0
$232$	20.7241	−	35.8952i	1.36061	−	2.35664i
$233$	18.2156	+	10.5168i	1.19335	+	0.688978i	0.959064	−	0.283191i	$-0.0913929\pi$
$233$	18.2156	+	10.5168i	1.19335	+	0.688978i	0.234282	+	0.972169i	$0.424726\pi$
$234$		0			0
$235$	4.77059	+	8.26291i	0.311199	+	0.539013i
$236$	−8.42392	−	14.5907i	−0.548350	−	0.949771i
$237$		0			0
$238$		0			0
$239$	7.51079	−	4.33636i	0.485832	−	0.280496i	−0.237011	−	0.971507i	$-0.576168\pi$
$239$	7.51079	−	4.33636i	0.485832	−	0.280496i	0.722844	+	0.691011i	$0.242835\pi$
$240$		0			0
$241$			8.47315i			0.545804i	0.962042	+	0.272902i	$0.0879834\pi$
$241$			8.47315i			0.545804i	−0.962042	+	0.272902i	$0.912017\pi$
$242$	23.8524	−	13.7712i	1.53329	−	0.885246i
$243$		0			0
$244$			68.2946i			4.37211i
$245$		0			0
$246$		0			0
$247$	2.33501			0.148573
$248$	8.77137	−	15.1925i	0.556982	−	0.964722i
$249$		0			0
$250$	−23.7246	+	13.6974i	−1.50047	+	0.866299i
$251$	23.4435			1.47974			0.739871	−	0.672749i	$-0.234887\pi$
$251$	23.4435			1.47974			0.739871	+	0.672749i	$0.234887\pi$
$252$		0			0
$253$	2.92891			0.184139
$254$	−6.58492	+	3.80180i	−0.413174	+	0.238546i
$255$		0			0
$256$	10.5170	−	18.2159i	0.657310	−	1.13849i
$257$	−24.5170			−1.52933			−0.764665	−	0.644428i	$-0.777096\pi$
$257$	−24.5170			−1.52933			−0.764665	+	0.644428i	$0.777096\pi$
$258$		0			0
$259$		0			0
$260$		−	7.27212i		−	0.450998i
$261$		0			0
$262$	36.4484	−	21.0435i	2.25179	−	1.30007i
$263$		−	10.5544i		−	0.650811i	−0.945575	−	0.325406i	$-0.894499\pi$
$263$		−	10.5544i		−	0.650811i	0.945575	−	0.325406i	$-0.105501\pi$
$264$		0			0
$265$	−3.35527	+	1.93716i	−0.206112	+	0.118999i
$266$		0			0
$267$		0			0
$268$	32.1703	+	55.7206i	1.96511	+	3.40367i
$269$	1.14451	+	1.98235i	0.0697821	+	0.120866i	0.898805	−	0.438348i	$-0.144436\pi$
$269$	1.14451	+	1.98235i	0.0697821	+	0.120866i	−0.829023	+	0.559214i	$0.811103\pi$
$270$		0			0
$271$	20.9239	+	12.0804i	1.27103	+	0.733831i	0.975182	−	0.221403i	$-0.0710635\pi$
$271$	20.9239	+	12.0804i	1.27103	+	0.733831i	0.295851	+	0.955234i	$0.404397\pi$
$272$	−19.6836	+	34.0929i	−1.19349	+	2.06719i
$273$		0			0
$274$	22.5672	+	39.0875i	1.36333	+	2.36136i
$275$		−	2.11549i		−	0.127569i
$276$		0			0
$277$	−11.3710			−0.683219			−0.341609	−	0.939842i	$-0.610972\pi$
$277$	−11.3710			−0.683219			−0.341609	+	0.939842i	$0.610972\pi$
$278$	−8.16481	+	14.1419i	−0.489693	+	0.848173i
$279$		0			0
$280$		0			0
$281$	−17.6382	−	10.1834i	−1.05221	−	0.607492i	−0.128941	−	0.991652i	$-0.541158\pi$
$281$	−17.6382	−	10.1834i	−1.05221	−	0.607492i	−0.923267	+	0.384160i	$0.874491\pi$
$282$		0			0
$283$	−10.5318	−	6.08055i	−0.626052	−	0.361451i	0.153169	−	0.988200i	$-0.451052\pi$
$283$	−10.5318	−	6.08055i	−0.626052	−	0.361451i	−0.779222	+	0.626749i	$0.784385\pi$
$284$	−42.6085	−	24.6000i	−2.52835	−	1.45974i
$285$		0			0
$286$	1.70105	+	0.982101i	0.100585	+	0.0580729i
$287$		0			0
$288$		0			0
$289$	−1.31257	+	2.27345i	−0.0772103	+	0.133732i
$290$	19.0482			1.11855
$291$		0			0
$292$			54.3043i			3.17792i
$293$	13.4674	+	23.3262i	0.786773	+	1.36273i	0.927934	+	0.372745i	$0.121583\pi$
$293$	13.4674	+	23.3262i	0.786773	+	1.36273i	−0.141161	+	0.989987i	$0.545083\pi$
$294$		0			0
$295$	2.23319	−	3.86799i	0.130021	−	0.225203i
$296$	−16.3159	−	9.41996i	−0.948340	−	0.547524i
$297$		0			0
$298$	−13.7807	−	23.8688i	−0.798293	−	1.38268i
$299$	−2.91570	−	5.05014i	−0.168619	−	0.292057i
$300$		0			0
$301$		0			0
$302$	21.3137	−	12.3054i	1.22646	−	0.708099i
$303$		0			0
$304$		−	16.8980i		−	0.969166i
$305$	−15.6793	+	9.05248i	−0.897797	+	0.518343i
$306$		0			0
$307$		−	21.3700i		−	1.21965i	−0.792536	−	0.609825i	$-0.791240\pi$
$307$		−	21.3700i		−	1.21965i	0.792536	−	0.609825i	$-0.208760\pi$
$308$		0			0
$309$		0			0
$310$	8.06206			0.457894
$311$	8.11558	−	14.0566i	0.460192	−	0.797076i	−0.538778	−	0.842448i	$-0.681114\pi$
$311$	8.11558	−	14.0566i	0.460192	−	0.797076i	0.998970	+	0.0453714i	$0.0144471\pi$
$312$		0			0
$313$	−12.1941	+	7.04027i	−0.689252	+	0.397940i	−0.803332	−	0.595532i	$-0.796941\pi$
$313$	−12.1941	+	7.04027i	−0.689252	+	0.397940i	0.114080	+	0.993472i	$0.463608\pi$
$314$	−61.7562			−3.48511
$315$		0			0
$316$	19.0563			1.07200
$317$	−17.5776	+	10.1484i	−0.987254	+	0.569991i	−0.904452	−	0.426575i	$-0.859720\pi$
$317$	−17.5776	+	10.1484i	−0.987254	+	0.569991i	−0.0828017	+	0.996566i	$0.526387\pi$
$318$		0			0
$319$	−1.80759	+	3.13083i	−0.101205	+	0.175293i
$320$	−6.66913			−0.372816
$321$		0			0
$322$		0			0
$323$		−	8.42392i		−	0.468720i
$324$		0			0
$325$	−3.64761	+	2.10595i	−0.202333	+	0.116817i
$326$			22.8802i			1.26722i
$327$		0			0
$328$	25.7158	−	14.8470i	1.41991	−	0.819788i
$329$		0			0
$330$		0			0
$331$	−13.2341	−	22.9221i	−0.727411	−	1.25991i	−0.957974	−	0.286856i	$-0.907390\pi$
$331$	−13.2341	−	22.9221i	−0.727411	−	1.25991i	0.230563	−	0.973057i	$-0.425943\pi$
$332$	−20.6439	−	35.7563i	−1.13298	−	1.96238i
$333$		0			0
$334$	−49.5642	−	28.6159i	−2.71203	−	1.56579i
$335$	−8.52836	+	14.7716i	−0.465954	+	0.807057i
$336$		0			0
$337$	−1.73659	−	3.00785i	−0.0945979	−	0.163848i	0.814843	−	0.579682i	$-0.196823\pi$
$337$	−1.73659	−	3.00785i	−0.0945979	−	0.163848i	−0.909441	+	0.415834i	$0.863490\pi$
$338$			29.8053i			1.62120i
$339$		0			0
$340$	−26.2354			−1.42281
$341$	−0.765051	+	1.32511i	−0.0414298	+	0.0717585i
$342$		0			0
$343$		0			0
$344$	27.5127	+	15.8844i	1.48338	+	0.856432i
$345$		0			0
$346$	9.13589	+	5.27461i	0.491149	+	0.283565i
$347$	−8.14765	−	4.70405i	−0.437389	−	0.252527i	0.265101	−	0.964221i	$-0.414595\pi$
$347$	−8.14765	−	4.70405i	−0.437389	−	0.252527i	−0.702489	+	0.711694i	$0.747928\pi$
$348$		0			0
$349$	12.3253	+	7.11603i	0.659759	+	0.380912i	0.792185	−	0.610281i	$-0.208943\pi$
$349$	12.3253	+	7.11603i	0.659759	+	0.380912i	−0.132426	+	0.991193i	$0.542277\pi$
$350$		0			0
$351$		0			0
$352$	2.74610	−	4.75639i	0.146368	−	0.253516i
$353$	17.1652			0.913614			0.456807	−	0.889566i	$-0.348993\pi$
$353$	17.1652			0.913614			0.456807	+	0.889566i	$0.348993\pi$
$354$		0			0
$355$		−	13.0430i		−	0.692250i
$356$	3.83422	+	6.64106i	0.203213	+	0.351975i
$357$		0			0
$358$	−10.7929	+	18.6939i	−0.570424	+	0.988003i
$359$	−24.4705	−	14.1281i	−1.29150	−	0.745650i	−0.312583	−	0.949890i	$-0.601194\pi$
$359$	−24.4705	−	14.1281i	−1.29150	−	0.745650i	−0.978921	+	0.204241i	$0.934528\pi$
$360$		0			0
$361$	−7.69205	−	13.3230i	−0.404845	−	0.701212i
$362$	−16.4302	−	28.4580i	−0.863554	−	1.49572i
$363$		0			0
$364$		0			0
$365$	−12.4674	+	7.19806i	−0.652574	+	0.376764i
$366$		0			0
$367$			23.0704i			1.20427i	0.798396	+	0.602133i	$0.205682\pi$
$367$			23.0704i			1.20427i	−0.798396	+	0.602133i	$0.794318\pi$
$368$	−36.5469	+	21.1004i	−1.90514	+	1.09993i
$369$		0			0
$370$		−	8.65820i		−	0.450118i
$371$		0			0
$372$		0			0
$373$	−13.8727			−0.718301			−0.359150	−	0.933280i	$-0.616933\pi$
$373$	−13.8727			−0.718301			−0.359150	+	0.933280i	$0.616933\pi$
$374$	3.54309	−	6.13682i	0.183209	−	0.317327i
$375$		0			0
$376$	46.6313	−	26.9226i	2.40482	−	1.38843i
$377$	7.19773			0.370702
$378$		0			0
$379$	22.7814			1.17020			0.585101	−	0.810961i	$-0.301055\pi$
$379$	22.7814			1.17020			0.585101	+	0.810961i	$0.301055\pi$
$380$	9.75258	−	5.63065i	0.500297	−	0.288846i
$381$		0			0
$382$	4.92838	−	8.53620i	0.252158	−	0.436750i
$383$	−15.2320			−0.778317			−0.389158	−	0.921171i	$-0.627234\pi$
$383$	−15.2320			−0.778317			−0.389158	+	0.921171i	$0.627234\pi$
$384$		0			0
$385$		0			0
$386$			17.6075i			0.896196i
$387$		0			0
$388$	41.4286	−	23.9188i	2.10322	−	1.21429i
$389$		−	14.1479i		−	0.717328i	−0.933467	−	0.358664i	$-0.883232\pi$
$389$		−	14.1479i		−	0.717328i	0.933467	−	0.358664i	$-0.116768\pi$
$390$		0			0
$391$	−18.2192	+	10.5189i	−0.921386	+	0.531962i
$392$		0			0
$393$		0			0
$394$	8.31817	+	14.4075i	0.419063	+	0.725839i
$395$	2.52592	+	4.37503i	0.127093	+	0.220131i
$396$		0			0
$397$	−8.40688	−	4.85371i	−0.421929	−	0.243601i	0.273973	−	0.961737i	$-0.411662\pi$
$397$	−8.40688	−	4.85371i	−0.421929	−	0.243601i	−0.695902	+	0.718136i	$0.744995\pi$
$398$	20.8018	−	36.0298i	1.04270	−	1.80601i
$399$		0			0
$400$	15.2403	+	26.3970i	0.762017	+	1.31985i
$401$		−	8.73133i		−	0.436022i	−0.975946	−	0.218011i	$-0.930043\pi$
$401$		−	8.73133i		−	0.436022i	0.975946	−	0.218011i	$-0.0699569\pi$
$402$		0			0
$403$	3.04640			0.151752
$404$	−4.04873	+	7.01261i	−0.201432	+	0.348890i
$405$		0			0
$406$		0			0
$407$	1.42309	+	0.821622i	0.0705400	+	0.0407263i
$408$		0			0
$409$	12.8967	+	7.44591i	0.637700	+	0.368176i	0.783728	−	0.621104i	$-0.213316\pi$
$409$	12.8967	+	7.44591i	0.637700	+	0.368176i	−0.146028	+	0.989280i	$0.546649\pi$
$410$	11.8181	+	6.82318i	0.583654	+	0.336973i
$411$		0			0
$412$	30.3114	+	17.5003i	1.49334	+	0.862178i
$413$		0			0
$414$		0			0
$415$	5.47272	−	9.47903i	0.268645	−	0.465307i
$416$	−10.9349			−0.536126
$417$		0			0
$418$			3.04168i			0.148774i
$419$	−2.13859	−	3.70414i	−0.104477	−	0.180959i	0.809048	−	0.587743i	$-0.199983\pi$
$419$	−2.13859	−	3.70414i	−0.104477	−	0.180959i	−0.913524	+	0.406784i	$0.866650\pi$
$420$		0			0
$421$	5.76681	−	9.98841i	0.281057	−	0.486805i	−0.690588	−	0.723248i	$-0.742648\pi$
$421$	5.76681	−	9.98841i	0.281057	−	0.486805i	0.971645	+	0.236443i	$0.0759816\pi$
$422$	−18.2412	−	10.5316i	−0.887969	−	0.512669i
$423$		0			0
$424$	10.9323	+	18.9353i	0.530919	+	0.919578i
$425$	7.59756	+	13.1594i	0.368536	+	0.638323i
$426$		0			0
$427$		0			0
$428$	0.622271	−	0.359268i	0.0300786	−	0.0173659i
$429$		0			0
$430$			14.5999i			0.704071i
$431$	14.4497	−	8.34254i	0.696018	−	0.401846i	−0.109845	−	0.993949i	$-0.535035\pi$
$431$	14.4497	−	8.34254i	0.696018	−	0.401846i	0.805863	+	0.592103i	$0.201702\pi$
$432$		0			0
$433$		−	12.3503i		−	0.593516i	−0.954953	−	0.296758i	$-0.904094\pi$
$433$		−	12.3503i		−	0.593516i	0.954953	−	0.296758i	$-0.0959055\pi$
$434$		0			0
$435$		0			0
$436$	25.5276			1.22255
$437$	4.51513	−	7.82044i	0.215988	−	0.374102i
$438$		0			0
$439$	19.1691	−	11.0673i	0.914892	−	0.528213i	0.0328902	−	0.999459i	$-0.489529\pi$
$439$	19.1691	−	11.0673i	0.914892	−	0.528213i	0.882002	+	0.471246i	$0.156195\pi$
$440$	5.46449			0.260509
$441$		0			0
$442$	−14.1085			−0.671071
$443$	4.22906	−	2.44165i	0.200929	−	0.116006i	−0.396160	−	0.918182i	$-0.629657\pi$
$443$	4.22906	−	2.44165i	0.200929	−	0.116006i	0.597089	+	0.802175i	$0.296324\pi$
$444$		0			0
$445$	−1.01645	+	1.76055i	−0.0481845	+	0.0834580i
$446$	20.8497			0.987260
$447$		0			0
$448$		0			0
$449$		−	12.4409i		−	0.587121i	−0.955941	−	0.293560i	$-0.905160\pi$
$449$		−	12.4409i		−	0.587121i	0.955941	−	0.293560i	$-0.0948401\pi$
$450$		0			0
$451$	−2.24296	+	1.29498i	−0.105617	+	0.0609780i
$452$		−	30.5841i		−	1.43855i
$453$		0			0
$454$	−46.7708	+	27.0031i	−2.19506	+	1.26732i
$455$		0			0
$456$		0			0
$457$	5.38774	+	9.33185i	0.252028	+	0.436525i	0.964084	−	0.265597i	$-0.0855691\pi$
$457$	5.38774	+	9.33185i	0.252028	+	0.436525i	−0.712056	+	0.702123i	$0.752236\pi$
$458$	−7.80549	−	13.5195i	−0.364727	−	0.631725i
$459$		0			0
$460$	−24.3559	−	14.0619i	−1.13560	−	0.655639i
$461$	−0.333303	+	0.577297i	−0.0155235	+	0.0268874i	−0.873683	−	0.486496i	$-0.838275\pi$
$461$	−0.333303	+	0.577297i	−0.0155235	+	0.0268874i	0.858159	+	0.513383i	$0.171608\pi$
$462$		0			0
$463$	−20.7892	−	36.0079i	−0.966155	−	1.67343i	−0.706479	−	0.707734i	$-0.749717\pi$
$463$	−20.7892	−	36.0079i	−0.966155	−	1.67343i	−0.259677	−	0.965696i	$-0.583616\pi$
$464$		−	52.0886i		−	2.41815i
$465$		0			0
$466$	54.5515			2.52705
$467$	19.6568	−	34.0465i	0.909606	−	1.57548i	0.0949943	−	0.995478i	$-0.469717\pi$
$467$	19.6568	−	34.0465i	0.909606	−	1.57548i	0.814612	−	0.580006i	$-0.196950\pi$
$468$		0			0
$469$		0			0
$470$	21.4302	+	12.3727i	0.988500	+	0.570711i
$471$		0			0
$472$	−21.8288	−	12.6029i	−1.00475	−	0.580094i
$473$	−2.39969	−	1.38546i	−0.110338	−	0.0637036i
$474$		0			0
$475$	−5.64854	−	3.26119i	−0.259173	−	0.149633i
$476$		0			0
$477$		0			0
$478$	11.2465	−	19.4795i	0.514403	−	0.890973i
$479$	−38.1153			−1.74153			−0.870767	−	0.491696i	$-0.836377\pi$
$479$	−38.1153			−1.74153			−0.870767	+	0.491696i	$0.836377\pi$
$480$		0			0
$481$		−	3.27167i		−	0.149175i
$482$	10.9877	+	19.0313i	0.500477	+	0.866852i
$483$		0			0
$484$	25.0965	−	43.4685i	1.14075	−	1.97584i
$485$	10.9828	+	6.34090i	0.498701	+	0.287925i
$486$		0			0
$487$	−3.80277	−	6.58659i	−0.172320	−	0.298467i	0.766911	−	0.641754i	$-0.221793\pi$
$487$	−3.80277	−	6.58659i	−0.172320	−	0.298467i	−0.939231	+	0.343287i	$0.888460\pi$
$488$	51.0872	+	88.4856i	2.31261	+	4.00555i
$489$		0			0
$490$		0			0
$491$	−3.33297	+	1.92429i	−0.150415	+	0.0868420i	−0.573318	−	0.819333i	$-0.694344\pi$
$491$	−3.33297	+	1.92429i	−0.150415	+	0.0868420i	0.422904	+	0.906175i	$0.361011\pi$
$492$		0			0
$493$		−	25.9670i		−	1.16950i
$494$	5.24459	−	3.02797i	0.235965	−	0.136235i
$495$		0			0
$496$		−	22.0462i		−	0.989904i
$497$		0			0
$498$		0			0
$499$	−32.1588			−1.43962			−0.719812	−	0.694169i	$-0.755772\pi$
$499$	−32.1588			−1.43962			−0.719812	+	0.694169i	$0.755772\pi$
$500$	−24.9620	+	43.2355i	−1.11634	+	1.93355i
$501$		0			0
$502$	52.6558	−	30.4009i	2.35014	−	1.35686i
$503$	−0.425693			−0.0189807			−0.00949035	−	0.999955i	$-0.503021\pi$
$503$	−0.425693			−0.0189807			−0.00949035	+	0.999955i	$0.503021\pi$
$504$		0			0
$505$	−2.14664			−0.0955243
$506$	6.57854	−	3.79812i	0.292452	−	0.168847i
$507$		0			0
$508$	−6.92838	+	12.0003i	−0.307397	+	0.532427i
$509$	−25.7926			−1.14323			−0.571617	−	0.820520i	$-0.693684\pi$
$509$	−25.7926			−1.14323			−0.571617	+	0.820520i	$0.693684\pi$
$510$		0			0
$511$		0			0
$512$		−	46.5411i		−	2.05684i
$513$		0			0
$514$	−55.0670	+	31.7929i	−2.42890	+	1.40233i
$515$			9.27868i			0.408868i
$516$		0			0
$517$	−4.06724	+	2.34822i	−0.178877	+	0.103275i
$518$		0			0
$519$		0			0
$520$	−5.43984	−	9.42209i	−0.238553	−	0.413186i
$521$	−9.07174	−	15.7127i	−0.397440	−	0.688386i	0.595969	−	0.803007i	$-0.296768\pi$
$521$	−9.07174	−	15.7127i	−0.397440	−	0.688386i	−0.993409	+	0.114621i	$0.963435\pi$
$522$		0			0
$523$	−12.0723	−	6.96997i	−0.527887	−	0.304776i	0.212269	−	0.977211i	$-0.431915\pi$
$523$	−12.0723	−	6.96997i	−0.527887	−	0.304776i	−0.740155	+	0.672436i	$0.765248\pi$
$524$	38.3495	−	66.4234i	1.67531	−	2.90172i
$525$		0			0
$526$	−13.6866	−	23.7059i	−0.596764	−	1.03363i
$527$		−	10.9904i		−	0.478749i
$528$		0			0
$529$	0.447980			0.0194774
$530$	−5.02411	+	8.70202i	−0.218234	+	0.377992i
$531$		0			0
$532$		0			0
$533$	4.46569	+	2.57827i	0.193431	+	0.111677i
$534$		0			0
$535$	0.164965	+	0.0952423i	0.00713204	+	0.00411769i
$536$	83.3625	+	48.1294i	3.60071	+	2.07887i
$537$		0			0
$538$	5.14131	+	2.96834i	0.221658	+	0.127974i
$539$		0			0
$540$		0			0
$541$	−14.8576	+	25.7341i	−0.638779	+	1.10640i	0.346922	+	0.937894i	$0.387227\pi$
$541$	−14.8576	+	25.7341i	−0.638779	+	1.10640i	−0.985701	+	0.168503i	$0.946107\pi$
$542$	62.6620			2.69156
$543$		0			0
$544$			39.4493i			1.69138i
$545$	3.38370	+	5.86074i	0.144942	+	0.251046i
$546$		0			0
$547$	−9.13516	+	15.8226i	−0.390591	+	0.676524i	−0.992528	−	0.122020i	$-0.961063\pi$
$547$	−9.13516	+	15.8226i	−0.390591	+	0.676524i	0.601937	+	0.798544i	$0.294396\pi$
$548$	71.2327	+	41.1262i	3.04291	+	1.75683i
$549$		0			0
$550$	−2.74330	−	4.75154i	−0.116975	−	0.202606i
$551$	5.57306	+	9.65282i	0.237420	+	0.411224i
$552$		0			0
$553$		0			0
$554$	−25.5401	+	14.7456i	−1.08510	+	0.626481i
$555$		0			0
$556$			29.7590i			1.26206i
$557$	0.359456	−	0.207532i	0.0152307	−	0.00879343i	−0.492365	−	0.870389i	$-0.663868\pi$
$557$	0.359456	−	0.207532i	0.0152307	−	0.00879343i	0.507596	+	0.861595i	$0.330534\pi$
$558$		0			0
$559$			5.51686i			0.233338i
$560$		0			0
$561$		0			0
$562$	−52.8222			−2.22817
$563$	1.82962	−	3.16900i	0.0771095	−	0.133558i	−0.824892	−	0.565290i	$-0.808764\pi$
$563$	1.82962	−	3.16900i	0.0771095	−	0.133558i	0.902002	+	0.431733i	$0.142098\pi$
$564$		0			0
$565$	7.02161	−	4.05393i	0.295401	−	0.170550i
$566$	−31.5403			−1.32574
$567$		0			0
$568$	−73.6074			−3.08850
$569$	−30.4692	+	17.5914i	−1.27733	+	0.737470i	−0.976358	−	0.216162i	$-0.930646\pi$
$569$	−30.4692	+	17.5914i	−1.27733	+	0.737470i	−0.300977	+	0.953631i	$0.597313\pi$
$570$		0			0
$571$	5.02680	−	8.70667i	0.210365	−	0.364363i	−0.741464	−	0.670993i	$-0.765868\pi$
$571$	5.02680	−	8.70667i	0.210365	−	0.364363i	0.951829	+	0.306630i	$0.0992014\pi$
$572$	3.57955			0.149668
$573$		0			0
$574$		0			0
$575$			16.2888i			0.679292i
$576$		0			0
$577$	−0.0597672	+	0.0345066i	−0.00248814	+	0.00143653i	−0.501244	−	0.865306i	$-0.667124\pi$
$577$	−0.0597672	+	0.0345066i	−0.00248814	+	0.00143653i	0.498755	+	0.866743i	$0.333791\pi$
$578$			6.80843i			0.283193i
$579$		0			0
$580$	30.0627	−	17.3567i	1.24828	−	0.720697i
$581$		0			0
$582$		0			0
$583$	−0.953529	−	1.65156i	−0.0394911	−	0.0684006i
$584$	40.6219	+	70.3591i	1.68094	+	2.91148i
$585$		0			0
$586$	60.4974	+	34.9282i	2.49913	+	1.44287i
$587$	−11.4799	+	19.8838i	−0.473827	+	0.820693i	−0.999551	−	0.0299626i	$-0.990461\pi$
$587$	−11.4799	+	19.8838i	−0.473827	+	0.820693i	0.525724	+	0.850655i	$0.323795\pi$
$588$		0			0
$589$	2.35877	+	4.08550i	0.0971913	+	0.168340i
$590$		−	11.5837i		−	0.476894i
$591$		0			0
$592$	−23.6764			−0.973094
$593$	14.3970	−	24.9363i	0.591213	−	1.02401i	−0.402856	−	0.915263i	$-0.631982\pi$
$593$	14.3970	−	24.9363i	0.591213	−	1.02401i	0.994069	−	0.108748i	$-0.0346843\pi$
$594$		0			0
$595$		0			0
$596$	−43.4984	−	25.1138i	−1.78176	−	1.02870i
$597$		0			0
$598$	−13.0977	−	7.56198i	−0.535606	−	0.309233i
$599$	33.1588	+	19.1442i	1.35483	+	0.782212i	0.988922	−	0.148438i	$-0.0474246\pi$
$599$	33.1588	+	19.1442i	1.35483	+	0.782212i	0.365910	+	0.930650i	$0.380758\pi$
$600$		0			0
$601$	−26.7618	−	15.4509i	−1.09164	−	0.630257i	−0.157625	−	0.987499i	$-0.550384\pi$
$601$	−26.7618	−	15.4509i	−1.09164	−	0.630257i	−0.934012	+	0.357242i	$0.883717\pi$
$602$		0			0
$603$		0			0
$604$	22.4254	−	38.8419i	0.912475	−	1.58045i
$605$	13.3062			0.540975
$606$		0			0
$607$		−	33.1791i		−	1.34670i	−0.739325	−	0.673349i	$-0.764855\pi$
$607$		−	33.1791i		−	1.34670i	0.739325	−	0.673349i	$-0.235145\pi$
$608$	−8.46664	−	14.6647i	−0.343368	−	0.594730i
$609$		0			0
$610$	−23.4780	+	40.6650i	−0.950595	+	1.64648i
$611$	8.09780	+	4.67527i	0.327602	+	0.189141i
$612$		0			0
$613$	−2.01164	−	3.48426i	−0.0812492	−	0.140728i	0.822538	−	0.568711i	$-0.192558\pi$
$613$	−2.01164	−	3.48426i	−0.0812492	−	0.140728i	−0.903787	+	0.427983i	$0.859224\pi$
$614$	−27.7120	−	47.9985i	−1.11836	−	1.93706i
$615$		0			0
$616$		0			0
$617$	−27.1191	+	15.6572i	−1.09177	+	0.630336i	−0.934048	−	0.357147i	$-0.883749\pi$
$617$	−27.1191	+	15.6572i	−1.09177	+	0.630336i	−0.157726	+	0.987483i	$0.550416\pi$
$618$		0			0
$619$			13.9310i			0.559934i	0.960010	+	0.279967i	$0.0903235\pi$
$619$			13.9310i			0.559934i	−0.960010	+	0.279967i	$0.909676\pi$
$620$	12.7238	−	7.34612i	0.511002	−	0.295027i
$621$		0			0
$622$		−	42.0962i		−	1.68790i
$623$		0			0
$624$		0			0
$625$	3.91523			0.156609
$626$	−18.2592	+	31.6259i	−0.729786	+	1.26403i
$627$		0			0
$628$	−97.4661	+	56.2721i	−3.88932	+	2.24550i
$629$	−11.8031			−0.470620
$630$		0			0
$631$	−4.61815			−0.183846			−0.0919229	−	0.995766i	$-0.529301\pi$
$631$	−4.61815			−0.183846			−0.0919229	+	0.995766i	$0.529301\pi$
$632$	24.6902	−	14.2549i	0.982124	−	0.567030i
$633$		0			0
$634$	−26.3203	+	45.5881i	−1.04531	+	1.81053i
$635$	−3.67344			−0.145776
$636$		0			0
$637$		0			0
$638$			9.37609i			0.371203i
$639$		0			0
$640$	4.34657	−	2.50949i	0.171813	−	0.0991964i
$641$		−	42.4724i		−	1.67756i	−0.544473	−	0.838779i	$-0.683270\pi$
$641$		−	42.4724i		−	1.67756i	0.544473	−	0.838779i	$-0.316730\pi$
$642$		0			0
$643$	3.13514	−	1.81008i	0.123638	−	0.0713825i	−0.436905	−	0.899507i	$-0.643926\pi$
$643$	3.13514	−	1.81008i	0.123638	−	0.0713825i	0.560544	+	0.828125i	$0.310592\pi$
$644$		0			0
$645$		0			0
$646$	−10.9239	−	18.9207i	−0.429795	−	0.744426i
$647$	6.00617	+	10.4030i	0.236127	+	0.408984i	0.959600	−	0.281369i	$-0.0907886\pi$
$647$	6.00617	+	10.4030i	0.236127	+	0.408984i	−0.723473	+	0.690353i	$0.757455\pi$
$648$		0			0
$649$	1.90394	+	1.09924i	0.0747361	+	0.0431489i
$650$	−5.46186	+	9.46022i	−0.214232	+	0.371060i
$651$		0			0
$652$	20.8484	+	36.1105i	0.816486	+	1.41420i
$653$			46.1822i			1.80725i	0.428324	+	0.903625i	$0.359104\pi$
$653$			46.1822i			1.80725i	−0.428324	+	0.903625i	$0.640896\pi$
$654$		0			0
$655$	20.3330			0.794476
$656$	18.6584	−	32.3174i	0.728490	−	1.26178i
$657$		0			0
$658$		0			0
$659$	16.3479	+	9.43847i	0.636824	+	0.367671i	0.783390	−	0.621530i	$-0.213489\pi$
$659$	16.3479	+	9.43847i	0.636824	+	0.367671i	−0.146566	+	0.989201i	$0.546822\pi$
$660$		0			0
$661$	−2.88202	−	1.66393i	−0.112097	−	0.0647195i	0.442903	−	0.896570i	$-0.353949\pi$
$661$	−2.88202	−	1.66393i	−0.112097	−	0.0647195i	−0.555000	+	0.831850i	$0.687282\pi$
$662$	−59.4494	−	34.3231i	−2.31057	−	1.33401i
$663$		0			0
$664$	−53.4944	−	30.8850i	−2.07599	−	1.19857i
$665$		0			0
$666$		0			0
$667$	13.9181	−	24.1068i	0.538909	−	0.933418i
$668$	−104.299			−4.03544
$669$		0			0
$670$			44.2373i			1.70904i
$671$	−4.45589	−	7.71783i	−0.172018	−	0.297944i
$672$		0			0
$673$	−16.3678	+	28.3499i	−0.630934	+	1.09281i	0.356427	+	0.934323i	$0.383995\pi$
$673$	−16.3678	+	28.3499i	−0.630934	+	1.09281i	−0.987361	+	0.158487i	$0.949339\pi$
$674$	−7.80099	−	4.50390i	−0.300483	−	0.173484i
$675$		0			0
$676$	27.1585	+	47.0399i	1.04456	+	1.80923i
$677$	−16.9228	−	29.3111i	−0.650396	−	1.12652i	−0.983027	−	0.183461i	$-0.941270\pi$
$677$	−16.9228	−	29.3111i	−0.650396	−	1.12652i	0.332631	−	0.943057i	$-0.392063\pi$
$678$		0			0
$679$		0			0
$680$	−33.9917	+	19.6251i	−1.30352	+	0.752590i
$681$		0			0
$682$			3.96838i			0.151957i
$683$	−4.79617	+	2.76907i	−0.183520	+	0.105956i	−0.588946	−	0.808173i	$-0.700457\pi$
$683$	−4.79617	+	2.76907i	−0.183520	+	0.105956i	0.405425	+	0.914128i	$0.367123\pi$
$684$		0			0
$685$			21.8052i			0.833133i
$686$		0			0
$687$		0			0
$688$	39.9244			1.52210
$689$	−1.89846	+	3.28822i	−0.0723254	+	0.125271i
$690$		0			0
$691$	−12.3417	+	7.12550i	−0.469502	+	0.271067i	−0.716031	−	0.698068i	$-0.754043\pi$
$691$	−12.3417	+	7.12550i	−0.469502	+	0.271067i	0.246530	+	0.969135i	$0.420710\pi$
$692$	19.2248			0.730818
$693$		0			0
$694$	−24.4003			−0.926222
$695$	−6.83219	+	3.94456i	−0.259160	+	0.149626i
$696$		0			0
$697$	9.30154	−	16.1107i	0.352321	−	0.610238i
$698$	36.9114			1.39712
$699$		0			0
$700$		0			0
$701$		−	18.6105i		−	0.702908i	−0.936205	−	0.351454i	$-0.885687\pi$
$701$		−	18.6105i		−	0.702908i	0.936205	−	0.351454i	$-0.114313\pi$
$702$		0			0
$703$	4.38760	−	2.53318i	0.165482	−	0.0955408i
$704$		−	3.28274i		−	0.123723i
$705$		0			0
$706$	38.5544	−	22.2594i	1.45101	−	0.837743i
$707$		0			0
$708$		0			0
$709$	6.74733	+	11.6867i	0.253401	+	0.438904i	0.964460	−	0.264229i	$-0.0851174\pi$
$709$	6.74733	+	11.6867i	0.253401	+	0.438904i	−0.711059	+	0.703133i	$0.751784\pi$
$710$	−16.9137	−	29.2955i	−0.634762	−	1.09944i
$711$		0			0
$712$	9.93557	+	5.73630i	0.372351	+	0.214977i
$713$	5.89074	−	10.2031i	0.220610	−	0.382107i
$714$		0			0
$715$	0.474470	+	0.821807i	0.0177442	+	0.0307338i
$716$			39.3379i			1.47013i
$717$		0			0
$718$	−73.2833			−2.73491
$719$	−18.8692	+	32.6824i	−0.703702	+	1.21885i	0.263456	+	0.964671i	$0.415137\pi$
$719$	−18.8692	+	32.6824i	−0.703702	+	1.21885i	−0.967158	+	0.254176i	$0.918196\pi$
$720$		0			0
$721$		0			0
$722$	−34.5538	−	19.9496i	−1.28596	−	0.742449i
$723$		0			0
$724$	−51.8617	−	29.9424i	−1.92742	−	1.11280i
$725$	−17.4118	−	10.0527i	−0.646659	−	0.373348i
$726$		0			0
$727$	−1.98480	−	1.14592i	−0.0736121	−	0.0424999i	0.462742	−	0.886493i	$-0.346866\pi$
$727$	−1.98480	−	1.14592i	−0.0736121	−	0.0424999i	−0.536354	+	0.843993i	$0.680199\pi$
$728$		0			0
$729$		0			0
$730$	−18.6685	+	32.3347i	−0.690950	+	1.19676i
$731$	19.9030			0.736138
$732$		0			0
$733$			24.7888i			0.915596i	0.889056	+	0.457798i	$0.151362\pi$
$733$			24.7888i			0.915596i	−0.889056	+	0.457798i	$0.848638\pi$
$734$	29.9170	+	51.8178i	1.10426	+	1.91263i
$735$		0			0
$736$	−21.1444	+	36.6232i	−0.779394	+	1.34995i
$737$	−7.27099	−	4.19791i	−0.267830	−	0.154632i
$738$		0			0
$739$	8.10081	+	14.0310i	0.297993	+	0.516139i	0.975677	−	0.219214i	$-0.0703494\pi$
$739$	8.10081	+	14.0310i	0.297993	+	0.516139i	−0.677684	+	0.735354i	$0.737016\pi$
$740$	−7.88932	−	13.6647i	−0.290017	−	0.502325i
$741$		0			0
$742$		0			0
$743$	18.8312	−	10.8722i	0.690848	−	0.398862i	−0.113081	−	0.993586i	$-0.536072\pi$
$743$	18.8312	−	10.8722i	0.690848	−	0.398862i	0.803930	+	0.594724i	$0.202739\pi$
$744$		0			0
$745$		−	13.3154i		−	0.487838i
$746$	−31.1591	+	17.9897i	−1.14081	+	0.658649i
$747$		0			0
$748$		−	12.9138i		−	0.472176i
$749$		0			0
$750$		0			0
$751$	−7.57995			−0.276596			−0.138298	−	0.990391i	$-0.544163\pi$
$751$	−7.57995			−0.276596			−0.138298	+	0.990391i	$0.544163\pi$
$752$	33.8340	−	58.6022i	1.23380	−	2.13700i
$753$		0			0
$754$	16.1666	−	9.33381i	0.588754	−	0.339917i
$755$	11.8900			0.432720
$756$		0			0
$757$	10.3436			0.375944			0.187972	−	0.982174i	$-0.439809\pi$
$757$	10.3436			0.375944			0.187972	+	0.982174i	$0.439809\pi$
$758$	51.1686	−	29.5422i	1.85853	−	1.07302i
$759$		0			0
$760$	8.42392	−	14.5907i	0.305568	−	0.529259i
$761$	−34.4339			−1.24823			−0.624114	−	0.781333i	$-0.714540\pi$
$761$	−34.4339			−1.24823			−0.624114	+	0.781333i	$0.714540\pi$
$762$		0			0
$763$		0			0
$764$		−	17.9629i		−	0.649874i
$765$		0			0
$766$	−34.2121	+	19.7523i	−1.23613	+	0.713681i
$767$		−	4.37713i		−	0.158049i
$768$		0			0
$769$	12.9344	−	7.46765i	0.466425	−	0.269290i	−0.248317	−	0.968679i	$-0.579877\pi$
$769$	12.9344	−	7.46765i	0.466425	−	0.269290i	0.714742	+	0.699388i	$0.246544\pi$
$770$		0			0
$771$		0			0
$772$	16.0439	+	27.7888i	0.577431	+	1.00014i
$773$	19.9924	+	34.6278i	0.719076	+	1.24548i	0.961366	+	0.275272i	$0.0887680\pi$
$773$	19.9924	+	34.6278i	0.719076	+	1.24548i	−0.242290	+	0.970204i	$0.577899\pi$
$774$		0			0
$775$	−7.36945	−	4.25476i	−0.264719	−	0.152835i
$776$	35.7845	−	61.9806i	1.28459	−	2.22497i
$777$		0			0
$778$	−18.3466	−	31.7772i	−0.657758	−	1.13927i
$779$			7.98521i			0.286100i
$780$		0			0
$781$	6.42013			0.229730
$782$	−27.2811	+	47.2523i	−0.975571	+	1.68974i
$783$		0			0
$784$		0			0
$785$	−25.8383	−	14.9178i	−0.922209	−	0.532438i
$786$		0			0
$787$	1.94091	+	1.12059i	0.0691860	+	0.0399446i	0.534194	−	0.845362i	$-0.320615\pi$
$787$	1.94091	+	1.12059i	0.0691860	+	0.0399446i	−0.465008	+	0.885307i	$0.653949\pi$
$788$	26.2561	+	15.1590i	0.935336	+	0.540016i
$789$		0			0
$790$	11.3468	+	6.55108i	0.403701	+	0.233077i
$791$		0			0
$792$		0			0
$793$	−8.87159	+	15.3660i	−0.315039	+	0.545664i
$794$	−25.1766			−0.893484
$795$		0			0
$796$		−	75.8182i		−	2.68731i
$797$	−22.1077	−	38.2916i	−0.783094	−	1.35636i	−0.930131	−	0.367227i	$-0.880307\pi$
$797$	−22.1077	−	38.2916i	−0.783094	−	1.35636i	0.147037	−	0.989131i	$-0.453026\pi$
$798$		0			0
$799$	16.8668	−	29.2142i	0.596705	−	1.03352i
$800$	26.4522	+	15.2722i	0.935226	+	0.539953i
$801$		0			0
$802$	−11.3225	−	19.6112i	−0.399812	−	0.692495i
$803$	−3.54309	−	6.13682i	−0.125033	−	0.216564i
$804$		0			0
$805$		0			0
$806$	6.84243	−	3.95048i	0.241014	−	0.139150i
$807$		0			0
$808$			12.1145i			0.426185i
$809$	−4.31478	+	2.49114i	−0.151699	+	0.0875837i	−0.573928	−	0.818906i	$-0.694581\pi$
$809$	−4.31478	+	2.49114i	−0.151699	+	0.0875837i	0.422229	+	0.906489i	$0.361248\pi$
$810$		0			0
$811$			36.5749i			1.28432i	0.766571	+	0.642160i	$0.221961\pi$
$811$			36.5749i			1.28432i	−0.766571	+	0.642160i	$0.778039\pi$
$812$		0			0
$813$		0			0
$814$	4.26182			0.149377
$815$	−5.52693	+	9.57292i	−0.193600	+	0.335325i
$816$		0			0
$817$	−7.39861	+	4.27159i	−0.258845	+	0.149444i
$818$	38.6225			1.35040
$819$		0			0
$820$	24.8690			0.868465
$821$	−34.8397	+	20.1147i	−1.21591	+	0.702008i	−0.964041	−	0.265753i	$-0.914379\pi$
$821$	−34.8397	+	20.1147i	−1.21591	+	0.702008i	−0.251872	+	0.967761i	$0.581046\pi$
$822$		0			0
$823$	17.9016	−	31.0065i	0.624011	−	1.08082i	−0.364720	−	0.931117i	$-0.618835\pi$
$823$	17.9016	−	31.0065i	0.624011	−	1.08082i	0.988731	−	0.149701i	$-0.0478313\pi$
$824$	52.3638			1.82418
$825$		0			0
$826$		0			0
$827$			32.0733i			1.11530i	0.830077	+	0.557648i	$0.188296\pi$
$827$			32.0733i			1.11530i	−0.830077	+	0.557648i	$0.811704\pi$
$828$		0			0
$829$	14.0640	−	8.11986i	0.488463	−	0.282014i	−0.235474	−	0.971881i	$-0.575664\pi$
$829$	14.0640	−	8.11986i	0.488463	−	0.282014i	0.723937	+	0.689866i	$0.242331\pi$
$830$		−	28.3874i		−	0.985343i
$831$		0			0
$832$	−5.66023	+	3.26793i	−0.196233	+	0.113295i
$833$		0			0
$834$		0			0
$835$	−13.8248	−	23.9453i	−0.478429	−	0.828663i
$836$	2.77157	+	4.80050i	0.0958568	+	0.166029i
$837$		0			0
$838$	−9.60684	−	5.54651i	−0.331863	−	0.191601i
$839$	−1.35145	+	2.34077i	−0.0466571	+	0.0808125i	−0.888411	−	0.459049i	$-0.848190\pi$
$839$	−1.35145	+	2.34077i	−0.0466571	+	0.0808125i	0.841754	+	0.539862i	$0.181523\pi$
$840$		0			0
$841$	2.67914	+	4.64041i	0.0923842	+	0.160014i
$842$		−	29.9129i		−	1.03087i
$843$		0			0
$844$	−38.3853			−1.32128
$845$	−7.19974	+	12.4703i	−0.247679	+	0.428992i
$846$		0			0
$847$		0			0
$848$	23.7962	+	13.7388i	0.817166	+	0.471791i
$849$		0			0
$850$	34.1293	+	19.7046i	1.17063	+	0.675861i
$851$	−10.9575	−	6.32632i	−0.375619	−	0.216864i
$852$		0			0
$853$	41.3187	+	23.8554i	1.41473	+	0.816793i	0.995829	−	0.0912411i	$-0.0290834\pi$
$853$	41.3187	+	23.8554i	1.41473	+	0.816793i	0.418897	+	0.908034i	$0.362417\pi$
$854$		0			0
$855$		0			0
$856$	0.537495	−	0.930969i	0.0183712	−	0.0318199i
$857$	17.8795			0.610751			0.305375	−	0.952232i	$-0.401218\pi$
$857$	17.8795			0.610751			0.305375	+	0.952232i	$0.401218\pi$
$858$		0			0
$859$		−	33.7058i		−	1.15003i	−0.818144	−	0.575014i	$-0.804997\pi$
$859$		−	33.7058i		−	1.15003i	0.818144	−	0.575014i	$-0.195003\pi$
$860$	13.3034	+	23.0422i	0.453642	+	0.785731i
$861$		0			0
$862$	21.6367	−	37.4759i	0.736950	−	1.27643i
$863$	16.4318	+	9.48693i	0.559347	+	0.322939i	0.752883	−	0.658154i	$-0.228662\pi$
$863$	16.4318	+	9.48693i	0.559347	+	0.322939i	−0.193537	+	0.981093i	$0.561996\pi$
$864$		0			0
$865$	2.54826	+	4.41371i	0.0866434	+	0.150071i
$866$	−16.0155	−	27.7396i	−0.544228	−	0.942630i
$867$		0			0
$868$		0			0
$869$	−2.15351	+	1.24333i	−0.0730530	+	0.0421772i
$870$		0			0
$871$			16.7159i			0.566397i
$872$	33.0748	−	19.0957i	1.12005	−	0.646663i
$873$		0			0
$874$		−	23.4204i		−	0.792206i
$875$		0			0
$876$		0			0
$877$	37.2376			1.25742			0.628712	−	0.777638i	$-0.283582\pi$
$877$	37.2376			1.25742			0.628712	+	0.777638i	$0.283582\pi$
$878$	28.7035	−	49.7159i	0.968695	−	1.67783i
$879$		0			0
$880$	5.94726	−	3.43365i	0.200482	−	0.115748i
$881$	−4.71527			−0.158862			−0.0794308	−	0.996840i	$-0.525310\pi$
$881$	−4.71527			−0.158862			−0.0794308	+	0.996840i	$0.525310\pi$
$882$		0			0
$883$	30.1766			1.01552			0.507762	−	0.861497i	$-0.330473\pi$
$883$	30.1766			1.01552			0.507762	+	0.861497i	$0.330473\pi$
$884$	−22.2665	+	12.8556i	−0.748904	+	0.432380i
$885$		0			0
$886$	6.33251	−	10.9682i	0.212745	−	0.368485i
$887$	38.4434			1.29080			0.645402	−	0.763843i	$-0.276690\pi$
$887$	38.4434			1.29080			0.645402	+	0.763843i	$0.276690\pi$
$888$		0			0
$889$		0			0
$890$			5.27243i			0.176732i
$891$		0			0
$892$	32.9058	−	18.9981i	1.10177	−	0.636105i
$893$			14.4799i			0.484550i
$894$		0			0
$895$	−9.03135	+	5.21425i	−0.301885	+	0.174293i
$896$		0			0
$897$		0			0
$898$	−16.1329	−	27.9431i	−0.538363	−	0.932472i
$899$	7.27098	+	12.5937i	0.242501	+	0.420023i
$900$		0			0
$901$	11.8628	+	6.84900i	0.395208	+	0.228173i
$902$	−3.35857	+	5.81721i	−0.111828	+	0.193692i
$903$		0			0
$904$	−22.8781	−	39.6261i	−0.760916	−	1.31794i
$905$		−	15.8755i		−	0.527719i
$906$		0			0
$907$	43.5902			1.44739			0.723695	−	0.690120i	$-0.242442\pi$
$907$	43.5902			1.44739			0.723695	+	0.690120i	$0.242442\pi$
$908$	−49.2103	+	85.2348i	−1.63310	+	2.82862i
$909$		0			0
$910$		0			0
$911$	1.67736	+	0.968423i	0.0555734	+	0.0320853i	0.527529	−	0.849537i	$-0.323119\pi$
$911$	1.67736	+	0.968423i	0.0555734	+	0.0320853i	−0.471956	+	0.881622i	$0.656452\pi$
$912$		0			0
$913$	4.66585	+	2.69383i	0.154417	+	0.0891528i
$914$	24.2025	+	13.9733i	0.800548	+	0.462197i
$915$		0			0
$916$	−24.6379	−	14.2247i	−0.814058	−	0.469997i
$917$		0			0
$918$		0			0
$919$	4.61421	−	7.99205i	0.152209	−	0.263634i	−0.779830	−	0.625991i	$-0.784695\pi$
$919$	4.61421	−	7.99205i	0.152209	−	0.263634i	0.932039	+	0.362357i	$0.118028\pi$
$920$	−42.0755			−1.38719
$921$		0			0
$922$			1.72887i			0.0569372i
$923$	−6.39118	−	11.0698i	−0.210368	−	0.364368i
$924$		0			0
$925$	−4.56937	+	7.91438i	−0.150240	+	0.260223i
$926$	−93.3880	−	53.9176i	−3.06892	−	1.77184i
$927$		0			0
$928$	−26.0987	−	45.2043i	−0.856732	−	1.48390i
$929$	26.6849	+	46.2197i	0.875504	+	1.51642i	0.856225	+	0.516603i	$0.172804\pi$
$929$	26.6849	+	46.2197i	0.875504	+	1.51642i	0.0192794	+	0.999814i	$0.493863\pi$
$930$		0			0
$931$		0			0
$932$	86.0952	−	49.7071i	2.82014	−	1.62821i
$933$		0			0
$934$		−	101.961i		−	3.33627i
$935$	2.96481	−	1.71173i	0.0969595	−	0.0559796i
$936$		0			0
$937$		−	28.6378i		−	0.935555i	−0.883846	−	0.467778i	$-0.845055\pi$
$937$		−	28.6378i		−	0.935555i	0.883846	−	0.467778i	$-0.154945\pi$
$938$		0			0
$939$		0			0
$940$	45.0959			1.47087
$941$	−0.688308	+	1.19218i	−0.0224382	+	0.0388641i	−0.877026	−	0.480442i	$-0.840476\pi$
$941$	−0.688308	+	1.19218i	−0.0224382	+	0.0388641i	0.854588	+	0.519306i	$0.173810\pi$
$942$		0			0
$943$	17.2704	−	9.97105i	0.562401	−	0.324702i
$944$	−31.6764			−1.03098
$945$		0			0
$946$	−7.18651			−0.233653
$947$	47.0080	−	27.1401i	1.52755	−	0.881933i	0.528090	−	0.849188i	$-0.322908\pi$
$947$	47.0080	−	27.1401i	1.52755	−	0.881933i	0.999464	−	0.0327450i	$-0.0104249\pi$
$948$		0			0
$949$	−7.05423	+	12.2183i	−0.228990	+	0.396622i
$950$	−16.9160			−0.548829
$951$		0			0
$952$		0			0
$953$		−	11.2998i		−	0.366036i	−0.983110	−	0.183018i	$-0.941413\pi$
$953$		−	11.2998i		−	0.366036i	0.983110	−	0.183018i	$-0.0585867\pi$
$954$		0			0
$955$	4.12399	−	2.38099i	0.133449	−	0.0770469i
$956$		−	40.9911i		−	1.32575i
$957$		0			0
$958$	−85.6097	+	49.4268i	−2.76592	+	1.59691i
$959$		0			0
$960$		0			0
$961$	−12.4226	−	21.5166i	−0.400729	−	0.694083i
$962$	−4.24260	−	7.34839i	−0.136787	−	0.236922i
$963$		0			0
$964$	34.6825	+	20.0240i	1.11705	+	0.644928i
$965$	−4.25324	+	7.36682i	−0.136917	+	0.237146i
$966$		0			0
$967$	5.93412	+	10.2782i	0.190829	+	0.330525i	0.945525	−	0.325549i	$-0.105549\pi$
$967$	5.93412	+	10.2782i	0.190829	+	0.330525i	−0.754696	+	0.656074i	$0.772216\pi$
$968$		−	75.0929i		−	2.41358i
$969$		0			0
$970$	32.8907			1.05606
$971$	28.0837	−	48.6424i	0.901249	−	1.56101i	0.0753736	−	0.997155i	$-0.475985\pi$
$971$	28.0837	−	48.6424i	0.901249	−	1.56101i	0.825875	−	0.563853i	$-0.190682\pi$
$972$		0			0
$973$		0			0
$974$	−17.0826	−	9.86263i	−0.547361	−	0.316019i
$975$		0			0
$976$	111.201	+	64.2020i	3.55946	+	2.05506i
$977$	−18.7626	−	10.8326i	−0.600268	−	0.346565i	0.168879	−	0.985637i	$-0.445985\pi$
$977$	−18.7626	−	10.8326i	−0.600268	−	0.346565i	−0.769147	+	0.639072i	$0.779319\pi$
$978$		0			0
$979$	−0.866594	−	0.500328i	−0.0276964	−	0.0159906i
$980$		0			0
$981$		0			0
$982$	−4.99072	+	8.64419i	−0.159260	+	0.275847i
$983$	−19.4001			−0.618768			−0.309384	−	0.950937i	$-0.600123\pi$
$983$	−19.4001			−0.618768			−0.309384	+	0.950937i	$0.600123\pi$
$984$		0			0
$985$			8.03731i			0.256090i
$986$	−33.6733	−	58.3238i	−1.07238	−	1.85741i
$987$		0			0
$988$	5.51814	−	9.55771i	0.175556	−	0.304071i
$989$	18.4771	+	10.6678i	0.587539	+	0.339216i
$990$		0			0
$991$	−12.6630	−	21.9330i	−0.402254	−	0.696725i	0.591743	−	0.806126i	$-0.298440\pi$
$991$	−12.6630	−	21.9330i	−0.402254	−	0.696725i	−0.993998	+	0.109402i	$0.965107\pi$
$992$	−11.0461	−	19.1325i	−0.350715	−	0.607456i
$993$		0			0
$994$		0			0
$995$	17.4066	−	10.0497i	0.551828	−	0.318598i
$996$		0			0
$997$			5.56584i			0.176272i	0.996108	+	0.0881360i	$0.0280910\pi$
$997$			5.56584i			0.176272i	−0.996108	+	0.0881360i	$0.971909\pi$
$998$	−72.2309	+	41.7025i	−2.28643	+	1.32007i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.b.656.5		10
3.2	odd	2		441.2.s.b.362.1		10
7.2	even	3		1323.2.o.c.440.1		10
7.3	odd	6		1323.2.i.b.521.5		10
7.4	even	3		189.2.i.b.143.5		10
7.5	odd	6		1323.2.o.d.440.1		10
7.6	odd	2		189.2.s.b.89.5		10
9.4	even	3		441.2.i.b.68.5		10
9.5	odd	6		1323.2.i.b.1097.1		10
21.2	odd	6		441.2.o.d.146.5		10
21.5	even	6		441.2.o.c.146.5		10
21.11	odd	6		63.2.i.b.38.1	yes	10
21.17	even	6		441.2.i.b.227.1		10
21.20	even	2		63.2.s.b.47.1	yes	10
28.11	odd	6		3024.2.ca.b.2033.2		10
28.27	even	2		3024.2.df.b.1601.2		10
63.4	even	3		63.2.s.b.59.1	yes	10
63.5	even	6		1323.2.o.c.881.1		10
63.11	odd	6		567.2.p.d.80.1		10
63.13	odd	6		63.2.i.b.5.5	✓	10
63.20	even	6		567.2.p.c.404.5		10
63.23	odd	6		1323.2.o.d.881.1		10
63.25	even	3		567.2.p.c.80.5		10
63.31	odd	6		441.2.s.b.374.1		10
63.32	odd	6		189.2.s.b.17.5		10
63.34	odd	6		567.2.p.d.404.1		10
63.40	odd	6		441.2.o.d.293.5		10
63.41	even	6		189.2.i.b.152.1		10
63.58	even	3		441.2.o.c.293.5		10
63.59	even	6	inner	1323.2.s.b.962.5		10
84.11	even	6		1008.2.ca.b.353.1		10
84.83	odd	2		1008.2.df.b.929.1		10
252.67	odd	6		1008.2.df.b.689.1		10
252.95	even	6		3024.2.df.b.17.2		10
252.139	even	6		1008.2.ca.b.257.1		10
252.167	odd	6		3024.2.ca.b.2609.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.5	✓	10	63.13	odd	6
63.2.i.b.38.1	yes	10	21.11	odd	6
63.2.s.b.47.1	yes	10	21.20	even	2
63.2.s.b.59.1	yes	10	63.4	even	3
189.2.i.b.143.5		10	7.4	even	3
189.2.i.b.152.1		10	63.41	even	6
189.2.s.b.17.5		10	63.32	odd	6
189.2.s.b.89.5		10	7.6	odd	2
441.2.i.b.68.5		10	9.4	even	3
441.2.i.b.227.1		10	21.17	even	6
441.2.o.c.146.5		10	21.5	even	6
441.2.o.c.293.5		10	63.58	even	3
441.2.o.d.146.5		10	21.2	odd	6
441.2.o.d.293.5		10	63.40	odd	6
441.2.s.b.362.1		10	3.2	odd	2
441.2.s.b.374.1		10	63.31	odd	6
567.2.p.c.80.5		10	63.25	even	3
567.2.p.c.404.5		10	63.20	even	6
567.2.p.d.80.1		10	63.11	odd	6
567.2.p.d.404.1		10	63.34	odd	6
1008.2.ca.b.257.1		10	252.139	even	6
1008.2.ca.b.353.1		10	84.11	even	6
1008.2.df.b.689.1		10	252.67	odd	6
1008.2.df.b.929.1		10	84.83	odd	2
1323.2.i.b.521.5		10	7.3	odd	6
1323.2.i.b.1097.1		10	9.5	odd	6
1323.2.o.c.440.1		10	7.2	even	3
1323.2.o.c.881.1		10	63.5	even	6
1323.2.o.d.440.1		10	7.5	odd	6
1323.2.o.d.881.1		10	63.23	odd	6
1323.2.s.b.656.5		10	1.1	even	1	trivial
1323.2.s.b.962.5		10	63.59	even	6	inner
3024.2.ca.b.2033.2		10	28.11	odd	6
3024.2.ca.b.2609.2		10	252.167	odd	6
3024.2.df.b.17.2		10	252.95	even	6
3024.2.df.b.1601.2		10	28.27	even	2

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.24607 - 1.29677i) q^{2} +(2.36322 - 4.09323i) q^{4} +1.25299 q^{5} -7.07116i q^{8} +O(q^{10})\)	\(q+(2.24607 - 1.29677i) q^{2} +(2.36322 - 4.09323i) q^{4} +1.25299 q^{5} -7.07116i q^{8} +(2.81429 - 1.62483i) q^{10} +0.616756i q^{11} +(1.06343 - 0.613974i) q^{13} +(-4.44321 - 7.69587i) q^{16} +(-2.21501 - 3.83652i) q^{17} +(1.64679 + 0.950775i) q^{19} +(2.96109 - 5.12875i) q^{20} +(0.799790 + 1.38528i) q^{22} -4.74890i q^{23} -3.43003 q^{25} +(1.59237 - 2.75806i) q^{26} +(5.07629 + 2.93080i) q^{29} +(2.14851 + 1.24044i) q^{31} +(-7.71195 - 4.45249i) q^{32} +(-9.95016 - 5.74473i) q^{34} +(1.33217 - 2.30738i) q^{37} +4.93175 q^{38} -8.86005i q^{40} +(2.09966 + 3.63671i) q^{41} +(-2.24637 + 3.89083i) q^{43} +(2.52452 + 1.45753i) q^{44} +(-6.15823 - 10.6664i) q^{46} +(3.80738 + 6.59458i) q^{47} +(-7.70409 + 4.44796i) q^{50} -5.80384i q^{52} +(-2.67782 + 1.54604i) q^{53} +0.772786i q^{55} +15.2023 q^{58} +(1.78229 - 3.08702i) q^{59} +(-12.5136 + 7.22473i) q^{61} +6.43428 q^{62} -5.32259 q^{64} +(1.33247 - 0.769301i) q^{65} +(-6.80644 + 11.7891i) q^{67} -20.9383 q^{68} -10.4095i q^{71} +(-9.95016 + 5.74473i) q^{73} -6.91006i q^{74} +(7.78348 - 4.49379i) q^{76} +(2.01592 + 3.49168i) q^{79} +(-5.56728 - 9.64281i) q^{80} +(9.43196 + 5.44554i) q^{82} +(4.36775 - 7.56516i) q^{83} +(-2.77538 - 4.80710i) q^{85} +11.6521i q^{86} +4.36118 q^{88} +(-0.811226 + 1.40508i) q^{89} +(-19.4383 - 11.2227i) q^{92} +(17.1033 + 9.87459i) q^{94} +(2.06341 + 1.19131i) q^{95} +(8.76527 + 5.06063i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4}+O(q^{10}) \) 10 * q + 4 * q^4	\( 10 q + 4 q^{4} + 15 q^{10} - 6 q^{13} - 6 q^{16} - 12 q^{17} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 14 q^{25} + 3 q^{26} + 15 q^{29} + 9 q^{31} - 48 q^{32} - 3 q^{34} + 6 q^{37} + 36 q^{38} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} + 15 q^{47} - 3 q^{50} + 9 q^{53} - 16 q^{58} - 18 q^{59} - 12 q^{61} + 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} - 54 q^{68} - 3 q^{73} - 9 q^{76} + 20 q^{79} - 30 q^{80} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 16 q^{88} + 24 q^{89} - 39 q^{92} + 3 q^{94} - 6 q^{97}+O(q^{100}) \) 10 * q + 4 * q^4 + 15 * q^10 - 6 * q^13 - 6 * q^16 - 12 * q^17 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 14 * q^25 + 3 * q^26 + 15 * q^29 + 9 * q^31 - 48 * q^32 - 3 * q^34 + 6 * q^37 + 36 * q^38 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 + 15 * q^47 - 3 * q^50 + 9 * q^53 - 16 * q^58 - 18 * q^59 - 12 * q^61 + 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 - 54 * q^68 - 3 * q^73 - 9 * q^76 + 20 * q^79 - 30 * q^80 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 16 * q^88 + 24 * q^89 - 39 * q^92 + 3 * q^94 - 6 * q^97

Introduction

L-functions

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