LMFDB - Embedded newform 684.3.s.a.445.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, degree $2$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.12
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99772 + 2.23810i) q^{3} +(0.267948 + 0.464100i) q^{5} +(4.62209 + 8.00569i) q^{7} +(-1.01820 - 8.94222i) q^{9} +O(q^{10})$	\(q+(-1.99772 + 2.23810i) q^{3} +(0.267948 + 0.464100i) q^{5} +(4.62209 + 8.00569i) q^{7} +(-1.01820 - 8.94222i) q^{9} +(6.99493 + 12.1156i) q^{11} -1.06489i q^{13} +(-1.57399 - 0.327448i) q^{15} +(-0.480422 + 0.832115i) q^{17} +(14.7192 + 12.0144i) q^{19} +(-27.1512 - 5.64845i) q^{21} -0.00791718 q^{23} +(12.3564 - 21.4019i) q^{25} +(22.0477 + 15.5852i) q^{27} +(17.0160 + 9.82417i) q^{29} +(-0.693935 - 0.400644i) q^{31} +(-41.0898 - 8.54820i) q^{33} +(-2.47696 + 4.29022i) q^{35} +14.3497i q^{37} +(2.38334 + 2.12736i) q^{39} +(-42.4984 + 24.5365i) q^{41} -15.1413 q^{43} +(3.87726 - 2.86860i) q^{45} +(-5.03942 + 8.72854i) q^{47} +(-18.2274 + 31.5708i) q^{49} +(-0.902609 - 2.73757i) q^{51} +(-40.3119 + 23.2741i) q^{53} +(-3.74856 + 6.49269i) q^{55} +(-56.2943 + 8.94146i) q^{57} +(-65.5017 + 37.8175i) q^{59} +(5.92027 - 10.2542i) q^{61} +(66.8824 - 49.4832i) q^{63} +(0.494217 - 0.285336i) q^{65} +25.7342i q^{67} +(0.0158163 - 0.0177195i) q^{69} +(-32.7913 - 18.9321i) q^{71} +(-17.6661 + 30.5985i) q^{73} +(23.2150 + 70.4100i) q^{75} +(-64.6624 + 111.999i) q^{77} +11.0432i q^{79} +(-78.9265 + 18.2100i) q^{81} +(-27.9268 - 48.3706i) q^{83} -0.514913 q^{85} +(-55.9807 + 18.4575i) q^{87} +(-42.2579 + 24.3976i) q^{89} +(8.52520 - 4.92203i) q^{91} +(2.28297 - 0.752723i) q^{93} +(-1.63193 + 10.0504i) q^{95} +92.5556i q^{97} +(101.218 - 74.8863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.99772	+	2.23810i	−0.665908	+	0.746034i
$3$	−1.99772	+	2.23810i	−0.665908	+	0.746034i
$4$		0			0
$5$	0.267948	+	0.464100i	0.0535896	+	0.0928200i	0.891576	−	0.452872i	$-0.149600\pi$
$5$	0.267948	+	0.464100i	0.0535896	+	0.0928200i	−0.837986	+	0.545692i	$0.816267\pi$
$6$		0			0
$7$	4.62209	+	8.00569i	0.660298	+	1.14367i	0.980537	+	0.196334i	$0.0629035\pi$
$7$	4.62209	+	8.00569i	0.660298	+	1.14367i	−0.320239	+	0.947337i	$0.603763\pi$
$8$		0			0
$9$	−1.01820	−	8.94222i	−0.113134	−	0.993580i
$10$		0			0
$11$	6.99493	+	12.1156i	0.635903	+	1.10142i	0.986323	+	0.164824i	$0.0527055\pi$
$11$	6.99493	+	12.1156i	0.635903	+	1.10142i	−0.350420	+	0.936593i	$0.613961\pi$
$12$		0			0
$13$		−	1.06489i		−	0.0819148i	−0.999161	−	0.0409574i	$-0.986959\pi$
$13$		−	1.06489i		−	0.0819148i	0.999161	−	0.0409574i	$-0.0130408\pi$
$14$		0			0
$15$	−1.57399	−	0.327448i	−0.104933	−	0.0218298i
$16$		0			0
$17$	−0.480422	+	0.832115i	−0.0282601	+	0.0489480i	−0.879810	−	0.475326i	$-0.842330\pi$
$17$	−0.480422	+	0.832115i	−0.0282601	+	0.0489480i	0.851549	+	0.524274i	$0.175663\pi$
$18$		0			0
$19$	14.7192	+	12.0144i	0.774692	+	0.632338i
$19$	14.7192	+	12.0144i	0.774692	+	0.632338i
$20$		0			0
$21$	−27.1512	−	5.64845i	−1.29291	−	0.268974i
$22$		0			0
$23$	−0.00791718			−0.000344225			−0.000172113	−	1.00000i	$-0.500055\pi$
$23$	−0.00791718			−0.000344225			−0.000172113		1.00000i	$0.500055\pi$
$24$		0			0
$25$	12.3564	−	21.4019i	0.494256	−	0.856077i
$26$		0			0
$27$	22.0477	+	15.5852i	0.816581	+	0.577231i
$28$		0			0
$29$	17.0160	+	9.82417i	0.586757	+	0.338765i	0.763814	−	0.645436i	$-0.223324\pi$
$29$	17.0160	+	9.82417i	0.586757	+	0.338765i	−0.177057	+	0.984201i	$0.556658\pi$
$30$		0			0
$31$	−0.693935	−	0.400644i	−0.0223850	−	0.0129240i	0.488766	−	0.872415i	$-0.337447\pi$
$31$	−0.693935	−	0.400644i	−0.0223850	−	0.0129240i	−0.511151	+	0.859491i	$0.670781\pi$
$32$		0			0
$33$	−41.0898	−	8.54820i	−1.24515	−	0.259036i
$34$		0			0
$35$	−2.47696	+	4.29022i	−0.0707703	+	0.122578i
$36$		0			0
$37$			14.3497i			0.387829i	0.981018	+	0.193914i	$0.0621184\pi$
$37$			14.3497i			0.387829i	−0.981018	+	0.193914i	$0.937882\pi$
$38$		0			0
$39$	2.38334	+	2.12736i	0.0611113	+	0.0545477i
$40$		0			0
$41$	−42.4984	+	24.5365i	−1.03655	+	0.598451i	−0.918853	−	0.394599i	$-0.870883\pi$
$41$	−42.4984	+	24.5365i	−1.03655	+	0.598451i	−0.117694	+	0.993050i	$0.537550\pi$
$42$		0			0
$43$	−15.1413			−0.352123			−0.176062	−	0.984379i	$-0.556336\pi$
$43$	−15.1413			−0.352123			−0.176062	+	0.984379i	$0.556336\pi$
$44$		0			0
$45$	3.87726	−	2.86860i	0.0861613	−	0.0637467i
$46$		0			0
$47$	−5.03942	+	8.72854i	−0.107222	+	0.185714i	−0.914644	−	0.404261i	$-0.867529\pi$
$47$	−5.03942	+	8.72854i	−0.107222	+	0.185714i	0.807422	+	0.589974i	$0.200862\pi$
$48$		0			0
$49$	−18.2274	+	31.5708i	−0.371988	+	0.644302i
$50$		0			0
$51$	−0.902609	−	2.73757i	−0.0176982	−	0.0536778i
$52$		0			0
$53$	−40.3119	+	23.2741i	−0.760602	+	0.439134i	−0.829512	−	0.558489i	$-0.811381\pi$
$53$	−40.3119	+	23.2741i	−0.760602	+	0.439134i	0.0689096	+	0.997623i	$0.478048\pi$
$54$		0			0
$55$	−3.74856	+	6.49269i	−0.0681556	+	0.118049i
$56$		0			0
$57$	−56.2943	+	8.94146i	−0.987620	+	0.156868i
$58$		0			0
$59$	−65.5017	+	37.8175i	−1.11020	+	0.640974i	−0.938881	−	0.344242i	$-0.888136\pi$
$59$	−65.5017	+	37.8175i	−1.11020	+	0.640974i	−0.171318	+	0.985216i	$0.554803\pi$
$60$		0			0
$61$	5.92027	−	10.2542i	0.0970537	−	0.168102i	−0.813410	−	0.581691i	$-0.802391\pi$
$61$	5.92027	−	10.2542i	0.0970537	−	0.168102i	0.910464	+	0.413589i	$0.135725\pi$
$62$		0			0
$63$	66.8824	−	49.4832i	1.06163	−	0.785447i
$64$		0			0
$65$	0.494217	−	0.285336i	0.00760333	−	0.00438979i
$66$		0			0
$67$			25.7342i			0.384093i	0.981386	+	0.192047i	$0.0615125\pi$
$67$			25.7342i			0.384093i	−0.981386	+	0.192047i	$0.938488\pi$
$68$		0			0
$69$	0.0158163	−	0.0177195i	0.000229222	−	0.000256804i
$70$		0			0
$71$	−32.7913	−	18.9321i	−0.461849	−	0.266649i	0.250972	−	0.967994i	$-0.419250\pi$
$71$	−32.7913	−	18.9321i	−0.461849	−	0.266649i	−0.712822	+	0.701345i	$0.752583\pi$
$72$		0			0
$73$	−17.6661	+	30.5985i	−0.242001	+	0.419158i	−0.961284	−	0.275559i	$-0.911137\pi$
$73$	−17.6661	+	30.5985i	−0.242001	+	0.419158i	0.719283	+	0.694717i	$0.244470\pi$
$74$		0			0
$75$	23.2150	+	70.4100i	0.309534	+	0.938800i
$76$		0			0
$77$	−64.6624	+	111.999i	−0.839771	+	1.45453i
$78$		0			0
$79$			11.0432i			0.139787i	0.997554	+	0.0698937i	$0.0222660\pi$
$79$			11.0432i			0.139787i	−0.997554	+	0.0698937i	$0.977734\pi$
$80$		0			0
$81$	−78.9265	+	18.2100i	−0.974401	+	0.224815i
$82$		0			0
$83$	−27.9268	−	48.3706i	−0.336467	−	0.582778i	0.647298	−	0.762237i	$-0.275899\pi$
$83$	−27.9268	−	48.3706i	−0.336467	−	0.582778i	−0.983766	+	0.179459i	$0.942565\pi$
$84$		0			0
$85$	−0.514913			−0.00605780
$86$		0			0
$87$	−55.9807	+	18.4575i	−0.643456	+	0.212155i
$88$		0			0
$89$	−42.2579	+	24.3976i	−0.474808	+	0.274131i	−0.718250	−	0.695785i	$-0.755057\pi$
$89$	−42.2579	+	24.3976i	−0.474808	+	0.274131i	0.243442	+	0.969915i	$0.421723\pi$
$90$		0			0
$91$	8.52520	−	4.92203i	0.0936836	−	0.0540882i
$92$		0			0
$93$	2.28297	−	0.752723i	0.0245481	−	0.00809379i
$94$		0			0
$95$	−1.63193	+	10.0504i	−0.0171782	+	0.105794i
$96$		0			0
$97$			92.5556i			0.954181i	0.878854	+	0.477091i	$0.158309\pi$
$97$			92.5556i			0.954181i	−0.878854	+	0.477091i	$0.841691\pi$
$98$		0			0
$99$	101.218	−	74.8863i	1.02240	−	0.756428i
$100$		0			0
$101$	23.1250	−	40.0536i	0.228960	−	0.396571i	−0.728540	−	0.685003i	$-0.759801\pi$
$101$	23.1250	−	40.0536i	0.228960	−	0.396571i	0.957500	+	0.288433i	$0.0931341\pi$
$102$		0			0
$103$	−43.5718	−	25.1562i	−0.423027	−	0.244235i	0.273344	−	0.961916i	$-0.411870\pi$
$103$	−43.5718	−	25.1562i	−0.423027	−	0.244235i	−0.696372	+	0.717681i	$0.745203\pi$
$104$		0			0
$105$	−4.65367	−	14.1144i	−0.0443207	−	0.134423i
$106$		0			0
$107$		−	38.3821i		−	0.358711i	−0.983784	−	0.179355i	$-0.942599\pi$
$107$		−	38.3821i		−	0.358711i	0.983784	−	0.179355i	$-0.0574012\pi$
$108$		0			0
$109$	74.4153	+	42.9637i	0.682709	+	0.394162i	0.800875	−	0.598832i	$-0.204368\pi$
$109$	74.4153	+	42.9637i	0.682709	+	0.394162i	−0.118166	+	0.992994i	$0.537701\pi$
$110$		0			0
$111$	−32.1160	−	28.6666i	−0.289333	−	0.258258i
$112$		0			0
$113$	−11.7708	−	6.79590i	−0.104167	−	0.0601407i	0.447012	−	0.894528i	$-0.352488\pi$
$113$	−11.7708	−	6.79590i	−0.104167	−	0.0601407i	−0.551178	+	0.834387i	$0.685822\pi$
$114$		0			0
$115$	−0.00212139	−	0.00367436i	−1.84469e−5	−	3.19510e-5i
$116$		0			0
$117$	−9.52250	+	1.08428i	−0.0813889	+	0.00926734i
$118$		0			0
$119$	−8.88221			−0.0746404
$120$		0			0
$121$	−37.3581	+	64.7062i	−0.308745	+	0.534762i
$122$		0			0
$123$	29.9849	−	144.133i	0.243780	−	1.17181i
$124$		0			0
$125$	26.6409			0.213127
$126$		0			0
$127$	26.7368	−	15.4365i	0.210526	−	0.121547i	−0.391030	−	0.920378i	$-0.627881\pi$
$127$	26.7368	−	15.4365i	0.210526	−	0.121547i	0.601556	+	0.798831i	$0.294548\pi$
$128$		0			0
$129$	30.2481	−	33.8878i	0.234482	−	0.262696i
$130$		0			0
$131$	−31.4707	−	54.5089i	−0.240235	−	0.416098i	0.720546	−	0.693407i	$-0.243891\pi$
$131$	−31.4707	−	54.5089i	−0.240235	−	0.416098i	−0.960781	+	0.277308i	$0.910558\pi$
$132$		0			0
$133$	−28.1506	+	173.369i	−0.211659	+	1.30352i
$134$		0			0
$135$	−1.32546	+	14.4084i	−0.00981826	+	0.106729i
$136$		0			0
$137$	−14.3073	+	24.7809i	−0.104433	+	0.180883i	−0.913506	−	0.406825i	$-0.866636\pi$
$137$	−14.3073	+	24.7809i	−0.104433	+	0.180883i	0.809074	+	0.587707i	$0.199969\pi$
$138$		0			0
$139$	230.669			1.65949			0.829745	−	0.558143i	$-0.188486\pi$
$139$	230.669			1.65949			0.829745	+	0.558143i	$0.188486\pi$
$140$		0			0
$141$	−9.46799	−	28.7159i	−0.0671488	−	0.203659i
$142$		0			0
$143$	12.9018	−	7.44885i	0.0902223	−	0.0520899i
$144$		0			0
$145$			10.5295i			0.0726171i
$146$		0			0
$147$	−34.2454	−	103.865i	−0.232962	−	0.706561i
$148$		0			0
$149$	−31.8858	−	55.2278i	−0.213999	−	0.370657i	0.738964	−	0.673745i	$-0.235316\pi$
$149$	−31.8858	−	55.2278i	−0.213999	−	0.370657i	−0.952962	+	0.303089i	$0.901982\pi$
$150$		0			0
$151$	−37.6539	+	21.7395i	−0.249363	+	0.143970i	−0.619473	−	0.785018i	$-0.712654\pi$
$151$	−37.6539	+	21.7395i	−0.249363	+	0.143970i	0.370109	+	0.928988i	$0.379320\pi$
$152$		0			0
$153$	7.93012	+	3.44877i	0.0518309	+	0.0225410i
$154$		0			0
$155$		−	0.429407i		−	0.00277037i
$156$		0			0
$157$	−113.699	−	196.932i	−0.724195	−	1.25434i	−0.959304	−	0.282374i	$-0.908878\pi$
$157$	−113.699	−	196.932i	−0.724195	−	1.25434i	0.235109	−	0.971969i	$-0.424455\pi$
$158$		0			0
$159$	28.4422	−	136.717i	0.178882	−	0.859858i
$160$		0			0
$161$	−0.0365939	−	0.0633825i	−0.000227291	−	0.000393680i
$162$		0			0
$163$	249.295			1.52942			0.764710	−	0.644375i	$-0.222882\pi$
$163$	249.295			1.52942			0.764710	+	0.644375i	$0.222882\pi$
$164$		0			0
$165$	−7.04273	−	21.3603i	−0.0426832	−	0.129456i
$166$		0			0
$167$			92.5036i			0.553914i	0.960882	+	0.276957i	$0.0893259\pi$
$167$			92.5036i			0.553914i	−0.960882	+	0.276957i	$0.910674\pi$
$168$		0			0
$169$	167.866			0.993290
$170$		0			0
$171$	92.4486	−	143.855i	0.540635	−	0.841257i
$172$		0			0
$173$			331.826i			1.91807i	0.283286	+	0.959035i	$0.408575\pi$
$173$			331.826i			1.91807i	−0.283286	+	0.959035i	$0.591425\pi$
$174$		0			0
$175$	228.450			1.30543
$176$		0			0
$177$	46.2150	−	222.148i	0.261102	−	1.25508i
$178$		0			0
$179$		−	227.494i		−	1.27091i	−0.772136	−	0.635457i	$-0.780812\pi$
$179$		−	227.494i		−	1.27091i	0.772136	−	0.635457i	$-0.219188\pi$
$180$		0			0
$181$	200.197	−	115.584i	1.10606	−	0.638585i	0.168255	−	0.985744i	$-0.446187\pi$
$181$	200.197	−	115.584i	1.10606	−	0.638585i	0.937806	+	0.347159i	$0.112854\pi$
$182$		0			0
$183$	11.1229	+	33.7353i	0.0607810	+	0.184346i
$184$		0			0
$185$	−6.65968	+	3.84497i	−0.0359982	+	0.0207836i
$186$		0			0
$187$	−13.4421			−0.0718828
$188$		0			0
$189$	−22.8642	+	248.543i	−0.120974	+	1.31504i
$190$		0			0
$191$	161.255	+	279.303i	0.844269	+	1.46232i	0.886254	+	0.463199i	$0.153298\pi$
$191$	161.255	+	279.303i	0.844269	+	1.46232i	−0.0419854	+	0.999118i	$0.513368\pi$
$192$		0			0
$193$	129.321	−	74.6635i	0.670057	−	0.386858i	−0.126041	−	0.992025i	$-0.540227\pi$
$193$	129.321	−	74.6635i	0.670057	−	0.386858i	0.796098	+	0.605167i	$0.206894\pi$
$194$		0			0
$195$	−0.348697	+	1.67613i	−0.00178819	+	0.00859554i
$196$		0			0
$197$	−256.813			−1.30362			−0.651811	−	0.758382i	$-0.725990\pi$
$197$	−256.813			−1.30362			−0.651811	+	0.758382i	$0.725990\pi$
$198$		0			0
$199$	116.477	+	201.743i	0.585309	+	1.01379i	0.994837	+	0.101488i	$0.0323603\pi$
$199$	116.477	+	201.743i	0.585309	+	1.01379i	−0.409527	+	0.912298i	$0.634306\pi$
$200$		0			0
$201$	−57.5959	−	51.4099i	−0.286547	−	0.255771i
$202$		0			0
$203$			181.633i			0.894743i
$204$		0			0
$205$	−22.7748	−	13.1490i	−0.111096	−	0.0641415i
$206$		0			0
$207$	0.00806131	+	0.0707972i	3.89435e−5	+	0.000342015i
$208$		0			0
$209$	−42.6023	+	262.371i	−0.203839	+	1.25536i
$210$		0			0
$211$	143.779	−	83.0108i	0.681417	−	0.393416i	−0.118972	−	0.992898i	$-0.537960\pi$
$211$	143.779	−	83.0108i	0.681417	−	0.393416i	0.800389	+	0.599481i	$0.204626\pi$
$212$		0			0
$213$	107.880	−	35.5693i	0.506478	−	0.166992i
$214$		0			0
$215$	−4.05709	−	7.02708i	−0.0188702	−	0.0326841i
$216$		0			0
$217$		−	7.40724i		−	0.0341347i
$218$		0			0
$219$	−33.1907	−	100.666i	−0.151556	−	0.459661i
$220$		0			0
$221$	0.886113	+	0.511598i	0.00400956	+	0.00231492i
$222$		0			0
$223$		−	30.8954i		−	0.138545i	−0.997598	−	0.0692723i	$-0.977932\pi$
$223$		−	30.8954i		−	0.138545i	0.997598	−	0.0692723i	$-0.0220677\pi$
$224$		0			0
$225$	−203.962	−	88.7022i	−0.906498	−	0.394232i
$226$		0			0
$227$	−130.385	+	75.2779i	−0.574384	+	0.331621i	−0.758898	−	0.651209i	$-0.774262\pi$
$227$	−130.385	+	75.2779i	−0.574384	+	0.331621i	0.184514	+	0.982830i	$0.440929\pi$
$228$		0			0
$229$	204.007	−	353.351i	0.890861	−	1.54302i	0.0520150	−	0.998646i	$-0.483436\pi$
$229$	204.007	−	353.351i	0.890861	−	1.54302i	0.838846	−	0.544369i	$-0.183231\pi$
$230$		0			0
$231$	−121.487	−	368.463i	−0.525916	−	1.59508i
$232$		0			0
$233$	123.041	−	213.113i	0.528072	−	0.914648i	−0.471392	−	0.881924i	$-0.656248\pi$
$233$	123.041	−	213.113i	0.528072	−	0.914648i	0.999464	−	0.0327244i	$-0.0104184\pi$
$234$		0			0
$235$	−5.40122			−0.0229839
$236$		0			0
$237$	−24.7158	−	22.0613i	−0.104286	−	0.0930855i
$238$		0			0
$239$	54.6527	−	94.6612i	0.228672	−	0.396072i	−0.728743	−	0.684788i	$-0.759895\pi$
$239$	54.6527	−	94.6612i	0.228672	−	0.396072i	0.957415	+	0.288716i	$0.0932282\pi$
$240$		0			0
$241$	−289.768	−	167.297i	−1.20236	−	0.694180i	−0.241277	−	0.970456i	$-0.577566\pi$
$241$	−289.768	−	167.297i	−1.20236	−	0.694180i	−0.961078	+	0.276276i	$0.910900\pi$
$242$		0			0
$243$	116.917	−	213.024i	0.481142	−	0.876643i
$244$		0			0
$245$	−19.5360			−0.0797388
$246$		0			0
$247$	12.7941	−	15.6743i	0.0517979	−	0.0634588i
$248$		0			0
$249$	164.048	+	34.1281i	0.658828	+	0.137061i
$250$		0			0
$251$	−26.1362	−	45.2693i	−0.104128	−	0.180356i	0.809253	−	0.587460i	$-0.199872\pi$
$251$	−26.1362	−	45.2693i	−0.104128	−	0.180356i	−0.913382	+	0.407104i	$0.866539\pi$
$252$		0			0
$253$	−0.0553801	−	0.0959212i	−0.000218894	−	0.000379135i
$254$		0			0
$255$	1.02865	−	1.15243i	0.00403393	−	0.00451932i
$256$		0			0
$257$		−	246.387i		−	0.958702i	−0.877623	−	0.479351i	$-0.840872\pi$
$257$		−	246.387i		−	0.958702i	0.877623	−	0.479351i	$-0.159128\pi$
$258$		0			0
$259$	−114.879	+	66.3254i	−0.443548	+	0.256083i
$260$		0			0
$261$	70.5242	−	162.163i	0.270207	−	0.621316i
$262$		0			0
$263$	−443.921			−1.68791			−0.843957	−	0.536412i	$-0.819779\pi$
$263$	−443.921			−1.68791			−0.843957	+	0.536412i	$0.819779\pi$
$264$		0			0
$265$	−21.6030	−	12.4725i	−0.0815208	−	0.0470661i
$266$		0			0
$267$	29.8153	−	143.317i	0.111668	−	0.536769i
$268$		0			0
$269$	−118.632	−	68.4924i	−0.441012	−	0.254619i	0.263015	−	0.964792i	$-0.415283\pi$
$269$	−118.632	−	68.4924i	−0.441012	−	0.254619i	−0.704027	+	0.710173i	$0.748617\pi$
$270$		0			0
$271$	25.1059	−	43.4847i	0.0926417	−	0.160460i	−0.815980	−	0.578080i	$-0.803802\pi$
$271$	25.1059	−	43.4847i	0.0926417	−	0.160460i	0.908622	+	0.417620i	$0.137136\pi$
$272$		0			0
$273$	−6.01499	+	28.9131i	−0.0220329	+	0.105909i
$274$		0			0
$275$	345.729			1.25720
$276$		0			0
$277$	84.5991	+	146.530i	0.305412	+	0.528989i	0.977353	−	0.211616i	$-0.0678725\pi$
$277$	84.5991	+	146.530i	0.305412	+	0.528989i	−0.671941	+	0.740605i	$0.734539\pi$
$278$		0			0
$279$	−2.87607	+	6.61325i	−0.0103085	+	0.0237034i
$280$		0			0
$281$	−236.557	−	136.576i	−0.841839	−	0.486036i	0.0160498	−	0.999871i	$-0.494891\pi$
$281$	−236.557	−	136.576i	−0.841839	−	0.486036i	−0.857889	+	0.513835i	$0.828224\pi$
$282$		0			0
$283$	79.5269	+	137.745i	0.281014	+	0.486730i	0.971635	−	0.236487i	$-0.0759960\pi$
$283$	79.5269	+	137.745i	0.281014	+	0.486730i	−0.690621	+	0.723217i	$0.742663\pi$
$284$		0			0
$285$	−19.2337	−	23.7303i	−0.0674866	−	0.0832644i
$286$		0			0
$287$	−392.863	−	226.820i	−1.36886	−	0.790312i
$288$		0			0
$289$	144.038	+	249.482i	0.498403	+	0.863259i
$290$		0			0
$291$	−207.149	−	184.900i	−0.711852	−	0.635397i
$292$		0			0
$293$	119.176	+	68.8065i	0.406745	+	0.234835i	0.689390	−	0.724390i	$-0.257879\pi$
$293$	119.176	+	68.8065i	0.406745	+	0.234835i	−0.282645	+	0.959225i	$0.591212\pi$
$294$		0			0
$295$	−35.1022	−	20.2662i	−0.118990	−	0.0686991i
$296$		0			0
$297$	−34.6020	+	376.138i	−0.116505	+	1.26646i
$298$		0			0
$299$			0.00843095i			2.81972e-5i
$300$		0			0
$301$	−69.9844	−	121.217i	−0.232506	−	0.402713i
$302$		0			0
$303$	43.4468	+	131.772i	0.143389	+	0.434892i
$304$		0			0
$305$	6.34531			0.0208043
$306$		0			0
$307$	−113.354	−	65.4449i	−0.369231	−	0.213176i	0.303891	−	0.952707i	$-0.401714\pi$
$307$	−113.354	−	65.4449i	−0.369231	−	0.213176i	−0.673123	+	0.739531i	$0.735047\pi$
$308$		0			0
$309$	143.347	−	47.2631i	0.463905	−	0.152955i
$310$		0			0
$311$	93.4810	−	161.914i	0.300582	−	0.520623i	−0.675686	−	0.737190i	$-0.736152\pi$
$311$	93.4810	−	161.914i	0.300582	−	0.520623i	0.976268	+	0.216566i	$0.0694857\pi$
$312$		0			0
$313$	−218.086	+	377.735i	−0.696759	+	1.20682i	0.272825	+	0.962064i	$0.412042\pi$
$313$	−218.086	+	377.735i	−0.696759	+	1.20682i	−0.969584	+	0.244758i	$0.921291\pi$
$314$		0			0
$315$	40.8862	+	17.7812i	0.129797	+	0.0564483i
$316$		0			0
$317$	411.913	+	237.818i	1.29941	+	0.750215i	0.980302	−	0.197504i	$-0.0632834\pi$
$317$	411.913	+	237.818i	1.29941	+	0.750215i	0.319108	+	0.947718i	$0.396617\pi$
$318$		0			0
$319$			274.878i			0.861685i
$320$		0			0
$321$	85.9030	+	76.6767i	0.267611	+	0.238868i
$322$		0			0
$323$	−17.0688	+	6.47603i	−0.0528446	+	0.0200496i
$324$		0			0
$325$	−22.7908	−	13.1582i	−0.0701254	−	0.0404869i
$326$		0			0
$327$	−244.818	+	80.7195i	−0.748680	+	0.246849i
$328$		0			0
$329$	−93.1707			−0.283193
$330$		0			0
$331$	568.161	−	328.028i	1.71650	−	0.991020i	0.791392	−	0.611309i	$-0.209357\pi$
$331$	568.161	−	328.028i	1.71650	−	0.991020i	0.925105	−	0.379711i	$-0.123977\pi$
$332$		0			0
$333$	128.318	−	14.6109i	0.385339	−	0.0438765i
$334$		0			0
$335$	−11.9433	+	6.89545i	−0.0356515	+	0.0205834i
$336$		0			0
$337$	−530.839	+	306.480i	−1.57519	+	0.909437i	−0.579674	+	0.814849i	$0.696820\pi$
$337$	−530.839	+	306.480i	−1.57519	+	0.909437i	−0.995517	+	0.0945880i	$0.969847\pi$
$338$		0			0
$339$	38.7248	−	12.7680i	0.114232	−	0.0376638i
$340$		0			0
$341$		−	11.2099i		−	0.0328736i
$342$		0			0
$343$	115.970			0.338104
$344$		0			0
$345$	0.0124616	+	0.00259246i	3.61205e−5	+	7.51438e-6i
$346$		0			0
$347$	326.309	+	565.183i	0.940371	+	1.62877i	0.764765	+	0.644309i	$0.222855\pi$
$347$	326.309	+	565.183i	0.940371	+	1.62877i	0.175605	+	0.984461i	$0.443812\pi$
$348$		0			0
$349$	229.539	+	397.573i	0.657705	+	1.13918i	0.981208	+	0.192952i	$0.0618060\pi$
$349$	229.539	+	397.573i	0.657705	+	1.13918i	−0.323503	+	0.946227i	$0.604861\pi$
$350$		0			0
$351$	16.5966	−	23.4784i	0.0472838	−	0.0668901i
$352$		0			0
$353$	164.479	+	284.885i	0.465945	+	0.807040i	0.999244	−	0.0388866i	$-0.0123811\pi$
$353$	164.479	+	284.885i	0.465945	+	0.807040i	−0.533299	+	0.845927i	$0.679048\pi$
$354$		0			0
$355$		−	20.2913i		−	0.0571585i
$356$		0			0
$357$	17.7442	−	19.8793i	0.0497036	−	0.0556843i
$358$		0			0
$359$	202.408	−	350.581i	0.563810	−	0.976547i	−0.433349	−	0.901226i	$-0.642668\pi$
$359$	202.408	−	350.581i	0.563810	−	0.976547i	0.997159	−	0.0753214i	$-0.0239983\pi$
$360$		0			0
$361$	72.3069	+	353.684i	0.200296	+	0.979735i
$362$		0			0
$363$	−70.1879	−	212.876i	−0.193355	−	0.586436i
$364$		0			0
$365$	−18.9344			−0.0518749
$366$		0			0
$367$	44.6648	−	77.3616i	0.121702	−	0.210795i	−0.798737	−	0.601681i	$-0.794498\pi$
$367$	44.6648	−	77.3616i	0.121702	−	0.210795i	0.920439	+	0.390886i	$0.127831\pi$
$368$		0			0
$369$	262.683	+	355.047i	0.711877	+	0.962187i
$370$		0			0
$371$	−372.651	−	215.150i	−1.00445	−	0.579919i
$372$		0			0
$373$	−588.402	−	339.714i	−1.57749	−	0.910762i	−0.995209	−	0.0977720i	$-0.968828\pi$
$373$	−588.402	−	339.714i	−1.57749	−	0.910762i	−0.582277	−	0.812990i	$-0.697838\pi$
$374$		0			0
$375$	−53.2212	+	59.6251i	−0.141923	+	0.159000i
$376$		0			0
$377$	10.4617	−	18.1202i	0.0277498	−	0.0480641i
$378$		0			0
$379$			217.761i			0.574566i	0.957846	+	0.287283i	$0.0927521\pi$
$379$			217.761i			0.574566i	−0.957846	+	0.287283i	$0.907248\pi$
$380$		0			0
$381$	−18.8643	+	90.6776i	−0.0495125	+	0.237999i
$382$		0			0
$383$	38.3141	−	22.1206i	0.100037	−	0.0577562i	−0.449147	−	0.893458i	$-0.648272\pi$
$383$	38.3141	−	22.1206i	0.100037	−	0.0577562i	0.549184	+	0.835702i	$0.314939\pi$
$384$		0			0
$385$	−69.3047			−0.180012
$386$		0			0
$387$	15.4169	+	135.397i	0.0398371	+	0.349863i
$388$		0			0
$389$	170.829	−	295.884i	0.439148	−	0.760627i	−0.558476	−	0.829521i	$-0.688614\pi$
$389$	170.829	−	295.884i	0.439148	−	0.760627i	0.997624	+	0.0688935i	$0.0219469\pi$
$390$		0			0
$391$	0.00380359	−	0.00658801i	9.72784e−6	−	1.68491e-5i
$392$		0			0
$393$	184.866	+	38.4590i	0.470398	+	0.0978600i
$394$		0			0
$395$	−5.12515	+	2.95901i	−0.0129751	+	0.00749116i
$396$		0			0
$397$	282.279	−	488.921i	0.711029	−	1.23154i	−0.253442	−	0.967351i	$-0.581563\pi$
$397$	282.279	−	488.921i	0.711029	−	1.23154i	0.964471	−	0.264188i	$-0.0851041\pi$
$398$		0			0
$399$	−331.780	−	409.347i	−0.831529	−	1.02593i
$400$		0			0
$401$	418.441	−	241.587i	1.04349	−	0.602462i	0.122674	−	0.992447i	$-0.460853\pi$
$401$	418.441	−	241.587i	1.04349	−	0.602462i	0.920821	+	0.389985i	$0.127520\pi$
$402$		0			0
$403$	−0.426642	+	0.738966i	−0.00105867	+	0.00183366i
$404$		0			0
$405$	−29.5995	−	31.7505i	−0.0730852	−	0.0783962i
$406$		0			0
$407$	−173.854	+	100.375i	−0.427161	+	0.246621i
$408$		0			0
$409$			406.107i			0.992926i	0.868058	+	0.496463i	$0.165368\pi$
$409$			406.107i			0.992926i	−0.868058	+	0.496463i	$0.834632\pi$
$410$		0			0
$411$	−26.8803	−	81.5265i	−0.0654021	−	0.198361i
$412$		0			0
$413$	−605.510	−	349.591i	−1.46613	−	0.846468i
$414$		0			0
$415$	14.9659	−	25.9216i	0.0360623	−	0.0624617i
$416$		0			0
$417$	−460.813	+	516.261i	−1.10507	+	1.23804i
$418$		0			0
$419$	0.161839	−	0.280314i	0.000386251	−	0.000669006i	−0.865832	−	0.500334i	$-0.833210\pi$
$419$	0.161839	−	0.280314i	0.000386251	−	0.000669006i	0.866218	+	0.499665i	$0.166544\pi$
$420$		0			0
$421$		−	258.491i		−	0.613994i	−0.951711	−	0.306997i	$-0.900676\pi$
$421$		−	258.491i		−	0.613994i	0.951711	−	0.306997i	$-0.0993241\pi$
$422$		0			0
$423$	83.1836	+	36.1762i	0.196652	+	0.0855229i
$424$		0			0
$425$	11.8726	+	20.5639i	0.0279355	+	0.0483857i
$426$		0			0
$427$	109.456			0.256338
$428$		0			0
$429$	−9.10291	+	43.7563i	−0.0212189	+	0.101996i
$430$		0			0
$431$	−441.525	+	254.914i	−1.02442	+	0.591448i	−0.915381	−	0.402589i	$-0.868110\pi$
$431$	−441.525	+	254.914i	−1.02442	+	0.591448i	−0.109038	+	0.994038i	$0.534777\pi$
$432$		0			0
$433$	−470.841	+	271.840i	−1.08739	+	0.627807i	−0.932881	−	0.360184i	$-0.882714\pi$
$433$	−470.841	+	271.840i	−1.08739	+	0.627807i	−0.154512	+	0.987991i	$0.549381\pi$
$434$		0			0
$435$	−23.5661	−	21.0350i	−0.0541748	−	0.0483563i
$436$		0			0
$437$	−0.116534	−	0.0951204i	−0.000266669	−	0.000217667i
$438$		0			0
$439$		−	470.760i		−	1.07235i	−0.844108	−	0.536173i	$-0.819869\pi$
$439$		−	470.760i		−	1.07235i	0.844108	−	0.536173i	$-0.180131\pi$
$440$		0			0
$441$	300.872	+	130.848i	0.682250	+	0.296707i
$442$		0			0
$443$	−381.060	+	660.015i	−0.860180	+	1.48988i	0.0115747	+	0.999933i	$0.496316\pi$
$443$	−381.060	+	660.015i	−0.860180	+	1.48988i	−0.871755	+	0.489943i	$0.837018\pi$
$444$		0			0
$445$	−22.6459	−	13.0746i	−0.0508896	−	0.0293811i
$446$		0			0
$447$	187.305	+	38.9662i	0.419026	+	0.0871728i
$448$		0			0
$449$		−	289.909i		−	0.645677i	−0.946454	−	0.322839i	$-0.895363\pi$
$449$		−	289.909i		−	0.645677i	0.946454	−	0.322839i	$-0.104637\pi$
$450$		0			0
$451$	−594.547	−	343.262i	−1.31829	−	0.761113i
$452$		0			0
$453$	26.5668	−	127.703i	0.0586464	−	0.281904i
$454$		0			0
$455$	4.56863	+	2.63770i	0.0100409	+	0.00579714i
$456$		0			0
$457$	−132.709	−	229.859i	−0.290392	−	0.502974i	0.683510	−	0.729941i	$-0.260452\pi$
$457$	−132.709	−	229.859i	−0.290392	−	0.502974i	−0.973902	+	0.226967i	$0.927119\pi$
$458$		0			0
$459$	−23.5609	+	10.8587i	−0.0513309	+	0.0236574i
$460$		0			0
$461$	634.203			1.37571			0.687856	−	0.725847i	$-0.258552\pi$
$461$	634.203			1.37571			0.687856	+	0.725847i	$0.258552\pi$
$462$		0			0
$463$	−82.6718	+	143.192i	−0.178557	+	0.309270i	−0.941386	−	0.337330i	$-0.890476\pi$
$463$	−82.6718	+	143.192i	−0.178557	+	0.309270i	0.762830	+	0.646600i	$0.223810\pi$
$464$		0			0
$465$	0.961057	+	0.857836i	0.00206679	+	0.00184481i
$466$		0			0
$467$	537.427			1.15081			0.575404	−	0.817869i	$-0.304845\pi$
$467$	537.427			1.15081			0.575404	+	0.817869i	$0.304845\pi$
$468$		0			0
$469$	−206.020	+	118.946i	−0.439276	+	0.253616i
$470$		0			0
$471$	667.892	+	138.946i	1.41803	+	0.295002i
$472$		0			0
$473$	−105.912	−	183.446i	−0.223916	−	0.387834i
$474$		0			0
$475$	439.008	−	166.563i	0.924227	−	0.350659i
$476$		0			0
$477$	249.168	+	336.780i	0.522364	+	0.706038i
$478$		0			0
$479$	−423.639	+	733.764i	−0.884423	+	1.53187i	−0.0380494	+	0.999276i	$0.512114\pi$
$479$	−423.639	+	733.764i	−0.884423	+	1.53187i	−0.846374	+	0.532590i	$0.821219\pi$
$480$		0			0
$481$	15.2808			0.0317689
$482$		0			0
$483$	0.214961	+	0.0447198i	0.000445054	+	9.25876e-5i
$484$		0			0
$485$	−42.9550	+	24.8001i	−0.0885671	+	0.0511342i
$486$		0			0
$487$		−	235.616i		−	0.483811i	−0.970300	−	0.241906i	$-0.922228\pi$
$487$		−	235.616i		−	0.483811i	0.970300	−	0.241906i	$-0.0777724\pi$
$488$		0			0
$489$	−498.023	+	557.949i	−1.01845	+	1.14100i
$490$		0			0
$491$	77.5516	+	134.323i	0.157946	+	0.273571i	0.934128	−	0.356938i	$-0.116179\pi$
$491$	77.5516	+	134.323i	0.157946	+	0.273571i	−0.776182	+	0.630509i	$0.782846\pi$
$492$		0			0
$493$	−16.3497	+	9.43950i	−0.0331637	+	0.0191471i
$494$		0			0
$495$	61.8759	+	26.9095i	0.125002	+	0.0543627i
$496$		0			0
$497$		−	350.023i		−	0.704271i
$498$		0			0
$499$	322.388	+	558.392i	0.646067	+	1.11902i	0.984054	+	0.177871i	$0.0569209\pi$
$499$	322.388	+	558.392i	0.646067	+	1.11902i	−0.337986	+	0.941151i	$0.609746\pi$
$500$		0			0
$501$	−207.032	−	184.797i	−0.413239	−	0.368855i
$502$		0			0
$503$	101.398	+	175.626i	0.201586	+	0.349157i	0.949040	−	0.315157i	$-0.102057\pi$
$503$	101.398	+	175.626i	0.201586	+	0.349157i	−0.747454	+	0.664314i	$0.768724\pi$
$504$		0			0
$505$	24.7852			0.0490796
$506$		0			0
$507$	−335.350	+	375.701i	−0.661439	+	0.741028i
$508$		0			0
$509$			656.308i			1.28941i	0.764433	+	0.644703i	$0.223019\pi$
$509$			656.308i			1.28941i	−0.764433	+	0.644703i	$0.776981\pi$
$510$		0			0
$511$	−326.616			−0.639171
$512$		0			0
$513$	137.276	+	494.292i	0.267594	+	0.963532i
$514$		0			0
$515$		−	26.9622i		−	0.0523539i
$516$		0			0
$517$	−141.002			−0.272731
$518$		0			0
$519$	−742.661	−	662.897i	−1.43095	−	1.27726i
$520$		0			0
$521$			13.7431i			0.0263782i	0.999913	+	0.0131891i	$0.00419835\pi$
$521$			13.7431i			0.0263782i	−0.999913	+	0.0131891i	$0.995802\pi$
$522$		0			0
$523$	−288.630	+	166.640i	−0.551873	+	0.318624i	−0.749877	−	0.661577i	$-0.769887\pi$
$523$	−288.630	+	166.640i	−0.551873	+	0.318624i	0.198004	+	0.980201i	$0.436554\pi$
$524$		0			0
$525$	−456.379	+	511.294i	−0.869294	+	0.973893i
$526$		0			0
$527$	0.666763	−	0.384956i	0.00126521	−	0.000730467i
$528$		0			0
$529$	−529.000			−1.00000
$530$		0			0
$531$	404.866	+	547.225i	0.762460	+	1.03056i
$532$		0			0
$533$	26.1287	+	45.2563i	0.0490220	+	0.0849086i
$534$		0			0
$535$	17.8131	−	10.2844i	0.0332955	−	0.0192232i
$536$		0			0
$537$	509.154	+	454.469i	0.948145	+	0.846311i
$538$		0			0
$539$	−509.998			−0.946193
$540$		0			0
$541$	−222.076	−	384.647i	−0.410491	−	0.710992i	0.584452	−	0.811428i	$-0.301310\pi$
$541$	−222.076	−	384.647i	−0.410491	−	0.710992i	−0.994944	+	0.100436i	$0.967976\pi$
$542$		0			0
$543$	−141.250	+	678.966i	−0.260129	+	1.25040i
$544$		0			0
$545$			46.0482i			0.0844921i
$546$		0			0
$547$	758.065	+	437.669i	1.38586	+	0.800127i	0.992846	−	0.119406i	$-0.0380989\pi$
$547$	758.065	+	437.669i	1.38586	+	0.800127i	0.393014	+	0.919532i	$0.371432\pi$
$548$		0			0
$549$	−97.7235	−	42.4995i	−0.178003	−	0.0774125i
$550$		0			0
$551$	132.429	+	349.041i	0.240343	+	0.633468i
$552$		0			0
$553$	−88.4085	+	51.0427i	−0.159871	+	0.0923014i
$554$		0			0
$555$	4.69876	−	22.5862i	0.00846624	−	0.0406959i
$556$		0			0
$557$	120.708	+	209.073i	0.216712	+	0.375356i	0.953801	−	0.300440i	$-0.0971335\pi$
$557$	120.708	+	209.073i	0.216712	+	0.375356i	−0.737089	+	0.675796i	$0.763800\pi$
$558$		0			0
$559$			16.1239i			0.0288441i
$560$		0			0
$561$	26.8535	−	30.0847i	0.0478673	−	0.0536270i
$562$		0			0
$563$	505.472	+	291.834i	0.897818	+	0.518356i	0.876492	−	0.481417i	$-0.159878\pi$
$563$	505.472	+	291.834i	0.897818	+	0.518356i	0.0213265	+	0.999773i	$0.493211\pi$
$564$		0			0
$565$		−	7.28380i		−	0.0128917i
$566$		0			0
$567$	−510.589	−	547.693i	−0.900510	−	0.965949i
$568$		0			0
$569$	199.116	−	114.960i	0.349941	−	0.202038i	−0.314718	−	0.949185i	$-0.601910\pi$
$569$	199.116	−	114.960i	0.349941	−	0.202038i	0.664659	+	0.747147i	$0.268577\pi$
$570$		0			0
$571$	306.824	−	531.434i	0.537344	−	0.930708i	−0.461702	−	0.887035i	$-0.652761\pi$
$571$	306.824	−	531.434i	0.537344	−	0.930708i	0.999046	−	0.0436724i	$-0.0139058\pi$
$572$		0			0
$573$	−947.251	−	197.063i	−1.65314	−	0.343915i
$574$		0			0
$575$	−0.0978279	+	0.169443i	−0.000170135	+	0.000294683i
$576$		0			0
$577$	−810.681			−1.40499			−0.702496	−	0.711688i	$-0.747931\pi$
$577$	−810.681			−1.40499			−0.702496	+	0.711688i	$0.747931\pi$
$578$		0			0
$579$	−91.2430	+	438.591i	−0.157587	+	0.757497i
$580$		0			0
$581$	258.160	−	447.146i	0.444337	−	0.769615i
$582$		0			0
$583$	−563.958	−	325.601i	−0.967338	−	0.558493i
$584$		0			0
$585$	−3.05475	−	4.12886i	−0.00522180	−	0.00705788i
$586$		0			0
$587$	−238.581			−0.406441			−0.203221	−	0.979133i	$-0.565141\pi$
$587$	−238.581			−0.406441			−0.203221	+	0.979133i	$0.565141\pi$
$588$		0			0
$589$	−5.40063	−	14.2344i	−0.00916915	−	0.0241670i
$590$		0			0
$591$	513.042	−	574.775i	0.868091	−	0.972546i
$592$		0			0
$593$	45.5918	+	78.9674i	0.0768833	+	0.133166i	0.901904	−	0.431937i	$-0.142170\pi$
$593$	45.5918	+	78.9674i	0.0768833	+	0.133166i	−0.825020	+	0.565103i	$0.808836\pi$
$594$		0			0
$595$	−2.37997	−	4.12223i	−0.00399995	−	0.00692812i
$596$		0			0
$597$	−684.210	−	142.341i	−1.14608	−	0.238427i
$598$		0			0
$599$		−	1105.03i		−	1.84479i	−0.386243	−	0.922397i	$-0.626228\pi$
$599$		−	1105.03i		−	1.84479i	0.386243	−	0.922397i	$-0.373772\pi$
$600$		0			0
$601$	−289.710	+	167.264i	−0.482047	+	0.278310i	−0.721269	−	0.692655i	$-0.756441\pi$
$601$	−289.710	+	167.264i	−0.482047	+	0.278310i	0.239222	+	0.970965i	$0.423108\pi$
$602$		0			0
$603$	230.121	−	26.2027i	0.381627	−	0.0434539i
$604$		0			0
$605$	−40.0402			−0.0661821
$606$		0			0
$607$	−41.3985	−	23.9014i	−0.0682018	−	0.0393763i	0.465511	−	0.885042i	$-0.345870\pi$
$607$	−41.3985	−	23.9014i	−0.0682018	−	0.0393763i	−0.533713	+	0.845666i	$0.679204\pi$
$608$		0			0
$609$	−406.513	−	362.852i	−0.667509	−	0.595816i
$610$		0			0
$611$	9.29496	+	5.36645i	0.0152127	+	0.00878305i
$612$		0			0
$613$	311.159	−	538.943i	0.507600	−	0.879189i	−0.492361	−	0.870391i	$-0.663866\pi$
$613$	311.159	−	538.943i	0.507600	−	0.879189i	0.999961	−	0.00879813i	$-0.00280057\pi$
$614$		0			0
$615$	74.9265	−	24.7042i	0.121832	−	0.0401694i
$616$		0			0
$617$	853.954			1.38404			0.692021	−	0.721878i	$-0.256721\pi$
$617$	853.954			1.38404			0.692021	+	0.721878i	$0.256721\pi$
$618$		0			0
$619$	−20.6289	−	35.7303i	−0.0333261	−	0.0577225i	0.848881	−	0.528584i	$-0.177277\pi$
$619$	−20.6289	−	35.7303i	−0.0333261	−	0.0577225i	−0.882207	+	0.470861i	$0.843943\pi$
$620$		0			0
$621$	−0.174556	−	0.123391i	−0.000281088	−	0.000198697i
$622$		0			0
$623$	−390.640	−	225.536i	−0.627030	−	0.362016i
$624$		0			0
$625$	−301.772	−	522.684i	−0.482835	−	0.836295i
$626$		0			0
$627$	−502.106	−	619.493i	−0.800807	−	0.988027i
$628$		0			0
$629$	−11.9406	−	6.89389i	−0.0189834	−	0.0109601i
$630$		0			0
$631$	165.135	+	286.023i	0.261704	+	0.453285i	0.966695	−	0.255932i	$-0.0823822\pi$
$631$	165.135	+	286.023i	0.261704	+	0.453285i	−0.704991	+	0.709216i	$0.749049\pi$
$632$		0			0
$633$	−101.444	+	487.625i	−0.160259	+	0.770339i
$634$		0			0
$635$	14.3282	+	8.27237i	0.0225640	+	0.0130274i
$636$		0			0
$637$	33.6195	+	19.4102i	0.0527779	+	0.0304713i
$638$		0			0
$639$	−135.906	+	312.504i	−0.212686	+	0.489051i
$640$		0			0
$641$		−	898.961i		−	1.40243i	−0.712948	−	0.701217i	$-0.752640\pi$
$641$		−	898.961i		−	1.40243i	0.712948	−	0.701217i	$-0.247360\pi$
$642$		0			0
$643$	155.442	+	269.234i	0.241745	+	0.418715i	0.961211	−	0.275812i	$-0.0889469\pi$
$643$	155.442	+	269.234i	0.241745	+	0.418715i	−0.719466	+	0.694527i	$0.755614\pi$
$644$		0			0
$645$	23.8323	+	4.95798i	0.0369492	+	0.00768680i
$646$		0			0
$647$	660.424			1.02075			0.510374	−	0.859953i	$-0.329507\pi$
$647$	660.424			1.02075			0.510374	+	0.859953i	$0.329507\pi$
$648$		0			0
$649$	−916.361	−	529.061i	−1.41196	−	0.815194i
$650$		0			0
$651$	16.5782	+	14.7976i	0.0254657	+	0.0227306i
$652$		0			0
$653$	348.598	−	603.789i	0.533840	−	0.924639i	−0.465378	−	0.885112i	$-0.654082\pi$
$653$	348.598	−	603.789i	0.533840	−	0.924639i	0.999219	−	0.0395267i	$-0.0125850\pi$
$654$		0			0
$655$	16.8651	−	29.2111i	0.0257482	−	0.0445971i
$656$		0			0
$657$	291.606	+	126.818i	0.443845	+	0.193026i
$658$		0			0
$659$	−836.364	−	482.875i	−1.26914	−	0.732739i	−0.294316	−	0.955708i	$-0.595092\pi$
$659$	−836.364	−	482.875i	−1.26914	−	0.732739i	−0.974825	+	0.222969i	$0.928425\pi$
$660$		0			0
$661$			840.507i			1.27157i	0.771867	+	0.635785i	$0.219323\pi$
$661$			840.507i			1.27157i	−0.771867	+	0.635785i	$0.780677\pi$
$662$		0			0
$663$	−2.91522	+	0.961182i	−0.00439701	+	0.00144975i
$664$		0			0
$665$	−88.0034	+	33.3892i	−0.132336	+	0.0502093i
$666$		0			0
$667$	−0.134718	−	0.0777797i	−0.000201977	−	0.000116611i
$668$		0			0
$669$	69.1472	+	61.7205i	0.103359	+	0.0922579i
$670$		0			0
$671$	165.648			0.246867
$672$		0			0
$673$	−110.214	+	63.6319i	−0.163765	+	0.0945497i	−0.579642	−	0.814871i	$-0.696808\pi$
$673$	−110.214	+	63.6319i	−0.163765	+	0.0945497i	0.415878	+	0.909421i	$0.363474\pi$
$674$		0			0
$675$	605.984	−	279.286i	0.897754	−	0.413756i
$676$		0			0
$677$	551.101	−	318.178i	0.814034	−	0.469983i	−0.0343210	−	0.999411i	$-0.510927\pi$
$677$	551.101	−	318.178i	0.814034	−	0.469983i	0.848355	+	0.529428i	$0.177594\pi$
$678$		0			0
$679$	−740.971	+	427.800i	−1.09127	+	0.630044i
$680$		0			0
$681$	91.9938	−	442.200i	0.135086	−	0.649339i
$682$		0			0
$683$			398.771i			0.583852i	0.956441	+	0.291926i	$0.0942961\pi$
$683$			398.771i			0.583852i	−0.956441	+	0.291926i	$0.905704\pi$
$684$		0			0
$685$	−15.3344			−0.0223860
$686$		0			0
$687$	383.285	+	1162.49i	0.557912	+	1.69212i
$688$		0			0
$689$	24.7844	+	42.9279i	0.0359716	+	0.0623046i
$690$		0			0
$691$	24.2134	+	41.9389i	0.0350411	+	0.0606930i	0.883014	−	0.469346i	$-0.155510\pi$
$691$	24.2134	+	41.9389i	0.0350411	+	0.0606930i	−0.847973	+	0.530039i	$0.822177\pi$
$692$		0			0
$693$	1067.35	+	464.188i	1.54019	+	0.669824i
$694$		0			0
$695$	61.8074	+	107.053i	0.0889314	+	0.154034i
$696$		0			0
$697$		−	47.1515i		−	0.0676491i
$698$		0			0
$699$	231.167	+	701.119i	0.330711	+	1.00303i
$700$		0			0
$701$	211.773	−	366.802i	0.302102	−	0.523255i	−0.674510	−	0.738266i	$-0.735645\pi$
$701$	211.773	−	366.802i	0.302102	−	0.523255i	0.976612	+	0.215010i	$0.0689785\pi$
$702$		0			0
$703$	−172.403	+	211.215i	−0.245239	+	0.300448i
$704$		0			0
$705$	10.7901	−	12.0885i	0.0153052	−	0.0171468i
$706$		0			0
$707$	427.543			0.604728
$708$		0			0
$709$	347.889	−	602.561i	0.490675	−	0.849874i	−0.509267	−	0.860608i	$-0.670083\pi$
$709$	347.889	−	602.561i	0.490675	−	0.849874i	0.999942	+	0.0107341i	$0.00341683\pi$
$710$		0			0
$711$	98.7508	−	11.2442i	0.138890	−	0.0158147i
$712$		0			0
$713$	0.00549401	+	0.00317197i	7.70548e−6	+	4.44876e-6i
$714$		0			0
$715$	6.91402	+	3.99181i	0.00966996	+	0.00558296i
$716$		0			0
$717$	102.681	+	311.425i	0.143209	+	0.434345i
$718$		0			0
$719$	421.427	−	729.933i	0.586129	−	1.01521i	−0.408604	−	0.912712i	$-0.633984\pi$
$719$	421.427	−	729.933i	0.586129	−	1.01521i	0.994734	−	0.102494i	$-0.0326823\pi$
$720$		0			0
$721$		−	465.097i		−	0.645072i
$722$		0			0
$723$	953.305	−	314.316i	1.31854	−	0.434738i
$724$		0			0
$725$	420.512	−	242.783i	0.580017	−	0.334873i
$726$		0			0
$727$	123.208			0.169475			0.0847375	−	0.996403i	$-0.472995\pi$
$727$	123.208			0.169475			0.0847375	+	0.996403i	$0.472995\pi$
$728$		0			0
$729$	243.201	+	687.237i	0.333609	+	0.942711i
$730$		0			0
$731$	7.27421	−	12.5993i	0.00995105	−	0.0172357i
$732$		0			0
$733$	−228.457	+	395.698i	−0.311673	+	0.539834i	−0.978725	−	0.205178i	$-0.934223\pi$
$733$	−228.457	+	395.698i	−0.311673	+	0.539834i	0.667051	+	0.745012i	$0.267556\pi$
$734$		0			0
$735$	39.0275	−	43.7236i	0.0530987	−	0.0594879i
$736$		0			0
$737$	−311.785	+	180.009i	−0.423046	+	0.244246i
$738$		0			0
$739$	−393.400	+	681.389i	−0.532341	+	0.922042i	0.466946	+	0.884286i	$0.345354\pi$
$739$	−393.400	+	681.389i	−0.532341	+	0.922042i	−0.999287	+	0.0377559i	$0.987979\pi$
$740$		0			0
$741$	9.52170	+	59.9474i	0.0128498	+	0.0809007i
$742$		0			0
$743$	1006.42	−	581.060i	1.35454	−	0.782045i	0.365660	−	0.930748i	$-0.380843\pi$
$743$	1006.42	−	581.060i	1.35454	−	0.782045i	0.988882	+	0.148703i	$0.0475098\pi$
$744$		0			0
$745$	17.0875	−	29.5964i	0.0229362	−	0.0397267i
$746$		0			0
$747$	−404.105	+	298.978i	−0.540971	+	0.400239i
$748$		0			0
$749$	307.275	−	177.405i	0.410247	−	0.236856i
$750$		0			0
$751$		−	575.775i		−	0.766678i	−0.923608	−	0.383339i	$-0.874774\pi$
$751$		−	575.775i		−	0.766678i	0.923608	−	0.383339i	$-0.125226\pi$
$752$		0			0
$753$	153.530	+	31.9399i	0.203891	+	0.0424169i
$754$		0			0
$755$	−20.1786	−	11.6501i	−0.0267266	−	0.0154306i
$756$		0			0
$757$	567.480	−	982.905i	0.749644	−	1.29842i	−0.198350	−	0.980131i	$-0.563558\pi$
$757$	567.480	−	982.905i	0.749644	−	1.29842i	0.947993	−	0.318290i	$-0.103109\pi$
$758$		0			0
$759$	0.325316	+	0.0676776i	0.000428611	+	8.91668e-5i
$760$		0			0
$761$	354.912	−	614.725i	0.466375	−	0.807786i	−0.532887	−	0.846186i	$-0.678893\pi$
$761$	354.912	−	614.725i	0.466375	−	0.807786i	0.999262	+	0.0384004i	$0.0122262\pi$
$762$		0			0
$763$			794.328i			1.04106i
$764$		0			0
$765$	0.524287	+	4.60446i	0.000685342	+	0.00601891i
$766$		0			0
$767$	40.2715	+	69.7523i	0.0525053	+	0.0909418i
$768$		0			0
$769$	534.659			0.695265			0.347633	−	0.937631i	$-0.386986\pi$
$769$	534.659			0.695265			0.347633	+	0.937631i	$0.386986\pi$
$770$		0			0
$771$	551.438	+	492.212i	0.715225	+	0.638407i
$772$		0			0
$773$	852.244	−	492.043i	1.10251	−	0.636537i	0.165634	−	0.986187i	$-0.447033\pi$
$773$	852.244	−	492.043i	1.10251	−	0.636537i	0.936880	+	0.349650i	$0.113699\pi$
$774$		0			0
$775$	−17.1491	+	9.90103i	−0.0221279	+	0.0127755i
$776$		0			0
$777$	81.0533	−	389.611i	0.104316	−	0.501429i
$778$		0			0
$779$	−920.333	−	149.438i	−1.18143	−	0.191833i
$780$		0			0
$781$		−	529.714i		−	0.678251i
$782$		0			0
$783$	222.051	+	481.798i	0.283590	+	0.615323i
$784$		0			0
$785$	60.9307	−	105.535i	0.0776188	−	0.134440i
$786$		0			0
$787$	−875.354	−	505.386i	−1.11227	−	0.642168i	−0.172852	−	0.984948i	$-0.555298\pi$
$787$	−875.354	−	505.386i	−1.11227	−	0.642168i	−0.939416	+	0.342780i	$0.888631\pi$
$788$		0			0
$789$	886.832	−	993.541i	1.12399	−	1.25924i
$790$		0			0
$791$		−	125.645i		−	0.158843i
$792$		0			0
$793$	−10.9196	−	6.30446i	−0.0137700	−	0.00795013i
$794$		0			0
$795$	71.0716	−	23.4331i	0.0893982	−	0.0294757i
$796$		0			0
$797$	1001.95	+	578.475i	1.25715	+	0.725816i	0.972519	−	0.232822i	$-0.0747959\pi$
$797$	1001.95	+	578.475i	1.25715	+	0.725816i	0.284630	+	0.958637i	$0.408129\pi$
$798$		0			0
$799$	−4.84210	−	8.38676i	−0.00606020	−	0.0104966i
$800$		0			0
$801$	261.196	+	353.038i	0.326087	+	0.440746i
$802$		0			0
$803$	−494.291			−0.615556
$804$		0			0
$805$	0.0196105	−	0.0339665i	2.43609e−5	−	4.21944e-5i
$806$		0			0
$807$	390.288	−	128.682i	0.483628	−	0.159458i
$808$		0			0
$809$	−151.961			−0.187838			−0.0939189	−	0.995580i	$-0.529939\pi$
$809$	−151.961			−0.187838			−0.0939189	+	0.995580i	$0.529939\pi$
$810$		0			0
$811$	−114.939	+	66.3602i	−0.141725	+	0.0818251i	−0.569186	−	0.822209i	$-0.692742\pi$
$811$	−114.939	+	66.3602i	−0.141725	+	0.0818251i	0.427461	+	0.904034i	$0.359408\pi$
$812$		0			0
$813$	47.1686	+	143.060i	0.0580179	+	0.175966i
$814$		0			0
$815$	66.7983	+	115.698i	0.0819611	+	0.141961i
$816$		0			0
$817$	−222.867	−	181.914i	−0.272787	−	0.222661i
$818$		0			0
$819$	−52.6943	−	71.2226i	−0.0643398	−	0.0869629i
$820$		0			0
$821$	214.022	−	370.697i	0.260685	−	0.451519i	−0.705739	−	0.708472i	$-0.749385\pi$
$821$	214.022	−	370.697i	0.260685	−	0.451519i	0.966424	+	0.256952i	$0.0827184\pi$
$822$		0			0
$823$	656.648			0.797871			0.398936	−	0.916979i	$-0.369380\pi$
$823$	656.648			0.797871			0.398936	+	0.916979i	$0.369380\pi$
$824$		0			0
$825$	−690.671	+	773.777i	−0.837177	+	0.937911i
$826$		0			0
$827$	643.114	−	371.302i	0.777647	−	0.448975i	−0.0579487	−	0.998320i	$-0.518456\pi$
$827$	643.114	−	371.302i	0.777647	−	0.448975i	0.835596	+	0.549345i	$0.185123\pi$
$828$		0			0
$829$		−	1614.02i		−	1.94695i	−0.228797	−	0.973474i	$-0.573479\pi$
$829$		−	1614.02i		−	1.94695i	0.228797	−	0.973474i	$-0.426521\pi$
$830$		0			0
$831$	−496.955	−	103.385i	−0.598020	−	0.124410i
$832$		0			0
$833$	−17.5137	−	30.3346i	−0.0210248	−	0.0364161i
$834$		0			0
$835$	−42.9309	+	24.7862i	−0.0514143	+	0.0296840i
$836$		0			0
$837$	−9.05554	−	19.6484i	−0.0108190	−	0.0234748i
$838$		0			0
$839$			681.396i			0.812152i	0.913839	+	0.406076i	$0.133103\pi$
$839$			681.396i			0.812152i	−0.913839	+	0.406076i	$0.866897\pi$
$840$		0			0
$841$	−227.471	−	393.992i	−0.270477	−	0.468480i
$842$		0			0
$843$	778.246	−	256.597i	0.923187	−	0.304386i
$844$		0			0
$845$	44.9794	+	77.9066i	0.0532301	+	0.0921972i
$846$		0			0
$847$	−690.691			−0.815455
$848$		0			0
$849$	−467.159	−	97.1863i	−0.550247	−	0.114471i
$850$		0			0
$851$		−	0.113609i		−	0.000133500i
$852$		0			0
$853$	−272.024			−0.318902			−0.159451	−	0.987206i	$-0.550972\pi$
$853$	−272.024			−0.318902			−0.159451	+	0.987206i	$0.550972\pi$
$854$		0			0
$855$	91.5345	+	4.35967i	0.107058	+	0.00509903i
$856$		0			0
$857$			814.261i			0.950130i	0.879951	+	0.475065i	$0.157575\pi$
$857$			814.261i			0.950130i	−0.879951	+	0.475065i	$0.842425\pi$
$858$		0			0
$859$	736.669			0.857590			0.428795	−	0.903402i	$-0.358938\pi$
$859$	736.669			0.857590			0.428795	+	0.903402i	$0.358938\pi$
$860$		0			0
$861$	1292.48	−	426.145i	1.50113	−	0.494942i
$862$		0			0
$863$			382.719i			0.443475i	0.975106	+	0.221738i	$0.0711729\pi$
$863$			382.719i			0.443475i	−0.975106	+	0.221738i	$0.928827\pi$
$864$		0			0
$865$	−154.001	+	88.9123i	−0.178035	+	0.102789i
$866$		0			0
$867$	−846.115	−	176.023i	−0.975911	−	0.203025i
$868$		0			0
$869$	−133.795	+	77.2465i	−0.153964	+	0.0888912i
$870$		0			0
$871$	27.4042			0.0314629
$872$		0			0
$873$	827.652	−	94.2405i	0.948055	−	0.107950i
$874$		0			0
$875$	123.137	+	213.279i	0.140728	+	0.243747i
$876$		0			0
$877$	201.266	−	116.201i	0.229494	−	0.132499i	−0.380845	−	0.924639i	$-0.624367\pi$
$877$	201.266	−	116.201i	0.229494	−	0.132499i	0.610339	+	0.792141i	$0.291033\pi$
$878$		0			0
$879$	−392.077	+	129.273i	−0.446049	+	0.147068i
$880$		0			0
$881$	−1435.66			−1.62958			−0.814792	−	0.579753i	$-0.803149\pi$
$881$	−1435.66			−1.62958			−0.814792	+	0.579753i	$0.803149\pi$
$882$		0			0
$883$	528.038	+	914.589i	0.598005	+	1.03577i	0.993115	+	0.117141i	$0.0373729\pi$
$883$	528.038	+	914.589i	0.598005	+	1.03577i	−0.395111	+	0.918634i	$0.629294\pi$
$884$		0			0
$885$	115.482	−	38.0759i	0.130488	−	0.0430236i
$886$		0			0
$887$		−	822.586i		−	0.927380i	−0.885998	−	0.463690i	$-0.846525\pi$
$887$		−	822.586i		−	0.927380i	0.885998	−	0.463690i	$-0.153475\pi$
$888$		0			0
$889$	247.160	+	142.698i	0.278020	+	0.160515i
$890$		0			0
$891$	−772.710	−	828.863i	−0.867240	−	0.930261i
$892$		0			0
$893$	−179.044	+	67.9309i	−0.200498	+	0.0760704i
$894$		0			0
$895$	105.580	−	60.9565i	0.117966	−	0.0681078i
$896$		0			0
$897$	−0.0188693	−	0.0168427i	−2.10360e−5	−	1.87767e-5i
$898$		0			0
$899$	−7.87198	−	13.6347i	−0.00875638	−	0.0151665i
$900$		0			0
$901$		−	44.7256i		−	0.0496399i
$902$		0			0
$903$	411.105	+	85.5249i	0.455265	+	0.0947119i
$904$		0			0
$905$	107.285	+	61.9409i	0.118547	+	0.0684430i
$906$		0			0
$907$		−	639.860i		−	0.705468i	−0.935724	−	0.352734i	$-0.885252\pi$
$907$		−	639.860i		−	0.705468i	0.935724	−	0.352734i	$-0.114748\pi$
$908$		0			0
$909$	−381.714	−	166.006i	−0.419928	−	0.182625i
$910$		0			0
$911$	1036.07	−	598.173i	1.13728	−	0.656612i	0.191528	−	0.981487i	$-0.438656\pi$
$911$	1036.07	−	598.173i	1.13728	−	0.656612i	0.945757	+	0.324875i	$0.105322\pi$
$912$		0			0
$913$	390.692	−	676.698i	0.427921	−	0.741181i
$914$		0			0
$915$	−12.6762	+	14.2014i	−0.0138537	+	0.0155207i
$916$		0			0
$917$	290.921	−	503.890i	0.317253	−	0.549498i
$918$		0			0
$919$	680.689			0.740685			0.370342	−	0.928895i	$-0.379240\pi$
$919$	680.689			0.740685			0.370342	+	0.928895i	$0.379240\pi$
$920$		0			0
$921$	372.922	−	122.957i	0.404910	−	0.133504i
$922$		0			0
$923$	−20.1606	+	34.9192i	−0.0218425	+	0.0378323i
$924$		0			0
$925$	307.110	+	177.310i	0.332011	+	0.191687i
$926$		0			0
$927$	−180.587	+	415.243i	−0.194808	+	0.447943i
$928$		0			0
$929$	−1074.38			−1.15649			−0.578247	−	0.815862i	$-0.696263\pi$
$929$	−1074.38			−1.15649			−0.578247	+	0.815862i	$0.696263\pi$
$930$		0			0
$931$	−647.597	+	245.703i	−0.695593	+	0.263914i
$932$		0			0
$933$	175.631	+	532.679i	0.188243	+	0.570932i
$934$		0			0
$935$	−3.60178	−	6.23847i	−0.00385217	−	0.00667216i
$936$		0			0
$937$	−235.778	−	408.380i	−0.251631	−	0.435838i	0.712344	−	0.701830i	$-0.247634\pi$
$937$	−235.778	−	408.380i	−0.251631	−	0.435838i	−0.963975	+	0.265993i	$0.914300\pi$
$938$		0			0
$939$	−409.736	−	1242.71i	−0.436353	−	1.32344i
$940$		0			0
$941$		−	1274.97i		−	1.35491i	−0.735566	−	0.677453i	$-0.763084\pi$
$941$		−	1274.97i		−	1.35491i	0.735566	−	0.677453i	$-0.236916\pi$
$942$		0			0
$943$	0.336468	−	0.194260i	0.000356806	−	0.000206002i
$944$		0			0
$945$	−121.475	+	55.9855i	−0.128545	+	0.0592439i
$946$		0			0
$947$	−1201.32			−1.26855			−0.634276	−	0.773106i	$-0.718702\pi$
$947$	−1201.32			−1.26855			−0.634276	+	0.773106i	$0.718702\pi$
$948$		0			0
$949$	32.5841	+	18.8125i	0.0343352	+	0.0198234i
$950$		0			0
$951$	−1355.15	+	446.809i	−1.42497	+	0.469830i
$952$		0			0
$953$	543.763	+	313.941i	0.570580	+	0.329424i	0.757381	−	0.652973i	$-0.226479\pi$
$953$	543.763	+	313.941i	0.570580	+	0.329424i	−0.186801	+	0.982398i	$0.559812\pi$
$954$		0			0
$955$	−86.4162	+	149.677i	−0.0904882	+	0.156730i
$956$		0			0
$957$	−615.204	−	549.129i	−0.642847	−	0.573803i
$958$		0			0
$959$	−264.518			−0.275827
$960$		0			0
$961$	−480.179	−	831.694i	−0.499666	−	0.865447i
$962$		0			0
$963$	−343.221	+	39.0808i	−0.356408	+	0.0405823i
$964$		0			0
$965$	69.3027	+	40.0119i	0.0718163	+	0.0414631i
$966$		0			0
$967$	−37.0438	−	64.1617i	−0.0383079	−	0.0663513i	0.846236	−	0.532809i	$-0.178863\pi$
$967$	−37.0438	−	64.1617i	−0.0383079	−	0.0663513i	−0.884544	+	0.466457i	$0.845530\pi$
$968$		0			0
$969$	19.6047	−	51.1390i	0.0202319	−	0.0527751i
$970$		0			0
$971$	−445.572	−	257.251i	−0.458879	−	0.264934i	0.252694	−	0.967546i	$-0.418684\pi$
$971$	−445.572	−	257.251i	−0.458879	−	0.264934i	−0.711573	+	0.702612i	$0.752017\pi$
$972$		0			0
$973$	1066.17	+	1846.67i	1.09576	+	1.89791i
$974$		0			0
$975$	74.9791	−	24.7215i	0.0769017	−	0.0253554i
$976$		0			0
$977$	1392.45	+	803.933i	1.42523	+	0.822859i	0.996740	−	0.0806858i	$-0.0257110\pi$
$977$	1392.45	+	803.933i	1.42523	+	0.822859i	0.428494	+	0.903545i	$0.359044\pi$
$978$		0			0
$979$	−591.183	−	341.319i	−0.603864	−	0.348641i
$980$		0			0
$981$	308.421	−	709.183i	0.314394	−	0.722919i
$982$		0			0
$983$			1337.82i			1.36096i	0.732768	+	0.680478i	$0.238228\pi$
$983$			1337.82i			1.36096i	−0.732768	+	0.680478i	$0.761772\pi$
$984$		0			0
$985$	−68.8127	−	119.187i	−0.0698606	−	0.121002i
$986$		0			0
$987$	186.129	−	208.525i	0.188581	−	0.211272i
$988$		0			0
$989$	0.119876			0.000121210
$990$		0			0
$991$	−476.228	−	274.950i	−0.480553	−	0.277447i	0.240094	−	0.970750i	$-0.422822\pi$
$991$	−476.228	−	274.950i	−0.480553	−	0.277447i	−0.720647	+	0.693302i	$0.756155\pi$
$992$		0			0
$993$	−400.868	+	1926.91i	−0.403694	+	1.94049i
$994$		0			0
$995$	−62.4194	+	108.114i	−0.0627331	+	0.108657i
$996$		0			0
$997$	781.574	−	1353.73i	0.783925	−	1.35780i	−0.145714	−	0.989327i	$-0.546548\pi$
$997$	781.574	−	1353.73i	0.783925	−	1.35780i	0.929639	−	0.368472i	$-0.120119\pi$
$998$		0			0
$999$	−223.643	+	316.377i	−0.223867	+	0.316694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.12	✓	80
3.2	odd	2		2052.3.s.a.901.19		80
9.2	odd	6		2052.3.bl.a.1585.22		80
9.7	even	3		684.3.bl.a.673.24	yes	80
19.12	odd	6		684.3.bl.a.373.24	yes	80
57.50	even	6		2052.3.bl.a.145.22		80
171.88	odd	6	inner	684.3.s.a.601.12	yes	80
171.164	even	6		2052.3.s.a.829.19		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.12	✓	80	1.1	even	1	trivial
684.3.s.a.601.12	yes	80	171.88	odd	6	inner
684.3.bl.a.373.24	yes	80	19.12	odd	6
684.3.bl.a.673.24	yes	80	9.7	even	3
2052.3.s.a.829.19		80	171.164	even	6
2052.3.s.a.901.19		80	3.2	odd	2
2052.3.bl.a.145.22		80	57.50	even	6
2052.3.bl.a.1585.22		80	9.2	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99772 + 2.23810i) q^{3} +(0.267948 + 0.464100i) q^{5} +(4.62209 + 8.00569i) q^{7} +(-1.01820 - 8.94222i) q^{9} +O(q^{10})\)	\(q+(-1.99772 + 2.23810i) q^{3} +(0.267948 + 0.464100i) q^{5} +(4.62209 + 8.00569i) q^{7} +(-1.01820 - 8.94222i) q^{9} +(6.99493 + 12.1156i) q^{11} -1.06489i q^{13} +(-1.57399 - 0.327448i) q^{15} +(-0.480422 + 0.832115i) q^{17} +(14.7192 + 12.0144i) q^{19} +(-27.1512 - 5.64845i) q^{21} -0.00791718 q^{23} +(12.3564 - 21.4019i) q^{25} +(22.0477 + 15.5852i) q^{27} +(17.0160 + 9.82417i) q^{29} +(-0.693935 - 0.400644i) q^{31} +(-41.0898 - 8.54820i) q^{33} +(-2.47696 + 4.29022i) q^{35} +14.3497i q^{37} +(2.38334 + 2.12736i) q^{39} +(-42.4984 + 24.5365i) q^{41} -15.1413 q^{43} +(3.87726 - 2.86860i) q^{45} +(-5.03942 + 8.72854i) q^{47} +(-18.2274 + 31.5708i) q^{49} +(-0.902609 - 2.73757i) q^{51} +(-40.3119 + 23.2741i) q^{53} +(-3.74856 + 6.49269i) q^{55} +(-56.2943 + 8.94146i) q^{57} +(-65.5017 + 37.8175i) q^{59} +(5.92027 - 10.2542i) q^{61} +(66.8824 - 49.4832i) q^{63} +(0.494217 - 0.285336i) q^{65} +25.7342i q^{67} +(0.0158163 - 0.0177195i) q^{69} +(-32.7913 - 18.9321i) q^{71} +(-17.6661 + 30.5985i) q^{73} +(23.2150 + 70.4100i) q^{75} +(-64.6624 + 111.999i) q^{77} +11.0432i q^{79} +(-78.9265 + 18.2100i) q^{81} +(-27.9268 - 48.3706i) q^{83} -0.514913 q^{85} +(-55.9807 + 18.4575i) q^{87} +(-42.2579 + 24.3976i) q^{89} +(8.52520 - 4.92203i) q^{91} +(2.28297 - 0.752723i) q^{93} +(-1.63193 + 10.0504i) q^{95} +92.5556i q^{97} +(101.218 - 74.8863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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