LMFDB - Embedded newform 484.2.e.b.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,2,Mod(9,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("484.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.e (of order $5$, degree $4$, not 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:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	484.9
Dual form			484.2.e.b.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{3} +(-0.927051 - 2.85317i) q^{5} +(1.61803 + 1.17557i) q^{7} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.927051 - 2.85317i) q^{5} +(1.61803 + 1.17557i) q^{7} +(-0.618034 + 1.90211i) q^{9} +(1.23607 - 3.80423i) q^{13} +(2.42705 + 1.76336i) q^{15} +(-1.85410 - 5.70634i) q^{17} +(6.47214 - 4.70228i) q^{19} -2.00000 q^{21} -3.00000 q^{23} +(-3.23607 + 2.35114i) q^{25} +(-1.54508 - 4.75528i) q^{27} +(1.54508 - 4.75528i) q^{31} +(1.85410 - 5.70634i) q^{35} +(0.809017 + 0.587785i) q^{37} +(1.23607 + 3.80423i) q^{39} +10.0000 q^{43} +6.00000 q^{45} +(-0.927051 - 2.85317i) q^{49} +(4.85410 + 3.52671i) q^{51} +(-1.85410 + 5.70634i) q^{53} +(-2.47214 + 7.60845i) q^{57} +(-2.42705 - 1.76336i) q^{59} +(1.23607 + 3.80423i) q^{61} +(-3.23607 + 2.35114i) q^{63} -12.0000 q^{65} -1.00000 q^{67} +(2.42705 - 1.76336i) q^{69} +(4.63525 + 14.2658i) q^{71} +(-3.23607 - 2.35114i) q^{73} +(1.23607 - 3.80423i) q^{75} +(-0.618034 + 1.90211i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-1.85410 - 5.70634i) q^{83} +(-14.5623 + 10.5801i) q^{85} -9.00000 q^{89} +(6.47214 - 4.70228i) q^{91} +(1.54508 + 4.75528i) q^{93} +(-19.4164 - 14.1068i) q^{95} +(-2.16312 + 6.65740i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 3 q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q - q^3 + 3 * q^5 + 2 * q^7 + 2 * q^9	$ 4 q - q^{3} + 3 q^{5} + 2 q^{7} + 2 q^{9} - 4 q^{13} + 3 q^{15} + 6 q^{17} + 8 q^{19} - 8 q^{21} - 12 q^{23} - 4 q^{25} + 5 q^{27} - 5 q^{31} - 6 q^{35} + q^{37} - 4 q^{39} + 40 q^{43} + 24 q^{45} + 3 q^{49} + 6 q^{51} + 6 q^{53} + 8 q^{57} - 3 q^{59} - 4 q^{61} - 4 q^{63} - 48 q^{65} - 4 q^{67} + 3 q^{69} - 15 q^{71} - 4 q^{73} - 4 q^{75} + 2 q^{79} - q^{81} + 6 q^{83} - 18 q^{85} - 36 q^{89} + 8 q^{91} - 5 q^{93} - 24 q^{95} + 7 q^{97}+O(q^{100}) $ 4 * q - q^3 + 3 * q^5 + 2 * q^7 + 2 * q^9 - 4 * q^13 + 3 * q^15 + 6 * q^17 + 8 * q^19 - 8 * q^21 - 12 * q^23 - 4 * q^25 + 5 * q^27 - 5 * q^31 - 6 * q^35 + q^37 - 4 * q^39 + 40 * q^43 + 24 * q^45 + 3 * q^49 + 6 * q^51 + 6 * q^53 + 8 * q^57 - 3 * q^59 - 4 * q^61 - 4 * q^63 - 48 * q^65 - 4 * q^67 + 3 * q^69 - 15 * q^71 - 4 * q^73 - 4 * q^75 + 2 * q^79 - q^81 + 6 * q^83 - 18 * q^85 - 36 * q^89 + 8 * q^91 - 5 * q^93 - 24 * q^95 + 7 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i	−0.796305	−	0.604896i	$-0.793215\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i	0.329218	+	0.944254i	$0.393215\pi$
$4$		0			0
$5$	−0.927051	−	2.85317i	−0.414590	−	1.27598i	−0.912617	−	0.408815i	$-0.865942\pi$
$5$	−0.927051	−	2.85317i	−0.414590	−	1.27598i	0.498027	−	0.867161i	$-0.334058\pi$
$6$		0			0
$7$	1.61803	+	1.17557i	0.611559	+	0.444324i	0.849963	−	0.526842i	$-0.176624\pi$
$7$	1.61803	+	1.17557i	0.611559	+	0.444324i	−0.238404	+	0.971166i	$0.576624\pi$
$8$		0			0
$9$	−0.618034	+	1.90211i	−0.206011	+	0.634038i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	1.23607	−	3.80423i	0.342824	−	1.05510i	−0.619915	−	0.784669i	$-0.712833\pi$
$13$	1.23607	−	3.80423i	0.342824	−	1.05510i	0.962739	−	0.270434i	$-0.0871670\pi$
$14$		0			0
$15$	2.42705	+	1.76336i	0.626662	+	0.455296i
$16$		0			0
$17$	−1.85410	−	5.70634i	−0.449686	−	1.38399i	−0.877262	−	0.480011i	$-0.840633\pi$
$17$	−1.85410	−	5.70634i	−0.449686	−	1.38399i	0.427576	−	0.903979i	$-0.359367\pi$
$18$		0			0
$19$	6.47214	−	4.70228i	1.48481	−	1.07878i	0.508843	−	0.860859i	$-0.330073\pi$
$19$	6.47214	−	4.70228i	1.48481	−	1.07878i	0.975967	−	0.217918i	$-0.0699265\pi$
$20$		0			0
$21$	−2.00000			−0.436436
$22$		0			0
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$		0			0
$25$	−3.23607	+	2.35114i	−0.647214	+	0.470228i
$26$		0			0
$27$	−1.54508	−	4.75528i	−0.297352	−	0.915155i
$28$		0			0
$29$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$29$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$30$		0			0
$31$	1.54508	−	4.75528i	0.277505	−	0.854074i	−0.711040	−	0.703151i	$-0.751776\pi$
$31$	1.54508	−	4.75528i	0.277505	−	0.854074i	0.988546	−	0.150923i	$-0.0482244\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.85410	−	5.70634i	0.313400	−	0.964547i
$36$		0			0
$37$	0.809017	+	0.587785i	0.133002	+	0.0966313i	0.652297	−	0.757964i	$-0.273806\pi$
$37$	0.809017	+	0.587785i	0.133002	+	0.0966313i	−0.519295	+	0.854595i	$0.673806\pi$
$38$		0			0
$39$	1.23607	+	3.80423i	0.197929	+	0.609164i
$40$		0			0
$41$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$41$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$42$		0			0
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$		0			0
$45$	6.00000			0.894427
$46$		0			0
$47$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$47$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$48$		0			0
$49$	−0.927051	−	2.85317i	−0.132436	−	0.407596i
$50$		0			0
$51$	4.85410	+	3.52671i	0.679710	+	0.493838i
$52$		0			0
$53$	−1.85410	+	5.70634i	−0.254680	+	0.783826i	0.739212	+	0.673473i	$0.235198\pi$
$53$	−1.85410	+	5.70634i	−0.254680	+	0.783826i	−0.993892	+	0.110353i	$0.964802\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.47214	+	7.60845i	−0.327442	+	1.00776i
$58$		0			0
$59$	−2.42705	−	1.76336i	−0.315975	−	0.229569i	0.418481	−	0.908226i	$-0.362563\pi$
$59$	−2.42705	−	1.76336i	−0.315975	−	0.229569i	−0.734456	+	0.678656i	$0.762563\pi$
$60$		0			0
$61$	1.23607	+	3.80423i	0.158262	+	0.487081i	0.998477	−	0.0551729i	$-0.0175710\pi$
$61$	1.23607	+	3.80423i	0.158262	+	0.487081i	−0.840215	+	0.542254i	$0.817571\pi$
$62$		0			0
$63$	−3.23607	+	2.35114i	−0.407706	+	0.296216i
$64$		0			0
$65$	−12.0000			−1.48842
$66$		0			0
$67$	−1.00000			−0.122169			−0.0610847	−	0.998133i	$-0.519456\pi$
$67$	−1.00000			−0.122169			−0.0610847	+	0.998133i	$0.519456\pi$
$68$		0			0
$69$	2.42705	−	1.76336i	0.292183	−	0.212283i
$70$		0			0
$71$	4.63525	+	14.2658i	0.550104	+	1.69304i	0.708536	+	0.705675i	$0.249356\pi$
$71$	4.63525	+	14.2658i	0.550104	+	1.69304i	−0.158432	+	0.987370i	$0.550644\pi$
$72$		0			0
$73$	−3.23607	−	2.35114i	−0.378753	−	0.275180i	0.382078	−	0.924130i	$-0.375209\pi$
$73$	−3.23607	−	2.35114i	−0.378753	−	0.275180i	−0.760831	+	0.648950i	$0.775209\pi$
$74$		0			0
$75$	1.23607	−	3.80423i	0.142729	−	0.439274i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.618034	+	1.90211i	−0.0695343	+	0.214004i	−0.979785	−	0.200053i	$-0.935889\pi$
$79$	−0.618034	+	1.90211i	−0.0695343	+	0.214004i	0.910251	+	0.414057i	$0.135889\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	−1.85410	−	5.70634i	−0.203514	−	0.626352i	−0.999771	−	0.0213936i	$-0.993190\pi$
$83$	−1.85410	−	5.70634i	−0.203514	−	0.626352i	0.796257	−	0.604959i	$-0.206810\pi$
$84$		0			0
$85$	−14.5623	+	10.5801i	−1.57950	+	1.14758i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$		0			0
$91$	6.47214	−	4.70228i	0.678464	−	0.492933i
$92$		0			0
$93$	1.54508	+	4.75528i	0.160218	+	0.493100i
$94$		0			0
$95$	−19.4164	−	14.1068i	−1.99208	−	1.44733i
$96$		0			0
$97$	−2.16312	+	6.65740i	−0.219631	+	0.675956i	0.779161	+	0.626824i	$0.215646\pi$
$97$	−2.16312	+	6.65740i	−0.219631	+	0.675956i	−0.998792	+	0.0491321i	$0.984354\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.56231	+	17.1190i	−0.553470	+	1.70341i	0.146480	+	0.989214i	$0.453206\pi$
$101$	−5.56231	+	17.1190i	−0.553470	+	1.70341i	−0.699950	+	0.714192i	$0.746794\pi$
$102$		0			0
$103$	−6.47214	−	4.70228i	−0.637719	−	0.463330i	0.221347	−	0.975195i	$-0.428955\pi$
$103$	−6.47214	−	4.70228i	−0.637719	−	0.463330i	−0.859066	+	0.511865i	$0.828955\pi$
$104$		0			0
$105$	1.85410	+	5.70634i	0.180942	+	0.556882i
$106$		0			0
$107$	4.85410	−	3.52671i	0.469264	−	0.340940i	−0.327891	−	0.944716i	$-0.606338\pi$
$107$	4.85410	−	3.52671i	0.469264	−	0.340940i	0.797154	+	0.603776i	$0.206338\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	−1.00000			−0.0949158
$112$		0			0
$113$	12.1353	−	8.81678i	1.14159	−	0.829413i	0.154249	−	0.988032i	$-0.450704\pi$
$113$	12.1353	−	8.81678i	1.14159	−	0.829413i	0.987340	+	0.158619i	$0.0507042\pi$
$114$		0			0
$115$	2.78115	+	8.55951i	0.259344	+	0.798178i
$116$		0			0
$117$	6.47214	+	4.70228i	0.598349	+	0.434726i
$118$		0			0
$119$	3.70820	−	11.4127i	0.339930	−	1.04620i
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.42705	−	1.76336i	−0.217082	−	0.157719i
$126$		0			0
$127$	4.94427	+	15.2169i	0.438733	+	1.35028i	0.889212	+	0.457495i	$0.151253\pi$
$127$	4.94427	+	15.2169i	0.438733	+	1.35028i	−0.450479	+	0.892787i	$0.648747\pi$
$128$		0			0
$129$	−8.09017	+	5.87785i	−0.712300	+	0.517516i
$130$		0			0
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$		0			0
$133$	16.0000			1.38738
$134$		0			0
$135$	−12.1353	+	8.81678i	−1.04444	+	0.758827i
$136$		0			0
$137$	2.78115	+	8.55951i	0.237610	+	0.731288i	0.996764	+	0.0803778i	$0.0256127\pi$
$137$	2.78115	+	8.55951i	0.237610	+	0.731288i	−0.759155	+	0.650910i	$0.774387\pi$
$138$		0			0
$139$	11.3262	+	8.22899i	0.960679	+	0.697974i	0.953308	−	0.301999i	$-0.0976538\pi$
$139$	11.3262	+	8.22899i	0.960679	+	0.697974i	0.00737063	+	0.999973i	$0.497654\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.42705	+	1.76336i	0.200180	+	0.145439i
$148$		0			0
$149$	−1.85410	−	5.70634i	−0.151894	−	0.467482i	0.845939	−	0.533280i	$-0.179041\pi$
$149$	−1.85410	−	5.70634i	−0.151894	−	0.467482i	−0.997833	+	0.0657982i	$0.979041\pi$
$150$		0			0
$151$	−8.09017	+	5.87785i	−0.658369	+	0.478333i	−0.866112	−	0.499851i	$-0.833388\pi$
$151$	−8.09017	+	5.87785i	−0.658369	+	0.478333i	0.207743	+	0.978183i	$0.433388\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$	−15.0000			−1.20483
$156$		0			0
$157$	−4.04508	+	2.93893i	−0.322833	+	0.234552i	−0.737383	−	0.675474i	$-0.763939\pi$
$157$	−4.04508	+	2.93893i	−0.322833	+	0.234552i	0.414550	+	0.910026i	$0.363939\pi$
$158$		0			0
$159$	−1.85410	−	5.70634i	−0.147040	−	0.452542i
$160$		0			0
$161$	−4.85410	−	3.52671i	−0.382557	−	0.277944i
$162$		0			0
$163$	−1.23607	+	3.80423i	−0.0968163	+	0.297970i	−0.987723	−	0.156217i	$-0.950070\pi$
$163$	−1.23607	+	3.80423i	−0.0968163	+	0.297970i	0.890906	+	0.454187i	$0.150070\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.70820	−	11.4127i	0.286949	−	0.883140i	−0.698858	−	0.715260i	$-0.746308\pi$
$167$	3.70820	−	11.4127i	0.286949	−	0.883140i	0.985808	−	0.167879i	$-0.0536919\pi$
$168$		0			0
$169$	−2.42705	−	1.76336i	−0.186696	−	0.135643i
$170$		0			0
$171$	4.94427	+	15.2169i	0.378098	+	1.16367i
$172$		0			0
$173$	14.5623	−	10.5801i	1.10715	−	0.804393i	0.124939	−	0.992164i	$-0.460127\pi$
$173$	14.5623	−	10.5801i	1.10715	−	0.804393i	0.982213	+	0.187772i	$0.0601265\pi$
$174$		0			0
$175$	−8.00000			−0.604743
$176$		0			0
$177$	3.00000			0.225494
$178$		0			0
$179$	7.28115	−	5.29007i	0.544219	−	0.395398i	−0.281431	−	0.959582i	$-0.590809\pi$
$179$	7.28115	−	5.29007i	0.544219	−	0.395398i	0.825649	+	0.564183i	$0.190809\pi$
$180$		0			0
$181$	−4.01722	−	12.3637i	−0.298598	−	0.918989i	−0.981989	−	0.188937i	$-0.939496\pi$
$181$	−4.01722	−	12.3637i	−0.298598	−	0.918989i	0.683392	−	0.730052i	$-0.260504\pi$
$182$		0			0
$183$	−3.23607	−	2.35114i	−0.239217	−	0.173801i
$184$		0			0
$185$	0.927051	−	2.85317i	0.0681581	−	0.209769i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	3.09017	−	9.51057i	0.224777	−	0.691792i
$190$		0			0
$191$	16.9894	+	12.3435i	1.22931	+	0.893144i	0.996838	−	0.0794603i	$-0.0253197\pi$
$191$	16.9894	+	12.3435i	1.22931	+	0.893144i	0.232469	+	0.972604i	$0.425320\pi$
$192$		0			0
$193$	−6.18034	−	19.0211i	−0.444871	−	1.36917i	−0.882626	−	0.470077i	$-0.844226\pi$
$193$	−6.18034	−	19.0211i	−0.444871	−	1.36917i	0.437755	−	0.899094i	$-0.355774\pi$
$194$		0			0
$195$	9.70820	−	7.05342i	0.695219	−	0.505106i
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$	0.809017	−	0.587785i	0.0570637	−	0.0414592i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.85410	−	5.70634i	0.128869	−	0.396618i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−6.18034	+	19.0211i	−0.425472	+	1.30947i	0.477069	+	0.878866i	$0.341699\pi$
$211$	−6.18034	+	19.0211i	−0.425472	+	1.30947i	−0.902541	+	0.430603i	$0.858301\pi$
$212$		0			0
$213$	−12.1353	−	8.81678i	−0.831494	−	0.604116i
$214$		0			0
$215$	−9.27051	−	28.5317i	−0.632244	−	1.94585i
$216$		0			0
$217$	8.09017	−	5.87785i	0.549197	−	0.399015i
$218$		0			0
$219$	4.00000			0.270295
$220$		0			0
$221$	−24.0000			−1.61441
$222$		0			0
$223$	−13.7533	+	9.99235i	−0.920988	+	0.669137i	−0.943770	−	0.330603i	$-0.892748\pi$
$223$	−13.7533	+	9.99235i	−0.920988	+	0.669137i	0.0227815	+	0.999740i	$0.492748\pi$
$224$		0			0
$225$	−2.47214	−	7.60845i	−0.164809	−	0.507230i
$226$		0			0
$227$	4.85410	+	3.52671i	0.322178	+	0.234076i	0.737104	−	0.675779i	$-0.236193\pi$
$227$	4.85410	+	3.52671i	0.322178	+	0.234076i	−0.414926	+	0.909855i	$0.636193\pi$
$228$		0			0
$229$	−4.01722	+	12.3637i	−0.265465	+	0.817019i	0.726120	+	0.687568i	$0.241321\pi$
$229$	−4.01722	+	12.3637i	−0.265465	+	0.817019i	−0.991586	+	0.129451i	$0.958679\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.41641	−	22.8254i	0.485865	−	1.49534i	−0.344859	−	0.938654i	$-0.612073\pi$
$233$	7.41641	−	22.8254i	0.485865	−	1.49534i	0.830724	−	0.556684i	$-0.187927\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.618034	−	1.90211i	−0.0401456	−	0.123556i
$238$		0			0
$239$	4.85410	−	3.52671i	0.313986	−	0.228124i	−0.419619	−	0.907700i	$-0.637836\pi$
$239$	4.85410	−	3.52671i	0.313986	−	0.228124i	0.733605	+	0.679576i	$0.237836\pi$
$240$		0			0
$241$	−8.00000			−0.515325			−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000			−0.515325			−0.257663	+	0.966235i	$0.582952\pi$
$242$		0			0
$243$	16.0000			1.02640
$244$		0			0
$245$	−7.28115	+	5.29007i	−0.465176	+	0.337970i
$246$		0			0
$247$	−9.88854	−	30.4338i	−0.629193	−	1.93646i
$248$		0			0
$249$	4.85410	+	3.52671i	0.307616	+	0.223496i
$250$		0			0
$251$	−2.78115	+	8.55951i	−0.175545	+	0.540271i	−0.999658	−	0.0261539i	$-0.991674\pi$
$251$	−2.78115	+	8.55951i	−0.175545	+	0.540271i	0.824113	+	0.566425i	$0.191674\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	5.56231	−	17.1190i	0.348325	−	1.07203i
$256$		0			0
$257$	14.5623	+	10.5801i	0.908372	+	0.659971i	0.940603	−	0.339510i	$-0.110261\pi$
$257$	14.5623	+	10.5801i	0.908372	+	0.659971i	−0.0322308	+	0.999480i	$0.510261\pi$
$258$		0			0
$259$	0.618034	+	1.90211i	0.0384028	+	0.118192i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−18.0000			−1.10993			−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000			−1.10993			−0.554964	+	0.831875i	$0.687268\pi$
$264$		0			0
$265$	18.0000			1.10573
$266$		0			0
$267$	7.28115	−	5.29007i	0.445599	−	0.323747i
$268$		0			0
$269$	−1.85410	−	5.70634i	−0.113047	−	0.347922i	0.878488	−	0.477764i	$-0.158553\pi$
$269$	−1.85410	−	5.70634i	−0.113047	−	0.347922i	−0.991535	+	0.129843i	$0.958553\pi$
$270$		0			0
$271$	16.1803	+	11.7557i	0.982886	+	0.714108i	0.958352	−	0.285591i	$-0.0921898\pi$
$271$	16.1803	+	11.7557i	0.982886	+	0.714108i	0.0245340	+	0.999699i	$0.492190\pi$
$272$		0			0
$273$	−2.47214	+	7.60845i	−0.149620	+	0.460484i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.09017	−	9.51057i	0.185670	−	0.571434i	−0.814289	−	0.580460i	$-0.802873\pi$
$277$	3.09017	−	9.51057i	0.185670	−	0.571434i	0.999959	+	0.00902525i	$0.00287287\pi$
$278$		0			0
$279$	8.09017	+	5.87785i	0.484346	+	0.351898i
$280$		0			0
$281$	5.56231	+	17.1190i	0.331819	+	1.02123i	0.968268	+	0.249916i	$0.0804029\pi$
$281$	5.56231	+	17.1190i	0.331819	+	1.02123i	−0.636448	+	0.771319i	$0.719597\pi$
$282$		0			0
$283$	−3.23607	+	2.35114i	−0.192364	+	0.139761i	−0.679799	−	0.733399i	$-0.737933\pi$
$283$	−3.23607	+	2.35114i	−0.192364	+	0.139761i	0.487434	+	0.873160i	$0.337933\pi$
$284$		0			0
$285$	24.0000			1.42164
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−15.3713	+	11.1679i	−0.904195	+	0.656936i
$290$		0			0
$291$	−2.16312	−	6.65740i	−0.126804	−	0.390263i
$292$		0			0
$293$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$293$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$294$		0			0
$295$	−2.78115	+	8.55951i	−0.161925	+	0.498354i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.70820	+	11.4127i	−0.214451	+	0.660012i
$300$		0			0
$301$	16.1803	+	11.7557i	0.932619	+	0.677588i
$302$		0			0
$303$	−5.56231	−	17.1190i	−0.319546	−	0.983462i
$304$		0			0
$305$	9.70820	−	7.05342i	0.555890	−	0.403878i
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	−9.70820	+	7.05342i	−0.550502	+	0.399963i	−0.827970	−	0.560772i	$-0.810505\pi$
$311$	−9.70820	+	7.05342i	−0.550502	+	0.399963i	0.277469	+	0.960735i	$0.410505\pi$
$312$		0			0
$313$	−0.309017	−	0.951057i	−0.0174667	−	0.0537569i	0.941943	−	0.335772i	$-0.108997\pi$
$313$	−0.309017	−	0.951057i	−0.0174667	−	0.0537569i	−0.959410	+	0.282015i	$0.908997\pi$
$314$		0			0
$315$	9.70820	+	7.05342i	0.546995	+	0.397415i
$316$		0			0
$317$	10.1976	−	31.3849i	0.572752	−	1.76275i	−0.0709570	−	0.997479i	$-0.522605\pi$
$317$	10.1976	−	31.3849i	0.572752	−	1.76275i	0.643709	−	0.765270i	$-0.277395\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.85410	+	5.70634i	−0.103486	+	0.318497i
$322$		0			0
$323$	−38.8328	−	28.2137i	−2.16072	−	1.56985i
$324$		0			0
$325$	4.94427	+	15.2169i	0.274259	+	0.844082i
$326$		0			0
$327$	1.61803	−	1.17557i	0.0894775	−	0.0650092i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−7.00000			−0.384755			−0.192377	−	0.981321i	$-0.561620\pi$
$331$	−7.00000			−0.384755			−0.192377	+	0.981321i	$0.561620\pi$
$332$		0			0
$333$	−1.61803	+	1.17557i	−0.0886677	+	0.0644209i
$334$		0			0
$335$	0.927051	+	2.85317i	0.0506502	+	0.155885i
$336$		0			0
$337$	1.61803	+	1.17557i	0.0881399	+	0.0640374i	0.630982	−	0.775797i	$-0.282652\pi$
$337$	1.61803	+	1.17557i	0.0881399	+	0.0640374i	−0.542843	+	0.839834i	$0.682652\pi$
$338$		0			0
$339$	−4.63525	+	14.2658i	−0.251752	+	0.774814i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	6.18034	−	19.0211i	0.333707	−	1.02704i
$344$		0			0
$345$	−7.28115	−	5.29007i	−0.392004	−	0.284808i
$346$		0			0
$347$	−3.70820	−	11.4127i	−0.199067	−	0.612665i	−0.999905	−	0.0137839i	$-0.995612\pi$
$347$	−3.70820	−	11.4127i	−0.199067	−	0.612665i	0.800838	−	0.598881i	$-0.204388\pi$
$348$		0			0
$349$	11.3262	−	8.22899i	0.606280	−	0.440488i	−0.241823	−	0.970320i	$-0.577745\pi$
$349$	11.3262	−	8.22899i	0.606280	−	0.440488i	0.848102	+	0.529833i	$0.177745\pi$
$350$		0			0
$351$	−20.0000			−1.06752
$352$		0			0
$353$	−21.0000			−1.11772			−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000			−1.11772			−0.558859	+	0.829263i	$0.688761\pi$
$354$		0			0
$355$	36.4058	−	26.4503i	1.93222	−	1.40384i
$356$		0			0
$357$	3.70820	+	11.4127i	0.196259	+	0.604023i
$358$		0			0
$359$	−29.1246	−	21.1603i	−1.53714	−	1.11680i	−0.952098	−	0.305792i	$-0.901079\pi$
$359$	−29.1246	−	21.1603i	−1.53714	−	1.11680i	−0.585040	−	0.811005i	$-0.698921\pi$
$360$		0			0
$361$	13.9058	−	42.7975i	0.731882	−	2.25250i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.70820	+	11.4127i	−0.194096	+	0.597367i
$366$		0			0
$367$	15.3713	+	11.1679i	0.802377	+	0.582961i	0.911610	−	0.411055i	$-0.134840\pi$
$367$	15.3713	+	11.1679i	0.802377	+	0.582961i	−0.109234	+	0.994016i	$0.534840\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9.70820	+	7.05342i	−0.504025	+	0.366195i
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$		0			0
$375$	3.00000			0.154919
$376$		0			0
$377$		0			0
$378$		0			0
$379$	8.96149	+	27.5806i	0.460321	+	1.41672i	0.864773	+	0.502163i	$0.167462\pi$
$379$	8.96149	+	27.5806i	0.460321	+	1.41672i	−0.404452	+	0.914559i	$0.632538\pi$
$380$		0			0
$381$	−12.9443	−	9.40456i	−0.663155	−	0.481810i
$382$		0			0
$383$	−8.34346	+	25.6785i	−0.426331	+	1.31211i	0.475383	+	0.879779i	$0.342309\pi$
$383$	−8.34346	+	25.6785i	−0.426331	+	1.31211i	−0.901714	+	0.432333i	$0.857691\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.18034	+	19.0211i	−0.314164	+	0.966898i
$388$		0			0
$389$	21.8435	+	15.8702i	1.10751	+	0.804651i	0.982269	−	0.187476i	$-0.0600305\pi$
$389$	21.8435	+	15.8702i	1.10751	+	0.804651i	0.125238	+	0.992127i	$0.460031\pi$
$390$		0			0
$391$	5.56231	+	17.1190i	0.281298	+	0.865746i
$392$		0			0
$393$	−4.85410	+	3.52671i	−0.244857	+	0.177899i
$394$		0			0
$395$	6.00000			0.301893
$396$		0			0
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$		0			0
$399$	−12.9443	+	9.40456i	−0.648024	+	0.470817i
$400$		0			0
$401$	5.56231	+	17.1190i	0.277768	+	0.854883i	0.988474	+	0.151393i	$0.0483759\pi$
$401$	5.56231	+	17.1190i	0.277768	+	0.854883i	−0.710705	+	0.703490i	$0.751624\pi$
$402$		0			0
$403$	−16.1803	−	11.7557i	−0.806000	−	0.585593i
$404$		0			0
$405$	−0.927051	+	2.85317i	−0.0460655	+	0.141775i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.618034	+	1.90211i	−0.0305598	+	0.0940534i	−0.965173	−	0.261612i	$-0.915746\pi$
$409$	−0.618034	+	1.90211i	−0.0305598	+	0.0940534i	0.934613	+	0.355666i	$0.115746\pi$
$410$		0			0
$411$	−7.28115	−	5.29007i	−0.359153	−	0.260940i
$412$		0			0
$413$	−1.85410	−	5.70634i	−0.0912344	−	0.280791i
$414$		0			0
$415$	−14.5623	+	10.5801i	−0.714835	+	0.519358i
$416$		0			0
$417$	−14.0000			−0.685583
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	8.09017	−	5.87785i	0.394291	−	0.286469i	−0.372921	−	0.927863i	$-0.621644\pi$
$421$	8.09017	−	5.87785i	0.394291	−	0.286469i	0.767211	+	0.641394i	$0.221644\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	19.4164	+	14.1068i	0.941834	+	0.684283i
$426$		0			0
$427$	−2.47214	+	7.60845i	−0.119635	+	0.368199i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.56231	+	17.1190i	−0.267927	+	0.824594i	0.723078	+	0.690767i	$0.242727\pi$
$431$	−5.56231	+	17.1190i	−0.267927	+	0.824594i	−0.991005	+	0.133827i	$0.957273\pi$
$432$		0			0
$433$	−23.4615	−	17.0458i	−1.12749	−	0.819168i	−0.142160	−	0.989844i	$-0.545405\pi$
$433$	−23.4615	−	17.0458i	−1.12749	−	0.819168i	−0.985327	+	0.170676i	$0.945405\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−19.4164	+	14.1068i	−0.928813	+	0.674822i
$438$		0			0
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$		0			0
$441$	6.00000			0.285714
$442$		0			0
$443$	16.9894	−	12.3435i	0.807189	−	0.586457i	−0.105825	−	0.994385i	$-0.533748\pi$
$443$	16.9894	−	12.3435i	0.807189	−	0.586457i	0.913014	+	0.407928i	$0.133748\pi$
$444$		0			0
$445$	8.34346	+	25.6785i	0.395518	+	1.21728i
$446$		0			0
$447$	4.85410	+	3.52671i	0.229591	+	0.166808i
$448$		0			0
$449$	0.927051	−	2.85317i	0.0437502	−	0.134649i	−0.926795	−	0.375566i	$-0.877448\pi$
$449$	0.927051	−	2.85317i	0.0437502	−	0.134649i	0.970546	+	0.240917i	$0.0774482\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	3.09017	−	9.51057i	0.145189	−	0.446845i
$454$		0			0
$455$	−19.4164	−	14.1068i	−0.910255	−	0.661339i
$456$		0			0
$457$	8.65248	+	26.6296i	0.404746	+	1.24568i	0.921107	+	0.389309i	$0.127286\pi$
$457$	8.65248	+	26.6296i	0.404746	+	1.24568i	−0.516362	+	0.856371i	$0.672714\pi$
$458$		0			0
$459$	−24.2705	+	17.6336i	−1.13285	+	0.823064i
$460$		0			0
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$		0			0
$463$	23.0000			1.06890			0.534450	−	0.845200i	$-0.320519\pi$
$463$	23.0000			1.06890			0.534450	+	0.845200i	$0.320519\pi$
$464$		0			0
$465$	12.1353	−	8.81678i	0.562759	−	0.408868i
$466$		0			0
$467$	0.927051	+	2.85317i	0.0428988	+	0.132029i	0.970212	−	0.242257i	$-0.0778878\pi$
$467$	0.927051	+	2.85317i	0.0428988	+	0.132029i	−0.927313	+	0.374286i	$0.877888\pi$
$468$		0			0
$469$	−1.61803	−	1.17557i	−0.0747139	−	0.0542828i
$470$		0			0
$471$	1.54508	−	4.75528i	0.0711938	−	0.219112i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−9.88854	+	30.4338i	−0.453718	+	1.39640i
$476$		0			0
$477$	−9.70820	−	7.05342i	−0.444508	−	0.322954i
$478$		0			0
$479$	3.70820	+	11.4127i	0.169432	+	0.521459i	0.999336	−	0.0364486i	$-0.0116045\pi$
$479$	3.70820	+	11.4127i	0.169432	+	0.521459i	−0.829903	+	0.557907i	$0.811605\pi$
$480$		0			0
$481$	3.23607	−	2.35114i	0.147552	−	0.107203i
$482$		0			0
$483$	6.00000			0.273009
$484$		0			0
$485$	21.0000			0.953561
$486$		0			0
$487$	−23.4615	+	17.0458i	−1.06314	+	0.772418i	−0.974667	−	0.223661i	$-0.928199\pi$
$487$	−23.4615	+	17.0458i	−1.06314	+	0.772418i	−0.0884747	+	0.996078i	$0.528199\pi$
$488$		0			0
$489$	−1.23607	−	3.80423i	−0.0558969	−	0.172033i
$490$		0			0
$491$	19.4164	+	14.1068i	0.876250	+	0.636633i	0.932257	−	0.361797i	$-0.117837\pi$
$491$	19.4164	+	14.1068i	0.876250	+	0.636633i	−0.0560065	+	0.998430i	$0.517837\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.27051	+	28.5317i	−0.415839	+	1.27982i
$498$		0			0
$499$	3.23607	+	2.35114i	0.144866	+	0.105252i	0.657858	−	0.753142i	$-0.271463\pi$
$499$	3.23607	+	2.35114i	0.144866	+	0.105252i	−0.512992	+	0.858394i	$0.671463\pi$
$500$		0			0
$501$	3.70820	+	11.4127i	0.165670	+	0.509881i
$502$		0			0
$503$	−24.2705	+	17.6336i	−1.08217	+	0.786241i	−0.978060	−	0.208324i	$-0.933199\pi$
$503$	−24.2705	+	17.6336i	−1.08217	+	0.786241i	−0.104109	+	0.994566i	$0.533199\pi$
$504$		0			0
$505$	54.0000			2.40297
$506$		0			0
$507$	3.00000			0.133235
$508$		0			0
$509$	16.9894	−	12.3435i	0.753040	−	0.547116i	−0.143728	−	0.989617i	$-0.545909\pi$
$509$	16.9894	−	12.3435i	0.753040	−	0.547116i	0.896768	+	0.442502i	$0.145909\pi$
$510$		0			0
$511$	−2.47214	−	7.60845i	−0.109361	−	0.336578i
$512$		0			0
$513$	−32.3607	−	23.5114i	−1.42876	−	1.03805i
$514$		0			0
$515$	−7.41641	+	22.8254i	−0.326806	+	1.00581i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−5.56231	+	17.1190i	−0.244158	+	0.751441i
$520$		0			0
$521$	21.8435	+	15.8702i	0.956979	+	0.695286i	0.952447	−	0.304704i	$-0.0985574\pi$
$521$	21.8435	+	15.8702i	0.956979	+	0.695286i	0.00453207	+	0.999990i	$0.498557\pi$
$522$		0			0
$523$	−2.47214	−	7.60845i	−0.108099	−	0.332694i	0.882346	−	0.470601i	$-0.155963\pi$
$523$	−2.47214	−	7.60845i	−0.108099	−	0.332694i	−0.990445	+	0.137906i	$0.955963\pi$
$524$		0			0
$525$	6.47214	−	4.70228i	0.282467	−	0.205224i
$526$		0			0
$527$	−30.0000			−1.30682
$528$		0			0
$529$	−14.0000			−0.608696
$530$		0			0
$531$	4.85410	−	3.52671i	0.210650	−	0.153046i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−14.5623	−	10.5801i	−0.629583	−	0.457419i
$536$		0			0
$537$	−2.78115	+	8.55951i	−0.120016	+	0.369370i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.94427	−	15.2169i	0.212571	−	0.654226i	−0.786746	−	0.617277i	$-0.788236\pi$
$541$	4.94427	−	15.2169i	0.212571	−	0.654226i	0.999317	−	0.0369493i	$-0.0117640\pi$
$542$		0			0
$543$	10.5172	+	7.64121i	0.451337	+	0.327916i
$544$		0			0
$545$	1.85410	+	5.70634i	0.0794210	+	0.244433i
$546$		0			0
$547$	6.47214	−	4.70228i	0.276729	−	0.201055i	−0.440761	−	0.897625i	$-0.645291\pi$
$547$	6.47214	−	4.70228i	0.276729	−	0.201055i	0.717489	+	0.696570i	$0.245291\pi$
$548$		0			0
$549$	−8.00000			−0.341432
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−3.23607	+	2.35114i	−0.137612	+	0.0999807i
$554$		0			0
$555$	0.927051	+	2.85317i	0.0393511	+	0.121110i
$556$		0			0
$557$	−14.5623	−	10.5801i	−0.617025	−	0.448295i	0.234856	−	0.972030i	$-0.424538\pi$
$557$	−14.5623	−	10.5801i	−0.617025	−	0.448295i	−0.851881	+	0.523735i	$0.824538\pi$
$558$		0			0
$559$	12.3607	−	38.0423i	0.522801	−	1.60902i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.1246	−	34.2380i	0.468846	−	1.44296i	−0.385233	−	0.922819i	$-0.625879\pi$
$563$	11.1246	−	34.2380i	0.468846	−	1.44296i	0.854080	−	0.520142i	$-0.174121\pi$
$564$		0			0
$565$	−36.4058	−	26.4503i	−1.53160	−	1.11277i
$566$		0			0
$567$	−0.618034	−	1.90211i	−0.0259550	−	0.0798812i
$568$		0			0
$569$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$569$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$570$		0			0
$571$	−44.0000			−1.84134			−0.920671	−	0.390339i	$-0.872358\pi$
$571$	−44.0000			−1.84134			−0.920671	+	0.390339i	$0.872358\pi$
$572$		0			0
$573$	−21.0000			−0.877288
$574$		0			0
$575$	9.70820	−	7.05342i	0.404860	−	0.294148i
$576$		0			0
$577$	5.25329	+	16.1680i	0.218697	+	0.673081i	0.998870	+	0.0475174i	$0.0151309\pi$
$577$	5.25329	+	16.1680i	0.218697	+	0.673081i	−0.780173	+	0.625564i	$0.784869\pi$
$578$		0			0
$579$	16.1803	+	11.7557i	0.672432	+	0.488550i
$580$		0			0
$581$	3.70820	−	11.4127i	0.153842	−	0.473478i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	7.41641	−	22.8254i	0.306631	−	0.943712i
$586$		0			0
$587$	9.70820	+	7.05342i	0.400700	+	0.291126i	0.769826	−	0.638254i	$-0.220343\pi$
$587$	9.70820	+	7.05342i	0.400700	+	0.291126i	−0.369126	+	0.929379i	$0.620343\pi$
$588$		0			0
$589$	−12.3607	−	38.0423i	−0.509313	−	1.56750i
$590$		0			0
$591$	4.85410	−	3.52671i	0.199671	−	0.145070i
$592$		0			0
$593$	36.0000			1.47834			0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000			1.47834			0.739171	+	0.673517i	$0.235217\pi$
$594$		0			0
$595$	−36.0000			−1.47586
$596$		0			0
$597$	−6.47214	+	4.70228i	−0.264887	+	0.192452i
$598$		0			0
$599$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$599$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$600$		0			0
$601$	21.0344	+	15.2824i	0.858013	+	0.623383i	0.927344	−	0.374211i	$-0.122086\pi$
$601$	21.0344	+	15.2824i	0.858013	+	0.623383i	−0.0693308	+	0.997594i	$0.522086\pi$
$602$		0			0
$603$	0.618034	−	1.90211i	0.0251683	−	0.0774600i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.32624	+	13.3148i	−0.175597	+	0.540431i	−0.999660	−	0.0260665i	$-0.991702\pi$
$607$	−4.32624	+	13.3148i	−0.175597	+	0.540431i	0.824064	+	0.566497i	$0.191702\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	25.8885	−	18.8091i	1.04563	−	0.759694i	0.0742521	−	0.997239i	$-0.476343\pi$
$613$	25.8885	−	18.8091i	1.04563	−	0.759694i	0.971376	+	0.237546i	$0.0763430\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$		0			0
$619$	−13.7533	+	9.99235i	−0.552791	+	0.401626i	−0.828814	−	0.559525i	$-0.810984\pi$
$619$	−13.7533	+	9.99235i	−0.552791	+	0.401626i	0.276022	+	0.961151i	$0.410984\pi$
$620$		0			0
$621$	4.63525	+	14.2658i	0.186006	+	0.572469i
$622$		0			0
$623$	−14.5623	−	10.5801i	−0.583426	−	0.423884i
$624$		0			0
$625$	−8.96149	+	27.5806i	−0.358460	+	1.10323i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.85410	−	5.70634i	0.0739279	−	0.227527i
$630$		0			0
$631$	34.7877	+	25.2748i	1.38488	+	1.00617i	0.996405	+	0.0847121i	$0.0269971\pi$
$631$	34.7877	+	25.2748i	1.38488	+	1.00617i	0.388472	+	0.921460i	$0.373003\pi$
$632$		0			0
$633$	−6.18034	−	19.0211i	−0.245646	−	0.756022i
$634$		0			0
$635$	38.8328	−	28.2137i	1.54103	−	1.11963i
$636$		0			0
$637$	−12.0000			−0.475457
$638$		0			0
$639$	−30.0000			−1.18678
$640$		0			0
$641$	−31.5517	+	22.9236i	−1.24622	+	0.905429i	−0.997996	−	0.0632750i	$-0.979845\pi$
$641$	−31.5517	+	22.9236i	−1.24622	+	0.905429i	−0.248220	+	0.968704i	$0.579845\pi$
$642$		0			0
$643$	−4.01722	−	12.3637i	−0.158424	−	0.487578i	0.840068	−	0.542481i	$-0.182515\pi$
$643$	−4.01722	−	12.3637i	−0.158424	−	0.487578i	−0.998492	+	0.0549031i	$0.982515\pi$
$644$		0			0
$645$	24.2705	+	17.6336i	0.955650	+	0.694321i
$646$		0			0
$647$	0.927051	−	2.85317i	0.0364461	−	0.112170i	−0.931178	−	0.364564i	$-0.881218\pi$
$647$	0.927051	−	2.85317i	0.0364461	−	0.112170i	0.967624	+	0.252394i	$0.0812180\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−3.09017	+	9.51057i	−0.121113	+	0.372748i
$652$		0			0
$653$	−2.42705	−	1.76336i	−0.0949778	−	0.0690054i	0.539283	−	0.842125i	$-0.318695\pi$
$653$	−2.42705	−	1.76336i	−0.0949778	−	0.0690054i	−0.634261	+	0.773119i	$0.718695\pi$
$654$		0			0
$655$	−5.56231	−	17.1190i	−0.217337	−	0.668895i
$656$		0			0
$657$	6.47214	−	4.70228i	0.252502	−	0.183453i
$658$		0			0
$659$	42.0000			1.63609			0.818044	−	0.575156i	$-0.195059\pi$
$659$	42.0000			1.63609			0.818044	+	0.575156i	$0.195059\pi$
$660$		0			0
$661$	17.0000			0.661223			0.330612	−	0.943767i	$-0.392745\pi$
$661$	17.0000			0.661223			0.330612	+	0.943767i	$0.392745\pi$
$662$		0			0
$663$	19.4164	−	14.1068i	0.754071	−	0.547865i
$664$		0			0
$665$	−14.8328	−	45.6507i	−0.575192	−	1.77026i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	5.25329	−	16.1680i	0.203104	−	0.625089i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	10.5066	−	32.3359i	0.404999	−	1.24646i	−0.515897	−	0.856650i	$-0.672541\pi$
$673$	10.5066	−	32.3359i	0.404999	−	1.24646i	0.920896	−	0.389808i	$-0.127459\pi$
$674$		0			0
$675$	16.1803	+	11.7557i	0.622782	+	0.452477i
$676$		0			0
$677$	12.9787	+	39.9444i	0.498812	+	1.53519i	0.810930	+	0.585143i	$0.198962\pi$
$677$	12.9787	+	39.9444i	0.498812	+	1.53519i	−0.312117	+	0.950044i	$0.601038\pi$
$678$		0			0
$679$	−11.3262	+	8.22899i	−0.434661	+	0.315800i
$680$		0			0
$681$	−6.00000			−0.229920
$682$		0			0
$683$	48.0000			1.83667			0.918334	−	0.395805i	$-0.129534\pi$
$683$	48.0000			1.83667			0.918334	+	0.395805i	$0.129534\pi$
$684$		0			0
$685$	21.8435	−	15.8702i	0.834596	−	0.606369i
$686$		0			0
$687$	−4.01722	−	12.3637i	−0.153267	−	0.471706i
$688$		0			0
$689$	19.4164	+	14.1068i	0.739706	+	0.537428i
$690$		0			0
$691$	−0.309017	+	0.951057i	−0.0117556	+	0.0361799i	−0.956762	−	0.290871i	$-0.906055\pi$
$691$	−0.309017	+	0.951057i	−0.0117556	+	0.0361799i	0.945007	+	0.327051i	$0.106055\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.9787	−	39.9444i	0.492311	−	1.51518i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	7.41641	+	22.8254i	0.280514	+	0.863334i
$700$		0			0
$701$	14.5623	−	10.5801i	0.550011	−	0.399606i	−0.277779	−	0.960645i	$-0.589598\pi$
$701$	14.5623	−	10.5801i	0.550011	−	0.399606i	0.827789	+	0.561039i	$0.189598\pi$
$702$		0			0
$703$	8.00000			0.301726
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−29.1246	+	21.1603i	−1.09534	+	0.795814i
$708$		0			0
$709$	−11.4336	−	35.1891i	−0.429399	−	1.32155i	−0.898719	−	0.438526i	$-0.855501\pi$
$709$	−11.4336	−	35.1891i	−0.429399	−	1.32155i	0.469320	−	0.883028i	$-0.344499\pi$
$710$		0			0
$711$	−3.23607	−	2.35114i	−0.121362	−	0.0881747i
$712$		0			0
$713$	−4.63525	+	14.2658i	−0.173592	+	0.534260i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.85410	+	5.70634i	−0.0692427	+	0.213107i
$718$		0			0
$719$	−36.4058	−	26.4503i	−1.35771	−	0.986431i	−0.998587	−	0.0531392i	$-0.983077\pi$
$719$	−36.4058	−	26.4503i	−1.35771	−	0.986431i	−0.359119	−	0.933292i	$-0.616923\pi$
$720$		0			0
$721$	−4.94427	−	15.2169i	−0.184134	−	0.566707i
$722$		0			0
$723$	6.47214	−	4.70228i	0.240701	−	0.174880i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	17.0000			0.630495			0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000			0.630495			0.315248	+	0.949009i	$0.397912\pi$
$728$		0			0
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$		0			0
$731$	−18.5410	−	57.0634i	−0.685764	−	2.11057i
$732$		0			0
$733$	−3.23607	−	2.35114i	−0.119527	−	0.0868414i	0.526416	−	0.850227i	$-0.323536\pi$
$733$	−3.23607	−	2.35114i	−0.119527	−	0.0868414i	−0.645943	+	0.763386i	$0.723536\pi$
$734$		0			0
$735$	2.78115	−	8.55951i	0.102584	−	0.315722i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	10.5066	−	32.3359i	0.386491	−	1.18950i	−0.548902	−	0.835886i	$-0.684954\pi$
$739$	10.5066	−	32.3359i	0.386491	−	1.18950i	0.935393	−	0.353610i	$-0.115046\pi$
$740$		0			0
$741$	25.8885	+	18.8091i	0.951039	+	0.690971i
$742$		0			0
$743$	−3.70820	−	11.4127i	−0.136041	−	0.418691i	0.859710	−	0.510783i	$-0.170644\pi$
$743$	−3.70820	−	11.4127i	−0.136041	−	0.418691i	−0.995750	+	0.0920925i	$0.970644\pi$
$744$		0			0
$745$	−14.5623	+	10.5801i	−0.533522	+	0.387626i
$746$		0			0
$747$	12.0000			0.439057
$748$		0			0
$749$	12.0000			0.438470
$750$		0			0
$751$	−28.3156	+	20.5725i	−1.03325	+	0.750701i	−0.968957	−	0.247230i	$-0.920480\pi$
$751$	−28.3156	+	20.5725i	−1.03325	+	0.750701i	−0.0642940	+	0.997931i	$0.520480\pi$
$752$		0			0
$753$	−2.78115	−	8.55951i	−0.101351	−	0.311926i
$754$		0			0
$755$	24.2705	+	17.6336i	0.883294	+	0.641751i
$756$		0			0
$757$	−6.79837	+	20.9232i	−0.247091	+	0.760468i	0.748194	+	0.663480i	$0.230921\pi$
$757$	−6.79837	+	20.9232i	−0.247091	+	0.760468i	−0.995285	+	0.0969886i	$0.969079\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.1246	+	34.2380i	−0.403267	+	1.24113i	0.519067	+	0.854734i	$0.326280\pi$
$761$	−11.1246	+	34.2380i	−0.403267	+	1.24113i	−0.922334	+	0.386394i	$0.873720\pi$
$762$		0			0
$763$	−3.23607	−	2.35114i	−0.117154	−	0.0851170i
$764$		0			0
$765$	−11.1246	−	34.2380i	−0.402211	−	1.23788i
$766$		0			0
$767$	−9.70820	+	7.05342i	−0.350543	+	0.254684i
$768$		0			0
$769$	−44.0000			−1.58668			−0.793340	−	0.608778i	$-0.791660\pi$
$769$	−44.0000			−1.58668			−0.793340	+	0.608778i	$0.791660\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$		0			0
$773$	−33.9787	+	24.6870i	−1.22213	+	0.887929i	−0.996275	−	0.0862321i	$-0.972517\pi$
$773$	−33.9787	+	24.6870i	−1.22213	+	0.887929i	−0.225854	+	0.974161i	$0.572517\pi$
$774$		0			0
$775$	6.18034	+	19.0211i	0.222004	+	0.683259i
$776$		0			0
$777$	−1.61803	−	1.17557i	−0.0580466	−	0.0421734i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	12.1353	+	8.81678i	0.433126	+	0.314684i
$786$		0			0
$787$	−9.88854	−	30.4338i	−0.352489	−	1.08485i	−0.957451	−	0.288594i	$-0.906812\pi$
$787$	−9.88854	−	30.4338i	−0.352489	−	1.08485i	0.604963	−	0.796254i	$-0.293188\pi$
$788$		0			0
$789$	14.5623	−	10.5801i	0.518432	−	0.376663i
$790$		0			0
$791$	30.0000			1.06668
$792$		0			0
$793$	16.0000			0.568177
$794$		0			0
$795$	−14.5623	+	10.5801i	−0.516472	+	0.375239i
$796$		0			0
$797$	2.78115	+	8.55951i	0.0985135	+	0.303193i	0.988153	−	0.153469i	$-0.0490446\pi$
$797$	2.78115	+	8.55951i	0.0985135	+	0.303193i	−0.889640	+	0.456663i	$0.849045\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	5.56231	−	17.1190i	0.196534	−	0.604871i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−5.56231	+	17.1190i	−0.196046	+	0.603366i
$806$		0			0
$807$	4.85410	+	3.52671i	0.170872	+	0.124146i
$808$		0			0
$809$	7.41641	+	22.8254i	0.260747	+	0.802497i	0.992643	+	0.121080i	$0.0386358\pi$
$809$	7.41641	+	22.8254i	0.260747	+	0.802497i	−0.731896	+	0.681417i	$0.761364\pi$
$810$		0			0
$811$	30.7426	−	22.3358i	1.07952	−	0.784317i	0.101921	−	0.994792i	$-0.467501\pi$
$811$	30.7426	−	22.3358i	1.07952	−	0.784317i	0.977599	+	0.210475i	$0.0675011\pi$
$812$		0			0
$813$	−20.0000			−0.701431
$814$		0			0
$815$	12.0000			0.420342
$816$		0			0
$817$	64.7214	−	47.0228i	2.26431	−	1.64512i
$818$		0			0
$819$	4.94427	+	15.2169i	0.172767	+	0.531722i
$820$		0			0
$821$	24.2705	+	17.6336i	0.847047	+	0.615415i	0.924330	−	0.381594i	$-0.124625\pi$
$821$	24.2705	+	17.6336i	0.847047	+	0.615415i	−0.0772835	+	0.997009i	$0.524625\pi$
$822$		0			0
$823$	−13.2877	+	40.8954i	−0.463181	+	1.42553i	0.398074	+	0.917353i	$0.369679\pi$
$823$	−13.2877	+	40.8954i	−0.463181	+	1.42553i	−0.861256	+	0.508172i	$0.830321\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.1246	−	34.2380i	0.386841	−	1.19057i	−0.548296	−	0.836285i	$-0.684723\pi$
$827$	11.1246	−	34.2380i	0.386841	−	1.19057i	0.935136	−	0.354288i	$-0.115277\pi$
$828$		0			0
$829$	15.3713	+	11.1679i	0.533868	+	0.387878i	0.821803	−	0.569772i	$-0.192969\pi$
$829$	15.3713	+	11.1679i	0.533868	+	0.387878i	−0.287935	+	0.957650i	$0.592969\pi$
$830$		0			0
$831$	3.09017	+	9.51057i	0.107197	+	0.329918i
$832$		0			0
$833$	−14.5623	+	10.5801i	−0.504554	+	0.366580i
$834$		0			0
$835$	−36.0000			−1.24583
$836$		0			0
$837$	−25.0000			−0.864126
$838$		0			0
$839$	31.5517	−	22.9236i	1.08928	−	0.791411i	0.110006	−	0.993931i	$-0.464913\pi$
$839$	31.5517	−	22.9236i	1.08928	−	0.791411i	0.979278	+	0.202519i	$0.0649129\pi$
$840$		0			0
$841$	−8.96149	−	27.5806i	−0.309017	−	0.951057i
$842$		0			0
$843$	−14.5623	−	10.5801i	−0.501552	−	0.364399i
$844$		0			0
$845$	−2.78115	+	8.55951i	−0.0956746	+	0.294456i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.23607	−	3.80423i	0.0424217	−	0.130561i
$850$		0			0
$851$	−2.42705	−	1.76336i	−0.0831982	−	0.0604471i
$852$		0			0
$853$	−11.7426	−	36.1401i	−0.402061	−	1.23742i	−0.923325	−	0.384020i	$-0.874539\pi$
$853$	−11.7426	−	36.1401i	−0.402061	−	1.23742i	0.521264	−	0.853395i	$-0.325461\pi$
$854$		0			0
$855$	38.8328	−	28.2137i	1.32805	−	0.964888i
$856$		0			0
$857$	−24.0000			−0.819824			−0.409912	−	0.912125i	$-0.634441\pi$
$857$	−24.0000			−0.819824			−0.409912	+	0.912125i	$0.634441\pi$
$858$		0			0
$859$	−25.0000			−0.852989			−0.426494	−	0.904490i	$-0.640252\pi$
$859$	−25.0000			−0.852989			−0.426494	+	0.904490i	$0.640252\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.8328	+	45.6507i	0.504915	+	1.55397i	0.800914	+	0.598780i	$0.204348\pi$
$863$	14.8328	+	45.6507i	0.504915	+	1.55397i	−0.295999	+	0.955188i	$0.595652\pi$
$864$		0			0
$865$	−43.6869	−	31.7404i	−1.48540	−	1.07921i
$866$		0			0
$867$	5.87132	−	18.0701i	0.199401	−	0.613692i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−1.23607	+	3.80423i	−0.0418826	+	0.128901i
$872$		0			0
$873$	−11.3262	−	8.22899i	−0.383335	−	0.278509i
$874$		0			0
$875$	−1.85410	−	5.70634i	−0.0626801	−	0.192909i
$876$		0			0
$877$	−42.0689	+	30.5648i	−1.42057	+	1.03210i	−0.428887	+	0.903358i	$0.641094\pi$
$877$	−42.0689	+	30.5648i	−1.42057	+	1.03210i	−0.991678	+	0.128743i	$0.958906\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−27.0000			−0.909653			−0.454827	−	0.890580i	$-0.650299\pi$
$881$	−27.0000			−0.909653			−0.454827	+	0.890580i	$0.650299\pi$
$882$		0			0
$883$	3.23607	−	2.35114i	0.108902	−	0.0791222i	−0.532001	−	0.846744i	$-0.678560\pi$
$883$	3.23607	−	2.35114i	0.108902	−	0.0791222i	0.640904	+	0.767621i	$0.278560\pi$
$884$		0			0
$885$	−2.78115	−	8.55951i	−0.0934874	−	0.287725i
$886$		0			0
$887$	24.2705	+	17.6336i	0.814924	+	0.592077i	0.915254	−	0.402877i	$-0.131990\pi$
$887$	24.2705	+	17.6336i	0.814924	+	0.592077i	−0.100330	+	0.994954i	$0.531990\pi$
$888$		0			0
$889$	−9.88854	+	30.4338i	−0.331651	+	1.02072i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−21.8435	−	15.8702i	−0.730146	−	0.530482i
$896$		0			0
$897$	−3.70820	−	11.4127i	−0.123813	−	0.381058i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	36.0000			1.19933
$902$		0			0
$903$	−20.0000			−0.665558
$904$		0			0
$905$	−31.5517	+	22.9236i	−1.04881	+	0.762007i
$906$		0			0
$907$	−1.23607	−	3.80423i	−0.0410430	−	0.126317i	0.928436	−	0.371493i	$-0.121154\pi$
$907$	−1.23607	−	3.80423i	−0.0410430	−	0.126317i	−0.969479	+	0.245176i	$0.921154\pi$
$908$		0			0
$909$	−29.1246	−	21.1603i	−0.966002	−	0.701842i
$910$		0			0
$911$	3.70820	−	11.4127i	0.122858	−	0.378119i	−0.870647	−	0.491909i	$-0.836299\pi$
$911$	3.70820	−	11.4127i	0.122858	−	0.378119i	0.993505	+	0.113790i	$0.0362992\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−3.70820	+	11.4127i	−0.122589	+	0.377292i
$916$		0			0
$917$	9.70820	+	7.05342i	0.320593	+	0.232925i
$918$		0			0
$919$	10.5066	+	32.3359i	0.346580	+	1.06666i	0.960732	+	0.277476i	$0.0894980\pi$
$919$	10.5066	+	32.3359i	0.346580	+	1.06666i	−0.614152	+	0.789187i	$0.710502\pi$
$920$		0			0
$921$	−12.9443	+	9.40456i	−0.426528	+	0.309891i
$922$		0			0
$923$	60.0000			1.97492
$924$		0			0
$925$	−4.00000			−0.131519
$926$		0			0
$927$	12.9443	−	9.40456i	0.425146	−	0.308886i
$928$		0			0
$929$	5.56231	+	17.1190i	0.182493	+	0.561657i	0.999896	−	0.0144098i	$-0.00458693\pi$
$929$	5.56231	+	17.1190i	0.182493	+	0.561657i	−0.817403	+	0.576066i	$0.804587\pi$
$930$		0			0
$931$	−19.4164	−	14.1068i	−0.636347	−	0.462333i
$932$		0			0
$933$	3.70820	−	11.4127i	0.121401	−	0.373634i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−9.88854	+	30.4338i	−0.323045	+	0.994229i	0.649271	+	0.760557i	$0.275074\pi$
$937$	−9.88854	+	30.4338i	−0.323045	+	0.994229i	−0.972316	+	0.233672i	$0.924926\pi$
$938$		0			0
$939$	0.809017	+	0.587785i	0.0264013	+	0.0191816i
$940$		0			0
$941$	9.27051	+	28.5317i	0.302210	+	0.930107i	0.980704	+	0.195500i	$0.0626331\pi$
$941$	9.27051	+	28.5317i	0.302210	+	0.930107i	−0.678494	+	0.734606i	$0.737367\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−30.0000			−0.975900
$946$		0			0
$947$	27.0000			0.877382			0.438691	−	0.898638i	$-0.355442\pi$
$947$	27.0000			0.877382			0.438691	+	0.898638i	$0.355442\pi$
$948$		0			0
$949$	−12.9443	+	9.40456i	−0.420189	+	0.305285i
$950$		0			0
$951$	10.1976	+	31.3849i	0.330679	+	1.01772i
$952$		0			0
$953$	33.9787	+	24.6870i	1.10068	+	0.799690i	0.981171	−	0.193143i	$-0.0618683\pi$
$953$	33.9787	+	24.6870i	1.10068	+	0.799690i	0.119508	+	0.992833i	$0.461868\pi$
$954$		0			0
$955$	19.4681	−	59.9166i	0.629972	−	1.93885i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.56231	+	17.1190i	−0.179616	+	0.552802i
$960$		0			0
$961$	4.85410	+	3.52671i	0.156584	+	0.113765i
$962$		0			0
$963$	3.70820	+	11.4127i	0.119495	+	0.367768i
$964$		0			0
$965$	−48.5410	+	35.2671i	−1.56259	+	1.13529i
$966$		0			0
$967$	16.0000			0.514525			0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000			0.514525			0.257263	+	0.966342i	$0.417179\pi$
$968$		0			0
$969$	48.0000			1.54198
$970$		0			0
$971$	12.1353	−	8.81678i	0.389439	−	0.282944i	−0.375787	−	0.926706i	$-0.622627\pi$
$971$	12.1353	−	8.81678i	0.389439	−	0.282944i	0.765226	+	0.643762i	$0.222627\pi$
$972$		0			0
$973$	8.65248	+	26.6296i	0.277386	+	0.853705i
$974$		0			0
$975$	−12.9443	−	9.40456i	−0.414548	−	0.301187i
$976$		0			0
$977$	13.9058	−	42.7975i	0.444885	−	1.36921i	−0.437725	−	0.899109i	$-0.644216\pi$
$977$	13.9058	−	42.7975i	0.444885	−	1.36921i	0.882610	−	0.470106i	$-0.155784\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.23607	−	3.80423i	0.0394646	−	0.121460i
$982$		0			0
$983$	−36.4058	−	26.4503i	−1.16116	−	0.843635i	−0.171239	−	0.985230i	$-0.554777\pi$
$983$	−36.4058	−	26.4503i	−1.16116	−	0.843635i	−0.989925	+	0.141595i	$0.954777\pi$
$984$		0			0
$985$	5.56231	+	17.1190i	0.177230	+	0.545457i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−30.0000			−0.953945
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$	5.66312	−	4.11450i	0.179714	−	0.130570i
$994$		0			0
$995$	−7.41641	−	22.8254i	−0.235116	−	0.723612i
$996$		0			0
$997$	−8.09017	−	5.87785i	−0.256218	−	0.186153i	0.452260	−	0.891886i	$-0.350618\pi$
$997$	−8.09017	−	5.87785i	−0.256218	−	0.186153i	−0.708478	+	0.705733i	$0.750618\pi$
$998$		0			0
$999$	1.54508	−	4.75528i	0.0488843	−	0.150450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.e.b.9.1		4
11.2	odd	10		484.2.e.a.245.1		4
11.3	even	5	inner	484.2.e.b.81.1		4
11.4	even	5		484.2.a.a.1.1		1
11.5	even	5	inner	484.2.e.b.269.1		4
11.6	odd	10		484.2.e.a.269.1		4
11.7	odd	10		44.2.a.a.1.1	✓	1
11.8	odd	10		484.2.e.a.81.1		4
11.9	even	5	inner	484.2.e.b.245.1		4
11.10	odd	2		484.2.e.a.9.1		4
33.26	odd	10		4356.2.a.j.1.1		1
33.29	even	10		396.2.a.c.1.1		1
44.7	even	10		176.2.a.a.1.1		1
44.15	odd	10		1936.2.a.c.1.1		1
55.7	even	20		1100.2.b.c.749.1		2
55.18	even	20		1100.2.b.c.749.2		2
55.29	odd	10		1100.2.a.b.1.1		1
77.18	odd	30		2156.2.i.b.177.1		2
77.40	even	30		2156.2.i.c.1145.1		2
77.51	odd	30		2156.2.i.b.1145.1		2
77.62	even	10		2156.2.a.a.1.1		1
77.73	even	30		2156.2.i.c.177.1		2
88.29	odd	10		704.2.a.f.1.1		1
88.37	even	10		7744.2.a.m.1.1		1
88.51	even	10		704.2.a.i.1.1		1
88.59	odd	10		7744.2.a.bc.1.1		1
99.7	odd	30		3564.2.i.j.2377.1		2
99.29	even	30		3564.2.i.a.2377.1		2
99.40	odd	30		3564.2.i.j.1189.1		2
99.95	even	30		3564.2.i.a.1189.1		2
132.95	odd	10		1584.2.a.p.1.1		1
143.51	odd	10		7436.2.a.d.1.1		1
165.29	even	10		9900.2.a.h.1.1		1
165.62	odd	20		9900.2.c.g.5149.2		2
165.128	odd	20		9900.2.c.g.5149.1		2
176.29	odd	20		2816.2.c.e.1409.2		2
176.51	even	20		2816.2.c.k.1409.1		2
176.117	odd	20		2816.2.c.e.1409.1		2
176.139	even	20		2816.2.c.k.1409.2		2
220.7	odd	20		4400.2.b.k.4049.2		2
220.139	even	10		4400.2.a.v.1.1		1
220.183	odd	20		4400.2.b.k.4049.1		2
264.29	even	10		6336.2.a.j.1.1		1
264.227	odd	10		6336.2.a.i.1.1		1
308.139	odd	10		8624.2.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.a.a.1.1	✓	1	11.7	odd	10
176.2.a.a.1.1		1	44.7	even	10
396.2.a.c.1.1		1	33.29	even	10
484.2.a.a.1.1		1	11.4	even	5
484.2.e.a.9.1		4	11.10	odd	2
484.2.e.a.81.1		4	11.8	odd	10
484.2.e.a.245.1		4	11.2	odd	10
484.2.e.a.269.1		4	11.6	odd	10
484.2.e.b.9.1		4	1.1	even	1	trivial
484.2.e.b.81.1		4	11.3	even	5	inner
484.2.e.b.245.1		4	11.9	even	5	inner
484.2.e.b.269.1		4	11.5	even	5	inner
704.2.a.f.1.1		1	88.29	odd	10
704.2.a.i.1.1		1	88.51	even	10
1100.2.a.b.1.1		1	55.29	odd	10
1100.2.b.c.749.1		2	55.7	even	20
1100.2.b.c.749.2		2	55.18	even	20
1584.2.a.p.1.1		1	132.95	odd	10
1936.2.a.c.1.1		1	44.15	odd	10
2156.2.a.a.1.1		1	77.62	even	10
2156.2.i.b.177.1		2	77.18	odd	30
2156.2.i.b.1145.1		2	77.51	odd	30
2156.2.i.c.177.1		2	77.73	even	30
2156.2.i.c.1145.1		2	77.40	even	30
2816.2.c.e.1409.1		2	176.117	odd	20
2816.2.c.e.1409.2		2	176.29	odd	20
2816.2.c.k.1409.1		2	176.51	even	20
2816.2.c.k.1409.2		2	176.139	even	20
3564.2.i.a.1189.1		2	99.95	even	30
3564.2.i.a.2377.1		2	99.29	even	30
3564.2.i.j.1189.1		2	99.40	odd	30
3564.2.i.j.2377.1		2	99.7	odd	30
4356.2.a.j.1.1		1	33.26	odd	10
4400.2.a.v.1.1		1	220.139	even	10
4400.2.b.k.4049.1		2	220.183	odd	20
4400.2.b.k.4049.2		2	220.7	odd	20
6336.2.a.i.1.1		1	264.227	odd	10
6336.2.a.j.1.1		1	264.29	even	10
7436.2.a.d.1.1		1	143.51	odd	10
7744.2.a.m.1.1		1	88.37	even	10
7744.2.a.bc.1.1		1	88.59	odd	10
8624.2.a.w.1.1		1	308.139	odd	10
9900.2.a.h.1.1		1	165.29	even	10
9900.2.c.g.5149.1		2	165.128	odd	20
9900.2.c.g.5149.2		2	165.62	odd	20

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.927051 - 2.85317i) q^{5} +(1.61803 + 1.17557i) q^{7} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.927051 - 2.85317i) q^{5} +(1.61803 + 1.17557i) q^{7} +(-0.618034 + 1.90211i) q^{9} +(1.23607 - 3.80423i) q^{13} +(2.42705 + 1.76336i) q^{15} +(-1.85410 - 5.70634i) q^{17} +(6.47214 - 4.70228i) q^{19} -2.00000 q^{21} -3.00000 q^{23} +(-3.23607 + 2.35114i) q^{25} +(-1.54508 - 4.75528i) q^{27} +(1.54508 - 4.75528i) q^{31} +(1.85410 - 5.70634i) q^{35} +(0.809017 + 0.587785i) q^{37} +(1.23607 + 3.80423i) q^{39} +10.0000 q^{43} +6.00000 q^{45} +(-0.927051 - 2.85317i) q^{49} +(4.85410 + 3.52671i) q^{51} +(-1.85410 + 5.70634i) q^{53} +(-2.47214 + 7.60845i) q^{57} +(-2.42705 - 1.76336i) q^{59} +(1.23607 + 3.80423i) q^{61} +(-3.23607 + 2.35114i) q^{63} -12.0000 q^{65} -1.00000 q^{67} +(2.42705 - 1.76336i) q^{69} +(4.63525 + 14.2658i) q^{71} +(-3.23607 - 2.35114i) q^{73} +(1.23607 - 3.80423i) q^{75} +(-0.618034 + 1.90211i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-1.85410 - 5.70634i) q^{83} +(-14.5623 + 10.5801i) q^{85} -9.00000 q^{89} +(6.47214 - 4.70228i) q^{91} +(1.54508 + 4.75528i) q^{93} +(-19.4164 - 14.1068i) q^{95} +(-2.16312 + 6.65740i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 3 q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q - q^3 + 3 * q^5 + 2 * q^7 + 2 * q^9	\( 4 q - q^{3} + 3 q^{5} + 2 q^{7} + 2 q^{9} - 4 q^{13} + 3 q^{15} + 6 q^{17} + 8 q^{19} - 8 q^{21} - 12 q^{23} - 4 q^{25} + 5 q^{27} - 5 q^{31} - 6 q^{35} + q^{37} - 4 q^{39} + 40 q^{43} + 24 q^{45} + 3 q^{49} + 6 q^{51} + 6 q^{53} + 8 q^{57} - 3 q^{59} - 4 q^{61} - 4 q^{63} - 48 q^{65} - 4 q^{67} + 3 q^{69} - 15 q^{71} - 4 q^{73} - 4 q^{75} + 2 q^{79} - q^{81} + 6 q^{83} - 18 q^{85} - 36 q^{89} + 8 q^{91} - 5 q^{93} - 24 q^{95} + 7 q^{97}+O(q^{100}) \) 4 * q - q^3 + 3 * q^5 + 2 * q^7 + 2 * q^9 - 4 * q^13 + 3 * q^15 + 6 * q^17 + 8 * q^19 - 8 * q^21 - 12 * q^23 - 4 * q^25 + 5 * q^27 - 5 * q^31 - 6 * q^35 + q^37 - 4 * q^39 + 40 * q^43 + 24 * q^45 + 3 * q^49 + 6 * q^51 + 6 * q^53 + 8 * q^57 - 3 * q^59 - 4 * q^61 - 4 * q^63 - 48 * q^65 - 4 * q^67 + 3 * q^69 - 15 * q^71 - 4 * q^73 - 4 * q^75 + 2 * q^79 - q^81 + 6 * q^83 - 18 * q^85 - 36 * q^89 + 8 * q^91 - 5 * q^93 - 24 * q^95 + 7 * q^97

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