LMFDB - Embedded newform 1224.2.f.c.613.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1224,2,Mod(613,1224)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1224, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1224.613"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1224.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,1,0,1,0,0,-12,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.77368920740$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.4469724736.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 2x^{5} - 4x^{4} + 4x^{3} - 8x + 16 $ x^8 - x^7 + 2x^5 - 4x^4 + 4x^3 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 136)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			613.8
Root			$1.33209 + 0.474920i$ of defining polynomial
Character	$\chi$	$=$	1224.613
Dual form			1224.2.f.c.613.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.33209 + 0.474920i) q^{2} +(1.54890 + 1.26527i) q^{4} -1.58069i q^{5} -5.01127 q^{7} +(1.46237 + 2.42105i) q^{8} +(0.750703 - 2.10562i) q^{10} +2.65428i q^{11} +6.34060i q^{13} +(-6.67544 - 2.37995i) q^{14} +(0.798200 + 3.91955i) q^{16} -1.00000 q^{17} +2.44834i q^{19} +(2.00000 - 2.44834i) q^{20} +(-1.26057 + 3.53573i) q^{22} -2.83821 q^{23} +2.50141 q^{25} +(-3.01127 + 8.44622i) q^{26} +(-7.76198 - 6.34060i) q^{28} +1.58069i q^{29} +1.68293 q^{31} +(-0.798200 + 5.60026i) q^{32} +(-1.33209 - 0.474920i) q^{34} +7.92129i q^{35} -1.16881i q^{37} +(-1.16277 + 3.26140i) q^{38} +(3.82694 - 2.31156i) q^{40} +3.50141 q^{41} +6.52280i q^{43} +(-3.35838 + 4.11123i) q^{44} +(-3.78074 - 1.34792i) q^{46} -8.82975 q^{47} +18.1129 q^{49} +(3.33209 + 1.18797i) q^{50} +(-8.02255 + 9.82097i) q^{52} +7.37263i q^{53} +4.19561 q^{55} +(-7.32834 - 12.1325i) q^{56} +(-0.750703 + 2.10562i) q^{58} -10.7815i q^{59} -1.58069i q^{61} +(2.24181 + 0.799257i) q^{62} +(-3.72294 + 7.08094i) q^{64} +10.0225 q^{65} -9.82097i q^{67} +(-1.54890 - 1.26527i) q^{68} +(-3.76198 + 10.5518i) q^{70} -2.51268 q^{71} -2.52114 q^{73} +(0.555091 - 1.55696i) q^{74} +(-3.09781 + 3.79224i) q^{76} -13.3013i q^{77} +0.815662 q^{79} +(6.19561 - 1.26171i) q^{80} +(4.66417 + 1.66289i) q^{82} +8.22246i q^{83} +1.58069i q^{85} +(-3.09781 + 8.68893i) q^{86} +(-6.42615 + 3.88155i) q^{88} -1.45337 q^{89} -31.7745i q^{91} +(-4.39611 - 3.59109i) q^{92} +(-11.7620 - 4.19342i) q^{94} +3.87008 q^{95} -7.15528 q^{97} +(24.1279 + 8.60215i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{4} - 12 q^{7} - 5 q^{8} - 8 q^{10} - 6 q^{14} + 9 q^{16} - 8 q^{17} + 16 q^{20} + 4 q^{22} + 16 q^{23} - 8 q^{25} + 4 q^{26} - 20 q^{28} + 24 q^{31} - 9 q^{32} - q^{34} - 18 q^{38} + 20 q^{40}+ \cdots + 57 q^{98}+O(q^{100}) $ 8 * q + q^2 + q^4 - 12 * q^7 - 5 * q^8 - 8 * q^10 - 6 * q^14 + 9 * q^16 - 8 * q^17 + 16 * q^20 + 4 * q^22 + 16 * q^23 - 8 * q^25 + 4 * q^26 - 20 * q^28 + 24 * q^31 - 9 * q^32 - q^34 - 18 * q^38 + 20 * q^40 + 10 * q^44 - 18 * q^46 - 4 * q^47 + 8 * q^49 + 17 * q^50 - 8 * q^52 - 12 * q^55 - 20 * q^56 + 8 * q^58 - 26 * q^62 + q^64 + 24 * q^65 - q^68 + 12 * q^70 + 36 * q^71 + 8 * q^73 + 36 * q^74 - 2 * q^76 + 24 * q^79 + 4 * q^80 + 18 * q^82 - 2 * q^86 + 10 * q^88 - 8 * q^89 + 28 * q^92 - 52 * q^94 - 32 * q^95 - 8 * q^97 + 57 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	1.33209	+	0.474920i	0.941927	+	0.335819i
$2$	1.33209	+	0.474920i	0.941927	+	0.335819i
$3$		0			0
$3$		0			0
$4$	1.54890	+	1.26527i	0.774451	+	0.632633i
$5$		−	1.58069i		−	0.706908i	−0.935452	−	0.353454i	$-0.885007\pi$
$5$		−	1.58069i		−	0.706908i	0.935452	−	0.353454i	$-0.114993\pi$
$6$		0			0
$7$	−5.01127			−1.89408			−0.947042	−	0.321110i	$-0.895944\pi$
$7$	−5.01127			−1.89408			−0.947042	+	0.321110i	$0.895944\pi$
$8$	1.46237	+	2.42105i	0.517026	+	0.855970i
$9$		0			0
$10$	0.750703	−	2.10562i	0.237393	−	0.665855i
$11$			2.65428i			0.800297i	0.916450	+	0.400148i	$0.131041\pi$
$11$			2.65428i			0.800297i	−0.916450	+	0.400148i	$0.868959\pi$
$12$		0			0
$13$			6.34060i			1.75857i	0.476300	+	0.879283i	$0.341978\pi$
$13$			6.34060i			1.75857i	−0.476300	+	0.879283i	$0.658022\pi$
$14$	−6.67544	−	2.37995i	−1.78409	−	0.636069i
$15$		0			0
$16$	0.798200	+	3.91955i	0.199550	+	0.979888i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$		0			0
$19$			2.44834i			0.561688i	0.959753	+	0.280844i	$0.0906144\pi$
$19$			2.44834i			0.561688i	−0.959753	+	0.280844i	$0.909386\pi$
$20$	2.00000	−	2.44834i	0.447214	−	0.547466i
$21$		0			0
$22$	−1.26057	+	3.53573i	−0.268755	+	0.753821i
$23$	−2.83821			−0.591808			−0.295904	−	0.955218i	$-0.595621\pi$
$23$	−2.83821			−0.591808			−0.295904	+	0.955218i	$0.595621\pi$
$24$		0			0
$25$	2.50141			0.500281
$26$	−3.01127	+	8.44622i	−0.590559	+	1.65644i
$27$		0			0
$28$	−7.76198	−	6.34060i	−1.46688	−	1.19826i
$29$			1.58069i			0.293528i	0.989172	+	0.146764i	$0.0468857\pi$
$29$			1.58069i			0.293528i	−0.989172	+	0.146764i	$0.953114\pi$
$30$		0			0
$31$	1.68293			0.302264			0.151132	−	0.988514i	$-0.451708\pi$
$31$	1.68293			0.302264			0.151132	+	0.988514i	$0.451708\pi$
$32$	−0.798200	+	5.60026i	−0.141103	+	0.989995i
$33$		0			0
$34$	−1.33209	−	0.474920i	−0.228451	−	0.0814480i
$35$			7.92129i			1.33894i
$36$		0			0
$37$		−	1.16881i		−	0.192151i	−0.995374	−	0.0960757i	$-0.969371\pi$
$37$		−	1.16881i		−	0.192151i	0.995374	−	0.0960757i	$-0.0306291\pi$
$38$	−1.16277	+	3.26140i	−0.188625	+	0.529069i
$39$		0			0
$40$	3.82694	−	2.31156i	0.605092	−	0.365490i
$41$	3.50141			0.546828			0.273414	−	0.961897i	$-0.411847\pi$
$41$	3.50141			0.546828			0.273414	+	0.961897i	$0.411847\pi$
$42$		0			0
$43$			6.52280i			0.994718i	0.867545	+	0.497359i	$0.165697\pi$
$43$			6.52280i			0.994718i	−0.867545	+	0.497359i	$0.834303\pi$
$44$	−3.35838	+	4.11123i	−0.506294	+	0.619791i
$45$		0			0
$46$	−3.78074	−	1.34792i	−0.557439	−	0.198740i
$47$	−8.82975			−1.28795			−0.643975	−	0.765046i	$-0.722716\pi$
$47$	−8.82975			−1.28795			−0.643975	+	0.765046i	$0.722716\pi$
$48$		0			0
$49$	18.1129			2.58755
$50$	3.33209	+	1.18797i	0.471228	+	0.168004i
$51$		0			0
$52$	−8.02255	+	9.82097i	−1.11253	+	1.36192i
$53$			7.37263i			1.01271i	0.862326	+	0.506354i	$0.169007\pi$
$53$			7.37263i			1.01271i	−0.862326	+	0.506354i	$0.830993\pi$
$54$		0			0
$55$	4.19561			0.565736
$56$	−7.32834	−	12.1325i	−0.979291	−	1.62128i
$57$		0			0
$58$	−0.750703	+	2.10562i	−0.0985721	+	0.276481i
$59$		−	10.7815i		−	1.40363i	−0.712357	−	0.701817i	$-0.752372\pi$
$59$		−	10.7815i		−	1.40363i	0.712357	−	0.701817i	$-0.247628\pi$
$60$		0			0
$61$		−	1.58069i		−	0.202387i	−0.994867	−	0.101194i	$-0.967734\pi$
$61$		−	1.58069i		−	0.202387i	0.994867	−	0.101194i	$-0.0322661\pi$
$62$	2.24181	+	0.799257i	0.284710	+	0.101506i
$63$		0			0
$64$	−3.72294	+	7.08094i	−0.465368	+	0.885117i
$65$	10.0225			1.24314
$66$		0			0
$67$		−	9.82097i		−	1.19982i	−0.800067	−	0.599911i	$-0.795203\pi$
$67$		−	9.82097i		−	1.19982i	0.800067	−	0.599911i	$-0.204797\pi$
$68$	−1.54890	−	1.26527i	−0.187832	−	0.153436i
$69$		0			0
$70$	−3.76198	+	10.5518i	−0.449642	+	1.26119i
$71$	−2.51268			−0.298200			−0.149100	−	0.988822i	$-0.547638\pi$
$71$	−2.51268			−0.298200			−0.149100	+	0.988822i	$0.547638\pi$
$72$		0			0
$73$	−2.52114			−0.295077			−0.147539	−	0.989056i	$-0.547135\pi$
$73$	−2.52114			−0.295077			−0.147539	+	0.989056i	$0.547135\pi$
$74$	0.555091	−	1.55696i	0.0645280	−	0.180992i
$75$		0			0
$76$	−3.09781	+	3.79224i	−0.355343	+	0.435000i
$77$		−	13.3013i		−	1.51583i
$78$		0			0
$79$	0.815662			0.0917692			0.0458846	−	0.998947i	$-0.485389\pi$
$79$	0.815662			0.0917692			0.0458846	+	0.998947i	$0.485389\pi$
$80$	6.19561	−	1.26171i	0.692690	−	0.141064i
$81$		0			0
$82$	4.66417	+	1.66289i	0.515071	+	0.183635i
$83$			8.22246i			0.902532i	0.892390	+	0.451266i	$0.149027\pi$
$83$			8.22246i			0.902532i	−0.892390	+	0.451266i	$0.850973\pi$
$84$		0			0
$85$			1.58069i			0.171450i
$86$	−3.09781	+	8.68893i	−0.334045	+	0.936951i
$87$		0			0
$88$	−6.42615	+	3.88155i	−0.685030	+	0.413774i
$89$	−1.45337			−0.154057			−0.0770286	−	0.997029i	$-0.524543\pi$
$89$	−1.45337			−0.154057			−0.0770286	+	0.997029i	$0.524543\pi$
$90$		0			0
$91$		−	31.7745i		−	3.33087i
$92$	−4.39611	−	3.59109i	−0.458326	−	0.374397i
$93$		0			0
$94$	−11.7620	−	4.19342i	−1.21316	−	0.432518i
$95$	3.87008			0.397062
$96$		0			0
$97$	−7.15528			−0.726508			−0.363254	−	0.931690i	$-0.618334\pi$
$97$	−7.15528			−0.726508			−0.363254	+	0.931690i	$0.618334\pi$
$98$	24.1279	+	8.60215i	2.43728	+	0.868949i
$99$		0			0
$100$	3.87443	+	3.16494i	0.387443	+	0.316494i
$101$		−	8.67822i		−	0.863515i	−0.901990	−	0.431758i	$-0.857894\pi$
$101$		−	8.67822i		−	0.863515i	0.901990	−	0.431758i	$-0.142106\pi$
$102$		0			0
$103$	−7.13273			−0.702809			−0.351404	−	0.936224i	$-0.614296\pi$
$103$	−7.13273			−0.702809			−0.351404	+	0.936224i	$0.614296\pi$
$104$	−15.3509	+	9.27231i	−1.50528	+	0.909224i
$105$		0			0
$106$	−3.50141	+	9.82097i	−0.340087	+	0.953897i
$107$		−	5.26701i		−	0.509181i	−0.967049	−	0.254590i	$-0.918059\pi$
$107$		−	5.26701i		−	0.509181i	0.967049	−	0.254590i	$-0.0819407\pi$
$108$		0			0
$109$		−	8.35100i		−	0.799880i	−0.916541	−	0.399940i	$-0.869031\pi$
$109$		−	8.35100i		−	0.799880i	0.916541	−	0.399940i	$-0.130969\pi$
$110$	5.58891	+	1.99258i	0.532882	+	0.189985i
$111$		0			0
$112$	−4.00000	−	19.6419i	−0.377964	−	1.85599i
$113$	8.02255			0.754698			0.377349	−	0.926071i	$-0.376836\pi$
$113$	8.02255			0.754698			0.377349	+	0.926071i	$0.376836\pi$
$114$		0			0
$115$			4.48634i			0.418354i
$116$	−2.00000	+	2.44834i	−0.185695	+	0.227323i
$117$		0			0
$118$	5.12035	−	14.3619i	0.471367	−	1.32212i
$119$	5.01127			0.459383
$120$		0			0
$121$	3.95478			0.359525
$122$	0.750703	−	2.10562i	0.0679654	−	0.190634i
$123$		0			0
$124$	2.60670	+	2.12936i	0.234088	+	0.191222i
$125$		−	11.8574i		−	1.06056i
$126$		0			0
$127$	13.5014			1.19806			0.599028	−	0.800728i	$-0.295554\pi$
$127$	13.5014			1.19806			0.599028	+	0.800728i	$0.295554\pi$
$128$	−8.32215	+	7.66432i	−0.735581	+	0.677436i
$129$		0			0
$130$	13.3509	+	4.75990i	1.17095	+	0.417471i
$131$			5.90498i			0.515920i	0.966156	+	0.257960i	$0.0830503\pi$
$131$			5.90498i			0.515920i	−0.966156	+	0.257960i	$0.916950\pi$
$132$		0			0
$133$		−	12.2693i		−	1.06388i
$134$	4.66417	−	13.0824i	0.402923	−	1.13014i
$135$		0			0
$136$	−1.46237	−	2.42105i	−0.125397	−	0.207603i
$137$	−1.56636			−0.133824			−0.0669118	−	0.997759i	$-0.521315\pi$
$137$	−1.56636			−0.133824			−0.0669118	+	0.997759i	$0.521315\pi$
$138$		0			0
$139$			3.29225i			0.279245i	0.990205	+	0.139623i	$0.0445889\pi$
$139$			3.29225i			0.279245i	−0.990205	+	0.139623i	$0.955411\pi$
$140$	−10.0225	+	12.2693i	−0.847060	+	1.03695i
$141$		0			0
$142$	−3.34710	−	1.19332i	−0.280883	−	0.100141i
$143$	−16.8297			−1.40737
$144$		0			0
$145$	2.49859			0.207497
$146$	−3.35838	−	1.19734i	−0.277941	−	0.0990925i
$147$		0			0
$148$	1.47886	−	1.81037i	0.121561	−	0.148812i
$149$		−	2.70203i		−	0.221359i	−0.993856	−	0.110679i	$-0.964697\pi$
$149$		−	2.70203i		−	0.221359i	0.993856	−	0.110679i	$-0.0353027\pi$
$150$		0			0
$151$	2.88982			0.235170			0.117585	−	0.993063i	$-0.462485\pi$
$151$	2.88982			0.235170			0.117585	+	0.993063i	$0.462485\pi$
$152$	−5.92755	+	3.58038i	−0.480788	+	0.290408i
$153$		0			0
$154$	6.31707	−	17.7185i	0.509044	−	1.42780i
$155$		−	2.66020i		−	0.213673i
$156$		0			0
$157$		−	1.01421i		−	0.0809428i	−0.999181	−	0.0404714i	$-0.987114\pi$
$157$		−	1.01421i		−	0.0809428i	0.999181	−	0.0404714i	$-0.0128860\pi$
$158$	1.08653	+	0.387374i	0.0864398	+	0.0308178i
$159$		0			0
$160$	8.85229	+	1.26171i	0.699835	+	0.0997470i
$161$	14.2230			1.12093
$162$		0			0
$163$			15.5259i			1.21608i	0.793905	+	0.608042i	$0.208045\pi$
$163$			15.5259i			1.21608i	−0.793905	+	0.608042i	$0.791955\pi$
$164$	5.42334	+	4.43021i	0.423491	+	0.345941i
$165$		0			0
$166$	−3.90500	+	10.9530i	−0.303087	+	0.850119i
$167$	15.9011			1.23046			0.615232	−	0.788346i	$-0.289062\pi$
$167$	15.9011			1.23046			0.615232	+	0.788346i	$0.289062\pi$
$168$		0			0
$169$	−27.2032			−2.09255
$170$	−0.750703	+	2.10562i	−0.0575763	+	0.161494i
$171$		0			0
$172$	−8.25308	+	10.1032i	−0.629292	+	0.770361i
$173$			21.1752i			1.60992i	0.593331	+	0.804959i	$0.297813\pi$
$173$			21.1752i			1.60992i	−0.593331	+	0.804959i	$0.702187\pi$
$174$		0			0
$175$	−12.5352			−0.947574
$176$	−10.4036	+	2.11865i	−0.784201	+	0.159699i
$177$		0			0
$178$	−1.93602	−	0.690235i	−0.145111	−	0.0517353i
$179$			16.5913i			1.24009i	0.784566	+	0.620045i	$0.212886\pi$
$179$			16.5913i			1.24009i	−0.784566	+	0.620045i	$0.787114\pi$
$180$		0			0
$181$			11.7859i			0.876042i	0.898965	+	0.438021i	$0.144321\pi$
$181$			11.7859i			0.876042i	−0.898965	+	0.438021i	$0.855679\pi$
$182$	15.0903	−	42.3263i	1.11857	−	3.13743i
$183$		0			0
$184$	−4.15052	−	6.87144i	−0.305980	−	0.506569i
$185$	−1.84753			−0.135833
$186$		0			0
$187$		−	2.65428i		−	0.194100i
$188$	−13.6764	−	11.1720i	−0.997455	−	0.814801i
$189$		0			0
$190$	5.15528	+	1.83798i	0.374003	+	0.133341i
$191$	−7.96248			−0.576145			−0.288072	−	0.957609i	$-0.593014\pi$
$191$	−7.96248			−0.576145			−0.288072	+	0.957609i	$0.593014\pi$
$192$		0			0
$193$	25.2229			1.81559			0.907793	−	0.419419i	$-0.137766\pi$
$193$	25.2229			1.81559			0.907793	+	0.419419i	$0.137766\pi$
$194$	−9.53144	−	3.39818i	−0.684318	−	0.243975i
$195$		0			0
$196$	28.0551	+	22.9176i	2.00393	+	1.63697i
$197$			12.8833i			0.917895i	0.888463	+	0.458948i	$0.151773\pi$
$197$			12.8833i			0.917895i	−0.888463	+	0.458948i	$0.848227\pi$
$198$		0			0
$199$	0.339615			0.0240747			0.0120373	−	0.999928i	$-0.496168\pi$
$199$	0.339615			0.0240747			0.0120373	+	0.999928i	$0.496168\pi$
$200$	3.65798	+	6.05602i	0.258658	+	0.428225i
$201$		0			0
$202$	4.12146	−	11.5601i	0.289985	−	0.813368i
$203$		−	7.92129i		−	0.555966i
$204$		0			0
$205$		−	5.53465i		−	0.386557i
$206$	−9.50141	−	3.38747i	−0.661994	−	0.236016i
$207$		0			0
$208$	−24.8523	+	5.06107i	−1.72320	+	0.350922i
$209$	−6.49859			−0.449517
$210$		0			0
$211$			6.36434i			0.438139i	0.975709	+	0.219069i	$0.0703021\pi$
$211$			6.36434i			0.438139i	−0.975709	+	0.219069i	$0.929698\pi$
$212$	−9.32834	+	11.4195i	−0.640673	+	0.784293i
$213$		0			0
$214$	2.50141	−	7.01611i	0.170993	−	0.479611i
$215$	10.3106			0.703174
$216$		0			0
$217$	−8.43364			−0.572512
$218$	3.96605	−	11.1242i	0.268615	−	0.753429i
$219$		0			0
$220$	6.49859	+	5.30857i	0.438135	+	0.357904i
$221$		−	6.34060i		−	0.426515i
$222$		0			0
$223$	13.0629			0.874755			0.437378	−	0.899278i	$-0.355907\pi$
$223$	13.0629			0.874755			0.437378	+	0.899278i	$0.355907\pi$
$224$	4.00000	−	28.0644i	0.267261	−	1.87513i
$225$		0			0
$226$	10.6867	+	3.81006i	0.710870	+	0.253442i
$227$		−	20.3705i		−	1.35204i	−0.736885	−	0.676018i	$-0.763704\pi$
$227$		−	20.3705i		−	1.35204i	0.736885	−	0.676018i	$-0.236296\pi$
$228$		0			0
$229$		−	17.9245i		−	1.18448i	−0.805761	−	0.592241i	$-0.798243\pi$
$229$		−	17.9245i		−	1.18448i	0.805761	−	0.592241i	$-0.201757\pi$
$230$	−2.13065	+	5.97619i	−0.140491	+	0.394058i
$231$		0			0
$232$	−3.82694	+	2.31156i	−0.251251	+	0.151761i
$233$	−15.8926			−1.04116			−0.520580	−	0.853813i	$-0.674284\pi$
$233$	−15.8926			−1.04116			−0.520580	+	0.853813i	$0.674284\pi$
$234$		0			0
$235$			13.9571i			0.910463i
$236$	13.6415	−	16.6995i	0.887986	−	1.08705i
$237$		0			0
$238$	6.67544	+	2.37995i	0.432705	+	0.154269i
$239$	16.3537			1.05783			0.528916	−	0.848674i	$-0.322598\pi$
$239$	16.3537			1.05783			0.528916	+	0.848674i	$0.322598\pi$
$240$		0			0
$241$	29.6820			1.91199			0.955994	−	0.293386i	$-0.0947820\pi$
$241$	29.6820			1.91199			0.955994	+	0.293386i	$0.0947820\pi$
$242$	5.26810	+	1.87820i	0.338646	+	0.120735i
$243$		0			0
$244$	2.00000	−	2.44834i	0.128037	−	0.156739i
$245$		−	28.6309i		−	1.82916i
$246$		0			0
$247$	−15.5240			−0.987765
$248$	2.46107	+	4.07446i	0.156278	+	0.258728i
$249$		0			0
$250$	5.63132	−	15.7951i	0.356156	−	0.998970i
$251$			23.7425i			1.49861i	0.662225	+	0.749305i	$0.269612\pi$
$251$			23.7425i			1.49861i	−0.662225	+	0.749305i	$0.730388\pi$
$252$		0			0
$253$		−	7.53342i		−	0.473622i
$254$	17.9850	+	6.41208i	1.12848	+	0.402330i
$255$		0			0
$256$	−14.7258	+	6.25717i	−0.920360	+	0.391073i
$257$	18.9548			1.18237			0.591183	−	0.806537i	$-0.298661\pi$
$257$	18.9548			1.18237			0.591183	+	0.806537i	$0.298661\pi$
$258$		0			0
$259$			5.85723i			0.363951i
$260$	15.5240	+	12.6812i	0.962755	+	0.786454i
$261$		0			0
$262$	−2.80439	+	7.86593i	−0.173256	+	0.485959i
$263$	−9.54650			−0.588662			−0.294331	−	0.955703i	$-0.595097\pi$
$263$	−9.54650			−0.588662			−0.294331	+	0.955703i	$0.595097\pi$
$264$		0			0
$265$	11.6539			0.715892
$266$	5.82694	−	16.3438i	0.357272	−	1.00210i
$267$		0			0
$268$	12.4261	−	15.2117i	0.759048	−	0.929204i
$269$		−	20.3467i		−	1.24056i	−0.784379	−	0.620282i	$-0.787018\pi$
$269$		−	20.3467i		−	1.24056i	0.784379	−	0.620282i	$-0.212982\pi$
$270$		0			0
$271$	28.8748			1.75402			0.877011	−	0.480471i	$-0.159534\pi$
$271$	28.8748			1.75402			0.877011	+	0.480471i	$0.159534\pi$
$272$	−0.798200	−	3.91955i	−0.0483980	−	0.237658i
$273$		0			0
$274$	−2.08653	−	0.743897i	−0.126052	−	0.0449405i
$275$			6.63944i			0.400373i
$276$		0			0
$277$			10.4151i			0.625780i	0.949789	+	0.312890i	$0.101297\pi$
$277$			10.4151i			0.625780i	−0.949789	+	0.312890i	$0.898703\pi$
$278$	−1.56355	+	4.38556i	−0.0937758	+	0.263028i
$279$		0			0
$280$	−19.1778	+	11.5839i	−1.14609	+	0.692269i
$281$	30.2032			1.80177			0.900885	−	0.434057i	$-0.142918\pi$
$281$	30.2032			1.80177			0.900885	+	0.434057i	$0.142918\pi$
$282$		0			0
$283$		−	26.6458i		−	1.58393i	−0.610568	−	0.791964i	$-0.709059\pi$
$283$		−	26.6458i		−	1.58393i	0.610568	−	0.791964i	$-0.290941\pi$
$284$	−3.89190	−	3.17921i	−0.230942	−	0.188651i
$285$		0			0
$286$	−22.4187	−	7.99278i	−1.32564	−	0.472623i
$287$	−17.5465			−1.03574
$288$		0			0
$289$	1.00000			0.0588235
$290$	3.32834	+	1.18663i	0.195447	+	0.0696814i
$291$		0			0
$292$	−3.90500	−	3.18992i	−0.228523	−	0.186676i
$293$		−	3.52580i		−	0.205979i	−0.994682	−	0.102990i	$-0.967159\pi$
$293$		−	3.52580i		−	0.205979i	0.994682	−	0.102990i	$-0.0328408\pi$
$294$		0			0
$295$	−17.0423			−0.992240
$296$	2.82975	−	1.70924i	0.164476	−	0.0993473i
$297$		0			0
$298$	1.28325	−	3.59933i	0.0743364	−	0.208504i
$299$		−	17.9959i		−	1.04073i
$300$		0			0
$301$		−	32.6875i		−	1.88408i
$302$	3.84948	+	1.37243i	0.221513	+	0.0789745i
$303$		0			0
$304$	−9.59640	+	1.95427i	−0.550391	+	0.112085i
$305$	−2.49859			−0.143069
$306$		0			0
$307$		−	1.34483i		−	0.0767534i	−0.999263	−	0.0383767i	$-0.987781\pi$
$307$		−	1.34483i		−	0.0767534i	0.999263	−	0.0383767i	$-0.0122187\pi$
$308$	16.8297	−	20.6025i	0.958964	−	1.17394i
$309$		0			0
$310$	1.26338	−	3.54362i	0.0717553	−	0.201264i
$311$	−32.5803			−1.84746			−0.923730	−	0.383044i	$-0.874876\pi$
$311$	−32.5803			−1.84746			−0.923730	+	0.383044i	$0.874876\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	0.481668	−	1.35101i	0.0271821	−	0.0762421i
$315$		0			0
$316$	1.26338	+	1.03203i	0.0710708	+	0.0580562i
$317$			25.8814i			1.45364i	0.686826	+	0.726822i	$0.259004\pi$
$317$			25.8814i			1.45364i	−0.686826	+	0.726822i	$0.740996\pi$
$318$		0			0
$319$	−4.19561			−0.234909
$320$	11.1928	+	5.88483i	0.625697	+	0.328972i
$321$		0			0
$322$	18.9463	+	6.75480i	1.05584	+	0.376430i
$323$		−	2.44834i		−	0.136229i
$324$		0			0
$325$			15.8604i			0.879777i
$326$	−7.37356	+	20.6819i	−0.408384	+	1.14546i
$327$		0			0
$328$	5.12035	+	8.47707i	0.282724	+	0.468068i
$329$	44.2483			2.43949
$330$		0			0
$331$			1.26171i			0.0693499i	0.999399	+	0.0346749i	$0.0110396\pi$
$331$			1.26171i			0.0693499i	−0.999399	+	0.0346749i	$0.988960\pi$
$332$	−10.4036	+	12.7358i	−0.570972	+	0.698967i
$333$		0			0
$334$	21.1816	+	7.55174i	1.15901	+	0.413213i
$335$	−15.5240			−0.848164
$336$		0			0
$337$	17.8120			0.970279			0.485140	−	0.874437i	$-0.338769\pi$
$337$	17.8120			0.970279			0.485140	+	0.874437i	$0.338769\pi$
$338$	−36.2370	−	12.9193i	−1.97103	−	0.702719i
$339$		0			0
$340$	−2.00000	+	2.44834i	−0.108465	+	0.132780i
$341$			4.46698i			0.241901i
$342$		0			0
$343$	−55.6896			−3.00696
$344$	−15.7920	+	9.53876i	−0.851448	+	0.514295i
$345$		0			0
$346$	−10.0565	+	28.2071i	−0.540641	+	1.51642i
$347$			4.34210i			0.233096i	0.993185	+	0.116548i	$0.0371829\pi$
$347$			4.34210i			0.233096i	−0.993185	+	0.116548i	$0.962817\pi$
$348$		0			0
$349$		−	12.4908i		−	0.668615i	−0.942464	−	0.334307i	$-0.891498\pi$
$349$		−	12.4908i		−	0.668615i	0.942464	−	0.334307i	$-0.108502\pi$
$350$	−16.6980	−	5.95322i	−0.892545	−	0.318213i
$351$		0			0
$352$	−14.8647	−	2.11865i	−0.792290	−	0.112924i
$353$	−10.2782			−0.547055			−0.273527	−	0.961864i	$-0.588190\pi$
$353$	−10.2782			−0.547055			−0.273527	+	0.961864i	$0.588190\pi$
$354$		0			0
$355$			3.97178i			0.210800i
$356$	−2.25113	−	1.83890i	−0.119310	−	0.0974617i
$357$		0			0
$358$	−7.87952	+	22.1010i	−0.416446	+	1.16807i
$359$	−7.45826			−0.393632			−0.196816	−	0.980440i	$-0.563060\pi$
$359$	−7.45826			−0.393632			−0.196816	+	0.980440i	$0.563060\pi$
$360$		0			0
$361$	13.0056			0.684506
$362$	−5.59738	+	15.6999i	−0.294192	+	0.825168i
$363$		0			0
$364$	40.2032	−	49.2156i	2.10722	−	2.57960i
$365$			3.98516i			0.208593i
$366$		0			0
$367$	−6.92083			−0.361264			−0.180632	−	0.983551i	$-0.557814\pi$
$367$	−6.92083			−0.361264			−0.180632	+	0.983551i	$0.557814\pi$
$368$	−2.26546	−	11.1245i	−0.118095	−	0.579905i
$369$		0			0
$370$	−2.46107	−	0.877429i	−0.127945	−	0.0456154i
$371$		−	36.9463i		−	1.91815i
$372$		0			0
$373$			22.0882i			1.14369i	0.820363	+	0.571843i	$0.193771\pi$
$373$			22.0882i			1.14369i	−0.820363	+	0.571843i	$0.806229\pi$
$374$	1.26057	−	3.53573i	0.0651826	−	0.182828i
$375$		0			0
$376$	−12.9124	−	21.3772i	−0.665904	−	1.10245i
$377$	−10.0225			−0.516187
$378$		0			0
$379$			35.4430i			1.82058i	0.413968	+	0.910291i	$0.364143\pi$
$379$			35.4430i			1.82058i	−0.413968	+	0.910291i	$0.635857\pi$
$380$	5.99438	+	4.89668i	0.307505	+	0.251195i
$381$		0			0
$382$	−10.6067	−	3.78154i	−0.542686	−	0.193480i
$383$	28.5493			1.45880			0.729401	−	0.684087i	$-0.239799\pi$
$383$	28.5493			1.45880			0.729401	+	0.684087i	$0.239799\pi$
$384$		0			0
$385$	−21.0254			−1.07155
$386$	33.5991	+	11.9789i	1.71015	+	0.609708i
$387$		0			0
$388$	−11.0828	−	9.05333i	−0.562645	−	0.459613i
$389$		−	19.0218i		−	0.964443i	−0.876049	−	0.482222i	$-0.839830\pi$
$389$		−	19.0218i		−	0.964443i	0.876049	−	0.482222i	$-0.160170\pi$
$390$		0			0
$391$	2.83821			0.143534
$392$	26.4877	+	43.8521i	1.33783	+	2.21487i
$393$		0			0
$394$	−6.11852	+	17.1616i	−0.308247	+	0.864590i
$395$		−	1.28931i		−	0.0648724i
$396$		0			0
$397$		−	6.52486i		−	0.327473i	−0.986504	−	0.163737i	$-0.947645\pi$
$397$		−	6.52486i		−	0.327473i	0.986504	−	0.163737i	$-0.0523547\pi$
$398$	0.452397	+	0.161290i	0.0226766	+	0.00808474i
$399$		0			0
$400$	1.99662	+	9.80438i	0.0998311	+	0.490219i
$401$	5.41096			0.270210			0.135105	−	0.990831i	$-0.456863\pi$
$401$	5.41096			0.270210			0.135105	+	0.990831i	$0.456863\pi$
$402$		0			0
$403$			10.6708i			0.531550i
$404$	10.9803	−	13.4417i	0.546288	−	0.668751i
$405$		0			0
$406$	3.76198	−	10.5518i	0.186704	−	0.523679i
$407$	3.10236			0.153778
$408$		0			0
$409$	−28.4307			−1.40581			−0.702904	−	0.711285i	$-0.748114\pi$
$409$	−28.4307			−1.40581			−0.702904	+	0.711285i	$0.748114\pi$
$410$	2.62851	−	7.37263i	0.129813	−	0.364108i
$411$		0			0
$412$	−11.0479	−	9.02481i	−0.544291	−	0.444620i
$413$			54.0291i			2.65860i
$414$		0			0
$415$	12.9972			0.638007
$416$	−35.5090	−	5.06107i	−1.74097	−	0.248139i
$417$		0			0
$418$	−8.65668	−	3.08631i	−0.423412	−	0.150956i
$419$			14.4224i			0.704581i	0.935891	+	0.352290i	$0.114597\pi$
$419$			14.4224i			0.704581i	−0.935891	+	0.352290i	$0.885403\pi$
$420$		0			0
$421$			21.2645i			1.03637i	0.855270	+	0.518183i	$0.173391\pi$
$421$			21.2645i			1.03637i	−0.855270	+	0.518183i	$0.826609\pi$
$422$	−3.02255	+	8.47784i	−0.147135	+	0.412695i
$423$		0			0
$424$	−17.8495	+	10.7815i	−0.866848	+	0.523597i
$425$	−2.50141			−0.121336
$426$		0			0
$427$			7.92129i			0.383338i
$428$	6.66417	−	8.15808i	0.322125	−	0.394336i
$429$		0			0
$430$	13.7345	+	4.89668i	0.662338	+	0.236139i
$431$	−18.4752			−0.889917			−0.444958	−	0.895551i	$-0.646782\pi$
$431$	−18.4752			−0.889917			−0.444958	+	0.895551i	$0.646782\pi$
$432$		0			0
$433$	−27.1580			−1.30513			−0.652564	−	0.757733i	$-0.726307\pi$
$433$	−27.1580			−1.30513			−0.652564	+	0.757733i	$0.726307\pi$
$434$	−11.2343	−	4.00530i	−0.539265	−	0.192260i
$435$		0			0
$436$	10.5662	−	12.9349i	0.506031	−	0.619469i
$437$		−	6.94891i		−	0.332411i
$438$		0			0
$439$	2.29647			0.109605			0.0548023	−	0.998497i	$-0.482547\pi$
$439$	2.29647			0.109605			0.0548023	+	0.998497i	$0.482547\pi$
$440$	6.13554	+	10.1578i	0.292500	+	0.484253i
$441$		0			0
$442$	3.01127	−	8.44622i	0.143232	−	0.401746i
$443$		−	14.9912i		−	0.712254i	−0.934438	−	0.356127i	$-0.884097\pi$
$443$		−	14.9912i		−	0.712254i	0.934438	−	0.356127i	$-0.115903\pi$
$444$		0			0
$445$			2.29734i			0.108904i
$446$	17.4009	+	6.20382i	0.823955	+	0.293759i
$447$		0			0
$448$	18.6567	−	35.4845i	0.881445	−	1.67649i
$449$	20.6567			0.974849			0.487425	−	0.873165i	$-0.337936\pi$
$449$	20.6567			0.974849			0.487425	+	0.873165i	$0.337936\pi$
$450$		0			0
$451$			9.29372i			0.437624i
$452$	12.4261	+	10.1507i	0.584477	+	0.477447i
$453$		0			0
$454$	9.67434	−	27.1352i	0.454039	−	1.27352i
$455$	−50.2257			−2.35462
$456$		0			0
$457$	26.4206			1.23590			0.617952	−	0.786216i	$-0.287963\pi$
$457$	26.4206			1.23590			0.617952	+	0.786216i	$0.287963\pi$
$458$	8.51268	−	23.8769i	0.397771	−	1.11570i
$459$		0			0
$460$	−5.67642	+	6.94891i	−0.264664	+	0.323995i
$461$		−	39.2364i		−	1.82742i	−0.406365	−	0.913711i	$-0.633204\pi$
$461$		−	39.2364i		−	1.82742i	0.406365	−	0.913711i	$-0.366796\pi$
$462$		0			0
$463$	7.30774			0.339620			0.169810	−	0.985477i	$-0.445685\pi$
$463$	7.30774			0.339620			0.169810	+	0.985477i	$0.445685\pi$
$464$	−6.19561	+	1.26171i	−0.287624	+	0.0585734i
$465$		0			0
$466$	−21.1703	−	7.54772i	−0.980697	−	0.349641i
$467$			24.3923i			1.12874i	0.825522	+	0.564370i	$0.190881\pi$
$467$			24.3923i			1.12874i	−0.825522	+	0.564370i	$0.809119\pi$
$468$		0			0
$469$			49.2156i			2.27256i
$470$	−6.62851	+	18.5921i	−0.305751	+	0.857589i
$471$		0			0
$472$	26.1026	−	15.7666i	1.20147	−	0.725716i
$473$	−17.3134			−0.796069
$474$		0			0
$475$			6.12430i			0.281002i
$476$	7.76198	+	6.34060i	0.355770	+	0.290621i
$477$		0			0
$478$	21.7845	+	7.76669i	0.996401	+	0.355240i
$479$	6.68012			0.305223			0.152611	−	0.988286i	$-0.451232\pi$
$479$	6.68012			0.305223			0.152611	+	0.988286i	$0.451232\pi$
$480$		0			0
$481$	7.41096			0.337911
$482$	39.5390	+	14.0966i	1.80095	+	0.642082i
$483$		0			0
$484$	6.12557	+	5.00385i	0.278435	+	0.227448i
$485$			11.3103i			0.513575i
$486$		0			0
$487$	17.2314			0.780829			0.390414	−	0.920639i	$-0.372332\pi$
$487$	17.2314			0.780829			0.390414	+	0.920639i	$0.372332\pi$
$488$	3.82694	−	2.31156i	0.173237	−	0.104639i
$489$		0			0
$490$	13.5974	−	38.1388i	0.614267	−	1.72294i
$491$		−	8.73548i		−	0.394227i	−0.980381	−	0.197113i	$-0.936843\pi$
$491$		−	8.73548i		−	0.394227i	0.980381	−	0.197113i	$-0.0631567\pi$
$492$		0			0
$493$		−	1.58069i		−	0.0711909i
$494$	−20.6792	−	7.37263i	−0.930403	−	0.331710i
$495$		0			0
$496$	1.34332	+	6.59634i	0.0603167	+	0.296184i
$497$	12.5917			0.564816
$498$		0			0
$499$			5.23137i			0.234188i	0.993121	+	0.117094i	$0.0373579\pi$
$499$			5.23137i			0.234188i	−0.993121	+	0.117094i	$0.962642\pi$
$500$	15.0028	−	18.3660i	0.670946	−	0.821353i
$501$		0			0
$502$	−11.2758	+	31.6270i	−0.503262	+	1.41158i
$503$	−2.39969			−0.106997			−0.0534984	−	0.998568i	$-0.517037\pi$
$503$	−2.39969			−0.106997			−0.0534984	+	0.998568i	$0.517037\pi$
$504$		0			0
$505$	−13.7176			−0.610426
$506$	3.57777	−	10.0352i	0.159051	−	0.446117i
$507$		0			0
$508$	20.9124	+	17.0829i	0.927836	+	0.757930i
$509$			6.72283i			0.297984i	0.988838	+	0.148992i	$0.0476029\pi$
$509$			6.72283i			0.297984i	−0.988838	+	0.148992i	$0.952397\pi$
$510$		0			0
$511$	12.6341			0.558901
$512$	−22.5876	+	1.34154i	−0.998241	+	0.0592883i
$513$		0			0
$514$	25.2494	+	9.00199i	1.11370	+	0.397061i
$515$			11.2747i			0.496821i
$516$		0			0
$517$		−	23.4367i		−	1.03074i
$518$	−2.78171	+	7.80233i	−0.122221	+	0.342815i
$519$		0			0
$520$	14.6567	+	24.2651i	0.642738	+	1.06409i
$521$	−23.2754			−1.01971			−0.509857	−	0.860259i	$-0.670302\pi$
$521$	−23.2754			−1.01971			−0.509857	+	0.860259i	$0.670302\pi$
$522$		0			0
$523$		−	3.46255i		−	0.151407i	−0.997130	−	0.0757034i	$-0.975880\pi$
$523$		−	3.46255i		−	0.151407i	0.997130	−	0.0757034i	$-0.0241202\pi$
$524$	−7.47137	+	9.14623i	−0.326388	+	0.399555i
$525$		0			0
$526$	−12.7168	−	4.53382i	−0.554477	−	0.197684i
$527$	−1.68293			−0.0733097
$528$		0			0
$529$	−14.9446			−0.649764
$530$	15.5240	+	5.53465i	0.674317	+	0.240410i
$531$		0			0
$532$	15.5240	−	19.0040i	0.673049	−	0.823927i
$533$			22.2010i			0.961632i
$534$		0			0
$535$	−8.32553			−0.359944
$536$	23.7770	−	14.3619i	1.02701	−	0.620340i
$537$		0			0
$538$	9.66307	−	27.1036i	0.416604	−	1.16852i
$539$			48.0767i			2.07081i
$540$		0			0
$541$		−	9.41268i		−	0.404683i	−0.979315	−	0.202341i	$-0.935145\pi$
$541$		−	9.41268i		−	0.404683i	0.979315	−	0.202341i	$-0.0648551\pi$
$542$	38.4638	+	13.7132i	1.65216	+	0.589034i
$543$		0			0
$544$	0.798200	−	5.60026i	0.0342226	−	0.240109i
$545$	−13.2004			−0.565442
$546$		0			0
$547$		−	8.92340i		−	0.381537i	−0.981635	−	0.190768i	$-0.938902\pi$
$547$		−	8.92340i		−	0.381537i	0.981635	−	0.190768i	$-0.0610980\pi$
$548$	−2.42615	−	1.98187i	−0.103640	−	0.0846613i
$549$		0			0
$550$	−3.15320	+	8.84430i	−0.134453	+	0.377122i
$551$	−3.87008			−0.164871
$552$		0			0
$553$	−4.08751			−0.173818
$554$	−4.94631	+	13.8737i	−0.210149	+	0.589439i
$555$		0			0
$556$	−4.16558	+	5.09938i	−0.176660	+	0.216262i
$557$			8.36902i			0.354607i	0.984156	+	0.177303i	$0.0567374\pi$
$557$			8.36902i			0.354607i	−0.984156	+	0.177303i	$0.943263\pi$
$558$		0			0
$559$	−41.3585			−1.74928
$560$	−31.0479	+	6.32278i	−1.31201	+	0.267186i
$561$		0			0
$562$	40.2332	+	14.3441i	1.69714	+	0.605069i
$563$			12.1127i			0.510488i	0.966877	+	0.255244i	$0.0821557\pi$
$563$			12.1127i			0.510488i	−0.966877	+	0.255244i	$0.917844\pi$
$564$		0			0
$565$		−	12.6812i		−	0.533502i
$566$	12.6546	−	35.4945i	0.531913	−	1.49194i
$567$		0			0
$568$	−3.67447	−	6.08332i	−0.154177	−	0.255250i
$569$	−18.8542			−0.790411			−0.395206	−	0.918593i	$-0.629327\pi$
$569$	−18.8542			−0.790411			−0.395206	+	0.918593i	$0.629327\pi$
$570$		0			0
$571$		−	3.35775i		−	0.140517i	−0.997529	−	0.0702587i	$-0.977618\pi$
$571$		−	3.35775i		−	0.140517i	0.997529	−	0.0702587i	$-0.0223825\pi$
$572$	−26.0676	−	21.2941i	−1.08994	−	0.890352i
$573$		0			0
$574$	−23.3734	−	8.33318i	−0.975588	−	0.347820i
$575$	−7.09951			−0.296070
$576$		0			0
$577$	−24.7442			−1.03011			−0.515057	−	0.857156i	$-0.672229\pi$
$577$	−24.7442			−1.03011			−0.515057	+	0.857156i	$0.672229\pi$
$578$	1.33209	+	0.474920i	0.0554074	+	0.0197540i
$579$		0			0
$580$	3.87008	+	3.16139i	0.160696	+	0.131270i
$581$		−	41.2050i		−	1.70947i
$582$		0			0
$583$	−19.5690			−0.810467
$584$	−3.68685	−	6.10381i	−0.152563	−	0.252577i
$585$		0			0
$586$	1.67447	−	4.69666i	0.0691717	−	0.194017i
$587$			25.2517i			1.04225i	0.853481	+	0.521124i	$0.174487\pi$
$587$			25.2517i			1.04225i	−0.853481	+	0.521124i	$0.825513\pi$
$588$		0			0
$589$			4.12039i			0.169778i
$590$	−22.7018	−	8.09371i	−0.934617	−	0.333213i
$591$		0			0
$592$	4.58121	−	0.932945i	0.188287	−	0.0383438i
$593$	−22.1581			−0.909924			−0.454962	−	0.890511i	$-0.650347\pi$
$593$	−22.1581			−0.909924			−0.454962	+	0.890511i	$0.650347\pi$
$594$		0			0
$595$		−	7.92129i		−	0.324741i
$596$	3.41879	−	4.18518i	0.140039	−	0.171432i
$597$		0			0
$598$	8.54663	−	23.9721i	0.349498	−	0.980294i
$599$	34.4007			1.40558			0.702788	−	0.711399i	$-0.251938\pi$
$599$	34.4007			1.40558			0.702788	+	0.711399i	$0.251938\pi$
$600$		0			0
$601$	−25.2908			−1.03163			−0.515817	−	0.856699i	$-0.672512\pi$
$601$	−25.2908			−1.03163			−0.515817	+	0.856699i	$0.672512\pi$
$602$	15.5240	−	43.5426i	0.632709	−	1.77466i
$603$		0			0
$604$	4.47605	+	3.65639i	0.182128	+	0.148776i
$605$		−	6.25129i		−	0.254151i
$606$		0			0
$607$	14.2041			0.576526			0.288263	−	0.957551i	$-0.406922\pi$
$607$	14.2041			0.576526			0.288263	+	0.957551i	$0.406922\pi$
$608$	−13.7113	−	1.95427i	−0.556068	−	0.0792560i
$609$		0			0
$610$	−3.32834	−	1.18663i	−0.134761	−	0.0480453i
$611$		−	55.9859i		−	2.26495i
$612$		0			0
$613$		−	33.8370i		−	1.36666i	−0.730108	−	0.683332i	$-0.760530\pi$
$613$		−	33.8370i		−	1.36666i	0.730108	−	0.683332i	$-0.239470\pi$
$614$	0.638685	−	1.79143i	0.0257752	−	0.0722961i
$615$		0			0
$616$	32.2032	−	19.4515i	1.29750	−	0.783723i
$617$	−33.3261			−1.34166			−0.670830	−	0.741611i	$-0.734062\pi$
$617$	−33.3261			−1.34166			−0.670830	+	0.741611i	$0.734062\pi$
$618$		0			0
$619$		−	17.9900i		−	0.723080i	−0.932357	−	0.361540i	$-0.882251\pi$
$619$		−	17.9900i		−	0.723080i	0.932357	−	0.361540i	$-0.117749\pi$
$620$	3.36586	−	4.12039i	0.135176	−	0.165479i
$621$		0			0
$622$	−43.3998	−	15.4730i	−1.74017	−	0.620412i
$623$	7.28325			0.291797
$624$		0			0
$625$	−6.23595			−0.249438
$626$	−7.99251	−	2.84952i	−0.319445	−	0.113890i
$627$		0			0
$628$	1.28325	−	1.57091i	0.0512071	−	0.0626862i
$629$			1.16881i			0.0466035i
$630$		0			0
$631$	−9.75904			−0.388501			−0.194251	−	0.980952i	$-0.562227\pi$
$631$	−9.75904			−0.388501			−0.194251	+	0.980952i	$0.562227\pi$
$632$	1.19280	+	1.97476i	0.0474471	+	0.0785516i
$633$		0			0
$634$	−12.2916	+	34.4762i	−0.488161	+	1.36923i
$635$		−	21.3416i		−	0.846915i
$636$		0			0
$637$			114.846i			4.55038i
$638$	−5.58891	−	1.99258i	−0.221267	−	0.0788869i
$639$		0			0
$640$	12.1149	+	13.1548i	0.478885	+	0.519988i
$641$	12.1525			0.479994			0.239997	−	0.970774i	$-0.422854\pi$
$641$	12.1525			0.479994			0.239997	+	0.970774i	$0.422854\pi$
$642$		0			0
$643$		−	20.1310i		−	0.793890i	−0.917842	−	0.396945i	$-0.870070\pi$
$643$		−	20.1310i		−	0.793890i	0.917842	−	0.396945i	$-0.129930\pi$
$644$	22.0301	+	17.9959i	0.868108	+	0.709140i
$645$		0			0
$646$	1.16277	−	3.26140i	0.0457484	−	0.128318i
$647$	−8.21254			−0.322868			−0.161434	−	0.986883i	$-0.551612\pi$
$647$	−8.21254			−0.322868			−0.161434	+	0.986883i	$0.551612\pi$
$648$		0			0
$649$	28.6172			1.12332
$650$	−7.53242	+	21.1274i	−0.295446	+	0.828685i
$651$		0			0
$652$	−19.6444	+	24.0481i	−0.769335	+	0.941798i
$653$			39.5293i			1.54690i	0.633856	+	0.773451i	$0.281471\pi$
$653$			39.5293i			1.54690i	−0.633856	+	0.773451i	$0.718529\pi$
$654$		0			0
$655$	9.33396			0.364708
$656$	2.79482	+	13.7239i	0.109119	+	0.535830i
$657$		0			0
$658$	58.9425	+	21.0144i	2.29782	+	0.819226i
$659$			15.5399i			0.605348i	0.953094	+	0.302674i	$0.0978793\pi$
$659$			15.5399i			0.605348i	−0.953094	+	0.302674i	$0.902121\pi$
$660$		0			0
$661$		−	46.1373i		−	1.79453i	−0.441489	−	0.897267i	$-0.645550\pi$
$661$		−	46.1373i		−	1.79453i	0.441489	−	0.897267i	$-0.354450\pi$
$662$	−0.599211	+	1.68071i	−0.0232890	+	0.0653225i
$663$		0			0
$664$	−19.9070	+	12.0243i	−0.772540	+	0.466633i
$665$	−19.3940			−0.752068
$666$		0			0
$667$		−	4.48634i		−	0.173712i
$668$	24.6292	+	20.1191i	0.952934	+	0.778432i
$669$		0			0
$670$	−20.6792	−	7.37263i	−0.798908	−	0.284829i
$671$	4.19561			0.161970
$672$		0			0
$673$	−32.0095			−1.23388			−0.616938	−	0.787012i	$-0.711627\pi$
$673$	−32.0095			−1.23388			−0.616938	+	0.787012i	$0.711627\pi$
$674$	23.7271	+	8.45925i	0.913932	+	0.325838i
$675$		0			0
$676$	−42.1351	−	34.4193i	−1.62058	−	1.32382i
$677$			13.7551i			0.528650i	0.964434	+	0.264325i	$0.0851491\pi$
$677$			13.7551i			0.528650i	−0.964434	+	0.264325i	$0.914851\pi$
$678$		0			0
$679$	35.8571			1.37607
$680$	−3.82694	+	2.31156i	−0.146756	+	0.0886443i
$681$		0			0
$682$	−2.12146	+	5.95040i	−0.0812348	+	0.227853i
$683$		−	23.7998i		−	0.910674i	−0.890319	−	0.455337i	$-0.849519\pi$
$683$		−	23.7998i		−	0.910674i	0.890319	−	0.455337i	$-0.150481\pi$
$684$		0			0
$685$			2.47594i			0.0946010i
$686$	−74.1833	−	26.4481i	−2.83233	−	1.00979i
$687$		0			0
$688$	−25.5664	+	5.20650i	−0.974712	+	0.198496i
$689$	−46.7469			−1.78091
$690$		0			0
$691$		−	37.8178i		−	1.43866i	−0.694671	−	0.719328i	$-0.744450\pi$
$691$		−	37.8178i		−	1.43866i	0.694671	−	0.719328i	$-0.255550\pi$
$692$	−26.7922	+	32.7983i	−1.01849	+	1.24680i
$693$		0			0
$694$	−2.06215	+	5.78405i	−0.0782781	+	0.219560i
$695$	5.20404			0.197401
$696$		0			0
$697$	−3.50141			−0.132625
$698$	5.93210	−	16.6387i	0.224533	−	0.629786i
$699$		0			0
$700$	−19.4158	−	15.8604i	−0.733850	−	0.599467i
$701$		−	4.14594i		−	0.156590i	−0.996930	−	0.0782950i	$-0.975052\pi$
$701$		−	4.14594i		−	0.156590i	0.996930	−	0.0782950i	$-0.0249476\pi$
$702$		0			0
$703$	2.86165			0.107929
$704$	−18.7948	−	9.88175i	−0.708357	−	0.372432i
$705$		0			0
$706$	−13.6915	−	4.88133i	−0.515286	−	0.183711i
$707$			43.4889i			1.63557i
$708$		0			0
$709$			47.2230i			1.77350i	0.462252	+	0.886748i	$0.347041\pi$
$709$			47.2230i			1.77350i	−0.462252	+	0.886748i	$0.652959\pi$
$710$	−1.88627	+	5.29075i	−0.0707906	+	0.198558i
$711$		0			0
$712$	−2.12537	−	3.51868i	−0.0796516	−	0.131868i
$713$	−4.77652			−0.178882
$714$		0			0
$715$			26.6027i			0.994884i
$716$	−20.9924	+	25.6983i	−0.784522	+	0.960389i
$717$		0			0
$718$	−9.93504	−	3.54207i	−0.370772	−	0.132189i
$719$	19.5647			0.729642			0.364821	−	0.931078i	$-0.381130\pi$
$719$	19.5647			0.729642			0.364821	+	0.931078i	$0.381130\pi$
$720$		0			0
$721$	35.7441			1.33118
$722$	17.3246	+	6.17662i	0.644755	+	0.229870i
$723$		0			0
$724$	−14.9124	+	18.2553i	−0.554214	+	0.678452i
$725$			3.95396i			0.146846i
$726$		0			0
$727$	2.57406			0.0954668			0.0477334	−	0.998860i	$-0.484800\pi$
$727$	2.57406			0.0954668			0.0477334	+	0.998860i	$0.484800\pi$
$728$	76.9275	−	46.4661i	2.85112	−	1.72215i
$729$		0			0
$730$	−1.89263	+	5.30857i	−0.0700493	+	0.196479i
$731$		−	6.52280i		−	0.241255i
$732$		0			0
$733$		−	8.78689i		−	0.324551i	−0.986745	−	0.162276i	$-0.948117\pi$
$733$		−	8.78689i		−	0.324551i	0.986745	−	0.162276i	$-0.0518833\pi$
$734$	−9.21913	−	3.28684i	−0.340284	−	0.121319i
$735$		0			0
$736$	2.26546	−	15.8947i	0.0835060	−	0.585887i
$737$	26.0676			0.960214
$738$		0			0
$739$			21.3574i			0.785643i	0.919615	+	0.392822i	$0.128501\pi$
$739$			21.3574i			0.785643i	−0.919615	+	0.392822i	$0.871499\pi$
$740$	−2.86165	−	2.33762i	−0.105196	−	0.0859327i
$741$		0			0
$742$	17.5465	−	49.2156i	0.644152	−	1.80676i
$743$	15.6886			0.575557			0.287779	−	0.957697i	$-0.407083\pi$
$743$	15.6886			0.575557			0.287779	+	0.957697i	$0.407083\pi$
$744$		0			0
$745$	−4.27108			−0.156480
$746$	−10.4901	+	29.4234i	−0.384071	+	1.07727i
$747$		0			0
$748$	3.35838	−	4.11123i	0.122794	−	0.150321i
$749$			26.3944i			0.964431i
$750$		0			0
$751$	−19.4799			−0.710832			−0.355416	−	0.934708i	$-0.615661\pi$
$751$	−19.4799			−0.710832			−0.355416	+	0.934708i	$0.615661\pi$
$752$	−7.04791	−	34.6086i	−0.257011	−	1.26205i
$753$		0			0
$754$	−13.3509	−	4.75990i	−0.486211	−	0.173345i
$755$		−	4.56792i		−	0.166244i
$756$		0			0
$757$			18.0194i			0.654927i	0.944864	+	0.327463i	$0.106194\pi$
$757$			18.0194i			0.654927i	−0.944864	+	0.327463i	$0.893806\pi$
$758$	−16.8326	+	47.2131i	−0.611386	+	1.71486i
$759$		0			0
$760$	5.65949	+	9.36965i	0.205291	+	0.339873i
$761$	31.8671			1.15518			0.577592	−	0.816326i	$-0.303993\pi$
$761$	31.8671			1.15518			0.577592	+	0.816326i	$0.303993\pi$
$762$		0			0
$763$			41.8491i			1.51504i
$764$	−12.3331	−	10.0747i	−0.446196	−	0.364488i
$765$		0			0
$766$	38.0301	+	13.5586i	1.37408	+	0.489893i
$767$	68.3613			2.46838
$768$		0			0
$769$	−2.60475			−0.0939296			−0.0469648	−	0.998897i	$-0.514955\pi$
$769$	−2.60475			−0.0939296			−0.0469648	+	0.998897i	$0.514955\pi$
$770$	−28.0076	−	9.98535i	−1.00932	−	0.359847i
$771$		0			0
$772$	39.0679	+	31.9137i	1.40608	+	1.14860i
$773$			9.40703i			0.338347i	0.985586	+	0.169174i	$0.0541099\pi$
$773$			9.40703i			0.338347i	−0.985586	+	0.169174i	$0.945890\pi$
$774$		0			0
$775$	4.20970			0.151217
$776$	−10.4637	−	17.3233i	−0.375624	−	0.621869i
$777$		0			0
$778$	9.03382	−	25.3387i	0.323878	−	0.908435i
$779$			8.57264i			0.307147i
$780$		0			0
$781$		−	6.66936i		−	0.238649i
$782$	3.78074	+	1.34792i	0.135199	+	0.0482016i
$783$		0			0
$784$	14.4577	+	70.9943i	0.516346	+	2.53551i
$785$	−1.60316			−0.0572191
$786$		0			0
$787$		−	3.38310i		−	0.120594i	−0.998180	−	0.0602972i	$-0.980795\pi$
$787$		−	3.38310i		−	0.120594i	0.998180	−	0.0602972i	$-0.0192048\pi$
$788$	−16.3008	+	19.9549i	−0.580691	+	0.710865i
$789$		0			0
$790$	0.612320	−	1.71747i	0.0217854	−	0.0611050i
$791$	−40.2032			−1.42946
$792$		0			0
$793$	10.0225			0.355911
$794$	3.09878	−	8.69166i	0.109972	−	0.308456i
$795$		0			0
$796$	0.526031	+	0.429704i	0.0186447	+	0.0152305i
$797$		−	20.3351i		−	0.720307i	−0.932893	−	0.360153i	$-0.882724\pi$
$797$		−	20.3351i		−	0.720307i	0.932893	−	0.360153i	$-0.117276\pi$
$798$		0			0
$799$	8.82975			0.312374
$800$	−1.99662	+	14.0085i	−0.0705913	+	0.495276i
$801$		0			0
$802$	7.20786	+	2.56977i	0.254518	+	0.0907418i
$803$		−	6.69183i		−	0.236149i
$804$		0			0
$805$		−	22.4823i		−	0.792397i
$806$	−5.06777	+	14.2144i	−0.178505	+	0.500681i
$807$		0			0
$808$	21.0104	−	12.6908i	0.739143	−	0.446460i
$809$	−44.1507			−1.55226			−0.776128	−	0.630576i	$-0.782819\pi$
$809$	−44.1507			−1.55226			−0.776128	+	0.630576i	$0.782819\pi$
$810$		0			0
$811$		−	7.73677i		−	0.271675i	−0.990731	−	0.135837i	$-0.956628\pi$
$811$		−	7.73677i		−	0.271675i	0.990731	−	0.135837i	$-0.0433725\pi$
$812$	10.0225	−	12.2693i	0.351722	−	0.430568i
$813$		0			0
$814$	4.13260	+	1.47337i	0.144848	+	0.0516416i
$815$	24.5417			0.859660
$816$		0			0
$817$	−15.9700			−0.558721
$818$	−37.8721	−	13.5023i	−1.32417	−	0.472097i
$819$		0			0
$820$	7.00281	−	8.57264i	0.244549	−	0.299369i
$821$			48.5660i			1.69496i	0.530824	+	0.847482i	$0.321882\pi$
$821$			48.5660i			1.69496i	−0.530824	+	0.847482i	$0.678118\pi$
$822$		0			0
$823$	−37.3368			−1.30148			−0.650740	−	0.759301i	$-0.725541\pi$
$823$	−37.3368			−1.30148			−0.650740	+	0.759301i	$0.725541\pi$
$824$	−10.4307	−	17.2687i	−0.363371	−	0.601583i
$825$		0			0
$826$	−25.6595	+	71.9714i	−0.892808	+	2.50421i
$827$		−	36.3380i		−	1.26360i	−0.775133	−	0.631798i	$-0.782317\pi$
$827$		−	36.3380i		−	1.26360i	0.775133	−	0.631798i	$-0.217683\pi$
$828$		0			0
$829$		−	10.6053i		−	0.368337i	−0.982895	−	0.184169i	$-0.941041\pi$
$829$		−	10.6053i		−	0.368337i	0.982895	−	0.184169i	$-0.0589593\pi$
$830$	17.3134	+	6.17262i	0.600956	+	0.214255i
$831$		0			0
$832$	−44.8974	−	23.6057i	−1.55654	−	0.818380i
$833$	−18.1129			−0.627574
$834$		0			0
$835$		−	25.1348i		−	0.869824i
$836$	−10.0657	−	8.22246i	−0.348129	−	0.284380i
$837$		0			0
$838$	−6.84948	+	19.2119i	−0.236611	+	0.663663i
$839$	43.2821			1.49426			0.747132	−	0.664676i	$-0.231430\pi$
$839$	43.2821			1.49426			0.747132	+	0.664676i	$0.231430\pi$
$840$		0			0
$841$	26.5014			0.913842
$842$	−10.0989	+	28.3261i	−0.348031	+	0.976181i
$843$		0			0
$844$	−8.05258	+	9.85774i	−0.277181	+	0.339317i
$845$			42.9999i			1.47924i
$846$		0			0
$847$	−19.8185			−0.680971
$848$	−28.8974	+	5.88483i	−0.992340	+	0.202086i
$849$		0			0
$850$	−3.33209	−	1.18797i	−0.114290	−	0.0407469i
$851$			3.31733i			0.113717i
$852$		0			0
$853$			39.7672i			1.36160i	0.732467	+	0.680802i	$0.238369\pi$
$853$			39.7672i			1.36160i	−0.732467	+	0.680802i	$0.761631\pi$
$854$	−3.76198	+	10.5518i	−0.128732	+	0.361076i
$855$		0			0
$856$	12.7517	−	7.70232i	0.435843	−	0.263260i
$857$	14.9672			0.511271			0.255636	−	0.966773i	$-0.417715\pi$
$857$	14.9672			0.511271			0.255636	+	0.966773i	$0.417715\pi$
$858$		0			0
$859$		−	47.5063i		−	1.62090i	−0.585811	−	0.810448i	$-0.699224\pi$
$859$		−	47.5063i		−	1.62090i	0.585811	−	0.810448i	$-0.300776\pi$
$860$	15.9700	+	13.0456i	0.544574	+	0.444851i
$861$		0			0
$862$	−24.6105	−	8.77421i	−0.838236	−	0.298851i
$863$	20.9221			0.712198			0.356099	−	0.934448i	$-0.384107\pi$
$863$	20.9221			0.712198			0.356099	+	0.934448i	$0.384107\pi$
$864$		0			0
$865$	33.4715			1.13806
$866$	−36.1767	−	12.8978i	−1.22934	−	0.438287i
$867$		0			0
$868$	−13.0629	−	10.6708i	−0.443383	−	0.362190i
$869$			2.16500i			0.0734426i
$870$		0			0
$871$	62.2708			2.10997
$872$	20.2182	−	12.2123i	0.684673	−	0.413559i
$873$		0			0
$874$	3.30017	−	9.25654i	0.111630	−	0.313107i
$875$			59.4208i			2.00879i
$876$		0			0
$877$		−	29.6926i		−	1.00265i	−0.865260	−	0.501324i	$-0.832847\pi$
$877$		−	29.6926i		−	1.00265i	0.865260	−	0.501324i	$-0.167153\pi$
$878$	3.05910	+	1.09064i	0.103239	+	0.0368073i
$879$		0			0
$880$	3.34894	+	16.4449i	0.112893	+	0.554358i
$881$	16.1976			0.545710			0.272855	−	0.962055i	$-0.412032\pi$
$881$	16.1976			0.545710			0.272855	+	0.962055i	$0.412032\pi$
$882$		0			0
$883$		−	37.4853i		−	1.26148i	−0.775993	−	0.630741i	$-0.782751\pi$
$883$		−	37.4853i		−	1.26148i	0.775993	−	0.630741i	$-0.217249\pi$
$884$	8.02255	−	9.82097i	0.269827	−	0.330315i
$885$		0			0
$886$	7.11962	−	19.9696i	0.239188	−	0.670891i
$887$	8.05161			0.270347			0.135173	−	0.990822i	$-0.456841\pi$
$887$	8.05161			0.270347			0.135173	+	0.990822i	$0.456841\pi$
$888$		0			0
$889$	−67.6592			−2.26922
$890$	−1.09105	+	3.06025i	−0.0365721	+	0.102580i
$891$		0			0
$892$	20.2331	+	16.5280i	0.677455	+	0.553399i
$893$		−	21.6182i		−	0.723427i
$894$		0			0
$895$	26.2257			0.876630
$896$	41.7046	−	38.4080i	1.39325	−	1.28312i
$897$		0			0
$898$	27.5165	+	9.81026i	0.918236	+	0.327373i
$899$			2.66020i			0.0887227i
$900$		0			0
$901$		−	7.37263i		−	0.245618i
$902$	−4.41377	+	12.3800i	−0.146962	+	0.412210i
$903$		0			0
$904$	11.7319	+	19.4230i	0.390199	+	0.645998i
$905$	18.6300			0.619281
$906$		0			0
$907$			33.3609i			1.10773i	0.832606	+	0.553865i	$0.186848\pi$
$907$			33.3609i			1.10773i	−0.832606	+	0.553865i	$0.813152\pi$
$908$	25.7741	−	31.5519i	0.855344	−	1.04709i
$909$		0			0
$910$	−66.9050	−	23.8532i	−2.21788	−	0.790725i
$911$	25.7866			0.854347			0.427174	−	0.904170i	$-0.359509\pi$
$911$	25.7866			0.854347			0.427174	+	0.904170i	$0.359509\pi$
$912$		0			0
$913$	−21.8247			−0.722293
$914$	35.1945	+	12.5477i	1.16413	+	0.415040i
$915$		0			0
$916$	22.6792	−	27.7633i	0.749343	−	0.917324i
$917$		−	29.5915i		−	0.977196i
$918$		0			0
$919$	−25.8720			−0.853440			−0.426720	−	0.904384i	$-0.640331\pi$
$919$	−25.8720			−0.853440			−0.426720	+	0.904384i	$0.640331\pi$
$920$	−10.8616	+	6.56070i	−0.358098	+	0.216300i
$921$		0			0
$922$	18.6341	−	52.2662i	0.613683	−	1.72130i
$923$		−	15.9319i		−	0.524404i
$924$		0			0
$925$		−	2.92367i		−	0.0961297i
$926$	9.73454	+	3.47059i	0.319897	+	0.114051i
$927$		0			0
$928$	−8.85229	−	1.26171i	−0.290591	−	0.0414177i
$929$	−40.6849			−1.33483			−0.667413	−	0.744687i	$-0.732599\pi$
$929$	−40.6849			−1.33483			−0.667413	+	0.744687i	$0.732599\pi$
$930$		0			0
$931$			44.3465i			1.45340i
$932$	−24.6161	−	20.1084i	−0.806328	−	0.658673i
$933$		0			0
$934$	−11.5844	+	32.4926i	−0.379052	+	1.06319i
$935$	−4.19561			−0.137211
$936$		0			0
$937$	−0.426795			−0.0139428			−0.00697140	−	0.999976i	$-0.502219\pi$
$937$	−0.426795			−0.0139428			−0.00697140	+	0.999976i	$0.502219\pi$
$938$	−23.3734	+	65.5593i	−0.763170	+	2.14059i
$939$		0			0
$940$	−17.6595	+	21.6182i	−0.575989	+	0.705109i
$941$		−	21.4487i		−	0.699208i	−0.936898	−	0.349604i	$-0.886316\pi$
$941$		−	21.4487i		−	0.699208i	0.936898	−	0.349604i	$-0.113684\pi$
$942$		0			0
$943$	−9.93772			−0.323617
$944$	42.2587	−	8.60581i	1.37540	−	0.280095i
$945$		0			0
$946$	−23.0629	−	8.22246i	−0.749839	−	0.267335i
$947$		−	45.9708i		−	1.49385i	−0.664908	−	0.746925i	$-0.731529\pi$
$947$		−	45.9708i		−	1.49385i	0.664908	−	0.746925i	$-0.268471\pi$
$948$		0			0
$949$		−	15.9856i		−	0.518913i
$950$	−2.90855	+	8.15808i	−0.0943657	+	0.264683i
$951$		0			0
$952$	7.32834	+	12.1325i	0.237513	+	0.393218i
$953$	−28.3714			−0.919038			−0.459519	−	0.888168i	$-0.651978\pi$
$953$	−28.3714			−0.919038			−0.459519	+	0.888168i	$0.651978\pi$
$954$		0			0
$955$			12.5862i			0.407281i
$956$	25.3303	+	20.6918i	0.819240	+	0.669220i
$957$		0			0
$958$	8.89849	+	3.17252i	0.287497	+	0.102499i
$959$	7.84948			0.253473
$960$		0			0
$961$	−28.1677			−0.908637
$962$	9.87203	+	3.51961i	0.318287	+	0.113477i
$963$		0			0
$964$	45.9746	+	37.5557i	1.48074	+	1.20959i
$965$		−	39.8697i		−	1.28345i
$966$		0			0
$967$	−29.4541			−0.947180			−0.473590	−	0.880745i	$-0.657042\pi$
$967$	−29.4541			−0.947180			−0.473590	+	0.880745i	$0.657042\pi$
$968$	5.78335	+	9.57470i	0.185884	+	0.307743i
$969$		0			0
$970$	−5.37149	+	15.0663i	−0.172468	+	0.483750i
$971$			38.8816i			1.24777i	0.781516	+	0.623885i	$0.214446\pi$
$971$			38.8816i			1.24777i	−0.781516	+	0.623885i	$0.785554\pi$
$972$		0			0
$973$		−	16.4984i		−	0.528914i
$974$	22.9537	+	8.18352i	0.735483	+	0.262217i
$975$		0			0
$976$	6.19561	−	1.26171i	0.198317	−	0.0403864i
$977$	−51.5465			−1.64912			−0.824559	−	0.565775i	$-0.808577\pi$
$977$	−51.5465			−1.64912			−0.824559	+	0.565775i	$0.808577\pi$
$978$		0			0
$979$		−	3.85766i		−	0.123291i
$980$	36.2257	−	44.3465i	1.15719	−	1.41660i
$981$		0			0
$982$	4.14865	−	11.6364i	0.132389	−	0.371333i
$983$	−39.7261			−1.26707			−0.633533	−	0.773716i	$-0.718396\pi$
$983$	−39.7261			−1.26707			−0.633533	+	0.773716i	$0.718396\pi$
$984$		0			0
$985$	20.3645			0.648868
$986$	0.750703	−	2.10562i	0.0239072	−	0.0670566i
$987$		0			0
$988$	−24.0451	−	19.6419i	−0.764976	−	0.624893i
$989$		−	18.5131i		−	0.588682i
$990$		0			0
$991$	8.01408			0.254576			0.127288	−	0.991866i	$-0.459373\pi$
$991$	8.01408			0.254576			0.127288	+	0.991866i	$0.459373\pi$
$992$	−1.34332	+	9.42485i	−0.0426504	+	0.299239i
$993$		0			0
$994$	16.7733	+	5.98006i	0.532015	+	0.189676i
$995$		−	0.536828i		−	0.0170186i
$996$		0			0
$997$		−	18.6589i		−	0.590934i	−0.955353	−	0.295467i	$-0.904525\pi$
$997$		−	18.6589i		−	0.590934i	0.955353	−	0.295467i	$-0.0954753\pi$
$998$	−2.48448	+	6.96863i	−0.0786448	+	0.220588i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.2.f.c.613.8		8
3.2	odd	2		136.2.c.b.69.1	✓	8
4.3	odd	2		4896.2.f.d.2449.3		8
8.3	odd	2		4896.2.f.d.2449.6		8
8.5	even	2	inner	1224.2.f.c.613.7		8
12.11	even	2		544.2.c.b.273.2		8
24.5	odd	2		136.2.c.b.69.2	yes	8
24.11	even	2		544.2.c.b.273.7		8
48.5	odd	4		4352.2.a.bf.1.7		8
48.11	even	4		4352.2.a.bb.1.2		8
48.29	odd	4		4352.2.a.bf.1.2		8
48.35	even	4		4352.2.a.bb.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.c.b.69.1	✓	8	3.2	odd	2
136.2.c.b.69.2	yes	8	24.5	odd	2
544.2.c.b.273.2		8	12.11	even	2
544.2.c.b.273.7		8	24.11	even	2
1224.2.f.c.613.7		8	8.5	even	2	inner
1224.2.f.c.613.8		8	1.1	even	1	trivial
4352.2.a.bb.1.2		8	48.11	even	4
4352.2.a.bb.1.7		8	48.35	even	4
4352.2.a.bf.1.2		8	48.29	odd	4
4352.2.a.bf.1.7		8	48.5	odd	4
4896.2.f.d.2449.3		8	4.3	odd	2
4896.2.f.d.2449.6		8	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33209 + 0.474920i) q^{2} +(1.54890 + 1.26527i) q^{4} -1.58069i q^{5} -5.01127 q^{7} +(1.46237 + 2.42105i) q^{8} +(0.750703 - 2.10562i) q^{10} +2.65428i q^{11} +6.34060i q^{13} +(-6.67544 - 2.37995i) q^{14} +(0.798200 + 3.91955i) q^{16} -1.00000 q^{17} +2.44834i q^{19} +(2.00000 - 2.44834i) q^{20} +(-1.26057 + 3.53573i) q^{22} -2.83821 q^{23} +2.50141 q^{25} +(-3.01127 + 8.44622i) q^{26} +(-7.76198 - 6.34060i) q^{28} +1.58069i q^{29} +1.68293 q^{31} +(-0.798200 + 5.60026i) q^{32} +(-1.33209 - 0.474920i) q^{34} +7.92129i q^{35} -1.16881i q^{37} +(-1.16277 + 3.26140i) q^{38} +(3.82694 - 2.31156i) q^{40} +3.50141 q^{41} +6.52280i q^{43} +(-3.35838 + 4.11123i) q^{44} +(-3.78074 - 1.34792i) q^{46} -8.82975 q^{47} +18.1129 q^{49} +(3.33209 + 1.18797i) q^{50} +(-8.02255 + 9.82097i) q^{52} +7.37263i q^{53} +4.19561 q^{55} +(-7.32834 - 12.1325i) q^{56} +(-0.750703 + 2.10562i) q^{58} -10.7815i q^{59} -1.58069i q^{61} +(2.24181 + 0.799257i) q^{62} +(-3.72294 + 7.08094i) q^{64} +10.0225 q^{65} -9.82097i q^{67} +(-1.54890 - 1.26527i) q^{68} +(-3.76198 + 10.5518i) q^{70} -2.51268 q^{71} -2.52114 q^{73} +(0.555091 - 1.55696i) q^{74} +(-3.09781 + 3.79224i) q^{76} -13.3013i q^{77} +0.815662 q^{79} +(6.19561 - 1.26171i) q^{80} +(4.66417 + 1.66289i) q^{82} +8.22246i q^{83} +1.58069i q^{85} +(-3.09781 + 8.68893i) q^{86} +(-6.42615 + 3.88155i) q^{88} -1.45337 q^{89} -31.7745i q^{91} +(-4.39611 - 3.59109i) q^{92} +(-11.7620 - 4.19342i) q^{94} +3.87008 q^{95} -7.15528 q^{97} +(24.1279 + 8.60215i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{4} - 12 q^{7} - 5 q^{8} - 8 q^{10} - 6 q^{14} + 9 q^{16} - 8 q^{17} + 16 q^{20} + 4 q^{22} + 16 q^{23} - 8 q^{25} + 4 q^{26} - 20 q^{28} + 24 q^{31} - 9 q^{32} - q^{34} - 18 q^{38} + 20 q^{40}+ \cdots + 57 q^{98}+O(q^{100}) \) 8 * q + q^2 + q^4 - 12 * q^7 - 5 * q^8 - 8 * q^10 - 6 * q^14 + 9 * q^16 - 8 * q^17 + 16 * q^20 + 4 * q^22 + 16 * q^23 - 8 * q^25 + 4 * q^26 - 20 * q^28 + 24 * q^31 - 9 * q^32 - q^34 - 18 * q^38 + 20 * q^40 + 10 * q^44 - 18 * q^46 - 4 * q^47 + 8 * q^49 + 17 * q^50 - 8 * q^52 - 12 * q^55 - 20 * q^56 + 8 * q^58 - 26 * q^62 + q^64 + 24 * q^65 - q^68 + 12 * q^70 + 36 * q^71 + 8 * q^73 + 36 * q^74 - 2 * q^76 + 24 * q^79 + 4 * q^80 + 18 * q^82 - 2 * q^86 + 10 * q^88 - 8 * q^89 + 28 * q^92 - 52 * q^94 - 32 * q^95 - 8 * q^97 + 57 * q^98

Introduction

L-functions

Modular forms

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Database

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