LMFDB - Embedded newform 513.2.f.h.406.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(163,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.163"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,1,0,-3,5,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 8x^{10} - x^{9} + 41x^{8} - 7x^{7} + 91x^{6} + 9x^{5} + 135x^{4} - 12x^{3} + 45x^{2} + 9x + 9 $ x^12 - x^11 + 8x^10 - x^9 + 41x^8 - 7x^7 + 91x^6 + 9x^5 + 135x^4 - 12x^3 + 45x^2 + 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.3
Root			$-0.216506 + 0.375000i$ of defining polynomial
Character	$\chi$	$=$	513.406
Dual form			513.2.f.h.163.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.216506 - 0.375000i) q^{2} +(0.906250 - 1.56967i) q^{4} +(-1.01591 - 1.75962i) q^{5} -1.15054 q^{7} -1.65086 q^{8} +(-0.439904 + 0.761936i) q^{10} -3.69231 q^{11} +(0.690484 - 1.19595i) q^{13} +(0.249099 + 0.431453i) q^{14} +(-1.45508 - 2.52027i) q^{16} +(-1.17158 - 2.02924i) q^{17} +(-0.532593 + 4.32624i) q^{19} -3.68269 q^{20} +(0.799408 + 1.38462i) q^{22} +(-1.26501 + 2.19107i) q^{23} +(0.435835 - 0.754889i) q^{25} -0.597977 q^{26} +(-1.04268 + 1.80597i) q^{28} +(-0.309936 + 0.536825i) q^{29} +0.936857 q^{31} +(-2.28093 + 3.95068i) q^{32} +(-0.507311 + 0.878688i) q^{34} +(1.16885 + 2.02451i) q^{35} +3.82480 q^{37} +(1.73765 - 0.736936i) q^{38} +(1.67713 + 2.90488i) q^{40} +(-2.51591 - 4.35769i) q^{41} +(-5.09449 - 8.82391i) q^{43} +(-3.34615 + 5.79571i) q^{44} +1.09553 q^{46} +(1.27868 - 2.21475i) q^{47} -5.67626 q^{49} -0.377445 q^{50} +(-1.25150 - 2.16767i) q^{52} +(5.39033 - 9.33633i) q^{53} +(3.75107 + 6.49704i) q^{55} +1.89938 q^{56} +0.268412 q^{58} +(-3.76726 - 6.52508i) q^{59} +(3.55352 - 6.15488i) q^{61} +(-0.202835 - 0.351321i) q^{62} -3.84497 q^{64} -2.80589 q^{65} +(-1.62526 + 2.81503i) q^{67} -4.24699 q^{68} +(0.506127 - 0.876638i) q^{70} +(3.97238 + 6.88037i) q^{71} +(2.37756 + 4.11806i) q^{73} +(-0.828094 - 1.43430i) q^{74} +(6.30811 + 4.75665i) q^{76} +4.24815 q^{77} +(-2.90796 - 5.03674i) q^{79} +(-2.95647 + 5.12076i) q^{80} +(-1.08942 + 1.88694i) q^{82} +16.8621 q^{83} +(-2.38046 + 4.12308i) q^{85} +(-2.20598 + 3.82087i) q^{86} +6.09549 q^{88} +(5.57992 - 9.66470i) q^{89} +(-0.794430 + 1.37599i) q^{91} +(2.29284 + 3.97131i) q^{92} -1.10737 q^{94} +(8.15359 - 3.45793i) q^{95} +(-5.51591 - 9.55384i) q^{97} +(1.22895 + 2.12860i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - 3 q^{4} + 5 q^{5} + 2 q^{7} - 12 q^{8} + q^{10} - 4 q^{11} - 5 q^{13} + 2 q^{14} + 3 q^{16} + 10 q^{17} - 9 q^{19} - 2 q^{20} - 4 q^{22} + 3 q^{23} - 5 q^{25} - 2 q^{26} - 2 q^{28} - 6 q^{29}+ \cdots - 59 q^{98}+O(q^{100}) $ 12 * q + q^2 - 3 * q^4 + 5 * q^5 + 2 * q^7 - 12 * q^8 + q^10 - 4 * q^11 - 5 * q^13 + 2 * q^14 + 3 * q^16 + 10 * q^17 - 9 * q^19 - 2 * q^20 - 4 * q^22 + 3 * q^23 - 5 * q^25 - 2 * q^26 - 2 * q^28 - 6 * q^29 - 4 * q^31 + 8 * q^32 + 4 * q^34 + 3 * q^35 + 26 * q^37 - 10 * q^38 - 6 * q^40 - 13 * q^41 - 3 * q^43 - 20 * q^44 - 10 * q^46 + 18 * q^47 + 26 * q^49 + 6 * q^50 - 22 * q^52 - q^53 - 6 * q^55 + 48 * q^56 + 28 * q^58 + 11 * q^59 - 13 * q^61 + 22 * q^62 - 72 * q^65 + 9 * q^67 - 10 * q^68 - 30 * q^70 - 6 * q^71 - 15 * q^73 + 43 * q^74 - 33 * q^76 - 58 * q^77 - 13 * q^79 + q^80 + 4 * q^82 - 16 * q^83 - 3 * q^85 - 7 * q^86 - 30 * q^88 + 29 * q^89 + 22 * q^91 + 21 * q^92 + 36 * q^94 + 22 * q^95 + 20 * q^97 - 59 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.216506	−	0.375000i	−0.153093	−	0.265165i	0.779270	−	0.626688i	$-0.215590\pi$
$2$	−0.216506	−	0.375000i	−0.153093	−	0.265165i	−0.932363	+	0.361523i	$0.882257\pi$
$3$		0			0
$3$		0			0
$4$	0.906250	−	1.56967i	0.453125	−	0.784836i
$5$	−1.01591	−	1.75962i	−0.454331	−	0.786924i	0.544319	−	0.838879i	$-0.316788\pi$
$5$	−1.01591	−	1.75962i	−0.454331	−	0.786924i	−0.998649	+	0.0519545i	$0.983455\pi$
$6$		0			0
$7$	−1.15054			−0.434863			−0.217432	−	0.976076i	$-0.569768\pi$
$7$	−1.15054			−0.434863			−0.217432	+	0.976076i	$0.569768\pi$
$8$	−1.65086			−0.583668
$9$		0			0
$10$	−0.439904	+	0.761936i	−0.139110	+	0.240945i
$11$	−3.69231			−1.11327			−0.556636	−	0.830756i	$-0.687908\pi$
$11$	−3.69231			−1.11327			−0.556636	+	0.830756i	$0.687908\pi$
$12$		0			0
$13$	0.690484	−	1.19595i	0.191506	−	0.331698i	−0.754244	−	0.656595i	$-0.771996\pi$
$13$	0.690484	−	1.19595i	0.191506	−	0.331698i	0.945749	+	0.324897i	$0.105330\pi$
$14$	0.249099	+	0.431453i	0.0665746	+	0.115311i
$15$		0			0
$16$	−1.45508	−	2.52027i	−0.363770	−	0.630067i
$17$	−1.17158	−	2.02924i	−0.284151	−	0.492164i	0.688252	−	0.725472i	$-0.258378\pi$
$17$	−1.17158	−	2.02924i	−0.284151	−	0.492164i	−0.972403	+	0.233308i	$0.925045\pi$
$18$		0			0
$19$	−0.532593	+	4.32624i	−0.122185	+	0.992507i
$19$	−0.532593	+	4.32624i	−0.122185	+	0.992507i
$20$	−3.68269			−0.823475
$21$		0			0
$22$	0.799408	+	1.38462i	0.170434	+	0.295201i
$23$	−1.26501	+	2.19107i	−0.263774	+	0.456869i	−0.967242	−	0.253858i	$-0.918301\pi$
$23$	−1.26501	+	2.19107i	−0.263774	+	0.456869i	0.703468	+	0.710727i	$0.251634\pi$
$24$		0			0
$25$	0.435835	−	0.754889i	0.0871671	−	0.150978i
$26$	−0.597977			−0.117273
$27$		0			0
$28$	−1.04268	+	1.80597i	−0.197047	+	0.341296i
$29$	−0.309936	+	0.536825i	−0.0575536	+	0.0996858i	−0.893367	−	0.449328i	$-0.851663\pi$
$29$	−0.309936	+	0.536825i	−0.0575536	+	0.0996858i	0.835813	+	0.549014i	$0.184997\pi$
$30$		0			0
$31$	0.936857			0.168264			0.0841322	−	0.996455i	$-0.473188\pi$
$31$	0.936857			0.168264			0.0841322	+	0.996455i	$0.473188\pi$
$32$	−2.28093	+	3.95068i	−0.403215	+	0.698389i
$33$		0			0
$34$	−0.507311	+	0.878688i	−0.0870031	+	0.150694i
$35$	1.16885	+	2.02451i	0.197572	+	0.342204i
$36$		0			0
$37$	3.82480			0.628794			0.314397	−	0.949292i	$-0.398198\pi$
$37$	3.82480			0.628794			0.314397	+	0.949292i	$0.398198\pi$
$38$	1.73765	−	0.736936i	0.281884	−	0.119547i
$39$		0			0
$40$	1.67713	+	2.90488i	0.265178	+	0.459302i
$41$	−2.51591	−	4.35769i	−0.392920	−	0.680557i	0.599913	−	0.800065i	$-0.295202\pi$
$41$	−2.51591	−	4.35769i	−0.392920	−	0.680557i	−0.992833	+	0.119508i	$0.961868\pi$
$42$		0			0
$43$	−5.09449	−	8.82391i	−0.776902	−	1.34563i	−0.933719	−	0.358007i	$-0.883457\pi$
$43$	−5.09449	−	8.82391i	−0.776902	−	1.34563i	0.156817	−	0.987628i	$-0.449877\pi$
$44$	−3.34615	+	5.79571i	−0.504452	+	0.873736i
$45$		0			0
$46$	1.09553			0.161528
$47$	1.27868	−	2.21475i	0.186515	−	0.323054i	−0.757571	−	0.652753i	$-0.773614\pi$
$47$	1.27868	−	2.21475i	0.186515	−	0.323054i	0.944086	+	0.329699i	$0.106947\pi$
$48$		0			0
$49$	−5.67626			−0.810894
$50$	−0.377445			−0.0533787
$51$		0			0
$52$	−1.25150	−	2.16767i	−0.173552	−	0.300601i
$53$	5.39033	−	9.33633i	0.740419	−	1.28244i	−0.211885	−	0.977295i	$-0.567960\pi$
$53$	5.39033	−	9.33633i	0.740419	−	1.28244i	0.952304	−	0.305149i	$-0.0987064\pi$
$54$		0			0
$55$	3.75107	+	6.49704i	0.505794	+	0.876061i
$56$	1.89938			0.253816
$57$		0			0
$58$	0.268412			0.0352443
$59$	−3.76726	−	6.52508i	−0.490455	−	0.849493i	0.509485	−	0.860480i	$-0.329836\pi$
$59$	−3.76726	−	6.52508i	−0.490455	−	0.849493i	−0.999940	+	0.0109866i	$0.996503\pi$
$60$		0			0
$61$	3.55352	−	6.15488i	0.454982	−	0.788052i	−0.543705	−	0.839276i	$-0.682979\pi$
$61$	3.55352	−	6.15488i	0.454982	−	0.788052i	0.998687	+	0.0512241i	$0.0163123\pi$
$62$	−0.202835	−	0.351321i	−0.0257601	−	0.0446179i
$63$		0			0
$64$	−3.84497			−0.480621
$65$	−2.80589			−0.348028
$66$		0			0
$67$	−1.62526	+	2.81503i	−0.198557	+	0.343911i	−0.948061	−	0.318089i	$-0.896959\pi$
$67$	−1.62526	+	2.81503i	−0.198557	+	0.343911i	0.749504	+	0.662000i	$0.230292\pi$
$68$	−4.24699			−0.515024
$69$		0			0
$70$	0.506127	−	0.876638i	0.0604938	−	0.104778i
$71$	3.97238	+	6.88037i	0.471435	+	0.816550i	0.999466	−	0.0326754i	$-0.0104028\pi$
$71$	3.97238	+	6.88037i	0.471435	+	0.816550i	−0.528031	+	0.849225i	$0.677069\pi$
$72$		0			0
$73$	2.37756	+	4.11806i	0.278273	+	0.481982i	0.970956	−	0.239260i	$-0.0769048\pi$
$73$	2.37756	+	4.11806i	0.278273	+	0.481982i	−0.692683	+	0.721242i	$0.743571\pi$
$74$	−0.828094	−	1.43430i	−0.0962640	−	0.166734i
$75$		0			0
$76$	6.30811	+	4.75665i	0.723590	+	0.545625i
$77$	4.24815			0.484122
$78$		0			0
$79$	−2.90796	−	5.03674i	−0.327171	−	0.566677i	0.654778	−	0.755821i	$-0.272762\pi$
$79$	−2.90796	−	5.03674i	−0.327171	−	0.566677i	−0.981949	+	0.189144i	$0.939429\pi$
$80$	−2.95647	+	5.12076i	−0.330543	+	0.572518i
$81$		0			0
$82$	−1.08942	+	1.88694i	−0.120307	+	0.208377i
$83$	16.8621			1.85086			0.925428	−	0.378924i	$-0.123706\pi$
$83$	16.8621			1.85086			0.925428	+	0.378924i	$0.123706\pi$
$84$		0			0
$85$	−2.38046	+	4.12308i	−0.258197	+	0.447210i
$86$	−2.20598	+	3.82087i	−0.237877	+	0.412015i
$87$		0			0
$88$	6.09549			0.649781
$89$	5.57992	−	9.66470i	0.591470	−	1.02446i	−0.402565	−	0.915392i	$-0.631881\pi$
$89$	5.57992	−	9.66470i	0.591470	−	1.02446i	0.994035	−	0.109065i	$-0.0347855\pi$
$90$		0			0
$91$	−0.794430	+	1.37599i	−0.0832789	+	0.144243i
$92$	2.29284	+	3.97131i	0.239045	+	0.414038i
$93$		0			0
$94$	−1.10737			−0.114217
$95$	8.15359	−	3.45793i	0.836540	−	0.354776i
$96$		0			0
$97$	−5.51591	−	9.55384i	−0.560056	−	0.970046i	−0.997491	−	0.0707955i	$-0.977446\pi$
$97$	−5.51591	−	9.55384i	−0.560056	−	0.970046i	0.437435	−	0.899250i	$-0.355887\pi$
$98$	1.22895	+	2.12860i	0.124142	+	0.215021i
$99$		0			0
$100$	−0.789952	−	1.36824i	−0.0789952	−	0.136824i
$101$	−4.00224	+	6.93209i	−0.398238	+	0.689769i	−0.993509	−	0.113757i	$-0.963712\pi$
$101$	−4.00224	+	6.93209i	−0.398238	+	0.689769i	0.595271	+	0.803525i	$0.297045\pi$
$102$		0			0
$103$	−13.5972			−1.33977			−0.669884	−	0.742466i	$-0.733656\pi$
$103$	−13.5972			−1.33977			−0.669884	+	0.742466i	$0.733656\pi$
$104$	−1.13989	+	1.97435i	−0.111776	+	0.193601i
$105$		0			0
$106$	−4.66817			−0.453412
$107$	11.7261			1.13360			0.566802	−	0.823854i	$-0.308181\pi$
$107$	11.7261			1.13360			0.566802	+	0.823854i	$0.308181\pi$
$108$		0			0
$109$	6.86196	+	11.8853i	0.657256	+	1.13840i	0.981323	+	0.192367i	$0.0616164\pi$
$109$	6.86196	+	11.8853i	0.657256	+	1.13840i	−0.324067	+	0.946034i	$0.605050\pi$
$110$	1.62426	−	2.81330i	0.154867	−	0.268238i
$111$		0			0
$112$	1.67413	+	2.89967i	0.158190	+	0.273993i
$113$	16.9792			1.59727			0.798635	−	0.601815i	$-0.205556\pi$
$113$	16.9792			1.59727			0.798635	+	0.601815i	$0.205556\pi$
$114$		0			0
$115$	5.14058			0.479362
$116$	0.561759	+	0.972994i	0.0521580	+	0.0903403i
$117$		0			0
$118$	−1.63127	+	2.82544i	−0.150171	+	0.260103i
$119$	1.34796	+	2.33473i	0.123567	+	0.214024i
$120$		0			0
$121$	2.63314			0.239376
$122$	−3.07744			−0.278619
$123$		0			0
$124$	0.849026	−	1.47056i	0.0762448	−	0.132060i
$125$	−11.9302			−1.06707
$126$		0			0
$127$	5.47243	−	9.47853i	0.485600	−	0.841084i	−0.514263	−	0.857632i	$-0.671935\pi$
$127$	5.47243	−	9.47853i	0.485600	−	0.841084i	0.999863	+	0.0165487i	$0.00526784\pi$
$128$	5.39432	+	9.34323i	0.476795	+	0.825833i
$129$		0			0
$130$	0.607493	+	1.05221i	0.0532807	+	0.0922848i
$131$	11.2352	+	19.4600i	0.981628	+	1.70023i	0.656057	+	0.754711i	$0.272223\pi$
$131$	11.2352	+	19.4600i	0.981628	+	1.70023i	0.325571	+	0.945518i	$0.394444\pi$
$132$		0			0
$133$	0.612770	−	4.97751i	0.0531339	−	0.431605i
$134$	1.40752			0.121591
$135$		0			0
$136$	1.93412	+	3.35000i	0.165850	+	0.287260i
$137$	3.30172	−	5.71875i	0.282085	−	0.488586i	−0.689813	−	0.723988i	$-0.742307\pi$
$137$	3.30172	−	5.71875i	0.282085	−	0.488586i	0.971898	+	0.235402i	$0.0756406\pi$
$138$		0			0
$139$	7.69199	−	13.3229i	0.652426	−	1.13003i	−0.330107	−	0.943944i	$-0.607085\pi$
$139$	7.69199	−	13.3229i	0.652426	−	1.13003i	0.982533	−	0.186091i	$-0.0595819\pi$
$140$	4.23708			0.358099
$141$		0			0
$142$	1.72009	−	2.97929i	0.144347	−	0.250016i
$143$	−2.54948	+	4.41583i	−0.213198	+	0.369270i
$144$		0			0
$145$	1.25947			0.104594
$146$	1.02952	−	1.78317i	0.0852033	−	0.147576i
$147$		0			0
$148$	3.46623	−	6.00368i	0.284922	−	0.493499i
$149$	−1.01811	−	1.76342i	−0.0834067	−	0.144465i	0.821304	−	0.570490i	$-0.193247\pi$
$149$	−1.01811	−	1.76342i	−0.0834067	−	0.144465i	−0.904711	+	0.426025i	$0.859913\pi$
$150$		0			0
$151$	−13.4553			−1.09498			−0.547490	−	0.836812i	$-0.684417\pi$
$151$	−13.4553			−1.09498			−0.547490	+	0.836812i	$0.684417\pi$
$152$	0.879237	−	7.14202i	0.0713155	−	0.579294i
$153$		0			0
$154$	−0.919751	−	1.59306i	−0.0741157	−	0.128372i
$155$	−0.951766	−	1.64851i	−0.0764477	−	0.132411i
$156$		0			0
$157$	3.92767	+	6.80293i	0.313463	+	0.542933i	0.979109	−	0.203334i	$-0.0651777\pi$
$157$	3.92767	+	6.80293i	0.313463	+	0.542933i	−0.665647	+	0.746267i	$0.731844\pi$
$158$	−1.25918	+	2.18097i	−0.100175	+	0.173509i
$159$		0			0
$160$	9.26891			0.732772
$161$	1.45545	−	2.52091i	0.114705	−	0.198676i
$162$		0			0
$163$	6.47140			0.506879			0.253440	−	0.967351i	$-0.418438\pi$
$163$	6.47140			0.506879			0.253440	+	0.967351i	$0.418438\pi$
$164$	−9.12019			−0.712167
$165$		0			0
$166$	−3.65075	−	6.32329i	−0.283353	−	0.490782i
$167$	8.59411	−	14.8854i	0.665032	−	1.15187i	−0.314245	−	0.949342i	$-0.601751\pi$
$167$	8.59411	−	14.8854i	0.665032	−	1.15187i	0.979277	−	0.202527i	$-0.0649154\pi$
$168$		0			0
$169$	5.54646	+	9.60676i	0.426651	+	0.738981i
$170$	2.06154			0.158113
$171$		0			0
$172$	−18.4675			−1.40814
$173$	−4.67341	−	8.09458i	−0.355313	−	0.615420i	0.631859	−	0.775084i	$-0.282292\pi$
$173$	−4.67341	−	8.09458i	−0.355313	−	0.615420i	−0.987171	+	0.159664i	$0.948959\pi$
$174$		0			0
$175$	−0.501446	+	0.868530i	−0.0379058	+	0.0656547i
$176$	5.37260	+	9.30561i	0.404975	+	0.701437i
$177$		0			0
$178$	−4.83235			−0.362200
$179$	−13.0265			−0.973643			−0.486822	−	0.873501i	$-0.661844\pi$
$179$	−13.0265			−0.973643			−0.486822	+	0.873501i	$0.661844\pi$
$180$		0			0
$181$	6.33448	−	10.9716i	0.470838	−	0.815515i	−0.528606	−	0.848867i	$-0.677285\pi$
$181$	6.33448	−	10.9716i	0.470838	−	0.815515i	0.999444	+	0.0333523i	$0.0106183\pi$
$182$	0.687996			0.0509977
$183$		0			0
$184$	2.08836	−	3.61715i	0.153956	−	0.266660i
$185$	−3.88567	−	6.73018i	−0.285680	−	0.494813i
$186$		0			0
$187$	4.32585	+	7.49259i	0.316338	+	0.547913i
$188$	−2.31762	−	4.01423i	−0.169030	−	0.292768i
$189$		0			0
$190$	−3.06203	−	2.30893i	−0.222143	−	0.167507i
$191$	−19.6919			−1.42486			−0.712429	−	0.701744i	$-0.752405\pi$
$191$	−19.6919			−1.42486			−0.712429	+	0.701744i	$0.752405\pi$
$192$		0			0
$193$	−0.766445	−	1.32752i	−0.0551699	−	0.0955571i	0.837121	−	0.547017i	$-0.184237\pi$
$193$	−0.766445	−	1.32752i	−0.0551699	−	0.0955571i	−0.892291	+	0.451460i	$0.850903\pi$
$194$	−2.38846	+	4.13694i	−0.171481	+	0.297015i
$195$		0			0
$196$	−5.14411	+	8.90986i	−0.367436	+	0.636418i
$197$	4.01965			0.286388			0.143194	−	0.989695i	$-0.454263\pi$
$197$	4.01965			0.286388			0.143194	+	0.989695i	$0.454263\pi$
$198$		0			0
$199$	−3.76763	+	6.52572i	−0.267080	+	0.462596i	−0.968107	−	0.250539i	$-0.919392\pi$
$199$	−3.76763	+	6.52572i	−0.267080	+	0.462596i	0.701026	+	0.713135i	$0.252726\pi$
$200$	−0.719504	+	1.24622i	−0.0508766	+	0.0881208i
$201$		0			0
$202$	3.46604			0.243870
$203$	0.356594	−	0.617638i	0.0250280	−	0.0433497i
$204$		0			0
$205$	−5.11191	+	8.85408i	−0.357031	+	0.618396i
$206$	2.94387	+	5.09893i	0.205109	+	0.355260i
$207$		0			0
$208$	−4.01883			−0.278656
$209$	1.96650	−	15.9738i	0.136025	−	1.10493i
$210$		0			0
$211$	1.59567	+	2.76379i	0.109851	+	0.190267i	0.915710	−	0.401841i	$-0.131629\pi$
$211$	1.59567	+	2.76379i	0.109851	+	0.190267i	−0.805859	+	0.592108i	$0.798296\pi$
$212$	−9.76998	−	16.9221i	−0.671005	−	1.16221i
$213$		0			0
$214$	−2.53877	−	4.39728i	−0.173547	−	0.300592i
$215$	−10.3511	+	17.9287i	−0.705941	+	1.22273i
$216$		0			0
$217$	−1.07789			−0.0731720
$218$	2.97131	−	5.14647i	0.201243	−	0.348563i
$219$		0			0
$220$	13.5976			0.916752
$221$	−3.23584			−0.217666
$222$		0			0
$223$	7.19749	+	12.4664i	0.481980	+	0.834813i	0.999786	−	0.0206844i	$-0.00658453\pi$
$223$	7.19749	+	12.4664i	0.481980	+	0.834813i	−0.517806	+	0.855498i	$0.673251\pi$
$224$	2.62430	−	4.54542i	0.175343	−	0.303704i
$225$		0			0
$226$	−3.67611	−	6.36721i	−0.244531	−	0.423540i
$227$	8.88794			0.589914			0.294957	−	0.955511i	$-0.404695\pi$
$227$	8.88794			0.589914			0.294957	+	0.955511i	$0.404695\pi$
$228$		0			0
$229$	−6.83849			−0.451900			−0.225950	−	0.974139i	$-0.572549\pi$
$229$	−6.83849			−0.451900			−0.225950	+	0.974139i	$0.572549\pi$
$230$	−1.11297	−	1.92772i	−0.0733870	−	0.127110i
$231$		0			0
$232$	0.511661	−	0.886223i	0.0335922	−	0.0581834i
$233$	−0.518688	−	0.898394i	−0.0339804	−	0.0588557i	0.848535	−	0.529139i	$-0.177485\pi$
$233$	−0.518688	−	0.898394i	−0.0339804	−	0.0588557i	−0.882515	+	0.470283i	$0.844152\pi$
$234$		0			0
$235$	−5.19614			−0.338959
$236$	−13.6563			−0.888950
$237$		0			0
$238$	0.583682	−	1.01097i	0.0378345	−	0.0655312i
$239$	−18.5956			−1.20285			−0.601426	−	0.798929i	$-0.705400\pi$
$239$	−18.5956			−1.20285			−0.601426	+	0.798929i	$0.705400\pi$
$240$		0			0
$241$	−13.3437	+	23.1120i	−0.859545	+	1.48878i	0.0128186	+	0.999918i	$0.495920\pi$
$241$	−13.3437	+	23.1120i	−0.859545	+	1.48878i	−0.872364	+	0.488858i	$0.837414\pi$
$242$	−0.570091	−	0.987426i	−0.0366468	−	0.0634742i
$243$		0			0
$244$	−6.44076	−	11.1557i	−0.412328	−	0.714172i
$245$	5.76659	+	9.98803i	0.368414	+	0.638112i
$246$		0			0
$247$	4.80623	+	3.62416i	0.305813	+	0.230599i
$248$	−1.54662			−0.0982105
$249$		0			0
$250$	2.58297	+	4.47384i	0.163361	+	0.282950i
$251$	−1.40097	+	2.42655i	−0.0884286	+	0.153163i	−0.906847	−	0.421460i	$-0.861518\pi$
$251$	−1.40097	+	2.42655i	−0.0884286	+	0.153163i	0.818418	+	0.574623i	$0.194851\pi$
$252$		0			0
$253$	4.67082	−	8.09010i	0.293652	−	0.508620i
$254$	−4.73927			−0.297368
$255$		0			0
$256$	−1.50916	+	2.61395i	−0.0943226	+	0.163372i
$257$	−3.80716	+	6.59420i	−0.237484	+	0.411335i	−0.959992	−	0.280028i	$-0.909656\pi$
$257$	−3.80716	+	6.59420i	−0.237484	+	0.411335i	0.722507	+	0.691363i	$0.242989\pi$
$258$		0			0
$259$	−4.40059			−0.273439
$260$	−2.54284	+	4.40433i	−0.157700	+	0.273145i
$261$		0			0
$262$	4.86500	−	8.42643i	0.300561	−	0.520587i
$263$	7.64649	+	13.2441i	0.471503	+	0.816667i	0.999469	−	0.0325986i	$-0.0103783\pi$
$263$	7.64649	+	13.2441i	0.471503	+	0.816667i	−0.527965	+	0.849266i	$0.677045\pi$
$264$		0			0
$265$	−21.9045			−1.34558
$266$	−1.99924	+	0.847875i	−0.122581	+	0.0519865i
$267$		0			0
$268$	2.94578	+	5.10224i	0.179942	+	0.311669i
$269$	−15.0110	−	25.9998i	−0.915237	−	1.58524i	−0.806554	−	0.591161i	$-0.798670\pi$
$269$	−15.0110	−	25.9998i	−0.915237	−	1.58524i	−0.108683	−	0.994076i	$-0.534663\pi$
$270$		0			0
$271$	6.22818	+	10.7875i	0.378335	+	0.655296i	0.990820	−	0.135186i	$-0.0431633\pi$
$271$	6.22818	+	10.7875i	0.378335	+	0.655296i	−0.612485	+	0.790482i	$0.709830\pi$
$272$	−3.40949	+	5.90542i	−0.206731	+	0.358068i
$273$		0			0
$274$	−2.85938			−0.172741
$275$	−1.60924	+	2.78728i	−0.0970407	+	0.168079i
$276$		0			0
$277$	11.0756			0.665466			0.332733	−	0.943021i	$-0.392029\pi$
$277$	11.0756			0.665466			0.332733	+	0.943021i	$0.392029\pi$
$278$	−6.66146			−0.399528
$279$		0			0
$280$	−1.92961	−	3.34218i	−0.115316	−	0.199734i
$281$	−8.34817	+	14.4595i	−0.498010	+	0.862579i	−0.999997	−	0.00229612i	$-0.999269\pi$
$281$	−8.34817	+	14.4595i	−0.498010	+	0.862579i	0.501987	+	0.864875i	$0.332602\pi$
$282$		0			0
$283$	−12.9129	−	22.3658i	−0.767593	−	1.32951i	−0.938865	−	0.344286i	$-0.888121\pi$
$283$	−12.9129	−	22.3658i	−0.767593	−	1.32951i	0.171272	−	0.985224i	$-0.445212\pi$
$284$	14.3999			0.854476
$285$		0			0
$286$	2.20791			0.130557
$287$	2.89466	+	5.01370i	0.170866	+	0.295949i
$288$		0			0
$289$	5.75478	−	9.96757i	0.338516	−	0.586328i
$290$	−0.272684	−	0.472302i	−0.0160126	−	0.0277346i
$291$		0			0
$292$	8.61867			0.504369
$293$	−27.9386			−1.63219			−0.816094	−	0.577919i	$-0.803865\pi$
$293$	−27.9386			−1.63219			−0.816094	+	0.577919i	$0.803865\pi$
$294$		0			0
$295$	−7.65442	+	13.2578i	−0.445658	+	0.771902i
$296$	−6.31422			−0.367006
$297$		0			0
$298$	−0.440854	+	0.763581i	−0.0255380	+	0.0442331i
$299$	1.74694	+	3.02580i	0.101028	+	0.174986i
$300$		0			0
$301$	5.86142	+	10.1523i	0.337846	+	0.585167i
$302$	2.91317	+	5.04576i	0.167634	+	0.290351i
$303$		0			0
$304$	11.6783	−	4.95274i	0.669794	−	0.284059i
$305$	−14.4403			−0.826850
$306$		0			0
$307$	−6.26206	−	10.8462i	−0.357394	−	0.619025i	0.630130	−	0.776489i	$-0.283001\pi$
$307$	−6.26206	−	10.8462i	−0.357394	−	0.619025i	−0.987525	+	0.157464i	$0.949668\pi$
$308$	3.84989	−	6.66820i	0.219368	−	0.379956i
$309$		0			0
$310$	−0.412127	+	0.713825i	−0.0234072	+	0.0405425i
$311$	−24.4906			−1.38873			−0.694366	−	0.719622i	$-0.744315\pi$
$311$	−24.4906			−1.38873			−0.694366	+	0.719622i	$0.744315\pi$
$312$		0			0
$313$	10.2334	−	17.7247i	0.578424	−	1.00186i	−0.417236	−	0.908798i	$-0.637001\pi$
$313$	10.2334	−	17.7247i	0.578424	−	1.00186i	0.995660	−	0.0930622i	$-0.0296655\pi$
$314$	1.70073	−	2.94576i	0.0959779	−	0.166239i
$315$		0			0
$316$	−10.5414			−0.592998
$317$	10.9981	−	19.0492i	0.617713	−	1.06991i	−0.372189	−	0.928157i	$-0.621393\pi$
$317$	10.9981	−	19.0492i	0.617713	−	1.06991i	0.989902	−	0.141753i	$-0.0452739\pi$
$318$		0			0
$319$	1.14438	−	1.98212i	0.0640729	−	0.110977i
$320$	3.90616	+	6.76567i	0.218361	+	0.378212i
$321$		0			0
$322$	−1.26046			−0.0702425
$323$	9.40297	−	3.98779i	0.523195	−	0.221887i
$324$		0			0
$325$	−0.601875	−	1.04248i	−0.0333860	−	0.0578263i
$326$	−1.40110	−	2.42677i	−0.0775997	−	0.134407i
$327$		0			0
$328$	4.15343	+	7.19394i	0.229335	+	0.397219i
$329$	−1.47118	+	2.54816i	−0.0811087	+	0.140484i
$330$		0			0
$331$	32.5077			1.78679			0.893393	−	0.449275i	$-0.148318\pi$
$331$	32.5077			1.78679			0.893393	+	0.449275i	$0.148318\pi$
$332$	15.2813	−	26.4679i	0.838669	−	1.45262i
$333$		0			0
$334$	−7.44271			−0.407247
$335$	6.60449			0.360842
$336$		0			0
$337$	−1.28184	−	2.22022i	−0.0698264	−	0.120943i	0.828998	−	0.559251i	$-0.188911\pi$
$337$	−1.28184	−	2.22022i	−0.0698264	−	0.120943i	−0.898825	+	0.438308i	$0.855578\pi$
$338$	2.40169	−	4.15985i	0.130635	−	0.226266i
$339$		0			0
$340$	4.31458	+	7.47308i	0.233991	+	0.405284i
$341$	−3.45916			−0.187324
$342$		0			0
$343$	14.5845			0.787491
$344$	8.41029	+	14.5671i	0.453453	+	0.785403i
$345$		0			0
$346$	−2.02365	+	3.50506i	−0.108792	+	0.188433i
$347$	4.67453	+	8.09652i	0.250942	+	0.434644i	0.963785	−	0.266679i	$-0.0859264\pi$
$347$	4.67453	+	8.09652i	0.250942	+	0.434644i	−0.712844	+	0.701323i	$0.752593\pi$
$348$		0			0
$349$	9.97826			0.534124			0.267062	−	0.963679i	$-0.413947\pi$
$349$	9.97826			0.534124			0.267062	+	0.963679i	$0.413947\pi$
$350$	0.434265			0.0232125
$351$		0			0
$352$	8.42189	−	14.5871i	0.448888	−	0.777497i
$353$	−27.7171			−1.47523			−0.737617	−	0.675219i	$-0.764049\pi$
$353$	−27.7171			−1.47523			−0.737617	+	0.675219i	$0.764049\pi$
$354$		0			0
$355$	8.07121	−	13.9797i	0.428375	−	0.741967i
$356$	−10.1136	−	17.5173i	−0.536020	−	0.928413i
$357$		0			0
$358$	2.82031	+	4.88492i	0.149058	+	0.258176i
$359$	17.1967	+	29.7856i	0.907609	+	1.57202i	0.817376	+	0.576104i	$0.195428\pi$
$359$	17.1967	+	29.7856i	0.907609	+	1.57202i	0.0902324	+	0.995921i	$0.471239\pi$
$360$		0			0
$361$	−18.4327	−	4.60825i	−0.970142	−	0.242539i
$362$	−5.48582			−0.288328
$363$		0			0
$364$	1.43990	+	2.49399i	0.0754715	+	0.130720i
$365$	4.83080	−	8.36719i	0.252856	−	0.437959i
$366$		0			0
$367$	−16.1477	+	27.9686i	−0.842901	+	1.45995i	0.0445302	+	0.999008i	$0.485821\pi$
$367$	−16.1477	+	27.9686i	−0.842901	+	1.45995i	−0.887431	+	0.460940i	$0.847512\pi$
$368$	7.36278			0.383811
$369$		0			0
$370$	−1.68255	+	2.91425i	−0.0874714	+	0.151505i
$371$	−6.20180	+	10.7418i	−0.321981	+	0.557688i
$372$		0			0
$373$	−35.2967			−1.82759			−0.913796	−	0.406173i	$-0.866863\pi$
$373$	−35.2967			−1.82759			−0.913796	+	0.406173i	$0.866863\pi$
$374$	1.87315	−	3.24439i	0.0968582	−	0.167763i
$375$		0			0
$376$	−2.11093	+	3.65624i	−0.108863	+	0.188556i
$377$	0.428011	+	0.741337i	0.0220437	+	0.0381808i
$378$		0			0
$379$	24.0421			1.23496			0.617479	−	0.786587i	$-0.288154\pi$
$379$	24.0421			1.23496			0.617479	+	0.786587i	$0.288154\pi$
$380$	1.96137	−	15.9322i	0.100616	−	0.817304i
$381$		0			0
$382$	4.26343	+	7.38448i	0.218136	+	0.377823i
$383$	−3.35932	−	5.81852i	−0.171653	−	0.297312i	0.767345	−	0.641235i	$-0.221578\pi$
$383$	−3.35932	−	5.81852i	−0.171653	−	0.297312i	−0.938998	+	0.343923i	$0.888244\pi$
$384$		0			0
$385$	−4.31576	−	7.47511i	−0.219951	−	0.380967i
$386$	−0.331881	+	0.574834i	−0.0168923	+	0.0292583i
$387$		0			0
$388$	−19.9952			−1.01510
$389$	18.2243	−	31.5655i	0.924010	−	1.60043i	0.130864	−	0.991400i	$-0.458225\pi$
$389$	18.2243	−	31.5655i	0.924010	−	1.60043i	0.793146	−	0.609032i	$-0.208442\pi$
$390$		0			0
$391$	5.92828			0.299806
$392$	9.37071			0.473292
$393$		0			0
$394$	−0.870280	−	1.50737i	−0.0438441	−	0.0759402i
$395$	−5.90848	+	10.2338i	−0.297288	+	0.514918i
$396$		0			0
$397$	−2.52467	−	4.37285i	−0.126709	−	0.219467i	0.795690	−	0.605703i	$-0.207108\pi$
$397$	−2.52467	−	4.37285i	−0.126709	−	0.219467i	−0.922400	+	0.386236i	$0.873775\pi$
$398$	3.26286			0.163553
$399$		0			0
$400$	−2.53670			−0.126835
$401$	5.57189	+	9.65080i	0.278247	+	0.481938i	0.970949	−	0.239286i	$-0.0769133\pi$
$401$	5.57189	+	9.65080i	0.278247	+	0.481938i	−0.692702	+	0.721224i	$0.743580\pi$
$402$		0			0
$403$	0.646885	−	1.12044i	0.0322236	−	0.0558129i
$404$	7.25407	+	12.5644i	0.360903	+	0.625103i
$405$		0			0
$406$	−0.308819			−0.0153264
$407$	−14.1223			−0.700019
$408$		0			0
$409$	−2.46203	+	4.26436i	−0.121740	+	0.210859i	−0.920454	−	0.390851i	$-0.872181\pi$
$409$	−2.46203	+	4.26436i	−0.121740	+	0.210859i	0.798714	+	0.601711i	$0.205514\pi$
$410$	4.42704			0.218636
$411$		0			0
$412$	−12.3224	+	21.3431i	−0.607082	+	1.05150i
$413$	4.33438	+	7.50737i	0.213281	+	0.369414i
$414$		0			0
$415$	−17.1304	−	29.6708i	−0.840901	−	1.45648i
$416$	3.14989	+	5.45577i	0.154436	+	0.267491i
$417$		0			0
$418$	−6.41594	+	2.72099i	−0.313814	+	0.133088i
$419$	14.1877			0.693116			0.346558	−	0.938029i	$-0.387350\pi$
$419$	14.1877			0.693116			0.346558	+	0.938029i	$0.387350\pi$
$420$		0			0
$421$	−8.50727	−	14.7350i	−0.414619	−	0.718141i	0.580770	−	0.814068i	$-0.302752\pi$
$421$	−8.50727	−	14.7350i	−0.414619	−	0.718141i	−0.995388	+	0.0959271i	$0.969418\pi$
$422$	0.690947	−	1.19675i	0.0336348	−	0.0582571i
$423$		0			0
$424$	−8.89869	+	15.4130i	−0.432159	+	0.748521i
$425$	−2.04247			−0.0990744
$426$		0			0
$427$	−4.08847	+	7.08144i	−0.197855	+	0.342695i
$428$	10.6268	−	18.4061i	0.513664	−	0.889692i
$429$		0			0
$430$	8.96434			0.432299
$431$	0.974953	−	1.68867i	0.0469618	−	0.0813403i	−0.841589	−	0.540118i	$-0.818379\pi$
$431$	0.974953	−	1.68867i	0.0469618	−	0.0813403i	0.888551	+	0.458778i	$0.151713\pi$
$432$		0			0
$433$	14.6802	−	25.4268i	0.705483	−	1.22193i	−0.261034	−	0.965330i	$-0.584063\pi$
$433$	14.6802	−	25.4268i	0.705483	−	1.22193i	0.966517	−	0.256603i	$-0.0826032\pi$
$434$	0.233370	+	0.404209i	0.0112021	+	0.0194027i
$435$		0			0
$436$	24.8746			1.19128
$437$	−8.80535	−	6.63970i	−0.421217	−	0.317620i
$438$		0			0
$439$	5.35767	+	9.27976i	0.255708	+	0.442899i	0.965087	−	0.261928i	$-0.0843582\pi$
$439$	5.35767	+	9.27976i	0.255708	+	0.442899i	−0.709380	+	0.704826i	$0.751025\pi$
$440$	−6.19249	−	10.7257i	−0.295216	−	0.511328i
$441$		0			0
$442$	0.700580	+	1.21344i	0.0333232	+	0.0577175i
$443$	−9.91739	+	17.1774i	−0.471190	+	0.816124i	−0.999457	−	0.0329538i	$-0.989509\pi$
$443$	−9.91739	+	17.1774i	−0.471190	+	0.816124i	0.528267	+	0.849078i	$0.322842\pi$
$444$		0			0
$445$	−22.6749			−1.07489
$446$	3.11661	−	5.39812i	0.147576	−	0.255608i
$447$		0			0
$448$	4.42379			0.209005
$449$	25.1068			1.18486			0.592431	−	0.805621i	$-0.298168\pi$
$449$	25.1068			1.18486			0.592431	+	0.805621i	$0.298168\pi$
$450$		0			0
$451$	9.28953	+	16.0899i	0.437427	+	0.757646i
$452$	15.3874	−	26.6518i	0.723763	−	1.25359i
$453$		0			0
$454$	−1.92430	−	3.33298i	−0.0903117	−	0.156424i
$455$	3.22829			0.151345
$456$		0			0
$457$	10.1416			0.474404			0.237202	−	0.971460i	$-0.423770\pi$
$457$	10.1416			0.474404			0.237202	+	0.971460i	$0.423770\pi$
$458$	1.48058	+	2.56443i	0.0691828	+	0.119828i
$459$		0			0
$460$	4.65865	−	8.06903i	0.217211	−	0.376220i
$461$	10.2604	+	17.7715i	0.477873	+	0.827700i	0.999678	−	0.0253645i	$-0.00807463\pi$
$461$	10.2604	+	17.7715i	0.477873	+	0.827700i	−0.521805	+	0.853065i	$0.674741\pi$
$462$		0			0
$463$	20.1006			0.934155			0.467077	−	0.884216i	$-0.345307\pi$
$463$	20.1006			0.934155			0.467077	+	0.884216i	$0.345307\pi$
$464$	1.80392			0.0837450
$465$		0			0
$466$	−0.224598	+	0.389016i	−0.0104043	+	0.0180208i
$467$	13.4426			0.622048			0.311024	−	0.950402i	$-0.399328\pi$
$467$	13.4426			0.622048			0.311024	+	0.950402i	$0.399328\pi$
$468$		0			0
$469$	1.86993	−	3.23881i	0.0863451	−	0.149554i
$470$	1.12500	+	1.94855i	0.0518922	+	0.0898800i
$471$		0			0
$472$	6.21922	+	10.7720i	0.286263	+	0.495822i
$473$	18.8104	+	32.5806i	0.864904	+	1.49806i
$474$		0			0
$475$	3.03371	+	2.28758i	0.139196	+	0.104961i
$476$	4.88634			0.223965
$477$		0			0
$478$	4.02607	+	6.97336i	0.184148	+	0.318954i
$479$	−0.662849	+	1.14809i	−0.0302864	+	0.0524575i	−0.880771	−	0.473542i	$-0.842975\pi$
$479$	−0.662849	+	1.14809i	−0.0302864	+	0.0524575i	0.850485	+	0.525999i	$0.176309\pi$
$480$		0			0
$481$	2.64096	−	4.57428i	0.120418	−	0.208569i
$482$	11.5560			0.526362
$483$		0			0
$484$	2.38628	−	4.13316i	0.108467	−	0.187871i
$485$	−11.2074	+	19.4118i	−0.508901	+	0.881443i
$486$		0			0
$487$	−5.65193			−0.256113			−0.128057	−	0.991767i	$-0.540874\pi$
$487$	−5.65193			−0.256113			−0.128057	+	0.991767i	$0.540874\pi$
$488$	−5.86637	+	10.1609i	−0.265558	+	0.459960i
$489$		0			0
$490$	2.49701	−	4.32494i	0.112803	−	0.195381i
$491$	20.7321	+	35.9090i	0.935626	+	1.62055i	0.773514	+	0.633779i	$0.218497\pi$
$491$	20.7321	+	35.9090i	0.935626	+	1.62055i	0.162112	+	0.986772i	$0.448169\pi$
$492$		0			0
$493$	1.45246			0.0654157
$494$	0.318478	−	2.58699i	0.0143290	−	0.116394i
$495$		0			0
$496$	−1.36320	−	2.36113i	−0.0612095	−	0.106018i
$497$	−4.57039	−	7.91615i	−0.205010	−	0.355088i
$498$		0			0
$499$	0.164582	+	0.285064i	0.00736769	+	0.0127612i	0.869686	−	0.493606i	$-0.164321\pi$
$499$	0.164582	+	0.285064i	0.00736769	+	0.0127612i	−0.862318	+	0.506367i	$0.830988\pi$
$500$	−10.8118	+	18.7265i	−0.483517	+	0.837476i
$501$		0			0
$502$	1.21328			0.0541512
$503$	9.08741	−	15.7399i	0.405188	−	0.701806i	−0.589156	−	0.808020i	$-0.700539\pi$
$503$	9.08741	−	15.7399i	0.405188	−	0.701806i	0.994343	+	0.106214i	$0.0338728\pi$
$504$		0			0
$505$	16.2637			0.723727
$506$	−4.04505			−0.179824
$507$		0			0
$508$	−9.91879	−	17.1798i	−0.440075	−	0.762232i
$509$	2.15475	−	3.73214i	0.0955076	−	0.165424i	−0.814313	−	0.580426i	$-0.802886\pi$
$509$	2.15475	−	3.73214i	0.0955076	−	0.165424i	0.909820	+	0.415002i	$0.136219\pi$
$510$		0			0
$511$	−2.73548	−	4.73799i	−0.121011	−	0.209597i
$512$	22.8842			1.01135
$513$		0			0
$514$	3.29710			0.145429
$515$	13.8135	+	23.9258i	0.608698	+	1.05430i
$516$		0			0
$517$	−4.72130	+	8.17753i	−0.207642	+	0.359647i
$518$	0.952756	+	1.65022i	0.0418617	+	0.0725065i
$519$		0			0
$520$	4.63214			0.203133
$521$	−36.6688			−1.60649			−0.803245	−	0.595649i	$-0.796895\pi$
$521$	−36.6688			−1.60649			−0.803245	+	0.595649i	$0.796895\pi$
$522$		0			0
$523$	−1.86705	+	3.23382i	−0.0816402	+	0.141405i	−0.903955	−	0.427628i	$-0.859349\pi$
$523$	−1.86705	+	3.23382i	−0.0816402	+	0.141405i	0.822314	+	0.569033i	$0.192683\pi$
$524$	40.7278			1.77920
$525$		0			0
$526$	3.31103	−	5.73487i	0.144368	−	0.250052i
$527$	−1.09761	−	1.90111i	−0.0478125	−	0.0828137i
$528$		0			0
$529$	8.29948	+	14.3751i	0.360847	+	0.625005i
$530$	4.74246	+	8.21418i	0.205999	+	0.356801i
$531$		0			0
$532$	−7.25774	−	5.47272i	−0.314663	−	0.237272i
$533$	−6.94879			−0.300986
$534$		0			0
$535$	−11.9127	−	20.6334i	−0.515031	−	0.892059i
$536$	2.68308	−	4.64722i	0.115891	−	0.200729i
$537$		0			0
$538$	−6.49996	+	11.2583i	−0.280233	+	0.485378i
$539$	20.9585			0.902746
$540$		0			0
$541$	−10.2951	+	17.8316i	−0.442620	+	0.766641i	−0.997883	−	0.0650344i	$-0.979284\pi$
$541$	−10.2951	+	17.8316i	−0.442620	+	0.766641i	0.555263	+	0.831675i	$0.312618\pi$
$542$	2.69688	−	4.67114i	0.115841	−	0.200643i
$543$		0			0
$544$	10.6892			0.458296
$545$	13.9423	−	24.1488i	0.597223	−	1.03442i
$546$		0			0
$547$	−7.42876	+	12.8670i	−0.317631	+	0.550153i	−0.979993	−	0.199031i	$-0.936221\pi$
$547$	−7.42876	+	12.8670i	−0.317631	+	0.550153i	0.662362	+	0.749184i	$0.269554\pi$
$548$	−5.98437	−	10.3652i	−0.255640	−	0.442781i
$549$		0			0
$550$	1.39364			0.0594251
$551$	−2.15736	−	1.62677i	−0.0919067	−	0.0693025i
$552$		0			0
$553$	3.34573	+	5.79497i	0.142275	+	0.246427i
$554$	−2.39793	−	4.15333i	−0.101878	−	0.176458i
$555$		0			0
$556$	−13.9417	−	24.1478i	−0.591261	−	1.02409i
$557$	6.31888	−	10.9446i	0.267740	−	0.463739i	−0.700538	−	0.713615i	$-0.747057\pi$
$557$	6.31888	−	10.9446i	0.267740	−	0.463739i	0.968278	+	0.249876i	$0.0803900\pi$
$558$		0			0
$559$	−14.0707			−0.595125
$560$	3.40154	−	5.89164i	0.143741	−	0.248967i
$561$		0			0
$562$	7.22973			0.304968
$563$	13.9053			0.586041			0.293020	−	0.956106i	$-0.405340\pi$
$563$	13.9053			0.586041			0.293020	+	0.956106i	$0.405340\pi$
$564$		0			0
$565$	−17.2494	−	29.8769i	−0.725689	−	1.25693i
$566$	−5.59146	+	9.68469i	−0.235026	+	0.407078i
$567$		0			0
$568$	−6.55785	−	11.3585i	−0.275161	−	0.476594i
$569$	−11.5682			−0.484963			−0.242482	−	0.970156i	$-0.577961\pi$
$569$	−11.5682			−0.484963			−0.242482	+	0.970156i	$0.577961\pi$
$570$		0			0
$571$	20.2650			0.848062			0.424031	−	0.905648i	$-0.360615\pi$
$571$	20.2650			0.848062			0.424031	+	0.905648i	$0.360615\pi$
$572$	4.62093	+	8.00369i	0.193211	+	0.334651i
$573$		0			0
$574$	1.25343	−	2.17100i	0.0523170	−	0.0906156i
$575$	1.10268	+	1.90989i	0.0459848	+	0.0796479i
$576$		0			0
$577$	−19.0894			−0.794702			−0.397351	−	0.917667i	$-0.630070\pi$
$577$	−19.0894			−0.794702			−0.397351	+	0.917667i	$0.630070\pi$
$578$	−4.98379			−0.207298
$579$		0			0
$580$	1.14140	−	1.97696i	0.0473939	−	0.0820887i
$581$	−19.4005			−0.804869
$582$		0			0
$583$	−19.9028	+	34.4726i	−0.824289	+	1.42771i
$584$	−3.92503	−	6.79835i	−0.162419	−	0.281318i
$585$		0			0
$586$	6.04888	+	10.4770i	0.249877	+	0.432799i
$587$	11.7053	+	20.2741i	0.483127	+	0.836801i	0.999812	−	0.0193744i	$-0.00616745\pi$
$587$	11.7053	+	20.2741i	0.483127	+	0.836801i	−0.516685	+	0.856176i	$0.672834\pi$
$588$		0			0
$589$	−0.498963	+	4.05307i	−0.0205594	+	0.167004i
$590$	6.62893			0.272909
$591$		0			0
$592$	−5.56538	−	9.63953i	−0.228736	−	0.396182i
$593$	8.18930	−	14.1843i	0.336294	−	0.582479i	−0.647438	−	0.762118i	$-0.724160\pi$
$593$	8.18930	−	14.1843i	0.336294	−	0.582479i	0.983733	+	0.179639i	$0.0574930\pi$
$594$		0			0
$595$	2.73881	−	4.74377i	0.112280	−	0.194475i
$596$	−3.69064			−0.151175
$597$		0			0
$598$	0.756449	−	1.31021i	0.0309335	−	0.0535784i
$599$	−9.08296	+	15.7322i	−0.371120	+	0.642798i	−0.989738	−	0.142893i	$-0.954359\pi$
$599$	−9.08296	+	15.7322i	−0.371120	+	0.642798i	0.618618	+	0.785692i	$0.287693\pi$
$600$		0			0
$601$	−7.00570			−0.285768			−0.142884	−	0.989739i	$-0.545638\pi$
$601$	−7.00570			−0.285768			−0.142884	+	0.989739i	$0.545638\pi$
$602$	2.53807	−	4.39606i	0.103444	−	0.179170i
$603$		0			0
$604$	−12.1939	+	21.1205i	−0.496163	+	0.859380i
$605$	−2.67504	−	4.63331i	−0.108756	−	0.188371i
$606$		0			0
$607$	10.8546			0.440576			0.220288	−	0.975435i	$-0.429300\pi$
$607$	10.8546			0.440576			0.220288	+	0.975435i	$0.429300\pi$
$608$	−15.8768	−	11.9719i	−0.643889	−	0.485527i
$609$		0			0
$610$	3.12642	+	5.41512i	0.126585	+	0.219252i
$611$	−1.76582	−	3.05849i	−0.0714375	−	0.123733i
$612$		0			0
$613$	24.4865	+	42.4119i	0.989002	+	1.71300i	0.622589	+	0.782549i	$0.286081\pi$
$613$	24.4865	+	42.4119i	0.989002	+	1.71300i	0.366413	+	0.930452i	$0.380586\pi$
$614$	−2.71155	+	4.69654i	−0.109429	+	0.189537i
$615$		0			0
$616$	−7.01310			−0.282566
$617$	18.4730	−	31.9962i	0.743697	−	1.28812i	−0.207104	−	0.978319i	$-0.566404\pi$
$617$	18.4730	−	31.9962i	0.743697	−	1.28812i	0.950801	−	0.309802i	$-0.100263\pi$
$618$		0			0
$619$	−38.4572			−1.54573			−0.772863	−	0.634573i	$-0.781176\pi$
$619$	−38.4572			−1.54573			−0.772863	+	0.634573i	$0.781176\pi$
$620$	−3.45015			−0.138561
$621$		0			0
$622$	5.30236	+	9.18396i	0.212605	+	0.368243i
$623$	−6.41992	+	11.1196i	−0.257209	+	0.445498i
$624$		0			0
$625$	9.94092	+	17.2182i	0.397637	+	0.688727i
$626$	−8.86236			−0.354211
$627$		0			0
$628$	14.2378			0.568151
$629$	−4.48108	−	7.76145i	−0.178672	−	0.309469i
$630$		0			0
$631$	−4.05213	+	7.01849i	−0.161313	+	0.279402i	−0.935340	−	0.353751i	$-0.884906\pi$
$631$	−4.05213	+	7.01849i	−0.161313	+	0.279402i	0.774027	+	0.633153i	$0.218239\pi$
$632$	4.80064	+	8.31496i	0.190959	+	0.330751i
$633$		0			0
$634$	−9.52460			−0.378270
$635$	−22.2381			−0.882492
$636$		0			0
$637$	−3.91936	+	6.78854i	−0.155291	+	0.268972i
$638$	−0.991061			−0.0392365
$639$		0			0
$640$	10.9603	−	18.9838i	0.433245	−	0.750403i
$641$	−4.91135	−	8.50671i	−0.193987	−	0.335995i	0.752581	−	0.658500i	$-0.228809\pi$
$641$	−4.91135	−	8.50671i	−0.193987	−	0.335995i	−0.946568	+	0.322505i	$0.895475\pi$
$642$		0			0
$643$	−13.5129	−	23.4050i	−0.532895	−	0.923002i	−0.999262	−	0.0384104i	$-0.987771\pi$
$643$	−13.5129	−	23.4050i	−0.532895	−	0.923002i	0.466367	−	0.884592i	$-0.345563\pi$
$644$	−2.63800	−	4.56915i	−0.103952	−	0.180050i
$645$		0			0
$646$	−3.53123	−	2.66273i	−0.138934	−	0.104764i
$647$	−43.8308			−1.72316			−0.861582	−	0.507618i	$-0.830526\pi$
$647$	−43.8308			−1.72316			−0.861582	+	0.507618i	$0.830526\pi$
$648$		0			0
$649$	13.9099	+	24.0926i	0.546010	+	0.945718i
$650$	−0.260619	+	0.451406i	−0.0102223	+	0.0177056i
$651$		0			0
$652$	5.86471	−	10.1580i	0.229680	−	0.397817i
$653$	−26.9486			−1.05458			−0.527291	−	0.849685i	$-0.676792\pi$
$653$	−26.9486			−1.05458			−0.527291	+	0.849685i	$0.676792\pi$
$654$		0			0
$655$	22.8281	−	39.5394i	0.891967	−	1.54493i
$656$	−7.32170	+	12.6816i	−0.285865	+	0.495132i
$657$		0			0
$658$	1.27408			0.0496687
$659$	18.9668	−	32.8514i	0.738840	−	1.27971i	−0.214178	−	0.976795i	$-0.568707\pi$
$659$	18.9668	−	32.8514i	0.738840	−	1.27971i	0.953018	−	0.302914i	$-0.0979593\pi$
$660$		0			0
$661$	6.18965	−	10.7208i	0.240749	−	0.416990i	−0.720179	−	0.693789i	$-0.755940\pi$
$661$	6.18965	−	10.7208i	0.240749	−	0.416990i	0.960928	+	0.276799i	$0.0892735\pi$
$662$	−7.03813	−	12.1904i	−0.273545	−	0.473793i
$663$		0			0
$664$	−27.8370			−1.08028
$665$	−9.38103	+	3.97849i	−0.363781	+	0.154279i
$666$		0			0
$667$	−0.784146	−	1.35818i	−0.0303623	−	0.0525890i
$668$	−15.5768	−	26.9798i	−0.602685	−	1.04388i
$669$		0			0
$670$	−1.42992	−	2.47669i	−0.0552424	−	0.0956827i
$671$	−13.1207	+	22.7257i	−0.506519	+	0.877317i
$672$		0			0
$673$	46.7887			1.80357			0.901786	−	0.432183i	$-0.142256\pi$
$673$	46.7887			1.80357			0.901786	+	0.432183i	$0.142256\pi$
$674$	−0.555054	+	0.961382i	−0.0213799	+	0.0370310i
$675$		0			0
$676$	20.1059			0.773305
$677$	34.4443			1.32380			0.661901	−	0.749591i	$-0.269750\pi$
$677$	34.4443			1.32380			0.661901	+	0.749591i	$0.269750\pi$
$678$		0			0
$679$	6.34628	+	10.9921i	0.243548	+	0.421837i
$680$	3.92981	−	6.80663i	0.150701	−	0.261022i
$681$		0			0
$682$	0.748931	+	1.29719i	0.0286780	+	0.0496718i
$683$	15.5415			0.594679			0.297339	−	0.954772i	$-0.403901\pi$
$683$	15.5415			0.594679			0.297339	+	0.954772i	$0.403901\pi$
$684$		0			0
$685$	−13.4171			−0.512640
$686$	−3.15765	−	5.46921i	−0.120560	−	0.208815i
$687$		0			0
$688$	−14.8258	+	25.6790i	−0.565227	+	0.979001i
$689$	−7.44388	−	12.8932i	−0.283589	−	0.491191i
$690$		0			0
$691$	−11.0740			−0.421273			−0.210637	−	0.977564i	$-0.567554\pi$
$691$	−11.0740			−0.421273			−0.210637	+	0.977564i	$0.567554\pi$
$692$	−16.9411			−0.644004
$693$		0			0
$694$	2.02413	−	3.50589i	0.0768349	−	0.133082i
$695$	−31.2576			−1.18567
$696$		0			0
$697$	−5.89521	+	10.2108i	−0.223297	+	0.386762i
$698$	−2.16036	−	3.74185i	−0.0817707	−	0.141631i
$699$		0			0
$700$	0.908871	+	1.57421i	0.0343521	+	0.0594996i
$701$	10.7354	+	18.5943i	0.405471	+	0.702296i	0.994376	−	0.105906i	$-0.0337744\pi$
$701$	10.7354	+	18.5943i	0.405471	+	0.702296i	−0.588906	+	0.808202i	$0.700441\pi$
$702$		0			0
$703$	−2.03706	+	16.5470i	−0.0768293	+	0.624082i
$704$	14.1968			0.535063
$705$		0			0
$706$	6.00094	+	10.3939i	0.225848	+	0.391181i
$707$	4.60474	−	7.97565i	0.173179	−	0.299955i
$708$		0			0
$709$	24.1154	−	41.7691i	0.905674	−	1.56867i	0.0856629	−	0.996324i	$-0.472699\pi$
$709$	24.1154	−	41.7691i	0.905674	−	1.56867i	0.820011	−	0.572348i	$-0.193967\pi$
$710$	−6.98987			−0.262325
$711$		0			0
$712$	−9.21167	+	15.9551i	−0.345222	+	0.597942i
$713$	−1.18514	+	2.05272i	−0.0443837	+	0.0768749i
$714$		0			0
$715$	10.3602			0.387450
$716$	−11.8052	+	20.4473i	−0.441182	+	0.764150i
$717$		0			0
$718$	7.44640	−	12.8976i	0.277897	−	0.481332i
$719$	−19.2396	−	33.3240i	−0.717517	−	1.24278i	−0.961981	−	0.273117i	$-0.911945\pi$
$719$	−19.2396	−	33.3240i	−0.717517	−	1.24278i	0.244464	−	0.969658i	$-0.421388\pi$
$720$		0			0
$721$	15.6441			0.582616
$722$	2.26270	+	7.90997i	0.0842090	+	0.294379i
$723$		0			0
$724$	−11.4812	−	19.8861i	−0.426697	−	0.739061i
$725$	0.270162	+	0.467934i	0.0100336	+	0.0173786i
$726$		0			0
$727$	−21.6478	−	37.4950i	−0.802872	−	1.39061i	−0.917719	−	0.397231i	$-0.869971\pi$
$727$	−21.6478	−	37.4950i	−0.802872	−	1.39061i	0.114847	−	0.993383i	$-0.463362\pi$
$728$	1.31149	−	2.27157i	0.0486072	−	0.0841901i
$729$		0			0
$730$	−4.18360			−0.154842
$731$	−11.9372	+	20.6759i	−0.441515	+	0.764727i
$732$		0			0
$733$	−13.5020			−0.498708			−0.249354	−	0.968412i	$-0.580218\pi$
$733$	−13.5020			−0.498708			−0.249354	+	0.968412i	$0.580218\pi$
$734$	13.9843			0.516170
$735$		0			0
$736$	−5.77081	−	9.99534i	−0.212715	−	0.368433i
$737$	6.00095	−	10.3940i	0.221048	−	0.382866i
$738$		0			0
$739$	4.89763	+	8.48294i	0.180162	+	0.312050i	0.941936	−	0.335793i	$-0.109004\pi$
$739$	4.89763	+	8.48294i	0.180162	+	0.312050i	−0.761773	+	0.647843i	$0.775671\pi$
$740$	−14.0856			−0.517795
$741$		0			0
$742$	5.37091			0.197172
$743$	4.56485	+	7.90655i	0.167468	+	0.290063i	0.937529	−	0.347907i	$-0.113108\pi$
$743$	4.56485	+	7.90655i	0.167468	+	0.290063i	−0.770061	+	0.637970i	$0.779774\pi$
$744$		0			0
$745$	−2.06862	+	3.58296i	−0.0757884	+	0.131269i
$746$	7.64195	+	13.2362i	0.279792	+	0.484614i
$747$		0			0
$748$	15.6812			0.573362
$749$	−13.4913			−0.492962
$750$		0			0
$751$	5.21254	−	9.02838i	0.190208	−	0.329450i	−0.755111	−	0.655597i	$-0.772417\pi$
$751$	5.21254	−	9.02838i	0.190208	−	0.329450i	0.945319	+	0.326147i	$0.105750\pi$
$752$	−7.44234			−0.271394
$753$		0			0
$754$	0.185334	−	0.321009i	0.00674948	−	0.0116904i
$755$	13.6695	+	23.6762i	0.497483	+	0.861667i
$756$		0			0
$757$	−3.89716	−	6.75008i	−0.141645	−	0.245336i	0.786471	−	0.617627i	$-0.211906\pi$
$757$	−3.89716	−	6.75008i	−0.141645	−	0.245336i	−0.928116	+	0.372291i	$0.878572\pi$
$758$	−5.20526	−	9.01577i	−0.189064	−	0.327468i
$759$		0			0
$760$	−13.4604	+	5.70856i	−0.488261	+	0.207071i
$761$	−36.7419			−1.33189			−0.665947	−	0.745999i	$-0.731972\pi$
$761$	−36.7419			−1.33189			−0.665947	+	0.745999i	$0.731972\pi$
$762$		0			0
$763$	−7.89496	−	13.6745i	−0.285817	−	0.495049i
$764$	−17.8458	+	30.9099i	−0.645639	+	1.11828i
$765$		0			0
$766$	−1.45463	+	2.51949i	−0.0525579	+	0.0910329i
$767$	−10.4049			−0.375700
$768$		0			0
$769$	−4.07642	+	7.06056i	−0.146999	+	0.254610i	−0.930117	−	0.367263i	$-0.880295\pi$
$769$	−4.07642	+	7.06056i	−0.146999	+	0.254610i	0.783118	+	0.621874i	$0.213628\pi$
$770$	−1.86878	+	3.23682i	−0.0673461	+	0.116647i
$771$		0			0
$772$	−2.77836			−0.0999955
$773$	−9.24856	+	16.0190i	−0.332648	+	0.576163i	−0.983030	−	0.183444i	$-0.941275\pi$
$773$	−9.24856	+	16.0190i	−0.332648	+	0.576163i	0.650382	+	0.759607i	$0.274609\pi$
$774$		0			0
$775$	0.408315	−	0.707223i	0.0146671	−	0.0254042i
$776$	9.10601	+	15.7721i	0.326887	+	0.566184i
$777$		0			0
$778$	−15.7827			−0.565838
$779$	20.1924	−	8.56357i	0.723467	−	0.306822i
$780$		0			0
$781$	−14.6673	−	25.4044i	−0.524836	−	0.909043i
$782$	−1.28351	−	2.22311i	−0.0458983	−	0.0794981i
$783$		0			0
$784$	8.25940	+	14.3057i	0.294978	+	0.510918i
$785$	7.98036	−	13.8224i	0.284831	−	0.493342i
$786$		0			0
$787$	16.0647			0.572643			0.286322	−	0.958134i	$-0.407567\pi$
$787$	16.0647			0.572643			0.286322	+	0.958134i	$0.407567\pi$
$788$	3.64281	−	6.30953i	0.129770	−	0.224768i
$789$		0			0
$790$	5.11690			0.182051
$791$	−19.5353			−0.694595
$792$		0			0
$793$	−4.90730	−	8.49970i	−0.174263	−	0.301833i
$794$	−1.09321	+	1.89350i	−0.0387967	+	0.0671978i
$795$		0			0
$796$	6.82883	+	11.8279i	0.242041	+	0.419228i
$797$	−6.01294			−0.212989			−0.106495	−	0.994313i	$-0.533963\pi$
$797$	−6.01294			−0.212989			−0.106495	+	0.994313i	$0.533963\pi$
$798$		0			0
$799$	−5.99235			−0.211994
$800$	1.98822	+	3.44370i	0.0702941	+	0.121753i
$801$		0			0
$802$	2.41270	−	4.17892i	0.0851954	−	0.147563i
$803$	−8.77869	−	15.2051i	−0.309793	−	0.536578i
$804$		0			0
$805$	−5.91445			−0.208457
$806$	−0.560219			−0.0197329
$807$		0			0
$808$	6.60715	−	11.4439i	0.232439	−	0.402596i
$809$	0.0546010			0.00191967			0.000959834	−	1.00000i	$-0.499694\pi$
$809$	0.0546010			0.00191967			0.000959834		1.00000i	$0.499694\pi$
$810$		0			0
$811$	13.0470	−	22.5981i	0.458143	−	0.793527i	−0.540720	−	0.841203i	$-0.681848\pi$
$811$	13.0470	−	22.5981i	0.458143	−	0.793527i	0.998863	+	0.0476759i	$0.0151815\pi$
$812$	−0.646326	−	1.11947i	−0.0226816	−	0.0392857i
$813$		0			0
$814$	3.05758	+	5.29588i	0.107168	+	0.185620i
$815$	−6.57439	−	11.3872i	−0.230291	−	0.398875i
$816$		0			0
$817$	40.8877	−	17.3404i	1.43048	−	0.606665i
$818$	2.13218			0.0745500
$819$		0			0
$820$	9.26533	+	16.0480i	0.323559	+	0.560421i
$821$	−12.2698	+	21.2520i	−0.428220	+	0.741699i	−0.996715	−	0.0809878i	$-0.974193\pi$
$821$	−12.2698	+	21.2520i	−0.428220	+	0.741699i	0.568495	+	0.822687i	$0.307526\pi$
$822$		0			0
$823$	−1.95109	+	3.37939i	−0.0680108	+	0.117798i	−0.898026	−	0.439943i	$-0.854999\pi$
$823$	−1.95109	+	3.37939i	−0.0680108	+	0.117798i	0.830015	+	0.557741i	$0.188332\pi$
$824$	22.4470			0.781979
$825$		0			0
$826$	1.87684	−	3.25079i	0.0653037	−	0.113109i
$827$	11.1046	−	19.2337i	0.386145	−	0.668822i	−0.605783	−	0.795630i	$-0.707140\pi$
$827$	11.1046	−	19.2337i	0.386145	−	0.668822i	0.991927	+	0.126808i	$0.0404732\pi$
$828$		0			0
$829$	40.1536			1.39459			0.697296	−	0.716784i	$-0.254387\pi$
$829$	40.1536			1.39459			0.697296	+	0.716784i	$0.254387\pi$
$830$	−7.41770	+	12.8478i	−0.257472	+	0.445955i
$831$		0			0
$832$	−2.65489	+	4.59841i	−0.0920418	+	0.159421i
$833$	6.65021	+	11.5185i	0.230416	+	0.399093i
$834$		0			0
$835$	−34.9235			−1.20858
$836$	−23.2915	−	17.5630i	−0.805553	−	0.607430i
$837$		0			0
$838$	−3.07173	−	5.32040i	−0.106111	−	0.183790i
$839$	−8.80697	−	15.2541i	−0.304050	−	0.526631i	0.672999	−	0.739643i	$-0.265006\pi$
$839$	−8.80697	−	15.2541i	−0.304050	−	0.526631i	−0.977049	+	0.213013i	$0.931672\pi$
$840$		0			0
$841$	14.3079	+	24.7820i	0.493375	+	0.854551i
$842$	−3.68376	+	6.38045i	−0.126951	+	0.219885i
$843$		0			0
$844$	5.78431			0.199104
$845$	11.2695	−	19.5193i	0.387681	−	0.671484i
$846$		0			0
$847$	−3.02953			−0.104096
$848$	−31.3734			−1.07737
$849$		0			0
$850$	0.442208	+	0.765927i	0.0151676	+	0.0262711i
$851$	−4.83843	+	8.38040i	−0.165859	+	0.287276i
$852$		0			0
$853$	1.55952	+	2.70117i	0.0533970	+	0.0924862i	0.891488	−	0.453044i	$-0.149662\pi$
$853$	1.55952	+	2.70117i	0.0533970	+	0.0924862i	−0.838091	+	0.545530i	$0.816328\pi$
$854$	3.54072			0.121161
$855$		0			0
$856$	−19.3581			−0.661647
$857$	−9.52181	−	16.4923i	−0.325259	−	0.563365i	0.656306	−	0.754495i	$-0.272118\pi$
$857$	−9.52181	−	16.4923i	−0.325259	−	0.563365i	−0.981565	+	0.191130i	$0.938785\pi$
$858$		0			0
$859$	9.75554	−	16.8971i	0.332855	−	0.576522i	−0.650216	−	0.759750i	$-0.725321\pi$
$859$	9.75554	−	16.8971i	0.332855	−	0.576522i	0.983070	+	0.183228i	$0.0586547\pi$
$860$	18.7614	+	32.4957i	0.639759	+	1.10810i
$861$		0			0
$862$	−0.844334			−0.0287581
$863$	−28.7796			−0.979670			−0.489835	−	0.871815i	$-0.662943\pi$
$863$	−28.7796			−0.979670			−0.489835	+	0.871815i	$0.662943\pi$
$864$		0			0
$865$	−9.49557	+	16.4468i	−0.322859	+	0.559208i
$866$	−12.7134			−0.432018
$867$		0			0
$868$	−0.976839	+	1.69194i	−0.0331561	+	0.0574280i
$869$	10.7371	+	18.5972i	0.364231	+	0.630866i
$870$		0			0
$871$	2.24443	+	3.88747i	0.0760496	+	0.131722i
$872$	−11.3281	−	19.6209i	−0.383619	−	0.664448i
$873$		0			0
$874$	−0.583474	+	4.73954i	−0.0197363	+	0.160317i
$875$	13.7262			0.464031
$876$		0			0
$877$	26.2114	+	45.3995i	0.885096	+	1.53303i	0.845604	+	0.533811i	$0.179240\pi$
$877$	26.2114	+	45.3995i	0.885096	+	1.53303i	0.0394915	+	0.999220i	$0.487426\pi$
$878$	2.31994	−	4.01825i	0.0782941	−	0.135609i
$879$		0			0
$880$	10.9162	−	18.9074i	0.367985	−	0.637369i
$881$	−10.4947			−0.353575			−0.176788	−	0.984249i	$-0.556571\pi$
$881$	−10.4947			−0.353575			−0.176788	+	0.984249i	$0.556571\pi$
$882$		0			0
$883$	−20.0002	+	34.6413i	−0.673059	+	1.16577i	0.303973	+	0.952681i	$0.401687\pi$
$883$	−20.0002	+	34.6413i	−0.673059	+	1.16577i	−0.977032	+	0.213092i	$0.931647\pi$
$884$	−2.93248	+	5.07921i	−0.0986300	+	0.170832i
$885$		0			0
$886$	8.58872			0.288544
$887$	6.27708	−	10.8722i	0.210764	−	0.365054i	−0.741190	−	0.671295i	$-0.765738\pi$
$887$	6.27708	−	10.8722i	0.210764	−	0.365054i	0.951954	+	0.306242i	$0.0990716\pi$
$888$		0			0
$889$	−6.29626	+	10.9054i	−0.211170	+	0.365757i
$890$	4.90925	+	8.50308i	0.164559	+	0.285024i
$891$		0			0
$892$	26.0909			0.873588
$893$	8.90051	+	6.71145i	0.297844	+	0.224590i
$894$		0			0
$895$	13.2338	+	22.9216i	0.442356	+	0.766183i
$896$	−6.20638	−	10.7498i	−0.207341	−	0.359124i
$897$		0			0
$898$	−5.43578	−	9.41504i	−0.181394	−	0.314184i
$899$	−0.290365	+	0.502928i	−0.00968423	+	0.0167736i
$900$		0			0
$901$	−25.2609			−0.841563
$902$	4.02249	−	6.96715i	0.133934	−	0.231981i
$903$		0			0
$904$	−28.0303			−0.932275
$905$	−25.7411			−0.855665
$906$		0			0
$907$	−16.5241	−	28.6206i	−0.548673	−	0.950330i	−0.998366	−	0.0571467i	$-0.981800\pi$
$907$	−16.5241	−	28.6206i	−0.548673	−	0.950330i	0.449692	−	0.893183i	$-0.351534\pi$
$908$	8.05470	−	13.9511i	0.267305	−	0.462985i
$909$		0			0
$910$	−0.698946	−	1.21061i	−0.0231698	−	0.0401313i
$911$	45.8125			1.51784			0.758918	−	0.651186i	$-0.225728\pi$
$911$	45.8125			1.51784			0.758918	+	0.651186i	$0.225728\pi$
$912$		0			0
$913$	−62.2600			−2.06051
$914$	−2.19572	−	3.80310i	−0.0726281	−	0.125795i
$915$		0			0
$916$	−6.19738	+	10.7342i	−0.204767	+	0.354667i
$917$	−12.9266	−	22.3895i	−0.426874	−	0.739367i
$918$		0			0
$919$	−41.5838			−1.37172			−0.685861	−	0.727733i	$-0.740574\pi$
$919$	−41.5838			−1.37172			−0.685861	+	0.727733i	$0.740574\pi$
$920$	−8.48639			−0.279788
$921$		0			0
$922$	4.44287	−	7.69527i	0.146318	−	0.253430i
$923$	10.9715			0.361130
$924$		0			0
$925$	1.66698	−	2.88730i	0.0548101	−	0.0949339i
$926$	−4.35191	−	7.53773i	−0.143013	−	0.247705i
$927$		0			0
$928$	−1.41388	−	2.44892i	−0.0464130	−	0.0803896i
$929$	4.29016	+	7.43077i	0.140755	+	0.243796i	0.927781	−	0.373124i	$-0.121714\pi$
$929$	4.29016	+	7.43077i	0.140755	+	0.243796i	−0.787026	+	0.616920i	$0.788380\pi$
$930$		0			0
$931$	3.02313	−	24.5568i	0.0990792	−	0.804818i
$932$	−1.88024			−0.0615894
$933$		0			0
$934$	−2.91040	−	5.04097i	−0.0952313	−	0.164945i
$935$	8.78939	−	15.2237i	0.287444	−	0.497867i
$936$		0			0
$937$	3.34450	−	5.79284i	0.109260	−	0.189244i	−0.806211	−	0.591629i	$-0.798485\pi$
$937$	3.34450	−	5.79284i	0.109260	−	0.189244i	0.915471	+	0.402385i	$0.131819\pi$
$938$	−1.61940			−0.0528754
$939$		0			0
$940$	−4.70900	+	8.15623i	−0.153591	+	0.266027i
$941$	6.78214	−	11.7470i	0.221091	−	0.382942i	−0.734048	−	0.679097i	$-0.762371\pi$
$941$	6.78214	−	11.7470i	0.221091	−	0.382942i	0.955140	+	0.296156i	$0.0957047\pi$
$942$		0			0
$943$	12.7307			0.414568
$944$	−10.9633	+	18.9890i	−0.356825	+	0.618039i
$945$		0			0
$946$	8.14515	−	14.1078i	0.264822	−	0.458685i
$947$	−13.1474	−	22.7720i	−0.427234	−	0.739990i	0.569392	−	0.822066i	$-0.307179\pi$
$947$	−13.1474	−	22.7720i	−0.427234	−	0.739990i	−0.996626	+	0.0820754i	$0.973845\pi$
$948$		0			0
$949$	6.56668			0.213163
$950$	0.201024	−	1.63292i	0.00652209	−	0.0529788i
$951$		0			0
$952$	−2.22529	−	3.85431i	−0.0721220	−	0.124919i
$953$	3.79223	+	6.56834i	0.122842	+	0.212769i	0.920888	−	0.389828i	$-0.127466\pi$
$953$	3.79223	+	6.56834i	0.122842	+	0.212769i	−0.798045	+	0.602598i	$0.794132\pi$
$954$		0			0
$955$	20.0053	+	34.6502i	0.647357	+	1.12126i
$956$	−16.8523	+	29.1890i	−0.545042	+	0.944040i
$957$		0			0
$958$	0.574044			0.0185465
$959$	−3.79876	+	6.57965i	−0.122669	+	0.212468i
$960$		0			0
$961$	−30.1223			−0.971687
$962$	−2.28714			−0.0737404
$963$		0			0
$964$	24.1855	+	41.8905i	0.778963	+	1.34920i
$965$	−1.55729	+	2.69730i	−0.0501308	+	0.0868291i
$966$		0			0
$967$	−1.07288	−	1.85829i	−0.0345016	−	0.0597584i	0.848259	−	0.529582i	$-0.177651\pi$
$967$	−1.07288	−	1.85829i	−0.0345016	−	0.0597584i	−0.882761	+	0.469823i	$0.844318\pi$
$968$	−4.34694			−0.139716
$969$		0			0
$970$	9.70589			0.311637
$971$	−9.55697	−	16.5532i	−0.306698	−	0.531216i	0.670940	−	0.741512i	$-0.265891\pi$
$971$	−9.55697	−	16.5532i	−0.306698	−	0.531216i	−0.977638	+	0.210295i	$0.932557\pi$
$972$		0			0
$973$	−8.84994	+	15.3285i	−0.283716	+	0.491411i
$974$	1.22368	+	2.11947i	0.0392092	+	0.0679123i
$975$		0			0
$976$	−20.6826			−0.662035
$977$	45.5157			1.45618			0.728089	−	0.685483i	$-0.240409\pi$
$977$	45.5157			1.45618			0.728089	+	0.685483i	$0.240409\pi$
$978$		0			0
$979$	−20.6028	+	35.6850i	−0.658467	+	1.14050i
$980$	20.9039			0.667750
$981$		0			0
$982$	8.97726	−	15.5491i	0.286476	−	0.496191i
$983$	−8.52072	−	14.7583i	−0.271769	−	0.470717i	0.697546	−	0.716540i	$-0.254275\pi$
$983$	−8.52072	−	14.7583i	−0.271769	−	0.470717i	−0.969315	+	0.245823i	$0.920942\pi$
$984$		0			0
$985$	−4.08362	−	7.07304i	−0.130115	−	0.225366i
$986$	−0.314468	−	0.544674i	−0.0100147	−	0.0173460i
$987$		0			0
$988$	10.0444	−	4.25981i	0.319554	−	0.135523i
$989$	25.7784			0.819705
$990$		0			0
$991$	5.64050	+	9.76963i	0.179176	+	0.310343i	0.941599	−	0.336737i	$-0.109323\pi$
$991$	5.64050	+	9.76963i	0.179176	+	0.310343i	−0.762422	+	0.647080i	$0.775990\pi$
$992$	−2.13690	+	3.70122i	−0.0678467	+	0.117514i
$993$		0			0
$994$	−1.97904	+	3.42779i	−0.0627712	+	0.108723i
$995$	15.3104			0.485371
$996$		0			0
$997$	26.1792	−	45.3437i	0.829104	−	1.43605i	−0.0696383	−	0.997572i	$-0.522185\pi$
$997$	26.1792	−	45.3437i	0.829104	−	1.43605i	0.898742	−	0.438478i	$-0.144482\pi$
$998$	0.0712660	−	0.123436i	0.00225589	−	0.00390731i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.f.h.406.3	yes	12
3.2	odd	2		513.2.f.f.406.4	yes	12
19.7	even	3		9747.2.a.bl.1.4		6
19.11	even	3	inner	513.2.f.h.163.3	yes	12
19.12	odd	6		9747.2.a.br.1.3		6
57.11	odd	6		513.2.f.f.163.4	✓	12
57.26	odd	6		9747.2.a.bs.1.3		6
57.50	even	6		9747.2.a.bm.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
513.2.f.f.163.4	✓	12	57.11	odd	6
513.2.f.f.406.4	yes	12	3.2	odd	2
513.2.f.h.163.3	yes	12	19.11	even	3	inner
513.2.f.h.406.3	yes	12	1.1	even	1	trivial
9747.2.a.bl.1.4		6	19.7	even	3
9747.2.a.bm.1.4		6	57.50	even	6
9747.2.a.br.1.3		6	19.12	odd	6
9747.2.a.bs.1.3		6	57.26	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.216506 - 0.375000i) q^{2} +(0.906250 - 1.56967i) q^{4} +(-1.01591 - 1.75962i) q^{5} -1.15054 q^{7} -1.65086 q^{8} +(-0.439904 + 0.761936i) q^{10} -3.69231 q^{11} +(0.690484 - 1.19595i) q^{13} +(0.249099 + 0.431453i) q^{14} +(-1.45508 - 2.52027i) q^{16} +(-1.17158 - 2.02924i) q^{17} +(-0.532593 + 4.32624i) q^{19} -3.68269 q^{20} +(0.799408 + 1.38462i) q^{22} +(-1.26501 + 2.19107i) q^{23} +(0.435835 - 0.754889i) q^{25} -0.597977 q^{26} +(-1.04268 + 1.80597i) q^{28} +(-0.309936 + 0.536825i) q^{29} +0.936857 q^{31} +(-2.28093 + 3.95068i) q^{32} +(-0.507311 + 0.878688i) q^{34} +(1.16885 + 2.02451i) q^{35} +3.82480 q^{37} +(1.73765 - 0.736936i) q^{38} +(1.67713 + 2.90488i) q^{40} +(-2.51591 - 4.35769i) q^{41} +(-5.09449 - 8.82391i) q^{43} +(-3.34615 + 5.79571i) q^{44} +1.09553 q^{46} +(1.27868 - 2.21475i) q^{47} -5.67626 q^{49} -0.377445 q^{50} +(-1.25150 - 2.16767i) q^{52} +(5.39033 - 9.33633i) q^{53} +(3.75107 + 6.49704i) q^{55} +1.89938 q^{56} +0.268412 q^{58} +(-3.76726 - 6.52508i) q^{59} +(3.55352 - 6.15488i) q^{61} +(-0.202835 - 0.351321i) q^{62} -3.84497 q^{64} -2.80589 q^{65} +(-1.62526 + 2.81503i) q^{67} -4.24699 q^{68} +(0.506127 - 0.876638i) q^{70} +(3.97238 + 6.88037i) q^{71} +(2.37756 + 4.11806i) q^{73} +(-0.828094 - 1.43430i) q^{74} +(6.30811 + 4.75665i) q^{76} +4.24815 q^{77} +(-2.90796 - 5.03674i) q^{79} +(-2.95647 + 5.12076i) q^{80} +(-1.08942 + 1.88694i) q^{82} +16.8621 q^{83} +(-2.38046 + 4.12308i) q^{85} +(-2.20598 + 3.82087i) q^{86} +6.09549 q^{88} +(5.57992 - 9.66470i) q^{89} +(-0.794430 + 1.37599i) q^{91} +(2.29284 + 3.97131i) q^{92} -1.10737 q^{94} +(8.15359 - 3.45793i) q^{95} +(-5.51591 - 9.55384i) q^{97} +(1.22895 + 2.12860i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - 3 q^{4} + 5 q^{5} + 2 q^{7} - 12 q^{8} + q^{10} - 4 q^{11} - 5 q^{13} + 2 q^{14} + 3 q^{16} + 10 q^{17} - 9 q^{19} - 2 q^{20} - 4 q^{22} + 3 q^{23} - 5 q^{25} - 2 q^{26} - 2 q^{28} - 6 q^{29}+ \cdots - 59 q^{98}+O(q^{100}) \) 12 * q + q^2 - 3 * q^4 + 5 * q^5 + 2 * q^7 - 12 * q^8 + q^10 - 4 * q^11 - 5 * q^13 + 2 * q^14 + 3 * q^16 + 10 * q^17 - 9 * q^19 - 2 * q^20 - 4 * q^22 + 3 * q^23 - 5 * q^25 - 2 * q^26 - 2 * q^28 - 6 * q^29 - 4 * q^31 + 8 * q^32 + 4 * q^34 + 3 * q^35 + 26 * q^37 - 10 * q^38 - 6 * q^40 - 13 * q^41 - 3 * q^43 - 20 * q^44 - 10 * q^46 + 18 * q^47 + 26 * q^49 + 6 * q^50 - 22 * q^52 - q^53 - 6 * q^55 + 48 * q^56 + 28 * q^58 + 11 * q^59 - 13 * q^61 + 22 * q^62 - 72 * q^65 + 9 * q^67 - 10 * q^68 - 30 * q^70 - 6 * q^71 - 15 * q^73 + 43 * q^74 - 33 * q^76 - 58 * q^77 - 13 * q^79 + q^80 + 4 * q^82 - 16 * q^83 - 3 * q^85 - 7 * q^86 - 30 * q^88 + 29 * q^89 + 22 * q^91 + 21 * q^92 + 36 * q^94 + 22 * q^95 + 20 * q^97 - 59 * q^98

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