LMFDB - Embedded newform 1456.2.cc.f.673.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.7
Root			$-1.77673i$ of defining polynomial
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.f.225.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.888364 + 1.53869i) q^{3} -3.82804i q^{5} +(0.866025 + 0.500000i) q^{7} +(-0.0783804 + 0.135759i) q^{9} +(3.74735 - 2.16353i) q^{11} +(-0.930395 + 3.48344i) q^{13} +(5.89018 - 3.40069i) q^{15} +(1.45744 - 2.52436i) q^{17} +(-4.72686 - 2.72905i) q^{19} +1.77673i q^{21} +(0.307112 + 0.531934i) q^{23} -9.65391 q^{25} +5.05166 q^{27} +(-4.62872 - 8.01717i) q^{29} +5.30753i q^{31} +(6.65802 + 3.84401i) q^{33} +(1.91402 - 3.31518i) q^{35} +(-0.974022 + 0.562352i) q^{37} +(-6.18647 + 1.66297i) q^{39} +(10.4130 - 6.01195i) q^{41} +(-0.641552 + 1.11120i) q^{43} +(0.519691 + 0.300044i) q^{45} -5.68074i q^{47} +(0.500000 + 0.866025i) q^{49} +5.17895 q^{51} -3.96013 q^{53} +(-8.28210 - 14.3450i) q^{55} -9.69757i q^{57} +(6.68359 + 3.85877i) q^{59} +(7.17308 - 12.4241i) q^{61} +(-0.135759 + 0.0783804i) q^{63} +(13.3348 + 3.56159i) q^{65} +(-0.468974 + 0.270762i) q^{67} +(-0.545654 + 0.945101i) q^{69} +(-7.96918 - 4.60101i) q^{71} +7.36798i q^{73} +(-8.57618 - 14.8544i) q^{75} +4.32707 q^{77} -0.331686 q^{79} +(4.72285 + 8.18022i) q^{81} +16.6777i q^{83} +(-9.66335 - 5.57914i) q^{85} +(8.22397 - 14.2443i) q^{87} +(2.55836 - 1.47707i) q^{89} +(-2.54747 + 2.55155i) q^{91} +(-8.16665 + 4.71502i) q^{93} +(-10.4469 + 18.0946i) q^{95} +(8.36220 + 4.82792i) q^{97} +0.678314i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} - 6 q^{15} + 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} + 42 q^{33} + 6 q^{35} + 12 q^{37} - 24 q^{39} + 36 q^{41} - 6 q^{43} - 30 q^{45} + 8 q^{49} + 4 q^{51} + 8 q^{53}+ \cdots - 42 q^{97}+O(q^{100}) $ 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 - 6 * q^15 + 2 * q^17 - 44 * q^25 + 12 * q^27 - 22 * q^29 + 42 * q^33 + 6 * q^35 + 12 * q^37 - 24 * q^39 + 36 * q^41 - 6 * q^43 - 30 * q^45 + 8 * q^49 + 4 * q^51 + 8 * q^53 - 2 * q^55 + 18 * q^59 + 4 * q^61 + 12 * q^63 - 30 * q^65 - 24 * q^67 - 52 * q^69 - 36 * q^71 + 10 * q^75 - 24 * q^77 - 8 * q^79 + 42 * q^85 - 26 * q^87 - 36 * q^89 + 2 * q^91 - 42 * q^93 + 30 * q^95 - 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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
$3$	0.888364	+	1.53869i	0.512897	+	0.888364i	0.999888	+	0.0149568i	$0.00476108\pi$
$3$	0.888364	+	1.53869i	0.512897	+	0.888364i	−0.486991	+	0.873407i	$0.661906\pi$
$4$		0			0
$5$		−	3.82804i		−	1.71195i	−0.517015	−	0.855976i	$-0.672957\pi$
$5$		−	3.82804i		−	1.71195i	0.517015	−	0.855976i	$-0.327043\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		0			0
$9$	−0.0783804	+	0.135759i	−0.0261268	+	0.0452529i
$10$		0			0
$11$	3.74735	−	2.16353i	1.12987	−	0.652330i	0.185966	−	0.982556i	$-0.440458\pi$
$11$	3.74735	−	2.16353i	1.12987	−	0.652330i	0.943902	+	0.330227i	$0.107125\pi$
$12$		0			0
$13$	−0.930395	+	3.48344i	−0.258045	+	0.966133i
$13$	−0.930395	+	3.48344i	−0.258045	+	0.966133i
$14$		0			0
$15$	5.89018	−	3.40069i	1.52084	−	0.878056i
$16$		0			0
$17$	1.45744	−	2.52436i	0.353481	−	0.612247i	−0.633376	−	0.773844i	$-0.718331\pi$
$17$	1.45744	−	2.52436i	0.353481	−	0.612247i	0.986857	+	0.161597i	$0.0516646\pi$
$18$		0			0
$19$	−4.72686	−	2.72905i	−1.08442	−	0.626088i	−0.152331	−	0.988329i	$-0.548678\pi$
$19$	−4.72686	−	2.72905i	−1.08442	−	0.626088i	−0.932084	+	0.362242i	$0.882011\pi$
$20$		0			0
$21$			1.77673i			0.387714i
$22$		0			0
$23$	0.307112	+	0.531934i	0.0640373	+	0.110916i	0.896267	−	0.443516i	$-0.146269\pi$
$23$	0.307112	+	0.531934i	0.0640373	+	0.110916i	−0.832229	+	0.554432i	$0.812936\pi$
$24$		0			0
$25$	−9.65391			−1.93078
$26$		0			0
$27$	5.05166			0.972193
$28$		0			0
$29$	−4.62872	−	8.01717i	−0.859531	−	1.48875i	−0.872377	−	0.488834i	$-0.837422\pi$
$29$	−4.62872	−	8.01717i	−0.859531	−	1.48875i	0.0128452	−	0.999917i	$-0.495911\pi$
$30$		0			0
$31$			5.30753i			0.953261i	0.879104	+	0.476630i	$0.158142\pi$
$31$			5.30753i			0.953261i	−0.879104	+	0.476630i	$0.841858\pi$
$32$		0			0
$33$	6.65802	+	3.84401i	1.15901	+	0.669156i
$34$		0			0
$35$	1.91402	−	3.31518i	0.323529	−	0.560368i
$36$		0			0
$37$	−0.974022	+	0.562352i	−0.160128	+	0.0924501i	−0.577923	−	0.816091i	$-0.696137\pi$
$37$	−0.974022	+	0.562352i	−0.160128	+	0.0924501i	0.417795	+	0.908542i	$0.362803\pi$
$38$		0			0
$39$	−6.18647	+	1.66297i	−0.990628	+	0.266289i
$40$		0			0
$41$	10.4130	−	6.01195i	1.62624	−	0.938909i	0.641037	−	0.767510i	$-0.278505\pi$
$41$	10.4130	−	6.01195i	1.62624	−	0.938909i	0.985202	−	0.171399i	$-0.0548287\pi$
$42$		0			0
$43$	−0.641552	+	1.11120i	−0.0978358	+	0.169457i	−0.910789	−	0.412873i	$-0.864525\pi$
$43$	−0.641552	+	1.11120i	−0.0978358	+	0.169457i	0.812953	+	0.582330i	$0.197859\pi$
$44$		0			0
$45$	0.519691	+	0.300044i	0.0774709	+	0.0447278i
$46$		0			0
$47$		−	5.68074i		−	0.828620i	−0.910136	−	0.414310i	$-0.864023\pi$
$47$		−	5.68074i		−	0.828620i	0.910136	−	0.414310i	$-0.135977\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	5.17895			0.725197
$52$		0			0
$53$	−3.96013			−0.543966			−0.271983	−	0.962302i	$-0.587679\pi$
$53$	−3.96013			−0.543966			−0.271983	+	0.962302i	$0.587679\pi$
$54$		0			0
$55$	−8.28210	−	14.3450i	−1.11676	−	1.93428i
$56$		0			0
$57$		−	9.69757i		−	1.28447i
$58$		0			0
$59$	6.68359	+	3.85877i	0.870129	+	0.502369i	0.867391	−	0.497627i	$-0.165795\pi$
$59$	6.68359	+	3.85877i	0.870129	+	0.502369i	0.00273800	+	0.999996i	$0.499128\pi$
$60$		0			0
$61$	7.17308	−	12.4241i	0.918419	−	1.59075i	0.116601	−	0.993179i	$-0.462800\pi$
$61$	7.17308	−	12.4241i	0.918419	−	1.59075i	0.801817	−	0.597569i	$-0.203867\pi$
$62$		0			0
$63$	−0.135759	+	0.0783804i	−0.0171040	+	0.00987500i
$64$		0			0
$65$	13.3348	+	3.56159i	1.65397	+	0.441761i
$66$		0			0
$67$	−0.468974	+	0.270762i	−0.0572943	+	0.0330789i	−0.528374	−	0.849012i	$-0.677198\pi$
$67$	−0.468974	+	0.270762i	−0.0572943	+	0.0330789i	0.471079	+	0.882091i	$0.343865\pi$
$68$		0			0
$69$	−0.545654	+	0.945101i	−0.0656891	+	0.113777i
$70$		0			0
$71$	−7.96918	−	4.60101i	−0.945768	−	0.546040i	−0.0540044	−	0.998541i	$-0.517199\pi$
$71$	−7.96918	−	4.60101i	−0.945768	−	0.546040i	−0.891764	+	0.452501i	$0.850532\pi$
$72$		0			0
$73$			7.36798i			0.862357i	0.902267	+	0.431179i	$0.141902\pi$
$73$			7.36798i			0.862357i	−0.902267	+	0.431179i	$0.858098\pi$
$74$		0			0
$75$	−8.57618	−	14.8544i	−0.990293	−	1.71524i
$76$		0			0
$77$	4.32707			0.493115
$78$		0			0
$79$	−0.331686			−0.0373176			−0.0186588	−	0.999826i	$-0.505940\pi$
$79$	−0.331686			−0.0373176			−0.0186588	+	0.999826i	$0.505940\pi$
$80$		0			0
$81$	4.72285	+	8.18022i	0.524762	+	0.908914i
$82$		0			0
$83$			16.6777i			1.83061i	0.402758	+	0.915306i	$0.368052\pi$
$83$			16.6777i			1.83061i	−0.402758	+	0.915306i	$0.631948\pi$
$84$		0			0
$85$	−9.66335	−	5.57914i	−1.04814	−	0.605143i
$86$		0			0
$87$	8.22397	−	14.2443i	0.881702	−	1.52715i
$88$		0			0
$89$	2.55836	−	1.47707i	0.271185	−	0.156569i	−0.358241	−	0.933629i	$-0.616623\pi$
$89$	2.55836	−	1.47707i	0.271185	−	0.156569i	0.629426	+	0.777060i	$0.283290\pi$
$90$		0			0
$91$	−2.54747	+	2.55155i	−0.267047	+	0.267475i
$92$		0			0
$93$	−8.16665	+	4.71502i	−0.846842	+	0.488925i
$94$		0			0
$95$	−10.4469	+	18.0946i	−1.07183	+	1.85647i
$96$		0			0
$97$	8.36220	+	4.82792i	0.849052	+	0.490201i	0.860331	−	0.509736i	$-0.170257\pi$
$97$	8.36220	+	4.82792i	0.849052	+	0.490201i	−0.0112787	+	0.999936i	$0.503590\pi$
$98$		0			0
$99$			0.678314i			0.0681731i
$100$		0			0
$101$	−3.17528	−	5.49975i	−0.315952	−	0.547246i	0.663687	−	0.748010i	$-0.268991\pi$
$101$	−3.17528	−	5.49975i	−0.315952	−	0.547246i	−0.979639	+	0.200765i	$0.935657\pi$
$102$		0			0
$103$	5.07117			0.499678			0.249839	−	0.968287i	$-0.419622\pi$
$103$	5.07117			0.499678			0.249839	+	0.968287i	$0.419622\pi$
$104$		0			0
$105$	6.80139			0.663748
$106$		0			0
$107$	−2.74289	−	4.75083i	−0.265166	−	0.459280i	0.702441	−	0.711742i	$-0.252093\pi$
$107$	−2.74289	−	4.75083i	−0.265166	−	0.459280i	−0.967607	+	0.252461i	$0.918760\pi$
$108$		0			0
$109$			6.80685i			0.651978i	0.945374	+	0.325989i	$0.105697\pi$
$109$			6.80685i			0.651978i	−0.945374	+	0.325989i	$0.894303\pi$
$110$		0			0
$111$	−1.73057	−	0.999146i	−0.164259	−	0.0948347i
$112$		0			0
$113$	3.28384	−	5.68778i	0.308918	−	0.535061i	−0.669208	−	0.743075i	$-0.733367\pi$
$113$	3.28384	−	5.68778i	0.308918	−	0.535061i	0.978126	+	0.208014i	$0.0666999\pi$
$114$		0			0
$115$	2.03626	−	1.17564i	0.189883	−	0.109629i
$116$		0			0
$117$	−0.399983	−	0.399343i	−0.0369785	−	0.0369193i
$118$		0			0
$119$	2.52436	−	1.45744i	0.231408	−	0.133603i
$120$		0			0
$121$	3.86175	−	6.68874i	0.351068	−	0.608067i
$122$		0			0
$123$	18.5011	+	10.6816i	1.66819	+	0.963128i
$124$		0			0
$125$			17.8154i			1.59346i
$126$		0			0
$127$	10.1425	+	17.5674i	0.900003	+	1.55885i	0.827488	+	0.561483i	$0.189769\pi$
$127$	10.1425	+	17.5674i	0.900003	+	1.55885i	0.0725145	+	0.997367i	$0.476898\pi$
$128$		0			0
$129$	−2.27973			−0.200719
$130$		0			0
$131$	−4.92442			−0.430249			−0.215124	−	0.976587i	$-0.569016\pi$
$131$	−4.92442			−0.430249			−0.215124	+	0.976587i	$0.569016\pi$
$132$		0			0
$133$	−2.72905	−	4.72686i	−0.236639	−	0.409871i
$134$		0			0
$135$		−	19.3380i		−	1.66435i
$136$		0			0
$137$	11.1993	+	6.46589i	0.956817	+	0.552419i	0.895192	−	0.445681i	$-0.147038\pi$
$137$	11.1993	+	6.46589i	0.956817	+	0.552419i	0.0616251	+	0.998099i	$0.480372\pi$
$138$		0			0
$139$	7.90466	−	13.6913i	0.670464	−	1.16128i	−0.307308	−	0.951610i	$-0.599428\pi$
$139$	7.90466	−	13.6913i	0.670464	−	1.16128i	0.977773	−	0.209668i	$-0.0672384\pi$
$140$		0			0
$141$	8.74090	−	5.04656i	0.736116	−	0.424997i
$142$		0			0
$143$	4.05003	+	15.0666i	0.338680	+	1.25993i
$144$		0			0
$145$	−30.6901	+	17.7189i	−2.54867	+	1.47148i
$146$		0			0
$147$	−0.888364	+	1.53869i	−0.0732710	+	0.126909i
$148$		0			0
$149$	13.7967	+	7.96552i	1.13027	+	0.652561i	0.944002	−	0.329939i	$-0.107028\pi$
$149$	13.7967	+	7.96552i	1.13027	+	0.652561i	0.186266	+	0.982499i	$0.440361\pi$
$150$		0			0
$151$			6.37358i			0.518675i	0.965787	+	0.259337i	$0.0835041\pi$
$151$			6.37358i			0.518675i	−0.965787	+	0.259337i	$0.916496\pi$
$152$		0			0
$153$	0.228469	+	0.395721i	0.0184707	+	0.0319921i
$154$		0			0
$155$	20.3175			1.63194
$156$		0			0
$157$	−7.38800			−0.589627			−0.294813	−	0.955555i	$-0.595257\pi$
$157$	−7.38800			−0.589627			−0.294813	+	0.955555i	$0.595257\pi$
$158$		0			0
$159$	−3.51804	−	6.09342i	−0.278999	−	0.483240i
$160$		0			0
$161$			0.614224i			0.0484076i
$162$		0			0
$163$	0.0758325	+	0.0437819i	0.00593966	+	0.00342926i	0.502967	−	0.864306i	$-0.332242\pi$
$163$	0.0758325	+	0.0437819i	0.00593966	+	0.00342926i	−0.497027	+	0.867735i	$0.665575\pi$
$164$		0			0
$165$	14.7150	−	25.4872i	1.14556	−	1.98417i
$166$		0			0
$167$	−16.0309	+	9.25542i	−1.24050	+	0.716206i	−0.969197	−	0.246287i	$-0.920789\pi$
$167$	−16.0309	+	9.25542i	−1.24050	+	0.716206i	−0.271308	+	0.962493i	$0.587456\pi$
$168$		0			0
$169$	−11.2687	−	6.48195i	−0.866826	−	0.498612i
$170$		0			0
$171$	0.740986	−	0.427808i	0.0566646	−	0.0327153i
$172$		0			0
$173$	0.205452	−	0.355853i	0.0156202	−	0.0270550i	−0.858110	−	0.513466i	$-0.828361\pi$
$173$	0.205452	−	0.355853i	0.0156202	−	0.0270550i	0.873730	+	0.486412i	$0.161694\pi$
$174$		0			0
$175$	−8.36053	−	4.82696i	−0.631997	−	0.364884i
$176$		0			0
$177$			13.7120i			1.03065i
$178$		0			0
$179$	−1.07738	−	1.86607i	−0.0805268	−	0.139477i	0.822950	−	0.568114i	$-0.192327\pi$
$179$	−1.07738	−	1.86607i	−0.0805268	−	0.139477i	−0.903476	+	0.428638i	$0.858994\pi$
$180$		0			0
$181$	6.50124			0.483233			0.241617	−	0.970372i	$-0.422322\pi$
$181$	6.50124			0.483233			0.241617	+	0.970372i	$0.422322\pi$
$182$		0			0
$183$	25.4892			1.88422
$184$		0			0
$185$	2.15271	+	3.72860i	0.158270	+	0.274132i
$186$		0			0
$187$		−	12.6129i		−	0.922344i
$188$		0			0
$189$	4.37487	+	2.52583i	0.318225	+	0.183727i
$190$		0			0
$191$	−9.38751	+	16.2596i	−0.679256	+	1.17651i	0.295949	+	0.955204i	$0.404364\pi$
$191$	−9.38751	+	16.2596i	−0.679256	+	1.17651i	−0.975205	+	0.221303i	$0.928969\pi$
$192$		0			0
$193$	−22.1852	+	12.8086i	−1.59693	+	0.921986i	−0.604851	+	0.796339i	$0.706767\pi$
$193$	−22.1852	+	12.8086i	−1.59693	+	0.921986i	−0.992075	+	0.125647i	$0.959899\pi$
$194$		0			0
$195$	6.36593	+	23.6821i	0.455874	+	1.69591i
$196$		0			0
$197$	−0.510570	+	0.294778i	−0.0363766	+	0.0210021i	−0.518078	−	0.855333i	$-0.673352\pi$
$197$	−0.510570	+	0.294778i	−0.0363766	+	0.0210021i	0.481701	+	0.876335i	$0.340019\pi$
$198$		0			0
$199$	−8.04513	+	13.9346i	−0.570304	+	0.987796i	0.426230	+	0.904615i	$0.359841\pi$
$199$	−8.04513	+	13.9346i	−0.570304	+	0.987796i	−0.996534	+	0.0831814i	$0.973492\pi$
$200$		0			0
$201$	−0.833240	−	0.481071i	−0.0587722	−	0.0339321i
$202$		0			0
$203$		−	9.25744i		−	0.649745i
$204$		0			0
$205$	−23.0140	−	39.8614i	−1.60737	−	2.78404i
$206$		0			0
$207$	−0.0962862			−0.00669236
$208$		0			0
$209$	−23.6176			−1.63366
$210$		0			0
$211$	−5.69247	−	9.85965i	−0.391886	−	0.678766i	0.600812	−	0.799390i	$-0.294844\pi$
$211$	−5.69247	−	9.85965i	−0.391886	−	0.678766i	−0.992698	+	0.120624i	$0.961510\pi$
$212$		0			0
$213$		−	16.3495i		−	1.12025i
$214$		0			0
$215$	4.25373	+	2.45589i	0.290102	+	0.167490i
$216$		0			0
$217$	−2.65377	+	4.59646i	−0.180149	+	0.312028i
$218$		0			0
$219$	−11.3370	+	6.54545i	−0.766087	+	0.442300i
$220$		0			0
$221$	7.43746	+	7.42556i	0.500298	+	0.499497i
$222$		0			0
$223$	2.03182	−	1.17307i	0.136060	−	0.0785545i	−0.430425	−	0.902626i	$-0.641636\pi$
$223$	2.03182	−	1.17307i	0.136060	−	0.0785545i	0.566485	+	0.824072i	$0.308303\pi$
$224$		0			0
$225$	0.756677	−	1.31060i	0.0504452	−	0.0873736i
$226$		0			0
$227$	7.14587	+	4.12567i	0.474288	+	0.273830i	0.718033	−	0.696009i	$-0.245043\pi$
$227$	7.14587	+	4.12567i	0.474288	+	0.273830i	−0.243745	+	0.969839i	$0.578376\pi$
$228$		0			0
$229$		−	17.2750i		−	1.14156i	−0.821103	−	0.570780i	$-0.806641\pi$
$229$		−	17.2750i		−	1.14156i	0.821103	−	0.570780i	$-0.193359\pi$
$230$		0			0
$231$	3.84401	+	6.65802i	0.252917	+	0.438065i
$232$		0			0
$233$	−4.13778			−0.271075			−0.135537	−	0.990772i	$-0.543276\pi$
$233$	−4.13778			−0.271075			−0.135537	+	0.990772i	$0.543276\pi$
$234$		0			0
$235$	−21.7461			−1.41856
$236$		0			0
$237$	−0.294658	−	0.510363i	−0.0191401	−	0.0331516i
$238$		0			0
$239$		−	5.83879i		−	0.377680i	−0.982008	−	0.188840i	$-0.939527\pi$
$239$		−	5.83879i		−	0.377680i	0.982008	−	0.188840i	$-0.0604727\pi$
$240$		0			0
$241$	24.6356	+	14.2234i	1.58692	+	0.916207i	0.993811	+	0.111084i	$0.0354322\pi$
$241$	24.6356	+	14.2234i	1.58692	+	0.916207i	0.593107	+	0.805124i	$0.297901\pi$
$242$		0			0
$243$	−0.813733	+	1.40943i	−0.0522010	+	0.0904148i
$244$		0			0
$245$	3.31518	−	1.91402i	0.211799	−	0.122282i
$246$		0			0
$247$	13.9043	−	13.9266i	0.884712	−	0.886131i
$248$		0			0
$249$	−25.6618	+	14.8158i	−1.62625	+	0.938916i
$250$		0			0
$251$	6.39001	−	11.0678i	0.403334	−	0.698595i	−0.590792	−	0.806824i	$-0.701185\pi$
$251$	6.39001	−	11.0678i	0.403334	−	0.698595i	0.994126	+	0.108229i	$0.0345180\pi$
$252$		0			0
$253$	2.30171	+	1.32889i	0.144707	+	0.0835468i
$254$		0			0
$255$		−	19.8252i		−	1.24150i
$256$		0			0
$257$	0.335695	+	0.581441i	0.0209401	+	0.0362693i	0.876306	−	0.481756i	$-0.160001\pi$
$257$	0.335695	+	0.581441i	0.0209401	+	0.0362693i	−0.855365	+	0.518025i	$0.826667\pi$
$258$		0			0
$259$	−1.12470			−0.0698857
$260$		0			0
$261$	1.45120			0.0898272
$262$		0			0
$263$	−9.48512	−	16.4287i	−0.584878	−	1.01304i	−0.994891	−	0.100958i	$-0.967809\pi$
$263$	−9.48512	−	16.4287i	−0.584878	−	1.01304i	0.410013	−	0.912080i	$-0.365524\pi$
$264$		0			0
$265$			15.1596i			0.931244i
$266$		0			0
$267$	4.54550	+	2.62435i	0.278180	+	0.160607i
$268$		0			0
$269$	4.79241	−	8.30070i	0.292198	−	0.506102i	−0.682131	−	0.731230i	$-0.738947\pi$
$269$	4.79241	−	8.30070i	0.292198	−	0.506102i	0.974329	+	0.225128i	$0.0722799\pi$
$270$		0			0
$271$	−9.06856	+	5.23574i	−0.550876	+	0.318048i	−0.749475	−	0.662032i	$-0.769694\pi$
$271$	−9.06856	+	5.23574i	−0.550876	+	0.318048i	0.198599	+	0.980081i	$0.436361\pi$
$272$		0			0
$273$	−6.18913	−	1.65306i	−0.374583	−	0.100048i
$274$		0			0
$275$	−36.1766	+	20.8866i	−2.18153	+	1.25951i
$276$		0			0
$277$	−9.66856	+	16.7464i	−0.580927	+	1.00620i	0.414443	+	0.910075i	$0.363977\pi$
$277$	−9.66856	+	16.7464i	−0.580927	+	1.00620i	−0.995370	+	0.0961199i	$0.969357\pi$
$278$		0			0
$279$	−0.720544	−	0.416006i	−0.0431379	−	0.0249057i
$280$		0			0
$281$			18.7039i			1.11578i	0.829915	+	0.557890i	$0.188389\pi$
$281$			18.7039i			1.11578i	−0.829915	+	0.557890i	$0.811611\pi$
$282$		0			0
$283$	−0.587956	−	1.01837i	−0.0349504	−	0.0605358i	0.848021	−	0.529962i	$-0.177794\pi$
$283$	−0.587956	−	1.01837i	−0.0349504	−	0.0605358i	−0.882971	+	0.469427i	$0.844461\pi$
$284$		0			0
$285$	−37.1227			−2.19896
$286$		0			0
$287$	12.0239			0.709749
$288$		0			0
$289$	4.25174	+	7.36423i	0.250102	+	0.433190i
$290$		0			0
$291$			17.1558i			1.00569i
$292$		0			0
$293$	−5.63521	−	3.25349i	−0.329213	−	0.190071i	0.326279	−	0.945274i	$-0.394205\pi$
$293$	−5.63521	−	3.25349i	−0.329213	−	0.190071i	−0.655491	+	0.755203i	$0.727538\pi$
$294$		0			0
$295$	14.7715	−	25.5851i	0.860033	−	1.48962i
$296$		0			0
$297$	18.9303	−	10.9294i	1.09845	−	0.634190i
$298$		0			0
$299$	−2.13869	+	0.574899i	−0.123684	+	0.0332472i
$300$		0			0
$301$	−1.11120	+	0.641552i	−0.0640486	+	0.0369785i
$302$		0			0
$303$	5.64161	−	9.77156i	0.324102	−	0.561361i
$304$		0			0
$305$	−47.5601	−	27.4589i	−2.72329	−	1.57229i
$306$		0			0
$307$		−	27.0573i		−	1.54424i	−0.635475	−	0.772121i	$-0.719196\pi$
$307$		−	27.0573i		−	1.54424i	0.635475	−	0.772121i	$-0.280804\pi$
$308$		0			0
$309$	4.50505	+	7.80297i	0.256283	+	0.443895i
$310$		0			0
$311$	−30.9061			−1.75253			−0.876263	−	0.481834i	$-0.839971\pi$
$311$	−30.9061			−1.75253			−0.876263	+	0.481834i	$0.839971\pi$
$312$		0			0
$313$	30.0816			1.70031			0.850157	−	0.526530i	$-0.176507\pi$
$313$	30.0816			1.70031			0.850157	+	0.526530i	$0.176507\pi$
$314$		0			0
$315$	0.300044	+	0.519691i	0.0169055	+	0.0292812i
$316$		0			0
$317$			3.78351i			0.212503i	0.994339	+	0.106251i	$0.0338848\pi$
$317$			3.78351i			0.212503i	−0.994339	+	0.106251i	$0.966115\pi$
$318$		0			0
$319$	−34.6908	−	20.0288i	−1.94231	−	1.12140i
$320$		0			0
$321$	4.87338	−	8.44093i	0.272005	−	0.471127i
$322$		0			0
$323$	−13.7782	+	7.95486i	−0.766641	+	0.442620i
$324$		0			0
$325$	8.98195	−	33.6288i	0.498229	−	1.86539i
$326$		0			0
$327$	−10.4736	+	6.04696i	−0.579194	+	0.334398i
$328$		0			0
$329$	2.84037	−	4.91966i	0.156595	−	0.271230i
$330$		0			0
$331$	−20.1396	−	11.6276i	−1.10697	−	0.639110i	−0.168928	−	0.985628i	$-0.554031\pi$
$331$	−20.1396	−	11.6276i	−1.10697	−	0.639110i	−0.938043	+	0.346518i	$0.887364\pi$
$332$		0			0
$333$		−	0.176309i		−	0.00966170i
$334$		0			0
$335$	1.03649	+	1.79525i	0.0566295	+	0.0980852i
$336$		0			0
$337$	6.51910			0.355118			0.177559	−	0.984110i	$-0.443180\pi$
$337$	6.51910			0.355118			0.177559	+	0.984110i	$0.443180\pi$
$338$		0			0
$339$	11.6690			0.633772
$340$		0			0
$341$	11.4830	+	19.8892i	0.621840	+	1.07706i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	3.61789	+	2.08879i	0.194780	+	0.112457i
$346$		0			0
$347$	−6.55696	+	11.3570i	−0.351996	+	0.609675i	−0.986599	−	0.163163i	$-0.947830\pi$
$347$	−6.55696	+	11.3570i	−0.351996	+	0.609675i	0.634603	+	0.772838i	$0.281164\pi$
$348$		0			0
$349$	8.41298	−	4.85724i	0.450336	−	0.260002i	−0.257636	−	0.966242i	$-0.582943\pi$
$349$	8.41298	−	4.85724i	0.450336	−	0.260002i	0.707972	+	0.706240i	$0.249610\pi$
$350$		0			0
$351$	−4.70004	+	17.5972i	−0.250869	+	0.939267i
$352$		0			0
$353$	−26.2632	+	15.1631i	−1.39785	+	0.807049i	−0.994167	−	0.107850i	$-0.965603\pi$
$353$	−26.2632	+	15.1631i	−1.39785	+	0.807049i	−0.403683	+	0.914899i	$0.632270\pi$
$354$		0			0
$355$	−17.6129	+	30.5064i	−0.934794	+	1.61911i
$356$		0			0
$357$	4.48510	+	2.58947i	0.237377	+	0.137049i
$358$		0			0
$359$			10.5854i			0.558677i	0.960193	+	0.279339i	$0.0901152\pi$
$359$			10.5854i			0.558677i	−0.960193	+	0.279339i	$0.909885\pi$
$360$		0			0
$361$	5.39545	+	9.34520i	0.283971	+	0.491853i
$362$		0			0
$363$	13.7225			0.720247
$364$		0			0
$365$	28.2050			1.47631
$366$		0			0
$367$	13.3188	+	23.0688i	0.695234	+	1.20418i	0.970102	+	0.242699i	$0.0780328\pi$
$367$	13.3188	+	23.0688i	0.695234	+	1.20418i	−0.274867	+	0.961482i	$0.588634\pi$
$368$		0			0
$369$			1.88488i			0.0981228i
$370$		0			0
$371$	−3.42958	−	1.98007i	−0.178055	−	0.102800i
$372$		0			0
$373$	3.07064	−	5.31851i	0.158992	−	0.275382i	−0.775514	−	0.631331i	$-0.782509\pi$
$373$	3.07064	−	5.31851i	0.158992	−	0.275382i	0.934505	+	0.355949i	$0.115842\pi$
$374$		0			0
$375$	−27.4124	+	15.8265i	−1.41557	+	0.817278i
$376$		0			0
$377$	32.2339	−	8.66473i	1.66013	−	0.446256i
$378$		0			0
$379$	−20.4175	+	11.7880i	−1.04877	+	0.605510i	−0.922306	−	0.386460i	$-0.873698\pi$
$379$	−20.4175	+	11.7880i	−1.04877	+	0.605510i	−0.126469	+	0.991971i	$0.540364\pi$
$380$		0			0
$381$	−18.0205	+	31.2124i	−0.923217	+	1.59906i
$382$		0			0
$383$	17.4736	+	10.0884i	0.892860	+	0.515493i	0.874877	−	0.484346i	$-0.160942\pi$
$383$	17.4736	+	10.0884i	0.892860	+	0.515493i	0.0179828	+	0.999838i	$0.494276\pi$
$384$		0			0
$385$		−	16.5642i		−	0.844189i
$386$		0			0
$387$	−0.100570	−	0.174193i	−0.00511227	−	0.00885472i
$388$		0			0
$389$	−32.8506			−1.66559			−0.832795	−	0.553581i	$-0.813261\pi$
$389$	−32.8506			−1.66559			−0.832795	+	0.553581i	$0.813261\pi$
$390$		0			0
$391$	1.79039			0.0905438
$392$		0			0
$393$	−4.37468	−	7.57716i	−0.220673	−	0.382217i
$394$		0			0
$395$			1.26971i			0.0638860i
$396$		0			0
$397$	21.8789	+	12.6318i	1.09807	+	0.633970i	0.935713	−	0.352762i	$-0.114758\pi$
$397$	21.8789	+	12.6318i	1.09807	+	0.633970i	0.162355	+	0.986732i	$0.448091\pi$
$398$		0			0
$399$	4.84878	−	8.39834i	0.242743	−	0.420443i
$400$		0			0
$401$	−25.3059	+	14.6104i	−1.26372	+	0.729608i	−0.973792	−	0.227441i	$-0.926964\pi$
$401$	−25.3059	+	14.6104i	−1.26372	+	0.729608i	−0.289926	+	0.957049i	$0.593631\pi$
$402$		0			0
$403$	−18.4885	−	4.93810i	−0.920977	−	0.245984i
$404$		0			0
$405$	31.3142	−	18.0793i	1.55602	−	0.898367i
$406$		0			0
$407$	−2.43333	+	4.21466i	−0.120616	+	0.208913i
$408$		0			0
$409$	23.6697	+	13.6657i	1.17039	+	0.675727i	0.953773	−	0.300529i	$-0.0971633\pi$
$409$	23.6697	+	13.6657i	1.17039	+	0.675727i	0.216620	+	0.976256i	$0.430497\pi$
$410$		0			0
$411$			22.9763i			1.13334i
$412$		0			0
$413$	3.85877	+	6.68359i	0.189878	+	0.328878i
$414$		0			0
$415$	63.8429			3.13392
$416$		0			0
$417$	28.0889			1.37552
$418$		0			0
$419$	10.1693	+	17.6137i	0.496802	+	0.860486i	0.999993	−	0.00368888i	$-0.00117421\pi$
$419$	10.1693	+	17.6137i	0.496802	+	0.860486i	−0.503191	+	0.864175i	$0.667841\pi$
$420$		0			0
$421$			21.0712i			1.02695i	0.858106	+	0.513473i	$0.171641\pi$
$421$			21.0712i			1.02695i	−0.858106	+	0.513473i	$0.828359\pi$
$422$		0			0
$423$	0.771210	+	0.445258i	0.0374975	+	0.0216492i
$424$		0			0
$425$	−14.0700	+	24.3699i	−0.682495	+	1.18212i
$426$		0			0
$427$	12.4241	−	7.17308i	0.601246	−	0.347130i
$428$		0			0
$429$	−19.5850	+	19.6164i	−0.945571	+	0.947087i
$430$		0			0
$431$	25.6632	−	14.8167i	1.23615	−	0.713694i	0.267848	−	0.963461i	$-0.413687\pi$
$431$	25.6632	−	14.8167i	1.23615	−	0.713694i	0.968306	+	0.249767i	$0.0803541\pi$
$432$		0			0
$433$	−14.2983	+	24.7653i	−0.687130	+	1.19014i	0.285632	+	0.958339i	$0.407796\pi$
$433$	−14.2983	+	24.7653i	−0.687130	+	1.19014i	−0.972762	+	0.231805i	$0.925537\pi$
$434$		0			0
$435$	−54.5279	−	31.4817i	−2.61441	−	1.50943i
$436$		0			0
$437$		−	3.35250i		−	0.160372i
$438$		0			0
$439$	10.9124	+	18.9009i	0.520821	+	0.902088i	0.999707	+	0.0242113i	$0.00770744\pi$
$439$	10.9124	+	18.9009i	0.520821	+	0.902088i	−0.478886	+	0.877877i	$0.658959\pi$
$440$		0			0
$441$	−0.156761			−0.00746480
$442$		0			0
$443$	6.32956			0.300726			0.150363	−	0.988631i	$-0.451956\pi$
$443$	6.32956			0.300726			0.150363	+	0.988631i	$0.451956\pi$
$444$		0			0
$445$	−5.65428	−	9.79350i	−0.268039	−	0.464256i
$446$		0			0
$447$			28.3051i			1.33879i
$448$		0			0
$449$	21.2777	+	12.2847i	1.00415	+	0.579749i	0.909475	−	0.415759i	$-0.136484\pi$
$449$	21.2777	+	12.2847i	1.00415	+	0.579749i	0.0946799	+	0.995508i	$0.469817\pi$
$450$		0			0
$451$	26.0141	−	45.0578i	1.22496	−	2.12169i
$452$		0			0
$453$	−9.80697	+	5.66206i	−0.460772	+	0.266027i
$454$		0			0
$455$	9.76745	+	9.75181i	0.457905	+	0.457172i
$456$		0			0
$457$	−3.90240	+	2.25305i	−0.182547	+	0.105393i	−0.588489	−	0.808505i	$-0.700277\pi$
$457$	−3.90240	+	2.25305i	−0.182547	+	0.105393i	0.405942	+	0.913899i	$0.366944\pi$
$458$		0			0
$459$	7.36249	−	12.7522i	0.343652	−	0.595222i
$460$		0			0
$461$	0.260026	+	0.150126i	0.0121106	+	0.00699206i	0.506043	−	0.862508i	$-0.331108\pi$
$461$	0.260026	+	0.150126i	0.0121106	+	0.00699206i	−0.493932	+	0.869500i	$0.664441\pi$
$462$		0			0
$463$			19.2907i			0.896514i	0.893905	+	0.448257i	$0.147955\pi$
$463$			19.2907i			0.896514i	−0.893905	+	0.448257i	$0.852045\pi$
$464$		0			0
$465$	18.0493	+	31.2623i	0.837016	+	1.44975i
$466$		0			0
$467$	−13.9509			−0.645570			−0.322785	−	0.946472i	$-0.604619\pi$
$467$	−13.9509			−0.645570			−0.322785	+	0.946472i	$0.604619\pi$
$468$		0			0
$469$	−0.541525			−0.0250053
$470$		0			0
$471$	−6.56323	−	11.3679i	−0.302418	−	0.523803i
$472$		0			0
$473$			5.55208i			0.255285i
$474$		0			0
$475$	45.6327	+	26.3460i	2.09377	+	1.20884i
$476$		0			0
$477$	0.310397	−	0.537623i	0.0142121	−	0.0246161i
$478$		0			0
$479$	23.7743	−	13.7261i	1.08627	−	0.627160i	0.153692	−	0.988119i	$-0.450884\pi$
$479$	23.7743	−	13.7261i	1.08627	−	0.627160i	0.932582	+	0.360959i	$0.117550\pi$
$480$		0			0
$481$	−1.05270	−	3.91616i	−0.0479988	−	0.178561i
$482$		0			0
$483$	−0.945101	+	0.545654i	−0.0430036	+	0.0248281i
$484$		0			0
$485$	18.4815	−	32.0108i	0.839200	−	1.45354i
$486$		0			0
$487$	−12.1206	−	6.99785i	−0.549238	−	0.317103i	0.199577	−	0.979882i	$-0.436043\pi$
$487$	−12.1206	−	6.99785i	−0.549238	−	0.317103i	−0.748815	+	0.662780i	$0.769377\pi$
$488$		0			0
$489$			0.155577i			0.00703543i
$490$		0			0
$491$	3.76330	+	6.51823i	0.169836	+	0.294164i	0.938362	−	0.345654i	$-0.112343\pi$
$491$	3.76330	+	6.51823i	0.169836	+	0.294164i	−0.768526	+	0.639818i	$0.779010\pi$
$492$		0			0
$493$	−26.9843			−1.21531
$494$		0			0
$495$	2.59662			0.116709
$496$		0			0
$497$	−4.60101	−	7.96918i	−0.206384	−	0.357467i
$498$		0			0
$499$		−	1.16848i		−	0.0523083i	−0.999658	−	0.0261541i	$-0.991674\pi$
$499$		−	1.16848i		−	0.0523083i	0.999658	−	0.0261541i	$-0.00832607\pi$
$500$		0			0
$501$	−28.4825	−	16.4444i	−1.27250	−	0.734680i
$502$		0			0
$503$	−5.30877	+	9.19505i	−0.236706	+	0.409987i	−0.959767	−	0.280797i	$-0.909401\pi$
$503$	−5.30877	+	9.19505i	−0.236706	+	0.409987i	0.723061	+	0.690784i	$0.242735\pi$
$504$		0			0
$505$	−21.0533	+	12.1551i	−0.936859	+	0.540896i
$506$		0			0
$507$	−0.0370126	−	23.0974i	−0.00164379	−	1.02579i
$508$		0			0
$509$	−21.0450	+	12.1503i	−0.932803	+	0.538554i	−0.887697	−	0.460428i	$-0.847696\pi$
$509$	−21.0450	+	12.1503i	−0.932803	+	0.538554i	−0.0451058	+	0.998982i	$0.514363\pi$
$510$		0			0
$511$	−3.68399	+	6.38086i	−0.162970	+	0.282273i
$512$		0			0
$513$	−23.8785	−	13.7862i	−1.05426	−	0.608678i
$514$		0			0
$515$		−	19.4127i		−	0.855424i
$516$		0			0
$517$	−12.2905	−	21.2877i	−0.540534	−	0.936232i
$518$		0			0
$519$	0.730063			0.0320462
$520$		0			0
$521$	11.3280			0.496289			0.248144	−	0.968723i	$-0.420179\pi$
$521$	11.3280			0.496289			0.248144	+	0.968723i	$0.420179\pi$
$522$		0			0
$523$	15.1328	+	26.2108i	0.661711	+	1.14612i	0.980166	+	0.198180i	$0.0635029\pi$
$523$	15.1328	+	26.2108i	0.661711	+	1.14612i	−0.318454	+	0.947938i	$0.603164\pi$
$524$		0			0
$525$		−	17.1524i		−	0.748591i
$526$		0			0
$527$	13.3981	+	7.73541i	0.583631	+	0.336960i
$528$		0			0
$529$	11.3114	−	19.5919i	0.491798	−	0.851820i
$530$		0			0
$531$	−1.04772	+	0.604904i	−0.0454674	+	0.0262506i
$532$		0			0
$533$	11.2541	+	41.8666i	0.487468	+	1.81344i
$534$		0			0
$535$	−18.1864	+	10.4999i	−0.786266	+	0.453951i
$536$		0			0
$537$	1.91420	−	3.31550i	0.0826039	−	0.143074i
$538$		0			0
$539$	3.74735	+	2.16353i	0.161410	+	0.0931899i
$540$		0			0
$541$		−	11.1529i		−	0.479500i	−0.970835	−	0.239750i	$-0.922935\pi$
$541$		−	11.1529i		−	0.479500i	0.970835	−	0.239750i	$-0.0770654\pi$
$542$		0			0
$543$	5.77546	+	10.0034i	0.247849	+	0.429287i
$544$		0			0
$545$	26.0569			1.11616
$546$		0			0
$547$	−4.87804			−0.208570			−0.104285	−	0.994547i	$-0.533255\pi$
$547$	−4.87804			−0.208570			−0.104285	+	0.994547i	$0.533255\pi$
$548$		0			0
$549$	1.12446	+	1.94762i	0.0479907	+	0.0831223i
$550$		0			0
$551$			50.5281i			2.15257i
$552$		0			0
$553$	−0.287249	−	0.165843i	−0.0122151	−	0.00705237i
$554$		0			0
$555$	−3.82477	+	6.62470i	−0.162353	+	0.281203i
$556$		0			0
$557$	2.62046	−	1.51293i	0.111033	−	0.0641047i	−0.443455	−	0.896297i	$-0.646248\pi$
$557$	2.62046	−	1.51293i	0.111033	−	0.0641047i	0.554488	+	0.832192i	$0.312914\pi$
$558$		0			0
$559$	−3.27391	−	3.26867i	−0.138472	−	0.138250i
$560$		0			0
$561$	19.4073	−	11.2048i	0.819377	−	0.473068i
$562$		0			0
$563$	13.6591	−	23.6583i	0.575664	−	0.997079i	−0.420305	−	0.907383i	$-0.638077\pi$
$563$	13.6591	−	23.6583i	0.575664	−	0.997079i	0.995969	−	0.0896963i	$-0.0285896\pi$
$564$		0			0
$565$	−21.7730	−	12.5707i	−0.915999	−	0.528852i
$566$		0			0
$567$			9.44571i			0.396682i
$568$		0			0
$569$	−6.46871	−	11.2041i	−0.271183	−	0.469702i	0.697982	−	0.716115i	$-0.254081\pi$
$569$	−6.46871	−	11.2041i	−0.271183	−	0.469702i	−0.969165	+	0.246413i	$0.920748\pi$
$570$		0			0
$571$	−10.6779			−0.446855			−0.223427	−	0.974721i	$-0.571725\pi$
$571$	−10.6779			−0.446855			−0.223427	+	0.974721i	$0.571725\pi$
$572$		0			0
$573$	−33.3581			−1.39355
$574$		0			0
$575$	−2.96483	−	5.13524i	−0.123642	−	0.214154i
$576$		0			0
$577$		−	4.76467i		−	0.198356i	−0.995070	−	0.0991778i	$-0.968379\pi$
$577$		−	4.76467i		−	0.198356i	0.995070	−	0.0991778i	$-0.0316213\pi$
$578$		0			0
$579$	−39.4171	−	22.7575i	−1.63812	−	0.945767i
$580$		0			0
$581$	−8.33884	+	14.4433i	−0.345953	+	0.599209i
$582$		0			0
$583$	−14.8400	+	8.56788i	−0.614610	+	0.354845i
$584$		0			0
$585$	−1.52870	+	1.53115i	−0.0632040	+	0.0633054i
$586$		0			0
$587$	−27.6495	+	15.9634i	−1.14122	+	0.658881i	−0.946731	−	0.322024i	$-0.895637\pi$
$587$	−27.6495	+	15.9634i	−1.14122	+	0.658881i	−0.194485	+	0.980906i	$0.562303\pi$
$588$		0			0
$589$	14.4845	−	25.0879i	0.596825	−	1.03373i
$590$		0			0
$591$	−0.907144	−	0.523740i	−0.0373149	−	0.0215438i
$592$		0			0
$593$		−	1.27362i		−	0.0523015i	−0.999658	−	0.0261508i	$-0.991675\pi$
$593$		−	1.27362i		−	0.0523015i	0.999658	−	0.0261508i	$-0.00832499\pi$
$594$		0			0
$595$	−5.57914	−	9.66335i	−0.228722	−	0.396159i
$596$		0			0
$597$	−28.5880			−1.17003
$598$		0			0
$599$	15.1462			0.618857			0.309428	−	0.950923i	$-0.399862\pi$
$599$	15.1462			0.618857			0.309428	+	0.950923i	$0.399862\pi$
$600$		0			0
$601$	−17.1425	−	29.6917i	−0.699258	−	1.21115i	−0.968724	−	0.248141i	$-0.920180\pi$
$601$	−17.1425	−	29.6917i	−0.699258	−	1.21115i	0.269466	−	0.963010i	$-0.413153\pi$
$602$		0			0
$603$		−	0.0848899i		−	0.00345698i
$604$		0			0
$605$	−25.6048	−	14.7829i	−1.04098	−	0.601012i
$606$		0			0
$607$	4.73737	−	8.20537i	0.192284	−	0.333046i	−0.753723	−	0.657192i	$-0.771744\pi$
$607$	4.73737	−	8.20537i	0.192284	−	0.333046i	0.946007	+	0.324147i	$0.105077\pi$
$608$		0			0
$609$	14.2443	−	8.22397i	0.577210	−	0.333252i
$610$		0			0
$611$	19.7885	+	5.28533i	0.800557	+	0.213821i
$612$		0			0
$613$	10.0837	−	5.82183i	0.407277	−	0.235141i	−0.282342	−	0.959314i	$-0.591111\pi$
$613$	10.0837	−	5.82183i	0.407277	−	0.235141i	0.689619	+	0.724172i	$0.257778\pi$
$614$		0			0
$615$	40.8896	−	70.8229i	1.64883	−	2.85586i
$616$		0			0
$617$	−5.54295	−	3.20023i	−0.223151	−	0.128836i	0.384257	−	0.923226i	$-0.374457\pi$
$617$	−5.54295	−	3.20023i	−0.223151	−	0.128836i	−0.607408	+	0.794390i	$0.707791\pi$
$618$		0			0
$619$			11.2065i			0.450425i	0.974310	+	0.225213i	$0.0723077\pi$
$619$			11.2065i			0.450425i	−0.974310	+	0.225213i	$0.927692\pi$
$620$		0			0
$621$	1.55143	+	2.68715i	0.0622566	+	0.107832i
$622$		0			0
$623$	2.95414			0.118355
$624$		0			0
$625$	19.9284			0.797138
$626$		0			0
$627$	−20.9810	−	36.3402i	−0.837900	−	1.45129i
$628$		0			0
$629$			3.27837i			0.130717i
$630$		0			0
$631$	−39.1148	−	22.5830i	−1.55714	−	0.899013i	−0.997529	−	0.0702554i	$-0.977619\pi$
$631$	−39.1148	−	22.5830i	−1.55714	−	0.899013i	−0.559608	−	0.828758i	$-0.689048\pi$
$632$		0			0
$633$	10.1140	−	17.5179i	0.401994	−	0.696274i
$634$		0			0
$635$	67.2486	−	38.8260i	2.66868	−	1.54076i
$636$		0			0
$637$	−3.48195	+	0.935975i	−0.137960	+	0.0370847i
$638$		0			0
$639$	1.24926	−	0.721258i	0.0494198	−	0.0285325i
$640$		0			0
$641$	−3.57997	+	6.20069i	−0.141400	+	0.244912i	−0.928024	−	0.372520i	$-0.878494\pi$
$641$	−3.57997	+	6.20069i	−0.141400	+	0.244912i	0.786624	+	0.617432i	$0.211827\pi$
$642$		0			0
$643$	35.9015	+	20.7278i	1.41582	+	0.817423i	0.995928	−	0.0901516i	$-0.0287352\pi$
$643$	35.9015	+	20.7278i	1.41582	+	0.817423i	0.419890	+	0.907575i	$0.362068\pi$
$644$		0			0
$645$			8.72690i			0.343621i
$646$		0			0
$647$	−7.79258	−	13.4971i	−0.306358	−	0.530627i	0.671205	−	0.741272i	$-0.265777\pi$
$647$	−7.79258	−	13.4971i	−0.306358	−	0.530627i	−0.977563	+	0.210645i	$0.932444\pi$
$648$		0			0
$649$	33.3943			1.31084
$650$		0			0
$651$	−9.43004			−0.369592
$652$		0			0
$653$	11.9121	+	20.6323i	0.466156	+	0.807406i	0.999253	−	0.0386482i	$-0.0123052\pi$
$653$	11.9121	+	20.6323i	0.466156	+	0.807406i	−0.533097	+	0.846054i	$0.678972\pi$
$654$		0			0
$655$			18.8509i			0.736565i
$656$		0			0
$657$	−1.00027	−	0.577505i	−0.0390242	−	0.0225306i
$658$		0			0
$659$	2.01861	−	3.49634i	0.0786340	−	0.136198i	−0.824027	−	0.566551i	$-0.808277\pi$
$659$	2.01861	−	3.49634i	0.0786340	−	0.136198i	0.902661	+	0.430353i	$0.141611\pi$
$660$		0			0
$661$	32.2144	−	18.5990i	1.25299	−	0.723416i	0.281290	−	0.959623i	$-0.409238\pi$
$661$	32.2144	−	18.5990i	1.25299	−	0.723416i	0.971703	+	0.236207i	$0.0759043\pi$
$662$		0			0
$663$	−4.81846	+	18.0406i	−0.187134	+	0.700637i
$664$		0			0
$665$	−18.0946	+	10.4469i	−0.701679	+	0.405115i
$666$		0			0
$667$	2.84307	−	4.92434i	0.110084	−	0.190671i
$668$		0			0
$669$	3.60998	+	2.08422i	0.139570	+	0.0805808i
$670$		0			0
$671$		−	62.0768i		−	2.39645i
$672$		0			0
$673$	−5.02863	−	8.70984i	−0.193839	−	0.335740i	0.752680	−	0.658387i	$-0.228761\pi$
$673$	−5.02863	−	8.70984i	−0.193839	−	0.335740i	−0.946519	+	0.322647i	$0.895427\pi$
$674$		0			0
$675$	−48.7683			−1.87709
$676$		0			0
$677$	−19.8807			−0.764076			−0.382038	−	0.924147i	$-0.624778\pi$
$677$	−19.8807			−0.764076			−0.382038	+	0.924147i	$0.624778\pi$
$678$		0			0
$679$	4.82792	+	8.36220i	0.185278	+	0.320912i
$680$		0			0
$681$			14.6604i			0.561787i
$682$		0			0
$683$	17.2194	+	9.94161i	0.658881	+	0.380405i	0.791850	−	0.610715i	$-0.209118\pi$
$683$	17.2194	+	9.94161i	0.658881	+	0.380405i	−0.132970	+	0.991120i	$0.542451\pi$
$684$		0			0
$685$	24.7517	−	42.8712i	0.945715	−	1.63803i
$686$		0			0
$687$	26.5808	−	15.3464i	1.01412	−	0.585503i
$688$		0			0
$689$	3.68449	−	13.7949i	0.140368	−	0.525544i
$690$		0			0
$691$	16.5968	−	9.58219i	0.631373	−	0.364524i	−0.149910	−	0.988700i	$-0.547899\pi$
$691$	16.5968	−	9.58219i	0.631373	−	0.364524i	0.781284	+	0.624176i	$0.214565\pi$
$692$		0			0
$693$	−0.339157	+	0.587437i	−0.0128835	+	0.0223149i
$694$		0			0
$695$	−52.4108	−	30.2594i	−1.98805	−	1.14780i
$696$		0			0
$697$		−	35.0482i		−	1.32755i
$698$		0			0
$699$	−3.67585	−	6.36676i	−0.139033	−	0.240813i
$700$		0			0
$701$	18.5012			0.698780			0.349390	−	0.936977i	$-0.386389\pi$
$701$	18.5012			0.698780			0.349390	+	0.936977i	$0.386389\pi$
$702$		0			0
$703$	6.13875			0.231527
$704$		0			0
$705$	−19.3184	−	33.4605i	−0.727575	−	1.26020i
$706$		0			0
$707$		−	6.35056i		−	0.238838i
$708$		0			0
$709$	−20.8032	−	12.0107i	−0.781279	−	0.451072i	0.0556043	−	0.998453i	$-0.482291\pi$
$709$	−20.8032	−	12.0107i	−0.781279	−	0.451072i	−0.836883	+	0.547381i	$0.815625\pi$
$710$		0			0
$711$	0.0259977	−	0.0450294i	0.000974990	−	0.00168873i
$712$		0			0
$713$	−2.82325	+	1.63001i	−0.105732	+	0.0610442i
$714$		0			0
$715$	57.6756	−	15.5037i	2.15695	−	0.579805i
$716$		0			0
$717$	8.98409	−	5.18697i	0.335517	−	0.193711i
$718$		0			0
$719$	−12.2149	+	21.1568i	−0.455538	+	0.789015i	−0.998719	−	0.0506008i	$-0.983886\pi$
$719$	−12.2149	+	21.1568i	−0.455538	+	0.789015i	0.543181	+	0.839616i	$0.317220\pi$
$720$		0			0
$721$	4.39176	+	2.53559i	0.163558	+	0.0944302i
$722$		0			0
$723$			50.5421i			1.87968i
$724$		0			0
$725$	44.6852	+	77.3971i	1.65957	+	2.87446i
$726$		0			0
$727$	−20.9000			−0.775138			−0.387569	−	0.921841i	$-0.626685\pi$
$727$	−20.9000			−0.775138			−0.387569	+	0.921841i	$0.626685\pi$
$728$		0			0
$729$	25.4456			0.942428
$730$		0			0
$731$	1.87005	+	3.23902i	0.0691662	+	0.119799i
$732$		0			0
$733$			7.08118i			0.261549i	0.991412	+	0.130775i	$0.0417465\pi$
$733$			7.08118i			0.261549i	−0.991412	+	0.130775i	$0.958254\pi$
$734$		0			0
$735$	5.89018	+	3.40069i	0.217262	+	0.125437i
$736$		0			0
$737$	−1.17161	+	2.02928i	−0.0431567	+	0.0747496i
$738$		0			0
$739$	20.5378	−	11.8575i	0.755496	−	0.436186i	−0.0721806	−	0.997392i	$-0.522996\pi$
$739$	20.5378	−	11.8575i	0.755496	−	0.436186i	0.827676	+	0.561206i	$0.189662\pi$
$740$		0			0
$741$	33.7809	+	9.02256i	1.24097	+	0.331452i
$742$		0			0
$743$	36.5813	−	21.1202i	1.34204	−	0.774825i	0.354931	−	0.934893i	$-0.384504\pi$
$743$	36.5813	−	21.1202i	1.34204	−	0.774825i	0.987106	+	0.160067i	$0.0511710\pi$
$744$		0			0
$745$	30.4923	−	52.8143i	1.11715	−	1.93497i
$746$		0			0
$747$	−2.26414	−	1.30720i	−0.0828406	−	0.0478281i
$748$		0			0
$749$		−	5.48579i		−	0.200446i
$750$		0			0
$751$	−12.0710	−	20.9076i	−0.440478	−	0.762930i	0.557247	−	0.830347i	$-0.311858\pi$
$751$	−12.0710	−	20.9076i	−0.440478	−	0.762930i	−0.997725	+	0.0674164i	$0.978524\pi$
$752$		0			0
$753$	22.7066			0.827475
$754$		0			0
$755$	24.3983			0.887947
$756$		0			0
$757$	15.9716	+	27.6636i	0.580497	+	1.00545i	0.995420	+	0.0955942i	$0.0304751\pi$
$757$	15.9716	+	27.6636i	0.580497	+	1.00545i	−0.414923	+	0.909856i	$0.636192\pi$
$758$		0			0
$759$			4.72216i			0.171404i
$760$		0			0
$761$	−36.6083	−	21.1358i	−1.32705	−	0.766172i	−0.342207	−	0.939625i	$-0.611174\pi$
$761$	−36.6083	−	21.1358i	−1.32705	−	0.766172i	−0.984842	+	0.173452i	$0.944508\pi$
$762$		0			0
$763$	−3.40342	+	5.89490i	−0.123212	+	0.213410i
$764$		0			0
$765$	1.51484	−	0.874590i	0.0547690	−	0.0316209i
$766$		0			0
$767$	−19.6602	+	19.6917i	−0.709888	+	0.711026i
$768$		0			0
$769$	−2.36768	+	1.36698i	−0.0853808	+	0.0492946i	−0.542083	−	0.840325i	$-0.682364\pi$
$769$	−2.36768	+	1.36698i	−0.0853808	+	0.0492946i	0.456702	+	0.889620i	$0.349031\pi$
$770$		0			0
$771$	−0.596439	+	1.03306i	−0.0214802	+	0.0372048i
$772$		0			0
$773$	−16.9343	−	9.77703i	−0.609085	−	0.351655i	0.163523	−	0.986540i	$-0.447714\pi$
$773$	−16.9343	−	9.77703i	−0.609085	−	0.351655i	−0.772607	+	0.634884i	$0.781048\pi$
$774$		0			0
$775$		−	51.2384i		−	1.84054i
$776$		0			0
$777$	−0.999146	−	1.73057i	−0.0358442	−	0.0620839i
$778$		0			0
$779$	−65.6277			−2.35136
$780$		0			0
$781$	−39.8177			−1.42479
$782$		0			0
$783$	−23.3827	−	40.5001i	−0.835630	−	1.44735i
$784$		0			0
$785$			28.2816i			1.00941i
$786$		0			0
$787$	−28.0930	−	16.2195i	−1.00141	−	0.578163i	−0.0927426	−	0.995690i	$-0.529563\pi$
$787$	−28.0930	−	16.2195i	−1.00141	−	0.578163i	−0.908664	+	0.417528i	$0.862897\pi$
$788$		0			0
$789$	16.8525	−	29.1893i	0.599964	−	1.03917i
$790$		0			0
$791$	5.68778	−	3.28384i	0.202234	−	0.116760i
$792$		0			0
$793$	36.6050	+	36.5464i	1.29988	+	1.29780i
$794$		0			0
$795$	−23.3259	+	13.4672i	−0.827284	+	0.477632i
$796$		0			0
$797$	12.9397	−	22.4123i	0.458349	−	0.793883i	−0.540525	−	0.841328i	$-0.681774\pi$
$797$	12.9397	−	22.4123i	0.458349	−	0.793883i	0.998874	+	0.0474447i	$0.0151078\pi$
$798$		0			0
$799$	−14.3402	−	8.27933i	−0.507320	−	0.292902i
$800$		0			0
$801$			0.463093i			0.0163626i
$802$		0			0
$803$	15.9409	+	27.6104i	0.562541	+	0.974350i
$804$		0			0
$805$	2.35128			0.0828716
$806$		0			0
$807$	17.0296			0.599471
$808$		0			0
$809$	−11.2066	−	19.4105i	−0.394004	−	0.682435i	0.598969	−	0.800772i	$-0.295577\pi$
$809$	−11.2066	−	19.4105i	−0.394004	−	0.682435i	−0.992974	+	0.118337i	$0.962244\pi$
$810$		0			0
$811$		−	5.44486i		−	0.191195i	−0.995420	−	0.0955974i	$-0.969524\pi$
$811$		−	5.44486i		−	0.191195i	0.995420	−	0.0955974i	$-0.0304761\pi$
$812$		0			0
$813$	−16.1124	−	9.30247i	−0.565085	−	0.326252i
$814$		0			0
$815$	0.167599	−	0.290290i	0.00587074	−	0.0101684i
$816$		0			0
$817$	6.06505	−	3.50166i	0.212189	−	0.122508i
$818$		0			0
$819$	−0.146724	−	0.545833i	−0.00512696	−	0.0190729i
$820$		0			0
$821$	26.6843	−	15.4062i	0.931288	−	0.537679i	0.0440690	−	0.999028i	$-0.485968\pi$
$821$	26.6843	−	15.4062i	0.931288	−	0.537679i	0.887219	+	0.461349i	$0.152635\pi$
$822$		0			0
$823$	−0.102850	+	0.178141i	−0.00358513	+	0.00620962i	−0.867812	−	0.496892i	$-0.834475\pi$
$823$	−0.102850	+	0.178141i	−0.00358513	+	0.00620962i	0.864227	+	0.503102i	$0.167808\pi$
$824$		0			0
$825$	−64.2759	−	37.1097i	−2.23780	−	1.29199i
$826$		0			0
$827$			9.66411i			0.336054i	0.985782	+	0.168027i	$0.0537396\pi$
$827$			9.66411i			0.336054i	−0.985782	+	0.168027i	$0.946260\pi$
$828$		0			0
$829$	15.2667	+	26.4427i	0.530234	+	0.918393i	0.999378	+	0.0352709i	$0.0112294\pi$
$829$	15.2667	+	26.4427i	0.530234	+	0.918393i	−0.469143	+	0.883122i	$0.655437\pi$
$830$		0			0
$831$	−34.3568			−1.19182
$832$		0			0
$833$	2.91488			0.100995
$834$		0			0
$835$	35.4301	+	61.3668i	1.22611	+	2.12369i
$836$		0			0
$837$			26.8119i			0.926753i
$838$		0			0
$839$	33.0722	+	19.0942i	1.14178	+	0.659206i	0.946871	−	0.321615i	$-0.104226\pi$
$839$	33.0722	+	19.0942i	1.14178	+	0.659206i	0.194909	+	0.980821i	$0.437559\pi$
$840$		0			0
$841$	−28.3501	+	49.1037i	−0.977588	+	1.69323i
$842$		0			0
$843$	−28.7795	+	16.6158i	−0.991218	+	0.572280i
$844$		0			0
$845$	−24.8132	+	43.1372i	−0.853599	+	1.48396i
$846$		0			0
$847$	6.68874	−	3.86175i	0.229828	−	0.132691i
$848$		0			0
$849$	1.04464	−	1.80937i	0.0358519	−	0.0620973i
$850$		0			0
$851$	−0.598268	−	0.345410i	−0.0205084	−	0.0118405i
$852$		0			0
$853$		−	28.3480i		−	0.970618i	−0.874343	−	0.485309i	$-0.838707\pi$
$853$		−	28.3480i		−	0.970618i	0.874343	−	0.485309i	$-0.161293\pi$
$854$		0			0
$855$	−1.63767	−	2.83653i	−0.0560071	−	0.0970071i
$856$		0			0
$857$	25.8488			0.882978			0.441489	−	0.897267i	$-0.354450\pi$
$857$	25.8488			0.882978			0.441489	+	0.897267i	$0.354450\pi$
$858$		0			0
$859$	−19.6084			−0.669029			−0.334514	−	0.942391i	$-0.608572\pi$
$859$	−19.6084			−0.669029			−0.334514	+	0.942391i	$0.608572\pi$
$860$		0			0
$861$	10.6816	+	18.5011i	0.364028	+	0.630515i
$862$		0			0
$863$		−	13.4368i		−	0.457395i	−0.973498	−	0.228697i	$-0.926553\pi$
$863$		−	13.4368i		−	0.457395i	0.973498	−	0.228697i	$-0.0734466\pi$
$864$		0			0
$865$	−1.36222	−	0.786477i	−0.0463168	−	0.0267410i
$866$		0			0
$867$	−7.55418	+	13.0842i	−0.256554	+	0.444364i
$868$		0			0
$869$	−1.24294	+	0.717614i	−0.0421640	+	0.0243434i
$870$		0			0
$871$	−0.506854	−	1.88556i	−0.0171741	−	0.0638898i
$872$		0			0
$873$	−1.31086	+	0.756828i	−0.0443660	+	0.0256147i
$874$		0			0
$875$	−8.90769	+	15.4286i	−0.301135	+	0.521581i
$876$		0			0
$877$	26.1038	+	15.0711i	0.881464	+	0.508914i	0.871141	−	0.491033i	$-0.163381\pi$
$877$	26.1038	+	15.0711i	0.881464	+	0.508914i	0.0103233	+	0.999947i	$0.496714\pi$
$878$		0			0
$879$		−	11.5611i		−	0.389947i
$880$		0			0
$881$	4.52477	+	7.83714i	0.152443	+	0.264040i	0.932125	−	0.362136i	$-0.117952\pi$
$881$	4.52477	+	7.83714i	0.152443	+	0.264040i	−0.779682	+	0.626176i	$0.784619\pi$
$882$		0			0
$883$	−47.3475			−1.59337			−0.796685	−	0.604395i	$-0.793415\pi$
$883$	−47.3475			−1.59337			−0.796685	+	0.604395i	$0.793415\pi$
$884$		0			0
$885$	52.4900			1.76443
$886$		0			0
$887$	18.9895	+	32.8908i	0.637605	+	1.10436i	0.985957	+	0.167001i	$0.0534082\pi$
$887$	18.9895	+	32.8908i	0.637605	+	1.10436i	−0.348352	+	0.937364i	$0.613258\pi$
$888$		0			0
$889$			20.2850i			0.680338i
$890$		0			0
$891$	35.3964	+	20.4361i	1.18582	+	0.684635i
$892$		0			0
$893$	−15.5030	+	26.8520i	−0.518789	+	0.898569i
$894$		0			0
$895$	−7.14339	+	4.12424i	−0.238777	+	0.137858i
$896$		0			0
$897$	−2.78453	−	2.78007i	−0.0929728	−	0.0928239i
$898$		0			0
$899$	42.5514	−	24.5671i	1.41917	−	0.819358i
$900$		0			0
$901$	−5.77165	+	9.99680i	−0.192282	+	0.333042i
$902$		0			0
$903$	−1.97430	−	1.13986i	−0.0657007	−	0.0379323i
$904$		0			0
$905$		−	24.8870i		−	0.827272i
$906$		0			0
$907$	−13.9433	−	24.1506i	−0.462981	−	0.801906i	0.536127	−	0.844137i	$-0.319887\pi$
$907$	−13.9433	−	24.1506i	−0.462981	−	0.801906i	−0.999108	+	0.0422309i	$0.986553\pi$
$908$		0			0
$909$	0.995519			0.0330193
$910$		0			0
$911$	26.1435			0.866172			0.433086	−	0.901353i	$-0.357425\pi$
$911$	26.1435			0.866172			0.433086	+	0.901353i	$0.357425\pi$
$912$		0			0
$913$	36.0827	+	62.4971i	1.19416	+	2.06835i
$914$		0			0
$915$		−	97.5738i		−	3.22569i
$916$		0			0
$917$	−4.26467	−	2.46221i	−0.140832	−	0.0813094i
$918$		0			0
$919$	−1.54406	+	2.67439i	−0.0509338	+	0.0882199i	−0.890368	−	0.455241i	$-0.849553\pi$
$919$	−1.54406	+	2.67439i	−0.0509338	+	0.0882199i	0.839434	+	0.543461i	$0.182886\pi$
$920$		0			0
$921$	41.6329	−	24.0367i	1.37185	−	0.792038i
$922$		0			0
$923$	23.4418	−	23.4794i	0.771598	−	0.772835i
$924$		0			0
$925$	9.40312	−	5.42889i	0.309173	−	0.178501i
$926$		0			0
$927$	−0.397481	+	0.688457i	−0.0130550	+	0.0226119i
$928$		0			0
$929$	33.4087	+	19.2885i	1.09610	+	0.632836i	0.935195	−	0.354133i	$-0.115224\pi$
$929$	33.4087	+	19.2885i	1.09610	+	0.632836i	0.160910	+	0.986969i	$0.448557\pi$
$930$		0			0
$931$		−	5.45810i		−	0.178882i
$932$		0			0
$933$	−27.4559	−	47.5550i	−0.898865	−	1.55688i
$934$		0			0
$935$	−48.2826			−1.57901
$936$		0			0
$937$	8.28836			0.270769			0.135384	−	0.990793i	$-0.456773\pi$
$937$	8.28836			0.270769			0.135384	+	0.990793i	$0.456773\pi$
$938$		0			0
$939$	26.7234	+	46.2863i	0.872086	+	1.51050i
$940$		0			0
$941$		−	7.72406i		−	0.251797i	−0.992043	−	0.125899i	$-0.959819\pi$
$941$		−	7.72406i		−	0.251797i	0.992043	−	0.125899i	$-0.0401814\pi$
$942$		0			0
$943$	6.39592	+	3.69269i	0.208280	+	0.120250i
$944$		0			0
$945$	9.66899	−	16.7472i	0.314532	−	0.544786i
$946$		0			0
$947$	−44.8430	+	25.8901i	−1.45720	+	0.841316i	−0.998873	−	0.0474661i	$-0.984885\pi$
$947$	−44.8430	+	25.8901i	−1.45720	+	0.841316i	−0.458330	+	0.888782i	$0.651552\pi$
$948$		0			0
$949$	−25.6659	−	6.85513i	−0.833152	−	0.222527i
$950$		0			0
$951$	−5.82165	+	3.36113i	−0.188780	+	0.108992i
$952$		0			0
$953$	24.3912	−	42.2468i	0.790109	−	1.36851i	−0.135791	−	0.990738i	$-0.543357\pi$
$953$	24.3912	−	42.2468i	0.790109	−	1.36851i	0.925899	−	0.377771i	$-0.123309\pi$
$954$		0			0
$955$	62.2426	+	35.9358i	2.01412	+	1.16285i
$956$		0			0
$957$		−	71.1713i		−	2.30064i
$958$		0			0
$959$	6.46589	+	11.1993i	0.208795	+	0.361643i
$960$		0			0
$961$	2.83011			0.0912938
$962$		0			0
$963$	0.859956			0.0277117
$964$		0			0
$965$	49.0320	+	84.9259i	1.57840	+	2.73386i
$966$		0			0
$967$		−	3.09186i		−	0.0994274i	−0.998764	−	0.0497137i	$-0.984169\pi$
$967$		−	3.09186i		−	0.0994274i	0.998764	−	0.0497137i	$-0.0158309\pi$
$968$		0			0
$969$	−24.4801	−	14.1336i	−0.786415	−	0.454037i
$970$		0			0
$971$	27.2381	−	47.1777i	0.874111	−	1.51400i	0.0164037	−	0.999865i	$-0.494778\pi$
$971$	27.2381	−	47.1777i	0.874111	−	1.51400i	0.857707	−	0.514139i	$-0.171888\pi$
$972$		0			0
$973$	13.6913	−	7.90466i	0.438922	−	0.253412i
$974$		0			0
$975$	59.7236	−	16.0542i	1.91269	−	0.514146i
$976$		0			0
$977$	16.7476	−	9.66925i	0.535804	−	0.309347i	−0.207573	−	0.978220i	$-0.566556\pi$
$977$	16.7476	−	9.66925i	0.535804	−	0.309347i	0.743377	+	0.668873i	$0.233223\pi$
$978$		0			0
$979$	6.39137	−	11.0702i	0.204269	−	0.353804i
$980$		0			0
$981$	−0.924090	−	0.533524i	−0.0295039	−	0.0170341i
$982$		0			0
$983$			4.93770i			0.157488i	0.996895	+	0.0787440i	$0.0250910\pi$
$983$			4.93770i			0.157488i	−0.996895	+	0.0787440i	$0.974909\pi$
$984$		0			0
$985$	1.12842	+	1.95449i	0.0359545	+	0.0622751i
$986$		0			0
$987$	10.0931			0.321268
$988$		0			0
$989$	−0.788114			−0.0250606
$990$		0			0
$991$	24.1717	+	41.8666i	0.767839	+	1.32994i	0.938733	+	0.344646i	$0.112001\pi$
$991$	24.1717	+	41.8666i	0.767839	+	1.32994i	−0.170894	+	0.985289i	$0.554666\pi$
$992$		0			0
$993$		−	41.3181i		−	1.31119i
$994$		0			0
$995$	53.3422	+	30.7971i	1.69106	+	0.976334i
$996$		0			0
$997$	21.6634	−	37.5222i	0.686088	−	1.18834i	−0.287005	−	0.957929i	$-0.592660\pi$
$997$	21.6634	−	37.5222i	0.686088	−	1.18834i	0.973094	−	0.230411i	$-0.0740069\pi$
$998$		0			0
$999$	−4.92043	+	2.84081i	−0.155675	+	0.0898793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.f.673.7		16
4.3	odd	2		364.2.u.a.309.2	yes	16
12.11	even	2		3276.2.cf.c.1765.7		16
13.4	even	6	inner	1456.2.cc.f.225.7		16
28.3	even	6		2548.2.bb.c.569.7		16
28.11	odd	6		2548.2.bb.d.569.2		16
28.19	even	6		2548.2.bq.c.361.2		16
28.23	odd	6		2548.2.bq.e.361.7		16
28.27	even	2		2548.2.u.c.1765.7		16
52.3	odd	6		4732.2.g.k.337.13		16
52.11	even	12		4732.2.a.t.1.7		8
52.15	even	12		4732.2.a.s.1.7		8
52.23	odd	6		4732.2.g.k.337.14		16
52.43	odd	6		364.2.u.a.225.2	✓	16
156.95	even	6		3276.2.cf.c.2773.2		16
364.95	odd	6		2548.2.bq.e.1941.7		16
364.199	even	6		2548.2.bq.c.1941.2		16
364.251	even	6		2548.2.u.c.589.7		16
364.303	odd	6		2548.2.bb.d.1733.2		16
364.355	even	6		2548.2.bb.c.1733.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.2	✓	16	52.43	odd	6
364.2.u.a.309.2	yes	16	4.3	odd	2
1456.2.cc.f.225.7		16	13.4	even	6	inner
1456.2.cc.f.673.7		16	1.1	even	1	trivial
2548.2.u.c.589.7		16	364.251	even	6
2548.2.u.c.1765.7		16	28.27	even	2
2548.2.bb.c.569.7		16	28.3	even	6
2548.2.bb.c.1733.7		16	364.355	even	6
2548.2.bb.d.569.2		16	28.11	odd	6
2548.2.bb.d.1733.2		16	364.303	odd	6
2548.2.bq.c.361.2		16	28.19	even	6
2548.2.bq.c.1941.2		16	364.199	even	6
2548.2.bq.e.361.7		16	28.23	odd	6
2548.2.bq.e.1941.7		16	364.95	odd	6
3276.2.cf.c.1765.7		16	12.11	even	2
3276.2.cf.c.2773.2		16	156.95	even	6
4732.2.a.s.1.7		8	52.15	even	12
4732.2.a.t.1.7		8	52.11	even	12
4732.2.g.k.337.13		16	52.3	odd	6
4732.2.g.k.337.14		16	52.23	odd	6

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.888364 + 1.53869i) q^{3} -3.82804i q^{5} +(0.866025 + 0.500000i) q^{7} +(-0.0783804 + 0.135759i) q^{9} +(3.74735 - 2.16353i) q^{11} +(-0.930395 + 3.48344i) q^{13} +(5.89018 - 3.40069i) q^{15} +(1.45744 - 2.52436i) q^{17} +(-4.72686 - 2.72905i) q^{19} +1.77673i q^{21} +(0.307112 + 0.531934i) q^{23} -9.65391 q^{25} +5.05166 q^{27} +(-4.62872 - 8.01717i) q^{29} +5.30753i q^{31} +(6.65802 + 3.84401i) q^{33} +(1.91402 - 3.31518i) q^{35} +(-0.974022 + 0.562352i) q^{37} +(-6.18647 + 1.66297i) q^{39} +(10.4130 - 6.01195i) q^{41} +(-0.641552 + 1.11120i) q^{43} +(0.519691 + 0.300044i) q^{45} -5.68074i q^{47} +(0.500000 + 0.866025i) q^{49} +5.17895 q^{51} -3.96013 q^{53} +(-8.28210 - 14.3450i) q^{55} -9.69757i q^{57} +(6.68359 + 3.85877i) q^{59} +(7.17308 - 12.4241i) q^{61} +(-0.135759 + 0.0783804i) q^{63} +(13.3348 + 3.56159i) q^{65} +(-0.468974 + 0.270762i) q^{67} +(-0.545654 + 0.945101i) q^{69} +(-7.96918 - 4.60101i) q^{71} +7.36798i q^{73} +(-8.57618 - 14.8544i) q^{75} +4.32707 q^{77} -0.331686 q^{79} +(4.72285 + 8.18022i) q^{81} +16.6777i q^{83} +(-9.66335 - 5.57914i) q^{85} +(8.22397 - 14.2443i) q^{87} +(2.55836 - 1.47707i) q^{89} +(-2.54747 + 2.55155i) q^{91} +(-8.16665 + 4.71502i) q^{93} +(-10.4469 + 18.0946i) q^{95} +(8.36220 + 4.82792i) q^{97} +0.678314i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} - 6 q^{15} + 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} + 42 q^{33} + 6 q^{35} + 12 q^{37} - 24 q^{39} + 36 q^{41} - 6 q^{43} - 30 q^{45} + 8 q^{49} + 4 q^{51} + 8 q^{53}+ \cdots - 42 q^{97}+O(q^{100}) \) 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 - 6 * q^15 + 2 * q^17 - 44 * q^25 + 12 * q^27 - 22 * q^29 + 42 * q^33 + 6 * q^35 + 12 * q^37 - 24 * q^39 + 36 * q^41 - 6 * q^43 - 30 * q^45 + 8 * q^49 + 4 * q^51 + 8 * q^53 - 2 * q^55 + 18 * q^59 + 4 * q^61 + 12 * q^63 - 30 * q^65 - 24 * q^67 - 52 * q^69 - 36 * q^71 + 10 * q^75 - 24 * q^77 - 8 * q^79 + 42 * q^85 - 26 * q^87 - 36 * q^89 + 2 * q^91 - 42 * q^93 + 30 * q^95 - 42 * q^97

Introduction

L-functions

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