LMFDB - Embedded newform 588.4.k.e.521.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,4,Mod(509,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("588.509");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	588.k (of order $6$, degree $2$, not 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:	$34.6931230834$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.2
Character	$\chi$	$=$	588.521
Dual form			588.4.k.e.509.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.15687 - 0.637690i) q^{3} +(-6.99365 - 12.1134i) q^{5} +(26.1867 + 6.57697i) q^{9} +O(q^{10})$	\(q+(-5.15687 - 0.637690i) q^{3} +(-6.99365 - 12.1134i) q^{5} +(26.1867 + 6.57697i) q^{9} +(-27.5333 - 15.8964i) q^{11} -31.1041i q^{13} +(28.3408 + 66.9269i) q^{15} +(61.5138 - 106.545i) q^{17} +(62.7653 - 36.2376i) q^{19} +(66.1240 - 38.1767i) q^{23} +(-35.3223 + 61.1801i) q^{25} +(-130.847 - 50.6156i) q^{27} -14.1082i q^{29} +(-267.941 - 154.696i) q^{31} +(131.849 + 99.5333i) q^{33} +(58.3602 + 101.083i) q^{37} +(-19.8347 + 160.400i) q^{39} +491.980 q^{41} +13.6538 q^{43} +(-103.471 - 363.206i) q^{45} +(43.4381 + 75.2370i) q^{47} +(-385.161 + 510.212i) q^{51} +(-388.989 - 224.583i) q^{53} +444.695i q^{55} +(-346.781 + 146.848i) q^{57} +(-128.392 + 222.381i) q^{59} +(-238.010 + 137.415i) q^{61} +(-376.775 + 217.531i) q^{65} +(-515.984 + 893.710i) q^{67} +(-365.338 + 154.706i) q^{69} -931.763i q^{71} +(-887.716 - 512.523i) q^{73} +(221.167 - 292.973i) q^{75} +(462.310 + 800.745i) q^{79} +(642.487 + 344.459i) q^{81} -991.698 q^{83} -1720.82 q^{85} +(-8.99667 + 72.7543i) q^{87} +(-125.394 - 217.188i) q^{89} +(1283.09 + 968.611i) q^{93} +(-877.917 - 506.866i) q^{95} +1059.27i q^{97} +(-616.457 - 597.359i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 64 q^{9}+O(q^{10}) $ 48 * q + 64 * q^9	$ 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99}+O(q^{100}) $ 48 * q + 64 * q^9 - 192 * q^15 - 456 * q^25 + 432 * q^37 - 688 * q^39 + 1248 * q^43 + 1536 * q^51 - 2720 * q^57 + 528 * q^67 - 3744 * q^79 - 3408 * q^81 + 13824 * q^85 + 5088 * q^93 - 15472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−5.15687	−	0.637690i	−0.992441	−	0.122723i
$3$	−5.15687	−	0.637690i	−0.992441	−	0.122723i
$4$		0			0
$5$	−6.99365	−	12.1134i	−0.625531	−	1.08345i	−0.988438	−	0.151626i	$-0.951549\pi$
$5$	−6.99365	−	12.1134i	−0.625531	−	1.08345i	0.362907	−	0.931826i	$-0.381784\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	26.1867	+	6.57697i	0.969878	+	0.243592i
$10$		0			0
$11$	−27.5333	−	15.8964i	−0.754692	−	0.435721i	0.0726950	−	0.997354i	$-0.476840\pi$
$11$	−27.5333	−	15.8964i	−0.754692	−	0.435721i	−0.827387	+	0.561633i	$0.810173\pi$
$12$		0			0
$13$		−	31.1041i		−	0.663593i	−0.943351	−	0.331797i	$-0.892345\pi$
$13$		−	31.1041i		−	0.663593i	0.943351	−	0.331797i	$-0.107655\pi$
$14$		0			0
$15$	28.3408	+	66.9269i	0.487838	+	1.15203i
$16$		0			0
$17$	61.5138	−	106.545i	0.877605	−	1.52006i	0.0236424	−	0.999720i	$-0.492474\pi$
$17$	61.5138	−	106.545i	0.877605	−	1.52006i	0.853962	−	0.520335i	$-0.174193\pi$
$18$		0			0
$19$	62.7653	−	36.2376i	0.757860	−	0.437551i	−0.0706666	−	0.997500i	$-0.522513\pi$
$19$	62.7653	−	36.2376i	0.757860	−	0.437551i	0.828527	+	0.559949i	$0.189179\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	66.1240	−	38.1767i	0.599470	−	0.346104i	−0.169363	−	0.985554i	$-0.554171\pi$
$23$	66.1240	−	38.1767i	0.599470	−	0.346104i	0.768833	+	0.639449i	$0.220838\pi$
$24$		0			0
$25$	−35.3223	+	61.1801i	−0.282579	+	0.489441i
$26$		0			0
$27$	−130.847	−	50.6156i	−0.932652	−	0.360777i
$28$		0			0
$29$		−	14.1082i		−	0.0903390i	−0.998979	−	0.0451695i	$-0.985617\pi$
$29$		−	14.1082i		−	0.0903390i	0.998979	−	0.0451695i	$-0.0143828\pi$
$30$		0			0
$31$	−267.941	−	154.696i	−1.55238	−	0.896265i	−0.997948	−	0.0640343i	$-0.979603\pi$
$31$	−267.941	−	154.696i	−1.55238	−	0.896265i	−0.554429	−	0.832231i	$-0.687063\pi$
$32$		0			0
$33$	131.849	+	99.5333i	0.695514	+	0.525046i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	58.3602	+	101.083i	0.259307	+	0.449133i	0.966056	−	0.258331i	$-0.0831726\pi$
$37$	58.3602	+	101.083i	0.259307	+	0.449133i	−0.706750	+	0.707464i	$0.749839\pi$
$38$		0			0
$39$	−19.8347	+	160.400i	−0.0814385	+	0.658577i
$40$		0			0
$41$	491.980			1.87401			0.937004	−	0.349319i	$-0.113587\pi$
$41$	491.980			1.87401			0.937004	+	0.349319i	$0.113587\pi$
$42$		0			0
$43$	13.6538			0.0484230			0.0242115	−	0.999707i	$-0.492292\pi$
$43$	13.6538			0.0484230			0.0242115	+	0.999707i	$0.492292\pi$
$44$		0			0
$45$	−103.471	−	363.206i	−0.342769	−	1.20319i
$46$		0			0
$47$	43.4381	+	75.2370i	0.134811	+	0.233499i	0.925525	−	0.378686i	$-0.123624\pi$
$47$	43.4381	+	75.2370i	0.134811	+	0.233499i	−0.790714	+	0.612185i	$0.790291\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−385.161	+	510.212i	−1.05752	+	1.40086i
$52$		0			0
$53$	−388.989	−	224.583i	−1.00815	−	0.582053i	−0.0974977	−	0.995236i	$-0.531084\pi$
$53$	−388.989	−	224.583i	−1.00815	−	0.582053i	−0.910648	+	0.413182i	$0.864417\pi$
$54$		0			0
$55$			444.695i			1.09023i
$56$		0			0
$57$	−346.781	+	146.848i	−0.805829	+	0.341236i
$58$		0			0
$59$	−128.392	+	222.381i	−0.283308	+	0.490704i	−0.972197	−	0.234162i	$-0.924765\pi$
$59$	−128.392	+	222.381i	−0.283308	+	0.490704i	0.688889	+	0.724866i	$0.258099\pi$
$60$		0			0
$61$	−238.010	+	137.415i	−0.499575	+	0.288430i	−0.728538	−	0.685005i	$-0.759800\pi$
$61$	−238.010	+	137.415i	−0.499575	+	0.288430i	0.228963	+	0.973435i	$0.426467\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−376.775	+	217.531i	−0.718972	+	0.415098i
$66$		0			0
$67$	−515.984	+	893.710i	−0.940857	+	1.62961i	−0.177016	+	0.984208i	$0.556644\pi$
$67$	−515.984	+	893.710i	−0.940857	+	1.62961i	−0.763841	+	0.645404i	$0.776689\pi$
$68$		0			0
$69$	−365.338	+	154.706i	−0.637414	+	0.269919i
$70$		0			0
$71$		−	931.763i		−	1.55746i	−0.627356	−	0.778732i	$-0.715863\pi$
$71$		−	931.763i		−	1.55746i	0.627356	−	0.778732i	$-0.284137\pi$
$72$		0			0
$73$	−887.716	−	512.523i	−1.42328	−	0.821730i	−0.426700	−	0.904393i	$-0.640324\pi$
$73$	−887.716	−	512.523i	−1.42328	−	0.821730i	−0.996578	+	0.0826631i	$0.973657\pi$
$74$		0			0
$75$	221.167	−	292.973i	0.340509	−	0.451062i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	462.310	+	800.745i	0.658405	+	1.14039i	0.981029	+	0.193863i	$0.0621018\pi$
$79$	462.310	+	800.745i	0.658405	+	1.14039i	−0.322624	+	0.946527i	$0.604565\pi$
$80$		0			0
$81$	642.487	+	344.459i	0.881326	+	0.472508i
$82$		0			0
$83$	−991.698			−1.31148			−0.655741	−	0.754986i	$-0.727644\pi$
$83$	−991.698			−1.31148			−0.655741	+	0.754986i	$0.727644\pi$
$84$		0			0
$85$	−1720.82			−2.19588
$86$		0			0
$87$	−8.99667	+	72.7543i	−0.0110867	+	0.0896561i
$88$		0			0
$89$	−125.394	−	217.188i	−0.149345	−	0.258673i	0.781641	−	0.623729i	$-0.214383\pi$
$89$	−125.394	−	217.188i	−0.149345	−	0.258673i	−0.930985	+	0.365056i	$0.881050\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1283.09	+	968.611i	1.43065	+	1.08000i
$94$		0			0
$95$	−877.917	−	506.866i	−0.948131	−	0.547404i
$96$		0			0
$97$			1059.27i			1.10879i	0.832252	+	0.554397i	$0.187051\pi$
$97$			1059.27i			1.10879i	−0.832252	+	0.554397i	$0.812949\pi$
$98$		0			0
$99$	−616.457	−	597.359i	−0.625821	−	0.606433i
$100$		0			0
$101$	764.116	−	1323.49i	0.752796	−	1.30388i	−0.193666	−	0.981067i	$-0.562038\pi$
$101$	764.116	−	1323.49i	0.752796	−	1.30388i	0.946462	−	0.322814i	$-0.104629\pi$
$102$		0			0
$103$	−164.739	+	95.1120i	−0.157594	+	0.0909870i	−0.576723	−	0.816940i	$-0.695669\pi$
$103$	−164.739	+	95.1120i	−0.157594	+	0.0909870i	0.419129	+	0.907927i	$0.362336\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	154.050	−	88.9408i	0.139183	−	0.0803573i	−0.428792	−	0.903403i	$-0.641061\pi$
$107$	154.050	−	88.9408i	0.139183	−	0.0803573i	0.567975	+	0.823046i	$0.307727\pi$
$108$		0			0
$109$	−96.5195	+	167.177i	−0.0848156	+	0.146905i	−0.905313	−	0.424746i	$-0.860363\pi$
$109$	−96.5195	+	167.177i	−0.0848156	+	0.146905i	0.820497	+	0.571651i	$0.193697\pi$
$110$		0			0
$111$	−236.497	−	558.487i	−0.202228	−	0.477561i
$112$		0			0
$113$		−	452.079i		−	0.376354i	−0.982135	−	0.188177i	$-0.939742\pi$
$113$		−	452.079i		−	0.376354i	0.982135	−	0.188177i	$-0.0602579\pi$
$114$		0			0
$115$	−924.897	−	533.989i	−0.749975	−	0.432998i
$116$		0			0
$117$	204.571	−	814.513i	0.161646	−	0.643605i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−160.111	−	277.320i	−0.120294	−	0.208355i
$122$		0			0
$123$	−2537.08	−	313.731i	−1.85984	−	0.229985i
$124$		0			0
$125$	−760.285			−0.544015
$126$		0			0
$127$	729.629			0.509796			0.254898	−	0.966968i	$-0.417958\pi$
$127$	729.629			0.509796			0.254898	+	0.966968i	$0.417958\pi$
$128$		0			0
$129$	−70.4110	−	8.70690i	−0.0480569	−	0.00594264i
$130$		0			0
$131$	−287.216	−	497.472i	−0.191558	−	0.331789i	0.754208	−	0.656635i	$-0.228021\pi$
$131$	−287.216	−	497.472i	−0.191558	−	0.331789i	−0.945767	+	0.324846i	$0.894687\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	301.976	+	1938.99i	0.192518	+	1.23616i
$136$		0			0
$137$	2102.50	+	1213.88i	1.31116	+	0.756998i	0.982288	−	0.187376i	$-0.0599984\pi$
$137$	2102.50	+	1213.88i	1.31116	+	0.756998i	0.328871	+	0.944375i	$0.393332\pi$
$138$		0			0
$139$			1453.63i			0.887014i	0.896271	+	0.443507i	$0.146266\pi$
$139$			1453.63i			0.887014i	−0.896271	+	0.443507i	$0.853734\pi$
$140$		0			0
$141$	−176.027	−	415.688i	−0.105136	−	0.248278i
$142$		0			0
$143$	−494.442	+	856.398i	−0.289142	+	0.500808i
$144$		0			0
$145$	−170.898	+	98.6680i	−0.0978779	+	0.0565098i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1704.20	+	983.920i	−0.937003	+	0.540979i	−0.889020	−	0.457869i	$-0.848613\pi$
$149$	−1704.20	+	983.920i	−0.937003	+	0.540979i	−0.0479834	+	0.998848i	$0.515279\pi$
$150$		0			0
$151$	−1086.40	+	1881.71i	−0.585499	+	1.01411i	0.409314	+	0.912394i	$0.365768\pi$
$151$	−1086.40	+	1881.71i	−0.585499	+	1.01411i	−0.994813	+	0.101720i	$0.967565\pi$
$152$		0			0
$153$	2311.59	−	2385.49i	1.22144	−	1.26049i
$154$		0			0
$155$			4327.56i			2.24257i
$156$		0			0
$157$	−2857.15	−	1649.57i	−1.45239	−	0.838538i	−0.453773	−	0.891117i	$-0.649922\pi$
$157$	−2857.15	−	1649.57i	−1.45239	−	0.838538i	−0.998617	+	0.0525797i	$0.983256\pi$
$158$		0			0
$159$	1862.75	+	1406.20i	0.929094	+	0.701377i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1399.63	−	2424.23i	−0.672562	−	1.16491i	−0.977175	−	0.212436i	$-0.931860\pi$
$163$	−1399.63	−	2424.23i	−0.672562	−	1.16491i	0.304612	−	0.952476i	$-0.401473\pi$
$164$		0			0
$165$	283.577	−	2293.23i	0.133797	−	1.08199i
$166$		0			0
$167$	1933.50			0.895921			0.447960	−	0.894053i	$-0.352151\pi$
$167$	1933.50			0.895921			0.447960	+	0.894053i	$0.352151\pi$
$168$		0			0
$169$	1229.54			0.559644
$170$		0			0
$171$	1881.95	−	536.137i	0.841616	−	0.239763i
$172$		0			0
$173$	1752.50	+	3035.43i	0.770176	+	1.33398i	0.937466	+	0.348076i	$0.113165\pi$
$173$	1752.50	+	3035.43i	0.770176	+	1.33398i	−0.167290	+	0.985908i	$0.553502\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	803.910	−	1064.92i	0.341387	−	0.452226i
$178$		0			0
$179$	1598.90	+	923.127i	0.667640	+	0.385462i	0.795182	−	0.606371i	$-0.207375\pi$
$179$	1598.90	+	923.127i	0.667640	+	0.385462i	−0.127542	+	0.991833i	$0.540709\pi$
$180$		0			0
$181$			369.402i			0.151699i	0.997119	+	0.0758493i	$0.0241668\pi$
$181$			369.402i			0.151699i	−0.997119	+	0.0758493i	$0.975833\pi$
$182$		0			0
$183$	1315.02	−	556.857i	0.531196	−	0.224940i
$184$		0			0
$185$	816.302	−	1413.88i	0.324409	−	0.561893i
$186$		0			0
$187$	−3387.36	+	1955.69i	−1.32464	+	0.764782i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	206.710	−	119.344i	0.0783088	−	0.0452116i	−0.460334	−	0.887746i	$-0.652270\pi$
$191$	206.710	−	119.344i	0.0783088	−	0.0452116i	0.538643	+	0.842534i	$0.318937\pi$
$192$		0			0
$193$	841.049	−	1456.74i	0.313679	−	0.543308i	−0.665477	−	0.746418i	$-0.731772\pi$
$193$	841.049	−	1456.74i	0.313679	−	0.543308i	0.979156	+	0.203111i	$0.0651051\pi$
$194$		0			0
$195$	2081.70	−	881.514i	0.764479	−	0.323726i
$196$		0			0
$197$		−	2988.01i		−	1.08065i	−0.841458	−	0.540323i	$-0.818302\pi$
$197$		−	2988.01i		−	1.08065i	0.841458	−	0.540323i	$-0.181698\pi$
$198$		0			0
$199$	1746.98	+	1008.62i	0.622312	+	0.359292i	0.777768	−	0.628551i	$-0.216352\pi$
$199$	1746.98	+	1008.62i	0.622312	+	0.359292i	−0.155457	+	0.987843i	$0.549685\pi$
$200$		0			0
$201$	3230.77	−	4279.71i	1.13374	−	1.50183i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3440.73	−	5959.53i	−1.17225	−	2.03040i
$206$		0			0
$207$	1982.66	−	564.827i	0.665721	−	0.189653i
$208$		0			0
$209$	−2304.18			−0.762601
$210$		0			0
$211$	4685.01			1.52858			0.764288	−	0.644875i	$-0.223091\pi$
$211$	4685.01			1.52858			0.764288	+	0.644875i	$0.223091\pi$
$212$		0			0
$213$	−594.176	+	4804.99i	−0.191137	+	1.54569i
$214$		0			0
$215$	−95.4901	−	165.394i	−0.0302901	−	0.0524640i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	4251.01	+	3209.10i	1.31167	+	0.990188i
$220$		0			0
$221$	−3313.98	−	1913.33i	−1.00870	−	0.582373i
$222$		0			0
$223$			17.2808i			0.00518927i	0.999997	+	0.00259463i	$0.000825899\pi$
$223$			17.2808i			0.00518927i	−0.999997	+	0.00259463i	$0.999174\pi$
$224$		0			0
$225$	−1327.36	+	1369.79i	−0.393290	+	0.405864i
$226$		0			0
$227$	−731.937	+	1267.75i	−0.214011	+	0.370677i	−0.952966	−	0.303077i	$-0.901986\pi$
$227$	−731.937	+	1267.75i	−0.214011	+	0.370677i	0.738956	+	0.673754i	$0.235319\pi$
$228$		0			0
$229$	−100.522	+	58.0363i	−0.0290073	+	0.0167474i	−0.514434	−	0.857530i	$-0.671998\pi$
$229$	−100.522	+	58.0363i	−0.0290073	+	0.0167474i	0.485426	+	0.874278i	$0.338664\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3248.11	−	1875.30i	0.913265	−	0.527274i	0.0317846	−	0.999495i	$-0.489881\pi$
$233$	3248.11	−	1875.30i	0.913265	−	0.527274i	0.881480	+	0.472221i	$0.156548\pi$
$234$		0			0
$235$	607.582	−	1052.36i	0.168656	−	0.292122i
$236$		0			0
$237$	−1873.45	−	4424.15i	−0.513475	−	1.21257i
$238$		0			0
$239$			5423.48i			1.46785i	0.679232	+	0.733924i	$0.262313\pi$
$239$			5423.48i			1.46785i	−0.679232	+	0.733924i	$0.737687\pi$
$240$		0			0
$241$	3933.77	+	2271.16i	1.05144	+	0.607048i	0.923051	−	0.384677i	$-0.125687\pi$
$241$	3933.77	+	2271.16i	1.05144	+	0.607048i	0.128386	+	0.991724i	$0.459020\pi$
$242$		0			0
$243$	−3093.57	−	2186.04i	−0.816676	−	0.577096i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1127.14	−	1952.26i	−0.290356	−	0.502911i
$248$		0			0
$249$	5114.06	+	632.396i	1.30157	+	0.160950i
$250$		0			0
$251$	−1115.63			−0.280549			−0.140275	−	0.990113i	$-0.544799\pi$
$251$	−1115.63			−0.280549			−0.140275	+	0.990113i	$0.544799\pi$
$252$		0			0
$253$	−2427.49			−0.603220
$254$		0			0
$255$	8874.07	+	1097.35i	2.17928	+	0.269486i
$256$		0			0
$257$	−3189.65	−	5524.63i	−0.774182	−	1.34092i	−0.935253	−	0.353979i	$-0.884828\pi$
$257$	−3189.65	−	5524.63i	−0.774182	−	1.34092i	0.161071	−	0.986943i	$-0.448505\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	92.7894	−	369.448i	0.0220058	−	0.0876178i
$262$		0			0
$263$	624.597	+	360.611i	0.146442	+	0.0845485i	0.571431	−	0.820650i	$-0.306389\pi$
$263$	624.597	+	360.611i	0.146442	+	0.0845485i	−0.424989	+	0.905199i	$0.639722\pi$
$264$		0			0
$265$			6282.62i			1.45637i
$266$		0			0
$267$	508.140	+	1199.97i	0.116471	+	0.275046i
$268$		0			0
$269$	−2373.32	+	4110.72i	−0.537933	+	0.931728i	0.461082	+	0.887358i	$0.347461\pi$
$269$	−2373.32	+	4110.72i	−0.537933	+	0.931728i	−0.999015	+	0.0443703i	$0.985872\pi$
$270$		0			0
$271$	−7124.62	+	4113.40i	−1.59701	+	0.922034i	−0.604951	+	0.796263i	$0.706807\pi$
$271$	−7124.62	+	4113.40i	−1.59701	+	0.922034i	−0.992059	+	0.125772i	$0.959859\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1945.08	−	1122.99i	0.426519	−	0.246251i
$276$		0			0
$277$	2551.88	−	4419.99i	0.553529	−	0.958741i	−0.444487	−	0.895785i	$-0.646614\pi$
$277$	2551.88	−	4419.99i	0.553529	−	0.958741i	0.998016	−	0.0629556i	$-0.0200526\pi$
$278$		0			0
$279$	−5999.07	−	5813.22i	−1.28729	−	1.24741i
$280$		0			0
$281$		−	6818.51i		−	1.44754i	−0.690042	−	0.723769i	$-0.742408\pi$
$281$		−	6818.51i		−	1.44754i	0.690042	−	0.723769i	$-0.257592\pi$
$282$		0			0
$283$	2317.66	+	1338.10i	0.486822	+	0.281067i	0.723255	−	0.690581i	$-0.242645\pi$
$283$	2317.66	+	1338.10i	0.486822	+	0.281067i	−0.236433	+	0.971648i	$0.575978\pi$
$284$		0			0
$285$	4204.09	+	3173.68i	0.873784	+	0.659624i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−5111.38	−	8853.18i	−1.04038	−	1.80199i
$290$		0			0
$291$	675.489	−	5462.55i	0.136075	−	1.10041i
$292$		0			0
$293$	1743.71			0.347674			0.173837	−	0.984774i	$-0.444383\pi$
$293$	1743.71			0.347674			0.173837	+	0.984774i	$0.444383\pi$
$294$		0			0
$295$	3591.71			0.708872
$296$		0			0
$297$	2798.06	+	3473.62i	0.546666	+	0.678652i
$298$		0			0
$299$	−1187.45	−	2056.73i	−0.229673	−	0.397804i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−4784.43	+	6337.79i	−0.907123	+	1.20164i
$304$		0			0
$305$	3329.12	+	1922.07i	0.625000	+	0.360844i
$306$		0			0
$307$			1503.17i			0.279448i	0.990191	+	0.139724i	$0.0446215\pi$
$307$			1503.17i			0.279448i	−0.990191	+	0.139724i	$0.955378\pi$
$308$		0			0
$309$	910.189	−	385.428i	0.167569	−	0.0709587i
$310$		0			0
$311$	−4370.72	+	7570.31i	−0.796916	+	1.38030i	0.124699	+	0.992195i	$0.460204\pi$
$311$	−4370.72	+	7570.31i	−0.796916	+	1.38030i	−0.921615	+	0.388105i	$0.873130\pi$
$312$		0			0
$313$	3230.92	−	1865.37i	0.583458	−	0.336860i	−0.179048	−	0.983840i	$-0.557302\pi$
$313$	3230.92	−	1865.37i	0.583458	−	0.336860i	0.762507	+	0.646980i	$0.223968\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4312.95	−	2490.08i	0.764163	−	0.441190i	−0.0666256	−	0.997778i	$-0.521223\pi$
$317$	4312.95	−	2490.08i	0.764163	−	0.441190i	0.830788	+	0.556589i	$0.187890\pi$
$318$		0			0
$319$	−224.269	+	388.446i	−0.0393626	+	0.0681781i
$320$		0			0
$321$	−851.133	+	360.421i	−0.147993	+	0.0626689i
$322$		0			0
$323$		−	8916.43i		−	1.53599i
$324$		0			0
$325$	1902.95	+	1098.67i	0.324790	+	0.187517i
$326$		0			0
$327$	604.346	−	800.560i	0.102203	−	0.135386i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−3097.27	−	5364.63i	−0.514324	−	0.890836i	−0.999862	−	0.0166199i	$-0.994709\pi$
$331$	−3097.27	−	5364.63i	−0.514324	−	0.890836i	0.485538	−	0.874216i	$-0.338624\pi$
$332$		0			0
$333$	863.442	+	3030.86i	0.142091	+	0.498769i
$334$		0			0
$335$	14434.4			2.35414
$336$		0			0
$337$	−2866.79			−0.463395			−0.231697	−	0.972788i	$-0.574428\pi$
$337$	−2866.79			−0.463395			−0.231697	+	0.972788i	$0.574428\pi$
$338$		0			0
$339$	−288.286	+	2331.31i	−0.0461875	+	0.373509i
$340$		0			0
$341$	4918.21	+	8518.59i	0.781044	+	1.35281i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	4429.06	+	3343.51i	0.691166	+	0.521764i
$346$		0			0
$347$	1253.66	+	723.803i	0.193949	+	0.111976i	0.593830	−	0.804591i	$-0.297615\pi$
$347$	1253.66	+	723.803i	0.193949	+	0.111976i	−0.399881	+	0.916567i	$0.630949\pi$
$348$		0			0
$349$			5343.79i			0.819618i	0.912171	+	0.409809i	$0.134405\pi$
$349$			5343.79i			0.819618i	−0.912171	+	0.409809i	$0.865595\pi$
$350$		0			0
$351$	−1574.35	+	4069.89i	−0.239409	+	0.618902i
$352$		0			0
$353$	2201.40	−	3812.93i	0.331922	−	0.574906i	−0.650966	−	0.759107i	$-0.725636\pi$
$353$	2201.40	−	3812.93i	0.331922	−	0.574906i	0.982889	+	0.184200i	$0.0589695\pi$
$354$		0			0
$355$	−11286.8	+	6516.43i	−1.68744	+	0.974243i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4640.81	+	2679.37i	−0.682263	+	0.393905i	−0.800707	−	0.599056i	$-0.795543\pi$
$359$	−4640.81	+	2679.37i	−0.682263	+	0.393905i	0.118444	+	0.992961i	$0.462209\pi$
$360$		0			0
$361$	−803.178	+	1391.14i	−0.117098	+	0.202820i
$362$		0			0
$363$	648.828	+	1532.21i	0.0938144	+	0.221543i
$364$		0			0
$365$			14337.6i			2.05607i
$366$		0			0
$367$	−7217.32	−	4166.92i	−1.02654	−	0.592674i	−0.110550	−	0.993871i	$-0.535261\pi$
$367$	−7217.32	−	4166.92i	−1.02654	−	0.592674i	−0.915992	+	0.401196i	$0.868595\pi$
$368$		0			0
$369$	12883.3	+	3235.74i	1.81756	+	0.456493i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−3597.98	−	6231.89i	−0.499454	−	0.865080i	0.500546	−	0.865710i	$-0.333133\pi$
$373$	−3597.98	−	6231.89i	−0.499454	−	0.865080i	−1.00000		0.000630094i	$0.999799\pi$
$374$		0			0
$375$	3920.69	+	484.826i	0.539903	+	0.0667635i
$376$		0			0
$377$	−438.823			−0.0599483
$378$		0			0
$379$	12312.1			1.66869			0.834343	−	0.551245i	$-0.185847\pi$
$379$	12312.1			1.66869			0.834343	+	0.551245i	$0.185847\pi$
$380$		0			0
$381$	−3762.61	−	465.277i	−0.505943	−	0.0625640i
$382$		0			0
$383$	−5365.18	−	9292.76i	−0.715791	−	1.23979i	−0.962654	−	0.270736i	$-0.912733\pi$
$383$	−5365.18	−	9292.76i	−0.715791	−	1.23979i	0.246863	−	0.969050i	$-0.420600\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	357.549	+	89.8008i	0.0469644	+	0.0117954i
$388$		0			0
$389$	−8674.30	−	5008.11i	−1.13060	−	0.652754i	−0.186516	−	0.982452i	$-0.559720\pi$
$389$	−8674.30	−	5008.11i	−1.13060	−	0.652754i	−0.944086	+	0.329698i	$0.893053\pi$
$390$		0			0
$391$		−	9393.58i		−	1.21497i
$392$		0			0
$393$	1163.90	+	2748.56i	0.149392	+	0.352790i
$394$		0			0
$395$	6466.47	−	11200.3i	0.823705	−	1.42670i
$396$		0			0
$397$	3240.86	−	1871.11i	0.409708	−	0.236545i	−0.280956	−	0.959721i	$-0.590652\pi$
$397$	3240.86	−	1871.11i	0.409708	−	0.236545i	0.690664	+	0.723176i	$0.257318\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8343.83	+	4817.31i	−1.03908	+	0.599913i	−0.919572	−	0.392920i	$-0.871465\pi$
$401$	−8343.83	+	4817.31i	−1.03908	+	0.599913i	−0.119507	+	0.992833i	$0.538131\pi$
$402$		0			0
$403$	−4811.67	+	8334.06i	−0.594756	+	1.03015i
$404$		0			0
$405$	−320.779	−	10191.7i	−0.0393571	−	1.25044i
$406$		0			0
$407$		−	3710.86i		−	0.451942i
$408$		0			0
$409$	−4547.71	−	2625.62i	−0.549803	−	0.317429i	0.199239	−	0.979951i	$-0.436153\pi$
$409$	−4547.71	−	2625.62i	−0.549803	−	0.317429i	−0.749043	+	0.662522i	$0.769486\pi$
$410$		0			0
$411$	−10068.3	−	7600.57i	−1.20835	−	0.912186i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	6935.59	+	12012.8i	0.820373	+	1.42093i
$416$		0			0
$417$	926.963	−	7496.17i	0.108858	−	0.880309i
$418$		0			0
$419$	−11867.1			−1.38364			−0.691819	−	0.722071i	$-0.743191\pi$
$419$	−11867.1			−1.38364			−0.691819	+	0.722071i	$0.743191\pi$
$420$		0			0
$421$	−8108.04			−0.938626			−0.469313	−	0.883032i	$-0.655498\pi$
$421$	−8108.04			−0.938626			−0.469313	+	0.883032i	$0.655498\pi$
$422$		0			0
$423$	642.669	+	2255.90i	0.0738715	+	0.259304i
$424$		0			0
$425$	4345.62	+	7526.83i	0.495985	+	0.859071i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	3095.89	−	4101.04i	0.348417	−	0.461538i
$430$		0			0
$431$	390.334	+	225.360i	0.0436235	+	0.0251860i	0.521653	−	0.853158i	$-0.325316\pi$
$431$	390.334	+	225.360i	0.0436235	+	0.0251860i	−0.478030	+	0.878344i	$0.658649\pi$
$432$		0			0
$433$			8133.13i			0.902664i	0.892356	+	0.451332i	$0.149051\pi$
$433$			8133.13i			0.902664i	−0.892356	+	0.451332i	$0.850949\pi$
$434$		0			0
$435$	944.219	−	399.838i	0.104073	−	0.0440708i
$436$		0			0
$437$	2766.86	−	4792.35i	0.302876	−	0.524597i
$438$		0			0
$439$	8016.30	−	4628.21i	0.871520	−	0.503172i	0.00366672	−	0.999993i	$-0.498833\pi$
$439$	8016.30	−	4628.21i	0.871520	−	0.503172i	0.867853	+	0.496821i	$0.165500\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8854.31	−	5112.04i	0.949618	−	0.548262i	0.0566558	−	0.998394i	$-0.481956\pi$
$443$	8854.31	−	5112.04i	0.949618	−	0.548262i	0.892962	+	0.450132i	$0.148623\pi$
$444$		0			0
$445$	−1753.92	+	3037.87i	−0.186840	+	0.323616i
$446$		0			0
$447$	9415.78	−	3987.20i	0.996311	−	0.421897i
$448$		0			0
$449$			2896.50i			0.304442i	0.988346	+	0.152221i	$0.0486425\pi$
$449$			2896.50i			0.304442i	−0.988346	+	0.152221i	$0.951357\pi$
$450$		0			0
$451$	−13545.8	−	7820.69i	−1.41430	−	0.816545i
$452$		0			0
$453$	6802.40	−	9010.94i	0.705529	−	0.934594i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3995.15	+	6919.80i	0.408939	+	0.708303i	0.994771	−	0.102129i	$-0.0325655\pi$
$457$	3995.15	+	6919.80i	0.408939	+	0.708303i	−0.585832	+	0.810432i	$0.699232\pi$
$458$		0			0
$459$	−13441.8	+	10827.6i	−1.36690	+	1.10106i
$460$		0			0
$461$	−4639.50			−0.468727			−0.234363	−	0.972149i	$-0.575301\pi$
$461$	−4639.50			−0.468727			−0.234363	+	0.972149i	$0.575301\pi$
$462$		0			0
$463$	4926.63			0.494514			0.247257	−	0.968950i	$-0.420471\pi$
$463$	4926.63			0.494514			0.247257	+	0.968950i	$0.420471\pi$
$464$		0			0
$465$	2759.64	−	22316.7i	0.275216	−	2.22562i
$466$		0			0
$467$	3404.64	+	5897.01i	0.337362	+	0.584328i	0.983936	−	0.178523i	$-0.0571320\pi$
$467$	3404.64	+	5897.01i	0.337362	+	0.584328i	−0.646574	+	0.762852i	$0.723799\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	13682.0	+	10328.6i	1.33850	+	1.01044i
$472$		0			0
$473$	−375.935	−	217.046i	−0.0365444	−	0.0210989i
$474$		0			0
$475$			5119.98i			0.494570i
$476$		0			0
$477$	−8709.26	−	8439.45i	−0.835995	−	0.810097i
$478$		0			0
$479$	−1116.45	+	1933.75i	−0.106497	+	0.184458i	−0.914349	−	0.404927i	$-0.867297\pi$
$479$	−1116.45	+	1933.75i	−0.106497	+	0.184458i	0.807852	+	0.589386i	$0.200630\pi$
$480$		0			0
$481$	3144.09	−	1815.24i	0.298042	−	0.172074i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	12831.4	−	7408.20i	1.20133	−	0.693586i
$486$		0			0
$487$	60.8391	−	105.376i	0.00566095	−	0.00980505i	−0.863181	−	0.504895i	$-0.831531\pi$
$487$	60.8391	−	105.376i	0.00566095	−	0.00980505i	0.868842	+	0.495089i	$0.164865\pi$
$488$		0			0
$489$	5671.82	+	13394.0i	0.524516	+	1.23865i
$490$		0			0
$491$			9638.92i			0.885944i	0.896535	+	0.442972i	$0.146076\pi$
$491$			9638.92i			0.885944i	−0.896535	+	0.442972i	$0.853924\pi$
$492$		0			0
$493$	−1503.16	−	867.849i	−0.137320	−	0.0792819i
$494$		0			0
$495$	−2924.74	+	11645.1i	−0.265571	+	1.05739i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1875.57	+	3248.58i	0.168261	+	0.291436i	0.937808	−	0.347153i	$-0.112852\pi$
$499$	1875.57	+	3248.58i	0.168261	+	0.291436i	−0.769548	+	0.638589i	$0.779518\pi$
$500$		0			0
$501$	−9970.82	−	1232.97i	−0.889148	−	0.109951i
$502$		0			0
$503$	−13881.9			−1.23054			−0.615272	−	0.788315i	$-0.710954\pi$
$503$	−13881.9			−1.23054			−0.615272	+	0.788315i	$0.710954\pi$
$504$		0			0
$505$	−21375.9			−1.88359
$506$		0			0
$507$	−6340.57	−	784.064i	−0.555413	−	0.0686814i
$508$		0			0
$509$	−3096.63	−	5363.52i	−0.269658	−	0.467061i	0.699116	−	0.715009i	$-0.253577\pi$
$509$	−3096.63	−	5363.52i	−0.269658	−	0.467061i	−0.968773	+	0.247948i	$0.920244\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−10046.9	+	1564.69i	−0.864678	+	0.134664i
$514$		0			0
$515$	2304.25	+	1330.36i	0.197160	+	0.113830i
$516$		0			0
$517$		−	2762.03i		−	0.234959i
$518$		0			0
$519$	−7101.78	−	16770.9i	−0.600643	−	1.41842i
$520$		0			0
$521$	−2256.61	+	3908.57i	−0.189758	+	0.328671i	−0.945170	−	0.326580i	$-0.894104\pi$
$521$	−2256.61	+	3908.57i	−0.189758	+	0.328671i	0.755411	+	0.655251i	$0.227437\pi$
$522$		0			0
$523$	−537.821	+	310.511i	−0.0449661	+	0.0259612i	−0.522315	−	0.852753i	$-0.674931\pi$
$523$	−537.821	+	310.511i	−0.0449661	+	0.0259612i	0.477348	+	0.878714i	$0.341598\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−32964.2	+	19031.9i	−2.72475	+	1.57313i
$528$		0			0
$529$	−3168.58	+	5488.13i	−0.260424	+	0.451067i
$530$		0			0
$531$	−4824.75	+	4979.00i	−0.394306	+	0.406912i
$532$		0			0
$533$		−	15302.6i		−	1.24358i
$534$		0			0
$535$	−2154.74	−	1244.04i	−0.174127	−	0.100532i
$536$		0			0
$537$	−7656.67	−	5780.06i	−0.615288	−	0.464484i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	5101.80	+	8836.58i	0.405441	+	0.702244i	0.994373	−	0.105938i	$-0.0337846\pi$
$541$	5101.80	+	8836.58i	0.405441	+	0.702244i	−0.588932	+	0.808183i	$0.700451\pi$
$542$		0			0
$543$	235.564	−	1904.96i	0.0186170	−	0.150552i
$544$		0			0
$545$	2700.10			0.212219
$546$		0			0
$547$	−6359.52			−0.497100			−0.248550	−	0.968619i	$-0.579954\pi$
$547$	−6359.52			−0.497100			−0.248550	+	0.968619i	$0.579954\pi$
$548$		0			0
$549$	−7136.48	+	2033.07i	−0.554786	+	0.158049i
$550$		0			0
$551$	−511.247	−	885.507i	−0.0395279	−	0.0684643i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−5111.18	+	6770.63i	−0.390914	+	0.517833i
$556$		0			0
$557$	18905.0	+	10914.8i	1.43812	+	0.830298i	0.997719	−	0.0675048i	$-0.0215038\pi$
$557$	18905.0	+	10914.8i	1.43812	+	0.830298i	0.440399	+	0.897802i	$0.354837\pi$
$558$		0			0
$559$		−	424.689i		−	0.0321332i
$560$		0			0
$561$	18715.3	−	7925.17i	1.40849	−	0.596436i
$562$		0			0
$563$	312.001	−	540.401i	0.0233557	−	0.0404533i	−0.854111	−	0.520090i	$-0.825898\pi$
$563$	312.001	−	540.401i	0.0233557	−	0.0404533i	0.877467	+	0.479637i	$0.159232\pi$
$564$		0			0
$565$	−5476.19	+	3161.68i	−0.407761	+	0.235421i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12198.4	+	7042.74i	−0.898739	+	0.518887i	−0.876791	−	0.480872i	$-0.840320\pi$
$569$	−12198.4	+	7042.74i	−0.898739	+	0.518887i	−0.0219483	+	0.999759i	$0.506987\pi$
$570$		0			0
$571$	−4105.50	+	7110.94i	−0.300893	+	0.521162i	−0.976338	−	0.216248i	$-0.930618\pi$
$571$	−4105.50	+	7110.94i	−0.300893	+	0.521162i	0.675445	+	0.737410i	$0.263951\pi$
$572$		0			0
$573$	−1142.08	+	483.625i	−0.0832654	+	0.0352595i
$574$		0			0
$575$			5393.96i			0.391207i
$576$		0			0
$577$	−9649.07	−	5570.89i	−0.696180	−	0.401940i	0.109743	−	0.993960i	$-0.464997\pi$
$577$	−9649.07	−	5570.89i	−0.696180	−	0.401940i	−0.805923	+	0.592020i	$0.798331\pi$
$578$		0			0
$579$	−5266.13	+	6975.89i	−0.377984	+	0.500705i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	7140.10	+	12367.0i	0.507226	+	0.878541i
$584$		0			0
$585$	−11297.2	+	3218.38i	−0.798429	+	0.227459i
$586$		0			0
$587$	−5198.19			−0.365507			−0.182753	−	0.983159i	$-0.558501\pi$
$587$	−5198.19			−0.365507			−0.182753	+	0.983159i	$0.558501\pi$
$588$		0			0
$589$	−22423.2			−1.56865
$590$		0			0
$591$	−1905.43	+	15408.8i	−0.132621	+	1.07248i
$592$		0			0
$593$	5485.15	+	9500.55i	0.379845	+	0.657910i	0.991039	−	0.133570i	$-0.0426441\pi$
$593$	5485.15	+	9500.55i	0.379845	+	0.657910i	−0.611195	+	0.791480i	$0.709311\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8365.76	−	6315.35i	−0.573514	−	0.432948i
$598$		0			0
$599$	−22359.1	−	12909.0i	−1.52515	−	0.880547i	−0.999555	−	0.0298138i	$-0.990509\pi$
$599$	−22359.1	−	12909.0i	−1.52515	−	0.880547i	−0.525597	−	0.850734i	$-0.676158\pi$
$600$		0			0
$601$			11968.5i			0.812323i	0.913801	+	0.406162i	$0.133133\pi$
$601$			11968.5i			0.812323i	−0.913801	+	0.406162i	$0.866867\pi$
$602$		0			0
$603$	−19389.8	+	20009.7i	−1.30948	+	1.35134i
$604$		0			0
$605$	−2239.52	+	3878.96i	−0.150495	+	0.260665i
$606$		0			0
$607$	5412.72	−	3125.04i	0.361937	−	0.208964i	−0.307993	−	0.951389i	$-0.599657\pi$
$607$	5412.72	−	3125.04i	0.361937	−	0.208964i	0.669930	+	0.742424i	$0.266324\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2340.18	−	1351.10i	0.154948	−	0.0894594i
$612$		0			0
$613$	−2469.83	+	4277.87i	−0.162733	+	0.281862i	−0.935848	−	0.352404i	$-0.885364\pi$
$613$	−2469.83	+	4277.87i	−0.162733	+	0.281862i	0.773115	+	0.634266i	$0.218698\pi$
$614$		0			0
$615$	13943.1	+	32926.7i	0.914212	+	2.15891i
$616$		0			0
$617$		−	14836.2i		−	0.968042i	−0.875056	−	0.484021i	$-0.839176\pi$
$617$		−	14836.2i		−	0.968042i	0.875056	−	0.484021i	$-0.160824\pi$
$618$		0			0
$619$	10534.4	+	6082.04i	0.684028	+	0.394924i	0.801371	−	0.598168i	$-0.204104\pi$
$619$	10534.4	+	6082.04i	0.684028	+	0.394924i	−0.117343	+	0.993091i	$0.537438\pi$
$620$		0			0
$621$	−10584.5	+	1648.42i	−0.683964	+	0.106520i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9732.46	+	16857.1i	0.622877	+	1.07886i
$626$		0			0
$627$	11882.4	+	1469.35i	0.756837	+	0.0935891i
$628$		0			0
$629$	14359.8			0.910276
$630$		0			0
$631$	8372.13			0.528192			0.264096	−	0.964496i	$-0.414926\pi$
$631$	8372.13			0.528192			0.264096	+	0.964496i	$0.414926\pi$
$632$		0			0
$633$	−24160.0	−	2987.58i	−1.51702	−	0.187592i
$634$		0			0
$635$	−5102.77	−	8838.26i	−0.318893	−	0.552340i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	6128.18	−	24399.8i	0.379385	−	1.51055i
$640$		0			0
$641$	12972.5	+	7489.69i	0.799351	+	0.461505i	0.843244	−	0.537531i	$-0.180643\pi$
$641$	12972.5	+	7489.69i	0.799351	+	0.461505i	−0.0438933	+	0.999036i	$0.513976\pi$
$642$		0			0
$643$		−	4861.62i		−	0.298170i	−0.988824	−	0.149085i	$-0.952367\pi$
$643$		−	4861.62i		−	0.298170i	0.988824	−	0.149085i	$-0.0476329\pi$
$644$		0			0
$645$	386.960	+	913.807i	0.0236226	+	0.0557847i
$646$		0			0
$647$	13592.4	−	23542.8i	0.825925	−	1.43054i	−0.0752852	−	0.997162i	$-0.523987\pi$
$647$	13592.4	−	23542.8i	0.825925	−	1.43054i	0.901210	−	0.433382i	$-0.142680\pi$
$648$		0			0
$649$	7070.10	−	4081.92i	0.427620	−	0.246887i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3755.80	−	2168.41i	0.225078	−	0.129949i	−0.383222	−	0.923656i	$-0.625185\pi$
$653$	3755.80	−	2168.41i	0.225078	−	0.129949i	0.608299	+	0.793708i	$0.291852\pi$
$654$		0			0
$655$	−4017.37	+	6958.30i	−0.239652	+	0.415089i
$656$		0			0
$657$	−19875.5	−	19259.8i	−1.18024	−	1.14368i
$658$		0			0
$659$		−	15562.8i		−	0.919939i	−0.887935	−	0.459969i	$-0.847860\pi$
$659$		−	15562.8i		−	0.919939i	0.887935	−	0.459969i	$-0.152140\pi$
$660$		0			0
$661$	12267.0	+	7082.34i	0.721830	+	0.416749i	0.815426	−	0.578861i	$-0.196503\pi$
$661$	12267.0	+	7082.34i	0.721830	+	0.416749i	−0.0935956	+	0.995610i	$0.529836\pi$
$662$		0			0
$663$	15869.7	+	11980.1i	0.929603	+	0.701761i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−538.606	−	932.892i	−0.0312667	−	0.0541555i
$668$		0			0
$669$	11.0198	−	89.1148i	0.000636845	−	0.00515004i
$670$		0			0
$671$	8737.62			0.502700
$672$		0			0
$673$	21045.6			1.20542			0.602710	−	0.797960i	$-0.294087\pi$
$673$	21045.6			1.20542			0.602710	+	0.797960i	$0.294087\pi$
$674$		0			0
$675$	7718.51	−	6217.40i	0.440127	−	0.354530i
$676$		0			0
$677$	−9037.10	−	15652.7i	−0.513034	−	0.888601i	−0.999886	−	0.0151166i	$-0.995188\pi$
$677$	−9037.10	−	15652.7i	−0.513034	−	0.888601i	0.486852	−	0.873485i	$-0.338145\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	4582.94	−	6070.89i	0.257884	−	0.341611i
$682$		0			0
$683$	−21428.1	−	12371.5i	−1.20047	−	0.693092i	−0.239811	−	0.970820i	$-0.577086\pi$
$683$	−21428.1	−	12371.5i	−1.20047	−	0.693092i	−0.960660	+	0.277727i	$0.910419\pi$
$684$		0			0
$685$		−	33957.8i		−	1.89410i
$686$		0			0
$687$	555.388	−	235.184i	0.0308433	−	0.0130609i
$688$		0			0
$689$	−6985.44	+	12099.1i	−0.386247	+	0.668999i
$690$		0			0
$691$	20190.9	−	11657.2i	1.11158	−	0.641769i	0.172339	−	0.985038i	$-0.444868\pi$
$691$	20190.9	−	11657.2i	1.11158	−	0.641769i	0.939237	+	0.343269i	$0.111534\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	17608.3	−	10166.2i	0.961038	−	0.554855i
$696$		0			0
$697$	30263.5	−	52418.0i	1.64464	−	2.84860i
$698$		0			0
$699$	−17945.9	+	7599.38i	−0.971070	+	0.411209i
$700$		0			0
$701$			901.167i			0.0485544i	0.999705	+	0.0242772i	$0.00772843\pi$
$701$			901.167i			0.0485544i	−0.999705	+	0.0242772i	$0.992272\pi$
$702$		0			0
$703$	7325.99	+	4229.66i	0.393037	+	0.226920i
$704$		0			0
$705$	−3804.30	+	5039.45i	−0.203232	+	0.269215i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	2917.65	+	5053.52i	0.154548	+	0.267685i	0.932894	−	0.360150i	$-0.117274\pi$
$709$	2917.65	+	5053.52i	0.154548	+	0.267685i	−0.778346	+	0.627835i	$0.783941\pi$
$710$		0			0
$711$	6839.90	+	24009.5i	0.360783	+	1.26642i
$712$		0			0
$713$	−23623.1			−1.24080
$714$		0			0
$715$	13831.8			0.723469
$716$		0			0
$717$	3458.50	−	27968.2i	0.180139	−	1.45675i
$718$		0			0
$719$	9234.41	+	15994.5i	0.478978	+	0.829615i	0.999709	−	0.0241060i	$-0.00767394\pi$
$719$	9234.41	+	15994.5i	0.478978	+	0.829615i	−0.520731	+	0.853721i	$0.674341\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−18837.7	−	14220.6i	−0.968991	−	0.731495i
$724$		0			0
$725$	863.142	+	498.335i	0.0442156	+	0.0255279i
$726$		0			0
$727$		−	32300.3i		−	1.64780i	−0.566735	−	0.823900i	$-0.691794\pi$
$727$		−	32300.3i		−	1.64780i	0.566735	−	0.823900i	$-0.308206\pi$
$728$		0			0
$729$	14559.1	+	13245.9i	0.739680	+	0.672959i
$730$		0			0
$731$	839.898	−	1454.75i	0.0424962	−	0.0736056i
$732$		0			0
$733$	−5189.33	+	2996.06i	−0.261490	+	0.150971i	−0.625014	−	0.780613i	$-0.714907\pi$
$733$	−5189.33	+	2996.06i	−0.261490	+	0.150971i	0.363524	+	0.931585i	$0.381573\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	28413.5	−	16404.5i	1.42011	−	0.819903i
$738$		0			0
$739$	653.898	−	1132.58i	0.0325494	−	0.0563772i	−0.849292	−	0.527924i	$-0.822971\pi$
$739$	653.898	−	1132.58i	0.0325494	−	0.0563772i	0.881841	+	0.471546i	$0.156304\pi$
$740$		0			0
$741$	4567.56	+	10786.3i	0.226442	+	0.534743i
$742$		0			0
$743$			30175.4i			1.48995i	0.667095	+	0.744973i	$0.267538\pi$
$743$			30175.4i			1.48995i	−0.667095	+	0.744973i	$0.732462\pi$
$744$		0			0
$745$	23837.2	+	13762.4i	1.17225	+	0.676798i
$746$		0			0
$747$	−25969.3	−	6522.37i	−1.27198	−	0.319466i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−536.353	−	928.990i	−0.0260610	−	0.0451389i	0.852701	−	0.522400i	$-0.174963\pi$
$751$	−536.353	−	928.990i	−0.0260610	−	0.0451389i	−0.878762	+	0.477261i	$0.841630\pi$
$752$		0			0
$753$	5753.16	+	711.425i	0.278428	+	0.0344300i
$754$		0			0
$755$	30391.7			1.46499
$756$		0			0
$757$	−7773.72			−0.373237			−0.186619	−	0.982432i	$-0.559753\pi$
$757$	−7773.72			−0.373237			−0.186619	+	0.982432i	$0.559753\pi$
$758$		0			0
$759$	12518.2	+	1547.98i	0.598660	+	0.0740293i
$760$		0			0
$761$	−10431.8	−	18068.4i	−0.496916	−	0.860683i	0.503078	−	0.864241i	$-0.332201\pi$
$761$	−10431.8	−	18068.4i	−0.496916	−	0.860683i	−0.999994	+	0.00355768i	$0.998868\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−45062.7	−	11317.8i	−2.12973	−	0.534897i
$766$		0			0
$767$	6916.95	+	3993.50i	0.325628	+	0.188001i
$768$		0			0
$769$		−	1423.15i		−	0.0667364i	−0.999443	−	0.0333682i	$-0.989377\pi$
$769$		−	1423.15i		−	0.0667364i	0.999443	−	0.0333682i	$-0.0106234\pi$
$770$		0			0
$771$	12925.6	+	30523.8i	0.603767	+	1.42580i
$772$		0			0
$773$	−2664.15	+	4614.44i	−0.123962	+	0.214709i	−0.921327	−	0.388789i	$-0.872893\pi$
$773$	−2664.15	+	4614.44i	−0.123962	+	0.214709i	0.797365	+	0.603498i	$0.206227\pi$
$774$		0			0
$775$	18928.6	−	10928.4i	0.877337	−	0.506531i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	30879.3	−	17828.1i	1.42024	−	0.819974i
$780$		0			0
$781$	−14811.7	+	25654.5i	−0.678621	+	1.17541i
$782$		0			0
$783$	−714.096	+	1846.02i	−0.0325922	+	0.0842548i
$784$		0			0
$785$			46146.2i			2.09813i
$786$		0			0
$787$	−9982.43	−	5763.36i	−0.452141	−	0.261044i	0.256593	−	0.966520i	$-0.417400\pi$
$787$	−9982.43	−	5763.36i	−0.452141	−	0.261044i	−0.708734	+	0.705476i	$0.750733\pi$
$788$		0			0
$789$	−2991.01	−	2257.93i	−0.134959	−	0.101881i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4274.17	+	7403.09i	0.191400	+	0.331515i
$794$		0			0
$795$	4006.36	−	32398.7i	0.178731	−	1.44536i
$796$		0			0
$797$	42557.4			1.89142			0.945709	−	0.325013i	$-0.105369\pi$
$797$	42557.4			1.89142			0.945709	+	0.325013i	$0.105369\pi$
$798$		0			0
$799$	10688.2			0.473242
$800$		0			0
$801$	−1855.20	−	6512.15i	−0.0818357	−	0.287260i
$802$		0			0
$803$	16294.5	+	28222.9i	0.716091	+	1.24031i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	14860.3	−	19685.0i	0.648212	−	0.858668i
$808$		0			0
$809$	−16963.5	−	9793.90i	−0.737214	−	0.425630i	0.0838418	−	0.996479i	$-0.473281\pi$
$809$	−16963.5	−	9793.90i	−0.737214	−	0.425630i	−0.821055	+	0.570849i	$0.806614\pi$
$810$		0			0
$811$		−	26034.2i		−	1.12723i	−0.826038	−	0.563615i	$-0.809410\pi$
$811$		−	26034.2i		−	1.12723i	0.826038	−	0.563615i	$-0.190590\pi$
$812$		0			0
$813$	39363.8	−	16669.0i	1.69809	−	0.719074i
$814$		0			0
$815$	−19577.1	+	33908.5i	−0.841418	+	1.45738i
$816$		0			0
$817$	856.986	−	494.781i	0.0366979	−	0.0211875i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25214.2	+	14557.4i	−1.07184	+	0.618827i	−0.928683	−	0.370874i	$-0.879058\pi$
$821$	−25214.2	+	14557.4i	−1.07184	+	0.618827i	−0.143156	+	0.989700i	$0.545725\pi$
$822$		0			0
$823$	14791.2	−	25619.1i	0.626475	−	1.08509i	−0.361779	−	0.932264i	$-0.617831\pi$
$823$	14791.2	−	25619.1i	0.626475	−	1.08509i	0.988254	−	0.152822i	$-0.0488361\pi$
$824$		0			0
$825$	−10746.7	+	4550.78i	−0.453516	+	0.192046i
$826$		0			0
$827$		−	33550.7i		−	1.41073i	−0.708845	−	0.705364i	$-0.750784\pi$
$827$		−	33550.7i		−	1.41073i	0.708845	−	0.705364i	$-0.249216\pi$
$828$		0			0
$829$	40841.4	+	23579.8i	1.71108	+	0.987890i	0.933116	+	0.359576i	$0.117079\pi$
$829$	40841.4	+	23579.8i	1.71108	+	0.987890i	0.777960	+	0.628314i	$0.216255\pi$
$830$		0			0
$831$	−15978.3	+	21166.0i	−0.667005	+	0.883563i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−13522.2	−	23421.2i	−0.560426	−	0.970687i
$836$		0			0
$837$	27229.4	+	33803.6i	1.12448	+	1.39597i
$838$		0			0
$839$	−4790.07			−0.197106			−0.0985528	−	0.995132i	$-0.531421\pi$
$839$	−4790.07			−0.197106			−0.0985528	+	0.995132i	$0.531421\pi$
$840$		0			0
$841$	24190.0			0.991839
$842$		0			0
$843$	−4348.10	+	35162.2i	−0.177647	+	1.43660i
$844$		0			0
$845$	−8598.96	−	14893.8i	−0.350075	−	0.606347i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−11098.6	−	8378.38i	−0.448649	−	0.338687i
$850$		0			0
$851$	7718.02	+	4456.00i	0.310894	+	0.179494i
$852$		0			0
$853$		−	4925.15i		−	0.197695i	−0.995103	−	0.0988475i	$-0.968484\pi$
$853$		−	4925.15i		−	0.197695i	0.995103	−	0.0988475i	$-0.0315156\pi$
$854$		0			0
$855$	−19656.1	−	19047.2i	−0.786228	−	0.761871i
$856$		0			0
$857$	−2465.89	+	4271.05i	−0.0982885	+	0.170241i	−0.910976	−	0.412459i	$-0.864670\pi$
$857$	−2465.89	+	4271.05i	−0.0982885	+	0.170241i	0.812688	+	0.582699i	$0.198003\pi$
$858$		0			0
$859$	30455.0	−	17583.2i	1.20968	−	0.698407i	0.246987	−	0.969019i	$-0.420559\pi$
$859$	30455.0	−	17583.2i	1.20968	−	0.698407i	0.962688	+	0.270612i	$0.0872261\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−27078.5	+	15633.8i	−1.06809	+	0.616664i	−0.927660	−	0.373426i	$-0.878183\pi$
$863$	−27078.5	+	15633.8i	−1.06809	+	0.616664i	−0.140433	+	0.990090i	$0.544850\pi$
$864$		0			0
$865$	24512.8	−	42457.4i	0.963538	−	1.66890i
$866$		0			0
$867$	20713.2	+	48914.2i	0.811369	+	1.91605i
$868$		0			0
$869$		−	29396.2i		−	1.14752i
$870$		0			0
$871$	27798.0	+	16049.2i	1.08140	+	0.624347i
$872$		0			0
$873$	−6966.82	+	27738.9i	−0.270093	+	1.07540i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6398.52	−	11082.6i	−0.246366	−	0.426718i	0.716149	−	0.697947i	$-0.245903\pi$
$877$	−6398.52	−	11082.6i	−0.246366	−	0.426718i	−0.962515	+	0.271230i	$0.912570\pi$
$878$		0			0
$879$	−8992.07	−	1111.94i	−0.345045	−	0.0426677i
$880$		0			0
$881$	−2497.90			−0.0955235			−0.0477618	−	0.998859i	$-0.515209\pi$
$881$	−2497.90			−0.0955235			−0.0477618	+	0.998859i	$0.515209\pi$
$882$		0			0
$883$	−8139.20			−0.310199			−0.155100	−	0.987899i	$-0.549570\pi$
$883$	−8139.20			−0.310199			−0.155100	+	0.987899i	$0.549570\pi$
$884$		0			0
$885$	−18522.0	−	2290.40i	−0.703514	−	0.0869953i
$886$		0			0
$887$	2928.50	+	5072.31i	0.110856	+	0.192008i	0.916116	−	0.400914i	$-0.131307\pi$
$887$	2928.50	+	5072.31i	0.110856	+	0.192008i	−0.805260	+	0.592922i	$0.797974\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−12214.2	−	19697.3i	−0.459248	−	0.740611i
$892$		0			0
$893$	5452.81	+	3148.18i	0.204335	+	0.117973i
$894$		0			0
$895$		−	25824.1i		−	0.964475i
$896$		0			0
$897$	4811.98	+	11363.5i	0.179116	+	0.422984i
$898$		0			0
$899$	−2182.48	+	3780.17i	−0.0809677	+	0.140240i
$900$		0			0
$901$	−47856.3	+	27629.9i	−1.76951	+	1.02163i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4474.70	−	2583.47i	0.164358	−	0.0948922i
$906$		0			0
$907$	11271.2	−	19522.3i	0.412629	−	0.714694i	−0.582547	−	0.812797i	$-0.697944\pi$
$907$	11271.2	−	19522.3i	0.412629	−	0.714694i	0.995176	+	0.0981025i	$0.0312773\pi$
$908$		0			0
$909$	28714.2	−	29632.2i	1.04773	−	1.08123i
$910$		0			0
$911$		−	14306.2i		−	0.520291i	−0.965569	−	0.260146i	$-0.916229\pi$
$911$		−	14306.2i		−	0.520291i	0.965569	−	0.260146i	$-0.0837706\pi$
$912$		0			0
$913$	27304.7	+	15764.4i	0.989765	+	0.571441i
$914$		0			0
$915$	−15942.2	−	12034.8i	−0.575991	−	0.434818i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−10485.9	−	18162.0i	−0.376384	−	0.651916i	0.614149	−	0.789190i	$-0.289499\pi$
$919$	−10485.9	−	18162.0i	−0.376384	−	0.651916i	−0.990533	+	0.137274i	$0.956166\pi$
$920$		0			0
$921$	958.557	−	7751.66i	0.0342948	−	0.277335i
$922$		0			0
$923$	−28981.6			−1.03352
$924$		0			0
$925$	−8245.67			−0.293098
$926$		0			0
$927$	−4939.52	+	1407.19i	−0.175011	+	0.0498577i
$928$		0			0
$929$	10933.3	+	18937.1i	0.386125	+	0.668789i	0.991925	−	0.126829i	$-0.0404798\pi$
$929$	10933.3	+	18937.1i	0.386125	+	0.668789i	−0.605799	+	0.795618i	$0.707147\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	27366.8	−	36252.0i	0.960288	−	1.27207i
$934$		0			0
$935$	47380.0	+	27354.8i	1.65721	+	0.956790i
$936$		0			0
$937$			32284.1i			1.12559i	0.826597	+	0.562794i	$0.190274\pi$
$937$			32284.1i			1.12559i	−0.826597	+	0.562794i	$0.809726\pi$
$938$		0			0
$939$	−17851.0	+	7559.17i	−0.620388	+	0.262709i
$940$		0			0
$941$	11899.7	−	20610.9i	0.412242	−	0.714024i	−0.582893	−	0.812549i	$-0.698079\pi$
$941$	11899.7	−	20610.9i	0.412242	−	0.714024i	0.995135	+	0.0985254i	$0.0314126\pi$
$942$		0			0
$943$	32531.7	−	18782.2i	1.12341	−	0.648602i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8449.22	+	4878.16i	−0.289929	+	0.167391i	−0.637910	−	0.770111i	$-0.720201\pi$
$947$	−8449.22	+	4878.16i	−0.289929	+	0.167391i	0.347981	+	0.937502i	$0.386867\pi$
$948$		0			0
$949$	−15941.5	+	27611.6i	−0.545295	+	0.944478i
$950$		0			0
$951$	−23829.3	+	10090.7i	−0.812531	+	0.344074i
$952$		0			0
$953$			36031.4i			1.22473i	0.790574	+	0.612367i	$0.209782\pi$
$953$			36031.4i			1.22473i	−0.790574	+	0.612367i	$0.790218\pi$
$954$		0			0
$955$	−2891.31	−	1669.30i	−0.0979692	−	0.0565626i
$956$		0			0
$957$	1404.24	−	1860.15i	0.0474321	−	0.0628320i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	32966.2	+	57099.1i	1.10658	+	1.91666i
$962$		0			0
$963$	4619.02	−	1315.88i	0.154565	−	0.0440330i
$964$		0			0
$965$	−23528.0			−0.784864
$966$		0			0
$967$	−24872.5			−0.827142			−0.413571	−	0.910472i	$-0.635719\pi$
$967$	−24872.5			−0.827142			−0.413571	+	0.910472i	$0.635719\pi$
$968$		0			0
$969$	−5685.92	+	45980.9i	−0.188502	+	1.52438i
$970$		0			0
$971$	−12506.4	−	21661.8i	−0.413337	−	0.715921i	0.581915	−	0.813249i	$-0.302303\pi$
$971$	−12506.4	−	21661.8i	−0.413337	−	0.715921i	−0.995252	+	0.0973288i	$0.968970\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−9112.66	−	6879.18i	−0.299322	−	0.225959i
$976$		0			0
$977$	−2276.88	−	1314.56i	−0.0745588	−	0.0430465i	0.462257	−	0.886746i	$-0.347040\pi$
$977$	−2276.88	−	1314.56i	−0.0745588	−	0.0430465i	−0.536816	+	0.843699i	$0.680373\pi$
$978$		0			0
$979$			7973.21i			0.260291i
$980$		0			0
$981$	−3627.05	+	3743.00i	−0.118046	+	0.121819i
$982$		0			0
$983$	−806.903	+	1397.60i	−0.0261813	+	0.0453473i	−0.878819	−	0.477155i	$-0.841668\pi$
$983$	−806.903	+	1397.60i	−0.0261813	+	0.0453473i	0.852638	+	0.522502i	$0.175001\pi$
$984$		0			0
$985$	−36194.9	+	20897.1i	−1.17083	+	0.675977i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	902.846	−	521.258i	0.0290281	−	0.0167594i
$990$		0			0
$991$	16663.5	−	28862.0i	0.534140	−	0.925157i	−0.465065	−	0.885277i	$-0.653969\pi$
$991$	16663.5	−	28862.0i	0.534140	−	0.925157i	0.999204	−	0.0398803i	$-0.0126977\pi$
$992$		0			0
$993$	12551.3	+	29639.8i	0.401110	+	0.947221i
$994$		0			0
$995$		−	28215.7i		−	0.898993i
$996$		0			0
$997$	41092.8	+	23724.9i	1.30534	+	0.753637i	0.981314	−	0.192412i	$-0.0616309\pi$
$997$	41092.8	+	23724.9i	1.30534	+	0.753637i	0.324024	+	0.946049i	$0.394964\pi$
$998$		0			0
$999$	−2519.91	−	16180.4i	−0.0798063	−	0.512437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.k.e.521.2		48
3.2	odd	2	inner	588.4.k.e.521.8		48
7.2	even	3	inner	588.4.k.e.509.17		48
7.3	odd	6		588.4.f.d.293.9	✓	24
7.4	even	3		588.4.f.d.293.16	yes	24
7.5	odd	6	inner	588.4.k.e.509.8		48
7.6	odd	2	inner	588.4.k.e.521.23		48
21.2	odd	6	inner	588.4.k.e.509.23		48
21.5	even	6	inner	588.4.k.e.509.2		48
21.11	odd	6		588.4.f.d.293.10	yes	24
21.17	even	6		588.4.f.d.293.15	yes	24
21.20	even	2	inner	588.4.k.e.521.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.4.f.d.293.9	✓	24	7.3	odd	6
588.4.f.d.293.10	yes	24	21.11	odd	6
588.4.f.d.293.15	yes	24	21.17	even	6
588.4.f.d.293.16	yes	24	7.4	even	3
588.4.k.e.509.2		48	21.5	even	6	inner
588.4.k.e.509.8		48	7.5	odd	6	inner
588.4.k.e.509.17		48	7.2	even	3	inner
588.4.k.e.509.23		48	21.2	odd	6	inner
588.4.k.e.521.2		48	1.1	even	1	trivial
588.4.k.e.521.8		48	3.2	odd	2	inner
588.4.k.e.521.17		48	21.20	even	2	inner
588.4.k.e.521.23		48	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.15687 - 0.637690i) q^{3} +(-6.99365 - 12.1134i) q^{5} +(26.1867 + 6.57697i) q^{9} +O(q^{10})\)	\(q+(-5.15687 - 0.637690i) q^{3} +(-6.99365 - 12.1134i) q^{5} +(26.1867 + 6.57697i) q^{9} +(-27.5333 - 15.8964i) q^{11} -31.1041i q^{13} +(28.3408 + 66.9269i) q^{15} +(61.5138 - 106.545i) q^{17} +(62.7653 - 36.2376i) q^{19} +(66.1240 - 38.1767i) q^{23} +(-35.3223 + 61.1801i) q^{25} +(-130.847 - 50.6156i) q^{27} -14.1082i q^{29} +(-267.941 - 154.696i) q^{31} +(131.849 + 99.5333i) q^{33} +(58.3602 + 101.083i) q^{37} +(-19.8347 + 160.400i) q^{39} +491.980 q^{41} +13.6538 q^{43} +(-103.471 - 363.206i) q^{45} +(43.4381 + 75.2370i) q^{47} +(-385.161 + 510.212i) q^{51} +(-388.989 - 224.583i) q^{53} +444.695i q^{55} +(-346.781 + 146.848i) q^{57} +(-128.392 + 222.381i) q^{59} +(-238.010 + 137.415i) q^{61} +(-376.775 + 217.531i) q^{65} +(-515.984 + 893.710i) q^{67} +(-365.338 + 154.706i) q^{69} -931.763i q^{71} +(-887.716 - 512.523i) q^{73} +(221.167 - 292.973i) q^{75} +(462.310 + 800.745i) q^{79} +(642.487 + 344.459i) q^{81} -991.698 q^{83} -1720.82 q^{85} +(-8.99667 + 72.7543i) q^{87} +(-125.394 - 217.188i) q^{89} +(1283.09 + 968.611i) q^{93} +(-877.917 - 506.866i) q^{95} +1059.27i q^{97} +(-616.457 - 597.359i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 64 q^{9}+O(q^{10}) \) 48 * q + 64 * q^9	\( 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99}+O(q^{100}) \) 48 * q + 64 * q^9 - 192 * q^15 - 456 * q^25 + 432 * q^37 - 688 * q^39 + 1248 * q^43 + 1536 * q^51 - 2720 * q^57 + 528 * q^67 - 3744 * q^79 - 3408 * q^81 + 13824 * q^85 + 5088 * q^93 - 15472 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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