LMFDB - Embedded newform 684.3.m.a.653.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(353,684)]

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, 1, 4]))

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

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.m (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			653.8
Character	$\chi$	$=$	684.653
Dual form			684.3.m.a.353.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.55262 + 1.57611i) q^{3} -9.08186i q^{5} +(3.71777 + 6.43936i) q^{7} +(4.03172 - 8.04644i) q^{9} +O(q^{10})$	\(q+(-2.55262 + 1.57611i) q^{3} -9.08186i q^{5} +(3.71777 + 6.43936i) q^{7} +(4.03172 - 8.04644i) q^{9} +(-3.75893 + 2.17022i) q^{11} +(5.81239 + 10.0674i) q^{13} +(14.3141 + 23.1825i) q^{15} +(18.6676 - 10.7777i) q^{17} +(-9.10009 + 16.6790i) q^{19} +(-19.6392 - 10.5776i) q^{21} +(-3.34831 + 1.93315i) q^{23} -57.4802 q^{25} +(2.39066 + 26.8940i) q^{27} -50.7205i q^{29} +(17.5657 - 30.4248i) q^{31} +(6.17460 - 11.4642i) q^{33} +(58.4814 - 33.7642i) q^{35} +22.6583 q^{37} +(-30.7041 - 16.5371i) q^{39} -39.2048i q^{41} +(3.94146 - 6.82682i) q^{43} +(-73.0766 - 36.6156i) q^{45} +66.6664i q^{47} +(-3.14360 + 5.44487i) q^{49} +(-30.6643 + 56.9337i) q^{51} +(10.7574 + 6.21080i) q^{53} +(19.7096 + 34.1381i) q^{55} +(-3.05893 - 56.9179i) q^{57} -113.530i q^{59} +100.522 q^{61} +(66.8030 - 3.95306i) q^{63} +(91.4303 - 52.7873i) q^{65} +(-36.7385 - 63.6330i) q^{67} +(5.50009 - 10.2119i) q^{69} +(-2.86289 + 1.65289i) q^{71} +(17.9246 + 31.0463i) q^{73} +(146.725 - 90.5953i) q^{75} +(-27.9496 - 16.1367i) q^{77} +(63.5801 - 110.124i) q^{79} +(-48.4904 - 64.8821i) q^{81} +(-76.8076 + 44.3449i) q^{83} +(-97.8819 - 169.536i) q^{85} +(79.9413 + 129.470i) q^{87} +(78.4512 + 45.2938i) q^{89} +(-43.2183 + 74.8562i) q^{91} +(3.11427 + 105.348i) q^{93} +(151.476 + 82.6457i) q^{95} +(29.8352 - 51.6761i) q^{97} +(2.30757 + 38.9957i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	−2.55262	+	1.57611i	−0.850873	+	0.525372i
$3$	−2.55262	+	1.57611i	−0.850873	+	0.525372i
$4$		0			0
$5$		−	9.08186i		−	1.81637i	−0.418567	−	0.908186i	$-0.637468\pi$
$5$		−	9.08186i		−	1.81637i	0.418567	−	0.908186i	$-0.362532\pi$
$6$		0			0
$7$	3.71777	+	6.43936i	0.531110	+	0.919909i	0.999341	+	0.0363030i	$0.0115581\pi$
$7$	3.71777	+	6.43936i	0.531110	+	0.919909i	−0.468231	+	0.883606i	$0.655109\pi$
$8$		0			0
$9$	4.03172	−	8.04644i	0.447969	−	0.894049i
$10$		0			0
$11$	−3.75893	+	2.17022i	−0.341721	+	0.197293i	−0.661033	−	0.750357i	$-0.729882\pi$
$11$	−3.75893	+	2.17022i	−0.341721	+	0.197293i	0.319312	+	0.947650i	$0.396548\pi$
$12$		0			0
$13$	5.81239	+	10.0674i	0.447107	+	0.774412i	0.998196	−	0.0600340i	$-0.0191209\pi$
$13$	5.81239	+	10.0674i	0.447107	+	0.774412i	−0.551089	+	0.834446i	$0.685788\pi$
$14$		0			0
$15$	14.3141	+	23.1825i	0.954270	+	1.54550i
$16$		0			0
$17$	18.6676	−	10.7777i	1.09809	−	0.633985i	0.162374	−	0.986729i	$-0.448085\pi$
$17$	18.6676	−	10.7777i	1.09809	−	0.633985i	0.935720	+	0.352745i	$0.114752\pi$
$18$		0			0
$19$	−9.10009	+	16.6790i	−0.478952	+	0.877841i
$19$	−9.10009	+	16.6790i	−0.478952	+	0.877841i
$20$		0			0
$21$	−19.6392	−	10.5776i	−0.935201	−	0.503696i
$22$		0			0
$23$	−3.34831	+	1.93315i	−0.145579	+	0.0840498i	−0.571020	−	0.820936i	$-0.693452\pi$
$23$	−3.34831	+	1.93315i	−0.145579	+	0.0840498i	0.425441	+	0.904986i	$0.360119\pi$
$24$		0			0
$25$	−57.4802			−2.29921
$26$		0			0
$27$	2.39066	+	26.8940i	0.0885428	+	0.996072i
$28$		0			0
$29$		−	50.7205i		−	1.74898i	−0.485042	−	0.874491i	$-0.661196\pi$
$29$		−	50.7205i		−	1.74898i	0.485042	−	0.874491i	$-0.338804\pi$
$30$		0			0
$31$	17.5657	−	30.4248i	0.566637	−	0.981444i	−0.430258	−	0.902706i	$-0.641578\pi$
$31$	17.5657	−	30.4248i	0.566637	−	0.981444i	0.996895	−	0.0787382i	$-0.0250891\pi$
$32$		0			0
$33$	6.17460	−	11.4642i	0.187109	−	0.347401i
$34$		0			0
$35$	58.4814	−	33.7642i	1.67090	−	0.964693i
$36$		0			0
$37$	22.6583			0.612388			0.306194	−	0.951969i	$-0.400944\pi$
$37$	22.6583			0.612388			0.306194	+	0.951969i	$0.400944\pi$
$38$		0			0
$39$	−30.7041	−	16.5371i	−0.787286	−	0.424029i
$40$		0			0
$41$		−	39.2048i		−	0.956214i	−0.878301	−	0.478107i	$-0.841323\pi$
$41$		−	39.2048i		−	0.956214i	0.878301	−	0.478107i	$-0.158677\pi$
$42$		0			0
$43$	3.94146	−	6.82682i	0.0916619	−	0.158763i	−0.816549	−	0.577277i	$-0.804115\pi$
$43$	3.94146	−	6.82682i	0.0916619	−	0.158763i	0.908211	+	0.418514i	$0.137449\pi$
$44$		0			0
$45$	−73.0766	−	36.6156i	−1.62393	−	0.813679i
$46$		0			0
$47$			66.6664i			1.41843i	0.704990	+	0.709217i	$0.250951\pi$
$47$			66.6664i			1.41843i	−0.704990	+	0.709217i	$0.749049\pi$
$48$		0			0
$49$	−3.14360	+	5.44487i	−0.0641551	+	0.111120i
$50$		0			0
$51$	−30.6643	+	56.9337i	−0.601261	+	1.11635i
$52$		0			0
$53$	10.7574	+	6.21080i	0.202970	+	0.117185i	0.598040	−	0.801466i	$-0.295946\pi$
$53$	10.7574	+	6.21080i	0.202970	+	0.117185i	−0.395070	+	0.918651i	$0.629280\pi$
$54$		0			0
$55$	19.7096	+	34.1381i	0.358357	+	0.620692i
$56$		0			0
$57$	−3.05893	−	56.9179i	−0.0536654	−	0.998559i
$58$		0			0
$59$		−	113.530i		−	1.92424i	−0.272626	−	0.962120i	$-0.587892\pi$
$59$		−	113.530i		−	1.92424i	0.272626	−	0.962120i	$-0.412108\pi$
$60$		0			0
$61$	100.522			1.64791			0.823955	−	0.566656i	$-0.191763\pi$
$61$	100.522			1.64791			0.823955	+	0.566656i	$0.191763\pi$
$62$		0			0
$63$	66.8030	−	3.95306i	1.06036	−	0.0627469i
$64$		0			0
$65$	91.4303	−	52.7873i	1.40662	−	0.812113i
$66$		0			0
$67$	−36.7385	−	63.6330i	−0.548336	−	0.949746i	−0.998389	−	0.0567438i	$-0.981928\pi$
$67$	−36.7385	−	63.6330i	−0.548336	−	0.949746i	0.450053	−	0.893002i	$-0.351405\pi$
$68$		0			0
$69$	5.50009	−	10.2119i	0.0797115	−	0.147999i
$70$		0			0
$71$	−2.86289	+	1.65289i	−0.0403224	+	0.0232802i	−0.520026	−	0.854151i	$-0.674078\pi$
$71$	−2.86289	+	1.65289i	−0.0403224	+	0.0232802i	0.479703	+	0.877431i	$0.340744\pi$
$72$		0			0
$73$	17.9246	+	31.0463i	0.245542	+	0.425292i	0.962284	−	0.272047i	$-0.0877007\pi$
$73$	17.9246	+	31.0463i	0.245542	+	0.425292i	−0.716742	+	0.697339i	$0.754367\pi$
$74$		0			0
$75$	146.725	−	90.5953i	1.95633	−	1.20794i
$76$		0			0
$77$	−27.9496	−	16.1367i	−0.362982	−	0.209568i
$78$		0			0
$79$	63.5801	−	110.124i	0.804812	−	1.39397i	−0.111607	−	0.993752i	$-0.535600\pi$
$79$	63.5801	−	110.124i	0.804812	−	1.39397i	0.916418	−	0.400222i	$-0.131067\pi$
$80$		0			0
$81$	−48.4904	−	64.8821i	−0.598647	−	0.801013i
$82$		0			0
$83$	−76.8076	+	44.3449i	−0.925393	+	0.534276i	−0.885351	−	0.464922i	$-0.846082\pi$
$83$	−76.8076	+	44.3449i	−0.925393	+	0.534276i	−0.0400412	+	0.999198i	$0.512749\pi$
$84$		0			0
$85$	−97.8819	−	169.536i	−1.15155	−	1.99455i
$86$		0			0
$87$	79.9413	+	129.470i	0.918865	+	1.48816i
$88$		0			0
$89$	78.4512	+	45.2938i	0.881474	+	0.508919i	0.871144	−	0.491027i	$-0.163379\pi$
$89$	78.4512	+	45.2938i	0.881474	+	0.508919i	0.0103298	+	0.999947i	$0.496712\pi$
$90$		0			0
$91$	−43.2183	+	74.8562i	−0.474926	+	0.822596i
$92$		0			0
$93$	3.11427	+	105.348i	0.0334867	+	1.13278i
$94$		0			0
$95$	151.476	+	82.6457i	1.59449	+	0.869955i
$96$		0			0
$97$	29.8352	−	51.6761i	0.307579	−	0.532743i	−0.670253	−	0.742133i	$-0.733814\pi$
$97$	29.8352	−	51.6761i	0.307579	−	0.532743i	0.977832	+	0.209390i	$0.0671477\pi$
$98$		0			0
$99$	2.30757	+	38.9957i	0.0233087	+	0.393896i
$100$		0			0
$101$		−	160.036i		−	1.58452i	−0.610185	−	0.792259i	$-0.708905\pi$
$101$		−	160.036i		−	1.58452i	0.610185	−	0.792259i	$-0.291095\pi$
$102$		0			0
$103$	−16.7614	+	29.0316i	−0.162732	+	0.281860i	−0.935848	−	0.352405i	$-0.885364\pi$
$103$	−16.7614	+	29.0316i	−0.162732	+	0.281860i	0.773116	+	0.634265i	$0.218697\pi$
$104$		0			0
$105$	−96.0644	+	178.361i	−0.914899	+	1.69867i
$106$		0			0
$107$		−	113.499i		−	1.06073i	−0.847768	−	0.530367i	$-0.822054\pi$
$107$		−	113.499i		−	1.06073i	0.847768	−	0.530367i	$-0.177946\pi$
$108$		0			0
$109$	−27.9996	−	48.4968i	−0.256877	−	0.444925i	0.708526	−	0.705684i	$-0.249360\pi$
$109$	−27.9996	−	48.4968i	−0.256877	−	0.444925i	−0.965404	+	0.260760i	$0.916027\pi$
$110$		0			0
$111$	−57.8381	+	35.7121i	−0.521064	+	0.321731i
$112$		0			0
$113$	27.7838	+	16.0410i	0.245874	+	0.141955i	0.617874	−	0.786278i	$-0.287994\pi$
$113$	27.7838	+	16.0410i	0.245874	+	0.141955i	−0.372000	+	0.928233i	$0.621328\pi$
$114$		0			0
$115$	17.5566	+	30.4089i	0.152666	+	0.264425i
$116$		0			0
$117$	104.440	−	6.18024i	0.892653	−	0.0528226i
$118$		0			0
$119$	138.804	+	80.1383i	1.16642	+	0.673431i
$120$		0			0
$121$	−51.0803	+	88.4737i	−0.422151	+	0.731187i
$122$		0			0
$123$	61.7912	+	100.075i	0.502368	+	0.813617i
$124$		0			0
$125$			294.980i			2.35984i
$126$		0			0
$127$	113.530	−	196.639i	0.893934	−	1.54834i	0.0588151	−	0.998269i	$-0.481268\pi$
$127$	113.530	−	196.639i	0.893934	−	1.54834i	0.835119	−	0.550070i	$-0.185399\pi$
$128$		0			0
$129$	0.698790	+	23.6385i	0.00541698	+	0.183244i
$130$		0			0
$131$		−	80.7881i		−	0.616703i	−0.951272	−	0.308352i	$-0.900223\pi$
$131$		−	80.7881i		−	0.616703i	0.951272	−	0.308352i	$-0.0997773\pi$
$132$		0			0
$133$	−141.234	+	3.40980i	−1.06191	+	0.0256376i
$134$		0			0
$135$	244.247	−	21.7116i	1.80924	−	0.160827i
$136$		0			0
$137$			200.994i			1.46711i	0.679631	+	0.733555i	$0.262140\pi$
$137$			200.994i			1.46711i	−0.679631	+	0.733555i	$0.737860\pi$
$138$		0			0
$139$	−115.620	−	200.259i	−0.831797	−	1.44072i	−0.896611	−	0.442818i	$-0.853979\pi$
$139$	−115.620	−	200.259i	−0.831797	−	1.44072i	0.0648140	−	0.997897i	$-0.479355\pi$
$140$		0			0
$141$	−105.074	−	170.174i	−0.745205	−	1.20691i
$142$		0			0
$143$	−43.6967	−	25.2283i	−0.305572	−	0.176422i
$144$		0			0
$145$	−460.636			−3.17680
$146$		0			0
$147$	−0.557335	−	18.8534i	−0.00379139	−	0.128254i
$148$		0			0
$149$			215.584i			1.44688i	0.690390	+	0.723438i	$0.257439\pi$
$149$			215.584i			1.44688i	−0.690390	+	0.723438i	$0.742561\pi$
$150$		0			0
$151$	37.9858	+	65.7932i	0.251561	+	0.435717i	0.963956	−	0.266062i	$-0.0857227\pi$
$151$	37.9858	+	65.7932i	0.251561	+	0.435717i	−0.712395	+	0.701779i	$0.752389\pi$
$152$		0			0
$153$	−11.4598	−	193.661i	−0.0749009	−	1.26576i
$154$		0			0
$155$	−276.313	−	159.530i	−1.78267	−	1.02922i
$156$		0			0
$157$	−77.9228			−0.496324			−0.248162	−	0.968719i	$-0.579826\pi$
$157$	−77.9228			−0.496324			−0.248162	+	0.968719i	$0.579826\pi$
$158$		0			0
$159$	−37.2485	+	1.10113i	−0.234268	+	0.00692532i
$160$		0			0
$161$	−24.8965	−	14.3740i	−0.154636	−	0.0892794i
$162$		0			0
$163$	13.6477			0.0837281			0.0418641	−	0.999123i	$-0.486670\pi$
$163$	13.6477			0.0837281			0.0418641	+	0.999123i	$0.486670\pi$
$164$		0			0
$165$	−104.117	−	56.0768i	−0.631010	−	0.339860i
$166$		0			0
$167$	55.3372	−	31.9490i	0.331361	−	0.191311i	−0.325084	−	0.945685i	$-0.605393\pi$
$167$	55.3372	−	31.9490i	0.331361	−	0.191311i	0.656445	+	0.754374i	$0.272059\pi$
$168$		0			0
$169$	16.9322	−	29.3274i	0.100190	−	0.173535i
$170$		0			0
$171$	97.5174	+	140.468i	0.570277	+	0.821453i
$172$		0			0
$173$	−149.313	−	86.2059i	−0.863081	−	0.498300i	0.00196174	−	0.999998i	$-0.499376\pi$
$173$	−149.313	−	86.2059i	−0.863081	−	0.498300i	−0.865043	+	0.501698i	$0.832709\pi$
$174$		0			0
$175$	−213.698	−	370.136i	−1.22113	−	2.11506i
$176$		0			0
$177$	178.937	+	289.799i	1.01094	+	1.63728i
$178$		0			0
$179$			58.2650i			0.325503i	0.986667	+	0.162751i	$0.0520369\pi$
$179$			58.2650i			0.325503i	−0.986667	+	0.162751i	$0.947963\pi$
$180$		0			0
$181$	−149.077	+	258.209i	−0.823631	+	1.42657i	0.0793295	+	0.996848i	$0.474722\pi$
$181$	−149.077	+	258.209i	−0.823631	+	1.42657i	−0.902961	+	0.429723i	$0.858611\pi$
$182$		0			0
$183$	−256.596	+	158.435i	−1.40216	+	0.865765i
$184$		0			0
$185$		−	205.780i		−	1.11232i
$186$		0			0
$187$	−46.7801	+	81.0255i	−0.250161	+	0.433291i
$188$		0			0
$189$	−164.292	+	115.380i	−0.869270	+	0.610475i
$190$		0			0
$191$	−108.988	+	62.9245i	−0.570620	+	0.329448i	−0.757397	−	0.652955i	$-0.773529\pi$
$191$	−108.988	+	62.9245i	−0.570620	+	0.329448i	0.186777	+	0.982402i	$0.440196\pi$
$192$		0			0
$193$	77.3511			0.400783			0.200391	−	0.979716i	$-0.435779\pi$
$193$	77.3511			0.400783			0.200391	+	0.979716i	$0.435779\pi$
$194$		0			0
$195$	−150.188	+	278.851i	−0.770194	+	1.43000i
$196$		0			0
$197$		−	107.228i		−	0.544304i	−0.962254	−	0.272152i	$-0.912265\pi$
$197$		−	107.228i		−	0.544304i	0.962254	−	0.272152i	$-0.0877354\pi$
$198$		0			0
$199$	−24.3491	+	42.1738i	−0.122357	+	0.211929i	−0.920697	−	0.390279i	$-0.872379\pi$
$199$	−24.3491	+	42.1738i	−0.122357	+	0.211929i	0.798340	+	0.602207i	$0.205712\pi$
$200$		0			0
$201$	194.072	+	104.527i	0.965534	+	0.520033i
$202$		0			0
$203$	326.608	−	188.567i	1.60890	−	0.928901i
$204$		0			0
$205$	−356.052			−1.73684
$206$		0			0
$207$	2.05549	+	34.7359i	0.00992990	+	0.167806i
$208$		0			0
$209$	−1.99045	−	82.4443i	−0.00952367	−	0.394470i
$210$		0			0
$211$	−9.00077			−0.0426577			−0.0213288	−	0.999773i	$-0.506790\pi$
$211$	−9.00077			−0.0426577			−0.0213288	+	0.999773i	$0.506790\pi$
$212$		0			0
$213$	4.70273	−	8.73145i	0.0220785	−	0.0409927i
$214$		0			0
$215$	−62.0002	−	35.7958i	−0.288373	−	0.166492i
$216$		0			0
$217$	261.221			1.20379
$218$		0			0
$219$	−94.6871	−	50.9981i	−0.432361	−	0.232868i
$220$		0			0
$221$	217.007	+	125.289i	0.981931	+	0.566918i
$222$		0			0
$223$	−116.684	+	202.102i	−0.523246	+	0.906288i	0.476388	+	0.879235i	$0.341946\pi$
$223$	−116.684	+	202.102i	−0.523246	+	0.906288i	−0.999634	+	0.0270532i	$0.991388\pi$
$224$		0			0
$225$	−231.744	+	462.511i	−1.02997	+	2.05560i
$226$		0			0
$227$	127.238	−	73.4611i	0.560522	−	0.323617i	−0.192833	−	0.981232i	$-0.561768\pi$
$227$	127.238	−	73.4611i	0.560522	−	0.323617i	0.753355	+	0.657614i	$0.228434\pi$
$228$		0			0
$229$	−109.935	+	190.413i	−0.480065	+	0.831496i	−0.999738	−	0.0228685i	$-0.992720\pi$
$229$	−109.935	+	190.413i	−0.480065	+	0.831496i	0.519674	+	0.854365i	$0.326053\pi$
$230$		0			0
$231$	96.7781	−	2.86091i	0.418953	−	0.0123849i
$232$		0			0
$233$	87.1319	−	50.3056i	0.373956	−	0.215904i	−0.301229	−	0.953552i	$-0.597397\pi$
$233$	87.1319	−	50.3056i	0.373956	−	0.215904i	0.675186	+	0.737648i	$0.264064\pi$
$234$		0			0
$235$	605.455			2.57640
$236$		0			0
$237$	11.2722	+	381.314i	0.0475622	+	1.60892i
$238$		0			0
$239$	224.956	+	129.878i	0.941237	+	0.543423i	0.890348	−	0.455281i	$-0.150461\pi$
$239$	224.956	+	129.878i	0.941237	+	0.543423i	0.0508891	+	0.998704i	$0.483794\pi$
$240$		0			0
$241$	80.0410			0.332120			0.166060	−	0.986116i	$-0.446895\pi$
$241$	80.0410			0.332120			0.166060	+	0.986116i	$0.446895\pi$
$242$		0			0
$243$	226.039	+	89.1928i	0.930202	+	0.367048i
$244$		0			0
$245$	49.4495	+	28.5497i	0.201835	+	0.116529i
$246$		0			0
$247$	−220.807	+	5.33092i	−0.893954	+	0.0215827i
$248$		0			0
$249$	126.168	−	234.253i	0.506698	−	0.940776i
$250$		0			0
$251$	−99.7198	−	57.5732i	−0.397290	−	0.229375i	0.288024	−	0.957623i	$-0.407002\pi$
$251$	−99.7198	−	57.5732i	−0.397290	−	0.229375i	−0.685314	+	0.728248i	$0.740335\pi$
$252$		0			0
$253$	8.39070	−	14.5331i	0.0331648	−	0.0574432i
$254$		0			0
$255$	517.064	+	278.489i	2.02770	+	1.09211i
$256$		0			0
$257$	283.621	−	163.749i	1.10358	−	0.637154i	0.166424	−	0.986054i	$-0.446778\pi$
$257$	283.621	−	163.749i	1.10358	−	0.637154i	0.937160	+	0.348900i	$0.113445\pi$
$258$		0			0
$259$	84.2385	+	145.905i	0.325245	+	0.563341i
$260$		0			0
$261$	−408.119	−	204.491i	−1.56368	−	0.783491i
$262$		0			0
$263$	−59.4198	−	34.3060i	−0.225931	−	0.130441i	0.382763	−	0.923847i	$-0.374973\pi$
$263$	−59.4198	−	34.3060i	−0.225931	−	0.130441i	−0.608693	+	0.793405i	$0.708306\pi$
$264$		0			0
$265$	56.4056	−	97.6974i	0.212851	−	0.368670i
$266$		0			0
$267$	−271.644	+	8.03023i	−1.01739	+	0.0300758i
$268$		0			0
$269$	59.6954	−	34.4652i	0.221916	−	0.128123i	−0.384921	−	0.922949i	$-0.625771\pi$
$269$	59.6954	−	34.4652i	0.221916	−	0.128123i	0.606837	+	0.794826i	$0.292438\pi$
$270$		0			0
$271$	156.478	+	271.029i	0.577411	+	1.00011i	0.995775	+	0.0918261i	$0.0292704\pi$
$271$	156.478	+	271.029i	0.577411	+	1.00011i	−0.418364	+	0.908280i	$0.637396\pi$
$272$		0			0
$273$	−7.66225	−	259.196i	−0.0280669	−	0.949437i
$274$		0			0
$275$	216.064	−	124.744i	0.785687	−	0.453616i
$276$		0			0
$277$	253.618	+	439.279i	0.915588	+	1.58584i	0.806039	+	0.591863i	$0.201607\pi$
$277$	253.618	+	439.279i	0.915588	+	1.58584i	0.109549	+	0.993981i	$0.465059\pi$
$278$		0			0
$279$	−173.991	−	264.006i	−0.623623	−	0.946258i
$280$		0			0
$281$			462.014i			1.64418i	0.569359	+	0.822089i	$0.307191\pi$
$281$			462.014i			1.64418i	−0.569359	+	0.822089i	$0.692809\pi$
$282$		0			0
$283$	52.1104			0.184136			0.0920678	−	0.995753i	$-0.470652\pi$
$283$	52.1104			0.184136			0.0920678	+	0.995753i	$0.470652\pi$
$284$		0			0
$285$	−516.920	+	27.7808i	−1.81375	+	0.0974764i
$286$		0			0
$287$	252.454	−	145.754i	0.879630	−	0.507855i
$288$		0			0
$289$	87.8193	−	152.108i	0.303873	−	0.526324i
$290$		0			0
$291$	5.28954	+	178.933i	0.0181771	+	0.614890i
$292$		0			0
$293$	209.042	+	120.691i	0.713455	+	0.411913i	0.812339	−	0.583186i	$-0.198194\pi$
$293$	209.042	+	120.691i	0.713455	+	0.411913i	−0.0988841	+	0.995099i	$0.531527\pi$
$294$		0			0
$295$	−1031.06			−3.49514
$296$		0			0
$297$	−67.3521	−	95.9042i	−0.226775	−	0.322910i
$298$		0			0
$299$	−38.9234	−	22.4724i	−0.130178	−	0.0751586i
$300$		0			0
$301$	58.6138			0.194730
$302$		0			0
$303$	252.236	+	408.512i	0.832461	+	1.34822i
$304$		0			0
$305$		−	912.931i		−	2.99322i
$306$		0			0
$307$	−10.6736	−	18.4872i	−0.0347673	−	0.0602187i	0.848118	−	0.529807i	$-0.177736\pi$
$307$	−10.6736	−	18.4872i	−0.0347673	−	0.0602187i	−0.882885	+	0.469588i	$0.844402\pi$
$308$		0			0
$309$	−2.97166	−	100.524i	−0.00961702	−	0.325322i
$310$		0			0
$311$	−228.456	−	131.899i	−0.734587	−	0.424114i	0.0855112	−	0.996337i	$-0.472748\pi$
$311$	−228.456	−	131.899i	−0.734587	−	0.424114i	−0.820098	+	0.572223i	$0.806081\pi$
$312$		0			0
$313$	−8.08946			−0.0258449			−0.0129225	−	0.999917i	$-0.504113\pi$
$313$	−8.08946			−0.0258449			−0.0129225	+	0.999917i	$0.504113\pi$
$314$		0			0
$315$	−35.9011	−	606.695i	−0.113972	−	1.92602i
$316$		0			0
$317$			13.8994i			0.0438466i	0.999760	+	0.0219233i	$0.00697897\pi$
$317$			13.8994i			0.0438466i	−0.999760	+	0.0219233i	$0.993021\pi$
$318$		0			0
$319$	110.075	+	190.655i	0.345061	+	0.597664i
$320$		0			0
$321$	178.887	+	289.719i	0.557280	+	0.902550i
$322$		0			0
$323$	9.88496	+	409.435i	0.0306036	+	1.26760i
$324$		0			0
$325$	−334.097	−	578.673i	−1.02799	−	1.78053i
$326$		0			0
$327$	147.909	+	79.6632i	0.452321	+	0.243618i
$328$		0			0
$329$	−429.289	+	247.850i	−1.30483	+	0.753344i
$330$		0			0
$331$	12.4470	+	21.5588i	0.0376041	+	0.0651322i	0.884215	−	0.467080i	$-0.154694\pi$
$331$	12.4470	+	21.5588i	0.0376041	+	0.0651322i	−0.846611	+	0.532212i	$0.821361\pi$
$332$		0			0
$333$	91.3522	−	182.319i	0.274331	−	0.547504i
$334$		0			0
$335$	−577.906	+	333.654i	−1.72509	+	0.995982i
$336$		0			0
$337$	435.422			1.29205			0.646027	−	0.763315i	$-0.276429\pi$
$337$	435.422			1.29205			0.646027	+	0.763315i	$0.276429\pi$
$338$		0			0
$339$	−96.2037	+	2.84393i	−0.283787	+	0.00838918i
$340$		0			0
$341$			152.486i			0.447173i
$342$		0			0
$343$	317.593			0.925926
$344$		0			0
$345$	−92.7431	−	49.9511i	−0.268820	−	0.144786i
$346$		0			0
$347$		−	295.665i		−	0.852060i	−0.904709	−	0.426030i	$-0.859912\pi$
$347$		−	295.665i		−	0.852060i	0.904709	−	0.426030i	$-0.140088\pi$
$348$		0			0
$349$	−331.114	−	573.506i	−0.948750	−	1.64328i	−0.748063	−	0.663628i	$-0.769016\pi$
$349$	−331.114	−	573.506i	−0.948750	−	1.64328i	−0.200687	−	0.979655i	$-0.564317\pi$
$350$		0			0
$351$	−256.856	+	180.386i	−0.731783	+	0.513920i
$352$		0			0
$353$	244.745	−	141.304i	0.693328	−	0.400293i	−0.111529	−	0.993761i	$-0.535575\pi$
$353$	244.745	−	141.304i	0.693328	−	0.400293i	0.804858	+	0.593468i	$0.202242\pi$
$354$		0			0
$355$	15.0113	+	26.0004i	0.0422855	+	0.0732406i
$356$		0			0
$357$	−480.620	+	14.2079i	−1.34627	+	0.0397980i
$358$		0			0
$359$	197.563	−	114.063i	0.550316	−	0.317725i	−0.198934	−	0.980013i	$-0.563748\pi$
$359$	197.563	−	114.063i	0.550316	−	0.317725i	0.749249	+	0.662288i	$0.230414\pi$
$360$		0			0
$361$	−195.377	−	303.560i	−0.541210	−	0.840888i
$362$		0			0
$363$	−9.05613	−	306.348i	−0.0249480	−	0.843934i
$364$		0			0
$365$	281.958	−	162.789i	0.772488	−	0.445996i
$366$		0			0
$367$	224.046			0.610479			0.305239	−	0.952276i	$-0.401264\pi$
$367$	224.046			0.610479			0.305239	+	0.952276i	$0.401264\pi$
$368$		0			0
$369$	−315.459	−	158.063i	−0.854902	−	0.428355i
$370$		0			0
$371$			92.3613i			0.248952i
$372$		0			0
$373$	−44.0874	+	76.3616i	−0.118197	+	0.204723i	−0.919053	−	0.394134i	$-0.871045\pi$
$373$	−44.0874	+	76.3616i	−0.118197	+	0.204723i	0.800856	+	0.598856i	$0.204378\pi$
$374$		0			0
$375$	−464.923	−	752.972i	−1.23979	−	2.00793i
$376$		0			0
$377$	510.621	−	294.807i	1.35443	−	0.781982i
$378$		0			0
$379$	−420.700			−1.11003			−0.555013	−	0.831841i	$-0.687287\pi$
$379$	−420.700			−1.11003			−0.555013	+	0.831841i	$0.687287\pi$
$380$		0			0
$381$	20.1279	+	680.880i	0.0528291	+	1.78709i
$382$		0			0
$383$			264.276i			0.690016i	0.938600	+	0.345008i	$0.112124\pi$
$383$			264.276i			0.690016i	−0.938600	+	0.345008i	$0.887876\pi$
$384$		0			0
$385$	−146.552	+	253.835i	−0.380653	+	0.659311i
$386$		0			0
$387$	−39.0407	−	59.2386i	−0.100880	−	0.153071i
$388$		0			0
$389$			201.953i			0.519160i	0.965722	+	0.259580i	$0.0835841\pi$
$389$			201.953i			0.519160i	−0.965722	+	0.259580i	$0.916416\pi$
$390$		0			0
$391$	−41.6699	+	72.1744i	−0.106573	+	0.184589i
$392$		0			0
$393$	127.331	+	206.221i	0.323998	+	0.524736i
$394$		0			0
$395$	−1000.13	−	577.426i	−2.53198	−	1.46184i
$396$		0			0
$397$	−190.682	−	330.271i	−0.480308	−	0.831918i	0.519437	−	0.854509i	$-0.326142\pi$
$397$	−190.682	−	330.271i	−0.480308	−	0.831918i	−0.999745	+	0.0225909i	$0.992808\pi$
$398$		0			0
$399$	355.142	−	231.305i	0.890081	−	0.579712i
$400$		0			0
$401$			632.695i			1.57779i	0.614526	+	0.788896i	$0.289347\pi$
$401$			632.695i			1.57779i	−0.614526	+	0.788896i	$0.710653\pi$
$402$		0			0
$403$	408.396			1.01339
$404$		0			0
$405$	−589.250	+	440.383i	−1.45494	+	1.08737i
$406$		0			0
$407$	−85.1711	+	49.1736i	−0.209266	+	0.120820i
$408$		0			0
$409$	105.950	+	183.511i	0.259047	+	0.448683i	0.965987	−	0.258591i	$-0.0832582\pi$
$409$	105.950	+	183.511i	0.259047	+	0.448683i	−0.706940	+	0.707274i	$0.749925\pi$
$410$		0			0
$411$	−316.790	−	513.061i	−0.770777	−	1.24832i
$412$		0			0
$413$	731.062	−	422.079i	1.77013	−	1.02198i
$414$		0			0
$415$	402.734	+	697.556i	0.970443	+	1.68086i
$416$		0			0
$417$	610.765	+	328.956i	1.46466	+	0.788863i
$418$		0			0
$419$	14.7373	+	8.50858i	0.0351726	+	0.0203069i	0.517483	−	0.855693i	$-0.326869\pi$
$419$	14.7373	+	8.50858i	0.0351726	+	0.0203069i	−0.482311	+	0.876000i	$0.660202\pi$
$420$		0			0
$421$	106.884	−	185.129i	0.253881	−	0.439735i	−0.710710	−	0.703485i	$-0.751626\pi$
$421$	106.884	−	185.129i	0.253881	−	0.439735i	0.964591	+	0.263750i	$0.0849594\pi$
$422$		0			0
$423$	536.427	+	268.781i	1.26815	+	0.635415i
$424$		0			0
$425$	−1073.02	+	619.506i	−2.52474	+	1.45766i
$426$		0			0
$427$	373.719	+	647.301i	0.875221	+	1.51593i
$428$		0			0
$429$	151.304	−	4.47278i	0.352690	−	0.0104261i
$430$		0			0
$431$	4.09834	+	2.36618i	0.00950891	+	0.00548997i	0.504747	−	0.863267i	$-0.331586\pi$
$431$	4.09834	+	2.36618i	0.00950891	+	0.00548997i	−0.495238	+	0.868757i	$0.664919\pi$
$432$		0			0
$433$	329.460	−	570.641i	0.760877	−	1.31788i	−0.181522	−	0.983387i	$-0.558102\pi$
$433$	329.460	−	570.641i	0.760877	−	1.31788i	0.942399	−	0.334491i	$-0.108564\pi$
$434$		0			0
$435$	1175.83	−	726.016i	2.70305	−	1.66900i
$436$		0			0
$437$	−1.77301	−	73.4382i	−0.00405724	−	0.168051i
$438$		0			0
$439$	146.973	−	254.565i	0.334791	−	0.579874i	−0.648654	−	0.761083i	$-0.724668\pi$
$439$	146.973	−	254.565i	0.334791	−	0.579874i	0.983445	+	0.181209i	$0.0580011\pi$
$440$		0			0
$441$	31.1377	+	47.2470i	0.0706070	+	0.107136i
$442$		0			0
$443$		−	387.744i		−	0.875269i	−0.899153	−	0.437634i	$-0.855816\pi$
$443$		−	387.744i		−	0.875269i	0.899153	−	0.437634i	$-0.144184\pi$
$444$		0			0
$445$	411.352	−	712.482i	0.924386	−	1.60108i
$446$		0			0
$447$	−339.786	−	550.305i	−0.760147	−	1.23111i
$448$		0			0
$449$			732.714i			1.63188i	0.578137	+	0.815940i	$0.303780\pi$
$449$			732.714i			1.63188i	−0.578137	+	0.815940i	$0.696220\pi$
$450$		0			0
$451$	85.0830	+	147.368i	0.188654	+	0.326758i
$452$		0			0
$453$	−200.661	−	108.075i	−0.442960	−	0.238577i
$454$		0			0
$455$	679.834	+	392.502i	1.49414	+	0.862642i
$456$		0			0
$457$	208.608	+	361.319i	0.456472	+	0.790632i	0.998772	−	0.0495528i	$-0.0157796\pi$
$457$	208.608	+	361.319i	0.456472	+	0.790632i	−0.542300	+	0.840185i	$0.682446\pi$
$458$		0			0
$459$	334.484	+	476.279i	0.728723	+	1.03765i
$460$		0			0
$461$	−389.307	−	224.767i	−0.844484	−	0.487563i	0.0143016	−	0.999898i	$-0.495448\pi$
$461$	−389.307	−	224.767i	−0.844484	−	0.487563i	−0.858786	+	0.512334i	$0.828781\pi$
$462$		0			0
$463$	−268.570	+	465.176i	−0.580064	+	1.00470i	0.415407	+	0.909636i	$0.363639\pi$
$463$	−268.570	+	465.176i	−0.580064	+	1.00470i	−0.995471	+	0.0950649i	$0.969694\pi$
$464$		0			0
$465$	956.760	−	28.2833i	2.05755	−	0.0608243i
$466$		0			0
$467$			582.780i			1.24792i	0.781455	+	0.623961i	$0.214478\pi$
$467$			582.780i			1.24792i	−0.781455	+	0.623961i	$0.785522\pi$
$468$		0			0
$469$	273.171	−	473.145i	0.582453	−	1.00884i
$470$		0			0
$471$	198.907	−	122.815i	0.422308	−	0.260754i
$472$		0			0
$473$			34.2153i			0.0723369i
$474$		0			0
$475$	523.075	−	958.710i	1.10121	−	2.01834i
$476$		0			0
$477$	93.3458	−	61.5187i	0.195694	−	0.128970i
$478$		0			0
$479$		−	46.4224i		−	0.0969153i	−0.998825	−	0.0484577i	$-0.984569\pi$
$479$		−	46.4224i		−	0.0969153i	0.998825	−	0.0484577i	$-0.0154306\pi$
$480$		0			0
$481$	131.699	+	228.110i	0.273803	+	0.474241i
$482$		0			0
$483$	86.2062	−	2.54839i	0.178481	−	0.00527617i
$484$		0			0
$485$	−469.315	−	270.959i	−0.967659	−	0.558678i
$486$		0			0
$487$	−98.2155			−0.201674			−0.100837	−	0.994903i	$-0.532152\pi$
$487$	−98.2155			−0.201674			−0.100837	+	0.994903i	$0.532152\pi$
$488$		0			0
$489$	−34.8373	+	21.5103i	−0.0712420	+	0.0439884i
$490$		0			0
$491$			669.171i			1.36287i	0.731877	+	0.681437i	$0.238644\pi$
$491$			669.171i			1.36287i	−0.731877	+	0.681437i	$0.761356\pi$
$492$		0			0
$493$	−546.652	−	946.829i	−1.10883	−	1.92055i
$494$		0			0
$495$	354.154	−	20.9570i	0.715462	−	0.0423373i
$496$		0			0
$497$	−21.2871	−	12.2901i	−0.0428313	−	0.0247287i
$498$		0			0
$499$	133.576			0.267686			0.133843	−	0.991003i	$-0.457268\pi$
$499$	133.576			0.267686			0.133843	+	0.991003i	$0.457268\pi$
$500$		0			0
$501$	−90.8996	+	168.771i	−0.181436	+	0.336869i
$502$		0			0
$503$	−768.121	−	443.475i	−1.52708	−	0.881659i	−0.999483	−	0.0321643i	$-0.989760\pi$
$503$	−768.121	−	443.475i	−1.52708	−	0.881659i	−0.527596	−	0.849495i	$-0.676907\pi$
$504$		0			0
$505$	−1453.43			−2.87807
$506$		0			0
$507$	3.00194	+	101.549i	0.00592098	+	0.200293i
$508$		0			0
$509$	−4.94903	+	2.85732i	−0.00972305	+	0.00561360i	−0.504854	−	0.863205i	$-0.668454\pi$
$509$	−4.94903	+	2.85732i	−0.00972305	+	0.00561360i	0.495131	+	0.868819i	$0.335120\pi$
$510$		0			0
$511$	−133.279	+	230.846i	−0.260820	+	0.451753i
$512$		0			0
$513$	−470.319	−	204.864i	−0.916801	−	0.399344i
$514$		0			0
$515$	263.661	+	152.225i	0.511963	+	0.295582i
$516$		0			0
$517$	−144.681	−	250.594i	−0.279847	−	0.484708i
$518$		0			0
$519$	517.010	−	15.2836i	0.996165	−	0.0294482i
$520$		0			0
$521$		−	399.843i		−	0.767453i	−0.923447	−	0.383726i	$-0.874641\pi$
$521$		−	399.843i		−	0.767453i	0.923447	−	0.383726i	$-0.125359\pi$
$522$		0			0
$523$	−199.151	+	344.940i	−0.380786	+	0.659541i	−0.991175	−	0.132561i	$-0.957680\pi$
$523$	−199.151	+	344.940i	−0.380786	+	0.659541i	0.610389	+	0.792102i	$0.291013\pi$
$524$		0			0
$525$	1128.87	+	608.003i	2.15022	+	1.15810i
$526$		0			0
$527$		−	757.276i		−	1.43696i
$528$		0			0
$529$	−257.026	+	445.182i	−0.485871	+	0.841554i
$530$		0			0
$531$	−913.514	−	457.722i	−1.72036	−	0.862001i
$532$		0			0
$533$	394.689	−	227.874i	0.740504	−	0.427530i
$534$		0			0
$535$	−1030.78			−1.92669
$536$		0			0
$537$	−91.8324	−	148.728i	−0.171010	−	0.276962i
$538$		0			0
$539$		−	27.2892i		−	0.0506293i
$540$		0			0
$541$	142.004	−	245.957i	0.262484	−	0.454635i	−0.704418	−	0.709786i	$-0.748792\pi$
$541$	142.004	−	245.957i	0.262484	−	0.454635i	0.966901	+	0.255151i	$0.0821251\pi$
$542$		0			0
$543$	−26.4302	−	894.073i	−0.0486744	−	1.64654i
$544$		0			0
$545$	−440.441	+	254.289i	−0.808149	+	0.466585i
$546$		0			0
$547$	688.387			1.25848			0.629239	−	0.777212i	$-0.283367\pi$
$547$	688.387			1.25848			0.629239	+	0.777212i	$0.283367\pi$
$548$		0			0
$549$	405.279	−	808.848i	0.738213	−	1.47331i
$550$		0			0
$551$	845.966	+	461.561i	1.53533	+	0.837679i
$552$		0			0
$553$	945.504			1.70977
$554$		0			0
$555$	324.333	+	525.278i	0.584383	+	0.946446i
$556$		0			0
$557$	−640.827	−	369.982i	−1.15050	−	0.664240i	−0.201489	−	0.979491i	$-0.564578\pi$
$557$	−640.827	−	369.982i	−1.15050	−	0.664240i	−0.949008	+	0.315251i	$0.897911\pi$
$558$		0			0
$559$	91.6373			0.163931
$560$		0			0
$561$	−8.29374	−	280.558i	−0.0147838	−	0.500103i
$562$		0			0
$563$	537.579	+	310.371i	0.954847	+	0.551281i	0.894583	−	0.446901i	$-0.147472\pi$
$563$	537.579	+	310.371i	0.954847	+	0.551281i	0.0602639	+	0.998182i	$0.480806\pi$
$564$		0			0
$565$	145.682	−	252.328i	0.257844	−	0.446599i
$566$		0			0
$567$	237.523	−	553.464i	0.418912	−	0.976126i
$568$		0			0
$569$	536.511	−	309.755i	0.942902	−	0.544385i	0.0520329	−	0.998645i	$-0.483430\pi$
$569$	536.511	−	309.755i	0.942902	−	0.544385i	0.890869	+	0.454261i	$0.150097\pi$
$570$		0			0
$571$	−87.0815	+	150.830i	−0.152507	+	0.264150i	−0.932148	−	0.362076i	$-0.882068\pi$
$571$	−87.0815	+	150.830i	−0.152507	+	0.264150i	0.779641	+	0.626226i	$0.215401\pi$
$572$		0			0
$573$	179.030	−	332.401i	0.312443	−	0.580106i
$574$		0			0
$575$	192.461	−	111.118i	0.334715	−	0.193248i
$576$		0			0
$577$	−715.882			−1.24070			−0.620348	−	0.784327i	$-0.713009\pi$
$577$	−715.882			−1.24070			−0.620348	+	0.784327i	$0.713009\pi$
$578$		0			0
$579$	−197.448	+	121.914i	−0.341015	+	0.210560i
$580$		0			0
$581$	−571.106	−	329.728i	−0.982970	−	0.567518i
$582$		0			0
$583$	−53.9152			−0.0924789
$584$		0			0
$585$	−56.1281	−	948.513i	−0.0959455	−	1.62139i
$586$		0			0
$587$	−699.883	−	404.077i	−1.19230	−	0.688377i	−0.233476	−	0.972363i	$-0.575010\pi$
$587$	−699.883	−	404.077i	−1.19230	−	0.688377i	−0.958829	+	0.283986i	$0.908343\pi$
$588$		0			0
$589$	347.604	+	569.847i	0.590160	+	0.967482i
$590$		0			0
$591$	169.003	+	273.712i	0.285962	+	0.463134i
$592$		0			0
$593$	−639.673	−	369.316i	−1.07871	−	0.622792i	−0.148160	−	0.988963i	$-0.547335\pi$
$593$	−639.673	−	369.316i	−1.07871	−	0.622792i	−0.930547	+	0.366172i	$0.880668\pi$
$594$		0			0
$595$	727.804	−	1260.59i	1.22320	−	2.11865i
$596$		0			0
$597$	−4.31689	−	146.031i	−0.00723098	−	0.244607i
$598$		0			0
$599$	728.812	−	420.780i	1.21671	−	0.702470i	0.252501	−	0.967597i	$-0.418747\pi$
$599$	728.812	−	420.780i	1.21671	−	0.702470i	0.964214	+	0.265126i	$0.0854137\pi$
$600$		0			0
$601$	−65.8638	−	114.079i	−0.109590	−	0.189816i	0.806014	−	0.591896i	$-0.201621\pi$
$601$	−65.8638	−	114.079i	−0.109590	−	0.189816i	−0.915604	+	0.402080i	$0.868287\pi$
$602$		0			0
$603$	−660.138	+	39.0636i	−1.09476	+	0.0647821i
$604$		0			0
$605$	803.505	+	463.904i	1.32811	+	0.766784i
$606$		0			0
$607$	−399.055	+	691.184i	−0.657422	+	1.13869i	0.323858	+	0.946106i	$0.395020\pi$
$607$	−399.055	+	691.184i	−0.657422	+	1.13869i	−0.981281	+	0.192583i	$0.938313\pi$
$608$		0			0
$609$	−536.501	+	996.111i	−0.880955	+	1.63565i
$610$		0			0
$611$	−671.155	+	387.491i	−1.09845	+	0.634192i
$612$		0			0
$613$	520.371	+	901.308i	0.848892	+	1.47032i	0.882198	+	0.470879i	$0.156063\pi$
$613$	520.371	+	901.308i	0.848892	+	1.47032i	−0.0333062	+	0.999445i	$0.510604\pi$
$614$		0			0
$615$	908.866	−	561.179i	1.47783	−	0.912487i
$616$		0			0
$617$	−463.269	+	267.468i	−0.750841	+	0.433498i	−0.825998	−	0.563673i	$-0.809388\pi$
$617$	−463.269	+	267.468i	−0.750841	+	0.433498i	0.0751567	+	0.997172i	$0.476054\pi$
$618$		0			0
$619$	57.3192	+	99.2797i	0.0925996	+	0.160387i	0.908604	−	0.417658i	$-0.137149\pi$
$619$	57.3192	+	99.2797i	0.0925996	+	0.160387i	−0.816005	+	0.578045i	$0.803816\pi$
$620$		0			0
$621$	−59.9946	−	85.4278i	−0.0966097	−	0.137565i
$622$		0			0
$623$			673.567i			1.08117i
$624$		0			0
$625$	1241.96			1.98714
$626$		0			0
$627$	135.022	+	207.312i	0.215347	+	0.330641i
$628$		0			0
$629$	422.977	−	244.206i	0.672459	−	0.388244i
$630$		0			0
$631$	−319.956	+	554.181i	−0.507063	+	0.878258i	0.492904	+	0.870084i	$0.335935\pi$
$631$	−319.956	+	554.181i	−0.507063	+	0.878258i	−0.999967	+	0.00817442i	$0.997398\pi$
$632$		0			0
$633$	22.9755	−	14.1862i	0.0362963	−	0.0224111i
$634$		0			0
$635$	−1785.85	−	1031.06i	−2.81236	−	1.62372i
$636$		0			0
$637$	−73.0873			−0.114737
$638$		0			0
$639$	1.75750	+	29.7001i	0.00275039	+	0.0464790i
$640$		0			0
$641$	252.396	+	145.721i	0.393754	+	0.227334i	0.683785	−	0.729683i	$-0.260332\pi$
$641$	252.396	+	145.721i	0.393754	+	0.227334i	−0.290031	+	0.957017i	$0.593666\pi$
$642$		0			0
$643$	913.504			1.42069			0.710346	−	0.703853i	$-0.248539\pi$
$643$	913.504			1.42069			0.710346	+	0.703853i	$0.248539\pi$
$644$		0			0
$645$	214.681	−	6.34631i	0.332839	−	0.00983924i
$646$		0			0
$647$			179.023i			0.276697i	0.990384	+	0.138349i	$0.0441795\pi$
$647$			179.023i			0.276697i	−0.990384	+	0.138349i	$0.955821\pi$
$648$		0			0
$649$	246.385	+	426.752i	0.379638	+	0.657553i
$650$		0			0
$651$	−666.799	+	411.715i	−1.02427	+	0.632435i
$652$		0			0
$653$	62.3253	+	35.9836i	0.0954446	+	0.0551050i	0.546963	−	0.837157i	$-0.315784\pi$
$653$	62.3253	+	35.9836i	0.0954446	+	0.0551050i	−0.451518	+	0.892262i	$0.649117\pi$
$654$		0			0
$655$	−733.706			−1.12016
$656$		0			0
$657$	322.079	−	19.0590i	0.490227	−	0.0290091i
$658$		0			0
$659$		−	33.4949i		−	0.0508269i	−0.999677	−	0.0254134i	$-0.991910\pi$
$659$		−	33.4949i		−	0.0508269i	0.999677	−	0.0254134i	$-0.00809022\pi$
$660$		0			0
$661$	−58.6617	−	101.605i	−0.0887469	−	0.153714i	0.818235	−	0.574884i	$-0.194953\pi$
$661$	−58.6617	−	101.605i	−0.0887469	−	0.153714i	−0.906982	+	0.421170i	$0.861620\pi$
$662$		0			0
$663$	−751.405	+	22.2127i	−1.13334	+	0.0335033i
$664$		0			0
$665$	30.9674	+	1282.67i	0.0465675	+	1.92882i
$666$		0			0
$667$	98.0501	+	169.828i	0.147002	+	0.254614i
$668$		0			0
$669$	−20.6871	−	699.797i	−0.0309224	−	1.04603i
$670$		0			0
$671$	−377.857	+	218.156i	−0.563125	+	0.325120i
$672$		0			0
$673$	194.081	+	336.158i	0.288382	+	0.499492i	0.973424	−	0.229012i	$-0.0735494\pi$
$673$	194.081	+	336.158i	0.288382	+	0.499492i	−0.685042	+	0.728504i	$0.740216\pi$
$674$		0			0
$675$	−137.415	−	1545.87i	−0.203578	−	2.29018i
$676$		0			0
$677$	−724.175	+	418.103i	−1.06968	+	0.617582i	−0.928095	−	0.372344i	$-0.878554\pi$
$677$	−724.175	+	418.103i	−1.06968	+	0.617582i	−0.141588	+	0.989926i	$0.545221\pi$
$678$		0			0
$679$	443.681			0.653433
$680$		0			0
$681$	−209.008	+	388.061i	−0.306913	+	0.569839i
$682$		0			0
$683$		−	911.489i		−	1.33454i	−0.744817	−	0.667268i	$-0.767463\pi$
$683$		−	911.489i		−	1.33454i	0.744817	−	0.667268i	$-0.232537\pi$
$684$		0			0
$685$	1825.40			2.66482
$686$		0			0
$687$	−19.4906	−	659.321i	−0.0283705	−	0.959710i
$688$		0			0
$689$			144.399i			0.209577i
$690$		0			0
$691$	617.578	+	1069.68i	0.893745	+	1.54801i	0.835350	+	0.549719i	$0.185265\pi$
$691$	617.578	+	1069.68i	0.893745	+	1.54801i	0.0583958	+	0.998294i	$0.481401\pi$
$692$		0			0
$693$	−242.529	+	159.836i	−0.349969	+	0.230644i
$694$		0			0
$695$	−1818.73	+	1050.04i	−2.61687	+	1.51085i
$696$		0			0
$697$	−422.539	−	731.859i	−0.606225	−	1.05001i
$698$		0			0
$699$	−143.127	+	265.741i	−0.204760	+	0.380173i
$700$		0			0
$701$	126.432	−	72.9953i	0.180359	−	0.104130i	−0.407102	−	0.913383i	$-0.633461\pi$
$701$	126.432	−	72.9953i	0.180359	−	0.104130i	0.587461	+	0.809252i	$0.300127\pi$
$702$		0			0
$703$	−206.193	+	377.918i	−0.293304	+	0.537579i
$704$		0			0
$705$	−1545.50	+	954.266i	−2.19219	+	1.35357i
$706$		0			0
$707$	1030.53	−	594.978i	1.45761	−	0.841553i
$708$		0			0
$709$	743.280			1.04835			0.524175	−	0.851611i	$-0.324374\pi$
$709$	743.280			1.04835			0.524175	+	0.851611i	$0.324374\pi$
$710$		0			0
$711$	−629.769	−	955.583i	−0.885750	−	1.34400i
$712$		0			0
$713$			135.829i			0.190503i
$714$		0			0
$715$	−229.120	+	396.848i	−0.320448	+	0.555032i
$716$		0			0
$717$	−778.929	+	23.0264i	−1.08637	+	0.0321149i
$718$		0			0
$719$	299.714	−	173.040i	0.416848	−	0.240667i	−0.276880	−	0.960905i	$-0.589300\pi$
$719$	299.714	−	173.040i	0.416848	−	0.240667i	0.693728	+	0.720237i	$0.255967\pi$
$720$		0			0
$721$	−249.260			−0.345714
$722$		0			0
$723$	−204.314	+	126.154i	−0.282592	+	0.174487i
$724$		0			0
$725$			2915.42i			4.02127i
$726$		0			0
$727$	−471.068	+	815.913i	−0.647961	+	1.12230i	0.335648	+	0.941987i	$0.391045\pi$
$727$	−471.068	+	815.913i	−0.647961	+	1.12230i	−0.983609	+	0.180314i	$0.942289\pi$
$728$		0			0
$729$	−717.570	+	128.588i	−0.984320	+	0.176390i
$730$		0			0
$731$		−	169.920i		−	0.232449i
$732$		0			0
$733$	−35.7338	+	61.8927i	−0.0487500	+	0.0844376i	−0.889371	−	0.457187i	$-0.848857\pi$
$733$	−35.7338	+	61.8927i	−0.0487500	+	0.0844376i	0.840621	+	0.541624i	$0.182190\pi$
$734$		0			0
$735$	−171.223	+	5.06163i	−0.232957	+	0.00688658i
$736$		0			0
$737$	276.195	+	159.461i	0.374756	+	0.216365i
$738$		0			0
$739$	0.461491	+	0.799326i	0.000624481	+	0.00108163i	0.866337	−	0.499459i	$-0.166468\pi$
$739$	0.461491	+	0.799326i	0.000624481	+	0.00108163i	−0.865713	+	0.500541i	$0.833135\pi$
$740$		0			0
$741$	555.233	−	361.624i	0.749302	−	0.488022i
$742$		0			0
$743$			373.582i			0.502802i	0.967883	+	0.251401i	$0.0808912\pi$
$743$			373.582i			0.502802i	−0.967883	+	0.251401i	$0.919109\pi$
$744$		0			0
$745$	1957.91			2.62806
$746$		0			0
$747$	47.1514	+	796.814i	0.0631210	+	1.06669i
$748$		0			0
$749$	730.858	−	421.961i	0.975779	−	0.563366i
$750$		0			0
$751$	−182.718	−	316.476i	−0.243299	−	0.421406i	0.718353	−	0.695679i	$-0.244896\pi$
$751$	−182.718	−	316.476i	−0.243299	−	0.421406i	−0.961652	+	0.274272i	$0.911563\pi$
$752$		0			0
$753$	345.289	−	10.2073i	0.458551	−	0.0135555i
$754$		0			0
$755$	597.525	−	344.981i	0.791424	−	0.456929i
$756$		0			0
$757$	−678.845	−	1175.79i	−0.896757	−	1.55323i	−0.831615	−	0.555353i	$-0.812583\pi$
$757$	−678.845	−	1175.79i	−0.896757	−	1.55323i	−0.0651422	−	0.997876i	$-0.520750\pi$
$758$		0			0
$759$	1.48760	+	50.3222i	0.00195995	+	0.0663007i
$760$		0			0
$761$	−795.277	−	459.153i	−1.04504	−	0.603355i	−0.123784	−	0.992309i	$-0.539503\pi$
$761$	−795.277	−	459.153i	−1.04504	−	0.603355i	−0.921257	+	0.388954i	$0.872836\pi$
$762$		0			0
$763$	208.192	−	360.600i	0.272860	−	0.472608i
$764$		0			0
$765$	−1758.80	+	104.077i	−2.29908	+	0.136048i
$766$		0			0
$767$	1142.95	−	659.882i	1.49016	−	0.860342i
$768$		0			0
$769$	31.3693	+	54.3333i	0.0407924	+	0.0706545i	0.885701	−	0.464257i	$-0.153678\pi$
$769$	31.3693	+	54.3333i	0.0407924	+	0.0706545i	−0.844908	+	0.534911i	$0.820345\pi$
$770$		0			0
$771$	−465.890	+	865.007i	−0.604267	+	1.12193i
$772$		0			0
$773$	−761.999	−	439.940i	−0.985769	−	0.569134i	−0.0817619	−	0.996652i	$-0.526055\pi$
$773$	−761.999	−	439.940i	−0.985769	−	0.569134i	−0.904007	+	0.427518i	$0.859388\pi$
$774$		0			0
$775$	−1009.68	+	1748.82i	−1.30282	+	2.25654i
$776$		0			0
$777$	−444.992	−	239.671i	−0.572705	−	0.308457i
$778$		0			0
$779$	653.896	+	356.767i	0.839404	+	0.457981i
$780$		0			0
$781$	7.17428	−	12.4262i	0.00918601	−	0.0159106i
$782$		0			0
$783$	1364.07	−	121.255i	1.74211	−	0.154860i
$784$		0			0
$785$			707.684i			0.901508i
$786$		0			0
$787$	−390.537	+	676.431i	−0.496236	+	0.859505i	−0.999991	−	0.00434131i	$-0.998618\pi$
$787$	−390.537	+	676.431i	−0.496236	+	0.859505i	0.503755	+	0.863847i	$0.331951\pi$
$788$		0			0
$789$	205.746	−	6.08219i	0.260769	−	0.00770873i
$790$		0			0
$791$			238.546i			0.301576i
$792$		0			0
$793$	584.276	+	1012.00i	0.736792	+	1.27616i
$794$		0			0
$795$	10.0003	+	338.286i	0.0125790	+	0.425517i
$796$		0			0
$797$	105.463	+	60.8893i	0.132326	+	0.0763982i	0.564701	−	0.825295i	$-0.308991\pi$
$797$	105.463	+	60.8893i	0.132326	+	0.0763982i	−0.432376	+	0.901693i	$0.642325\pi$
$798$		0			0
$799$	718.513	+	1244.50i	0.899266	+	1.55757i
$800$		0			0
$801$	680.747	−	448.640i	0.849872	−	0.560100i
$802$		0			0
$803$	−134.754	−	77.8005i	−0.167814	−	0.0968873i
$804$		0			0
$805$	−130.542	+	226.106i	−0.162165	+	0.280877i
$806$		0			0
$807$	−98.0586	+	182.063i	−0.121510	+	0.225605i
$808$		0			0
$809$		−	100.026i		−	0.123641i	−0.998087	−	0.0618206i	$-0.980309\pi$
$809$		−	100.026i		−	0.123641i	0.998087	−	0.0618206i	$-0.0196907\pi$
$810$		0			0
$811$	−418.778	+	725.345i	−0.516373	+	0.894384i	0.483447	+	0.875374i	$0.339385\pi$
$811$	−418.778	+	725.345i	−0.516373	+	0.894384i	−0.999819	+	0.0190097i	$0.993949\pi$
$812$		0			0
$813$	−826.602	−	445.205i	−1.01673	−	0.547607i
$814$		0			0
$815$		−	123.946i		−	0.152081i
$816$		0			0
$817$	77.9967	+	127.864i	0.0954671	+	0.156505i
$818$		0			0
$819$	428.082	+	649.553i	0.522689	+	0.793105i
$820$		0			0
$821$			444.733i			0.541697i	0.962622	+	0.270848i	$0.0873042\pi$
$821$			444.733i			0.541697i	−0.962622	+	0.270848i	$0.912696\pi$
$822$		0			0
$823$	−664.390	−	1150.76i	−0.807279	−	1.39825i	−0.914742	−	0.404038i	$-0.867606\pi$
$823$	−664.390	−	1150.76i	−0.807279	−	1.39825i	0.107463	−	0.994209i	$-0.465727\pi$
$824$		0			0
$825$	−354.917	+	658.966i	−0.430202	+	0.798747i
$826$		0			0
$827$	20.0177	+	11.5572i	0.0242052	+	0.0139749i	0.512054	−	0.858953i	$-0.328885\pi$
$827$	20.0177	+	11.5572i	0.0242052	+	0.0139749i	−0.487849	+	0.872928i	$0.662218\pi$
$828$		0			0
$829$	536.977			0.647741			0.323870	−	0.946101i	$-0.395016\pi$
$829$	536.977			0.647741			0.323870	+	0.946101i	$0.395016\pi$
$830$		0			0
$831$	−1339.74	−	721.581i	−1.61221	−	0.868328i
$832$		0			0
$833$			135.524i			0.162693i
$834$		0			0
$835$	−290.156	−	502.565i	−0.347492	−	0.601874i
$836$		0			0
$837$	860.236	+	399.677i	1.02776	+	0.477512i
$838$		0			0
$839$	−886.610	−	511.884i	−1.05675	−	0.610112i	−0.132215	−	0.991221i	$-0.542209\pi$
$839$	−886.610	−	511.884i	−1.05675	−	0.610112i	−0.924530	+	0.381109i	$0.875542\pi$
$840$		0			0
$841$	−1731.57			−2.05894
$842$		0			0
$843$	−728.187	−	1179.35i	−0.863804	−	1.39899i
$844$		0			0
$845$	−266.347	−	153.776i	−0.315204	−	0.181983i
$846$		0			0
$847$	−759.619			−0.896835
$848$		0			0
$849$	−133.018	+	82.1319i	−0.156676	+	0.0967396i
$850$		0			0
$851$	−75.8671	+	43.8019i	−0.0891505	+	0.0514711i
$852$		0			0
$853$	577.893	−	1000.94i	0.677483	−	1.17344i	−0.298253	−	0.954487i	$-0.596404\pi$
$853$	577.893	−	1000.94i	0.677483	−	1.17344i	0.975736	−	0.218949i	$-0.0702627\pi$
$854$		0			0
$855$	1275.71	−	885.639i	1.49206	−	1.03583i
$856$		0			0
$857$	−486.622	−	280.952i	−0.567821	−	0.327832i	0.188458	−	0.982081i	$-0.439651\pi$
$857$	−486.622	−	280.952i	−0.567821	−	0.327832i	−0.756279	+	0.654250i	$0.772984\pi$
$858$		0			0
$859$	379.879	+	657.969i	0.442233	+	0.765971i	0.997855	−	0.0654645i	$-0.0208529\pi$
$859$	379.879	+	657.969i	0.442233	+	0.765971i	−0.555621	+	0.831435i	$0.687520\pi$
$860$		0			0
$861$	−414.693	+	769.951i	−0.481641	+	0.894253i
$862$		0			0
$863$		−	1588.53i		−	1.84071i	−0.391089	−	0.920353i	$-0.627902\pi$
$863$		−	1588.53i		−	1.84071i	0.391089	−	0.920353i	$-0.372098\pi$
$864$		0			0
$865$	−782.910	+	1356.04i	−0.905098	+	1.56768i
$866$		0			0
$867$	15.5697	+	526.686i	0.0179581	+	0.607481i
$868$		0			0
$869$			551.931i			0.635133i
$870$		0			0
$871$	427.077	−	739.720i	0.490330	−	0.849276i
$872$		0			0
$873$	−295.521	−	448.411i	−0.338512	−	0.513644i
$874$		0			0
$875$	−1899.48	+	1096.67i	−2.17084	+	1.25333i
$876$		0			0
$877$	−159.031			−0.181335			−0.0906676	−	0.995881i	$-0.528900\pi$
$877$	−159.031			−0.181335			−0.0906676	+	0.995881i	$0.528900\pi$
$878$		0			0
$879$	−723.827	+	21.3975i	−0.823467	+	0.0243430i
$880$		0			0
$881$		−	1052.85i		−	1.19506i	−0.801848	−	0.597529i	$-0.796149\pi$
$881$		−	1052.85i		−	1.19506i	0.801848	−	0.597529i	$-0.203851\pi$
$882$		0			0
$883$	598.786	−	1037.13i	0.678127	−	1.17455i	−0.297418	−	0.954747i	$-0.596125\pi$
$883$	598.786	−	1037.13i	0.678127	−	1.17455i	0.975544	−	0.219802i	$-0.0705413\pi$
$884$		0			0
$885$	2631.92	−	1625.08i	2.97392	−	1.83624i
$886$		0			0
$887$	−1372.55	+	792.445i	−1.54741	+	0.893399i	−0.549074	+	0.835774i	$0.685020\pi$
$887$	−1372.55	+	792.445i	−1.54741	+	0.893399i	−0.998338	+	0.0576255i	$0.981647\pi$
$888$		0			0
$889$	1688.31			1.89911
$890$		0			0
$891$	323.080	+	138.652i	0.362604	+	0.155614i
$892$		0			0
$893$	−1111.93	−	606.670i	−1.24516	−	0.679362i
$894$		0			0
$895$	529.155			0.591234
$896$		0			0
$897$	134.776	−	3.98418i	0.150252	−	0.00444167i
$898$		0			0
$899$	−1543.16	−	890.943i	−1.71653	−	0.991038i
$900$		0			0
$901$	267.754			0.297174
$902$		0			0
$903$	−149.619	+	92.3821i	−0.165691	+	0.102306i
$904$		0			0
$905$	2345.02	+	1353.90i	2.59118	+	1.49602i
$906$		0			0
$907$	−603.276	+	1044.91i	−0.665134	+	1.15205i	0.314115	+	0.949385i	$0.398292\pi$
$907$	−603.276	+	1044.91i	−0.665134	+	1.15205i	−0.979249	+	0.202661i	$0.935041\pi$
$908$		0			0
$909$	−1287.72	−	645.223i	−1.41664	−	0.709816i
$910$		0			0
$911$	−1358.72	+	784.455i	−1.49145	+	0.861092i	−0.999952	−	0.00978430i	$-0.996886\pi$
$911$	−1358.72	+	784.455i	−1.49145	+	0.861092i	−0.491503	+	0.870876i	$0.663552\pi$
$912$		0			0
$913$	192.476	−	333.378i	0.210817	−	0.365146i
$914$		0			0
$915$	1438.88	+	2330.36i	1.57255	+	2.54685i
$916$		0			0
$917$	520.224	−	300.351i	0.567311	−	0.327537i
$918$		0			0
$919$	−191.924			−0.208840			−0.104420	−	0.994533i	$-0.533299\pi$
$919$	−191.924			−0.208840			−0.104420	+	0.994533i	$0.533299\pi$
$920$		0			0
$921$	56.3834	+	30.3679i	0.0612198	+	0.0329727i
$922$		0			0
$923$	−33.2805	−	19.2145i	−0.0360569	−	0.0208175i
$924$		0			0
$925$	−1302.41			−1.40801
$926$		0			0
$927$	166.024	+	251.917i	0.179098	+	0.271755i
$928$		0			0
$929$	1180.04	+	681.296i	1.27023	+	0.733365i	0.975030	−	0.222072i	$-0.0712819\pi$
$929$	1180.04	+	681.296i	1.27023	+	0.733365i	0.295195	+	0.955437i	$0.404615\pi$
$930$		0			0
$931$	−62.2079	−	101.981i	−0.0668183	−	0.109539i
$932$		0			0
$933$	791.051	−	23.3847i	0.847857	−	0.0250640i
$934$		0			0
$935$	735.862	+	424.850i	0.787018	+	0.454385i
$936$		0			0
$937$	−862.482	+	1493.86i	−0.920472	+	1.59430i	−0.121787	+	0.992556i	$0.538862\pi$
$937$	−862.482	+	1493.86i	−0.920472	+	1.59430i	−0.798686	+	0.601748i	$0.794471\pi$
$938$		0			0
$939$	20.6493	−	12.7499i	0.0219908	−	0.0135782i
$940$		0			0
$941$	886.266	−	511.686i	0.941834	−	0.543768i	0.0512992	−	0.998683i	$-0.483664\pi$
$941$	886.266	−	511.686i	0.941834	−	0.543768i	0.890535	+	0.454915i	$0.150330\pi$
$942$		0			0
$943$	75.7886	+	131.270i	0.0803697	+	0.139204i
$944$		0			0
$945$	1047.86	+	1492.08i	1.10885	+	1.57892i
$946$		0			0
$947$	−622.249	−	359.256i	−0.657074	−	0.379362i	0.134087	−	0.990970i	$-0.457190\pi$
$947$	−622.249	−	359.256i	−0.657074	−	0.379362i	−0.791161	+	0.611608i	$0.790523\pi$
$948$		0			0
$949$	−208.369	+	360.907i	−0.219567	+	0.380302i
$950$		0			0
$951$	−21.9070	−	35.4798i	−0.0230358	−	0.0373079i
$952$		0			0
$953$	−203.586	+	117.541i	−0.213627	+	0.123337i	−0.602996	−	0.797744i	$-0.706026\pi$
$953$	−203.586	+	117.541i	−0.213627	+	0.123337i	0.389369	+	0.921082i	$0.372693\pi$
$954$		0			0
$955$	571.471	+	989.818i	0.598399	+	1.03646i
$956$		0			0
$957$	−581.472	−	313.179i	−0.607599	−	0.327250i
$958$		0			0
$959$	−1294.27	+	747.249i	−1.34961	+	0.779196i
$960$		0			0
$961$	−136.611	−	236.617i	−0.142155	−	0.246219i
$962$		0			0
$963$	−913.259	−	457.595i	−0.948348	−	0.475176i
$964$		0			0
$965$		−	702.491i		−	0.727970i
$966$		0			0
$967$	943.049			0.975232			0.487616	−	0.873058i	$-0.337867\pi$
$967$	943.049			0.975232			0.487616	+	0.873058i	$0.337867\pi$
$968$		0			0
$969$	−670.549	−	1029.55i	−0.692001	−	1.06249i
$970$		0			0
$971$	−620.444	+	358.213i	−0.638974	+	0.368912i	−0.784219	−	0.620484i	$-0.786936\pi$
$971$	−620.444	+	358.213i	−0.638974	+	0.368912i	0.145245	+	0.989396i	$0.453603\pi$
$972$		0			0
$973$	859.696	−	1489.04i	0.883551	−	1.53036i
$974$		0			0
$975$	1764.88	+	950.557i	1.81013	+	0.974930i
$976$		0			0
$977$	39.2042	+	22.6345i	0.0401271	+	0.0231674i	0.519929	−	0.854209i	$-0.325958\pi$
$977$	39.2042	+	22.6345i	0.0401271	+	0.0231674i	−0.479802	+	0.877377i	$0.659292\pi$
$978$		0			0
$979$	−393.190			−0.401624
$980$		0			0
$981$	−503.113	+	29.7717i	−0.512858	+	0.0303483i
$982$		0			0
$983$	1053.36	+	608.160i	1.07158	+	0.618677i	0.928613	−	0.371050i	$-0.121002\pi$
$983$	1053.36	+	608.160i	1.07158	+	0.618677i	0.142968	+	0.989727i	$0.454335\pi$
$984$		0			0
$985$	−973.829			−0.988659
$986$		0			0
$987$	705.171	−	1309.28i	0.714459	−	1.32652i
$988$		0			0
$989$			30.4777i			0.0308167i
$990$		0			0
$991$	−317.064	−	549.171i	−0.319944	−	0.554159i	0.660532	−	0.750798i	$-0.270331\pi$
$991$	−317.064	−	549.171i	−0.319944	−	0.554159i	−0.980476	+	0.196639i	$0.936997\pi$
$992$		0			0
$993$	−65.7514	−	35.4135i	−0.0662149	−	0.0356631i
$994$		0			0
$995$	383.017	+	221.135i	0.384941	+	0.222246i
$996$		0			0
$997$	−292.131			−0.293010			−0.146505	−	0.989210i	$-0.546802\pi$
$997$	−292.131			−0.293010			−0.146505	+	0.989210i	$0.546802\pi$
$998$		0			0
$999$	54.1683	+	609.372i	0.0542225	+	0.609982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.653.8	yes	80
3.2	odd	2		2052.3.m.a.881.39		80
9.2	odd	6		684.3.be.a.425.34	yes	80
9.7	even	3		2052.3.be.a.197.39		80
19.11	even	3		684.3.be.a.581.34	yes	80
57.11	odd	6		2052.3.be.a.125.39		80
171.11	odd	6	inner	684.3.m.a.353.8	✓	80
171.106	even	3		2052.3.m.a.1493.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.8	✓	80	171.11	odd	6	inner
684.3.m.a.653.8	yes	80	1.1	even	1	trivial
684.3.be.a.425.34	yes	80	9.2	odd	6
684.3.be.a.581.34	yes	80	19.11	even	3
2052.3.m.a.881.39		80	3.2	odd	2
2052.3.m.a.1493.2		80	171.106	even	3
2052.3.be.a.125.39		80	57.11	odd	6
2052.3.be.a.197.39		80	9.7	even	3

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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.55262 + 1.57611i) q^{3} -9.08186i q^{5} +(3.71777 + 6.43936i) q^{7} +(4.03172 - 8.04644i) q^{9} +O(q^{10})\)	\(q+(-2.55262 + 1.57611i) q^{3} -9.08186i q^{5} +(3.71777 + 6.43936i) q^{7} +(4.03172 - 8.04644i) q^{9} +(-3.75893 + 2.17022i) q^{11} +(5.81239 + 10.0674i) q^{13} +(14.3141 + 23.1825i) q^{15} +(18.6676 - 10.7777i) q^{17} +(-9.10009 + 16.6790i) q^{19} +(-19.6392 - 10.5776i) q^{21} +(-3.34831 + 1.93315i) q^{23} -57.4802 q^{25} +(2.39066 + 26.8940i) q^{27} -50.7205i q^{29} +(17.5657 - 30.4248i) q^{31} +(6.17460 - 11.4642i) q^{33} +(58.4814 - 33.7642i) q^{35} +22.6583 q^{37} +(-30.7041 - 16.5371i) q^{39} -39.2048i q^{41} +(3.94146 - 6.82682i) q^{43} +(-73.0766 - 36.6156i) q^{45} +66.6664i q^{47} +(-3.14360 + 5.44487i) q^{49} +(-30.6643 + 56.9337i) q^{51} +(10.7574 + 6.21080i) q^{53} +(19.7096 + 34.1381i) q^{55} +(-3.05893 - 56.9179i) q^{57} -113.530i q^{59} +100.522 q^{61} +(66.8030 - 3.95306i) q^{63} +(91.4303 - 52.7873i) q^{65} +(-36.7385 - 63.6330i) q^{67} +(5.50009 - 10.2119i) q^{69} +(-2.86289 + 1.65289i) q^{71} +(17.9246 + 31.0463i) q^{73} +(146.725 - 90.5953i) q^{75} +(-27.9496 - 16.1367i) q^{77} +(63.5801 - 110.124i) q^{79} +(-48.4904 - 64.8821i) q^{81} +(-76.8076 + 44.3449i) q^{83} +(-97.8819 - 169.536i) q^{85} +(79.9413 + 129.470i) q^{87} +(78.4512 + 45.2938i) q^{89} +(-43.2183 + 74.8562i) q^{91} +(3.11427 + 105.348i) q^{93} +(151.476 + 82.6457i) q^{95} +(29.8352 - 51.6761i) q^{97} +(2.30757 + 38.9957i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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