LMFDB - Embedded newform 1452.2.i.l.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.l.1237.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{3} +(0.618034 + 1.90211i) q^{5} +(1.61803 + 1.17557i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	$q+(0.809017 - 0.587785i) q^{3} +(0.618034 + 1.90211i) q^{5} +(1.61803 + 1.17557i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-1.85410 + 5.70634i) q^{13} +(1.61803 + 1.17557i) q^{15} +(1.23607 + 3.80423i) q^{17} +(-1.61803 + 1.17557i) q^{19} +2.00000 q^{21} -8.00000 q^{23} +(0.809017 - 0.587785i) q^{25} +(-0.309017 - 0.951057i) q^{27} +(-1.23607 + 3.80423i) q^{35} +(4.85410 + 3.52671i) q^{37} +(1.85410 + 5.70634i) q^{39} -10.0000 q^{43} +2.00000 q^{45} +(-0.927051 - 2.85317i) q^{49} +(3.23607 + 2.35114i) q^{51} +(4.32624 - 13.3148i) q^{53} +(-0.618034 + 1.90211i) q^{57} +(9.70820 + 7.05342i) q^{59} +(4.32624 + 13.3148i) q^{61} +(1.61803 - 1.17557i) q^{63} -12.0000 q^{65} +4.00000 q^{67} +(-6.47214 + 4.70228i) q^{69} +(4.85410 + 3.52671i) q^{73} +(0.309017 - 0.951057i) q^{75} +(-0.618034 + 1.90211i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-4.94427 - 15.2169i) q^{83} +(-6.47214 + 4.70228i) q^{85} -14.0000 q^{89} +(-9.70820 + 7.05342i) q^{91} +(-3.23607 - 2.35114i) q^{95} +(-0.618034 + 1.90211i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 6 q^{13} + 2 q^{15} - 4 q^{17} - 2 q^{19} + 8 q^{21} - 32 q^{23} + q^{25} + q^{27} + 4 q^{35} + 6 q^{37} - 6 q^{39} - 40 q^{43} + 8 q^{45} + 3 q^{49} + 4 q^{51} - 14 q^{53} + 2 q^{57} + 12 q^{59} - 14 q^{61} + 2 q^{63} - 48 q^{65} + 16 q^{67} - 8 q^{69} + 6 q^{73} - q^{75} + 2 q^{79} - q^{81} + 16 q^{83} - 8 q^{85} - 56 q^{89} - 12 q^{91} - 4 q^{95} + 2 q^{97}+O(q^{100}) $ 4 * q + q^3 - 2 * q^5 + 2 * q^7 - q^9 + 6 * q^13 + 2 * q^15 - 4 * q^17 - 2 * q^19 + 8 * q^21 - 32 * q^23 + q^25 + q^27 + 4 * q^35 + 6 * q^37 - 6 * q^39 - 40 * q^43 + 8 * q^45 + 3 * q^49 + 4 * q^51 - 14 * q^53 + 2 * q^57 + 12 * q^59 - 14 * q^61 + 2 * q^63 - 48 * q^65 + 16 * q^67 - 8 * q^69 + 6 * q^73 - q^75 + 2 * q^79 - q^81 + 16 * q^83 - 8 * q^85 - 56 * q^89 - 12 * q^91 - 4 * 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
$13$	−1.85410	+	5.70634i	−0.514235	+	1.58265i	0.270434	+	0.962739i	$0.412833\pi$
$13$	−1.85410	+	5.70634i	−0.514235	+	1.58265i	−0.784669	+	0.619915i	$0.787167\pi$
$14$		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
$19$	−1.61803	+	1.17557i	−0.371202	+	0.269694i	−0.757709	−	0.652592i	$-0.773682\pi$
$19$	−1.61803	+	1.17557i	−0.371202	+	0.269694i	0.386507	+	0.922287i	$0.373682\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$		0			0
$23$	−8.00000			−1.66812			−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$24$		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
$29$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$29$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$30$		0			0
$31$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$31$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.23607	+	3.80423i	−0.208934	+	0.643032i
$36$		0			0
$37$	4.85410	+	3.52671i	0.798009	+	0.579788i	0.910330	−	0.413884i	$-0.135828\pi$
$37$	4.85410	+	3.52671i	0.798009	+	0.579788i	−0.112320	+	0.993672i	$0.535828\pi$
$38$		0			0
$39$	1.85410	+	5.70634i	0.296894	+	0.913746i
$40$		0			0
$41$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$41$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$42$		0			0
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$		0			0
$45$	2.00000			0.298142
$46$		0			0
$47$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$47$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$48$		0			0
$49$	−0.927051	−	2.85317i	−0.132436	−	0.407596i
$50$		0			0
$51$	3.23607	+	2.35114i	0.453140	+	0.329226i
$52$		0			0
$53$	4.32624	−	13.3148i	0.594254	−	1.82893i	0.0358519	−	0.999357i	$-0.488586\pi$
$53$	4.32624	−	13.3148i	0.594254	−	1.82893i	0.558403	−	0.829570i	$-0.311414\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.618034	+	1.90211i	−0.0818606	+	0.251941i
$58$		0			0
$59$	9.70820	+	7.05342i	1.26390	+	0.918277i	0.998942	−	0.0459824i	$-0.0146418\pi$
$59$	9.70820	+	7.05342i	1.26390	+	0.918277i	0.264958	+	0.964260i	$0.414642\pi$
$60$		0			0
$61$	4.32624	+	13.3148i	0.553918	+	1.70478i	0.698784	+	0.715333i	$0.253725\pi$
$61$	4.32624	+	13.3148i	0.553918	+	1.70478i	−0.144866	+	0.989451i	$0.546275\pi$
$62$		0			0
$63$	1.61803	−	1.17557i	0.203853	−	0.148108i
$64$		0			0
$65$	−12.0000			−1.48842
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$		0			0
$69$	−6.47214	+	4.70228i	−0.779154	+	0.566088i
$70$		0			0
$71$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$71$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$72$		0			0
$73$	4.85410	+	3.52671i	0.568130	+	0.412770i	0.834425	−	0.551121i	$-0.185800\pi$
$73$	4.85410	+	3.52671i	0.568130	+	0.412770i	−0.266296	+	0.963891i	$0.585800\pi$
$74$		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	$-0.758802\pi$
$83$	−4.94427	−	15.2169i	−0.542704	−	1.67027i	0.183682	−	0.982986i	$-0.441198\pi$
$84$		0			0
$85$	−6.47214	+	4.70228i	−0.702002	+	0.510034i
$86$		0			0
$87$		0			0
$88$		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
$91$	−9.70820	+	7.05342i	−1.01770	+	0.739400i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.23607	−	2.35114i	−0.332014	−	0.241222i
$96$		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
$101$	−2.47214	+	7.60845i	−0.245987	+	0.757069i	0.749486	+	0.662020i	$0.230301\pi$
$101$	−2.47214	+	7.60845i	−0.245987	+	0.757069i	−0.995473	+	0.0950490i	$0.969699\pi$
$102$		0			0
$103$	9.70820	+	7.05342i	0.956578	+	0.694994i	0.952353	−	0.304997i	$-0.0986553\pi$
$103$	9.70820	+	7.05342i	0.956578	+	0.694994i	0.00422434	+	0.999991i	$0.498655\pi$
$104$		0			0
$105$	1.23607	+	3.80423i	0.120628	+	0.371254i
$106$		0			0
$107$	12.9443	−	9.40456i	1.25137	−	0.909174i	0.253069	−	0.967448i	$-0.418560\pi$
$107$	12.9443	−	9.40456i	1.25137	−	0.909174i	0.998301	+	0.0582746i	$0.0185599\pi$
$108$		0			0
$109$	18.0000			1.72409			0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000			1.72409			0.862044	+	0.506834i	$0.169184\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$		0			0
$113$	8.09017	−	5.87785i	0.761059	−	0.552942i	−0.138176	−	0.990408i	$-0.544124\pi$
$113$	8.09017	−	5.87785i	0.761059	−	0.552942i	0.899235	+	0.437466i	$0.144124\pi$
$114$		0			0
$115$	−4.94427	−	15.2169i	−0.461056	−	1.41898i
$116$		0			0
$117$	4.85410	+	3.52671i	0.448762	+	0.326045i
$118$		0			0
$119$	−2.47214	+	7.60845i	−0.226620	+	0.697466i
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.70820	+	7.05342i	0.868328	+	0.630877i
$126$		0			0
$127$	1.85410	+	5.70634i	0.164525	+	0.506356i	0.999001	−	0.0446885i	$-0.0142295\pi$
$127$	1.85410	+	5.70634i	0.164525	+	0.506356i	−0.834476	+	0.551044i	$0.814230\pi$
$128$		0			0
$129$	−8.09017	+	5.87785i	−0.712300	+	0.517516i
$130$		0			0
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$	−4.00000			−0.346844
$134$		0			0
$135$	1.61803	−	1.17557i	0.139258	−	0.101177i
$136$		0			0
$137$	4.32624	+	13.3148i	0.369615	+	1.13756i	0.947040	+	0.321115i	$0.104058\pi$
$137$	4.32624	+	13.3148i	0.369615	+	1.13756i	−0.577425	+	0.816444i	$0.695942\pi$
$138$		0			0
$139$	11.3262	+	8.22899i	0.960679	+	0.697974i	0.953308	−	0.301999i	$-0.0976538\pi$
$139$	11.3262	+	8.22899i	0.960679	+	0.697974i	0.00737063	+	0.999973i	$0.497654\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−2.42705	−	1.76336i	−0.200180	−	0.145439i
$148$		0			0
$149$	1.23607	+	3.80423i	0.101263	+	0.311654i	0.988835	−	0.149014i	$-0.0476099\pi$
$149$	1.23607	+	3.80423i	0.101263	+	0.311654i	−0.887572	+	0.460668i	$0.847610\pi$
$150$		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
$155$		0			0
$156$		0			0
$157$	8.09017	−	5.87785i	0.645666	−	0.469104i	−0.216126	−	0.976365i	$-0.569342\pi$
$157$	8.09017	−	5.87785i	0.645666	−	0.469104i	0.861792	+	0.507262i	$0.169342\pi$
$158$		0			0
$159$	−4.32624	−	13.3148i	−0.343093	−	1.05593i
$160$		0			0
$161$	−12.9443	−	9.40456i	−1.02015	−	0.741183i
$162$		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
$169$	−18.6074	−	13.5191i	−1.43134	−	1.03993i
$170$		0			0
$171$	0.618034	+	1.90211i	0.0472622	+	0.145458i
$172$		0			0
$173$	6.47214	−	4.70228i	0.492067	−	0.357508i	−0.313911	−	0.949452i	$-0.601639\pi$
$173$	6.47214	−	4.70228i	0.492067	−	0.357508i	0.805979	+	0.591944i	$0.201639\pi$
$174$		0			0
$175$	2.00000			0.151186
$176$		0			0
$177$	12.0000			0.901975
$178$		0			0
$179$	3.23607	−	2.35114i	0.241875	−	0.175733i	−0.460243	−	0.887793i	$-0.652238\pi$
$179$	3.23607	−	2.35114i	0.241875	−	0.175733i	0.702118	+	0.712060i	$0.252238\pi$
$180$		0			0
$181$	6.79837	+	20.9232i	0.505319	+	1.55521i	0.800233	+	0.599689i	$0.204709\pi$
$181$	6.79837	+	20.9232i	0.505319	+	1.55521i	−0.294914	+	0.955524i	$0.595291\pi$
$182$		0			0
$183$	11.3262	+	8.22899i	0.837260	+	0.608305i
$184$		0			0
$185$	−3.70820	+	11.4127i	−0.272633	+	0.839077i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.618034	−	1.90211i	0.0449554	−	0.138358i
$190$		0			0
$191$	−19.4164	−	14.1068i	−1.40492	−	1.02074i	−0.994036	−	0.109049i	$-0.965220\pi$
$191$	−19.4164	−	14.1068i	−1.40492	−	1.02074i	−0.410886	−	0.911687i	$-0.634780\pi$
$192$		0			0
$193$	−3.09017	−	9.51057i	−0.222435	−	0.684585i	−0.998542	−	0.0539836i	$-0.982808\pi$
$193$	−3.09017	−	9.51057i	−0.222435	−	0.684585i	0.776107	−	0.630602i	$-0.217192\pi$
$194$		0			0
$195$	−9.70820	+	7.05342i	−0.695219	+	0.505106i
$196$		0			0
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$	3.23607	−	2.35114i	0.228255	−	0.165837i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.47214	+	7.60845i	−0.171825	+	0.528824i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	3.09017	−	9.51057i	0.212736	−	0.654734i	−0.786571	−	0.617500i	$-0.788145\pi$
$211$	3.09017	−	9.51057i	0.212736	−	0.654734i	0.999307	−	0.0372338i	$-0.0118546\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.18034	−	19.0211i	−0.421496	−	1.29723i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	6.00000			0.405442
$220$		0			0
$221$	−24.0000			−1.61441
$222$		0			0
$223$	−9.70820	+	7.05342i	−0.650109	+	0.472332i	−0.863308	−	0.504677i	$-0.831612\pi$
$223$	−9.70820	+	7.05342i	−0.650109	+	0.472332i	0.213199	+	0.977009i	$0.431612\pi$
$224$		0			0
$225$	−0.309017	−	0.951057i	−0.0206011	−	0.0634038i
$226$		0			0
$227$	−19.4164	−	14.1068i	−1.28871	−	0.936304i	−0.288934	−	0.957349i	$-0.593301\pi$
$227$	−19.4164	−	14.1068i	−1.28871	−	0.936304i	−0.999779	+	0.0210448i	$0.993301\pi$
$228$		0			0
$229$	0.618034	−	1.90211i	0.0408408	−	0.125695i	−0.928557	−	0.371189i	$-0.878950\pi$
$229$	0.618034	−	1.90211i	0.0408408	−	0.125695i	0.969398	+	0.245494i	$0.0789502\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.94427	+	15.2169i	−0.323910	+	0.996893i	0.648020	+	0.761623i	$0.275597\pi$
$233$	−4.94427	+	15.2169i	−0.323910	+	0.996893i	−0.971930	+	0.235269i	$0.924403\pi$
$234$		0			0
$235$		0			0
$236$		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
$241$	2.00000			0.128831			0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000			0.128831			0.0644157	+	0.997923i	$0.479482\pi$
$242$		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	−0.982458	−	0.186485i	$-0.940291\pi$
$251$	−1.23607	+	3.80423i	−0.0780199	+	0.240121i	0.904438	+	0.426605i	$0.140291\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−2.47214	+	7.60845i	−0.154811	+	0.476460i
$256$		0			0
$257$	−1.61803	−	1.17557i	−0.100930	−	0.0733301i	0.536175	−	0.844107i	$-0.319869\pi$
$257$	−1.61803	−	1.17557i	−0.100930	−	0.0733301i	−0.637106	+	0.770776i	$0.719869\pi$
$258$		0			0
$259$	3.70820	+	11.4127i	0.230417	+	0.709149i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$		0			0
$265$	28.0000			1.72003
$266$		0			0
$267$	−11.3262	+	8.22899i	−0.693155	+	0.503606i
$268$		0			0
$269$	4.32624	+	13.3148i	0.263775	+	0.811817i	0.991973	+	0.126450i	$0.0403583\pi$
$269$	4.32624	+	13.3148i	0.263775	+	0.811817i	−0.728198	+	0.685367i	$0.759642\pi$
$270$		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
$273$	−3.70820	+	11.4127i	−0.224431	+	0.690727i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.09017	−	9.51057i	0.185670	−	0.571434i	−0.814289	−	0.580460i	$-0.802873\pi$
$277$	3.09017	−	9.51057i	0.185670	−	0.571434i	0.999959	+	0.00902525i	$0.00287287\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.88854	−	30.4338i	−0.589901	−	1.81553i	−0.578627	−	0.815592i	$-0.696411\pi$
$281$	−9.88854	−	30.4338i	−0.589901	−	1.81553i	−0.0112742	−	0.999936i	$-0.503589\pi$
$282$		0			0
$283$	−11.3262	+	8.22899i	−0.673275	+	0.489163i	−0.871120	−	0.491070i	$-0.836606\pi$
$283$	−11.3262	+	8.22899i	−0.673275	+	0.489163i	0.197845	+	0.980233i	$0.436606\pi$
$284$		0			0
$285$	−4.00000			−0.236940
$286$		0			0
$287$		0			0
$288$		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
$299$	14.8328	−	45.6507i	0.857804	−	2.64005i
$300$		0			0
$301$	−16.1803	−	11.7557i	−0.932619	−	0.677588i
$302$		0			0
$303$	2.47214	+	7.60845i	0.142020	+	0.437094i
$304$		0			0
$305$	−22.6525	+	16.4580i	−1.29708	+	0.942382i
$306$		0			0
$307$	26.0000			1.48390			0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000			1.48390			0.741949	+	0.670456i	$0.233902\pi$
$308$		0			0
$309$	12.0000			0.682656
$310$		0			0
$311$	6.47214	−	4.70228i	0.367001	−	0.266642i	−0.388965	−	0.921252i	$-0.627167\pi$
$311$	6.47214	−	4.70228i	0.367001	−	0.266642i	0.755966	+	0.654611i	$0.227167\pi$
$312$		0			0
$313$	4.32624	+	13.3148i	0.244533	+	0.752596i	0.995713	+	0.0924984i	$0.0294853\pi$
$313$	4.32624	+	13.3148i	0.244533	+	0.752596i	−0.751179	+	0.660098i	$0.770515\pi$
$314$		0			0
$315$	3.23607	+	2.35114i	0.182332	+	0.132472i
$316$		0			0
$317$	5.56231	−	17.1190i	0.312410	−	0.961500i	−0.664397	−	0.747380i	$-0.731312\pi$
$317$	5.56231	−	17.1190i	0.312410	−	0.961500i	0.976807	−	0.214120i	$-0.0686884\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	4.94427	−	15.2169i	0.275962	−	0.849325i
$322$		0			0
$323$	−6.47214	−	4.70228i	−0.360119	−	0.261642i
$324$		0			0
$325$	1.85410	+	5.70634i	0.102847	+	0.316531i
$326$		0			0
$327$	14.5623	−	10.5801i	0.805297	−	0.585083i
$328$		0			0
$329$		0			0
$330$		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
$333$	4.85410	−	3.52671i	0.266003	−	0.193263i
$334$		0			0
$335$	2.47214	+	7.60845i	0.135067	+	0.415694i
$336$		0			0
$337$	−14.5623	−	10.5801i	−0.793259	−	0.576337i	0.115670	−	0.993288i	$-0.463099\pi$
$337$	−14.5623	−	10.5801i	−0.793259	−	0.576337i	−0.908929	+	0.416951i	$0.863099\pi$
$338$		0			0
$339$	3.09017	−	9.51057i	0.167835	−	0.516543i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	6.18034	−	19.0211i	0.333707	−	1.02704i
$344$		0			0
$345$	−12.9443	−	9.40456i	−0.696896	−	0.506325i
$346$		0			0
$347$	−9.88854	−	30.4338i	−0.530845	−	1.63377i	−0.752460	−	0.658638i	$-0.771133\pi$
$347$	−9.88854	−	30.4338i	−0.530845	−	1.63377i	0.221615	−	0.975134i	$-0.428867\pi$
$348$		0			0
$349$	−4.85410	+	3.52671i	−0.259834	+	0.188781i	−0.710074	−	0.704127i	$-0.751338\pi$
$349$	−4.85410	+	3.52671i	−0.259834	+	0.188781i	0.450240	+	0.892908i	$0.351338\pi$
$350$		0			0
$351$	6.00000			0.320256
$352$		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
$355$		0			0
$356$		0			0
$357$	2.47214	+	7.60845i	0.130839	+	0.402682i
$358$		0			0
$359$	19.4164	+	14.1068i	1.02476	+	0.744531i	0.967253	−	0.253814i	$-0.0816852\pi$
$359$	19.4164	+	14.1068i	1.02476	+	0.744531i	0.0575058	+	0.998345i	$0.481685\pi$
$360$		0			0
$361$	−4.63525	+	14.2658i	−0.243961	+	0.750834i
$362$		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
$369$		0			0
$370$		0			0
$371$	22.6525	−	16.4580i	1.17606	−	0.854456i
$372$		0			0
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$		0			0
$375$	12.0000			0.619677
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−4.94427	−	15.2169i	−0.253970	−	0.781640i	−0.994031	−	0.109100i	$-0.965203\pi$
$379$	−4.94427	−	15.2169i	−0.253970	−	0.781640i	0.740061	−	0.672540i	$-0.234797\pi$
$380$		0			0
$381$	4.85410	+	3.52671i	0.248683	+	0.180679i
$382$		0			0
$383$	2.47214	−	7.60845i	0.126320	−	0.388774i	−0.867819	−	0.496880i	$-0.834479\pi$
$383$	2.47214	−	7.60845i	0.126320	−	0.388774i	0.994139	+	0.108107i	$0.0344788\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.09017	+	9.51057i	−0.157082	+	0.483449i
$388$		0			0
$389$	−14.5623	−	10.5801i	−0.738338	−	0.536434i	0.153852	−	0.988094i	$-0.450832\pi$
$389$	−14.5623	−	10.5801i	−0.738338	−	0.536434i	−0.892190	+	0.451660i	$0.850832\pi$
$390$		0			0
$391$	−9.88854	−	30.4338i	−0.500085	−	1.53910i
$392$		0			0
$393$	−3.23607	+	2.35114i	−0.163238	+	0.118599i
$394$		0			0
$395$	−4.00000			−0.201262
$396$		0			0
$397$	−14.0000			−0.702640			−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000			−0.702640			−0.351320	+	0.936255i	$0.614267\pi$
$398$		0			0
$399$	−3.23607	+	2.35114i	−0.162006	+	0.117704i
$400$		0			0
$401$	−0.618034	−	1.90211i	−0.0308631	−	0.0949870i	0.934438	−	0.356125i	$-0.115902\pi$
$401$	−0.618034	−	1.90211i	−0.0308631	−	0.0949870i	−0.965301	+	0.261138i	$0.915902\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.618034	−	1.90211i	0.0307104	−	0.0945168i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−6.79837	+	20.9232i	−0.336158	+	1.03459i	0.629991	+	0.776603i	$0.283059\pi$
$409$	−6.79837	+	20.9232i	−0.336158	+	1.03459i	−0.966149	+	0.257985i	$0.916941\pi$
$410$		0			0
$411$	11.3262	+	8.22899i	0.558682	+	0.405906i
$412$		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
$417$	14.0000			0.685583
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	8.09017	−	5.87785i	0.394291	−	0.286469i	−0.372921	−	0.927863i	$-0.621644\pi$
$421$	8.09017	−	5.87785i	0.394291	−	0.286469i	0.767211	+	0.641394i	$0.221644\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.23607	+	2.35114i	0.156972	+	0.114047i
$426$		0			0
$427$	−8.65248	+	26.6296i	−0.418723	+	1.28870i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	3.70820	−	11.4127i	0.178618	−	0.549729i	−0.821162	−	0.570695i	$-0.806674\pi$
$431$	3.70820	−	11.4127i	0.178618	−	0.549729i	0.999780	+	0.0209654i	$0.00667397\pi$
$432$		0			0
$433$	−11.3262	−	8.22899i	−0.544304	−	0.395460i	0.281377	−	0.959597i	$-0.409209\pi$
$433$	−11.3262	−	8.22899i	−0.544304	−	0.395460i	−0.825681	+	0.564137i	$0.809209\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.9443	−	9.40456i	0.619208	−	0.449881i
$438$		0			0
$439$	2.00000			0.0954548			0.0477274	−	0.998860i	$-0.484802\pi$
$439$	2.00000			0.0954548			0.0477274	+	0.998860i	$0.484802\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	−3.23607	+	2.35114i	−0.153750	+	0.111706i	−0.662001	−	0.749503i	$-0.730292\pi$
$443$	−3.23607	+	2.35114i	−0.153750	+	0.111706i	0.508250	+	0.861209i	$0.330292\pi$
$444$		0			0
$445$	−8.65248	−	26.6296i	−0.410167	−	1.26236i
$446$		0			0
$447$	3.23607	+	2.35114i	0.153061	+	0.111205i
$448$		0			0
$449$	−6.79837	+	20.9232i	−0.320835	+	0.987429i	0.652451	+	0.757831i	$0.273741\pi$
$449$	−6.79837	+	20.9232i	−0.320835	+	0.987429i	−0.973286	+	0.229598i	$0.926259\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	3.09017	−	9.51057i	0.145189	−	0.446845i
$454$		0			0
$455$	−19.4164	−	14.1068i	−0.910255	−	0.661339i
$456$		0			0
$457$	−6.79837	−	20.9232i	−0.318015	−	0.978748i	−0.974496	−	0.224406i	$-0.927956\pi$
$457$	−6.79837	−	20.9232i	−0.318015	−	0.978748i	0.656481	−	0.754342i	$-0.272044\pi$
$458$		0			0
$459$	3.23607	−	2.35114i	0.151047	−	0.109742i
$460$		0			0
$461$	28.0000			1.30409			0.652045	−	0.758180i	$-0.273911\pi$
$461$	28.0000			1.30409			0.652045	+	0.758180i	$0.273911\pi$
$462$		0			0
$463$	−12.0000			−0.557687			−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000			−0.557687			−0.278844	+	0.960337i	$0.589951\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.70820	−	11.4127i	−0.171595	−	0.528116i	0.827866	−	0.560925i	$-0.189555\pi$
$467$	−3.70820	−	11.4127i	−0.171595	−	0.528116i	−0.999462	+	0.0328096i	$0.989555\pi$
$468$		0			0
$469$	6.47214	+	4.70228i	0.298855	+	0.217131i
$470$		0			0
$471$	3.09017	−	9.51057i	0.142388	−	0.438224i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.618034	+	1.90211i	−0.0283573	+	0.0872749i
$476$		0			0
$477$	−11.3262	−	8.22899i	−0.518593	−	0.376780i
$478$		0			0
$479$	3.70820	+	11.4127i	0.169432	+	0.521459i	0.999336	−	0.0364486i	$-0.0116045\pi$
$479$	3.70820	+	11.4127i	0.169432	+	0.521459i	−0.829903	+	0.557907i	$0.811605\pi$
$480$		0			0
$481$	−29.1246	+	21.1603i	−1.32797	+	0.964825i
$482$		0			0
$483$	−16.0000			−0.728025
$484$		0			0
$485$	−4.00000			−0.181631
$486$		0			0
$487$	12.9443	−	9.40456i	0.586561	−	0.426161i	−0.254523	−	0.967067i	$-0.581918\pi$
$487$	12.9443	−	9.40456i	0.586561	−	0.426161i	0.841083	+	0.540905i	$0.181918\pi$
$488$		0			0
$489$	−4.94427	−	15.2169i	−0.223588	−	0.688132i
$490$		0			0
$491$	−12.9443	−	9.40456i	−0.584167	−	0.424422i	0.256057	−	0.966662i	$-0.417576\pi$
$491$	−12.9443	−	9.40456i	−0.584167	−	0.424422i	−0.840224	+	0.542240i	$0.817576\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	3.23607	+	2.35114i	0.144866	+	0.105252i	0.657858	−	0.753142i	$-0.271463\pi$
$499$	3.23607	+	2.35114i	0.144866	+	0.105252i	−0.512992	+	0.858394i	$0.671463\pi$
$500$		0			0
$501$	−3.70820	−	11.4127i	−0.165670	−	0.509881i
$502$		0			0
$503$	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
$505$	−16.0000			−0.711991
$506$		0			0
$507$	−23.0000			−1.02147
$508$		0			0
$509$	−11.3262	+	8.22899i	−0.502027	+	0.364744i	−0.809791	−	0.586719i	$-0.800419\pi$
$509$	−11.3262	+	8.22899i	−0.502027	+	0.364744i	0.307764	+	0.951463i	$0.400419\pi$
$510$		0			0
$511$	3.70820	+	11.4127i	0.164041	+	0.504867i
$512$		0			0
$513$	1.61803	+	1.17557i	0.0714379	+	0.0519027i
$514$		0			0
$515$	−7.41641	+	22.8254i	−0.326806	+	1.00581i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	2.47214	−	7.60845i	0.108515	−	0.333974i
$520$		0			0
$521$	33.9787	+	24.6870i	1.48863	+	1.08156i	0.974644	+	0.223760i	$0.0718333\pi$
$521$	33.9787	+	24.6870i	1.48863	+	1.08156i	0.513990	+	0.857796i	$0.328167\pi$
$522$		0			0
$523$	6.79837	+	20.9232i	0.297272	+	0.914910i	0.982449	+	0.186533i	$0.0597250\pi$
$523$	6.79837	+	20.9232i	0.297272	+	0.914910i	−0.685177	+	0.728377i	$0.740275\pi$
$524$		0			0
$525$	1.61803	−	1.17557i	0.0706168	−	0.0513061i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	41.0000			1.78261
$530$		0			0
$531$	9.70820	−	7.05342i	0.421300	−	0.306092i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	25.8885	+	18.8091i	1.11926	+	0.813190i
$536$		0			0
$537$	1.23607	−	3.80423i	0.0533403	−	0.164164i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	8.03444	−	24.7275i	0.345428	−	1.06312i	−0.615927	−	0.787803i	$-0.711218\pi$
$541$	8.03444	−	24.7275i	0.345428	−	1.06312i	0.961354	−	0.275314i	$-0.0887817\pi$
$542$		0			0
$543$	17.7984	+	12.9313i	0.763801	+	0.554934i
$544$		0			0
$545$	11.1246	+	34.2380i	0.476526	+	1.46660i
$546$		0			0
$547$	−17.7984	+	12.9313i	−0.761004	+	0.552901i	−0.899218	−	0.437501i	$-0.855864\pi$
$547$	−17.7984	+	12.9313i	−0.761004	+	0.552901i	0.138214	+	0.990402i	$0.455864\pi$
$548$		0			0
$549$	14.0000			0.597505
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−3.23607	+	2.35114i	−0.137612	+	0.0999807i
$554$		0			0
$555$	3.70820	+	11.4127i	0.157404	+	0.484441i
$556$		0			0
$557$	9.70820	+	7.05342i	0.411350	+	0.298863i	0.774148	−	0.633005i	$-0.218179\pi$
$557$	9.70820	+	7.05342i	0.411350	+	0.298863i	−0.362798	+	0.931868i	$0.618179\pi$
$558$		0			0
$559$	18.5410	−	57.0634i	0.784202	−	2.41352i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.23607	+	3.80423i	−0.0520941	+	0.160329i	−0.973719	−	0.227753i	$-0.926862\pi$
$563$	−1.23607	+	3.80423i	−0.0520941	+	0.160329i	0.921625	+	0.388082i	$0.126862\pi$
$564$		0			0
$565$	16.1803	+	11.7557i	0.680712	+	0.494566i
$566$		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
$571$	−34.0000			−1.42286			−0.711428	−	0.702759i	$-0.751951\pi$
$571$	−34.0000			−1.42286			−0.711428	+	0.702759i	$0.751951\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$		0			0
$575$	−6.47214	+	4.70228i	−0.269907	+	0.196099i
$576$		0			0
$577$	0.618034	+	1.90211i	0.0257291	+	0.0791860i	0.963097	−	0.269156i	$-0.0867448\pi$
$577$	0.618034	+	1.90211i	0.0257291	+	0.0791860i	−0.937367	+	0.348342i	$0.886745\pi$
$578$		0			0
$579$	−8.09017	−	5.87785i	−0.336216	−	0.244275i
$580$		0			0
$581$	9.88854	−	30.4338i	0.410246	−	1.26261i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−3.70820	+	11.4127i	−0.153315	+	0.471856i
$586$		0			0
$587$	9.70820	+	7.05342i	0.400700	+	0.291126i	0.769826	−	0.638254i	$-0.220343\pi$
$587$	9.70820	+	7.05342i	0.400700	+	0.291126i	−0.369126	+	0.929379i	$0.620343\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−12.9443	+	9.40456i	−0.532456	+	0.386852i
$592$		0			0
$593$	−24.0000			−0.985562			−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000			−0.985562			−0.492781	+	0.870153i	$0.664020\pi$
$594$		0			0
$595$	−16.0000			−0.655936
$596$		0			0
$597$	6.47214	−	4.70228i	0.264887	−	0.192452i
$598$		0			0
$599$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$599$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$600$		0			0
$601$	−11.3262	−	8.22899i	−0.462007	−	0.335668i	0.332311	−	0.943170i	$-0.392172\pi$
$601$	−11.3262	−	8.22899i	−0.462007	−	0.335668i	−0.794318	+	0.607502i	$0.792172\pi$
$602$		0			0
$603$	1.23607	−	3.80423i	0.0503366	−	0.154920i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−10.5066	+	32.3359i	−0.426449	+	1.31247i	0.475151	+	0.879904i	$0.342393\pi$
$607$	−10.5066	+	32.3359i	−0.426449	+	1.31247i	−0.901600	+	0.432570i	$0.857607\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	33.9787	−	24.6870i	1.37239	−	0.997098i	0.374841	−	0.927089i	$-0.377697\pi$
$613$	33.9787	−	24.6870i	1.37239	−	0.997098i	0.997546	−	0.0700086i	$-0.0223027\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	38.0000			1.52982			0.764911	−	0.644136i	$-0.222783\pi$
$617$	38.0000			1.52982			0.764911	+	0.644136i	$0.222783\pi$
$618$		0			0
$619$	−25.8885	+	18.8091i	−1.04055	+	0.756003i	−0.970393	−	0.241533i	$-0.922350\pi$
$619$	−25.8885	+	18.8091i	−1.04055	+	0.756003i	−0.0701559	+	0.997536i	$0.522350\pi$
$620$		0			0
$621$	2.47214	+	7.60845i	0.0992034	+	0.305317i
$622$		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
$629$	−7.41641	+	22.8254i	−0.295712	+	0.910107i
$630$		0			0
$631$	6.47214	+	4.70228i	0.257652	+	0.187195i	0.709111	−	0.705097i	$-0.249096\pi$
$631$	6.47214	+	4.70228i	0.257652	+	0.187195i	−0.451459	+	0.892292i	$0.649096\pi$
$632$		0			0
$633$	−3.09017	−	9.51057i	−0.122823	−	0.378011i
$634$		0			0
$635$	−9.70820	+	7.05342i	−0.385258	+	0.279907i
$636$		0			0
$637$	18.0000			0.713186
$638$		0			0
$639$		0			0
$640$		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
$643$	9.88854	+	30.4338i	0.389966	+	1.20019i	0.932813	+	0.360361i	$0.117346\pi$
$643$	9.88854	+	30.4338i	0.389966	+	1.20019i	−0.542847	+	0.839832i	$0.682654\pi$
$644$		0			0
$645$	−16.1803	−	11.7557i	−0.637100	−	0.462880i
$646$		0			0
$647$	2.47214	−	7.60845i	0.0971897	−	0.299119i	−0.890628	−	0.454732i	$-0.849735\pi$
$647$	2.47214	−	7.60845i	0.0971897	−	0.299119i	0.987818	+	0.155613i	$0.0497351\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	33.9787	+	24.6870i	1.32969	+	0.966076i	0.999756	+	0.0220720i	$0.00702631\pi$
$653$	33.9787	+	24.6870i	1.32969	+	0.966076i	0.329933	+	0.944004i	$0.392974\pi$
$654$		0			0
$655$	−2.47214	−	7.60845i	−0.0965943	−	0.297287i
$656$		0			0
$657$	4.85410	−	3.52671i	0.189377	−	0.137590i
$658$		0			0
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−18.0000			−0.700119			−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000			−0.700119			−0.350059	+	0.936727i	$0.613839\pi$
$662$		0			0
$663$	−19.4164	+	14.1068i	−0.754071	+	0.547865i
$664$		0			0
$665$	−2.47214	−	7.60845i	−0.0958653	−	0.295043i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−3.70820	+	11.4127i	−0.143367	+	0.441240i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−8.03444	+	24.7275i	−0.309705	+	0.953174i	0.668174	+	0.744005i	$0.267076\pi$
$673$	−8.03444	+	24.7275i	−0.309705	+	0.953174i	−0.977879	+	0.209169i	$0.932924\pi$
$674$		0			0
$675$	−0.809017	−	0.587785i	−0.0311391	−	0.0226239i
$676$		0			0
$677$	9.88854	+	30.4338i	0.380048	+	1.16967i	0.940010	+	0.341148i	$0.110816\pi$
$677$	9.88854	+	30.4338i	0.380048	+	1.16967i	−0.559962	+	0.828518i	$0.689184\pi$
$678$		0			0
$679$	−3.23607	+	2.35114i	−0.124189	+	0.0902285i
$680$		0			0
$681$	−24.0000			−0.919682
$682$		0			0
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		0			0
$685$	−22.6525	+	16.4580i	−0.865507	+	0.628827i
$686$		0			0
$687$	−0.618034	−	1.90211i	−0.0235795	−	0.0725701i
$688$		0			0
$689$	67.9574	+	49.3740i	2.58897	+	1.88100i
$690$		0			0
$691$	7.41641	−	22.8254i	0.282133	−	0.868317i	−0.705110	−	0.709098i	$-0.749102\pi$
$691$	7.41641	−	22.8254i	0.282133	−	0.868317i	0.987243	−	0.159219i	$-0.0508977\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.65248	+	26.6296i	−0.328207	+	1.01012i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	4.94427	+	15.2169i	0.187010	+	0.575556i
$700$		0			0
$701$	−9.70820	+	7.05342i	−0.366674	+	0.266404i	−0.755830	−	0.654768i	$-0.772767\pi$
$701$	−9.70820	+	7.05342i	−0.366674	+	0.266404i	0.389157	+	0.921172i	$0.372767\pi$
$702$		0			0
$703$	−12.0000			−0.452589
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−12.9443	+	9.40456i	−0.486819	+	0.353695i
$708$		0			0
$709$	5.56231	+	17.1190i	0.208897	+	0.642918i	0.999531	+	0.0306292i	$0.00975110\pi$
$709$	5.56231	+	17.1190i	0.208897	+	0.642918i	−0.790634	+	0.612289i	$0.790249\pi$
$710$		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
$719$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$719$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$720$		0			0
$721$	7.41641	+	22.8254i	0.276201	+	0.850061i
$722$		0			0
$723$	1.61803	−	1.17557i	0.0601753	−	0.0437199i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−48.0000			−1.78022			−0.890111	−	0.455744i	$-0.849373\pi$
$727$	−48.0000			−1.78022			−0.890111	+	0.455744i	$0.849373\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−12.3607	−	38.0423i	−0.457176	−	1.40704i
$732$		0			0
$733$	−27.5066	−	19.9847i	−1.01598	−	0.738152i	−0.0505240	−	0.998723i	$-0.516089\pi$
$733$	−27.5066	−	19.9847i	−1.01598	−	0.738152i	−0.965455	+	0.260571i	$0.916089\pi$
$734$		0			0
$735$	1.85410	−	5.70634i	0.0683896	−	0.210481i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−8.03444	+	24.7275i	−0.295552	+	0.909615i	0.687484	+	0.726200i	$0.258715\pi$
$739$	−8.03444	+	24.7275i	−0.295552	+	0.909615i	−0.983036	+	0.183415i	$0.941285\pi$
$740$		0			0
$741$	−9.70820	−	7.05342i	−0.356640	−	0.259114i
$742$		0			0
$743$	2.47214	+	7.60845i	0.0906939	+	0.279127i	0.986108	−	0.166108i	$-0.0531201\pi$
$743$	2.47214	+	7.60845i	0.0906939	+	0.279127i	−0.895414	+	0.445235i	$0.853120\pi$
$744$		0			0
$745$	−6.47214	+	4.70228i	−0.237121	+	0.172278i
$746$		0			0
$747$	−16.0000			−0.585409
$748$		0			0
$749$	32.0000			1.16925
$750$		0			0
$751$	32.3607	−	23.5114i	1.18086	−	0.857944i	0.188590	−	0.982056i	$-0.439608\pi$
$751$	32.3607	−	23.5114i	1.18086	−	0.857944i	0.992268	+	0.124112i	$0.0396083\pi$
$752$		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
$757$	11.7426	−	36.1401i	0.426794	−	1.31354i	−0.474473	−	0.880270i	$-0.657361\pi$
$757$	11.7426	−	36.1401i	0.426794	−	1.31354i	0.901266	−	0.433266i	$-0.142639\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.1246	+	34.2380i	−0.403267	+	1.24113i	0.519067	+	0.854734i	$0.326280\pi$
$761$	−11.1246	+	34.2380i	−0.403267	+	1.24113i	−0.922334	+	0.386394i	$0.873720\pi$
$762$		0			0
$763$	29.1246	+	21.1603i	1.05438	+	0.766053i
$764$		0			0
$765$	2.47214	+	7.60845i	0.0893803	+	0.275084i
$766$		0			0
$767$	−58.2492	+	42.3205i	−2.10326	+	1.52811i
$768$		0			0
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$	−2.00000			−0.0720282
$772$		0			0
$773$	14.5623	−	10.5801i	0.523770	−	0.380541i	−0.294252	−	0.955728i	$-0.595071\pi$
$773$	14.5623	−	10.5801i	0.523770	−	0.380541i	0.818022	+	0.575187i	$0.195071\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	9.70820	+	7.05342i	0.348280	+	0.253040i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	16.1803	+	11.7557i	0.577501	+	0.419579i
$786$		0			0
$787$	11.7426	+	36.1401i	0.418580	+	1.28826i	0.909009	+	0.416776i	$0.136840\pi$
$787$	11.7426	+	36.1401i	0.418580	+	1.28826i	−0.490429	+	0.871481i	$0.663160\pi$
$788$		0			0
$789$	9.70820	−	7.05342i	0.345621	−	0.251109i
$790$		0			0
$791$	20.0000			0.711118
$792$		0			0
$793$	−84.0000			−2.98293
$794$		0			0
$795$	22.6525	−	16.4580i	0.803401	−	0.583705i
$796$		0			0
$797$	−1.85410	−	5.70634i	−0.0656757	−	0.202129i	0.912834	−	0.408332i	$-0.133889\pi$
$797$	−1.85410	−	5.70634i	−0.0656757	−	0.202129i	−0.978509	+	0.206203i	$0.933889\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−4.32624	+	13.3148i	−0.152860	+	0.470455i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	9.88854	−	30.4338i	0.348525	−	1.07265i
$806$		0			0
$807$	11.3262	+	8.22899i	0.398702	+	0.289674i
$808$		0			0
$809$	13.5967	+	41.8465i	0.478036	+	1.47124i	0.841819	+	0.539760i	$0.181485\pi$
$809$	13.5967	+	41.8465i	0.478036	+	1.47124i	−0.363783	+	0.931484i	$0.618515\pi$
$810$		0			0
$811$	30.7426	−	22.3358i	1.07952	−	0.784317i	0.101921	−	0.994792i	$-0.467501\pi$
$811$	30.7426	−	22.3358i	1.07952	−	0.784317i	0.977599	+	0.210475i	$0.0675011\pi$
$812$		0			0
$813$	−10.0000			−0.350715
$814$		0			0
$815$	32.0000			1.12091
$816$		0			0
$817$	16.1803	−	11.7557i	0.566078	−	0.411280i
$818$		0			0
$819$	3.70820	+	11.4127i	0.129575	+	0.398791i
$820$		0			0
$821$	32.3607	+	23.5114i	1.12940	+	0.820554i	0.985607	−	0.169055i	$-0.0540714\pi$
$821$	32.3607	+	23.5114i	1.12940	+	0.820554i	0.143789	+	0.989608i	$0.454071\pi$
$822$		0			0
$823$	−8.65248	+	26.6296i	−0.301606	+	0.928249i	0.679315	+	0.733846i	$0.262277\pi$
$823$	−8.65248	+	26.6296i	−0.301606	+	0.928249i	−0.980922	+	0.194403i	$0.937723\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.94427	−	15.2169i	0.171929	−	0.529144i	−0.827551	−	0.561391i	$-0.810266\pi$
$827$	4.94427	−	15.2169i	0.171929	−	0.529144i	0.999480	+	0.0322473i	$0.0102664\pi$
$828$		0			0
$829$	11.3262	+	8.22899i	0.393377	+	0.285805i	0.766838	−	0.641841i	$-0.221829\pi$
$829$	11.3262	+	8.22899i	0.393377	+	0.285805i	−0.373461	+	0.927646i	$0.621829\pi$
$830$		0			0
$831$	−3.09017	−	9.51057i	−0.107197	−	0.329918i
$832$		0			0
$833$	9.70820	−	7.05342i	0.336369	−	0.244387i
$834$		0			0
$835$	24.0000			0.830554
$836$		0			0
$837$		0			0
$838$		0			0
$839$	19.4164	−	14.1068i	0.670329	−	0.487022i	−0.199806	−	0.979835i	$-0.564031\pi$
$839$	19.4164	−	14.1068i	0.670329	−	0.487022i	0.870135	+	0.492813i	$0.164031\pi$
$840$		0			0
$841$	−8.96149	−	27.5806i	−0.309017	−	0.951057i
$842$		0			0
$843$	−25.8885	−	18.8091i	−0.891649	−	0.647821i
$844$		0			0
$845$	14.2148	−	43.7486i	0.489003	−	1.50500i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−4.32624	+	13.3148i	−0.148476	+	0.456962i
$850$		0			0
$851$	−38.8328	−	28.2137i	−1.33117	−	0.967153i
$852$		0			0
$853$	−5.56231	−	17.1190i	−0.190450	−	0.586144i	0.809550	−	0.587051i	$-0.199711\pi$
$853$	−5.56231	−	17.1190i	−0.190450	−	0.586144i	−1.00000		0.000907135i	$0.999711\pi$
$854$		0			0
$855$	−3.23607	+	2.35114i	−0.110671	+	0.0804073i
$856$		0			0
$857$	−44.0000			−1.50301			−0.751506	−	0.659727i	$-0.770672\pi$
$857$	−44.0000			−1.50301			−0.751506	+	0.659727i	$0.770672\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.47214	+	7.60845i	0.0841525	+	0.258995i	0.984275	−	0.176642i	$-0.0565234\pi$
$863$	2.47214	+	7.60845i	0.0841525	+	0.258995i	−0.900123	+	0.435636i	$0.856523\pi$
$864$		0			0
$865$	12.9443	+	9.40456i	0.440118	+	0.319765i
$866$		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
$877$	14.5623	−	10.5801i	0.491734	−	0.357266i	−0.314117	−	0.949384i	$-0.601708\pi$
$877$	14.5623	−	10.5801i	0.491734	−	0.357266i	0.805851	+	0.592119i	$0.201708\pi$
$878$		0			0
$879$	−20.0000			−0.674583
$880$		0			0
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		0			0
$883$	35.5967	−	25.8626i	1.19793	−	0.870344i	0.203847	−	0.979003i	$-0.434656\pi$
$883$	35.5967	−	25.8626i	1.19793	−	0.870344i	0.994079	+	0.108659i	$0.0346555\pi$
$884$		0			0
$885$	7.41641	+	22.8254i	0.249300	+	0.767266i
$886$		0			0
$887$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$887$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$888$		0			0
$889$	−3.70820	+	11.4127i	−0.124369	+	0.382769i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	6.47214	+	4.70228i	0.216340	+	0.157180i
$896$		0			0
$897$	−14.8328	−	45.6507i	−0.495253	−	1.52423i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	56.0000			1.86563
$902$		0			0
$903$	−20.0000			−0.665558
$904$		0			0
$905$	−35.5967	+	25.8626i	−1.18328	+	0.859700i
$906$		0			0
$907$	4.94427	+	15.2169i	0.164172	+	0.505269i	0.998974	−	0.0452806i	$-0.0144182\pi$
$907$	4.94427	+	15.2169i	0.164172	+	0.505269i	−0.834802	+	0.550550i	$0.814418\pi$
$908$		0			0
$909$	6.47214	+	4.70228i	0.214667	+	0.155965i
$910$		0			0
$911$	−14.8328	+	45.6507i	−0.491433	+	1.51248i	0.331009	+	0.943627i	$0.392611\pi$
$911$	−14.8328	+	45.6507i	−0.491433	+	1.51248i	−0.822443	+	0.568848i	$0.807389\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−8.65248	+	26.6296i	−0.286042	+	0.880347i
$916$		0			0
$917$	−6.47214	−	4.70228i	−0.213729	−	0.155283i
$918$		0			0
$919$	10.5066	+	32.3359i	0.346580	+	1.06666i	0.960732	+	0.277476i	$0.0894980\pi$
$919$	10.5066	+	32.3359i	0.346580	+	1.06666i	−0.614152	+	0.789187i	$0.710502\pi$
$920$		0			0
$921$	21.0344	−	15.2824i	0.693108	−	0.503573i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	6.00000			0.197279
$926$		0			0
$927$	9.70820	−	7.05342i	0.318859	−	0.231665i
$928$		0			0
$929$	−12.9787	−	39.9444i	−0.425818	−	1.31053i	−0.902209	−	0.431299i	$-0.858055\pi$
$929$	−12.9787	−	39.9444i	−0.425818	−	1.31053i	0.476391	−	0.879233i	$-0.341945\pi$
$930$		0			0
$931$	4.85410	+	3.52671i	0.159087	+	0.115583i
$932$		0			0
$933$	2.47214	−	7.60845i	0.0809341	−	0.249090i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	11.7426	−	36.1401i	0.383616	−	1.18065i	−0.553864	−	0.832607i	$-0.686847\pi$
$937$	11.7426	−	36.1401i	0.383616	−	1.18065i	0.937480	−	0.348040i	$-0.113153\pi$
$938$		0			0
$939$	11.3262	+	8.22899i	0.369618	+	0.268543i
$940$		0			0
$941$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$941$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	4.00000			0.130120
$946$		0			0
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$	−29.1246	+	21.1603i	−0.945425	+	0.686891i
$950$		0			0
$951$	−5.56231	−	17.1190i	−0.180370	−	0.555122i
$952$		0			0
$953$	9.70820	+	7.05342i	0.314480	+	0.228483i	0.733816	−	0.679348i	$-0.237737\pi$
$953$	9.70820	+	7.05342i	0.314480	+	0.228483i	−0.419337	+	0.907831i	$0.637737\pi$
$954$		0			0
$955$	14.8328	−	45.6507i	0.479979	−	1.47722i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−8.65248	+	26.6296i	−0.279403	+	0.859914i
$960$		0			0
$961$	25.0795	+	18.2213i	0.809017	+	0.587785i
$962$		0			0
$963$	−4.94427	−	15.2169i	−0.159327	−	0.490358i
$964$		0			0
$965$	16.1803	−	11.7557i	0.520864	−	0.378430i
$966$		0			0
$967$	−34.0000			−1.09337			−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000			−1.09337			−0.546683	+	0.837340i	$0.684110\pi$
$968$		0			0
$969$	−8.00000			−0.256997
$970$		0			0
$971$	−48.5410	+	35.2671i	−1.55776	+	1.13178i	−0.619936	+	0.784652i	$0.712841\pi$
$971$	−48.5410	+	35.2671i	−1.55776	+	1.13178i	−0.937820	+	0.347123i	$0.887159\pi$
$972$		0			0
$973$	8.65248	+	26.6296i	0.277386	+	0.853705i
$974$		0			0
$975$	4.85410	+	3.52671i	0.155456	+	0.112945i
$976$		0			0
$977$	−3.09017	+	9.51057i	−0.0988633	+	0.304270i	−0.988241	−	0.152903i	$-0.951138\pi$
$977$	−3.09017	+	9.51057i	−0.0988633	+	0.304270i	0.889378	+	0.457173i	$0.151138\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	5.56231	−	17.1190i	0.177591	−	0.546568i
$982$		0			0
$983$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$983$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$984$		0			0
$985$	−9.88854	−	30.4338i	−0.315075	−	0.969702i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	80.0000			2.54385
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$	6.47214	−	4.70228i	0.205387	−	0.149222i
$994$		0			0
$995$	4.94427	+	15.2169i	0.156744	+	0.482408i
$996$		0			0
$997$	8.09017	+	5.87785i	0.256218	+	0.186153i	0.708478	−	0.705733i	$-0.249382\pi$
$997$	8.09017	+	5.87785i	0.256218	+	0.186153i	−0.452260	+	0.891886i	$0.649382\pi$
$998$		0			0
$999$	1.85410	−	5.70634i	0.0586612	−	0.180541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1452.2.i.l.493.1		4
11.2	odd	10		1452.2.i.k.1213.1		4
11.3	even	5	inner	1452.2.i.l.565.1		4
11.4	even	5		1452.2.a.c.1.1		1
11.5	even	5	inner	1452.2.i.l.1237.1		4
11.6	odd	10		1452.2.i.k.1237.1		4
11.7	odd	10		132.2.a.a.1.1	✓	1
11.8	odd	10		1452.2.i.k.565.1		4
11.9	even	5	inner	1452.2.i.l.1213.1		4
11.10	odd	2		1452.2.i.k.493.1		4
33.26	odd	10		4356.2.a.c.1.1		1
33.29	even	10		396.2.a.b.1.1		1
44.7	even	10		528.2.a.h.1.1		1
44.15	odd	10		5808.2.a.bf.1.1		1
55.7	even	20		3300.2.c.c.1849.2		2
55.18	even	20		3300.2.c.c.1849.1		2
55.29	odd	10		3300.2.a.k.1.1		1
77.62	even	10		6468.2.a.l.1.1		1
88.29	odd	10		2112.2.a.t.1.1		1
88.51	even	10		2112.2.a.b.1.1		1
99.7	odd	30		3564.2.i.b.2377.1		2
99.29	even	30		3564.2.i.g.2377.1		2
99.40	odd	30		3564.2.i.b.1189.1		2
99.95	even	30		3564.2.i.g.1189.1		2
132.95	odd	10		1584.2.a.c.1.1		1
165.29	even	10		9900.2.a.g.1.1		1
165.62	odd	20		9900.2.c.k.5149.2		2
165.128	odd	20		9900.2.c.k.5149.1		2
264.29	even	10		6336.2.a.cf.1.1		1
264.227	odd	10		6336.2.a.bz.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.a.a.1.1	✓	1	11.7	odd	10
396.2.a.b.1.1		1	33.29	even	10
528.2.a.h.1.1		1	44.7	even	10
1452.2.a.c.1.1		1	11.4	even	5
1452.2.i.k.493.1		4	11.10	odd	2
1452.2.i.k.565.1		4	11.8	odd	10
1452.2.i.k.1213.1		4	11.2	odd	10
1452.2.i.k.1237.1		4	11.6	odd	10
1452.2.i.l.493.1		4	1.1	even	1	trivial
1452.2.i.l.565.1		4	11.3	even	5	inner
1452.2.i.l.1213.1		4	11.9	even	5	inner
1452.2.i.l.1237.1		4	11.5	even	5	inner
1584.2.a.c.1.1		1	132.95	odd	10
2112.2.a.b.1.1		1	88.51	even	10
2112.2.a.t.1.1		1	88.29	odd	10
3300.2.a.k.1.1		1	55.29	odd	10
3300.2.c.c.1849.1		2	55.18	even	20
3300.2.c.c.1849.2		2	55.7	even	20
3564.2.i.b.1189.1		2	99.40	odd	30
3564.2.i.b.2377.1		2	99.7	odd	30
3564.2.i.g.1189.1		2	99.95	even	30
3564.2.i.g.2377.1		2	99.29	even	30
4356.2.a.c.1.1		1	33.26	odd	10
5808.2.a.bf.1.1		1	44.15	odd	10
6336.2.a.bz.1.1		1	264.227	odd	10
6336.2.a.cf.1.1		1	264.29	even	10
6468.2.a.l.1.1		1	77.62	even	10
9900.2.a.g.1.1		1	165.29	even	10
9900.2.c.k.5149.1		2	165.128	odd	20
9900.2.c.k.5149.2		2	165.62	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1452.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{3} +(0.618034 + 1.90211i) q^{5} +(1.61803 + 1.17557i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{3} +(0.618034 + 1.90211i) q^{5} +(1.61803 + 1.17557i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-1.85410 + 5.70634i) q^{13} +(1.61803 + 1.17557i) q^{15} +(1.23607 + 3.80423i) q^{17} +(-1.61803 + 1.17557i) q^{19} +2.00000 q^{21} -8.00000 q^{23} +(0.809017 - 0.587785i) q^{25} +(-0.309017 - 0.951057i) q^{27} +(-1.23607 + 3.80423i) q^{35} +(4.85410 + 3.52671i) q^{37} +(1.85410 + 5.70634i) q^{39} -10.0000 q^{43} +2.00000 q^{45} +(-0.927051 - 2.85317i) q^{49} +(3.23607 + 2.35114i) q^{51} +(4.32624 - 13.3148i) q^{53} +(-0.618034 + 1.90211i) q^{57} +(9.70820 + 7.05342i) q^{59} +(4.32624 + 13.3148i) q^{61} +(1.61803 - 1.17557i) q^{63} -12.0000 q^{65} +4.00000 q^{67} +(-6.47214 + 4.70228i) q^{69} +(4.85410 + 3.52671i) q^{73} +(0.309017 - 0.951057i) q^{75} +(-0.618034 + 1.90211i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-4.94427 - 15.2169i) q^{83} +(-6.47214 + 4.70228i) q^{85} -14.0000 q^{89} +(-9.70820 + 7.05342i) q^{91} +(-3.23607 - 2.35114i) q^{95} +(-0.618034 + 1.90211i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 2 q^{5} + 2 q^{7} - q^{9}+O(q^{10}) \) 4 * q + q^3 - 2 * q^5 + 2 * q^7 - q^9	\( 4 q + q^{3} - 2 q^{5} + 2 q^{7} - q^{9} + 6 q^{13} + 2 q^{15} - 4 q^{17} - 2 q^{19} + 8 q^{21} - 32 q^{23} + q^{25} + q^{27} + 4 q^{35} + 6 q^{37} - 6 q^{39} - 40 q^{43} + 8 q^{45} + 3 q^{49} + 4 q^{51} - 14 q^{53} + 2 q^{57} + 12 q^{59} - 14 q^{61} + 2 q^{63} - 48 q^{65} + 16 q^{67} - 8 q^{69} + 6 q^{73} - q^{75} + 2 q^{79} - q^{81} + 16 q^{83} - 8 q^{85} - 56 q^{89} - 12 q^{91} - 4 q^{95} + 2 q^{97}+O(q^{100}) \) 4 * q + q^3 - 2 * q^5 + 2 * q^7 - q^9 + 6 * q^13 + 2 * q^15 - 4 * q^17 - 2 * q^19 + 8 * q^21 - 32 * q^23 + q^25 + q^27 + 4 * q^35 + 6 * q^37 - 6 * q^39 - 40 * q^43 + 8 * q^45 + 3 * q^49 + 4 * q^51 - 14 * q^53 + 2 * q^57 + 12 * q^59 - 14 * q^61 + 2 * q^63 - 48 * q^65 + 16 * q^67 - 8 * q^69 + 6 * q^73 - q^75 + 2 * q^79 - q^81 + 16 * q^83 - 8 * q^85 - 56 * q^89 - 12 * q^91 - 4 * q^95 + 2 * q^97

Introduction

L-functions

Modular forms

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