LMFDB - Embedded newform 756.2.bo.a.169.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(85,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("756.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bo (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.3
Character	$\chi$	$=$	756.169
Dual form			756.2.bo.a.85.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42882 - 0.979012i) q^{3} +(-0.0286316 - 0.162378i) q^{5} +(0.766044 + 0.642788i) q^{7} +(1.08307 + 2.79767i) q^{9} +O(q^{10})$	\(q+(-1.42882 - 0.979012i) q^{3} +(-0.0286316 - 0.162378i) q^{5} +(0.766044 + 0.642788i) q^{7} +(1.08307 + 2.79767i) q^{9} +(0.534112 - 3.02910i) q^{11} +(-6.00062 - 2.18405i) q^{13} +(-0.118060 + 0.260040i) q^{15} +(0.807949 + 1.39941i) q^{17} +(3.03868 - 5.26315i) q^{19} +(-0.465245 - 1.66840i) q^{21} +(-2.43235 + 2.04098i) q^{23} +(4.67292 - 1.70080i) q^{25} +(1.19144 - 5.05771i) q^{27} +(-5.10566 + 1.85831i) q^{29} +(-1.91748 + 1.60896i) q^{31} +(-3.72868 + 3.80515i) q^{33} +(0.0824414 - 0.142793i) q^{35} +(-3.30926 - 5.73181i) q^{37} +(6.43562 + 8.99530i) q^{39} +(-9.10515 - 3.31400i) q^{41} +(0.285097 - 1.61686i) q^{43} +(0.423270 - 0.255968i) q^{45} +(-9.84038 - 8.25706i) q^{47} +(0.173648 + 0.984808i) q^{49} +(0.215622 - 2.79050i) q^{51} -13.5267 q^{53} -0.507152 q^{55} +(-9.49442 + 4.54520i) q^{57} +(-0.456799 - 2.59063i) q^{59} +(-5.98718 - 5.02384i) q^{61} +(-0.968627 + 2.83932i) q^{63} +(-0.182834 + 1.03690i) q^{65} +(9.02897 + 3.28628i) q^{67} +(5.47354 - 0.534904i) q^{69} +(3.36760 + 5.83286i) q^{71} +(-1.81178 + 3.13809i) q^{73} +(-8.34188 - 2.14470i) q^{75} +(2.35622 - 1.97711i) q^{77} +(11.2223 - 4.08460i) q^{79} +(-6.65392 + 6.06015i) q^{81} +(8.01162 - 2.91599i) q^{83} +(0.204100 - 0.171260i) q^{85} +(9.11439 + 2.34331i) q^{87} +(4.35416 - 7.54162i) q^{89} +(-3.19286 - 5.53020i) q^{91} +(4.31493 - 0.421679i) q^{93} +(-0.941621 - 0.342722i) q^{95} +(-1.39099 + 7.88871i) q^{97} +(9.05291 - 1.78646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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
$3$	−1.42882	−	0.979012i	−0.824931	−	0.565233i
$3$	−1.42882	−	0.979012i	−0.824931	−	0.565233i
$4$		0			0
$5$	−0.0286316	−	0.162378i	−0.0128044	−	0.0726176i	0.977736	−	0.209839i	$-0.0672940\pi$
$5$	−0.0286316	−	0.162378i	−0.0128044	−	0.0726176i	−0.990540	+	0.137221i	$0.956183\pi$
$6$		0			0
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$		0			0
$9$	1.08307	+	2.79767i	0.361024	+	0.932557i
$10$		0			0
$11$	0.534112	−	3.02910i	0.161041	−	0.913309i	−0.792012	−	0.610505i	$-0.790966\pi$
$11$	0.534112	−	3.02910i	0.161041	−	0.913309i	0.953053	−	0.302803i	$-0.0979225\pi$
$12$		0			0
$13$	−6.00062	−	2.18405i	−1.66427	−	0.605746i	−0.673247	−	0.739418i	$-0.735101\pi$
$13$	−6.00062	−	2.18405i	−1.66427	−	0.605746i	−0.991026	+	0.133672i	$0.957323\pi$
$14$		0			0
$15$	−0.118060	+	0.260040i	−0.0304831	+	0.0671420i
$16$		0			0
$17$	0.807949	+	1.39941i	0.195956	+	0.339406i	0.947214	−	0.320603i	$-0.103886\pi$
$17$	0.807949	+	1.39941i	0.195956	+	0.339406i	−0.751257	+	0.660010i	$0.770552\pi$
$18$		0			0
$19$	3.03868	−	5.26315i	0.697121	−	1.20745i	−0.272340	−	0.962201i	$-0.587797\pi$
$19$	3.03868	−	5.26315i	0.697121	−	1.20745i	0.969460	−	0.245248i	$-0.0788692\pi$
$20$		0			0
$21$	−0.465245	−	1.66840i	−0.101525	−	0.364074i
$22$		0			0
$23$	−2.43235	+	2.04098i	−0.507179	+	0.425574i	−0.860135	−	0.510066i	$-0.829621\pi$
$23$	−2.43235	+	2.04098i	−0.507179	+	0.425574i	0.352956	+	0.935640i	$0.385177\pi$
$24$		0			0
$25$	4.67292	−	1.70080i	0.934583	−	0.340160i
$26$		0			0
$27$	1.19144	−	5.05771i	0.229292	−	0.973358i
$28$		0			0
$29$	−5.10566	+	1.85831i	−0.948097	+	0.345079i	−0.769358	−	0.638817i	$-0.779424\pi$
$29$	−5.10566	+	1.85831i	−0.948097	+	0.345079i	−0.178739	+	0.983897i	$0.557202\pi$
$30$		0			0
$31$	−1.91748	+	1.60896i	−0.344390	+	0.288978i	−0.798533	−	0.601951i	$-0.794390\pi$
$31$	−1.91748	+	1.60896i	−0.344390	+	0.288978i	0.454143	+	0.890929i	$0.349946\pi$
$32$		0			0
$33$	−3.72868	+	3.80515i	−0.649080	+	0.662391i
$34$		0			0
$35$	0.0824414	−	0.142793i	0.0139351	−	0.0241364i
$36$		0			0
$37$	−3.30926	−	5.73181i	−0.544039	−	0.942303i	−0.998667	−	0.0516217i	$-0.983561\pi$
$37$	−3.30926	−	5.73181i	−0.544039	−	0.942303i	0.454628	−	0.890682i	$-0.349772\pi$
$38$		0			0
$39$	6.43562	+	8.99530i	1.03052	+	1.44040i
$40$		0			0
$41$	−9.10515	−	3.31400i	−1.42199	−	0.517561i	−0.487363	−	0.873200i	$-0.662041\pi$
$41$	−9.10515	−	3.31400i	−1.42199	−	0.517561i	−0.934623	+	0.355639i	$0.884263\pi$
$42$		0			0
$43$	0.285097	−	1.61686i	0.0434769	−	0.246570i	−0.955322	−	0.295567i	$-0.904491\pi$
$43$	0.285097	−	1.61686i	0.0434769	−	0.246570i	0.998799	+	0.0489973i	$0.0156026\pi$
$44$		0			0
$45$	0.423270	−	0.255968i	0.0630973	−	0.0381575i
$46$		0			0
$47$	−9.84038	−	8.25706i	−1.43537	−	1.20442i	−0.942453	−	0.334338i	$-0.891487\pi$
$47$	−9.84038	−	8.25706i	−1.43537	−	1.20442i	−0.492914	−	0.870078i	$-0.664068\pi$
$48$		0			0
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$		0			0
$51$	0.215622	−	2.79050i	0.0301931	−	0.390748i
$52$		0			0
$53$	−13.5267			−1.85804			−0.929019	−	0.370032i	$-0.879347\pi$
$53$	−13.5267			−1.85804			−0.929019	+	0.370032i	$0.879347\pi$
$54$		0			0
$55$	−0.507152			−0.0683843
$56$		0			0
$57$	−9.49442	+	4.54520i	−1.25757	+	0.602027i
$58$		0			0
$59$	−0.456799	−	2.59063i	−0.0594701	−	0.337272i	0.940527	−	0.339719i	$-0.110332\pi$
$59$	−0.456799	−	2.59063i	−0.0594701	−	0.337272i	−0.999997	+	0.00244740i	$0.999221\pi$
$60$		0			0
$61$	−5.98718	−	5.02384i	−0.766579	−	0.643236i	0.173251	−	0.984878i	$-0.444573\pi$
$61$	−5.98718	−	5.02384i	−0.766579	−	0.643236i	−0.939830	+	0.341641i	$0.889017\pi$
$62$		0			0
$63$	−0.968627	+	2.83932i	−0.122036	+	0.357721i
$64$		0			0
$65$	−0.182834	+	1.03690i	−0.0226777	+	0.128612i
$66$		0			0
$67$	9.02897	+	3.28628i	1.10306	+	0.401482i	0.828445	−	0.560071i	$-0.189226\pi$
$67$	9.02897	+	3.28628i	1.10306	+	0.401482i	0.274619	+	0.961553i	$0.411448\pi$
$68$		0			0
$69$	5.47354	−	0.534904i	0.658936	−	0.0643949i
$70$		0			0
$71$	3.36760	+	5.83286i	0.399661	+	0.692233i	0.993684	−	0.112215i	$-0.0357946\pi$
$71$	3.36760	+	5.83286i	0.399661	+	0.692233i	−0.594023	+	0.804448i	$0.702461\pi$
$72$		0			0
$73$	−1.81178	+	3.13809i	−0.212053	+	0.367286i	−0.952357	−	0.304986i	$-0.901348\pi$
$73$	−1.81178	+	3.13809i	−0.212053	+	0.367286i	0.740304	+	0.672272i	$0.234682\pi$
$74$		0			0
$75$	−8.34188	−	2.14470i	−0.963237	−	0.247648i
$76$		0			0
$77$	2.35622	−	1.97711i	0.268517	−	0.225312i
$78$		0			0
$79$	11.2223	−	4.08460i	1.26261	−	0.459553i	0.377967	−	0.925819i	$-0.376623\pi$
$79$	11.2223	−	4.08460i	1.26261	−	0.459553i	0.884645	+	0.466266i	$0.154401\pi$
$80$		0			0
$81$	−6.65392	+	6.06015i	−0.739324	+	0.673350i
$82$		0			0
$83$	8.01162	−	2.91599i	0.879390	−	0.320072i	0.137426	−	0.990512i	$-0.456117\pi$
$83$	8.01162	−	2.91599i	0.879390	−	0.320072i	0.741964	+	0.670440i	$0.233895\pi$
$84$		0			0
$85$	0.204100	−	0.171260i	0.0221378	−	0.0185758i
$86$		0			0
$87$	9.11439	+	2.34331i	0.977165	+	0.251229i
$88$		0			0
$89$	4.35416	−	7.54162i	0.461540	−	0.799411i	−0.537498	−	0.843265i	$-0.680630\pi$
$89$	4.35416	−	7.54162i	0.461540	−	0.799411i	0.999038	+	0.0438545i	$0.0139638\pi$
$90$		0			0
$91$	−3.19286	−	5.53020i	−0.334703	−	0.579723i
$92$		0			0
$93$	4.31493	−	0.421679i	0.447438	−	0.0437261i
$94$		0			0
$95$	−0.941621	−	0.342722i	−0.0966082	−	0.0351625i
$96$		0			0
$97$	−1.39099	+	7.88871i	−0.141234	+	0.800977i	0.829080	+	0.559130i	$0.188865\pi$
$97$	−1.39099	+	7.88871i	−0.141234	+	0.800977i	−0.970314	+	0.241848i	$0.922247\pi$
$98$		0			0
$99$	9.05291	−	1.78646i	0.909852	−	0.179546i
$100$		0			0
$101$	11.8127	+	9.91201i	1.17540	+	0.986282i	0.999998	+	0.00178559i	$0.000568371\pi$
$101$	11.8127	+	9.91201i	1.17540	+	0.986282i	0.175406	+	0.984496i	$0.443876\pi$
$102$		0			0
$103$	−1.06669	−	6.04948i	−0.105104	−	0.596073i	−0.991179	−	0.132531i	$-0.957689\pi$
$103$	−1.06669	−	6.04948i	−0.105104	−	0.596073i	0.886075	−	0.463542i	$-0.153422\pi$
$104$		0			0
$105$	−0.257590	+	0.123314i	−0.0251382	+	0.0120342i
$106$		0			0
$107$	−1.66675			−0.161131			−0.0805653	−	0.996749i	$-0.525673\pi$
$107$	−1.66675			−0.161131			−0.0805653	+	0.996749i	$0.525673\pi$
$108$		0			0
$109$	4.72279			0.452361			0.226180	−	0.974085i	$-0.427376\pi$
$109$	4.72279			0.452361			0.226180	+	0.974085i	$0.427376\pi$
$110$		0			0
$111$	−0.883161	+	11.4295i	−0.0838259	+	1.08484i
$112$		0			0
$113$	−0.261497	−	1.48302i	−0.0245996	−	0.139511i	0.970034	−	0.242968i	$-0.0781208\pi$
$113$	−0.261497	−	1.48302i	−0.0245996	−	0.139511i	−0.994634	+	0.103457i	$0.967010\pi$
$114$		0			0
$115$	0.401052	+	0.336523i	0.0373983	+	0.0313809i
$116$		0			0
$117$	−0.388852	−	19.1532i	−0.0359494	−	1.77072i
$118$		0			0
$119$	−0.280598	+	1.59135i	−0.0257224	+	0.145879i
$120$		0			0
$121$	1.44643	+	0.526459i	0.131494	+	0.0478599i
$122$		0			0
$123$	9.76520	+	13.6492i	0.880499	+	1.23071i
$124$		0			0
$125$	−0.822173	−	1.42404i	−0.0735373	−	0.127370i
$126$		0			0
$127$	2.57741	−	4.46420i	0.228708	−	0.396134i	−0.728717	−	0.684814i	$-0.759883\pi$
$127$	2.57741	−	4.46420i	0.228708	−	0.396134i	0.957425	+	0.288681i	$0.0932166\pi$
$128$		0			0
$129$	−1.99028	+	2.03110i	−0.175235	+	0.178828i
$130$		0			0
$131$	−15.9517	+	13.3850i	−1.39370	+	1.16946i	−0.429887	+	0.902883i	$0.641447\pi$
$131$	−15.9517	+	13.3850i	−1.39370	+	1.16946i	−0.963815	+	0.266572i	$0.914109\pi$
$132$		0			0
$133$	5.71085	−	2.07858i	0.495193	−	0.180236i
$134$		0			0
$135$	−0.855373	−	0.0486525i	−0.0736188	−	0.00418734i
$136$		0			0
$137$	2.94732	−	1.07274i	0.251807	−	0.0916501i	−0.213033	−	0.977045i	$-0.568334\pi$
$137$	2.94732	−	1.07274i	0.251807	−	0.0916501i	0.464840	+	0.885395i	$0.346112\pi$
$138$		0			0
$139$	16.4064	−	13.7666i	1.39157	−	1.16767i	0.426873	−	0.904312i	$-0.359615\pi$
$139$	16.4064	−	13.7666i	1.39157	−	1.16767i	0.964699	−	0.263355i	$-0.0848292\pi$
$140$		0			0
$141$	5.97640	+	21.4317i	0.503304	+	1.80488i
$142$		0			0
$143$	−9.82071	+	17.0100i	−0.821249	+	1.42244i
$144$		0			0
$145$	0.447931	+	0.775840i	0.0371987	+	0.0644300i
$146$		0			0
$147$	0.716026	−	1.57712i	0.0590568	−	0.130079i
$148$		0			0
$149$	−5.61883	−	2.04509i	−0.460312	−	0.167540i	0.101447	−	0.994841i	$-0.467653\pi$
$149$	−5.61883	−	2.04509i	−0.460312	−	0.167540i	−0.561759	+	0.827301i	$0.689875\pi$
$150$		0			0
$151$	3.01664	−	17.1082i	0.245491	−	1.39225i	−0.573860	−	0.818954i	$-0.694554\pi$
$151$	3.01664	−	17.1082i	0.245491	−	1.39225i	0.819350	−	0.573293i	$-0.194334\pi$
$152$		0			0
$153$	−3.04002	+	3.77603i	−0.245771	+	0.305274i
$154$		0			0
$155$	0.316160	+	0.265290i	0.0253946	+	0.0213086i
$156$		0			0
$157$	2.47372	+	14.0292i	0.197425	+	1.11965i	0.908923	+	0.416963i	$0.136906\pi$
$157$	2.47372	+	14.0292i	0.197425	+	1.11965i	−0.711499	+	0.702687i	$0.751983\pi$
$158$		0			0
$159$	19.3273	+	13.2428i	1.53275	+	1.05022i
$160$		0			0
$161$	−3.17520			−0.250241
$162$		0			0
$163$	−5.21846			−0.408741			−0.204371	−	0.978894i	$-0.565515\pi$
$163$	−5.21846			−0.408741			−0.204371	+	0.978894i	$0.565515\pi$
$164$		0			0
$165$	0.724630	+	0.496508i	0.0564124	+	0.0386531i
$166$		0			0
$167$	−3.82378	−	21.6857i	−0.295893	−	1.67809i	−0.663551	−	0.748131i	$-0.730952\pi$
$167$	−3.82378	−	21.6857i	−0.295893	−	1.67809i	0.367659	−	0.929961i	$-0.380160\pi$
$168$		0			0
$169$	21.2788	+	17.8550i	1.63683	+	1.37346i
$170$		0			0
$171$	18.0157	+	2.80086i	1.37769	+	0.214187i
$172$		0			0
$173$	0.761111	−	4.31647i	0.0578662	−	0.328175i	−0.942108	−	0.335308i	$-0.891159\pi$
$173$	0.761111	−	4.31647i	0.0578662	−	0.328175i	0.999975	+	0.00713314i	$0.00227057\pi$
$174$		0			0
$175$	4.67292	+	1.70080i	0.353239	+	0.128569i
$176$		0			0
$177$	−1.88358	+	4.14877i	−0.141578	+	0.311841i
$178$		0			0
$179$	6.35326	+	11.0042i	0.474865	+	0.822491i	0.999586	−	0.0287838i	$-0.00916345\pi$
$179$	6.35326	+	11.0042i	0.474865	+	0.822491i	−0.524720	+	0.851275i	$0.675830\pi$
$180$		0			0
$181$	8.63501	−	14.9563i	0.641836	−	1.11169i	−0.343187	−	0.939267i	$-0.611507\pi$
$181$	8.63501	−	14.9563i	0.641836	−	1.11169i	0.985023	−	0.172425i	$-0.0551601\pi$
$182$		0			0
$183$	3.63622	+	13.0397i	0.268797	+	0.963922i
$184$		0			0
$185$	−0.835969	+	0.701461i	−0.0614617	+	0.0515725i
$186$		0			0
$187$	4.67049	−	1.69992i	0.341540	−	0.124310i
$188$		0			0
$189$	4.16373	−	3.10859i	0.302867	−	0.226117i
$190$		0			0
$191$	21.4676	−	7.81355i	1.55334	−	0.565369i	0.584140	−	0.811653i	$-0.301432\pi$
$191$	21.4676	−	7.81355i	1.55334	−	0.565369i	0.969198	+	0.246284i	$0.0792096\pi$
$192$		0			0
$193$	−15.3088	+	12.8456i	−1.10195	+	0.924645i	−0.997555	−	0.0698913i	$-0.977735\pi$
$193$	−15.3088	+	12.8456i	−1.10195	+	0.924645i	−0.104394	+	0.994536i	$0.533290\pi$
$194$		0			0
$195$	1.27637	−	1.30255i	0.0914031	−	0.0932776i
$196$		0			0
$197$	−1.69377	+	2.93369i	−0.120676	+	0.209017i	−0.920034	−	0.391837i	$-0.871840\pi$
$197$	−1.69377	+	2.93369i	−0.120676	+	0.209017i	0.799358	+	0.600854i	$0.205173\pi$
$198$		0			0
$199$	−8.59322	−	14.8839i	−0.609157	−	1.05509i	−0.991380	−	0.131021i	$-0.958174\pi$
$199$	−8.59322	−	14.8839i	−0.609157	−	1.05509i	0.382222	−	0.924070i	$-0.375159\pi$
$200$		0			0
$201$	−9.68349	−	13.5350i	−0.683021	−	0.954683i
$202$		0			0
$203$	−5.10566	−	1.85831i	−0.358347	−	0.130428i
$204$		0			0
$205$	−0.277426	+	1.57336i	−0.0193763	+	0.109888i
$206$		0			0
$207$	−8.34439	−	4.59438i	−0.579975	−	0.319331i
$208$		0			0
$209$	−14.3196	−	12.0156i	−0.990508	−	0.831135i
$210$		0			0
$211$	1.37113	+	7.77609i	0.0943928	+	0.535328i	0.994932	+	0.100553i	$0.0320611\pi$
$211$	1.37113	+	7.77609i	0.0943928	+	0.535328i	−0.900539	+	0.434775i	$0.856828\pi$
$212$		0			0
$213$	0.898731	−	11.6310i	0.0615800	−	0.796946i
$214$		0			0
$215$	−0.270706			−0.0184620
$216$		0			0
$217$	−2.50310			−0.169921
$218$		0			0
$219$	5.66095	−	2.71003i	0.382531	−	0.183127i
$220$		0			0
$221$	−1.79182	−	10.1619i	−0.120531	−	0.683565i
$222$		0			0
$223$	1.81492	+	1.52289i	0.121536	+	0.101981i	0.701530	−	0.712640i	$-0.252501\pi$
$223$	1.81492	+	1.52289i	0.121536	+	0.101981i	−0.579994	+	0.814621i	$0.696945\pi$
$224$		0			0
$225$	9.81938	+	11.2312i	0.654625	+	0.748746i
$226$		0			0
$227$	−1.42095	+	8.05862i	−0.0943119	+	0.534869i	0.900644	+	0.434557i	$0.143095\pi$
$227$	−1.42095	+	8.05862i	−0.0943119	+	0.534869i	−0.994956	+	0.100312i	$0.968016\pi$
$228$		0			0
$229$	−14.1418	−	5.14720i	−0.934517	−	0.340136i	−0.170519	−	0.985354i	$-0.554544\pi$
$229$	−14.1418	−	5.14720i	−0.934517	−	0.340136i	−0.763999	+	0.645218i	$0.776767\pi$
$230$		0			0
$231$	−5.30224	+	0.518164i	−0.348862	+	0.0340927i
$232$		0			0
$233$	5.98265	+	10.3623i	0.391937	+	0.678854i	0.992705	−	0.120569i	$-0.0384719\pi$
$233$	5.98265	+	10.3623i	0.391937	+	0.678854i	−0.600768	+	0.799423i	$0.705139\pi$
$234$		0			0
$235$	−1.05902	+	1.83427i	−0.0690827	+	0.119655i
$236$		0			0
$237$	−20.0336	−	5.15064i	−1.30132	−	0.334570i
$238$		0			0
$239$	−20.7058	+	17.3742i	−1.33935	+	1.12385i	−0.357555	+	0.933892i	$0.616390\pi$
$239$	−20.7058	+	17.3742i	−1.33935	+	1.12385i	−0.981793	+	0.189954i	$0.939166\pi$
$240$		0			0
$241$	5.30262	−	1.92999i	0.341571	−	0.124322i	−0.165538	−	0.986203i	$-0.552936\pi$
$241$	5.30262	−	1.92999i	0.341571	−	0.124322i	0.507110	+	0.861882i	$0.330714\pi$
$242$		0			0
$243$	15.4402	−	2.14462i	0.990491	−	0.137577i
$244$		0			0
$245$	0.154939	−	0.0563932i	0.00989870	−	0.00360283i
$246$		0			0
$247$	−29.7289	+	24.9455i	−1.89161	+	1.58725i
$248$		0			0
$249$	−14.3020	−	3.67704i	−0.906351	−	0.233023i
$250$		0			0
$251$	−9.63955	+	16.6962i	−0.608443	+	1.05385i	0.383054	+	0.923726i	$0.374872\pi$
$251$	−9.63955	+	16.6962i	−0.608443	+	1.05385i	−0.991497	+	0.130128i	$0.958461\pi$
$252$		0			0
$253$	4.88319	+	8.45794i	0.307004	+	0.531746i
$254$		0			0
$255$	−0.459289	+	0.0448842i	−0.0287618	+	0.00281076i
$256$		0			0
$257$	21.0745	+	7.67049i	1.31459	+	0.478472i	0.901721	−	0.432318i	$-0.142304\pi$
$257$	21.0745	+	7.67049i	1.31459	+	0.478472i	0.412870	+	0.910790i	$0.364526\pi$
$258$		0			0
$259$	1.14929	−	6.51797i	0.0714137	−	0.405007i
$260$		0			0
$261$	−10.7287	−	12.2713i	−0.664091	−	0.759573i
$262$		0			0
$263$	10.7610	+	9.02956i	0.663553	+	0.556787i	0.911149	−	0.412076i	$-0.135196\pi$
$263$	10.7610	+	9.02956i	0.663553	+	0.556787i	−0.247597	+	0.968863i	$0.579641\pi$
$264$		0			0
$265$	0.387292	+	2.19644i	0.0237911	+	0.134926i
$266$		0			0
$267$	−13.6047	+	6.51287i	−0.832592	+	0.398581i
$268$		0			0
$269$	28.9395			1.76447			0.882237	−	0.470806i	$-0.156037\pi$
$269$	28.9395			1.76447			0.882237	+	0.470806i	$0.156037\pi$
$270$		0			0
$271$	−3.68386			−0.223778			−0.111889	−	0.993721i	$-0.535690\pi$
$271$	−3.68386			−0.223778			−0.111889	+	0.993721i	$0.535690\pi$
$272$		0			0
$273$	−0.852098	+	11.0275i	−0.0515713	+	0.667417i
$274$		0			0
$275$	−2.65604	−	15.0632i	−0.160165	−	0.908343i
$276$		0			0
$277$	10.2756	+	8.62226i	0.617401	+	0.518061i	0.896985	−	0.442060i	$-0.145752\pi$
$277$	10.2756	+	8.62226i	0.617401	+	0.518061i	−0.279584	+	0.960121i	$0.590197\pi$
$278$		0			0
$279$	−6.57810	−	3.62187i	−0.393821	−	0.216836i
$280$		0			0
$281$	5.13440	−	29.1186i	0.306292	−	1.73707i	−0.311066	−	0.950388i	$-0.600686\pi$
$281$	5.13440	−	29.1186i	0.306292	−	1.73707i	0.617358	−	0.786682i	$-0.288203\pi$
$282$		0			0
$283$	−3.65751	−	1.33123i	−0.217417	−	0.0791332i	0.231015	−	0.972950i	$-0.425795\pi$
$283$	−3.65751	−	1.33123i	−0.217417	−	0.0791332i	−0.448432	+	0.893817i	$0.648017\pi$
$284$		0			0
$285$	1.00988	+	1.41155i	0.0598201	+	0.0836128i
$286$		0			0
$287$	−4.84475	−	8.39135i	−0.285977	−	0.495326i
$288$		0			0
$289$	7.19444	−	12.4611i	0.423202	−	0.733008i
$290$		0			0
$291$	9.71063	−	9.90978i	0.569247	−	0.580921i
$292$		0			0
$293$	−14.1829	+	11.9009i	−0.828573	+	0.695255i	−0.954963	−	0.296725i	$-0.904105\pi$
$293$	−14.1829	+	11.9009i	−0.828573	+	0.695255i	0.126390	+	0.991981i	$0.459661\pi$
$294$		0			0
$295$	−0.407583	+	0.148348i	−0.0237304	+	0.00863715i
$296$		0			0
$297$	−14.6840	−	6.31037i	−0.852051	−	0.366165i
$298$		0			0
$299$	19.0532	−	6.93479i	1.10187	−	0.401049i
$300$		0			0
$301$	1.25770	−	1.05533i	0.0724925	−	0.0608284i
$302$		0			0
$303$	−7.17424	−	25.7273i	−0.412149	−	1.47799i
$304$		0			0
$305$	−0.644337	+	1.11603i	−0.0368947	+	0.0639034i
$306$		0			0
$307$	−5.48391	−	9.49842i	−0.312984	−	0.542103i	0.666023	−	0.745931i	$-0.267995\pi$
$307$	−5.48391	−	9.49842i	−0.312984	−	0.542103i	−0.979007	+	0.203828i	$0.934662\pi$
$308$		0			0
$309$	−4.39841	+	9.68794i	−0.250217	+	0.551128i
$310$		0			0
$311$	8.15998	+	2.96999i	0.462710	+	0.168413i	0.562847	−	0.826561i	$-0.309706\pi$
$311$	8.15998	+	2.96999i	0.462710	+	0.168413i	−0.100137	+	0.994974i	$0.531928\pi$
$312$		0			0
$313$	−0.125627	+	0.712466i	−0.00710086	+	0.0402710i	−0.988152	−	0.153476i	$-0.950953\pi$
$313$	−0.125627	+	0.712466i	−0.00710086	+	0.0402710i	0.981051	+	0.193747i	$0.0620642\pi$
$314$		0			0
$315$	0.488777	+	0.0759893i	0.0275394	+	0.00428151i
$316$		0			0
$317$	−4.78174	−	4.01236i	−0.268570	−	0.225357i	0.498550	−	0.866861i	$-0.333866\pi$
$317$	−4.78174	−	4.01236i	−0.268570	−	0.225357i	−0.767119	+	0.641504i	$0.778311\pi$
$318$		0			0
$319$	2.90201	+	16.4581i	0.162481	+	0.921478i
$320$		0			0
$321$	2.38149	+	1.63177i	0.132922	+	0.0910763i
$322$		0			0
$323$	9.82039			0.546421
$324$		0			0
$325$	−31.7550			−1.76145
$326$		0			0
$327$	−6.74802	−	4.62366i	−0.373167	−	0.255689i
$328$		0			0
$329$	−2.23063	−	12.6506i	−0.122979	−	0.697448i
$330$		0			0
$331$	−4.68103	−	3.92785i	−0.257293	−	0.215894i	0.505012	−	0.863112i	$-0.331488\pi$
$331$	−4.68103	−	3.92785i	−0.257293	−	0.215894i	−0.762305	+	0.647218i	$0.775932\pi$
$332$		0			0
$333$	12.4515	−	15.4662i	0.682340	−	0.847541i
$334$		0			0
$335$	0.275105	−	1.56020i	0.0150306	−	0.0852426i
$336$		0			0
$337$	6.26566	+	2.28051i	0.341312	+	0.124227i	0.506989	−	0.861953i	$-0.330759\pi$
$337$	6.26566	+	2.28051i	0.341312	+	0.124227i	−0.165677	+	0.986180i	$0.552981\pi$
$338$		0			0
$339$	−1.07826	+	2.37499i	−0.0585633	+	0.128991i
$340$		0			0
$341$	3.84955	+	6.66762i	0.208465	+	0.361072i
$342$		0			0
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$		0			0
$345$	−0.243573	−	0.873466i	−0.0131135	−	0.0470258i
$346$		0			0
$347$	−0.896284	+	0.752072i	−0.0481151	+	0.0403733i	−0.666528	−	0.745480i	$-0.732220\pi$
$347$	−0.896284	+	0.752072i	−0.0481151	+	0.0403733i	0.618413	+	0.785853i	$0.287776\pi$
$348$		0			0
$349$	8.92783	−	3.24946i	0.477896	−	0.173940i	−0.0918299	−	0.995775i	$-0.529272\pi$
$349$	8.92783	−	3.24946i	0.477896	−	0.173940i	0.569726	+	0.821835i	$0.307049\pi$
$350$		0			0
$351$	−18.1956	+	27.7473i	−0.971212	+	1.48104i
$352$		0			0
$353$	−8.86804	+	3.22770i	−0.471998	+	0.171793i	−0.567057	−	0.823678i	$-0.691918\pi$
$353$	−8.86804	+	3.22770i	−0.471998	+	0.171793i	0.0950593	+	0.995472i	$0.469696\pi$
$354$		0			0
$355$	0.850707	−	0.713828i	0.0451508	−	0.0378860i
$356$		0			0
$357$	1.95887	−	1.99905i	0.103675	−	0.105801i
$358$		0			0
$359$	−11.5182	+	19.9502i	−0.607909	+	1.05293i	0.383675	+	0.923468i	$0.374658\pi$
$359$	−11.5182	+	19.9502i	−0.607909	+	1.05293i	−0.991584	+	0.129461i	$0.958675\pi$
$360$		0			0
$361$	−8.96714	−	15.5315i	−0.471955	−	0.817450i
$362$		0			0
$363$	−1.55129	−	2.16829i	−0.0814215	−	0.113806i
$364$		0			0
$365$	0.561431	+	0.204344i	0.0293866	+	0.0106959i
$366$		0			0
$367$	−1.26851	+	7.19407i	−0.0662156	+	0.375527i	0.933635	+	0.358227i	$0.116618\pi$
$367$	−1.26851	+	7.19407i	−0.0662156	+	0.375527i	−0.999850	+	0.0173009i	$0.994493\pi$
$368$		0			0
$369$	−0.590031	−	29.0625i	−0.0307158	−	1.51293i
$370$		0			0
$371$	−10.3621	−	8.69481i	−0.537972	−	0.451412i
$372$		0			0
$373$	−3.60398	−	20.4392i	−0.186607	−	1.05830i	−0.923873	−	0.382699i	$-0.874995\pi$
$373$	−3.60398	−	20.4392i	−0.186607	−	1.05830i	0.737266	−	0.675603i	$-0.236116\pi$
$374$		0			0
$375$	−0.219418	+	2.83962i	−0.0113307	+	0.146638i
$376$		0			0
$377$	34.6958			1.78692
$378$		0			0
$379$	10.4447			0.536508			0.268254	−	0.963348i	$-0.413553\pi$
$379$	10.4447			0.536508			0.268254	+	0.963348i	$0.413553\pi$
$380$		0			0
$381$	−8.05317	+	3.85524i	−0.412576	+	0.197510i
$382$		0			0
$383$	−3.37101	−	19.1179i	−0.172251	−	0.976881i	−0.941270	−	0.337656i	$-0.890366\pi$
$383$	−3.37101	−	19.1179i	−0.172251	−	0.976881i	0.769019	−	0.639226i	$-0.220745\pi$
$384$		0			0
$385$	−0.388501	−	0.325991i	−0.0197998	−	0.0166140i
$386$		0			0
$387$	4.83223	−	0.953572i	0.245636	−	0.0484728i
$388$		0			0
$389$	2.91533	−	16.5337i	0.147813	−	0.838290i	−0.817252	−	0.576280i	$-0.804504\pi$
$389$	2.91533	−	16.5337i	0.147813	−	0.838290i	0.965065	−	0.262010i	$-0.0843852\pi$
$390$		0			0
$391$	−4.82138	−	1.75484i	−0.243828	−	0.0887460i
$392$		0			0
$393$	35.8962	−	3.50797i	1.81072	−	0.176954i
$394$		0			0
$395$	−0.984561	−	1.70531i	−0.0495387	−	0.0858035i
$396$		0			0
$397$	−9.80115	+	16.9761i	−0.491906	+	0.852006i	−0.999957	−	0.00932133i	$-0.997033\pi$
$397$	−9.80115	+	16.9761i	−0.491906	+	0.852006i	0.508051	+	0.861327i	$0.330366\pi$
$398$		0			0
$399$	−10.1947	−	2.62107i	−0.510376	−	0.131218i
$400$		0			0
$401$	−4.59501	+	3.85567i	−0.229464	+	0.192543i	−0.750269	−	0.661132i	$-0.770076\pi$
$401$	−4.59501	+	3.85567i	−0.229464	+	0.192543i	0.520805	+	0.853675i	$0.325632\pi$
$402$		0			0
$403$	15.0201	−	5.46688i	0.748206	−	0.272325i
$404$		0			0
$405$	1.17455	+	0.906937i	0.0583637	+	0.0450661i
$406$		0			0
$407$	−19.1297	+	6.96266i	−0.948226	+	0.345126i
$408$		0			0
$409$	−22.2205	+	18.6452i	−1.09873	+	0.921947i	−0.997339	−	0.0728996i	$-0.976775\pi$
$409$	−22.2205	+	18.6452i	−1.09873	+	0.921947i	−0.101394	+	0.994846i	$0.532330\pi$
$410$		0			0
$411$	−5.26142	−	1.35271i	−0.259527	−	0.0667243i
$412$		0			0
$413$	1.31530	−	2.27817i	0.0647217	−	0.112101i
$414$		0			0
$415$	−0.702878	−	1.21742i	−0.0345029	−	0.0597608i
$416$		0			0
$417$	−36.9195	+	3.60797i	−1.80795	+	0.176683i
$418$		0			0
$419$	3.96385	+	1.44272i	0.193647	+	0.0704817i	0.437023	−	0.899450i	$-0.356033\pi$
$419$	3.96385	+	1.44272i	0.193647	+	0.0704817i	−0.243376	+	0.969932i	$0.578255\pi$
$420$		0			0
$421$	−2.32150	+	13.1659i	−0.113143	+	0.641665i	0.874510	+	0.485007i	$0.161183\pi$
$421$	−2.32150	+	13.1659i	−0.113143	+	0.641665i	−0.987653	+	0.156658i	$0.949928\pi$
$422$		0			0
$423$	12.4427	−	36.4731i	0.604985	−	1.77338i
$424$		0			0
$425$	6.15560	+	5.16516i	0.298590	+	0.250547i
$426$		0			0
$427$	−1.35718	−	7.69696i	−0.0656787	−	0.372482i
$428$		0			0
$429$	30.6850	−	14.6896i	1.48149	−	0.709222i
$430$		0			0
$431$	−21.4839			−1.03484			−0.517422	−	0.855730i	$-0.673108\pi$
$431$	−21.4839			−1.03484			−0.517422	+	0.855730i	$0.673108\pi$
$432$		0			0
$433$	8.22905			0.395463			0.197731	−	0.980256i	$-0.436643\pi$
$433$	8.22905			0.395463			0.197731	+	0.980256i	$0.436643\pi$
$434$		0			0
$435$	0.119542	−	1.54707i	0.00573160	−	0.0741762i
$436$		0			0
$437$	3.35086	+	19.0037i	0.160293	+	0.909069i
$438$		0			0
$439$	5.07779	+	4.26077i	0.242350	+	0.203355i	0.755870	−	0.654722i	$-0.227214\pi$
$439$	5.07779	+	4.26077i	0.242350	+	0.203355i	−0.513520	+	0.858078i	$0.671659\pi$
$440$		0			0
$441$	−2.56709	+	1.55243i	−0.122243	+	0.0739251i
$442$		0			0
$443$	2.54379	−	14.4265i	0.120859	−	0.685425i	−0.862823	−	0.505507i	$-0.831306\pi$
$443$	2.54379	−	14.4265i	0.120859	−	0.685425i	0.983682	−	0.179918i	$-0.0575833\pi$
$444$		0			0
$445$	−1.34926	−	0.491090i	−0.0639610	−	0.0232799i
$446$		0			0
$447$	6.02615	+	8.42297i	0.285027	+	0.398393i
$448$		0			0
$449$	3.92525	+	6.79874i	0.185244	+	0.320852i	0.943659	−	0.330920i	$-0.107359\pi$
$449$	3.92525	+	6.79874i	0.185244	+	0.320852i	−0.758415	+	0.651772i	$0.774026\pi$
$450$		0			0
$451$	−14.9016	+	25.8104i	−0.701691	+	1.21536i
$452$		0			0
$453$	−21.0594	+	21.4913i	−0.989457	+	1.00975i
$454$		0			0
$455$	−0.806565	+	0.676789i	−0.0378124	+	0.0317283i
$456$		0			0
$457$	−38.3808	+	13.9695i	−1.79538	+	0.653464i	−0.796576	+	0.604538i	$0.793358\pi$
$457$	−38.3808	+	13.9695i	−1.79538	+	0.653464i	−0.998802	+	0.0489259i	$0.984420\pi$
$458$		0			0
$459$	8.04043	−	2.41907i	0.375295	−	0.112912i
$460$		0			0
$461$	16.4401	−	5.98371i	0.765693	−	0.278689i	0.0704990	−	0.997512i	$-0.477541\pi$
$461$	16.4401	−	5.98371i	0.765693	−	0.278689i	0.695194	+	0.718823i	$0.255319\pi$
$462$		0			0
$463$	8.02433	−	6.73321i	0.372922	−	0.312919i	−0.436994	−	0.899464i	$-0.643957\pi$
$463$	8.02433	−	6.73321i	0.372922	−	0.312919i	0.809916	+	0.586546i	$0.199512\pi$
$464$		0			0
$465$	−0.192015	−	0.688576i	−0.00890447	−	0.0319320i
$466$		0			0
$467$	−2.14759	+	3.71973i	−0.0993784	+	0.172129i	−0.911428	−	0.411461i	$-0.865019\pi$
$467$	−2.14759	+	3.71973i	−0.0993784	+	0.172129i	0.812049	+	0.583589i	$0.198352\pi$
$468$		0			0
$469$	4.80421	+	8.32114i	0.221838	+	0.384235i
$470$		0			0
$471$	10.2002	−	22.4670i	0.470001	−	1.03523i
$472$		0			0
$473$	−4.74537	−	1.72718i	−0.218193	−	0.0794156i
$474$		0			0
$475$	5.24792	−	29.7624i	0.240791	−	1.36559i
$476$		0			0
$477$	−14.6504	−	37.8433i	−0.670795	−	1.73273i
$478$		0			0
$479$	31.7737	+	26.6613i	1.45178	+	1.21819i	0.931269	+	0.364332i	$0.118703\pi$
$479$	31.7737	+	26.6613i	1.45178	+	1.21819i	0.520510	+	0.853856i	$0.325742\pi$
$480$		0			0
$481$	7.33908	+	41.6220i	0.334633	+	1.89780i
$482$		0			0
$483$	4.53680	+	3.10856i	0.206432	+	0.141444i
$484$		0			0
$485$	1.32078			0.0599735
$486$		0			0
$487$	−4.09801			−0.185699			−0.0928494	−	0.995680i	$-0.529597\pi$
$487$	−4.09801			−0.185699			−0.0928494	+	0.995680i	$0.529597\pi$
$488$		0			0
$489$	7.45625	+	5.10893i	0.337183	+	0.231034i
$490$		0			0
$491$	−5.87105	−	33.2964i	−0.264957	−	1.50264i	−0.769158	−	0.639058i	$-0.779324\pi$
$491$	−5.87105	−	33.2964i	−0.264957	−	1.50264i	0.504201	−	0.863586i	$-0.331787\pi$
$492$		0			0
$493$	−6.72565	−	5.64349i	−0.302908	−	0.254170i
$494$		0			0
$495$	−0.549281	−	1.41884i	−0.0246883	−	0.0637722i
$496$		0			0
$497$	−1.16956	+	6.63288i	−0.0524617	+	0.297525i
$498$		0			0
$499$	−27.9770	−	10.1828i	−1.25242	−	0.455844i	−0.371202	−	0.928552i	$-0.621054\pi$
$499$	−27.9770	−	10.1828i	−1.25242	−	0.455844i	−0.881219	+	0.472708i	$0.843276\pi$
$500$		0			0
$501$	−15.7671	+	34.7286i	−0.704421	+	1.55156i
$502$		0			0
$503$	−10.0893	−	17.4752i	−0.449861	−	0.779182i	0.548516	−	0.836140i	$-0.315193\pi$
$503$	−10.0893	−	17.4752i	−0.449861	−	0.779182i	−0.998377	+	0.0569584i	$0.981860\pi$
$504$		0			0
$505$	1.27127	−	2.20191i	0.0565710	−	0.0979838i
$506$		0			0
$507$	−12.9233	−	46.3439i	−0.573946	−	2.05820i
$508$		0			0
$509$	18.9242	−	15.8793i	0.838801	−	0.703838i	−0.118493	−	0.992955i	$-0.537806\pi$
$509$	18.9242	−	15.8793i	0.838801	−	0.703838i	0.957294	+	0.289117i	$0.0933618\pi$
$510$		0			0
$511$	−3.40503	+	1.23933i	−0.150630	+	0.0548247i
$512$		0			0
$513$	−22.9991	−	21.6395i	−1.01544	−	0.955406i
$514$		0			0
$515$	−0.951761	+	0.346413i	−0.0419396	+	0.0152648i
$516$		0			0
$517$	−30.2674	+	25.3973i	−1.33116	+	1.11697i
$518$		0			0
$519$	−5.31337	+	5.42234i	−0.233231	+	0.238014i
$520$		0			0
$521$	2.32879	−	4.03358i	0.102026	−	0.176715i	−0.810493	−	0.585748i	$-0.800801\pi$
$521$	2.32879	−	4.03358i	0.102026	−	0.176715i	0.912519	+	0.409034i	$0.134134\pi$
$522$		0			0
$523$	−14.0320	−	24.3042i	−0.613578	−	1.06275i	−0.990632	−	0.136557i	$-0.956396\pi$
$523$	−14.0320	−	24.3042i	−0.613578	−	1.06275i	0.377054	−	0.926191i	$-0.376937\pi$
$524$		0			0
$525$	−5.01166	−	7.00499i	−0.218727	−	0.305723i
$526$		0			0
$527$	−3.80082	−	1.38338i	−0.165566	−	0.0602612i
$528$		0			0
$529$	−2.24320	+	12.7218i	−0.0975306	+	0.553123i
$530$		0			0
$531$	6.75300	−	4.08381i	0.293055	−	0.177222i
$532$		0			0
$533$	47.3986	+	39.7722i	2.05306	+	1.72272i
$534$		0			0
$535$	0.0477216	+	0.270643i	0.00206319	+	0.0117009i
$536$		0			0
$537$	1.69553	−	21.9429i	0.0731676	−	0.946908i
$538$		0			0
$539$	3.07583			0.132485
$540$		0			0
$541$	0.663158			0.0285114			0.0142557	−	0.999898i	$-0.495462\pi$
$541$	0.663158			0.0285114			0.0142557	+	0.999898i	$0.495462\pi$
$542$		0			0
$543$	−26.9803	+	12.9161i	−1.15784	+	0.554283i
$544$		0			0
$545$	−0.135221	−	0.766876i	−0.00579223	−	0.0328493i
$546$		0			0
$547$	−3.27467	−	2.74777i	−0.140015	−	0.117486i	0.570090	−	0.821582i	$-0.306908\pi$
$547$	−3.27467	−	2.74777i	−0.140015	−	0.117486i	−0.710105	+	0.704096i	$0.751353\pi$
$548$		0			0
$549$	7.57050	−	22.1913i	0.323101	−	0.947102i
$550$		0			0
$551$	−5.73391	+	32.5186i	−0.244273	+	1.38534i
$552$		0			0
$553$	11.2223	+	4.08460i	0.477222	+	0.173695i
$554$		0			0
$555$	1.88119	−	0.183840i	0.0798521	−	0.00780358i
$556$		0			0
$557$	−16.0234	−	27.7534i	−0.678934	−	1.17595i	−0.975302	−	0.220874i	$-0.929109\pi$
$557$	−16.0234	−	27.7534i	−0.678934	−	1.17595i	0.296369	−	0.955074i	$-0.404224\pi$
$558$		0			0
$559$	−5.24207	+	9.07953i	−0.221716	+	0.384023i
$560$		0			0
$561$	−8.33754	−	2.14358i	−0.352011	−	0.0905021i
$562$		0			0
$563$	−2.49585	+	2.09427i	−0.105188	+	0.0882630i	−0.693865	−	0.720105i	$-0.744093\pi$
$563$	−2.49585	+	2.09427i	−0.105188	+	0.0882630i	0.588677	+	0.808368i	$0.299649\pi$
$564$		0			0
$565$	−0.233323	+	0.0849226i	−0.00981597	+	0.00357272i
$566$		0			0
$567$	−8.99258	+	0.365288i	−0.377653	+	0.0153407i
$568$		0			0
$569$	33.7981	−	12.3015i	1.41689	−	0.515706i	0.483746	−	0.875208i	$-0.339276\pi$
$569$	33.7981	−	12.3015i	1.41689	−	0.515706i	0.933144	+	0.359503i	$0.117054\pi$
$570$		0			0
$571$	20.0374	−	16.8134i	0.838540	−	0.703619i	−0.118695	−	0.992931i	$-0.537871\pi$
$571$	20.0374	−	16.8134i	0.838540	−	0.703619i	0.957235	+	0.289312i	$0.0934266\pi$
$572$		0			0
$573$	−38.3229	−	9.85282i	−1.60096	−	0.411607i
$574$		0			0
$575$	−7.89484	+	13.6743i	−0.329238	+	0.570257i
$576$		0			0
$577$	0.949118	+	1.64392i	0.0395123	+	0.0684373i	0.885105	−	0.465391i	$-0.154086\pi$
$577$	0.949118	+	1.64392i	0.0395123	+	0.0684373i	−0.845593	+	0.533828i	$0.820753\pi$
$578$		0			0
$579$	34.4495	−	3.36659i	1.43167	−	0.139911i
$580$		0			0
$581$	8.01162	+	2.91599i	0.332378	+	0.120976i
$582$		0			0
$583$	−7.22479	+	40.9738i	−0.299220	+	1.69696i
$584$		0			0
$585$	−3.09893	+	0.611528i	−0.128125	+	0.0252836i
$586$		0			0
$587$	−10.6030	−	8.89698i	−0.437633	−	0.367218i	0.397190	−	0.917737i	$-0.369985\pi$
$587$	−10.6030	−	8.89698i	−0.437633	−	0.367218i	−0.834823	+	0.550519i	$0.814430\pi$
$588$		0			0
$589$	2.64157	+	14.9811i	0.108844	+	0.617286i
$590$		0			0
$591$	5.29222	−	2.53351i	0.217693	−	0.104215i
$592$		0			0
$593$	−15.0344			−0.617387			−0.308693	−	0.951162i	$-0.599892\pi$
$593$	−15.0344			−0.617387			−0.308693	+	0.951162i	$0.599892\pi$
$594$		0			0
$595$	0.266434			0.0109227
$596$		0			0
$597$	−2.29332	+	29.6793i	−0.0938594	+	1.21469i
$598$		0			0
$599$	−0.465704	−	2.64114i	−0.0190282	−	0.107914i	0.973814	−	0.227344i	$-0.0730043\pi$
$599$	−0.465704	−	2.64114i	−0.0190282	−	0.107914i	−0.992843	+	0.119430i	$0.961893\pi$
$600$		0			0
$601$	29.9413	+	25.1237i	1.22133	+	1.02482i	0.998754	+	0.0499021i	$0.0158909\pi$
$601$	29.9413	+	25.1237i	1.22133	+	1.02482i	0.222576	+	0.974915i	$0.428554\pi$
$602$		0			0
$603$	0.585094	+	28.8193i	0.0238269	+	1.17361i
$604$		0			0
$605$	0.0440716	−	0.249942i	0.00179176	−	0.0101616i
$606$		0			0
$607$	−1.97987	−	0.720614i	−0.0803605	−	0.0292488i	0.301527	−	0.953458i	$-0.402504\pi$
$607$	−1.97987	−	0.720614i	−0.0803605	−	0.0292488i	−0.381888	+	0.924209i	$0.624726\pi$
$608$		0			0
$609$	5.47578	+	7.65370i	0.221890	+	0.310143i
$610$		0			0
$611$	41.0146	+	71.0394i	1.65927	+	2.87394i
$612$		0			0
$613$	12.4644	−	21.5890i	0.503432	−	0.871970i	−0.496560	−	0.868002i	$-0.665404\pi$
$613$	12.4644	−	21.5890i	0.503432	−	0.871970i	0.999992	−	0.00396747i	$-0.00126289\pi$
$614$		0			0
$615$	1.93673	−	1.97645i	0.0780965	−	0.0796982i
$616$		0			0
$617$	2.08918	−	1.75303i	0.0841073	−	0.0705744i	−0.599765	−	0.800176i	$-0.704739\pi$
$617$	2.08918	−	1.75303i	0.0841073	−	0.0705744i	0.683872	+	0.729602i	$0.260295\pi$
$618$		0			0
$619$	−24.7908	+	9.02311i	−0.996426	+	0.362669i	−0.788205	−	0.615412i	$-0.788989\pi$
$619$	−24.7908	+	9.02311i	−0.996426	+	0.362669i	−0.208221	+	0.978082i	$0.566767\pi$
$620$		0			0
$621$	7.42471	+	14.7338i	0.297943	+	0.591247i
$622$		0			0
$623$	8.18314	−	2.97842i	0.327851	−	0.119328i
$624$		0			0
$625$	18.8393	−	15.8080i	0.753572	−	0.632322i
$626$		0			0
$627$	8.69679	+	31.1872i	0.347316	+	1.24550i
$628$		0			0
$629$	5.34743	−	9.26202i	0.213216	−	0.369301i
$630$		0			0
$631$	−4.27751	−	7.40887i	−0.170285	−	0.294942i	0.768234	−	0.640169i	$-0.221136\pi$
$631$	−4.27751	−	7.40887i	−0.170285	−	0.294942i	−0.938519	+	0.345226i	$0.887802\pi$
$632$		0			0
$633$	5.65378	−	12.4530i	0.224717	−	0.494963i
$634$		0			0
$635$	−0.798683	−	0.290697i	−0.0316948	−	0.0115359i
$636$		0			0
$637$	1.10887	−	6.28871i	0.0439350	−	0.249168i
$638$		0			0
$639$	−12.6711	+	15.7388i	−0.501259	+	0.622619i
$640$		0			0
$641$	−26.3596	−	22.1183i	−1.04114	−	0.873620i	−0.0490060	−	0.998798i	$-0.515605\pi$
$641$	−26.3596	−	22.1183i	−1.04114	−	0.873620i	−0.992134	+	0.125178i	$0.960050\pi$
$642$		0			0
$643$	3.16590	+	17.9547i	0.124851	+	0.708064i	0.981396	+	0.191993i	$0.0614950\pi$
$643$	3.16590	+	17.9547i	0.124851	+	0.708064i	−0.856546	+	0.516071i	$0.827394\pi$
$644$		0			0
$645$	0.386791	+	0.265024i	0.0152299	+	0.0104353i
$646$		0			0
$647$	3.49575			0.137432			0.0687160	−	0.997636i	$-0.478110\pi$
$647$	3.49575			0.137432			0.0687160	+	0.997636i	$0.478110\pi$
$648$		0			0
$649$	−8.09128			−0.317611
$650$		0			0
$651$	3.57648	+	2.45056i	0.140173	+	0.0960450i
$652$		0			0
$653$	2.24846	+	12.7517i	0.0879891	+	0.499011i	0.996671	+	0.0815230i	$0.0259784\pi$
$653$	2.24846	+	12.7517i	0.0879891	+	0.499011i	−0.908682	+	0.417488i	$0.862910\pi$
$654$		0			0
$655$	2.63015	+	2.20696i	0.102769	+	0.0862331i
$656$		0			0
$657$	−10.7416	−	1.66998i	−0.419071	−	0.0651523i
$658$		0			0
$659$	6.24842	−	35.4366i	0.243404	−	1.38041i	−0.580766	−	0.814071i	$-0.697247\pi$
$659$	6.24842	−	35.4366i	0.243404	−	1.38041i	0.824170	−	0.566342i	$-0.191642\pi$
$660$		0			0
$661$	5.58758	+	2.03371i	0.217332	+	0.0791023i	0.448391	−	0.893837i	$-0.351997\pi$
$661$	5.58758	+	2.03371i	0.217332	+	0.0791023i	−0.231060	+	0.972940i	$0.574219\pi$
$662$		0			0
$663$	−7.38845	+	16.2738i	−0.286944	+	0.632022i
$664$		0			0
$665$	−0.501026	−	0.867802i	−0.0194289	−	0.0336519i
$666$		0			0
$667$	8.62596	−	14.9406i	0.333999	−	0.578503i
$668$		0			0
$669$	−1.10226	−	3.95277i	−0.0426159	−	0.152823i
$670$		0			0
$671$	−18.4155	+	15.4525i	−0.710924	+	0.596536i
$672$		0			0
$673$	18.5041	−	6.73494i	0.713280	−	0.259613i	0.0402098	−	0.999191i	$-0.487197\pi$
$673$	18.5041	−	6.73494i	0.713280	−	0.259613i	0.673070	+	0.739579i	$0.264975\pi$
$674$		0			0
$675$	−3.03469	−	25.6607i	−0.116805	−	0.987680i
$676$		0			0
$677$	−1.98965	+	0.724173i	−0.0764684	+	0.0278322i	−0.379971	−	0.924998i	$-0.624066\pi$
$677$	−1.98965	+	0.724173i	−0.0764684	+	0.0278322i	0.303503	+	0.952831i	$0.401844\pi$
$678$		0			0
$679$	−6.13633	+	5.14899i	−0.235491	+	0.197600i
$680$		0			0
$681$	9.91977	−	10.1232i	0.380126	−	0.387922i
$682$		0			0
$683$	21.8799	−	37.8972i	0.837212	−	1.45009i	−0.0550038	−	0.998486i	$-0.517517\pi$
$683$	21.8799	−	37.8972i	0.837212	−	1.45009i	0.892216	−	0.451608i	$-0.149150\pi$
$684$		0			0
$685$	−0.258575	−	0.447866i	−0.00987965	−	0.0171121i
$686$		0			0
$687$	15.1670	+	21.1994i	0.578656	+	0.808809i
$688$		0			0
$689$	81.1687	+	29.5430i	3.09228	+	1.12550i
$690$		0			0
$691$	5.53148	−	31.3706i	0.210427	−	1.19339i	−0.678240	−	0.734841i	$-0.737257\pi$
$691$	5.53148	−	31.3706i	0.210427	−	1.19339i	0.888667	−	0.458553i	$-0.151632\pi$
$692$		0			0
$693$	8.08325	+	4.45059i	0.307057	+	0.169064i
$694$		0			0
$695$	−2.70513	−	2.26987i	−0.102611	−	0.0861012i
$696$		0			0
$697$	−2.71885	−	15.4194i	−0.102984	−	0.584051i
$698$		0			0
$699$	1.59662	−	20.6629i	0.0603899	−	0.781544i
$700$		0			0
$701$	−28.9856			−1.09477			−0.547386	−	0.836880i	$-0.684377\pi$
$701$	−28.9856			−1.09477			−0.547386	+	0.836880i	$0.684377\pi$
$702$		0			0
$703$	−40.2231			−1.51704
$704$		0			0
$705$	3.30892	−	1.58406i	0.124621	−	0.0596591i
$706$		0			0
$707$	2.67772	+	15.1861i	0.100706	+	0.571131i
$708$		0			0
$709$	28.5166	+	23.9283i	1.07096	+	0.898645i	0.995139	−	0.0984767i	$-0.0313970\pi$
$709$	28.5166	+	23.9283i	1.07096	+	0.898645i	0.0758235	+	0.997121i	$0.475841\pi$
$710$		0			0
$711$	23.5819	+	26.9725i	0.884392	+	1.01155i
$712$		0			0
$713$	1.38013	−	7.82709i	0.0516862	−	0.293127i
$714$		0			0
$715$	3.04322	+	1.10764i	0.113810	+	0.0414235i
$716$		0			0
$717$	46.5945	−	4.55347i	1.74010	−	0.170053i
$718$		0			0
$719$	12.0241	+	20.8263i	0.448422	+	0.776690i	0.998284	−	0.0585657i	$-0.0186527\pi$
$719$	12.0241	+	20.8263i	0.448422	+	0.776690i	−0.549861	+	0.835256i	$0.685319\pi$
$720$		0			0
$721$	3.07140	−	5.31983i	0.114385	−	0.198121i
$722$		0			0
$723$	−9.46599	−	2.43370i	−0.352044	−	0.0905104i
$724$		0			0
$725$	−20.6977	+	17.3674i	−0.768694	+	0.645011i
$726$		0			0
$727$	−5.94746	+	2.16470i	−0.220579	+	0.0802842i	−0.449946	−	0.893056i	$-0.648557\pi$
$727$	−5.94746	+	2.16470i	−0.220579	+	0.0802842i	0.229367	+	0.973340i	$0.426334\pi$
$728$		0			0
$729$	−24.1610	−	12.0519i	−0.894850	−	0.446366i
$730$		0			0
$731$	2.49300	−	0.907377i	0.0922069	−	0.0335606i
$732$		0			0
$733$	5.19100	−	4.35576i	0.191734	−	0.160884i	−0.541867	−	0.840464i	$-0.682283\pi$
$733$	5.19100	−	4.35576i	0.191734	−	0.160884i	0.733601	+	0.679580i	$0.237838\pi$
$734$		0			0
$735$	−0.276590	−	0.0711113i	−0.0102022	−	0.00262298i
$736$		0			0
$737$	14.7769	−	25.5944i	0.544316	−	0.942783i
$738$		0			0
$739$	20.5683	+	35.6253i	0.756617	+	1.31050i	0.944567	+	0.328320i	$0.106482\pi$
$739$	20.5683	+	35.6253i	0.756617	+	1.31050i	−0.187950	+	0.982179i	$0.560184\pi$
$740$		0			0
$741$	66.8993	−	6.53777i	2.45761	−	0.240171i
$742$		0			0
$743$	−10.2277	−	3.72259i	−0.375219	−	0.136569i	0.147525	−	0.989058i	$-0.452869\pi$
$743$	−10.2277	−	3.72259i	−0.375219	−	0.136569i	−0.522744	+	0.852490i	$0.675092\pi$
$744$		0			0
$745$	−0.171201	+	0.970927i	−0.00627231	+	0.0355720i
$746$		0			0
$747$	16.8351	+	19.2557i	0.615965	+	0.704527i
$748$		0			0
$749$	−1.27680	−	1.07136i	−0.0466534	−	0.0391468i
$750$		0			0
$751$	−4.28357	−	24.2934i	−0.156310	−	0.886477i	−0.957578	−	0.288173i	$-0.906952\pi$
$751$	−4.28357	−	24.2934i	−0.156310	−	0.886477i	0.801269	−	0.598305i	$-0.204159\pi$
$752$		0			0
$753$	30.1190	−	14.4187i	1.09760	−	0.525445i
$754$		0			0
$755$	−2.86437			−0.104245
$756$		0			0
$757$	22.3696			0.813038			0.406519	−	0.913642i	$-0.366742\pi$
$757$	22.3696			0.813038			0.406519	+	0.913642i	$0.366742\pi$
$758$		0			0
$759$	1.30321	−	16.8656i	0.0473034	−	0.612183i
$760$		0			0
$761$	−2.97061	−	16.8472i	−0.107685	−	0.610709i	−0.990114	−	0.140265i	$-0.955205\pi$
$761$	−2.97061	−	16.8472i	−0.107685	−	0.610709i	0.882430	−	0.470445i	$-0.155906\pi$
$762$		0			0
$763$	3.61786	+	3.03575i	0.130975	+	0.109901i
$764$		0			0
$765$	0.700185	+	0.385518i	0.0253152	+	0.0139384i
$766$		0			0
$767$	−2.91699	+	16.5431i	−0.105326	+	0.597336i
$768$		0			0
$769$	5.55919	+	2.02338i	0.200470	+	0.0729649i	0.440304	−	0.897849i	$-0.354871\pi$
$769$	5.55919	+	2.02338i	0.200470	+	0.0729649i	−0.239834	+	0.970814i	$0.577093\pi$
$770$		0			0
$771$	−22.6022	−	31.5920i	−0.813999	−	1.13776i
$772$		0			0
$773$	16.3239	+	28.2737i	0.587128	+	1.01694i	0.994606	+	0.103721i	$0.0330749\pi$
$773$	16.3239	+	28.2737i	0.587128	+	1.01694i	−0.407478	+	0.913215i	$0.633592\pi$
$774$		0			0
$775$	−6.22371	+	10.7798i	−0.223562	+	0.387221i
$776$		0			0
$777$	−8.02331	+	8.18785i	−0.287835	+	0.293738i
$778$		0			0
$779$	−45.1097	+	37.8516i	−1.61622	+	1.35617i
$780$		0			0
$781$	19.4670	−	7.08541i	0.696584	−	0.253536i
$782$		0			0
$783$	3.31572	+	28.0370i	0.118494	+	1.00196i
$784$		0			0
$785$	2.20720	−	0.803355i	0.0787784	−	0.0286730i
$786$		0			0
$787$	−21.4182	+	17.9720i	−0.763475	+	0.640631i	−0.939029	−	0.343838i	$-0.888273\pi$
$787$	−21.4182	+	17.9720i	−0.763475	+	0.640631i	0.175554	+	0.984470i	$0.443828\pi$
$788$		0			0
$789$	−6.53553	−	23.4368i	−0.232671	−	0.834373i
$790$		0			0
$791$	0.752950	−	1.30415i	0.0267718	−	0.0463702i
$792$		0			0
$793$	24.9545	+	43.2224i	0.886159	+	1.53487i
$794$		0			0
$795$	1.59697	−	3.51749i	0.0566387	−	0.124752i
$796$		0			0
$797$	17.3550	+	6.31672i	0.614747	+	0.223750i	0.630579	−	0.776125i	$-0.282817\pi$
$797$	17.3550	+	6.31672i	0.614747	+	0.223750i	−0.0158319	+	0.999875i	$0.505040\pi$
$798$		0			0
$799$	3.60448	−	20.4420i	0.127517	−	0.723186i
$800$		0			0
$801$	25.8148	+	4.01339i	0.912122	+	0.141806i
$802$		0			0
$803$	8.53792	+	7.16416i	0.301296	+	0.252818i
$804$		0			0
$805$	0.0909111	+	0.515582i	0.00320420	+	0.0181719i
$806$		0			0
$807$	−41.3495	−	28.3321i	−1.45557	−	0.997339i
$808$		0			0
$809$	47.5716			1.67253			0.836264	−	0.548327i	$-0.184735\pi$
$809$	47.5716			1.67253			0.836264	+	0.548327i	$0.184735\pi$
$810$		0			0
$811$	10.0033			0.351264			0.175632	−	0.984456i	$-0.443803\pi$
$811$	10.0033			0.351264			0.175632	+	0.984456i	$0.443803\pi$
$812$		0			0
$813$	5.26358	+	3.60654i	0.184602	+	0.126487i
$814$		0			0
$815$	0.149413	+	0.847362i	0.00523370	+	0.0296818i
$816$		0			0
$817$	−7.64348	−	6.41364i	−0.267411	−	0.224385i
$818$		0			0
$819$	12.0136	−	14.9222i	0.419789	−	0.521423i
$820$		0			0
$821$	1.16108	−	6.58480i	0.0405219	−	0.229811i	−0.957820	−	0.287368i	$-0.907220\pi$
$821$	1.16108	−	6.58480i	0.0405219	−	0.229811i	0.998342	+	0.0575565i	$0.0183309\pi$
$822$		0			0
$823$	38.5780	+	14.0412i	1.34474	+	0.489447i	0.911304	−	0.411735i	$-0.135077\pi$
$823$	38.5780	+	14.0412i	1.34474	+	0.489447i	0.433441	+	0.901182i	$0.357299\pi$
$824$		0			0
$825$	−10.9520	+	24.1229i	−0.381300	+	0.839851i
$826$		0			0
$827$	−17.1930	−	29.7791i	−0.597858	−	1.03552i	−0.993137	−	0.116959i	$-0.962685\pi$
$827$	−17.1930	−	29.7791i	−0.597858	−	1.03552i	0.395279	−	0.918561i	$-0.370648\pi$
$828$		0			0
$829$	−4.12407	+	7.14309i	−0.143235	+	0.248090i	−0.928713	−	0.370799i	$-0.879084\pi$
$829$	−4.12407	+	7.14309i	−0.143235	+	0.248090i	0.785478	+	0.618889i	$0.212417\pi$
$830$		0			0
$831$	−6.24073	−	22.3796i	−0.216488	−	0.776340i
$832$		0			0
$833$	−1.23785	+	1.03868i	−0.0428890	+	0.0359881i
$834$		0			0
$835$	−3.41180	+	1.24179i	−0.118070	+	0.0429740i
$836$		0			0
$837$	5.85310	+	11.6151i	0.202313	+	0.401475i
$838$		0			0
$839$	7.20339	−	2.62182i	0.248689	−	0.0905153i	−0.214668	−	0.976687i	$-0.568867\pi$
$839$	7.20339	−	2.62182i	0.248689	−	0.0905153i	0.463357	+	0.886172i	$0.346645\pi$
$840$		0			0
$841$	0.399174	−	0.334947i	0.0137646	−	0.0115499i
$842$		0			0
$843$	−35.8436	+	36.5787i	−1.23452	+	1.25984i
$844$		0			0
$845$	2.29002	−	3.96642i	0.0787790	−	0.136449i
$846$		0			0
$847$	0.769632	+	1.33304i	0.0264449	+	0.0458038i
$848$		0			0
$849$	3.92265	+	5.48284i	0.134625	+	0.188171i
$850$		0			0
$851$	19.7478	+	7.18760i	0.676945	+	0.246388i
$852$		0			0
$853$	−9.12056	+	51.7253i	−0.312282	+	1.77104i	0.274789	+	0.961505i	$0.411392\pi$
$853$	−9.12056	+	51.7253i	−0.312282	+	1.77104i	−0.587071	+	0.809535i	$0.699719\pi$
$854$		0			0
$855$	−0.0610188	−	3.00554i	−0.00208680	−	0.102787i
$856$		0			0
$857$	−12.8846	−	10.8115i	−0.440129	−	0.369312i	0.395628	−	0.918411i	$-0.370527\pi$
$857$	−12.8846	−	10.8115i	−0.440129	−	0.369312i	−0.835758	+	0.549098i	$0.814971\pi$
$858$		0			0
$859$	8.82599	+	50.0547i	0.301139	+	1.70784i	0.641145	+	0.767420i	$0.278460\pi$
$859$	8.82599	+	50.0547i	0.301139	+	1.70784i	−0.340006	+	0.940423i	$0.610429\pi$
$860$		0			0
$861$	−1.29295	+	16.7328i	−0.0440635	+	0.570253i
$862$		0			0
$863$	32.9716			1.12237			0.561183	−	0.827692i	$-0.310346\pi$
$863$	32.9716			1.12237			0.561183	+	0.827692i	$0.310346\pi$
$864$		0			0
$865$	−0.722691			−0.0245722
$866$		0			0
$867$	−22.4792	+	10.7613i	−0.763433	+	0.365473i
$868$		0			0
$869$	−6.37867	−	36.1752i	−0.216382	−	1.22716i
$870$		0			0
$871$	−47.0020	−	39.4394i	−1.59260	−	1.33635i
$872$		0			0
$873$	−23.5766	+	4.65249i	−0.797946	+	0.157463i
$874$		0			0
$875$	0.285538	−	1.61936i	0.00965293	−	0.0547445i
$876$		0			0
$877$	−38.4584	−	13.9977i	−1.29865	−	0.472670i	−0.402093	−	0.915599i	$-0.631717\pi$
$877$	−38.4584	−	13.9977i	−1.29865	−	0.472670i	−0.896557	+	0.442929i	$0.853939\pi$
$878$		0			0
$879$	31.9159	−	3.11900i	1.07650	−	0.105201i
$880$		0			0
$881$	−1.99561	−	3.45650i	−0.0672339	−	0.116453i	0.830449	−	0.557095i	$-0.188084\pi$
$881$	−1.99561	−	3.45650i	−0.0672339	−	0.116453i	−0.897683	+	0.440642i	$0.854751\pi$
$882$		0			0
$883$	7.04650	−	12.2049i	0.237133	−	0.410727i	−0.722757	−	0.691102i	$-0.757125\pi$
$883$	7.04650	−	12.2049i	0.237133	−	0.410727i	0.959891	+	0.280375i	$0.0904588\pi$
$884$		0			0
$885$	0.727598	+	0.187065i	0.0244579	+	0.00628814i
$886$		0			0
$887$	−1.22214	+	1.02550i	−0.0410355	+	0.0344329i	−0.663075	−	0.748553i	$-0.730749\pi$
$887$	−1.22214	+	1.02550i	−0.0410355	+	0.0344329i	0.622039	+	0.782986i	$0.286304\pi$
$888$		0			0
$889$	4.84394	−	1.76305i	0.162461	−	0.0591308i
$890$		0			0
$891$	14.8029	+	23.3922i	0.495915	+	0.783668i
$892$		0			0
$893$	−73.3599	+	26.7008i	−2.45490	+	0.893509i
$894$		0			0
$895$	1.60493	−	1.34670i	0.0536469	−	0.0450151i
$896$		0			0
$897$	−34.0129	−	8.74471i	−1.13566	−	0.291977i
$898$		0			0
$899$	6.80007	−	11.7781i	0.226795	−	0.392821i
$900$		0			0
$901$	−10.9289	−	18.9294i	−0.364095	−	0.630630i
$902$		0			0
$903$	−2.83021	+	0.276584i	−0.0941835	+	0.00920413i
$904$		0			0
$905$	−2.67580	−	0.973913i	−0.0889467	−	0.0323740i
$906$		0			0
$907$	0.787156	−	4.46419i	0.0261371	−	0.148231i	−0.968946	−	0.247271i	$-0.920466\pi$
$907$	0.787156	−	4.46419i	0.0261371	−	0.148231i	0.995083	+	0.0990403i	$0.0315773\pi$
$908$		0			0
$909$	−14.9366	+	43.7834i	−0.495415	+	1.45220i
$910$		0			0
$911$	−41.9114	−	35.1678i	−1.38859	−	1.16516i	−0.965909	−	0.258883i	$-0.916646\pi$
$911$	−41.9114	−	35.1678i	−1.38859	−	1.16516i	−0.422678	−	0.906280i	$-0.638910\pi$
$912$		0			0
$913$	−4.55373	−	25.8255i	−0.150706	−	0.854699i
$914$		0			0
$915$	2.01325	−	0.963788i	0.0665559	−	0.0318619i
$916$		0			0
$917$	−20.8234			−0.687649
$918$		0			0
$919$	37.4026			1.23380			0.616899	−	0.787043i	$-0.288389\pi$
$919$	37.4026			1.23380			0.616899	+	0.787043i	$0.288389\pi$
$920$		0			0
$921$	−1.46352	+	18.9404i	−0.0482247	+	0.624107i
$922$		0			0
$923$	−7.46846	−	42.3558i	−0.245827	−	1.39416i
$924$		0			0
$925$	−25.2126	−	21.1559i	−0.828984	−	0.695600i
$926$		0			0
$927$	15.7692	−	9.53625i	0.517927	−	0.313212i
$928$		0			0
$929$	−8.66155	+	49.1221i	−0.284176	+	1.61164i	0.424037	+	0.905645i	$0.360613\pi$
$929$	−8.66155	+	49.1221i	−0.284176	+	1.61164i	−0.708213	+	0.705998i	$0.750499\pi$
$930$		0			0
$931$	5.71085	+	2.07858i	0.187166	+	0.0681227i
$932$		0			0
$933$	−8.75151	−	12.2323i	−0.286512	−	0.400468i
$934$		0			0
$935$	−0.409753	−	0.709712i	−0.0134003	−	0.0232101i
$936$		0			0
$937$	20.2238	−	35.0287i	0.660683	−	1.14434i	−0.319754	−	0.947501i	$-0.603600\pi$
$937$	20.2238	−	35.0287i	0.660683	−	1.14434i	0.980437	−	0.196835i	$-0.0630665\pi$
$938$		0			0
$939$	0.877012	−	0.894998i	0.0286202	−	0.0292072i
$940$		0			0
$941$	−15.0509	+	12.6292i	−0.490645	+	0.411700i	−0.854257	−	0.519850i	$-0.825988\pi$
$941$	−15.0509	+	12.6292i	−0.490645	+	0.411700i	0.363612	+	0.931550i	$0.381543\pi$
$942$		0			0
$943$	28.9107	−	10.5226i	0.941462	−	0.342664i
$944$		0			0
$945$	−0.623981	−	0.587093i	−0.0202981	−	0.0190982i
$946$		0			0
$947$	3.70569	−	1.34876i	0.120419	−	0.0438289i	−0.281108	−	0.959676i	$-0.590702\pi$
$947$	3.70569	−	1.34876i	0.120419	−	0.0438289i	0.401527	+	0.915847i	$0.368480\pi$
$948$		0			0
$949$	17.7255	−	14.8735i	0.575396	−	0.482814i
$950$		0			0
$951$	2.90412	+	10.4143i	0.0941725	+	0.337708i
$952$		0			0
$953$	14.7510	−	25.5494i	0.477831	−	0.827628i	−0.521846	−	0.853040i	$-0.674756\pi$
$953$	14.7510	−	25.5494i	0.477831	−	0.827628i	0.999677	+	0.0254119i	$0.00808974\pi$
$954$		0			0
$955$	−1.88340	−	3.26214i	−0.0609453	−	0.105560i
$956$		0			0
$957$	11.9662	−	26.3568i	0.386813	−	0.851996i
$958$		0			0
$959$	2.94732	+	1.07274i	0.0951740	+	0.0346405i
$960$		0			0
$961$	−4.29510	+	24.3587i	−0.138552	+	0.785766i
$962$		0			0
$963$	−1.80521	−	4.66301i	−0.0581719	−	0.150263i
$964$		0			0
$965$	2.52415	+	2.11801i	0.0812553	+	0.0681813i
$966$		0			0
$967$	−7.06544	−	40.0701i	−0.227209	−	1.28857i	−0.858416	−	0.512953i	$-0.828551\pi$
$967$	−7.06544	−	40.0701i	−0.227209	−	1.28857i	0.631207	−	0.775614i	$-0.282560\pi$
$968$		0			0
$969$	−14.0316	−	9.61428i	−0.450760	−	0.308855i
$970$		0			0
$971$	−53.9664			−1.73186			−0.865932	−	0.500161i	$-0.833274\pi$
$971$	−53.9664			−1.73186			−0.865932	+	0.500161i	$0.833274\pi$
$972$		0			0
$973$	21.4170			0.686598
$974$		0			0
$975$	45.3723	+	31.0886i	1.45308	+	0.995631i
$976$		0			0
$977$	−9.19342	−	52.1385i	−0.294124	−	1.66806i	−0.670743	−	0.741690i	$-0.734024\pi$
$977$	−9.19342	−	52.1385i	−0.294124	−	1.66806i	0.376619	−	0.926368i	$-0.377087\pi$
$978$		0			0
$979$	−20.5187	−	17.2173i	−0.655782	−	0.550266i
$980$		0			0
$981$	5.11511	+	13.2128i	0.163313	+	0.421852i
$982$		0			0
$983$	−1.43559	+	8.14166i	−0.0457883	+	0.259678i	−0.999105	−	0.0422931i	$-0.986534\pi$
$983$	−1.43559	+	8.14166i	−0.0457883	+	0.259678i	0.953317	+	0.301972i	$0.0976448\pi$
$984$		0			0
$985$	0.524862	+	0.191034i	0.0167235	+	0.00608685i
$986$		0			0
$987$	−9.19786	+	20.2592i	−0.292771	+	0.644858i
$988$		0			0
$989$	2.60654	+	4.51465i	0.0828830	+	0.143558i
$990$		0			0
$991$	−14.1219	+	24.4598i	−0.448596	+	0.776990i	−0.998295	−	0.0583722i	$-0.981409\pi$
$991$	−14.1219	+	24.4598i	−0.448596	+	0.776990i	0.549699	+	0.835363i	$0.314742\pi$
$992$		0			0
$993$	2.84295	+	10.1950i	0.0902183	+	0.323528i
$994$		0			0
$995$	−2.17078	+	1.82150i	−0.0688183	+	0.0577454i
$996$		0			0
$997$	−2.87758	+	1.04735i	−0.0911340	+	0.0331701i	−0.387185	−	0.922002i	$-0.626552\pi$
$997$	−2.87758	+	1.04735i	−0.0911340	+	0.0331701i	0.296051	+	0.955172i	$0.404330\pi$
$998$		0			0
$999$	−32.9326	+	9.90821i	−1.04194	+	0.313482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.a.169.3	yes	54
27.4	even	9	inner	756.2.bo.a.85.3	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.a.85.3	✓	54	27.4	even	9	inner
756.2.bo.a.169.3	yes	54	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42882 - 0.979012i) q^{3} +(-0.0286316 - 0.162378i) q^{5} +(0.766044 + 0.642788i) q^{7} +(1.08307 + 2.79767i) q^{9} +O(q^{10})\)	\(q+(-1.42882 - 0.979012i) q^{3} +(-0.0286316 - 0.162378i) q^{5} +(0.766044 + 0.642788i) q^{7} +(1.08307 + 2.79767i) q^{9} +(0.534112 - 3.02910i) q^{11} +(-6.00062 - 2.18405i) q^{13} +(-0.118060 + 0.260040i) q^{15} +(0.807949 + 1.39941i) q^{17} +(3.03868 - 5.26315i) q^{19} +(-0.465245 - 1.66840i) q^{21} +(-2.43235 + 2.04098i) q^{23} +(4.67292 - 1.70080i) q^{25} +(1.19144 - 5.05771i) q^{27} +(-5.10566 + 1.85831i) q^{29} +(-1.91748 + 1.60896i) q^{31} +(-3.72868 + 3.80515i) q^{33} +(0.0824414 - 0.142793i) q^{35} +(-3.30926 - 5.73181i) q^{37} +(6.43562 + 8.99530i) q^{39} +(-9.10515 - 3.31400i) q^{41} +(0.285097 - 1.61686i) q^{43} +(0.423270 - 0.255968i) q^{45} +(-9.84038 - 8.25706i) q^{47} +(0.173648 + 0.984808i) q^{49} +(0.215622 - 2.79050i) q^{51} -13.5267 q^{53} -0.507152 q^{55} +(-9.49442 + 4.54520i) q^{57} +(-0.456799 - 2.59063i) q^{59} +(-5.98718 - 5.02384i) q^{61} +(-0.968627 + 2.83932i) q^{63} +(-0.182834 + 1.03690i) q^{65} +(9.02897 + 3.28628i) q^{67} +(5.47354 - 0.534904i) q^{69} +(3.36760 + 5.83286i) q^{71} +(-1.81178 + 3.13809i) q^{73} +(-8.34188 - 2.14470i) q^{75} +(2.35622 - 1.97711i) q^{77} +(11.2223 - 4.08460i) q^{79} +(-6.65392 + 6.06015i) q^{81} +(8.01162 - 2.91599i) q^{83} +(0.204100 - 0.171260i) q^{85} +(9.11439 + 2.34331i) q^{87} +(4.35416 - 7.54162i) q^{89} +(-3.19286 - 5.53020i) q^{91} +(4.31493 - 0.421679i) q^{93} +(-0.941621 - 0.342722i) q^{95} +(-1.39099 + 7.88871i) q^{97} +(9.05291 - 1.78646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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