LMFDB - Embedded newform 207.2.i.a.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			55.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	207.55
Dual form			207.2.i.a.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.459493 - 0.134919i) q^{2} +(-1.48958 + 0.957293i) q^{4} +(-0.480602 - 3.34266i) q^{5} +(1.88533 - 4.12830i) q^{7} +(-1.18251 + 1.36469i) q^{8} +O(q^{10})$	\(q+(0.459493 - 0.134919i) q^{2} +(-1.48958 + 0.957293i) q^{4} +(-0.480602 - 3.34266i) q^{5} +(1.88533 - 4.12830i) q^{7} +(-1.18251 + 1.36469i) q^{8} +(-0.671822 - 1.47109i) q^{10} +(0.942270 + 0.276675i) q^{11} +(-0.188515 - 0.412791i) q^{13} +(0.309309 - 2.15129i) q^{14} +(1.11189 - 2.43470i) q^{16} +(2.76321 + 1.77580i) q^{17} +(1.41042 - 0.906424i) q^{19} +(3.91579 + 4.51907i) q^{20} +0.470295 q^{22} +(-4.59385 + 1.37715i) q^{23} +(-6.14491 + 1.80431i) q^{25} +(-0.142315 - 0.164240i) q^{26} +(1.14365 + 7.95423i) q^{28} +(1.15189 + 0.740277i) q^{29} +(-4.23404 + 4.88634i) q^{31} +(0.696384 - 4.84346i) q^{32} +(1.50926 + 0.443160i) q^{34} +(-14.7056 - 4.31795i) q^{35} +(0.506627 - 3.52367i) q^{37} +(0.525785 - 0.606789i) q^{38} +(5.12999 + 3.29685i) q^{40} +(0.821738 + 5.71531i) q^{41} +(7.20584 + 8.31598i) q^{43} +(-1.66844 + 0.489899i) q^{44} +(-1.92504 + 1.25259i) q^{46} +10.0618 q^{47} +(-8.90436 - 10.2762i) q^{49} +(-2.58011 + 1.65814i) q^{50} +(0.675969 + 0.434419i) q^{52} +(5.11162 - 11.1929i) q^{53} +(0.471975 - 3.28266i) q^{55} +(3.40442 + 7.45463i) q^{56} +(0.629165 + 0.184739i) q^{58} +(4.41863 + 9.67544i) q^{59} +(-3.65011 + 4.21246i) q^{61} +(-1.28625 + 2.81649i) q^{62} +(0.428340 + 2.97917i) q^{64} +(-1.28922 + 0.828529i) q^{65} +(7.43903 - 2.18430i) q^{67} -5.81597 q^{68} -7.33969 q^{70} +(2.86847 - 0.842258i) q^{71} +(-3.27850 + 2.10697i) q^{73} +(-0.242620 - 1.68746i) q^{74} +(-1.23322 + 2.70038i) q^{76} +(2.91869 - 3.36835i) q^{77} +(-3.61897 - 7.92444i) q^{79} +(-8.67273 - 2.54654i) q^{80} +(1.14869 + 2.51528i) q^{82} +(-1.06526 + 7.40902i) q^{83} +(4.60791 - 10.0899i) q^{85} +(4.43302 + 2.84893i) q^{86} +(-1.49182 + 0.958732i) q^{88} +(-4.73727 - 5.46710i) q^{89} -2.05954 q^{91} +(5.52455 - 6.44903i) q^{92} +(4.62333 - 1.35753i) q^{94} +(-3.70772 - 4.27893i) q^{95} +(0.801906 + 5.57738i) q^{97} +(-5.47795 - 3.52046i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 14 q^{4} + 3 q^{5} + 6 q^{7} + 7 q^{8}+O(q^{10}) $ 10 * q - 4 * q^2 - 14 * q^4 + 3 * q^5 + 6 * q^7 + 7 * q^8	$ 10 q - 4 q^{2} - 14 q^{4} + 3 q^{5} + 6 q^{7} + 7 q^{8} + 12 q^{10} + 15 q^{11} + 8 q^{13} - 9 q^{14} + 12 q^{16} - q^{17} - 9 q^{19} + 9 q^{20} - 28 q^{22} - 21 q^{23} - 4 q^{25} - q^{26} + 29 q^{28} + 8 q^{29} - 23 q^{31} + q^{32} - 15 q^{34} - 18 q^{35} + 3 q^{37} - 3 q^{38} - 32 q^{40} + 15 q^{41} + 22 q^{43} + q^{44} + 26 q^{46} - 4 q^{47} - 29 q^{49} - 49 q^{50} + 2 q^{52} - 29 q^{53} + 43 q^{55} + 2 q^{56} + 21 q^{58} + 54 q^{59} - 30 q^{61} + 7 q^{62} - 31 q^{64} + 9 q^{65} + q^{67} + 30 q^{68} - 94 q^{70} + 3 q^{71} - 47 q^{73} + 12 q^{74} + 50 q^{76} - 13 q^{77} + 18 q^{79} - 3 q^{80} - 28 q^{82} - 18 q^{83} + 58 q^{85} + 16 q^{88} - 25 q^{89} + 18 q^{91} + 3 q^{92} + 39 q^{94} + 16 q^{95} + 21 q^{97} + 27 q^{98}+O(q^{100}) $ 10 * q - 4 * q^2 - 14 * q^4 + 3 * q^5 + 6 * q^7 + 7 * q^8 + 12 * q^10 + 15 * q^11 + 8 * q^13 - 9 * q^14 + 12 * q^16 - q^17 - 9 * q^19 + 9 * q^20 - 28 * q^22 - 21 * q^23 - 4 * q^25 - q^26 + 29 * q^28 + 8 * q^29 - 23 * q^31 + q^32 - 15 * q^34 - 18 * q^35 + 3 * q^37 - 3 * q^38 - 32 * q^40 + 15 * q^41 + 22 * q^43 + q^44 + 26 * q^46 - 4 * q^47 - 29 * q^49 - 49 * q^50 + 2 * q^52 - 29 * q^53 + 43 * q^55 + 2 * q^56 + 21 * q^58 + 54 * q^59 - 30 * q^61 + 7 * q^62 - 31 * q^64 + 9 * q^65 + q^67 + 30 * q^68 - 94 * q^70 + 3 * q^71 - 47 * q^73 + 12 * q^74 + 50 * q^76 - 13 * q^77 + 18 * q^79 - 3 * q^80 - 28 * q^82 - 18 * q^83 + 58 * q^85 + 16 * q^88 - 25 * q^89 + 18 * q^91 + 3 * q^92 + 39 * q^94 + 16 * q^95 + 21 * q^97 + 27 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	0.459493	−	0.134919i	0.324911	−	0.0954024i	−0.115210	−	0.993341i	$-0.536754\pi$
$2$	0.459493	−	0.134919i	0.324911	−	0.0954024i	0.440120	+	0.897939i	$0.354936\pi$
$3$		0			0
$3$		0			0
$4$	−1.48958	+	0.957293i	−0.744788	+	0.478646i
$5$	−0.480602	−	3.34266i	−0.214932	−	1.49488i	−0.756372	−	0.654142i	$-0.773030\pi$
$5$	−0.480602	−	3.34266i	−0.214932	−	1.49488i	0.541440	−	0.840739i	$-0.317879\pi$
$6$		0			0
$7$	1.88533	−	4.12830i	0.712588	−	1.56035i	−0.111420	−	0.993773i	$-0.535540\pi$
$7$	1.88533	−	4.12830i	0.712588	−	1.56035i	0.824009	−	0.566577i	$-0.191733\pi$
$8$	−1.18251	+	1.36469i	−0.418079	+	0.482489i
$9$		0			0
$10$	−0.671822	−	1.47109i	−0.212449	−	0.465198i
$11$	0.942270	+	0.276675i	0.284105	+	0.0834208i	0.420680	−	0.907209i	$-0.361791\pi$
$11$	0.942270	+	0.276675i	0.284105	+	0.0834208i	−0.136575	+	0.990630i	$0.543610\pi$
$12$		0			0
$13$	−0.188515	−	0.412791i	−0.0522847	−	0.114488i	0.881687	−	0.471835i	$-0.156408\pi$
$13$	−0.188515	−	0.412791i	−0.0522847	−	0.114488i	−0.933971	+	0.357348i	$0.883681\pi$
$14$	0.309309	−	2.15129i	0.0826664	−	0.574957i
$15$		0			0
$16$	1.11189	−	2.43470i	0.277972	−	0.608674i
$17$	2.76321	+	1.77580i	0.670176	+	0.430696i	0.830989	−	0.556289i	$-0.187775\pi$
$17$	2.76321	+	1.77580i	0.670176	+	0.430696i	−0.160813	+	0.986985i	$0.551412\pi$
$18$		0			0
$19$	1.41042	−	0.906424i	0.323573	−	0.207948i	−0.368762	−	0.929524i	$-0.620218\pi$
$19$	1.41042	−	0.906424i	0.323573	−	0.207948i	0.692335	+	0.721576i	$0.256582\pi$
$20$	3.91579	+	4.51907i	0.875598	+	1.01049i
$21$		0			0
$22$	0.470295			0.100267
$23$	−4.59385	+	1.37715i	−0.957884	+	0.287156i
$23$	−4.59385	+	1.37715i	−0.957884	+	0.287156i
$24$		0			0
$25$	−6.14491	+	1.80431i	−1.22898	+	0.360862i
$26$	−0.142315	−	0.164240i	−0.0279102	−	0.0322101i
$27$		0			0
$28$	1.14365	+	7.95423i	0.216129	+	1.50321i
$29$	1.15189	+	0.740277i	0.213901	+	0.137466i	0.643205	−	0.765694i	$-0.277604\pi$
$29$	1.15189	+	0.740277i	0.213901	+	0.137466i	−0.429303	+	0.903160i	$0.641241\pi$
$30$		0			0
$31$	−4.23404	+	4.88634i	−0.760456	+	0.877613i	−0.995538	−	0.0943622i	$-0.969919\pi$
$31$	−4.23404	+	4.88634i	−0.760456	+	0.877613i	0.235082	+	0.971976i	$0.424464\pi$
$32$	0.696384	−	4.84346i	0.123104	−	0.856211i
$33$		0			0
$34$	1.50926	+	0.443160i	0.258837	+	0.0760013i
$35$	−14.7056	−	4.31795i	−2.48570	−	0.729867i
$36$		0			0
$37$	0.506627	−	3.52367i	0.0832890	−	0.579288i	−0.904851	−	0.425729i	$-0.860018\pi$
$37$	0.506627	−	3.52367i	0.0832890	−	0.579288i	0.988140	−	0.153559i	$-0.0490734\pi$
$38$	0.525785	−	0.606789i	0.0852937	−	0.0984341i
$39$		0			0
$40$	5.12999	+	3.29685i	0.811123	+	0.521277i
$41$	0.821738	+	5.71531i	0.128334	+	0.892582i	0.947666	+	0.319263i	$0.103435\pi$
$41$	0.821738	+	5.71531i	0.128334	+	0.892582i	−0.819332	+	0.573319i	$0.805656\pi$
$42$		0			0
$43$	7.20584	+	8.31598i	1.09888	+	1.26817i	0.960646	+	0.277775i	$0.0895970\pi$
$43$	7.20584	+	8.31598i	1.09888	+	1.26817i	0.138233	+	0.990400i	$0.455858\pi$
$44$	−1.66844	+	0.489899i	−0.251527	+	0.0738551i
$45$		0			0
$46$	−1.92504	+	1.25259i	−0.283831	+	0.184684i
$47$	10.0618			1.46767			0.733833	−	0.679330i	$-0.237730\pi$
$47$	10.0618			1.46767			0.733833	+	0.679330i	$0.237730\pi$
$48$		0			0
$49$	−8.90436	−	10.2762i	−1.27205	−	1.46803i
$50$	−2.58011	+	1.65814i	−0.364882	+	0.234496i
$51$		0			0
$52$	0.675969	+	0.434419i	0.0937401	+	0.0602431i
$53$	5.11162	−	11.1929i	0.702135	−	1.53746i	−0.135229	−	0.990814i	$-0.543177\pi$
$53$	5.11162	−	11.1929i	0.702135	−	1.53746i	0.837364	−	0.546646i	$-0.184096\pi$
$54$		0			0
$55$	0.471975	−	3.28266i	0.0636411	−	0.442633i
$56$	3.40442	+	7.45463i	0.454934	+	0.996167i
$57$		0			0
$58$	0.629165	+	0.184739i	0.0826134	+	0.0242575i
$59$	4.41863	+	9.67544i	0.575256	+	1.25964i	0.943951	+	0.330085i	$0.107077\pi$
$59$	4.41863	+	9.67544i	0.575256	+	1.25964i	−0.368695	+	0.929550i	$0.620195\pi$
$60$		0			0
$61$	−3.65011	+	4.21246i	−0.467349	+	0.539350i	−0.939672	−	0.342076i	$-0.888870\pi$
$61$	−3.65011	+	4.21246i	−0.467349	+	0.539350i	0.472323	+	0.881425i	$0.343416\pi$
$62$	−1.28625	+	2.81649i	−0.163354	+	0.357695i
$63$		0			0
$64$	0.428340	+	2.97917i	0.0535425	+	0.372396i
$65$	−1.28922	+	0.828529i	−0.159908	+	0.102766i
$66$		0			0
$67$	7.43903	−	2.18430i	0.908822	−	0.266854i	0.206277	−	0.978494i	$-0.433865\pi$
$67$	7.43903	−	2.18430i	0.908822	−	0.266854i	0.702545	+	0.711639i	$0.252047\pi$
$68$	−5.81597			−0.705290
$69$		0			0
$70$	−7.33969			−0.877260
$71$	2.86847	−	0.842258i	0.340424	−	0.0999576i	−0.107052	−	0.994253i	$-0.534141\pi$
$71$	2.86847	−	0.842258i	0.340424	−	0.0999576i	0.447476	+	0.894296i	$0.352323\pi$
$72$		0			0
$73$	−3.27850	+	2.10697i	−0.383720	+	0.246602i	−0.718253	−	0.695782i	$-0.755058\pi$
$73$	−3.27850	+	2.10697i	−0.383720	+	0.246602i	0.334533	+	0.942384i	$0.391421\pi$
$74$	−0.242620	−	1.68746i	−0.0282039	−	0.196163i
$75$		0			0
$76$	−1.23322	+	2.70038i	−0.141460	+	0.309754i
$77$	2.91869	−	3.36835i	0.332616	−	0.383859i
$78$		0			0
$79$	−3.61897	−	7.92444i	−0.407166	−	0.891570i	−0.996493	−	0.0836750i	$-0.973334\pi$
$79$	−3.61897	−	7.92444i	−0.407166	−	0.891570i	0.589327	−	0.807895i	$-0.299393\pi$
$80$	−8.67273	−	2.54654i	−0.969641	−	0.284712i
$81$		0			0
$82$	1.14869	+	2.51528i	0.126851	+	0.277766i
$83$	−1.06526	+	7.40902i	−0.116927	+	0.813246i	0.843980	+	0.536375i	$0.180207\pi$
$83$	−1.06526	+	7.40902i	−0.116927	+	0.813246i	−0.960907	+	0.276871i	$0.910703\pi$
$84$		0			0
$85$	4.60791	−	10.0899i	0.499798	−	1.09440i
$86$	4.43302	+	2.84893i	0.478024	+	0.307208i
$87$		0			0
$88$	−1.49182	+	0.958732i	−0.159028	+	0.102201i
$89$	−4.73727	−	5.46710i	−0.502150	−	0.579512i	0.446922	−	0.894573i	$-0.352520\pi$
$89$	−4.73727	−	5.46710i	−0.502150	−	0.579512i	−0.949071	+	0.315062i	$0.897975\pi$
$90$		0			0
$91$	−2.05954			−0.215898
$92$	5.52455	−	6.44903i	0.575974	−	0.672358i
$93$		0			0
$94$	4.62333	−	1.35753i	0.476860	−	0.140019i
$95$	−3.70772	−	4.27893i	−0.380404	−	0.439009i
$96$		0			0
$97$	0.801906	+	5.57738i	0.0814212	+	0.566297i	0.989169	+	0.146781i	$0.0468912\pi$
$97$	0.801906	+	5.57738i	0.0814212	+	0.566297i	−0.907748	+	0.419516i	$0.862200\pi$
$98$	−5.47795	−	3.52046i	−0.553356	−	0.355620i
$99$		0			0
$100$	7.42607	−	8.57014i	0.742607	−	0.857014i
$101$	1.12323	−	7.81224i	0.111766	−	0.777347i	−0.854435	−	0.519558i	$-0.826097\pi$
$101$	1.12323	−	7.81224i	0.111766	−	0.777347i	0.966201	−	0.257790i	$-0.0829942\pi$
$102$		0			0
$103$	8.63913	+	2.53668i	0.851239	+	0.249946i	0.678117	−	0.734954i	$-0.262796\pi$
$103$	8.63913	+	2.53668i	0.851239	+	0.249946i	0.173122	+	0.984900i	$0.444615\pi$
$104$	0.786250	+	0.230864i	0.0770982	+	0.0226381i
$105$		0			0
$106$	0.838617	−	5.83271i	0.0814536	−	0.566523i
$107$	−2.36779	+	2.73258i	−0.228903	+	0.264168i	−0.858569	−	0.512697i	$-0.828646\pi$
$107$	−2.36779	+	2.73258i	−0.228903	+	0.264168i	0.629666	+	0.776866i	$0.283192\pi$
$108$		0			0
$109$	1.07332	+	0.689779i	0.102805	+	0.0660688i	0.591033	−	0.806647i	$-0.298720\pi$
$109$	1.07332	+	0.689779i	0.102805	+	0.0660688i	−0.488228	+	0.872716i	$0.662357\pi$
$110$	−0.226025	−	1.57204i	−0.0215506	−	0.149888i
$111$		0			0
$112$	−7.95488	−	9.18042i	−0.751666	−	0.867468i
$113$	−1.13788	+	0.334113i	−0.107043	+	0.0314307i	−0.334815	−	0.942284i	$-0.608674\pi$
$113$	−1.13788	+	0.334113i	−0.107043	+	0.0314307i	0.227772	+	0.973714i	$0.426856\pi$
$114$		0			0
$115$	6.81116	+	14.6938i	0.635144	+	1.37020i
$116$	−2.42450			−0.225109
$117$		0			0
$118$	3.33573	+	3.84964i	0.307079	+	0.354388i
$119$	12.5406	−	8.05936i	1.14960	−	0.738801i
$120$		0			0
$121$	−8.44247	−	5.42564i	−0.767497	−	0.493240i
$122$	−1.10886	+	2.42806i	−0.100391	+	0.219827i
$123$		0			0
$124$	1.62927	−	11.3318i	0.146312	−	1.01763i
$125$	1.97010	+	4.31391i	0.176211	+	0.385848i
$126$		0			0
$127$	−2.74514	−	0.806046i	−0.243592	−	0.0715250i	0.157658	−	0.987494i	$-0.449606\pi$
$127$	−2.74514	−	0.806046i	−0.243592	−	0.0715250i	−0.401249	+	0.915969i	$0.631424\pi$
$128$	4.66424	+	10.2133i	0.412264	+	0.902733i
$129$		0			0
$130$	−0.480602	+	0.554644i	−0.0421515	+	0.0486455i
$131$	−0.160212	+	0.350814i	−0.0139977	+	0.0306508i	−0.916502	−	0.400031i	$-0.868999\pi$
$131$	−0.160212	+	0.350814i	−0.0139977	+	0.0306508i	0.902504	+	0.430681i	$0.141727\pi$
$132$		0			0
$133$	−1.08287	−	7.53156i	−0.0938972	−	0.653069i
$134$	3.12348	−	2.00734i	0.269828	−	0.173408i
$135$		0			0
$136$	−5.69093	+	1.67101i	−0.487993	+	0.143288i
$137$	−20.4664			−1.74856			−0.874282	−	0.485419i	$-0.838667\pi$
$137$	−20.4664			−1.74856			−0.874282	+	0.485419i	$0.838667\pi$
$138$		0			0
$139$	10.1030			0.856927			0.428463	−	0.903559i	$-0.359055\pi$
$139$	10.1030			0.856927			0.428463	+	0.903559i	$0.359055\pi$
$140$	26.0386	−	7.64563i	2.20067	−	0.646174i
$141$		0			0
$142$	1.20440	−	0.774023i	0.101071	−	0.0649546i
$143$	−0.0634232	−	0.441118i	−0.00530371	−	0.0368881i
$144$		0			0
$145$	1.92089	−	4.20616i	0.159521	−	0.349303i
$146$	−1.22218	+	1.41047i	−0.101148	+	0.116731i
$147$		0			0
$148$	2.61852	+	5.73377i	0.215241	+	0.471313i
$149$	−9.88733	−	2.90318i	−0.810001	−	0.237838i	−0.149596	−	0.988747i	$-0.547797\pi$
$149$	−9.88733	−	2.90318i	−0.810001	−	0.237838i	−0.660405	+	0.750909i	$0.729615\pi$
$150$		0			0
$151$	0.207860	+	0.455151i	0.0169154	+	0.0370396i	0.917901	−	0.396809i	$-0.129882\pi$
$151$	0.207860	+	0.455151i	0.0169154	+	0.0370396i	−0.900986	+	0.433849i	$0.857155\pi$
$152$	−0.430851	+	2.99664i	−0.0349467	+	0.243059i
$153$		0			0
$154$	0.886663	−	1.94152i	0.0714493	−	0.156452i
$155$	18.3683	+	11.8046i	1.47537	+	0.948165i
$156$		0			0
$157$	−13.1111	+	8.42597i	−1.04638	+	0.672466i	−0.946556	−	0.322540i	$-0.895463\pi$
$157$	−13.1111	+	8.42597i	−1.04638	+	0.672466i	−0.0998213	+	0.995005i	$0.531827\pi$
$158$	−2.73205	−	3.15296i	−0.217350	−	0.250836i
$159$		0			0
$160$	−16.5247			−1.30639
$161$	−2.97563	+	21.5612i	−0.234512	+	1.69926i
$162$		0			0
$163$	6.51437	−	1.91279i	0.510245	−	0.149821i	−0.0164685	−	0.999864i	$-0.505242\pi$
$163$	6.51437	−	1.91279i	0.510245	−	0.149821i	0.526713	+	0.850043i	$0.323424\pi$
$164$	−6.69527	−	7.72675i	−0.522813	−	0.603358i
$165$		0			0
$166$	0.510142	+	3.54812i	0.0395947	+	0.275387i
$167$	−16.8646	−	10.8382i	−1.30502	−	0.838688i	−0.311274	−	0.950320i	$-0.600756\pi$
$167$	−16.8646	−	10.8382i	−1.30502	−	0.838688i	−0.993750	+	0.111633i	$0.964392\pi$
$168$		0			0
$169$	8.37833	−	9.66911i	0.644487	−	0.743778i
$170$	0.755977	−	5.25794i	0.0579808	−	0.403265i
$171$		0			0
$172$	−18.6945	−	5.48919i	−1.42544	−	0.418547i
$173$	9.96585	+	2.92624i	0.757690	+	0.222478i	0.637687	−	0.770296i	$-0.279891\pi$
$173$	9.96585	+	2.92624i	0.757690	+	0.222478i	0.120003	+	0.992774i	$0.461710\pi$
$174$		0			0
$175$	−4.13647	+	28.7698i	−0.312688	+	2.17479i
$176$	1.72132	−	1.98651i	0.129749	−	0.149739i
$177$		0			0
$178$	−2.91436	−	1.87295i	−0.218441	−	0.140383i
$179$	0.597086	+	4.15282i	0.0446283	+	0.310396i	0.999893	+	0.0146436i	$0.00466138\pi$
$179$	0.597086	+	4.15282i	0.0446283	+	0.310396i	−0.955265	+	0.295753i	$0.904430\pi$
$180$		0			0
$181$	0.398786	+	0.460224i	0.0296415	+	0.0342081i	0.770377	−	0.637589i	$-0.220068\pi$
$181$	0.398786	+	0.460224i	0.0296415	+	0.0342081i	−0.740735	+	0.671797i	$0.765523\pi$
$182$	−0.946343	+	0.277871i	−0.0701476	+	0.0205972i
$183$		0			0
$184$	3.55288	−	7.89765i	0.261922	−	0.582223i
$185$	−12.0219			−0.883868
$186$		0			0
$187$	2.11237	+	2.43780i	0.154471	+	0.178270i
$188$	−14.9878	+	9.63209i	−1.09310	+	0.702493i
$189$		0			0
$190$	−2.28098	−	1.46590i	−0.165480	−	0.106347i
$191$	−0.608314	+	1.33202i	−0.0440161	+	0.0963817i	−0.930363	−	0.366641i	$-0.880508\pi$
$191$	−0.608314	+	1.33202i	−0.0440161	+	0.0963817i	0.886347	+	0.463022i	$0.153235\pi$
$192$		0			0
$193$	−3.02393	+	21.0319i	−0.217667	+	1.51391i	0.528948	+	0.848654i	$0.322587\pi$
$193$	−3.02393	+	21.0319i	−0.217667	+	1.51391i	−0.746616	+	0.665256i	$0.768323\pi$
$194$	1.12097	+	2.45457i	0.0804807	+	0.176228i
$195$		0			0
$196$	23.1010	+	6.78308i	1.65007	+	0.484506i
$197$	2.52646	+	5.53217i	0.180003	+	0.394151i	0.978028	−	0.208473i	$-0.0668492\pi$
$197$	2.52646	+	5.53217i	0.180003	+	0.394151i	−0.798025	+	0.602624i	$0.794122\pi$
$198$		0			0
$199$	−7.57550	+	8.74259i	−0.537013	+	0.619746i	−0.957808	−	0.287410i	$-0.907206\pi$
$199$	−7.57550	+	8.74259i	−0.537013	+	0.619746i	0.420795	+	0.907156i	$0.361751\pi$
$200$	4.80409	−	10.5195i	0.339700	−	0.743840i
$201$		0			0
$202$	−0.537906	−	3.74122i	−0.0378469	−	0.263231i
$203$	5.22779	−	3.35970i	0.366919	−	0.235804i
$204$		0			0
$205$	18.7094	−	5.49357i	1.30672	−	0.383688i
$206$	4.31187			0.300422
$207$		0			0
$208$	−1.21463			−0.0842193
$209$	1.57979	−	0.463867i	0.109276	−	0.0320863i
$210$		0			0
$211$	−2.32817	+	1.49622i	−0.160278	+	0.103004i	−0.618321	−	0.785926i	$-0.712187\pi$
$211$	−2.32817	+	1.49622i	−0.160278	+	0.103004i	0.458043	+	0.888930i	$0.348550\pi$
$212$	3.10072	+	21.5660i	0.212958	+	1.48116i
$213$		0			0
$214$	−0.719307	+	1.57506i	−0.0491708	+	0.107669i
$215$	24.3343	−	28.0833i	1.65959	−	1.91527i
$216$		0			0
$217$	12.1897	+	26.6918i	0.827492	+	1.81196i
$218$	0.586246	+	0.172137i	0.0397056	+	0.0116586i
$219$		0			0
$220$	2.43942	+	5.34159i	0.164466	+	0.360130i
$221$	0.212129	−	1.47539i	0.0142694	−	0.0992456i
$222$		0			0
$223$	−7.66126	+	16.7758i	−0.513036	+	1.12339i	0.458973	+	0.888450i	$0.348217\pi$
$223$	−7.66126	+	16.7758i	−0.513036	+	1.12339i	−0.972009	+	0.234942i	$0.924510\pi$
$224$	−18.6823	−	12.0064i	−1.24827	−	0.802212i
$225$		0			0
$226$	−0.477771	+	0.307045i	−0.0317809	+	0.0204243i
$227$	4.74799	+	5.47948i	0.315135	+	0.363686i	0.891114	−	0.453779i	$-0.149924\pi$
$227$	4.74799	+	5.47948i	0.315135	+	0.363686i	−0.575979	+	0.817465i	$0.695379\pi$
$228$		0			0
$229$	9.95723			0.657992			0.328996	−	0.944331i	$-0.393290\pi$
$229$	9.95723			0.657992			0.328996	+	0.944331i	$0.393290\pi$
$230$	5.11216	+	5.83274i	0.337086	+	0.384600i
$231$		0			0
$232$	−2.37237	+	0.696590i	−0.155754	+	0.0457334i
$233$	3.53680	+	4.08169i	0.231704	+	0.267400i	0.859681	−	0.510831i	$-0.170662\pi$
$233$	3.53680	+	4.08169i	0.231704	+	0.267400i	−0.627977	+	0.778232i	$0.716117\pi$
$234$		0			0
$235$	−4.83572	−	33.6332i	−0.315448	−	2.19399i
$236$	−15.8441	−	10.1824i	−1.03136	−	0.662817i
$237$		0			0
$238$	4.67496	−	5.39519i	0.303033	−	0.349718i
$239$	−2.10857	+	14.6654i	−0.136392	+	0.948626i	0.800581	+	0.599224i	$0.204524\pi$
$239$	−2.10857	+	14.6654i	−0.136392	+	0.948626i	−0.936973	+	0.349402i	$0.886385\pi$
$240$		0			0
$241$	−14.0591	−	4.12814i	−0.905629	−	0.265917i	−0.204429	−	0.978881i	$-0.565534\pi$
$241$	−14.0591	−	4.12814i	−0.905629	−	0.265917i	−0.701200	+	0.712965i	$0.747352\pi$
$242$	−4.61128	−	1.35399i	−0.296424	−	0.0870380i
$243$		0			0
$244$	1.40457	−	9.76900i	0.0899184	−	0.625396i
$245$	−30.0703	+	34.7030i	−1.92112	+	2.21709i
$246$		0			0
$247$	−0.640050	−	0.411335i	−0.0407254	−	0.0261726i
$248$	−1.66154	−	11.5563i	−0.105508	−	0.733824i
$249$		0			0
$250$	1.48728	+	1.71641i	0.0940636	+	0.108555i
$251$	0.924463	−	0.271447i	0.0583516	−	0.0171336i	−0.252426	−	0.967616i	$-0.581229\pi$
$251$	0.924463	−	0.271447i	0.0583516	−	0.0171336i	0.310778	+	0.950483i	$0.399410\pi$
$252$		0			0
$253$	−4.70967	+	0.0266443i	−0.296095	+	0.00167511i
$254$	−1.37012			−0.0859692
$255$		0			0
$256$	−0.420855	−	0.485693i	−0.0263035	−	0.0303558i
$257$	0.188128	−	0.120903i	0.0117351	−	0.00754171i	−0.534760	−	0.845004i	$-0.679598\pi$
$257$	0.188128	−	0.120903i	0.0117351	−	0.00754171i	0.546495	+	0.837462i	$0.315962\pi$
$258$		0			0
$259$	−13.5916	−	8.73480i	−0.844542	−	0.542754i
$260$	1.12724	−	2.46832i	0.0699086	−	0.153078i
$261$		0			0
$262$	−0.0262844	+	0.182812i	−0.00162386	+	0.0112942i
$263$	9.27832	+	20.3167i	0.572126	+	1.25278i	0.945658	+	0.325163i	$0.105419\pi$
$263$	9.27832	+	20.3167i	0.572126	+	1.25278i	−0.373532	+	0.927617i	$0.621853\pi$
$264$		0			0
$265$	−39.8706	−	11.7071i	−2.44923	−	0.719160i
$266$	−1.51373	−	3.31460i	−0.0928125	−	0.203231i
$267$		0			0
$268$	−8.99000	+	10.3750i	−0.549151	+	0.633755i
$269$	9.85399	−	21.5772i	0.600808	−	1.31559i	−0.327878	−	0.944720i	$-0.606333\pi$
$269$	9.85399	−	21.5772i	0.600808	−	1.31559i	0.928686	−	0.370867i	$-0.120939\pi$
$270$		0			0
$271$	1.63660	+	11.3828i	0.0994161	+	0.691454i	0.977188	+	0.212376i	$0.0681201\pi$
$271$	1.63660	+	11.3828i	0.0994161	+	0.691454i	−0.877772	+	0.479079i	$0.840971\pi$
$272$	7.39592	−	4.75307i	0.448444	−	0.288197i
$273$		0			0
$274$	−9.40417	+	2.76131i	−0.568127	+	0.166817i
$275$	−6.28938			−0.379264
$276$		0			0
$277$	−6.25528			−0.375843			−0.187922	−	0.982184i	$-0.560175\pi$
$277$	−6.25528			−0.375843			−0.187922	+	0.982184i	$0.560175\pi$
$278$	4.64227	−	1.36309i	0.278425	−	0.0817528i
$279$		0			0
$280$	23.2821	−	14.9625i	1.39137	−	0.894180i
$281$	−3.04681	−	21.1911i	−0.181758	−	1.26415i	−0.852604	−	0.522557i	$-0.824978\pi$
$281$	−3.04681	−	21.1911i	−0.181758	−	1.26415i	0.670847	−	0.741596i	$-0.265931\pi$
$282$		0			0
$283$	3.01441	−	6.60063i	0.179188	−	0.392367i	−0.798630	−	0.601822i	$-0.794442\pi$
$283$	3.01441	−	6.60063i	0.179188	−	0.392367i	0.977818	+	0.209455i	$0.0671690\pi$
$284$	−3.46651	+	4.00057i	−0.205700	+	0.237390i
$285$		0			0
$286$	−0.0886578	−	0.194134i	−0.00524245	−	0.0114794i
$287$	25.1438	+	7.38288i	1.48419	+	0.435797i
$288$		0			0
$289$	−2.58023	−	5.64991i	−0.151778	−	0.332348i
$290$	0.315143	−	2.19187i	0.0185058	−	0.128711i
$291$		0			0
$292$	2.86660	−	6.27698i	0.167755	−	0.367332i
$293$	0.329271	+	0.211609i	0.0192362	+	0.0123624i	0.550224	−	0.835017i	$-0.314542\pi$
$293$	0.329271	+	0.211609i	0.0192362	+	0.0123624i	−0.530987	+	0.847380i	$0.678179\pi$
$294$		0			0
$295$	30.2181	−	19.4200i	1.75937	−	1.13068i
$296$	4.20961	+	4.85815i	0.244679	+	0.282374i
$297$		0			0
$298$	−4.93485			−0.285868
$299$	1.43449	+	1.63668i	0.0829585	+	0.0946519i
$300$		0			0
$301$	47.9162	−	14.0695i	2.76185	−	0.810951i
$302$	0.156919	+	0.181094i	0.00902968	+	0.0104208i
$303$		0			0
$304$	−0.638634	−	4.44180i	−0.0366282	−	0.254754i
$305$	15.8350	+	10.1766i	0.906712	+	0.582709i
$306$		0			0
$307$	−0.843569	+	0.973531i	−0.0481450	+	0.0555623i	−0.779311	−	0.626637i	$-0.784431\pi$
$307$	−0.843569	+	0.973531i	−0.0481450	+	0.0555623i	0.731166	+	0.682199i	$0.238976\pi$
$308$	−1.12312	+	7.81145i	−0.0639956	+	0.445099i
$309$		0			0
$310$	10.0328	+	2.94588i	0.569822	+	0.167315i
$311$	−1.20852	−	0.354853i	−0.0685288	−	0.0201219i	0.247288	−	0.968942i	$-0.420460\pi$
$311$	−1.20852	−	0.354853i	−0.0685288	−	0.0201219i	−0.315817	+	0.948820i	$0.602279\pi$
$312$		0			0
$313$	1.48565	−	10.3330i	0.0839742	−	0.584053i	−0.903776	−	0.428007i	$-0.859216\pi$
$313$	1.48565	−	10.3330i	0.0839742	−	0.584053i	0.987750	−	0.156046i	$-0.0498750\pi$
$314$	−4.88762	+	5.64061i	−0.275824	+	0.318318i
$315$		0			0
$316$	12.9767	+	8.33965i	0.729999	+	0.469142i
$317$	−3.85904	−	26.8402i	−0.216745	−	1.50750i	−0.749941	−	0.661505i	$-0.769918\pi$
$317$	−3.85904	−	26.8402i	−0.216745	−	1.50750i	0.533196	−	0.845992i	$-0.320991\pi$
$318$		0			0
$319$	0.880579	+	1.01624i	0.0493029	+	0.0568986i
$320$	9.75248	−	2.86359i	0.545180	−	0.160079i
$321$		0			0
$322$	1.54174	+	10.3087i	0.0859177	+	0.574480i
$323$	5.50692			0.306413
$324$		0			0
$325$	1.90321	+	2.19642i	0.105571	+	0.121836i
$326$	2.73523	−	1.75783i	0.151491	−	0.0973571i
$327$		0			0
$328$	−8.77132	−	5.63698i	−0.484315	−	0.311250i
$329$	18.9698	−	41.5382i	1.04584	−	2.29007i
$330$		0			0
$331$	1.06491	−	7.40664i	0.0585330	−	0.407106i	−0.939399	−	0.342826i	$-0.888616\pi$
$331$	1.06491	−	7.40664i	0.0585330	−	0.407106i	0.997932	−	0.0642799i	$-0.0204751\pi$
$332$	−5.50582	−	12.0561i	−0.302171	−	0.661662i
$333$		0			0
$334$	−9.21146	−	2.70473i	−0.504029	−	0.147996i
$335$	−10.8766	−	23.8164i	−0.594250	−	1.30123i
$336$		0			0
$337$	16.8366	−	19.4305i	0.917150	−	1.05845i	−0.0809434	−	0.996719i	$-0.525793\pi$
$337$	16.8366	−	19.4305i	0.917150	−	1.05845i	0.998093	−	0.0617284i	$-0.0196613\pi$
$338$	2.54523	−	5.57329i	0.138443	−	0.303147i
$339$		0			0
$340$	2.79517	+	19.4408i	0.151589	+	1.05433i
$341$	−5.34154	+	3.43280i	−0.289261	+	0.185897i
$342$		0			0
$343$	−28.7287	+	8.43551i	−1.55120	+	0.455475i
$344$	−19.8696			−1.07130
$345$		0			0
$346$	4.97404			0.267406
$347$	−23.6140	+	6.93370i	−1.26767	+	0.372220i	−0.845342	−	0.534225i	$-0.820604\pi$
$347$	−23.6140	+	6.93370i	−1.26767	+	0.372220i	−0.422324	+	0.906445i	$0.638785\pi$
$348$		0			0
$349$	−16.2708	+	10.4566i	−0.870956	+	0.559730i	−0.898045	−	0.439903i	$-0.855013\pi$
$349$	−16.2708	+	10.4566i	−0.870956	+	0.559730i	0.0270889	+	0.999633i	$0.491376\pi$
$350$	1.98092	+	13.7776i	0.105885	+	0.736443i
$351$		0			0
$352$	1.99625	−	4.37117i	0.106400	−	0.232984i
$353$	−15.4031	+	17.7761i	−0.819823	+	0.946126i	−0.999291	−	0.0376379i	$-0.988017\pi$
$353$	−15.4031	+	17.7761i	−0.819823	+	0.946126i	0.179469	+	0.983764i	$0.442562\pi$
$354$		0			0
$355$	−4.19397	−	9.18351i	−0.222593	−	0.487410i
$356$	12.2901	+	3.60871i	0.651376	+	0.191261i
$357$		0			0
$358$	0.834652	+	1.82763i	0.0441127	+	0.0965934i
$359$	−0.860321	+	5.98367i	−0.0454060	+	0.315806i	0.954442	+	0.298395i	$0.0964513\pi$
$359$	−0.860321	+	5.98367i	−0.0454060	+	0.315806i	−0.999848	+	0.0174106i	$0.994458\pi$
$360$		0			0
$361$	−6.72520	+	14.7261i	−0.353958	+	0.775059i
$362$	0.245332	+	0.157666i	0.0128944	+	0.00828672i
$363$		0			0
$364$	3.06784	−	1.97158i	0.160798	−	0.103339i
$365$	8.61852	+	9.94630i	0.451114	+	0.520613i
$366$		0			0
$367$	3.17802			0.165891			0.0829457	−	0.996554i	$-0.473567\pi$
$367$	3.17802			0.165891			0.0829457	+	0.996554i	$0.473567\pi$
$368$	−1.75490	+	12.7159i	−0.0914805	+	0.662861i
$369$		0			0
$370$	−5.52398	+	1.62199i	−0.287178	+	0.0843231i
$371$	−36.5705	−	42.2046i	−1.89864	−	2.19115i
$372$		0			0
$373$	0.0788258	+	0.548246i	0.00408145	+	0.0283871i	0.991760	−	0.128107i	$-0.0408900\pi$
$373$	0.0788258	+	0.548246i	0.00408145	+	0.0283871i	−0.987679	+	0.156494i	$0.949981\pi$
$374$	1.29952	+	0.835153i	0.0671967	+	0.0431847i
$375$		0			0
$376$	−11.8982	+	13.7312i	−0.613601	+	0.708133i
$377$	0.0884301	−	0.615045i	0.00455438	−	0.0316764i
$378$		0			0
$379$	−2.23321	−	0.655730i	−0.114712	−	0.0336826i	0.223873	−	0.974618i	$-0.428130\pi$
$379$	−2.23321	−	0.655730i	−0.114712	−	0.0336826i	−0.338585	+	0.940936i	$0.609948\pi$
$380$	9.61912	+	2.82443i	0.493450	+	0.144890i
$381$		0			0
$382$	−0.0998005	+	0.694128i	−0.00510624	+	0.0355147i
$383$	−19.1738	+	22.1278i	−0.979736	+	1.13068i	0.0116804	+	0.999932i	$0.496282\pi$
$383$	−19.1738	+	22.1278i	−0.979736	+	1.13068i	−0.991416	+	0.130744i	$0.958264\pi$
$384$		0			0
$385$	−12.6620	−	8.13735i	−0.645313	−	0.414718i
$386$	1.44813	+	10.0720i	0.0737081	+	0.512651i
$387$		0			0
$388$	−6.53368	−	7.54027i	−0.331697	−	0.382799i
$389$	9.77736	−	2.87089i	0.495732	−	0.145560i	−0.0243038	−	0.999705i	$-0.507737\pi$
$389$	9.77736	−	2.87089i	0.495732	−	0.145560i	0.520035	+	0.854145i	$0.325919\pi$
$390$		0			0
$391$	−15.1393	−	4.35242i	−0.765628	−	0.220112i
$392$	24.5532			1.24013
$393$		0			0
$394$	1.90729	+	2.20113i	0.0960878	+	0.110891i
$395$	−24.7494	+	15.9055i	−1.24528	+	0.800292i
$396$		0			0
$397$	29.0435	+	18.6651i	1.45765	+	0.936775i	0.998836	+	0.0482421i	$0.0153619\pi$
$397$	29.0435	+	18.6651i	1.45765	+	0.936775i	0.458814	+	0.888532i	$0.348274\pi$
$398$	−2.30134	+	5.03924i	−0.115356	+	0.252594i
$399$		0			0
$400$	−2.43951	+	16.9672i	−0.121976	+	0.848360i
$401$	−3.73436	−	8.17710i	−0.186485	−	0.408345i	0.793180	−	0.608988i	$-0.208424\pi$
$401$	−3.73436	−	8.17710i	−0.186485	−	0.408345i	−0.979664	+	0.200643i	$0.935697\pi$
$402$		0			0
$403$	2.81522	+	0.826623i	0.140236	+	0.0411770i
$404$	5.80547	+	12.7122i	0.288833	+	0.632455i
$405$		0			0
$406$	1.94884	−	2.24909i	0.0967195	−	0.111620i
$407$	1.45229	−	3.18008i	0.0719875	−	0.157631i
$408$		0			0
$409$	−3.18911	−	22.1808i	−0.157691	−	1.09677i	−0.902873	−	0.429907i	$-0.858546\pi$
$409$	−3.18911	−	22.1808i	−0.157691	−	1.09677i	0.745182	−	0.666861i	$-0.232363\pi$
$410$	7.85565	−	5.04852i	0.387963	−	0.249329i
$411$		0			0
$412$	−15.2970	+	4.49160i	−0.753629	+	0.221285i
$413$	48.2737			2.37539
$414$		0			0
$415$	25.2778			1.24084
$416$	−2.13061	+	0.625605i	−0.104462	+	0.0306728i
$417$		0			0
$418$	0.663316	−	0.426287i	0.0324438	−	0.0208504i
$419$	1.45242	+	10.1018i	0.0709555	+	0.493506i	0.994049	+	0.108931i	$0.0347428\pi$
$419$	1.45242	+	10.1018i	0.0709555	+	0.493506i	−0.923094	+	0.384575i	$0.874348\pi$
$420$		0			0
$421$	6.66427	−	14.5927i	0.324797	−	0.711205i	−0.674846	−	0.737959i	$-0.735790\pi$
$421$	6.66427	−	14.5927i	0.324797	−	0.711205i	0.999642	+	0.0267538i	$0.00851702\pi$
$422$	−0.867907	+	1.00162i	−0.0422491	+	0.0487580i
$423$		0			0
$424$	9.23024	+	20.2114i	0.448260	+	0.981553i
$425$	−20.1838	−	5.92649i	−0.979056	−	0.287477i
$426$		0			0
$427$	10.5086	+	23.0106i	0.508547	+	1.11356i
$428$	0.911131	−	6.33706i	0.0440412	−	0.306313i
$429$		0			0
$430$	7.39247	−	16.1873i	0.356497	−	0.780619i
$431$	32.3600	+	20.7965i	1.55873	+	1.00173i	0.982895	+	0.184165i	$0.0589580\pi$
$431$	32.3600	+	20.7965i	1.55873	+	1.00173i	0.575832	+	0.817568i	$0.304678\pi$
$432$		0			0
$433$	−6.54040	+	4.20326i	−0.314311	+	0.201996i	−0.688279	−	0.725446i	$-0.741633\pi$
$433$	−6.54040	+	4.20326i	−0.314311	+	0.201996i	0.373968	+	0.927442i	$0.377997\pi$
$434$	9.20233	+	10.6201i	0.441726	+	0.509779i
$435$		0			0
$436$	−2.25911			−0.108192
$437$	−5.23099	+	6.10634i	−0.250232	+	0.292106i
$438$		0			0
$439$	−33.5580	+	9.85352i	−1.60164	+	0.470283i	−0.956001	−	0.293363i	$-0.905226\pi$
$439$	−33.5580	+	9.85352i	−1.60164	+	0.470283i	−0.645635	+	0.763646i	$0.723407\pi$
$440$	3.92168	+	4.52586i	0.186959	+	0.215762i
$441$		0			0
$442$	−0.101587	−	0.706553i	−0.00483200	−	0.0336073i
$443$	8.46340	+	5.43910i	0.402108	+	0.258419i	0.726028	−	0.687665i	$-0.241364\pi$
$443$	8.46340	+	5.43910i	0.402108	+	0.258419i	−0.323919	+	0.946085i	$0.605001\pi$
$444$		0			0
$445$	−15.9979	+	18.4626i	−0.758373	+	0.875210i
$446$	−1.25691	+	8.74203i	−0.0595166	+	0.413947i
$447$		0			0
$448$	13.1065	+	3.84841i	0.619222	+	0.181820i
$449$	−16.3702	−	4.80672i	−0.772557	−	0.226843i	−0.128386	−	0.991724i	$-0.540980\pi$
$449$	−16.3702	−	4.80672i	−0.772557	−	0.226843i	−0.644172	+	0.764881i	$0.722798\pi$
$450$		0			0
$451$	−0.806988	+	5.61272i	−0.0379996	+	0.264293i
$452$	1.37512	−	1.58697i	0.0646802	−	0.0746449i
$453$		0			0
$454$	2.92096	+	1.87719i	0.137087	+	0.0881007i
$455$	0.989817	+	6.88433i	0.0464033	+	0.322742i
$456$		0			0
$457$	15.9633	+	18.4226i	0.746732	+	0.861774i	0.994247	−	0.107110i	$-0.0341596\pi$
$457$	15.9633	+	18.4226i	0.746732	+	0.861774i	−0.247515	+	0.968884i	$0.579614\pi$
$458$	4.57528	−	1.34342i	0.213789	−	0.0627740i
$459$		0			0
$460$	−24.2120	−	15.3673i	−1.12889	−	0.716503i
$461$	−38.0631			−1.77278			−0.886388	−	0.462943i	$-0.846793\pi$
$461$	−38.0631			−1.77278			−0.886388	+	0.462943i	$0.846793\pi$
$462$		0			0
$463$	−9.34715	−	10.7872i	−0.434399	−	0.501323i	0.495770	−	0.868454i	$-0.334886\pi$
$463$	−9.34715	−	10.7872i	−0.434399	−	0.501323i	−0.930169	+	0.367130i	$0.880340\pi$
$464$	3.08313	−	1.98141i	0.143131	−	0.0919845i
$465$		0			0
$466$	2.17583	+	1.39832i	0.100794	+	0.0647761i
$467$	1.62177	−	3.55117i	0.0750463	−	0.164329i	−0.868390	−	0.495881i	$-0.834845\pi$
$467$	1.62177	−	3.55117i	0.0750463	−	0.164329i	0.943437	+	0.331553i	$0.107572\pi$
$468$		0			0
$469$	5.00761	−	34.8287i	0.231230	−	1.60824i
$470$	−6.75974	−	14.8018i	−0.311804	−	0.682755i
$471$		0			0
$472$	−18.4290	−	5.41124i	−0.848263	−	0.249073i
$473$	4.48902	+	9.82958i	0.206405	+	0.451964i
$474$		0			0
$475$	−7.03146	+	8.11474i	−0.322626	+	0.372330i
$476$	−10.9650	+	24.0101i	−0.502582	+	1.10050i
$477$		0			0
$478$	1.00977	+	7.02313i	0.0461860	+	0.321231i
$479$	−15.4838	+	9.95081i	−0.707471	+	0.454664i	−0.844258	−	0.535936i	$-0.819959\pi$
$479$	−15.4838	+	9.95081i	−0.707471	+	0.454664i	0.136787	+	0.990600i	$0.456322\pi$
$480$		0			0
$481$	−1.55005	+	0.455134i	−0.0706760	+	0.0207523i
$482$	−7.01704			−0.319618
$483$		0			0
$484$	17.7696			0.807710
$485$	18.2579	−	5.36099i	0.829047	−	0.243430i
$486$		0			0
$487$	10.9745	−	7.05285i	0.497300	−	0.319595i	−0.267835	−	0.963465i	$-0.586308\pi$
$487$	10.9745	−	7.05285i	0.497300	−	0.319595i	0.765135	+	0.643869i	$0.222672\pi$
$488$	−1.43239	−	9.96252i	−0.0648414	−	0.450982i
$489$		0			0
$490$	−9.13499	+	20.0028i	−0.412677	+	0.903636i
$491$	15.6987	−	18.1173i	0.708473	−	0.817621i	−0.281398	−	0.959591i	$-0.590798\pi$
$491$	15.6987	−	18.1173i	0.708473	−	0.817621i	0.989871	+	0.141970i	$0.0453437\pi$
$492$		0			0
$493$	1.86833	+	4.09108i	0.0841455	+	0.184253i
$494$	−0.349595	−	0.102650i	−0.0157290	−	0.00461846i
$495$		0			0
$496$	7.18898	+	15.7417i	0.322795	+	0.706822i
$497$	1.93092	−	13.4298i	0.0866135	−	0.602410i
$498$		0			0
$499$	−3.65609	+	8.00571i	−0.163669	+	0.358385i	−0.973642	−	0.228082i	$-0.926754\pi$
$499$	−3.65609	+	8.00571i	−0.163669	+	0.358385i	0.809973	+	0.586467i	$0.199482\pi$
$500$	−7.06429	−	4.53994i	−0.315924	−	0.203032i
$501$		0			0
$502$	0.388161	−	0.249456i	0.0173245	−	0.0111338i
$503$	−23.6324	−	27.2732i	−1.05372	−	1.21605i	−0.975702	−	0.219102i	$-0.929687\pi$
$503$	−23.6324	−	27.2732i	−1.05372	−	1.21605i	−0.0780145	−	0.996952i	$-0.524858\pi$
$504$		0			0
$505$	−26.6535			−1.18606
$506$	−2.16047	+	0.647668i	−0.0960444	+	0.0287924i
$507$		0			0
$508$	4.86072	−	1.42724i	0.215659	−	0.0633233i
$509$	22.5009	+	25.9674i	0.997335	+	1.15099i	0.988530	+	0.151025i	$0.0482574\pi$
$509$	22.5009	+	25.9674i	0.997335	+	1.15099i	0.00880523	+	0.999961i	$0.497197\pi$
$510$		0			0
$511$	2.51712	+	17.5070i	0.111351	+	0.774463i
$512$	−19.1499	−	12.3069i	−0.846315	−	0.543894i
$513$		0			0
$514$	0.0701316	−	0.0809361i	0.00309337	−	0.00356994i
$515$	4.32726	−	30.0968i	0.190682	−	1.32622i
$516$		0			0
$517$	9.48094	+	2.78385i	0.416971	+	0.122434i
$518$	−7.42374	−	2.17981i	−0.326181	−	0.0957752i
$519$		0			0
$520$	0.393826	−	2.73912i	0.0172704	−	0.120118i
$521$	19.3174	−	22.2934i	0.846310	−	0.976694i	−0.153625	−	0.988129i	$-0.549095\pi$
$521$	19.3174	−	22.2934i	0.846310	−	0.976694i	0.999935	+	0.0114355i	$0.00364012\pi$
$522$		0			0
$523$	17.1736	+	11.0368i	0.750949	+	0.482606i	0.859278	−	0.511509i	$-0.170913\pi$
$523$	17.1736	+	11.0368i	0.750949	+	0.482606i	−0.108329	+	0.994115i	$0.534550\pi$
$524$	−0.0971846	−	0.675934i	−0.00424553	−	0.0295283i
$525$		0			0
$526$	7.00444	+	8.08355i	0.305408	+	0.352460i
$527$	−20.3767	+	5.98315i	−0.887624	+	0.260630i
$528$		0			0
$529$	19.2069	−	12.6529i	0.835083	−	0.550124i
$530$	−19.8998			−0.864391
$531$		0			0
$532$	8.82293	+	10.1822i	0.382523	+	0.441455i
$533$	2.20432	−	1.41663i	0.0954796	−	0.0613610i
$534$		0			0
$535$	10.2720	+	6.60144i	0.444099	+	0.285405i
$536$	−5.81583	+	12.7349i	−0.251206	+	0.550063i
$537$		0			0
$538$	1.61665	−	11.2441i	0.0696989	−	0.484767i
$539$	−5.54715	−	12.1466i	−0.238933	−	0.523189i
$540$		0			0
$541$	18.7902	+	5.51730i	0.807854	+	0.237207i	0.659478	−	0.751724i	$-0.270777\pi$
$541$	18.7902	+	5.51730i	0.807854	+	0.237207i	0.148376	+	0.988931i	$0.452595\pi$
$542$	2.28776	+	5.00950i	0.0982677	+	0.215176i
$543$		0			0
$544$	10.5253	−	12.1468i	0.451268	−	0.520791i
$545$	1.78986	−	3.91924i	0.0766690	−	0.167882i
$546$		0			0
$547$	−6.16443	−	42.8745i	−0.263572	−	1.83318i	−0.505425	−	0.862870i	$-0.668664\pi$
$547$	−6.16443	−	42.8745i	−0.263572	−	1.83318i	0.241853	−	0.970313i	$-0.422245\pi$
$548$	30.4863	−	19.5923i	1.30231	−	0.836943i
$549$		0			0
$550$	−2.88992	+	0.848558i	−0.123227	+	0.0361827i
$551$	2.29566			0.0977985
$552$		0			0
$553$	−39.5374			−1.68130
$554$	−2.87425	+	0.843957i	−0.122115	+	0.0358563i
$555$		0			0
$556$	−15.0492	+	9.67155i	−0.638229	+	0.410165i
$557$	5.05359	+	35.1485i	0.214128	+	1.48929i	0.759176	+	0.650885i	$0.225602\pi$
$557$	5.05359	+	35.1485i	0.214128	+	1.48929i	−0.545049	+	0.838404i	$0.683489\pi$
$558$		0			0
$559$	2.07435	−	4.54219i	0.0877356	−	0.192114i
$560$	−26.8639	+	31.0026i	−1.13521	+	1.31010i
$561$		0			0
$562$	−4.25907	−	9.32607i	−0.179658	−	0.393397i
$563$	13.0802	+	3.84069i	0.551264	+	0.161866i	0.545490	−	0.838118i	$-0.316344\pi$
$563$	13.0802	+	3.84069i	0.551264	+	0.161866i	0.00577455	+	0.999983i	$0.498162\pi$
$564$		0			0
$565$	1.66369	+	3.64298i	0.0699921	+	0.153261i
$566$	0.494547	−	3.43965i	0.0207873	−	0.144579i
$567$		0			0
$568$	−2.24257	+	4.91053i	−0.0940960	+	0.206041i
$569$	12.8326	+	8.24698i	0.537969	+	0.345732i	0.781244	−	0.624226i	$-0.214585\pi$
$569$	12.8326	+	8.24698i	0.537969	+	0.345732i	−0.243275	+	0.969957i	$0.578222\pi$
$570$		0			0
$571$	−2.37190	+	1.52433i	−0.0992610	+	0.0637912i	−0.589330	−	0.807893i	$-0.700608\pi$
$571$	−2.37190	+	1.52433i	−0.0992610	+	0.0637912i	0.490069	+	0.871684i	$0.336972\pi$
$572$	0.516753	+	0.596364i	0.0216065	+	0.0249352i
$573$		0			0
$574$	12.5495			0.523805
$575$	25.7440	−	16.7512i	1.07360	−	0.698574i
$576$		0			0
$577$	−5.15667	+	1.51414i	−0.214675	+	0.0630343i	−0.387302	−	0.921953i	$-0.626593\pi$
$577$	−5.15667	+	1.51414i	−0.214675	+	0.0630343i	0.172627	+	0.984987i	$0.444775\pi$
$578$	−1.94788	−	2.24797i	−0.0810211	−	0.0935033i
$579$		0			0
$580$	1.16522	+	8.10426i	0.0483830	+	0.336511i
$581$	28.5783	+	18.3662i	1.18563	+	0.761957i
$582$		0			0
$583$	7.91332	−	9.13246i	0.327736	−	0.378228i
$584$	1.00151	−	6.96563i	0.0414426	−	0.288240i
$585$		0			0
$586$	0.179848	+	0.0528081i	0.00742944	+	0.00218148i
$587$	6.92857	+	2.03441i	0.285973	+	0.0839691i	0.421573	−	0.906794i	$-0.361478\pi$
$587$	6.92857	+	2.03441i	0.285973	+	0.0839691i	−0.135600	+	0.990764i	$0.543296\pi$
$588$		0			0
$589$	−1.54269	+	10.7297i	−0.0635655	+	0.442108i
$590$	11.2649	−	13.0004i	0.463767	−	0.535216i
$591$		0			0
$592$	−8.01576	−	5.15141i	−0.329446	−	0.211722i
$593$	−0.228182	−	1.58704i	−0.00937031	−	0.0651720i	0.984600	−	0.174824i	$-0.0559355\pi$
$593$	−0.228182	−	1.58704i	−0.00937031	−	0.0651720i	−0.993970	+	0.109652i	$0.965026\pi$
$594$		0			0
$595$	−32.9667	−	38.0456i	−1.35150	−	1.55972i
$596$	17.5071	−	5.14055i	0.717120	−	0.210565i
$597$		0			0
$598$	0.879957	+	0.558505i	0.0359841	+	0.0228390i
$599$	−7.66948			−0.313366			−0.156683	−	0.987649i	$-0.550080\pi$
$599$	−7.66948			−0.313366			−0.156683	+	0.987649i	$0.550080\pi$
$600$		0			0
$601$	−17.9986	−	20.7715i	−0.734177	−	0.847285i	0.258758	−	0.965942i	$-0.416687\pi$
$601$	−17.9986	−	20.7715i	−0.734177	−	0.847285i	−0.992935	+	0.118657i	$0.962141\pi$
$602$	20.1189	−	12.9297i	0.819986	−	0.526973i
$603$		0			0
$604$	−0.745336	−	0.478999i	−0.0303273	−	0.0194902i
$605$	−14.0786	+	30.8278i	−0.572377	+	1.25333i
$606$		0			0
$607$	5.02072	−	34.9199i	0.203785	−	1.41735i	−0.589138	−	0.808032i	$-0.700533\pi$
$607$	5.02072	−	34.9199i	0.203785	−	1.41735i	0.792923	−	0.609322i	$-0.208558\pi$
$608$	−3.40803	−	7.46255i	−0.138214	−	0.302646i
$609$		0			0
$610$	8.64911	+	2.53961i	0.350192	+	0.102826i
$611$	−1.89680	−	4.15342i	−0.0767364	−	0.168029i
$612$		0			0
$613$	4.08485	−	4.71417i	0.164986	−	0.190404i	−0.667237	−	0.744846i	$-0.732523\pi$
$613$	4.08485	−	4.71417i	0.164986	−	0.190404i	0.832222	+	0.554442i	$0.187068\pi$
$614$	−0.256266	+	0.561144i	−0.0103421	+	0.0226459i
$615$		0			0
$616$	1.14537	+	7.96619i	0.0461481	+	0.320967i
$617$	−27.3775	+	17.5944i	−1.10218	+	0.708325i	−0.959574	−	0.281455i	$-0.909183\pi$
$617$	−27.3775	+	17.5944i	−1.10218	+	0.708325i	−0.142601	+	0.989780i	$0.545546\pi$
$618$		0			0
$619$	35.2718	−	10.3567i	1.41769	−	0.416272i	0.518971	−	0.854792i	$-0.326315\pi$
$619$	35.2718	−	10.3567i	1.41769	−	0.416272i	0.898722	+	0.438519i	$0.144497\pi$
$620$	−38.6614			−1.55268
$621$		0			0
$622$	−0.603182			−0.0241854
$623$	−31.5012	+	9.24957i	−1.26207	+	0.370576i
$624$		0			0
$625$	−13.4653	+	8.65359i	−0.538610	+	0.346144i
$626$	−0.711467	−	4.94836i	−0.0284360	−	0.197776i
$627$		0			0
$628$	11.4638	−	25.1023i	0.457456	−	1.00169i
$629$	7.65727	−	8.83696i	0.305315	−	0.352353i
$630$		0			0
$631$	−13.2756	−	29.0695i	−0.528493	−	1.15724i	−0.966123	−	0.258082i	$-0.916909\pi$
$631$	−13.2756	−	29.0695i	−0.528493	−	1.15724i	0.437630	−	0.899155i	$-0.355818\pi$
$632$	15.0938	+	4.43195i	0.600401	+	0.176294i
$633$		0			0
$634$	−5.39446	−	11.8122i	−0.214242	−	0.469124i
$635$	−1.37502	+	9.56345i	−0.0545658	+	0.379514i
$636$		0			0
$637$	−2.56330	+	5.61285i	−0.101562	+	0.222389i
$638$	0.541730	+	0.348149i	0.0214473	+	0.0137833i
$639$		0			0
$640$	31.8978	−	20.4995i	1.26087	−	0.810312i
$641$	−2.99133	−	3.45217i	−0.118150	−	0.136353i	0.693593	−	0.720367i	$-0.256027\pi$
$641$	−2.99133	−	3.45217i	−0.118150	−	0.136353i	−0.811743	+	0.584014i	$0.801481\pi$
$642$		0			0
$643$	11.6990			0.461362			0.230681	−	0.973029i	$-0.425905\pi$
$643$	11.6990			0.461362			0.230681	+	0.973029i	$0.425905\pi$
$644$	−16.2079	−	34.9656i	−0.638682	−	1.37784i
$645$		0			0
$646$	2.53039	−	0.742990i	0.0995570	−	0.0292326i
$647$	17.4405	+	20.1274i	0.685656	+	0.791289i	0.986740	−	0.162309i	$-0.0518941\pi$
$647$	17.4405	+	20.1274i	0.685656	+	0.791289i	−0.301084	+	0.953597i	$0.597349\pi$
$648$		0			0
$649$	1.48658	+	10.3394i	0.0583535	+	0.405857i
$650$	1.17085	+	0.752461i	0.0459246	+	0.0295140i
$651$		0			0
$652$	−7.87255	+	9.08541i	−0.308313	+	0.355812i
$653$	5.73066	−	39.8576i	0.224258	−	1.55975i	−0.497413	−	0.867514i	$-0.665717\pi$
$653$	5.73066	−	39.8576i	0.224258	−	1.55975i	0.721671	−	0.692236i	$-0.243374\pi$
$654$		0			0
$655$	1.24965	+	0.366930i	0.0488279	+	0.0143372i
$656$	14.8287	+	4.35411i	0.578965	+	0.169999i
$657$		0			0
$658$	3.11221	−	21.6459i	0.121327	−	0.843844i
$659$	32.0467	−	36.9838i	1.24836	−	1.44069i	0.395568	−	0.918437i	$-0.370548\pi$
$659$	32.0467	−	36.9838i	1.24836	−	1.44069i	0.852793	−	0.522249i	$-0.174907\pi$
$660$		0			0
$661$	−5.50297	−	3.53654i	−0.214041	−	0.137556i	0.429228	−	0.903196i	$-0.358786\pi$
$661$	−5.50297	−	3.53654i	−0.214041	−	0.137556i	−0.643269	+	0.765641i	$0.722422\pi$
$662$	−0.509979	−	3.54698i	−0.0198209	−	0.137857i
$663$		0			0
$664$	−8.85131	−	10.2150i	−0.343498	−	0.396417i
$665$	−24.6550	+	7.23936i	−0.956080	+	0.280730i
$666$		0			0
$667$	−6.31110	−	1.81439i	−0.244367	−	0.0702534i
$668$	35.4965			1.37340
$669$		0			0
$670$	−8.21099	−	9.47599i	−0.317218	−	0.366089i
$671$	−4.60488	+	2.95937i	−0.177769	+	0.114245i
$672$		0			0
$673$	32.9821	+	21.1963i	1.27137	+	0.817058i	0.989797	−	0.142482i	$-0.0455085\pi$
$673$	32.9821	+	21.1963i	1.27137	+	0.817058i	0.281570	+	0.959541i	$0.409145\pi$
$674$	5.11476	−	11.1998i	0.197013	−	0.431399i
$675$		0			0
$676$	−3.22400	+	22.4234i	−0.124000	+	0.862438i
$677$	16.0459	+	35.1357i	0.616696	+	1.35038i	0.917899	+	0.396815i	$0.129885\pi$
$677$	16.0459	+	35.1357i	0.616696	+	1.35038i	−0.301203	+	0.953560i	$0.597388\pi$
$678$		0			0
$679$	24.5369	+	7.20470i	0.941642	+	0.276491i
$680$	8.32067	+	18.2197i	0.319083	+	0.698695i
$681$		0			0
$682$	−1.99125	+	2.29803i	−0.0762489	+	0.0879959i
$683$	−10.5331	+	23.0643i	−0.403038	+	0.882531i	0.593915	+	0.804528i	$0.297582\pi$
$683$	−10.5331	+	23.0643i	−0.403038	+	0.882531i	−0.996953	+	0.0780028i	$0.975146\pi$
$684$		0			0
$685$	9.83619	+	68.4122i	0.375821	+	2.61390i
$686$	−12.0625	+	7.75211i	−0.460549	+	0.295977i
$687$		0			0
$688$	28.2590	−	8.29758i	1.07736	−	0.316342i
$689$	−5.58394			−0.212731
$690$		0			0
$691$	−46.4896			−1.76855			−0.884273	−	0.466970i	$-0.845346\pi$
$691$	−46.4896			−1.76855			−0.884273	+	0.466970i	$0.845346\pi$
$692$	−17.6462	+	5.18138i	−0.670806	+	0.196967i
$693$		0			0
$694$	−9.91498	+	6.37197i	−0.376367	+	0.241877i
$695$	−4.85553	−	33.7709i	−0.184181	−	1.28100i
$696$		0			0
$697$	−7.87865	+	17.2518i	−0.298425	+	0.653460i
$698$	−6.06552	+	6.99999i	−0.229583	+	0.264953i
$699$		0			0
$700$	−21.3795	−	46.8146i	−0.808069	−	1.76942i
$701$	−36.2960	−	10.6575i	−1.37088	−	0.402526i	−0.488294	−	0.872679i	$-0.662381\pi$
$701$	−36.2960	−	10.6575i	−1.37088	−	0.402526i	−0.882585	+	0.470153i	$0.844199\pi$
$702$		0			0
$703$	−2.47938	−	5.42909i	−0.0935116	−	0.204762i
$704$	−0.420651	+	2.92569i	−0.0158539	+	0.110266i
$705$		0			0
$706$	−4.67926	+	10.2462i	−0.176106	+	0.385619i
$707$	−30.1336	−	19.3657i	−1.13329	−	0.728322i
$708$		0			0
$709$	−32.8040	+	21.0818i	−1.23198	+	0.791745i	−0.984198	−	0.177071i	$-0.943338\pi$
$709$	−32.8040	+	21.0818i	−1.23198	+	0.791745i	−0.247782	+	0.968816i	$0.579702\pi$
$710$	−3.16613	−	3.65391i	−0.118823	−	0.137129i
$711$		0			0
$712$	13.0627			0.489547
$713$	12.7213	−	28.2781i	0.476417	−	1.05902i
$714$		0			0
$715$	−1.44402	+	0.424004i	−0.0540035	+	0.0158568i
$716$	−4.86487	−	5.61436i	−0.181809	−	0.209818i
$717$		0			0
$718$	0.412001	+	2.86553i	0.0153757	+	0.106941i
$719$	−6.53058	−	4.19695i	−0.243550	−	0.156520i	0.413172	−	0.910653i	$-0.364421\pi$
$719$	−6.53058	−	4.19695i	−0.243550	−	0.156520i	−0.656721	+	0.754133i	$0.728057\pi$
$720$		0			0
$721$	26.7598	−	30.8824i	0.996587	−	1.15012i
$722$	−1.10334	+	7.67391i	−0.0410621	+	0.285593i
$723$		0			0
$724$	−1.03459	−	0.303783i	−0.0384503	−	0.0112900i
$725$	−8.41398	−	2.47057i	−0.312487	−	0.0917545i
$726$		0			0
$727$	−4.82471	+	33.5566i	−0.178939	+	1.24454i	0.680286	+	0.732947i	$0.261855\pi$
$727$	−4.82471	+	33.5566i	−0.178939	+	1.24454i	−0.859225	+	0.511598i	$0.829054\pi$
$728$	2.43542	−	2.81062i	0.0902626	−	0.104169i
$729$		0			0
$730$	5.30210	+	3.40745i	0.196239	+	0.126115i
$731$	5.14366	+	35.7749i	0.190245	+	1.32318i
$732$		0			0
$733$	18.6038	+	21.4699i	0.687146	+	0.793008i	0.986956	−	0.160991i	$-0.0514689\pi$
$733$	18.6038	+	21.4699i	0.687146	+	0.793008i	−0.299810	+	0.953999i	$0.596923\pi$
$734$	1.46028	−	0.428776i	0.0538999	−	0.0158264i
$735$		0			0
$736$	3.47110	+	23.2091i	0.127946	+	0.855500i
$737$	7.61392			0.280462
$738$		0			0
$739$	25.4735	+	29.3980i	0.937059	+	1.08142i	0.996533	+	0.0831944i	$0.0265122\pi$
$739$	25.4735	+	29.3980i	0.937059	+	1.08142i	−0.0594739	+	0.998230i	$0.518942\pi$
$740$	17.9076	−	11.5085i	0.658295	−	0.423060i
$741$		0			0
$742$	−22.4981	−	14.4586i	−0.825931	−	0.530794i
$743$	−9.44697	+	20.6860i	−0.346576	+	0.758895i	0.653422	+	0.756993i	$0.273333\pi$
$743$	−9.44697	+	20.6860i	−0.346576	+	0.758895i	−0.999998	+	0.00190149i	$0.999395\pi$
$744$		0			0
$745$	−4.95247	+	34.4452i	−0.181445	+	1.26197i
$746$	0.110189	+	0.241280i	0.00403430	+	0.00883388i
$747$		0			0
$748$	−5.48022	−	1.60914i	−0.200377	−	0.0588359i
$749$	6.81683	+	14.9268i	0.249082	+	0.545413i
$750$		0			0
$751$	2.10873	−	2.43360i	0.0769485	−	0.0888033i	−0.715970	−	0.698131i	$-0.754015\pi$
$751$	2.10873	−	2.43360i	0.0769485	−	0.0888033i	0.792918	+	0.609328i	$0.208561\pi$
$752$	11.1876	−	24.4974i	0.407970	−	0.893330i
$753$		0			0
$754$	−0.0423484	−	0.294540i	−0.00154224	−	0.0107265i
$755$	1.42151	−	0.913552i	0.0517342	−	0.0332476i
$756$		0			0
$757$	−33.3481	+	9.79188i	−1.21206	+	0.355892i	−0.824451	−	0.565933i	$-0.808516\pi$
$757$	−33.3481	+	9.79188i	−1.21206	+	0.355892i	−0.387606	+	0.921825i	$0.626698\pi$
$758$	−1.11462			−0.0404847
$759$		0			0
$760$	10.2238			0.370856
$761$	27.7524	−	8.14883i	1.00602	−	0.295395i	0.263098	−	0.964769i	$-0.415256\pi$
$761$	27.7524	−	8.14883i	1.00602	−	0.295395i	0.742925	+	0.669374i	$0.233438\pi$
$762$		0			0
$763$	4.87117	−	3.13051i	0.176348	−	0.113332i
$764$	−0.369005	−	2.56648i	−0.0133501	−	0.0928521i
$765$		0			0
$766$	−5.82477	+	12.7545i	−0.210457	+	0.460838i
$767$	3.16095	−	3.64794i	0.114135	−	0.131719i
$768$		0			0
$769$	8.52205	+	18.6607i	0.307313	+	0.672921i	0.998775	−	0.0494918i	$-0.0157602\pi$
$769$	8.52205	+	18.6607i	0.307313	+	0.672921i	−0.691462	+	0.722413i	$0.743033\pi$
$770$	−6.91597	−	2.03071i	−0.249234	−	0.0731818i
$771$		0			0
$772$	−15.6293	−	34.2234i	−0.562511	−	1.23173i
$773$	−4.27604	+	29.7405i	−0.153799	+	1.06969i	0.755979	+	0.654596i	$0.227161\pi$
$773$	−4.27604	+	29.7405i	−0.153799	+	1.06969i	−0.909777	+	0.415097i	$0.863748\pi$
$774$		0			0
$775$	17.2013	−	37.6657i	0.617890	−	1.35299i
$776$	−8.55963	−	5.50094i	−0.307273	−	0.197472i
$777$		0			0
$778$	4.10529	−	2.63831i	0.147182	−	0.0945879i
$779$	6.33949	+	7.31617i	0.227136	+	0.262129i
$780$		0			0
$781$	2.93590			0.105055
$782$	−7.54363	+	0.0426770i	−0.269760	+	0.00152613i
$783$		0			0
$784$	−34.9200	+	10.2535i	−1.24714	+	0.366195i
$785$	34.4663	+	39.7763i	1.23016	+	1.41968i
$786$		0			0
$787$	−2.52433	−	17.5571i	−0.0899826	−	0.625843i	−0.984048	−	0.177905i	$-0.943068\pi$
$787$	−2.52433	−	17.5571i	−0.0899826	−	0.625843i	0.894065	−	0.447937i	$-0.147841\pi$
$788$	−9.05926	−	5.82204i	−0.322723	−	0.207401i
$789$		0			0
$790$	−9.22623	+	10.6476i	−0.328254	+	0.378826i
$791$	−0.765970	+	5.32744i	−0.0272347	+	0.189422i
$792$		0			0
$793$	2.42696	+	0.712621i	0.0861840	+	0.0253059i
$794$	15.8635	+	4.65796i	0.562976	+	0.165305i
$795$		0			0
$796$	2.91507	−	20.2747i	0.103322	−	0.718619i
$797$	18.4548	−	21.2980i	0.653704	−	0.754414i	−0.328031	−	0.944667i	$-0.606385\pi$
$797$	18.4548	−	21.2980i	0.653704	−	0.754414i	0.981735	+	0.190252i	$0.0609306\pi$
$798$		0			0
$799$	27.8028	+	17.8678i	0.983594	+	0.632117i
$800$	4.45988	+	31.0191i	0.157680	+	1.09669i
$801$		0			0
$802$	−2.81916	−	3.25348i	−0.0995480	−	0.114884i
$803$	−3.67218	+	1.07825i	−0.129589	+	0.0380506i
$804$		0			0
$805$	73.5017	−	0.415825i	2.59060	−	0.0146559i
$806$	1.40510			0.0494926
$807$		0			0
$808$	9.33303	+	10.7709i	0.328335	+	0.378919i
$809$	−11.6653	+	7.49681i	−0.410129	+	0.263574i	−0.729397	−	0.684091i	$-0.760199\pi$
$809$	−11.6653	+	7.49681i	−0.410129	+	0.263574i	0.319268	+	0.947664i	$0.396563\pi$
$810$		0			0
$811$	−28.7636	−	18.4852i	−1.01003	−	0.649105i	−0.0726267	−	0.997359i	$-0.523138\pi$
$811$	−28.7636	−	18.4852i	−1.01003	−	0.649105i	−0.937400	+	0.348254i	$0.886775\pi$
$812$	−4.57098	+	10.0090i	−0.160410	+	0.351249i
$813$		0			0
$814$	0.238265	−	1.65717i	0.00835117	−	0.0580836i
$815$	−9.52462	−	20.8560i	−0.333633	−	0.730554i
$816$		0			0
$817$	17.7011	+	5.19751i	0.619282	+	0.181838i
$818$	−4.45799	−	9.76163i	−0.155870	−	0.341307i
$819$		0			0
$820$	−22.6101	+	26.0935i	−0.789580	+	0.911223i
$821$	−9.10007	+	19.9264i	−0.317595	+	0.695435i	−0.999346	−	0.0361483i	$-0.988491\pi$
$821$	−9.10007	+	19.9264i	−0.317595	+	0.695435i	0.681752	+	0.731584i	$0.261218\pi$
$822$		0			0
$823$	−7.94565	−	55.2632i	−0.276968	−	1.92635i	−0.366599	−	0.930379i	$-0.619478\pi$
$823$	−7.94565	−	55.2632i	−0.276968	−	1.92635i	0.0896310	−	0.995975i	$-0.471431\pi$
$824$	−13.6776	+	8.79006i	−0.476482	+	0.306216i
$825$		0			0
$826$	22.1814	−	6.51306i	0.771791	−	0.226618i
$827$	14.1505			0.492060			0.246030	−	0.969262i	$-0.420874\pi$
$827$	14.1505			0.492060			0.246030	+	0.969262i	$0.420874\pi$
$828$		0			0
$829$	−14.1731			−0.492253			−0.246126	−	0.969238i	$-0.579158\pi$
$829$	−14.1731			−0.492253			−0.246126	+	0.969238i	$0.579158\pi$
$830$	11.6150	−	3.41046i	0.403161	−	0.118379i
$831$		0			0
$832$	1.14902	−	0.738433i	0.0398353	−	0.0256006i
$833$	−6.35610	−	44.2076i	−0.220226	−	1.53170i
$834$		0			0
$835$	−28.1233	+	61.5815i	−0.973248	+	2.13112i
$836$	−1.90915	+	2.20328i	−0.0660295	+	0.0762021i
$837$		0			0
$838$	2.03031	+	4.44575i	0.0701358	+	0.153576i
$839$	4.71989	+	1.38588i	0.162949	+	0.0478460i	0.362189	−	0.932105i	$-0.382029\pi$
$839$	4.71989	+	1.38588i	0.162949	+	0.0478460i	−0.199241	+	0.979951i	$0.563848\pi$
$840$		0			0
$841$	−11.2682	−	24.6739i	−0.388558	−	0.850824i
$842$	1.09335	−	7.60439i	0.0376792	−	0.262064i
$843$		0			0
$844$	2.03566	−	4.45748i	0.0700703	−	0.153433i
$845$	−36.3472	−	23.3589i	−1.25038	−	0.803571i
$846$		0			0
$847$	−38.3155	+	24.6239i	−1.31654	+	0.846087i
$848$	−21.5677	−	24.8905i	−0.740639	−	0.854743i
$849$		0			0
$850$	−10.0739			−0.345532
$851$	2.52526	+	16.8849i	0.0865649	+	0.578807i
$852$		0			0
$853$	−3.81247	+	1.11944i	−0.130537	+	0.0383290i	−0.346348	−	0.938106i	$-0.612578\pi$
$853$	−3.81247	+	1.11944i	−0.130537	+	0.0383290i	0.215812	+	0.976435i	$0.430760\pi$
$854$	7.93321	+	9.15541i	0.271469	+	0.313292i
$855$		0			0
$856$	−0.929180	−	6.46259i	−0.0317587	−	0.220887i
$857$	28.6259	+	18.3968i	0.977843	+	0.628421i	0.928881	−	0.370379i	$-0.120772\pi$
$857$	28.6259	+	18.3968i	0.977843	+	0.628421i	0.0489622	+	0.998801i	$0.484409\pi$
$858$		0			0
$859$	−23.4721	+	27.0883i	−0.800858	+	0.924240i	−0.998428	−	0.0560492i	$-0.982150\pi$
$859$	−23.4721	+	27.0883i	−0.800858	+	0.924240i	0.197570	+	0.980289i	$0.436695\pi$
$860$	−9.36389	+	65.1273i	−0.319306	+	2.22082i
$861$		0			0
$862$	17.6751	+	5.18986i	0.602015	+	0.176767i
$863$	−8.55323	−	2.51146i	−0.291155	−	0.0854909i	0.132893	−	0.991130i	$-0.457573\pi$
$863$	−8.55323	−	2.51146i	−0.291155	−	0.0854909i	−0.424049	+	0.905639i	$0.639391\pi$
$864$		0			0
$865$	4.99181	−	34.7188i	0.169726	−	1.18047i
$866$	−2.43817	+	2.81379i	−0.0828522	+	0.0956166i
$867$		0			0
$868$	−43.7094	−	28.0903i	−1.48359	−	0.953447i
$869$	−1.21755	−	8.46825i	−0.0413026	−	0.287266i
$870$		0			0
$871$	−2.30403	−	2.65899i	−0.0780690	−	0.0900964i
$872$	−2.21054	+	0.649072i	−0.0748582	+	0.0219804i
$873$		0			0
$874$	−1.57974	+	3.51158i	−0.0534355	+	0.118781i
$875$	21.5234			0.727624
$876$		0			0
$877$	27.3868	+	31.6060i	0.924785	+	1.06726i	0.997553	+	0.0699099i	$0.0222712\pi$
$877$	27.3868	+	31.6060i	0.924785	+	1.06726i	−0.0727683	+	0.997349i	$0.523183\pi$
$878$	−14.0902	+	9.05525i	−0.475523	+	0.305600i
$879$		0			0
$880$	−7.46749	−	4.79906i	−0.251729	−	0.161776i
$881$	−16.5934	+	36.3344i	−0.559045	+	1.22414i	0.393383	+	0.919375i	$0.371305\pi$
$881$	−16.5934	+	36.3344i	−0.559045	+	1.22414i	−0.952428	+	0.304763i	$0.901423\pi$
$882$		0			0
$883$	−7.73017	+	53.7645i	−0.260141	+	1.80932i	0.271597	+	0.962411i	$0.412448\pi$
$883$	−7.73017	+	53.7645i	−0.260141	+	1.80932i	−0.531738	+	0.846909i	$0.678461\pi$
$884$	1.09640	+	2.40078i	0.0368759	+	0.0807469i
$885$		0			0
$886$	4.62271	+	1.35735i	0.155303	+	0.0456011i
$887$	−17.4644	−	38.2417i	−0.586397	−	1.28403i	−0.937595	−	0.347729i	$-0.886953\pi$
$887$	−17.4644	−	38.2417i	−0.586397	−	1.28403i	0.351198	−	0.936301i	$-0.385774\pi$
$888$		0			0
$889$	−8.50310	+	9.81309i	−0.285185	+	0.329121i
$890$	−4.85997	+	10.6418i	−0.162907	+	0.356715i
$891$		0			0
$892$	−4.64734	−	32.3230i	−0.155604	−	1.08225i
$893$	14.1914	−	9.12026i	0.474897	−	0.305198i
$894$		0			0
$895$	13.5945	−	3.99170i	0.454414	−	0.133428i
$896$	50.9570			1.70235
$897$		0			0
$898$	−8.17051			−0.272654
$899$	−8.49442	+	2.49419i	−0.283305	+	0.0831858i
$900$		0			0
$901$	34.0008	−	21.8510i	1.13273	−	0.727963i
$902$	0.386459	+	2.68788i	0.0128677	+	0.0894968i
$903$		0			0
$904$	0.889596	−	1.94794i	0.0295875	−	0.0647876i
$905$	1.34671	−	1.55419i	0.0447662	−	0.0516630i
$906$		0			0
$907$	−4.45205	−	9.74862i	−0.147828	−	0.323698i	0.821204	−	0.570635i	$-0.193303\pi$
$907$	−4.45205	−	9.74862i	−0.147828	−	0.323698i	−0.969031	+	0.246938i	$0.920576\pi$
$908$	−12.3180	−	3.61688i	−0.408786	−	0.120030i
$909$		0			0
$910$	1.38364	+	3.02975i	0.0458673	+	0.100435i
$911$	0.661955	−	4.60400i	0.0219316	−	0.152537i	−0.975913	−	0.218160i	$-0.929994\pi$
$911$	0.661955	−	4.60400i	0.0219316	−	0.152537i	0.997844	+	0.0656231i	$0.0209035\pi$
$912$		0			0
$913$	−3.05365	+	6.68657i	−0.101061	+	0.221293i
$914$	9.82059	+	6.31131i	0.324836	+	0.208760i
$915$		0			0
$916$	−14.8320	+	9.53198i	−0.490065	+	0.314945i
$917$	1.14621	+	1.32280i	0.0378513	+	0.0436828i
$918$		0			0
$919$	45.2701			1.49332			0.746661	−	0.665205i	$-0.231656\pi$
$919$	45.2701			1.49332			0.746661	+	0.665205i	$0.231656\pi$
$920$	−28.1067	−	8.08043i	−0.926649	−	0.266404i
$921$		0			0
$922$	−17.4897	+	5.13545i	−0.575994	+	0.169127i
$923$	−0.888426	−	1.02530i	−0.0292429	−	0.0337481i
$924$		0			0
$925$	3.24461	+	22.5668i	0.106682	+	0.741991i
$926$	−5.75035	−	3.69553i	−0.188968	−	0.121443i
$927$		0			0
$928$	4.38766	−	5.06363i	0.144032	−	0.166222i
$929$	−4.77406	+	33.2043i	−0.156632	+	1.08940i	0.748152	+	0.663528i	$0.230941\pi$
$929$	−4.77406	+	33.2043i	−0.156632	+	1.08940i	−0.904784	+	0.425871i	$0.859968\pi$
$930$		0			0
$931$	−21.8735	−	6.42264i	−0.716875	−	0.210493i
$932$	−9.17571	−	2.69423i	−0.300560	−	0.0882525i
$933$		0			0
$934$	0.266068	−	1.85055i	0.00870602	−	0.0605517i
$935$	7.13352	−	8.23252i	0.233291	−	0.269232i
$936$		0			0
$937$	3.73421	+	2.39983i	0.121991	+	0.0783991i	0.600214	−	0.799840i	$-0.295082\pi$
$937$	3.73421	+	2.39983i	0.121991	+	0.0783991i	−0.478222	+	0.878239i	$0.658719\pi$
$938$	−2.39810	−	16.6792i	−0.0783008	−	0.544594i
$939$		0			0
$940$	39.4000	+	45.4700i	1.28508	+	1.48307i
$941$	17.2470	−	5.06418i	0.562236	−	0.165087i	0.0117490	−	0.999931i	$-0.496260\pi$
$941$	17.2470	−	5.06418i	0.562236	−	0.165087i	0.550487	+	0.834843i	$0.314442\pi$
$942$		0			0
$943$	−11.6458	−	25.1236i	−0.379239	−	0.818138i
$944$	28.4698			0.926613
$945$		0			0
$946$	3.38887	+	3.91097i	0.110182	+	0.127156i
$947$	2.72766	−	1.75296i	0.0886370	−	0.0569635i	−0.495572	−	0.868567i	$-0.665041\pi$
$947$	2.72766	−	1.75296i	0.0886370	−	0.0569635i	0.584209	+	0.811604i	$0.301405\pi$
$948$		0			0
$949$	1.48778	+	0.956141i	0.0482955	+	0.0310376i
$950$	−2.13607	+	4.67734i	−0.0693033	+	0.151753i
$951$		0			0
$952$	−3.83087	+	26.6443i	−0.124159	+	0.863545i
$953$	−5.50230	−	12.0484i	−0.178237	−	0.390285i	0.799335	−	0.600886i	$-0.205185\pi$
$953$	−5.50230	−	12.0484i	−0.178237	−	0.390285i	−0.977572	+	0.210601i	$0.932458\pi$
$954$		0			0
$955$	4.74485	+	1.39321i	0.153540	+	0.0450833i
$956$	−10.8982	−	23.8637i	−0.352473	−	0.771809i
$957$		0			0
$958$	−5.77212	+	6.66138i	−0.186489	+	0.215220i
$959$	−38.5860	+	84.4915i	−1.24601	+	2.72837i
$960$		0			0
$961$	−1.53749	−	10.6935i	−0.0495966	−	0.344952i
$962$	−0.650829	+	0.418262i	−0.0209836	+	0.0134853i
$963$		0			0
$964$	24.8940	−	7.30954i	0.801782	−	0.235424i
$965$	71.7557			2.30990
$966$		0			0
$967$	31.9173			1.02639			0.513196	−	0.858272i	$-0.328461\pi$
$967$	31.9173			1.02639			0.513196	+	0.858272i	$0.328461\pi$
$968$	17.3876	−	5.10545i	0.558858	−	0.164095i
$969$		0			0
$970$	7.66606	−	4.92668i	0.246142	−	0.158186i
$971$	−7.94033	−	55.2262i	−0.254817	−	1.77229i	−0.568420	−	0.822738i	$-0.692445\pi$
$971$	−7.94033	−	55.2262i	−0.254817	−	1.77229i	0.313603	−	0.949554i	$-0.398464\pi$
$972$		0			0
$973$	19.0475	−	41.7083i	0.610636	−	1.33711i
$974$	4.09112	−	4.72140i	0.131088	−	0.151284i
$975$		0			0
$976$	6.19753	+	13.5707i	0.198378	+	0.434388i
$977$	−20.0943	−	5.90022i	−0.642874	−	0.188765i	−0.0559840	−	0.998432i	$-0.517830\pi$
$977$	−20.0943	−	5.90022i	−0.642874	−	0.188765i	−0.586890	+	0.809667i	$0.699648\pi$
$978$		0			0
$979$	−2.95118	−	6.46217i	−0.0943200	−	0.206532i
$980$	11.5711	−	80.4788i	0.369625	−	2.57080i
$981$		0			0
$982$	4.76907	−	10.4428i	0.152187	−	0.333244i
$983$	−19.0495	−	12.2424i	−0.607585	−	0.390471i	0.200366	−	0.979721i	$-0.435787\pi$
$983$	−19.0495	−	12.2424i	−0.607585	−	0.390471i	−0.807951	+	0.589250i	$0.799423\pi$
$984$		0			0
$985$	17.2779	−	11.1039i	0.550521	−	0.353798i
$986$	1.41045	+	1.62775i	0.0449179	+	0.0518380i
$987$		0			0
$988$	1.34717			0.0428592
$989$	−44.5549	−	28.2788i	−1.41676	−	0.899214i
$990$		0			0
$991$	−36.8257	+	10.8130i	−1.16981	+	0.343486i	−0.808236	−	0.588859i	$-0.799577\pi$
$991$	−36.8257	+	10.8130i	−1.16981	+	0.343486i	−0.361570	+	0.932345i	$0.617759\pi$
$992$	20.7183	+	23.9102i	0.657806	+	0.759149i
$993$		0			0
$994$	−0.924700	−	6.43143i	−0.0293297	−	0.203993i
$995$	32.8643	+	21.1206i	1.04187	+	0.669568i
$996$		0			0
$997$	31.2609	−	36.0770i	0.990044	−	1.14257i	0.000259238	−	1.00000i	$-0.499917\pi$
$997$	31.2609	−	36.0770i	0.990044	−	1.14257i	0.989785	−	0.142571i	$-0.0455371\pi$
$998$	−0.599821	+	4.17185i	−0.0189870	+	0.132057i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.a.55.1		10
3.2	odd	2		69.2.e.b.55.1	✓	10
23.8	even	11		4761.2.a.bp.1.3		5
23.15	odd	22		4761.2.a.bm.1.3		5
23.18	even	11	inner	207.2.i.a.64.1		10
69.8	odd	22		1587.2.a.q.1.3		5
69.38	even	22		1587.2.a.r.1.3		5
69.41	odd	22		69.2.e.b.64.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.b.55.1	✓	10	3.2	odd	2
69.2.e.b.64.1	yes	10	69.41	odd	22
207.2.i.a.55.1		10	1.1	even	1	trivial
207.2.i.a.64.1		10	23.18	even	11	inner
1587.2.a.q.1.3		5	69.8	odd	22
1587.2.a.r.1.3		5	69.38	even	22
4761.2.a.bm.1.3		5	23.15	odd	22
4761.2.a.bp.1.3		5	23.8	even	11

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.459493 - 0.134919i) q^{2} +(-1.48958 + 0.957293i) q^{4} +(-0.480602 - 3.34266i) q^{5} +(1.88533 - 4.12830i) q^{7} +(-1.18251 + 1.36469i) q^{8} +O(q^{10})\)	\(q+(0.459493 - 0.134919i) q^{2} +(-1.48958 + 0.957293i) q^{4} +(-0.480602 - 3.34266i) q^{5} +(1.88533 - 4.12830i) q^{7} +(-1.18251 + 1.36469i) q^{8} +(-0.671822 - 1.47109i) q^{10} +(0.942270 + 0.276675i) q^{11} +(-0.188515 - 0.412791i) q^{13} +(0.309309 - 2.15129i) q^{14} +(1.11189 - 2.43470i) q^{16} +(2.76321 + 1.77580i) q^{17} +(1.41042 - 0.906424i) q^{19} +(3.91579 + 4.51907i) q^{20} +0.470295 q^{22} +(-4.59385 + 1.37715i) q^{23} +(-6.14491 + 1.80431i) q^{25} +(-0.142315 - 0.164240i) q^{26} +(1.14365 + 7.95423i) q^{28} +(1.15189 + 0.740277i) q^{29} +(-4.23404 + 4.88634i) q^{31} +(0.696384 - 4.84346i) q^{32} +(1.50926 + 0.443160i) q^{34} +(-14.7056 - 4.31795i) q^{35} +(0.506627 - 3.52367i) q^{37} +(0.525785 - 0.606789i) q^{38} +(5.12999 + 3.29685i) q^{40} +(0.821738 + 5.71531i) q^{41} +(7.20584 + 8.31598i) q^{43} +(-1.66844 + 0.489899i) q^{44} +(-1.92504 + 1.25259i) q^{46} +10.0618 q^{47} +(-8.90436 - 10.2762i) q^{49} +(-2.58011 + 1.65814i) q^{50} +(0.675969 + 0.434419i) q^{52} +(5.11162 - 11.1929i) q^{53} +(0.471975 - 3.28266i) q^{55} +(3.40442 + 7.45463i) q^{56} +(0.629165 + 0.184739i) q^{58} +(4.41863 + 9.67544i) q^{59} +(-3.65011 + 4.21246i) q^{61} +(-1.28625 + 2.81649i) q^{62} +(0.428340 + 2.97917i) q^{64} +(-1.28922 + 0.828529i) q^{65} +(7.43903 - 2.18430i) q^{67} -5.81597 q^{68} -7.33969 q^{70} +(2.86847 - 0.842258i) q^{71} +(-3.27850 + 2.10697i) q^{73} +(-0.242620 - 1.68746i) q^{74} +(-1.23322 + 2.70038i) q^{76} +(2.91869 - 3.36835i) q^{77} +(-3.61897 - 7.92444i) q^{79} +(-8.67273 - 2.54654i) q^{80} +(1.14869 + 2.51528i) q^{82} +(-1.06526 + 7.40902i) q^{83} +(4.60791 - 10.0899i) q^{85} +(4.43302 + 2.84893i) q^{86} +(-1.49182 + 0.958732i) q^{88} +(-4.73727 - 5.46710i) q^{89} -2.05954 q^{91} +(5.52455 - 6.44903i) q^{92} +(4.62333 - 1.35753i) q^{94} +(-3.70772 - 4.27893i) q^{95} +(0.801906 + 5.57738i) q^{97} +(-5.47795 - 3.52046i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 14 q^{4} + 3 q^{5} + 6 q^{7} + 7 q^{8}+O(q^{10}) \) 10 * q - 4 * q^2 - 14 * q^4 + 3 * q^5 + 6 * q^7 + 7 * q^8	\( 10 q - 4 q^{2} - 14 q^{4} + 3 q^{5} + 6 q^{7} + 7 q^{8} + 12 q^{10} + 15 q^{11} + 8 q^{13} - 9 q^{14} + 12 q^{16} - q^{17} - 9 q^{19} + 9 q^{20} - 28 q^{22} - 21 q^{23} - 4 q^{25} - q^{26} + 29 q^{28} + 8 q^{29} - 23 q^{31} + q^{32} - 15 q^{34} - 18 q^{35} + 3 q^{37} - 3 q^{38} - 32 q^{40} + 15 q^{41} + 22 q^{43} + q^{44} + 26 q^{46} - 4 q^{47} - 29 q^{49} - 49 q^{50} + 2 q^{52} - 29 q^{53} + 43 q^{55} + 2 q^{56} + 21 q^{58} + 54 q^{59} - 30 q^{61} + 7 q^{62} - 31 q^{64} + 9 q^{65} + q^{67} + 30 q^{68} - 94 q^{70} + 3 q^{71} - 47 q^{73} + 12 q^{74} + 50 q^{76} - 13 q^{77} + 18 q^{79} - 3 q^{80} - 28 q^{82} - 18 q^{83} + 58 q^{85} + 16 q^{88} - 25 q^{89} + 18 q^{91} + 3 q^{92} + 39 q^{94} + 16 q^{95} + 21 q^{97} + 27 q^{98}+O(q^{100}) \) 10 * q - 4 * q^2 - 14 * q^4 + 3 * q^5 + 6 * q^7 + 7 * q^8 + 12 * q^10 + 15 * q^11 + 8 * q^13 - 9 * q^14 + 12 * q^16 - q^17 - 9 * q^19 + 9 * q^20 - 28 * q^22 - 21 * q^23 - 4 * q^25 - q^26 + 29 * q^28 + 8 * q^29 - 23 * q^31 + q^32 - 15 * q^34 - 18 * q^35 + 3 * q^37 - 3 * q^38 - 32 * q^40 + 15 * q^41 + 22 * q^43 + q^44 + 26 * q^46 - 4 * q^47 - 29 * q^49 - 49 * q^50 + 2 * q^52 - 29 * q^53 + 43 * q^55 + 2 * q^56 + 21 * q^58 + 54 * q^59 - 30 * q^61 + 7 * q^62 - 31 * q^64 + 9 * q^65 + q^67 + 30 * q^68 - 94 * q^70 + 3 * q^71 - 47 * q^73 + 12 * q^74 + 50 * q^76 - 13 * q^77 + 18 * q^79 - 3 * q^80 - 28 * q^82 - 18 * q^83 + 58 * q^85 + 16 * q^88 - 25 * q^89 + 18 * q^91 + 3 * q^92 + 39 * q^94 + 16 * q^95 + 21 * q^97 + 27 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more