LMFDB - Embedded newform 882.2.f.q.295.1

Newspace parameters

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	882.295
Dual form			882.2.f.q.589.1

$q$-expansion

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.517638 + 0.896575i) q^{5} +(0.448288 - 1.67303i) q^{6} +1.00000 q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.517638 + 0.896575i) q^{5} +(0.448288 - 1.67303i) q^{6} +1.00000 q^{8} +(2.59808 - 1.50000i) q^{9} -1.03528 q^{10} +(0.133975 - 0.232051i) q^{11} +(1.22474 + 1.22474i) q^{12} +(-0.896575 - 1.55291i) q^{13} +(-1.26795 - 1.26795i) q^{15} +(-0.500000 + 0.866025i) q^{16} -6.83083 q^{17} +3.00000i q^{18} +4.38134 q^{19} +(0.517638 - 0.896575i) q^{20} +(0.133975 + 0.232051i) q^{22} +(-2.73205 - 4.73205i) q^{23} +(-1.67303 + 0.448288i) q^{24} +(1.96410 - 3.40192i) q^{25} +1.79315 q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.00000 - 3.46410i) q^{29} +(1.73205 - 0.464102i) q^{30} +(-3.34607 - 5.79555i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.120118 + 0.448288i) q^{33} +(3.41542 - 5.91567i) q^{34} +(-2.59808 - 1.50000i) q^{36} +7.46410 q^{37} +(-2.19067 + 3.79435i) q^{38} +(2.19615 + 2.19615i) q^{39} +(0.517638 + 0.896575i) q^{40} +(4.31199 + 7.46859i) q^{41} +(-0.133975 + 0.232051i) q^{43} -0.267949 q^{44} +(2.68973 + 1.55291i) q^{45} +5.46410 q^{46} +(-0.378937 + 0.656339i) q^{47} +(0.448288 - 1.67303i) q^{48} +(1.96410 + 3.40192i) q^{50} +(11.4282 - 3.06218i) q^{51} +(-0.896575 + 1.55291i) q^{52} +10.9282 q^{53} +(-1.34486 - 5.01910i) q^{54} +0.277401 q^{55} +(-7.33013 + 1.96410i) q^{57} +(2.00000 + 3.46410i) q^{58} +(0.637756 + 1.10463i) q^{59} +(-0.464102 + 1.73205i) q^{60} +(6.31319 - 10.9348i) q^{61} +6.69213 q^{62} +1.00000 q^{64} +(0.928203 - 1.60770i) q^{65} +(-0.328169 - 0.328169i) q^{66} +(-6.23205 - 10.7942i) q^{67} +(3.41542 + 5.91567i) q^{68} +(6.69213 + 6.69213i) q^{69} +9.46410 q^{71} +(2.59808 - 1.50000i) q^{72} +5.41662 q^{73} +(-3.73205 + 6.46410i) q^{74} +(-1.76097 + 6.57201i) q^{75} +(-2.19067 - 3.79435i) q^{76} +(-3.00000 + 0.803848i) q^{78} +(-4.46410 + 7.73205i) q^{79} -1.03528 q^{80} +(4.50000 - 7.79423i) q^{81} -8.62398 q^{82} +(-3.29530 + 5.70762i) q^{83} +(-3.53590 - 6.12436i) q^{85} +(-0.133975 - 0.232051i) q^{86} +(-1.79315 + 6.69213i) q^{87} +(0.133975 - 0.232051i) q^{88} +7.07107 q^{89} +(-2.68973 + 1.55291i) q^{90} +(-2.73205 + 4.73205i) q^{92} +(8.19615 + 8.19615i) q^{93} +(-0.378937 - 0.656339i) q^{94} +(2.26795 + 3.92820i) q^{95} +(1.22474 + 1.22474i) q^{96} +(9.07227 - 15.7136i) q^{97} -0.803848i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 8 q^{11} - 24 q^{15} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 12 q^{25} + 16 q^{29} - 4 q^{32} + 32 q^{37} - 24 q^{39} - 8 q^{43} - 16 q^{44} + 16 q^{46} - 12 q^{50} + 36 q^{51} + 32 q^{53} - 24 q^{57} + 16 q^{58} + 24 q^{60} + 8 q^{64} - 48 q^{65} - 36 q^{67} + 48 q^{71} - 16 q^{74} - 24 q^{78} - 8 q^{79} + 36 q^{81} - 56 q^{85} - 8 q^{86} + 8 q^{88} - 8 q^{92} + 24 q^{93} + 32 q^{95}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 8 * q^11 - 24 * q^15 - 4 * q^16 + 8 * q^22 - 8 * q^23 - 12 * q^25 + 16 * q^29 - 4 * q^32 + 32 * q^37 - 24 * q^39 - 8 * q^43 - 16 * q^44 + 16 * q^46 - 12 * q^50 + 36 * q^51 + 32 * q^53 - 24 * q^57 + 16 * q^58 + 24 * q^60 + 8 * q^64 - 48 * q^65 - 36 * q^67 + 48 * q^71 - 16 * q^74 - 24 * q^78 - 8 * q^79 + 36 * q^81 - 56 * q^85 - 8 * q^86 + 8 * q^88 - 8 * q^92 + 24 * q^93 + 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.67303	+	0.448288i	−0.965926	+	0.258819i
$3$	−1.67303	+	0.448288i	−0.965926	+	0.258819i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.517638	+	0.896575i	0.231495	+	0.400961i	0.958248	−	0.285938i	$-0.0923050\pi$
$5$	0.517638	+	0.896575i	0.231495	+	0.400961i	−0.726753	+	0.686898i	$0.758972\pi$
$6$	0.448288	−	1.67303i	0.183013	−	0.683013i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	2.59808	−	1.50000i	0.866025	−	0.500000i
$10$	−1.03528			−0.327383
$11$	0.133975	−	0.232051i	0.0403949	−	0.0699660i	−0.845121	−	0.534575i	$-0.820472\pi$
$11$	0.133975	−	0.232051i	0.0403949	−	0.0699660i	0.885516	+	0.464609i	$0.153805\pi$
$12$	1.22474	+	1.22474i	0.353553	+	0.353553i
$13$	−0.896575	−	1.55291i	−0.248665	−	0.430701i	0.714490	−	0.699645i	$-0.246659\pi$
$13$	−0.896575	−	1.55291i	−0.248665	−	0.430701i	−0.963156	+	0.268944i	$0.913325\pi$
$14$		0			0
$15$	−1.26795	−	1.26795i	−0.327383	−	0.327383i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.83083			−1.65672			−0.828360	−	0.560196i	$-0.810726\pi$
$17$	−6.83083			−1.65672			−0.828360	+	0.560196i	$0.810726\pi$
$18$			3.00000i			0.707107i
$19$	4.38134			1.00515			0.502574	−	0.864534i	$-0.332386\pi$
$19$	4.38134			1.00515			0.502574	+	0.864534i	$0.332386\pi$
$20$	0.517638	−	0.896575i	0.115747	−	0.200480i
$21$		0			0
$22$	0.133975	+	0.232051i	0.0285635	+	0.0494734i
$23$	−2.73205	−	4.73205i	−0.569672	−	0.986701i	−0.996598	−	0.0824143i	$-0.973737\pi$
$23$	−2.73205	−	4.73205i	−0.569672	−	0.986701i	0.426926	−	0.904286i	$-0.359596\pi$
$24$	−1.67303	+	0.448288i	−0.341506	+	0.0915064i
$25$	1.96410	−	3.40192i	0.392820	−	0.680385i
$26$	1.79315			0.351666
$27$	−3.67423	+	3.67423i	−0.707107	+	0.707107i
$28$		0			0
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	−0.618389	−	0.785872i	$-0.712214\pi$
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	0.989780	+	0.142605i	$0.0455477\pi$
$30$	1.73205	−	0.464102i	0.316228	−	0.0847330i
$31$	−3.34607	−	5.79555i	−0.600971	−	1.04091i	−0.992674	−	0.120821i	$-0.961447\pi$
$31$	−3.34607	−	5.79555i	−0.600971	−	1.04091i	0.391703	−	0.920092i	$-0.371886\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.120118	+	0.448288i	−0.0209099	+	0.0780369i
$34$	3.41542	−	5.91567i	0.585739	−	1.01453i
$35$		0			0
$36$	−2.59808	−	1.50000i	−0.433013	−	0.250000i
$37$	7.46410			1.22709			0.613545	−	0.789659i	$-0.289743\pi$
$37$	7.46410			1.22709			0.613545	+	0.789659i	$0.289743\pi$
$38$	−2.19067	+	3.79435i	−0.355374	+	0.615525i
$39$	2.19615	+	2.19615i	0.351666	+	0.351666i
$40$	0.517638	+	0.896575i	0.0818458	+	0.141761i
$41$	4.31199	+	7.46859i	0.673420	+	1.16640i	0.976928	+	0.213569i	$0.0685087\pi$
$41$	4.31199	+	7.46859i	0.673420	+	1.16640i	−0.303508	+	0.952829i	$0.598158\pi$
$42$		0			0
$43$	−0.133975	+	0.232051i	−0.0204309	+	0.0353874i	−0.876060	−	0.482202i	$-0.839837\pi$
$43$	−0.133975	+	0.232051i	−0.0204309	+	0.0353874i	0.855629	+	0.517589i	$0.173170\pi$
$44$	−0.267949			−0.0403949
$45$	2.68973	+	1.55291i	0.400961	+	0.231495i
$46$	5.46410			0.805638
$47$	−0.378937	+	0.656339i	−0.0552737	+	0.0957369i	−0.892338	−	0.451367i	$-0.850936\pi$
$47$	−0.378937	+	0.656339i	−0.0552737	+	0.0957369i	0.837065	+	0.547104i	$0.184270\pi$
$48$	0.448288	−	1.67303i	0.0647048	−	0.241481i
$49$		0			0
$50$	1.96410	+	3.40192i	0.277766	+	0.481105i
$51$	11.4282	−	3.06218i	1.60027	−	0.428791i
$52$	−0.896575	+	1.55291i	−0.124333	+	0.215350i
$53$	10.9282			1.50110			0.750552	−	0.660811i	$-0.229788\pi$
$53$	10.9282			1.50110			0.750552	+	0.660811i	$0.229788\pi$
$54$	−1.34486	−	5.01910i	−0.183013	−	0.683013i
$55$	0.277401			0.0374048
$56$		0			0
$57$	−7.33013	+	1.96410i	−0.970899	+	0.260152i
$58$	2.00000	+	3.46410i	0.262613	+	0.454859i
$59$	0.637756	+	1.10463i	0.0830288	+	0.143810i	0.904550	−	0.426369i	$-0.140207\pi$
$59$	0.637756	+	1.10463i	0.0830288	+	0.143810i	−0.821521	+	0.570179i	$0.806874\pi$
$60$	−0.464102	+	1.73205i	−0.0599153	+	0.223607i
$61$	6.31319	−	10.9348i	0.808322	−	1.40005i	−0.105704	−	0.994398i	$-0.533710\pi$
$61$	6.31319	−	10.9348i	0.808322	−	1.40005i	0.914026	−	0.405656i	$-0.132957\pi$
$62$	6.69213			0.849901
$63$		0			0
$64$	1.00000			0.125000
$65$	0.928203	−	1.60770i	0.115129	−	0.199410i
$66$	−0.328169	−	0.328169i	−0.0403949	−	0.0403949i
$67$	−6.23205	−	10.7942i	−0.761366	−	1.31872i	−0.942146	−	0.335201i	$-0.891196\pi$
$67$	−6.23205	−	10.7942i	−0.761366	−	1.31872i	0.180780	−	0.983524i	$-0.442138\pi$
$68$	3.41542	+	5.91567i	0.414180	+	0.717381i
$69$	6.69213	+	6.69213i	0.805638	+	0.805638i
$70$		0			0
$71$	9.46410			1.12318			0.561591	−	0.827415i	$-0.310189\pi$
$71$	9.46410			1.12318			0.561591	+	0.827415i	$0.310189\pi$
$72$	2.59808	−	1.50000i	0.306186	−	0.176777i
$73$	5.41662			0.633967			0.316984	−	0.948431i	$-0.397330\pi$
$73$	5.41662			0.633967			0.316984	+	0.948431i	$0.397330\pi$
$74$	−3.73205	+	6.46410i	−0.433842	+	0.751437i
$75$	−1.76097	+	6.57201i	−0.203339	+	0.758871i
$76$	−2.19067	−	3.79435i	−0.251287	−	0.435242i
$77$		0			0
$78$	−3.00000	+	0.803848i	−0.339683	+	0.0910178i
$79$	−4.46410	+	7.73205i	−0.502251	+	0.869924i	0.497746	+	0.867323i	$0.334161\pi$
$79$	−4.46410	+	7.73205i	−0.502251	+	0.869924i	−0.999997	+	0.00260080i	$0.999172\pi$
$80$	−1.03528			−0.115747
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	−8.62398			−0.952360
$83$	−3.29530	+	5.70762i	−0.361706	+	0.626493i	−0.988242	−	0.152900i	$-0.951139\pi$
$83$	−3.29530	+	5.70762i	−0.361706	+	0.626493i	0.626536	+	0.779393i	$0.284472\pi$
$84$		0			0
$85$	−3.53590	−	6.12436i	−0.383522	−	0.664280i
$86$	−0.133975	−	0.232051i	−0.0144469	−	0.0250227i
$87$	−1.79315	+	6.69213i	−0.192246	+	0.717472i
$88$	0.133975	−	0.232051i	0.0142817	−	0.0247367i
$89$	7.07107			0.749532			0.374766	−	0.927119i	$-0.377723\pi$
$89$	7.07107			0.749532			0.374766	+	0.927119i	$0.377723\pi$
$90$	−2.68973	+	1.55291i	−0.283522	+	0.163692i
$91$		0			0
$92$	−2.73205	+	4.73205i	−0.284836	+	0.493350i
$93$	8.19615	+	8.19615i	0.849901	+	0.849901i
$94$	−0.378937	−	0.656339i	−0.0390844	−	0.0676962i
$95$	2.26795	+	3.92820i	0.232687	+	0.403025i
$96$	1.22474	+	1.22474i	0.125000	+	0.125000i
$97$	9.07227	−	15.7136i	0.921149	−	1.59548i	0.123510	−	0.992343i	$-0.460585\pi$
$97$	9.07227	−	15.7136i	0.921149	−	1.59548i	0.797640	−	0.603134i	$-0.206082\pi$
$98$		0			0
$99$		−	0.803848i		−	0.0807897i
$100$	−3.92820			−0.392820
$101$	2.44949	−	4.24264i	0.243733	−	0.422159i	−0.718041	−	0.696000i	$-0.754961\pi$
$101$	2.44949	−	4.24264i	0.243733	−	0.422159i	0.961775	+	0.273842i	$0.0882945\pi$
$102$	−3.06218	+	11.4282i	−0.303201	+	1.13156i
$103$	−6.17449	−	10.6945i	−0.608391	−	1.05376i	−0.991506	−	0.130063i	$-0.958482\pi$
$103$	−6.17449	−	10.6945i	−0.608391	−	1.05376i	0.383115	−	0.923701i	$-0.374851\pi$
$104$	−0.896575	−	1.55291i	−0.0879165	−	0.152276i
$105$		0			0
$106$	−5.46410	+	9.46410i	−0.530720	+	0.919235i
$107$	−17.3923			−1.68138			−0.840689	−	0.541519i	$-0.817850\pi$
$107$	−17.3923			−1.68138			−0.840689	+	0.541519i	$0.817850\pi$
$108$	5.01910	+	1.34486i	0.482963	+	0.129410i
$109$	4.92820			0.472036			0.236018	−	0.971749i	$-0.424158\pi$
$109$	4.92820			0.472036			0.236018	+	0.971749i	$0.424158\pi$
$110$	−0.138701	+	0.240237i	−0.0132246	+	0.0229057i
$111$	−12.4877	+	3.34607i	−1.18528	+	0.317594i
$112$		0			0
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	0.981689	−	0.190490i	$-0.0610077\pi$
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	−0.655814	+	0.754923i	$0.727674\pi$
$114$	1.96410	−	7.33013i	0.183955	−	0.686529i
$115$	2.82843	−	4.89898i	0.263752	−	0.456832i
$116$	−4.00000			−0.371391
$117$	−4.65874	−	2.68973i	−0.430701	−	0.248665i
$118$	−1.27551			−0.117420
$119$		0			0
$120$	−1.26795	−	1.26795i	−0.115747	−	0.115747i
$121$	5.46410	+	9.46410i	0.496737	+	0.860373i
$122$	6.31319	+	10.9348i	0.571570	+	0.989988i
$123$	−10.5622	−	10.5622i	−0.952360	−	0.952360i
$124$	−3.34607	+	5.79555i	−0.300486	+	0.520456i
$125$	9.24316			0.826733
$126$		0			0
$127$	13.4641			1.19475			0.597373	−	0.801964i	$-0.296211\pi$
$127$	13.4641			1.19475			0.597373	+	0.801964i	$0.296211\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	0.120118	−	0.448288i	0.0105758	−	0.0394695i
$130$	0.928203	+	1.60770i	0.0814088	+	0.141004i
$131$	−5.46739	−	9.46979i	−0.477688	−	0.827379i	0.521985	−	0.852955i	$-0.325192\pi$
$131$	−5.46739	−	9.46979i	−0.477688	−	0.827379i	−0.999673	+	0.0255752i	$0.991858\pi$
$132$	0.448288	−	0.120118i	0.0390184	−	0.0104550i
$133$		0			0
$134$	12.4641			1.07673
$135$	−5.19615	−	1.39230i	−0.447214	−	0.119831i
$136$	−6.83083			−0.585739
$137$	−4.33013	+	7.50000i	−0.369948	+	0.640768i	−0.989557	−	0.144142i	$-0.953958\pi$
$137$	−4.33013	+	7.50000i	−0.369948	+	0.640768i	0.619609	+	0.784910i	$0.287291\pi$
$138$	−9.14162	+	2.44949i	−0.778186	+	0.208514i
$139$	−0.397520	−	0.688524i	−0.0337172	−	0.0583999i	0.848674	−	0.528916i	$-0.177401\pi$
$139$	−0.397520	−	0.688524i	−0.0337172	−	0.0583999i	−0.882392	+	0.470516i	$0.844068\pi$
$140$		0			0
$141$	0.339746	−	1.26795i	0.0286118	−	0.106781i
$142$	−4.73205	+	8.19615i	−0.397105	+	0.687806i
$143$	−0.480473			−0.0401792
$144$			3.00000i			0.250000i
$145$	4.14110			0.343900
$146$	−2.70831	+	4.69093i	−0.224141	+	0.388224i
$147$		0			0
$148$	−3.73205	−	6.46410i	−0.306773	−	0.531346i
$149$	−11.4641	−	19.8564i	−0.939176	−	1.62670i	−0.767013	−	0.641632i	$-0.778258\pi$
$149$	−11.4641	−	19.8564i	−0.939176	−	1.62670i	−0.172163	−	0.985068i	$-0.555076\pi$
$150$	−4.81105	−	4.81105i	−0.392820	−	0.392820i
$151$	−9.19615	+	15.9282i	−0.748372	+	1.29622i	0.200230	+	0.979749i	$0.435831\pi$
$151$	−9.19615	+	15.9282i	−0.748372	+	1.29622i	−0.948603	+	0.316470i	$0.897502\pi$
$152$	4.38134			0.355374
$153$	−17.7470	+	10.2462i	−1.43476	+	0.828360i
$154$		0			0
$155$	3.46410	−	6.00000i	0.278243	−	0.481932i
$156$	0.803848	−	3.00000i	0.0643593	−	0.240192i
$157$	−4.76028	−	8.24504i	−0.379912	−	0.658026i	0.611137	−	0.791524i	$-0.290712\pi$
$157$	−4.76028	−	8.24504i	−0.379912	−	0.658026i	−0.991049	+	0.133498i	$0.957379\pi$
$158$	−4.46410	−	7.73205i	−0.355145	−	0.615129i
$159$	−18.2832	+	4.89898i	−1.44996	+	0.388514i
$160$	0.517638	−	0.896575i	0.0409229	−	0.0708805i
$161$		0			0
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	−13.3205			−1.04334			−0.521671	−	0.853147i	$-0.674691\pi$
$163$	−13.3205			−1.04334			−0.521671	+	0.853147i	$0.674691\pi$
$164$	4.31199	−	7.46859i	0.336710	−	0.583199i
$165$	−0.464102	+	0.124356i	−0.0361303	+	0.00968107i
$166$	−3.29530	−	5.70762i	−0.255765	−	0.442997i
$167$	−0.757875	−	1.31268i	−0.0586461	−	0.101578i	0.835212	−	0.549928i	$-0.185345\pi$
$167$	−0.757875	−	1.31268i	−0.0586461	−	0.101578i	−0.893858	+	0.448350i	$0.852012\pi$
$168$		0			0
$169$	4.89230	−	8.47372i	0.376331	−	0.651825i
$170$	7.07180			0.542382
$171$	11.3831	−	6.57201i	0.870484	−	0.502574i
$172$	0.267949			0.0204309
$173$	−3.34607	+	5.79555i	−0.254397	+	0.440628i	−0.964731	−	0.263236i	$-0.915210\pi$
$173$	−3.34607	+	5.79555i	−0.254397	+	0.440628i	0.710335	+	0.703864i	$0.248544\pi$
$174$	−4.89898	−	4.89898i	−0.371391	−	0.371391i
$175$		0			0
$176$	0.133975	+	0.232051i	0.0100987	+	0.0174915i
$177$	−1.56218	−	1.56218i	−0.117420	−	0.117420i
$178$	−3.53553	+	6.12372i	−0.264999	+	0.458993i
$179$	5.07180			0.379084			0.189542	−	0.981873i	$-0.439300\pi$
$179$	5.07180			0.379084			0.189542	+	0.981873i	$0.439300\pi$
$180$		−	3.10583i		−	0.231495i
$181$	−16.9706			−1.26141			−0.630706	−	0.776022i	$-0.717235\pi$
$181$	−16.9706			−1.26141			−0.630706	+	0.776022i	$0.717235\pi$
$182$		0			0
$183$	−5.66025	+	21.1244i	−0.418418	+	1.56156i
$184$	−2.73205	−	4.73205i	−0.201409	−	0.348851i
$185$	3.86370	+	6.69213i	0.284065	+	0.492015i
$186$	−11.1962	+	3.00000i	−0.820942	+	0.219971i
$187$	−0.915158	+	1.58510i	−0.0669230	+	0.115914i
$188$	0.757875			0.0552737
$189$		0			0
$190$	−4.53590			−0.329069
$191$	−7.46410	+	12.9282i	−0.540083	+	0.935452i	0.458815	+	0.888532i	$0.348274\pi$
$191$	−7.46410	+	12.9282i	−0.540083	+	0.935452i	−0.998899	+	0.0469202i	$0.985059\pi$
$192$	−1.67303	+	0.448288i	−0.120741	+	0.0323524i
$193$	−7.52628	−	13.0359i	−0.541753	−	0.938344i	−0.998804	−	0.0489035i	$-0.984427\pi$
$193$	−7.52628	−	13.0359i	−0.541753	−	0.938344i	0.457050	−	0.889441i	$-0.348906\pi$
$194$	9.07227	+	15.7136i	0.651351	+	1.12817i
$195$	−0.832204	+	3.10583i	−0.0595954	+	0.222413i
$196$		0			0
$197$	−16.9282			−1.20608			−0.603042	−	0.797709i	$-0.706045\pi$
$197$	−16.9282			−1.20608			−0.603042	+	0.797709i	$0.706045\pi$
$198$	0.696152	+	0.401924i	0.0494734	+	0.0285635i
$199$	26.2880			1.86351			0.931755	−	0.363087i	$-0.118277\pi$
$199$	26.2880			1.86351			0.931755	+	0.363087i	$0.118277\pi$
$200$	1.96410	−	3.40192i	0.138883	−	0.240552i
$201$	15.2653	+	15.2653i	1.07673	+	1.07673i
$202$	2.44949	+	4.24264i	0.172345	+	0.298511i
$203$		0			0
$204$	−8.36603	−	8.36603i	−0.585739	−	0.585739i
$205$	−4.46410	+	7.73205i	−0.311786	+	0.540030i
$206$	12.3490			0.860395
$207$	−14.1962	−	8.19615i	−0.986701	−	0.569672i
$208$	1.79315			0.124333
$209$	0.586988	−	1.01669i	0.0406028	−	0.0703262i
$210$		0			0
$211$	−9.46410	−	16.3923i	−0.651536	−	1.12849i	−0.982750	−	0.184937i	$-0.940792\pi$
$211$	−9.46410	−	16.3923i	−0.651536	−	1.12849i	0.331215	−	0.943555i	$-0.392542\pi$
$212$	−5.46410	−	9.46410i	−0.375276	−	0.649997i
$213$	−15.8338	+	4.24264i	−1.08491	+	0.290701i
$214$	8.69615	−	15.0622i	0.594457	−	1.02963i
$215$	−0.277401			−0.0189186
$216$	−3.67423	+	3.67423i	−0.250000	+	0.250000i
$217$		0			0
$218$	−2.46410	+	4.26795i	−0.166890	+	0.289062i
$219$	−9.06218	+	2.42820i	−0.612365	+	0.164083i
$220$	−0.138701	−	0.240237i	−0.00935120	−	0.0161968i
$221$	6.12436	+	10.6077i	0.411969	+	0.713551i
$222$	3.34607	−	12.4877i	0.224573	−	0.838119i
$223$	3.58630	−	6.21166i	0.240157	−	0.415963i	−0.720602	−	0.693349i	$-0.756135\pi$
$223$	3.58630	−	6.21166i	0.240157	−	0.415963i	0.960759	+	0.277385i	$0.0894679\pi$
$224$		0			0
$225$		−	11.7846i		−	0.785641i
$226$	−6.92820			−0.460857
$227$	13.8325	−	23.9587i	0.918098	−	1.59019i	0.115798	−	0.993273i	$-0.463057\pi$
$227$	13.8325	−	23.9587i	0.918098	−	1.59019i	0.802300	−	0.596920i	$-0.203609\pi$
$228$	5.36603	+	5.36603i	0.355374	+	0.355374i
$229$	−0.240237	−	0.416102i	−0.0158753	−	0.0274968i	0.857979	−	0.513685i	$-0.171720\pi$
$229$	−0.240237	−	0.416102i	−0.0158753	−	0.0274968i	−0.873854	+	0.486189i	$0.838387\pi$
$230$	2.82843	+	4.89898i	0.186501	+	0.323029i
$231$		0			0
$232$	2.00000	−	3.46410i	0.131306	−	0.227429i
$233$	0.124356			0.00814681			0.00407340	−	0.999992i	$-0.498703\pi$
$233$	0.124356			0.00814681			0.00407340	+	0.999992i	$0.498703\pi$
$234$	4.65874	−	2.68973i	0.304552	−	0.175833i
$235$	−0.784610			−0.0511823
$236$	0.637756	−	1.10463i	0.0415144	−	0.0719051i
$237$	4.00240	−	14.9372i	0.259984	−	0.970274i
$238$		0			0
$239$	−0.464102	−	0.803848i	−0.0300202	−	0.0519966i	0.850625	−	0.525773i	$-0.176224\pi$
$239$	−0.464102	−	0.803848i	−0.0300202	−	0.0519966i	−0.880645	+	0.473776i	$0.842891\pi$
$240$	1.73205	−	0.464102i	0.111803	−	0.0299576i
$241$	−3.13801	+	5.43520i	−0.202137	+	0.350112i	−0.949217	−	0.314623i	$-0.898122\pi$
$241$	−3.13801	+	5.43520i	−0.202137	+	0.350112i	0.747080	+	0.664735i	$0.231455\pi$
$242$	−10.9282			−0.702492
$243$	−4.03459	+	15.0573i	−0.258819	+	0.965926i
$244$	−12.6264			−0.808322
$245$		0			0
$246$	14.4282	−	3.86603i	0.919909	−	0.246489i
$247$	−3.92820	−	6.80385i	−0.249946	−	0.432918i
$248$	−3.34607	−	5.79555i	−0.212475	−	0.368018i
$249$	2.95448	−	11.0263i	0.187233	−	0.698762i
$250$	−4.62158	+	8.00481i	−0.292294	+	0.506269i
$251$	0.795040			0.0501824			0.0250912	−	0.999685i	$-0.492012\pi$
$251$	0.795040			0.0501824			0.0250912	+	0.999685i	$0.492012\pi$
$252$		0			0
$253$	−1.46410			−0.0920473
$254$	−6.73205	+	11.6603i	−0.422406	+	0.731629i
$255$	8.66115	+	8.66115i	0.542382	+	0.542382i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.01910	−	8.69333i	−0.313083	−	0.542275i	0.665945	−	0.746001i	$-0.268028\pi$
$257$	−5.01910	−	8.69333i	−0.313083	−	0.542275i	−0.979028	+	0.203725i	$0.934695\pi$
$258$	0.328169	+	0.328169i	0.0204309	+	0.0204309i
$259$		0			0
$260$	−1.85641			−0.115129
$261$		−	12.0000i		−	0.742781i
$262$	10.9348			0.675552
$263$	4.26795	−	7.39230i	0.263173	−	0.455829i	−0.703910	−	0.710289i	$-0.748564\pi$
$263$	4.26795	−	7.39230i	0.263173	−	0.455829i	0.967083	+	0.254460i	$0.0818977\pi$
$264$	−0.120118	+	0.448288i	−0.00739277	+	0.0275902i
$265$	5.65685	+	9.79796i	0.347498	+	0.601884i
$266$		0			0
$267$	−11.8301	+	3.16987i	−0.723992	+	0.193993i
$268$	−6.23205	+	10.7942i	−0.380683	+	0.659362i
$269$	−5.65685			−0.344904			−0.172452	−	0.985018i	$-0.555169\pi$
$269$	−5.65685			−0.344904			−0.172452	+	0.985018i	$0.555169\pi$
$270$	3.80385	−	3.80385i	0.231495	−	0.231495i
$271$	13.1069			0.796185			0.398093	−	0.917345i	$-0.369672\pi$
$271$	13.1069			0.796185			0.398093	+	0.917345i	$0.369672\pi$
$272$	3.41542	−	5.91567i	0.207090	−	0.358690i
$273$		0			0
$274$	−4.33013	−	7.50000i	−0.261593	−	0.453092i
$275$	−0.526279	−	0.911543i	−0.0317358	−	0.0549681i
$276$	2.44949	−	9.14162i	0.147442	−	0.550261i
$277$	−15.7321	+	27.2487i	−0.945247	+	1.63722i	−0.189992	+	0.981786i	$0.560846\pi$
$277$	−15.7321	+	27.2487i	−0.945247	+	1.63722i	−0.755255	+	0.655431i	$0.772487\pi$
$278$	0.795040			0.0476833
$279$	−17.3867	−	10.0382i	−1.04091	−	0.600971i
$280$		0			0
$281$	−8.92820	+	15.4641i	−0.532612	+	0.922511i	0.466663	+	0.884435i	$0.345456\pi$
$281$	−8.92820	+	15.4641i	−0.532612	+	0.922511i	−0.999275	+	0.0380757i	$0.987877\pi$
$282$	0.928203	+	0.928203i	0.0552737	+	0.0552737i
$283$	7.53794	+	13.0561i	0.448084	+	0.776104i	0.998261	−	0.0589437i	$-0.0187732\pi$
$283$	7.53794	+	13.0561i	0.448084	+	0.776104i	−0.550177	+	0.835048i	$0.685440\pi$
$284$	−4.73205	−	8.19615i	−0.280796	−	0.486352i
$285$	−5.55532	−	5.55532i	−0.329069	−	0.329069i
$286$	0.240237	−	0.416102i	0.0142055	−	0.0246046i
$287$		0			0
$288$	−2.59808	−	1.50000i	−0.153093	−	0.0883883i
$289$	29.6603			1.74472
$290$	−2.07055	+	3.58630i	−0.121587	+	0.210595i
$291$	−8.13397	+	30.3564i	−0.476822	+	1.77952i
$292$	−2.70831	−	4.69093i	−0.158492	−	0.274516i
$293$	4.62158	+	8.00481i	0.269995	+	0.467646i	0.968860	−	0.247608i	$-0.0796445\pi$
$293$	4.62158	+	8.00481i	0.269995	+	0.467646i	−0.698865	+	0.715254i	$0.746311\pi$
$294$		0			0
$295$	−0.660254	+	1.14359i	−0.0384415	+	0.0665826i
$296$	7.46410			0.433842
$297$	0.360355	+	1.34486i	0.0209099	+	0.0780369i
$298$	22.9282			1.32820
$299$	−4.89898	+	8.48528i	−0.283315	+	0.490716i
$300$	6.57201	−	1.76097i	0.379435	−	0.101669i
$301$		0			0
$302$	−9.19615	−	15.9282i	−0.529179	−	0.916565i
$303$	−2.19615	+	8.19615i	−0.126166	+	0.470857i
$304$	−2.19067	+	3.79435i	−0.125644	+	0.217621i
$305$	13.0718			0.748489
$306$		−	20.4925i		−	1.17148i
$307$	1.17398			0.0670024			0.0335012	−	0.999439i	$-0.489334\pi$
$307$	1.17398			0.0670024			0.0335012	+	0.999439i	$0.489334\pi$
$308$		0			0
$309$	15.1244	+	15.1244i	0.860395	+	0.860395i
$310$	3.46410	+	6.00000i	0.196748	+	0.340777i
$311$	3.72500	+	6.45189i	0.211226	+	0.365853i	0.952098	−	0.305792i	$-0.0989212\pi$
$311$	3.72500	+	6.45189i	0.211226	+	0.365853i	−0.740873	+	0.671645i	$0.765588\pi$
$312$	2.19615	+	2.19615i	0.124333	+	0.124333i
$313$	−3.13801	+	5.43520i	−0.177371	+	0.307216i	−0.940979	−	0.338464i	$-0.890093\pi$
$313$	−3.13801	+	5.43520i	−0.177371	+	0.307216i	0.763608	+	0.645680i	$0.223426\pi$
$314$	9.52056			0.537276
$315$		0			0
$316$	8.92820			0.502251
$317$	13.0000	−	22.5167i	0.730153	−	1.26466i	−0.226665	−	0.973973i	$-0.572782\pi$
$317$	13.0000	−	22.5167i	0.730153	−	1.26466i	0.956818	−	0.290689i	$-0.0938844\pi$
$318$	4.89898	−	18.2832i	0.274721	−	1.02527i
$319$	−0.535898	−	0.928203i	−0.0300045	−	0.0519694i
$320$	0.517638	+	0.896575i	0.0289368	+	0.0501201i
$321$	29.0979	−	7.79676i	1.62409	−	0.435173i
$322$		0			0
$323$	−29.9282			−1.66525
$324$	−9.00000			−0.500000
$325$	−7.04386			−0.390723
$326$	6.66025	−	11.5359i	0.368877	−	0.638914i
$327$	−8.24504	+	2.20925i	−0.455952	+	0.122172i
$328$	4.31199	+	7.46859i	0.238090	+	0.412384i
$329$		0			0
$330$	0.124356	−	0.464102i	0.00684555	−	0.0255480i
$331$	5.73205	−	9.92820i	0.315062	−	0.545703i	−0.664389	−	0.747387i	$-0.731308\pi$
$331$	5.73205	−	9.92820i	0.315062	−	0.545703i	0.979451	+	0.201684i	$0.0646413\pi$
$332$	6.59059			0.361706
$333$	19.3923	−	11.1962i	1.06269	−	0.613545i
$334$	1.51575			0.0829381
$335$	6.45189	−	11.1750i	0.352505	−	0.610556i
$336$		0			0
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	0.945468	−	0.325714i	$-0.105605\pi$
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	−0.754811	+	0.655942i	$0.772271\pi$
$338$	4.89230	+	8.47372i	0.266106	+	0.460910i
$339$	−8.48528	−	8.48528i	−0.460857	−	0.460857i
$340$	−3.53590	+	6.12436i	−0.191761	+	0.332140i
$341$	−1.79315			−0.0971046
$342$			13.1440i			0.710747i
$343$		0			0
$344$	−0.133975	+	0.232051i	−0.00722343	+	0.0125113i
$345$	−2.53590	+	9.46410i	−0.136528	+	0.509530i
$346$	−3.34607	−	5.79555i	−0.179886	−	0.311571i
$347$	4.79423	+	8.30385i	0.257368	+	0.445774i	0.965536	−	0.260270i	$-0.0838115\pi$
$347$	4.79423	+	8.30385i	0.257368	+	0.445774i	−0.708168	+	0.706044i	$0.750478\pi$
$348$	6.69213	−	1.79315i	0.358736	−	0.0961230i
$349$	4.00240	−	6.93237i	0.214244	−	0.371081i	−0.738795	−	0.673931i	$-0.764605\pi$
$349$	4.00240	−	6.93237i	0.214244	−	0.371081i	0.953038	+	0.302850i	$0.0979380\pi$
$350$		0			0
$351$	9.00000	+	2.41154i	0.480384	+	0.128719i
$352$	−0.267949			−0.0142817
$353$	−12.5063	+	21.6615i	−0.665641	+	1.15292i	0.313470	+	0.949598i	$0.398509\pi$
$353$	−12.5063	+	21.6615i	−0.665641	+	1.15292i	−0.979111	+	0.203327i	$0.934825\pi$
$354$	2.13397	−	0.571797i	0.113419	−	0.0303907i
$355$	4.89898	+	8.48528i	0.260011	+	0.450352i
$356$	−3.53553	−	6.12372i	−0.187383	−	0.324557i
$357$		0			0
$358$	−2.53590	+	4.39230i	−0.134026	+	0.232141i
$359$	7.46410			0.393940			0.196970	−	0.980409i	$-0.436890\pi$
$359$	7.46410			0.393940			0.196970	+	0.980409i	$0.436890\pi$
$360$	2.68973	+	1.55291i	0.141761	+	0.0818458i
$361$	0.196152			0.0103238
$362$	8.48528	−	14.6969i	0.445976	−	0.772454i
$363$	−13.3843	−	13.3843i	−0.702492	−	0.702492i
$364$		0			0
$365$	2.80385	+	4.85641i	0.146760	+	0.254196i
$366$	−15.4641	−	15.4641i	−0.808322	−	0.808322i
$367$	−9.28032	+	16.0740i	−0.484429	+	0.839055i	−0.999840	−	0.0178877i	$-0.994306\pi$
$367$	−9.28032	+	16.0740i	−0.484429	+	0.839055i	0.515411	+	0.856943i	$0.327639\pi$
$368$	5.46410			0.284836
$369$	22.4058	+	12.9360i	1.16640	+	0.673420i
$370$	−7.72741			−0.401729
$371$		0			0
$372$	3.00000	−	11.1962i	0.155543	−	0.580493i
$373$	5.39230	+	9.33975i	0.279203	+	0.483594i	0.971187	−	0.238319i	$-0.0765964\pi$
$373$	5.39230	+	9.33975i	0.279203	+	0.483594i	−0.691984	+	0.721913i	$0.743263\pi$
$374$	−0.915158	−	1.58510i	−0.0473217	−	0.0819636i
$375$	−15.4641	+	4.14359i	−0.798563	+	0.213974i
$376$	−0.378937	+	0.656339i	−0.0195422	+	0.0338481i
$377$	−7.17260			−0.369408
$378$		0			0
$379$	13.5885			0.697992			0.348996	−	0.937124i	$-0.386523\pi$
$379$	13.5885			0.697992			0.348996	+	0.937124i	$0.386523\pi$
$380$	2.26795	−	3.92820i	0.116343	−	0.201513i
$381$	−22.5259	+	6.03579i	−1.15404	+	0.309223i
$382$	−7.46410	−	12.9282i	−0.381897	−	0.661464i
$383$	−13.6617	−	23.6627i	−0.698078	−	1.20911i	−0.969132	−	0.246543i	$-0.920705\pi$
$383$	−13.6617	−	23.6627i	−0.698078	−	1.20911i	0.271054	−	0.962564i	$-0.412628\pi$
$384$	0.448288	−	1.67303i	0.0228766	−	0.0853766i
$385$		0			0
$386$	15.0526			0.766155
$387$			0.803848i			0.0408619i
$388$	−18.1445			−0.921149
$389$	−4.00000	+	6.92820i	−0.202808	+	0.351274i	−0.949432	−	0.313972i	$-0.898340\pi$
$389$	−4.00000	+	6.92820i	−0.202808	+	0.351274i	0.746624	+	0.665246i	$0.231673\pi$
$390$	−2.27362	−	2.27362i	−0.115129	−	0.115129i
$391$	18.6622	+	32.3238i	0.943787	+	1.63469i
$392$		0			0
$393$	13.3923	+	13.3923i	0.675552	+	0.675552i
$394$	8.46410	−	14.6603i	0.426415	−	0.738573i
$395$	−9.24316			−0.465074
$396$	−0.696152	+	0.401924i	−0.0349830	+	0.0201974i
$397$	13.1069			0.657814			0.328907	−	0.944362i	$-0.393320\pi$
$397$	13.1069			0.657814			0.328907	+	0.944362i	$0.393320\pi$
$398$	−13.1440	+	22.7661i	−0.658850	+	1.14116i
$399$		0			0
$400$	1.96410	+	3.40192i	0.0982051	+	0.170096i
$401$	11.8923	+	20.5981i	0.593873	+	1.02862i	0.993705	+	0.112030i	$0.0357353\pi$
$401$	11.8923	+	20.5981i	0.593873	+	1.02862i	−0.399831	+	0.916589i	$0.630931\pi$
$402$	−20.8528	+	5.58750i	−1.04005	+	0.278679i
$403$	−6.00000	+	10.3923i	−0.298881	+	0.517678i
$404$	−4.89898			−0.243733
$405$	9.31749			0.462990
$406$		0			0
$407$	1.00000	−	1.73205i	0.0495682	−	0.0858546i
$408$	11.4282	−	3.06218i	0.565780	−	0.151600i
$409$	−2.24144	−	3.88229i	−0.110832	−	0.191967i	0.805274	−	0.592903i	$-0.202018\pi$
$409$	−2.24144	−	3.88229i	−0.110832	−	0.191967i	−0.916106	+	0.400936i	$0.868685\pi$
$410$	−4.46410	−	7.73205i	−0.220466	−	0.381859i
$411$	3.88229	−	14.4889i	0.191499	−	0.714684i
$412$	−6.17449	+	10.6945i	−0.304195	+	0.526882i
$413$		0			0
$414$	14.1962	−	8.19615i	0.697703	−	0.402819i
$415$	−6.82309			−0.334932
$416$	−0.896575	+	1.55291i	−0.0439582	+	0.0761379i
$417$	0.973721	+	0.973721i	0.0476833	+	0.0476833i
$418$	0.586988	+	1.01669i	0.0287105	+	0.0497281i
$419$	−18.0938	−	31.3393i	−0.883939	−	1.53103i	−0.846925	−	0.531712i	$-0.821549\pi$
$419$	−18.0938	−	31.3393i	−0.883939	−	1.53103i	−0.0370132	−	0.999315i	$-0.511784\pi$
$420$		0			0
$421$	−3.80385	+	6.58846i	−0.185388	+	0.321102i	−0.943707	−	0.330782i	$-0.892688\pi$
$421$	−3.80385	+	6.58846i	−0.185388	+	0.321102i	0.758319	+	0.651884i	$0.226021\pi$
$422$	18.9282			0.921411
$423$			2.27362i			0.110547i
$424$	10.9282			0.530720
$425$	−13.4164	+	23.2380i	−0.650793	+	1.12721i
$426$	4.24264	−	15.8338i	0.205557	−	0.767148i
$427$		0			0
$428$	8.69615	+	15.0622i	0.420344	+	0.728058i
$429$	0.803848	−	0.215390i	0.0388101	−	0.0103991i
$430$	0.138701	−	0.240237i	0.00668874	−	0.0115852i
$431$	−10.1436			−0.488600			−0.244300	−	0.969700i	$-0.578558\pi$
$431$	−10.1436			−0.488600			−0.244300	+	0.969700i	$0.578558\pi$
$432$	−1.34486	−	5.01910i	−0.0647048	−	0.241481i
$433$	−19.8362			−0.953265			−0.476632	−	0.879103i	$-0.658143\pi$
$433$	−19.8362			−0.953265			−0.476632	+	0.879103i	$0.658143\pi$
$434$		0			0
$435$	−6.92820	+	1.85641i	−0.332182	+	0.0890079i
$436$	−2.46410	−	4.26795i	−0.118009	−	0.204398i
$437$	−11.9700	−	20.7327i	−0.572605	−	0.991781i
$438$	2.42820	−	9.06218i	0.116024	−	0.433008i
$439$	−9.79796	+	16.9706i	−0.467631	+	0.809961i	−0.999316	−	0.0369815i	$-0.988226\pi$
$439$	−9.79796	+	16.9706i	−0.467631	+	0.809961i	0.531685	+	0.846942i	$0.321559\pi$
$440$	0.277401			0.0132246
$441$		0			0
$442$	−12.2487			−0.582612
$443$	−8.16025	+	14.1340i	−0.387705	+	0.671525i	−0.992140	−	0.125129i	$-0.960066\pi$
$443$	−8.16025	+	14.1340i	−0.387705	+	0.671525i	0.604435	+	0.796654i	$0.293399\pi$
$444$	9.14162	+	9.14162i	0.433842	+	0.433842i
$445$	3.66025	+	6.33975i	0.173513	+	0.300533i
$446$	3.58630	+	6.21166i	0.169816	+	0.294130i
$447$	28.0812	+	28.0812i	1.32820	+	1.32820i
$448$		0			0
$449$	23.7846			1.12247			0.561233	−	0.827658i	$-0.310327\pi$
$449$	23.7846			1.12247			0.561233	+	0.827658i	$0.310327\pi$
$450$	10.2058	+	5.89230i	0.481105	+	0.277766i
$451$	2.31079			0.108811
$452$	3.46410	−	6.00000i	0.162938	−	0.282216i
$453$	8.24504	−	30.7709i	0.387386	−	1.44574i
$454$	13.8325	+	23.9587i	0.649194	+	1.12444i
$455$		0			0
$456$	−7.33013	+	1.96410i	−0.343265	+	0.0919775i
$457$	15.5263	−	26.8923i	0.726289	−	1.25797i	−0.232153	−	0.972679i	$-0.574577\pi$
$457$	15.5263	−	26.8923i	0.726289	−	1.25797i	0.958441	−	0.285290i	$-0.0920898\pi$
$458$	0.480473			0.0224510
$459$	25.0981	−	25.0981i	1.17148	−	1.17148i
$460$	−5.65685			−0.263752
$461$	5.51815	−	9.55772i	0.257006	−	0.445148i	−0.708432	−	0.705779i	$-0.750597\pi$
$461$	5.51815	−	9.55772i	0.257006	−	0.445148i	0.965438	+	0.260631i	$0.0839306\pi$
$462$		0			0
$463$	15.3205	+	26.5359i	0.712004	+	1.23323i	0.964104	+	0.265526i	$0.0855457\pi$
$463$	15.3205	+	26.5359i	0.712004	+	1.23323i	−0.252099	+	0.967701i	$0.581121\pi$
$464$	2.00000	+	3.46410i	0.0928477	+	0.160817i
$465$	−3.10583	+	11.5911i	−0.144029	+	0.537525i
$466$	−0.0621778	+	0.107695i	−0.00288033	+	0.00498888i
$467$	9.17878			0.424744			0.212372	−	0.977189i	$-0.431881\pi$
$467$	9.17878			0.424744			0.212372	+	0.977189i	$0.431881\pi$
$468$			5.37945i			0.248665i
$469$		0			0
$470$	0.392305	−	0.679492i	0.0180957	−	0.0313426i
$471$	11.6603	+	11.6603i	0.537276	+	0.537276i
$472$	0.637756	+	1.10463i	0.0293551	+	0.0508446i
$473$	0.0358984	+	0.0621778i	0.00165061	+	0.00285894i
$474$	10.9348	+	10.9348i	0.502251	+	0.502251i
$475$	8.60540	−	14.9050i	0.394843	−	0.683888i
$476$		0			0
$477$	28.3923	−	16.3923i	1.29999	−	0.750552i
$478$	0.928203			0.0424550
$479$	2.07055	−	3.58630i	0.0946060	−	0.163862i	−0.814838	−	0.579689i	$-0.803174\pi$
$479$	2.07055	−	3.58630i	0.0946060	−	0.163862i	0.909444	+	0.415826i	$0.136508\pi$
$480$	−0.464102	+	1.73205i	−0.0211832	+	0.0790569i
$481$	−6.69213	−	11.5911i	−0.305135	−	0.528509i
$482$	−3.13801	−	5.43520i	−0.142933	−	0.247567i
$483$		0			0
$484$	5.46410	−	9.46410i	0.248368	−	0.430186i
$485$	18.7846			0.852965
$486$	−11.0227	−	11.0227i	−0.500000	−	0.500000i
$487$	−2.78461			−0.126183			−0.0630914	−	0.998008i	$-0.520096\pi$
$487$	−2.78461			−0.126183			−0.0630914	+	0.998008i	$0.520096\pi$
$488$	6.31319	−	10.9348i	0.285785	−	0.494994i
$489$	22.2856	−	5.97142i	1.00779	−	0.270037i
$490$		0			0
$491$	−9.69615	−	16.7942i	−0.437581	−	0.757913i	0.559921	−	0.828546i	$-0.310831\pi$
$491$	−9.69615	−	16.7942i	−0.437581	−	0.757913i	−0.997502	+	0.0706330i	$0.977498\pi$
$492$	−3.86603	+	14.4282i	−0.174294	+	0.650474i
$493$	−13.6617	+	23.6627i	−0.615290	+	1.06571i
$494$	7.85641			0.353476
$495$	0.720710	−	0.416102i	0.0323935	−	0.0187024i
$496$	6.69213			0.300486
$497$		0			0
$498$	8.07180	+	8.07180i	0.361706	+	0.361706i
$499$	−16.6962	−	28.9186i	−0.747422	−	1.29457i	−0.949054	−	0.315112i	$-0.897958\pi$
$499$	−16.6962	−	28.9186i	−0.747422	−	1.29457i	0.201632	−	0.979461i	$-0.435376\pi$
$500$	−4.62158	−	8.00481i	−0.206683	−	0.357986i
$501$	1.85641	+	1.85641i	0.0829381	+	0.0829381i
$502$	−0.397520	+	0.688524i	−0.0177422	+	0.0307303i
$503$	−12.3490			−0.550614			−0.275307	−	0.961356i	$-0.588780\pi$
$503$	−12.3490			−0.550614			−0.275307	+	0.961356i	$0.588780\pi$
$504$		0			0
$505$	5.07180			0.225692
$506$	0.732051	−	1.26795i	0.0325436	−	0.0563672i
$507$	−4.38632	+	16.3700i	−0.194803	+	0.727016i
$508$	−6.73205	−	11.6603i	−0.298686	−	0.517340i
$509$	−10.7961	−	18.6993i	−0.478527	−	0.828834i	0.521169	−	0.853453i	$-0.325496\pi$
$509$	−10.7961	−	18.6993i	−0.478527	−	0.828834i	−0.999697	+	0.0246194i	$0.992163\pi$
$510$	−11.8313	+	3.17020i	−0.523901	+	0.140379i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−16.0981	+	16.0981i	−0.710747	+	0.710747i
$514$	10.0382			0.442766
$515$	6.39230	−	11.0718i	0.281679	−	0.487882i
$516$	−0.448288	+	0.120118i	−0.0197348	+	0.00528791i
$517$	0.101536	+	0.175865i	0.00446555	+	0.00773455i
$518$		0			0
$519$	3.00000	−	11.1962i	0.131685	−	0.491457i
$520$	0.928203	−	1.60770i	0.0407044	−	0.0705021i
$521$	−33.7752			−1.47972			−0.739860	−	0.672761i	$-0.765108\pi$
$521$	−33.7752			−1.47972			−0.739860	+	0.672761i	$0.765108\pi$
$522$	10.3923	+	6.00000i	0.454859	+	0.262613i
$523$	20.7327			0.906579			0.453289	−	0.891363i	$-0.350250\pi$
$523$	20.7327			0.906579			0.453289	+	0.891363i	$0.350250\pi$
$524$	−5.46739	+	9.46979i	−0.238844	+	0.413690i
$525$		0			0
$526$	4.26795	+	7.39230i	0.186091	+	0.322320i
$527$	22.8564	+	39.5885i	0.995641	+	1.72450i
$528$	−0.328169	−	0.328169i	−0.0142817	−	0.0142817i
$529$	−3.42820	+	5.93782i	−0.149052	+	0.258166i
$530$	−11.3137			−0.491436
$531$	3.31388	+	1.91327i	0.143810	+	0.0830288i
$532$		0			0
$533$	7.73205	−	13.3923i	0.334912	−	0.580085i
$534$	3.16987	−	11.8301i	0.137174	−	0.511940i
$535$	−9.00292	−	15.5935i	−0.389230	−	0.674166i
$536$	−6.23205	−	10.7942i	−0.269184	−	0.466240i
$537$	−8.48528	+	2.27362i	−0.366167	+	0.0981141i
$538$	2.82843	−	4.89898i	0.121942	−	0.211210i
$539$		0			0
$540$	1.39230	+	5.19615i	0.0599153	+	0.223607i
$541$	15.3205			0.658680			0.329340	−	0.944211i	$-0.393174\pi$
$541$	15.3205			0.658680			0.329340	+	0.944211i	$0.393174\pi$
$542$	−6.55343	+	11.3509i	−0.281494	+	0.487562i
$543$	28.3923	−	7.60770i	1.21843	−	0.326477i
$544$	3.41542	+	5.91567i	0.146435	+	0.253632i
$545$	2.55103	+	4.41851i	0.109274	+	0.189268i
$546$		0			0
$547$	−17.1865	+	29.7679i	−0.734843	+	1.27279i	0.219949	+	0.975511i	$0.429411\pi$
$547$	−17.1865	+	29.7679i	−0.734843	+	1.27279i	−0.954792	+	0.297274i	$0.903922\pi$
$548$	8.66025			0.369948
$549$		−	37.8792i		−	1.61664i
$550$	1.05256			0.0448813
$551$	8.76268	−	15.1774i	0.373303	−	0.646579i
$552$	6.69213	+	6.69213i	0.284836	+	0.284836i
$553$		0			0
$554$	−15.7321	−	27.2487i	−0.668391	−	1.15769i
$555$	−9.46410	−	9.46410i	−0.401729	−	0.401729i
$556$	−0.397520	+	0.688524i	−0.0168586	+	0.0291999i
$557$	−6.92820			−0.293557			−0.146779	−	0.989169i	$-0.546891\pi$
$557$	−6.92820			−0.293557			−0.146779	+	0.989169i	$0.546891\pi$
$558$	17.3867	−	10.0382i	0.736036	−	0.424951i
$559$	0.480473			0.0203219
$560$		0			0
$561$	0.820508	−	3.06218i	0.0346419	−	0.129285i
$562$	−8.92820	−	15.4641i	−0.376614	−	0.652314i
$563$	9.12304	+	15.8016i	0.384490	+	0.665957i	0.991698	−	0.128586i	$-0.0410439\pi$
$563$	9.12304	+	15.8016i	0.384490	+	0.665957i	−0.607208	+	0.794543i	$0.707711\pi$
$564$	−1.26795	+	0.339746i	−0.0533903	+	0.0143059i
$565$	−3.58630	+	6.21166i	−0.150877	+	0.261326i
$566$	−15.0759			−0.633686
$567$		0			0
$568$	9.46410			0.397105
$569$	12.8923	−	22.3301i	0.540474	−	0.936128i	−0.458403	−	0.888744i	$-0.651578\pi$
$569$	12.8923	−	22.3301i	0.540474	−	0.936128i	0.998877	−	0.0473833i	$-0.0150882\pi$
$570$	7.58871	−	2.03339i	0.317856	−	0.0851692i
$571$	16.5263	+	28.6244i	0.691603	+	1.19789i	0.971312	+	0.237807i	$0.0764286\pi$
$571$	16.5263	+	28.6244i	0.691603	+	1.19789i	−0.279709	+	0.960085i	$0.590238\pi$
$572$	0.240237	+	0.416102i	0.0100448	+	0.0173981i
$573$	6.69213	−	24.9754i	0.279568	−	1.04336i
$574$		0			0
$575$	−21.4641			−0.895115
$576$	2.59808	−	1.50000i	0.108253	−	0.0625000i
$577$	−27.4892			−1.14439			−0.572196	−	0.820117i	$-0.693908\pi$
$577$	−27.4892			−1.14439			−0.572196	+	0.820117i	$0.693908\pi$
$578$	−14.8301	+	25.6865i	−0.616852	+	1.06842i
$579$	18.4355	+	18.4355i	0.766155	+	0.766155i
$580$	−2.07055	−	3.58630i	−0.0859750	−	0.148913i
$581$		0			0
$582$	−22.2224	−	22.2224i	−0.921149	−	0.921149i
$583$	1.46410	−	2.53590i	0.0606369	−	0.105026i
$584$	5.41662			0.224141
$585$		−	5.56922i		−	0.230259i
$586$	−9.24316			−0.381831
$587$	20.9408	−	36.2705i	0.864319	−	1.49704i	−0.00340370	−	0.999994i	$-0.501083\pi$
$587$	20.9408	−	36.2705i	0.864319	−	1.49704i	0.867722	−	0.497049i	$-0.165583\pi$
$588$		0			0
$589$	−14.6603	−	25.3923i	−0.604065	−	1.04627i
$590$	−0.660254	−	1.14359i	−0.0271822	−	0.0470810i
$591$	28.3214	−	7.58871i	1.16499	−	0.312158i
$592$	−3.73205	+	6.46410i	−0.153386	+	0.265673i
$593$	16.8690			0.692728			0.346364	−	0.938100i	$-0.387416\pi$
$593$	16.8690			0.692728			0.346364	+	0.938100i	$0.387416\pi$
$594$	−1.34486	−	0.360355i	−0.0551804	−	0.0147855i
$595$		0			0
$596$	−11.4641	+	19.8564i	−0.469588	+	0.813350i
$597$	−43.9808	+	11.7846i	−1.80001	+	0.482312i
$598$	−4.89898	−	8.48528i	−0.200334	−	0.346989i
$599$	−2.39230	−	4.14359i	−0.0977469	−	0.169303i	0.813005	−	0.582257i	$-0.197830\pi$
$599$	−2.39230	−	4.14359i	−0.0977469	−	0.169303i	−0.910752	+	0.412954i	$0.864497\pi$
$600$	−1.76097	+	6.57201i	−0.0718911	+	0.268301i
$601$	1.67303	−	2.89778i	0.0682444	−	0.118203i	−0.829884	−	0.557936i	$-0.811594\pi$
$601$	1.67303	−	2.89778i	0.0682444	−	0.118203i	0.898129	+	0.439733i	$0.144927\pi$
$602$		0			0
$603$	−32.3827	−	18.6962i	−1.31872	−	0.761366i
$604$	18.3923			0.748372
$605$	−5.65685	+	9.79796i	−0.229984	+	0.398344i
$606$	−6.00000	−	6.00000i	−0.243733	−	0.243733i
$607$	1.13681	+	1.96902i	0.0461418	+	0.0799199i	0.888174	−	0.459507i	$-0.151974\pi$
$607$	1.13681	+	1.96902i	0.0461418	+	0.0799199i	−0.842032	+	0.539427i	$0.818641\pi$
$608$	−2.19067	−	3.79435i	−0.0888434	−	0.153881i
$609$		0			0
$610$	−6.53590	+	11.3205i	−0.264631	+	0.458354i
$611$	1.35898			0.0549786
$612$	17.7470	+	10.2462i	0.717381	+	0.414180i
$613$	24.9282			1.00684			0.503420	−	0.864042i	$-0.332075\pi$
$613$	24.9282			1.00684			0.503420	+	0.864042i	$0.332075\pi$
$614$	−0.586988	+	1.01669i	−0.0236889	+	0.0410304i
$615$	4.00240	−	14.9372i	0.161393	−	0.602325i
$616$		0			0
$617$	1.57180	+	2.72243i	0.0632782	+	0.109601i	0.895929	−	0.444197i	$-0.146511\pi$
$617$	1.57180	+	2.72243i	0.0632782	+	0.109601i	−0.832651	+	0.553798i	$0.813178\pi$
$618$	−20.6603	+	5.53590i	−0.831077	+	0.222686i
$619$	15.8523	−	27.4570i	0.637159	−	1.10359i	−0.348894	−	0.937162i	$-0.613443\pi$
$619$	15.8523	−	27.4570i	0.637159	−	1.10359i	0.986053	−	0.166430i	$-0.0532239\pi$
$620$	−6.92820			−0.278243
$621$	27.4249	+	7.34847i	1.10052	+	0.294884i
$622$	−7.45001			−0.298718
$623$		0			0
$624$	−3.00000	+	0.803848i	−0.120096	+	0.0321797i
$625$	−5.03590	−	8.72243i	−0.201436	−	0.348897i
$626$	−3.13801	−	5.43520i	−0.125420	−	0.217234i
$627$	−0.526279	+	1.96410i	−0.0210176	+	0.0784387i
$628$	−4.76028	+	8.24504i	−0.189956	+	0.329013i
$629$	−50.9860			−2.03295
$630$		0			0
$631$	−19.7128			−0.784755			−0.392377	−	0.919804i	$-0.628347\pi$
$631$	−19.7128			−0.784755			−0.392377	+	0.919804i	$0.628347\pi$
$632$	−4.46410	+	7.73205i	−0.177572	+	0.307564i
$633$	23.1822	+	23.1822i	0.921411	+	0.921411i
$634$	13.0000	+	22.5167i	0.516296	+	0.894251i
$635$	6.96953	+	12.0716i	0.276577	+	0.479046i
$636$	13.3843	+	13.3843i	0.530720	+	0.530720i
$637$		0			0
$638$	1.07180			0.0424328
$639$	24.5885	−	14.1962i	0.972704	−	0.561591i
$640$	−1.03528			−0.0409229
$641$	−2.03590	+	3.52628i	−0.0804132	+	0.139280i	−0.903427	−	0.428741i	$-0.858957\pi$
$641$	−2.03590	+	3.52628i	−0.0804132	+	0.139280i	0.823014	+	0.568021i	$0.192291\pi$
$642$	−7.79676	+	29.0979i	−0.307713	+	1.14840i
$643$	22.4565	+	38.8959i	0.885599	+	1.53390i	0.845025	+	0.534726i	$0.179585\pi$
$643$	22.4565	+	38.8959i	0.885599	+	1.53390i	0.0405737	+	0.999177i	$0.487081\pi$
$644$		0			0
$645$	0.464102	−	0.124356i	0.0182740	−	0.00489650i
$646$	14.9641	−	25.9186i	0.588755	−	1.01975i
$647$	21.8695			0.859780			0.429890	−	0.902881i	$-0.358552\pi$
$647$	21.8695			0.859780			0.429890	+	0.902881i	$0.358552\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	0.341773			0.0134157
$650$	3.52193	−	6.10016i	0.138141	−	0.239268i
$651$		0			0
$652$	6.66025	+	11.5359i	0.260836	+	0.451781i
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	0.801337	−	0.598213i	$-0.204122\pi$
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	−0.918736	+	0.394872i	$0.870789\pi$
$654$	2.20925	−	8.24504i	0.0863886	−	0.322407i
$655$	5.66025	−	9.80385i	0.221164	−	0.383068i
$656$	−8.62398			−0.336710
$657$	14.0728	−	8.12493i	0.549032	−	0.316984i
$658$		0			0
$659$	24.1244	−	41.7846i	0.939751	−	1.62770i	0.173818	−	0.984778i	$-0.444390\pi$
$659$	24.1244	−	41.7846i	0.939751	−	1.62770i	0.765934	−	0.642919i	$-0.222277\pi$
$660$	0.339746	+	0.339746i	0.0132246	+	0.0132246i
$661$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$661$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$662$	5.73205	+	9.92820i	0.222782	+	0.385871i
$663$	−15.0015	−	15.0015i	−0.582612	−	0.582612i
$664$	−3.29530	+	5.70762i	−0.127882	+	0.221499i
$665$		0			0
$666$			22.3923i			0.867684i
$667$	−21.8564			−0.846283
$668$	−0.757875	+	1.31268i	−0.0293231	+	0.0507890i
$669$	−3.21539	+	12.0000i	−0.124314	+	0.463947i
$670$	6.45189	+	11.1750i	0.249258	+	0.431728i
$671$	−1.69161	−	2.92996i	−0.0653041	−	0.113110i
$672$		0			0
$673$	−20.7846	+	36.0000i	−0.801188	+	1.38770i	0.117647	+	0.993055i	$0.462465\pi$
$673$	−20.7846	+	36.0000i	−0.801188	+	1.38770i	−0.918835	+	0.394643i	$0.870868\pi$
$674$	−7.00000			−0.269630
$675$	5.28290	+	19.7160i	0.203339	+	0.758871i
$676$	−9.78461			−0.376331
$677$	2.68973	−	4.65874i	0.103375	−	0.179050i	−0.809698	−	0.586846i	$-0.800369\pi$
$677$	2.68973	−	4.65874i	0.103375	−	0.179050i	0.913073	+	0.407796i	$0.133703\pi$
$678$	11.5911	−	3.10583i	0.445154	−	0.119279i
$679$		0			0
$680$	−3.53590	−	6.12436i	−0.135596	−	0.234858i
$681$	−12.4019	+	46.2846i	−0.475243	+	1.77363i
$682$	0.896575	−	1.55291i	0.0343316	−	0.0594642i
$683$	−38.3205			−1.46629			−0.733147	−	0.680070i	$-0.761949\pi$
$683$	−38.3205			−1.46629			−0.733147	+	0.680070i	$0.761949\pi$
$684$	−11.3831	−	6.57201i	−0.435242	−	0.251287i
$685$	−8.96575			−0.342564
$686$		0			0
$687$	0.588457	+	0.588457i	0.0224510	+	0.0224510i
$688$	−0.133975	−	0.232051i	−0.00510773	−	0.00884685i
$689$	−9.79796	−	16.9706i	−0.373273	−	0.646527i
$690$	−6.92820	−	6.92820i	−0.263752	−	0.263752i
$691$	−12.1595	+	21.0609i	−0.462570	+	0.801194i	−0.999088	−	0.0426942i	$-0.986406\pi$
$691$	−12.1595	+	21.0609i	−0.462570	+	0.801194i	0.536518	+	0.843889i	$0.319739\pi$
$692$	6.69213			0.254397
$693$		0			0
$694$	−9.58846			−0.363973
$695$	0.411543	−	0.712813i	0.0156107	−	0.0270385i
$696$	−1.79315	+	6.69213i	−0.0679692	+	0.253665i
$697$	−29.4545	−	51.0167i	−1.11567	−	1.93239i
$698$	4.00240	+	6.93237i	0.151493	+	0.262394i
$699$	−0.208051	+	0.0557471i	−0.00786921	+	0.00210855i
$700$		0			0
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$	−6.58846	+	6.58846i	−0.248665	+	0.248665i
$703$	32.7028			1.23341
$704$	0.133975	−	0.232051i	0.00504936	−	0.00874574i
$705$	1.31268	−	0.351731i	0.0494383	−	0.0132470i
$706$	−12.5063	−	21.6615i	−0.470680	−	0.815241i
$707$		0			0
$708$	−0.571797	+	2.13397i	−0.0214894	+	0.0801997i
$709$	6.19615	−	10.7321i	0.232701	−	0.403051i	−0.725901	−	0.687799i	$-0.758577\pi$
$709$	6.19615	−	10.7321i	0.232701	−	0.403051i	0.958602	+	0.284749i	$0.0919102\pi$
$710$	−9.79796			−0.367711
$711$			26.7846i			1.00450i
$712$	7.07107			0.264999
$713$	−18.2832	+	31.6675i	−0.684713	+	1.18596i
$714$		0			0
$715$	−0.248711	−	0.430781i	−0.00930128	−	0.0161103i
$716$	−2.53590	−	4.39230i	−0.0947710	−	0.164148i
$717$	1.13681	+	1.13681i	0.0424550	+	0.0424550i
$718$	−3.73205	+	6.46410i	−0.139279	+	0.241238i
$719$	−49.6733			−1.85250			−0.926251	−	0.376906i	$-0.876988\pi$
$719$	−49.6733			−1.85250			−0.926251	+	0.376906i	$0.876988\pi$
$720$	−2.68973	+	1.55291i	−0.100240	+	0.0578737i
$721$		0			0
$722$	−0.0980762	+	0.169873i	−0.00365002	+	0.00632202i
$723$	2.81347	−	10.5000i	0.104634	−	0.390499i
$724$	8.48528	+	14.6969i	0.315353	+	0.546207i
$725$	−7.85641	−	13.6077i	−0.291780	−	0.505377i
$726$	18.2832	−	4.89898i	0.678555	−	0.181818i
$727$	−16.3514	+	28.3214i	−0.606439	+	1.05038i	0.385383	+	0.922757i	$0.374069\pi$
$727$	−16.3514	+	28.3214i	−0.606439	+	1.05038i	−0.991822	+	0.127627i	$0.959264\pi$
$728$		0			0
$729$		−	27.0000i		−	1.00000i
$730$	−5.60770			−0.207550
$731$	0.915158	−	1.58510i	0.0338483	−	0.0586270i
$732$	21.1244	−	5.66025i	0.780779	−	0.209209i
$733$	−4.00240	−	6.93237i	−0.147832	−	0.256053i	0.782594	−	0.622533i	$-0.213896\pi$
$733$	−4.00240	−	6.93237i	−0.147832	−	0.256053i	−0.930426	+	0.366480i	$0.880563\pi$
$734$	−9.28032	−	16.0740i	−0.342543	−	0.593302i
$735$		0			0
$736$	−2.73205	+	4.73205i	−0.100705	+	0.174426i
$737$	−3.33975			−0.123021
$738$	−22.4058	+	12.9360i	−0.824768	+	0.476180i
$739$	6.12436			0.225288			0.112644	−	0.993635i	$-0.464068\pi$
$739$	6.12436			0.225288			0.112644	+	0.993635i	$0.464068\pi$
$740$	3.86370	−	6.69213i	0.142033	−	0.246008i
$741$	9.62209	+	9.62209i	0.353476	+	0.353476i
$742$		0			0
$743$	15.7846	+	27.3397i	0.579081	+	1.00300i	0.995585	+	0.0938641i	$0.0299219\pi$
$743$	15.7846	+	27.3397i	0.579081	+	1.00300i	−0.416504	+	0.909134i	$0.636745\pi$
$744$	8.19615	+	8.19615i	0.300486	+	0.300486i
$745$	11.8685	−	20.5569i	0.434829	−	0.753145i
$746$	−10.7846			−0.394853
$747$			19.7718i			0.723412i
$748$	1.83032			0.0669230
$749$		0			0
$750$	4.14359	−	15.4641i	0.151303	−	0.564669i
$751$	−17.3923	−	30.1244i	−0.634654	−	1.09925i	−0.986588	−	0.163229i	$-0.947809\pi$
$751$	−17.3923	−	30.1244i	−0.634654	−	1.09925i	0.351934	−	0.936025i	$-0.385524\pi$
$752$	−0.378937	−	0.656339i	−0.0138184	−	0.0239342i
$753$	−1.33013	+	0.356406i	−0.0484725	+	0.0129882i
$754$	3.58630	−	6.21166i	0.130605	−	0.226215i
$755$	−19.0411			−0.692977
$756$		0			0
$757$	19.3205			0.702216			0.351108	−	0.936335i	$-0.385805\pi$
$757$	19.3205			0.702216			0.351108	+	0.936335i	$0.385805\pi$
$758$	−6.79423	+	11.7679i	−0.246777	+	0.427431i
$759$	2.44949	−	0.656339i	0.0889108	−	0.0238236i
$760$	2.26795	+	3.92820i	0.0822672	+	0.142491i
$761$	20.1272	+	34.8613i	0.729609	+	1.26372i	0.957049	+	0.289928i	$0.0936312\pi$
$761$	20.1272	+	34.8613i	0.729609	+	1.26372i	−0.227440	+	0.973792i	$0.573035\pi$
$762$	6.03579	−	22.5259i	0.218654	−	0.816027i
$763$		0			0
$764$	14.9282			0.540083
$765$	−18.3731	−	10.6077i	−0.664280	−	0.383522i
$766$	27.3233			0.987232
$767$	1.14359	−	1.98076i	0.0412928	−	0.0715212i
$768$	1.22474	+	1.22474i	0.0441942	+	0.0441942i
$769$	−19.0919	−	33.0681i	−0.688471	−	1.19247i	−0.972332	−	0.233601i	$-0.924949\pi$
$769$	−19.0919	−	33.0681i	−0.688471	−	1.19247i	0.283862	−	0.958865i	$-0.408384\pi$
$770$		0			0
$771$	12.2942	+	12.2942i	0.442766	+	0.442766i
$772$	−7.52628	+	13.0359i	−0.270877	+	0.469172i
$773$	39.3949			1.41694			0.708468	−	0.705743i	$-0.249387\pi$
$773$	39.3949			1.41694			0.708468	+	0.705743i	$0.249387\pi$
$774$	−0.696152	−	0.401924i	−0.0250227	−	0.0144469i
$775$	−26.2880			−0.944295
$776$	9.07227	−	15.7136i	0.325676	−	0.564087i
$777$		0			0
$778$	−4.00000	−	6.92820i	−0.143407	−	0.248388i
$779$	18.8923	+	32.7224i	0.676887	+	1.17240i
$780$	3.10583	−	0.832204i	0.111207	−	0.0297977i

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.517638 + 0.896575i) q^{5} +(0.448288 - 1.67303i) q^{6} +1.00000 q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.517638 + 0.896575i) q^{5} +(0.448288 - 1.67303i) q^{6} +1.00000 q^{8} +(2.59808 - 1.50000i) q^{9} -1.03528 q^{10} +(0.133975 - 0.232051i) q^{11} +(1.22474 + 1.22474i) q^{12} +(-0.896575 - 1.55291i) q^{13} +(-1.26795 - 1.26795i) q^{15} +(-0.500000 + 0.866025i) q^{16} -6.83083 q^{17} +3.00000i q^{18} +4.38134 q^{19} +(0.517638 - 0.896575i) q^{20} +(0.133975 + 0.232051i) q^{22} +(-2.73205 - 4.73205i) q^{23} +(-1.67303 + 0.448288i) q^{24} +(1.96410 - 3.40192i) q^{25} +1.79315 q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.00000 - 3.46410i) q^{29} +(1.73205 - 0.464102i) q^{30} +(-3.34607 - 5.79555i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.120118 + 0.448288i) q^{33} +(3.41542 - 5.91567i) q^{34} +(-2.59808 - 1.50000i) q^{36} +7.46410 q^{37} +(-2.19067 + 3.79435i) q^{38} +(2.19615 + 2.19615i) q^{39} +(0.517638 + 0.896575i) q^{40} +(4.31199 + 7.46859i) q^{41} +(-0.133975 + 0.232051i) q^{43} -0.267949 q^{44} +(2.68973 + 1.55291i) q^{45} +5.46410 q^{46} +(-0.378937 + 0.656339i) q^{47} +(0.448288 - 1.67303i) q^{48} +(1.96410 + 3.40192i) q^{50} +(11.4282 - 3.06218i) q^{51} +(-0.896575 + 1.55291i) q^{52} +10.9282 q^{53} +(-1.34486 - 5.01910i) q^{54} +0.277401 q^{55} +(-7.33013 + 1.96410i) q^{57} +(2.00000 + 3.46410i) q^{58} +(0.637756 + 1.10463i) q^{59} +(-0.464102 + 1.73205i) q^{60} +(6.31319 - 10.9348i) q^{61} +6.69213 q^{62} +1.00000 q^{64} +(0.928203 - 1.60770i) q^{65} +(-0.328169 - 0.328169i) q^{66} +(-6.23205 - 10.7942i) q^{67} +(3.41542 + 5.91567i) q^{68} +(6.69213 + 6.69213i) q^{69} +9.46410 q^{71} +(2.59808 - 1.50000i) q^{72} +5.41662 q^{73} +(-3.73205 + 6.46410i) q^{74} +(-1.76097 + 6.57201i) q^{75} +(-2.19067 - 3.79435i) q^{76} +(-3.00000 + 0.803848i) q^{78} +(-4.46410 + 7.73205i) q^{79} -1.03528 q^{80} +(4.50000 - 7.79423i) q^{81} -8.62398 q^{82} +(-3.29530 + 5.70762i) q^{83} +(-3.53590 - 6.12436i) q^{85} +(-0.133975 - 0.232051i) q^{86} +(-1.79315 + 6.69213i) q^{87} +(0.133975 - 0.232051i) q^{88} +7.07107 q^{89} +(-2.68973 + 1.55291i) q^{90} +(-2.73205 + 4.73205i) q^{92} +(8.19615 + 8.19615i) q^{93} +(-0.378937 - 0.656339i) q^{94} +(2.26795 + 3.92820i) q^{95} +(1.22474 + 1.22474i) q^{96} +(9.07227 - 15.7136i) q^{97} -0.803848i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 8 q^{11} - 24 q^{15} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 12 q^{25} + 16 q^{29} - 4 q^{32} + 32 q^{37} - 24 q^{39} - 8 q^{43} - 16 q^{44} + 16 q^{46} - 12 q^{50} + 36 q^{51} + 32 q^{53} - 24 q^{57} + 16 q^{58} + 24 q^{60} + 8 q^{64} - 48 q^{65} - 36 q^{67} + 48 q^{71} - 16 q^{74} - 24 q^{78} - 8 q^{79} + 36 q^{81} - 56 q^{85} - 8 q^{86} + 8 q^{88} - 8 q^{92} + 24 q^{93} + 32 q^{95}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 8 * q^11 - 24 * q^15 - 4 * q^16 + 8 * q^22 - 8 * q^23 - 12 * q^25 + 16 * q^29 - 4 * q^32 + 32 * q^37 - 24 * q^39 - 8 * q^43 - 16 * q^44 + 16 * q^46 - 12 * q^50 + 36 * q^51 + 32 * q^53 - 24 * q^57 + 16 * q^58 + 24 * q^60 + 8 * q^64 - 48 * q^65 - 36 * q^67 + 48 * q^71 - 16 * q^74 - 24 * q^78 - 8 * q^79 + 36 * q^81 - 56 * q^85 - 8 * q^86 + 8 * q^88 - 8 * q^92 + 24 * q^93 + 32 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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