LMFDB - Embedded newform 441.2.e.g.361.1

Newspace parameters

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.e (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
Defining polynomial:	$x^{4} + 2 x^{2} + 4$
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	441.361
Dual form			441.2.e.g.226.1

$q$-expansion

$f(q)$	$=$	$q+(-1.20711 - 2.09077i) q^{2} +(-1.91421 + 3.31552i) q^{4} +(0.292893 + 0.507306i) q^{5} +4.41421 q^{8} +O(q^{10})$	\(q+(-1.20711 - 2.09077i) q^{2} +(-1.91421 + 3.31552i) q^{4} +(0.292893 + 0.507306i) q^{5} +4.41421 q^{8} +(0.707107 - 1.22474i) q^{10} +(-1.00000 + 1.73205i) q^{11} +5.41421 q^{13} +(-1.50000 - 2.59808i) q^{16} +(3.12132 - 5.40629i) q^{17} +(-1.41421 - 2.44949i) q^{19} -2.24264 q^{20} +4.82843 q^{22} +(1.82843 + 3.16693i) q^{23} +(2.32843 - 4.03295i) q^{25} +(-6.53553 - 11.3199i) q^{26} +1.17157 q^{29} +(3.41421 - 5.91359i) q^{31} +(0.792893 - 1.37333i) q^{32} -15.0711 q^{34} +(2.00000 + 3.46410i) q^{37} +(-3.41421 + 5.91359i) q^{38} +(1.29289 + 2.23936i) q^{40} +2.24264 q^{41} -5.65685 q^{43} +(-3.82843 - 6.63103i) q^{44} +(4.41421 - 7.64564i) q^{46} +(1.41421 + 2.44949i) q^{47} -11.2426 q^{50} +(-10.3640 + 17.9509i) q^{52} +(-1.00000 + 1.73205i) q^{53} -1.17157 q^{55} +(-1.41421 - 2.44949i) q^{58} +(-3.41421 + 5.91359i) q^{59} +(-1.87868 - 3.25397i) q^{61} -16.4853 q^{62} -9.82843 q^{64} +(1.58579 + 2.74666i) q^{65} +(-2.82843 + 4.89898i) q^{67} +(11.9497 + 20.6976i) q^{68} +13.3137 q^{71} +(2.94975 - 5.10911i) q^{73} +(4.82843 - 8.36308i) q^{74} +10.8284 q^{76} +(-1.17157 - 2.02922i) q^{79} +(0.878680 - 1.52192i) q^{80} +(-2.70711 - 4.68885i) q^{82} +15.3137 q^{83} +3.65685 q^{85} +(6.82843 + 11.8272i) q^{86} +(-4.41421 + 7.64564i) q^{88} +(-2.87868 - 4.98602i) q^{89} -14.0000 q^{92} +(3.41421 - 5.91359i) q^{94} +(0.828427 - 1.43488i) q^{95} +5.41421 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4q - 2q^{2} - 2q^{4} + 4q^{5} + 12q^{8} + O(q^{10}) $	$ 4q - 2q^{2} - 2q^{4} + 4q^{5} + 12q^{8} - 4q^{11} + 16q^{13} - 6q^{16} + 4q^{17} + 8q^{20} + 8q^{22} - 4q^{23} - 2q^{25} - 12q^{26} + 16q^{29} + 8q^{31} + 6q^{32} - 32q^{34} + 8q^{37} - 8q^{38} + 8q^{40} - 8q^{41} - 4q^{44} + 12q^{46} - 28q^{50} - 16q^{52} - 4q^{53} - 16q^{55} - 8q^{59} - 16q^{61} - 32q^{62} - 28q^{64} + 12q^{65} + 28q^{68} + 8q^{71} - 8q^{73} + 8q^{74} + 32q^{76} - 16q^{79} + 12q^{80} - 8q^{82} + 16q^{83} - 8q^{85} + 16q^{86} - 12q^{88} - 20q^{89} - 56q^{92} + 8q^{94} - 8q^{95} + 16q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.20711	−	2.09077i	−0.853553	−	1.47840i	−0.877981	−	0.478696i	$-0.841110\pi$
$2$	−1.20711	−	2.09077i	−0.853553	−	1.47840i	0.0244272	−	0.999702i	$-0.492224\pi$
$3$		0			0
$3$		0			0
$4$	−1.91421	+	3.31552i	−0.957107	+	1.65776i
$5$	0.292893	+	0.507306i	0.130986	+	0.226874i	0.924057	−	0.382255i	$-0.124852\pi$
$5$	0.292893	+	0.507306i	0.130986	+	0.226874i	−0.793071	+	0.609129i	$0.791519\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	4.41421			1.56066
$9$		0			0
$10$	0.707107	−	1.22474i	0.223607	−	0.387298i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	5.41421			1.50163			0.750816	−	0.660511i	$-0.229660\pi$
$13$	5.41421			1.50163			0.750816	+	0.660511i	$0.229660\pi$
$14$		0			0
$15$		0			0
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	3.12132	−	5.40629i	0.757031	−	1.31122i	−0.187327	−	0.982298i	$-0.559982\pi$
$17$	3.12132	−	5.40629i	0.757031	−	1.31122i	0.944358	−	0.328919i	$-0.106684\pi$
$18$		0			0
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	0.656957	−	0.753928i	$-0.271843\pi$
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	−0.981399	+	0.191977i	$0.938510\pi$
$20$	−2.24264			−0.501470
$21$		0			0
$22$	4.82843			1.02942
$23$	1.82843	+	3.16693i	0.381253	+	0.660350i	0.991242	−	0.132060i	$-0.0421592\pi$
$23$	1.82843	+	3.16693i	0.381253	+	0.660350i	−0.609988	+	0.792410i	$0.708826\pi$
$24$		0			0
$25$	2.32843	−	4.03295i	0.465685	−	0.806591i
$26$	−6.53553	−	11.3199i	−1.28172	−	2.22001i
$27$		0			0
$28$		0			0
$29$	1.17157			0.217556			0.108778	−	0.994066i	$-0.465306\pi$
$29$	1.17157			0.217556			0.108778	+	0.994066i	$0.465306\pi$
$30$		0			0
$31$	3.41421	−	5.91359i	0.613211	−	1.06211i	−0.377485	−	0.926016i	$-0.623211\pi$
$31$	3.41421	−	5.91359i	0.613211	−	1.06211i	0.990696	−	0.136097i	$-0.0434557\pi$
$32$	0.792893	−	1.37333i	0.140165	−	0.242773i
$33$		0			0
$34$	−15.0711			−2.58467
$35$		0			0
$36$		0			0
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	−3.41421	+	5.91359i	−0.553859	+	0.959311i
$39$		0			0
$40$	1.29289	+	2.23936i	0.204424	+	0.354073i
$41$	2.24264			0.350242			0.175121	−	0.984547i	$-0.443968\pi$
$41$	2.24264			0.350242			0.175121	+	0.984547i	$0.443968\pi$
$42$		0			0
$43$	−5.65685			−0.862662			−0.431331	−	0.902194i	$-0.641956\pi$
$43$	−5.65685			−0.862662			−0.431331	+	0.902194i	$0.641956\pi$
$44$	−3.82843	−	6.63103i	−0.577157	−	0.999665i
$45$		0			0
$46$	4.41421	−	7.64564i	0.650840	−	1.12729i
$47$	1.41421	+	2.44949i	0.206284	+	0.357295i	0.950541	−	0.310599i	$-0.100530\pi$
$47$	1.41421	+	2.44949i	0.206284	+	0.357295i	−0.744257	+	0.667893i	$0.767196\pi$
$48$		0			0
$49$		0			0
$50$	−11.2426			−1.58995
$51$		0			0
$52$	−10.3640	+	17.9509i	−1.43722	+	2.48934i
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$		0			0
$55$	−1.17157			−0.157975
$56$		0			0
$57$		0			0
$58$	−1.41421	−	2.44949i	−0.185695	−	0.321634i
$59$	−3.41421	+	5.91359i	−0.444493	+	0.769884i	−0.998017	−	0.0629492i	$-0.979949\pi$
$59$	−3.41421	+	5.91359i	−0.444493	+	0.769884i	0.553524	+	0.832833i	$0.313283\pi$
$60$		0			0
$61$	−1.87868	−	3.25397i	−0.240540	−	0.416628i	0.720328	−	0.693634i	$-0.243991\pi$
$61$	−1.87868	−	3.25397i	−0.240540	−	0.416628i	−0.960868	+	0.277006i	$0.910658\pi$
$62$	−16.4853			−2.09363
$63$		0			0
$64$	−9.82843			−1.22855
$65$	1.58579	+	2.74666i	0.196693	+	0.340682i
$66$		0			0
$67$	−2.82843	+	4.89898i	−0.345547	+	0.598506i	−0.985453	−	0.169948i	$-0.945640\pi$
$67$	−2.82843	+	4.89898i	−0.345547	+	0.598506i	0.639906	+	0.768453i	$0.278973\pi$
$68$	11.9497	+	20.6976i	1.44912	+	2.50995i
$69$		0			0
$70$		0			0
$71$	13.3137			1.58005			0.790023	−	0.613077i	$-0.210068\pi$
$71$	13.3137			1.58005			0.790023	+	0.613077i	$0.210068\pi$
$72$		0			0
$73$	2.94975	−	5.10911i	0.345242	−	0.597976i	−0.640156	−	0.768245i	$-0.721130\pi$
$73$	2.94975	−	5.10911i	0.345242	−	0.597976i	0.985398	+	0.170269i	$0.0544636\pi$
$74$	4.82843	−	8.36308i	0.561293	−	0.972188i
$75$		0			0
$76$	10.8284			1.24211
$77$		0			0
$78$		0			0
$79$	−1.17157	−	2.02922i	−0.131812	−	0.228306i	0.792563	−	0.609790i	$-0.208746\pi$
$79$	−1.17157	−	2.02922i	−0.131812	−	0.228306i	−0.924375	+	0.381485i	$0.875413\pi$
$80$	0.878680	−	1.52192i	0.0982394	−	0.170156i
$81$		0			0
$82$	−2.70711	−	4.68885i	−0.298950	−	0.517796i
$83$	15.3137			1.68090			0.840449	−	0.541891i	$-0.182291\pi$
$83$	15.3137			1.68090			0.840449	+	0.541891i	$0.182291\pi$
$84$		0			0
$85$	3.65685			0.396642
$86$	6.82843	+	11.8272i	0.736328	+	1.27536i
$87$		0			0
$88$	−4.41421	+	7.64564i	−0.470557	+	0.815028i
$89$	−2.87868	−	4.98602i	−0.305139	−	0.528517i	0.672153	−	0.740412i	$-0.265370\pi$
$89$	−2.87868	−	4.98602i	−0.305139	−	0.528517i	−0.977292	+	0.211895i	$0.932036\pi$
$90$		0			0
$91$		0			0
$92$	−14.0000			−1.45960
$93$		0			0
$94$	3.41421	−	5.91359i	0.352149	−	0.609940i
$95$	0.828427	−	1.43488i	0.0849948	−	0.147215i
$96$		0			0
$97$	5.41421			0.549730			0.274865	−	0.961483i	$-0.411367\pi$
$97$	5.41421			0.549730			0.274865	+	0.961483i	$0.411367\pi$
$98$		0			0
$99$		0			0
$100$	8.91421	+	15.4399i	0.891421	+	1.54399i
$101$	8.53553	−	14.7840i	0.849317	−	1.47106i	−0.0325010	−	0.999472i	$-0.510347\pi$
$101$	8.53553	−	14.7840i	0.849317	−	1.47106i	0.881818	−	0.471589i	$-0.156319\pi$
$102$		0			0
$103$	6.24264	+	10.8126i	0.615106	+	1.06539i	0.990366	+	0.138475i	$0.0442200\pi$
$103$	6.24264	+	10.8126i	0.615106	+	1.06539i	−0.375260	+	0.926919i	$0.622447\pi$
$104$	23.8995			2.34354
$105$		0			0
$106$	4.82843			0.468978
$107$	−5.82843	−	10.0951i	−0.563455	−	0.975933i	−0.997192	−	0.0748933i	$-0.976138\pi$
$107$	−5.82843	−	10.0951i	−0.563455	−	0.975933i	0.433736	−	0.901040i	$-0.357195\pi$
$108$		0			0
$109$	−2.82843	+	4.89898i	−0.270914	+	0.469237i	−0.969096	−	0.246683i	$-0.920659\pi$
$109$	−2.82843	+	4.89898i	−0.270914	+	0.469237i	0.698182	+	0.715920i	$0.253993\pi$
$110$	1.41421	+	2.44949i	0.134840	+	0.233550i
$111$		0			0
$112$		0			0
$113$	−17.3137			−1.62874			−0.814368	−	0.580348i	$-0.802916\pi$
$113$	−17.3137			−1.62874			−0.814368	+	0.580348i	$0.802916\pi$
$114$		0			0
$115$	−1.07107	+	1.85514i	−0.0998776	+	0.172993i
$116$	−2.24264	+	3.88437i	−0.208224	+	0.360654i
$117$		0			0
$118$	16.4853			1.51759
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−4.53553	+	7.85578i	−0.410628	+	0.711228i
$123$		0			0
$124$	13.0711	+	22.6398i	1.17382	+	2.03311i
$125$	5.65685			0.505964
$126$		0			0
$127$	9.65685			0.856907			0.428454	−	0.903564i	$-0.359059\pi$
$127$	9.65685			0.856907			0.428454	+	0.903564i	$0.359059\pi$
$128$	10.2782	+	17.8023i	0.908471	+	1.57352i
$129$		0			0
$130$	3.82843	−	6.63103i	0.335775	−	0.581580i
$131$	3.65685	+	6.33386i	0.319501	+	0.553392i	0.980384	−	0.197097i	$-0.0631514\pi$
$131$	3.65685	+	6.33386i	0.319501	+	0.553392i	−0.660883	+	0.750489i	$0.729818\pi$
$132$		0			0
$133$		0			0
$134$	13.6569			1.17977
$135$		0			0
$136$	13.7782	−	23.8645i	1.18147	−	2.04636i
$137$	−7.07107	+	12.2474i	−0.604122	+	1.04637i	0.388067	+	0.921631i	$0.373143\pi$
$137$	−7.07107	+	12.2474i	−0.604122	+	1.04637i	−0.992190	+	0.124739i	$0.960191\pi$
$138$		0			0
$139$	−6.34315			−0.538019			−0.269009	−	0.963138i	$-0.586696\pi$
$139$	−6.34315			−0.538019			−0.269009	+	0.963138i	$0.586696\pi$
$140$		0			0
$141$		0			0
$142$	−16.0711	−	27.8359i	−1.34865	−	2.33594i
$143$	−5.41421	+	9.37769i	−0.452759	+	0.784202i
$144$		0			0
$145$	0.343146	+	0.594346i	0.0284967	+	0.0493577i
$146$	−14.2426			−1.17873
$147$		0			0
$148$	−15.3137			−1.25878
$149$	−2.65685	−	4.60181i	−0.217658	−	0.376995i	0.736434	−	0.676510i	$-0.236508\pi$
$149$	−2.65685	−	4.60181i	−0.217658	−	0.376995i	−0.954092	+	0.299515i	$0.903175\pi$
$150$		0			0
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	−0.999909	−	0.0134886i	$-0.995706\pi$
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	0.511636	+	0.859202i	$0.329040\pi$
$152$	−6.24264	−	10.8126i	−0.506345	−	0.877015i
$153$		0			0
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	−10.1213	+	17.5306i	−0.807769	+	1.39910i	0.106636	+	0.994298i	$0.465992\pi$
$157$	−10.1213	+	17.5306i	−0.807769	+	1.39910i	−0.914406	+	0.404799i	$0.867341\pi$
$158$	−2.82843	+	4.89898i	−0.225018	+	0.389742i
$159$		0			0
$160$	0.928932			0.0734385
$161$		0			0
$162$		0			0
$163$	−5.65685	−	9.79796i	−0.443079	−	0.767435i	0.554837	−	0.831959i	$-0.312781\pi$
$163$	−5.65685	−	9.79796i	−0.443079	−	0.767435i	−0.997916	+	0.0645236i	$0.979447\pi$
$164$	−4.29289	+	7.43551i	−0.335219	+	0.580616i
$165$		0			0
$166$	−18.4853	−	32.0174i	−1.43474	−	2.48504i
$167$	−19.7990			−1.53209			−0.766046	−	0.642786i	$-0.777779\pi$
$167$	−19.7990			−1.53209			−0.766046	+	0.642786i	$0.777779\pi$
$168$		0			0
$169$	16.3137			1.25490
$170$	−4.41421	−	7.64564i	−0.338555	−	0.586394i
$171$		0			0
$172$	10.8284	−	18.7554i	0.825660	−	1.43008i
$173$	3.46447	+	6.00063i	0.263398	+	0.456220i	0.967143	−	0.254234i	$-0.0818233\pi$
$173$	3.46447	+	6.00063i	0.263398	+	0.456220i	−0.703744	+	0.710453i	$0.748490\pi$
$174$		0			0
$175$		0			0
$176$	6.00000			0.452267
$177$		0			0
$178$	−6.94975	+	12.0373i	−0.520906	+	0.902235i
$179$	−4.17157	+	7.22538i	−0.311798	+	0.540050i	−0.978752	−	0.205049i	$-0.934265\pi$
$179$	−4.17157	+	7.22538i	−0.311798	+	0.540050i	0.666954	+	0.745099i	$0.267598\pi$
$180$		0			0
$181$	−5.41421			−0.402435			−0.201218	−	0.979547i	$-0.564490\pi$
$181$	−5.41421			−0.402435			−0.201218	+	0.979547i	$0.564490\pi$
$182$		0			0
$183$		0			0
$184$	8.07107	+	13.9795i	0.595007	+	1.03058i
$185$	−1.17157	+	2.02922i	−0.0861358	+	0.149191i
$186$		0			0
$187$	6.24264	+	10.8126i	0.456507	+	0.790693i
$188$	−10.8284			−0.789744
$189$		0			0
$190$	−4.00000			−0.290191
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$		0			0
$193$	8.65685	−	14.9941i	0.623134	−	1.07930i	−0.365765	−	0.930707i	$-0.619192\pi$
$193$	8.65685	−	14.9941i	0.623134	−	1.07930i	0.988899	−	0.148592i	$-0.0474742\pi$
$194$	−6.53553	−	11.3199i	−0.469224	−	0.812720i
$195$		0			0
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	−5.17157	+	8.95743i	−0.366603	+	0.634975i	−0.989032	−	0.147701i	$-0.952813\pi$
$199$	−5.17157	+	8.95743i	−0.366603	+	0.634975i	0.622429	+	0.782676i	$0.286146\pi$
$200$	10.2782	−	17.8023i	0.726777	−	1.25881i
$201$		0			0
$202$	−41.2132			−2.89975
$203$		0			0
$204$		0			0
$205$	0.656854	+	1.13770i	0.0458767	+	0.0794608i
$206$	15.0711	−	26.1039i	1.05005	−	1.81874i
$207$		0			0
$208$	−8.12132	−	14.0665i	−0.563112	−	0.975339i
$209$	5.65685			0.391293
$210$		0			0
$211$	−20.9706			−1.44367			−0.721837	−	0.692064i	$-0.756702\pi$
$211$	−20.9706			−1.44367			−0.721837	+	0.692064i	$0.756702\pi$
$212$	−3.82843	−	6.63103i	−0.262937	−	0.455421i
$213$		0			0
$214$	−14.0711	+	24.3718i	−0.961878	+	1.66602i
$215$	−1.65685	−	2.86976i	−0.112997	−	0.195716i
$216$		0			0
$217$		0			0
$218$	13.6569			0.924959
$219$		0			0
$220$	2.24264	−	3.88437i	0.151199	−	0.261884i
$221$	16.8995	−	29.2708i	1.13678	−	1.96897i
$222$		0			0
$223$	−8.97056			−0.600713			−0.300357	−	0.953827i	$-0.597106\pi$
$223$	−8.97056			−0.600713			−0.300357	+	0.953827i	$0.597106\pi$
$224$		0			0
$225$		0			0
$226$	20.8995	+	36.1990i	1.39021	+	2.40792i
$227$	−7.89949	+	13.6823i	−0.524308	+	0.908128i	0.475292	+	0.879828i	$0.342343\pi$
$227$	−7.89949	+	13.6823i	−0.524308	+	0.908128i	−0.999599	+	0.0282996i	$0.990991\pi$
$228$		0			0
$229$	−4.12132	−	7.13834i	−0.272345	−	0.471715i	0.697117	−	0.716957i	$-0.254466\pi$
$229$	−4.12132	−	7.13834i	−0.272345	−	0.471715i	−0.969462	+	0.245243i	$0.921132\pi$
$230$	5.17157			0.341003
$231$		0			0
$232$	5.17157			0.339530
$233$	11.0711	+	19.1757i	0.725290	+	1.25624i	0.958855	+	0.283898i	$0.0916275\pi$
$233$	11.0711	+	19.1757i	0.725290	+	1.25624i	−0.233565	+	0.972341i	$0.575039\pi$
$234$		0			0
$235$	−0.828427	+	1.43488i	−0.0540406	+	0.0936011i
$236$	−13.0711	−	22.6398i	−0.850854	−	1.47372i
$237$		0			0
$238$		0			0
$239$	4.34315			0.280935			0.140467	−	0.990085i	$-0.455139\pi$
$239$	4.34315			0.280935			0.140467	+	0.990085i	$0.455139\pi$
$240$		0			0
$241$	3.87868	−	6.71807i	0.249848	−	0.432749i	−0.713636	−	0.700517i	$-0.752953\pi$
$241$	3.87868	−	6.71807i	0.249848	−	0.432749i	0.963483	+	0.267768i	$0.0862861\pi$
$242$	8.44975	−	14.6354i	0.543170	−	0.940799i
$243$		0			0
$244$	14.3848			0.920891
$245$		0			0
$246$		0			0
$247$	−7.65685	−	13.2621i	−0.487194	−	0.843845i
$248$	15.0711	−	26.1039i	0.957014	−	1.65760i
$249$		0			0
$250$	−6.82843	−	11.8272i	−0.431868	−	0.748017i
$251$	−4.48528			−0.283108			−0.141554	−	0.989931i	$-0.545210\pi$
$251$	−4.48528			−0.283108			−0.141554	+	0.989931i	$0.545210\pi$
$252$		0			0
$253$	−7.31371			−0.459809
$254$	−11.6569	−	20.1903i	−0.731416	−	1.26685i
$255$		0			0
$256$	14.9853	−	25.9553i	0.936580	−	1.62220i
$257$	−9.60660	−	16.6391i	−0.599243	−	1.03792i	−0.992933	−	0.118677i	$-0.962135\pi$
$257$	−9.60660	−	16.6391i	−0.599243	−	1.03792i	0.393690	−	0.919243i	$-0.371198\pi$
$258$		0			0
$259$		0			0
$260$	−12.1421			−0.753023
$261$		0			0
$262$	8.82843	−	15.2913i	0.545422	−	0.944699i
$263$	−8.65685	+	14.9941i	−0.533805	+	0.924577i	0.465416	+	0.885092i	$0.345905\pi$
$263$	−8.65685	+	14.9941i	−0.533805	+	0.924577i	−0.999220	+	0.0394843i	$0.987428\pi$
$264$		0			0
$265$	−1.17157			−0.0719691
$266$		0			0
$267$		0			0
$268$	−10.8284	−	18.7554i	−0.661451	−	1.14567i
$269$	5.36396	−	9.29065i	0.327046	−	0.566461i	−0.654878	−	0.755735i	$-0.727280\pi$
$269$	5.36396	−	9.29065i	0.327046	−	0.566461i	0.981924	+	0.189274i	$0.0606133\pi$
$270$		0			0
$271$	−9.07107	−	15.7116i	−0.551028	−	0.954409i	−0.998201	−	0.0599610i	$-0.980902\pi$
$271$	−9.07107	−	15.7116i	−0.551028	−	0.954409i	0.447173	−	0.894448i	$-0.352431\pi$
$272$	−18.7279			−1.13555
$273$		0			0
$274$	34.1421			2.06260
$275$	4.65685	+	8.06591i	0.280819	+	0.486393i
$276$		0			0
$277$	−6.65685	+	11.5300i	−0.399972	+	0.692771i	−0.993722	−	0.111878i	$-0.964313\pi$
$277$	−6.65685	+	11.5300i	−0.399972	+	0.692771i	0.593750	+	0.804649i	$0.297647\pi$
$278$	7.65685	+	13.2621i	0.459228	+	0.795406i
$279$		0			0
$280$		0			0
$281$	16.4853			0.983429			0.491715	−	0.870756i	$-0.336370\pi$
$281$	16.4853			0.983429			0.491715	+	0.870756i	$0.336370\pi$
$282$		0			0
$283$	−4.24264	+	7.34847i	−0.252199	+	0.436821i	−0.964131	−	0.265427i	$-0.914487\pi$
$283$	−4.24264	+	7.34847i	−0.252199	+	0.436821i	0.711932	+	0.702248i	$0.247820\pi$
$284$	−25.4853	+	44.1418i	−1.51227	+	2.61933i
$285$		0			0
$286$	26.1421			1.54582
$287$		0			0
$288$		0			0
$289$	−10.9853	−	19.0271i	−0.646193	−	1.11924i
$290$	0.828427	−	1.43488i	0.0486469	−	0.0842589i
$291$		0			0
$292$	11.2929	+	19.5599i	0.660867	+	1.14465i
$293$	−19.4142			−1.13419			−0.567095	−	0.823652i	$-0.691933\pi$
$293$	−19.4142			−1.13419			−0.567095	+	0.823652i	$0.691933\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	8.82843	+	15.2913i	0.513142	+	0.888788i
$297$		0			0
$298$	−6.41421	+	11.1097i	−0.371565	+	0.643570i
$299$	9.89949	+	17.1464i	0.572503	+	0.991604i
$300$		0			0
$301$		0			0
$302$	28.9706			1.66707
$303$		0			0
$304$	−4.24264	+	7.34847i	−0.243332	+	0.421464i
$305$	1.10051	−	1.90613i	0.0630147	−	0.109145i
$306$		0			0
$307$	1.85786			0.106034			0.0530170	−	0.998594i	$-0.483116\pi$
$307$	1.85786			0.106034			0.0530170	+	0.998594i	$0.483116\pi$
$308$		0			0
$309$		0			0
$310$	−4.82843	−	8.36308i	−0.274236	−	0.474991i
$311$	−11.0711	+	19.1757i	−0.627783	+	1.08735i	0.360213	+	0.932870i	$0.382704\pi$
$311$	−11.0711	+	19.1757i	−0.627783	+	1.08735i	−0.987996	+	0.154481i	$0.950629\pi$
$312$		0			0
$313$	8.94975	+	15.5014i	0.505870	+	0.876192i	0.999977	+	0.00679098i	$0.00216165\pi$
$313$	8.94975	+	15.5014i	0.505870	+	0.876192i	−0.494107	+	0.869401i	$0.664505\pi$
$314$	48.8701			2.75790
$315$		0			0
$316$	8.97056			0.504634
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	0.971589	−	0.236675i	$-0.0760576\pi$
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	−0.690761	+	0.723083i	$0.742724\pi$
$318$		0			0
$319$	−1.17157	+	2.02922i	−0.0655955	+	0.113615i
$320$	−2.87868	−	4.98602i	−0.160923	−	0.278727i
$321$		0			0
$322$		0			0
$323$	−17.6569			−0.982454
$324$		0			0
$325$	12.6066	−	21.8353i	0.699288	−	1.21120i
$326$	−13.6569	+	23.6544i	−0.756383	+	1.31009i
$327$		0			0
$328$	9.89949			0.546608
$329$		0			0
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	−29.3137	+	50.7728i	−1.60880	+	2.78652i
$333$		0			0
$334$	23.8995	+	41.3951i	1.30772	+	2.26504i
$335$	−3.31371			−0.181047
$336$		0			0
$337$	−18.3431			−0.999215			−0.499607	−	0.866252i	$-0.666522\pi$
$337$	−18.3431			−0.999215			−0.499607	+	0.866252i	$0.666522\pi$
$338$	−19.6924	−	34.1082i	−1.07112	−	1.85524i
$339$		0			0
$340$	−7.00000	+	12.1244i	−0.379628	+	0.657536i
$341$	6.82843	+	11.8272i	0.369780	+	0.640478i
$342$		0			0
$343$		0			0
$344$	−24.9706			−1.34632
$345$		0			0
$346$	8.36396	−	14.4868i	0.449649	−	0.778815i
$347$	5.34315	−	9.25460i	0.286835	−	0.496813i	−0.686217	−	0.727396i	$-0.740730\pi$
$347$	5.34315	−	9.25460i	0.286835	−	0.496813i	0.973053	+	0.230584i	$0.0740635\pi$
$348$		0			0
$349$	9.89949			0.529908			0.264954	−	0.964261i	$-0.414643\pi$
$349$	9.89949			0.529908			0.264954	+	0.964261i	$0.414643\pi$
$350$		0			0
$351$		0			0
$352$	1.58579	+	2.74666i	0.0845227	+	0.146398i
$353$	5.36396	−	9.29065i	0.285495	−	0.494492i	−0.687234	−	0.726436i	$-0.741175\pi$
$353$	5.36396	−	9.29065i	0.285495	−	0.494492i	0.972729	+	0.231944i	$0.0745087\pi$
$354$		0			0
$355$	3.89949	+	6.75412i	0.206964	+	0.358472i
$356$	22.0416			1.16820
$357$		0			0
$358$	20.1421			1.06454
$359$	−5.82843	−	10.0951i	−0.307613	−	0.532801i	0.670227	−	0.742156i	$-0.266197\pi$
$359$	−5.82843	−	10.0951i	−0.307613	−	0.532801i	−0.977840	+	0.209355i	$0.932863\pi$
$360$		0			0
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$	6.53553	+	11.3199i	0.343500	+	0.594960i
$363$		0			0
$364$		0			0
$365$	3.45584			0.180887
$366$		0			0
$367$	−9.65685	+	16.7262i	−0.504084	+	0.873099i	0.495905	+	0.868377i	$0.334836\pi$
$367$	−9.65685	+	16.7262i	−0.504084	+	0.873099i	−0.999989	+	0.00472187i	$0.998497\pi$
$368$	5.48528	−	9.50079i	0.285940	−	0.495263i
$369$		0			0
$370$	5.65685			0.294086
$371$		0			0
$372$		0			0
$373$	16.6569	+	28.8505i	0.862459	+	1.49382i	0.869548	+	0.493848i	$0.164410\pi$
$373$	16.6569	+	28.8505i	0.862459	+	1.49382i	−0.00708885	+	0.999975i	$0.502256\pi$
$374$	15.0711	−	26.1039i	0.779306	−	1.34980i
$375$		0			0
$376$	6.24264	+	10.8126i	0.321940	+	0.557616i
$377$	6.34315			0.326689
$378$		0			0
$379$	31.3137			1.60848			0.804239	−	0.594307i	$-0.202573\pi$
$379$	31.3137			1.60848			0.804239	+	0.594307i	$0.202573\pi$
$380$	3.17157	+	5.49333i	0.162698	+	0.281802i
$381$		0			0
$382$	−21.7279	+	37.6339i	−1.11170	+	1.92552i
$383$	−14.8284	−	25.6836i	−0.757697	−	1.31237i	−0.944022	−	0.329882i	$-0.892991\pi$
$383$	−14.8284	−	25.6836i	−0.757697	−	1.31237i	0.186325	−	0.982488i	$-0.440342\pi$
$384$		0			0
$385$		0			0
$386$	−41.7990			−2.12751
$387$		0			0
$388$	−10.3640	+	17.9509i	−0.526150	+	0.911319i
$389$	5.07107	−	8.78335i	0.257113	−	0.445333i	−0.708354	−	0.705857i	$-0.750562\pi$
$389$	5.07107	−	8.78335i	0.257113	−	0.445333i	0.965467	+	0.260524i	$0.0838953\pi$
$390$		0			0
$391$	22.8284			1.15448
$392$		0			0
$393$		0			0
$394$	2.41421	+	4.18154i	0.121626	+	0.210663i
$395$	0.686292	−	1.18869i	0.0345311	−	0.0598096i
$396$		0			0
$397$	−17.1924	−	29.7781i	−0.862861	−	1.49452i	−0.869155	−	0.494539i	$-0.835337\pi$
$397$	−17.1924	−	29.7781i	−0.862861	−	1.49452i	0.00629405	−	0.999980i	$-0.497997\pi$
$398$	24.9706			1.25166
$399$		0			0
$400$	−13.9706			−0.698528
$401$	11.0711	+	19.1757i	0.552863	+	0.957586i	0.998066	+	0.0621570i	$0.0197980\pi$
$401$	11.0711	+	19.1757i	0.552863	+	0.957586i	−0.445204	+	0.895429i	$0.646869\pi$
$402$		0			0
$403$	18.4853	−	32.0174i	0.920817	−	1.59490i
$404$	32.6777	+	56.5994i	1.62577	+	2.81592i
$405$		0			0
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	9.29289	−	16.0958i	0.459504	−	0.795884i	−0.539431	−	0.842030i	$-0.681361\pi$
$409$	9.29289	−	16.0958i	0.459504	−	0.795884i	0.998935	+	0.0461457i	$0.0146939\pi$
$410$	1.58579	−	2.74666i	0.0783164	−	0.135648i
$411$		0			0
$412$	−47.7990			−2.35489
$413$		0			0
$414$		0			0
$415$	4.48528	+	7.76874i	0.220174	+	0.381352i
$416$	4.29289	−	7.43551i	0.210476	−	0.364556i
$417$		0			0
$418$	−6.82843	−	11.8272i	−0.333989	−	0.578486i
$419$	−38.8284			−1.89689			−0.948446	−	0.316938i	$-0.897345\pi$
$419$	−38.8284			−1.89689			−0.948446	+	0.316938i	$0.897345\pi$
$420$		0			0
$421$	−28.6274			−1.39521			−0.697607	−	0.716480i	$-0.745752\pi$
$421$	−28.6274			−1.39521			−0.697607	+	0.716480i	$0.745752\pi$
$422$	25.3137	+	43.8446i	1.23225	+	2.13432i
$423$		0			0
$424$	−4.41421	+	7.64564i	−0.214373	+	0.371305i
$425$	−14.5355	−	25.1763i	−0.705077	−	1.22123i
$426$		0			0
$427$		0			0
$428$	44.6274			2.15715
$429$		0			0
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$	3.48528	−	6.03668i	0.167880	−	0.290777i	−0.769794	−	0.638292i	$-0.779641\pi$
$431$	3.48528	−	6.03668i	0.167880	−	0.290777i	0.937674	+	0.347515i	$0.112975\pi$
$432$		0			0
$433$	−11.7574			−0.565023			−0.282511	−	0.959264i	$-0.591167\pi$
$433$	−11.7574			−0.565023			−0.282511	+	0.959264i	$0.591167\pi$
$434$		0			0
$435$		0			0
$436$	−10.8284	−	18.7554i	−0.518588	−	0.898220i
$437$	5.17157	−	8.95743i	0.247390	−	0.428492i
$438$		0			0
$439$	−17.6569	−	30.5826i	−0.842716	−	1.45963i	−0.887590	−	0.460634i	$-0.847622\pi$
$439$	−17.6569	−	30.5826i	−0.842716	−	1.45963i	0.0448746	−	0.998993i	$-0.485711\pi$
$440$	−5.17157			−0.246545
$441$		0			0
$442$	−81.5980			−3.88122
$443$	0.514719	+	0.891519i	0.0244550	+	0.0423573i	0.877994	−	0.478672i	$-0.158882\pi$
$443$	0.514719	+	0.891519i	0.0244550	+	0.0423573i	−0.853539	+	0.521029i	$0.825548\pi$
$444$		0			0
$445$	1.68629	−	2.92074i	0.0799379	−	0.138456i
$446$	10.8284	+	18.7554i	0.512741	+	0.888093i
$447$		0			0
$448$		0			0
$449$	−17.3137			−0.817084			−0.408542	−	0.912739i	$-0.633963\pi$
$449$	−17.3137			−0.817084			−0.408542	+	0.912739i	$0.633963\pi$
$450$		0			0
$451$	−2.24264	+	3.88437i	−0.105602	+	0.182908i
$452$	33.1421	−	57.4039i	1.55887	−	2.70005i
$453$		0			0
$454$	38.1421			1.79010
$455$		0			0
$456$		0			0
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	−9.94975	+	17.2335i	−0.464921	+	0.805267i
$459$		0			0
$460$	−4.10051	−	7.10228i	−0.191187	−	0.331146i
$461$	19.4142			0.904210			0.452105	−	0.891965i	$-0.350673\pi$
$461$	19.4142			0.904210			0.452105	+	0.891965i	$0.350673\pi$
$462$		0			0
$463$	18.6274			0.865689			0.432845	−	0.901468i	$-0.357510\pi$
$463$	18.6274			0.865689			0.432845	+	0.901468i	$0.357510\pi$
$464$	−1.75736	−	3.04384i	−0.0815834	−	0.141307i
$465$		0			0
$466$	26.7279	−	46.2941i	1.23815	−	2.14453i
$467$	19.8995	+	34.4669i	0.920839	+	1.59494i	0.798120	+	0.602498i	$0.205828\pi$
$467$	19.8995	+	34.4669i	0.920839	+	1.59494i	0.122718	+	0.992442i	$0.460839\pi$
$468$		0			0
$469$		0			0
$470$	4.00000			0.184506
$471$		0			0
$472$	−15.0711	+	26.1039i	−0.693702	+	1.20153i
$473$	5.65685	−	9.79796i	0.260102	−	0.450511i
$474$		0			0
$475$	−13.1716			−0.604353
$476$		0			0
$477$		0			0
$478$	−5.24264	−	9.08052i	−0.239793	−	0.415333i
$479$	15.0711	−	26.1039i	0.688615	−	1.19272i	−0.283671	−	0.958922i	$-0.591553\pi$
$479$	15.0711	−	26.1039i	0.688615	−	1.19272i	0.972286	−	0.233794i	$-0.0751142\pi$
$480$		0			0
$481$	10.8284	+	18.7554i	0.493734	+	0.855172i
$482$	−18.7279			−0.853033
$483$		0			0
$484$	−26.7990			−1.21814
$485$	1.58579	+	2.74666i	0.0720069	+	0.124720i
$486$		0			0
$487$	9.31371	−	16.1318i	0.422044	−	0.731002i	−0.574095	−	0.818789i	$-0.694646\pi$
$487$	9.31371	−	16.1318i	0.422044	−	0.731002i	0.996139	+	0.0877864i	$0.0279793\pi$
$488$	−8.29289	−	14.3637i	−0.375402	−	0.650215i
$489$		0			0
$490$		0			0
$491$	−38.9706			−1.75872			−0.879358	−	0.476160i	$-0.842028\pi$
$491$	−38.9706			−1.75872			−0.879358	+	0.476160i	$0.842028\pi$
$492$		0			0
$493$	3.65685	−	6.33386i	0.164696	−	0.285263i
$494$	−18.4853	+	32.0174i	−0.831692	+	1.44053i
$495$		0			0
$496$	−20.4853			−0.919816
$497$		0			0
$498$		0			0
$499$	9.65685	+	16.7262i	0.432300	+	0.748766i	0.997071	−	0.0764820i	$-0.0243688\pi$
$499$	9.65685	+	16.7262i	0.432300	+	0.748766i	−0.564771	+	0.825248i	$0.691035\pi$
$500$	−10.8284	+	18.7554i	−0.484262	+	0.838766i
$501$		0			0
$502$	5.41421	+	9.37769i	0.241648	+	0.418547i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	8.82843	+	15.2913i	0.392471	+	0.679781i
$507$		0			0
$508$	−18.4853	+	32.0174i	−0.820152	+	1.42054i
$509$	−12.7782	−	22.1324i	−0.566383	−	0.981003i	−0.996920	−	0.0784305i	$-0.975009\pi$
$509$	−12.7782	−	22.1324i	−0.566383	−	0.981003i	0.430537	−	0.902573i	$-0.358324\pi$
$510$		0			0
$511$		0			0
$512$	−31.2426			−1.38074
$513$		0			0
$514$	−23.1924	+	40.1704i	−1.02297	+	1.77184i
$515$	−3.65685	+	6.33386i	−0.161140	+	0.279103i
$516$		0			0
$517$	−5.65685			−0.248788
$518$		0			0
$519$		0			0
$520$	7.00000	+	12.1244i	0.306970	+	0.531688i
$521$	−16.2929	+	28.2201i	−0.713805	+	1.23635i	0.249614	+	0.968345i	$0.419696\pi$
$521$	−16.2929	+	28.2201i	−0.713805	+	1.23635i	−0.963419	+	0.268000i	$0.913637\pi$
$522$		0			0
$523$	7.17157	+	12.4215i	0.313591	+	0.543156i	0.979137	−	0.203201i	$-0.0651346\pi$
$523$	7.17157	+	12.4215i	0.313591	+	0.543156i	−0.665546	+	0.746357i	$0.731801\pi$
$524$	−28.0000			−1.22319
$525$		0			0
$526$	41.7990			1.82252
$527$	−21.3137	−	36.9164i	−0.928440	−	1.60810i
$528$		0			0
$529$	4.81371	−	8.33759i	0.209292	−	0.362504i
$530$	1.41421	+	2.44949i	0.0614295	+	0.106399i
$531$		0			0
$532$		0			0
$533$	12.1421			0.525934
$534$		0			0
$535$	3.41421	−	5.91359i	0.147609	−	0.255667i
$536$	−12.4853	+	21.6251i	−0.539282	+	0.934064i
$537$		0			0
$538$	−25.8995			−1.11661
$539$		0			0
$540$		0			0
$541$	2.65685	+	4.60181i	0.114227	+	0.197847i	0.917471	−	0.397804i	$-0.130228\pi$
$541$	2.65685	+	4.60181i	0.114227	+	0.197847i	−0.803243	+	0.595651i	$0.796894\pi$
$542$	−21.8995	+	37.9310i	−0.940664	+	1.62928i
$543$		0			0
$544$	−4.94975	−	8.57321i	−0.212219	−	0.367574i
$545$	−3.31371			−0.141944
$546$		0			0
$547$	−3.02944			−0.129529			−0.0647647	−	0.997901i	$-0.520630\pi$
$547$	−3.02944			−0.129529			−0.0647647	+	0.997901i	$0.520630\pi$
$548$	−27.0711	−	46.8885i	−1.15642	−	2.00298i
$549$		0			0
$550$	11.2426	−	19.4728i	0.479388	−	0.830324i
$551$	−1.65685	−	2.86976i	−0.0705844	−	0.122256i
$552$		0			0
$553$		0			0
$554$	32.1421			1.36559
$555$		0			0
$556$	12.1421	−	21.0308i	0.514941	−	0.891904i
$557$	13.0000	−	22.5167i	0.550828	−	0.954062i	−0.447387	−	0.894340i	$-0.647645\pi$
$557$	13.0000	−	22.5167i	0.550828	−	0.954062i	0.998215	−	0.0597213i	$-0.0190212\pi$
$558$		0			0
$559$	−30.6274			−1.29540
$560$		0			0
$561$		0			0
$562$	−19.8995	−	34.4669i	−0.839410	−	1.45390i
$563$	−3.41421	+	5.91359i	−0.143892	+	0.249228i	−0.928959	−	0.370183i	$-0.879295\pi$
$563$	−3.41421	+	5.91359i	−0.143892	+	0.249228i	0.785067	+	0.619411i	$0.212628\pi$
$564$		0			0
$565$	−5.07107	−	8.78335i	−0.213341	−	0.369518i
$566$	20.4853			0.861061
$567$		0			0
$568$	58.7696			2.46592
$569$	0.242641	+	0.420266i	0.0101720	+	0.0176185i	0.871067	−	0.491165i	$-0.163429\pi$
$569$	0.242641	+	0.420266i	0.0101720	+	0.0176185i	−0.860895	+	0.508783i	$0.830095\pi$
$570$		0			0
$571$	−16.8284	+	29.1477i	−0.704248	+	1.21979i	0.262715	+	0.964874i	$0.415382\pi$
$571$	−16.8284	+	29.1477i	−0.704248	+	1.21979i	−0.966962	+	0.254919i	$0.917951\pi$
$572$	−20.7279	−	35.9018i	−0.866678	−	1.50113i
$573$		0			0
$574$		0			0
$575$	17.0294			0.710177
$576$		0			0
$577$	7.05025	−	12.2114i	0.293506	−	0.508367i	−0.681130	−	0.732162i	$-0.738511\pi$
$577$	7.05025	−	12.2114i	0.293506	−	0.508367i	0.974636	+	0.223795i	$0.0718446\pi$
$578$	−26.5208	+	45.9354i	−1.10312	+	1.91066i
$579$		0			0
$580$	−2.62742			−0.109098
$581$		0			0
$582$		0			0
$583$	−2.00000	−	3.46410i	−0.0828315	−	0.143468i
$584$	13.0208	−	22.5527i	0.538805	−	0.933238i
$585$		0			0
$586$	23.4350	+	40.5907i	0.968092	+	1.67678i
$587$	17.1716			0.708747			0.354373	−	0.935104i	$-0.384694\pi$
$587$	17.1716			0.708747			0.354373	+	0.935104i	$0.384694\pi$
$588$		0			0
$589$	−19.3137			−0.795807
$590$	4.82843	+	8.36308i	0.198783	+	0.344303i
$591$		0			0
$592$	6.00000	−	10.3923i	0.246598	−	0.427121i
$593$	−10.5355	−	18.2481i	−0.432643	−	0.749359i	0.564457	−	0.825462i	$-0.309085\pi$
$593$	−10.5355	−	18.2481i	−0.432643	−	0.749359i	−0.997100	+	0.0761034i	$0.975752\pi$
$594$		0			0
$595$		0			0
$596$	20.3431			0.833288
$597$		0			0
$598$	23.8995	−	41.3951i	0.977323	−	1.69277i
$599$	−1.00000	+	1.73205i	−0.0408589	+	0.0707697i	−0.885732	−	0.464198i	$-0.846343\pi$
$599$	−1.00000	+	1.73205i	−0.0408589	+	0.0707697i	0.844873	+	0.534967i	$0.179676\pi$
$600$		0			0
$601$	−0.928932			−0.0378919			−0.0189460	−	0.999821i	$-0.506031\pi$
$601$	−0.928932			−0.0378919			−0.0189460	+	0.999821i	$0.506031\pi$
$602$		0			0
$603$		0			0
$604$	−22.9706	−	39.7862i	−0.934659	−	1.61888i
$605$	−2.05025	+	3.55114i	−0.0833546	+	0.144374i
$606$		0			0
$607$	14.8284	+	25.6836i	0.601867	+	1.04246i	0.992538	+	0.121934i	$0.0389097\pi$
$607$	14.8284	+	25.6836i	0.601867	+	1.04246i	−0.390671	+	0.920530i	$0.627757\pi$
$608$	−4.48528			−0.181902
$609$		0			0
$610$	−5.31371			−0.215146
$611$	7.65685	+	13.2621i	0.309763	+	0.536526i
$612$		0			0
$613$	−13.6569	+	23.6544i	−0.551595	+	0.955391i	0.446565	+	0.894751i	$0.352647\pi$
$613$	−13.6569	+	23.6544i	−0.551595	+	0.955391i	−0.998160	+	0.0606394i	$0.980686\pi$
$614$	−2.24264	−	3.88437i	−0.0905056	−	0.156760i
$615$		0			0
$616$		0			0
$617$	7.51472			0.302531			0.151266	−	0.988493i	$-0.451665\pi$
$617$	7.51472			0.302531			0.151266	+	0.988493i	$0.451665\pi$
$618$		0			0
$619$	2.48528	−	4.30463i	0.0998919	−	0.173018i	−0.811748	−	0.584008i	$-0.801484\pi$
$619$	2.48528	−	4.30463i	0.0998919	−	0.173018i	0.911640	+	0.410990i	$0.134817\pi$
$620$	−7.65685	+	13.2621i	−0.307507	+	0.532617i
$621$		0			0
$622$	53.4558			2.14338
$623$		0			0
$624$		0			0
$625$	−9.98528	−	17.2950i	−0.399411	−	0.691801i
$626$	21.6066	−	37.4237i	0.863573	−	1.49575i
$627$		0			0
$628$	−38.7487	−	67.1148i	−1.54624	−	2.67817i
$629$	24.9706			0.995642
$630$		0			0
$631$	0.686292			0.0273208			0.0136604	−	0.999907i	$-0.495652\pi$
$631$	0.686292			0.0273208			0.0136604	+	0.999907i	$0.495652\pi$
$632$	−5.17157	−	8.95743i	−0.205714	−	0.356307i
$633$		0			0
$634$	12.0711	−	20.9077i	0.479403	−	0.830351i
$635$	2.82843	+	4.89898i	0.112243	+	0.194410i
$636$		0			0
$637$		0			0
$638$	5.65685			0.223957
$639$		0			0
$640$	−6.02082	+	10.4284i	−0.237994	+	0.412217i
$641$	−2.58579	+	4.47871i	−0.102132	+	0.176899i	−0.912563	−	0.408936i	$-0.865900\pi$
$641$	−2.58579	+	4.47871i	−0.102132	+	0.176899i	0.810431	+	0.585835i	$0.199233\pi$
$642$		0			0
$643$	50.4264			1.98862			0.994312	−	0.106510i	$-0.0339675\pi$
$643$	50.4264			1.98862			0.994312	+	0.106510i	$0.0339675\pi$
$644$		0			0
$645$		0			0
$646$	21.3137	+	36.9164i	0.838577	+	1.45246i
$647$	10.5858	−	18.3351i	0.416170	−	0.720828i	−0.579380	−	0.815057i	$-0.696705\pi$
$647$	10.5858	−	18.3351i	0.416170	−	0.720828i	0.995551	+	0.0942294i	$0.0300387\pi$
$648$		0			0
$649$	−6.82843	−	11.8272i	−0.268039	−	0.464258i
$650$	−60.8701			−2.38752
$651$		0			0
$652$	43.3137			1.69630
$653$	9.75736	+	16.9002i	0.381835	+	0.661358i	0.991325	−	0.131436i	$-0.0419589\pi$
$653$	9.75736	+	16.9002i	0.381835	+	0.661358i	−0.609490	+	0.792794i	$0.708626\pi$
$654$		0			0
$655$	−2.14214	+	3.71029i	−0.0837002	+	0.144973i
$656$	−3.36396	−	5.82655i	−0.131341	−	0.227489i
$657$		0			0
$658$		0			0
$659$	13.3137			0.518628			0.259314	−	0.965793i	$-0.416503\pi$
$659$	13.3137			0.518628			0.259314	+	0.965793i	$0.416503\pi$
$660$		0			0
$661$	−3.77817	+	6.54399i	−0.146954	+	0.254532i	−0.930100	−	0.367306i	$-0.880280\pi$
$661$	−3.77817	+	6.54399i	−0.146954	+	0.254532i	0.783146	+	0.621838i	$0.213614\pi$
$662$	4.82843	−	8.36308i	0.187662	−	0.325040i
$663$		0			0
$664$	67.5980			2.62331
$665$		0			0
$666$		0			0
$667$	2.14214	+	3.71029i	0.0829438	+	0.143663i
$668$	37.8995	−	65.6439i	1.46638	−	2.53984i
$669$		0			0
$670$	4.00000	+	6.92820i	0.154533	+	0.267660i
$671$	7.51472			0.290102
$672$		0			0
$673$	0.686292			0.0264546			0.0132273	−	0.999913i	$-0.495789\pi$
$673$	0.686292			0.0264546			0.0132273	+	0.999913i	$0.495789\pi$
$674$	22.1421	+	38.3513i	0.852883	+	1.47724i
$675$		0			0
$676$	−31.2279	+	54.0883i	−1.20107	+	2.08032i
$677$	14.2929	+	24.7560i	0.549321	+	0.951451i	0.998321	+	0.0579196i	$0.0184467\pi$
$677$	14.2929	+	24.7560i	0.549321	+	0.951451i	−0.449001	+	0.893531i	$0.648220\pi$
$678$		0			0
$679$		0			0
$680$	16.1421			0.619023
$681$		0			0
$682$	16.4853	−	28.5533i	0.631254	−	1.09336i
$683$	−4.17157	+	7.22538i	−0.159621	+	0.276471i	−0.934732	−	0.355354i	$-0.884360\pi$
$683$	−4.17157	+	7.22538i	−0.159621	+	0.276471i	0.775111	+	0.631825i	$0.217694\pi$
$684$		0			0
$685$	−8.28427			−0.316526
$686$		0			0
$687$		0			0
$688$	8.48528	+	14.6969i	0.323498	+	0.560316i
$689$	−5.41421	+	9.37769i	−0.206265	+	0.357262i
$690$		0			0
$691$	11.6569	+	20.1903i	0.443448	+	0.768074i	0.997943	−	0.0641132i	$-0.0204219\pi$
$691$	11.6569	+	20.1903i	0.443448	+	0.768074i	−0.554495	+	0.832187i	$0.687089\pi$
$692$	−26.5269			−1.00840
$693$		0			0
$694$	−25.7990			−0.979316
$695$	−1.85786	−	3.21792i	−0.0704728	−	0.122062i
$696$		0			0
$697$	7.00000	−	12.1244i	0.265144	−	0.459243i
$698$	−11.9497	−	20.6976i	−0.452305	−	0.783415i
$699$		0			0
$700$		0			0
$701$	22.8284			0.862218			0.431109	−	0.902300i	$-0.358122\pi$
$701$	22.8284			0.862218			0.431109	+	0.902300i	$0.358122\pi$
$702$		0			0
$703$	5.65685	−	9.79796i	0.213352	−	0.369537i
$704$	9.82843	−	17.0233i	0.370423	−	0.641591i
$705$		0			0
$706$	−25.8995			−0.974740
$707$		0			0
$708$		0			0
$709$	−10.1421	−	17.5667i	−0.380896	−	0.659731i	0.610295	−	0.792174i	$-0.291051\pi$
$709$	−10.1421	−	17.5667i	−0.380896	−	0.659731i	−0.991191	+	0.132443i	$0.957718\pi$
$710$	9.41421	−	16.3059i	0.353309	−	0.611949i
$711$		0			0
$712$	−12.7071	−	22.0094i	−0.476219	−	0.824835i
$713$	24.9706			0.935155
$714$		0			0
$715$	−6.34315			−0.237220
$716$	−15.9706	−	27.6618i	−0.596848	−	1.03377i
$717$		0			0
$718$	−14.0711	+	24.3718i	−0.525128	+	0.909548i
$719$	−12.9706	−	22.4657i	−0.483720	−	0.837828i	0.516105	−	0.856525i	$-0.327381\pi$
$719$	−12.9706	−	22.4657i	−0.483720	−	0.837828i	−0.999825	+	0.0186972i	$0.994048\pi$
$720$		0			0
$721$		0			0
$722$	−26.5563			−0.988325
$723$		0			0
$724$	10.3640	−	17.9509i	0.385174	−	0.667140i
$725$	2.72792	−	4.72490i	0.101312	−	0.175478i
$726$		0			0
$727$	−4.48528			−0.166350			−0.0831749	−	0.996535i	$-0.526506\pi$
$727$	−4.48528			−0.166350			−0.0831749	+	0.996535i	$0.526506\pi$
$728$		0			0
$729$		0			0
$730$	−4.17157	−	7.22538i	−0.154397	−	0.267423i
$731$	−17.6569	+	30.5826i	−0.653062	+	1.13114i
$732$		0			0
$733$	4.84924	+	8.39913i	0.179111	+	0.310229i	0.941576	−	0.336800i	$-0.109345\pi$
$733$	4.84924	+	8.39913i	0.179111	+	0.310229i	−0.762465	+	0.647029i	$0.776011\pi$
$734$	46.6274			1.72105
$735$		0			0
$736$	5.79899			0.213754
$737$	−5.65685	−	9.79796i	−0.208373	−	0.360912i
$738$		0			0
$739$	−13.6569	+	23.6544i	−0.502376	+	0.870140i	0.497621	+	0.867395i	$0.334207\pi$
$739$	−13.6569	+	23.6544i	−0.502376	+	0.870140i	−0.999996	+	0.00274517i	$0.999126\pi$
$740$	−4.48528	−	7.76874i	−0.164882	−	0.285584i
$741$		0			0
$742$		0			0
$743$	17.0294			0.624749			0.312375	−	0.949959i	$-0.398876\pi$
$743$	17.0294			0.624749			0.312375	+	0.949959i	$0.398876\pi$
$744$		0			0
$745$	1.55635	−	2.69568i	0.0570202	−	0.0987619i
$746$	40.2132	−	69.6513i	1.47231	−	2.55012i
$747$		0			0
$748$	−47.7990			−1.74770
$749$		0			0
$750$		0			0
$751$	−1.17157	−	2.02922i	−0.0427513	−	0.0740474i	0.843858	−	0.536567i	$-0.180279\pi$
$751$	−1.17157	−	2.02922i	−0.0427513	−	0.0740474i	−0.886609	+	0.462519i	$0.846946\pi$
$752$	4.24264	−	7.34847i	0.154713	−	0.267971i
$753$		0			0
$754$	−7.65685	−	13.2621i	−0.278846	−	0.482976i
$755$	−7.02944			−0.255827
$756$		0			0
$757$	37.6569			1.36866			0.684331	−	0.729172i	$-0.260094\pi$
$757$	37.6569			1.36866			0.684331	+	0.729172i	$0.260094\pi$
$758$	−37.7990	−	65.4698i	−1.37292	−	2.37797i
$759$		0			0
$760$	3.65685	−	6.33386i	0.132648	−	0.229753i
$761$	23.2635	+	40.2935i	0.843300	+	1.46064i	0.887090	+	0.461597i	$0.152723\pi$
$761$	23.2635	+	40.2935i	0.843300	+	1.46064i	−0.0437901	+	0.999041i	$0.513943\pi$
$762$		0			0
$763$		0			0
$764$	68.9117			2.49314
$765$		0			0
$766$	−35.7990	+	62.0057i	−1.29347	+	2.24036i
$767$	−18.4853	+	32.0174i	−0.667465	+	1.15608i
$768$		0			0
$769$	−29.6985			−1.07095			−0.535477	−	0.844550i	$-0.679868\pi$
$769$	−29.6985			−1.07095			−0.535477	+	0.844550i	$0.679868\pi$
$770$		0			0
$771$		0			0
$772$	33.1421	+	57.4039i	1.19281	+	2.06601i
$773$	10.7782	−	18.6683i	0.387664	−	0.671454i	−0.604471	−	0.796627i	$-0.706615\pi$
$773$	10.7782	−	18.6683i	0.387664	−	0.671454i	0.992135	+	0.125174i	$0.0399488\pi$
$774$		0			0
$775$	−15.8995	−	27.5387i	−0.571127	−	0.989220i
$776$	23.8995			0.857942
$777$		0			0
$778$	−24.4853			−0.877840
$779$	−3.17157	−	5.49333i	−0.113633	−	0.196819i
$780$		0			0
$781$	−13.3137	+	23.0600i	−0.476402	+	0.825152i
$782$	−27.5563	−	47.7290i	−0.985413	−	1.70679i
$783$		0			0
$784$		0			0
$785$	−11.8579			−0.423225
$786$		0			0
$787$	−23.6569	+	40.9749i	−0.843276	+	1.46060i	0.0438344	+	0.999039i	$0.486043\pi$
$787$	−23.6569	+	40.9749i	−0.843276	+	1.46060i	−0.887110	+	0.461558i	$0.847291\pi$
$788$	3.82843	−	6.63103i	0.136382	−	0.236221i
$789$		0			0
$790$	−3.31371			−0.117896
$791$		0			0
$792$		0			0
$793$	−10.1716	−	17.6177i	−0.361203	−	0.625622i
$794$	−41.5061	+	71.8907i	−1.47300	+

Overview	Random
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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