LMFDB - Embedded newform 1452.2.i.e.565.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1452,2,Mod(493,1452)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1452, 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("1452.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1452 = 2^{2} \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1452.i (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:	$11.5942783735$
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 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			565.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	1452.565
Dual form			1452.2.i.e.1213.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{3} +(-1.61803 + 1.17557i) q^{5} +(-0.618034 - 1.90211i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{3} +(-1.61803 + 1.17557i) q^{5} +(-0.618034 - 1.90211i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(1.61803 + 1.17557i) q^{13} +(0.618034 + 1.90211i) q^{15} +(-3.23607 + 2.35114i) q^{17} +(-1.85410 + 5.70634i) q^{19} -2.00000 q^{21} +(-0.309017 + 0.951057i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(-2.47214 - 7.60845i) q^{29} +(6.47214 + 4.70228i) q^{31} +(3.23607 + 2.35114i) q^{35} +(3.09017 + 9.51057i) q^{37} +(1.61803 - 1.17557i) q^{39} +(2.47214 - 7.60845i) q^{41} -2.00000 q^{43} +2.00000 q^{45} +(-2.47214 + 7.60845i) q^{47} +(2.42705 - 1.76336i) q^{49} +(1.23607 + 3.80423i) q^{51} +(1.61803 + 1.17557i) q^{53} +(4.85410 + 3.52671i) q^{57} +(3.70820 + 11.4127i) q^{59} +(-8.09017 + 5.87785i) q^{61} +(-0.618034 + 1.90211i) q^{63} -4.00000 q^{65} +12.0000 q^{67} +(-6.47214 + 4.70228i) q^{71} +(1.85410 + 5.70634i) q^{73} +(0.809017 + 0.587785i) q^{75} +(1.61803 + 1.17557i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-12.9443 + 9.40456i) q^{83} +(2.47214 - 7.60845i) q^{85} -8.00000 q^{87} -14.0000 q^{89} +(1.23607 - 3.80423i) q^{91} +(6.47214 - 4.70228i) q^{93} +(-3.70820 - 11.4127i) q^{95} +(1.61803 + 1.17557i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 2 q^{5} + 2 q^{7} - q^{9}+O(q^{10}) $ 4 * q - q^3 - 2 * q^5 + 2 * q^7 - q^9	$ 4 q - q^{3} - 2 q^{5} + 2 q^{7} - q^{9} + 2 q^{13} - 2 q^{15} - 4 q^{17} + 6 q^{19} - 8 q^{21} + q^{25} - q^{27} + 8 q^{29} + 8 q^{31} + 4 q^{35} - 10 q^{37} + 2 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} + 3 q^{49} - 4 q^{51} + 2 q^{53} + 6 q^{57} - 12 q^{59} - 10 q^{61} + 2 q^{63} - 16 q^{65} + 48 q^{67} - 8 q^{71} - 6 q^{73} + q^{75} + 2 q^{79} - q^{81} - 16 q^{83} - 8 q^{85} - 32 q^{87} - 56 q^{89} - 4 q^{91} + 8 q^{93} + 12 q^{95} + 2 q^{97}+O(q^{100}) $ 4 * q - q^3 - 2 * q^5 + 2 * q^7 - q^9 + 2 * q^13 - 2 * q^15 - 4 * q^17 + 6 * q^19 - 8 * q^21 + q^25 - q^27 + 8 * q^29 + 8 * q^31 + 4 * q^35 - 10 * q^37 + 2 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 + 3 * q^49 - 4 * q^51 + 2 * q^53 + 6 * q^57 - 12 * q^59 - 10 * q^61 + 2 * q^63 - 16 * q^65 + 48 * q^67 - 8 * q^71 - 6 * q^73 + q^75 + 2 * q^79 - q^81 - 16 * q^83 - 8 * q^85 - 32 * q^87 - 56 * q^89 - 4 * q^91 + 8 * q^93 + 12 * q^95 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1452\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$1333$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$		0			0
$5$	−1.61803	+	1.17557i	−0.723607	+	0.525731i	−0.887535	−	0.460741i	$-0.847584\pi$
$5$	−1.61803	+	1.17557i	−0.723607	+	0.525731i	0.163928	+	0.986472i	$0.447584\pi$
$6$		0			0
$7$	−0.618034	−	1.90211i	−0.233595	−	0.718931i	−0.997305	−	0.0733714i	$-0.976624\pi$
$7$	−0.618034	−	1.90211i	−0.233595	−	0.718931i	0.763710	−	0.645560i	$-0.223376\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	1.61803	+	1.17557i	0.448762	+	0.326045i	0.789107	−	0.614256i	$-0.210544\pi$
$13$	1.61803	+	1.17557i	0.448762	+	0.326045i	−0.340345	+	0.940301i	$0.610544\pi$
$14$		0			0
$15$	0.618034	+	1.90211i	0.159576	+	0.491123i
$16$		0			0
$17$	−3.23607	+	2.35114i	−0.784862	+	0.570235i	−0.906434	−	0.422347i	$-0.861206\pi$
$17$	−3.23607	+	2.35114i	−0.784862	+	0.570235i	0.121572	+	0.992583i	$0.461206\pi$
$18$		0			0
$19$	−1.85410	+	5.70634i	−0.425360	+	1.30912i	0.477289	+	0.878746i	$0.341620\pi$
$19$	−1.85410	+	5.70634i	−0.425360	+	1.30912i	−0.902649	+	0.430377i	$0.858380\pi$
$20$		0			0
$21$	−2.00000			−0.436436
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$		0			0
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$		0			0
$29$	−2.47214	−	7.60845i	−0.459064	−	1.41285i	−0.866297	−	0.499530i	$-0.833506\pi$
$29$	−2.47214	−	7.60845i	−0.459064	−	1.41285i	0.407233	−	0.913324i	$-0.366494\pi$
$30$		0			0
$31$	6.47214	+	4.70228i	1.16243	+	0.844555i	0.990083	−	0.140482i	$-0.0448651\pi$
$31$	6.47214	+	4.70228i	1.16243	+	0.844555i	0.172347	+	0.985036i	$0.444865\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.23607	+	2.35114i	0.546995	+	0.397415i
$36$		0			0
$37$	3.09017	+	9.51057i	0.508021	+	1.56353i	0.795632	+	0.605780i	$0.207139\pi$
$37$	3.09017	+	9.51057i	0.508021	+	1.56353i	−0.287611	+	0.957747i	$0.592861\pi$
$38$		0			0
$39$	1.61803	−	1.17557i	0.259093	−	0.188242i
$40$		0			0
$41$	2.47214	−	7.60845i	0.386083	−	1.18824i	−0.549609	−	0.835422i	$-0.685223\pi$
$41$	2.47214	−	7.60845i	0.386083	−	1.18824i	0.935692	−	0.352819i	$-0.114777\pi$
$42$		0			0
$43$	−2.00000			−0.304997			−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$		0			0
$45$	2.00000			0.298142
$46$		0			0
$47$	−2.47214	+	7.60845i	−0.360598	+	1.10981i	0.592094	+	0.805869i	$0.298301\pi$
$47$	−2.47214	+	7.60845i	−0.360598	+	1.10981i	−0.952692	+	0.303938i	$0.901699\pi$
$48$		0			0
$49$	2.42705	−	1.76336i	0.346722	−	0.251908i
$50$		0			0
$51$	1.23607	+	3.80423i	0.173084	+	0.532698i
$52$		0			0
$53$	1.61803	+	1.17557i	0.222254	+	0.161477i	0.693341	−	0.720610i	$-0.256138\pi$
$53$	1.61803	+	1.17557i	0.222254	+	0.161477i	−0.471087	+	0.882087i	$0.656138\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	4.85410	+	3.52671i	0.642942	+	0.467124i
$58$		0			0
$59$	3.70820	+	11.4127i	0.482767	+	1.48580i	0.835189	+	0.549963i	$0.185358\pi$
$59$	3.70820	+	11.4127i	0.482767	+	1.48580i	−0.352422	+	0.935841i	$0.614642\pi$
$60$		0			0
$61$	−8.09017	+	5.87785i	−1.03584	+	0.752582i	−0.969469	−	0.245213i	$-0.921142\pi$
$61$	−8.09017	+	5.87785i	−1.03584	+	0.752582i	−0.0663709	+	0.997795i	$0.521142\pi$
$62$		0			0
$63$	−0.618034	+	1.90211i	−0.0778650	+	0.239644i
$64$		0			0
$65$	−4.00000			−0.496139
$66$		0			0
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.47214	+	4.70228i	−0.768101	+	0.558058i	−0.901384	−	0.433020i	$-0.857448\pi$
$71$	−6.47214	+	4.70228i	−0.768101	+	0.558058i	0.133283	+	0.991078i	$0.457448\pi$
$72$		0			0
$73$	1.85410	+	5.70634i	0.217006	+	0.667876i	0.999005	+	0.0445966i	$0.0142003\pi$
$73$	1.85410	+	5.70634i	0.217006	+	0.667876i	−0.781999	+	0.623280i	$0.785800\pi$
$74$		0			0
$75$	0.809017	+	0.587785i	0.0934172	+	0.0678716i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.61803	+	1.17557i	0.182043	+	0.132262i	0.675075	−	0.737749i	$-0.264111\pi$
$79$	1.61803	+	1.17557i	0.182043	+	0.132262i	−0.493032	+	0.870011i	$0.664111\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−12.9443	+	9.40456i	−1.42082	+	1.03229i	−0.429183	+	0.903218i	$0.641198\pi$
$83$	−12.9443	+	9.40456i	−1.42082	+	1.03229i	−0.991636	+	0.129067i	$0.958802\pi$
$84$		0			0
$85$	2.47214	−	7.60845i	0.268141	−	0.825253i
$86$		0			0
$87$	−8.00000			−0.857690
$88$		0			0
$89$	−14.0000			−1.48400			−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000			−1.48400			−0.741999	+	0.670402i	$0.766122\pi$
$90$		0			0
$91$	1.23607	−	3.80423i	0.129575	−	0.398791i
$92$		0			0
$93$	6.47214	−	4.70228i	0.671129	−	0.487604i
$94$		0			0
$95$	−3.70820	−	11.4127i	−0.380454	−	1.17092i
$96$		0			0
$97$	1.61803	+	1.17557i	0.164286	+	0.119361i	0.666891	−	0.745155i	$-0.267625\pi$
$97$	1.61803	+	1.17557i	0.164286	+	0.119361i	−0.502604	+	0.864517i	$0.667625\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	12.9443	+	9.40456i	1.28800	+	0.935789i	0.999763	−	0.0217690i	$-0.00692985\pi$
$101$	12.9443	+	9.40456i	1.28800	+	0.935789i	0.288240	+	0.957558i	$0.406930\pi$
$102$		0			0
$103$	1.23607	+	3.80423i	0.121793	+	0.374842i	0.993303	−	0.115536i	$-0.0368587\pi$
$103$	1.23607	+	3.80423i	0.121793	+	0.374842i	−0.871510	+	0.490378i	$0.836859\pi$
$104$		0			0
$105$	3.23607	−	2.35114i	0.315808	−	0.229448i
$106$		0			0
$107$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$107$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$	10.0000			0.949158
$112$		0			0
$113$	1.85410	−	5.70634i	0.174419	−	0.536807i	−0.825187	−	0.564859i	$-0.808930\pi$
$113$	1.85410	−	5.70634i	0.174419	−	0.536807i	0.999606	+	0.0280521i	$0.00893043\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.618034	−	1.90211i	−0.0571373	−	0.175850i
$118$		0			0
$119$	6.47214	+	4.70228i	0.593300	+	0.431057i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−6.47214	−	4.70228i	−0.583573	−	0.423990i
$124$		0			0
$125$	−3.70820	−	11.4127i	−0.331672	−	1.02078i
$126$		0			0
$127$	8.09017	−	5.87785i	0.717886	−	0.521575i	−0.167822	−	0.985817i	$-0.553673\pi$
$127$	8.09017	−	5.87785i	0.717886	−	0.521575i	0.885708	+	0.464242i	$0.153673\pi$
$128$		0			0
$129$	−0.618034	+	1.90211i	−0.0544149	+	0.167472i
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	12.0000			1.04053
$134$		0			0
$135$	0.618034	−	1.90211i	0.0531919	−	0.163708i
$136$		0			0
$137$	1.61803	−	1.17557i	0.138238	−	0.100436i	−0.516517	−	0.856277i	$-0.672772\pi$
$137$	1.61803	−	1.17557i	0.138238	−	0.100436i	0.654755	+	0.755841i	$0.272772\pi$
$138$		0			0
$139$	−1.85410	−	5.70634i	−0.157263	−	0.484005i	0.841120	−	0.540848i	$-0.181897\pi$
$139$	−1.85410	−	5.70634i	−0.157263	−	0.484005i	−0.998383	+	0.0568428i	$0.981897\pi$
$140$		0			0
$141$	6.47214	+	4.70228i	0.545052	+	0.396004i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	12.9443	+	9.40456i	1.07496	+	0.781007i
$146$		0			0
$147$	−0.927051	−	2.85317i	−0.0764619	−	0.235325i
$148$		0			0
$149$	−16.1803	+	11.7557i	−1.32555	+	0.963065i	−0.325700	+	0.945473i	$0.605600\pi$
$149$	−16.1803	+	11.7557i	−1.32555	+	0.963065i	−0.999845	+	0.0175917i	$0.994400\pi$
$150$		0			0
$151$	−3.09017	+	9.51057i	−0.251474	+	0.773959i	0.743029	+	0.669259i	$0.233388\pi$
$151$	−3.09017	+	9.51057i	−0.251474	+	0.773959i	−0.994504	+	0.104700i	$0.966612\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$	−16.0000			−1.28515
$156$		0			0
$157$	1.85410	−	5.70634i	0.147973	−	0.455415i	−0.849408	−	0.527737i	$-0.823041\pi$
$157$	1.85410	−	5.70634i	0.147973	−	0.455415i	0.997381	+	0.0723214i	$0.0230407\pi$
$158$		0			0
$159$	1.61803	−	1.17557i	0.128318	−	0.0932288i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−12.9443	−	9.40456i	−1.01387	−	0.736622i	−0.0488556	−	0.998806i	$-0.515557\pi$
$163$	−12.9443	−	9.40456i	−1.01387	−	0.736622i	−0.965018	+	0.262184i	$0.915557\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.70820	−	7.05342i	−0.751243	−	0.545810i	0.144969	−	0.989436i	$-0.453692\pi$
$167$	−9.70820	−	7.05342i	−0.751243	−	0.545810i	−0.896212	+	0.443626i	$0.853692\pi$
$168$		0			0
$169$	−2.78115	−	8.55951i	−0.213935	−	0.658424i
$170$		0			0
$171$	4.85410	−	3.52671i	0.371202	−	0.269694i
$172$		0			0
$173$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$173$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$174$		0			0
$175$	2.00000			0.151186
$176$		0			0
$177$	12.0000			0.901975
$178$		0			0
$179$	−3.70820	+	11.4127i	−0.277164	+	0.853024i	0.711474	+	0.702712i	$0.248028\pi$
$179$	−3.70820	+	11.4127i	−0.277164	+	0.853024i	−0.988639	+	0.150312i	$0.951972\pi$
$180$		0			0
$181$	8.09017	−	5.87785i	0.601338	−	0.436897i	−0.245016	−	0.969519i	$-0.578793\pi$
$181$	8.09017	−	5.87785i	0.601338	−	0.436897i	0.846353	+	0.532622i	$0.178793\pi$
$182$		0			0
$183$	3.09017	+	9.51057i	0.228432	+	0.703041i
$184$		0			0
$185$	−16.1803	−	11.7557i	−1.18960	−	0.864297i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	1.61803	+	1.17557i	0.117695	+	0.0855102i
$190$		0			0
$191$	4.94427	+	15.2169i	0.357755	+	1.10106i	0.954395	+	0.298547i	$0.0965021\pi$
$191$	4.94427	+	15.2169i	0.357755	+	1.10106i	−0.596640	+	0.802509i	$0.703498\pi$
$192$		0			0
$193$	17.7984	−	12.9313i	1.28115	−	0.930814i	0.281568	−	0.959541i	$-0.409146\pi$
$193$	17.7984	−	12.9313i	1.28115	−	0.930814i	0.999587	+	0.0287278i	$0.00914559\pi$
$194$		0			0
$195$	−1.23607	+	3.80423i	−0.0885167	+	0.272426i
$196$		0			0
$197$	24.0000			1.70993			0.854965	−	0.518686i	$-0.173579\pi$
$197$	24.0000			1.70993			0.854965	+	0.518686i	$0.173579\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$		0			0
$201$	3.70820	−	11.4127i	0.261557	−	0.804988i
$202$		0			0
$203$	−12.9443	+	9.40456i	−0.908510	+	0.660071i
$204$		0			0
$205$	4.94427	+	15.2169i	0.345323	+	1.06279i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−14.5623	−	10.5801i	−1.00251	−	0.728366i	−0.0398855	−	0.999204i	$-0.512699\pi$
$211$	−14.5623	−	10.5801i	−1.00251	−	0.728366i	−0.962625	+	0.270838i	$0.912699\pi$
$212$		0			0
$213$	2.47214	+	7.60845i	0.169388	+	0.521323i
$214$		0			0
$215$	3.23607	−	2.35114i	0.220698	−	0.160346i
$216$		0			0
$217$	4.94427	−	15.2169i	0.335639	−	1.03299i
$218$		0			0
$219$	6.00000			0.405442
$220$		0			0
$221$	−8.00000			−0.538138
$222$		0			0
$223$	−1.23607	+	3.80423i	−0.0827732	+	0.254750i	−0.983875	−	0.178858i	$-0.942760\pi$
$223$	−1.23607	+	3.80423i	−0.0827732	+	0.254750i	0.901102	+	0.433608i	$0.142760\pi$
$224$		0			0
$225$	0.809017	−	0.587785i	0.0539345	−	0.0391857i
$226$		0			0
$227$	−7.41641	−	22.8254i	−0.492244	−	1.51497i	−0.821208	−	0.570629i	$-0.806699\pi$
$227$	−7.41641	−	22.8254i	−0.492244	−	1.51497i	0.328963	−	0.944343i	$-0.393301\pi$
$228$		0			0
$229$	11.3262	+	8.22899i	0.748459	+	0.543787i	0.895349	−	0.445366i	$-0.146926\pi$
$229$	11.3262	+	8.22899i	0.748459	+	0.543787i	−0.146890	+	0.989153i	$0.546926\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−19.4164	−	14.1068i	−1.27201	−	0.924170i	−0.272730	−	0.962090i	$-0.587927\pi$
$233$	−19.4164	−	14.1068i	−1.27201	−	0.924170i	−0.999281	+	0.0379203i	$0.987927\pi$
$234$		0			0
$235$	−4.94427	−	15.2169i	−0.322529	−	0.992641i
$236$		0			0
$237$	1.61803	−	1.17557i	0.105103	−	0.0763615i
$238$		0			0
$239$	1.23607	−	3.80423i	0.0799546	−	0.246075i	−0.903087	−	0.429458i	$-0.858705\pi$
$239$	1.23607	−	3.80423i	0.0799546	−	0.246075i	0.983042	+	0.183383i	$0.0587048\pi$
$240$		0			0
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−1.85410	+	5.70634i	−0.118454	+	0.364565i
$246$		0			0
$247$	−9.70820	+	7.05342i	−0.617718	+	0.448799i
$248$		0			0
$249$	4.94427	+	15.2169i	0.313331	+	0.964332i
$250$		0			0
$251$	−3.23607	−	2.35114i	−0.204259	−	0.148403i	0.480953	−	0.876746i	$-0.340291\pi$
$251$	−3.23607	−	2.35114i	−0.204259	−	0.148403i	−0.685212	+	0.728343i	$0.740291\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−6.47214	−	4.70228i	−0.405301	−	0.294468i
$256$		0			0
$257$	−9.27051	−	28.5317i	−0.578279	−	1.77976i	−0.624734	−	0.780838i	$-0.714792\pi$
$257$	−9.27051	−	28.5317i	−0.578279	−	1.77976i	0.0464552	−	0.998920i	$-0.485208\pi$
$258$		0			0
$259$	16.1803	−	11.7557i	1.00540	−	0.730464i
$260$		0			0
$261$	−2.47214	+	7.60845i	−0.153021	+	0.470951i
$262$		0			0
$263$	−4.00000			−0.246651			−0.123325	−	0.992366i	$-0.539356\pi$
$263$	−4.00000			−0.246651			−0.123325	+	0.992366i	$0.539356\pi$
$264$		0			0
$265$	−4.00000			−0.245718
$266$		0			0
$267$	−4.32624	+	13.3148i	−0.264761	+	0.814852i
$268$		0			0
$269$	1.61803	−	1.17557i	0.0986533	−	0.0716758i	−0.537365	−	0.843350i	$-0.680580\pi$
$269$	1.61803	−	1.17557i	0.0986533	−	0.0716758i	0.636018	+	0.771674i	$0.280580\pi$
$270$		0			0
$271$	3.09017	+	9.51057i	0.187714	+	0.577726i	0.999985	−	0.00555577i	$-0.00176847\pi$
$271$	3.09017	+	9.51057i	0.187714	+	0.577726i	−0.812270	+	0.583281i	$0.801768\pi$
$272$		0			0
$273$	−3.23607	−	2.35114i	−0.195856	−	0.142298i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−11.3262	−	8.22899i	−0.680528	−	0.494432i	0.193005	−	0.981198i	$-0.438177\pi$
$277$	−11.3262	−	8.22899i	−0.680528	−	0.494432i	−0.873533	+	0.486765i	$0.838177\pi$
$278$		0			0
$279$	−2.47214	−	7.60845i	−0.148003	−	0.455506i
$280$		0			0
$281$	6.47214	−	4.70228i	0.386095	−	0.280515i	−0.377758	−	0.925904i	$-0.623305\pi$
$281$	6.47214	−	4.70228i	0.386095	−	0.280515i	0.763854	+	0.645390i	$0.223305\pi$
$282$		0			0
$283$	−8.03444	+	24.7275i	−0.477598	+	1.46990i	0.364824	+	0.931077i	$0.381129\pi$
$283$	−8.03444	+	24.7275i	−0.477598	+	1.46990i	−0.842422	+	0.538819i	$0.818871\pi$
$284$		0			0
$285$	−12.0000			−0.710819
$286$		0			0
$287$	−16.0000			−0.944450
$288$		0			0
$289$	−0.309017	+	0.951057i	−0.0181775	+	0.0559445i
$290$		0			0
$291$	1.61803	−	1.17557i	0.0948508	−	0.0689132i
$292$		0			0
$293$	6.18034	+	19.0211i	0.361059	+	1.11123i	0.952412	+	0.304813i	$0.0985941\pi$
$293$	6.18034	+	19.0211i	0.361059	+	1.11123i	−0.591353	+	0.806413i	$0.701406\pi$
$294$		0			0
$295$	−19.4164	−	14.1068i	−1.13047	−	0.821332i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	1.23607	+	3.80423i	0.0712458	+	0.219272i
$302$		0			0
$303$	12.9443	−	9.40456i	0.743629	−	0.540278i
$304$		0			0
$305$	6.18034	−	19.0211i	0.353885	−	1.08915i
$306$		0			0
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$		0			0
$311$	−4.94427	+	15.2169i	−0.280364	+	0.862871i	0.707386	+	0.706827i	$0.249874\pi$
$311$	−4.94427	+	15.2169i	−0.280364	+	0.862871i	−0.987750	+	0.156044i	$0.950126\pi$
$312$		0			0
$313$	14.5623	−	10.5801i	0.823110	−	0.598025i	−0.0944915	−	0.995526i	$-0.530123\pi$
$313$	14.5623	−	10.5801i	0.823110	−	0.598025i	0.917602	+	0.397501i	$0.130123\pi$
$314$		0			0
$315$	−1.23607	−	3.80423i	−0.0696445	−	0.214344i
$316$		0			0
$317$	11.3262	+	8.22899i	0.636145	+	0.462186i	0.858524	−	0.512774i	$-0.171382\pi$
$317$	11.3262	+	8.22899i	0.636145	+	0.462186i	−0.222379	+	0.974960i	$0.571382\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−7.41641	−	22.8254i	−0.412660	−	1.27004i
$324$		0			0
$325$	−1.61803	+	1.17557i	−0.0897524	+	0.0652089i
$326$		0			0
$327$	−3.09017	+	9.51057i	−0.170887	+	0.525935i
$328$		0			0
$329$	16.0000			0.882109
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$		0			0
$333$	3.09017	−	9.51057i	0.169340	−	0.521176i
$334$		0			0
$335$	−19.4164	+	14.1068i	−1.06083	+	0.770739i
$336$		0			0
$337$	4.32624	+	13.3148i	0.235665	+	0.725303i	0.997032	+	0.0769821i	$0.0245284\pi$
$337$	4.32624	+	13.3148i	0.235665	+	0.725303i	−0.761367	+	0.648321i	$0.775472\pi$
$338$		0			0
$339$	−4.85410	−	3.52671i	−0.263639	−	0.191545i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−16.1803	−	11.7557i	−0.873656	−	0.634748i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$347$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$348$		0			0
$349$	−4.32624	+	13.3148i	−0.231578	+	0.712724i	0.765979	+	0.642866i	$0.222255\pi$
$349$	−4.32624	+	13.3148i	−0.231578	+	0.712724i	−0.997557	+	0.0698585i	$0.977745\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$	4.94427	−	15.2169i	0.262415	−	0.807629i
$356$		0			0
$357$	6.47214	−	4.70228i	0.342542	−	0.248871i
$358$		0			0
$359$	−2.47214	−	7.60845i	−0.130474	−	0.401559i	0.864384	−	0.502832i	$-0.167708\pi$
$359$	−2.47214	−	7.60845i	−0.130474	−	0.401559i	−0.994859	+	0.101273i	$0.967708\pi$
$360$		0			0
$361$	−13.7533	−	9.99235i	−0.723857	−	0.525913i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−9.70820	−	7.05342i	−0.508151	−	0.369193i
$366$		0			0
$367$	−1.23607	−	3.80423i	−0.0645222	−	0.198579i	0.913598	−	0.406618i	$-0.133292\pi$
$367$	−1.23607	−	3.80423i	−0.0645222	−	0.198579i	−0.978121	+	0.208039i	$0.933292\pi$
$368$		0			0
$369$	−6.47214	+	4.70228i	−0.336926	+	0.244791i
$370$		0			0
$371$	1.23607	−	3.80423i	0.0641735	−	0.197506i
$372$		0			0
$373$	34.0000			1.76045			0.880227	−	0.474554i	$-0.157390\pi$
$373$	34.0000			1.76045			0.880227	+	0.474554i	$0.157390\pi$
$374$		0			0
$375$	−12.0000			−0.619677
$376$		0			0
$377$	4.94427	−	15.2169i	0.254643	−	0.783710i
$378$		0			0
$379$	−12.9443	+	9.40456i	−0.664903	+	0.483080i	−0.868315	−	0.496013i	$-0.834797\pi$
$379$	−12.9443	+	9.40456i	−0.664903	+	0.483080i	0.203412	+	0.979093i	$0.434797\pi$
$380$		0			0
$381$	−3.09017	−	9.51057i	−0.158314	−	0.487241i
$382$		0			0
$383$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$383$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.61803	+	1.17557i	0.0822493	+	0.0597576i
$388$		0			0
$389$	−4.32624	−	13.3148i	−0.219349	−	0.675087i	−0.998816	−	0.0486437i	$-0.984510\pi$
$389$	−4.32624	−	13.3148i	−0.219349	−	0.675087i	0.779467	−	0.626443i	$-0.215490\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	3.70820	−	11.4127i	0.187054	−	0.575693i
$394$		0			0
$395$	−4.00000			−0.201262
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$		0			0
$399$	3.70820	−	11.4127i	0.185642	−	0.571349i
$400$		0			0
$401$	14.5623	−	10.5801i	0.727207	−	0.528347i	−0.161472	−	0.986877i	$-0.551624\pi$
$401$	14.5623	−	10.5801i	0.727207	−	0.528347i	0.888679	+	0.458531i	$0.151624\pi$
$402$		0			0
$403$	4.94427	+	15.2169i	0.246292	+	0.758008i
$404$		0			0
$405$	−1.61803	−	1.17557i	−0.0804008	−	0.0584146i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	8.09017	+	5.87785i	0.400033	+	0.290641i	0.769554	−	0.638581i	$-0.220478\pi$
$409$	8.09017	+	5.87785i	0.400033	+	0.290641i	−0.369521	+	0.929222i	$0.620478\pi$
$410$		0			0
$411$	−0.618034	−	1.90211i	−0.0304854	−	0.0938243i
$412$		0			0
$413$	19.4164	−	14.1068i	0.955419	−	0.694153i
$414$		0			0
$415$	9.88854	−	30.4338i	0.485410	−	1.49394i
$416$		0			0
$417$	−6.00000			−0.293821
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	1.85410	−	5.70634i	0.0903634	−	0.278110i	−0.895654	−	0.444751i	$-0.853292\pi$
$421$	1.85410	−	5.70634i	0.0903634	−	0.278110i	0.986018	+	0.166641i	$0.0532921\pi$
$422$		0			0
$423$	6.47214	−	4.70228i	0.314686	−	0.228633i
$424$		0			0
$425$	−1.23607	−	3.80423i	−0.0599581	−	0.184532i
$426$		0			0
$427$	16.1803	+	11.7557i	0.783022	+	0.568898i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	3.23607	+	2.35114i	0.155876	+	0.113250i	0.662989	−	0.748629i	$-0.269287\pi$
$431$	3.23607	+	2.35114i	0.155876	+	0.113250i	−0.507113	+	0.861879i	$0.669287\pi$
$432$		0			0
$433$	−5.56231	−	17.1190i	−0.267307	−	0.822687i	−0.991153	−	0.132725i	$-0.957627\pi$
$433$	−5.56231	−	17.1190i	−0.267307	−	0.822687i	0.723845	−	0.689962i	$-0.242373\pi$
$434$		0			0
$435$	12.9443	−	9.40456i	0.620630	−	0.450914i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	34.0000			1.62273			0.811366	−	0.584539i	$-0.198725\pi$
$439$	34.0000			1.62273			0.811366	+	0.584539i	$0.198725\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	3.70820	−	11.4127i	0.176182	−	0.542233i	−0.823503	−	0.567311i	$-0.807984\pi$
$443$	3.70820	−	11.4127i	0.176182	−	0.542233i	0.999685	+	0.0250786i	$0.00798361\pi$
$444$		0			0
$445$	22.6525	−	16.4580i	1.07383	−	0.780183i
$446$		0			0
$447$	6.18034	+	19.0211i	0.292320	+	0.899669i
$448$		0			0
$449$	−33.9787	−	24.6870i	−1.60355	−	1.16505i	−0.880236	−	0.474536i	$-0.842616\pi$
$449$	−33.9787	−	24.6870i	−1.60355	−	1.16505i	−0.723319	−	0.690514i	$-0.757384\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	8.09017	+	5.87785i	0.380109	+	0.276166i
$454$		0			0
$455$	2.47214	+	7.60845i	0.115896	+	0.356690i
$456$		0			0
$457$	−17.7984	+	12.9313i	−0.832573	+	0.604900i	−0.920286	−	0.391246i	$-0.872044\pi$
$457$	−17.7984	+	12.9313i	−0.832573	+	0.604900i	0.0877132	+	0.996146i	$0.472044\pi$
$458$		0			0
$459$	1.23607	−	3.80423i	0.0576947	−	0.177566i
$460$		0			0
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$		0			0
$465$	−4.94427	+	15.2169i	−0.229285	+	0.705667i
$466$		0			0
$467$	16.1803	−	11.7557i	0.748737	−	0.543989i	−0.146698	−	0.989181i	$-0.546865\pi$
$467$	16.1803	−	11.7557i	0.748737	−	0.543989i	0.895435	+	0.445192i	$0.146865\pi$
$468$		0			0
$469$	−7.41641	−	22.8254i	−0.342458	−	1.05398i
$470$		0			0
$471$	−4.85410	−	3.52671i	−0.223665	−	0.162502i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−4.85410	−	3.52671i	−0.222721	−	0.161817i
$476$		0			0
$477$	−0.618034	−	1.90211i	−0.0282978	−	0.0870918i
$478$		0			0
$479$	−22.6525	+	16.4580i	−1.03502	+	0.751985i	−0.969307	−	0.245854i	$-0.920932\pi$
$479$	−22.6525	+	16.4580i	−1.03502	+	0.751985i	−0.0657112	+	0.997839i	$0.520932\pi$
$480$		0			0
$481$	−6.18034	+	19.0211i	−0.281799	+	0.867289i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.00000			−0.181631
$486$		0			0
$487$	−2.47214	+	7.60845i	−0.112023	+	0.344772i	−0.991315	−	0.131512i	$-0.958017\pi$
$487$	−2.47214	+	7.60845i	−0.112023	+	0.344772i	0.879291	+	0.476284i	$0.158017\pi$
$488$		0			0
$489$	−12.9443	+	9.40456i	−0.585360	+	0.425289i
$490$		0			0
$491$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$491$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$492$		0			0
$493$	25.8885	+	18.8091i	1.16596	+	0.847121i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.9443	+	9.40456i	0.580630	+	0.421852i
$498$		0			0
$499$	1.23607	+	3.80423i	0.0553340	+	0.170301i	0.974904	−	0.222626i	$-0.0714628\pi$
$499$	1.23607	+	3.80423i	0.0553340	+	0.170301i	−0.919570	+	0.392926i	$0.871463\pi$
$500$		0			0
$501$	−9.70820	+	7.05342i	−0.433731	+	0.315124i
$502$		0			0
$503$	−6.18034	+	19.0211i	−0.275568	+	0.848110i	0.713501	+	0.700654i	$0.247108\pi$
$503$	−6.18034	+	19.0211i	−0.275568	+	0.848110i	−0.989069	+	0.147456i	$0.952892\pi$
$504$		0			0
$505$	−32.0000			−1.42398
$506$		0			0
$507$	−9.00000			−0.399704
$508$		0			0
$509$	−0.618034	+	1.90211i	−0.0273939	+	0.0843097i	−0.963819	−	0.266558i	$-0.914113\pi$
$509$	−0.618034	+	1.90211i	−0.0273939	+	0.0843097i	0.936425	+	0.350868i	$0.114113\pi$
$510$		0			0
$511$	9.70820	−	7.05342i	0.429466	−	0.312025i
$512$		0			0
$513$	−1.85410	−	5.70634i	−0.0818606	−	0.251941i
$514$		0			0
$515$	−6.47214	−	4.70228i	−0.285196	−	0.207207i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.85410	+	5.70634i	0.0812297	+	0.249999i	0.983421	−	0.181337i	$-0.0580424\pi$
$521$	1.85410	+	5.70634i	0.0812297	+	0.249999i	−0.902191	+	0.431336i	$0.858042\pi$
$522$		0			0
$523$	27.5066	−	19.9847i	1.20278	−	0.873870i	0.208224	−	0.978081i	$-0.433232\pi$
$523$	27.5066	−	19.9847i	1.20278	−	0.873870i	0.994555	+	0.104211i	$0.0332319\pi$
$524$		0			0
$525$	0.618034	−	1.90211i	0.0269732	−	0.0830150i
$526$		0			0
$527$	−32.0000			−1.39394
$528$		0			0
$529$	−23.0000			−1.00000
$530$		0			0
$531$	3.70820	−	11.4127i	0.160922	−	0.495268i
$532$		0			0
$533$	12.9443	−	9.40456i	0.560679	−	0.407357i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	9.70820	+	7.05342i	0.418940	+	0.304378i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	14.5623	+	10.5801i	0.626082	+	0.454876i	0.855041	−	0.518561i	$-0.173532\pi$
$541$	14.5623	+	10.5801i	0.626082	+	0.454876i	−0.228958	+	0.973436i	$0.573532\pi$
$542$		0			0
$543$	−3.09017	−	9.51057i	−0.132612	−	0.408137i
$544$		0			0
$545$	16.1803	−	11.7557i	0.693090	−	0.503559i
$546$		0			0
$547$	−0.618034	+	1.90211i	−0.0264252	+	0.0813285i	−0.963399	−	0.268070i	$-0.913614\pi$
$547$	−0.618034	+	1.90211i	−0.0264252	+	0.0813285i	0.936974	+	0.349399i	$0.113614\pi$
$548$		0			0
$549$	10.0000			0.426790
$550$		0			0
$551$	48.0000			2.04487
$552$		0			0
$553$	1.23607	−	3.80423i	0.0525630	−	0.161772i
$554$		0			0
$555$	−16.1803	+	11.7557i	−0.686817	+	0.499002i
$556$		0			0
$557$	6.18034	+	19.0211i	0.261869	+	0.805951i	0.992398	+	0.123069i	$0.0392737\pi$
$557$	6.18034	+	19.0211i	0.261869	+	0.805951i	−0.730529	+	0.682882i	$0.760726\pi$
$558$		0			0
$559$	−3.23607	−	2.35114i	−0.136871	−	0.0994427i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	29.1246	+	21.1603i	1.22746	+	0.891799i	0.996697	−	0.0812119i	$-0.0258790\pi$
$563$	29.1246	+	21.1603i	1.22746	+	0.891799i	0.230759	+	0.973011i	$0.425879\pi$
$564$		0			0
$565$	3.70820	+	11.4127i	0.156005	+	0.480135i
$566$		0			0
$567$	1.61803	−	1.17557i	0.0679510	−	0.0493693i
$568$		0			0
$569$	6.18034	−	19.0211i	0.259093	−	0.797407i	−0.733902	−	0.679255i	$-0.762303\pi$
$569$	6.18034	−	19.0211i	0.259093	−	0.797407i	0.992996	−	0.118152i	$-0.0376970\pi$
$570$		0			0
$571$	−10.0000			−0.418487			−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000			−0.418487			−0.209243	+	0.977864i	$0.567100\pi$
$572$		0			0
$573$	16.0000			0.668410
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−27.5066	+	19.9847i	−1.14511	+	0.831974i	−0.987824	−	0.155579i	$-0.950276\pi$
$577$	−27.5066	+	19.9847i	−1.14511	+	0.831974i	−0.157290	+	0.987552i	$0.550276\pi$
$578$		0			0
$579$	−6.79837	−	20.9232i	−0.282531	−	0.869540i
$580$		0			0
$581$	25.8885	+	18.8091i	1.07404	+	0.780334i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	3.23607	+	2.35114i	0.133795	+	0.0972077i
$586$		0			0
$587$	13.5967	+	41.8465i	0.561198	+	1.72719i	0.678987	+	0.734151i	$0.262419\pi$
$587$	13.5967	+	41.8465i	0.561198	+	1.72719i	−0.117789	+	0.993039i	$0.537581\pi$
$588$		0			0
$589$	−38.8328	+	28.2137i	−1.60008	+	1.16252i
$590$		0			0
$591$	7.41641	−	22.8254i	0.305070	−	0.938910i
$592$		0			0
$593$	−16.0000			−0.657041			−0.328521	−	0.944497i	$-0.606550\pi$
$593$	−16.0000			−0.657041			−0.328521	+	0.944497i	$0.606550\pi$
$594$		0			0
$595$	−16.0000			−0.655936
$596$		0			0
$597$	−4.94427	+	15.2169i	−0.202356	+	0.622786i
$598$		0			0
$599$	−19.4164	+	14.1068i	−0.793333	+	0.576390i	−0.908951	−	0.416904i	$-0.863115\pi$
$599$	−19.4164	+	14.1068i	−0.793333	+	0.576390i	0.115618	+	0.993294i	$0.463115\pi$
$600$		0			0
$601$	−9.27051	−	28.5317i	−0.378152	−	1.16383i	−0.941327	−	0.337495i	$-0.890420\pi$
$601$	−9.27051	−	28.5317i	−0.378152	−	1.16383i	0.563175	−	0.826337i	$-0.309580\pi$
$602$		0			0
$603$	−9.70820	−	7.05342i	−0.395349	−	0.287238i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.3262	−	8.22899i	−0.459718	−	0.334005i	0.333703	−	0.942678i	$-0.391702\pi$
$607$	−11.3262	−	8.22899i	−0.459718	−	0.334005i	−0.793421	+	0.608674i	$0.791702\pi$
$608$		0			0
$609$	4.94427	+	15.2169i	0.200352	+	0.616620i
$610$		0			0
$611$	−12.9443	+	9.40456i	−0.523669	+	0.380468i
$612$		0			0
$613$	0.618034	−	1.90211i	0.0249622	−	0.0768256i	−0.937799	−	0.347178i	$-0.887140\pi$
$613$	0.618034	−	1.90211i	0.0249622	−	0.0768256i	0.962762	+	0.270352i	$0.0871401\pi$
$614$		0			0
$615$	16.0000			0.645182
$616$		0			0
$617$	−10.0000			−0.402585			−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000			−0.402585			−0.201292	+	0.979531i	$0.564514\pi$
$618$		0			0
$619$	−9.88854	+	30.4338i	−0.397454	+	1.22324i	0.529580	+	0.848260i	$0.322350\pi$
$619$	−9.88854	+	30.4338i	−0.397454	+	1.22324i	−0.927034	+	0.374978i	$0.877650\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.65248	+	26.6296i	0.346654	+	1.06689i
$624$		0			0
$625$	15.3713	+	11.1679i	0.614853	+	0.446717i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−32.3607	−	23.5114i	−1.29030	−	0.937461i
$630$		0			0
$631$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$631$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$632$		0			0
$633$	−14.5623	+	10.5801i	−0.578800	+	0.420523i
$634$		0			0
$635$	−6.18034	+	19.0211i	−0.245259	+	0.754831i
$636$		0			0
$637$	6.00000			0.237729
$638$		0			0
$639$	8.00000			0.316475
$640$		0			0
$641$	−1.85410	+	5.70634i	−0.0732326	+	0.225387i	−0.980973	−	0.194147i	$-0.937806\pi$
$641$	−1.85410	+	5.70634i	−0.0732326	+	0.225387i	0.907740	+	0.419533i	$0.137806\pi$
$642$		0			0
$643$	12.9443	−	9.40456i	0.510472	−	0.370880i	−0.302530	−	0.953140i	$-0.597831\pi$
$643$	12.9443	−	9.40456i	0.510472	−	0.370880i	0.813003	+	0.582260i	$0.197831\pi$
$644$		0			0
$645$	−1.23607	−	3.80423i	−0.0486701	−	0.149791i
$646$		0			0
$647$	12.9443	+	9.40456i	0.508892	+	0.369732i	0.812403	−	0.583096i	$-0.198159\pi$
$647$	12.9443	+	9.40456i	0.508892	+	0.369732i	−0.303511	+	0.952828i	$0.598159\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−12.9443	−	9.40456i	−0.507326	−	0.368594i
$652$		0			0
$653$	1.85410	+	5.70634i	0.0725566	+	0.223306i	0.980758	−	0.195227i	$-0.0625443\pi$
$653$	1.85410	+	5.70634i	0.0725566	+	0.223306i	−0.908201	+	0.418533i	$0.862544\pi$
$654$		0			0
$655$	−19.4164	+	14.1068i	−0.758662	+	0.551200i
$656$		0			0
$657$	1.85410	−	5.70634i	0.0723354	−	0.222625i
$658$		0			0
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$		0			0
$661$	30.0000			1.16686			0.583432	−	0.812162i	$-0.301709\pi$
$661$	30.0000			1.16686			0.583432	+	0.812162i	$0.301709\pi$
$662$		0			0
$663$	−2.47214	+	7.60845i	−0.0960098	+	0.295488i
$664$		0			0
$665$	−19.4164	+	14.1068i	−0.752936	+	0.547040i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	3.23607	+	2.35114i	0.125114	+	0.0909004i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	17.7984	+	12.9313i	0.686077	+	0.498464i	0.875368	−	0.483457i	$-0.160619\pi$
$673$	17.7984	+	12.9313i	0.686077	+	0.498464i	−0.189291	+	0.981921i	$0.560619\pi$
$674$		0			0
$675$	−0.309017	−	0.951057i	−0.0118941	−	0.0366062i
$676$		0			0
$677$	−6.47214	+	4.70228i	−0.248744	+	0.180723i	−0.705170	−	0.709038i	$-0.749129\pi$
$677$	−6.47214	+	4.70228i	−0.248744	+	0.180723i	0.456426	+	0.889761i	$0.349129\pi$
$678$		0			0
$679$	1.23607	−	3.80423i	0.0474359	−	0.145993i
$680$		0			0
$681$	−24.0000			−0.919682
$682$		0			0
$683$	44.0000			1.68361			0.841807	−	0.539779i	$-0.181492\pi$
$683$	44.0000			1.68361			0.841807	+	0.539779i	$0.181492\pi$
$684$		0			0
$685$	−1.23607	+	3.80423i	−0.0472277	+	0.145352i
$686$		0			0
$687$	11.3262	−	8.22899i	0.432123	−	0.313956i
$688$		0			0
$689$	1.23607	+	3.80423i	0.0470904	+	0.144929i
$690$		0			0
$691$	6.47214	+	4.70228i	0.246212	+	0.178883i	0.704046	−	0.710154i	$-0.251375\pi$
$691$	6.47214	+	4.70228i	0.246212	+	0.178883i	−0.457835	+	0.889037i	$0.651375\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	9.70820	+	7.05342i	0.368253	+	0.267552i
$696$		0			0
$697$	9.88854	+	30.4338i	0.374555	+	1.15276i
$698$		0			0
$699$	−19.4164	+	14.1068i	−0.734396	+	0.533570i
$700$		0			0
$701$	−11.1246	+	34.2380i	−0.420171	+	1.29315i	0.487372	+	0.873194i	$0.337955\pi$
$701$	−11.1246	+	34.2380i	−0.420171	+	1.29315i	−0.907543	+	0.419959i	$0.862045\pi$
$702$		0			0
$703$	−60.0000			−2.26294
$704$		0			0
$705$	−16.0000			−0.602595
$706$		0			0
$707$	9.88854	−	30.4338i	0.371897	−	1.14458i
$708$		0			0
$709$	−27.5066	+	19.9847i	−1.03303	+	0.750541i	−0.968913	−	0.247401i	$-0.920423\pi$
$709$	−27.5066	+	19.9847i	−1.03303	+	0.750541i	−0.0641181	+	0.997942i	$0.520423\pi$
$710$		0			0
$711$	−0.618034	−	1.90211i	−0.0231781	−	0.0713348i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−3.23607	−	2.35114i	−0.120853	−	0.0878050i
$718$		0			0
$719$	12.3607	+	38.0423i	0.460976	+	1.41874i	0.863974	+	0.503536i	$0.167968\pi$
$719$	12.3607	+	38.0423i	0.460976	+	1.41874i	−0.402999	+	0.915201i	$0.632032\pi$
$720$		0			0
$721$	6.47214	−	4.70228i	0.241035	−	0.175122i
$722$		0			0
$723$	−5.56231	+	17.1190i	−0.206864	+	0.636663i
$724$		0			0
$725$	8.00000			0.297113
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	6.47214	−	4.70228i	0.239381	−	0.173920i
$732$		0			0
$733$	−8.03444	−	24.7275i	−0.296759	−	0.913330i	−0.982625	−	0.185602i	$-0.940576\pi$
$733$	−8.03444	−	24.7275i	−0.296759	−	0.913330i	0.685866	−	0.727728i	$-0.259424\pi$
$734$		0			0
$735$	4.85410	+	3.52671i	0.179046	+	0.130085i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	27.5066	+	19.9847i	1.01185	+	0.735149i	0.964595	−	0.263734i	$-0.0849541\pi$
$739$	27.5066	+	19.9847i	1.01185	+	0.735149i	0.0472504	+	0.998883i	$0.484954\pi$
$740$		0			0
$741$	3.70820	+	11.4127i	0.136224	+	0.419255i
$742$		0			0
$743$	32.3607	−	23.5114i	1.18720	−	0.862550i	0.194233	−	0.980955i	$-0.437778\pi$
$743$	32.3607	−	23.5114i	1.18720	−	0.862550i	0.992965	+	0.118405i	$0.0377783\pi$
$744$		0			0
$745$	12.3607	−	38.0423i	0.452860	−	1.39376i
$746$		0			0
$747$	16.0000			0.585409
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−9.88854	+	30.4338i	−0.360838	+	1.11055i	0.591708	+	0.806152i	$0.298454\pi$
$751$	−9.88854	+	30.4338i	−0.360838	+	1.11055i	−0.952546	+	0.304393i	$0.901546\pi$
$752$		0			0
$753$	−3.23607	+	2.35114i	−0.117929	+	0.0856803i
$754$		0			0
$755$	−6.18034	−	19.0211i	−0.224926	−	0.692250i
$756$		0			0
$757$	−43.6869	−	31.7404i	−1.58783	−	1.15362i	−0.906959	−	0.421220i	$-0.861602\pi$
$757$	−43.6869	−	31.7404i	−1.58783	−	1.15362i	−0.680869	−	0.732405i	$-0.738398\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.1803	+	11.7557i	0.586537	+	0.426144i	0.841075	−	0.540919i	$-0.181923\pi$
$761$	16.1803	+	11.7557i	0.586537	+	0.426144i	−0.254538	+	0.967063i	$0.581923\pi$
$762$		0			0
$763$	6.18034	+	19.0211i	0.223743	+	0.688611i
$764$		0			0
$765$	−6.47214	+	4.70228i	−0.234001	+	0.170011i
$766$		0			0
$767$	−7.41641	+	22.8254i	−0.267791	+	0.824176i
$768$		0			0
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$	−30.0000			−1.08042
$772$		0			0
$773$	−0.618034	+	1.90211i	−0.0222291	+	0.0684143i	−0.961556	−	0.274610i	$-0.911451\pi$
$773$	−0.618034	+	1.90211i	−0.0222291	+	0.0684143i	0.939327	+	0.343024i	$0.111451\pi$
$774$		0			0
$775$	−6.47214	+	4.70228i	−0.232486	+	0.168911i
$776$		0			0
$777$	−6.18034	−	19.0211i	−0.221718	−	0.682379i
$778$		0			0
$779$	38.8328	+	28.2137i	1.39133	+	1.01086i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	6.47214	+	4.70228i	0.231295	+	0.168046i
$784$		0			0
$785$	3.70820	+	11.4127i	0.132351	+	0.407336i
$786$		0			0
$787$	−11.3262	+	8.22899i	−0.403737	+	0.293332i	−0.771061	−	0.636761i	$-0.780274\pi$
$787$	−11.3262	+	8.22899i	−0.403737	+	0.293332i	0.367325	+	0.930093i	$0.380274\pi$
$788$		0			0
$789$	−1.23607	+	3.80423i	−0.0440052	+	0.135434i
$790$		0			0
$791$	−12.0000			−0.426671
$792$		0			0
$793$	−20.0000			−0.710221
$794$		0			0
$795$	−1.23607	+	3.80423i	−0.0438388	+	0.134922i
$796$		0			0
$797$	30.7426	−	22.3358i	1.08896	−	0.791176i	0.109737	−	0.993961i	$-0.464999\pi$
$797$	30.7426	−	22.3358i	1.08896	−	0.791176i	0.979223	+	0.202785i	$0.0649991\pi$
$798$		0			0
$799$	−9.88854	−	30.4338i	−0.349832	−	1.07667i
$800$		0			0
$801$	11.3262	+	8.22899i	0.400193	+	0.290757i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.618034	−	1.90211i	−0.0217558	−	0.0669575i
$808$		0			0
$809$	16.1803	−	11.7557i	0.568870	−	0.413309i	−0.265824	−	0.964022i	$-0.585644\pi$
$809$	16.1803	−	11.7557i	0.568870	−	0.413309i	0.834695	+	0.550713i	$0.185644\pi$
$810$		0			0
$811$	5.56231	−	17.1190i	0.195319	−	0.601130i	−0.804654	−	0.593744i	$-0.797649\pi$
$811$	5.56231	−	17.1190i	0.195319	−	0.601130i	0.999973	−	0.00738566i	$-0.00235095\pi$
$812$		0			0
$813$	10.0000			0.350715
$814$		0			0
$815$	32.0000			1.12091
$816$		0			0
$817$	3.70820	−	11.4127i	0.129734	−	0.399279i
$818$		0			0
$819$	−3.23607	+	2.35114i	−0.113077	+	0.0821555i
$820$		0			0
$821$	4.94427	+	15.2169i	0.172556	+	0.531074i	0.999513	−	0.0311913i	$-0.00993012\pi$
$821$	4.94427	+	15.2169i	0.172556	+	0.531074i	−0.826957	+	0.562265i	$0.809930\pi$
$822$		0			0
$823$	9.70820	+	7.05342i	0.338407	+	0.245867i	0.743989	−	0.668192i	$-0.232931\pi$
$823$	9.70820	+	7.05342i	0.338407	+	0.245867i	−0.405583	+	0.914058i	$0.632931\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	38.8328	+	28.2137i	1.35035	+	0.981086i	0.998994	+	0.0448440i	$0.0142791\pi$
$827$	38.8328	+	28.2137i	1.35035	+	0.981086i	0.351355	+	0.936242i	$0.385721\pi$
$828$		0			0
$829$	5.56231	+	17.1190i	0.193187	+	0.594568i	0.999993	+	0.00375172i	$0.00119421\pi$
$829$	5.56231	+	17.1190i	0.193187	+	0.594568i	−0.806806	+	0.590816i	$0.798806\pi$
$830$		0			0
$831$	−11.3262	+	8.22899i	−0.392903	+	0.285461i
$832$		0			0
$833$	−3.70820	+	11.4127i	−0.128482	+	0.395426i
$834$		0			0
$835$	24.0000			0.830554
$836$		0			0
$837$	−8.00000			−0.276520
$838$		0			0
$839$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$839$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$840$		0			0
$841$	−28.3156	+	20.5725i	−0.976400	+	0.709396i
$842$		0			0
$843$	−2.47214	−	7.60845i	−0.0851449	−	0.262049i
$844$		0			0
$845$	14.5623	+	10.5801i	0.500959	+	0.363968i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	21.0344	+	15.2824i	0.721900	+	0.524491i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	4.85410	−	3.52671i	0.166201	−	0.120752i	−0.501576	−	0.865114i	$-0.667246\pi$
$853$	4.85410	−	3.52671i	0.166201	−	0.120752i	0.667777	+	0.744362i	$0.267246\pi$
$854$		0			0
$855$	−3.70820	+	11.4127i	−0.126818	+	0.390305i
$856$		0			0
$857$	−28.0000			−0.956462			−0.478231	−	0.878234i	$-0.658722\pi$
$857$	−28.0000			−0.956462			−0.478231	+	0.878234i	$0.658722\pi$
$858$		0			0
$859$	−8.00000			−0.272956			−0.136478	−	0.990643i	$-0.543578\pi$
$859$	−8.00000			−0.272956			−0.136478	+	0.990643i	$0.543578\pi$
$860$		0			0
$861$	−4.94427	+	15.2169i	−0.168500	+	0.518591i
$862$		0			0
$863$	38.8328	−	28.2137i	1.32188	−	0.960405i	0.321978	−	0.946747i	$-0.395652\pi$
$863$	38.8328	−	28.2137i	1.32188	−	0.960405i	0.999907	−	0.0136580i	$-0.00434761\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	0.809017	+	0.587785i	0.0274757	+	0.0199622i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	19.4164	+	14.1068i	0.657900	+	0.477992i
$872$		0			0
$873$	−0.618034	−	1.90211i	−0.0209173	−	0.0643768i
$874$		0			0
$875$	−19.4164	+	14.1068i	−0.656394	+	0.476898i
$876$		0			0
$877$	−11.7426	+	36.1401i	−0.396521	+	1.22037i	0.531250	+	0.847215i	$0.321723\pi$
$877$	−11.7426	+	36.1401i	−0.396521	+	1.22037i	−0.927771	+	0.373151i	$0.878277\pi$
$878$		0			0
$879$	20.0000			0.674583
$880$		0			0
$881$	46.0000			1.54978			0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000			1.54978			0.774890	+	0.632096i	$0.217805\pi$
$882$		0			0
$883$	13.5967	−	41.8465i	0.457567	−	1.40825i	−0.410528	−	0.911848i	$-0.634656\pi$
$883$	13.5967	−	41.8465i	0.457567	−	1.40825i	0.868095	−	0.496398i	$-0.165344\pi$
$884$		0			0
$885$	−19.4164	+	14.1068i	−0.652675	+	0.474196i
$886$		0			0
$887$	−14.8328	−	45.6507i	−0.498037	−	1.53280i	−0.812169	−	0.583422i	$-0.801714\pi$
$887$	−14.8328	−	45.6507i	−0.498037	−	1.53280i	0.314132	−	0.949379i	$-0.398286\pi$
$888$		0			0
$889$	−16.1803	−	11.7557i	−0.542671	−	0.394274i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−38.8328	−	28.2137i	−1.29949	−	0.944135i
$894$		0			0
$895$	−7.41641	−	22.8254i	−0.247903	−	0.762968i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	19.7771	−	60.8676i	0.659603	−	2.03005i
$900$		0			0
$901$	−8.00000			−0.266519
$902$		0			0
$903$	4.00000			0.133112
$904$		0			0
$905$	−6.18034	+	19.0211i	−0.205441	+	0.632284i
$906$		0			0
$907$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$907$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$908$		0			0
$909$	−4.94427	−	15.2169i	−0.163991	−	0.504713i
$910$		0			0
$911$	−6.47214	−	4.70228i	−0.214431	−	0.155794i	0.475385	−	0.879778i	$-0.342309\pi$
$911$	−6.47214	−	4.70228i	−0.214431	−	0.155794i	−0.689816	+	0.723984i	$0.742309\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−16.1803	−	11.7557i	−0.534906	−	0.388632i
$916$		0			0
$917$	−7.41641	−	22.8254i	−0.244911	−	0.753760i
$918$		0			0
$919$	−40.4508	+	29.3893i	−1.33435	+	0.969462i	−0.334719	+	0.942318i	$0.608641\pi$
$919$	−40.4508	+	29.3893i	−1.33435	+	0.969462i	−0.999632	+	0.0271443i	$0.991359\pi$
$920$		0			0
$921$	0.618034	−	1.90211i	0.0203649	−	0.0626768i
$922$		0			0
$923$	−16.0000			−0.526646
$924$		0			0
$925$	−10.0000			−0.328798
$926$		0			0
$927$	1.23607	−	3.80423i	0.0405978	−	0.124947i
$928$		0			0
$929$	−4.85410	+	3.52671i	−0.159258	+	0.115708i	−0.664560	−	0.747235i	$-0.731381\pi$
$929$	−4.85410	+	3.52671i	−0.159258	+	0.115708i	0.505302	+	0.862942i	$0.331381\pi$
$930$		0			0
$931$	5.56231	+	17.1190i	0.182297	+	0.561053i
$932$		0			0
$933$	12.9443	+	9.40456i	0.423776	+	0.307892i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	30.7426	+	22.3358i	1.00432	+	0.729680i	0.963010	−	0.269466i	$-0.0868473\pi$
$937$	30.7426	+	22.3358i	1.00432	+	0.729680i	0.0413087	+	0.999146i	$0.486847\pi$
$938$		0			0
$939$	−5.56231	−	17.1190i	−0.181519	−	0.558658i
$940$		0			0
$941$	19.4164	−	14.1068i	0.632957	−	0.459870i	−0.224467	−	0.974482i	$-0.572064\pi$
$941$	19.4164	−	14.1068i	0.632957	−	0.459870i	0.857423	+	0.514612i	$0.172064\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−4.00000			−0.130120
$946$		0			0
$947$	52.0000			1.68977			0.844886	−	0.534946i	$-0.179668\pi$
$947$	52.0000			1.68977			0.844886	+	0.534946i	$0.179668\pi$
$948$		0			0
$949$	−3.70820	+	11.4127i	−0.120373	+	0.370471i
$950$		0			0
$951$	11.3262	−	8.22899i	0.367278	−	0.266843i
$952$		0			0
$953$	11.1246	+	34.2380i	0.360362	+	1.10908i	0.952835	+	0.303489i	$0.0981515\pi$
$953$	11.1246	+	34.2380i	0.360362	+	1.10908i	−0.592473	+	0.805590i	$0.701849\pi$
$954$		0			0
$955$	−25.8885	−	18.8091i	−0.837734	−	0.608649i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.23607	−	2.35114i	−0.104498	−	0.0759223i
$960$		0			0
$961$	10.1976	+	31.3849i	0.328954	+	1.01242i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−13.5967	+	41.8465i	−0.437695	+	1.34709i
$966$		0			0
$967$	14.0000			0.450210			0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000			0.450210			0.225105	+	0.974335i	$0.427728\pi$
$968$		0			0
$969$	−24.0000			−0.770991
$970$		0			0
$971$	6.18034	−	19.0211i	0.198337	−	0.610417i	−0.801585	−	0.597881i	$-0.796010\pi$
$971$	6.18034	−	19.0211i	0.198337	−	0.610417i	0.999921	−	0.0125361i	$-0.00399048\pi$
$972$		0			0
$973$	−9.70820	+	7.05342i	−0.311231	+	0.226122i
$974$		0			0
$975$	0.618034	+	1.90211i	0.0197929	+	0.0609164i
$976$		0			0
$977$	−30.7426	−	22.3358i	−0.983544	−	0.714587i	−0.0250464	−	0.999686i	$-0.507973\pi$
$977$	−30.7426	−	22.3358i	−0.983544	−	0.714587i	−0.958498	+	0.285099i	$0.907973\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	8.09017	+	5.87785i	0.258299	+	0.187665i
$982$		0			0
$983$	2.47214	+	7.60845i	0.0788489	+	0.242672i	0.982709	−	0.185156i	$-0.0592790\pi$
$983$	2.47214	+	7.60845i	0.0788489	+	0.242672i	−0.903860	+	0.427828i	$0.859279\pi$
$984$		0			0
$985$	−38.8328	+	28.2137i	−1.23732	+	0.898963i
$986$		0			0
$987$	4.94427	−	15.2169i	0.157378	−	0.484359i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−56.0000			−1.77890			−0.889449	−	0.457034i	$-0.848912\pi$
$991$	−56.0000			−1.77890			−0.889449	+	0.457034i	$0.848912\pi$
$992$		0			0
$993$	2.47214	−	7.60845i	0.0784509	−	0.241447i
$994$		0			0
$995$	25.8885	−	18.8091i	0.820722	−	0.596289i
$996$		0			0
$997$	0.618034	+	1.90211i	0.0195733	+	0.0602405i	0.960366	−	0.278742i	$-0.0899173\pi$
$997$	0.618034	+	1.90211i	0.0195733	+	0.0602405i	−0.940793	+	0.338982i	$0.889917\pi$
$998$		0			0
$999$	−8.09017	−	5.87785i	−0.255962	−	0.185967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1452.2.i.e.565.1		4
11.2	odd	10		1452.2.i.d.1237.1		4
11.3	even	5	inner	1452.2.i.e.1213.1		4
11.4	even	5	inner	1452.2.i.e.493.1		4
11.5	even	5		132.2.a.b.1.1	✓	1
11.6	odd	10		1452.2.a.f.1.1		1
11.7	odd	10		1452.2.i.d.493.1		4
11.8	odd	10		1452.2.i.d.1213.1		4
11.9	even	5	inner	1452.2.i.e.1237.1		4
11.10	odd	2		1452.2.i.d.565.1		4
33.5	odd	10		396.2.a.a.1.1		1
33.17	even	10		4356.2.a.d.1.1		1
44.27	odd	10		528.2.a.e.1.1		1
44.39	even	10		5808.2.a.m.1.1		1
55.27	odd	20		3300.2.c.j.1849.1		2
55.38	odd	20		3300.2.c.j.1849.2		2
55.49	even	10		3300.2.a.f.1.1		1
77.27	odd	10		6468.2.a.b.1.1		1
88.5	even	10		2112.2.a.c.1.1		1
88.27	odd	10		2112.2.a.u.1.1		1
99.5	odd	30		3564.2.i.i.1189.1		2
99.16	even	15		3564.2.i.d.2377.1		2
99.38	odd	30		3564.2.i.i.2377.1		2
99.49	even	15		3564.2.i.d.1189.1		2
132.71	even	10		1584.2.a.e.1.1		1
165.38	even	20		9900.2.c.f.5149.2		2
165.104	odd	10		9900.2.a.w.1.1		1
165.137	even	20		9900.2.c.f.5149.1		2
264.5	odd	10		6336.2.a.ca.1.1		1
264.203	even	10		6336.2.a.cg.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.a.b.1.1	✓	1	11.5	even	5
396.2.a.a.1.1		1	33.5	odd	10
528.2.a.e.1.1		1	44.27	odd	10
1452.2.a.f.1.1		1	11.6	odd	10
1452.2.i.d.493.1		4	11.7	odd	10
1452.2.i.d.565.1		4	11.10	odd	2
1452.2.i.d.1213.1		4	11.8	odd	10
1452.2.i.d.1237.1		4	11.2	odd	10
1452.2.i.e.493.1		4	11.4	even	5	inner
1452.2.i.e.565.1		4	1.1	even	1	trivial
1452.2.i.e.1213.1		4	11.3	even	5	inner
1452.2.i.e.1237.1		4	11.9	even	5	inner
1584.2.a.e.1.1		1	132.71	even	10
2112.2.a.c.1.1		1	88.5	even	10
2112.2.a.u.1.1		1	88.27	odd	10
3300.2.a.f.1.1		1	55.49	even	10
3300.2.c.j.1849.1		2	55.27	odd	20
3300.2.c.j.1849.2		2	55.38	odd	20
3564.2.i.d.1189.1		2	99.49	even	15
3564.2.i.d.2377.1		2	99.16	even	15
3564.2.i.i.1189.1		2	99.5	odd	30
3564.2.i.i.2377.1		2	99.38	odd	30
4356.2.a.d.1.1		1	33.17	even	10
5808.2.a.m.1.1		1	44.39	even	10
6336.2.a.ca.1.1		1	264.5	odd	10
6336.2.a.cg.1.1		1	264.203	even	10
6468.2.a.b.1.1		1	77.27	odd	10
9900.2.a.w.1.1		1	165.104	odd	10
9900.2.c.f.5149.1		2	165.137	even	20
9900.2.c.f.5149.2		2	165.38	even	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:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1452.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{3} +(-1.61803 + 1.17557i) q^{5} +(-0.618034 - 1.90211i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{3} +(-1.61803 + 1.17557i) q^{5} +(-0.618034 - 1.90211i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(1.61803 + 1.17557i) q^{13} +(0.618034 + 1.90211i) q^{15} +(-3.23607 + 2.35114i) q^{17} +(-1.85410 + 5.70634i) q^{19} -2.00000 q^{21} +(-0.309017 + 0.951057i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(-2.47214 - 7.60845i) q^{29} +(6.47214 + 4.70228i) q^{31} +(3.23607 + 2.35114i) q^{35} +(3.09017 + 9.51057i) q^{37} +(1.61803 - 1.17557i) q^{39} +(2.47214 - 7.60845i) q^{41} -2.00000 q^{43} +2.00000 q^{45} +(-2.47214 + 7.60845i) q^{47} +(2.42705 - 1.76336i) q^{49} +(1.23607 + 3.80423i) q^{51} +(1.61803 + 1.17557i) q^{53} +(4.85410 + 3.52671i) q^{57} +(3.70820 + 11.4127i) q^{59} +(-8.09017 + 5.87785i) q^{61} +(-0.618034 + 1.90211i) q^{63} -4.00000 q^{65} +12.0000 q^{67} +(-6.47214 + 4.70228i) q^{71} +(1.85410 + 5.70634i) q^{73} +(0.809017 + 0.587785i) q^{75} +(1.61803 + 1.17557i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-12.9443 + 9.40456i) q^{83} +(2.47214 - 7.60845i) q^{85} -8.00000 q^{87} -14.0000 q^{89} +(1.23607 - 3.80423i) q^{91} +(6.47214 - 4.70228i) q^{93} +(-3.70820 - 11.4127i) q^{95} +(1.61803 + 1.17557i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 2 q^{5} + 2 q^{7} - q^{9}+O(q^{10}) \) 4 * q - q^3 - 2 * q^5 + 2 * q^7 - q^9	\( 4 q - q^{3} - 2 q^{5} + 2 q^{7} - q^{9} + 2 q^{13} - 2 q^{15} - 4 q^{17} + 6 q^{19} - 8 q^{21} + q^{25} - q^{27} + 8 q^{29} + 8 q^{31} + 4 q^{35} - 10 q^{37} + 2 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} + 3 q^{49} - 4 q^{51} + 2 q^{53} + 6 q^{57} - 12 q^{59} - 10 q^{61} + 2 q^{63} - 16 q^{65} + 48 q^{67} - 8 q^{71} - 6 q^{73} + q^{75} + 2 q^{79} - q^{81} - 16 q^{83} - 8 q^{85} - 32 q^{87} - 56 q^{89} - 4 q^{91} + 8 q^{93} + 12 q^{95} + 2 q^{97}+O(q^{100}) \) 4 * q - q^3 - 2 * q^5 + 2 * q^7 - q^9 + 2 * q^13 - 2 * q^15 - 4 * q^17 + 6 * q^19 - 8 * q^21 + q^25 - q^27 + 8 * q^29 + 8 * q^31 + 4 * q^35 - 10 * q^37 + 2 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 + 3 * q^49 - 4 * q^51 + 2 * q^53 + 6 * q^57 - 12 * q^59 - 10 * q^61 + 2 * q^63 - 16 * q^65 + 48 * q^67 - 8 * q^71 - 6 * q^73 + q^75 + 2 * q^79 - q^81 - 16 * q^83 - 8 * q^85 - 32 * q^87 - 56 * q^89 - 4 * q^91 + 8 * q^93 + 12 * q^95 + 2 * q^97

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