LMFDB - Embedded newform 693.2.m.i.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.2
Root			$-0.206962 - 0.636964i$ of defining polynomial
Character	$\chi$	$=$	693.379
Dual form			693.2.m.i.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.206962 - 0.636964i) q^{2} +(1.25514 - 0.911915i) q^{4} +(-0.662464 + 2.03885i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-1.92429 - 1.39808i) q^{8} +O(q^{10})$	\(q+(-0.206962 - 0.636964i) q^{2} +(1.25514 - 0.911915i) q^{4} +(-0.662464 + 2.03885i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-1.92429 - 1.39808i) q^{8} +1.43578 q^{10} +(1.08444 + 3.13432i) q^{11} +(0.781276 + 2.40452i) q^{13} +(0.541834 + 0.393666i) q^{14} +(0.466573 - 1.43596i) q^{16} +(0.553425 - 1.70327i) q^{17} +(5.44258 + 3.95427i) q^{19} +(1.02778 + 3.16317i) q^{20} +(1.77201 - 1.33944i) q^{22} +3.16429 q^{23} +(0.327016 + 0.237591i) q^{25} +(1.36990 - 0.995290i) q^{26} +(-0.479422 + 1.47551i) q^{28} +(-0.747669 + 0.543213i) q^{29} +(0.927602 + 2.85487i) q^{31} -5.76834 q^{32} -1.19946 q^{34} +(-0.662464 - 2.03885i) q^{35} +(1.21933 - 0.885898i) q^{37} +(1.39232 - 4.28511i) q^{38} +(4.12526 - 2.99718i) q^{40} +(4.49897 + 3.26870i) q^{41} -8.42985 q^{43} +(4.21937 + 2.94511i) q^{44} +(-0.654888 - 2.01554i) q^{46} +(3.55782 + 2.58491i) q^{47} +(0.309017 - 0.951057i) q^{49} +(0.0836570 - 0.257470i) q^{50} +(3.17333 + 2.30556i) q^{52} +(-0.206244 - 0.634755i) q^{53} +(-7.10883 + 0.134639i) q^{55} +2.37856 q^{56} +(0.500747 + 0.363814i) q^{58} +(-0.298010 + 0.216517i) q^{59} +(1.54863 - 4.76621i) q^{61} +(1.62647 - 1.18170i) q^{62} +(0.260682 + 0.802296i) q^{64} -5.42003 q^{65} -0.902129 q^{67} +(-0.858607 - 2.64252i) q^{68} +(-1.16157 + 0.843932i) q^{70} +(4.59489 - 14.1416i) q^{71} +(-6.50301 + 4.72471i) q^{73} +(-0.816641 - 0.593325i) q^{74} +10.4372 q^{76} +(-2.71964 - 1.89830i) q^{77} +(1.25358 + 3.85813i) q^{79} +(2.61863 + 1.90255i) q^{80} +(1.15092 - 3.54218i) q^{82} +(1.25193 - 3.85305i) q^{83} +(3.10609 + 2.25670i) q^{85} +(1.74466 + 5.36951i) q^{86} +(2.29526 - 7.54749i) q^{88} +8.30727 q^{89} +(-2.04541 - 1.48608i) q^{91} +(3.97163 - 2.88556i) q^{92} +(0.910159 - 2.80118i) q^{94} +(-11.6677 + 8.47707i) q^{95} +(2.63154 + 8.09904i) q^{97} -0.669744 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.206962	−	0.636964i	−0.146344	−	0.450402i	0.850837	−	0.525430i	$-0.176095\pi$
$2$	−0.206962	−	0.636964i	−0.146344	−	0.450402i	−0.997181	+	0.0750279i	$0.976095\pi$
$3$		0			0
$3$		0			0
$4$	1.25514	−	0.911915i	0.627572	−	0.455958i
$5$	−0.662464	+	2.03885i	−0.296263	+	0.911803i	0.686531	+	0.727100i	$0.259132\pi$
$5$	−0.662464	+	2.03885i	−0.296263	+	0.911803i	−0.982794	+	0.184703i	$0.940868\pi$
$6$		0			0
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	−1.92429	−	1.39808i	−0.680340	−	0.494296i
$9$		0			0
$10$	1.43578			0.454034
$11$	1.08444	+	3.13432i	0.326971	+	0.945034i
$11$	1.08444	+	3.13432i	0.326971	+	0.945034i
$12$		0			0
$13$	0.781276	+	2.40452i	0.216687	+	0.666894i	0.999030	+	0.0440455i	$0.0140247\pi$
$13$	0.781276	+	2.40452i	0.216687	+	0.666894i	−0.782343	+	0.622848i	$0.785975\pi$
$14$	0.541834	+	0.393666i	0.144811	+	0.105212i
$15$		0			0
$16$	0.466573	−	1.43596i	0.116643	−	0.358991i
$17$	0.553425	−	1.70327i	0.134225	−	0.413103i	−0.861244	−	0.508193i	$-0.830314\pi$
$17$	0.553425	−	1.70327i	0.134225	−	0.413103i	0.995469	+	0.0950899i	$0.0303138\pi$
$18$		0			0
$19$	5.44258	+	3.95427i	1.24861	+	0.907171i	0.998141	−	0.0609525i	$-0.0194138\pi$
$19$	5.44258	+	3.95427i	1.24861	+	0.907171i	0.250473	+	0.968124i	$0.419414\pi$
$20$	1.02778	+	3.16317i	0.229818	+	0.707306i
$21$		0			0
$22$	1.77201	−	1.33944i	0.377795	−	0.285569i
$23$	3.16429			0.659799			0.329900	−	0.944016i	$-0.392985\pi$
$23$	3.16429			0.659799			0.329900	+	0.944016i	$0.392985\pi$
$24$		0			0
$25$	0.327016	+	0.237591i	0.0654031	+	0.0475182i
$26$	1.36990	−	0.995290i	0.268659	−	0.195192i
$27$		0			0
$28$	−0.479422	+	1.47551i	−0.0906023	+	0.278845i
$29$	−0.747669	+	0.543213i	−0.138839	+	0.100872i	−0.655037	−	0.755597i	$-0.727347\pi$
$29$	−0.747669	+	0.543213i	−0.138839	+	0.100872i	0.516198	+	0.856469i	$0.327347\pi$
$30$		0			0
$31$	0.927602	+	2.85487i	0.166602	+	0.512749i	0.999151	−	0.0412031i	$-0.0131191\pi$
$31$	0.927602	+	2.85487i	0.166602	+	0.512749i	−0.832549	+	0.553952i	$0.813119\pi$
$32$	−5.76834			−1.01971
$33$		0			0
$34$	−1.19946			−0.205705
$35$	−0.662464	−	2.03885i	−0.111977	−	0.344629i
$36$		0			0
$37$	1.21933	−	0.885898i	0.200457	−	0.145641i	−0.483028	−	0.875605i	$-0.660463\pi$
$37$	1.21933	−	0.885898i	0.200457	−	0.145641i	0.683486	+	0.729964i	$0.260463\pi$
$38$	1.39232	−	4.28511i	0.225864	−	0.695137i
$39$		0			0
$40$	4.12526	−	2.99718i	0.652261	−	0.473895i
$41$	4.49897	+	3.26870i	0.702622	+	0.510485i	0.880785	−	0.473516i	$-0.157016\pi$
$41$	4.49897	+	3.26870i	0.702622	+	0.510485i	−0.178163	+	0.984001i	$0.557016\pi$
$42$		0			0
$43$	−8.42985			−1.28554			−0.642770	−	0.766059i	$-0.722215\pi$
$43$	−8.42985			−1.28554			−0.642770	+	0.766059i	$0.722215\pi$
$44$	4.21937	+	2.94511i	0.636094	+	0.443992i
$45$		0			0
$46$	−0.654888	−	2.01554i	−0.0965579	−	0.297175i
$47$	3.55782	+	2.58491i	0.518961	+	0.377047i	0.816212	−	0.577752i	$-0.196070\pi$
$47$	3.55782	+	2.58491i	0.518961	+	0.377047i	−0.297251	+	0.954799i	$0.596070\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	0.0836570	−	0.257470i	0.0118309	−	0.0364117i
$51$		0			0
$52$	3.17333	+	2.30556i	0.440062	+	0.319724i
$53$	−0.206244	−	0.634755i	−0.0283298	−	0.0871903i	0.935892	−	0.352287i	$-0.114596\pi$
$53$	−0.206244	−	0.634755i	−0.0283298	−	0.0871903i	−0.964222	+	0.265097i	$0.914596\pi$
$54$		0			0
$55$	−7.10883	+	0.134639i	−0.958555	+	0.0181547i
$56$	2.37856			0.317848
$57$		0			0
$58$	0.500747	+	0.363814i	0.0657513	+	0.0477711i
$59$	−0.298010	+	0.216517i	−0.0387976	+	0.0281881i	−0.607015	−	0.794690i	$-0.707633\pi$
$59$	−0.298010	+	0.216517i	−0.0387976	+	0.0281881i	0.568217	+	0.822878i	$0.307633\pi$
$60$		0			0
$61$	1.54863	−	4.76621i	0.198282	−	0.610250i	−0.801640	−	0.597807i	$-0.796039\pi$
$61$	1.54863	−	4.76621i	0.198282	−	0.610250i	0.999923	−	0.0124435i	$-0.00396099\pi$
$62$	1.62647	−	1.18170i	0.206562	−	0.150076i
$63$		0			0
$64$	0.260682	+	0.802296i	0.0325852	+	0.100287i
$65$	−5.42003			−0.672273
$66$		0			0
$67$	−0.902129			−0.110213			−0.0551063	−	0.998480i	$-0.517550\pi$
$67$	−0.902129			−0.110213			−0.0551063	+	0.998480i	$0.517550\pi$
$68$	−0.858607	−	2.64252i	−0.104121	−	0.320453i
$69$		0			0
$70$	−1.16157	+	0.843932i	−0.138834	+	0.100869i
$71$	4.59489	−	14.1416i	0.545313	−	1.67830i	−0.174932	−	0.984580i	$-0.555971\pi$
$71$	4.59489	−	14.1416i	0.545313	−	1.67830i	0.720245	−	0.693720i	$-0.244029\pi$
$72$		0			0
$73$	−6.50301	+	4.72471i	−0.761119	+	0.552986i	−0.899254	−	0.437428i	$-0.855890\pi$
$73$	−6.50301	+	4.72471i	−0.761119	+	0.552986i	0.138134	+	0.990414i	$0.455890\pi$
$74$	−0.816641	−	0.593325i	−0.0949326	−	0.0689726i
$75$		0			0
$76$	10.4372			1.19723
$77$	−2.71964	−	1.89830i	−0.309932	−	0.216332i
$78$		0			0
$79$	1.25358	+	3.85813i	0.141039	+	0.434074i	0.996480	−	0.0838261i	$-0.0267140\pi$
$79$	1.25358	+	3.85813i	0.141039	+	0.434074i	−0.855441	+	0.517900i	$0.826714\pi$
$80$	2.61863	+	1.90255i	0.292772	+	0.212711i
$81$		0			0
$82$	1.15092	−	3.54218i	0.127098	−	0.391169i
$83$	1.25193	−	3.85305i	0.137418	−	0.422928i	−0.858541	−	0.512745i	$-0.828628\pi$
$83$	1.25193	−	3.85305i	0.137418	−	0.422928i	0.995958	+	0.0898178i	$0.0286285\pi$
$84$		0			0
$85$	3.10609	+	2.25670i	0.336902	+	0.244774i
$86$	1.74466	+	5.36951i	0.188132	+	0.579009i
$87$		0			0
$88$	2.29526	−	7.54749i	0.244675	−	0.804566i
$89$	8.30727			0.880569			0.440284	−	0.897858i	$-0.354878\pi$
$89$	8.30727			0.880569			0.440284	+	0.897858i	$0.354878\pi$
$90$		0			0
$91$	−2.04541	−	1.48608i	−0.214417	−	0.155783i
$92$	3.97163	−	2.88556i	0.414071	−	0.300840i
$93$		0			0
$94$	0.910159	−	2.80118i	0.0938758	−	0.288920i
$95$	−11.6677	+	8.47707i	−1.19708	+	0.869729i
$96$		0			0
$97$	2.63154	+	8.09904i	0.267192	+	0.822333i	0.991180	+	0.132520i	$0.0423070\pi$
$97$	2.63154	+	8.09904i	0.267192	+	0.822333i	−0.723988	+	0.689812i	$0.757693\pi$
$98$	−0.669744			−0.0676544
$99$		0			0
$100$	0.627115			0.0627115
$101$	1.24443	+	3.82997i	0.123826	+	0.381096i	0.993685	−	0.112203i	$-0.0357907\pi$
$101$	1.24443	+	3.82997i	0.123826	+	0.381096i	−0.869860	+	0.493299i	$0.835791\pi$
$102$		0			0
$103$	14.2596	−	10.3602i	1.40504	−	1.02082i	0.411020	−	0.911626i	$-0.365173\pi$
$103$	14.2596	−	10.3602i	1.40504	−	1.02082i	0.994020	−	0.109195i	$-0.0348272\pi$
$104$	1.85831	−	5.71929i	0.182222	−	0.560822i
$105$		0			0
$106$	−0.361631	+	0.262741i	−0.0351248	+	0.0255196i
$107$	−12.4619	−	9.05408i	−1.20473	−	0.875291i	−0.209993	−	0.977703i	$-0.567344\pi$
$107$	−12.4619	−	9.05408i	−1.20473	−	0.875291i	−0.994742	+	0.102412i	$0.967344\pi$
$108$		0			0
$109$	−18.9265			−1.81283			−0.906416	−	0.422386i	$-0.861193\pi$
$109$	−18.9265			−1.81283			−0.906416	+	0.422386i	$0.861193\pi$
$110$	1.55702	+	4.50021i	0.148456	+	0.429078i
$111$		0			0
$112$	0.466573	+	1.43596i	0.0440870	+	0.135686i
$113$	1.35965	+	0.987844i	0.127905	+	0.0929286i	0.649898	−	0.760021i	$-0.274811\pi$
$113$	1.35965	+	0.987844i	0.127905	+	0.0929286i	−0.521993	+	0.852950i	$0.674811\pi$
$114$		0			0
$115$	−2.09623	+	6.45152i	−0.195474	+	0.601607i
$116$	−0.443068	+	1.36362i	−0.0411378	+	0.126609i
$117$		0			0
$118$	0.199590	+	0.145011i	0.0183738	+	0.0133493i
$119$	0.553425	+	1.70327i	0.0507324	+	0.156138i
$120$		0			0
$121$	−8.64798	+	6.79797i	−0.786180	+	0.617998i
$122$	−3.35641			−0.303875
$123$		0			0
$124$	3.76767	+	2.73737i	0.338347	+	0.245823i
$125$	−9.37282	+	6.80975i	−0.838330	+	0.609082i
$126$		0			0
$127$	5.42848	−	16.7071i	0.481699	−	1.48252i	−0.355006	−	0.934864i	$-0.615521\pi$
$127$	5.42848	−	16.7071i	0.481699	−	1.48252i	0.836705	−	0.547654i	$-0.184479\pi$
$128$	−8.87628	+	6.44900i	−0.784560	+	0.570016i
$129$		0			0
$130$	1.12174	+	3.45237i	0.0983833	+	0.302793i
$131$	−6.72557			−0.587616			−0.293808	−	0.955865i	$-0.594923\pi$
$131$	−6.72557			−0.587616			−0.293808	+	0.955865i	$0.594923\pi$
$132$		0			0
$133$	−6.72740			−0.583340
$134$	0.186707	+	0.574624i	0.0161290	+	0.0496400i
$135$		0			0
$136$	−3.44625	+	2.50385i	−0.295514	+	0.214703i
$137$	−4.28533	+	13.1889i	−0.366121	+	1.12680i	0.583156	+	0.812360i	$0.301818\pi$
$137$	−4.28533	+	13.1889i	−0.366121	+	1.12680i	−0.949276	+	0.314443i	$0.898182\pi$
$138$		0			0
$139$	−11.5453	+	8.38812i	−0.979256	+	0.711471i	−0.957542	−	0.288293i	$-0.906912\pi$
$139$	−11.5453	+	8.38812i	−0.979256	+	0.711471i	−0.0217140	+	0.999764i	$0.506912\pi$
$140$	−2.69075	−	1.95494i	−0.227410	−	0.165223i
$141$		0			0
$142$	−9.95867			−0.835713
$143$	−6.68930	+	5.05633i	−0.559387	+	0.422832i
$144$		0			0
$145$	−0.612229	−	1.88425i	−0.0508429	−	0.156478i
$146$	4.35535	+	3.16435i	0.360451	+	0.261883i
$147$		0			0
$148$	0.722575	−	2.22386i	0.0593953	−	0.182800i
$149$	−0.810527	+	2.49455i	−0.0664010	+	0.204361i	−0.978752	−	0.205048i	$-0.934265\pi$
$149$	−0.810527	+	2.49455i	−0.0664010	+	0.204361i	0.912351	+	0.409409i	$0.134265\pi$
$150$		0			0
$151$	2.41864	+	1.75724i	0.196826	+	0.143002i	0.681833	−	0.731508i	$-0.261183\pi$
$151$	2.41864	+	1.75724i	0.196826	+	0.143002i	−0.485007	+	0.874510i	$0.661183\pi$
$152$	−4.94474	−	15.2183i	−0.401071	−	1.23437i
$153$		0			0
$154$	−0.646289	+	2.12519i	−0.0520794	+	0.171253i
$155$	−6.43516			−0.516884
$156$		0			0
$157$	−9.10524	−	6.61534i	−0.726677	−	0.527962i	0.161833	−	0.986818i	$-0.448259\pi$
$157$	−9.10524	−	6.61534i	−0.726677	−	0.527962i	−0.888511	+	0.458856i	$0.848259\pi$
$158$	2.19805	−	1.59698i	0.174867	−	0.127049i
$159$		0			0
$160$	3.82131	−	11.7608i	0.302101	−	0.929773i
$161$	−2.55996	+	1.85992i	−0.201753	+	0.146582i
$162$		0			0
$163$	−5.62502	−	17.3120i	−0.440586	−	1.35598i	−0.887253	−	0.461283i	$-0.847389\pi$
$163$	−5.62502	−	17.3120i	−0.440586	−	1.35598i	0.446667	−	0.894700i	$-0.352611\pi$
$164$	8.62763			0.673705
$165$		0			0
$166$	−2.71336			−0.210598
$167$	−6.15909	−	18.9557i	−0.476605	−	1.46684i	−0.843781	−	0.536687i	$-0.819675\pi$
$167$	−6.15909	−	18.9557i	−0.476605	−	1.46684i	0.367176	−	0.930151i	$-0.380325\pi$
$168$		0			0
$169$	5.34590	−	3.88402i	0.411223	−	0.298771i
$170$	0.794597	−	2.44552i	0.0609428	−	0.187563i
$171$		0			0
$172$	−10.5807	+	7.68731i	−0.806769	+	0.586152i
$173$	4.84607	+	3.52088i	0.368440	+	0.267687i	0.756564	−	0.653920i	$-0.226877\pi$
$173$	4.84607	+	3.52088i	0.368440	+	0.267687i	−0.388124	+	0.921607i	$0.626877\pi$
$174$		0			0
$175$	−0.404214			−0.0305557
$176$	5.00675	−	0.0948260i	0.377398	−	0.00714778i
$177$		0			0
$178$	−1.71929	−	5.29143i	−0.128866	−	0.396610i
$179$	−1.30975	−	0.951588i	−0.0978952	−	0.0711251i	0.537761	−	0.843097i	$-0.319270\pi$
$179$	−1.30975	−	0.951588i	−0.0978952	−	0.0711251i	−0.635656	+	0.771972i	$0.719270\pi$
$180$		0			0
$181$	0.749929	−	2.30804i	0.0557418	−	0.171556i	−0.919309	−	0.393535i	$-0.871252\pi$
$181$	0.749929	−	2.30804i	0.0557418	−	0.171556i	0.975051	+	0.221980i	$0.0712519\pi$
$182$	−0.523255	+	1.61041i	−0.0387862	+	0.119372i
$183$		0			0
$184$	−6.08901	−	4.42393i	−0.448888	−	0.326136i
$185$	0.998452	+	3.07292i	0.0734077	+	0.225926i
$186$		0			0
$187$	5.93874	−	0.112478i	0.434284	−	0.00822518i
$188$	6.82279			0.497603
$189$		0			0
$190$	7.81436	+	5.67747i	0.566914	+	0.411887i
$191$	10.2753	−	7.46541i	0.743492	−	0.540178i	−0.150311	−	0.988639i	$-0.548027\pi$
$191$	10.2753	−	7.46541i	0.743492	−	0.540178i	0.893803	+	0.448460i	$0.148027\pi$
$192$		0			0
$193$	−0.543657	+	1.67320i	−0.0391333	+	0.120440i	−0.968715	−	0.248177i	$-0.920169\pi$
$193$	−0.543657	+	1.67320i	−0.0391333	+	0.120440i	0.929581	+	0.368617i	$0.120169\pi$
$194$	4.61417	−	3.35239i	0.331278	−	0.240688i
$195$		0			0
$196$	−0.479422	−	1.47551i	−0.0342444	−	0.105394i
$197$	0.903053			0.0643399			0.0321699	−	0.999482i	$-0.489758\pi$
$197$	0.903053			0.0643399			0.0321699	+	0.999482i	$0.489758\pi$
$198$		0			0
$199$	−15.6296			−1.10795			−0.553976	−	0.832533i	$-0.686890\pi$
$199$	−15.6296			−1.10795			−0.553976	+	0.832533i	$0.686890\pi$
$200$	−0.297103	−	0.914389i	−0.0210084	−	0.0646571i
$201$		0			0
$202$	2.18200	−	1.58532i	0.153525	−	0.111543i
$203$	0.285584	−	0.878938i	0.0200441	−	0.0616893i
$204$		0			0
$205$	−9.64480	+	7.00736i	−0.673622	+	0.489415i
$206$	−9.55028	−	6.93868i	−0.665399	−	0.483441i
$207$		0			0
$208$	3.81733			0.264684
$209$	−6.49180	+	21.3470i	−0.449047	+	1.47660i
$210$		0			0
$211$	4.56378	+	14.0459i	0.314184	+	0.966958i	0.976089	+	0.217371i	$0.0697480\pi$
$211$	4.56378	+	14.0459i	0.314184	+	0.966958i	−0.661905	+	0.749587i	$0.730252\pi$
$212$	−0.837709	−	0.608631i	−0.0575341	−	0.0418010i
$213$		0			0
$214$	−3.18799	+	9.81162i	−0.217926	+	0.670709i
$215$	5.58447	−	17.1872i	0.380858	−	1.17216i
$216$		0			0
$217$	−2.42849	−	1.76440i	−0.164857	−	0.119776i
$218$	3.91708	+	12.0555i	0.265298	+	0.816503i
$219$		0			0
$220$	−8.79983	+	6.65165i	−0.593284	+	0.448454i
$221$	4.52791			0.304581
$222$		0			0
$223$	1.49293	+	1.08468i	0.0999743	+	0.0726356i	0.636649	−	0.771153i	$-0.280320\pi$
$223$	1.49293	+	1.08468i	0.0999743	+	0.0726356i	−0.536675	+	0.843789i	$0.680320\pi$
$224$	4.66668	−	3.39054i	0.311806	−	0.226540i
$225$		0			0
$226$	0.347825	−	1.07050i	0.0231370	−	0.0712083i
$227$	−17.7498	+	12.8960i	−1.17809	+	0.855936i	−0.991955	−	0.126588i	$-0.959597\pi$
$227$	−17.7498	+	12.8960i	−1.17809	+	0.855936i	−0.186139	+	0.982523i	$0.559597\pi$
$228$		0			0
$229$	−6.25815	−	19.2606i	−0.413550	−	1.27278i	−0.913541	−	0.406746i	$-0.866663\pi$
$229$	−6.25815	−	19.2606i	−0.413550	−	1.27278i	0.499991	−	0.866030i	$-0.333337\pi$
$230$	4.54323			0.299571
$231$		0			0
$232$	2.19819			0.144318
$233$	−6.50870	−	20.0317i	−0.426399	−	1.31232i	−0.901648	−	0.432470i	$-0.857642\pi$
$233$	−6.50870	−	20.0317i	−0.426399	−	1.31232i	0.475250	−	0.879851i	$-0.342358\pi$
$234$		0			0
$235$	−7.62718	+	5.54147i	−0.497542	+	0.361486i
$236$	−0.176600	+	0.543519i	−0.0114957	+	0.0353801i
$237$		0			0
$238$	0.970382	−	0.705023i	0.0629005	−	0.0456999i
$239$	12.5370	+	9.10863i	0.810948	+	0.589188i	0.914105	−	0.405477i	$-0.132894\pi$
$239$	12.5370	+	9.10863i	0.810948	+	0.589188i	−0.103157	+	0.994665i	$0.532894\pi$
$240$		0			0
$241$	14.0848			0.907283			0.453641	−	0.891184i	$-0.350125\pi$
$241$	14.0848			0.907283			0.453641	+	0.891184i	$0.350125\pi$
$242$	6.11987	+	4.10153i	0.393400	+	0.263656i
$243$		0			0
$244$	−2.40262	−	7.39450i	−0.153812	−	0.473384i
$245$	1.73435	+	1.26008i	0.110804	+	0.0805036i
$246$		0			0
$247$	−5.25596	+	16.1762i	−0.334429	+	1.02927i
$248$	2.20635	−	6.79046i	0.140104	−	0.431195i
$249$		0			0
$250$	6.27739	+	4.56079i	0.397017	+	0.288450i
$251$	0.332894	+	1.02454i	0.0210121	+	0.0646686i	0.961013	−	0.276504i	$-0.0891759\pi$
$251$	0.332894	+	1.02454i	0.0210121	+	0.0646686i	−0.940001	+	0.341173i	$0.889176\pi$
$252$		0			0
$253$	3.43148	+	9.91790i	0.215735	+	0.623533i
$254$	−11.7653			−0.738223
$255$		0			0
$256$	7.30978	+	5.31087i	0.456861	+	0.331929i
$257$	10.5828	−	7.68883i	0.660135	−	0.479616i	−0.206574	−	0.978431i	$-0.566231\pi$
$257$	10.5828	−	7.68883i	0.660135	−	0.479616i	0.866708	+	0.498815i	$0.166231\pi$
$258$		0			0
$259$	−0.465744	+	1.43341i	−0.0289399	+	0.0890679i
$260$	−6.80292	+	4.94261i	−0.421899	+	0.306528i
$261$		0			0
$262$	1.39194	+	4.28395i	0.0859943	+	0.264663i
$263$	9.57216			0.590245			0.295122	−	0.955459i	$-0.404640\pi$
$263$	9.57216			0.590245			0.295122	+	0.955459i	$0.404640\pi$
$264$		0			0
$265$	1.43080			0.0878935
$266$	1.39232	+	4.28511i	0.0853685	+	0.262737i
$267$		0			0
$268$	−1.13230	+	0.822665i	−0.0691663	+	0.0502523i
$269$	1.47356	−	4.53514i	0.0898444	−	0.276513i	−0.896031	−	0.443991i	$-0.853562\pi$
$269$	1.47356	−	4.53514i	0.0898444	−	0.276513i	0.985876	+	0.167478i	$0.0535623\pi$
$270$		0			0
$271$	16.2226	−	11.7864i	0.985455	−	0.715975i	0.0265341	−	0.999648i	$-0.491553\pi$
$271$	16.2226	−	11.7864i	0.985455	−	0.715975i	0.958921	+	0.283673i	$0.0915530\pi$
$272$	−2.18762	−	1.58940i	−0.132644	−	0.0963713i
$273$		0			0
$274$	9.28776			0.561094
$275$	−0.390058	+	1.28263i	−0.0235214	+	0.0773453i
$276$		0			0
$277$	−3.58535	−	11.0346i	−0.215423	−	0.663004i	−0.999123	−	0.0418647i	$-0.986670\pi$
$277$	−3.58535	−	11.0346i	−0.215423	−	0.663004i	0.783700	−	0.621139i	$-0.213330\pi$
$278$	7.73237	+	5.61789i	0.463757	+	0.336939i
$279$		0			0
$280$	−1.57571	+	4.84953i	−0.0941666	+	0.289815i
$281$	−3.73256	+	11.4876i	−0.222666	+	0.685295i	0.775854	+	0.630912i	$0.217319\pi$
$281$	−3.73256	+	11.4876i	−0.222666	+	0.685295i	−0.998520	+	0.0543830i	$0.982681\pi$
$282$		0			0
$283$	−17.7929	−	12.9273i	−1.05768	−	0.768448i	−0.0840200	−	0.996464i	$-0.526776\pi$
$283$	−17.7929	−	12.9273i	−1.05768	−	0.768448i	−0.973657	+	0.228017i	$0.926776\pi$
$284$	−7.12871	−	21.9399i	−0.423011	−	1.30189i
$285$		0			0
$286$	4.60513	+	3.21438i	0.272307	+	0.190070i
$287$	−5.56104			−0.328258
$288$		0			0
$289$	11.1585	+	8.10709i	0.656380	+	0.476888i
$290$	−1.07349	+	0.779936i	−0.0630375	+	0.0457994i
$291$		0			0
$292$	−3.85367	+	11.8604i	−0.225519	+	0.694077i
$293$	1.14654	−	0.833014i	0.0669819	−	0.0486652i	−0.553790	−	0.832656i	$-0.686819\pi$
$293$	1.14654	−	0.833014i	0.0669819	−	0.0486652i	0.620772	+	0.783991i	$0.286819\pi$
$294$		0			0
$295$	−0.244025	−	0.751033i	−0.0142077	−	0.0437268i
$296$	−3.58491			−0.208369
$297$		0			0
$298$	1.75669			0.101762
$299$	2.47218	+	7.60859i	0.142970	+	0.440016i
$300$		0			0
$301$	6.81989	−	4.95494i	0.393092	−	0.285598i
$302$	0.618734	−	1.90427i	0.0356041	−	0.109578i
$303$		0			0
$304$	8.21755	−	5.97040i	0.471309	−	0.342426i
$305$	8.69169	+	6.31488i	0.497685	+	0.361589i
$306$		0			0
$307$	29.4646			1.68163			0.840817	−	0.541319i	$-0.182075\pi$
$307$	29.4646			1.68163			0.840817	+	0.541319i	$0.182075\pi$
$308$	−5.14463	+	0.0974375i	−0.293143	+	0.00555202i
$309$		0			0
$310$	1.33183	+	4.09897i	0.0756431	+	0.232806i
$311$	21.7453	+	15.7989i	1.23306	+	0.895873i	0.997116	−	0.0758927i	$-0.0241807\pi$
$311$	21.7453	+	15.7989i	1.23306	+	0.895873i	0.235948	+	0.971766i	$0.424181\pi$
$312$		0			0
$313$	−1.38832	+	4.27281i	−0.0784725	+	0.241514i	−0.982595	−	0.185759i	$-0.940526\pi$
$313$	−1.38832	+	4.27281i	−0.0784725	+	0.241514i	0.904123	+	0.427273i	$0.140526\pi$
$314$	−2.32930	+	7.16884i	−0.131450	+	0.404561i
$315$		0			0
$316$	5.09172	+	3.69935i	0.286431	+	0.208105i
$317$	3.38376	+	10.4141i	0.190051	+	0.584916i	0.999999	−	0.00158586i	$-0.000504795\pi$
$317$	3.38376	+	10.4141i	0.190051	+	0.584916i	−0.809948	+	0.586502i	$0.800505\pi$
$318$		0			0
$319$	−2.51341	−	1.75436i	−0.140724	−	0.0982250i
$320$	−1.80846			−0.101096
$321$		0			0
$322$	1.71452	+	1.24567i	0.0955464	+	0.0694185i
$323$	9.74723	−	7.08177i	0.542350	−	0.394040i
$324$		0			0
$325$	−0.315802	+	0.971940i	−0.0175176	+	0.0539135i
$326$	−9.86298	+	7.16588i	−0.546260	+	0.396881i
$327$		0			0
$328$	−4.08744	−	12.5799i	−0.225691	−	0.694607i
$329$	−4.39771			−0.242453
$330$		0			0
$331$	16.5226			0.908166			0.454083	−	0.890959i	$-0.349967\pi$
$331$	16.5226			0.908166			0.454083	+	0.890959i	$0.349967\pi$
$332$	−1.94230	−	5.97779i	−0.106598	−	0.328074i
$333$		0			0
$334$	−10.7994	+	7.84624i	−0.590918	+	0.429327i
$335$	0.597628	−	1.83931i	0.0326519	−	0.100492i
$336$		0			0
$337$	9.80588	−	7.12439i	0.534160	−	0.388090i	−0.287751	−	0.957705i	$-0.592908\pi$
$337$	9.80588	−	7.12439i	0.534160	−	0.388090i	0.821912	+	0.569615i	$0.192908\pi$
$338$	−3.58038	−	2.60130i	−0.194747	−	0.141492i
$339$		0			0
$340$	5.95651			0.323037
$341$	−7.94214	+	6.00334i	−0.430091	+	0.325099i
$342$		0			0
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	16.2215	+	11.7856i	0.874605	+	0.635437i
$345$		0			0
$346$	1.23972	−	3.81547i	0.0666478	−	0.205121i
$347$	7.50452	−	23.0965i	0.402864	−	1.23989i	−0.519802	−	0.854287i	$-0.673994\pi$
$347$	7.50452	−	23.0965i	0.402864	−	1.23989i	0.922666	−	0.385600i	$-0.126006\pi$
$348$		0			0
$349$	2.68497	+	1.95074i	0.143723	+	0.104421i	0.657323	−	0.753609i	$-0.271689\pi$
$349$	2.68497	+	1.95074i	0.143723	+	0.104421i	−0.513600	+	0.858030i	$0.671689\pi$
$350$	0.0836570	+	0.257470i	0.00447165	+	0.0137623i
$351$		0			0
$352$	−6.25542	−	18.0798i	−0.333415	−	0.963658i
$353$	−20.3272			−1.08191			−0.540955	−	0.841051i	$-0.681937\pi$
$353$	−20.3272			−1.08191			−0.540955	+	0.841051i	$0.681937\pi$
$354$		0			0
$355$	25.7887	+	18.7366i	1.36872	+	0.994436i
$356$	10.4268	−	7.57553i	0.552620	−	0.401502i
$357$		0			0
$358$	−0.335059	+	1.03121i	−0.0177084	+	0.0545009i
$359$	23.4949	−	17.0700i	1.24001	−	0.900921i	0.242412	−	0.970173i	$-0.422062\pi$
$359$	23.4949	−	17.0700i	1.24001	−	0.900921i	0.997599	+	0.0692529i	$0.0220615\pi$
$360$		0			0
$361$	8.11414	+	24.9728i	0.427060	+	1.31436i
$362$	−1.62535			−0.0854264
$363$		0			0
$364$	−3.92246			−0.205593
$365$	−5.32499	−	16.3886i	−0.278723	−	0.857821i
$366$		0			0
$367$	18.4122	−	13.3773i	0.961111	−	0.698288i	0.00770265	−	0.999970i	$-0.497548\pi$
$367$	18.4122	−	13.3773i	0.961111	−	0.698288i	0.953409	+	0.301682i	$0.0975481\pi$
$368$	1.47637	−	4.54380i	0.0769611	−	0.236862i
$369$		0			0
$370$	1.75070	−	1.27196i	0.0910145	−	0.0661259i
$371$	0.539955	+	0.392300i	0.0280331	+	0.0203672i
$372$		0			0
$373$	−22.2412			−1.15160			−0.575802	−	0.817589i	$-0.695310\pi$
$373$	−22.2412			−1.15160			−0.575802	+	0.817589i	$0.695310\pi$
$374$	−1.30074	−	3.75949i	−0.0672597	−	0.194399i
$375$		0			0
$376$	−3.23238	−	9.94824i	−0.166697	−	0.513041i
$377$	−1.89030	−	1.37339i	−0.0973556	−	0.0707330i
$378$		0			0
$379$	10.3430	−	31.8325i	0.531285	−	1.63513i	−0.220258	−	0.975442i	$-0.570690\pi$
$379$	10.3430	−	31.8325i	0.531285	−	1.63513i	0.751543	−	0.659685i	$-0.229310\pi$
$380$	−6.91426	+	21.2799i	−0.354694	+	1.09164i
$381$		0			0
$382$	−6.88179	−	4.99992i	−0.352103	−	0.255818i
$383$	1.89919	+	5.84512i	0.0970443	+	0.298672i	0.987781	−	0.155848i	$-0.0498110\pi$
$383$	1.89919	+	5.84512i	0.0970443	+	0.298672i	−0.890737	+	0.454520i	$0.849811\pi$
$384$		0			0
$385$	5.67203	−	4.28739i	0.289073	−	0.218506i
$386$	1.17829			0.0599733
$387$		0			0
$388$	10.6886	+	7.76572i	0.542631	+	0.394245i
$389$	5.98967	−	4.35175i	0.303689	−	0.220643i	−0.425495	−	0.904961i	$-0.639900\pi$
$389$	5.98967	−	4.35175i	0.303689	−	0.220643i	0.729184	+	0.684318i	$0.239900\pi$
$390$		0			0
$391$	1.75119	−	5.38962i	0.0885617	−	0.272565i
$392$	−1.92429	+	1.39808i	−0.0971915	+	0.0706138i
$393$		0			0
$394$	−0.186898	−	0.575213i	−0.00941578	−	0.0289788i
$395$	−8.69662			−0.437575
$396$		0			0
$397$	17.8079			0.893752			0.446876	−	0.894596i	$-0.352537\pi$
$397$	17.8079			0.893752			0.446876	+	0.894596i	$0.352537\pi$
$398$	3.23473	+	9.95549i	0.162143	+	0.499024i
$399$		0			0
$400$	0.493749	−	0.358729i	0.0246874	−	0.0179365i
$401$	−7.93520	+	24.4220i	−0.396265	+	1.21958i	0.531707	+	0.846929i	$0.321551\pi$
$401$	−7.93520	+	24.4220i	−0.396265	+	1.21958i	−0.927972	+	0.372650i	$0.878449\pi$
$402$		0			0
$403$	−6.13987	+	4.46088i	−0.305849	+	0.222212i
$404$	5.05455	+	3.67235i	0.251473	+	0.182706i
$405$		0			0
$406$	−0.618957			−0.0307183
$407$	4.09899	+	2.86108i	0.203179	+	0.141819i
$408$		0			0
$409$	0.413324	+	1.27208i	0.0204376	+	0.0629003i	0.960755	−	0.277398i	$-0.0894720\pi$
$409$	0.413324	+	1.27208i	0.0204376	+	0.0629003i	−0.940318	+	0.340298i	$0.889472\pi$
$410$	6.45955	+	4.69314i	0.319014	+	0.231778i
$411$		0			0
$412$	8.45022	−	26.0071i	0.416312	−	1.28128i
$413$	0.113830	−	0.350331i	0.00560119	−	0.0172387i
$414$		0			0
$415$	7.02646	+	5.10502i	0.344915	+	0.250596i
$416$	−4.50666	−	13.8701i	−0.220957	−	0.680037i
$417$		0			0
$418$	14.9408	−	0.282974i	0.730780	−	0.0138407i
$419$	−37.4618			−1.83013			−0.915064	−	0.403310i	$-0.867860\pi$
$419$	−37.4618			−1.83013			−0.915064	+	0.403310i	$0.867860\pi$
$420$		0			0
$421$	−6.68374	−	4.85602i	−0.325746	−	0.236668i	0.412878	−	0.910787i	$-0.364524\pi$
$421$	−6.68374	−	4.85602i	−0.325746	−	0.236668i	−0.738623	+	0.674118i	$0.764524\pi$
$422$	8.00219	−	5.81393i	0.389541	−	0.283018i
$423$		0			0
$424$	−0.490564	+	1.50980i	−0.0238239	+	0.0733224i
$425$	0.585659	−	0.425506i	0.0284086	−	0.0206401i
$426$		0			0
$427$	1.54863	+	4.76621i	0.0749437	+	0.230653i
$428$	−23.8980			−1.15515
$429$		0			0
$430$	−12.1034			−0.583679
$431$	−10.0914	−	31.0581i	−0.486085	−	1.49602i	−0.830403	−	0.557164i	$-0.811890\pi$
$431$	−10.0914	−	31.0581i	−0.486085	−	1.49602i	0.344317	−	0.938853i	$-0.388110\pi$
$432$		0			0
$433$	−12.7786	+	9.28422i	−0.614102	+	0.446171i	−0.850856	−	0.525398i	$-0.823916\pi$
$433$	−12.7786	+	9.28422i	−0.614102	+	0.446171i	0.236754	+	0.971570i	$0.423916\pi$
$434$	−0.621256	+	1.91203i	−0.0298212	+	0.0917803i
$435$		0			0
$436$	−23.7555	+	17.2594i	−1.13768	+	0.826575i
$437$	17.2219	+	12.5124i	0.823834	+	0.598551i
$438$		0			0
$439$	−20.6942			−0.987678			−0.493839	−	0.869553i	$-0.664407\pi$
$439$	−20.6942			−0.987678			−0.493839	+	0.869553i	$0.664407\pi$
$440$	13.8677	+	9.67964i	0.661118	+	0.461459i
$441$		0			0
$442$	−0.937107	−	2.88412i	−0.0445737	−	0.137184i
$443$	24.3477	+	17.6897i	1.15680	+	0.840462i	0.989370	−	0.145423i	$-0.0464543\pi$
$443$	24.3477	+	17.6897i	1.15680	+	0.840462i	0.167427	+	0.985885i	$0.446454\pi$
$444$		0			0
$445$	−5.50327	+	16.9373i	−0.260880	+	0.802906i
$446$	0.381922	−	1.17543i	0.0180845	−	0.0556584i
$447$		0			0
$448$	−0.682474	−	0.495846i	−0.0322438	−	0.0234265i
$449$	−11.2465	−	34.6132i	−0.530755	−	1.63350i	−0.752647	−	0.658424i	$-0.771223\pi$
$449$	−11.2465	−	34.6132i	−0.530755	−	1.63350i	0.221892	−	0.975071i	$-0.428777\pi$
$450$		0			0
$451$	−5.36629	+	17.6460i	−0.252689	+	0.830915i
$452$	2.60739			0.122641
$453$		0			0
$454$	11.8878	+	8.63700i	0.557922	+	0.405354i
$455$	4.38490	−	3.18582i	0.205567	−	0.149353i
$456$		0			0
$457$	−3.02652	+	9.31466i	−0.141574	+	0.435721i	−0.996555	−	0.0829393i	$-0.973569\pi$
$457$	−3.02652	+	9.31466i	−0.141574	+	0.435721i	0.854980	+	0.518661i	$0.173569\pi$
$458$	−10.9731	+	7.97243i	−0.512740	+	0.372527i
$459$		0			0
$460$	3.25217	+	10.0092i	0.151633	+	0.466680i
$461$	21.8596			1.01810			0.509052	−	0.860736i	$-0.329996\pi$
$461$	21.8596			1.01810			0.509052	+	0.860736i	$0.329996\pi$
$462$		0			0
$463$	6.75889			0.314112			0.157056	−	0.987590i	$-0.449800\pi$
$463$	6.75889			0.314112			0.157056	+	0.987590i	$0.449800\pi$
$464$	0.431193	+	1.32707i	0.0200176	+	0.0616079i
$465$		0			0
$466$	−11.4124	+	8.29161i	−0.528670	+	0.384102i
$467$	9.27768	−	28.5538i	0.429320	−	1.32131i	−0.469477	−	0.882945i	$-0.655558\pi$
$467$	9.27768	−	28.5538i	0.429320	−	1.32131i	0.898797	−	0.438366i	$-0.144442\pi$
$468$		0			0
$469$	0.729838	−	0.530258i	0.0337008	−	0.0244850i
$470$	5.10826	+	3.71136i	0.235626	+	0.171192i
$471$		0			0
$472$	0.876166			0.0403288
$473$	−9.14167	−	26.4219i	−0.420334	−	1.21488i
$474$		0			0
$475$	0.840312	+	2.58622i	0.0385562	+	0.118664i
$476$	2.24786	+	1.63317i	0.103031	+	0.0748561i
$477$		0			0
$478$	3.20720	−	9.87074i	0.146694	−	0.451477i
$479$	1.85519	−	5.70970i	0.0847659	−	0.260883i	−0.899686	−	0.436538i	$-0.856204\pi$
$479$	1.85519	−	5.70970i	0.0847659	−	0.260883i	0.984452	+	0.175655i	$0.0562044\pi$
$480$		0			0
$481$	3.08280	+	2.23978i	0.140563	+	0.102125i
$482$	−2.91503	−	8.97153i	−0.132776	−	0.408642i
$483$		0			0
$484$	−4.65528	+	16.4187i	−0.211604	+	0.746303i
$485$	−18.2561			−0.828965
$486$		0			0
$487$	−5.15120	−	3.74256i	−0.233423	−	0.169592i	0.464925	−	0.885350i	$-0.346081\pi$
$487$	−5.15120	−	3.74256i	−0.233423	−	0.169592i	−0.698348	+	0.715758i	$0.746081\pi$
$488$	−9.64357	+	7.00646i	−0.436544	+	0.317168i
$489$		0			0
$490$	0.443681	−	1.36551i	0.0200435	−	0.0616875i
$491$	10.0131	−	7.27496i	0.451886	−	0.328314i	−0.338454	−	0.940983i	$-0.609904\pi$
$491$	10.0131	−	7.27496i	0.451886	−	0.328314i	0.790340	+	0.612669i	$0.209904\pi$
$492$		0			0
$493$	0.511458	+	1.57411i	0.0230349	+	0.0708942i
$494$	11.3914			0.512525
$495$		0			0
$496$	4.53228			0.203505
$497$	4.59489	+	14.1416i	0.206109	+	0.634338i
$498$		0			0
$499$	11.5525	−	8.39337i	0.517160	−	0.375739i	−0.298373	−	0.954449i	$-0.596444\pi$
$499$	11.5525	−	8.39337i	0.517160	−	0.375739i	0.815533	+	0.578711i	$0.196444\pi$
$500$	−5.55432	+	17.0944i	−0.248397	+	0.764486i
$501$		0			0
$502$	0.583701	−	0.424084i	0.0260519	−	0.0189278i
$503$	4.79402	+	3.48306i	0.213755	+	0.155302i	0.689511	−	0.724275i	$-0.257826\pi$
$503$	4.79402	+	3.48306i	0.213755	+	0.155302i	−0.475756	+	0.879577i	$0.657826\pi$
$504$		0			0
$505$	−8.63314			−0.384170
$506$	5.60716	−	4.23836i	0.249269	−	0.188418i
$507$		0			0
$508$	−8.42197	−	25.9202i	−0.373665	−	1.15002i
$509$	24.9772	+	18.1470i	1.10709	+	0.804351i	0.982204	−	0.187820i	$-0.0601420\pi$
$509$	24.9772	+	18.1470i	1.10709	+	0.804351i	0.124891	+	0.992171i	$0.460142\pi$
$510$		0			0
$511$	2.48393	−	7.64474i	0.109883	−	0.338184i
$512$	−4.91089	+	15.1142i	−0.217033	+	0.667958i
$513$		0			0
$514$	−7.08774	−	5.14955i	−0.312627	−	0.227137i
$515$	11.6765	+	35.9365i	0.514527	+	1.58355i
$516$		0			0
$517$	−4.24370	+	13.9545i	−0.186637	+	0.613720i
$518$	1.00942			0.0443516
$519$		0			0
$520$	10.4297	+	7.57765i	0.457374	+	0.332302i
$521$	15.2799	−	11.1015i	0.669423	−	0.486365i	−0.200409	−	0.979712i	$-0.564227\pi$
$521$	15.2799	−	11.1015i	0.669423	−	0.486365i	0.869832	+	0.493348i	$0.164227\pi$
$522$		0			0
$523$	−2.45424	+	7.55337i	−0.107316	+	0.330286i	−0.990267	−	0.139180i	$-0.955553\pi$
$523$	−2.45424	+	7.55337i	−0.107316	+	0.330286i	0.882951	+	0.469466i	$0.155553\pi$
$524$	−8.44156	+	6.13315i	−0.368771	+	0.267928i
$525$		0			0
$526$	−1.98108	−	6.09712i	−0.0863790	−	0.265847i
$527$	5.37595			0.234180
$528$		0			0
$529$	−12.9873			−0.564665
$530$	−0.296122	−	0.911370i	−0.0128627	−	0.0395874i
$531$		0			0
$532$	−8.44386	+	6.13482i	−0.366088	+	0.265978i
$533$	−4.34471	+	13.3716i	−0.188190	+	0.579190i
$534$		0			0
$535$	26.7155	−	19.4099i	1.15501	−	0.839165i
$536$	1.73596	+	1.26125i	0.0749821	+	0.0544777i
$537$		0			0
$538$	−3.19370			−0.137690
$539$	3.31603	−	0.0628044i	0.142832	−	0.00270518i
$540$		0			0
$541$	2.34904	+	7.22960i	0.100993	+	0.310825i	0.988769	−	0.149451i	$-0.0477506\pi$
$541$	2.34904	+	7.22960i	0.100993	+	0.310825i	−0.887776	+	0.460276i	$0.847751\pi$
$542$	−10.8650	−	7.89389i	−0.466692	−	0.339072i
$543$		0			0
$544$	−3.19234	+	9.82501i	−0.136870	+	0.421244i
$545$	12.5381	−	38.5884i	0.537075	−	1.65295i
$546$		0			0
$547$	−17.5548	−	12.7543i	−0.750590	−	0.545335i	0.145420	−	0.989370i	$-0.453547\pi$
$547$	−17.5548	−	12.7543i	−0.750590	−	0.545335i	−0.896010	+	0.444035i	$0.853547\pi$
$548$	6.64845	+	20.4618i	0.284008	+	0.874086i
$549$		0			0
$550$	0.897714	−	0.0170024i	0.0382787	−	0.000724984i
$551$	−6.21726			−0.264864
$552$		0			0
$553$	−3.28192	−	2.38446i	−0.139562	−	0.101397i
$554$	−6.28660	+	4.56749i	−0.267092	+	0.194054i
$555$		0			0
$556$	−6.84170	+	21.0566i	−0.290153	+	0.892999i
$557$	−32.8569	+	23.8719i	−1.39219	+	1.01149i	−0.396571	+	0.918004i	$0.629800\pi$
$557$	−32.8569	+	23.8719i	−1.39219	+	1.01149i	−0.995621	+	0.0934825i	$0.970200\pi$
$558$		0			0
$559$	−6.58604	−	20.2697i	−0.278560	−	0.857319i
$560$	−3.23681			−0.136780
$561$		0			0
$562$	8.08972			0.341244
$563$	7.24004	+	22.2825i	0.305131	+	0.939097i	0.979628	+	0.200820i	$0.0643606\pi$
$563$	7.24004	+	22.2825i	0.305131	+	0.939097i	−0.674497	+	0.738278i	$0.735639\pi$
$564$		0			0
$565$	−2.91479	+	2.11772i	−0.122626	+	0.0890931i
$566$	−4.55177	+	14.0089i	−0.191325	+	0.588838i
$567$		0			0
$568$	−28.6130	+	20.7886i	−1.20058	+	0.872269i
$569$	−9.01678	−	6.55107i	−0.378003	−	0.274635i	0.382519	−	0.923948i	$-0.375057\pi$
$569$	−9.01678	−	6.55107i	−0.378003	−	0.274635i	−0.760522	+	0.649313i	$0.775057\pi$
$570$		0			0
$571$	−6.15846			−0.257724			−0.128862	−	0.991663i	$-0.541132\pi$
$571$	−6.15846			−0.257724			−0.128862	+	0.991663i	$0.541132\pi$
$572$	−3.78509	+	12.4465i	−0.158262	+	0.520414i
$573$		0			0
$574$	1.15092	+	3.54218i	0.0480387	+	0.147848i
$575$	1.03477	+	0.751805i	0.0431529	+	0.0313524i
$576$		0			0
$577$	−4.47585	+	13.7752i	−0.186332	+	0.573471i	−0.999969	−	0.00790255i	$-0.997485\pi$
$577$	−4.47585	+	13.7752i	−0.186332	+	0.573471i	0.813637	+	0.581374i	$0.197485\pi$
$578$	2.85455	−	8.78540i	0.118734	−	0.365424i
$579$		0			0
$580$	−2.48671	−	1.80670i	−0.103255	−	0.0750192i
$581$	1.25193	+	3.85305i	0.0519389	+	0.159852i
$582$		0			0
$583$	1.76587	−	1.33479i	0.0731348	−	0.0552814i
$584$	19.1192			0.791159
$585$		0			0
$586$	−0.767891	−	0.557906i	−0.0317213	−	0.0230469i
$587$	12.8285	−	9.32048i	0.529491	−	0.384698i	−0.290676	−	0.956821i	$-0.593880\pi$
$587$	12.8285	−	9.32048i	0.529491	−	0.384698i	0.820167	+	0.572124i	$0.193880\pi$
$588$		0			0
$589$	−6.24035	+	19.2058i	−0.257129	+	0.791362i
$590$	−0.427877	+	0.310871i	−0.0176154	+	0.0127984i
$591$		0			0
$592$	−0.703209	−	2.16426i	−0.0289017	−	0.0889503i
$593$	−22.9285			−0.941560			−0.470780	−	0.882251i	$-0.656027\pi$
$593$	−22.9285			−0.941560			−0.470780	+	0.882251i	$0.656027\pi$
$594$		0			0
$595$	−3.83934			−0.157397
$596$	1.25749	+	3.87015i	0.0515087	+	0.158527i
$597$		0			0
$598$	4.33475	−	3.14938i	0.177261	−	0.128788i
$599$	−4.06395	+	12.5075i	−0.166048	+	0.511044i	−0.999112	−	0.0421329i	$-0.986585\pi$
$599$	−4.06395	+	12.5075i	−0.166048	+	0.511044i	0.833064	+	0.553177i	$0.186585\pi$
$600$		0			0
$601$	−22.1286	+	16.0774i	−0.902645	+	0.655810i	−0.939144	−	0.343524i	$-0.888379\pi$
$601$	−22.1286	+	16.0774i	−0.902645	+	0.655810i	0.0364993	+	0.999334i	$0.488379\pi$
$602$	−4.56758	−	3.31854i	−0.186161	−	0.135254i
$603$		0			0
$604$	4.63819			0.188725
$605$	−8.13111	−	22.1354i	−0.330577	−	0.899931i
$606$		0			0
$607$	−14.4850	−	44.5801i	−0.587926	−	1.80945i	−0.587186	−	0.809452i	$-0.699764\pi$
$607$	−14.4850	−	44.5801i	−0.587926	−	1.80945i	−0.000740345	−	1.00000i	$-0.500236\pi$
$608$	−31.3946	−	22.8095i	−1.27322	−	0.925049i
$609$		0			0
$610$	2.22350	−	6.84324i	0.0900270	−	0.277075i
$611$	−3.43582	+	10.5744i	−0.138999	+	0.427793i
$612$		0			0
$613$	16.5601	+	12.0316i	0.668857	+	0.485953i	0.869642	−	0.493682i	$-0.164349\pi$
$613$	16.5601	+	12.0316i	0.668857	+	0.485953i	−0.200786	+	0.979635i	$0.564349\pi$
$614$	−6.09806	−	18.7679i	−0.246098	−	0.757411i
$615$		0			0
$616$	2.57940	+	7.45517i	0.103927	+	0.300377i
$617$	−44.1691			−1.77818			−0.889090	−	0.457733i	$-0.848662\pi$
$617$	−44.1691			−1.77818			−0.889090	+	0.457733i	$0.848662\pi$
$618$		0			0
$619$	−0.551413	−	0.400625i	−0.0221632	−	0.0161025i	0.576649	−	0.816992i	$-0.304360\pi$
$619$	−0.551413	−	0.400625i	−0.0221632	−	0.0161025i	−0.598812	+	0.800890i	$0.704360\pi$
$620$	−8.07705	+	5.86832i	−0.324382	+	0.235677i
$621$		0			0
$622$	5.56287	−	17.1208i	0.223051	−	0.686480i
$623$	−6.72072	+	4.88289i	−0.269260	+	0.195629i
$624$		0			0
$625$	−7.05039	−	21.6989i	−0.282016	−	0.867955i
$626$	3.00896			0.120262
$627$		0			0
$628$	−17.4610			−0.696770
$629$	−0.834110	−	2.56713i	−0.0332582	−	0.102358i
$630$		0			0
$631$	29.8299	−	21.6727i	1.18751	−	0.862776i	0.194511	−	0.980900i	$-0.437688\pi$
$631$	29.8299	−	21.6727i	1.18751	−	0.862776i	0.992999	+	0.118124i	$0.0376880\pi$
$632$	2.98172	−	9.17679i	0.118606	−	0.365033i
$633$		0			0
$634$	5.93312	−	4.31066i	0.235634	−	0.171198i
$635$	30.4672	+	22.1357i	1.20906	+	0.878430i
$636$		0			0
$637$	2.52826			0.100173
$638$	−0.597281	+	1.96404i	−0.0236466	+	0.0777570i
$639$		0			0
$640$	−7.26835	−	22.3697i	−0.287307	−	0.884239i
$641$	−16.5951	−	12.0570i	−0.655466	−	0.476224i	0.209663	−	0.977774i	$-0.432763\pi$
$641$	−16.5951	−	12.0570i	−0.655466	−	0.476224i	−0.865129	+	0.501550i	$0.832763\pi$
$642$		0			0
$643$	−2.35984	+	7.26283i	−0.0930629	+	0.286418i	−0.986744	−	0.162284i	$-0.948114\pi$
$643$	−2.35984	+	7.26283i	−0.0930629	+	0.286418i	0.893681	+	0.448703i	$0.148114\pi$
$644$	−1.51703	+	4.66894i	−0.0597793	+	0.183982i
$645$		0			0
$646$	−6.52815	−	4.74298i	−0.256846	−	0.186610i
$647$	−4.53724	−	13.9642i	−0.178377	−	0.548989i	0.821394	−	0.570361i	$-0.193197\pi$
$647$	−4.53724	−	13.9642i	−0.178377	−	0.548989i	−0.999772	+	0.0213717i	$0.993197\pi$
$648$		0			0
$649$	−1.00181	−	0.699260i	−0.0393244	−	0.0274483i
$650$	0.684450			0.0268463
$651$		0			0
$652$	−22.8473	−	16.5996i	−0.894770	−	0.650089i
$653$	0.911790	−	0.662454i	0.0356811	−	0.0259238i	−0.569802	−	0.821782i	$-0.692980\pi$
$653$	0.911790	−	0.662454i	0.0356811	−	0.0259238i	0.605483	+	0.795858i	$0.292980\pi$
$654$		0			0
$655$	4.45545	−	13.7125i	0.174089	−	0.535790i
$656$	6.79283	−	4.93528i	0.265215	−	0.192690i
$657$		0			0
$658$	0.910159	+	2.80118i	0.0354817	+	0.109201i
$659$	−10.0215			−0.390384			−0.195192	−	0.980765i	$-0.562533\pi$
$659$	−10.0215			−0.390384			−0.195192	+	0.980765i	$0.562533\pi$
$660$		0			0
$661$	15.7371			0.612101			0.306050	−	0.952015i	$-0.400992\pi$
$661$	15.7371			0.612101			0.306050	+	0.952015i	$0.400992\pi$
$662$	−3.41956	−	10.5243i	−0.132905	−	0.409040i
$663$		0			0
$664$	−7.79597	+	5.66410i	−0.302542	+	0.219810i
$665$	4.45666	−	13.7162i	0.172822	−	0.531891i
$666$		0			0
$667$	−2.36584	+	1.71888i	−0.0916056	+	0.0665554i
$668$	−25.0166	−	18.1756i	−0.967920	−	0.703235i
$669$		0			0
$670$	−1.29526			−0.0500403
$671$	16.6182	−	0.314744i	0.641540	−	0.0121505i
$672$		0			0
$673$	9.89226	+	30.4452i	0.381319	+	1.17358i	0.939116	+	0.343601i	$0.111647\pi$
$673$	9.89226	+	30.4452i	0.381319	+	1.17358i	−0.557797	+	0.829977i	$0.688353\pi$
$674$	−6.56743	−	4.77152i	−0.252968	−	0.183792i
$675$		0			0
$676$	3.16797	−	9.75001i	0.121845	−	0.375000i
$677$	4.74033	−	14.5892i	0.182186	−	0.560710i	−0.817703	−	0.575641i	$-0.804753\pi$
$677$	4.74033	−	14.5892i	0.182186	−	0.560710i	0.999889	+	0.0149305i	$0.00475269\pi$
$678$		0			0
$679$	−6.88945	−	5.00548i	−0.264393	−	0.192093i
$680$	−2.82197	−	8.68512i	−0.108218	−	0.333059i
$681$		0			0
$682$	5.46763	+	3.81640i	0.209367	+	0.146137i
$683$	−1.04764			−0.0400868			−0.0200434	−	0.999799i	$-0.506380\pi$
$683$	−1.04764			−0.0400868			−0.0200434	+	0.999799i	$0.506380\pi$
$684$		0			0
$685$	−24.0514	−	17.4743i	−0.918955	−	0.667660i
$686$	0.541834	−	0.393666i	0.0206873	−	0.0150302i
$687$		0			0
$688$	−3.93314	+	12.1050i	−0.149950	+	0.461497i
$689$	1.36515	−	0.991838i	0.0520080	−	0.0377860i
$690$		0			0
$691$	9.01969	+	27.7597i	0.343125	+	1.05603i	0.962580	+	0.270998i	$0.0873537\pi$
$691$	9.01969	+	27.7597i	0.343125	+	1.05603i	−0.619455	+	0.785032i	$0.712646\pi$
$692$	9.29326			0.353277
$693$		0			0
$694$	−16.2648			−0.617404
$695$	−9.45384	−	29.0959i	−0.358605	−	1.10367i
$696$		0			0
$697$	8.05730	−	5.85397i	0.305192	−	0.221735i
$698$	0.686867	−	2.11396i	0.0259983	−	0.0800145i
$699$		0			0
$700$	−0.507346	+	0.368609i	−0.0191759	+	0.0139321i
$701$	10.3380	+	7.51100i	0.390461	+	0.283687i	0.765644	−	0.643264i	$-0.222420\pi$
$701$	10.3380	+	7.51100i	0.390461	+	0.283687i	−0.375183	+	0.926951i	$0.622420\pi$
$702$		0			0
$703$	10.1394			0.382415
$704$	−2.23196	+	1.68710i	−0.0841202	+	0.0635851i
$705$		0			0
$706$	4.20697	+	12.9477i	0.158332	+	0.487294i
$707$	−3.25797	−	2.36705i	−0.122528	−	0.0890221i
$708$		0			0
$709$	11.7646	−	36.2076i	0.441828	−	1.35981i	−0.444098	−	0.895978i	$-0.646476\pi$
$709$	11.7646	−	36.2076i	0.441828	−	1.35981i	0.885925	−	0.463828i	$-0.153524\pi$
$710$	6.59726	−	20.3043i	0.247591	−	0.762006i
$711$		0			0
$712$	−15.9856	−	11.6142i	−0.599087	−	0.435262i
$713$	2.93520	+	9.03361i	0.109924	+	0.338311i
$714$		0			0
$715$	−5.87770	−	16.9881i	−0.219814	−	0.635321i
$716$	−2.51169			−0.0938663
$717$		0			0
$718$	−15.7355	−	11.4325i	−0.587245	−	0.426658i
$719$	−31.7696	+	23.0819i	−1.18481	+	0.860811i	−0.992706	−	0.120564i	$-0.961530\pi$
$719$	−31.7696	+	23.0819i	−1.18481	+	0.860811i	−0.192100	+	0.981375i	$0.561530\pi$
$720$		0			0
$721$	−5.44668	+	16.7632i	−0.202845	+	0.624293i
$722$	14.2274	−	10.3368i	0.529491	−	0.384697i
$723$		0			0
$724$	−1.16347	−	3.58080i	−0.0432401	−	0.133079i
$725$	−0.373562			−0.0138737
$726$		0			0
$727$	−28.4699			−1.05589			−0.527946	−	0.849278i	$-0.677037\pi$
$727$	−28.4699			−1.05589			−0.527946	+	0.849278i	$0.677037\pi$
$728$	1.85831	+	5.71929i	0.0688735	+	0.211971i
$729$		0			0
$730$	−9.33691	+	6.78366i	−0.345574	+	0.251074i
$731$	−4.66529	+	14.3583i	−0.172552	+	0.531060i
$732$		0			0
$733$	2.42168	−	1.75946i	0.0894470	−	0.0649870i	−0.542163	−	0.840273i	$-0.682394\pi$
$733$	2.42168	−	1.75946i	0.0894470	−	0.0649870i	0.631610	+	0.775286i	$0.282394\pi$
$734$	−12.3315	−	8.95935i	−0.455163	−	0.330696i
$735$		0			0
$736$	−18.2527			−0.672802
$737$	−0.978305	−	2.82757i	−0.0360363	−	0.104155i
$738$		0			0
$739$	−15.6773	−	48.2498i	−0.576700	−	1.77490i	−0.630318	−	0.776337i	$-0.717075\pi$
$739$	−15.6773	−	48.2498i	−0.576700	−	1.77490i	0.0536180	−	0.998562i	$-0.482925\pi$
$740$	4.05544	+	2.94645i	0.149081	+	0.108314i
$741$		0			0
$742$	0.138131	−	0.425123i	0.00507095	−	0.0156068i
$743$	0.118625	−	0.365089i	0.00435191	−	0.0133938i	−0.948857	−	0.315706i	$-0.897759\pi$
$743$	0.118625	−	0.365089i	0.00435191	−	0.0133938i	0.953209	+	0.302312i	$0.0977586\pi$
$744$		0			0
$745$	−4.54907	−	3.30510i	−0.166665	−	0.121089i
$746$	4.60309	+	14.1668i	0.168531	+	0.518685i
$747$		0			0
$748$	7.35141	−	5.55681i	0.268794	−	0.203177i
$749$	15.4037			0.562840
$750$		0			0
$751$	31.8404	+	23.1334i	1.16187	+	0.844151i	0.990014	−	0.140970i	$-0.0450221\pi$
$751$	31.8404	+	23.1334i	1.16187	+	0.844151i	0.171861	+	0.985121i	$0.445022\pi$
$752$	5.37182	−	3.90285i	0.195890	−	0.142322i
$753$		0			0
$754$	−0.483576	+	1.48830i	−0.0176108	+	0.0542005i
$755$	−5.18502	+	3.76714i	−0.188702	+	0.137100i
$756$		0			0
$757$	3.51868	+	10.8294i	0.127889	+	0.393600i	0.994416	−	0.105528i	$-0.0336534\pi$
$757$	3.51868	+	10.8294i	0.127889	+	0.393600i	−0.866528	+	0.499129i	$0.833653\pi$
$758$	−22.4168			−0.814214
$759$		0			0
$760$	34.3037			1.24433
$761$	2.31196	+	7.11547i	0.0838083	+	0.257936i	0.984176	−	0.177195i	$-0.0567023\pi$
$761$	2.31196	+	7.11547i	0.0838083	+	0.257936i	−0.900367	+	0.435130i	$0.856702\pi$
$762$		0			0
$763$	15.3119	−	11.1247i	0.554327	−	0.402742i
$764$	6.08911	−	18.7403i	0.220296	−	0.678002i
$765$		0			0
$766$	3.33007	−	2.41944i	0.120320	−	0.0874179i
$767$	−0.753447	−	0.547411i	−0.0272054	−	0.0197659i
$768$		0			0
$769$	−26.8378			−0.967798			−0.483899	−	0.875124i	$-0.660780\pi$
$769$	−26.8378			−0.967798			−0.483899	+	0.875124i	$0.660780\pi$
$770$	−3.90481	−	2.72555i	−0.140720	−	0.0982221i
$771$		0			0
$772$	0.843453	+	2.59588i	0.0303565	+	0.0934278i
$773$	3.61453	+	2.62611i	0.130006	+	0.0944546i	0.650888	−	0.759174i	$-0.274397\pi$
$773$	3.61453	+	2.62611i	0.130006	+	0.0944546i	−0.520882	+	0.853629i	$0.674397\pi$
$774$		0			0
$775$	−0.374949	+	1.15398i	−0.0134686	+	0.0414520i
$776$	6.25926	−	19.2640i	0.224694	−	0.691538i
$777$		0			0
$778$	−4.01155	−	2.91456i	−0.143821	−	0.104492i
$779$	11.5607	+	35.5803i	0.414206	+	1.27480i
$780$		0			0
$781$	49.3073	−	0.933862i	1.76435	−	0.0334162i
$782$	−3.79543			−0.135724
$783$		0			0
$784$	−1.22150	−	0.887475i	−0.0436251	−	0.0316955i
$785$	19.5196	−	14.1818i	0.696685	−	0.506171i
$786$		0			0
$787$	−4.16738	+	12.8259i	−0.148551	+	0.457193i	−0.997451	−	0.0713611i	$-0.977266\pi$
$787$	−4.16738	+	12.8259i	−0.148551	+	0.457193i	0.848899	+	0.528554i	$0.177266\pi$
$788$	1.13346	−	0.823508i	0.0403779	−	0.0293363i
$789$		0			0
$790$	1.79987	+	5.53944i	0.0640366	+	0.197084i
$791$	−1.68062			−0.0597560
$792$		0			0
$793$	12.6704			0.449937
$794$	−3.68556	−	11.3430i	−0.130796	−	0.402547i
$795$		0			0
$796$	−19.6174	+	14.2529i	−0.695320	+	0.505179i
$797$	−16.2250	+	49.9354i	−0.574719	+	1.76880i	0.0624156	+	0.998050i	$0.480120\pi$
$797$	−16.2250	+	49.9354i	−0.574719	+	1.76880i	−0.637134	+	0.770753i	$0.719880\pi$
$798$		0			0
$799$	6.37177	−	4.62936i	0.225417	−	0.163775i
$800$	−1.88634	−	1.37050i	−0.0666921	−	0.0484546i
$801$		0			0
$802$	17.1983			0.607292
$803$	−21.8609	−	15.2589i	−0.771454	−	0.538474i
$804$		0			0
$805$	−2.09623	−	6.45152i	−0.0738822	−	0.227386i
$806$	4.11214	+	2.98764i	0.144844	+	0.105235i
$807$		0			0
$808$	2.95995	−	9.10980i	0.104131	−	0.320482i
$809$	0.398583	−	1.22671i	0.0140134	−	0.0431289i	−0.943805	−	0.330502i	$-0.892782\pi$
$809$	0.398583	−	1.22671i	0.0140134	−	0.0431289i	0.957819	+	0.287373i	$0.0927820\pi$
$810$		0			0
$811$	27.6585	+	20.0951i	0.971220	+	0.705633i	0.955729	−	0.294247i	$-0.0950689\pi$
$811$	27.6585	+	20.0951i	0.971220	+	0.705633i	0.0154910	+	0.999880i	$0.495069\pi$
$812$	−0.443068	−	1.36362i	−0.0155486	−	0.0478538i
$813$		0			0
$814$	0.974073	−	3.20304i	0.0341412	−	0.112267i
$815$	39.0231			1.36692
$816$		0			0
$817$	−45.8801	−	33.3339i	−1.60514	−	1.16620i
$818$	0.724728	−	0.526545i	0.0253395	−	0.0184102i
$819$		0			0
$820$	−5.71550	+	17.5905i	−0.199594	+	0.614287i
$821$	32.0856	−	23.3115i	1.11979	−	0.813578i	0.135616	−	0.990761i	$-0.456699\pi$
$821$	32.0856	−	23.3115i	1.11979	−	0.813578i	0.984178	+	0.177184i	$0.0566987\pi$
$822$		0			0
$823$	−2.85134	−	8.77554i	−0.0993916	−	0.305896i	0.888982	−	0.457943i	$-0.151414\pi$
$823$	−2.85134	−	8.77554i	−0.0993916	−	0.305896i	−0.988373	+	0.152047i	$0.951414\pi$
$824$	−41.9241			−1.46049
$825$		0			0
$826$	−0.246707			−0.00858403
$827$	7.94043	+	24.4381i	0.276116	+	0.849797i	0.988922	+	0.148436i	$0.0474239\pi$
$827$	7.94043	+	24.4381i	0.276116	+	0.849797i	−0.712806	+	0.701361i	$0.752576\pi$
$828$		0			0
$829$	−8.84945	+	6.42950i	−0.307354	+	0.223306i	−0.730760	−	0.682634i	$-0.760834\pi$
$829$	−8.84945	+	6.42950i	−0.307354	+	0.223306i	0.423406	+	0.905940i	$0.360834\pi$
$830$	1.79750	−	5.53215i	0.0623923	−	0.192024i
$831$		0			0
$832$	−1.72547	+	1.25363i	−0.0598200	+	0.0434618i
$833$	−1.44888	−	1.05268i	−0.0502009	−	0.0364731i
$834$		0			0
$835$	42.7282			1.47867
$836$	11.3185	+	32.7135i	0.391458	+	1.13142i
$837$		0			0
$838$	7.75317	+	23.8618i	0.267829	+	0.824293i
$839$	−28.1031	−	20.4181i	−0.970228	−	0.704912i	−0.0147243	−	0.999892i	$-0.504687\pi$
$839$	−28.1031	−	20.4181i	−0.970228	−	0.704912i	−0.955503	+	0.294980i	$0.904687\pi$
$840$		0			0
$841$	−8.69756	+	26.7684i	−0.299916	+	0.923047i
$842$	−1.70983	+	5.26232i	−0.0589247	+	0.181351i
$843$		0			0
$844$	18.5369	+	13.4678i	0.638065	+	0.463581i
$845$	4.37749	+	13.4725i	0.150590	+	0.463469i
$846$		0			0
$847$	3.00061	−	10.5828i	0.103102	−	0.363630i
$848$	−1.00771			−0.0346050
$849$		0			0
$850$	−0.392241	−	0.284980i	−0.0134538	−	0.00977474i
$851$	3.85832	−	2.80323i	0.132262	−	0.0960936i
$852$		0			0
$853$	−6.37880	+	19.6319i	−0.218406	+	0.672185i	0.780488	+	0.625171i	$0.214971\pi$
$853$	−6.37880	+	19.6319i	−0.218406	+	0.672185i	−0.998894	+	0.0470143i	$0.985029\pi$
$854$	2.71539	−	1.97285i	0.0929189	−	0.0675095i
$855$		0			0
$856$	11.3220	+	34.8454i	0.386977	+	1.19099i
$857$	34.1512			1.16658			0.583291	−	0.812263i	$-0.301765\pi$
$857$	34.1512			1.16658			0.583291	+	0.812263i	$0.301765\pi$
$858$		0			0
$859$	−33.4493			−1.14127			−0.570637	−	0.821202i	$-0.693304\pi$
$859$	−33.4493			−1.14127			−0.570637	+	0.821202i	$0.693304\pi$
$860$	−8.66399	−	26.6650i	−0.295440	−	0.909269i
$861$		0			0
$862$	−17.6944	+	12.8557i	−0.602673	+	0.437868i
$863$	10.5171	−	32.3683i	0.358006	−	1.10183i	−0.596240	−	0.802806i	$-0.703340\pi$
$863$	10.5171	−	32.3683i	0.358006	−	1.10183i	0.954246	−	0.299022i	$-0.0966605\pi$
$864$		0			0
$865$	−10.3889	+	7.54799i	−0.353234	+	0.256639i
$866$	8.55841	+	6.21805i	0.290827	+	0.211298i
$867$		0			0
$868$	−4.65710			−0.158072
$869$	−10.7332	+	8.11305i	−0.364099	+	0.275216i
$870$		0			0
$871$	−0.704812	−	2.16919i	−0.0238816	−	0.0735001i
$872$	36.4202	+	26.4608i	1.23334	+	0.896076i
$873$		0			0
$874$	4.40569	−	13.5593i	0.149025	−	0.458651i
$875$	3.58010	−	11.0184i	0.121029	−	0.372490i
$876$		0			0
$877$	−6.36458	−	4.62414i	−0.214917	−	0.156146i	0.475119	−	0.879922i	$-0.342405\pi$
$877$	−6.36458	−	4.62414i	−0.214917	−	0.156146i	−0.690035	+	0.723776i	$0.742405\pi$
$878$	4.28291	+	13.1814i	0.144541	+	0.444852i
$879$		0			0
$880$	−3.12345	+	10.2708i	−0.105292	+	0.346230i
$881$	−13.3289			−0.449063			−0.224531	−	0.974467i	$-0.572085\pi$
$881$	−13.3289			−0.449063			−0.224531	+	0.974467i	$0.572085\pi$
$882$		0			0
$883$	13.8340	+	10.0510i	0.465552	+	0.338243i	0.795705	−	0.605684i	$-0.207100\pi$
$883$	13.8340	+	10.0510i	0.465552	+	0.338243i	−0.330153	+	0.943927i	$0.607100\pi$
$884$	5.68318	−	4.12908i	0.191146	−	0.138876i
$885$		0			0
$886$	6.22863	−	19.1697i	0.209255	−	0.644020i
$887$	−21.4539	+	15.5872i	−0.720351	+	0.523366i	−0.886496	−	0.462736i	$-0.846868\pi$
$887$	−21.4539	+	15.5872i	−0.720351	+	0.523366i	0.166145	+	0.986101i	$0.446868\pi$
$888$		0			0
$889$	5.42848	+	16.7071i	0.182065	+	0.560339i
$890$	11.9274			0.399808
$891$		0			0
$892$	2.86298			0.0958598
$893$	9.14231	+	28.1371i	0.305936	+	0.941573i
$894$		0			0
$895$	2.80781	−	2.03999i	0.0938548	−	0.0681895i
$896$	3.39044	−	10.4347i	0.113267	−	0.348599i
$897$		0			0
$898$	−19.7197	+	14.3272i	−0.658056	+	0.478106i
$899$	−2.24434	−	1.63061i	−0.0748529	−	0.0543838i
$900$		0			0
$901$	−1.19530			−0.0398211
$902$	12.3505	−	0.233913i	0.411225	−	0.00778846i
$903$		0			0
$904$	−1.23528	−	3.80180i	−0.0410848	−	0.126446i
$905$	4.20896	+	3.05799i	0.139911	+	0.101651i
$906$		0			0
$907$	2.73559	−	8.41928i	0.0908338	−	0.279558i	−0.895312	−	0.445440i	$-0.853047\pi$
$907$	2.73559	−	8.41928i	0.0908338	−	0.279558i	0.986146	+	0.165882i	$0.0530472\pi$
$908$	−10.5185	+	32.3726i	−0.349068	+	1.07432i
$909$		0			0
$910$	−2.93676	−	2.13368i	−0.0973526	−	0.0707308i
$911$	17.2740	+	53.1639i	0.572313	+	1.76140i	0.645151	+	0.764055i	$0.276794\pi$
$911$	17.2740	+	53.1639i	0.572313	+	1.76140i	−0.0728381	+	0.997344i	$0.523206\pi$
$912$		0			0
$913$	13.4344	−	0.254442i	0.444613	−	0.00842081i
$914$	6.55948			0.216968
$915$		0			0
$916$	−25.4189	−	18.4679i	−0.839865	−	0.610197i
$917$	5.44110	−	3.95319i	0.179681	−	0.130546i
$918$		0			0
$919$	14.9495	−	46.0098i	0.493139	−	1.51772i	−0.326699	−	0.945128i	$-0.605936\pi$
$919$	14.9495	−	46.0098i	0.493139	−	1.51772i	0.819838	−	0.572596i	$-0.194064\pi$
$920$	13.0535	−	9.48392i	0.430361	−	0.312676i
$921$		0			0
$922$	−4.52412	−	13.9238i	−0.148994	−	0.458556i
$923$	37.5937			1.23741
$924$		0			0
$925$	0.609223			0.0200311
$926$	−1.39884	−	4.30517i	−0.0459686	−	0.141477i
$927$		0			0
$928$	4.31281	−	3.13344i	0.141575	−	0.102860i
$929$	−0.267082	+	0.821994i	−0.00876267	+	0.0269687i	−0.955342	−	0.295502i	$-0.904513\pi$
$929$	−0.267082	+	0.821994i	−0.00876267	+	0.0269687i	0.946580	+	0.322470i	$0.104513\pi$
$930$		0			0
$931$	5.44258	−	3.95427i	0.178373	−	0.129596i
$932$	−26.4366	−	19.2073i	−0.865959	−	0.629156i
$933$		0			0
$934$	−20.1079			−0.657949
$935$	−3.70488	+	12.1827i	−0.121162	+	0.398418i
$936$		0			0
$937$	16.5194	+	50.8416i	0.539667	+	1.66092i	0.733344	+	0.679858i	$0.237958\pi$
$937$	16.5194	+	50.8416i	0.539667	+	1.66092i	−0.193678	+	0.981065i	$0.562042\pi$
$938$	−0.488804	−	0.355137i	−0.0159600	−	0.0115956i
$939$		0			0
$940$	−4.51985	+	13.9107i	−0.147421	+	0.453716i
$941$	−4.23353	+	13.0295i	−0.138009	+	0.424749i	−0.996046	−	0.0888397i	$-0.971684\pi$
$941$	−4.23353	+	13.0295i	−0.138009	+	0.424749i	0.858037	+	0.513588i	$0.171684\pi$
$942$		0			0
$943$	14.2360	+	10.3431i	0.463589	+	0.336817i
$944$	0.171867	+	0.528952i	0.00559379	+	0.0172159i
$945$		0			0
$946$	−14.9378	+	11.2912i	−0.485670	+	0.367110i
$947$	−31.6444			−1.02830			−0.514152	−	0.857699i	$-0.671893\pi$
$947$	−31.6444			−1.02830			−0.514152	+	0.857699i	$0.671893\pi$
$948$		0			0
$949$	−16.4413	−	11.9453i	−0.533707	−	0.387761i
$950$	1.47341	−	1.07050i	0.0478039	−	0.0347315i
$951$		0			0
$952$	1.31635	−	4.05132i	0.0426632	−	0.131304i
$953$	26.4856	−	19.2429i	0.857951	−	0.623338i	−0.0693755	−	0.997591i	$-0.522101\pi$
$953$	26.4856	−	19.2429i	0.857951	−	0.623338i	0.927327	+	0.374253i	$0.122101\pi$
$954$		0			0
$955$	8.41390	+	25.8953i	0.272268	+	0.837953i
$956$	24.0420			0.777573
$957$		0			0
$958$	−4.02083			−0.129907
$959$	−4.28533	−	13.1889i	−0.138381	−	0.425892i
$960$		0			0
$961$	17.7897	−	12.9250i	0.573862	−	0.416935i
$962$	0.788639	−	2.42718i	0.0254267	−	0.0782555i
$963$		0			0
$964$	17.6785	−	12.8442i	0.569385	−	0.413683i
$965$	−3.05127	−	2.21688i	−0.0982238	−	0.0713637i
$966$		0			0
$967$	−32.3487			−1.04026			−0.520132	−	0.854086i	$-0.674117\pi$
$967$	−32.3487			−1.04026			−0.520132	+	0.854086i	$0.674117\pi$
$968$	26.1454	−	0.990723i	0.840344	−	0.0318430i
$969$		0			0
$970$	3.77832	+	11.6285i	0.121314	+	0.373367i
$971$	−23.8069	−	17.2968i	−0.764001	−	0.555079i	0.136134	−	0.990690i	$-0.456532\pi$
$971$	−23.8069	−	17.2968i	−0.764001	−	0.555079i	−0.900135	+	0.435611i	$0.856532\pi$
$972$		0			0
$973$	4.40990	−	13.5723i	0.141375	−	0.435107i
$974$	−1.31778	+	4.05570i	−0.0422243	+	0.129953i
$975$		0			0
$976$	−6.12155	−	4.44757i	−0.195946	−	0.142363i
$977$	−4.23181	−	13.0242i	−0.135388	−	0.416681i	0.860262	−	0.509852i	$-0.170300\pi$
$977$	−4.23181	−	13.0242i	−0.135388	−	0.416681i	−0.995650	+	0.0931709i	$0.970300\pi$
$978$		0			0
$979$	9.00874	+	26.0377i	0.287920	+	0.832168i
$980$	3.32595			0.106244
$981$		0			0
$982$	−6.70622	−	4.87236i	−0.214004	−	0.155483i
$983$	13.7791	−	10.0111i	0.439486	−	0.319305i	−0.345945	−	0.938255i	$-0.612442\pi$
$983$	13.7791	−	10.0111i	0.439486	−	0.319305i	0.785431	+	0.618950i	$0.212442\pi$
$984$		0			0
$985$	−0.598240	+	1.84119i	−0.0190615	+	0.0586653i
$986$	0.896797	−	0.651561i	0.0285598	−	0.0207499i
$987$		0			0
$988$	8.15432	+	25.0964i	0.259423	+	0.798423i
$989$	−26.6744			−0.848198
$990$		0			0
$991$	23.2202			0.737614			0.368807	−	0.929506i	$-0.379766\pi$
$991$	23.2202			0.737614			0.368807	+	0.929506i	$0.379766\pi$
$992$	−5.35072	−	16.4678i	−0.169886	−	0.522854i
$993$		0			0
$994$	8.05673	−	5.85356i	0.255544	−	0.185664i
$995$	10.3540	−	31.8665i	0.328245	−	1.01023i
$996$		0			0
$997$	14.8678	−	10.8021i	0.470868	−	0.342105i	−0.326912	−	0.945055i	$-0.606008\pi$
$997$	14.8678	−	10.8021i	0.470868	−	0.342105i	0.797779	+	0.602949i	$0.206008\pi$
$998$	−7.73720	−	5.62141i	−0.244917	−	0.177943i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.i.379.2		16
3.2	odd	2		77.2.f.b.71.3	yes	16
11.3	even	5		7623.2.a.ct.1.4		8
11.8	odd	10		7623.2.a.cw.1.5		8
11.9	even	5	inner	693.2.m.i.64.2		16
21.2	odd	6		539.2.q.g.214.3		32
21.5	even	6		539.2.q.f.214.3		32
21.11	odd	6		539.2.q.g.324.2		32
21.17	even	6		539.2.q.f.324.2		32
21.20	even	2		539.2.f.e.148.3		16
33.2	even	10		847.2.f.x.372.2		16
33.5	odd	10		847.2.f.w.323.2		16
33.8	even	10		847.2.a.o.1.4		8
33.14	odd	10		847.2.a.p.1.5		8
33.17	even	10		847.2.f.v.323.3		16
33.20	odd	10		77.2.f.b.64.3	✓	16
33.26	odd	10		847.2.f.w.729.2		16
33.29	even	10		847.2.f.v.729.3		16
33.32	even	2		847.2.f.x.148.2		16
231.20	even	10		539.2.f.e.295.3		16
231.41	odd	10		5929.2.a.bs.1.4		8
231.53	odd	30		539.2.q.g.471.3		32
231.86	odd	30		539.2.q.g.361.2		32
231.146	even	10		5929.2.a.bt.1.5		8
231.152	even	30		539.2.q.f.361.2		32
231.185	even	30		539.2.q.f.471.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.3	✓	16	33.20	odd	10
77.2.f.b.71.3	yes	16	3.2	odd	2
539.2.f.e.148.3		16	21.20	even	2
539.2.f.e.295.3		16	231.20	even	10
539.2.q.f.214.3		32	21.5	even	6
539.2.q.f.324.2		32	21.17	even	6
539.2.q.f.361.2		32	231.152	even	30
539.2.q.f.471.3		32	231.185	even	30
539.2.q.g.214.3		32	21.2	odd	6
539.2.q.g.324.2		32	21.11	odd	6
539.2.q.g.361.2		32	231.86	odd	30
539.2.q.g.471.3		32	231.53	odd	30
693.2.m.i.64.2		16	11.9	even	5	inner
693.2.m.i.379.2		16	1.1	even	1	trivial
847.2.a.o.1.4		8	33.8	even	10
847.2.a.p.1.5		8	33.14	odd	10
847.2.f.v.323.3		16	33.17	even	10
847.2.f.v.729.3		16	33.29	even	10
847.2.f.w.323.2		16	33.5	odd	10
847.2.f.w.729.2		16	33.26	odd	10
847.2.f.x.148.2		16	33.32	even	2
847.2.f.x.372.2		16	33.2	even	10
5929.2.a.bs.1.4		8	231.41	odd	10
5929.2.a.bt.1.5		8	231.146	even	10
7623.2.a.ct.1.4		8	11.3	even	5
7623.2.a.cw.1.5		8	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.206962 - 0.636964i) q^{2} +(1.25514 - 0.911915i) q^{4} +(-0.662464 + 2.03885i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-1.92429 - 1.39808i) q^{8} +O(q^{10})\)	\(q+(-0.206962 - 0.636964i) q^{2} +(1.25514 - 0.911915i) q^{4} +(-0.662464 + 2.03885i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-1.92429 - 1.39808i) q^{8} +1.43578 q^{10} +(1.08444 + 3.13432i) q^{11} +(0.781276 + 2.40452i) q^{13} +(0.541834 + 0.393666i) q^{14} +(0.466573 - 1.43596i) q^{16} +(0.553425 - 1.70327i) q^{17} +(5.44258 + 3.95427i) q^{19} +(1.02778 + 3.16317i) q^{20} +(1.77201 - 1.33944i) q^{22} +3.16429 q^{23} +(0.327016 + 0.237591i) q^{25} +(1.36990 - 0.995290i) q^{26} +(-0.479422 + 1.47551i) q^{28} +(-0.747669 + 0.543213i) q^{29} +(0.927602 + 2.85487i) q^{31} -5.76834 q^{32} -1.19946 q^{34} +(-0.662464 - 2.03885i) q^{35} +(1.21933 - 0.885898i) q^{37} +(1.39232 - 4.28511i) q^{38} +(4.12526 - 2.99718i) q^{40} +(4.49897 + 3.26870i) q^{41} -8.42985 q^{43} +(4.21937 + 2.94511i) q^{44} +(-0.654888 - 2.01554i) q^{46} +(3.55782 + 2.58491i) q^{47} +(0.309017 - 0.951057i) q^{49} +(0.0836570 - 0.257470i) q^{50} +(3.17333 + 2.30556i) q^{52} +(-0.206244 - 0.634755i) q^{53} +(-7.10883 + 0.134639i) q^{55} +2.37856 q^{56} +(0.500747 + 0.363814i) q^{58} +(-0.298010 + 0.216517i) q^{59} +(1.54863 - 4.76621i) q^{61} +(1.62647 - 1.18170i) q^{62} +(0.260682 + 0.802296i) q^{64} -5.42003 q^{65} -0.902129 q^{67} +(-0.858607 - 2.64252i) q^{68} +(-1.16157 + 0.843932i) q^{70} +(4.59489 - 14.1416i) q^{71} +(-6.50301 + 4.72471i) q^{73} +(-0.816641 - 0.593325i) q^{74} +10.4372 q^{76} +(-2.71964 - 1.89830i) q^{77} +(1.25358 + 3.85813i) q^{79} +(2.61863 + 1.90255i) q^{80} +(1.15092 - 3.54218i) q^{82} +(1.25193 - 3.85305i) q^{83} +(3.10609 + 2.25670i) q^{85} +(1.74466 + 5.36951i) q^{86} +(2.29526 - 7.54749i) q^{88} +8.30727 q^{89} +(-2.04541 - 1.48608i) q^{91} +(3.97163 - 2.88556i) q^{92} +(0.910159 - 2.80118i) q^{94} +(-11.6677 + 8.47707i) q^{95} +(2.63154 + 8.09904i) q^{97} -0.669744 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more