LMFDB - Embedded newform 810.3.j.h.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.h.539.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.24042 - 2.64931i) q^{5} +(8.20611 + 4.73780i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.24042 - 2.64931i) q^{5} +(8.20611 + 4.73780i) q^{7} +2.82843 q^{8} +(0.246293 + 7.06678i) q^{10} +(17.6547 + 10.1930i) q^{11} +(-5.29129 + 3.05493i) q^{13} +(-11.6052 + 6.70026i) q^{14} +(-2.00000 + 3.46410i) q^{16} -24.0002 q^{17} +16.0752 q^{19} +(-8.82915 - 4.69532i) q^{20} +(-24.9676 + 14.4150i) q^{22} +(21.6389 + 37.4798i) q^{23} +(10.9624 - 22.4683i) q^{25} -8.64064i q^{26} -18.9512i q^{28} +(-16.9927 - 9.81073i) q^{29} +(-15.2536 - 26.4200i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(16.9707 - 29.3941i) q^{34} +(47.3492 - 1.65023i) q^{35} -44.8335i q^{37} +(-11.3669 + 19.6880i) q^{38} +(11.9937 - 7.49337i) q^{40} +(-41.6479 + 24.0454i) q^{41} +(41.6597 + 24.0522i) q^{43} -40.7719i q^{44} -61.2042 q^{46} +(-34.0385 + 58.9564i) q^{47} +(20.3935 + 35.3225i) q^{49} +(19.7664 + 29.3136i) q^{50} +(10.5826 + 6.10986i) q^{52} +61.7484 q^{53} +(101.868 - 3.55032i) q^{55} +(23.2104 + 13.4005i) q^{56} +(24.0313 - 13.8745i) q^{58} +(43.6833 - 25.2206i) q^{59} +(24.4987 - 42.4330i) q^{61} +43.1438 q^{62} +8.00000 q^{64} +(-14.3439 + 26.9724i) q^{65} +(-47.7100 + 27.5454i) q^{67} +(24.0002 + 41.5696i) q^{68} +(-31.4599 + 59.1576i) q^{70} +23.5982i q^{71} -40.4303i q^{73} +(54.9096 + 31.7021i) q^{74} +(-16.0752 - 27.8430i) q^{76} +(96.5844 + 167.289i) q^{77} +(-16.6169 + 28.7813i) q^{79} +(0.696621 + 19.9879i) q^{80} -68.0107i q^{82} +(-11.3572 + 19.6713i) q^{83} +(-101.771 + 63.5839i) q^{85} +(-58.9157 + 34.0150i) q^{86} +(49.9351 + 28.8301i) q^{88} +79.5266i q^{89} -57.8946 q^{91} +(43.2779 - 74.9595i) q^{92} +(-48.1377 - 83.3770i) q^{94} +(68.1655 - 42.5880i) q^{95} +(-103.825 - 59.9431i) q^{97} -57.6815 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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^{40} - 24 q^{43} - 36 q^{49} - 96 q^{52} + 216 q^{55} + 396 q^{58} - 60 q^{61} + 192 q^{64} - 1032 q^{67} + 288 q^{70} - 240 q^{79} - 48 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^40 - 24 * q^43 - 36 * q^49 - 96 * q^52 + 216 * q^55 + 396 * q^58 - 60 * q^61 + 192 * q^64 - 1032 * q^67 + 288 * q^70 - 240 * q^79 - 48 * 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
$5$	4.24042	−	2.64931i	0.848084	−	0.529861i
$5$	4.24042	−	2.64931i	0.848084	−	0.529861i
$6$		0			0
$7$	8.20611	+	4.73780i	1.17230	+	0.676828i	0.954221	−	0.299102i	$-0.0966872\pi$
$7$	8.20611	+	4.73780i	1.17230	+	0.676828i	0.218080	+	0.975931i	$0.430021\pi$
$8$	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	$0.0439775\pi$
$11$	17.6547	+	10.1930i	1.60498	+	0.926633i	0.614505	+	0.788913i	$0.289356\pi$
$12$		0			0
$13$	−5.29129	+	3.05493i	−0.407023	+	0.234995i	−0.689510	−	0.724277i	$-0.742174\pi$
$13$	−5.29129	+	3.05493i	−0.407023	+	0.234995i	0.282487	+	0.959271i	$0.408841\pi$
$14$	−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	$0.360966\pi$
$20$	−8.82915	−	4.69532i	−0.441458	−	0.234766i
$21$		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
$25$	10.9624	−	22.4683i	0.438494	−	0.898734i
$26$		−	8.64064i		−	0.332332i
$27$		0			0
$28$		−	18.9512i		−	0.676828i
$29$	−16.9927	−	9.81073i	−0.585954	−	0.338301i	0.177542	−	0.984113i	$-0.443186\pi$
$29$	−16.9927	−	9.81073i	−0.585954	−	0.338301i	−0.763496	+	0.645812i	$0.776519\pi$
$30$		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	$-0.792830\pi$
$37$		−	44.8335i		−	1.21172i	0.795573	−	0.605858i	$-0.207170\pi$
$38$	−11.3669	+	19.6880i	−0.299128	+	0.518105i
$39$		0			0
$40$	11.9937	−	7.49337i	0.299843	−	0.187334i
$41$	−41.6479	+	24.0454i	−1.01580	+	0.586473i	−0.912885	−	0.408217i	$-0.866151\pi$
$41$	−41.6479	+	24.0454i	−1.01580	+	0.586473i	−0.102917	+	0.994690i	$0.532818\pi$
$42$		0			0
$43$	41.6597	+	24.0522i	0.968830	+	0.559354i	0.898879	−	0.438196i	$-0.144382\pi$
$43$	41.6597	+	24.0522i	0.968830	+	0.559354i	0.0699506	+	0.997550i	$0.477716\pi$
$44$		−	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
$50$	19.7664	+	29.3136i	0.395329	+	0.586272i
$51$		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	−0.0818182	−	0.996647i	$-0.526073\pi$
$59$	43.6833	−	25.2206i	0.740395	−	0.427467i	0.822213	+	0.569180i	$0.192739\pi$
$60$		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
$65$	−14.3439	+	26.9724i	−0.220675	+	0.414961i
$66$		0			0
$67$	−47.7100	+	27.5454i	−0.712089	+	0.411125i	−0.811834	−	0.583888i	$-0.801531\pi$
$67$	−47.7100	+	27.5454i	−0.712089	+	0.411125i	0.0997448	+	0.995013i	$0.468197\pi$
$68$	24.0002	+	41.5696i	0.352944	+	0.611317i
$69$		0			0
$70$	−31.4599	+	59.1576i	−0.449427	+	0.845109i
$71$			23.5982i			0.332369i	0.986095	+	0.166184i	$0.0531447\pi$
$71$			23.5982i			0.332369i	−0.986095	+	0.166184i	$0.946855\pi$
$72$		0			0
$73$		−	40.4303i		−	0.553840i	−0.960893	−	0.276920i	$-0.910686\pi$
$73$		−	40.4303i		−	0.553840i	0.960893	−	0.276920i	$-0.0893137\pi$
$74$	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
$85$	−101.771	+	63.5839i	−1.19731	+	0.748046i
$86$	−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	$0.147429\pi$
$89$			79.5266i			0.893557i	−0.894644	+	0.446779i	$0.852571\pi$
$90$		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
$95$	68.1655	−	42.5880i	0.717532	−	0.448295i
$96$		0			0
$97$	−103.825	−	59.9431i	−1.07036	−	0.617970i	−0.142077	−	0.989856i	$-0.545378\pi$
$97$	−103.825	−	59.9431i	−1.07036	−	0.617970i	−0.928279	+	0.371885i	$0.878711\pi$
$98$	−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	0.402353	−	0.915485i	$-0.368192\pi$
$101$	−19.1196	−	11.0387i	−0.189303	−	0.109294i	−0.591656	+	0.806190i	$0.701526\pi$
$102$		0			0
$103$	15.9238	−	9.19358i	0.154600	−	0.0892581i	−0.420705	−	0.907198i	$-0.638217\pi$
$103$	15.9238	−	9.19358i	0.154600	−	0.0892581i	0.575304	+	0.817940i	$0.304884\pi$
$104$	−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	$0.379626\pi$
$110$	−67.6832	+	127.273i	−0.615302	+	1.15702i
$111$		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
$115$	191.054	+	101.602i	1.66134	+	0.883494i
$116$			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	$0.0932576\pi$
$127$			73.3562i			0.577608i	−0.957388	+	0.288804i	$0.906742\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−22.8917	−	36.6400i	−0.176090	−	0.281846i
$131$	78.8523	−	45.5254i	0.601926	−	0.347522i	−0.167873	−	0.985809i	$-0.553690\pi$
$131$	78.8523	−	45.5254i	0.601926	−	0.347522i	0.769799	+	0.638286i	$0.220356\pi$
$132$		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	$0.873212\pi$
$140$	−50.2075	−	80.3611i	−0.358625	−	0.574008i
$141$		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	−0.500921	−	0.865493i	$-0.667005\pi$
$149$	−0.274589	+	0.158534i	−0.00184288	+	0.00106399i	0.499078	+	0.866557i	$0.333672\pi$
$150$		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
$155$	−134.677	−	71.6206i	−0.868881	−	0.462069i
$156$		0			0
$157$	−39.4927	+	22.8011i	−0.251546	+	0.145230i	−0.620472	−	0.784229i	$-0.713059\pi$
$157$	−39.4927	+	22.8011i	−0.251546	+	0.145230i	0.368926	+	0.929459i	$0.379726\pi$
$158$	−23.4998	−	40.7029i	−0.148733	−	0.257613i
$159$		0			0
$160$	−24.9726	−	13.2804i	−0.156079	−	0.0830023i
$161$			410.084i			2.54711i
$162$		0			0
$163$		−	152.794i		−	0.937384i	−0.883362	−	0.468692i	$-0.844725\pi$
$163$		−	152.794i		−	0.937384i	0.883362	−	0.468692i	$-0.155275\pi$
$164$	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
$175$	196.409	−	132.440i	1.12234	−	0.756802i
$176$	−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	$-0.944174\pi$
$179$		−	62.4650i		−	0.348967i	0.984660	−	0.174483i	$-0.0558255\pi$
$180$		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
$185$	−118.778	−	190.113i	−0.642041	−	1.02764i
$186$		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	0.528377	−	0.849010i	$-0.322801\pi$
$191$	10.9445	+	6.31882i	0.0573012	+	0.0330829i	−0.471076	+	0.882093i	$0.656134\pi$
$192$		0			0
$193$	145.600	−	84.0622i	0.754405	−	0.435556i	−0.0728786	−	0.997341i	$-0.523219\pi$
$193$	145.600	−	84.0622i	0.754405	−	0.435556i	0.827283	+	0.561785i	$0.189885\pi$
$194$	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	$0.302088\pi$
$200$	31.0062	−	63.5501i	0.155031	−	0.317750i
$201$		0			0
$202$	27.0392	−	15.6111i	0.133858	−	0.0772827i
$203$	−92.9625	−	161.016i	−0.457943	−	0.793181i
$204$		0			0
$205$	−112.901	+	212.301i	−0.550736	+	1.03561i
$206$			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
$220$	−108.017	−	172.890i	−0.490987	−	0.785863i
$221$	126.992	−	73.3189i	0.574625	−	0.331760i
$222$		0			0
$223$	13.6598	+	7.88652i	0.0612549	+	0.0353655i	0.530315	−	0.847801i	$-0.322074\pi$
$223$	13.6598	+	7.88652i	0.0612549	+	0.0353655i	−0.469060	+	0.883166i	$0.655407\pi$
$224$		−	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	$0.918044\pi$
$230$	−259.532	+	162.149i	−1.12840	+	0.704994i
$231$		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	−0.699987	−	0.714156i	$-0.746811\pi$
$239$	−103.129	+	59.5417i	−0.431503	+	0.249128i	0.268484	+	0.963284i	$0.413477\pi$
$240$		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
$245$	180.057	+	95.7539i	0.734927	+	0.390832i
$246$		0			0
$247$	−85.0584	+	49.1085i	−0.344366	+	0.198820i
$248$	−43.1438	−	74.7272i	−0.173967	−	0.301319i
$249$		0			0
$250$	161.479	+	71.9347i	0.645915	+	0.287739i
$251$			148.193i			0.590411i	0.955434	+	0.295206i	$0.0953882\pi$
$251$			148.193i			0.590411i	−0.955434	+	0.295206i	$0.904612\pi$
$252$		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
$265$	261.839	−	163.590i	0.988072	−	0.617322i
$266$	−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	$-0.837784\pi$
$269$		−	262.460i		−	0.975687i	0.872931	−	0.487844i	$-0.162216\pi$
$270$		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
$275$	422.557	−	284.934i	1.53657	−	1.03612i
$276$		0			0
$277$	−126.760	−	73.1851i	−0.457619	−	0.264206i	0.253424	−	0.967355i	$-0.418443\pi$
$277$	−126.760	−	73.1851i	−0.457619	−	0.264206i	−0.711042	+	0.703149i	$0.751777\pi$
$278$	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	0.373017	−	0.927825i	$-0.378323\pi$
$281$	−68.5625	−	39.5846i	−0.243995	−	0.140870i	−0.617011	+	0.786954i	$0.711657\pi$
$282$		0			0
$283$	−187.343	+	108.163i	−0.661991	+	0.382201i	−0.793035	−	0.609176i	$-0.791500\pi$
$283$	−187.343	+	108.163i	−0.661991	+	0.382201i	0.131044	+	0.991377i	$0.458167\pi$
$284$	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
$290$	65.1451	−	122.500i	0.224638	−	0.422413i
$291$		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
$295$	118.419	−	222.676i	0.401419	−	0.754834i
$296$		−	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	$-0.818417\pi$
$307$		−	331.571i		−	1.08004i	0.841653	−	0.540018i	$-0.181583\pi$
$308$	193.169	−	334.578i	0.627172	−	1.08629i
$309$		0			0
$310$	182.948	−	114.301i	0.590154	−	0.368713i
$311$	−340.840	+	196.784i	−1.09595	+	0.632745i	−0.935154	−	0.354243i	$-0.884739\pi$
$311$	−340.840	+	196.784i	−1.09595	+	0.632745i	−0.160794	+	0.986988i	$0.551405\pi$
$312$		0			0
$313$	−220.083	−	127.065i	−0.703141	−	0.405959i	0.105375	−	0.994433i	$-0.466396\pi$
$313$	−220.083	−	127.065i	−0.703141	−	0.405959i	−0.808516	+	0.588474i	$0.799729\pi$
$314$		−	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
$320$	33.9234	−	21.1944i	0.106011	−	0.0662326i
$321$		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
$335$	−129.334	+	243.202i	−0.386073	+	0.725977i
$336$		0			0
$337$	−220.065	+	127.055i	−0.653013	+	0.377017i	−0.789610	−	0.613609i	$-0.789717\pi$
$337$	−220.065	+	127.055i	−0.653013	+	0.377017i	0.136597	+	0.990627i	$0.456384\pi$
$338$	−93.1045	−	161.262i	−0.275457	−	0.477106i
$339$		0			0
$340$	211.901	+	112.689i	0.623240	+	0.331437i
$341$		−	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
$355$	62.5188	+	100.066i	0.176109	+	0.281877i
$356$	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	$0.348413\pi$
$359$			638.110i			1.77746i	−0.458427	+	0.888732i	$0.651587\pi$
$360$		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
$365$	−107.112	−	171.442i	−0.293458	−	0.469703i
$366$		0			0
$367$	−320.949	−	185.300i	−0.874519	−	0.504904i	−0.00567194	−	0.999984i	$-0.501805\pi$
$367$	−320.949	−	185.300i	−0.874519	−	0.504904i	−0.868847	+	0.495080i	$0.835139\pi$
$368$	−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	0.235510	−	0.971872i	$-0.424324\pi$
$373$	445.709	−	257.330i	1.19493	−	0.689894i	0.959421	+	0.281978i	$0.0909906\pi$
$374$	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	$0.567519\pi$
$380$	−141.930	−	75.4781i	−0.373500	−	0.198627i
$381$		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
$385$	852.759	+	453.495i	2.21496	+	1.17791i
$386$			237.764i			0.615969i
$387$		0			0
$388$			239.772i			0.617970i
$389$	−483.961	−	279.415i	−1.24412	−	0.718291i	−0.274187	−	0.961676i	$-0.588409\pi$
$389$	−483.961	−	279.415i	−1.24412	−	0.718291i	−0.969930	+	0.243385i	$0.921742\pi$
$390$		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	$-0.891199\pi$
$397$		−	266.143i		−	0.670385i	0.942150	−	0.335192i	$-0.108801\pi$
$398$	−163.922	+	283.922i	−0.411865	+	0.713372i
$399$		0			0
$400$	55.9079	+	82.9114i	0.139770	+	0.207279i
$401$	15.0865	−	8.71018i	0.0376222	−	0.0217212i	−0.481071	−	0.876682i	$-0.659752\pi$
$401$	15.0865	−	8.71018i	0.0376222	−	0.0217212i	0.518693	+	0.854961i	$0.326419\pi$
$402$		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	$0.649885\pi$
$410$	−180.181	−	288.394i	−0.439466	−	0.703400i
$411$		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	−0.0828141	−	0.996565i	$-0.526391\pi$
$419$	309.570	−	178.730i	0.738830	−	0.426563i	0.821644	+	0.570002i	$0.193057\pi$
$420$		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
$425$	−263.099	+	539.245i	−0.619056	+	1.26881i
$426$		0			0
$427$	402.078	−	232.140i	0.941636	−	0.543654i
$428$	−60.8601	−	105.413i	−0.142196	−	0.246292i
$429$		0			0
$430$	−159.711	+	300.324i	−0.371422	+	0.698427i
$431$			181.318i			0.420691i	0.977627	+	0.210346i	$0.0674589\pi$
$431$			181.318i			0.420691i	−0.977627	+	0.210346i	$0.932541\pi$
$432$		0			0
$433$		−	705.627i		−	1.62962i	−0.579726	−	0.814811i	$-0.696840\pi$
$433$		−	705.627i		−	1.62962i	0.579726	−	0.814811i	$-0.303160\pi$
$434$	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
$445$	210.690	+	337.226i	0.473461	+	0.757812i
$446$	−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	$-0.809547\pi$
$449$		−	505.807i		−	1.12652i	0.826280	−	0.563260i	$-0.190453\pi$
$450$		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
$455$	−245.497	+	153.380i	−0.539555	+	0.337100i
$456$		0			0
$457$	−615.467	−	355.340i	−1.34676	−	0.777550i	−0.358967	−	0.933350i	$-0.616871\pi$
$457$	−615.467	−	355.340i	−1.34676	−	0.777550i	−0.987788	+	0.155801i	$0.950204\pi$
$458$	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	0.623659	−	0.781696i	$-0.285645\pi$
$461$	119.178	+	68.8073i	0.258520	+	0.149257i	−0.365139	+	0.930953i	$0.618979\pi$
$462$		0			0
$463$	−298.053	+	172.081i	−0.643743	+	0.371665i	−0.786055	−	0.618157i	$-0.787880\pi$
$463$	−298.053	+	172.081i	−0.643743	+	0.371665i	0.142312	+	0.989822i	$0.454546\pi$
$464$	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
$470$	−425.015	−	226.022i	−0.904288	−	0.480898i
$471$		0			0
$472$	123.555	−	71.3345i	0.261769	−	0.151132i
$473$	490.327	+	849.272i	1.03663	+	1.79550i
$474$		0			0
$475$	176.222	−	361.183i	0.370993	−	0.760384i
$476$			454.832i			0.955530i
$477$		0			0
$478$		−	168.409i		−	0.352321i
$479$	−73.7251	−	42.5652i	−0.153915	−	0.0888626i	0.421065	−	0.907031i	$-0.361657\pi$
$479$	−73.7251	−	42.5652i	−0.153915	−	0.0888626i	−0.574979	+	0.818168i	$0.694990\pi$
$480$		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	$-0.851774\pi$
$487$		−	437.344i		−	0.898037i	0.893522	−	0.449018i	$-0.148226\pi$
$488$	69.2929	−	120.019i	0.141994	−	0.245940i
$489$		0			0
$490$	−244.594	+	152.816i	−0.499171	+	0.311869i
$491$	588.443	−	339.738i	1.19846	−	0.691930i	0.238247	−	0.971205i	$-0.423427\pi$
$491$	588.443	−	339.738i	1.19846	−	0.691930i	0.960211	+	0.279275i	$0.0900940\pi$
$492$		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	$0.930708\pi$
$500$	−202.284	+	146.905i	−0.404569	+	0.293810i
$501$		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	−0.905167	−	0.425057i	$-0.860254\pi$
$509$	−503.727	+	290.827i	−0.989640	+	0.571369i	−0.0844732	+	0.996426i	$0.526921\pi$
$510$		0			0
$511$	191.551	−	331.776i	0.374855	−	0.649267i
$512$	22.6274			0.0441942
$513$		0			0
$514$	416.225			0.809777
$515$	43.1668	−	81.1716i	0.0838191	−	0.157615i
$516$		0			0
$517$	−1201.88	+	693.907i	−2.32472	+	1.34218i
$518$	300.396	+	520.301i	0.579915	+	1.00444i
$519$		0			0
$520$	−40.5706	+	76.2896i	−0.0780204	+	0.146711i
$521$		−	1006.68i		−	1.93222i	−0.258138	−	0.966108i	$-0.583109\pi$
$521$		−	1006.68i		−	1.93222i	0.258138	−	0.966108i	$-0.416891\pi$
$522$		0			0
$523$			674.227i			1.28915i	0.764540	+	0.644576i	$0.222966\pi$
$523$			674.227i			1.28915i	−0.764540	+	0.644576i	$0.777034\pi$
$524$	−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
$535$	258.072	−	161.237i	0.482378	−	0.301378i
$536$	−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
$545$	341.308	−	213.240i	0.626253	−	0.391267i
$546$		0			0
$547$	178.531	+	103.075i	0.326381	+	0.188436i	0.654233	−	0.756293i	$-0.272991\pi$
$547$	178.531	+	103.075i	0.326381	+	0.188436i	−0.327852	+	0.944729i	$0.606325\pi$
$548$	−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
$560$	−88.9819	+	167.323i	−0.158896	+	0.298791i
$561$		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
$565$	100.456	+	53.4225i	0.177799	+	0.0945531i
$566$		−	305.931i		−	0.540513i
$567$		0			0
$568$			66.7457i			0.117510i
$569$	349.661	+	201.877i	0.614518	+	0.354792i	0.774732	−	0.632290i	$-0.217885\pi$
$569$	349.661	+	201.877i	0.614518	+	0.354792i	−0.160214	+	0.987082i	$0.551218\pi$
$570$		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	$0.0290679\pi$
$577$			105.236i			0.182386i	−0.995833	+	0.0911928i	$0.970932\pi$
$578$	−202.946	+	351.514i	−0.351118	+	0.608155i
$579$		0			0
$580$	103.966	+	166.407i	0.179253	+	0.286908i
$581$	−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
$590$	188.987	+	302.488i	0.320317	+	0.512692i
$591$		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	$0.731744\pi$
$599$	−985.107	+	568.752i	−1.64459	+	0.949502i	−0.979173	+	0.203026i	$0.934922\pi$
$600$		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
$605$	1300.47	+	691.588i	2.14954	+	1.14312i
$606$		0			0
$607$	−856.430	+	494.460i	−1.41092	+	0.814597i	−0.995475	−	0.0950207i	$-0.969708\pi$
$607$	−856.430	+	494.460i	−1.41092	+	0.814597i	−0.415447	+	0.909617i	$0.636375\pi$
$608$	−45.4674	−	78.7519i	−0.0747820	−	0.129526i
$609$		0			0
$610$	305.899	+	162.676i	0.501473	+	0.266682i
$611$		−	415.941i		−	0.680754i
$612$		0			0
$613$		−	131.155i		−	0.213956i	−0.994261	−	0.106978i	$-0.965882\pi$
$613$		−	131.155i		−	0.213956i	0.994261	−	0.106978i	$-0.0341175\pi$
$614$	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
$625$	−384.653	−	492.612i	−0.615446	−	0.788179i
$626$	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
$635$	194.343	+	311.061i	0.306052	+	0.489860i
$636$		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	0.704003	−	0.710197i	$-0.251394\pi$
$641$	282.653	+	163.190i	0.440957	+	0.254586i	−0.263047	+	0.964783i	$0.584727\pi$
$642$		0			0
$643$	483.731	−	279.282i	0.752303	−	0.434342i	−0.0742223	−	0.997242i	$-0.523647\pi$
$643$	483.731	−	279.282i	0.752303	−	0.434342i	0.826525	+	0.562899i	$0.190314\pi$
$644$	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
$650$	−194.141	−	94.7218i	−0.298679	−	0.145726i
$651$		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
$655$	213.756	−	401.951i	0.326346	−	0.613666i
$656$		−	192.363i		−	0.293237i
$657$		0			0
$658$		−	912.267i		−	1.38642i
$659$	−110.583	−	63.8450i	−0.167804	−	0.0968817i	0.413746	−	0.910392i	$-0.364220\pi$
$659$	−110.583	−	63.8450i	−0.167804	−	0.0968817i	−0.581550	+	0.813511i	$0.697554\pi$
$660$		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
$670$	−206.408	−	330.372i	−0.308071	−	0.493092i
$671$	865.037	−	499.430i	1.28918	−	0.744306i
$672$		0			0
$673$	−1073.07	−	619.539i	−1.59446	−	0.920562i	−0.992528	−	0.122016i	$-0.961064\pi$
$673$	−1073.07	−	619.539i	−1.59446	−	0.920562i	−0.601933	−	0.798547i	$-0.705603\pi$
$674$		−	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
$680$	−287.852	+	179.842i	−0.423311	+	0.264474i
$681$		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
$695$	−153.353	−	81.5528i	−0.220652	−	0.117342i
$696$		0			0
$697$	999.557	−	577.095i	1.43409	−	0.827969i
$698$	−215.331	−	372.965i	−0.308497	−	0.534333i
$699$		0			0
$700$	−425.802	−	207.750i	−0.608289	−	0.296785i
$701$		−	319.512i		−	0.455795i	−0.973685	−	0.227898i	$-0.926815\pi$
$701$		−	319.512i		−	0.455795i	0.973685	−	0.227898i	$-0.0731851\pi$
$702$		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
$715$	−528.166	+	329.985i	−0.738694	+	0.461517i
$716$	−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	$-0.757652\pi$
$719$		−	992.085i		−	1.37981i	0.723899	−	0.689906i	$-0.242348\pi$
$720$		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
$725$	−406.711	+	274.249i	−0.560980	+	0.378274i
$726$		0			0
$727$	6.01986	+	3.47557i	0.00828041	+	0.00478070i	0.504134	−	0.863625i	$-0.331812\pi$
$727$	6.01986	+	3.47557i	0.00828041	+	0.00478070i	−0.495854	+	0.868406i	$0.665145\pi$
$728$	−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	−0.640116	−	0.768278i	$-0.721114\pi$
$733$	−216.107	+	124.770i	−0.294826	+	0.170218i	0.345290	+	0.938496i	$0.387780\pi$
$734$	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	$0.725400\pi$
$740$	−210.508	+	395.842i	−0.284470	+	0.534921i
$741$		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
$745$	−0.744369	+	1.39972i	−0.000999153	+	0.00187882i
$746$			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	$-0.912357\pi$
$757$		−	411.616i		−	0.543746i	0.962333	−	0.271873i	$-0.0876431\pi$
$758$	112.842	−	195.448i	0.148868	−	0.257847i
$759$		0			0
$760$	192.801	−	120.457i	0.253686	−	0.158496i
$761$	−463.859	+	267.809i	−0.609539	+	0.351918i	−0.772785	−	0.634668i	$-0.781137\pi$
$761$	−463.859	+	267.809i	−0.609539	+	0.351918i	0.163246	+	0.986585i	$0.447804\pi$
$762$		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	$0.584997\pi$
$770$	−1158.41	+	723.743i	−1.50442	+	0.939926i
$771$		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
$785$	−107.059	+	201.315i	−0.136380	+	0.256452i
$786$		0			0
$787$	352.266	−	203.381i	0.447607	−	0.258426i	−0.259212	−	0.965820i	$-0.583463\pi$
$787$	352.266	−	203.381i	0.447607	−	0.258426i	0.706819	+	0.707395i	$0.250130\pi$
$788$	372.044	+	644.400i	0.472138	+	0.817766i
$789$		0			0
$790$	−207.484	−	110.339i	−0.262637	−	0.139670i
$791$			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
$805$	1086.44	+	1738.93i	1.34961	+	2.16016i
$806$	−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	$-0.827729\pi$
$809$		−	833.545i		−	1.03034i	0.857088	−	0.515170i	$-0.172271\pi$
$810$		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
$815$	−404.797	−	647.909i	−0.496683	−	0.794981i
$816$		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	0.579340	−	0.815086i	$-0.303310\pi$
$821$	133.926	+	77.3220i	0.163125	+	0.0941803i	−0.416215	+	0.909266i	$0.636644\pi$
$822$		0			0
$823$	955.975	−	551.932i	1.16157	−	0.670635i	0.209893	−	0.977724i	$-0.432688\pi$
$823$	955.975	−	551.932i	1.16157	−	0.670635i	0.951681	+	0.307090i	$0.0993551\pi$
$824$	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	$0.437055\pi$
$830$	−141.810	−	75.4140i	−0.170855	−	0.0908602i
$831$		0			0
$832$	−42.3303	+	24.4394i	−0.0508778	+	0.0293743i
$833$	−489.447	−	847.748i	−0.587572	−	1.01770i
$834$		0			0
$835$	60.6051	+	32.2296i	0.0725809	+	0.0385983i
$836$		−	655.415i		−	0.783989i
$837$		0			0
$838$			505.525i			0.603252i
$839$	−1050.83	−	606.698i	−1.25248	−	0.723121i	−0.280880	−	0.959743i	$-0.590626\pi$
$839$	−1050.83	−	606.698i	−1.25248	−	0.723121i	−0.971602	+	0.236622i	$0.923960\pi$
$840$		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
$850$	−474.399	−	703.533i	−0.558116	−	0.827685i
$851$	1680.35	−	970.149i	1.97456	−	1.14001i
$852$		0			0
$853$	−30.3535	−	17.5246i	−0.0355844	−	0.0205446i	0.482102	−	0.876115i	$-0.339873\pi$
$853$	−30.3535	−	17.5246i	−0.0355844	−	0.0205446i	−0.517687	+	0.855570i	$0.673207\pi$
$854$			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	$-0.343111\pi$
$860$	−254.887	−	407.966i	−0.296380	−	0.474380i
$861$		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
$875$	481.981	−	1081.95i	0.550836	−	1.23651i
$876$		0			0
$877$	1045.75	−	603.765i	1.19242	−	0.688443i	0.233564	−	0.972341i	$-0.424961\pi$
$877$	1045.75	−	603.765i	1.19242	−	0.688443i	0.958854	+	0.283898i	$0.0916278\pi$
$878$	−201.917	−	349.730i	−0.229973	−	0.398326i
$879$		0			0
$880$	−191.437	+	359.981i	−0.217542	+	0.409069i
$881$		−	407.569i		−	0.462621i	−0.972880	−	0.231311i	$-0.925699\pi$
$881$		−	407.569i		−	0.462621i	0.972880	−	0.231311i	$-0.0743013\pi$
$882$		0			0
$883$			85.9086i			0.0972918i	0.998816	+	0.0486459i	$0.0154906\pi$
$883$			85.9086i			0.0972918i	−0.998816	+	0.0486459i	$0.984509\pi$
$884$	−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
$895$	−165.489	−	264.878i	−0.184904	−	0.295953i
$896$	−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
$905$	1454.59	−	908.789i	1.60728	−	1.00419i
$906$		0			0
$907$	−1034.37	−	597.195i	−1.14043	−	0.658429i	−0.193895	−	0.981022i	$-0.562112\pi$
$907$	−1034.37	−	597.195i	−1.14043	−	0.658429i	−0.946538	+	0.322593i	$0.895446\pi$
$908$	−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	0.977279	−	0.211956i	$-0.0679833\pi$
$911$	1168.23	+	674.478i	1.28236	+	0.740371i	0.305080	+	0.952327i	$0.401317\pi$
$912$		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	$0.173614\pi$
$920$	540.381	+	287.373i	0.587371	+	0.312362i
$921$		0			0
$922$	−168.543	+	97.3082i	−0.182801	+	0.105540i
$923$	−72.0907	−	124.865i	−0.0781048	−	0.135282i
$924$		0			0
$925$	−1007.33	−	491.481i	−1.08901	−	0.531330i
$926$		−	486.718i		−	0.525614i
$927$		0			0
$928$			110.996i			0.119607i
$929$	−217.900	−	125.805i	−0.234554	−	0.135420i	0.378117	−	0.925758i	$-0.376572\pi$
$929$	−217.900	−	125.805i	−0.234554	−	0.135420i	−0.612671	+	0.790338i	$0.709905\pi$
$930$		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	$0.323112\pi$
$937$			1592.01i			1.69905i	−0.527546	+	0.849526i	$0.676888\pi$
$938$	369.122	−	639.339i	0.393521	−	0.681598i
$939$		0			0
$940$	577.350	−	360.714i	0.614203	−	0.383738i
$941$	−883.684	+	510.195i	−0.939091	+	0.542184i	−0.889675	−	0.456594i	$-0.849069\pi$
$941$	−883.684	+	510.195i	−0.939091	+	0.542184i	−0.0494154	+	0.998778i	$0.515736\pi$
$942$		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
$950$	317.749	+	471.221i	0.334473	+	0.496022i
$951$		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
$965$	394.699	−	742.199i	0.409015	−	0.769118i
$966$		0			0
$967$	881.781	−	509.096i	0.911873	−	0.526470i	0.0308394	−	0.999524i	$-0.490182\pi$
$967$	881.781	−	509.096i	0.911873	−	0.526470i	0.881033	+	0.473054i	$0.156849\pi$
$968$	416.608	+	721.586i	0.430380	+	0.745440i
$969$		0			0
$970$	398.033	−	748.468i	0.410344	−	0.771617i
$971$			997.549i			1.02734i	0.857987	+	0.513671i	$0.171715\pi$
$971$			997.549i			1.02734i	−0.857987	+	0.513671i	$0.828285\pi$
$972$		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
$985$	−1577.63	+	985.659i	−1.60165	+	1.00067i
$986$	−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
$995$	983.020	−	614.165i	0.987960	−	0.617252i
$996$		0			0
$997$	650.499	+	375.566i	0.652456	+	0.376696i	0.789397	−	0.613884i	$-0.210394\pi$
$997$	650.499	+	375.566i	0.652456	+	0.376696i	−0.136941	+	0.990579i	$0.543727\pi$
$998$	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.h.269.6		24
3.2	odd	2	inner	810.3.j.h.269.12		24
5.4	even	2		810.3.j.g.269.12		24
9.2	odd	6		810.3.b.c.809.7	✓	24
9.4	even	3		810.3.j.g.539.6		24
9.5	odd	6		810.3.j.g.539.12		24
9.7	even	3		810.3.b.c.809.18	yes	24
15.14	odd	2		810.3.j.g.269.6		24
45.4	even	6	inner	810.3.j.h.539.12		24
45.14	odd	6	inner	810.3.j.h.539.6		24
45.29	odd	6		810.3.b.c.809.17	yes	24
45.34	even	6		810.3.b.c.809.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.3.b.c.809.7	✓	24	9.2	odd	6
810.3.b.c.809.8	yes	24	45.34	even	6
810.3.b.c.809.17	yes	24	45.29	odd	6
810.3.b.c.809.18	yes	24	9.7	even	3
810.3.j.g.269.6		24	15.14	odd	2
810.3.j.g.269.12		24	5.4	even	2
810.3.j.g.539.6		24	9.4	even	3
810.3.j.g.539.12		24	9.5	odd	6
810.3.j.h.269.6		24	1.1	even	1	trivial
810.3.j.h.269.12		24	3.2	odd	2	inner
810.3.j.h.539.6		24	45.14	odd	6	inner
810.3.j.h.539.12		24	45.4	even	6	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.24042 - 2.64931i) q^{5} +(8.20611 + 4.73780i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.24042 - 2.64931i) q^{5} +(8.20611 + 4.73780i) q^{7} +2.82843 q^{8} +(0.246293 + 7.06678i) q^{10} +(17.6547 + 10.1930i) q^{11} +(-5.29129 + 3.05493i) q^{13} +(-11.6052 + 6.70026i) q^{14} +(-2.00000 + 3.46410i) q^{16} -24.0002 q^{17} +16.0752 q^{19} +(-8.82915 - 4.69532i) q^{20} +(-24.9676 + 14.4150i) q^{22} +(21.6389 + 37.4798i) q^{23} +(10.9624 - 22.4683i) q^{25} -8.64064i q^{26} -18.9512i q^{28} +(-16.9927 - 9.81073i) q^{29} +(-15.2536 - 26.4200i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(16.9707 - 29.3941i) q^{34} +(47.3492 - 1.65023i) q^{35} -44.8335i q^{37} +(-11.3669 + 19.6880i) q^{38} +(11.9937 - 7.49337i) q^{40} +(-41.6479 + 24.0454i) q^{41} +(41.6597 + 24.0522i) q^{43} -40.7719i q^{44} -61.2042 q^{46} +(-34.0385 + 58.9564i) q^{47} +(20.3935 + 35.3225i) q^{49} +(19.7664 + 29.3136i) q^{50} +(10.5826 + 6.10986i) q^{52} +61.7484 q^{53} +(101.868 - 3.55032i) q^{55} +(23.2104 + 13.4005i) q^{56} +(24.0313 - 13.8745i) q^{58} +(43.6833 - 25.2206i) q^{59} +(24.4987 - 42.4330i) q^{61} +43.1438 q^{62} +8.00000 q^{64} +(-14.3439 + 26.9724i) q^{65} +(-47.7100 + 27.5454i) q^{67} +(24.0002 + 41.5696i) q^{68} +(-31.4599 + 59.1576i) q^{70} +23.5982i q^{71} -40.4303i q^{73} +(54.9096 + 31.7021i) q^{74} +(-16.0752 - 27.8430i) q^{76} +(96.5844 + 167.289i) q^{77} +(-16.6169 + 28.7813i) q^{79} +(0.696621 + 19.9879i) q^{80} -68.0107i q^{82} +(-11.3572 + 19.6713i) q^{83} +(-101.771 + 63.5839i) q^{85} +(-58.9157 + 34.0150i) q^{86} +(49.9351 + 28.8301i) q^{88} +79.5266i q^{89} -57.8946 q^{91} +(43.2779 - 74.9595i) q^{92} +(-48.1377 - 83.3770i) q^{94} +(68.1655 - 42.5880i) q^{95} +(-103.825 - 59.9431i) q^{97} -57.6815 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 24 q^{7}+O(q^{10}) \) 24 * q - 24 * q^4 + 24 * q^7	\( 24 q - 24 q^{4} + 24 q^{7} - 12 q^{10} + 48 q^{13} - 48 q^{16} - 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{40} - 24 q^{43} - 36 q^{49} - 96 q^{52} + 216 q^{55} + 396 q^{58} - 60 q^{61} + 192 q^{64} - 1032 q^{67} + 288 q^{70} - 240 q^{79} - 48 q^{85} + 240 q^{88} + 48 q^{91} - 48 q^{94} - 1440 q^{97}+O(q^{100}) \) 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^40 - 24 * q^43 - 36 * q^49 - 96 * q^52 + 216 * q^55 + 396 * q^58 - 60 * q^61 + 192 * q^64 - 1032 * q^67 + 288 * q^70 - 240 * q^79 - 48 * 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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