LMFDB - Embedded newform 504.2.bs.a.353.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(257,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.257"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bs (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.23
Character	$\chi$	$=$	504.353
Dual form			504.2.bs.a.257.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72860 + 0.109329i) q^{3} +(2.05742 - 3.56356i) q^{5} +(1.89056 + 1.85089i) q^{7} +(2.97609 + 0.377972i) q^{9} +(-5.04147 + 2.91069i) q^{11} +(2.52259 - 1.45642i) q^{13} +(3.94605 - 5.93502i) q^{15} +(-1.58162 + 2.73945i) q^{17} +(0.722488 - 0.417129i) q^{19} +(3.06566 + 3.40613i) q^{21} +(-6.14668 - 3.54879i) q^{23} +(-5.96595 - 10.3333i) q^{25} +(5.10314 + 0.978735i) q^{27} +(-1.91234 - 1.10409i) q^{29} +4.23424i q^{31} +(-9.03289 + 4.48023i) q^{33} +(10.4854 - 2.92907i) q^{35} +(1.82507 + 3.16112i) q^{37} +(4.51977 - 2.24177i) q^{39} +(-2.04811 - 3.54743i) q^{41} +(0.155460 - 0.269265i) q^{43} +(7.47000 - 9.82783i) q^{45} +1.00467 q^{47} +(0.148439 + 6.99843i) q^{49} +(-3.03349 + 4.56249i) q^{51} +(1.94801 + 1.12469i) q^{53} +23.9541i q^{55} +(1.29450 - 0.642058i) q^{57} +5.03496 q^{59} +4.60348i q^{61} +(4.92690 + 6.22299i) q^{63} -11.9859i q^{65} -9.99453 q^{67} +(-10.2371 - 6.80644i) q^{69} +11.4186i q^{71} +(-3.04990 - 1.76086i) q^{73} +(-9.18299 - 18.5144i) q^{75} +(-14.9186 - 3.82834i) q^{77} -1.15870 q^{79} +(8.71427 + 2.24976i) q^{81} +(7.57669 - 13.1232i) q^{83} +(6.50813 + 11.2724i) q^{85} +(-3.18496 - 2.11760i) q^{87} +(-4.82266 - 8.35309i) q^{89} +(7.46478 + 1.91558i) q^{91} +(-0.462926 + 7.31930i) q^{93} -3.43284i q^{95} +(-5.06969 - 2.92699i) q^{97} +(-16.1040 + 6.75696i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75}+ \cdots - 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.72860	+	0.109329i	0.998006	+	0.0631212i
$3$	1.72860	+	0.109329i	0.998006	+	0.0631212i
$4$		0			0
$5$	2.05742	−	3.56356i	0.920106	−	1.59367i	0.120858	−	0.992670i	$-0.461436\pi$
$5$	2.05742	−	3.56356i	0.920106	−	1.59367i	0.799248	−	0.601001i	$-0.205231\pi$
$6$		0			0
$7$	1.89056	+	1.85089i	0.714565	+	0.699569i
$7$	1.89056	+	1.85089i	0.714565	+	0.699569i
$8$		0			0
$9$	2.97609	+	0.377972i	0.992031	+	0.125991i
$10$		0			0
$11$	−5.04147	+	2.91069i	−1.52006	+	0.877607i	−0.520339	+	0.853960i	$0.674194\pi$
$11$	−5.04147	+	2.91069i	−1.52006	+	0.877607i	−0.999720	+	0.0236471i	$0.992472\pi$
$12$		0			0
$13$	2.52259	−	1.45642i	0.699641	−	0.403938i	−0.107573	−	0.994197i	$-0.534308\pi$
$13$	2.52259	−	1.45642i	0.699641	−	0.403938i	0.807214	+	0.590259i	$0.200975\pi$
$14$		0			0
$15$	3.94605	−	5.93502i	1.01887	−	1.53241i
$16$		0			0
$17$	−1.58162	+	2.73945i	−0.383600	+	0.664415i	−0.991574	−	0.129542i	$-0.958649\pi$
$17$	−1.58162	+	2.73945i	−0.383600	+	0.664415i	0.607974	+	0.793957i	$0.291983\pi$
$18$		0			0
$19$	0.722488	−	0.417129i	0.165750	−	0.0956959i	−0.414830	−	0.909899i	$-0.636159\pi$
$19$	0.722488	−	0.417129i	0.165750	−	0.0956959i	0.580580	+	0.814203i	$0.302826\pi$
$20$		0			0
$21$	3.06566	+	3.40613i	0.668982	+	0.743278i
$22$		0			0
$23$	−6.14668	−	3.54879i	−1.28167	−	0.739973i	−0.304518	−	0.952507i	$-0.598495\pi$
$23$	−6.14668	−	3.54879i	−1.28167	−	0.739973i	−0.977154	+	0.212533i	$0.931829\pi$
$24$		0			0
$25$	−5.96595	−	10.3333i	−1.19319	−	2.06667i
$26$		0			0
$27$	5.10314	+	0.978735i	0.982100	+	0.188358i
$28$		0			0
$29$	−1.91234	−	1.10409i	−0.355113	−	0.205025i	0.311822	−	0.950141i	$-0.399061\pi$
$29$	−1.91234	−	1.10409i	−0.355113	−	0.205025i	−0.666935	+	0.745116i	$0.732394\pi$
$30$		0			0
$31$			4.23424i			0.760493i	0.924885	+	0.380246i	$0.124161\pi$
$31$			4.23424i			0.760493i	−0.924885	+	0.380246i	$0.875839\pi$
$32$		0			0
$33$	−9.03289	+	4.48023i	−1.57242	+	0.779909i
$34$		0			0
$35$	10.4854	−	2.92907i	1.77236	−	0.495103i
$36$		0			0
$37$	1.82507	+	3.16112i	0.300040	+	0.519684i	0.976145	−	0.217121i	$-0.0696667\pi$
$37$	1.82507	+	3.16112i	0.300040	+	0.519684i	−0.676105	+	0.736806i	$0.736333\pi$
$38$		0			0
$39$	4.51977	−	2.24177i	0.723743	−	0.358970i
$40$		0			0
$41$	−2.04811	−	3.54743i	−0.319861	−	0.554016i	0.660598	−	0.750740i	$-0.270303\pi$
$41$	−2.04811	−	3.54743i	−0.319861	−	0.554016i	−0.980459	+	0.196724i	$0.936970\pi$
$42$		0			0
$43$	0.155460	−	0.269265i	0.0237074	−	0.0410625i	−0.853928	−	0.520391i	$-0.825786\pi$
$43$	0.155460	−	0.269265i	0.0237074	−	0.0410625i	0.877636	+	0.479328i	$0.159120\pi$
$44$		0			0
$45$	7.47000	−	9.82783i	1.11356	−	1.46505i
$46$		0			0
$47$	1.00467			0.146546			0.0732731	−	0.997312i	$-0.476656\pi$
$47$	1.00467			0.146546			0.0732731	+	0.997312i	$0.476656\pi$
$48$		0			0
$49$	0.148439	+	6.99843i	0.0212055	+	0.999775i
$50$		0			0
$51$	−3.03349	+	4.56249i	−0.424774	+	0.638876i
$52$		0			0
$53$	1.94801	+	1.12469i	0.267580	+	0.154487i	0.627787	−	0.778385i	$-0.283961\pi$
$53$	1.94801	+	1.12469i	0.267580	+	0.154487i	−0.360207	+	0.932872i	$0.617294\pi$
$54$		0			0
$55$			23.9541i			3.22997i
$56$		0			0
$57$	1.29450	−	0.642058i	0.171460	−	0.0850427i
$58$		0			0
$59$	5.03496			0.655496			0.327748	−	0.944765i	$-0.393710\pi$
$59$	5.03496			0.655496			0.327748	+	0.944765i	$0.393710\pi$
$60$		0			0
$61$			4.60348i			0.589416i	0.955587	+	0.294708i	$0.0952224\pi$
$61$			4.60348i			0.589416i	−0.955587	+	0.294708i	$0.904778\pi$
$62$		0			0
$63$	4.92690	+	6.22299i	0.620731	+	0.784023i
$64$		0			0
$65$		−	11.9859i		−	1.48666i
$66$		0			0
$67$	−9.99453			−1.22103			−0.610513	−	0.792006i	$-0.709037\pi$
$67$	−9.99453			−1.22103			−0.610513	+	0.792006i	$0.709037\pi$
$68$		0			0
$69$	−10.2371	−	6.80644i	−1.23241	−	0.819398i
$70$		0			0
$71$			11.4186i			1.35514i	0.735458	+	0.677571i	$0.236967\pi$
$71$			11.4186i			1.35514i	−0.735458	+	0.677571i	$0.763033\pi$
$72$		0			0
$73$	−3.04990	−	1.76086i	−0.356964	−	0.206093i	0.310784	−	0.950480i	$-0.399408\pi$
$73$	−3.04990	−	1.76086i	−0.356964	−	0.206093i	−0.667748	+	0.744387i	$0.732742\pi$
$74$		0			0
$75$	−9.18299	−	18.5144i	−1.06036	−	2.13786i
$76$		0			0
$77$	−14.9186	−	3.82834i	−1.70013	−	0.436280i
$78$		0			0
$79$	−1.15870			−0.130364			−0.0651820	−	0.997873i	$-0.520763\pi$
$79$	−1.15870			−0.130364			−0.0651820	+	0.997873i	$0.520763\pi$
$80$		0			0
$81$	8.71427	+	2.24976i	0.968253	+	0.249973i
$82$		0			0
$83$	7.57669	−	13.1232i	0.831650	−	1.44046i	−0.0650797	−	0.997880i	$-0.520730\pi$
$83$	7.57669	−	13.1232i	0.831650	−	1.44046i	0.896729	−	0.442579i	$-0.145937\pi$
$84$		0			0
$85$	6.50813	+	11.2724i	0.705905	+	1.22266i
$86$		0			0
$87$	−3.18496	−	2.11760i	−0.341464	−	0.227031i
$88$		0			0
$89$	−4.82266	−	8.35309i	−0.511201	−	0.885426i	−0.999916	−	0.0129824i	$-0.995867\pi$
$89$	−4.82266	−	8.35309i	−0.511201	−	0.885426i	0.488715	−	0.872444i	$-0.337466\pi$
$90$		0			0
$91$	7.46478	+	1.91558i	0.782521	+	0.200808i
$92$		0			0
$93$	−0.462926	+	7.31930i	−0.0480032	+	0.758976i
$94$		0			0
$95$		−	3.43284i		−	0.352201i
$96$		0			0
$97$	−5.06969	−	2.92699i	−0.514749	−	0.297190i	0.220035	−	0.975492i	$-0.429383\pi$
$97$	−5.06969	−	2.92699i	−0.514749	−	0.297190i	−0.734784	+	0.678302i	$0.762716\pi$
$98$		0			0
$99$	−16.1040	+	6.75696i	−1.61852	+	0.679100i
$100$		0			0
$101$	2.92632	+	5.06853i	0.291180	+	0.504338i	0.974089	−	0.226165i	$-0.0726189\pi$
$101$	2.92632	+	5.06853i	0.291180	+	0.504338i	−0.682909	+	0.730503i	$0.739286\pi$
$102$		0			0
$103$	−0.675732	−	0.390134i	−0.0665818	−	0.0384410i	0.466340	−	0.884606i	$-0.345573\pi$
$103$	−0.675732	−	0.390134i	−0.0665818	−	0.0384410i	−0.532921	+	0.846165i	$0.678906\pi$
$104$		0			0
$105$	18.4453	−	3.91682i	1.80008	−	0.382242i
$106$		0			0
$107$	7.15538	−	4.13116i	0.691737	−	0.399374i	−0.112526	−	0.993649i	$-0.535894\pi$
$107$	7.15538	−	4.13116i	0.691737	−	0.399374i	0.804262	+	0.594274i	$0.202561\pi$
$108$		0			0
$109$	3.63584	−	6.29745i	0.348250	−	0.603187i	−0.637689	−	0.770294i	$-0.720109\pi$
$109$	3.63584	−	6.29745i	0.348250	−	0.603187i	0.985939	+	0.167107i	$0.0534427\pi$
$110$		0			0
$111$	2.80921	+	5.66383i	0.266639	+	0.537587i
$112$		0			0
$113$	−16.0816	+	9.28474i	−1.51283	+	0.873435i	−0.512947	+	0.858421i	$0.671446\pi$
$113$	−16.0816	+	9.28474i	−1.51283	+	0.873435i	−0.999887	+	0.0150145i	$0.995221\pi$
$114$		0			0
$115$	−25.2926	+	14.6027i	−2.35855	+	1.36171i
$116$		0			0
$117$	8.05795	−	3.38097i	0.744958	−	0.312571i
$118$		0			0
$119$	−8.06057	+	2.25169i	−0.738911	+	0.206412i
$120$		0			0
$121$	11.4443	−	19.8220i	1.04039	−	1.80200i
$122$		0			0
$123$	−3.15252	−	6.35600i	−0.284253	−	0.573101i
$124$		0			0
$125$	−28.5237			−2.55124
$126$		0			0
$127$	4.38363			0.388984			0.194492	−	0.980904i	$-0.437694\pi$
$127$	4.38363			0.388984			0.194492	+	0.980904i	$0.437694\pi$
$128$		0			0
$129$	0.298166	−	0.448454i	0.0262521	−	0.0394841i
$130$		0			0
$131$	−7.85419	+	13.6039i	−0.686224	+	1.18857i	0.286827	+	0.957982i	$0.407400\pi$
$131$	−7.85419	+	13.6039i	−0.686224	+	1.18857i	−0.973051	+	0.230592i	$0.925934\pi$
$132$		0			0
$133$	2.13797	+	0.548636i	0.185385	+	0.0475728i
$134$		0			0
$135$	13.9871	−	16.1717i	1.20382	−	1.39184i
$136$		0			0
$137$	−15.9901	+	9.23190i	−1.36613	+	0.788734i	−0.990431	−	0.138008i	$-0.955930\pi$
$137$	−15.9901	+	9.23190i	−1.36613	+	0.788734i	−0.375697	+	0.926743i	$0.622597\pi$
$138$		0			0
$139$	−3.80522	+	2.19695i	−0.322755	+	0.186343i	−0.652620	−	0.757685i	$-0.726330\pi$
$139$	−3.80522	+	2.19695i	−0.322755	+	0.186343i	0.329865	+	0.944028i	$0.392997\pi$
$140$		0			0
$141$	1.73667	+	0.109840i	0.146254	+	0.00925018i
$142$		0			0
$143$	−8.47837	+	14.6850i	−0.708997	+	1.22802i
$144$		0			0
$145$	−7.86898	+	4.54316i	−0.653483	+	0.377289i
$146$		0			0
$147$	−0.508542	+	12.1137i	−0.0419438	+	0.999120i
$148$		0			0
$149$	17.7580	+	10.2526i	1.45479	+	0.839922i	0.998747	−	0.0500363i	$-0.0159337\pi$
$149$	17.7580	+	10.2526i	1.45479	+	0.839922i	0.456041	+	0.889959i	$0.349267\pi$
$150$		0			0
$151$	−2.70776	−	4.68998i	−0.220354	−	0.381665i	0.734561	−	0.678542i	$-0.237388\pi$
$151$	−2.70776	−	4.68998i	−0.220354	−	0.381665i	−0.954916	+	0.296877i	$0.904055\pi$
$152$		0			0
$153$	−5.74250	+	7.55506i	−0.464253	+	0.610790i
$154$		0			0
$155$	15.0890	+	8.71162i	1.21197	+	0.699734i
$156$		0			0
$157$			11.2537i			0.898140i	0.893497	+	0.449070i	$0.148245\pi$
$157$			11.2537i			0.898140i	−0.893497	+	0.449070i	$0.851755\pi$
$158$		0			0
$159$	3.24437	+	2.15710i	0.257295	+	0.171069i
$160$		0			0
$161$	−5.05227	−	18.0860i	−0.398175	−	1.42538i
$162$		0			0
$163$	−1.25819	−	2.17924i	−0.0985487	−	0.170691i	0.812535	−	0.582912i	$-0.198087\pi$
$163$	−1.25819	−	2.17924i	−0.0985487	−	0.170691i	−0.911084	+	0.412220i	$0.864753\pi$
$164$		0			0
$165$	−2.61888	+	41.4069i	−0.203879	+	3.22352i
$166$		0			0
$167$	−9.38259	−	16.2511i	−0.726047	−	1.25755i	−0.958542	−	0.284952i	$-0.908022\pi$
$167$	−9.38259	−	16.2511i	−0.726047	−	1.25755i	0.232495	−	0.972598i	$-0.425311\pi$
$168$		0			0
$169$	−2.25769	+	3.91043i	−0.173668	+	0.300803i
$170$		0			0
$171$	2.30786	−	0.968334i	0.176486	−	0.0740503i
$172$		0			0
$173$	9.71715			0.738781			0.369391	−	0.929274i	$-0.379566\pi$
$173$	9.71715			0.738781			0.369391	+	0.929274i	$0.379566\pi$
$174$		0			0
$175$	7.84683	−	30.5781i	0.593165	−	2.31149i
$176$		0			0
$177$	8.70341	+	0.550468i	0.654189	+	0.0413757i
$178$		0			0
$179$	9.24569	+	5.33800i	0.691055	+	0.398981i	0.804007	−	0.594619i	$-0.202697\pi$
$179$	9.24569	+	5.33800i	0.691055	+	0.398981i	−0.112952	+	0.993600i	$0.536031\pi$
$180$		0			0
$181$			4.34901i			0.323259i	0.986851	+	0.161630i	$0.0516750\pi$
$181$			4.34901i			0.323259i	−0.986851	+	0.161630i	$0.948325\pi$
$182$		0			0
$183$	−0.503295	+	7.95757i	−0.0372046	+	0.588240i
$184$		0			0
$185$	15.0198			1.10427
$186$		0			0
$187$		−	18.4145i		−	1.34660i
$188$		0			0
$189$	7.83627	+	11.2957i	0.570005	+	0.821641i
$190$		0			0
$191$		−	24.7918i		−	1.79387i	−0.442159	−	0.896937i	$-0.645787\pi$
$191$		−	24.7918i		−	1.79387i	0.442159	−	0.896937i	$-0.354213\pi$
$192$		0			0
$193$	26.6512			1.91840			0.959198	−	0.282736i	$-0.0912419\pi$
$193$	26.6512			1.91840			0.959198	+	0.282736i	$0.0912419\pi$
$194$		0			0
$195$	1.31040	−	20.7187i	0.0938400	−	1.48370i
$196$		0			0
$197$			6.11068i			0.435368i	0.976019	+	0.217684i	$0.0698502\pi$
$197$			6.11068i			0.435368i	−0.976019	+	0.217684i	$0.930150\pi$
$198$		0			0
$199$	−0.385220	−	0.222407i	−0.0273075	−	0.0157660i	0.486284	−	0.873801i	$-0.338352\pi$
$199$	−0.385220	−	0.222407i	−0.0273075	−	0.0157660i	−0.513592	+	0.858035i	$0.671685\pi$
$200$		0			0
$201$	−17.2765	−	1.09269i	−1.21859	−	0.0770727i
$202$		0			0
$203$	−1.57185	−	5.62688i	−0.110322	−	0.394930i
$204$		0			0
$205$	−16.8553			−1.17723
$206$		0			0
$207$	−16.9518	−	12.8848i	−1.17823	−	0.895556i
$208$		0			0
$209$	−2.42827	+	4.20588i	−0.167967	+	0.290927i
$210$		0			0
$211$	−4.23912	−	7.34236i	−0.291833	−	0.505469i	0.682410	−	0.730969i	$-0.260932\pi$
$211$	−4.23912	−	7.34236i	−0.291833	−	0.505469i	−0.974243	+	0.225500i	$0.927598\pi$
$212$		0			0
$213$	−1.24839	+	19.7382i	−0.0855382	+	1.35244i
$214$		0			0
$215$	−0.639693	−	1.10798i	−0.0436267	−	0.0755636i
$216$		0			0
$217$	−7.83710	+	8.00509i	−0.532017	+	0.543421i
$218$		0			0
$219$	−5.07953	−	3.37726i	−0.343243	−	0.228214i
$220$		0			0
$221$			9.21402i			0.619802i
$222$		0			0
$223$	7.25738	+	4.19005i	0.485990	+	0.280587i	0.722909	−	0.690943i	$-0.242804\pi$
$223$	7.25738	+	4.19005i	0.485990	+	0.280587i	−0.236919	+	0.971529i	$0.576138\pi$
$224$		0			0
$225$	−13.8495	−	33.0079i	−0.923302	−	2.20053i
$226$		0			0
$227$	−1.11075	−	1.92388i	−0.0737233	−	0.127693i	0.826807	−	0.562486i	$-0.190155\pi$
$227$	−1.11075	−	1.92388i	−0.0737233	−	0.127693i	−0.900530	+	0.434793i	$0.856822\pi$
$228$		0			0
$229$	−20.4417	−	11.8020i	−1.35082	−	0.779898i	−0.362458	−	0.932000i	$-0.618062\pi$
$229$	−20.4417	−	11.8020i	−1.35082	−	0.779898i	−0.988365	+	0.152102i	$0.951396\pi$
$230$		0			0
$231$	−25.3696	−	8.24870i	−1.66920	−	0.542724i
$232$		0			0
$233$	6.69275	−	3.86406i	0.438457	−	0.253143i	−0.264486	−	0.964390i	$-0.585202\pi$
$233$	6.69275	−	3.86406i	0.438457	−	0.253143i	0.702943	+	0.711246i	$0.251869\pi$
$234$		0			0
$235$	2.06703	−	3.58020i	0.134838	−	0.233546i
$236$		0			0
$237$	−2.00293	−	0.126680i	−0.130104	−	0.00822874i
$238$		0			0
$239$	16.2873	−	9.40346i	1.05354	−	0.608259i	0.129899	−	0.991527i	$-0.458535\pi$
$239$	16.2873	−	9.40346i	1.05354	−	0.608259i	0.923637	+	0.383268i	$0.125201\pi$
$240$		0			0
$241$	21.5749	−	12.4563i	1.38976	−	0.802379i	0.396473	−	0.918047i	$-0.370234\pi$
$241$	21.5749	−	12.4563i	1.38976	−	0.802379i	0.993288	+	0.115668i	$0.0369008\pi$
$242$		0			0
$243$	14.8175	+	4.84165i	0.950543	+	0.310592i
$244$		0			0
$245$	25.2447	+	13.8697i	1.61282	+	0.886105i
$246$		0			0
$247$	1.21503	−	2.10449i	0.0773104	−	0.133906i
$248$		0			0
$249$	14.5318	−	21.8564i	0.920915	−	1.38509i
$250$		0			0
$251$	3.39294			0.214161			0.107080	−	0.994250i	$-0.465850\pi$
$251$	3.39294			0.214161			0.107080	+	0.994250i	$0.465850\pi$
$252$		0			0
$253$	41.3177			2.59762
$254$		0			0
$255$	10.0175	+	20.1970i	0.627322	+	1.26478i
$256$		0			0
$257$	2.47711	−	4.29047i	0.154518	−	0.267632i	−0.778366	−	0.627811i	$-0.783951\pi$
$257$	2.47711	−	4.29047i	0.154518	−	0.267632i	0.932883	+	0.360179i	$0.117284\pi$
$258$		0			0
$259$	−2.40046	+	9.35428i	−0.149157	+	0.581247i
$260$		0			0
$261$	−5.27400	−	4.00869i	−0.326452	−	0.248132i
$262$		0			0
$263$	2.52396	−	1.45721i	0.155634	−	0.0898553i	−0.420160	−	0.907450i	$-0.638026\pi$
$263$	2.52396	−	1.45721i	0.155634	−	0.0898553i	0.575794	+	0.817595i	$0.304693\pi$
$264$		0			0
$265$	8.01576	−	4.62790i	0.492404	−	0.284290i
$266$		0			0
$267$	−7.42320	−	14.9664i	−0.454292	−	0.915928i
$268$		0			0
$269$	9.41429	−	16.3060i	0.573999	−	0.994196i	−0.422150	−	0.906526i	$-0.638724\pi$
$269$	9.41429	−	16.3060i	0.573999	−	0.994196i	0.996150	−	0.0876702i	$-0.0279422\pi$
$270$		0			0
$271$	−13.6959	+	7.90734i	−0.831967	+	0.480336i	−0.854526	−	0.519409i	$-0.826152\pi$
$271$	−13.6959	+	7.90734i	−0.831967	+	0.480336i	0.0225585	+	0.999746i	$0.492819\pi$
$272$		0			0
$273$	12.6942	+	4.12739i	0.768286	+	0.249801i
$274$		0			0
$275$	60.1543	+	34.7301i	3.62744	+	2.09430i
$276$		0			0
$277$	2.45231	+	4.24753i	0.147345	+	0.255209i	0.930245	−	0.366938i	$-0.119594\pi$
$277$	2.45231	+	4.24753i	0.147345	+	0.255209i	−0.782900	+	0.622147i	$0.786261\pi$
$278$		0			0
$279$	−1.60043	+	12.6015i	−0.0958150	+	0.754433i
$280$		0			0
$281$	2.77186	+	1.60034i	0.165355	+	0.0954680i	0.580394	−	0.814336i	$-0.302899\pi$
$281$	2.77186	+	1.60034i	0.165355	+	0.0954680i	−0.415039	+	0.909804i	$0.636232\pi$
$282$		0			0
$283$			5.06740i			0.301226i	0.988593	+	0.150613i	$0.0481247\pi$
$283$			5.06740i			0.301226i	−0.988593	+	0.150613i	$0.951875\pi$
$284$		0			0
$285$	0.375309	−	5.93399i	0.0222314	−	0.351499i
$286$		0			0
$287$	2.69382	−	10.4975i	0.159011	−	0.619646i
$288$		0			0
$289$	3.49694	+	6.05687i	0.205702	+	0.356287i
$290$		0			0
$291$	−8.44344	−	5.61384i	−0.494963	−	0.329089i
$292$		0			0
$293$	12.3751	+	21.4343i	0.722961	+	1.25221i	0.959808	+	0.280658i	$0.0905527\pi$
$293$	12.3751	+	21.4343i	0.722961	+	1.25221i	−0.236847	+	0.971547i	$0.576114\pi$
$294$		0			0
$295$	10.3590	−	17.9424i	0.603126	−	1.04464i
$296$		0			0
$297$	−28.5761	+	9.91942i	−1.65816	+	0.575583i
$298$		0			0
$299$	−20.6741			−1.19561
$300$		0			0
$301$	0.792285	−	0.221322i	0.0456665	−	0.0127568i
$302$		0			0
$303$	4.50429	+	9.08138i	0.258765	+	0.521712i
$304$		0			0
$305$	16.4048	+	9.47130i	0.939335	+	0.542325i
$306$		0			0
$307$			19.8011i			1.13011i	0.825054	+	0.565055i	$0.191145\pi$
$307$			19.8011i			1.13011i	−0.825054	+	0.565055i	$0.808855\pi$
$308$		0			0
$309$	−1.12541	−	0.748261i	−0.0640226	−	0.0425671i
$310$		0			0
$311$	−12.0490			−0.683235			−0.341617	−	0.939839i	$-0.610975\pi$
$311$	−12.0490			−0.683235			−0.341617	+	0.939839i	$0.610975\pi$
$312$		0			0
$313$		−	30.0873i		−	1.70064i	−0.526269	−	0.850318i	$-0.676410\pi$
$313$		−	30.0873i		−	1.70064i	0.526269	−	0.850318i	$-0.323590\pi$
$314$		0			0
$315$	32.3127	−	4.75399i	1.82061	−	0.267857i
$316$		0			0
$317$		−	12.6887i		−	0.712669i	−0.934358	−	0.356335i	$-0.884026\pi$
$317$		−	12.6887i		−	0.712669i	0.934358	−	0.356335i	$-0.115974\pi$
$318$		0			0
$319$	12.8547			0.719724
$320$		0			0
$321$	12.8204	−	6.35882i	0.715566	−	0.354915i
$322$		0			0
$323$			2.63896i			0.146836i
$324$		0			0
$325$	−30.0993	−	17.3778i	−1.66961	−	0.963950i
$326$		0			0
$327$	6.97339	−	10.4883i	0.385629	−	0.580002i
$328$		0			0
$329$	1.89939	+	1.85953i	0.104717	+	0.102519i
$330$		0			0
$331$	−5.90816			−0.324742			−0.162371	−	0.986730i	$-0.551914\pi$
$331$	−5.90816			−0.324742			−0.162371	+	0.986730i	$0.551914\pi$
$332$		0			0
$333$	4.23677	+	10.0976i	0.232174	+	0.553346i
$334$		0			0
$335$	−20.5629	+	35.6161i	−1.12347	+	1.94591i
$336$		0			0
$337$	−10.5675	−	18.3034i	−0.575647	−	0.997051i	−0.995971	−	0.0896763i	$-0.971417\pi$
$337$	−10.5675	−	18.3034i	−0.575647	−	0.997051i	0.420323	−	0.907374i	$-0.361917\pi$
$338$		0			0
$339$	−28.8138	+	14.2914i	−1.56495	+	0.776201i
$340$		0			0
$341$	−12.3246	−	21.3468i	−0.667414	−	1.15599i
$342$		0			0
$343$	−12.6727	+	13.5057i	−0.684259	+	0.729239i
$344$		0			0
$345$	−45.3172	+	22.4769i	−2.43980	+	1.21012i
$346$		0			0
$347$		−	29.5975i		−	1.58888i	−0.607344	−	0.794439i	$-0.707765\pi$
$347$		−	29.5975i		−	1.58888i	0.607344	−	0.794439i	$-0.292235\pi$
$348$		0			0
$349$	6.60232	+	3.81185i	0.353414	+	0.204044i	0.666188	−	0.745784i	$-0.267925\pi$
$349$	6.60232	+	3.81185i	0.353414	+	0.204044i	−0.312774	+	0.949828i	$0.601258\pi$
$350$		0			0
$351$	14.2986	−	4.96336i	0.763202	−	0.264925i
$352$		0			0
$353$	5.24727	+	9.08854i	0.279284	+	0.483734i	0.971207	−	0.238237i	$-0.0765695\pi$
$353$	5.24727	+	9.08854i	0.279284	+	0.483734i	−0.691923	+	0.721971i	$0.743236\pi$
$354$		0			0
$355$	40.6909	+	23.4929i	2.15965	+	1.24687i
$356$		0			0
$357$	−14.1796	+	3.01102i	−0.750467	+	0.159360i
$358$		0			0
$359$	−4.65028	+	2.68484i	−0.245432	+	0.141700i	−0.617671	−	0.786437i	$-0.711924\pi$
$359$	−4.65028	+	2.68484i	−0.245432	+	0.141700i	0.372239	+	0.928137i	$0.378590\pi$
$360$		0			0
$361$	−9.15201	+	15.8517i	−0.481685	+	0.834302i
$362$		0			0
$363$	21.9496	−	33.0131i	1.15206	−	1.73274i
$364$		0			0
$365$	−12.5498	+	7.24566i	−0.656889	+	0.379255i
$366$		0			0
$367$	9.61757	−	5.55271i	0.502033	−	0.289849i	−0.227520	−	0.973773i	$-0.573062\pi$
$367$	9.61757	−	5.55271i	0.502033	−	0.289849i	0.729553	+	0.683925i	$0.239728\pi$
$368$		0			0
$369$	−4.75454	−	11.3316i	−0.247512	−	0.589901i
$370$		0			0
$371$	1.60117	+	5.73184i	0.0831286	+	0.297582i
$372$		0			0
$373$	17.7021	−	30.6610i	0.916580	−	1.58756i	0.112010	−	0.993707i	$-0.464271\pi$
$373$	17.7021	−	30.6610i	0.916580	−	1.58756i	0.804571	−	0.593857i	$-0.202395\pi$
$374$		0			0
$375$	−49.3059	−	3.11847i	−2.54615	−	0.161037i
$376$		0			0
$377$	−6.43208			−0.331269
$378$		0			0
$379$	−26.5906			−1.36587			−0.682933	−	0.730481i	$-0.739296\pi$
$379$	−26.5906			−1.36587			−0.682933	+	0.730481i	$0.739296\pi$
$380$		0			0
$381$	7.57753	+	0.479259i	0.388209	+	0.0245532i
$382$		0			0
$383$	−12.2956	+	21.2967i	−0.628277	+	1.08821i	0.359620	+	0.933099i	$0.382906\pi$
$383$	−12.2956	+	21.2967i	−0.628277	+	1.08821i	−0.987897	+	0.155110i	$0.950427\pi$
$384$		0			0
$385$	−44.3363	+	45.2866i	−2.25958	+	2.30802i
$386$		0			0
$387$	0.564438	−	0.742597i	0.0286920	−	0.0377483i
$388$		0			0
$389$	16.5400	−	9.54936i	0.838611	−	0.484172i	−0.0181812	−	0.999835i	$-0.505788\pi$
$389$	16.5400	−	9.54936i	0.838611	−	0.484172i	0.856792	+	0.515663i	$0.172454\pi$
$390$		0			0
$391$	19.4435	−	11.2257i	0.983298	−	0.567708i
$392$		0			0
$393$	−15.0640	+	22.6569i	−0.759880	+	1.14289i
$394$		0			0
$395$	−2.38394	+	4.12910i	−0.119949	+	0.207757i
$396$		0			0
$397$	17.8857	−	10.3263i	0.897655	−	0.518261i	0.0212165	−	0.999775i	$-0.493246\pi$
$397$	17.8857	−	10.3263i	0.897655	−	0.518261i	0.876439	+	0.481513i	$0.159913\pi$
$398$		0			0
$399$	3.63570	+	1.18211i	0.182013	+	0.0591797i
$400$		0			0
$401$	−13.3677	−	7.71786i	−0.667553	−	0.385412i	0.127596	−	0.991826i	$-0.459274\pi$
$401$	−13.3677	−	7.71786i	−0.667553	−	0.385412i	−0.795149	+	0.606414i	$0.792607\pi$
$402$		0			0
$403$	6.16683	+	10.6813i	0.307192	+	0.532072i
$404$		0			0
$405$	25.9461	−	26.4251i	1.28927	−	1.31307i
$406$		0			0
$407$	−18.4021	−	10.6244i	−0.912157	−	0.526634i
$408$		0			0
$409$		−	18.6613i		−	0.922741i	−0.887208	−	0.461370i	$-0.847358\pi$
$409$		−	18.6613i		−	0.922741i	0.887208	−	0.461370i	$-0.152642\pi$
$410$		0			0
$411$	−28.6498	+	14.2100i	−1.41319	+	0.700930i
$412$		0			0
$413$	9.51889	+	9.31914i	0.468394	+	0.458565i
$414$		0			0
$415$	−31.1769	−	53.9999i	−1.53041	−	2.65075i
$416$		0			0
$417$	−6.81789	+	3.38161i	−0.333874	+	0.165598i
$418$		0			0
$419$	−14.3576	−	24.8681i	−0.701414	−	1.21488i	−0.967970	−	0.251065i	$-0.919219\pi$
$419$	−14.3576	−	24.8681i	−0.701414	−	1.21488i	0.266557	−	0.963819i	$-0.414114\pi$
$420$		0			0
$421$	12.8338	−	22.2287i	0.625479	−	1.08336i	−0.362969	−	0.931801i	$-0.618237\pi$
$421$	12.8338	−	22.2287i	0.625479	−	1.08336i	0.988448	−	0.151560i	$-0.0484296\pi$
$422$		0			0
$423$	2.98999	+	0.379737i	0.145379	+	0.0184635i
$424$		0			0
$425$	37.7436			1.83083
$426$		0			0
$427$	−8.52053	+	8.70317i	−0.412337	+	0.421176i
$428$		0			0
$429$	−16.2612	+	24.4575i	−0.785097	+	1.18082i
$430$		0			0
$431$	17.0243	+	9.82896i	0.820030	+	0.473444i	0.850427	−	0.526094i	$-0.176344\pi$
$431$	17.0243	+	9.82896i	0.820030	+	0.473444i	−0.0303970	+	0.999538i	$0.509677\pi$
$432$		0			0
$433$			7.07732i			0.340114i	0.985434	+	0.170057i	$0.0543952\pi$
$433$			7.07732i			0.340114i	−0.985434	+	0.170057i	$0.945605\pi$
$434$		0			0
$435$	−14.0990	+	6.99298i	−0.675995	+	0.335288i
$436$		0			0
$437$	−5.92120			−0.283250
$438$		0			0
$439$		−	19.4414i		−	0.927889i	−0.885864	−	0.463945i	$-0.846434\pi$
$439$		−	19.4414i		−	0.927889i	0.885864	−	0.463945i	$-0.153566\pi$
$440$		0			0
$441$	−2.20344	+	20.8841i	−0.104926	+	0.994480i
$442$		0			0
$443$			34.5199i			1.64009i	0.572299	+	0.820045i	$0.306052\pi$
$443$			34.5199i			1.64009i	−0.572299	+	0.820045i	$0.693948\pi$
$444$		0			0
$445$	−39.6889			−1.88144
$446$		0			0
$447$	29.5754	+	19.6640i	1.39887	+	0.930076i
$448$		0			0
$449$			10.9491i			0.516720i	0.966049	+	0.258360i	$0.0831821\pi$
$449$			10.9491i			0.516720i	−0.966049	+	0.258360i	$0.916818\pi$
$450$		0			0
$451$	20.6510	+	11.9228i	0.972417	+	0.561425i
$452$		0			0
$453$	−4.16787	−	8.40312i	−0.195824	−	0.394813i
$454$		0			0
$455$	22.1845	−	22.6600i	1.04002	−	1.06232i
$456$		0			0
$457$	−19.1923			−0.897776			−0.448888	−	0.893588i	$-0.648180\pi$
$457$	−19.1923			−0.897776			−0.448888	+	0.893588i	$0.648180\pi$
$458$		0			0
$459$	−10.7524	+	12.4318i	−0.501881	+	0.580268i
$460$		0			0
$461$	−16.2492	+	28.1444i	−0.756799	+	1.31081i	0.187676	+	0.982231i	$0.439905\pi$
$461$	−16.2492	+	28.1444i	−0.756799	+	1.31081i	−0.944475	+	0.328584i	$0.893429\pi$
$462$		0			0
$463$	13.9136	+	24.0991i	0.646621	+	1.11998i	0.983924	+	0.178585i	$0.0571519\pi$
$463$	13.9136	+	24.0991i	0.646621	+	1.11998i	−0.337303	+	0.941396i	$0.609515\pi$
$464$		0			0
$465$	25.1303	+	16.7085i	1.16539	+	0.774840i
$466$		0			0
$467$	0.0869153	+	0.150542i	0.00402196	+	0.00696624i	0.868029	−	0.496513i	$-0.165386\pi$
$467$	0.0869153	+	0.150542i	0.00402196	+	0.00696624i	−0.864007	+	0.503479i	$0.832053\pi$
$468$		0			0
$469$	−18.8953	−	18.4987i	−0.872502	−	0.854192i
$470$		0			0
$471$	−1.23035	+	19.4530i	−0.0566917	+	0.896349i
$472$		0			0
$473$			1.80998i			0.0832232i
$474$		0			0
$475$	−8.62066	−	4.97714i	−0.395543	−	0.228367i
$476$		0			0
$477$	5.37237	+	4.08346i	0.245984	+	0.186969i
$478$		0			0
$479$	−1.46598	−	2.53915i	−0.0669822	−	0.116017i	0.830589	−	0.556885i	$-0.188004\pi$
$479$	−1.46598	−	2.53915i	−0.0669822	−	0.116017i	−0.897572	+	0.440869i	$0.854670\pi$
$480$		0			0
$481$	9.20782	+	5.31614i	0.419840	+	0.242395i
$482$		0			0
$483$	−6.75601	−	31.8158i	−0.307409	−	1.44767i
$484$		0			0
$485$	−20.8610	+	12.0441i	−0.947247	+	0.546893i
$486$		0			0
$487$	18.7014	−	32.3917i	0.847440	−	1.46781i	−0.0360460	−	0.999350i	$-0.511476\pi$
$487$	18.7014	−	32.3917i	0.847440	−	1.46781i	0.883486	−	0.468458i	$-0.155190\pi$
$488$		0			0
$489$	−1.93664	−	3.90459i	−0.0875780	−	0.176572i
$490$		0			0
$491$	−7.27844	+	4.20221i	−0.328472	+	0.189643i	−0.655162	−	0.755488i	$-0.727400\pi$
$491$	−7.27844	+	4.20221i	−0.328472	+	0.189643i	0.326691	+	0.945131i	$0.394066\pi$
$492$		0			0
$493$	6.04921	−	3.49251i	0.272443	−	0.157295i
$494$		0			0
$495$	−9.05397	+	71.2896i	−0.406946	+	3.20423i
$496$		0			0
$497$	−21.1346	+	21.5876i	−0.948015	+	0.968336i
$498$		0			0
$499$	0.0176239	−	0.0305256i	0.000788956	−	0.00136651i	−0.865631	−	0.500683i	$-0.833082\pi$
$499$	0.0176239	−	0.0305256i	0.000788956	−	0.00136651i	0.866420	+	0.499317i	$0.166416\pi$
$500$		0			0
$501$	−14.4420	−	29.1174i	−0.645221	−	1.30087i
$502$		0			0
$503$	14.9085			0.664736			0.332368	−	0.943150i	$-0.392152\pi$
$503$	14.9085			0.664736			0.332368	+	0.943150i	$0.392152\pi$
$504$		0			0
$505$	24.0827			1.07166
$506$		0			0
$507$	−4.33016	+	6.51273i	−0.192309	+	0.289241i
$508$		0			0
$509$	−7.20640	+	12.4818i	−0.319418	+	0.553248i	−0.980367	−	0.197183i	$-0.936821\pi$
$509$	−7.20640	+	12.4818i	−0.319418	+	0.553248i	0.660949	+	0.750431i	$0.270154\pi$
$510$		0			0
$511$	−2.50687	−	8.97403i	−0.110897	−	0.396988i
$512$		0			0
$513$	4.09522	−	1.42154i	0.180808	−	0.0627627i
$514$		0			0
$515$	−2.78053	+	1.60534i	−0.122525	+	0.0707397i
$516$		0			0
$517$	−5.06501	+	2.92429i	−0.222759	+	0.128610i
$518$		0			0
$519$	16.7970	+	1.06237i	0.737308	+	0.0466328i
$520$		0			0
$521$	10.4159	−	18.0409i	0.456330	−	0.790386i	−0.542434	−	0.840098i	$-0.682497\pi$
$521$	10.4159	−	18.0409i	0.456330	−	0.790386i	0.998764	+	0.0497124i	$0.0158305\pi$
$522$		0			0
$523$	12.6684	−	7.31408i	0.553949	−	0.319822i	−0.196764	−	0.980451i	$-0.563043\pi$
$523$	12.6684	−	7.31408i	0.553949	−	0.319822i	0.750713	+	0.660628i	$0.229710\pi$
$524$		0			0
$525$	16.9071	−	51.9993i	0.737886	−	2.26944i
$526$		0			0
$527$	−11.5995	−	6.69698i	−0.505282	−	0.291725i
$528$		0			0
$529$	13.6878	+	23.7079i	0.595121	+	1.03078i
$530$		0			0
$531$	14.9845	+	1.90307i	0.650272	+	0.0825864i
$532$		0			0
$533$	−10.3331	−	5.96582i	−0.447576	−	0.258408i
$534$		0			0
$535$		−	33.9981i		−	1.46987i
$536$		0			0
$537$	15.3985	+	10.2381i	0.664493	+	0.441806i
$538$		0			0
$539$	−21.1186	−	34.8503i	−0.909643	−	1.50111i
$540$		0			0
$541$	3.60713	+	6.24773i	0.155083	+	0.268611i	0.933089	−	0.359645i	$-0.117102\pi$
$541$	3.60713	+	6.24773i	0.155083	+	0.268611i	−0.778006	+	0.628256i	$0.783769\pi$
$542$		0			0
$543$	−0.475473	+	7.51768i	−0.0204045	+	0.322615i
$544$		0			0
$545$	−14.9609	−	25.9130i	−0.640854	−	1.10999i
$546$		0			0
$547$	3.81987	−	6.61620i	0.163326	−	0.282888i	−0.772734	−	0.634730i	$-0.781111\pi$
$547$	3.81987	−	6.61620i	0.163326	−	0.282888i	0.936059	+	0.351842i	$0.114445\pi$
$548$		0			0
$549$	−1.73999	+	13.7004i	−0.0742609	+	0.584719i
$550$		0			0
$551$	−1.84219			−0.0784801
$552$		0			0
$553$	−2.19060	−	2.14462i	−0.0931536	−	0.0911987i
$554$		0			0
$555$	25.9631	+	1.64210i	1.10207	+	0.0697032i
$556$		0			0
$557$	8.13965	+	4.69943i	0.344888	+	0.199121i	0.662432	−	0.749122i	$-0.269525\pi$
$557$	8.13965	+	4.69943i	0.344888	+	0.199121i	−0.317543	+	0.948244i	$0.602858\pi$
$558$		0			0
$559$		−	0.905659i		−	0.0383053i
$560$		0			0
$561$	2.01324	−	31.8312i	0.0849990	−	1.34391i
$562$		0			0
$563$	4.12705			0.173934			0.0869671	−	0.996211i	$-0.472282\pi$
$563$	4.12705			0.173934			0.0869671	+	0.996211i	$0.472282\pi$
$564$		0			0
$565$			76.4104i			3.21461i
$566$		0			0
$567$	12.3108	+	20.3824i	0.517005	+	0.855982i
$568$		0			0
$569$		−	18.2143i		−	0.763583i	−0.924248	−	0.381792i	$-0.875307\pi$
$569$		−	18.2143i		−	0.763583i	0.924248	−	0.381792i	$-0.124693\pi$
$570$		0			0
$571$	−45.1826			−1.89083			−0.945417	−	0.325864i	$-0.894345\pi$
$571$	−45.1826			−1.89083			−0.945417	+	0.325864i	$0.894345\pi$
$572$		0			0
$573$	2.71047	−	42.8551i	0.113231	−	1.79030i
$574$		0			0
$575$			84.6876i			3.53172i
$576$		0			0
$577$	7.04322	+	4.06641i	0.293213	+	0.169287i	0.639390	−	0.768883i	$-0.279187\pi$
$577$	7.04322	+	4.06641i	0.293213	+	0.169287i	−0.346177	+	0.938169i	$0.612520\pi$
$578$		0			0
$579$	46.0692	+	2.91375i	1.91457	+	0.121091i
$580$		0			0
$581$	38.6138	−	10.7866i	1.60197	−	0.447505i
$582$		0			0
$583$	−13.0945			−0.542317
$584$		0			0
$585$	4.53032	−	35.6710i	0.187306	−	1.47482i
$586$		0			0
$587$	−12.4379	+	21.5430i	−0.513366	+	0.889175i	0.486514	+	0.873673i	$0.338268\pi$
$587$	−12.4379	+	21.5430i	−0.513366	+	0.889175i	−0.999880	+	0.0155026i	$0.995065\pi$
$588$		0			0
$589$	1.76622	+	3.05919i	0.0727760	+	0.126052i
$590$		0			0
$591$	−0.668075	+	10.5629i	−0.0274809	+	0.434499i
$592$		0			0
$593$	15.6229	+	27.0596i	0.641554	+	1.11120i	0.985086	+	0.172063i	$0.0550432\pi$
$593$	15.6229	+	27.0596i	0.641554	+	1.11120i	−0.343532	+	0.939141i	$0.611623\pi$
$594$		0			0
$595$	−8.55993	+	33.3570i	−0.350923	+	1.36750i
$596$		0			0
$597$	−0.641575	−	0.426568i	−0.0262579	−	0.0174583i
$598$		0			0
$599$			6.39849i			0.261435i	0.991420	+	0.130718i	$0.0417281\pi$
$599$			6.39849i			0.261435i	−0.991420	+	0.130718i	$0.958272\pi$
$600$		0			0
$601$	−36.0541	−	20.8158i	−1.47068	−	0.849095i	−0.471218	−	0.882017i	$-0.656186\pi$
$601$	−36.0541	−	20.8158i	−1.47068	−	0.849095i	−0.999458	+	0.0329215i	$0.989519\pi$
$602$		0			0
$603$	−29.7447	−	3.77765i	−1.21130	−	0.153838i
$604$		0			0
$605$	−47.0913	−	81.5645i	−1.91453	−	3.31607i
$606$		0			0
$607$	−21.7167	−	12.5381i	−0.881452	−	0.508907i	−0.0103153	−	0.999947i	$-0.503284\pi$
$607$	−21.7167	−	12.5381i	−0.881452	−	0.508907i	−0.871137	+	0.491040i	$0.836617\pi$
$608$		0			0
$609$	−2.10192	−	9.89846i	−0.0851739	−	0.401106i
$610$		0			0
$611$	2.53437	−	1.46322i	0.102530	−	0.0591956i
$612$		0			0
$613$	15.3779	−	26.6352i	0.621106	−	1.07579i	−0.368174	−	0.929757i	$-0.620017\pi$
$613$	15.3779	−	26.6352i	0.621106	−	1.07579i	0.989280	−	0.146030i	$-0.0466497\pi$
$614$		0			0
$615$	−29.1360	−	1.84278i	−1.17488	−	0.0743079i
$616$		0			0
$617$	−10.1910	+	5.88375i	−0.410272	+	0.236871i	−0.690907	−	0.722944i	$-0.742788\pi$
$617$	−10.1910	+	5.88375i	−0.410272	+	0.236871i	0.280634	+	0.959815i	$0.409455\pi$
$618$		0			0
$619$	6.14617	−	3.54849i	0.247035	−	0.142626i	−0.371371	−	0.928485i	$-0.621112\pi$
$619$	6.14617	−	3.54849i	0.247035	−	0.142626i	0.618406	+	0.785859i	$0.287779\pi$
$620$		0			0
$621$	−27.8941	−	24.1259i	−1.11935	−	0.968141i
$622$		0			0
$623$	6.34309	−	24.7182i	0.254131	−	0.990315i
$624$		0			0
$625$	−28.8554	+	49.9791i	−1.15422	+	1.99916i
$626$		0			0
$627$	−4.65732	+	7.00479i	−0.185995	+	0.279744i
$628$		0			0
$629$	−11.5463			−0.460381
$630$		0			0
$631$	13.0686			0.520252			0.260126	−	0.965575i	$-0.416236\pi$
$631$	13.0686			0.520252			0.260126	+	0.965575i	$0.416236\pi$
$632$		0			0
$633$	−6.52499	−	13.1554i	−0.259345	−	0.522882i
$634$		0			0
$635$	9.01897	−	15.6213i	0.357907	−	0.619913i
$636$		0			0
$637$	10.5671	+	17.4380i	0.418683	+	0.690918i
$638$		0			0
$639$	−4.31592	+	33.9829i	−0.170735	+	1.34434i
$640$		0			0
$641$	10.9219	−	6.30573i	0.431387	−	0.249062i	−0.268550	−	0.963266i	$-0.586545\pi$
$641$	10.9219	−	6.30573i	0.431387	−	0.249062i	0.699937	+	0.714204i	$0.253211\pi$
$642$		0			0
$643$	−12.3449	+	7.12736i	−0.486837	+	0.281076i	−0.723261	−	0.690574i	$-0.757358\pi$
$643$	−12.3449	+	7.12736i	−0.486837	+	0.281076i	0.236424	+	0.971650i	$0.424025\pi$
$644$		0			0
$645$	−0.984636	−	1.98519i	−0.0387700	−	0.0781667i
$646$		0			0
$647$	20.0060	−	34.6515i	0.786519	−	1.36229i	−0.141569	−	0.989928i	$-0.545215\pi$
$647$	20.0060	−	34.6515i	0.786519	−	1.36229i	0.928088	−	0.372362i	$-0.121452\pi$
$648$		0			0
$649$	−25.3836	+	14.6552i	−0.996392	+	0.575267i
$650$		0			0
$651$	−14.4224	+	12.9808i	−0.565258	+	0.508756i
$652$		0			0
$653$	−12.6726	−	7.31656i	−0.495919	−	0.286319i	0.231108	−	0.972928i	$-0.425765\pi$
$653$	−12.6726	−	7.31656i	−0.495919	−	0.286319i	−0.727027	+	0.686609i	$0.759098\pi$
$654$		0			0
$655$	32.3187	+	55.9777i	1.26280	+	2.18723i
$656$		0			0
$657$	−8.41123	−	6.39326i	−0.328153	−	0.249425i
$658$		0			0
$659$	−23.7553	−	13.7151i	−0.925374	−	0.534265i	−0.0400285	−	0.999199i	$-0.512745\pi$
$659$	−23.7553	−	13.7151i	−0.925374	−	0.534265i	−0.885346	+	0.464934i	$0.846078\pi$
$660$		0			0
$661$			35.6097i			1.38506i	0.721391	+	0.692528i	$0.243503\pi$
$661$			35.6097i			1.38506i	−0.721391	+	0.692528i	$0.756497\pi$
$662$		0			0
$663$	−1.00736	+	15.9273i	−0.0391227	+	0.618566i
$664$		0			0
$665$	6.35379	−	6.48998i	0.246389	−	0.251671i
$666$		0			0
$667$	7.83637	+	13.5730i	0.303426	+	0.525548i
$668$		0			0
$669$	12.0870	+	8.03635i	0.467310	+	0.310703i
$670$		0			0
$671$	−13.3993	−	23.2083i	−0.517275	−	0.895947i
$672$		0			0
$673$	6.35937	−	11.0147i	0.245136	−	0.424587i	−0.717034	−	0.697038i	$-0.754501\pi$
$673$	6.35937	−	11.0147i	0.245136	−	0.424587i	0.962170	+	0.272451i	$0.0878342\pi$
$674$		0			0
$675$	−20.3315	−	58.5716i	−0.782560	−	2.25442i
$676$		0			0
$677$	28.0556			1.07826			0.539131	−	0.842222i	$-0.318753\pi$
$677$	28.0556			1.07826			0.539131	+	0.842222i	$0.318753\pi$
$678$		0			0
$679$	−4.16703	−	14.9171i	−0.159916	−	0.572464i
$680$		0			0
$681$	−1.70971	−	3.44705i	−0.0655162	−	0.132091i
$682$		0			0
$683$	14.4564	+	8.34638i	0.553157	+	0.319365i	0.750394	−	0.660990i	$-0.229864\pi$
$683$	14.4564	+	8.34638i	0.553157	+	0.319365i	−0.197237	+	0.980356i	$0.563197\pi$
$684$		0			0
$685$			75.9756i			2.90288i
$686$		0			0
$687$	−34.0451	−	22.6358i	−1.29890	−	0.863608i
$688$		0			0
$689$	6.55205			0.249613
$690$		0			0
$691$		−	30.4437i		−	1.15813i	−0.815281	−	0.579066i	$-0.803417\pi$
$691$		−	30.4437i		−	1.15813i	0.815281	−	0.579066i	$-0.196583\pi$
$692$		0			0
$693$	−42.9520	−	17.0323i	−1.63161	−	0.647004i
$694$		0			0
$695$			18.0802i			0.685820i
$696$		0			0
$697$	12.9574			0.490795
$698$		0			0
$699$	11.9915	−	5.94769i	0.453561	−	0.224962i
$700$		0			0
$701$		−	6.16940i		−	0.233015i	−0.993190	−	0.116507i	$-0.962830\pi$
$701$		−	6.16940i		−	0.233015i	0.993190	−	0.116507i	$-0.0371699\pi$
$702$		0			0
$703$	2.63719	+	1.52258i	0.0994633	+	0.0574252i
$704$		0			0
$705$	3.96448	−	5.96274i	0.149311	−	0.224570i
$706$		0			0
$707$	−3.84890	+	14.9987i	−0.144753	+	0.564082i
$708$		0			0
$709$	25.4973			0.957572			0.478786	−	0.877932i	$-0.341077\pi$
$709$	25.4973			0.957572			0.478786	+	0.877932i	$0.341077\pi$
$710$		0			0
$711$	−3.44840	−	0.437957i	−0.129325	−	0.0164247i
$712$		0			0
$713$	15.0264	−	26.0265i	0.562744	−	0.974702i
$714$		0			0
$715$	34.8871	+	60.4263i	1.30471	+	2.25982i
$716$		0			0
$717$	29.1822	−	14.4741i	1.08983	−	0.540546i
$718$		0			0
$719$	−12.1263	−	21.0034i	−0.452236	−	0.783296i	0.546289	−	0.837597i	$-0.316040\pi$
$719$	−12.1263	−	21.0034i	−0.452236	−	0.783296i	−0.998525	+	0.0543012i	$0.982707\pi$
$720$		0			0
$721$	−0.555418	−	1.98827i	−0.0206849	−	0.0740472i
$722$		0			0
$723$	38.6561	−	19.1731i	1.43764	−	0.713055i
$724$		0			0
$725$			26.3478i			0.978534i
$726$		0			0
$727$	13.5251	+	7.80870i	0.501617	+	0.289609i	0.729381	−	0.684108i	$-0.239808\pi$
$727$	13.5251	+	7.80870i	0.501617	+	0.289609i	−0.227764	+	0.973716i	$0.573141\pi$
$728$		0			0
$729$	25.0842	+	9.98925i	0.929043	+	0.369972i
$730$		0			0
$731$	0.491758	+	0.851750i	0.0181883	+	0.0315031i
$732$		0			0
$733$	30.9202	+	17.8518i	1.14206	+	0.659371i	0.946941	−	0.321408i	$-0.104156\pi$
$733$	30.9202	+	17.8518i	1.14206	+	0.659371i	0.195123	+	0.980779i	$0.437489\pi$
$734$		0			0
$735$	42.1215	+	26.7352i	1.55368	+	0.986141i
$736$		0			0
$737$	50.3871	−	29.0910i	1.85603	−	1.07158i
$738$		0			0
$739$	7.27883	−	12.6073i	0.267756	−	0.463767i	−0.700526	−	0.713627i	$-0.747051\pi$
$739$	7.27883	−	12.6073i	0.267756	−	0.463767i	0.968282	+	0.249860i	$0.0803846\pi$
$740$		0			0
$741$	2.33038	−	3.50498i	0.0856085	−	0.128759i
$742$		0			0
$743$	0.0287226	−	0.0165830i	0.00105373	−	0.000608372i	−0.499473	−	0.866329i	$-0.666473\pi$
$743$	0.0287226	−	0.0165830i	0.00105373	−	0.000608372i	0.500527	+	0.865721i	$0.333140\pi$
$744$		0			0
$745$	73.0711	−	42.1876i	2.67712	−	1.54564i
$746$		0			0
$747$	27.5091	−	36.1921i	1.00651	−	1.32420i
$748$		0			0
$749$	21.1740	+	5.43359i	0.773681	+	0.198539i
$750$		0			0
$751$	−11.8949	+	20.6027i	−0.434053	+	0.751801i	−0.997218	−	0.0745430i	$-0.976250\pi$
$751$	−11.8949	+	20.6027i	−0.434053	+	0.751801i	0.563165	+	0.826344i	$0.309584\pi$
$752$		0			0
$753$	5.86503	+	0.370948i	0.213734	+	0.0135181i
$754$		0			0
$755$	−22.2840			−0.810998
$756$		0			0
$757$	−33.2060			−1.20689			−0.603446	−	0.797404i	$-0.706206\pi$
$757$	−33.2060			−1.20689			−0.603446	+	0.797404i	$0.706206\pi$
$758$		0			0
$759$	71.4217	+	4.51723i	2.59244	+	0.163965i
$760$		0			0
$761$	−21.2837	+	36.8645i	−0.771535	+	1.33634i	0.165187	+	0.986262i	$0.447177\pi$
$761$	−21.2837	+	36.8645i	−0.771535	+	1.33634i	−0.936722	+	0.350075i	$0.886156\pi$
$762$		0			0
$763$	18.5296	−	5.17620i	0.670818	−	0.187391i
$764$		0			0
$765$	15.1081	+	36.0076i	0.546236	+	1.30186i
$766$		0			0
$767$	12.7011	−	7.33301i	0.458612	−	0.264780i
$768$		0			0
$769$	−27.1091	+	15.6514i	−0.977578	+	0.564405i	−0.901538	−	0.432700i	$-0.857561\pi$
$769$	−27.1091	+	15.6514i	−0.977578	+	0.564405i	−0.0760402	+	0.997105i	$0.524228\pi$
$770$		0			0
$771$	4.75099	−	7.14568i	0.171103	−	0.257345i
$772$		0			0
$773$	−0.165130	+	0.286014i	−0.00593932	+	0.0102872i	−0.868980	−	0.494848i	$-0.835224\pi$
$773$	−0.165130	+	0.286014i	−0.00593932	+	0.0102872i	0.863040	+	0.505135i	$0.168557\pi$
$774$		0			0
$775$	43.7539	−	25.2613i	1.57168	−	0.907413i
$776$		0			0
$777$	−5.17212	+	15.9073i	−0.185549	+	0.570673i
$778$		0			0
$779$	−2.95947	−	1.70865i	−0.106034	−	0.0612188i
$780$		0			0
$781$	−33.2361	−	57.5666i	−1.18928	−	2.05990i
$782$		0			0
$783$	−8.67835	−	7.50601i	−0.310139	−	0.268243i
$784$		0			0
$785$	40.1031	+	23.1535i	1.43134	+	0.826384i
$786$		0			0
$787$		−	7.50934i		−	0.267679i	−0.991003	−	0.133840i	$-0.957269\pi$
$787$		−	7.50934i		−	0.267679i	0.991003	−	0.133840i	$-0.0427307\pi$
$788$		0			0
$789$	4.52222	−	2.24298i	0.160995	−	0.0798523i
$790$		0			0
$791$	−47.5883	−	12.2119i	−1.69205	−	0.434206i
$792$		0			0
$793$	6.70460	+	11.6127i	0.238087	+	0.412379i
$794$		0			0
$795$	14.3620	−	7.12342i	0.509367	−	0.252642i
$796$		0			0
$797$	−3.58136	−	6.20310i	−0.126858	−	0.219725i	0.795600	−	0.605823i	$-0.207156\pi$
$797$	−3.58136	−	6.20310i	−0.126858	−	0.219725i	−0.922458	+	0.386098i	$0.873823\pi$
$798$		0			0
$799$	−1.58901	+	2.75225i	−0.0562151	+	0.0973675i
$800$		0			0
$801$	−11.1955	−	26.6824i	−0.395572	−	0.942777i
$802$		0			0
$803$	20.5013			0.723475
$804$		0			0
$805$	−74.8451	−	19.2065i	−2.63794	−	0.676939i
$806$		0			0
$807$	18.0562	−	27.1573i	0.635610	−	0.955982i
$808$		0			0
$809$	−39.9767	−	23.0806i	−1.40551	−	0.811469i	−0.410556	−	0.911836i	$-0.634665\pi$
$809$	−39.9767	−	23.0806i	−1.40551	−	0.811469i	−0.994951	+	0.100366i	$0.967999\pi$
$810$		0			0
$811$		−	22.8560i		−	0.802581i	−0.915951	−	0.401290i	$-0.868562\pi$
$811$		−	22.8560i		−	0.802581i	0.915951	−	0.401290i	$-0.131438\pi$
$812$		0			0
$813$	−24.5392	+	12.1712i	−0.860628	+	0.426864i
$814$		0			0
$815$	−10.3545			−0.362701
$816$		0			0
$817$		−	0.259387i		−	0.00907481i
$818$		0			0
$819$	21.4918	+	8.52243i	0.750986	+	0.297798i
$820$		0			0
$821$		−	1.91410i		−	0.0668026i	−0.999442	−	0.0334013i	$-0.989366\pi$
$821$		−	1.91410i		−	0.0668026i	0.999442	−	0.0334013i	$-0.0106339\pi$
$822$		0			0
$823$	−15.0947			−0.526168			−0.263084	−	0.964773i	$-0.584740\pi$
$823$	−15.0947			−0.526168			−0.263084	+	0.964773i	$0.584740\pi$
$824$		0			0
$825$	100.186	+	66.6110i	3.48801	+	2.31910i
$826$		0			0
$827$		−	14.4077i		−	0.501004i	−0.968116	−	0.250502i	$-0.919404\pi$
$827$		−	14.4077i		−	0.501004i	0.968116	−	0.250502i	$-0.0805956\pi$
$828$		0			0
$829$	−37.1450	−	21.4457i	−1.29010	−	0.744840i	−0.311429	−	0.950270i	$-0.600807\pi$
$829$	−37.1450	−	21.4457i	−1.29010	−	0.744840i	−0.978672	+	0.205430i	$0.934141\pi$
$830$		0			0
$831$	3.77468	+	7.61037i	0.130942	+	0.264001i
$832$		0			0
$833$	−19.4066	−	10.6622i	−0.672400	−	0.369424i
$834$		0			0
$835$	−77.2157			−2.67216
$836$		0			0
$837$	−4.14420	+	21.6080i	−0.143245	+	0.746880i
$838$		0			0
$839$	12.5327	−	21.7073i	0.432678	−	0.749421i	−0.564425	−	0.825485i	$-0.690902\pi$
$839$	12.5327	−	21.7073i	0.432678	−	0.749421i	0.997103	+	0.0760639i	$0.0242353\pi$
$840$		0			0
$841$	−12.0620	−	20.8919i	−0.415930	−	0.720412i
$842$		0			0
$843$	4.61647	+	3.06938i	0.159000	+	0.105715i
$844$		0			0
$845$	9.29003	+	16.0908i	0.319587	+	0.553541i
$846$		0			0
$847$	58.3244	−	16.2927i	2.00405	−	0.559825i
$848$		0			0
$849$	−0.554015	+	8.75950i	−0.0190137	+	0.300625i
$850$		0			0
$851$		−	25.9072i		−	0.888086i
$852$		0			0
$853$	14.9013	+	8.60328i	0.510211	+	0.294571i	0.732920	−	0.680314i	$-0.238157\pi$
$853$	14.9013	+	8.60328i	0.510211	+	0.294571i	−0.222709	+	0.974885i	$0.571490\pi$
$854$		0			0
$855$	1.29752	−	10.2164i	0.0443741	−	0.349395i
$856$		0			0
$857$	24.3484	+	42.1727i	0.831726	+	1.44059i	0.896669	+	0.442702i	$0.145980\pi$
$857$	24.3484	+	42.1727i	0.831726	+	1.44059i	−0.0649433	+	0.997889i	$0.520687\pi$
$858$		0			0
$859$	−2.68282	−	1.54893i	−0.0915366	−	0.0528487i	0.453533	−	0.891239i	$-0.350163\pi$
$859$	−2.68282	−	1.54893i	−0.0915366	−	0.0528487i	−0.545070	+	0.838391i	$0.683497\pi$
$860$		0			0
$861$	5.80420	−	17.8514i	0.197807	−	0.608373i
$862$		0			0
$863$	−22.2443	+	12.8427i	−0.757203	+	0.437172i	−0.828291	−	0.560299i	$-0.810686\pi$
$863$	−22.2443	+	12.8427i	−0.757203	+	0.437172i	0.0710874	+	0.997470i	$0.477353\pi$
$864$		0			0
$865$	19.9923	−	34.6276i	0.679757	−	1.17737i
$866$		0			0
$867$	5.38260	+	10.8522i	0.182803	+	0.368560i
$868$		0			0
$869$	5.84156	−	3.37262i	0.198161	−	0.114408i
$870$		0			0
$871$	−25.2121	+	14.5562i	−0.854280	+	0.493219i
$872$		0			0
$873$	−13.9815	−	10.6272i	−0.473204	−	0.359676i
$874$		0			0
$875$	−53.9257	−	52.7941i	−1.82302	−	1.78477i
$876$		0			0
$877$	−0.626626	+	1.08535i	−0.0211597	+	0.0366496i	−0.876411	−	0.481563i	$-0.840069\pi$
$877$	−0.626626	+	1.08535i	−0.0211597	+	0.0366496i	0.855252	+	0.518213i	$0.173403\pi$
$878$		0			0
$879$	19.0482	+	38.4042i	0.642479	+	1.29534i
$880$		0			0
$881$	−18.7429			−0.631464			−0.315732	−	0.948848i	$-0.602250\pi$
$881$	−18.7429			−0.631464			−0.315732	+	0.948848i	$0.602250\pi$
$882$		0			0
$883$	39.3701			1.32491			0.662454	−	0.749103i	$-0.269515\pi$
$883$	39.3701			1.32491			0.662454	+	0.749103i	$0.269515\pi$
$884$		0			0
$885$	19.8682	−	29.8826i	0.667862	−	1.00449i
$886$		0			0
$887$	−18.5954	+	32.2083i	−0.624374	+	1.08145i	0.364288	+	0.931286i	$0.381313\pi$
$887$	−18.5954	+	32.2083i	−0.624374	+	1.08145i	−0.988662	+	0.150161i	$0.952021\pi$
$888$		0			0
$889$	8.28752	+	8.11360i	0.277955	+	0.272122i
$890$		0			0
$891$	−50.4811	+	14.0225i	−1.69118	+	0.469771i
$892$		0			0
$893$	0.725863	−	0.419077i	0.0242901	−	0.0140239i
$894$		0			0
$895$	38.0445	−	21.9650i	1.27169	−	0.734210i
$896$		0			0
$897$	−35.7372	−	2.26028i	−1.19323	−	0.0754686i
$898$		0			0
$899$	4.67499	−	8.09732i	0.155920	−	0.270061i
$900$		0			0
$901$	−6.16204	+	3.55766i	−0.205287	+	0.118523i
$902$		0			0
$903$	1.39374	−	0.295957i	0.0463807	−	0.00984883i
$904$		0			0
$905$	15.4979	+	8.94774i	0.515169	+	0.297433i
$906$		0			0
$907$	15.4295	+	26.7247i	0.512328	+	0.887378i	0.999898	+	0.0142940i	$0.00455008\pi$
$907$	15.4295	+	26.7247i	0.512328	+	0.887378i	−0.487570	+	0.873084i	$0.662117\pi$
$908$		0			0
$909$	6.79324	+	16.1905i	0.225317	+	0.537005i
$910$		0			0
$911$	−14.7486	−	8.51511i	−0.488643	−	0.282118i	0.235368	−	0.971906i	$-0.424370\pi$
$911$	−14.7486	−	8.51511i	−0.488643	−	0.282118i	−0.724011	+	0.689788i	$0.757704\pi$
$912$		0			0
$913$			88.2136i			2.91945i
$914$		0			0
$915$	27.3218	+	18.1656i	0.903229	+	0.600536i
$916$		0			0
$917$	−40.0280	+	11.1817i	−1.32184	+	0.369252i
$918$		0			0
$919$	−8.44635	−	14.6295i	−0.278619	−	0.482583i	0.692422	−	0.721492i	$-0.256543\pi$
$919$	−8.44635	−	14.6295i	−0.278619	−	0.482583i	−0.971042	+	0.238909i	$0.923210\pi$
$920$		0			0
$921$	−2.16484	+	34.2281i	−0.0713339	+	1.12786i
$922$		0			0
$923$	16.6303	+	28.8045i	0.547393	+	0.948112i
$924$		0			0
$925$	21.7766	−	37.7182i	0.716010	−	1.24017i
$926$		0			0
$927$	−1.86358	−	1.41648i	−0.0612081	−	0.0465234i
$928$		0			0
$929$	−6.79356			−0.222889			−0.111445	−	0.993771i	$-0.535548\pi$
$929$	−6.79356			−0.222889			−0.111445	+	0.993771i	$0.535548\pi$
$930$		0			0
$931$	3.02649	+	4.99436i	0.0991892	+	0.163684i
$932$		0			0
$933$	−20.8278	−	1.31730i	−0.681872	−	0.0431266i
$934$		0			0
$935$	−65.6210	−	37.8863i	−2.14604	−	1.23901i
$936$		0			0
$937$		−	5.14535i		−	0.168091i	−0.996462	−	0.0840456i	$-0.973216\pi$
$937$		−	5.14535i		−	0.168091i	0.996462	−	0.0840456i	$-0.0267841\pi$
$938$		0			0
$939$	3.28942	−	52.0088i	0.107346	−	1.69724i
$940$		0			0
$941$	0.920907			0.0300207			0.0150104	−	0.999887i	$-0.495222\pi$
$941$	0.920907			0.0300207			0.0150104	+	0.999887i	$0.495222\pi$
$942$		0			0
$943$			29.0733i			0.946756i
$944$		0			0
$945$	56.3754	−	4.68501i	1.83389	−	0.152403i
$946$		0			0
$947$			24.4835i			0.795606i	0.917471	+	0.397803i	$0.130227\pi$
$947$			24.4835i			0.795606i	−0.917471	+	0.397803i	$0.869773\pi$
$948$		0			0
$949$	−10.2582			−0.332995
$950$		0			0
$951$	1.38725	−	21.9337i	0.0449846	−	0.711248i
$952$		0			0
$953$			9.80916i			0.317750i	0.987299	+	0.158875i	$0.0507866\pi$
$953$			9.80916i			0.317750i	−0.987299	+	0.158875i	$0.949213\pi$
$954$		0			0
$955$	−88.3471	−	51.0072i	−2.85884	−	1.65055i
$956$		0			0
$957$	22.2206	+	1.40539i	0.718289	+	0.0454299i
$958$		0			0
$959$	−47.3175	−	12.1424i	−1.52796	−	0.392099i
$960$		0			0
$961$	13.0712			0.421651
$962$		0			0
$963$	22.8565	−	9.59019i	0.736542	−	0.309040i
$964$		0			0
$965$	54.8327	−	94.9731i	1.76513	−	3.05729i
$966$		0			0
$967$	−18.1376	−	31.4152i	−0.583264	−	1.01024i	−0.995089	−	0.0989807i	$-0.968442\pi$
$967$	−18.1376	−	31.4152i	−0.583264	−	1.01024i	0.411825	−	0.911263i	$-0.364892\pi$
$968$		0			0
$969$	−0.288515	+	4.56170i	−0.00926845	+	0.146543i
$970$		0			0
$971$	1.09772	+	1.90130i	0.0352274	+	0.0610157i	0.883102	−	0.469182i	$-0.155451\pi$
$971$	1.09772	+	1.90130i	0.0352274	+	0.0610157i	−0.847874	+	0.530198i	$0.822118\pi$
$972$		0			0
$973$	−11.2603	−	2.88958i	−0.360989	−	0.0926356i
$974$		0			0
$975$	−50.1297	−	33.3300i	−1.60543	−	1.06742i
$976$		0			0
$977$			42.7181i			1.36667i	0.730103	+	0.683337i	$0.239472\pi$
$977$			42.7181i			1.36667i	−0.730103	+	0.683337i	$0.760528\pi$
$978$		0			0
$979$	48.6266	+	28.0746i	1.55411	+	0.897267i
$980$		0			0
$981$	13.2009	−	17.3676i	0.421471	−	0.554504i
$982$		0			0
$983$	22.8781	+	39.6260i	0.729698	+	1.26387i	0.957011	+	0.290052i	$0.0936727\pi$
$983$	22.8781	+	39.6260i	0.729698	+	1.26387i	−0.227313	+	0.973822i	$0.572994\pi$
$984$		0			0
$985$	21.7757	+	12.5722i	0.693832	+	0.400584i
$986$		0			0
$987$	3.07998	+	3.42204i	0.0980368	+	0.108925i
$988$		0			0
$989$	−1.91113	+	1.10339i	−0.0607703	+	0.0350857i
$990$		0			0
$991$	−8.30690	+	14.3880i	−0.263877	+	0.457049i	−0.967269	−	0.253754i	$-0.918335\pi$
$991$	−8.30690	+	14.3880i	−0.263877	+	0.457049i	0.703392	+	0.710803i	$0.251668\pi$
$992$		0			0
$993$	−10.2128	−	0.645934i	−0.324094	−	0.0204981i
$994$		0			0
$995$	−1.58512	+	0.915169i	−0.0502517	+	0.0290128i
$996$		0			0
$997$	−18.6045	+	10.7413i	−0.589210	+	0.340181i	−0.764785	−	0.644285i	$-0.777155\pi$
$997$	−18.6045	+	10.7413i	−0.589210	+	0.340181i	0.175575	+	0.984466i	$0.443822\pi$
$998$		0			0
$999$	6.21971	+	17.9179i	0.196783	+	0.566897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.353.23	yes	48
3.2	odd	2		1512.2.bs.a.521.1		48
4.3	odd	2		1008.2.ca.e.353.2		48
7.5	odd	6		504.2.cx.a.425.17	yes	48
9.4	even	3		1512.2.cx.a.17.1		48
9.5	odd	6		504.2.cx.a.185.17	yes	48
12.11	even	2		3024.2.ca.e.2033.1		48
21.5	even	6		1512.2.cx.a.89.1		48
28.19	even	6		1008.2.df.e.929.8		48
36.23	even	6		1008.2.df.e.689.8		48
36.31	odd	6		3024.2.df.e.17.1		48
63.5	even	6	inner	504.2.bs.a.257.23	✓	48
63.40	odd	6		1512.2.bs.a.1097.1		48
84.47	odd	6		3024.2.df.e.1601.1		48
252.103	even	6		3024.2.ca.e.2609.1		48
252.131	odd	6		1008.2.ca.e.257.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.23	✓	48	63.5	even	6	inner
504.2.bs.a.353.23	yes	48	1.1	even	1	trivial
504.2.cx.a.185.17	yes	48	9.5	odd	6
504.2.cx.a.425.17	yes	48	7.5	odd	6
1008.2.ca.e.257.2		48	252.131	odd	6
1008.2.ca.e.353.2		48	4.3	odd	2
1008.2.df.e.689.8		48	36.23	even	6
1008.2.df.e.929.8		48	28.19	even	6
1512.2.bs.a.521.1		48	3.2	odd	2
1512.2.bs.a.1097.1		48	63.40	odd	6
1512.2.cx.a.17.1		48	9.4	even	3
1512.2.cx.a.89.1		48	21.5	even	6
3024.2.ca.e.2033.1		48	12.11	even	2
3024.2.ca.e.2609.1		48	252.103	even	6
3024.2.df.e.17.1		48	36.31	odd	6
3024.2.df.e.1601.1		48	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72860 + 0.109329i) q^{3} +(2.05742 - 3.56356i) q^{5} +(1.89056 + 1.85089i) q^{7} +(2.97609 + 0.377972i) q^{9} +(-5.04147 + 2.91069i) q^{11} +(2.52259 - 1.45642i) q^{13} +(3.94605 - 5.93502i) q^{15} +(-1.58162 + 2.73945i) q^{17} +(0.722488 - 0.417129i) q^{19} +(3.06566 + 3.40613i) q^{21} +(-6.14668 - 3.54879i) q^{23} +(-5.96595 - 10.3333i) q^{25} +(5.10314 + 0.978735i) q^{27} +(-1.91234 - 1.10409i) q^{29} +4.23424i q^{31} +(-9.03289 + 4.48023i) q^{33} +(10.4854 - 2.92907i) q^{35} +(1.82507 + 3.16112i) q^{37} +(4.51977 - 2.24177i) q^{39} +(-2.04811 - 3.54743i) q^{41} +(0.155460 - 0.269265i) q^{43} +(7.47000 - 9.82783i) q^{45} +1.00467 q^{47} +(0.148439 + 6.99843i) q^{49} +(-3.03349 + 4.56249i) q^{51} +(1.94801 + 1.12469i) q^{53} +23.9541i q^{55} +(1.29450 - 0.642058i) q^{57} +5.03496 q^{59} +4.60348i q^{61} +(4.92690 + 6.22299i) q^{63} -11.9859i q^{65} -9.99453 q^{67} +(-10.2371 - 6.80644i) q^{69} +11.4186i q^{71} +(-3.04990 - 1.76086i) q^{73} +(-9.18299 - 18.5144i) q^{75} +(-14.9186 - 3.82834i) q^{77} -1.15870 q^{79} +(8.71427 + 2.24976i) q^{81} +(7.57669 - 13.1232i) q^{83} +(6.50813 + 11.2724i) q^{85} +(-3.18496 - 2.11760i) q^{87} +(-4.82266 - 8.35309i) q^{89} +(7.46478 + 1.91558i) q^{91} +(-0.462926 + 7.31930i) q^{93} -3.43284i q^{95} +(-5.06969 - 2.92699i) q^{97} +(-16.1040 + 6.75696i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75}+ \cdots - 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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