LMFDB - Embedded newform 588.3.p.i.557.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,3,Mod(557,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.557"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 3, names="a")

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

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-4,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 18x^{14} + 201x^{12} - 1606x^{10} + 9216x^{8} - 21516x^{6} + 38173x^{4} - 134064x^{2} + 194481 $ x^16 - 18x^14 + 201x^12 - 1606x^10 + 9216x^8 - 21516x^6 + 38173x^4 - 134064*x^2 + 194481
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			557.7
Root			$0.858455 + 1.31213i$ of defining polynomial
Character	$\chi$	$=$	588.557
Dual form			588.3.p.i.569.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.68280 - 1.34261i) q^{3} +(-5.28547 + 3.05157i) q^{5} +(5.39478 - 7.20391i) q^{9} +(-14.9496 - 8.63114i) q^{11} +19.2674 q^{13} +(-10.0828 + 15.2831i) q^{15} +(-17.8430 - 10.3017i) q^{17} +(-6.09819 - 10.5624i) q^{19} +(-16.8055 + 9.70264i) q^{23} +(6.12414 - 10.6073i) q^{25} +(4.80102 - 26.5697i) q^{27} -3.24407i q^{29} +(4.24264 - 7.34847i) q^{31} +(-51.6949 - 3.08409i) q^{33} +(-33.8724 - 58.6688i) q^{37} +(51.6906 - 25.8687i) q^{39} -55.6650i q^{41} -49.7449 q^{43} +(-6.53072 + 54.5386i) q^{45} +(39.6591 - 22.8972i) q^{47} +(-61.7002 - 3.68100i) q^{51} +(-28.9456 - 16.7117i) q^{53} +105.354 q^{55} +(-30.5414 - 20.1492i) q^{57} +(58.8145 + 33.9565i) q^{59} +(-9.10218 - 15.7654i) q^{61} +(-101.838 + 58.7959i) q^{65} +(-33.0000 + 57.1577i) q^{67} +(-32.0587 + 48.5934i) q^{69} +93.8415i q^{71} +(-3.88667 + 6.73190i) q^{73} +(2.18828 - 36.6796i) q^{75} +(-52.4966 - 90.9267i) q^{79} +(-22.7927 - 77.7270i) q^{81} +51.1190i q^{83} +125.745 q^{85} +(-4.35553 - 8.70317i) q^{87} +(-130.150 + 75.1423i) q^{89} +(1.51598 - 25.4107i) q^{93} +(64.4636 + 37.2181i) q^{95} +188.793 q^{97} +(-142.828 + 61.1323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{9} - 64 q^{15} - 48 q^{25} - 104 q^{37} + 240 q^{39} + 80 q^{43} + 44 q^{51} - 440 q^{57} - 528 q^{67} - 256 q^{79} + 496 q^{81} + 1136 q^{85} - 24 q^{93} - 1312 q^{99}+O(q^{100}) $ 16 * q - 4 * q^9 - 64 * q^15 - 48 * q^25 - 104 * q^37 + 240 * q^39 + 80 * q^43 + 44 * q^51 - 440 * q^57 - 528 * q^67 - 256 * q^79 + 496 * q^81 + 1136 * q^85 - 24 * q^93 - 1312 * q^99

Character values

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

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.68280	−	1.34261i	0.894265	−	0.447538i
$3$	2.68280	−	1.34261i	0.894265	−	0.447538i
$4$		0			0
$5$	−5.28547	+	3.05157i	−1.05709	+	0.610314i	−0.924627	−	0.380874i	$-0.875623\pi$
$5$	−5.28547	+	3.05157i	−1.05709	+	0.610314i	−0.132467	+	0.991187i	$0.542290\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	5.39478	−	7.20391i	0.599420	−	0.800435i
$10$		0			0
$11$	−14.9496	−	8.63114i	−1.35905	−	0.784649i	−0.369556	−	0.929208i	$-0.620490\pi$
$11$	−14.9496	−	8.63114i	−1.35905	−	0.784649i	−0.989496	+	0.144559i	$0.953824\pi$
$12$		0			0
$13$	19.2674			1.48211			0.741056	−	0.671444i	$-0.234325\pi$
$13$	19.2674			1.48211			0.741056	+	0.671444i	$0.234325\pi$
$14$		0			0
$15$	−10.0828	+	15.2831i	−0.672184	+	1.01887i
$16$		0			0
$17$	−17.8430	−	10.3017i	−1.04959	−	0.605980i	−0.127054	−	0.991896i	$-0.540552\pi$
$17$	−17.8430	−	10.3017i	−1.04959	−	0.605980i	−0.922534	+	0.385916i	$0.873885\pi$
$18$		0			0
$19$	−6.09819	−	10.5624i	−0.320957	−	0.555915i	0.659728	−	0.751504i	$-0.270671\pi$
$19$	−6.09819	−	10.5624i	−0.320957	−	0.555915i	−0.980686	+	0.195590i	$0.937338\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−16.8055	+	9.70264i	−0.730673	+	0.421854i	−0.818668	−	0.574267i	$-0.805287\pi$
$23$	−16.8055	+	9.70264i	−0.730673	+	0.421854i	0.0879956	+	0.996121i	$0.471954\pi$
$24$		0			0
$25$	6.12414	−	10.6073i	0.244966	−	0.424293i
$26$		0			0
$27$	4.80102	−	26.5697i	0.177816	−	0.984064i
$28$		0			0
$29$		−	3.24407i		−	0.111864i	−0.998435	−	0.0559322i	$-0.982187\pi$
$29$		−	3.24407i		−	0.111864i	0.998435	−	0.0559322i	$-0.0178131\pi$
$30$		0			0
$31$	4.24264	−	7.34847i	0.136859	−	0.237047i	−0.789447	−	0.613819i	$-0.789632\pi$
$31$	4.24264	−	7.34847i	0.136859	−	0.237047i	0.926306	+	0.376772i	$0.122966\pi$
$32$		0			0
$33$	−51.6949	−	3.08409i	−1.56651	−	0.0934572i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−33.8724	−	58.6688i	−0.915471	−	1.58564i	−0.806210	−	0.591629i	$-0.798485\pi$
$37$	−33.8724	−	58.6688i	−0.915471	−	1.58564i	−0.109261	−	0.994013i	$-0.534848\pi$
$38$		0			0
$39$	51.6906	−	25.8687i	1.32540	−	0.663301i
$40$		0			0
$41$		−	55.6650i		−	1.35768i	−0.734285	−	0.678841i	$-0.762482\pi$
$41$		−	55.6650i		−	1.35768i	0.734285	−	0.678841i	$-0.237518\pi$
$42$		0			0
$43$	−49.7449			−1.15686			−0.578429	−	0.815733i	$-0.696334\pi$
$43$	−49.7449			−1.15686			−0.578429	+	0.815733i	$0.696334\pi$
$44$		0			0
$45$	−6.53072	+	54.5386i	−0.145127	+	1.21197i
$46$		0			0
$47$	39.6591	−	22.8972i	0.843812	−	0.487175i	−0.0147465	−	0.999891i	$-0.504694\pi$
$47$	39.6591	−	22.8972i	0.843812	−	0.487175i	0.858558	+	0.512716i	$0.171361\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−61.7002	−	3.68100i	−1.20981	−	0.0721764i
$52$		0			0
$53$	−28.9456	−	16.7117i	−0.546143	−	0.315316i	0.201422	−	0.979505i	$-0.435444\pi$
$53$	−28.9456	−	16.7117i	−0.546143	−	0.315316i	−0.747565	+	0.664189i	$0.768777\pi$
$54$		0			0
$55$	105.354			1.91553
$56$		0			0
$57$	−30.5414	−	20.1492i	−0.535814	−	0.353494i
$58$		0			0
$59$	58.8145	+	33.9565i	0.996855	+	0.575535i	0.907316	−	0.420449i	$-0.138127\pi$
$59$	58.8145	+	33.9565i	0.996855	+	0.575535i	0.0895389	+	0.995983i	$0.471461\pi$
$60$		0			0
$61$	−9.10218	−	15.7654i	−0.149216	−	0.258450i	0.781722	−	0.623627i	$-0.214342\pi$
$61$	−9.10218	−	15.7654i	−0.149216	−	0.258450i	−0.930938	+	0.365177i	$0.881008\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−101.838	+	58.7959i	−1.56673	+	0.904553i
$66$		0			0
$67$	−33.0000	+	57.1577i	−0.492537	+	0.853100i	−0.999963	−	0.00859584i	$-0.997264\pi$
$67$	−33.0000	+	57.1577i	−0.492537	+	0.853100i	0.507426	+	0.861695i	$0.330597\pi$
$68$		0			0
$69$	−32.0587	+	48.5934i	−0.464619	+	0.704253i
$70$		0			0
$71$			93.8415i			1.32171i	0.750513	+	0.660855i	$0.229806\pi$
$71$			93.8415i			1.32171i	−0.750513	+	0.660855i	$0.770194\pi$
$72$		0			0
$73$	−3.88667	+	6.73190i	−0.0532420	+	0.0922178i	−0.891418	−	0.453182i	$-0.850289\pi$
$73$	−3.88667	+	6.73190i	−0.0532420	+	0.0922178i	0.838176	+	0.545400i	$0.183622\pi$
$74$		0			0
$75$	2.18828	−	36.6796i	0.0291771	−	0.489062i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−52.4966	−	90.9267i	−0.664514	−	1.15097i	−0.979417	−	0.201848i	$-0.935305\pi$
$79$	−52.4966	−	90.9267i	−0.664514	−	1.15097i	0.314903	−	0.949124i	$-0.398028\pi$
$80$		0			0
$81$	−22.7927	−	77.7270i	−0.281391	−	0.959593i
$82$		0			0
$83$			51.1190i			0.615892i	0.951404	+	0.307946i	$0.0996415\pi$
$83$			51.1190i			0.615892i	−0.951404	+	0.307946i	$0.900358\pi$
$84$		0			0
$85$	125.745			1.47935
$86$		0			0
$87$	−4.35553	−	8.70317i	−0.0500635	−	0.100036i
$88$		0			0
$89$	−130.150	+	75.1423i	−1.46236	+	0.844295i	−0.999120	−	0.0419368i	$-0.986647\pi$
$89$	−130.150	+	75.1423i	−1.46236	+	0.844295i	−0.463242	+	0.886232i	$0.653314\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.51598	−	25.4107i	0.0163009	−	0.273233i
$94$		0			0
$95$	64.4636	+	37.2181i	0.678565	+	0.391769i
$96$		0			0
$97$	188.793			1.94632			0.973158	−	0.230138i	$-0.0739177\pi$
$97$	188.793			1.94632			0.973158	+	0.230138i	$0.0739177\pi$
$98$		0			0
$99$	−142.828	+	61.1323i	−1.44270	+	0.617498i
$100$		0			0
$101$	35.6498	+	20.5824i	0.352968	+	0.203786i	0.665992	−	0.745959i	$-0.268009\pi$
$101$	35.6498	+	20.5824i	0.352968	+	0.203786i	−0.313024	+	0.949745i	$0.601342\pi$
$102$		0			0
$103$	43.3091	+	75.0135i	0.420476	+	0.728287i	0.995986	−	0.0895084i	$-0.0285296\pi$
$103$	43.3091	+	75.0135i	0.420476	+	0.728287i	−0.575510	+	0.817795i	$0.695196\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	128.025	−	73.9152i	1.19649	−	0.690796i	0.236723	−	0.971577i	$-0.423927\pi$
$107$	128.025	−	73.9152i	1.19649	−	0.690796i	0.959772	+	0.280781i	$0.0905934\pi$
$108$		0			0
$109$	−12.1276	+	21.0056i	−0.111262	+	0.192712i	−0.916279	−	0.400540i	$-0.868823\pi$
$109$	−12.1276	+	21.0056i	−0.111262	+	0.192712i	0.805017	+	0.593251i	$0.202156\pi$
$110$		0			0
$111$	−169.642	−	111.919i	−1.52831	−	1.00828i
$112$		0			0
$113$		−	133.753i		−	1.18366i	−0.806064	−	0.591828i	$-0.798407\pi$
$113$		−	133.753i		−	1.18366i	0.806064	−	0.591828i	$-0.201593\pi$
$114$		0			0
$115$	59.2166	−	102.566i	0.514927	−	0.891879i
$116$		0			0
$117$	103.944	−	138.801i	0.888407	−	1.18633i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	88.4932	+	153.275i	0.731348	+	1.26673i
$122$		0			0
$123$	−74.7366	−	149.338i	−0.607614	−	1.21413i
$124$		0			0
$125$		−	77.8255i		−	0.622604i
$126$		0			0
$127$	−2.99315			−0.0235681			−0.0117841	−	0.999931i	$-0.503751\pi$
$127$	−2.99315			−0.0235681			−0.0117841	+	0.999931i	$0.503751\pi$
$128$		0			0
$129$	−133.455	+	66.7881i	−1.03454	+	0.517737i
$130$		0			0
$131$	−35.0479	+	20.2349i	−0.267541	+	0.154465i	−0.627770	−	0.778399i	$-0.716032\pi$
$131$	−35.0479	+	20.2349i	−0.267541	+	0.154465i	0.360228	+	0.932864i	$0.382699\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	55.7037	+	155.084i	0.412620	+	1.14877i
$136$		0			0
$137$	58.8447	+	33.9740i	0.429524	+	0.247986i	0.699144	−	0.714981i	$-0.253565\pi$
$137$	58.8447	+	33.9740i	0.429524	+	0.247986i	−0.269620	+	0.962967i	$0.586898\pi$
$138$		0			0
$139$	−134.862			−0.970233			−0.485117	−	0.874449i	$-0.661223\pi$
$139$	−134.862			−0.970233			−0.485117	+	0.874449i	$0.661223\pi$
$140$		0			0
$141$	75.6553	−	114.675i	0.536562	−	0.813301i
$142$		0			0
$143$	−288.040	−	166.300i	−2.01427	−	1.16294i
$144$		0			0
$145$	9.89949	+	17.1464i	0.0682724	+	0.118251i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	167.204	−	96.5350i	1.12217	−	0.647886i	0.180217	−	0.983627i	$-0.442320\pi$
$149$	167.204	−	96.5350i	1.12217	−	0.647886i	0.941954	+	0.335741i	$0.108987\pi$
$150$		0			0
$151$	−136.745	+	236.849i	−0.905595	+	1.56854i	−0.0854787	+	0.996340i	$0.527242\pi$
$151$	−136.745	+	236.849i	−0.905595	+	1.56854i	−0.820116	+	0.572197i	$0.806091\pi$
$152$		0			0
$153$	−170.471	+	72.9642i	−1.11419	+	0.476890i
$154$		0			0
$155$			51.7868i			0.334109i
$156$		0			0
$157$	72.3907	−	125.384i	0.461087	−	0.798626i	−0.537928	−	0.842991i	$-0.680793\pi$
$157$	72.3907	−	125.384i	0.461087	−	0.798626i	0.999015	+	0.0443644i	$0.0141263\pi$
$158$		0			0
$159$	−100.093	−	5.97146i	−0.629513	−	0.0375563i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.120719	+	0.209091i	0.000740607	+	0.00128277i	0.866395	−	0.499358i	$-0.166431\pi$
$163$	0.120719	+	0.209091i	0.000740607	+	0.00128277i	−0.865655	+	0.500641i	$0.833098\pi$
$164$		0			0
$165$	282.643	−	141.450i	1.71299	−	0.857271i
$166$		0			0
$167$			76.1847i			0.456196i	0.973638	+	0.228098i	$0.0732506\pi$
$167$			76.1847i			0.456196i	−0.973638	+	0.228098i	$0.926749\pi$
$168$		0			0
$169$	202.235			1.19665
$170$		0			0
$171$	−108.989	−	13.0509i	−0.637362	−	0.0763208i
$172$		0			0
$173$	147.957	−	85.4230i	0.855243	−	0.493775i	−0.00717350	−	0.999974i	$-0.502283\pi$
$173$	147.957	−	85.4230i	0.855243	−	0.493775i	0.862416	+	0.506200i	$0.168950\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	203.378	+	12.1334i	1.14903	+	0.0685502i
$178$		0			0
$179$	64.4124	+	37.1885i	0.359846	+	0.207757i	0.669013	−	0.743251i	$-0.266717\pi$
$179$	64.4124	+	37.1885i	0.359846	+	0.207757i	−0.309167	+	0.951008i	$0.600050\pi$
$180$		0			0
$181$	98.8242			0.545990			0.272995	−	0.962015i	$-0.411986\pi$
$181$	98.8242			0.545990			0.272995	+	0.962015i	$0.411986\pi$
$182$		0			0
$183$	−45.5862	−	30.0747i	−0.249105	−	0.164343i
$184$		0			0
$185$	358.064	+	206.728i	1.93548	+	1.11745i
$186$		0			0
$187$	177.830	+	308.011i	0.950963	+	1.64712i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−15.9543	+	9.21123i	−0.0835305	+	0.0482263i	−0.541183	−	0.840905i	$-0.682024\pi$
$191$	−15.9543	+	9.21123i	−0.0835305	+	0.0482263i	0.457653	+	0.889131i	$0.348690\pi$
$192$		0			0
$193$	−105.121	+	182.074i	−0.544667	+	0.943391i	0.453961	+	0.891022i	$0.350011\pi$
$193$	−105.121	+	182.074i	−0.544667	+	0.943391i	−0.998628	+	0.0523692i	$0.983323\pi$
$194$		0			0
$195$	−194.269	+	294.466i	−0.996252	+	1.51008i
$196$		0			0
$197$			109.079i			0.553700i	0.960913	+	0.276850i	$0.0892906\pi$
$197$			109.079i			0.553700i	−0.960913	+	0.276850i	$0.910709\pi$
$198$		0			0
$199$	90.1488	−	156.142i	0.453009	−	0.784635i	−0.545562	−	0.838070i	$-0.683684\pi$
$199$	90.1488	−	156.142i	0.453009	−	0.784635i	0.998571	+	0.0534353i	$0.0170171\pi$
$200$		0			0
$201$	−11.7916	+	197.649i	−0.0586646	+	0.983326i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	169.866	+	294.216i	0.828613	+	1.43520i
$206$		0			0
$207$	−20.7648	+	173.409i	−0.100313	+	0.837723i
$208$		0			0
$209$			210.537i			1.00736i
$210$		0			0
$211$	216.497			1.02605			0.513025	−	0.858374i	$-0.328525\pi$
$211$	216.497			1.02605			0.513025	+	0.858374i	$0.328525\pi$
$212$		0			0
$213$	125.993	+	251.757i	0.591516	+	1.18196i
$214$		0			0
$215$	262.925	−	151.800i	1.22291	−	0.706046i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.38879	+	23.2786i	−0.00634149	+	0.106295i
$220$		0			0
$221$	−343.789	−	198.487i	−1.55561	−	0.898130i
$222$		0			0
$223$	−57.6123			−0.258351			−0.129175	−	0.991622i	$-0.541233\pi$
$223$	−57.6123			−0.258351			−0.129175	+	0.991622i	$0.541233\pi$
$224$		0			0
$225$	−43.3759	−	101.342i	−0.192782	−	0.450409i
$226$		0			0
$227$	−38.8763	−	22.4452i	−0.171261	−	0.0988776i	0.411919	−	0.911220i	$-0.364859\pi$
$227$	−38.8763	−	22.4452i	−0.171261	−	0.0988776i	−0.583180	+	0.812343i	$0.698192\pi$
$228$		0			0
$229$	38.0887	+	65.9716i	0.166326	+	0.288086i	0.937125	−	0.348993i	$-0.113476\pi$
$229$	38.0887	+	65.9716i	0.166326	+	0.288086i	−0.770799	+	0.637078i	$0.780143\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−64.5660	+	37.2772i	−0.277107	+	0.159988i	−0.632113	−	0.774876i	$-0.717812\pi$
$233$	−64.5660	+	37.2772i	−0.277107	+	0.159988i	0.355006	+	0.934864i	$0.384479\pi$
$234$		0			0
$235$	−139.745	+	242.045i	−0.594659	+	1.02998i
$236$		0			0
$237$	−262.917	−	173.455i	−1.10935	−	0.731879i
$238$		0			0
$239$		−	451.081i		−	1.88737i	−0.330851	−	0.943683i	$-0.607336\pi$
$239$		−	451.081i		−	1.88737i	0.330851	−	0.943683i	$-0.392664\pi$
$240$		0			0
$241$	−131.507	+	227.777i	−0.545674	+	0.945134i	0.452891	+	0.891566i	$0.350393\pi$
$241$	−131.507	+	227.777i	−0.545674	+	0.945134i	−0.998564	+	0.0535683i	$0.982941\pi$
$242$		0			0
$243$	−165.506	−	177.924i	−0.681093	−	0.732197i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−117.497	−	203.510i	−0.475695	−	0.823927i
$248$		0			0
$249$	68.6330	+	137.142i	0.275635	+	0.550770i
$250$		0			0
$251$			360.864i			1.43770i	0.695163	+	0.718852i	$0.255332\pi$
$251$			360.864i			1.43770i	−0.695163	+	0.718852i	$0.744668\pi$
$252$		0			0
$253$	334.979			1.32403
$254$		0			0
$255$	337.348	−	168.827i	1.32293	−	0.662066i
$256$		0			0
$257$	138.169	−	79.7719i	0.537622	−	0.310396i	−0.206492	−	0.978448i	$-0.566205\pi$
$257$	138.169	−	79.7719i	0.537622	−	0.310396i	0.744115	+	0.668052i	$0.232872\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−23.3700	−	17.5010i	−0.0895401	−	0.0670538i
$262$		0			0
$263$	301.801	+	174.245i	1.14753	+	0.662528i	0.948285	−	0.317421i	$-0.102817\pi$
$263$	301.801	+	174.245i	1.14753	+	0.662528i	0.199247	+	0.979949i	$0.436150\pi$
$264$		0			0
$265$	203.988			0.769767
$266$		0			0
$267$	−248.279	+	376.333i	−0.929885	+	1.40949i
$268$		0			0
$269$	−258.988	−	149.527i	−0.962781	−	0.555862i	−0.0657533	−	0.997836i	$-0.520945\pi$
$269$	−258.988	−	149.527i	−0.962781	−	0.555862i	−0.897028	+	0.441974i	$0.854278\pi$
$270$		0			0
$271$	−7.42220	−	12.8556i	−0.0273882	−	0.0474377i	0.852006	−	0.523531i	$-0.175386\pi$
$271$	−7.42220	−	12.8556i	−0.0273882	−	0.0474377i	−0.879395	+	0.476094i	$0.842052\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−183.107	+	105.717i	−0.665842	+	0.384424i
$276$		0			0
$277$	176.490	−	305.689i	0.637147	−	1.10357i	−0.348909	−	0.937157i	$-0.613448\pi$
$277$	176.490	−	305.689i	0.637147	−	1.10357i	0.986056	−	0.166414i	$-0.0532189\pi$
$278$		0			0
$279$	−30.0496	−	70.2070i	−0.107705	−	0.251638i
$280$		0			0
$281$		−	59.2578i		−	0.210882i	−0.994426	−	0.105441i	$-0.966375\pi$
$281$		−	59.2578i		−	0.210882i	0.994426	−	0.105441i	$-0.0336254\pi$
$282$		0			0
$283$	23.7710	−	41.1726i	0.0839965	−	0.145486i	−0.820967	−	0.570976i	$-0.806565\pi$
$283$	23.7710	−	41.1726i	0.0839965	−	0.145486i	0.904963	+	0.425490i	$0.139898\pi$
$284$		0			0
$285$	222.912	+	13.2988i	0.782148	+	0.0466625i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	67.7483	+	117.343i	0.234423	+	0.406033i
$290$		0			0
$291$	506.492	−	253.476i	1.74052	−	0.871050i
$292$		0			0
$293$		−	385.971i		−	1.31731i	−0.752446	−	0.658654i	$-0.771126\pi$
$293$		−	385.971i		−	1.31731i	0.752446	−	0.658654i	$-0.228874\pi$
$294$		0			0
$295$	−414.483			−1.40503
$296$		0			0
$297$	−301.100	+	355.768i	−1.01381	+	1.19787i
$298$		0			0
$299$	−323.799	+	186.945i	−1.08294	+	0.625235i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	123.275	+	7.35453i	0.406849	+	0.0242724i
$304$		0			0
$305$	96.2187	+	55.5519i	0.315471	+	0.182137i
$306$		0			0
$307$	−267.457			−0.871196			−0.435598	−	0.900141i	$-0.643463\pi$
$307$	−267.457			−0.871196			−0.435598	+	0.900141i	$0.643463\pi$
$308$		0			0
$309$	216.904	+	143.099i	0.701953	+	0.463102i
$310$		0			0
$311$	−59.5249	−	34.3667i	−0.191398	−	0.110504i	0.401239	−	0.915974i	$-0.368580\pi$
$311$	−59.5249	−	34.3667i	−0.191398	−	0.110504i	−0.592637	+	0.805470i	$0.701913\pi$
$312$		0			0
$313$	−50.1949	−	86.9401i	−0.160367	−	0.277764i	0.774633	−	0.632411i	$-0.217934\pi$
$313$	−50.1949	−	86.9401i	−0.160367	−	0.277764i	−0.935000	+	0.354647i	$0.884601\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	161.789	−	93.4092i	0.510377	−	0.294666i	−0.222612	−	0.974907i	$-0.571458\pi$
$317$	161.789	−	93.4092i	0.510377	−	0.294666i	0.732989	+	0.680241i	$0.238125\pi$
$318$		0			0
$319$	−28.0000	+	48.4974i	−0.0877743	+	0.152030i
$320$		0			0
$321$	244.225	−	370.187i	0.760826	−	1.15323i
$322$		0			0
$323$			251.286i			0.777975i
$324$		0			0
$325$	117.997	−	204.376i	0.363067	−	0.628850i
$326$		0			0
$327$	−4.33343	+	72.6363i	−0.0132521	+	0.222129i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−73.3690	−	127.079i	−0.221659	−	0.383924i	0.733653	−	0.679524i	$-0.237814\pi$
$331$	−73.3690	−	127.079i	−0.221659	−	0.383924i	−0.955312	+	0.295600i	$0.904480\pi$
$332$		0			0
$333$	−605.379	−	72.4911i	−1.81795	−	0.217691i
$334$		0			0
$335$		−	402.807i		−	1.20241i
$336$		0			0
$337$	−365.717			−1.08522			−0.542608	−	0.839986i	$-0.682563\pi$
$337$	−365.717			−1.08522			−0.542608	+	0.839986i	$0.682563\pi$
$338$		0			0
$339$	−179.579	−	358.832i	−0.529731	−	1.05850i
$340$		0			0
$341$	−126.851	+	73.2377i	−0.371998	+	0.214773i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	21.1593	−	354.669i	0.0613313	−	1.02803i
$346$		0			0
$347$	−506.481	−	292.417i	−1.45960	−	0.842700i	−0.460607	−	0.887604i	$-0.652368\pi$
$347$	−506.481	−	292.417i	−1.45960	−	0.842700i	−0.998991	+	0.0449042i	$0.985702\pi$
$348$		0			0
$349$	353.002			1.01147			0.505734	−	0.862689i	$-0.331222\pi$
$349$	353.002			1.01147			0.505734	+	0.862689i	$0.331222\pi$
$350$		0			0
$351$	92.5034	−	511.931i	0.263543	−	1.45849i
$352$		0			0
$353$	−143.491	−	82.8443i	−0.406489	−	0.234687i	0.282791	−	0.959182i	$-0.408740\pi$
$353$	−143.491	−	82.8443i	−0.406489	−	0.234687i	−0.689280	+	0.724495i	$0.742073\pi$
$354$		0			0
$355$	−286.364	−	495.997i	−0.806658	−	1.39717i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−364.255	+	210.303i	−1.01464	+	0.585802i	−0.912546	−	0.408973i	$-0.865887\pi$
$359$	−364.255	+	210.303i	−1.01464	+	0.585802i	−0.102092	+	0.994775i	$0.532554\pi$
$360$		0			0
$361$	106.124	−	183.812i	0.293973	−	0.509176i
$362$		0			0
$363$	443.198	+	292.392i	1.22093	+	0.805489i
$364$		0			0
$365$		−	47.4417i		−	0.129977i
$366$		0			0
$367$	−65.5951	+	113.614i	−0.178733	+	0.309575i	−0.941447	−	0.337161i	$-0.890533\pi$
$367$	−65.5951	+	113.614i	−0.178733	+	0.309575i	0.762714	+	0.646736i	$0.223867\pi$
$368$		0			0
$369$	−401.006	−	300.300i	−1.08674	−	0.813822i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−296.476	−	513.512i	−0.794842	−	1.37671i	−0.922940	−	0.384945i	$-0.874220\pi$
$373$	−296.476	−	513.512i	−0.794842	−	1.37671i	0.128098	−	0.991762i	$-0.459113\pi$
$374$		0			0
$375$	−104.489	−	208.790i	−0.278639	−	0.556773i
$376$		0			0
$377$		−	62.5049i		−	0.165796i
$378$		0			0
$379$	−170.228			−0.449150			−0.224575	−	0.974457i	$-0.572099\pi$
$379$	−170.228			−0.449150			−0.224575	+	0.974457i	$0.572099\pi$
$380$		0			0
$381$	−8.03001	+	4.01864i	−0.0210761	+	0.0105476i
$382$		0			0
$383$	−350.117	+	202.140i	−0.914144	+	0.527781i	−0.881762	−	0.471694i	$-0.843643\pi$
$383$	−350.117	+	202.140i	−0.914144	+	0.527781i	−0.0323821	+	0.999476i	$0.510309\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−268.363	+	358.358i	−0.693443	+	0.925989i
$388$		0			0
$389$	−81.1667	−	46.8616i	−0.208655	−	0.120467i	0.392031	−	0.919952i	$-0.371772\pi$
$389$	−81.1667	−	46.8616i	−0.208655	−	0.120467i	−0.600686	+	0.799485i	$0.705106\pi$
$390$		0			0
$391$	399.813			1.02254
$392$		0			0
$393$	−66.8587	+	101.342i	−0.170124	+	0.257868i
$394$		0			0
$395$	554.938	+	320.394i	1.40491	+	0.811124i
$396$		0			0
$397$	−21.4887	−	37.2195i	−0.0541276	−	0.0937518i	0.837692	−	0.546143i	$-0.183904\pi$
$397$	−21.4887	−	37.2195i	−0.0541276	−	0.0937518i	−0.891820	+	0.452391i	$0.850571\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	542.901	−	313.444i	1.35387	−	0.781656i	0.365079	−	0.930976i	$-0.381042\pi$
$401$	542.901	−	313.444i	1.35387	−	0.781656i	0.988789	+	0.149320i	$0.0477085\pi$
$402$		0			0
$403$	81.7449	−	141.586i	0.202841	−	0.351331i
$404$		0			0
$405$	357.660	+	341.271i	0.883110	+	0.842643i
$406$		0			0
$407$			1169.43i			2.87329i
$408$		0			0
$409$	58.8703	−	101.966i	0.143937	−	0.249306i	−0.785039	−	0.619447i	$-0.787357\pi$
$409$	58.8703	−	101.966i	0.143937	−	0.249306i	0.928976	+	0.370140i	$0.120690\pi$
$410$		0			0
$411$	203.482	+	12.1396i	0.495091	+	0.0295368i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−155.993	−	270.188i	−0.375887	−	0.651056i
$416$		0			0
$417$	−361.808	+	181.068i	−0.867646	+	0.434216i
$418$		0			0
$419$		−	314.902i		−	0.751556i	−0.926710	−	0.375778i	$-0.877375\pi$
$419$		−	314.902i		−	0.751556i	0.926710	−	0.375778i	$-0.122625\pi$
$420$		0			0
$421$	−200.524			−0.476304			−0.238152	−	0.971228i	$-0.576542\pi$
$421$	−200.524			−0.476304			−0.238152	+	0.971228i	$0.576542\pi$
$422$		0			0
$423$	49.0028	−	409.226i	0.115846	−	0.967438i
$424$		0			0
$425$	−218.546	+	126.178i	−0.514226	+	0.296889i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−996.029	−	59.4225i	−2.32175	−	0.138514i
$430$		0			0
$431$	269.246	+	155.449i	0.624700	+	0.360671i	0.778697	−	0.627400i	$-0.215881\pi$
$431$	269.246	+	155.449i	0.624700	+	0.360671i	−0.153996	+	0.988071i	$0.549214\pi$
$432$		0			0
$433$	−100.068			−0.231103			−0.115552	−	0.993301i	$-0.536864\pi$
$433$	−100.068			−0.231103			−0.115552	+	0.993301i	$0.536864\pi$
$434$		0			0
$435$	49.5793	+	32.7092i	0.113975	+	0.0751935i
$436$		0			0
$437$	204.966	+	118.337i	0.469030	+	0.270794i
$438$		0			0
$439$	207.187	+	358.859i	0.471952	+	0.817446i	0.999485	−	0.0320892i	$-0.0102161\pi$
$439$	207.187	+	358.859i	0.471952	+	0.817446i	−0.527533	+	0.849535i	$0.676883\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	34.6157	−	19.9854i	0.0781392	−	0.0451137i	−0.460421	−	0.887701i	$-0.652302\pi$
$443$	34.6157	−	19.9854i	0.0781392	−	0.0451137i	0.538561	+	0.842587i	$0.318968\pi$
$444$		0			0
$445$	458.604	−	794.325i	1.03057	−	1.78500i
$446$		0			0
$447$	318.964	−	483.473i	0.713565	−	1.08160i
$448$		0			0
$449$			38.5741i			0.0859111i	0.999077	+	0.0429556i	$0.0136774\pi$
$449$			38.5741i			0.0859111i	−0.999077	+	0.0429556i	$0.986323\pi$
$450$		0			0
$451$	−480.452	+	832.168i	−1.06530	+	1.84516i
$452$		0			0
$453$	−48.8618	+	819.013i	−0.107863	+	1.80798i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	213.631	+	370.020i	0.467464	+	0.809671i	0.999309	−	0.0371705i	$-0.0118345\pi$
$457$	213.631	+	370.020i	0.467464	+	0.809671i	−0.531845	+	0.846842i	$0.678501\pi$
$458$		0			0
$459$	−359.377	+	424.625i	−0.782956	+	0.925109i
$460$		0			0
$461$			224.426i			0.486825i	0.969923	+	0.243412i	$0.0782668\pi$
$461$			224.426i			0.486825i	−0.969923	+	0.243412i	$0.921733\pi$
$462$		0			0
$463$	94.4966			0.204096			0.102048	−	0.994779i	$-0.467460\pi$
$463$	94.4966			0.204096			0.102048	+	0.994779i	$0.467460\pi$
$464$		0			0
$465$	69.5297	+	138.933i	0.149526	+	0.298782i
$466$		0			0
$467$	344.375	−	198.825i	0.737419	−	0.425749i	−0.0837110	−	0.996490i	$-0.526677\pi$
$467$	344.375	−	198.825i	0.737419	−	0.425749i	0.821130	+	0.570741i	$0.193344\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	25.8667	−	433.573i	0.0549187	−	0.920537i
$472$		0			0
$473$	743.664	+	429.355i	1.57223	+	0.907727i
$474$		0			0
$475$	−149.385			−0.314494
$476$		0			0
$477$	−276.545	+	118.365i	−0.579759	+	0.248145i
$478$		0			0
$479$	−191.553	−	110.593i	−0.399902	−	0.230884i	0.286540	−	0.958068i	$-0.407495\pi$
$479$	−191.553	−	110.593i	−0.399902	−	0.230884i	−0.686442	+	0.727185i	$0.740828\pi$
$480$		0			0
$481$	−652.635	−	1130.40i	−1.35683	−	2.35010i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−997.858	+	576.114i	−2.05744	+	1.18786i
$486$		0			0
$487$	83.7517	−	145.062i	0.171975	−	0.297869i	−0.767135	−	0.641485i	$-0.778319\pi$
$487$	83.7517	−	145.062i	0.171975	−	0.297869i	0.939110	+	0.343616i	$0.111652\pi$
$488$		0			0
$489$	0.604593	+	0.398871i	0.00123639	+	0.000815686i
$490$		0			0
$491$		−	641.712i		−	1.30695i	−0.756949	−	0.653474i	$-0.773311\pi$
$491$		−	641.712i		−	1.30695i	0.756949	−	0.653474i	$-0.226689\pi$
$492$		0			0
$493$	−33.4193	+	57.8839i	−0.0677876	+	0.117412i
$494$		0			0
$495$	568.362	−	758.961i	1.14821	−	1.53326i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−353.241	−	611.832i	−0.707899	−	1.22612i	−0.965635	−	0.259901i	$-0.916310\pi$
$499$	−353.241	−	611.832i	−0.707899	−	1.22612i	0.257737	−	0.966215i	$-0.417023\pi$
$500$		0			0
$501$	102.287	+	204.388i	0.204165	+	0.407960i
$502$		0			0
$503$			77.8255i			0.154723i	0.997003	+	0.0773613i	$0.0246495\pi$
$503$			77.8255i			0.154723i	−0.997003	+	0.0773613i	$0.975351\pi$
$504$		0			0
$505$	−251.235			−0.497494
$506$		0			0
$507$	542.554	−	271.523i	1.07013	−	0.535548i
$508$		0			0
$509$	85.6626	−	49.4574i	0.168296	−	0.0971657i	−0.413486	−	0.910510i	$-0.635689\pi$
$509$	85.6626	−	49.4574i	0.168296	−	0.0971657i	0.581782	+	0.813345i	$0.302356\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−309.917	+	111.317i	−0.604127	+	0.216992i
$514$		0			0
$515$	−457.818	−	264.321i	−0.888967	−	0.513245i
$516$		0			0
$517$	−790.516			−1.52905
$518$		0			0
$519$	282.248	−	427.822i	0.543831	−	0.824319i
$520$		0			0
$521$	416.842	+	240.664i	0.800080	+	0.461927i	0.843499	−	0.537130i	$-0.180492\pi$
$521$	416.842	+	240.664i	0.800080	+	0.461927i	−0.0434189	+	0.999057i	$0.513825\pi$
$522$		0			0
$523$	−65.8560	−	114.066i	−0.125920	−	0.218099i	0.796172	−	0.605070i	$-0.206855\pi$
$523$	−65.8560	−	114.066i	−0.125920	−	0.218099i	−0.922092	+	0.386971i	$0.873521\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−151.403	+	87.4125i	−0.287292	+	0.165868i
$528$		0			0
$529$	−76.2175	+	132.013i	−0.144078	+	0.249551i
$530$		0			0
$531$	561.911	−	240.506i	1.05821	−	0.452931i
$532$		0			0
$533$		−	1072.52i		−	2.01224i
$534$		0			0
$535$	−451.115	+	781.354i	−0.843205	+	1.46047i
$536$		0			0
$537$	222.735	+	13.2882i	0.414777	+	0.0247453i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	178.248	+	308.735i	0.329479	+	0.570675i	0.982409	−	0.186744i	$-0.0597935\pi$
$541$	178.248	+	308.735i	0.329479	+	0.570675i	−0.652929	+	0.757419i	$0.726460\pi$
$542$		0			0
$543$	265.125	−	132.683i	0.488260	−	0.244351i
$544$		0			0
$545$		−	148.032i		−	0.271619i
$546$		0			0
$547$	−799.731			−1.46203			−0.731016	−	0.682361i	$-0.760953\pi$
$547$	−799.731			−1.46203			−0.731016	+	0.682361i	$0.760953\pi$
$548$		0			0
$549$	−162.677	−	19.4798i	−0.296315	−	0.0354823i
$550$		0			0
$551$	−34.2651	+	19.7829i	−0.0621870	+	0.0359037i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1238.17	+	73.8683i	2.23093	+	0.133096i
$556$		0			0
$557$	234.528	+	135.405i	0.421055	+	0.243096i	0.695529	−	0.718498i	$-0.255170\pi$
$557$	234.528	+	135.405i	0.421055	+	0.243096i	−0.274473	+	0.961595i	$0.588504\pi$
$558$		0			0
$559$	−958.457			−1.71459
$560$		0			0
$561$	890.621	+	587.573i	1.58756	+	1.04737i
$562$		0			0
$563$	−114.294	−	65.9876i	−0.203009	−	0.117207i	0.395049	−	0.918660i	$-0.370727\pi$
$563$	−114.294	−	65.9876i	−0.203009	−	0.117207i	−0.598058	+	0.801453i	$0.704061\pi$
$564$		0			0
$565$	408.157	+	706.948i	0.722401	+	1.25124i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−77.7621	+	44.8960i	−0.136665	+	0.0789033i	−0.566773	−	0.823874i	$-0.691808\pi$
$569$	−77.7621	+	44.8960i	−0.136665	+	0.0789033i	0.430109	+	0.902777i	$0.358475\pi$
$570$		0			0
$571$	190.362	−	329.717i	0.333384	−	0.577438i	−0.649789	−	0.760114i	$-0.725143\pi$
$571$	190.362	−	329.717i	0.333384	−	0.577438i	0.983173	+	0.182677i	$0.0584762\pi$
$572$		0			0
$573$	−30.4351	+	46.1323i	−0.0531153	+	0.0805102i
$574$		0			0
$575$			237.682i			0.413359i
$576$		0			0
$577$	483.105	−	836.763i	0.837271	−	1.45020i	−0.0548972	−	0.998492i	$-0.517483\pi$
$577$	483.105	−	836.763i	0.837271	−	1.45020i	0.892168	−	0.451704i	$-0.149184\pi$
$578$		0			0
$579$	−37.5618	+	629.605i	−0.0648736	+	1.08740i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	288.483	+	499.667i	0.494825	+	0.857062i
$584$		0			0
$585$	−125.830	+	1050.82i	−0.215095	+	1.79627i
$586$		0			0
$587$		−	235.937i		−	0.401938i	−0.979598	−	0.200969i	$-0.935591\pi$
$587$		−	235.937i		−	0.401938i	0.979598	−	0.200969i	$-0.0644090\pi$
$588$		0			0
$589$	−103.490			−0.175704
$590$		0			0
$591$	146.451	+	292.637i	0.247802	+	0.495155i
$592$		0			0
$593$	−82.6896	+	47.7409i	−0.139443	+	0.0805073i	−0.568098	−	0.822961i	$-0.692321\pi$
$593$	−82.6896	+	47.7409i	−0.139443	+	0.0805073i	0.428656	+	0.903468i	$0.358987\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	32.2121	−	539.933i	0.0539566	−	0.904411i
$598$		0			0
$599$	−331.700	−	191.507i	−0.553756	−	0.319711i	0.196879	−	0.980428i	$-0.436919\pi$
$599$	−331.700	−	191.507i	−0.553756	−	0.319711i	−0.750636	+	0.660716i	$0.770253\pi$
$600$		0			0
$601$	−131.142			−0.218206			−0.109103	−	0.994030i	$-0.534798\pi$
$601$	−131.142			−0.218206			−0.109103	+	0.994030i	$0.534798\pi$
$602$		0			0
$603$	233.731	+	546.082i	0.387614	+	0.905609i
$604$		0			0
$605$	−935.456	−	540.086i	−1.54621	−	0.892704i
$606$		0			0
$607$	269.554	+	466.882i	0.444076	+	0.769162i	0.997987	−	0.0634134i	$-0.0201987\pi$
$607$	269.554	+	466.882i	0.444076	+	0.769162i	−0.553911	+	0.832576i	$0.686865\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	764.131	−	441.171i	1.25062	−	0.722047i
$612$		0			0
$613$	112.624	−	195.071i	0.183726	−	0.318223i	−0.759420	−	0.650600i	$-0.774517\pi$
$613$	112.624	−	195.071i	0.183726	−	0.318223i	0.943147	+	0.332377i	$0.107851\pi$
$614$		0			0
$615$	850.733	+	561.257i	1.38331	+	0.912613i
$616$		0			0
$617$			1021.48i			1.65556i	0.561051	+	0.827781i	$0.310397\pi$
$617$			1021.48i			1.65556i	−0.561051	+	0.827781i	$0.689603\pi$
$618$		0			0
$619$	−105.464	+	182.668i	−0.170377	+	0.295102i	−0.938552	−	0.345138i	$-0.887832\pi$
$619$	−105.464	+	182.668i	−0.170377	+	0.295102i	0.768174	+	0.640241i	$0.221165\pi$
$620$		0			0
$621$	177.113	+	493.099i	0.285206	+	0.794041i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	390.593	+	676.527i	0.624949	+	1.08244i
$626$		0			0
$627$	282.670	+	564.829i	0.450830	+	0.900843i
$628$		0			0
$629$			1395.77i			2.21903i
$630$		0			0
$631$	1084.40			1.71854			0.859272	−	0.511520i	$-0.170917\pi$
$631$	1084.40			1.71854			0.859272	+	0.511520i	$0.170917\pi$
$632$		0			0
$633$	580.816	−	290.671i	0.917561	−	0.459196i
$634$		0			0
$635$	15.8202	−	9.13380i	0.0249137	−	0.0143839i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	676.026	+	506.254i	1.05794	+	0.792260i
$640$		0			0
$641$	−804.775	−	464.637i	−1.25550	−	0.724863i	−0.283303	−	0.959031i	$-0.591430\pi$
$641$	−804.775	−	464.637i	−1.25550	−	0.724863i	−0.972196	+	0.234168i	$0.924763\pi$
$642$		0			0
$643$	−887.946			−1.38094			−0.690471	−	0.723360i	$-0.742597\pi$
$643$	−887.946			−1.38094			−0.690471	+	0.723360i	$0.742597\pi$
$644$		0			0
$645$	501.566	−	760.255i	0.777621	−	1.17869i
$646$		0			0
$647$	−170.484	−	98.4288i	−0.263499	−	0.152131i	0.362431	−	0.932011i	$-0.381947\pi$
$647$	−170.484	−	98.4288i	−0.263499	−	0.152131i	−0.625929	+	0.779880i	$0.715280\pi$
$648$		0			0
$649$	−586.167	−	1015.27i	−0.903185	−	1.56436i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	376.651	−	217.460i	0.576801	−	0.333016i	−0.183060	−	0.983102i	$-0.558600\pi$
$653$	376.651	−	217.460i	0.576801	−	0.333016i	0.759861	+	0.650085i	$0.225267\pi$
$654$		0			0
$655$	123.497	−	213.902i	0.188544	−	0.326568i
$656$		0			0
$657$	27.5283	+	64.3163i	0.0419000	+	0.0978940i
$658$		0			0
$659$		−	662.337i		−	1.00506i	−0.864559	−	0.502532i	$-0.832402\pi$
$659$		−	662.337i		−	1.00506i	0.864559	−	0.502532i	$-0.167598\pi$
$660$		0			0
$661$	519.614	−	899.998i	0.786103	−	1.36157i	−0.142235	−	0.989833i	$-0.545429\pi$
$661$	519.614	−	899.998i	0.786103	−	1.36157i	0.928338	−	0.371737i	$-0.121238\pi$
$662$		0			0
$663$	−1188.81	−	70.9234i	−1.79307	−	0.106973i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	31.4760	+	54.5181i	0.0471904	+	0.0817362i
$668$		0			0
$669$	−154.562	+	77.3510i	−0.231034	+	0.115622i
$670$		0			0
$671$			314.249i			0.468329i
$672$		0			0
$673$	−1210.47			−1.79862			−0.899308	−	0.437315i	$-0.855930\pi$
$673$	−1210.47			−1.79862			−0.899308	+	0.437315i	$0.855930\pi$
$674$		0			0
$675$	−252.432	−	213.643i	−0.373973	−	0.316508i
$676$		0			0
$677$	1081.96	−	624.668i	1.59816	−	0.922700i	0.606321	−	0.795220i	$-0.292645\pi$
$677$	1081.96	−	624.668i	1.59816	−	0.922700i	0.991841	−	0.127480i	$-0.0406888\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−134.432	−	8.02015i	−0.197404	−	0.0117770i
$682$		0			0
$683$	−339.226	−	195.852i	−0.496671	−	0.286753i	0.230667	−	0.973033i	$-0.425909\pi$
$683$	−339.226	−	195.852i	−0.496671	−	0.286753i	−0.727338	+	0.686280i	$0.759243\pi$
$684$		0			0
$685$	−414.696			−0.605396
$686$		0			0
$687$	190.759	+	125.850i	0.277669	+	0.183188i
$688$		0			0
$689$	−557.708	−	321.993i	−0.809445	−	0.467333i
$690$		0			0
$691$	336.844	+	583.430i	0.487473	+	0.844328i	0.999896	−	0.0144052i	$-0.00458547\pi$
$691$	336.844	+	583.430i	0.487473	+	0.844328i	−0.512423	+	0.858733i	$0.671252\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	712.812	−	411.542i	1.02563	−	0.592147i
$696$		0			0
$697$	−573.442	+	993.230i	−0.822729	+	1.42501i
$698$		0			0
$699$	−123.169	+	186.694i	−0.176207	+	0.267088i
$700$		0			0
$701$		−	499.209i		−	0.712139i	−0.934459	−	0.356070i	$-0.884117\pi$
$701$		−	499.209i		−	0.712139i	0.934459	−	0.356070i	$-0.115883\pi$
$702$		0			0
$703$	−413.121	+	715.547i	−0.587654	+	1.01785i
$704$		0			0
$705$	−49.9338	+	836.981i	−0.0708280	+	1.18721i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	394.879	+	683.951i	0.556952	+	0.964670i	0.997749	+	0.0670628i	$0.0213628\pi$
$709$	394.879	+	683.951i	0.556952	+	0.964670i	−0.440796	+	0.897607i	$0.645304\pi$
$710$		0			0
$711$	−938.236	−	112.349i	−1.31960	−	0.158015i
$712$		0			0
$713$			164.659i			0.230939i
$714$		0			0
$715$	2029.90			2.83903
$716$		0			0
$717$	−605.627	−	1210.16i	−0.844668	−	1.68781i
$718$		0			0
$719$	503.215	−	290.531i	0.699882	−	0.404077i	−0.107422	−	0.994214i	$-0.534259\pi$
$719$	503.215	−	290.531i	0.699882	−	0.404077i	0.807303	+	0.590137i	$0.200926\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−46.9903	+	787.644i	−0.0649935	+	1.08941i
$724$		0			0
$725$	−34.4109	−	19.8671i	−0.0474633	−	0.0274029i
$726$		0			0
$727$	−21.5256			−0.0296088			−0.0148044	−	0.999890i	$-0.504713\pi$
$727$	−21.5256			−0.0296088			−0.0148044	+	0.999890i	$0.504713\pi$
$728$		0			0
$729$	−682.900	−	255.124i	−0.936763	−	0.349964i
$730$		0			0
$731$	887.597	+	512.455i	1.21422	+	0.701032i
$732$		0			0
$733$	99.4024	+	172.170i	0.135610	+	0.234884i	0.925830	−	0.377939i	$-0.123367\pi$
$733$	99.4024	+	172.170i	0.135610	+	0.234884i	−0.790220	+	0.612823i	$0.790034\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	986.672	−	569.655i	1.33877	−	0.772938i
$738$		0			0
$739$	195.114	−	337.947i	0.264024	−	0.457303i	−0.703283	−	0.710910i	$-0.748283\pi$
$739$	195.114	−	337.947i	0.264024	−	0.457303i	0.967308	+	0.253606i	$0.0816168\pi$
$740$		0			0
$741$	−588.455	−	388.223i	−0.794136	−	0.523918i
$742$		0			0
$743$		−	228.637i		−	0.307721i	−0.988093	−	0.153860i	$-0.950829\pi$
$743$		−	228.637i		−	0.307721i	0.988093	−	0.153860i	$-0.0491706\pi$
$744$		0			0
$745$	−589.166	+	1020.47i	−0.790827	+	1.36975i
$746$		0			0
$747$	368.257	+	275.776i	0.492981	+	0.369178i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	670.193	+	1160.81i	0.892401	+	1.54568i	0.836988	+	0.547221i	$0.184314\pi$
$751$	670.193	+	1160.81i	0.892401	+	1.54568i	0.0554134	+	0.998463i	$0.482352\pi$
$752$		0			0
$753$	484.500	+	968.123i	0.643427	+	1.28569i
$754$		0			0
$755$		−	1669.15i		−	2.21079i
$756$		0			0
$757$	−550.187			−0.726799			−0.363399	−	0.931633i	$-0.618384\pi$
$757$	−550.187			−0.726799			−0.363399	+	0.931633i	$0.618384\pi$
$758$		0			0
$759$	898.681	−	449.748i	1.18403	−	0.592553i
$760$		0			0
$761$	−227.696	+	131.460i	−0.299206	+	0.172747i	−0.642086	−	0.766632i	$-0.721931\pi$
$761$	−227.696	+	131.460i	−0.299206	+	0.172747i	0.342880	+	0.939379i	$0.388598\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	678.366	−	905.855i	0.886753	−	1.18412i
$766$		0			0
$767$	1133.20	+	654.256i	1.47745	+	0.853006i
$768$		0			0
$769$	−1415.55			−1.84077			−0.920384	−	0.391016i	$-0.872124\pi$
$769$	−1415.55			−1.84077			−0.920384	+	0.391016i	$0.872124\pi$
$770$		0			0
$771$	263.576	−	399.519i	0.341863	−	0.518183i
$772$		0			0
$773$	−31.3146	−	18.0795i	−0.0405105	−	0.0233887i	0.479608	−	0.877483i	$-0.340779\pi$
$773$	−31.3146	−	18.0795i	−0.0405105	−	0.0233887i	−0.520118	+	0.854094i	$0.674112\pi$
$774$		0			0
$775$	−51.9651	−	90.0062i	−0.0670517	−	0.116137i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−587.955	+	339.456i	−0.754756	+	0.435758i
$780$		0			0
$781$	809.959	−	1402.89i	1.03708	−	1.79627i
$782$		0			0
$783$	−86.1940	−	15.5748i	−0.110082	−	0.0198912i
$784$		0			0
$785$			883.620i			1.12563i
$786$		0			0
$787$	70.9813	−	122.943i	0.0901922	−	0.156218i	−0.817400	−	0.576071i	$-0.804585\pi$
$787$	70.9813	−	122.943i	0.0901922	−	0.156218i	0.907592	+	0.419853i	$0.137919\pi$
$788$		0			0
$789$	1043.61	+	62.2613i	1.32270	+	0.0789117i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−175.376	−	303.760i	−0.221155	−	0.383052i
$794$		0			0
$795$	547.259	−	273.877i	0.688376	−	0.344500i
$796$		0			0
$797$			811.299i			1.01794i	0.860784	+	0.508971i	$0.169974\pi$
$797$			811.299i			1.01794i	−0.860784	+	0.508971i	$0.830026\pi$
$798$		0			0
$799$	−943.517			−1.18087
$800$		0			0
$801$	−160.813	+	1342.97i	−0.200766	+	1.67661i
$802$		0			0
$803$	116.208	−	67.0927i	0.144717	−	0.0835526i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−895.569	−	53.4291i	−1.10975	−	0.0662070i
$808$		0			0
$809$	823.775	+	475.607i	1.01826	+	0.587895i	0.913600	−	0.406613i	$-0.133290\pi$
$809$	823.775	+	475.607i	1.01826	+	0.587895i	0.104663	+	0.994508i	$0.466624\pi$
$810$		0			0
$811$	518.407			0.639220			0.319610	−	0.947549i	$-0.396448\pi$
$811$	518.407			0.639220			0.319610	+	0.947549i	$0.396448\pi$
$812$		0			0
$813$	−37.1724	−	24.5239i	−0.0457225	−	0.0301647i
$814$		0			0
$815$	−1.27611	−	0.736765i	−0.00156578	−	0.000904006i
$816$		0			0
$817$	303.354	+	525.424i	0.371302	+	0.643114i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1116.66	+	644.701i	−1.36012	+	0.785263i	−0.989639	−	0.143579i	$-0.954139\pi$
$821$	−1116.66	+	644.701i	−1.36012	+	0.785263i	−0.370477	+	0.928842i	$0.620806\pi$
$822$		0			0
$823$	−251.248	+	435.175i	−0.305283	+	0.528766i	−0.977324	−	0.211748i	$-0.932085\pi$
$823$	−251.248	+	435.175i	−0.305283	+	0.528766i	0.672041	+	0.740514i	$0.265418\pi$
$824$		0			0
$825$	−349.301	+	529.458i	−0.423395	+	0.641767i
$826$		0			0
$827$		−	1533.34i		−	1.85409i	−0.374946	−	0.927047i	$-0.622339\pi$
$827$		−	1533.34i		−	1.85409i	0.374946	−	0.927047i	$-0.377661\pi$
$828$		0			0
$829$	559.031	−	968.271i	0.674344	−	1.16800i	−0.302316	−	0.953208i	$-0.597760\pi$
$829$	559.031	−	968.271i	0.674344	−	1.16800i	0.976660	−	0.214791i	$-0.0689070\pi$
$830$		0			0
$831$	63.0635	−	1057.06i	0.0758886	−	1.27203i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−232.483	−	402.672i	−0.278423	−	0.482242i
$836$		0			0
$837$	−174.878	−	148.006i	−0.208934	−	0.176829i
$838$		0			0
$839$			1008.87i			1.20246i	0.799074	+	0.601232i	$0.205323\pi$
$839$			1008.87i			1.20246i	−0.799074	+	0.601232i	$0.794677\pi$
$840$		0			0
$841$	830.476			0.987486
$842$		0			0
$843$	−79.5603	−	158.977i	−0.0943776	−	0.188584i
$844$		0			0
$845$	−1068.91	+	617.133i	−1.26498	+	0.730335i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	8.49388	−	142.373i	0.0100046	−	0.167695i
$850$		0			0
$851$	1138.48	+	657.304i	1.33782	+	0.772390i
$852$		0			0
$853$	389.811			0.456988			0.228494	−	0.973545i	$-0.426620\pi$
$853$	389.811			0.456988			0.228494	+	0.973545i	$0.426620\pi$
$854$		0			0
$855$	615.883	−	263.607i	0.720331	−	0.308312i
$856$		0			0
$857$	379.038	+	218.838i	0.442285	+	0.255353i	0.704566	−	0.709638i	$-0.251142\pi$
$857$	379.038	+	218.838i	0.442285	+	0.255353i	−0.262282	+	0.964991i	$0.584475\pi$
$858$		0			0
$859$	−581.142	−	1006.57i	−0.676533	−	1.17179i	−0.976018	−	0.217689i	$-0.930148\pi$
$859$	−581.142	−	1006.57i	−0.676533	−	1.17179i	0.299485	−	0.954101i	$-0.403185\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−156.222	+	90.1947i	−0.181022	+	0.104513i	−0.587773	−	0.809026i	$-0.699995\pi$
$863$	−156.222	+	90.1947i	−0.181022	+	0.104513i	0.406751	+	0.913539i	$0.366662\pi$
$864$		0			0
$865$	−521.348	+	903.002i	−0.602715	+	1.04393i
$866$		0			0
$867$	339.302	+	223.849i	0.391351	+	0.258188i
$868$		0			0
$869$			1812.42i			2.08564i
$870$		0			0
$871$	−635.826	+	1101.28i	−0.729995	+	1.26439i
$872$		0			0
$873$	1018.49	−	1360.05i	1.16666	−	1.55790i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−555.080	−	961.426i	−0.632930	−	1.09627i	−0.986950	−	0.161029i	$-0.948519\pi$
$877$	−555.080	−	961.426i	−0.632930	−	1.09627i	0.354020	−	0.935238i	$-0.384815\pi$
$878$		0			0
$879$	−518.210	−	1035.48i	−0.589545	−	1.17802i
$880$		0			0
$881$		−	1491.08i		−	1.69249i	−0.532794	−	0.846245i	$-0.678858\pi$
$881$		−	1491.08i		−	1.69249i	0.532794	−	0.846245i	$-0.321142\pi$
$882$		0			0
$883$	334.027			0.378287			0.189143	−	0.981949i	$-0.439429\pi$
$883$	334.027			0.378287			0.189143	+	0.981949i	$0.439429\pi$
$884$		0			0
$885$	−1111.97	+	556.490i	−1.25647	+	0.628802i
$886$		0			0
$887$	−198.223	+	114.444i	−0.223476	+	0.129024i	−0.607559	−	0.794275i	$-0.707851\pi$
$887$	−198.223	+	114.444i	−0.223476	+	0.129024i	0.384083	+	0.923299i	$0.374518\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−330.132	+	1358.71i	−0.370518	+	1.52493i
$892$		0			0
$893$	−483.698	−	279.263i	−0.541655	−	0.312725i
$894$		0			0
$895$	−453.933			−0.507188
$896$		0			0
$897$	−617.690	+	936.272i	−0.688618	+	1.04378i
$898$		0			0
$899$	−23.8389	−	13.7634i	−0.0265172	−	0.0153097i
$900$		0			0
$901$	344.317	+	596.375i	0.382150	+	0.661904i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−522.333	+	301.569i	−0.577163	+	0.333225i
$906$		0			0
$907$	−461.228	+	798.870i	−0.508520	+	0.880783i	0.491431	+	0.870916i	$0.336474\pi$
$907$	−461.228	+	798.870i	−0.508520	+	0.880783i	−0.999951	+	0.00986628i	$0.996859\pi$
$908$		0			0
$909$	340.597	−	145.780i	0.374694	−	0.160374i
$910$		0			0
$911$		−	1277.11i		−	1.40188i	−0.713220	−	0.700940i	$-0.752764\pi$
$911$		−	1277.11i		−	1.40188i	0.713220	−	0.700940i	$-0.247236\pi$
$912$		0			0
$913$	441.215	−	764.207i	0.483259	−	0.837029i
$914$		0			0
$915$	332.720	+	19.8498i	0.363628	+	0.0216938i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−647.704	−	1121.86i	−0.704792	−	1.22074i	−0.966767	−	0.255661i	$-0.917707\pi$
$919$	−647.704	−	1121.86i	−0.704792	−	1.22074i	0.261975	−	0.965075i	$-0.415626\pi$
$920$		0			0
$921$	−717.533	+	359.091i	−0.779080	+	0.389893i
$922$		0			0
$923$			1808.09i			1.95892i
$924$		0			0
$925$	−829.759			−0.897036
$926$		0			0
$927$	774.034	+	92.6866i	0.834988	+	0.0999856i
$928$		0			0
$929$	−795.758	+	459.431i	−0.856574	+	0.494543i	−0.862864	−	0.505437i	$-0.831331\pi$
$929$	−795.758	+	459.431i	−0.856574	+	0.494543i	0.00628921	+	0.999980i	$0.497998\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−205.834	−	12.2799i	−0.220616	−	0.0131618i
$934$		0			0
$935$	−1879.83	−	1085.32i	−2.01052	−	1.16077i
$936$		0			0
$937$	1066.99			1.13873			0.569365	−	0.822085i	$-0.307189\pi$
$937$	1066.99			1.13873			0.569365	+	0.822085i	$0.307189\pi$
$938$		0			0
$939$	−251.390	−	165.850i	−0.267721	−	0.176624i
$940$		0			0
$941$	751.632	+	433.955i	0.798759	+	0.461164i	0.843037	−	0.537856i	$-0.180765\pi$
$941$	751.632	+	433.955i	0.798759	+	0.461164i	−0.0442781	+	0.999019i	$0.514099\pi$
$942$		0			0
$943$	540.098	+	935.476i	0.572744	+	0.992022i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	30.3087	−	17.4988i	0.0320050	−	0.0184781i	−0.483912	−	0.875117i	$-0.660785\pi$
$947$	30.3087	−	17.4988i	0.0320050	−	0.0184781i	0.515917	+	0.856638i	$0.327451\pi$
$948$		0			0
$949$	−74.8861	+	129.707i	−0.0789106	+	0.136677i
$950$		0			0
$951$	308.636	−	467.818i	0.324538	−	0.491923i
$952$		0			0
$953$			482.989i			0.506809i	0.967360	+	0.253405i	$0.0815504\pi$
$953$			482.989i			0.506809i	−0.967360	+	0.253405i	$0.918450\pi$
$954$		0			0
$955$	56.2174	−	97.3714i	0.0588664	−	0.101960i
$956$		0			0
$957$	−10.0050	+	167.702i	−0.0104545	+	0.175237i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	444.500	+	769.897i	0.462539	+	0.801141i
$962$		0			0
$963$	158.187	−	1321.04i	0.164265	−	1.37179i
$964$		0			0
$965$		−	1283.13i		−	1.32967i
$966$		0			0
$967$	−567.394			−0.586757			−0.293378	−	0.955996i	$-0.594780\pi$
$967$	−567.394			−0.586757			−0.293378	+	0.955996i	$0.594780\pi$
$968$		0			0
$969$	337.380	+	674.149i	0.348173	+	0.695716i
$970$		0			0
$971$	−774.869	+	447.371i	−0.798012	+	0.460732i	−0.842775	−	0.538265i	$-0.819080\pi$
$971$	−774.869	+	447.371i	−0.798012	+	0.460732i	0.0447638	+	0.998998i	$0.485746\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	42.1627	−	706.723i	0.0432438	−	0.724844i
$976$		0			0
$977$	811.533	+	468.539i	0.830637	+	0.479569i	0.854071	−	0.520157i	$-0.174126\pi$
$977$	811.533	+	468.539i	0.830637	+	0.479569i	−0.0234335	+	0.999725i	$0.507460\pi$
$978$		0			0
$979$	2594.25			2.64990
$980$		0			0
$981$	85.8967	+	200.686i	0.0875603	+	0.204573i
$982$		0			0
$983$	1569.53	+	906.170i	1.59668	+	0.921841i	0.992122	+	0.125276i	$0.0399817\pi$
$983$	1569.53	+	906.170i	1.59668	+	0.921841i	0.604553	+	0.796565i	$0.293352\pi$
$984$		0			0
$985$	−332.862	−	576.534i	−0.337931	−	0.585314i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	835.986	−	482.657i	0.845284	−	0.488025i
$990$		0			0
$991$	494.455	−	856.422i	0.498946	−	0.864200i	−0.501053	−	0.865416i	$-0.667054\pi$
$991$	494.455	−	856.422i	0.498946	−	0.864200i	0.999999	+	0.00121664i	$0.000387268\pi$
$992$		0			0
$993$	−367.452	−	242.420i	−0.370042	−	0.244129i
$994$		0			0
$995$			1100.38i			1.10591i
$996$		0			0
$997$	692.821	−	1200.00i	0.694906	−	1.20361i	−0.275307	−	0.961356i	$-0.588779\pi$
$997$	692.821	−	1200.00i	0.694906	−	1.20361i	0.970212	−	0.242256i	$-0.0778873\pi$
$998$		0			0
$999$	−1721.44	+	618.311i	−1.72316	+	0.618930i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.p.i.557.7		16
3.2	odd	2	inner	588.3.p.i.557.4		16
7.2	even	3	inner	588.3.p.i.569.4		16
7.3	odd	6		588.3.c.j.197.8	yes	8
7.4	even	3		588.3.c.j.197.1	✓	8
7.5	odd	6	inner	588.3.p.i.569.5		16
7.6	odd	2	inner	588.3.p.i.557.2		16
21.2	odd	6	inner	588.3.p.i.569.7		16
21.5	even	6	inner	588.3.p.i.569.2		16
21.11	odd	6		588.3.c.j.197.2	yes	8
21.17	even	6		588.3.c.j.197.7	yes	8
21.20	even	2	inner	588.3.p.i.557.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.3.c.j.197.1	✓	8	7.4	even	3
588.3.c.j.197.2	yes	8	21.11	odd	6
588.3.c.j.197.7	yes	8	21.17	even	6
588.3.c.j.197.8	yes	8	7.3	odd	6
588.3.p.i.557.2		16	7.6	odd	2	inner
588.3.p.i.557.4		16	3.2	odd	2	inner
588.3.p.i.557.5		16	21.20	even	2	inner
588.3.p.i.557.7		16	1.1	even	1	trivial
588.3.p.i.569.2		16	21.5	even	6	inner
588.3.p.i.569.4		16	7.2	even	3	inner
588.3.p.i.569.5		16	7.5	odd	6	inner
588.3.p.i.569.7		16	21.2	odd	6	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(2.68280 - 1.34261i) q^{3} +(-5.28547 + 3.05157i) q^{5} +(5.39478 - 7.20391i) q^{9} +(-14.9496 - 8.63114i) q^{11} +19.2674 q^{13} +(-10.0828 + 15.2831i) q^{15} +(-17.8430 - 10.3017i) q^{17} +(-6.09819 - 10.5624i) q^{19} +(-16.8055 + 9.70264i) q^{23} +(6.12414 - 10.6073i) q^{25} +(4.80102 - 26.5697i) q^{27} -3.24407i q^{29} +(4.24264 - 7.34847i) q^{31} +(-51.6949 - 3.08409i) q^{33} +(-33.8724 - 58.6688i) q^{37} +(51.6906 - 25.8687i) q^{39} -55.6650i q^{41} -49.7449 q^{43} +(-6.53072 + 54.5386i) q^{45} +(39.6591 - 22.8972i) q^{47} +(-61.7002 - 3.68100i) q^{51} +(-28.9456 - 16.7117i) q^{53} +105.354 q^{55} +(-30.5414 - 20.1492i) q^{57} +(58.8145 + 33.9565i) q^{59} +(-9.10218 - 15.7654i) q^{61} +(-101.838 + 58.7959i) q^{65} +(-33.0000 + 57.1577i) q^{67} +(-32.0587 + 48.5934i) q^{69} +93.8415i q^{71} +(-3.88667 + 6.73190i) q^{73} +(2.18828 - 36.6796i) q^{75} +(-52.4966 - 90.9267i) q^{79} +(-22.7927 - 77.7270i) q^{81} +51.1190i q^{83} +125.745 q^{85} +(-4.35553 - 8.70317i) q^{87} +(-130.150 + 75.1423i) q^{89} +(1.51598 - 25.4107i) q^{93} +(64.4636 + 37.2181i) q^{95} +188.793 q^{97} +(-142.828 + 61.1323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{9} - 64 q^{15} - 48 q^{25} - 104 q^{37} + 240 q^{39} + 80 q^{43} + 44 q^{51} - 440 q^{57} - 528 q^{67} - 256 q^{79} + 496 q^{81} + 1136 q^{85} - 24 q^{93} - 1312 q^{99}+O(q^{100}) \) 16 * q - 4 * q^9 - 64 * q^15 - 48 * q^25 - 104 * q^37 + 240 * q^39 + 80 * q^43 + 44 * q^51 - 440 * q^57 - 528 * q^67 - 256 * q^79 + 496 * q^81 + 1136 * q^85 - 24 * q^93 - 1312 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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