LMFDB - Embedded newform 300.2.x.a.53.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(17,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 13]))

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

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

chi := DirichletCharacter("300.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			53.5
Character	$\chi$	$=$	300.53
Dual form			300.2.x.a.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.351313 + 1.69605i) q^{3} +(2.22846 + 0.184289i) q^{5} +(-2.84010 + 2.84010i) q^{7} +(-2.75316 - 1.19169i) q^{9} +O(q^{10})$	\(q+(-0.351313 + 1.69605i) q^{3} +(2.22846 + 0.184289i) q^{5} +(-2.84010 + 2.84010i) q^{7} +(-2.75316 - 1.19169i) q^{9} +(4.71560 + 1.53219i) q^{11} +(-0.188444 + 0.369843i) q^{13} +(-1.09545 + 3.71483i) q^{15} +(-7.50930 - 1.18936i) q^{17} +(2.68725 + 3.69868i) q^{19} +(-3.81918 - 5.81471i) q^{21} +(0.153636 + 0.301528i) q^{23} +(4.93208 + 0.821362i) q^{25} +(2.98838 - 4.25083i) q^{27} +(0.836442 + 0.607711i) q^{29} +(-2.24457 + 1.63078i) q^{31} +(-4.25532 + 7.45960i) q^{33} +(-6.85245 + 5.80565i) q^{35} +(4.31832 + 2.20029i) q^{37} +(-0.561068 - 0.449541i) q^{39} +(5.67438 - 1.84372i) q^{41} +(2.46472 + 2.46472i) q^{43} +(-5.91569 - 3.16301i) q^{45} +(-1.21046 - 7.64252i) q^{47} -9.13235i q^{49} +(4.65532 - 12.3183i) q^{51} +(8.21858 - 1.30170i) q^{53} +(10.2262 + 4.28346i) q^{55} +(-7.21721 + 3.25831i) q^{57} +(-3.09959 - 9.53955i) q^{59} +(3.00345 - 9.24368i) q^{61} +(11.2038 - 4.43473i) q^{63} +(-0.488099 + 0.789452i) q^{65} +(1.15518 - 7.29349i) q^{67} +(-0.565381 + 0.154644i) q^{69} +(-1.25910 + 1.73301i) q^{71} +(12.7520 - 6.49745i) q^{73} +(-3.12577 + 8.07648i) q^{75} +(-17.7443 + 9.04119i) q^{77} +(-4.46331 + 6.14322i) q^{79} +(6.15976 + 6.56181i) q^{81} +(-1.02557 + 6.47518i) q^{83} +(-16.5150 - 4.03432i) q^{85} +(-1.32456 + 1.20515i) q^{87} +(4.13129 - 12.7148i) q^{89} +(-0.515190 - 1.58559i) q^{91} +(-1.97733 - 4.37982i) q^{93} +(5.30680 + 8.73760i) q^{95} +(2.19961 - 0.348384i) q^{97} +(-11.1569 - 9.83788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q - 2 * q^3 + 4 * q^7	$ 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) $ 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.351313	+	1.69605i	−0.202831	+	0.979214i
$3$	−0.351313	+	1.69605i	−0.202831	+	0.979214i
$4$		0			0
$5$	2.22846	+	0.184289i	0.996598	+	0.0824166i
$5$	2.22846	+	0.184289i	0.996598	+	0.0824166i
$6$		0			0
$7$	−2.84010	+	2.84010i	−1.07346	+	1.07346i	−0.0763784	+	0.997079i	$0.524336\pi$
$7$	−2.84010	+	2.84010i	−1.07346	+	1.07346i	−0.997079	+	0.0763784i	$0.975664\pi$
$8$		0			0
$9$	−2.75316	−	1.19169i	−0.917719	−	0.397230i
$10$		0			0
$11$	4.71560	+	1.53219i	1.42181	+	0.461973i	0.916175	−	0.400778i	$-0.131260\pi$
$11$	4.71560	+	1.53219i	1.42181	+	0.461973i	0.505630	+	0.862750i	$0.331260\pi$
$12$		0			0
$13$	−0.188444	+	0.369843i	−0.0522651	+	0.102576i	−0.915662	−	0.401950i	$-0.868333\pi$
$13$	−0.188444	+	0.369843i	−0.0522651	+	0.102576i	0.863397	+	0.504526i	$0.168333\pi$
$14$		0			0
$15$	−1.09545	+	3.71483i	−0.282844	+	0.959166i
$16$		0			0
$17$	−7.50930	−	1.18936i	−1.82127	−	0.288461i	−0.850062	−	0.526683i	$-0.823436\pi$
$17$	−7.50930	−	1.18936i	−1.82127	−	0.288461i	−0.971211	+	0.238222i	$0.923436\pi$
$18$		0			0
$19$	2.68725	+	3.69868i	0.616497	+	0.848536i	0.997092	−	0.0762063i	$-0.0242808\pi$
$19$	2.68725	+	3.69868i	0.616497	+	0.848536i	−0.380595	+	0.924742i	$0.624281\pi$
$20$		0			0
$21$	−3.81918	−	5.81471i	−0.833414	−	1.26887i
$22$		0			0
$23$	0.153636	+	0.301528i	0.0320354	+	0.0628730i	0.906469	−	0.422271i	$-0.138767\pi$
$23$	0.153636	+	0.301528i	0.0320354	+	0.0628730i	−0.874434	+	0.485144i	$0.838767\pi$
$24$		0			0
$25$	4.93208	+	0.821362i	0.986415	+	0.164272i
$26$		0			0
$27$	2.98838	−	4.25083i	0.575114	−	0.818073i
$28$		0			0
$29$	0.836442	+	0.607711i	0.155323	+	0.112849i	0.662732	−	0.748856i	$-0.269397\pi$
$29$	0.836442	+	0.607711i	0.155323	+	0.112849i	−0.507409	+	0.861705i	$0.669397\pi$
$30$		0			0
$31$	−2.24457	+	1.63078i	−0.403138	+	0.292897i	−0.770818	−	0.637056i	$-0.780152\pi$
$31$	−2.24457	+	1.63078i	−0.403138	+	0.292897i	0.367680	+	0.929952i	$0.380152\pi$
$32$		0			0
$33$	−4.25532	+	7.45960i	−0.740756	+	1.29855i
$34$		0			0
$35$	−6.85245	+	5.80565i	−1.15828	+	0.981335i
$36$		0			0
$37$	4.31832	+	2.20029i	0.709928	+	0.361726i	0.771372	−	0.636384i	$-0.219571\pi$
$37$	4.31832	+	2.20029i	0.709928	+	0.361726i	−0.0614445	+	0.998111i	$0.519571\pi$
$38$		0			0
$39$	−0.561068	−	0.449541i	−0.0898428	−	0.0719842i
$40$		0			0
$41$	5.67438	−	1.84372i	0.886189	−	0.287940i	0.169664	−	0.985502i	$-0.445732\pi$
$41$	5.67438	−	1.84372i	0.886189	−	0.287940i	0.716525	+	0.697562i	$0.245732\pi$
$42$		0			0
$43$	2.46472	+	2.46472i	0.375866	+	0.375866i	0.869608	−	0.493742i	$-0.164371\pi$
$43$	2.46472	+	2.46472i	0.375866	+	0.375866i	−0.493742	+	0.869608i	$0.664371\pi$
$44$		0			0
$45$	−5.91569	−	3.16301i	−0.881859	−	0.471513i
$46$		0			0
$47$	−1.21046	−	7.64252i	−0.176563	−	1.11478i	−0.903663	−	0.428245i	$-0.859132\pi$
$47$	−1.21046	−	7.64252i	−0.176563	−	1.11478i	0.727100	−	0.686532i	$-0.240868\pi$
$48$		0			0
$49$		−	9.13235i		−	1.30462i
$50$		0			0
$51$	4.65532	−	12.3183i	0.651875	−	1.72491i
$52$		0			0
$53$	8.21858	−	1.30170i	1.12891	−	0.178802i	0.436083	−	0.899906i	$-0.356365\pi$
$53$	8.21858	−	1.30170i	1.12891	−	0.178802i	0.692826	+	0.721105i	$0.256365\pi$
$54$		0			0
$55$	10.2262	+	4.28346i	1.37889	+	0.577581i
$56$		0			0
$57$	−7.21721	+	3.25831i	−0.955942	+	0.431573i
$58$		0			0
$59$	−3.09959	−	9.53955i	−0.403532	−	1.24194i	−0.922115	−	0.386917i	$-0.873540\pi$
$59$	−3.09959	−	9.53955i	−0.403532	−	1.24194i	0.518583	−	0.855028i	$-0.326460\pi$
$60$		0			0
$61$	3.00345	−	9.24368i	0.384553	−	1.18353i	−0.552251	−	0.833678i	$-0.686231\pi$
$61$	3.00345	−	9.24368i	0.384553	−	1.18353i	0.936804	−	0.349855i	$-0.113769\pi$
$62$		0			0
$63$	11.2038	−	4.43473i	1.41154	−	0.558724i
$64$		0			0
$65$	−0.488099	+	0.789452i	−0.0605412	+	0.0979195i
$66$		0			0
$67$	1.15518	−	7.29349i	0.141127	−	0.891041i	−0.810935	−	0.585136i	$-0.801041\pi$
$67$	1.15518	−	7.29349i	0.141127	−	0.891041i	0.952062	−	0.305905i	$-0.0989590\pi$
$68$		0			0
$69$	−0.565381	+	0.154644i	−0.0680639	+	0.0186169i
$70$		0			0
$71$	−1.25910	+	1.73301i	−0.149428	+	0.205670i	−0.877169	−	0.480182i	$-0.840570\pi$
$71$	−1.25910	+	1.73301i	−0.149428	+	0.205670i	0.727741	+	0.685852i	$0.240570\pi$
$72$		0			0
$73$	12.7520	−	6.49745i	1.49250	−	0.760469i	0.498201	−	0.867061i	$-0.333994\pi$
$73$	12.7520	−	6.49745i	1.49250	−	0.760469i	0.994303	+	0.106592i	$0.0339940\pi$
$74$		0			0
$75$	−3.12577	+	8.07648i	−0.360933	+	0.932592i
$76$		0			0
$77$	−17.7443	+	9.04119i	−2.02216	+	1.03034i
$78$		0			0
$79$	−4.46331	+	6.14322i	−0.502162	+	0.691166i	−0.982573	−	0.185877i	$-0.940487\pi$
$79$	−4.46331	+	6.14322i	−0.502162	+	0.691166i	0.480411	+	0.877043i	$0.340487\pi$
$80$		0			0
$81$	6.15976	+	6.56181i	0.684417	+	0.729090i
$82$		0			0
$83$	−1.02557	+	6.47518i	−0.112571	+	0.710743i	0.865256	+	0.501329i	$0.167156\pi$
$83$	−1.02557	+	6.47518i	−0.112571	+	0.710743i	−0.977827	+	0.209414i	$0.932844\pi$
$84$		0			0
$85$	−16.5150	−	4.03432i	−1.79130	−	0.437583i
$86$		0			0
$87$	−1.32456	+	1.20515i	−0.142008	+	0.129206i
$88$		0			0
$89$	4.13129	−	12.7148i	0.437916	−	1.34777i	−0.452153	−	0.891941i	$-0.649344\pi$
$89$	4.13129	−	12.7148i	0.437916	−	1.34777i	0.890069	−	0.455826i	$-0.150656\pi$
$90$		0			0
$91$	−0.515190	−	1.58559i	−0.0540066	−	0.166215i
$92$		0			0
$93$	−1.97733	−	4.37982i	−0.205040	−	0.454166i
$94$		0			0
$95$	5.30680	+	8.73760i	0.544466	+	0.896458i
$96$		0			0
$97$	2.19961	−	0.348384i	0.223337	−	0.0353730i	−0.0437632	−	0.999042i	$-0.513935\pi$
$97$	2.19961	−	0.348384i	0.223337	−	0.0353730i	0.267100	+	0.963669i	$0.413935\pi$
$98$		0			0
$99$	−11.1569	−	9.83788i	−1.12131	−	0.988744i
$100$		0			0
$101$			12.5854i			1.25230i	0.779704	+	0.626149i	$0.215370\pi$
$101$			12.5854i			1.25230i	−0.779704	+	0.626149i	$0.784630\pi$
$102$		0			0
$103$	0.211229	+	1.33365i	0.0208130	+	0.131408i	0.995907	−	0.0903839i	$-0.0288094\pi$
$103$	0.211229	+	1.33365i	0.0208130	+	0.131408i	−0.975094	+	0.221792i	$0.928809\pi$
$104$		0			0
$105$	−7.43931	−	13.6617i	−0.726002	−	1.33324i
$106$		0			0
$107$	2.51075	+	2.51075i	0.242723	+	0.242723i	0.817976	−	0.575253i	$-0.195096\pi$
$107$	2.51075	+	2.51075i	0.242723	+	0.242723i	−0.575253	+	0.817976i	$0.695096\pi$
$108$		0			0
$109$	−10.8158	+	3.51428i	−1.03597	+	0.336607i	−0.777148	−	0.629318i	$-0.783334\pi$
$109$	−10.8158	+	3.51428i	−1.03597	+	0.336607i	−0.258822	+	0.965925i	$0.583334\pi$
$110$		0			0
$111$	−5.24889	+	6.55109i	−0.498203	+	0.621802i
$112$		0			0
$113$	−6.91215	−	3.52192i	−0.650240	−	0.331314i	0.0975678	−	0.995229i	$-0.468894\pi$
$113$	−6.91215	−	3.52192i	−0.650240	−	0.331314i	−0.747808	+	0.663915i	$0.768894\pi$
$114$		0			0
$115$	0.286804	+	0.700258i	0.0267446	+	0.0652994i
$116$		0			0
$117$	0.959555	−	0.793669i	0.0887108	−	0.0733747i
$118$		0			0
$119$	24.7051	−	17.9493i	2.26471	−	1.64541i
$120$		0			0
$121$	10.9900	+	7.98474i	0.999095	+	0.725885i
$122$		0			0
$123$	1.13355	+	10.2717i	0.102209	+	0.926172i
$124$		0			0
$125$	10.8396	+	2.73930i	0.969520	+	0.245011i
$126$		0			0
$127$	8.79185	+	17.2550i	0.780151	+	1.53113i	0.845928	+	0.533297i	$0.179047\pi$
$127$	8.79185	+	17.2550i	0.780151	+	1.53113i	−0.0657772	+	0.997834i	$0.520953\pi$
$128$		0			0
$129$	−5.04618	+	3.31440i	−0.444291	+	0.291816i
$130$		0			0
$131$	−1.96392	−	2.70310i	−0.171588	−	0.236171i	0.714558	−	0.699576i	$-0.246628\pi$
$131$	−1.96392	−	2.70310i	−0.171588	−	0.236171i	−0.886147	+	0.463405i	$0.846628\pi$
$132$		0			0
$133$	−18.1367	−	2.87257i	−1.57265	−	0.249083i
$134$		0			0
$135$	7.44287	−	8.92209i	0.640581	−	0.767891i
$136$		0			0
$137$	−1.08309	+	2.12568i	−0.0925343	+	0.181609i	−0.932635	−	0.360822i	$-0.882496\pi$
$137$	−1.08309	+	2.12568i	−0.0925343	+	0.181609i	0.840100	+	0.542431i	$0.182496\pi$
$138$		0			0
$139$	−1.62858	−	0.529159i	−0.138135	−	0.0448827i	0.239134	−	0.970987i	$-0.423137\pi$
$139$	−1.62858	−	0.529159i	−0.138135	−	0.0448827i	−0.377268	+	0.926104i	$0.623137\pi$
$140$		0			0
$141$	13.3873	+	0.631928i	1.12742	+	0.0532179i
$142$		0			0
$143$	−1.45530	+	1.45530i	−0.121698	+	0.121698i
$144$		0			0
$145$	1.75198	+	1.50841i	0.145494	+	0.125266i
$146$		0			0
$147$	15.4889	+	3.20832i	1.27750	+	0.264617i
$148$		0			0
$149$	−7.67808			−0.629012			−0.314506	−	0.949255i	$-0.601839\pi$
$149$	−7.67808			−0.629012			−0.314506	+	0.949255i	$0.601839\pi$
$150$		0			0
$151$	−18.9987			−1.54609			−0.773045	−	0.634352i	$-0.781267\pi$
$151$	−18.9987			−1.54609			−0.773045	+	0.634352i	$0.781267\pi$
$152$		0			0
$153$	19.2569	+	12.2232i	1.55683	+	0.988190i
$154$		0			0
$155$	−5.30248	+	3.22048i	−0.425906	+	0.258675i
$156$		0			0
$157$	−3.65415	+	3.65415i	−0.291633	+	0.291633i	−0.837725	−	0.546092i	$-0.816115\pi$
$157$	−3.65415	+	3.65415i	−0.291633	+	0.291633i	0.546092	+	0.837725i	$0.316115\pi$
$158$		0			0
$159$	−0.679559	+	14.3964i	−0.0538926	+	1.14171i
$160$		0			0
$161$	−1.29271	−	0.420028i	−0.101880	−	0.0331029i
$162$		0			0
$163$	1.70981	−	3.35569i	0.133923	−	0.262838i	−0.814300	−	0.580444i	$-0.802879\pi$
$163$	1.70981	−	3.35569i	0.133923	−	0.262838i	0.948223	+	0.317606i	$0.102879\pi$
$164$		0			0
$165$	−10.8575	+	15.8392i	−0.845258	+	1.23308i
$166$		0			0
$167$	−3.33491	−	0.528199i	−0.258063	−	0.0408732i	0.0260621	−	0.999660i	$-0.491703\pi$
$167$	−3.33491	−	0.528199i	−0.258063	−	0.0408732i	−0.284126	+	0.958787i	$0.591703\pi$
$168$		0			0
$169$	7.53994	+	10.3778i	0.579995	+	0.798295i
$170$		0			0
$171$	−2.99074	−	13.3854i	−0.228708	−	1.02361i
$172$		0			0
$173$	−5.42968	−	10.6563i	−0.412811	−	0.810187i	−1.00000		0.000736755i	$-0.999765\pi$
$173$	−5.42968	−	10.6563i	−0.412811	−	0.810187i	0.587189	−	0.809450i	$-0.300235\pi$
$174$		0			0
$175$	−16.3403	+	11.6748i	−1.23521	+	0.882535i
$176$		0			0
$177$	17.2685	−	1.90568i	1.29798	−	0.143240i
$178$		0			0
$179$	−1.75204	−	1.27293i	−0.130954	−	0.0951434i	0.520380	−	0.853935i	$-0.325790\pi$
$179$	−1.75204	−	1.27293i	−0.130954	−	0.0951434i	−0.651334	+	0.758791i	$0.725790\pi$
$180$		0			0
$181$	−0.486921	+	0.353769i	−0.0361925	+	0.0262954i	−0.605734	−	0.795667i	$-0.707121\pi$
$181$	−0.486921	+	0.353769i	−0.0361925	+	0.0262954i	0.569542	+	0.821962i	$0.307121\pi$
$182$		0			0
$183$	14.6226	+	8.34143i	1.08093	+	0.616616i
$184$		0			0
$185$	9.21772	+	5.69909i	0.677700	+	0.419005i
$186$		0			0
$187$	−33.5885	−	17.1142i	−2.45623	−	1.25151i
$188$		0			0
$189$	3.58549	+	20.5601i	0.260806	+	1.49553i
$190$		0			0
$191$	−20.1158	+	6.53603i	−1.45553	+	0.472931i	−0.926702	−	0.375798i	$-0.877369\pi$
$191$	−20.1158	+	6.53603i	−1.45553	+	0.472931i	−0.528829	+	0.848728i	$0.677369\pi$
$192$		0			0
$193$	0.525247	+	0.525247i	0.0378081	+	0.0378081i	0.725758	−	0.687950i	$-0.241489\pi$
$193$	0.525247	+	0.525247i	0.0378081	+	0.0378081i	−0.687950	+	0.725758i	$0.741489\pi$
$194$		0			0
$195$	−1.16747	−	1.10518i	−0.0836045	−	0.0791439i
$196$		0			0
$197$	0.380297	+	2.40110i	0.0270950	+	0.171071i	0.997525	−	0.0703111i	$-0.0223992\pi$
$197$	0.380297	+	2.40110i	0.0270950	+	0.171071i	−0.970430	+	0.241382i	$0.922399\pi$
$198$		0			0
$199$		−	26.6540i		−	1.88945i	−0.327865	−	0.944725i	$-0.606329\pi$
$199$		−	26.6540i		−	1.88945i	0.327865	−	0.944725i	$-0.393671\pi$
$200$		0			0
$201$	11.9643	+	4.52153i	0.843895	+	0.318924i
$202$		0			0
$203$	−4.10154	+	0.649620i	−0.287872	+	0.0455944i
$204$		0			0
$205$	12.9849	−	3.06293i	0.906905	−	0.213924i
$206$		0			0
$207$	−0.0636573	−	1.01324i	−0.00442449	−	0.0704252i
$208$		0			0
$209$	7.00490	+	21.5589i	0.484539	+	1.49126i
$210$		0			0
$211$	−2.55687	+	7.86925i	−0.176022	+	0.541741i	−0.999679	−	0.0253480i	$-0.991931\pi$
$211$	−2.55687	+	7.86925i	−0.176022	+	0.541741i	0.823656	+	0.567089i	$0.191931\pi$
$212$		0			0
$213$	−2.49692	−	2.74433i	−0.171086	−	0.188038i
$214$		0			0
$215$	5.03831	+	5.94676i	0.343610	+	0.405565i
$216$		0			0
$217$	1.74324	−	11.0064i	0.118339	−	0.747163i
$218$		0			0
$219$	6.54005	+	23.9106i	0.441936	+	1.61573i
$220$		0			0
$221$	1.85496	−	2.55313i	0.124778	−	0.171742i
$222$		0			0
$223$	−11.3838	+	5.80036i	−0.762319	+	0.388421i	−0.791513	−	0.611153i	$-0.790706\pi$
$223$	−11.3838	+	5.80036i	−0.762319	+	0.388421i	0.0291937	+	0.999574i	$0.490706\pi$
$224$		0			0
$225$	−12.6000	−	8.13884i	−0.839998	−	0.542589i
$226$		0			0
$227$	21.6298	−	11.0209i	1.43562	−	0.731484i	0.448848	−	0.893608i	$-0.351835\pi$
$227$	21.6298	−	11.0209i	1.43562	−	0.731484i	0.986770	+	0.162124i	$0.0518346\pi$
$228$		0			0
$229$	4.36425	−	6.00687i	0.288398	−	0.396945i	−0.640095	−	0.768296i	$-0.721105\pi$
$229$	4.36425	−	6.00687i	0.288398	−	0.396945i	0.928493	+	0.371350i	$0.121105\pi$
$230$		0			0
$231$	−9.10047	−	33.2715i	−0.598767	−	2.18911i
$232$		0			0
$233$	2.77715	−	17.5342i	0.181937	−	1.14871i	−0.712553	−	0.701618i	$-0.752461\pi$
$233$	2.77715	−	17.5342i	0.181937	−	1.14871i	0.894490	−	0.447087i	$-0.147539\pi$
$234$		0			0
$235$	−1.28902	−	17.2541i	−0.0840865	−	1.12554i
$236$		0			0
$237$	−8.85118	−	9.72819i	−0.574946	−	0.631914i
$238$		0			0
$239$	−0.224620	+	0.691308i	−0.0145294	+	0.0447170i	−0.958058	−	0.286573i	$-0.907484\pi$
$239$	−0.224620	+	0.691308i	−0.0145294	+	0.0447170i	0.943529	+	0.331290i	$0.107484\pi$
$240$		0			0
$241$	−4.44165	−	13.6700i	−0.286112	−	0.880561i	−0.986063	−	0.166371i	$-0.946795\pi$
$241$	−4.44165	−	13.6700i	−0.286112	−	0.880561i	0.699951	−	0.714190i	$-0.253205\pi$
$242$		0			0
$243$	−13.2932	+	8.14199i	−0.852756	+	0.522309i
$244$		0			0
$245$	1.68299	−	20.3511i	0.107522	−	1.30018i
$246$		0			0
$247$	−1.87433	+	0.296864i	−0.119261	+	0.0188890i
$248$		0			0
$249$	−10.6219	−	4.01423i	−0.673137	−	0.254391i
$250$		0			0
$251$			10.6776i			0.673961i	0.941512	+	0.336981i	$0.109406\pi$
$251$			10.6776i			0.673961i	−0.941512	+	0.336981i	$0.890594\pi$
$252$		0			0
$253$	0.262488	+	1.65729i	0.0165025	+	0.104193i
$254$		0			0
$255$	12.6443	−	26.5929i	0.791819	−	1.66531i
$256$		0			0
$257$	−9.29989	−	9.29989i	−0.580111	−	0.580111i	0.354822	−	0.934934i	$-0.384541\pi$
$257$	−9.29989	−	9.29989i	−0.580111	−	0.580111i	−0.934934	+	0.354822i	$0.884541\pi$
$258$		0			0
$259$	−18.5135	+	6.01541i	−1.15037	+	0.373779i
$260$		0			0
$261$	−1.57866	−	2.66990i	−0.0977163	−	0.165263i
$262$		0			0
$263$	−23.1320	−	11.7863i	−1.42638	−	0.726776i	−0.441055	−	0.897480i	$-0.645396\pi$
$263$	−23.1320	−	11.7863i	−1.42638	−	0.726776i	−0.985322	+	0.170704i	$0.945396\pi$
$264$		0			0
$265$	18.5547	−	1.38618i	1.13980	−	0.0851525i
$266$		0			0
$267$	20.1135	+	11.4738i	1.23093	+	0.702182i
$268$		0			0
$269$	−13.6649	+	9.92811i	−0.833162	+	0.605328i	−0.920452	−	0.390855i	$-0.872179\pi$
$269$	−13.6649	+	9.92811i	−0.833162	+	0.605328i	0.0872901	+	0.996183i	$0.472179\pi$
$270$		0			0
$271$	12.7884	+	9.29128i	0.776837	+	0.564405i	0.904028	−	0.427473i	$-0.140596\pi$
$271$	12.7884	+	9.29128i	0.776837	+	0.564405i	−0.127191	+	0.991878i	$0.540596\pi$
$272$		0			0
$273$	2.87023	−	0.316748i	0.173714	−	0.0191704i
$274$		0			0
$275$	21.9992	+	11.4301i	1.32660	+	0.689260i
$276$		0			0
$277$	7.77059	+	15.2506i	0.466890	+	0.916323i	0.997631	+	0.0687889i	$0.0219135\pi$
$277$	7.77059	+	15.2506i	0.466890	+	0.916323i	−0.530742	+	0.847534i	$0.678087\pi$
$278$		0			0
$279$	8.12305	−	1.81496i	0.486314	−	0.108659i
$280$		0			0
$281$	16.0338	+	22.0687i	0.956499	+	1.31651i	0.948580	+	0.316539i	$0.102521\pi$
$281$	16.0338	+	22.0687i	0.956499	+	1.31651i	0.00791912	+	0.999969i	$0.497479\pi$
$282$		0			0
$283$	−3.01460	−	0.477465i	−0.179199	−	0.0283824i	0.0661898	−	0.997807i	$-0.478916\pi$
$283$	−3.01460	−	0.477465i	−0.179199	−	0.0283824i	−0.245389	+	0.969425i	$0.578916\pi$
$284$		0			0
$285$	−16.6837	+	5.93096i	−0.988259	+	0.351320i
$286$		0			0
$287$	−10.8795	+	21.3522i	−0.642195	+	1.26038i
$288$		0			0
$289$	38.8070	+	12.6092i	2.28277	+	0.741716i
$290$		0			0
$291$	−0.181876	+	3.85304i	−0.0106618	+	0.225869i
$292$		0			0
$293$	10.5577	−	10.5577i	0.616788	−	0.616788i	−0.327918	−	0.944706i	$-0.606347\pi$
$293$	10.5577	−	10.5577i	0.616788	−	0.616788i	0.944706	+	0.327918i	$0.106347\pi$
$294$		0			0
$295$	−5.14928	−	21.8297i	−0.299802	−	1.27098i
$296$		0			0
$297$	20.6051	−	15.4664i	1.19563	−	0.897454i
$298$		0			0
$299$	−0.140470			−0.00812359
$300$		0			0
$301$	−14.0001			−0.806953
$302$		0			0
$303$	−21.3455	−	4.42143i	−1.22627	−	0.254005i
$304$		0			0
$305$	8.39659	−	20.0457i	0.480787	−	1.14781i
$306$		0			0
$307$	17.3293	−	17.3293i	0.989033	−	0.989033i	−0.0109073	−	0.999941i	$-0.503472\pi$
$307$	17.3293	−	17.3293i	0.989033	−	0.989033i	0.999941	+	0.0109073i	$0.00347197\pi$
$308$		0			0
$309$	−2.33614	−	0.110273i	−0.132898	−	0.00627324i
$310$		0			0
$311$	−4.35394	−	1.41468i	−0.246889	−	0.0802191i	0.182958	−	0.983121i	$-0.441433\pi$
$311$	−4.35394	−	1.41468i	−0.246889	−	0.0802191i	−0.429847	+	0.902902i	$0.641433\pi$
$312$		0			0
$313$	−4.00451	+	7.85929i	−0.226348	+	0.444233i	−0.976051	−	0.217541i	$-0.930196\pi$
$313$	−4.00451	+	7.85929i	−0.226348	+	0.444233i	0.749703	+	0.661774i	$0.230196\pi$
$314$		0			0
$315$	25.7844	−	7.81789i	1.45279	−	0.440488i
$316$		0			0
$317$	−17.3151	−	2.74245i	−0.972515	−	0.154031i	−0.350095	−	0.936714i	$-0.613851\pi$
$317$	−17.3151	−	2.74245i	−0.972515	−	0.154031i	−0.622420	+	0.782683i	$0.713851\pi$
$318$		0			0
$319$	3.01319	+	4.14731i	0.168707	+	0.232205i
$320$		0			0
$321$	−5.14041	+	3.37629i	−0.286910	+	0.188446i
$322$		0			0
$323$	−15.7803	−	30.9706i	−0.878040	−	1.72325i
$324$		0			0
$325$	−1.23320	+	1.66931i	−0.0684054	+	0.0925967i
$326$		0			0
$327$	−2.16064	−	19.5788i	−0.119484	−	1.08271i
$328$		0			0
$329$	25.1434	+	18.2677i	1.38620	+	1.00713i
$330$		0			0
$331$	12.7358	−	9.25307i	0.700020	−	0.508595i	−0.179918	−	0.983682i	$-0.557583\pi$
$331$	12.7358	−	9.25307i	0.700020	−	0.508595i	0.879939	+	0.475087i	$0.157583\pi$
$332$		0			0
$333$	−9.26696	−	11.2039i	−0.507826	−	0.613967i
$334$		0			0
$335$	3.91837	−	16.0404i	0.214084	−	0.876379i
$336$		0			0
$337$	3.48017	+	1.77323i	0.189577	+	0.0965942i	0.546203	−	0.837653i	$-0.316073\pi$
$337$	3.48017	+	1.77323i	0.189577	+	0.0965942i	−0.356626	+	0.934247i	$0.616073\pi$
$338$		0			0
$339$	8.40167	−	10.4860i	0.456316	−	0.569524i
$340$		0			0
$341$	−13.0832	+	4.25098i	−0.708493	+	0.230203i
$342$		0			0
$343$	6.05609	+	6.05609i	0.326998	+	0.326998i
$344$		0			0
$345$	−1.28843	+	0.240424i	−0.0693667	+	0.0129440i
$346$		0			0
$347$	0.587119	+	3.70692i	0.0315182	+	0.198998i	0.998423	−	0.0561397i	$-0.0178792\pi$
$347$	0.587119	+	3.70692i	0.0315182	+	0.198998i	−0.966905	+	0.255138i	$0.917879\pi$
$348$		0			0
$349$		−	12.9374i		−	0.692525i	−0.938138	−	0.346262i	$-0.887451\pi$
$349$		−	12.9374i		−	0.692525i	0.938138	−	0.346262i	$-0.112549\pi$
$350$		0			0
$351$	1.00900	+	1.90628i	0.0538562	+	0.101750i
$352$		0			0
$353$	−26.1583	+	4.14307i	−1.39227	+	0.220513i	−0.807107	−	0.590405i	$-0.798968\pi$
$353$	−26.1583	+	4.14307i	−1.39227	+	0.220513i	−0.585159	+	0.810919i	$0.698968\pi$
$354$		0			0
$355$	−3.12523	+	3.62990i	−0.165870	+	0.192655i
$356$		0			0
$357$	21.7636	+	48.2068i	1.15185	+	2.55137i
$358$		0			0
$359$	−1.48360	−	4.56607i	−0.0783016	−	0.240988i	0.904242	−	0.427021i	$-0.140437\pi$
$359$	−1.48360	−	4.56607i	−0.0783016	−	0.240988i	−0.982543	+	0.186033i	$0.940437\pi$
$360$		0			0
$361$	−0.587610	+	1.80848i	−0.0309269	+	0.0951831i
$362$		0			0
$363$	−17.4034	+	15.8345i	−0.913444	+	0.831096i
$364$		0			0
$365$	29.6147	−	12.1293i	1.55010	−	0.634875i
$366$		0			0
$367$	4.19594	−	26.4921i	0.219026	−	1.38288i	−0.595782	−	0.803146i	$-0.703158\pi$
$367$	4.19594	−	26.4921i	0.219026	−	1.38288i	0.814808	−	0.579731i	$-0.196842\pi$
$368$		0			0
$369$	−17.8196	−	1.68605i	−0.927651	−	0.0877721i
$370$		0			0
$371$	−19.6447	+	27.0386i	−1.01990	+	1.40377i
$372$		0			0
$373$	2.97876	−	1.51776i	0.154234	−	0.0785864i	−0.375170	−	0.926956i	$-0.622416\pi$
$373$	2.97876	−	1.51776i	0.154234	−	0.0785864i	0.529404	+	0.848370i	$0.322416\pi$
$374$		0			0
$375$	−8.45407	+	17.4221i	−0.436566	+	0.899672i
$376$		0			0
$377$	−0.382380	+	0.194832i	−0.0196936	+	0.0100344i
$378$		0			0
$379$	−1.47681	+	2.03266i	−0.0758588	+	0.104411i	−0.845260	−	0.534355i	$-0.820555\pi$
$379$	−1.47681	+	2.03266i	−0.0758588	+	0.104411i	0.769401	+	0.638766i	$0.220555\pi$
$380$		0			0
$381$	−32.3540	+	8.84950i	−1.65754	+	0.453373i
$382$		0			0
$383$	1.45004	−	9.15521i	0.0740938	−	0.467810i	−0.922545	−	0.385889i	$-0.873895\pi$
$383$	1.45004	−	9.15521i	0.0740938	−	0.467810i	0.996639	−	0.0819203i	$-0.0261053\pi$
$384$		0			0
$385$	−41.2088	+	16.8779i	−2.10019	+	0.860175i
$386$		0			0
$387$	−3.84859	−	9.72295i	−0.195635	−	0.494245i
$388$		0			0
$389$	−3.53033	+	10.8652i	−0.178995	+	0.550890i	−0.999793	−	0.0203282i	$-0.993529\pi$
$389$	−3.53033	+	10.8652i	−0.178995	+	0.550890i	0.820798	+	0.571218i	$0.193529\pi$
$390$		0			0
$391$	−0.795077	−	2.44700i	−0.0402088	−	0.123750i
$392$		0			0
$393$	5.27454	−	2.38127i	0.266066	−	0.120119i
$394$		0			0
$395$	−11.0784	+	12.8674i	−0.557417	+	0.647429i
$396$		0			0
$397$	−9.67691	+	1.53267i	−0.485670	+	0.0769226i	−0.394468	−	0.918910i	$-0.629071\pi$
$397$	−9.67691	+	1.53267i	−0.485670	+	0.0769226i	−0.0912023	+	0.995832i	$0.529071\pi$
$398$		0			0
$399$	11.2437	−	29.7515i	0.562888	−	1.48944i
$400$		0			0
$401$		−	27.1537i		−	1.35599i	−0.735066	−	0.677996i	$-0.762849\pi$
$401$		−	27.1537i		−	1.35599i	0.735066	−	0.677996i	$-0.237151\pi$
$402$		0			0
$403$	−0.180155	−	1.13745i	−0.00897414	−	0.0566605i
$404$		0			0
$405$	12.5175	+	15.7579i	0.622000	+	0.783017i
$406$		0			0
$407$	16.9922	+	16.9922i	0.842271	+	0.842271i
$408$		0			0
$409$	−30.0764	+	9.77241i	−1.48718	+	0.483215i	−0.936250	−	0.351335i	$-0.885728\pi$
$409$	−30.0764	+	9.77241i	−1.48718	+	0.483215i	−0.550932	+	0.834550i	$0.685728\pi$
$410$		0			0
$411$	−3.22475	−	2.58374i	−0.159065	−	0.127447i
$412$		0			0
$413$	35.8964	+	18.2902i	1.76635	+	0.900000i
$414$		0			0
$415$	−3.47874	+	14.2407i	−0.170765	+	0.699047i
$416$		0			0
$417$	1.46962	−	2.57626i	0.0719677	−	0.126160i
$418$		0			0
$419$	−13.3040	+	9.66590i	−0.649941	+	0.472210i	−0.863251	−	0.504775i	$-0.831576\pi$
$419$	−13.3040	+	9.66590i	−0.649941	+	0.472210i	0.213310	+	0.976985i	$0.431576\pi$
$420$		0			0
$421$	11.1129	+	8.07400i	0.541610	+	0.393503i	0.824683	−	0.565596i	$-0.191354\pi$
$421$	11.1129	+	8.07400i	0.541610	+	0.393503i	−0.283073	+	0.959098i	$0.591354\pi$
$422$		0			0
$423$	−5.77493	+	22.4836i	−0.280787	+	1.09319i
$424$		0			0
$425$	−36.0595	−	12.0338i	−1.74914	−	0.583727i
$426$		0			0
$427$	17.7229	+	34.7831i	0.857670	+	1.68327i
$428$		0			0
$429$	−1.95699	−	2.97952i	−0.0944843	−	0.143852i
$430$		0			0
$431$	2.67787	+	3.68577i	0.128989	+	0.177537i	0.868626	−	0.495468i	$-0.165003\pi$
$431$	2.67787	+	3.68577i	0.128989	+	0.177537i	−0.739638	+	0.673005i	$0.765003\pi$
$432$		0			0
$433$	21.2003	+	3.35781i	1.01882	+	0.161366i	0.643434	−	0.765501i	$-0.277509\pi$
$433$	21.2003	+	3.35781i	1.01882	+	0.161366i	0.375389	+	0.926867i	$0.377509\pi$
$434$		0			0
$435$	−3.17383	+	2.44153i	−0.152173	+	0.117062i
$436$		0			0
$437$	−0.702398	+	1.37853i	−0.0336003	+	0.0659442i
$438$		0			0
$439$	10.5185	+	3.41768i	0.502022	+	0.163117i	0.549071	−	0.835776i	$-0.314982\pi$
$439$	10.5185	+	3.41768i	0.502022	+	0.163117i	−0.0470490	+	0.998893i	$0.514982\pi$
$440$		0			0
$441$	−10.8829	+	25.1428i	−0.518234	+	1.19728i
$442$		0			0
$443$	11.3624	−	11.3624i	0.539846	−	0.539846i	−0.383638	−	0.923484i	$-0.625329\pi$
$443$	11.3624	−	11.3624i	0.539846	−	0.539846i	0.923484	+	0.383638i	$0.125329\pi$
$444$		0			0
$445$	11.5496	−	27.5731i	0.547505	−	1.30709i
$446$		0			0
$447$	2.69741	−	13.0224i	0.127583	−	0.615938i
$448$		0			0
$449$	16.5317			0.780178			0.390089	−	0.920777i	$-0.372444\pi$
$449$	16.5317			0.780178			0.390089	+	0.920777i	$0.372444\pi$
$450$		0			0
$451$	29.5830			1.39301
$452$		0			0
$453$	6.67448	−	32.2226i	0.313595	−	1.51395i
$454$		0			0
$455$	−0.855873	−	3.62837i	−0.0401240	−	0.170101i
$456$		0			0
$457$	−16.5635	+	16.5635i	−0.774807	+	0.774807i	−0.978943	−	0.204136i	$-0.934562\pi$
$457$	−16.5635	+	16.5635i	−0.774807	+	0.774807i	0.204136	+	0.978943i	$0.434562\pi$
$458$		0			0
$459$	−27.4964	+	28.3665i	−1.28342	+	1.32404i
$460$		0			0
$461$	−14.5158	−	4.71648i	−0.676070	−	0.219669i	−0.0491963	−	0.998789i	$-0.515666\pi$
$461$	−14.5158	−	4.71648i	−0.676070	−	0.219669i	−0.626874	+	0.779121i	$0.715666\pi$
$462$		0			0
$463$	−1.93184	+	3.79146i	−0.0897804	+	0.176204i	−0.931530	−	0.363664i	$-0.881526\pi$
$463$	−1.93184	+	3.79146i	−0.0897804	+	0.176204i	0.841750	+	0.539868i	$0.181526\pi$
$464$		0			0
$465$	−3.59925	−	10.1247i	−0.166911	−	0.469520i
$466$		0			0
$467$	30.6114	+	4.84837i	1.41653	+	0.224356i	0.817295	−	0.576219i	$-0.195472\pi$
$467$	30.6114	+	4.84837i	1.41653	+	0.224356i	0.599233	+	0.800575i	$0.295472\pi$
$468$		0			0
$469$	17.4334	+	23.9951i	0.805001	+	1.10799i
$470$		0			0
$471$	−4.91387	−	7.48137i	−0.226419	−	0.344723i
$472$		0			0
$473$	7.84621	+	15.3990i	0.360769	+	0.708049i
$474$		0			0
$475$	10.2158	+	20.4494i	0.468731	+	0.938282i
$476$		0			0
$477$	−24.1783	−	6.21022i	−1.10705	−	0.284346i
$478$		0			0
$479$	−23.7090	−	17.2256i	−1.08329	−	0.787059i	−0.105039	−	0.994468i	$-0.533497\pi$
$479$	−23.7090	−	17.2256i	−1.08329	−	0.787059i	−0.978254	+	0.207409i	$0.933497\pi$
$480$		0			0
$481$	−1.62753	+	1.18247i	−0.0742088	+	0.0539159i
$482$		0			0
$483$	1.16654	−	2.04494i	0.0530792	−	0.0930482i
$484$		0			0
$485$	4.96595	−	0.370996i	0.225492	−	0.0168460i
$486$		0			0
$487$	18.5821	+	9.46803i	0.842033	+	0.429037i	0.821128	−	0.570744i	$-0.193345\pi$
$487$	18.5821	+	9.46803i	0.842033	+	0.429037i	0.0209053	+	0.999781i	$0.493345\pi$
$488$		0			0
$489$	5.09073	+	4.07882i	0.230211	+	0.184451i
$490$		0			0
$491$	8.67143	−	2.81752i	0.391336	−	0.127153i	−0.106738	−	0.994287i	$-0.534041\pi$
$491$	8.67143	−	2.81752i	0.391336	−	0.127153i	0.498074	+	0.867134i	$0.334041\pi$
$492$		0			0
$493$	−5.55831	−	5.55831i	−0.250334	−	0.250334i
$494$		0			0
$495$	−23.0497	−	23.9794i	−1.03601	−	1.07780i
$496$		0			0
$497$	−1.34593	−	8.49789i	−0.0603734	−	0.381183i
$498$		0			0
$499$			9.70109i			0.434280i	0.976140	+	0.217140i	$0.0696729\pi$
$499$			9.70109i			0.434280i	−0.976140	+	0.217140i	$0.930327\pi$
$500$		0			0
$501$	2.06745	−	5.47061i	0.0923669	−	0.244409i
$502$		0			0
$503$	8.01914	−	1.27011i	0.357556	−	0.0566313i	0.0249274	−	0.999689i	$-0.492065\pi$
$503$	8.01914	−	1.27011i	0.357556	−	0.0566313i	0.332628	+	0.943058i	$0.392065\pi$
$504$		0			0
$505$	−2.31936	+	28.0461i	−0.103210	+	1.24804i
$506$		0			0
$507$	−20.2502	+	9.14222i	−0.899342	+	0.406020i
$508$		0			0
$509$	11.1835	+	34.4193i	0.495700	+	1.52561i	0.815863	+	0.578245i	$0.196262\pi$
$509$	11.1835	+	34.4193i	0.495700	+	1.52561i	−0.320163	+	0.947362i	$0.603738\pi$
$510$		0			0
$511$	−17.7634	+	54.6703i	−0.785809	+	2.41847i
$512$		0			0
$513$	23.7530	−	0.369972i	1.04872	−	0.0163347i
$514$		0			0
$515$	0.224939	+	3.01091i	0.00991198	+	0.132676i
$516$		0			0
$517$	6.00177	−	37.8937i	0.263958	−	1.66656i
$518$		0			0
$519$	19.9812	−	5.46528i	0.877077	−	0.239899i
$520$		0			0
$521$	−9.60734	+	13.2234i	−0.420905	+	0.579326i	−0.965836	−	0.259155i	$-0.916556\pi$
$521$	−9.60734	+	13.2234i	−0.420905	+	0.579326i	0.544930	+	0.838481i	$0.316556\pi$
$522$		0			0
$523$	−9.11004	+	4.64180i	−0.398354	+	0.202972i	−0.641679	−	0.766973i	$-0.721762\pi$
$523$	−9.11004	+	4.64180i	−0.398354	+	0.202972i	0.243325	+	0.969945i	$0.421762\pi$
$524$		0			0
$525$	−14.0605	−	31.8155i	−0.613651	−	1.38854i
$526$		0			0
$527$	18.7948	−	9.57641i	0.818713	−	0.417155i
$528$		0			0
$529$	13.4517	−	18.5147i	0.584859	−	0.804989i
$530$		0			0
$531$	−2.83452	+	29.9576i	−0.123008	+	1.30005i
$532$		0			0
$533$	−0.387419	+	2.44607i	−0.0167810	+	0.105951i
$534$		0			0
$535$	5.13240	+	6.05781i	0.221893	+	0.261902i
$536$		0			0
$537$	2.77447	−	2.52435i	0.119727	−	0.108934i
$538$		0			0
$539$	13.9925	−	43.0645i	0.602699	−	1.85492i
$540$		0			0
$541$	5.41906	+	16.6781i	0.232983	+	0.717049i	0.997383	+	0.0723059i	$0.0230358\pi$
$541$	5.41906	+	16.6781i	0.232983	+	0.717049i	−0.764399	+	0.644743i	$0.776964\pi$
$542$		0			0
$543$	−0.428947	−	0.950125i	−0.0184079	−	0.0407738i
$544$		0			0
$545$	−24.7503	+	5.83819i	−1.06019	+	0.250081i
$546$		0			0
$547$	16.0041	−	2.53481i	0.684288	−	0.108381i	0.195395	−	0.980725i	$-0.437401\pi$
$547$	16.0041	−	2.53481i	0.684288	−	0.108381i	0.488893	+	0.872344i	$0.337401\pi$
$548$		0			0
$549$	−19.2846	+	21.8701i	−0.823046	+	0.933395i
$550$		0			0
$551$			4.72680i			0.201369i
$552$		0			0
$553$	−4.77111	−	30.1236i	−0.202888	−	1.28099i
$554$		0			0
$555$	−12.9042	+	13.6315i	−0.547754	+	0.578626i
$556$		0			0
$557$	−0.351406	−	0.351406i	−0.0148895	−	0.0148895i	0.699623	−	0.714512i	$-0.253351\pi$
$557$	−0.351406	−	0.351406i	−0.0148895	−	0.0148895i	−0.714512	+	0.699623i	$0.753351\pi$
$558$		0			0
$559$	−1.37602	+	0.447097i	−0.0581995	+	0.0189102i
$560$		0			0
$561$	40.8266	−	50.9553i	1.72370	−	2.15133i
$562$		0			0
$563$	−9.57089	−	4.87661i	−0.403365	−	0.205525i	0.240525	−	0.970643i	$-0.422680\pi$
$563$	−9.57089	−	4.87661i	−0.403365	−	0.205525i	−0.643890	+	0.765118i	$0.722680\pi$
$564$		0			0
$565$	−14.7544	−	9.12229i	−0.620722	−	0.383777i
$566$		0			0
$567$	−36.1305	−	1.14188i	−1.51734	−	0.0479546i
$568$		0			0
$569$	34.5553	−	25.1059i	1.44863	−	1.05249i	0.462484	−	0.886628i	$-0.346958\pi$
$569$	34.5553	−	25.1059i	1.44863	−	1.05249i	0.986148	−	0.165865i	$-0.0530417\pi$
$570$		0			0
$571$	−37.4429	−	27.2039i	−1.56694	−	1.13845i	−0.930017	−	0.367517i	$-0.880208\pi$
$571$	−37.4429	−	27.2039i	−1.56694	−	1.13845i	−0.636920	−	0.770930i	$-0.719792\pi$
$572$		0			0
$573$	−4.01846	−	36.4136i	−0.167874	−	1.52120i
$574$		0			0
$575$	0.510082	+	1.61335i	0.0212719	+	0.0672814i
$576$		0			0
$577$	−3.73707	−	7.33441i	−0.155576	−	0.305335i	0.800042	−	0.599944i	$-0.204811\pi$
$577$	−3.73707	−	7.33441i	−0.155576	−	0.305335i	−0.955618	+	0.294609i	$0.904811\pi$
$578$		0			0
$579$	−1.07537	+	0.706318i	−0.0446909	+	0.0293536i
$580$		0			0
$581$	−15.4774	−	21.3029i	−0.642113	−	0.883792i
$582$		0			0
$583$	40.7500	+	6.45416i	1.68769	+	0.267304i
$584$		0			0
$585$	2.28459	−	1.59182i	0.0944563	−	0.0658138i
$586$		0			0
$587$	−0.885671	+	1.73823i	−0.0365556	+	0.0717444i	−0.908562	−	0.417750i	$-0.862819\pi$
$587$	−0.885671	+	1.73823i	−0.0365556	+	0.0717444i	0.872006	+	0.489495i	$0.162819\pi$
$588$		0			0
$589$	−12.0635	−	3.91966i	−0.497066	−	0.161507i
$590$		0			0
$591$	−4.20599	−	0.198537i	−0.173011	−	0.00816671i
$592$		0			0
$593$	−26.3630	+	26.3630i	−1.08260	+	1.08260i	−0.0863319	+	0.996266i	$0.527515\pi$
$593$	−26.3630	+	26.3630i	−1.08260	+	1.08260i	−0.996266	+	0.0863319i	$0.972485\pi$
$594$		0			0
$595$	58.3621	−	35.4464i	2.39261	−	1.45316i
$596$		0			0
$597$	45.2064	+	9.36389i	1.85017	+	0.383239i
$598$		0			0
$599$	−27.2293			−1.11256			−0.556280	−	0.830995i	$-0.687772\pi$
$599$	−27.2293			−1.11256			−0.556280	+	0.830995i	$0.687772\pi$
$600$		0			0
$601$	−0.707518			−0.0288602			−0.0144301	−	0.999896i	$-0.504593\pi$
$601$	−0.707518			−0.0288602			−0.0144301	+	0.999896i	$0.504593\pi$
$602$		0			0
$603$	−11.8719	+	18.7035i	−0.483463	+	0.761666i
$604$		0			0
$605$	23.0194	+	19.8190i	0.935871	+	0.805758i
$606$		0			0
$607$	−15.7536	+	15.7536i	−0.639418	+	0.639418i	−0.950412	−	0.310994i	$-0.899338\pi$
$607$	−15.7536	+	15.7536i	−0.639418	+	0.639418i	0.310994	+	0.950412i	$0.399338\pi$
$608$		0			0
$609$	0.339139	−	7.18463i	0.0137426	−	0.291136i
$610$		0			0
$611$	3.05464	+	0.992512i	0.123577	+	0.0401527i
$612$		0			0
$613$	−7.04615	+	13.8288i	−0.284591	+	0.558542i	−0.988405	−	0.151843i	$-0.951479\pi$
$613$	−7.04615	+	13.8288i	−0.284591	+	0.558542i	0.703813	+	0.710385i	$0.251479\pi$
$614$		0			0
$615$	0.633098	+	23.0991i	0.0255290	+	0.931445i
$616$		0			0
$617$	−30.2739	−	4.79492i	−1.21878	−	0.193036i	−0.486282	−	0.873802i	$-0.661647\pi$
$617$	−30.2739	−	4.79492i	−1.21878	−	0.193036i	−0.732501	+	0.680766i	$0.761647\pi$
$618$		0			0
$619$	−24.7268	−	34.0335i	−0.993852	−	1.36792i	−0.929022	−	0.370024i	$-0.879350\pi$
$619$	−24.7268	−	34.0335i	−0.993852	−	1.36792i	−0.0648299	−	0.997896i	$-0.520650\pi$
$620$		0			0
$621$	1.74087	+	0.248000i	0.0698588	+	0.00995188i
$622$		0			0
$623$	24.3781	+	47.8446i	0.976686	+	1.91685i
$624$		0			0
$625$	23.6507	+	8.10204i	0.946029	+	0.324082i
$626$		0			0
$627$	−39.0258	+	4.30673i	−1.55854	+	0.171994i
$628$		0			0
$629$	−29.8106	−	21.6587i	−1.18863	−	0.863589i
$630$		0			0
$631$	35.3783	−	25.7038i	1.40839	−	1.02325i	0.414834	−	0.909897i	$-0.363840\pi$
$631$	35.3783	−	25.7038i	1.40839	−	1.02325i	0.993554	−	0.113357i	$-0.0361603\pi$
$632$		0			0
$633$	−12.4484	−	7.10115i	−0.494778	−	0.282246i
$634$		0			0
$635$	16.4124	+	40.0723i	0.651306	+	1.59022i
$636$		0			0
$637$	3.37753	+	1.72094i	0.133823	+	0.0681861i
$638$		0			0
$639$	5.53171	−	3.27078i	0.218831	−	0.129390i
$640$		0			0
$641$	41.9572	−	13.6327i	1.65721	−	0.538460i	0.676924	−	0.736053i	$-0.263313\pi$
$641$	41.9572	−	13.6327i	1.65721	−	0.538460i	0.980284	+	0.197593i	$0.0633125\pi$
$642$		0			0
$643$	−21.6567	−	21.6567i	−0.854057	−	0.854057i	0.136573	−	0.990630i	$-0.456391\pi$
$643$	−21.6567	−	21.6567i	−0.854057	−	0.854057i	−0.990630	+	0.136573i	$0.956391\pi$
$644$		0			0
$645$	−11.8560	+	6.45605i	−0.466830	+	0.254207i
$646$		0			0
$647$	4.83284	+	30.5133i	0.189998	+	1.19960i	0.879707	+	0.475516i	$0.157739\pi$
$647$	4.83284	+	30.5133i	0.189998	+	1.19960i	−0.689709	+	0.724087i	$0.742261\pi$
$648$		0			0
$649$		−	49.7338i		−	1.95222i
$650$		0			0
$651$	18.0550	+	6.82332i	0.707629	+	0.267427i
$652$		0			0
$653$	−29.5562	+	4.68124i	−1.15662	+	0.183191i	−0.705127	−	0.709081i	$-0.749110\pi$
$653$	−29.5562	+	4.68124i	−1.15662	+	0.183191i	−0.451497	+	0.892272i	$0.649110\pi$
$654$		0			0
$655$	−3.87836	−	6.38569i	−0.151540	−	0.249510i
$656$		0			0
$657$	−42.8511	+	2.69214i	−1.67178	+	0.105030i
$658$		0			0
$659$	−3.30930	−	10.1850i	−0.128912	−	0.396750i	0.865682	−	0.500595i	$-0.166885\pi$
$659$	−3.30930	−	10.1850i	−0.128912	−	0.396750i	−0.994594	+	0.103845i	$0.966885\pi$
$660$		0			0
$661$	8.67556	−	26.7006i	0.337440	−	1.03853i	−0.628067	−	0.778159i	$-0.716154\pi$
$661$	8.67556	−	26.7006i	0.337440	−	1.03853i	0.965507	−	0.260375i	$-0.0838463\pi$
$662$		0			0
$663$	3.67856	+	4.04305i	0.142864	+	0.157019i
$664$		0			0
$665$	−39.8875	−	9.74380i	−1.54677	−	0.377848i
$666$		0			0
$667$	−0.0547341	+	0.345578i	−0.00211931	+	0.0133808i
$668$		0			0
$669$	−5.83839	−	21.3453i	−0.225725	−	0.825257i
$670$		0			0
$671$	28.3262	−	38.9876i	1.09352	−	1.50510i
$672$		0			0
$673$	−22.9797	+	11.7087i	−0.885803	+	0.451339i	−0.836831	−	0.547461i	$-0.815594\pi$
$673$	−22.9797	+	11.7087i	−0.885803	+	0.451339i	−0.0489715	+	0.998800i	$0.515594\pi$
$674$		0			0
$675$	18.2304	−	18.5109i	0.701688	−	0.712484i
$676$		0			0
$677$	3.98966	−	2.03283i	0.153335	−	0.0781281i	−0.375639	−	0.926766i	$-0.622577\pi$
$677$	3.98966	−	2.03283i	0.153335	−	0.0781281i	0.528974	+	0.848638i	$0.322577\pi$
$678$		0			0
$679$	−5.25767	+	7.23656i	−0.201771	+	0.277714i
$680$		0			0
$681$	11.0932	+	40.5569i	0.425092	+	1.55414i
$682$		0			0
$683$	4.57286	−	28.8719i	0.174976	−	1.10475i	−0.731297	−	0.682059i	$-0.761085\pi$
$683$	4.57286	−	28.8719i	0.174976	−	1.10475i	0.906273	−	0.422693i	$-0.138915\pi$
$684$		0			0
$685$	−2.80535	+	4.53739i	−0.107187	+	0.173365i
$686$		0			0
$687$	8.65473	+	9.51227i	0.330198	+	0.362916i
$688$		0			0
$689$	−1.06732	+	3.28488i	−0.0406618	+	0.125144i
$690$		0			0
$691$	−7.71677	−	23.7498i	−0.293560	−	0.903484i	−0.983701	−	0.179810i	$-0.942452\pi$
$691$	−7.71677	−	23.7498i	−0.293560	−	0.903484i	0.690141	−	0.723674i	$-0.257548\pi$
$692$		0			0
$693$	59.6273	−	3.74610i	2.26505	−	0.142303i
$694$		0			0
$695$	−3.53172	−	1.47934i	−0.133966	−	0.0561146i
$696$		0			0
$697$	−44.8035	+	7.09617i	−1.69705	+	0.268787i
$698$		0			0
$699$	28.7632	+	10.8702i	1.08793	+	0.411148i
$700$		0			0
$701$		−	6.88847i		−	0.260174i	−0.991503	−	0.130087i	$-0.958474\pi$
$701$		−	6.88847i		−	0.260174i	0.991503	−	0.130087i	$-0.0415257\pi$
$702$		0			0
$703$	3.46622	+	21.8848i	0.130731	+	0.825402i
$704$		0			0
$705$	29.7167	+	3.87537i	1.11920	+	0.145955i
$706$		0			0
$707$	−35.7439	−	35.7439i	−1.34429	−	1.34429i
$708$		0			0
$709$	−3.31523	+	1.07719i	−0.124506	+	0.0404545i	−0.370607	−	0.928790i	$-0.620850\pi$
$709$	−3.31523	+	1.07719i	−0.124506	+	0.0404545i	0.246101	+	0.969244i	$0.420850\pi$
$710$		0			0
$711$	19.6090	−	11.5944i	0.735395	−	0.434823i
$712$		0			0
$713$	−0.836575	−	0.426256i	−0.0313300	−	0.0159634i
$714$		0			0
$715$	−3.51127	+	2.97488i	−0.131314	+	0.111254i
$716$		0			0
$717$	−1.09358	−	0.623832i	−0.0408405	−	0.0232974i
$718$		0			0
$719$	−13.0340	+	9.46973i	−0.486085	+	0.353161i	−0.803677	−	0.595066i	$-0.797126\pi$
$719$	−13.0340	+	9.46973i	−0.486085	+	0.353161i	0.317592	+	0.948228i	$0.397126\pi$
$720$		0			0
$721$	−4.38760	−	3.18778i	−0.163403	−	0.118719i
$722$		0			0
$723$	24.7454	−	2.73080i	0.920290	−	0.101560i
$724$		0			0
$725$	3.62624	+	3.68430i	0.134675	+	0.136831i
$726$		0			0
$727$	12.5508	+	24.6324i	0.465484	+	0.913564i	0.997754	+	0.0669890i	$0.0213392\pi$
$727$	12.5508	+	24.6324i	0.465484	+	0.913564i	−0.532270	+	0.846575i	$0.678661\pi$
$728$		0			0
$729$	−9.13914	−	25.4062i	−0.338487	−	0.940971i
$730$		0			0
$731$	−15.5769	−	21.4398i	−0.576132	−	0.792978i
$732$		0			0
$733$	19.6261	+	3.10847i	0.724907	+	0.114814i	0.507974	−	0.861372i	$-0.330395\pi$
$733$	19.6261	+	3.10847i	0.724907	+	0.114814i	0.216933	+	0.976186i	$0.430395\pi$
$734$		0			0
$735$	33.9252	+	10.0040i	1.25135	+	0.369005i
$736$		0			0
$737$	16.6223	−	32.6232i	0.612292	−	1.20169i
$738$		0			0
$739$	40.3184	+	13.1002i	1.48313	+	0.481900i	0.935048	−	0.354522i	$-0.115356\pi$
$739$	40.3184	+	13.1002i	1.48313	+	0.481900i	0.548087	+	0.836421i	$0.315356\pi$
$740$		0			0
$741$	0.154980	−	3.28324i	0.00569334	−	0.120613i
$742$		0			0
$743$	−27.1592	+	27.1592i	−0.996375	+	0.996375i	−0.999993	−	0.00361798i	$-0.998848\pi$
$743$	−27.1592	+	27.1592i	−0.996375	+	0.996375i	0.00361798	+	0.999993i	$0.498848\pi$
$744$		0			0
$745$	−17.1103	−	1.41499i	−0.626873	−	0.0518411i
$746$		0			0
$747$	10.5399	−	16.6050i	0.385636	−	0.607546i
$748$		0			0
$749$	−14.2616			−0.521106
$750$		0			0
$751$	−7.33413			−0.267626			−0.133813	−	0.991007i	$-0.542722\pi$
$751$	−7.33413			−0.267626			−0.133813	+	0.991007i	$0.542722\pi$
$752$		0			0
$753$	−18.1096	−	3.75117i	−0.659952	−	0.136700i
$754$		0			0
$755$	−42.3378	−	3.50125i	−1.54083	−	0.127423i
$756$		0			0
$757$	15.2951	−	15.2951i	0.555911	−	0.555911i	−0.372230	−	0.928141i	$-0.621407\pi$
$757$	15.2951	−	15.2951i	0.555911	−	0.555911i	0.928141	+	0.372230i	$0.121407\pi$
$758$		0			0
$759$	−2.90305	−	0.137034i	−0.105374	−	0.00497402i
$760$		0			0
$761$	10.8598	+	3.52857i	0.393669	+	0.127911i	0.499161	−	0.866509i	$-0.333642\pi$
$761$	10.8598	+	3.52857i	0.393669	+	0.127911i	−0.105492	+	0.994420i	$0.533642\pi$
$762$		0			0
$763$	20.7372	−	40.6990i	0.750736	−	1.47340i
$764$		0			0
$765$	40.6607	+	30.7878i	1.47009	+	1.11314i
$766$		0			0
$767$	4.11224	+	0.651314i	0.148484	+	0.0235176i
$768$		0			0
$769$	13.6293	+	18.7591i	0.491485	+	0.676471i	0.980661	−	0.195714i	$-0.0627025\pi$
$769$	13.6293	+	18.7591i	0.491485	+	0.676471i	−0.489176	+	0.872185i	$0.662702\pi$
$770$		0			0
$771$	19.0402	−	12.5059i	0.685717	−	0.450388i
$772$		0			0
$773$	15.7994	+	31.0081i	0.568265	+	1.11528i	0.979063	+	0.203556i	$0.0652499\pi$
$773$	15.7994	+	31.0081i	0.568265	+	1.11528i	−0.410799	+	0.911726i	$0.634750\pi$
$774$		0			0
$775$	−12.4099	+	6.19952i	−0.445776	+	0.222693i
$776$		0			0
$777$	−3.69838	−	33.5131i	−0.132678	−	1.20228i
$778$		0			0
$779$	22.0678	+	16.0332i	0.790661	+	0.574449i
$780$		0			0
$781$	−8.59271	+	6.24297i	−0.307471	+	0.223391i
$782$		0			0
$783$	5.08289	−	1.73950i	0.181648	−	0.0621648i
$784$		0			0
$785$	−8.81656	+	7.46972i	−0.314677	+	0.266606i
$786$		0			0
$787$	−38.3652	−	19.5480i	−1.36757	−	0.696812i	−0.392718	−	0.919659i	$-0.628465\pi$
$787$	−38.3652	−	19.5480i	−1.36757	−	0.696812i	−0.974854	+	0.222847i	$0.928465\pi$
$788$		0			0
$789$	28.1167	−	35.0922i	1.00098	−	1.24932i
$790$		0			0
$791$	29.6338	−	9.62861i	1.05366	−	0.342354i
$792$		0			0
$793$	2.85273	+	2.85273i	0.101303	+	0.101303i
$794$		0			0
$795$	−4.16747	+	31.9566i	−0.147805	+	1.13338i
$796$		0			0
$797$	−5.41838	−	34.2103i	−0.191929	−	1.21179i	−0.875976	−	0.482354i	$-0.839782\pi$
$797$	−5.41838	−	34.2103i	−0.191929	−	1.21179i	0.684047	−	0.729438i	$-0.260218\pi$
$798$		0			0
$799$			58.8297i			2.08124i
$800$		0			0
$801$	−26.5262	+	30.0827i	−0.937257	+	1.06292i
$802$		0			0
$803$	70.0884	−	11.1009i	2.47337	−	0.391743i
$804$		0			0
$805$	−2.80336	−	1.17425i	−0.0988053	−	0.0413869i
$806$		0			0
$807$	−12.0379	−	26.6642i	−0.423754	−	0.938623i
$808$		0			0
$809$	−2.65484	−	8.17077i	−0.0933393	−	0.287269i	0.893478	−	0.449107i	$-0.148258\pi$
$809$	−2.65484	−	8.17077i	−0.0933393	−	0.287269i	−0.986817	+	0.161838i	$0.948258\pi$
$810$		0			0
$811$	−6.69438	+	20.6032i	−0.235072	+	0.723476i	0.762040	+	0.647530i	$0.224198\pi$
$811$	−6.69438	+	20.6032i	−0.235072	+	0.723476i	−0.997112	+	0.0759463i	$0.975802\pi$
$812$		0			0
$813$	−20.2512	+	18.4255i	−0.710240	+	0.646211i
$814$		0			0
$815$	4.42866	−	7.16292i	0.155129	−	0.250906i
$816$		0			0
$817$	−2.49290	+	15.7395i	−0.0872155	+	0.550657i
$818$		0			0
$819$	−0.471132	+	4.97933i	−0.0164627	+	0.173992i
$820$		0			0
$821$	26.5748	−	36.5770i	0.927466	−	1.27655i	−0.0333736	−	0.999443i	$-0.510625\pi$
$821$	26.5748	−	36.5770i	0.927466	−	1.27655i	0.960840	−	0.277105i	$-0.0893749\pi$
$822$		0			0
$823$	−2.87584	+	1.46531i	−0.100245	+	0.0510776i	−0.503394	−	0.864057i	$-0.667916\pi$
$823$	−2.87584	+	1.46531i	−0.100245	+	0.0510776i	0.403149	+	0.915134i	$0.367916\pi$
$824$		0			0
$825$	−27.1146	+	33.2961i	−0.944009	+	1.15922i
$826$		0			0
$827$	−18.7516	+	9.55443i	−0.652058	+	0.332240i	−0.748535	−	0.663095i	$-0.769242\pi$
$827$	−18.7516	+	9.55443i	−0.652058	+	0.332240i	0.0964773	+	0.995335i	$0.469242\pi$
$828$		0			0
$829$	−32.8299	+	45.1864i	−1.14023	+	1.56939i	−0.373232	+	0.927738i	$0.621750\pi$
$829$	−32.8299	+	45.1864i	−1.14023	+	1.56939i	−0.766997	+	0.641651i	$0.778250\pi$
$830$		0			0
$831$	−28.5957	+	7.82154i	−0.991975	+	0.271326i
$832$		0			0
$833$	−10.8616	+	68.5775i	−0.376333	+	2.37607i
$834$		0			0
$835$	−7.33438	−	1.79166i	−0.253817	−	0.0620029i
$836$		0			0
$837$	0.224520	+	14.4147i	0.00776056	+	0.498245i
$838$		0			0
$839$	−8.34410	+	25.6805i	−0.288070	+	0.886590i	0.697391	+	0.716691i	$0.254344\pi$
$839$	−8.34410	+	25.6805i	−0.288070	+	0.886590i	−0.985461	+	0.169899i	$0.945656\pi$
$840$		0			0
$841$	−8.63117	−	26.5640i	−0.297627	−	0.916000i
$842$		0			0
$843$	−43.0625	+	19.4411i	−1.48315	+	0.669588i
$844$		0			0
$845$	14.8899	+	24.5161i	0.512229	+	0.843380i
$846$		0			0
$847$	−53.8903	+	8.53538i	−1.85169	+	0.293279i
$848$		0			0
$849$	1.86887	−	4.94516i	0.0641395	−	0.169718i
$850$		0			0
$851$			1.64014i			0.0562234i
$852$		0			0
$853$	−3.65179	−	23.0565i	−0.125035	−	0.789439i	−0.967904	−	0.251320i	$-0.919135\pi$
$853$	−3.65179	−	23.0565i	−0.125035	−	0.789439i	0.842869	−	0.538119i	$-0.180865\pi$
$854$		0			0
$855$	−4.19797	−	30.3800i	−0.143568	−	1.03898i
$856$		0			0
$857$	23.9274	+	23.9274i	0.817343	+	0.817343i	0.985722	−	0.168379i	$-0.0538534\pi$
$857$	23.9274	+	23.9274i	0.817343	+	0.817343i	−0.168379	+	0.985722i	$0.553853\pi$
$858$		0			0
$859$	12.3998	−	4.02894i	0.423076	−	0.137466i	−0.0897381	−	0.995965i	$-0.528603\pi$
$859$	12.3998	−	4.02894i	0.423076	−	0.137466i	0.512814	+	0.858500i	$0.328603\pi$
$860$		0			0
$861$	−32.3922	−	25.9534i	−1.10392	−	0.884489i
$862$		0			0
$863$	48.0446	+	24.4799i	1.63546	+	0.833307i	0.998026	+	0.0627991i	$0.0200027\pi$
$863$	48.0446	+	24.4799i	1.63546	+	0.833307i	0.637431	+	0.770508i	$0.279997\pi$
$864$		0			0
$865$	−10.1360	−	24.7479i	−0.344633	−	0.841453i
$866$		0			0
$867$	−35.0192	+	61.3888i	−1.18931	+	2.08487i
$868$		0			0
$869$	−30.4598	+	22.1303i	−1.03328	+	0.750719i
$870$		0			0
$871$	2.47976	+	1.80165i	0.0840234	+	0.0610466i
$872$		0			0
$873$	−6.47104	−	1.66209i	−0.219011	−	0.0562534i
$874$		0			0
$875$	−38.5654	+	23.0056i	−1.30375	+	0.777730i
$876$		0			0
$877$	22.3043	+	43.7747i	0.753163	+	1.47817i	0.874225	+	0.485521i	$0.161370\pi$
$877$	22.3043	+	43.7747i	0.753163	+	1.47817i	−0.121062	+	0.992645i	$0.538630\pi$
$878$		0			0
$879$	14.1973	+	21.6155i	0.478864	+	0.729071i
$880$		0			0
$881$	6.95200	+	9.56861i	0.234219	+	0.322375i	0.909907	−	0.414813i	$-0.136153\pi$
$881$	6.95200	+	9.56861i	0.234219	+	0.322375i	−0.675688	+	0.737188i	$0.736153\pi$
$882$		0			0
$883$	−20.9091	−	3.31167i	−0.703647	−	0.111447i	−0.205650	−	0.978626i	$-0.565931\pi$
$883$	−20.9091	−	3.31167i	−0.703647	−	0.111447i	−0.497997	+	0.867179i	$0.665931\pi$
$884$		0			0
$885$	38.8333	−	1.06434i	1.30537	−	0.0357774i
$886$		0			0
$887$	12.0304	−	23.6111i	0.403943	−	0.792782i	−0.596005	−	0.802981i	$-0.703246\pi$
$887$	12.0304	−	23.6111i	0.403943	−	0.792782i	0.999948	+	0.0101983i	$0.00324627\pi$
$888$		0			0
$889$	−73.9756	−	24.0361i	−2.48106	−	0.806146i
$890$		0			0
$891$	18.9930	+	40.3808i	0.636289	+	1.35281i
$892$		0			0
$893$	25.0145	−	25.0145i	0.837077	−	0.837077i
$894$		0			0
$895$	−3.66977	−	3.15956i	−0.122667	−	0.105613i
$896$		0			0
$897$	0.0493490	−	0.238244i	0.00164772	−	0.00795473i
$898$		0			0
$899$	−2.86850			−0.0956698
$900$		0			0
$901$	−63.2640			−2.10763
$902$		0			0
$903$	4.91843	−	23.7449i	0.163675	−	0.790180i
$904$		0			0
$905$	−1.15028	+	0.698625i	−0.0382366	+	0.0232231i
$906$		0			0
$907$	24.4142	−	24.4142i	0.810659	−	0.810659i	−0.174073	−	0.984733i	$-0.555693\pi$
$907$	24.4142	−	24.4142i	0.810659	−	0.810659i	0.984733	+	0.174073i	$0.0556929\pi$
$908$		0			0
$909$	14.9979	−	34.6497i	0.497450	−	1.14926i
$910$		0			0
$911$	29.3166	+	9.52554i	0.971303	+	0.315595i	0.751342	−	0.659913i	$-0.229407\pi$
$911$	29.3166	+	9.52554i	0.971303	+	0.315595i	0.219961	+	0.975509i	$0.429407\pi$
$912$		0			0
$913$	−14.7574	+	28.9630i	−0.488397	+	0.958534i
$914$		0			0
$915$	31.0486	+	21.2833i	1.02644	+	0.703606i
$916$		0			0
$917$	13.2548	+	2.09936i	0.437713	+	0.0693269i
$918$		0			0
$919$	−15.8783	−	21.8546i	−0.523777	−	0.720918i	0.462389	−	0.886677i	$-0.346992\pi$
$919$	−15.8783	−	21.8546i	−0.523777	−	0.720918i	−0.986166	+	0.165760i	$0.946992\pi$
$920$		0			0
$921$	23.3033	+	35.4793i	0.767869	+	1.16908i
$922$		0			0
$923$	−0.403669	−	0.792245i	−0.0132869	−	0.0260771i
$924$		0			0
$925$	19.4910	+	14.3989i	0.640862	+	0.473434i
$926$		0			0
$927$	1.00774	−	3.92346i	0.0330987	−	0.128863i
$928$		0			0
$929$	−8.85751	−	6.43535i	−0.290605	−	0.211137i	0.432925	−	0.901430i	$-0.357482\pi$
$929$	−8.85751	−	6.43535i	−0.290605	−	0.211137i	−0.723530	+	0.690293i	$0.757482\pi$
$930$		0			0
$931$	33.7776	−	24.5409i	1.10702	−	0.804295i
$932$		0			0
$933$	3.92896	−	6.88749i	0.128628	−	0.225486i
$934$		0			0
$935$	−71.6967	−	44.3283i	−2.34473	−	1.44969i
$936$		0			0
$937$	8.29377	+	4.22589i	0.270946	+	0.138054i	0.584185	−	0.811620i	$-0.301414\pi$
$937$	8.29377	+	4.22589i	0.270946	+	0.138054i	−0.313239	+	0.949674i	$0.601414\pi$
$938$		0			0
$939$	−11.9229	−	9.55291i	−0.389089	−	0.311747i
$940$		0			0
$941$	16.5696	−	5.38379i	0.540153	−	0.175506i	−0.0262187	−	0.999656i	$-0.508347\pi$
$941$	16.5696	−	5.38379i	0.540153	−	0.175506i	0.566372	+	0.824150i	$0.308347\pi$
$942$		0			0
$943$	1.42772	+	1.42772i	0.0464931	+	0.0464931i
$944$		0			0
$945$	4.20111	+	46.4781i	0.136662	+	1.51193i
$946$		0			0
$947$	−4.45223	−	28.1103i	−0.144678	−	0.913462i	−0.948082	−	0.318027i	$-0.896980\pi$
$947$	−4.45223	−	28.1103i	−0.144678	−	0.913462i	0.803403	−	0.595435i	$-0.203020\pi$
$948$		0			0
$949$			5.94063i			0.192841i
$950$		0			0
$951$	10.7344	−	28.4038i	0.348086	−	0.921058i
$952$		0			0
$953$	10.3056	−	1.63224i	0.333830	−	0.0528735i	0.0127306	−	0.999919i	$-0.495948\pi$
$953$	10.3056	−	1.63224i	0.333830	−	0.0528735i	0.321099	+	0.947045i	$0.395948\pi$
$954$		0			0
$955$	−46.0319	+	10.8582i	−1.48956	+	0.351362i
$956$		0			0
$957$	−8.09261	+	3.65352i	−0.261597	+	0.118101i
$958$		0			0
$959$	−2.96106	−	9.11321i	−0.0956177	−	0.294281i
$960$		0			0
$961$	−7.20085	+	22.1619i	−0.232286	+	0.714901i
$962$		0			0
$963$	−3.92046	−	9.90452i	−0.126335	−	0.319169i
$964$		0			0
$965$	1.07370	+	1.26729i	0.0345635	+	0.0407955i
$966$		0			0
$967$	3.51292	−	22.1797i	0.112968	−	0.713251i	−0.864573	−	0.502507i	$-0.832411\pi$
$967$	3.51292	−	22.1797i	0.112968	−	0.713251i	0.977541	−	0.210744i	$-0.0675887\pi$
$968$		0			0
$969$	58.0715	−	15.8838i	1.86552	−	0.510260i
$970$		0			0
$971$	−11.1728	+	15.3781i	−0.358554	+	0.493507i	−0.949745	−	0.313025i	$-0.898658\pi$
$971$	−11.1728	+	15.3781i	−0.358554	+	0.493507i	0.591191	+	0.806531i	$0.298658\pi$
$972$		0			0
$973$	6.12821	−	3.12248i	0.196461	−	0.100102i
$974$		0			0
$975$	−2.39799	−	2.67801i	−0.0767973	−	0.0857650i
$976$		0			0
$977$	−19.9407	+	10.1603i	−0.637958	+	0.325056i	−0.742880	−	0.669425i	$-0.766541\pi$
$977$	−19.9407	+	10.1603i	−0.637958	+	0.325056i	0.104922	+	0.994480i	$0.466541\pi$
$978$		0			0
$979$	38.9630	−	53.6280i	1.24526	−	1.71396i
$980$		0			0
$981$	33.9657	+	3.21375i	1.08444	+	0.102607i
$982$		0			0
$983$	0.682136	−	4.30684i	0.0217568	−	0.137367i	−0.974419	−	0.224739i	$-0.927847\pi$
$983$	0.682136	−	4.30684i	0.0217568	−	0.137367i	0.996176	+	0.0873723i	$0.0278470\pi$
$984$		0			0
$985$	0.404980	+	5.42084i	0.0129037	+	0.172722i
$986$		0			0
$987$	−39.8161	+	36.2267i	−1.26736	+	1.15311i
$988$		0			0
$989$	−0.364513	+	1.12185i	−0.0115908	+	0.0356729i
$990$		0			0
$991$	−16.7179	−	51.4526i	−0.531063	−	1.63444i	−0.752005	−	0.659157i	$-0.770913\pi$
$991$	−16.7179	−	51.4526i	−0.531063	−	1.63444i	0.220942	−	0.975287i	$-0.429087\pi$
$992$		0			0
$993$	11.2194	+	24.8512i	0.356037	+	0.788628i
$994$		0			0
$995$	4.91204	−	59.3973i	0.155722	−	1.88302i
$996$		0			0
$997$	−5.05321	+	0.800350i	−0.160037	+	0.0253473i	−0.235939	−	0.971768i	$-0.575816\pi$
$997$	−5.05321	+	0.800350i	−0.160037	+	0.0253473i	0.0759018	+	0.997115i	$0.475816\pi$
$998$		0			0
$999$	22.2579	−	11.7811i	0.704208	−	0.372739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.53.5	yes	80
3.2	odd	2	inner	300.2.x.a.53.7	yes	80
25.17	odd	20	inner	300.2.x.a.17.7	yes	80
75.17	even	20	inner	300.2.x.a.17.5	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.17.5	✓	80	75.17	even	20	inner
300.2.x.a.17.7	yes	80	25.17	odd	20	inner
300.2.x.a.53.5	yes	80	1.1	even	1	trivial
300.2.x.a.53.7	yes	80	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.351313 + 1.69605i) q^{3} +(2.22846 + 0.184289i) q^{5} +(-2.84010 + 2.84010i) q^{7} +(-2.75316 - 1.19169i) q^{9} +O(q^{10})\)	\(q+(-0.351313 + 1.69605i) q^{3} +(2.22846 + 0.184289i) q^{5} +(-2.84010 + 2.84010i) q^{7} +(-2.75316 - 1.19169i) q^{9} +(4.71560 + 1.53219i) q^{11} +(-0.188444 + 0.369843i) q^{13} +(-1.09545 + 3.71483i) q^{15} +(-7.50930 - 1.18936i) q^{17} +(2.68725 + 3.69868i) q^{19} +(-3.81918 - 5.81471i) q^{21} +(0.153636 + 0.301528i) q^{23} +(4.93208 + 0.821362i) q^{25} +(2.98838 - 4.25083i) q^{27} +(0.836442 + 0.607711i) q^{29} +(-2.24457 + 1.63078i) q^{31} +(-4.25532 + 7.45960i) q^{33} +(-6.85245 + 5.80565i) q^{35} +(4.31832 + 2.20029i) q^{37} +(-0.561068 - 0.449541i) q^{39} +(5.67438 - 1.84372i) q^{41} +(2.46472 + 2.46472i) q^{43} +(-5.91569 - 3.16301i) q^{45} +(-1.21046 - 7.64252i) q^{47} -9.13235i q^{49} +(4.65532 - 12.3183i) q^{51} +(8.21858 - 1.30170i) q^{53} +(10.2262 + 4.28346i) q^{55} +(-7.21721 + 3.25831i) q^{57} +(-3.09959 - 9.53955i) q^{59} +(3.00345 - 9.24368i) q^{61} +(11.2038 - 4.43473i) q^{63} +(-0.488099 + 0.789452i) q^{65} +(1.15518 - 7.29349i) q^{67} +(-0.565381 + 0.154644i) q^{69} +(-1.25910 + 1.73301i) q^{71} +(12.7520 - 6.49745i) q^{73} +(-3.12577 + 8.07648i) q^{75} +(-17.7443 + 9.04119i) q^{77} +(-4.46331 + 6.14322i) q^{79} +(6.15976 + 6.56181i) q^{81} +(-1.02557 + 6.47518i) q^{83} +(-16.5150 - 4.03432i) q^{85} +(-1.32456 + 1.20515i) q^{87} +(4.13129 - 12.7148i) q^{89} +(-0.515190 - 1.58559i) q^{91} +(-1.97733 - 4.37982i) q^{93} +(5.30680 + 8.73760i) q^{95} +(2.19961 - 0.348384i) q^{97} +(-11.1569 - 9.83788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q - 2 * q^3 + 4 * q^7	\( 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) \) 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more