LMFDB - Embedded newform 1452.2.i.e.493.1

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			493.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	1452.493
Dual form			1452.2.i.e.1237.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{3} +(0.618034 + 1.90211i) q^{5} +(1.61803 + 1.17557i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{3} +(0.618034 + 1.90211i) q^{5} +(1.61803 + 1.17557i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-0.618034 + 1.90211i) q^{13} +(-1.61803 - 1.17557i) q^{15} +(1.23607 + 3.80423i) q^{17} +(4.85410 - 3.52671i) q^{19} -2.00000 q^{21} +(0.809017 - 0.587785i) q^{25} +(0.309017 + 0.951057i) q^{27} +(6.47214 + 4.70228i) q^{29} +(-2.47214 + 7.60845i) q^{31} +(-1.23607 + 3.80423i) q^{35} +(-8.09017 - 5.87785i) q^{37} +(-0.618034 - 1.90211i) q^{39} +(-6.47214 + 4.70228i) q^{41} -2.00000 q^{43} +2.00000 q^{45} +(6.47214 - 4.70228i) q^{47} +(-0.927051 - 2.85317i) q^{49} +(-3.23607 - 2.35114i) q^{51} +(-0.618034 + 1.90211i) q^{53} +(-1.85410 + 5.70634i) q^{57} +(-9.70820 - 7.05342i) q^{59} +(3.09017 + 9.51057i) q^{61} +(1.61803 - 1.17557i) q^{63} -4.00000 q^{65} +12.0000 q^{67} +(2.47214 + 7.60845i) q^{71} +(-4.85410 - 3.52671i) q^{73} +(-0.309017 + 0.951057i) q^{75} +(-0.618034 + 1.90211i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(4.94427 + 15.2169i) q^{83} +(-6.47214 + 4.70228i) q^{85} -8.00000 q^{87} -14.0000 q^{89} +(-3.23607 + 2.35114i) q^{91} +(-2.47214 - 7.60845i) q^{93} +(9.70820 + 7.05342i) q^{95} +(-0.618034 + 1.90211i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1452\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$1333$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$		0			0
$5$	0.618034	+	1.90211i	0.276393	+	0.850651i	0.988847	+	0.148932i	$0.0475836\pi$
$5$	0.618034	+	1.90211i	0.276393	+	0.850651i	−0.712454	+	0.701719i	$0.752416\pi$
$6$		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
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	−0.618034	+	1.90211i	−0.171412	+	0.527551i	−0.999451	−	0.0331183i	$-0.989456\pi$
$13$	−0.618034	+	1.90211i	−0.171412	+	0.527551i	0.828040	+	0.560670i	$0.189456\pi$
$14$		0			0
$15$	−1.61803	−	1.17557i	−0.417775	−	0.303531i
$16$		0			0
$17$	1.23607	+	3.80423i	0.299791	+	0.922660i	0.981570	+	0.191103i	$0.0612063\pi$
$17$	1.23607	+	3.80423i	0.299791	+	0.922660i	−0.681780	+	0.731558i	$0.738794\pi$
$18$		0			0
$19$	4.85410	−	3.52671i	1.11361	−	0.809083i	0.130379	−	0.991464i	$-0.458380\pi$
$19$	4.85410	−	3.52671i	1.11361	−	0.809083i	0.983228	+	0.182381i	$0.0583804\pi$
$20$		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
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$		0			0
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$		0			0
$29$	6.47214	+	4.70228i	1.20185	+	0.873192i	0.994465	−	0.105069i	$-0.0335062\pi$
$29$	6.47214	+	4.70228i	1.20185	+	0.873192i	0.207380	+	0.978260i	$0.433506\pi$
$30$		0			0
$31$	−2.47214	+	7.60845i	−0.444009	+	1.36652i	0.439558	+	0.898214i	$0.355135\pi$
$31$	−2.47214	+	7.60845i	−0.444009	+	1.36652i	−0.883567	+	0.468304i	$0.844865\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.23607	+	3.80423i	−0.208934	+	0.643032i
$36$		0			0
$37$	−8.09017	−	5.87785i	−1.33002	−	0.966313i	−0.999749	−	0.0224255i	$-0.992861\pi$
$37$	−8.09017	−	5.87785i	−1.33002	−	0.966313i	−0.330267	−	0.943887i	$-0.607139\pi$
$38$		0			0
$39$	−0.618034	−	1.90211i	−0.0989646	−	0.304582i
$40$		0			0
$41$	−6.47214	+	4.70228i	−1.01078	+	0.734373i	−0.964372	−	0.264550i	$-0.914777\pi$
$41$	−6.47214	+	4.70228i	−1.01078	+	0.734373i	−0.0464057	+	0.998923i	$0.514777\pi$
$42$		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
$47$	6.47214	−	4.70228i	0.944058	−	0.685898i	−0.00533600	−	0.999986i	$-0.501699\pi$
$47$	6.47214	−	4.70228i	0.944058	−	0.685898i	0.949394	+	0.314087i	$0.101699\pi$
$48$		0			0
$49$	−0.927051	−	2.85317i	−0.132436	−	0.407596i
$50$		0			0
$51$	−3.23607	−	2.35114i	−0.453140	−	0.329226i
$52$		0			0
$53$	−0.618034	+	1.90211i	−0.0848935	+	0.261275i	−0.984488	−	0.175450i	$-0.943862\pi$
$53$	−0.618034	+	1.90211i	−0.0848935	+	0.261275i	0.899595	+	0.436726i	$0.143862\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.85410	+	5.70634i	−0.245582	+	0.755823i
$58$		0			0
$59$	−9.70820	−	7.05342i	−1.26390	−	0.918277i	−0.264958	−	0.964260i	$-0.585358\pi$
$59$	−9.70820	−	7.05342i	−1.26390	−	0.918277i	−0.998942	+	0.0459824i	$0.985358\pi$
$60$		0			0
$61$	3.09017	+	9.51057i	0.395656	+	1.21770i	0.928450	+	0.371458i	$0.121142\pi$
$61$	3.09017	+	9.51057i	0.395656	+	1.21770i	−0.532794	+	0.846245i	$0.678858\pi$
$62$		0			0
$63$	1.61803	−	1.17557i	0.203853	−	0.148108i
$64$		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
$71$	2.47214	+	7.60845i	0.293389	+	0.902957i	0.983758	+	0.179500i	$0.0574480\pi$
$71$	2.47214	+	7.60845i	0.293389	+	0.902957i	−0.690369	+	0.723457i	$0.742552\pi$
$72$		0			0
$73$	−4.85410	−	3.52671i	−0.568130	−	0.412770i	0.266296	−	0.963891i	$-0.414200\pi$
$73$	−4.85410	−	3.52671i	−0.568130	−	0.412770i	−0.834425	+	0.551121i	$0.814200\pi$
$74$		0			0
$75$	−0.309017	+	0.951057i	−0.0356822	+	0.109819i
$76$		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
$83$	4.94427	+	15.2169i	0.542704	+	1.67027i	0.726386	+	0.687287i	$0.241198\pi$
$83$	4.94427	+	15.2169i	0.542704	+	1.67027i	−0.183682	+	0.982986i	$0.558802\pi$
$84$		0			0
$85$	−6.47214	+	4.70228i	−0.702002	+	0.510034i
$86$		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
$91$	−3.23607	+	2.35114i	−0.339232	+	0.246467i
$92$		0			0
$93$	−2.47214	−	7.60845i	−0.256349	−	0.788960i
$94$		0			0
$95$	9.70820	+	7.05342i	0.996041	+	0.723666i
$96$		0			0
$97$	−0.618034	+	1.90211i	−0.0627518	+	0.193130i	−0.977517	−	0.210855i	$-0.932375\pi$
$97$	−0.618034	+	1.90211i	−0.0627518	+	0.193130i	0.914766	+	0.403985i	$0.132375\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.94427	+	15.2169i	−0.491973	+	1.51414i	0.329647	+	0.944104i	$0.393070\pi$
$101$	−4.94427	+	15.2169i	−0.491973	+	1.51414i	−0.821621	+	0.570034i	$0.806930\pi$
$102$		0			0
$103$	−3.23607	−	2.35114i	−0.318859	−	0.231665i	0.416829	−	0.908985i	$-0.363141\pi$
$103$	−3.23607	−	2.35114i	−0.318859	−	0.231665i	−0.735689	+	0.677320i	$0.763141\pi$
$104$		0			0
$105$	−1.23607	−	3.80423i	−0.120628	−	0.371254i
$106$		0			0
$107$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$107$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$108$		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
$113$	−4.85410	+	3.52671i	−0.456636	+	0.331765i	−0.792210	−	0.610249i	$-0.791070\pi$
$113$	−4.85410	+	3.52671i	−0.456636	+	0.331765i	0.335575	+	0.942014i	$0.391070\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.61803	+	1.17557i	0.149587	+	0.108682i
$118$		0			0
$119$	−2.47214	+	7.60845i	−0.226620	+	0.697466i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	2.47214	−	7.60845i	0.222905	−	0.686031i
$124$		0			0
$125$	9.70820	+	7.05342i	0.868328	+	0.630877i
$126$		0			0
$127$	−3.09017	−	9.51057i	−0.274208	−	0.843926i	−0.989428	−	0.145026i	$-0.953673\pi$
$127$	−3.09017	−	9.51057i	−0.274208	−	0.843926i	0.715220	−	0.698900i	$-0.246327\pi$
$128$		0			0
$129$	1.61803	−	1.17557i	0.142460	−	0.103503i
$130$		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
$135$	−1.61803	+	1.17557i	−0.139258	+	0.101177i
$136$		0			0
$137$	−0.618034	−	1.90211i	−0.0528022	−	0.162508i	0.921178	−	0.389141i	$-0.127228\pi$
$137$	−0.618034	−	1.90211i	−0.0528022	−	0.162508i	−0.973980	+	0.226633i	$0.927228\pi$
$138$		0			0
$139$	4.85410	+	3.52671i	0.411720	+	0.299132i	0.774298	−	0.632822i	$-0.218103\pi$
$139$	4.85410	+	3.52671i	0.411720	+	0.299132i	−0.362578	+	0.931953i	$0.618103\pi$
$140$		0			0
$141$	−2.47214	+	7.60845i	−0.208191	+	0.640747i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−4.94427	+	15.2169i	−0.410599	+	1.26370i
$146$		0			0
$147$	2.42705	+	1.76336i	0.200180	+	0.145439i
$148$		0			0
$149$	6.18034	+	19.0211i	0.506313	+	1.55827i	0.798552	+	0.601926i	$0.205600\pi$
$149$	6.18034	+	19.0211i	0.506313	+	1.55827i	−0.292239	+	0.956345i	$0.594400\pi$
$150$		0			0
$151$	8.09017	−	5.87785i	0.658369	−	0.478333i	−0.207743	−	0.978183i	$-0.566612\pi$
$151$	8.09017	−	5.87785i	0.658369	−	0.478333i	0.866112	+	0.499851i	$0.166612\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$	−16.0000			−1.28515
$156$		0			0
$157$	−4.85410	+	3.52671i	−0.387400	+	0.281462i	−0.764389	−	0.644755i	$-0.776959\pi$
$157$	−4.85410	+	3.52671i	−0.387400	+	0.281462i	0.376990	+	0.926218i	$0.376959\pi$
$158$		0			0
$159$	−0.618034	−	1.90211i	−0.0490133	−	0.150847i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.94427	−	15.2169i	0.387265	−	1.19188i	−0.547558	−	0.836768i	$-0.684443\pi$
$163$	4.94427	−	15.2169i	0.387265	−	1.19188i	0.934824	−	0.355112i	$-0.115557\pi$
$164$		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
$169$	7.28115	+	5.29007i	0.560089	+	0.406928i
$170$		0			0
$171$	−1.85410	−	5.70634i	−0.141787	−	0.436375i
$172$		0			0
$173$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$173$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$174$		0			0
$175$	2.00000			0.151186
$176$		0			0
$177$	12.0000			0.901975
$178$		0			0
$179$	9.70820	−	7.05342i	0.725625	−	0.527198i	−0.162551	−	0.986700i	$-0.551972\pi$
$179$	9.70820	−	7.05342i	0.725625	−	0.527198i	0.888176	+	0.459503i	$0.151972\pi$
$180$		0			0
$181$	−3.09017	−	9.51057i	−0.229691	−	0.706915i	−0.997781	−	0.0665740i	$-0.978793\pi$
$181$	−3.09017	−	9.51057i	−0.229691	−	0.706915i	0.768091	−	0.640341i	$-0.221207\pi$
$182$		0			0
$183$	−8.09017	−	5.87785i	−0.598043	−	0.434503i
$184$		0			0
$185$	6.18034	−	19.0211i	0.454388	−	1.39846i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−0.618034	+	1.90211i	−0.0449554	+	0.138358i
$190$		0			0
$191$	−12.9443	−	9.40456i	−0.936615	−	0.680490i	0.0109887	−	0.999940i	$-0.496502\pi$
$191$	−12.9443	−	9.40456i	−0.936615	−	0.680490i	−0.947603	+	0.319449i	$0.896502\pi$
$192$		0			0
$193$	−6.79837	−	20.9232i	−0.489358	−	1.50609i	−0.825569	−	0.564301i	$-0.809146\pi$
$193$	−6.79837	−	20.9232i	−0.489358	−	1.50609i	0.336211	−	0.941787i	$-0.390854\pi$
$194$		0			0
$195$	3.23607	−	2.35114i	0.231740	−	0.168369i
$196$		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
$201$	−9.70820	+	7.05342i	−0.684764	+	0.497510i
$202$		0			0
$203$	4.94427	+	15.2169i	0.347020	+	1.06802i
$204$		0			0
$205$	−12.9443	−	9.40456i	−0.904067	−	0.656843i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	5.56231	−	17.1190i	0.382925	−	1.17852i	−0.555050	−	0.831817i	$-0.687301\pi$
$211$	5.56231	−	17.1190i	0.382925	−	1.17852i	0.937974	−	0.346704i	$-0.112699\pi$
$212$		0			0
$213$	−6.47214	−	4.70228i	−0.443463	−	0.322195i
$214$		0			0
$215$	−1.23607	−	3.80423i	−0.0842991	−	0.259446i
$216$		0			0
$217$	−12.9443	+	9.40456i	−0.878714	+	0.638423i
$218$		0			0
$219$	6.00000			0.405442
$220$		0			0
$221$	−8.00000			−0.538138
$222$		0			0
$223$	3.23607	−	2.35114i	0.216703	−	0.157444i	−0.474138	−	0.880450i	$-0.657240\pi$
$223$	3.23607	−	2.35114i	0.216703	−	0.157444i	0.690841	+	0.723006i	$0.257240\pi$
$224$		0			0
$225$	−0.309017	−	0.951057i	−0.0206011	−	0.0634038i
$226$		0			0
$227$	19.4164	+	14.1068i	1.28871	+	0.936304i	0.999779	−	0.0210448i	$-0.00669928\pi$
$227$	19.4164	+	14.1068i	1.28871	+	0.936304i	0.288934	+	0.957349i	$0.406699\pi$
$228$		0			0
$229$	−4.32624	+	13.3148i	−0.285886	+	0.879866i	0.700246	+	0.713902i	$0.253074\pi$
$229$	−4.32624	+	13.3148i	−0.285886	+	0.879866i	−0.986132	+	0.165964i	$0.946926\pi$
$230$		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
$235$	12.9443	+	9.40456i	0.844391	+	0.613486i
$236$		0			0
$237$	−0.618034	−	1.90211i	−0.0401456	−	0.123556i
$238$		0			0
$239$	−3.23607	+	2.35114i	−0.209324	+	0.152083i	−0.687508	−	0.726177i	$-0.741295\pi$
$239$	−3.23607	+	2.35114i	−0.209324	+	0.152083i	0.478184	+	0.878260i	$0.341295\pi$
$240$		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
$245$	4.85410	−	3.52671i	0.310117	−	0.225313i
$246$		0			0
$247$	3.70820	+	11.4127i	0.235947	+	0.726171i
$248$		0			0
$249$	−12.9443	−	9.40456i	−0.820310	−	0.595990i
$250$		0			0
$251$	1.23607	−	3.80423i	0.0780199	−	0.240121i	−0.904438	−	0.426605i	$-0.859709\pi$
$251$	1.23607	−	3.80423i	0.0780199	−	0.240121i	0.982458	+	0.186485i	$0.0597094\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	2.47214	−	7.60845i	0.154811	−	0.476460i
$256$		0			0
$257$	24.2705	+	17.6336i	1.51395	+	1.09995i	0.964385	+	0.264502i	$0.0852075\pi$
$257$	24.2705	+	17.6336i	1.51395	+	1.09995i	0.549568	+	0.835449i	$0.314792\pi$
$258$		0			0
$259$	−6.18034	−	19.0211i	−0.384028	−	1.18192i
$260$		0			0
$261$	6.47214	−	4.70228i	0.400615	−	0.291064i
$262$		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
$267$	11.3262	−	8.22899i	0.693155	−	0.503606i
$268$		0			0
$269$	−0.618034	−	1.90211i	−0.0376822	−	0.115974i	0.930446	−	0.366429i	$-0.119420\pi$
$269$	−0.618034	−	1.90211i	−0.0376822	−	0.115974i	−0.968128	+	0.250455i	$0.919420\pi$
$270$		0			0
$271$	−8.09017	−	5.87785i	−0.491443	−	0.357054i	0.314296	−	0.949325i	$-0.398232\pi$
$271$	−8.09017	−	5.87785i	−0.491443	−	0.357054i	−0.805739	+	0.592271i	$0.798232\pi$
$272$		0			0
$273$	1.23607	−	3.80423i	0.0748102	−	0.230242i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	4.32624	−	13.3148i	0.259938	−	0.800008i	−0.732878	−	0.680360i	$-0.761823\pi$
$277$	4.32624	−	13.3148i	0.259938	−	0.800008i	0.992816	−	0.119648i	$-0.0381766\pi$
$278$		0			0
$279$	6.47214	+	4.70228i	0.387477	+	0.281518i
$280$		0			0
$281$	−2.47214	−	7.60845i	−0.147475	−	0.453882i	0.849846	−	0.527032i	$-0.176695\pi$
$281$	−2.47214	−	7.60845i	−0.147475	−	0.453882i	−0.997321	+	0.0731493i	$0.976695\pi$
$282$		0			0
$283$	21.0344	−	15.2824i	1.25037	−	0.908445i	0.252125	−	0.967695i	$-0.418871\pi$
$283$	21.0344	−	15.2824i	1.25037	−	0.908445i	0.998243	+	0.0592494i	$0.0188707\pi$
$284$		0			0
$285$	−12.0000			−0.710819
$286$		0			0
$287$	−16.0000			−0.944450
$288$		0			0
$289$	0.809017	−	0.587785i	0.0475892	−	0.0345756i
$290$		0			0
$291$	−0.618034	−	1.90211i	−0.0362298	−	0.111504i
$292$		0			0
$293$	−16.1803	−	11.7557i	−0.945266	−	0.686776i	0.00441682	−	0.999990i	$-0.498594\pi$
$293$	−16.1803	−	11.7557i	−0.945266	−	0.686776i	−0.949682	+	0.313215i	$0.898594\pi$
$294$		0			0
$295$	7.41641	−	22.8254i	0.431800	−	1.32894i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−3.23607	−	2.35114i	−0.186524	−	0.135518i
$302$		0			0
$303$	−4.94427	−	15.2169i	−0.284041	−	0.874188i
$304$		0			0
$305$	−16.1803	+	11.7557i	−0.926484	+	0.673130i
$306$		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
$311$	12.9443	−	9.40456i	0.734002	−	0.533284i	−0.156825	−	0.987626i	$-0.550126\pi$
$311$	12.9443	−	9.40456i	0.734002	−	0.533284i	0.890827	+	0.454343i	$0.150126\pi$
$312$		0			0
$313$	−5.56231	−	17.1190i	−0.314400	−	0.967624i	−0.976001	−	0.217768i	$-0.930123\pi$
$313$	−5.56231	−	17.1190i	−0.314400	−	0.967624i	0.661601	−	0.749856i	$-0.269877\pi$
$314$		0			0
$315$	3.23607	+	2.35114i	0.182332	+	0.132472i
$316$		0			0
$317$	−4.32624	+	13.3148i	−0.242986	+	0.747833i	0.752975	+	0.658049i	$0.228618\pi$
$317$	−4.32624	+	13.3148i	−0.242986	+	0.747833i	−0.995961	+	0.0897846i	$0.971382\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	19.4164	+	14.1068i	1.08036	+	0.784926i
$324$		0			0
$325$	0.618034	+	1.90211i	0.0342824	+	0.105510i
$326$		0			0
$327$	8.09017	−	5.87785i	0.447387	−	0.325046i
$328$		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
$333$	−8.09017	+	5.87785i	−0.443339	+	0.322104i
$334$		0			0
$335$	7.41641	+	22.8254i	0.405202	+	1.24708i
$336$		0			0
$337$	−11.3262	−	8.22899i	−0.616979	−	0.448262i	0.234886	−	0.972023i	$-0.424528\pi$
$337$	−11.3262	−	8.22899i	−0.616979	−	0.448262i	−0.851865	+	0.523761i	$0.824528\pi$
$338$		0			0
$339$	1.85410	−	5.70634i	0.100701	−	0.309926i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	6.18034	−	19.0211i	0.333707	−	1.02704i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$347$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$348$		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
$351$	−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
$355$	−12.9443	+	9.40456i	−0.687011	+	0.499142i
$356$		0			0
$357$	−2.47214	−	7.60845i	−0.130839	−	0.402682i
$358$		0			0
$359$	6.47214	+	4.70228i	0.341586	+	0.248177i	0.745331	−	0.666695i	$-0.232292\pi$
$359$	6.47214	+	4.70228i	0.341586	+	0.248177i	−0.403745	+	0.914872i	$0.632292\pi$
$360$		0			0
$361$	5.25329	−	16.1680i	0.276489	−	0.850945i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.70820	−	11.4127i	0.194096	−	0.597367i
$366$		0			0
$367$	3.23607	+	2.35114i	0.168921	+	0.122729i	0.669034	−	0.743232i	$-0.266708\pi$
$367$	3.23607	+	2.35114i	0.168921	+	0.122729i	−0.500113	+	0.865960i	$0.666708\pi$
$368$		0			0
$369$	2.47214	+	7.60845i	0.128694	+	0.396080i
$370$		0			0
$371$	−3.23607	+	2.35114i	−0.168008	+	0.122065i
$372$		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
$377$	−12.9443	+	9.40456i	−0.666664	+	0.484360i
$378$		0			0
$379$	4.94427	+	15.2169i	0.253970	+	0.781640i	0.994031	+	0.109100i	$0.0347968\pi$
$379$	4.94427	+	15.2169i	0.253970	+	0.781640i	−0.740061	+	0.672540i	$0.765203\pi$
$380$		0			0
$381$	8.09017	+	5.87785i	0.414472	+	0.301132i
$382$		0			0
$383$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$383$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.618034	+	1.90211i	−0.0314164	+	0.0966898i
$388$		0			0
$389$	11.3262	+	8.22899i	0.574263	+	0.417227i	0.836651	−	0.547736i	$-0.184510\pi$
$389$	11.3262	+	8.22899i	0.574263	+	0.417227i	−0.262388	+	0.964962i	$0.584510\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−9.70820	+	7.05342i	−0.489714	+	0.355798i
$394$		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
$399$	−9.70820	+	7.05342i	−0.486018	+	0.353113i
$400$		0			0
$401$	−5.56231	−	17.1190i	−0.277768	−	0.854883i	−0.988474	−	0.151393i	$-0.951624\pi$
$401$	−5.56231	−	17.1190i	−0.277768	−	0.854883i	0.710705	−	0.703490i	$-0.248376\pi$
$402$		0			0
$403$	−12.9443	−	9.40456i	−0.644800	−	0.468475i
$404$		0			0
$405$	0.618034	−	1.90211i	0.0307104	−	0.0945168i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−3.09017	+	9.51057i	−0.152799	+	0.470267i	−0.997931	−	0.0642902i	$-0.979522\pi$
$409$	−3.09017	+	9.51057i	−0.152799	+	0.470267i	0.845132	+	0.534557i	$0.179522\pi$
$410$		0			0
$411$	1.61803	+	1.17557i	0.0798117	+	0.0579866i
$412$		0			0
$413$	−7.41641	−	22.8254i	−0.364938	−	1.12316i
$414$		0			0
$415$	−25.8885	+	18.8091i	−1.27082	+	0.923304i
$416$		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
$421$	−4.85410	+	3.52671i	−0.236574	+	0.171881i	−0.699756	−	0.714382i	$-0.746708\pi$
$421$	−4.85410	+	3.52671i	−0.236574	+	0.171881i	0.463181	+	0.886264i	$0.346708\pi$
$422$		0			0
$423$	−2.47214	−	7.60845i	−0.120199	−	0.369936i
$424$		0			0
$425$	3.23607	+	2.35114i	0.156972	+	0.114047i
$426$		0			0
$427$	−6.18034	+	19.0211i	−0.299088	+	0.920497i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.23607	+	3.80423i	−0.0595393	+	0.183243i	−0.976403	−	0.215958i	$-0.930713\pi$
$431$	−1.23607	+	3.80423i	−0.0595393	+	0.183243i	0.916863	+	0.399201i	$0.130713\pi$
$432$		0			0
$433$	14.5623	+	10.5801i	0.699820	+	0.508449i	0.879874	−	0.475208i	$-0.157627\pi$
$433$	14.5623	+	10.5801i	0.699820	+	0.508449i	−0.180054	+	0.983657i	$0.557627\pi$
$434$		0			0
$435$	−4.94427	−	15.2169i	−0.237060	−	0.729595i
$436$		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
$443$	−9.70820	+	7.05342i	−0.461251	+	0.335118i	−0.794022	−	0.607889i	$-0.792016\pi$
$443$	−9.70820	+	7.05342i	−0.461251	+	0.335118i	0.332771	+	0.943008i	$0.392016\pi$
$444$		0			0
$445$	−8.65248	−	26.6296i	−0.410167	−	1.26236i
$446$		0			0
$447$	−16.1803	−	11.7557i	−0.765304	−	0.556026i
$448$		0			0
$449$	12.9787	−	39.9444i	0.612503	−	1.88509i	0.179303	−	0.983794i	$-0.442616\pi$
$449$	12.9787	−	39.9444i	0.612503	−	1.88509i	0.433200	−	0.901298i	$-0.357384\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−3.09017	+	9.51057i	−0.145189	+	0.446845i
$454$		0			0
$455$	−6.47214	−	4.70228i	−0.303418	−	0.220446i
$456$		0			0
$457$	6.79837	+	20.9232i	0.318015	+	0.978748i	0.974496	+	0.224406i	$0.0720441\pi$
$457$	6.79837	+	20.9232i	0.318015	+	0.978748i	−0.656481	+	0.754342i	$0.727956\pi$
$458$		0			0
$459$	−3.23607	+	2.35114i	−0.151047	+	0.109742i
$460$		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
$465$	12.9443	−	9.40456i	0.600276	−	0.436126i
$466$		0			0
$467$	−6.18034	−	19.0211i	−0.285992	−	0.880193i	−0.986100	−	0.166156i	$-0.946865\pi$
$467$	−6.18034	−	19.0211i	−0.285992	−	0.880193i	0.700108	−	0.714037i	$-0.253135\pi$
$468$		0			0
$469$	19.4164	+	14.1068i	0.896566	+	0.651394i
$470$		0			0
$471$	1.85410	−	5.70634i	0.0854325	−	0.262934i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	1.85410	−	5.70634i	0.0850720	−	0.261825i
$476$		0			0
$477$	1.61803	+	1.17557i	0.0740847	+	0.0538257i
$478$		0			0
$479$	8.65248	+	26.6296i	0.395342	+	1.21674i	0.928695	+	0.370844i	$0.120932\pi$
$479$	8.65248	+	26.6296i	0.395342	+	1.21674i	−0.533353	+	0.845893i	$0.679068\pi$
$480$		0			0
$481$	16.1803	−	11.7557i	0.737760	−	0.536014i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.00000			−0.181631
$486$		0			0
$487$	6.47214	−	4.70228i	0.293280	−	0.213081i	−0.431409	−	0.902157i	$-0.641983\pi$
$487$	6.47214	−	4.70228i	0.293280	−	0.213081i	0.724689	+	0.689076i	$0.241983\pi$
$488$		0			0
$489$	4.94427	+	15.2169i	0.223588	+	0.688132i
$490$		0			0
$491$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$491$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$492$		0			0
$493$	−9.88854	+	30.4338i	−0.445358	+	1.37067i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.94427	+	15.2169i	−0.221781	+	0.682571i
$498$		0			0
$499$	−3.23607	−	2.35114i	−0.144866	−	0.105252i	0.512992	−	0.858394i	$-0.328537\pi$
$499$	−3.23607	−	2.35114i	−0.144866	−	0.105252i	−0.657858	+	0.753142i	$0.728537\pi$
$500$		0			0
$501$	3.70820	+	11.4127i	0.165670	+	0.509881i
$502$		0			0
$503$	16.1803	−	11.7557i	0.721446	−	0.524161i	−0.165400	−	0.986227i	$-0.552892\pi$
$503$	16.1803	−	11.7557i	0.721446	−	0.524161i	0.886846	+	0.462066i	$0.152892\pi$
$504$		0			0
$505$	−32.0000			−1.42398
$506$		0			0
$507$	−9.00000			−0.399704
$508$		0			0
$509$	1.61803	−	1.17557i	0.0717181	−	0.0521062i	−0.551349	−	0.834275i	$-0.685887\pi$
$509$	1.61803	−	1.17557i	0.0717181	−	0.0521062i	0.623067	+	0.782169i	$0.285887\pi$
$510$		0			0
$511$	−3.70820	−	11.4127i	−0.164041	−	0.504867i
$512$		0			0
$513$	4.85410	+	3.52671i	0.214314	+	0.155708i
$514$		0			0
$515$	2.47214	−	7.60845i	0.108935	−	0.335268i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4.85410	−	3.52671i	−0.212662	−	0.154508i	0.476355	−	0.879253i	$-0.341958\pi$
$521$	−4.85410	−	3.52671i	−0.212662	−	0.154508i	−0.689017	+	0.724745i	$0.741958\pi$
$522$		0			0
$523$	−10.5066	−	32.3359i	−0.459421	−	1.41395i	−0.865866	−	0.500276i	$-0.833232\pi$
$523$	−10.5066	−	32.3359i	−0.459421	−	1.41395i	0.406445	−	0.913675i	$-0.366768\pi$
$524$		0			0
$525$	−1.61803	+	1.17557i	−0.0706168	+	0.0513061i
$526$		0			0
$527$	−32.0000			−1.39394
$528$		0			0
$529$	−23.0000			−1.00000
$530$		0			0
$531$	−9.70820	+	7.05342i	−0.421300	+	0.306092i
$532$		0			0
$533$	−4.94427	−	15.2169i	−0.214160	−	0.659117i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.70820	+	11.4127i	−0.160021	+	0.492493i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−5.56231	+	17.1190i	−0.239142	+	0.736004i	0.757403	+	0.652948i	$0.226468\pi$
$541$	−5.56231	+	17.1190i	−0.239142	+	0.736004i	−0.996545	+	0.0830560i	$0.973532\pi$
$542$		0			0
$543$	8.09017	+	5.87785i	0.347182	+	0.252243i
$544$		0			0
$545$	−6.18034	−	19.0211i	−0.264737	−	0.814776i
$546$		0			0
$547$	1.61803	−	1.17557i	0.0691821	−	0.0502638i	−0.552657	−	0.833409i	$-0.686386\pi$
$547$	1.61803	−	1.17557i	0.0691821	−	0.0502638i	0.621839	+	0.783145i	$0.286386\pi$
$548$		0			0
$549$	10.0000			0.426790
$550$		0			0
$551$	48.0000			2.04487
$552$		0			0
$553$	−3.23607	+	2.35114i	−0.137612	+	0.0999807i
$554$		0			0
$555$	6.18034	+	19.0211i	0.262341	+	0.807402i
$556$		0			0
$557$	−16.1803	−	11.7557i	−0.685583	−	0.498105i	0.189622	−	0.981857i	$-0.439274\pi$
$557$	−16.1803	−	11.7557i	−0.685583	−	0.498105i	−0.875205	+	0.483752i	$0.839274\pi$
$558$		0			0
$559$	1.23607	−	3.80423i	0.0522801	−	0.160902i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11.1246	+	34.2380i	−0.468846	+	1.44296i	0.385233	+	0.922819i	$0.374121\pi$
$563$	−11.1246	+	34.2380i	−0.468846	+	1.44296i	−0.854080	+	0.520142i	$0.825879\pi$
$564$		0			0
$565$	−9.70820	−	7.05342i	−0.408427	−	0.296740i
$566$		0			0
$567$	−0.618034	−	1.90211i	−0.0259550	−	0.0798812i
$568$		0			0
$569$	−16.1803	+	11.7557i	−0.678315	+	0.492825i	−0.872798	−	0.488081i	$-0.837697\pi$
$569$	−16.1803	+	11.7557i	−0.678315	+	0.492825i	0.194483	+	0.980906i	$0.437697\pi$
$570$		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
$577$	10.5066	+	32.3359i	0.437395	+	1.34616i	0.890613	+	0.454762i	$0.150276\pi$
$577$	10.5066	+	32.3359i	0.437395	+	1.34616i	−0.453218	+	0.891400i	$0.649724\pi$
$578$		0			0
$579$	17.7984	+	12.9313i	0.739675	+	0.537405i
$580$		0			0
$581$	−9.88854	+	30.4338i	−0.410246	+	1.26261i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−1.23607	+	3.80423i	−0.0511051	+	0.157285i
$586$		0			0
$587$	−35.5967	−	25.8626i	−1.46924	−	1.06746i	−0.980835	−	0.194842i	$-0.937581\pi$
$587$	−35.5967	−	25.8626i	−1.46924	−	1.06746i	−0.488400	−	0.872620i	$-0.662419\pi$
$588$		0			0
$589$	14.8328	+	45.6507i	0.611176	+	1.88100i
$590$		0			0
$591$	−19.4164	+	14.1068i	−0.798684	+	0.580278i
$592$		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
$597$	12.9443	−	9.40456i	0.529774	−	0.384903i
$598$		0			0
$599$	7.41641	+	22.8254i	0.303026	+	0.932619i	0.980406	+	0.196986i	$0.0631152\pi$
$599$	7.41641	+	22.8254i	0.303026	+	0.932619i	−0.677380	+	0.735633i	$0.736885\pi$
$600$		0			0
$601$	24.2705	+	17.6336i	0.990015	+	0.719288i	0.959924	−	0.280259i	$-0.0904205\pi$
$601$	24.2705	+	17.6336i	0.990015	+	0.719288i	0.0300904	+	0.999547i	$0.490420\pi$
$602$		0			0
$603$	3.70820	−	11.4127i	0.151010	−	0.464760i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	4.32624	−	13.3148i	0.175597	−	0.540431i	−0.824064	−	0.566497i	$-0.808298\pi$
$607$	4.32624	−	13.3148i	0.175597	−	0.540431i	0.999660	+	0.0260665i	$0.00829818\pi$
$608$		0			0
$609$	−12.9443	−	9.40456i	−0.524528	−	0.381092i
$610$		0			0
$611$	4.94427	+	15.2169i	0.200024	+	0.615610i
$612$		0			0
$613$	−1.61803	+	1.17557i	−0.0653518	+	0.0474808i	−0.619982	−	0.784616i	$-0.712860\pi$
$613$	−1.61803	+	1.17557i	−0.0653518	+	0.0474808i	0.554630	+	0.832097i	$0.312860\pi$
$614$		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
$619$	25.8885	−	18.8091i	1.04055	−	0.756003i	0.0701559	−	0.997536i	$-0.477650\pi$
$619$	25.8885	−	18.8091i	1.04055	−	0.756003i	0.970393	+	0.241533i	$0.0776503\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−22.6525	−	16.4580i	−0.907552	−	0.659375i
$624$		0			0
$625$	−5.87132	+	18.0701i	−0.234853	+	0.722803i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	12.3607	−	38.0423i	0.492853	−	1.51684i
$630$		0			0
$631$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$631$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$632$		0			0
$633$	5.56231	+	17.1190i	0.221082	+	0.680420i
$634$		0			0
$635$	16.1803	−	11.7557i	0.642097	−	0.466511i
$636$		0			0
$637$	6.00000			0.237729
$638$		0			0
$639$	8.00000			0.316475
$640$		0			0
$641$	4.85410	−	3.52671i	0.191726	−	0.139297i	−0.487781	−	0.872966i	$-0.662194\pi$
$641$	4.85410	−	3.52671i	0.191726	−	0.139297i	0.679507	+	0.733669i	$0.262194\pi$
$642$		0			0
$643$	−4.94427	−	15.2169i	−0.194983	−	0.600096i	−0.999977	−	0.00681282i	$-0.997831\pi$
$643$	−4.94427	−	15.2169i	−0.194983	−	0.600096i	0.804994	−	0.593283i	$-0.202169\pi$
$644$		0			0
$645$	3.23607	+	2.35114i	0.127420	+	0.0925761i
$646$		0			0
$647$	−4.94427	+	15.2169i	−0.194379	+	0.598238i	0.805604	+	0.592455i	$0.201841\pi$
$647$	−4.94427	+	15.2169i	−0.194379	+	0.598238i	−0.999983	+	0.00578370i	$0.998159\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	4.94427	−	15.2169i	0.193781	−	0.596397i
$652$		0			0
$653$	−4.85410	−	3.52671i	−0.189956	−	0.138011i	0.488743	−	0.872428i	$-0.337456\pi$
$653$	−4.85410	−	3.52671i	−0.189956	−	0.138011i	−0.678698	+	0.734417i	$0.737456\pi$
$654$		0			0
$655$	7.41641	+	22.8254i	0.289783	+	0.891860i
$656$		0			0
$657$	−4.85410	+	3.52671i	−0.189377	+	0.137590i
$658$		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
$663$	6.47214	−	4.70228i	0.251357	−	0.182622i
$664$		0			0
$665$	7.41641	+	22.8254i	0.287596	+	0.885129i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−1.23607	+	3.80423i	−0.0477891	+	0.147080i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−6.79837	+	20.9232i	−0.262058	+	0.806532i	0.730299	+	0.683128i	$0.239381\pi$
$673$	−6.79837	+	20.9232i	−0.262058	+	0.806532i	−0.992357	+	0.123404i	$0.960619\pi$
$674$		0			0
$675$	0.809017	+	0.587785i	0.0311391	+	0.0226239i
$676$		0			0
$677$	2.47214	+	7.60845i	0.0950119	+	0.292417i	0.987257	−	0.159135i	$-0.0508706\pi$
$677$	2.47214	+	7.60845i	0.0950119	+	0.292417i	−0.892245	+	0.451552i	$0.850871\pi$
$678$		0			0
$679$	−3.23607	+	2.35114i	−0.124189	+	0.0902285i
$680$		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
$685$	3.23607	−	2.35114i	0.123644	−	0.0898325i
$686$		0			0
$687$	−4.32624	−	13.3148i	−0.165056	−	0.507991i
$688$		0			0
$689$	−3.23607	−	2.35114i	−0.123284	−	0.0895713i
$690$		0			0
$691$	−2.47214	+	7.60845i	−0.0940445	+	0.289439i	−0.987003	−	0.160699i	$-0.948625\pi$
$691$	−2.47214	+	7.60845i	−0.0940445	+	0.289439i	0.892959	+	0.450138i	$0.148625\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.70820	+	11.4127i	−0.140660	+	0.432908i
$696$		0			0
$697$	−25.8885	−	18.8091i	−0.980599	−	0.712447i
$698$		0			0
$699$	7.41641	+	22.8254i	0.280514	+	0.863334i
$700$		0			0
$701$	29.1246	−	21.1603i	1.10002	−	0.799212i	0.118958	−	0.992899i	$-0.462045\pi$
$701$	29.1246	−	21.1603i	1.10002	−	0.799212i	0.981063	+	0.193687i	$0.0620446\pi$
$702$		0			0
$703$	−60.0000			−2.26294
$704$		0			0
$705$	−16.0000			−0.602595
$706$		0			0
$707$	−25.8885	+	18.8091i	−0.973639	+	0.707390i
$708$		0			0
$709$	10.5066	+	32.3359i	0.394583	+	1.21440i	0.929286	+	0.369361i	$0.120423\pi$
$709$	10.5066	+	32.3359i	0.394583	+	1.21440i	−0.534703	+	0.845040i	$0.679577\pi$
$710$		0			0
$711$	1.61803	+	1.17557i	0.0606810	+	0.0440873i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.23607	−	3.80423i	0.0461618	−	0.142071i
$718$		0			0
$719$	−32.3607	−	23.5114i	−1.20685	−	0.876828i	−0.211909	−	0.977289i	$-0.567968\pi$
$719$	−32.3607	−	23.5114i	−1.20685	−	0.876828i	−0.994941	+	0.100462i	$0.967968\pi$
$720$		0			0
$721$	−2.47214	−	7.60845i	−0.0920672	−	0.283354i
$722$		0			0
$723$	14.5623	−	10.5801i	0.541578	−	0.393479i
$724$		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
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−2.47214	−	7.60845i	−0.0914353	−	0.281409i
$732$		0			0
$733$	21.0344	+	15.2824i	0.776925	+	0.564469i	0.904055	−	0.427417i	$-0.140576\pi$
$733$	21.0344	+	15.2824i	0.776925	+	0.564469i	−0.127130	+	0.991886i	$0.540576\pi$
$734$		0			0
$735$	−1.85410	+	5.70634i	−0.0683896	+	0.210481i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−10.5066	+	32.3359i	−0.386491	+	1.18950i	0.548902	+	0.835886i	$0.315046\pi$
$739$	−10.5066	+	32.3359i	−0.386491	+	1.18950i	−0.935393	+	0.353610i	$0.884954\pi$
$740$		0			0
$741$	−9.70820	−	7.05342i	−0.356640	−	0.259114i
$742$		0			0
$743$	−12.3607	−	38.0423i	−0.453469	−	1.39564i	−0.872923	−	0.487858i	$-0.837778\pi$
$743$	−12.3607	−	38.0423i	−0.453469	−	1.39564i	0.419453	−	0.907777i	$-0.362222\pi$
$744$		0			0
$745$	−32.3607	+	23.5114i	−1.18560	+	0.861391i
$746$		0			0
$747$	16.0000			0.585409
$748$		0			0
$749$		0			0
$750$		0			0
$751$	25.8885	−	18.8091i	0.944686	−	0.686355i	−0.00485778	−	0.999988i	$-0.501546\pi$
$751$	25.8885	−	18.8091i	0.944686	−	0.686355i	0.949544	+	0.313633i	$0.101546\pi$
$752$		0			0
$753$	1.23607	+	3.80423i	0.0450448	+	0.138634i
$754$		0			0
$755$	16.1803	+	11.7557i	0.588863	+	0.427834i
$756$		0			0
$757$	16.6869	−	51.3571i	0.606496	−	1.86660i	0.120338	−	0.992733i	$-0.461602\pi$
$757$	16.6869	−	51.3571i	0.606496	−	1.86660i	0.486158	−	0.873871i	$-0.338398\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6.18034	+	19.0211i	−0.224037	+	0.689515i	0.774351	+	0.632757i	$0.218077\pi$
$761$	−6.18034	+	19.0211i	−0.224037	+	0.689515i	−0.998388	+	0.0567589i	$0.981923\pi$
$762$		0			0
$763$	−16.1803	−	11.7557i	−0.585768	−	0.425585i
$764$		0			0
$765$	2.47214	+	7.60845i	0.0893803	+	0.275084i
$766$		0			0
$767$	19.4164	−	14.1068i	0.701086	−	0.509369i
$768$		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
$773$	1.61803	−	1.17557i	0.0581966	−	0.0422823i	−0.558307	−	0.829635i	$-0.688549\pi$
$773$	1.61803	−	1.17557i	0.0581966	−	0.0422823i	0.616503	+	0.787352i	$0.288549\pi$
$774$		0			0
$775$	2.47214	+	7.60845i	0.0888017	+	0.273304i
$776$		0			0
$777$	16.1803	+	11.7557i	0.580466	+	0.421734i
$778$		0			0
$779$	−14.8328	+	45.6507i	−0.531441	+	1.63561i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−2.47214	+	7.60845i	−0.0883469	+	0.271904i
$784$		0			0
$785$	−9.70820	−	7.05342i	−0.346501	−	0.251747i
$786$		0			0
$787$	4.32624	+	13.3148i	0.154214	+	0.474621i	0.998080	−	0.0619319i	$-0.0197262\pi$
$787$	4.32624	+	13.3148i	0.154214	+	0.474621i	−0.843867	+	0.536553i	$0.819726\pi$
$788$		0			0
$789$	3.23607	−	2.35114i	0.115207	−	0.0837028i
$790$		0			0
$791$	−12.0000			−0.426671
$792$		0			0
$793$	−20.0000			−0.710221
$794$		0			0
$795$	3.23607	−	2.35114i	0.114772	−	0.0833864i
$796$		0			0
$797$	−11.7426	−	36.1401i	−0.415946	−	1.28015i	−0.911402	−	0.411517i	$-0.864999\pi$
$797$	−11.7426	−	36.1401i	−0.415946	−	1.28015i	0.495456	−	0.868633i	$-0.335001\pi$
$798$		0			0
$799$	25.8885	+	18.8091i	0.915871	+	0.665419i
$800$		0			0
$801$	−4.32624	+	13.3148i	−0.152860	+	0.470455i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.61803	+	1.17557i	0.0569575	+	0.0413820i
$808$		0			0
$809$	−6.18034	−	19.0211i	−0.217289	−	0.668747i	−0.998983	−	0.0450851i	$-0.985644\pi$
$809$	−6.18034	−	19.0211i	−0.217289	−	0.668747i	0.781694	−	0.623662i	$-0.214356\pi$
$810$		0			0
$811$	−14.5623	+	10.5801i	−0.511352	+	0.371519i	−0.813336	−	0.581794i	$-0.802351\pi$
$811$	−14.5623	+	10.5801i	−0.511352	+	0.371519i	0.301984	+	0.953313i	$0.402351\pi$
$812$		0			0
$813$	10.0000			0.350715
$814$		0			0
$815$	32.0000			1.12091
$816$		0			0
$817$	−9.70820	+	7.05342i	−0.339647	+	0.246768i
$818$		0			0
$819$	1.23607	+	3.80423i	0.0431917	+	0.132930i
$820$		0			0
$821$	−12.9443	−	9.40456i	−0.451758	−	0.328222i	0.338531	−	0.940955i	$-0.390070\pi$
$821$	−12.9443	−	9.40456i	−0.451758	−	0.328222i	−0.790290	+	0.612734i	$0.790070\pi$
$822$		0			0
$823$	−3.70820	+	11.4127i	−0.129260	+	0.397821i	−0.994653	−	0.103272i	$-0.967069\pi$
$823$	−3.70820	+	11.4127i	−0.129260	+	0.397821i	0.865393	+	0.501093i	$0.167069\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−14.8328	+	45.6507i	−0.515788	+	1.58743i	0.266057	+	0.963957i	$0.414279\pi$
$827$	−14.8328	+	45.6507i	−0.515788	+	1.58743i	−0.781844	+	0.623474i	$0.785721\pi$
$828$		0			0
$829$	−14.5623	−	10.5801i	−0.505770	−	0.367463i	0.305447	−	0.952209i	$-0.401194\pi$
$829$	−14.5623	−	10.5801i	−0.505770	−	0.367463i	−0.811217	+	0.584746i	$0.801194\pi$
$830$		0			0
$831$	4.32624	+	13.3148i	0.150076	+	0.461885i
$832$		0			0
$833$	9.70820	−	7.05342i	0.336369	−	0.244387i
$834$		0			0
$835$	24.0000			0.830554
$836$		0			0
$837$	−8.00000			−0.276520
$838$		0			0
$839$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$839$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$840$		0			0
$841$	10.8156	+	33.2870i	0.372952	+	1.14783i
$842$		0			0
$843$	6.47214	+	4.70228i	0.222912	+	0.161955i
$844$		0			0
$845$	−5.56231	+	17.1190i	−0.191349	+	0.588912i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−8.03444	+	24.7275i	−0.275741	+	0.848645i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−1.85410	−	5.70634i	−0.0634832	−	0.195381i	0.914284	−	0.405073i	$-0.132754\pi$
$853$	−1.85410	−	5.70634i	−0.0634832	−	0.195381i	−0.977768	+	0.209692i	$0.932754\pi$
$854$		0			0
$855$	9.70820	−	7.05342i	0.332014	−	0.241222i
$856$		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
$861$	12.9443	−	9.40456i	0.441140	−	0.320507i
$862$		0			0
$863$	−14.8328	−	45.6507i	−0.504915	−	1.55397i	−0.800914	−	0.598780i	$-0.795652\pi$
$863$	−14.8328	−	45.6507i	−0.504915	−	1.55397i	0.295999	−	0.955188i	$-0.404348\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.309017	+	0.951057i	−0.0104948	+	0.0322996i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−7.41641	+	22.8254i	−0.251295	+	0.773408i
$872$		0			0
$873$	1.61803	+	1.17557i	0.0547622	+	0.0397870i
$874$		0			0
$875$	7.41641	+	22.8254i	0.250720	+	0.771638i
$876$		0			0
$877$	30.7426	−	22.3358i	1.03811	−	0.754228i	0.0681906	−	0.997672i	$-0.478277\pi$
$877$	30.7426	−	22.3358i	1.03811	−	0.754228i	0.969915	+	0.243445i	$0.0782774\pi$
$878$		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
$883$	−35.5967	+	25.8626i	−1.19793	+	0.870344i	−0.994079	−	0.108659i	$-0.965344\pi$
$883$	−35.5967	+	25.8626i	−1.19793	+	0.870344i	−0.203847	+	0.979003i	$0.565344\pi$
$884$		0			0
$885$	7.41641	+	22.8254i	0.249300	+	0.767266i
$886$		0			0
$887$	38.8328	+	28.2137i	1.30388	+	0.947323i	0.999986	−	0.00538315i	$-0.00171352\pi$
$887$	38.8328	+	28.2137i	1.30388	+	0.947323i	0.303893	+	0.952706i	$0.401714\pi$
$888$		0			0
$889$	6.18034	−	19.0211i	0.207282	−	0.637948i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	14.8328	−	45.6507i	0.496361	−	1.52764i
$894$		0			0
$895$	19.4164	+	14.1068i	0.649019	+	0.471540i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−51.7771	+	37.6183i	−1.72686	+	1.25464i
$900$		0			0
$901$	−8.00000			−0.266519
$902$		0			0
$903$	4.00000			0.133112
$904$		0			0
$905$	16.1803	−	11.7557i	0.537853	−	0.390773i
$906$		0			0
$907$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$907$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$908$		0			0
$909$	12.9443	+	9.40456i	0.429334	+	0.311930i
$910$		0			0
$911$	2.47214	−	7.60845i	0.0819055	−	0.252079i	−0.901715	−	0.432331i	$-0.857691\pi$
$911$	2.47214	−	7.60845i	0.0819055	−	0.252079i	0.983621	+	0.180252i	$0.0576912\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	6.18034	−	19.0211i	0.204316	−	0.628819i
$916$		0			0
$917$	19.4164	+	14.1068i	0.641186	+	0.465849i
$918$		0			0
$919$	15.4508	+	47.5528i	0.509677	+	1.56862i	0.792764	+	0.609529i	$0.208641\pi$
$919$	15.4508	+	47.5528i	0.509677	+	1.56862i	−0.283087	+	0.959094i	$0.591359\pi$
$920$		0			0
$921$	−1.61803	+	1.17557i	−0.0533160	+	0.0387364i
$922$		0			0
$923$	−16.0000			−0.526646
$924$		0			0
$925$	−10.0000			−0.328798
$926$		0			0
$927$	−3.23607	+	2.35114i	−0.106286	+	0.0772216i
$928$		0			0
$929$	1.85410	+	5.70634i	0.0608311	+	0.187219i	0.976854	−	0.213907i	$-0.0686190\pi$
$929$	1.85410	+	5.70634i	0.0608311	+	0.187219i	−0.916023	+	0.401126i	$0.868619\pi$
$930$		0			0
$931$	−14.5623	−	10.5801i	−0.477260	−	0.346750i
$932$		0			0
$933$	−4.94427	+	15.2169i	−0.161868	+	0.498179i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−11.7426	+	36.1401i	−0.383616	+	1.18065i	0.553864	+	0.832607i	$0.313153\pi$
$937$	−11.7426	+	36.1401i	−0.383616	+	1.18065i	−0.937480	+	0.348040i	$0.886847\pi$
$938$		0			0
$939$	14.5623	+	10.5801i	0.475223	+	0.345270i
$940$		0			0
$941$	−7.41641	−	22.8254i	−0.241768	−	0.744085i	−0.996151	−	0.0876511i	$-0.972064\pi$
$941$	−7.41641	−	22.8254i	−0.241768	−	0.744085i	0.754383	−	0.656434i	$-0.227936\pi$
$942$		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
$949$	9.70820	−	7.05342i	0.315142	−	0.228964i
$950$		0			0
$951$	−4.32624	−	13.3148i	−0.140288	−	0.431762i
$952$		0			0
$953$	−29.1246	−	21.1603i	−0.943439	−	0.685448i	0.00580723	−	0.999983i	$-0.498151\pi$
$953$	−29.1246	−	21.1603i	−0.943439	−	0.685448i	−0.949246	+	0.314535i	$0.898151\pi$
$954$		0			0
$955$	9.88854	−	30.4338i	0.319986	−	0.984815i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.23607	−	3.80423i	0.0399147	−	0.122845i
$960$		0			0
$961$	−26.6976	−	19.3969i	−0.861212	−	0.625707i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	35.5967	−	25.8626i	1.14590	−	0.832545i
$966$		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
$971$	−16.1803	+	11.7557i	−0.519252	+	0.377259i	−0.816322	−	0.577597i	$-0.803990\pi$
$971$	−16.1803	+	11.7557i	−0.519252	+	0.377259i	0.297070	+	0.954856i	$0.403990\pi$
$972$		0			0
$973$	3.70820	+	11.4127i	0.118880	+	0.365874i
$974$		0			0
$975$	−1.61803	−	1.17557i	−0.0518186	−	0.0376484i
$976$		0			0
$977$	11.7426	−	36.1401i	0.375681	−	1.15623i	−0.567338	−	0.823485i	$-0.692027\pi$
$977$	11.7426	−	36.1401i	0.375681	−	1.15623i	0.943018	−	0.332741i	$-0.107973\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−3.09017	+	9.51057i	−0.0986615	+	0.303649i
$982$		0			0
$983$	−6.47214	−	4.70228i	−0.206429	−	0.149980i	0.479767	−	0.877396i	$-0.340721\pi$
$983$	−6.47214	−	4.70228i	−0.206429	−	0.149980i	−0.686197	+	0.727416i	$0.740721\pi$
$984$		0			0
$985$	14.8328	+	45.6507i	0.472613	+	1.45455i
$986$		0			0
$987$	−12.9443	+	9.40456i	−0.412021	+	0.299351i
$988$		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
$993$	−6.47214	+	4.70228i	−0.205387	+	0.149222i
$994$		0			0
$995$	−9.88854	−	30.4338i	−0.313488	−	0.964817i
$996$		0			0
$997$	−1.61803	−	1.17557i	−0.0512437	−	0.0372307i	0.561869	−	0.827227i	$-0.310083\pi$
$997$	−1.61803	−	1.17557i	−0.0512437	−	0.0372307i	−0.613112	+	0.789996i	$0.710083\pi$
$998$		0			0
$999$	3.09017	−	9.51057i	0.0977687	−	0.300901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1452.2.i.e.493.1		4
11.2	odd	10		1452.2.i.d.1213.1		4
11.3	even	5	inner	1452.2.i.e.565.1		4
11.4	even	5		132.2.a.b.1.1	✓	1
11.5	even	5	inner	1452.2.i.e.1237.1		4
11.6	odd	10		1452.2.i.d.1237.1		4
11.7	odd	10		1452.2.a.f.1.1		1
11.8	odd	10		1452.2.i.d.565.1		4
11.9	even	5	inner	1452.2.i.e.1213.1		4
11.10	odd	2		1452.2.i.d.493.1		4
33.26	odd	10		396.2.a.a.1.1		1
33.29	even	10		4356.2.a.d.1.1		1
44.7	even	10		5808.2.a.m.1.1		1
44.15	odd	10		528.2.a.e.1.1		1
55.4	even	10		3300.2.a.f.1.1		1
55.37	odd	20		3300.2.c.j.1849.1		2
55.48	odd	20		3300.2.c.j.1849.2		2
77.48	odd	10		6468.2.a.b.1.1		1
88.37	even	10		2112.2.a.c.1.1		1
88.59	odd	10		2112.2.a.u.1.1		1
99.4	even	15		3564.2.i.d.1189.1		2
99.59	odd	30		3564.2.i.i.1189.1		2
99.70	even	15		3564.2.i.d.2377.1		2
99.92	odd	30		3564.2.i.i.2377.1		2
132.59	even	10		1584.2.a.e.1.1		1
165.59	odd	10		9900.2.a.w.1.1		1
165.92	even	20		9900.2.c.f.5149.1		2
165.158	even	20		9900.2.c.f.5149.2		2
264.59	even	10		6336.2.a.cg.1.1		1
264.125	odd	10		6336.2.a.ca.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.a.b.1.1	✓	1	11.4	even	5
396.2.a.a.1.1		1	33.26	odd	10
528.2.a.e.1.1		1	44.15	odd	10
1452.2.a.f.1.1		1	11.7	odd	10
1452.2.i.d.493.1		4	11.10	odd	2
1452.2.i.d.565.1		4	11.8	odd	10
1452.2.i.d.1213.1		4	11.2	odd	10
1452.2.i.d.1237.1		4	11.6	odd	10
1452.2.i.e.493.1		4	1.1	even	1	trivial
1452.2.i.e.565.1		4	11.3	even	5	inner
1452.2.i.e.1213.1		4	11.9	even	5	inner
1452.2.i.e.1237.1		4	11.5	even	5	inner
1584.2.a.e.1.1		1	132.59	even	10
2112.2.a.c.1.1		1	88.37	even	10
2112.2.a.u.1.1		1	88.59	odd	10
3300.2.a.f.1.1		1	55.4	even	10
3300.2.c.j.1849.1		2	55.37	odd	20
3300.2.c.j.1849.2		2	55.48	odd	20
3564.2.i.d.1189.1		2	99.4	even	15
3564.2.i.d.2377.1		2	99.70	even	15
3564.2.i.i.1189.1		2	99.59	odd	30
3564.2.i.i.2377.1		2	99.92	odd	30
4356.2.a.d.1.1		1	33.29	even	10
5808.2.a.m.1.1		1	44.7	even	10
6336.2.a.ca.1.1		1	264.125	odd	10
6336.2.a.cg.1.1		1	264.59	even	10
6468.2.a.b.1.1		1	77.48	odd	10
9900.2.a.w.1.1		1	165.59	odd	10
9900.2.c.f.5149.1		2	165.92	even	20
9900.2.c.f.5149.2		2	165.158	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} +(0.618034 + 1.90211i) q^{5} +(1.61803 + 1.17557i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{3} +(0.618034 + 1.90211i) q^{5} +(1.61803 + 1.17557i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-0.618034 + 1.90211i) q^{13} +(-1.61803 - 1.17557i) q^{15} +(1.23607 + 3.80423i) q^{17} +(4.85410 - 3.52671i) q^{19} -2.00000 q^{21} +(0.809017 - 0.587785i) q^{25} +(0.309017 + 0.951057i) q^{27} +(6.47214 + 4.70228i) q^{29} +(-2.47214 + 7.60845i) q^{31} +(-1.23607 + 3.80423i) q^{35} +(-8.09017 - 5.87785i) q^{37} +(-0.618034 - 1.90211i) q^{39} +(-6.47214 + 4.70228i) q^{41} -2.00000 q^{43} +2.00000 q^{45} +(6.47214 - 4.70228i) q^{47} +(-0.927051 - 2.85317i) q^{49} +(-3.23607 - 2.35114i) q^{51} +(-0.618034 + 1.90211i) q^{53} +(-1.85410 + 5.70634i) q^{57} +(-9.70820 - 7.05342i) q^{59} +(3.09017 + 9.51057i) q^{61} +(1.61803 - 1.17557i) q^{63} -4.00000 q^{65} +12.0000 q^{67} +(2.47214 + 7.60845i) q^{71} +(-4.85410 - 3.52671i) q^{73} +(-0.309017 + 0.951057i) q^{75} +(-0.618034 + 1.90211i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(4.94427 + 15.2169i) q^{83} +(-6.47214 + 4.70228i) q^{85} -8.00000 q^{87} -14.0000 q^{89} +(-3.23607 + 2.35114i) q^{91} +(-2.47214 - 7.60845i) q^{93} +(9.70820 + 7.05342i) q^{95} +(-0.618034 + 1.90211i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 2 q^{5} + 2 q^{7} - q^{9}+O(q^{10}) \) 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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