LMFDB - Embedded newform 1452.2.i.n.1237.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1452,2,Mod(493,1452)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [4,0,1,0,1,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1237.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	1452.1237
Dual form			1452.2.i.n.493.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{3} +(-0.309017 + 0.951057i) q^{5} +(1.61803 - 1.17557i) q^{7} +(0.309017 + 0.951057i) q^{9} +(0.927051 + 2.85317i) q^{13} +(-0.809017 + 0.587785i) q^{15} +(2.16312 - 6.65740i) q^{17} +(3.23607 + 2.35114i) q^{19} +2.00000 q^{21} -2.00000 q^{23} +(3.23607 + 2.35114i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(2.42705 - 1.76336i) q^{29} +(0.618034 + 1.90211i) q^{35} +(-7.28115 + 5.29007i) q^{37} +(-0.927051 + 2.85317i) q^{39} +(7.28115 + 5.29007i) q^{41} +2.00000 q^{43} -1.00000 q^{45} +(9.70820 + 7.05342i) q^{47} +(-0.927051 + 2.85317i) q^{49} +(5.66312 - 4.11450i) q^{51} +(-4.01722 - 12.3637i) q^{53} +(1.23607 + 3.80423i) q^{57} +(4.85410 - 3.52671i) q^{59} +(0.618034 - 1.90211i) q^{61} +(1.61803 + 1.17557i) q^{63} -3.00000 q^{65} -14.0000 q^{67} +(-1.61803 - 1.17557i) q^{69} +(-1.85410 + 5.70634i) q^{71} +(4.85410 - 3.52671i) q^{73} +(1.23607 + 3.80423i) q^{75} +(4.94427 + 15.2169i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(2.47214 - 7.60845i) q^{83} +(5.66312 + 4.11450i) q^{85} +3.00000 q^{87} +1.00000 q^{89} +(4.85410 + 3.52671i) q^{91} +(-3.23607 + 2.35114i) q^{95} +(2.16312 + 6.65740i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} + q^{5} + 2 q^{7} - q^{9} - 3 q^{13} - q^{15} - 7 q^{17} + 4 q^{19} + 8 q^{21} - 8 q^{23} + 4 q^{25} + q^{27} + 3 q^{29} - 2 q^{35} - 9 q^{37} + 3 q^{39} + 9 q^{41} + 8 q^{43} - 4 q^{45}+ \cdots - 7 q^{97}+O(q^{100}) $ 4 * q + q^3 + q^5 + 2 * q^7 - q^9 - 3 * q^13 - q^15 - 7 * q^17 + 4 * q^19 + 8 * q^21 - 8 * q^23 + 4 * q^25 + q^27 + 3 * q^29 - 2 * q^35 - 9 * q^37 + 3 * q^39 + 9 * q^41 + 8 * q^43 - 4 * q^45 + 12 * q^47 + 3 * q^49 + 7 * q^51 + 13 * q^53 - 4 * q^57 + 6 * q^59 - 2 * q^61 + 2 * q^63 - 12 * q^65 - 56 * q^67 - 2 * q^69 + 6 * q^71 + 6 * q^73 - 4 * q^75 - 16 * q^79 - q^81 - 8 * q^83 + 7 * q^85 + 12 * q^87 + 4 * q^89 + 6 * q^91 - 4 * q^95 - 7 * q^97

Character values

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

$n$	$485$	$727$	$1333$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i	−0.996074	−	0.0885298i	$-0.971783\pi$
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i	0.857877	+	0.513855i	$0.171783\pi$
$6$		0			0
$7$	1.61803	−	1.17557i	0.611559	−	0.444324i	−0.238404	−	0.971166i	$-0.576624\pi$
$7$	1.61803	−	1.17557i	0.611559	−	0.444324i	0.849963	+	0.526842i	$0.176624\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	0.927051	+	2.85317i	0.257118	+	0.791327i	0.993405	+	0.114658i	$0.0365772\pi$
$13$	0.927051	+	2.85317i	0.257118	+	0.791327i	−0.736287	+	0.676669i	$0.763423\pi$
$14$		0			0
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$		0			0
$17$	2.16312	−	6.65740i	0.524633	−	1.61466i	−0.240406	−	0.970672i	$-0.577281\pi$
$17$	2.16312	−	6.65740i	0.524633	−	1.61466i	0.765040	−	0.643983i	$-0.222719\pi$
$18$		0			0
$19$	3.23607	+	2.35114i	0.742405	+	0.539389i	0.893463	−	0.449136i	$-0.148268\pi$
$19$	3.23607	+	2.35114i	0.742405	+	0.539389i	−0.151058	+	0.988525i	$0.548268\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$		0			0
$23$	−2.00000			−0.417029			−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000			−0.417029			−0.208514	+	0.978019i	$0.566863\pi$
$24$		0			0
$25$	3.23607	+	2.35114i	0.647214	+	0.470228i
$26$		0			0
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$		0			0
$29$	2.42705	−	1.76336i	0.450692	−	0.327447i	−0.339177	−	0.940723i	$-0.610149\pi$
$29$	2.42705	−	1.76336i	0.450692	−	0.327447i	0.789869	+	0.613276i	$0.210149\pi$
$30$		0			0
$31$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$31$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.618034	+	1.90211i	0.104467	+	0.321516i
$36$		0			0
$37$	−7.28115	+	5.29007i	−1.19701	+	0.869682i	−0.993988	−	0.109492i	$-0.965078\pi$
$37$	−7.28115	+	5.29007i	−1.19701	+	0.869682i	−0.203026	+	0.979173i	$0.565078\pi$
$38$		0			0
$39$	−0.927051	+	2.85317i	−0.148447	+	0.456873i
$40$		0			0
$41$	7.28115	+	5.29007i	1.13713	+	0.826170i	0.986716	−	0.162454i	$-0.0519410\pi$
$41$	7.28115	+	5.29007i	1.13713	+	0.826170i	0.150409	+	0.988624i	$0.451941\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	9.70820	+	7.05342i	1.41609	+	1.02885i	0.992402	+	0.123038i	$0.0392637\pi$
$47$	9.70820	+	7.05342i	1.41609	+	1.02885i	0.423685	+	0.905810i	$0.360736\pi$
$48$		0			0
$49$	−0.927051	+	2.85317i	−0.132436	+	0.407596i
$50$		0			0
$51$	5.66312	−	4.11450i	0.792995	−	0.576145i
$52$		0			0
$53$	−4.01722	−	12.3637i	−0.551808	−	1.69829i	−0.704228	−	0.709974i	$-0.748707\pi$
$53$	−4.01722	−	12.3637i	−0.551808	−	1.69829i	0.152420	−	0.988316i	$-0.451293\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.23607	+	3.80423i	0.163721	+	0.503882i
$58$		0			0
$59$	4.85410	−	3.52671i	0.631950	−	0.459139i	−0.225125	−	0.974330i	$-0.572279\pi$
$59$	4.85410	−	3.52671i	0.631950	−	0.459139i	0.857075	+	0.515191i	$0.172279\pi$
$60$		0			0
$61$	0.618034	−	1.90211i	0.0791311	−	0.243541i	−0.903663	−	0.428244i	$-0.859132\pi$
$61$	0.618034	−	1.90211i	0.0791311	−	0.243541i	0.982794	+	0.184703i	$0.0591324\pi$
$62$		0			0
$63$	1.61803	+	1.17557i	0.203853	+	0.148108i
$64$		0			0
$65$	−3.00000			−0.372104
$66$		0			0
$67$	−14.0000			−1.71037			−0.855186	−	0.518321i	$-0.826557\pi$
$67$	−14.0000			−1.71037			−0.855186	+	0.518321i	$0.826557\pi$
$68$		0			0
$69$	−1.61803	−	1.17557i	−0.194788	−	0.141522i
$70$		0			0
$71$	−1.85410	+	5.70634i	−0.220041	+	0.677218i	0.778716	+	0.627377i	$0.215871\pi$
$71$	−1.85410	+	5.70634i	−0.220041	+	0.677218i	−0.998757	+	0.0498409i	$0.984129\pi$
$72$		0			0
$73$	4.85410	−	3.52671i	0.568130	−	0.412770i	−0.266296	−	0.963891i	$-0.585800\pi$
$73$	4.85410	−	3.52671i	0.568130	−	0.412770i	0.834425	+	0.551121i	$0.185800\pi$
$74$		0			0
$75$	1.23607	+	3.80423i	0.142729	+	0.439274i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.94427	+	15.2169i	0.556274	+	1.71204i	0.692555	+	0.721365i	$0.256485\pi$
$79$	4.94427	+	15.2169i	0.556274	+	1.71204i	−0.136281	+	0.990670i	$0.543515\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	2.47214	−	7.60845i	0.271352	−	0.835136i	−0.718809	−	0.695207i	$-0.755313\pi$
$83$	2.47214	−	7.60845i	0.271352	−	0.835136i	0.990162	−	0.139929i	$-0.0446874\pi$
$84$		0			0
$85$	5.66312	+	4.11450i	0.614251	+	0.446280i
$86$		0			0
$87$	3.00000			0.321634
$88$		0			0
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$		0			0
$91$	4.85410	+	3.52671i	0.508848	+	0.369700i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.23607	+	2.35114i	−0.332014	+	0.241222i
$96$		0			0
$97$	2.16312	+	6.65740i	0.219631	+	0.675956i	0.998792	+	0.0491321i	$0.0156455\pi$
$97$	2.16312	+	6.65740i	0.219631	+	0.675956i	−0.779161	+	0.626824i	$0.784354\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.618034	−	1.90211i	−0.0614967	−	0.189267i	0.915588	−	0.402117i	$-0.131726\pi$
$101$	−0.618034	−	1.90211i	−0.0614967	−	0.189267i	−0.977085	+	0.212850i	$0.931726\pi$
$102$		0			0
$103$	4.85410	−	3.52671i	0.478289	−	0.347497i	−0.322374	−	0.946612i	$-0.604481\pi$
$103$	4.85410	−	3.52671i	0.478289	−	0.347497i	0.800663	+	0.599115i	$0.204481\pi$
$104$		0			0
$105$	−0.618034	+	1.90211i	−0.0603139	+	0.185627i
$106$		0			0
$107$	−11.3262	−	8.22899i	−1.09495	−	0.795527i	−0.114721	−	0.993398i	$-0.536597\pi$
$107$	−11.3262	−	8.22899i	−1.09495	−	0.795527i	−0.980228	+	0.197871i	$0.936597\pi$
$108$		0			0
$109$	3.00000			0.287348			0.143674	−	0.989625i	$-0.454108\pi$
$109$	3.00000			0.287348			0.143674	+	0.989625i	$0.454108\pi$
$110$		0			0
$111$	−9.00000			−0.854242
$112$		0			0
$113$	15.3713	+	11.1679i	1.44601	+	1.05059i	0.986743	+	0.162293i	$0.0518889\pi$
$113$	15.3713	+	11.1679i	1.44601	+	1.05059i	0.459270	+	0.888297i	$0.348111\pi$
$114$		0			0
$115$	0.618034	−	1.90211i	0.0576320	−	0.177373i
$116$		0			0
$117$	−2.42705	+	1.76336i	−0.224381	+	0.163022i
$118$		0			0
$119$	−4.32624	−	13.3148i	−0.396586	−	1.22056i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	2.78115	+	8.55951i	0.250768	+	0.771785i
$124$		0			0
$125$	−7.28115	+	5.29007i	−0.651246	+	0.473158i
$126$		0			0
$127$	−3.70820	+	11.4127i	−0.329050	+	1.01271i	0.640529	+	0.767934i	$0.278715\pi$
$127$	−3.70820	+	11.4127i	−0.329050	+	1.01271i	−0.969579	+	0.244778i	$0.921285\pi$
$128$		0			0
$129$	1.61803	+	1.17557i	0.142460	+	0.103503i
$130$		0			0
$131$	−22.0000			−1.92215			−0.961074	−	0.276289i	$-0.910895\pi$
$131$	−22.0000			−1.92215			−0.961074	+	0.276289i	$0.910895\pi$
$132$		0			0
$133$	8.00000			0.693688
$134$		0			0
$135$	−0.809017	−	0.587785i	−0.0696291	−	0.0505885i
$136$		0			0
$137$	−3.09017	+	9.51057i	−0.264011	+	0.812542i	0.727909	+	0.685674i	$0.240493\pi$
$137$	−3.09017	+	9.51057i	−0.264011	+	0.812542i	−0.991920	+	0.126868i	$0.959507\pi$
$138$		0			0
$139$	11.3262	−	8.22899i	0.960679	−	0.697974i	0.00737063	−	0.999973i	$-0.497654\pi$
$139$	11.3262	−	8.22899i	0.960679	−	0.697974i	0.953308	+	0.301999i	$0.0976538\pi$
$140$		0			0
$141$	3.70820	+	11.4127i	0.312287	+	0.961121i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	0.927051	+	2.85317i	0.0769874	+	0.236943i
$146$		0			0
$147$	−2.42705	+	1.76336i	−0.200180	+	0.145439i
$148$		0			0
$149$	4.01722	−	12.3637i	0.329104	−	1.01288i	−0.640451	−	0.767999i	$-0.721252\pi$
$149$	4.01722	−	12.3637i	0.329104	−	1.01288i	0.969554	−	0.244877i	$-0.0787476\pi$
$150$		0			0
$151$	−6.47214	−	4.70228i	−0.526695	−	0.382666i	0.292425	−	0.956288i	$-0.405538\pi$
$151$	−6.47214	−	4.70228i	−0.526695	−	0.382666i	−0.819120	+	0.573622i	$0.805538\pi$
$152$		0			0
$153$	7.00000			0.565916
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−11.3262	−	8.22899i	−0.903932	−	0.656745i	0.0355408	−	0.999368i	$-0.488685\pi$
$157$	−11.3262	−	8.22899i	−0.903932	−	0.656745i	−0.939473	+	0.342623i	$0.888685\pi$
$158$		0			0
$159$	4.01722	−	12.3637i	0.318586	−	0.980508i
$160$		0			0
$161$	−3.23607	+	2.35114i	−0.255038	+	0.185296i
$162$		0			0
$163$	−0.618034	−	1.90211i	−0.0484082	−	0.148985i	0.923931	−	0.382560i	$-0.124958\pi$
$163$	−0.618034	−	1.90211i	−0.0484082	−	0.148985i	−0.972339	+	0.233575i	$0.924958\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.56231	−	17.1190i	−0.430424	−	1.32471i	−0.897704	−	0.440600i	$-0.854766\pi$
$167$	−5.56231	−	17.1190i	−0.430424	−	1.32471i	0.467280	−	0.884110i	$-0.345234\pi$
$168$		0			0
$169$	3.23607	−	2.35114i	0.248928	−	0.180857i
$170$		0			0
$171$	−1.23607	+	3.80423i	−0.0945245	+	0.290916i
$172$		0			0
$173$	11.3262	+	8.22899i	0.861118	+	0.625639i	0.928189	−	0.372109i	$-0.121365\pi$
$173$	11.3262	+	8.22899i	0.861118	+	0.625639i	−0.0670709	+	0.997748i	$0.521365\pi$
$174$		0			0
$175$	8.00000			0.604743
$176$		0			0
$177$	6.00000			0.450988
$178$		0			0
$179$	−6.47214	−	4.70228i	−0.483750	−	0.351465i	0.319026	−	0.947746i	$-0.396644\pi$
$179$	−6.47214	−	4.70228i	−0.483750	−	0.351465i	−0.802776	+	0.596281i	$0.796644\pi$
$180$		0			0
$181$	4.01722	−	12.3637i	0.298598	−	0.918989i	−0.683392	−	0.730052i	$-0.739496\pi$
$181$	4.01722	−	12.3637i	0.298598	−	0.918989i	0.981989	−	0.188937i	$-0.0605042\pi$
$182$		0			0
$183$	1.61803	−	1.17557i	0.119609	−	0.0869007i
$184$		0			0
$185$	−2.78115	−	8.55951i	−0.204474	−	0.629308i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.618034	+	1.90211i	0.0449554	+	0.138358i
$190$		0			0
$191$	9.70820	−	7.05342i	0.702461	−	0.510368i	−0.178272	−	0.983981i	$-0.557051\pi$
$191$	9.70820	−	7.05342i	0.702461	−	0.510368i	0.880733	+	0.473614i	$0.157051\pi$
$192$		0			0
$193$	1.54508	−	4.75528i	0.111218	−	0.342293i	−0.879922	−	0.475119i	$-0.842405\pi$
$193$	1.54508	−	4.75528i	0.111218	−	0.342293i	0.991139	+	0.132826i	$0.0424051\pi$
$194$		0			0
$195$	−2.42705	−	1.76336i	−0.173805	−	0.126277i
$196$		0			0
$197$	−7.00000			−0.498729			−0.249365	−	0.968410i	$-0.580222\pi$
$197$	−7.00000			−0.498729			−0.249365	+	0.968410i	$0.580222\pi$
$198$		0			0
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$		0			0
$201$	−11.3262	−	8.22899i	−0.798891	−	0.580428i
$202$		0			0
$203$	1.85410	−	5.70634i	0.130132	−	0.400506i
$204$		0			0
$205$	−7.28115	+	5.29007i	−0.508538	+	0.369474i
$206$		0			0
$207$	−0.618034	−	1.90211i	−0.0429563	−	0.132206i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−4.32624	−	13.3148i	−0.297831	−	0.916628i	−0.982256	−	0.187545i	$-0.939947\pi$
$211$	−4.32624	−	13.3148i	−0.297831	−	0.916628i	0.684425	−	0.729083i	$-0.260053\pi$
$212$		0			0
$213$	−4.85410	+	3.52671i	−0.332598	+	0.241646i
$214$		0			0
$215$	−0.618034	+	1.90211i	−0.0421496	+	0.129723i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	6.00000			0.405442
$220$		0			0
$221$	21.0000			1.41261
$222$		0			0
$223$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$223$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$224$		0			0
$225$	−1.23607	+	3.80423i	−0.0824045	+	0.253615i
$226$		0			0
$227$	−14.5623	+	10.5801i	−0.966534	+	0.702228i	−0.954659	−	0.297701i	$-0.903780\pi$
$227$	−14.5623	+	10.5801i	−0.966534	+	0.702228i	−0.0118751	+	0.999929i	$0.503780\pi$
$228$		0			0
$229$	8.96149	+	27.5806i	0.592192	+	1.82258i	0.568234	+	0.822867i	$0.307627\pi$
$229$	8.96149	+	27.5806i	0.592192	+	1.82258i	0.0239580	+	0.999713i	$0.492373\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.72542	−	23.7764i	−0.506109	−	1.55764i	−0.798897	−	0.601467i	$-0.794583\pi$
$233$	−7.72542	−	23.7764i	−0.506109	−	1.55764i	0.292788	−	0.956177i	$-0.405417\pi$
$234$		0			0
$235$	−9.70820	+	7.05342i	−0.633293	+	0.460115i
$236$		0			0
$237$	−4.94427	+	15.2169i	−0.321165	+	0.988444i
$238$		0			0
$239$	−12.9443	−	9.40456i	−0.837295	−	0.608331i	0.0843185	−	0.996439i	$-0.473129\pi$
$239$	−12.9443	−	9.40456i	−0.837295	−	0.608331i	−0.921614	+	0.388108i	$0.873129\pi$
$240$		0			0
$241$	26.0000			1.67481			0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.0000			1.67481			0.837404	+	0.546585i	$0.184072\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−2.42705	−	1.76336i	−0.155059	−	0.112657i
$246$		0			0
$247$	−3.70820	+	11.4127i	−0.235947	+	0.726171i
$248$		0			0
$249$	6.47214	−	4.70228i	0.410155	−	0.297995i
$250$		0			0
$251$	−3.09017	−	9.51057i	−0.195050	−	0.600302i	−0.999976	−	0.00692663i	$-0.997795\pi$
$251$	−3.09017	−	9.51057i	−0.195050	−	0.600302i	0.804926	−	0.593375i	$-0.202205\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	2.16312	+	6.65740i	0.135460	+	0.416902i
$256$		0			0
$257$	5.66312	−	4.11450i	0.353256	−	0.256655i	−0.396978	−	0.917828i	$-0.629941\pi$
$257$	5.66312	−	4.11450i	0.353256	−	0.256655i	0.750234	+	0.661173i	$0.229941\pi$
$258$		0			0
$259$	−5.56231	+	17.1190i	−0.345625	+	1.06372i
$260$		0			0
$261$	2.42705	+	1.76336i	0.150231	+	0.109149i
$262$		0			0
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$		0			0
$265$	13.0000			0.798584
$266$		0			0
$267$	0.809017	+	0.587785i	0.0495110	+	0.0359719i
$268$		0			0
$269$	−0.309017	+	0.951057i	−0.0188411	+	0.0579869i	−0.960035	−	0.279880i	$-0.909705\pi$
$269$	−0.309017	+	0.951057i	−0.0188411	+	0.0579869i	0.941194	+	0.337867i	$0.109705\pi$
$270$		0			0
$271$	−17.7984	+	12.9313i	−1.08117	+	0.785519i	−0.977887	−	0.209133i	$-0.932936\pi$
$271$	−17.7984	+	12.9313i	−1.08117	+	0.785519i	−0.103287	+	0.994652i	$0.532936\pi$
$272$		0			0
$273$	1.85410	+	5.70634i	0.112215	+	0.345363i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.25329	−	16.1680i	−0.315640	−	0.971439i	−0.975490	−	0.220042i	$-0.929381\pi$
$277$	−5.25329	−	16.1680i	−0.315640	−	0.971439i	0.659851	−	0.751397i	$-0.270619\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.79837	−	20.9232i	0.405557	−	1.24818i	−0.514872	−	0.857267i	$-0.672161\pi$
$281$	6.79837	−	20.9232i	0.405557	−	1.24818i	0.920429	−	0.390909i	$-0.127839\pi$
$282$		0			0
$283$	−11.3262	−	8.22899i	−0.673275	−	0.489163i	0.197845	−	0.980233i	$-0.436606\pi$
$283$	−11.3262	−	8.22899i	−0.673275	−	0.489163i	−0.871120	+	0.491070i	$0.836606\pi$
$284$		0			0
$285$	−4.00000			−0.236940
$286$		0			0
$287$	18.0000			1.06251
$288$		0			0
$289$	−25.8885	−	18.8091i	−1.52286	−	1.10642i
$290$		0			0
$291$	−2.16312	+	6.65740i	−0.126804	+	0.390263i
$292$		0			0
$293$	−13.7533	+	9.99235i	−0.803476	+	0.583759i	−0.911932	−	0.410342i	$-0.865409\pi$
$293$	−13.7533	+	9.99235i	−0.803476	+	0.583759i	0.108456	+	0.994101i	$0.465409\pi$
$294$		0			0
$295$	1.85410	+	5.70634i	0.107950	+	0.332236i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.85410	−	5.70634i	−0.107225	−	0.330006i
$300$		0			0
$301$	3.23607	−	2.35114i	0.186524	−	0.135518i
$302$		0			0
$303$	0.618034	−	1.90211i	0.0355051	−	0.109274i
$304$		0			0
$305$	1.61803	+	1.17557i	0.0926484	+	0.0673130i
$306$		0			0
$307$	−22.0000			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$		0			0
$309$	6.00000			0.341328
$310$		0			0
$311$	−22.6525	−	16.4580i	−1.28450	−	0.933247i	−0.284825	−	0.958580i	$-0.591935\pi$
$311$	−22.6525	−	16.4580i	−1.28450	−	0.933247i	−0.999679	+	0.0253327i	$0.991935\pi$
$312$		0			0
$313$	−0.309017	+	0.951057i	−0.0174667	+	0.0537569i	−0.959410	−	0.282015i	$-0.908997\pi$
$313$	−0.309017	+	0.951057i	−0.0174667	+	0.0537569i	0.941943	+	0.335772i	$0.108997\pi$
$314$		0			0
$315$	−1.61803	+	1.17557i	−0.0911659	+	0.0662359i
$316$		0			0
$317$	−1.85410	−	5.70634i	−0.104137	−	0.320500i	0.885390	−	0.464849i	$-0.153891\pi$
$317$	−1.85410	−	5.70634i	−0.104137	−	0.320500i	−0.989527	+	0.144349i	$0.953891\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−4.32624	−	13.3148i	−0.241467	−	0.743159i
$322$		0			0
$323$	22.6525	−	16.4580i	1.26042	−	0.915747i
$324$		0			0
$325$	−3.70820	+	11.4127i	−0.205694	+	0.633061i
$326$		0			0
$327$	2.42705	+	1.76336i	0.134216	+	0.0975138i
$328$		0			0
$329$	24.0000			1.32316
$330$		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
$333$	−7.28115	−	5.29007i	−0.399005	−	0.289894i
$334$		0			0
$335$	4.32624	−	13.3148i	0.236368	−	0.727465i
$336$		0			0
$337$	12.1353	−	8.81678i	0.661049	−	0.480281i	−0.205968	−	0.978559i	$-0.566034\pi$
$337$	12.1353	−	8.81678i	0.661049	−	0.480281i	0.867017	+	0.498278i	$0.166034\pi$
$338$		0			0
$339$	5.87132	+	18.0701i	0.318886	+	0.981432i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	6.18034	+	19.0211i	0.333707	+	1.02704i
$344$		0			0
$345$	1.61803	−	1.17557i	0.0871120	−	0.0632906i
$346$		0			0
$347$	−2.47214	+	7.60845i	−0.132711	+	0.408443i	−0.995227	−	0.0975871i	$-0.968888\pi$
$347$	−2.47214	+	7.60845i	−0.132711	+	0.408443i	0.862516	+	0.506030i	$0.168888\pi$
$348$		0			0
$349$	−2.42705	−	1.76336i	−0.129917	−	0.0943903i	0.520929	−	0.853600i	$-0.325586\pi$
$349$	−2.42705	−	1.76336i	−0.129917	−	0.0943903i	−0.650846	+	0.759210i	$0.725586\pi$
$350$		0			0
$351$	−3.00000			−0.160128
$352$		0			0
$353$	−3.00000			−0.159674			−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000			−0.159674			−0.0798369	+	0.996808i	$0.525440\pi$
$354$		0			0
$355$	−4.85410	−	3.52671i	−0.257629	−	0.187178i
$356$		0			0
$357$	4.32624	−	13.3148i	0.228969	−	0.704693i
$358$		0			0
$359$	−24.2705	+	17.6336i	−1.28095	+	0.930664i	−0.999581	−	0.0289366i	$-0.990788\pi$
$359$	−24.2705	+	17.6336i	−1.28095	+	0.930664i	−0.281367	+	0.959600i	$0.590788\pi$
$360$		0			0
$361$	−0.927051	−	2.85317i	−0.0487922	−	0.150167i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.85410	+	5.70634i	0.0970481	+	0.298683i
$366$		0			0
$367$	8.09017	−	5.87785i	0.422303	−	0.306821i	−0.356261	−	0.934387i	$-0.615948\pi$
$367$	8.09017	−	5.87785i	0.422303	−	0.306821i	0.778564	+	0.627565i	$0.215948\pi$
$368$		0			0
$369$	−2.78115	+	8.55951i	−0.144781	+	0.445590i
$370$		0			0
$371$	−21.0344	−	15.2824i	−1.09205	−	0.793424i
$372$		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
$375$	−9.00000			−0.464758
$376$		0			0
$377$	7.28115	+	5.29007i	0.374998	+	0.272452i
$378$		0			0
$379$	8.03444	−	24.7275i	0.412702	−	1.27016i	−0.501589	−	0.865106i	$-0.667251\pi$
$379$	8.03444	−	24.7275i	0.412702	−	1.27016i	0.914291	−	0.405059i	$-0.132749\pi$
$380$		0			0
$381$	−9.70820	+	7.05342i	−0.497366	+	0.361358i
$382$		0			0
$383$	−3.09017	−	9.51057i	−0.157900	−	0.485967i	0.840543	−	0.541745i	$-0.182236\pi$
$383$	−3.09017	−	9.51057i	−0.157900	−	0.485967i	−0.998443	+	0.0557778i	$0.982236\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.618034	+	1.90211i	0.0314164	+	0.0966898i
$388$		0			0
$389$	−12.1353	+	8.81678i	−0.615282	+	0.447028i	−0.851270	−	0.524727i	$-0.824167\pi$
$389$	−12.1353	+	8.81678i	−0.615282	+	0.447028i	0.235988	+	0.971756i	$0.424167\pi$
$390$		0			0
$391$	−4.32624	+	13.3148i	−0.218787	+	0.673358i
$392$		0			0
$393$	−17.7984	−	12.9313i	−0.897809	−	0.652297i
$394$		0			0
$395$	−16.0000			−0.805047
$396$		0			0
$397$	25.0000			1.25471			0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000			1.25471			0.627357	+	0.778732i	$0.284137\pi$
$398$		0			0
$399$	6.47214	+	4.70228i	0.324012	+	0.235409i
$400$		0			0
$401$	−3.39919	+	10.4616i	−0.169747	+	0.522428i	−0.999355	−	0.0359187i	$-0.988564\pi$
$401$	−3.39919	+	10.4616i	−0.169747	+	0.522428i	0.829607	+	0.558347i	$0.188564\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−9.57953	−	29.4828i	−0.473677	−	1.45783i	−0.847734	−	0.530422i	$-0.822033\pi$
$409$	−9.57953	−	29.4828i	−0.473677	−	1.45783i	0.374056	−	0.927406i	$-0.377967\pi$
$410$		0			0
$411$	−8.09017	+	5.87785i	−0.399059	+	0.289933i
$412$		0			0
$413$	3.70820	−	11.4127i	0.182469	−	0.561581i
$414$		0			0
$415$	6.47214	+	4.70228i	0.317705	+	0.230826i
$416$		0			0
$417$	14.0000			0.685583
$418$		0			0
$419$	−18.0000			−0.879358			−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000			−0.879358			−0.439679	+	0.898155i	$0.644908\pi$
$420$		0			0
$421$	−4.04508	−	2.93893i	−0.197145	−	0.143235i	0.484833	−	0.874607i	$-0.338880\pi$
$421$	−4.04508	−	2.93893i	−0.197145	−	0.143235i	−0.681979	+	0.731372i	$0.738880\pi$
$422$		0			0
$423$	−3.70820	+	11.4127i	−0.180299	+	0.554903i
$424$		0			0
$425$	22.6525	−	16.4580i	1.09881	−	0.798330i
$426$		0			0
$427$	−1.23607	−	3.80423i	−0.0598175	−	0.184099i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.27051	−	28.5317i	−0.446545	−	1.37432i	−0.880781	−	0.473524i	$-0.842982\pi$
$431$	−9.27051	−	28.5317i	−0.446545	−	1.37432i	0.434236	−	0.900799i	$-0.357018\pi$
$432$		0			0
$433$	−8.89919	+	6.46564i	−0.427668	+	0.310719i	−0.780716	−	0.624886i	$-0.785145\pi$
$433$	−8.89919	+	6.46564i	−0.427668	+	0.310719i	0.353048	+	0.935605i	$0.385145\pi$
$434$		0			0
$435$	−0.927051	+	2.85317i	−0.0444487	+	0.136799i
$436$		0			0
$437$	−6.47214	−	4.70228i	−0.309604	−	0.224941i
$438$		0			0
$439$	−4.00000			−0.190910			−0.0954548	−	0.995434i	$-0.530431\pi$
$439$	−4.00000			−0.190910			−0.0954548	+	0.995434i	$0.530431\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	1.61803	+	1.17557i	0.0768751	+	0.0558530i	0.625559	−	0.780177i	$-0.284871\pi$
$443$	1.61803	+	1.17557i	0.0768751	+	0.0558530i	−0.548684	+	0.836030i	$0.684871\pi$
$444$		0			0
$445$	−0.309017	+	0.951057i	−0.0146488	+	0.0450844i
$446$		0			0
$447$	10.5172	−	7.64121i	0.497447	−	0.361417i
$448$		0			0
$449$	8.96149	+	27.5806i	0.422919	+	1.30161i	0.904973	+	0.425469i	$0.139891\pi$
$449$	8.96149	+	27.5806i	0.422919	+	1.30161i	−0.482054	+	0.876142i	$0.660109\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−2.47214	−	7.60845i	−0.116151	−	0.357476i
$454$		0			0
$455$	−4.85410	+	3.52671i	−0.227564	+	0.165335i
$456$		0			0
$457$	−2.16312	+	6.65740i	−0.101186	+	0.311420i	−0.988816	−	0.149137i	$-0.952350\pi$
$457$	−2.16312	+	6.65740i	−0.101186	+	0.311420i	0.887630	+	0.460557i	$0.152350\pi$
$458$		0			0
$459$	5.66312	+	4.11450i	0.264332	+	0.192048i
$460$		0			0
$461$	−11.0000			−0.512321			−0.256161	−	0.966634i	$-0.582458\pi$
$461$	−11.0000			−0.512321			−0.256161	+	0.966634i	$0.582458\pi$
$462$		0			0
$463$	−30.0000			−1.39422			−0.697109	−	0.716965i	$-0.745531\pi$
$463$	−30.0000			−1.39422			−0.697109	+	0.716965i	$0.745531\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.27051	−	28.5317i	0.428988	−	1.32029i	−0.470135	−	0.882594i	$-0.655795\pi$
$467$	9.27051	−	28.5317i	0.428988	−	1.32029i	0.899123	−	0.437695i	$-0.144205\pi$
$468$		0			0
$469$	−22.6525	+	16.4580i	−1.04599	+	0.759959i
$470$		0			0
$471$	−4.32624	−	13.3148i	−0.199343	−	0.613513i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	4.94427	+	15.2169i	0.226859	+	0.698199i
$476$		0			0
$477$	10.5172	−	7.64121i	0.481550	−	0.349867i
$478$		0			0
$479$	−9.27051	+	28.5317i	−0.423580	+	1.30365i	0.480767	+	0.876849i	$0.340358\pi$
$479$	−9.27051	+	28.5317i	−0.423580	+	1.30365i	−0.904347	+	0.426798i	$0.859642\pi$
$480$		0			0
$481$	−21.8435	−	15.8702i	−0.995976	−	0.723619i
$482$		0			0
$483$	−4.00000			−0.182006
$484$		0			0
$485$	−7.00000			−0.317854
$486$		0			0
$487$	−1.61803	−	1.17557i	−0.0733201	−	0.0532702i	0.550521	−	0.834821i	$-0.314429\pi$
$487$	−1.61803	−	1.17557i	−0.0733201	−	0.0532702i	−0.623842	+	0.781551i	$0.714429\pi$
$488$		0			0
$489$	0.618034	−	1.90211i	0.0279485	−	0.0860165i
$490$		0			0
$491$	6.47214	−	4.70228i	0.292083	−	0.212211i	−0.432087	−	0.901832i	$-0.642223\pi$
$491$	6.47214	−	4.70228i	0.292083	−	0.212211i	0.724171	+	0.689621i	$0.242223\pi$
$492$		0			0
$493$	−6.48936	−	19.9722i	−0.292266	−	0.899502i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.70820	+	11.4127i	0.166336	+	0.511929i
$498$		0			0
$499$	8.09017	−	5.87785i	0.362166	−	0.263129i	−0.391789	−	0.920055i	$-0.628144\pi$
$499$	8.09017	−	5.87785i	0.362166	−	0.263129i	0.753955	+	0.656926i	$0.228144\pi$
$500$		0			0
$501$	5.56231	−	17.1190i	0.248506	−	0.764821i
$502$		0			0
$503$	11.3262	+	8.22899i	0.505012	+	0.366913i	0.810928	−	0.585146i	$-0.198963\pi$
$503$	11.3262	+	8.22899i	0.505012	+	0.366913i	−0.305916	+	0.952058i	$0.598963\pi$
$504$		0			0
$505$	2.00000			0.0889988
$506$		0			0
$507$	4.00000			0.177646
$508$		0			0
$509$	−1.61803	−	1.17557i	−0.0717181	−	0.0521062i	0.551349	−	0.834275i	$-0.314113\pi$
$509$	−1.61803	−	1.17557i	−0.0717181	−	0.0521062i	−0.623067	+	0.782169i	$0.714113\pi$
$510$		0			0
$511$	3.70820	−	11.4127i	0.164041	−	0.504867i
$512$		0			0
$513$	−3.23607	+	2.35114i	−0.142876	+	0.103805i
$514$		0			0
$515$	1.85410	+	5.70634i	0.0817015	+	0.251451i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	4.32624	+	13.3148i	0.189901	+	0.584454i
$520$		0			0
$521$	24.2705	−	17.6336i	1.06331	−	0.772540i	0.0886124	−	0.996066i	$-0.471757\pi$
$521$	24.2705	−	17.6336i	1.06331	−	0.772540i	0.974698	+	0.223526i	$0.0717568\pi$
$522$		0			0
$523$	12.3607	−	38.0423i	0.540495	−	1.66347i	−0.190973	−	0.981595i	$-0.561164\pi$
$523$	12.3607	−	38.0423i	0.540495	−	1.66347i	0.731467	−	0.681877i	$-0.238836\pi$
$524$		0			0
$525$	6.47214	+	4.70228i	0.282467	+	0.205224i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−19.0000			−0.826087
$530$		0			0
$531$	4.85410	+	3.52671i	0.210650	+	0.153046i
$532$		0			0
$533$	−8.34346	+	25.6785i	−0.361395	+	1.11226i
$534$		0			0
$535$	11.3262	−	8.22899i	0.489676	−	0.355770i
$536$		0			0
$537$	−2.47214	−	7.60845i	−0.106681	−	0.328329i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	8.03444	+	24.7275i	0.345428	+	1.06312i	0.961354	+	0.275314i	$0.0887817\pi$
$541$	8.03444	+	24.7275i	0.345428	+	1.06312i	−0.615927	+	0.787803i	$0.711218\pi$
$542$		0			0
$543$	10.5172	−	7.64121i	0.451337	−	0.327916i
$544$		0			0
$545$	−0.927051	+	2.85317i	−0.0397105	+	0.122216i
$546$		0			0
$547$	6.47214	+	4.70228i	0.276729	+	0.201055i	0.717489	−	0.696570i	$-0.245291\pi$
$547$	6.47214	+	4.70228i	0.276729	+	0.201055i	−0.440761	+	0.897625i	$0.645291\pi$
$548$		0			0
$549$	2.00000			0.0853579
$550$		0			0
$551$	12.0000			0.511217
$552$		0			0
$553$	25.8885	+	18.8091i	1.10089	+	0.799845i
$554$		0			0
$555$	2.78115	−	8.55951i	0.118053	−	0.363331i
$556$		0			0
$557$	14.5623	−	10.5801i	0.617025	−	0.448295i	−0.234856	−	0.972030i	$-0.575462\pi$
$557$	14.5623	−	10.5801i	0.617025	−	0.448295i	0.851881	+	0.523735i	$0.175462\pi$
$558$		0			0
$559$	1.85410	+	5.70634i	0.0784202	+	0.241352i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.618034	+	1.90211i	0.0260470	+	0.0801645i	0.963235	−	0.268660i	$-0.0865809\pi$
$563$	0.618034	+	1.90211i	0.0260470	+	0.0801645i	−0.937188	+	0.348825i	$0.886581\pi$
$564$		0			0
$565$	−15.3713	+	11.1679i	−0.646676	+	0.469838i
$566$		0			0
$567$	−0.618034	+	1.90211i	−0.0259550	+	0.0798812i
$568$		0			0
$569$	17.7984	+	12.9313i	0.746147	+	0.542107i	0.894630	−	0.446808i	$-0.147439\pi$
$569$	17.7984	+	12.9313i	0.746147	+	0.542107i	−0.148483	+	0.988915i	$0.547439\pi$
$570$		0			0
$571$	14.0000			0.585882			0.292941	−	0.956131i	$-0.405366\pi$
$571$	14.0000			0.585882			0.292941	+	0.956131i	$0.405366\pi$
$572$		0			0
$573$	12.0000			0.501307
$574$		0			0
$575$	−6.47214	−	4.70228i	−0.269907	−	0.196099i
$576$		0			0
$577$	−4.01722	+	12.3637i	−0.167239	+	0.514709i	−0.999194	−	0.0401338i	$-0.987222\pi$
$577$	−4.01722	+	12.3637i	−0.167239	+	0.514709i	0.831955	+	0.554843i	$0.187222\pi$
$578$		0			0
$579$	4.04508	−	2.93893i	0.168108	−	0.122138i
$580$		0			0
$581$	−4.94427	−	15.2169i	−0.205123	−	0.631304i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−0.927051	−	2.85317i	−0.0383288	−	0.117964i
$586$		0			0
$587$	−19.4164	+	14.1068i	−0.801401	+	0.582252i	−0.911325	−	0.411688i	$-0.864939\pi$
$587$	−19.4164	+	14.1068i	−0.801401	+	0.582252i	0.109924	+	0.993940i	$0.464939\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−5.66312	−	4.11450i	−0.232950	−	0.169248i
$592$		0			0
$593$	3.00000			0.123195			0.0615976	−	0.998101i	$-0.480380\pi$
$593$	3.00000			0.123195			0.0615976	+	0.998101i	$0.480380\pi$
$594$		0			0
$595$	14.0000			0.573944
$596$		0			0
$597$	−8.09017	−	5.87785i	−0.331109	−	0.240564i
$598$		0			0
$599$	−7.41641	+	22.8254i	−0.303026	+	0.932619i	0.677380	+	0.735633i	$0.263115\pi$
$599$	−7.41641	+	22.8254i	−0.303026	+	0.932619i	−0.980406	+	0.196986i	$0.936885\pi$
$600$		0			0
$601$	−4.04508	+	2.93893i	−0.165002	+	0.119881i	−0.667222	−	0.744859i	$-0.732517\pi$
$601$	−4.04508	+	2.93893i	−0.165002	+	0.119881i	0.502220	+	0.864740i	$0.332517\pi$
$602$		0			0
$603$	−4.32624	−	13.3148i	−0.176178	−	0.542220i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	2.47214	+	7.60845i	0.100341	+	0.308818i	0.988609	−	0.150508i	$-0.0480910\pi$
$607$	2.47214	+	7.60845i	0.100341	+	0.308818i	−0.888268	+	0.459326i	$0.848091\pi$
$608$		0			0
$609$	4.85410	−	3.52671i	0.196698	−	0.142910i
$610$		0			0
$611$	−11.1246	+	34.2380i	−0.450054	+	1.38512i
$612$		0			0
$613$	26.6976	+	19.3969i	1.07830	+	0.783434i	0.977386	−	0.211461i	$-0.0678221\pi$
$613$	26.6976	+	19.3969i	1.07830	+	0.783434i	0.100918	+	0.994895i	$0.467822\pi$
$614$		0			0
$615$	−9.00000			−0.362915
$616$		0			0
$617$	−7.00000			−0.281809			−0.140905	−	0.990023i	$-0.545001\pi$
$617$	−7.00000			−0.281809			−0.140905	+	0.990023i	$0.545001\pi$
$618$		0			0
$619$	17.7984	+	12.9313i	0.715377	+	0.519752i	0.884904	−	0.465774i	$-0.154224\pi$
$619$	17.7984	+	12.9313i	0.715377	+	0.519752i	−0.169527	+	0.985526i	$0.554224\pi$
$620$		0			0
$621$	0.618034	−	1.90211i	0.0248008	−	0.0763292i
$622$		0			0
$623$	1.61803	−	1.17557i	0.0648252	−	0.0470982i
$624$		0			0
$625$	3.39919	+	10.4616i	0.135967	+	0.418465i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	19.4681	+	59.9166i	0.776243	+	2.38903i
$630$		0			0
$631$	−17.7984	+	12.9313i	−0.708542	+	0.514786i	−0.882703	−	0.469931i	$-0.844279\pi$
$631$	−17.7984	+	12.9313i	−0.708542	+	0.514786i	0.174161	+	0.984717i	$0.444279\pi$
$632$		0			0
$633$	4.32624	−	13.3148i	0.171953	−	0.529215i
$634$		0			0
$635$	−9.70820	−	7.05342i	−0.385258	−	0.279907i
$636$		0			0
$637$	−9.00000			−0.356593
$638$		0			0
$639$	−6.00000			−0.237356
$640$		0			0
$641$	31.5517	+	22.9236i	1.24622	+	0.905429i	0.997996	−	0.0632750i	$-0.0201545\pi$
$641$	31.5517	+	22.9236i	1.24622	+	0.905429i	0.248220	+	0.968704i	$0.420155\pi$
$642$		0			0
$643$	−12.3607	+	38.0423i	−0.487458	+	1.50024i	0.340932	+	0.940088i	$0.389257\pi$
$643$	−12.3607	+	38.0423i	−0.487458	+	1.50024i	−0.828390	+	0.560152i	$0.810743\pi$
$644$		0			0
$645$	−1.61803	+	1.17557i	−0.0637100	+	0.0462880i
$646$		0			0
$647$	9.88854	+	30.4338i	0.388759	+	1.19648i	0.933717	+	0.358013i	$0.116546\pi$
$647$	9.88854	+	30.4338i	0.388759	+	1.19648i	−0.544958	+	0.838463i	$0.683454\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−33.9787	+	24.6870i	−1.32969	+	0.966076i	−0.329933	+	0.944004i	$0.607026\pi$
$653$	−33.9787	+	24.6870i	−1.32969	+	0.966076i	−0.999756	+	0.0220720i	$0.992974\pi$
$654$		0			0
$655$	6.79837	−	20.9232i	0.265634	−	0.817539i
$656$		0			0
$657$	4.85410	+	3.52671i	0.189377	+	0.137590i
$658$		0			0
$659$	48.0000			1.86981			0.934907	−	0.354892i	$-0.115482\pi$
$659$	48.0000			1.86981			0.934907	+	0.354892i	$0.115482\pi$
$660$		0			0
$661$	−3.00000			−0.116686			−0.0583432	−	0.998297i	$-0.518582\pi$
$661$	−3.00000			−0.116686			−0.0583432	+	0.998297i	$0.518582\pi$
$662$		0			0
$663$	16.9894	+	12.3435i	0.659812	+	0.479381i
$664$		0			0
$665$	−2.47214	+	7.60845i	−0.0958653	+	0.295043i
$666$		0			0
$667$	−4.85410	+	3.52671i	−0.187952	+	0.136555i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−11.7426	−	36.1401i	−0.452646	−	1.39310i	−0.873877	−	0.486147i	$-0.838402\pi$
$673$	−11.7426	−	36.1401i	−0.452646	−	1.39310i	0.421231	−	0.906953i	$-0.361598\pi$
$674$		0			0
$675$	−3.23607	+	2.35114i	−0.124556	+	0.0904955i
$676$		0			0
$677$	5.25329	−	16.1680i	0.201900	−	0.621385i	−0.797926	−	0.602755i	$-0.794070\pi$
$677$	5.25329	−	16.1680i	0.201900	−	0.621385i	0.999826	−	0.0186300i	$-0.00593045\pi$
$678$		0			0
$679$	11.3262	+	8.22899i	0.434661	+	0.315800i
$680$		0			0
$681$	−18.0000			−0.689761
$682$		0			0
$683$	−6.00000			−0.229584			−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000			−0.229584			−0.114792	+	0.993390i	$0.536620\pi$
$684$		0			0
$685$	−8.09017	−	5.87785i	−0.309110	−	0.224581i
$686$		0			0
$687$	−8.96149	+	27.5806i	−0.341902	+	1.05227i
$688$		0			0
$689$	31.5517	−	22.9236i	1.20202	−	0.873321i
$690$		0			0
$691$	−5.56231	−	17.1190i	−0.211600	−	0.651238i	−0.999378	−	0.0352781i	$-0.988768\pi$
$691$	−5.56231	−	17.1190i	−0.211600	−	0.651238i	0.787777	−	0.615960i	$-0.211232\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.32624	+	13.3148i	0.164104	+	0.505059i
$696$		0			0
$697$	50.9681	−	37.0305i	1.93055	−	1.40263i
$698$		0			0
$699$	7.72542	−	23.7764i	0.292202	−	0.899307i
$700$		0			0
$701$	21.8435	+	15.8702i	0.825016	+	0.599409i	0.918145	−	0.396245i	$-0.129687\pi$
$701$	21.8435	+	15.8702i	0.825016	+	0.599409i	−0.0931288	+	0.995654i	$0.529687\pi$
$702$		0			0
$703$	−36.0000			−1.35777
$704$		0			0
$705$	−12.0000			−0.451946
$706$		0			0
$707$	−3.23607	−	2.35114i	−0.121705	−	0.0884238i
$708$		0			0
$709$	1.85410	−	5.70634i	0.0696323	−	0.214306i	−0.910185	−	0.414202i	$-0.864061\pi$
$709$	1.85410	−	5.70634i	0.0696323	−	0.214306i	0.979817	+	0.199896i	$0.0640606\pi$
$710$		0			0
$711$	−12.9443	+	9.40456i	−0.485448	+	0.352699i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−4.94427	−	15.2169i	−0.184647	−	0.568286i
$718$		0			0
$719$	−33.9787	+	24.6870i	−1.26719	+	0.920669i	−0.999087	−	0.0427206i	$-0.986397\pi$
$719$	−33.9787	+	24.6870i	−1.26719	+	0.920669i	−0.268105	+	0.963390i	$0.586397\pi$
$720$		0			0
$721$	3.70820	−	11.4127i	0.138101	−	0.425030i
$722$		0			0
$723$	21.0344	+	15.2824i	0.782279	+	0.568359i
$724$		0			0
$725$	12.0000			0.445669
$726$		0			0
$727$	−6.00000			−0.222528			−0.111264	−	0.993791i	$-0.535490\pi$
$727$	−6.00000			−0.222528			−0.111264	+	0.993791i	$0.535490\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	4.32624	−	13.3148i	0.160012	−	0.492465i
$732$		0			0
$733$	13.7533	−	9.99235i	0.507989	−	0.369076i	−0.304071	−	0.952649i	$-0.598346\pi$
$733$	13.7533	−	9.99235i	0.507989	−	0.369076i	0.812060	+	0.583574i	$0.198346\pi$
$734$		0			0
$735$	−0.927051	−	2.85317i	−0.0341948	−	0.105241i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	12.3607	+	38.0423i	0.454695	+	1.39941i	0.871493	+	0.490408i	$0.163152\pi$
$739$	12.3607	+	38.0423i	0.454695	+	1.39941i	−0.416798	+	0.908999i	$0.636848\pi$
$740$		0			0
$741$	−9.70820	+	7.05342i	−0.356640	+	0.259114i
$742$		0			0
$743$	8.03444	−	24.7275i	0.294755	−	0.907163i	−0.688549	−	0.725190i	$-0.741752\pi$
$743$	8.03444	−	24.7275i	0.294755	−	0.907163i	0.983304	−	0.181973i	$-0.0582482\pi$
$744$		0			0
$745$	10.5172	+	7.64121i	0.385321	+	0.279952i
$746$		0			0
$747$	8.00000			0.292705
$748$		0			0
$749$	−28.0000			−1.02310
$750$		0			0
$751$	27.5066	+	19.9847i	1.00373	+	0.729252i	0.962885	−	0.269913i	$-0.0869951\pi$
$751$	27.5066	+	19.9847i	1.00373	+	0.729252i	0.0408447	+	0.999166i	$0.486995\pi$
$752$		0			0
$753$	3.09017	−	9.51057i	0.112612	−	0.346584i
$754$		0			0
$755$	6.47214	−	4.70228i	0.235545	−	0.171134i
$756$		0			0
$757$	−13.2877	−	40.8954i	−0.482951	−	1.48637i	−0.834927	−	0.550361i	$-0.814490\pi$
$757$	−13.2877	−	40.8954i	−0.482951	−	1.48637i	0.351976	−	0.936009i	$-0.385510\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	8.34346	+	25.6785i	0.302450	+	0.930846i	0.980616	+	0.195937i	$0.0627749\pi$
$761$	8.34346	+	25.6785i	0.302450	+	0.930846i	−0.678166	+	0.734909i	$0.737225\pi$
$762$		0			0
$763$	4.85410	−	3.52671i	0.175730	−	0.127676i
$764$		0			0
$765$	−2.16312	+	6.65740i	−0.0782077	+	0.240699i
$766$		0			0
$767$	14.5623	+	10.5801i	0.525814	+	0.382027i
$768$		0			0
$769$	41.0000			1.47850			0.739249	−	0.673432i	$-0.235181\pi$
$769$	41.0000			1.47850			0.739249	+	0.673432i	$0.235181\pi$
$770$		0			0
$771$	7.00000			0.252099
$772$		0			0
$773$	24.2705	+	17.6336i	0.872950	+	0.634235i	0.931377	−	0.364057i	$-0.118609\pi$
$773$	24.2705	+	17.6336i	0.872950	+	0.634235i	−0.0584272	+	0.998292i	$0.518609\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−14.5623	+	10.5801i	−0.522420	+	0.379560i
$778$		0			0
$779$	11.1246	+	34.2380i	0.398581	+	1.22670i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.927051	+	2.85317i	0.0331301	+	0.101964i
$784$		0			0
$785$	11.3262	−	8.22899i	0.404251	−	0.293705i
$786$		0			0
$787$	9.88854	−	30.4338i	0.352489	−	1.08485i	−0.604963	−	0.796254i	$-0.706812\pi$
$787$	9.88854	−	30.4338i	0.352489	−	1.08485i	0.957451	−	0.288594i	$-0.0931879\pi$
$788$		0			0
$789$	−9.70820	−	7.05342i	−0.345621	−	0.251109i
$790$		0			0
$791$	38.0000			1.35112
$792$		0			0
$793$	6.00000			0.213066
$794$		0			0
$795$	10.5172	+	7.64121i	0.373007	+	0.271006i
$796$		0			0
$797$	12.9787	−	39.9444i	0.459730	−	1.41490i	−0.405762	−	0.913979i	$-0.632994\pi$
$797$	12.9787	−	39.9444i	0.459730	−	1.41490i	0.865492	−	0.500924i	$-0.167006\pi$
$798$		0			0
$799$	67.9574	−	49.3740i	2.40416	−	1.74673i
$800$		0			0
$801$	0.309017	+	0.951057i	0.0109186	+	0.0336039i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−1.23607	−	3.80423i	−0.0435657	−	0.134081i
$806$		0			0
$807$	−0.809017	+	0.587785i	−0.0284787	+	0.0206910i
$808$		0			0
$809$	−10.5066	+	32.3359i	−0.369392	+	1.13687i	0.577793	+	0.816183i	$0.303914\pi$
$809$	−10.5066	+	32.3359i	−0.369392	+	1.13687i	−0.947185	+	0.320687i	$0.896086\pi$
$810$		0			0
$811$	16.1803	+	11.7557i	0.568169	+	0.412799i	0.834439	−	0.551100i	$-0.185792\pi$
$811$	16.1803	+	11.7557i	0.568169	+	0.412799i	−0.266271	+	0.963898i	$0.585792\pi$
$812$		0			0
$813$	−22.0000			−0.771574
$814$		0			0
$815$	2.00000			0.0700569
$816$		0			0
$817$	6.47214	+	4.70228i	0.226431	+	0.164512i
$818$		0			0
$819$	−1.85410	+	5.70634i	−0.0647876	+	0.199396i
$820$		0			0
$821$	8.09017	−	5.87785i	0.282349	−	0.205138i	−0.437592	−	0.899173i	$-0.644169\pi$
$821$	8.09017	−	5.87785i	0.282349	−	0.205138i	0.719941	+	0.694035i	$0.244169\pi$
$822$		0			0
$823$	−10.5066	−	32.3359i	−0.366236	−	1.12716i	−0.949203	−	0.314664i	$-0.898108\pi$
$823$	−10.5066	−	32.3359i	−0.366236	−	1.12716i	0.582967	−	0.812496i	$-0.301892\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.618034	−	1.90211i	−0.0214911	−	0.0661430i	0.939736	−	0.341902i	$-0.111071\pi$
$827$	−0.618034	−	1.90211i	−0.0214911	−	0.0661430i	−0.961227	+	0.275759i	$0.911071\pi$
$828$		0			0
$829$	−39.6418	+	28.8015i	−1.37682	+	1.00032i	−0.379648	+	0.925131i	$0.623955\pi$
$829$	−39.6418	+	28.8015i	−1.37682	+	1.00032i	−0.997170	+	0.0751857i	$0.976045\pi$
$830$		0			0
$831$	5.25329	−	16.1680i	0.182235	−	0.560860i
$832$		0			0
$833$	16.9894	+	12.3435i	0.588646	+	0.427677i
$834$		0			0
$835$	18.0000			0.622916
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−38.8328	−	28.2137i	−1.34066	−	0.974045i	−0.999420	−	0.0340680i	$-0.989154\pi$
$839$	−38.8328	−	28.2137i	−1.34066	−	0.974045i	−0.341238	−	0.939977i	$-0.610846\pi$
$840$		0			0
$841$	−6.18034	+	19.0211i	−0.213115	+	0.655901i
$842$		0			0
$843$	17.7984	−	12.9313i	0.613009	−	0.445377i
$844$		0			0
$845$	1.23607	+	3.80423i	0.0425220	+	0.130869i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−4.32624	−	13.3148i	−0.148476	−	0.456962i
$850$		0			0
$851$	14.5623	−	10.5801i	0.499189	−	0.362682i
$852$		0			0
$853$	4.63525	−	14.2658i	0.158708	−	0.488453i	−0.839810	−	0.542881i	$-0.817333\pi$
$853$	4.63525	−	14.2658i	0.158708	−	0.488453i	0.998518	+	0.0544277i	$0.0173334\pi$
$854$		0			0
$855$	−3.23607	−	2.35114i	−0.110671	−	0.0804073i
$856$		0			0
$857$	10.0000			0.341593			0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000			0.341593			0.170797	+	0.985306i	$0.445366\pi$
$858$		0			0
$859$	22.0000			0.750630			0.375315	−	0.926897i	$-0.377534\pi$
$859$	22.0000			0.750630			0.375315	+	0.926897i	$0.377534\pi$
$860$		0			0
$861$	14.5623	+	10.5801i	0.496282	+	0.360570i
$862$		0			0
$863$	−3.09017	+	9.51057i	−0.105191	+	0.323743i	−0.989775	−	0.142636i	$-0.954442\pi$
$863$	−3.09017	+	9.51057i	−0.105191	+	0.323743i	0.884585	+	0.466380i	$0.154442\pi$
$864$		0			0
$865$	−11.3262	+	8.22899i	−0.385104	+	0.279794i
$866$		0			0
$867$	−9.88854	−	30.4338i	−0.335833	−	1.03359i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−12.9787	−	39.9444i	−0.439767	−	1.35346i
$872$		0			0
$873$	−5.66312	+	4.11450i	−0.191668	+	0.139255i
$874$		0			0
$875$	−5.56231	+	17.1190i	−0.188040	+	0.578728i
$876$		0			0
$877$	−12.1353	−	8.81678i	−0.409778	−	0.297721i	0.363734	−	0.931503i	$-0.381502\pi$
$877$	−12.1353	−	8.81678i	−0.409778	−	0.297721i	−0.773512	+	0.633782i	$0.781502\pi$
$878$		0			0
$879$	−17.0000			−0.573396
$880$		0			0
$881$	−23.0000			−0.774890			−0.387445	−	0.921893i	$-0.626642\pi$
$881$	−23.0000			−0.774890			−0.387445	+	0.921893i	$0.626642\pi$
$882$		0			0
$883$	35.5967	+	25.8626i	1.19793	+	0.870344i	0.994079	−	0.108659i	$-0.0346555\pi$
$883$	35.5967	+	25.8626i	1.19793	+	0.870344i	0.203847	+	0.979003i	$0.434656\pi$
$884$		0			0
$885$	−1.85410	+	5.70634i	−0.0623250	+	0.191816i
$886$		0			0
$887$	4.85410	−	3.52671i	0.162985	−	0.118415i	−0.503303	−	0.864110i	$-0.667882\pi$
$887$	4.85410	−	3.52671i	0.162985	−	0.118415i	0.666288	+	0.745694i	$0.267882\pi$
$888$		0			0
$889$	7.41641	+	22.8254i	0.248738	+	0.765538i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	14.8328	+	45.6507i	0.496361	+	1.52764i
$894$		0			0
$895$	6.47214	−	4.70228i	0.216340	−	0.157180i
$896$		0			0
$897$	1.85410	−	5.70634i	0.0619067	−	0.190529i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−91.0000			−3.03165
$902$		0			0
$903$	4.00000			0.133112
$904$		0			0
$905$	10.5172	+	7.64121i	0.349604	+	0.254002i
$906$		0			0
$907$	−8.03444	+	24.7275i	−0.266779	+	0.821062i	0.724499	+	0.689276i	$0.242071\pi$
$907$	−8.03444	+	24.7275i	−0.266779	+	0.821062i	−0.991278	+	0.131786i	$0.957929\pi$
$908$		0			0
$909$	1.61803	−	1.17557i	0.0536668	−	0.0389912i
$910$		0			0
$911$	9.27051	+	28.5317i	0.307146	+	0.945297i	0.978868	+	0.204494i	$0.0655549\pi$
$911$	9.27051	+	28.5317i	0.307146	+	0.945297i	−0.671722	+	0.740803i	$0.734445\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.618034	+	1.90211i	0.0204316	+	0.0628819i
$916$		0			0
$917$	−35.5967	+	25.8626i	−1.17551	+	0.854057i
$918$		0			0
$919$	−8.03444	+	24.7275i	−0.265032	+	0.815684i	0.726654	+	0.687003i	$0.241074\pi$
$919$	−8.03444	+	24.7275i	−0.265032	+	0.815684i	−0.991686	+	0.128681i	$0.958926\pi$
$920$		0			0
$921$	−17.7984	−	12.9313i	−0.586476	−	0.426100i
$922$		0			0
$923$	−18.0000			−0.592477
$924$		0			0
$925$	−36.0000			−1.18367
$926$		0			0
$927$	4.85410	+	3.52671i	0.159430	+	0.115832i
$928$		0			0
$929$	2.78115	−	8.55951i	0.0912467	−	0.280828i	−0.895011	−	0.446045i	$-0.852832\pi$
$929$	2.78115	−	8.55951i	0.0912467	−	0.280828i	0.986257	+	0.165216i	$0.0528322\pi$
$930$		0			0
$931$	−9.70820	+	7.05342i	−0.318174	+	0.231167i
$932$		0			0
$933$	−8.65248	−	26.6296i	−0.283269	−	0.871813i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	8.96149	+	27.5806i	0.292759	+	0.901020i	0.983965	+	0.178362i	$0.0570799\pi$
$937$	8.96149	+	27.5806i	0.292759	+	0.901020i	−0.691206	+	0.722658i	$0.742920\pi$
$938$		0			0
$939$	−0.809017	+	0.587785i	−0.0264013	+	0.0191816i
$940$		0			0
$941$	−8.34346	+	25.6785i	−0.271989	+	0.837096i	0.718011	+	0.696031i	$0.245053\pi$
$941$	−8.34346	+	25.6785i	−0.271989	+	0.837096i	−0.990000	+	0.141065i	$0.954947\pi$
$942$		0			0
$943$	−14.5623	−	10.5801i	−0.474214	−	0.344537i
$944$		0			0
$945$	−2.00000			−0.0650600
$946$		0			0
$947$	−18.0000			−0.584921			−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000			−0.584921			−0.292461	+	0.956278i	$0.594474\pi$
$948$		0			0
$949$	14.5623	+	10.5801i	0.472712	+	0.343446i
$950$		0			0
$951$	1.85410	−	5.70634i	0.0601234	−	0.185041i
$952$		0			0
$953$	26.6976	−	19.3969i	0.864819	−	0.628328i	−0.0643728	−	0.997926i	$-0.520505\pi$
$953$	26.6976	−	19.3969i	0.864819	−	0.628328i	0.929192	+	0.369598i	$0.120505\pi$
$954$		0			0
$955$	3.70820	+	11.4127i	0.119995	+	0.369306i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.18034	+	19.0211i	0.199574	+	0.614224i
$960$		0			0
$961$	25.0795	−	18.2213i	0.809017	−	0.587785i
$962$		0			0
$963$	4.32624	−	13.3148i	0.139411	−	0.429063i
$964$		0			0
$965$	4.04508	+	2.93893i	0.130216	+	0.0946074i
$966$		0			0
$967$	62.0000			1.99379			0.996893	−	0.0787703i	$-0.0250994\pi$
$967$	62.0000			1.99379			0.996893	+	0.0787703i	$0.0250994\pi$
$968$		0			0
$969$	28.0000			0.899490
$970$		0			0
$971$	−33.9787	−	24.6870i	−1.09043	−	0.792243i	−0.110957	−	0.993825i	$-0.535392\pi$
$971$	−33.9787	−	24.6870i	−1.09043	−	0.792243i	−0.979472	+	0.201582i	$0.935392\pi$
$972$		0			0
$973$	8.65248	−	26.6296i	0.277386	−	0.853705i
$974$		0			0
$975$	−9.70820	+	7.05342i	−0.310911	+	0.225890i
$976$		0			0
$977$	12.6697	+	38.9933i	0.405340	+	1.24751i	0.920611	+	0.390480i	$0.127691\pi$
$977$	12.6697	+	38.9933i	0.405340	+	1.24751i	−0.515272	+	0.857027i	$0.672309\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.927051	+	2.85317i	0.0295985	+	0.0910947i
$982$		0			0
$983$	29.1246	−	21.1603i	0.928931	−	0.674908i	−0.0168000	−	0.999859i	$-0.505348\pi$
$983$	29.1246	−	21.1603i	0.928931	−	0.674908i	0.945731	+	0.324951i	$0.105348\pi$
$984$		0			0
$985$	2.16312	−	6.65740i	0.0689227	−	0.212122i
$986$		0			0
$987$	19.4164	+	14.1068i	0.618031	+	0.449026i
$988$		0			0
$989$	−4.00000			−0.127193
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$		0			0
$993$	6.47214	+	4.70228i	0.205387	+	0.149222i
$994$		0			0
$995$	3.09017	−	9.51057i	0.0979650	−	0.301505i
$996$		0			0
$997$	−47.7320	+	34.6793i	−1.51169	+	1.09831i	−0.546266	+	0.837612i	$0.683951\pi$
$997$	−47.7320	+	34.6793i	−1.51169	+	1.09831i	−0.965422	+	0.260694i	$0.916049\pi$
$998$		0			0
$999$	−2.78115	−	8.55951i	−0.0879918	−	0.270811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1452.2.i.n.1237.1		4
11.2	odd	10		1452.2.i.m.493.1		4
11.3	even	5		1452.2.a.a.1.1	✓	1
11.4	even	5	inner	1452.2.i.n.1213.1		4
11.5	even	5	inner	1452.2.i.n.565.1		4
11.6	odd	10		1452.2.i.m.565.1		4
11.7	odd	10		1452.2.i.m.1213.1		4
11.8	odd	10		1452.2.a.b.1.1	yes	1
11.9	even	5	inner	1452.2.i.n.493.1		4
11.10	odd	2		1452.2.i.m.1237.1		4
33.8	even	10		4356.2.a.i.1.1		1
33.14	odd	10		4356.2.a.h.1.1		1
44.3	odd	10		5808.2.a.y.1.1		1
44.19	even	10		5808.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1452.2.a.a.1.1	✓	1	11.3	even	5
1452.2.a.b.1.1	yes	1	11.8	odd	10
1452.2.i.m.493.1		4	11.2	odd	10
1452.2.i.m.565.1		4	11.6	odd	10
1452.2.i.m.1213.1		4	11.7	odd	10
1452.2.i.m.1237.1		4	11.10	odd	2
1452.2.i.n.493.1		4	11.9	even	5	inner
1452.2.i.n.565.1		4	11.5	even	5	inner
1452.2.i.n.1213.1		4	11.4	even	5	inner
1452.2.i.n.1237.1		4	1.1	even	1	trivial
4356.2.a.h.1.1		1	33.14	odd	10
4356.2.a.i.1.1		1	33.8	even	10
5808.2.a.v.1.1		1	44.19	even	10
5808.2.a.y.1.1		1	44.3	odd	10

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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{3} +(-0.309017 + 0.951057i) q^{5} +(1.61803 - 1.17557i) q^{7} +(0.309017 + 0.951057i) q^{9} +(0.927051 + 2.85317i) q^{13} +(-0.809017 + 0.587785i) q^{15} +(2.16312 - 6.65740i) q^{17} +(3.23607 + 2.35114i) q^{19} +2.00000 q^{21} -2.00000 q^{23} +(3.23607 + 2.35114i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(2.42705 - 1.76336i) q^{29} +(0.618034 + 1.90211i) q^{35} +(-7.28115 + 5.29007i) q^{37} +(-0.927051 + 2.85317i) q^{39} +(7.28115 + 5.29007i) q^{41} +2.00000 q^{43} -1.00000 q^{45} +(9.70820 + 7.05342i) q^{47} +(-0.927051 + 2.85317i) q^{49} +(5.66312 - 4.11450i) q^{51} +(-4.01722 - 12.3637i) q^{53} +(1.23607 + 3.80423i) q^{57} +(4.85410 - 3.52671i) q^{59} +(0.618034 - 1.90211i) q^{61} +(1.61803 + 1.17557i) q^{63} -3.00000 q^{65} -14.0000 q^{67} +(-1.61803 - 1.17557i) q^{69} +(-1.85410 + 5.70634i) q^{71} +(4.85410 - 3.52671i) q^{73} +(1.23607 + 3.80423i) q^{75} +(4.94427 + 15.2169i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(2.47214 - 7.60845i) q^{83} +(5.66312 + 4.11450i) q^{85} +3.00000 q^{87} +1.00000 q^{89} +(4.85410 + 3.52671i) q^{91} +(-3.23607 + 2.35114i) q^{95} +(2.16312 + 6.65740i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} + q^{5} + 2 q^{7} - q^{9} - 3 q^{13} - q^{15} - 7 q^{17} + 4 q^{19} + 8 q^{21} - 8 q^{23} + 4 q^{25} + q^{27} + 3 q^{29} - 2 q^{35} - 9 q^{37} + 3 q^{39} + 9 q^{41} + 8 q^{43} - 4 q^{45}+ \cdots - 7 q^{97}+O(q^{100}) \) 4 * q + q^3 + q^5 + 2 * q^7 - q^9 - 3 * q^13 - q^15 - 7 * q^17 + 4 * q^19 + 8 * q^21 - 8 * q^23 + 4 * q^25 + q^27 + 3 * q^29 - 2 * q^35 - 9 * q^37 + 3 * q^39 + 9 * q^41 + 8 * q^43 - 4 * q^45 + 12 * q^47 + 3 * q^49 + 7 * q^51 + 13 * q^53 - 4 * q^57 + 6 * q^59 - 2 * q^61 + 2 * q^63 - 12 * q^65 - 56 * q^67 - 2 * q^69 + 6 * q^71 + 6 * q^73 - 4 * q^75 - 16 * q^79 - q^81 - 8 * q^83 + 7 * q^85 + 12 * q^87 + 4 * q^89 + 6 * q^91 - 4 * q^95 - 7 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more