LMFDB - Embedded newform 1350.2.e.f.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(451,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1350.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.7798042729$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 450)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			901.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1350.901
Dual form			1350.2.e.f.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{11} +(-2.00000 + 3.46410i) q^{13} +(2.00000 - 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} -3.00000 q^{17} -4.00000 q^{19} +(-1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} -4.00000 q^{26} +4.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{34} -8.00000 q^{37} +(-2.00000 - 3.46410i) q^{38} +(-3.00000 + 5.19615i) q^{41} +(-0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +6.00000 q^{46} +(-6.00000 - 10.3923i) q^{47} +(-4.50000 + 7.79423i) q^{49} +(-2.00000 - 3.46410i) q^{52} +(2.00000 + 3.46410i) q^{56} +(3.00000 - 5.19615i) q^{58} +(-4.50000 + 7.79423i) q^{59} +(-4.00000 - 6.92820i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +6.00000 q^{71} -14.0000 q^{73} +(-4.00000 - 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(6.00000 - 10.3923i) q^{77} +(-4.00000 - 6.92820i) q^{79} -6.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +(0.500000 - 0.866025i) q^{86} +(-1.50000 - 2.59808i) q^{88} +9.00000 q^{89} +16.0000 q^{91} +(3.00000 + 5.19615i) q^{92} +(6.00000 - 10.3923i) q^{94} +(-3.50000 - 6.06218i) q^{97} -9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 4 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - 4 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - 4 q^{7} - 2 q^{8} + 3 q^{11} - 4 q^{13} + 4 q^{14} - q^{16} - 6 q^{17} - 8 q^{19} - 3 q^{22} + 6 q^{23} - 8 q^{26} + 8 q^{28} - 6 q^{29} - 8 q^{31} + q^{32} - 3 q^{34} - 16 q^{37} - 4 q^{38} - 6 q^{41} - q^{43} - 6 q^{44} + 12 q^{46} - 12 q^{47} - 9 q^{49} - 4 q^{52} + 4 q^{56} + 6 q^{58} - 9 q^{59} - 8 q^{61} - 16 q^{62} + 2 q^{64} - 4 q^{67} + 3 q^{68} + 12 q^{71} - 28 q^{73} - 8 q^{74} + 4 q^{76} + 12 q^{77} - 8 q^{79} - 12 q^{82} + 9 q^{83} + q^{86} - 3 q^{88} + 18 q^{89} + 32 q^{91} + 6 q^{92} + 12 q^{94} - 7 q^{97} - 18 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - 4 * q^7 - 2 * q^8 + 3 * q^11 - 4 * q^13 + 4 * q^14 - q^16 - 6 * q^17 - 8 * q^19 - 3 * q^22 + 6 * q^23 - 8 * q^26 + 8 * q^28 - 6 * q^29 - 8 * q^31 + q^32 - 3 * q^34 - 16 * q^37 - 4 * q^38 - 6 * q^41 - q^43 - 6 * q^44 + 12 * q^46 - 12 * q^47 - 9 * q^49 - 4 * q^52 + 4 * q^56 + 6 * q^58 - 9 * q^59 - 8 * q^61 - 16 * q^62 + 2 * q^64 - 4 * q^67 + 3 * q^68 + 12 * q^71 - 28 * q^73 - 8 * q^74 + 4 * q^76 + 12 * q^77 - 8 * q^79 - 12 * q^82 + 9 * q^83 + q^86 - 3 * q^88 + 18 * q^89 + 32 * q^91 + 6 * q^92 + 12 * q^94 - 7 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	0.188982	−	0.981981i	$-0.439481\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	0.443227	+	0.896410i	$0.353834\pi$
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	2.00000	−	3.46410i	0.534522	−	0.925820i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$		0			0
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$		0			0
$26$	−4.00000			−0.784465
$27$		0			0
$28$	4.00000			0.755929
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$		0			0
$36$		0			0
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$	−2.00000	−	3.46410i	−0.324443	−	0.561951i
$39$		0			0
$40$		0			0
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	6.00000			0.884652
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.856560	−	0.516047i	$-0.827403\pi$
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.0186297	−	0.999826i	$-0.505930\pi$
$48$		0			0
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$		0			0
$51$		0			0
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$		0			0
$56$	2.00000	+	3.46410i	0.267261	+	0.462910i
$57$		0			0
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	0.408919	+	0.912571i	$0.365906\pi$
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	−0.994769	+	0.102151i	$0.967427\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	6.00000	−	10.3923i	0.683763	−	1.18431i
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$		0			0
$81$		0			0
$82$	−6.00000			−0.662589
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$		0			0
$85$		0			0
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$		0			0
$91$	16.0000			1.67726
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$		0			0
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$		0			0
$96$		0			0
$97$	−3.50000	−	6.06218i	−0.355371	−	0.615521i	0.631810	−	0.775123i	$-0.282312\pi$
$97$	−3.50000	−	6.06218i	−0.355371	−	0.615521i	−0.987181	+	0.159602i	$0.948979\pi$
$98$	−9.00000			−0.909137
$99$		0			0
$100$		0			0
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$		0			0
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$	2.00000	−	3.46410i	0.196116	−	0.339683i
$105$		0			0
$106$		0			0
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$		0			0
$112$	−2.00000	+	3.46410i	−0.188982	+	0.327327i
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	−0.927914	−	0.372794i	$-0.878400\pi$
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	0.786806	+	0.617200i	$0.211733\pi$
$114$		0			0
$115$		0			0
$116$	6.00000			0.557086
$117$		0			0
$118$	−9.00000			−0.828517
$119$	6.00000	+	10.3923i	0.550019	+	0.952661i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	4.00000	−	6.92820i	0.362143	−	0.627250i
$123$		0			0
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$		0			0
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$	8.00000	+	13.8564i	0.693688	+	1.20150i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	3.00000			0.257248
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$		0			0
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	−0.999268	−	0.0382553i	$-0.987820\pi$
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	0.532764	+	0.846264i	$0.321153\pi$
$140$		0			0
$141$		0			0
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$	−12.0000			−1.00349
$144$		0			0
$145$		0			0
$146$	−7.00000	−	12.1244i	−0.579324	−	1.00342i
$147$		0			0
$148$	4.00000	−	6.92820i	0.328798	−	0.569495i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$	4.00000			0.324443
$153$		0			0
$154$	12.0000			0.966988
$155$		0			0
$156$		0			0
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	−0.934731	−	0.355357i	$-0.884359\pi$
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	0.775113	+	0.631822i	$0.217693\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$		0			0
$160$		0			0
$161$	−24.0000			−1.89146
$162$		0			0
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	0.273252	+	0.961943i	$0.411901\pi$
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	−0.969693	+	0.244328i	$0.921432\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$		0			0
$171$		0			0
$172$	1.00000			0.0762493
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$		0			0
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$		0			0
$178$	4.50000	+	7.79423i	0.337289	+	0.584202i
$179$	3.00000			0.224231			0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000			0.224231			0.112115	+	0.993695i	$0.464237\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	8.00000	+	13.8564i	0.592999	+	1.02711i
$183$		0			0
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$		0			0
$186$		0			0
$187$	−4.50000	−	7.79423i	−0.329073	−	0.569970i
$188$	12.0000			0.875190
$189$		0			0
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	2.50000	−	4.33013i	0.179954	−	0.311689i	−0.761911	−	0.647682i	$-0.775738\pi$
$193$	2.50000	−	4.33013i	0.179954	−	0.311689i	0.941865	+	0.335993i	$0.109072\pi$
$194$	3.50000	−	6.06218i	0.251285	−	0.435239i
$195$		0			0
$196$	−4.50000	−	7.79423i	−0.321429	−	0.556731i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$		0			0
$201$		0			0
$202$	−6.00000	+	10.3923i	−0.422159	+	0.731200i
$203$	−12.0000	+	20.7846i	−0.842235	+	1.45879i
$204$		0			0
$205$		0			0
$206$	8.00000			0.557386
$207$		0			0
$208$	4.00000			0.277350
$209$	−6.00000	−	10.3923i	−0.415029	−	0.718851i
$210$		0			0
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	0.133226	+	0.991086i	$0.457467\pi$
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	−0.924918	+	0.380166i	$0.875867\pi$
$212$		0			0
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$		0			0
$216$		0			0
$217$	32.0000			2.17230
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$		0			0
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	0.897564	−	0.440884i	$-0.145335\pi$
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	−0.830599	+	0.556871i	$0.812002\pi$
$224$	−4.00000			−0.267261
$225$		0			0
$226$	−3.00000			−0.199557
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.832529	+	0.553981i	$0.186892\pi$
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.0634974	+	0.997982i	$0.479775\pi$
$228$		0			0
$229$	−4.00000	+	6.92820i	−0.264327	+	0.457829i	−0.967387	−	0.253302i	$-0.918483\pi$
$229$	−4.00000	+	6.92820i	−0.264327	+	0.457829i	0.703060	+	0.711131i	$0.251817\pi$
$230$		0			0
$231$		0			0
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	15.0000			0.982683			0.491341	−	0.870967i	$-0.336507\pi$
$233$	15.0000			0.982683			0.491341	+	0.870967i	$0.336507\pi$
$234$		0			0
$235$		0			0
$236$	−4.50000	−	7.79423i	−0.292925	−	0.507361i
$237$		0			0
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$	9.00000	−	15.5885i	0.582162	−	1.00833i	−0.413061	−	0.910703i	$-0.635540\pi$
$239$	9.00000	−	15.5885i	0.582162	−	1.00833i	0.995223	−	0.0976302i	$-0.0311262\pi$
$240$		0			0
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	−0.892058	−	0.451920i	$-0.850739\pi$
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	0.0546547	−	0.998505i	$-0.482594\pi$
$242$	2.00000			0.128565
$243$		0			0
$244$	8.00000			0.512148
$245$		0			0
$246$		0			0
$247$	8.00000	−	13.8564i	0.509028	−	0.881662i
$248$	4.00000	−	6.92820i	0.254000	−	0.439941i
$249$		0			0
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$	8.00000	+	13.8564i	0.501965	+	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$		0			0
$259$	16.0000	+	27.7128i	0.994192	+	1.72199i
$260$		0			0
$261$		0			0
$262$	12.0000			0.741362
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$		0			0
$265$		0			0
$266$	−8.00000	+	13.8564i	−0.490511	+	0.849591i
$267$		0			0
$268$	−2.00000	−	3.46410i	−0.122169	−	0.211604i
$269$	12.0000			0.731653			0.365826	−	0.930683i	$-0.380786\pi$
$269$	12.0000			0.731653			0.365826	+	0.930683i	$0.380786\pi$
$270$		0			0
$271$	−4.00000			−0.242983			−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000			−0.242983			−0.121491	+	0.992592i	$0.538768\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$		0			0
$274$	9.00000	−	15.5885i	0.543710	−	0.941733i
$275$		0			0
$276$		0			0
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	−11.0000			−0.659736
$279$		0			0
$280$		0			0
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	−0.999069	−	0.0431402i	$-0.986264\pi$
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	0.462174	−	0.886789i	$-0.347070\pi$
$282$		0			0
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	−0.880504	−	0.474039i	$-0.842796\pi$
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	0.850782	+	0.525519i	$0.176129\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$	24.0000			1.41668
$288$		0			0
$289$	−8.00000			−0.470588
$290$		0			0
$291$		0			0
$292$	7.00000	−	12.1244i	0.409644	−	0.709524i
$293$	6.00000	−	10.3923i	0.350524	−	0.607125i	−0.635818	−	0.771839i	$-0.719337\pi$
$293$	6.00000	−	10.3923i	0.350524	−	0.607125i	0.986341	+	0.164714i	$0.0526703\pi$
$294$		0			0
$295$		0			0
$296$	8.00000			0.464991
$297$		0			0
$298$	−6.00000			−0.347571
$299$	12.0000	+	20.7846i	0.693978	+	1.20201i
$300$		0			0
$301$	−2.00000	+	3.46410i	−0.115278	+	0.199667i
$302$	−5.00000	+	8.66025i	−0.287718	+	0.498342i
$303$		0			0
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$		0			0
$306$		0			0
$307$	1.00000			0.0570730			0.0285365	−	0.999593i	$-0.490915\pi$
$307$	1.00000			0.0570730			0.0285365	+	0.999593i	$0.490915\pi$
$308$	6.00000	+	10.3923i	0.341882	+	0.592157i
$309$		0			0
$310$		0			0
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	0.999748	−	0.0224310i	$-0.00714060\pi$
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	−0.519300	+	0.854592i	$0.673807\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	8.00000			0.450035
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$		0			0
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$		0			0
$322$	−12.0000	−	20.7846i	−0.668734	−	1.15828i
$323$	12.0000			0.667698
$324$		0			0
$325$		0			0
$326$	−5.50000	−	9.52628i	−0.304617	−	0.527612i
$327$		0			0
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	−24.0000	+	41.5692i	−1.32316	+	2.29179i
$330$		0			0
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	0.532096	−	0.846684i	$-0.321405\pi$
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	−0.999298	+	0.0374662i	$0.988071\pi$
$332$	−9.00000			−0.493939
$333$		0			0
$334$	−18.0000			−0.984916
$335$		0			0
$336$		0			0
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	−0.986960	−	0.160968i	$-0.948538\pi$
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	0.632882	+	0.774248i	$0.281872\pi$
$338$	1.50000	−	2.59808i	0.0815892	−	0.141317i
$339$		0			0
$340$		0			0
$341$	−24.0000			−1.29967
$342$		0			0
$343$	8.00000			0.431959
$344$	0.500000	+	0.866025i	0.0269582	+	0.0466930i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−13.5000	+	23.3827i	−0.724718	+	1.25525i	0.234372	+	0.972147i	$0.424697\pi$
$347$	−13.5000	+	23.3827i	−0.724718	+	1.25525i	−0.959090	+	0.283101i	$0.908637\pi$
$348$		0			0
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$		0			0
$351$		0			0
$352$	3.00000			0.159901
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	0.960574	−	0.278024i	$-0.0896796\pi$
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	−0.721063	+	0.692869i	$0.756346\pi$
$354$		0			0
$355$		0			0
$356$	−4.50000	+	7.79423i	−0.238500	+	0.413093i
$357$		0			0
$358$	1.50000	+	2.59808i	0.0792775	+	0.137313i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	1.00000	+	1.73205i	0.0525588	+	0.0910346i
$363$		0			0
$364$	−8.00000	+	13.8564i	−0.419314	+	0.726273i
$365$		0			0
$366$		0			0
$367$	13.0000	+	22.5167i	0.678594	+	1.17536i	0.975404	+	0.220423i	$0.0707439\pi$
$367$	13.0000	+	22.5167i	0.678594	+	1.17536i	−0.296810	+	0.954937i	$0.595923\pi$
$368$	−6.00000			−0.312772
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.00000	−	6.92820i	0.207112	−	0.358729i	−0.743691	−	0.668523i	$-0.766927\pi$
$373$	4.00000	−	6.92820i	0.207112	−	0.358729i	0.950804	+	0.309794i	$0.100260\pi$
$374$	4.50000	−	7.79423i	0.232689	−	0.403030i
$375$		0			0
$376$	6.00000	+	10.3923i	0.309426	+	0.535942i
$377$	24.0000			1.23606
$378$		0			0
$379$	29.0000			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$380$		0			0
$381$		0			0
$382$	−3.00000	+	5.19615i	−0.153493	+	0.265858i
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	−0.998954	−	0.0457244i	$-0.985440\pi$
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	0.539076	+	0.842257i	$0.318774\pi$
$384$		0			0
$385$		0			0
$386$	5.00000			0.254493
$387$		0			0
$388$	7.00000			0.355371
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.455150	+	0.788342i
$392$	4.50000	−	7.79423i	0.227284	−	0.393668i
$393$		0			0
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$		0			0
$396$		0			0
$397$	−14.0000			−0.702640			−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000			−0.702640			−0.351320	+	0.936255i	$0.614267\pi$
$398$	1.00000	+	1.73205i	0.0501255	+	0.0868199i
$399$		0			0
$400$		0			0
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	−0.990257	−	0.139253i	$-0.955530\pi$
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	0.615725	+	0.787961i	$0.288863\pi$
$402$		0			0
$403$	−16.0000	−	27.7128i	−0.797017	−	1.38047i
$404$	−12.0000			−0.597022
$405$		0			0
$406$	−24.0000			−1.19110
$407$	−12.0000	−	20.7846i	−0.594818	−	1.03025i
$408$		0			0
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	−0.454759	−	0.890614i	$-0.650275\pi$
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	0.998674	−	0.0514740i	$-0.0163919\pi$
$410$		0			0
$411$		0			0
$412$	4.00000	+	6.92820i	0.197066	+	0.341328i
$413$	36.0000			1.77144
$414$		0			0
$415$		0			0
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$		0			0
$418$	6.00000	−	10.3923i	0.293470	−	0.508304i
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	−0.734919	−	0.678155i	$-0.762780\pi$
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	0.954759	+	0.297382i	$0.0961133\pi$
$420$		0			0
$421$	−16.0000	−	27.7128i	−0.779792	−	1.35064i	−0.932061	−	0.362301i	$-0.881991\pi$
$421$	−16.0000	−	27.7128i	−0.779792	−	1.35064i	0.152269	−	0.988339i	$-0.451342\pi$
$422$	−23.0000			−1.11962
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−16.0000	+	27.7128i	−0.774294	+	1.34112i
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$		0			0
$431$	−6.00000			−0.289010			−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000			−0.289010			−0.144505	+	0.989504i	$0.546159\pi$
$432$		0			0
$433$	7.00000			0.336399			0.168199	−	0.985753i	$-0.446205\pi$
$433$	7.00000			0.336399			0.168199	+	0.985753i	$0.446205\pi$
$434$	16.0000	+	27.7128i	0.768025	+	1.33026i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	−12.0000	+	20.7846i	−0.574038	+	0.994263i
$438$		0			0
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	0.649218	−	0.760602i	$-0.275096\pi$
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	−0.983310	+	0.181938i	$0.941763\pi$
$440$		0			0
$441$		0			0
$442$	12.0000			0.570782
$443$	−4.50000	−	7.79423i	−0.213801	−	0.370315i	0.739100	−	0.673596i	$-0.235251\pi$
$443$	−4.50000	−	7.79423i	−0.213801	−	0.370315i	−0.952901	+	0.303281i	$0.901918\pi$
$444$		0			0
$445$		0			0
$446$	−1.00000	+	1.73205i	−0.0473514	+	0.0820150i
$447$		0			0
$448$	−2.00000	−	3.46410i	−0.0944911	−	0.163663i
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	−18.0000			−0.847587
$452$	−1.50000	−	2.59808i	−0.0705541	−	0.122203i
$453$		0			0
$454$	−13.5000	+	23.3827i	−0.633586	+	1.09740i
$455$		0			0
$456$		0			0
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	0.725059	−	0.688686i	$-0.241812\pi$
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	−8.00000			−0.373815
$459$		0			0
$460$		0			0
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	0.787668	−	0.616100i	$-0.211288\pi$
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	−0.927392	+	0.374091i	$0.877955\pi$
$462$		0			0
$463$	7.00000	−	12.1244i	0.325318	−	0.563467i	−0.656259	−	0.754536i	$-0.727862\pi$
$463$	7.00000	−	12.1244i	0.325318	−	0.563467i	0.981577	+	0.191069i	$0.0611955\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	7.50000	+	12.9904i	0.347431	+	0.601768i
$467$	9.00000			0.416470			0.208235	−	0.978079i	$-0.433228\pi$
$467$	9.00000			0.416470			0.208235	+	0.978079i	$0.433228\pi$
$468$		0			0
$469$	16.0000			0.738811
$470$		0			0
$471$		0			0
$472$	4.50000	−	7.79423i	0.207129	−	0.358758i
$473$	1.50000	−	2.59808i	0.0689701	−	0.119460i
$474$		0			0
$475$		0			0
$476$	−12.0000			−0.550019
$477$		0			0
$478$	18.0000			0.823301
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	0.695773	−	0.718262i	$-0.255062\pi$
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	−0.969920	+	0.243426i	$0.921729\pi$
$480$		0			0
$481$	16.0000	−	27.7128i	0.729537	−	1.26360i
$482$	13.0000	−	22.5167i	0.592134	−	1.02561i
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$		0			0
$486$		0			0
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$	4.00000	+	6.92820i	0.181071	+	0.313625i
$489$		0			0
$490$		0			0
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	−0.984145	−	0.177365i	$-0.943243\pi$
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	0.645675	+	0.763612i	$0.276576\pi$
$492$		0			0
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	16.0000			0.719874
$495$		0			0
$496$	8.00000			0.359211
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$		0			0
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	0.716258	+	0.697835i	$0.245853\pi$
$500$		0			0
$501$		0			0
$502$	6.00000	+	10.3923i	0.267793	+	0.463831i
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$		0			0
$506$	9.00000	+	15.5885i	0.400099	+	0.692991i
$507$		0			0
$508$	−8.00000	+	13.8564i	−0.354943	+	0.614779i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$		0			0
$511$	28.0000	+	48.4974i	1.23865	+	2.14540i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−3.00000			−0.132324
$515$		0			0
$516$		0			0
$517$	18.0000	−	31.1769i	0.791639	−	1.37116i
$518$	−16.0000	+	27.7128i	−0.703000	+	1.21763i
$519$		0			0
$520$		0			0
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$		0			0
$523$	−29.0000			−1.26808			−0.634041	−	0.773300i	$-0.718605\pi$
$523$	−29.0000			−1.26808			−0.634041	+	0.773300i	$0.718605\pi$
$524$	6.00000	+	10.3923i	0.262111	+	0.453990i
$525$		0			0
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$	12.0000	−	20.7846i	0.522728	−	0.905392i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$		0			0
$532$	−16.0000			−0.693688
$533$	−12.0000	−	20.7846i	−0.519778	−	0.900281i
$534$		0			0
$535$		0			0
$536$	2.00000	−	3.46410i	0.0863868	−	0.149626i
$537$		0			0
$538$	6.00000	+	10.3923i	0.258678	+	0.448044i
$539$	−27.0000			−1.16297
$540$		0			0
$541$	8.00000			0.343947			0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000			0.343947			0.171973	+	0.985102i	$0.444986\pi$
$542$	−2.00000	−	3.46410i	−0.0859074	−	0.148796i
$543$		0			0
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$		0			0
$546$		0			0
$547$	10.0000	+	17.3205i	0.427569	+	0.740571i	0.996657	−	0.0817056i	$-0.0260367\pi$
$547$	10.0000	+	17.3205i	0.427569	+	0.740571i	−0.569087	+	0.822277i	$0.692703\pi$
$548$	18.0000			0.768922
$549$		0			0
$550$		0			0
$551$	12.0000	+	20.7846i	0.511217	+	0.885454i
$552$		0			0
$553$	−16.0000	+	27.7128i	−0.680389	+	1.17847i
$554$	−1.00000	+	1.73205i	−0.0424859	+	0.0735878i
$555$		0			0
$556$	−5.50000	−	9.52628i	−0.233252	−	0.404004i
$557$	−6.00000			−0.254228			−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000			−0.254228			−0.127114	+	0.991888i	$0.540571\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$		0			0
$561$		0			0
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	−0.832684	−	0.553748i	$-0.813197\pi$
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	0.895902	+	0.444252i	$0.146530\pi$
$564$		0			0
$565$		0			0
$566$	−1.00000			−0.0420331
$567$		0			0
$568$	−6.00000			−0.251754
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	−0.996961	−	0.0779066i	$-0.975176\pi$
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	0.431011	−	0.902347i	$-0.358157\pi$
$570$		0			0
$571$	12.5000	−	21.6506i	0.523109	−	0.906051i	−0.476530	−	0.879158i	$-0.658105\pi$
$571$	12.5000	−	21.6506i	0.523109	−	0.906051i	0.999638	−	0.0268925i	$-0.00856117\pi$
$572$	6.00000	−	10.3923i	0.250873	−	0.434524i
$573$		0			0
$574$	12.0000	+	20.7846i	0.500870	+	0.867533i
$575$		0			0
$576$		0			0
$577$	−38.0000			−1.58196			−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000			−1.58196			−0.790980	+	0.611842i	$0.790429\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$		0			0
$581$	18.0000	−	31.1769i	0.746766	−	1.29344i
$582$		0			0
$583$		0			0
$584$	14.0000			0.579324
$585$		0			0
$586$	12.0000			0.495715
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	0.895320	−	0.445424i	$-0.146947\pi$
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	−0.833408	+	0.552658i	$0.813614\pi$
$588$		0			0
$589$	16.0000	−	27.7128i	0.659269	−	1.14189i
$590$		0			0
$591$		0			0
$592$	4.00000	+	6.92820i	0.164399	+	0.284747i
$593$	−45.0000			−1.84793			−0.923964	−	0.382479i	$-0.875070\pi$
$593$	−45.0000			−1.84793			−0.923964	+	0.382479i	$0.875070\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$	−12.0000	+	20.7846i	−0.490716	+	0.849946i
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	−0.621480	−	0.783430i	$-0.713468\pi$
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	0.989210	+	0.146503i	$0.0468017\pi$
$600$		0			0
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	0.945558	+	0.325455i	$0.105517\pi$
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	−0.190927	+	0.981604i	$0.561149\pi$
$602$	−4.00000			−0.163028
$603$		0			0
$604$	−10.0000			−0.406894
$605$		0			0
$606$		0			0
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	−0.981454	−	0.191700i	$-0.938600\pi$
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	0.656744	+	0.754114i	$0.271933\pi$
$608$	−2.00000	+	3.46410i	−0.0811107	+	0.140488i
$609$		0			0
$610$		0			0
$611$	48.0000			1.94187
$612$		0			0
$613$	−14.0000			−0.565455			−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000			−0.565455			−0.282727	+	0.959200i	$0.591239\pi$
$614$	0.500000	+	0.866025i	0.0201784	+	0.0349499i
$615$		0			0
$616$	−6.00000	+	10.3923i	−0.241747	+	0.418718i
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$		0			0
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	−0.967271	−	0.253744i	$-0.918338\pi$
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	0.263887	−	0.964554i	$-0.414995\pi$
$620$		0			0
$621$		0			0
$622$	6.00000			0.240578
$623$	−18.0000	−	31.1769i	−0.721155	−	1.24908i
$624$		0			0
$625$		0			0
$626$	−8.50000	+	14.7224i	−0.339728	+	0.588427i
$627$		0			0
$628$	−2.00000	−	3.46410i	−0.0798087	−	0.138233i
$629$	24.0000			0.956943
$630$		0			0
$631$	38.0000			1.51276			0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000			1.51276			0.756378	+	0.654135i	$0.226967\pi$
$632$	4.00000	+	6.92820i	0.159111	+	0.275589i
$633$		0			0
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$		0			0
$636$		0			0
$637$	−18.0000	−	31.1769i	−0.713186	−	1.23527i
$638$	18.0000			0.712627
$639$		0			0
$640$		0			0
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	−0.999247	−	0.0387913i	$-0.987649\pi$
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	0.466029	−	0.884769i	$-0.345684\pi$
$642$		0			0
$643$	11.5000	−	19.9186i	0.453516	−	0.785512i	−0.545086	−	0.838380i	$-0.683503\pi$
$643$	11.5000	−	19.9186i	0.453516	−	0.785512i	0.998602	+	0.0528680i	$0.0168363\pi$
$644$	12.0000	−	20.7846i	0.472866	−	0.819028i
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$		0			0
$649$	−27.0000			−1.05984
$650$		0			0
$651$		0			0
$652$	5.50000	−	9.52628i	0.215397	−	0.373078i
$653$	12.0000	−	20.7846i	0.469596	−	0.813365i	−0.529799	−	0.848123i	$-0.677733\pi$
$653$	12.0000	−	20.7846i	0.469596	−	0.813365i	0.999396	+	0.0347583i	$0.0110661\pi$
$654$		0			0
$655$		0			0
$656$	6.00000			0.234261
$657$		0			0
$658$	−48.0000			−1.87123
$659$	−22.5000	−	38.9711i	−0.876476	−	1.51810i	−0.855183	−	0.518327i	$-0.826555\pi$
$659$	−22.5000	−	38.9711i	−0.876476	−	1.51810i	−0.0212930	−	0.999773i	$-0.506778\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$	8.50000	−	14.7224i	0.330362	−	0.572204i
$663$		0			0
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$		0			0
$666$		0			0
$667$	−36.0000			−1.39393
$668$	−9.00000	−	15.5885i	−0.348220	−	0.603136i
$669$		0			0
$670$		0			0
$671$	12.0000	−	20.7846i	0.463255	−	0.802381i
$672$		0			0
$673$	−23.0000	−	39.8372i	−0.886585	−	1.53561i	−0.843886	−	0.536522i	$-0.819738\pi$
$673$	−23.0000	−	39.8372i	−0.886585	−	1.53561i	−0.0426985	−	0.999088i	$-0.513595\pi$
$674$	−13.0000			−0.500741
$675$		0			0
$676$	3.00000			0.115385
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	0.639618	−	0.768693i	$-0.279092\pi$
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	−0.985517	+	0.169580i	$0.945759\pi$
$678$		0			0
$679$	−14.0000	+	24.2487i	−0.537271	+	0.930580i
$680$		0			0
$681$		0			0
$682$	−12.0000	−	20.7846i	−0.459504	−	0.795884i
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$		0			0
$686$	4.00000	+	6.92820i	0.152721	+	0.264520i
$687$		0			0
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$		0			0
$690$		0			0
$691$	9.50000	+	16.4545i	0.361397	+	0.625958i	0.988191	−	0.153227i	$-0.0489666\pi$
$691$	9.50000	+	16.4545i	0.361397	+	0.625958i	−0.626794	+	0.779185i	$0.715633\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−27.0000			−1.02491
$695$		0			0
$696$		0			0
$697$	9.00000	−	15.5885i	0.340899	−	0.590455i
$698$	7.00000	−	12.1244i	0.264954	−	0.458914i
$699$		0			0
$700$		0			0
$701$	−48.0000			−1.81293			−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000			−1.81293			−0.906467	+	0.422276i	$0.861231\pi$
$702$		0			0
$703$	32.0000			1.20690
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	−4.50000	+	7.79423i	−0.169360	+	0.293340i
$707$	24.0000	−	41.5692i	0.902613	−	1.56337i
$708$		0			0
$709$	26.0000	+	45.0333i	0.976450	+	1.69126i	0.675063	+	0.737760i	$0.264116\pi$
$709$	26.0000	+	45.0333i	0.976450	+	1.69126i	0.301388	+	0.953502i	$0.402550\pi$
$710$		0			0
$711$		0			0
$712$	−9.00000			−0.337289
$713$	24.0000	+	41.5692i	0.898807	+	1.55678i
$714$		0			0
$715$		0			0
$716$	−1.50000	+	2.59808i	−0.0560576	+	0.0970947i
$717$		0			0
$718$		0			0
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$		0			0
$721$	−32.0000			−1.19174
$722$	−1.50000	−	2.59808i	−0.0558242	−	0.0966904i
$723$		0			0
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$		0			0
$726$		0			0
$727$	7.00000	+	12.1244i	0.259616	+	0.449667i	0.966139	−	0.258022i	$-0.0830708\pi$
$727$	7.00000	+	12.1244i	0.259616	+	0.449667i	−0.706523	+	0.707690i	$0.749737\pi$
$728$	−16.0000			−0.592999
$729$		0			0
$730$		0			0
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$		0			0
$733$	−2.00000	+	3.46410i	−0.0738717	+	0.127950i	−0.900595	−	0.434659i	$-0.856869\pi$
$733$	−2.00000	+	3.46410i	−0.0738717	+	0.127950i	0.826723	+	0.562609i	$0.190202\pi$
$734$	−13.0000	+	22.5167i	−0.479839	+	0.831105i
$735$		0			0
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$	−12.0000			−0.442026
$738$		0			0
$739$	−25.0000			−0.919640			−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000			−0.919640			−0.459820	+	0.888012i	$0.652086\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$743$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$744$		0			0
$745$		0			0
$746$	8.00000			0.292901
$747$		0			0
$748$	9.00000			0.329073
$749$	−24.0000	−	41.5692i	−0.876941	−	1.51891i
$750$		0			0
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	−0.369084	−	0.929396i	$-0.620328\pi$
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	0.989423	−	0.145062i	$-0.0463382\pi$
$752$	−6.00000	+	10.3923i	−0.218797	+	0.378968i
$753$		0			0
$754$	12.0000	+	20.7846i	0.437014	+	0.756931i
$755$		0			0
$756$		0			0
$757$	−20.0000			−0.726912			−0.363456	−	0.931611i	$-0.618403\pi$
$757$	−20.0000			−0.726912			−0.363456	+	0.931611i	$0.618403\pi$
$758$	14.5000	+	25.1147i	0.526664	+	0.912208i
$759$		0			0
$760$		0			0
$761$	−19.5000	+	33.7750i	−0.706874	+	1.22434i	0.259136	+	0.965841i	$0.416562\pi$
$761$	−19.5000	+	33.7750i	−0.706874	+	1.22434i	−0.966011	+	0.258502i	$0.916771\pi$
$762$		0			0
$763$	−4.00000	−	6.92820i	−0.144810	−	0.250818i
$764$	−6.00000			−0.217072
$765$		0			0
$766$	−18.0000			−0.650366
$767$	−18.0000	−	31.1769i	−0.649942	−	1.12573i
$768$		0			0
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	−0.907575	−	0.419890i	$-0.862069\pi$
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	0.817423	+	0.576038i	$0.195402\pi$
$770$		0			0
$771$		0			0
$772$	2.50000	+	4.33013i	0.0899770	+	0.155845i
$773$	−42.0000			−1.51064			−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000			−1.51064			−0.755318	+	0.655359i	$0.772517\pi$
$774$		0			0
$775$		0			0
$776$	3.50000	+	6.06218i	0.125643	+	0.217620i
$777$		0			0
$778$	3.00000	−	5.19615i	0.107555	−	0.186291i
$779$	12.0000	−	20.7846i	0.429945	−	0.744686i
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$	−18.0000			−0.643679
$783$		0			0
$784$	9.00000			0.321429
$785$		0			0
$786$		0			0
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	−0.899468	−	0.436987i	$-0.856046\pi$
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	0.828176	+	0.560469i	$0.189379\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$		0			0
$790$		0			0
$791$	12.0000			0.426671
$792$		0			0
$793$	32.0000			1.13635
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$		0			0
$796$	−1.00000	+	1.73205i	−0.0354441	+	0.0613909i
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	−0.952506	−	0.304520i	$-0.901504\pi$
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	0.739975	+	0.672634i	$0.234837\pi$
$798$		0			0
$799$	18.0000	+	31.1769i	0.636794	+	1.10296i
$800$		0			0
$801$		0			0
$802$	−15.0000			−0.529668
$803$	−21.0000	−	36.3731i	−0.741074	−	1.28358i
$804$		0			0
$805$		0			0
$806$	16.0000	−	27.7128i	0.563576	−	0.976142i
$807$		0			0
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	−45.0000			−1.58212			−0.791058	−	0.611741i	$-0.790469\pi$
$809$	−45.0000			−1.58212			−0.791058	+	0.611741i	$0.790469\pi$
$810$		0			0
$811$	5.00000			0.175574			0.0877869	−	0.996139i	$-0.472021\pi$
$811$	5.00000			0.175574			0.0877869	+	0.996139i	$0.472021\pi$
$812$	−12.0000	−	20.7846i	−0.421117	−	0.729397i
$813$		0			0
$814$	12.0000	−	20.7846i	0.420600	−	0.728500i
$815$		0			0
$816$		0			0
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$	22.0000			0.769212
$819$		0			0
$820$		0			0
$821$	12.0000	+	20.7846i	0.418803	+	0.725388i	0.995819	−	0.0913446i	$-0.0291165\pi$
$821$	12.0000	+	20.7846i	0.418803	+	0.725388i	−0.577016	+	0.816733i	$0.695783\pi$
$822$		0			0
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$		0			0
$826$	18.0000	+	31.1769i	0.626300	+	1.08478i
$827$	15.0000			0.521601			0.260801	−	0.965393i	$-0.416014\pi$
$827$	15.0000			0.521601			0.260801	+	0.965393i	$0.416014\pi$
$828$		0			0
$829$	20.0000			0.694629			0.347314	−	0.937749i	$-0.387094\pi$
$829$	20.0000			0.694629			0.347314	+	0.937749i	$0.387094\pi$
$830$		0			0
$831$		0			0
$832$	−2.00000	+	3.46410i	−0.0693375	+	0.120096i
$833$	13.5000	−	23.3827i	0.467747	−	0.810162i
$834$		0			0
$835$		0			0
$836$	12.0000			0.415029
$837$		0			0
$838$	9.00000			0.310900
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	0.899158	+	0.437623i	$0.144180\pi$
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	−0.0705865	+	0.997506i	$0.522487\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	16.0000	−	27.7128i	0.551396	−	0.955047i
$843$		0			0
$844$	−11.5000	−	19.9186i	−0.395846	−	0.685626i
$845$		0			0
$846$		0			0
$847$	−8.00000			−0.274883
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−24.0000	+	41.5692i	−0.822709	+	1.42497i
$852$		0			0
$853$	−23.0000	−	39.8372i	−0.787505	−	1.36400i	−0.927491	−	0.373845i	$-0.878039\pi$
$853$	−23.0000	−	39.8372i	−0.787505	−	1.36400i	0.139986	−	0.990153i	$-0.455294\pi$
$854$	−32.0000			−1.09502
$855$		0			0
$856$	−12.0000			−0.410152
$857$	13.5000	+	23.3827i	0.461151	+	0.798737i	0.999019	−	0.0442921i	$-0.0141032\pi$
$857$	13.5000	+	23.3827i	0.461151	+	0.798737i	−0.537867	+	0.843029i	$0.680770\pi$
$858$		0			0
$859$	8.00000	−	13.8564i	0.272956	−	0.472774i	−0.696661	−	0.717400i	$-0.745332\pi$
$859$	8.00000	−	13.8564i	0.272956	−	0.472774i	0.969618	+	0.244626i	$0.0786652\pi$
$860$		0			0
$861$		0			0
$862$	−3.00000	−	5.19615i	−0.102180	−	0.176982i
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$		0			0
$866$	3.50000	+	6.06218i	0.118935	+	0.206001i
$867$		0			0
$868$	−16.0000	+	27.7128i	−0.543075	+	0.940634i
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	−2.00000			−0.0677285
$873$		0			0
$874$	−24.0000			−0.811812
$875$		0			0
$876$		0			0
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	−0.968898	−	0.247462i	$-0.920404\pi$
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	0.698757	+	0.715359i	$0.253737\pi$
$878$	7.00000	−	12.1244i	0.236239	−	0.409177i
$879$		0			0
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	13.0000			0.437485			0.218742	−	0.975783i	$-0.429805\pi$
$883$	13.0000			0.437485			0.218742	+	0.975783i	$0.429805\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$		0			0
$886$	4.50000	−	7.79423i	0.151180	−	0.261852i
$887$	−15.0000	+	25.9808i	−0.503651	+	0.872349i	0.496340	+	0.868128i	$0.334677\pi$
$887$	−15.0000	+	25.9808i	−0.503651	+	0.872349i	−0.999991	+	0.00422062i	$0.998657\pi$
$888$		0			0
$889$	−32.0000	−	55.4256i	−1.07325	−	1.85892i
$890$		0			0
$891$		0			0
$892$	−2.00000			−0.0669650
$893$	24.0000	+	41.5692i	0.803129	+	1.39106i
$894$		0			0
$895$		0			0
$896$	2.00000	−	3.46410i	0.0668153	−	0.115728i
$897$		0			0
$898$	−9.00000	−	15.5885i	−0.300334	−	0.520194i
$899$	48.0000			1.60089
$900$		0			0
$901$		0			0
$902$	−9.00000	−	15.5885i	−0.299667	−	0.519039i
$903$		0			0
$904$	1.50000	−	2.59808i	0.0498893	−	0.0864107i
$905$		0			0
$906$		0			0
$907$	8.50000	+	14.7224i	0.282238	+	0.488850i	0.971936	−	0.235247i	$-0.0755899\pi$
$907$	8.50000	+	14.7224i	0.282238	+	0.488850i	−0.689698	+	0.724097i	$0.742257\pi$
$908$	−27.0000			−0.896026
$909$		0			0
$910$		0			0
$911$	−9.00000	−	15.5885i	−0.298183	−	0.516469i	0.677537	−	0.735489i	$-0.263047\pi$
$911$	−9.00000	−	15.5885i	−0.298183	−	0.516469i	−0.975720	+	0.219020i	$0.929714\pi$
$912$		0			0
$913$	−13.5000	+	23.3827i	−0.446785	+	0.773854i
$914$	5.00000	−	8.66025i	0.165385	−	0.286456i
$915$		0			0
$916$	−4.00000	−	6.92820i	−0.132164	−	0.228914i
$917$	−48.0000			−1.58510
$918$		0			0
$919$	−46.0000			−1.51740			−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000			−1.51740			−0.758700	+	0.651440i	$0.774165\pi$
$920$		0			0
$921$		0			0
$922$	3.00000	−	5.19615i	0.0987997	−	0.171126i
$923$	−12.0000	+	20.7846i	−0.394985	+	0.684134i
$924$		0			0
$925$		0			0
$926$	14.0000			0.460069
$927$		0			0
$928$	−6.00000			−0.196960
$929$	21.0000	+	36.3731i	0.688988	+	1.19336i	0.972166	+	0.234294i	$0.0752779\pi$
$929$	21.0000	+	36.3731i	0.688988	+	1.19336i	−0.283178	+	0.959067i	$0.591389\pi$
$930$		0			0
$931$	18.0000	−	31.1769i	0.589926	−	1.02178i
$932$	−7.50000	+	12.9904i	−0.245671	+	0.425514i
$933$		0			0
$934$	4.50000	+	7.79423i	0.147244	+	0.255035i
$935$		0			0
$936$		0			0
$937$	37.0000			1.20874			0.604369	−	0.796705i	$-0.293425\pi$
$937$	37.0000			1.20874			0.604369	+	0.796705i	$0.293425\pi$
$938$	8.00000	+	13.8564i	0.261209	+	0.452428i
$939$		0			0
$940$		0			0
$941$	12.0000	−	20.7846i	0.391189	−	0.677559i	−0.601418	−	0.798935i	$-0.705397\pi$
$941$	12.0000	−	20.7846i	0.391189	−	0.677559i	0.992607	+	0.121376i	$0.0387306\pi$
$942$		0			0
$943$	18.0000	+	31.1769i	0.586161	+	1.01526i
$944$	9.00000			0.292925
$945$		0			0
$946$	3.00000			0.0975384
$947$	4.50000	+	7.79423i	0.146230	+	0.253278i	0.929831	−	0.367986i	$-0.119953\pi$
$947$	4.50000	+	7.79423i	0.146230	+	0.253278i	−0.783601	+	0.621264i	$0.786619\pi$
$948$		0			0
$949$	28.0000	−	48.4974i	0.908918	−	1.57429i
$950$		0			0
$951$		0			0
$952$	−6.00000	−	10.3923i	−0.194461	−	0.336817i
$953$	−27.0000			−0.874616			−0.437308	−	0.899312i	$-0.644068\pi$
$953$	−27.0000			−0.874616			−0.437308	+	0.899312i	$0.644068\pi$
$954$		0			0
$955$		0			0
$956$	9.00000	+	15.5885i	0.291081	+	0.504167i
$957$		0			0
$958$	6.00000	−	10.3923i	0.193851	−	0.335760i
$959$	−36.0000	+	62.3538i	−1.16250	+	2.01351i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	32.0000			1.03172
$963$		0			0
$964$	26.0000			0.837404
$965$		0			0
$966$		0			0
$967$	−14.0000	+	24.2487i	−0.450210	+	0.779786i	−0.998399	−	0.0565684i	$-0.981984\pi$
$967$	−14.0000	+	24.2487i	−0.450210	+	0.779786i	0.548189	+	0.836354i	$0.315317\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$		0			0
$970$		0			0
$971$	27.0000			0.866471			0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000			0.866471			0.433236	+	0.901281i	$0.357372\pi$
$972$		0			0
$973$	44.0000			1.41058
$974$	−1.00000	−	1.73205i	−0.0320421	−	0.0554985i
$975$		0			0
$976$	−4.00000	+	6.92820i	−0.128037	+	0.221766i
$977$	27.0000	−	46.7654i	0.863807	−	1.49616i	−0.00442082	−	0.999990i	$-0.501407\pi$
$977$	27.0000	−	46.7654i	0.863807	−	1.49616i	0.868227	−	0.496167i	$-0.165259\pi$
$978$		0			0
$979$	13.5000	+	23.3827i	0.431462	+	0.747314i
$980$		0			0
$981$		0			0
$982$	−15.0000			−0.478669
$983$	−27.0000	−	46.7654i	−0.861166	−	1.49158i	−0.870804	−	0.491630i	$-0.836401\pi$
$983$	−27.0000	−	46.7654i	−0.861166	−	1.49158i	0.00963785	−	0.999954i	$-0.496932\pi$
$984$		0			0
$985$		0			0
$986$	−9.00000	+	15.5885i	−0.286618	+	0.496438i
$987$		0			0
$988$	8.00000	+	13.8564i	0.254514	+	0.440831i
$989$	−6.00000			−0.190789
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$		0			0
$994$	12.0000	−	20.7846i	0.380617	−	0.659248i
$995$		0			0
$996$		0			0
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	0.775923	−	0.630828i	$-0.217285\pi$
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	−0.934274	+	0.356555i	$0.883951\pi$
$998$	−11.0000			−0.348199
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.e.f.901.1		2
3.2	odd	2		450.2.e.a.301.1	yes	2
5.2	odd	4		1350.2.j.d.199.1		4
5.3	odd	4		1350.2.j.d.199.2		4
5.4	even	2		1350.2.e.e.901.1		2
9.2	odd	6		450.2.e.a.151.1	✓	2
9.4	even	3		4050.2.a.p.1.1		1
9.5	odd	6		4050.2.a.bj.1.1		1
9.7	even	3	inner	1350.2.e.f.451.1		2
15.2	even	4		450.2.j.d.49.2		4
15.8	even	4		450.2.j.d.49.1		4
15.14	odd	2		450.2.e.h.301.1	yes	2
45.2	even	12		450.2.j.d.349.1		4
45.4	even	6		4050.2.a.t.1.1		1
45.7	odd	12		1350.2.j.d.1099.2		4
45.13	odd	12		4050.2.c.e.649.2		2
45.14	odd	6		4050.2.a.b.1.1		1
45.22	odd	12		4050.2.c.e.649.1		2
45.23	even	12		4050.2.c.q.649.1		2
45.29	odd	6		450.2.e.h.151.1	yes	2
45.32	even	12		4050.2.c.q.649.2		2
45.34	even	6		1350.2.e.e.451.1		2
45.38	even	12		450.2.j.d.349.2		4
45.43	odd	12		1350.2.j.d.1099.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.e.a.151.1	✓	2	9.2	odd	6
450.2.e.a.301.1	yes	2	3.2	odd	2
450.2.e.h.151.1	yes	2	45.29	odd	6
450.2.e.h.301.1	yes	2	15.14	odd	2
450.2.j.d.49.1		4	15.8	even	4
450.2.j.d.49.2		4	15.2	even	4
450.2.j.d.349.1		4	45.2	even	12
450.2.j.d.349.2		4	45.38	even	12
1350.2.e.e.451.1		2	45.34	even	6
1350.2.e.e.901.1		2	5.4	even	2
1350.2.e.f.451.1		2	9.7	even	3	inner
1350.2.e.f.901.1		2	1.1	even	1	trivial
1350.2.j.d.199.1		4	5.2	odd	4
1350.2.j.d.199.2		4	5.3	odd	4
1350.2.j.d.1099.1		4	45.43	odd	12
1350.2.j.d.1099.2		4	45.7	odd	12
4050.2.a.b.1.1		1	45.14	odd	6
4050.2.a.p.1.1		1	9.4	even	3
4050.2.a.t.1.1		1	45.4	even	6
4050.2.a.bj.1.1		1	9.5	odd	6
4050.2.c.e.649.1		2	45.22	odd	12
4050.2.c.e.649.2		2	45.13	odd	12
4050.2.c.q.649.1		2	45.23	even	12
4050.2.c.q.649.2		2	45.32	even	12

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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{11} +(-2.00000 + 3.46410i) q^{13} +(2.00000 - 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} -3.00000 q^{17} -4.00000 q^{19} +(-1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} -4.00000 q^{26} +4.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{34} -8.00000 q^{37} +(-2.00000 - 3.46410i) q^{38} +(-3.00000 + 5.19615i) q^{41} +(-0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +6.00000 q^{46} +(-6.00000 - 10.3923i) q^{47} +(-4.50000 + 7.79423i) q^{49} +(-2.00000 - 3.46410i) q^{52} +(2.00000 + 3.46410i) q^{56} +(3.00000 - 5.19615i) q^{58} +(-4.50000 + 7.79423i) q^{59} +(-4.00000 - 6.92820i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +6.00000 q^{71} -14.0000 q^{73} +(-4.00000 - 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(6.00000 - 10.3923i) q^{77} +(-4.00000 - 6.92820i) q^{79} -6.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +(0.500000 - 0.866025i) q^{86} +(-1.50000 - 2.59808i) q^{88} +9.00000 q^{89} +16.0000 q^{91} +(3.00000 + 5.19615i) q^{92} +(6.00000 - 10.3923i) q^{94} +(-3.50000 - 6.06218i) q^{97} -9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 4 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - 4 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - 4 q^{7} - 2 q^{8} + 3 q^{11} - 4 q^{13} + 4 q^{14} - q^{16} - 6 q^{17} - 8 q^{19} - 3 q^{22} + 6 q^{23} - 8 q^{26} + 8 q^{28} - 6 q^{29} - 8 q^{31} + q^{32} - 3 q^{34} - 16 q^{37} - 4 q^{38} - 6 q^{41} - q^{43} - 6 q^{44} + 12 q^{46} - 12 q^{47} - 9 q^{49} - 4 q^{52} + 4 q^{56} + 6 q^{58} - 9 q^{59} - 8 q^{61} - 16 q^{62} + 2 q^{64} - 4 q^{67} + 3 q^{68} + 12 q^{71} - 28 q^{73} - 8 q^{74} + 4 q^{76} + 12 q^{77} - 8 q^{79} - 12 q^{82} + 9 q^{83} + q^{86} - 3 q^{88} + 18 q^{89} + 32 q^{91} + 6 q^{92} + 12 q^{94} - 7 q^{97} - 18 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - 4 * q^7 - 2 * q^8 + 3 * q^11 - 4 * q^13 + 4 * q^14 - q^16 - 6 * q^17 - 8 * q^19 - 3 * q^22 + 6 * q^23 - 8 * q^26 + 8 * q^28 - 6 * q^29 - 8 * q^31 + q^32 - 3 * q^34 - 16 * q^37 - 4 * q^38 - 6 * q^41 - q^43 - 6 * q^44 + 12 * q^46 - 12 * q^47 - 9 * q^49 - 4 * q^52 + 4 * q^56 + 6 * q^58 - 9 * q^59 - 8 * q^61 - 16 * q^62 + 2 * q^64 - 4 * q^67 + 3 * q^68 + 12 * q^71 - 28 * q^73 - 8 * q^74 + 4 * q^76 + 12 * q^77 - 8 * q^79 - 12 * q^82 + 9 * q^83 + q^86 - 3 * q^88 + 18 * q^89 + 32 * q^91 + 6 * q^92 + 12 * q^94 - 7 * q^97 - 18 * q^98

Introduction

L-functions

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