LMFDB - Embedded newform 216.2.l.b.179.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(35,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("216.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.6
Root			$-0.533474 + 1.30973i$ of defining polynomial
Character	$\chi$	$=$	216.179
Dual form			216.2.l.b.35.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.867527 + 1.11687i) q^{2} +(-0.494795 + 1.93783i) q^{4} +(-0.895377 + 1.55084i) q^{5} +(-2.08793 + 1.20546i) q^{7} +(-2.59355 + 1.12850i) q^{8} +O(q^{10})$	\(q+(0.867527 + 1.11687i) q^{2} +(-0.494795 + 1.93783i) q^{4} +(-0.895377 + 1.55084i) q^{5} +(-2.08793 + 1.20546i) q^{7} +(-2.59355 + 1.12850i) q^{8} +(-2.50885 + 0.345375i) q^{10} +(1.36975 - 0.790826i) q^{11} +(5.35491 + 3.09166i) q^{13} +(-3.15768 - 1.28617i) q^{14} +(-3.51036 - 1.91766i) q^{16} -3.69943i q^{17} +3.12941 q^{19} +(-2.56223 - 2.50243i) q^{20} +(2.07154 + 0.843770i) q^{22} +(1.36036 - 2.35622i) q^{23} +(0.896599 + 1.55296i) q^{25} +(1.19255 + 8.66283i) q^{26} +(-1.30289 - 4.64250i) q^{28} +(2.55291 + 4.42177i) q^{29} +(-5.95312 - 3.43703i) q^{31} +(-0.903557 - 5.58423i) q^{32} +(4.13178 - 3.20936i) q^{34} -4.31738i q^{35} -5.24328i q^{37} +(2.71485 + 3.49514i) q^{38} +(0.572089 - 5.03261i) q^{40} +(5.32220 + 3.07278i) q^{41} +(-0.452455 - 0.783675i) q^{43} +(0.854739 + 3.04564i) q^{44} +(3.81174 - 0.524733i) q^{46} +(-4.88993 - 8.46960i) q^{47} +(-0.593711 + 1.02834i) q^{49} +(-0.956625 + 2.34861i) q^{50} +(-8.64069 + 8.84716i) q^{52} +7.05913 q^{53} +2.83235i q^{55} +(4.05478 - 5.48265i) q^{56} +(-2.72382 + 6.68727i) q^{58} +(6.10118 + 3.52252i) q^{59} +(-3.05109 + 1.76155i) q^{61} +(-1.32577 - 9.63057i) q^{62} +(5.45299 - 5.85362i) q^{64} +(-9.58933 + 5.53640i) q^{65} +(1.03786 - 1.79762i) q^{67} +(7.16886 + 1.83046i) q^{68} +(4.82195 - 3.74544i) q^{70} -3.31507 q^{71} +0.631029 q^{73} +(5.85606 - 4.54868i) q^{74} +(-1.54842 + 6.06426i) q^{76} +(-1.90662 + 3.30237i) q^{77} +(7.82515 - 4.51785i) q^{79} +(6.11707 - 3.72697i) q^{80} +(1.18526 + 8.60992i) q^{82} +(-13.5542 + 7.82551i) q^{83} +(5.73722 + 3.31239i) q^{85} +(0.482746 - 1.18519i) q^{86} +(-2.66007 + 3.59680i) q^{88} +1.16402i q^{89} -14.9075 q^{91} +(3.89284 + 3.80199i) q^{92} +(5.21730 - 12.8090i) q^{94} +(-2.80200 + 4.85321i) q^{95} +(-6.72981 - 11.6564i) q^{97} +(-1.66358 + 0.229013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) $ 16 * q + 3 * q^2 - 5 * q^4	$ 16 q + 3 q^{2} - 5 q^{4} - 12 q^{11} + 18 q^{14} + 7 q^{16} - 4 q^{19} - 18 q^{20} - q^{22} - 14 q^{25} - 12 q^{28} - 27 q^{32} - 13 q^{34} + 15 q^{38} - 12 q^{40} + 36 q^{41} + 8 q^{43} + 12 q^{46} + 10 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 12 q^{59} + 34 q^{64} + 6 q^{65} - 16 q^{67} + 9 q^{68} + 18 q^{70} - 4 q^{73} + 60 q^{74} - 7 q^{76} - 22 q^{82} - 54 q^{83} + 51 q^{86} - 13 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 16 * q + 3 * q^2 - 5 * q^4 - 12 * q^11 + 18 * q^14 + 7 * q^16 - 4 * q^19 - 18 * q^20 - q^22 - 14 * q^25 - 12 * q^28 - 27 * q^32 - 13 * q^34 + 15 * q^38 - 12 * q^40 + 36 * q^41 + 8 * q^43 + 12 * q^46 + 10 * q^49 - 51 * q^50 - 18 * q^52 + 66 * q^56 + 12 * q^58 - 12 * q^59 + 34 * q^64 + 6 * q^65 - 16 * q^67 + 9 * q^68 + 18 * q^70 - 4 * q^73 + 60 * q^74 - 7 * q^76 - 22 * q^82 - 54 * q^83 + 51 * q^86 - 13 * q^88 - 36 * q^91 - 84 * q^92 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.867527	+	1.11687i	0.613434	+	0.789746i
$2$	0.867527	+	1.11687i	0.613434	+	0.789746i
$3$		0			0
$3$		0			0
$4$	−0.494795	+	1.93783i	−0.247397	+	0.968914i
$5$	−0.895377	+	1.55084i	−0.400425	+	0.693556i	−0.993777	−	0.111387i	$-0.964471\pi$
$5$	−0.895377	+	1.55084i	−0.400425	+	0.693556i	0.593352	+	0.804943i	$0.297804\pi$
$6$		0			0
$7$	−2.08793	+	1.20546i	−0.789162	+	0.455623i	−0.839667	−	0.543101i	$-0.817250\pi$
$7$	−2.08793	+	1.20546i	−0.789162	+	0.455623i	0.0505056	+	0.998724i	$0.483917\pi$
$8$	−2.59355	+	1.12850i	−0.916958	+	0.398984i
$9$		0			0
$10$	−2.50885	+	0.345375i	−0.793368	+	0.109217i
$11$	1.36975	−	0.790826i	0.412995	−	0.238443i	−0.279081	−	0.960268i	$-0.590030\pi$
$11$	1.36975	−	0.790826i	0.412995	−	0.238443i	0.692076	+	0.721825i	$0.256696\pi$
$12$		0			0
$13$	5.35491	+	3.09166i	1.48519	+	0.857472i	0.999858	−	0.0168604i	$-0.00536707\pi$
$13$	5.35491	+	3.09166i	1.48519	+	0.857472i	0.485327	+	0.874332i	$0.338700\pi$
$14$	−3.15768	−	1.28617i	−0.843925	−	0.343743i
$15$		0			0
$16$	−3.51036	−	1.91766i	−0.877589	−	0.479414i
$17$		−	3.69943i		−	0.897244i	−0.893722	−	0.448622i	$-0.851915\pi$
$17$		−	3.69943i		−	0.897244i	0.893722	−	0.448622i	$-0.148085\pi$
$18$		0			0
$19$	3.12941			0.717936			0.358968	−	0.933350i	$-0.383129\pi$
$19$	3.12941			0.717936			0.358968	+	0.933350i	$0.383129\pi$
$20$	−2.56223	−	2.50243i	−0.572932	−	0.559561i
$21$		0			0
$22$	2.07154	+	0.843770i	0.441655	+	0.179892i
$23$	1.36036	−	2.35622i	0.283655	−	0.491305i	−0.688627	−	0.725116i	$-0.741786\pi$
$23$	1.36036	−	2.35622i	0.283655	−	0.491305i	0.972282	+	0.233811i	$0.0751196\pi$
$24$		0			0
$25$	0.896599	+	1.55296i	0.179320	+	0.310591i
$26$	1.19255	+	8.66283i	0.233878	+	1.69892i
$27$		0			0
$28$	−1.30289	−	4.64250i	−0.246223	−	0.877350i
$29$	2.55291	+	4.42177i	0.474064	+	0.821102i	0.999559	−	0.0296942i	$-0.00945336\pi$
$29$	2.55291	+	4.42177i	0.474064	+	0.821102i	−0.525495	+	0.850796i	$0.676120\pi$
$30$		0			0
$31$	−5.95312	−	3.43703i	−1.06921	−	0.617310i	−0.141246	−	0.989975i	$-0.545111\pi$
$31$	−5.95312	−	3.43703i	−1.06921	−	0.617310i	−0.927966	+	0.372665i	$0.878444\pi$
$32$	−0.903557	−	5.58423i	−0.159728	−	0.987161i
$33$		0			0
$34$	4.13178	−	3.20936i	0.708595	−	0.550400i
$35$		−	4.31738i		−	0.729771i
$36$		0			0
$37$		−	5.24328i		−	0.861990i	−0.902354	−	0.430995i	$-0.858163\pi$
$37$		−	5.24328i		−	0.861990i	0.902354	−	0.430995i	$-0.141837\pi$
$38$	2.71485	+	3.49514i	0.440406	+	0.566987i
$39$		0			0
$40$	0.572089	−	5.03261i	0.0904552	−	0.795725i
$41$	5.32220	+	3.07278i	0.831189	+	0.479887i	0.854260	−	0.519847i	$-0.174011\pi$
$41$	5.32220	+	3.07278i	0.831189	+	0.479887i	−0.0230708	+	0.999734i	$0.507344\pi$
$42$		0			0
$43$	−0.452455	−	0.783675i	−0.0689987	−	0.119509i	0.829462	−	0.558563i	$-0.188647\pi$
$43$	−0.452455	−	0.783675i	−0.0689987	−	0.119509i	−0.898461	+	0.439054i	$0.855314\pi$
$44$	0.854739	+	3.04564i	0.128857	+	0.459147i
$45$		0			0
$46$	3.81174	−	0.524733i	0.562010	−	0.0773677i
$47$	−4.88993	−	8.46960i	−0.713269	−	1.23542i	−0.963623	−	0.267264i	$-0.913880\pi$
$47$	−4.88993	−	8.46960i	−0.713269	−	1.23542i	0.250354	−	0.968154i	$-0.419453\pi$
$48$		0			0
$49$	−0.593711	+	1.02834i	−0.0848159	+	0.146905i
$50$	−0.956625	+	2.34861i	−0.135287	+	0.332144i
$51$		0			0
$52$	−8.64069	+	8.84716i	−1.19825	+	1.22688i
$53$	7.05913			0.969646			0.484823	−	0.874612i	$-0.338884\pi$
$53$	7.05913			0.969646			0.484823	+	0.874612i	$0.338884\pi$
$54$		0			0
$55$			2.83235i			0.381914i
$56$	4.05478	−	5.48265i	0.541842	−	0.732650i
$57$		0			0
$58$	−2.72382	+	6.68727i	−0.357655	+	0.878082i
$59$	6.10118	+	3.52252i	0.794306	+	0.458593i	0.841476	−	0.540294i	$-0.181687\pi$
$59$	6.10118	+	3.52252i	0.794306	+	0.458593i	−0.0471702	+	0.998887i	$0.515020\pi$
$60$		0			0
$61$	−3.05109	+	1.76155i	−0.390652	+	0.225543i	−0.682443	−	0.730939i	$-0.739082\pi$
$61$	−3.05109	+	1.76155i	−0.390652	+	0.225543i	0.291790	+	0.956482i	$0.405749\pi$
$62$	−1.32577	−	9.63057i	−0.168373	−	1.22308i
$63$		0			0
$64$	5.45299	−	5.85362i	0.681624	−	0.731703i
$65$	−9.58933	+	5.53640i	−1.18941	+	0.686706i
$66$		0			0
$67$	1.03786	−	1.79762i	0.126794	−	0.219614i	−0.795639	−	0.605772i	$-0.792865\pi$
$67$	1.03786	−	1.79762i	0.126794	−	0.219614i	0.922433	+	0.386158i	$0.126198\pi$
$68$	7.16886	+	1.83046i	0.869353	+	0.221976i
$69$		0			0
$70$	4.82195	−	3.74544i	0.576334	−	0.447666i
$71$	−3.31507			−0.393426			−0.196713	−	0.980461i	$-0.563027\pi$
$71$	−3.31507			−0.393426			−0.196713	+	0.980461i	$0.563027\pi$
$72$		0			0
$73$	0.631029			0.0738563			0.0369282	−	0.999318i	$-0.488243\pi$
$73$	0.631029			0.0738563			0.0369282	+	0.999318i	$0.488243\pi$
$74$	5.85606	−	4.54868i	0.680753	−	0.528774i
$75$		0			0
$76$	−1.54842	+	6.06426i	−0.177615	+	0.695618i
$77$	−1.90662	+	3.30237i	−0.217280	+	0.376340i
$78$		0			0
$79$	7.82515	−	4.51785i	0.880398	−	0.508298i	0.00960849	−	0.999954i	$-0.496941\pi$
$79$	7.82515	−	4.51785i	0.880398	−	0.508298i	0.870790	+	0.491656i	$0.163608\pi$
$80$	6.11707	−	3.72697i	0.683909	−	0.416688i
$81$		0			0
$82$	1.18526	+	8.60992i	0.130891	+	0.950807i
$83$	−13.5542	+	7.82551i	−1.48776	+	0.858961i	−0.999903	−	0.0139604i	$-0.995556\pi$
$83$	−13.5542	+	7.82551i	−1.48776	+	0.858961i	−0.487861	+	0.872921i	$0.662223\pi$
$84$		0			0
$85$	5.73722	+	3.31239i	0.622289	+	0.359279i
$86$	0.482746	−	1.18519i	0.0520558	−	0.127803i
$87$		0			0
$88$	−2.66007	+	3.59680i	−0.283564	+	0.383420i
$89$			1.16402i			0.123386i	0.998095	+	0.0616929i	$0.0196499\pi$
$89$			1.16402i			0.123386i	−0.998095	+	0.0616929i	$0.980350\pi$
$90$		0			0
$91$	−14.9075			−1.56274
$92$	3.89284	+	3.80199i	0.405857	+	0.396385i
$93$		0			0
$94$	5.21730	−	12.8090i	0.538123	−	1.32115i
$95$	−2.80200	+	4.85321i	−0.287479	+	0.497929i
$96$		0			0
$97$	−6.72981	−	11.6564i	−0.683309	−	1.18353i	−0.973965	−	0.226698i	$-0.927207\pi$
$97$	−6.72981	−	11.6564i	−0.683309	−	1.18353i	0.290656	−	0.956827i	$-0.406126\pi$
$98$	−1.66358	+	0.229013i	−0.168047	+	0.0231338i
$99$		0			0
$100$	−3.45299	+	0.969060i	−0.345299	+	0.0969060i
$101$	−3.28047	−	5.68195i	−0.326419	−	0.565375i	0.655379	−	0.755300i	$-0.272509\pi$
$101$	−3.28047	−	5.68195i	−0.326419	−	0.565375i	−0.981799	+	0.189925i	$0.939175\pi$
$102$		0			0
$103$	−5.12167	−	2.95700i	−0.504653	−	0.291361i	0.225980	−	0.974132i	$-0.427442\pi$
$103$	−5.12167	−	2.95700i	−0.504653	−	0.291361i	−0.730633	+	0.682771i	$0.760775\pi$
$104$	−17.3772	−	1.97537i	−1.70397	−	0.193701i
$105$		0			0
$106$	6.12398	+	7.88413i	0.594814	+	0.765774i
$107$			1.01487i			0.0981111i	0.998796	+	0.0490555i	$0.0156211\pi$
$107$			1.01487i			0.0981111i	−0.998796	+	0.0490555i	$0.984379\pi$
$108$		0			0
$109$		−	4.46314i		−	0.427491i	−0.976889	−	0.213746i	$-0.931434\pi$
$109$		−	4.46314i		−	0.427491i	0.976889	−	0.213746i	$-0.0685664\pi$
$110$	−3.16336	+	2.45714i	−0.301615	+	0.234279i
$111$		0			0
$112$	9.64103	−	0.227688i	0.910991	−	0.0215145i
$113$	−7.35628	−	4.24715i	−0.692021	−	0.399538i	0.112348	−	0.993669i	$-0.464163\pi$
$113$	−7.35628	−	4.24715i	−0.692021	−	0.399538i	−0.804369	+	0.594131i	$0.797496\pi$
$114$		0			0
$115$	2.43607	+	4.21940i	0.227165	+	0.393462i
$116$	−9.83180	+	2.75923i	−0.912860	+	0.256188i
$117$		0			0
$118$	1.35874	+	9.87010i	0.125082	+	0.908616i
$119$	4.45953	+	7.72414i	0.408805	+	0.708071i
$120$		0			0
$121$	−4.24919	+	7.35981i	−0.386290	+	0.669074i
$122$	−4.61432	−	1.87948i	−0.417761	−	0.170160i
$123$		0			0
$124$	9.60595	−	9.83549i	0.862640	−	0.883253i
$125$	−12.1650			−1.08807
$126$		0			0
$127$			15.9098i			1.41176i	0.708329	+	0.705882i	$0.249449\pi$
$127$			15.9098i			1.41176i	−0.708329	+	0.705882i	$0.750551\pi$
$128$	11.2683	+	1.01211i	0.995991	+	0.0894587i
$129$		0			0
$130$	−14.5024	−	5.90706i	−1.27195	−	0.518083i
$131$	−1.38769	−	0.801182i	−0.121243	−	0.0699996i	0.438152	−	0.898901i	$-0.355633\pi$
$131$	−1.38769	−	0.801182i	−0.121243	−	0.0699996i	−0.559395	+	0.828901i	$0.688966\pi$
$132$		0			0
$133$	−6.53397	+	3.77239i	−0.566567	+	0.327108i
$134$	2.90807	−	0.400333i	0.251219	−	0.0345835i
$135$		0			0
$136$	4.17480	+	9.59466i	0.357986	+	0.822735i
$137$	10.6153	−	6.12877i	0.906930	−	0.523616i	0.0274877	−	0.999622i	$-0.491249\pi$
$137$	10.6153	−	6.12877i	0.906930	−	0.523616i	0.879442	+	0.476006i	$0.157916\pi$
$138$		0			0
$139$	−0.618940	+	1.07204i	−0.0524978	+	0.0909289i	−0.891080	−	0.453846i	$-0.850052\pi$
$139$	−0.618940	+	1.07204i	−0.0524978	+	0.0909289i	0.838582	+	0.544775i	$0.183385\pi$
$140$	8.36634	+	2.13622i	0.707085	+	0.180543i
$141$		0			0
$142$	−2.87591	−	3.70250i	−0.241341	−	0.310707i
$143$	9.77985			0.817832
$144$		0			0
$145$	−9.14327			−0.759307
$146$	0.547434	+	0.704777i	0.0453060	+	0.0583277i
$147$		0			0
$148$	10.1606	+	2.59435i	0.835194	+	0.213254i
$149$	2.96982	−	5.14387i	0.243297	−	0.421402i	−0.718355	−	0.695677i	$-0.755104\pi$
$149$	2.96982	−	5.14387i	0.243297	−	0.421402i	0.961651	+	0.274275i	$0.0884378\pi$
$150$		0			0
$151$	11.9663	−	6.90874i	0.973803	−	0.562226i	0.0734098	−	0.997302i	$-0.476612\pi$
$151$	11.9663	−	6.90874i	0.973803	−	0.562226i	0.900394	+	0.435076i	$0.143279\pi$
$152$	−8.11627	+	3.53153i	−0.658317	+	0.286445i
$153$		0			0
$154$	−5.34236	+	0.735444i	−0.430500	+	0.0592637i
$155$	10.6606	−	6.15488i	0.856278	−	0.494372i
$156$		0			0
$157$	−4.98995	−	2.88095i	−0.398241	−	0.229925i	0.287483	−	0.957786i	$-0.407181\pi$
$157$	−4.98995	−	2.88095i	−0.398241	−	0.229925i	−0.685725	+	0.727861i	$0.740515\pi$
$158$	11.8344	+	4.82031i	0.941493	+	0.383484i
$159$		0			0
$160$	9.46926	+	3.59872i	0.748611	+	0.284504i
$161$			6.55947i			0.516959i
$162$		0			0
$163$	11.2888			0.884209			0.442104	−	0.896964i	$-0.354232\pi$
$163$	11.2888			0.884209			0.442104	+	0.896964i	$0.354232\pi$
$164$	−8.58791	+	8.79312i	−0.670603	+	0.686628i
$165$		0			0
$166$	−20.4987	−	8.34941i	−1.59101	−	0.648040i
$167$	0.378448	−	0.655492i	0.0292852	−	0.0507235i	−0.851011	−	0.525147i	$-0.824010\pi$
$167$	0.378448	−	0.655492i	0.0292852	−	0.0507235i	0.880297	+	0.474424i	$0.157344\pi$
$168$		0			0
$169$	12.6167	+	21.8528i	0.970517	+	1.68098i
$170$	1.27769	+	9.28132i	0.0979943	+	0.711844i
$171$		0			0
$172$	1.74250	−	0.489021i	0.132864	−	0.0372875i
$173$	−4.62735	−	8.01480i	−0.351811	−	0.609354i	0.634756	−	0.772713i	$-0.281101\pi$
$173$	−4.62735	−	8.01480i	−0.351811	−	0.609354i	−0.986567	+	0.163359i	$0.947767\pi$
$174$		0			0
$175$	−3.74406	−	2.16164i	−0.283025	−	0.163404i
$176$	−6.32484	+	0.149371i	−0.476753	+	0.0112593i
$177$		0			0
$178$	−1.30006	+	1.00982i	−0.0974434	+	0.0756890i
$179$		−	1.56530i		−	0.116996i	−0.998288	−	0.0584980i	$-0.981369\pi$
$179$		−	1.56530i		−	0.116996i	0.998288	−	0.0584980i	$-0.0186311\pi$
$180$		0			0
$181$		−	3.68300i		−	0.273755i	−0.990588	−	0.136878i	$-0.956293\pi$
$181$		−	3.68300i		−	0.273755i	0.990588	−	0.136878i	$-0.0437067\pi$
$182$	−12.9327	−	16.6498i	−0.958635	−	1.23416i
$183$		0			0
$184$	−0.869185	+	7.64613i	−0.0640771	+	0.563680i
$185$	8.13148	+	4.69471i	0.597838	+	0.345162i
$186$		0			0
$187$	−2.92561	−	5.06730i	−0.213941	−	0.370558i
$188$	18.8321	−	5.28512i	1.37348	−	0.385457i
$189$		0			0
$190$	−7.85121	+	1.08082i	−0.569587	+	0.0784108i
$191$	11.8678	+	20.5556i	0.858722	+	1.48735i	0.873148	+	0.487455i	$0.162075\pi$
$191$	11.8678	+	20.5556i	0.858722	+	1.48735i	−0.0144258	+	0.999896i	$0.504592\pi$
$192$		0			0
$193$	12.8012	−	22.1723i	0.921451	−	1.59600i	0.124279	−	0.992247i	$-0.460338\pi$
$193$	12.8012	−	22.1723i	0.921451	−	1.59600i	0.797172	−	0.603752i	$-0.206328\pi$
$194$	7.18036	−	17.6285i	0.515520	−	1.26566i
$195$		0			0
$196$	−1.69898	−	1.65933i	−0.121355	−	0.118523i
$197$	−5.76656			−0.410850			−0.205425	−	0.978673i	$-0.565858\pi$
$197$	−5.76656			−0.410850			−0.205425	+	0.978673i	$0.565858\pi$
$198$		0			0
$199$		−	1.24163i		−	0.0880169i	−0.999031	−	0.0440085i	$-0.985987\pi$
$199$		−	1.24163i		−	0.0880169i	0.999031	−	0.0440085i	$-0.0140129\pi$
$200$	−4.07788	−	3.01586i	−0.288349	−	0.213253i
$201$		0			0
$202$	3.50010	−	8.59310i	0.246266	−	0.604609i
$203$	−10.6606	−	6.15488i	−0.748226	−	0.431988i
$204$		0			0
$205$	−9.53076	+	5.50259i	−0.665657	+	0.384317i
$206$	−1.14060	−	8.28550i	−0.0794696	−	0.577278i
$207$		0			0
$208$	−12.8689	−	21.1217i	−0.892298	−	1.46453i
$209$	4.28651	−	2.47482i	0.296504	−	0.171187i
$210$		0			0
$211$	1.62194	−	2.80928i	0.111659	−	0.193399i	−0.804780	−	0.593573i	$-0.797717\pi$
$211$	1.62194	−	2.80928i	0.111659	−	0.193399i	0.916439	+	0.400174i	$0.131050\pi$
$212$	−3.49282	+	13.6794i	−0.239888	+	0.939504i
$213$		0			0
$214$	−1.13348	+	0.880426i	−0.0774828	+	0.0601847i
$215$	1.62047			0.110515
$216$		0			0
$217$	16.5729			1.12504
$218$	4.98474	−	3.87189i	0.337610	−	0.262238i
$219$		0			0
$220$	−5.48861	−	1.40143i	−0.370042	−	0.0944845i
$221$	11.4374	−	19.8101i	0.769362	−	1.33257i
$222$		0			0
$223$	12.1221	−	6.99871i	0.811758	−	0.468669i	−0.0358081	−	0.999359i	$-0.511401\pi$
$223$	12.1221	−	6.99871i	0.811758	−	0.468669i	0.847566	+	0.530690i	$0.178067\pi$
$224$	8.61815	+	10.5702i	0.575824	+	0.706254i
$225$		0			0
$226$	−1.63826	−	11.9005i	−0.108975	−	0.791611i
$227$	8.75366	−	5.05393i	0.581001	−	0.335441i	−0.180530	−	0.983569i	$-0.557781\pi$
$227$	8.75366	−	5.05393i	0.581001	−	0.335441i	0.761531	+	0.648128i	$0.224448\pi$
$228$		0			0
$229$	−9.93043	−	5.73334i	−0.656221	−	0.378869i	0.134615	−	0.990898i	$-0.457020\pi$
$229$	−9.93043	−	5.73334i	−0.656221	−	0.378869i	−0.790836	+	0.612029i	$0.790354\pi$
$230$	−2.59916	+	6.38122i	−0.171384	+	0.420765i
$231$		0			0
$232$	−11.6110	−	8.58713i	−0.762303	−	0.563773i
$233$		−	6.74860i		−	0.442115i	−0.975261	−	0.221058i	$-0.929049\pi$
$233$		−	6.74860i		−	0.442115i	0.975261	−	0.221058i	$-0.0709509\pi$
$234$		0			0
$235$	17.5133			1.14244
$236$	−9.84487	+	10.0801i	−0.640846	+	0.656160i
$237$		0			0
$238$	−4.75809	+	11.6816i	−0.308421	+	0.757207i
$239$	0.0677896	−	0.117415i	0.00438494	−	0.00759495i	−0.863825	−	0.503793i	$-0.831938\pi$
$239$	0.0677896	−	0.117415i	0.00438494	−	0.00759495i	0.868210	+	0.496198i	$0.165271\pi$
$240$		0			0
$241$	−9.71742	−	16.8311i	−0.625954	−	1.08418i	−0.988355	−	0.152163i	$-0.951376\pi$
$241$	−9.71742	−	16.8311i	−0.625954	−	1.08418i	0.362401	−	0.932022i	$-0.381957\pi$
$242$	−11.9062	+	1.63904i	−0.765362	+	0.105362i
$243$		0			0
$244$	−1.90391	−	6.78410i	−0.121886	−	0.434307i
$245$	−1.06319	−	1.84150i	−0.0679248	−	0.117649i
$246$		0			0
$247$	16.7577	+	9.67507i	1.06627	+	0.615610i
$248$	19.3184	+	2.19605i	1.22672	+	0.139449i
$249$		0			0
$250$	−10.5534	−	13.5867i	−0.667457	−	0.859296i
$251$			18.7837i			1.18561i	0.805344	+	0.592807i	$0.201980\pi$
$251$			18.7837i			1.18561i	−0.805344	+	0.592807i	$0.798020\pi$
$252$		0			0
$253$		−	4.30324i		−	0.270542i
$254$	−17.7691	+	13.8022i	−1.11494	+	0.866024i
$255$		0			0
$256$	8.64520	+	13.4633i	0.540325	+	0.841457i
$257$	−18.6937	−	10.7928i	−1.16608	−	0.673238i	−0.213329	−	0.976981i	$-0.568430\pi$
$257$	−18.6937	−	10.7928i	−1.16608	−	0.673238i	−0.952754	+	0.303742i	$0.901764\pi$
$258$		0			0
$259$	6.32058	+	10.9476i	0.392742	+	0.680249i
$260$	−5.98385	−	21.3219i	−0.371102	−	1.32233i
$261$		0			0
$262$	−0.309041	−	2.24491i	−0.0190926	−	0.138691i
$263$	−8.56995	−	14.8436i	−0.528446	−	0.915295i	−0.999450	−	0.0331642i	$-0.989442\pi$
$263$	−8.56995	−	14.8436i	−0.528446	−	0.915295i	0.471004	−	0.882131i	$-0.343892\pi$
$264$		0			0
$265$	−6.32058	+	10.9476i	−0.388270	+	0.672504i
$266$	−9.88166	−	4.02494i	−0.605884	−	0.246785i
$267$		0			0
$268$	2.96995	+	2.90064i	0.181419	+	0.177185i
$269$	20.1271			1.22717			0.613585	−	0.789629i	$-0.289727\pi$
$269$	20.1271			1.22717			0.613585	+	0.789629i	$0.289727\pi$
$270$		0			0
$271$			6.20336i			0.376827i	0.982090	+	0.188414i	$0.0603345\pi$
$271$			6.20336i			0.376827i	−0.982090	+	0.188414i	$0.939665\pi$
$272$	−7.09424	+	12.9863i	−0.430151	+	0.787412i
$273$		0			0
$274$	16.0541	+	6.53908i	0.969865	+	0.395040i
$275$	2.45623	+	1.41811i	0.148116	+	0.0855151i
$276$		0			0
$277$	−10.6060	+	6.12340i	−0.637256	+	0.367920i	−0.783557	−	0.621320i	$-0.786597\pi$
$277$	−10.6060	+	6.12340i	−0.637256	+	0.367920i	0.146301	+	0.989240i	$0.453263\pi$
$278$	−1.73427	+	0.238744i	−0.104015	+	0.0143189i
$279$		0			0
$280$	4.87215	+	11.1973i	0.291167	+	0.669169i
$281$	15.1623	−	8.75399i	0.904510	−	0.522219i	0.0258492	−	0.999666i	$-0.491771\pi$
$281$	15.1623	−	8.75399i	0.904510	−	0.522219i	0.878661	+	0.477447i	$0.158438\pi$
$282$		0			0
$283$	−3.79698	+	6.57656i	−0.225707	+	0.390936i	−0.956531	−	0.291630i	$-0.905802\pi$
$283$	−3.79698	+	6.57656i	−0.225707	+	0.390936i	0.730824	+	0.682565i	$0.239136\pi$
$284$	1.64028	−	6.42403i	0.0973326	−	0.381196i
$285$		0			0
$286$	8.48428	+	10.9228i	0.501686	+	0.645880i
$287$	−14.8165			−0.874590
$288$		0			0
$289$	3.31420			0.194953
$290$	−7.93203	−	10.2118i	−0.465785	−	0.599660i
$291$		0			0
$292$	−0.312230	+	1.22283i	−0.0182719	+	0.0715604i
$293$	−12.6164	+	21.8523i	−0.737061	+	1.27663i	0.216753	+	0.976227i	$0.430454\pi$
$293$	−12.6164	+	21.8523i	−0.737061	+	1.27663i	−0.953813	+	0.300400i	$0.902880\pi$
$294$		0			0
$295$	−10.9257	+	6.30797i	−0.636120	+	0.367264i
$296$	5.91702	+	13.5987i	0.343920	+	0.790408i
$297$		0			0
$298$	8.32143	−	1.14555i	0.482047	−	0.0663599i
$299$	14.5692	−	8.41155i	0.842561	−	0.486453i
$300$		0			0
$301$	1.88938	+	1.09084i	0.108902	+	0.0628748i
$302$	18.0972	+	7.37127i	1.04138	+	0.424169i
$303$		0			0
$304$	−10.9853	−	6.00113i	−0.630052	−	0.344188i
$305$		−	6.30900i		−	0.361253i
$306$		0			0
$307$	−29.5997			−1.68934			−0.844671	−	0.535286i	$-0.820204\pi$
$307$	−29.5997			−1.68934			−0.844671	+	0.535286i	$0.820204\pi$
$308$	−5.45604	−	5.32871i	−0.310887	−	0.303631i
$309$		0			0
$310$	16.1225	+	6.56694i	0.915698	+	0.372977i
$311$	−10.3607	+	17.9453i	−0.587502	+	1.01758i	0.407057	+	0.913403i	$0.366555\pi$
$311$	−10.3607	+	17.9453i	−0.587502	+	1.01758i	−0.994558	+	0.104180i	$0.966778\pi$
$312$		0			0
$313$	1.73680	+	3.00823i	0.0981700	+	0.170035i	0.910927	−	0.412567i	$-0.135368\pi$
$313$	1.73680	+	3.00823i	0.0981700	+	0.170035i	−0.812757	+	0.582603i	$0.802034\pi$
$314$	−1.11127	−	8.07242i	−0.0627126	−	0.455553i
$315$		0			0
$316$	4.88298	+	17.3992i	0.274689	+	0.978782i
$317$	7.64385	+	13.2395i	0.429321	+	0.743606i	0.996813	−	0.0797728i	$-0.0254195\pi$
$317$	7.64385	+	13.2395i	0.429321	+	0.743606i	−0.567492	+	0.823379i	$0.692086\pi$
$318$		0			0
$319$	6.99370	+	4.03781i	0.391572	+	0.226074i
$320$	4.19554	+	13.6979i	0.234538	+	0.765737i
$321$		0			0
$322$	−7.32607	+	5.69052i	−0.408266	+	0.317120i
$323$		−	11.5770i		−	0.644164i
$324$		0			0
$325$			11.0879i			0.615047i
$326$	9.79335	+	12.6081i	0.542404	+	0.698300i
$327$		0			0
$328$	−17.2710	−	1.96331i	−0.953632	−	0.108406i
$329$	20.4196	+	11.7893i	1.12577	+	0.649963i
$330$		0			0
$331$	3.09986	+	5.36912i	0.170384	+	0.295114i	0.938554	−	0.345132i	$-0.112166\pi$
$331$	3.09986	+	5.36912i	0.170384	+	0.295114i	−0.768170	+	0.640246i	$0.778833\pi$
$332$	−8.45795	−	30.1377i	−0.464190	−	1.65402i
$333$		0			0
$334$	1.06041	−	0.145979i	0.0580232	−	0.00798763i
$335$	1.85854	+	3.21909i	0.101543	+	0.175878i
$336$		0			0
$337$	−9.63097	+	16.6813i	−0.524632	+	0.908690i	0.474956	+	0.880009i	$0.342464\pi$
$337$	−9.63097	+	16.6813i	−0.524632	+	0.908690i	−0.999589	+	0.0286803i	$0.990870\pi$
$338$	−13.4614	+	33.0491i	−0.732203	+	1.79763i
$339$		0			0
$340$	−9.25759	+	9.47880i	−0.502063	+	0.514060i
$341$	−10.8724			−0.588772
$342$		0			0
$343$		−	19.7393i		−	1.06582i
$344$	2.05784	+	1.52191i	0.110951	+	0.0820556i
$345$		0			0
$346$	4.93714	−	12.1212i	0.265422	−	0.651640i
$347$	−22.9191	−	13.2323i	−1.23036	−	0.710349i	−0.263255	−	0.964726i	$-0.584796\pi$
$347$	−22.9191	−	13.2323i	−1.23036	−	0.710349i	−0.967105	+	0.254378i	$0.918129\pi$
$348$		0			0
$349$	14.8362	−	8.56568i	0.794164	−	0.458511i	−0.0472627	−	0.998882i	$-0.515050\pi$
$349$	14.8362	−	8.56568i	0.794164	−	0.458511i	0.841426	+	0.540372i	$0.181716\pi$
$350$	−0.833810	−	6.05691i	−0.0445690	−	0.323755i
$351$		0			0
$352$	−5.65380	−	6.93444i	−0.301348	−	0.369607i
$353$	−26.8134	+	15.4807i	−1.42713	+	0.823955i	−0.996894	−	0.0787597i	$-0.974904\pi$
$353$	−26.8134	+	15.4807i	−1.42713	+	0.823955i	−0.430239	+	0.902715i	$0.641571\pi$
$354$		0			0
$355$	2.96823	−	5.14113i	0.157538	−	0.272863i
$356$	−2.25567	−	0.575950i	−0.119550	−	0.0305253i
$357$		0			0
$358$	1.74824	−	1.35794i	0.0923972	−	0.0717694i
$359$	6.43781			0.339775			0.169887	−	0.985463i	$-0.445660\pi$
$359$	6.43781			0.339775			0.169887	+	0.985463i	$0.445660\pi$
$360$		0			0
$361$	−9.20680			−0.484569
$362$	4.11343	−	3.19510i	0.216197	−	0.167931i
$363$		0			0
$364$	7.37618	−	28.8883i	0.386617	−	1.51416i
$365$	−0.565009	+	0.978624i	−0.0295739	+	0.0512235i
$366$		0			0
$367$	−23.8725	+	13.7828i	−1.24614	+	0.719457i	−0.970337	−	0.241758i	$-0.922276\pi$
$367$	−23.8725	+	13.7828i	−1.24614	+	0.719457i	−0.275800	+	0.961215i	$0.588943\pi$
$368$	−9.29376	+	5.66245i	−0.484471	+	0.295176i
$369$		0			0
$370$	1.81089	+	13.1546i	0.0941439	+	0.683875i
$371$	−14.7389	+	8.50953i	−0.765208	+	0.441793i
$372$		0			0
$373$	23.2547	+	13.4261i	1.20408	+	0.695178i	0.961461	−	0.274942i	$-0.0886587\pi$
$373$	23.2547	+	13.4261i	1.20408	+	0.695178i	0.242623	+	0.970121i	$0.421992\pi$
$374$	3.12147	−	7.66354i	0.161407	−	0.396272i
$375$		0			0
$376$	22.2402	+	16.4481i	1.14695	+	0.848244i
$377$			31.5709i			1.62599i
$378$		0			0
$379$	4.63966			0.238323			0.119162	−	0.992875i	$-0.461979\pi$
$379$	4.63966			0.238323			0.119162	+	0.992875i	$0.461979\pi$
$380$	−8.01827	−	7.83114i	−0.411328	−	0.401729i
$381$		0			0
$382$	−12.6623	+	31.0873i	−0.647860	+	1.59056i
$383$	17.7531	−	30.7493i	0.907141	−	1.57122i	0.0891248	−	0.996020i	$-0.471593\pi$
$383$	17.7531	−	30.7493i	0.907141	−	1.57122i	0.818017	−	0.575195i	$-0.195074\pi$
$384$		0			0
$385$	−3.41430	−	5.91373i	−0.174009	−	0.301392i
$386$	35.8690	−	4.93782i	1.82568	−	0.251328i
$387$		0			0
$388$	25.9179	−	7.27370i	1.31578	−	0.369266i
$389$	3.19920	+	5.54117i	0.162206	+	0.280949i	0.935659	−	0.352904i	$-0.114806\pi$
$389$	3.19920	+	5.54117i	0.162206	+	0.280949i	−0.773454	+	0.633853i	$0.781473\pi$
$390$		0			0
$391$	−8.71666	−	5.03257i	−0.440821	−	0.254508i
$392$	0.379344	−	3.33705i	0.0191597	−	0.168546i
$393$		0			0
$394$	−5.00264	−	6.44049i	−0.252029	−	0.324467i
$395$			16.1807i			0.814141i
$396$		0			0
$397$		−	3.01894i		−	0.151516i	−0.997126	−	0.0757581i	$-0.975862\pi$
$397$		−	3.01894i		−	0.151516i	0.997126	−	0.0757581i	$-0.0241377\pi$
$398$	1.38674	−	1.07715i	0.0695110	−	0.0539926i
$399$		0			0
$400$	−0.169349	−	7.17079i	−0.00846747	−	0.358540i
$401$	−25.1191	−	14.5025i	−1.25439	−	0.724222i	−0.282411	−	0.959294i	$-0.591134\pi$
$401$	−25.1191	−	14.5025i	−1.25439	−	0.724222i	−0.971978	+	0.235072i	$0.924467\pi$
$402$		0			0
$403$	−21.2523	−	36.8100i	−1.05865	−	1.83364i
$404$	12.6338	−	3.54560i	0.628555	−	0.176400i
$405$		0			0
$406$	−2.37413	−	17.2460i	−0.117826	−	0.855904i
$407$	−4.14652	−	7.18198i	−0.205535	−	0.355998i
$408$		0			0
$409$	−0.662169	+	1.14691i	−0.0327422	+	0.0567111i	−0.881932	−	0.471376i	$-0.843757\pi$
$409$	−0.662169	+	1.14691i	−0.0327422	+	0.0567111i	0.849190	+	0.528087i	$0.177091\pi$
$410$	−14.4139	−	5.87098i	−0.711850	−	0.289947i
$411$		0			0
$412$	8.26432	−	8.46180i	0.407154	−	0.416883i
$413$	−16.9851			−0.835781
$414$		0			0
$415$		−	28.0271i		−	1.37580i
$416$	12.4261	−	32.6965i	0.609238	−	1.60308i
$417$		0			0
$418$	6.48271	+	2.64050i	0.317080	+	0.129151i
$419$	27.2974	+	15.7602i	1.33357	+	0.769935i	0.985844	−	0.167663i	$-0.0536219\pi$
$419$	27.2974	+	15.7602i	1.33357	+	0.769935i	0.347722	+	0.937598i	$0.386955\pi$
$420$		0			0
$421$	30.9851	−	17.8893i	1.51012	−	0.871869i	0.510192	−	0.860061i	$-0.329574\pi$
$421$	30.9851	−	17.8893i	1.51012	−	0.871869i	0.999930	−	0.0118087i	$-0.00375891\pi$
$422$	4.54468	−	0.625632i	0.221231	−	0.0304553i
$423$		0			0
$424$	−18.3082	+	7.96620i	−0.889125	+	0.386873i
$425$	5.74505	−	3.31691i	0.278676	−	0.160894i
$426$		0			0
$427$	4.24697	−	7.35597i	0.205525	−	0.355980i
$428$	−1.96664	−	0.502152i	−0.0950612	−	0.0242724i
$429$		0			0
$430$	1.40580	+	1.80985i	0.0677938	+	0.0872789i
$431$	−17.1129			−0.824301			−0.412150	−	0.911116i	$-0.635222\pi$
$431$	−17.1129			−0.824301			−0.412150	+	0.911116i	$0.635222\pi$
$432$		0			0
$433$	−19.1099			−0.918363			−0.459182	−	0.888342i	$-0.651857\pi$
$433$	−19.1099			−0.918363			−0.459182	+	0.888342i	$0.651857\pi$
$434$	14.3774	+	18.5098i	0.690138	+	0.888497i
$435$		0			0
$436$	8.64880	+	2.20834i	0.414202	+	0.105760i
$437$	4.25713	−	7.37356i	0.203646	−	0.352725i
$438$		0			0
$439$	−29.4886	+	17.0253i	−1.40742	+	0.812572i	−0.995138	−	0.0984868i	$-0.968600\pi$
$439$	−29.4886	+	17.0253i	−1.40742	+	0.812572i	−0.412277	+	0.911058i	$0.635266\pi$
$440$	−3.19630	−	7.34584i	−0.152377	−	0.350199i
$441$		0			0
$442$	32.0476	−	4.41175i	1.52435	−	0.209846i
$443$	−17.1586	+	9.90651i	−0.815229	+	0.470673i	−0.848768	−	0.528765i	$-0.822655\pi$
$443$	−17.1586	+	9.90651i	−0.815229	+	0.470673i	0.0335394	+	0.999437i	$0.489322\pi$
$444$		0			0
$445$	−1.80521	−	1.04224i	−0.0855749	−	0.0494067i
$446$	18.3329	+	7.46727i	0.868089	+	0.353585i
$447$		0			0
$448$	−4.32911	+	18.7953i	−0.204531	+	0.887995i
$449$			8.73916i			0.412426i	0.978507	+	0.206213i	$0.0661140\pi$
$449$			8.73916i			0.412426i	−0.978507	+	0.206213i	$0.933886\pi$
$450$		0			0
$451$	9.72012			0.457703
$452$	11.8701	−	12.1537i	0.558323	−	0.571664i
$453$		0			0
$454$	13.2386	+	5.39228i	0.621319	+	0.253072i
$455$	13.3479	−	23.1192i	0.625758	−	1.08384i
$456$		0			0
$457$	−1.25081	−	2.16647i	−0.0585104	−	0.101343i	0.835287	−	0.549815i	$-0.185302\pi$
$457$	−1.25081	−	2.16647i	−0.0585104	−	0.101343i	−0.893797	+	0.448472i	$0.851968\pi$
$458$	−2.21152	−	16.0648i	−0.103338	−	0.750659i
$459$		0			0
$460$	−9.38184	+	2.63295i	−0.437430	+	0.122762i
$461$	−2.63419	−	4.56255i	−0.122686	−	0.212499i	0.798140	−	0.602472i	$-0.205818\pi$
$461$	−2.63419	−	4.56255i	−0.122686	−	0.212499i	−0.920826	+	0.389973i	$0.872484\pi$
$462$		0			0
$463$	−15.2227	−	8.78883i	−0.707459	−	0.408451i	0.102661	−	0.994716i	$-0.467264\pi$
$463$	−15.2227	−	8.78883i	−0.707459	−	0.408451i	−0.810119	+	0.586265i	$0.800598\pi$
$464$	−0.482193	−	20.4176i	−0.0223852	−	0.947863i
$465$		0			0
$466$	7.53731	−	5.85459i	0.349159	−	0.271209i
$467$			2.29842i			0.106358i	0.998585	+	0.0531791i	$0.0169354\pi$
$467$			2.29842i			0.106358i	−0.998585	+	0.0531791i	$0.983065\pi$
$468$		0			0
$469$			5.00439i			0.231081i
$470$	15.1933	+	19.5601i	0.700813	+	0.902240i
$471$		0			0
$472$	−19.7989	−	2.25066i	−0.911316	−	0.103595i
$473$	−1.23950	−	0.715626i	−0.0569923	−	0.0329045i
$474$		0			0
$475$	2.80582	+	4.85983i	0.128740	+	0.222984i
$476$	−17.1746	+	4.81995i	−0.787197	+	0.220922i
$477$		0			0
$478$	0.189947	−	0.0261485i	0.00868795	−	0.00119601i
$479$	−18.0219	−	31.2149i	−0.823442	−	1.42624i	−0.903104	−	0.429422i	$-0.858717\pi$
$479$	−18.0219	−	31.2149i	−0.823442	−	1.42624i	0.0796622	−	0.996822i	$-0.474616\pi$
$480$		0			0
$481$	16.2104	−	28.0773i	0.739132	−	1.28021i
$482$	10.3680	−	25.4545i	0.472249	−	1.15942i
$483$		0			0
$484$	−12.1596	−	11.8758i	−0.552708	−	0.539809i
$485$	24.1029			1.09446
$486$		0			0
$487$		−	2.72292i		−	0.123387i	−0.998095	−	0.0616937i	$-0.980350\pi$
$487$		−	2.72292i		−	0.123387i	0.998095	−	0.0616937i	$-0.0196502\pi$
$488$	5.92526	−	8.01181i	0.268224	−	0.362678i
$489$		0			0
$490$	1.13437	−	2.78500i	0.0512456	−	0.125813i
$491$	−13.1715	−	7.60457i	−0.594421	−	0.343189i	0.172422	−	0.985023i	$-0.444841\pi$
$491$	−13.1715	−	7.60457i	−0.594421	−	0.343189i	−0.766844	+	0.641834i	$0.778174\pi$
$492$		0			0
$493$	16.3580	−	9.44432i	0.736729	−	0.425351i
$494$	3.73197	+	27.1095i	0.167909	+	1.21972i
$495$		0			0
$496$	14.3065	+	23.4812i	0.642382	+	1.05434i
$497$	6.92161	−	3.99619i	0.310477	−	0.179254i
$498$		0			0
$499$	−19.7305	+	34.1743i	−0.883260	+	1.52985i	−0.0355642	+	0.999367i	$0.511323\pi$
$499$	−19.7305	+	34.1743i	−0.883260	+	1.52985i	−0.847695	+	0.530483i	$0.822010\pi$
$500$	6.01916	−	23.5736i	0.269185	−	1.05424i
$501$		0			0
$502$	−20.9789	+	16.2953i	−0.936334	+	0.727296i
$503$	18.4749			0.823756			0.411878	−	0.911239i	$-0.364873\pi$
$503$	18.4749			0.823756			0.411878	+	0.911239i	$0.364873\pi$
$504$		0			0
$505$	11.7490			0.522826
$506$	4.80615	−	3.73317i	0.213660	−	0.165960i
$507$		0			0
$508$	−30.8304	−	7.87208i	−1.36788	−	0.349267i
$509$	−17.0068	+	29.4566i	−0.753813	+	1.30564i	0.192149	+	0.981366i	$0.438454\pi$
$509$	−17.0068	+	29.4566i	−0.753813	+	1.30564i	−0.945962	+	0.324277i	$0.894879\pi$
$510$		0			0
$511$	−1.31754	+	0.760683i	−0.0582846	+	0.0336506i
$512$	−7.53681	+	21.3353i	−0.333083	+	0.942897i
$513$		0			0
$514$	−4.16313	−	30.2415i	−0.183628	−	1.33390i
$515$	9.17165	−	5.29525i	0.404151	−	0.233337i
$516$		0			0
$517$	−13.3960	−	7.73416i	−0.589153	−	0.340148i
$518$	−6.74374	+	16.5566i	−0.296303	+	0.727454i
$519$		0			0
$520$	18.6226	−	25.1805i	0.816655	−	1.10424i
$521$		−	12.0788i		−	0.529182i	−0.964361	−	0.264591i	$-0.914763\pi$
$521$		−	12.0788i		−	0.529182i	0.964361	−	0.264591i	$-0.0852369\pi$
$522$		0			0
$523$	5.27483			0.230652			0.115326	−	0.993328i	$-0.463209\pi$
$523$	5.27483			0.230652			0.115326	+	0.993328i	$0.463209\pi$
$524$	2.23917	−	2.29268i	0.0978188	−	0.100156i
$525$		0			0
$526$	9.14370	−	22.4487i	0.398684	−	0.978811i
$527$	−12.7151	+	22.0232i	−0.553877	+	0.959344i
$528$		0			0
$529$	7.79883	+	13.5080i	0.339080	+	0.587303i
$530$	−17.7103	+	2.43804i	−0.769286	+	0.105902i
$531$		0			0
$532$	−4.07727	−	14.5283i	−0.176772	−	0.629881i
$533$	19.0000	+	32.9089i	0.822980	+	1.42544i
$534$		0			0
$535$	−1.57390	−	0.908690i	−0.0680455	−	0.0392861i
$536$	−0.663123	+	5.83343i	−0.0286426	+	0.251966i
$537$		0			0
$538$	17.4608	+	22.4793i	0.752787	+	0.969152i
$539$			1.87809i			0.0808950i
$540$		0			0
$541$			23.6734i			1.01780i	0.860826	+	0.508900i	$0.169948\pi$
$541$			23.6734i			1.01780i	−0.860826	+	0.508900i	$0.830052\pi$
$542$	−6.92834	+	5.38158i	−0.297598	+	0.231159i
$543$		0			0
$544$	−20.6585	+	3.34265i	−0.885725	+	0.143315i
$545$	6.92161	+	3.99619i	0.296489	+	0.171178i
$546$		0			0
$547$	10.5319	+	18.2418i	0.450312	+	0.779964i	0.998405	−	0.0564536i	$-0.0179793\pi$
$547$	10.5319	+	18.2418i	0.450312	+	0.779964i	−0.548093	+	0.836417i	$0.684646\pi$
$548$	6.62409	+	23.6032i	0.282967	+	1.00828i
$549$		0			0
$550$	0.547007	+	3.97354i	0.0233245	+	0.169432i
$551$	7.98910	+	13.8375i	0.340347	+	0.589498i
$552$		0			0
$553$	−10.8922	+	18.8659i	−0.463184	+	0.802259i
$554$	−16.0401	−	6.53335i	−0.681477	−	0.277576i
$555$		0			0
$556$	−1.77117	−	1.72984i	−0.0751144	−	0.0733614i
$557$	9.64427			0.408641			0.204321	−	0.978904i	$-0.434502\pi$
$557$	9.64427			0.408641			0.204321	+	0.978904i	$0.434502\pi$
$558$		0			0
$559$		−	5.59535i		−	0.236658i
$560$	−8.27925	+	15.1555i	−0.349862	+	0.640439i
$561$		0			0
$562$	22.9308	+	9.34005i	0.967277	+	0.393986i
$563$	36.8534	+	21.2773i	1.55319	+	0.896733i	0.997880	+	0.0650873i	$0.0207326\pi$
$563$	36.8534	+	21.2773i	1.55319	+	0.896733i	0.555307	+	0.831645i	$0.312601\pi$
$564$		0			0
$565$	13.1733	−	7.60561i	0.554205	−	0.319970i
$566$	−10.6391	+	1.46461i	−0.447196	+	0.0615622i
$567$		0			0
$568$	8.59779	−	3.74104i	0.360755	−	0.156971i
$569$	8.25996	−	4.76889i	0.346275	−	0.199922i	−0.316768	−	0.948503i	$-0.602598\pi$
$569$	8.25996	−	4.76889i	0.346275	−	0.199922i	0.663044	+	0.748581i	$0.269264\pi$
$570$		0			0
$571$	13.4455	−	23.2882i	0.562675	−	0.974582i	−0.434587	−	0.900630i	$-0.643106\pi$
$571$	13.4455	−	23.2882i	0.562675	−	0.974582i	0.997262	−	0.0739518i	$-0.0235611\pi$
$572$	−4.83902	+	18.9517i	−0.202330	+	0.792409i
$573$		0			0
$574$	−12.8537	−	16.5481i	−0.536503	−	0.690704i
$575$	4.87880			0.203460
$576$		0			0
$577$	−8.52363			−0.354843			−0.177422	−	0.984135i	$-0.556776\pi$
$577$	−8.52363			−0.354843			−0.177422	+	0.984135i	$0.556776\pi$
$578$	2.87516	+	3.70153i	0.119591	+	0.153963i
$579$		0			0
$580$	4.52404	−	17.7181i	0.187851	−	0.735704i
$581$	18.8667	−	32.6781i	0.782724	−	1.35572i
$582$		0			0
$583$	9.66924	−	5.58254i	0.400459	−	0.231205i
$584$	−1.63660	+	0.712114i	−0.0677232	+	0.0294675i
$585$		0			0
$586$	−35.3513	+	4.86655i	−1.46035	+	0.201035i
$587$	19.4568	−	11.2334i	0.803067	−	0.463651i	−0.0414756	−	0.999140i	$-0.513206\pi$
$587$	19.4568	−	11.2334i	0.803067	−	0.463651i	0.844542	+	0.535489i	$0.179873\pi$
$588$		0			0
$589$	−18.6297	−	10.7559i	−0.767625	−	0.443189i
$590$	−16.5235	−	6.73027i	−0.680263	−	0.277081i
$591$		0			0
$592$	−10.0548	+	18.4058i	−0.413250	+	0.756473i
$593$		−	28.8424i		−	1.18442i	−0.805785	−	0.592208i	$-0.798257\pi$
$593$		−	28.8424i		−	1.18442i	0.805785	−	0.592208i	$-0.201743\pi$
$594$		0			0
$595$	−15.9719			−0.654783
$596$	8.49849	+	8.30015i	0.348112	+	0.339987i
$597$		0			0
$598$	22.0338	+	8.97469i	0.901029	+	0.367002i
$599$	−8.40225	+	14.5531i	−0.343307	+	0.594625i	−0.985045	−	0.172299i	$-0.944880\pi$
$599$	−8.40225	+	14.5531i	−0.343307	+	0.594625i	0.641738	+	0.766924i	$0.278214\pi$
$600$		0			0
$601$	14.8802	+	25.7732i	0.606974	+	1.05131i	0.991736	+	0.128294i	$0.0409502\pi$
$601$	14.8802	+	25.7732i	0.606974	+	1.05131i	−0.384762	+	0.923016i	$0.625716\pi$
$602$	0.420769	+	3.05653i	0.0171493	+	0.124575i
$603$		0			0
$604$	7.46710	+	26.6070i	0.303832	+	1.08263i
$605$	−7.60926	−	13.1796i	−0.309360	−	0.535828i
$606$		0			0
$607$	20.9599	+	12.1012i	0.850737	+	0.491173i	0.860899	−	0.508775i	$-0.169902\pi$
$607$	20.9599	+	12.1012i	0.850737	+	0.491173i	−0.0101625	+	0.999948i	$0.503235\pi$
$608$	−2.82760	−	17.4753i	−0.114674	−	0.708718i
$609$		0			0
$610$	7.04633	−	5.47323i	0.285298	−	0.221605i
$611$		−	60.4720i		−	2.44643i
$612$		0			0
$613$			38.3189i			1.54769i	0.633377	+	0.773843i	$0.281668\pi$
$613$			38.3189i			1.54769i	−0.633377	+	0.773843i	$0.718332\pi$
$614$	−25.6785	−	33.0589i	−1.03630	−	1.33415i
$615$		0			0
$616$	1.21821	−	10.7165i	0.0490831	−	0.431779i
$617$	7.31357	+	4.22249i	0.294433	+	0.169991i	0.639939	−	0.768425i	$-0.278959\pi$
$617$	7.31357	+	4.22249i	0.294433	+	0.169991i	−0.345506	+	0.938417i	$0.612293\pi$
$618$		0			0
$619$	4.12431	+	7.14352i	0.165770	+	0.287122i	0.936929	−	0.349521i	$-0.113656\pi$
$619$	4.12431	+	7.14352i	0.165770	+	0.287122i	−0.771158	+	0.636643i	$0.780322\pi$
$620$	6.65231	+	23.7038i	0.267163	+	0.951966i
$621$		0			0
$622$	−29.0307	+	3.99644i	−1.16403	+	0.160243i
$623$	−1.40318	−	2.43038i	−0.0562173	−	0.0973713i
$624$		0			0
$625$	6.40923	−	11.1011i	0.256369	−	0.444044i
$626$	−1.85308	+	4.54951i	−0.0740640	+	0.181835i
$627$		0			0
$628$	8.05179	−	8.24419i	0.321301	−	0.328979i
$629$	−19.3972			−0.773415
$630$		0			0
$631$			34.0954i			1.35732i	0.734454	+	0.678659i	$0.237439\pi$
$631$			34.0954i			1.35732i	−0.734454	+	0.678659i	$0.762561\pi$
$632$	−15.1965	+	20.5479i	−0.604486	+	0.817353i
$633$		0			0
$634$	−8.15559	+	20.0228i	−0.323900	+	0.795208i
$635$	−24.6735	−	14.2452i	−0.979138	−	0.565305i
$636$		0			0
$637$	−6.35854	+	3.67111i	−0.251935	+	0.145455i
$638$	1.55751	+	11.3140i	0.0616624	+	0.447924i
$639$		0			0
$640$	−11.6590	+	16.5692i	−0.460864	+	0.654954i
$641$	−20.9715	+	12.1079i	−0.828324	+	0.478233i	−0.853279	−	0.521455i	$-0.825389\pi$
$641$	−20.9715	+	12.1079i	−0.828324	+	0.478233i	0.0249544	+	0.999689i	$0.492056\pi$
$642$		0			0
$643$	11.3299	−	19.6240i	0.446808	−	0.773895i	−0.551368	−	0.834262i	$-0.685894\pi$
$643$	11.3299	−	19.6240i	0.446808	−	0.773895i	0.998176	+	0.0603676i	$0.0192273\pi$
$644$	−12.7111	−	3.24559i	−0.500889	−	0.127894i
$645$		0			0
$646$	12.9300	−	10.0434i	0.508726	−	0.395152i
$647$	−38.6020			−1.51760			−0.758800	−	0.651323i	$-0.774214\pi$
$647$	−38.6020			−1.51760			−0.758800	+	0.651323i	$0.774214\pi$
$648$		0			0
$649$	11.1428			0.437393
$650$	−12.3838	+	9.61906i	−0.485731	+	0.377291i
$651$		0			0
$652$	−5.58565	+	21.8758i	−0.218751	+	0.856722i
$653$	−13.1416	+	22.7619i	−0.514271	+	0.890743i	0.485592	+	0.874185i	$0.338604\pi$
$653$	−13.1416	+	22.7619i	−0.514271	+	0.890743i	−0.999863	+	0.0165576i	$0.994729\pi$
$654$		0			0
$655$	2.48501	−	1.43472i	0.0970973	−	0.0560592i
$656$	−12.7903	−	20.9927i	−0.499378	−	0.819627i
$657$		0			0
$658$	4.54748	+	33.0335i	0.177279	+	1.28778i
$659$	−33.1862	+	19.1601i	−1.29275	+	0.746370i	−0.979141	−	0.203182i	$-0.934872\pi$
$659$	−33.1862	+	19.1601i	−1.29275	+	0.746370i	−0.313610	+	0.949552i	$0.601538\pi$
$660$		0			0
$661$	−38.7145	−	22.3518i	−1.50582	−	0.869385i	−0.999977	−	0.00675901i	$-0.997849\pi$
$661$	−38.7145	−	22.3518i	−1.50582	−	0.869385i	−0.505842	−	0.862626i	$-0.668818\pi$
$662$	−3.30739	+	8.12000i	−0.128546	+	0.315593i
$663$		0			0
$664$	26.3224	−	35.5917i	1.02151	−	1.38122i
$665$		−	13.5109i		−	0.523928i
$666$		0			0
$667$	13.8915			0.537882
$668$	1.08298	+	1.05770i	0.0419016	+	0.0409237i
$669$		0			0
$670$	−1.98297	+	4.86840i	−0.0766088	+	0.188083i
$671$	−2.78616	+	4.82576i	−0.107558	+	0.186297i
$672$		0			0
$673$	−12.8138	−	22.1942i	−0.493937	−	0.855524i	0.506039	−	0.862511i	$-0.331109\pi$
$673$	−12.8138	−	22.1942i	−0.493937	−	0.855524i	−0.999976	+	0.00698696i	$0.997776\pi$
$674$	−26.9860	+	3.71496i	−1.03946	+	0.143095i
$675$		0			0
$676$	−48.5897	+	13.6364i	−1.86883	+	0.524476i
$677$	−11.1613	−	19.3320i	−0.428964	−	0.742988i	0.567817	−	0.823155i	$-0.307788\pi$
$677$	−11.1613	−	19.3320i	−0.428964	−	0.742988i	−0.996781	+	0.0801666i	$0.974455\pi$
$678$		0			0
$679$	28.1027	+	16.2251i	1.07848	+	0.622662i
$680$	−18.6178	−	2.11640i	−0.713960	−	0.0811604i
$681$		0			0
$682$	−9.43208	−	12.1430i	−0.361173	−	0.464981i
$683$		−	20.5229i		−	0.785288i	−0.919691	−	0.392644i	$-0.871560\pi$
$683$		−	20.5229i		−	0.785288i	0.919691	−	0.392644i	$-0.128440\pi$
$684$		0			0
$685$			21.9502i			0.838676i
$686$	22.0462	−	17.1244i	0.841728	−	0.653811i
$687$		0			0
$688$	0.0854595	+	3.61863i	0.00325811	+	0.137959i
$689$	37.8010	+	21.8244i	1.44010	+	0.831444i
$690$		0			0
$691$	−5.97960	−	10.3570i	−0.227475	−	0.393998i	0.729584	−	0.683891i	$-0.239714\pi$
$691$	−5.97960	−	10.3570i	−0.227475	−	0.393998i	−0.957059	+	0.289893i	$0.906380\pi$
$692$	17.8209	−	5.00132i	0.677449	−	0.190122i
$693$		0			0
$694$	−5.10412	−	37.0770i	−0.193750	−	1.40742i
$695$	−1.10837	−	1.91975i	−0.0420429	−	0.0728204i
$696$		0			0
$697$	11.3675	−	19.6891i	0.430576	−	0.745779i
$698$	22.4376	+	9.13914i	0.849274	+	0.345922i
$699$		0			0
$700$	6.04142	−	6.18579i	0.228344	−	0.233801i
$701$	41.9171			1.58319			0.791593	−	0.611049i	$-0.209252\pi$
$701$	41.9171			1.58319			0.791593	+	0.611049i	$0.209252\pi$
$702$		0			0
$703$		−	16.4084i		−	0.618853i
$704$	2.84004	−	12.3304i	0.107038	−	0.464718i
$705$		0			0
$706$	−40.5513	−	16.5171i	−1.52617	−	0.621630i
$707$	13.6988	+	7.90899i	0.515195	+	0.297448i
$708$		0			0
$709$	−4.41486	+	2.54892i	−0.165803	+	0.0957266i	−0.580606	−	0.814185i	$-0.697184\pi$
$709$	−4.41486	+	2.54892i	−0.165803	+	0.0957266i	0.414802	+	0.909912i	$0.363851\pi$
$710$	8.31700	−	1.14494i	0.312131	−	0.0429688i
$711$		0			0
$712$	−1.31359	−	3.01894i	−0.0492289	−	0.113140i
$713$	−16.1968	+	9.35122i	−0.606575	+	0.350206i
$714$		0			0
$715$	−8.75666	+	15.1670i	−0.327480	+	0.567213i
$716$	3.03328	+	0.774503i	0.113359	+	0.0289445i
$717$		0			0
$718$	5.58497	+	7.19020i	0.208429	+	0.268336i
$719$	35.1676			1.31153			0.655765	−	0.754965i	$-0.272346\pi$
$719$	35.1676			1.31153			0.655765	+	0.754965i	$0.272346\pi$
$720$		0			0
$721$	14.2582			0.531003
$722$	−7.98715	−	10.2828i	−0.297251	−	0.382686i
$723$		0			0
$724$	7.13702	+	1.82233i	0.265245	+	0.0677264i
$725$	−4.57787	+	7.92911i	−0.170018	+	0.294480i
$726$		0			0
$727$	19.9209	−	11.5013i	0.738826	−	0.426561i	−0.0828164	−	0.996565i	$-0.526391\pi$
$727$	19.9209	−	11.5013i	0.738826	−	0.426561i	0.821642	+	0.570003i	$0.193058\pi$
$728$	38.6634	−	16.8231i	1.43296	−	0.623506i
$729$		0			0
$730$	−1.58316	+	0.217941i	−0.0585952	+	0.00806637i
$731$	−2.89915	+	1.67383i	−0.107229	+	0.0619087i
$732$		0			0
$733$	7.38177	+	4.26187i	0.272652	+	0.157416i	0.630092	−	0.776520i	$-0.283017\pi$
$733$	7.38177	+	4.26187i	0.272652	+	0.157416i	−0.357440	+	0.933936i	$0.616350\pi$
$734$	−36.1037	−	14.7055i	−1.33261	−	0.542792i
$735$		0			0
$736$	−14.3868	−	5.46759i	−0.530305	−	0.201538i
$737$		−	3.28305i		−	0.120933i
$738$		0			0
$739$	32.3956			1.19169			0.595846	−	0.803099i	$-0.296817\pi$
$739$	32.3956			1.19169			0.595846	+	0.803099i	$0.296817\pi$
$740$	−13.1210	+	13.4345i	−0.482336	+	0.493862i
$741$		0			0
$742$	−22.2905	−	9.07923i	−0.818308	−	0.333309i
$743$	−2.22350	+	3.85122i	−0.0815725	+	0.141288i	−0.903926	−	0.427690i	$-0.859328\pi$
$743$	−2.22350	+	3.85122i	−0.0815725	+	0.141288i	0.822353	+	0.568978i	$0.192661\pi$
$744$		0			0
$745$	5.31821	+	9.21141i	0.194844	+	0.337480i
$746$	5.17887	+	37.6200i	0.189612	+	1.37737i
$747$		0			0
$748$	11.2671	−	3.16205i	0.411967	−	0.115616i
$749$	−1.22339	−	2.11897i	−0.0447016	−	0.0774255i
$750$		0			0
$751$	32.3801	+	18.6946i	1.18157	+	0.682177i	0.956376	−	0.292138i	$-0.0943666\pi$
$751$	32.3801	+	18.6946i	1.18157	+	0.682177i	0.225189	+	0.974315i	$0.427700\pi$
$752$	0.923608	+	39.1085i	0.0336805	+	1.42614i
$753$		0			0
$754$	−35.2606	+	27.3886i	−1.28412	+	0.997435i
$755$			24.7437i			0.900517i
$756$		0			0
$757$		−	46.7837i		−	1.70038i	−0.526474	−	0.850191i	$-0.676486\pi$
$757$		−	46.7837i		−	1.70038i	0.526474	−	0.850191i	$-0.323514\pi$
$758$	4.02503	+	5.18190i	0.146196	+	0.188215i
$759$		0			0
$760$	1.79030	−	15.7491i	0.0649410	−	0.571279i
$761$	−5.83226	−	3.36726i	−0.211419	−	0.122063i	0.390552	−	0.920581i	$-0.372284\pi$
$761$	−5.83226	−	3.36726i	−0.211419	−	0.122063i	−0.601971	+	0.798518i	$0.705618\pi$
$762$		0			0
$763$	5.38016	+	9.31870i	0.194775	+	0.337360i
$764$	−45.7053	+	12.8269i	−1.65356	+	0.464061i
$765$		0			0
$766$	49.7442	−	6.84792i	1.79733	−	0.247425i
$767$	21.7809	+	37.7255i	0.786461	+	1.36219i
$768$		0			0
$769$	−8.91160	+	15.4353i	−0.321361	+	0.556613i	−0.980769	−	0.195172i	$-0.937473\pi$
$769$	−8.91160	+	15.4353i	−0.321361	+	0.556613i	0.659408	+	0.751785i	$0.270807\pi$
$770$	3.64288	−	8.94364i	0.131280	−	0.322307i
$771$		0			0
$772$	36.6322	+	35.7773i	1.31842	+	1.28765i
$773$	−18.9682			−0.682237			−0.341119	−	0.940020i	$-0.610806\pi$
$773$	−18.9682			−0.682237			−0.341119	+	0.940020i	$0.610806\pi$
$774$		0			0
$775$		−	12.3266i		−	0.442783i
$776$	30.6083	+	22.6368i	1.09877	+	0.812614i
$777$		0			0
$778$	−3.41338	+	8.38020i	−0.122375	+	0.300445i
$779$	16.6554	+	9.61597i	0.596740	+	0.344528i
$780$		0			0
$781$	−4.54081	+	2.62164i	−0.162483	+	0.0938096i
$782$	−1.94122	−	14.1013i	−0.0694178	−	0.504260i
$783$		0			0
$784$	4.05614	−	2.47130i	0.144862	−	0.0882607i
$785$	8.93578	−	5.15907i	0.318932	−	0.184135i
$786$		0			0
$787$	−1.03810	+	1.79804i	−0.0370041	+	0.0640931i	−0.883934	−	0.467611i	$-0.845115\pi$
$787$	−1.03810	+	1.79804i	−0.0370041	+	0.0640931i	0.846930	+	0.531704i	$0.178448\pi$
$788$	2.85326	−	11.1746i	0.101643	−	0.398079i
$789$		0			0
$790$	−18.0718	+	14.0372i	−0.642965	+	0.499422i
$791$	20.4792			0.728155
$792$		0			0
$793$	−21.7844			−0.773588
$794$	3.37176	−	2.61901i	0.119659	−	0.0929452i
$795$		0			0
$796$	2.40607	+	0.614353i	0.0852808	+	0.0217752i
$797$	17.7593	−	30.7601i	0.629068	−	1.08958i	−0.358671	−	0.933464i	$-0.616770\pi$
$797$	17.7593	−	30.7601i	0.629068	−	1.08958i	0.987739	−	0.156113i	$-0.0498965\pi$
$798$		0			0
$799$	−31.3327	+	18.0900i	−1.10847	+	0.639977i
$800$	7.86192	−	6.40999i	0.277961	−	0.226628i
$801$		0			0
$802$	−5.59407	−	40.6361i	−0.197533	−	1.43491i
$803$	0.864352	−	0.499034i	0.0305023	−	0.0176105i
$804$		0			0
$805$	−10.1727	−	5.87320i	−0.358540	−	0.207003i
$806$	22.6751	−	55.6697i	0.798696	−	1.96088i
$807$		0			0
$808$	14.9201	+	11.0344i	0.524888	+	0.388189i
$809$		−	41.7225i		−	1.46688i	−0.679752	−	0.733442i	$-0.737913\pi$
$809$		−	41.7225i		−	1.46688i	0.679752	−	0.733442i	$-0.262087\pi$
$810$		0			0
$811$	−3.03064			−0.106420			−0.0532102	−	0.998583i	$-0.516945\pi$
$811$	−3.03064			−0.106420			−0.0532102	+	0.998583i	$0.516945\pi$
$812$	17.2019	−	17.6130i	0.603669	−	0.618093i
$813$		0			0
$814$	4.42412	−	10.8617i	0.155065	−	0.380702i
$815$	−10.1078	+	17.5071i	−0.354059	+	0.613248i
$816$		0			0
$817$	−1.41592	−	2.45244i	−0.0495366	−	0.0858000i
$818$	−1.85540	+	0.255419i	−0.0648725	+	0.00893052i
$819$		0			0
$820$	−5.94730	−	21.1916i	−0.207689	−	0.740044i
$821$	−25.9259	−	44.9049i	−0.904819	−	1.56719i	−0.821160	−	0.570698i	$-0.806673\pi$
$821$	−25.9259	−	44.9049i	−0.904819	−	1.56719i	−0.0836589	−	0.996494i	$-0.526661\pi$
$822$		0			0
$823$	−28.3812	−	16.3859i	−0.989307	−	0.571177i	−0.0842401	−	0.996445i	$-0.526846\pi$
$823$	−28.3812	−	16.3859i	−0.989307	−	0.571177i	−0.905067	+	0.425269i	$0.860180\pi$
$824$	16.6202	+	1.88933i	0.578994	+	0.0658180i
$825$		0			0
$826$	−14.7350	−	18.9701i	−0.512697	−	0.660055i
$827$			52.8295i			1.83706i	0.395350	+	0.918531i	$0.370623\pi$
$827$			52.8295i			1.83706i	−0.395350	+	0.918531i	$0.629377\pi$
$828$		0			0
$829$		−	0.0144624i		−	0.000502300i	−1.00000		0.000251150i	$-0.999920\pi$
$829$		−	0.0144624i		−	0.000502300i	1.00000		0.000251150i	$-7.99435e-5\pi$
$830$	31.3026	−	24.3143i	1.08653	−	0.843961i
$831$		0			0
$832$	47.2977	−	14.4868i	1.63975	−	0.502240i
$833$	3.80427	+	2.19639i	0.131810	+	0.0761006i
$834$		0			0
$835$	0.677708	+	1.17382i	0.0234531	+	0.0406219i
$836$	2.67483	+	9.53104i	0.0925108	+	0.329638i
$837$		0			0
$838$	6.07919	+	44.1600i	0.210002	+	1.52548i
$839$	16.6802	+	28.8909i	0.575864	+	0.997425i	0.995947	+	0.0899399i	$0.0286675\pi$
$839$	16.6802	+	28.8909i	0.575864	+	0.997425i	−0.420083	+	0.907486i	$0.637999\pi$
$840$		0			0
$841$	1.46530	−	2.53797i	0.0505275	−	0.0875162i
$842$	46.8604	+	19.0869i	1.61492	+	0.657779i
$843$		0			0
$844$	4.64138	+	4.53306i	0.159763	+	0.156034i
$845$	−45.1869			−1.55448
$846$		0			0
$847$		−	20.4890i		−	0.704010i
$848$	−24.7801	−	13.5370i	−0.850951	−	0.464862i
$849$		0			0
$850$	8.68854	+	3.53897i	0.298014	+	0.121386i
$851$	−12.3543	−	7.13276i	−0.423500	−	0.244508i
$852$		0			0
$853$	−32.7219	+	18.8920i	−1.12038	+	0.646850i	−0.941497	−	0.337021i	$-0.890581\pi$
$853$	−32.7219	+	18.8920i	−1.12038	+	0.646850i	−0.178880	+	0.983871i	$0.557247\pi$
$854$	11.9000	−	1.63819i	0.407210	−	0.0560576i
$855$		0			0
$856$	−1.14528	−	2.63211i	−0.0391447	−	0.0899637i
$857$	−9.00665	+	5.19999i	−0.307661	+	0.177628i	−0.645879	−	0.763439i	$-0.723509\pi$
$857$	−9.00665	+	5.19999i	−0.307661	+	0.177628i	0.338218	+	0.941068i	$0.390176\pi$
$858$		0			0
$859$	−10.3547	+	17.9348i	−0.353297	+	0.611929i	−0.986825	−	0.161791i	$-0.948273\pi$
$859$	−10.3547	+	17.9348i	−0.353297	+	0.611929i	0.633528	+	0.773720i	$0.281606\pi$
$860$	−0.801801	+	3.14019i	−0.0273412	+	0.107080i
$861$		0			0
$862$	−14.8459	−	19.1129i	−0.505654	−	0.650988i
$863$	4.67705			0.159209			0.0796043	−	0.996827i	$-0.474634\pi$
$863$	4.67705			0.159209			0.0796043	+	0.996827i	$0.474634\pi$
$864$		0			0
$865$	16.5729			0.563495
$866$	−16.5784	−	21.3433i	−0.563355	−	0.725274i
$867$		0			0
$868$	−8.20018	+	32.1154i	−0.278332	+	1.09007i
$869$	7.14567	−	12.3767i	0.242400	−	0.419849i
$870$		0			0
$871$	11.1152	−	6.41739i	0.376626	−	0.217445i
$872$	5.03664	+	11.5754i	0.170562	+	0.391992i
$873$		0			0
$874$	11.9285	−	1.64211i	0.403487	−	0.0555450i
$875$	25.3995	−	14.6644i	0.858660	−	0.495748i
$876$		0			0
$877$	9.04467	+	5.22194i	0.305417	+	0.176333i	0.644874	−	0.764289i	$-0.276910\pi$
$877$	9.04467	+	5.22194i	0.305417	+	0.176333i	−0.339457	+	0.940622i	$0.610243\pi$
$878$	−44.5972	−	18.1651i	−1.50508	−	0.613042i
$879$		0			0
$880$	5.43147	−	9.94255i	0.183095	−	0.335163i
$881$			29.7734i			1.00309i	0.865131	+	0.501546i	$0.167235\pi$
$881$			29.7734i			1.00309i	−0.865131	+	0.501546i	$0.832765\pi$
$882$		0			0
$883$	−52.9294			−1.78122			−0.890608	−	0.454772i	$-0.849721\pi$
$883$	−52.9294			−1.78122			−0.890608	+	0.454772i	$0.849721\pi$
$884$	32.7295	+	31.9656i	1.10081	+	1.07512i
$885$		0			0
$886$	−25.9498	−	10.5697i	−0.871801	−	0.355097i
$887$	22.4416	−	38.8700i	0.753515	−	1.30513i	−0.192594	−	0.981278i	$-0.561690\pi$
$887$	22.4416	−	38.8700i	0.753515	−	1.30513i	0.946109	−	0.323848i	$-0.104977\pi$
$888$		0			0
$889$	−19.1787	−	33.2184i	−0.643232	−	1.11411i
$890$	−0.402022	−	2.92035i	−0.0134758	−	0.0978902i
$891$		0			0
$892$	7.56434	+	26.9535i	0.253273	+	0.902471i
$893$	−15.3026	−	26.5048i	−0.512081	−	0.886951i
$894$		0			0
$895$	2.42753	+	1.40153i	0.0811434	+	0.0468481i
$896$	−24.7475	+	11.4704i	−0.826757	+	0.383199i
$897$		0			0
$898$	−9.76050	+	7.58145i	−0.325712	+	0.252996i
$899$		−	35.0978i		−	1.17058i
$900$		0			0
$901$		−	26.1148i		−	0.870009i
$902$	8.43246	+	10.8561i	0.280770	+	0.361469i
$903$		0			0
$904$	23.8718	+	2.71366i	0.793963	+	0.0902549i
$905$	5.71174	+	3.29768i	0.189865	+	0.109618i
$906$		0			0
$907$	−8.19627	−	14.1964i	−0.272153	−	0.471382i	0.697260	−	0.716818i	$-0.254402\pi$
$907$	−8.19627	−	14.1964i	−0.272153	−	0.471382i	−0.969413	+	0.245436i	$0.921069\pi$
$908$	5.46238	+	19.4637i	0.181275	+	0.645927i
$909$		0			0
$910$	37.4008	−	5.14869i	1.23982	−	0.170677i
$911$	−13.4518	−	23.2991i	−0.445677	−	0.771935i	0.552422	−	0.833564i	$-0.313704\pi$
$911$	−13.4518	−	23.2991i	−0.445677	−	0.771935i	−0.998099	+	0.0616295i	$0.980370\pi$
$912$		0			0
$913$	−12.3772	+	21.4380i	−0.409626	+	0.709493i
$914$	1.33455	−	3.27646i	0.0441430	−	0.108376i
$915$		0			0
$916$	16.0237	−	16.4066i	0.529439	−	0.542091i
$917$	3.86319			0.127574
$918$		0			0
$919$		−	22.2518i		−	0.734020i	−0.930217	−	0.367010i	$-0.880381\pi$
$919$		−	22.2518i		−	0.734020i	0.930217	−	0.367010i	$-0.119619\pi$
$920$	−11.0797	−	8.19413i	−0.365286	−	0.270153i
$921$		0			0
$922$	2.81054	−	6.90017i	0.0925603	−	0.227245i
$923$	−17.7519	−	10.2491i	−0.584310	−	0.337352i
$924$		0			0
$925$	8.14257	−	4.70112i	0.267726	−	0.154572i
$926$	−3.39012	−	24.6263i	−0.111406	−	0.809271i
$927$		0			0
$928$	22.3855	−	18.2513i	0.734839	−	0.599130i
$929$	8.55489	−	4.93917i	0.280677	−	0.162049i	−0.353053	−	0.935603i	$-0.614856\pi$
$929$	8.55489	−	4.93917i	0.280677	−	0.162049i	0.633730	+	0.773555i	$0.281523\pi$
$930$		0			0
$931$	−1.85796	+	3.21809i	−0.0608923	+	0.105469i
$932$	13.0776	+	3.33917i	0.428372	+	0.109378i
$933$		0			0
$934$	−2.56703	+	1.99394i	−0.0839959	+	0.0652437i
$935$	10.4781			0.342670
$936$		0			0
$937$	−2.11802			−0.0691926			−0.0345963	−	0.999401i	$-0.511015\pi$
$937$	−2.11802			−0.0691926			−0.0345963	+	0.999401i	$0.511015\pi$
$938$	−5.58925	+	4.34144i	−0.182496	+	0.141753i
$939$		0			0
$940$	−8.66550	+	33.9378i	−0.282637	+	1.10693i
$941$	3.56180	−	6.16922i	0.116111	−	0.201111i	−0.802112	−	0.597173i	$-0.796290\pi$
$941$	3.56180	−	6.16922i	0.116111	−	0.201111i	0.918223	+	0.396063i	$0.129624\pi$
$942$		0			0
$943$	14.4803	−	8.36018i	0.471542	−	0.272245i
$944$	−14.6623	−	24.0653i	−0.477219	−	0.783257i
$945$		0			0
$946$	−0.276039	−	2.00518i	−0.00897480	−	0.0651942i
$947$	−44.5581	+	25.7256i	−1.44794	+	0.835970i	−0.998359	−	0.0572679i	$-0.981761\pi$
$947$	−44.5581	+	25.7256i	−1.44794	+	0.835970i	−0.449584	+	0.893238i	$0.648428\pi$
$948$		0			0
$949$	3.37910	+	1.95093i	0.109690	+	0.0633297i
$950$	−2.99367	+	7.34977i	−0.0971274	+	0.238458i
$951$		0			0
$952$	−20.2827	−	15.0004i	−0.657366	−	0.486165i
$953$			45.3652i			1.46952i	0.678326	+	0.734761i	$0.262706\pi$
$953$			45.3652i			1.46952i	−0.678326	+	0.734761i	$0.737294\pi$
$954$		0			0
$955$	−42.5046			−1.37542
$956$	0.193988	+	0.189461i	0.00627403	+	0.00612761i
$957$		0			0
$958$	19.2284	−	47.2078i	0.621243	−	1.52522i
$959$	−14.7760	+	25.5928i	−0.477143	+	0.826436i
$960$		0			0
$961$	8.12641	+	14.0754i	0.262142	+	0.454044i
$962$	45.4216	−	6.25286i	1.46445	−	0.201600i
$963$		0			0
$964$	37.4239	−	10.5028i	1.20534	−	0.338271i
$965$	22.9238	+	39.7052i	0.737944	+	1.27816i
$966$		0			0
$967$	2.55341	+	1.47421i	0.0821121	+	0.0474075i	0.540494	−	0.841348i	$-0.318237\pi$
$967$	2.55341	+	1.47421i	0.0821121	+	0.0474075i	−0.458382	+	0.888755i	$0.651571\pi$
$968$	2.71496	−	23.8832i	0.0872622	−	0.767636i
$969$		0			0
$970$	20.9099	+	26.9198i	0.671376	+	0.864342i
$971$			21.8052i			0.699763i	0.936794	+	0.349882i	$0.113778\pi$
$971$			21.8052i			0.699763i	−0.936794	+	0.349882i	$0.886222\pi$
$972$		0			0
$973$		−	2.98444i		−	0.0956768i
$974$	3.04115	−	2.36221i	0.0974447	−	0.0756901i
$975$		0			0
$976$	14.0885	−	0.332721i	0.450961	−	0.0106501i
$977$	−26.7110	−	15.4216i	−0.854560	−	0.493381i	0.00762657	−	0.999971i	$-0.497572\pi$
$977$	−26.7110	−	15.4216i	−0.854560	−	0.493381i	−0.862187	+	0.506590i	$0.830906\pi$
$978$		0			0
$979$	0.920536	+	1.59441i	0.0294204	+	0.0509577i
$980$	4.09457	−	1.14912i	0.130796	−	0.0367072i
$981$		0			0
$982$	−2.93332	−	21.3080i	−0.0936059	−	0.679966i
$983$	−6.49316	−	11.2465i	−0.207100	−	0.358707i	0.743700	−	0.668513i	$-0.233069\pi$
$983$	−6.49316	−	11.2465i	−0.207100	−	0.358707i	−0.950800	+	0.309806i	$0.899736\pi$
$984$		0			0
$985$	5.16324	−	8.94300i	0.164515	−	0.284948i
$986$	24.7391	+	10.0766i	0.787854	+	0.320904i
$987$		0			0
$988$	−27.0402	+	27.6864i	−0.860265	+	0.880821i
$989$	−2.46201			−0.0782873
$990$		0			0
$991$			47.5865i			1.51163i	0.654783	+	0.755817i	$0.272760\pi$
$991$			47.5865i			1.51163i	−0.654783	+	0.755817i	$0.727240\pi$
$992$	−13.8142	+	36.3491i	−0.438601	+	1.15409i
$993$		0			0
$994$	10.4679	+	4.26373i	0.332022	+	0.135237i
$995$	1.92557	+	1.11173i	0.0610447	+	0.0352442i
$996$		0			0
$997$	7.41748	−	4.28248i	0.234914	−	0.135628i	−0.377923	−	0.925837i	$-0.623362\pi$
$997$	7.41748	−	4.28248i	0.234914	−	0.135628i	0.612837	+	0.790209i	$0.290028\pi$
$998$	−55.2850	+	7.61067i	−1.75001	+	0.240912i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.l.b.179.6		16
3.2	odd	2		72.2.l.b.59.3	yes	16
4.3	odd	2		864.2.p.b.719.3		16
8.3	odd	2	inner	216.2.l.b.179.2		16
8.5	even	2		864.2.p.b.719.6		16
9.2	odd	6	inner	216.2.l.b.35.2		16
9.4	even	3		648.2.f.b.323.2		16
9.5	odd	6		648.2.f.b.323.15		16
9.7	even	3		72.2.l.b.11.7	yes	16
12.11	even	2		288.2.p.b.239.2		16
24.5	odd	2		288.2.p.b.239.1		16
24.11	even	2		72.2.l.b.59.7	yes	16
36.7	odd	6		288.2.p.b.47.1		16
36.11	even	6		864.2.p.b.143.6		16
36.23	even	6		2592.2.f.b.1295.6		16
36.31	odd	6		2592.2.f.b.1295.12		16
72.5	odd	6		2592.2.f.b.1295.11		16
72.11	even	6	inner	216.2.l.b.35.6		16
72.13	even	6		2592.2.f.b.1295.5		16
72.29	odd	6		864.2.p.b.143.3		16
72.43	odd	6		72.2.l.b.11.3	✓	16
72.59	even	6		648.2.f.b.323.1		16
72.61	even	6		288.2.p.b.47.2		16
72.67	odd	6		648.2.f.b.323.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.3	✓	16	72.43	odd	6
72.2.l.b.11.7	yes	16	9.7	even	3
72.2.l.b.59.3	yes	16	3.2	odd	2
72.2.l.b.59.7	yes	16	24.11	even	2
216.2.l.b.35.2		16	9.2	odd	6	inner
216.2.l.b.35.6		16	72.11	even	6	inner
216.2.l.b.179.2		16	8.3	odd	2	inner
216.2.l.b.179.6		16	1.1	even	1	trivial
288.2.p.b.47.1		16	36.7	odd	6
288.2.p.b.47.2		16	72.61	even	6
288.2.p.b.239.1		16	24.5	odd	2
288.2.p.b.239.2		16	12.11	even	2
648.2.f.b.323.1		16	72.59	even	6
648.2.f.b.323.2		16	9.4	even	3
648.2.f.b.323.15		16	9.5	odd	6
648.2.f.b.323.16		16	72.67	odd	6
864.2.p.b.143.3		16	72.29	odd	6
864.2.p.b.143.6		16	36.11	even	6
864.2.p.b.719.3		16	4.3	odd	2
864.2.p.b.719.6		16	8.5	even	2
2592.2.f.b.1295.5		16	72.13	even	6
2592.2.f.b.1295.6		16	36.23	even	6
2592.2.f.b.1295.11		16	72.5	odd	6
2592.2.f.b.1295.12		16	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.867527 + 1.11687i) q^{2} +(-0.494795 + 1.93783i) q^{4} +(-0.895377 + 1.55084i) q^{5} +(-2.08793 + 1.20546i) q^{7} +(-2.59355 + 1.12850i) q^{8} +O(q^{10})\)	\(q+(0.867527 + 1.11687i) q^{2} +(-0.494795 + 1.93783i) q^{4} +(-0.895377 + 1.55084i) q^{5} +(-2.08793 + 1.20546i) q^{7} +(-2.59355 + 1.12850i) q^{8} +(-2.50885 + 0.345375i) q^{10} +(1.36975 - 0.790826i) q^{11} +(5.35491 + 3.09166i) q^{13} +(-3.15768 - 1.28617i) q^{14} +(-3.51036 - 1.91766i) q^{16} -3.69943i q^{17} +3.12941 q^{19} +(-2.56223 - 2.50243i) q^{20} +(2.07154 + 0.843770i) q^{22} +(1.36036 - 2.35622i) q^{23} +(0.896599 + 1.55296i) q^{25} +(1.19255 + 8.66283i) q^{26} +(-1.30289 - 4.64250i) q^{28} +(2.55291 + 4.42177i) q^{29} +(-5.95312 - 3.43703i) q^{31} +(-0.903557 - 5.58423i) q^{32} +(4.13178 - 3.20936i) q^{34} -4.31738i q^{35} -5.24328i q^{37} +(2.71485 + 3.49514i) q^{38} +(0.572089 - 5.03261i) q^{40} +(5.32220 + 3.07278i) q^{41} +(-0.452455 - 0.783675i) q^{43} +(0.854739 + 3.04564i) q^{44} +(3.81174 - 0.524733i) q^{46} +(-4.88993 - 8.46960i) q^{47} +(-0.593711 + 1.02834i) q^{49} +(-0.956625 + 2.34861i) q^{50} +(-8.64069 + 8.84716i) q^{52} +7.05913 q^{53} +2.83235i q^{55} +(4.05478 - 5.48265i) q^{56} +(-2.72382 + 6.68727i) q^{58} +(6.10118 + 3.52252i) q^{59} +(-3.05109 + 1.76155i) q^{61} +(-1.32577 - 9.63057i) q^{62} +(5.45299 - 5.85362i) q^{64} +(-9.58933 + 5.53640i) q^{65} +(1.03786 - 1.79762i) q^{67} +(7.16886 + 1.83046i) q^{68} +(4.82195 - 3.74544i) q^{70} -3.31507 q^{71} +0.631029 q^{73} +(5.85606 - 4.54868i) q^{74} +(-1.54842 + 6.06426i) q^{76} +(-1.90662 + 3.30237i) q^{77} +(7.82515 - 4.51785i) q^{79} +(6.11707 - 3.72697i) q^{80} +(1.18526 + 8.60992i) q^{82} +(-13.5542 + 7.82551i) q^{83} +(5.73722 + 3.31239i) q^{85} +(0.482746 - 1.18519i) q^{86} +(-2.66007 + 3.59680i) q^{88} +1.16402i q^{89} -14.9075 q^{91} +(3.89284 + 3.80199i) q^{92} +(5.21730 - 12.8090i) q^{94} +(-2.80200 + 4.85321i) q^{95} +(-6.72981 - 11.6564i) q^{97} +(-1.66358 + 0.229013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) \) 16 * q + 3 * q^2 - 5 * q^4	\( 16 q + 3 q^{2} - 5 q^{4} - 12 q^{11} + 18 q^{14} + 7 q^{16} - 4 q^{19} - 18 q^{20} - q^{22} - 14 q^{25} - 12 q^{28} - 27 q^{32} - 13 q^{34} + 15 q^{38} - 12 q^{40} + 36 q^{41} + 8 q^{43} + 12 q^{46} + 10 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 12 q^{59} + 34 q^{64} + 6 q^{65} - 16 q^{67} + 9 q^{68} + 18 q^{70} - 4 q^{73} + 60 q^{74} - 7 q^{76} - 22 q^{82} - 54 q^{83} + 51 q^{86} - 13 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 16 * q + 3 * q^2 - 5 * q^4 - 12 * q^11 + 18 * q^14 + 7 * q^16 - 4 * q^19 - 18 * q^20 - q^22 - 14 * q^25 - 12 * q^28 - 27 * q^32 - 13 * q^34 + 15 * q^38 - 12 * q^40 + 36 * q^41 + 8 * q^43 + 12 * q^46 + 10 * q^49 - 51 * q^50 - 18 * q^52 + 66 * q^56 + 12 * q^58 - 12 * q^59 + 34 * q^64 + 6 * q^65 - 16 * q^67 + 9 * q^68 + 18 * q^70 - 4 * q^73 + 60 * q^74 - 7 * q^76 - 22 * q^82 - 54 * q^83 + 51 * q^86 - 13 * q^88 - 36 * q^91 - 84 * q^92 + 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more