LMFDB - Embedded newform 684.2.l.a.121.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(121,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("684.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.19
Character	$\chi$	$=$	684.121
Dual form			684.2.l.a.277.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72309 + 0.176004i) q^{3} +1.40487 q^{5} +(1.81436 + 3.14256i) q^{7} +(2.93805 + 0.606538i) q^{9} +(-2.95551 - 5.11909i) q^{11} +(2.62282 + 4.54285i) q^{13} +(2.42071 + 0.247262i) q^{15} +(-0.0900422 - 0.155958i) q^{17} +(-2.73055 - 3.39766i) q^{19} +(2.57319 + 5.73423i) q^{21} +(1.41468 + 2.45030i) q^{23} -3.02634 q^{25} +(4.95575 + 1.56222i) q^{27} -1.35158 q^{29} +(-1.44710 + 2.50646i) q^{31} +(-4.19162 - 9.34081i) q^{33} +(2.54894 + 4.41489i) q^{35} -5.72791 q^{37} +(3.71978 + 8.28935i) q^{39} -0.130472 q^{41} +(5.73992 - 9.94183i) q^{43} +(4.12757 + 0.852107i) q^{45} +7.47588 q^{47} +(-3.08379 + 5.34129i) q^{49} +(-0.127701 - 0.284576i) q^{51} +(3.35526 - 5.81148i) q^{53} +(-4.15210 - 7.19165i) q^{55} +(-4.10697 - 6.33505i) q^{57} -0.859576 q^{59} -5.00809 q^{61} +(3.42458 + 10.3335i) q^{63} +(3.68472 + 6.38211i) q^{65} +(-0.409661 - 0.709554i) q^{67} +(2.00635 + 4.47106i) q^{69} +(-4.84083 - 8.38457i) q^{71} +(5.48215 + 9.49536i) q^{73} +(-5.21465 - 0.532647i) q^{75} +(10.7247 - 18.5757i) q^{77} +(-2.42611 + 4.20215i) q^{79} +(8.26422 + 3.56407i) q^{81} +(-5.76363 - 9.98290i) q^{83} +(-0.126497 - 0.219100i) q^{85} +(-2.32889 - 0.237883i) q^{87} +(-5.84756 + 10.1283i) q^{89} +(-9.51747 + 16.4847i) q^{91} +(-2.93463 + 4.06415i) q^{93} +(-3.83606 - 4.77327i) q^{95} +(-1.15391 + 1.99864i) q^{97} +(-5.57850 - 16.8328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{3} - q^{7} + q^{9} - q^{11} - q^{13} + 10 q^{15} + 5 q^{17} + q^{19} + 6 q^{21} - 4 q^{23} + 40 q^{25} + 7 q^{27} + 18 q^{29} + 2 q^{31} - 7 q^{33} - 6 q^{35} + 2 q^{37} + 3 q^{39} + 50 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) $ 40 * q + q^3 - q^7 + q^9 - q^11 - q^13 + 10 * q^15 + 5 * q^17 + q^19 + 6 * q^21 - 4 * q^23 + 40 * q^25 + 7 * q^27 + 18 * q^29 + 2 * q^31 - 7 * q^33 - 6 * q^35 + 2 * q^37 + 3 * q^39 + 50 * q^41 + 8 * q^43 + 44 * q^45 + 20 * q^47 - 21 * q^49 - 17 * q^51 - 8 * q^53 + 15 * q^57 + 44 * q^59 + 14 * q^61 - 26 * q^63 - 6 * q^65 - 10 * q^67 + 38 * q^69 - 5 * q^71 - 10 * q^73 - 10 * q^77 - q^79 + q^81 + q^83 - 52 * q^87 - 34 * q^89 + 16 * q^91 + 46 * q^93 - 54 * q^95 - q^97 - 8 * q^99

Character values

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

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

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
$3$	1.72309	+	0.176004i	0.994824	+	0.101616i
$3$	1.72309	+	0.176004i	0.994824	+	0.101616i
$4$		0			0
$5$	1.40487			0.628276			0.314138	−	0.949377i	$-0.398284\pi$
$5$	1.40487			0.628276			0.314138	+	0.949377i	$0.398284\pi$
$6$		0			0
$7$	1.81436	+	3.14256i	0.685763	+	1.18778i	0.973196	+	0.229976i	$0.0738647\pi$
$7$	1.81436	+	3.14256i	0.685763	+	1.18778i	−0.287433	+	0.957801i	$0.592802\pi$
$8$		0			0
$9$	2.93805	+	0.606538i	0.979348	+	0.202179i
$10$		0			0
$11$	−2.95551	−	5.11909i	−0.891120	−	1.54346i	−0.838535	−	0.544848i	$-0.816587\pi$
$11$	−2.95551	−	5.11909i	−0.891120	−	1.54346i	−0.0525849	−	0.998616i	$-0.516746\pi$
$12$		0			0
$13$	2.62282	+	4.54285i	0.727439	+	1.25996i	0.957962	+	0.286894i	$0.0926229\pi$
$13$	2.62282	+	4.54285i	0.727439	+	1.25996i	−0.230523	+	0.973067i	$0.574044\pi$
$14$		0			0
$15$	2.42071	+	0.247262i	0.625024	+	0.0638428i
$16$		0			0
$17$	−0.0900422	−	0.155958i	−0.0218384	−	0.0378253i	0.854900	−	0.518793i	$-0.173619\pi$
$17$	−0.0900422	−	0.155958i	−0.0218384	−	0.0378253i	−0.876738	+	0.480968i	$0.840285\pi$
$18$		0			0
$19$	−2.73055	−	3.39766i	−0.626431	−	0.779477i
$19$	−2.73055	−	3.39766i	−0.626431	−	0.779477i
$20$		0			0
$21$	2.57319	+	5.73423i	0.561517	+	1.25131i
$22$		0			0
$23$	1.41468	+	2.45030i	0.294981	+	0.510922i	0.974980	−	0.222290i	$-0.0713533\pi$
$23$	1.41468	+	2.45030i	0.294981	+	0.510922i	−0.679999	+	0.733213i	$0.738020\pi$
$24$		0			0
$25$	−3.02634			−0.605269
$26$		0			0
$27$	4.95575	+	1.56222i	0.953734	+	0.300650i
$28$		0			0
$29$	−1.35158			−0.250982			−0.125491	−	0.992095i	$-0.540051\pi$
$29$	−1.35158			−0.250982			−0.125491	+	0.992095i	$0.540051\pi$
$30$		0			0
$31$	−1.44710	+	2.50646i	−0.259908	+	0.450173i	−0.966217	−	0.257730i	$-0.917025\pi$
$31$	−1.44710	+	2.50646i	−0.259908	+	0.450173i	0.706309	+	0.707903i	$0.250359\pi$
$32$		0			0
$33$	−4.19162	−	9.34081i	−0.729667	−	1.62603i
$34$		0			0
$35$	2.54894	+	4.41489i	0.430849	+	0.746252i
$36$		0			0
$37$	−5.72791			−0.941663			−0.470831	−	0.882223i	$-0.656046\pi$
$37$	−5.72791			−0.941663			−0.470831	+	0.882223i	$0.656046\pi$
$38$		0			0
$39$	3.71978	+	8.28935i	0.595642	+	1.32736i
$40$		0			0
$41$	−0.130472			−0.0203762			−0.0101881	−	0.999948i	$-0.503243\pi$
$41$	−0.130472			−0.0203762			−0.0101881	+	0.999948i	$0.503243\pi$
$42$		0			0
$43$	5.73992	−	9.94183i	0.875329	−	1.51611i	0.0189180	−	0.999821i	$-0.493978\pi$
$43$	5.73992	−	9.94183i	0.875329	−	1.51611i	0.856411	−	0.516294i	$-0.172689\pi$
$44$		0			0
$45$	4.12757	+	0.852107i	0.615302	+	0.127025i
$46$		0			0
$47$	7.47588			1.09047			0.545235	−	0.838283i	$-0.316441\pi$
$47$	7.47588			1.09047			0.545235	+	0.838283i	$0.316441\pi$
$48$		0			0
$49$	−3.08379	+	5.34129i	−0.440542	+	0.763041i
$50$		0			0
$51$	−0.127701	−	0.284576i	−0.0178817	−	0.0398486i
$52$		0			0
$53$	3.35526	−	5.81148i	0.460880	−	0.798268i	−0.538125	−	0.842865i	$-0.680867\pi$
$53$	3.35526	−	5.81148i	0.460880	−	0.798268i	0.999005	+	0.0445971i	$0.0142004\pi$
$54$		0			0
$55$	−4.15210	−	7.19165i	−0.559869	−	0.969722i
$56$		0			0
$57$	−4.10697	−	6.33505i	−0.543981	−	0.839097i
$58$		0			0
$59$	−0.859576			−0.111907			−0.0559536	−	0.998433i	$-0.517820\pi$
$59$	−0.859576			−0.111907			−0.0559536	+	0.998433i	$0.517820\pi$
$60$		0			0
$61$	−5.00809			−0.641220			−0.320610	−	0.947211i	$-0.603888\pi$
$61$	−5.00809			−0.641220			−0.320610	+	0.947211i	$0.603888\pi$
$62$		0			0
$63$	3.42458	+	10.3335i	0.431457	+	1.30189i
$64$		0			0
$65$	3.68472	+	6.38211i	0.457033	+	0.791604i
$66$		0			0
$67$	−0.409661	−	0.709554i	−0.0500481	−	0.0866858i	0.839916	−	0.542716i	$-0.182604\pi$
$67$	−0.409661	−	0.709554i	−0.0500481	−	0.0866858i	−0.889964	+	0.456031i	$0.849271\pi$
$68$		0			0
$69$	2.00635	+	4.47106i	0.241536	+	0.538252i
$70$		0			0
$71$	−4.84083	−	8.38457i	−0.574501	−	0.995065i	−0.996096	−	0.0882807i	$-0.971863\pi$
$71$	−4.84083	−	8.38457i	−0.574501	−	0.995065i	0.421595	−	0.906784i	$-0.361471\pi$
$72$		0			0
$73$	5.48215	+	9.49536i	0.641637	+	1.11135i	0.985067	+	0.172170i	$0.0550778\pi$
$73$	5.48215	+	9.49536i	0.641637	+	1.11135i	−0.343430	+	0.939178i	$0.611589\pi$
$74$		0			0
$75$	−5.21465	−	0.532647i	−0.602136	−	0.0615048i
$76$		0			0
$77$	10.7247	−	18.5757i	1.22219	−	2.11690i
$78$		0			0
$79$	−2.42611	+	4.20215i	−0.272959	+	0.472779i	−0.969618	−	0.244623i	$-0.921336\pi$
$79$	−2.42611	+	4.20215i	−0.272959	+	0.472779i	0.696659	+	0.717402i	$0.254669\pi$
$80$		0			0
$81$	8.26422	+	3.56407i	0.918247	+	0.396008i
$82$		0			0
$83$	−5.76363	−	9.98290i	−0.632641	−	1.09577i	−0.987010	−	0.160660i	$-0.948638\pi$
$83$	−5.76363	−	9.98290i	−0.632641	−	1.09577i	0.354369	−	0.935106i	$-0.384696\pi$
$84$		0			0
$85$	−0.126497	−	0.219100i	−0.0137206	−	0.0237647i
$86$		0			0
$87$	−2.32889	−	0.237883i	−0.249683	−	0.0255037i
$88$		0			0
$89$	−5.84756	+	10.1283i	−0.619840	+	1.07360i	0.369674	+	0.929162i	$0.379469\pi$
$89$	−5.84756	+	10.1283i	−0.619840	+	1.07360i	−0.989514	+	0.144434i	$0.953864\pi$
$90$		0			0
$91$	−9.51747	+	16.4847i	−0.997702	+	1.72807i
$92$		0			0
$93$	−2.93463	+	4.06415i	−0.304307	+	0.421432i
$94$		0			0
$95$	−3.83606	−	4.77327i	−0.393572	−	0.489727i
$96$		0			0
$97$	−1.15391	+	1.99864i	−0.117162	+	0.202931i	−0.918642	−	0.395091i	$-0.870713\pi$
$97$	−1.15391	+	1.99864i	−0.117162	+	0.202931i	0.801480	+	0.598022i	$0.204046\pi$
$98$		0			0
$99$	−5.57850	−	16.8328i	−0.560660	−	1.69176i
$100$		0			0
$101$	−8.62235			−0.857956			−0.428978	−	0.903315i	$-0.641126\pi$
$101$	−8.62235			−0.857956			−0.428978	+	0.903315i	$0.641126\pi$
$102$		0			0
$103$	−0.960084	+	1.66291i	−0.0945999	+	0.163852i	−0.909442	−	0.415832i	$-0.863491\pi$
$103$	−0.960084	+	1.66291i	−0.0945999	+	0.163852i	0.814842	+	0.579684i	$0.196824\pi$
$104$		0			0
$105$	3.61500	+	8.05585i	0.352788	+	0.786170i
$106$		0			0
$107$	3.22783			0.312046			0.156023	−	0.987753i	$-0.450133\pi$
$107$	3.22783			0.312046			0.156023	+	0.987753i	$0.450133\pi$
$108$		0			0
$109$	1.70495	+	2.95305i	0.163304	+	0.282851i	0.936052	−	0.351862i	$-0.114451\pi$
$109$	1.70495	+	2.95305i	0.163304	+	0.282851i	−0.772748	+	0.634714i	$0.781118\pi$
$110$		0			0
$111$	−9.86968	−	1.00813i	−0.936788	−	0.0956877i
$112$		0			0
$113$	8.09494	−	14.0208i	0.761507	−	1.31897i	−0.180566	−	0.983563i	$-0.557793\pi$
$113$	8.09494	−	14.0208i	0.761507	−	1.31897i	0.942073	−	0.335407i	$-0.108874\pi$
$114$		0			0
$115$	1.98744	+	3.44235i	0.185330	+	0.321000i
$116$		0			0
$117$	4.95054	+	14.9380i	0.457678	+	1.38101i
$118$		0			0
$119$	0.326738	−	0.565926i	0.0299520	−	0.0518784i
$120$		0			0
$121$	−11.9701	+	20.7328i	−1.08819	+	1.88480i
$122$		0			0
$123$	−0.224814	−	0.0229635i	−0.0202708	−	0.00207054i
$124$		0			0
$125$	−11.2760			−1.00855
$126$		0			0
$127$	8.05593	−	13.9533i	0.714848	−	1.23815i	−0.248170	−	0.968717i	$-0.579829\pi$
$127$	8.05593	−	13.9533i	0.714848	−	1.23815i	0.963018	−	0.269437i	$-0.0868376\pi$
$128$		0			0
$129$	11.6402	−	16.1204i	1.02486	−	1.41932i
$130$		0			0
$131$	2.93443			0.256382			0.128191	−	0.991749i	$-0.459083\pi$
$131$	2.93443			0.256382			0.128191	+	0.991749i	$0.459083\pi$
$132$		0			0
$133$	5.72316	−	14.7455i	0.496261	−	1.27860i
$134$		0			0
$135$	6.96218	+	2.19472i	0.599209	+	0.188891i
$136$		0			0
$137$	−16.6830			−1.42533			−0.712664	−	0.701506i	$-0.752511\pi$
$137$	−16.6830			−1.42533			−0.712664	+	0.701506i	$0.752511\pi$
$138$		0			0
$139$	−4.23771	−	7.33993i	−0.359438	−	0.622564i	0.628429	−	0.777867i	$-0.283698\pi$
$139$	−4.23771	−	7.33993i	−0.359438	−	0.622564i	−0.987867	+	0.155302i	$0.950365\pi$
$140$		0			0
$141$	12.8816	+	1.31578i	1.08482	+	0.110809i
$142$		0			0
$143$	15.5035	−	26.8529i	1.29647	−	2.24555i
$144$		0			0
$145$	−1.89879			−0.157686
$146$		0			0
$147$	−6.25373	+	8.66074i	−0.515799	+	0.714326i
$148$		0			0
$149$	15.9847			1.30952			0.654758	−	0.755838i	$-0.272770\pi$
$149$	15.9847			1.30952			0.654758	+	0.755838i	$0.272770\pi$
$150$		0			0
$151$	−6.91211	−	11.9721i	−0.562500	−	0.974278i	−0.997277	−	0.0737405i	$-0.976506\pi$
$151$	−6.91211	−	11.9721i	−0.562500	−	0.974278i	0.434778	−	0.900538i	$-0.356827\pi$
$152$		0			0
$153$	−0.169954	−	0.512825i	−0.0137399	−	0.0414594i
$154$		0			0
$155$	−2.03299	+	3.52125i	−0.163294	+	0.282833i
$156$		0			0
$157$	−7.16778			−0.572051			−0.286025	−	0.958222i	$-0.592334\pi$
$157$	−7.16778			−0.572051			−0.286025	+	0.958222i	$0.592334\pi$
$158$		0			0
$159$	6.80424	−	9.42314i	0.539611	−	0.747303i
$160$		0			0
$161$	−5.13347	+	8.89143i	−0.404574	+	0.700743i
$162$		0			0
$163$	−19.6317			−1.53768			−0.768838	−	0.639444i	$-0.779165\pi$
$163$	−19.6317			−1.53768			−0.768838	+	0.639444i	$0.779165\pi$
$164$		0			0
$165$	−5.88867	−	13.1226i	−0.458432	−	1.02159i
$166$		0			0
$167$	8.72959	+	15.1201i	0.675516	+	1.17003i	0.976318	+	0.216341i	$0.0694124\pi$
$167$	8.72959	+	15.1201i	0.675516	+	1.17003i	−0.300802	+	0.953687i	$0.597254\pi$
$168$		0			0
$169$	−7.25835	+	12.5718i	−0.558335	+	0.967064i
$170$		0			0
$171$	−5.96167	−	11.6387i	−0.455900	−	0.890031i
$172$		0			0
$173$	−9.84582	+	17.0535i	−0.748564	+	1.29655i	0.199947	+	0.979807i	$0.435923\pi$
$173$	−9.84582	+	17.0535i	−0.748564	+	1.29655i	−0.948511	+	0.316744i	$0.897410\pi$
$174$		0			0
$175$	−5.49087	−	9.51047i	−0.415071	−	0.718924i
$176$		0			0
$177$	−1.48112	−	0.151288i	−0.111328	−	0.0113715i
$178$		0			0
$179$	−15.5819			−1.16464			−0.582322	−	0.812958i	$-0.697856\pi$
$179$	−15.5819			−1.16464			−0.582322	+	0.812958i	$0.697856\pi$
$180$		0			0
$181$	4.97858	−	8.62316i	0.370055	−	0.640955i	−0.619518	−	0.784982i	$-0.712672\pi$
$181$	4.97858	−	8.62316i	0.370055	−	0.640955i	0.989574	+	0.144028i	$0.0460054\pi$
$182$		0			0
$183$	−8.62936	−	0.881442i	−0.637901	−	0.0651580i
$184$		0			0
$185$	−8.04696			−0.591624
$186$		0			0
$187$	−0.532241	+	0.921868i	−0.0389213	+	0.0674137i
$188$		0			0
$189$	4.08212	+	18.4082i	0.296931	+	1.33900i
$190$		0			0
$191$	−13.6381	−	23.6219i	−0.986818	−	1.70922i	−0.633562	−	0.773692i	$-0.718408\pi$
$191$	−13.6381	−	23.6219i	−0.986818	−	1.70922i	−0.353256	−	0.935527i	$-0.614926\pi$
$192$		0			0
$193$	6.05927			0.436156			0.218078	−	0.975931i	$-0.430021\pi$
$193$	6.05927			0.436156			0.218078	+	0.975931i	$0.430021\pi$
$194$		0			0
$195$	5.22580	+	11.6455i	0.374228	+	0.833948i
$196$		0			0
$197$	−20.6193			−1.46907			−0.734534	−	0.678572i	$-0.762599\pi$
$197$	−20.6193			−1.46907			−0.734534	+	0.678572i	$0.762599\pi$
$198$		0			0
$199$	−7.27737	+	12.6048i	−0.515879	+	0.893528i	0.483951	+	0.875095i	$0.339201\pi$
$199$	−7.27737	+	12.6048i	−0.515879	+	0.893528i	−0.999830	+	0.0184334i	$0.994132\pi$
$200$		0			0
$201$	−0.580997	−	1.29472i	−0.0409804	−	0.0913228i
$202$		0			0
$203$	−2.45225	−	4.24742i	−0.172114	−	0.298111i
$204$		0			0
$205$	−0.183295			−0.0128019
$206$		0			0
$207$	2.67019	+	8.05714i	0.185591	+	0.560010i
$208$		0			0
$209$	−9.32277	+	24.0198i	−0.644870	+	1.66148i
$210$		0			0
$211$	0.399930			0.0275323			0.0137662	−	0.999905i	$-0.495618\pi$
$211$	0.399930			0.0275323			0.0137662	+	0.999905i	$0.495618\pi$
$212$		0			0
$213$	−6.86545	−	15.2993i	−0.470413	−	1.04829i
$214$		0			0
$215$	8.06383	−	13.9670i	0.549949	−	0.952539i
$216$		0			0
$217$	−10.5023			−0.712940
$218$		0			0
$219$	7.77499	+	17.3262i	0.525385	+	1.17080i
$220$		0			0
$221$	0.472329	−	0.818097i	0.0317723	−	0.0550312i
$222$		0			0
$223$	−12.4090	+	21.4930i	−0.830967	+	1.43928i	0.0663044	+	0.997799i	$0.478879\pi$
$223$	−12.4090	+	21.4930i	−0.830967	+	1.43928i	−0.897272	+	0.441478i	$0.854454\pi$
$224$		0			0
$225$	−8.89154	−	1.83559i	−0.592769	−	0.122373i
$226$		0			0
$227$	13.9652	+	24.1884i	0.926903	+	1.60544i	0.788471	+	0.615072i	$0.210873\pi$
$227$	13.9652	+	24.1884i	0.926903	+	1.60544i	0.138432	+	0.990372i	$0.455794\pi$
$228$		0			0
$229$	1.49584	−	2.59088i	0.0988482	−	0.171210i	−0.812360	−	0.583156i	$-0.801818\pi$
$229$	1.49584	−	2.59088i	0.0988482	−	0.171210i	0.911208	+	0.411946i	$0.135151\pi$
$230$		0			0
$231$	21.7490	−	30.1200i	1.43098	−	1.98175i
$232$		0			0
$233$	−4.97555	−	8.61791i	−0.325959	−	0.564578i	0.655747	−	0.754981i	$-0.272354\pi$
$233$	−4.97555	−	8.61791i	−0.325959	−	0.564578i	−0.981706	+	0.190403i	$0.939021\pi$
$234$		0			0
$235$	10.5026			0.685116
$236$		0			0
$237$	−4.91999	+	6.81366i	−0.319588	+	0.442595i
$238$		0			0
$239$	12.9990	−	22.5149i	0.840834	−	1.45637i	−0.0483572	−	0.998830i	$-0.515399\pi$
$239$	12.9990	−	22.5149i	0.840834	−	1.45637i	0.889191	−	0.457536i	$-0.151268\pi$
$240$		0			0
$241$	24.9893			1.60970			0.804851	−	0.593477i	$-0.202245\pi$
$241$	24.9893			1.60970			0.804851	+	0.593477i	$0.202245\pi$
$242$		0			0
$243$	13.6127	+	7.59574i	0.873253	+	0.487267i
$244$		0			0
$245$	−4.33233	+	7.50381i	−0.276782	+	0.479401i
$246$		0			0
$247$	8.27334	−	21.3159i	0.526420	−	1.35630i
$248$		0			0
$249$	−8.17420	−	18.2158i	−0.518019	−	1.15438i
$250$		0			0
$251$	11.0018	−	19.0556i	0.694425	−	1.20278i	−0.275950	−	0.961172i	$-0.588992\pi$
$251$	11.0018	−	19.0556i	0.694425	−	1.20278i	0.970374	−	0.241607i	$-0.0776744\pi$
$252$		0			0
$253$	8.36220	−	14.4838i	0.525727	−	0.910586i
$254$		0			0
$255$	−0.179403	−	0.399792i	−0.0112347	−	0.0250359i
$256$		0			0
$257$	7.72786	+	13.3850i	0.482051	+	0.834936i	0.999788	−	0.0206037i	$-0.00655883\pi$
$257$	7.72786	+	13.3850i	0.482051	+	0.834936i	−0.517737	+	0.855540i	$0.673225\pi$
$258$		0			0
$259$	−10.3925	−	18.0003i	−0.645758	−	1.11848i
$260$		0			0
$261$	−3.97100	−	0.819785i	−0.245799	−	0.0507434i
$262$		0			0
$263$	1.44932	−	2.51030i	0.0893691	−	0.154792i	−0.817876	−	0.575395i	$-0.804848\pi$
$263$	1.44932	−	2.51030i	0.0893691	−	0.154792i	0.907245	+	0.420603i	$0.138182\pi$
$264$		0			0
$265$	4.71370	−	8.16437i	0.289560	−	0.501533i
$266$		0			0
$267$	−11.8585	+	16.4227i	−0.725726	+	1.00505i
$268$		0			0
$269$	1.04169	+	1.80426i	0.0635130	+	0.110008i	0.896033	−	0.443987i	$-0.146436\pi$
$269$	1.04169	+	1.80426i	0.0635130	+	0.110008i	−0.832520	+	0.553994i	$0.813103\pi$
$270$		0			0
$271$	7.60652	+	13.1749i	0.462063	+	0.800317i	0.999064	−	0.0432648i	$-0.0137759\pi$
$271$	7.60652	+	13.1749i	0.462063	+	0.800317i	−0.537000	+	0.843582i	$0.680443\pi$
$272$		0			0
$273$	−19.3008	+	26.7295i	−1.16814	+	1.61774i
$274$		0			0
$275$	8.94439	+	15.4921i	0.539367	+	0.934211i
$276$		0			0
$277$	14.0404	+	24.3187i	0.843607	+	1.46117i	0.886825	+	0.462105i	$0.152906\pi$
$277$	14.0404	+	24.3187i	0.843607	+	1.46117i	−0.0432181	+	0.999066i	$0.513761\pi$
$278$		0			0
$279$	−5.77192	+	6.48637i	−0.345556	+	0.388329i
$280$		0			0
$281$	−3.14530			−0.187633			−0.0938164	−	0.995590i	$-0.529907\pi$
$281$	−3.14530			−0.187633			−0.0938164	+	0.995590i	$0.529907\pi$
$282$		0			0
$283$	−13.0286			−0.774469			−0.387235	−	0.921981i	$-0.626570\pi$
$283$	−13.0286			−0.774469			−0.387235	+	0.921981i	$0.626570\pi$
$284$		0			0
$285$	−5.76975	−	8.89991i	−0.341771	−	0.527185i
$286$		0			0
$287$	−0.236722	−	0.410015i	−0.0139733	−	0.0242024i
$288$		0			0
$289$	8.48378	−	14.6943i	0.499046	−	0.864373i
$290$		0			0
$291$	−2.34006	+	3.24073i	−0.137177	+	0.189975i
$292$		0			0
$293$	−0.891775	+	1.54460i	−0.0520981	+	0.0902365i	−0.890898	−	0.454203i	$-0.849924\pi$
$293$	−0.891775	+	1.54460i	−0.0520981	+	0.0902365i	0.838800	+	0.544439i	$0.183258\pi$
$294$		0			0
$295$	−1.20759			−0.0703087
$296$		0			0
$297$	−6.64960	−	29.9861i	−0.385849	−	1.73997i
$298$		0			0
$299$	−7.42089	+	12.8534i	−0.429161	+	0.743329i
$300$		0			0
$301$	41.6571			2.40107
$302$		0			0
$303$	−14.8570	−	1.51757i	−0.853515	−	0.0871818i
$304$		0			0
$305$	−7.03571			−0.402863
$306$		0			0
$307$	−6.80462	−	11.7859i	−0.388360	−	0.672660i	0.603869	−	0.797084i	$-0.293625\pi$
$307$	−6.80462	−	11.7859i	−0.388360	−	0.672660i	−0.992229	+	0.124424i	$0.960292\pi$
$308$		0			0
$309$	−1.94699	+	2.69637i	−0.110760	+	0.153391i
$310$		0			0
$311$	−4.44015	+	7.69057i	−0.251778	+	0.436092i	−0.964015	−	0.265846i	$-0.914349\pi$
$311$	−4.44015	+	7.69057i	−0.251778	+	0.436092i	0.712237	+	0.701939i	$0.247682\pi$
$312$		0			0
$313$	−5.09526			−0.288001			−0.144001	−	0.989578i	$-0.545997\pi$
$313$	−5.09526			−0.288001			−0.144001	+	0.989578i	$0.545997\pi$
$314$		0			0
$315$	4.81109	+	14.5172i	0.271074	+	0.817950i
$316$		0			0
$317$	32.1676			1.80671			0.903356	−	0.428892i	$-0.141096\pi$
$317$	32.1676			1.80671			0.903356	+	0.428892i	$0.141096\pi$
$318$		0			0
$319$	3.99461	+	6.91886i	0.223655	+	0.387382i
$320$		0			0
$321$	5.56183	+	0.568110i	0.310431	+	0.0317088i
$322$		0			0
$323$	−0.284026	+	0.731783i	−0.0158037	+	0.0407175i
$324$		0			0
$325$	−7.93755	−	13.7482i	−0.440296	−	0.762615i
$326$		0			0
$327$	2.41802	+	5.38844i	0.133717	+	0.297981i
$328$		0			0
$329$	13.5639	+	23.4934i	0.747804	+	1.29523i
$330$		0			0
$331$	1.63433	+	2.83073i	0.0898307	+	0.155591i	0.907439	−	0.420183i	$-0.138034\pi$
$331$	1.63433	+	2.83073i	0.0898307	+	0.155591i	−0.817609	+	0.575774i	$0.804701\pi$
$332$		0			0
$333$	−16.8289	−	3.47420i	−0.922216	−	0.190385i
$334$		0			0
$335$	−0.575520	−	0.996830i	−0.0314440	−	0.0544626i
$336$		0			0
$337$	29.8630			1.62674			0.813370	−	0.581747i	$-0.197630\pi$
$337$	29.8630			1.62674			0.813370	+	0.581747i	$0.197630\pi$
$338$		0			0
$339$	16.4160	−	22.7344i	0.891594	−	1.23476i
$340$		0			0
$341$	17.1077			0.926435
$342$		0			0
$343$	3.02058			0.163096
$344$		0			0
$345$	2.81866	+	6.28125i	0.151752	+	0.338171i
$346$		0			0
$347$	32.6930			1.75505			0.877526	−	0.479530i	$-0.159193\pi$
$347$	32.6930			1.75505			0.877526	+	0.479530i	$0.159193\pi$
$348$		0			0
$349$	4.14348	+	7.17672i	0.221795	+	0.384161i	0.955353	−	0.295466i	$-0.0954750\pi$
$349$	4.14348	+	7.17672i	0.221795	+	0.384161i	−0.733558	+	0.679627i	$0.762142\pi$
$350$		0			0
$351$	5.90107	+	26.6107i	0.314976	+	1.42037i
$352$		0			0
$353$	9.59980	+	16.6273i	0.510946	+	0.884984i	0.999920	+	0.0126858i	$0.00403812\pi$
$353$	9.59980	+	16.6273i	0.510946	+	0.884984i	−0.488974	+	0.872299i	$0.662629\pi$
$354$		0			0
$355$	−6.80073	−	11.7792i	−0.360946	−	0.625176i
$356$		0			0
$357$	0.662602	−	0.917632i	0.0350686	−	0.0485662i
$358$		0			0
$359$	−0.448167	−	0.776248i	−0.0236533	−	0.0409688i	0.853956	−	0.520345i	$-0.174196\pi$
$359$	−0.448167	−	0.776248i	−0.0236533	−	0.0409688i	−0.877610	+	0.479376i	$0.840863\pi$
$360$		0			0
$361$	−4.08820	+	18.5550i	−0.215168	+	0.976577i
$362$		0			0
$363$	−24.2745	+	33.6176i	−1.27408	+	1.76446i
$364$		0			0
$365$	7.70170	+	13.3397i	0.403125	+	0.698234i
$366$		0			0
$367$	10.0806			0.526201			0.263101	−	0.964768i	$-0.415255\pi$
$367$	10.0806			0.526201			0.263101	+	0.964768i	$0.415255\pi$
$368$		0			0
$369$	−0.383331	−	0.0791360i	−0.0199554	−	0.00411965i
$370$		0			0
$371$	24.3506			1.26422
$372$		0			0
$373$	−0.693763	+	1.20163i	−0.0359217	+	0.0622182i	−0.883427	−	0.468568i	$-0.844770\pi$
$373$	−0.693763	+	1.20163i	−0.0359217	+	0.0622182i	0.847506	+	0.530786i	$0.178103\pi$
$374$		0			0
$375$	−19.4294	−	1.98461i	−1.00333	−	0.102485i
$376$		0			0
$377$	−3.54495	−	6.14003i	−0.182574	−	0.316228i
$378$		0			0
$379$	19.6830			1.01105			0.505523	−	0.862813i	$-0.331300\pi$
$379$	19.6830			1.01105			0.505523	+	0.862813i	$0.331300\pi$
$380$		0			0
$381$	16.3369	−	22.6248i	0.836964	−	1.15910i
$382$		0			0
$383$	−31.3873			−1.60382			−0.801909	−	0.597447i	$-0.796182\pi$
$383$	−31.3873			−1.60382			−0.801909	+	0.597447i	$0.796182\pi$
$384$		0			0
$385$	15.0668	−	26.0965i	0.767876	−	1.33000i
$386$		0			0
$387$	22.8942	−	25.7281i	1.16378	−	1.30783i
$388$		0			0
$389$	−11.9247			−0.604608			−0.302304	−	0.953212i	$-0.597756\pi$
$389$	−11.9247			−0.604608			−0.302304	+	0.953212i	$0.597756\pi$
$390$		0			0
$391$	0.254762	−	0.441260i	0.0128838	−	0.0223155i
$392$		0			0
$393$	5.05627	+	0.516470i	0.255055	+	0.0260524i
$394$		0			0
$395$	−3.40837	+	5.90347i	−0.171494	+	0.297036i
$396$		0			0
$397$	18.7373	+	32.4540i	0.940399	+	1.62882i	0.764712	+	0.644372i	$0.222881\pi$
$397$	18.7373	+	32.4540i	0.940399	+	1.62882i	0.175686	+	0.984446i	$0.443786\pi$
$398$		0			0
$399$	12.4568	−	24.4004i	0.623618	−	1.22155i
$400$		0			0
$401$	−1.69724			−0.0847562			−0.0423781	−	0.999102i	$-0.513493\pi$
$401$	−1.69724			−0.0847562			−0.0423781	+	0.999102i	$0.513493\pi$
$402$		0			0
$403$	−15.1820			−0.756268
$404$		0			0
$405$	11.6101	+	5.00706i	0.576913	+	0.248803i
$406$		0			0
$407$	16.9289	+	29.3217i	0.839134	+	1.45342i
$408$		0			0
$409$	16.3211	+	28.2689i	0.807025	+	1.39781i	0.914915	+	0.403646i	$0.132257\pi$
$409$	16.3211	+	28.2689i	0.807025	+	1.39781i	−0.107890	+	0.994163i	$0.534409\pi$
$410$		0			0
$411$	−28.7463	−	2.93627i	−1.41795	−	0.144836i
$412$		0			0
$413$	−1.55958	−	2.70127i	−0.0767418	−	0.132921i
$414$		0			0
$415$	−8.09715	−	14.0247i	−0.397473	−	0.688444i
$416$		0			0
$417$	−6.01008	−	13.3932i	−0.294315	−	0.655866i
$418$		0			0
$419$	−7.49198	+	12.9765i	−0.366007	+	0.633943i	−0.988937	−	0.148334i	$-0.952609\pi$
$419$	−7.49198	+	12.9765i	−0.366007	+	0.633943i	0.622930	+	0.782278i	$0.285942\pi$
$420$		0			0
$421$	1.41058	−	2.44319i	0.0687473	−	0.119074i	−0.829603	−	0.558354i	$-0.811433\pi$
$421$	1.41058	−	2.44319i	0.0687473	−	0.119074i	0.898350	+	0.439280i	$0.144766\pi$
$422$		0			0
$423$	21.9645	+	4.53441i	1.06795	+	0.220471i
$424$		0			0
$425$	0.272499	+	0.471981i	0.0132181	+	0.0228945i
$426$		0			0
$427$	−9.08647	−	15.7382i	−0.439725	−	0.761626i
$428$		0			0
$429$	31.4401	−	43.5412i	1.51794	−	2.10219i
$430$		0			0
$431$	−16.0987	+	27.8838i	−0.775447	+	1.34311i	0.159096	+	0.987263i	$0.449142\pi$
$431$	−16.0987	+	27.8838i	−0.775447	+	1.34311i	−0.934543	+	0.355850i	$0.884191\pi$
$432$		0			0
$433$	−4.51311	+	7.81694i	−0.216886	+	0.375658i	−0.953854	−	0.300269i	$-0.902923\pi$
$433$	−4.51311	+	7.81694i	−0.216886	+	0.375658i	0.736968	+	0.675927i	$0.236257\pi$
$434$		0			0
$435$	−3.27178	−	0.334194i	−0.156870	−	0.0160234i
$436$		0			0
$437$	4.46242	−	11.4973i	0.213467	−	0.549988i
$438$		0			0
$439$	0.0997940	−	0.172848i	0.00476291	−	0.00824960i	−0.863634	−	0.504119i	$-0.831817\pi$
$439$	0.0997940	−	0.172848i	0.00476291	−	0.00824960i	0.868397	+	0.495870i	$0.165151\pi$
$440$		0			0
$441$	−12.3000	+	13.8225i	−0.585716	+	0.658215i
$442$		0			0
$443$	15.9752			0.759006			0.379503	−	0.925190i	$-0.376095\pi$
$443$	15.9752			0.759006			0.379503	+	0.925190i	$0.376095\pi$
$444$		0			0
$445$	−8.21506	+	14.2289i	−0.389431	+	0.674515i
$446$		0			0
$447$	27.5430	+	2.81336i	1.30274	+	0.133068i
$448$		0			0
$449$	−33.1626			−1.56504			−0.782520	−	0.622625i	$-0.786066\pi$
$449$	−33.1626			−1.56504			−0.782520	+	0.622625i	$0.786066\pi$
$450$		0			0
$451$	0.385610	+	0.667896i	0.0181577	+	0.0314500i
$452$		0			0
$453$	−9.80302	−	21.8456i	−0.460586	−	1.02639i
$454$		0			0
$455$	−13.3708	+	23.1589i	−0.626832	+	1.08571i
$456$		0			0
$457$	0.0126390	+	0.0218915i	0.000591229	+	0.00102404i	0.866321	−	0.499488i	$-0.166478\pi$
$457$	0.0126390	+	0.0218915i	0.000591229	+	0.00102404i	−0.865730	+	0.500512i	$0.833145\pi$
$458$		0			0
$459$	−0.202586	−	0.913553i	−0.00945589	−	0.0426410i
$460$		0			0
$461$	9.55209	−	16.5447i	0.444885	−	0.770564i	−0.553159	−	0.833076i	$-0.686578\pi$
$461$	9.55209	−	16.5447i	0.444885	−	0.770564i	0.998044	+	0.0625118i	$0.0199111\pi$
$462$		0			0
$463$	−11.6344	+	20.1514i	−0.540698	+	0.936516i	0.458167	+	0.888866i	$0.348506\pi$
$463$	−11.6344	+	20.1514i	−0.540698	+	0.936516i	−0.998864	+	0.0476493i	$0.984827\pi$
$464$		0			0
$465$	−4.12277	+	5.70959i	−0.191189	+	0.264776i
$466$		0			0
$467$	−2.81178			−0.130113			−0.0650567	−	0.997882i	$-0.520723\pi$
$467$	−2.81178			−0.130113			−0.0650567	+	0.997882i	$0.520723\pi$
$468$		0			0
$469$	1.48654	−	2.57477i	0.0686422	−	0.118892i
$470$		0			0
$471$	−12.3507	−	1.26155i	−0.569090	−	0.0581294i
$472$		0			0
$473$	−67.8575			−3.12009
$474$		0			0
$475$	8.26358	+	10.2825i	0.379159	+	0.471793i
$476$		0			0
$477$	13.3828	−	15.0393i	0.612756	−	0.688602i
$478$		0			0
$479$	−15.6822			−0.716539			−0.358269	−	0.933618i	$-0.616633\pi$
$479$	−15.6822			−0.716539			−0.358269	+	0.933618i	$0.616633\pi$
$480$		0			0
$481$	−15.0233	−	26.0211i	−0.685002	−	1.18646i
$482$		0			0
$483$	−10.4103	+	14.4172i	−0.473687	+	0.656005i
$484$		0			0
$485$	−1.62110	+	2.80782i	−0.0736102	+	0.127497i
$486$		0			0
$487$	43.4927			1.97084			0.985421	−	0.170133i	$-0.0544199\pi$
$487$	43.4927			1.97084			0.985421	+	0.170133i	$0.0544199\pi$
$488$		0			0
$489$	−33.8271	−	3.45525i	−1.52972	−	0.156252i
$490$		0			0
$491$	5.07169			0.228882			0.114441	−	0.993430i	$-0.463492\pi$
$491$	5.07169			0.228882			0.114441	+	0.993430i	$0.463492\pi$
$492$		0			0
$493$	0.121699	+	0.210789i	0.00548106	+	0.00949347i
$494$		0			0
$495$	−7.83705	−	23.6478i	−0.352249	−	1.06289i
$496$		0			0
$497$	17.5660	−	30.4252i	0.787943	−	1.36476i
$498$		0			0
$499$	−3.81013			−0.170565			−0.0852824	−	0.996357i	$-0.527179\pi$
$499$	−3.81013			−0.170565			−0.0852824	+	0.996357i	$0.527179\pi$
$500$		0			0
$501$	12.3806	+	27.5896i	0.553126	+	1.23261i
$502$		0			0
$503$	16.9720	−	29.3963i	0.756742	−	1.31072i	−0.187761	−	0.982215i	$-0.560123\pi$
$503$	16.9720	−	29.3963i	0.756742	−	1.31072i	0.944504	−	0.328501i	$-0.106544\pi$
$504$		0			0
$505$	−12.1133			−0.539034
$506$		0			0
$507$	−14.7194	+	20.3848i	−0.653714	+	0.905323i
$508$		0			0
$509$	−6.42078	−	11.1211i	−0.284596	−	0.492935i	0.687915	−	0.725791i	$-0.258526\pi$
$509$	−6.42078	−	11.1211i	−0.284596	−	0.492935i	−0.972511	+	0.232856i	$0.925193\pi$
$510$		0			0
$511$	−19.8932	+	34.4560i	−0.880022	+	1.52424i
$512$		0			0
$513$	−8.22401	−	21.1037i	−0.363099	−	0.931751i
$514$		0			0
$515$	−1.34879	+	2.33618i	−0.0594349	+	0.102944i
$516$		0			0
$517$	−22.0950	−	38.2697i	−0.971739	−	1.68310i
$518$		0			0
$519$	−19.9667	+	27.6517i	−0.876439	+	1.21377i
$520$		0			0
$521$	4.58441			0.200846			0.100423	−	0.994945i	$-0.467980\pi$
$521$	4.58441			0.200846			0.100423	+	0.994945i	$0.467980\pi$
$522$		0			0
$523$	−3.92387	+	6.79635i	−0.171579	+	0.297183i	−0.938972	−	0.343993i	$-0.888220\pi$
$523$	−3.92387	+	6.79635i	−0.171579	+	0.297183i	0.767393	+	0.641177i	$0.221554\pi$
$524$		0			0
$525$	−7.78736	−	17.3538i	−0.339868	−	0.757380i
$526$		0			0
$527$	0.521202			0.0227039
$528$		0			0
$529$	7.49736	−	12.9858i	0.325972	−	0.564601i
$530$		0			0
$531$	−2.52547	−	0.521366i	−0.109596	−	0.0226253i
$532$		0			0
$533$	−0.342203	−	0.592713i	−0.0148225	−	0.0256733i
$534$		0			0
$535$	4.53468			0.196051
$536$		0			0
$537$	−26.8489	−	2.74247i	−1.15862	−	0.118346i
$538$		0			0
$539$	36.4567			1.57030
$540$		0			0
$541$	12.9942	−	22.5066i	0.558663	−	0.967633i	−0.438945	−	0.898514i	$-0.644648\pi$
$541$	12.9942	−	22.5066i	0.558663	−	0.967633i	0.997608	−	0.0691195i	$-0.0220190\pi$
$542$		0			0
$543$	10.0962	−	13.9822i	0.433271	−	0.600033i
$544$		0			0
$545$	2.39523	+	4.14865i	0.102600	+	0.177709i
$546$		0			0
$547$	44.9646			1.92255			0.961273	−	0.275598i	$-0.0888760\pi$
$547$	44.9646			1.92255			0.961273	+	0.275598i	$0.0888760\pi$
$548$		0			0
$549$	−14.7140	−	3.03760i	−0.627978	−	0.129642i
$550$		0			0
$551$	3.69056	+	4.59221i	0.157223	+	0.195635i
$552$		0			0
$553$	−17.6074			−0.748741
$554$		0			0
$555$	−13.8656	−	1.41629i	−0.588562	−	0.0601184i
$556$		0			0
$557$	−6.08361	+	10.5371i	−0.257771	+	0.446472i	−0.965644	−	0.259867i	$-0.916321\pi$
$557$	−6.08361	+	10.5371i	−0.257771	+	0.446472i	0.707874	+	0.706339i	$0.249655\pi$
$558$		0			0
$559$	60.2191			2.54699
$560$		0			0
$561$	−1.07935	+	1.49478i	−0.0455701	+	0.0631097i
$562$		0			0
$563$	−12.3945	+	21.4679i	−0.522366	+	0.904765i	0.477295	+	0.878743i	$0.341617\pi$
$563$	−12.3945	+	21.4679i	−0.522366	+	0.904765i	−0.999661	+	0.0260218i	$0.991716\pi$
$564$		0			0
$565$	11.3723	−	19.6974i	0.478437	−	0.828678i
$566$		0			0
$567$	3.79394	+	32.4373i	0.159330	+	1.36224i
$568$		0			0
$569$	−14.7622	−	25.5689i	−0.618864	−	1.07190i	−0.989693	−	0.143203i	$-0.954260\pi$
$569$	−14.7622	−	25.5689i	−0.618864	−	1.07190i	0.370830	−	0.928701i	$-0.379073\pi$
$570$		0			0
$571$	17.1164	−	29.6465i	0.716301	−	1.24067i	−0.246155	−	0.969231i	$-0.579167\pi$
$571$	17.1164	−	29.6465i	0.716301	−	1.24067i	0.962456	−	0.271439i	$-0.0874995\pi$
$572$		0			0
$573$	−19.3421	−	43.1029i	−0.808026	−	1.80065i
$574$		0			0
$575$	−4.28131	−	7.41544i	−0.178543	−	0.309245i
$576$		0			0
$577$	−0.203463			−0.00847026			−0.00423513	−	0.999991i	$-0.501348\pi$
$577$	−0.203463			−0.00847026			−0.00423513	+	0.999991i	$0.501348\pi$
$578$		0			0
$579$	10.4406	+	1.06645i	0.433898	+	0.0443203i
$580$		0			0
$581$	20.9146	−	36.2251i	0.867683	−	1.50287i
$582$		0			0
$583$	−39.6660			−1.64280
$584$		0			0
$585$	6.95486	+	20.9859i	0.287548	+	0.867659i
$586$		0			0
$587$	−16.8567	+	29.1967i	−0.695752	+	1.20508i	0.274175	+	0.961680i	$0.411595\pi$
$587$	−16.8567	+	29.1967i	−0.695752	+	1.20508i	−0.969927	+	0.243398i	$0.921738\pi$
$588$		0			0
$589$	12.4675	−	1.92724i	0.513714	−	0.0794105i
$590$		0			0
$591$	−35.5289	−	3.62908i	−1.46146	−	0.149280i
$592$		0			0
$593$	−10.0852	+	17.4681i	−0.414150	+	0.717329i	−0.995339	−	0.0964395i	$-0.969255\pi$
$593$	−10.0852	+	17.4681i	−0.414150	+	0.717329i	0.581189	+	0.813769i	$0.302588\pi$
$594$		0			0
$595$	0.459023	−	0.795052i	0.0188181	−	0.0325940i
$596$		0			0
$597$	−14.7580	+	20.4382i	−0.604005	+	0.836482i
$598$		0			0
$599$	20.3298	+	35.2123i	0.830654	+	1.43874i	0.897520	+	0.440973i	$0.145367\pi$
$599$	20.3298	+	35.2123i	0.830654	+	1.43874i	−0.0668662	+	0.997762i	$0.521300\pi$
$600$		0			0
$601$	−11.1288	−	19.2756i	−0.453953	−	0.786269i	0.544675	−	0.838647i	$-0.316653\pi$
$601$	−11.1288	−	19.2756i	−0.453953	−	0.786269i	−0.998627	+	0.0523784i	$0.983320\pi$
$602$		0			0
$603$	−0.773231	−	2.33318i	−0.0314884	−	0.0950143i
$604$		0			0
$605$	−16.8164	+	29.1268i	−0.683683	+	1.18417i
$606$		0			0
$607$	−1.80987	+	3.13479i	−0.0734605	+	0.127237i	−0.900416	−	0.435030i	$-0.856738\pi$
$607$	−1.80987	+	3.13479i	−0.0734605	+	0.127237i	0.826955	+	0.562268i	$0.190071\pi$
$608$		0			0
$609$	−3.47787	−	7.75028i	−0.140931	−	0.314057i
$610$		0			0
$611$	19.6079	+	33.9618i	0.793250	+	1.37395i
$612$		0			0
$613$	−2.84219	−	4.92281i	−0.114795	−	0.198830i	0.802903	−	0.596110i	$-0.203288\pi$
$613$	−2.84219	−	4.92281i	−0.114795	−	0.198830i	−0.917698	+	0.397279i	$0.869954\pi$
$614$		0			0
$615$	−0.315834	−	0.0322606i	−0.0127356	−	0.00130087i
$616$		0			0
$617$	−13.8171	−	23.9319i	−0.556255	−	0.963463i	−0.997805	−	0.0662257i	$-0.978904\pi$
$617$	−13.8171	−	23.9319i	−0.556255	−	0.963463i	0.441549	−	0.897237i	$-0.354429\pi$
$618$		0			0
$619$	−21.6612	−	37.5183i	−0.870637	−	1.50799i	−0.861339	−	0.508031i	$-0.830374\pi$
$619$	−21.6612	−	37.5183i	−0.870637	−	1.50799i	−0.00929791	−	0.999957i	$-0.502960\pi$
$620$		0			0
$621$	3.18289	+	14.3531i	0.127725	+	0.575970i
$622$		0			0
$623$	−42.4383			−1.70025
$624$		0			0
$625$	−0.709526			−0.0283811
$626$		0			0
$627$	−20.2915	+	39.7472i	−0.810364	+	1.58735i
$628$		0			0
$629$	0.515754	+	0.893311i	0.0205644	+	0.0356187i
$630$		0			0
$631$	−11.2686	+	19.5177i	−0.448595	+	0.776989i	−0.998295	−	0.0583730i	$-0.981409\pi$
$631$	−11.2686	+	19.5177i	−0.448595	+	0.776989i	0.549700	+	0.835362i	$0.314742\pi$
$632$		0			0
$633$	0.689113	+	0.0703891i	0.0273898	+	0.00279772i
$634$		0			0
$635$	11.3175	−	19.6025i	0.449122	−	0.777903i
$636$		0			0
$637$	−32.3529			−1.28187
$638$		0			0
$639$	−9.13702	−	27.5704i	−0.361455	−	1.09067i
$640$		0			0
$641$	−20.4375	+	35.3987i	−0.807231	+	1.39817i	0.107543	+	0.994200i	$0.465702\pi$
$641$	−20.4375	+	35.3987i	−0.807231	+	1.39817i	−0.914775	+	0.403965i	$0.867632\pi$
$642$		0			0
$643$	−18.6922			−0.737148			−0.368574	−	0.929598i	$-0.620154\pi$
$643$	−18.6922			−0.737148			−0.368574	+	0.929598i	$0.620154\pi$
$644$		0			0
$645$	16.3529	−	22.6470i	0.643895	−	0.891725i
$646$		0			0
$647$	−4.68590			−0.184222			−0.0921108	−	0.995749i	$-0.529361\pi$
$647$	−4.68590			−0.184222			−0.0921108	+	0.995749i	$0.529361\pi$
$648$		0			0
$649$	2.54048	+	4.40025i	0.0997227	+	0.172725i
$650$		0			0
$651$	−18.0963	−	1.84844i	−0.709250	−	0.0724460i
$652$		0			0
$653$	6.69758	−	11.6006i	0.262097	−	0.453965i	−0.704702	−	0.709503i	$-0.748919\pi$
$653$	6.69758	−	11.6006i	0.262097	−	0.453965i	0.966799	+	0.255538i	$0.0822527\pi$
$654$		0			0
$655$	4.12248			0.161079
$656$		0			0
$657$	10.3475	+	31.2229i	0.403695	+	1.21812i
$658$		0			0
$659$	36.9886			1.44087			0.720435	−	0.693523i	$-0.243942\pi$
$659$	36.9886			1.44087			0.720435	+	0.693523i	$0.243942\pi$
$660$		0			0
$661$	−2.16552	−	3.75080i	−0.0842292	−	0.145889i	0.820833	−	0.571168i	$-0.193509\pi$
$661$	−2.16552	−	3.75080i	−0.0842292	−	0.145889i	−0.905062	+	0.425279i	$0.860176\pi$
$662$		0			0
$663$	0.957850	−	1.32652i	0.0371998	−	0.0515177i
$664$		0			0
$665$	8.04029	−	20.7155i	0.311789	−	0.803312i
$666$		0			0
$667$	−1.91205	−	3.31177i	−0.0740350	−	0.128232i
$668$		0			0
$669$	−25.1646	+	34.8502i	−0.972919	+	1.34739i
$670$		0			0
$671$	14.8015	+	25.6369i	0.571404	+	0.989700i
$672$		0			0
$673$	7.34639	+	12.7243i	0.283183	+	0.490487i	0.972167	−	0.234290i	$-0.0752764\pi$
$673$	7.34639	+	12.7243i	0.283183	+	0.490487i	−0.688984	+	0.724776i	$0.741943\pi$
$674$		0			0
$675$	−14.9978	−	4.72783i	−0.577266	−	0.181974i
$676$		0			0
$677$	12.8772	+	22.3039i	0.494910	+	0.857209i	0.999983	−	0.00586780i	$-0.00186779\pi$
$677$	12.8772	+	22.3039i	0.494910	+	0.857209i	−0.505073	+	0.863077i	$0.668534\pi$
$678$		0			0
$679$	−8.37445			−0.321382
$680$		0			0
$681$	19.8060	+	44.1367i	0.758967	+	1.69132i
$682$		0			0
$683$	−7.56905			−0.289622			−0.144811	−	0.989459i	$-0.546257\pi$
$683$	−7.56905			−0.289622			−0.144811	+	0.989459i	$0.546257\pi$
$684$		0			0
$685$	−23.4375			−0.895500
$686$		0			0
$687$	3.03347	−	4.20103i	0.115734	−	0.160279i
$688$		0			0
$689$	35.2009			1.34105
$690$		0			0
$691$	−22.8116	−	39.5108i	−0.867793	−	1.50306i	−0.864247	−	0.503069i	$-0.832204\pi$
$691$	−22.8116	−	39.5108i	−0.867793	−	1.50306i	−0.00354685	−	0.999994i	$-0.501129\pi$
$692$		0			0
$693$	42.7766	−	48.0714i	1.62495	−	1.82608i
$694$		0			0
$695$	−5.95342	−	10.3116i	−0.225826	−	0.391143i
$696$		0			0
$697$	0.0117479	+	0.0203480i	0.000444985	+	0.000770736i
$698$		0			0
$699$	−7.05652	−	15.7251i	−0.266902	−	0.594778i
$700$		0			0
$701$	−5.32010	−	9.21469i	−0.200937	−	0.348034i	0.747893	−	0.663819i	$-0.231065\pi$
$701$	−5.32010	−	9.21469i	−0.200937	−	0.348034i	−0.948831	+	0.315785i	$0.897732\pi$
$702$		0			0
$703$	15.6403	+	19.4615i	0.589887	+	0.734004i
$704$		0			0
$705$	18.0969	+	1.84850i	0.681570	+	0.0696186i
$706$		0			0
$707$	−15.6440	−	27.0963i	−0.588355	−	1.01906i
$708$		0			0
$709$	21.3937			0.803457			0.401729	−	0.915759i	$-0.368409\pi$
$709$	21.3937			0.803457			0.401729	+	0.915759i	$0.368409\pi$
$710$		0			0
$711$	−9.67680	+	10.8746i	−0.362908	+	0.407829i
$712$		0			0
$713$	−8.18876			−0.306671
$714$		0			0
$715$	21.7804	−	37.7248i	0.814542	−	1.41083i
$716$		0			0
$717$	26.3610	−	36.5072i	0.984471	−	1.36339i
$718$		0			0
$719$	−12.9572	−	22.4425i	−0.483220	−	0.836962i	0.516594	−	0.856231i	$-0.327200\pi$
$719$	−12.9572	−	22.4425i	−0.483220	−	0.836962i	−0.999814	+	0.0192681i	$0.993866\pi$
$720$		0			0
$721$	−6.96775			−0.259493
$722$		0			0
$723$	43.0587	+	4.39821i	1.60137	+	0.163571i
$724$		0			0
$725$	4.09034			0.151912
$726$		0			0
$727$	−7.62649	+	13.2095i	−0.282851	+	0.489912i	−0.972086	−	0.234626i	$-0.924614\pi$
$727$	−7.62649	+	13.2095i	−0.282851	+	0.489912i	0.689235	+	0.724538i	$0.257947\pi$
$728$		0			0
$729$	22.1189	+	15.4840i	0.819219	+	0.573481i
$730$		0			0
$731$	−2.06734			−0.0764633
$732$		0			0
$733$	13.2841	−	23.0087i	0.490658	−	0.849845i	−0.509284	−	0.860599i	$-0.670090\pi$
$733$	13.2841	−	23.0087i	0.490658	−	0.849845i	0.999942	+	0.0107536i	$0.00342305\pi$
$734$		0			0
$735$	−8.78567	+	12.1672i	−0.324064	+	0.448794i
$736$		0			0
$737$	−2.42151	+	4.19419i	−0.0891976	+	0.154495i
$738$		0			0
$739$	−8.38134	−	14.5169i	−0.308313	−	0.534013i	0.669681	−	0.742649i	$-0.266431\pi$
$739$	−8.38134	−	14.5169i	−0.308313	−	0.534013i	−0.977993	+	0.208636i	$0.933098\pi$
$740$		0			0
$741$	18.0074	−	35.2730i	0.661517	−	1.29579i
$742$		0			0
$743$	−6.59695			−0.242019			−0.121009	−	0.992651i	$-0.538613\pi$
$743$	−6.59695			−0.242019			−0.121009	+	0.992651i	$0.538613\pi$
$744$		0			0
$745$	22.4564			0.822739
$746$		0			0
$747$	−10.8788	−	32.8261i	−0.398034	−	1.20104i
$748$		0			0
$749$	5.85645	+	10.1437i	0.213990	+	0.370641i
$750$		0			0
$751$	22.2261	+	38.4967i	0.811041	+	1.40476i	0.912136	+	0.409888i	$0.134432\pi$
$751$	22.2261	+	38.4967i	0.811041	+	1.40476i	−0.101095	+	0.994877i	$0.532234\pi$
$752$		0			0
$753$	22.3108	−	30.8981i	0.813051	−	1.12599i
$754$		0			0
$755$	−9.71061	−	16.8193i	−0.353405	−	0.612116i
$756$		0			0
$757$	−2.06830	−	3.58240i	−0.0751736	−	0.130204i	0.825988	−	0.563687i	$-0.190618\pi$
$757$	−2.06830	−	3.58240i	−0.0751736	−	0.130204i	−0.901162	+	0.433483i	$0.857284\pi$
$758$		0			0
$759$	16.9580	−	23.4850i	0.615535	−	0.852450i
$760$		0			0
$761$	−18.0127	+	31.1989i	−0.652959	+	1.13096i	0.329442	+	0.944176i	$0.393139\pi$
$761$	−18.0127	+	31.1989i	−0.652959	+	1.13096i	−0.982401	+	0.186783i	$0.940194\pi$
$762$		0			0
$763$	−6.18677	+	10.7158i	−0.223976	+	0.387938i
$764$		0			0
$765$	−0.238763	−	0.720451i	−0.00863248	−	0.0260480i
$766$		0			0
$767$	−2.25451	−	3.90493i	−0.0814057	−	0.140999i
$768$		0			0
$769$	8.66529	+	15.0087i	0.312478	+	0.541228i	0.978898	−	0.204348i	$-0.0655075\pi$
$769$	8.66529	+	15.0087i	0.312478	+	0.541228i	−0.666420	+	0.745577i	$0.732174\pi$
$770$		0			0
$771$	10.9599	+	24.4237i	0.394713	+	0.879598i
$772$		0			0
$773$	7.97650	−	13.8157i	0.286895	−	0.496916i	−0.686172	−	0.727439i	$-0.740710\pi$
$773$	7.97650	−	13.8157i	0.286895	−	0.496916i	0.973067	+	0.230523i	$0.0740436\pi$
$774$		0			0
$775$	4.37944	−	7.58541i	0.157314	−	0.272476i
$776$		0			0
$777$	−14.7390	−	32.8452i	−0.528759	−	1.17831i
$778$		0			0
$779$	0.356259	+	0.443298i	0.0127643	+	0.0158828i
$780$		0			0
$781$	−28.6143	+	49.5613i	−1.02390	+	1.77344i
$782$		0			0
$783$	−6.69809	−	2.11147i	−0.239370	−	0.0754578i
$784$		0			0
$785$	−10.0698			−0.359406
$786$		0			0
$787$	−23.1822	+	40.1528i	−0.826357	+	1.43129i	0.0745211	+	0.997219i	$0.476257\pi$
$787$	−23.1822	+	40.1528i	−0.826357	+	1.43129i	−0.900878	+	0.434073i	$0.857076\pi$
$788$		0			0
$789$	2.93913	−	4.07038i	0.104636	−	0.144909i
$790$		0			0
$791$	58.7485			2.08886
$792$		0			0
$793$	−13.1353	−	22.7510i	−0.466448	−	0.807912i
$794$		0			0
$795$	9.55906	−	13.2383i	0.339025	−	0.469513i
$796$		0			0
$797$	−4.51728	+	7.82416i	−0.160010	+	0.277146i	−0.934872	−	0.354985i	$-0.884486\pi$
$797$	−4.51728	+	7.82416i	−0.160010	+	0.277146i	0.774862	+	0.632131i	$0.217819\pi$
$798$		0			0
$799$	−0.673145	−	1.16592i	−0.0238141	−	0.0412473i
$800$		0			0
$801$	−23.3236	+	26.2106i	−0.824099	+	0.926105i
$802$		0			0
$803$	32.4051	−	56.1273i	1.14355	−	1.98069i
$804$		0			0
$805$	−7.21185	+	12.4913i	−0.254184	+	0.440260i
$806$		0			0
$807$	1.47737	+	3.29224i	0.0520058	+	0.115892i
$808$		0			0
$809$	−30.1309			−1.05935			−0.529673	−	0.848202i	$-0.677685\pi$
$809$	−30.1309			−1.05935			−0.529673	+	0.848202i	$0.677685\pi$
$810$		0			0
$811$	12.5895	−	21.8057i	0.442078	−	0.765702i	−0.555765	−	0.831339i	$-0.687575\pi$
$811$	12.5895	−	21.8057i	0.442078	−	0.765702i	0.997844	+	0.0656370i	$0.0209079\pi$
$812$		0			0
$813$	10.7879	+	24.0402i	0.378347	+	0.843128i
$814$		0			0
$815$	−27.5800			−0.966085
$816$		0			0
$817$	−49.4521	+	7.64437i	−1.73011	+	0.267443i
$818$		0			0
$819$	−37.9614	+	42.6602i	−1.32648	+	1.49067i
$820$		0			0
$821$	−30.8343			−1.07612			−0.538062	−	0.842906i	$-0.680843\pi$
$821$	−30.8343			−1.07612			−0.538062	+	0.842906i	$0.680843\pi$
$822$		0			0
$823$	−3.34245	−	5.78929i	−0.116510	−	0.201802i	0.801872	−	0.597496i	$-0.203838\pi$
$823$	−3.34245	−	5.78929i	−0.116510	−	0.201802i	−0.918383	+	0.395694i	$0.870504\pi$
$824$		0			0
$825$	12.6853	+	28.2685i	0.441644	+	0.984183i
$826$		0			0
$827$	6.12508	−	10.6089i	0.212990	−	0.368909i	−0.739659	−	0.672982i	$-0.765013\pi$
$827$	6.12508	−	10.6089i	0.212990	−	0.368909i	0.952649	+	0.304073i	$0.0983466\pi$
$828$		0			0
$829$	25.4887			0.885259			0.442629	−	0.896705i	$-0.354046\pi$
$829$	25.4887			0.885259			0.442629	+	0.896705i	$0.354046\pi$
$830$		0			0
$831$	19.9127	+	44.3744i	0.690763	+	1.53933i
$832$		0			0
$833$	1.11069			0.0384830
$834$		0			0
$835$	12.2639	+	21.2417i	0.424411	+	0.735101i
$836$		0			0
$837$	−11.0871	+	10.1607i	−0.383228	+	0.351205i
$838$		0			0
$839$	−17.6200	+	30.5187i	−0.608309	+	1.05362i	0.383211	+	0.923661i	$0.374818\pi$
$839$	−17.6200	+	30.5187i	−0.608309	+	1.05362i	−0.991519	+	0.129960i	$0.958515\pi$
$840$		0			0
$841$	−27.1732			−0.937008
$842$		0			0
$843$	−5.41962	−	0.553584i	−0.186662	−	0.0190664i
$844$		0			0
$845$	−10.1970	+	17.6618i	−0.350789	+	0.607584i
$846$		0			0
$847$	−86.8720			−2.98496
$848$		0			0
$849$	−22.4494	−	2.29308i	−0.770461	−	0.0786983i
$850$		0			0
$851$	−8.10316	−	14.0351i	−0.277773	−	0.481116i
$852$		0			0
$853$	−1.72366	+	2.98546i	−0.0590169	+	0.102220i	−0.894024	−	0.448018i	$-0.852130\pi$
$853$	−1.72366	+	2.98546i	−0.0590169	+	0.102220i	0.835007	+	0.550239i	$0.185463\pi$
$854$		0			0
$855$	−8.37536	−	16.3508i	−0.286431	−	0.559185i
$856$		0			0
$857$	26.2498	−	45.4659i	0.896675	−	1.55309i	0.0649565	−	0.997888i	$-0.479309\pi$
$857$	26.2498	−	45.4659i	0.896675	−	1.55309i	0.831718	−	0.555198i	$-0.187358\pi$
$858$		0			0
$859$	13.8084	+	23.9168i	0.471135	+	0.816029i	0.999455	−	0.0330159i	$-0.0105112\pi$
$859$	13.8084	+	23.9168i	0.471135	+	0.816029i	−0.528320	+	0.849045i	$0.677178\pi$
$860$		0			0
$861$	−0.335728	−	0.748154i	−0.0114416	−	0.0254970i
$862$		0			0
$863$	−54.5817			−1.85798			−0.928992	−	0.370101i	$-0.879323\pi$
$863$	−54.5817			−1.85798			−0.928992	+	0.370101i	$0.879323\pi$
$864$		0			0
$865$	−13.8321	+	23.9579i	−0.470305	+	0.814592i
$866$		0			0
$867$	17.2045	−	23.8264i	0.584297	−	0.809188i
$868$		0			0
$869$	28.6816			0.972957
$870$		0			0
$871$	2.14893	−	3.72206i	0.0728138	−	0.126117i
$872$		0			0
$873$	−4.60250	+	5.17219i	−0.155771	+	0.175052i
$874$		0			0
$875$	−20.4586	−	35.4354i	−0.691628	−	1.19794i
$876$		0			0
$877$	41.8650			1.41368			0.706841	−	0.707372i	$-0.250120\pi$
$877$	41.8650			1.41368			0.706841	+	0.707372i	$0.250120\pi$
$878$		0			0
$879$	−1.80846	+	2.50452i	−0.0609978	+	0.0844754i
$880$		0			0
$881$	12.2805			0.413740			0.206870	−	0.978368i	$-0.433672\pi$
$881$	12.2805			0.413740			0.206870	+	0.978368i	$0.433672\pi$
$882$		0			0
$883$	−9.96692	+	17.2632i	−0.335414	+	0.580953i	−0.983564	−	0.180559i	$-0.942209\pi$
$883$	−9.96692	+	17.2632i	−0.335414	+	0.580953i	0.648151	+	0.761512i	$0.275543\pi$
$884$		0			0
$885$	−2.08078	−	0.212540i	−0.0699447	−	0.00714447i
$886$		0			0
$887$	3.32825	+	5.76469i	0.111752	+	0.193559i	0.916477	−	0.400088i	$-0.131021\pi$
$887$	3.32825	+	5.76469i	0.111752	+	0.193559i	−0.804725	+	0.593648i	$0.797687\pi$
$888$		0			0
$889$	58.4654			1.96087
$890$		0			0
$891$	−6.18016	−	52.8390i	−0.207043	−	1.77017i
$892$		0			0
$893$	−20.4133	−	25.4005i	−0.683104	−	0.849996i
$894$		0			0
$895$	−21.8905			−0.731718
$896$		0			0
$897$	−15.0491	+	20.8413i	−0.502474	+	0.695872i
$898$		0			0
$899$	1.95588	−	3.38768i	0.0652322	−	0.112985i
$900$		0			0
$901$	−1.20846			−0.0402596
$902$		0			0
$903$	71.7787	+	7.33180i	2.38865	+	0.243987i
$904$		0			0
$905$	6.99426	−	12.1144i	0.232497	−	0.402697i
$906$		0			0
$907$	−9.30046	+	16.1089i	−0.308817	+	0.534886i	−0.978104	−	0.208118i	$-0.933266\pi$
$907$	−9.30046	+	16.1089i	−0.308817	+	0.534886i	0.669287	+	0.743004i	$0.266600\pi$
$908$		0			0
$909$	−25.3329	−	5.22979i	−0.840238	−	0.173461i
$910$		0			0
$911$	−13.5585	−	23.4840i	−0.449214	−	0.778061i	0.549121	−	0.835743i	$-0.314962\pi$
$911$	−13.5585	−	23.4840i	−0.449214	−	0.778061i	−0.998335	+	0.0576818i	$0.981629\pi$
$912$		0			0
$913$	−34.0689	+	59.0091i	−1.12752	+	1.95292i
$914$		0			0
$915$	−12.1231	−	1.23831i	−0.400778	−	0.0409373i
$916$		0			0
$917$	5.32410	+	9.22162i	0.175817	+	0.304525i
$918$		0			0
$919$	−21.0393			−0.694022			−0.347011	−	0.937861i	$-0.612803\pi$
$919$	−21.0393			−0.694022			−0.347011	+	0.937861i	$0.612803\pi$
$920$		0			0
$921$	−9.65057	−	21.5058i	−0.317997	−	0.708641i
$922$		0			0
$923$	25.3932	−	43.9824i	0.835829	−	1.44770i
$924$		0			0
$925$	17.3346			0.569959
$926$		0			0
$927$	−3.82939	+	4.30339i	−0.125774	+	0.141342i
$928$		0			0
$929$	−4.45950	+	7.72408i	−0.146311	+	0.253419i	−0.929861	−	0.367910i	$-0.880074\pi$
$929$	−4.45950	+	7.72408i	−0.146311	+	0.253419i	0.783550	+	0.621329i	$0.213407\pi$
$930$		0			0
$931$	26.5683	−	4.10697i	0.870742	−	0.134600i
$932$		0			0
$933$	−9.00433	+	12.4700i	−0.294789	+	0.408250i
$934$		0			0
$935$	−0.747729	+	1.29510i	−0.0244533	+	0.0423544i
$936$		0			0
$937$	−0.301295	+	0.521858i	−0.00984287	+	0.0170484i	−0.870905	−	0.491452i	$-0.836466\pi$
$937$	−0.301295	+	0.521858i	−0.00984287	+	0.0170484i	0.861062	+	0.508500i	$0.169800\pi$
$938$		0			0
$939$	−8.77957	−	0.896785i	−0.286510	−	0.0292655i
$940$		0			0
$941$	−0.420517	−	0.728356i	−0.0137085	−	0.0237437i	0.859090	−	0.511825i	$-0.171030\pi$
$941$	−0.420517	−	0.728356i	−0.0137085	−	0.0237437i	−0.872798	+	0.488081i	$0.837697\pi$
$942$		0			0
$943$	−0.184575	−	0.319694i	−0.00601060	−	0.0104107i
$944$		0			0
$945$	5.73485	+	25.8611i	0.186555	+	0.841261i
$946$		0			0
$947$	−4.88645	+	8.46358i	−0.158788	+	0.275029i	−0.934432	−	0.356142i	$-0.884092\pi$
$947$	−4.88645	+	8.46358i	−0.158788	+	0.275029i	0.775644	+	0.631171i	$0.217425\pi$
$948$		0			0
$949$	−28.7574	+	49.8092i	−0.933503	+	1.61688i
$950$		0			0
$951$	55.4275	+	5.66161i	1.79736	+	0.183590i
$952$		0			0
$953$	−5.70692	−	9.88468i	−0.184865	−	0.320196i	0.758666	−	0.651480i	$-0.225852\pi$
$953$	−5.70692	−	9.88468i	−0.184865	−	0.320196i	−0.943531	+	0.331284i	$0.892518\pi$
$954$		0			0
$955$	−19.1597	−	33.1856i	−0.619994	−	1.07386i
$956$		0			0
$957$	5.66530	+	12.6249i	0.183133	+	0.408104i
$958$		0			0
$959$	−30.2690	−	52.4274i	−0.977437	−	1.69297i
$960$		0			0
$961$	11.3118	+	19.5926i	0.364896	+	0.632018i
$962$		0			0
$963$	9.48352	+	1.95780i	0.305602	+	0.0630894i
$964$		0			0
$965$	8.51248			0.274027
$966$		0			0
$967$	50.1293			1.61205			0.806024	−	0.591883i	$-0.201615\pi$
$967$	50.1293			1.61205			0.806024	+	0.591883i	$0.201615\pi$
$968$		0			0
$969$	−0.618198	+	1.21093i	−0.0198594	+	0.0389008i
$970$		0			0
$971$	26.1596	+	45.3097i	0.839500	+	1.45406i	0.890313	+	0.455349i	$0.150486\pi$
$971$	26.1596	+	45.3097i	0.839500	+	1.45406i	−0.0508124	+	0.998708i	$0.516181\pi$
$972$		0			0
$973$	15.3774	−	26.6345i	0.492978	−	0.853863i
$974$		0			0
$975$	−11.2573	−	25.0864i	−0.360523	−	0.803409i
$976$		0			0
$977$	16.9698	−	29.3925i	0.542911	−	0.940349i	−0.455825	−	0.890070i	$-0.650656\pi$
$977$	16.9698	−	29.3925i	0.542911	−	0.940349i	0.998735	−	0.0502791i	$-0.0160111\pi$
$978$		0			0
$979$	69.1301			2.20941
$980$		0			0
$981$	3.21807	+	9.71032i	0.102745	+	0.310027i
$982$		0			0
$983$	20.6004	−	35.6809i	0.657050	−	1.13804i	−0.324326	−	0.945945i	$-0.605137\pi$
$983$	20.6004	−	35.6809i	0.657050	−	1.13804i	0.981376	−	0.192098i	$-0.0615293\pi$
$984$		0			0
$985$	−28.9675			−0.922980
$986$		0			0
$987$	19.2369	+	42.8685i	0.612317	+	1.36452i
$988$		0			0
$989$	32.4806			1.03282
$990$		0			0
$991$	20.2099	+	35.0046i	0.641989	+	1.11196i	0.984988	+	0.172622i	$0.0552241\pi$
$991$	20.2099	+	35.0046i	0.641989	+	1.11196i	−0.342999	+	0.939336i	$0.611443\pi$
$992$		0			0
$993$	2.31786	+	5.16524i	0.0735551	+	0.163914i
$994$		0			0
$995$	−10.2237	+	17.7080i	−0.324115	+	0.561383i
$996$		0			0
$997$	17.8339			0.564804			0.282402	−	0.959296i	$-0.408869\pi$
$997$	17.8339			0.564804			0.282402	+	0.959296i	$0.408869\pi$
$998$		0			0
$999$	−28.3861	−	8.94828i	−0.898096	−	0.283111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.l.a.121.19	yes	40
3.2	odd	2		2052.2.l.a.577.7		40
9.2	odd	6		2052.2.j.a.1261.14		40
9.7	even	3		684.2.j.a.349.8	yes	40
19.11	even	3		684.2.j.a.49.8	✓	40
57.11	odd	6		2052.2.j.a.1873.14		40
171.11	odd	6		2052.2.l.a.505.7		40
171.106	even	3	inner	684.2.l.a.277.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.j.a.49.8	✓	40	19.11	even	3
684.2.j.a.349.8	yes	40	9.7	even	3
684.2.l.a.121.19	yes	40	1.1	even	1	trivial
684.2.l.a.277.19	yes	40	171.106	even	3	inner
2052.2.j.a.1261.14		40	9.2	odd	6
2052.2.j.a.1873.14		40	57.11	odd	6
2052.2.l.a.505.7		40	171.11	odd	6
2052.2.l.a.577.7		40	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72309 + 0.176004i) q^{3} +1.40487 q^{5} +(1.81436 + 3.14256i) q^{7} +(2.93805 + 0.606538i) q^{9} +(-2.95551 - 5.11909i) q^{11} +(2.62282 + 4.54285i) q^{13} +(2.42071 + 0.247262i) q^{15} +(-0.0900422 - 0.155958i) q^{17} +(-2.73055 - 3.39766i) q^{19} +(2.57319 + 5.73423i) q^{21} +(1.41468 + 2.45030i) q^{23} -3.02634 q^{25} +(4.95575 + 1.56222i) q^{27} -1.35158 q^{29} +(-1.44710 + 2.50646i) q^{31} +(-4.19162 - 9.34081i) q^{33} +(2.54894 + 4.41489i) q^{35} -5.72791 q^{37} +(3.71978 + 8.28935i) q^{39} -0.130472 q^{41} +(5.73992 - 9.94183i) q^{43} +(4.12757 + 0.852107i) q^{45} +7.47588 q^{47} +(-3.08379 + 5.34129i) q^{49} +(-0.127701 - 0.284576i) q^{51} +(3.35526 - 5.81148i) q^{53} +(-4.15210 - 7.19165i) q^{55} +(-4.10697 - 6.33505i) q^{57} -0.859576 q^{59} -5.00809 q^{61} +(3.42458 + 10.3335i) q^{63} +(3.68472 + 6.38211i) q^{65} +(-0.409661 - 0.709554i) q^{67} +(2.00635 + 4.47106i) q^{69} +(-4.84083 - 8.38457i) q^{71} +(5.48215 + 9.49536i) q^{73} +(-5.21465 - 0.532647i) q^{75} +(10.7247 - 18.5757i) q^{77} +(-2.42611 + 4.20215i) q^{79} +(8.26422 + 3.56407i) q^{81} +(-5.76363 - 9.98290i) q^{83} +(-0.126497 - 0.219100i) q^{85} +(-2.32889 - 0.237883i) q^{87} +(-5.84756 + 10.1283i) q^{89} +(-9.51747 + 16.4847i) q^{91} +(-2.93463 + 4.06415i) q^{93} +(-3.83606 - 4.77327i) q^{95} +(-1.15391 + 1.99864i) q^{97} +(-5.57850 - 16.8328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{3} - q^{7} + q^{9} - q^{11} - q^{13} + 10 q^{15} + 5 q^{17} + q^{19} + 6 q^{21} - 4 q^{23} + 40 q^{25} + 7 q^{27} + 18 q^{29} + 2 q^{31} - 7 q^{33} - 6 q^{35} + 2 q^{37} + 3 q^{39} + 50 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) \) 40 * q + q^3 - q^7 + q^9 - q^11 - q^13 + 10 * q^15 + 5 * q^17 + q^19 + 6 * q^21 - 4 * q^23 + 40 * q^25 + 7 * q^27 + 18 * q^29 + 2 * q^31 - 7 * q^33 - 6 * q^35 + 2 * q^37 + 3 * q^39 + 50 * q^41 + 8 * q^43 + 44 * q^45 + 20 * q^47 - 21 * q^49 - 17 * q^51 - 8 * q^53 + 15 * q^57 + 44 * q^59 + 14 * q^61 - 26 * q^63 - 6 * q^65 - 10 * q^67 + 38 * q^69 - 5 * q^71 - 10 * q^73 - 10 * q^77 - q^79 + q^81 + q^83 - 52 * q^87 - 34 * q^89 + 16 * q^91 + 46 * q^93 - 54 * q^95 - q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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