LMFDB - Embedded newform 684.3.t.a.265.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(265,684)]

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, 3]))

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

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

chi := DirichletCharacter("684.265");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.t (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			265.17
Character	$\chi$	$=$	684.265
Dual form			684.3.t.a.493.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.960366 - 2.84213i) q^{3} +(4.33807 - 7.51375i) q^{5} +(-2.48195 - 4.29886i) q^{7} +(-7.15540 + 5.45897i) q^{9} +O(q^{10})$	\(q+(-0.960366 - 2.84213i) q^{3} +(4.33807 - 7.51375i) q^{5} +(-2.48195 - 4.29886i) q^{7} +(-7.15540 + 5.45897i) q^{9} +(-5.84041 - 10.1159i) q^{11} +(-2.45073 - 1.41493i) q^{13} +(-25.5212 - 5.11340i) q^{15} -27.2126 q^{17} +(12.6074 + 14.2145i) q^{19} +(-9.83434 + 11.1825i) q^{21} +(-4.73905 + 8.20828i) q^{23} +(-25.1377 - 43.5397i) q^{25} +(22.3869 + 15.0940i) q^{27} +(40.9359 - 23.6343i) q^{29} +(48.2087 + 27.8333i) q^{31} +(-23.1417 + 26.3142i) q^{33} -43.0674 q^{35} -19.0327i q^{37} +(-1.66781 + 8.32413i) q^{39} +(-55.3669 - 31.9661i) q^{41} +(11.2303 + 19.4514i) q^{43} +(9.97674 + 77.4453i) q^{45} +(0.297483 + 0.515256i) q^{47} +(12.1799 - 21.0962i) q^{49} +(26.1340 + 77.3417i) q^{51} +46.8587i q^{53} -101.344 q^{55} +(28.2918 - 49.4831i) q^{57} +(30.2212 + 17.4482i) q^{59} +(3.32779 + 5.76390i) q^{61} +(41.2266 + 17.2112i) q^{63} +(-21.2628 + 12.2761i) q^{65} +(-10.5087 - 6.06721i) q^{67} +(27.8802 + 5.58605i) q^{69} +56.3185i q^{71} +77.7499 q^{73} +(-99.6042 + 113.259i) q^{75} +(-28.9912 + 50.2142i) q^{77} +(-118.896 + 68.6448i) q^{79} +(21.3994 - 78.1221i) q^{81} +(-77.2040 - 133.721i) q^{83} +(-118.050 + 204.469i) q^{85} +(-106.485 - 93.6475i) q^{87} -158.272i q^{89} +14.0471i q^{91} +(32.8079 - 163.745i) q^{93} +(161.496 - 33.0656i) q^{95} +(-159.698 + 92.2018i) q^{97} +(97.0128 + 40.5006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 2 * q^7 + 4 * q^9	$ 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) $ 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.960366	−	2.84213i	−0.320122	−	0.947376i
$3$	−0.960366	−	2.84213i	−0.320122	−	0.947376i
$4$		0			0
$5$	4.33807	−	7.51375i	0.867614	−	1.50275i	0.00318527	−	0.999995i	$-0.498986\pi$
$5$	4.33807	−	7.51375i	0.867614	−	1.50275i	0.864428	−	0.502756i	$-0.167681\pi$
$6$		0			0
$7$	−2.48195	−	4.29886i	−0.354564	−	0.614123i	0.632479	−	0.774577i	$-0.282037\pi$
$7$	−2.48195	−	4.29886i	−0.354564	−	0.614123i	−0.987043	+	0.160454i	$0.948704\pi$
$8$		0			0
$9$	−7.15540	+	5.45897i	−0.795044	+	0.606552i
$10$		0			0
$11$	−5.84041	−	10.1159i	−0.530947	−	0.919627i	−0.999348	−	0.0361107i	$-0.988503\pi$
$11$	−5.84041	−	10.1159i	−0.530947	−	0.919627i	0.468401	−	0.883516i	$-0.344830\pi$
$12$		0			0
$13$	−2.45073	−	1.41493i	−0.188517	−	0.108841i	0.402771	−	0.915301i	$-0.368047\pi$
$13$	−2.45073	−	1.41493i	−0.188517	−	0.108841i	−0.591288	+	0.806460i	$0.701380\pi$
$14$		0			0
$15$	−25.5212	−	5.11340i	−1.70141	−	0.340893i
$16$		0			0
$17$	−27.2126			−1.60074			−0.800370	−	0.599506i	$-0.795364\pi$
$17$	−27.2126			−1.60074			−0.800370	+	0.599506i	$0.795364\pi$
$18$		0			0
$19$	12.6074	+	14.2145i	0.663549	+	0.748133i
$19$	12.6074	+	14.2145i	0.663549	+	0.748133i
$20$		0			0
$21$	−9.83434	+	11.1825i	−0.468302	+	0.532500i
$22$		0			0
$23$	−4.73905	+	8.20828i	−0.206046	+	0.356882i	−0.950465	−	0.310830i	$-0.899393\pi$
$23$	−4.73905	+	8.20828i	−0.206046	+	0.356882i	0.744420	+	0.667712i	$0.232726\pi$
$24$		0			0
$25$	−25.1377	−	43.5397i	−1.00551	−	1.74159i
$26$		0			0
$27$	22.3869	+	15.0940i	0.829144	+	0.559035i
$28$		0			0
$29$	40.9359	−	23.6343i	1.41158	−	0.814977i	0.416045	−	0.909344i	$-0.363416\pi$
$29$	40.9359	−	23.6343i	1.41158	−	0.814977i	0.995538	+	0.0943667i	$0.0300826\pi$
$30$		0			0
$31$	48.2087	+	27.8333i	1.55512	+	0.897848i	0.997712	+	0.0676090i	$0.0215370\pi$
$31$	48.2087	+	27.8333i	1.55512	+	0.897848i	0.557407	+	0.830239i	$0.311796\pi$
$32$		0			0
$33$	−23.1417	+	26.3142i	−0.701265	+	0.797399i
$34$		0			0
$35$	−43.0674			−1.23050
$36$		0			0
$37$		−	19.0327i		−	0.514396i	−0.966359	−	0.257198i	$-0.917201\pi$
$37$		−	19.0327i		−	0.514396i	0.966359	−	0.257198i	$-0.0827993\pi$
$38$		0			0
$39$	−1.66781	+	8.32413i	−0.0427645	+	0.213439i
$40$		0			0
$41$	−55.3669	−	31.9661i	−1.35041	−	0.779661i	−0.362105	−	0.932137i	$-0.617942\pi$
$41$	−55.3669	−	31.9661i	−1.35041	−	0.779661i	−0.988307	+	0.152477i	$0.951275\pi$
$42$		0			0
$43$	11.2303	+	19.4514i	0.261169	+	0.452359i	0.966553	−	0.256467i	$-0.0825586\pi$
$43$	11.2303	+	19.4514i	0.261169	+	0.452359i	−0.705384	+	0.708826i	$0.749225\pi$
$44$		0			0
$45$	9.97674	+	77.4453i	0.221705	+	1.72101i
$46$		0			0
$47$	0.297483	+	0.515256i	0.00632943	+	0.0109629i	0.869173	−	0.494509i	$-0.164652\pi$
$47$	0.297483	+	0.515256i	0.00632943	+	0.0109629i	−0.862843	+	0.505471i	$0.831319\pi$
$48$		0			0
$49$	12.1799	−	21.0962i	0.248569	−	0.430534i
$50$		0			0
$51$	26.1340	+	77.3417i	0.512432	+	1.51650i
$52$		0			0
$53$			46.8587i			0.884127i	0.896984	+	0.442064i	$0.145753\pi$
$53$			46.8587i			0.884127i	−0.896984	+	0.442064i	$0.854247\pi$
$54$		0			0
$55$	−101.344			−1.84263
$56$		0			0
$57$	28.2918	−	49.4831i	0.496347	−	0.868124i
$58$		0			0
$59$	30.2212	+	17.4482i	0.512224	+	0.295733i	0.733747	−	0.679422i	$-0.237770\pi$
$59$	30.2212	+	17.4482i	0.512224	+	0.295733i	−0.221523	+	0.975155i	$0.571103\pi$
$60$		0			0
$61$	3.32779	+	5.76390i	0.0545539	+	0.0944902i	0.892013	−	0.452010i	$-0.149293\pi$
$61$	3.32779	+	5.76390i	0.0545539	+	0.0944902i	−0.837459	+	0.546500i	$0.815960\pi$
$62$		0			0
$63$	41.2266	+	17.2112i	0.654391	+	0.273193i
$64$		0			0
$65$	−21.2628	+	12.2761i	−0.327121	+	0.188863i
$66$		0			0
$67$	−10.5087	−	6.06721i	−0.156846	−	0.0905554i	0.419522	−	0.907745i	$-0.362198\pi$
$67$	−10.5087	−	6.06721i	−0.156846	−	0.0905554i	−0.576369	+	0.817190i	$0.695531\pi$
$68$		0			0
$69$	27.8802	+	5.58605i	0.404061	+	0.0809572i
$70$		0			0
$71$			56.3185i			0.793219i	0.917987	+	0.396609i	$0.129813\pi$
$71$			56.3185i			0.793219i	−0.917987	+	0.396609i	$0.870187\pi$
$72$		0			0
$73$	77.7499			1.06507			0.532534	−	0.846409i	$-0.321240\pi$
$73$	77.7499			1.06507			0.532534	+	0.846409i	$0.321240\pi$
$74$		0			0
$75$	−99.6042	+	113.259i	−1.32806	+	1.51011i
$76$		0			0
$77$	−28.9912	+	50.2142i	−0.376509	+	0.652133i
$78$		0			0
$79$	−118.896	+	68.6448i	−1.50502	+	0.868921i	−0.505033	+	0.863100i	$0.668520\pi$
$79$	−118.896	+	68.6448i	−1.50502	+	0.868921i	−0.999983	+	0.00582122i	$0.998147\pi$
$80$		0			0
$81$	21.3994	−	78.1221i	0.264190	−	0.964471i
$82$		0			0
$83$	−77.2040	−	133.721i	−0.930169	−	1.61110i	−0.783030	−	0.621983i	$-0.786327\pi$
$83$	−77.2040	−	133.721i	−0.930169	−	1.61110i	−0.147138	−	0.989116i	$-0.547006\pi$
$84$		0			0
$85$	−118.050	+	204.469i	−1.38882	+	2.40551i
$86$		0			0
$87$	−106.485	−	93.6475i	−1.22397	−	1.07641i
$88$		0			0
$89$		−	158.272i		−	1.77834i	−0.457577	−	0.889170i	$-0.651283\pi$
$89$		−	158.272i		−	1.77834i	0.457577	−	0.889170i	$-0.348717\pi$
$90$		0			0
$91$			14.0471i			0.154364i
$92$		0			0
$93$	32.8079	−	163.745i	0.352773	−	1.76070i
$94$		0			0
$95$	161.496	−	33.0656i	1.69996	−	0.348059i
$96$		0			0
$97$	−159.698	+	92.2018i	−1.64637	+	0.950535i	−0.667878	+	0.744271i	$0.732797\pi$
$97$	−159.698	+	92.2018i	−1.64637	+	0.950535i	−0.978497	+	0.206263i	$0.933870\pi$
$98$		0			0
$99$	97.0128	+	40.5006i	0.979927	+	0.409097i
$100$		0			0
$101$	−49.6534	−	86.0023i	−0.491618	−	0.851508i	0.508335	−	0.861159i	$-0.330261\pi$
$101$	−49.6534	−	86.0023i	−0.491618	−	0.851508i	−0.999953	+	0.00965159i	$0.996928\pi$
$102$		0			0
$103$	−139.875	−	80.7568i	−1.35801	−	0.784046i	−0.368653	−	0.929567i	$-0.620181\pi$
$103$	−139.875	−	80.7568i	−1.35801	−	0.784046i	−0.989355	+	0.145521i	$0.953514\pi$
$104$		0			0
$105$	41.3605	+	122.403i	0.393909	+	1.16574i
$106$		0			0
$107$			100.411i			0.938421i	0.883086	+	0.469210i	$0.155461\pi$
$107$			100.411i			0.938421i	−0.883086	+	0.469210i	$0.844539\pi$
$108$		0			0
$109$		−	10.0693i		−	0.0923791i	−0.998933	−	0.0461896i	$-0.985292\pi$
$109$		−	10.0693i		−	0.0923791i	0.998933	−	0.0461896i	$-0.0147078\pi$
$110$		0			0
$111$	−54.0933	+	18.2783i	−0.487327	+	0.164669i
$112$		0			0
$113$	−52.6100	−	30.3744i	−0.465575	−	0.268800i	0.248810	−	0.968552i	$-0.419960\pi$
$113$	−52.6100	−	30.3744i	−0.465575	−	0.268800i	−0.714386	+	0.699752i	$0.753294\pi$
$114$		0			0
$115$	41.1167	+	71.2162i	0.357536	+	0.619271i
$116$		0			0
$117$	25.2600	−	3.25407i	0.215897	−	0.0278125i
$118$		0			0
$119$	67.5402	+	116.983i	0.567565	+	0.983051i
$120$		0			0
$121$	−7.72085	+	13.3729i	−0.0638087	+	0.110520i
$122$		0			0
$123$	−37.6793	+	188.059i	−0.306336	+	1.52893i
$124$		0			0
$125$	−219.292			−1.75434
$126$		0			0
$127$			30.4094i			0.239444i	0.992807	+	0.119722i	$0.0382004\pi$
$127$			30.4094i			0.239444i	−0.992807	+	0.119722i	$0.961800\pi$
$128$		0			0
$129$	44.4983	−	50.5984i	0.344948	−	0.392236i
$130$		0			0
$131$	113.936	−	197.343i	0.869742	−	1.50644i	0.00748187	−	0.999972i	$-0.497618\pi$
$131$	113.936	−	197.343i	0.869742	−	1.50644i	0.862260	−	0.506465i	$-0.169048\pi$
$132$		0			0
$133$	29.8152	−	89.4773i	0.224175	−	0.672762i
$134$		0			0
$135$	210.528	−	102.731i	1.55947	−	0.760970i
$136$		0			0
$137$	93.2895	+	161.582i	0.680945	+	1.17943i	0.974693	+	0.223549i	$0.0717642\pi$
$137$	93.2895	+	161.582i	0.680945	+	1.17943i	−0.293748	+	0.955883i	$0.594902\pi$
$138$		0			0
$139$	−65.2083	+	112.944i	−0.469125	+	0.812548i	−0.999377	−	0.0352922i	$-0.988764\pi$
$139$	−65.2083	+	112.944i	−0.469125	+	0.812548i	0.530252	+	0.847840i	$0.322097\pi$
$140$		0			0
$141$	1.17873	−	1.34032i	0.00835979	−	0.00950581i
$142$		0			0
$143$			33.0551i			0.231154i
$144$		0			0
$145$		−	410.110i		−	2.82834i
$146$		0			0
$147$	−71.6551	−	14.3567i	−0.487450	−	0.0976649i
$148$		0			0
$149$	48.6250	−	84.2210i	0.326342	−	0.565242i	−0.655441	−	0.755247i	$-0.727517\pi$
$149$	48.6250	−	84.2210i	0.326342	−	0.565242i	0.981783	+	0.190005i	$0.0608504\pi$
$150$		0			0
$151$	89.2805	−	51.5461i	0.591261	−	0.341365i	−0.174335	−	0.984686i	$-0.555777\pi$
$151$	89.2805	−	51.5461i	0.591261	−	0.341365i	0.765596	+	0.643322i	$0.222444\pi$
$152$		0			0
$153$	194.717	−	148.553i	1.27266	−	0.970932i
$154$		0			0
$155$	418.265	−	241.485i	2.69848	−	1.55797i
$156$		0			0
$157$	−66.5134	+	115.205i	−0.423652	+	0.733787i	−0.996293	−	0.0860190i	$-0.972585\pi$
$157$	−66.5134	+	115.205i	−0.423652	+	0.733787i	0.572641	+	0.819806i	$0.305919\pi$
$158$		0			0
$159$	133.179	−	45.0015i	0.837601	−	0.283028i
$160$		0			0
$161$	47.0483			0.292226
$162$		0			0
$163$	−61.0567			−0.374581			−0.187291	−	0.982305i	$-0.559971\pi$
$163$	−61.0567			−0.374581			−0.187291	+	0.982305i	$0.559971\pi$
$164$		0			0
$165$	97.3277	+	288.034i	0.589865	+	1.74566i
$166$		0			0
$167$	203.678	+	117.594i	1.21963	+	0.704153i	0.964839	−	0.262843i	$-0.0846601\pi$
$167$	203.678	+	117.594i	1.21963	+	0.704153i	0.254791	+	0.966996i	$0.417993\pi$
$168$		0			0
$169$	−80.4960	−	139.423i	−0.476307	−	0.824989i
$170$		0			0
$171$	−167.808	−	32.8870i	−0.981332	−	0.192321i
$172$		0			0
$173$	−21.6447	+	12.4966i	−0.125114	+	0.0722346i	−0.561251	−	0.827646i	$-0.689680\pi$
$173$	−21.6447	+	12.4966i	−0.125114	+	0.0722346i	0.436137	+	0.899880i	$0.356346\pi$
$174$		0			0
$175$	−124.781	+	216.127i	−0.713033	+	1.23501i
$176$		0			0
$177$	20.5667	−	102.649i	0.116196	−	0.579939i
$178$		0			0
$179$		−	36.3803i		−	0.203242i	−0.994823	−	0.101621i	$-0.967597\pi$
$179$		−	36.3803i		−	0.203242i	0.994823	−	0.101621i	$-0.0324029\pi$
$180$		0			0
$181$		−	42.5984i		−	0.235350i	−0.993052	−	0.117675i	$-0.962456\pi$
$181$		−	42.5984i		−	0.235350i	0.993052	−	0.117675i	$-0.0375441\pi$
$182$		0			0
$183$	13.1859	−	14.9935i	0.0720538	−	0.0819315i
$184$		0			0
$185$	−143.007	−	82.5650i	−0.773009	−	0.446297i
$186$		0			0
$187$	158.933	+	275.280i	0.849908	+	1.47208i
$188$		0			0
$189$	9.32372	−	133.700i	0.0493318	−	0.707410i
$190$		0			0
$191$	−86.2073	−	149.315i	−0.451347	−	0.781756i	0.547123	−	0.837052i	$-0.315723\pi$
$191$	−86.2073	−	149.315i	−0.451347	−	0.781756i	−0.998470	+	0.0552963i	$0.982390\pi$
$192$		0			0
$193$	−18.4568	−	10.6560i	−0.0956310	−	0.0552126i	0.451422	−	0.892311i	$-0.350917\pi$
$193$	−18.4568	−	10.6560i	−0.0956310	−	0.0552126i	−0.547053	+	0.837098i	$0.684250\pi$
$194$		0			0
$195$	55.3104	+	48.6422i	0.283643	+	0.249447i
$196$		0			0
$197$	99.3815			0.504474			0.252237	−	0.967665i	$-0.418834\pi$
$197$	99.3815			0.504474			0.252237	+	0.967665i	$0.418834\pi$
$198$		0			0
$199$	45.5383			0.228836			0.114418	−	0.993433i	$-0.463500\pi$
$199$	45.5383			0.228836			0.114418	+	0.993433i	$0.463500\pi$
$200$		0			0
$201$	−7.15158	+	35.6939i	−0.0355800	+	0.177581i
$202$		0			0
$203$	−203.201	−	117.318i	−1.00099	−	0.577923i
$204$		0			0
$205$	−480.371	+	277.342i	−2.34327	+	1.35289i
$206$		0			0
$207$	−10.8989	−	84.6038i	−0.0526518	−	0.408714i
$208$		0			0
$209$	70.1599	−	210.554i	0.335693	−	1.00744i
$210$		0			0
$211$	−169.598	−	97.9174i	−0.803782	−	0.464064i	0.0410102	−	0.999159i	$-0.486942\pi$
$211$	−169.598	−	97.9174i	−0.803782	−	0.464064i	−0.844792	+	0.535095i	$0.820276\pi$
$212$		0			0
$213$	160.065	−	54.0864i	0.751477	−	0.253927i
$214$		0			0
$215$	194.871			0.906376
$216$		0			0
$217$		−	276.323i		−	1.27338i
$218$		0			0
$219$	−74.6684	−	220.975i	−0.340951	−	1.00902i
$220$		0			0
$221$	66.6906	+	38.5039i	0.301768	+	0.174226i
$222$		0			0
$223$	249.710	−	144.170i	1.11978	−	0.646503i	0.178432	−	0.983952i	$-0.442898\pi$
$223$	249.710	−	144.170i	1.11978	−	0.646503i	0.941344	+	0.337450i	$0.109564\pi$
$224$		0			0
$225$	417.552	+	174.318i	1.85579	+	0.774748i
$226$		0			0
$227$	62.3055	−	35.9721i	0.274473	−	0.158467i	−0.356445	−	0.934316i	$-0.616011\pi$
$227$	62.3055	−	35.9721i	0.274473	−	0.158467i	0.630919	+	0.775849i	$0.282678\pi$
$228$		0			0
$229$	52.7384	−	91.3456i	0.230299	−	0.398889i	−0.727597	−	0.686005i	$-0.759363\pi$
$229$	52.7384	−	91.3456i	0.230299	−	0.398889i	0.957896	+	0.287115i	$0.0926963\pi$
$230$		0			0
$231$	170.557	+	34.1727i	0.738344	+	0.147934i
$232$		0			0
$233$	−273.916			−1.17561			−0.587804	−	0.809004i	$-0.700007\pi$
$233$	−273.916			−1.17561			−0.587804	+	0.809004i	$0.700007\pi$
$234$		0			0
$235$	5.16201			0.0219660
$236$		0			0
$237$	309.281	+	271.994i	1.30498	+	1.14766i
$238$		0			0
$239$	179.884	−	311.567i	0.752651	−	1.30363i	−0.193883	−	0.981025i	$-0.562108\pi$
$239$	179.884	−	311.567i	0.752651	−	1.30363i	0.946534	−	0.322605i	$-0.104558\pi$
$240$		0			0
$241$	107.059	−	61.8105i	0.444228	−	0.256475i	−0.261162	−	0.965295i	$-0.584106\pi$
$241$	107.059	−	61.8105i	0.444228	−	0.256475i	0.705389	+	0.708820i	$0.250772\pi$
$242$		0			0
$243$	−242.584	+	14.2060i	−0.998290	+	0.0584610i
$244$		0			0
$245$	−105.674	−	183.033i	−0.431323	−	0.747074i
$246$		0			0
$247$	−10.7849	−	52.6745i	−0.0436634	−	0.213257i
$248$		0			0
$249$	−305.909	+	347.845i	−1.22855	+	1.39697i
$250$		0			0
$251$	−71.4343			−0.284599			−0.142299	−	0.989824i	$-0.545450\pi$
$251$	−71.4343			−0.284599			−0.142299	+	0.989824i	$0.545450\pi$
$252$		0			0
$253$	110.712			0.437597
$254$		0			0
$255$	694.498	+	139.149i	2.72352	+	0.545682i
$256$		0			0
$257$	−244.351	−	141.076i	−0.950784	−	0.548935i	−0.0574595	−	0.998348i	$-0.518300\pi$
$257$	−244.351	−	141.076i	−0.950784	−	0.548935i	−0.893324	+	0.449413i	$0.851633\pi$
$258$		0			0
$259$	−81.8187	+	47.2381i	−0.315902	+	0.182386i
$260$		0			0
$261$	−163.893	+	392.581i	−0.627944	+	1.50414i
$262$		0			0
$263$	170.207	+	294.807i	0.647175	+	1.12094i	0.983795	+	0.179299i	$0.0573830\pi$
$263$	170.207	+	294.807i	0.647175	+	1.12094i	−0.336620	+	0.941641i	$0.609284\pi$
$264$		0			0
$265$	352.085	+	203.276i	1.32862	+	0.767081i
$266$		0			0
$267$	−449.830	+	151.999i	−1.68476	+	0.569286i
$268$		0			0
$269$		−	348.158i		−	1.29427i	−0.762376	−	0.647135i	$-0.775967\pi$
$269$		−	348.158i		−	1.29427i	0.762376	−	0.647135i	$-0.224033\pi$
$270$		0			0
$271$	−138.917			−0.512609			−0.256305	−	0.966596i	$-0.582505\pi$
$271$	−138.917			−0.512609			−0.256305	+	0.966596i	$0.582505\pi$
$272$		0			0
$273$	39.9237	−	13.4904i	0.146241	−	0.0494152i
$274$		0			0
$275$	−293.629	+	508.580i	−1.06774	+	1.84938i
$276$		0			0
$277$	−72.2969	−	125.222i	−0.261000	−	0.452064i	0.705508	−	0.708702i	$-0.250719\pi$
$277$	−72.2969	−	125.222i	−0.261000	−	0.452064i	−0.966508	+	0.256637i	$0.917385\pi$
$278$		0			0
$279$	−496.893	+	64.0113i	−1.78098	+	0.229431i
$280$		0			0
$281$	225.900	−	130.423i	0.803914	−	0.464140i	−0.0409241	−	0.999162i	$-0.513030\pi$
$281$	225.900	−	130.423i	0.803914	−	0.464140i	0.844838	+	0.535022i	$0.179697\pi$
$282$		0			0
$283$	93.9224	−	162.678i	0.331881	−	0.574835i	−0.650999	−	0.759078i	$-0.725650\pi$
$283$	93.9224	−	162.678i	0.331881	−	0.574835i	0.982881	+	0.184243i	$0.0589833\pi$
$284$		0			0
$285$	−249.072	−	427.238i	−0.873938	−	1.49908i
$286$		0			0
$287$			317.353i			1.10576i
$288$		0			0
$289$	451.525			1.56237
$290$		0			0
$291$	415.418	+	365.336i	1.42755	+	1.25545i
$292$		0			0
$293$	145.591	+	84.0569i	0.496897	+	0.286884i	0.727431	−	0.686181i	$-0.240714\pi$
$293$	145.591	+	84.0569i	0.496897	+	0.286884i	−0.230534	+	0.973064i	$0.574047\pi$
$294$		0			0
$295$	262.203	−	151.383i	0.888825	−	0.513163i
$296$		0			0
$297$	21.9402	−	314.618i	0.0738726	−	1.05932i
$298$		0			0
$299$	23.2283	−	13.4108i	0.0776865	−	0.0448523i
$300$		0			0
$301$	55.7459	−	96.5548i	0.185202	−	0.320780i
$302$		0			0
$303$	−196.744	+	223.715i	−0.649321	+	0.738334i
$304$		0			0
$305$	57.7447			0.189327
$306$		0			0
$307$			226.808i			0.738790i	0.929273	+	0.369395i	$0.120435\pi$
$307$			226.808i			0.738790i	−0.929273	+	0.369395i	$0.879565\pi$
$308$		0			0
$309$	−95.1902	+	475.098i	−0.308059	+	1.53754i
$310$		0			0
$311$	49.5527	−	85.8278i	0.159333	−	0.275974i	−0.775295	−	0.631599i	$-0.782399\pi$
$311$	49.5527	−	85.8278i	0.159333	−	0.275974i	0.934629	+	0.355626i	$0.115732\pi$
$312$		0			0
$313$	33.1262	+	57.3763i	0.105835	+	0.183311i	0.914079	−	0.405536i	$-0.132915\pi$
$313$	33.1262	+	57.3763i	0.105835	+	0.183311i	−0.808244	+	0.588847i	$0.799582\pi$
$314$		0			0
$315$	308.165	−	235.104i	0.978300	−	0.746361i
$316$		0			0
$317$	158.685	−	91.6170i	0.500584	−	0.289013i	−0.228370	−	0.973574i	$-0.573340\pi$
$317$	158.685	−	91.6170i	0.500584	−	0.289013i	0.728955	+	0.684562i	$0.240006\pi$
$318$		0			0
$319$	−478.165	−	276.069i	−1.49895	−	0.865419i
$320$		0			0
$321$	285.381	−	96.4313i	0.889038	−	0.300409i
$322$		0			0
$323$	−343.081	−	386.814i	−1.06217	−	1.19757i
$324$		0			0
$325$			142.272i			0.437760i
$326$		0			0
$327$	−28.6183	+	9.67023i	−0.0875178	+	0.0295726i
$328$		0			0
$329$	1.47668	−	2.55768i	0.00448837	−	0.00777409i
$330$		0			0
$331$	0.338861	−	0.195641i	0.00102375	−	0.000591062i	−0.499488	−	0.866321i	$-0.666479\pi$
$331$	0.338861	−	0.195641i	0.00102375	−	0.000591062i	0.500512	+	0.865730i	$0.333145\pi$
$332$		0			0
$333$	103.899	+	136.186i	0.312008	+	0.408968i
$334$		0			0
$335$	−91.1750	+	52.6399i	−0.272164	+	0.157134i
$336$		0			0
$337$	−114.430	−	66.0664i	−0.339556	−	0.196043i	0.320520	−	0.947242i	$-0.396142\pi$
$337$	−114.430	−	66.0664i	−0.339556	−	0.196043i	−0.660076	+	0.751199i	$0.729476\pi$
$338$		0			0
$339$	−35.8031	+	178.695i	−0.105614	+	0.527124i
$340$		0			0
$341$		−	650.232i		−	1.90684i
$342$		0			0
$343$	−364.150			−1.06166
$344$		0			0
$345$	162.918	−	185.252i	0.472227	−	0.536964i
$346$		0			0
$347$	−84.7430	+	146.779i	−0.244216	+	0.422995i	−0.961911	−	0.273363i	$-0.911864\pi$
$347$	−84.7430	+	146.779i	−0.244216	+	0.422995i	0.717695	+	0.696358i	$0.245197\pi$
$348$		0			0
$349$	240.268	+	416.156i	0.688446	+	1.19242i	0.972341	+	0.233567i	$0.0750399\pi$
$349$	240.268	+	416.156i	0.688446	+	1.19242i	−0.283895	+	0.958855i	$0.591627\pi$
$350$		0			0
$351$	−33.5073	−	68.6670i	−0.0954623	−	0.195632i
$352$		0			0
$353$	−158.614	−	274.728i	−0.449333	−	0.778267i	0.549010	−	0.835816i	$-0.315005\pi$
$353$	−158.614	−	274.728i	−0.449333	−	0.778267i	−0.998343	+	0.0575488i	$0.981672\pi$
$354$		0			0
$355$	423.164	+	244.314i	1.19201	+	0.688207i
$356$		0			0
$357$	267.618	−	304.305i	0.749630	−	0.852394i
$358$		0			0
$359$	−669.670			−1.86538			−0.932689	−	0.360683i	$-0.882544\pi$
$359$	−669.670			−1.86538			−0.932689	+	0.360683i	$0.882544\pi$
$360$		0			0
$361$	−43.1052	+	358.417i	−0.119405	+	0.992846i
$362$		0			0
$363$	45.4224	+	9.10078i	0.125131	+	0.0250710i
$364$		0			0
$365$	337.284	−	584.194i	0.924067	−	1.60053i
$366$		0			0
$367$	60.8175	+	105.339i	0.165715	+	0.287027i	0.936909	−	0.349573i	$-0.113673\pi$
$367$	60.8175	+	105.339i	0.165715	+	0.287027i	−0.771194	+	0.636600i	$0.780340\pi$
$368$		0			0
$369$	570.674	−	73.5160i	1.54654	−	0.199230i
$370$		0			0
$371$	201.439	−	116.301i	0.542963	−	0.313480i
$372$		0			0
$373$	−41.1683	−	23.7686i	−0.110371	−	0.0637227i	0.443798	−	0.896127i	$-0.353631\pi$
$373$	−41.1683	−	23.7686i	−0.110371	−	0.0637227i	−0.554169	+	0.832404i	$0.686964\pi$
$374$		0			0
$375$	210.601	+	623.257i	0.561602	+	1.66202i
$376$		0			0
$377$	−133.764			−0.354811
$378$		0			0
$379$			227.549i			0.600392i	0.953878	+	0.300196i	$0.0970521\pi$
$379$			227.549i			0.600392i	−0.953878	+	0.300196i	$0.902948\pi$
$380$		0			0
$381$	86.4275	−	29.2042i	0.226844	−	0.0766514i
$382$		0			0
$383$	−99.9855	−	57.7267i	−0.261059	−	0.150722i	0.363759	−	0.931493i	$-0.381493\pi$
$383$	−99.9855	−	57.7267i	−0.261059	−	0.150722i	−0.624817	+	0.780771i	$0.714827\pi$
$384$		0			0
$385$	251.532	+	435.666i	0.653329	+	1.13160i
$386$		0			0
$387$	−186.542	−	77.8769i	−0.482020	−	0.201232i
$388$		0			0
$389$	−240.435	−	416.445i	−0.618084	−	1.07055i	−0.989835	−	0.142221i	$-0.954576\pi$
$389$	−240.435	−	416.445i	−0.618084	−	1.07055i	0.371751	−	0.928333i	$-0.378758\pi$
$390$		0			0
$391$	128.962	−	223.369i	0.329826	−	0.571275i
$392$		0			0
$393$	−670.296	−	134.300i	−1.70559	−	0.341730i
$394$		0			0
$395$			1191.14i			3.01555i
$396$		0			0
$397$	61.4000			0.154660			0.0773300	−	0.997006i	$-0.475361\pi$
$397$	61.4000			0.154660			0.0773300	+	0.997006i	$0.475361\pi$
$398$		0			0
$399$	−282.940	+	1.19218i	−0.709122	+	0.00298792i
$400$		0			0
$401$	−35.8656	−	20.7070i	−0.0894404	−	0.0516385i	0.454613	−	0.890689i	$-0.349778\pi$
$401$	−35.8656	−	20.7070i	−0.0894404	−	0.0516385i	−0.544053	+	0.839051i	$0.683111\pi$
$402$		0			0
$403$	−78.7642	−	136.424i	−0.195445	−	0.338520i
$404$		0			0
$405$	−494.159	−	499.689i	−1.22014	−	1.23380i
$406$		0			0
$407$	−192.532	+	111.159i	−0.473052	+	0.273117i
$408$		0			0
$409$	−435.012	−	251.155i	−1.06360	−	0.614070i	−0.137174	−	0.990547i	$-0.543802\pi$
$409$	−435.012	−	251.155i	−1.06360	−	0.614070i	−0.926426	+	0.376477i	$0.877135\pi$
$410$		0			0
$411$	369.645	−	420.319i	0.899380	−	1.02267i
$412$		0			0
$413$		−	173.222i		−	0.419425i
$414$		0			0
$415$	−1339.66			−3.22811
$416$		0			0
$417$	383.626	+	76.8628i	0.919966	+	0.184323i
$418$		0			0
$419$	145.560	−	252.118i	0.347399	−	0.601713i	−0.638388	−	0.769715i	$-0.720398\pi$
$419$	145.560	−	252.118i	0.347399	−	0.601713i	0.985787	+	0.168002i	$0.0537316\pi$
$420$		0			0
$421$	540.164	−	311.864i	1.28305	−	0.740769i	0.305645	−	0.952146i	$-0.401128\pi$
$421$	540.164	−	311.864i	1.28305	−	0.740769i	0.977405	+	0.211377i	$0.0677947\pi$
$422$		0			0
$423$	−4.94137	−	2.06291i	−0.0116817	−	0.00487685i
$424$		0			0
$425$	684.061	+	1184.83i	1.60956	+	2.78783i
$426$		0			0
$427$	16.5188	−	28.6114i	0.0386857	−	0.0670056i
$428$		0			0
$429$	93.9467	−	31.7449i	0.218990	−	0.0739975i
$430$		0			0
$431$			191.714i			0.444812i	0.974954	+	0.222406i	$0.0713910\pi$
$431$			191.714i			0.444812i	−0.974954	+	0.222406i	$0.928609\pi$
$432$		0			0
$433$			540.808i			1.24898i	0.781033	+	0.624490i	$0.214693\pi$
$433$			540.808i			1.24898i	−0.781033	+	0.624490i	$0.785307\pi$
$434$		0			0
$435$	−1165.58	+	393.855i	−2.67950	+	0.905414i
$436$		0			0
$437$	−176.424	+	36.1220i	−0.403716	+	0.0826590i
$438$		0			0
$439$	399.683	−	230.757i	0.910440	−	0.525643i	0.0298676	−	0.999554i	$-0.490491\pi$
$439$	399.683	−	230.757i	0.910440	−	0.525643i	0.880573	+	0.473911i	$0.157158\pi$
$440$		0			0
$441$	28.0114	+	217.441i	0.0635179	+	0.493063i
$442$		0			0
$443$	103.892	+	179.946i	0.234519	+	0.406199i	0.959133	−	0.282956i	$-0.0913151\pi$
$443$	103.892	+	179.946i	0.234519	+	0.406199i	−0.724614	+	0.689155i	$0.757982\pi$
$444$		0			0
$445$	−1189.22	−	686.596i	−2.67240	−	1.54291i
$446$		0			0
$447$	−286.065	−	57.3156i	−0.639966	−	0.128223i
$448$		0			0
$449$			691.304i			1.53965i	0.638254	+	0.769826i	$0.279657\pi$
$449$			691.304i			1.53965i	−0.638254	+	0.769826i	$0.720343\pi$
$450$		0			0
$451$			746.781i			1.65583i
$452$		0			0
$453$	−232.243	−	204.244i	−0.512677	−	0.450869i
$454$		0			0
$455$	105.547	+	60.9373i	0.231970	+	0.133928i
$456$		0			0
$457$	−22.2648	−	38.5637i	−0.0487195	−	0.0843846i	0.840637	−	0.541599i	$-0.182181\pi$
$457$	−22.2648	−	38.5637i	−0.0487195	−	0.0843846i	−0.889357	+	0.457214i	$0.848847\pi$
$458$		0			0
$459$	−609.205	−	410.746i	−1.32724	−	0.894871i
$460$		0			0
$461$	−75.3988	−	130.595i	−0.163555	−	0.283285i	0.772586	−	0.634910i	$-0.218963\pi$
$461$	−75.3988	−	130.595i	−0.163555	−	0.283285i	−0.936141	+	0.351624i	$0.885629\pi$
$462$		0			0
$463$	145.724	−	252.402i	0.314739	−	0.545144i	−0.664643	−	0.747161i	$-0.731416\pi$
$463$	145.724	−	252.402i	0.314739	−	0.545144i	0.979382	+	0.202017i	$0.0647497\pi$
$464$		0			0
$465$	−1088.02	−	956.849i	−2.33983	−	2.05774i
$466$		0			0
$467$	557.987			1.19483			0.597417	−	0.801931i	$-0.296194\pi$
$467$	557.987			1.19483			0.597417	+	0.801931i	$0.296194\pi$
$468$		0			0
$469$			60.2340i			0.128431i
$470$		0			0
$471$	391.303	+	78.4011i	0.830793	+	0.166457i
$472$		0			0
$473$	131.179	−	227.209i	0.277334	−	0.480357i
$474$		0			0
$475$	301.975	−	906.244i	0.635736	−	1.90788i
$476$		0			0
$477$	−255.800	−	335.293i	−0.536269	−	0.702920i
$478$		0			0
$479$	190.550	+	330.042i	0.397807	+	0.689022i	0.993455	−	0.114223i	$-0.0364380\pi$
$479$	190.550	+	330.042i	0.397807	+	0.689022i	−0.595648	+	0.803246i	$0.703105\pi$
$480$		0			0
$481$	−26.9298	+	46.6439i	−0.0559872	+	0.0969727i
$482$		0			0
$483$	−45.1836	−	133.717i	−0.0935478	−	0.276848i
$484$		0			0
$485$			1599.91i			3.29879i
$486$		0			0
$487$		−	533.197i		−	1.09486i	−0.836852	−	0.547430i	$-0.815606\pi$
$487$		−	533.197i		−	1.09486i	0.836852	−	0.547430i	$-0.184394\pi$
$488$		0			0
$489$	58.6368	+	173.531i	0.119912	+	0.354869i
$490$		0			0
$491$	152.400	−	263.964i	0.310387	−	0.537606i	−0.668059	−	0.744108i	$-0.732875\pi$
$491$	152.400	−	263.964i	0.310387	−	0.537606i	0.978446	+	0.206502i	$0.0662081\pi$
$492$		0			0
$493$	−1113.97	+	643.152i	−2.25958	+	1.30457i
$494$		0			0
$495$	725.160	−	553.236i	1.46497	−	1.11765i
$496$		0			0
$497$	242.105	−	139.780i	0.487134	−	0.281247i
$498$		0			0
$499$	208.809	−	361.669i	0.418456	−	0.724787i	−0.577329	−	0.816512i	$-0.695905\pi$
$499$	208.809	−	361.669i	0.418456	−	0.724787i	0.995784	+	0.0917253i	$0.0292382\pi$
$500$		0			0
$501$	138.611	−	691.812i	0.276668	−	1.38086i
$502$		0			0
$503$	192.169			0.382046			0.191023	−	0.981586i	$-0.438819\pi$
$503$	192.169			0.382046			0.191023	+	0.981586i	$0.438819\pi$
$504$		0			0
$505$	−861.600			−1.70614
$506$		0			0
$507$	−318.953	+	362.677i	−0.629098	+	0.715339i
$508$		0			0
$509$	−316.776	−	182.891i	−0.622349	−	0.359314i	0.155434	−	0.987846i	$-0.450322\pi$
$509$	−316.776	−	182.891i	−0.622349	−	0.359314i	−0.777783	+	0.628533i	$0.783656\pi$
$510$		0			0
$511$	−192.971	−	334.236i	−0.377635	−	0.654082i
$512$		0			0
$513$	67.6879	+	508.515i	0.131945	+	0.991257i
$514$		0			0
$515$	−1213.57	+	700.657i	−2.35645	+	1.36050i
$516$		0			0
$517$	3.47485	−	6.01861i	0.00672118	−	0.0116414i
$518$		0			0
$519$	56.3038	+	49.5158i	0.108485	+	0.0954062i
$520$		0			0
$521$			470.648i			0.903356i	0.892181	+	0.451678i	$0.149174\pi$
$521$			470.648i			0.903356i	−0.892181	+	0.451678i	$0.850826\pi$
$522$		0			0
$523$		−	176.573i		−	0.337616i	−0.985649	−	0.168808i	$-0.946008\pi$
$523$		−	176.573i		−	0.337616i	0.985649	−	0.168808i	$-0.0539918\pi$
$524$		0			0
$525$	734.095	+	147.082i	1.39828	+	0.280157i
$526$		0			0
$527$	−1311.88	−	757.416i	−2.48934	−	1.43722i
$528$		0			0
$529$	219.583	+	380.328i	0.415090	+	0.718957i
$530$		0			0
$531$	−311.494	+	40.1276i	−0.586618	+	0.0755699i
$532$		0			0
$533$	90.4594	+	156.680i	0.169717	+	0.293959i
$534$		0			0
$535$	754.464	+	435.590i	1.41021	+	0.814187i
$536$		0			0
$537$	−103.397	+	34.9384i	−0.192546	+	0.0650621i
$538$		0			0
$539$	−284.542			−0.527907
$540$		0			0
$541$	−131.774			−0.243575			−0.121787	−	0.992556i	$-0.538863\pi$
$541$	−131.774			−0.243575			−0.121787	+	0.992556i	$0.538863\pi$
$542$		0			0
$543$	−121.070	+	40.9100i	−0.222965	+	0.0753407i
$544$		0			0
$545$	−75.6584	−	43.6814i	−0.138823	−	0.0801494i
$546$		0			0
$547$	−395.503	+	228.344i	−0.723041	+	0.417448i	−0.815871	−	0.578234i	$-0.803742\pi$
$547$	−395.503	+	228.344i	−0.723041	+	0.417448i	0.0928302	+	0.995682i	$0.470409\pi$
$548$		0			0
$549$	−55.2766	−	23.0767i	−0.100686	−	0.0420341i
$550$		0			0
$551$	852.047	+	283.916i	1.54637	+	0.515273i
$552$		0			0
$553$	590.189	+	340.746i	1.06725	+	0.616176i
$554$		0			0
$555$	−97.3216	+	485.736i	−0.175354	+	0.875200i
$556$		0			0
$557$	−89.4812			−0.160649			−0.0803243	−	0.996769i	$-0.525596\pi$
$557$	−89.4812			−0.160649			−0.0803243	+	0.996769i	$0.525596\pi$
$558$		0			0
$559$		−	63.5602i		−	0.113703i
$560$		0			0
$561$	629.747	−	716.077i	1.12254	−	1.27643i
$562$		0			0
$563$	−150.680	−	86.9952i	−0.267638	−	0.154521i	0.360176	−	0.932884i	$-0.382717\pi$
$563$	−150.680	−	86.9952i	−0.267638	−	0.154521i	−0.627814	+	0.778364i	$0.716050\pi$
$564$		0			0
$565$	−456.452	+	263.533i	−0.807879	+	0.466429i
$566$		0			0
$567$	−388.948	+	101.902i	−0.685976	+	0.179722i
$568$		0			0
$569$	148.195	−	85.5604i	0.260448	−	0.150370i	−0.364091	−	0.931363i	$-0.618620\pi$
$569$	148.195	−	85.5604i	0.260448	−	0.150370i	0.624539	+	0.780994i	$0.285287\pi$
$570$		0			0
$571$	230.825	−	399.801i	0.404247	−	0.700176i	−0.589987	−	0.807413i	$-0.700867\pi$
$571$	230.825	−	399.801i	0.404247	−	0.700176i	0.994234	+	0.107237i	$0.0342003\pi$
$572$		0			0
$573$	−341.583	+	388.410i	−0.596131	+	0.677853i
$574$		0			0
$575$	476.515			0.828722
$576$		0			0
$577$	845.752			1.46578			0.732888	−	0.680350i	$-0.238172\pi$
$577$	845.752			1.46578			0.732888	+	0.680350i	$0.238172\pi$
$578$		0			0
$579$	−12.5605	+	62.6902i	−0.0216935	+	0.108273i
$580$		0			0
$581$	−383.233	+	663.778i	−0.659609	+	1.14248i
$582$		0			0
$583$	474.018	−	273.674i	0.813067	−	0.469424i
$584$		0			0
$585$	85.1292	−	203.914i	0.145520	−	0.348570i
$586$		0			0
$587$	335.918	+	581.828i	0.572263	+	0.991189i	0.996333	+	0.0855593i	$0.0272677\pi$
$587$	335.918	+	581.828i	0.572263	+	0.991189i	−0.424070	+	0.905629i	$0.639399\pi$
$588$		0			0
$589$	212.151	+	1036.17i	0.360188	+	1.75920i
$590$		0			0
$591$	−95.4425	−	282.455i	−0.161493	−	0.477927i
$592$		0			0
$593$	−692.927			−1.16851			−0.584255	−	0.811570i	$-0.698613\pi$
$593$	−692.927			−1.16851			−0.584255	+	0.811570i	$0.698613\pi$
$594$		0			0
$595$	1171.98			1.96971
$596$		0			0
$597$	−43.7335	−	129.426i	−0.0732554	−	0.216794i
$598$		0			0
$599$	878.797	+	507.374i	1.46711	+	0.847035i	0.999322	−	0.0368074i	$-0.0117188\pi$
$599$	878.797	+	507.374i	1.46711	+	0.847035i	0.467785	+	0.883842i	$0.345052\pi$
$600$		0			0
$601$	669.637	−	386.615i	1.11420	−	0.643286i	0.174289	−	0.984694i	$-0.444237\pi$
$601$	669.637	−	386.615i	1.11420	−	0.643286i	0.939915	+	0.341408i	$0.110904\pi$
$602$		0			0
$603$	108.315	−	13.9534i	0.179626	−	0.0231400i
$604$		0			0
$605$	66.9872	+	116.025i	0.110723	+	0.191777i
$606$		0			0
$607$	278.810	+	160.971i	0.459324	+	0.265191i	0.711760	−	0.702423i	$-0.247898\pi$
$607$	278.810	+	160.971i	0.459324	+	0.265191i	−0.252436	+	0.967614i	$0.581232\pi$
$608$		0			0
$609$	−138.286	+	690.193i	−0.227071	+	1.13332i
$610$		0			0
$611$		−	1.68367i		−	0.00275560i
$612$		0			0
$613$	−554.613			−0.904752			−0.452376	−	0.891827i	$-0.649424\pi$
$613$	−554.613			−0.904752			−0.452376	+	0.891827i	$0.649424\pi$
$614$		0			0
$615$	1249.57	+	1098.93i	2.03183	+	1.78687i
$616$		0			0
$617$	165.574	−	286.782i	0.268353	−	0.464800i	−0.700084	−	0.714060i	$-0.746854\pi$
$617$	165.574	−	286.782i	0.268353	−	0.464800i	0.968437	+	0.249260i	$0.0801875\pi$
$618$		0			0
$619$	455.349	+	788.687i	0.735620	+	1.27413i	0.954451	+	0.298368i	$0.0964423\pi$
$619$	455.349	+	788.687i	0.735620	+	1.27413i	−0.218831	+	0.975763i	$0.570224\pi$
$620$		0			0
$621$	−229.988	+	112.227i	−0.370351	+	0.180719i
$622$		0			0
$623$	−680.390	+	392.823i	−1.09212	+	0.630535i
$624$		0			0
$625$	−322.863	+	559.216i	−0.516581	+	0.894745i
$626$		0			0
$627$	−665.801	+	2.80539i	−1.06188	+	0.00447431i
$628$		0			0
$629$			517.928i			0.823415i
$630$		0			0
$631$	946.323			1.49972			0.749860	−	0.661597i	$-0.230121\pi$
$631$	946.323			1.49972			0.749860	+	0.661597i	$0.230121\pi$
$632$		0			0
$633$	−115.418	+	576.056i	−0.182335	+	0.910041i
$634$		0			0
$635$	228.489	+	131.918i	0.359825	+	0.207745i
$636$		0			0
$637$	−59.6991	+	34.4673i	−0.0937191	+	0.0541088i
$638$		0			0
$639$	−307.441	−	402.981i	−0.481128	−	0.630644i
$640$		0			0
$641$	831.699	−	480.182i	1.29750	−	0.749113i	0.317530	−	0.948248i	$-0.397147\pi$
$641$	831.699	−	480.182i	1.29750	−	0.749113i	0.979972	+	0.199135i	$0.0638133\pi$
$642$		0			0
$643$	590.021	−	1021.95i	0.917607	−	1.58934i	0.114568	−	0.993415i	$-0.463452\pi$
$643$	590.021	−	1021.95i	0.917607	−	1.58934i	0.803039	−	0.595926i	$-0.203215\pi$
$644$		0			0
$645$	−187.147	−	553.848i	−0.290151	−	0.858680i
$646$		0			0
$647$	588.156			0.909051			0.454525	−	0.890734i	$-0.349809\pi$
$647$	588.156			0.909051			0.454525	+	0.890734i	$0.349809\pi$
$648$		0			0
$649$		−	407.619i		−	0.628073i
$650$		0			0
$651$	−785.346	+	265.371i	−1.20637	+	0.407636i
$652$		0			0
$653$	318.237	−	551.203i	0.487346	−	0.844108i	−0.512548	−	0.858659i	$-0.671298\pi$
$653$	318.237	−	551.203i	0.487346	−	0.844108i	0.999894	+	0.0145502i	$0.00463164\pi$
$654$		0			0
$655$	−988.526	−	1712.18i	−1.50920	−	2.61401i
$656$		0			0
$657$	−556.331	+	424.434i	−0.846775	+	0.646019i
$658$		0			0
$659$	677.911	−	391.392i	1.02870	−	0.593918i	0.112085	−	0.993699i	$-0.464247\pi$
$659$	677.911	−	391.392i	1.02870	−	0.593918i	0.916611	+	0.399781i	$0.130914\pi$
$660$		0			0
$661$	−257.653	−	148.756i	−0.389792	−	0.225047i	0.292278	−	0.956333i	$-0.405587\pi$
$661$	−257.653	−	148.756i	−0.389792	−	0.225047i	−0.682070	+	0.731287i	$0.738920\pi$
$662$		0			0
$663$	45.3855	−	226.521i	0.0684548	−	0.341661i
$664$		0			0
$665$	−542.970	−	612.183i	−0.816496	−	0.920576i
$666$		0			0
$667$			448.018i			0.671691i
$668$		0			0
$669$	−649.563	−	571.252i	−0.970946	−	0.853889i
$670$		0			0
$671$	38.8713	−	67.3271i	0.0579304	−	0.100338i
$672$		0			0
$673$	−930.283	+	537.099i	−1.38229	+	0.798067i	−0.992431	−	0.122806i	$-0.960811\pi$
$673$	−930.283	+	537.099i	−1.38229	+	0.798067i	−0.389862	+	0.920873i	$0.627477\pi$
$674$		0			0
$675$	94.4325	−	1354.15i	0.139900	−	2.00614i
$676$		0			0
$677$	−283.955	+	163.942i	−0.419432	+	0.242159i	−0.694834	−	0.719170i	$-0.744522\pi$
$677$	−283.955	+	163.942i	−0.419432	+	0.242159i	0.275402	+	0.961329i	$0.411189\pi$
$678$		0			0
$679$	792.726	+	457.680i	1.16749	+	0.674051i
$680$		0			0
$681$	−162.073	−	142.534i	−0.237993	−	0.209301i
$682$		0			0
$683$		−	38.4411i		−	0.0562827i	−0.999604	−	0.0281413i	$-0.991041\pi$
$683$		−	38.4411i		−	0.0562827i	0.999604	−	0.0281413i	$-0.00895885\pi$
$684$		0			0
$685$	1618.78			2.36319
$686$		0			0
$687$	−310.264	−	62.1642i	−0.451622	−	0.0904865i
$688$		0			0
$689$	66.3017	−	114.838i	0.0962289	−	0.166673i
$690$		0			0
$691$	−28.8388	−	49.9502i	−0.0417348	−	0.0722868i	0.844403	−	0.535708i	$-0.179955\pi$
$691$	−28.8388	−	49.9502i	−0.0417348	−	0.0722868i	−0.886138	+	0.463421i	$0.846622\pi$
$692$		0			0
$693$	−66.6743	−	517.565i	−0.0962111	−	0.746847i
$694$		0			0
$695$	565.756	+	979.919i	0.814038	+	1.40995i
$696$		0			0
$697$	1506.68	+	869.880i	2.16166	+	1.24803i
$698$		0			0
$699$	263.060	+	778.506i	0.376338	+	1.11374i
$700$		0			0
$701$	−478.201			−0.682170			−0.341085	−	0.940032i	$-0.610794\pi$
$701$	−478.201			−0.682170			−0.341085	+	0.940032i	$0.610794\pi$
$702$		0			0
$703$	270.540	−	239.953i	0.384837	−	0.341327i
$704$		0			0
$705$	−4.95741	−	14.6711i	−0.00703179	−	0.0208101i
$706$		0			0
$707$	−246.474	+	426.906i	−0.348620	+	0.603828i
$708$		0			0
$709$	−208.291	−	360.771i	−0.293781	−	0.508844i	0.680919	−	0.732358i	$-0.261580\pi$
$709$	−208.291	−	360.771i	−0.293781	−	0.508844i	−0.974701	+	0.223514i	$0.928247\pi$
$710$		0			0
$711$	476.020	−	1140.23i	0.669508	−	1.60370i
$712$		0			0
$713$	−456.927	+	263.807i	−0.640851	+	0.369996i
$714$		0			0
$715$	248.368	+	143.395i	0.347367	+	0.200553i
$716$		0			0
$717$	−1058.27	−	212.034i	−1.47597	−	0.295723i
$718$		0			0
$719$	−196.088			−0.272723			−0.136362	−	0.990659i	$-0.543541\pi$
$719$	−196.088			−0.272723			−0.136362	+	0.990659i	$0.543541\pi$
$720$		0			0
$721$			801.736i			1.11198i
$722$		0			0
$723$	−278.489	−	244.914i	−0.385185	−	0.338748i
$724$		0			0
$725$	−2058.07	−	1188.22i	−2.83871	−	1.63893i
$726$		0			0
$727$	−340.110	−	589.088i	−0.467827	−	0.810300i	0.531497	−	0.847060i	$-0.321630\pi$
$727$	−340.110	−	589.088i	−0.467827	−	0.810300i	−0.999324	+	0.0367599i	$0.988296\pi$
$728$		0			0
$729$	273.345	+	675.813i	0.374959	+	0.927041i
$730$		0			0
$731$	−305.605	−	529.323i	−0.418064	−	0.724109i
$732$		0			0
$733$	469.602	−	813.374i	0.640657	−	1.10965i	−0.344629	−	0.938739i	$-0.611995\pi$
$733$	469.602	−	813.374i	0.640657	−	1.10965i	0.985286	−	0.170912i	$-0.0546715\pi$
$734$		0			0
$735$	−418.718	+	476.118i	−0.569684	+	0.647780i
$736$		0			0
$737$			141.740i			0.192320i
$738$		0			0
$739$	−504.159			−0.682218			−0.341109	−	0.940024i	$-0.610803\pi$
$739$	−504.159			−0.682218			−0.341109	+	0.940024i	$0.610803\pi$
$740$		0			0
$741$	−139.350	+	81.2388i	−0.188057	+	0.109634i
$742$		0			0
$743$	−171.388	−	98.9510i	−0.230670	−	0.133178i	0.380211	−	0.924900i	$-0.375851\pi$
$743$	−171.388	−	98.9510i	−0.230670	−	0.133178i	−0.610881	+	0.791722i	$0.709185\pi$
$744$		0			0
$745$	−421.877	−	730.713i	−0.566278	−	0.980823i
$746$		0			0
$747$	1282.40	+	535.374i	1.71674	+	0.716699i
$748$		0			0
$749$	431.653	−	249.215i	0.576306	−	0.332730i
$750$		0			0
$751$	−320.148	−	184.838i	−0.426296	−	0.246122i	0.271471	−	0.962447i	$-0.412490\pi$
$751$	−320.148	−	184.838i	−0.426296	−	0.246122i	−0.697767	+	0.716324i	$0.745823\pi$
$752$		0			0
$753$	68.6030	+	203.025i	0.0911063	+	0.269622i
$754$		0			0
$755$		−	894.442i		−	1.18469i
$756$		0			0
$757$	989.420			1.30703			0.653514	−	0.756914i	$-0.273294\pi$
$757$	989.420			1.30703			0.653514	+	0.756914i	$0.273294\pi$
$758$		0			0
$759$	−106.324	−	314.658i	−0.140084	−	0.414569i
$760$		0			0
$761$	−284.900	+	493.462i	−0.374376	+	0.648438i	−0.990233	−	0.139419i	$-0.955476\pi$
$761$	−284.900	+	493.462i	−0.374376	+	0.648438i	0.615857	+	0.787858i	$0.288810\pi$
$762$		0			0
$763$	−43.2866	+	24.9915i	−0.0567321	+	0.0327543i
$764$		0			0
$765$	−271.493	−	2107.49i	−0.354893	−	2.75488i
$766$		0			0
$767$	−49.3760	−	85.5217i	−0.0643755	−	0.111502i
$768$		0			0
$769$	−308.994	+	535.194i	−0.401813	+	0.695961i	−0.993945	−	0.109880i	$-0.964953\pi$
$769$	−308.994	+	535.194i	−0.401813	+	0.695961i	0.592132	+	0.805841i	$0.298287\pi$
$770$		0			0
$771$	−166.291	+	829.963i	−0.215682	+	1.07648i
$772$		0			0
$773$		−	1209.25i		−	1.56436i	−0.623055	−	0.782178i	$-0.714109\pi$
$773$		−	1209.25i		−	1.56436i	0.623055	−	0.782178i	$-0.285891\pi$
$774$		0			0
$775$		−	2798.66i		−	3.61117i
$776$		0			0
$777$	212.833	+	187.174i	0.273916	+	0.240893i
$778$		0			0
$779$	−243.652	−	1190.02i	−0.312775	−	1.52763i
$780$		0			0
$781$	569.712	−	328.924i	0.729465	−	0.421157i
$782$		0			0
$783$	1273.16	+	88.7851i	1.62601	+	0.113391i
$784$		0			0
$785$	577.079	+	999.530i	0.735133	+	1.27329i
$786$		0			0
$787$	−307.233	−	177.381i	−0.390385	−	0.225389i	0.291942	−	0.956436i	$-0.405699\pi$
$787$	−307.233	−	177.381i	−0.390385	−	0.225389i	−0.682327	+	0.731047i	$0.739032\pi$
$788$		0			0
$789$	674.419	−	766.873i	0.854777	−	0.971956i
$790$		0			0
$791$			301.551i			0.381227i
$792$		0			0
$793$		−	18.8343i		−	0.0237507i
$794$		0			0
$795$	239.607	−	1195.89i	0.301393	−	1.50427i
$796$		0			0
$797$	−1002.04	−	578.529i	−1.25727	−	0.725883i	−0.284724	−	0.958610i	$-0.591902\pi$
$797$	−1002.04	−	578.529i	−1.25727	−	0.725883i	−0.972542	+	0.232727i	$0.925235\pi$
$798$		0			0
$799$	−8.09529	−	14.0214i	−0.0101318	−	0.0175487i
$800$		0			0
$801$	864.003	+	1132.50i	1.07866	+	1.41386i
$802$		0			0
$803$	−454.092	−	786.510i	−0.565494	−	0.979464i
$804$		0			0
$805$	204.099	−	353.510i	0.253539	−	0.439142i
$806$		0			0
$807$	−989.511	+	334.359i	−1.22616	+	0.414324i
$808$		0			0
$809$	−1060.71			−1.31114			−0.655569	−	0.755135i	$-0.727571\pi$
$809$	−1060.71			−1.31114			−0.655569	+	0.755135i	$0.727571\pi$
$810$		0			0
$811$			156.898i			0.193463i	0.995311	+	0.0967313i	$0.0308388\pi$
$811$			156.898i			0.193463i	−0.995311	+	0.0967313i	$0.969161\pi$
$812$		0			0
$813$	133.411	+	394.820i	0.164097	+	0.485634i
$814$		0			0
$815$	−264.868	+	458.765i	−0.324992	+	0.562902i
$816$		0			0
$817$	−134.908	+	404.866i	−0.165126	+	0.495552i
$818$		0			0
$819$	−76.6827	−	100.513i	−0.0936297	−	0.122726i
$820$		0			0
$821$	464.939	+	805.298i	0.566308	+	0.980875i	0.996927	+	0.0783408i	$0.0249622\pi$
$821$	464.939	+	805.298i	0.566308	+	0.980875i	−0.430618	+	0.902534i	$0.641704\pi$
$822$		0			0
$823$	423.501	−	733.525i	0.514582	−	0.891282i	−0.485275	−	0.874362i	$-0.661280\pi$
$823$	423.501	−	733.525i	0.514582	−	0.891282i	0.999857	−	0.0169204i	$-0.00538618\pi$
$824$		0			0
$825$	1727.44	+	346.108i	2.09387	+	0.419525i
$826$		0			0
$827$			323.004i			0.390574i	0.980746	+	0.195287i	$0.0625638\pi$
$827$			323.004i			0.390574i	−0.980746	+	0.195287i	$0.937436\pi$
$828$		0			0
$829$			928.549i			1.12008i	0.828465	+	0.560041i	$0.189215\pi$
$829$			928.549i			1.12008i	−0.828465	+	0.560041i	$0.810785\pi$
$830$		0			0
$831$	−286.465	+	325.736i	−0.344723	+	0.391980i
$832$		0			0
$833$	−331.446	+	574.081i	−0.397894	+	0.689173i
$834$		0			0
$835$	1767.14	−	1020.26i	2.11633	−	1.22187i
$836$		0			0
$837$	659.128	+	1350.76i	0.787488	+	1.61381i
$838$		0			0
$839$	159.634	−	92.1648i	0.190267	−	0.109851i	−0.401841	−	0.915710i	$-0.631629\pi$
$839$	159.634	−	92.1648i	0.190267	−	0.109851i	0.592108	+	0.805859i	$0.298296\pi$
$840$		0			0
$841$	696.665	−	1206.66i	0.828376	−	1.43479i
$842$		0			0
$843$	−587.626	−	516.782i	−0.697065	−	0.613028i
$844$		0			0
$845$	−1396.79			−1.65300
$846$		0			0
$847$	76.6510			0.0904971
$848$		0			0
$849$	−552.553	−	110.709i	−0.650828	−	0.130399i
$850$		0			0
$851$	156.225	+	90.1968i	0.183579	+	0.105989i
$852$		0			0
$853$	229.777	+	397.986i	0.269376	+	0.466572i	0.968701	−	0.248231i	$-0.0798493\pi$
$853$	229.777	+	397.986i	0.269376	+	0.466572i	−0.699325	+	0.714804i	$0.746516\pi$
$854$		0			0
$855$	−975.066	+	1118.20i	−1.14043	+	1.30784i
$856$		0			0
$857$	1089.92	−	629.268i	1.27179	−	0.734268i	0.296465	−	0.955044i	$-0.404192\pi$
$857$	1089.92	−	629.268i	1.27179	−	0.734268i	0.975325	+	0.220775i	$0.0708587\pi$
$858$		0			0
$859$	−488.155	+	845.509i	−0.568283	+	0.984295i	0.428453	+	0.903564i	$0.359059\pi$
$859$	−488.155	+	845.509i	−0.568283	+	0.984295i	−0.996736	+	0.0807308i	$0.974275\pi$
$860$		0			0
$861$	901.957	−	304.775i	1.04757	−	0.353977i
$862$		0			0
$863$			1576.74i			1.82705i	0.406783	+	0.913525i	$0.366651\pi$
$863$			1576.74i			1.82705i	−0.406783	+	0.913525i	$0.633349\pi$
$864$		0			0
$865$			216.844i			0.250687i
$866$		0			0
$867$	−433.629	−	1283.29i	−0.500149	−	1.48015i
$868$		0			0
$869$	1388.81	+	801.828i	1.59817	+	0.922702i
$870$		0			0
$871$	17.1693	+	29.7382i	0.0197122	+	0.0341425i
$872$		0			0
$873$	639.378	−	1531.53i	0.732391	−	1.75433i
$874$		0			0
$875$	544.272	+	942.707i	0.622025	+	1.07738i
$876$		0			0
$877$	830.690	+	479.599i	0.947195	+	0.546863i	0.892208	−	0.451624i	$-0.149155\pi$
$877$	830.690	+	479.599i	0.947195	+	0.546863i	0.0549864	+	0.998487i	$0.482488\pi$
$878$		0			0
$879$	99.0801	−	494.513i	0.112719	−	0.562586i
$880$		0			0
$881$	1178.74			1.33796			0.668979	−	0.743282i	$-0.266732\pi$
$881$	1178.74			1.33796			0.668979	+	0.743282i	$0.266732\pi$
$882$		0			0
$883$	358.364			0.405848			0.202924	−	0.979194i	$-0.434956\pi$
$883$	358.364			0.405848			0.202924	+	0.979194i	$0.434956\pi$
$884$		0			0
$885$	−682.062	−	599.833i	−0.770691	−	0.677777i
$886$		0			0
$887$	−80.0085	−	46.1929i	−0.0902012	−	0.0520777i	0.454221	−	0.890889i	$-0.349918\pi$
$887$	−80.0085	−	46.1929i	−0.0902012	−	0.0520777i	−0.544422	+	0.838811i	$0.683251\pi$
$888$		0			0
$889$	130.726	−	75.4746i	0.147048	−	0.0848983i
$890$		0			0
$891$	−915.256	+	239.792i	−1.02722	+	0.269127i
$892$		0			0
$893$	−3.57362	+	10.7246i	−0.00400181	+	0.0120097i
$894$		0			0
$895$	−273.353	−	157.820i	−0.305422	−	0.176335i
$896$		0			0
$897$	−60.4229	−	53.1384i	−0.0673611	−	0.0592401i
$898$		0			0
$899$	2631.29			2.92690
$900$		0			0
$901$		−	1275.15i		−	1.41526i
$902$		0			0
$903$	−327.958	−	65.7093i	−0.363187	−	0.0727677i
$904$		0			0
$905$	−320.074	−	184.795i	−0.353673	−	0.204193i
$906$		0			0
$907$	576.628	−	332.917i	0.635754	−	0.367052i	−0.147223	−	0.989103i	$-0.547034\pi$
$907$	576.628	−	332.917i	0.635754	−	0.367052i	0.782977	+	0.622051i	$0.213700\pi$
$908$		0			0
$909$	824.774	+	344.324i	0.907342	+	0.378794i
$910$		0			0
$911$	−542.594	+	313.267i	−0.595603	+	0.343872i	−0.767310	−	0.641277i	$-0.778405\pi$
$911$	−542.594	+	313.267i	−0.595603	+	0.343872i	0.171707	+	0.985148i	$0.445072\pi$
$912$		0			0
$913$	−901.807	+	1561.97i	−0.987740	+	1.71082i
$914$		0			0
$915$	−55.4560	−	164.118i	−0.0606077	−	0.179364i
$916$		0			0
$917$	−1131.13			−1.23352
$918$		0			0
$919$	−791.268			−0.861010			−0.430505	−	0.902588i	$-0.641664\pi$
$919$	−791.268			−0.861010			−0.430505	+	0.902588i	$0.641664\pi$
$920$		0			0
$921$	644.619	−	217.819i	0.699912	−	0.236503i
$922$		0			0
$923$	79.6867	−	138.021i	0.0863344	−	0.149536i
$924$		0			0
$925$	−828.677	+	478.437i	−0.895867	+	0.517229i
$926$		0			0
$927$	1441.71	−	185.725i	1.55524	−	0.200351i
$928$		0			0
$929$	580.633	+	1005.69i	0.625009	+	1.08255i	0.988539	+	0.150964i	$0.0482379\pi$
$929$	580.633	+	1005.69i	0.625009	+	1.08255i	−0.363531	+	0.931582i	$0.618429\pi$
$930$		0			0
$931$	453.429	−	92.8374i	0.487034	−	0.0997179i
$932$		0			0
$933$	−291.522	−	58.4091i	−0.312457	−	0.0626036i
$934$		0			0
$935$	2757.84			2.94957
$936$		0			0
$937$	786.926			0.839836			0.419918	−	0.907562i	$-0.362059\pi$
$937$	786.926			0.839836			0.419918	+	0.907562i	$0.362059\pi$
$938$		0			0
$939$	131.258	−	149.251i	0.139784	−	0.158947i
$940$		0			0
$941$	722.821	+	417.321i	0.768142	+	0.443487i	0.832211	−	0.554459i	$-0.187075\pi$
$941$	722.821	+	417.321i	0.768142	+	0.443487i	−0.0640696	+	0.997945i	$0.520408\pi$
$942$		0			0
$943$	524.773	−	302.978i	0.556493	−	0.321292i
$944$		0			0
$945$	−964.146	−	650.058i	−1.02026	−	0.687892i
$946$		0			0
$947$	−494.200	−	855.980i	−0.521859	−	0.903885i	−0.999677	−	0.0254267i	$-0.991906\pi$
$947$	−494.200	−	855.980i	−0.521859	−	0.903885i	0.477818	−	0.878459i	$-0.341428\pi$
$948$		0			0
$949$	−190.544	−	110.011i	−0.200784	−	0.115923i
$950$		0			0
$951$	−412.783	−	363.018i	−0.434052	−	0.381723i
$952$		0			0
$953$		−	1518.27i		−	1.59314i	−0.604544	−	0.796572i	$-0.706645\pi$
$953$		−	1518.27i		−	1.59314i	0.604544	−	0.796572i	$-0.293355\pi$
$954$		0			0
$955$	−1495.89			−1.56638
$956$		0			0
$957$	−325.410	+	1624.13i	−0.340031	+	1.69711i
$958$		0			0
$959$	463.079	−	802.077i	0.482877	−	0.836368i
$960$		0			0
$961$	1068.88	+	1851.36i	1.11226	+	1.92650i
$962$		0			0
$963$	−548.140	−	718.481i	−0.569201	−	0.746086i
$964$		0			0
$965$	−160.134	+	92.4531i	−0.165942	+	0.0958064i
$966$		0			0
$967$	−762.081	+	1319.96i	−0.788088	+	1.36501i	0.139049	+	0.990286i	$0.455595\pi$
$967$	−762.081	+	1319.96i	−0.788088	+	1.36501i	−0.927137	+	0.374723i	$0.877738\pi$
$968$		0			0
$969$	−769.892	+	1346.56i	−0.794522	+	1.38964i
$970$		0			0
$971$			208.549i			0.214777i	0.994217	+	0.107389i	$0.0342489\pi$
$971$			208.549i			0.214777i	−0.994217	+	0.107389i	$0.965751\pi$
$972$		0			0
$973$	647.375			0.665339
$974$		0			0
$975$	404.355	−	136.633i	0.414723	−	0.140137i
$976$		0			0
$977$	789.549	+	455.846i	0.808136	+	0.466577i	0.846308	−	0.532694i	$-0.178820\pi$
$977$	789.549	+	455.846i	0.808136	+	0.466577i	−0.0381724	+	0.999271i	$0.512154\pi$
$978$		0			0
$979$	−1601.07	+	924.375i	−1.63541	+	0.944204i
$980$		0			0
$981$	54.9681	+	72.0500i	0.0560327	+	0.0734455i
$982$		0			0
$983$	−188.330	+	108.733i	−0.191587	+	0.110613i	−0.592725	−	0.805405i	$-0.701948\pi$
$983$	−188.330	+	108.733i	−0.191587	+	0.110613i	0.401138	+	0.916018i	$0.368615\pi$
$984$		0			0
$985$	431.124	−	746.728i	0.437689	−	0.758099i
$986$		0			0
$987$	−8.68739	−	1.74060i	−0.00880182	−	0.00176352i
$988$		0			0
$989$	−212.884			−0.215251
$990$		0			0
$991$			1152.62i			1.16309i	0.813515	+	0.581544i	$0.197551\pi$
$991$			1152.62i			1.16309i	−0.813515	+	0.581544i	$0.802449\pi$
$992$		0			0
$993$	−0.881469	−	0.775199i	−0.000887682	−	0.000780664i
$994$		0			0
$995$	197.548	−	342.164i	0.198541	−	0.343883i
$996$		0			0
$997$	−831.022	−	1439.37i	−0.833522	−	1.44370i	−0.895228	−	0.445608i	$-0.852987\pi$
$997$	−831.022	−	1439.37i	−0.833522	−	1.44370i	0.0617058	−	0.998094i	$-0.480346\pi$
$998$		0			0
$999$	287.278	−	426.082i	0.287566	−	0.426508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.t.a.265.17	✓	80
3.2	odd	2		2052.3.t.a.37.1		80
9.2	odd	6		2052.3.t.a.721.2		80
9.7	even	3	inner	684.3.t.a.493.24	yes	80
19.18	odd	2	inner	684.3.t.a.265.24	yes	80
57.56	even	2		2052.3.t.a.37.2		80
171.56	even	6		2052.3.t.a.721.1		80
171.151	odd	6	inner	684.3.t.a.493.17	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.t.a.265.17	✓	80	1.1	even	1	trivial
684.3.t.a.265.24	yes	80	19.18	odd	2	inner
684.3.t.a.493.17	yes	80	171.151	odd	6	inner
684.3.t.a.493.24	yes	80	9.7	even	3	inner
2052.3.t.a.37.1		80	3.2	odd	2
2052.3.t.a.37.2		80	57.56	even	2
2052.3.t.a.721.1		80	171.56	even	6
2052.3.t.a.721.2		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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.960366 - 2.84213i) q^{3} +(4.33807 - 7.51375i) q^{5} +(-2.48195 - 4.29886i) q^{7} +(-7.15540 + 5.45897i) q^{9} +O(q^{10})\)	\(q+(-0.960366 - 2.84213i) q^{3} +(4.33807 - 7.51375i) q^{5} +(-2.48195 - 4.29886i) q^{7} +(-7.15540 + 5.45897i) q^{9} +(-5.84041 - 10.1159i) q^{11} +(-2.45073 - 1.41493i) q^{13} +(-25.5212 - 5.11340i) q^{15} -27.2126 q^{17} +(12.6074 + 14.2145i) q^{19} +(-9.83434 + 11.1825i) q^{21} +(-4.73905 + 8.20828i) q^{23} +(-25.1377 - 43.5397i) q^{25} +(22.3869 + 15.0940i) q^{27} +(40.9359 - 23.6343i) q^{29} +(48.2087 + 27.8333i) q^{31} +(-23.1417 + 26.3142i) q^{33} -43.0674 q^{35} -19.0327i q^{37} +(-1.66781 + 8.32413i) q^{39} +(-55.3669 - 31.9661i) q^{41} +(11.2303 + 19.4514i) q^{43} +(9.97674 + 77.4453i) q^{45} +(0.297483 + 0.515256i) q^{47} +(12.1799 - 21.0962i) q^{49} +(26.1340 + 77.3417i) q^{51} +46.8587i q^{53} -101.344 q^{55} +(28.2918 - 49.4831i) q^{57} +(30.2212 + 17.4482i) q^{59} +(3.32779 + 5.76390i) q^{61} +(41.2266 + 17.2112i) q^{63} +(-21.2628 + 12.2761i) q^{65} +(-10.5087 - 6.06721i) q^{67} +(27.8802 + 5.58605i) q^{69} +56.3185i q^{71} +77.7499 q^{73} +(-99.6042 + 113.259i) q^{75} +(-28.9912 + 50.2142i) q^{77} +(-118.896 + 68.6448i) q^{79} +(21.3994 - 78.1221i) q^{81} +(-77.2040 - 133.721i) q^{83} +(-118.050 + 204.469i) q^{85} +(-106.485 - 93.6475i) q^{87} -158.272i q^{89} +14.0471i q^{91} +(32.8079 - 163.745i) q^{93} +(161.496 - 33.0656i) q^{95} +(-159.698 + 92.2018i) q^{97} +(97.0128 + 40.5006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 2 * q^7 + 4 * q^9	\( 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) \) 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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