LMFDB - Embedded newform 729.2.e.q.649.2

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 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			649.2
Root			$0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.q.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.118782 - 0.673648i) q^{2} +(1.43969 + 0.524005i) q^{4} +(0.802823 - 0.673648i) q^{5} +(0.113341 - 0.0412527i) q^{7} +(1.20805 - 2.09240i) q^{8} +O(q^{10})$	\(q+(0.118782 - 0.673648i) q^{2} +(1.43969 + 0.524005i) q^{4} +(0.802823 - 0.673648i) q^{5} +(0.113341 - 0.0412527i) q^{7} +(1.20805 - 2.09240i) q^{8} +(-0.358441 - 0.620838i) q^{10} +(-4.16247 - 3.49273i) q^{11} +(-0.794263 - 4.50449i) q^{13} +(-0.0143269 - 0.0812519i) q^{14} +(1.08125 + 0.907278i) q^{16} +(-2.38917 - 4.13816i) q^{17} +(0.294263 - 0.509678i) q^{19} +(1.50881 - 0.549163i) q^{20} +(-2.84730 + 2.38917i) q^{22} +(7.32580 + 2.66637i) q^{23} +(-0.677519 + 3.84240i) q^{25} -3.12879 q^{26} +0.184793 q^{28} +(0.880352 - 4.99273i) q^{29} +(8.23055 + 2.99568i) q^{31} +(4.44129 - 3.72668i) q^{32} +(-3.07145 + 1.11792i) q^{34} +(0.0632028 - 0.109470i) q^{35} +(1.09240 + 1.89209i) q^{37} +(-0.308391 - 0.258770i) q^{38} +(-0.439693 - 2.49362i) q^{40} +(1.31250 + 7.44356i) q^{41} +(-1.00000 - 0.839100i) q^{43} +(-4.16247 - 7.20961i) q^{44} +(2.66637 - 4.61830i) q^{46} +(-2.27038 + 0.826352i) q^{47} +(-5.35117 + 4.49016i) q^{49} +(2.50795 + 0.912818i) q^{50} +(1.21688 - 6.90128i) q^{52} -3.04628 q^{53} -5.69459 q^{55} +(0.0506039 - 0.286989i) q^{56} +(-3.25877 - 1.18610i) q^{58} +(-0.0336295 + 0.0282185i) q^{59} +(9.59627 - 3.49276i) q^{61} +(2.99568 - 5.18866i) q^{62} +(-0.571452 - 0.989783i) q^{64} +(-3.67209 - 3.08125i) q^{65} +(-0.322948 - 1.83153i) q^{67} +(-1.27125 - 7.20961i) q^{68} +(-0.0662372 - 0.0555796i) q^{70} +(3.25519 + 5.63816i) q^{71} +(-6.11721 + 10.5953i) q^{73} +(1.40436 - 0.511144i) q^{74} +(0.690722 - 0.579585i) q^{76} +(-0.615862 - 0.224155i) q^{77} +(0.121959 - 0.691663i) q^{79} +1.47924 q^{80} +5.17024 q^{82} +(1.17674 - 6.67365i) q^{83} +(-4.70574 - 1.71275i) q^{85} +(-0.684040 + 0.573978i) q^{86} +(-12.3366 + 4.49016i) q^{88} +(-3.42782 + 5.93717i) q^{89} +(-0.275845 - 0.477777i) q^{91} +(9.14971 + 7.67752i) q^{92} +(0.286989 + 1.62760i) q^{94} +(-0.107103 - 0.607411i) q^{95} +(-6.91534 - 5.80266i) q^{97} +(2.38917 + 4.13816i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 12 q^{7}+O(q^{10}) $ 12 * q + 6 * q^4 - 12 * q^7	$ 12 q + 6 q^{4} - 12 q^{7} + 12 q^{10} - 30 q^{13} + 18 q^{16} + 24 q^{19} - 30 q^{22} + 42 q^{25} - 12 q^{28} + 24 q^{31} - 36 q^{34} + 6 q^{37} + 6 q^{40} - 12 q^{43} - 6 q^{46} - 12 q^{49} - 18 q^{52} - 60 q^{55} + 6 q^{58} + 60 q^{61} - 6 q^{64} + 78 q^{67} - 66 q^{70} - 12 q^{73} + 48 q^{76} + 6 q^{79} - 24 q^{82} - 36 q^{85} - 24 q^{88} - 12 q^{94} + 6 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 - 12 * q^7 + 12 * q^10 - 30 * q^13 + 18 * q^16 + 24 * q^19 - 30 * q^22 + 42 * q^25 - 12 * q^28 + 24 * q^31 - 36 * q^34 + 6 * q^37 + 6 * q^40 - 12 * q^43 - 6 * q^46 - 12 * q^49 - 18 * q^52 - 60 * q^55 + 6 * q^58 + 60 * q^61 - 6 * q^64 + 78 * q^67 - 66 * q^70 - 12 * q^73 + 48 * q^76 + 6 * q^79 - 24 * q^82 - 36 * q^85 - 24 * q^88 - 12 * q^94 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.118782	−	0.673648i	0.0839918	−	0.476341i	−0.913578	−	0.406664i	$-0.866692\pi$
$2$	0.118782	−	0.673648i	0.0839918	−	0.476341i	0.997570	−	0.0696772i	$-0.0221969\pi$
$3$		0			0
$3$		0			0
$4$	1.43969	+	0.524005i	0.719846	+	0.262003i
$5$	0.802823	−	0.673648i	0.359033	−	0.301265i	−0.445372	−	0.895346i	$-0.646929\pi$
$5$	0.802823	−	0.673648i	0.359033	−	0.301265i	0.804405	+	0.594081i	$0.202484\pi$
$6$		0			0
$7$	0.113341	−	0.0412527i	0.0428388	−	0.0155920i	−0.320512	−	0.947244i	$-0.603855\pi$
$7$	0.113341	−	0.0412527i	0.0428388	−	0.0155920i	0.363351	+	0.931652i	$0.381633\pi$
$8$	1.20805	−	2.09240i	0.427109	−	0.739774i
$9$		0			0
$10$	−0.358441	−	0.620838i	−0.113349	−	0.196326i
$11$	−4.16247	−	3.49273i	−1.25503	−	1.05310i	−0.996193	−	0.0871759i	$-0.972216\pi$
$11$	−4.16247	−	3.49273i	−1.25503	−	1.05310i	−0.258839	−	0.965921i	$-0.583340\pi$
$12$		0			0
$13$	−0.794263	−	4.50449i	−0.220289	−	1.24932i	−0.871489	−	0.490415i	$-0.836845\pi$
$13$	−0.794263	−	4.50449i	−0.220289	−	1.24932i	0.651200	−	0.758906i	$-0.274266\pi$
$14$	−0.0143269	−	0.0812519i	−0.00382903	−	0.0217155i
$15$		0			0
$16$	1.08125	+	0.907278i	0.270313	+	0.226820i
$17$	−2.38917	−	4.13816i	−0.579458	−	1.00365i	−0.995542	−	0.0943239i	$-0.969931\pi$
$17$	−2.38917	−	4.13816i	−0.579458	−	1.00365i	0.416084	−	0.909326i	$-0.363402\pi$
$18$		0			0
$19$	0.294263	−	0.509678i	0.0675085	−	0.116928i	−0.830295	−	0.557323i	$-0.811828\pi$
$19$	0.294263	−	0.509678i	0.0675085	−	0.116928i	0.897804	+	0.440395i	$0.145162\pi$
$20$	1.50881	−	0.549163i	0.337381	−	0.122797i
$21$		0			0
$22$	−2.84730	+	2.38917i	−0.607046	+	0.509372i
$23$	7.32580	+	2.66637i	1.52754	+	0.555977i	0.963016	−	0.269443i	$-0.0868394\pi$
$23$	7.32580	+	2.66637i	1.52754	+	0.555977i	0.564519	+	0.825420i	$0.309062\pi$
$24$		0			0
$25$	−0.677519	+	3.84240i	−0.135504	+	0.768480i
$26$	−3.12879			−0.613605
$27$		0			0
$28$	0.184793			0.0349225
$29$	0.880352	−	4.99273i	0.163477	−	0.927126i	−0.787143	−	0.616770i	$-0.788441\pi$
$29$	0.880352	−	4.99273i	0.163477	−	0.927126i	0.950621	−	0.310356i	$-0.100448\pi$
$30$		0			0
$31$	8.23055	+	2.99568i	1.47825	+	0.538039i	0.950327	−	0.311253i	$-0.100749\pi$
$31$	8.23055	+	2.99568i	1.47825	+	0.538039i	0.527924	+	0.849292i	$0.322971\pi$
$32$	4.44129	−	3.72668i	0.785116	−	0.658790i
$33$		0			0
$34$	−3.07145	+	1.11792i	−0.526750	+	0.191721i
$35$	0.0632028	−	0.109470i	0.0106832	−	0.0185039i
$36$		0			0
$37$	1.09240	+	1.89209i	0.179589	+	0.311057i	0.941740	−	0.336342i	$-0.109190\pi$
$37$	1.09240	+	1.89209i	0.179589	+	0.311057i	−0.762151	+	0.647399i	$0.775857\pi$
$38$	−0.308391	−	0.258770i	−0.0500276	−	0.0419781i
$39$		0			0
$40$	−0.439693	−	2.49362i	−0.0695215	−	0.394276i
$41$	1.31250	+	7.44356i	0.204978	+	1.16249i	0.897474	+	0.441067i	$0.145400\pi$
$41$	1.31250	+	7.44356i	0.204978	+	1.16249i	−0.692496	+	0.721422i	$0.743489\pi$
$42$		0			0
$43$	−1.00000	−	0.839100i	−0.152499	−	0.127961i	0.563346	−	0.826221i	$-0.309514\pi$
$43$	−1.00000	−	0.839100i	−0.152499	−	0.127961i	−0.715845	+	0.698259i	$0.753958\pi$
$44$	−4.16247	−	7.20961i	−0.627516	−	1.08689i
$45$		0			0
$46$	2.66637	−	4.61830i	0.393135	−	0.680931i
$47$	−2.27038	+	0.826352i	−0.331169	+	0.120536i	−0.502253	−	0.864721i	$-0.667495\pi$
$47$	−2.27038	+	0.826352i	−0.331169	+	0.120536i	0.171084	+	0.985257i	$0.445273\pi$
$48$		0			0
$49$	−5.35117	+	4.49016i	−0.764452	+	0.641452i
$50$	2.50795	+	0.912818i	0.354677	+	0.129092i
$51$		0			0
$52$	1.21688	−	6.90128i	0.168751	−	0.957035i
$53$	−3.04628			−0.418439			−0.209219	−	0.977869i	$-0.567092\pi$
$53$	−3.04628			−0.418439			−0.209219	+	0.977869i	$0.567092\pi$
$54$		0			0
$55$	−5.69459			−0.767859
$56$	0.0506039	−	0.286989i	0.00676223	−	0.0383505i
$57$		0			0
$58$	−3.25877	−	1.18610i	−0.427898	−	0.155742i
$59$	−0.0336295	+	0.0282185i	−0.00437819	+	0.00367373i	−0.644974	−	0.764204i	$-0.723132\pi$
$59$	−0.0336295	+	0.0282185i	−0.00437819	+	0.00367373i	0.640596	+	0.767878i	$0.278687\pi$
$60$		0			0
$61$	9.59627	−	3.49276i	1.22868	−	0.447202i	0.355532	−	0.934664i	$-0.384300\pi$
$61$	9.59627	−	3.49276i	1.22868	−	0.447202i	0.873144	+	0.487463i	$0.162077\pi$
$62$	2.99568	−	5.18866i	0.380451	−	0.658961i
$63$		0			0
$64$	−0.571452	−	0.989783i	−0.0714315	−	0.123723i
$65$	−3.67209	−	3.08125i	−0.455467	−	0.382182i
$66$		0			0
$67$	−0.322948	−	1.83153i	−0.0394544	−	0.223757i	0.958705	−	0.284403i	$-0.0917952\pi$
$67$	−0.322948	−	1.83153i	−0.0394544	−	0.223757i	−0.998159	+	0.0606455i	$0.980684\pi$
$68$	−1.27125	−	7.20961i	−0.154162	−	0.874293i
$69$		0			0
$70$	−0.0662372	−	0.0555796i	−0.00791686	−	0.00664303i
$71$	3.25519	+	5.63816i	0.386320	+	0.669126i	0.991951	−	0.126619i	$-0.0404127\pi$
$71$	3.25519	+	5.63816i	0.386320	+	0.669126i	−0.605631	+	0.795745i	$0.707079\pi$
$72$		0			0
$73$	−6.11721	+	10.5953i	−0.715965	+	1.24009i	0.246621	+	0.969112i	$0.420680\pi$
$73$	−6.11721	+	10.5953i	−0.715965	+	1.24009i	−0.962586	+	0.270976i	$0.912653\pi$
$74$	1.40436	−	0.511144i	0.163253	−	0.0594193i
$75$		0			0
$76$	0.690722	−	0.579585i	0.0792313	−	0.0664829i
$77$	−0.615862	−	0.224155i	−0.0701840	−	0.0255449i
$78$		0			0
$79$	0.121959	−	0.691663i	0.0137215	−	0.0778182i	−0.977178	−	0.212422i	$-0.931865\pi$
$79$	0.121959	−	0.691663i	0.0137215	−	0.0778182i	0.990900	+	0.134603i	$0.0429761\pi$
$80$	1.47924			0.165384
$81$		0			0
$82$	5.17024			0.570958
$83$	1.17674	−	6.67365i	0.129164	−	0.732528i	−0.849582	−	0.527456i	$-0.823146\pi$
$83$	1.17674	−	6.67365i	0.129164	−	0.732528i	0.978747	−	0.205072i	$-0.0657429\pi$
$84$		0			0
$85$	−4.70574	−	1.71275i	−0.510409	−	0.185774i
$86$	−0.684040	+	0.573978i	−0.0737620	+	0.0618936i
$87$		0			0
$88$	−12.3366	+	4.49016i	−1.31509	+	0.478653i
$89$	−3.42782	+	5.93717i	−0.363349	+	0.629338i	−0.988510	−	0.151157i	$-0.951700\pi$
$89$	−3.42782	+	5.93717i	−0.363349	+	0.629338i	0.625161	+	0.780496i	$0.285033\pi$
$90$		0			0
$91$	−0.275845	−	0.477777i	−0.0289164	−	0.0500846i
$92$	9.14971	+	7.67752i	0.953923	+	0.800437i
$93$		0			0
$94$	0.286989	+	1.62760i	0.0296007	+	0.167874i
$95$	−0.107103	−	0.607411i	−0.0109885	−	0.0623191i
$96$		0			0
$97$	−6.91534	−	5.80266i	−0.702147	−	0.589171i	0.220237	−	0.975446i	$-0.429317\pi$
$97$	−6.91534	−	5.80266i	−0.702147	−	0.589171i	−0.922384	+	0.386275i	$0.873761\pi$
$98$	2.38917	+	4.13816i	0.241342	+	0.418017i
$99$		0			0
$100$	−2.98886	+	5.17685i	−0.298886	+	0.517685i
$101$	−12.2086	+	4.44356i	−1.21480	+	0.442151i	−0.868366	−	0.495923i	$-0.834830\pi$
$101$	−12.2086	+	4.44356i	−1.21480	+	0.442151i	−0.346434	+	0.938074i	$0.612607\pi$
$102$		0			0
$103$	6.94949	−	5.83132i	0.684754	−	0.574577i	−0.232637	−	0.972564i	$-0.574735\pi$
$103$	6.94949	−	5.83132i	0.684754	−	0.574577i	0.917391	+	0.397987i	$0.130291\pi$
$104$	−10.3847	−	3.77972i	−1.01830	−	0.370632i
$105$		0			0
$106$	−0.361844	+	2.05212i	−0.0351454	+	0.199320i
$107$	11.3865			1.10077			0.550386	−	0.834911i	$-0.314481\pi$
$107$	11.3865			1.10077			0.550386	+	0.834911i	$0.314481\pi$
$108$		0			0
$109$	2.89899			0.277672			0.138836	−	0.990315i	$-0.455664\pi$
$109$	2.89899			0.277672			0.138836	+	0.990315i	$0.455664\pi$
$110$	−0.676417	+	3.83615i	−0.0644938	+	0.365763i
$111$		0			0
$112$	0.159978	+	0.0582271i	0.0151165	+	0.00550194i
$113$	−8.87089	+	7.44356i	−0.834503	+	0.700232i	−0.956320	−	0.292321i	$-0.905572\pi$
$113$	−8.87089	+	7.44356i	−0.834503	+	0.700232i	0.121817	+	0.992553i	$0.461128\pi$
$114$		0			0
$115$	7.67752	−	2.79439i	0.715932	−	0.260578i
$116$	3.88365	−	6.72668i	0.360588	−	0.624557i
$117$		0			0
$118$	0.0150147	+	0.0260063i	0.00138222	+	0.00239407i
$119$	−0.441500	−	0.370462i	−0.0404722	−	0.0339602i
$120$		0			0
$121$	3.21688	+	18.2438i	0.292444	+	1.65853i
$122$	−1.21302	−	6.87939i	−0.109822	−	0.622830i
$123$		0			0
$124$	10.2797	+	8.62571i	0.923146	+	0.774611i
$125$	4.66452	+	8.07919i	0.417208	+	0.722625i
$126$		0			0
$127$	7.70961	−	13.3534i	0.684117	−	1.18493i	−0.289596	−	0.957149i	$-0.593521\pi$
$127$	7.70961	−	13.3534i	0.684117	−	1.18493i	0.973713	−	0.227777i	$-0.0731456\pi$
$128$	10.1614	−	3.69846i	0.898153	−	0.326901i
$129$		0			0
$130$	−2.51186	+	2.10770i	−0.220305	+	0.184858i
$131$	−12.5506	−	4.56805i	−1.09655	−	0.399112i	−0.270508	−	0.962718i	$-0.587192\pi$
$131$	−12.5506	−	4.56805i	−1.09655	−	0.399112i	−0.826044	+	0.563606i	$0.809414\pi$
$132$		0			0
$133$	0.0123264	−	0.0699065i	0.00106883	−	0.00606166i
$134$	−1.27217			−0.109899
$135$		0			0
$136$	−11.5449			−0.989965
$137$	−3.40760	+	19.3255i	−0.291131	+	1.65109i	0.391393	+	0.920224i	$0.371993\pi$
$137$	−3.40760	+	19.3255i	−0.291131	+	1.65109i	−0.682524	+	0.730863i	$0.739118\pi$
$138$		0			0
$139$	−15.3229	−	5.57710i	−1.29968	−	0.473043i	−0.402784	−	0.915295i	$-0.631958\pi$
$139$	−15.3229	−	5.57710i	−1.29968	−	0.473043i	−0.896891	+	0.442252i	$0.854180\pi$
$140$	0.148356	−	0.124485i	0.0125383	−	0.0105209i
$141$		0			0
$142$	4.18479	−	1.52314i	0.351180	−	0.127819i
$143$	−12.4269	+	21.5239i	−1.03919	+	1.79992i
$144$		0			0
$145$	−2.65657	−	4.60132i	−0.220616	−	0.382119i
$146$	6.41090	+	5.37939i	0.530570	+	0.445201i
$147$		0			0
$148$	0.581252	+	3.29644i	0.0477786	+	0.270966i
$149$	1.91841	+	10.8799i	0.157162	+	0.891312i	0.956782	+	0.290806i	$0.0939233\pi$
$149$	1.91841	+	10.8799i	0.157162	+	0.891312i	−0.799620	+	0.600507i	$0.794966\pi$
$150$		0			0
$151$	−5.20961	−	4.37138i	−0.423952	−	0.355738i	0.405712	−	0.914001i	$-0.367024\pi$
$151$	−5.20961	−	4.37138i	−0.423952	−	0.355738i	−0.829664	+	0.558263i	$0.811468\pi$
$152$	−0.710966	−	1.23143i	−0.0576670	−	0.0998821i
$153$		0			0
$154$	−0.224155	+	0.388249i	−0.0180630	+	0.0312860i
$155$	8.62571	−	3.13950i	0.692833	−	0.252171i
$156$		0			0
$157$	12.9363	−	10.8548i	1.03243	−	0.866310i	0.0412904	−	0.999147i	$-0.486853\pi$
$157$	12.9363	−	10.8548i	1.03243	−	0.866310i	0.991138	+	0.132837i	$0.0424087\pi$
$158$	−0.451451	−	0.164315i	−0.0359155	−	0.0130722i
$159$		0			0
$160$	1.05509	−	5.98373i	0.0834124	−	0.473055i
$161$	0.940307			0.0741066
$162$		0			0
$163$	8.41147			0.658838			0.329419	−	0.944184i	$-0.393147\pi$
$163$	8.41147			0.658838			0.329419	+	0.944184i	$0.393147\pi$
$164$	−2.01087	+	11.4042i	−0.157022	+	0.890518i
$165$		0			0
$166$	−4.35591	−	1.58542i	−0.338085	−	0.123053i
$167$	−2.01087	+	1.68732i	−0.155606	+	0.130569i	−0.717267	−	0.696799i	$-0.754607\pi$
$167$	−2.01087	+	1.68732i	−0.155606	+	0.130569i	0.561661	+	0.827368i	$0.310163\pi$
$168$		0			0
$169$	−7.44356	+	2.70924i	−0.572582	+	0.208403i
$170$	−1.71275	+	2.96657i	−0.131362	+	0.227525i
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	10.0377	+	8.42262i	0.763151	+	0.640360i	0.938945	−	0.344067i	$-0.111805\pi$
$173$	10.0377	+	8.42262i	0.763151	+	0.640360i	−0.175794	+	0.984427i	$0.556249\pi$
$174$		0			0
$175$	0.0817187	+	0.463450i	0.00617736	+	0.0350335i
$176$	−1.33180	−	7.55303i	−0.100388	−	0.569331i
$177$		0			0
$178$	3.59240	+	3.01438i	0.269261	+	0.225937i
$179$	11.0494	+	19.1382i	0.825872	+	1.43045i	0.901251	+	0.433298i	$0.142650\pi$
$179$	11.0494	+	19.1382i	0.825872	+	1.43045i	−0.0753784	+	0.997155i	$0.524016\pi$
$180$		0			0
$181$	1.02956	−	1.78325i	0.0765268	−	0.132548i	−0.825222	−	0.564808i	$-0.808950\pi$
$181$	1.02956	−	1.78325i	0.0765268	−	0.132548i	0.901749	+	0.432260i	$0.142284\pi$
$182$	−0.354619	+	0.129071i	−0.0262861	+	0.00956736i
$183$		0			0
$184$	14.4290	−	12.1074i	1.06372	−	0.892568i
$185$	2.15160	+	0.783119i	0.158189	+	0.0575760i
$186$		0			0
$187$	−4.50862	+	25.5696i	−0.329703	+	1.86984i
$188$	−3.70167			−0.269972
$189$		0			0
$190$	−0.421903			−0.0306081
$191$	−0.685768	+	3.88919i	−0.0496205	+	0.281412i	−0.999514	−	0.0311609i	$-0.990080\pi$
$191$	−0.685768	+	3.88919i	−0.0496205	+	0.281412i	0.949894	+	0.312572i	$0.101191\pi$
$192$		0			0
$193$	7.93717	+	2.88889i	0.571330	+	0.207947i	0.611498	−	0.791246i	$-0.290567\pi$
$193$	7.93717	+	2.88889i	0.571330	+	0.207947i	−0.0401684	+	0.999193i	$0.512789\pi$
$194$	−4.73037	+	3.96926i	−0.339621	+	0.284976i
$195$		0			0
$196$	−10.0569	+	3.66041i	−0.718350	+	0.261458i
$197$	1.14749	−	1.98751i	0.0817553	−	0.141604i	−0.822249	−	0.569128i	$-0.807281\pi$
$197$	1.14749	−	1.98751i	0.0817553	−	0.141604i	0.904004	+	0.427524i	$0.140614\pi$
$198$		0			0
$199$	11.7515	+	20.3542i	0.833042	+	1.44287i	0.895615	+	0.444830i	$0.146736\pi$
$199$	11.7515	+	20.3542i	0.833042	+	1.44287i	−0.0625736	+	0.998040i	$0.519931\pi$
$200$	7.22135	+	6.05943i	0.510626	+	0.428466i
$201$		0			0
$202$	1.54323	+	8.75211i	0.108582	+	0.615796i
$203$	−0.106183	−	0.602196i	−0.00745262	−	0.0422659i
$204$		0			0
$205$	6.06805	+	5.09170i	0.423811	+	0.355620i
$206$	−3.10278	−	5.37417i	−0.216181	−	0.374436i
$207$		0			0
$208$	3.22803	−	5.59110i	0.223823	−	0.387673i
$209$	−3.00503	+	1.09374i	−0.207862	+	0.0756556i
$210$		0			0
$211$	−1.27719	+	1.07169i	−0.0879253	+	0.0737781i	−0.685691	−	0.727893i	$-0.740500\pi$
$211$	−1.27719	+	1.07169i	−0.0879253	+	0.0737781i	0.597766	+	0.801671i	$0.296055\pi$
$212$	−4.38571	−	1.59627i	−0.301212	−	0.109632i
$213$		0			0
$214$	1.35251	−	7.67047i	0.0924557	−	0.524343i
$215$	−1.36808			−0.0933023
$216$		0			0
$217$	1.05644			0.0717156
$218$	0.344348	−	1.95290i	0.0233222	−	0.132267i
$219$		0			0
$220$	−8.19846	−	2.98400i	−0.552740	−	0.201181i
$221$	−16.7427	+	14.0488i	−1.12623	+	0.945021i
$222$		0			0
$223$	9.20961	−	3.35202i	0.616721	−	0.224468i	−0.0147205	−	0.999892i	$-0.504686\pi$
$223$	9.20961	−	3.35202i	0.616721	−	0.224468i	0.631441	+	0.775424i	$0.282464\pi$
$224$	0.349643	−	0.605600i	0.0233615	−	0.0404634i
$225$		0			0
$226$	3.96064	+	6.86002i	0.263458	+	0.456322i
$227$	−11.8589	−	9.95084i	−0.787106	−	0.660460i	0.157921	−	0.987452i	$-0.449521\pi$
$227$	−11.8589	−	9.95084i	−0.787106	−	0.660460i	−0.945027	+	0.326991i	$0.893965\pi$
$228$		0			0
$229$	−1.95424	−	11.0830i	−0.129140	−	0.732388i	−0.978763	−	0.204997i	$-0.934281\pi$
$229$	−1.95424	−	11.0830i	−0.129140	−	0.732388i	0.849623	−	0.527391i	$-0.176830\pi$
$230$	−0.970481	−	5.50387i	−0.0639916	−	0.362914i
$231$		0			0
$232$	−9.38326	−	7.87349i	−0.616041	−	0.516920i
$233$	2.61738	+	4.53343i	0.171470	+	0.296995i	0.938934	−	0.344097i	$-0.111815\pi$
$233$	2.61738	+	4.53343i	0.171470	+	0.296995i	−0.767464	+	0.641092i	$0.778482\pi$
$234$		0			0
$235$	−1.26604	+	2.19285i	−0.0825876	+	0.143046i
$236$	−0.0632028	+	0.0230039i	−0.00411415	+	0.00149743i
$237$		0			0
$238$	−0.302004	+	0.253411i	−0.0195760	+	0.0164262i
$239$	−9.68804	−	3.52616i	−0.626667	−	0.228088i	0.00911276	−	0.999958i	$-0.497099\pi$
$239$	−9.68804	−	3.52616i	−0.626667	−	0.228088i	−0.635780	+	0.771870i	$0.719321\pi$
$240$		0			0
$241$	1.86571	−	10.5810i	0.120181	−	0.681582i	−0.863873	−	0.503710i	$-0.831968\pi$
$241$	1.86571	−	10.5810i	0.120181	−	0.681582i	0.984054	−	0.177871i	$-0.0569211\pi$
$242$	12.6720			0.814590
$243$		0			0
$244$	15.6459			1.00163
$245$	−1.27125	+	7.20961i	−0.0812171	+	0.460605i
$246$		0			0
$247$	−2.52956	−	0.920686i	−0.160952	−	0.0585818i
$248$	16.2110	−	13.6027i	1.02940	−	0.863770i
$249$		0			0
$250$	5.99660	−	2.18258i	0.379258	−	0.138039i
$251$	7.53644	−	13.0535i	0.475696	−	0.823930i	−0.523916	−	0.851770i	$-0.675530\pi$
$251$	7.53644	−	13.0535i	0.475696	−	0.823930i	0.999612	+	0.0278401i	$0.00886291\pi$
$252$		0			0
$253$	−21.1805	−	36.6857i	−1.33161	−	2.30641i
$254$	−8.07975	−	6.77972i	−0.506969	−	0.425397i
$255$		0			0
$256$	−1.68139	−	9.53563i	−0.105087	−	0.595977i
$257$	0.576937	+	3.27197i	0.0359884	+	0.204100i	0.997500	−	0.0706633i	$-0.0225116\pi$
$257$	0.576937	+	3.27197i	0.0359884	+	0.204100i	−0.961512	+	0.274763i	$0.911400\pi$
$258$		0			0
$259$	0.201867	+	0.169386i	0.0125434	+	0.0105251i
$260$	−3.67209	−	6.36025i	−0.227734	−	0.394446i
$261$		0			0
$262$	−4.56805	+	7.91209i	−0.282215	+	0.488811i
$263$	8.30564	−	3.02300i	0.512147	−	0.186406i	−0.0730022	−	0.997332i	$-0.523258\pi$
$263$	8.30564	−	3.02300i	0.512147	−	0.186406i	0.585150	+	0.810925i	$0.301036\pi$
$264$		0			0
$265$	−2.44562	+	2.05212i	−0.150233	+	0.126061i
$266$	−0.0456282	−	0.0166073i	−0.00279765	−	0.00101826i
$267$		0			0
$268$	0.494785	−	2.80607i	0.0302238	−	0.171408i
$269$	−8.09267			−0.493419			−0.246709	−	0.969090i	$-0.579349\pi$
$269$	−8.09267			−0.493419			−0.246709	+	0.969090i	$0.579349\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	1.17117	−	6.64203i	0.0710125	−	0.402732i
$273$		0			0
$274$	12.6138	+	4.59105i	0.762028	+	0.277356i
$275$	16.2406	−	13.6275i	0.979345	−	0.821768i
$276$		0			0
$277$	3.97431	−	1.44653i	0.238793	−	0.0869135i	−0.219852	−	0.975533i	$-0.570557\pi$
$277$	3.97431	−	1.44653i	0.238793	−	0.0869135i	0.458645	+	0.888620i	$0.348335\pi$
$278$	−5.57710	+	9.65982i	−0.334492	+	0.579357i
$279$		0			0
$280$	−0.152704	−	0.264490i	−0.00912579	−	0.0158063i
$281$	−5.59375	−	4.69372i	−0.333695	−	0.280004i	0.460508	−	0.887655i	$-0.347667\pi$
$281$	−5.59375	−	4.69372i	−0.333695	−	0.280004i	−0.794204	+	0.607652i	$0.792112\pi$
$282$		0			0
$283$	2.78194	+	15.7771i	0.165369	+	0.937854i	0.948683	+	0.316228i	$0.102416\pi$
$283$	2.78194	+	15.7771i	0.165369	+	0.937854i	−0.783314	+	0.621626i	$0.786472\pi$
$284$	1.73205	+	9.82295i	0.102778	+	0.582885i
$285$		0			0
$286$	13.0235	+	10.9280i	0.770094	+	0.646186i
$287$	0.455827	+	0.789515i	0.0269066	+	0.0466036i
$288$		0			0
$289$	−2.91622	+	5.05104i	−0.171542	+	0.297120i
$290$	−3.41523	+	1.24304i	−0.200549	+	0.0729939i
$291$		0			0
$292$	−14.3589	+	12.0486i	−0.840292	+	0.705088i
$293$	16.9187	+	6.15792i	0.988403	+	0.359749i	0.785102	−	0.619367i	$-0.212611\pi$
$293$	16.9187	+	6.15792i	0.988403	+	0.359749i	0.203302	+	0.979116i	$0.434833\pi$
$294$		0			0
$295$	−0.00798918	+	0.0453089i	−0.000465148	+	0.00263799i
$296$	5.27866			0.306816
$297$		0			0
$298$	7.55707			0.437769
$299$	6.19204	−	35.1168i	0.358095	−	2.03086i
$300$		0			0
$301$	−0.147956	−	0.0538515i	−0.00852804	−	0.00310395i
$302$	−3.56358	+	2.99020i	−0.205061	+	0.172067i
$303$		0			0
$304$	0.780592	−	0.284112i	0.0447700	−	0.0162950i
$305$	5.35121	−	9.26857i	0.306409	−	0.530717i
$306$		0			0
$307$	6.75537	+	11.7006i	0.385549	+	0.667791i	0.991845	−	0.127448i	$-0.0406787\pi$
$307$	6.75537	+	11.7006i	0.385549	+	0.667791i	−0.606296	+	0.795239i	$0.707345\pi$
$308$	−0.769193	−	0.645430i	−0.0438288	−	0.0367768i
$309$		0			0
$310$	−1.09034	−	6.18361i	−0.0619270	−	0.351205i
$311$	−2.85170	−	16.1728i	−0.161705	−	0.917074i	−0.952397	−	0.304860i	$-0.901390\pi$
$311$	−2.85170	−	16.1728i	−0.161705	−	0.917074i	0.790692	−	0.612214i	$-0.209721\pi$
$312$		0			0
$313$	−14.9875	−	12.5760i	−0.847144	−	0.710838i	0.112015	−	0.993707i	$-0.464270\pi$
$313$	−14.9875	−	12.5760i	−0.847144	−	0.710838i	−0.959159	+	0.282868i	$0.908714\pi$
$314$	−5.77574	−	10.0039i	−0.325944	−	0.564551i
$315$		0			0
$316$	0.538019	−	0.931876i	0.0302659	−	0.0524221i
$317$	−22.9084	+	8.33796i	−1.28666	+	0.468307i	−0.892630	−	0.450790i	$-0.851142\pi$
$317$	−22.9084	+	8.33796i	−1.28666	+	0.468307i	−0.394032	+	0.919097i	$0.628920\pi$
$318$		0			0
$319$	−21.1027	+	17.7072i	−1.18152	+	0.991415i
$320$	−1.12554	−	0.409663i	−0.0629196	−	0.0229009i
$321$		0			0
$322$	0.111692	−	0.633436i	0.00622435	−	0.0353000i
$323$	−2.81217			−0.156473
$324$		0			0
$325$	17.8462			0.989927
$326$	0.999135	−	5.66637i	0.0553370	−	0.313831i
$327$		0			0
$328$	17.1604	+	6.24589i	0.947527	+	0.344872i
$329$	−0.223238	+	0.187319i	−0.0123075	+	0.0103272i
$330$		0			0
$331$	−26.7802	+	9.74719i	−1.47197	+	0.535754i	−0.948635	−	0.316372i	$-0.897535\pi$
$331$	−26.7802	+	9.74719i	−1.47197	+	0.535754i	−0.523337	+	0.852126i	$0.675313\pi$
$332$	5.19118	−	8.99138i	0.284903	−	0.493466i
$333$		0			0
$334$	0.897804	+	1.55504i	0.0491256	+	0.0850881i
$335$	−1.49308	−	1.25284i	−0.0815755	−	0.0684500i
$336$		0			0
$337$	−3.02956	−	17.1815i	−0.165031	−	0.935936i	−0.949033	−	0.315178i	$-0.897936\pi$
$337$	−3.02956	−	17.1815i	−0.165031	−	0.935936i	0.784002	−	0.620758i	$-0.213175\pi$
$338$	0.940908	+	5.33615i	0.0511786	+	0.290248i
$339$		0			0
$340$	−5.87733	−	4.93166i	−0.318743	−	0.267457i
$341$	−23.7963	−	41.2165i	−1.28864	−	2.23200i
$342$		0			0
$343$	−0.843426	+	1.46086i	−0.0455407	+	0.0788788i
$344$	−2.96377	+	1.07873i	−0.159796	+	0.0581610i
$345$		0			0
$346$	6.86618	−	5.76141i	0.369128	−	0.309735i
$347$	23.6699	+	8.61515i	1.27067	+	0.462486i	0.887335	−	0.461125i	$-0.152554\pi$
$347$	23.6699	+	8.61515i	1.27067	+	0.462486i	0.383333	+	0.923610i	$0.374776\pi$
$348$		0			0
$349$	−2.05809	+	11.6720i	−0.110167	+	0.624787i	0.878863	+	0.477074i	$0.158302\pi$
$349$	−2.05809	+	11.6720i	−0.110167	+	0.624787i	−0.989030	+	0.147713i	$0.952809\pi$
$350$	0.321909			0.0172068
$351$		0			0
$352$	−31.5030			−1.67912
$353$	1.45821	−	8.26991i	0.0776126	−	0.440163i	−0.921095	−	0.389338i	$-0.872704\pi$
$353$	1.45821	−	8.26991i	0.0776126	−	0.440163i	0.998708	−	0.0508251i	$-0.0161851\pi$
$354$		0			0
$355$	6.41147	+	2.33359i	0.340286	+	0.123854i
$356$	−8.04612	+	6.75150i	−0.426444	+	0.357829i
$357$		0			0
$358$	14.2049	−	5.17015i	0.750750	−	0.273251i
$359$	1.32012	−	2.28652i	0.0696735	−	0.120678i	−0.829084	−	0.559124i	$-0.811138\pi$
$359$	1.32012	−	2.28652i	0.0696735	−	0.120678i	0.898758	+	0.438446i	$0.144471\pi$
$360$		0			0
$361$	9.32682	+	16.1545i	0.490885	+	0.850238i
$362$	−1.07899	−	0.905382i	−0.0567106	−	0.0475858i
$363$		0			0
$364$	−0.146774	−	0.832396i	−0.00769304	−	0.0436294i
$365$	2.22648	+	12.6270i	0.116539	+	0.660928i
$366$		0			0
$367$	7.04576	+	5.91209i	0.367786	+	0.308609i	0.807885	−	0.589340i	$-0.200612\pi$
$367$	7.04576	+	5.91209i	0.367786	+	0.308609i	−0.440099	+	0.897949i	$0.645057\pi$
$368$	5.50190	+	9.52956i	0.286806	+	0.496763i
$369$		0			0
$370$	0.783119	−	1.35640i	0.0407124	−	0.0705159i
$371$	−0.345268	+	0.125667i	−0.0179254	+	0.00652432i
$372$		0			0
$373$	−20.5232	+	17.2210i	−1.06265	+	0.891671i	−0.994367	−	0.105995i	$-0.966197\pi$
$373$	−20.5232	+	17.2210i	−1.06265	+	0.891671i	−0.0682855	+	0.997666i	$0.521753\pi$
$374$	16.6894	+	6.07444i	0.862988	+	0.314102i
$375$		0			0
$376$	−1.01367	+	5.74881i	−0.0522761	+	0.296472i
$377$	−23.1889			−1.19429
$378$		0			0
$379$	−27.1242			−1.39328			−0.696639	−	0.717422i	$-0.745322\pi$
$379$	−27.1242			−1.39328			−0.696639	+	0.717422i	$0.745322\pi$
$380$	0.164091	−	0.930608i	0.00841770	−	0.0477392i
$381$		0			0
$382$	2.53849	+	0.923933i	0.129880	+	0.0472725i
$383$	26.3725	−	22.1291i	1.34757	−	1.13075i	0.367959	−	0.929842i	$-0.380057\pi$
$383$	26.3725	−	22.1291i	1.34757	−	1.13075i	0.979611	−	0.200904i	$-0.0643878\pi$
$384$		0			0
$385$	−0.645430	+	0.234917i	−0.0328941	+	0.0119725i
$386$	2.88889	−	5.00371i	0.147041	−	0.254682i
$387$		0			0
$388$	−6.91534	−	11.9777i	−0.351073	−	0.608077i
$389$	0.579585	+	0.486329i	0.0293861	+	0.0246579i	0.657362	−	0.753575i	$-0.271672\pi$
$389$	0.579585	+	0.486329i	0.0293861	+	0.0246579i	−0.627976	+	0.778232i	$0.716117\pi$
$390$		0			0
$391$	−6.46868	−	36.6857i	−0.327135	−	1.85528i
$392$	2.93075	+	16.6211i	0.148025	+	0.839491i
$393$		0			0
$394$	−1.20258	−	1.00909i	−0.0605852	−	0.0508370i
$395$	−0.368026	−	0.637441i	−0.0185174	−	0.0320731i
$396$		0			0
$397$	−3.50387	+	6.06888i	−0.175854	+	0.304588i	−0.940457	−	0.339914i	$-0.889602\pi$
$397$	−3.50387	+	6.06888i	−0.175854	+	0.304588i	0.764602	+	0.644502i	$0.222935\pi$
$398$	15.1074	−	5.49866i	0.757267	−	0.275623i
$399$		0			0
$400$	−4.21869	+	3.53990i	−0.210935	+	0.176995i
$401$	8.88084	+	3.23236i	0.443488	+	0.161417i	0.554105	−	0.832447i	$-0.313060\pi$
$401$	8.88084	+	3.23236i	0.443488	+	0.161417i	−0.110617	+	0.993863i	$0.535283\pi$
$402$		0			0
$403$	6.95677	−	39.4538i	0.346541	−	1.96533i
$404$	−19.9051			−0.990314
$405$		0			0
$406$	−0.418281			−0.0207590
$407$	2.06147	−	11.6912i	0.102183	−	0.579511i
$408$		0			0
$409$	−5.18479	−	1.88711i	−0.256371	−	0.0933116i	0.210637	−	0.977564i	$-0.432446\pi$
$409$	−5.18479	−	1.88711i	−0.256371	−	0.0933116i	−0.467009	+	0.884253i	$0.654668\pi$
$410$	4.15079	−	3.48293i	0.204993	−	0.172009i
$411$		0			0
$412$	13.0608	−	4.75373i	0.643458	−	0.234200i
$413$	−0.00264750	+	0.00458561i	−0.000130275	+	0.000225643i
$414$		0			0
$415$	−3.55097	−	6.15047i	−0.174310	−	0.301915i
$416$	−20.3143	−	17.0458i	−0.995993	−	0.835737i
$417$		0			0
$418$	0.379852	+	2.15425i	0.0185792	+	0.105368i
$419$	−0.0809857	−	0.459293i	−0.00395641	−	0.0224379i	0.982766	−	0.184856i	$-0.0591818\pi$
$419$	−0.0809857	−	0.459293i	−0.00395641	−	0.0224379i	−0.986722	+	0.162418i	$0.948071\pi$
$420$		0			0
$421$	−1.84936	−	1.55179i	−0.0901321	−	0.0756298i	0.596608	−	0.802533i	$-0.296515\pi$
$421$	−1.84936	−	1.55179i	−0.0901321	−	0.0756298i	−0.686740	+	0.726903i	$0.740959\pi$
$422$	0.570234	+	0.987674i	0.0277585	+	0.0480792i
$423$		0			0
$424$	−3.68004	+	6.37402i	−0.178719	+	0.309550i
$425$	17.5191	−	6.37645i	0.849804	−	0.309303i
$426$		0			0
$427$	0.943563	−	0.791743i	0.0456622	−	0.0383151i
$428$	16.3930	+	5.96657i	0.792386	+	0.288405i
$429$		0			0
$430$	−0.162504	+	0.921605i	−0.00783663	+	0.0444437i
$431$	12.0992			0.582796			0.291398	−	0.956602i	$-0.405880\pi$
$431$	12.0992			0.582796			0.291398	+	0.956602i	$0.405880\pi$
$432$		0			0
$433$	33.3509			1.60274			0.801371	−	0.598167i	$-0.204104\pi$
$433$	33.3509			1.60274			0.801371	+	0.598167i	$0.204104\pi$
$434$	0.125486	−	0.711667i	0.00602352	−	0.0341611i
$435$		0			0
$436$	4.17365	+	1.51908i	0.199881	+	0.0727509i
$437$	3.51471	−	2.94919i	0.168131	−	0.141079i
$438$		0			0
$439$	8.49912	−	3.09343i	0.405641	−	0.147641i	−0.131138	−	0.991364i	$-0.541863\pi$
$439$	8.49912	−	3.09343i	0.405641	−	0.147641i	0.536779	+	0.843723i	$0.319641\pi$
$440$	−6.87933	+	11.9153i	−0.327959	+	0.568042i
$441$		0			0
$442$	7.47519	+	12.9474i	0.355558	+	0.615845i
$443$	3.58288	+	3.00640i	0.170228	+	0.142838i	0.723922	−	0.689882i	$-0.242338\pi$
$443$	3.58288	+	3.00640i	0.170228	+	0.142838i	−0.553694	+	0.832720i	$0.686782\pi$
$444$		0			0
$445$	1.24763	+	7.07564i	0.0591432	+	0.335417i
$446$	−1.16415	−	6.60220i	−0.0551239	−	0.312623i
$447$		0			0
$448$	−0.105600	−	0.0886089i	−0.00498913	−	0.00418638i
$449$	−13.3534	−	23.1288i	−0.630187	−	1.09152i	−0.987513	−	0.157537i	$-0.949645\pi$
$449$	−13.3534	−	23.1288i	−0.630187	−	1.09152i	0.357326	−	0.933980i	$-0.383689\pi$
$450$		0			0
$451$	20.5351	−	35.5678i	0.966959	−	1.67482i
$452$	−16.6718	+	6.06805i	−0.784177	+	0.285417i
$453$		0			0
$454$	−8.11200	+	6.80677i	−0.380715	+	0.319458i
$455$	−0.543308	−	0.197748i	−0.0254707	−	0.00927056i
$456$		0			0
$457$	−0.114218	+	0.647763i	−0.00534290	+	0.0303011i	−0.987363	−	0.158477i	$-0.949342\pi$
$457$	−0.114218	+	0.647763i	−0.00534290	+	0.0303011i	0.982020	+	0.188778i	$0.0604527\pi$
$458$	−7.69820			−0.359713
$459$		0			0
$460$	12.5175			0.583633
$461$	−3.59516	+	20.3892i	−0.167443	+	0.949619i	0.779066	+	0.626942i	$0.215694\pi$
$461$	−3.59516	+	20.3892i	−0.167443	+	0.949619i	−0.946509	+	0.322677i	$0.895417\pi$
$462$		0			0
$463$	23.3268	+	8.49027i	1.08409	+	0.394576i	0.821428	−	0.570312i	$-0.193178\pi$
$463$	23.3268	+	8.49027i	1.08409	+	0.394576i	0.262661	+	0.964888i	$0.415400\pi$
$464$	5.48167	−	4.59967i	0.254480	−	0.213534i
$465$		0			0
$466$	3.36484	−	1.22470i	0.155873	−	0.0567332i
$467$	13.3365	−	23.0994i	0.617138	−	1.06891i	−0.372868	−	0.927884i	$-0.621625\pi$
$467$	13.3365	−	23.0994i	0.617138	−	1.06891i	0.990005	−	0.141029i	$-0.0450412\pi$
$468$		0			0
$469$	−0.112159	−	0.194265i	−0.00517901	−	0.00897031i
$470$	1.32683	+	1.11334i	0.0612020	+	0.0513546i
$471$		0			0
$472$	0.0184183	+	0.104455i	0.000847772	+	0.00480795i
$473$	1.23172	+	6.98545i	0.0566347	+	0.321191i
$474$		0			0
$475$	1.75902	+	1.47599i	0.0807093	+	0.0677232i
$476$	−0.441500	−	0.764700i	−0.0202361	−	0.0350500i
$477$		0			0
$478$	−3.52616	+	6.10749i	−0.161283	+	0.279350i
$479$	−3.03195	+	1.10354i	−0.138533	+	0.0504221i	−0.410356	−	0.911925i	$-0.634596\pi$
$479$	−3.03195	+	1.10354i	−0.138533	+	0.0504221i	0.271823	+	0.962347i	$0.412373\pi$
$480$		0			0
$481$	7.65523	−	6.42350i	0.349048	−	0.292886i
$482$	−6.90625	−	2.51367i	−0.314571	−	0.114495i
$483$		0			0
$484$	−4.92855	+	27.9512i	−0.224025	+	1.27051i
$485$	−9.46075			−0.429590
$486$		0			0
$487$	−7.77930			−0.352514			−0.176257	−	0.984344i	$-0.556399\pi$
$487$	−7.77930			−0.352514			−0.176257	+	0.984344i	$0.556399\pi$
$488$	4.28450	−	24.2986i	0.193950	−	1.09995i
$489$		0			0
$490$	4.70574	+	1.71275i	0.212584	+	0.0773741i
$491$	−13.0580	+	10.9569i	−0.589297	+	0.494479i	−0.887985	−	0.459872i	$-0.847895\pi$
$491$	−13.0580	+	10.9569i	−0.589297	+	0.494479i	0.298688	+	0.954351i	$0.403451\pi$
$492$		0			0
$493$	−22.7640	+	8.28541i	−1.02524	+	0.373156i
$494$	−0.920686	+	1.59467i	−0.0414236	+	0.0717478i
$495$		0			0
$496$	6.18139	+	10.7065i	0.277553	+	0.480735i
$497$	0.601535	+	0.504748i	0.0269825	+	0.0226410i
$498$		0			0
$499$	1.37716	+	7.81028i	0.0616503	+	0.349636i	0.999992	+	0.00392784i	$0.00125027\pi$
$499$	1.37716	+	7.81028i	0.0616503	+	0.349636i	−0.938342	+	0.345708i	$0.887639\pi$
$500$	2.48194	+	14.0758i	0.110996	+	0.629488i
$501$		0			0
$502$	−7.89827	−	6.62744i	−0.352517	−	0.295797i
$503$	12.4748	+	21.6070i	0.556224	+	0.963409i	0.997807	+	0.0661881i	$0.0210837\pi$
$503$	12.4748	+	21.6070i	0.556224	+	0.963409i	−0.441583	+	0.897220i	$0.645583\pi$
$504$		0			0
$505$	−6.80793	+	11.7917i	−0.302949	+	0.524723i
$506$	−27.2291	+	9.91060i	−1.21048	+	0.440580i
$507$		0			0
$508$	18.0967	−	15.1850i	0.802913	−	0.673724i
$509$	−38.0284	−	13.8412i	−1.68558	−	0.613501i	−0.691521	−	0.722356i	$-0.743059\pi$
$509$	−38.0284	−	13.8412i	−1.68558	−	0.613501i	−0.994058	+	0.108855i	$0.965281\pi$
$510$		0			0
$511$	−0.256244	+	1.45323i	−0.0113356	+	0.0642873i
$512$	15.0038			0.663080
$513$		0			0
$514$	2.27269			0.100244
$515$	1.65095	−	9.36303i	0.0727497	−	0.412584i
$516$		0			0
$517$	12.3366	+	4.49016i	0.542564	+	0.197477i
$518$	0.138085	−	0.115867i	0.00606710	−	0.00509090i
$519$		0			0
$520$	−10.8833	+	3.96118i	−0.477262	+	0.173709i
$521$	12.6837	−	21.9688i	0.555684	−	0.962473i	−0.442166	−	0.896933i	$-0.645790\pi$
$521$	12.6837	−	21.9688i	0.555684	−	0.962473i	0.997850	−	0.0655394i	$-0.0208768\pi$
$522$		0			0
$523$	−6.36097	−	11.0175i	−0.278146	−	0.481762i	0.692778	−	0.721151i	$-0.256386\pi$
$523$	−6.36097	−	11.0175i	−0.278146	−	0.481762i	−0.970924	+	0.239388i	$0.923053\pi$
$524$	−15.6753	−	13.1532i	−0.684780	−	0.574599i
$525$		0			0
$526$	−1.04988	−	5.95416i	−0.0457769	−	0.259614i
$527$	−7.26758	−	41.2165i	−0.316581	−	1.79542i
$528$		0			0
$529$	28.9388	+	24.2825i	1.25821	+	1.05576i
$530$	1.09191	+	1.89124i	0.0474296	+	0.0821504i
$531$		0			0
$532$	0.0543776	−	0.0941848i	0.00235757	−	0.00408343i
$533$	32.4870	−	11.8243i	1.40717	−	0.512167i
$534$		0			0
$535$	9.14131	−	7.67047i	0.395213	−	0.331623i
$536$	−4.22242	−	1.53684i	−0.182381	−	0.0663812i
$537$		0			0
$538$	−0.961266	+	5.45161i	−0.0414431	+	0.235036i
$539$	37.9570			1.63492
$540$		0			0
$541$	2.09327			0.0899969			0.0449984	−	0.998987i	$-0.485672\pi$
$541$	2.09327			0.0899969			0.0449984	+	0.998987i	$0.485672\pi$
$542$	−2.25686	+	12.7993i	−0.0969406	+	0.549778i
$543$		0			0
$544$	−26.0326	−	9.47508i	−1.11614	−	0.406241i
$545$	2.32737	−	1.95290i	0.0996936	−	0.0836529i
$546$		0			0
$547$	−3.24288	+	1.18031i	−0.138655	+	0.0504665i	−0.410416	−	0.911899i	$-0.634616\pi$
$547$	−3.24288	+	1.18031i	−0.138655	+	0.0504665i	0.271760	+	0.962365i	$0.412394\pi$
$548$	−15.0326	+	26.0371i	−0.642159	+	1.11225i
$549$		0			0
$550$	−7.25103	−	12.5592i	−0.309185	−	0.535524i
$551$	−2.28563	−	1.91787i	−0.0973711	−	0.0817040i
$552$		0			0
$553$	−0.0147100	−	0.0834248i	−0.000625535	−	0.00354758i
$554$	−0.502374	−	2.84911i	−0.0213438	−	0.121047i
$555$		0			0
$556$	−19.1379	−	16.0586i	−0.811628	−	0.681037i
$557$	−5.55017	−	9.61318i	−0.235168	−	0.407323i	0.724153	−	0.689639i	$-0.242231\pi$
$557$	−5.55017	−	9.61318i	−0.235168	−	0.407323i	−0.959322	+	0.282316i	$0.908897\pi$
$558$		0			0
$559$	−2.98545	+	5.17095i	−0.126271	+	0.218708i
$560$	0.167658	−	0.0610226i	0.00708485	−	0.00257868i
$561$		0			0
$562$	−3.82635	+	3.21069i	−0.161405	+	0.135435i
$563$	22.8446	+	8.31474i	0.962784	+	0.350425i	0.775124	−	0.631810i	$-0.217688\pi$
$563$	22.8446	+	8.31474i	0.962784	+	0.350425i	0.187660	+	0.982234i	$0.439910\pi$
$564$		0			0
$565$	−2.10741	+	11.9517i	−0.0886594	+	0.502813i
$566$	10.9587			0.460628
$567$		0			0
$568$	15.7297			0.660002
$569$	−7.42588	+	42.1143i	−0.311309	+	1.76552i	0.280899	+	0.959737i	$0.409367\pi$
$569$	−7.42588	+	42.1143i	−0.311309	+	1.76552i	−0.592208	+	0.805785i	$0.701744\pi$
$570$		0			0
$571$	−16.9410	−	6.16603i	−0.708960	−	0.258040i	−0.0377286	−	0.999288i	$-0.512012\pi$
$571$	−16.9410	−	6.16603i	−0.708960	−	0.258040i	−0.671232	+	0.741248i	$0.734234\pi$
$572$	−29.1695	+	24.4761i	−1.21964	+	1.02340i
$573$		0			0
$574$	0.586000	−	0.213286i	0.0244592	−	0.00890240i
$575$	−15.2086	+	26.3421i	−0.634244	+	1.09854i
$576$		0			0
$577$	−12.6382	−	21.8899i	−0.526133	−	0.911290i	−0.999536	−	0.0304438i	$-0.990308\pi$
$577$	−12.6382	−	21.8899i	−0.526133	−	0.911290i	0.473403	−	0.880846i	$-0.343025\pi$
$578$	3.05623	+	2.56448i	0.127122	+	0.106668i
$579$		0			0
$580$	−1.41353	−	8.01655i	−0.0586938	−	0.332869i
$581$	−0.141933	−	0.804940i	−0.00588836	−	0.0333946i
$582$		0			0
$583$	12.6800	+	10.6398i	0.525154	+	0.440656i
$584$	14.7797	+	25.5993i	0.611590	+	1.05930i
$585$		0			0
$586$	6.15792	−	10.6658i	0.254381	−	0.440601i
$587$	26.8426	−	9.76991i	1.10791	−	0.403248i	0.277686	−	0.960672i	$-0.410433\pi$
$587$	26.8426	−	9.76991i	1.10791	−	0.403248i	0.830228	+	0.557424i	$0.188210\pi$
$588$		0			0
$589$	3.94878	−	3.31342i	0.162707	−	0.136527i
$590$	0.0295733	+	0.0107638i	0.00121751	+	0.000443138i
$591$		0			0
$592$	−0.535492	+	3.03693i	−0.0220086	+	0.124817i
$593$	−20.6009			−0.845977			−0.422989	−	0.906135i	$-0.639019\pi$
$593$	−20.6009			−0.845977			−0.422989	+	0.906135i	$0.639019\pi$
$594$		0			0
$595$	−0.604007			−0.0247619
$596$	−2.93918	+	16.6689i	−0.120393	+	0.682785i
$597$		0			0
$598$	−22.9209	−	8.34251i	−0.937304	−	0.341151i
$599$	11.0883	−	9.30423i	0.453057	−	0.380160i	−0.387512	−	0.921865i	$-0.626665\pi$
$599$	11.0883	−	9.30423i	0.453057	−	0.380160i	0.840569	+	0.541705i	$0.182221\pi$
$600$		0			0
$601$	12.5496	−	4.56769i	0.511910	−	0.186320i	−0.0731331	−	0.997322i	$-0.523300\pi$
$601$	12.5496	−	4.56769i	0.511910	−	0.186320i	0.585043	+	0.811002i	$0.301078\pi$
$602$	−0.0538515	+	0.0932736i	−0.00219483	+	0.00380155i
$603$		0			0
$604$	−5.20961	−	9.02330i	−0.211976	−	0.367153i
$605$	14.8725	+	12.4795i	0.604654	+	0.507365i
$606$		0			0
$607$	5.42009	+	30.7389i	0.219995	+	1.24765i	0.872026	+	0.489460i	$0.162806\pi$
$607$	5.42009	+	30.7389i	0.219995	+	1.24765i	−0.652031	+	0.758192i	$0.726083\pi$
$608$	−0.592503	−	3.36025i	−0.0240292	−	0.136276i
$609$		0			0
$610$	−5.60813	−	4.70578i	−0.227066	−	0.190531i
$611$	5.52557	+	9.57057i	0.223541	+	0.387184i
$612$		0			0
$613$	−15.0326	+	26.0372i	−0.607159	+	1.05163i	0.384547	+	0.923105i	$0.374358\pi$
$613$	−15.0326	+	26.0372i	−0.607159	+	1.05163i	−0.991706	+	0.128525i	$0.958976\pi$
$614$	8.68453	−	3.16091i	0.350479	−	0.127564i
$615$		0			0
$616$	−1.21301	+	1.01784i	−0.0488736	+	0.0410098i
$617$	−39.6115	−	14.4174i	−1.59470	−	0.580423i	−0.616366	−	0.787460i	$-0.711396\pi$
$617$	−39.6115	−	14.4174i	−1.59470	−	0.580423i	−0.978333	+	0.207037i	$0.933618\pi$
$618$		0			0
$619$	2.01620	−	11.4344i	0.0810378	−	0.459588i	−0.917104	−	0.398649i	$-0.869479\pi$
$619$	2.01620	−	11.4344i	0.0810378	−	0.459588i	0.998141	−	0.0609394i	$-0.0194096\pi$
$620$	14.0635			0.564803
$621$		0			0
$622$	−11.2335			−0.450422
$623$	−0.143588	+	0.814330i	−0.00575275	+	0.0326254i
$624$		0			0
$625$	−9.14455	−	3.32834i	−0.365782	−	0.133134i
$626$	−10.2521	+	8.60250i	−0.409755	+	0.343825i
$627$		0			0
$628$	24.3123	−	8.84894i	0.970165	−	0.353111i
$629$	5.21983	−	9.04101i	0.208128	−	0.360489i
$630$		0			0
$631$	14.6552	+	25.3836i	0.583415	+	1.01051i	0.995071	+	0.0991657i	$0.0316174\pi$
$631$	14.6552	+	25.3836i	0.583415	+	1.01051i	−0.411655	+	0.911340i	$0.635049\pi$
$632$	−1.29990	−	1.09075i	−0.0517073	−	0.0433876i
$633$		0			0
$634$	2.89574	+	16.4226i	0.115005	+	0.652224i
$635$	−2.80607	−	15.9140i	−0.111355	−	0.631528i
$636$		0			0
$637$	24.4761	+	20.5379i	0.969779	+	0.813741i
$638$	9.42182	+	16.3191i	0.373014	+	0.646078i
$639$		0			0
$640$	5.66637	−	9.81445i	0.223983	−	0.387950i
$641$	−29.2224	+	10.6361i	−1.15422	+	0.420101i	−0.847028	−	0.531548i	$-0.821610\pi$
$641$	−29.2224	+	10.6361i	−1.15422	+	0.420101i	−0.307189	+	0.951649i	$0.599388\pi$
$642$		0			0
$643$	32.2290	−	27.0433i	1.27099	−	1.06648i	0.276566	−	0.960995i	$-0.410804\pi$
$643$	32.2290	−	27.0433i	1.27099	−	1.06648i	0.994420	−	0.105489i	$-0.0336408\pi$
$644$	1.35375	+	0.492726i	0.0533454	+	0.0194161i
$645$		0			0
$646$	−0.334036	+	1.89441i	−0.0131425	+	0.0745347i
$647$	−4.66717			−0.183485			−0.0917427	−	0.995783i	$-0.529244\pi$
$647$	−4.66717			−0.183485			−0.0917427	+	0.995783i	$0.529244\pi$
$648$		0			0
$649$	0.238541			0.00936356
$650$	2.11981	−	12.0220i	0.0831458	−	0.471543i
$651$		0			0
$652$	12.1099	+	4.40766i	0.474262	+	0.172617i
$653$	−2.39322	+	2.00815i	−0.0936540	+	0.0785850i	−0.688413	−	0.725319i	$-0.741692\pi$
$653$	−2.39322	+	2.00815i	−0.0936540	+	0.0785850i	0.594759	+	0.803904i	$0.297248\pi$
$654$		0			0
$655$	−13.1532	+	4.78736i	−0.513937	+	0.187058i
$656$	−5.33424	+	9.23917i	−0.208267	+	0.360729i
$657$		0			0
$658$	0.0996702	+	0.172634i	0.00388555	+	0.00672997i
$659$	28.6724	+	24.0590i	1.11692	+	0.937206i	0.998445	−	0.0557508i	$-0.0177552\pi$
$659$	28.6724	+	24.0590i	1.11692	+	0.937206i	0.118474	+	0.992957i	$0.462200\pi$
$660$		0			0
$661$	4.60173	+	26.0977i	0.178987	+	1.01508i	0.933441	+	0.358731i	$0.116790\pi$
$661$	4.60173	+	26.0977i	0.178987	+	1.01508i	−0.754455	+	0.656352i	$0.772099\pi$
$662$	3.38516	+	19.1982i	0.131568	+	0.746160i
$663$		0			0
$664$	−12.5424	−	10.5243i	−0.486738	−	0.408422i
$665$	−0.0371965	−	0.0644262i	−0.00144242	−	0.00249834i
$666$		0			0
$667$	19.7618	−	34.2284i	0.765179	−	1.32533i
$668$	−3.77920	+	1.37551i	−0.146221	+	0.0532203i
$669$		0			0
$670$	−1.02133	+	0.856994i	−0.0394572	+	0.0331085i
$671$	−52.1434	−	18.9786i	−2.01297	−	0.732662i
$672$		0			0
$673$	0.298849	−	1.69485i	0.0115198	−	0.0653318i	−0.978506	−	0.206219i	$-0.933884\pi$
$673$	0.298849	−	1.69485i	0.0115198	−	0.0653318i	0.990026	+	0.140887i	$0.0449953\pi$
$674$	−11.9341			−0.459686
$675$		0			0
$676$	−12.1361			−0.466773
$677$	−4.91063	+	27.8496i	−0.188731	+	1.07035i	0.732337	+	0.680943i	$0.238430\pi$
$677$	−4.91063	+	27.8496i	−0.188731	+	1.07035i	−0.921067	+	0.389403i	$0.872681\pi$
$678$		0			0
$679$	−1.02317	−	0.372402i	−0.0392655	−	0.0142915i
$680$	−9.26849	+	7.77719i	−0.355430	+	0.298242i
$681$		0			0
$682$	−30.5920	+	11.1346i	−1.17143	+	0.426365i
$683$	−12.3569	+	21.4029i	−0.472825	+	0.818958i	−0.999516	−	0.0310993i	$-0.990099\pi$
$683$	−12.3569	+	21.4029i	−0.472825	+	0.818958i	0.526691	+	0.850057i	$0.323433\pi$
$684$		0			0
$685$	10.2829	+	17.8105i	0.392888	+	0.680502i
$686$	0.883919	+	0.741696i	0.0337482	+	0.0283181i
$687$		0			0
$688$	−0.319955	−	1.81456i	−0.0121982	−	0.0691793i
$689$	2.41955	+	13.7219i	0.0921774	+	0.522764i
$690$		0			0
$691$	−33.5317	−	28.1364i	−1.27561	−	1.07036i	−0.993834	−	0.110878i	$-0.964634\pi$
$691$	−33.5317	−	28.1364i	−1.27561	−	1.07036i	−0.281771	−	0.959482i	$-0.590922\pi$
$692$	10.0377	+	17.3858i	0.381576	+	0.660908i
$693$		0			0
$694$	8.61515	−	14.9219i	0.327027	−	0.566427i
$695$	−16.0586	+	5.84486i	−0.609138	+	0.221708i
$696$		0			0
$697$	27.6668	−	23.2152i	1.04796	−	0.879340i
$698$	7.61835	+	2.77285i	0.288359	+	0.104954i
$699$		0			0
$700$	−0.125200	+	0.710047i	−0.00473213	+	0.0268372i
$701$	14.6504			0.553338			0.276669	−	0.960965i	$-0.410769\pi$
$701$	14.6504			0.553338			0.276669	+	0.960965i	$0.410769\pi$
$702$		0			0
$703$	1.28581			0.0484951
$704$	−1.07839	+	6.11587i	−0.0406434	+	0.230500i
$705$		0			0
$706$	−5.39780	−	1.96464i	−0.203149	−	0.0739402i
$707$	−1.20042	+	1.00727i	−0.0451465	+	0.0378824i
$708$		0			0
$709$	−4.76769	+	1.73530i	−0.179054	+	0.0651705i	−0.429992	−	0.902833i	$-0.641483\pi$
$709$	−4.76769	+	1.73530i	−0.179054	+	0.0651705i	0.250937	+	0.968003i	$0.419261\pi$
$710$	2.33359	−	4.04189i	0.0875779	−	0.151689i
$711$		0			0
$712$	8.28194	+	14.3447i	0.310379	+	0.537592i
$713$	52.3078	+	43.8915i	1.95894	+	1.64375i
$714$		0			0
$715$	4.52300	+	25.6512i	0.169151	+	0.959302i
$716$	5.87927	+	33.3430i	0.219719	+	1.24609i
$717$		0			0
$718$	−1.38350	−	1.16090i	−0.0516319	−	0.0433243i
$719$	−2.66858	−	4.62212i	−0.0995213	−	0.172376i	0.811965	−	0.583706i	$-0.198398\pi$
$719$	−2.66858	−	4.62212i	−0.0995213	−	0.172376i	−0.911487	+	0.411330i	$0.865064\pi$
$720$		0			0
$721$	0.547104	−	0.947611i	0.0203752	−	0.0352909i
$722$	11.9903	−	4.36412i	0.446234	−	0.162416i
$723$		0			0
$724$	2.41669	−	2.02784i	0.0898155	−	0.0753642i
$725$	18.5876	+	6.76533i	0.690326	+	0.251258i
$726$		0			0
$727$	6.44578	−	36.5559i	0.239061	−	1.35578i	−0.594830	−	0.803852i	$-0.702780\pi$
$727$	6.44578	−	36.5559i	0.239061	−	1.35578i	0.833890	−	0.551930i	$-0.186108\pi$
$728$	−1.33293			−0.0494017
$729$		0			0
$730$	8.77063			0.324616
$731$	−1.08316	+	6.14290i	−0.0400621	+	0.227203i
$732$		0			0
$733$	−28.1403	−	10.2422i	−1.03938	−	0.378305i	−0.234738	−	0.972059i	$-0.575423\pi$
$733$	−28.1403	−	10.2422i	−1.03938	−	0.378305i	−0.804647	+	0.593754i	$0.797645\pi$
$734$	4.81958	−	4.04411i	0.177894	−	0.149271i
$735$		0			0
$736$	42.4727	−	15.4588i	1.56557	−	0.569819i
$737$	−5.05277	+	8.75166i	−0.186121	+	0.322371i
$738$		0			0
$739$	14.3050	+	24.7770i	0.526218	+	0.911436i	0.999533	+	0.0305431i	$0.00972368\pi$
$739$	14.3050	+	24.7770i	0.526218	+	0.911436i	−0.473316	+	0.880893i	$0.656943\pi$
$740$	2.68729	+	2.25490i	0.0987866	+	0.0828918i
$741$		0			0
$742$	0.0436438	+	0.247516i	0.00160221	+	0.00908660i
$743$	−8.62052	−	48.8894i	−0.316256	−	1.79358i	−0.565087	−	0.825031i	$-0.691157\pi$
$743$	−8.62052	−	48.8894i	−0.316256	−	1.79358i	0.248831	−	0.968547i	$-0.419954\pi$
$744$		0			0
$745$	8.86934	+	7.44226i	0.324947	+	0.272663i
$746$	9.16312	+	15.8710i	0.335486	+	0.581078i
$747$		0			0
$748$	−19.8897	+	34.4499i	−0.727238	+	1.25961i
$749$	1.29055	−	0.469722i	0.0471557	−	0.0171633i
$750$		0			0
$751$	−24.2251	+	20.3273i	−0.883986	+	0.741752i	−0.966995	−	0.254796i	$-0.917992\pi$
$751$	−24.2251	+	20.3273i	−0.883986	+	0.741752i	0.0830087	+	0.996549i	$0.473547\pi$
$752$	−3.20459	−	1.16637i	−0.116859	−	0.0425333i
$753$		0			0
$754$	−2.75443	+	15.6212i	−0.100311	+	0.568889i
$755$	−7.12716			−0.259384
$756$		0			0
$757$	3.04189			0.110559			0.0552797	−	0.998471i	$-0.482395\pi$
$757$	3.04189			0.110559			0.0552797	+	0.998471i	$0.482395\pi$
$758$	−3.22188	+	18.2722i	−0.117024	+	0.663676i
$759$		0			0
$760$	−1.40033	−	0.509678i	−0.0507953	−	0.0184880i
$761$	−29.0548	+	24.3799i	−1.05323	+	0.883769i	−0.993430	−	0.114441i	$-0.963492\pi$
$761$	−29.0548	+	24.3799i	−1.05323	+	0.883769i	−0.0598048	+	0.998210i	$0.519048\pi$
$762$		0			0
$763$	0.328573	−	0.119591i	0.0118952	−	0.00432948i
$764$	−3.02525	+	5.23989i	−0.109450	+	0.189572i
$765$		0			0
$766$	−11.7747	−	20.3943i	−0.425436	−	0.736877i
$767$	0.153821	+	0.129071i	0.00555414	+	0.00466048i
$768$		0			0
$769$	−3.54030	−	20.0780i	−0.127666	−	0.724032i	−0.979688	−	0.200526i	$-0.935735\pi$
$769$	−3.54030	−	20.0780i	−0.127666	−	0.724032i	0.852022	−	0.523506i	$-0.175376\pi$
$770$	0.0815859	+	0.462697i	0.00294015	+	0.0166744i
$771$		0			0
$772$	9.91329	+	8.31823i	0.356787	+	0.299380i
$773$	12.2332	+	21.1885i	0.439997	+	0.762097i	0.997689	−	0.0679509i	$-0.0216461\pi$
$773$	12.2332	+	21.1885i	0.439997	+	0.762097i	−0.557692	+	0.830048i	$0.688313\pi$
$774$		0			0
$775$	−17.0869	+	29.5954i	−0.613781	+	1.06310i
$776$	−20.4955	+	7.45976i	−0.735746	+	0.267790i
$777$		0			0
$778$	0.396459	−	0.332669i	0.0142138	−	0.0119268i
$779$	4.18004	+	1.52141i	0.149766	+	0.0545102i
$780$		0			0
$781$	6.14290	−	34.8381i	0.219810	−	1.24661i
$782$	−25.4816			−0.911221
$783$		0			0
$784$	−9.85978			−0.352135
$785$	3.07321	−	17.4290i	0.109687	−	0.622068i
$786$		0			0
$787$	−35.3089	−	12.8514i	−1.25863	−	0.458102i	−0.375318	−	0.926896i	$-0.622466\pi$
$787$	−35.3089	−	12.8514i	−1.25863	−	0.458102i	−0.883307	+	0.468794i	$0.844689\pi$
$788$	2.69350	−	2.26011i	0.0959520	−	0.0805133i
$789$		0			0
$790$	−0.473126	+	0.172204i	−0.0168331	+	0.00612673i
$791$	−0.698367	+	1.20961i	−0.0248311	+	0.0430087i
$792$		0			0
$793$	−23.3550	−	40.4521i	−0.829362	−	1.43650i
$794$	3.67209	+	3.08125i	0.130318	+	0.109350i
$795$		0			0
$796$	6.25284	+	35.4616i	0.221626	+	1.25690i
$797$	−0.400247	−	2.26991i	−0.0141775	−	0.0804045i	0.976898	−	0.213706i	$-0.0685534\pi$
$797$	−0.400247	−	2.26991i	−0.0141775	−	0.0804045i	−0.991076	+	0.133301i	$0.957442\pi$
$798$		0			0
$799$	8.84389	+	7.42091i	0.312874	+	0.262533i
$800$	11.3103	+	19.5901i	0.399881	+	0.692614i
$801$		0			0
$802$	3.23236	−	5.59862i	0.114139	−	0.197694i
$803$	62.4693	−	22.7369i	2.20449	−	0.802369i
$804$		0			0
$805$	0.754900	−	0.633436i	0.0266067	−	0.0223257i
$806$	−25.7516	−	9.37283i	−0.907062	−	0.330144i
$807$		0			0
$808$	−5.45084	+	30.9132i	−0.191760	+	1.08752i
$809$	28.8614			1.01471			0.507356	−	0.861736i	$-0.330623\pi$
$809$	28.8614			1.01471			0.507356	+	0.861736i	$0.330623\pi$
$810$		0			0
$811$	−51.8631			−1.82116			−0.910580	−	0.413334i	$-0.864364\pi$
$811$	−51.8631			−1.82116			−0.910580	+	0.413334i	$0.864364\pi$
$812$	0.162683	−	0.922618i	0.00570904	−	0.0323776i
$813$		0			0
$814$	−7.63088	−	2.77741i	−0.267462	−	0.0973483i
$815$	6.75292	−	5.66637i	0.236545	−	0.198484i
$816$		0			0
$817$	−0.721934	+	0.262762i	−0.0252573	+	0.00919289i
$818$	−1.88711	+	3.26857i	−0.0659813	+	0.114283i
$819$		0			0
$820$	6.06805	+	10.5102i	0.211905	+	0.367031i
$821$	−14.1267	−	11.8537i	−0.493025	−	0.413697i	0.362084	−	0.932145i	$-0.382065\pi$
$821$	−14.1267	−	11.8537i	−0.493025	−	0.413697i	−0.855109	+	0.518449i	$0.826510\pi$
$822$		0			0
$823$	−6.03714	−	34.2383i	−0.210442	−	1.19347i	−0.888644	−	0.458598i	$-0.848352\pi$
$823$	−6.03714	−	34.2383i	−0.210442	−	1.19347i	0.678202	−	0.734875i	$-0.262759\pi$
$824$	−3.80612	−	21.5856i	−0.132593	−	0.751970i
$825$		0			0
$826$	0.00277461	+	0.00232818i	9.65411e−5	+	8.10076e-5i
$827$	−16.3886	−	28.3859i	−0.569889	−	0.987076i	−0.996576	−	0.0826770i	$-0.973653\pi$
$827$	−16.3886	−	28.3859i	−0.569889	−	0.987076i	0.426688	−	0.904399i	$-0.359680\pi$
$828$		0			0
$829$	−2.67634	+	4.63555i	−0.0929530	+	0.160999i	−0.908752	−	0.417336i	$-0.862964\pi$
$829$	−2.67634	+	4.63555i	−0.0929530	+	0.160999i	0.815799	+	0.578335i	$0.196297\pi$
$830$	−4.56504	+	1.66154i	−0.158455	+	0.0576729i
$831$		0			0
$832$	−4.00459	+	3.36025i	−0.138834	+	0.116496i
$833$	31.3658	+	11.4162i	1.08676	+	0.395549i
$834$		0			0
$835$	−0.477711	+	2.70924i	−0.0165319	+	0.0937570i
$836$	−4.89944			−0.169451
$837$		0			0
$838$	−0.319022			−0.0110204
$839$	−0.944364	+	5.35575i	−0.0326031	+	0.184901i	−0.996760	−	0.0804308i	$-0.974370\pi$
$839$	−0.944364	+	5.35575i	−0.0326031	+	0.184901i	0.964157	+	0.265332i	$0.0854815\pi$
$840$		0			0
$841$	3.09879	+	1.12787i	0.106855	+	0.0388920i
$842$	−1.26503	+	1.06149i	−0.0435959	+	0.0365813i
$843$		0			0
$844$	−2.40033	+	0.873649i	−0.0826228	+	0.0300722i
$845$	−4.15079	+	7.18938i	−0.142791	+	0.247322i
$846$		0			0
$847$	1.11721	+	1.93507i	0.0383878	+	0.0664897i
$848$	−3.29380	−	2.76382i	−0.113109	−	0.0949101i
$849$		0			0
$850$	−2.21452	−	12.5592i	−0.0759573	−	0.430775i
$851$	2.95767	+	16.7738i	0.101388	+	0.574998i
$852$		0			0
$853$	−36.0938	−	30.2863i	−1.23583	−	1.03698i	−0.997838	−	0.0657152i	$-0.979067\pi$
$853$	−36.0938	−	30.2863i	−1.23583	−	1.03698i	−0.237990	−	0.971268i	$-0.576488\pi$
$854$	−0.421278	−	0.729675i	−0.0144158	−	0.0249690i
$855$		0			0
$856$	13.7554	−	23.8250i	0.470149	−	0.814322i
$857$	−44.1242	+	16.0599i	−1.50725	+	0.548596i	−0.957927	−	0.287012i	$-0.907338\pi$
$857$	−44.1242	+	16.0599i	−1.50725	+	0.548596i	−0.549327	+	0.835607i	$0.685116\pi$
$858$		0			0
$859$	5.48751	−	4.60457i	0.187231	−	0.157106i	−0.544354	−	0.838856i	$-0.683225\pi$
$859$	5.48751	−	4.60457i	0.187231	−	0.157106i	0.731585	+	0.681750i	$0.238781\pi$
$860$	−1.96962	−	0.716881i	−0.0671633	−	0.0244455i
$861$		0			0
$862$	1.43717	−	8.15058i	0.0489501	−	0.277610i
$863$	35.4309			1.20608			0.603041	−	0.797710i	$-0.293955\pi$
$863$	35.4309			1.20608			0.603041	+	0.797710i	$0.293955\pi$
$864$		0			0
$865$	13.7324			0.466914
$866$	3.96150	−	22.4668i	0.134617	−	0.763452i
$867$		0			0
$868$	1.52094	+	0.553579i	0.0516242	+	0.0187897i
$869$	−2.92344	+	2.45306i	−0.0991710	+	0.0832143i
$870$		0			0
$871$	−7.99360	+	2.90943i	−0.270853	+	0.0985824i
$872$	3.50211	−	6.06583i	0.118596	−	0.205415i
$873$		0			0
$874$	−1.56923	−	2.71799i	−0.0530800	−	0.0919373i
$875$	0.861969	+	0.723278i	0.0291399	+	0.0244513i
$876$		0			0
$877$	1.41921	+	8.04877i	0.0479235	+	0.271788i	0.999348	−	0.0360932i	$-0.0114913\pi$
$877$	1.41921	+	8.04877i	0.0479235	+	0.271788i	−0.951425	+	0.307881i	$0.900380\pi$
$878$	−1.07434	−	6.09286i	−0.0362571	−	0.205624i
$879$		0			0
$880$	−6.15729	−	5.16658i	−0.207562	−	0.174165i
$881$	−16.6153	−	28.7786i	−0.559785	−	0.969575i	−0.997514	−	0.0704686i	$-0.977551\pi$
$881$	−16.6153	−	28.7786i	−0.559785	−	0.969575i	0.437729	−	0.899107i	$-0.355783\pi$
$882$		0			0
$883$	−16.5239	+	28.6203i	−0.556075	+	0.963150i	0.441744	+	0.897141i	$0.354360\pi$
$883$	−16.5239	+	28.6203i	−0.556075	+	0.963150i	−0.997819	+	0.0660087i	$0.978973\pi$
$884$	−31.4659	+	11.4526i	−1.05831	+	0.385194i
$885$		0			0
$886$	2.45084	−	2.05650i	0.0823375	−	0.0690893i
$887$	−46.7471	−	17.0145i	−1.56961	−	0.571293i	−0.596701	−	0.802464i	$-0.703522\pi$
$887$	−46.7471	−	17.0145i	−1.56961	−	0.571293i	−0.972913	+	0.231171i	$0.925744\pi$
$888$		0			0
$889$	0.322948	−	1.83153i	0.0108313	−	0.0614276i
$890$	4.91469			0.164741
$891$		0			0
$892$	15.0155			0.502756
$893$	−0.246916	+	1.40033i	−0.00826273	+	0.0468602i
$894$		0			0
$895$	21.7631	+	7.92112i	0.727460	+	0.264774i
$896$	0.999135	−	0.838374i	0.0333787	−	0.0280081i
$897$		0			0
$898$	−17.1668	+	6.24822i	−0.572865	+	0.208506i
$899$	22.2024	−	38.4556i	0.740491	−	1.28257i
$900$		0			0
$901$	7.27807	+	12.6060i	0.242468	+	0.419966i
$902$	−21.5210	−	18.0582i	−0.716570	−	0.601274i
$903$		0			0
$904$	4.85844	+	27.5536i	0.161589	+	0.916419i
$905$	−0.374730	−	2.12520i	−0.0124565	−	0.0706441i
$906$		0			0
$907$	26.4657	+	22.2074i	0.878779	+	0.737383i	0.965928	−	0.258812i	$-0.0833311\pi$
$907$	26.4657	+	22.2074i	0.878779	+	0.737383i	−0.0871488	+	0.996195i	$0.527776\pi$
$908$	−11.8589	−	20.5403i	−0.393553	−	0.681654i
$909$		0			0
$910$	−0.197748	+	0.342509i	−0.00655528	+	0.0113541i
$911$	−12.8145	+	4.66410i	−0.424563	+	0.154528i	−0.545460	−	0.838137i	$-0.683645\pi$
$911$	−12.8145	+	4.66410i	−0.424563	+	0.154528i	0.120897	+	0.992665i	$0.461423\pi$
$912$		0			0
$913$	−28.2074	+	23.6688i	−0.933528	+	0.783323i
$914$	0.422797	+	0.153886i	0.0139849	+	0.00509009i
$915$		0			0
$916$	2.99407	−	16.9802i	0.0989269	−	0.561042i
$917$	−1.61094			−0.0531979
$918$		0			0
$919$	32.7701			1.08099			0.540493	−	0.841348i	$-0.318238\pi$
$919$	32.7701			1.08099			0.540493	+	0.841348i	$0.318238\pi$
$920$	3.42782	−	19.4402i	0.113012	−	0.640923i
$921$		0			0
$922$	13.3081	+	4.84375i	0.438279	+	0.159520i
$923$	22.8115	−	19.1411i	0.750851	−	0.630039i
$924$		0			0
$925$	−8.01027	+	2.91550i	−0.263376	+	0.0958610i
$926$	8.49027	−	14.7056i	0.279008	−	0.483255i
$927$		0			0
$928$	−14.6964	−	25.4549i	−0.482433	−	0.835599i
$929$	−4.23735	−	3.55556i	−0.139023	−	0.116654i	0.570624	−	0.821211i	$-0.306701\pi$
$929$	−4.23735	−	3.55556i	−0.139023	−	0.116654i	−0.709647	+	0.704557i	$0.751146\pi$
$930$		0			0
$931$	0.713888	+	4.04866i	0.0233967	+	0.132690i
$932$	1.39268	+	7.89827i	0.0456187	+	0.258716i
$933$		0			0
$934$	−13.9767	−	11.7279i	−0.457333	−	0.383748i
$935$	13.6053	+	23.5651i	0.444942	+	0.770662i
$936$		0			0
$937$	0.497007	−	0.860841i	0.0162365	−	0.0281225i	−0.857793	−	0.513995i	$-0.828165\pi$
$937$	0.497007	−	0.860841i	0.0162365	−	0.0281225i	0.874029	+	0.485873i	$0.161498\pi$
$938$	−0.144189	+	0.0524803i	−0.00470792	+	0.00171354i
$939$		0			0
$940$	−2.97178	+	2.49362i	−0.0969288	+	0.0813329i
$941$	10.7662	+	3.91859i	0.350969	+	0.127742i	0.511488	−	0.859291i	$-0.329095\pi$
$941$	10.7662	+	3.91859i	0.350969	+	0.127742i	−0.160519	+	0.987033i	$0.551317\pi$
$942$		0			0
$943$	−10.2322	+	58.0297i	−0.333206	+	1.88971i
$944$	−0.0619640			−0.00201676
$945$		0			0
$946$	4.85204			0.157754
$947$	7.93312	−	44.9910i	0.257792	−	1.46201i	−0.531012	−	0.847365i	$-0.678188\pi$
$947$	7.93312	−	44.9910i	0.257792	−	1.46201i	0.788803	−	0.614646i	$-0.210701\pi$
$948$		0			0
$949$	52.5852	+	19.1394i	1.70699	+	0.621293i
$950$	1.20324	−	1.00964i	0.0390383	−	0.0327570i
$951$		0			0
$952$	−1.30851	+	0.476257i	−0.0424089	+	0.0154356i
$953$	−7.25265	+	12.5620i	−0.234936	+	0.406922i	−0.959254	−	0.282545i	$-0.908822\pi$
$953$	−7.25265	+	12.5620i	−0.234936	+	0.406922i	0.724318	+	0.689466i	$0.242155\pi$
$954$		0			0
$955$	2.06939	+	3.58429i	0.0669640	+	0.115985i
$956$	−12.1001	−	10.1532i	−0.391344	−	0.328377i
$957$		0			0
$958$	0.383256	+	2.17355i	0.0123824	+	0.0702242i
$959$	0.411007	+	2.33094i	0.0132721	+	0.0752699i
$960$		0			0
$961$	35.0205	+	29.3857i	1.12969	+	0.947926i
$962$	−3.41787	−	5.91993i	−0.110197	−	0.190866i
$963$		0			0
$964$	8.23055	−	14.2557i	0.265088	−	0.459146i
$965$	8.31823	−	3.02759i	0.267773	−	0.0974616i
$966$		0			0
$967$	−19.1793	+	16.0934i	−0.616766	+	0.517528i	−0.896785	−	0.442467i	$-0.854104\pi$
$967$	−19.1793	+	16.0934i	−0.616766	+	0.517528i	0.280019	+	0.959994i	$0.409659\pi$
$968$	42.0595	+	15.3084i	1.35184	+	0.492031i
$969$		0			0
$970$	−1.12377	+	6.37322i	−0.0360821	+	0.204632i
$971$	−27.0907			−0.869383			−0.434692	−	0.900579i	$-0.643143\pi$
$971$	−27.0907			−0.869383			−0.434692	+	0.900579i	$0.643143\pi$
$972$		0			0
$973$	−1.96679			−0.0630522
$974$	−0.924044	+	5.24051i	−0.0296083	+	0.167917i
$975$		0			0
$976$	13.5449	+	4.92993i	0.433561	+	0.157803i
$977$	1.89473	−	1.58987i	0.0606179	−	0.0508644i	−0.611975	−	0.790877i	$-0.709625\pi$
$977$	1.89473	−	1.58987i	0.0606179	−	0.0508644i	0.672593	+	0.740012i	$0.265180\pi$
$978$		0			0
$979$	35.0051	−	12.7408i	1.11877	−	0.407198i
$980$	−5.60808	+	9.71348i	−0.179144	+	0.310286i
$981$		0			0
$982$	5.83006	+	10.0980i	0.186045	+	0.322239i
$983$	−14.6376	−	12.2824i	−0.466867	−	0.391748i	0.378783	−	0.925485i	$-0.376343\pi$
$983$	−14.6376	−	12.2824i	−0.466867	−	0.391748i	−0.845650	+	0.533738i	$0.820787\pi$
$984$		0			0
$985$	−0.417652	−	2.36862i	−0.0133075	−	0.0754706i
$986$	2.87749	+	16.3191i	0.0916381	+	0.519705i
$987$		0			0
$988$	−3.15935	−	2.65101i	−0.100512	−	0.0843398i
$989$	−5.08845	−	8.81345i	−0.161803	−	0.280251i
$990$		0			0
$991$	19.1582	−	33.1830i	0.608581	−	1.05409i	−0.382894	−	0.923792i	$-0.625072\pi$
$991$	19.1582	−	33.1830i	0.608581	−	1.05409i	0.991475	−	0.130301i	$-0.0415943\pi$
$992$	47.7182	−	17.3680i	1.51505	−	0.551434i
$993$		0			0
$994$	0.411474	−	0.345268i	0.0130512	−	0.0109512i
$995$	23.1459	+	8.42443i	0.733775	+	0.267072i
$996$		0			0
$997$	7.18463	−	40.7461i	0.227540	−	1.29044i	−0.630231	−	0.776408i	$-0.717040\pi$
$997$	7.18463	−	40.7461i	0.227540	−	1.29044i	0.857770	−	0.514033i	$-0.171849\pi$
$998$	5.42497			0.171724
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.q.649.2		12
3.2	odd	2	inner	729.2.e.q.649.1		12
9.2	odd	6		729.2.e.m.163.2		12
9.4	even	3		729.2.e.r.406.2		12
9.5	odd	6		729.2.e.r.406.1		12
9.7	even	3		729.2.e.m.163.1		12
27.2	odd	18		729.2.c.c.487.4		12
27.4	even	9		729.2.e.r.325.2		12
27.5	odd	18		729.2.e.m.568.2		12
27.7	even	9		729.2.c.c.244.3		12
27.11	odd	18		729.2.a.c.1.3	✓	6
27.13	even	9	inner	729.2.e.q.82.2		12
27.14	odd	18	inner	729.2.e.q.82.1		12
27.16	even	9		729.2.a.c.1.4	yes	6
27.20	odd	18		729.2.c.c.244.4		12
27.22	even	9		729.2.e.m.568.1		12
27.23	odd	18		729.2.e.r.325.1		12
27.25	even	9		729.2.c.c.487.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.c.1.3	✓	6	27.11	odd	18
729.2.a.c.1.4	yes	6	27.16	even	9
729.2.c.c.244.3		12	27.7	even	9
729.2.c.c.244.4		12	27.20	odd	18
729.2.c.c.487.3		12	27.25	even	9
729.2.c.c.487.4		12	27.2	odd	18
729.2.e.m.163.1		12	9.7	even	3
729.2.e.m.163.2		12	9.2	odd	6
729.2.e.m.568.1		12	27.22	even	9
729.2.e.m.568.2		12	27.5	odd	18
729.2.e.q.82.1		12	27.14	odd	18	inner
729.2.e.q.82.2		12	27.13	even	9	inner
729.2.e.q.649.1		12	3.2	odd	2	inner
729.2.e.q.649.2		12	1.1	even	1	trivial
729.2.e.r.325.1		12	27.23	odd	18
729.2.e.r.325.2		12	27.4	even	9
729.2.e.r.406.1		12	9.5	odd	6
729.2.e.r.406.2		12	9.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(0.118782 - 0.673648i) q^{2} +(1.43969 + 0.524005i) q^{4} +(0.802823 - 0.673648i) q^{5} +(0.113341 - 0.0412527i) q^{7} +(1.20805 - 2.09240i) q^{8} +O(q^{10})\)	\(q+(0.118782 - 0.673648i) q^{2} +(1.43969 + 0.524005i) q^{4} +(0.802823 - 0.673648i) q^{5} +(0.113341 - 0.0412527i) q^{7} +(1.20805 - 2.09240i) q^{8} +(-0.358441 - 0.620838i) q^{10} +(-4.16247 - 3.49273i) q^{11} +(-0.794263 - 4.50449i) q^{13} +(-0.0143269 - 0.0812519i) q^{14} +(1.08125 + 0.907278i) q^{16} +(-2.38917 - 4.13816i) q^{17} +(0.294263 - 0.509678i) q^{19} +(1.50881 - 0.549163i) q^{20} +(-2.84730 + 2.38917i) q^{22} +(7.32580 + 2.66637i) q^{23} +(-0.677519 + 3.84240i) q^{25} -3.12879 q^{26} +0.184793 q^{28} +(0.880352 - 4.99273i) q^{29} +(8.23055 + 2.99568i) q^{31} +(4.44129 - 3.72668i) q^{32} +(-3.07145 + 1.11792i) q^{34} +(0.0632028 - 0.109470i) q^{35} +(1.09240 + 1.89209i) q^{37} +(-0.308391 - 0.258770i) q^{38} +(-0.439693 - 2.49362i) q^{40} +(1.31250 + 7.44356i) q^{41} +(-1.00000 - 0.839100i) q^{43} +(-4.16247 - 7.20961i) q^{44} +(2.66637 - 4.61830i) q^{46} +(-2.27038 + 0.826352i) q^{47} +(-5.35117 + 4.49016i) q^{49} +(2.50795 + 0.912818i) q^{50} +(1.21688 - 6.90128i) q^{52} -3.04628 q^{53} -5.69459 q^{55} +(0.0506039 - 0.286989i) q^{56} +(-3.25877 - 1.18610i) q^{58} +(-0.0336295 + 0.0282185i) q^{59} +(9.59627 - 3.49276i) q^{61} +(2.99568 - 5.18866i) q^{62} +(-0.571452 - 0.989783i) q^{64} +(-3.67209 - 3.08125i) q^{65} +(-0.322948 - 1.83153i) q^{67} +(-1.27125 - 7.20961i) q^{68} +(-0.0662372 - 0.0555796i) q^{70} +(3.25519 + 5.63816i) q^{71} +(-6.11721 + 10.5953i) q^{73} +(1.40436 - 0.511144i) q^{74} +(0.690722 - 0.579585i) q^{76} +(-0.615862 - 0.224155i) q^{77} +(0.121959 - 0.691663i) q^{79} +1.47924 q^{80} +5.17024 q^{82} +(1.17674 - 6.67365i) q^{83} +(-4.70574 - 1.71275i) q^{85} +(-0.684040 + 0.573978i) q^{86} +(-12.3366 + 4.49016i) q^{88} +(-3.42782 + 5.93717i) q^{89} +(-0.275845 - 0.477777i) q^{91} +(9.14971 + 7.67752i) q^{92} +(0.286989 + 1.62760i) q^{94} +(-0.107103 - 0.607411i) q^{95} +(-6.91534 - 5.80266i) q^{97} +(2.38917 + 4.13816i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 12 q^{7}+O(q^{10}) \) 12 * q + 6 * q^4 - 12 * q^7	\( 12 q + 6 q^{4} - 12 q^{7} + 12 q^{10} - 30 q^{13} + 18 q^{16} + 24 q^{19} - 30 q^{22} + 42 q^{25} - 12 q^{28} + 24 q^{31} - 36 q^{34} + 6 q^{37} + 6 q^{40} - 12 q^{43} - 6 q^{46} - 12 q^{49} - 18 q^{52} - 60 q^{55} + 6 q^{58} + 60 q^{61} - 6 q^{64} + 78 q^{67} - 66 q^{70} - 12 q^{73} + 48 q^{76} + 6 q^{79} - 24 q^{82} - 36 q^{85} - 24 q^{88} - 12 q^{94} + 6 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 - 12 * q^7 + 12 * q^10 - 30 * q^13 + 18 * q^16 + 24 * q^19 - 30 * q^22 + 42 * q^25 - 12 * q^28 + 24 * q^31 - 36 * q^34 + 6 * q^37 + 6 * q^40 - 12 * q^43 - 6 * q^46 - 12 * q^49 - 18 * q^52 - 60 * q^55 + 6 * q^58 + 60 * q^61 - 6 * q^64 + 78 * q^67 - 66 * q^70 - 12 * q^73 + 48 * q^76 + 6 * q^79 - 24 * q^82 - 36 * q^85 - 24 * q^88 - 12 * q^94 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more