LMFDB - Embedded newform 684.3.bl.a.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(373,684)]

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, 5]))

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

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

chi := DirichletCharacter("684.373");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.bl (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			373.2
Character	$\chi$	$=$	684.373
Dual form			684.3.bl.a.673.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.95765 + 0.502306i) q^{3} +5.96221 q^{5} +(6.83689 + 11.8418i) q^{7} +(8.49538 - 2.97129i) q^{9} +O(q^{10})$	\(q+(-2.95765 + 0.502306i) q^{3} +5.96221 q^{5} +(6.83689 + 11.8418i) q^{7} +(8.49538 - 2.97129i) q^{9} +(-0.0305186 - 0.0528598i) q^{11} +(17.8742 - 10.3197i) q^{13} +(-17.6341 + 2.99485i) q^{15} +(15.1064 + 26.1650i) q^{17} +(-16.6230 - 9.20190i) q^{19} +(-26.1694 - 31.5898i) q^{21} +(0.855542 + 1.48184i) q^{23} +10.5479 q^{25} +(-23.6338 + 13.0553i) q^{27} -50.9509i q^{29} +(-2.97698 - 1.71876i) q^{31} +(0.116815 + 0.141011i) q^{33} +(40.7629 + 70.6035i) q^{35} -18.8728i q^{37} +(-47.6819 + 39.5003i) q^{39} +43.2335i q^{41} +(20.5707 - 35.6295i) q^{43} +(50.6512 - 17.7155i) q^{45} -8.12095 q^{47} +(-68.9861 + 119.487i) q^{49} +(-57.8222 - 69.7989i) q^{51} +(38.9115 + 22.4656i) q^{53} +(-0.181958 - 0.315161i) q^{55} +(53.7873 + 18.8661i) q^{57} +46.4391i q^{59} +76.9545 q^{61} +(93.2675 + 80.2865i) q^{63} +(106.570 - 61.5280i) q^{65} +(35.6393 - 20.5764i) q^{67} +(-3.27473 - 3.95303i) q^{69} +(-35.0078 + 20.2118i) q^{71} +(19.3561 + 33.5258i) q^{73} +(-31.1970 + 5.29828i) q^{75} +(0.417305 - 0.722793i) q^{77} +(-21.7113 - 12.5350i) q^{79} +(63.3428 - 50.4845i) q^{81} +(17.9661 + 31.1181i) q^{83} +(90.0673 + 156.001i) q^{85} +(25.5929 + 150.695i) q^{87} +(-35.8967 - 20.7250i) q^{89} +(244.408 + 141.109i) q^{91} +(9.66820 + 3.58813i) q^{93} +(-99.1099 - 54.8636i) q^{95} +(-109.866 - 63.4310i) q^{97} +(-0.416329 - 0.358384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.95765	+	0.502306i	−0.985883	+	0.167435i
$3$	−2.95765	+	0.502306i	−0.985883	+	0.167435i
$4$		0			0
$5$	5.96221			1.19244			0.596221	−	0.802821i	$-0.296668\pi$
$5$	5.96221			1.19244			0.596221	+	0.802821i	$0.296668\pi$
$6$		0			0
$7$	6.83689	+	11.8418i	0.976699	+	1.69169i	0.674212	+	0.738538i	$0.264483\pi$
$7$	6.83689	+	11.8418i	0.976699	+	1.69169i	0.302487	+	0.953154i	$0.402183\pi$
$8$		0			0
$9$	8.49538	−	2.97129i	0.943931	−	0.330144i
$10$		0			0
$11$	−0.0305186	−	0.0528598i	−0.00277442	−	0.00480544i	0.864635	−	0.502401i	$-0.167550\pi$
$11$	−0.0305186	−	0.0528598i	−0.00277442	−	0.00480544i	−0.867409	+	0.497595i	$0.834216\pi$
$12$		0			0
$13$	17.8742	−	10.3197i	1.37494	−	0.793821i	0.383393	−	0.923585i	$-0.374756\pi$
$13$	17.8742	−	10.3197i	1.37494	−	0.793821i	0.991545	+	0.129765i	$0.0414222\pi$
$14$		0			0
$15$	−17.6341	+	2.99485i	−1.17561	+	0.199657i
$16$		0			0
$17$	15.1064	+	26.1650i	0.888610	+	1.53912i	0.841519	+	0.540227i	$0.181662\pi$
$17$	15.1064	+	26.1650i	0.888610	+	1.53912i	0.0470906	+	0.998891i	$0.485005\pi$
$18$		0			0
$19$	−16.6230	−	9.20190i	−0.874896	−	0.484310i
$19$	−16.6230	−	9.20190i	−0.874896	−	0.484310i
$20$		0			0
$21$	−26.1694	−	31.5898i	−1.24616	−	1.50428i
$22$		0			0
$23$	0.855542	+	1.48184i	0.0371975	+	0.0644279i	0.884025	−	0.467440i	$-0.154824\pi$
$23$	0.855542	+	1.48184i	0.0371975	+	0.0644279i	−0.846827	+	0.531868i	$0.821490\pi$
$24$		0			0
$25$	10.5479			0.421916
$26$		0			0
$27$	−23.6338	+	13.0553i	−0.875328	+	0.483530i
$28$		0			0
$29$		−	50.9509i		−	1.75693i	−0.477810	−	0.878463i	$-0.658569\pi$
$29$		−	50.9509i		−	1.75693i	0.477810	−	0.878463i	$-0.341431\pi$
$30$		0			0
$31$	−2.97698	−	1.71876i	−0.0960316	−	0.0554439i	0.451215	−	0.892415i	$-0.350991\pi$
$31$	−2.97698	−	1.71876i	−0.0960316	−	0.0554439i	−0.547247	+	0.836971i	$0.684324\pi$
$32$		0			0
$33$	0.116815	+	0.141011i	0.00353985	+	0.00427306i
$34$		0			0
$35$	40.7629	+	70.6035i	1.16466	+	2.01724i
$36$		0			0
$37$		−	18.8728i		−	0.510077i	−0.966931	−	0.255038i	$-0.917912\pi$
$37$		−	18.8728i		−	0.510077i	0.966931	−	0.255038i	$-0.0820881\pi$
$38$		0			0
$39$	−47.6819	+	39.5003i	−1.22261	+	1.01283i
$40$		0			0
$41$			43.2335i			1.05448i	0.849718	+	0.527238i	$0.176772\pi$
$41$			43.2335i			1.05448i	−0.849718	+	0.527238i	$0.823228\pi$
$42$		0			0
$43$	20.5707	−	35.6295i	0.478389	−	0.828594i	−0.521304	−	0.853371i	$-0.674554\pi$
$43$	20.5707	−	35.6295i	0.478389	−	0.828594i	0.999693	+	0.0247770i	$0.00788756\pi$
$44$		0			0
$45$	50.6512	−	17.7155i	1.12558	−	0.393677i
$46$		0			0
$47$	−8.12095			−0.172786			−0.0863931	−	0.996261i	$-0.527534\pi$
$47$	−8.12095			−0.172786			−0.0863931	+	0.996261i	$0.527534\pi$
$48$		0			0
$49$	−68.9861	+	119.487i	−1.40788	+	2.43852i
$50$		0			0
$51$	−57.8222	−	69.7989i	−1.13377	−	1.36861i
$52$		0			0
$53$	38.9115	+	22.4656i	0.734180	+	0.423879i	0.819949	−	0.572436i	$-0.194002\pi$
$53$	38.9115	+	22.4656i	0.734180	+	0.423879i	−0.0857695	+	0.996315i	$0.527335\pi$
$54$		0			0
$55$	−0.181958	−	0.315161i	−0.00330833	−	0.00573020i
$56$		0			0
$57$	53.7873	+	18.8661i	0.943636	+	0.330985i
$58$		0			0
$59$			46.4391i			0.787104i	0.919302	+	0.393552i	$0.128754\pi$
$59$			46.4391i			0.787104i	−0.919302	+	0.393552i	$0.871246\pi$
$60$		0			0
$61$	76.9545			1.26155			0.630775	−	0.775966i	$-0.282737\pi$
$61$	76.9545			1.26155			0.630775	+	0.775966i	$0.282737\pi$
$62$		0			0
$63$	93.2675	+	80.2865i	1.48044	+	1.27439i
$64$		0			0
$65$	106.570	−	61.5280i	1.63953	−	0.946585i
$66$		0			0
$67$	35.6393	−	20.5764i	0.531930	−	0.307110i	−0.209872	−	0.977729i	$-0.567305\pi$
$67$	35.6393	−	20.5764i	0.531930	−	0.307110i	0.741802	+	0.670619i	$0.233971\pi$
$68$		0			0
$69$	−3.27473	−	3.95303i	−0.0474599	−	0.0572902i
$70$		0			0
$71$	−35.0078	+	20.2118i	−0.493068	+	0.284673i	−0.725846	−	0.687857i	$-0.758552\pi$
$71$	−35.0078	+	20.2118i	−0.493068	+	0.284673i	0.232778	+	0.972530i	$0.425218\pi$
$72$		0			0
$73$	19.3561	+	33.5258i	0.265152	+	0.459257i	0.967603	−	0.252475i	$-0.0812445\pi$
$73$	19.3561	+	33.5258i	0.265152	+	0.459257i	−0.702451	+	0.711732i	$0.747911\pi$
$74$		0			0
$75$	−31.1970	+	5.29828i	−0.415960	+	0.0706437i
$76$		0			0
$77$	0.417305	−	0.722793i	0.00541954	−	0.00938693i
$78$		0			0
$79$	−21.7113	−	12.5350i	−0.274826	−	0.158671i	0.356253	−	0.934390i	$-0.384054\pi$
$79$	−21.7113	−	12.5350i	−0.274826	−	0.158671i	−0.631079	+	0.775719i	$0.717388\pi$
$80$		0			0
$81$	63.3428	−	50.4845i	0.782010	−	0.623265i
$82$		0			0
$83$	17.9661	+	31.1181i	0.216459	+	0.374917i	0.953723	−	0.300687i	$-0.0972160\pi$
$83$	17.9661	+	31.1181i	0.216459	+	0.374917i	−0.737264	+	0.675605i	$0.763883\pi$
$84$		0			0
$85$	90.0673	+	156.001i	1.05962	+	1.83531i
$86$		0			0
$87$	25.5929	+	150.695i	0.294172	+	1.73212i
$88$		0			0
$89$	−35.8967	−	20.7250i	−0.403334	−	0.232865i	0.284588	−	0.958650i	$-0.408143\pi$
$89$	−35.8967	−	20.7250i	−0.403334	−	0.232865i	−0.687921	+	0.725785i	$0.741477\pi$
$90$		0			0
$91$	244.408	+	141.109i	2.68580	+	1.55065i
$92$		0			0
$93$	9.66820	+	3.58813i	0.103959	+	0.0385821i
$94$		0			0
$95$	−99.1099	−	54.8636i	−1.04326	−	0.577512i
$96$		0			0
$97$	−109.866	−	63.4310i	−1.13264	−	0.653928i	−0.188040	−	0.982161i	$-0.560213\pi$
$97$	−109.866	−	63.4310i	−1.13264	−	0.653928i	−0.944597	+	0.328233i	$0.893547\pi$
$98$		0			0
$99$	−0.416329	−	0.358384i	−0.00420534	−	0.00362004i
$100$		0			0
$101$	−184.431			−1.82605			−0.913026	−	0.407900i	$-0.866261\pi$
$101$	−184.431			−1.82605			−0.913026	+	0.407900i	$0.866261\pi$
$102$		0			0
$103$	145.759	+	84.1540i	1.41514	+	0.817030i	0.995866	−	0.0908319i	$-0.0289526\pi$
$103$	145.759	+	84.1540i	1.41514	+	0.817030i	0.419270	+	0.907861i	$0.362286\pi$
$104$		0			0
$105$	−156.027	−	188.345i	−1.48597	−	1.79376i
$106$		0			0
$107$			84.5050i			0.789767i	0.918731	+	0.394883i	$0.129215\pi$
$107$			84.5050i			0.789767i	−0.918731	+	0.394883i	$0.870785\pi$
$108$		0			0
$109$	−96.1522	+	55.5135i	−0.882130	+	0.509298i	−0.871360	−	0.490644i	$-0.836762\pi$
$109$	−96.1522	+	55.5135i	−0.882130	+	0.509298i	−0.0107698	+	0.999942i	$0.503428\pi$
$110$		0			0
$111$	9.47994	+	55.8192i	0.0854049	+	0.502876i
$112$		0			0
$113$	46.3810	+	26.7781i	0.410452	+	0.236974i	0.690984	−	0.722870i	$-0.257178\pi$
$113$	46.3810	+	26.7781i	0.410452	+	0.236974i	−0.280532	+	0.959845i	$0.590511\pi$
$114$		0			0
$115$	5.10092	+	8.83505i	0.0443558	+	0.0768265i
$116$		0			0
$117$	121.185	−	140.779i	1.03577	−	1.20324i
$118$		0			0
$119$	−206.561	+	357.774i	−1.73581	+	3.00651i
$120$		0			0
$121$	60.4981	−	104.786i	0.499985	−	0.865999i
$122$		0			0
$123$	−21.7165	−	127.870i	−0.176557	−	1.03959i
$124$		0			0
$125$	−86.1664			−0.689331
$126$		0			0
$127$	−78.0863	−	45.0832i	−0.614853	−	0.354985i	0.160009	−	0.987115i	$-0.448848\pi$
$127$	−78.0863	−	45.0832i	−0.614853	−	0.354985i	−0.774862	+	0.632130i	$0.782181\pi$
$128$		0			0
$129$	−42.9440	+	115.713i	−0.332900	+	0.896996i
$130$		0			0
$131$	−29.6584			−0.226400			−0.113200	−	0.993572i	$-0.536110\pi$
$131$	−29.6584			−0.226400			−0.113200	+	0.993572i	$0.536110\pi$
$132$		0			0
$133$	−4.68242	−	259.760i	−0.0352062	−	1.95308i
$134$		0			0
$135$	−140.910	+	77.8385i	−1.04378	+	0.576582i
$136$		0			0
$137$	180.800			1.31971			0.659854	−	0.751394i	$-0.270618\pi$
$137$	180.800			1.31971			0.659854	+	0.751394i	$0.270618\pi$
$138$		0			0
$139$	−43.5844	−	75.4905i	−0.313557	−	0.543097i	0.665573	−	0.746333i	$-0.268187\pi$
$139$	−43.5844	−	75.4905i	−0.313557	−	0.543097i	−0.979130	+	0.203236i	$0.934854\pi$
$140$		0			0
$141$	24.0189	−	4.07920i	0.170347	−	0.0289305i
$142$		0			0
$143$	−1.09099	−	0.629884i	−0.00762931	−	0.00440478i
$144$		0			0
$145$		−	303.780i		−	2.09503i
$146$		0			0
$147$	144.017	−	388.054i	0.979710	−	2.63982i
$148$		0			0
$149$	−46.7893			−0.314022			−0.157011	−	0.987597i	$-0.550186\pi$
$149$	−46.7893			−0.314022			−0.157011	+	0.987597i	$0.550186\pi$
$150$		0			0
$151$	155.846	−	89.9778i	1.03209	−	0.595880i	0.114510	−	0.993422i	$-0.463470\pi$
$151$	155.846	−	89.9778i	1.03209	−	0.595880i	0.917584	+	0.397543i	$0.130137\pi$
$152$		0			0
$153$	206.078	+	177.396i	1.34692	+	1.15945i
$154$		0			0
$155$	−17.7494	−	10.2476i	−0.114512	−	0.0661135i
$156$		0			0
$157$	−79.7566			−0.508004			−0.254002	−	0.967204i	$-0.581747\pi$
$157$	−79.7566			−0.508004			−0.254002	+	0.967204i	$0.581747\pi$
$158$		0			0
$159$	−126.371	−	46.8998i	−0.794788	−	0.294967i
$160$		0			0
$161$	−11.6985	+	20.2624i	−0.0726615	+	0.125853i
$162$		0			0
$163$	−46.4827			−0.285170			−0.142585	−	0.989783i	$-0.545541\pi$
$163$	−46.4827			−0.285170			−0.142585	+	0.989783i	$0.545541\pi$
$164$		0			0
$165$	0.696476	+	0.840737i	0.00422107	+	0.00509538i
$166$		0			0
$167$	−79.9901	+	46.1823i	−0.478983	+	0.276541i	−0.719993	−	0.693982i	$-0.755855\pi$
$167$	−79.9901	+	46.1823i	−0.478983	+	0.276541i	0.241010	+	0.970523i	$0.422521\pi$
$168$		0			0
$169$	128.491	−	222.553i	0.760303	−	1.31688i
$170$		0			0
$171$	−168.560	−	28.7817i	−0.985733	−	0.168314i
$172$		0			0
$173$	−75.6930	−	43.7014i	−0.437532	−	0.252609i	0.265018	−	0.964243i	$-0.414622\pi$
$173$	−75.6930	−	43.7014i	−0.437532	−	0.252609i	−0.702550	+	0.711634i	$0.747955\pi$
$174$		0			0
$175$	72.1149	+	124.907i	0.412085	+	0.713752i
$176$		0			0
$177$	−23.3267	−	137.351i	−0.131789	−	0.775993i
$178$		0			0
$179$			155.213i			0.867109i	0.901127	+	0.433555i	$0.142741\pi$
$179$			155.213i			0.867109i	−0.901127	+	0.433555i	$0.857259\pi$
$180$		0			0
$181$	58.5550	+	33.8067i	0.323508	+	0.186778i	0.652955	−	0.757397i	$-0.273529\pi$
$181$	58.5550	+	33.8067i	0.323508	+	0.186778i	−0.329447	+	0.944174i	$0.606862\pi$
$182$		0			0
$183$	−227.604	+	38.6548i	−1.24374	+	0.211228i
$184$		0			0
$185$		−	112.524i		−	0.608236i
$186$		0			0
$187$	0.922051	−	1.59704i	0.00493075	−	0.00854032i
$188$		0			0
$189$	−316.181	−	190.610i	−1.67292	−	1.00852i
$190$		0			0
$191$	−73.8255	−	127.869i	−0.386521	−	0.669474i	0.605458	−	0.795877i	$-0.292990\pi$
$191$	−73.8255	−	127.869i	−0.386521	−	0.669474i	−0.991979	+	0.126403i	$0.959657\pi$
$192$		0			0
$193$		−	105.302i		−	0.545607i	−0.962070	−	0.272803i	$-0.912049\pi$
$193$		−	105.302i		−	0.545607i	0.962070	−	0.272803i	$-0.0879509\pi$
$194$		0			0
$195$	−284.290	+	235.509i	−1.45790	+	1.20774i
$196$		0			0
$197$	−289.808			−1.47111			−0.735553	−	0.677467i	$-0.763078\pi$
$197$	−289.808			−1.47111			−0.735553	+	0.677467i	$0.763078\pi$
$198$		0			0
$199$	184.816	−	320.111i	0.928725	−	1.60860i	0.143268	−	0.989684i	$-0.454239\pi$
$199$	184.816	−	320.111i	0.928725	−	1.60860i	0.785457	−	0.618916i	$-0.212428\pi$
$200$		0			0
$201$	−95.0729	+	78.7595i	−0.472999	+	0.391838i
$202$		0			0
$203$	603.352	−	348.345i	2.97218	−	1.71599i
$204$		0			0
$205$			257.767i			1.25740i
$206$		0			0
$207$	11.6711	+	10.0467i	0.0563823	+	0.0485350i
$208$		0			0
$209$	0.0209015	+	1.15952i	0.000100007	+	0.00554794i
$210$		0			0
$211$		−	31.6844i		−	0.150163i	−0.997177	−	0.0750814i	$-0.976078\pi$
$211$		−	31.6844i		−	0.150163i	0.997177	−	0.0750814i	$-0.0239217\pi$
$212$		0			0
$213$	93.3884	−	77.3640i	0.438443	−	0.363211i
$214$		0			0
$215$	122.647	−	212.431i	0.570451	−	0.988050i
$216$		0			0
$217$		−	47.0039i		−	0.216608i
$218$		0			0
$219$	−74.0888	−	89.4347i	−0.338305	−	0.408378i
$220$		0			0
$221$	540.028	+	311.785i	2.44357	+	1.41079i
$222$		0			0
$223$	4.10878	+	2.37220i	0.0184250	+	0.0106377i	0.509184	−	0.860658i	$-0.329947\pi$
$223$	4.10878	+	2.37220i	0.0184250	+	0.0106377i	−0.490759	+	0.871295i	$0.663281\pi$
$224$		0			0
$225$	89.6084	−	31.3409i	0.398260	−	0.139293i
$226$		0			0
$227$	−215.175	+	124.231i	−0.947908	+	0.547275i	−0.892430	−	0.451185i	$-0.851001\pi$
$227$	−215.175	+	124.231i	−0.947908	+	0.547275i	−0.0554775	+	0.998460i	$0.517668\pi$
$228$		0			0
$229$	21.6534	−	37.5047i	0.0945562	−	0.163776i	−0.814867	−	0.579648i	$-0.803190\pi$
$229$	21.6534	−	37.5047i	0.0945562	−	0.163776i	0.909423	+	0.415872i	$0.136523\pi$
$230$		0			0
$231$	−0.871178	+	2.34738i	−0.00377133	+	0.0101618i
$232$		0			0
$233$	74.3349	+	128.752i	0.319034	+	0.552583i	0.980287	−	0.197580i	$-0.0633083\pi$
$233$	74.3349	+	128.752i	0.319034	+	0.552583i	−0.661253	+	0.750163i	$0.729975\pi$
$234$		0			0
$235$	−48.4188			−0.206037
$236$		0			0
$237$	70.5107	+	26.1684i	0.297514	+	0.110415i
$238$		0			0
$239$	111.083	−	192.401i	0.464781	−	0.805023i	−0.534411	−	0.845225i	$-0.679467\pi$
$239$	111.083	−	192.401i	0.464781	−	0.805023i	0.999192	+	0.0402012i	$0.0127999\pi$
$240$		0			0
$241$		−	103.268i		−	0.428500i	−0.976779	−	0.214250i	$-0.931269\pi$
$241$		−	103.268i		−	0.428500i	0.976779	−	0.214250i	$-0.0687307\pi$
$242$		0			0
$243$	−161.987	+	181.133i	−0.666614	+	0.745403i
$244$		0			0
$245$	−411.310	+	712.409i	−1.67881	+	2.90779i
$246$		0			0
$247$	−392.084	+	7.06769i	−1.58738	+	0.0286141i
$248$		0			0
$249$	−68.7682	−	83.0121i	−0.276177	−	0.333382i
$250$		0			0
$251$	−65.3474	+	113.185i	−0.260348	+	0.450937i	−0.966334	−	0.257289i	$-0.917171\pi$
$251$	−65.3474	+	113.185i	−0.260348	+	0.450937i	0.705986	+	0.708226i	$0.250504\pi$
$252$		0			0
$253$	0.0522199	−	0.0904476i	0.000206403	−	0.000357500i
$254$		0			0
$255$	−344.748	−	416.155i	−1.35195	−	1.63198i
$256$		0			0
$257$	−294.809	+	170.208i	−1.14712	+	0.662287i	−0.948183	−	0.317726i	$-0.897081\pi$
$257$	−294.809	+	170.208i	−1.14712	+	0.662287i	−0.198933	+	0.980013i	$0.563748\pi$
$258$		0			0
$259$	223.489	−	129.031i	0.862892	−	0.498191i
$260$		0			0
$261$	−151.390	−	432.847i	−0.580038	−	1.65842i
$262$		0			0
$263$	−199.254	+	345.118i	−0.757619	+	1.31223i	0.186443	+	0.982466i	$0.440304\pi$
$263$	−199.254	+	345.118i	−0.757619	+	1.31223i	−0.944062	+	0.329768i	$0.893029\pi$
$264$		0			0
$265$	231.999	+	133.944i	0.875466	+	0.505451i
$266$		0			0
$267$	116.580	+	43.2661i	0.436630	+	0.162045i
$268$		0			0
$269$	413.044	−	238.471i	1.53548	−	0.886509i	0.536383	−	0.843975i	$-0.319790\pi$
$269$	413.044	−	238.471i	1.53548	−	0.886509i	0.999095	−	0.0425337i	$-0.0135430\pi$
$270$		0			0
$271$	45.3497	+	78.5479i	0.167342	+	0.289845i	0.937484	−	0.348027i	$-0.113148\pi$
$271$	45.3497	+	78.5479i	0.167342	+	0.289845i	−0.770143	+	0.637872i	$0.779815\pi$
$272$		0			0
$273$	−793.752	−	294.583i	−2.90752	−	1.07906i
$274$		0			0
$275$	−0.321907	−	0.557560i	−0.00117057	−	0.00202749i
$276$		0			0
$277$	140.593	+	243.515i	0.507557	+	0.879115i	0.999962	+	0.00874854i	$0.00278478\pi$
$277$	140.593	+	243.515i	0.507557	+	0.879115i	−0.492404	+	0.870367i	$0.663882\pi$
$278$		0			0
$279$	−30.3975	−	5.75604i	−0.108952	−	0.0206310i
$280$		0			0
$281$			66.6712i			0.237264i	0.992938	+	0.118632i	$0.0378509\pi$
$281$			66.6712i			0.237264i	−0.992938	+	0.118632i	$0.962149\pi$
$282$		0			0
$283$	88.0549			0.311148			0.155574	−	0.987824i	$-0.450277\pi$
$283$	88.0549			0.311148			0.155574	+	0.987824i	$0.450277\pi$
$284$		0			0
$285$	320.691	+	112.484i	1.12523	+	0.394680i
$286$		0			0
$287$	−511.964	+	295.583i	−1.78385	+	1.02991i
$288$		0			0
$289$	−311.905	+	540.235i	−1.07926	+	1.86932i
$290$		0			0
$291$	356.806	+	132.420i	1.22614	+	0.455053i
$292$		0			0
$293$	−141.493	−	81.6909i	−0.482910	−	0.278808i	0.238718	−	0.971089i	$-0.423273\pi$
$293$	−141.493	−	81.6909i	−0.482910	−	0.278808i	−0.721629	+	0.692280i	$0.756606\pi$
$294$		0			0
$295$			276.880i			0.938575i
$296$		0			0
$297$	1.41137	+	0.850850i	0.00475210	+	0.00286481i
$298$		0			0
$299$	30.5842	+	17.6578i	0.102288	+	0.0590563i
$300$		0			0
$301$	562.559			1.86897
$302$		0			0
$303$	545.483	−	92.6410i	1.80027	−	0.305746i
$304$		0			0
$305$	458.819			1.50432
$306$		0			0
$307$	199.159	−	114.984i	0.648725	−	0.374542i	−0.139242	−	0.990258i	$-0.544467\pi$
$307$	199.159	−	114.984i	0.648725	−	0.374542i	0.787968	+	0.615717i	$0.211133\pi$
$308$		0			0
$309$	−473.375	−	175.682i	−1.53196	−	0.568551i
$310$		0			0
$311$	−28.8869	+	50.0336i	−0.0928840	+	0.160880i	−0.908724	−	0.417399i	$-0.862942\pi$
$311$	−28.8869	+	50.0336i	−0.0928840	+	0.160880i	0.815840	+	0.578278i	$0.196275\pi$
$312$		0			0
$313$	84.4539			0.269821			0.134910	−	0.990858i	$-0.456925\pi$
$313$	84.4539			0.269821			0.134910	+	0.990858i	$0.456925\pi$
$314$		0			0
$315$	556.080	+	478.685i	1.76533	+	1.51963i
$316$		0			0
$317$		−	459.347i		−	1.44905i	−0.689251	−	0.724523i	$-0.742060\pi$
$317$		−	459.347i		−	1.44905i	0.689251	−	0.724523i	$-0.257940\pi$
$318$		0			0
$319$	−2.69325	+	1.55495i	−0.00844280	+	0.00487445i
$320$		0			0
$321$	−42.4474	−	249.936i	−0.132235	−	0.778617i
$322$		0			0
$323$	−10.3460	−	573.949i	−0.0320309	−	1.77693i
$324$		0			0
$325$	188.535	−	108.851i	0.580108	−	0.334926i
$326$		0			0
$327$	256.500	−	212.487i	0.784402	−	0.649808i
$328$		0			0
$329$	−55.5220	−	96.1670i	−0.168760	−	0.292301i
$330$		0			0
$331$	33.9831	−	19.6202i	0.102668	−	0.0592755i	−0.447787	−	0.894140i	$-0.647788\pi$
$331$	33.9831	−	19.6202i	0.102668	−	0.0592755i	0.550455	+	0.834865i	$0.314454\pi$
$332$		0			0
$333$	−56.0767	−	160.332i	−0.168398	−	0.481477i
$334$		0			0
$335$	212.489	−	122.680i	0.634295	−	0.366210i
$336$		0			0
$337$		−	531.335i		−	1.57666i	−0.615252	−	0.788330i	$-0.710946\pi$
$337$		−	531.335i		−	1.57666i	0.615252	−	0.788330i	$-0.289054\pi$
$338$		0			0
$339$	−150.630	−	55.9027i	−0.444335	−	0.164905i
$340$		0			0
$341$			0.209817i			0.000615298i
$342$		0			0
$343$	−1216.59			−3.54690
$344$		0			0
$345$	−19.5246	−	23.5688i	−0.0565931	−	0.0683152i
$346$		0			0
$347$	424.279			1.22271			0.611353	−	0.791358i	$-0.290625\pi$
$347$	424.279			1.22271			0.611353	+	0.791358i	$0.290625\pi$
$348$		0			0
$349$	328.765	+	569.438i	0.942020	+	1.63163i	0.761611	+	0.648034i	$0.224409\pi$
$349$	328.765	+	569.438i	0.942020	+	1.63163i	0.180409	+	0.983592i	$0.442258\pi$
$350$		0			0
$351$	−287.709	+	477.247i	−0.819684	+	1.35968i
$352$		0			0
$353$	10.2091	+	17.6827i	0.0289210	+	0.0500926i	0.880124	−	0.474745i	$-0.157460\pi$
$353$	10.2091	+	17.6827i	0.0289210	+	0.0500926i	−0.851203	+	0.524837i	$0.824126\pi$
$354$		0			0
$355$	−208.724	+	120.507i	−0.587955	+	0.339456i
$356$		0			0
$357$	431.223	−	1161.93i	1.20791	−	3.25470i
$358$		0			0
$359$	−177.673	−	307.739i	−0.494911	−	0.857211i	0.505072	−	0.863077i	$-0.331466\pi$
$359$	−177.673	−	307.739i	−0.494911	−	0.857211i	−0.999983	+	0.00586638i	$0.998133\pi$
$360$		0			0
$361$	191.650	+	305.927i	0.530887	+	0.847443i
$362$		0			0
$363$	−126.298	+	340.308i	−0.347927	+	0.937489i
$364$		0			0
$365$	115.405	+	199.887i	0.316178	+	0.547637i
$366$		0			0
$367$	−540.288			−1.47217			−0.736087	−	0.676887i	$-0.763329\pi$
$367$	−540.288			−1.47217			−0.736087	+	0.676887i	$0.763329\pi$
$368$		0			0
$369$	128.459	+	367.285i	0.348128	+	0.995352i
$370$		0			0
$371$			614.379i			1.65601i
$372$		0			0
$373$	−317.781	−	183.471i	−0.851961	−	0.491880i	0.00935134	−	0.999956i	$-0.497023\pi$
$373$	−317.781	−	183.471i	−0.851961	−	0.491880i	−0.861312	+	0.508077i	$0.830357\pi$
$374$		0			0
$375$	254.850	−	43.2819i	0.679600	−	0.115418i
$376$		0			0
$377$	−525.796	−	910.705i	−1.39468	−	2.41566i
$378$		0			0
$379$		−	495.103i		−	1.30634i	−0.757211	−	0.653170i	$-0.773439\pi$
$379$		−	495.103i		−	1.30634i	0.757211	−	0.653170i	$-0.226561\pi$
$380$		0			0
$381$	253.597	+	94.1169i	0.665610	+	0.247026i
$382$		0			0
$383$		−	602.533i		−	1.57319i	−0.617467	−	0.786597i	$-0.711841\pi$
$383$		−	602.533i		−	1.57319i	0.617467	−	0.786597i	$-0.288159\pi$
$384$		0			0
$385$	2.48806	−	4.30944i	0.00646249	−	0.0111934i
$386$		0			0
$387$	68.8903	−	363.808i	0.178011	−	0.940072i
$388$		0			0
$389$	−591.183			−1.51975			−0.759876	−	0.650068i	$-0.774740\pi$
$389$	−591.183			−1.51975			−0.759876	+	0.650068i	$0.774740\pi$
$390$		0			0
$391$	−25.8483	+	44.7705i	−0.0661081	+	0.114503i
$392$		0			0
$393$	87.7191	−	14.8976i	0.223204	−	0.0379074i
$394$		0			0
$395$	−129.447	−	74.7363i	−0.327714	−	0.189206i
$396$		0			0
$397$	111.011	+	192.276i	0.279624	+	0.484322i	0.971291	−	0.237894i	$-0.0764570\pi$
$397$	111.011	+	192.276i	0.279624	+	0.484322i	−0.691668	+	0.722216i	$0.743124\pi$
$398$		0			0
$399$	144.328	+	765.926i	0.361724	+	1.91961i
$400$		0			0
$401$			293.337i			0.731513i	0.930711	+	0.365757i	$0.119190\pi$
$401$			293.337i			0.731513i	−0.930711	+	0.365757i	$0.880810\pi$
$402$		0			0
$403$	−70.9481			−0.176050
$404$		0			0
$405$	377.663	−	300.999i	0.932502	−	0.743207i
$406$		0			0
$407$	−0.997614	+	0.575973i	−0.00245114	+	0.00141517i
$408$		0			0
$409$	−49.7824	+	28.7419i	−0.121717	+	0.0702735i	−0.559623	−	0.828748i	$-0.689054\pi$
$409$	−49.7824	+	28.7419i	−0.121717	+	0.0702735i	0.437905	+	0.899021i	$0.355721\pi$
$410$		0			0
$411$	−534.743	+	90.8170i	−1.30108	+	0.220966i
$412$		0			0
$413$	−549.925	+	317.499i	−1.33154	+	0.768763i
$414$		0			0
$415$	107.117	+	185.533i	0.258114	+	0.447067i
$416$		0			0
$417$	166.827	+	201.382i	0.400064	+	0.482929i
$418$		0			0
$419$	198.879	−	344.468i	0.474650	−	0.822119i	−0.524928	−	0.851147i	$-0.675908\pi$
$419$	198.879	−	344.468i	0.474650	−	0.822119i	0.999579	+	0.0290278i	$0.00924113\pi$
$420$		0			0
$421$	−121.075	−	69.9029i	−0.287590	−	0.166040i	0.349265	−	0.937024i	$-0.386431\pi$
$421$	−121.075	−	69.9029i	−0.287590	−	0.166040i	−0.636854	+	0.770984i	$0.719765\pi$
$422$		0			0
$423$	−68.9905	+	24.1297i	−0.163098	+	0.0570442i
$424$		0			0
$425$	159.341	+	275.986i	0.374919	+	0.649379i
$426$		0			0
$427$	526.130	+	911.283i	1.23215	+	2.13415i
$428$		0			0
$429$	3.54316	+	1.31496i	0.00825912	+	0.00306518i
$430$		0			0
$431$	644.642	+	372.184i	1.49569	+	0.863536i	0.999988	−	0.00495690i	$-0.00157784\pi$
$431$	644.642	+	372.184i	1.49569	+	0.863536i	0.495701	+	0.868493i	$0.334911\pi$
$432$		0			0
$433$	475.819	+	274.714i	1.09889	+	0.634444i	0.935929	−	0.352188i	$-0.114562\pi$
$433$	475.819	+	274.714i	1.09889	+	0.634444i	0.162961	+	0.986633i	$0.447896\pi$
$434$		0			0
$435$	152.590	+	898.473i	0.350783	+	2.06546i
$436$		0			0
$437$	−0.585940	−	32.5053i	−0.00134082	−	0.0743829i
$438$		0			0
$439$	−631.963	−	364.864i	−1.43955	−	0.831125i	−0.441733	−	0.897147i	$-0.645636\pi$
$439$	−631.963	−	364.864i	−1.43955	−	0.831125i	−0.997818	+	0.0660215i	$0.978969\pi$
$440$		0			0
$441$	−231.031	+	1220.07i	−0.523880	+	2.76660i
$442$		0			0
$443$	−119.035			−0.268703			−0.134351	−	0.990934i	$-0.542895\pi$
$443$	−119.035			−0.268703			−0.134351	+	0.990934i	$0.542895\pi$
$444$		0			0
$445$	−214.024	−	123.567i	−0.480952	−	0.277678i
$446$		0			0
$447$	138.386	−	23.5025i	0.309589	−	0.0525784i
$448$		0			0
$449$			141.672i			0.315529i	0.987477	+	0.157764i	$0.0504286\pi$
$449$			141.672i			0.315529i	−0.987477	+	0.157764i	$0.949571\pi$
$450$		0			0
$451$	2.28531	−	1.31943i	0.00506722	−	0.00292556i
$452$		0			0
$453$	−415.742	+	344.405i	−0.917752	+	0.760277i
$454$		0			0
$455$	1457.21	+	841.320i	3.20266	+	1.84906i
$456$		0			0
$457$	18.8326	+	32.6191i	0.0412093	+	0.0713766i	0.885894	−	0.463887i	$-0.153546\pi$
$457$	18.8326	+	32.6191i	0.0412093	+	0.0713766i	−0.844685	+	0.535264i	$0.820212\pi$
$458$		0			0
$459$	−698.614	−	421.161i	−1.52203	−	0.917562i
$460$		0			0
$461$	247.430	−	428.561i	0.536724	−	0.929633i	−0.462354	−	0.886695i	$-0.652995\pi$
$461$	247.430	−	428.561i	0.536724	−	0.929633i	0.999078	−	0.0429373i	$-0.0136716\pi$
$462$		0			0
$463$	265.993	−	460.714i	0.574500	−	0.995063i	−0.421596	−	0.906784i	$-0.638530\pi$
$463$	265.993	−	460.714i	0.574500	−	0.995063i	0.996096	−	0.0882791i	$-0.0281367\pi$
$464$		0			0
$465$	57.6438	+	21.3932i	0.123965	+	0.0460068i
$466$		0			0
$467$	−472.877			−1.01258			−0.506292	−	0.862362i	$-0.668984\pi$
$467$	−472.877			−1.01258			−0.506292	+	0.862362i	$0.668984\pi$
$468$		0			0
$469$	487.324	+	281.356i	1.03907	+	0.599907i
$470$		0			0
$471$	235.892	−	40.0622i	0.500832	−	0.0850578i
$472$		0			0
$473$	−2.51116			−0.00530901
$474$		0			0
$475$	−175.338	−	97.0607i	−0.369133	−	0.204338i
$476$		0			0
$477$	397.320	+	75.2361i	0.832956	+	0.157728i
$478$		0			0
$479$	534.382			1.11562			0.557810	−	0.829969i	$-0.311642\pi$
$479$	534.382			1.11562			0.557810	+	0.829969i	$0.311642\pi$
$480$		0			0
$481$	−194.761	−	337.337i	−0.404909	−	0.701324i
$482$		0			0
$483$	24.4221	−	65.8053i	0.0505634	−	0.136243i
$484$		0			0
$485$	−655.042	−	378.189i	−1.35060	−	0.779771i
$486$		0			0
$487$		−	519.550i		−	1.06684i	−0.845851	−	0.533419i	$-0.820907\pi$
$487$		−	519.550i		−	1.06684i	0.845851	−	0.533419i	$-0.179093\pi$
$488$		0			0
$489$	137.480	−	23.3486i	0.281144	−	0.0477476i
$490$		0			0
$491$	−329.798			−0.671685			−0.335843	−	0.941918i	$-0.609021\pi$
$491$	−329.798			−0.671685			−0.335843	+	0.941918i	$0.609021\pi$
$492$		0			0
$493$	1333.13	−	769.682i	2.70412	−	1.56122i
$494$		0			0
$495$	−2.48224	−	2.13676i	−0.00501463	−	0.00431669i
$496$		0			0
$497$	−478.689	−	276.371i	−0.963158	−	0.556079i
$498$		0			0
$499$	502.951			1.00792			0.503959	−	0.863727i	$-0.331876\pi$
$499$	502.951			1.00792			0.503959	+	0.863727i	$0.331876\pi$
$500$		0			0
$501$	213.385	−	176.771i	0.425918	−	0.352836i
$502$		0			0
$503$	182.006	−	315.244i	0.361842	−	0.626729i	−0.626422	−	0.779484i	$-0.715481\pi$
$503$	182.006	−	315.244i	0.361842	−	0.626729i	0.988264	+	0.152755i	$0.0488147\pi$
$504$		0			0
$505$	−1099.62			−2.17746
$506$		0			0
$507$	−268.242	+	722.776i	−0.529076	+	1.42559i
$508$		0			0
$509$	−600.445	+	346.667i	−1.17966	+	0.681075i	−0.955935	−	0.293578i	$-0.905154\pi$
$509$	−600.445	+	346.667i	−1.17966	+	0.681075i	−0.223721	+	0.974653i	$0.571821\pi$
$510$		0			0
$511$	−264.671	+	458.424i	−0.517947	+	0.897111i
$512$		0			0
$513$	513.000	+	0.457206i	1.00000	+	0.000891239i
$514$		0			0
$515$	869.046	+	501.744i	1.68747	+	0.974260i
$516$		0			0
$517$	0.247840	+	0.429272i	0.000479381	+	0.000830313i
$518$		0			0
$519$	245.825	+	91.2323i	0.473651	+	0.175785i
$520$		0			0
$521$			456.825i			0.876823i	0.898774	+	0.438411i	$0.144459\pi$
$521$			456.825i			0.876823i	−0.898774	+	0.438411i	$0.855541\pi$
$522$		0			0
$523$	−177.780	−	102.641i	−0.339924	−	0.196255i	0.320315	−	0.947311i	$-0.396211\pi$
$523$	−177.780	−	102.641i	−0.339924	−	0.196255i	−0.660238	+	0.751056i	$0.729545\pi$
$524$		0			0
$525$	−276.032	−	333.206i	−0.525775	−	0.634678i
$526$		0			0
$527$		−	103.857i		−	0.197072i
$528$		0			0
$529$	263.036	−	455.592i	0.497233	−	0.861232i
$530$		0			0
$531$	137.984	+	394.518i	0.259857	+	0.742972i
$532$		0			0
$533$	446.156	+	772.764i	0.837065	+	1.44984i
$534$		0			0
$535$			503.836i			0.941750i
$536$		0			0
$537$	−77.9643	−	459.064i	−0.145185	−	0.854868i
$538$		0			0
$539$	8.42145			0.0156242
$540$		0			0
$541$	101.226	−	175.329i	0.187109	−	0.324082i	−0.757176	−	0.653211i	$-0.773422\pi$
$541$	101.226	−	175.329i	0.187109	−	0.324082i	0.944285	+	0.329128i	$0.106755\pi$
$542$		0			0
$543$	−190.166	−	70.5759i	−0.350214	−	0.129974i
$544$		0			0
$545$	−573.279	+	330.983i	−1.05189	+	0.607308i
$546$		0			0
$547$		−	36.2433i		−	0.0662583i	−0.999451	−	0.0331291i	$-0.989453\pi$
$547$		−	36.2433i		−	0.0662583i	0.999451	−	0.0331291i	$-0.0105473\pi$
$548$		0			0
$549$	653.758	−	228.654i	1.19082	−	0.416492i
$550$		0			0
$551$	−468.845	+	846.958i	−0.850898	+	1.53713i
$552$		0			0
$553$		−	342.802i		−	0.619895i
$554$		0			0
$555$	56.5214	+	332.806i	0.101840	+	0.599650i
$556$		0			0
$557$	220.256	−	381.495i	0.395433	−	0.684910i	−0.597724	−	0.801702i	$-0.703928\pi$
$557$	220.256	−	381.495i	0.395433	−	0.684910i	0.993156	+	0.116793i	$0.0372613\pi$
$558$		0			0
$559$		−	849.132i		−	1.51902i
$560$		0			0
$561$	−1.92490	+	5.18663i	−0.00343120	+	0.00924534i
$562$		0			0
$563$	489.577	+	282.657i	0.869586	+	0.502056i	0.867211	−	0.497941i	$-0.165911\pi$
$563$	489.577	+	282.657i	0.869586	+	0.502056i	0.00237548	+	0.999997i	$0.499244\pi$
$564$		0			0
$565$	276.533	+	159.657i	0.489440	+	0.282578i
$566$		0			0
$567$	1030.90	+	404.939i	1.81816	+	0.714178i
$568$		0			0
$569$	457.777	−	264.298i	0.804529	−	0.464495i	−0.0405235	−	0.999179i	$-0.512903\pi$
$569$	457.777	−	264.298i	0.804529	−	0.464495i	0.845052	+	0.534684i	$0.179569\pi$
$570$		0			0
$571$	−254.349	+	440.545i	−0.445444	+	0.771532i	−0.998083	−	0.0618886i	$-0.980288\pi$
$571$	−254.349	+	440.545i	−0.445444	+	0.771532i	0.552639	+	0.833421i	$0.313621\pi$
$572$		0			0
$573$	282.580	+	341.110i	0.493158	+	0.595306i
$574$		0			0
$575$	9.02418	+	15.6303i	0.0156942	+	0.0271832i
$576$		0			0
$577$	696.388			1.20691			0.603456	−	0.797396i	$-0.293790\pi$
$577$	696.388			1.20691			0.603456	+	0.797396i	$0.293790\pi$
$578$		0			0
$579$	52.8939	+	311.447i	0.0913539	+	0.537904i
$580$		0			0
$581$	−245.664	+	425.503i	−0.422830	+	0.732362i
$582$		0			0
$583$		−	2.74247i		−	0.00470407i
$584$		0			0
$585$	722.531	−	839.353i	1.23510	−	1.43479i
$586$		0			0
$587$	511.342	−	885.670i	0.871110	−	1.50881i	0.0102613	−	0.999947i	$-0.496734\pi$
$587$	511.342	−	885.670i	0.871110	−	1.50881i	0.860849	−	0.508860i	$-0.169933\pi$
$588$		0			0
$589$	33.6706	+	55.9648i	0.0571656	+	0.0950167i
$590$		0			0
$591$	857.150	−	145.572i	1.45034	−	0.246315i
$592$		0			0
$593$	−10.7225	+	18.5719i	−0.0180817	+	0.0313185i	−0.874925	−	0.484259i	$-0.839089\pi$
$593$	−10.7225	+	18.5719i	−0.0180817	+	0.0313185i	0.856843	+	0.515578i	$0.172423\pi$
$594$		0			0
$595$	−1231.56	+	2133.12i	−2.06985	+	3.58508i
$596$		0			0
$597$	−385.828	+	1039.61i	−0.646278	+	1.74139i
$598$		0			0
$599$	406.542	−	234.717i	0.678702	−	0.391849i	−0.120664	−	0.992693i	$-0.538502\pi$
$599$	406.542	−	234.717i	0.678702	−	0.391849i	0.799366	+	0.600845i	$0.205169\pi$
$600$		0			0
$601$	−446.289	+	257.665i	−0.742577	+	0.428727i	−0.823006	−	0.568033i	$-0.807705\pi$
$601$	−446.289	+	257.665i	−0.742577	+	0.428727i	0.0804283	+	0.996760i	$0.474371\pi$
$602$		0			0
$603$	241.631	−	280.699i	0.400714	−	0.465503i
$604$		0			0
$605$	360.702	−	624.755i	0.596202	−	1.03265i
$606$		0			0
$607$	−676.578	−	390.622i	−1.11463	−	0.643529i	−0.174602	−	0.984639i	$-0.555864\pi$
$607$	−676.578	−	390.622i	−1.11463	−	0.643529i	−0.940023	+	0.341110i	$0.889197\pi$
$608$		0			0
$609$	−1609.53	+	1333.35i	−2.64290	+	2.18941i
$610$		0			0
$611$	−145.155	+	83.8055i	−0.237570	+	0.137161i
$612$		0			0
$613$	−442.760	−	766.882i	−0.722283	−	1.25103i	−0.960082	−	0.279717i	$-0.909759\pi$
$613$	−442.760	−	766.882i	−0.722283	−	1.25103i	0.237799	−	0.971314i	$-0.423574\pi$
$614$		0			0
$615$	−129.478	−	762.385i	−0.210533	−	1.23965i
$616$		0			0
$617$	281.038	+	486.773i	0.455492	+	0.788935i	0.998716	−	0.0506526i	$-0.0161301\pi$
$617$	281.038	+	486.773i	0.455492	+	0.788935i	−0.543225	+	0.839587i	$0.682797\pi$
$618$		0			0
$619$	−276.310	−	478.582i	−0.446381	−	0.773154i	0.551767	−	0.833998i	$-0.313954\pi$
$619$	−276.310	−	478.582i	−0.446381	−	0.773154i	−0.998147	+	0.0608448i	$0.980621\pi$
$620$		0			0
$621$	−39.5657	−	23.8523i	−0.0637128	−	0.0384094i
$622$		0			0
$623$		−	566.777i		−	0.909755i
$624$		0			0
$625$	−777.439			−1.24390
$626$		0			0
$627$	−0.644253	−	3.41895i	−0.00102752	−	0.00545287i
$628$		0			0
$629$	493.808	−	285.100i	0.785068	−	0.453259i
$630$		0			0
$631$	365.132	−	632.427i	0.578656	−	1.00226i	−0.416978	−	0.908916i	$-0.636911\pi$
$631$	365.132	−	632.427i	0.578656	−	1.00226i	0.995634	−	0.0933444i	$-0.0297558\pi$
$632$		0			0
$633$	15.9153	+	93.7112i	0.0251426	+	0.148043i
$634$		0			0
$635$	−465.567	−	268.795i	−0.733176	−	0.423299i
$636$		0			0
$637$			2847.66i			4.47042i
$638$		0			0
$639$	−237.350	+	275.725i	−0.371439	+	0.431495i
$640$		0			0
$641$	−604.563	−	349.045i	−0.943156	−	0.544531i	−0.0522078	−	0.998636i	$-0.516626\pi$
$641$	−604.563	−	349.045i	−0.943156	−	0.544531i	−0.890948	+	0.454105i	$0.849959\pi$
$642$		0			0
$643$	−389.541			−0.605817			−0.302909	−	0.953020i	$-0.597958\pi$
$643$	−389.541			−0.605817			−0.302909	+	0.953020i	$0.597958\pi$
$644$		0			0
$645$	−256.041	+	689.902i	−0.396963	+	1.06962i
$646$		0			0
$647$	−535.718			−0.828002			−0.414001	−	0.910276i	$-0.635869\pi$
$647$	−535.718			−0.828002			−0.414001	+	0.910276i	$0.635869\pi$
$648$		0			0
$649$	2.45476	−	1.41726i	0.00378238	−	0.00218376i
$650$		0			0
$651$	23.6104	+	139.021i	0.0362678	+	0.213550i
$652$		0			0
$653$	387.113	−	670.499i	0.592822	−	1.02680i	−0.401028	−	0.916066i	$-0.631347\pi$
$653$	387.113	−	670.499i	0.592822	−	1.02680i	0.993850	−	0.110733i	$-0.0353197\pi$
$654$		0			0
$655$	−176.829			−0.269969
$656$		0			0
$657$	264.052	+	227.301i	0.401906	+	0.345968i
$658$		0			0
$659$		−	137.735i		−	0.209007i	−0.994525	−	0.104503i	$-0.966675\pi$
$659$		−	137.735i		−	0.209007i	0.994525	−	0.104503i	$-0.0333253\pi$
$660$		0			0
$661$	955.488	−	551.651i	1.44552	−	0.834571i	0.447309	−	0.894380i	$-0.352382\pi$
$661$	955.488	−	551.651i	1.44552	−	0.834571i	0.998210	+	0.0598090i	$0.0190492\pi$
$662$		0			0
$663$	−1753.83	−	650.892i	−2.64529	−	0.981738i
$664$		0			0
$665$	−27.9176	−	1548.74i	−0.0419813	−	2.32893i
$666$		0			0
$667$	75.5011	−	43.5906i	0.113195	−	0.0653532i
$668$		0			0
$669$	−13.3439	−	4.95228i	−0.0199460	−	0.00740251i
$670$		0			0
$671$	−2.34855	−	4.06780i	−0.00350007	−	0.00606230i
$672$		0			0
$673$	−793.377	+	458.056i	−1.17887	+	0.680618i	−0.955752	−	0.294174i	$-0.904955\pi$
$673$	−793.377	+	458.056i	−1.17887	+	0.680618i	−0.223114	+	0.974792i	$0.571622\pi$
$674$		0			0
$675$	−249.288	+	137.706i	−0.369315	+	0.204009i
$676$		0			0
$677$	−518.834	+	299.549i	−0.766372	+	0.442465i	−0.831579	−	0.555407i	$-0.812563\pi$
$677$	−518.834	+	299.549i	−0.766372	+	0.442465i	0.0652071	+	0.997872i	$0.479229\pi$
$678$		0			0
$679$		−	1734.68i		−	2.55476i
$680$		0			0
$681$	574.010	−	475.517i	0.842893	−	0.698262i
$682$		0			0
$683$		−	884.634i		−	1.29522i	−0.761973	−	0.647609i	$-0.775769\pi$
$683$		−	884.634i		−	1.29522i	0.761973	−	0.647609i	$-0.224231\pi$
$684$		0			0
$685$	1077.97			1.57367
$686$		0			0
$687$	−45.2042	+	121.802i	−0.0657994	+	0.177296i
$688$		0			0
$689$	927.349			1.34594
$690$		0			0
$691$	341.903	+	592.194i	0.494795	+	0.857010i	0.999982	−	0.00600019i	$-0.00190993\pi$
$691$	341.903	+	592.194i	0.494795	+	0.857010i	−0.505187	+	0.863010i	$0.668577\pi$
$692$		0			0
$693$	1.39753	−	7.38034i	0.00201664	−	0.0106498i
$694$		0			0
$695$	−259.859	−	450.090i	−0.373898	−	0.647611i
$696$		0			0
$697$	−1131.20	+	653.101i	−1.62296	+	0.937018i
$698$		0			0
$699$	−284.529	−	343.464i	−0.407052	−	0.491365i
$700$		0			0
$701$	−424.494	−	735.244i	−0.605554	−	1.04885i	−0.991964	−	0.126523i	$-0.959618\pi$
$701$	−424.494	−	735.244i	−0.605554	−	1.04885i	0.386409	−	0.922327i	$-0.373715\pi$
$702$		0			0
$703$	−173.666	+	313.724i	−0.247035	+	0.446264i
$704$		0			0
$705$	143.206	−	24.3211i	0.203129	−	0.0344980i
$706$		0			0
$707$	−1260.94	−	2184.01i	−1.78350	−	3.08912i
$708$		0			0
$709$	−1310.98			−1.84905			−0.924526	−	0.381119i	$-0.875539\pi$
$709$	−1310.98			−1.84905			−0.924526	+	0.381119i	$0.875539\pi$
$710$		0			0
$711$	−221.691	−	41.9791i	−0.311801	−	0.0590423i
$712$		0			0
$713$		−	5.88188i		−	0.00824949i
$714$		0			0
$715$	−6.50471	−	3.75550i	−0.00909750	−	0.00525245i
$716$		0			0
$717$	−231.899	+	624.851i	−0.323430	+	0.871480i
$718$		0			0
$719$	266.689	+	461.919i	0.370916	+	0.642446i	0.989707	−	0.143110i	$-0.0457103\pi$
$719$	266.689	+	461.919i	0.370916	+	0.642446i	−0.618790	+	0.785556i	$0.712377\pi$
$720$		0			0
$721$			2301.41i			3.19197i
$722$		0			0
$723$	51.8724	+	305.432i	0.0717461	+	0.422451i
$724$		0			0
$725$		−	537.425i		−	0.741276i
$726$		0			0
$727$	260.552	−	451.289i	0.358393	−	0.620755i	−0.629299	−	0.777163i	$-0.716658\pi$
$727$	260.552	−	451.289i	0.358393	−	0.620755i	0.987693	+	0.156408i	$0.0499914\pi$
$728$		0			0
$729$	388.117	−	617.095i	0.532397	−	0.846495i
$730$		0			0
$731$	1243.00			1.70040
$732$		0			0
$733$	−50.8982	+	88.1583i	−0.0694382	+	0.120271i	−0.898654	−	0.438658i	$-0.855454\pi$
$733$	−50.8982	+	88.1583i	−0.0694382	+	0.120271i	0.829216	+	0.558928i	$0.188787\pi$
$734$		0			0
$735$	858.662	−	2313.66i	1.16825	−	3.14784i
$736$		0			0
$737$	−2.17532	−	1.25592i	−0.00295159	−	0.00170410i
$738$		0			0
$739$	−190.049	−	329.174i	−0.257170	−	0.445432i	0.708313	−	0.705899i	$-0.249457\pi$
$739$	−190.049	−	329.174i	−0.257170	−	0.445432i	−0.965483	+	0.260467i	$0.916123\pi$
$740$		0			0
$741$	1156.10	−	217.850i	1.56018	−	0.293994i
$742$		0			0
$743$			549.604i			0.739709i	0.929090	+	0.369855i	$0.120593\pi$
$743$			549.604i			0.739709i	−0.929090	+	0.369855i	$0.879407\pi$
$744$		0			0
$745$	−278.967			−0.374453
$746$		0			0
$747$	245.090	+	210.978i	0.328098	+	0.282434i
$748$		0			0
$749$	−1000.70	+	577.752i	−1.33604	+	0.771364i
$750$		0			0
$751$	−1102.86	+	636.737i	−1.46852	+	0.847852i	−0.999378	−	0.0352683i	$-0.988771\pi$
$751$	−1102.86	+	636.737i	−1.46852	+	0.847852i	−0.469146	+	0.883121i	$0.655438\pi$
$752$		0			0
$753$	136.421	−	367.586i	0.181170	−	0.488162i
$754$		0			0
$755$	929.187	−	536.466i	1.23071	−	0.710551i
$756$		0			0
$757$	−265.936	−	460.615i	−0.351303	−	0.608474i	0.635175	−	0.772368i	$-0.280928\pi$
$757$	−265.936	−	460.615i	−0.351303	−	0.608474i	−0.986478	+	0.163894i	$0.947595\pi$
$758$		0			0
$759$	−0.109016	+	0.293743i	−0.000143631	+	0.000387013i
$760$		0			0
$761$	323.880	−	560.976i	0.425598	−	0.737157i	−0.570878	−	0.821035i	$-0.693397\pi$
$761$	323.880	−	560.976i	0.425598	−	0.737157i	0.996476	+	0.0838780i	$0.0267306\pi$
$762$		0			0
$763$	−1314.76	−	759.079i	−1.72315	−	0.994861i
$764$		0			0
$765$	1228.68	+	1057.67i	1.60612	+	1.38258i
$766$		0			0
$767$	479.237	+	830.062i	0.624819	+	1.08222i
$768$		0			0
$769$	72.8899	+	126.249i	0.0947853	+	0.164173i	0.909519	−	0.415662i	$-0.136450\pi$
$769$	72.8899	+	126.249i	0.0947853	+	0.164173i	−0.814734	+	0.579835i	$0.803117\pi$
$770$		0			0
$771$	786.444	−	651.499i	1.02003	−	0.845006i
$772$		0			0
$773$	499.283	+	288.261i	0.645903	+	0.372912i	0.786885	−	0.617100i	$-0.211693\pi$
$773$	499.283	+	288.261i	0.645903	+	0.372912i	−0.140982	+	0.990012i	$0.545026\pi$
$774$		0			0
$775$	−31.4009	−	18.1293i	−0.0405173	−	0.0233927i
$776$		0			0
$777$	−596.189	+	493.890i	−0.767296	+	0.635637i
$778$		0			0
$779$	397.830	−	718.672i	0.510694	−	0.922557i
$780$		0			0
$781$	2.13678	+	1.23367i	0.00273596	+	0.00157960i
$782$		0			0
$783$	665.180	+	1204.16i	0.849527	+	1.53789i
$784$		0			0
$785$	−475.525			−0.605765
$786$		0			0
$787$	622.039	+	359.134i	0.790392	+	0.456333i	0.840101	−	0.542431i	$-0.182496\pi$
$787$	622.039	+	359.134i	0.790392	+	0.456333i	−0.0497083	+	0.998764i	$0.515829\pi$
$788$		0			0
$789$	415.968	−	1120.82i	0.527209	−	1.42056i
$790$		0			0
$791$			732.316i			0.925810i
$792$		0			0
$793$	1375.50	−	794.145i	1.73455	−	1.00144i
$794$		0			0
$795$	−753.452	−	279.626i	−0.947738	−	0.351731i
$796$		0			0
$797$	1164.66	+	672.418i	1.46131	+	0.843687i	0.999072	−	0.0430699i	$-0.0137138\pi$
$797$	1164.66	+	672.418i	1.46131	+	0.843687i	0.462236	+	0.886757i	$0.347047\pi$
$798$		0			0
$799$	−122.678	−	212.485i	−0.153539	−	0.265938i
$800$		0			0
$801$	−366.536	−	69.4068i	−0.457598	−	0.0866502i
$802$		0			0
$803$	1.18144	−	2.04632i	0.00147129	−	0.00254834i
$804$		0			0
$805$	−69.7488	+	120.809i	−0.0866445	+	0.150073i
$806$		0			0
$807$	−1101.85	+	912.787i	−1.36537	+	1.13109i
$808$		0			0
$809$	280.641			0.346899			0.173449	−	0.984843i	$-0.444509\pi$
$809$	280.641			0.346899			0.173449	+	0.984843i	$0.444509\pi$
$810$		0			0
$811$	−107.506	−	62.0685i	−0.132559	−	0.0765333i	0.432254	−	0.901752i	$-0.357718\pi$
$811$	−107.506	−	62.0685i	−0.132559	−	0.0765333i	−0.564813	+	0.825219i	$0.691052\pi$
$812$		0			0
$813$	−173.583	−	209.538i	−0.213510	−	0.257734i
$814$		0			0
$815$	−277.140			−0.340049
$816$		0			0
$817$	−669.807	+	402.981i	−0.819837	+	0.493245i
$818$		0			0
$819$	2495.61	+	472.566i	3.04714	+	0.577004i
$820$		0			0
$821$	407.988			0.496940			0.248470	−	0.968640i	$-0.420072\pi$
$821$	407.988			0.496940			0.248470	+	0.968640i	$0.420072\pi$
$822$		0			0
$823$	−672.867	−	1165.44i	−0.817578	−	1.41609i	−0.907462	−	0.420134i	$-0.861983\pi$
$823$	−672.867	−	1165.44i	−0.817578	−	1.41609i	0.0898838	−	0.995952i	$-0.471350\pi$
$824$		0			0
$825$	1.23216	+	1.48737i	0.00149352	+	0.00180287i
$826$		0			0
$827$	−925.108	−	534.111i	−1.11863	−	0.645842i	−0.177580	−	0.984106i	$-0.556827\pi$
$827$	−925.108	−	534.111i	−1.11863	−	0.645842i	−0.941051	+	0.338264i	$0.890160\pi$
$828$		0			0
$829$		−	463.384i		−	0.558968i	−0.960150	−	0.279484i	$-0.909837\pi$
$829$		−	463.384i		−	0.558968i	0.960150	−	0.279484i	$-0.0901634\pi$
$830$		0			0
$831$	−538.145	−	649.611i	−0.647587	−	0.781722i
$832$		0			0
$833$	−4168.52			−5.00423
$834$		0			0
$835$	−476.918	+	275.349i	−0.571159	+	0.329759i
$836$		0			0
$837$	92.7964	+	1.75548i	0.110868	+	0.00209735i
$838$		0			0
$839$	104.327	+	60.2334i	0.124347	+	0.0717919i	0.560883	−	0.827895i	$-0.310462\pi$
$839$	104.327	+	60.2334i	0.124347	+	0.0717919i	−0.436536	+	0.899687i	$0.643795\pi$
$840$		0			0
$841$	−1754.99			−2.08679
$842$		0			0
$843$	−33.4894	−	197.190i	−0.0397264	−	0.233915i
$844$		0			0
$845$	766.091	−	1326.91i	0.906616	−	1.57031i
$846$		0			0
$847$	1654.48			1.95334
$848$		0			0
$849$	−260.436	+	44.2306i	−0.306756	+	0.0520972i
$850$		0			0
$851$	27.9666	−	16.1465i	0.0328632	−	0.0189736i
$852$		0			0
$853$	−411.634	+	712.971i	−0.482572	+	0.835840i	−0.999800	−	0.0200083i	$-0.993631\pi$
$853$	−411.634	+	712.971i	−0.482572	+	0.835840i	0.517228	+	0.855848i	$0.326964\pi$
$854$		0			0
$855$	−1004.99	−	171.602i	−1.17543	−	0.200705i
$856$		0			0
$857$	242.598	+	140.064i	0.283078	+	0.163435i	0.634816	−	0.772663i	$-0.281076\pi$
$857$	242.598	+	140.064i	0.283078	+	0.163435i	−0.351738	+	0.936098i	$0.614409\pi$
$858$		0			0
$859$	306.566	+	530.988i	0.356887	+	0.618147i	0.987439	−	0.158000i	$-0.0505046\pi$
$859$	306.566	+	530.988i	0.356887	+	0.618147i	−0.630552	+	0.776147i	$0.717171\pi$
$860$		0			0
$861$	1365.74	−	1131.39i	1.58622	−	1.31405i
$862$		0			0
$863$		−	825.559i		−	0.956615i	−0.878192	−	0.478308i	$-0.841250\pi$
$863$		−	825.559i		−	0.956615i	0.878192	−	0.478308i	$-0.158750\pi$
$864$		0			0
$865$	−451.297	−	260.557i	−0.521731	−	0.301222i
$866$		0			0
$867$	651.141	−	1754.50i	0.751028	−	2.02364i
$868$		0			0
$869$			1.53020i			0.00176088i
$870$		0			0
$871$	424.682	−	735.571i	0.487580	−	0.844513i
$872$		0			0
$873$	−1121.82	−	212.427i	−1.28502	−	0.243330i
$874$		0			0
$875$	−589.110	−	1020.37i	−0.673269	−	1.16614i
$876$		0			0
$877$			602.546i			0.687053i	0.939143	+	0.343527i	$0.111622\pi$
$877$			602.546i			0.687053i	−0.939143	+	0.343527i	$0.888378\pi$
$878$		0			0
$879$	459.520	+	170.540i	0.522776	+	0.194016i
$880$		0			0
$881$	−649.481			−0.737209			−0.368605	−	0.929586i	$-0.620164\pi$
$881$	−649.481			−0.737209			−0.368605	+	0.929586i	$0.620164\pi$
$882$		0			0
$883$	−24.3325	+	42.1452i	−0.0275567	+	0.0477295i	−0.879475	−	0.475945i	$-0.842106\pi$
$883$	−24.3325	+	42.1452i	−0.0275567	+	0.0477295i	0.851918	+	0.523675i	$0.175439\pi$
$884$		0			0
$885$	−139.078	−	818.913i	−0.157151	−	0.925326i
$886$		0			0
$887$	1307.46	−	754.862i	1.47402	−	0.851028i	0.474452	−	0.880281i	$-0.342646\pi$
$887$	1307.46	−	754.862i	1.47402	−	0.851028i	0.999572	+	0.0292530i	$0.00931286\pi$
$888$		0			0
$889$		−	1232.91i		−	1.38686i
$890$		0			0
$891$	−4.60174	−	1.80757i	−0.00516469	−	0.00202870i
$892$		0			0
$893$	134.995	+	74.7281i	0.151170	+	0.0836821i
$894$		0			0
$895$			925.409i			1.03398i
$896$		0			0
$897$	−99.3271	−	36.8630i	−0.110733	−	0.0410959i
$898$		0			0
$899$	−87.5723	+	151.680i	−0.0974108	+	0.168720i
$900$		0			0
$901$			1357.49i			1.50665i
$902$		0			0
$903$	−1663.85	+	282.577i	−1.84258	+	0.312931i
$904$		0			0
$905$	349.117	+	201.563i	0.385764	+	0.222721i
$906$		0			0
$907$	−220.691	−	127.416i	−0.243320	−	0.140481i	0.373382	−	0.927678i	$-0.378198\pi$
$907$	−220.691	−	127.416i	−0.243320	−	0.140481i	−0.616702	+	0.787197i	$0.711531\pi$
$908$		0			0
$909$	−1566.81	+	547.999i	−1.72367	+	0.602860i
$910$		0			0
$911$	−1421.30	+	820.588i	−1.56015	+	0.900755i	−0.562912	+	0.826517i	$0.690319\pi$
$911$	−1421.30	+	820.588i	−1.56015	+	0.900755i	−0.997241	+	0.0742381i	$0.976348\pi$
$912$		0			0
$913$	1.09660	−	1.89937i	0.00120109	−	0.00208036i
$914$		0			0
$915$	−1357.02	+	230.468i	−1.48309	+	0.251877i
$916$		0			0
$917$	−202.771	−	351.210i	−0.221124	−	0.382999i
$918$		0			0
$919$	970.835			1.05640			0.528202	−	0.849119i	$-0.322866\pi$
$919$	970.835			1.05640			0.528202	+	0.849119i	$0.322866\pi$
$920$		0			0
$921$	−531.284	+	440.122i	−0.576856	+	0.477874i
$922$		0			0
$923$	−417.158	+	722.538i	−0.451959	+	0.782815i
$924$		0			0
$925$		−	199.069i		−	0.215210i
$926$		0			0
$927$	1488.32	+	281.827i	1.60553	+	0.304021i
$928$		0			0
$929$	188.836	−	327.073i	0.203268	−	0.352070i	−0.746312	−	0.665597i	$-0.768177\pi$
$929$	188.836	−	327.073i	0.203268	−	0.352070i	0.949579	+	0.313527i	$0.101510\pi$
$930$		0			0
$931$	2246.27	−	1351.44i	2.41275	−	1.45160i
$932$		0			0
$933$	60.3052	−	162.492i	0.0646358	−	0.174161i
$934$		0			0
$935$	5.49746	−	9.52188i	0.00587963	−	0.0101838i
$936$		0			0
$937$	472.636	−	818.629i	0.504414	−	0.873671i	−0.495573	−	0.868566i	$-0.665042\pi$
$937$	472.636	−	818.629i	0.504414	−	0.873671i	0.999987	−	0.00510436i	$-0.00162477\pi$
$938$		0			0
$939$	−249.785	+	42.4217i	−0.266012	+	0.0451776i
$940$		0			0
$941$	270.948	−	156.432i	0.287936	−	0.166240i	−0.349075	−	0.937095i	$-0.613504\pi$
$941$	270.948	−	156.432i	0.287936	−	0.166240i	0.637011	+	0.770855i	$0.280171\pi$
$942$		0			0
$943$	−64.0653	+	36.9881i	−0.0679377	+	0.0392239i
$944$		0			0
$945$	−1885.14	−	1136.46i	−1.99485	−	1.20260i
$946$		0			0
$947$	−141.229	+	244.616i	−0.149133	+	0.258306i	−0.930907	−	0.365256i	$-0.880982\pi$
$947$	−141.229	+	244.616i	−0.149133	+	0.258306i	0.781774	+	0.623562i	$0.214315\pi$
$948$		0			0
$949$	691.949	+	399.497i	0.729135	+	0.420966i
$950$		0			0
$951$	230.733	+	1358.59i	0.242622	+	1.42859i
$952$		0			0
$953$	−1014.92	+	585.963i	−1.06497	+	0.614862i	−0.926803	−	0.375547i	$-0.877455\pi$
$953$	−1014.92	+	585.963i	−1.06497	+	0.614862i	−0.138169	+	0.990409i	$0.544122\pi$
$954$		0			0
$955$	−440.163	−	762.384i	−0.460903	−	0.798308i
$956$		0			0
$957$	7.18463	−	5.95183i	0.00750745	−	0.00621926i
$958$		0			0
$959$	1236.11	+	2141.01i	1.28896	+	2.23254i
$960$		0			0
$961$	−474.592	−	822.017i	−0.493852	−	0.855377i
$962$		0			0
$963$	251.089	+	717.902i	0.260736	+	0.745485i
$964$		0			0
$965$		−	627.833i		−	0.650604i
$966$		0			0
$967$	−1057.37			−1.09345			−0.546725	−	0.837312i	$-0.684126\pi$
$967$	−1057.37			−1.09345			−0.546725	+	0.837312i	$0.684126\pi$
$968$		0			0
$969$	318.898	+	1692.34i	0.329100	+	1.74648i
$970$		0			0
$971$	−402.603	+	232.443i	−0.414628	+	0.239385i	−0.692776	−	0.721153i	$-0.743613\pi$
$971$	−402.603	+	232.443i	−0.414628	+	0.239385i	0.278148	+	0.960538i	$0.410279\pi$
$972$		0			0
$973$	595.964	−	1032.24i	0.612502	−	1.06088i
$974$		0			0
$975$	−502.945	+	416.645i	−0.515841	+	0.427328i
$976$		0			0
$977$	374.179	+	216.032i	0.382988	+	0.221118i	0.679117	−	0.734030i	$-0.262363\pi$
$977$	374.179	+	216.032i	0.382988	+	0.221118i	−0.296130	+	0.955148i	$0.595696\pi$
$978$		0			0
$979$			2.52999i			0.00258426i
$980$		0			0
$981$	−651.902	+	757.304i	−0.664528	+	0.771971i
$982$		0			0
$983$	556.873	+	321.511i	0.566504	+	0.327071i	0.755752	−	0.654858i	$-0.227272\pi$
$983$	556.873	+	321.511i	0.566504	+	0.327071i	−0.189248	+	0.981929i	$0.560605\pi$
$984$		0			0
$985$	−1727.89			−1.75421
$986$		0			0
$987$	212.520	+	256.539i	0.215319	+	0.259918i
$988$		0			0
$989$	70.3965			0.0711795
$990$		0			0
$991$	138.794	−	80.1330i	0.140055	−	0.0808607i	−0.428335	−	0.903620i	$-0.640900\pi$
$991$	138.794	−	80.1330i	0.140055	−	0.0808607i	0.568390	+	0.822759i	$0.307566\pi$
$992$		0			0
$993$	−90.6549	+	75.0995i	−0.0912939	+	0.0756289i
$994$		0			0
$995$	1101.91	−	1908.57i	1.10745	−	1.91816i
$996$		0			0
$997$	234.440			0.235146			0.117573	−	0.993064i	$-0.462489\pi$
$997$	234.440			0.235146			0.117573	+	0.993064i	$0.462489\pi$
$998$		0			0
$999$	246.391	+	446.038i	0.246638	+	0.446484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.bl.a.373.2	yes	80
3.2	odd	2		2052.3.bl.a.145.8		80
9.2	odd	6		2052.3.s.a.829.33		80
9.7	even	3		684.3.s.a.601.13	yes	80
19.8	odd	6		684.3.s.a.445.13	✓	80
57.8	even	6		2052.3.s.a.901.33		80
171.65	even	6		2052.3.bl.a.1585.8		80
171.160	odd	6	inner	684.3.bl.a.673.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.13	✓	80	19.8	odd	6
684.3.s.a.601.13	yes	80	9.7	even	3
684.3.bl.a.373.2	yes	80	1.1	even	1	trivial
684.3.bl.a.673.2	yes	80	171.160	odd	6	inner
2052.3.s.a.829.33		80	9.2	odd	6
2052.3.s.a.901.33		80	57.8	even	6
2052.3.bl.a.145.8		80	3.2	odd	2
2052.3.bl.a.1585.8		80	171.65	even	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.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.95765 + 0.502306i) q^{3} +5.96221 q^{5} +(6.83689 + 11.8418i) q^{7} +(8.49538 - 2.97129i) q^{9} +O(q^{10})\)	\(q+(-2.95765 + 0.502306i) q^{3} +5.96221 q^{5} +(6.83689 + 11.8418i) q^{7} +(8.49538 - 2.97129i) q^{9} +(-0.0305186 - 0.0528598i) q^{11} +(17.8742 - 10.3197i) q^{13} +(-17.6341 + 2.99485i) q^{15} +(15.1064 + 26.1650i) q^{17} +(-16.6230 - 9.20190i) q^{19} +(-26.1694 - 31.5898i) q^{21} +(0.855542 + 1.48184i) q^{23} +10.5479 q^{25} +(-23.6338 + 13.0553i) q^{27} -50.9509i q^{29} +(-2.97698 - 1.71876i) q^{31} +(0.116815 + 0.141011i) q^{33} +(40.7629 + 70.6035i) q^{35} -18.8728i q^{37} +(-47.6819 + 39.5003i) q^{39} +43.2335i q^{41} +(20.5707 - 35.6295i) q^{43} +(50.6512 - 17.7155i) q^{45} -8.12095 q^{47} +(-68.9861 + 119.487i) q^{49} +(-57.8222 - 69.7989i) q^{51} +(38.9115 + 22.4656i) q^{53} +(-0.181958 - 0.315161i) q^{55} +(53.7873 + 18.8661i) q^{57} +46.4391i q^{59} +76.9545 q^{61} +(93.2675 + 80.2865i) q^{63} +(106.570 - 61.5280i) q^{65} +(35.6393 - 20.5764i) q^{67} +(-3.27473 - 3.95303i) q^{69} +(-35.0078 + 20.2118i) q^{71} +(19.3561 + 33.5258i) q^{73} +(-31.1970 + 5.29828i) q^{75} +(0.417305 - 0.722793i) q^{77} +(-21.7113 - 12.5350i) q^{79} +(63.3428 - 50.4845i) q^{81} +(17.9661 + 31.1181i) q^{83} +(90.0673 + 156.001i) q^{85} +(25.5929 + 150.695i) q^{87} +(-35.8967 - 20.7250i) q^{89} +(244.408 + 141.109i) q^{91} +(9.66820 + 3.58813i) q^{93} +(-99.1099 - 54.8636i) q^{95} +(-109.866 - 63.4310i) q^{97} +(-0.416329 - 0.358384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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