LMFDB - Embedded newform 1323.2.o.d.881.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (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			881.1
Root			$1.07065 - 1.85442i$ of defining polynomial
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.d.440.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24607 + 1.29677i) q^{2} +(2.36322 - 4.09323i) q^{4} +(0.626493 - 1.08512i) q^{5} +7.07116i q^{8} +O(q^{10})$	\(q+(-2.24607 + 1.29677i) q^{2} +(2.36322 - 4.09323i) q^{4} +(0.626493 - 1.08512i) q^{5} +7.07116i q^{8} +3.24967i q^{10} +(-0.534126 + 0.308378i) q^{11} +(-1.06343 - 0.613974i) q^{13} +(-4.44321 - 7.69587i) q^{16} -4.43003 q^{17} -1.90155i q^{19} +(-2.96109 - 5.12875i) q^{20} +(0.799790 - 1.38528i) q^{22} +(-4.11267 - 2.37445i) q^{23} +(1.71501 + 2.97049i) q^{25} +3.18473 q^{26} +(5.07629 - 2.93080i) q^{29} +(2.14851 + 1.24044i) q^{31} +(7.71195 + 4.45249i) q^{32} +(9.95016 - 5.74473i) q^{34} -2.66433 q^{37} +(2.46587 + 4.27102i) q^{38} +(7.67303 + 4.43003i) q^{40} +(-2.09966 + 3.63671i) q^{41} +(-2.24637 - 3.89083i) q^{43} +2.91506i q^{44} +12.3165 q^{46} +(-3.80738 - 6.59458i) q^{47} +(-7.70409 - 4.44796i) q^{50} +(-5.02627 + 2.90192i) q^{52} +3.09208i q^{53} +0.772786i q^{55} +(-7.60114 + 13.1656i) q^{58} +(-1.78229 + 3.08702i) q^{59} +(-12.5136 + 7.22473i) q^{61} -6.43428 q^{62} -5.32259 q^{64} +(-1.33247 + 0.769301i) q^{65} +(-6.80644 + 11.7891i) q^{67} +(-10.4692 + 18.1331i) q^{68} +10.4095i q^{71} -11.4895i q^{73} +(5.98429 - 3.45503i) q^{74} +(-7.78348 - 4.49379i) q^{76} +(2.01592 + 3.49168i) q^{79} -11.1346 q^{80} -10.8911i q^{82} +(-4.36775 - 7.56516i) q^{83} +(-2.77538 + 4.80710i) q^{85} +(10.0910 + 5.82605i) q^{86} +(-2.18059 - 3.77689i) q^{88} -1.62245 q^{89} +(-19.4383 + 11.2227i) q^{92} +(17.1033 + 9.87459i) q^{94} +(-2.06341 - 1.19131i) q^{95} +(-8.76527 + 5.06063i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4}+O(q^{10}) $ 10 * q + 4 * q^4	$ 10 q + 4 q^{4} - 12 q^{11} + 6 q^{13} - 6 q^{16} - 24 q^{17} + 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 6 q^{26} + 15 q^{29} + 9 q^{31} + 48 q^{32} + 3 q^{34} - 12 q^{37} + 18 q^{38} + 15 q^{40} + 9 q^{41} + 3 q^{43} + 26 q^{46} - 15 q^{47} - 3 q^{50} - 12 q^{52} + 8 q^{58} + 18 q^{59} - 12 q^{61} - 12 q^{62} + 6 q^{64} - 3 q^{65} - 10 q^{67} - 27 q^{68} - 30 q^{74} + 9 q^{76} + 20 q^{79} - 60 q^{80} + 15 q^{83} + 18 q^{85} + 54 q^{86} - 8 q^{88} + 48 q^{89} - 39 q^{92} + 3 q^{94} + 6 q^{97}+O(q^{100}) $ 10 * q + 4 * q^4 - 12 * q^11 + 6 * q^13 - 6 * q^16 - 24 * q^17 + 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 6 * q^26 + 15 * q^29 + 9 * q^31 + 48 * q^32 + 3 * q^34 - 12 * q^37 + 18 * q^38 + 15 * q^40 + 9 * q^41 + 3 * q^43 + 26 * q^46 - 15 * q^47 - 3 * q^50 - 12 * q^52 + 8 * q^58 + 18 * q^59 - 12 * q^61 - 12 * q^62 + 6 * q^64 - 3 * q^65 - 10 * q^67 - 27 * q^68 - 30 * q^74 + 9 * q^76 + 20 * q^79 - 60 * q^80 + 15 * q^83 + 18 * q^85 + 54 * q^86 - 8 * q^88 + 48 * 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 $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

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

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	$0.702694\pi$
$2$	−2.24607	+	1.29677i	−1.58821	+	0.916955i	−0.993602	+	0.112941i	$0.963973\pi$
$3$		0			0
$3$		0			0
$4$	2.36322	−	4.09323i	1.18161	−	2.04661i
$5$	0.626493	−	1.08512i	0.280176	−	0.485279i	−0.691252	−	0.722614i	$-0.742941\pi$
$5$	0.626493	−	1.08512i	0.280176	−	0.485279i	0.971428	+	0.237335i	$0.0762738\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			7.07116i			2.50003i
$9$		0			0
$10$			3.24967i			1.02763i
$11$	−0.534126	+	0.308378i	−0.161045	+	0.0929794i	−0.578357	−	0.815784i	$-0.696306\pi$
$11$	−0.534126	+	0.308378i	−0.161045	+	0.0929794i	0.417311	+	0.908764i	$0.362972\pi$
$12$		0			0
$13$	−1.06343	−	0.613974i	−0.294944	−	0.170286i	0.345226	−	0.938520i	$-0.387802\pi$
$13$	−1.06343	−	0.613974i	−0.294944	−	0.170286i	−0.640169	+	0.768234i	$0.721136\pi$
$14$		0			0
$15$		0			0
$16$	−4.44321	−	7.69587i	−1.11080	−	1.92397i
$17$	−4.43003			−1.07444			−0.537220	−	0.843442i	$-0.680525\pi$
$17$	−4.43003			−1.07444			−0.537220	+	0.843442i	$0.680525\pi$
$18$		0			0
$19$		−	1.90155i		−	0.436246i	−0.975921	−	0.218123i	$-0.930007\pi$
$19$		−	1.90155i		−	0.436246i	0.975921	−	0.218123i	$-0.0699933\pi$
$20$	−2.96109	−	5.12875i	−0.662119	−	1.14682i
$21$		0			0
$22$	0.799790	−	1.38528i	0.170516	−	0.295342i
$23$	−4.11267	−	2.37445i	−0.857550	−	0.495107i	0.00564111	−	0.999984i	$-0.498204\pi$
$23$	−4.11267	−	2.37445i	−0.857550	−	0.495107i	−0.863191	+	0.504877i	$0.831538\pi$
$24$		0			0
$25$	1.71501	+	2.97049i	0.343003	+	0.594098i
$26$	3.18473			0.624578
$27$		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	0.680375	−	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
$37$	−2.66433			−0.438014			−0.219007	−	0.975723i	$-0.570282\pi$
$37$	−2.66433			−0.438014			−0.219007	+	0.975723i	$0.570282\pi$
$38$	2.46587	+	4.27102i	0.400018	+	0.692851i
$39$		0			0
$40$	7.67303	+	4.43003i	1.21321	+	0.700449i
$41$	−2.09966	+	3.63671i	−0.327911	+	0.567959i	−0.982097	−	0.188375i	$-0.939678\pi$
$41$	−2.09966	+	3.63671i	−0.327911	+	0.567959i	0.654186	+	0.756334i	$0.273011\pi$
$42$		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	$0.944630\pi$
$44$			2.91506i			0.439463i
$45$		0			0
$46$	12.3165			1.81596
$47$	−3.80738	−	6.59458i	−0.555364	−	0.961918i	−0.997875	−	0.0651551i	$-0.979246\pi$
$47$	−3.80738	−	6.59458i	−0.555364	−	0.961918i	0.442512	−	0.896763i	$-0.354088\pi$
$48$		0			0
$49$		0			0
$50$	−7.70409	−	4.44796i	−1.08952	−	0.629036i
$51$		0			0
$52$	−5.02627	+	2.90192i	−0.697018	+	0.402424i
$53$			3.09208i			0.424730i	0.977190	+	0.212365i	$0.0681165\pi$
$53$			3.09208i			0.424730i	−0.977190	+	0.212365i	$0.931883\pi$
$54$		0			0
$55$			0.772786i			0.104202i
$56$		0			0
$57$		0			0
$58$	−7.60114	+	13.1656i	−0.998078	+	1.72872i
$59$	−1.78229	+	3.08702i	−0.232035	+	0.401896i	−0.958407	−	0.285406i	$-0.907872\pi$
$59$	−1.78229	+	3.08702i	−0.232035	+	0.401896i	0.726372	+	0.687302i	$0.241205\pi$
$60$		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	$0.854127\pi$
$68$	−10.4692	+	18.1331i	−1.26957	+	2.19896i
$69$		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
$73$		−	11.4895i		−	1.34474i	−0.740216	−	0.672369i	$-0.765277\pi$
$73$		−	11.4895i		−	1.34474i	0.740216	−	0.672369i	$-0.234723\pi$
$74$	5.98429	−	3.45503i	0.695659	−	0.401639i
$75$		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	$0.760504\pi$
$80$	−11.1346			−1.24488
$81$		0			0
$82$		−	10.8911i		−	1.20272i
$83$	−4.36775	−	7.56516i	−0.479422	−	0.830384i	0.520299	−	0.853984i	$-0.325820\pi$
$83$	−4.36775	−	7.56516i	−0.479422	−	0.830384i	−0.999721	+	0.0236001i	$0.992487\pi$
$84$		0			0
$85$	−2.77538	+	4.80710i	−0.301032	+	0.521403i
$86$	10.0910	+	5.82605i	1.08814	+	0.628240i
$87$		0			0
$88$	−2.18059	−	3.77689i	−0.232451	−	0.402618i
$89$	−1.62245			−0.171979			−0.0859897	−	0.996296i	$-0.527405\pi$
$89$	−1.62245			−0.171979			−0.0859897	+	0.996296i	$0.527405\pi$
$90$		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	$-0.838440\pi$
$97$	−8.76527	+	5.06063i	−0.889979	+	0.513829i	−0.0160431	+	0.999871i	$0.505107\pi$
$98$		0			0
$99$		0			0
$100$	16.2119			1.62119
$101$	−0.856611	−	1.48369i	−0.0852360	−	0.147633i	0.820256	−	0.571997i	$-0.193831\pi$
$101$	−0.856611	−	1.48369i	−0.0852360	−	0.147633i	−0.905492	+	0.424364i	$0.860498\pi$
$102$		0			0
$103$	−6.41315	−	3.70263i	−0.631906	−	0.364831i	0.149584	−	0.988749i	$-0.452207\pi$
$103$	−6.41315	−	3.70263i	−0.631906	−	0.364831i	−0.781490	+	0.623918i	$0.785540\pi$
$104$	4.34151	−	7.51971i	0.425720	−	0.737368i
$105$		0			0
$106$	−4.00972	−	6.94503i	−0.389458	−	0.674561i
$107$			0.152025i			0.0146968i	0.999973	+	0.00734839i	$0.00233909\pi$
$107$			0.152025i			0.0146968i	−0.999973	+	0.00734839i	$0.997661\pi$
$108$		0			0
$109$	−5.40102			−0.517324			−0.258662	−	0.965968i	$-0.583282\pi$
$109$	−5.40102			−0.517324			−0.258662	+	0.965968i	$0.583282\pi$
$110$	−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
$115$	−5.15311	+	2.97515i	−0.480530	+	0.277434i
$116$		−	27.7045i		−	2.57230i
$117$		0			0
$118$		−	9.24490i		−	0.851062i
$119$		0			0
$120$		0			0
$121$	−5.30981	+	9.19685i	−0.482710	+	0.836078i
$122$	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
$131$	8.11382	−	14.0535i	0.708908	−	1.22786i	−0.256355	−	0.966583i	$-0.582522\pi$
$131$	8.11382	−	14.0535i	0.708908	−	1.22786i	0.965263	−	0.261281i	$-0.0841450\pi$
$132$		0			0
$133$		0			0
$134$		−	35.3055i		−	3.04993i
$135$		0			0
$136$		−	31.3254i		−	2.68613i
$137$	−15.0711	+	8.70129i	−1.28761	+	0.743402i	−0.978227	−	0.207536i	$-0.933456\pi$
$137$	−15.0711	+	8.70129i	−1.28761	+	0.743402i	−0.309382	+	0.950938i	$0.600122\pi$
$138$		0			0
$139$	5.45273	+	3.14813i	0.462494	+	0.267021i	0.713092	−	0.701070i	$-0.247294\pi$
$139$	5.45273	+	3.14813i	0.462494	+	0.267021i	−0.250598	+	0.968091i	$0.580627\pi$
$140$		0			0
$141$		0			0
$142$	−13.4988	−	23.3805i	−1.13279	−	1.96205i
$143$	0.757344			0.0633323
$144$		0			0
$145$		−	7.34449i		−	0.609927i
$146$	14.8992	+	25.8061i	1.23306	+	2.13573i
$147$		0			0
$148$	−6.29642	+	10.9057i	−0.517563	+	0.896445i
$149$	−9.20319	−	5.31346i	−0.753954	−	0.435296i	0.0731665	−	0.997320i	$-0.476690\pi$
$149$	−9.20319	−	5.31346i	−0.753954	−	0.435296i	−0.827121	+	0.562024i	$0.810023\pi$
$150$		0			0
$151$	−4.74465	−	8.21798i	−0.386114	−	0.668770i	0.605809	−	0.795610i	$-0.292850\pi$
$151$	−4.74465	−	8.21798i	−0.386114	−	0.668770i	−0.991923	+	0.126841i	$0.959516\pi$
$152$	13.4462			1.09063
$153$		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
$163$	8.82201			0.690993			0.345497	−	0.938420i	$-0.387710\pi$
$163$	8.82201			0.690993			0.345497	+	0.938420i	$0.387710\pi$
$164$	9.92392	+	17.1887i	0.774928	+	1.34221i
$165$		0			0
$166$	19.6205	+	11.3279i	1.52285	+	0.879217i
$167$	11.0335	−	19.1106i	0.853800	−	1.47883i	−0.0239535	−	0.999713i	$-0.507625\pi$
$167$	11.0335	−	19.1106i	0.853800	−	1.47883i	0.877754	−	0.479112i	$-0.159041\pi$
$168$		0			0
$169$	−5.74607	−	9.95249i	−0.442005	−	0.765576i
$170$		−	14.3961i		−	1.10413i
$171$		0			0
$172$	−21.2347			−1.61913
$173$	−2.03375	−	3.52256i	−0.154623	−	0.267815i	0.778299	−	0.627894i	$-0.216083\pi$
$173$	−2.03375	−	3.52256i	−0.154623	−	0.267815i	−0.932922	+	0.360079i	$0.882750\pi$
$174$		0			0
$175$		0			0
$176$	4.74647	+	2.74038i	0.357779	+	0.206564i
$177$		0			0
$178$	3.64414	−	2.10395i	0.273140	−	0.157697i
$179$			8.32293i			0.622085i	0.950396	+	0.311042i	$0.100678\pi$
$179$			8.32293i			0.622085i	−0.950396	+	0.311042i	$0.899322\pi$
$180$		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
$184$	16.7901	−	29.0813i	1.23778	−	2.14390i
$185$	−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	$-0.710573\pi$
$191$	−3.29133	+	1.90025i	−0.238152	+	0.137497i	0.376175	+	0.926549i	$0.377239\pi$
$192$		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	$0.245238\pi$
$194$	13.1250	−	22.7331i	0.942317	−	1.63214i
$195$		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
$199$			16.0413i			1.13714i	0.822637	+	0.568568i	$0.192502\pi$
$199$			16.0413i			1.13714i	−0.822637	+	0.568568i	$0.807498\pi$
$200$	−21.0048	+	12.1271i	−1.48526	+	0.857518i
$201$		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
$206$	19.2058			1.33813
$207$		0			0
$208$			10.9121i			0.756616i
$209$	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	$0.256852\pi$
$212$	12.6566	+	7.30728i	0.869257	+	0.501866i
$213$		0			0
$214$	−0.197141	−	0.341458i	−0.0134763	−	0.0233416i
$215$	−5.62934			−0.383918
$216$		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	$-0.753415\pi$
$223$	−6.96205	+	4.01954i	−0.466213	+	0.269168i	0.248440	+	0.968647i	$0.420082\pi$
$224$		0			0
$225$		0			0
$226$	−16.7824			−1.11635
$227$	−10.4117	−	18.0336i	−0.691048	−	1.19693i	−0.971495	−	0.237061i	$-0.923816\pi$
$227$	−10.4117	−	18.0336i	−0.691048	−	1.19693i	0.280447	−	0.959870i	$-0.409517\pi$
$228$		0			0
$229$	5.21276	+	3.00959i	0.344469	+	0.198879i	0.662247	−	0.749286i	$-0.269603\pi$
$229$	5.21276	+	3.00959i	0.344469	+	0.198879i	−0.317777	+	0.948165i	$0.602936\pi$
$230$	7.71617	−	13.3648i	0.508789	−	0.881248i
$231$		0			0
$232$	20.7241	+	35.8952i	1.36061	+	2.35664i
$233$			21.0336i			1.37796i	0.724782	+	0.688978i	$0.241940\pi$
$233$			21.0336i			1.37796i	−0.724782	+	0.688978i	$0.758060\pi$
$234$		0			0
$235$	−9.54118			−0.622398
$236$	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
$241$	7.33797	−	4.23658i	0.472680	−	0.272902i	−0.244681	−	0.969604i	$-0.578683\pi$
$241$	7.33797	−	4.23658i	0.472680	−	0.272902i	0.717361	+	0.696702i	$0.245350\pi$
$242$		−	27.5424i		−	1.77049i
$243$		0			0
$244$			68.2946i			4.37211i
$245$		0			0
$246$		0			0
$247$	−1.16750	+	2.02217i	−0.0742864	+	0.128668i
$248$	−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	$-0.765113\pi$
$251$	−23.4435			−1.47974			−0.739871	+	0.672749i	$0.765113\pi$
$252$		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
$257$	−12.2585	+	21.2324i	−0.764665	+	1.32444i	0.175758	+	0.984433i	$0.443762\pi$
$257$	−12.2585	+	21.2324i	−0.764665	+	1.32444i	−0.940423	+	0.340005i	$0.889571\pi$
$258$		0			0
$259$		0			0
$260$			7.27212i			0.450998i
$261$		0			0
$262$			42.0870i			2.60014i
$263$	9.14036	−	5.27719i	0.563619	−	0.325406i	−0.190978	−	0.981594i	$-0.561166\pi$
$263$	9.14036	−	5.27719i	0.563619	−	0.325406i	0.754597	+	0.656189i	$0.227833\pi$
$264$		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
$269$	2.28902			0.139564			0.0697821	−	0.997562i	$-0.477770\pi$
$269$	2.28902			0.139564			0.0697821	+	0.997562i	$0.477770\pi$
$270$		0			0
$271$		−	24.1608i		−	1.46766i	−0.679332	−	0.733831i	$-0.737730\pi$
$271$		−	24.1608i		−	1.46766i	0.679332	−	0.733831i	$-0.262270\pi$
$272$	19.6836	+	34.0929i	1.19349	+	2.06719i
$273$		0			0
$274$	22.5672	−	39.0875i	1.36333	−	2.36136i
$275$	−1.83207	−	1.05774i	−0.110478	−	0.0637844i
$276$		0			0
$277$	5.68551	+	9.84760i	0.341609	+	0.591685i	0.984732	−	0.174079i	$-0.0556947\pi$
$277$	5.68551	+	9.84760i	0.341609	+	0.591685i	−0.643122	+	0.765763i	$0.722361\pi$
$278$	−16.3296			−0.979386
$279$		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	0.153169	−	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
$289$	2.62515			0.154421
$290$	9.52411	+	16.4962i	0.559275	+	0.968693i
$291$		0			0
$292$	−47.0289	−	27.1522i	−2.75216	−	1.58896i
$293$	−13.4674	+	23.3262i	−0.786773	+	1.36273i	0.141161	+	0.989987i	$0.454917\pi$
$293$	−13.4674	+	23.3262i	−0.786773	+	1.36273i	−0.927934	+	0.372745i	$0.878417\pi$
$294$		0			0
$295$	2.23319	+	3.86799i	0.130021	+	0.225203i
$296$		−	18.8399i		−	1.09505i
$297$		0			0
$298$	27.5614			1.59659
$299$	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
$304$	−14.6341	+	8.44899i	−0.839322	+	0.484583i
$305$			18.1050i			1.03669i
$306$		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
$310$	−4.03103	+	6.98195i	−0.228947	+	0.396548i
$311$	−8.11558	+	14.0566i	−0.460192	+	0.797076i	−0.998970	−	0.0453714i	$-0.985553\pi$
$311$	−8.11558	+	14.0566i	−0.460192	+	0.797076i	0.538778	+	0.842448i	$0.318886\pi$
$312$		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	0.0828017	−	0.996566i	$-0.473613\pi$
$317$	17.5776	−	10.1484i	0.987254	−	0.569991i	0.904452	+	0.426575i	$0.140280\pi$
$318$		0			0
$319$	−1.80759	+	3.13083i	−0.101205	+	0.175293i
$320$	−3.33456	+	5.77563i	−0.186408	+	0.322868i
$321$		0			0
$322$		0			0
$323$			8.42392i			0.468720i
$324$		0			0
$325$		−	4.21190i		−	0.233634i
$326$	−19.8149	+	11.4401i	−1.09744	+	0.633610i
$327$		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	$-0.425943\pi$
$332$	−41.2879			−2.26597
$333$		0			0
$334$			57.2318i			3.13158i
$335$	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	$0.196823\pi$
$338$	25.8122	+	14.9027i	1.40400	+	0.810598i
$339$		0			0
$340$	13.1177	+	22.7205i	0.711407	+	1.23219i
$341$	−1.53010			−0.0828596
$342$		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	$-0.252072\pi$
$347$	8.14765	+	4.70405i	0.437389	+	0.252527i	−0.265101	+	0.964221i	$0.585405\pi$
$348$		0			0
$349$	−12.3253	+	7.11603i	−0.659759	+	0.380912i	−0.792185	−	0.610281i	$-0.791057\pi$
$349$	−12.3253	+	7.11603i	−0.659759	+	0.380912i	0.132426	+	0.991193i	$0.457723\pi$
$350$		0			0
$351$		0			0
$352$	−5.49220			−0.292735
$353$	8.58262	+	14.8655i	0.456807	+	0.791213i	0.998790	−	0.0491765i	$-0.0156597\pi$
$353$	8.58262	+	14.8655i	0.456807	+	0.791213i	−0.541983	+	0.840389i	$0.682326\pi$
$354$		0			0
$355$	11.2956	+	6.52149i	0.599506	+	0.346125i
$356$	−3.83422	+	6.64106i	−0.203213	+	0.351975i
$357$		0			0
$358$	−10.7929	−	18.6939i	−0.570424	−	0.988003i
$359$		−	28.2561i		−	1.49130i	−0.666338	−	0.745650i	$-0.732139\pi$
$359$		−	28.2561i		−	1.49130i	0.666338	−	0.745650i	$-0.267861\pi$
$360$		0			0
$361$	15.3841			0.809690
$362$	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
$367$	19.9796	−	11.5352i	1.04293	−	0.602133i	0.122265	−	0.992498i	$-0.460984\pi$
$367$	19.9796	−	11.5352i	1.04293	−	0.602133i	0.920661	+	0.390364i	$0.127651\pi$
$368$			42.2007i			2.19986i
$369$		0			0
$370$		−	8.65820i		−	0.450118i
$371$		0			0
$372$		0			0
$373$	6.93635	−	12.0141i	0.359150	−	0.622067i	−0.628669	−	0.777673i	$-0.716400\pi$
$373$	6.93635	−	12.0141i	0.359150	−	0.622067i	0.987819	+	0.155607i	$0.0497332\pi$
$374$	−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
$383$	−7.61598	+	13.1913i	−0.389158	+	0.674042i	−0.992337	−	0.123564i	$-0.960567\pi$
$383$	−7.61598	+	13.1913i	−0.389158	+	0.674042i	0.603178	+	0.797606i	$0.293901\pi$
$384$		0			0
$385$		0			0
$386$		−	17.6075i		−	0.896196i
$387$		0			0
$388$			47.8376i			2.42859i
$389$	12.2525	−	7.07396i	0.621224	−	0.358664i	−0.156121	−	0.987738i	$-0.549899\pi$
$389$	12.2525	−	7.07396i	0.621224	−	0.358664i	0.777346	+	0.629074i	$0.216566\pi$
$390$		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
$395$	5.05184			0.254186
$396$		0			0
$397$			9.70742i			0.487202i	0.969876	+	0.243601i	$0.0783287\pi$
$397$			9.70742i			0.487202i	−0.969876	+	0.243601i	$0.921671\pi$
$398$	−20.8018	−	36.0298i	−1.04270	−	1.80601i
$399$		0			0
$400$	15.2403	−	26.3970i	0.762017	−	1.31985i
$401$	−7.56156	−	4.36567i	−0.377606	−	0.218011i	0.299170	−	0.954200i	$-0.403290\pi$
$401$	−7.56156	−	4.36567i	−0.377606	−	0.218011i	−0.676776	+	0.736189i	$0.736624\pi$
$402$		0			0
$403$	−1.52320	−	2.63826i	−0.0758760	−	0.131421i
$404$	−8.09746			−0.402864
$405$		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
$415$	−10.9454			−0.537291
$416$	−5.46743	−	9.46987i	−0.268063	−	0.464299i
$417$		0			0
$418$	−2.63418	−	1.52084i	−0.128842	−	0.0743868i
$419$	2.13859	−	3.70414i	0.104477	−	0.180959i	−0.809048	−	0.587743i	$-0.800017\pi$
$419$	2.13859	−	3.70414i	0.104477	−	0.180959i	0.913524	+	0.406784i	$0.133350\pi$
$420$		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	$0.742648\pi$
$422$		−	21.0632i		−	1.02534i
$423$		0			0
$424$	−21.8646			−1.06184
$425$	−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
$430$	12.6439	−	7.29996i	0.609743	−	0.352035i
$431$		−	16.6851i		−	0.803692i	−0.915707	−	0.401846i	$-0.868369\pi$
$431$		−	16.6851i		−	0.803692i	0.915707	−	0.401846i	$-0.131631\pi$
$432$		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
$436$	−12.7638	+	22.1076i	−0.611276	+	1.05876i
$437$	−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	−0.597089	−	0.802175i	$-0.703676\pi$
$443$	−4.22906	+	2.44165i	−0.200929	+	0.116006i	0.396160	+	0.918182i	$0.370343\pi$
$444$		0			0
$445$	−1.01645	+	1.76055i	−0.0481845	+	0.0834580i
$446$	10.4248	−	18.0563i	0.493630	−	0.854993i
$447$		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
$451$		−	2.58995i		−	0.121956i
$452$	26.4866	−	15.2920i	1.24582	−	0.719277i
$453$		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	$0.752236\pi$
$458$	−15.6110			−0.729454
$459$		0			0
$460$			28.1238i			1.31128i
$461$	0.333303	+	0.577297i	0.0155235	+	0.0268874i	0.873683	−	0.486496i	$-0.161725\pi$
$461$	0.333303	+	0.577297i	0.0155235	+	0.0268874i	−0.858159	+	0.513383i	$0.828392\pi$
$462$		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	$0.749717\pi$
$464$	−45.1101	−	26.0443i	−2.09418	−	1.20908i
$465$		0			0
$466$	−27.2757	−	47.2429i	−1.26352	−	2.18849i
$467$	39.3135			1.81921			0.909606	−	0.415471i	$-0.136383\pi$
$467$	39.3135			1.81921			0.909606	+	0.415471i	$0.136383\pi$
$468$		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
$478$	−22.4930			−1.02881
$479$	−19.0577	−	33.0088i	−0.870767	−	1.50821i	−0.861205	−	0.508258i	$-0.830290\pi$
$479$	−19.0577	−	33.0088i	−0.870767	−	1.50821i	−0.00956182	−	0.999954i	$-0.503044\pi$
$480$		0			0
$481$	2.83335	+	1.63583i	0.129189	+	0.0745875i
$482$	−10.9877	+	19.0313i	−0.500477	+	0.866852i
$483$		0			0
$484$	25.0965	+	43.4685i	1.14075	+	1.97584i
$485$			12.6818i			0.575851i
$486$		0			0
$487$	7.60554			0.344640			0.172320	−	0.985041i	$-0.444874\pi$
$487$	7.60554			0.344640			0.172320	+	0.985041i	$0.444874\pi$
$488$	−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
$493$	−22.4881	+	12.9835i	−1.01281	+	0.584748i
$494$		−	6.05593i		−	0.272469i
$495$		0			0
$496$		−	22.0462i		−	0.989904i
$497$		0			0
$498$		0			0
$499$	16.0794	−	27.8503i	0.719812	−	1.24675i	−0.241262	−	0.970460i	$-0.577561\pi$
$499$	16.0794	−	27.8503i	0.719812	−	1.24675i	0.961074	−	0.276291i	$-0.0891053\pi$
$500$	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	$-0.496979\pi$
$503$	0.425693			0.0189807			0.00949035	+	0.999955i	$0.496979\pi$
$504$		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
$509$	−12.8963	+	22.3370i	−0.571617	+	0.990071i	0.424783	+	0.905295i	$0.360351\pi$
$509$	−12.8963	+	22.3370i	−0.571617	+	0.990071i	−0.996400	+	0.0847751i	$0.972983\pi$
$510$		0			0
$511$		0			0
$512$			46.5411i			2.05684i
$513$		0			0
$514$		−	63.5859i		−	2.80465i
$515$	−8.03558	+	4.63934i	−0.354090	+	0.204434i
$516$		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
$521$	−18.1435			−0.794880			−0.397440	−	0.917628i	$-0.630101\pi$
$521$	−18.1435			−0.794880			−0.397440	+	0.917628i	$0.630101\pi$
$522$		0			0
$523$			13.9399i			0.609551i	0.952424	+	0.304776i	$0.0985814\pi$
$523$			13.9399i			0.609551i	−0.952424	+	0.304776i	$0.901419\pi$
$524$	−38.3495	−	66.4234i	−1.67531	−	2.90172i
$525$		0			0
$526$	−13.6866	+	23.7059i	−0.596764	+	1.03363i
$527$	−9.51796	−	5.49520i	−0.414609	−	0.239375i
$528$		0			0
$529$	−0.223990	−	0.387962i	−0.00973870	−	0.0168679i
$530$	−10.0482			−0.436467
$531$		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
$541$	29.7152			1.27756			0.638779	−	0.769390i	$-0.279440\pi$
$541$	29.7152			1.27756			0.638779	+	0.769390i	$0.279440\pi$
$542$	31.3310	+	54.2668i	1.34578	+	2.33096i
$543$		0			0
$544$	−34.1641	−	19.7247i	−1.46478	−	0.845688i
$545$	−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	$0.961063\pi$
$548$			82.2524i			3.51365i
$549$		0			0
$550$	5.48661			0.233950
$551$	−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
$556$	25.7720	−	14.8795i	1.09298	−	0.631031i
$557$		−	0.415065i		−	0.0175869i	−0.999961	−	0.00879343i	$-0.997201\pi$
$557$		−	0.415065i		−	0.0175869i	0.999961	−	0.00879343i	$-0.00279907\pi$
$558$		0			0
$559$			5.51686i			0.233338i
$560$		0			0
$561$		0			0
$562$	26.4111	−	45.7454i	1.11409	−	1.92965i
$563$	−1.82962	+	3.16900i	−0.0771095	+	0.133558i	−0.902002	−	0.431733i	$-0.857902\pi$
$563$	−1.82962	+	3.16900i	−0.0771095	+	0.133558i	0.824892	+	0.565290i	$0.191236\pi$
$564$		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	$-0.402687\pi$
$569$	30.4692	−	17.5914i	1.27733	−	0.737470i	0.976358	+	0.216162i	$0.0693538\pi$
$570$		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	$0.0992014\pi$
$572$	1.78977	−	3.09998i	0.0748342	−	0.129617i
$573$		0			0
$574$		0			0
$575$		−	16.2888i		−	0.679292i
$576$		0			0
$577$		−	0.0690132i		−	0.00287306i	−0.999999	−	0.00143653i	$-0.999543\pi$
$577$		−	0.0690132i		−	0.00287306i	0.999999	−	0.00143653i	$-0.000457261\pi$
$578$	−5.89627	+	3.40421i	−0.245253	+	0.141597i
$579$		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
$584$	81.2437			3.36189
$585$		0			0
$586$		−	69.8564i		−	2.88574i
$587$	11.4799	+	19.8838i	0.473827	+	0.820693i	0.999551	−	0.0299626i	$-0.00953881\pi$
$587$	11.4799	+	19.8838i	0.473827	+	0.820693i	−0.525724	+	0.850655i	$0.676205\pi$
$588$		0			0
$589$	2.35877	−	4.08550i	0.0971913	−	0.168340i
$590$	−10.0318	−	5.79186i	−0.413003	−	0.238447i
$591$		0			0
$592$	11.8382	+	20.5044i	0.486547	+	0.842725i
$593$	28.7940			1.18243			0.591213	−	0.806515i	$-0.298649\pi$
$593$	28.7940			1.18243			0.591213	+	0.806515i	$0.298649\pi$
$594$		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	$-0.619242\pi$
$599$	−33.1588	−	19.1442i	−1.35483	−	0.782212i	−0.988922	+	0.148438i	$0.952575\pi$
$600$		0			0
$601$	26.7618	−	15.4509i	1.09164	−	0.630257i	0.157625	−	0.987499i	$-0.449616\pi$
$601$	26.7618	−	15.4509i	1.09164	−	0.630257i	0.934012	+	0.357242i	$0.116283\pi$
$602$		0			0
$603$		0			0
$604$	−44.8507			−1.82495
$605$	6.65311	+	11.5235i	0.270487	+	0.468498i
$606$		0			0
$607$	28.7339	+	16.5895i	1.16627	+	0.673349i	0.952800	−	0.303600i	$-0.0981886\pi$
$607$	28.7339	+	16.5895i	1.16627	+	0.673349i	0.213475	+	0.976949i	$0.431522\pi$
$608$	8.46664	−	14.6647i	0.343368	−	0.594730i
$609$		0			0
$610$	−23.4780	−	40.6650i	−0.950595	−	1.64648i
$611$			9.35053i			0.378282i
$612$		0			0
$613$	4.02327			0.162498			0.0812492	−	0.996694i	$-0.474109\pi$
$613$	4.02327			0.162498			0.0812492	+	0.996694i	$0.474109\pi$
$614$	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
$619$	12.0646	−	6.96550i	0.484917	−	0.279967i	−0.237546	−	0.971376i	$-0.576343\pi$
$619$	12.0646	−	6.96550i	0.484917	−	0.279967i	0.722463	+	0.691409i	$0.243010\pi$
$620$		−	14.6922i		−	0.590054i
$621$		0			0
$622$		−	42.0962i		−	1.68790i
$623$		0			0
$624$		0			0
$625$	−1.95762	+	3.39069i	−0.0783047	+	0.135628i
$626$	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
$635$	−1.83672	+	3.18129i	−0.0728879	+	0.126246i
$636$		0			0
$637$		0			0
$638$		−	9.37609i		−	0.371203i
$639$		0			0
$640$			5.01899i			0.198393i
$641$	36.7821	−	21.2362i	1.45281	−	0.838779i	0.454167	−	0.890917i	$-0.349937\pi$
$641$	36.7821	−	21.2362i	1.45281	−	0.838779i	0.998640	+	0.0521380i	$0.0166036\pi$
$642$		0			0
$643$	−3.13514	−	1.81008i	−0.123638	−	0.0713825i	0.436905	−	0.899507i	$-0.356074\pi$
$643$	−3.13514	−	1.81008i	−0.123638	−	0.0713825i	−0.560544	+	0.828125i	$0.689408\pi$
$644$		0			0
$645$		0			0
$646$	−10.9239	−	18.9207i	−0.429795	−	0.744426i
$647$	12.0123			0.472254			0.236127	−	0.971722i	$-0.424122\pi$
$647$	12.0123			0.472254			0.236127	+	0.971722i	$0.424122\pi$
$648$		0			0
$649$		−	2.19848i		−	0.0862979i
$650$	5.46186	+	9.46022i	0.214232	+	0.371060i
$651$		0			0
$652$	20.8484	−	36.1105i	0.816486	−	1.41420i
$653$	39.9950	+	23.0911i	1.56512	+	0.903625i	0.996724	+	0.0808728i	$0.0257707\pi$
$653$	39.9950	+	23.0911i	1.56512	+	0.903625i	0.568400	+	0.822752i	$0.307563\pi$
$654$		0			0
$655$	−10.1665	−	17.6089i	−0.397238	−	0.688036i
$656$	37.3169			1.45698
$657$		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	0.442903	−	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
$667$	−27.8361			−1.07782
$668$	−52.1494	−	90.3254i	−2.01772	−	3.49480i
$669$		0			0
$670$	−38.3106	−	22.1187i	−1.48007	−	0.854518i
$671$	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	$-0.383995\pi$
$674$		−	9.00781i		−	0.346968i
$675$		0			0
$676$	−54.3170			−2.08912
$677$	16.9228	+	29.3111i	0.650396	+	1.12652i	0.983027	+	0.183461i	$0.0587302\pi$
$677$	16.9228	+	29.3111i	0.650396	+	1.12652i	−0.332631	+	0.943057i	$0.607937\pi$
$678$		0			0
$679$		0			0
$680$	−33.9917	−	19.6251i	−1.30352	−	0.752590i
$681$		0			0
$682$	3.43672	−	1.98419i	0.131599	−	0.0759785i
$683$			5.53814i			0.211911i	0.994371	+	0.105956i	$0.0337901\pi$
$683$			5.53814i			0.211911i	−0.994371	+	0.105956i	$0.966210\pi$
$684$		0			0
$685$			21.8052i			0.833133i
$686$		0			0
$687$		0			0
$688$	−19.9622	+	34.5756i	−0.761052	+	1.31818i
$689$	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
$698$	18.4557	−	31.9662i	0.698559	−	1.20994i
$699$		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
$703$			5.06637i			0.191082i
$704$	2.84293	−	1.64137i	0.107147	−	0.0618614i
$705$		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	$0.751784\pi$
$710$	−33.8275			−1.26952
$711$		0			0
$712$		−	11.4726i		−	0.429954i
$713$	−5.89074	−	10.2031i	−0.220610	−	0.382107i
$714$		0			0
$715$	0.474470	−	0.821807i	0.0177442	−	0.0307338i
$716$	34.0676	+	19.6689i	1.27317	+	0.735063i
$717$		0			0
$718$	36.6417	+	63.4652i	1.36745	+	2.36850i
$719$	−37.7384			−1.40740			−0.703702	−	0.710496i	$-0.748471\pi$
$719$	−37.7384			−1.40740			−0.703702	+	0.710496i	$0.748471\pi$
$720$		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	$-0.653134\pi$
$727$	1.98480	−	1.14592i	0.0736121	−	0.0424999i	0.536354	+	0.843993i	$0.319801\pi$
$728$		0			0
$729$		0			0
$730$	37.3369			1.38190
$731$	9.95149	+	17.2365i	0.368069	+	0.637514i
$732$		0			0
$733$	−21.4678	−	12.3944i	−0.792930	−	0.457798i	0.0480633	−	0.998844i	$-0.484695\pi$
$733$	−21.4678	−	12.3944i	−0.792930	−	0.457798i	−0.840993	+	0.541046i	$0.818028\pi$
$734$	−29.9170	+	51.8178i	−1.10426	+	1.91263i
$735$		0			0
$736$	−21.1444	−	36.6232i	−0.779394	−	1.34995i
$737$		−	8.39582i		−	0.309264i
$738$		0			0
$739$	−16.2016			−0.595986			−0.297993	−	0.954568i	$-0.596317\pi$
$739$	−16.2016			−0.595986			−0.297993	+	0.954568i	$0.596317\pi$
$740$	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
$745$	−11.5315	+	6.65769i	−0.422480	+	0.243919i
$746$			35.9794i			1.31730i
$747$		0			0
$748$		−	12.9138i		−	0.472176i
$749$		0			0
$750$		0			0
$751$	3.78997	−	6.56443i	0.138298	−	0.239539i	−0.788554	−	0.614965i	$-0.789170\pi$
$751$	3.78997	−	6.56443i	0.138298	−	0.239539i	0.926853	+	0.375426i	$0.122503\pi$
$752$	−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
$761$	−17.2169	+	29.8206i	−0.624114	+	1.08100i	0.364598	+	0.931165i	$0.381207\pi$
$761$	−17.2169	+	29.8206i	−0.624114	+	1.08100i	−0.988711	+	0.149832i	$0.952127\pi$
$762$		0			0
$763$		0			0
$764$			17.9629i			0.649874i
$765$		0			0
$766$		−	39.5047i		−	1.42736i
$767$	3.79070	−	2.18856i	0.136874	−	0.0790245i
$768$		0			0
$769$	−12.9344	−	7.46765i	−0.466425	−	0.269290i	0.248317	−	0.968679i	$-0.420123\pi$
$769$	−12.9344	−	7.46765i	−0.466425	−	0.269290i	−0.714742	+	0.699388i	$0.753456\pi$
$770$		0			0
$771$		0			0
$772$	16.0439	+	27.7888i	0.577431	+	1.00014i
$773$	39.9848			1.43815			0.719076	−	0.694931i	$-0.244565\pi$
$773$	39.9848			1.43815			0.719076	+	0.694931i	$0.244565\pi$
$774$		0			0
$775$			8.50951i			0.305671i
$776$	−35.7845	−	61.9806i	−1.28459	−	2.22497i
$777$		0			0
$778$	−18.3466	+	31.7772i	−0.657758	+	1.13927i
$779$	6.91539	+	3.99260i	0.247770	+	0.143050i
$780$		0			0
$781$	−3.21007	−	5.56000i	−0.114865	−	0.198952i
$782$	−54.5622			−1.95114
$783$		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
$793$	17.7432			0.630079
$794$	−12.5883	−	21.8036i	−0.446742	−	0.773780i
$795$		0			0
$796$	65.6605	+	37.9091i	2.32727	+	1.34365i
$797$	22.1077	−	38.2916i	0.783094	−	1.35636i	−0.147037	−	0.989131i	$-0.546974\pi$
$797$	22.1077	−	38.2916i	0.783094	−	1.35636i	0.930131	−	0.367227i	$-0.119693\pi$
$798$		0			0
$799$	16.8668	+	29.2142i	0.596705	+	1.03352i
$800$			30.5444i			1.07991i
$801$		0			0
$802$	22.6451			0.799625
$803$	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
$808$	10.4914	−	6.05723i	0.369087	−	0.213093i
$809$			4.98227i			0.175167i	0.996157	+	0.0875837i	$0.0279145\pi$
$809$			4.98227i			0.175167i	−0.996157	+	0.0875837i	$0.972085\pi$
$810$		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
$814$	−2.13091	+	3.69084i	−0.0746883	+	0.129364i
$815$	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	$-0.418954\pi$
$821$	34.8397	−	20.1147i	1.21591	−	0.702008i	0.964041	+	0.265753i	$0.0856205\pi$
$822$		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	$-0.0478313\pi$
$824$	26.1819	−	45.3483i	0.912089	−	1.57978i
$825$		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
$829$			16.2397i			0.564029i	0.959410	+	0.282014i	$0.0910026\pi$
$829$			16.2397i			0.564029i	−0.959410	+	0.282014i	$0.908997\pi$
$830$	24.5842	−	14.1937i	0.853332	−	0.492671i
$831$		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
$836$	5.54314			0.191714
$837$		0			0
$838$			11.0930i			0.383202i
$839$	1.35145	+	2.34077i	0.0466571	+	0.0808125i	0.888411	−	0.459049i	$-0.151810\pi$
$839$	1.35145	+	2.34077i	0.0466571	+	0.0808125i	−0.841754	+	0.539862i	$0.818477\pi$
$840$		0			0
$841$	2.67914	−	4.64041i	0.0923842	−	0.160014i
$842$	−25.9053	−	14.9565i	−0.892757	−	0.515434i
$843$		0			0
$844$	19.1927	+	33.2427i	0.660639	+	1.14426i
$845$	−14.3995			−0.495357
$846$		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	$-0.970917\pi$
$853$	−41.3187	+	23.8554i	−1.41473	+	0.816793i	−0.418897	+	0.908034i	$0.637583\pi$
$854$		0			0
$855$		0			0
$856$	−1.07499			−0.0367424
$857$	8.93973	+	15.4841i	0.305375	+	0.528926i	0.977345	−	0.211653i	$-0.0678847\pi$
$857$	8.93973	+	15.4841i	0.305375	+	0.528926i	−0.671969	+	0.740579i	$0.734551\pi$
$858$		0			0
$859$	29.1901	+	16.8529i	0.995953	+	0.575014i	0.907048	−	0.421026i	$-0.138330\pi$
$859$	29.1901	+	16.8529i	0.995953	+	0.575014i	0.0889047	+	0.996040i	$0.471663\pi$
$860$	−13.3034	+	23.0422i	−0.453642	+	0.785731i
$861$		0			0
$862$	21.6367	+	37.4759i	0.736950	+	1.27643i
$863$			18.9739i			0.645878i	0.946420	+	0.322939i	$0.104671\pi$
$863$			18.9739i			0.645878i	−0.946420	+	0.322939i	$0.895329\pi$
$864$		0			0
$865$	−5.09652			−0.173287
$866$	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
$871$	14.4764	−	8.35795i	0.490514	−	0.283198i
$872$		−	38.1915i		−	1.29333i
$873$		0			0
$874$		−	23.4204i		−	0.792206i
$875$		0			0
$876$		0			0
$877$	−18.6188	+	32.2487i	−0.628712	+	1.08896i	0.359098	+	0.933300i	$0.383084\pi$
$877$	−18.6188	+	32.2487i	−0.628712	+	1.08896i	−0.987810	+	0.155662i	$0.950249\pi$
$878$	−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	$-0.474690\pi$
$881$	4.71527			0.158862			0.0794308	+	0.996840i	$0.474690\pi$
$882$		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
$887$	19.2217	−	33.2930i	0.645402	−	1.11787i	−0.338806	−	0.940856i	$-0.610023\pi$
$887$	19.2217	−	33.2930i	0.645402	−	1.11787i	0.984208	−	0.177013i	$-0.0566436\pi$
$888$		0			0
$889$		0			0
$890$		−	5.27243i		−	0.176732i
$891$		0			0
$892$			37.9963i			1.27221i
$893$	−12.5399	+	7.23993i	−0.419632	+	0.242275i
$894$		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
$899$	14.5420			0.485001
$900$		0			0
$901$		−	13.6980i		−	0.456346i
$902$	3.35857	+	5.81721i	0.111828	+	0.193692i
$903$		0			0
$904$	−22.8781	+	39.6261i	−0.760916	+	1.31794i
$905$	−13.7486	−	7.93774i	−0.457018	−	0.263859i
$906$		0			0
$907$	−21.7951	−	37.7503i	−0.723695	−	1.25348i	−0.959509	−	0.281678i	$-0.909109\pi$
$907$	−21.7951	−	37.7503i	−0.723695	−	1.25348i	0.235814	−	0.971798i	$-0.424224\pi$
$908$	−98.4206			−3.26620
$909$		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
$919$	−9.22843			−0.304418			−0.152209	−	0.988348i	$-0.548639\pi$
$919$	−9.22843			−0.304418			−0.152209	+	0.988348i	$0.548639\pi$
$920$	−21.0377	−	36.4384i	−0.693594	−	1.20134i
$921$		0			0
$922$	−1.49724	−	0.864434i	−0.0493091	−	0.0284686i
$923$	6.39118	−	11.0698i	0.210368	−	0.364368i
$924$		0			0
$925$	−4.56937	−	7.91438i	−0.150240	−	0.260223i
$926$		−	107.835i		−	3.54368i
$927$		0			0
$928$	52.1974			1.71346
$929$	−26.6849	−	46.2197i	−0.875504	−	1.51642i	−0.856225	−	0.516603i	$-0.827196\pi$
$929$	−26.6849	−	46.2197i	−0.875504	−	1.51642i	−0.0192794	−	0.999814i	$-0.506137\pi$
$930$		0			0
$931$		0			0
$932$	86.0952	+	49.7071i	2.82014	+	1.62821i
$933$		0			0
$934$	−88.3010	+	50.9806i	−2.88930	+	1.66814i
$935$		−	3.42346i		−	0.111959i
$936$		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
$940$	−22.5480	+	39.0542i	−0.735433	+	1.27381i
$941$	0.688308	−	1.19218i	0.0224382	−	0.0388641i	−0.854588	−	0.519306i	$-0.826190\pi$
$941$	0.688308	−	1.19218i	0.0224382	−	0.0388641i	0.877026	+	0.480442i	$0.159524\pi$
$942$		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	$0.677092\pi$
$947$	−47.0080	+	27.1401i	−1.52755	+	0.881933i	−0.999464	+	0.0327450i	$0.989575\pi$
$948$		0			0
$949$	−7.05423	+	12.2183i	−0.228990	+	0.396622i
$950$	−8.45802	+	14.6497i	−0.274414	+	0.475300i
$951$		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
$955$			4.76197i			0.154094i
$956$	35.4994	−	20.4956i	1.14813	−	0.662874i
$957$		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
$962$	−8.48519			−0.273574
$963$		0			0
$964$		−	40.0479i		−	1.28986i
$965$	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	$0.105549\pi$
$968$	−65.0324	−	37.5465i	−2.09022	−	1.20679i
$969$		0			0
$970$	−16.4454	−	28.4842i	−0.528029	−	0.914573i
$971$	56.1674			1.80250			0.901249	−	0.433302i	$-0.142652\pi$
$971$	56.1674			1.80250			0.901249	+	0.433302i	$0.142652\pi$
$972$		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	$-0.220681\pi$
$977$	18.7626	+	10.8326i	0.600268	+	0.346565i	−0.168879	+	0.985637i	$0.554015\pi$
$978$		0			0
$979$	0.866594	−	0.500328i	0.0276964	−	0.0159906i
$980$		0			0
$981$		0			0
$982$	9.98145			0.318521
$983$	−9.70006	−	16.8010i	−0.309384	−	0.535869i	0.668844	−	0.743403i	$-0.266789\pi$
$983$	−9.70006	−	16.8010i	−0.309384	−	0.535869i	−0.978228	+	0.207534i	$0.933456\pi$
$984$		0			0
$985$	−6.96052	−	4.01866i	−0.221781	−	0.128045i
$986$	33.6733	−	58.3238i	1.07238	−	1.85741i
$987$		0			0
$988$	5.51814	+	9.55771i	0.175556	+	0.304071i
$989$			21.3356i			0.678432i
$990$		0			0
$991$	25.3261			0.804509			0.402254	−	0.915528i	$-0.368227\pi$
$991$	25.3261			0.804509			0.402254	+	0.915528i	$0.368227\pi$
$992$	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
$997$	4.82016	−	2.78292i	0.152656	−	0.0881360i	−0.421726	−	0.906723i	$-0.638576\pi$
$997$	4.82016	−	2.78292i	0.152656	−	0.0881360i	0.574382	+	0.818587i	$0.305242\pi$
$998$			83.4050i			2.64014i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.5	✓	10	21.17	even	6
63.2.i.b.38.1	yes	10	63.16	even	3
63.2.s.b.47.1	yes	10	63.52	odd	6
63.2.s.b.59.1	yes	10	21.2	odd	6
189.2.i.b.143.5		10	63.2	odd	6
189.2.i.b.152.1		10	7.3	odd	6
189.2.s.b.17.5		10	7.2	even	3
189.2.s.b.89.5		10	63.38	even	6
441.2.i.b.68.5		10	21.11	odd	6
441.2.i.b.227.1		10	63.61	odd	6
441.2.o.c.146.5		10	63.34	odd	6
441.2.o.c.293.5		10	3.2	odd	2
441.2.o.d.146.5		10	9.7	even	3
441.2.o.d.293.5		10	21.20	even	2
441.2.s.b.362.1		10	63.25	even	3
441.2.s.b.374.1		10	21.5	even	6
567.2.p.c.80.5		10	63.23	odd	6
567.2.p.c.404.5		10	63.31	odd	6
567.2.p.d.80.1		10	63.58	even	3
567.2.p.d.404.1		10	63.59	even	6
1008.2.ca.b.257.1		10	84.59	odd	6
1008.2.ca.b.353.1		10	252.79	odd	6
1008.2.df.b.689.1		10	84.23	even	6
1008.2.df.b.929.1		10	252.115	even	6
1323.2.i.b.521.5		10	63.47	even	6
1323.2.i.b.1097.1		10	7.4	even	3
1323.2.o.c.440.1		10	9.2	odd	6
1323.2.o.c.881.1		10	7.6	odd	2
1323.2.o.d.440.1		10	63.20	even	6	inner
1323.2.o.d.881.1		10	1.1	even	1	trivial
1323.2.s.b.656.5		10	63.11	odd	6
1323.2.s.b.962.5		10	7.5	odd	6
3024.2.ca.b.2033.2		10	252.191	even	6
3024.2.ca.b.2609.2		10	28.3	even	6
3024.2.df.b.17.2		10	28.23	odd	6
3024.2.df.b.1601.2		10	252.227	odd	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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.24607 + 1.29677i) q^{2} +(2.36322 - 4.09323i) q^{4} +(0.626493 - 1.08512i) q^{5} +7.07116i q^{8} +O(q^{10})\)	\(q+(-2.24607 + 1.29677i) q^{2} +(2.36322 - 4.09323i) q^{4} +(0.626493 - 1.08512i) q^{5} +7.07116i q^{8} +3.24967i q^{10} +(-0.534126 + 0.308378i) q^{11} +(-1.06343 - 0.613974i) q^{13} +(-4.44321 - 7.69587i) q^{16} -4.43003 q^{17} -1.90155i q^{19} +(-2.96109 - 5.12875i) q^{20} +(0.799790 - 1.38528i) q^{22} +(-4.11267 - 2.37445i) q^{23} +(1.71501 + 2.97049i) q^{25} +3.18473 q^{26} +(5.07629 - 2.93080i) q^{29} +(2.14851 + 1.24044i) q^{31} +(7.71195 + 4.45249i) q^{32} +(9.95016 - 5.74473i) q^{34} -2.66433 q^{37} +(2.46587 + 4.27102i) q^{38} +(7.67303 + 4.43003i) q^{40} +(-2.09966 + 3.63671i) q^{41} +(-2.24637 - 3.89083i) q^{43} +2.91506i q^{44} +12.3165 q^{46} +(-3.80738 - 6.59458i) q^{47} +(-7.70409 - 4.44796i) q^{50} +(-5.02627 + 2.90192i) q^{52} +3.09208i q^{53} +0.772786i q^{55} +(-7.60114 + 13.1656i) q^{58} +(-1.78229 + 3.08702i) q^{59} +(-12.5136 + 7.22473i) q^{61} -6.43428 q^{62} -5.32259 q^{64} +(-1.33247 + 0.769301i) q^{65} +(-6.80644 + 11.7891i) q^{67} +(-10.4692 + 18.1331i) q^{68} +10.4095i q^{71} -11.4895i q^{73} +(5.98429 - 3.45503i) q^{74} +(-7.78348 - 4.49379i) q^{76} +(2.01592 + 3.49168i) q^{79} -11.1346 q^{80} -10.8911i q^{82} +(-4.36775 - 7.56516i) q^{83} +(-2.77538 + 4.80710i) q^{85} +(10.0910 + 5.82605i) q^{86} +(-2.18059 - 3.77689i) q^{88} -1.62245 q^{89} +(-19.4383 + 11.2227i) q^{92} +(17.1033 + 9.87459i) q^{94} +(-2.06341 - 1.19131i) q^{95} +(-8.76527 + 5.06063i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4}+O(q^{10}) \) 10 * q + 4 * q^4	\( 10 q + 4 q^{4} - 12 q^{11} + 6 q^{13} - 6 q^{16} - 24 q^{17} + 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 6 q^{26} + 15 q^{29} + 9 q^{31} + 48 q^{32} + 3 q^{34} - 12 q^{37} + 18 q^{38} + 15 q^{40} + 9 q^{41} + 3 q^{43} + 26 q^{46} - 15 q^{47} - 3 q^{50} - 12 q^{52} + 8 q^{58} + 18 q^{59} - 12 q^{61} - 12 q^{62} + 6 q^{64} - 3 q^{65} - 10 q^{67} - 27 q^{68} - 30 q^{74} + 9 q^{76} + 20 q^{79} - 60 q^{80} + 15 q^{83} + 18 q^{85} + 54 q^{86} - 8 q^{88} + 48 q^{89} - 39 q^{92} + 3 q^{94} + 6 q^{97}+O(q^{100}) \) 10 * q + 4 * q^4 - 12 * q^11 + 6 * q^13 - 6 * q^16 - 24 * q^17 + 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 6 * q^26 + 15 * q^29 + 9 * q^31 + 48 * q^32 + 3 * q^34 - 12 * q^37 + 18 * q^38 + 15 * q^40 + 9 * q^41 + 3 * q^43 + 26 * q^46 - 15 * q^47 - 3 * q^50 - 12 * q^52 + 8 * q^58 + 18 * q^59 - 12 * q^61 - 12 * q^62 + 6 * q^64 - 3 * q^65 - 10 * q^67 - 27 * q^68 - 30 * q^74 + 9 * q^76 + 20 * q^79 - 60 * q^80 + 15 * q^83 + 18 * q^85 + 54 * q^86 - 8 * q^88 + 48 * q^89 - 39 * q^92 + 3 * q^94 + 6 * q^97

Introduction

L-functions

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