LMFDB - Embedded newform 1040.2.da.f.881.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16 $ x^16 + 22x^14 + 183x^12 + 730x^10 + 1485x^8 + 1552x^6 + 812x^4 + 192*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 520)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.1
Root			$1.97402i$ of defining polynomial
Character	$\chi$	$=$	1040.881
Dual form			1040.2.da.f.641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43538 - 2.48615i) q^{3} -1.00000i q^{5} +(-0.0113994 - 0.00658143i) q^{7} +(-2.62062 + 4.53905i) q^{9} +O(q^{10})$	\(q+(-1.43538 - 2.48615i) q^{3} -1.00000i q^{5} +(-0.0113994 - 0.00658143i) q^{7} +(-2.62062 + 4.53905i) q^{9} +(-0.541191 + 0.312457i) q^{11} +(1.97232 + 3.01827i) q^{13} +(-2.48615 + 1.43538i) q^{15} +(-3.78024 + 6.54756i) q^{17} +(-6.29517 - 3.63452i) q^{19} +0.0377874i q^{21} +(1.22985 + 2.13017i) q^{23} -1.00000 q^{25} +6.43407 q^{27} +(-1.15977 - 2.00878i) q^{29} +8.02362i q^{31} +(1.55363 + 0.896987i) q^{33} +(-0.00658143 + 0.0113994i) q^{35} +(-3.65201 + 2.10849i) q^{37} +(4.67284 - 9.23584i) q^{39} +(3.29811 - 1.90416i) q^{41} +(-1.39758 + 2.42068i) q^{43} +(4.53905 + 2.62062i) q^{45} +4.00926i q^{47} +(-3.49991 - 6.06203i) q^{49} +21.7043 q^{51} +6.25234 q^{53} +(0.312457 + 0.541191i) q^{55} +20.8676i q^{57} +(11.6836 + 6.74554i) q^{59} +(3.28736 - 5.69387i) q^{61} +(0.0597469 - 0.0344949i) q^{63} +(3.01827 - 1.97232i) q^{65} +(-5.81605 + 3.35790i) q^{67} +(3.53061 - 6.11520i) q^{69} +(-13.2257 - 7.63585i) q^{71} +2.98937i q^{73} +(1.43538 + 2.48615i) q^{75} +0.00822564 q^{77} -2.02435 q^{79} +(-1.37345 - 2.37889i) q^{81} -2.35696i q^{83} +(6.54756 + 3.78024i) q^{85} +(-3.32941 + 5.76671i) q^{87} +(4.50245 - 2.59949i) q^{89} +(-0.00261866 - 0.0473870i) q^{91} +(19.9479 - 11.5169i) q^{93} +(-3.63452 + 6.29517i) q^{95} +(7.02150 + 4.05387i) q^{97} -3.27532i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9	$ 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) $ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^17 - 30 * q^19 - 6 * q^23 - 16 * q^25 - 44 * q^27 - 16 * q^29 + 24 * q^33 + 6 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 - 6 * q^43 + 12 * q^45 - 4 * q^49 + 40 * q^51 + 4 * q^53 + 6 * q^55 - 12 * q^59 - 2 * q^61 + 60 * q^63 - 10 * q^65 + 6 * q^67 + 52 * q^69 - 72 * q^71 - 4 * q^75 + 32 * q^77 - 36 * q^79 - 28 * q^81 + 22 * q^87 + 24 * q^89 + 22 * q^91 - 96 * q^93 - 10 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.43538	−	2.48615i	−0.828716	−	1.43538i	−0.899046	−	0.437855i	$-0.855738\pi$
$3$	−1.43538	−	2.48615i	−0.828716	−	1.43538i	0.0703297	−	0.997524i	$-0.477595\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−0.0113994	−	0.00658143i	−0.00430856	−	0.00248755i	0.497844	−	0.867266i	$-0.334125\pi$
$7$	−0.0113994	−	0.00658143i	−0.00430856	−	0.00248755i	−0.502153	+	0.864779i	$0.667458\pi$
$8$		0			0
$9$	−2.62062	+	4.53905i	−0.873541	+	1.51302i
$10$		0			0
$11$	−0.541191	+	0.312457i	−0.163175	+	0.0942092i	−0.579364	−	0.815069i	$-0.696699\pi$
$11$	−0.541191	+	0.312457i	−0.163175	+	0.0942092i	0.416189	+	0.909278i	$0.363366\pi$
$12$		0			0
$13$	1.97232	+	3.01827i	0.547023	+	0.837118i
$13$	1.97232	+	3.01827i	0.547023	+	0.837118i
$14$		0			0
$15$	−2.48615	+	1.43538i	−0.641921	+	0.370613i
$16$		0			0
$17$	−3.78024	+	6.54756i	−0.916842	+	1.58802i	−0.112661	+	0.993633i	$0.535937\pi$
$17$	−3.78024	+	6.54756i	−0.916842	+	1.58802i	−0.804181	+	0.594384i	$0.797396\pi$
$18$		0			0
$19$	−6.29517	−	3.63452i	−1.44421	−	0.833815i	−0.446084	−	0.894991i	$-0.647182\pi$
$19$	−6.29517	−	3.63452i	−1.44421	−	0.833815i	−0.998127	+	0.0611757i	$0.980515\pi$
$20$		0			0
$21$			0.0377874i			0.00824588i
$22$		0			0
$23$	1.22985	+	2.13017i	0.256442	+	0.444171i	0.965286	−	0.261194i	$-0.0841163\pi$
$23$	1.22985	+	2.13017i	0.256442	+	0.444171i	−0.708844	+	0.705365i	$0.750783\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	6.43407			1.23824
$28$		0			0
$29$	−1.15977	−	2.00878i	−0.215364	−	0.373021i	0.738021	−	0.674777i	$-0.235760\pi$
$29$	−1.15977	−	2.00878i	−0.215364	−	0.373021i	−0.953385	+	0.301757i	$0.902427\pi$
$30$		0			0
$31$			8.02362i			1.44109i	0.693411	+	0.720543i	$0.256107\pi$
$31$			8.02362i			1.44109i	−0.693411	+	0.720543i	$0.743893\pi$
$32$		0			0
$33$	1.55363	+	0.896987i	0.270452	+	0.156145i
$34$		0			0
$35$	−0.00658143	+	0.0113994i	−0.00111246	+	0.00192684i
$36$		0			0
$37$	−3.65201	+	2.10849i	−0.600387	+	0.346634i	−0.769194	−	0.639016i	$-0.779342\pi$
$37$	−3.65201	+	2.10849i	−0.600387	+	0.346634i	0.168807	+	0.985649i	$0.446009\pi$
$38$		0			0
$39$	4.67284	−	9.23584i	0.748254	−	1.47892i
$40$		0			0
$41$	3.29811	−	1.90416i	0.515078	−	0.297380i	−0.219840	−	0.975536i	$-0.570554\pi$
$41$	3.29811	−	1.90416i	0.515078	−	0.297380i	0.734919	+	0.678155i	$0.237220\pi$
$42$		0			0
$43$	−1.39758	+	2.42068i	−0.213129	+	0.369151i	−0.952692	−	0.303937i	$-0.901699\pi$
$43$	−1.39758	+	2.42068i	−0.213129	+	0.369151i	0.739563	+	0.673087i	$0.235032\pi$
$44$		0			0
$45$	4.53905	+	2.62062i	0.676642	+	0.390659i
$46$		0			0
$47$			4.00926i			0.584810i	0.956295	+	0.292405i	$0.0944556\pi$
$47$			4.00926i			0.584810i	−0.956295	+	0.292405i	$0.905544\pi$
$48$		0			0
$49$	−3.49991	−	6.06203i	−0.499988	−	0.866004i
$50$		0			0
$51$	21.7043			3.03921
$52$		0			0
$53$	6.25234			0.858824			0.429412	−	0.903109i	$-0.358721\pi$
$53$	6.25234			0.858824			0.429412	+	0.903109i	$0.358721\pi$
$54$		0			0
$55$	0.312457	+	0.541191i	0.0421316	+	0.0729741i
$56$		0			0
$57$			20.8676i			2.76399i
$58$		0			0
$59$	11.6836	+	6.74554i	1.52108	+	0.878195i	0.999691	+	0.0248747i	$0.00791868\pi$
$59$	11.6836	+	6.74554i	1.52108	+	0.878195i	0.521387	+	0.853320i	$0.325415\pi$
$60$		0			0
$61$	3.28736	−	5.69387i	0.420903	−	0.729025i	−0.575125	−	0.818065i	$-0.695047\pi$
$61$	3.28736	−	5.69387i	0.420903	−	0.729025i	0.996028	+	0.0890404i	$0.0283800\pi$
$62$		0			0
$63$	0.0597469	−	0.0344949i	0.00752740	−	0.00434594i
$64$		0			0
$65$	3.01827	−	1.97232i	0.374370	−	0.244636i
$66$		0			0
$67$	−5.81605	+	3.35790i	−0.710544	+	0.410233i	−0.811262	−	0.584682i	$-0.801219\pi$
$67$	−5.81605	+	3.35790i	−0.710544	+	0.410233i	0.100718	+	0.994915i	$0.467886\pi$
$68$		0			0
$69$	3.53061	−	6.11520i	0.425036	−	0.736183i
$70$		0			0
$71$	−13.2257	−	7.63585i	−1.56960	−	0.906209i	−0.996215	−	0.0869220i	$-0.972297\pi$
$71$	−13.2257	−	7.63585i	−1.56960	−	0.906209i	−0.573384	−	0.819287i	$-0.694370\pi$
$72$		0			0
$73$			2.98937i			0.349879i	0.984579	+	0.174940i	$0.0559730\pi$
$73$			2.98937i			0.349879i	−0.984579	+	0.174940i	$0.944027\pi$
$74$		0			0
$75$	1.43538	+	2.48615i	0.165743	+	0.287076i
$76$		0			0
$77$	0.00822564			0.000937399
$78$		0			0
$79$	−2.02435			−0.227758			−0.113879	−	0.993495i	$-0.536328\pi$
$79$	−2.02435			−0.227758			−0.113879	+	0.993495i	$0.536328\pi$
$80$		0			0
$81$	−1.37345	−	2.37889i	−0.152606	−	0.264321i
$82$		0			0
$83$		−	2.35696i		−	0.258710i	−0.991598	−	0.129355i	$-0.958709\pi$
$83$		−	2.35696i		−	0.258710i	0.991598	−	0.129355i	$-0.0412907\pi$
$84$		0			0
$85$	6.54756	+	3.78024i	0.710183	+	0.410024i
$86$		0			0
$87$	−3.32941	+	5.76671i	−0.356951	+	0.618257i
$88$		0			0
$89$	4.50245	−	2.59949i	0.477259	−	0.275545i	−0.242015	−	0.970273i	$-0.577808\pi$
$89$	4.50245	−	2.59949i	0.477259	−	0.275545i	0.719273	+	0.694727i	$0.244475\pi$
$90$		0			0
$91$	−0.00261866	−	0.0473870i	−0.000274510	−	0.00496751i
$92$		0			0
$93$	19.9479	−	11.5169i	2.06850	−	1.19425i
$94$		0			0
$95$	−3.63452	+	6.29517i	−0.372894	+	0.645871i
$96$		0			0
$97$	7.02150	+	4.05387i	0.712925	+	0.411608i	0.812143	−	0.583458i	$-0.198301\pi$
$97$	7.02150	+	4.05387i	0.712925	+	0.411608i	−0.0992179	+	0.995066i	$0.531634\pi$
$98$		0			0
$99$		−	3.27532i		−	0.329182i
$100$		0			0
$101$	−5.68537	−	9.84736i	−0.565716	−	0.979848i	−0.996983	−	0.0776241i	$-0.975267\pi$
$101$	−5.68537	−	9.84736i	−0.565716	−	0.979848i	0.431267	−	0.902224i	$-0.358067\pi$
$102$		0			0
$103$	−13.9614			−1.37566			−0.687829	−	0.725873i	$-0.741436\pi$
$103$	−13.9614			−1.37566			−0.687829	+	0.725873i	$0.741436\pi$
$104$		0			0
$105$	0.0377874			0.00368767
$106$		0			0
$107$	7.33282	+	12.7008i	0.708891	+	1.22783i	0.965269	+	0.261258i	$0.0841374\pi$
$107$	7.33282	+	12.7008i	0.708891	+	1.22783i	−0.256378	+	0.966576i	$0.582529\pi$
$108$		0			0
$109$			6.16019i			0.590039i	0.955491	+	0.295020i	$0.0953262\pi$
$109$			6.16019i			0.590039i	−0.955491	+	0.295020i	$0.904674\pi$
$110$		0			0
$111$	10.4840	+	6.05296i	0.995101	+	0.574522i
$112$		0			0
$113$	−3.38917	+	5.87021i	−0.318826	+	0.552223i	−0.980243	−	0.197795i	$-0.936622\pi$
$113$	−3.38917	+	5.87021i	−0.318826	+	0.552223i	0.661417	+	0.750018i	$0.269955\pi$
$114$		0			0
$115$	2.13017	−	1.22985i	0.198639	−	0.114684i
$116$		0			0
$117$	−18.8688	+	1.04271i	−1.74442	+	0.0963984i
$118$		0			0
$119$	0.0861846	−	0.0497587i	0.00790053	−	0.00456137i
$120$		0			0
$121$	−5.30474	+	9.18808i	−0.482249	+	0.835280i
$122$		0			0
$123$	−9.46807	−	5.46639i	−0.853707	−	0.492888i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	1.52888	+	2.64810i	0.135666	+	0.234981i	0.925852	−	0.377887i	$-0.123349\pi$
$127$	1.52888	+	2.64810i	0.135666	+	0.234981i	−0.790185	+	0.612868i	$0.790016\pi$
$128$		0			0
$129$	8.02424			0.706495
$130$		0			0
$131$	15.5729			1.36061			0.680307	−	0.732927i	$-0.261846\pi$
$131$	15.5729			1.36061			0.680307	+	0.732927i	$0.261846\pi$
$132$		0			0
$133$	0.0478406	+	0.0828624i	0.00414831	+	0.00718508i
$134$		0			0
$135$		−	6.43407i		−	0.553756i
$136$		0			0
$137$	−15.4959	−	8.94656i	−1.32390	−	0.764356i	−0.339555	−	0.940586i	$-0.610276\pi$
$137$	−15.4959	−	8.94656i	−1.32390	−	0.764356i	−0.984349	+	0.176230i	$0.943610\pi$
$138$		0			0
$139$	−10.4203	+	18.0485i	−0.883841	+	1.53086i	−0.0368049	+	0.999322i	$0.511718\pi$
$139$	−10.4203	+	18.0485i	−0.883841	+	1.53086i	−0.847036	+	0.531535i	$0.821615\pi$
$140$		0			0
$141$	9.96761	−	5.75480i	0.839424	−	0.484642i
$142$		0			0
$143$	−2.01048	−	1.01720i	−0.168125	−	0.0850622i
$144$		0			0
$145$	−2.00878	+	1.15977i	−0.166820	+	0.0963135i
$146$		0			0
$147$	−10.0474	+	17.4026i	−0.828696	+	1.43534i
$148$		0			0
$149$	−14.1504	−	8.16975i	−1.15925	−	0.669292i	−0.208125	−	0.978102i	$-0.566736\pi$
$149$	−14.1504	−	8.16975i	−1.15925	−	0.669292i	−0.951124	+	0.308810i	$0.900069\pi$
$150$		0			0
$151$		−	6.34453i		−	0.516311i	−0.966103	−	0.258155i	$-0.916885\pi$
$151$		−	6.34453i		−	0.516311i	0.966103	−	0.258155i	$-0.0831147\pi$
$152$		0			0
$153$	−19.8132	−	34.3174i	−1.60180	−	2.77440i
$154$		0			0
$155$	8.02362			0.644473
$156$		0			0
$157$	−0.454894			−0.0363045			−0.0181523	−	0.999835i	$-0.505778\pi$
$157$	−0.454894			−0.0363045			−0.0181523	+	0.999835i	$0.505778\pi$
$158$		0			0
$159$	−8.97447	−	15.5442i	−0.711722	−	1.23274i
$160$		0			0
$161$		−	0.0323768i		−	0.00255165i
$162$		0			0
$163$	−8.27406	−	4.77703i	−0.648074	−	0.374166i	0.139644	−	0.990202i	$-0.455404\pi$
$163$	−8.27406	−	4.77703i	−0.648074	−	0.374166i	−0.787718	+	0.616036i	$0.788738\pi$
$164$		0			0
$165$	0.896987	−	1.55363i	0.0698303	−	0.120950i
$166$		0			0
$167$	−8.71320	+	5.03057i	−0.674248	+	0.389277i	−0.797684	−	0.603075i	$-0.793942\pi$
$167$	−8.71320	+	5.03057i	−0.674248	+	0.389277i	0.123436	+	0.992352i	$0.460609\pi$
$168$		0			0
$169$	−5.21992	+	11.9060i	−0.401532	+	0.915845i
$170$		0			0
$171$	32.9945	−	19.0494i	2.52315	−	1.45674i
$172$		0			0
$173$	2.81853	−	4.88184i	0.214289	−	0.371159i	−0.738763	−	0.673965i	$-0.764590\pi$
$173$	2.81853	−	4.88184i	0.214289	−	0.371159i	0.953052	+	0.302805i	$0.0979232\pi$
$174$		0			0
$175$	0.0113994	+	0.00658143i	0.000861711	+	0.000497509i
$176$		0			0
$177$		−	38.7296i		−	2.91110i
$178$		0			0
$179$	2.05404	+	3.55770i	0.153526	+	0.265915i	0.932521	−	0.361115i	$-0.117604\pi$
$179$	2.05404	+	3.55770i	0.153526	+	0.265915i	−0.778995	+	0.627030i	$0.784270\pi$
$180$		0			0
$181$	−26.2588			−1.95180			−0.975899	−	0.218222i	$-0.929974\pi$
$181$	−26.2588			−1.95180			−0.975899	+	0.218222i	$0.929974\pi$
$182$		0			0
$183$	−18.8744			−1.39524
$184$		0			0
$185$	2.10849	+	3.65201i	0.155019	+	0.268501i
$186$		0			0
$187$		−	4.72464i		−	0.345500i
$188$		0			0
$189$	−0.0733443	−	0.0423453i	−0.00533501	−	0.00308017i
$190$		0			0
$191$	7.89188	−	13.6691i	0.571037	−	0.989064i	−0.425423	−	0.904995i	$-0.639875\pi$
$191$	7.89188	−	13.6691i	0.571037	−	0.989064i	0.996460	−	0.0840699i	$-0.0267919\pi$
$192$		0			0
$193$	0.684803	−	0.395371i	0.0492932	−	0.0284594i	−0.475151	−	0.879904i	$-0.657607\pi$
$193$	0.684803	−	0.395371i	0.0492932	−	0.0284594i	0.524444	+	0.851445i	$0.324273\pi$
$194$		0			0
$195$	−9.23584	−	4.67284i	−0.661392	−	0.334629i
$196$		0			0
$197$	2.71134	−	1.56539i	0.193175	−	0.111530i	−0.400293	−	0.916387i	$-0.631092\pi$
$197$	2.71134	−	1.56539i	0.193175	−	0.111530i	0.593468	+	0.804858i	$0.297758\pi$
$198$		0			0
$199$	−3.01204	+	5.21701i	−0.213518	+	0.369824i	−0.952813	−	0.303557i	$-0.901826\pi$
$199$	−3.01204	+	5.21701i	−0.213518	+	0.369824i	0.739295	+	0.673382i	$0.235159\pi$
$200$		0			0
$201$	16.6965	+	9.63971i	1.17768	+	0.679933i
$202$		0			0
$203$			0.0305317i			0.00214291i
$204$		0			0
$205$	−1.90416	−	3.29811i	−0.132993	−	0.230350i
$206$		0			0
$207$	−12.8919			−0.896051
$208$		0			0
$209$	4.54252			0.314212
$210$		0			0
$211$	−12.5479	−	21.7335i	−0.863830	−	1.49620i	−0.868204	−	0.496207i	$-0.834726\pi$
$211$	−12.5479	−	21.7335i	−0.863830	−	1.49620i	0.00437417	−	0.999990i	$-0.498608\pi$
$212$		0			0
$213$			43.8413i			3.00396i
$214$		0			0
$215$	2.42068	+	1.39758i	0.165089	+	0.0953144i
$216$		0			0
$217$	0.0528069	−	0.0914642i	0.00358477	−	0.00620900i
$218$		0			0
$219$	7.43201	−	4.29088i	0.502209	−	0.289950i
$220$		0			0
$221$	−27.2182	+	1.50410i	−1.83089	+	0.101177i
$222$		0			0
$223$	0.211215	−	0.121945i	0.0141440	−	0.00816606i	−0.492911	−	0.870080i	$-0.664067\pi$
$223$	0.211215	−	0.121945i	0.0141440	−	0.00816606i	0.507055	+	0.861913i	$0.330734\pi$
$224$		0			0
$225$	2.62062	−	4.53905i	0.174708	−	0.302603i
$226$		0			0
$227$	−7.79411	−	4.49993i	−0.517313	−	0.298671i	0.218521	−	0.975832i	$-0.429877\pi$
$227$	−7.79411	−	4.49993i	−0.517313	−	0.298671i	−0.735835	+	0.677161i	$0.763210\pi$
$228$		0			0
$229$		−	23.1995i		−	1.53306i	−0.642206	−	0.766532i	$-0.721981\pi$
$229$		−	23.1995i		−	1.53306i	0.642206	−	0.766532i	$-0.278019\pi$
$230$		0			0
$231$	−0.0118069	−	0.0204502i	−0.000776837	−	0.00134552i
$232$		0			0
$233$	3.05984			0.200457			0.100228	−	0.994964i	$-0.468043\pi$
$233$	3.05984			0.200457			0.100228	+	0.994964i	$0.468043\pi$
$234$		0			0
$235$	4.00926			0.261535
$236$		0			0
$237$	2.90572	+	5.03285i	0.188746	+	0.326918i
$238$		0			0
$239$			14.5625i			0.941967i	0.882142	+	0.470983i	$0.156101\pi$
$239$			14.5625i			0.941967i	−0.882142	+	0.470983i	$0.843899\pi$
$240$		0			0
$241$	18.7917	+	10.8494i	1.21048	+	0.698872i	0.962864	−	0.269986i	$-0.0870191\pi$
$241$	18.7917	+	10.8494i	1.21048	+	0.698872i	0.247617	+	0.968858i	$0.420352\pi$
$242$		0			0
$243$	5.70825	−	9.88698i	0.366184	−	0.634250i
$244$		0			0
$245$	−6.06203	+	3.49991i	−0.387289	+	0.223601i
$246$		0			0
$247$	−1.44612	−	26.1690i	−0.0920146	−	1.66509i
$248$		0			0
$249$	−5.85976	+	3.38313i	−0.371347	+	0.214397i
$250$		0			0
$251$	−6.66885	+	11.5508i	−0.420934	+	0.729079i	−0.996031	−	0.0890063i	$-0.971631\pi$
$251$	−6.66885	+	11.5508i	−0.420934	+	0.729079i	0.575097	+	0.818085i	$0.304964\pi$
$252$		0			0
$253$	−1.33117	−	0.768552i	−0.0836900	−	0.0483184i
$254$		0			0
$255$		−	21.7043i		−	1.35918i
$256$		0			0
$257$	10.6087	+	18.3747i	0.661750	+	1.14619i	0.980155	+	0.198230i	$0.0635194\pi$
$257$	10.6087	+	18.3747i	0.661750	+	1.14619i	−0.318405	+	0.947955i	$0.603147\pi$
$258$		0			0
$259$	0.0555075			0.00344907
$260$		0			0
$261$	12.1573			0.752516
$262$		0			0
$263$	5.15581	+	8.93013i	0.317921	+	0.550656i	0.980054	−	0.198731i	$-0.0636820\pi$
$263$	5.15581	+	8.93013i	0.317921	+	0.550656i	−0.662133	+	0.749386i	$0.730349\pi$
$264$		0			0
$265$		−	6.25234i		−	0.384078i
$266$		0			0
$267$	−12.9254	−	7.46251i	−0.791024	−	0.456698i
$268$		0			0
$269$	−13.7790	+	23.8659i	−0.840119	+	1.45513i	0.0496753	+	0.998765i	$0.484181\pi$
$269$	−13.7790	+	23.8659i	−0.840119	+	1.45513i	−0.889794	+	0.456363i	$0.849152\pi$
$270$		0			0
$271$	−9.57787	+	5.52978i	−0.581814	+	0.335910i	−0.761854	−	0.647749i	$-0.775711\pi$
$271$	−9.57787	+	5.52978i	−0.581814	+	0.335910i	0.180040	+	0.983659i	$0.442377\pi$
$272$		0			0
$273$	−0.114052	+	0.0745287i	−0.00690277	+	0.00451068i
$274$		0			0
$275$	0.541191	−	0.312457i	0.0326350	−	0.0188418i
$276$		0			0
$277$	−11.9360	+	20.6738i	−0.717165	+	1.24217i	0.244953	+	0.969535i	$0.421227\pi$
$277$	−11.9360	+	20.6738i	−0.717165	+	1.24217i	−0.962118	+	0.272632i	$0.912106\pi$
$278$		0			0
$279$	−36.4196	−	21.0269i	−2.18039	−	1.25885i
$280$		0			0
$281$		−	2.59106i		−	0.154570i	−0.997009	−	0.0772848i	$-0.975375\pi$
$281$		−	2.59106i		−	0.154570i	0.997009	−	0.0772848i	$-0.0246251\pi$
$282$		0			0
$283$	7.56534	+	13.1036i	0.449713	+	0.778925i	0.998367	−	0.0571240i	$-0.0181930\pi$
$283$	7.56534	+	13.1036i	0.449713	+	0.778925i	−0.548654	+	0.836049i	$0.684860\pi$
$284$		0			0
$285$	20.8676			1.23609
$286$		0			0
$287$	−0.0501285			−0.00295899
$288$		0			0
$289$	−20.0804	−	34.7803i	−1.18120	−	2.04590i
$290$		0			0
$291$		−	23.2753i		−	1.36442i
$292$		0			0
$293$	27.7087	+	15.9976i	1.61876	+	0.934590i	0.987242	+	0.159226i	$0.0508997\pi$
$293$	27.7087	+	15.9976i	1.61876	+	0.934590i	0.631514	+	0.775364i	$0.282434\pi$
$294$		0			0
$295$	6.74554	−	11.6836i	0.392741	−	0.680247i
$296$		0			0
$297$	−3.48206	+	2.01037i	−0.202049	+	0.116653i
$298$		0			0
$299$	−4.00376	+	7.91341i	−0.231544	+	0.457644i
$300$		0			0
$301$	0.0318631	−	0.0183962i	0.00183656	−	0.00106034i
$302$		0			0
$303$	−16.3213	+	28.2694i	−0.937636	+	1.62403i
$304$		0			0
$305$	−5.69387	−	3.28736i	−0.326030	−	0.188233i
$306$		0			0
$307$		−	19.7355i		−	1.12637i	−0.826332	−	0.563183i	$-0.809577\pi$
$307$		−	19.7355i		−	1.12637i	0.826332	−	0.563183i	$-0.190423\pi$
$308$		0			0
$309$	20.0399	+	34.7101i	1.14003	+	1.97459i
$310$		0			0
$311$	24.2206			1.37342			0.686711	−	0.726930i	$-0.259054\pi$
$311$	24.2206			1.37342			0.686711	+	0.726930i	$0.259054\pi$
$312$		0			0
$313$	17.0003			0.960915			0.480457	−	0.877018i	$-0.340471\pi$
$313$	17.0003			0.960915			0.480457	+	0.877018i	$0.340471\pi$
$314$		0			0
$315$	−0.0344949	−	0.0597469i	−0.00194357	−	0.00336635i
$316$		0			0
$317$		−	29.1303i		−	1.63612i	−0.575131	−	0.818061i	$-0.695049\pi$
$317$		−	29.1303i		−	1.63612i	0.575131	−	0.818061i	$-0.304951\pi$
$318$		0			0
$319$	1.25531	+	0.724755i	0.0702840	+	0.0405785i
$320$		0			0
$321$	21.0507	−	36.4610i	1.17494	−	2.03505i
$322$		0			0
$323$	47.5945	−	27.4787i	2.64823	−	1.52895i
$324$		0			0
$325$	−1.97232	−	3.01827i	−0.109405	−	0.167424i
$326$		0			0
$327$	15.3151	−	8.84220i	0.846930	−	0.488975i
$328$		0			0
$329$	0.0263866	−	0.0457030i	0.00145474	−	0.00251969i
$330$		0			0
$331$	−1.23105	−	0.710748i	−0.0676647	−	0.0390662i	0.465786	−	0.884897i	$-0.345772\pi$
$331$	−1.23105	−	0.710748i	−0.0676647	−	0.0390662i	−0.533451	+	0.845831i	$0.679105\pi$
$332$		0			0
$333$		−	22.1022i		−	1.21119i
$334$		0			0
$335$	3.35790	+	5.81605i	0.183462	+	0.317765i
$336$		0			0
$337$	−20.5875			−1.12147			−0.560735	−	0.827995i	$-0.689481\pi$
$337$	−20.5875			−1.12147			−0.560735	+	0.827995i	$0.689481\pi$
$338$		0			0
$339$	19.4590			1.05687
$340$		0			0
$341$	−2.50703	−	4.34231i	−0.135763	−	0.235149i
$342$		0			0
$343$			0.184278i			0.00995006i
$344$		0			0
$345$	−6.11520	−	3.53061i	−0.329231	−	0.190082i
$346$		0			0
$347$	2.06238	−	3.57214i	0.110714	−	0.191763i	−0.805344	−	0.592807i	$-0.798020\pi$
$347$	2.06238	−	3.57214i	0.110714	−	0.191763i	0.916058	+	0.401045i	$0.131353\pi$
$348$		0			0
$349$	−8.23537	+	4.75470i	−0.440829	+	0.254513i	−0.703949	−	0.710250i	$-0.748582\pi$
$349$	−8.23537	+	4.75470i	−0.440829	+	0.254513i	0.263120	+	0.964763i	$0.415249\pi$
$350$		0			0
$351$	12.6900	+	19.4198i	0.677344	+	1.03655i
$352$		0			0
$353$	−17.8996	+	10.3343i	−0.952700	+	0.550041i	−0.893918	−	0.448230i	$-0.852055\pi$
$353$	−17.8996	+	10.3343i	−0.952700	+	0.550041i	−0.0587811	+	0.998271i	$0.518721\pi$
$354$		0			0
$355$	−7.63585	+	13.2257i	−0.405269	+	0.701946i
$356$		0			0
$357$	−0.247415	−	0.142845i	−0.0130946	−	0.00756017i
$358$		0			0
$359$			4.18621i			0.220939i	0.993879	+	0.110470i	$0.0352355\pi$
$359$			4.18621i			0.220939i	−0.993879	+	0.110470i	$0.964764\pi$
$360$		0			0
$361$	16.9194	+	29.3053i	0.890497	+	1.54239i
$362$		0			0
$363$	30.4572			1.59859
$364$		0			0
$365$	2.98937			0.156471
$366$		0			0
$367$	4.18853	+	7.25476i	0.218640	+	0.378695i	0.954392	−	0.298555i	$-0.0965047\pi$
$367$	4.18853	+	7.25476i	0.218640	+	0.378695i	−0.735753	+	0.677250i	$0.763171\pi$
$368$		0			0
$369$			19.9604i			1.03910i
$370$		0			0
$371$	−0.0712727	−	0.0411493i	−0.00370029	−	0.00213636i
$372$		0			0
$373$	−16.8805	+	29.2379i	−0.874040	+	1.51388i	−0.0162579	+	0.999868i	$0.505175\pi$
$373$	−16.8805	+	29.2379i	−0.874040	+	1.51388i	−0.857782	+	0.514014i	$0.828158\pi$
$374$		0			0
$375$	2.48615	−	1.43538i	0.128384	−	0.0741226i
$376$		0			0
$377$	3.77560	−	7.46245i	0.194453	−	0.384336i
$378$		0			0
$379$	2.75279	−	1.58932i	0.141401	−	0.0816380i	−0.427630	−	0.903954i	$-0.640652\pi$
$379$	2.75279	−	1.58932i	0.141401	−	0.0816380i	0.569032	+	0.822316i	$0.307318\pi$
$380$		0			0
$381$	4.38905	−	7.60206i	0.224858	−	0.389465i
$382$		0			0
$383$	21.2084	+	12.2447i	1.08370	+	0.625675i	0.931892	−	0.362735i	$-0.118157\pi$
$383$	21.2084	+	12.2447i	1.08370	+	0.625675i	0.151809	+	0.988410i	$0.451490\pi$
$384$		0			0
$385$		−	0.00822564i		−	0.000419217i
$386$		0			0
$387$	−7.32507	−	12.6874i	−0.372354	−	0.644937i
$388$		0			0
$389$	−10.9858			−0.557005			−0.278502	−	0.960436i	$-0.589838\pi$
$389$	−10.9858			−0.557005			−0.278502	+	0.960436i	$0.589838\pi$
$390$		0			0
$391$	−18.5966			−0.940469
$392$		0			0
$393$	−22.3531	−	38.7166i	−1.12756	−	1.95300i
$394$		0			0
$395$			2.02435i			0.101856i
$396$		0			0
$397$	−24.6162	−	14.2122i	−1.23545	−	0.713289i	−0.267291	−	0.963616i	$-0.586128\pi$
$397$	−24.6162	−	14.2122i	−1.23545	−	0.713289i	−0.968161	+	0.250327i	$0.919462\pi$
$398$		0			0
$399$	0.137339	−	0.237878i	0.00687554	−	0.0119088i
$400$		0			0
$401$	17.2287	−	9.94697i	0.860358	−	0.496728i	−0.00377395	−	0.999993i	$-0.501201\pi$
$401$	17.2287	−	9.94697i	0.860358	−	0.496728i	0.864132	+	0.503265i	$0.167868\pi$
$402$		0			0
$403$	−24.2175	+	15.8251i	−1.20636	+	0.788307i
$404$		0			0
$405$	−2.37889	+	1.37345i	−0.118208	+	0.0682475i
$406$		0			0
$407$	1.31762	−	2.28219i	0.0653122	−	0.113124i
$408$		0			0
$409$	20.6919	+	11.9464i	1.02315	+	0.590714i	0.915014	−	0.403423i	$-0.132180\pi$
$409$	20.6919	+	11.9464i	1.02315	+	0.590714i	0.108133	+	0.994136i	$0.465513\pi$
$410$		0			0
$411$			51.3668i			2.53374i
$412$		0			0
$413$	−0.0887906	−	0.153790i	−0.00436910	−	0.00756750i
$414$		0			0
$415$	−2.35696			−0.115699
$416$		0			0
$417$	59.8285			2.92981
$418$		0			0
$419$	5.67470	+	9.82886i	0.277227	+	0.480171i	0.970695	−	0.240317i	$-0.0772512\pi$
$419$	5.67470	+	9.82886i	0.277227	+	0.480171i	−0.693467	+	0.720488i	$0.743918\pi$
$420$		0			0
$421$		−	23.8328i		−	1.16154i	−0.814068	−	0.580769i	$-0.802752\pi$
$421$		−	23.8328i		−	1.16154i	0.814068	−	0.580769i	$-0.197248\pi$
$422$		0			0
$423$	−18.1982	−	10.5067i	−0.884828	−	0.510855i
$424$		0			0
$425$	3.78024	−	6.54756i	0.183368	−	0.317604i
$426$		0			0
$427$	−0.0749475	+	0.0432710i	−0.00362697	+	0.00209403i
$428$		0			0
$429$	0.356898	+	6.45841i	0.0172312	+	0.311815i
$430$		0			0
$431$	−1.44588	+	0.834781i	−0.0696457	+	0.0402100i	−0.534418	−	0.845220i	$-0.679469\pi$
$431$	−1.44588	+	0.834781i	−0.0696457	+	0.0402100i	0.464773	+	0.885430i	$0.346136\pi$
$432$		0			0
$433$	−13.5317	+	23.4376i	−0.650292	+	1.12634i	0.332760	+	0.943012i	$0.392020\pi$
$433$	−13.5317	+	23.4376i	−0.650292	+	1.12634i	−0.983052	+	0.183328i	$0.941313\pi$
$434$		0			0
$435$	5.76671	+	3.32941i	0.276493	+	0.159633i
$436$		0			0
$437$		−	17.8797i		−	0.855302i
$438$		0			0
$439$	2.17711	+	3.77087i	0.103908	+	0.179974i	0.913291	−	0.407307i	$-0.133532\pi$
$439$	2.17711	+	3.77087i	0.103908	+	0.179974i	−0.809384	+	0.587280i	$0.800199\pi$
$440$		0			0
$441$	36.6878			1.74704
$442$		0			0
$443$	−26.7538			−1.27111			−0.635556	−	0.772055i	$-0.719229\pi$
$443$	−26.7538			−1.27111			−0.635556	+	0.772055i	$0.719229\pi$
$444$		0			0
$445$	−2.59949	−	4.50245i	−0.123228	−	0.213437i
$446$		0			0
$447$			46.9067i			2.21861i
$448$		0			0
$449$	−6.11442	−	3.53016i	−0.288557	−	0.166599i	0.348734	−	0.937222i	$-0.386612\pi$
$449$	−6.11442	−	3.53016i	−0.288557	−	0.166599i	−0.637291	+	0.770623i	$0.719945\pi$
$450$		0			0
$451$	−1.18994	+	2.06103i	−0.0560319	+	0.0970502i
$452$		0			0
$453$	−15.7735	+	9.10681i	−0.741102	+	0.427875i
$454$		0			0
$455$	−0.0473870	+	0.00261866i	−0.00222154	+	0.000122764i
$456$		0			0
$457$	−24.8408	+	14.3419i	−1.16200	+	0.670884i	−0.951784	−	0.306770i	$-0.900752\pi$
$457$	−24.8408	+	14.3419i	−1.16200	+	0.670884i	−0.210221	+	0.977654i	$0.567418\pi$
$458$		0			0
$459$	−24.3223	+	42.1275i	−1.13527	+	1.96634i
$460$		0			0
$461$	11.3018	+	6.52508i	0.526376	+	0.303903i	0.739539	−	0.673113i	$-0.235043\pi$
$461$	11.3018	+	6.52508i	0.526376	+	0.303903i	−0.213163	+	0.977017i	$0.568377\pi$
$462$		0			0
$463$		−	30.1313i		−	1.40032i	−0.713985	−	0.700161i	$-0.753112\pi$
$463$		−	30.1313i		−	1.40032i	0.713985	−	0.700161i	$-0.246888\pi$
$464$		0			0
$465$	−11.5169	−	19.9479i	−0.534085	−	0.925063i
$466$		0			0
$467$	21.4253			0.991446			0.495723	−	0.868481i	$-0.334903\pi$
$467$	21.4253			0.991446			0.495723	+	0.868481i	$0.334903\pi$
$468$		0			0
$469$	0.0883991			0.00408189
$470$		0			0
$471$	0.652946	+	1.13093i	0.0300861	+	0.0521107i
$472$		0			0
$473$		−	1.74674i		−	0.0803150i
$474$		0			0
$475$	6.29517	+	3.63452i	0.288842	+	0.166763i
$476$		0			0
$477$	−16.3850	+	28.3797i	−0.750218	+	1.29942i
$478$		0			0
$479$	24.6440	−	14.2282i	1.12602	−	0.650105i	0.183085	−	0.983097i	$-0.441392\pi$
$479$	24.6440	−	14.2282i	1.12602	−	0.650105i	0.942930	+	0.332992i	$0.108058\pi$
$480$		0			0
$481$	−13.5669	−	6.86415i	−0.618599	−	0.312978i
$482$		0			0
$483$	−0.0804935	+	0.0464729i	−0.00366258	+	0.00211459i
$484$		0			0
$485$	4.05387	−	7.02150i	0.184077	−	0.318830i
$486$		0			0
$487$	−19.2632	−	11.1216i	−0.872901	−	0.503969i	−0.00458955	−	0.999989i	$-0.501461\pi$
$487$	−19.2632	−	11.1216i	−0.872901	−	0.503969i	−0.868311	+	0.496020i	$0.834794\pi$
$488$		0			0
$489$			27.4274i			1.24031i
$490$		0			0
$491$	−18.4112	−	31.8892i	−0.830887	−	1.43914i	−0.897336	−	0.441349i	$-0.854500\pi$
$491$	−18.4112	−	31.8892i	−0.830887	−	1.43914i	0.0664487	−	0.997790i	$-0.478833\pi$
$492$		0			0
$493$	17.5368			0.789818
$494$		0			0
$495$	−3.27532			−0.147215
$496$		0			0
$497$	0.100510	+	0.174088i	0.00450847	+	0.00780890i
$498$		0			0
$499$			19.2718i			0.862725i	0.902179	+	0.431362i	$0.141967\pi$
$499$			19.2718i			0.862725i	−0.902179	+	0.431362i	$0.858033\pi$
$500$		0			0
$501$	25.0135	+	14.4415i	1.11752	+	0.645201i
$502$		0			0
$503$	4.00312	−	6.93361i	0.178490	−	0.309155i	−0.762873	−	0.646548i	$-0.776212\pi$
$503$	4.00312	−	6.93361i	0.178490	−	0.309155i	0.941364	+	0.337394i	$0.109545\pi$
$504$		0			0
$505$	−9.84736	+	5.68537i	−0.438202	+	0.252996i
$506$		0			0
$507$	37.0926	−	4.11211i	1.64734	−	0.182625i
$508$		0			0
$509$	−15.3822	+	8.88090i	−0.681803	+	0.393639i	−0.800534	−	0.599287i	$-0.795451\pi$
$509$	−15.3822	+	8.88090i	−0.681803	+	0.393639i	0.118731	+	0.992926i	$0.462117\pi$
$510$		0			0
$511$	0.0196743	−	0.0340769i	0.000870340	−	0.00150747i
$512$		0			0
$513$	−40.5035	−	23.3847i	−1.78827	−	1.03246i
$514$		0			0
$515$			13.9614i			0.615213i
$516$		0			0
$517$	−1.25272	−	2.16977i	−0.0550945	−	0.0954265i
$518$		0			0
$519$	−16.1826			−0.710339
$520$		0			0
$521$	6.32264			0.277000			0.138500	−	0.990362i	$-0.455772\pi$
$521$	6.32264			0.277000			0.138500	+	0.990362i	$0.455772\pi$
$522$		0			0
$523$	6.41474	+	11.1107i	0.280497	+	0.485835i	0.971507	−	0.237010i	$-0.0761674\pi$
$523$	6.41474	+	11.1107i	0.280497	+	0.485835i	−0.691010	+	0.722845i	$0.742834\pi$
$524$		0			0
$525$		−	0.0377874i		−	0.00164918i
$526$		0			0
$527$	−52.5352	−	30.3312i	−2.28847	−	1.32125i
$528$		0			0
$529$	8.47492	−	14.6790i	0.368475	−	0.638217i
$530$		0			0
$531$	−61.2367	+	35.3550i	−2.65745	+	1.53428i
$532$		0			0
$533$	12.2522	+	6.19897i	0.530702	+	0.268507i
$534$		0			0
$535$	12.7008	−	7.33282i	0.549104	−	0.317026i
$536$		0			0
$537$	5.89665	−	10.2133i	0.254459	−	0.440736i
$538$		0			0
$539$	3.78824	+	2.18714i	0.163171	+	0.0942069i
$540$		0			0
$541$		−	26.8783i		−	1.15559i	−0.816183	−	0.577793i	$-0.803914\pi$
$541$		−	26.8783i		−	1.15559i	0.816183	−	0.577793i	$-0.196086\pi$
$542$		0			0
$543$	37.6913	+	65.2832i	1.61749	+	2.80157i
$544$		0			0
$545$	6.16019			0.263874
$546$		0			0
$547$	−18.7581			−0.802039			−0.401020	−	0.916069i	$-0.631344\pi$
$547$	−18.7581			−0.802039			−0.401020	+	0.916069i	$0.631344\pi$
$548$		0			0
$549$	17.2298	+	29.8429i	0.735351	+	1.27367i
$550$		0			0
$551$			16.8608i			0.718294i
$552$		0			0
$553$	0.0230764	+	0.0133231i	0.000981307	+	0.000566558i
$554$		0			0
$555$	6.05296	−	10.4840i	0.256934	−	0.445023i
$556$		0			0
$557$	−0.562910	+	0.324996i	−0.0238513	+	0.0137705i	−0.511878	−	0.859058i	$-0.671050\pi$
$557$	−0.562910	+	0.324996i	−0.0238513	+	0.0137705i	0.488027	+	0.872829i	$0.337717\pi$
$558$		0			0
$559$	−10.0628	+	0.556078i	−0.425609	+	0.0235196i
$560$		0			0
$561$	−11.7462	+	6.78165i	−0.495923	+	0.286321i
$562$		0			0
$563$	2.06346	−	3.57402i	0.0869645	−	0.150627i	−0.819262	−	0.573419i	$-0.805617\pi$
$563$	2.06346	−	3.57402i	0.0869645	−	0.150627i	0.906227	+	0.422792i	$0.138950\pi$
$564$		0			0
$565$	5.87021	+	3.38917i	0.246962	+	0.142583i
$566$		0			0
$567$			0.0361571i			0.00151846i
$568$		0			0
$569$	17.6625	+	30.5923i	0.740449	+	1.28250i	0.952291	+	0.305191i	$0.0987204\pi$
$569$	17.6625	+	30.5923i	0.740449	+	1.28250i	−0.211842	+	0.977304i	$0.567946\pi$
$570$		0			0
$571$	−21.7114			−0.908596			−0.454298	−	0.890850i	$-0.650110\pi$
$571$	−21.7114			−0.908596			−0.454298	+	0.890850i	$0.650110\pi$
$572$		0			0
$573$	−45.3114			−1.89291
$574$		0			0
$575$	−1.22985	−	2.13017i	−0.0512885	−	0.0888342i
$576$		0			0
$577$			27.7388i			1.15478i	0.816468	+	0.577390i	$0.195929\pi$
$577$			27.7388i			1.15478i	−0.816468	+	0.577390i	$0.804071\pi$
$578$		0			0
$579$	−1.96590	−	1.13501i	−0.0817002	−	0.0471696i
$580$		0			0
$581$	−0.0155122	+	0.0268679i	−0.000643554	+	0.00111467i
$582$		0			0
$583$	−3.38371	+	1.95358i	−0.140139	+	0.0809092i
$584$		0			0
$585$	1.04271	+	18.8688i	0.0431107	+	0.780128i
$586$		0			0
$587$	26.3980	−	15.2409i	1.08956	−	0.629058i	0.156102	−	0.987741i	$-0.450107\pi$
$587$	26.3980	−	15.2409i	1.08956	−	0.629058i	0.933460	+	0.358683i	$0.116774\pi$
$588$		0			0
$589$	29.1620	−	50.5101i	1.20160	−	2.08123i
$590$		0			0
$591$	−7.78360	−	4.49386i	−0.320174	−	0.184853i
$592$		0			0
$593$		−	25.3371i		−	1.04047i	−0.854024	−	0.520234i	$-0.825845\pi$
$593$		−	25.3371i		−	1.04047i	0.854024	−	0.520234i	$-0.174155\pi$
$594$		0			0
$595$	−0.0497587	−	0.0861846i	−0.00203991	−	0.00353323i
$596$		0			0
$597$	17.2937			0.707784
$598$		0			0
$599$	13.4736			0.550517			0.275259	−	0.961370i	$-0.411236\pi$
$599$	13.4736			0.550517			0.275259	+	0.961370i	$0.411236\pi$
$600$		0			0
$601$	−19.4499	−	33.6883i	−0.793380	−	1.37417i	−0.923863	−	0.382724i	$-0.874986\pi$
$601$	−19.4499	−	33.6883i	−0.793380	−	1.37417i	0.130483	−	0.991451i	$-0.458347\pi$
$602$		0			0
$603$		−	35.1991i		−	1.43342i
$604$		0			0
$605$	9.18808	+	5.30474i	0.373549	+	0.215668i
$606$		0			0
$607$	1.14512	−	1.98340i	0.0464789	−	0.0805039i	−0.841850	−	0.539712i	$-0.818533\pi$
$607$	1.14512	−	1.98340i	0.0464789	−	0.0805039i	0.888329	+	0.459208i	$0.151867\pi$
$608$		0			0
$609$	0.0759064	−	0.0438246i	0.00307588	−	0.00177586i
$610$		0			0
$611$	−12.1010	+	7.90753i	−0.489555	+	0.319905i
$612$		0			0
$613$	31.1861	−	18.0053i	1.25960	−	0.727228i	0.286599	−	0.958051i	$-0.407475\pi$
$613$	31.1861	−	18.0053i	1.25960	−	0.727228i	0.972996	+	0.230823i	$0.0741418\pi$
$614$		0			0
$615$	−5.46639	+	9.46807i	−0.220426	+	0.381789i
$616$		0			0
$617$	11.2592	+	6.50050i	0.453278	+	0.261700i	0.709214	−	0.704994i	$-0.249050\pi$
$617$	11.2592	+	6.50050i	0.453278	+	0.261700i	−0.255935	+	0.966694i	$0.582383\pi$
$618$		0			0
$619$			24.6297i			0.989952i	0.868907	+	0.494976i	$0.164823\pi$
$619$			24.6297i			0.989952i	−0.868907	+	0.494976i	$0.835177\pi$
$620$		0			0
$621$	7.91296	+	13.7057i	0.317536	+	0.549989i
$622$		0			0
$623$	−0.0684334			−0.00274173
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−6.52023	−	11.2934i	−0.260393	−	0.451014i
$628$		0			0
$629$		−	31.8824i		−	1.27123i
$630$		0			0
$631$	28.6992	+	16.5695i	1.14250	+	0.659621i	0.947048	−	0.321093i	$-0.104050\pi$
$631$	28.6992	+	16.5695i	1.14250	+	0.659621i	0.195449	+	0.980714i	$0.437384\pi$
$632$		0			0
$633$	−36.0218	+	62.3917i	−1.43174	+	2.47985i
$634$		0			0
$635$	2.64810	−	1.52888i	0.105087	−	0.0606719i
$636$		0			0
$637$	11.3939	−	22.5199i	0.451443	−	0.892272i
$638$		0			0
$639$	69.3190	−	40.0214i	2.74222	−	1.58322i
$640$		0			0
$641$	−18.9022	+	32.7395i	−0.746591	+	1.29313i	0.202857	+	0.979208i	$0.434977\pi$
$641$	−18.9022	+	32.7395i	−0.746591	+	1.29313i	−0.949448	+	0.313925i	$0.898356\pi$
$642$		0			0
$643$	16.3067	+	9.41467i	0.643073	+	0.371278i	0.785797	−	0.618484i	$-0.212253\pi$
$643$	16.3067	+	9.41467i	0.643073	+	0.371278i	−0.142724	+	0.989762i	$0.545586\pi$
$644$		0			0
$645$		−	8.02424i		−	0.315954i
$646$		0			0
$647$	6.03457	+	10.4522i	0.237243	+	0.410917i	0.959922	−	0.280266i	$-0.0904228\pi$
$647$	6.03457	+	10.4522i	0.237243	+	0.410917i	−0.722679	+	0.691184i	$0.757089\pi$
$648$		0			0
$649$	−8.43076			−0.330936
$650$		0			0
$651$	−0.303191			−0.0118830
$652$		0			0
$653$	0.180156	+	0.312039i	0.00705004	+	0.0122110i	0.869529	−	0.493882i	$-0.164423\pi$
$653$	0.180156	+	0.312039i	0.00705004	+	0.0122110i	−0.862479	+	0.506093i	$0.831089\pi$
$654$		0			0
$655$		−	15.5729i		−	0.608485i
$656$		0			0
$657$	−13.5689	−	7.83401i	−0.529373	−	0.305634i
$658$		0			0
$659$	−8.14247	+	14.1032i	−0.317185	+	0.549381i	−0.979900	−	0.199491i	$-0.936071\pi$
$659$	−8.14247	+	14.1032i	−0.317185	+	0.549381i	0.662714	+	0.748872i	$0.269404\pi$
$660$		0			0
$661$	−12.1249	+	7.00033i	−0.471605	+	0.272281i	−0.716911	−	0.697164i	$-0.754445\pi$
$661$	−12.1249	+	7.00033i	−0.471605	+	0.272281i	0.245306	+	0.969446i	$0.421111\pi$
$662$		0			0
$663$	42.8078	+	65.5094i	1.66252	+	2.54417i
$664$		0			0
$665$	0.0828624	−	0.0478406i	0.00321327	−	0.00185518i
$666$		0			0
$667$	2.85269	−	4.94101i	0.110457	−	0.191317i
$668$		0			0
$669$	−0.606348	−	0.350075i	−0.0234428	−	0.0135347i
$670$		0			0
$671$			4.10862i			0.158612i
$672$		0			0
$673$	−2.40870	−	4.17199i	−0.0928485	−	0.160818i	0.815860	−	0.578249i	$-0.196264\pi$
$673$	−2.40870	−	4.17199i	−0.0928485	−	0.160818i	−0.908709	+	0.417431i	$0.862931\pi$
$674$		0			0
$675$	−6.43407			−0.247647
$676$		0			0
$677$	1.69491			0.0651407			0.0325703	−	0.999469i	$-0.489631\pi$
$677$	1.69491			0.0651407			0.0325703	+	0.999469i	$0.489631\pi$
$678$		0			0
$679$	−0.0533604	−	0.0924230i	−0.00204779	−	0.00354687i
$680$		0			0
$681$			25.8364i			0.990054i
$682$		0			0
$683$	−20.9247	−	12.0809i	−0.800661	−	0.462262i	0.0430412	−	0.999073i	$-0.486295\pi$
$683$	−20.9247	−	12.0809i	−0.800661	−	0.462262i	−0.843702	+	0.536811i	$0.819629\pi$
$684$		0			0
$685$	−8.94656	+	15.4959i	−0.341830	+	0.592068i
$686$		0			0
$687$	−57.6773	+	33.3000i	−2.20053	+	1.27048i
$688$		0			0
$689$	12.3316	+	18.8712i	0.469797	+	0.718937i
$690$		0			0
$691$	3.68354	−	2.12669i	0.140128	−	0.0809032i	−0.428297	−	0.903638i	$-0.640886\pi$
$691$	3.68354	−	2.12669i	0.140128	−	0.0809032i	0.568425	+	0.822735i	$0.307553\pi$
$692$		0			0
$693$	−0.0215563	+	0.0373366i	−0.000818856	+	0.00141830i
$694$		0			0
$695$	18.0485	+	10.4203i	0.684620	+	0.395266i
$696$		0			0
$697$			28.7928i			1.09060i
$698$		0			0
$699$	−4.39203	−	7.60722i	−0.166122	−	0.287732i
$700$		0			0
$701$	49.9032			1.88482			0.942408	−	0.334465i	$-0.108556\pi$
$701$	49.9032			1.88482			0.942408	+	0.334465i	$0.108556\pi$
$702$		0			0
$703$	30.6534			1.15611
$704$		0			0
$705$	−5.75480	−	9.96761i	−0.216738	−	0.375402i
$706$		0			0
$707$			0.149671i			0.00562898i
$708$		0			0
$709$	−29.5571	−	17.0648i	−1.11004	−	0.640881i	−0.171199	−	0.985236i	$-0.554764\pi$
$709$	−29.5571	−	17.0648i	−1.11004	−	0.640881i	−0.938839	+	0.344355i	$0.888098\pi$
$710$		0			0
$711$	5.30507	−	9.18865i	0.198956	−	0.344601i
$712$		0			0
$713$	−17.0917	+	9.86789i	−0.640088	+	0.369555i
$714$		0			0
$715$	−1.01720	+	2.01048i	−0.0380410	+	0.0751876i
$716$		0			0
$717$	36.2044	−	20.9026i	1.35208	−	0.780623i
$718$		0			0
$719$	2.72873	−	4.72630i	0.101765	−	0.176261i	−0.810647	−	0.585535i	$-0.800885\pi$
$719$	2.72873	−	4.72630i	0.101765	−	0.176261i	0.912412	+	0.409274i	$0.134218\pi$
$720$		0			0
$721$	0.159151	+	0.0918859i	0.00592710	+	0.00342201i
$722$		0			0
$723$		−	62.2920i		−	2.31667i
$724$		0			0
$725$	1.15977	+	2.00878i	0.0430727	+	0.0746041i
$726$		0			0
$727$	35.0650			1.30049			0.650244	−	0.759725i	$-0.274667\pi$
$727$	35.0650			1.30049			0.650244	+	0.759725i	$0.274667\pi$
$728$		0			0
$729$	−41.0147			−1.51906
$730$		0			0
$731$	−10.5664	−	18.3015i	−0.390812	−	0.676906i
$732$		0			0
$733$		−	11.5520i		−	0.426683i	−0.976978	−	0.213341i	$-0.931565\pi$
$733$		−	11.5520i		−	0.426683i	0.976978	−	0.213341i	$-0.0684346\pi$
$734$		0			0
$735$	17.4026	+	10.0474i	0.641905	+	0.370604i
$736$		0			0
$737$	2.09840	−	3.63453i	0.0772954	−	0.133880i
$738$		0			0
$739$	9.81858	−	5.66876i	0.361182	−	0.208529i	−0.308417	−	0.951251i	$-0.599799\pi$
$739$	9.81858	−	5.66876i	0.361182	−	0.208529i	0.669599	+	0.742723i	$0.266466\pi$
$740$		0			0
$741$	−62.9842	+	41.1576i	−2.31378	+	1.51196i
$742$		0			0
$743$	−2.22973	+	1.28734i	−0.0818009	+	0.0472278i	−0.540343	−	0.841445i	$-0.681705\pi$
$743$	−2.22973	+	1.28734i	−0.0818009	+	0.0472278i	0.458542	+	0.888673i	$0.348372\pi$
$744$		0			0
$745$	−8.16975	+	14.1504i	−0.299317	+	0.518432i
$746$		0			0
$747$	10.6984	+	6.17671i	0.391433	+	0.225994i
$748$		0			0
$749$		−	0.193042i		−	0.00705359i
$750$		0			0
$751$	−21.2324	−	36.7756i	−0.774782	−	1.34196i	−0.934917	−	0.354866i	$-0.884526\pi$
$751$	−21.2324	−	36.7756i	−0.774782	−	1.34196i	0.160135	−	0.987095i	$-0.448807\pi$
$752$		0			0
$753$	38.2893			1.39534
$754$		0			0
$755$	−6.34453			−0.230901
$756$		0			0
$757$	22.8791	+	39.6278i	0.831556	+	1.44030i	0.896804	+	0.442428i	$0.145883\pi$
$757$	22.8791	+	39.6278i	0.831556	+	1.44030i	−0.0652482	+	0.997869i	$0.520784\pi$
$758$		0			0
$759$			4.41265i			0.160169i
$760$		0			0
$761$	−7.27193	−	4.19845i	−0.263607	−	0.152194i	0.362372	−	0.932034i	$-0.381967\pi$
$761$	−7.27193	−	4.19845i	−0.263607	−	0.152194i	−0.625979	+	0.779840i	$0.715300\pi$
$762$		0			0
$763$	0.0405428	−	0.0702223i	0.00146775	−	0.00254222i
$764$		0			0
$765$	−34.3174	+	19.8132i	−1.24075	+	0.716346i
$766$		0			0
$767$	2.68395	+	48.5687i	0.0969120	+	1.75371i
$768$		0			0
$769$	33.3508	−	19.2551i	1.20266	−	0.694356i	0.241514	−	0.970397i	$-0.422356\pi$
$769$	33.3508	−	19.2551i	1.20266	−	0.694356i	0.961146	+	0.276042i	$0.0890229\pi$
$770$		0			0
$771$	30.4549	−	52.7494i	1.09681	−	1.89972i
$772$		0			0
$773$	−13.8690	−	8.00728i	−0.498834	−	0.288002i	0.229398	−	0.973333i	$-0.426324\pi$
$773$	−13.8690	−	8.00728i	−0.498834	−	0.288002i	−0.728232	+	0.685331i	$0.759658\pi$
$774$		0			0
$775$		−	8.02362i		−	0.288217i
$776$		0			0
$777$	−0.0796743	−	0.138000i	−0.00285830	−	0.00495072i
$778$		0			0
$779$	−27.6829			−0.991842
$780$		0			0
$781$	9.54348			0.341493
$782$		0			0
$783$	−7.46203	−	12.9246i	−0.266671	−	0.461888i
$784$		0			0
$785$			0.454894i			0.0162359i
$786$		0			0
$787$	−22.9063	−	13.2249i	−0.816520	−	0.471418i	0.0326948	−	0.999465i	$-0.489591\pi$
$787$	−22.9063	−	13.2249i	−0.816520	−	0.471418i	−0.849215	+	0.528047i	$0.822924\pi$
$788$		0			0
$789$	14.8011	−	25.6362i	0.526933	−	0.912674i
$790$		0			0
$791$	0.0772688	−	0.0446111i	0.00274736	−	0.00158619i
$792$		0			0
$793$	23.6693	−	1.30799i	0.840523	−	0.0464481i
$794$		0			0
$795$	−15.5442	+	8.97447i	−0.551297	+	0.318292i
$796$		0			0
$797$	27.7925	−	48.1380i	0.984461	−	1.70514i	0.340156	−	0.940369i	$-0.389520\pi$
$797$	27.7925	−	48.1380i	0.984461	−	1.70514i	0.644306	−	0.764768i	$-0.277146\pi$
$798$		0			0
$799$	−26.2509	−	15.1559i	−0.928689	−	0.536179i
$800$		0			0
$801$			27.2491i			0.962801i
$802$		0			0
$803$	−0.934048	−	1.61782i	−0.0329618	−	0.0570916i
$804$		0			0
$805$	−0.0323768			−0.00114113
$806$		0			0
$807$	79.1121			2.78488
$808$		0			0
$809$	3.88462	+	6.72836i	0.136576	+	0.236557i	0.926198	−	0.377036i	$-0.123057\pi$
$809$	3.88462	+	6.72836i	0.136576	+	0.236557i	−0.789622	+	0.613593i	$0.789724\pi$
$810$		0			0
$811$		−	37.0763i		−	1.30192i	−0.759110	−	0.650962i	$-0.774366\pi$
$811$		−	37.0763i		−	1.30192i	0.759110	−	0.650962i	$-0.225634\pi$
$812$		0			0
$813$	27.4957	+	15.8747i	0.964317	+	0.556749i
$814$		0			0
$815$	−4.77703	+	8.27406i	−0.167332	+	0.289828i
$816$		0			0
$817$	17.5960	−	10.1591i	0.615607	−	0.355421i
$818$		0			0
$819$	0.221955	+	0.112297i	0.00775572	+	0.00392399i
$820$		0			0
$821$	14.0800	−	8.12908i	0.491395	−	0.283707i	−0.233758	−	0.972295i	$-0.575102\pi$
$821$	14.0800	−	8.12908i	0.491395	−	0.283707i	0.725153	+	0.688588i	$0.241769\pi$
$822$		0			0
$823$	4.45988	−	7.72473i	0.155461	−	0.269267i	−0.777765	−	0.628555i	$-0.783647\pi$
$823$	4.45988	−	7.72473i	0.155461	−	0.269267i	0.933227	+	0.359287i	$0.116980\pi$
$824$		0			0
$825$	−1.55363	−	0.896987i	−0.0540903	−	0.0312291i
$826$		0			0
$827$		−	5.70031i		−	0.198219i	−0.995077	−	0.0991097i	$-0.968401\pi$
$827$		−	5.70031i		−	0.198219i	0.995077	−	0.0991097i	$-0.0315995\pi$
$828$		0			0
$829$	−3.93952	−	6.82346i	−0.136825	−	0.236988i	0.789468	−	0.613792i	$-0.210357\pi$
$829$	−3.93952	−	6.82346i	−0.136825	−	0.236988i	−0.926293	+	0.376803i	$0.877023\pi$
$830$		0			0
$831$	68.5308			2.37731
$832$		0			0
$833$	52.9220			1.83364
$834$		0			0
$835$	5.03057	+	8.71320i	0.174090	+	0.301533i
$836$		0			0
$837$			51.6245i			1.78440i
$838$		0			0
$839$	−27.3107	−	15.7678i	−0.942869	−	0.544366i	−0.0520106	−	0.998647i	$-0.516563\pi$
$839$	−27.3107	−	15.7678i	−0.942869	−	0.544366i	−0.890859	+	0.454281i	$0.849896\pi$
$840$		0			0
$841$	11.8099	−	20.4553i	0.407237	−	0.705355i
$842$		0			0
$843$	−6.44176	+	3.71915i	−0.221866	+	0.128094i
$844$		0			0
$845$	11.9060	+	5.21992i	0.409578	+	0.179571i
$846$		0			0
$847$	0.120941	−	0.0698255i	0.00415560	−	0.00239923i
$848$		0			0
$849$	21.7182	−	37.6171i	0.745368	−	1.29102i
$850$		0			0
$851$	−8.98288	−	5.18627i	−0.307929	−	0.177783i
$852$		0			0
$853$		−	19.4521i		−	0.666026i	−0.942922	−	0.333013i	$-0.891935\pi$
$853$		−	19.4521i		−	0.666026i	0.942922	−	0.333013i	$-0.108065\pi$
$854$		0			0
$855$	−19.0494	−	32.9945i	−0.651476	−	1.12839i
$856$		0			0
$857$	7.12075			0.243240			0.121620	−	0.992577i	$-0.461191\pi$
$857$	7.12075			0.243240			0.121620	+	0.992577i	$0.461191\pi$
$858$		0			0
$859$	−39.0322			−1.33176			−0.665881	−	0.746058i	$-0.731944\pi$
$859$	−39.0322			−1.33176			−0.665881	+	0.746058i	$0.731944\pi$
$860$		0			0
$861$	0.0719533	+	0.124627i	0.00245216	+	0.00424727i
$862$		0			0
$863$		−	56.6348i		−	1.92787i	−0.266136	−	0.963935i	$-0.585747\pi$
$863$		−	56.6348i		−	1.92787i	0.266136	−	0.963935i	$-0.414253\pi$
$864$		0			0
$865$	−4.88184	−	2.81853i	−0.165988	−	0.0958330i
$866$		0			0
$867$	−57.6459	+	99.8457i	−1.95776	+	3.39094i
$868$		0			0
$869$	1.09556	−	0.632523i	0.0371644	−	0.0214569i
$870$		0			0
$871$	−21.6062	−	10.9316i	−0.732097	−	0.370402i
$872$		0			0
$873$	−36.8014	+	21.2473i	−1.24554	+	0.719112i
$874$		0			0
$875$	0.00658143	−	0.0113994i	0.000222493	−	0.000385369i
$876$		0			0
$877$	−21.2565	−	12.2725i	−0.717783	−	0.414412i	0.0961534	−	0.995367i	$-0.469346\pi$
$877$	−21.2565	−	12.2725i	−0.717783	−	0.414412i	−0.813936	+	0.580955i	$0.802679\pi$
$878$		0			0
$879$		−	91.8504i		−	3.09804i
$880$		0			0
$881$	17.9634	+	31.1135i	0.605201	+	1.04824i	0.992020	+	0.126083i	$0.0402406\pi$
$881$	17.9634	+	31.1135i	0.605201	+	1.04824i	−0.386819	+	0.922156i	$0.626426\pi$
$882$		0			0
$883$	54.3701			1.82970			0.914850	−	0.403794i	$-0.132309\pi$
$883$	54.3701			1.82970			0.914850	+	0.403794i	$0.132309\pi$
$884$		0			0
$885$	−38.7296			−1.30188
$886$		0			0
$887$	5.20320	+	9.01221i	0.174707	+	0.302601i	0.940060	−	0.341010i	$-0.110769\pi$
$887$	5.20320	+	9.01221i	0.174707	+	0.302601i	−0.765353	+	0.643611i	$0.777436\pi$
$888$		0			0
$889$		−	0.0402489i		−	0.00134991i
$890$		0			0
$891$	1.48660	+	0.858289i	0.0498030	+	0.0287538i
$892$		0			0
$893$	14.5717	−	25.2389i	0.487624	−	0.844589i
$894$		0			0
$895$	3.55770	−	2.05404i	0.118921	−	0.0686590i
$896$		0			0
$897$	25.4208	−	1.40478i	0.848776	−	0.0469042i
$898$		0			0
$899$	16.1177	−	9.30555i	0.537555	−	0.310357i
$900$		0			0
$901$	−23.6353	+	40.9376i	−0.787407	+	1.36383i
$902$		0			0
$903$	−0.0914712	−	0.0528109i	−0.00304397	−	0.00175744i
$904$		0			0
$905$			26.2588i			0.872871i
$906$		0			0
$907$	11.3808	+	19.7121i	0.377892	+	0.654529i	0.990755	−	0.135660i	$-0.0433156\pi$
$907$	11.3808	+	19.7121i	0.377892	+	0.654529i	−0.612863	+	0.790189i	$0.709982\pi$
$908$		0			0
$909$	59.5969			1.97670
$910$		0			0
$911$	−43.1903			−1.43096			−0.715480	−	0.698634i	$-0.753792\pi$
$911$	−43.1903			−1.43096			−0.715480	+	0.698634i	$0.753792\pi$
$912$		0			0
$913$	0.736449	+	1.27557i	0.0243729	+	0.0422151i
$914$		0			0
$915$			18.8744i			0.623968i
$916$		0			0
$917$	−0.177522	−	0.102492i	−0.00586228	−	0.00338459i
$918$		0			0
$919$	26.6446	−	46.1497i	0.878923	−	1.52234i	0.0263987	−	0.999651i	$-0.491596\pi$
$919$	26.6446	−	46.1497i	0.878923	−	1.52234i	0.852524	−	0.522688i	$-0.175071\pi$
$920$		0			0
$921$	−49.0654	+	28.3279i	−1.61676	+	0.933438i
$922$		0			0
$923$	−3.03819	−	54.9790i	−0.100003	−	1.80966i
$924$		0			0
$925$	3.65201	−	2.10849i	0.120077	−	0.0693267i
$926$		0			0
$927$	36.5876	−	63.3715i	1.20169	−	2.08139i
$928$		0			0
$929$	30.7343	+	17.7444i	1.00836	+	0.582176i	0.910711	−	0.413045i	$-0.135535\pi$
$929$	30.7343	+	17.7444i	1.00836	+	0.582176i	0.0976482	+	0.995221i	$0.468868\pi$
$930$		0			0
$931$			50.8820i			1.66759i
$932$		0			0
$933$	−34.7657	−	60.2159i	−1.13818	−	1.97138i
$934$		0			0
$935$	−4.72464			−0.154512
$936$		0			0
$937$	−41.0349			−1.34055			−0.670277	−	0.742111i	$-0.733825\pi$
$937$	−41.0349			−1.34055			−0.670277	+	0.742111i	$0.733825\pi$
$938$		0			0
$939$	−24.4019	−	42.2653i	−0.796326	−	1.37928i
$940$		0			0
$941$		−	37.8638i		−	1.23432i	−0.786836	−	0.617162i	$-0.788282\pi$
$941$		−	37.8638i		−	1.23432i	0.786836	−	0.617162i	$-0.211718\pi$
$942$		0			0
$943$	8.11239	+	4.68369i	0.264176	+	0.152522i
$944$		0			0
$945$	−0.0423453	+	0.0733443i	−0.00137749	+	0.00238589i
$946$		0			0
$947$	−15.8835	+	9.17032i	−0.516143	+	0.297995i	−0.735355	−	0.677682i	$-0.762985\pi$
$947$	−15.8835	+	9.17032i	−0.516143	+	0.297995i	0.219212	+	0.975677i	$0.429651\pi$
$948$		0			0
$949$	−9.02272	+	5.89599i	−0.292890	+	0.191392i
$950$		0			0
$951$	−72.4223	+	41.8131i	−2.34846	+	1.35588i
$952$		0			0
$953$	12.6426	−	21.8976i	0.409534	−	0.709334i	−0.585303	−	0.810815i	$-0.699025\pi$
$953$	12.6426	−	21.8976i	0.409534	−	0.709334i	0.994838	+	0.101480i	$0.0323578\pi$
$954$		0			0
$955$	−13.6691	−	7.89188i	−0.442323	−	0.255375i
$956$		0			0
$957$		−	4.16119i		−	0.134512i
$958$		0			0
$959$	0.117762	+	0.203970i	0.00380274	+	0.00658654i
$960$		0			0
$961$	−33.3785			−1.07673
$962$		0			0
$963$	−76.8662			−2.47698
$964$		0			0
$965$	−0.395371	−	0.684803i	−0.0127275	−	0.0220446i
$966$		0			0
$967$			28.2771i			0.909329i	0.890663	+	0.454664i	$0.150241\pi$
$967$			28.2771i			0.909329i	−0.890663	+	0.454664i	$0.849759\pi$
$968$		0			0
$969$	−136.632	−	78.8846i	−4.38926	−	2.53414i
$970$		0			0
$971$	27.2902	−	47.2680i	0.875783	−	1.51690i	0.0198574	−	0.999803i	$-0.493679\pi$
$971$	27.2902	−	47.2680i	0.875783	−	1.51690i	0.855926	−	0.517098i	$-0.172988\pi$
$972$		0			0
$973$	0.237570	−	0.137161i	0.00761616	−	0.00439719i
$974$		0			0
$975$	−4.67284	+	9.23584i	−0.149651	+	0.295784i
$976$		0			0
$977$	0.465407	−	0.268703i	0.0148897	−	0.00859657i	−0.492537	−	0.870292i	$-0.663930\pi$
$977$	0.465407	−	0.268703i	0.0148897	−	0.00859657i	0.507426	+	0.861695i	$0.330597\pi$
$978$		0			0
$979$	−1.62446	+	2.81364i	−0.0519178	+	0.0899243i
$980$		0			0
$981$	−27.9614	−	16.1435i	−0.892739	−	0.515423i
$982$		0			0
$983$			23.5796i			0.752074i	0.926605	+	0.376037i	$0.122713\pi$
$983$			23.5796i			0.752074i	−0.926605	+	0.376037i	$0.877287\pi$
$984$		0			0
$985$	−1.56539	−	2.71134i	−0.0498776	−	0.0863905i
$986$		0			0
$987$	−0.151499			−0.00482227
$988$		0			0
$989$	−6.87529			−0.218622
$990$		0			0
$991$	8.05890	+	13.9584i	0.255999	+	0.443404i	0.965167	−	0.261636i	$-0.0842621\pi$
$991$	8.05890	+	13.9584i	0.255999	+	0.443404i	−0.709167	+	0.705041i	$0.750929\pi$
$992$		0			0
$993$			4.08077i			0.129499i
$994$		0			0
$995$	5.21701	+	3.01204i	0.165390	+	0.0954882i
$996$		0			0
$997$	−6.24465	+	10.8160i	−0.197770	+	0.342548i	−0.947805	−	0.318850i	$-0.896703\pi$
$997$	−6.24465	+	10.8160i	−0.197770	+	0.342548i	0.750035	+	0.661398i	$0.230037\pi$
$998$		0			0
$999$	−23.4973	+	13.5662i	−0.743421	+	0.429214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.f.881.1		16
4.3	odd	2		520.2.bu.b.361.8	yes	16
13.4	even	6	inner	1040.2.da.f.641.1		16
52.11	even	12		6760.2.a.bl.1.1		8
52.15	even	12		6760.2.a.bk.1.1		8
52.43	odd	6		520.2.bu.b.121.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.bu.b.121.8	✓	16	52.43	odd	6
520.2.bu.b.361.8	yes	16	4.3	odd	2
1040.2.da.f.641.1		16	13.4	even	6	inner
1040.2.da.f.881.1		16	1.1	even	1	trivial
6760.2.a.bk.1.1		8	52.15	even	12
6760.2.a.bl.1.1		8	52.11	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.43538 - 2.48615i) q^{3} -1.00000i q^{5} +(-0.0113994 - 0.00658143i) q^{7} +(-2.62062 + 4.53905i) q^{9} +O(q^{10})\)	\(q+(-1.43538 - 2.48615i) q^{3} -1.00000i q^{5} +(-0.0113994 - 0.00658143i) q^{7} +(-2.62062 + 4.53905i) q^{9} +(-0.541191 + 0.312457i) q^{11} +(1.97232 + 3.01827i) q^{13} +(-2.48615 + 1.43538i) q^{15} +(-3.78024 + 6.54756i) q^{17} +(-6.29517 - 3.63452i) q^{19} +0.0377874i q^{21} +(1.22985 + 2.13017i) q^{23} -1.00000 q^{25} +6.43407 q^{27} +(-1.15977 - 2.00878i) q^{29} +8.02362i q^{31} +(1.55363 + 0.896987i) q^{33} +(-0.00658143 + 0.0113994i) q^{35} +(-3.65201 + 2.10849i) q^{37} +(4.67284 - 9.23584i) q^{39} +(3.29811 - 1.90416i) q^{41} +(-1.39758 + 2.42068i) q^{43} +(4.53905 + 2.62062i) q^{45} +4.00926i q^{47} +(-3.49991 - 6.06203i) q^{49} +21.7043 q^{51} +6.25234 q^{53} +(0.312457 + 0.541191i) q^{55} +20.8676i q^{57} +(11.6836 + 6.74554i) q^{59} +(3.28736 - 5.69387i) q^{61} +(0.0597469 - 0.0344949i) q^{63} +(3.01827 - 1.97232i) q^{65} +(-5.81605 + 3.35790i) q^{67} +(3.53061 - 6.11520i) q^{69} +(-13.2257 - 7.63585i) q^{71} +2.98937i q^{73} +(1.43538 + 2.48615i) q^{75} +0.00822564 q^{77} -2.02435 q^{79} +(-1.37345 - 2.37889i) q^{81} -2.35696i q^{83} +(6.54756 + 3.78024i) q^{85} +(-3.32941 + 5.76671i) q^{87} +(4.50245 - 2.59949i) q^{89} +(-0.00261866 - 0.0473870i) q^{91} +(19.9479 - 11.5169i) q^{93} +(-3.63452 + 6.29517i) q^{95} +(7.02150 + 4.05387i) q^{97} -3.27532i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9	\( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) \) 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^17 - 30 * q^19 - 6 * q^23 - 16 * q^25 - 44 * q^27 - 16 * q^29 + 24 * q^33 + 6 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 - 6 * q^43 + 12 * q^45 - 4 * q^49 + 40 * q^51 + 4 * q^53 + 6 * q^55 - 12 * q^59 - 2 * q^61 + 60 * q^63 - 10 * q^65 + 6 * q^67 + 52 * q^69 - 72 * q^71 - 4 * q^75 + 32 * q^77 - 36 * q^79 - 28 * q^81 + 22 * q^87 + 24 * q^89 + 22 * q^91 - 96 * q^93 - 10 * q^95 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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