LMFDB - Embedded newform 756.2.bx.a.41.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(41,756)]

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, 17, 9]))

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

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

chi := DirichletCharacter("756.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bx (of order $18$, 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:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.11
Character	$\chi$	$=$	756.41
Dual form			756.2.bx.a.461.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.481075 + 1.66390i) q^{3} +(-1.62248 - 1.36143i) q^{5} +(-0.358949 + 2.62129i) q^{7} +(-2.53713 - 1.60092i) q^{9} +O(q^{10})$	\(q+(-0.481075 + 1.66390i) q^{3} +(-1.62248 - 1.36143i) q^{5} +(-0.358949 + 2.62129i) q^{7} +(-2.53713 - 1.60092i) q^{9} +(-3.33628 - 3.97603i) q^{11} +(4.86998 + 0.858708i) q^{13} +(3.04581 - 2.04471i) q^{15} +(1.84048 - 3.18781i) q^{17} +(-7.14590 + 4.12569i) q^{19} +(-4.18888 - 1.85829i) q^{21} +(-1.32510 - 3.64069i) q^{23} +(-0.0892661 - 0.506253i) q^{25} +(3.88433 - 3.45138i) q^{27} +(5.74315 - 1.01267i) q^{29} +(-2.85576 - 7.84614i) q^{31} +(8.22072 - 3.63848i) q^{33} +(4.15108 - 3.76432i) q^{35} +(4.57500 - 7.92413i) q^{37} +(-3.77163 + 7.69006i) q^{39} +(0.222124 - 1.25973i) q^{41} +(-0.873681 + 0.733106i) q^{43} +(1.93692 + 6.05159i) q^{45} +(-5.12890 - 1.86677i) q^{47} +(-6.74231 - 1.88182i) q^{49} +(4.41879 + 4.59596i) q^{51} +10.3606i q^{53} +10.9931i q^{55} +(-3.42702 - 13.8748i) q^{57} +(3.45773 + 2.90138i) q^{59} +(-0.327957 + 0.901055i) q^{61} +(5.10718 - 6.07591i) q^{63} +(-6.73239 - 8.02336i) q^{65} +(0.122990 - 0.697511i) q^{67} +(6.69522 - 0.453395i) q^{69} +(-2.81439 - 1.62489i) q^{71} +(1.13616 - 0.655964i) q^{73} +(0.885299 + 0.0950158i) q^{75} +(11.6199 - 7.31817i) q^{77} +(-2.11975 - 12.0217i) q^{79} +(3.87410 + 8.12351i) q^{81} +(-2.33990 - 13.2702i) q^{83} +(-7.32612 + 2.66649i) q^{85} +(-1.07790 + 10.0432i) q^{87} +(-2.71716 - 4.70627i) q^{89} +(-3.99900 + 12.4574i) q^{91} +(14.4290 - 0.977124i) q^{93} +(17.2109 + 3.03475i) q^{95} +(-3.13633 - 3.73773i) q^{97} +(2.09929 + 15.4288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$1$

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
$3$	−0.481075	+	1.66390i	−0.277749	+	0.960654i
$3$	−0.481075	+	1.66390i	−0.277749	+	0.960654i
$4$		0			0
$5$	−1.62248	−	1.36143i	−0.725597	−	0.608848i	0.203330	−	0.979110i	$-0.434823\pi$
$5$	−1.62248	−	1.36143i	−0.725597	−	0.608848i	−0.928927	+	0.370262i	$0.879268\pi$
$6$		0			0
$7$	−0.358949	+	2.62129i	−0.135670	+	0.990754i
$7$	−0.358949	+	2.62129i	−0.135670	+	0.990754i
$8$		0			0
$9$	−2.53713	−	1.60092i	−0.845711	−	0.533641i
$10$		0			0
$11$	−3.33628	−	3.97603i	−1.00593	−	1.19882i	−0.979968	−	0.199155i	$-0.936180\pi$
$11$	−3.33628	−	3.97603i	−1.00593	−	1.19882i	−0.0259593	−	0.999663i	$-0.508264\pi$
$12$		0			0
$13$	4.86998	+	0.858708i	1.35069	+	0.238163i	0.801730	−	0.597687i	$-0.203913\pi$
$13$	4.86998	+	0.858708i	1.35069	+	0.238163i	0.548959	+	0.835849i	$0.315024\pi$
$14$		0			0
$15$	3.04581	−	2.04471i	0.786426	−	0.527941i
$16$		0			0
$17$	1.84048	−	3.18781i	0.446383	−	0.773158i	−0.551765	−	0.834000i	$-0.686045\pi$
$17$	1.84048	−	3.18781i	0.446383	−	0.773158i	0.998147	+	0.0608423i	$0.0193787\pi$
$18$		0			0
$19$	−7.14590	+	4.12569i	−1.63938	+	0.946498i	−0.658336	+	0.752724i	$0.728739\pi$
$19$	−7.14590	+	4.12569i	−1.63938	+	0.946498i	−0.981046	+	0.193773i	$0.937927\pi$
$20$		0			0
$21$	−4.18888	−	1.85829i	−0.914089	−	0.405513i
$22$		0			0
$23$	−1.32510	−	3.64069i	−0.276303	−	0.759136i	−0.997774	−	0.0666910i	$-0.978756\pi$
$23$	−1.32510	−	3.64069i	−0.276303	−	0.759136i	0.721471	−	0.692445i	$-0.243466\pi$
$24$		0			0
$25$	−0.0892661	−	0.506253i	−0.0178532	−	0.101251i
$26$		0			0
$27$	3.88433	−	3.45138i	0.747539	−	0.664218i
$28$		0			0
$29$	5.74315	−	1.01267i	1.06648	−	0.188049i	0.387248	−	0.921975i	$-0.373426\pi$
$29$	5.74315	−	1.01267i	1.06648	−	0.188049i	0.679228	+	0.733927i	$0.262315\pi$
$30$		0			0
$31$	−2.85576	−	7.84614i	−0.512910	−	1.40921i	−0.878190	−	0.478311i	$-0.841249\pi$
$31$	−2.85576	−	7.84614i	−0.512910	−	1.40921i	0.365280	−	0.930898i	$-0.380973\pi$
$32$		0			0
$33$	8.22072	−	3.63848i	1.43104	−	0.633378i
$34$		0			0
$35$	4.15108	−	3.76432i	0.701661	−	0.636286i
$36$		0			0
$37$	4.57500	−	7.92413i	0.752125	−	1.30272i	−0.194666	−	0.980870i	$-0.562362\pi$
$37$	4.57500	−	7.92413i	0.752125	−	1.30272i	0.946791	−	0.321849i	$-0.104304\pi$
$38$		0			0
$39$	−3.77163	+	7.69006i	−0.603944	+	1.23139i
$40$		0			0
$41$	0.222124	−	1.25973i	0.0346899	−	0.196736i	−0.962538	−	0.271148i	$-0.912597\pi$
$41$	0.222124	−	1.25973i	0.0346899	−	0.196736i	0.997228	+	0.0744116i	$0.0237079\pi$
$42$		0			0
$43$	−0.873681	+	0.733106i	−0.133235	+	0.111798i	−0.706970	−	0.707244i	$-0.749938\pi$
$43$	−0.873681	+	0.733106i	−0.133235	+	0.111798i	0.573735	+	0.819041i	$0.305494\pi$
$44$		0			0
$45$	1.93692	+	6.05159i	0.288739	+	0.902118i
$46$		0			0
$47$	−5.12890	−	1.86677i	−0.748127	−	0.272296i	−0.0603096	−	0.998180i	$-0.519209\pi$
$47$	−5.12890	−	1.86677i	−0.748127	−	0.272296i	−0.687817	+	0.725884i	$0.741431\pi$
$48$		0			0
$49$	−6.74231	−	1.88182i	−0.963187	−	0.268832i
$50$		0			0
$51$	4.41879	+	4.59596i	0.618754	+	0.643563i
$52$		0			0
$53$			10.3606i			1.42314i	0.702613	+	0.711572i	$0.252016\pi$
$53$			10.3606i			1.42314i	−0.702613	+	0.711572i	$0.747984\pi$
$54$		0			0
$55$			10.9931i			1.48232i
$56$		0			0
$57$	−3.42702	−	13.8748i	−0.453920	−	1.83777i
$58$		0			0
$59$	3.45773	+	2.90138i	0.450158	+	0.377727i	0.839494	−	0.543368i	$-0.182851\pi$
$59$	3.45773	+	2.90138i	0.450158	+	0.377727i	−0.389337	+	0.921095i	$0.627296\pi$
$60$		0			0
$61$	−0.327957	+	0.901055i	−0.0419906	+	0.115368i	−0.958916	−	0.283691i	$-0.908441\pi$
$61$	−0.327957	+	0.901055i	−0.0419906	+	0.115368i	0.916925	+	0.399059i	$0.130663\pi$
$62$		0			0
$63$	5.10718	−	6.07591i	0.643444	−	0.765493i
$64$		0			0
$65$	−6.73239	−	8.02336i	−0.835051	−	0.995175i
$66$		0			0
$67$	0.122990	−	0.697511i	0.0150256	−	0.0852145i	−0.976373	−	0.216093i	$-0.930669\pi$
$67$	0.122990	−	0.697511i	0.0150256	−	0.0852145i	0.991398	+	0.130878i	$0.0417797\pi$
$68$		0			0
$69$	6.69522	−	0.453395i	0.806009	−	0.0545824i
$70$		0			0
$71$	−2.81439	−	1.62489i	−0.334006	−	0.192839i	0.323612	−	0.946190i	$-0.395103\pi$
$71$	−2.81439	−	1.62489i	−0.334006	−	0.192839i	−0.657618	+	0.753351i	$0.728436\pi$
$72$		0			0
$73$	1.13616	−	0.655964i	0.132978	−	0.0767748i	−0.432035	−	0.901857i	$-0.642204\pi$
$73$	1.13616	−	0.655964i	0.132978	−	0.0767748i	0.565013	+	0.825082i	$0.308871\pi$
$74$		0			0
$75$	0.885299	+	0.0950158i	0.102226	+	0.0109715i
$76$		0			0
$77$	11.6199	−	7.31817i	1.32421	−	0.833983i
$78$		0			0
$79$	−2.11975	−	12.0217i	−0.238490	−	1.35255i	−0.835137	−	0.550041i	$-0.814612\pi$
$79$	−2.11975	−	12.0217i	−0.238490	−	1.35255i	0.596647	−	0.802504i	$-0.296499\pi$
$80$		0			0
$81$	3.87410	+	8.12351i	0.430455	+	0.902612i
$82$		0			0
$83$	−2.33990	−	13.2702i	−0.256837	−	1.45660i	−0.791313	−	0.611411i	$-0.790602\pi$
$83$	−2.33990	−	13.2702i	−0.256837	−	1.45660i	0.534476	−	0.845184i	$-0.320509\pi$
$84$		0			0
$85$	−7.32612	+	2.66649i	−0.794630	+	0.289222i
$86$		0			0
$87$	−1.07790	+	10.0432i	−0.115563	+	1.07675i
$88$		0			0
$89$	−2.71716	−	4.70627i	−0.288019	−	0.498863i	0.685318	−	0.728244i	$-0.259663\pi$
$89$	−2.71716	−	4.70627i	−0.288019	−	0.498863i	−0.973337	+	0.229381i	$0.926330\pi$
$90$		0			0
$91$	−3.99900	+	12.4574i	−0.419209	+	1.30589i
$92$		0			0
$93$	14.4290	−	0.977124i	1.49622	−	0.101323i
$94$		0			0
$95$	17.2109	+	3.03475i	1.76580	+	0.311359i
$96$		0			0
$97$	−3.13633	−	3.73773i	−0.318446	−	0.379509i	0.582948	−	0.812510i	$-0.301899\pi$
$97$	−3.13633	−	3.73773i	−0.318446	−	0.379509i	−0.901394	+	0.433001i	$0.857455\pi$
$98$		0			0
$99$	2.09929	+	15.4288i	0.210986	+	1.55066i
$100$		0			0
$101$	−16.1748	−	5.88715i	−1.60945	−	0.585793i	−0.628121	−	0.778116i	$-0.716176\pi$
$101$	−16.1748	−	5.88715i	−1.60945	−	0.585793i	−0.981332	+	0.192323i	$0.938398\pi$
$102$		0			0
$103$	−5.81638	+	6.93170i	−0.573105	+	0.683000i	−0.972265	−	0.233881i	$-0.924857\pi$
$103$	−5.81638	+	6.93170i	−0.573105	+	0.683000i	0.399160	+	0.916881i	$0.369302\pi$
$104$		0			0
$105$	4.26647	+	8.71791i	0.416365	+	0.850781i
$106$		0			0
$107$			5.71955i			0.552930i	0.961024	+	0.276465i	$0.0891630\pi$
$107$			5.71955i			0.552930i	−0.961024	+	0.276465i	$0.910837\pi$
$108$		0			0
$109$	−11.2183			−1.07451			−0.537257	−	0.843419i	$-0.680539\pi$
$109$	−11.2183			−1.07451			−0.537257	+	0.843419i	$0.680539\pi$
$110$		0			0
$111$	10.9841	+	11.4244i	1.04256	+	1.08436i
$112$		0			0
$113$	1.59599	−	1.90203i	0.150138	−	0.178928i	−0.685733	−	0.727853i	$-0.740518\pi$
$113$	1.59599	−	1.90203i	0.150138	−	0.178928i	0.835872	+	0.548925i	$0.184963\pi$
$114$		0			0
$115$	−2.80657	+	7.71099i	−0.261714	+	0.719053i
$116$		0			0
$117$	−10.9811	−	9.97511i	−1.01520	−	0.922199i
$118$		0			0
$119$	7.69553	+	5.96870i	0.705448	+	0.547150i
$120$		0			0
$121$	−2.76788	+	15.6974i	−0.251626	+	1.42704i
$122$		0			0
$123$	1.98920	+	0.975615i	0.179360	+	0.0879683i
$124$		0			0
$125$	−5.83940	+	10.1141i	−0.522292	+	0.904636i
$126$		0			0
$127$	8.46998	+	14.6704i	0.751589	+	1.30179i	0.947052	+	0.321079i	$0.104046\pi$
$127$	8.46998	+	14.6704i	0.751589	+	1.30179i	−0.195464	+	0.980711i	$0.562621\pi$
$128$		0			0
$129$	−0.799509	−	1.80640i	−0.0703929	−	0.159044i
$130$		0			0
$131$	−1.67086	+	0.608145i	−0.145984	+	0.0531338i	−0.413979	−	0.910287i	$-0.635861\pi$
$131$	−1.67086	+	0.608145i	−0.145984	+	0.0531338i	0.267995	+	0.963420i	$0.413639\pi$
$132$		0			0
$133$	−8.24960	−	20.2124i	−0.715331	−	1.75264i
$134$		0			0
$135$	−11.0011	+	0.311580i	−0.946820	+	0.0268165i
$136$		0			0
$137$	−14.5539	+	2.56625i	−1.24343	+	0.219250i	−0.756384	−	0.654128i	$-0.773036\pi$
$137$	−14.5539	+	2.56625i	−1.24343	+	0.219250i	−0.487043	+	0.873378i	$0.661925\pi$
$138$		0			0
$139$	2.82087	+	7.75028i	0.239263	+	0.657370i	0.999966	+	0.00826955i	$0.00263231\pi$
$139$	2.82087	+	7.75028i	0.239263	+	0.657370i	−0.760703	+	0.649100i	$0.775145\pi$
$140$		0			0
$141$	5.57350	−	7.63593i	0.469373	−	0.643061i
$142$		0			0
$143$	−12.8334	−	22.2281i	−1.07318	−	1.85880i
$144$		0			0
$145$	−10.6969	−	6.17583i	−0.888325	−	0.512875i
$146$		0			0
$147$	6.37472	−	10.3132i	0.525778	−	0.850622i
$148$		0			0
$149$	7.36279	+	1.29826i	0.603183	+	0.106358i	0.466897	−	0.884312i	$-0.345372\pi$
$149$	7.36279	+	1.29826i	0.603183	+	0.106358i	0.136287	+	0.990669i	$0.456483\pi$
$150$		0			0
$151$	2.24500	−	1.88378i	0.182696	−	0.153300i	−0.546853	−	0.837228i	$-0.684174\pi$
$151$	2.24500	−	1.88378i	0.182696	−	0.153300i	0.729549	+	0.683929i	$0.239730\pi$
$152$		0			0
$153$	−9.77299	+	5.14143i	−0.790099	+	0.415660i
$154$		0			0
$155$	−6.04851	+	16.6182i	−0.485828	+	1.33480i
$156$		0			0
$157$	−7.00418	+	8.34726i	−0.558994	+	0.666184i	−0.969333	−	0.245749i	$-0.920966\pi$
$157$	−7.00418	+	8.34726i	−0.558994	+	0.666184i	0.410339	+	0.911933i	$0.365410\pi$
$158$		0			0
$159$	−17.2391	−	4.98425i	−1.36715	−	0.395276i
$160$		0			0
$161$	10.0189	−	2.16665i	0.789603	−	0.170756i
$162$		0			0
$163$	18.7083			1.46534			0.732672	−	0.680581i	$-0.238273\pi$
$163$	18.7083			1.46534			0.732672	+	0.680581i	$0.238273\pi$
$164$		0			0
$165$	−18.2915	−	5.28853i	−1.42399	−	0.411711i
$166$		0			0
$167$	−12.7189	−	10.6724i	−0.984216	−	0.825855i	0.000504182	−	1.00000i	$-0.499840\pi$
$167$	−12.7189	−	10.6724i	−0.984216	−	0.825855i	−0.984720	+	0.174145i	$0.944284\pi$
$168$		0			0
$169$	10.7633	+	3.91752i	0.827946	+	0.301348i
$170$		0			0
$171$	24.7350	+	0.972608i	1.89153	+	0.0743772i
$172$		0			0
$173$	1.27984	−	1.07391i	0.0973046	−	0.0816482i	−0.592838	−	0.805322i	$-0.701992\pi$
$173$	1.27984	−	1.07391i	0.0973046	−	0.0816482i	0.690142	+	0.723674i	$0.257548\pi$
$174$		0			0
$175$	1.35908	−	0.0522729i	0.102737	−	0.00395146i
$176$		0			0
$177$	−6.49103	+	4.35754i	−0.487896	+	0.327532i
$178$		0			0
$179$	15.5901	+	9.00095i	1.16526	+	0.672763i	0.952559	−	0.304355i	$-0.0984408\pi$
$179$	15.5901	+	9.00095i	1.16526	+	0.672763i	0.212701	+	0.977117i	$0.431774\pi$
$180$		0			0
$181$	−6.02159	+	3.47657i	−0.447581	+	0.258411i	−0.706808	−	0.707405i	$-0.749866\pi$
$181$	−6.02159	+	3.47657i	−0.447581	+	0.258411i	0.259227	+	0.965816i	$0.416532\pi$
$182$		0			0
$183$	−1.34149	−	0.979163i	−0.0991661	−	0.0723818i
$184$		0			0
$185$	−18.2110	+	6.62825i	−1.33890	+	0.487319i
$186$		0			0
$187$	−18.8152	+	3.31763i	−1.37590	+	0.242609i
$188$		0			0
$189$	7.65278	+	11.4208i	0.556658	+	0.830742i
$190$		0			0
$191$	−19.6207	+	3.45966i	−1.41970	+	0.250332i	−0.830215	−	0.557444i	$-0.811782\pi$
$191$	−19.6207	+	3.45966i	−1.41970	+	0.250332i	−0.589490	+	0.807776i	$0.700671\pi$
$192$		0			0
$193$	2.73861	−	0.996771i	0.197129	−	0.0717491i	−0.241569	−	0.970384i	$-0.577662\pi$
$193$	2.73861	−	0.996771i	0.197129	−	0.0717491i	0.438698	+	0.898635i	$0.355440\pi$
$194$		0			0
$195$	16.5889	−	7.34220i	1.18795	−	0.525786i
$196$		0			0
$197$	−19.6589	+	11.3500i	−1.40064	+	0.808658i	−0.994458	−	0.105136i	$-0.966472\pi$
$197$	−19.6589	+	11.3500i	−1.40064	+	0.808658i	−0.406178	+	0.913794i	$0.633139\pi$
$198$		0			0
$199$	8.66203	+	5.00103i	0.614035	+	0.354513i	0.774543	−	0.632521i	$-0.217980\pi$
$199$	8.66203	+	5.00103i	0.614035	+	0.354513i	−0.160508	+	0.987035i	$0.551313\pi$
$200$		0			0
$201$	1.10142	+	0.540198i	0.0776883	+	0.0381026i
$202$		0			0
$203$	0.593006	+	15.4180i	0.0416209	+	1.08213i
$204$		0			0
$205$	−2.07542	+	1.74148i	−0.144953	+	0.121630i
$206$		0			0
$207$	−2.46650	+	11.3583i	−0.171433	+	0.789456i
$208$		0			0
$209$	40.2446	+	14.6478i	2.78378	+	1.01321i
$210$		0			0
$211$	2.91122	+	2.44280i	0.200416	+	0.168169i	0.737472	−	0.675377i	$-0.236019\pi$
$211$	2.91122	+	2.44280i	0.200416	+	0.168169i	−0.537056	+	0.843547i	$0.680464\pi$
$212$		0			0
$213$	4.05758	−	3.90117i	0.278021	−	0.267304i
$214$		0			0
$215$	2.41560			0.164743
$216$		0			0
$217$	21.5921	−	4.66941i	1.46577	−	0.316980i
$218$		0			0
$219$	0.544880	+	2.20603i	0.0368196	+	0.149070i
$220$		0			0
$221$	11.7005	−	13.9441i	0.787061	−	0.937983i
$222$		0			0
$223$	3.43414	−	9.43521i	0.229967	−	0.631829i	−0.770014	−	0.638027i	$-0.779751\pi$
$223$	3.43414	−	9.43521i	0.229967	−	0.631829i	0.999981	+	0.00619843i	$0.00197303\pi$
$224$		0			0
$225$	−0.583992	+	1.42734i	−0.0389328	+	0.0951561i
$226$		0			0
$227$	8.21348	−	6.89192i	0.545148	−	0.457433i	−0.328146	−	0.944627i	$-0.606424\pi$
$227$	8.21348	−	6.89192i	0.545148	−	0.457433i	0.873294	+	0.487194i	$0.161979\pi$
$228$		0			0
$229$	−9.17169	−	1.61722i	−0.606082	−	0.106869i	−0.137819	−	0.990457i	$-0.544009\pi$
$229$	−9.17169	−	1.61722i	−0.606082	−	0.106869i	−0.468264	+	0.883589i	$0.655120\pi$
$230$		0			0
$231$	6.58668	+	22.8549i	0.433372	+	1.50374i
$232$		0			0
$233$	16.3400	+	9.43389i	1.07047	+	0.618034i	0.928309	−	0.371810i	$-0.121263\pi$
$233$	16.3400	+	9.43389i	1.07047	+	0.618034i	0.142158	+	0.989844i	$0.454596\pi$
$234$		0			0
$235$	5.78010	+	10.0114i	0.377052	+	0.653073i
$236$		0			0
$237$	21.0226	+	2.25628i	1.36557	+	0.146561i
$238$		0			0
$239$	−10.0326	−	27.5644i	−0.648957	−	1.78299i	−0.621557	−	0.783369i	$-0.713499\pi$
$239$	−10.0326	−	27.5644i	−0.648957	−	1.78299i	−0.0274000	−	0.999625i	$-0.508723\pi$
$240$		0			0
$241$	27.1904	−	4.79440i	1.75149	−	0.308834i	0.796314	−	0.604883i	$-0.206780\pi$
$241$	27.1904	−	4.79440i	1.75149	−	0.308834i	0.955173	+	0.296049i	$0.0956691\pi$
$242$		0			0
$243$	−15.3804	+	2.53810i	−0.986656	+	0.162819i
$244$		0			0
$245$	8.37733	+	12.2324i	0.535208	+	0.781498i
$246$		0			0
$247$	−38.3431	+	13.9558i	−2.43972	+	0.887984i
$248$		0			0
$249$	23.2060	+	2.49061i	1.47062	+	0.157836i
$250$		0			0
$251$	−0.252278	−	0.436958i	−0.0159237	−	0.0275806i	0.857954	−	0.513727i	$-0.171736\pi$
$251$	−0.252278	−	0.436958i	−0.0159237	−	0.0275806i	−0.873877	+	0.486146i	$0.838402\pi$
$252$		0			0
$253$	−10.0546	+	17.4150i	−0.632125	+	1.09487i
$254$		0			0
$255$	−0.912363	−	13.4727i	−0.0571344	−	0.843695i
$256$		0			0
$257$	2.53417	−	14.3720i	0.158077	−	0.896501i	−0.797841	−	0.602868i	$-0.794024\pi$
$257$	2.53417	−	14.3720i	0.158077	−	0.896501i	0.955918	−	0.293633i	$-0.0948644\pi$
$258$		0			0
$259$	19.1292	+	14.8368i	1.18863	+	0.921911i
$260$		0			0
$261$	−16.1924	−	6.62505i	−1.00228	−	0.410081i
$262$		0			0
$263$	9.10779	−	25.0234i	0.561610	−	1.54301i	−0.255666	−	0.966765i	$-0.582295\pi$
$263$	9.10779	−	25.0234i	0.561610	−	1.54301i	0.817276	−	0.576247i	$-0.195483\pi$
$264$		0			0
$265$	14.1053	−	16.8100i	0.866479	−	1.03263i
$266$		0			0
$267$	9.13792	−	2.25703i	0.559232	−	0.138128i
$268$		0			0
$269$	−3.99054			−0.243308			−0.121654	−	0.992573i	$-0.538820\pi$
$269$	−3.99054			−0.243308			−0.121654	+	0.992573i	$0.538820\pi$
$270$		0			0
$271$		−	1.22254i		−	0.0742641i	−0.999310	−	0.0371320i	$-0.988178\pi$
$271$		−	1.22254i		−	0.0742641i	0.999310	−	0.0371320i	$-0.0118222\pi$
$272$		0			0
$273$	−18.8040	−	12.6469i	−1.13807	−	0.765424i
$274$		0			0
$275$	−1.71506	+	2.04393i	−0.103422	+	0.123254i
$276$		0			0
$277$	−3.51685	−	1.28003i	−0.211307	−	0.0769094i	0.234198	−	0.972189i	$-0.424754\pi$
$277$	−3.51685	−	1.28003i	−0.211307	−	0.0769094i	−0.445505	+	0.895279i	$0.646976\pi$
$278$		0			0
$279$	−5.31561	+	24.4786i	−0.318237	+	1.46549i
$280$		0			0
$281$	−17.9630	−	21.4075i	−1.07158	−	1.27706i	−0.958995	−	0.283423i	$-0.908530\pi$
$281$	−17.9630	−	21.4075i	−1.07158	−	1.27706i	−0.112589	−	0.993642i	$-0.535914\pi$
$282$		0			0
$283$	−15.3139	−	2.70026i	−0.910318	−	0.160514i	−0.301170	−	0.953570i	$-0.597377\pi$
$283$	−15.3139	−	2.70026i	−0.910318	−	0.160514i	−0.609148	+	0.793057i	$0.708488\pi$
$284$		0			0
$285$	−13.3293	+	27.1773i	−0.789558	+	1.60985i
$286$		0			0
$287$	3.22238	+	1.03443i	0.190211	+	0.0610604i
$288$		0			0
$289$	1.72524	+	2.98821i	0.101485	+	0.175777i
$290$		0			0
$291$	7.72802	−	3.42041i	0.453025	−	0.200508i
$292$		0			0
$293$	9.94911	−	3.62118i	0.581233	−	0.211552i	−0.0346360	−	0.999400i	$-0.511027\pi$
$293$	9.94911	−	3.62118i	0.581233	−	0.211552i	0.615869	+	0.787848i	$0.288805\pi$
$294$		0			0
$295$	−1.66010	−	9.41488i	−0.0966546	−	0.548155i
$296$		0			0
$297$	−26.6820	−	3.92942i	−1.54825	−	0.228008i
$298$		0			0
$299$	−3.32693	−	18.8679i	−0.192401	−	1.09116i
$300$		0			0
$301$	−1.60807	−	2.55332i	−0.0926879	−	0.147171i
$302$		0			0
$303$	17.5769	−	24.0811i	1.00977	−	1.38342i
$304$		0			0
$305$	1.75883	−	1.01546i	0.100710	−	0.0581450i
$306$		0			0
$307$	−0.734793	−	0.424233i	−0.0419369	−	0.0242123i	0.478885	−	0.877878i	$-0.341041\pi$
$307$	−0.734793	−	0.424233i	−0.0419369	−	0.0242123i	−0.520822	+	0.853665i	$0.674374\pi$
$308$		0			0
$309$	−8.73554	−	13.0126i	−0.496948	−	0.740258i
$310$		0			0
$311$	1.13796	−	6.45367i	0.0645276	−	0.365954i	−0.935396	−	0.353602i	$-0.884957\pi$
$311$	1.13796	−	6.45367i	0.0645276	−	0.365954i	0.999924	−	0.0123526i	$-0.00393205\pi$
$312$		0			0
$313$	−5.53859	−	6.60064i	−0.313060	−	0.373090i	0.586454	−	0.809983i	$-0.300523\pi$
$313$	−5.53859	−	6.60064i	−0.313060	−	0.373090i	−0.899514	+	0.436892i	$0.856079\pi$
$314$		0			0
$315$	−16.5582	+	2.90502i	−0.932950	+	0.163679i
$316$		0			0
$317$	2.86658	−	7.87586i	0.161003	−	0.442352i	−0.832791	−	0.553588i	$-0.813258\pi$
$317$	2.86658	−	7.87586i	0.161003	−	0.442352i	0.993794	+	0.111235i	$0.0354806\pi$
$318$		0			0
$319$	−23.1872	−	19.4564i	−1.29823	−	1.08935i
$320$		0			0
$321$	−9.51677	−	2.75153i	−0.531174	−	0.153576i
$322$		0			0
$323$			30.3730i			1.69000i
$324$		0			0
$325$		−	2.54210i		−	0.141010i
$326$		0			0
$327$	5.39682	−	18.6661i	0.298445	−	1.03224i
$328$		0			0
$329$	6.73435	−	12.7743i	0.371277	−	0.704267i
$330$		0			0
$331$	23.4010	+	8.51725i	1.28623	+	0.468151i	0.892489	−	0.451069i	$-0.148957\pi$
$331$	23.4010	+	8.51725i	1.28623	+	0.468151i	0.393744	+	0.919220i	$0.371180\pi$
$332$		0			0
$333$	−24.2933	+	12.7804i	−1.33126	+	0.700359i
$334$		0			0
$335$	−1.14916	+	0.964259i	−0.0627853	+	0.0526831i
$336$		0			0
$337$	0.796781	−	4.51877i	0.0434035	−	0.246153i	−0.955385	−	0.295363i	$-0.904559\pi$
$337$	0.796781	−	4.51877i	0.0434035	−	0.246153i	0.998788	+	0.0492101i	$0.0156704\pi$
$338$		0			0
$339$	2.39700	+	3.57060i	0.130187	+	0.193928i
$340$		0			0
$341$	−21.6689	+	37.5316i	−1.17343	+	2.03245i
$342$		0			0
$343$	7.35294	−	16.9981i	0.397022	−	0.917809i
$344$		0			0
$345$	−11.4801	−	8.37942i	−0.618070	−	0.451133i
$346$		0			0
$347$	1.73463	+	4.76584i	0.0931196	+	0.255844i	0.977505	−	0.210914i	$-0.0676441\pi$
$347$	1.73463	+	4.76584i	0.0931196	+	0.255844i	−0.884385	+	0.466758i	$0.845422\pi$
$348$		0			0
$349$	28.8243	−	5.08250i	1.54293	−	0.272060i	0.663531	−	0.748149i	$-0.269057\pi$
$349$	28.8243	−	5.08250i	1.54293	−	0.272060i	0.879397	+	0.476089i	$0.157946\pi$
$350$		0			0
$351$	21.8803	−	13.4726i	1.16788	−	0.719115i
$352$		0			0
$353$	4.42014	+	25.0679i	0.235261	+	1.33423i	0.842064	+	0.539377i	$0.181340\pi$
$353$	4.42014	+	25.0679i	0.235261	+	1.33423i	−0.606804	+	0.794852i	$0.707549\pi$
$354$		0			0
$355$	2.35414	+	6.46794i	0.124945	+	0.343282i
$356$		0			0
$357$	−13.6335	+	9.93321i	−0.721559	+	0.525721i
$358$		0			0
$359$	18.4947	−	10.6779i	0.976111	−	0.563558i	0.0750174	−	0.997182i	$-0.476099\pi$
$359$	18.4947	−	10.6779i	0.976111	−	0.563558i	0.901094	+	0.433624i	$0.142765\pi$
$360$		0			0
$361$	24.5426	−	42.5090i	1.29172	−	2.23732i
$362$		0			0
$363$	−24.7874	−	12.1571i	−1.30100	−	0.638083i
$364$		0			0
$365$	−2.73645	−	0.482510i	−0.143232	−	0.0252557i
$366$		0			0
$367$	−1.97806	−	2.35736i	−0.103254	−	0.123053i	0.711943	−	0.702238i	$-0.247816\pi$
$367$	−1.97806	−	2.35736i	−0.103254	−	0.123053i	−0.815197	+	0.579184i	$0.803371\pi$
$368$		0			0
$369$	−2.58028	+	2.84049i	−0.134324	+	0.147870i
$370$		0			0
$371$	−27.1582	−	3.71895i	−1.40999	−	0.193078i
$372$		0			0
$373$	−3.14017	−	2.63492i	−0.162592	−	0.136431i	0.557862	−	0.829934i	$-0.311622\pi$
$373$	−3.14017	−	2.63492i	−0.162592	−	0.136431i	−0.720454	+	0.693503i	$0.756066\pi$
$374$		0			0
$375$	−14.0197	−	14.5818i	−0.723976	−	0.753003i
$376$		0			0
$377$	28.8386			1.48526
$378$		0			0
$379$	32.3702			1.66275			0.831374	−	0.555713i	$-0.187555\pi$
$379$	32.3702			1.66275			0.831374	+	0.555713i	$0.187555\pi$
$380$		0			0
$381$	−28.4848	+	7.03563i	−1.45932	+	0.360446i
$382$		0			0
$383$	6.02897	+	5.05891i	0.308066	+	0.258498i	0.783692	−	0.621149i	$-0.213334\pi$
$383$	6.02897	+	5.05891i	0.308066	+	0.258498i	−0.475626	+	0.879648i	$0.657778\pi$
$384$		0			0
$385$	−28.8162	−	3.94598i	−1.46861	−	0.201106i
$386$		0			0
$387$	3.39029	−	0.461292i	0.172338	−	0.0234488i
$388$		0			0
$389$	1.24756	+	1.48679i	0.0632539	+	0.0753831i	0.796744	−	0.604318i	$-0.206554\pi$
$389$	1.24756	+	1.48679i	0.0632539	+	0.0753831i	−0.733490	+	0.679701i	$0.762110\pi$
$390$		0			0
$391$	−14.0446	−	2.47645i	−0.710268	−	0.125239i
$392$		0			0
$393$	−0.208082	−	3.07272i	−0.0104963	−	0.154998i
$394$		0			0
$395$	−12.9274	+	22.3909i	−0.650447	+	1.12661i
$396$		0			0
$397$	13.9021	−	8.02639i	0.697727	−	0.402833i	−0.108773	−	0.994067i	$-0.534692\pi$
$397$	13.9021	−	8.02639i	0.697727	−	0.402833i	0.806500	+	0.591234i	$0.201359\pi$
$398$		0			0
$399$	37.6001	−	4.00285i	1.88236	−	0.200393i
$400$		0			0
$401$	5.79906	+	15.9328i	0.289591	+	0.795645i	0.996124	+	0.0879644i	$0.0280362\pi$
$401$	5.79906	+	15.9328i	0.289591	+	0.795645i	−0.706533	+	0.707681i	$0.749742\pi$
$402$		0			0
$403$	−7.16995	−	40.6628i	−0.357161	−	2.02556i
$404$		0			0
$405$	4.77389	−	18.4546i	0.237217	−	0.917015i
$406$		0			0
$407$	−46.7701	+	8.24682i	−2.31831	+	0.408780i
$408$		0			0
$409$	−7.33472	−	20.1520i	−0.362679	−	0.996452i	−0.978079	−	0.208237i	$-0.933228\pi$
$409$	−7.33472	−	20.1520i	−0.362679	−	0.996452i	0.615400	−	0.788215i	$-0.288995\pi$
$410$		0			0
$411$	2.73155	−	25.4509i	0.134737	−	1.25540i
$412$		0			0
$413$	−8.84650	+	8.02225i	−0.435308	+	0.394749i
$414$		0			0
$415$	−14.2700	+	24.7163i	−0.700485	+	1.21328i
$416$		0			0
$417$	−14.2527	+	0.965185i	−0.697960	+	0.0472653i
$418$		0			0
$419$	−4.67151	+	26.4934i	−0.228218	+	1.29429i	0.628218	+	0.778037i	$0.283784\pi$
$419$	−4.67151	+	26.4934i	−0.228218	+	1.29429i	−0.856437	+	0.516252i	$0.827327\pi$
$420$		0			0
$421$	2.23085	−	1.87191i	0.108725	−	0.0912313i	−0.586804	−	0.809729i	$-0.699614\pi$
$421$	2.23085	−	1.87191i	0.108725	−	0.0912313i	0.695530	+	0.718497i	$0.255170\pi$
$422$		0			0
$423$	10.0242	+	12.9472i	0.487391	+	0.629515i
$424$		0			0
$425$	−1.77813	−	0.647187i	−0.0862521	−	0.0313932i
$426$		0			0
$427$	−2.24421	−	1.18310i	−0.108605	−	0.0572544i
$428$		0			0
$429$	43.1591	−	10.6601i	2.08374	−	0.514675i
$430$		0			0
$431$			1.22259i			0.0588901i	0.999566	+	0.0294450i	$0.00937400\pi$
$431$			1.22259i			0.0588901i	−0.999566	+	0.0294450i	$0.990626\pi$
$432$		0			0
$433$		−	9.48559i		−	0.455848i	−0.973679	−	0.227924i	$-0.926806\pi$
$433$		−	9.48559i		−	0.455848i	0.973679	−	0.227924i	$-0.0731938\pi$
$434$		0			0
$435$	15.4220	−	14.8275i	0.739427	−	0.710923i
$436$		0			0
$437$	24.4894	+	20.5490i	1.17149	+	0.982994i
$438$		0			0
$439$	−0.174317	+	0.478932i	−0.00831969	+	0.0228582i	−0.943783	−	0.330566i	$-0.892760\pi$
$439$	−0.174317	+	0.478932i	−0.00831969	+	0.0228582i	0.935463	+	0.353424i	$0.114983\pi$
$440$		0			0
$441$	14.0935	+	15.5683i	0.671119	+	0.741350i
$442$		0			0
$443$	0.870518	+	1.03744i	0.0413595	+	0.0492904i	0.786328	−	0.617810i	$-0.211980\pi$
$443$	0.870518	+	1.03744i	0.0413595	+	0.0492904i	−0.744968	+	0.667100i	$0.767535\pi$
$444$		0			0
$445$	−1.99868	+	11.3351i	−0.0947464	+	0.537333i
$446$		0			0
$447$	−5.70223	+	11.6264i	−0.269706	+	0.549910i
$448$		0			0
$449$	−27.0191	−	15.5995i	−1.27511	−	0.736187i	−0.299167	−	0.954201i	$-0.596709\pi$
$449$	−27.0191	−	15.5995i	−1.27511	−	0.736187i	−0.975946	+	0.218014i	$0.930042\pi$
$450$		0			0
$451$	−5.74978	+	3.31964i	−0.270746	+	0.156316i
$452$		0			0
$453$	2.05441	+	4.64170i	0.0965245	+	0.218086i
$454$		0			0
$455$	23.4481	−	14.7676i	1.09926	−	0.692314i
$456$		0			0
$457$	3.36827	+	19.1024i	0.157561	+	0.893573i	0.956407	+	0.292037i	$0.0943332\pi$
$457$	3.36827	+	19.1024i	0.157561	+	0.893573i	−0.798846	+	0.601536i	$0.794556\pi$
$458$		0			0
$459$	−3.85329	−	18.7347i	−0.179856	−	0.874461i
$460$		0			0
$461$	−1.93052	−	10.9485i	−0.0899131	−	0.509923i	−0.996188	−	0.0872337i	$-0.972197\pi$
$461$	−1.93052	−	10.9485i	−0.0899131	−	0.509923i	0.906275	−	0.422689i	$-0.138914\pi$
$462$		0			0
$463$	8.22825	−	2.99484i	0.382399	−	0.139182i	−0.143666	−	0.989626i	$-0.545889\pi$
$463$	8.22825	−	2.99484i	0.382399	−	0.139182i	0.526065	+	0.850444i	$0.323667\pi$
$464$		0			0
$465$	−24.7412	−	18.0587i	−1.14734	−	0.837453i
$466$		0			0
$467$	−0.725247	−	1.25617i	−0.0335604	−	0.0581284i	0.848757	−	0.528783i	$-0.177351\pi$
$467$	−0.725247	−	1.25617i	−0.0335604	−	0.0581284i	−0.882318	+	0.470654i	$0.844018\pi$
$468$		0			0
$469$	1.78423	+	0.572764i	0.0823881	+	0.0264478i
$470$		0			0
$471$	−10.5195	−	15.6699i	−0.484712	−	0.722032i
$472$		0			0
$473$	5.82970	+	1.02793i	0.268050	+	0.0472644i
$474$		0			0
$475$	2.72653	+	3.24935i	0.125102	+	0.149091i
$476$		0			0
$477$	16.5866	−	26.2863i	0.759448	−	1.20357i
$478$		0			0
$479$	34.1784	+	12.4399i	1.56165	+	0.568395i	0.971114	−	0.238615i	$-0.0766935\pi$
$479$	34.1784	+	12.4399i	1.56165	+	0.568395i	0.590538	+	0.807010i	$0.298916\pi$
$480$		0			0
$481$	29.0847	−	34.6617i	1.32615	−	1.58044i
$482$		0			0
$483$	−1.21477	+	17.7128i	−0.0552737	+	0.805962i
$484$		0			0
$485$			10.3343i			0.469256i
$486$		0			0
$487$	−25.6160			−1.16077			−0.580387	−	0.814341i	$-0.697099\pi$
$487$	−25.6160			−1.16077			−0.580387	+	0.814341i	$0.697099\pi$
$488$		0			0
$489$	−9.00008	+	31.1287i	−0.406998	+	1.40769i
$490$		0			0
$491$	19.7664	−	23.5567i	0.892047	−	1.06310i	−0.105591	−	0.994410i	$-0.533674\pi$
$491$	19.7664	−	23.5567i	0.892047	−	1.06310i	0.997638	−	0.0686901i	$-0.0218820\pi$
$492$		0			0
$493$	7.34197	−	20.1719i	0.330666	−	0.908496i
$494$		0			0
$495$	17.5992	−	27.8911i	0.791024	−	1.25361i
$496$		0			0
$497$	5.26952	−	6.79407i	0.236370	−	0.304756i
$498$		0			0
$499$	−0.268069	+	1.52030i	−0.0120004	+	0.0680578i	−0.990220	−	0.139516i	$-0.955445\pi$
$499$	−0.268069	+	1.52030i	−0.0120004	+	0.0680578i	0.978219	+	0.207573i	$0.0665566\pi$
$500$		0			0
$501$	23.8766	−	16.0287i	1.06673	−	0.716110i
$502$		0			0
$503$	−12.2041	+	21.1382i	−0.544156	+	0.942505i	0.454504	+	0.890745i	$0.349817\pi$
$503$	−12.2041	+	21.1382i	−0.544156	+	0.942505i	−0.998660	+	0.0517603i	$0.983517\pi$
$504$		0			0
$505$	18.2284	+	31.5726i	0.811155	+	1.40496i
$506$		0			0
$507$	−11.6963	+	16.0244i	−0.519452	+	0.711670i
$508$		0			0
$509$	−23.3284	+	8.49085i	−1.03401	+	0.376350i	−0.802608	−	0.596507i	$-0.796555\pi$
$509$	−23.3284	+	8.49085i	−1.03401	+	0.376350i	−0.231406	+	0.972857i	$0.574332\pi$
$510$		0			0
$511$	1.31165	+	3.21367i	0.0580238	+	0.142164i
$512$		0			0
$513$	−13.5177	+	40.6887i	−0.596822	+	1.79645i
$514$		0			0
$515$	18.8740	−	3.32799i	0.831687	−	0.146649i
$516$		0			0
$517$	9.68915	+	26.6207i	0.426128	+	1.17078i
$518$		0			0
$519$	1.17119	+	2.64616i	0.0514095	+	0.116154i
$520$		0			0
$521$	−7.37907	−	12.7809i	−0.323283	−	0.559942i	0.657881	−	0.753122i	$-0.271453\pi$
$521$	−7.37907	−	12.7809i	−0.323283	−	0.559942i	−0.981163	+	0.193180i	$0.938120\pi$
$522$		0			0
$523$	−5.76889	−	3.33067i	−0.252256	−	0.145640i	0.368541	−	0.929612i	$-0.379857\pi$
$523$	−5.76889	−	3.33067i	−0.252256	−	0.145640i	−0.620797	+	0.783972i	$0.713191\pi$
$524$		0			0
$525$	−0.566842	+	2.28652i	−0.0247390	+	0.0997919i
$526$		0			0
$527$	−30.2680	−	5.33707i	−1.31849	−	0.232486i
$528$		0			0
$529$	6.12031	−	5.13555i	0.266101	−	0.223285i
$530$		0			0
$531$	−4.12784	−	12.8967i	−0.179133	−	0.559671i
$532$		0			0
$533$	2.16348	−	5.94410i	0.0937106	−	0.257468i
$534$		0			0
$535$	7.78675	−	9.27989i	0.336650	−	0.401204i
$536$		0			0
$537$	−22.4767	+	21.6103i	−0.969941	+	0.932552i
$538$		0			0
$539$	15.0121	+	33.0859i	0.646616	+	1.42511i
$540$		0			0
$541$	−1.77614			−0.0763621			−0.0381811	−	0.999271i	$-0.512156\pi$
$541$	−1.77614			−0.0763621			−0.0381811	+	0.999271i	$0.512156\pi$
$542$		0			0
$543$	−2.88783	−	11.6918i	−0.123929	−	0.501744i
$544$		0			0
$545$	18.2014	+	15.2728i	0.779664	+	0.654216i
$546$		0			0
$547$	−20.1912	−	7.34899i	−0.863313	−	0.314220i	−0.127857	−	0.991793i	$-0.540810\pi$
$547$	−20.1912	−	7.34899i	−0.863313	−	0.314220i	−0.735456	+	0.677573i	$0.763032\pi$
$548$		0			0
$549$	2.27459	−	1.76106i	0.0970771	−	0.0751603i
$550$		0			0
$551$	−36.8620	+	30.9309i	−1.57038	+	1.31770i
$552$		0			0
$553$	32.2732	−	1.24129i	1.37240	−	0.0527851i
$554$		0			0
$555$	−2.26791	−	33.4900i	−0.0962676	−	1.42157i
$556$		0			0
$557$	−6.42694	−	3.71060i	−0.272318	−	0.157223i	0.357622	−	0.933866i	$-0.383588\pi$
$557$	−6.42694	−	3.71060i	−0.272318	−	0.157223i	−0.629941	+	0.776643i	$0.716921\pi$
$558$		0			0
$559$	−4.88433	+	2.81997i	−0.206585	+	0.119272i
$560$		0			0
$561$	3.53132	−	32.9027i	0.149092	−	1.38915i
$562$		0			0
$563$	−3.64853	+	1.32796i	−0.153767	+	0.0559667i	−0.417757	−	0.908559i	$-0.637184\pi$
$563$	−3.64853	+	1.32796i	−0.153767	+	0.0559667i	0.263990	+	0.964525i	$0.414961\pi$
$564$		0			0
$565$	−5.17895	+	0.913189i	−0.217880	+	0.0384181i
$566$		0			0
$567$	−22.6847	+	7.23920i	−0.952666	+	0.304018i
$568$		0			0
$569$	−24.2144	+	4.26965i	−1.01512	+	0.178993i	−0.656369	−	0.754440i	$-0.727908\pi$
$569$	−24.2144	+	4.26965i	−1.01512	+	0.178993i	−0.358751	+	0.933433i	$0.616797\pi$
$570$		0			0
$571$	−37.9814	+	13.8241i	−1.58947	+	0.578521i	−0.977236	−	0.212153i	$-0.931952\pi$
$571$	−37.9814	+	13.8241i	−1.58947	+	0.578521i	−0.612237	+	0.790674i	$0.709730\pi$
$572$		0			0
$573$	3.68250	−	34.3113i	0.153838	−	1.43337i
$574$		0			0
$575$	−1.72482	+	0.995827i	−0.0719301	+	0.0415289i
$576$		0			0
$577$	−11.0712	−	6.39195i	−0.460899	−	0.266100i	0.251523	−	0.967851i	$-0.419069\pi$
$577$	−11.0712	−	6.39195i	−0.460899	−	0.266100i	−0.712422	+	0.701751i	$0.752402\pi$
$578$		0			0
$579$	0.341054	+	5.03629i	0.0141737	+	0.209301i
$580$		0			0
$581$	35.6250	−	1.37021i	1.47797	−	0.0568458i
$582$		0			0
$583$	41.1942	−	34.5661i	1.70609	−	1.43158i
$584$		0			0
$585$	4.23622	+	31.1344i	0.175146	+	1.28725i
$586$		0			0
$587$	−23.6906	−	8.62268i	−0.977816	−	0.355896i	−0.196825	−	0.980439i	$-0.563063\pi$
$587$	−23.6906	−	8.62268i	−0.977816	−	0.355896i	−0.780991	+	0.624543i	$0.785285\pi$
$588$		0			0
$589$	52.7777	+	44.2858i	2.17467	+	1.82476i
$590$		0			0
$591$	−9.42797	−	38.1706i	−0.387815	−	1.57013i
$592$		0			0
$593$	25.8300			1.06071			0.530356	−	0.847775i	$-0.322058\pi$
$593$	25.8300			1.06071			0.530356	+	0.847775i	$0.322058\pi$
$594$		0			0
$595$	−4.35993	−	20.1610i	−0.178740	−	0.826521i
$596$		0			0
$597$	−12.4883	+	12.0069i	−0.511112	+	0.491409i
$598$		0			0
$599$	4.62777	−	5.51517i	0.189086	−	0.225344i	−0.663170	−	0.748469i	$-0.730789\pi$
$599$	4.62777	−	5.51517i	0.189086	−	0.225344i	0.852256	+	0.523125i	$0.175234\pi$
$600$		0			0
$601$	−0.815903	+	2.24168i	−0.0332814	+	0.0914399i	−0.955220	−	0.295895i	$-0.904382\pi$
$601$	−0.815903	+	2.24168i	−0.0332814	+	0.0914399i	0.921939	+	0.387335i	$0.126604\pi$
$602$		0			0
$603$	−1.42870	+	1.57278i	−0.0581813	+	0.0640486i
$604$		0			0
$605$	25.8617	−	21.7006i	1.05143	−	0.882254i
$606$		0			0
$607$	21.4284	+	3.77841i	0.869753	+	0.153361i	0.590677	−	0.806908i	$-0.298861\pi$
$607$	21.4284	+	3.77841i	0.869753	+	0.153361i	0.279076	+	0.960269i	$0.409972\pi$
$608$		0			0
$609$	−25.9392	−	6.43049i	−1.05111	−	0.260577i
$610$		0			0
$611$	−23.3746	−	13.4953i	−0.945636	−	0.545963i
$612$		0			0
$613$	16.1568	+	27.9844i	0.652568	+	1.13028i	0.982498	+	0.186275i	$0.0596416\pi$
$613$	16.1568	+	27.9844i	0.652568	+	1.13028i	−0.329930	+	0.944005i	$0.607025\pi$
$614$		0			0
$615$	−1.89922	−	4.29107i	−0.0765841	−	0.173033i
$616$		0			0
$617$	10.1692	+	27.9396i	0.409396	+	1.12481i	0.957509	+	0.288402i	$0.0931240\pi$
$617$	10.1692	+	27.9396i	0.409396	+	1.12481i	−0.548113	+	0.836404i	$0.684654\pi$
$618$		0			0
$619$	12.2199	−	2.15469i	0.491158	−	0.0866044i	0.0774165	−	0.996999i	$-0.475333\pi$
$619$	12.2199	−	2.15469i	0.491158	−	0.0866044i	0.413741	+	0.910394i	$0.364222\pi$
$620$		0			0
$621$	−17.7125	−	9.56820i	−0.710779	−	0.383959i
$622$		0			0
$623$	13.3118	−	5.43316i	0.533326	−	0.217675i
$624$		0			0
$625$	20.8287	−	7.58102i	0.833147	−	0.303241i
$626$		0			0
$627$	−43.7332	+	59.9163i	−1.74654	+	2.39283i
$628$		0			0
$629$	−16.8404	−	29.1684i	−0.671471	−	1.16302i
$630$		0			0
$631$	−2.13813	+	3.70334i	−0.0851175	+	0.147428i	−0.905441	−	0.424472i	$-0.860460\pi$
$631$	−2.13813	+	3.70334i	−0.0851175	+	0.147428i	0.820324	+	0.571899i	$0.193793\pi$
$632$		0			0
$633$	−5.46509	+	3.66880i	−0.217218	+	0.145822i
$634$		0			0
$635$	6.23030	−	35.3338i	0.247242	−	1.40218i
$636$		0			0
$637$	−31.2190	−	14.9541i	−1.23694	−	0.592503i
$638$		0			0
$639$	4.53916	+	8.62817i	0.179566	+	0.341325i
$640$		0			0
$641$	−13.6743	+	37.5699i	−0.540104	+	1.48392i	0.306590	+	0.951842i	$0.400812\pi$
$641$	−13.6743	+	37.5699i	−0.540104	+	1.48392i	−0.846693	+	0.532081i	$0.821410\pi$
$642$		0			0
$643$	11.8228	−	14.0899i	0.466246	−	0.555651i	−0.480765	−	0.876849i	$-0.659641\pi$
$643$	11.8228	−	14.0899i	0.466246	−	0.555651i	0.947012	+	0.321198i	$0.104086\pi$
$644$		0			0
$645$	−1.16209	+	4.01933i	−0.0457571	+	0.158261i
$646$		0			0
$647$	41.2616			1.62216			0.811081	−	0.584934i	$-0.198880\pi$
$647$	41.2616			1.62216			0.811081	+	0.584934i	$0.198880\pi$
$648$		0			0
$649$		−	23.4278i		−	0.919623i
$650$		0			0
$651$	−2.61797	+	38.1734i	−0.102606	+	1.49613i
$652$		0			0
$653$	−12.5912	+	15.0056i	−0.492733	+	0.587216i	−0.953910	−	0.300092i	$-0.902983\pi$
$653$	−12.5912	+	15.0056i	−0.492733	+	0.587216i	0.461177	+	0.887308i	$0.347427\pi$
$654$		0			0
$655$	3.53889	+	1.28805i	0.138276	+	0.0503284i
$656$		0			0
$657$	−3.93274	−	0.154640i	−0.153431	−	0.00603308i
$658$		0			0
$659$	−3.69352	−	4.40176i	−0.143879	−	0.171468i	0.689292	−	0.724483i	$-0.257922\pi$
$659$	−3.69352	−	4.40176i	−0.143879	−	0.171468i	−0.833171	+	0.553015i	$0.813477\pi$
$660$		0			0
$661$	−9.95640	−	1.75558i	−0.387259	−	0.0682842i	−0.0233708	−	0.999727i	$-0.507440\pi$
$661$	−9.95640	−	1.75558i	−0.387259	−	0.0682842i	−0.363888	+	0.931443i	$0.618551\pi$
$662$		0			0
$663$	17.5728	+	26.1767i	0.682472	+	1.01662i
$664$		0			0
$665$	−14.1328	+	44.0255i	−0.548047	+	1.70724i
$666$		0			0
$667$	−11.2971	−	19.5671i	−0.437425	−	0.757642i
$668$		0			0
$669$	14.0472	+	10.2531i	0.543095	+	0.396408i
$670$		0			0
$671$	4.67678	−	1.70221i	0.180545	−	0.0657130i
$672$		0			0
$673$	2.87208	+	16.2883i	0.110710	+	0.627870i	0.988785	+	0.149346i	$0.0477168\pi$
$673$	2.87208	+	16.2883i	0.110710	+	0.627870i	−0.878075	+	0.478524i	$0.841172\pi$
$674$		0			0
$675$	−2.09401	−	1.65836i	−0.0805985	−	0.0638304i
$676$		0			0
$677$	1.31076	+	7.43367i	0.0503764	+	0.285699i	0.999581	−	0.0289622i	$-0.00922023\pi$
$677$	1.31076	+	7.43367i	0.0503764	+	0.285699i	−0.949204	+	0.314661i	$0.898109\pi$
$678$		0			0
$679$	10.9235	−	6.87956i	0.419204	−	0.264013i
$680$		0			0
$681$	7.51618	+	16.9819i	0.288021	+	0.650750i
$682$		0			0
$683$	37.4517	−	21.6227i	1.43305	−	0.827370i	0.435696	−	0.900094i	$-0.356502\pi$
$683$	37.4517	−	21.6227i	1.43305	−	0.827370i	0.997352	+	0.0727236i	$0.0231691\pi$
$684$		0			0
$685$	27.1073	+	15.6504i	1.03572	+	0.597971i
$686$		0			0
$687$	7.10316	−	14.4828i	0.271002	−	0.552553i
$688$		0			0
$689$	−8.89677	+	50.4561i	−0.338940	+	1.92222i
$690$		0			0
$691$	18.0902	+	21.5591i	0.688184	+	0.820146i	0.991135	−	0.132860i	$-0.0424162\pi$
$691$	18.0902	+	21.5591i	0.688184	+	0.820146i	−0.302951	+	0.953006i	$0.597972\pi$
$692$		0			0
$693$	−41.1970	−	0.0353383i	−1.56494	−	0.00134239i
$694$		0			0
$695$	5.97461	−	16.4151i	0.226630	−	0.622661i
$696$		0			0
$697$	−3.60696	−	3.02659i	−0.136623	−	0.114640i
$698$		0			0
$699$	−23.5578	+	22.6497i	−0.891038	+	0.856690i
$700$		0			0
$701$		−	3.40155i		−	0.128475i	−0.997935	−	0.0642373i	$-0.979539\pi$
$701$		−	3.40155i		−	0.128475i	0.997935	−	0.0642373i	$-0.0204615\pi$
$702$		0			0
$703$			75.5000i			2.84754i
$704$		0			0
$705$	−19.4387	+	4.80127i	−0.732103	+	0.180826i
$706$		0			0
$707$	21.2378	−	40.2856i	0.798731	−	1.51510i
$708$		0			0
$709$	7.17379	+	2.61104i	0.269417	+	0.0980598i	0.473196	−	0.880957i	$-0.343100\pi$
$709$	7.17379	+	2.61104i	0.269417	+	0.0980598i	−0.203779	+	0.979017i	$0.565322\pi$
$710$		0			0
$711$	−13.8677	+	33.8942i	−0.520079	+	1.27113i
$712$		0			0
$713$	−24.7812	+	20.7939i	−0.928063	+	0.778737i
$714$		0			0
$715$	−9.43991	+	53.5364i	−0.353033	+	2.00215i
$716$		0			0
$717$	50.6909	−	3.43275i	1.89309	−	0.128198i
$718$		0			0
$719$	1.02799	−	1.78053i	0.0383374	−	0.0664024i	−0.846220	−	0.532834i	$-0.821127\pi$
$719$	1.02799	−	1.78053i	0.0383374	−	0.0664024i	0.884557	+	0.466431i	$0.154460\pi$
$720$		0			0
$721$	−16.0822	−	17.7346i	−0.598932	−	0.660469i
$722$		0			0
$723$	−5.10321	+	47.5486i	−0.189790	+	1.76835i
$724$		0			0
$725$	−1.02534	−	2.81709i	−0.0380801	−	0.104624i
$726$		0			0
$727$	−20.3018	+	3.57976i	−0.752952	+	0.132766i	−0.536935	−	0.843624i	$-0.680418\pi$
$727$	−20.3018	+	3.57976i	−0.752952	+	0.132766i	−0.216017	+	0.976390i	$0.569307\pi$
$728$		0			0
$729$	3.17600	−	26.8126i	0.117630	−	0.993058i
$730$		0			0
$731$	0.729006	+	4.13440i	0.0269633	+	0.152916i
$732$		0			0
$733$	−1.81117	−	4.97615i	−0.0668971	−	0.183798i	0.901740	−	0.432280i	$-0.142291\pi$
$733$	−1.81117	−	4.97615i	−0.0668971	−	0.183798i	−0.968637	+	0.248482i	$0.920068\pi$
$734$		0			0
$735$	−24.3836	+	8.05436i	−0.899403	+	0.297090i
$736$		0			0
$737$	−3.18365	+	1.83808i	−0.117271	+	0.0677067i
$738$		0			0
$739$	3.61690	−	6.26466i	0.133050	−	0.230449i	−0.791801	−	0.610779i	$-0.790856\pi$
$739$	3.61690	−	6.26466i	0.133050	−	0.230449i	0.924851	+	0.380330i	$0.124190\pi$
$740$		0			0
$741$	−4.77509	−	70.5130i	−0.175417	−	2.59036i
$742$		0			0
$743$	−34.4508	−	6.07461i	−1.26388	−	0.222856i	−0.498757	−	0.866742i	$-0.666210\pi$
$743$	−34.4508	−	6.07461i	−1.26388	−	0.222856i	−0.765122	+	0.643886i	$0.777321\pi$
$744$		0			0
$745$	−10.1785	−	12.1303i	−0.372913	−	0.444420i
$746$		0			0
$747$	−15.3079	+	37.4143i	−0.560089	+	1.36892i
$748$		0			0
$749$	−14.9926	−	2.05303i	−0.547818	−	0.0750161i
$750$		0			0
$751$	−10.2333	−	8.58676i	−0.373418	−	0.313335i	0.436694	−	0.899610i	$-0.356149\pi$
$751$	−10.2333	−	8.58676i	−0.373418	−	0.313335i	−0.810112	+	0.586275i	$0.800594\pi$
$752$		0			0
$753$	0.848420	−	0.209556i	0.0309182	−	0.00763665i
$754$		0			0
$755$	−6.20710			−0.225900
$756$		0			0
$757$	−23.2054			−0.843416			−0.421708	−	0.906732i	$-0.638569\pi$
$757$	−23.2054			−0.843416			−0.421708	+	0.906732i	$0.638569\pi$
$758$		0			0
$759$	−24.1399	−	25.1077i	−0.876221	−	0.911352i
$760$		0			0
$761$	39.4403	+	33.0944i	1.42971	+	1.19967i	0.945884	+	0.324506i	$0.105198\pi$
$761$	39.4403	+	33.0944i	1.42971	+	1.19967i	0.483827	+	0.875164i	$0.339246\pi$
$762$		0			0
$763$	4.02679	−	29.4063i	0.145779	−	1.06458i
$764$		0			0
$765$	22.8562	+	4.96331i	0.826368	+	0.179449i
$766$		0			0
$767$	14.3476	+	17.0988i	0.518062	+	0.617403i
$768$		0			0
$769$	−45.1010	−	7.95252i	−1.62638	−	0.286775i	−0.715244	−	0.698875i	$-0.753684\pi$
$769$	−45.1010	−	7.95252i	−1.62638	−	0.286775i	−0.911139	+	0.412100i	$0.864796\pi$
$770$		0			0
$771$	22.6945	+	11.1306i	0.817322	+	0.400860i
$772$		0			0
$773$	13.5983	−	23.5529i	0.489096	−	0.847140i	−0.510825	−	0.859685i	$-0.670660\pi$
$773$	13.5983	−	23.5529i	0.489096	−	0.847140i	0.999921	+	0.0125451i	$0.00399334\pi$
$774$		0			0
$775$	−3.71721	+	2.14613i	−0.133526	+	0.0770914i
$776$		0			0
$777$	−33.8895	+	24.6916i	−1.21578	+	0.885805i
$778$		0			0
$779$	3.60996	+	9.91830i	0.129340	+	0.355360i
$780$		0			0
$781$	2.92900	+	16.6112i	0.104808	+	0.594395i
$782$		0			0
$783$	18.8132	−	23.7553i	0.672328	−	0.848946i
$784$		0			0
$785$	22.7283	−	4.00762i	0.811210	−	0.143038i
$786$		0			0
$787$	−8.49646	−	23.3438i	−0.302866	−	0.832118i	−0.993999	−	0.109390i	$-0.965110\pi$
$787$	−8.49646	−	23.3438i	−0.302866	−	0.832118i	0.691133	−	0.722728i	$-0.257112\pi$
$788$		0			0
$789$	37.2550	+	27.1926i	1.32631	+	0.968083i
$790$		0			0
$791$	4.41289	+	4.86629i	0.156904	+	0.173026i
$792$		0			0
$793$	−2.37089	+	4.10650i	−0.0841927	+	0.145826i
$794$		0			0
$795$	21.1845	+	31.5566i	0.751336	+	1.11920i
$796$		0			0
$797$	−3.33095	+	18.8908i	−0.117988	+	0.669145i	0.867239	+	0.497893i	$0.165893\pi$
$797$	−3.33095	+	18.8908i	−0.117988	+	0.669145i	−0.985227	+	0.171253i	$0.945218\pi$
$798$		0			0
$799$	−15.3906	+	12.9142i	−0.544479	+	0.456872i
$800$		0			0
$801$	−0.640556	+	16.2904i	−0.0226330	+	0.575593i
$802$		0			0
$803$	−6.39869	−	2.32893i	−0.225805	−	0.0821863i
$804$		0			0
$805$	−19.2053	−	10.1247i	−0.676898	−	0.356848i
$806$		0			0
$807$	1.91975	−	6.63987i	0.0675784	−	0.233734i
$808$		0			0
$809$			10.2158i			0.359167i	0.983743	+	0.179584i	$0.0574751\pi$
$809$			10.2158i			0.359167i	−0.983743	+	0.179584i	$0.942525\pi$
$810$		0			0
$811$			5.03056i			0.176647i	0.996092	+	0.0883234i	$0.0281509\pi$
$811$			5.03056i			0.176647i	−0.996092	+	0.0883234i	$0.971849\pi$
$812$		0			0
$813$	2.03419	+	0.588134i	0.0713421	+	0.0206268i
$814$		0			0
$815$	−30.3539	−	25.4699i	−1.06325	−	0.892173i
$816$		0			0
$817$	3.21867	−	8.84324i	0.112607	−	0.309386i
$818$		0			0
$819$	30.0893	−	25.2040i	1.05141	−	0.880698i
$820$		0			0
$821$	−13.9616	−	16.6388i	−0.487264	−	0.580699i	0.465255	−	0.885177i	$-0.345963\pi$
$821$	−13.9616	−	16.6388i	−0.487264	−	0.580699i	−0.952520	+	0.304478i	$0.901518\pi$
$822$		0			0
$823$	6.06408	−	34.3911i	0.211381	−	1.19880i	−0.675697	−	0.737179i	$-0.736157\pi$
$823$	6.06408	−	34.3911i	0.211381	−	1.19880i	0.887078	−	0.461620i	$-0.152732\pi$
$824$		0			0
$825$	−2.57582	−	3.83697i	−0.0896787	−	0.133586i
$826$		0			0
$827$	7.24287	+	4.18168i	0.251859	+	0.145411i	0.620615	−	0.784115i	$-0.286883\pi$
$827$	7.24287	+	4.18168i	0.251859	+	0.145411i	−0.368756	+	0.929526i	$0.620216\pi$
$828$		0			0
$829$	−30.6277	+	17.6829i	−1.06374	+	0.614153i	−0.926465	−	0.376380i	$-0.877169\pi$
$829$	−30.6277	+	17.6829i	−1.06374	+	0.614153i	−0.137278	+	0.990533i	$0.543835\pi$
$830$		0			0
$831$	3.82171	−	5.23590i	0.132574	−	0.181631i
$832$		0			0
$833$	−18.4080	+	18.0297i	−0.637799	+	0.624694i
$834$		0			0
$835$	6.10649	+	34.6316i	0.211324	+	1.19848i
$836$		0			0
$837$	−38.1727	−	20.6207i	−1.31944	−	0.712755i
$838$		0			0
$839$	5.08181	+	28.8204i	0.175444	+	0.994990i	0.937631	+	0.347633i	$0.113015\pi$
$839$	5.08181	+	28.8204i	0.175444	+	0.994990i	−0.762187	+	0.647357i	$0.775874\pi$
$840$		0			0
$841$	4.70721	−	1.71329i	0.162318	−	0.0590788i
$842$		0			0
$843$	44.2615	−	19.5901i	1.52445	−	0.674718i
$844$		0			0
$845$	−12.1299	−	21.0095i	−0.417280	−	0.722750i
$846$		0			0
$847$	−40.1540	−	12.8900i	−1.37971	−	0.442906i
$848$		0			0
$849$	11.8601	−	24.1818i	0.407038	−	0.829918i
$850$		0			0
$851$	−34.9116	−	6.15586i	−1.19675	−	0.211020i
$852$		0			0
$853$	9.76232	+	11.6343i	0.334255	+	0.398350i	0.906826	−	0.421505i	$-0.138498\pi$
$853$	9.76232	+	11.6343i	0.334255	+	0.398350i	−0.572571	+	0.819855i	$0.694054\pi$
$854$		0			0
$855$	−38.8080	−	35.2529i	−1.32721	−	1.20562i
$856$		0			0
$857$	15.4157	+	5.61084i	0.526589	+	0.191663i	0.591615	−	0.806221i	$-0.298491\pi$
$857$	15.4157	+	5.61084i	0.526589	+	0.191663i	−0.0650255	+	0.997884i	$0.520713\pi$
$858$		0			0
$859$	−15.6296	+	18.6266i	−0.533275	+	0.635532i	−0.963666	−	0.267111i	$-0.913931\pi$
$859$	−15.6296	+	18.6266i	−0.533275	+	0.635532i	0.430391	+	0.902642i	$0.358376\pi$
$860$		0			0
$861$	−3.27139	+	4.86408i	−0.111489	+	0.165767i
$862$		0			0
$863$		−	11.3903i		−	0.387730i	−0.981028	−	0.193865i	$-0.937898\pi$
$863$		−	11.3903i		−	0.387730i	0.981028	−	0.193865i	$-0.0621023\pi$
$864$		0			0
$865$	−3.53858			−0.120315
$866$		0			0
$867$	−5.80206	+	1.43308i	−0.197048	+	0.0486700i
$868$		0			0
$869$	−40.7265	+	48.5359i	−1.38155	+	1.64647i
$870$		0			0
$871$	1.19792	−	3.29125i	0.0405899	−	0.111520i
$872$		0			0
$873$	1.97347	+	14.5041i	0.0667918	+	0.490891i
$874$		0			0
$875$	−24.4160	−	18.9372i	−0.825413	−	0.640195i
$876$		0			0
$877$	1.30107	−	7.37871i	0.0439339	−	0.249161i	−0.954929	−	0.296834i	$-0.904069\pi$
$877$	1.30107	−	7.37871i	0.0439339	−	0.249161i	0.998863	+	0.0476725i	$0.0151804\pi$
$878$		0			0
$879$	1.23902	+	18.2964i	0.0417911	+	0.617122i
$880$		0			0
$881$	11.7812	−	20.4056i	0.396918	−	0.687482i	−0.596426	−	0.802668i	$-0.703413\pi$
$881$	11.7812	−	20.4056i	0.396918	−	0.687482i	0.993344	+	0.115186i	$0.0367463\pi$
$882$		0			0
$883$	21.6320	+	37.4678i	0.727976	+	1.26089i	0.957737	+	0.287644i	$0.0928721\pi$
$883$	21.6320	+	37.4678i	0.727976	+	1.26089i	−0.229761	+	0.973247i	$0.573795\pi$
$884$		0			0
$885$	16.4641	+	1.76702i	0.553433	+	0.0593979i
$886$		0			0
$887$	11.4946	−	4.18368i	0.385950	−	0.140474i	−0.141755	−	0.989902i	$-0.545275\pi$
$887$	11.4946	−	4.18368i	0.385950	−	0.140474i	0.527706	+	0.849427i	$0.323052\pi$
$888$		0			0
$889$	−41.4957	+	16.9363i	−1.39172	+	0.568026i
$890$		0			0
$891$	19.3742	−	42.5058i	0.649060	−	1.42400i
$892$		0			0
$893$	44.3523	−	7.82051i	1.48419	−	0.261703i
$894$		0			0
$895$	−13.0406	−	35.8287i	−0.435898	−	1.19762i
$896$		0			0
$897$	32.9949	+	3.54122i	1.10167	+	0.118238i
$898$		0			0
$899$	−24.3467	−	42.1697i	−0.812007	−	1.40644i
$900$		0			0
$901$	33.0278	+	19.0686i	1.10031	+	0.635267i
$902$		0			0
$903$	5.02207	−	1.44734i	0.167124	−	0.0481644i
$904$		0			0
$905$	14.5030	+	2.55728i	0.482097	+	0.0850067i
$906$		0			0
$907$	19.0255	−	15.9643i	0.631730	−	0.530084i	−0.269736	−	0.962934i	$-0.586936\pi$
$907$	19.0255	−	15.9643i	0.631730	−	0.530084i	0.901466	+	0.432850i	$0.142492\pi$
$908$		0			0
$909$	31.6128	+	40.8311i	1.04853	+	1.35428i
$910$		0			0
$911$	−14.2331	+	39.1052i	−0.471564	+	1.29561i	0.444930	+	0.895565i	$0.353228\pi$
$911$	−14.2331	+	39.1052i	−0.471564	+	1.29561i	−0.916495	+	0.400047i	$0.868994\pi$
$912$		0			0
$913$	−44.9562	+	53.5767i	−1.48783	+	1.77313i
$914$		0			0
$915$	0.843495	+	3.41502i	0.0278851	+	0.112897i
$916$		0			0
$917$	−0.994367	−	4.59811i	−0.0328369	−	0.151843i
$918$		0			0
$919$	53.0126			1.74873			0.874363	−	0.485273i	$-0.161280\pi$
$919$	53.0126			1.74873			0.874363	+	0.485273i	$0.161280\pi$
$920$		0			0
$921$	1.05937	−	1.01854i	0.0349075	−	0.0335619i
$922$		0			0
$923$	−12.3107	−	10.3299i	−0.405212	−	0.340013i
$924$		0			0
$925$	−4.42001	−	1.60875i	−0.145329	−	0.0528954i
$926$		0			0
$927$	25.8541	−	8.27507i	0.849159	−	0.271789i
$928$		0			0
$929$	18.0970	−	15.1852i	0.593744	−	0.498210i	−0.295684	−	0.955286i	$-0.595548\pi$
$929$	18.0970	−	15.1852i	0.593744	−	0.498210i	0.889428	+	0.457076i	$0.151103\pi$
$930$		0			0
$931$	55.9437	−	14.3694i	1.83348	−	0.470937i
$932$		0			0
$933$	10.1908	+	4.99815i	0.333633	+	0.163632i
$934$		0			0
$935$	35.0441	+	20.2327i	1.14606	+	0.661680i
$936$		0			0
$937$	38.3227	−	22.1256i	1.25195	−	0.722812i	0.280451	−	0.959868i	$-0.409516\pi$
$937$	38.3227	−	22.1256i	1.25195	−	0.722812i	0.971496	+	0.237056i	$0.0761826\pi$
$938$		0			0
$939$	13.6473	−	6.04027i	0.445362	−	0.197117i
$940$		0			0
$941$	−31.7300	+	11.5488i	−1.03437	+	0.376480i	−0.802743	−	0.596325i	$-0.796627\pi$
$941$	−31.7300	+	11.5488i	−1.03437	+	0.376480i	−0.231627	+	0.972805i	$0.574405\pi$
$942$		0			0
$943$	−4.88061	+	0.860583i	−0.158934	+	0.0280244i
$944$		0			0
$945$	3.13208	−	28.9488i	0.101887	−	0.941704i
$946$		0			0
$947$	−27.9123	+	4.92169i	−0.907027	+	0.159933i	−0.607653	−	0.794203i	$-0.707889\pi$
$947$	−27.9123	+	4.92169i	−0.907027	+	0.159933i	−0.299374	+	0.954136i	$0.596778\pi$
$948$		0			0
$949$	6.09637	−	2.21890i	0.197896	−	0.0720284i
$950$		0			0
$951$	11.7256	+	8.55858i	0.380229	+	0.277531i
$952$		0			0
$953$	−28.7475	+	16.5974i	−0.931223	+	0.537642i	−0.887198	−	0.461389i	$-0.847351\pi$
$953$	−28.7475	+	16.5974i	−0.931223	+	0.537642i	−0.0440245	+	0.999030i	$0.514018\pi$
$954$		0			0
$955$	36.5444	+	21.0989i	1.18255	+	0.682744i
$956$		0			0
$957$	43.5283	−	29.2212i	1.40707	−	0.944589i
$958$		0			0
$959$	−1.50276	−	39.0712i	−0.0485266	−	1.26168i
$960$		0			0
$961$	−29.6592	+	24.8870i	−0.956749	+	0.802808i
$962$		0			0
$963$	9.15656	−	14.5113i	0.295066	−	0.467619i
$964$		0			0
$965$	−5.80037	−	2.11116i	−0.186721	−	0.0679608i
$966$		0			0
$967$	−34.5341	−	28.9776i	−1.11054	−	0.931856i	−0.112454	−	0.993657i	$-0.535871\pi$
$967$	−34.5341	−	28.9776i	−1.11054	−	0.931856i	−0.998088	+	0.0618014i	$0.980315\pi$
$968$		0			0
$969$	−50.5377	−	14.6117i	−1.62351	−	0.469396i
$970$		0			0
$971$	51.7359			1.66028			0.830142	−	0.557552i	$-0.188259\pi$
$971$	51.7359			1.66028			0.830142	+	0.557552i	$0.188259\pi$
$972$		0			0
$973$	−21.3283	+	4.61236i	−0.683753	+	0.147865i
$974$		0			0
$975$	4.22980	+	1.22294i	0.135462	+	0.0391654i
$976$		0			0
$977$	−12.9438	+	15.4259i	−0.414110	+	0.493518i	−0.932268	−	0.361767i	$-0.882173\pi$
$977$	−12.9438	+	15.4259i	−0.414110	+	0.493518i	0.518158	+	0.855285i	$0.326618\pi$
$978$		0			0
$979$	−9.64702	+	26.5050i	−0.308320	+	0.847102i
$980$		0			0
$981$	28.4622	+	17.9596i	0.908729	+	0.573404i
$982$		0			0
$983$	19.7330	−	16.5580i	0.629385	−	0.528117i	−0.271353	−	0.962480i	$-0.587471\pi$
$983$	19.7330	−	16.5580i	0.629385	−	0.528117i	0.900738	+	0.434363i	$0.143027\pi$
$984$		0			0
$985$	47.3485	+	8.34881i	1.50865	+	0.266015i
$986$		0			0
$987$	18.0154	+	17.3507i	0.573436	+	0.552278i
$988$		0			0
$989$	3.82673	+	2.20936i	0.121683	+	0.0702536i
$990$		0			0
$991$	−10.3791	−	17.9772i	−0.329704	−	0.571064i	0.652749	−	0.757574i	$-0.273616\pi$
$991$	−10.3791	−	17.9772i	−0.329704	−	0.571064i	−0.982453	+	0.186510i	$0.940282\pi$
$992$		0			0
$993$	−25.4295	+	34.8394i	−0.806980	+	1.10560i
$994$		0			0
$995$	−7.24548	−	19.9068i	−0.229697	−	0.631088i
$996$		0			0
$997$	5.04729	−	0.889974i	0.159849	−	0.0281858i	−0.0931507	−	0.995652i	$-0.529694\pi$
$997$	5.04729	−	0.889974i	0.159849	−	0.0281858i	0.253000	+	0.967466i	$0.418583\pi$
$998$		0			0
$999$	−9.57836	−	46.5700i	−0.303046	−	1.47341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bx.a.41.11	✓	144
7.6	odd	2	inner	756.2.bx.a.41.14	yes	144
27.2	odd	18	inner	756.2.bx.a.461.14	yes	144
189.83	even	18	inner	756.2.bx.a.461.11	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bx.a.41.11	✓	144	1.1	even	1	trivial
756.2.bx.a.41.14	yes	144	7.6	odd	2	inner
756.2.bx.a.461.11	yes	144	189.83	even	18	inner
756.2.bx.a.461.14	yes	144	27.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bx (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.481075 + 1.66390i) q^{3} +(-1.62248 - 1.36143i) q^{5} +(-0.358949 + 2.62129i) q^{7} +(-2.53713 - 1.60092i) q^{9} +O(q^{10})\)	\(q+(-0.481075 + 1.66390i) q^{3} +(-1.62248 - 1.36143i) q^{5} +(-0.358949 + 2.62129i) q^{7} +(-2.53713 - 1.60092i) q^{9} +(-3.33628 - 3.97603i) q^{11} +(4.86998 + 0.858708i) q^{13} +(3.04581 - 2.04471i) q^{15} +(1.84048 - 3.18781i) q^{17} +(-7.14590 + 4.12569i) q^{19} +(-4.18888 - 1.85829i) q^{21} +(-1.32510 - 3.64069i) q^{23} +(-0.0892661 - 0.506253i) q^{25} +(3.88433 - 3.45138i) q^{27} +(5.74315 - 1.01267i) q^{29} +(-2.85576 - 7.84614i) q^{31} +(8.22072 - 3.63848i) q^{33} +(4.15108 - 3.76432i) q^{35} +(4.57500 - 7.92413i) q^{37} +(-3.77163 + 7.69006i) q^{39} +(0.222124 - 1.25973i) q^{41} +(-0.873681 + 0.733106i) q^{43} +(1.93692 + 6.05159i) q^{45} +(-5.12890 - 1.86677i) q^{47} +(-6.74231 - 1.88182i) q^{49} +(4.41879 + 4.59596i) q^{51} +10.3606i q^{53} +10.9931i q^{55} +(-3.42702 - 13.8748i) q^{57} +(3.45773 + 2.90138i) q^{59} +(-0.327957 + 0.901055i) q^{61} +(5.10718 - 6.07591i) q^{63} +(-6.73239 - 8.02336i) q^{65} +(0.122990 - 0.697511i) q^{67} +(6.69522 - 0.453395i) q^{69} +(-2.81439 - 1.62489i) q^{71} +(1.13616 - 0.655964i) q^{73} +(0.885299 + 0.0950158i) q^{75} +(11.6199 - 7.31817i) q^{77} +(-2.11975 - 12.0217i) q^{79} +(3.87410 + 8.12351i) q^{81} +(-2.33990 - 13.2702i) q^{83} +(-7.32612 + 2.66649i) q^{85} +(-1.07790 + 10.0432i) q^{87} +(-2.71716 - 4.70627i) q^{89} +(-3.99900 + 12.4574i) q^{91} +(14.4290 - 0.977124i) q^{93} +(17.2109 + 3.03475i) q^{95} +(-3.13633 - 3.73773i) q^{97} +(2.09929 + 15.4288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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