LMFDB - Embedded newform 572.2.n.b.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.1
Character	$\chi$	$=$	572.157
Dual form			572.2.n.b.521.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05349 - 3.24229i) q^{3} +(-2.42026 - 1.75842i) q^{5} +(1.07034 - 3.29416i) q^{7} +(-6.97559 + 5.06806i) q^{9} +O(q^{10})$	\(q+(-1.05349 - 3.24229i) q^{3} +(-2.42026 - 1.75842i) q^{5} +(1.07034 - 3.29416i) q^{7} +(-6.97559 + 5.06806i) q^{9} +(-0.426312 - 3.28911i) q^{11} +(0.809017 - 0.587785i) q^{13} +(-3.15161 + 9.69965i) q^{15} +(4.85851 + 3.52991i) q^{17} +(-1.26857 - 3.90425i) q^{19} -11.8082 q^{21} +5.25830 q^{23} +(1.22052 + 3.75637i) q^{25} +(15.5067 + 11.2662i) q^{27} +(-0.600613 + 1.84850i) q^{29} +(1.80890 - 1.31424i) q^{31} +(-10.2152 + 4.84726i) q^{33} +(-8.38302 + 6.09062i) q^{35} +(2.33336 - 7.18133i) q^{37} +(-2.75806 - 2.00385i) q^{39} +(1.01929 + 3.13704i) q^{41} -8.24966 q^{43} +25.7945 q^{45} +(1.98019 + 6.09440i) q^{47} +(-4.04278 - 2.93725i) q^{49} +(6.32665 - 19.4714i) q^{51} +(-5.36329 + 3.89666i) q^{53} +(-4.75186 + 8.71013i) q^{55} +(-11.3223 + 8.22615i) q^{57} +(-1.43034 + 4.40213i) q^{59} +(-4.02359 - 2.92331i) q^{61} +(9.22879 + 28.4033i) q^{63} -2.99160 q^{65} +1.08509 q^{67} +(-5.53954 - 17.0490i) q^{69} +(-2.26168 - 1.64320i) q^{71} +(4.53789 - 13.9662i) q^{73} +(10.8935 - 7.91456i) q^{75} +(-11.2912 - 2.11612i) q^{77} +(0.308350 - 0.224030i) q^{79} +(12.1991 - 37.5451i) q^{81} +(2.85383 + 2.07343i) q^{83} +(-5.55177 - 17.0866i) q^{85} +6.62611 q^{87} +4.38192 q^{89} +(-1.07034 - 3.29416i) q^{91} +(-6.16682 - 4.48045i) q^{93} +(-3.79505 + 11.6800i) q^{95} +(-4.79011 + 3.48022i) q^{97} +(19.6432 + 20.7829i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.05349	−	3.24229i	−0.608230	−	1.87194i	−0.472843	−	0.881147i	$-0.656772\pi$
$3$	−1.05349	−	3.24229i	−0.608230	−	1.87194i	−0.135387	−	0.990793i	$-0.543228\pi$
$4$		0			0
$5$	−2.42026	−	1.75842i	−1.08237	−	0.786389i	−0.104277	−	0.994548i	$-0.533253\pi$
$5$	−2.42026	−	1.75842i	−1.08237	−	0.786389i	−0.978095	+	0.208159i	$0.933253\pi$
$6$		0			0
$7$	1.07034	−	3.29416i	0.404550	−	1.24508i	−0.516720	−	0.856154i	$-0.672847\pi$
$7$	1.07034	−	3.29416i	0.404550	−	1.24508i	0.921270	−	0.388923i	$-0.127153\pi$
$8$		0			0
$9$	−6.97559	+	5.06806i	−2.32520	+	1.68935i
$10$		0			0
$11$	−0.426312	−	3.28911i	−0.128538	−	0.991705i
$11$	−0.426312	−	3.28911i	−0.128538	−	0.991705i
$12$		0			0
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$		0			0
$15$	−3.15161	+	9.69965i	−0.813742	+	2.50444i
$16$		0			0
$17$	4.85851	+	3.52991i	1.17836	+	0.856130i	0.991986	−	0.126349i	$-0.0403259\pi$
$17$	4.85851	+	3.52991i	1.17836	+	0.856130i	0.186375	+	0.982479i	$0.440326\pi$
$18$		0			0
$19$	−1.26857	−	3.90425i	−0.291030	−	0.895697i	−0.984526	−	0.175237i	$-0.943931\pi$
$19$	−1.26857	−	3.90425i	−0.291030	−	0.895697i	0.693497	−	0.720460i	$-0.256069\pi$
$20$		0			0
$21$	−11.8082			−2.57677
$22$		0			0
$23$	5.25830			1.09643			0.548216	−	0.836337i	$-0.315307\pi$
$23$	5.25830			1.09643			0.548216	+	0.836337i	$0.315307\pi$
$24$		0			0
$25$	1.22052	+	3.75637i	0.244104	+	0.751274i
$26$		0			0
$27$	15.5067	+	11.2662i	2.98426	+	2.16819i
$28$		0			0
$29$	−0.600613	+	1.84850i	−0.111531	+	0.343257i	−0.991208	−	0.132315i	$-0.957759\pi$
$29$	−0.600613	+	1.84850i	−0.111531	+	0.343257i	0.879677	+	0.475572i	$0.157759\pi$
$30$		0			0
$31$	1.80890	−	1.31424i	0.324888	−	0.236045i	−0.413370	−	0.910563i	$-0.635648\pi$
$31$	1.80890	−	1.31424i	0.324888	−	0.236045i	0.738258	+	0.674518i	$0.235648\pi$
$32$		0			0
$33$	−10.2152	+	4.84726i	−1.77823	+	0.843799i
$34$		0			0
$35$	−8.38302	+	6.09062i	−1.41699	+	1.02950i
$36$		0			0
$37$	2.33336	−	7.18133i	0.383601	−	1.18060i	−0.553889	−	0.832591i	$-0.686857\pi$
$37$	2.33336	−	7.18133i	0.383601	−	1.18060i	0.937490	−	0.348013i	$-0.113143\pi$
$38$		0			0
$39$	−2.75806	−	2.00385i	−0.441643	−	0.320872i
$40$		0			0
$41$	1.01929	+	3.13704i	0.159186	+	0.489923i	0.998561	−	0.0536294i	$-0.0170789\pi$
$41$	1.01929	+	3.13704i	0.159186	+	0.489923i	−0.839375	+	0.543552i	$0.817079\pi$
$42$		0			0
$43$	−8.24966			−1.25806			−0.629031	−	0.777380i	$-0.716548\pi$
$43$	−8.24966			−1.25806			−0.629031	+	0.777380i	$0.716548\pi$
$44$		0			0
$45$	25.7945			3.84522
$46$		0			0
$47$	1.98019	+	6.09440i	0.288841	+	0.888960i	0.985221	+	0.171287i	$0.0547927\pi$
$47$	1.98019	+	6.09440i	0.288841	+	0.888960i	−0.696380	+	0.717673i	$0.745207\pi$
$48$		0			0
$49$	−4.04278	−	2.93725i	−0.577539	−	0.419607i
$50$		0			0
$51$	6.32665	−	19.4714i	0.885908	−	2.72654i
$52$		0			0
$53$	−5.36329	+	3.89666i	−0.736705	+	0.535247i	−0.891677	−	0.452671i	$-0.850471\pi$
$53$	−5.36329	+	3.89666i	−0.736705	+	0.535247i	0.154973	+	0.987919i	$0.450471\pi$
$54$		0			0
$55$	−4.75186	+	8.71013i	−0.640740	+	1.17447i
$56$		0			0
$57$	−11.3223	+	8.22615i	−1.49968	+	1.08958i
$58$		0			0
$59$	−1.43034	+	4.40213i	−0.186214	+	0.573108i	−0.999967	−	0.00810267i	$-0.997421\pi$
$59$	−1.43034	+	4.40213i	−0.186214	+	0.573108i	0.813753	+	0.581211i	$0.197421\pi$
$60$		0			0
$61$	−4.02359	−	2.92331i	−0.515168	−	0.374292i	0.299612	−	0.954061i	$-0.403143\pi$
$61$	−4.02359	−	2.92331i	−0.515168	−	0.374292i	−0.814781	+	0.579769i	$0.803143\pi$
$62$		0			0
$63$	9.22879	+	28.4033i	1.16272	+	3.57848i
$64$		0			0
$65$	−2.99160			−0.371063
$66$		0			0
$67$	1.08509			0.132565			0.0662824	−	0.997801i	$-0.478886\pi$
$67$	1.08509			0.132565			0.0662824	+	0.997801i	$0.478886\pi$
$68$		0			0
$69$	−5.53954	−	17.0490i	−0.666883	−	2.05245i
$70$		0			0
$71$	−2.26168	−	1.64320i	−0.268412	−	0.195012i	0.445435	−	0.895314i	$-0.353049\pi$
$71$	−2.26168	−	1.64320i	−0.268412	−	0.195012i	−0.713847	+	0.700302i	$0.753049\pi$
$72$		0			0
$73$	4.53789	−	13.9662i	0.531120	−	1.63462i	−0.220767	−	0.975327i	$-0.570856\pi$
$73$	4.53789	−	13.9662i	0.531120	−	1.63462i	0.751887	−	0.659292i	$-0.229144\pi$
$74$		0			0
$75$	10.8935	−	7.91456i	1.25787	−	0.913895i
$76$		0			0
$77$	−11.2912	−	2.11612i	−1.28675	−	0.241155i
$78$		0			0
$79$	0.308350	−	0.224030i	0.0346921	−	0.0252053i	−0.570304	−	0.821434i	$-0.693175\pi$
$79$	0.308350	−	0.224030i	0.0346921	−	0.0252053i	0.604996	+	0.796228i	$0.293175\pi$
$80$		0			0
$81$	12.1991	−	37.5451i	1.35546	−	4.17167i
$82$		0			0
$83$	2.85383	+	2.07343i	0.313249	+	0.227588i	0.733289	−	0.679917i	$-0.237984\pi$
$83$	2.85383	+	2.07343i	0.313249	+	0.227588i	−0.420041	+	0.907505i	$0.637984\pi$
$84$		0			0
$85$	−5.55177	−	17.0866i	−0.602174	−	1.85330i
$86$		0			0
$87$	6.62611			0.710394
$88$		0			0
$89$	4.38192			0.464482			0.232241	−	0.972658i	$-0.425394\pi$
$89$	4.38192			0.464482			0.232241	+	0.972658i	$0.425394\pi$
$90$		0			0
$91$	−1.07034	−	3.29416i	−0.112202	−	0.345322i
$92$		0			0
$93$	−6.16682	−	4.48045i	−0.639469	−	0.464601i
$94$		0			0
$95$	−3.79505	+	11.6800i	−0.389364	+	1.19834i
$96$		0			0
$97$	−4.79011	+	3.48022i	−0.486362	+	0.353363i	−0.803784	−	0.594922i	$-0.797183\pi$
$97$	−4.79011	+	3.48022i	−0.486362	+	0.353363i	0.317421	+	0.948285i	$0.397183\pi$
$98$		0			0
$99$	19.6432	+	20.7829i	1.97422	+	2.08876i
$100$		0			0
$101$	−6.92083	+	5.02827i	−0.688648	+	0.500332i	−0.876215	−	0.481920i	$-0.839940\pi$
$101$	−6.92083	+	5.02827i	−0.688648	+	0.500332i	0.187567	+	0.982252i	$0.439940\pi$
$102$		0			0
$103$	1.30176	−	4.00642i	0.128267	−	0.394764i	−0.866215	−	0.499671i	$-0.833454\pi$
$103$	1.30176	−	4.00642i	0.128267	−	0.394764i	0.994482	+	0.104907i	$0.0334544\pi$
$104$		0			0
$105$	28.5790	+	20.7638i	2.78902	+	2.02634i
$106$		0			0
$107$	−4.16031	−	12.8041i	−0.402193	−	1.23782i	−0.923217	−	0.384280i	$-0.874450\pi$
$107$	−4.16031	−	12.8041i	−0.402193	−	1.23782i	0.521024	−	0.853542i	$-0.325550\pi$
$108$		0			0
$109$	14.0855			1.34915			0.674574	−	0.738207i	$-0.264327\pi$
$109$	14.0855			1.34915			0.674574	+	0.738207i	$0.264327\pi$
$110$		0			0
$111$	−25.7421			−2.44334
$112$		0			0
$113$	−4.55029	−	14.0044i	−0.428055	−	1.31742i	−0.900038	−	0.435811i	$-0.856462\pi$
$113$	−4.55029	−	14.0044i	−0.428055	−	1.31742i	0.471983	−	0.881608i	$-0.343538\pi$
$114$		0			0
$115$	−12.7264	−	9.24630i	−1.18675	−	0.862222i
$116$		0			0
$117$	−2.66444	+	8.20030i	−0.246327	+	0.758118i
$118$		0			0
$119$	16.8284	−	12.2265i	1.54265	−	1.12080i
$120$		0			0
$121$	−10.6365	+	2.80437i	−0.966956	+	0.254943i
$122$		0			0
$123$	9.09740	−	6.60965i	0.820285	−	0.595972i
$124$		0			0
$125$	−0.970973	+	2.98835i	−0.0868465	+	0.267286i
$126$		0			0
$127$	−1.22947	−	0.893263i	−0.109098	−	0.0792643i	0.531899	−	0.846808i	$-0.321479\pi$
$127$	−1.22947	−	0.893263i	−0.109098	−	0.0792643i	−0.640997	+	0.767544i	$0.721479\pi$
$128$		0			0
$129$	8.69090	+	26.7478i	0.765191	+	2.35502i
$130$		0			0
$131$	5.42306			0.473815			0.236907	−	0.971532i	$-0.423866\pi$
$131$	5.42306			0.473815			0.236907	+	0.971532i	$0.423866\pi$
$132$		0			0
$133$	−14.2191			−1.23295
$134$		0			0
$135$	−17.7193	−	54.5344i	−1.52503	−	4.69357i
$136$		0			0
$137$	−5.92461	−	4.30448i	−0.506173	−	0.367756i	0.305197	−	0.952289i	$-0.401278\pi$
$137$	−5.92461	−	4.30448i	−0.506173	−	0.367756i	−0.811370	+	0.584533i	$0.801278\pi$
$138$		0			0
$139$	0.902779	−	2.77847i	0.0765727	−	0.235667i	−0.905442	−	0.424469i	$-0.860461\pi$
$139$	0.902779	−	2.77847i	0.0765727	−	0.235667i	0.982015	+	0.188803i	$0.0604607\pi$
$140$		0			0
$141$	17.6737	−	12.8407i	1.48840	−	1.08138i
$142$		0			0
$143$	−2.27818	−	2.41037i	−0.190511	−	0.201565i
$144$		0			0
$145$	4.70407	−	3.41771i	0.390652	−	0.283825i
$146$		0			0
$147$	−5.26442	+	16.2022i	−0.434202	+	1.33634i
$148$		0			0
$149$	−0.811079	−	0.589283i	−0.0664462	−	0.0482760i	0.554066	−	0.832473i	$-0.313075\pi$
$149$	−0.811079	−	0.589283i	−0.0664462	−	0.0482760i	−0.620513	+	0.784197i	$0.713075\pi$
$150$		0			0
$151$	0.211929	+	0.652250i	0.0172465	+	0.0530793i	0.959309	−	0.282357i	$-0.0911163\pi$
$151$	0.211929	+	0.652250i	0.0172465	+	0.0530793i	−0.942063	+	0.335436i	$0.891116\pi$
$152$		0			0
$153$	−51.7808			−4.18623
$154$		0			0
$155$	−6.68900			−0.537273
$156$		0			0
$157$	5.24430	+	16.1403i	0.418541	+	1.28814i	0.909045	+	0.416697i	$0.136812\pi$
$157$	5.24430	+	16.1403i	0.418541	+	1.28814i	−0.490505	+	0.871438i	$0.663188\pi$
$158$		0			0
$159$	18.2843	+	13.2843i	1.45004	+	1.05351i
$160$		0			0
$161$	5.62817	−	17.3217i	0.443562	−	1.36514i
$162$		0			0
$163$	−8.45101	+	6.14002i	−0.661934	+	0.480923i	−0.867316	−	0.497759i	$-0.834157\pi$
$163$	−8.45101	+	6.14002i	−0.661934	+	0.480923i	0.205381	+	0.978682i	$0.434157\pi$
$164$		0			0
$165$	33.2468	+	6.23092i	2.58826	+	0.485076i
$166$		0			0
$167$	−2.04694	+	1.48719i	−0.158397	+	0.115082i	−0.664160	−	0.747590i	$-0.731211\pi$
$167$	−2.04694	+	1.48719i	−0.158397	+	0.115082i	0.505764	+	0.862672i	$0.331211\pi$
$168$		0			0
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$		0			0
$171$	28.6360	+	20.8053i	2.18985	+	1.59102i
$172$		0			0
$173$	4.61391	+	14.2001i	0.350789	+	1.07962i	0.958411	+	0.285391i	$0.0921235\pi$
$173$	4.61391	+	14.2001i	0.350789	+	1.07962i	−0.607622	+	0.794226i	$0.707877\pi$
$174$		0			0
$175$	13.6805			1.03415
$176$		0			0
$177$	15.7798			1.18608
$178$		0			0
$179$	−0.0191360	−	0.0588945i	−0.00143029	−	0.00440198i	0.950339	−	0.311217i	$-0.100737\pi$
$179$	−0.0191360	−	0.0588945i	−0.00143029	−	0.00440198i	−0.951769	+	0.306815i	$0.900737\pi$
$180$		0			0
$181$	17.4407	+	12.6714i	1.29636	+	0.941859i	0.999913	−	0.0131915i	$-0.00419910\pi$
$181$	17.4407	+	12.6714i	1.29636	+	0.941859i	0.296444	+	0.955050i	$0.404199\pi$
$182$		0			0
$183$	−5.23944	+	16.1253i	−0.387311	+	1.19202i
$184$		0			0
$185$	−18.2751	+	13.2776i	−1.34361	+	0.976192i
$186$		0			0
$187$	9.53904	−	17.4850i	0.697564	−	1.27863i
$188$		0			0
$189$	53.7102	−	39.0228i	3.90684	−	2.83849i
$190$		0			0
$191$	7.27810	−	22.3997i	0.526625	−	1.62078i	−0.234456	−	0.972127i	$-0.575331\pi$
$191$	7.27810	−	22.3997i	0.526625	−	1.62078i	0.761081	−	0.648657i	$-0.224669\pi$
$192$		0			0
$193$	3.81845	+	2.77426i	0.274858	+	0.199696i	0.716671	−	0.697411i	$-0.245665\pi$
$193$	3.81845	+	2.77426i	0.274858	+	0.199696i	−0.441814	+	0.897107i	$0.645665\pi$
$194$		0			0
$195$	3.15161	+	9.69965i	0.225691	+	0.694607i
$196$		0			0
$197$	15.1947			1.08258			0.541289	−	0.840837i	$-0.317937\pi$
$197$	15.1947			1.08258			0.541289	+	0.840837i	$0.317937\pi$
$198$		0			0
$199$	3.14455			0.222911			0.111456	−	0.993769i	$-0.464449\pi$
$199$	3.14455			0.222911			0.111456	+	0.993769i	$0.464449\pi$
$200$		0			0
$201$	−1.14313	−	3.51818i	−0.0806298	−	0.248153i
$202$		0			0
$203$	5.44640	+	3.95704i	0.382262	+	0.277730i
$204$		0			0
$205$	3.04930	−	9.38477i	0.212972	−	0.655461i
$206$		0			0
$207$	−36.6798	+	26.6494i	−2.54942	+	1.85226i
$208$		0			0
$209$	−12.3007	+	5.83689i	−0.850859	+	0.403746i
$210$		0			0
$211$	1.12722	−	0.818973i	0.0776010	−	0.0563804i	−0.548308	−	0.836276i	$-0.684728\pi$
$211$	1.12722	−	0.818973i	0.0776010	−	0.0563804i	0.625909	+	0.779896i	$0.284728\pi$
$212$		0			0
$213$	−2.94511	+	9.06411i	−0.201796	+	0.621063i
$214$		0			0
$215$	19.9663	+	14.5064i	1.36169	+	0.989326i
$216$		0			0
$217$	−2.39320	−	7.36550i	−0.162461	−	0.500003i
$218$		0			0
$219$	−50.0631			−3.38295
$220$		0			0
$221$	6.00545			0.403970
$222$		0			0
$223$	0.659030	+	2.02829i	0.0441319	+	0.135824i	0.970695	−	0.240316i	$-0.0772511\pi$
$223$	0.659030	+	2.02829i	0.0441319	+	0.135824i	−0.926563	+	0.376140i	$0.877251\pi$
$224$		0			0
$225$	−27.5514	−	20.0172i	−1.83676	−	1.33448i
$226$		0			0
$227$	0.411872	−	1.26761i	0.0273369	−	0.0841344i	−0.936457	−	0.350782i	$-0.885916\pi$
$227$	0.411872	−	1.26761i	0.0273369	−	0.0841344i	0.963794	+	0.266647i	$0.0859159\pi$
$228$		0			0
$229$	3.61788	−	2.62854i	0.239076	−	0.173699i	−0.461795	−	0.886986i	$-0.652795\pi$
$229$	3.61788	−	2.62854i	0.239076	−	0.173699i	0.700872	+	0.713287i	$0.252795\pi$
$230$		0			0
$231$	5.03399	+	38.8386i	0.331212	+	2.55539i
$232$		0			0
$233$	−23.4010	+	17.0018i	−1.53305	+	1.11383i	−0.578535	+	0.815657i	$0.696375\pi$
$233$	−23.4010	+	17.0018i	−1.53305	+	1.11383i	−0.954513	+	0.298168i	$0.903625\pi$
$234$		0			0
$235$	5.92395	−	18.2320i	0.386436	−	1.18933i
$236$		0			0
$237$	−1.05121	−	0.763750i	−0.0682836	−	0.0496109i
$238$		0			0
$239$	5.72031	+	17.6053i	0.370016	+	1.13879i	0.946780	+	0.321882i	$0.104315\pi$
$239$	5.72031	+	17.6053i	0.370016	+	1.13879i	−0.576764	+	0.816911i	$0.695685\pi$
$240$		0			0
$241$	−19.6851			−1.26803			−0.634014	−	0.773321i	$-0.718594\pi$
$241$	−19.6851			−1.26803			−0.634014	+	0.773321i	$0.718594\pi$
$242$		0			0
$243$	−77.0819			−4.94481
$244$		0			0
$245$	4.61964	+	14.2178i	0.295138	+	0.908341i
$246$		0			0
$247$	−3.32116	−	2.41296i	−0.211320	−	0.153533i
$248$		0			0
$249$	3.71620	−	11.4373i	0.235505	−	0.724808i
$250$		0			0
$251$	13.9185	−	10.1124i	0.878529	−	0.638289i	−0.0543331	−	0.998523i	$-0.517303\pi$
$251$	13.9185	−	10.1124i	0.878529	−	0.638289i	0.932862	+	0.360234i	$0.117303\pi$
$252$		0			0
$253$	−2.24167	−	17.2951i	−0.140933	−	1.08734i
$254$		0			0
$255$	−49.5510	+	36.0009i	−3.10301	+	2.25447i
$256$		0			0
$257$	0.278498	−	0.857128i	0.0173722	−	0.0534662i	−0.941995	−	0.335628i	$-0.891051\pi$
$257$	0.278498	−	0.857128i	0.0173722	−	0.0534662i	0.959367	+	0.282162i	$0.0910515\pi$
$258$		0			0
$259$	−21.1590	−	15.3729i	−1.31476	−	0.955226i
$260$		0			0
$261$	−5.17867	−	15.9383i	−0.320552	−	0.986557i
$262$		0			0
$263$	−1.15980			−0.0715166			−0.0357583	−	0.999360i	$-0.511385\pi$
$263$	−1.15980			−0.0715166			−0.0357583	+	0.999360i	$0.511385\pi$
$264$		0			0
$265$	19.8325			1.21830
$266$		0			0
$267$	−4.61629	−	14.2075i	−0.282512	−	0.869483i
$268$		0			0
$269$	−2.88333	−	2.09486i	−0.175800	−	0.127726i	0.496406	−	0.868091i	$-0.334653\pi$
$269$	−2.88333	−	2.09486i	−0.175800	−	0.127726i	−0.672205	+	0.740365i	$0.734653\pi$
$270$		0			0
$271$	−4.83159	+	14.8701i	−0.293498	+	0.903295i	0.690224	+	0.723596i	$0.257512\pi$
$271$	−4.83159	+	14.8701i	−0.293498	+	0.903295i	−0.983722	+	0.179698i	$0.942488\pi$
$272$		0			0
$273$	−9.55306	+	6.94071i	−0.578178	+	0.420071i
$274$		0			0
$275$	11.8348	−	5.61581i	0.713665	−	0.338646i
$276$		0			0
$277$	4.05839	−	2.94859i	0.243845	−	0.177164i	−0.459150	−	0.888359i	$-0.651846\pi$
$277$	4.05839	−	2.94859i	0.243845	−	0.177164i	0.702995	+	0.711195i	$0.251846\pi$
$278$		0			0
$279$	−5.95748	+	18.3353i	−0.356665	+	1.09770i
$280$		0			0
$281$	−19.0768	−	13.8601i	−1.13803	−	0.826826i	−0.151185	−	0.988506i	$-0.548309\pi$
$281$	−19.0768	−	13.8601i	−1.13803	−	0.826826i	−0.986843	+	0.161680i	$0.948309\pi$
$282$		0			0
$283$	−3.29531	−	10.1419i	−0.195886	−	0.602874i	−0.999965	−	0.00835214i	$-0.997341\pi$
$283$	−3.29531	−	10.1419i	−0.195886	−	0.602874i	0.804080	−	0.594522i	$-0.202659\pi$
$284$		0			0
$285$	41.8679			2.48004
$286$		0			0
$287$	11.4249			0.674390
$288$		0			0
$289$	5.89153	+	18.1323i	0.346561	+	1.06660i
$290$		0			0
$291$	16.3302	+	11.8646i	0.957294	+	0.695515i
$292$		0			0
$293$	−6.38461	+	19.6498i	−0.372993	+	1.14795i	0.571830	+	0.820372i	$0.306234\pi$
$293$	−6.38461	+	19.6498i	−0.372993	+	1.14795i	−0.944823	+	0.327582i	$0.893766\pi$
$294$		0			0
$295$	11.2026	−	8.13914i	0.652239	−	0.473879i
$296$		0			0
$297$	30.4453	−	55.8061i	1.76661	−	3.23820i
$298$		0			0
$299$	4.25406	−	3.09075i	0.246018	−	0.178743i
$300$		0			0
$301$	−8.82994	+	27.1757i	−0.508949	+	1.56638i
$302$		0			0
$303$	23.5941	+	17.1421i	1.35545	+	0.984790i
$304$		0			0
$305$	4.59772	+	14.1503i	0.263265	+	0.810246i
$306$		0			0
$307$	4.28073			0.244314			0.122157	−	0.992511i	$-0.461019\pi$
$307$	4.28073			0.244314			0.122157	+	0.992511i	$0.461019\pi$
$308$		0			0
$309$	−14.3614			−0.816990
$310$		0			0
$311$	−5.09798	−	15.6900i	−0.289080	−	0.889697i	−0.985146	−	0.171719i	$-0.945068\pi$
$311$	−5.09798	−	15.6900i	−0.289080	−	0.889697i	0.696066	−	0.717978i	$-0.254932\pi$
$312$		0			0
$313$	−19.2319	−	13.9728i	−1.08705	−	0.789790i	−0.108153	−	0.994134i	$-0.534494\pi$
$313$	−19.2319	−	13.9728i	−1.08705	−	0.789790i	−0.978899	+	0.204345i	$0.934494\pi$
$314$		0			0
$315$	27.6089	−	84.9713i	1.55558	−	4.78759i
$316$		0			0
$317$	−15.6900	+	11.3994i	−0.881238	+	0.640257i	−0.933579	−	0.358373i	$-0.883332\pi$
$317$	−15.6900	+	11.3994i	−0.881238	+	0.640257i	0.0523409	+	0.998629i	$0.483332\pi$
$318$		0			0
$319$	6.33597	+	1.18745i	0.354746	+	0.0664844i
$320$		0			0
$321$	−37.1319	+	26.9779i	−2.07250	+	1.50576i
$322$		0			0
$323$	7.61832	−	23.4468i	0.423895	−	1.30461i
$324$		0			0
$325$	3.19536	+	2.32156i	0.177247	+	0.128777i
$326$		0			0
$327$	−14.8389	−	45.6694i	−0.820593	−	2.52553i
$328$		0			0
$329$	22.1954			1.22367
$330$		0			0
$331$	1.19772			0.0658327			0.0329164	−	0.999458i	$-0.489521\pi$
$331$	1.19772			0.0658327			0.0329164	+	0.999458i	$0.489521\pi$
$332$		0			0
$333$	20.1189	+	61.9196i	1.10251	+	3.39317i
$334$		0			0
$335$	−2.62619	−	1.90804i	−0.143484	−	0.104247i
$336$		0			0
$337$	−6.70627	+	20.6398i	−0.365314	+	1.12432i	0.584470	+	0.811415i	$0.301302\pi$
$337$	−6.70627	+	20.6398i	−0.365314	+	1.12432i	−0.949784	+	0.312906i	$0.898698\pi$
$338$		0			0
$339$	−40.6126	+	29.5068i	−2.20577	+	1.60259i
$340$		0			0
$341$	−5.09385	−	5.38940i	−0.275847	−	0.291852i
$342$		0			0
$343$	5.61237	−	4.07762i	0.303039	−	0.220171i
$344$		0			0
$345$	−16.5721	+	51.0037i	−0.892212	+	2.74595i
$346$		0			0
$347$	5.78825	+	4.20541i	0.310729	+	0.225758i	0.732209	−	0.681080i	$-0.238489\pi$
$347$	5.78825	+	4.20541i	0.310729	+	0.225758i	−0.421480	+	0.906838i	$0.638489\pi$
$348$		0			0
$349$	−9.76700	−	30.0597i	−0.522815	−	1.60906i	−0.768596	−	0.639735i	$-0.779044\pi$
$349$	−9.76700	−	30.0597i	−0.522815	−	1.60906i	0.245781	−	0.969326i	$-0.420956\pi$
$350$		0			0
$351$	19.1673			1.02307
$352$		0			0
$353$	10.2675			0.546483			0.273242	−	0.961945i	$-0.411904\pi$
$353$	10.2675			0.546483			0.273242	+	0.961945i	$0.411904\pi$
$354$		0			0
$355$	2.58440	+	7.95395i	0.137165	+	0.422152i
$356$		0			0
$357$	−57.3704	−	41.6820i	−3.03636	−	2.20605i
$358$		0			0
$359$	4.57132	−	14.0691i	0.241265	−	0.742538i	−0.754963	−	0.655767i	$-0.772345\pi$
$359$	4.57132	−	14.0691i	0.241265	−	0.742538i	0.996228	−	0.0867708i	$-0.0276548\pi$
$360$		0			0
$361$	1.73739	−	1.26229i	0.0914418	−	0.0664364i
$362$		0			0
$363$	20.2980	+	31.5324i	1.06537	+	1.65502i
$364$		0			0
$365$	−35.5413	+	25.8223i	−1.86032	+	1.35160i
$366$		0			0
$367$	5.18323	−	15.9523i	0.270563	−	0.832706i	−0.719797	−	0.694185i	$-0.755765\pi$
$367$	5.18323	−	15.9523i	0.270563	−	0.832706i	0.990359	−	0.138521i	$-0.0442349\pi$
$368$		0			0
$369$	−23.0088	−	16.7169i	−1.19779	−	0.870246i
$370$		0			0
$371$	7.09570	+	21.8383i	0.368390	+	1.13379i
$372$		0			0
$373$	37.2795			1.93026			0.965130	−	0.261769i	$-0.0843060\pi$
$373$	37.2795			1.93026			0.965130	+	0.261769i	$0.0843060\pi$
$374$		0			0
$375$	10.7120			0.553166
$376$		0			0
$377$	0.600613	+	1.84850i	0.0309332	+	0.0952025i
$378$		0			0
$379$	−26.5166	−	19.2654i	−1.36206	−	0.989598i	−0.998311	−	0.0581031i	$-0.981495\pi$
$379$	−26.5166	−	19.2654i	−1.36206	−	0.989598i	−0.363754	−	0.931495i	$-0.618505\pi$
$380$		0			0
$381$	−1.60099	+	4.92735i	−0.0820213	+	0.252436i
$382$		0			0
$383$	−16.1534	+	11.7361i	−0.825400	+	0.599688i	−0.918254	−	0.395992i	$-0.870401\pi$
$383$	−16.1534	+	11.7361i	−0.825400	+	0.599688i	0.0928544	+	0.995680i	$0.470401\pi$
$384$		0			0
$385$	23.6065	+	24.9762i	1.20310	+	1.27290i
$386$		0			0
$387$	57.5463	−	41.8098i	2.92524	−	2.12531i
$388$		0			0
$389$	4.55284	−	14.0122i	0.230838	−	0.710446i	−0.766808	−	0.641876i	$-0.778156\pi$
$389$	4.55284	−	14.0122i	0.230838	−	0.710446i	0.997646	−	0.0685700i	$-0.0218437\pi$
$390$		0			0
$391$	25.5475	+	18.5613i	1.29199	+	0.938688i
$392$		0			0
$393$	−5.71311	−	17.5831i	−0.288188	−	0.886952i
$394$		0			0
$395$	−1.14022			−0.0573709
$396$		0			0
$397$	27.3620			1.37326			0.686629	−	0.727008i	$-0.259089\pi$
$397$	27.3620			1.37326			0.686629	+	0.727008i	$0.259089\pi$
$398$		0			0
$399$	14.9796	+	46.1024i	0.749916	+	2.30800i
$400$		0			0
$401$	−5.88104	−	4.27282i	−0.293685	−	0.213375i	0.431179	−	0.902266i	$-0.358098\pi$
$401$	−5.88104	−	4.27282i	−0.293685	−	0.213375i	−0.724864	+	0.688892i	$0.758098\pi$
$402$		0			0
$403$	0.690939	−	2.12649i	0.0344181	−	0.105928i
$404$		0			0
$405$	−95.5450	+	69.4175i	−4.74767	+	3.44938i
$406$		0			0
$407$	−24.6149	−	4.61318i	−1.22012	−	0.228667i
$408$		0			0
$409$	26.9102	−	19.5514i	1.33062	−	0.966755i	0.330891	−	0.943669i	$-0.392651\pi$
$409$	26.9102	−	19.5514i	1.33062	−	0.966755i	0.999733	−	0.0230861i	$-0.00734919\pi$
$410$		0			0
$411$	−7.71490	+	23.7440i	−0.380548	+	1.17121i
$412$		0			0
$413$	12.9704	+	9.42354i	0.638231	+	0.463702i
$414$		0			0
$415$	−3.26104	−	10.0365i	−0.160078	−	0.492670i
$416$		0			0
$417$	−9.95968			−0.487727
$418$		0			0
$419$	5.67635			0.277308			0.138654	−	0.990341i	$-0.455722\pi$
$419$	5.67635			0.277308			0.138654	+	0.990341i	$0.455722\pi$
$420$		0			0
$421$	1.34988	+	4.15452i	0.0657893	+	0.202479i	0.978547	−	0.206022i	$-0.0660518\pi$
$421$	1.34988	+	4.15452i	0.0657893	+	0.202479i	−0.912758	+	0.408501i	$0.866052\pi$
$422$		0			0
$423$	−44.6998	−	32.4763i	−2.17338	−	1.57905i
$424$		0			0
$425$	−7.32976	+	22.5587i	−0.355546	+	1.09426i
$426$		0			0
$427$	−13.9365	+	10.1254i	−0.674434	+	0.490005i
$428$		0			0
$429$	−5.41509	+	9.92583i	−0.261443	+	0.479224i
$430$		0			0
$431$	24.4882	−	17.7917i	1.17955	−	0.856996i	0.187433	−	0.982277i	$-0.439983\pi$
$431$	24.4882	−	17.7917i	1.17955	−	0.856996i	0.992121	+	0.125281i	$0.0399833\pi$
$432$		0			0
$433$	−3.99273	+	12.2884i	−0.191878	+	0.590541i	0.808120	+	0.589017i	$0.200485\pi$
$433$	−3.99273	+	12.2884i	−0.191878	+	0.590541i	−0.999999	+	0.00152375i	$0.999515\pi$
$434$		0			0
$435$	−16.0369	−	11.6515i	−0.768910	−	0.558646i
$436$		0			0
$437$	−6.67052	−	20.5297i	−0.319094	−	0.982071i
$438$		0			0
$439$	29.5168			1.40876			0.704380	−	0.709824i	$-0.251225\pi$
$439$	29.5168			1.40876			0.704380	+	0.709824i	$0.251225\pi$
$440$		0			0
$441$	43.0869			2.05176
$442$		0			0
$443$	−5.45019	−	16.7740i	−0.258946	−	0.796955i	−0.993026	−	0.117892i	$-0.962386\pi$
$443$	−5.45019	−	16.7740i	−0.258946	−	0.796955i	0.734080	−	0.679063i	$-0.237614\pi$
$444$		0			0
$445$	−10.6054	−	7.70525i	−0.502742	−	0.365264i
$446$		0			0
$447$	−1.05617	+	3.25056i	−0.0499551	+	0.153746i
$448$		0			0
$449$	13.1894	−	9.58270i	0.622449	−	0.452235i	−0.231327	−	0.972876i	$-0.574307\pi$
$449$	13.1894	−	9.58270i	0.622449	−	0.452235i	0.853776	+	0.520641i	$0.174307\pi$
$450$		0			0
$451$	9.88354	−	4.68990i	0.465397	−	0.220839i
$452$		0			0
$453$	1.89152	−	1.37427i	0.0888715	−	0.0645689i
$454$		0			0
$455$	−3.20203	+	9.85483i	−0.150113	+	0.462001i
$456$		0			0
$457$	16.7038	+	12.1361i	0.781373	+	0.567700i	0.905391	−	0.424579i	$-0.139578\pi$
$457$	16.7038	+	12.1361i	0.781373	+	0.567700i	−0.124018	+	0.992280i	$0.539578\pi$
$458$		0			0
$459$	35.5703	+	109.474i	1.66028	+	5.10982i
$460$		0			0
$461$	−4.54374			−0.211623			−0.105812	−	0.994386i	$-0.533744\pi$
$461$	−4.54374			−0.211623			−0.105812	+	0.994386i	$0.533744\pi$
$462$		0			0
$463$	25.0385			1.16364			0.581820	−	0.813318i	$-0.302341\pi$
$463$	25.0385			1.16364			0.581820	+	0.813318i	$0.302341\pi$
$464$		0			0
$465$	7.04676	+	21.6877i	0.326786	+	1.00574i
$466$		0			0
$467$	31.7046	+	23.0347i	1.46711	+	1.06592i	0.981438	+	0.191779i	$0.0614256\pi$
$467$	31.7046	+	23.0347i	1.46711	+	1.06592i	0.485674	+	0.874140i	$0.338574\pi$
$468$		0			0
$469$	1.16141	−	3.57446i	0.0536291	−	0.165053i
$470$		0			0
$471$	46.8068	−	34.0071i	2.15674	−	1.56697i
$472$		0			0
$473$	3.51693	+	27.1341i	0.161708	+	1.24763i
$474$		0			0
$475$	13.1175	−	9.53043i	0.601873	−	0.437286i
$476$		0			0
$477$	17.6636	−	54.3630i	0.808761	−	2.48911i
$478$		0			0
$479$	−4.34796	−	3.15898i	−0.198663	−	0.144337i	0.484006	−	0.875064i	$-0.339181\pi$
$479$	−4.34796	−	3.15898i	−0.198663	−	0.144337i	−0.682670	+	0.730727i	$0.739181\pi$
$480$		0			0
$481$	−2.33336	−	7.18133i	−0.106392	−	0.327440i
$482$		0			0
$483$	−62.0913			−2.82525
$484$		0			0
$485$	17.7130			0.804305
$486$		0			0
$487$	−0.0254728	−	0.0783974i	−0.00115428	−	0.00355252i	0.950478	−	0.310793i	$-0.100594\pi$
$487$	−0.0254728	−	0.0783974i	−0.00115428	−	0.00355252i	−0.951632	+	0.307240i	$0.900594\pi$
$488$		0			0
$489$	28.8108	+	20.9322i	1.30287	+	0.946589i
$490$		0			0
$491$	−9.04943	+	27.8513i	−0.408395	+	1.25691i	0.509632	+	0.860393i	$0.329782\pi$
$491$	−9.04943	+	27.8513i	−0.408395	+	1.25691i	−0.918027	+	0.396518i	$0.870218\pi$
$492$		0			0
$493$	−9.44312	+	6.86083i	−0.425297	+	0.308996i
$494$		0			0
$495$	−10.9965	−	84.8410i	−0.494256	−	3.81332i
$496$		0			0
$497$	−7.83375	+	5.69155i	−0.351392	+	0.255301i
$498$		0			0
$499$	8.46445	−	26.0509i	0.378921	−	1.16620i	−0.561874	−	0.827223i	$-0.689919\pi$
$499$	8.46445	−	26.0509i	0.378921	−	1.16620i	0.940795	−	0.338976i	$-0.110081\pi$
$500$		0			0
$501$	6.97831	+	5.07004i	0.311768	+	0.226513i
$502$		0			0
$503$	10.4457	+	32.1485i	0.465750	+	1.43343i	0.858037	+	0.513587i	$0.171684\pi$
$503$	10.4457	+	32.1485i	0.465750	+	1.43343i	−0.392288	+	0.919843i	$0.628316\pi$
$504$		0			0
$505$	25.5920			1.13883
$506$		0			0
$507$	−3.40915			−0.151406
$508$		0			0
$509$	3.17142	+	9.76062i	0.140571	+	0.432632i	0.996415	−	0.0846017i	$-0.0269618\pi$
$509$	3.17142	+	9.76062i	0.140571	+	0.432632i	−0.855844	+	0.517234i	$0.826962\pi$
$510$		0			0
$511$	−41.1498	−	29.8971i	−1.82036	−	1.32257i
$512$		0			0
$513$	24.3150	−	74.8339i	1.07353	−	3.30400i
$514$		0			0
$515$	−10.1956	+	7.40751i	−0.449270	+	0.326414i
$516$		0			0
$517$	19.2010	−	9.11119i	0.844459	−	0.400710i
$518$		0			0
$519$	41.1804	−	29.9193i	1.80762	−	1.31331i
$520$		0			0
$521$	4.53366	−	13.9532i	0.198623	−	0.611299i	−0.801292	−	0.598273i	$-0.795854\pi$
$521$	4.53366	−	13.9532i	0.198623	−	0.611299i	0.999915	−	0.0130257i	$-0.00414634\pi$
$522$		0			0
$523$	−33.2096	−	24.1282i	−1.45216	−	1.05505i	−0.985321	−	0.170709i	$-0.945394\pi$
$523$	−33.2096	−	24.1282i	−1.45216	−	1.05505i	−0.466835	−	0.884344i	$-0.654606\pi$
$524$		0			0
$525$	−14.4122	−	44.3561i	−0.628999	−	1.93586i
$526$		0			0
$527$	13.4277			0.584921
$528$		0			0
$529$	4.64974			0.202163
$530$		0			0
$531$	−12.3328	−	37.9565i	−0.535198	−	1.64717i
$532$		0			0
$533$	2.66852	+	1.93880i	0.115587	+	0.0839786i
$534$		0			0
$535$	−12.4460	+	38.3048i	−0.538087	+	1.65606i
$536$		0			0
$537$	−0.170794	+	0.124089i	−0.00737030	+	0.00535484i
$538$		0			0
$539$	−7.93746	+	14.5493i	−0.341890	+	0.626684i
$540$		0			0
$541$	−7.92704	+	5.75933i	−0.340810	+	0.247613i	−0.745003	−	0.667061i	$-0.767552\pi$
$541$	−7.92704	+	5.75933i	−0.340810	+	0.247613i	0.404194	+	0.914673i	$0.367552\pi$
$542$		0			0
$543$	22.7109	−	69.8970i	0.974619	−	2.99957i
$544$		0			0
$545$	−34.0906	−	24.7683i	−1.46028	−	1.06096i
$546$		0			0
$547$	8.64964	+	26.6208i	0.369832	+	1.13822i	0.946900	+	0.321529i	$0.104197\pi$
$547$	8.64964	+	26.6208i	0.369832	+	1.13822i	−0.577068	+	0.816696i	$0.695803\pi$
$548$		0			0
$549$	42.8825			1.83018
$550$		0			0
$551$	7.97892			0.339914
$552$		0			0
$553$	−0.407951	−	1.25554i	−0.0173478	−	0.0533912i
$554$		0			0
$555$	62.3026	+	45.2655i	2.64460	+	1.92141i
$556$		0			0
$557$	−10.1331	+	31.1865i	−0.429354	+	1.32141i	0.469410	+	0.882980i	$0.344467\pi$
$557$	−10.1331	+	31.1865i	−0.429354	+	1.32141i	−0.898763	+	0.438434i	$0.855533\pi$
$558$		0			0
$559$	−6.67412	+	4.84903i	−0.282285	+	0.205092i
$560$		0			0
$561$	−66.7408	−	12.5082i	−2.81780	−	0.528095i
$562$		0			0
$563$	29.2275	−	21.2350i	1.23179	−	0.894950i	0.234769	−	0.972051i	$-0.424567\pi$
$563$	29.2275	−	21.2350i	1.23179	−	0.894950i	0.997023	+	0.0771016i	$0.0245666\pi$
$564$		0			0
$565$	−13.6127	+	41.8954i	−0.572689	+	1.76255i
$566$		0			0
$567$	−110.622	−	80.3719i	−4.64570	−	3.37530i
$568$		0			0
$569$	−7.80481	−	24.0207i	−0.327195	−	1.00700i	−0.970440	−	0.241342i	$-0.922413\pi$
$569$	−7.80481	−	24.0207i	−0.327195	−	1.00700i	0.643246	−	0.765660i	$-0.277587\pi$
$570$		0			0
$571$	−20.2018			−0.845419			−0.422709	−	0.906265i	$-0.638921\pi$
$571$	−20.2018			−0.845419			−0.422709	+	0.906265i	$0.638921\pi$
$572$		0			0
$573$	−80.2937			−3.35432
$574$		0			0
$575$	6.41786	+	19.7521i	0.267643	+	0.823721i
$576$		0			0
$577$	−21.8639	−	15.8850i	−0.910206	−	0.661303i	0.0308613	−	0.999524i	$-0.490175\pi$
$577$	−21.8639	−	15.8850i	−0.910206	−	0.661303i	−0.941067	+	0.338221i	$0.890175\pi$
$578$		0			0
$579$	4.97230	−	15.3032i	0.206642	−	0.635978i
$580$		0			0
$581$	9.88478	−	7.18171i	0.410090	−	0.297948i
$582$		0			0
$583$	15.1030	+	15.9793i	0.625502	+	0.661794i
$584$		0			0
$585$	20.8682	−	15.1616i	0.862793	−	0.626856i
$586$		0			0
$587$	7.64878	−	23.5405i	0.315699	−	0.971622i	−0.659767	−	0.751471i	$-0.729345\pi$
$587$	7.64878	−	23.5405i	0.315699	−	0.971622i	0.975466	−	0.220151i	$-0.0706552\pi$
$588$		0			0
$589$	−7.42586	−	5.39520i	−0.305977	−	0.222305i
$590$		0			0
$591$	−16.0074	−	49.2657i	−0.658456	−	2.02652i
$592$		0			0
$593$	−9.38104			−0.385233			−0.192617	−	0.981274i	$-0.561697\pi$
$593$	−9.38104			−0.385233			−0.192617	+	0.981274i	$0.561697\pi$
$594$		0			0
$595$	−62.2283			−2.55111
$596$		0			0
$597$	−3.31274	−	10.1956i	−0.135581	−	0.417276i
$598$		0			0
$599$	−3.84874	−	2.79627i	−0.157255	−	0.114253i	0.506375	−	0.862313i	$-0.330985\pi$
$599$	−3.84874	−	2.79627i	−0.157255	−	0.114253i	−0.663630	+	0.748061i	$0.730985\pi$
$600$		0			0
$601$	−12.7397	+	39.2087i	−0.519662	+	1.59935i	0.254975	+	0.966948i	$0.417933\pi$
$601$	−12.7397	+	39.2087i	−0.519662	+	1.59935i	−0.774636	+	0.632407i	$0.782067\pi$
$602$		0			0
$603$	−7.56914	+	5.49930i	−0.308239	+	0.223949i
$604$		0			0
$605$	30.6744	+	11.9162i	1.24709	+	0.484461i
$606$		0			0
$607$	11.8903	−	8.63882i	0.482613	−	0.350639i	−0.319723	−	0.947511i	$-0.603590\pi$
$607$	11.8903	−	8.63882i	0.482613	−	0.350639i	0.802336	+	0.596872i	$0.203590\pi$
$608$		0			0
$609$	7.09219	−	21.8275i	0.287390	−	0.884495i
$610$		0			0
$611$	5.18421	+	3.76655i	0.209731	+	0.152378i
$612$		0			0
$613$	−9.18599	−	28.2716i	−0.371019	−	1.14188i	−0.946126	−	0.323800i	$-0.895039\pi$
$613$	−9.18599	−	28.2716i	−0.371019	−	1.14188i	0.575107	−	0.818078i	$-0.304961\pi$
$614$		0			0
$615$	−33.6406			−1.35652
$616$		0			0
$617$	32.3194			1.30113			0.650565	−	0.759450i	$-0.274532\pi$
$617$	32.3194			1.30113			0.650565	+	0.759450i	$0.274532\pi$
$618$		0			0
$619$	−7.12895	−	21.9406i	−0.286537	−	0.881869i	−0.985934	−	0.167136i	$-0.946548\pi$
$619$	−7.12895	−	21.9406i	−0.286537	−	0.881869i	0.699397	−	0.714733i	$-0.253452\pi$
$620$		0			0
$621$	81.5387	+	59.2413i	3.27203	+	2.37727i
$622$		0			0
$623$	4.69014	−	14.4348i	0.187906	−	0.578316i
$624$		0			0
$625$	23.5816	−	17.1330i	0.943263	−	0.685321i
$626$		0			0
$627$	31.8836	+	33.7335i	1.27331	+	1.34719i
$628$		0			0
$629$	36.6861	−	26.6540i	1.46277	−	1.06276i
$630$		0			0
$631$	8.58840	−	26.4324i	0.341899	−	1.05226i	−0.621324	−	0.783554i	$-0.713405\pi$
$631$	8.58840	−	26.4324i	0.341899	−	1.05226i	0.963223	−	0.268703i	$-0.0865951\pi$
$632$		0			0
$633$	−3.84286	−	2.79200i	−0.152740	−	0.110972i
$634$		0			0
$635$	1.40490	+	4.32385i	0.0557519	+	0.171587i
$636$		0			0
$637$	−4.99714			−0.197994
$638$		0			0
$639$	24.1044			0.953555
$640$		0			0
$641$	−10.3891	−	31.9743i	−0.410344	−	1.26291i	−0.916349	−	0.400380i	$-0.868878\pi$
$641$	−10.3891	−	31.9743i	−0.410344	−	1.26291i	0.506005	−	0.862531i	$-0.331122\pi$
$642$		0			0
$643$	5.53338	+	4.02024i	0.218215	+	0.158543i	0.691523	−	0.722354i	$-0.256940\pi$
$643$	5.53338	+	4.02024i	0.218215	+	0.158543i	−0.473308	+	0.880897i	$0.656940\pi$
$644$		0			0
$645$	25.9997	−	80.0189i	1.02374	−	3.15074i
$646$		0			0
$647$	−24.0429	+	17.4682i	−0.945224	+	0.686745i	−0.949672	−	0.313245i	$-0.898584\pi$
$647$	−24.0429	+	17.4682i	−0.945224	+	0.686745i	0.00444846	+	0.999990i	$0.498584\pi$
$648$		0			0
$649$	15.0889	+	2.82786i	0.592289	+	0.111003i
$650$		0			0
$651$	−21.3599	+	15.5189i	−0.837162	+	0.608234i
$652$		0			0
$653$	−0.998906	+	3.07432i	−0.0390902	+	0.120307i	−0.968697	−	0.248245i	$-0.920146\pi$
$653$	−0.998906	+	3.07432i	−0.0390902	+	0.120307i	0.929607	+	0.368552i	$0.120146\pi$
$654$		0			0
$655$	−13.1252	−	9.53601i	−0.512844	−	0.372603i
$656$		0			0
$657$	39.1271	+	120.421i	1.52649	+	4.69806i
$658$		0			0
$659$	−11.5331			−0.449264			−0.224632	−	0.974444i	$-0.572118\pi$
$659$	−11.5331			−0.449264			−0.224632	+	0.974444i	$0.572118\pi$
$660$		0			0
$661$	−41.0038			−1.59486			−0.797431	−	0.603410i	$-0.793808\pi$
$661$	−41.0038			−1.59486			−0.797431	+	0.603410i	$0.793808\pi$
$662$		0			0
$663$	−6.32665	−	19.4714i	−0.245707	−	0.756207i
$664$		0			0
$665$	34.4138	+	25.0031i	1.33451	+	0.969577i
$666$		0			0
$667$	−3.15821	+	9.71996i	−0.122286	+	0.376358i
$668$		0			0
$669$	5.88203	−	4.27354i	0.227412	−	0.165225i
$670$		0			0
$671$	−7.89980	+	14.4803i	−0.304968	+	0.559006i
$672$		0			0
$673$	−7.36681	+	5.35230i	−0.283970	+	0.206316i	−0.720647	−	0.693302i	$-0.756155\pi$
$673$	−7.36681	+	5.35230i	−0.283970	+	0.206316i	0.436677	+	0.899618i	$0.356155\pi$
$674$		0			0
$675$	−23.3940	+	71.9994i	−0.900436	+	2.77126i
$676$		0			0
$677$	9.01288	+	6.54824i	0.346393	+	0.251669i	0.747354	−	0.664426i	$-0.231324\pi$
$677$	9.01288	+	6.54824i	0.346393	+	0.251669i	−0.400961	+	0.916095i	$0.631324\pi$
$678$		0			0
$679$	6.33738	+	19.5044i	0.243206	+	0.748512i
$680$		0			0
$681$	−4.54387			−0.174122
$682$		0			0
$683$	22.0121			0.842271			0.421136	−	0.906998i	$-0.361632\pi$
$683$	22.0121			0.842271			0.421136	+	0.906998i	$0.361632\pi$
$684$		0			0
$685$	6.76999	+	20.8359i	0.258668	+	0.796098i
$686$		0			0
$687$	−12.3339	−	8.96109i	−0.470567	−	0.341887i
$688$		0			0
$689$	−2.04859	+	6.30493i	−0.0780452	+	0.240199i
$690$		0			0
$691$	30.5427	−	22.1906i	1.16190	−	0.844169i	0.171882	−	0.985118i	$-0.445015\pi$
$691$	30.5427	−	22.1906i	1.16190	−	0.844169i	0.990017	+	0.140948i	$0.0450152\pi$
$692$		0			0
$693$	89.4873	−	42.4632i	3.39934	−	1.61304i
$694$		0			0
$695$	−7.07067	+	5.13714i	−0.268206	+	0.194863i
$696$		0			0
$697$	−6.12126	+	18.8393i	−0.231859	+	0.713590i
$698$		0			0
$699$	79.7774	+	57.9617i	3.01746	+	2.19231i
$700$		0			0
$701$	0.839467	+	2.58361i	0.0317062	+	0.0975818i	0.965657	−	0.259819i	$-0.0836630\pi$
$701$	0.839467	+	2.58361i	0.0317062	+	0.0975818i	−0.933951	+	0.357401i	$0.883663\pi$
$702$		0			0
$703$	−30.9978			−1.16910
$704$		0			0
$705$	−65.3544			−2.46139
$706$		0			0
$707$	9.15633	+	28.1803i	0.344359	+	1.05983i
$708$		0			0
$709$	−17.2416	−	12.5268i	−0.647523	−	0.470453i	0.214904	−	0.976635i	$-0.431056\pi$
$709$	−17.2416	−	12.5268i	−0.647523	−	0.470453i	−0.862426	+	0.506182i	$0.831056\pi$
$710$		0			0
$711$	−1.01553	+	3.12548i	−0.0380853	+	0.117215i
$712$		0			0
$713$	9.51175	−	6.91069i	0.356218	−	0.258807i
$714$		0			0
$715$	1.27535	+	9.83971i	0.0476955	+	0.367984i
$716$		0			0
$717$	51.0553	−	37.0939i	1.90670	−	1.38530i
$718$		0			0
$719$	−8.48930	+	26.1274i	−0.316598	+	0.974387i	0.658494	+	0.752586i	$0.271194\pi$
$719$	−8.48930	+	26.1274i	−0.316598	+	0.974387i	−0.975092	+	0.221801i	$0.928806\pi$
$720$		0			0
$721$	−11.8045	−	8.57645i	−0.439621	−	0.319404i
$722$		0			0
$723$	20.7380	+	63.8249i	0.771253	+	2.37367i
$724$		0			0
$725$	−7.67670			−0.285106
$726$		0			0
$727$	−32.8448			−1.21815			−0.609073	−	0.793114i	$-0.708458\pi$
$727$	−32.8448			−1.21815			−0.609073	+	0.793114i	$0.708458\pi$
$728$		0			0
$729$	44.6073	+	137.287i	1.65212	+	5.08471i
$730$		0			0
$731$	−40.0811	−	29.1206i	−1.48245	−	1.07706i
$732$		0			0
$733$	0.589415	−	1.81403i	0.0217705	−	0.0670028i	−0.939581	−	0.342327i	$-0.888785\pi$
$733$	0.589415	−	1.81403i	0.0217705	−	0.0670028i	0.961352	+	0.275324i	$0.0887851\pi$
$734$		0			0
$735$	41.2315	−	29.9565i	1.52085	−	1.10496i
$736$		0			0
$737$	−0.462586	−	3.56898i	−0.0170396	−	0.131465i
$738$		0			0
$739$	−39.8399	+	28.9453i	−1.46553	+	1.06477i	−0.483654	+	0.875259i	$0.660691\pi$
$739$	−39.8399	+	28.9453i	−1.46553	+	1.06477i	−0.981878	+	0.189513i	$0.939309\pi$
$740$		0			0
$741$	−4.32474	+	13.3102i	−0.158873	+	0.488962i
$742$		0			0
$743$	−22.5275	−	16.3672i	−0.826453	−	0.600453i	0.0921005	−	0.995750i	$-0.470642\pi$
$743$	−22.5275	−	16.3672i	−0.826453	−	0.600453i	−0.918554	+	0.395296i	$0.870642\pi$
$744$		0			0
$745$	0.926812	+	2.85243i	0.0339558	+	0.104505i
$746$		0			0
$747$	−30.4154			−1.11284
$748$		0			0
$749$	−46.6318			−1.70389
$750$		0			0
$751$	−6.56733	−	20.2122i	−0.239645	−	0.737553i	−0.996471	−	0.0839360i	$-0.973251\pi$
$751$	−6.56733	−	20.2122i	−0.239645	−	0.737553i	0.756826	−	0.653617i	$-0.226749\pi$
$752$		0			0
$753$	−47.4503	−	34.4747i	−1.72919	−	1.25633i
$754$		0			0
$755$	0.634007	−	1.95127i	0.0230739	−	0.0710141i
$756$		0			0
$757$	−3.43065	+	2.49251i	−0.124689	+	0.0905919i	−0.648382	−	0.761315i	$-0.724554\pi$
$757$	−3.43065	+	2.49251i	−0.124689	+	0.0905919i	0.523693	+	0.851907i	$0.324554\pi$
$758$		0			0
$759$	−53.7144	+	25.4884i	−1.94971	+	0.925169i
$760$		0			0
$761$	10.6900	−	7.76675i	0.387513	−	0.281545i	−0.376923	−	0.926245i	$-0.623018\pi$
$761$	10.6900	−	7.76675i	0.387513	−	0.281545i	0.764436	+	0.644700i	$0.223018\pi$
$762$		0			0
$763$	15.0763	−	46.4000i	0.545798	−	1.67979i
$764$		0			0
$765$	125.323	+	91.0523i	4.53106	+	3.29200i
$766$		0			0
$767$	1.43034	+	4.40213i	0.0516465	+	0.158952i
$768$		0			0
$769$	33.1577			1.19570			0.597849	−	0.801609i	$-0.296022\pi$
$769$	33.1577			1.19570			0.597849	+	0.801609i	$0.296022\pi$
$770$		0			0
$771$	−3.07246			−0.110652
$772$		0			0
$773$	−10.9919	−	33.8297i	−0.395352	−	1.21677i	−0.928687	−	0.370864i	$-0.879062\pi$
$773$	−10.9919	−	33.8297i	−0.395352	−	1.21677i	0.533335	−	0.845904i	$-0.320938\pi$
$774$		0			0
$775$	7.14458	+	5.19084i	0.256641	+	0.186461i
$776$		0			0
$777$	−27.5528	+	84.7988i	−0.988452	+	3.04214i
$778$		0			0
$779$	10.9548	−	7.95910i	0.392495	−	0.285164i
$780$		0			0
$781$	−4.44050	+	8.13942i	−0.158894	+	0.291252i
$782$		0			0
$783$	−30.1391	+	21.8974i	−1.07708	+	0.782548i
$784$		0			0
$785$	15.6889	−	48.2853i	0.559959	−	1.72338i
$786$		0			0
$787$	−30.4888	−	22.1514i	−1.08681	−	0.789612i	−0.107951	−	0.994156i	$-0.534429\pi$
$787$	−30.4888	−	22.1514i	−1.08681	−	0.789612i	−0.978857	+	0.204544i	$0.934429\pi$
$788$		0			0
$789$	1.22184	+	3.76043i	0.0434985	+	0.133875i
$790$		0			0
$791$	−51.0030			−1.81346
$792$		0			0
$793$	−4.97344			−0.176612
$794$		0			0
$795$	−20.8932	−	64.3028i	−0.741007	−	2.28059i
$796$		0			0
$797$	12.3738	+	8.99007i	0.438301	+	0.318445i	0.784960	−	0.619547i	$-0.212684\pi$
$797$	12.3738	+	8.99007i	0.438301	+	0.318445i	−0.346658	+	0.937991i	$0.612684\pi$
$798$		0			0
$799$	−11.8919	+	36.5996i	−0.420706	+	1.29480i
$800$		0			0
$801$	−30.5665	+	22.2078i	−1.08001	+	0.784675i
$802$		0			0
$803$	−47.8709	−	8.97168i	−1.68933	−	0.316604i
$804$		0			0
$805$	−44.0804	+	32.0263i	−1.55363	+	1.12878i
$806$		0			0
$807$	−3.75461	+	11.5555i	−0.132169	+	0.406773i
$808$		0			0
$809$	−39.6630	−	28.8168i	−1.39448	−	1.01315i	−0.995358	−	0.0962458i	$-0.969317\pi$
$809$	−39.6630	−	28.8168i	−1.39448	−	1.01315i	−0.399118	−	0.916900i	$-0.630683\pi$
$810$		0			0
$811$	2.90313	+	8.93491i	0.101943	+	0.313747i	0.989001	−	0.147911i	$-0.0472548\pi$
$811$	2.90313	+	8.93491i	0.101943	+	0.313747i	−0.887058	+	0.461658i	$0.847255\pi$
$812$		0			0
$813$	53.3033			1.86943
$814$		0			0
$815$	31.2503			1.09465
$816$		0			0
$817$	10.4653	+	32.2088i	0.366133	+	1.12684i
$818$		0			0
$819$	24.1613	+	17.5542i	0.844263	+	0.613393i
$820$		0			0
$821$	1.07619	−	3.31216i	0.0375592	−	0.115595i	−0.930519	−	0.366243i	$-0.880644\pi$
$821$	1.07619	−	3.31216i	0.0375592	−	0.115595i	0.968078	+	0.250648i	$0.0806437\pi$
$822$		0			0
$823$	27.9472	−	20.3049i	0.974179	−	0.707783i	0.0177790	−	0.999842i	$-0.494340\pi$
$823$	27.9472	−	20.3049i	0.974179	−	0.707783i	0.956400	+	0.292059i	$0.0943405\pi$
$824$		0			0
$825$	−30.6759	−	32.4557i	−1.06800	−	1.12996i
$826$		0			0
$827$	−35.6396	+	25.8937i	−1.23931	+	0.900412i	−0.997552	−	0.0699244i	$-0.977724\pi$
$827$	−35.6396	+	25.8937i	−1.23931	+	0.900412i	−0.241759	+	0.970336i	$0.577724\pi$
$828$		0			0
$829$	−12.4675	+	38.3711i	−0.433015	+	1.33268i	0.462092	+	0.886832i	$0.347099\pi$
$829$	−12.4675	+	38.3711i	−0.433015	+	1.33268i	−0.895107	+	0.445851i	$0.852901\pi$
$830$		0			0
$831$	−13.8357	−	10.0522i	−0.479954	−	0.348707i
$832$		0			0
$833$	−9.27363	−	28.5413i	−0.321312	−	0.988897i
$834$		0			0
$835$	7.56920			0.261943
$836$		0			0
$837$	42.8566			1.48134
$838$		0			0
$839$	3.95832	+	12.1825i	0.136656	+	0.420585i	0.995844	−	0.0910757i	$-0.0290305\pi$
$839$	3.95832	+	12.1825i	0.136656	+	0.420585i	−0.859188	+	0.511661i	$0.829031\pi$
$840$		0			0
$841$	20.4053	+	14.8253i	0.703630	+	0.511217i
$842$		0			0
$843$	−24.8414	+	76.4541i	−0.855585	+	2.63322i
$844$		0			0
$845$	−2.42026	+	1.75842i	−0.0832594	+	0.0604915i
$846$		0			0
$847$	−2.14661	+	38.0401i	−0.0737585	+	1.30707i
$848$		0			0
$849$	−29.4115	+	21.3687i	−1.00940	+	0.733372i
$850$		0			0
$851$	12.2695	−	37.7616i	0.420593	−	1.29445i
$852$		0			0
$853$	8.64210	+	6.27886i	0.295900	+	0.214984i	0.725823	−	0.687882i	$-0.241459\pi$
$853$	8.64210	+	6.27886i	0.295900	+	0.214984i	−0.429923	+	0.902866i	$0.641459\pi$
$854$		0			0
$855$	−32.7221	−	100.708i	−1.11907	−	3.44415i
$856$		0			0
$857$	48.6806			1.66290			0.831449	−	0.555602i	$-0.187512\pi$
$857$	48.6806			1.66290			0.831449	+	0.555602i	$0.187512\pi$
$858$		0			0
$859$	17.7081			0.604193			0.302096	−	0.953277i	$-0.402314\pi$
$859$	17.7081			0.604193			0.302096	+	0.953277i	$0.402314\pi$
$860$		0			0
$861$	−12.0360	−	37.0429i	−0.410184	−	1.26242i
$862$		0			0
$863$	−9.25687	−	6.72551i	−0.315108	−	0.228939i	0.418977	−	0.907997i	$-0.362389\pi$
$863$	−9.25687	−	6.72551i	−0.315108	−	0.228939i	−0.734085	+	0.679058i	$0.762389\pi$
$864$		0			0
$865$	13.8030	−	42.4812i	0.469315	−	1.44440i
$866$		0			0
$867$	52.5835	−	38.2041i	1.78583	−	1.29748i
$868$		0			0
$869$	−0.868312	−	0.918692i	−0.0294555	−	0.0311645i
$870$		0			0
$871$	0.877856	−	0.637799i	0.0297450	−	0.0216110i
$872$		0			0
$873$	15.7759	−	48.5532i	0.533933	−	1.64328i
$874$		0			0
$875$	8.80484	+	6.39709i	0.297658	+	0.216261i
$876$		0			0
$877$	11.8934	+	36.6043i	0.401613	+	1.23604i	0.923690	+	0.383140i	$0.125157\pi$
$877$	11.8934	+	36.6043i	0.401613	+	1.23604i	−0.522077	+	0.852898i	$0.674843\pi$
$878$		0			0
$879$	70.4365			2.37576
$880$		0			0
$881$	17.7509			0.598044			0.299022	−	0.954246i	$-0.403340\pi$
$881$	17.7509			0.598044			0.299022	+	0.954246i	$0.403340\pi$
$882$		0			0
$883$	6.35750	+	19.5664i	0.213947	+	0.658461i	0.999227	+	0.0393197i	$0.0125191\pi$
$883$	6.35750	+	19.5664i	0.213947	+	0.658461i	−0.785280	+	0.619141i	$0.787481\pi$
$884$		0			0
$885$	−38.1912	−	27.7476i	−1.28378	−	0.932724i
$886$		0			0
$887$	−2.46718	+	7.59319i	−0.0828397	+	0.254954i	−0.983894	−	0.178751i	$-0.942794\pi$
$887$	−2.46718	+	7.59319i	−0.0828397	+	0.254954i	0.901055	+	0.433706i	$0.142794\pi$
$888$		0			0
$889$	−4.25851	+	3.09399i	−0.142826	+	0.103769i
$890$		0			0
$891$	−128.691	−	24.1184i	−4.31130	−	0.807997i
$892$		0			0
$893$	21.2821	−	15.4623i	0.712178	−	0.517428i
$894$		0			0
$895$	−0.0572473	+	0.176189i	−0.00191357	+	0.00588935i
$896$		0			0
$897$	−14.5027	−	10.5368i	−0.484232	−	0.351815i
$898$		0			0
$899$	1.34293	+	4.13310i	0.0447891	+	0.137847i
$900$		0			0
$901$	−39.8125			−1.32635
$902$		0			0
$903$	97.4140			3.24173
$904$		0			0
$905$	−19.9293	−	61.3361i	−0.662473	−	2.03888i
$906$		0			0
$907$	−13.6903	−	9.94658i	−0.454579	−	0.330271i	0.336822	−	0.941568i	$-0.390648\pi$
$907$	−13.6903	−	9.94658i	−0.454579	−	0.330271i	−0.791401	+	0.611298i	$0.790648\pi$
$908$		0			0
$909$	22.7932	−	70.1504i	0.756004	−	2.32674i
$910$		0			0
$911$	39.7583	−	28.8861i	1.31725	−	0.957039i	0.317290	−	0.948329i	$-0.397227\pi$
$911$	39.7583	−	28.8861i	1.31725	−	0.957039i	0.999962	−	0.00871069i	$-0.00277273\pi$
$912$		0			0
$913$	5.60312	−	10.2705i	0.185436	−	0.339904i
$914$		0			0
$915$	41.0359	−	29.8143i	1.35661	−	0.985632i
$916$		0			0
$917$	5.80451	−	17.8644i	0.191682	−	0.589936i
$918$		0			0
$919$	26.0649	+	18.9373i	0.859803	+	0.624684i	0.927831	−	0.373000i	$-0.121671\pi$
$919$	26.0649	+	18.9373i	0.859803	+	0.624684i	−0.0680283	+	0.997683i	$0.521671\pi$
$920$		0			0
$921$	−4.50969	−	13.8794i	−0.148599	−	0.457342i
$922$		0			0
$923$	−2.79559			−0.0920178
$924$		0			0
$925$	29.8236			0.980595
$926$		0			0
$927$	11.2242	+	34.5446i	0.368651	+	1.13459i
$928$		0			0
$929$	−18.6469	−	13.5478i	−0.611786	−	0.444489i	0.238257	−	0.971202i	$-0.423424\pi$
$929$	−18.6469	−	13.5478i	−0.611786	−	0.444489i	−0.850043	+	0.526714i	$0.823424\pi$
$930$		0			0
$931$	−6.33922	+	19.5101i	−0.207760	+	0.639418i
$932$		0			0
$933$	−45.5009	+	33.0583i	−1.48963	+	1.08228i
$934$		0			0
$935$	−53.8329	+	25.5446i	−1.76053	+	0.835398i
$936$		0			0
$937$	10.2922	−	7.47773i	0.336232	−	0.244287i	−0.406838	−	0.913500i	$-0.633369\pi$
$937$	10.2922	−	7.47773i	0.336232	−	0.244287i	0.743070	+	0.669213i	$0.233369\pi$
$938$		0			0
$939$	−25.0434	+	77.0757i	−0.817261	+	2.51527i
$940$		0			0
$941$	−23.8847	−	17.3532i	−0.778618	−	0.565699i	0.125946	−	0.992037i	$-0.459803\pi$
$941$	−23.8847	−	17.3532i	−0.778618	−	0.565699i	−0.904564	+	0.426338i	$0.859803\pi$
$942$		0			0
$943$	5.35971	+	16.4955i	0.174536	+	0.537167i
$944$		0			0
$945$	−198.611			−6.46081
$946$		0			0
$947$	−56.4744			−1.83517			−0.917585	−	0.397539i	$-0.869865\pi$
$947$	−56.4744			−1.83517			−0.917585	+	0.397539i	$0.869865\pi$
$948$		0			0
$949$	−4.53789	−	13.9662i	−0.147306	−	0.453362i
$950$		0			0
$951$	53.4895	+	38.8624i	1.73452	+	1.26020i
$952$		0			0
$953$	−9.02580	+	27.7786i	−0.292374	+	0.899836i	0.691716	+	0.722169i	$0.256855\pi$
$953$	−9.02580	+	27.7786i	−0.292374	+	0.899836i	−0.984091	+	0.177666i	$0.943145\pi$
$954$		0			0
$955$	−57.0029	+	41.4150i	−1.84457	+	1.34016i
$956$		0			0
$957$	−2.82479	−	21.7940i	−0.0913124	−	0.704501i
$958$		0			0
$959$	−20.5210	+	14.9094i	−0.662657	+	0.481449i
$960$		0			0
$961$	−8.03464	+	24.7281i	−0.259182	+	0.797680i
$962$		0			0
$963$	93.9127	+	68.2316i	3.02630	+	2.19873i
$964$		0			0
$965$	−4.36330	−	13.4289i	−0.140460	−	0.432290i
$966$		0			0
$967$	26.2505			0.844160			0.422080	−	0.906559i	$-0.361300\pi$
$967$	26.2505			0.844160			0.422080	+	0.906559i	$0.361300\pi$
$968$		0			0
$969$	−84.0472			−2.69998
$970$		0			0
$971$	−1.72461	−	5.30781i	−0.0553455	−	0.170336i	0.919563	−	0.392943i	$-0.128543\pi$
$971$	−1.72461	−	5.30781i	−0.0553455	−	0.170336i	−0.974908	+	0.222607i	$0.928543\pi$
$972$		0			0
$973$	−8.18645	−	5.94781i	−0.262446	−	0.190678i
$974$		0			0
$975$	4.16093	−	12.8060i	0.133256	−	0.410121i
$976$		0			0
$977$	−28.5293	+	20.7277i	−0.912733	+	0.663139i	−0.941705	−	0.336441i	$-0.890777\pi$
$977$	−28.5293	+	20.7277i	−0.912733	+	0.663139i	0.0289718	+	0.999580i	$0.490777\pi$
$978$		0			0
$979$	−1.86806	−	14.4126i	−0.0597035	−	0.460629i
$980$		0			0
$981$	−98.2549	+	71.3863i	−3.13704	+	2.27919i
$982$		0			0
$983$	17.9239	−	55.1641i	0.571683	−	1.75946i	−0.0755209	−	0.997144i	$-0.524062\pi$
$983$	17.9239	−	55.1641i	0.571683	−	1.75946i	0.647204	−	0.762317i	$-0.275938\pi$
$984$		0			0
$985$	−36.7751	−	26.7187i	−1.17175	−	0.851327i
$986$		0			0
$987$	−23.3826	−	71.9642i	−0.744276	−	2.29064i
$988$		0			0
$989$	−43.3792			−1.37938
$990$		0			0
$991$	27.6564			0.878534			0.439267	−	0.898357i	$-0.355238\pi$
$991$	27.6564			0.878534			0.439267	+	0.898357i	$0.355238\pi$
$992$		0			0
$993$	−1.26178	−	3.88337i	−0.0400414	−	0.123235i
$994$		0			0
$995$	−7.61062	−	5.52944i	−0.241273	−	0.175295i
$996$		0			0
$997$	−15.0404	+	46.2896i	−0.476334	+	1.46601i	0.367815	+	0.929899i	$0.380106\pi$
$997$	−15.0404	+	46.2896i	−0.476334	+	1.46601i	−0.844150	+	0.536107i	$0.819894\pi$
$998$		0			0
$999$	117.089	−	85.0702i	3.70454	−	2.69150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.b.157.1	✓	28
11.2	odd	10		6292.2.a.y.1.1		14
11.4	even	5	inner	572.2.n.b.521.1	yes	28
11.9	even	5		6292.2.a.z.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.b.157.1	✓	28	1.1	even	1	trivial
572.2.n.b.521.1	yes	28	11.4	even	5	inner
6292.2.a.y.1.1		14	11.2	odd	10
6292.2.a.z.1.1		14	11.9	even	5

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05349 - 3.24229i) q^{3} +(-2.42026 - 1.75842i) q^{5} +(1.07034 - 3.29416i) q^{7} +(-6.97559 + 5.06806i) q^{9} +O(q^{10})\)	\(q+(-1.05349 - 3.24229i) q^{3} +(-2.42026 - 1.75842i) q^{5} +(1.07034 - 3.29416i) q^{7} +(-6.97559 + 5.06806i) q^{9} +(-0.426312 - 3.28911i) q^{11} +(0.809017 - 0.587785i) q^{13} +(-3.15161 + 9.69965i) q^{15} +(4.85851 + 3.52991i) q^{17} +(-1.26857 - 3.90425i) q^{19} -11.8082 q^{21} +5.25830 q^{23} +(1.22052 + 3.75637i) q^{25} +(15.5067 + 11.2662i) q^{27} +(-0.600613 + 1.84850i) q^{29} +(1.80890 - 1.31424i) q^{31} +(-10.2152 + 4.84726i) q^{33} +(-8.38302 + 6.09062i) q^{35} +(2.33336 - 7.18133i) q^{37} +(-2.75806 - 2.00385i) q^{39} +(1.01929 + 3.13704i) q^{41} -8.24966 q^{43} +25.7945 q^{45} +(1.98019 + 6.09440i) q^{47} +(-4.04278 - 2.93725i) q^{49} +(6.32665 - 19.4714i) q^{51} +(-5.36329 + 3.89666i) q^{53} +(-4.75186 + 8.71013i) q^{55} +(-11.3223 + 8.22615i) q^{57} +(-1.43034 + 4.40213i) q^{59} +(-4.02359 - 2.92331i) q^{61} +(9.22879 + 28.4033i) q^{63} -2.99160 q^{65} +1.08509 q^{67} +(-5.53954 - 17.0490i) q^{69} +(-2.26168 - 1.64320i) q^{71} +(4.53789 - 13.9662i) q^{73} +(10.8935 - 7.91456i) q^{75} +(-11.2912 - 2.11612i) q^{77} +(0.308350 - 0.224030i) q^{79} +(12.1991 - 37.5451i) q^{81} +(2.85383 + 2.07343i) q^{83} +(-5.55177 - 17.0866i) q^{85} +6.62611 q^{87} +4.38192 q^{89} +(-1.07034 - 3.29416i) q^{91} +(-6.16682 - 4.48045i) q^{93} +(-3.79505 + 11.6800i) q^{95} +(-4.79011 + 3.48022i) q^{97} +(19.6432 + 20.7829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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