LMFDB - Embedded newform 1323.2.s.b.962.5

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			962.5
Root			$1.07065 - 1.85442i$ of defining polynomial
Character	$\chi$	$=$	1323.962
Dual form			1323.2.s.b.656.5

$q$-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 $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

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

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	0.993602	+	0.112941i	$0.0360271\pi$
$2$	2.24607	+	1.29677i	1.58821	+	0.916955i	0.594611	+	0.804014i	$0.297306\pi$
$3$		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	$-0.970361\pi$
$11$		−	0.616756i		−	0.185959i	0.995668	−	0.0929794i	$-0.0296391\pi$
$12$		0			0
$13$	1.06343	+	0.613974i	0.294944	+	0.170286i	0.640169	−	0.768234i	$-0.278864\pi$
$13$	1.06343	+	0.613974i	0.294944	+	0.170286i	−0.345226	+	0.938520i	$0.612198\pi$
$14$		0			0
$15$		0			0
$16$	−4.44321	+	7.69587i	−1.11080	+	1.92397i
$17$	−2.21501	+	3.83652i	−0.537220	+	0.930492i	0.461833	+	0.886967i	$0.347192\pi$
$17$	−2.21501	+	3.83652i	−0.537220	+	0.930492i	−0.999052	+	0.0435249i	$0.986141\pi$
$18$		0			0
$19$	1.64679	−	0.950775i	0.377800	−	0.218123i	−0.299061	−	0.954234i	$-0.596673\pi$
$19$	1.64679	−	0.950775i	0.377800	−	0.218123i	0.676861	+	0.736111i	$0.263340\pi$
$20$	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	$0.164871\pi$
$23$			4.74890i			0.990213i	−0.868832	+	0.495107i	$0.835129\pi$
$24$		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	0.0518553	−	0.998655i	$-0.483487\pi$
$29$	5.07629	−	2.93080i	0.942643	−	0.544235i	0.890788	+	0.454419i	$0.150153\pi$
$30$		0			0
$31$	2.14851	−	1.24044i	0.385884	−	0.222790i	−0.294491	−	0.955654i	$-0.595150\pi$
$31$	2.14851	−	1.24044i	0.385884	−	0.222790i	0.680375	+	0.732864i	$0.261817\pi$
$32$	−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	0.954505	−	0.298196i	$-0.0963849\pi$
$37$	1.33217	+	2.30738i	0.219007	+	0.379331i	−0.735498	+	0.677527i	$0.763052\pi$
$38$	4.93175			0.800035
$39$		0			0
$40$			8.86005i			1.40090i
$41$	2.09966	−	3.63671i	0.327911	−	0.567959i	−0.654186	−	0.756334i	$-0.726989\pi$
$41$	2.09966	−	3.63671i	0.327911	−	0.567959i	0.982097	+	0.188375i	$0.0603220\pi$
$42$		0			0
$43$	−2.24637	−	3.89083i	−0.342568	−	0.593346i	0.642340	−	0.766419i	$-0.277964\pi$
$43$	−2.24637	−	3.89083i	−0.342568	−	0.593346i	−0.984909	+	0.173073i	$0.944630\pi$
$44$	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	−0.442512	−	0.896763i	$-0.645912\pi$
$47$	3.80738	−	6.59458i	0.555364	−	0.961918i	0.997875	−	0.0651551i	$-0.0207542\pi$
$48$		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	0.304682	−	0.952454i	$-0.401450\pi$
$53$	−2.67782	−	1.54604i	−0.367827	−	0.212365i	−0.672509	+	0.740089i	$0.734783\pi$
$54$		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	0.958407	−	0.285406i	$-0.0921283\pi$
$59$	1.78229	+	3.08702i	0.232035	+	0.401896i	−0.726372	+	0.687302i	$0.758795\pi$
$60$		0			0
$61$	−12.5136	−	7.22473i	−1.60220	−	0.925032i	−0.991046	−	0.133521i	$-0.957372\pi$
$61$	−12.5136	−	7.22473i	−1.60220	−	0.925032i	−0.611156	−	0.791510i	$-0.709295\pi$
$62$	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	−0.896818	−	0.442400i	$-0.854127\pi$
$67$	−6.80644	−	11.7891i	−0.831539	−	1.44027i	0.0652791	−	0.997867i	$-0.479206\pi$
$68$	−20.9383			−2.53914
$69$		0			0
$70$		0			0
$71$			10.4095i			1.23538i	0.786420	+	0.617692i	$0.211932\pi$
$71$			10.4095i			1.23538i	−0.786420	+	0.617692i	$0.788068\pi$
$72$		0			0
$73$	−9.95016	−	5.74473i	−1.16458	−	0.672369i	−0.212181	−	0.977230i	$-0.568057\pi$
$73$	−9.95016	−	5.74473i	−1.16458	−	0.672369i	−0.952397	+	0.304861i	$0.901390\pi$
$74$			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	−0.730052	−	0.683392i	$-0.760504\pi$
$79$	2.01592	−	3.49168i	0.226809	−	0.392845i	0.956861	+	0.290547i	$0.0938373\pi$
$80$	−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	0.999721	−	0.0236001i	$-0.00751285\pi$
$83$	4.36775	+	7.56516i	0.479422	+	0.830384i	−0.520299	+	0.853984i	$0.674180\pi$
$84$		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	0.819823	−	0.572617i	$-0.194072\pi$
$89$	−0.811226	−	1.40508i	−0.0859897	−	0.148939i	−0.905813	+	0.423679i	$0.860739\pi$
$90$		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	0.0160431	−	0.999871i	$-0.494893\pi$
$97$	8.76527	−	5.06063i	0.889979	−	0.513829i	0.873936	+	0.486042i	$0.161560\pi$
$98$		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	$-0.881127\pi$
$103$		−	7.40526i		−	0.729662i	0.931074	−	0.364831i	$-0.118873\pi$
$104$	−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	−0.493623	−	0.869676i	$-0.664328\pi$
$107$	0.131657	−	0.0760123i	0.0127278	−	0.00734839i	0.506350	+	0.862328i	$0.330994\pi$
$108$		0			0
$109$	2.70051	−	4.67742i	0.258662	−	0.448016i	−0.707222	−	0.706992i	$-0.750052\pi$
$109$	2.70051	−	4.67742i	0.258662	−	0.448016i	0.965884	+	0.258976i	$0.0833851\pi$
$110$	1.00213	−	1.73573i	0.0955489	−	0.165496i
$111$		0			0
$112$		0			0
$113$	5.60391	+	3.23542i	0.527171	+	0.304362i	0.739864	−	0.672757i	$-0.234890\pi$
$113$	5.60391	+	3.23542i	0.527171	+	0.304362i	−0.212693	+	0.977119i	$0.568223\pi$
$114$		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	$-0.733211\pi$
$137$		−	17.4026i		−	1.48680i	0.668845	−	0.743402i	$-0.266789\pi$
$138$		0			0
$139$	−5.45273	−	3.14813i	−0.462494	−	0.267021i	0.250598	−	0.968091i	$-0.419373\pi$
$139$	−5.45273	−	3.14813i	−0.462494	−	0.267021i	−0.713092	+	0.701070i	$0.752706\pi$
$140$		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	$0.143356\pi$
$149$			10.6269i			0.870592i	−0.900287	+	0.435296i	$0.856644\pi$
$150$		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	−0.667040	+	0.745022i	$0.732439\pi$
$157$	−20.6214	+	11.9058i	−1.64577	+	0.950185i	−0.978728	+	0.205163i	$0.934228\pi$
$158$	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	0.639947	−	0.768419i	$-0.278956\pi$
$163$	−4.41101	−	7.64009i	−0.345497	−	0.598418i	−0.985444	+	0.170001i	$0.945623\pi$
$164$	19.8478			1.54986
$165$		0			0
$166$			22.6558i			1.75843i
$167$	−11.0335	+	19.1106i	−0.853800	+	1.47883i	0.0239535	+	0.999713i	$0.492375\pi$
$167$	−11.0335	+	19.1106i	−0.853800	+	1.47883i	−0.877754	+	0.479112i	$0.840959\pi$
$168$		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	−0.778299	−	0.627894i	$-0.783917\pi$
$173$	2.03375	−	3.52256i	0.154623	−	0.267815i	0.932922	+	0.360079i	$0.117250\pi$
$174$		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	0.205827	−	0.978588i	$-0.434011\pi$
$179$	−7.20787	−	4.16146i	−0.538741	−	0.311042i	−0.744569	+	0.667546i	$0.767345\pi$
$180$		0			0
$181$			12.6701i			0.941763i	0.882196	+	0.470881i	$0.156064\pi$
$181$			12.6701i			0.941763i	−0.882196	+	0.470881i	$0.843936\pi$
$182$		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	0.614327	−	0.789051i	$-0.289427\pi$
$191$	3.29133	+	1.90025i	0.238152	+	0.137497i	−0.376175	+	0.926549i	$0.622761\pi$
$192$		0			0
$193$	−3.39448	−	5.87942i	−0.244340	−	0.423210i	0.717606	−	0.696450i	$-0.245238\pi$
$193$	−3.39448	−	5.87942i	−0.244340	−	0.423210i	−0.961946	+	0.273240i	$0.911905\pi$
$194$	26.2499			1.88463
$195$		0			0
$196$		0			0
$197$		−	6.41453i		−	0.457017i	−0.973542	−	0.228508i	$-0.926615\pi$
$197$		−	6.41453i		−	0.457017i	0.973542	−	0.228508i	$-0.0733848\pi$
$198$		0			0
$199$	13.8921	+	8.02063i	0.984788	+	0.568568i	0.903712	−	0.428140i	$-0.140831\pi$
$199$	13.8921	+	8.02063i	0.984788	+	0.568568i	0.0810756	+	0.996708i	$0.474164\pi$
$200$		−	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	−0.971273	−	0.237968i	$-0.923519\pi$
$211$	−4.06070	+	7.03333i	−0.279550	+	0.484194i	0.691723	+	0.722163i	$0.256852\pi$
$212$		−	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	−0.248440	−	0.968647i	$-0.579918\pi$
$223$	6.96205	−	4.01954i	0.466213	−	0.269168i	0.714653	+	0.699479i	$0.246585\pi$
$224$		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	$0.0637302\pi$
$229$			6.01918i			0.397759i	−0.980024	+	0.198879i	$0.936270\pi$
$230$	−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	0.234282	−	0.972169i	$-0.424726\pi$
$233$	18.2156	−	10.5168i	1.19335	−	0.688978i	0.959064	+	0.283191i	$0.0913929\pi$
$234$		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	0.722844	−	0.691011i	$-0.242835\pi$
$239$	7.51079	+	4.33636i	0.485832	+	0.280496i	−0.237011	+	0.971507i	$0.576168\pi$
$240$		0			0
$241$		−	8.47315i		−	0.545804i	−0.962042	−	0.272902i	$-0.912017\pi$
$241$		−	8.47315i		−	0.545804i	0.962042	−	0.272902i	$-0.0879834\pi$
$242$	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	$0.105501\pi$
$263$			10.5544i			0.650811i	−0.945575	+	0.325406i	$0.894499\pi$
$264$		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	−0.829023	−	0.559214i	$-0.811103\pi$
$269$	1.14451	−	1.98235i	0.0697821	−	0.120866i	0.898805	+	0.438348i	$0.144436\pi$
$270$		0			0
$271$	20.9239	−	12.0804i	1.27103	−	0.733831i	0.295851	−	0.955234i	$-0.404397\pi$
$271$	20.9239	−	12.0804i	1.27103	−	0.733831i	0.975182	+	0.221403i	$0.0710635\pi$
$272$	−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	−0.923267	−	0.384160i	$-0.874491\pi$
$281$	−17.6382	+	10.1834i	−1.05221	+	0.607492i	−0.128941	+	0.991652i	$0.541158\pi$
$282$		0			0
$283$	−10.5318	+	6.08055i	−0.626052	+	0.361451i	−0.779222	−	0.626749i	$-0.784385\pi$
$283$	−10.5318	+	6.08055i	−0.626052	+	0.361451i	0.153169	+	0.988200i	$0.451052\pi$
$284$	−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	−0.141161	−	0.989987i	$-0.545083\pi$
$293$	13.4674	−	23.3262i	0.786773	−	1.36273i	0.927934	−	0.372745i	$-0.121583\pi$
$294$		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	$0.208760\pi$
$307$			21.3700i			1.21965i	−0.792536	+	0.609825i	$0.791240\pi$
$308$		0			0
$309$		0			0
$310$	8.06206			0.457894
$311$	8.11558	+	14.0566i	0.460192	+	0.797076i	0.998970	−	0.0453714i	$-0.0144471\pi$
$311$	8.11558	+	14.0566i	0.460192	+	0.797076i	−0.538778	+	0.842448i	$0.681114\pi$
$312$		0			0
$313$	−12.1941	−	7.04027i	−0.689252	−	0.397940i	0.114080	−	0.993472i	$-0.463608\pi$
$313$	−12.1941	−	7.04027i	−0.689252	−	0.397940i	−0.803332	+	0.595532i	$0.796941\pi$
$314$	−61.7562			−3.48511
$315$		0			0
$316$	19.0563			1.07200
$317$	−17.5776	−	10.1484i	−0.987254	−	0.569991i	−0.0828017	−	0.996566i	$-0.526387\pi$
$317$	−17.5776	−	10.1484i	−0.987254	−	0.569991i	−0.904452	+	0.426575i	$0.859720\pi$
$318$		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	0.230563	+	0.973057i	$0.425943\pi$
$331$	−13.2341	+	22.9221i	−0.727411	+	1.25991i	−0.957974	+	0.286856i	$0.907390\pi$
$332$	−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	−0.909441	−	0.415834i	$-0.863490\pi$
$337$	−1.73659	+	3.00785i	−0.0945979	+	0.163848i	0.814843	+	0.579682i	$0.196823\pi$
$338$		−	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	−0.702489	−	0.711694i	$-0.747928\pi$
$347$	−8.14765	+	4.70405i	−0.437389	+	0.252527i	0.265101	+	0.964221i	$0.414595\pi$
$348$		0			0
$349$	12.3253	−	7.11603i	0.659759	−	0.380912i	−0.132426	−	0.991193i	$-0.542277\pi$
$349$	12.3253	−	7.11603i	0.659759	−	0.380912i	0.792185	+	0.610281i	$0.208943\pi$
$350$		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	−0.978921	−	0.204241i	$-0.934528\pi$
$359$	−24.4705	+	14.1281i	−1.29150	+	0.745650i	−0.312583	+	0.949890i	$0.601194\pi$
$360$		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	$-0.794318\pi$
$367$		−	23.0704i		−	1.20427i	0.798396	−	0.602133i	$-0.205682\pi$
$368$	−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	$0.116768\pi$
$389$			14.1479i			0.717328i	−0.933467	+	0.358664i	$0.883232\pi$
$390$		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	−0.695902	−	0.718136i	$-0.744995\pi$
$397$	−8.40688	+	4.85371i	−0.421929	+	0.243601i	0.273973	+	0.961737i	$0.411662\pi$
$398$	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	$0.0699569\pi$
$401$			8.73133i			0.436022i	−0.975946	+	0.218011i	$0.930043\pi$
$402$		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	−0.146028	−	0.989280i	$-0.546649\pi$
$409$	12.8967	−	7.44591i	0.637700	−	0.368176i	0.783728	+	0.621104i	$0.213316\pi$
$410$	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	−0.913524	−	0.406784i	$-0.866650\pi$
$419$	−2.13859	+	3.70414i	−0.104477	+	0.180959i	0.809048	+	0.587743i	$0.199983\pi$
$420$		0			0
$421$	5.76681	+	9.98841i	0.281057	+	0.486805i	0.971645	−	0.236443i	$-0.0759816\pi$
$421$	5.76681	+	9.98841i	0.281057	+	0.486805i	−0.690588	+	0.723248i	$0.742648\pi$
$422$	−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	0.805863	−	0.592103i	$-0.201702\pi$
$431$	14.4497	+	8.34254i	0.696018	+	0.401846i	−0.109845	+	0.993949i	$0.535035\pi$
$432$		0			0
$433$			12.3503i			0.593516i	0.954953	+	0.296758i	$0.0959055\pi$
$433$			12.3503i			0.593516i	−0.954953	+	0.296758i	$0.904094\pi$
$434$		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	0.882002	−	0.471246i	$-0.156195\pi$
$439$	19.1691	+	11.0673i	0.914892	+	0.528213i	0.0328902	+	0.999459i	$0.489529\pi$
$440$	5.46449			0.260509
$441$		0			0
$442$	−14.1085			−0.671071
$443$	4.22906	+	2.44165i	0.200929	+	0.116006i	0.597089	−	0.802175i	$-0.296324\pi$
$443$	4.22906	+	2.44165i	0.200929	+	0.116006i	−0.396160	+	0.918182i	$0.629657\pi$
$444$		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	$0.0948401\pi$
$449$			12.4409i			0.587121i	−0.955941	+	0.293560i	$0.905160\pi$
$450$		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	−0.712056	−	0.702123i	$-0.752236\pi$
$457$	5.38774	−	9.33185i	0.252028	−	0.436525i	0.964084	+	0.265597i	$0.0855691\pi$
$458$	−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	0.858159	−	0.513383i	$-0.171608\pi$
$461$	−0.333303	−	0.577297i	−0.0155235	−	0.0268874i	−0.873683	+	0.486496i	$0.838275\pi$
$462$		0			0
$463$	−20.7892	+	36.0079i	−0.966155	+	1.67343i	−0.259677	+	0.965696i	$0.583616\pi$
$463$	−20.7892	+	36.0079i	−0.966155	+	1.67343i	−0.706479	+	0.707734i	$0.749717\pi$
$464$			52.0886i			2.41815i
$465$		0			0
$466$	54.5515			2.52705
$467$	19.6568	+	34.0465i	0.909606	+	1.57548i	0.814612	+	0.580006i	$0.196950\pi$
$467$	19.6568	+	34.0465i	0.909606	+	1.57548i	0.0949943	+	0.995478i	$0.469717\pi$
$468$		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	−0.939231	−	0.343287i	$-0.888460\pi$
$487$	−3.80277	+	6.58659i	−0.172320	+	0.298467i	0.766911	+	0.641754i	$0.221793\pi$
$488$	51.0872	−	88.4856i	2.31261	−	4.00555i
$489$		0			0
$490$		0			0
$491$	−3.33297	−	1.92429i	−0.150415	−	0.0868420i	0.422904	−	0.906175i	$-0.361011\pi$
$491$	−3.33297	−	1.92429i	−0.150415	−	0.0868420i	−0.573318	+	0.819333i	$0.694344\pi$
$492$		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	−0.993409	−	0.114621i	$-0.963435\pi$
$521$	−9.07174	+	15.7127i	−0.397440	+	0.688386i	0.595969	+	0.803007i	$0.296768\pi$
$522$		0			0
$523$	−12.0723	+	6.96997i	−0.527887	+	0.304776i	−0.740155	−	0.672436i	$-0.765248\pi$
$523$	−12.0723	+	6.96997i	−0.527887	+	0.304776i	0.212269	+	0.977211i	$0.431915\pi$
$524$	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	−0.985701	−	0.168503i	$-0.946107\pi$
$541$	−14.8576	−	25.7341i	−0.638779	−	1.10640i	0.346922	−	0.937894i	$-0.387227\pi$
$542$	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	0.601937	−	0.798544i	$-0.294396\pi$
$547$	−9.13516	−	15.8226i	−0.390591	−	0.676524i	−0.992528	+	0.122020i	$0.961063\pi$
$548$	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	0.507596	−	0.861595i	$-0.330534\pi$
$557$	0.359456	+	0.207532i	0.0152307	+	0.00879343i	−0.492365	+	0.870389i	$0.663868\pi$
$558$		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	0.902002	−	0.431733i	$-0.142098\pi$
$563$	1.82962	+	3.16900i	0.0771095	+	0.133558i	−0.824892	+	0.565290i	$0.808764\pi$
$564$		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	−0.300977	−	0.953631i	$-0.597313\pi$
$569$	−30.4692	−	17.5914i	−1.27733	−	0.737470i	−0.976358	+	0.216162i	$0.930646\pi$
$570$		0			0
$571$	5.02680	+	8.70667i	0.210365	+	0.364363i	0.951829	−	0.306630i	$-0.0992014\pi$
$571$	5.02680	+	8.70667i	0.210365	+	0.364363i	−0.741464	+	0.670993i	$0.765868\pi$
$572$	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	0.498755	−	0.866743i	$-0.333791\pi$
$577$	−0.0597672	−	0.0345066i	−0.00248814	−	0.00143653i	−0.501244	+	0.865306i	$0.667124\pi$
$578$		−	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	0.525724	−	0.850655i	$-0.323795\pi$
$587$	−11.4799	−	19.8838i	−0.473827	−	0.820693i	−0.999551	+	0.0299626i	$0.990461\pi$
$588$		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	0.994069	+	0.108748i	$0.0346843\pi$
$593$	14.3970	+	24.9363i	0.591213	+	1.02401i	−0.402856	+	0.915263i	$0.631982\pi$
$594$		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	0.365910	−	0.930650i	$-0.380758\pi$
$599$	33.1588	−	19.1442i	1.35483	−	0.782212i	0.988922	+	0.148438i	$0.0474246\pi$
$600$		0			0
$601$	−26.7618	+	15.4509i	−1.09164	+	0.630257i	−0.934012	−	0.357242i	$-0.883717\pi$
$601$	−26.7618	+	15.4509i	−1.09164	+	0.630257i	−0.157625	+	0.987499i	$0.550384\pi$
$602$		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	$0.235145\pi$
$607$			33.1791i			1.34670i	−0.739325	+	0.673349i	$0.764855\pi$
$608$	−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	−0.903787	−	0.427983i	$-0.859224\pi$
$613$	−2.01164	+	3.48426i	−0.0812492	+	0.140728i	0.822538	+	0.568711i	$0.192558\pi$
$614$	−27.7120	+	47.9985i	−1.11836	+	1.93706i
$615$		0			0
$616$		0			0
$617$	−27.1191	−	15.6572i	−1.09177	−	0.630336i	−0.157726	−	0.987483i	$-0.550416\pi$
$617$	−27.1191	−	15.6572i	−1.09177	−	0.630336i	−0.934048	+	0.357147i	$0.883749\pi$
$618$		0			0
$619$		−	13.9310i		−	0.559934i	−0.960010	−	0.279967i	$-0.909676\pi$
$619$		−	13.9310i		−	0.559934i	0.960010	−	0.279967i	$-0.0903235\pi$
$620$	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	$0.316730\pi$
$641$			42.4724i			1.67756i	−0.544473	+	0.838779i	$0.683270\pi$
$642$		0			0
$643$	3.13514	+	1.81008i	0.123638	+	0.0713825i	0.560544	−	0.828125i	$-0.310592\pi$
$643$	3.13514	+	1.81008i	0.123638	+	0.0713825i	−0.436905	+	0.899507i	$0.643926\pi$
$644$		0			0
$645$		0			0
$646$	−10.9239	+	18.9207i	−0.429795	+	0.744426i
$647$	6.00617	−	10.4030i	0.236127	−	0.408984i	−0.723473	−	0.690353i	$-0.757455\pi$
$647$	6.00617	−	10.4030i	0.236127	−	0.408984i	0.959600	+	0.281369i	$0.0907886\pi$
$648$		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	$-0.640896\pi$
$653$		−	46.1822i		−	1.80725i	0.428324	−	0.903625i	$-0.359104\pi$
$654$		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	−0.146566	−	0.989201i	$-0.546822\pi$
$659$	16.3479	−	9.43847i	0.636824	−	0.367671i	0.783390	+	0.621530i	$0.213489\pi$
$660$		0			0
$661$	−2.88202	+	1.66393i	−0.112097	+	0.0647195i	−0.555000	−	0.831850i	$-0.687282\pi$
$661$	−2.88202	+	1.66393i	−0.112097	+	0.0647195i	0.442903	+	0.896570i	$0.353949\pi$
$662$	−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	−0.987361	−	0.158487i	$-0.949339\pi$
$673$	−16.3678	−	28.3499i	−0.630934	−	1.09281i	0.356427	−	0.934323i	$-0.383995\pi$
$674$	−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	0.332631	+	0.943057i	$0.392063\pi$
$677$	−16.9228	+	29.3111i	−0.650396	+	1.12652i	−0.983027	+	0.183461i	$0.941270\pi$
$678$		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	0.405425	−	0.914128i	$-0.367123\pi$
$683$	−4.79617	−	2.76907i	−0.183520	−	0.105956i	−0.588946	+	0.808173i	$0.700457\pi$
$684$		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	0.246530	−	0.969135i	$-0.420710\pi$
$691$	−12.3417	−	7.12550i	−0.469502	−	0.271067i	−0.716031	+	0.698068i	$0.754043\pi$
$692$	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	$0.114313\pi$
$701$			18.6105i			0.702908i	−0.936205	+	0.351454i	$0.885687\pi$
$702$		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	−0.711059	−	0.703133i	$-0.751784\pi$
$709$	6.74733	−	11.6867i	0.253401	−	0.438904i	0.964460	+	0.264229i	$0.0851174\pi$
$710$	−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	−0.967158	−	0.254176i	$-0.918196\pi$
$719$	−18.8692	−	32.6824i	−0.703702	−	1.21885i	0.263456	−	0.964671i	$-0.415137\pi$
$720$		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	−0.536354	−	0.843993i	$-0.680199\pi$
$727$	−1.98480	+	1.14592i	−0.0736121	+	0.0424999i	0.462742	+	0.886493i	$0.346866\pi$
$728$		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	$-0.848638\pi$
$733$		−	24.7888i		−	0.915596i	0.889056	−	0.457798i	$-0.151362\pi$
$734$	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	−0.677684	−	0.735354i	$-0.737016\pi$
$739$	8.10081	−	14.0310i	0.297993	−	0.516139i	0.975677	+	0.219214i	$0.0703494\pi$
$740$	−7.88932	+	13.6647i	−0.290017	+	0.502325i
$741$		0			0
$742$		0			0
$743$	18.8312	+	10.8722i	0.690848	+	0.398862i	0.803930	−	0.594724i	$-0.202739\pi$
$743$	18.8312	+	10.8722i	0.690848	+	0.398862i	−0.113081	+	0.993586i	$0.536072\pi$
$744$		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	0.714742	−	0.699388i	$-0.246544\pi$
$769$	12.9344	+	7.46765i	0.466425	+	0.269290i	−0.248317	+	0.968679i	$0.579877\pi$
$770$		0			0
$771$		0			0
$772$	16.0439	−	27.7888i	0.577431	−	1.00014i
$773$	19.9924	−	34.6278i	0.719076	−	1.24548i	−0.242290	−	0.970204i	$-0.577899\pi$
$773$	19.9924	−	34.6278i	0.719076	−	1.24548i	0.961366	−	0.275272i	$-0.0887680\pi$
$774$		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	−0.465008	−	0.885307i	$-0.653949\pi$
$787$	1.94091	−	1.12059i	0.0691860	−	0.0399446i	0.534194	+	0.845362i	$0.320615\pi$
$788$	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	0.147037	+	0.989131i	$0.453026\pi$
$797$	−22.1077	+	38.2916i	−0.783094	+	1.35636i	−0.930131	+	0.367227i	$0.880307\pi$
$798$		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	0.422229	−	0.906489i	$-0.361248\pi$
$809$	−4.31478	−	2.49114i	−0.151699	−	0.0875837i	−0.573928	+	0.818906i	$0.694581\pi$
$810$		0			0
$811$		−	36.5749i		−	1.28432i	−0.766571	−	0.642160i	$-0.778039\pi$
$811$		−	36.5749i		−	1.28432i	0.766571	−	0.642160i	$-0.221961\pi$
$812$		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	−0.251872	−	0.967761i	$-0.581046\pi$
$821$	−34.8397	−	20.1147i	−1.21591	−	0.702008i	−0.964041	+	0.265753i	$0.914379\pi$
$822$		0			0
$823$	17.9016	+	31.0065i	0.624011	+	1.08082i	0.988731	+	0.149701i	$0.0478313\pi$
$823$	17.9016	+	31.0065i	0.624011	+	1.08082i	−0.364720	+	0.931117i	$0.618835\pi$
$824$	52.3638			1.82418
$825$		0			0
$826$		0			0
$827$		−	32.0733i		−	1.11530i	−0.830077	−	0.557648i	$-0.811704\pi$
$827$		−	32.0733i		−	1.11530i	0.830077	−	0.557648i	$-0.188296\pi$
$828$		0			0
$829$	14.0640	+	8.11986i	0.488463	+	0.282014i	0.723937	−	0.689866i	$-0.242331\pi$
$829$	14.0640	+	8.11986i	0.488463	+	0.282014i	−0.235474	+	0.971881i	$0.575664\pi$
$830$			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	0.841754	−	0.539862i	$-0.181523\pi$
$839$	−1.35145	−	2.34077i	−0.0466571	−	0.0808125i	−0.888411	+	0.459049i	$0.848190\pi$
$840$		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	0.418897	−	0.908034i	$-0.362417\pi$
$853$	41.3187	−	23.8554i	1.41473	−	0.816793i	0.995829	+	0.0912411i	$0.0290834\pi$
$854$		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	$0.195003\pi$
$859$			33.7058i			1.15003i	−0.818144	+	0.575014i	$0.804997\pi$
$860$	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	−0.193537	−	0.981093i	$-0.561996\pi$
$863$	16.4318	−	9.48693i	0.559347	−	0.322939i	0.752883	+	0.658154i	$0.228662\pi$
$864$		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	−0.471956	−	0.881622i	$-0.656452\pi$
$911$	1.67736	−	0.968423i	0.0555734	−	0.0320853i	0.527529	+	0.849537i	$0.323119\pi$
$912$		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	0.932039	−	0.362357i	$-0.118028\pi$
$919$	4.61421	+	7.99205i	0.152209	+	0.263634i	−0.779830	+	0.625991i	$0.784695\pi$
$920$	−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	0.0192794	−	0.999814i	$-0.493863\pi$
$929$	26.6849	−	46.2197i	0.875504	−	1.51642i	0.856225	−	0.516603i	$-0.172804\pi$
$930$		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	$0.154945\pi$
$937$			28.6378i			0.935555i	−0.883846	+	0.467778i	$0.845055\pi$
$938$		0			0
$939$		0			0
$940$	45.0959			1.47087
$941$	−0.688308	−	1.19218i	−0.0224382	−	0.0388641i	0.854588	−	0.519306i	$-0.173810\pi$
$941$	−0.688308	−	1.19218i	−0.0224382	−	0.0388641i	−0.877026	+	0.480442i	$0.840476\pi$
$942$		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	0.999464	+	0.0327450i	$0.0104249\pi$
$947$	47.0080	+	27.1401i	1.52755	+	0.881933i	0.528090	+	0.849188i	$0.322908\pi$
$948$		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	$0.0585867\pi$
$953$			11.2998i			0.366036i	−0.983110	+	0.183018i	$0.941413\pi$
$954$		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	−0.754696	−	0.656074i	$-0.772216\pi$
$967$	5.93412	−	10.2782i	0.190829	−	0.330525i	0.945525	+	0.325549i	$0.105549\pi$
$968$			75.0929i			2.41358i
$969$		0			0
$970$	32.8907			1.05606
$971$	28.0837	+	48.6424i	0.901249	+	1.56101i	0.825875	+	0.563853i	$0.190682\pi$
$971$	28.0837	+	48.6424i	0.901249	+	1.56101i	0.0753736	+	0.997155i	$0.475985\pi$
$972$		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	−0.769147	−	0.639072i	$-0.779319\pi$
$977$	−18.7626	+	10.8326i	−0.600268	+	0.346565i	0.168879	+	0.985637i	$0.445985\pi$
$978$		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	−0.993998	−	0.109402i	$-0.965107\pi$
$991$	−12.6630	+	21.9330i	−0.402254	+	0.696725i	0.591743	+	0.806126i	$0.298440\pi$
$992$	−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	$-0.971909\pi$
$997$		−	5.56584i		−	0.176272i	0.996108	−	0.0881360i	$-0.0280910\pi$
$998$	−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.962.5		10
3.2	odd	2		441.2.s.b.374.1		10
7.2	even	3		189.2.i.b.152.1		10
7.3	odd	6		1323.2.o.d.881.1		10
7.4	even	3		1323.2.o.c.881.1		10
7.5	odd	6		1323.2.i.b.1097.1		10
7.6	odd	2		189.2.s.b.17.5		10
9.2	odd	6		1323.2.i.b.521.5		10
9.7	even	3		441.2.i.b.227.1		10
21.2	odd	6		63.2.i.b.5.5	✓	10
21.5	even	6		441.2.i.b.68.5		10
21.11	odd	6		441.2.o.d.293.5		10
21.17	even	6		441.2.o.c.293.5		10
21.20	even	2		63.2.s.b.59.1	yes	10
28.23	odd	6		3024.2.ca.b.2609.2		10
28.27	even	2		3024.2.df.b.17.2		10
63.2	odd	6		189.2.s.b.89.5		10
63.11	odd	6		1323.2.o.d.440.1		10
63.13	odd	6		567.2.p.d.80.1		10
63.16	even	3		63.2.s.b.47.1	yes	10
63.20	even	6		189.2.i.b.143.5		10
63.23	odd	6		567.2.p.d.404.1		10
63.25	even	3		441.2.o.c.146.5		10
63.34	odd	6		63.2.i.b.38.1	yes	10
63.38	even	6		1323.2.o.c.440.1		10
63.41	even	6		567.2.p.c.80.5		10
63.47	even	6	inner	1323.2.s.b.656.5		10
63.52	odd	6		441.2.o.d.146.5		10
63.58	even	3		567.2.p.c.404.5		10
63.61	odd	6		441.2.s.b.362.1		10
84.23	even	6		1008.2.ca.b.257.1		10
84.83	odd	2		1008.2.df.b.689.1		10
252.79	odd	6		1008.2.df.b.929.1		10
252.83	odd	6		3024.2.ca.b.2033.2		10
252.191	even	6		3024.2.df.b.1601.2		10
252.223	even	6		1008.2.ca.b.353.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.5	✓	10	21.2	odd	6
63.2.i.b.38.1	yes	10	63.34	odd	6
63.2.s.b.47.1	yes	10	63.16	even	3
63.2.s.b.59.1	yes	10	21.20	even	2
189.2.i.b.143.5		10	63.20	even	6
189.2.i.b.152.1		10	7.2	even	3
189.2.s.b.17.5		10	7.6	odd	2
189.2.s.b.89.5		10	63.2	odd	6
441.2.i.b.68.5		10	21.5	even	6
441.2.i.b.227.1		10	9.7	even	3
441.2.o.c.146.5		10	63.25	even	3
441.2.o.c.293.5		10	21.17	even	6
441.2.o.d.146.5		10	63.52	odd	6
441.2.o.d.293.5		10	21.11	odd	6
441.2.s.b.362.1		10	63.61	odd	6
441.2.s.b.374.1		10	3.2	odd	2
567.2.p.c.80.5		10	63.41	even	6
567.2.p.c.404.5		10	63.58	even	3
567.2.p.d.80.1		10	63.13	odd	6
567.2.p.d.404.1		10	63.23	odd	6
1008.2.ca.b.257.1		10	84.23	even	6
1008.2.ca.b.353.1		10	252.223	even	6
1008.2.df.b.689.1		10	84.83	odd	2
1008.2.df.b.929.1		10	252.79	odd	6
1323.2.i.b.521.5		10	9.2	odd	6
1323.2.i.b.1097.1		10	7.5	odd	6
1323.2.o.c.440.1		10	63.38	even	6
1323.2.o.c.881.1		10	7.4	even	3
1323.2.o.d.440.1		10	63.11	odd	6
1323.2.o.d.881.1		10	7.3	odd	6
1323.2.s.b.656.5		10	63.47	even	6	inner
1323.2.s.b.962.5		10	1.1	even	1	trivial
3024.2.ca.b.2033.2		10	252.83	odd	6
3024.2.ca.b.2609.2		10	28.23	odd	6
3024.2.df.b.17.2		10	28.27	even	2
3024.2.df.b.1601.2		10	252.191	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
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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