LMFDB - Embedded newform 729.2.e.o.406.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			406.2
Root			$0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.o.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32683 + 1.11334i) q^{2} +(0.173648 + 0.984808i) q^{4} +(1.62760 + 0.592396i) q^{5} +(0.347296 - 1.96962i) q^{7} +(0.866025 - 1.50000i) q^{8} +O(q^{10})$	\(q+(1.32683 + 1.11334i) q^{2} +(0.173648 + 0.984808i) q^{4} +(1.62760 + 0.592396i) q^{5} +(0.347296 - 1.96962i) q^{7} +(0.866025 - 1.50000i) q^{8} +(1.50000 + 2.59808i) q^{10} +(3.25519 - 1.18479i) q^{11} +(-0.766044 + 0.642788i) q^{13} +(2.65366 - 2.22668i) q^{14} +(4.69846 - 1.71010i) q^{16} +(-2.59808 - 4.50000i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-0.300767 + 1.70574i) q^{20} +(5.63816 + 2.05212i) q^{22} +(0.601535 + 3.41147i) q^{23} +(-1.53209 - 1.28558i) q^{25} -1.73205 q^{26} +2.00000 q^{28} +(1.32683 + 1.11334i) q^{29} +(1.38919 + 7.87846i) q^{31} +(4.88279 + 1.77719i) q^{32} +(1.56283 - 8.86327i) q^{34} +(1.73205 - 3.00000i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-3.25519 + 1.18479i) q^{38} +(2.29813 - 1.92836i) q^{40} +(-5.30731 + 4.45336i) q^{41} +(-1.87939 + 0.684040i) q^{43} +(1.73205 + 3.00000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(1.20307 - 6.82295i) q^{47} +(2.81908 + 1.02606i) q^{49} +(-0.601535 - 3.41147i) q^{50} +(-0.766044 - 0.642788i) q^{52} +6.00000 q^{55} +(-2.65366 - 2.22668i) q^{56} +(0.520945 + 2.95442i) q^{58} +(-13.0208 - 4.73917i) q^{59} +(-1.21554 + 6.89365i) q^{61} +(-6.92820 + 12.0000i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-1.62760 + 0.592396i) q^{65} +(-7.66044 + 6.42788i) q^{67} +(3.98048 - 3.34002i) q^{68} +(5.63816 - 2.05212i) q^{70} +(5.19615 + 9.00000i) q^{71} +(3.50000 - 6.06218i) q^{73} +(-2.10537 + 11.9402i) q^{74} +(-1.87939 - 0.684040i) q^{76} +(-1.20307 - 6.82295i) q^{77} +(1.53209 + 1.28558i) q^{79} +8.66025 q^{80} -12.0000 q^{82} +(-10.6146 - 8.90673i) q^{83} +(-1.56283 - 8.86327i) q^{85} +(-3.25519 - 1.18479i) q^{86} +(1.04189 - 5.90885i) q^{88} +(2.59808 - 4.50000i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-3.25519 + 1.18479i) q^{92} +(9.19253 - 7.71345i) q^{94} +(-2.65366 + 2.22668i) q^{95} +(-1.87939 + 0.684040i) q^{97} +(2.59808 + 4.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 18 q^{10} - 12 q^{19} + 24 q^{28} + 42 q^{37} - 36 q^{46} + 72 q^{55} - 6 q^{64} + 42 q^{73} - 144 q^{82} + 12 q^{91}+O(q^{100}) $ 12 * q + 18 * q^10 - 12 * q^19 + 24 * q^28 + 42 * q^37 - 36 * q^46 + 72 * q^55 - 6 * q^64 + 42 * q^73 - 144 * q^82 + 12 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	1.32683	+	1.11334i	0.938209	+	0.787251i	0.977273	−	0.211986i	$-0.0679931\pi$
$2$	1.32683	+	1.11334i	0.938209	+	0.787251i	−0.0390637	+	0.999237i	$0.512438\pi$
$3$		0			0
$3$		0			0
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	1.62760	+	0.592396i	0.727883	+	0.264928i	0.679268	−	0.733890i	$-0.262297\pi$
$5$	1.62760	+	0.592396i	0.727883	+	0.264928i	0.0486144	+	0.998818i	$0.484519\pi$
$6$		0			0
$7$	0.347296	−	1.96962i	0.131266	−	0.744445i	−0.846122	−	0.532989i	$-0.821069\pi$
$7$	0.347296	−	1.96962i	0.131266	−	0.744445i	0.977388	−	0.211455i	$-0.0678203\pi$
$8$	0.866025	−	1.50000i	0.306186	−	0.530330i
$9$		0			0
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	3.25519	−	1.18479i	0.981477	−	0.357228i	0.199063	−	0.979987i	$-0.436210\pi$
$11$	3.25519	−	1.18479i	0.981477	−	0.357228i	0.782414	+	0.622758i	$0.213988\pi$
$12$		0			0
$13$	−0.766044	+	0.642788i	−0.212463	+	0.178277i	−0.742808	−	0.669504i	$-0.766507\pi$
$13$	−0.766044	+	0.642788i	−0.212463	+	0.178277i	0.530346	+	0.847781i	$0.322062\pi$
$14$	2.65366	−	2.22668i	0.709219	−	0.595106i
$15$		0			0
$16$	4.69846	−	1.71010i	1.17462	−	0.427525i
$17$	−2.59808	−	4.50000i	−0.630126	−	1.09141i	−0.987526	−	0.157459i	$-0.949670\pi$
$17$	−2.59808	−	4.50000i	−0.630126	−	1.09141i	0.357400	−	0.933952i	$-0.383663\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	−0.300767	+	1.70574i	−0.0672537	+	0.381414i
$21$		0			0
$22$	5.63816	+	2.05212i	1.20206	+	0.437514i
$23$	0.601535	+	3.41147i	0.125429	+	0.711342i	0.981052	+	0.193743i	$0.0620628\pi$
$23$	0.601535	+	3.41147i	0.125429	+	0.711342i	−0.855624	+	0.517599i	$0.826826\pi$
$24$		0			0
$25$	−1.53209	−	1.28558i	−0.306418	−	0.257115i
$26$	−1.73205			−0.339683
$27$		0			0
$28$	2.00000			0.377964
$29$	1.32683	+	1.11334i	0.246386	+	0.206742i	0.757614	−	0.652703i	$-0.226365\pi$
$29$	1.32683	+	1.11334i	0.246386	+	0.206742i	−0.511228	+	0.859445i	$0.670809\pi$
$30$		0			0
$31$	1.38919	+	7.87846i	0.249505	+	1.41501i	0.809793	+	0.586716i	$0.199579\pi$
$31$	1.38919	+	7.87846i	0.249505	+	1.41501i	−0.560288	+	0.828298i	$0.689310\pi$
$32$	4.88279	+	1.77719i	0.863163	+	0.314166i
$33$		0			0
$34$	1.56283	−	8.86327i	0.268024	−	1.52004i
$35$	1.73205	−	3.00000i	0.292770	−	0.507093i
$36$		0			0
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	−3.25519	+	1.18479i	−0.528062	+	0.192199i
$39$		0			0
$40$	2.29813	−	1.92836i	0.363367	−	0.304901i
$41$	−5.30731	+	4.45336i	−0.828863	+	0.695498i	−0.955030	−	0.296511i	$-0.904177\pi$
$41$	−5.30731	+	4.45336i	−0.828863	+	0.695498i	0.126167	+	0.992009i	$0.459733\pi$
$42$		0			0
$43$	−1.87939	+	0.684040i	−0.286604	+	0.104315i	−0.481322	−	0.876544i	$-0.659843\pi$
$43$	−1.87939	+	0.684040i	−0.286604	+	0.104315i	0.194718	+	0.980859i	$0.437621\pi$
$44$	1.73205	+	3.00000i	0.261116	+	0.452267i
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	1.20307	−	6.82295i	0.175486	−	0.995229i	−0.762096	−	0.647464i	$-0.775830\pi$
$47$	1.20307	−	6.82295i	0.175486	−	0.995229i	0.937582	−	0.347765i	$-0.113059\pi$
$48$		0			0
$49$	2.81908	+	1.02606i	0.402725	+	0.146580i
$50$	−0.601535	−	3.41147i	−0.0850699	−	0.482455i
$51$		0			0
$52$	−0.766044	−	0.642788i	−0.106231	−	0.0891386i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$	−2.65366	−	2.22668i	−0.354610	−	0.297553i
$57$		0			0
$58$	0.520945	+	2.95442i	0.0684034	+	0.387935i
$59$	−13.0208	−	4.73917i	−1.69516	−	0.616987i	−0.699899	−	0.714241i	$-0.746772\pi$
$59$	−13.0208	−	4.73917i	−1.69516	−	0.616987i	−0.995260	+	0.0972541i	$0.968994\pi$
$60$		0			0
$61$	−1.21554	+	6.89365i	−0.155634	+	0.882642i	0.802571	+	0.596557i	$0.203465\pi$
$61$	−1.21554	+	6.89365i	−0.155634	+	0.882642i	−0.958204	+	0.286085i	$0.907646\pi$
$62$	−6.92820	+	12.0000i	−0.879883	+	1.52400i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.62760	+	0.592396i	−0.201878	+	0.0734777i
$66$		0			0
$67$	−7.66044	+	6.42788i	−0.935872	+	0.785290i	−0.976862	−	0.213870i	$-0.931393\pi$
$67$	−7.66044	+	6.42788i	−0.935872	+	0.785290i	0.0409900	+	0.999160i	$0.486949\pi$
$68$	3.98048	−	3.34002i	0.482705	−	0.405037i
$69$		0			0
$70$	5.63816	−	2.05212i	0.673889	−	0.245275i
$71$	5.19615	+	9.00000i	0.616670	+	1.06810i	0.990089	+	0.140441i	$0.0448520\pi$
$71$	5.19615	+	9.00000i	0.616670	+	1.06810i	−0.373419	+	0.927663i	$0.621815\pi$
$72$		0			0
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$	−2.10537	+	11.9402i	−0.244745	+	1.38802i
$75$		0			0
$76$	−1.87939	−	0.684040i	−0.215580	−	0.0784648i
$77$	−1.20307	−	6.82295i	−0.137103	−	0.777547i
$78$		0			0
$79$	1.53209	+	1.28558i	0.172373	+	0.144639i	0.724893	−	0.688861i	$-0.241889\pi$
$79$	1.53209	+	1.28558i	0.172373	+	0.144639i	−0.552520	+	0.833500i	$0.686334\pi$
$80$	8.66025			0.968246
$81$		0			0
$82$	−12.0000			−1.32518
$83$	−10.6146	−	8.90673i	−1.16511	−	0.977640i	−0.165143	−	0.986270i	$-0.552809\pi$
$83$	−10.6146	−	8.90673i	−1.16511	−	0.977640i	−0.999963	+	0.00862932i	$0.997253\pi$
$84$		0			0
$85$	−1.56283	−	8.86327i	−0.169513	−	0.961357i
$86$	−3.25519	−	1.18479i	−0.351016	−	0.127759i
$87$		0			0
$88$	1.04189	−	5.90885i	0.111066	−	0.629885i
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	−0.694839	−	0.719165i	$-0.744525\pi$
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	0.970235	+	0.242166i	$0.0778579\pi$
$90$		0			0
$91$	1.00000	+	1.73205i	0.104828	+	0.181568i
$92$	−3.25519	+	1.18479i	−0.339377	+	0.123523i
$93$		0			0
$94$	9.19253	−	7.71345i	0.948137	−	0.795582i
$95$	−2.65366	+	2.22668i	−0.272259	+	0.228453i
$96$		0			0
$97$	−1.87939	+	0.684040i	−0.190823	+	0.0694538i	−0.435664	−	0.900109i	$-0.643486\pi$
$97$	−1.87939	+	0.684040i	−0.190823	+	0.0694538i	0.244841	+	0.969563i	$0.421264\pi$
$98$	2.59808	+	4.50000i	0.262445	+	0.454569i
$99$		0			0
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	1.20307	−	6.82295i	0.119710	−	0.678909i	−0.864600	−	0.502461i	$-0.832428\pi$
$101$	1.20307	−	6.82295i	0.119710	−	0.678909i	0.984310	−	0.176448i	$-0.0564607\pi$
$102$		0			0
$103$	−7.51754	−	2.73616i	−0.740725	−	0.269602i	−0.0560277	−	0.998429i	$-0.517844\pi$
$103$	−7.51754	−	2.73616i	−0.740725	−	0.269602i	−0.684698	+	0.728827i	$0.740066\pi$
$104$	0.300767	+	1.70574i	0.0294927	+	0.167261i
$105$		0			0
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	11.0000			1.05361			0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000			1.05361			0.526804	+	0.849987i	$0.323390\pi$
$110$	7.96097	+	6.68004i	0.759048	+	0.636917i
$111$		0			0
$112$	−1.73648	−	9.84808i	−0.164082	−	0.930556i
$113$	1.62760	+	0.592396i	0.153111	+	0.0557280i	0.417439	−	0.908705i	$-0.362928\pi$
$113$	1.62760	+	0.592396i	0.153111	+	0.0557280i	−0.264328	+	0.964433i	$0.585150\pi$
$114$		0			0
$115$	−1.04189	+	5.90885i	−0.0971567	+	0.551003i
$116$	−0.866025	+	1.50000i	−0.0804084	+	0.139272i
$117$		0			0
$118$	−12.0000	−	20.7846i	−1.10469	−	1.91338i
$119$	−9.76557	+	3.55438i	−0.895209	+	0.325829i
$120$		0			0
$121$	0.766044	−	0.642788i	0.0696404	−	0.0584352i
$122$	−9.28780	+	7.79339i	−0.840877	+	0.705580i
$123$		0			0
$124$	−7.51754	+	2.73616i	−0.675095	+	0.245715i
$125$	−6.06218	−	10.5000i	−0.542218	−	0.939149i
$126$		0			0
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	0.818241	+	0.574875i	$0.194949\pi$
$128$	2.10537	−	11.9402i	0.186090	−	1.05537i
$129$		0			0
$130$	−2.81908	−	1.02606i	−0.247249	−	0.0899915i
$131$	0.601535	+	3.41147i	0.0525564	+	0.298062i	0.999744	−	0.0226174i	$-0.00719995\pi$
$131$	0.601535	+	3.41147i	0.0525564	+	0.298062i	−0.947188	+	0.320679i	$0.896089\pi$
$132$		0			0
$133$	3.06418	+	2.57115i	0.265698	+	0.222947i
$134$	−17.3205			−1.49626
$135$		0			0
$136$	−9.00000			−0.771744
$137$	1.32683	+	1.11334i	0.113359	+	0.0951191i	0.697705	−	0.716385i	$-0.254205\pi$
$137$	1.32683	+	1.11334i	0.113359	+	0.0951191i	−0.584346	+	0.811504i	$0.698649\pi$
$138$		0			0
$139$	1.38919	+	7.87846i	0.117829	+	0.668242i	0.985310	+	0.170773i	$0.0546264\pi$
$139$	1.38919	+	7.87846i	0.117829	+	0.668242i	−0.867481	+	0.497470i	$0.834263\pi$
$140$	3.25519	+	1.18479i	0.275114	+	0.100133i
$141$		0			0
$142$	−3.12567	+	17.7265i	−0.262300	+	1.48758i
$143$	−1.73205	+	3.00000i	−0.144841	+	0.250873i
$144$		0			0
$145$	1.50000	+	2.59808i	0.124568	+	0.215758i
$146$	11.3932	−	4.14677i	0.942905	−	0.343189i
$147$		0			0
$148$	−5.36231	+	4.49951i	−0.440779	+	0.369858i
$149$	6.63414	−	5.56670i	0.543490	−	0.456042i	−0.329239	−	0.944246i	$-0.606792\pi$
$149$	6.63414	−	5.56670i	0.543490	−	0.456042i	0.872729	+	0.488204i	$0.162348\pi$
$150$		0			0
$151$	−18.7939	+	6.84040i	−1.52942	+	0.556664i	−0.963480	−	0.267781i	$-0.913710\pi$
$151$	−18.7939	+	6.84040i	−1.52942	+	0.556664i	−0.565942	+	0.824445i	$0.691487\pi$
$152$	1.73205	+	3.00000i	0.140488	+	0.243332i
$153$		0			0
$154$	6.00000	−	10.3923i	0.483494	−	0.837436i
$155$	−2.40614	+	13.6459i	−0.193266	+	1.09606i
$156$		0			0
$157$	−15.9748	−	5.81434i	−1.27493	−	0.464035i	−0.386175	−	0.922426i	$-0.626204\pi$
$157$	−15.9748	−	5.81434i	−1.27493	−	0.464035i	−0.888751	+	0.458391i	$0.848426\pi$
$158$	0.601535	+	3.41147i	0.0478555	+	0.271402i
$159$		0			0
$160$	6.89440	+	5.78509i	0.545050	+	0.457351i
$161$	6.92820			0.546019
$162$		0			0
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	−5.30731	−	4.45336i	−0.414431	−	0.347749i
$165$		0			0
$166$	−4.16756	−	23.6354i	−0.323465	−	1.83446i
$167$	16.2760	+	5.92396i	1.25947	+	0.458410i	0.883592	−	0.468259i	$-0.155118\pi$
$167$	16.2760	+	5.92396i	1.25947	+	0.458410i	0.375880	+	0.926669i	$0.377341\pi$
$168$		0			0
$169$	−2.08378	+	11.8177i	−0.160291	+	0.909053i
$170$	7.79423	−	13.5000i	0.597790	−	1.03540i
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	17.9035	−	6.51636i	1.36118	−	0.495430i	0.444762	−	0.895649i	$-0.353288\pi$
$173$	17.9035	−	6.51636i	1.36118	−	0.495430i	0.916419	+	0.400219i	$0.131066\pi$
$174$		0			0
$175$	−3.06418	+	2.57115i	−0.231630	+	0.194361i
$176$	13.2683	−	11.1334i	1.00013	−	0.839212i
$177$		0			0
$178$	8.45723	−	3.07818i	0.633896	−	0.230719i
$179$	−10.3923	−	18.0000i	−0.776757	−	1.34538i	−0.933801	−	0.357792i	$-0.883530\pi$
$179$	−10.3923	−	18.0000i	−0.776757	−	1.34538i	0.157044	−	0.987592i	$-0.449804\pi$
$180$		0			0
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	−0.900794	−	0.434246i	$-0.857015\pi$
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	0.826465	+	0.562988i	$0.190348\pi$
$182$	−0.601535	+	3.41147i	−0.0445887	+	0.252875i
$183$		0			0
$184$	5.63816	+	2.05212i	0.415650	+	0.151284i
$185$	2.10537	+	11.9402i	0.154790	+	0.877858i
$186$		0			0
$187$	−13.7888	−	11.5702i	−1.00834	−	0.846095i
$188$	6.92820			0.505291
$189$		0			0
$190$	−6.00000			−0.435286
$191$	13.2683	+	11.1334i	0.960059	+	0.805585i	0.980963	−	0.194196i	$-0.0622099\pi$
$191$	13.2683	+	11.1334i	0.960059	+	0.805585i	−0.0209037	+	0.999781i	$0.506654\pi$
$192$		0			0
$193$	−0.173648	−	0.984808i	−0.0124995	−	0.0708880i	0.977920	−	0.208980i	$-0.0670143\pi$
$193$	−0.173648	−	0.984808i	−0.0124995	−	0.0708880i	−0.990419	+	0.138092i	$0.955903\pi$
$194$	−3.25519	−	1.18479i	−0.233709	−	0.0850631i
$195$		0			0
$196$	−0.520945	+	2.95442i	−0.0372103	+	0.211030i
$197$	2.59808	−	4.50000i	0.185105	−	0.320612i	−0.758507	−	0.651665i	$-0.774071\pi$
$197$	2.59808	−	4.50000i	0.185105	−	0.320612i	0.943612	+	0.331053i	$0.107404\pi$
$198$		0			0
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$	−3.25519	+	1.18479i	−0.230177	+	0.0837775i
$201$		0			0
$202$	9.19253	−	7.71345i	0.646784	−	0.542717i
$203$	2.65366	−	2.22668i	0.186250	−	0.156282i
$204$		0			0
$205$	−11.2763	+	4.10424i	−0.787572	+	0.286653i
$206$	−6.92820	−	12.0000i	−0.482711	−	0.836080i
$207$		0			0
$208$	−2.50000	+	4.33013i	−0.173344	+	0.300240i
$209$	−1.20307	+	6.82295i	−0.0832181	+	0.471953i
$210$		0			0
$211$	9.39693	+	3.42020i	0.646911	+	0.235456i	0.644575	−	0.764541i	$-0.277034\pi$
$211$	9.39693	+	3.42020i	0.646911	+	0.235456i	0.00233585	+	0.999997i	$0.499256\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.46410			−0.236250
$216$		0			0
$217$	16.0000			1.08615
$218$	14.5951	+	12.2467i	0.988505	+	0.829454i
$219$		0			0
$220$	1.04189	+	5.90885i	0.0702441	+	0.398374i
$221$	4.88279	+	1.77719i	0.328452	+	0.119547i
$222$		0			0
$223$	0.347296	−	1.96962i	0.0232567	−	0.131895i	−0.970969	−	0.239206i	$-0.923113\pi$
$223$	0.347296	−	1.96962i	0.0232567	−	0.131895i	0.994226	+	0.107311i	$0.0342240\pi$
$224$	5.19615	−	9.00000i	0.347183	−	0.601338i
$225$		0			0
$226$	1.50000	+	2.59808i	0.0997785	+	0.172821i
$227$	3.25519	−	1.18479i	0.216055	−	0.0786374i	−0.231725	−	0.972781i	$-0.574437\pi$
$227$	3.25519	−	1.18479i	0.216055	−	0.0786374i	0.447780	+	0.894144i	$0.352215\pi$
$228$		0			0
$229$	−0.766044	+	0.642788i	−0.0506216	+	0.0424766i	−0.667747	−	0.744388i	$-0.732741\pi$
$229$	−0.766044	+	0.642788i	−0.0506216	+	0.0424766i	0.617126	+	0.786864i	$0.288297\pi$
$230$	−7.96097	+	6.68004i	−0.524931	+	0.440469i
$231$		0			0
$232$	2.81908	−	1.02606i	0.185082	−	0.0673642i
$233$	12.9904	+	22.5000i	0.851028	+	1.47402i	0.880281	+	0.474452i	$0.157354\pi$
$233$	12.9904	+	22.5000i	0.851028	+	1.47402i	−0.0292532	+	0.999572i	$0.509313\pi$
$234$		0			0
$235$	6.00000	−	10.3923i	0.391397	−	0.677919i
$236$	2.40614	−	13.6459i	0.156626	−	0.888272i
$237$		0			0
$238$	−16.9145	−	6.15636i	−1.09640	−	0.399058i
$239$	−4.81228	−	27.2918i	−0.311280	−	1.76536i	−0.592359	−	0.805674i	$-0.701803\pi$
$239$	−4.81228	−	27.2918i	−0.311280	−	1.76536i	0.281078	−	0.959685i	$-0.409308\pi$
$240$		0			0
$241$	22.2153	+	18.6408i	1.43101	+	1.20076i	0.945111	+	0.326748i	$0.105953\pi$
$241$	22.2153	+	18.6408i	1.43101	+	1.20076i	0.485901	+	0.874014i	$0.338491\pi$
$242$	1.73205			0.111340
$243$		0			0
$244$	−7.00000			−0.448129
$245$	3.98048	+	3.34002i	0.254304	+	0.213386i
$246$		0			0
$247$	−0.347296	−	1.96962i	−0.0220979	−	0.125324i
$248$	13.0208	+	4.73917i	0.826819	+	0.300938i
$249$		0			0
$250$	3.64661	−	20.6810i	0.230632	−	1.30798i
$251$	−5.19615	+	9.00000i	−0.327978	+	0.568075i	−0.982111	−	0.188305i	$-0.939701\pi$
$251$	−5.19615	+	9.00000i	−0.327978	+	0.568075i	0.654132	+	0.756380i	$0.273034\pi$
$252$		0			0
$253$	6.00000	+	10.3923i	0.377217	+	0.653359i
$254$	−3.25519	+	1.18479i	−0.204249	+	0.0743405i
$255$		0			0
$256$	14.5548	−	12.2130i	0.909678	−	0.763310i
$257$	6.63414	−	5.56670i	0.413826	−	0.347241i	−0.411982	−	0.911192i	$-0.635164\pi$
$257$	6.63414	−	5.56670i	0.413826	−	0.347241i	0.825809	+	0.563950i	$0.190719\pi$
$258$		0			0
$259$	13.1557	−	4.78828i	0.817455	−	0.297529i
$260$	−0.866025	−	1.50000i	−0.0537086	−	0.0930261i
$261$		0			0
$262$	−3.00000	+	5.19615i	−0.185341	+	0.321019i
$263$	1.20307	−	6.82295i	0.0741845	−	0.420721i	−0.924986	−	0.380001i	$-0.875924\pi$
$263$	1.20307	−	6.82295i	0.0741845	−	0.420721i	0.999171	−	0.0407201i	$-0.0129652\pi$
$264$		0			0
$265$		0			0
$266$	1.20307	+	6.82295i	0.0737649	+	0.418342i
$267$		0			0
$268$	−7.66044	−	6.42788i	−0.467936	−	0.392645i
$269$	−15.5885			−0.950445			−0.475223	−	0.879866i	$-0.657632\pi$
$269$	−15.5885			−0.950445			−0.475223	+	0.879866i	$0.657632\pi$
$270$		0			0
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	−19.9024	−	16.7001i	−1.20676	−	1.01259i
$273$		0			0
$274$	0.520945	+	2.95442i	0.0314714	+	0.178483i
$275$	−6.51038	−	2.36959i	−0.392591	−	0.142891i
$276$		0			0
$277$	0.347296	−	1.96962i	0.0208670	−	0.118343i	−0.972595	−	0.232506i	$-0.925308\pi$
$277$	0.347296	−	1.96962i	0.0208670	−	0.118343i	0.993462	+	0.114163i	$0.0364186\pi$
$278$	−6.92820	+	12.0000i	−0.415526	+	0.719712i
$279$		0			0
$280$	−3.00000	−	5.19615i	−0.179284	−	0.310530i
$281$	−11.3932	+	4.14677i	−0.679659	+	0.247376i	−0.658701	−	0.752405i	$-0.728894\pi$
$281$	−11.3932	+	4.14677i	−0.679659	+	0.247376i	−0.0209581	+	0.999780i	$0.506672\pi$
$282$		0			0
$283$	−21.4492	+	17.9981i	−1.27503	+	1.06987i	−0.281116	+	0.959674i	$0.590704\pi$
$283$	−21.4492	+	17.9981i	−1.27503	+	1.06987i	−0.993910	+	0.110199i	$0.964851\pi$
$284$	−7.96097	+	6.68004i	−0.472397	+	0.396388i
$285$		0			0
$286$	−5.63816	+	2.05212i	−0.333391	+	0.121344i
$287$	6.92820	+	12.0000i	0.408959	+	0.708338i
$288$		0			0
$289$	−5.00000	+	8.66025i	−0.294118	+	0.509427i
$290$	−0.902302	+	5.11721i	−0.0529850	+	0.300493i
$291$		0			0
$292$	6.57785	+	2.39414i	0.384939	+	0.140107i
$293$	3.30844	+	18.7631i	0.193281	+	1.09615i	0.914845	+	0.403805i	$0.132312\pi$
$293$	3.30844	+	18.7631i	0.193281	+	1.09615i	−0.721564	+	0.692348i	$0.756576\pi$
$294$		0			0
$295$	−18.3851	−	15.4269i	−1.07042	−	0.898189i
$296$	12.1244			0.704714
$297$		0			0
$298$	15.0000			0.868927
$299$	−2.65366	−	2.22668i	−0.153465	−	0.128772i
$300$		0			0
$301$	0.694593	+	3.93923i	0.0400357	+	0.227054i
$302$	−32.5519	−	11.8479i	−1.87315	−	0.681771i
$303$		0			0
$304$	−1.73648	+	9.84808i	−0.0995941	+	0.564826i
$305$	−6.06218	+	10.5000i	−0.347119	+	0.601228i
$306$		0			0
$307$	8.00000	+	13.8564i	0.456584	+	0.790827i	0.998778	−	0.0494267i	$-0.0157394\pi$
$307$	8.00000	+	13.8564i	0.456584	+	0.790827i	−0.542194	+	0.840254i	$0.682406\pi$
$308$	6.51038	−	2.36959i	0.370963	−	0.135020i
$309$		0			0
$310$	−18.3851	+	15.4269i	−1.04420	+	0.876189i
$311$	−5.30731	+	4.45336i	−0.300950	+	0.252527i	−0.780740	−	0.624857i	$-0.785157\pi$
$311$	−5.30731	+	4.45336i	−0.300950	+	0.252527i	0.479790	+	0.877384i	$0.340713\pi$
$312$		0			0
$313$	23.4923	−	8.55050i	1.32786	−	0.483303i	0.421894	−	0.906645i	$-0.361365\pi$
$313$	23.4923	−	8.55050i	1.32786	−	0.483303i	0.905970	+	0.423342i	$0.139143\pi$
$314$	−14.7224	−	25.5000i	−0.830835	−	1.43905i
$315$		0			0
$316$	−1.00000	+	1.73205i	−0.0562544	+	0.0974355i
$317$	−1.50384	+	8.52869i	−0.0844639	+	0.479019i	0.913007	+	0.407944i	$0.133754\pi$
$317$	−1.50384	+	8.52869i	−0.0844639	+	0.479019i	−0.997471	+	0.0710749i	$0.977357\pi$
$318$		0			0
$319$	5.63816	+	2.05212i	0.315676	+	0.114897i
$320$	−0.300767	−	1.70574i	−0.0168134	−	0.0953536i
$321$		0			0
$322$	9.19253	+	7.71345i	0.512280	+	0.429854i
$323$	10.3923			0.578243
$324$		0			0
$325$	2.00000			0.110940
$326$	−21.2292	−	17.8135i	−1.17578	−	0.986596i
$327$		0			0
$328$	2.08378	+	11.8177i	0.115057	+	0.652523i
$329$	−13.0208	−	4.73917i	−0.717858	−	0.261279i
$330$		0			0
$331$	0.347296	−	1.96962i	0.0190891	−	0.108260i	−0.973774	−	0.227516i	$-0.926940\pi$
$331$	0.347296	−	1.96962i	0.0190891	−	0.108260i	0.992864	+	0.119256i	$0.0380508\pi$
$332$	6.92820	−	12.0000i	0.380235	−	0.658586i
$333$		0			0
$334$	15.0000	+	25.9808i	0.820763	+	1.42160i
$335$	−16.2760	+	5.92396i	−0.889250	+	0.323661i
$336$		0			0
$337$	19.9172	−	16.7125i	1.08496	−	0.910387i	0.0886337	−	0.996064i	$-0.471750\pi$
$337$	19.9172	−	16.7125i	1.08496	−	0.910387i	0.996323	+	0.0856776i	$0.0273055\pi$
$338$	−15.9219	+	13.3601i	−0.866039	+	0.726693i
$339$		0			0
$340$	8.45723	−	3.07818i	0.458658	−	0.166938i
$341$	13.8564	+	24.0000i	0.750366	+	1.29967i
$342$		0			0
$343$	10.0000	−	17.3205i	0.539949	−	0.935220i
$344$	−0.601535	+	3.41147i	−0.0324326	+	0.183934i
$345$		0			0
$346$	31.0099	+	11.2867i	1.66710	+	0.606775i
$347$	0.601535	+	3.41147i	0.0322921	+	0.183138i	0.996687	−	0.0813271i	$-0.0259159\pi$
$347$	0.601535	+	3.41147i	0.0322921	+	0.183138i	−0.964395	+	0.264465i	$0.914805\pi$
$348$		0			0
$349$	1.53209	+	1.28558i	0.0820108	+	0.0688153i	0.682871	−	0.730539i	$-0.260731\pi$
$349$	1.53209	+	1.28558i	0.0820108	+	0.0688153i	−0.600861	+	0.799354i	$0.705175\pi$
$350$	−6.92820			−0.370328
$351$		0			0
$352$	18.0000			0.959403
$353$	−10.6146	−	8.90673i	−0.564959	−	0.474057i	0.315010	−	0.949089i	$-0.397992\pi$
$353$	−10.6146	−	8.90673i	−0.564959	−	0.474057i	−0.879969	+	0.475031i	$0.842437\pi$
$354$		0			0
$355$	3.12567	+	17.7265i	0.165893	+	0.940827i
$356$	4.88279	+	1.77719i	0.258787	+	0.0941908i
$357$		0			0
$358$	6.25133	−	35.4531i	0.330393	−	1.87375i
$359$	−5.19615	+	9.00000i	−0.274242	+	0.475002i	−0.969944	−	0.243329i	$-0.921760\pi$
$359$	−5.19615	+	9.00000i	−0.274242	+	0.475002i	0.695701	+	0.718331i	$0.255094\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−3.25519	+	1.18479i	−0.171089	+	0.0622713i
$363$		0			0
$364$	−1.53209	+	1.28558i	−0.0803033	+	0.0673825i
$365$	9.28780	−	7.79339i	0.486145	−	0.407924i
$366$		0			0
$367$	−18.7939	+	6.84040i	−0.981031	+	0.357066i	−0.782241	−	0.622976i	$-0.785923\pi$
$367$	−18.7939	+	6.84040i	−0.981031	+	0.357066i	−0.198790	+	0.980042i	$0.563701\pi$
$368$	8.66025	+	15.0000i	0.451447	+	0.781929i
$369$		0			0
$370$	−10.5000	+	18.1865i	−0.545869	+	0.945473i
$371$		0			0
$372$		0			0
$373$	9.39693	+	3.42020i	0.486554	+	0.177091i	0.573637	−	0.819110i	$-0.305532\pi$
$373$	9.39693	+	3.42020i	0.486554	+	0.177091i	−0.0870824	+	0.996201i	$0.527754\pi$
$374$	−5.41381	−	30.7033i	−0.279942	−	1.58763i
$375$		0			0
$376$	−9.19253	−	7.71345i	−0.474069	−	0.397791i
$377$	−1.73205			−0.0892052
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	−2.65366	−	2.22668i	−0.136130	−	0.114226i
$381$		0			0
$382$	5.20945	+	29.5442i	0.266538	+	1.51161i
$383$	16.2760	+	5.92396i	0.831662	+	0.302700i	0.722541	−	0.691328i	$-0.242974\pi$
$383$	16.2760	+	5.92396i	0.831662	+	0.302700i	0.109121	+	0.994028i	$0.465196\pi$
$384$		0			0
$385$	2.08378	−	11.8177i	0.106199	−	0.602285i
$386$	0.866025	−	1.50000i	0.0440795	−	0.0763480i
$387$		0			0
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	−26.0415	+	9.47834i	−1.32036	+	0.480571i	−0.903573	−	0.428434i	$-0.859065\pi$
$389$	−26.0415	+	9.47834i	−1.32036	+	0.480571i	−0.416785	+	0.909005i	$0.636843\pi$
$390$		0			0
$391$	13.7888	−	11.5702i	0.697330	−	0.585129i
$392$	3.98048	−	3.34002i	0.201045	−	0.168697i
$393$		0			0
$394$	8.45723	−	3.07818i	0.426069	−	0.155077i
$395$	1.73205	+	3.00000i	0.0871489	+	0.150946i
$396$		0			0
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	−0.957839	+	0.287307i	$0.907240\pi$
$398$	6.01535	−	34.1147i	0.301522	−	1.71002i
$399$		0			0
$400$	−9.39693	−	3.42020i	−0.469846	−	0.171010i
$401$	−2.10537	−	11.9402i	−0.105137	−	0.596263i	−0.991165	−	0.132632i	$-0.957657\pi$
$401$	−2.10537	−	11.9402i	−0.105137	−	0.596263i	0.886028	−	0.463631i	$-0.153454\pi$
$402$		0			0
$403$	−6.12836	−	5.14230i	−0.305275	−	0.256156i
$404$	6.92820			0.344691
$405$		0			0
$406$	6.00000			0.297775
$407$	18.5756	+	15.5868i	0.920758	+	0.772608i
$408$		0			0
$409$	−3.29932	−	18.7113i	−0.163141	−	0.925217i	−0.950961	−	0.309311i	$-0.899901\pi$
$409$	−3.29932	−	18.7113i	−0.163141	−	0.925217i	0.787820	−	0.615905i	$-0.211210\pi$
$410$	−19.5311	−	7.10876i	−0.964574	−	0.351076i
$411$		0			0
$412$	1.38919	−	7.87846i	0.0684403	−	0.388144i
$413$	−13.8564	+	24.0000i	−0.681829	+	1.18096i
$414$		0			0
$415$	−12.0000	−	20.7846i	−0.589057	−	1.02028i
$416$	−4.88279	+	1.77719i	−0.239398	+	0.0871338i
$417$		0			0
$418$	−9.19253	+	7.71345i	−0.449622	+	0.377277i
$419$	−5.30731	+	4.45336i	−0.259279	+	0.217561i	−0.763156	−	0.646215i	$-0.776351\pi$
$419$	−5.30731	+	4.45336i	−0.259279	+	0.217561i	0.503877	+	0.863776i	$0.331907\pi$
$420$		0			0
$421$	23.4923	−	8.55050i	1.14495	−	0.416726i	0.301248	−	0.953546i	$-0.402597\pi$
$421$	23.4923	−	8.55050i	1.14495	−	0.416726i	0.843697	+	0.536820i	$0.180374\pi$
$422$	8.66025	+	15.0000i	0.421575	+	0.730189i
$423$		0			0
$424$		0			0
$425$	−1.80460	+	10.2344i	−0.0875362	+	0.496442i
$426$		0			0
$427$	13.1557	+	4.78828i	0.636649	+	0.231721i
$428$		0			0
$429$		0			0
$430$	−4.59627	−	3.85673i	−0.221652	−	0.185988i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	11.0000			0.528626			0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000			0.528626			0.264313	+	0.964437i	$0.414855\pi$
$434$	21.2292	+	17.8135i	1.01904	+	0.855073i
$435$		0			0
$436$	1.91013	+	10.8329i	0.0914786	+	0.518801i
$437$	−6.51038	−	2.36959i	−0.311434	−	0.113353i
$438$		0			0
$439$	3.47296	−	19.6962i	0.165756	−	0.940046i	−0.782527	−	0.622617i	$-0.786069\pi$
$439$	3.47296	−	19.6962i	0.165756	−	0.940046i	0.948282	−	0.317429i	$-0.102820\pi$
$440$	5.19615	−	9.00000i	0.247717	−	0.429058i
$441$		0			0
$442$	4.50000	+	7.79423i	0.214043	+	0.370734i
$443$	32.5519	−	11.8479i	1.54659	−	0.562912i	0.578974	−	0.815346i	$-0.303453\pi$
$443$	32.5519	−	11.8479i	1.54659	−	0.562912i	0.967614	+	0.252434i	$0.0812311\pi$
$444$		0			0
$445$	6.89440	−	5.78509i	0.326826	−	0.274239i
$446$	2.65366	−	2.22668i	0.125654	−	0.105436i
$447$		0			0
$448$	−1.87939	+	0.684040i	−0.0887926	+	0.0323179i
$449$	−10.3923	−	18.0000i	−0.490443	−	0.849473i	0.509496	−	0.860473i	$-0.329832\pi$
$449$	−10.3923	−	18.0000i	−0.490443	−	0.849473i	−0.999939	+	0.0110003i	$0.996498\pi$
$450$		0			0
$451$	−12.0000	+	20.7846i	−0.565058	+	0.978709i
$452$	−0.300767	+	1.70574i	−0.0141469	+	0.0802311i
$453$		0			0
$454$	5.63816	+	2.05212i	0.264612	+	0.0963108i
$455$	0.601535	+	3.41147i	0.0282004	+	0.159932i
$456$		0			0
$457$	22.2153	+	18.6408i	1.03919	+	0.871982i	0.991915	−	0.126900i	$-0.0405028\pi$
$457$	22.2153	+	18.6408i	1.03919	+	0.871982i	0.0472719	+	0.998882i	$0.484947\pi$
$458$	−1.73205			−0.0809334
$459$		0			0
$460$	−6.00000			−0.279751
$461$	−10.6146	−	8.90673i	−0.494372	−	0.414828i	0.361218	−	0.932481i	$-0.382361\pi$
$461$	−10.6146	−	8.90673i	−0.494372	−	0.414828i	−0.855590	+	0.517654i	$0.826806\pi$
$462$		0			0
$463$	1.38919	+	7.87846i	0.0645609	+	0.366143i	0.999922	+	0.0124502i	$0.00396312\pi$
$463$	1.38919	+	7.87846i	0.0645609	+	0.366143i	−0.935362	+	0.353693i	$0.884926\pi$
$464$	8.13798	+	2.96198i	0.377796	+	0.137507i
$465$		0			0
$466$	−7.81417	+	44.3163i	−0.361984	+	2.05292i
$467$	10.3923	−	18.0000i	0.480899	−	0.832941i	−0.518861	−	0.854858i	$-0.673644\pi$
$467$	10.3923	−	18.0000i	0.480899	−	0.832941i	0.999760	+	0.0219178i	$0.00697721\pi$
$468$		0			0
$469$	10.0000	+	17.3205i	0.461757	+	0.799787i
$470$	19.5311	−	7.10876i	0.900905	−	0.327902i
$471$		0			0
$472$	−18.3851	+	15.4269i	−0.846241	+	0.710081i
$473$	−5.30731	+	4.45336i	−0.244030	+	0.204766i
$474$		0			0
$475$	3.75877	−	1.36808i	0.172464	−	0.0627718i
$476$	−5.19615	−	9.00000i	−0.238165	−	0.412514i
$477$		0			0
$478$	24.0000	−	41.5692i	1.09773	−	1.90133i
$479$	−4.21074	+	23.8803i	−0.192394	+	1.09112i	0.723688	+	0.690128i	$0.242446\pi$
$479$	−4.21074	+	23.8803i	−0.192394	+	1.09112i	−0.916082	+	0.400992i	$0.868666\pi$
$480$		0			0
$481$	−6.57785	−	2.39414i	−0.299924	−	0.109163i
$482$	8.72226	+	49.4664i	0.397288	+	2.25313i
$483$		0			0
$484$	0.766044	+	0.642788i	0.0348202	+	0.0292176i
$485$	−3.46410			−0.157297
$486$		0			0
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	9.28780	+	7.79339i	0.420439	+	0.352790i
$489$		0			0
$490$	1.56283	+	8.86327i	0.0706016	+	0.400402i
$491$	16.2760	+	5.92396i	0.734524	+	0.267345i	0.682078	−	0.731279i	$-0.261076\pi$
$491$	16.2760	+	5.92396i	0.734524	+	0.267345i	0.0524452	+	0.998624i	$0.483299\pi$
$492$		0			0
$493$	1.56283	−	8.86327i	0.0703865	−	0.399182i
$494$	1.73205	−	3.00000i	0.0779287	−	0.134976i
$495$		0			0
$496$	20.0000	+	34.6410i	0.898027	+	1.55543i
$497$	19.5311	−	7.10876i	0.876092	−	0.318871i
$498$		0			0
$499$	−7.66044	+	6.42788i	−0.342929	+	0.287751i	−0.797943	−	0.602733i	$-0.794079\pi$
$499$	−7.66044	+	6.42788i	−0.342929	+	0.287751i	0.455015	+	0.890484i	$0.349634\pi$
$500$	9.28780	−	7.79339i	0.415363	−	0.348531i
$501$		0			0
$502$	−16.9145	+	6.15636i	−0.754930	+	0.274772i
$503$	−10.3923	−	18.0000i	−0.463370	−	0.802580i	0.535756	−	0.844373i	$-0.320027\pi$
$503$	−10.3923	−	18.0000i	−0.463370	−	0.802580i	−0.999126	+	0.0417923i	$0.986693\pi$
$504$		0			0
$505$	6.00000	−	10.3923i	0.266996	−	0.462451i
$506$	−3.60921	+	20.4688i	−0.160449	+	0.909951i
$507$		0			0
$508$	−1.87939	−	0.684040i	−0.0833842	−	0.0303494i
$509$	−4.81228	−	27.2918i	−0.213301	−	1.20969i	−0.883831	−	0.467806i	$-0.845045\pi$
$509$	−4.81228	−	27.2918i	−0.213301	−	1.20969i	0.670531	−	0.741882i	$-0.266066\pi$
$510$		0			0
$511$	−10.7246	−	8.99903i	−0.474429	−	0.398093i
$512$	8.66025			0.382733
$513$		0			0
$514$	15.0000			0.661622
$515$	−10.6146	−	8.90673i	−0.467736	−	0.392477i
$516$		0			0
$517$	−4.16756	−	23.6354i	−0.183289	−	1.03948i
$518$	22.7863	+	8.29355i	1.00117	+	0.364398i
$519$		0			0
$520$	−0.520945	+	2.95442i	−0.0228449	+	0.129560i
$521$	10.3923	−	18.0000i	0.455295	−	0.788594i	−0.543410	−	0.839467i	$-0.682867\pi$
$521$	10.3923	−	18.0000i	0.455295	−	0.788594i	0.998705	+	0.0508731i	$0.0162004\pi$
$522$		0			0
$523$	−19.0000	−	32.9090i	−0.830812	−	1.43901i	−0.897395	−	0.441228i	$-0.854543\pi$
$523$	−19.0000	−	32.9090i	−0.830812	−	1.43901i	0.0665832	−	0.997781i	$-0.478790\pi$
$524$	−3.25519	+	1.18479i	−0.142204	+	0.0517579i
$525$		0			0
$526$	9.19253	−	7.71345i	0.400813	−	0.336322i
$527$	31.8439	−	26.7202i	1.38714	−	1.16395i
$528$		0			0
$529$	10.3366	−	3.76222i	0.449418	−	0.163575i
$530$		0			0
$531$		0			0
$532$	−2.00000	+	3.46410i	−0.0867110	+	0.150188i
$533$	1.20307	−	6.82295i	0.0521107	−	0.295535i
$534$		0			0
$535$		0			0
$536$	3.00767	+	17.0574i	0.129912	+	0.736766i
$537$		0			0
$538$	−20.6832	−	17.3553i	−0.891716	−	0.748239i
$539$	10.3923			0.447628
$540$		0			0
$541$	11.0000			0.472927			0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000			0.472927			0.236463	+	0.971640i	$0.424012\pi$
$542$	2.65366	+	2.22668i	0.113984	+	0.0956442i
$543$		0			0
$544$	−4.68850	−	26.5898i	−0.201018	−	1.14003i
$545$	17.9035	+	6.51636i	0.766904	+	0.279130i
$546$		0			0
$547$	3.47296	−	19.6962i	0.148493	−	0.842147i	−0.816003	−	0.578048i	$-0.803815\pi$
$547$	3.47296	−	19.6962i	0.148493	−	0.842147i	0.964496	−	0.264098i	$-0.0850744\pi$
$548$	−0.866025	+	1.50000i	−0.0369948	+	0.0640768i
$549$		0			0
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	−3.25519	+	1.18479i	−0.138676	+	0.0504739i
$552$		0			0
$553$	3.06418	−	2.57115i	0.130302	−	0.109336i
$554$	2.65366	−	2.22668i	0.112743	−	0.0946026i
$555$		0			0
$556$	−7.51754	+	2.73616i	−0.318815	+	0.116039i
$557$	−18.1865	−	31.5000i	−0.770588	−	1.33470i	−0.937241	−	0.348682i	$-0.886629\pi$
$557$	−18.1865	−	31.5000i	−0.770588	−	1.33470i	0.166653	−	0.986016i	$-0.446704\pi$
$558$		0			0
$559$	1.00000	−	1.73205i	0.0422955	−	0.0732579i
$560$	3.00767	−	17.0574i	0.127097	−	0.720805i
$561$		0			0
$562$	−19.7335	−	7.18242i	−0.832409	−	0.302972i
$563$	6.01535	+	34.1147i	0.253517	+	1.43776i	0.799851	+	0.600198i	$0.204912\pi$
$563$	6.01535	+	34.1147i	0.253517	+	1.43776i	−0.546335	+	0.837567i	$0.683977\pi$
$564$		0			0
$565$	2.29813	+	1.92836i	0.0966832	+	0.0811268i
$566$	−48.4974			−2.03850
$567$		0			0
$568$	18.0000			0.755263
$569$	25.2097	+	21.1535i	1.05685	+	0.886800i	0.993797	−	0.111211i	$-0.0354728\pi$
$569$	25.2097	+	21.1535i	1.05685	+	0.886800i	0.0630500	+	0.998010i	$0.479917\pi$
$570$		0			0
$571$	1.38919	+	7.87846i	0.0581356	+	0.329703i	0.999980	−	0.00634631i	$-0.00202011\pi$
$571$	1.38919	+	7.87846i	0.0581356	+	0.329703i	−0.941844	+	0.336050i	$0.890909\pi$
$572$	−3.25519	−	1.18479i	−0.136106	−	0.0495387i
$573$		0			0
$574$	−4.16756	+	23.6354i	−0.173950	+	0.986522i
$575$	3.46410	−	6.00000i	0.144463	−	0.250217i
$576$		0			0
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−16.2760	+	5.92396i	−0.676990	+	0.246404i
$579$		0			0
$580$	−2.29813	+	1.92836i	−0.0954248	+	0.0800709i
$581$	−21.2292	+	17.8135i	−0.880738	+	0.739027i
$582$		0			0
$583$		0			0
$584$	−6.06218	−	10.5000i	−0.250855	−	0.434493i
$585$		0			0
$586$	−16.5000	+	28.5788i	−0.681609	+	1.18058i
$587$	6.61688	−	37.5262i	0.273108	−	1.54887i	−0.471800	−	0.881706i	$-0.656396\pi$
$587$	6.61688	−	37.5262i	0.273108	−	1.54887i	0.744908	−	0.667167i	$-0.232493\pi$
$588$		0			0
$589$	−15.0351	−	5.47232i	−0.619510	−	0.225483i
$590$	−7.21842	−	40.9377i	−0.297178	−	1.68538i
$591$		0			0
$592$	26.8116	+	22.4976i	1.10195	+	0.924644i
$593$	15.5885			0.640141			0.320071	−	0.947394i	$-0.396293\pi$
$593$	15.5885			0.640141			0.320071	+	0.947394i	$0.396293\pi$
$594$		0			0
$595$	−18.0000			−0.737928
$596$	6.63414	+	5.56670i	0.271745	+	0.228021i
$597$		0			0
$598$	−1.04189	−	5.90885i	−0.0426060	−	0.241631i
$599$	−13.0208	−	4.73917i	−0.532014	−	0.193637i	0.0620234	−	0.998075i	$-0.480245\pi$
$599$	−13.0208	−	4.73917i	−0.532014	−	0.193637i	−0.594037	+	0.804437i	$0.702467\pi$
$600$		0			0
$601$	−4.34120	+	24.6202i	−0.177081	+	1.00428i	0.758632	+	0.651519i	$0.225868\pi$
$601$	−4.34120	+	24.6202i	−0.177081	+	1.00428i	−0.935714	+	0.352760i	$0.885243\pi$
$602$	−3.46410	+	6.00000i	−0.141186	+	0.244542i
$603$		0			0
$604$	−10.0000	−	17.3205i	−0.406894	−	0.704761i
$605$	1.62760	−	0.592396i	0.0661712	−	0.0240843i
$606$		0			0
$607$	19.9172	−	16.7125i	0.808412	−	0.678339i	−0.141816	−	0.989893i	$-0.545294\pi$
$607$	19.9172	−	16.7125i	0.808412	−	0.678339i	0.950228	+	0.311555i	$0.100850\pi$
$608$	−7.96097	+	6.68004i	−0.322860	+	0.270912i
$609$		0			0
$610$	−19.7335	+	7.18242i	−0.798988	+	0.290808i
$611$	3.46410	+	6.00000i	0.140143	+	0.242734i
$612$		0			0
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	−0.286300	−	0.958140i	$-0.592425\pi$
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	0.972924	−	0.231127i	$-0.0742412\pi$
$614$	−4.81228	+	27.2918i	−0.194208	+	1.10141i
$615$		0			0
$616$	−11.2763	−	4.10424i	−0.454336	−	0.165365i
$617$	−2.10537	−	11.9402i	−0.0847591	−	0.480693i	−0.997408	−	0.0719490i	$-0.977078\pi$
$617$	−2.10537	−	11.9402i	−0.0847591	−	0.480693i	0.912649	−	0.408744i	$-0.134033\pi$
$618$		0			0
$619$	15.3209	+	12.8558i	0.615799	+	0.516716i	0.896480	−	0.443085i	$-0.146116\pi$
$619$	15.3209	+	12.8558i	0.615799	+	0.516716i	−0.280681	+	0.959801i	$0.590560\pi$
$620$	−13.8564			−0.556487
$621$		0			0
$622$	−12.0000			−0.481156
$623$	−7.96097	−	6.68004i	−0.318949	−	0.267630i
$624$		0			0
$625$	−1.91013	−	10.8329i	−0.0764052	−	0.433315i
$626$	40.6899	+	14.8099i	1.62629	+	0.591923i
$627$		0			0
$628$	2.95202	−	16.7417i	0.117798	−	0.668068i
$629$	18.1865	−	31.5000i	0.725145	−	1.25599i
$630$		0			0
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	0.595397	−	0.803432i	$-0.296995\pi$
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	−0.993491	+	0.113913i	$0.963661\pi$
$632$	3.25519	−	1.18479i	0.129485	−	0.0471285i
$633$		0			0
$634$	−11.4907	+	9.64181i	−0.456353	+	0.382925i
$635$	−2.65366	+	2.22668i	−0.105307	+	0.0883632i
$636$		0			0
$637$	−2.81908	+	1.02606i	−0.111696	+	0.0406540i
$638$	5.19615	+	9.00000i	0.205718	+	0.356313i
$639$		0			0
$640$	10.5000	−	18.1865i	0.415049	−	0.718886i
$641$	3.90998	−	22.1746i	0.154435	−	0.875843i	−0.804866	−	0.593457i	$-0.797763\pi$
$641$	3.90998	−	22.1746i	0.154435	−	0.875843i	0.959301	−	0.282387i	$-0.0911261\pi$
$642$		0			0
$643$	−7.51754	−	2.73616i	−0.296463	−	0.107904i	0.189507	−	0.981879i	$-0.439311\pi$
$643$	−7.51754	−	2.73616i	−0.296463	−	0.107904i	−0.485969	+	0.873976i	$0.661533\pi$
$644$	1.20307	+	6.82295i	0.0474076	+	0.268862i
$645$		0			0
$646$	13.7888	+	11.5702i	0.542513	+	0.455223i
$647$	−31.1769			−1.22569			−0.612845	−	0.790203i	$-0.709975\pi$
$647$	−31.1769			−1.22569			−0.612845	+	0.790203i	$0.709975\pi$
$648$		0			0
$649$	−48.0000			−1.88416
$650$	2.65366	+	2.22668i	0.104085	+	0.0873376i
$651$		0			0
$652$	−2.77837	−	15.7569i	−0.108809	−	0.617089i
$653$	−13.0208	−	4.73917i	−0.509542	−	0.185458i	0.0744389	−	0.997226i	$-0.476283\pi$
$653$	−13.0208	−	4.73917i	−0.509542	−	0.185458i	−0.583981	+	0.811768i	$0.698506\pi$
$654$		0			0
$655$	−1.04189	+	5.90885i	−0.0407100	+	0.230878i
$656$	−17.3205	+	30.0000i	−0.676252	+	1.17130i
$657$		0			0
$658$	−12.0000	−	20.7846i	−0.467809	−	0.810268i
$659$	3.25519	−	1.18479i	0.126804	−	0.0461530i	−0.277839	−	0.960628i	$-0.589618\pi$
$659$	3.25519	−	1.18479i	0.126804	−	0.0461530i	0.404643	+	0.914475i	$0.367396\pi$
$660$		0			0
$661$	13.0228	−	10.9274i	0.506526	−	0.425026i	−0.353378	−	0.935480i	$-0.614967\pi$
$661$	13.0228	−	10.9274i	0.506526	−	0.425026i	0.859905	+	0.510454i	$0.170523\pi$
$662$	2.65366	−	2.22668i	0.103137	−	0.0865424i
$663$		0			0
$664$	−22.5526	+	8.20848i	−0.875212	+	0.318551i
$665$	3.46410	+	6.00000i	0.134332	+	0.232670i
$666$		0			0
$667$	−3.00000	+	5.19615i	−0.116160	+	0.201196i
$668$	−3.00767	+	17.0574i	−0.116370	+	0.659969i
$669$		0			0
$670$	−28.1908	−	10.2606i	−1.08910	−	0.396402i
$671$	4.21074	+	23.8803i	0.162554	+	0.921889i
$672$		0			0
$673$	−19.1511	−	16.0697i	−0.738221	−	0.619441i	0.194138	−	0.980974i	$-0.437809\pi$
$673$	−19.1511	−	16.0697i	−0.738221	−	0.619441i	−0.932359	+	0.361533i	$0.882253\pi$
$674$	45.0333			1.73462
$675$		0			0
$676$	−12.0000			−0.461538
$677$	−10.6146	−	8.90673i	−0.407953	−	0.342313i	0.415605	−	0.909545i	$-0.363570\pi$
$677$	−10.6146	−	8.90673i	−0.407953	−	0.342313i	−0.823558	+	0.567232i	$0.808014\pi$
$678$		0			0
$679$	0.694593	+	3.93923i	0.0266560	+	0.151174i
$680$	−14.6484	−	5.33157i	−0.561739	−	0.204456i
$681$		0			0
$682$	−8.33511	+	47.2708i	−0.319168	+	1.81009i
$683$	10.3923	−	18.0000i	0.397650	−	0.688751i	−0.595785	−	0.803144i	$-0.703159\pi$
$683$	10.3923	−	18.0000i	0.397650	−	0.688751i	0.993436	+	0.114393i	$0.0364923\pi$
$684$		0			0
$685$	1.50000	+	2.59808i	0.0573121	+	0.0992674i
$686$	32.5519	−	11.8479i	1.24284	−	0.452356i
$687$		0			0
$688$	−7.66044	+	6.42788i	−0.292052	+	0.245060i
$689$		0			0
$690$		0			0
$691$	−1.87939	+	0.684040i	−0.0714952	+	0.0260221i	−0.377520	−	0.926001i	$-0.623223\pi$
$691$	−1.87939	+	0.684040i	−0.0714952	+	0.0260221i	0.306025	+	0.952023i	$0.401001\pi$
$692$	9.52628	+	16.5000i	0.362135	+	0.627236i
$693$		0			0
$694$	−3.00000	+	5.19615i	−0.113878	+	0.197243i
$695$	−2.40614	+	13.6459i	−0.0912701	+	0.517618i
$696$		0			0
$697$	33.8289	+	12.3127i	1.28136	+	0.466378i
$698$	0.601535	+	3.41147i	0.0227684	+	0.129126i
$699$		0			0
$700$	−3.06418	−	2.57115i	−0.115815	−	0.0971804i
$701$	46.7654			1.76630			0.883152	−	0.469087i	$-0.155417\pi$
$701$	46.7654			1.76630			0.883152	+	0.469087i	$0.155417\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	−2.65366	−	2.22668i	−0.100013	−	0.0839212i
$705$		0			0
$706$	−4.16756	−	23.6354i	−0.156848	−	0.889529i
$707$	−13.0208	−	4.73917i	−0.489696	−	0.178235i
$708$		0			0
$709$	−4.34120	+	24.6202i	−0.163037	+	0.924631i	0.788028	+	0.615640i	$0.211102\pi$
$709$	−4.34120	+	24.6202i	−0.163037	+	0.924631i	−0.951065	+	0.308991i	$0.900009\pi$
$710$	−15.5885	+	27.0000i	−0.585024	+	1.01329i
$711$		0			0
$712$	−4.50000	−	7.79423i	−0.168645	−	0.292101i
$713$	−26.0415	+	9.47834i	−0.975263	+	0.354967i
$714$		0			0
$715$	−4.59627	+	3.85673i	−0.171891	+	0.144233i
$716$	15.9219	−	13.3601i	0.595031	−	0.499290i
$717$		0			0
$718$	−16.9145	+	6.15636i	−0.631242	+	0.229753i
$719$	5.19615	+	9.00000i	0.193784	+	0.335643i	0.946501	−	0.322700i	$-0.104591\pi$
$719$	5.19615	+	9.00000i	0.193784	+	0.335643i	−0.752717	+	0.658344i	$0.771257\pi$
$720$		0			0
$721$	−8.00000	+	13.8564i	−0.297936	+	0.516040i
$722$	−4.51151	+	25.5861i	−0.167901	+	0.952214i
$723$		0			0
$724$	−1.87939	−	0.684040i	−0.0698468	−	0.0254222i
$725$	−0.601535	−	3.41147i	−0.0223404	−	0.126699i
$726$		0			0
$727$	−26.0455	−	21.8548i	−0.965975	−	0.810549i	0.0159401	−	0.999873i	$-0.494926\pi$
$727$	−26.0455	−	21.8548i	−0.965975	−	0.810549i	−0.981915	+	0.189324i	$0.939370\pi$
$728$	3.46410			0.128388
$729$		0			0
$730$	21.0000			0.777245
$731$	7.96097	+	6.68004i	0.294447	+	0.247070i
$732$		0			0
$733$	−7.98782	−	45.3012i	−0.295037	−	1.67324i	−0.667053	−	0.745010i	$-0.732445\pi$
$733$	−7.98782	−	45.3012i	−0.295037	−	1.67324i	0.372016	−	0.928226i	$-0.378667\pi$
$734$	−32.5519	−	11.8479i	−1.20151	−	0.437315i
$735$		0			0
$736$	−3.12567	+	17.7265i	−0.115214	+	0.653409i
$737$	−17.3205	+	30.0000i	−0.638009	+	1.10506i
$738$		0			0
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$	−11.3932	+	4.14677i	−0.418821	+	0.152438i
$741$		0			0
$742$		0			0
$743$	−5.30731	+	4.45336i	−0.194706	+	0.163378i	−0.734929	−	0.678144i	$-0.762785\pi$
$743$	−5.30731	+	4.45336i	−0.194706	+	0.163378i	0.540223	+	0.841522i	$0.318340\pi$
$744$		0			0
$745$	14.0954	−	5.13030i	0.516415	−	0.187960i
$746$	8.66025	+	15.0000i	0.317074	+	0.549189i
$747$		0			0
$748$	9.00000	−	15.5885i	0.329073	−	0.569970i
$749$		0			0
$750$		0			0
$751$	9.39693	+	3.42020i	0.342899	+	0.124805i	0.507729	−	0.861517i	$-0.330485\pi$
$751$	9.39693	+	3.42020i	0.342899	+	0.124805i	−0.164830	+	0.986322i	$0.552708\pi$
$752$	−6.01535	−	34.1147i	−0.219357	−	1.24404i
$753$		0			0
$754$	−2.29813	−	1.92836i	−0.0836931	−	0.0702268i
$755$	−34.6410			−1.26072
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−21.2292	−	17.8135i	−0.771081	−	0.647014i
$759$		0			0
$760$	1.04189	+	5.90885i	0.0377933	+	0.214336i
$761$	−27.6691	−	10.0707i	−1.00300	−	0.365064i	−0.212262	−	0.977213i	$-0.568083\pi$
$761$	−27.6691	−	10.0707i	−1.00300	−	0.365064i	−0.790743	+	0.612149i	$0.790305\pi$
$762$		0			0
$763$	3.82026	−	21.6658i	0.138303	−	0.784354i
$764$	−8.66025	+	15.0000i	−0.313317	+	0.542681i
$765$		0			0
$766$	15.0000	+	25.9808i	0.541972	+	0.938723i
$767$	13.0208	−	4.73917i	0.470152	−	0.171122i
$768$		0			0
$769$	−0.766044	+	0.642788i	−0.0276243	+	0.0231795i	−0.656495	−	0.754330i	$-0.727962\pi$
$769$	−0.766044	+	0.642788i	−0.0276243	+	0.0231795i	0.628871	+	0.777510i	$0.283517\pi$
$770$	15.9219	−	13.3601i	0.573787	−	0.481464i
$771$		0			0
$772$	0.939693	−	0.342020i	0.0338203	−	0.0123096i
$773$	12.9904	+	22.5000i	0.467232	+	0.809269i	0.999299	−	0.0374331i	$-0.0119181\pi$
$773$	12.9904	+	22.5000i	0.467232	+	0.809269i	−0.532068	+	0.846702i	$0.678585\pi$
$774$		0			0
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$	−0.601535	+	3.41147i	−0.0215938	+	0.122465i
$777$		0			0
$778$	−45.1052	−	16.4170i	−1.61710	−	0.588577i
$779$	−2.40614	−	13.6459i	−0.0862089	−	0.488915i
$780$		0			0
$781$	27.5776	+	23.1404i	0.986804	+	0.828027i
$782$	31.1769			1.11488
$783$		0			0
$784$	15.0000			0.535714
$785$	−22.5561	−	18.9268i	−0.805061	−	0.675526i
$786$		0			0
$787$	4.51485	+	25.6050i	0.160937	+	0.912720i	0.953155	+	0.302482i	$0.0978151\pi$
$787$	4.51485	+	25.6050i	0.160937	+	0.912720i	−0.792218	+	0.610238i	$0.791074\pi$
$788$	4.88279	+	1.77719i	0.173942	+	0.0633097i
$789$		0			0
$790$	−1.04189	+	5.90885i	−0.0370687	+	0.210227i
$791$	1.73205	−	3.00000i	0.0615846	−	0.106668i
$792$		0			0
$793$	−3.50000	−	6.06218i	−0.124289	−	0.215274i
$794$	−47.2003	+	17.1795i	−1.67507	+	0.609677i
$795$		0			0
$796$	15.3209	−	12.8558i	0.543035	−	0.455660i
$797$	−41.1317	+	34.5136i	−1.45696	+	1.22253i	−0.529660	+	0.848210i	$0.677680\pi$
$797$	−41.1317	+	34.5136i	−1.45696	+	1.22253i	−0.927298	+	0.374323i	$0.877875\pi$
$798$		0			0
$799$	−33.8289	+	12.3127i	−1.19678	+	0.435593i
$800$	−5.19615	−	9.00000i	−0.183712	−	0.318198i
$801$		0			0
$802$	10.5000	−	18.1865i	0.370768	−	0.642189i
$803$	4.21074	−	23.8803i	0.148594	−	0.842718i
$804$		0			0
$805$	11.2763	+	4.10424i	0.397438	+	0.144656i
$806$	−2.40614	−	13.6459i	−0.0847527	−	0.480656i
$807$		0			0
$808$	−9.19253	−	7.71345i	−0.323392	−	0.271358i
$809$	−46.7654			−1.64418			−0.822091	−	0.569355i	$-0.807193\pi$
$809$	−46.7654			−1.64418			−0.822091	+	0.569355i	$0.807193\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	2.65366	+	2.22668i	0.0931251	+	0.0781412i
$813$		0			0
$814$	7.29322	+	41.3619i	0.255627	+	1.44973i
$815$	−26.0415	−	9.47834i	−0.912195	−	0.332012i
$816$		0			0
$817$	0.694593	−	3.93923i	0.0243007	−	0.137816i
$818$	16.4545	−	28.5000i	0.575317	−	0.996479i
$819$		0			0
$820$	−6.00000	−	10.3923i	−0.209529	−	0.362915i
$821$	−11.3932	+	4.14677i	−0.397624	+	0.144723i	−0.533090	−	0.846059i	$-0.678969\pi$
$821$	−11.3932	+	4.14677i	−0.397624	+	0.144723i	0.135466	+	0.990782i	$0.456747\pi$
$822$		0			0
$823$	−21.4492	+	17.9981i	−0.747674	+	0.627373i	−0.934887	−	0.354947i	$-0.884499\pi$
$823$	−21.4492	+	17.9981i	−0.747674	+	0.627373i	0.187213	+	0.982319i	$0.440055\pi$
$824$	−10.6146	+	8.90673i	−0.369778	+	0.310281i
$825$		0			0
$826$	−45.1052	+	16.4170i	−1.56941	+	0.571219i
$827$	5.19615	+	9.00000i	0.180688	+	0.312961i	0.942115	−	0.335290i	$-0.108834\pi$
$827$	5.19615	+	9.00000i	0.180688	+	0.312961i	−0.761427	+	0.648251i	$0.775501\pi$
$828$		0			0
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	0.848137	+	0.529777i	$0.177724\pi$
$830$	7.21842	−	40.9377i	0.250555	−	1.42097i
$831$		0			0
$832$	0.939693	+	0.342020i	0.0325780	+	0.0118574i
$833$	−2.70691	−	15.3516i	−0.0937888	−	0.531903i
$834$		0			0
$835$	22.9813	+	19.2836i	0.795302	+	0.667337i
$836$	−6.92820			−0.239617
$837$		0			0
$838$	−12.0000			−0.414533
$839$	−34.4975	−	28.9469i	−1.19099	−	0.999357i	−0.999842	−	0.0177948i	$-0.994335\pi$
$839$	−34.4975	−	28.9469i	−1.19099	−	0.999357i	−0.191145	−	0.981562i	$-0.561220\pi$
$840$		0			0
$841$	−4.51485	−	25.6050i	−0.155685	−	0.882931i
$842$	40.6899	+	14.8099i	1.40227	+	0.510383i
$843$		0			0
$844$	−1.73648	+	9.84808i	−0.0597722	+	0.338985i
$845$	−10.3923	+	18.0000i	−0.357506	+	0.619219i
$846$		0			0
$847$	−1.00000	−	1.73205i	−0.0343604	−	0.0595140i
$848$		0			0
$849$		0			0
$850$	−13.7888	+	11.5702i	−0.472952	+	0.396854i
$851$	−18.5756	+	15.5868i	−0.636763	+	0.534308i
$852$		0			0
$853$	31.9495	−	11.6287i	1.09393	−	0.398159i	0.268856	−	0.963180i	$-0.413354\pi$
$853$	31.9495	−	11.6287i	1.09393	−	0.398159i	0.825076	+	0.565022i	$0.191132\pi$
$854$	12.1244	+	21.0000i	0.414887	+	0.718605i
$855$		0			0
$856$		0			0
$857$	3.90998	−	22.1746i	0.133562	−	0.757469i	−0.842288	−	0.539028i	$-0.818792\pi$
$857$	3.90998	−	22.1746i	0.133562	−	0.757469i	0.975850	−	0.218441i	$-0.0700972\pi$
$858$		0			0
$859$	−41.3465	−	15.0489i	−1.41072	−	0.513461i	−0.479381	−	0.877607i	$-0.659139\pi$
$859$	−41.3465	−	15.0489i	−1.41072	−	0.513461i	−0.931342	+	0.364145i	$0.881361\pi$
$860$	−0.601535	−	3.41147i	−0.0205122	−	0.116330i
$861$		0			0
$862$		0			0
$863$	31.1769			1.06127			0.530637	−	0.847599i	$-0.321953\pi$
$863$	31.1769			1.06127			0.530637	+	0.847599i	$0.321953\pi$
$864$		0			0
$865$	33.0000			1.12203
$866$	14.5951	+	12.2467i	0.495962	+	0.416161i
$867$		0			0
$868$	2.77837	+	15.7569i	0.0943041	+	0.534825i
$869$	6.51038	+	2.36959i	0.220850	+	0.0803827i
$870$		0			0
$871$	1.73648	−	9.84808i	0.0588384	−	0.333689i
$872$	9.52628	−	16.5000i	0.322601	−	0.558761i
$873$		0			0
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$	−22.7863	+	8.29355i	−0.770319	+	0.280373i
$876$		0			0
$877$	40.6004	−	34.0677i	1.37098	−	1.15039i	0.398558	−	0.917143i	$-0.369511\pi$
$877$	40.6004	−	34.0677i	1.37098	−	1.15039i	0.972419	−	0.233243i	$-0.0749337\pi$
$878$	26.5366	−	22.2668i	0.895565	−	0.751469i
$879$		0			0
$880$	28.1908	−	10.2606i	0.950311	−	0.345885i
$881$	−10.3923	−	18.0000i	−0.350126	−	0.606435i	0.636146	−	0.771569i	$-0.280528\pi$
$881$	−10.3923	−	18.0000i	−0.350126	−	0.606435i	−0.986271	+	0.165134i	$0.947194\pi$
$882$		0			0
$883$	−28.0000	+	48.4974i	−0.942275	+	1.63207i	−0.181158	+	0.983454i	$0.557984\pi$
$883$	−28.0000	+	48.4974i	−0.942275	+	1.63207i	−0.761117	+	0.648614i	$0.775349\pi$
$884$	−0.902302	+	5.11721i	−0.0303477	+	0.172110i
$885$		0			0
$886$	56.3816	+	20.5212i	1.89418	+	0.689423i
$887$	0.601535	+	3.41147i	0.0201976	+	0.114546i	0.993240	−	0.116081i	$-0.0370333\pi$
$887$	0.601535	+	3.41147i	0.0201976	+	0.114546i	−0.973042	+	0.230627i	$0.925922\pi$
$888$		0			0
$889$	3.06418	+	2.57115i	0.102769	+	0.0862336i
$890$	15.5885			0.522526
$891$		0			0
$892$	2.00000			0.0669650
$893$	10.6146	+	8.90673i	0.355205	+	0.298052i
$894$		0			0
$895$	−6.25133	−	35.4531i	−0.208959	−	1.18507i
$896$	−22.7863	−	8.29355i	−0.761238	−	0.277068i
$897$		0			0
$898$	6.25133	−	35.4531i	0.208610	−	1.18308i
$899$	−6.92820	+	12.0000i	−0.231069	+	0.400222i
$900$		0			0
$901$		0			0
$902$	−39.0623	+	14.2175i	−1.30063	+	0.473391i
$903$		0			0
$904$	2.29813	−	1.92836i	0.0764348	−	0.0641364i
$905$	−2.65366	+	2.22668i	−0.0882105	+	0.0740174i
$906$		0			0
$907$	48.8640	−	17.7850i	1.62250	−	0.590543i	0.638646	−	0.769500i	$-0.279495\pi$
$907$	48.8640	−	17.7850i	1.62250	−	0.590543i	0.983857	+	0.178958i	$0.0572725\pi$
$908$	1.73205	+	3.00000i	0.0574801	+	0.0995585i
$909$		0			0
$910$	−3.00000	+	5.19615i	−0.0994490	+	0.172251i
$911$	−4.21074	+	23.8803i	−0.139508	+	0.791190i	0.832106	+	0.554617i	$0.187135\pi$
$911$	−4.21074	+	23.8803i	−0.139508	+	0.791190i	−0.971614	+	0.236573i	$0.923976\pi$
$912$		0			0
$913$	−45.1052	−	16.4170i	−1.49277	−	0.543322i
$914$	8.72226	+	49.4664i	0.288507	+	1.63620i
$915$		0			0
$916$	−0.766044	−	0.642788i	−0.0253108	−	0.0212383i
$917$	6.92820			0.228789
$918$		0			0
$919$	2.00000			0.0659739			0.0329870	−	0.999456i	$-0.489498\pi$
$919$	2.00000			0.0659739			0.0329870	+	0.999456i	$0.489498\pi$
$920$	7.96097	+	6.68004i	0.262465	+	0.220235i
$921$		0			0
$922$	−4.16756	−	23.6354i	−0.137251	−	0.778390i
$923$	−9.76557	−	3.55438i	−0.321438	−	0.116994i
$924$		0			0
$925$	2.43107	−	13.7873i	0.0799332	−	0.453324i
$926$	−6.92820	+	12.0000i	−0.227675	+	0.394344i
$927$		0			0
$928$	4.50000	+	7.79423i	0.147720	+	0.255858i
$929$	47.2003	−	17.1795i	1.54859	−	0.563641i	0.580504	−	0.814257i	$-0.302856\pi$
$929$	47.2003	−	17.1795i	1.54859	−	0.563641i	0.968086	+	0.250617i	$0.0806333\pi$
$930$		0			0
$931$	−4.59627	+	3.85673i	−0.150637	+	0.126399i
$932$	−19.9024	+	16.7001i	−0.651925	+	0.547030i
$933$		0			0
$934$	33.8289	−	12.3127i	1.10692	−	0.402885i
$935$	−15.5885	−	27.0000i	−0.509797	−	0.882994i
$936$		0			0
$937$	12.5000	−	21.6506i	0.408357	−	0.707295i	−0.586349	−	0.810059i	$-0.699435\pi$
$937$	12.5000	−	21.6506i	0.408357	−	0.707295i	0.994706	+	0.102763i	$0.0327685\pi$
$938$	−6.01535	+	34.1147i	−0.196408	+	1.11389i
$939$		0			0
$940$	11.2763	+	4.10424i	0.367793	+	0.133866i
$941$	8.72226	+	49.4664i	0.284337	+	1.61256i	0.707643	+	0.706571i	$0.249759\pi$
$941$	8.72226	+	49.4664i	0.284337	+	1.61256i	−0.423305	+	0.905987i	$0.639130\pi$
$942$		0			0
$943$	−18.3851	−	15.4269i	−0.598700	−	0.502369i
$944$	−69.2820			−2.25494
$945$		0			0
$946$	−12.0000			−0.390154
$947$	13.2683	+	11.1334i	0.431161	+	0.361787i	0.832390	−	0.554191i	$-0.186972\pi$
$947$	13.2683	+	11.1334i	0.431161	+	0.361787i	−0.401229	+	0.915978i	$0.631417\pi$
$948$		0			0
$949$	1.21554	+	6.89365i	0.0394580	+	0.223777i
$950$	6.51038	+	2.36959i	0.211225	+	0.0768795i
$951$		0			0
$952$	−3.12567	+	17.7265i	−0.101303	+	0.574520i
$953$	2.59808	−	4.50000i	0.0841599	−	0.145769i	−0.820873	−	0.571111i	$-0.806513\pi$
$953$	2.59808	−	4.50000i	0.0841599	−	0.145769i	0.905033	+	0.425341i	$0.139846\pi$
$954$		0			0
$955$	15.0000	+	25.9808i	0.485389	+	0.840718i
$956$	26.0415	−	9.47834i	0.842243	−	0.306551i
$957$		0			0
$958$	−32.1739	+	26.9971i	−1.03949	+	0.872236i
$959$	2.65366	−	2.22668i	0.0856910	−	0.0719033i
$960$		0			0
$961$	−31.0099	+	11.2867i	−1.00032	+	0.364086i
$962$	−6.06218	−	10.5000i	−0.195452	−	0.338534i
$963$		0			0
$964$	−14.5000	+	25.1147i	−0.467014	+	0.808891i
$965$	0.300767	−	1.70574i	0.00968205	−	0.0549096i
$966$		0			0
$967$	43.2259	+	15.7329i	1.39005	+	0.505937i	0.925209	−	0.379457i	$-0.123889\pi$
$967$	43.2259	+	15.7329i	1.39005	+	0.505937i	0.464841	+	0.885394i	$0.346112\pi$
$968$	−0.300767	−	1.70574i	−0.00966703	−	0.0548245i
$969$		0			0
$970$	−4.59627	−	3.85673i	−0.147577	−	0.123832i
$971$	31.1769			1.00051			0.500257	−	0.865877i	$-0.333239\pi$
$971$	31.1769			1.00051			0.500257	+	0.865877i	$0.333239\pi$
$972$		0			0
$973$	16.0000			0.512936
$974$	−21.2292	−	17.8135i	−0.680229	−	0.570780i
$975$		0			0
$976$	6.07769	+	34.4683i	0.194542	+	1.10330i
$977$	45.5727	+	16.5871i	1.45800	+	0.530668i	0.944813	−	0.327609i	$-0.106243\pi$
$977$	45.5727	+	16.5871i	1.45800	+	0.530668i	0.513186	+	0.858278i	$0.328465\pi$
$978$		0			0
$979$	3.12567	−	17.7265i	0.0998968	−	0.566543i
$980$	−2.59808	+	4.50000i	−0.0829925	+	0.143747i
$981$		0			0
$982$	15.0000	+	25.9808i	0.478669	+	0.829079i
$983$	32.5519	−	11.8479i	1.03824	−	0.377890i	0.234030	−	0.972229i	$-0.424809\pi$
$983$	32.5519	−	11.8479i	1.03824	−	0.377890i	0.804214	+	0.594339i	$0.202586\pi$
$984$		0			0
$985$	6.89440	−	5.78509i	0.219674	−	0.184328i
$986$	11.9415	−	10.0201i	0.380293	−	0.319104i
$987$		0			0
$988$	1.87939	−	0.684040i	0.0597912	−	0.0217622i
$989$	−3.46410	−	6.00000i	−0.110152	−	0.190789i
$990$		0			0
$991$	17.0000	−	29.4449i	0.540023	−	0.935347i	−0.458879	−	0.888499i	$-0.651749\pi$
$991$	17.0000	−	29.4449i	0.540023	−	0.935347i	0.998902	−	0.0468483i	$-0.0149177\pi$
$992$	−7.21842	+	40.9377i	−0.229185	+	1.29977i
$993$		0			0
$994$	33.8289	+	12.3127i	1.07299	+	0.390536i
$995$	−6.01535	−	34.1147i	−0.190699	−	1.08151i
$996$		0			0
$997$	−5.36231	−	4.49951i	−0.169826	−	0.142501i	0.553913	−	0.832574i	$-0.313134\pi$
$997$	−5.36231	−	4.49951i	−0.169826	−	0.142501i	−0.723740	+	0.690073i	$0.757578\pi$
$998$	−17.3205			−0.548271
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.o.406.2		12
3.2	odd	2	inner	729.2.e.o.406.1		12
9.2	odd	6	inner	729.2.e.o.649.1		12
9.4	even	3	inner	729.2.e.o.163.1		12
9.5	odd	6	inner	729.2.e.o.163.2		12
9.7	even	3	inner	729.2.e.o.649.2		12
27.2	odd	18		81.2.c.b.28.2		4
27.4	even	9	inner	729.2.e.o.82.2		12
27.5	odd	18	inner	729.2.e.o.325.1		12
27.7	even	9		81.2.a.a.1.2	yes	2
27.11	odd	18		81.2.c.b.55.2		4
27.13	even	9	inner	729.2.e.o.568.1		12
27.14	odd	18	inner	729.2.e.o.568.2		12
27.16	even	9		81.2.c.b.55.1		4
27.20	odd	18		81.2.a.a.1.1	✓	2
27.22	even	9	inner	729.2.e.o.325.2		12
27.23	odd	18	inner	729.2.e.o.82.1		12
27.25	even	9		81.2.c.b.28.1		4
108.7	odd	18		1296.2.a.o.1.1		2
108.11	even	18		1296.2.i.s.865.1		4
108.43	odd	18		1296.2.i.s.865.2		4
108.47	even	18		1296.2.a.o.1.2		2
108.79	odd	18		1296.2.i.s.433.2		4
108.83	even	18		1296.2.i.s.433.1		4
135.7	odd	36		2025.2.b.k.649.4		4
135.34	even	18		2025.2.a.j.1.1		2
135.47	even	36		2025.2.b.k.649.2		4
135.74	odd	18		2025.2.a.j.1.2		2
135.88	odd	36		2025.2.b.k.649.1		4
135.128	even	36		2025.2.b.k.649.3		4
189.20	even	18		3969.2.a.i.1.1		2
189.34	odd	18		3969.2.a.i.1.2		2
216.61	even	18		5184.2.a.br.1.2		2
216.101	odd	18		5184.2.a.br.1.1		2
216.115	odd	18		5184.2.a.bq.1.2		2
216.155	even	18		5184.2.a.bq.1.1		2
297.142	odd	18		9801.2.a.v.1.1		2
297.263	even	18		9801.2.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.a.a.1.1	✓	2	27.20	odd	18
81.2.a.a.1.2	yes	2	27.7	even	9
81.2.c.b.28.1		4	27.25	even	9
81.2.c.b.28.2		4	27.2	odd	18
81.2.c.b.55.1		4	27.16	even	9
81.2.c.b.55.2		4	27.11	odd	18
729.2.e.o.82.1		12	27.23	odd	18	inner
729.2.e.o.82.2		12	27.4	even	9	inner
729.2.e.o.163.1		12	9.4	even	3	inner
729.2.e.o.163.2		12	9.5	odd	6	inner
729.2.e.o.325.1		12	27.5	odd	18	inner
729.2.e.o.325.2		12	27.22	even	9	inner
729.2.e.o.406.1		12	3.2	odd	2	inner
729.2.e.o.406.2		12	1.1	even	1	trivial
729.2.e.o.568.1		12	27.13	even	9	inner
729.2.e.o.568.2		12	27.14	odd	18	inner
729.2.e.o.649.1		12	9.2	odd	6	inner
729.2.e.o.649.2		12	9.7	even	3	inner
1296.2.a.o.1.1		2	108.7	odd	18
1296.2.a.o.1.2		2	108.47	even	18
1296.2.i.s.433.1		4	108.83	even	18
1296.2.i.s.433.2		4	108.79	odd	18
1296.2.i.s.865.1		4	108.11	even	18
1296.2.i.s.865.2		4	108.43	odd	18
2025.2.a.j.1.1		2	135.34	even	18
2025.2.a.j.1.2		2	135.74	odd	18
2025.2.b.k.649.1		4	135.88	odd	36
2025.2.b.k.649.2		4	135.47	even	36
2025.2.b.k.649.3		4	135.128	even	36
2025.2.b.k.649.4		4	135.7	odd	36
3969.2.a.i.1.1		2	189.20	even	18
3969.2.a.i.1.2		2	189.34	odd	18
5184.2.a.bq.1.1		2	216.155	even	18
5184.2.a.bq.1.2		2	216.115	odd	18
5184.2.a.br.1.1		2	216.101	odd	18
5184.2.a.br.1.2		2	216.61	even	18
9801.2.a.v.1.1		2	297.142	odd	18
9801.2.a.v.1.2		2	297.263	even	18

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32683 + 1.11334i) q^{2} +(0.173648 + 0.984808i) q^{4} +(1.62760 + 0.592396i) q^{5} +(0.347296 - 1.96962i) q^{7} +(0.866025 - 1.50000i) q^{8} +O(q^{10})\)	\(q+(1.32683 + 1.11334i) q^{2} +(0.173648 + 0.984808i) q^{4} +(1.62760 + 0.592396i) q^{5} +(0.347296 - 1.96962i) q^{7} +(0.866025 - 1.50000i) q^{8} +(1.50000 + 2.59808i) q^{10} +(3.25519 - 1.18479i) q^{11} +(-0.766044 + 0.642788i) q^{13} +(2.65366 - 2.22668i) q^{14} +(4.69846 - 1.71010i) q^{16} +(-2.59808 - 4.50000i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-0.300767 + 1.70574i) q^{20} +(5.63816 + 2.05212i) q^{22} +(0.601535 + 3.41147i) q^{23} +(-1.53209 - 1.28558i) q^{25} -1.73205 q^{26} +2.00000 q^{28} +(1.32683 + 1.11334i) q^{29} +(1.38919 + 7.87846i) q^{31} +(4.88279 + 1.77719i) q^{32} +(1.56283 - 8.86327i) q^{34} +(1.73205 - 3.00000i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-3.25519 + 1.18479i) q^{38} +(2.29813 - 1.92836i) q^{40} +(-5.30731 + 4.45336i) q^{41} +(-1.87939 + 0.684040i) q^{43} +(1.73205 + 3.00000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(1.20307 - 6.82295i) q^{47} +(2.81908 + 1.02606i) q^{49} +(-0.601535 - 3.41147i) q^{50} +(-0.766044 - 0.642788i) q^{52} +6.00000 q^{55} +(-2.65366 - 2.22668i) q^{56} +(0.520945 + 2.95442i) q^{58} +(-13.0208 - 4.73917i) q^{59} +(-1.21554 + 6.89365i) q^{61} +(-6.92820 + 12.0000i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-1.62760 + 0.592396i) q^{65} +(-7.66044 + 6.42788i) q^{67} +(3.98048 - 3.34002i) q^{68} +(5.63816 - 2.05212i) q^{70} +(5.19615 + 9.00000i) q^{71} +(3.50000 - 6.06218i) q^{73} +(-2.10537 + 11.9402i) q^{74} +(-1.87939 - 0.684040i) q^{76} +(-1.20307 - 6.82295i) q^{77} +(1.53209 + 1.28558i) q^{79} +8.66025 q^{80} -12.0000 q^{82} +(-10.6146 - 8.90673i) q^{83} +(-1.56283 - 8.86327i) q^{85} +(-3.25519 - 1.18479i) q^{86} +(1.04189 - 5.90885i) q^{88} +(2.59808 - 4.50000i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-3.25519 + 1.18479i) q^{92} +(9.19253 - 7.71345i) q^{94} +(-2.65366 + 2.22668i) q^{95} +(-1.87939 + 0.684040i) q^{97} +(2.59808 + 4.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 18 q^{10} - 12 q^{19} + 24 q^{28} + 42 q^{37} - 36 q^{46} + 72 q^{55} - 6 q^{64} + 42 q^{73} - 144 q^{82} + 12 q^{91}+O(q^{100}) \) 12 * q + 18 * q^10 - 12 * q^19 + 24 * q^28 + 42 * q^37 - 36 * q^46 + 72 * q^55 - 6 * q^64 + 42 * q^73 - 144 * q^82 + 12 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more