LMFDB - Embedded newform 1148.2.n.d.57.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			57.4
Character	$\chi$	$=$	1148.57
Dual form			1148.2.n.d.141.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.14291 q^{3} +(-1.88811 - 1.37180i) q^{5} +(0.309017 + 0.951057i) q^{7} -1.69375 q^{9} +O(q^{10})$	\(q+1.14291 q^{3} +(-1.88811 - 1.37180i) q^{5} +(0.309017 + 0.951057i) q^{7} -1.69375 q^{9} +(-1.48187 + 1.07664i) q^{11} +(-0.348317 + 1.07201i) q^{13} +(-2.15795 - 1.56784i) q^{15} +(-1.87008 + 1.35869i) q^{17} +(0.684060 + 2.10532i) q^{19} +(0.353179 + 1.08697i) q^{21} +(-1.08092 + 3.32674i) q^{23} +(0.138069 + 0.424932i) q^{25} -5.36454 q^{27} +(6.21745 + 4.51724i) q^{29} +(-7.82825 + 5.68755i) q^{31} +(-1.69365 + 1.23051i) q^{33} +(0.721196 - 2.21961i) q^{35} +(-4.87706 - 3.54339i) q^{37} +(-0.398095 + 1.22521i) q^{39} +(5.74276 - 2.83209i) q^{41} +(-2.98688 + 9.19267i) q^{43} +(3.19800 + 2.32348i) q^{45} +(-0.394042 + 1.21274i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-2.13733 + 1.55286i) q^{51} +(-9.49030 - 6.89511i) q^{53} +4.27489 q^{55} +(0.781820 + 2.40619i) q^{57} +(-0.0268701 + 0.0826976i) q^{59} +(2.19602 + 6.75864i) q^{61} +(-0.523399 - 1.61086i) q^{63} +(2.12824 - 1.54626i) q^{65} +(12.4813 + 9.06823i) q^{67} +(-1.23540 + 3.80216i) q^{69} +(8.95791 - 6.50830i) q^{71} -13.6494 q^{73} +(0.157800 + 0.485660i) q^{75} +(-1.48187 - 1.07664i) q^{77} -13.4658 q^{79} -1.04994 q^{81} -1.47244 q^{83} +5.39476 q^{85} +(7.10599 + 5.16281i) q^{87} +(0.511574 + 1.57446i) q^{89} -1.12718 q^{91} +(-8.94699 + 6.50037i) q^{93} +(1.59648 - 4.91347i) q^{95} +(6.26110 + 4.54895i) q^{97} +(2.50993 - 1.82357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	1.14291			0.659860			0.329930	−	0.944005i	$-0.392975\pi$
$3$	1.14291			0.659860			0.329930	+	0.944005i	$0.392975\pi$
$4$		0			0
$5$	−1.88811	−	1.37180i	−0.844391	−	0.613486i	0.0792031	−	0.996858i	$-0.474762\pi$
$5$	−1.88811	−	1.37180i	−0.844391	−	0.613486i	−0.923594	+	0.383373i	$0.874762\pi$
$6$		0			0
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$		0			0
$9$	−1.69375			−0.564584
$10$		0			0
$11$	−1.48187	+	1.07664i	−0.446802	+	0.324621i	−0.788332	−	0.615250i	$-0.789055\pi$
$11$	−1.48187	+	1.07664i	−0.446802	+	0.324621i	0.341530	+	0.939871i	$0.389055\pi$
$12$		0			0
$13$	−0.348317	+	1.07201i	−0.0966057	+	0.297322i	−0.987669	−	0.156558i	$-0.949960\pi$
$13$	−0.348317	+	1.07201i	−0.0966057	+	0.297322i	0.891063	+	0.453879i	$0.149960\pi$
$14$		0			0
$15$	−2.15795	−	1.56784i	−0.557180	−	0.404815i
$16$		0			0
$17$	−1.87008	+	1.35869i	−0.453560	+	0.329531i	−0.791000	−	0.611817i	$-0.790439\pi$
$17$	−1.87008	+	1.35869i	−0.453560	+	0.329531i	0.337440	+	0.941347i	$0.390439\pi$
$18$		0			0
$19$	0.684060	+	2.10532i	0.156934	+	0.482993i	0.998352	−	0.0573920i	$-0.0182785\pi$
$19$	0.684060	+	2.10532i	0.156934	+	0.482993i	−0.841418	+	0.540385i	$0.818278\pi$
$20$		0			0
$21$	0.353179	+	1.08697i	0.0770700	+	0.237197i
$22$		0			0
$23$	−1.08092	+	3.32674i	−0.225388	+	0.693672i	0.772864	+	0.634571i	$0.218823\pi$
$23$	−1.08092	+	3.32674i	−0.225388	+	0.693672i	−0.998252	+	0.0591009i	$0.981177\pi$
$24$		0			0
$25$	0.138069	+	0.424932i	0.0276138	+	0.0849864i
$26$		0			0
$27$	−5.36454			−1.03241
$28$		0			0
$29$	6.21745	+	4.51724i	1.15455	+	0.838830i	0.989079	−	0.147384i	$-0.0470853\pi$
$29$	6.21745	+	4.51724i	1.15455	+	0.838830i	0.165472	+	0.986215i	$0.447085\pi$
$30$		0			0
$31$	−7.82825	+	5.68755i	−1.40599	+	1.02151i	−0.412105	+	0.911136i	$0.635206\pi$
$31$	−7.82825	+	5.68755i	−1.40599	+	1.02151i	−0.993890	+	0.110379i	$0.964794\pi$
$32$		0			0
$33$	−1.69365	+	1.23051i	−0.294827	+	0.214204i
$34$		0			0
$35$	0.721196	−	2.21961i	0.121904	−	0.375183i
$36$		0			0
$37$	−4.87706	−	3.54339i	−0.801784	−	0.582530i	0.109653	−	0.993970i	$-0.465026\pi$
$37$	−4.87706	−	3.54339i	−0.801784	−	0.582530i	−0.911437	+	0.411440i	$0.865026\pi$
$38$		0			0
$39$	−0.398095	+	1.22521i	−0.0637462	+	0.196191i
$40$		0			0
$41$	5.74276	−	2.83209i	0.896868	−	0.442298i
$41$	5.74276	−	2.83209i	0.896868	−	0.442298i
$42$		0			0
$43$	−2.98688	+	9.19267i	−0.455495	+	1.40187i	0.415058	+	0.909795i	$0.363761\pi$
$43$	−2.98688	+	9.19267i	−0.455495	+	1.40187i	−0.870553	+	0.492074i	$0.836239\pi$
$44$		0			0
$45$	3.19800	+	2.32348i	0.476730	+	0.346364i
$46$		0			0
$47$	−0.394042	+	1.21274i	−0.0574769	+	0.176896i	−0.975673	−	0.219230i	$-0.929646\pi$
$47$	−0.394042	+	1.21274i	−0.0574769	+	0.176896i	0.918196	+	0.396126i	$0.129646\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$		0			0
$51$	−2.13733	+	1.55286i	−0.299286	+	0.217444i
$52$		0			0
$53$	−9.49030	−	6.89511i	−1.30359	−	0.947116i	−0.303610	−	0.952797i	$-0.598192\pi$
$53$	−9.49030	−	6.89511i	−1.30359	−	0.947116i	−0.999984	+	0.00568039i	$0.998192\pi$
$54$		0			0
$55$	4.27489			0.576426
$56$		0			0
$57$	0.781820	+	2.40619i	0.103555	+	0.318708i
$58$		0			0
$59$	−0.0268701	+	0.0826976i	−0.00349819	+	0.0107663i	−0.952790	−	0.303629i	$-0.901802\pi$
$59$	−0.0268701	+	0.0826976i	−0.00349819	+	0.0107663i	0.949292	+	0.314395i	$0.101802\pi$
$60$		0			0
$61$	2.19602	+	6.75864i	0.281171	+	0.865356i	0.987520	+	0.157492i	$0.0503409\pi$
$61$	2.19602	+	6.75864i	0.281171	+	0.865356i	−0.706349	+	0.707864i	$0.749659\pi$
$62$		0			0
$63$	−0.523399	−	1.61086i	−0.0659420	−	0.202949i
$64$		0			0
$65$	2.12824	−	1.54626i	0.263975	−	0.191789i
$66$		0			0
$67$	12.4813	+	9.06823i	1.52484	+	1.10786i	0.959023	+	0.283329i	$0.0914389\pi$
$67$	12.4813	+	9.06823i	1.52484	+	1.10786i	0.565816	+	0.824531i	$0.308561\pi$
$68$		0			0
$69$	−1.23540	+	3.80216i	−0.148724	+	0.457727i
$70$		0			0
$71$	8.95791	−	6.50830i	1.06311	−	0.772393i	0.0884473	−	0.996081i	$-0.471810\pi$
$71$	8.95791	−	6.50830i	1.06311	−	0.772393i	0.974661	+	0.223688i	$0.0718095\pi$
$72$		0			0
$73$	−13.6494			−1.59754			−0.798771	−	0.601635i	$-0.794516\pi$
$73$	−13.6494			−1.59754			−0.798771	+	0.601635i	$0.794516\pi$
$74$		0			0
$75$	0.157800	+	0.485660i	0.0182212	+	0.0560792i
$76$		0			0
$77$	−1.48187	−	1.07664i	−0.168875	−	0.122695i
$78$		0			0
$79$	−13.4658			−1.51502			−0.757512	−	0.652821i	$-0.773586\pi$
$79$	−13.4658			−1.51502			−0.757512	+	0.652821i	$0.773586\pi$
$80$		0			0
$81$	−1.04994			−0.116660
$82$		0			0
$83$	−1.47244			−0.161621			−0.0808105	−	0.996729i	$-0.525751\pi$
$83$	−1.47244			−0.161621			−0.0808105	+	0.996729i	$0.525751\pi$
$84$		0			0
$85$	5.39476			0.585144
$86$		0			0
$87$	7.10599	+	5.16281i	0.761842	+	0.553511i
$88$		0			0
$89$	0.511574	+	1.57446i	0.0542267	+	0.166893i	0.974502	−	0.224379i	$-0.0720353\pi$
$89$	0.511574	+	1.57446i	0.0542267	+	0.166893i	−0.920275	+	0.391272i	$0.872035\pi$
$90$		0			0
$91$	−1.12718			−0.118160
$92$		0			0
$93$	−8.94699	+	6.50037i	−0.927760	+	0.674057i
$94$		0			0
$95$	1.59648	−	4.91347i	0.163796	−	0.504112i
$96$		0			0
$97$	6.26110	+	4.54895i	0.635718	+	0.461876i	0.858377	−	0.513020i	$-0.171473\pi$
$97$	6.26110	+	4.54895i	0.635718	+	0.461876i	−0.222658	+	0.974897i	$0.571473\pi$
$98$		0			0
$99$	2.50993	−	1.82357i	0.252257	−	0.183276i
$100$		0			0
$101$	−3.46883	−	10.6760i	−0.345161	−	1.06230i	−0.961497	−	0.274814i	$-0.911384\pi$
$101$	−3.46883	−	10.6760i	−0.345161	−	1.06230i	0.616336	−	0.787483i	$-0.288616\pi$
$102$		0			0
$103$	−0.430786	−	1.32582i	−0.0424466	−	0.130637i	0.927587	−	0.373606i	$-0.121879\pi$
$103$	−0.430786	−	1.32582i	−0.0424466	−	0.130637i	−0.970034	+	0.242969i	$0.921879\pi$
$104$		0			0
$105$	0.824263	−	2.53682i	0.0804398	−	0.247568i
$106$		0			0
$107$	−4.62018	−	14.2194i	−0.446649	−	1.37465i	−0.880665	−	0.473740i	$-0.842904\pi$
$107$	−4.62018	−	14.2194i	−0.446649	−	1.37465i	0.434015	−	0.900906i	$-0.357096\pi$
$108$		0			0
$109$	−6.39357			−0.612393			−0.306197	−	0.951968i	$-0.599056\pi$
$109$	−6.39357			−0.612393			−0.306197	+	0.951968i	$0.599056\pi$
$110$		0			0
$111$	−5.57405	−	4.04978i	−0.529065	−	0.384388i
$112$		0			0
$113$	15.5025	−	11.2632i	1.45835	−	1.05955i	0.474564	−	0.880221i	$-0.342606\pi$
$113$	15.5025	−	11.2632i	1.45835	−	1.05955i	0.983788	−	0.179334i	$-0.0573942\pi$
$114$		0			0
$115$	6.60451	−	4.79845i	0.615873	−	0.447458i
$116$		0			0
$117$	0.589963	−	1.81572i	0.0545421	−	0.167863i
$118$		0			0
$119$	−1.87008	−	1.35869i	−0.171430	−	0.124551i
$120$		0			0
$121$	−2.36240	+	7.27072i	−0.214764	+	0.660974i
$122$		0			0
$123$	6.56346	−	3.23683i	0.591808	−	0.291855i
$124$		0			0
$125$	−3.28375	+	10.1063i	−0.293707	+	0.903938i
$126$		0			0
$127$	9.70447	+	7.05071i	0.861132	+	0.625649i	0.928193	−	0.372100i	$-0.121362\pi$
$127$	9.70447	+	7.05071i	0.861132	+	0.625649i	−0.0670606	+	0.997749i	$0.521362\pi$
$128$		0			0
$129$	−3.41374	+	10.5064i	−0.300563	+	0.925038i
$130$		0			0
$131$	−9.07876	+	6.59611i	−0.793215	+	0.576305i	−0.908916	−	0.416980i	$-0.863089\pi$
$131$	−9.07876	+	6.59611i	−0.793215	+	0.576305i	0.115701	+	0.993284i	$0.463089\pi$
$132$		0			0
$133$	−1.79089	+	1.30116i	−0.155290	+	0.112825i
$134$		0			0
$135$	10.1289	+	7.35906i	0.871755	+	0.633367i
$136$		0			0
$137$	−2.41346			−0.206196			−0.103098	−	0.994671i	$-0.532875\pi$
$137$	−2.41346			−0.206196			−0.103098	+	0.994671i	$0.532875\pi$
$138$		0			0
$139$	−6.37500	−	19.6202i	−0.540720	−	1.66417i	−0.730954	−	0.682427i	$-0.760924\pi$
$139$	−6.37500	−	19.6202i	−0.540720	−	1.66417i	0.190233	−	0.981739i	$-0.439076\pi$
$140$		0			0
$141$	−0.450355	+	1.38605i	−0.0379267	+	0.116727i
$142$		0			0
$143$	−0.638011	−	1.96360i	−0.0533532	−	0.164204i
$144$		0			0
$145$	−5.54252	−	17.0581i	−0.460282	−	1.41660i
$146$		0			0
$147$	−0.924635	+	0.671787i	−0.0762626	+	0.0554080i
$148$		0			0
$149$	−12.4380	−	9.03673i	−1.01896	−	0.740317i	−0.0528902	−	0.998600i	$-0.516843\pi$
$149$	−12.4380	−	9.03673i	−1.01896	−	0.740317i	−0.966069	+	0.258283i	$0.916843\pi$
$150$		0			0
$151$	0.245624	−	0.755954i	0.0199886	−	0.0615187i	−0.940565	−	0.339615i	$-0.889703\pi$
$151$	0.245624	−	0.755954i	0.0199886	−	0.0615187i	0.960553	+	0.278096i	$0.0897033\pi$
$152$		0			0
$153$	3.16745	−	2.30128i	0.256073	−	0.186048i
$154$		0			0
$155$	22.5828			1.81389
$156$		0			0
$157$	0.775709	+	2.38739i	0.0619083	+	0.190534i	0.977227	−	0.212196i	$-0.0680614\pi$
$157$	0.775709	+	2.38739i	0.0619083	+	0.190534i	−0.915319	+	0.402730i	$0.868061\pi$
$158$		0			0
$159$	−10.8466	−	7.88050i	−0.860190	−	0.624964i
$160$		0			0
$161$	−3.49794			−0.275676
$162$		0			0
$163$	18.6063			1.45736			0.728679	−	0.684855i	$-0.240135\pi$
$163$	18.6063			1.45736			0.728679	+	0.684855i	$0.240135\pi$
$164$		0			0
$165$	4.88582			0.380360
$166$		0			0
$167$	−16.7491			−1.29608			−0.648042	−	0.761604i	$-0.724412\pi$
$167$	−16.7491			−1.29608			−0.648042	+	0.761604i	$0.724412\pi$
$168$		0			0
$169$	9.48934	+	6.89441i	0.729949	+	0.530339i
$170$		0			0
$171$	−1.15863	−	3.56589i	−0.0886025	−	0.272691i
$172$		0			0
$173$	−1.64581			−0.125129			−0.0625644	−	0.998041i	$-0.519928\pi$
$173$	−1.64581			−0.125129			−0.0625644	+	0.998041i	$0.519928\pi$
$174$		0			0
$175$	−0.361469	+	0.262623i	−0.0273245	+	0.0198524i
$176$		0			0
$177$	−0.0307101	+	0.0945161i	−0.00230831	+	0.00710426i
$178$		0			0
$179$	5.32989	+	3.87239i	0.398375	+	0.289436i	0.768879	−	0.639395i	$-0.220815\pi$
$179$	5.32989	+	3.87239i	0.398375	+	0.289436i	−0.370504	+	0.928831i	$0.620815\pi$
$180$		0			0
$181$	−10.2352	+	7.43630i	−0.760775	+	0.552736i	−0.899148	−	0.437645i	$-0.855813\pi$
$181$	−10.2352	+	7.43630i	−0.760775	+	0.552736i	0.138373	+	0.990380i	$0.455813\pi$
$182$		0			0
$183$	2.50985	+	7.72453i	0.185534	+	0.571014i
$184$		0			0
$185$	4.34764	+	13.3807i	0.319645	+	0.983766i
$186$		0			0
$187$	1.30839	−	4.02681i	0.0956790	−	0.294470i
$188$		0			0
$189$	−1.65774	−	5.10199i	−0.120583	−	0.371115i
$190$		0			0
$191$	23.4642			1.69781			0.848904	−	0.528547i	$-0.177263\pi$
$191$	23.4642			1.69781			0.848904	+	0.528547i	$0.177263\pi$
$192$		0			0
$193$	3.39185	+	2.46432i	0.244151	+	0.177386i	0.703130	−	0.711061i	$-0.251785\pi$
$193$	3.39185	+	2.46432i	0.244151	+	0.177386i	−0.458980	+	0.888447i	$0.651785\pi$
$194$		0			0
$195$	2.43239	−	1.76723i	0.174187	−	0.126554i
$196$		0			0
$197$	−13.7208	+	9.96877i	−0.977569	+	0.710245i	−0.957164	−	0.289547i	$-0.906495\pi$
$197$	−13.7208	+	9.96877i	−0.977569	+	0.710245i	−0.0204047	+	0.999792i	$0.506495\pi$
$198$		0			0
$199$	3.61810	−	11.1354i	0.256480	−	0.789365i	−0.737054	−	0.675834i	$-0.763784\pi$
$199$	3.61810	−	11.1354i	0.256480	−	0.789365i	0.993534	−	0.113531i	$-0.0362163\pi$
$200$		0			0
$201$	14.2651	+	10.3642i	1.00618	+	0.731033i
$202$		0			0
$203$	−2.37485	+	7.30905i	−0.166682	+	0.512995i
$204$		0			0
$205$	−14.7280	−	2.53058i	−1.02865	−	0.176743i
$206$		0			0
$207$	1.83082	−	5.63467i	0.127250	−	0.391637i
$208$		0			0
$209$	−3.28037	−	2.38333i	−0.226908	−	0.164858i
$210$		0			0
$211$	−1.55261	+	4.77844i	−0.106886	+	0.328962i	−0.990168	−	0.139880i	$-0.955328\pi$
$211$	−1.55261	+	4.77844i	−0.106886	+	0.328962i	0.883282	+	0.468841i	$0.155328\pi$
$212$		0			0
$213$	10.2381	−	7.43841i	0.701503	−	0.509672i
$214$		0			0
$215$	18.2500	−	13.2594i	1.24464	−	0.904285i
$216$		0			0
$217$	−7.82825	−	5.68755i	−0.531416	−	0.386096i
$218$		0			0
$219$	−15.6001			−1.05416
$220$		0			0
$221$	−0.805148	−	2.47799i	−0.0541601	−	0.166688i
$222$		0			0
$223$	4.04176	−	12.4393i	0.270657	−	0.832995i	−0.719679	−	0.694307i	$-0.755711\pi$
$223$	4.04176	−	12.4393i	0.270657	−	0.832995i	0.990336	−	0.138689i	$-0.0442888\pi$
$224$		0			0
$225$	−0.233855	−	0.719730i	−0.0155903	−	0.0479820i
$226$		0			0
$227$	−2.99408	−	9.21484i	−0.198724	−	0.611610i	−0.999913	−	0.0131984i	$-0.995799\pi$
$227$	−2.99408	−	9.21484i	−0.198724	−	0.611610i	0.801189	−	0.598412i	$-0.204201\pi$
$228$		0			0
$229$	−20.3652	+	14.7962i	−1.34577	+	0.977759i	−0.346559	+	0.938028i	$0.612650\pi$
$229$	−20.3652	+	14.7962i	−1.34577	+	0.977759i	−0.999210	+	0.0397304i	$0.987350\pi$
$230$		0			0
$231$	−1.69365	−	1.23051i	−0.111434	−	0.0809616i
$232$		0			0
$233$	1.56148	−	4.80575i	0.102296	−	0.314835i	−0.886790	−	0.462172i	$-0.847070\pi$
$233$	1.56148	−	4.80575i	0.102296	−	0.314835i	0.989086	+	0.147337i	$0.0470702\pi$
$234$		0			0
$235$	2.40762	−	1.74924i	0.157056	−	0.114108i
$236$		0			0
$237$	−15.3903			−0.999705
$238$		0			0
$239$	1.98963	+	6.12345i	0.128698	+	0.396093i	0.994557	−	0.104196i	$-0.0332270\pi$
$239$	1.98963	+	6.12345i	0.128698	+	0.396093i	−0.865858	+	0.500289i	$0.833227\pi$
$240$		0			0
$241$	9.92632	+	7.21190i	0.639411	+	0.464559i	0.859648	−	0.510887i	$-0.170683\pi$
$241$	9.92632	+	7.21190i	0.639411	+	0.464559i	−0.220237	+	0.975446i	$0.570683\pi$
$242$		0			0
$243$	14.8936			0.955428
$244$		0			0
$245$	2.33384			0.149103
$246$		0			0
$247$	−2.49519			−0.158765
$248$		0			0
$249$	−1.68287			−0.106647
$250$		0			0
$251$	10.1725	+	7.39072i	0.642080	+	0.466498i	0.860564	−	0.509342i	$-0.170111\pi$
$251$	10.1725	+	7.39072i	0.642080	+	0.466498i	−0.218484	+	0.975840i	$0.570111\pi$
$252$		0			0
$253$	−1.97992	−	6.09357i	−0.124477	−	0.383100i
$254$		0			0
$255$	6.16573			0.386113
$256$		0			0
$257$	11.1209	−	8.07978i	0.693700	−	0.504003i	−0.184174	−	0.982894i	$-0.558961\pi$
$257$	11.1209	−	8.07978i	0.693700	−	0.504003i	0.877874	+	0.478891i	$0.158961\pi$
$258$		0			0
$259$	1.86287	−	5.73333i	0.115753	−	0.356252i
$260$		0			0
$261$	−10.5308	−	7.65109i	−0.651842	−	0.473591i
$262$		0			0
$263$	10.1728	−	7.39097i	0.627281	−	0.455747i	−0.228176	−	0.973620i	$-0.573276\pi$
$263$	10.1728	−	7.39097i	0.627281	−	0.455747i	0.855457	+	0.517873i	$0.173276\pi$
$264$		0			0
$265$	8.46010	+	26.0375i	0.519700	+	1.59947i
$266$		0			0
$267$	0.584684	+	1.79947i	0.0357821	+	0.110126i
$268$		0			0
$269$	1.94423	−	5.98373i	0.118542	−	0.364834i	−0.874127	−	0.485697i	$-0.838566\pi$
$269$	1.94423	−	5.98373i	0.118542	−	0.364834i	0.992669	+	0.120862i	$0.0385659\pi$
$270$		0			0
$271$	1.78290	+	5.48720i	0.108303	+	0.333324i	0.990492	−	0.137574i	$-0.0439303\pi$
$271$	1.78290	+	5.48720i	0.108303	+	0.333324i	−0.882188	+	0.470897i	$0.843930\pi$
$272$		0			0
$273$	−1.28826			−0.0779692
$274$		0			0
$275$	−0.662102	−	0.481045i	−0.0399262	−	0.0290081i
$276$		0			0
$277$	−21.8752	+	15.8933i	−1.31435	+	0.954935i	−0.314371	+	0.949300i	$0.601793\pi$
$277$	−21.8752	+	15.8933i	−1.31435	+	0.954935i	−0.999984	+	0.00563433i	$0.998207\pi$
$278$		0			0
$279$	13.2591	−	9.63331i	0.793803	−	0.576731i
$280$		0			0
$281$	3.72115	−	11.4525i	0.221985	−	0.683199i	−0.776599	−	0.629996i	$-0.783057\pi$
$281$	3.72115	−	11.4525i	0.221985	−	0.683199i	0.998584	−	0.0532038i	$-0.0169433\pi$
$282$		0			0
$283$	17.9820	+	13.0647i	1.06892	+	0.776616i	0.975718	−	0.219031i	$-0.0702896\pi$
$283$	17.9820	+	13.0647i	1.06892	+	0.776616i	0.0932026	+	0.995647i	$0.470290\pi$
$284$		0			0
$285$	1.82464	−	5.61567i	0.108082	−	0.332643i
$286$		0			0
$287$	4.46809	+	4.58652i	0.263743	+	0.270734i
$288$		0			0
$289$	−3.60214	+	11.0863i	−0.211891	+	0.652133i
$290$		0			0
$291$	7.15588	+	5.19905i	0.419485	+	0.304774i
$292$		0			0
$293$	1.98371	−	6.10522i	0.115889	−	0.356671i	−0.876242	−	0.481871i	$-0.839957\pi$
$293$	1.98371	−	6.10522i	0.115889	−	0.356671i	0.992131	+	0.125200i	$0.0399573\pi$
$294$		0			0
$295$	0.164178	−	0.119282i	0.00955881	−	0.00694489i
$296$		0			0
$297$	7.94958	−	5.77571i	0.461282	−	0.335141i
$298$		0			0
$299$	−3.18979	−	2.31751i	−0.184470	−	0.134025i
$300$		0			0
$301$	−9.66575			−0.557124
$302$		0			0
$303$	−3.96456	−	12.2017i	−0.227758	−	0.700968i
$304$		0			0
$305$	5.12515	−	15.7736i	0.293465	−	0.903193i
$306$		0			0
$307$	1.42076	+	4.37266i	0.0810872	+	0.249561i	0.983379	−	0.181565i	$-0.0581164\pi$
$307$	1.42076	+	4.37266i	0.0810872	+	0.249561i	−0.902292	+	0.431126i	$0.858116\pi$
$308$		0			0
$309$	−0.492351	−	1.51530i	−0.0280089	−	0.0862024i
$310$		0			0
$311$	1.57261	−	1.14257i	0.0891744	−	0.0647890i	−0.542305	−	0.840182i	$-0.682448\pi$
$311$	1.57261	−	1.14257i	0.0891744	−	0.0647890i	0.631479	+	0.775393i	$0.282448\pi$
$312$		0			0
$313$	−22.0560	−	16.0246i	−1.24668	−	0.905766i	−0.248655	−	0.968592i	$-0.579989\pi$
$313$	−22.0560	−	16.0246i	−1.24668	−	0.905766i	−0.998024	+	0.0628262i	$0.979989\pi$
$314$		0			0
$315$	−1.22153	+	3.75948i	−0.0688253	+	0.211822i
$316$		0			0
$317$	23.7135	−	17.2289i	1.33188	−	0.967669i	0.332181	−	0.943216i	$-0.392216\pi$
$317$	23.7135	−	17.2289i	1.33188	−	0.967669i	0.999701	−	0.0244532i	$-0.00778446\pi$
$318$		0			0
$319$	−14.0769			−0.788157
$320$		0			0
$321$	−5.28045	−	16.2516i	−0.294726	−	0.907074i
$322$		0			0
$323$	−4.13972	−	3.00768i	−0.230340	−	0.167352i
$324$		0			0
$325$	−0.503623			−0.0279360
$326$		0			0
$327$	−7.30729			−0.404094
$328$		0			0
$329$	−1.27515			−0.0703011
$330$		0			0
$331$	20.6927			1.13738			0.568688	−	0.822553i	$-0.307451\pi$
$331$	20.6927			1.13738			0.568688	+	0.822553i	$0.307451\pi$
$332$		0			0
$333$	8.26054	+	6.00163i	0.452675	+	0.328887i
$334$		0			0
$335$	−11.1265	−	34.2437i	−0.607903	−	1.87093i
$336$		0			0
$337$	19.5549			1.06522			0.532611	−	0.846360i	$-0.321211\pi$
$337$	19.5549			1.06522			0.532611	+	0.846360i	$0.321211\pi$
$338$		0			0
$339$	17.7180	−	12.8729i	0.962309	−	0.699158i
$340$		0			0
$341$	5.47700	−	16.8565i	0.296596	−	0.912830i
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$		0			0
$345$	7.54836	−	5.48421i	0.406390	−	0.295260i
$346$		0			0
$347$	7.28275	+	22.4140i	0.390959	+	1.20325i	0.932064	+	0.362292i	$0.118006\pi$
$347$	7.28275	+	22.4140i	0.390959	+	1.20325i	−0.541106	+	0.840955i	$0.681994\pi$
$348$		0			0
$349$	−10.7197	−	32.9918i	−0.573811	−	1.76601i	−0.640191	−	0.768216i	$-0.721145\pi$
$349$	−10.7197	−	32.9918i	−0.573811	−	1.76601i	0.0663798	−	0.997794i	$-0.478855\pi$
$350$		0			0
$351$	1.86856	−	5.75084i	0.0997364	−	0.306957i
$352$		0			0
$353$	0.533557	+	1.64212i	0.0283984	+	0.0874011i	0.964251	−	0.264990i	$-0.0853687\pi$
$353$	0.533557	+	1.64212i	0.0283984	+	0.0874011i	−0.935853	+	0.352391i	$0.885369\pi$
$354$		0			0
$355$	−25.8416			−1.37153
$356$		0			0
$357$	−2.13733	−	1.55286i	−0.113120	−	0.0821861i
$358$		0			0
$359$	−6.30583	+	4.58145i	−0.332809	+	0.241800i	−0.741621	−	0.670819i	$-0.765943\pi$
$359$	−6.30583	+	4.58145i	−0.332809	+	0.241800i	0.408813	+	0.912618i	$0.365943\pi$
$360$		0			0
$361$	11.4069	−	8.28759i	0.600363	−	0.436189i
$362$		0			0
$363$	−2.70001	+	8.30978i	−0.141714	+	0.436151i
$364$		0			0
$365$	25.7717	+	18.7242i	1.34895	+	0.980070i
$366$		0			0
$367$	5.28385	−	16.2620i	0.275815	−	0.848871i	−0.713188	−	0.700973i	$-0.752749\pi$
$367$	5.28385	−	16.2620i	0.275815	−	0.848871i	0.989003	−	0.147898i	$-0.0472506\pi$
$368$		0			0
$369$	−9.72682	+	4.79686i	−0.506358	+	0.249715i
$370$		0			0
$371$	3.62497	−	11.1565i	0.188199	−	0.579218i
$372$		0			0
$373$	−7.40164	−	5.37761i	−0.383242	−	0.278442i	0.379438	−	0.925217i	$-0.376117\pi$
$373$	−7.40164	−	5.37761i	−0.383242	−	0.278442i	−0.762681	+	0.646775i	$0.776117\pi$
$374$		0			0
$375$	−3.75303	+	11.5506i	−0.193806	+	0.596473i
$376$		0			0
$377$	−7.00816	+	5.09173i	−0.360939	+	0.262237i
$378$		0			0
$379$	7.02254	−	5.10217i	0.360724	−	0.262081i	−0.392630	−	0.919696i	$-0.628435\pi$
$379$	7.02254	−	5.10217i	0.360724	−	0.262081i	0.753354	+	0.657615i	$0.228435\pi$
$380$		0			0
$381$	11.0913	+	8.05833i	0.568227	+	0.412841i
$382$		0			0
$383$	−21.9116			−1.11963			−0.559815	−	0.828617i	$-0.689128\pi$
$383$	−21.9116			−1.11963			−0.559815	+	0.828617i	$0.689128\pi$
$384$		0			0
$385$	1.32101	+	4.06566i	0.0673250	+	0.207205i
$386$		0			0
$387$	5.05904	−	15.5701i	0.257165	−	0.791473i
$388$		0			0
$389$	−1.37652	−	4.23648i	−0.0697922	−	0.214798i	0.910077	−	0.414439i	$-0.136022\pi$
$389$	−1.37652	−	4.23648i	−0.0697922	−	0.214798i	−0.979869	+	0.199641i	$0.936022\pi$
$390$		0			0
$391$	−2.49859	−	7.68988i	−0.126359	−	0.388894i
$392$		0			0
$393$	−10.3762	+	7.53877i	−0.523411	+	0.380280i
$394$		0			0
$395$	25.4250	+	18.4724i	1.27927	+	0.929446i
$396$		0			0
$397$	2.08771	−	6.42532i	0.104779	−	0.322478i	−0.884899	−	0.465782i	$-0.845773\pi$
$397$	2.08771	−	6.42532i	0.104779	−	0.322478i	0.989679	+	0.143305i	$0.0457729\pi$
$398$		0			0
$399$	−2.04683	+	1.48711i	−0.102470	+	0.0744486i
$400$		0			0
$401$	−7.90623			−0.394818			−0.197409	−	0.980321i	$-0.563253\pi$
$401$	−7.90623			−0.394818			−0.197409	+	0.980321i	$0.563253\pi$
$402$		0			0
$403$	−3.37040	−	10.3730i	−0.167891	−	0.516717i
$404$		0			0
$405$	1.98241	+	1.44030i	0.0985065	+	0.0715692i
$406$		0			0
$407$	11.0422			0.547340
$408$		0			0
$409$	11.9788			0.592311			0.296156	−	0.955140i	$-0.404295\pi$
$409$	11.9788			0.592311			0.296156	+	0.955140i	$0.404295\pi$
$410$		0			0
$411$	−2.75837			−0.136060
$412$		0			0
$413$	−0.0869534			−0.00427870
$414$		0			0
$415$	2.78013	+	2.01988i	0.136471	+	0.0991521i
$416$		0			0
$417$	−7.28606	−	22.4242i	−0.356800	−	1.09812i
$418$		0			0
$419$	−20.1035			−0.982119			−0.491059	−	0.871126i	$-0.663390\pi$
$419$	−20.1035			−0.982119			−0.491059	+	0.871126i	$0.663390\pi$
$420$		0			0
$421$	−1.66685	+	1.21104i	−0.0812374	+	0.0590225i	−0.627663	−	0.778485i	$-0.715988\pi$
$421$	−1.66685	+	1.21104i	−0.0812374	+	0.0590225i	0.546425	+	0.837508i	$0.315988\pi$
$422$		0			0
$423$	0.667410	−	2.05408i	0.0324506	−	0.0998726i
$424$		0			0
$425$	−0.835550	−	0.607063i	−0.0405301	−	0.0294469i
$426$		0			0
$427$	−5.74925	+	4.17707i	−0.278225	+	0.202143i
$428$		0			0
$429$	−0.729190	−	2.24422i	−0.0352056	−	0.108352i
$430$		0			0
$431$	11.7040	+	36.0213i	0.563763	+	1.73508i	0.671600	+	0.740914i	$0.265608\pi$
$431$	11.7040	+	36.0213i	0.563763	+	1.73508i	−0.107837	+	0.994169i	$0.534392\pi$
$432$		0			0
$433$	−9.35052	+	28.7779i	−0.449357	+	1.38298i	0.428277	+	0.903648i	$0.359121\pi$
$433$	−9.35052	+	28.7779i	−0.449357	+	1.38298i	−0.877634	+	0.479332i	$0.840879\pi$
$434$		0			0
$435$	−6.33461	−	19.4959i	−0.303722	−	0.934759i
$436$		0			0
$437$	−7.74326			−0.370410
$438$		0			0
$439$	13.1895	+	9.58271i	0.629499	+	0.457358i	0.856227	−	0.516601i	$-0.172803\pi$
$439$	13.1895	+	9.58271i	0.629499	+	0.457358i	−0.226728	+	0.973958i	$0.572803\pi$
$440$		0			0
$441$	1.37028	−	0.995563i	0.0652512	−	0.0474078i
$442$		0			0
$443$	−28.5637	+	20.7528i	−1.35710	+	0.985994i	−0.358481	+	0.933537i	$0.616705\pi$
$443$	−28.5637	+	20.7528i	−1.35710	+	0.985994i	−0.998623	+	0.0524574i	$0.983295\pi$
$444$		0			0
$445$	1.19393	−	3.67454i	0.0565977	−	0.174190i
$446$		0			0
$447$	−14.2155	−	10.3282i	−0.672371	−	0.488506i
$448$		0			0
$449$	−6.82136	+	20.9940i	−0.321920	+	0.990768i	0.650892	+	0.759171i	$0.274395\pi$
$449$	−6.82136	+	20.9940i	−0.321920	+	0.990768i	−0.972812	+	0.231597i	$0.925605\pi$
$450$		0			0
$451$	−5.46089	+	10.3797i	−0.257143	+	0.488762i
$452$		0			0
$453$	0.280727	−	0.863988i	0.0131897	−	0.0405937i
$454$		0			0
$455$	2.12824	+	1.54626i	0.0997734	+	0.0724896i
$456$		0			0
$457$	−10.2483	+	31.5411i	−0.479397	+	1.47543i	0.360537	+	0.932745i	$0.382593\pi$
$457$	−10.2483	+	31.5411i	−0.479397	+	1.47543i	−0.839934	+	0.542688i	$0.817407\pi$
$458$		0			0
$459$	10.0321	−	7.28875i	0.468258	−	0.340210i
$460$		0			0
$461$	−30.6849	+	22.2939i	−1.42914	+	1.03833i	−0.438964	+	0.898505i	$0.644654\pi$
$461$	−30.6849	+	22.2939i	−1.42914	+	1.03833i	−0.990176	+	0.139826i	$0.955346\pi$
$462$		0			0
$463$	13.9783	+	10.1559i	0.649628	+	0.471983i	0.863145	−	0.504957i	$-0.168492\pi$
$463$	13.9783	+	10.1559i	0.649628	+	0.471983i	−0.213516	+	0.976940i	$0.568492\pi$
$464$		0			0
$465$	25.8101			1.19692
$466$		0			0
$467$	−3.65085	−	11.2362i	−0.168941	−	0.519947i	0.830364	−	0.557221i	$-0.188133\pi$
$467$	−3.65085	−	11.2362i	−0.168941	−	0.519947i	−0.999305	+	0.0372740i	$0.988133\pi$
$468$		0			0
$469$	−4.76745	+	14.6727i	−0.220140	+	0.677522i
$470$		0			0
$471$	0.886567	+	2.72857i	0.0408508	+	0.125726i
$472$		0			0
$473$	−5.47106	−	16.8382i	−0.251560	−	0.774221i
$474$		0			0
$475$	−0.800171	+	0.581358i	−0.0367143	+	0.0266745i
$476$		0			0
$477$	16.0742	+	11.6786i	0.735989	+	0.534727i
$478$		0			0
$479$	−2.66846	+	8.21268i	−0.121925	+	0.375247i	−0.993328	−	0.115321i	$-0.963210\pi$
$479$	−2.66846	+	8.21268i	−0.121925	+	0.375247i	0.871403	+	0.490567i	$0.163210\pi$
$480$		0			0
$481$	5.49731	−	3.99403i	0.250656	−	0.182112i
$482$		0			0
$483$	−3.99783			−0.181908
$484$		0			0
$485$	−5.58144	−	17.1779i	−0.253440	−	0.780008i
$486$		0			0
$487$	3.18040	+	2.31070i	0.144118	+	0.104708i	0.657508	−	0.753448i	$-0.271611\pi$
$487$	3.18040	+	2.31070i	0.144118	+	0.104708i	−0.513390	+	0.858155i	$0.671611\pi$
$488$		0			0
$489$	21.2654			0.961653
$490$		0			0
$491$	42.0384			1.89717			0.948583	−	0.316528i	$-0.102517\pi$
$491$	42.0384			1.89717			0.948583	+	0.316528i	$0.102517\pi$
$492$		0			0
$493$	−17.7646			−0.800078
$494$		0			0
$495$	−7.24060			−0.325441
$496$		0			0
$497$	8.95791	+	6.50830i	0.401817	+	0.291937i
$498$		0			0
$499$	4.98571	+	15.3444i	0.223191	+	0.686911i	0.998470	+	0.0552923i	$0.0176091\pi$
$499$	4.98571	+	15.3444i	0.223191	+	0.686911i	−0.775279	+	0.631618i	$0.782391\pi$
$500$		0			0
$501$	−19.1427			−0.855235
$502$		0			0
$503$	−31.9156	+	23.1880i	−1.42305	+	1.03390i	−0.431787	+	0.901976i	$0.642117\pi$
$503$	−31.9156	+	23.1880i	−1.42305	+	1.03390i	−0.991259	+	0.131928i	$0.957883\pi$
$504$		0			0
$505$	−8.09568	+	24.9160i	−0.360253	+	1.10875i
$506$		0			0
$507$	10.8455	+	7.87970i	0.481665	+	0.349950i
$508$		0			0
$509$	−25.0473	+	18.1980i	−1.11020	+	0.806611i	−0.982696	−	0.185227i	$-0.940698\pi$
$509$	−25.0473	+	18.1980i	−1.11020	+	0.806611i	−0.127508	+	0.991837i	$0.540698\pi$
$510$		0			0
$511$	−4.21790	−	12.9814i	−0.186589	−	0.574262i
$512$		0			0
$513$	−3.66967	−	11.2941i	−0.162020	−	0.498646i
$514$		0			0
$515$	−1.00539	+	3.09426i	−0.0443026	+	0.136349i
$516$		0			0
$517$	−0.721766	−	2.22137i	−0.0317432	−	0.0976956i
$518$		0			0
$519$	−1.88102			−0.0825676
$520$		0			0
$521$	29.5089	+	21.4395i	1.29281	+	0.939281i	0.999858	−	0.0168460i	$-0.00536251\pi$
$521$	29.5089	+	21.4395i	1.29281	+	0.939281i	0.292952	+	0.956127i	$0.405363\pi$
$522$		0			0
$523$	−15.4024	+	11.1905i	−0.673501	+	0.489327i	−0.871195	−	0.490937i	$-0.836655\pi$
$523$	−15.4024	+	11.1905i	−0.673501	+	0.489327i	0.197694	+	0.980264i	$0.436655\pi$
$524$		0			0
$525$	−0.413127	+	0.300154i	−0.0180303	+	0.0130998i
$526$		0			0
$527$	6.91179	−	21.2723i	0.301082	−	0.926636i
$528$		0			0
$529$	8.70861	+	6.32718i	0.378635	+	0.275095i
$530$		0			0
$531$	0.0455113	−	0.140069i	0.00197502	−	0.00607849i
$532$		0			0
$533$	1.03573	+	7.14275i	0.0448622	+	0.309387i
$534$		0			0
$535$	−10.7827	+	33.1859i	−0.466179	+	1.43475i
$536$		0			0
$537$	6.09159	+	4.42580i	0.262872	+	0.190987i
$538$		0			0
$539$	0.566026	−	1.74205i	0.0243805	−	0.0750353i
$540$		0			0
$541$	−18.7837	+	13.6471i	−0.807573	+	0.586736i	−0.913126	−	0.407678i	$-0.866339\pi$
$541$	−18.7837	+	13.6471i	−0.807573	+	0.586736i	0.105553	+	0.994414i	$0.466339\pi$
$542$		0			0
$543$	−11.6979	+	8.49903i	−0.502005	+	0.364728i
$544$		0			0
$545$	12.0718	+	8.77067i	0.517099	+	0.375694i
$546$		0			0
$547$	−16.0659			−0.686929			−0.343464	−	0.939166i	$-0.611601\pi$
$547$	−16.0659			−0.686929			−0.343464	+	0.939166i	$0.611601\pi$
$548$		0			0
$549$	−3.71951	−	11.4475i	−0.158745	−	0.488566i
$550$		0			0
$551$	−5.25713	+	16.1798i	−0.223961	+	0.689282i
$552$		0			0
$553$	−4.16117	−	12.8068i	−0.176951	−	0.544599i
$554$		0			0
$555$	4.96897	+	15.2929i	0.210921	+	0.649148i
$556$		0			0
$557$	−11.9198	+	8.66022i	−0.505057	+	0.366945i	−0.810945	−	0.585122i	$-0.801047\pi$
$557$	−11.9198	+	8.66022i	−0.505057	+	0.366945i	0.305888	+	0.952067i	$0.401047\pi$
$558$		0			0
$559$	−8.81424	−	6.40392i	−0.372803	−	0.270857i
$560$		0			0
$561$	1.49538	−	4.60229i	0.0631348	−	0.194309i
$562$		0			0
$563$	17.6460	−	12.8205i	0.743689	−	0.540321i	−0.150176	−	0.988659i	$-0.547984\pi$
$563$	17.6460	−	12.8205i	0.743689	−	0.540321i	0.893864	+	0.448338i	$0.147984\pi$
$564$		0			0
$565$	−44.7213			−1.88144
$566$		0			0
$567$	−0.324449	−	0.998552i	−0.0136256	−	0.0419352i
$568$		0			0
$569$	−3.82908	−	2.78199i	−0.160524	−	0.116627i	0.504624	−	0.863339i	$-0.331631\pi$
$569$	−3.82908	−	2.78199i	−0.160524	−	0.116627i	−0.665147	+	0.746712i	$0.731631\pi$
$570$		0			0
$571$	9.47170			0.396378			0.198189	−	0.980164i	$-0.436494\pi$
$571$	9.47170			0.396378			0.198189	+	0.980164i	$0.436494\pi$
$572$		0			0
$573$	26.8175			1.12032
$574$		0			0
$575$	−1.56288			−0.0651765
$576$		0			0
$577$	−43.1158			−1.79493			−0.897466	−	0.441083i	$-0.854594\pi$
$577$	−43.1158			−1.79493			−0.897466	+	0.441083i	$0.854594\pi$
$578$		0			0
$579$	3.87658	+	2.81650i	0.161105	+	0.117050i
$580$		0			0
$581$	−0.455008	−	1.40037i	−0.0188769	−	0.0580972i
$582$		0			0
$583$	21.4870			0.889902
$584$		0			0
$585$	−3.60471	+	2.61898i	−0.149036	+	0.108281i
$586$		0			0
$587$	−4.16538	+	12.8197i	−0.171923	+	0.529126i	−0.999480	−	0.0322570i	$-0.989731\pi$
$587$	−4.16538	+	12.8197i	−0.171923	+	0.529126i	0.827556	+	0.561383i	$0.189731\pi$
$588$		0			0
$589$	−17.3291	−	12.5903i	−0.714033	−	0.518776i
$590$		0			0
$591$	−15.6817	+	11.3934i	−0.645059	+	0.468663i
$592$		0			0
$593$	−2.10223	−	6.47001i	−0.0863284	−	0.265691i	0.898569	−	0.438833i	$-0.144608\pi$
$593$	−2.10223	−	6.47001i	−0.0863284	−	0.265691i	−0.984897	+	0.173142i	$0.944608\pi$
$594$		0			0
$595$	1.66707	+	5.13072i	0.0683433	+	0.210339i
$596$		0			0
$597$	4.13517	−	12.7267i	0.169241	−	0.520871i
$598$		0			0
$599$	0.824046	+	2.53615i	0.0336696	+	0.103624i	0.966479	−	0.256746i	$-0.0826504\pi$
$599$	0.824046	+	2.53615i	0.0336696	+	0.103624i	−0.932809	+	0.360370i	$0.882650\pi$
$600$		0			0
$601$	10.3654			0.422812			0.211406	−	0.977398i	$-0.432196\pi$
$601$	10.3654			0.422812			0.211406	+	0.977398i	$0.432196\pi$
$602$		0			0
$603$	−21.1403	−	15.3593i	−0.860900	−	0.625481i
$604$		0			0
$605$	14.4344	−	10.4872i	0.586842	−	0.426366i
$606$		0			0
$607$	−23.9797	+	17.4223i	−0.973306	+	0.707149i	−0.956203	−	0.292705i	$-0.905445\pi$
$607$	−23.9797	+	17.4223i	−0.973306	+	0.707149i	−0.0171037	+	0.999854i	$0.505445\pi$
$608$		0			0
$609$	−2.71425	+	8.35360i	−0.109987	+	0.338505i
$610$		0			0
$611$	−1.16281	−	0.844833i	−0.0470424	−	0.0341783i
$612$		0			0
$613$	−4.72158	+	14.5315i	−0.190703	+	0.586923i	−1.00000		0.000476535i	$-0.999848\pi$
$613$	−4.72158	+	14.5315i	−0.190703	+	0.586923i	0.809297	+	0.587400i	$0.199848\pi$
$614$		0			0
$615$	−16.8328	−	2.89223i	−0.678766	−	0.116626i
$616$		0			0
$617$	−4.86061	+	14.9594i	−0.195681	+	0.602243i	0.804287	+	0.594241i	$0.202547\pi$
$617$	−4.86061	+	14.9594i	−0.195681	+	0.602243i	−0.999968	+	0.00800248i	$0.997453\pi$
$618$		0			0
$619$	−28.2246	−	20.5064i	−1.13444	−	0.824222i	−0.148109	−	0.988971i	$-0.547319\pi$
$619$	−28.2246	−	20.5064i	−1.13444	−	0.824222i	−0.986336	+	0.164749i	$0.947319\pi$
$620$		0			0
$621$	5.79865	−	17.8464i	0.232692	−	0.716152i
$622$		0			0
$623$	−1.33932	+	0.973071i	−0.0536586	+	0.0389853i
$624$		0			0
$625$	21.8713	−	15.8904i	0.874851	−	0.635616i
$626$		0			0
$627$	−3.74918	−	2.72394i	−0.149728	−	0.108783i
$628$		0			0
$629$	13.9348			0.555618
$630$		0			0
$631$	7.17784	+	22.0911i	0.285745	+	0.879434i	0.986174	+	0.165712i	$0.0529922\pi$
$631$	7.17784	+	22.0911i	0.285745	+	0.879434i	−0.700429	+	0.713722i	$0.747008\pi$
$632$		0			0
$633$	−1.77450	+	5.46134i	−0.0705299	+	0.217069i
$634$		0			0
$635$	−8.65102	−	26.6251i	−0.343305	−	1.05658i
$636$		0			0
$637$	−0.348317	−	1.07201i	−0.0138008	−	0.0424745i
$638$		0			0
$639$	−15.1725	+	11.0235i	−0.600214	+	0.436081i
$640$		0			0
$641$	16.9114	+	12.2868i	0.667959	+	0.485301i	0.869341	−	0.494212i	$-0.164543\pi$
$641$	16.9114	+	12.2868i	0.667959	+	0.485301i	−0.201382	+	0.979513i	$0.564543\pi$
$642$		0			0
$643$	−9.55494	+	29.4071i	−0.376810	+	1.15970i	0.565439	+	0.824790i	$0.308707\pi$
$643$	−9.55494	+	29.4071i	−0.376810	+	1.15970i	−0.942249	+	0.334912i	$0.891293\pi$
$644$		0			0
$645$	20.8582	−	15.1544i	0.821290	−	0.596702i
$646$		0			0
$647$	−15.9453			−0.626874			−0.313437	−	0.949609i	$-0.601480\pi$
$647$	−15.9453			−0.626874			−0.313437	+	0.949609i	$0.601480\pi$
$648$		0			0
$649$	−0.0492179	−	0.151477i	−0.00193197	−	0.00594599i
$650$		0			0
$651$	−8.94699	−	6.50037i	−0.350660	−	0.254770i
$652$		0			0
$653$	12.1599			0.475853			0.237926	−	0.971283i	$-0.423532\pi$
$653$	12.1599			0.475853			0.237926	+	0.971283i	$0.423532\pi$
$654$		0			0
$655$	26.1903			1.02334
$656$		0			0
$657$	23.1187			0.901948
$658$		0			0
$659$	−19.4339			−0.757036			−0.378518	−	0.925594i	$-0.623566\pi$
$659$	−19.4339			−0.757036			−0.378518	+	0.925594i	$0.623566\pi$
$660$		0			0
$661$	16.7541	+	12.1725i	0.651657	+	0.473457i	0.863835	−	0.503774i	$-0.168056\pi$
$661$	16.7541	+	12.1725i	0.651657	+	0.473457i	−0.212178	+	0.977231i	$0.568056\pi$
$662$		0			0
$663$	−0.920213	−	2.83212i	−0.0357381	−	0.109991i
$664$		0			0
$665$	5.16633			0.200342
$666$		0			0
$667$	−21.7482	+	15.8010i	−0.842095	+	0.611818i
$668$		0			0
$669$	4.61938	−	14.2170i	0.178596	−	0.549661i
$670$		0			0
$671$	−10.5309	−	7.65113i	−0.406540	−	0.295369i
$672$		0			0
$673$	12.4027	−	9.01112i	0.478090	−	0.347353i	−0.322495	−	0.946571i	$-0.604522\pi$
$673$	12.4027	−	9.01112i	0.478090	−	0.347353i	0.800586	+	0.599218i	$0.204522\pi$
$674$		0			0
$675$	−0.740676	−	2.27957i	−0.0285086	−	0.0877406i
$676$		0			0
$677$	1.98178	+	6.09928i	0.0761658	+	0.234414i	0.981890	−	0.189454i	$-0.0606719\pi$
$677$	1.98178	+	6.09928i	0.0761658	+	0.234414i	−0.905724	+	0.423869i	$0.860672\pi$
$678$		0			0
$679$	−2.39153	+	7.36036i	−0.0917784	+	0.282465i
$680$		0			0
$681$	−3.42197	−	10.5317i	−0.131130	−	0.403577i
$682$		0			0
$683$	−29.8608			−1.14259			−0.571296	−	0.820744i	$-0.693559\pi$
$683$	−29.8608			−1.14259			−0.571296	+	0.820744i	$0.693559\pi$
$684$		0			0
$685$	4.55689	+	3.31077i	0.174110	+	0.126498i
$686$		0			0
$687$	−23.2756	+	16.9107i	−0.888020	+	0.645184i
$688$		0			0
$689$	10.6972	−	7.77201i	0.407533	−	0.296090i
$690$		0			0
$691$	3.37158	−	10.3767i	0.128261	−	0.394747i	−0.866220	−	0.499663i	$-0.833457\pi$
$691$	3.37158	−	10.3767i	0.128261	−	0.394747i	0.994481	+	0.104916i	$0.0334574\pi$
$692$		0			0
$693$	2.50993	+	1.82357i	0.0953444	+	0.0692717i
$694$		0			0
$695$	−14.8782	+	45.7904i	−0.564363	+	1.73693i
$696$		0			0
$697$	−6.89146	+	13.0988i	−0.261033	+	0.496154i
$698$		0			0
$699$	1.78464	−	5.49255i	0.0675012	−	0.207747i
$700$		0			0
$701$	5.39429	+	3.91918i	0.203739	+	0.148025i	0.684977	−	0.728565i	$-0.259812\pi$
$701$	5.39429	+	3.91918i	0.203739	+	0.148025i	−0.481237	+	0.876590i	$0.659812\pi$
$702$		0			0
$703$	4.12377	−	12.6917i	0.155531	−	0.478675i
$704$		0			0
$705$	2.75170	−	1.99923i	0.103635	−	0.0752953i
$706$		0			0
$707$	9.08151	−	6.59810i	0.341545	−	0.248147i
$708$		0			0
$709$	−7.28406	−	5.29218i	−0.273559	−	0.198752i	0.442544	−	0.896747i	$-0.354076\pi$
$709$	−7.28406	−	5.29218i	−0.273559	−	0.198752i	−0.716103	+	0.697995i	$0.754076\pi$
$710$		0			0
$711$	22.8078			0.855360
$712$		0			0
$713$	−10.4593	−	32.1903i	−0.391703	−	1.20554i
$714$		0			0
$715$	−1.48901	+	4.58271i	−0.0556860	+	0.171384i
$716$		0			0
$717$	2.27397	+	6.99856i	0.0849230	+	0.261366i
$718$		0			0
$719$	−6.16370	−	18.9699i	−0.229867	−	0.707459i	−0.997761	−	0.0668814i	$-0.978695\pi$
$719$	−6.16370	−	18.9699i	−0.229867	−	0.707459i	0.767894	−	0.640577i	$-0.221305\pi$
$720$		0			0
$721$	1.12781	−	0.819404i	0.0420020	−	0.0305162i
$722$		0			0
$723$	11.3449	+	8.24256i	0.421922	+	0.306544i
$724$		0			0
$725$	−1.06108	+	3.26568i	−0.0394077	+	0.121284i
$726$		0			0
$727$	18.9368	−	13.7584i	0.702327	−	0.510271i	−0.178362	−	0.983965i	$-0.557080\pi$
$727$	18.9368	−	13.7584i	0.702327	−	0.510271i	0.880689	+	0.473694i	$0.157080\pi$
$728$		0			0
$729$	20.1719			0.747109
$730$		0			0
$731$	−6.90429	−	21.2492i	−0.255364	−	0.785931i
$732$		0			0
$733$	−28.2165	−	20.5005i	−1.04220	−	0.757202i	−0.0714850	−	0.997442i	$-0.522774\pi$
$733$	−28.2165	−	20.5005i	−1.04220	−	0.757202i	−0.970713	+	0.240240i	$0.922774\pi$
$734$		0			0
$735$	2.66737			0.0983874
$736$		0			0
$737$	−28.2591			−1.04094
$738$		0			0
$739$	24.9062			0.916189			0.458094	−	0.888904i	$-0.348532\pi$
$739$	24.9062			0.916189			0.458094	+	0.888904i	$0.348532\pi$
$740$		0			0
$741$	−2.85178			−0.104763
$742$		0			0
$743$	4.59569	+	3.33897i	0.168600	+	0.122495i	0.668885	−	0.743366i	$-0.266772\pi$
$743$	4.59569	+	3.33897i	0.168600	+	0.122495i	−0.500286	+	0.865860i	$0.666772\pi$
$744$		0			0
$745$	11.0878	+	34.1247i	0.406226	+	1.25023i
$746$		0			0
$747$	2.49395			0.0912487
$748$		0			0
$749$	12.0958	−	8.78810i	0.441970	−	0.321110i
$750$		0			0
$751$	4.09213	−	12.5943i	0.149324	−	0.459572i	−0.848218	−	0.529648i	$-0.822324\pi$
$751$	4.09213	−	12.5943i	0.149324	−	0.459572i	0.997542	+	0.0700759i	$0.0223241\pi$
$752$		0			0
$753$	11.6262	+	8.44694i	0.423683	+	0.307824i
$754$		0			0
$755$	−1.50078	+	1.09038i	−0.0546190	+	0.0396830i
$756$		0			0
$757$	−6.90553	−	21.2530i	−0.250986	−	0.772455i	−0.994594	−	0.103839i	$-0.966887\pi$
$757$	−6.90553	−	21.2530i	−0.250986	−	0.772455i	0.743608	−	0.668615i	$-0.233113\pi$
$758$		0			0
$759$	−2.26288	−	6.96442i	−0.0821372	−	0.252792i
$760$		0			0
$761$	−1.59568	+	4.91098i	−0.0578432	+	0.178023i	−0.975804	−	0.218649i	$-0.929835\pi$
$761$	−1.59568	+	4.91098i	−0.0578432	+	0.178023i	0.917960	+	0.396672i	$0.129835\pi$
$762$		0			0
$763$	−1.97572	−	6.08065i	−0.0715260	−	0.220134i
$764$		0			0
$765$	−9.13739			−0.330363
$766$		0			0
$767$	−0.0792933	−	0.0576099i	−0.00286311	−	0.00208017i
$768$		0			0
$769$	−37.6708	+	27.3695i	−1.35844	+	0.986968i	−0.359903	+	0.932990i	$0.617190\pi$
$769$	−37.6708	+	27.3695i	−1.35844	+	0.986968i	−0.998542	+	0.0539783i	$0.982810\pi$
$770$		0			0
$771$	12.7102	−	9.23447i	0.457745	−	0.332571i
$772$		0			0
$773$	−10.9292	+	33.6365i	−0.393094	+	1.20982i	0.537341	+	0.843365i	$0.319429\pi$
$773$	−10.9292	+	33.6365i	−0.393094	+	1.20982i	−0.930436	+	0.366455i	$0.880571\pi$
$774$		0			0
$775$	−3.49766	−	2.54120i	−0.125640	−	0.0912826i
$776$		0			0
$777$	2.12910	−	6.55269i	0.0763809	−	0.235076i
$778$		0			0
$779$	9.89084	+	10.1530i	0.354376	+	0.363770i
$780$		0			0
$781$	−6.26737	+	19.2890i	−0.224264	+	0.690214i
$782$		0			0
$783$	−33.3538	−	24.2329i	−1.19197	−	0.866015i
$784$		0			0
$785$	1.81038	−	5.57178i	0.0646152	−	0.198865i
$786$		0			0
$787$	−5.23657	+	3.80459i	−0.186663	+	0.135619i	−0.677192	−	0.735806i	$-0.736804\pi$
$787$	−5.23657	+	3.80459i	−0.186663	+	0.135619i	0.490529	+	0.871425i	$0.336804\pi$
$788$		0			0
$789$	11.6266	−	8.44722i	0.413918	−	0.300729i
$790$		0			0
$791$	15.5025	+	11.2632i	0.551205	+	0.400474i
$792$		0			0
$793$	−8.01023			−0.284452
$794$		0			0
$795$	9.66915	+	29.7586i	0.342929	+	1.05543i
$796$		0			0
$797$	5.95812	−	18.3372i	0.211048	−	0.649538i	−0.788363	−	0.615210i	$-0.789071\pi$
$797$	5.95812	−	18.3372i	0.211048	−	0.649538i	0.999411	−	0.0343274i	$-0.0109289\pi$
$798$		0			0
$799$	−0.910844	−	2.80329i	−0.0322233	−	0.0991732i
$800$		0			0
$801$	−0.866480	−	2.66675i	−0.0306156	−	0.0942250i
$802$		0			0
$803$	20.2267	−	14.6956i	0.713785	−	0.518595i
$804$		0			0
$805$	6.60451	+	4.79845i	0.232778	+	0.169123i
$806$		0			0
$807$	2.22208	−	6.83887i	0.0782211	−	0.240740i
$808$		0			0
$809$	25.6953	−	18.6687i	0.903398	−	0.656357i	−0.0359385	−	0.999354i	$-0.511442\pi$
$809$	25.6953	−	18.6687i	0.903398	−	0.656357i	0.939337	+	0.342997i	$0.111442\pi$
$810$		0			0
$811$	29.4357			1.03363			0.516814	−	0.856097i	$-0.327118\pi$
$811$	29.4357			1.03363			0.516814	+	0.856097i	$0.327118\pi$
$812$		0			0
$813$	2.03770	+	6.27138i	0.0714651	+	0.219947i
$814$		0			0
$815$	−35.1308	−	25.5240i	−1.23058	−	0.894068i
$816$		0			0
$817$	−21.3967			−0.748576
$818$		0			0
$819$	1.90916			0.0667114
$820$		0			0
$821$	13.4039			0.467800			0.233900	−	0.972261i	$-0.424851\pi$
$821$	13.4039			0.467800			0.233900	+	0.972261i	$0.424851\pi$
$822$		0			0
$823$	0.326547			0.0113827			0.00569135	−	0.999984i	$-0.498188\pi$
$823$	0.326547			0.0113827			0.00569135	+	0.999984i	$0.498188\pi$
$824$		0			0
$825$	−0.756724	−	0.549792i	−0.0263457	−	0.0191413i
$826$		0			0
$827$	−10.3509	−	31.8568i	−0.359936	−	1.10777i	−0.953092	−	0.302681i	$-0.902118\pi$
$827$	−10.3509	−	31.8568i	−0.359936	−	1.10777i	0.593156	−	0.805087i	$-0.297882\pi$
$828$		0			0
$829$	−4.25920			−0.147928			−0.0739640	−	0.997261i	$-0.523565\pi$
$829$	−4.25920			−0.147928			−0.0739640	+	0.997261i	$0.523565\pi$
$830$		0			0
$831$	−25.0014	+	18.1646i	−0.867290	+	0.630123i
$832$		0			0
$833$	0.714305	−	2.19841i	0.0247492	−	0.0761702i
$834$		0			0
$835$	31.6242	+	22.9763i	1.09440	+	0.795129i
$836$		0			0
$837$	41.9950	−	30.5111i	1.45156	−	1.05462i
$838$		0			0
$839$	−11.7973	−	36.3083i	−0.407288	−	1.25350i	−0.918970	−	0.394328i	$-0.870977\pi$
$839$	−11.7973	−	36.3083i	−0.407288	−	1.25350i	0.511682	−	0.859175i	$-0.329023\pi$
$840$		0			0
$841$	9.28971	+	28.5908i	0.320335	+	0.985889i
$842$		0			0
$843$	4.25294	−	13.0892i	0.146479	−	0.450816i
$844$		0			0
$845$	−8.45924	−	26.0349i	−0.291007	−	0.895627i
$846$		0			0
$847$	−7.64488			−0.262681
$848$		0			0
$849$	20.5519	+	14.9318i	0.705338	+	0.512458i
$850$		0			0
$851$	17.0596	−	12.3946i	0.584797	−	0.424880i
$852$		0			0
$853$	10.8791	−	7.90416i	0.372495	−	0.270633i	−0.385750	−	0.922603i	$-0.626057\pi$
$853$	10.8791	−	7.90416i	0.372495	−	0.270633i	0.758245	+	0.651970i	$0.226057\pi$
$854$		0			0
$855$	−2.70405	+	8.32221i	−0.0924766	+	0.284614i
$856$		0			0
$857$	15.6787	+	11.3912i	0.535574	+	0.389118i	0.822439	−	0.568854i	$-0.192613\pi$
$857$	15.6787	+	11.3912i	0.535574	+	0.389118i	−0.286864	+	0.957971i	$0.592613\pi$
$858$		0			0
$859$	−15.2594	+	46.9637i	−0.520645	+	1.60238i	0.252126	+	0.967694i	$0.418870\pi$
$859$	−15.2594	+	46.9637i	−0.520645	+	1.60238i	−0.772771	+	0.634686i	$0.781130\pi$
$860$		0			0
$861$	5.10663	+	5.24199i	0.174033	+	0.178647i
$862$		0			0
$863$	−2.80747	+	8.64050i	−0.0955674	+	0.294126i	−0.987401	−	0.158237i	$-0.949419\pi$
$863$	−2.80747	+	8.64050i	−0.0955674	+	0.294126i	0.891834	+	0.452363i	$0.149419\pi$
$864$		0			0
$865$	3.10748	+	2.25772i	0.105658	+	0.0767648i
$866$		0			0
$867$	−4.11693	+	12.6706i	−0.139818	+	0.430317i
$868$		0			0
$869$	19.9547	−	14.4979i	0.676916	−	0.491808i
$870$		0			0
$871$	−14.0687	+	10.2215i	−0.476699	+	0.346342i
$872$		0			0
$873$	−10.6048	−	7.70481i	−0.358917	−	0.260768i
$874$		0			0
$875$	−10.6264			−0.359239
$876$		0			0
$877$	5.08680	+	15.6556i	0.171769	+	0.528650i	0.999471	−	0.0325171i	$-0.0103523\pi$
$877$	5.08680	+	15.6556i	0.171769	+	0.528650i	−0.827702	+	0.561168i	$0.810352\pi$
$878$		0			0
$879$	2.26720	−	6.97773i	0.0764708	−	0.235353i
$880$		0			0
$881$	9.62665	+	29.6278i	0.324330	+	0.998186i	0.971742	+	0.236045i	$0.0758514\pi$
$881$	9.62665	+	29.6278i	0.324330	+	0.998186i	−0.647412	+	0.762140i	$0.724149\pi$
$882$		0			0
$883$	3.99827	+	12.3054i	0.134553	+	0.414110i	0.995520	−	0.0945495i	$-0.0301411\pi$
$883$	3.99827	+	12.3054i	0.134553	+	0.414110i	−0.860968	+	0.508660i	$0.830141\pi$
$884$		0			0
$885$	0.187641	−	0.136329i	0.00630748	−	0.00458265i
$886$		0			0
$887$	43.8245	+	31.8403i	1.47148	+	1.06909i	0.980181	+	0.198103i	$0.0634781\pi$
$887$	43.8245	+	31.8403i	1.47148	+	1.06909i	0.491300	+	0.870990i	$0.336522\pi$
$888$		0			0
$889$	−3.70678	+	11.4083i	−0.124321	+	0.382622i
$890$		0			0
$891$	1.55588	−	1.13041i	0.0521239	−	0.0378702i
$892$		0			0
$893$	−2.82275			−0.0944596
$894$		0			0
$895$	−4.75131	−	14.6230i	−0.158819	−	0.488794i
$896$		0			0
$897$	−3.64564	−	2.64871i	−0.121724	−	0.0884380i
$898$		0			0
$899$	−74.3638			−2.48017
$900$		0			0
$901$	27.1159			0.903361
$902$		0			0
$903$	−11.0471			−0.367624
$904$		0			0
$905$	29.5263			0.981487
$906$		0			0
$907$	−24.3083	−	17.6610i	−0.807142	−	0.586423i	0.105858	−	0.994381i	$-0.466241\pi$
$907$	−24.3083	−	17.6610i	−0.807142	−	0.586423i	−0.913001	+	0.407958i	$0.866241\pi$
$908$		0			0
$909$	5.87534	+	18.0824i	0.194873	+	0.599757i
$910$		0			0
$911$	23.3178			0.772552			0.386276	−	0.922383i	$-0.373761\pi$
$911$	23.3178			0.772552			0.386276	+	0.922383i	$0.373761\pi$
$912$		0			0
$913$	2.18197	−	1.58529i	0.0722126	−	0.0524655i
$914$		0			0
$915$	5.85759	−	18.0278i	0.193646	−	0.595981i
$916$		0			0
$917$	−9.07876	−	6.59611i	−0.299807	−	0.217823i
$918$		0			0
$919$	−5.11575	+	3.71681i	−0.168753	+	0.122606i	−0.668956	−	0.743302i	$-0.733259\pi$
$919$	−5.11575	+	3.71681i	−0.168753	+	0.122606i	0.500203	+	0.865908i	$0.333259\pi$
$920$		0			0
$921$	1.62381	+	4.99756i	0.0535062	+	0.164675i
$922$		0			0
$923$	3.85677	+	11.8699i	0.126947	+	0.390703i
$924$		0			0
$925$	0.832331	−	2.56165i	0.0273669	−	0.0842266i
$926$		0			0
$927$	0.729646	+	2.24562i	0.0239647	+	0.0737558i
$928$		0			0
$929$	42.1654			1.38340			0.691701	−	0.722184i	$-0.256862\pi$
$929$	42.1654			1.38340			0.691701	+	0.722184i	$0.256862\pi$
$930$		0			0
$931$	−1.79089	−	1.30116i	−0.0586941	−	0.0426438i
$932$		0			0
$933$	1.79735	−	1.30585i	0.0588426	−	0.0427517i
$934$		0			0
$935$	−7.99436	+	5.80824i	−0.261443	+	0.189950i
$936$		0			0
$937$	3.47236	−	10.6868i	0.113437	−	0.349124i	−0.878181	−	0.478329i	$-0.841243\pi$
$937$	3.47236	−	10.6868i	0.113437	−	0.349124i	0.991618	+	0.129205i	$0.0412427\pi$
$938$		0			0
$939$	−25.2081	−	18.3147i	−0.822634	−	0.597679i
$940$		0			0
$941$	−7.01635	+	21.5941i	−0.228727	+	0.703948i	0.769165	+	0.639050i	$0.220672\pi$
$941$	−7.01635	+	21.5941i	−0.228727	+	0.703948i	−0.997892	+	0.0648982i	$0.979328\pi$
$942$		0			0
$943$	3.21414	+	22.1659i	0.104667	+	0.721821i
$944$		0			0
$945$	−3.86889	+	11.9072i	−0.125855	+	0.387341i
$946$		0			0
$947$	−36.6897	−	26.6566i	−1.19226	−	0.866224i	−0.198755	−	0.980049i	$-0.563690\pi$
$947$	−36.6897	−	26.6566i	−1.19226	−	0.866224i	−0.993501	+	0.113825i	$0.963690\pi$
$948$		0			0
$949$	4.75432	−	14.6323i	0.154332	−	0.474984i
$950$		0			0
$951$	27.1024	−	19.6911i	0.878856	−	0.638526i
$952$		0			0
$953$	22.1961	−	16.1264i	0.719001	−	0.522385i	−0.167064	−	0.985946i	$-0.553429\pi$
$953$	22.1961	−	16.1264i	0.719001	−	0.522385i	0.886065	+	0.463561i	$0.153429\pi$
$954$		0			0
$955$	−44.3030	−	32.1880i	−1.43361	−	1.04158i
$956$		0			0
$957$	−16.0887			−0.520074
$958$		0			0
$959$	−0.745800	−	2.29533i	−0.0240831	−	0.0741202i
$960$		0			0
$961$	19.3537	−	59.5644i	0.624311	−	1.92143i
$962$		0			0
$963$	7.82544	+	24.0842i	0.252171	+	0.776104i
$964$		0			0
$965$	−3.02365	−	9.30585i	−0.0973348	−	0.299566i
$966$		0			0
$967$	25.3869	−	18.4447i	0.816388	−	0.593140i	−0.0992878	−	0.995059i	$-0.531656\pi$
$967$	25.3869	−	18.4447i	0.816388	−	0.593140i	0.915676	+	0.401918i	$0.131656\pi$
$968$		0			0
$969$	−4.73133	−	3.43751i	−0.151992	−	0.110429i
$970$		0			0
$971$	−5.45065	+	16.7754i	−0.174920	+	0.538348i	−0.999630	−	0.0272082i	$-0.991338\pi$
$971$	−5.45065	+	16.7754i	−0.174920	+	0.538348i	0.824710	+	0.565556i	$0.191338\pi$
$972$		0			0
$973$	16.6900	−	12.1260i	0.535056	−	0.388741i
$974$		0			0
$975$	−0.575596			−0.0184338
$976$		0			0
$977$	−13.1766	−	40.5534i	−0.421557	−	1.29742i	−0.906253	−	0.422736i	$-0.861070\pi$
$977$	−13.1766	−	40.5534i	−0.421557	−	1.29742i	0.484696	−	0.874683i	$-0.338930\pi$
$978$		0			0
$979$	−2.45323	−	1.78237i	−0.0784054	−	0.0569649i
$980$		0			0
$981$	10.8291			0.345748
$982$		0			0
$983$	36.8991			1.17690			0.588449	−	0.808534i	$-0.299739\pi$
$983$	36.8991			1.17690			0.588449	+	0.808534i	$0.299739\pi$
$984$		0			0
$985$	39.5816			1.26117
$986$		0			0
$987$	−1.45738			−0.0463889
$988$		0			0
$989$	−27.3530	−	19.8731i	−0.869775	−	0.631928i
$990$		0			0
$991$	−2.59059	−	7.97301i	−0.0822928	−	0.253271i	0.901442	−	0.432901i	$-0.142510\pi$
$991$	−2.59059	−	7.97301i	−0.0822928	−	0.253271i	−0.983734	+	0.179630i	$0.942510\pi$
$992$		0			0
$993$	23.6500			0.750509
$994$		0			0
$995$	−22.1068	+	16.0616i	−0.700834	+	0.509186i
$996$		0			0
$997$	3.94865	−	12.1527i	0.125055	−	0.384880i	−0.868856	−	0.495065i	$-0.835144\pi$
$997$	3.94865	−	12.1527i	0.125055	−	0.384880i	0.993911	+	0.110185i	$0.0351443\pi$
$998$		0			0
$999$	26.1632	+	19.0087i	0.827767	+	0.601408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.d.57.4	✓	24
41.18	even	5	inner	1148.2.n.d.141.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.d.57.4	✓	24	1.1	even	1	trivial
1148.2.n.d.141.4	yes	24	41.18	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.14291 q^{3} +(-1.88811 - 1.37180i) q^{5} +(0.309017 + 0.951057i) q^{7} -1.69375 q^{9} +O(q^{10})\)	\(q+1.14291 q^{3} +(-1.88811 - 1.37180i) q^{5} +(0.309017 + 0.951057i) q^{7} -1.69375 q^{9} +(-1.48187 + 1.07664i) q^{11} +(-0.348317 + 1.07201i) q^{13} +(-2.15795 - 1.56784i) q^{15} +(-1.87008 + 1.35869i) q^{17} +(0.684060 + 2.10532i) q^{19} +(0.353179 + 1.08697i) q^{21} +(-1.08092 + 3.32674i) q^{23} +(0.138069 + 0.424932i) q^{25} -5.36454 q^{27} +(6.21745 + 4.51724i) q^{29} +(-7.82825 + 5.68755i) q^{31} +(-1.69365 + 1.23051i) q^{33} +(0.721196 - 2.21961i) q^{35} +(-4.87706 - 3.54339i) q^{37} +(-0.398095 + 1.22521i) q^{39} +(5.74276 - 2.83209i) q^{41} +(-2.98688 + 9.19267i) q^{43} +(3.19800 + 2.32348i) q^{45} +(-0.394042 + 1.21274i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-2.13733 + 1.55286i) q^{51} +(-9.49030 - 6.89511i) q^{53} +4.27489 q^{55} +(0.781820 + 2.40619i) q^{57} +(-0.0268701 + 0.0826976i) q^{59} +(2.19602 + 6.75864i) q^{61} +(-0.523399 - 1.61086i) q^{63} +(2.12824 - 1.54626i) q^{65} +(12.4813 + 9.06823i) q^{67} +(-1.23540 + 3.80216i) q^{69} +(8.95791 - 6.50830i) q^{71} -13.6494 q^{73} +(0.157800 + 0.485660i) q^{75} +(-1.48187 - 1.07664i) q^{77} -13.4658 q^{79} -1.04994 q^{81} -1.47244 q^{83} +5.39476 q^{85} +(7.10599 + 5.16281i) q^{87} +(0.511574 + 1.57446i) q^{89} -1.12718 q^{91} +(-8.94699 + 6.50037i) q^{93} +(1.59648 - 4.91347i) q^{95} +(6.26110 + 4.54895i) q^{97} +(2.50993 - 1.82357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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