LMFDB - Embedded newform 224.2.t.a.177.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(81,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("224.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.t (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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.951588245534976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 $ x^12 - x^11 + 2x^10 - 9x^9 + 8x^8 - 13x^7 + 35x^6 - 26x^5 + 32x^4 - 72x^3 + 32x^2 - 32x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			177.3
Root			$-0.390636 + 1.35919i$ of defining polynomial
Character	$\chi$	$=$	224.177
Dual form			224.2.t.a.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.591141 + 0.341295i) q^{3} +(-2.80486 - 1.61939i) q^{5} +(-1.47779 + 2.19457i) q^{7} +(-1.26704 + 2.19457i) q^{9} +O(q^{10})$	\(q+(-0.591141 + 0.341295i) q^{3} +(-2.80486 - 1.61939i) q^{5} +(-1.47779 + 2.19457i) q^{7} +(-1.26704 + 2.19457i) q^{9} +(-2.08913 + 1.20616i) q^{11} +3.09491i q^{13} +2.21076 q^{15} +(-1.97779 - 3.42563i) q^{17} +(-2.33831 - 1.35002i) q^{19} +(0.124586 - 1.80166i) q^{21} +(1.37241 - 2.37709i) q^{23} +(2.74483 + 4.75418i) q^{25} -3.77750i q^{27} +2.01745i q^{29} +(-1.10538 - 1.91457i) q^{31} +(0.823314 - 1.42602i) q^{33} +(7.69885 - 3.76234i) q^{35} +(4.30285 + 2.48425i) q^{37} +(-1.05628 - 1.82953i) q^{39} -2.11256 q^{41} +11.5899i q^{43} +(7.10771 - 4.10364i) q^{45} +(-3.31613 + 5.74371i) q^{47} +(-2.63227 - 6.48623i) q^{49} +(2.33831 + 1.35002i) q^{51} +(2.23998 - 1.29325i) q^{53} +7.81297 q^{55} +1.84302 q^{57} +(10.6283 - 6.13625i) q^{59} +(-7.54801 - 4.35784i) q^{61} +(-2.94372 - 6.02371i) q^{63} +(5.01186 - 8.68080i) q^{65} +(-5.01858 + 2.89748i) q^{67} +1.87359i q^{69} -6.64663 q^{71} +(4.77890 + 8.27729i) q^{73} +(-3.24516 - 1.87359i) q^{75} +(0.440297 - 6.36720i) q^{77} +(0.838343 - 1.45205i) q^{79} +(-2.51186 - 4.35067i) q^{81} +6.47755i q^{83} +12.8112i q^{85} +(-0.688547 - 1.19260i) q^{87} +(-6.98965 + 12.1064i) q^{89} +(-6.79200 - 4.57363i) q^{91} +(1.30687 + 0.754520i) q^{93} +(4.37241 + 7.57324i) q^{95} -1.37709 q^{97} -6.11300i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{7}+O(q^{10}) $ 12 * q + 4 * q^7	$ 12 q + 4 q^{7} + 20 q^{15} - 2 q^{17} - 2 q^{23} - 4 q^{25} - 10 q^{31} - 14 q^{33} - 4 q^{39} - 8 q^{41} - 30 q^{47} - 12 q^{49} - 4 q^{55} - 4 q^{57} - 44 q^{63} + 8 q^{65} - 32 q^{71} - 10 q^{73} + 22 q^{79} + 22 q^{81} + 20 q^{87} - 10 q^{89} + 34 q^{95} + 40 q^{97}+O(q^{100}) $ 12 * q + 4 * q^7 + 20 * q^15 - 2 * q^17 - 2 * q^23 - 4 * q^25 - 10 * q^31 - 14 * q^33 - 4 * q^39 - 8 * q^41 - 30 * q^47 - 12 * q^49 - 4 * q^55 - 4 * q^57 - 44 * q^63 + 8 * q^65 - 32 * q^71 - 10 * q^73 + 22 * q^79 + 22 * q^81 + 20 * q^87 - 10 * q^89 + 34 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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
$3$	−0.591141	+	0.341295i	−0.341295	+	0.197047i	−0.660845	−	0.750523i	$-0.729802\pi$
$3$	−0.591141	+	0.341295i	−0.341295	+	0.197047i	0.319549	+	0.947570i	$0.396468\pi$
$4$		0			0
$5$	−2.80486	−	1.61939i	−1.25437	−	0.724212i	−0.282397	−	0.959298i	$-0.591130\pi$
$5$	−2.80486	−	1.61939i	−1.25437	−	0.724212i	−0.971975	+	0.235086i	$0.924463\pi$
$6$		0			0
$7$	−1.47779	+	2.19457i	−0.558552	+	0.829469i
$7$	−1.47779	+	2.19457i	−0.558552	+	0.829469i
$8$		0			0
$9$	−1.26704	+	2.19457i	−0.422345	+	0.731523i
$10$		0			0
$11$	−2.08913	+	1.20616i	−0.629897	+	0.363671i	−0.780712	−	0.624891i	$-0.785144\pi$
$11$	−2.08913	+	1.20616i	−0.629897	+	0.363671i	0.150815	+	0.988562i	$0.451810\pi$
$12$		0			0
$13$			3.09491i			0.858375i	0.903216	+	0.429187i	$0.141200\pi$
$13$			3.09491i			0.858375i	−0.903216	+	0.429187i	$0.858800\pi$
$14$		0			0
$15$	2.21076			0.570815
$16$		0			0
$17$	−1.97779	−	3.42563i	−0.479685	−	0.830838i	0.520044	−	0.854140i	$-0.325916\pi$
$17$	−1.97779	−	3.42563i	−0.479685	−	0.830838i	−0.999728	+	0.0233012i	$0.992582\pi$
$18$		0			0
$19$	−2.33831	−	1.35002i	−0.536444	−	0.309716i	0.207192	−	0.978300i	$-0.433567\pi$
$19$	−2.33831	−	1.35002i	−0.536444	−	0.309716i	−0.743637	+	0.668584i	$0.766901\pi$
$20$		0			0
$21$	0.124586	−	1.80166i	0.0271870	−	0.393155i
$22$		0			0
$23$	1.37241	−	2.37709i	0.286168	−	0.495657i	−0.686724	−	0.726918i	$-0.740952\pi$
$23$	1.37241	−	2.37709i	0.286168	−	0.495657i	0.972892	+	0.231261i	$0.0742852\pi$
$24$		0			0
$25$	2.74483	+	4.75418i	0.548965	+	0.950836i
$26$		0			0
$27$		−	3.77750i		−	0.726981i
$28$		0			0
$29$			2.01745i			0.374631i	0.982300	+	0.187316i	$0.0599787\pi$
$29$			2.01745i			0.374631i	−0.982300	+	0.187316i	$0.940021\pi$
$30$		0			0
$31$	−1.10538	−	1.91457i	−0.198532	−	0.343867i	0.749521	−	0.661981i	$-0.230284\pi$
$31$	−1.10538	−	1.91457i	−0.198532	−	0.343867i	−0.948053	+	0.318114i	$0.896951\pi$
$32$		0			0
$33$	0.823314	−	1.42602i	0.143321	−	0.248239i
$34$		0			0
$35$	7.69885	−	3.76234i	1.30134	−	0.635952i
$36$		0			0
$37$	4.30285	+	2.48425i	0.707385	+	0.408409i	0.810092	−	0.586303i	$-0.199417\pi$
$37$	4.30285	+	2.48425i	0.707385	+	0.408409i	−0.102707	+	0.994712i	$0.532751\pi$
$38$		0			0
$39$	−1.05628	−	1.82953i	−0.169140	−	0.292959i
$40$		0			0
$41$	−2.11256			−0.329926			−0.164963	−	0.986300i	$-0.552751\pi$
$41$	−2.11256			−0.329926			−0.164963	+	0.986300i	$0.552751\pi$
$42$		0			0
$43$			11.5899i			1.76745i	0.468011	+	0.883723i	$0.344971\pi$
$43$			11.5899i			1.76745i	−0.468011	+	0.883723i	$0.655029\pi$
$44$		0			0
$45$	7.10771	−	4.10364i	1.05956	−	0.611734i
$46$		0			0
$47$	−3.31613	+	5.74371i	−0.483708	+	0.837807i	−0.999825	−	0.0187115i	$-0.994044\pi$
$47$	−3.31613	+	5.74371i	−0.483708	+	0.837807i	0.516117	+	0.856518i	$0.327377\pi$
$48$		0			0
$49$	−2.63227	−	6.48623i	−0.376038	−	0.926604i
$50$		0			0
$51$	2.33831	+	1.35002i	0.327428	+	0.189041i
$52$		0			0
$53$	2.23998	−	1.29325i	0.307684	−	0.177642i	−0.338205	−	0.941072i	$-0.609820\pi$
$53$	2.23998	−	1.29325i	0.307684	−	0.177642i	0.645890	+	0.763431i	$0.276487\pi$
$54$		0			0
$55$	7.81297			1.05350
$56$		0			0
$57$	1.84302			0.244114
$58$		0			0
$59$	10.6283	−	6.13625i	1.38369	−	0.798872i	0.391093	−	0.920351i	$-0.372097\pi$
$59$	10.6283	−	6.13625i	1.38369	−	0.798872i	0.992594	+	0.121479i	$0.0387638\pi$
$60$		0			0
$61$	−7.54801	−	4.35784i	−0.966424	−	0.557965i	−0.0682795	−	0.997666i	$-0.521751\pi$
$61$	−7.54801	−	4.35784i	−0.966424	−	0.557965i	−0.898144	+	0.439701i	$0.855084\pi$
$62$		0			0
$63$	−2.94372	−	6.02371i	−0.370874	−	0.758916i
$64$		0			0
$65$	5.01186	−	8.68080i	0.621645	−	1.07672i
$66$		0			0
$67$	−5.01858	+	2.89748i	−0.613117	+	0.353983i	−0.774184	−	0.632960i	$-0.781840\pi$
$67$	−5.01858	+	2.89748i	−0.613117	+	0.353983i	0.161067	+	0.986943i	$0.448506\pi$
$68$		0			0
$69$			1.87359i			0.225554i
$70$		0			0
$71$	−6.64663			−0.788810			−0.394405	−	0.918937i	$-0.629049\pi$
$71$	−6.64663			−0.788810			−0.394405	+	0.918937i	$0.629049\pi$
$72$		0			0
$73$	4.77890	+	8.27729i	0.559328	+	0.968784i	0.997553	+	0.0699184i	$0.0222739\pi$
$73$	4.77890	+	8.27729i	0.559328	+	0.968784i	−0.438225	+	0.898865i	$0.644393\pi$
$74$		0			0
$75$	−3.24516	−	1.87359i	−0.374718	−	0.216344i
$76$		0			0
$77$	0.440297	−	6.36720i	0.0501765	−	0.725610i
$78$		0			0
$79$	0.838343	−	1.45205i	0.0943209	−	0.163369i	−0.815004	−	0.579455i	$-0.803265\pi$
$79$	0.838343	−	1.45205i	0.0943209	−	0.163369i	0.909325	+	0.416087i	$0.136599\pi$
$80$		0			0
$81$	−2.51186	−	4.35067i	−0.279096	−	0.483408i
$82$		0			0
$83$			6.47755i			0.711003i	0.934676	+	0.355502i	$0.115690\pi$
$83$			6.47755i			0.711003i	−0.934676	+	0.355502i	$0.884310\pi$
$84$		0			0
$85$			12.8112i			1.38957i
$86$		0			0
$87$	−0.688547	−	1.19260i	−0.0738200	−	0.127860i
$88$		0			0
$89$	−6.98965	+	12.1064i	−0.740902	+	1.28328i	0.211184	+	0.977446i	$0.432268\pi$
$89$	−6.98965	+	12.1064i	−0.740902	+	1.28328i	−0.952085	+	0.305833i	$0.901065\pi$
$90$		0			0
$91$	−6.79200	−	4.57363i	−0.711995	−	0.479447i
$92$		0			0
$93$	1.30687	+	0.754520i	0.135516	+	0.0782401i
$94$		0			0
$95$	4.37241	+	7.57324i	0.448600	+	0.776998i
$96$		0			0
$97$	−1.37709			−0.139823			−0.0699113	−	0.997553i	$-0.522272\pi$
$97$	−1.37709			−0.139823			−0.0699113	+	0.997553i	$0.522272\pi$
$98$		0			0
$99$		−	6.11300i		−	0.614379i
$100$		0			0
$101$	0.689470	−	0.398066i	0.0686048	−	0.0396090i	−0.465305	−	0.885150i	$-0.654055\pi$
$101$	0.689470	−	0.398066i	0.0686048	−	0.0396090i	0.533910	+	0.845541i	$0.320722\pi$
$102$		0			0
$103$	−1.32799	+	2.30015i	−0.130851	+	0.226641i	−0.924005	−	0.382381i	$-0.875104\pi$
$103$	−1.32799	+	2.30015i	−0.130851	+	0.226641i	0.793154	+	0.609022i	$0.208438\pi$
$104$		0			0
$105$	−3.26704	+	4.85166i	−0.318830	+	0.473473i
$106$		0			0
$107$	−4.70287	−	2.71520i	−0.454643	−	0.262489i	0.255146	−	0.966903i	$-0.417877\pi$
$107$	−4.70287	−	2.71520i	−0.454643	−	0.262489i	−0.709789	+	0.704414i	$0.751210\pi$
$108$		0			0
$109$	−11.9614	+	6.90593i	−1.14570	+	0.661468i	−0.947835	−	0.318762i	$-0.896733\pi$
$109$	−11.9614	+	6.90593i	−1.14570	+	0.661468i	−0.197862	+	0.980230i	$0.563400\pi$
$110$		0			0
$111$	−3.39145			−0.321903
$112$		0			0
$113$	4.53407			0.426529			0.213265	−	0.976994i	$-0.431590\pi$
$113$	4.53407			0.426529			0.213265	+	0.976994i	$0.431590\pi$
$114$		0			0
$115$	−7.69885	+	4.44493i	−0.717922	+	0.414492i
$116$		0			0
$117$	−6.79200	−	3.92136i	−0.627921	−	0.362530i
$118$		0			0
$119$	10.4406	+	0.721973i	0.957084	+	0.0661831i
$120$		0			0
$121$	−2.59035	+	4.48662i	−0.235486	+	0.407874i
$122$		0			0
$123$	1.24882	−	0.721006i	0.112602	−	0.0650109i
$124$		0			0
$125$		−	1.58587i		−	0.141845i
$126$		0			0
$127$	15.4897			1.37448			0.687242	−	0.726428i	$-0.258821\pi$
$127$	15.4897			1.37448			0.687242	+	0.726428i	$0.258821\pi$
$128$		0			0
$129$	−3.95558	−	6.85127i	−0.348270	−	0.603221i
$130$		0			0
$131$	−14.5574	−	8.40471i	−1.27189	−	0.734323i	−0.296543	−	0.955020i	$-0.595834\pi$
$131$	−14.5574	−	8.40471i	−1.27189	−	0.734323i	−0.975343	+	0.220696i	$0.929167\pi$
$132$		0			0
$133$	6.41824	−	3.13652i	0.556532	−	0.271971i
$134$		0			0
$135$	−6.11724	+	10.5954i	−0.526488	+	0.911904i
$136$		0			0
$137$	0.443721	+	0.768547i	0.0379096	+	0.0656614i	0.884358	−	0.466810i	$-0.154597\pi$
$137$	0.443721	+	0.768547i	0.0379096	+	0.0656614i	−0.846448	+	0.532471i	$0.821263\pi$
$138$		0			0
$139$			2.44264i			0.207182i	0.994620	+	0.103591i	$0.0330333\pi$
$139$			2.44264i			0.207182i	−0.994620	+	0.103591i	$0.966967\pi$
$140$		0			0
$141$		−	4.52712i		−	0.381253i
$142$		0			0
$143$	−3.73296	−	6.46568i	−0.312166	−	0.540688i
$144$		0			0
$145$	3.26704	−	5.65867i	0.271312	−	0.469927i
$146$		0			0
$147$	3.76976	+	2.93589i	0.310925	+	0.242148i
$148$		0			0
$149$	−8.16541	−	4.71430i	−0.668936	−	0.386210i	0.126737	−	0.991936i	$-0.459549\pi$
$149$	−8.16541	−	4.71430i	−0.668936	−	0.386210i	−0.795673	+	0.605726i	$0.792883\pi$
$150$		0			0
$151$	−3.52689	−	6.10875i	−0.287014	−	0.497123i	0.686081	−	0.727525i	$-0.259329\pi$
$151$	−3.52689	−	6.10875i	−0.287014	−	0.497123i	−0.973096	+	0.230402i	$0.925996\pi$
$152$		0			0
$153$	10.0237			0.810370
$154$		0			0
$155$			7.16014i			0.575116i
$156$		0			0
$157$	−7.54801	+	4.35784i	−0.602397	+	0.347794i	−0.769984	−	0.638063i	$-0.779736\pi$
$157$	−7.54801	+	4.35784i	−0.602397	+	0.347794i	0.167587	+	0.985857i	$0.446402\pi$
$158$		0			0
$159$	−0.882761	+	1.52899i	−0.0700075	+	0.121257i
$160$		0			0
$161$	3.18855	+	6.52470i	0.251293	+	0.514218i
$162$		0			0
$163$	17.1711	+	9.91376i	1.34495	+	0.776505i	0.987529	−	0.157439i	$-0.0503239\pi$
$163$	17.1711	+	9.91376i	1.34495	+	0.776505i	0.357418	+	0.933945i	$0.383657\pi$
$164$		0			0
$165$	−4.61856	+	2.66653i	−0.359555	+	0.207589i
$166$		0			0
$167$	−22.1600			−1.71479			−0.857396	−	0.514657i	$-0.827919\pi$
$167$	−22.1600			−1.71479			−0.857396	+	0.514657i	$0.827919\pi$
$168$		0			0
$169$	3.42151			0.263193
$170$		0			0
$171$	5.92543	−	3.42105i	0.453129	−	0.261614i
$172$		0			0
$173$	18.8200	+	10.8657i	1.43086	+	0.826105i	0.997186	−	0.0749674i	$-0.0238853\pi$
$173$	18.8200	+	10.8657i	1.43086	+	0.826105i	0.433669	+	0.901072i	$0.357219\pi$
$174$		0			0
$175$	−14.4897	−	1.00197i	−1.09531	−	0.0757419i
$176$		0			0
$177$	−4.18855	+	7.25478i	−0.314830	+	0.545302i
$178$		0			0
$179$	3.27141	−	1.88875i	0.244517	−	0.141172i	−0.372734	−	0.927938i	$-0.621580\pi$
$179$	3.27141	−	1.88875i	0.244517	−	0.141172i	0.617251	+	0.786766i	$0.288246\pi$
$180$		0			0
$181$		−	14.0326i		−	1.04303i	−0.853242	−	0.521516i	$-0.825367\pi$
$181$		−	14.0326i		−	1.04303i	0.853242	−	0.521516i	$-0.174633\pi$
$182$		0			0
$183$	5.94925			0.439781
$184$		0			0
$185$	−8.04593	−	13.9360i	−0.591549	−	1.02459i
$186$		0			0
$187$	8.26374	+	4.77107i	0.604304	+	0.348895i
$188$		0			0
$189$	8.28999	+	5.58236i	0.603008	+	0.406057i
$190$		0			0
$191$	3.63945	−	6.30371i	0.263341	−	0.456120i	−0.703786	−	0.710412i	$-0.748509\pi$
$191$	3.63945	−	6.30371i	0.263341	−	0.456120i	0.967128	+	0.254291i	$0.0818422\pi$
$192$		0			0
$193$	−4.76704	−	8.25675i	−0.343139	−	0.594334i	0.641875	−	0.766809i	$-0.278157\pi$
$193$	−4.76704	−	8.25675i	−0.343139	−	0.594334i	−0.985014	+	0.172476i	$0.944823\pi$
$194$		0			0
$195$			6.84210i			0.489973i
$196$		0			0
$197$		−	11.6667i		−	0.831221i	−0.909543	−	0.415611i	$-0.863568\pi$
$197$		−	11.6667i		−	0.831221i	0.909543	−	0.415611i	$-0.136432\pi$
$198$		0			0
$199$	9.48247	+	16.4241i	0.672195	+	1.16428i	0.977280	+	0.211950i	$0.0679815\pi$
$199$	9.48247	+	16.4241i	0.672195	+	1.16428i	−0.305086	+	0.952325i	$0.598685\pi$
$200$		0			0
$201$	1.97779	−	3.42563i	0.139503	−	0.241626i
$202$		0			0
$203$	−4.42744	−	2.98137i	−0.310745	−	0.209251i
$204$		0			0
$205$	5.92543	+	3.42105i	0.413850	+	0.238936i
$206$		0			0
$207$	3.47779	+	6.02371i	0.241723	+	0.418677i
$208$		0			0
$209$	6.51337			0.450540
$210$		0			0
$211$		−	16.1268i		−	1.11022i	−0.831778	−	0.555109i	$-0.812677\pi$
$211$		−	16.1268i		−	1.11022i	0.831778	−	0.555109i	$-0.187323\pi$
$212$		0			0
$213$	3.92909	−	2.26846i	0.269217	−	0.155433i
$214$		0			0
$215$	18.7685	−	32.5081i	1.28000	−	2.21703i
$216$		0			0
$217$	5.83518	+	0.403507i	0.396118	+	0.0273918i
$218$		0			0
$219$	−5.65000	−	3.26203i	−0.381792	−	0.220428i
$220$		0			0
$221$	10.6020	−	6.12109i	0.713170	−	0.411749i
$222$		0			0
$223$	7.71477			0.516619			0.258310	−	0.966062i	$-0.416835\pi$
$223$	7.71477			0.516619			0.258310	+	0.966062i	$0.416835\pi$
$224$		0			0
$225$	−13.9112			−0.927411
$226$		0			0
$227$	1.83996	−	1.06230i	0.122122	−	0.0705074i	−0.437694	−	0.899124i	$-0.644205\pi$
$227$	1.83996	−	1.06230i	0.122122	−	0.0705074i	0.559817	+	0.828616i	$0.310871\pi$
$228$		0			0
$229$	8.11289	+	4.68398i	0.536115	+	0.309526i	0.743503	−	0.668733i	$-0.233163\pi$
$229$	8.11289	+	4.68398i	0.536115	+	0.309526i	−0.207388	+	0.978259i	$0.566496\pi$
$230$		0			0
$231$	1.91282	+	3.91418i	0.125854	+	0.257534i
$232$		0			0
$233$	4.41366	−	7.64469i	0.289149	−	0.500820i	−0.684458	−	0.729052i	$-0.739961\pi$
$233$	4.41366	−	7.64469i	0.289149	−	0.500820i	0.973607	+	0.228232i	$0.0732945\pi$
$234$		0			0
$235$	18.6026	−	10.7402i	1.21350	−	0.700614i
$236$		0			0
$237$			1.14449i			0.0743426i
$238$		0			0
$239$	−5.93489			−0.383896			−0.191948	−	0.981405i	$-0.561480\pi$
$239$	−5.93489			−0.383896			−0.191948	+	0.981405i	$0.561480\pi$
$240$		0			0
$241$	5.34302	+	9.25439i	0.344174	+	0.596128i	0.985203	−	0.171389i	$-0.0548255\pi$
$241$	5.34302	+	9.25439i	0.344174	+	0.596128i	−0.641029	+	0.767517i	$0.721492\pi$
$242$		0			0
$243$	12.7840	+	7.38083i	0.820092	+	0.473480i
$244$		0			0
$245$	−3.12057	+	22.4556i	−0.199366	+	1.43464i
$246$		0			0
$247$	4.17820	−	7.23685i	0.265852	−	0.460470i
$248$		0			0
$249$	−2.21076	−	3.82914i	−0.140101	−	0.242662i
$250$		0			0
$251$			3.82402i			0.241370i	0.992691	+	0.120685i	$0.0385091\pi$
$251$			3.82402i			0.241370i	−0.992691	+	0.120685i	$0.961491\pi$
$252$		0			0
$253$			6.62141i			0.416284i
$254$		0			0
$255$	−4.37241	−	7.57324i	−0.273811	−	0.474255i
$256$		0			0
$257$	−6.20291	+	10.7438i	−0.386927	+	0.670177i	−0.992034	−	0.125967i	$-0.959797\pi$
$257$	−6.20291	+	10.7438i	−0.386927	+	0.670177i	0.605108	+	0.796144i	$0.293130\pi$
$258$		0			0
$259$	−11.8106	+	5.77170i	−0.733874	+	0.358636i
$260$		0			0
$261$	−4.42744	−	2.55618i	−0.274052	−	0.158224i
$262$		0			0
$263$	−0.672005	−	1.16395i	−0.0414376	−	0.0717720i	0.844563	−	0.535457i	$-0.179860\pi$
$263$	−0.672005	−	1.16395i	−0.0414376	−	0.0717720i	−0.886000	+	0.463685i	$0.846527\pi$
$264$		0			0
$265$	−8.37709			−0.514601
$266$		0			0
$267$		−	9.54214i		−	0.583970i
$268$		0			0
$269$	−1.68912	+	0.975212i	−0.102987	+	0.0594597i	−0.550609	−	0.834763i	$-0.685604\pi$
$269$	−1.68912	+	0.975212i	−0.102987	+	0.0594597i	0.447622	+	0.894223i	$0.352271\pi$
$270$		0			0
$271$	−13.0190	+	22.5496i	−0.790850	+	1.36979i	0.134590	+	0.990901i	$0.457028\pi$
$271$	−13.0190	+	22.5496i	−0.790850	+	1.36979i	−0.925441	+	0.378892i	$0.876305\pi$
$272$		0			0
$273$	5.57599	+	0.385584i	0.337474	+	0.0233366i
$274$		0			0
$275$	−11.4686	−	6.62141i	−0.691583	−	0.399286i
$276$		0			0
$277$	13.9578	−	8.05852i	0.838641	−	0.484189i	−0.0181613	−	0.999835i	$-0.505781\pi$
$277$	13.9578	−	8.05852i	0.838641	−	0.484189i	0.856802	+	0.515646i	$0.172448\pi$
$278$		0			0
$279$	5.60221			0.335396
$280$		0			0
$281$	−16.1313			−0.962312			−0.481156	−	0.876635i	$-0.659783\pi$
$281$	−16.1313			−0.962312			−0.481156	+	0.876635i	$0.659783\pi$
$282$		0			0
$283$	−22.7949	+	13.1606i	−1.35501	+	0.782318i	−0.988947	−	0.148270i	$-0.952629\pi$
$283$	−22.7949	+	13.1606i	−1.35501	+	0.782318i	−0.366068	+	0.930588i	$0.619296\pi$
$284$		0			0
$285$	−5.16942	−	2.98457i	−0.306210	−	0.176791i
$286$		0			0
$287$	3.12192	−	4.63616i	0.184281	−	0.273664i
$288$		0			0
$289$	0.676686	−	1.17205i	0.0398050	−	0.0689444i
$290$		0			0
$291$	0.814056	−	0.469996i	0.0477208	−	0.0275516i
$292$		0			0
$293$			9.64929i			0.563718i	0.959456	+	0.281859i	$0.0909510\pi$
$293$			9.64929i			0.563718i	−0.959456	+	0.281859i	$0.909049\pi$
$294$		0			0
$295$	−39.7479			−2.31421
$296$		0			0
$297$	4.55628	+	7.89171i	0.264382	+	0.457923i
$298$		0			0
$299$	7.35688	+	4.24750i	0.425460	+	0.245639i
$300$		0			0
$301$	−25.4349	−	17.1275i	−1.46604	−	0.987211i
$302$		0			0
$303$	−0.271716	+	0.470626i	−0.0156097	+	0.0270367i
$304$		0			0
$305$	14.1141	+	24.4463i	0.808169	+	1.39979i
$306$		0			0
$307$		−	25.2741i		−	1.44247i	−0.692691	−	0.721235i	$-0.743575\pi$
$307$		−	25.2741i		−	1.44247i	0.692691	−	0.721235i	$-0.256425\pi$
$308$		0			0
$309$		−	1.81295i		−	0.103135i
$310$		0			0
$311$	11.2742	+	19.5275i	0.639302	+	1.10730i	0.985586	+	0.169174i	$0.0541100\pi$
$311$	11.2742	+	19.5275i	0.639302	+	1.10730i	−0.346284	+	0.938130i	$0.612557\pi$
$312$		0			0
$313$	12.6901	−	21.9798i	0.717285	−	1.24237i	−0.244787	−	0.969577i	$-0.578718\pi$
$313$	12.6901	−	21.9798i	0.717285	−	1.24237i	0.962072	−	0.272797i	$-0.0879486\pi$
$314$		0			0
$315$	−1.49799	+	21.6627i	−0.0844023	+	1.22055i
$316$		0			0
$317$	−14.8384	−	8.56693i	−0.833405	−	0.481167i	0.0216120	−	0.999766i	$-0.493120\pi$
$317$	−14.8384	−	8.56693i	−0.833405	−	0.481167i	−0.855017	+	0.518600i	$0.826453\pi$
$318$		0			0
$319$	−2.43337	−	4.21473i	−0.136243	−	0.235979i
$320$		0			0
$321$	3.70674			0.206890
$322$		0			0
$323$			10.6802i			0.594264i
$324$		0			0
$325$	−14.7138	+	8.49500i	−0.816173	+	0.471218i
$326$		0			0
$327$	4.71392	−	8.16475i	0.260681	−	0.451512i
$328$		0			0
$329$	−7.70442	−	15.7655i	−0.424758	−	0.869180i
$330$		0			0
$331$	−7.43566	−	4.29298i	−0.408701	−	0.235963i	0.281531	−	0.959552i	$-0.409158\pi$
$331$	−7.43566	−	4.29298i	−0.408701	−	0.235963i	−0.690231	+	0.723589i	$0.742491\pi$
$332$		0			0
$333$	−10.9037	+	6.29527i	−0.597521	+	0.344979i
$334$		0			0
$335$	18.7685			1.02544
$336$		0			0
$337$	−3.18070			−0.173264			−0.0866319	−	0.996240i	$-0.527610\pi$
$337$	−3.18070			−0.173264			−0.0866319	+	0.996240i	$0.527610\pi$
$338$		0			0
$339$	−2.68027	+	1.54746i	−0.145572	+	0.0840463i
$340$		0			0
$341$	4.61856	+	2.66653i	0.250109	+	0.144401i
$342$		0			0
$343$	18.1244	+	3.80860i	0.978627	+	0.205645i
$344$		0			0
$345$	3.03407	−	5.25516i	0.163349	−	0.282929i
$346$		0			0
$347$	−19.0373	+	10.9912i	−1.02198	+	0.590039i	−0.914676	−	0.404187i	$-0.867554\pi$
$347$	−19.0373	+	10.9912i	−1.02198	+	0.590039i	−0.107302	+	0.994226i	$0.534221\pi$
$348$		0			0
$349$		−	15.5480i		−	0.832265i	−0.909304	−	0.416132i	$-0.863385\pi$
$349$		−	15.5480i		−	0.832265i	0.909304	−	0.416132i	$-0.136615\pi$
$350$		0			0
$351$	11.6910			0.624022
$352$		0			0
$353$	13.2804	+	23.0023i	0.706845	+	1.22429i	0.966022	+	0.258461i	$0.0832155\pi$
$353$	13.2804	+	23.0023i	0.706845	+	1.22429i	−0.259177	+	0.965830i	$0.583451\pi$
$354$		0			0
$355$	18.6429	+	10.7635i	0.989460	+	0.571265i
$356$		0			0
$357$	−6.41824	+	3.13652i	−0.339689	+	0.166002i
$358$		0			0
$359$	−15.5062	+	26.8575i	−0.818386	+	1.41749i	0.0884855	+	0.996077i	$0.471797\pi$
$359$	−15.5062	+	26.8575i	−0.818386	+	1.41749i	−0.906871	+	0.421408i	$0.861536\pi$
$360$		0			0
$361$	−5.85488	−	10.1410i	−0.308152	−	0.533735i
$362$		0			0
$363$		−	3.53630i		−	0.185607i
$364$		0			0
$365$		−	30.9555i		−	1.62029i
$366$		0			0
$367$	−6.38677	−	11.0622i	−0.333387	−	0.577443i	0.649787	−	0.760117i	$-0.274858\pi$
$367$	−6.38677	−	11.0622i	−0.333387	−	0.577443i	−0.983174	+	0.182674i	$0.941525\pi$
$368$		0			0
$369$	2.67669	−	4.63616i	0.139343	−	0.241349i
$370$		0			0
$371$	−0.472088	+	6.82694i	−0.0245096	+	0.354437i
$372$		0			0
$373$	5.73431	+	3.31070i	0.296911	+	0.171422i	0.641054	−	0.767495i	$-0.278497\pi$
$373$	5.73431	+	3.31070i	0.296911	+	0.171422i	−0.344143	+	0.938917i	$0.611831\pi$
$374$		0			0
$375$	0.541251	+	0.937474i	0.0279501	+	0.0484109i
$376$		0			0
$377$	−6.24384			−0.321574
$378$		0			0
$379$		−	18.7804i		−	0.964683i	−0.875983	−	0.482341i	$-0.839786\pi$
$379$		−	18.7804i		−	0.964683i	0.875983	−	0.482341i	$-0.160214\pi$
$380$		0			0
$381$	−9.15656	+	5.28654i	−0.469105	+	0.270838i
$382$		0			0
$383$	−10.2179	+	17.6980i	−0.522112	+	0.904325i	0.477557	+	0.878601i	$0.341522\pi$
$383$	−10.2179	+	17.6980i	−0.522112	+	0.904325i	−0.999669	+	0.0257240i	$0.991811\pi$
$384$		0			0
$385$	−11.5459	+	17.1461i	−0.588435	+	0.873846i
$386$		0			0
$387$	−25.4349	−	14.6848i	−1.29293	−	0.746472i
$388$		0			0
$389$	2.05734	−	1.18781i	0.104311	−	0.0602242i	−0.446937	−	0.894566i	$-0.647485\pi$
$389$	2.05734	−	1.18781i	0.104311	−	0.0602242i	0.551248	+	0.834341i	$0.314152\pi$
$390$		0			0
$391$	−10.8574			−0.549082
$392$		0			0
$393$	11.4740			0.578785
$394$		0			0
$395$	−4.70287	+	2.71520i	−0.236627	+	0.136617i
$396$		0			0
$397$	19.1993	+	11.0847i	0.963583	+	0.556325i	0.897274	−	0.441474i	$-0.145544\pi$
$397$	19.1993	+	11.0847i	0.963583	+	0.556325i	0.0663091	+	0.997799i	$0.478878\pi$
$398$		0			0
$399$	−2.72360	+	4.04464i	−0.136351	+	0.202485i
$400$		0			0
$401$	−13.1585	+	22.7912i	−0.657104	+	1.13814i	0.324258	+	0.945969i	$0.394885\pi$
$401$	−13.1585	+	22.7912i	−0.657104	+	1.13814i	−0.981362	+	0.192168i	$0.938448\pi$
$402$		0			0
$403$	5.92543	−	3.42105i	0.295167	−	0.170415i
$404$		0			0
$405$			16.2707i			0.808497i
$406$		0			0
$407$	−11.9856			−0.594106
$408$		0			0
$409$	0.331162	+	0.573590i	0.0163749	+	0.0283622i	0.874097	−	0.485752i	$-0.161454\pi$
$409$	0.331162	+	0.573590i	0.0163749	+	0.0283622i	−0.857722	+	0.514114i	$0.828121\pi$
$410$		0			0
$411$	−0.524603	−	0.302880i	−0.0258768	−	0.0149399i
$412$		0			0
$413$	−2.23998	+	32.3926i	−0.110222	+	1.59394i
$414$		0			0
$415$	10.4897	−	18.1686i	0.514917	−	0.891862i
$416$		0			0
$417$	−0.833662	−	1.44395i	−0.0408246	−	0.0707103i
$418$		0			0
$419$		−	7.55501i		−	0.369086i	−0.982824	−	0.184543i	$-0.940919\pi$
$419$		−	7.55501i		−	0.369086i	0.982824	−	0.184543i	$-0.0590805\pi$
$420$		0			0
$421$		−	12.5905i		−	0.613625i	−0.951770	−	0.306813i	$-0.900737\pi$
$421$		−	12.5905i		−	0.613625i	0.951770	−	0.306813i	$-0.0992625\pi$
$422$		0			0
$423$	−8.40332	−	14.5550i	−0.408583	−	0.707687i
$424$		0			0
$425$	10.8574	−	18.8055i	0.526661	−	0.912203i
$426$		0			0
$427$	20.7180	−	10.1246i	1.00261	−	0.489966i
$428$		0			0
$429$	4.41342	+	2.54809i	0.213082	+	0.123023i
$430$		0			0
$431$	−6.45241	−	11.1759i	−0.310802	−	0.538325i	0.667734	−	0.744400i	$-0.267264\pi$
$431$	−6.45241	−	11.1759i	−0.310802	−	0.538325i	−0.978536	+	0.206075i	$0.933931\pi$
$432$		0			0
$433$	−40.5815			−1.95022			−0.975112	−	0.221715i	$-0.928835\pi$
$433$	−40.5815			−1.95022			−0.975112	+	0.221715i	$0.928835\pi$
$434$		0			0
$435$			4.46009i			0.213845i
$436$		0			0
$437$	−6.41824	+	3.70557i	−0.307026	+	0.177262i
$438$		0			0
$439$	18.2273	−	31.5706i	0.869941	−	1.50678i	0.00788596	−	0.999969i	$-0.497490\pi$
$439$	18.2273	−	31.5706i	0.869941	−	1.50678i	0.862055	−	0.506814i	$-0.169177\pi$
$440$		0			0
$441$	17.5697	+	2.44159i	0.836650	+	0.116266i
$442$		0			0
$443$	28.1274	+	16.2393i	1.33637	+	0.771555i	0.986267	−	0.165156i	$-0.0528128\pi$
$443$	28.1274	+	16.2393i	1.33637	+	0.771555i	0.350104	+	0.936711i	$0.386146\pi$
$444$		0			0
$445$	39.2100	−	22.6379i	1.85873	−	1.07314i
$446$		0			0
$447$	6.43587			0.304406
$448$		0			0
$449$	25.9823			1.22618			0.613091	−	0.790012i	$-0.289926\pi$
$449$	25.9823			1.22618			0.613091	+	0.790012i	$0.289926\pi$
$450$		0			0
$451$	4.41342	−	2.54809i	0.207820	−	0.119985i
$452$		0			0
$453$	4.16978	+	2.40742i	0.195913	+	0.113111i
$454$		0			0
$455$	11.6441	+	23.8273i	0.545885	+	1.11704i
$456$		0			0
$457$	5.73448	−	9.93241i	0.268248	−	0.464618i	−0.700162	−	0.713984i	$-0.746889\pi$
$457$	5.73448	−	9.93241i	0.268248	−	0.464618i	0.968409	+	0.249366i	$0.0802221\pi$
$458$		0			0
$459$	−12.9403	+	7.47111i	−0.604004	+	0.348722i
$460$		0			0
$461$			25.1973i			1.17355i	0.809749	+	0.586777i	$0.199604\pi$
$461$			25.1973i			1.17355i	−0.809749	+	0.586777i	$0.800396\pi$
$462$		0			0
$463$	31.8223			1.47891			0.739454	−	0.673207i	$-0.235084\pi$
$463$	31.8223			1.47891			0.739454	+	0.673207i	$0.235084\pi$
$464$		0			0
$465$	−2.44372	−	4.23265i	−0.113325	−	0.196284i
$466$		0			0
$467$	12.3089	+	7.10656i	0.569589	+	0.328852i	0.756985	−	0.653432i	$-0.226671\pi$
$467$	12.3089	+	7.10656i	0.569589	+	0.328852i	−0.187396	+	0.982284i	$0.560005\pi$
$468$		0			0
$469$	1.05770	−	15.2955i	0.0488398	−	0.706280i
$470$		0			0
$471$	2.97462	−	5.15220i	0.137063	−	0.237401i
$472$		0			0
$473$	−13.9793	−	24.2129i	−0.642769	−	1.11331i
$474$		0			0
$475$		−	14.8223i		−	0.680094i
$476$		0			0
$477$			6.55438i			0.300104i
$478$		0			0
$479$	−5.77020	−	9.99428i	−0.263647	−	0.456650i	0.703561	−	0.710635i	$-0.251592\pi$
$479$	−5.77020	−	9.99428i	−0.263647	−	0.456650i	−0.967208	+	0.253984i	$0.918259\pi$
$480$		0			0
$481$	−7.68855	+	13.3170i	−0.350568	+	0.607201i
$482$		0			0
$483$	−4.11173	−	2.76878i	−0.187090	−	0.125984i
$484$		0			0
$485$	3.86255	+	2.23005i	0.175390	+	0.101261i
$486$		0			0
$487$	−8.80829	−	15.2564i	−0.399142	−	0.691333i	0.594479	−	0.804111i	$-0.297358\pi$
$487$	−8.80829	−	15.2564i	−0.399142	−	0.691333i	−0.993620	+	0.112778i	$0.964025\pi$
$488$		0			0
$489$	−13.5341			−0.612032
$490$		0			0
$491$		−	26.8502i		−	1.21173i	−0.795567	−	0.605866i	$-0.792827\pi$
$491$		−	26.8502i		−	1.21173i	0.795567	−	0.605866i	$-0.207173\pi$
$492$		0			0
$493$	6.91105	−	3.99010i	0.311258	−	0.179705i
$494$		0			0
$495$	−9.89930	+	17.1461i	−0.444941	+	0.770660i
$496$		0			0
$497$	9.82233	−	14.5865i	0.440592	−	0.654293i
$498$		0			0
$499$	2.21925	+	1.28129i	0.0993474	+	0.0573583i	0.548851	−	0.835921i	$-0.315066\pi$
$499$	2.21925	+	1.28129i	0.0993474	+	0.0573583i	−0.449503	+	0.893279i	$0.648399\pi$
$500$		0			0
$501$	13.0997	−	7.56310i	0.585251	−	0.337895i
$502$		0			0
$503$	14.6941			0.655176			0.327588	−	0.944821i	$-0.393764\pi$
$503$	14.6941			0.655176			0.327588	+	0.944821i	$0.393764\pi$
$504$		0			0
$505$	−2.57849			−0.114741
$506$		0			0
$507$	−2.02259	+	1.16775i	−0.0898266	+	0.0518614i
$508$		0			0
$509$	−11.0283	−	6.36720i	−0.488821	−	0.282221i	0.235264	−	0.971932i	$-0.424405\pi$
$509$	−11.0283	−	6.36720i	−0.488821	−	0.282221i	−0.724085	+	0.689710i	$0.757738\pi$
$510$		0			0
$511$	−25.2273	−	1.74449i	−1.11599	−	0.0771716i
$512$		0			0
$513$	−5.09971	+	8.83296i	−0.225158	+	0.389985i
$514$		0			0
$515$	7.44968	−	4.30107i	0.328272	−	0.189528i
$516$		0			0
$517$		−	15.9992i		−	0.703643i
$518$		0			0
$519$	−14.8337			−0.651126
$520$		0			0
$521$	−17.0134	−	29.4680i	−0.745369	−	1.29102i	−0.950022	−	0.312183i	$-0.898940\pi$
$521$	−17.0134	−	29.4680i	−0.745369	−	1.29102i	0.204652	−	0.978835i	$-0.434394\pi$
$522$		0			0
$523$	5.88515	+	3.39779i	0.257340	+	0.148575i	0.623120	−	0.782126i	$-0.285865\pi$
$523$	5.88515	+	3.39779i	0.257340	+	0.148575i	−0.365781	+	0.930701i	$0.619198\pi$
$524$		0			0
$525$	8.90739	−	4.35294i	0.388750	−	0.189978i
$526$		0			0
$527$	−4.37241	+	7.57324i	−0.190465	+	0.329896i
$528$		0			0
$529$	7.73296	+	13.3939i	0.336216	+	0.582343i
$530$		0			0
$531$			31.0994i			1.34960i
$532$		0			0
$533$		−	6.53819i		−	0.283200i
$534$		0			0
$535$	8.79392	+	15.2315i	0.380195	+	0.658516i
$536$		0			0
$537$	−1.28924	+	2.23304i	−0.0556350	+	0.0963626i
$538$		0			0
$539$	13.3226	+	10.3757i	0.573845	+	0.446911i
$540$		0			0
$541$	21.3952	+	12.3525i	0.919852	+	0.531077i	0.883588	−	0.468266i	$-0.155121\pi$
$541$	21.3952	+	12.3525i	0.919852	+	0.531077i	0.0362640	+	0.999342i	$0.488454\pi$
$542$		0			0
$543$	4.78924	+	8.29521i	0.205526	+	0.355982i
$544$		0			0
$545$	44.7335			1.91617
$546$		0			0
$547$			27.5793i			1.17920i	0.807694	+	0.589602i	$0.200716\pi$
$547$			27.5793i			1.17920i	−0.807694	+	0.589602i	$0.799284\pi$
$548$		0			0
$549$	19.1272	−	11.0431i	0.816328	−	0.471307i
$550$		0			0
$551$	2.72360	−	4.71742i	0.116029	−	0.200969i
$552$		0			0
$553$	1.94773	+	3.98563i	0.0828261	+	0.169486i
$554$		0			0
$555$	9.51256	+	5.49208i	0.403785	+	0.233126i
$556$		0			0
$557$	−39.1575	+	22.6076i	−1.65916	+	0.957914i	−0.686050	+	0.727555i	$0.740657\pi$
$557$	−39.1575	+	22.6076i	−1.65916	+	0.957914i	−0.973106	+	0.230359i	$0.926010\pi$
$558$		0			0
$559$	−35.8698			−1.51713
$560$		0			0
$561$	−6.51337			−0.274995
$562$		0			0
$563$	13.1895	−	7.61497i	0.555872	−	0.320933i	−0.195615	−	0.980681i	$-0.562670\pi$
$563$	13.1895	−	7.61497i	0.555872	−	0.320933i	0.751487	+	0.659748i	$0.229337\pi$
$564$		0			0
$565$	−12.7174	−	7.34241i	−0.535026	−	0.308898i
$566$		0			0
$567$	13.2599	+	0.916930i	0.556862	+	0.0385074i
$568$		0			0
$569$	−7.04343	+	12.1996i	−0.295276	+	0.511433i	−0.975049	−	0.221989i	$-0.928745\pi$
$569$	−7.04343	+	12.1996i	−0.295276	+	0.511433i	0.679773	+	0.733423i	$0.262078\pi$
$570$		0			0
$571$	19.2480	−	11.1129i	0.805505	−	0.465058i	−0.0398876	−	0.999204i	$-0.512700\pi$
$571$	19.2480	−	11.1129i	0.805505	−	0.465058i	0.845392	+	0.534146i	$0.179367\pi$
$572$		0			0
$573$			4.96851i			0.207562i
$574$		0			0
$575$	15.0681			0.628385
$576$		0			0
$577$	−4.68070	−	8.10721i	−0.194860	−	0.337507i	0.751995	−	0.659169i	$-0.229092\pi$
$577$	−4.68070	−	8.10721i	−0.194860	−	0.337507i	−0.946855	+	0.321662i	$0.895759\pi$
$578$		0			0
$579$	5.63598	+	3.25393i	0.234223	+	0.135229i
$580$		0			0
$581$	−14.2154	−	9.57246i	−0.589755	−	0.397133i
$582$		0			0
$583$	−3.11974	+	5.40355i	−0.129206	+	0.223792i
$584$		0			0
$585$	12.7004	+	21.9978i	0.525097	+	0.909495i
$586$		0			0
$587$			13.0157i			0.537217i	0.963249	+	0.268608i	$0.0865637\pi$
$587$			13.0157i			0.537217i	−0.963249	+	0.268608i	$0.913436\pi$
$588$		0			0
$589$			5.96914i			0.245954i
$590$		0			0
$591$	3.98180	+	6.89669i	0.163790	+	0.283692i
$592$		0			0
$593$	0.698895	−	1.21052i	0.0287002	−	0.0497101i	−0.851319	−	0.524649i	$-0.824197\pi$
$593$	0.698895	−	1.21052i	0.0287002	−	0.0497101i	0.880019	+	0.474939i	$0.157530\pi$
$594$		0			0
$595$	−28.1151	−	18.9323i	−1.15261	−	0.776150i
$596$		0			0
$597$	−11.2110	−	6.47265i	−0.458834	−	0.264908i
$598$		0			0
$599$	−15.9302	−	27.5919i	−0.650891	−	1.12738i	−0.982907	−	0.184102i	$-0.941062\pi$
$599$	−15.9302	−	27.5919i	−0.650891	−	1.12738i	0.332017	−	0.943274i	$-0.392271\pi$
$600$		0			0
$601$	34.4927			1.40699			0.703493	−	0.710702i	$-0.251623\pi$
$601$	34.4927			1.40699			0.703493	+	0.710702i	$0.251623\pi$
$602$		0			0
$603$		−	14.6848i		−	0.598012i
$604$		0			0
$605$	14.5311	−	8.38955i	0.590775	−	0.341084i
$606$		0			0
$607$	−4.61573	+	7.99467i	−0.187347	+	0.324494i	−0.944365	−	0.328900i	$-0.893322\pi$
$607$	−4.61573	+	7.99467i	−0.187347	+	0.324494i	0.757018	+	0.653394i	$0.226655\pi$
$608$		0			0
$609$	3.63477	+	0.251347i	0.147288	+	0.0101851i
$610$		0			0
$611$	−17.7763	−	10.2631i	−0.719152	−	0.415202i
$612$		0			0
$613$	−28.0431	+	16.1907i	−1.13265	+	0.653935i	−0.944600	−	0.328225i	$-0.893550\pi$
$613$	−28.0431	+	16.1907i	−1.13265	+	0.653935i	−0.188049	+	0.982160i	$0.560216\pi$
$614$		0			0
$615$	−4.67035			−0.188327
$616$		0			0
$617$	−10.1600			−0.409026			−0.204513	−	0.978864i	$-0.565561\pi$
$617$	−10.1600			−0.409026			−0.204513	+	0.978864i	$0.565561\pi$
$618$		0			0
$619$	−32.1866	+	18.5829i	−1.29369	+	0.746911i	−0.979306	−	0.202385i	$-0.935131\pi$
$619$	−32.1866	+	18.5829i	−1.29369	+	0.746911i	−0.314382	+	0.949297i	$0.601797\pi$
$620$		0			0
$621$	−8.97946	−	5.18430i	−0.360333	−	0.208039i
$622$		0			0
$623$	−16.2392	−	33.2301i	−0.650608	−	1.33133i
$624$		0			0
$625$	11.1560	−	19.3227i	0.446240	−	0.772910i
$626$		0			0
$627$	−3.85032	+	2.22298i	−0.153767	+	0.0887774i
$628$		0			0
$629$		−	19.6533i		−	0.783630i
$630$		0			0
$631$	7.31198			0.291085			0.145543	−	0.989352i	$-0.453507\pi$
$631$	7.31198			0.291085			0.145543	+	0.989352i	$0.453507\pi$
$632$		0			0
$633$	5.50401	+	9.53323i	0.218765	+	0.378912i
$634$		0			0
$635$	−43.4463	−	25.0837i	−1.72411	−	0.995418i
$636$		0			0
$637$	20.0743	−	8.14664i	0.795373	−	0.322782i
$638$		0			0
$639$	8.42151	−	14.5865i	0.333150	−	0.577032i
$640$		0			0
$641$	−6.85337	−	11.8704i	−0.270692	−	0.468852i	0.698347	−	0.715759i	$-0.253919\pi$
$641$	−6.85337	−	11.8704i	−0.270692	−	0.468852i	−0.969039	+	0.246907i	$0.920586\pi$
$642$		0			0
$643$		−	30.5812i		−	1.20600i	−0.797740	−	0.603002i	$-0.793971\pi$
$643$		−	30.5812i		−	1.20600i	0.797740	−	0.603002i	$-0.206029\pi$
$644$		0			0
$645$			25.6225i			1.00888i
$646$		0			0
$647$	21.2979	+	36.8891i	0.837308	+	1.45026i	0.892137	+	0.451765i	$0.149205\pi$
$647$	21.2979	+	36.8891i	0.837308	+	1.45026i	−0.0548287	+	0.998496i	$0.517461\pi$
$648$		0			0
$649$	−14.8026	+	25.6389i	−0.581054	+	1.00641i
$650$		0			0
$651$	−3.58712	+	1.75299i	−0.140591	+	0.0687050i
$652$		0			0
$653$	−26.9273	−	15.5465i	−1.05375	−	0.608381i	−0.130051	−	0.991507i	$-0.541514\pi$
$653$	−26.9273	−	15.5465i	−1.05375	−	0.608381i	−0.923696	+	0.383126i	$0.874848\pi$
$654$		0			0
$655$	27.2210	+	47.1481i	1.06361	+	1.84223i
$656$		0			0
$657$	−24.2201			−0.944917
$658$		0			0
$659$			35.8472i			1.39641i	0.715899	+	0.698204i	$0.246017\pi$
$659$			35.8472i			1.39641i	−0.715899	+	0.698204i	$0.753983\pi$
$660$		0			0
$661$	−23.6297	+	13.6426i	−0.919087	+	0.530635i	−0.883344	−	0.468726i	$-0.844713\pi$
$661$	−23.6297	+	13.6426i	−0.919087	+	0.530635i	−0.0357432	+	0.999361i	$0.511380\pi$
$662$		0			0
$663$	−4.17820	+	7.23685i	−0.162268	+	0.281056i
$664$		0			0
$665$	−23.0815	−	1.59611i	−0.895063	−	0.0618943i
$666$		0			0
$667$	4.79566	+	2.76878i	0.185689	+	0.107208i
$668$		0			0
$669$	−4.56051	+	2.63301i	−0.176320	+	0.101798i
$670$		0			0
$671$	21.0251			0.811663
$672$		0			0
$673$	−32.2963			−1.24493			−0.622465	−	0.782648i	$-0.713869\pi$
$673$	−32.2963			−1.24493			−0.622465	+	0.782648i	$0.713869\pi$
$674$		0			0
$675$	17.9589	−	10.3686i	0.691239	−	0.399087i
$676$		0			0
$677$	13.5785	+	7.83953i	0.521863	+	0.301298i	0.737697	−	0.675132i	$-0.235914\pi$
$677$	13.5785	+	7.83953i	0.521863	+	0.301298i	−0.215834	+	0.976430i	$0.569247\pi$
$678$		0			0
$679$	2.03506	−	3.02213i	0.0780983	−	0.115979i
$680$		0			0
$681$	−0.725117	+	1.25594i	−0.0277865	+	0.0481277i
$682$		0			0
$683$	−16.5012	+	9.52698i	−0.631401	+	0.364540i	−0.781295	−	0.624162i	$-0.785440\pi$
$683$	−16.5012	+	9.52698i	−0.631401	+	0.364540i	0.149893	+	0.988702i	$0.452107\pi$
$684$		0			0
$685$		−	2.87422i		−	0.109818i
$686$		0			0
$687$	−6.39448			−0.243965
$688$		0			0
$689$	4.00250	+	6.93253i	0.152483	+	0.264108i
$690$		0			0
$691$	−26.9066	−	15.5345i	−1.02358	−	0.590961i	−0.108438	−	0.994103i	$-0.534585\pi$
$691$	−26.9066	−	15.5345i	−1.02358	−	0.590961i	−0.915138	+	0.403142i	$0.867918\pi$
$692$		0			0
$693$	13.4154	+	9.03373i	0.509609	+	0.343163i
$694$		0			0
$695$	3.95558	−	6.85127i	0.150044	−	0.259883i
$696$		0			0
$697$	4.17820	+	7.23685i	0.158261	+	0.274115i
$698$		0			0
$699$			6.02545i			0.227903i
$700$		0			0
$701$			33.5258i			1.26625i	0.774048	+	0.633127i	$0.218229\pi$
$701$			33.5258i			1.26625i	−0.774048	+	0.633127i	$0.781771\pi$
$702$		0			0
$703$	−6.70759	−	11.6179i	−0.252981	−	0.438177i
$704$		0			0
$705$	−7.33116	+	12.6979i	−0.276108	+	0.478232i
$706$		0			0
$707$	−0.145310	+	2.10135i	−0.00546494	+	0.0790293i
$708$		0			0
$709$	7.16576	+	4.13715i	0.269116	+	0.155374i	0.628486	−	0.777821i	$-0.283675\pi$
$709$	7.16576	+	4.13715i	0.269116	+	0.155374i	−0.359370	+	0.933195i	$0.617008\pi$
$710$		0			0
$711$	2.12442	+	3.67960i	0.0796720	+	0.137996i
$712$		0			0
$713$	−6.06814			−0.227254
$714$		0			0
$715$			24.1805i			0.904298i
$716$		0			0
$717$	3.50835	−	2.02555i	0.131022	−	0.0756455i
$718$		0			0
$719$	−1.81462	+	3.14301i	−0.0676739	+	0.117215i	−0.897877	−	0.440246i	$-0.854891\pi$
$719$	−1.81462	+	3.14301i	−0.0676739	+	0.117215i	0.830203	+	0.557461i	$0.188224\pi$
$720$		0			0
$721$	−3.08535	−	6.31352i	−0.114904	−	0.235128i
$722$		0			0
$723$	−6.31696	−	3.64710i	−0.234930	−	0.135637i
$724$		0			0
$725$	−9.59133	+	5.53756i	−0.356213	+	0.205660i
$726$		0			0
$727$	−28.1550			−1.04421			−0.522106	−	0.852881i	$-0.674853\pi$
$727$	−28.1550			−1.04421			−0.522106	+	0.852881i	$0.674853\pi$
$728$		0			0
$729$	4.99500			0.185000
$730$		0			0
$731$	39.7028	−	22.9224i	1.46846	−	0.847816i
$732$		0			0
$733$	−25.4264	−	14.6799i	−0.939145	−	0.542215i	−0.0494525	−	0.998776i	$-0.515748\pi$
$733$	−25.4264	−	14.6799i	−0.939145	−	0.542215i	−0.889692	+	0.456561i	$0.849081\pi$
$734$		0			0
$735$	−5.81930	−	14.3395i	−0.214648	−	0.528919i
$736$		0			0
$737$	6.98965	−	12.1064i	0.257467	−	0.445946i
$738$		0			0
$739$	−11.2457	+	6.49271i	−0.413680	+	0.238838i	−0.692370	−	0.721543i	$-0.743433\pi$
$739$	−11.2457	+	6.49271i	−0.413680	+	0.238838i	0.278690	+	0.960381i	$0.410100\pi$
$740$		0			0
$741$			5.70400i			0.209542i
$742$		0			0
$743$	−21.8510			−0.801637			−0.400819	−	0.916157i	$-0.631274\pi$
$743$	−21.8510			−0.801637			−0.400819	+	0.916157i	$0.631274\pi$
$744$		0			0
$745$	15.2685	+	26.4459i	0.559396	+	0.968903i
$746$		0			0
$747$	−14.2154	−	8.20728i	−0.520115	−	0.300289i
$748$		0			0
$749$	12.9086	−	6.30827i	0.471668	−	0.230499i
$750$		0			0
$751$	6.03724	−	10.4568i	0.220302	−	0.381574i	−0.734598	−	0.678503i	$-0.762629\pi$
$751$	6.03724	−	10.4568i	0.220302	−	0.381574i	0.954900	+	0.296929i	$0.0959624\pi$
$752$		0			0
$753$	−1.30512	−	2.26053i	−0.0475612	−	0.0823783i
$754$		0			0
$755$			22.8456i			0.831436i
$756$		0			0
$757$			27.2309i			0.989725i	0.868971	+	0.494862i	$0.164782\pi$
$757$			27.2309i			0.989725i	−0.868971	+	0.494862i	$0.835218\pi$
$758$		0			0
$759$	−2.25985	−	3.91418i	−0.0820275	−	0.142076i
$760$		0			0
$761$	−15.2423	+	26.4005i	−0.552534	+	0.957017i	0.445557	+	0.895254i	$0.353006\pi$
$761$	−15.2423	+	26.4005i	−0.552534	+	0.957017i	−0.998091	+	0.0617632i	$0.980328\pi$
$762$		0			0
$763$	2.52094	−	36.4557i	0.0912642	−	1.31978i
$764$		0			0
$765$	−28.1151	−	16.2323i	−1.01650	−	0.586879i
$766$		0			0
$767$	18.9912	+	32.8937i	0.685731	+	1.18772i
$768$		0			0
$769$	36.6991			1.32340			0.661701	−	0.749768i	$-0.269835\pi$
$769$	36.6991			1.32340			0.661701	+	0.749768i	$0.269835\pi$
$770$		0			0
$771$		−	8.46809i		−	0.304971i
$772$		0			0
$773$	28.6220	−	16.5249i	1.02946	−	0.594359i	0.112631	−	0.993637i	$-0.464072\pi$
$773$	28.6220	−	16.5249i	1.02946	−	0.594359i	0.916830	+	0.399277i	$0.130739\pi$
$774$		0			0
$775$	6.06814	−	10.5103i	0.217974	−	0.377542i
$776$		0			0
$777$	5.01186	−	7.44278i	0.179800	−	0.267008i
$778$		0			0
$779$	4.93981	+	2.85200i	0.176987	+	0.102183i
$780$		0			0
$781$	13.8857	−	8.01691i	0.496869	−	0.286867i
$782$		0			0
$783$	7.62093			0.272350
$784$		0			0
$785$	28.2281			1.00751
$786$		0			0
$787$	14.9922	−	8.65572i	0.534413	−	0.308543i	−0.208399	−	0.978044i	$-0.566825\pi$
$787$	14.9922	−	8.65572i	0.534413	−	0.308543i	0.742811	+	0.669501i	$0.233492\pi$
$788$		0			0
$789$	0.794499	+	0.458704i	0.0282849	+	0.0163303i
$790$		0			0
$791$	−6.70041	+	9.95033i	−0.238239	+	0.353793i
$792$		0			0
$793$	13.4872	−	23.3604i	0.478943	−	0.829553i
$794$		0			0
$795$	4.95204	−	2.85906i	0.175631	−	0.101400i
$796$		0			0
$797$		−	41.7331i		−	1.47826i	−0.673561	−	0.739131i	$-0.735236\pi$
$797$		−	41.7331i		−	1.47826i	0.673561	−	0.739131i	$-0.264764\pi$
$798$		0			0
$799$	26.2345			0.928109
$800$		0			0
$801$	−17.7123	−	30.6786i	−0.625832	−	1.08397i
$802$		0			0
$803$	−19.9675	−	11.5282i	−0.704638	−	0.406823i
$804$		0			0
$805$	1.62258	−	23.4643i	0.0571884	−	0.827010i
$806$		0			0
$807$	0.665670	−	1.15297i	0.0234327	−	0.0405866i
$808$		0			0
$809$	4.86273	+	8.42250i	0.170965	+	0.296119i	0.938757	−	0.344579i	$-0.111978\pi$
$809$	4.86273	+	8.42250i	0.170965	+	0.296119i	−0.767793	+	0.640698i	$0.778645\pi$
$810$		0			0
$811$			55.3405i			1.94327i	0.236492	+	0.971633i	$0.424002\pi$
$811$			55.3405i			1.94327i	−0.236492	+	0.971633i	$0.575998\pi$
$812$		0			0
$813$		−	17.7733i		−	0.623339i
$814$		0			0
$815$	−32.1084	−	55.6134i	−1.12471	−	1.94805i
$816$		0			0
$817$	15.6466	−	27.1008i	0.547406	−	0.948135i
$818$		0			0
$819$	18.6429	−	9.11056i	0.651434	−	0.318349i
$820$		0			0
$821$	36.5157	+	21.0823i	1.27441	+	0.735779i	0.975814	−	0.218602i	$-0.0701496\pi$
$821$	36.5157	+	21.0823i	1.27441	+	0.735779i	0.298592	+	0.954381i	$0.403483\pi$
$822$		0			0
$823$	7.60689	+	13.1755i	0.265160	+	0.459270i	0.967605	−	0.252467i	$-0.0812420\pi$
$823$	7.60689	+	13.1755i	0.265160	+	0.459270i	−0.702446	+	0.711737i	$0.747909\pi$
$824$		0			0
$825$	9.03942			0.314712
$826$		0			0
$827$			1.24390i			0.0432548i	0.999766	+	0.0216274i	$0.00688475\pi$
$827$			1.24390i			0.0432548i	−0.999766	+	0.0216274i	$0.993115\pi$
$828$		0			0
$829$	−18.4517	+	10.6531i	−0.640855	+	0.369998i	−0.784944	−	0.619567i	$-0.787308\pi$
$829$	−18.4517	+	10.6531i	−0.640855	+	0.369998i	0.144089	+	0.989565i	$0.453975\pi$
$830$		0			0
$831$	−5.50067	+	9.52744i	−0.190816	+	0.330503i
$832$		0			0
$833$	−17.0134	+	21.8456i	−0.589478	+	0.756905i
$834$		0			0
$835$	62.1557	+	35.8856i	2.15099	+	1.24187i
$836$		0			0
$837$	−7.23230	+	4.17557i	−0.249985	+	0.144329i
$838$		0			0
$839$	20.9379			0.722857			0.361429	−	0.932400i	$-0.382289\pi$
$839$	20.9379			0.722857			0.361429	+	0.932400i	$0.382289\pi$
$840$		0			0
$841$	24.9299			0.859651
$842$		0			0
$843$	9.53586	−	5.50553i	0.328432	−	0.189621i
$844$		0			0
$845$	−9.59686	−	5.54075i	−0.330142	−	0.190608i
$846$		0			0
$847$	−6.01820	−	12.3150i	−0.206788	−	0.423148i
$848$		0			0
$849$	8.98332	−	15.5596i	0.308307	−	0.534003i
$850$		0			0
$851$	11.8106	−	6.81884i	0.404861	−	0.233747i
$852$		0			0
$853$			17.4758i			0.598361i	0.954197	+	0.299180i	$0.0967133\pi$
$853$			17.4758i			0.598361i	−0.954197	+	0.299180i	$0.903287\pi$
$854$		0			0
$855$	−22.1600			−0.757856
$856$		0			0
$857$	−1.75517	−	3.04005i	−0.0599556	−	0.103846i	0.834490	−	0.551024i	$-0.185763\pi$
$857$	−1.75517	−	3.04005i	−0.0599556	−	0.103846i	−0.894445	+	0.447177i	$0.852429\pi$
$858$		0			0
$859$	4.45370	+	2.57134i	0.151958	+	0.0877331i	0.574051	−	0.818819i	$-0.305371\pi$
$859$	4.45370	+	2.57134i	0.151958	+	0.0877331i	−0.422093	+	0.906553i	$0.638704\pi$
$860$		0			0
$861$	−0.263196	+	3.80612i	−0.00896970	+	0.129712i
$862$		0			0
$863$	−20.1410	+	34.8852i	−0.685606	+	1.18750i	0.287640	+	0.957739i	$0.407129\pi$
$863$	−20.1410	+	34.8852i	−0.685606	+	1.18750i	−0.973246	+	0.229766i	$0.926204\pi$
$864$		0			0
$865$	−35.1916	−	60.9536i	−1.19655	−	2.07248i
$866$		0			0
$867$			0.923798i			0.0313738i
$868$		0			0
$869$			4.04471i			0.137207i
$870$		0			0
$871$	−8.96744	−	15.5321i	−0.303850	−	0.526284i
$872$		0			0
$873$	1.74483	−	3.02213i	0.0590534	−	0.102284i
$874$		0			0
$875$	3.48031	+	2.34359i	0.117656	+	0.0792277i
$876$		0			0
$877$	36.3471	+	20.9850i	1.22735	+	0.708613i	0.966476	−	0.256759i	$-0.0826546\pi$
$877$	36.3471	+	20.9850i	1.22735	+	0.708613i	0.260878	+	0.965372i	$0.415988\pi$
$878$		0			0
$879$	−3.29326	−	5.70409i	−0.111079	−	0.192394i
$880$		0			0
$881$	−16.5992			−0.559241			−0.279620	−	0.960111i	$-0.590209\pi$
$881$	−16.5992			−0.559241			−0.279620	+	0.960111i	$0.590209\pi$
$882$		0			0
$883$			12.8210i			0.431462i	0.976453	+	0.215731i	$0.0692135\pi$
$883$			12.8210i			0.431462i	−0.976453	+	0.215731i	$0.930787\pi$
$884$		0			0
$885$	23.4966	−	13.5658i	0.789829	−	0.456008i
$886$		0			0
$887$	4.14980	−	7.18766i	0.139337	−	0.241338i	−0.787909	−	0.615792i	$-0.788836\pi$
$887$	4.14980	−	7.18766i	0.139337	−	0.241338i	0.927246	+	0.374454i	$0.122170\pi$
$888$		0			0
$889$	−22.8905	+	33.9931i	−0.767722	+	1.14009i
$890$		0			0
$891$	10.4952	+	6.05942i	0.351603	+	0.202998i
$892$		0			0
$893$	15.5083	−	8.95370i	0.518964	−	0.299624i
$894$		0			0
$895$	−12.2345			−0.408954
$896$		0			0
$897$	−5.79861			−0.193610
$898$		0			0
$899$	3.86255	−	2.23005i	0.128823	−	0.0743762i
$900$		0			0
$901$	−8.86041	−	5.11556i	−0.295183	−	0.170424i
$902$		0			0
$903$	20.8811	+	1.44395i	0.694880	+	0.0480515i
$904$		0			0
$905$	−22.7241	+	39.3593i	−0.755376	+	1.30835i
$906$		0			0
$907$	14.2277	−	8.21434i	0.472422	−	0.272753i	−0.244831	−	0.969566i	$-0.578733\pi$
$907$	14.2277	−	8.21434i	0.472422	−	0.272753i	0.717253	+	0.696813i	$0.245399\pi$
$908$		0			0
$909$			2.01745i			0.0669147i
$910$		0			0
$911$	37.1630			1.23127			0.615633	−	0.788033i	$-0.288900\pi$
$911$	37.1630			1.23127			0.615633	+	0.788033i	$0.288900\pi$
$912$		0			0
$913$	−7.81297	−	13.5325i	−0.258571	−	0.447859i
$914$		0			0
$915$	−16.6868	−	9.63413i	−0.551649	−	0.318495i
$916$		0			0
$917$	39.9575	−	19.5268i	1.31951	−	0.644831i
$918$		0			0
$919$	−18.1528	+	31.4416i	−0.598806	+	1.03716i	0.394191	+	0.919028i	$0.371025\pi$
$919$	−18.1528	+	31.4416i	−0.598806	+	1.03716i	−0.992998	+	0.118135i	$0.962309\pi$
$920$		0			0
$921$	8.62593	+	14.9406i	0.284234	+	0.492308i
$922$		0			0
$923$		−	20.5707i		−	0.677094i
$924$		0			0
$925$			27.2754i			0.896809i
$926$		0			0
$927$	−3.36523	−	5.82875i	−0.110529	−	0.191441i
$928$		0			0
$929$	10.8263	−	18.7518i	0.355201	−	0.615226i	−0.631952	−	0.775008i	$-0.717746\pi$
$929$	10.8263	−	18.7518i	0.355201	−	0.615226i	0.987152	+	0.159782i	$0.0510792\pi$
$930$		0			0
$931$	−2.60150	+	18.7204i	−0.0852608	+	0.613536i
$932$		0			0
$933$	−13.3293	−	7.69567i	−0.436382	−	0.251945i
$934$		0			0
$935$	−15.4524	−	26.7644i	−0.505348	−	0.875288i
$936$		0			0
$937$	−15.8637			−0.518245			−0.259123	−	0.965844i	$-0.583433\pi$
$937$	−15.8637			−0.518245			−0.259123	+	0.965844i	$0.583433\pi$
$938$		0			0
$939$			17.3242i			0.565355i
$940$		0			0
$941$	12.7230	−	7.34561i	0.414757	−	0.239460i	−0.278075	−	0.960559i	$-0.589696\pi$
$941$	12.7230	−	7.34561i	0.414757	−	0.239460i	0.692832	+	0.721099i	$0.256363\pi$
$942$		0			0
$943$	−2.89930	+	5.02174i	−0.0944143	+	0.163530i
$944$		0			0
$945$	−14.2123	−	29.0824i	−0.462325	−	0.946052i
$946$		0			0
$947$	−12.0598	−	6.96270i	−0.391889	−	0.226257i	0.291089	−	0.956696i	$-0.405982\pi$
$947$	−12.0598	−	6.96270i	−0.391889	−	0.226257i	−0.682978	+	0.730439i	$0.739316\pi$
$948$		0			0
$949$	−25.6175	+	14.7903i	−0.831579	+	0.480112i
$950$		0			0
$951$	11.6954			0.379250
$952$		0			0
$953$	11.2883			0.365663			0.182831	−	0.983144i	$-0.441474\pi$
$953$	11.2883			0.365663			0.182831	+	0.983144i	$0.441474\pi$
$954$		0			0
$955$	−20.4163	+	11.7873i	−0.660655	+	0.381430i
$956$		0			0
$957$	2.87693	+	1.66100i	0.0929980	+	0.0536924i
$958$		0			0
$959$	−2.34236	−	0.161976i	−0.0756386	−	0.00523047i
$960$		0			0
$961$	13.0563	−	22.6141i	0.421170	−	0.729488i
$962$		0			0
$963$	11.9174	−	6.88051i	0.384033	−	0.221721i
$964$		0			0
$965$			30.8787i			0.994020i
$966$		0			0
$967$	36.4276			1.17143			0.585716	−	0.810517i	$-0.300813\pi$
$967$	36.4276			1.17143			0.585716	+	0.810517i	$0.300813\pi$
$968$		0			0
$969$	−3.64512	−	6.31352i	−0.117098	−	0.202820i
$970$		0			0
$971$	5.75503	+	3.32267i	0.184688	+	0.106629i	0.589493	−	0.807773i	$-0.299327\pi$
$971$	5.75503	+	3.32267i	0.184688	+	0.106629i	−0.404806	+	0.914403i	$0.632661\pi$
$972$		0			0
$973$	−5.36055	−	3.60971i	−0.171851	−	0.115722i
$974$		0			0
$975$	5.79861	−	10.0435i	0.185704	−	0.321649i
$976$		0			0
$977$	22.7226	+	39.3567i	0.726961	+	1.25913i	0.958162	+	0.286227i	$0.0924012\pi$
$977$	22.7226	+	39.3567i	0.726961	+	1.25913i	−0.231201	+	0.972906i	$0.574265\pi$
$978$		0			0
$979$		−	33.7226i		−	1.07778i
$980$		0			0
$981$		−	35.0002i		−	1.11747i
$982$		0			0
$983$	−9.26538	−	16.0481i	−0.295520	−	0.511855i	0.679586	−	0.733596i	$-0.262159\pi$
$983$	−9.26538	−	16.0481i	−0.295520	−	0.511855i	−0.975106	+	0.221741i	$0.928826\pi$
$984$		0			0
$985$	−18.8930	+	32.7236i	−0.601980	+	1.04266i
$986$		0			0
$987$	9.93508	+	6.69014i	0.316237	+	0.212950i
$988$		0			0
$989$	27.5503	+	15.9061i	0.876047	+	0.505786i
$990$		0			0
$991$	−18.2392	−	31.5911i	−0.579386	−	1.00353i	−0.995550	−	0.0942363i	$-0.969959\pi$
$991$	−18.2392	−	31.5911i	−0.579386	−	1.00353i	0.416164	−	0.909290i	$-0.363374\pi$
$992$		0			0
$993$	5.86069			0.185983
$994$		0			0
$995$		−	61.4232i		−	1.94724i
$996$		0			0
$997$	−13.2738	+	7.66365i	−0.420386	+	0.242710i	−0.695243	−	0.718775i	$-0.744703\pi$
$997$	−13.2738	+	7.66365i	−0.420386	+	0.242710i	0.274856	+	0.961485i	$0.411370\pi$
$998$		0			0
$999$	9.38427	−	16.2540i	0.296905	−	0.514255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.t.a.177.3		12
3.2	odd	2		2016.2.cr.c.1297.6		12
4.3	odd	2		56.2.p.a.37.5	yes	12
7.2	even	3		1568.2.b.f.785.3		6
7.3	odd	6		1568.2.t.g.753.3		12
7.4	even	3	inner	224.2.t.a.81.4		12
7.5	odd	6		1568.2.b.e.785.4		6
7.6	odd	2		1568.2.t.g.177.4		12
8.3	odd	2		56.2.p.a.37.1	✓	12
8.5	even	2	inner	224.2.t.a.177.4		12
12.11	even	2		504.2.cj.c.37.2		12
21.11	odd	6		2016.2.cr.c.1873.1		12
24.5	odd	2		2016.2.cr.c.1297.1		12
24.11	even	2		504.2.cj.c.37.6		12
28.3	even	6		392.2.p.g.165.1		12
28.11	odd	6		56.2.p.a.53.1	yes	12
28.19	even	6		392.2.b.f.197.3		6
28.23	odd	6		392.2.b.e.197.3		6
28.27	even	2		392.2.p.g.373.5		12
56.3	even	6		392.2.p.g.165.5		12
56.5	odd	6		1568.2.b.e.785.3		6
56.11	odd	6		56.2.p.a.53.5	yes	12
56.13	odd	2		1568.2.t.g.177.3		12
56.19	even	6		392.2.b.f.197.4		6
56.27	even	2		392.2.p.g.373.1		12
56.37	even	6		1568.2.b.f.785.4		6
56.45	odd	6		1568.2.t.g.753.4		12
56.51	odd	6		392.2.b.e.197.4		6
56.53	even	6	inner	224.2.t.a.81.3		12
84.11	even	6		504.2.cj.c.109.6		12
168.11	even	6		504.2.cj.c.109.2		12
168.53	odd	6		2016.2.cr.c.1873.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.1	✓	12	8.3	odd	2
56.2.p.a.37.5	yes	12	4.3	odd	2
56.2.p.a.53.1	yes	12	28.11	odd	6
56.2.p.a.53.5	yes	12	56.11	odd	6
224.2.t.a.81.3		12	56.53	even	6	inner
224.2.t.a.81.4		12	7.4	even	3	inner
224.2.t.a.177.3		12	1.1	even	1	trivial
224.2.t.a.177.4		12	8.5	even	2	inner
392.2.b.e.197.3		6	28.23	odd	6
392.2.b.e.197.4		6	56.51	odd	6
392.2.b.f.197.3		6	28.19	even	6
392.2.b.f.197.4		6	56.19	even	6
392.2.p.g.165.1		12	28.3	even	6
392.2.p.g.165.5		12	56.3	even	6
392.2.p.g.373.1		12	56.27	even	2
392.2.p.g.373.5		12	28.27	even	2
504.2.cj.c.37.2		12	12.11	even	2
504.2.cj.c.37.6		12	24.11	even	2
504.2.cj.c.109.2		12	168.11	even	6
504.2.cj.c.109.6		12	84.11	even	6
1568.2.b.e.785.3		6	56.5	odd	6
1568.2.b.e.785.4		6	7.5	odd	6
1568.2.b.f.785.3		6	7.2	even	3
1568.2.b.f.785.4		6	56.37	even	6
1568.2.t.g.177.3		12	56.13	odd	2
1568.2.t.g.177.4		12	7.6	odd	2
1568.2.t.g.753.3		12	7.3	odd	6
1568.2.t.g.753.4		12	56.45	odd	6
2016.2.cr.c.1297.1		12	24.5	odd	2
2016.2.cr.c.1297.6		12	3.2	odd	2
2016.2.cr.c.1873.1		12	21.11	odd	6
2016.2.cr.c.1873.6		12	168.53	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.591141 + 0.341295i) q^{3} +(-2.80486 - 1.61939i) q^{5} +(-1.47779 + 2.19457i) q^{7} +(-1.26704 + 2.19457i) q^{9} +O(q^{10})\)	\(q+(-0.591141 + 0.341295i) q^{3} +(-2.80486 - 1.61939i) q^{5} +(-1.47779 + 2.19457i) q^{7} +(-1.26704 + 2.19457i) q^{9} +(-2.08913 + 1.20616i) q^{11} +3.09491i q^{13} +2.21076 q^{15} +(-1.97779 - 3.42563i) q^{17} +(-2.33831 - 1.35002i) q^{19} +(0.124586 - 1.80166i) q^{21} +(1.37241 - 2.37709i) q^{23} +(2.74483 + 4.75418i) q^{25} -3.77750i q^{27} +2.01745i q^{29} +(-1.10538 - 1.91457i) q^{31} +(0.823314 - 1.42602i) q^{33} +(7.69885 - 3.76234i) q^{35} +(4.30285 + 2.48425i) q^{37} +(-1.05628 - 1.82953i) q^{39} -2.11256 q^{41} +11.5899i q^{43} +(7.10771 - 4.10364i) q^{45} +(-3.31613 + 5.74371i) q^{47} +(-2.63227 - 6.48623i) q^{49} +(2.33831 + 1.35002i) q^{51} +(2.23998 - 1.29325i) q^{53} +7.81297 q^{55} +1.84302 q^{57} +(10.6283 - 6.13625i) q^{59} +(-7.54801 - 4.35784i) q^{61} +(-2.94372 - 6.02371i) q^{63} +(5.01186 - 8.68080i) q^{65} +(-5.01858 + 2.89748i) q^{67} +1.87359i q^{69} -6.64663 q^{71} +(4.77890 + 8.27729i) q^{73} +(-3.24516 - 1.87359i) q^{75} +(0.440297 - 6.36720i) q^{77} +(0.838343 - 1.45205i) q^{79} +(-2.51186 - 4.35067i) q^{81} +6.47755i q^{83} +12.8112i q^{85} +(-0.688547 - 1.19260i) q^{87} +(-6.98965 + 12.1064i) q^{89} +(-6.79200 - 4.57363i) q^{91} +(1.30687 + 0.754520i) q^{93} +(4.37241 + 7.57324i) q^{95} -1.37709 q^{97} -6.11300i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{7}+O(q^{10}) \) 12 * q + 4 * q^7	\( 12 q + 4 q^{7} + 20 q^{15} - 2 q^{17} - 2 q^{23} - 4 q^{25} - 10 q^{31} - 14 q^{33} - 4 q^{39} - 8 q^{41} - 30 q^{47} - 12 q^{49} - 4 q^{55} - 4 q^{57} - 44 q^{63} + 8 q^{65} - 32 q^{71} - 10 q^{73} + 22 q^{79} + 22 q^{81} + 20 q^{87} - 10 q^{89} + 34 q^{95} + 40 q^{97}+O(q^{100}) \) 12 * q + 4 * q^7 + 20 * q^15 - 2 * q^17 - 2 * q^23 - 4 * q^25 - 10 * q^31 - 14 * q^33 - 4 * q^39 - 8 * q^41 - 30 * q^47 - 12 * q^49 - 4 * q^55 - 4 * q^57 - 44 * q^63 + 8 * q^65 - 32 * q^71 - 10 * q^73 + 22 * q^79 + 22 * q^81 + 20 * q^87 - 10 * q^89 + 34 * q^95 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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