LMFDB - Embedded newform 810.3.j.g.269.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(269,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("810.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.j (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:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.6
Character	$\chi$	$=$	810.269
Dual form			810.3.j.g.539.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.41458 + 2.34766i) q^{5} +(-8.20611 - 4.73780i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.41458 + 2.34766i) q^{5} +(-8.20611 - 4.73780i) q^{7} +2.82843 q^{8} +(0.246293 - 7.06678i) q^{10} +(-17.6547 - 10.1930i) q^{11} +(5.29129 - 3.05493i) q^{13} +(11.6052 - 6.70026i) q^{14} +(-2.00000 + 3.46410i) q^{16} -24.0002 q^{17} +16.0752 q^{19} +(8.48084 + 5.29861i) q^{20} +(24.9676 - 14.4150i) q^{22} +(21.6389 + 37.4798i) q^{23} +(13.9770 - 20.7279i) q^{25} +8.64064i q^{26} +18.9512i q^{28} +(16.9927 + 9.81073i) q^{29} +(-15.2536 - 26.4200i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(16.9707 - 29.3941i) q^{34} +(47.3492 + 1.65023i) q^{35} +44.8335i q^{37} +(-11.3669 + 19.6880i) q^{38} +(-12.4863 + 6.64019i) q^{40} +(41.6479 - 24.0454i) q^{41} +(-41.6597 - 24.0522i) q^{43} +40.7719i q^{44} -61.2042 q^{46} +(-34.0385 + 58.9564i) q^{47} +(20.3935 + 35.3225i) q^{49} +(15.5031 + 31.7750i) q^{50} +(-10.5826 - 6.10986i) q^{52} +61.7484 q^{53} +(101.868 + 3.55032i) q^{55} +(-23.2104 - 13.4005i) q^{56} +(-24.0313 + 13.8745i) q^{58} +(-43.6833 + 25.2206i) q^{59} +(24.4987 - 42.4330i) q^{61} +43.1438 q^{62} +8.00000 q^{64} +(-16.1869 + 25.9084i) q^{65} +(47.7100 - 27.5454i) q^{67} +(24.0002 + 41.5696i) q^{68} +(-35.5021 + 56.8239i) q^{70} -23.5982i q^{71} +40.4303i q^{73} +(-54.9096 - 31.7021i) q^{74} +(-16.0752 - 27.8430i) q^{76} +(96.5844 + 167.289i) q^{77} +(-16.6169 + 28.7813i) q^{79} +(0.696621 - 19.9879i) q^{80} +68.0107i q^{82} +(-11.3572 + 19.6713i) q^{83} +(105.951 - 56.3443i) q^{85} +(58.9157 - 34.0150i) q^{86} +(-49.9351 - 28.8301i) q^{88} -79.5266i q^{89} -57.8946 q^{91} +(43.2779 - 74.9595i) q^{92} +(-48.1377 - 83.3770i) q^{94} +(-70.9651 + 37.7390i) q^{95} +(103.825 + 59.9431i) q^{97} -57.6815 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) $ 24 * q - 24 * q^4 - 24 * q^7	$ 24 q - 24 q^{4} - 24 q^{7} - 12 q^{10} - 48 q^{13} - 48 q^{16} + 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{43} - 36 q^{49} + 96 q^{52} + 216 q^{55} - 396 q^{58} - 60 q^{61} + 192 q^{64} + 1032 q^{67} - 480 q^{70} - 240 q^{79} - 396 q^{85} - 240 q^{88} + 48 q^{91} - 48 q^{94} + 1440 q^{97}+O(q^{100}) $ 24 * q - 24 * q^4 - 24 * q^7 - 12 * q^10 - 48 * q^13 - 48 * q^16 + 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^43 - 36 * q^49 + 96 * q^52 + 216 * q^55 - 396 * q^58 - 60 * q^61 + 192 * q^64 + 1032 * q^67 - 480 * q^70 - 240 * q^79 - 396 * q^85 - 240 * q^88 + 48 * q^91 - 48 * q^94 + 1440 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−4.41458	+	2.34766i	−0.882915	+	0.469532i
$5$	−4.41458	+	2.34766i	−0.882915	+	0.469532i
$6$		0			0
$7$	−8.20611	−	4.73780i	−1.17230	−	0.676828i	−0.218080	−	0.975931i	$-0.569979\pi$
$7$	−8.20611	−	4.73780i	−1.17230	−	0.676828i	−0.954221	+	0.299102i	$0.903313\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$	0.246293	−	7.06678i	0.0246293	−	0.706678i
$11$	−17.6547	−	10.1930i	−1.60498	−	0.926633i	−0.990471	−	0.137720i	$-0.956023\pi$
$11$	−17.6547	−	10.1930i	−1.60498	−	0.926633i	−0.614505	−	0.788913i	$-0.710644\pi$
$12$		0			0
$13$	5.29129	−	3.05493i	0.407023	−	0.234995i	−0.282487	−	0.959271i	$-0.591159\pi$
$13$	5.29129	−	3.05493i	0.407023	−	0.234995i	0.689510	+	0.724277i	$0.257826\pi$
$14$	11.6052	−	6.70026i	0.828942	−	0.478590i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−24.0002			−1.41178			−0.705888	−	0.708323i	$-0.749452\pi$
$17$	−24.0002			−1.41178			−0.705888	+	0.708323i	$0.749452\pi$
$18$		0			0
$19$	16.0752			0.846062			0.423031	−	0.906115i	$-0.360966\pi$
$19$	16.0752			0.846062			0.423031	+	0.906115i	$0.360966\pi$
$20$	8.48084	+	5.29861i	0.424042	+	0.264931i
$21$		0			0
$22$	24.9676	−	14.4150i	1.13489	−	0.655229i
$23$	21.6389	+	37.4798i	0.940824	+	1.62955i	0.763905	+	0.645329i	$0.223280\pi$
$23$	21.6389	+	37.4798i	0.940824	+	1.62955i	0.176919	+	0.984225i	$0.443387\pi$
$24$		0			0
$25$	13.9770	−	20.7279i	0.559079	−	0.829114i
$26$			8.64064i			0.332332i
$27$		0			0
$28$			18.9512i			0.676828i
$29$	16.9927	+	9.81073i	0.585954	+	0.338301i	0.763496	−	0.645812i	$-0.223481\pi$
$29$	16.9927	+	9.81073i	0.585954	+	0.338301i	−0.177542	+	0.984113i	$0.556814\pi$
$30$		0			0
$31$	−15.2536	−	26.4200i	−0.492052	−	0.852260i	0.507906	−	0.861413i	$-0.330420\pi$
$31$	−15.2536	−	26.4200i	−0.492052	−	0.852260i	−0.999958	+	0.00915307i	$0.997086\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$		0			0
$34$	16.9707	−	29.3941i	0.499138	−	0.864533i
$35$	47.3492	+	1.65023i	1.35284	+	0.0471493i
$36$		0			0
$37$			44.8335i			1.21172i	0.795573	+	0.605858i	$0.207170\pi$
$37$			44.8335i			1.21172i	−0.795573	+	0.605858i	$0.792830\pi$
$38$	−11.3669	+	19.6880i	−0.299128	+	0.518105i
$39$		0			0
$40$	−12.4863	+	6.64019i	−0.312158	+	0.166005i
$41$	41.6479	−	24.0454i	1.01580	−	0.586473i	0.102917	−	0.994690i	$-0.467182\pi$
$41$	41.6479	−	24.0454i	1.01580	−	0.586473i	0.912885	+	0.408217i	$0.133849\pi$
$42$		0			0
$43$	−41.6597	−	24.0522i	−0.968830	−	0.559354i	−0.0699506	−	0.997550i	$-0.522284\pi$
$43$	−41.6597	−	24.0522i	−0.968830	−	0.559354i	−0.898879	+	0.438196i	$0.855618\pi$
$44$			40.7719i			0.926633i
$45$		0			0
$46$	−61.2042			−1.33053
$47$	−34.0385	+	58.9564i	−0.724223	+	1.25439i	0.235070	+	0.971979i	$0.424468\pi$
$47$	−34.0385	+	58.9564i	−0.724223	+	1.25439i	−0.959293	+	0.282413i	$0.908865\pi$
$48$		0			0
$49$	20.3935	+	35.3225i	0.416193	+	0.720868i
$50$	15.5031	+	31.7750i	0.310062	+	0.635501i
$51$		0			0
$52$	−10.5826	−	6.10986i	−0.203511	−	0.117497i
$53$	61.7484			1.16506			0.582532	−	0.812808i	$-0.302062\pi$
$53$	61.7484			1.16506			0.582532	+	0.812808i	$0.302062\pi$
$54$		0			0
$55$	101.868	+	3.55032i	1.85214	+	0.0645512i
$56$	−23.2104	−	13.4005i	−0.414471	−	0.239295i
$57$		0			0
$58$	−24.0313	+	13.8745i	−0.414332	+	0.239215i
$59$	−43.6833	+	25.2206i	−0.740395	+	0.427467i	−0.822213	−	0.569180i	$-0.807261\pi$
$59$	−43.6833	+	25.2206i	−0.740395	+	0.427467i	0.0818182	+	0.996647i	$0.473927\pi$
$60$		0			0
$61$	24.4987	−	42.4330i	0.401619	−	0.695624i	−0.592303	−	0.805715i	$-0.701781\pi$
$61$	24.4987	−	42.4330i	0.401619	−	0.695624i	0.993921	+	0.110092i	$0.0351144\pi$
$62$	43.1438			0.695867
$63$		0			0
$64$	8.00000			0.125000
$65$	−16.1869	+	25.9084i	−0.249029	+	0.398590i
$66$		0			0
$67$	47.7100	−	27.5454i	0.712089	−	0.411125i	−0.0997448	−	0.995013i	$-0.531803\pi$
$67$	47.7100	−	27.5454i	0.712089	−	0.411125i	0.811834	+	0.583888i	$0.198469\pi$
$68$	24.0002	+	41.5696i	0.352944	+	0.611317i
$69$		0			0
$70$	−35.5021	+	56.8239i	−0.507172	+	0.811769i
$71$		−	23.5982i		−	0.332369i	−0.986095	−	0.166184i	$-0.946855\pi$
$71$		−	23.5982i		−	0.332369i	0.986095	−	0.166184i	$-0.0531447\pi$
$72$		0			0
$73$			40.4303i			0.553840i	0.960893	+	0.276920i	$0.0893137\pi$
$73$			40.4303i			0.553840i	−0.960893	+	0.276920i	$0.910686\pi$
$74$	−54.9096	−	31.7021i	−0.742021	−	0.428406i
$75$		0			0
$76$	−16.0752	−	27.8430i	−0.211515	−	0.366355i
$77$	96.5844	+	167.289i	1.25434	+	2.17259i
$78$		0			0
$79$	−16.6169	+	28.7813i	−0.210340	+	0.364320i	−0.951821	−	0.306654i	$-0.900791\pi$
$79$	−16.6169	+	28.7813i	−0.210340	+	0.364320i	0.741481	+	0.670974i	$0.234124\pi$
$80$	0.696621	−	19.9879i	0.00870776	−	0.249848i
$81$		0			0
$82$			68.0107i			0.829399i
$83$	−11.3572	+	19.6713i	−0.136834	+	0.237003i	−0.926296	−	0.376795i	$-0.877026\pi$
$83$	−11.3572	+	19.6713i	−0.136834	+	0.237003i	0.789463	+	0.613799i	$0.210359\pi$
$84$		0			0
$85$	105.951	−	56.3443i	1.24648	−	0.662874i
$86$	58.9157	−	34.0150i	0.685066	−	0.395523i
$87$		0			0
$88$	−49.9351	−	28.8301i	−0.567445	−	0.327614i
$89$		−	79.5266i		−	0.893557i	−0.894644	−	0.446779i	$-0.852571\pi$
$89$		−	79.5266i		−	0.893557i	0.894644	−	0.446779i	$-0.147429\pi$
$90$		0			0
$91$	−57.8946			−0.636204
$92$	43.2779	−	74.9595i	0.470412	−	0.814777i
$93$		0			0
$94$	−48.1377	−	83.3770i	−0.512103	−	0.886989i
$95$	−70.9651	+	37.7390i	−0.747001	+	0.397253i
$96$		0			0
$97$	103.825	+	59.9431i	1.07036	+	0.617970i	0.928279	−	0.371885i	$-0.121289\pi$
$97$	103.825	+	59.9431i	1.07036	+	0.617970i	0.142077	+	0.989856i	$0.454622\pi$
$98$	−57.6815			−0.588586
$99$		0			0
$100$	−49.8787	−	3.48099i	−0.498787	−	0.0348099i
$101$	19.1196	+	11.0387i	0.189303	+	0.109294i	0.591656	−	0.806190i	$-0.298474\pi$
$101$	19.1196	+	11.0387i	0.189303	+	0.109294i	−0.402353	+	0.915485i	$0.631808\pi$
$102$		0			0
$103$	−15.9238	+	9.19358i	−0.154600	+	0.0892581i	−0.575304	−	0.817940i	$-0.695116\pi$
$103$	−15.9238	+	9.19358i	−0.154600	+	0.0892581i	0.420705	+	0.907198i	$0.361783\pi$
$104$	14.9660	−	8.64064i	0.143904	−	0.0830831i
$105$		0			0
$106$	−43.6627	+	75.6260i	−0.411912	+	0.713453i
$107$	60.8601			0.568786			0.284393	−	0.958708i	$-0.408208\pi$
$107$	60.8601			0.568786			0.284393	+	0.958708i	$0.408208\pi$
$108$		0			0
$109$	80.4892			0.738433			0.369216	−	0.929343i	$-0.379626\pi$
$109$	80.4892			0.738433			0.369216	+	0.929343i	$0.379626\pi$
$110$	−76.3797	+	122.252i	−0.694361	+	1.11138i
$111$		0			0
$112$	32.8244	−	18.9512i	0.293075	−	0.169207i
$113$	11.3778	+	19.7069i	0.100689	+	0.174398i	0.911969	−	0.410260i	$-0.134562\pi$
$113$	11.3778	+	19.7069i	0.100689	+	0.174398i	−0.811280	+	0.584658i	$0.801229\pi$
$114$		0			0
$115$	−183.517	−	114.656i	−1.59580	−	0.997012i
$116$		−	39.2429i		−	0.338301i
$117$		0			0
$118$		−	71.3345i		−	0.604530i
$119$	196.948	+	113.708i	1.65503	+	0.955530i
$120$		0			0
$121$	147.293	+	255.119i	1.21730	+	2.10842i
$122$	34.6464	+	60.0094i	0.283987	+	0.491880i
$123$		0			0
$124$	−30.5072	+	52.8401i	−0.246026	+	0.426130i
$125$	−13.0405	+	124.318i	−0.104324	+	0.994543i
$126$		0			0
$127$		−	73.3562i		−	0.577608i	−0.957388	−	0.288804i	$-0.906742\pi$
$127$		−	73.3562i		−	0.577608i	0.957388	−	0.288804i	$-0.0932576\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−20.2853	−	38.1448i	−0.156041	−	0.293421i
$131$	−78.8523	+	45.5254i	−0.601926	+	0.347522i	−0.769799	−	0.638286i	$-0.779644\pi$
$131$	−78.8523	+	45.5254i	−0.601926	+	0.347522i	0.167873	+	0.985809i	$0.446310\pi$
$132$		0			0
$133$	−131.915	−	76.1609i	−0.991839	−	0.572639i
$134$			77.9101i			0.581419i
$135$		0			0
$136$	−67.8828			−0.499138
$137$	13.9419	−	24.1480i	0.101765	−	0.176263i	−0.810647	−	0.585536i	$-0.800884\pi$
$137$	13.9419	−	24.1480i	0.101765	−	0.176263i	0.912412	+	0.409273i	$0.134218\pi$
$138$		0			0
$139$	−17.3690	−	30.0839i	−0.124957	−	0.216431i	0.796759	−	0.604297i	$-0.206546\pi$
$139$	−17.3690	−	30.0839i	−0.124957	−	0.216431i	−0.921716	+	0.387866i	$0.873212\pi$
$140$	−44.4910	−	83.6615i	−0.317793	−	0.597582i
$141$		0			0
$142$	28.9017	+	16.6864i	0.203533	+	0.117510i
$143$	−124.555			−0.871015
$144$		0			0
$145$	−98.0477	−	3.41718i	−0.676191	−	0.0235668i
$146$	−49.5168	−	28.5886i	−0.339156	−	0.195812i
$147$		0			0
$148$	77.6539	−	44.8335i	0.524688	−	0.302929i
$149$	0.274589	−	0.158534i	0.00184288	−	0.00106399i	−0.499078	−	0.866557i	$-0.666328\pi$
$149$	0.274589	−	0.158534i	0.00184288	−	0.00106399i	0.500921	+	0.865493i	$0.332995\pi$
$150$		0			0
$151$	52.6638	−	91.2164i	0.348767	−	0.604082i	−0.637264	−	0.770646i	$-0.719934\pi$
$151$	52.6638	−	91.2164i	0.348767	−	0.604082i	0.986031	+	0.166564i	$0.0532671\pi$
$152$	45.4674			0.299128
$153$		0			0
$154$	−273.182			−1.77391
$155$	129.364	+	80.8230i	0.834604	+	0.521439i
$156$		0			0
$157$	39.4927	−	22.8011i	0.251546	−	0.145230i	−0.368926	−	0.929459i	$-0.620274\pi$
$157$	39.4927	−	22.8011i	0.251546	−	0.145230i	0.620472	+	0.784229i	$0.286941\pi$
$158$	−23.4998	−	40.7029i	−0.148733	−	0.257613i
$159$		0			0
$160$	23.9874	+	14.9867i	0.149922	+	0.0936671i
$161$		−	410.084i		−	2.54711i
$162$		0			0
$163$			152.794i			0.937384i	0.883362	+	0.468692i	$0.155275\pi$
$163$			152.794i			0.937384i	−0.883362	+	0.468692i	$0.844725\pi$
$164$	−83.2957	−	48.0908i	−0.507901	−	0.293237i
$165$		0			0
$166$	−16.0615	−	27.8194i	−0.0967561	−	0.167587i
$167$	6.86420	+	11.8891i	0.0411030	+	0.0711925i	0.885845	−	0.463981i	$-0.153579\pi$
$167$	6.86420	+	11.8891i	0.0411030	+	0.0711925i	−0.844742	+	0.535174i	$0.820246\pi$
$168$		0			0
$169$	−65.8348	+	114.029i	−0.389555	+	0.674729i
$170$	−5.91107	+	169.604i	−0.0347710	+	0.997671i
$171$		0			0
$172$			96.2089i			0.559354i
$173$	5.21536	−	9.03326i	0.0301466	−	0.0522154i	−0.850558	−	0.525880i	$-0.823736\pi$
$173$	5.21536	−	9.03326i	0.0301466	−	0.0522154i	0.880705	+	0.473665i	$0.157069\pi$
$174$		0			0
$175$	−212.901	+	103.875i	−1.21658	+	0.593571i
$176$	70.6189	−	40.7719i	0.401244	−	0.231658i
$177$		0			0
$178$	97.3998	+	56.2338i	0.547190	+	0.315920i
$179$			62.4650i			0.348967i	0.984660	+	0.174483i	$0.0558255\pi$
$179$			62.4650i			0.348967i	−0.984660	+	0.174483i	$0.944174\pi$
$180$		0			0
$181$	343.029			1.89519			0.947594	−	0.319477i	$-0.103507\pi$
$181$	343.029			1.89519			0.947594	+	0.319477i	$0.103507\pi$
$182$	40.9376	−	70.9061i	0.224932	−	0.389594i
$183$		0			0
$184$	61.2042	+	106.009i	0.332631	+	0.576135i
$185$	−105.254	−	197.921i	−0.568939	−	1.06984i
$186$		0			0
$187$	423.717	+	244.633i	2.26587	+	1.30820i
$188$	136.154			0.724223
$189$		0			0
$190$	3.95920	−	113.600i	0.0208379	−	0.597893i
$191$	−10.9445	−	6.31882i	−0.0573012	−	0.0330829i	0.471076	−	0.882093i	$-0.343866\pi$
$191$	−10.9445	−	6.31882i	−0.0573012	−	0.0330829i	−0.528377	+	0.849010i	$0.677199\pi$
$192$		0			0
$193$	−145.600	+	84.0622i	−0.754405	+	0.435556i	−0.827283	−	0.561785i	$-0.810115\pi$
$193$	−145.600	+	84.0622i	−0.754405	+	0.435556i	0.0728786	+	0.997341i	$0.476781\pi$
$194$	−146.830	+	84.7724i	−0.756856	+	0.436971i
$195$		0			0
$196$	40.7869	−	70.6451i	0.208097	−	0.360434i
$197$	−372.044			−1.88855			−0.944275	−	0.329157i	$-0.893235\pi$
$197$	−372.044			−1.88855			−0.944275	+	0.329157i	$0.893235\pi$
$198$		0			0
$199$	231.821			1.16493			0.582466	−	0.812855i	$-0.302088\pi$
$199$	231.821			1.16493			0.582466	+	0.812855i	$0.302088\pi$
$200$	39.5329	−	58.6272i	0.197664	−	0.293136i
$201$		0			0
$202$	−27.0392	+	15.6111i	−0.133858	+	0.0772827i
$203$	−92.9625	−	161.016i	−0.457943	−	0.793181i
$204$		0			0
$205$	−127.407	+	203.925i	−0.621499	+	0.994758i
$206$		−	26.0034i		−	0.126230i
$207$		0			0
$208$			24.4394i			0.117497i
$209$	−283.803	−	163.854i	−1.35791	−	0.783989i
$210$		0			0
$211$	−10.4506	−	18.1010i	−0.0495289	−	0.0857866i	0.840198	−	0.542280i	$-0.182439\pi$
$211$	−10.4506	−	18.1010i	−0.0495289	−	0.0857866i	−0.889727	+	0.456493i	$0.849105\pi$
$212$	−61.7484	−	106.951i	−0.291266	−	0.504487i
$213$		0			0
$214$	−43.0346	+	74.5381i	−0.201096	+	0.348309i
$215$	240.376	+	8.37765i	1.11803	+	0.0389658i
$216$		0			0
$217$			289.074i			1.33214i
$218$	−56.9144	+	98.5787i	−0.261075	+	0.452196i
$219$		0			0
$220$	−95.7185	−	179.991i	−0.435084	−	0.818139i
$221$	−126.992	+	73.3189i	−0.574625	+	0.331760i
$222$		0			0
$223$	−13.6598	−	7.88652i	−0.0612549	−	0.0353655i	0.469060	−	0.883166i	$-0.344593\pi$
$223$	−13.6598	−	7.88652i	−0.0612549	−	0.0353655i	−0.530315	+	0.847801i	$0.677926\pi$
$224$			53.6021i			0.239295i
$225$		0			0
$226$	−32.1813			−0.142395
$227$	170.673	−	295.614i	0.751863	−	1.30227i	−0.195056	−	0.980792i	$-0.562489\pi$
$227$	170.673	−	295.614i	0.751863	−	1.30227i	0.946919	−	0.321473i	$-0.104178\pi$
$228$		0			0
$229$	−60.2263	−	104.315i	−0.262997	−	0.455524i	0.704040	−	0.710160i	$-0.251378\pi$
$229$	−60.2263	−	104.315i	−0.262997	−	0.455524i	−0.967037	+	0.254636i	$0.918044\pi$
$230$	270.191	−	143.687i	1.17474	−	0.624724i
$231$		0			0
$232$	48.0626	+	27.7489i	0.207166	+	0.119607i
$233$	307.400			1.31931			0.659657	−	0.751567i	$-0.270702\pi$
$233$	307.400			1.31931			0.659657	+	0.751567i	$0.270702\pi$
$234$		0			0
$235$	11.8560	−	340.178i	0.0504509	−	1.44757i
$236$	87.3666	+	50.4411i	0.370197	+	0.213734i
$237$		0			0
$238$	−278.527	+	160.808i	−1.17028	+	0.675662i
$239$	103.129	−	59.5417i	0.431503	−	0.249128i	−0.268484	−	0.963284i	$-0.586523\pi$
$239$	103.129	−	59.5417i	0.431503	−	0.249128i	0.699987	+	0.714156i	$0.253189\pi$
$240$		0			0
$241$	157.300	−	272.452i	0.652697	−	1.13050i	−0.329769	−	0.944062i	$-0.606971\pi$
$241$	157.300	−	272.452i	0.652697	−	1.13050i	0.982466	−	0.186443i	$-0.0596958\pi$
$242$	−416.608			−1.72152
$243$		0			0
$244$	−97.9949			−0.401619
$245$	−172.954	−	108.057i	−0.705934	−	0.441049i
$246$		0			0
$247$	85.0584	−	49.1085i	0.344366	−	0.198820i
$248$	−43.1438	−	74.7272i	−0.173967	−	0.301319i
$249$		0			0
$250$	−143.037	−	103.877i	−0.572147	−	0.415509i
$251$		−	148.193i		−	0.590411i	−0.955434	−	0.295206i	$-0.904612\pi$
$251$		−	148.193i		−	0.590411i	0.955434	−	0.295206i	$-0.0953882\pi$
$252$		0			0
$253$		−	882.260i		−	3.48719i
$254$	89.8427	+	51.8707i	0.353711	+	0.204215i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−147.158	−	254.885i	−0.572598	−	0.991770i	−0.996298	−	0.0859668i	$-0.972602\pi$
$257$	−147.158	−	254.885i	−0.572598	−	0.991770i	0.423700	−	0.905803i	$-0.360731\pi$
$258$		0			0
$259$	212.412	−	367.908i	0.820123	−	1.42050i
$260$	61.0615	+	2.12813i	0.234852	+	0.00818511i
$261$		0			0
$262$		−	128.765i		−	0.491471i
$263$	34.7322	−	60.1580i	0.132062	−	0.228738i	−0.792409	−	0.609990i	$-0.791174\pi$
$263$	34.7322	−	60.1580i	0.132062	−	0.228738i	0.924471	+	0.381252i	$0.124507\pi$
$264$		0			0
$265$	−272.593	+	144.964i	−1.02865	+	0.547035i
$266$	186.555	−	107.708i	0.701336	−	0.404917i
$267$		0			0
$268$	−95.4200	−	55.0907i	−0.356045	−	0.205562i
$269$			262.460i			0.975687i	0.872931	+	0.487844i	$0.162216\pi$
$269$			262.460i			0.975687i	−0.872931	+	0.487844i	$0.837784\pi$
$270$		0			0
$271$	−375.110			−1.38417			−0.692084	−	0.721817i	$-0.743307\pi$
$271$	−375.110			−1.38417			−0.692084	+	0.721817i	$0.743307\pi$
$272$	48.0004	−	83.1391i	0.176472	−	0.305659i
$273$		0			0
$274$	19.7168	+	34.1504i	0.0719590	+	0.124637i
$275$	−458.038	+	223.478i	−1.66559	+	0.812647i
$276$		0			0
$277$	126.760	+	73.1851i	0.457619	+	0.264206i	0.711042	−	0.703149i	$-0.248223\pi$
$277$	126.760	+	73.1851i	0.457619	+	0.264206i	−0.253424	+	0.967355i	$0.581557\pi$
$278$	49.1268			0.176715
$279$		0			0
$280$	133.924	+	4.66754i	0.478300	+	0.0166698i
$281$	68.5625	+	39.5846i	0.243995	+	0.140870i	0.617011	−	0.786954i	$-0.288343\pi$
$281$	68.5625	+	39.5846i	0.243995	+	0.140870i	−0.373017	+	0.927825i	$0.621677\pi$
$282$		0			0
$283$	187.343	−	108.163i	0.661991	−	0.382201i	−0.131044	−	0.991377i	$-0.541833\pi$
$283$	187.343	−	108.163i	0.661991	−	0.382201i	0.793035	+	0.609176i	$0.208500\pi$
$284$	−40.8732	+	23.5982i	−0.143920	+	0.0830921i
$285$		0			0
$286$	88.0738	−	152.548i	0.307950	−	0.533386i
$287$	−455.689			−1.58777
$288$		0			0
$289$	287.010			0.993113
$290$	73.5154	−	117.667i	0.253501	−	0.405749i
$291$		0			0
$292$	70.0274	−	40.4303i	0.239820	−	0.138460i
$293$	−208.166	−	360.554i	−0.710464	−	1.23056i	−0.964683	−	0.263413i	$-0.915152\pi$
$293$	−208.166	−	360.554i	−0.710464	−	1.23056i	0.254220	−	0.967147i	$-0.418181\pi$
$294$		0			0
$295$	133.634	−	213.892i	0.452996	−	0.725056i
$296$			126.808i			0.428406i
$297$		0			0
$298$			0.448403i			0.00150471i
$299$	228.996	+	132.211i	0.765873	+	0.442177i
$300$		0			0
$301$	227.909	+	394.750i	0.757174	+	1.31146i
$302$	74.4779	+	129.000i	0.246616	+	0.427151i
$303$		0			0
$304$	−32.1503	+	55.6860i	−0.105758	+	0.183178i
$305$	−8.53317	+	244.839i	−0.0279776	+	0.802750i
$306$		0			0
$307$			331.571i			1.08004i	0.841653	+	0.540018i	$0.181583\pi$
$307$			331.571i			1.08004i	−0.841653	+	0.540018i	$0.818417\pi$
$308$	193.169	−	334.578i	0.627172	−	1.08629i
$309$		0			0
$310$	−190.461	+	101.287i	−0.614392	+	0.326732i
$311$	340.840	−	196.784i	1.09595	−	0.632745i	0.160794	−	0.986988i	$-0.448595\pi$
$311$	340.840	−	196.784i	1.09595	−	0.632745i	0.935154	+	0.354243i	$0.115261\pi$
$312$		0			0
$313$	220.083	+	127.065i	0.703141	+	0.405959i	0.808516	−	0.588474i	$-0.200271\pi$
$313$	220.083	+	127.065i	0.703141	+	0.405959i	−0.105375	+	0.994433i	$0.533604\pi$
$314$			64.4914i			0.205387i
$315$		0			0
$316$	66.4675			0.210340
$317$	215.992	−	374.108i	0.681361	−	1.18015i	−0.293204	−	0.956050i	$-0.594722\pi$
$317$	215.992	−	374.108i	0.681361	−	1.18015i	0.974566	−	0.224103i	$-0.0719451\pi$
$318$		0			0
$319$	−200.001	−	346.412i	−0.626962	−	1.08593i
$320$	−35.3166	+	18.7813i	−0.110364	+	0.0586915i
$321$		0			0
$322$	502.248	+	289.973i	1.55978	+	0.900538i
$323$	−385.807			−1.19445
$324$		0			0
$325$	10.6342	−	152.376i	0.0327206	−	0.468849i
$326$	−187.133	−	108.041i	−0.574028	−	0.331415i
$327$		0			0
$328$	117.798	−	68.0107i	0.359140	−	0.207350i
$329$	558.647	−	322.535i	1.69802	−	0.980350i
$330$		0			0
$331$	−95.8658	+	166.044i	−0.289625	+	0.501645i	−0.973720	−	0.227748i	$-0.926864\pi$
$331$	−95.8658	+	166.044i	−0.289625	+	0.501645i	0.684095	+	0.729393i	$0.260197\pi$
$332$	45.4288			0.136834
$333$		0			0
$334$	−19.4149			−0.0581284
$335$	−145.952	+	233.608i	−0.435678	+	0.697337i
$336$		0			0
$337$	220.065	−	127.055i	0.653013	−	0.377017i	−0.136597	−	0.990627i	$-0.543616\pi$
$337$	220.065	−	127.055i	0.653013	−	0.377017i	0.789610	+	0.613609i	$0.210283\pi$
$338$	−93.1045	−	161.262i	−0.275457	−	0.477106i
$339$		0			0
$340$	−203.542	−	127.168i	−0.598653	−	0.374023i
$341$			621.919i			1.82381i
$342$		0			0
$343$			77.8236i			0.226891i
$344$	−117.831	−	68.0300i	−0.342533	−	0.197762i
$345$		0			0
$346$	7.37563	+	12.7750i	0.0213168	+	0.0369219i
$347$	160.397	+	277.817i	0.462241	+	0.800624i	0.999072	−	0.0430652i	$-0.0137123\pi$
$347$	160.397	+	277.817i	0.462241	+	0.800624i	−0.536832	+	0.843689i	$0.680379\pi$
$348$		0			0
$349$	−152.262	+	263.726i	−0.436281	+	0.755661i	−0.997399	−	0.0720745i	$-0.977038\pi$
$349$	−152.262	+	263.726i	−0.436281	+	0.755661i	0.561118	+	0.827736i	$0.310371\pi$
$350$	23.3235	−	334.200i	0.0666387	−	0.954857i
$351$		0			0
$352$			115.320i			0.327614i
$353$	−107.879	+	186.852i	−0.305607	+	0.529326i	−0.977396	−	0.211416i	$-0.932193\pi$
$353$	−107.879	+	186.852i	−0.305607	+	0.529326i	0.671790	+	0.740742i	$0.265526\pi$
$354$		0			0
$355$	55.4005	+	104.176i	0.156058	+	0.293453i
$356$	−137.744	+	79.5266i	−0.386922	+	0.223389i
$357$		0			0
$358$	−76.5037	−	44.1695i	−0.213698	−	0.123378i
$359$		−	638.110i		−	1.77746i	−0.458427	−	0.888732i	$-0.651587\pi$
$359$		−	638.110i		−	1.77746i	0.458427	−	0.888732i	$-0.348413\pi$
$360$		0			0
$361$	−102.589			−0.284180
$362$	−242.558	+	420.123i	−0.670050	+	1.16056i
$363$		0			0
$364$	57.8946	+	100.276i	0.159051	+	0.275484i
$365$	−94.9167	−	178.483i	−0.260046	−	0.488994i
$366$		0			0
$367$	320.949	+	185.300i	0.874519	+	0.504904i	0.868847	−	0.495080i	$-0.164861\pi$
$367$	320.949	+	185.300i	0.874519	+	0.504904i	0.00567194	+	0.999984i	$0.498195\pi$
$368$	−173.112			−0.470412
$369$		0			0
$370$	316.828	+	11.0422i	0.856292	+	0.0298437i
$371$	−506.714	−	292.551i	−1.36581	−	0.788548i
$372$		0			0
$373$	−445.709	+	257.330i	−1.19493	+	0.689894i	−0.959421	−	0.281978i	$-0.909009\pi$
$373$	−445.709	+	257.330i	−1.19493	+	0.689894i	−0.235510	+	0.971872i	$0.575676\pi$
$374$	−599.227	+	345.964i	−1.60221	+	0.925036i
$375$		0			0
$376$	−96.2754	+	166.754i	−0.256052	+	0.443494i
$377$	119.884			0.317996
$378$		0			0
$379$	−159.583			−0.421063			−0.210532	−	0.977587i	$-0.567519\pi$
$379$	−159.583			−0.421063			−0.210532	+	0.977587i	$0.567519\pi$
$380$	136.331	+	85.1761i	0.358766	+	0.224148i
$381$		0			0
$382$	15.4779	−	8.93617i	0.0405181	−	0.0233931i
$383$	−224.022	−	388.017i	−0.584913	−	1.01310i	−0.994886	−	0.101001i	$-0.967795\pi$
$383$	−224.022	−	388.017i	−0.584913	−	1.01310i	0.409973	−	0.912098i	$-0.365538\pi$
$384$		0			0
$385$	−819.118	−	511.763i	−2.12758	−	1.32926i
$386$		−	237.764i		−	0.615969i
$387$		0			0
$388$		−	239.772i		−	0.617970i
$389$	483.961	+	279.415i	1.24412	+	0.718291i	0.969930	−	0.243385i	$-0.0782580\pi$
$389$	483.961	+	279.415i	1.24412	+	0.718291i	0.274187	+	0.961676i	$0.411591\pi$
$390$		0			0
$391$	−519.339	−	899.522i	−1.32823	−	2.30057i
$392$	57.6815	+	99.9072i	0.147147	+	0.254865i
$393$		0			0
$394$	263.075	−	455.659i	0.667703	−	1.15650i
$395$	5.78784	−	166.068i	0.0146527	−	0.420425i
$396$		0			0
$397$			266.143i			0.670385i	0.942150	+	0.335192i	$0.108801\pi$
$397$			266.143i			0.670385i	−0.942150	+	0.335192i	$0.891199\pi$
$398$	−163.922	+	283.922i	−0.411865	+	0.713372i
$399$		0			0
$400$	43.8494	+	89.8734i	0.109624	+	0.224683i
$401$	−15.0865	+	8.71018i	−0.0376222	+	0.0217212i	−0.518693	−	0.854961i	$-0.673581\pi$
$401$	−15.0865	+	8.71018i	−0.0376222	+	0.0217212i	0.481071	+	0.876682i	$0.340248\pi$
$402$		0			0
$403$	−161.423	−	93.1975i	−0.400553	−	0.231259i
$404$		−	44.1549i		−	0.109294i
$405$		0			0
$406$	262.938			0.647630
$407$	456.986	−	791.523i	1.12282	−	1.94477i
$408$		0			0
$409$	222.882	+	386.042i	0.544943	+	0.943869i	0.998610	+	0.0526980i	$0.0167821\pi$
$409$	222.882	+	386.042i	0.544943	+	0.943869i	−0.453667	+	0.891171i	$0.649885\pi$
$410$	−159.666	−	300.238i	−0.389429	−	0.732289i
$411$		0			0
$412$	31.8475	+	18.3872i	0.0772998	+	0.0446290i
$413$	477.960			1.15729
$414$		0			0
$415$	3.95583	−	113.503i	0.00953213	−	0.273502i
$416$	−29.9321	−	17.2813i	−0.0719521	−	0.0415416i
$417$		0			0
$418$	401.358	−	231.724i	0.960186	−	0.554364i
$419$	−309.570	+	178.730i	−0.738830	+	0.426563i	−0.821644	−	0.570002i	$-0.806943\pi$
$419$	−309.570	+	178.730i	−0.738830	+	0.426563i	0.0828141	+	0.996565i	$0.473609\pi$
$420$		0			0
$421$	−287.514	+	497.988i	−0.682930	+	1.18287i	0.291152	+	0.956677i	$0.405961\pi$
$421$	−287.514	+	497.988i	−0.682930	+	1.18287i	−0.974083	+	0.226193i	$0.927372\pi$
$422$	29.5588			0.0700445
$423$		0			0
$424$	174.651			0.411912
$425$	−335.450	+	497.473i	−0.789295	+	1.17052i
$426$		0			0
$427$	−402.078	+	232.140i	−0.941636	+	0.543654i
$428$	−60.8601	−	105.413i	−0.142196	−	0.246292i
$429$		0			0
$430$	−180.232	+	288.476i	−0.419145	+	0.670874i
$431$		−	181.318i		−	0.420691i	−0.977627	−	0.210346i	$-0.932541\pi$
$431$		−	181.318i		−	0.420691i	0.977627	−	0.210346i	$-0.0674589\pi$
$432$		0			0
$433$			705.627i			1.62962i	0.579726	+	0.814811i	$0.303160\pi$
$433$			705.627i			1.62962i	−0.579726	+	0.814811i	$0.696840\pi$
$434$	−354.042	−	204.406i	−0.815766	−	0.470983i
$435$		0			0
$436$	−80.4892	−	139.411i	−0.184608	−	0.319751i
$437$	347.850	+	602.493i	0.795995	+	1.37870i
$438$		0			0
$439$	−142.777	+	247.296i	−0.325231	+	0.563317i	−0.981559	−	0.191159i	$-0.938776\pi$
$439$	−142.777	+	247.296i	−0.325231	+	0.563317i	0.656328	+	0.754476i	$0.272109\pi$
$440$	288.126	+	10.0418i	0.654831	+	0.0228223i
$441$		0			0
$442$		−	207.377i		−	0.469179i
$443$	−353.052	+	611.504i	−0.796957	+	1.38037i	0.124632	+	0.992203i	$0.460225\pi$
$443$	−353.052	+	611.504i	−0.796957	+	1.38037i	−0.921589	+	0.388167i	$0.873108\pi$
$444$		0			0
$445$	186.701	+	351.076i	0.419554	+	0.788936i
$446$	19.3179	−	11.1532i	0.0433138	−	0.0250072i
$447$		0			0
$448$	−65.6489	−	37.9024i	−0.146538	−	0.0846035i
$449$			505.807i			1.12652i	0.826280	+	0.563260i	$0.190453\pi$
$449$			505.807i			1.12652i	−0.826280	+	0.563260i	$0.809547\pi$
$450$		0			0
$451$	−980.376			−2.17378
$452$	22.7556	−	39.4139i	0.0503443	−	0.0871989i
$453$		0			0
$454$	241.368	+	418.062i	0.531648	+	0.920841i
$455$	255.580	−	135.917i	0.561714	−	0.298718i
$456$		0			0
$457$	615.467	+	355.340i	1.34676	+	0.777550i	0.987788	−	0.155801i	$-0.0497958\pi$
$457$	615.467	+	355.340i	1.34676	+	0.777550i	0.358967	+	0.933350i	$0.383129\pi$
$458$	170.346			0.371934
$459$		0			0
$460$	−15.0741	+	432.516i	−0.0327699	+	0.940253i
$461$	−119.178	−	68.8073i	−0.258520	−	0.149257i	0.365139	−	0.930953i	$-0.381021\pi$
$461$	−119.178	−	68.8073i	−0.258520	−	0.149257i	−0.623659	+	0.781696i	$0.714355\pi$
$462$		0			0
$463$	298.053	−	172.081i	0.643743	−	0.371665i	−0.142312	−	0.989822i	$-0.545454\pi$
$463$	298.053	−	172.081i	0.643743	−	0.371665i	0.786055	+	0.618157i	$0.212120\pi$
$464$	−67.9707	+	39.2429i	−0.146489	+	0.0845752i
$465$		0			0
$466$	−217.365	+	376.487i	−0.466448	+	0.807912i
$467$	322.715			0.691038			0.345519	−	0.938412i	$-0.387703\pi$
$467$	322.715			0.691038			0.345519	+	0.938412i	$0.387703\pi$
$468$		0			0
$469$	−522.018			−1.11304
$470$	408.248	+	255.063i	0.868614	+	0.542687i
$471$		0			0
$472$	−123.555	+	71.3345i	−0.261769	+	0.151132i
$473$	490.327	+	849.272i	1.03663	+	1.79550i
$474$		0			0
$475$	224.682	−	333.204i	0.473016	−	0.701482i
$476$		−	454.832i		−	0.955530i
$477$		0			0
$478$			168.409i			0.352321i
$479$	73.7251	+	42.5652i	0.153915	+	0.0888626i	0.574979	−	0.818168i	$-0.305010\pi$
$479$	73.7251	+	42.5652i	0.153915	+	0.0888626i	−0.421065	+	0.907031i	$0.638343\pi$
$480$		0			0
$481$	136.963	+	237.227i	0.284747	+	0.493196i
$482$	222.456	+	385.305i	0.461526	+	0.799387i
$483$		0			0
$484$	294.586	−	510.238i	0.608649	−	1.05421i
$485$	−599.067	−	20.8788i	−1.23519	−	0.0430491i
$486$		0			0
$487$			437.344i			0.898037i	0.893522	+	0.449018i	$0.148226\pi$
$487$			437.344i			0.898037i	−0.893522	+	0.449018i	$0.851774\pi$
$488$	69.2929	−	120.019i	0.141994	−	0.245940i
$489$		0			0
$490$	254.639	−	135.416i	0.519672	−	0.276360i
$491$	−588.443	+	339.738i	−1.19846	+	0.691930i	−0.960211	−	0.279275i	$-0.909906\pi$
$491$	−588.443	+	339.738i	−1.19846	+	0.691930i	−0.238247	+	0.971205i	$0.576573\pi$
$492$		0			0
$493$	−407.828	−	235.459i	−0.827237	−	0.477605i
$494$			138.900i			0.281174i
$495$		0			0
$496$	122.029			0.246026
$497$	−111.803	+	193.649i	−0.224956	+	0.389636i
$498$		0			0
$499$	−150.280	−	260.293i	−0.301162	−	0.521629i	0.675237	−	0.737601i	$-0.264041\pi$
$499$	−150.280	−	260.293i	−0.301162	−	0.521629i	−0.976400	+	0.215972i	$0.930708\pi$
$500$	228.365	−	101.731i	0.456731	−	0.203462i
$501$		0			0
$502$	181.499	+	104.788i	0.361552	+	0.208742i
$503$	371.067			0.737707			0.368853	−	0.929488i	$-0.379750\pi$
$503$	371.067			0.737707			0.368853	+	0.929488i	$0.379750\pi$
$504$		0			0
$505$	−110.320	−	3.84490i	−0.218456	−	0.00761367i
$506$	1080.54	+	623.852i	2.13546	+	1.23291i
$507$		0			0
$508$	−127.057	+	73.3562i	−0.250112	+	0.144402i
$509$	503.727	−	290.827i	0.989640	−	0.571369i	0.0844732	−	0.996426i	$-0.473079\pi$
$509$	503.727	−	290.827i	0.989640	−	0.571369i	0.905167	+	0.425057i	$0.139746\pi$
$510$		0			0
$511$	191.551	−	331.776i	0.374855	−	0.649267i
$512$	22.6274			0.0441942
$513$		0			0
$514$	416.225			0.809777
$515$	48.7132	−	77.9693i	0.0945888	−	0.151397i
$516$		0			0
$517$	1201.88	−	693.907i	2.32472	−	1.34218i
$518$	300.396	+	520.301i	0.579915	+	1.00444i
$519$		0			0
$520$	−45.7834	+	73.2800i	−0.0880450	+	0.140923i
$521$			1006.68i			1.93222i	0.258138	+	0.966108i	$0.416891\pi$
$521$			1006.68i			1.93222i	−0.258138	+	0.966108i	$0.583109\pi$
$522$		0			0
$523$		−	674.227i		−	1.28915i	−0.764540	−	0.644576i	$-0.777034\pi$
$523$		−	674.227i		−	1.28915i	0.764540	−	0.644576i	$-0.222966\pi$
$524$	157.705	+	91.0508i	0.300963	+	0.173761i
$525$		0			0
$526$	49.1188	+	85.0763i	0.0933817	+	0.161742i
$527$	366.090	+	634.086i	0.694668	+	1.20320i
$528$		0			0
$529$	−671.988	+	1163.92i	−1.27030	+	2.20022i
$530$	15.2082	−	436.362i	0.0286947	−	0.823325i
$531$		0			0
$532$			304.644i			0.572639i
$533$	146.914	−	254.463i	0.275636	−	0.477416i
$534$		0			0
$535$	−268.672	+	142.879i	−0.502190	+	0.267063i
$536$	134.944	−	77.9101i	0.251762	−	0.145355i
$537$		0			0
$538$	−321.446	−	185.587i	−0.597484	−	0.344958i
$539$		−	831.480i		−	1.54263i
$540$		0			0
$541$	178.075			0.329159			0.164579	−	0.986364i	$-0.447373\pi$
$541$	178.075			0.329159			0.164579	+	0.986364i	$0.447373\pi$
$542$	265.243	−	459.414i	0.489378	−	0.847627i
$543$		0			0
$544$	67.8828	+	117.576i	0.124785	+	0.216133i
$545$	−355.326	+	188.961i	−0.651974	+	0.346718i
$546$		0			0
$547$	−178.531	−	103.075i	−0.326381	−	0.188436i	0.327852	−	0.944729i	$-0.393675\pi$
$547$	−178.531	−	103.075i	−0.326381	−	0.188436i	−0.654233	+	0.756293i	$0.727009\pi$
$548$	−55.7674			−0.101765
$549$		0			0
$550$	50.1786	−	719.003i	0.0912338	−	1.30728i
$551$	273.160	+	157.709i	0.495754	+	0.286223i
$552$		0			0
$553$	272.720	−	157.455i	0.493164	−	0.284729i
$554$	−179.266	+	103.499i	−0.323585	+	0.186822i
$555$		0			0
$556$	−34.7379	+	60.1679i	−0.0624783	+	0.108216i
$557$	37.8724			0.0679935			0.0339968	−	0.999422i	$-0.489176\pi$
$557$	37.8724			0.0679935			0.0339968	+	0.999422i	$0.489176\pi$
$558$		0			0
$559$	−293.911			−0.525781
$560$	−100.415	+	160.722i	−0.179313	+	0.287004i
$561$		0			0
$562$	−96.9621	+	55.9811i	−0.172530	+	0.0996105i
$563$	158.628	+	274.751i	0.281754	+	0.488012i	0.971817	−	0.235737i	$-0.0757505\pi$
$563$	158.628	+	274.751i	0.281754	+	0.488012i	−0.690063	+	0.723749i	$0.742417\pi$
$564$		0			0
$565$	−96.4935	−	60.2866i	−0.170785	−	0.106702i
$566$			305.931i			0.540513i
$567$		0			0
$568$		−	66.7457i		−	0.117510i
$569$	−349.661	−	201.877i	−0.614518	−	0.354792i	0.160214	−	0.987082i	$-0.448782\pi$
$569$	−349.661	−	201.877i	−0.614518	−	0.354792i	−0.774732	+	0.632290i	$0.782115\pi$
$570$		0			0
$571$	−142.037	−	246.015i	−0.248751	−	0.430849i	0.714429	−	0.699708i	$-0.246687\pi$
$571$	−142.037	−	246.015i	−0.248751	−	0.430849i	−0.963180	+	0.268859i	$0.913353\pi$
$572$	124.555	+	215.736i	0.217754	+	0.377161i
$573$		0			0
$574$	322.221	−	558.103i	0.561361	−	0.972305i
$575$	1079.32	+	75.3250i	1.87708	+	0.131000i
$576$		0			0
$577$		−	105.236i		−	0.182386i	−0.995833	−	0.0911928i	$-0.970932\pi$
$577$		−	105.236i		−	0.182386i	0.995833	−	0.0911928i	$-0.0290679\pi$
$578$	−202.946	+	351.514i	−0.351118	+	0.608155i
$579$		0			0
$580$	92.1290	+	173.241i	0.158843	+	0.298691i
$581$	186.397	−	107.616i	0.320821	−	0.185226i
$582$		0			0
$583$	−1090.15	−	629.399i	−1.86990	−	1.07959i
$584$			114.354i			0.195812i
$585$		0			0
$586$	588.782			1.00475
$587$	−438.787	+	760.001i	−0.747508	+	1.29472i	0.201507	+	0.979487i	$0.435416\pi$
$587$	−438.787	+	760.001i	−0.747508	+	1.29472i	−0.949014	+	0.315234i	$0.897917\pi$
$588$		0			0
$589$	−245.205	−	424.707i	−0.416307	−	0.721064i
$590$	167.469	+	314.912i	0.283846	+	0.533749i
$591$		0			0
$592$	−155.308	−	89.6669i	−0.262344	−	0.151464i
$593$	47.7971			0.0806022			0.0403011	−	0.999188i	$-0.487168\pi$
$593$	47.7971			0.0806022			0.0403011	+	0.999188i	$0.487168\pi$
$594$		0			0
$595$	−1136.39	−	39.6057i	−1.90990	−	0.0665643i
$596$	−0.549179	−	0.317069i	−0.000921441	−	0.000531994i
$597$		0			0
$598$	−323.849	+	186.974i	−0.541554	+	0.312666i
$599$	985.107	−	568.752i	1.64459	−	0.949502i	0.665412	−	0.746476i	$-0.268256\pi$
$599$	985.107	−	568.752i	1.64459	−	0.949502i	0.979173	−	0.203026i	$-0.0650777\pi$
$600$		0			0
$601$	−95.3631	+	165.174i	−0.158674	+	0.274832i	−0.934391	−	0.356250i	$-0.884055\pi$
$601$	−95.3631	+	165.174i	−0.158674	+	0.274832i	0.775717	+	0.631081i	$0.217389\pi$
$602$	−644.625			−1.07081
$603$		0			0
$604$	−210.655			−0.348767
$605$	−1249.17	−	780.449i	−2.06474	−	1.29000i
$606$		0			0
$607$	856.430	−	494.460i	1.41092	−	0.814597i	0.415447	−	0.909617i	$-0.363625\pi$
$607$	856.430	−	494.460i	1.41092	−	0.814597i	0.995475	+	0.0950207i	$0.0302917\pi$
$608$	−45.4674	−	78.7519i	−0.0747820	−	0.129526i
$609$		0			0
$610$	−293.831	−	183.578i	−0.481690	−	0.300948i
$611$			415.941i			0.680754i
$612$		0			0
$613$			131.155i			0.213956i	0.994261	+	0.106978i	$0.0341175\pi$
$613$			131.155i			0.213956i	−0.994261	+	0.106978i	$0.965882\pi$
$614$	−406.090	−	234.456i	−0.661384	−	0.381850i
$615$		0			0
$616$	273.182	+	473.165i	0.443477	+	0.768125i
$617$	−216.658	−	375.263i	−0.351148	−	0.608207i	0.635303	−	0.772263i	$-0.280875\pi$
$617$	−216.658	−	375.263i	−0.351148	−	0.608207i	−0.986451	+	0.164057i	$0.947542\pi$
$618$		0			0
$619$	−289.947	+	502.202i	−0.468411	+	0.811312i	−0.999348	−	0.0360992i	$-0.988507\pi$
$619$	−289.947	+	502.202i	−0.468411	+	0.811312i	0.530937	+	0.847411i	$0.321840\pi$
$620$	10.6260	−	304.887i	0.0171387	−	0.491754i
$621$		0			0
$622$			556.589i			0.894837i
$623$	−376.781	+	652.604i	−0.604785	+	1.04752i
$624$		0			0
$625$	−234.288	−	579.426i	−0.374861	−	0.927081i
$626$	−311.245	+	179.697i	−0.497196	+	0.287056i
$627$		0			0
$628$	−78.9855	−	45.6023i	−0.125773	−	0.0726151i
$629$		−	1076.01i		−	1.71067i
$630$		0			0
$631$	1026.45			1.62671			0.813354	−	0.581768i	$-0.197639\pi$
$631$	1026.45			1.62671			0.813354	+	0.581768i	$0.197639\pi$
$632$	−46.9997	+	81.4058i	−0.0743665	+	0.128807i
$633$		0			0
$634$	305.458	+	529.069i	0.481795	+	0.834494i
$635$	172.215	+	323.837i	0.271206	+	0.509979i
$636$		0			0
$637$	215.816	+	124.601i	0.338800	+	0.195606i
$638$	565.688			0.886658
$639$		0			0
$640$	1.97034	−	56.5342i	0.00307866	−	0.0883347i
$641$	−282.653	−	163.190i	−0.440957	−	0.254586i	0.263047	−	0.964783i	$-0.415273\pi$
$641$	−282.653	−	163.190i	−0.440957	−	0.254586i	−0.704003	+	0.710197i	$0.748606\pi$
$642$		0			0
$643$	−483.731	+	279.282i	−0.752303	+	0.434342i	−0.826525	−	0.562899i	$-0.809686\pi$
$643$	−483.731	+	279.282i	−0.752303	+	0.434342i	0.0742223	+	0.997242i	$0.476353\pi$
$644$	−710.286	+	410.084i	−1.10293	+	0.636776i
$645$		0			0
$646$	272.807	−	472.516i	0.422302	−	0.731448i
$647$	−404.040			−0.624483			−0.312241	−	0.950003i	$-0.601080\pi$
$647$	−404.040			−0.624483			−0.312241	+	0.950003i	$0.601080\pi$
$648$		0			0
$649$	1028.29			1.58442
$650$	179.102	+	120.770i	0.275542	+	0.185800i
$651$		0			0
$652$	264.646	−	152.794i	0.405899	−	0.234346i
$653$	357.001	+	618.344i	0.546709	+	0.946928i	0.998497	+	0.0548026i	$0.0174530\pi$
$653$	357.001	+	618.344i	0.546709	+	0.946928i	−0.451788	+	0.892125i	$0.649214\pi$
$654$		0			0
$655$	241.222	−	386.094i	0.368277	−	0.589456i
$656$			192.363i			0.293237i
$657$		0			0
$658$			912.267i			1.38642i
$659$	110.583	+	63.8450i	0.167804	+	0.0968817i	0.581550	−	0.813511i	$-0.302446\pi$
$659$	110.583	+	63.8450i	0.167804	+	0.0968817i	−0.413746	+	0.910392i	$0.635780\pi$
$660$		0			0
$661$	202.346	+	350.474i	0.306121	+	0.530217i	0.977510	−	0.210888i	$-0.0676354\pi$
$661$	202.346	+	350.474i	0.306121	+	0.530217i	−0.671389	+	0.741105i	$0.734302\pi$
$662$	−135.575	−	234.822i	−0.204796	−	0.354716i
$663$		0			0
$664$	−32.1230	+	55.6387i	−0.0483781	+	0.0837933i
$665$	761.147	+	26.5277i	1.14458	+	0.0398912i
$666$		0			0
$667$			849.175i			1.27313i
$668$	13.7284	−	23.7783i	0.0205515	−	0.0355962i
$669$		0			0
$670$	−182.906	−	343.940i	−0.272995	−	0.513343i
$671$	−865.037	+	499.430i	−1.28918	+	0.744306i
$672$		0			0
$673$	1073.07	+	619.539i	1.59446	+	0.920562i	0.992528	+	0.122016i	$0.0389358\pi$
$673$	1073.07	+	619.539i	1.59446	+	0.920562i	0.601933	+	0.798547i	$0.294397\pi$
$674$			359.365i			0.533183i
$675$		0			0
$676$	263.339			0.389555
$677$	−339.544	+	588.107i	−0.501541	+	0.868695i	0.498457	+	0.866914i	$0.333900\pi$
$677$	−339.544	+	588.107i	−0.501541	+	0.868695i	−0.999998	+	0.00178078i	$0.999433\pi$
$678$		0			0
$679$	−567.997	−	983.799i	−0.836520	−	1.44889i
$680$	299.674	−	159.366i	0.440697	−	0.234361i
$681$		0			0
$682$	−761.692	−	439.763i	−1.11685	−	0.644814i
$683$	−439.600			−0.643632			−0.321816	−	0.946802i	$-0.604293\pi$
$683$	−439.600			−0.643632			−0.321816	+	0.946802i	$0.604293\pi$
$684$		0			0
$685$	−4.85610	+	139.334i	−0.00708919	+	0.203407i
$686$	−95.3141	−	55.0296i	−0.138942	−	0.0802181i
$687$		0			0
$688$	166.639	−	96.2089i	0.242207	−	0.139839i
$689$	326.729	−	188.637i	0.474207	−	0.273784i
$690$		0			0
$691$	162.345	−	281.189i	0.234941	−	0.406931i	−0.724314	−	0.689470i	$-0.757843\pi$
$691$	162.345	−	281.189i	0.234941	−	0.406931i	0.959256	+	0.282539i	$0.0911768\pi$
$692$	−20.8614			−0.0301466
$693$		0			0
$694$	−453.673			−0.653707
$695$	147.303	+	92.0314i	0.211947	+	0.132419i
$696$		0			0
$697$	−999.557	+	577.095i	−1.43409	+	0.827969i
$698$	−215.331	−	372.965i	−0.308497	−	0.534333i
$699$		0			0
$700$	392.818	+	264.881i	0.561168	+	0.378401i
$701$			319.512i			0.455795i	0.973685	+	0.227898i	$0.0731851\pi$
$701$			319.512i			0.455795i	−0.973685	+	0.227898i	$0.926815\pi$
$702$		0			0
$703$			720.706i			1.02519i
$704$	−141.238	−	81.5437i	−0.200622	−	0.115829i
$705$		0			0
$706$	−152.564	−	264.249i	−0.216096	−	0.374290i
$707$	−104.598	−	181.170i	−0.147947	−	0.256252i
$708$		0			0
$709$	553.311	−	958.363i	0.780411	−	1.35171i	−0.151292	−	0.988489i	$-0.548343\pi$
$709$	553.311	−	958.363i	0.780411	−	1.35171i	0.931703	−	0.363222i	$-0.118323\pi$
$710$	−166.763	−	5.81206i	−0.234877	−	0.00818600i
$711$		0			0
$712$		−	224.935i		−	0.315920i
$713$	660.145	−	1143.40i	0.925869	−	1.60365i
$714$		0			0
$715$	549.858	−	292.413i	0.769033	−	0.408970i
$716$	108.193	−	62.4650i	0.151107	−	0.0872417i
$717$		0			0
$718$	781.522	+	451.212i	1.08847	+	0.628429i
$719$			992.085i			1.37981i	0.723899	+	0.689906i	$0.242348\pi$
$719$			992.085i			1.37981i	−0.723899	+	0.689906i	$0.757652\pi$
$720$		0			0
$721$	174.229			0.241650
$722$	72.5413	−	125.645i	0.100473	−	0.174024i
$723$		0			0
$724$	−343.029	−	594.144i	−0.473797	−	0.820641i
$725$	440.862	−	215.097i	0.608085	−	0.296686i
$726$		0			0
$727$	−6.01986	−	3.47557i	−0.00828041	−	0.00478070i	0.495854	−	0.868406i	$-0.334855\pi$
$727$	−6.01986	−	3.47557i	−0.00828041	−	0.00478070i	−0.504134	+	0.863625i	$0.668188\pi$
$728$	−163.751			−0.224932
$729$		0			0
$730$	285.712	+	9.95769i	0.391386	+	0.0136407i
$731$	999.841	+	577.258i	1.36777	+	0.789683i
$732$		0			0
$733$	216.107	−	124.770i	0.294826	−	0.170218i	−0.345290	−	0.938496i	$-0.612220\pi$
$733$	216.107	−	124.770i	0.294826	−	0.170218i	0.640116	+	0.768278i	$0.278886\pi$
$734$	−453.890	+	262.053i	−0.618379	+	0.357021i
$735$		0			0
$736$	122.408	−	212.018i	0.166316	−	0.288067i
$737$	−1123.08			−1.52385
$738$		0			0
$739$	−961.297			−1.30081			−0.650404	−	0.759588i	$-0.725400\pi$
$739$	−961.297			−1.30081			−0.650404	+	0.759588i	$0.725400\pi$
$740$	−237.555	+	380.226i	−0.321021	+	0.513819i
$741$		0			0
$742$	716.602	−	413.730i	0.965770	−	0.557588i
$743$	−398.376	−	690.008i	−0.536172	−	0.928678i	−0.999106	−	0.0422847i	$-0.986536\pi$
$743$	−398.376	−	690.008i	−0.536172	−	0.928678i	0.462933	−	0.886393i	$-0.346797\pi$
$744$		0			0
$745$	−0.840012	+	1.34450i	−0.00112753	+	0.00180470i
$746$		−	727.840i		−	0.975657i
$747$		0			0
$748$		−	978.533i		−	1.30820i
$749$	−499.424	−	288.343i	−0.666788	−	0.384970i
$750$		0			0
$751$	−153.068	−	265.122i	−0.203820	−	0.353026i	0.745936	−	0.666017i	$-0.232002\pi$
$751$	−153.068	−	265.122i	−0.203820	−	0.353026i	−0.949756	+	0.312991i	$0.898669\pi$
$752$	−136.154	−	235.826i	−0.181056	−	0.313598i
$753$		0			0
$754$	−84.7710	+	146.828i	−0.112428	+	0.194732i
$755$	−18.3434	+	526.319i	−0.0242958	+	0.697111i
$756$		0			0
$757$			411.616i			0.543746i	0.962333	+	0.271873i	$0.0876431\pi$
$757$			411.616i			0.543746i	−0.962333	+	0.271873i	$0.912357\pi$
$758$	112.842	−	195.448i	0.148868	−	0.257847i
$759$		0			0
$760$	−200.720	+	106.742i	−0.264105	+	0.140450i
$761$	463.859	−	267.809i	0.609539	−	0.351918i	−0.163246	−	0.986585i	$-0.552196\pi$
$761$	463.859	−	267.809i	0.609539	−	0.351918i	0.772785	+	0.634668i	$0.218863\pi$
$762$		0			0
$763$	−660.503	−	381.341i	−0.865665	−	0.499792i
$764$			25.2753i			0.0330829i
$765$		0			0
$766$	633.629			0.827192
$767$	−154.094	+	266.899i	−0.200905	+	0.347977i
$768$		0			0
$769$	540.916	+	936.894i	0.703402	+	1.21833i	0.967265	+	0.253768i	$0.0816700\pi$
$769$	540.916	+	936.894i	0.703402	+	1.21833i	−0.263863	+	0.964560i	$0.584997\pi$
$770$	1205.98	−	641.339i	1.56621	−	0.832907i
$771$		0			0
$772$	291.200	+	168.124i	0.377202	+	0.217778i
$773$	−166.623			−0.215554			−0.107777	−	0.994175i	$-0.534373\pi$
$773$	−166.623			−0.215554			−0.107777	+	0.994175i	$0.534373\pi$
$774$		0			0
$775$	−760.830	−	53.0977i	−0.981717	−	0.0685132i
$776$	293.660	+	169.545i	0.378428	+	0.218485i
$777$		0			0
$778$	−684.425	+	395.153i	−0.879723	+	0.507908i
$779$	669.497	−	386.534i	0.859431	−	0.496193i
$780$		0			0
$781$	−240.535	+	416.619i	−0.307984	+	0.533444i
$782$	1468.91			1.87841
$783$		0			0
$784$	−163.148			−0.208097
$785$	−120.814	+	193.373i	−0.153904	+	0.246335i
$786$		0			0
$787$	−352.266	+	203.381i	−0.447607	+	0.258426i	−0.706819	−	0.707395i	$-0.749870\pi$
$787$	−352.266	+	203.381i	−0.447607	+	0.258426i	0.259212	+	0.965820i	$0.416537\pi$
$788$	372.044	+	644.400i	0.472138	+	0.817766i
$789$		0			0
$790$	199.298	+	124.516i	0.252276	+	0.157616i
$791$		−	215.623i		−	0.272596i
$792$		0			0
$793$		−	299.368i		−	0.377513i
$794$	−325.957	−	188.191i	−0.410525	−	0.237017i
$795$		0			0
$796$	−231.821	−	401.526i	−0.291233	−	0.504430i
$797$	51.6178	+	89.4047i	0.0647652	+	0.112177i	0.896590	−	0.442862i	$-0.146037\pi$
$797$	51.6178	+	89.4047i	0.0647652	+	0.112177i	−0.831825	+	0.555039i	$0.812704\pi$
$798$		0			0
$799$	816.931	−	1414.97i	1.02244	−	1.77092i
$800$	−141.078	−	9.84573i	−0.176348	−	0.0123072i
$801$		0			0
$802$		−	24.6361i		−	0.0307184i
$803$	412.105	−	713.787i	0.513207	−	0.888900i
$804$		0			0
$805$	962.738	+	1810.35i	1.19595	+	2.24888i
$806$	228.286	−	131.801i	0.283234	−	0.163525i
$807$		0			0
$808$	54.0784	+	31.2222i	0.0669288	+	0.0386413i
$809$			833.545i			1.03034i	0.857088	+	0.515170i	$0.172271\pi$
$809$			833.545i			1.03034i	−0.857088	+	0.515170i	$0.827729\pi$
$810$		0			0
$811$	814.193			1.00394			0.501968	−	0.864886i	$-0.332609\pi$
$811$	814.193			1.00394			0.501968	+	0.864886i	$0.332609\pi$
$812$	−185.925	+	322.032i	−0.228972	+	0.396591i
$813$		0			0
$814$	646.276	+	1119.38i	0.793951	+	1.37516i
$815$	−358.707	−	674.519i	−0.440132	−	0.827631i
$816$		0			0
$817$	−669.687	−	386.644i	−0.819690	−	0.473248i
$818$	−630.405			−0.770666
$819$		0			0
$820$	480.616	+	16.7505i	0.586118	+	0.0204275i
$821$	−133.926	−	77.3220i	−0.163125	−	0.0941803i	0.416215	−	0.909266i	$-0.363356\pi$
$821$	−133.926	−	77.3220i	−0.163125	−	0.0941803i	−0.579340	+	0.815086i	$0.696690\pi$
$822$		0			0
$823$	−955.975	+	551.932i	−1.16157	+	0.670635i	−0.951681	−	0.307090i	$-0.900645\pi$
$823$	−955.975	+	551.932i	−1.16157	+	0.670635i	−0.209893	+	0.977724i	$0.567312\pi$
$824$	−45.0392	+	26.0034i	−0.0546592	+	0.0315575i
$825$		0			0
$826$	−337.969	+	585.379i	−0.409163	+	0.708691i
$827$	423.629			0.512248			0.256124	−	0.966644i	$-0.417554\pi$
$827$	423.629			0.512248			0.256124	+	0.966644i	$0.417554\pi$
$828$		0			0
$829$	325.734			0.392924			0.196462	−	0.980511i	$-0.437055\pi$
$829$	325.734			0.392924			0.196462	+	0.980511i	$0.437055\pi$
$830$	136.215	+	85.1037i	0.164115	+	0.102535i
$831$		0			0
$832$	42.3303	−	24.4394i	0.0508778	−	0.0293743i
$833$	−489.447	−	847.748i	−0.587572	−	1.01770i
$834$		0			0
$835$	−58.2142	−	36.3707i	−0.0697176	−	0.0435578i
$836$			655.415i			0.783989i
$837$		0			0
$838$		−	505.525i		−	0.603252i
$839$	1050.83	+	606.698i	1.25248	+	0.723121i	0.971602	−	0.236622i	$-0.0760403\pi$
$839$	1050.83	+	606.698i	1.25248	+	0.723121i	0.280880	+	0.959743i	$0.409374\pi$
$840$		0			0
$841$	−227.999	−	394.906i	−0.271105	−	0.469567i
$842$	−406.606	−	704.261i	−0.482904	−	0.836415i
$843$		0			0
$844$	−20.9012	+	36.2020i	−0.0247645	+	0.0428933i
$845$	22.9310	−	657.949i	0.0271372	−	0.778637i
$846$		0			0
$847$		−	2791.38i		−	3.29561i
$848$	−123.497	+	213.903i	−0.145633	+	0.252244i
$849$		0			0
$850$	−372.078	−	762.607i	−0.437739	−	0.897185i
$851$	−1680.35	+	970.149i	−1.97456	+	1.14001i
$852$		0			0
$853$	30.3535	+	17.5246i	0.0355844	+	0.0205446i	0.517687	−	0.855570i	$-0.326793\pi$
$853$	30.3535	+	17.5246i	0.0355844	+	0.0205446i	−0.482102	+	0.876115i	$0.660127\pi$
$854$		−	656.591i		−	0.768842i
$855$		0			0
$856$	172.138			0.201096
$857$	548.707	−	950.388i	0.640265	−	1.10897i	−0.345109	−	0.938563i	$-0.612158\pi$
$857$	548.707	−	950.388i	0.640265	−	1.10897i	0.985374	−	0.170408i	$-0.0545087\pi$
$858$		0			0
$859$	−452.145	−	783.137i	−0.526362	−	0.911685i	−0.999528	−	0.0307121i	$-0.990223\pi$
$859$	−452.145	−	783.137i	−0.526362	−	0.911685i	0.473167	−	0.880973i	$-0.343111\pi$
$860$	−225.866	−	424.722i	−0.262635	−	0.493862i
$861$		0			0
$862$	222.068	+	128.211i	0.257620	+	0.148737i
$863$	179.328			0.207796			0.103898	−	0.994588i	$-0.466868\pi$
$863$	179.328			0.207796			0.103898	+	0.994588i	$0.466868\pi$
$864$		0			0
$865$	−1.81656	+	52.1219i	−0.00210007	+	0.0602566i
$866$	−864.213	−	498.953i	−0.997936	−	0.576159i
$867$		0			0
$868$	500.691	−	289.074i	0.576833	−	0.333035i
$869$	586.733	−	338.751i	0.675182	−	0.389817i
$870$		0			0
$871$	168.298	−	291.501i	0.193224	−	0.334674i
$872$	227.658			0.261075
$873$		0			0
$874$	−983.868			−1.12571
$875$	696.005	−	958.383i	0.795434	−	1.09529i
$876$		0			0
$877$	−1045.75	+	603.765i	−1.19242	+	0.688443i	−0.958854	−	0.283898i	$-0.908372\pi$
$877$	−1045.75	+	603.765i	−1.19242	+	0.688443i	−0.233564	+	0.972341i	$0.575039\pi$
$878$	−201.917	−	349.730i	−0.229973	−	0.398326i
$879$		0			0
$880$	−216.034	+	345.780i	−0.245494	+	0.392932i
$881$			407.569i			0.462621i	0.972880	+	0.231311i	$0.0743013\pi$
$881$			407.569i			0.462621i	−0.972880	+	0.231311i	$0.925699\pi$
$882$		0			0
$883$		−	85.9086i		−	0.0972918i	−0.998816	−	0.0486459i	$-0.984509\pi$
$883$		−	85.9086i		−	0.0972918i	0.998816	−	0.0486459i	$-0.0154906\pi$
$884$	253.984	+	146.638i	0.287312	+	0.165880i
$885$		0			0
$886$	−499.291	−	864.797i	−0.563534	−	0.976069i
$887$	199.282	+	345.167i	0.224670	+	0.389140i	0.956220	−	0.292647i	$-0.0945362\pi$
$887$	199.282	+	345.167i	0.224670	+	0.389140i	−0.731550	+	0.681787i	$0.761203\pi$
$888$		0			0
$889$	−347.547	+	601.969i	−0.390942	+	0.677131i
$890$	−561.997	−	19.5868i	−0.631457	−	0.0220077i
$891$		0			0
$892$			31.5461i			0.0353655i
$893$	−547.175	+	947.734i	−0.612738	+	1.06129i
$894$		0			0
$895$	−146.647	−	275.757i	−0.163851	−	0.308108i
$896$	92.8415	−	53.6021i	0.103618	−	0.0598237i
$897$		0			0
$898$	−619.485	−	357.660i	−0.689850	−	0.398285i
$899$		−	598.596i		−	0.665847i
$900$		0			0
$901$	−1481.97			−1.64481
$902$	693.231	−	1200.71i	0.768548	−	1.33116i
$903$		0			0
$904$	32.1813	+	55.7397i	0.0355988	+	0.0616589i
$905$	−1514.33	+	805.316i	−1.67329	+	0.889852i
$906$		0			0
$907$	1034.37	+	597.195i	1.14043	+	0.658429i	0.946538	−	0.322593i	$-0.104554\pi$
$907$	1034.37	+	597.195i	1.14043	+	0.658429i	0.193895	+	0.981022i	$0.437888\pi$
$908$	−682.692			−0.751863
$909$		0			0
$910$	−14.2590	+	409.128i	−0.0156692	+	0.449591i
$911$	−1168.23	−	674.478i	−1.28236	−	0.740371i	−0.305080	−	0.952327i	$-0.598683\pi$
$911$	−1168.23	−	674.478i	−1.28236	−	0.740371i	−0.977279	+	0.211956i	$0.932017\pi$
$912$		0			0
$913$	401.017	−	231.527i	0.439230	−	0.253590i
$914$	−870.402	+	502.527i	−0.952300	+	0.549811i
$915$		0			0
$916$	−120.453	+	208.630i	−0.131498	+	0.227762i
$917$	862.761			0.940852
$918$		0			0
$919$	1571.32			1.70982			0.854908	−	0.518780i	$-0.173614\pi$
$919$	1571.32			1.70982			0.854908	+	0.518780i	$0.173614\pi$
$920$	−519.063	−	324.297i	−0.564199	−	0.352497i
$921$		0			0
$922$	168.543	−	97.3082i	0.182801	−	0.105540i
$923$	−72.0907	−	124.865i	−0.0781048	−	0.135282i
$924$		0			0
$925$	929.302	+	626.637i	1.00465	+	0.677445i
$926$			486.718i			0.525614i
$927$		0			0
$928$		−	110.996i		−	0.119607i
$929$	217.900	+	125.805i	0.234554	+	0.135420i	0.612671	−	0.790338i	$-0.290095\pi$
$929$	217.900	+	125.805i	0.234554	+	0.135420i	−0.378117	+	0.925758i	$0.623428\pi$
$930$		0			0
$931$	327.829	+	567.816i	0.352125	+	0.609899i
$932$	−307.400	−	532.433i	−0.329829	−	0.571280i
$933$		0			0
$934$	−228.194	+	395.243i	−0.244319	+	0.423173i
$935$	−2444.85	−	85.2083i	−2.61481	−	0.0911319i
$936$		0			0
$937$		−	1592.01i		−	1.69905i	−0.527546	−	0.849526i	$-0.676888\pi$
$937$		−	1592.01i		−	1.69905i	0.527546	−	0.849526i	$-0.323112\pi$
$938$	369.122	−	639.339i	0.393521	−	0.681598i
$939$		0			0
$940$	−601.062	+	319.643i	−0.639428	+	0.340046i
$941$	883.684	−	510.195i	0.939091	−	0.542184i	0.0494154	−	0.998778i	$-0.484264\pi$
$941$	883.684	−	510.195i	0.939091	−	0.542184i	0.889675	+	0.456594i	$0.150931\pi$
$942$		0			0
$943$	1802.43	+	1040.63i	1.91138	+	1.10354i
$944$		−	201.764i		−	0.213734i
$945$		0			0
$946$	−1386.85			−1.46602
$947$	337.033	−	583.758i	0.355895	−	0.616429i	−0.631375	−	0.775477i	$-0.717509\pi$
$947$	337.033	−	583.758i	0.355895	−	0.616429i	0.987271	+	0.159048i	$0.0508426\pi$
$948$		0			0
$949$	123.512	+	213.929i	0.130149	+	0.225425i
$950$	249.215	+	510.789i	0.262332	+	0.537673i
$951$		0			0
$952$	557.054	+	321.615i	0.585140	+	0.337831i
$953$	−836.522			−0.877778			−0.438889	−	0.898541i	$-0.644628\pi$
$953$	−836.522			−0.877778			−0.438889	+	0.898541i	$0.644628\pi$
$954$		0			0
$955$	63.1499	+	2.20091i	0.0661256	+	0.00230462i
$956$	−206.258	−	119.083i	−0.215751	−	0.124564i
$957$		0			0
$958$	−104.263	+	60.1963i	−0.108834	+	0.0628353i
$959$	−228.817	+	132.107i	−0.238599	+	0.137755i
$960$		0			0
$961$	15.1541	−	26.2477i	0.0157691	−	0.0273129i
$962$	−387.390			−0.402692
$963$		0			0
$964$	−629.200			−0.652697
$965$	445.413	−	712.919i	0.461568	−	0.738776i
$966$		0			0
$967$	−881.781	+	509.096i	−0.911873	+	0.526470i	−0.881033	−	0.473054i	$-0.843151\pi$
$967$	−881.781	+	509.096i	−0.911873	+	0.526470i	−0.0308394	+	0.999524i	$0.509818\pi$
$968$	416.608	+	721.586i	0.430380	+	0.745440i
$969$		0			0
$970$	449.176	−	718.941i	0.463068	−	0.741176i
$971$		−	997.549i		−	1.02734i	−0.857987	−	0.513671i	$-0.828285\pi$
$971$		−	997.549i		−	1.02734i	0.857987	−	0.513671i	$-0.171715\pi$
$972$		0			0
$973$			329.163i			0.338297i
$974$	−535.635	−	309.249i	−0.549933	−	0.317504i
$975$		0			0
$976$	97.9949	+	169.732i	0.100405	+	0.173906i
$977$	−552.008	−	956.105i	−0.565003	−	0.978613i	−0.997049	−	0.0767621i	$-0.975542\pi$
$977$	−552.008	−	956.105i	−0.565003	−	0.978613i	0.432047	−	0.901851i	$-0.357792\pi$
$978$		0			0
$979$	−810.612	+	1404.02i	−0.828000	+	1.43414i
$980$	−14.2065	+	407.622i	−0.0144965	+	0.415941i
$981$		0			0
$982$		−	960.923i		−	0.978537i
$983$	608.302	−	1053.61i	0.618822	−	1.07183i	−0.370879	−	0.928681i	$-0.620944\pi$
$983$	608.302	−	1053.61i	0.618822	−	1.07183i	0.989701	−	0.143150i	$-0.0457230\pi$
$984$		0			0
$985$	1642.42	−	873.434i	1.66743	−	0.886735i
$986$	576.755	−	332.990i	0.584945	−	0.337718i
$987$		0			0
$988$	−170.117	−	98.2170i	−0.172183	−	0.0994099i
$989$		−	2081.86i		−	2.10502i
$990$		0			0
$991$	736.595			0.743285			0.371642	−	0.928376i	$-0.378795\pi$
$991$	736.595			0.743285			0.371642	+	0.928376i	$0.378795\pi$
$992$	−86.2875	+	149.454i	−0.0869834	+	0.150660i
$993$		0			0
$994$	−158.114	−	273.861i	−0.159068	−	0.275514i
$995$	−1023.39	+	544.238i	−1.02854	+	0.546972i
$996$		0			0
$997$	−650.499	−	375.566i	−0.652456	−	0.376696i	0.136941	−	0.990579i	$-0.456273\pi$
$997$	−650.499	−	375.566i	−0.652456	−	0.376696i	−0.789397	+	0.613884i	$0.789606\pi$
$998$	425.056			0.425908
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.g.269.6		24
3.2	odd	2	inner	810.3.j.g.269.12		24
5.4	even	2		810.3.j.h.269.12		24
9.2	odd	6		810.3.b.c.809.8	yes	24
9.4	even	3		810.3.j.h.539.6		24
9.5	odd	6		810.3.j.h.539.12		24
9.7	even	3		810.3.b.c.809.17	yes	24
15.14	odd	2		810.3.j.h.269.6		24
45.4	even	6	inner	810.3.j.g.539.12		24
45.14	odd	6	inner	810.3.j.g.539.6		24
45.29	odd	6		810.3.b.c.809.18	yes	24
45.34	even	6		810.3.b.c.809.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.3.b.c.809.7	✓	24	45.34	even	6
810.3.b.c.809.8	yes	24	9.2	odd	6
810.3.b.c.809.17	yes	24	9.7	even	3
810.3.b.c.809.18	yes	24	45.29	odd	6
810.3.j.g.269.6		24	1.1	even	1	trivial
810.3.j.g.269.12		24	3.2	odd	2	inner
810.3.j.g.539.6		24	45.14	odd	6	inner
810.3.j.g.539.12		24	45.4	even	6	inner
810.3.j.h.269.6		24	15.14	odd	2
810.3.j.h.269.12		24	5.4	even	2
810.3.j.h.539.6		24	9.4	even	3
810.3.j.h.539.12		24	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.41458 + 2.34766i) q^{5} +(-8.20611 - 4.73780i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.41458 + 2.34766i) q^{5} +(-8.20611 - 4.73780i) q^{7} +2.82843 q^{8} +(0.246293 - 7.06678i) q^{10} +(-17.6547 - 10.1930i) q^{11} +(5.29129 - 3.05493i) q^{13} +(11.6052 - 6.70026i) q^{14} +(-2.00000 + 3.46410i) q^{16} -24.0002 q^{17} +16.0752 q^{19} +(8.48084 + 5.29861i) q^{20} +(24.9676 - 14.4150i) q^{22} +(21.6389 + 37.4798i) q^{23} +(13.9770 - 20.7279i) q^{25} +8.64064i q^{26} +18.9512i q^{28} +(16.9927 + 9.81073i) q^{29} +(-15.2536 - 26.4200i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(16.9707 - 29.3941i) q^{34} +(47.3492 + 1.65023i) q^{35} +44.8335i q^{37} +(-11.3669 + 19.6880i) q^{38} +(-12.4863 + 6.64019i) q^{40} +(41.6479 - 24.0454i) q^{41} +(-41.6597 - 24.0522i) q^{43} +40.7719i q^{44} -61.2042 q^{46} +(-34.0385 + 58.9564i) q^{47} +(20.3935 + 35.3225i) q^{49} +(15.5031 + 31.7750i) q^{50} +(-10.5826 - 6.10986i) q^{52} +61.7484 q^{53} +(101.868 + 3.55032i) q^{55} +(-23.2104 - 13.4005i) q^{56} +(-24.0313 + 13.8745i) q^{58} +(-43.6833 + 25.2206i) q^{59} +(24.4987 - 42.4330i) q^{61} +43.1438 q^{62} +8.00000 q^{64} +(-16.1869 + 25.9084i) q^{65} +(47.7100 - 27.5454i) q^{67} +(24.0002 + 41.5696i) q^{68} +(-35.5021 + 56.8239i) q^{70} -23.5982i q^{71} +40.4303i q^{73} +(-54.9096 - 31.7021i) q^{74} +(-16.0752 - 27.8430i) q^{76} +(96.5844 + 167.289i) q^{77} +(-16.6169 + 28.7813i) q^{79} +(0.696621 - 19.9879i) q^{80} +68.0107i q^{82} +(-11.3572 + 19.6713i) q^{83} +(105.951 - 56.3443i) q^{85} +(58.9157 - 34.0150i) q^{86} +(-49.9351 - 28.8301i) q^{88} -79.5266i q^{89} -57.8946 q^{91} +(43.2779 - 74.9595i) q^{92} +(-48.1377 - 83.3770i) q^{94} +(-70.9651 + 37.7390i) q^{95} +(103.825 + 59.9431i) q^{97} -57.6815 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) \) 24 * q - 24 * q^4 - 24 * q^7	\( 24 q - 24 q^{4} - 24 q^{7} - 12 q^{10} - 48 q^{13} - 48 q^{16} + 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{43} - 36 q^{49} + 96 q^{52} + 216 q^{55} - 396 q^{58} - 60 q^{61} + 192 q^{64} + 1032 q^{67} - 480 q^{70} - 240 q^{79} - 396 q^{85} - 240 q^{88} + 48 q^{91} - 48 q^{94} + 1440 q^{97}+O(q^{100}) \) 24 * q - 24 * q^4 - 24 * q^7 - 12 * q^10 - 48 * q^13 - 48 * q^16 + 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^43 - 36 * q^49 + 96 * q^52 + 216 * q^55 - 396 * q^58 - 60 * q^61 + 192 * q^64 + 1032 * q^67 - 480 * q^70 - 240 * q^79 - 396 * q^85 - 240 * q^88 + 48 * q^91 - 48 * q^94 + 1440 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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