LMFDB - Embedded newform 684.3.be.a.425.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(425,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("684.425");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.be (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			425.3
Character	$\chi$	$=$	684.425
Dual form			684.3.be.a.581.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.83801 + 0.972476i) q^{3} +(4.92443 + 2.84312i) q^{5} +(-1.27053 + 2.20061i) q^{7} +(7.10858 - 5.51979i) q^{9} +O(q^{10})$	\(q+(-2.83801 + 0.972476i) q^{3} +(4.92443 + 2.84312i) q^{5} +(-1.27053 + 2.20061i) q^{7} +(7.10858 - 5.51979i) q^{9} +(-16.6159 - 9.59321i) q^{11} +15.3309 q^{13} +(-16.7405 - 3.27991i) q^{15} +(23.5119 - 13.5746i) q^{17} +(-3.43177 - 18.6875i) q^{19} +(1.46572 - 7.48092i) q^{21} +14.0875i q^{23} +(3.66670 + 6.35091i) q^{25} +(-14.8064 + 22.5781i) q^{27} +(3.83381 - 2.21345i) q^{29} +(0.818629 + 1.41791i) q^{31} +(56.4853 + 11.0670i) q^{33} +(-12.5132 + 7.22452i) q^{35} -10.2519 q^{37} +(-43.5093 + 14.9090i) q^{39} +(-41.3655 - 23.8824i) q^{41} +27.6865 q^{43} +(50.6992 - 6.97126i) q^{45} +(63.5252 - 36.6763i) q^{47} +(21.2715 + 36.8434i) q^{49} +(-53.5260 + 61.3896i) q^{51} +(25.9371 + 14.9748i) q^{53} +(-54.5494 - 94.4823i) q^{55} +(27.9125 + 49.6980i) q^{57} +(94.3617 + 54.4798i) q^{59} +(-27.4453 - 47.5366i) q^{61} +(3.11529 + 22.6563i) q^{63} +(75.4962 + 43.5878i) q^{65} +38.5522 q^{67} +(-13.6998 - 39.9804i) q^{69} +(101.956 - 58.8645i) q^{71} +(43.2124 + 74.8461i) q^{73} +(-16.5822 - 14.4582i) q^{75} +(42.2219 - 24.3768i) q^{77} +126.252 q^{79} +(20.0639 - 78.4757i) q^{81} +(-35.1083 - 20.2698i) q^{83} +154.377 q^{85} +(-8.72786 + 10.0101i) q^{87} +(-99.4601 - 57.4233i) q^{89} +(-19.4783 + 33.7375i) q^{91} +(-3.70215 - 3.22793i) q^{93} +(36.2314 - 101.782i) q^{95} +48.6430 q^{97} +(-171.068 + 23.5223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.83801	+	0.972476i	−0.946003	+	0.324159i
$3$	−2.83801	+	0.972476i	−0.946003	+	0.324159i
$4$		0			0
$5$	4.92443	+	2.84312i	0.984887	+	0.568625i	0.903742	−	0.428078i	$-0.140809\pi$
$5$	4.92443	+	2.84312i	0.984887	+	0.568625i	0.0811448	+	0.996702i	$0.474142\pi$
$6$		0			0
$7$	−1.27053	+	2.20061i	−0.181504	+	0.314373i	−0.942393	−	0.334508i	$-0.891430\pi$
$7$	−1.27053	+	2.20061i	−0.181504	+	0.314373i	0.760889	+	0.648882i	$0.224763\pi$
$8$		0			0
$9$	7.10858	−	5.51979i	0.789842	−	0.613310i
$10$		0			0
$11$	−16.6159	−	9.59321i	−1.51054	−	0.872110i	−0.999924	−	0.0123002i	$-0.996085\pi$
$11$	−16.6159	−	9.59321i	−1.51054	−	0.872110i	−0.510614	−	0.859810i	$-0.670582\pi$
$12$		0			0
$13$	15.3309			1.17930			0.589652	−	0.807658i	$-0.299265\pi$
$13$	15.3309			1.17930			0.589652	+	0.807658i	$0.299265\pi$
$14$		0			0
$15$	−16.7405	−	3.27991i	−1.11603	−	0.218661i
$16$		0			0
$17$	23.5119	−	13.5746i	1.38305	−	0.798506i	0.390533	−	0.920589i	$-0.372291\pi$
$17$	23.5119	−	13.5746i	1.38305	−	0.798506i	0.992520	+	0.122083i	$0.0389575\pi$
$18$		0			0
$19$	−3.43177	−	18.6875i	−0.180619	−	0.983553i
$19$	−3.43177	−	18.6875i	−0.180619	−	0.983553i
$20$		0			0
$21$	1.46572	−	7.48092i	0.0697961	−	0.356234i
$22$		0			0
$23$			14.0875i			0.612500i	0.951951	+	0.306250i	$0.0990744\pi$
$23$			14.0875i			0.612500i	−0.951951	+	0.306250i	$0.900926\pi$
$24$		0			0
$25$	3.66670	+	6.35091i	0.146668	+	0.254036i
$26$		0			0
$27$	−14.8064	+	22.5781i	−0.548384	+	0.836227i
$28$		0			0
$29$	3.83381	−	2.21345i	0.132200	−	0.0763260i	−0.432441	−	0.901662i	$-0.642348\pi$
$29$	3.83381	−	2.21345i	0.132200	−	0.0763260i	0.564642	+	0.825336i	$0.309014\pi$
$30$		0			0
$31$	0.818629	+	1.41791i	0.0264074	+	0.0457389i	0.878927	−	0.476956i	$-0.158260\pi$
$31$	0.818629	+	1.41791i	0.0264074	+	0.0457389i	−0.852520	+	0.522695i	$0.824927\pi$
$32$		0			0
$33$	56.4853	+	11.0670i	1.71168	+	0.335364i
$34$		0			0
$35$	−12.5132	+	7.22452i	−0.357521	+	0.206415i
$36$		0			0
$37$	−10.2519			−0.277079			−0.138540	−	0.990357i	$-0.544241\pi$
$37$	−10.2519			−0.277079			−0.138540	+	0.990357i	$0.544241\pi$
$38$		0			0
$39$	−43.5093	+	14.9090i	−1.11562	+	0.382281i
$40$		0			0
$41$	−41.3655	−	23.8824i	−1.00892	−	0.582498i	−0.0980416	−	0.995182i	$-0.531258\pi$
$41$	−41.3655	−	23.8824i	−1.00892	−	0.582498i	−0.910874	+	0.412685i	$0.864591\pi$
$42$		0			0
$43$	27.6865			0.643873			0.321936	−	0.946761i	$-0.395666\pi$
$43$	27.6865			0.643873			0.321936	+	0.946761i	$0.395666\pi$
$44$		0			0
$45$	50.6992	−	6.97126i	1.12665	−	0.154917i
$46$		0			0
$47$	63.5252	−	36.6763i	1.35160	−	0.780347i	0.363127	−	0.931740i	$-0.381709\pi$
$47$	63.5252	−	36.6763i	1.35160	−	0.780347i	0.988474	+	0.151393i	$0.0483758\pi$
$48$		0			0
$49$	21.2715	+	36.8434i	0.434113	+	0.751906i
$50$		0			0
$51$	−53.5260	+	61.3896i	−1.04953	+	1.20372i
$52$		0			0
$53$	25.9371	+	14.9748i	0.489379	+	0.282543i	0.724317	−	0.689467i	$-0.242155\pi$
$53$	25.9371	+	14.9748i	0.489379	+	0.282543i	−0.234938	+	0.972010i	$0.575489\pi$
$54$		0			0
$55$	−54.5494	−	94.4823i	−0.991806	−	1.71786i
$56$		0			0
$57$	27.9125	+	49.6980i	0.489694	+	0.871895i
$58$		0			0
$59$	94.3617	+	54.4798i	1.59935	+	0.923386i	0.991612	+	0.129249i	$0.0412565\pi$
$59$	94.3617	+	54.4798i	1.59935	+	0.923386i	0.607739	+	0.794137i	$0.292077\pi$
$60$		0			0
$61$	−27.4453	−	47.5366i	−0.449923	−	0.779289i	0.548458	−	0.836178i	$-0.315215\pi$
$61$	−27.4453	−	47.5366i	−0.449923	−	0.779289i	−0.998381	+	0.0568892i	$0.981882\pi$
$62$		0			0
$63$	3.11529	+	22.6563i	0.0494491	+	0.359623i
$64$		0			0
$65$	75.4962	+	43.5878i	1.16148	+	0.670581i
$66$		0			0
$67$	38.5522			0.575406			0.287703	−	0.957720i	$-0.407108\pi$
$67$	38.5522			0.575406			0.287703	+	0.957720i	$0.407108\pi$
$68$		0			0
$69$	−13.6998	−	39.9804i	−0.198547	−	0.579427i
$70$		0			0
$71$	101.956	−	58.8645i	1.43600	−	0.829077i	0.438435	−	0.898763i	$-0.355533\pi$
$71$	101.956	−	58.8645i	1.43600	−	0.829077i	0.997569	+	0.0696859i	$0.0221997\pi$
$72$		0			0
$73$	43.2124	+	74.8461i	0.591951	+	1.02529i	0.993969	+	0.109657i	$0.0349753\pi$
$73$	43.2124	+	74.8461i	0.591951	+	1.02529i	−0.402019	+	0.915631i	$0.631691\pi$
$74$		0			0
$75$	−16.5822	−	14.4582i	−0.221096	−	0.192775i
$76$		0			0
$77$	42.2219	−	24.3768i	0.548337	−	0.316582i
$78$		0			0
$79$	126.252			1.59813			0.799064	−	0.601246i	$-0.205329\pi$
$79$	126.252			1.59813			0.799064	+	0.601246i	$0.205329\pi$
$80$		0			0
$81$	20.0639	−	78.4757i	0.247702	−	0.968836i
$82$		0			0
$83$	−35.1083	−	20.2698i	−0.422992	−	0.244214i	0.273365	−	0.961910i	$-0.411863\pi$
$83$	−35.1083	−	20.2698i	−0.422992	−	0.244214i	−0.696357	+	0.717696i	$0.745197\pi$
$84$		0			0
$85$	154.377			1.81620
$86$		0			0
$87$	−8.72786	+	10.0101i	−0.100320	+	0.115058i
$88$		0			0
$89$	−99.4601	−	57.4233i	−1.11753	−	0.645206i	−0.176760	−	0.984254i	$-0.556562\pi$
$89$	−99.4601	−	57.4233i	−1.11753	−	0.645206i	−0.940769	+	0.339048i	$0.889895\pi$
$90$		0			0
$91$	−19.4783	+	33.7375i	−0.214048	+	0.370742i
$92$		0			0
$93$	−3.70215	−	3.22793i	−0.0398081	−	0.0347090i
$94$		0			0
$95$	36.2314	−	101.782i	0.381383	−	1.07139i
$96$		0			0
$97$	48.6430			0.501474			0.250737	−	0.968055i	$-0.419327\pi$
$97$	48.6430			0.501474			0.250737	+	0.968055i	$0.419327\pi$
$98$		0			0
$99$	−171.068	+	23.5223i	−1.72796	+	0.237599i
$100$		0			0
$101$	−19.6614	+	11.3515i	−0.194667	+	0.112391i	−0.594165	−	0.804343i	$-0.702518\pi$
$101$	−19.6614	+	11.3515i	−0.194667	+	0.112391i	0.399499	+	0.916734i	$0.369184\pi$
$102$		0			0
$103$	25.6106	+	44.3589i	0.248647	+	0.430668i	0.963151	−	0.268963i	$-0.0866809\pi$
$103$	25.6106	+	44.3589i	0.248647	+	0.430668i	−0.714504	+	0.699631i	$0.753348\pi$
$104$		0			0
$105$	28.4870	−	32.6721i	0.271305	−	0.311163i
$106$		0			0
$107$		−	67.3620i		−	0.629552i	−0.949166	−	0.314776i	$-0.898071\pi$
$107$		−	67.3620i		−	0.629552i	0.949166	−	0.314776i	$-0.101929\pi$
$108$		0			0
$109$	24.1043	+	41.7498i	0.221140	+	0.383026i	0.955154	−	0.296108i	$-0.0956889\pi$
$109$	24.1043	+	41.7498i	0.221140	+	0.383026i	−0.734014	+	0.679134i	$0.762356\pi$
$110$		0			0
$111$	29.0951	−	9.96976i	0.262118	−	0.0898177i
$112$		0			0
$113$	−15.2621	+	8.81158i	−0.135063	+	0.0779785i	−0.566009	−	0.824399i	$-0.691513\pi$
$113$	−15.2621	+	8.81158i	−0.135063	+	0.0779785i	0.430946	+	0.902378i	$0.358180\pi$
$114$		0			0
$115$	−40.0525	+	69.3730i	−0.348283	+	0.603243i
$116$		0			0
$117$	108.981	−	84.6235i	0.931464	−	0.723278i
$118$		0			0
$119$			68.9875i			0.579727i
$120$		0			0
$121$	123.559	+	214.011i	1.02115	+	1.76869i
$122$		0			0
$123$	140.621	+	27.5515i	1.14326	+	0.223996i
$124$		0			0
$125$		−	100.457i		−	0.803653i
$126$		0			0
$127$	−75.5505	+	130.857i	−0.594885	+	1.03037i	0.398678	+	0.917091i	$0.369469\pi$
$127$	−75.5505	+	130.857i	−0.594885	+	1.03037i	−0.993563	+	0.113281i	$0.963864\pi$
$128$		0			0
$129$	−78.5746	+	26.9245i	−0.609105	+	0.208717i
$130$		0			0
$131$	−171.741	−	99.1549i	−1.31100	−	0.756907i	−0.328740	−	0.944421i	$-0.606624\pi$
$131$	−171.741	−	99.1549i	−1.31100	−	0.756907i	−0.982262	+	0.187513i	$0.939957\pi$
$132$		0			0
$133$	45.4841	+	16.1910i	0.341986	+	0.121737i
$134$		0			0
$135$	−137.105	+	69.0882i	−1.01559	+	0.511765i
$136$		0			0
$137$	−10.8433	+	6.26037i	−0.0791480	+	0.0456961i	−0.539052	−	0.842273i	$-0.681217\pi$
$137$	−10.8433	+	6.26037i	−0.0791480	+	0.0456961i	0.459904	+	0.887969i	$0.347884\pi$
$138$		0			0
$139$	91.1354			0.655650			0.327825	−	0.944738i	$-0.393684\pi$
$139$	91.1354			0.655650			0.327825	+	0.944738i	$0.393684\pi$
$140$		0			0
$141$	−144.618	+	165.864i	−1.02566	+	1.17634i
$142$		0			0
$143$	−254.738	−	147.073i	−1.78138	−	1.02848i
$144$		0			0
$145$	25.1725			0.173603
$146$		0			0
$147$	−96.1981	−	83.8757i	−0.654409	−	0.570583i
$148$		0			0
$149$	−157.715	−	91.0570i	−1.05849	−	0.611121i	−0.133478	−	0.991052i	$-0.542614\pi$
$149$	−157.715	−	91.0570i	−1.05849	−	0.611121i	−0.925015	+	0.379931i	$0.875948\pi$
$150$		0			0
$151$	−123.511	+	213.927i	−0.817951	+	1.41673i	0.0892386	+	0.996010i	$0.471557\pi$
$151$	−123.511	+	213.927i	−0.817951	+	1.41673i	−0.907189	+	0.420722i	$0.861777\pi$
$152$		0			0
$153$	92.2073	−	226.277i	0.602662	−	1.47893i
$154$		0			0
$155$			9.30985i			0.0600635i
$156$		0			0
$157$	104.590	−	181.155i	0.666178	−	1.15385i	−0.312787	−	0.949823i	$-0.601263\pi$
$157$	104.590	−	181.155i	0.666178	−	1.15385i	0.978965	−	0.204030i	$-0.0654040\pi$
$158$		0			0
$159$	−88.1724	−	17.2754i	−0.554543	−	0.108650i
$160$		0			0
$161$	−31.0012	−	17.8985i	−0.192554	−	0.111171i
$162$		0			0
$163$	−18.8681			−0.115755			−0.0578776	−	0.998324i	$-0.518433\pi$
$163$	−18.8681			−0.115755			−0.0578776	+	0.998324i	$0.518433\pi$
$164$		0			0
$165$	246.693	+	215.093i	1.49511	+	1.30360i
$166$		0			0
$167$		−	224.543i		−	1.34457i	−0.740293	−	0.672284i	$-0.765313\pi$
$167$		−	224.543i		−	1.34457i	0.740293	−	0.672284i	$-0.234687\pi$
$168$		0			0
$169$	66.0377			0.390756
$170$		0			0
$171$	−127.546	−	113.899i	−0.745884	−	0.666076i
$172$		0			0
$173$			73.9870i			0.427670i	0.976870	+	0.213835i	$0.0685955\pi$
$173$			73.9870i			0.427670i	−0.976870	+	0.213835i	$0.931404\pi$
$174$		0			0
$175$	−18.6345			−0.106483
$176$		0			0
$177$	−320.780	−	62.8495i	−1.81231	−	0.355082i
$178$		0			0
$179$			196.345i			1.09690i	0.836184	+	0.548449i	$0.184782\pi$
$179$			196.345i			1.09690i	−0.836184	+	0.548449i	$0.815218\pi$
$180$		0			0
$181$	−20.4913	+	35.4920i	−0.113212	+	0.196088i	−0.917063	−	0.398741i	$-0.869447\pi$
$181$	−20.4913	+	35.4920i	−0.113212	+	0.196088i	0.803852	+	0.594830i	$0.202780\pi$
$182$		0			0
$183$	124.118	+	108.219i	0.678241	+	0.591363i
$184$		0			0
$185$	−50.4850	−	29.1475i	−0.272892	−	0.157554i
$186$		0			0
$187$	−520.896			−2.78554
$188$		0			0
$189$	−30.8739	−	61.2692i	−0.163354	−	0.324175i
$190$		0			0
$191$	71.5656	+	41.3184i	0.374689	+	0.216327i	0.675505	−	0.737355i	$-0.263926\pi$
$191$	71.5656	+	41.3184i	0.374689	+	0.216327i	−0.300816	+	0.953682i	$0.597259\pi$
$192$		0			0
$193$	−163.937	+	283.947i	−0.849412	+	1.47123i	0.0323211	+	0.999478i	$0.489710\pi$
$193$	−163.937	+	283.947i	−0.849412	+	1.47123i	−0.881733	+	0.471748i	$0.843623\pi$
$194$		0			0
$195$	−256.647	−	50.2842i	−1.31614	−	0.257868i
$196$		0			0
$197$		−	247.337i		−	1.25552i	−0.778407	−	0.627760i	$-0.783972\pi$
$197$		−	247.337i		−	1.25552i	0.778407	−	0.627760i	$-0.216028\pi$
$198$		0			0
$199$	70.5278	−	122.158i	0.354411	−	0.613858i	−0.632606	−	0.774474i	$-0.718015\pi$
$199$	70.5278	−	122.158i	0.354411	−	0.613858i	0.987017	+	0.160616i	$0.0513481\pi$
$200$		0			0
$201$	−109.411	+	37.4911i	−0.544336	+	0.186523i
$202$		0			0
$203$			11.2490i			0.0554138i
$204$		0			0
$205$	−135.801	−	235.215i	−0.662445	−	1.14739i
$206$		0			0
$207$	77.7600	+	100.142i	0.375652	+	0.483779i
$208$		0			0
$209$	−122.251	+	343.432i	−0.584934	+	1.64321i
$210$		0			0
$211$	96.9990	−	168.007i	0.459711	−	0.796243i	−0.539235	−	0.842156i	$-0.681286\pi$
$211$	96.9990	−	168.007i	0.459711	−	0.796243i	0.998945	+	0.0459131i	$0.0146197\pi$
$212$		0			0
$213$	−232.108	+	266.208i	−1.08971	+	1.24980i
$214$		0			0
$215$	136.340	+	78.7162i	0.634142	+	0.366122i
$216$		0			0
$217$	−4.16035			−0.0191721
$218$		0			0
$219$	−195.423	−	170.391i	−0.892343	−	0.778040i
$220$		0			0
$221$	360.459	−	208.111i	1.63104	−	0.941680i
$222$		0			0
$223$	330.514			1.48212			0.741062	−	0.671436i	$-0.234322\pi$
$223$	330.514			1.48212			0.741062	+	0.671436i	$0.234322\pi$
$224$		0			0
$225$	61.1207	+	24.9066i	0.271648	+	0.110696i
$226$		0			0
$227$	80.2262	+	46.3186i	0.353419	+	0.204047i	0.666190	−	0.745782i	$-0.267924\pi$
$227$	80.2262	+	46.3186i	0.353419	+	0.204047i	−0.312771	+	0.949829i	$0.601257\pi$
$228$		0			0
$229$	−27.5909	−	47.7889i	−0.120484	−	0.208685i	0.799474	−	0.600700i	$-0.205111\pi$
$229$	−27.5909	−	47.7889i	−0.120484	−	0.208685i	−0.919959	+	0.392015i	$0.871778\pi$
$230$		0			0
$231$	−96.1203	+	110.241i	−0.416105	+	0.477236i
$232$		0			0
$233$	24.3726	−	14.0715i	0.104603	−	0.0603927i	−0.446786	−	0.894641i	$-0.647431\pi$
$233$	24.3726	−	14.0715i	0.104603	−	0.0603927i	0.551389	+	0.834248i	$0.314098\pi$
$234$		0			0
$235$	417.101			1.77490
$236$		0			0
$237$	−358.305	+	122.777i	−1.51183	+	0.518047i
$238$		0			0
$239$	25.2620	−	14.5850i	0.105699	−	0.0610251i	−0.446219	−	0.894924i	$-0.647230\pi$
$239$	25.2620	−	14.5850i	0.105699	−	0.0610251i	0.551917	+	0.833899i	$0.313896\pi$
$240$		0			0
$241$	−3.98576	−	6.90354i	−0.0165384	−	0.0286454i	0.857638	−	0.514254i	$-0.171931\pi$
$241$	−3.98576	−	6.90354i	−0.0165384	−	0.0286454i	−0.874176	+	0.485609i	$0.838598\pi$
$242$		0			0
$243$	19.3743	+	242.226i	0.0797296	+	0.996817i
$244$		0			0
$245$			241.910i			0.987389i
$246$		0			0
$247$	−52.6122	−	286.497i	−0.213005	−	1.15991i
$248$		0			0
$249$	119.350	+	23.3839i	0.479316	+	0.0939111i
$250$		0			0
$251$	−254.626	−	147.009i	−1.01445	−	0.585692i	−0.101957	−	0.994789i	$-0.532510\pi$
$251$	−254.626	−	147.009i	−1.01445	−	0.585692i	−0.912491	+	0.409097i	$0.865844\pi$
$252$		0			0
$253$	135.144	−	234.077i	0.534167	−	0.925205i
$254$		0			0
$255$	−438.123	+	150.128i	−1.71813	+	0.588737i
$256$		0			0
$257$			53.6039i			0.208575i	0.994547	+	0.104288i	$0.0332563\pi$
$257$			53.6039i			0.208575i	−0.994547	+	0.104288i	$0.966744\pi$
$258$		0			0
$259$	13.0253	−	22.5606i	0.0502909	−	0.0871064i
$260$		0			0
$261$	15.0352	−	36.8963i	0.0576061	−	0.141365i
$262$		0			0
$263$		−	499.348i		−	1.89866i	−0.314278	−	0.949331i	$-0.601762\pi$
$263$		−	499.348i		−	1.89866i	0.314278	−	0.949331i	$-0.398238\pi$
$264$		0			0
$265$	85.1504	+	147.485i	0.321322	+	0.556546i
$266$		0			0
$267$	338.111	+	66.2453i	1.26633	+	0.248110i
$268$		0			0
$269$	215.111	−	124.195i	0.799670	−	0.461690i	−0.0436856	−	0.999045i	$-0.513910\pi$
$269$	215.111	−	124.195i	0.799670	−	0.461690i	0.843356	+	0.537355i	$0.180577\pi$
$270$		0			0
$271$	103.664	+	179.551i	0.382524	+	0.662552i	0.991422	−	0.130697i	$-0.0417215\pi$
$271$	103.664	+	179.551i	0.382524	+	0.662552i	−0.608898	+	0.793248i	$0.708388\pi$
$272$		0			0
$273$	22.4708	−	114.689i	0.0823107	−	0.420108i
$274$		0			0
$275$		−	140.702i		−	0.511642i
$276$		0			0
$277$	−214.427	+	371.398i	−0.774104	+	1.34079i	0.161193	+	0.986923i	$0.448466\pi$
$277$	−214.427	+	371.398i	−0.774104	+	1.34079i	−0.935297	+	0.353864i	$0.884868\pi$
$278$		0			0
$279$	13.6458	+	5.56065i	0.0489098	+	0.0199306i
$280$		0			0
$281$	423.424	−	244.464i	1.50685	−	0.869978i	0.506877	−	0.862018i	$-0.330800\pi$
$281$	423.424	−	244.464i	1.50685	−	0.869978i	0.999968	−	0.00795961i	$-0.00253365\pi$
$282$		0			0
$283$	−174.925	+	302.980i	−0.618111	+	1.07060i	0.371719	+	0.928345i	$0.378768\pi$
$283$	−174.925	+	302.980i	−0.618111	+	1.07060i	−0.989830	+	0.142254i	$0.954565\pi$
$284$		0			0
$285$	−3.84411	+	324.093i	−0.0134881	+	1.13717i
$286$		0			0
$287$	105.112	−	60.6864i	0.366244	−	0.211451i
$288$		0			0
$289$	224.039	−	388.048i	0.775223	−	1.34273i
$290$		0			0
$291$	−138.049	+	47.3041i	−0.474396	+	0.162557i
$292$		0			0
$293$	−24.7663	+	14.2988i	−0.0845266	+	0.0488015i	−0.541668	−	0.840593i	$-0.682207\pi$
$293$	−24.7663	+	14.2988i	−0.0845266	+	0.0488015i	0.457141	+	0.889394i	$0.348873\pi$
$294$		0			0
$295$	309.785	+	536.564i	1.05012	+	1.81886i
$296$		0			0
$297$	462.618	−	233.116i	1.55764	−	0.784903i
$298$		0			0
$299$			215.975i			0.722323i
$300$		0			0
$301$	−35.1764	+	60.9274i	−0.116865	+	0.202417i
$302$		0			0
$303$	44.7600	−	51.3358i	0.147723	−	0.169425i
$304$		0			0
$305$		−	312.121i		−	1.02335i
$306$		0			0
$307$	−98.3532	−	170.353i	−0.320369	−	0.554895i	0.660195	−	0.751094i	$-0.270473\pi$
$307$	−98.3532	−	170.353i	−0.320369	−	0.554895i	−0.980564	+	0.196199i	$0.937140\pi$
$308$		0			0
$309$	−115.821	−	100.985i	−0.374825	−	0.326813i
$310$		0			0
$311$	−184.438	+	106.485i	−0.593047	+	0.342396i	−0.766301	−	0.642481i	$-0.777905\pi$
$311$	−184.438	+	106.485i	−0.593047	+	0.342396i	0.173254	+	0.984877i	$0.444572\pi$
$312$		0			0
$313$	−202.221	−	350.256i	−0.646072	−	1.11903i	−0.984053	−	0.177877i	$-0.943077\pi$
$313$	−202.221	−	350.256i	−0.646072	−	1.11903i	0.337980	−	0.941153i	$-0.390256\pi$
$314$		0			0
$315$	−49.0735	+	120.427i	−0.155789	+	0.382306i
$316$		0			0
$317$	−184.527	+	106.537i	−0.582104	+	0.336078i	−0.761969	−	0.647613i	$-0.775767\pi$
$317$	−184.527	+	106.537i	−0.582104	+	0.336078i	0.179865	+	0.983691i	$0.442434\pi$
$318$		0			0
$319$	−84.9365			−0.266259
$320$		0			0
$321$	65.5079	+	191.174i	0.204075	+	0.595558i
$322$		0			0
$323$	−334.363	−	392.794i	−1.03518	−	1.21608i
$324$		0			0
$325$	56.2139	+	97.3654i	0.172966	+	0.299586i
$326$		0			0
$327$	−109.009	−	95.0455i	−0.333360	−	0.290659i
$328$		0			0
$329$			186.393i			0.566543i
$330$		0			0
$331$	23.2252	−	40.2273i	0.0701669	−	0.121533i	−0.828807	−	0.559534i	$-0.810980\pi$
$331$	23.2252	−	40.2273i	0.0701669	−	0.121533i	0.898974	+	0.438001i	$0.144313\pi$
$332$		0			0
$333$	−72.8767	+	56.5885i	−0.218849	+	0.169936i
$334$		0			0
$335$	189.848	+	109.609i	0.566710	+	0.327190i
$336$		0			0
$337$	−283.898	+	491.725i	−0.842427	+	1.45913i	0.0454104	+	0.998968i	$0.485540\pi$
$337$	−283.898	+	491.725i	−0.842427	+	1.45913i	−0.887837	+	0.460158i	$0.847793\pi$
$338$		0			0
$339$	34.7449	−	39.8493i	0.102492	−	0.117550i
$340$		0			0
$341$		−	31.4131i		−	0.0921205i
$342$		0			0
$343$	−232.616			−0.678179
$344$		0			0
$345$	46.2058	−	235.831i	0.133930	−	0.683569i
$346$		0			0
$347$	−197.965	−	114.295i	−0.570504	−	0.329381i	0.186847	−	0.982389i	$-0.440173\pi$
$347$	−197.965	−	114.295i	−0.570504	−	0.329381i	−0.757351	+	0.653009i	$0.773507\pi$
$348$		0			0
$349$	−125.287	+	217.003i	−0.358988	+	0.621786i	−0.987792	−	0.155778i	$-0.950212\pi$
$349$	−125.287	+	217.003i	−0.358988	+	0.621786i	0.628804	+	0.777564i	$0.283545\pi$
$350$		0			0
$351$	−226.995	+	346.144i	−0.646710	+	0.986165i
$352$		0			0
$353$	−135.138	−	78.0218i	−0.382826	−	0.221025i	0.296221	−	0.955119i	$-0.404274\pi$
$353$	−135.138	−	78.0218i	−0.382826	−	0.221025i	−0.679047	+	0.734095i	$0.737607\pi$
$354$		0			0
$355$	669.436			1.88573
$356$		0			0
$357$	−67.0887	−	195.787i	−0.187923	−	0.548423i
$358$		0			0
$359$	−262.509	+	151.560i	−0.731222	+	0.422171i	−0.818869	−	0.573980i	$-0.805399\pi$
$359$	−262.509	+	151.560i	−0.731222	+	0.422171i	0.0876469	+	0.996152i	$0.472065\pi$
$360$		0			0
$361$	−337.446	+	128.262i	−0.934753	+	0.355297i
$362$		0			0
$363$	−558.783	−	487.207i	−1.53935	−	1.34217i
$364$		0			0
$365$			491.433i			1.34639i
$366$		0			0
$367$	−11.1332	−	19.2833i	−0.0303358	−	0.0525432i	0.850459	−	0.526041i	$-0.176324\pi$
$367$	−11.1332	−	19.2833i	−0.0303358	−	0.0525432i	−0.880795	+	0.473498i	$0.842991\pi$
$368$		0			0
$369$	−425.876	+	58.5590i	−1.15414	+	0.158696i
$370$		0			0
$371$	−65.9075	+	38.0517i	−0.177648	+	0.102565i
$372$		0			0
$373$	−242.162	−	419.437i	−0.649229	−	1.12450i	−0.983307	−	0.181952i	$-0.941759\pi$
$373$	−242.162	−	419.437i	−0.649229	−	1.12450i	0.334079	−	0.942545i	$-0.391575\pi$
$374$		0			0
$375$	97.6917	+	285.097i	0.260511	+	0.760258i
$376$		0			0
$377$	58.7760	−	33.9343i	0.155904	−	0.0900114i
$378$		0			0
$379$	−515.865			−1.36112			−0.680561	−	0.732692i	$-0.738264\pi$
$379$	−515.865			−1.36112			−0.680561	+	0.732692i	$0.738264\pi$
$380$		0			0
$381$	87.1573	−	444.845i	0.228759	−	1.16757i
$382$		0			0
$383$	−172.390	−	99.5296i	−0.450105	−	0.259868i	0.257769	−	0.966206i	$-0.417013\pi$
$383$	−172.390	−	99.5296i	−0.450105	−	0.259868i	−0.707875	+	0.706338i	$0.750346\pi$
$384$		0			0
$385$	277.225			0.720066
$386$		0			0
$387$	196.812	−	152.824i	0.508558	−	0.394893i
$388$		0			0
$389$	156.994	−	90.6403i	0.403583	−	0.233008i	−0.284446	−	0.958692i	$-0.591810\pi$
$389$	156.994	−	90.6403i	0.403583	−	0.233008i	0.688029	+	0.725684i	$0.258476\pi$
$390$		0			0
$391$	191.232	+	331.224i	0.489085	+	0.847120i
$392$		0			0
$393$	583.829	+	114.388i	1.48557	+	0.291064i
$394$		0			0
$395$	621.720	+	358.950i	1.57398	+	0.908735i
$396$		0			0
$397$	−224.772	−	389.316i	−0.566176	−	0.980645i	−0.996939	−	0.0781804i	$-0.975089\pi$
$397$	−224.772	−	389.316i	−0.566176	−	0.980645i	0.430763	−	0.902465i	$-0.358244\pi$
$398$		0			0
$399$	−144.830	−	1.71784i	−0.362982	−	0.00430537i
$400$		0			0
$401$	96.1997	+	55.5409i	0.239900	+	0.138506i	0.615131	−	0.788425i	$-0.289103\pi$
$401$	96.1997	+	55.5409i	0.239900	+	0.138506i	−0.375231	+	0.926931i	$0.622437\pi$
$402$		0			0
$403$	12.5503	+	21.7378i	0.0311423	+	0.0539400i
$404$		0			0
$405$	321.919	−	329.404i	0.794863	−	0.813344i
$406$		0			0
$407$	170.345	+	98.3490i	0.418539	+	0.241644i
$408$		0			0
$409$	502.935			1.22967			0.614835	−	0.788655i	$-0.289222\pi$
$409$	502.935			1.22967			0.614835	+	0.788655i	$0.289222\pi$
$410$		0			0
$411$	24.6852	−	28.3118i	0.0600614	−	0.0688851i
$412$		0			0
$413$	−239.778	+	138.436i	−0.580576	+	0.335196i
$414$		0			0
$415$	−115.259	−	199.635i	−0.277733	−	0.481047i
$416$		0			0
$417$	−258.643	+	88.6270i	−0.620247	+	0.212535i
$418$		0			0
$419$	−411.162	+	237.385i	−0.981295	+	0.566551i	−0.902661	−	0.430353i	$-0.858389\pi$
$419$	−411.162	+	237.385i	−0.981295	+	0.566551i	−0.0786339	+	0.996904i	$0.525056\pi$
$420$		0			0
$421$	703.876			1.67191			0.835957	−	0.548795i	$-0.184913\pi$
$421$	703.876			1.67191			0.835957	+	0.548795i	$0.184913\pi$
$422$		0			0
$423$	249.129	−	611.362i	0.588957	−	1.44530i
$424$		0			0
$425$	172.422	+	99.5479i	0.405699	+	0.234230i
$426$		0			0
$427$	139.480			0.326650
$428$		0			0
$429$	865.973	+	169.668i	2.01858	+	0.395496i
$430$		0			0
$431$	704.096	+	406.510i	1.63363	+	0.943178i	0.982960	+	0.183820i	$0.0588462\pi$
$431$	704.096	+	406.510i	1.63363	+	0.943178i	0.650672	+	0.759359i	$0.274487\pi$
$432$		0			0
$433$	124.092	−	214.934i	0.286588	−	0.496384i	−0.686405	−	0.727219i	$-0.740812\pi$
$433$	124.092	−	214.934i	0.286588	−	0.496384i	0.972993	+	0.230835i	$0.0741457\pi$
$434$		0			0
$435$	−71.4397	+	24.4796i	−0.164229	+	0.0562750i
$436$		0			0
$437$	263.260	−	48.3450i	0.602426	−	0.110629i
$438$		0			0
$439$	−68.9527			−0.157068			−0.0785339	−	0.996911i	$-0.525024\pi$
$439$	−68.9527			−0.157068			−0.0785339	+	0.996911i	$0.525024\pi$
$440$		0			0
$441$	354.578	+	144.490i	0.804032	+	0.327641i
$442$		0			0
$443$	182.038	−	105.100i	0.410922	−	0.237246i	−0.280264	−	0.959923i	$-0.590422\pi$
$443$	182.038	−	105.100i	0.410922	−	0.237246i	0.691186	+	0.722677i	$0.257089\pi$
$444$		0			0
$445$	−326.523	−	565.554i	−0.733760	−	1.27091i
$446$		0			0
$447$	536.148	+	105.046i	1.19944	+	0.235003i
$448$		0			0
$449$		−	478.696i		−	1.06614i	−0.846072	−	0.533069i	$-0.821039\pi$
$449$		−	478.696i		−	1.06614i	0.846072	−	0.533069i	$-0.178961\pi$
$450$		0			0
$451$	458.218	+	793.657i	1.01600	+	1.75977i
$452$		0			0
$453$	142.486	−	727.237i	0.314538	−	1.60538i
$454$		0			0
$455$	−191.840	+	110.759i	−0.421626	+	0.243426i
$456$		0			0
$457$	221.421	−	383.512i	0.484510	−	0.839195i	−0.515332	−	0.856991i	$-0.672331\pi$
$457$	221.421	−	383.512i	0.484510	−	0.839195i	0.999842	+	0.0177952i	$0.00566470\pi$
$458$		0			0
$459$	−41.6364	+	731.845i	−0.0907112	+	1.59443i
$460$		0			0
$461$			717.965i			1.55741i	0.627392	+	0.778704i	$0.284122\pi$
$461$			717.965i			1.55741i	−0.627392	+	0.778704i	$0.715878\pi$
$462$		0			0
$463$	−409.863	−	709.903i	−0.885232	−	1.53327i	−0.845447	−	0.534059i	$-0.820666\pi$
$463$	−409.863	−	709.903i	−0.885232	−	1.53327i	−0.0397854	−	0.999208i	$-0.512667\pi$
$464$		0			0
$465$	−9.05360	−	26.4214i	−0.0194701	−	0.0568203i
$466$		0			0
$467$		−	928.612i		−	1.98846i	−0.107255	−	0.994232i	$-0.534206\pi$
$467$		−	928.612i		−	1.98846i	0.107255	−	0.994232i	$-0.465794\pi$
$468$		0			0
$469$	−48.9815	+	84.8385i	−0.104438	+	0.180892i
$470$		0			0
$471$	−120.658	+	615.830i	−0.256174	+	1.30750i
$472$		0			0
$473$	−460.037	−	265.603i	−0.972595	−	0.561528i
$474$		0			0
$475$	106.099	−	90.3163i	0.223367	−	0.190140i
$476$		0			0
$477$	267.034	−	36.7178i	0.559819	−	0.0769765i
$478$		0			0
$479$	395.774	−	228.500i	0.826251	−	0.477036i	−0.0263164	−	0.999654i	$-0.508378\pi$
$479$	395.774	−	228.500i	0.826251	−	0.477036i	0.852567	+	0.522617i	$0.175044\pi$
$480$		0			0
$481$	−157.172			−0.326761
$482$		0			0
$483$	105.387	+	20.6483i	0.218193	+	0.0427501i
$484$		0			0
$485$	239.539	+	138.298i	0.493895	+	0.285151i
$486$		0			0
$487$	540.475			1.10980			0.554902	−	0.831916i	$-0.312756\pi$
$487$	540.475			1.10980			0.554902	+	0.831916i	$0.312756\pi$
$488$		0			0
$489$	53.5478	−	18.3488i	0.109505	−	0.0375231i
$490$		0			0
$491$	−768.591	−	443.746i	−1.56536	−	0.903760i	−0.996699	−	0.0811879i	$-0.974129\pi$
$491$	−768.591	−	443.746i	−1.56536	−	0.903760i	−0.568660	−	0.822573i	$-0.692538\pi$
$492$		0			0
$493$	60.0935	−	104.085i	0.121893	−	0.211126i
$494$		0			0
$495$	−909.291	−	370.534i	−1.83695	−	0.748553i
$496$		0			0
$497$			299.155i			0.601922i
$498$		0			0
$499$	65.2082	−	112.944i	0.130678	−	0.226340i	−0.793260	−	0.608883i	$-0.791618\pi$
$499$	65.2082	−	112.944i	0.130678	−	0.226340i	0.923938	+	0.382542i	$0.124951\pi$
$500$		0			0
$501$	218.362	+	637.254i	0.435853	+	1.27196i
$502$		0			0
$503$	246.777	+	142.477i	0.490609	+	0.283254i	0.724827	−	0.688931i	$-0.241920\pi$
$503$	246.777	+	142.477i	0.490609	+	0.283254i	−0.234218	+	0.972184i	$0.575253\pi$
$504$		0			0
$505$	−129.095			−0.255633
$506$		0			0
$507$	−187.416	+	64.2201i	−0.369656	+	0.126667i
$508$		0			0
$509$			352.715i			0.692957i	0.938058	+	0.346479i	$0.112623\pi$
$509$			352.715i			0.692957i	−0.938058	+	0.346479i	$0.887377\pi$
$510$		0			0
$511$	−219.610			−0.429765
$512$		0			0
$513$	472.741	+	199.211i	0.921522	+	0.388326i
$514$		0			0
$515$			291.256i			0.565546i
$516$		0			0
$517$	−1407.37			−2.72219
$518$		0			0
$519$	−71.9505	−	209.976i	−0.138633	−	0.404577i
$520$		0			0
$521$			479.212i			0.919793i	0.887973	+	0.459897i	$0.152114\pi$
$521$			479.212i			0.919793i	−0.887973	+	0.459897i	$0.847886\pi$
$522$		0			0
$523$	−372.327	+	644.890i	−0.711907	+	1.23306i	0.252234	+	0.967666i	$0.418835\pi$
$523$	−372.327	+	644.890i	−0.711907	+	1.23306i	−0.964140	+	0.265392i	$0.914498\pi$
$524$		0			0
$525$	52.8850	−	18.1216i	0.100733	−	0.0345174i
$526$		0			0
$527$	38.4950	+	22.2251i	0.0730456	+	0.0421729i
$528$		0			0
$529$	330.542			0.624844
$530$		0			0
$531$	971.495	−	133.583i	1.82956	−	0.251568i
$532$		0			0
$533$	−634.173	−	366.140i	−1.18982	−	0.686941i
$534$		0			0
$535$	191.519	−	331.720i	0.357979	−	0.620037i
$536$		0			0
$537$	−190.941	−	557.228i	−0.355569	−	1.03767i
$538$		0			0
$539$		−	816.249i		−	1.51438i
$540$		0			0
$541$	−49.4363	+	85.6262i	−0.0913795	+	0.158274i	−0.908092	−	0.418771i	$-0.862461\pi$
$541$	−49.4363	+	85.6262i	−0.0913795	+	0.158274i	0.816712	+	0.577045i	$0.195794\pi$
$542$		0			0
$543$	23.6394	−	120.654i	0.0435348	−	0.222198i
$544$		0			0
$545$			274.125i			0.502983i
$546$		0			0
$547$	189.203	+	327.710i	0.345893	+	0.599104i	0.985516	−	0.169585i	$-0.0542427\pi$
$547$	189.203	+	327.710i	0.345893	+	0.599104i	−0.639623	+	0.768689i	$0.720909\pi$
$548$		0			0
$549$	−457.489	−	186.426i	−0.833314	−	0.339574i
$550$		0			0
$551$	−54.5207	−	64.0484i	−0.0989486	−	0.116240i
$552$		0			0
$553$	−160.407	+	277.832i	−0.290066	+	0.502409i
$554$		0			0
$555$	171.622	+	33.6255i	0.309229	+	0.0605865i
$556$		0			0
$557$	314.531	+	181.594i	0.564687	+	0.326022i	0.755025	−	0.655696i	$-0.227625\pi$
$557$	314.531	+	181.594i	0.564687	+	0.326022i	−0.190337	+	0.981719i	$0.560958\pi$
$558$		0			0
$559$	424.460			0.759321
$560$		0			0
$561$	1478.31	−	506.559i	2.63513	−	0.902956i
$562$		0			0
$563$	−451.834	+	260.866i	−0.802546	+	0.463350i	−0.844361	−	0.535775i	$-0.820020\pi$
$563$	−451.834	+	260.866i	−0.802546	+	0.463350i	0.0418144	+	0.999125i	$0.486686\pi$
$564$		0			0
$565$	−100.210			−0.177362
$566$		0			0
$567$	147.203	+	143.858i	0.259618	+	0.253718i
$568$		0			0
$569$	274.251	+	158.339i	0.481988	+	0.278276i	0.721244	−	0.692681i	$-0.243570\pi$
$569$	274.251	+	158.339i	0.481988	+	0.278276i	−0.239257	+	0.970956i	$0.576904\pi$
$570$		0			0
$571$	425.013	+	736.145i	0.744331	+	1.28922i	0.950506	+	0.310705i	$0.100565\pi$
$571$	425.013	+	736.145i	0.744331	+	1.28922i	−0.206175	+	0.978515i	$0.566102\pi$
$572$		0			0
$573$	−243.285	−	47.6662i	−0.424581	−	0.0831870i
$574$		0			0
$575$	−89.4684	+	51.6546i	−0.155597	+	0.0898341i
$576$		0			0
$577$	939.590			1.62841			0.814203	−	0.580581i	$-0.197174\pi$
$577$	939.590			1.62841			0.814203	+	0.580581i	$0.197174\pi$
$578$		0			0
$579$	189.122	−	965.267i	0.326636	−	1.66713i
$580$		0			0
$581$	89.2120	−	51.5066i	0.153549	−	0.0886516i
$582$		0			0
$583$	−287.313	−	497.640i	−0.492818	−	0.853585i
$584$		0			0
$585$	777.266	−	106.876i	1.32866	−	0.182694i
$586$		0			0
$587$		−	205.221i		−	0.349610i	−0.984603	−	0.174805i	$-0.944070\pi$
$587$		−	205.221i		−	0.349610i	0.984603	−	0.174805i	$-0.0559295\pi$
$588$		0			0
$589$	23.6878	−	20.1641i	0.0402170	−	0.0342344i
$590$		0			0
$591$	240.530	+	701.946i	0.406988	+	1.18773i
$592$		0			0
$593$	710.973	+	410.481i	1.19894	+	0.692210i	0.960320	−	0.278902i	$-0.0899705\pi$
$593$	710.973	+	410.481i	1.19894	+	0.692210i	0.238623	+	0.971112i	$0.423304\pi$
$594$		0			0
$595$	−196.140	+	339.724i	−0.329647	+	0.570965i
$596$		0			0
$597$	−81.3630	+	415.271i	−0.136286	+	0.695597i
$598$		0			0
$599$		−	380.778i		−	0.635689i	−0.948143	−	0.317845i	$-0.897041\pi$
$599$		−	380.778i		−	0.635689i	0.948143	−	0.317845i	$-0.102959\pi$
$600$		0			0
$601$	−205.436	+	355.826i	−0.341824	+	0.592057i	−0.984771	−	0.173854i	$-0.944378\pi$
$601$	−205.436	+	355.826i	−0.341824	+	0.592057i	0.642947	+	0.765910i	$0.277711\pi$
$602$		0			0
$603$	274.051	−	212.800i	0.454480	−	0.352902i
$604$		0			0
$605$			1405.18i			2.32261i
$606$		0			0
$607$	−176.593	−	305.869i	−0.290928	−	0.503902i	0.683101	−	0.730324i	$-0.260631\pi$
$607$	−176.593	−	305.869i	−0.290928	−	0.503902i	−0.974029	+	0.226421i	$0.927297\pi$
$608$		0			0
$609$	−10.9394	−	31.9247i	−0.0179628	−	0.0524216i
$610$		0			0
$611$	973.902	−	562.282i	1.59395	−	0.920266i
$612$		0			0
$613$	84.7338	+	146.763i	0.138228	+	0.239418i	0.926826	−	0.375491i	$-0.122526\pi$
$613$	84.7338	+	146.763i	0.138228	+	0.239418i	−0.788598	+	0.614909i	$0.789193\pi$
$614$		0			0
$615$	614.146	+	535.478i	0.998611	+	0.870695i
$616$		0			0
$617$			128.808i			0.208766i	0.994537	+	0.104383i	$0.0332867\pi$
$617$			128.808i			0.208766i	−0.994537	+	0.104383i	$0.966713\pi$
$618$		0			0
$619$	185.687	−	321.619i	0.299978	−	0.519578i	−0.676152	−	0.736762i	$-0.736354\pi$
$619$	185.687	−	321.619i	0.299978	−	0.519578i	0.976131	+	0.217184i	$0.0696872\pi$
$620$		0			0
$621$	−318.069	−	208.585i	−0.512189	−	0.335885i
$622$		0			0
$623$	252.733	−	145.916i	0.405671	−	0.234214i
$624$		0			0
$625$	377.278	−	653.465i	0.603645	−	1.04554i
$626$		0			0
$627$	12.9707	−	1093.55i	0.0206870	−	1.74410i
$628$		0			0
$629$	−241.042	+	139.166i	−0.383215	+	0.221250i
$630$		0			0
$631$	−120.458	+	208.640i	−0.190900	+	0.330649i	−0.945549	−	0.325480i	$-0.894474\pi$
$631$	−120.458	+	208.640i	−0.190900	+	0.330649i	0.754649	+	0.656129i	$0.227807\pi$
$632$		0			0
$633$	−111.901	+	571.135i	−0.176779	+	0.902267i
$634$		0			0
$635$	−744.086	+	429.599i	−1.17179	+	0.676533i
$636$		0			0
$637$	326.113	+	564.844i	0.511951	+	0.886725i
$638$		0			0
$639$	399.845	−	981.220i	0.625736	−	1.53556i
$640$		0			0
$641$			510.534i			0.796465i	0.917285	+	0.398232i	$0.130376\pi$
$641$			510.534i			0.796465i	−0.917285	+	0.398232i	$0.869624\pi$
$642$		0			0
$643$	24.9822	−	43.2704i	0.0388525	−	0.0672946i	−0.845945	−	0.533270i	$-0.820963\pi$
$643$	24.9822	−	43.2704i	0.0388525	−	0.0672946i	0.884798	+	0.465975i	$0.154296\pi$
$644$		0			0
$645$	−463.485	−	90.8094i	−0.718581	−	0.140790i
$646$		0			0
$647$			1066.24i			1.64798i	0.566602	+	0.823991i	$0.308258\pi$
$647$			1066.24i			1.64798i	−0.566602	+	0.823991i	$0.691742\pi$
$648$		0			0
$649$	−1045.27	−	1810.46i	−1.61059	−	2.78962i
$650$		0			0
$651$	11.8071	−	4.04584i	0.0181369	−	0.00621481i
$652$		0			0
$653$	−689.970	+	398.354i	−1.05661	+	0.610037i	−0.924494	−	0.381197i	$-0.875512\pi$
$653$	−689.970	+	398.354i	−1.05661	+	0.610037i	−0.132121	+	0.991234i	$0.542179\pi$
$654$		0			0
$655$	−563.819	−	976.563i	−0.860792	−	1.49094i
$656$		0			0
$657$	720.313	+	293.526i	1.09637	+	0.446767i
$658$		0			0
$659$	−944.767	+	545.461i	−1.43364	+	0.827711i	−0.997396	−	0.0721190i	$-0.977024\pi$
$659$	−944.767	+	545.461i	−1.43364	+	0.827711i	−0.436241	+	0.899830i	$0.643691\pi$
$660$		0			0
$661$	−39.9813			−0.0604861			−0.0302431	−	0.999543i	$-0.509628\pi$
$661$	−39.9813			−0.0604861			−0.0302431	+	0.999543i	$0.509628\pi$
$662$		0			0
$663$	−820.604	+	941.160i	−1.23771	+	1.41955i
$664$		0			0
$665$	177.951	+	209.048i	0.267595	+	0.314358i
$666$		0			0
$667$	31.1820	+	54.0088i	0.0467497	+	0.0809728i
$668$		0			0
$669$	−938.001	+	321.417i	−1.40209	+	0.480443i
$670$		0			0
$671$			1053.15i			1.56953i
$672$		0			0
$673$	−529.340	+	916.844i	−0.786538	+	1.36232i	0.141538	+	0.989933i	$0.454795\pi$
$673$	−529.340	+	916.844i	−0.786538	+	1.36232i	−0.928076	+	0.372391i	$0.878538\pi$
$674$		0			0
$675$	−197.682	−	11.2466i	−0.292862	−	0.0166616i
$676$		0			0
$677$	−844.755	−	487.719i	−1.24779	−	0.720413i	−0.277123	−	0.960834i	$-0.589381\pi$
$677$	−844.755	−	487.719i	−1.24779	−	0.720413i	−0.970669	+	0.240422i	$0.922714\pi$
$678$		0			0
$679$	−61.8022	+	107.044i	−0.0910194	+	0.157650i
$680$		0			0
$681$	−272.726	−	53.4346i	−0.400479	−	0.0784648i
$682$		0			0
$683$		−	991.533i		−	1.45173i	−0.687836	−	0.725866i	$-0.741439\pi$
$683$		−	991.533i		−	1.45173i	0.687836	−	0.725866i	$-0.258561\pi$
$684$		0			0
$685$	−71.1960			−0.103936
$686$		0			0
$687$	124.777	+	108.794i	0.181626	+	0.158361i
$688$		0			0
$689$	397.640	+	229.578i	0.577127	+	0.333204i
$690$		0			0
$691$	−482.918	+	836.438i	−0.698868	+	1.21047i	0.269991	+	0.962863i	$0.412979\pi$
$691$	−482.918	+	836.438i	−0.698868	+	1.21047i	−0.968859	+	0.247612i	$0.920354\pi$
$692$		0			0
$693$	165.583	−	406.341i	0.238936	−	0.586350i
$694$		0			0
$695$	448.790	+	259.109i	0.645741	+	0.372819i
$696$		0			0
$697$	−1296.78			−1.86051
$698$		0			0
$699$	−55.4853	+	63.6368i	−0.0793782	+	0.0910397i
$700$		0			0
$701$	−271.500	+	156.751i	−0.387304	+	0.223610i	−0.680991	−	0.732292i	$-0.738451\pi$
$701$	−271.500	+	156.751i	−0.387304	+	0.223610i	0.293688	+	0.955901i	$0.405117\pi$
$702$		0			0
$703$	35.1823	+	191.583i	0.0500459	+	0.272522i
$704$		0			0
$705$	−1183.74	+	405.621i	−1.67906	+	0.575348i
$706$		0			0
$707$		−	57.6894i		−	0.0815975i
$708$		0			0
$709$	−498.245	−	862.985i	−0.702743	−	1.21719i	−0.967500	−	0.252871i	$-0.918625\pi$
$709$	−498.245	−	862.985i	−0.702743	−	1.21719i	0.264757	−	0.964315i	$-0.414708\pi$
$710$		0			0
$711$	897.474	−	696.885i	1.26227	−	0.980148i
$712$		0			0
$713$	−19.9748	+	11.5324i	−0.0280151	+	0.0161745i
$714$		0			0
$715$	−836.293	−	1448.50i	−1.16964	−	2.02588i
$716$		0			0
$717$	−57.5101	+	65.9590i	−0.0802094	+	0.0919931i
$718$		0			0
$719$	864.450	−	499.090i	1.20229	−	0.694145i	0.241230	−	0.970468i	$-0.422449\pi$
$719$	864.450	−	499.090i	1.20229	−	0.694145i	0.961065	+	0.276323i	$0.0891159\pi$
$720$		0			0
$721$	−130.156			−0.180521
$722$		0			0
$723$	18.0251	+	15.7162i	0.0249310	+	0.0217376i
$724$		0			0
$725$	28.1149	+	16.2321i	0.0387791	+	0.0223891i
$726$		0			0
$727$	738.667			1.01605			0.508024	−	0.861343i	$-0.330376\pi$
$727$	738.667			1.01605			0.508024	+	0.861343i	$0.330376\pi$
$728$		0			0
$729$	−290.544	−	668.600i	−0.398551	−	0.917146i
$730$		0			0
$731$	650.963	−	375.833i	0.890510	−	0.514136i
$732$		0			0
$733$	−428.638	−	742.423i	−0.584773	−	1.01286i	−0.994904	−	0.100829i	$-0.967850\pi$
$733$	−428.638	−	742.423i	−0.584773	−	1.01286i	0.410131	−	0.912027i	$-0.365483\pi$
$734$		0			0
$735$	−235.252	−	686.544i	−0.320071	−	0.934073i
$736$		0			0
$737$	−640.581	−	369.839i	−0.869173	−	0.501817i
$738$		0			0
$739$	320.378	+	554.910i	0.433529	+	0.750894i	0.997174	−	0.0751231i	$-0.0239350\pi$
$739$	320.378	+	554.910i	0.433529	+	0.750894i	−0.563646	+	0.826017i	$0.690602\pi$
$740$		0			0
$741$	427.925	+	761.917i	0.577497	+	1.02823i
$742$		0			0
$743$	−1085.64	−	626.793i	−1.46115	−	0.843598i	−0.462090	−	0.886833i	$-0.652900\pi$
$743$	−1085.64	−	626.793i	−1.46115	−	0.843598i	−0.999065	+	0.0432348i	$0.986234\pi$
$744$		0			0
$745$	−517.773	−	896.809i	−0.694997	−	1.20377i
$746$		0			0
$747$	−361.455	+	49.7010i	−0.483876	+	0.0665341i
$748$		0			0
$749$	148.238	+	85.5852i	0.197914	+	0.114266i
$750$		0			0
$751$	−250.171			−0.333117			−0.166558	−	0.986032i	$-0.553265\pi$
$751$	−250.171			−0.333117			−0.166558	+	0.986032i	$0.553265\pi$
$752$		0			0
$753$	865.594	+	169.594i	1.14953	+	0.225224i
$754$		0			0
$755$	−1216.44	+	702.312i	−1.61118	+	0.930214i
$756$		0			0
$757$	64.0809	+	110.991i	0.0846512	+	0.146620i	0.905243	−	0.424895i	$-0.139689\pi$
$757$	64.0809	+	110.991i	0.0846512	+	0.146620i	−0.820591	+	0.571515i	$0.806356\pi$
$758$		0			0
$759$	−155.907	+	795.737i	−0.205411	+	1.04840i
$760$		0			0
$761$	−157.748	+	91.0757i	−0.207290	+	0.119679i	−0.600051	−	0.799962i	$-0.704853\pi$
$761$	−157.748	+	91.0757i	−0.207290	+	0.119679i	0.392761	+	0.919640i	$0.371520\pi$
$762$		0			0
$763$	−122.500			−0.160551
$764$		0			0
$765$	1097.40	−	852.128i	1.43451	−	1.11389i
$766$		0			0
$767$	1446.65	+	835.226i	1.88612	+	1.08895i
$768$		0			0
$769$	1084.06			1.40970			0.704849	−	0.709357i	$-0.251015\pi$
$769$	1084.06			1.40970			0.704849	+	0.709357i	$0.251015\pi$
$770$		0			0
$771$	−52.1285	−	152.128i	−0.0676115	−	0.197313i
$772$		0			0
$773$	524.842	+	303.018i	0.678968	+	0.392002i	0.799466	−	0.600711i	$-0.205116\pi$
$773$	524.842	+	303.018i	0.678968	+	0.392002i	−0.120498	+	0.992714i	$0.538449\pi$
$774$		0			0
$775$	−6.00333	+	10.3981i	−0.00774623	+	0.0134169i
$776$		0			0
$777$	−15.0264	+	76.6939i	−0.0193391	+	0.0987052i
$778$		0			0
$779$	−304.346	+	854.978i	−0.390688	+	1.09753i
$780$		0			0
$781$	−2258.80			−2.89219
$782$		0			0
$783$	−6.78917	+	119.333i	−0.00867071	+	0.152405i
$784$		0			0
$785$	1030.09	−	594.724i	1.31222	−	0.757610i
$786$		0			0
$787$	431.411	+	747.227i	0.548172	+	0.949462i	0.998400	+	0.0565482i	$0.0180095\pi$
$787$	431.411	+	747.227i	0.548172	+	0.949462i	−0.450228	+	0.892914i	$0.648657\pi$
$788$		0			0
$789$	485.604	+	1417.15i	0.615468	+	1.79614i
$790$		0			0
$791$		−	44.7813i		−	0.0566136i
$792$		0			0
$793$	−420.762	−	728.781i	−0.530595	−	0.919018i
$794$		0			0
$795$	−385.083	−	335.756i	−0.484381	−	0.422335i
$796$		0			0
$797$	28.8187	−	16.6385i	0.0361590	−	0.0208764i	−0.481812	−	0.876275i	$-0.660021\pi$
$797$	28.8187	−	16.6385i	0.0361590	−	0.0208764i	0.517971	+	0.855398i	$0.326688\pi$
$798$		0			0
$799$	995.732	−	1724.66i	1.24622	−	2.15852i
$800$		0			0
$801$	−1023.98	+	140.800i	−1.27838	+	0.175781i
$802$		0			0
$803$		−	1658.18i		−	2.06498i
$804$		0			0
$805$	−101.775	−	176.280i	−0.126429	−	0.218982i
$806$		0			0
$807$	−489.711	+	561.656i	−0.606830	+	0.695980i
$808$		0			0
$809$		−	797.081i		−	0.985267i	−0.870237	−	0.492633i	$-0.836034\pi$
$809$		−	797.081i		−	0.985267i	0.870237	−	0.492633i	$-0.163966\pi$
$810$		0			0
$811$	−233.636	+	404.670i	−0.288084	+	0.498977i	−0.973352	−	0.229314i	$-0.926352\pi$
$811$	−233.636	+	404.670i	−0.288084	+	0.498977i	0.685268	+	0.728291i	$0.259685\pi$
$812$		0			0
$813$	−468.809	−	408.758i	−0.576641	−	0.502777i
$814$		0			0
$815$	−92.9147	−	53.6443i	−0.114006	−	0.0658213i
$816$		0			0
$817$	−95.0137	−	517.392i	−0.116296	−	0.633283i
$818$		0			0
$819$	47.7604	+	347.342i	0.0583155	+	0.424105i
$820$		0			0
$821$	−611.361	+	352.970i	−0.744655	+	0.429927i	−0.823759	−	0.566940i	$-0.808127\pi$
$821$	−611.361	+	352.970i	−0.744655	+	0.429927i	0.0791046	+	0.996866i	$0.474794\pi$
$822$		0			0
$823$	−43.3500			−0.0526732			−0.0263366	−	0.999653i	$-0.508384\pi$
$823$	−43.3500			−0.0526732			−0.0263366	+	0.999653i	$0.508384\pi$
$824$		0			0
$825$	136.829	+	399.312i	0.165853	+	0.484015i
$826$		0			0
$827$	272.721	+	157.455i	0.329771	+	0.190393i	0.655739	−	0.754987i	$-0.272357\pi$
$827$	272.721	+	157.455i	0.329771	+	0.190393i	−0.325968	+	0.945381i	$0.605690\pi$
$828$		0			0
$829$	−175.140			−0.211266			−0.105633	−	0.994405i	$-0.533687\pi$
$829$	−175.140			−0.211266			−0.105633	+	0.994405i	$0.533687\pi$
$830$		0			0
$831$	247.369	−	1262.56i	0.297677	−	1.51932i
$832$		0			0
$833$	1000.27	+	577.505i	1.20080	+	0.693283i
$834$		0			0
$835$	638.403	−	1105.75i	0.764554	−	1.32425i
$836$		0			0
$837$	−44.1346	−	2.51092i	−0.0527295	−	0.00299991i
$838$		0			0
$839$			223.819i			0.266769i	0.991064	+	0.133385i	$0.0425846\pi$
$839$			223.819i			0.266769i	−0.991064	+	0.133385i	$0.957415\pi$
$840$		0			0
$841$	−410.701	+	711.355i	−0.488349	+	0.845845i
$842$		0			0
$843$	−963.945	+	1105.56i	−1.14347	+	1.31146i
$844$		0			0
$845$	325.198	+	187.753i	0.384850	+	0.222193i
$846$		0			0
$847$	−627.941			−0.741371
$848$		0			0
$849$	201.799	−	1029.97i	0.237691	−	1.21316i
$850$		0			0
$851$		−	144.424i		−	0.169711i
$852$		0			0
$853$	−1180.41			−1.38383			−0.691916	−	0.721978i	$-0.743233\pi$
$853$	−1180.41			−1.38383			−0.691916	+	0.721978i	$0.743233\pi$
$854$		0			0
$855$	−304.263	−	923.518i	−0.355863	−	1.08014i
$856$		0			0
$857$			565.357i			0.659693i	0.944035	+	0.329847i	$0.106997\pi$
$857$			565.357i			0.659693i	−0.944035	+	0.329847i	$0.893003\pi$
$858$		0			0
$859$	−704.601			−0.820258			−0.410129	−	0.912028i	$-0.634516\pi$
$859$	−704.601			−0.820258			−0.410129	+	0.912028i	$0.634516\pi$
$860$		0			0
$861$	−239.292	+	274.447i	−0.277924	+	0.318754i
$862$		0			0
$863$			585.783i			0.678775i	0.940647	+	0.339388i	$0.110220\pi$
$863$			585.783i			0.678775i	−0.940647	+	0.339388i	$0.889780\pi$
$864$		0			0
$865$	−210.354	+	364.344i	−0.243184	+	0.421207i
$866$		0			0
$867$	−258.459	+	1319.16i	−0.298107	+	1.52152i
$868$		0			0
$869$	−2097.80	−	1211.16i	−2.41404	−	1.39374i
$870$		0			0
$871$	591.042			0.678578
$872$		0			0
$873$	345.783	−	268.499i	0.396086	−	0.307559i
$874$		0			0
$875$	221.066	+	127.633i	0.252647	+	0.145866i
$876$		0			0
$877$	−675.042	+	1169.21i	−0.769717	+	1.33319i	0.168000	+	0.985787i	$0.446269\pi$
$877$	−675.042	+	1169.21i	−0.769717	+	1.33319i	−0.937716	+	0.347401i	$0.887064\pi$
$878$		0			0
$879$	56.3817	−	64.6648i	0.0641430	−	0.0735664i
$880$		0			0
$881$			1018.07i			1.15558i	0.816185	+	0.577790i	$0.196085\pi$
$881$			1018.07i			1.15558i	−0.816185	+	0.577790i	$0.803915\pi$
$882$		0			0
$883$	−792.523	+	1372.69i	−0.897535	+	1.55458i	−0.0668992	+	0.997760i	$0.521311\pi$
$883$	−792.523	+	1372.69i	−0.897535	+	1.55458i	−0.830636	+	0.556816i	$0.812023\pi$
$884$		0			0
$885$	−1400.97	−	1221.51i	−1.58302	−	1.38024i
$886$		0			0
$887$			1174.84i			1.32451i	0.749277	+	0.662256i	$0.230401\pi$
$887$			1174.84i			1.32451i	−0.749277	+	0.662256i	$0.769599\pi$
$888$		0			0
$889$	−191.978	−	332.515i	−0.215948	−	0.374032i
$890$		0			0
$891$	−1086.21	+	1111.47i	−1.21910	+	1.24744i
$892$		0			0
$893$	−903.393	−	1061.26i	−1.01164	−	1.18843i
$894$		0			0
$895$	−558.232	+	966.887i	−0.623723	+	1.08032i
$896$		0			0
$897$	−210.030	−	612.938i	−0.234147	−	0.683320i
$898$		0			0
$899$	6.27694	+	3.62399i	0.00698213	+	0.00403114i
$900$		0			0
$901$	813.107			0.902450
$902$		0			0
$903$	40.5806	−	207.121i	0.0449398	−	0.229369i
$904$		0			0
$905$	−201.816	+	116.519i	−0.223001	+	0.128750i
$906$		0			0
$907$	953.908			1.05172			0.525859	−	0.850572i	$-0.323744\pi$
$907$	953.908			1.05172			0.525859	+	0.850572i	$0.323744\pi$
$908$		0			0
$909$	−77.1065	+	189.219i	−0.0848257	+	0.208162i
$910$		0			0
$911$	28.1810	+	16.2703i	0.0309342	+	0.0178599i	0.515387	−	0.856957i	$-0.327648\pi$
$911$	28.1810	+	16.2703i	0.0309342	+	0.0178599i	−0.484453	+	0.874817i	$0.660981\pi$
$912$		0			0
$913$	388.905	+	673.603i	0.425964	+	0.737791i
$914$		0			0
$915$	303.530	+	885.803i	0.331727	+	0.968091i
$916$		0			0
$917$	436.403	−	251.958i	0.475903	−	0.274763i
$918$		0			0
$919$	−1215.43			−1.32256			−0.661280	−	0.750139i	$-0.729986\pi$
$919$	−1215.43			−1.32256			−0.661280	+	0.750139i	$0.729986\pi$
$920$		0			0
$921$	444.791	+	387.816i	0.482944	+	0.421082i
$922$		0			0
$923$	1563.09	−	902.448i	1.69348	−	0.977733i
$924$		0			0
$925$	−37.5908	−	65.1091i	−0.0406387	−	0.0703883i
$926$		0			0
$927$	426.906	+	173.963i	0.460525	+	0.187663i
$928$		0			0
$929$			1180.08i			1.27027i	0.772402	+	0.635134i	$0.219055\pi$
$929$			1180.08i			1.27027i	−0.772402	+	0.635134i	$0.780945\pi$
$930$		0			0
$931$	615.512	−	523.950i	0.661130	−	0.562782i
$932$		0			0
$933$	419.881	−	481.567i	0.450033	−	0.516149i
$934$		0			0
$935$	−2565.12	−	1480.97i	−2.74344	−	1.58393i
$936$		0			0
$937$	339.618	−	588.236i	0.362453	−	0.627786i	−0.625911	−	0.779894i	$-0.715273\pi$
$937$	339.618	−	588.236i	0.362453	−	0.627786i	0.988364	+	0.152108i	$0.0486062\pi$
$938$		0			0
$939$	914.520	+	797.376i	0.973929	+	0.849176i
$940$		0			0
$941$			529.877i			0.563100i	0.959547	+	0.281550i	$0.0908485\pi$
$941$			529.877i			0.563100i	−0.959547	+	0.281550i	$0.909152\pi$
$942$		0			0
$943$	336.443	−	582.737i	0.356780	−	0.617961i
$944$		0			0
$945$	22.1593	−	389.494i	0.0234490	−	0.412163i
$946$		0			0
$947$		−	114.564i		−	0.120976i	−0.998169	−	0.0604880i	$-0.980734\pi$
$947$		−	114.564i		−	0.120976i	0.998169	−	0.0604880i	$-0.0192657\pi$
$948$		0			0
$949$	662.487	+	1147.46i	0.698089	+	1.20913i
$950$		0			0
$951$	420.085	−	481.800i	0.441730	−	0.506625i
$952$		0			0
$953$	178.049	−	102.797i	0.186830	−	0.107867i	−0.403668	−	0.914906i	$-0.632265\pi$
$953$	178.049	−	102.797i	0.186830	−	0.107867i	0.590498	+	0.807039i	$0.298931\pi$
$954$		0			0
$955$	234.947	+	406.939i	0.246017	+	0.426115i
$956$		0			0
$957$	241.050	−	82.5987i	0.251881	−	0.0863100i
$958$		0			0
$959$		−	31.8158i		−	0.0331760i
$960$		0			0
$961$	479.160	−	829.929i	0.498605	−	0.863610i
$962$		0			0
$963$	−371.824	−	478.849i	−0.386110	−	0.497247i
$964$		0			0
$965$	−1614.59	+	932.184i	−1.67315	+	0.965994i
$966$		0			0
$967$	−603.557	+	1045.39i	−0.624154	+	1.08107i	0.364550	+	0.931184i	$0.381223\pi$
$967$	−603.557	+	1045.39i	−0.624154	+	1.08107i	−0.988704	+	0.149882i	$0.952110\pi$
$968$		0			0
$969$	1330.91	+	789.593i	1.37348	+	0.814853i
$970$		0			0
$971$	−247.794	+	143.064i	−0.255194	+	0.147337i	−0.622140	−	0.782906i	$-0.713737\pi$
$971$	−247.794	+	143.064i	−0.255194	+	0.147337i	0.366946	+	0.930242i	$0.380403\pi$
$972$		0			0
$973$	−115.790	+	200.554i	−0.119003	+	0.206119i
$974$		0			0
$975$	−254.221	−	221.657i	−0.260740	−	0.227341i
$976$		0			0
$977$	−239.324	+	138.174i	−0.244958	+	0.141427i	−0.617453	−	0.786607i	$-0.711836\pi$
$977$	−239.324	+	138.174i	−0.244958	+	0.141427i	0.372495	+	0.928034i	$0.378502\pi$
$978$		0			0
$979$	1101.75	+	1908.28i	1.12538	+	1.94922i
$980$		0			0
$981$	401.797	+	163.731i	0.409579	+	0.166903i
$982$		0			0
$983$			1014.26i			1.03180i	0.856650	+	0.515899i	$0.172542\pi$
$983$			1014.26i			1.03180i	−0.856650	+	0.515899i	$0.827458\pi$
$984$		0			0
$985$	703.211	−	1218.00i	0.713920	−	1.23655i
$986$		0			0
$987$	−181.262	−	528.984i	−0.183650	−	0.535951i
$988$		0			0
$989$			390.034i			0.394372i
$990$		0			0
$991$	−668.318	−	1157.56i	−0.674388	−	1.16807i	−0.976647	−	0.214848i	$-0.931074\pi$
$991$	−668.318	−	1157.56i	−0.674388	−	1.16807i	0.302260	−	0.953226i	$-0.402259\pi$
$992$		0			0
$993$	−26.7934	+	136.751i	−0.0269822	+	0.137715i
$994$		0			0
$995$	694.619	−	401.038i	0.698109	−	0.403054i
$996$		0			0
$997$	30.0956	+	52.1270i	0.0301861	+	0.0522839i	0.880724	−	0.473630i	$-0.157057\pi$
$997$	30.0956	+	52.1270i	0.0301861	+	0.0522839i	−0.850538	+	0.525914i	$0.823723\pi$
$998$		0			0
$999$	151.794	−	231.470i	0.151946	−	0.231701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.be.a.425.3	yes	80
3.2	odd	2		2052.3.be.a.197.11		80
9.4	even	3		2052.3.m.a.881.11		80
9.5	odd	6		684.3.m.a.653.31	yes	80
19.11	even	3		684.3.m.a.353.31	✓	80
57.11	odd	6		2052.3.m.a.1493.30		80
171.49	even	3		2052.3.be.a.125.11		80
171.68	odd	6	inner	684.3.be.a.581.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.31	✓	80	19.11	even	3
684.3.m.a.653.31	yes	80	9.5	odd	6
684.3.be.a.425.3	yes	80	1.1	even	1	trivial
684.3.be.a.581.3	yes	80	171.68	odd	6	inner
2052.3.m.a.881.11		80	9.4	even	3
2052.3.m.a.1493.30		80	57.11	odd	6
2052.3.be.a.125.11		80	171.49	even	3
2052.3.be.a.197.11		80	3.2	odd	2

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

\(f(q)\)	\(=\)	\(q+(-2.83801 + 0.972476i) q^{3} +(4.92443 + 2.84312i) q^{5} +(-1.27053 + 2.20061i) q^{7} +(7.10858 - 5.51979i) q^{9} +O(q^{10})\)	\(q+(-2.83801 + 0.972476i) q^{3} +(4.92443 + 2.84312i) q^{5} +(-1.27053 + 2.20061i) q^{7} +(7.10858 - 5.51979i) q^{9} +(-16.6159 - 9.59321i) q^{11} +15.3309 q^{13} +(-16.7405 - 3.27991i) q^{15} +(23.5119 - 13.5746i) q^{17} +(-3.43177 - 18.6875i) q^{19} +(1.46572 - 7.48092i) q^{21} +14.0875i q^{23} +(3.66670 + 6.35091i) q^{25} +(-14.8064 + 22.5781i) q^{27} +(3.83381 - 2.21345i) q^{29} +(0.818629 + 1.41791i) q^{31} +(56.4853 + 11.0670i) q^{33} +(-12.5132 + 7.22452i) q^{35} -10.2519 q^{37} +(-43.5093 + 14.9090i) q^{39} +(-41.3655 - 23.8824i) q^{41} +27.6865 q^{43} +(50.6992 - 6.97126i) q^{45} +(63.5252 - 36.6763i) q^{47} +(21.2715 + 36.8434i) q^{49} +(-53.5260 + 61.3896i) q^{51} +(25.9371 + 14.9748i) q^{53} +(-54.5494 - 94.4823i) q^{55} +(27.9125 + 49.6980i) q^{57} +(94.3617 + 54.4798i) q^{59} +(-27.4453 - 47.5366i) q^{61} +(3.11529 + 22.6563i) q^{63} +(75.4962 + 43.5878i) q^{65} +38.5522 q^{67} +(-13.6998 - 39.9804i) q^{69} +(101.956 - 58.8645i) q^{71} +(43.2124 + 74.8461i) q^{73} +(-16.5822 - 14.4582i) q^{75} +(42.2219 - 24.3768i) q^{77} +126.252 q^{79} +(20.0639 - 78.4757i) q^{81} +(-35.1083 - 20.2698i) q^{83} +154.377 q^{85} +(-8.72786 + 10.0101i) q^{87} +(-99.4601 - 57.4233i) q^{89} +(-19.4783 + 33.7375i) q^{91} +(-3.70215 - 3.22793i) q^{93} +(36.2314 - 101.782i) q^{95} +48.6430 q^{97} +(-171.068 + 23.5223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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