LMFDB - Embedded newform 1350.2.j.d.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(199,1350)]

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([2, 3]))

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

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

chi := DirichletCharacter("1350.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 450)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1350.199
Dual form			1350.2.j.d.1099.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(1.50000 + 2.59808i) q^{11} +(-3.46410 - 2.00000i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.00000i q^{17} +4.00000 q^{19} +(2.59808 + 1.50000i) q^{22} +(5.19615 + 3.00000i) q^{23} -4.00000 q^{26} +4.00000i q^{28} +(3.00000 + 5.19615i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.50000 + 2.59808i) q^{34} +8.00000i q^{37} +(3.46410 - 2.00000i) q^{38} +(-3.00000 + 5.19615i) q^{41} +(0.866025 - 0.500000i) q^{43} +3.00000 q^{44} +6.00000 q^{46} +(-10.3923 + 6.00000i) q^{47} +(4.50000 - 7.79423i) q^{49} +(-3.46410 + 2.00000i) q^{52} +(2.00000 + 3.46410i) q^{56} +(5.19615 + 3.00000i) q^{58} +(4.50000 - 7.79423i) q^{59} +(-4.00000 - 6.92820i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(3.46410 + 2.00000i) q^{67} +(2.59808 + 1.50000i) q^{68} +6.00000 q^{71} -14.0000i q^{73} +(4.00000 + 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-10.3923 - 6.00000i) q^{77} +(4.00000 + 6.92820i) q^{79} +6.00000i q^{82} +(-7.79423 + 4.50000i) q^{83} +(0.500000 - 0.866025i) q^{86} +(2.59808 - 1.50000i) q^{88} -9.00000 q^{89} +16.0000 q^{91} +(5.19615 - 3.00000i) q^{92} +(-6.00000 + 10.3923i) q^{94} +(-6.06218 + 3.50000i) q^{97} -9.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} + 6 q^{11} - 8 q^{14} - 2 q^{16} + 16 q^{19} - 16 q^{26} + 12 q^{29} - 16 q^{31} + 6 q^{34} - 12 q^{41} + 12 q^{44} + 24 q^{46} + 18 q^{49} + 8 q^{56} + 18 q^{59} - 16 q^{61} - 4 q^{64} + 24 q^{71} + 16 q^{74} + 8 q^{76} + 16 q^{79} + 2 q^{86} - 36 q^{89} + 64 q^{91} - 24 q^{94}+O(q^{100}) $ 4 * q + 2 * q^4 + 6 * q^11 - 8 * q^14 - 2 * q^16 + 16 * q^19 - 16 * q^26 + 12 * q^29 - 16 * q^31 + 6 * q^34 - 12 * q^41 + 12 * q^44 + 24 * q^46 + 18 * q^49 + 8 * q^56 + 18 * q^59 - 16 * q^61 - 4 * q^64 + 24 * q^71 + 16 * q^74 + 8 * q^76 + 16 * q^79 + 2 * q^86 - 36 * q^89 + 64 * q^91 - 24 * q^94

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.46410	+	2.00000i	−1.30931	+	0.755929i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$	−3.46410	+	2.00000i	−1.30931	+	0.755929i	−0.327327	+	0.944911i	$0.606148\pi$
$8$		−	1.00000i		−	0.353553i
$9$		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
$13$	−3.46410	−	2.00000i	−0.960769	−	0.554700i	−0.0643593	−	0.997927i	$-0.520500\pi$
$13$	−3.46410	−	2.00000i	−0.960769	−	0.554700i	−0.896410	+	0.443227i	$0.853834\pi$
$14$	−2.00000	+	3.46410i	−0.534522	+	0.925820i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			3.00000i			0.727607i	0.931476	+	0.363803i	$0.118522\pi$
$17$			3.00000i			0.727607i	−0.931476	+	0.363803i	$0.881478\pi$
$18$		0			0
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$		0			0
$21$		0			0
$22$	2.59808	+	1.50000i	0.553912	+	0.319801i
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.931831	−	0.362892i	$-0.118211\pi$
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.151642	+	0.988436i	$0.451544\pi$
$24$		0			0
$25$		0			0
$26$	−4.00000			−0.784465
$27$		0			0
$28$			4.00000i			0.755929i
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		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	$0.911532\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	1.50000	+	2.59808i	0.257248	+	0.445566i
$35$		0			0
$36$		0			0
$37$			8.00000i			1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$	3.46410	−	2.00000i	0.561951	−	0.324443i
$39$		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
$43$	0.866025	−	0.500000i	0.132068	−	0.0762493i	−0.432511	−	0.901629i	$-0.642372\pi$
$43$	0.866025	−	0.500000i	0.132068	−	0.0762493i	0.564578	+	0.825380i	$0.309039\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	6.00000			0.884652
$47$	−10.3923	+	6.00000i	−1.51587	+	0.875190i	−0.516047	+	0.856560i	$0.672597\pi$
$47$	−10.3923	+	6.00000i	−1.51587	+	0.875190i	−0.999826	+	0.0186297i	$0.994070\pi$
$48$		0			0
$49$	4.50000	−	7.79423i	0.642857	−	1.11346i
$50$		0			0
$51$		0			0
$52$	−3.46410	+	2.00000i	−0.480384	+	0.277350i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$		0			0
$56$	2.00000	+	3.46410i	0.267261	+	0.462910i
$57$		0			0
$58$	5.19615	+	3.00000i	0.682288	+	0.393919i
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	−0.408919	−	0.912571i	$-0.634094\pi$
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	0.994769	−	0.102151i	$-0.0325726\pi$
$60$		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	$-0.337817\pi$
$62$			8.00000i			1.01600i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	3.46410	+	2.00000i	0.423207	+	0.244339i	0.696449	−	0.717607i	$-0.254762\pi$
$67$	3.46410	+	2.00000i	0.423207	+	0.244339i	−0.273241	+	0.961946i	$0.588096\pi$
$68$	2.59808	+	1.50000i	0.315063	+	0.181902i
$69$		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
$73$		−	14.0000i		−	1.63858i	−0.573382	−	0.819288i	$-0.694369\pi$
$73$		−	14.0000i		−	1.63858i	0.573382	−	0.819288i	$-0.305631\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	−10.3923	−	6.00000i	−1.18431	−	0.683763i
$78$		0			0
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$		0			0
$81$		0			0
$82$			6.00000i			0.662589i
$83$	−7.79423	+	4.50000i	−0.855528	+	0.493939i	−0.862512	−	0.506036i	$-0.831110\pi$
$83$	−7.79423	+	4.50000i	−0.855528	+	0.493939i	0.00698436	+	0.999976i	$0.497777\pi$
$84$		0			0
$85$		0			0
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$		0			0
$88$	2.59808	−	1.50000i	0.276956	−	0.159901i
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$		0			0
$91$	16.0000			1.67726
$92$	5.19615	−	3.00000i	0.541736	−	0.312772i
$93$		0			0
$94$	−6.00000	+	10.3923i	−0.618853	+	1.07188i
$95$		0			0
$96$		0			0
$97$	−6.06218	+	3.50000i	−0.615521	+	0.355371i	−0.775123	−	0.631810i	$-0.782312\pi$
$97$	−6.06218	+	3.50000i	−0.615521	+	0.355371i	0.159602	+	0.987181i	$0.448979\pi$
$98$		−	9.00000i		−	0.909137i
$99$		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
$103$	6.92820	+	4.00000i	0.682656	+	0.394132i	0.800855	−	0.598858i	$-0.204379\pi$
$103$	6.92820	+	4.00000i	0.682656	+	0.394132i	−0.118199	+	0.992990i	$0.537712\pi$
$104$	−2.00000	+	3.46410i	−0.196116	+	0.339683i
$105$		0			0
$106$		0			0
$107$		−	12.0000i		−	1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$		−	12.0000i		−	1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$		0			0
$112$	3.46410	+	2.00000i	0.327327	+	0.188982i
$113$	−2.59808	−	1.50000i	−0.244406	−	0.141108i	0.372794	−	0.927914i	$-0.378400\pi$
$113$	−2.59808	−	1.50000i	−0.244406	−	0.141108i	−0.617200	+	0.786806i	$0.711733\pi$
$114$		0			0
$115$		0			0
$116$	6.00000			0.557086
$117$		0			0
$118$		−	9.00000i		−	0.828517i
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−6.92820	−	4.00000i	−0.627250	−	0.362143i
$123$		0			0
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$		0			0
$126$		0			0
$127$		−	16.0000i		−	1.41977i	−0.704317	−	0.709885i	$-0.748747\pi$
$127$		−	16.0000i		−	1.41977i	0.704317	−	0.709885i	$-0.251253\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		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
$133$	−13.8564	+	8.00000i	−1.20150	+	0.693688i
$134$	4.00000			0.345547
$135$		0			0
$136$	3.00000			0.257248
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.985577	−	0.169226i	$-0.945873\pi$
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.346235	+	0.938148i	$0.612540\pi$
$138$		0			0
$139$	5.50000	−	9.52628i	0.466504	−	0.808008i	−0.532764	−	0.846264i	$-0.678847\pi$
$139$	5.50000	−	9.52628i	0.466504	−	0.808008i	0.999268	+	0.0382553i	$0.0121800\pi$
$140$		0			0
$141$		0			0
$142$	5.19615	−	3.00000i	0.436051	−	0.251754i
$143$		−	12.0000i		−	1.00349i
$144$		0			0
$145$		0			0
$146$	−7.00000	−	12.1244i	−0.579324	−	1.00342i
$147$		0			0
$148$	6.92820	+	4.00000i	0.569495	+	0.328798i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		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	$0.699945\pi$
$152$		−	4.00000i		−	0.324443i
$153$		0			0
$154$	−12.0000			−0.966988
$155$		0			0
$156$		0			0
$157$	3.46410	+	2.00000i	0.276465	+	0.159617i	0.631822	−	0.775113i	$-0.282307\pi$
$157$	3.46410	+	2.00000i	0.276465	+	0.159617i	−0.355357	+	0.934731i	$0.615641\pi$
$158$	6.92820	+	4.00000i	0.551178	+	0.318223i
$159$		0			0
$160$		0			0
$161$	−24.0000			−1.89146
$162$		0			0
$163$		−	11.0000i		−	0.861586i	−0.902451	−	0.430793i	$-0.858234\pi$
$163$		−	11.0000i		−	0.861586i	0.902451	−	0.430793i	$-0.141766\pi$
$164$	3.00000	+	5.19615i	0.234261	+	0.405751i
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	15.5885	+	9.00000i	1.20627	+	0.696441i	0.961943	−	0.273252i	$-0.0880992\pi$
$167$	15.5885	+	9.00000i	1.20627	+	0.696441i	0.244328	+	0.969693i	$0.421432\pi$
$168$		0			0
$169$	1.50000	+	2.59808i	0.115385	+	0.199852i
$170$		0			0
$171$		0			0
$172$		−	1.00000i		−	0.0762493i
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	−0.684349	−	0.729155i	$-0.739913\pi$
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	0.289292	+	0.957241i	$0.406580\pi$
$174$		0			0
$175$		0			0
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$		0			0
$178$	−7.79423	+	4.50000i	−0.584202	+	0.337289i
$179$	−3.00000			−0.224231			−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000			−0.224231			−0.112115	+	0.993695i	$0.535763\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	13.8564	−	8.00000i	1.02711	−	0.592999i
$183$		0			0
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$		0			0
$186$		0			0
$187$	−7.79423	+	4.50000i	−0.569970	+	0.329073i
$188$			12.0000i			0.875190i
$189$		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
$193$	4.33013	+	2.50000i	0.311689	+	0.179954i	0.647682	−	0.761911i	$-0.275738\pi$
$193$	4.33013	+	2.50000i	0.311689	+	0.179954i	−0.335993	+	0.941865i	$0.609072\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$		0			0
$196$	−4.50000	−	7.79423i	−0.321429	−	0.556731i
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$		0			0
$199$	−2.00000			−0.141776			−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000			−0.141776			−0.0708881	+	0.997484i	$0.522583\pi$
$200$		0			0
$201$		0			0
$202$	10.3923	+	6.00000i	0.731200	+	0.422159i
$203$	−20.7846	−	12.0000i	−1.45879	−	0.842235i
$204$		0			0
$205$		0			0
$206$	8.00000			0.557386
$207$		0			0
$208$			4.00000i			0.277350i
$209$	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
$217$		−	32.0000i		−	2.17230i
$218$	−1.73205	+	1.00000i	−0.117309	+	0.0677285i
$219$		0			0
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	−1.73205	+	1.00000i	−0.115987	+	0.0669650i	−0.556871	−	0.830599i	$-0.687998\pi$
$223$	−1.73205	+	1.00000i	−0.115987	+	0.0669650i	0.440884	+	0.897564i	$0.354665\pi$
$224$	4.00000			0.267261
$225$		0			0
$226$	−3.00000			−0.199557
$227$	23.3827	−	13.5000i	1.55196	−	0.896026i	0.553981	−	0.832529i	$-0.313108\pi$
$227$	23.3827	−	13.5000i	1.55196	−	0.896026i	0.997982	−	0.0634974i	$-0.0202255\pi$
$228$		0			0
$229$	4.00000	−	6.92820i	0.264327	−	0.457829i	−0.703060	−	0.711131i	$-0.748183\pi$
$229$	4.00000	−	6.92820i	0.264327	−	0.457829i	0.967387	+	0.253302i	$0.0815167\pi$
$230$		0			0
$231$		0			0
$232$	5.19615	−	3.00000i	0.341144	−	0.196960i
$233$			15.0000i			0.982683i	0.870967	+	0.491341i	$0.163493\pi$
$233$			15.0000i			0.982683i	−0.870967	+	0.491341i	$0.836507\pi$
$234$		0			0
$235$		0			0
$236$	−4.50000	−	7.79423i	−0.292925	−	0.507361i
$237$		0			0
$238$	−10.3923	−	6.00000i	−0.673633	−	0.388922i
$239$	−9.00000	+	15.5885i	−0.582162	+	1.00833i	0.413061	+	0.910703i	$0.364460\pi$
$239$	−9.00000	+	15.5885i	−0.582162	+	1.00833i	−0.995223	+	0.0976302i	$0.968874\pi$
$240$		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	$-0.482594\pi$
$242$		−	2.00000i		−	0.128565i
$243$		0			0
$244$	−8.00000			−0.512148
$245$		0			0
$246$		0			0
$247$	−13.8564	−	8.00000i	−0.881662	−	0.509028i
$248$	6.92820	+	4.00000i	0.439941	+	0.254000i
$249$		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
$253$			18.0000i			1.13165i
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.59808	+	1.50000i	0.162064	+	0.0935674i	0.578838	−	0.815442i	$-0.303506\pi$
$257$	2.59808	+	1.50000i	0.162064	+	0.0935674i	−0.416775	+	0.909010i	$0.636840\pi$
$258$		0			0
$259$	−16.0000	−	27.7128i	−0.994192	−	1.72199i
$260$		0			0
$261$		0			0
$262$		−	12.0000i		−	0.741362i
$263$	20.7846	−	12.0000i	1.28163	−	0.739952i	0.304487	−	0.952517i	$-0.401515\pi$
$263$	20.7846	−	12.0000i	1.28163	−	0.739952i	0.977147	+	0.212565i	$0.0681817\pi$
$264$		0			0
$265$		0			0
$266$	−8.00000	+	13.8564i	−0.490511	+	0.849591i
$267$		0			0
$268$	3.46410	−	2.00000i	0.211604	−	0.122169i
$269$	−12.0000			−0.731653			−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000			−0.731653			−0.365826	+	0.930683i	$0.619214\pi$
$270$		0			0
$271$	−4.00000			−0.242983			−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000			−0.242983			−0.121491	+	0.992592i	$0.538768\pi$
$272$	2.59808	−	1.50000i	0.157532	−	0.0909509i
$273$		0			0
$274$	−9.00000	+	15.5885i	−0.543710	+	0.941733i
$275$		0			0
$276$		0			0
$277$	1.73205	−	1.00000i	0.104069	−	0.0600842i	−0.447062	−	0.894503i	$-0.647530\pi$
$277$	1.73205	−	1.00000i	0.104069	−	0.0600842i	0.551131	+	0.834419i	$0.314196\pi$
$278$		−	11.0000i		−	0.659736i
$279$		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
$283$	−0.866025	−	0.500000i	−0.0514799	−	0.0297219i	0.474039	−	0.880504i	$-0.342796\pi$
$283$	−0.866025	−	0.500000i	−0.0514799	−	0.0297219i	−0.525519	+	0.850782i	$0.676129\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$		−	24.0000i		−	1.41668i
$288$		0			0
$289$	8.00000			0.470588
$290$		0			0
$291$		0			0
$292$	−12.1244	−	7.00000i	−0.709524	−	0.409644i
$293$	10.3923	+	6.00000i	0.607125	+	0.350524i	0.771839	−	0.635818i	$-0.219337\pi$
$293$	10.3923	+	6.00000i	0.607125	+	0.350524i	−0.164714	+	0.986341i	$0.552670\pi$
$294$		0			0
$295$		0			0
$296$	8.00000			0.464991
$297$		0			0
$298$		−	6.00000i		−	0.347571i
$299$	−12.0000	−	20.7846i	−0.693978	−	1.20201i
$300$		0			0
$301$	−2.00000	+	3.46410i	−0.115278	+	0.199667i
$302$	8.66025	+	5.00000i	0.498342	+	0.287718i
$303$		0			0
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$		0			0
$306$		0			0
$307$		−	1.00000i		−	0.0570730i	−0.999593	−	0.0285365i	$-0.990915\pi$
$307$		−	1.00000i		−	0.0570730i	0.999593	−	0.0285365i	$-0.00908469\pi$
$308$	−10.3923	+	6.00000i	−0.592157	+	0.341882i
$309$		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
$313$	−14.7224	+	8.50000i	−0.832161	+	0.480448i	−0.854592	−	0.519300i	$-0.826193\pi$
$313$	−14.7224	+	8.50000i	−0.832161	+	0.480448i	0.0224310	+	0.999748i	$0.492859\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	8.00000			0.450035
$317$	15.5885	−	9.00000i	0.875535	−	0.505490i	0.00635137	−	0.999980i	$-0.497978\pi$
$317$	15.5885	−	9.00000i	0.875535	−	0.505490i	0.869184	+	0.494489i	$0.164645\pi$
$318$		0			0
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$		0			0
$321$		0			0
$322$	−20.7846	+	12.0000i	−1.15828	+	0.668734i
$323$			12.0000i			0.667698i
$324$		0			0
$325$		0			0
$326$	−5.50000	−	9.52628i	−0.304617	−	0.527612i
$327$		0			0
$328$	5.19615	+	3.00000i	0.286910	+	0.165647i
$329$	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	$0.988071\pi$
$332$			9.00000i			0.493939i
$333$		0			0
$334$	18.0000			0.984916
$335$		0			0
$336$		0			0
$337$	11.2583	+	6.50000i	0.613280	+	0.354078i	0.774248	−	0.632882i	$-0.218128\pi$
$337$	11.2583	+	6.50000i	0.613280	+	0.354078i	−0.160968	+	0.986960i	$0.551462\pi$
$338$	2.59808	+	1.50000i	0.141317	+	0.0815892i
$339$		0			0
$340$		0			0
$341$	−24.0000			−1.29967
$342$		0			0
$343$			8.00000i			0.431959i
$344$	−0.500000	−	0.866025i	−0.0269582	−	0.0466930i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	23.3827	+	13.5000i	1.25525	+	0.724718i	0.972147	−	0.234372i	$-0.0753034\pi$
$347$	23.3827	+	13.5000i	1.25525	+	0.724718i	0.283101	+	0.959090i	$0.408637\pi$
$348$		0			0
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	0.990282	−	0.139072i	$-0.0444119\pi$
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	−0.615581	+	0.788074i	$0.711079\pi$
$350$		0			0
$351$		0			0
$352$		−	3.00000i		−	0.159901i
$353$	−7.79423	+	4.50000i	−0.414845	+	0.239511i	−0.692869	−	0.721063i	$-0.743654\pi$
$353$	−7.79423	+	4.50000i	−0.414845	+	0.239511i	0.278024	+	0.960574i	$0.410320\pi$
$354$		0			0
$355$		0			0
$356$	−4.50000	+	7.79423i	−0.238500	+	0.413093i
$357$		0			0
$358$	−2.59808	+	1.50000i	−0.137313	+	0.0792775i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	1.73205	−	1.00000i	0.0910346	−	0.0525588i
$363$		0			0
$364$	8.00000	−	13.8564i	0.419314	−	0.726273i
$365$		0			0
$366$		0			0
$367$	22.5167	−	13.0000i	1.17536	−	0.678594i	0.220423	−	0.975404i	$-0.429256\pi$
$367$	22.5167	−	13.0000i	1.17536	−	0.678594i	0.954937	+	0.296810i	$0.0959227\pi$
$368$		−	6.00000i		−	0.312772i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	6.92820	+	4.00000i	0.358729	+	0.207112i	0.668523	−	0.743691i	$-0.266927\pi$
$373$	6.92820	+	4.00000i	0.358729	+	0.207112i	−0.309794	+	0.950804i	$0.600260\pi$
$374$	−4.50000	+	7.79423i	−0.232689	+	0.403030i
$375$		0			0
$376$	6.00000	+	10.3923i	0.309426	+	0.535942i
$377$		−	24.0000i		−	1.23606i
$378$		0			0
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$		0			0
$381$		0			0
$382$	5.19615	+	3.00000i	0.265858	+	0.153493i
$383$	−15.5885	−	9.00000i	−0.796533	−	0.459879i	0.0457244	−	0.998954i	$-0.485440\pi$
$383$	−15.5885	−	9.00000i	−0.796533	−	0.459879i	−0.842257	+	0.539076i	$0.818774\pi$
$384$		0			0
$385$		0			0
$386$	5.00000			0.254493
$387$		0			0
$388$			7.00000i			0.355371i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.455150	+	0.788342i
$392$	−7.79423	−	4.50000i	−0.393668	−	0.227284i
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$		0			0
$396$		0			0
$397$			14.0000i			0.702640i	0.936255	+	0.351320i	$0.114267\pi$
$397$			14.0000i			0.702640i	−0.936255	+	0.351320i	$0.885733\pi$
$398$	−1.73205	+	1.00000i	−0.0868199	+	0.0501255i
$399$		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
$403$	27.7128	−	16.0000i	1.38047	−	0.797017i
$404$	12.0000			0.597022
$405$		0			0
$406$	−24.0000			−1.19110
$407$	−20.7846	+	12.0000i	−1.03025	+	0.594818i
$408$		0			0
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	0.454759	+	0.890614i	$0.349725\pi$
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	−0.998674	+	0.0514740i	$0.983608\pi$
$410$		0			0
$411$		0			0
$412$	6.92820	−	4.00000i	0.341328	−	0.197066i
$413$			36.0000i			1.77144i
$414$		0			0
$415$		0			0
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$		0			0
$418$	10.3923	+	6.00000i	0.508304	+	0.293470i
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	−0.954759	−	0.297382i	$-0.903887\pi$
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	0.734919	+	0.678155i	$0.237220\pi$
$420$		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	$-0.451342\pi$
$422$			23.0000i			1.11962i
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	27.7128	+	16.0000i	1.34112	+	0.774294i
$428$	−10.3923	−	6.00000i	−0.502331	−	0.290021i
$429$		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
$433$			7.00000i			0.336399i	0.985753	+	0.168199i	$0.0537952\pi$
$433$			7.00000i			0.336399i	−0.985753	+	0.168199i	$0.946205\pi$
$434$	−16.0000	−	27.7128i	−0.768025	−	1.33026i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	20.7846	+	12.0000i	0.994263	+	0.574038i
$438$		0			0
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	0.983310	−	0.181938i	$-0.0582371\pi$
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	−0.649218	+	0.760602i	$0.724904\pi$
$440$		0			0
$441$		0			0
$442$		−	12.0000i		−	0.570782i
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	−0.303281	−	0.952901i	$-0.598082\pi$
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	0.673596	+	0.739100i	$0.264749\pi$
$444$		0			0
$445$		0			0
$446$	−1.00000	+	1.73205i	−0.0473514	+	0.0820150i
$447$		0			0
$448$	3.46410	−	2.00000i	0.163663	−	0.0944911i
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	−18.0000			−0.847587
$452$	−2.59808	+	1.50000i	−0.122203	+	0.0705541i
$453$		0			0
$454$	13.5000	−	23.3827i	0.633586	−	1.09740i
$455$		0			0
$456$		0			0
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	−0.688686	−	0.725059i	$-0.741812\pi$
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	0.283577	+	0.958950i	$0.408479\pi$
$458$		−	8.00000i		−	0.373815i
$459$		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
$463$	12.1244	+	7.00000i	0.563467	+	0.325318i	0.754536	−	0.656259i	$-0.227862\pi$
$463$	12.1244	+	7.00000i	0.563467	+	0.325318i	−0.191069	+	0.981577i	$0.561195\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$		0			0
$466$	7.50000	+	12.9904i	0.347431	+	0.601768i
$467$		−	9.00000i		−	0.416470i	−0.978079	−	0.208235i	$-0.933228\pi$
$467$		−	9.00000i		−	0.416470i	0.978079	−	0.208235i	$-0.0667719\pi$
$468$		0			0
$469$	−16.0000			−0.738811
$470$		0			0
$471$		0			0
$472$	−7.79423	−	4.50000i	−0.358758	−	0.207129i
$473$	2.59808	+	1.50000i	0.119460	+	0.0689701i
$474$		0			0
$475$		0			0
$476$	−12.0000			−0.550019
$477$		0			0
$478$			18.0000i			0.823301i
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$		0			0
$481$	16.0000	−	27.7128i	0.729537	−	1.26360i
$482$	−22.5167	−	13.0000i	−1.02561	−	0.592134i
$483$		0			0
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$		0			0
$486$		0			0
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$	−6.92820	+	4.00000i	−0.313625	+	0.181071i
$489$		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
$493$	−15.5885	+	9.00000i	−0.702069	+	0.405340i
$494$	−16.0000			−0.719874
$495$		0			0
$496$	8.00000			0.359211
$497$	−20.7846	+	12.0000i	−0.932317	+	0.538274i
$498$		0			0
$499$	5.50000	−	9.52628i	0.246214	−	0.426455i	−0.716258	−	0.697835i	$-0.754147\pi$
$499$	5.50000	−	9.52628i	0.246214	−	0.426455i	0.962472	+	0.271380i	$0.0874801\pi$
$500$		0			0
$501$		0			0
$502$	10.3923	−	6.00000i	0.463831	−	0.267793i
$503$		−	12.0000i		−	0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$		−	12.0000i		−	0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$		0			0
$505$		0			0
$506$	9.00000	+	15.5885i	0.400099	+	0.692991i
$507$		0			0
$508$	−13.8564	−	8.00000i	−0.614779	−	0.354943i
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	0.314459	+	0.949271i	$0.398177\pi$
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	−0.979322	+	0.202306i	$0.935156\pi$
$510$		0			0
$511$	28.0000	+	48.4974i	1.23865	+	2.14540i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	3.00000			0.132324
$515$		0			0
$516$		0			0
$517$	−31.1769	−	18.0000i	−1.37116	−	0.791639i
$518$	−27.7128	−	16.0000i	−1.21763	−	0.703000i
$519$		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
$523$		−	29.0000i		−	1.26808i	−0.773300	−	0.634041i	$-0.781395\pi$
$523$		−	29.0000i		−	1.26808i	0.773300	−	0.634041i	$-0.218605\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$		0			0
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$	−20.7846	−	12.0000i	−0.905392	−	0.522728i
$528$		0			0
$529$	6.50000	+	11.2583i	0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$			16.0000i			0.693688i
$533$	20.7846	−	12.0000i	0.900281	−	0.519778i
$534$		0			0
$535$		0			0
$536$	2.00000	−	3.46410i	0.0863868	−	0.149626i
$537$		0			0
$538$	−10.3923	+	6.00000i	−0.448044	+	0.258678i
$539$	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	$0.444986\pi$
$542$	−3.46410	+	2.00000i	−0.148796	+	0.0859074i
$543$		0			0
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$		0			0
$546$		0			0
$547$	17.3205	−	10.0000i	0.740571	−	0.427569i	−0.0817056	−	0.996657i	$-0.526037\pi$
$547$	17.3205	−	10.0000i	0.740571	−	0.427569i	0.822277	+	0.569087i	$0.192703\pi$
$548$			18.0000i			0.768922i
$549$		0			0
$550$		0			0
$551$	12.0000	+	20.7846i	0.511217	+	0.885454i
$552$		0			0
$553$	−27.7128	−	16.0000i	−1.17847	−	0.680389i
$554$	1.00000	−	1.73205i	0.0424859	−	0.0735878i
$555$		0			0
$556$	−5.50000	−	9.52628i	−0.233252	−	0.404004i
$557$			6.00000i			0.254228i	0.991888	+	0.127114i	$0.0405714\pi$
$557$			6.00000i			0.254228i	−0.991888	+	0.127114i	$0.959429\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$		0			0
$561$		0			0
$562$	−15.5885	−	9.00000i	−0.657559	−	0.379642i
$563$	2.59808	+	1.50000i	0.109496	+	0.0632175i	0.553748	−	0.832684i	$-0.313197\pi$
$563$	2.59808	+	1.50000i	0.109496	+	0.0632175i	−0.444252	+	0.895902i	$0.646530\pi$
$564$		0			0
$565$		0			0
$566$	−1.00000			−0.0420331
$567$		0			0
$568$		−	6.00000i		−	0.251754i
$569$	13.5000	+	23.3827i	0.565949	+	0.980253i	0.996961	+	0.0779066i	$0.0248236\pi$
$569$	13.5000	+	23.3827i	0.565949	+	0.980253i	−0.431011	+	0.902347i	$0.641843\pi$
$570$		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	$-0.00856117\pi$
$572$	−10.3923	−	6.00000i	−0.434524	−	0.250873i
$573$		0			0
$574$	−12.0000	−	20.7846i	−0.500870	−	0.867533i
$575$		0			0
$576$		0			0
$577$			38.0000i			1.58196i	0.611842	+	0.790980i	$0.290429\pi$
$577$			38.0000i			1.58196i	−0.611842	+	0.790980i	$0.709571\pi$
$578$	6.92820	−	4.00000i	0.288175	−	0.166378i
$579$		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
$587$	2.59808	−	1.50000i	0.107234	−	0.0619116i	−0.445424	−	0.895320i	$-0.646947\pi$
$587$	2.59808	−	1.50000i	0.107234	−	0.0619116i	0.552658	+	0.833408i	$0.313614\pi$
$588$		0			0
$589$	−16.0000	+	27.7128i	−0.659269	+	1.14189i
$590$		0			0
$591$		0			0
$592$	6.92820	−	4.00000i	0.284747	−	0.164399i
$593$		−	45.0000i		−	1.84793i	−0.382479	−	0.923964i	$-0.624930\pi$
$593$		−	45.0000i		−	1.84793i	0.382479	−	0.923964i	$-0.375070\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$	−20.7846	−	12.0000i	−0.849946	−	0.490716i
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	−0.989210	−	0.146503i	$-0.953198\pi$
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	0.621480	+	0.783430i	$0.286532\pi$
$600$		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	$0.561149\pi$
$602$			4.00000i			0.163028i
$603$		0			0
$604$	10.0000			0.406894
$605$		0			0
$606$		0			0
$607$	13.8564	+	8.00000i	0.562414	+	0.324710i	0.754114	−	0.656744i	$-0.228067\pi$
$607$	13.8564	+	8.00000i	0.562414	+	0.324710i	−0.191700	+	0.981454i	$0.561400\pi$
$608$	−3.46410	−	2.00000i	−0.140488	−	0.0811107i
$609$		0			0
$610$		0			0
$611$	48.0000			1.94187
$612$		0			0
$613$		−	14.0000i		−	0.565455i	−0.959200	−	0.282727i	$-0.908761\pi$
$613$		−	14.0000i		−	0.565455i	0.959200	−	0.282727i	$-0.0912392\pi$
$614$	−0.500000	−	0.866025i	−0.0201784	−	0.0349499i
$615$		0			0
$616$	−6.00000	+	10.3923i	−0.241747	+	0.418718i
$617$	23.3827	+	13.5000i	0.941351	+	0.543490i	0.890384	−	0.455211i	$-0.150436\pi$
$617$	23.3827	+	13.5000i	0.941351	+	0.543490i	0.0509678	+	0.998700i	$0.483769\pi$
$618$		0			0
$619$	17.5000	+	30.3109i	0.703384	+	1.21830i	0.967271	+	0.253744i	$0.0816620\pi$
$619$	17.5000	+	30.3109i	0.703384	+	1.21830i	−0.263887	+	0.964554i	$0.585005\pi$
$620$		0			0
$621$		0			0
$622$		−	6.00000i		−	0.240578i
$623$	31.1769	−	18.0000i	1.24908	−	0.721155i
$624$		0			0
$625$		0			0
$626$	−8.50000	+	14.7224i	−0.339728	+	0.588427i
$627$		0			0
$628$	3.46410	−	2.00000i	0.138233	−	0.0798087i
$629$	−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	$0.226967\pi$
$632$	6.92820	−	4.00000i	0.275589	−	0.159111i
$633$		0			0
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$		0			0
$636$		0			0
$637$	−31.1769	+	18.0000i	−1.23527	+	0.713186i
$638$			18.0000i			0.712627i
$639$		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
$643$	19.9186	+	11.5000i	0.785512	+	0.453516i	0.838380	−	0.545086i	$-0.183503\pi$
$643$	19.9186	+	11.5000i	0.785512	+	0.453516i	−0.0528680	+	0.998602i	$0.516836\pi$
$644$	−12.0000	+	20.7846i	−0.472866	+	0.819028i
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$		−	12.0000i		−	0.471769i	−0.971781	−	0.235884i	$-0.924201\pi$
$647$		−	12.0000i		−	0.471769i	0.971781	−	0.235884i	$-0.0757987\pi$
$648$		0			0
$649$	27.0000			1.05984
$650$		0			0
$651$		0			0
$652$	−9.52628	−	5.50000i	−0.373078	−	0.215397i
$653$	20.7846	+	12.0000i	0.813365	+	0.469596i	0.848123	−	0.529799i	$-0.177733\pi$
$653$	20.7846	+	12.0000i	0.813365	+	0.469596i	−0.0347583	+	0.999396i	$0.511066\pi$
$654$		0			0
$655$		0			0
$656$	6.00000			0.234261
$657$		0			0
$658$		−	48.0000i		−	1.87123i
$659$	22.5000	+	38.9711i	0.876476	+	1.51810i	0.855183	+	0.518327i	$0.173445\pi$
$659$	22.5000	+	38.9711i	0.876476	+	1.51810i	0.0212930	+	0.999773i	$0.493222\pi$
$660$		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	$0.104366\pi$
$662$	−14.7224	−	8.50000i	−0.572204	−	0.330362i
$663$		0			0
$664$	4.50000	+	7.79423i	0.174634	+	0.302475i
$665$		0			0
$666$		0			0
$667$			36.0000i			1.39393i
$668$	15.5885	−	9.00000i	0.603136	−	0.348220i
$669$		0			0
$670$		0			0
$671$	12.0000	−	20.7846i	0.463255	−	0.802381i
$672$		0			0
$673$	39.8372	−	23.0000i	1.53561	−	0.886585i	0.536522	−	0.843886i	$-0.319738\pi$
$673$	39.8372	−	23.0000i	1.53561	−	0.886585i	0.999088	−	0.0426985i	$-0.0135955\pi$
$674$	13.0000			0.500741
$675$		0			0
$676$	3.00000			0.115385
$677$	−15.5885	+	9.00000i	−0.599113	+	0.345898i	−0.768693	−	0.639618i	$-0.779092\pi$
$677$	−15.5885	+	9.00000i	−0.599113	+	0.345898i	0.169580	+	0.985517i	$0.445759\pi$
$678$		0			0
$679$	14.0000	−	24.2487i	0.537271	−	0.930580i
$680$		0			0
$681$		0			0
$682$	−20.7846	+	12.0000i	−0.795884	+	0.459504i
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$		0			0
$685$		0			0
$686$	4.00000	+	6.92820i	0.152721	+	0.264520i
$687$		0			0
$688$	−0.866025	−	0.500000i	−0.0330169	−	0.0190623i
$689$		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	$0.715633\pi$
$692$			6.00000i			0.228086i
$693$		0			0
$694$	27.0000			1.02491
$695$		0			0
$696$		0			0
$697$	−15.5885	−	9.00000i	−0.590455	−	0.340899i
$698$	12.1244	+	7.00000i	0.458914	+	0.264954i
$699$		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
$703$			32.0000i			1.20690i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	−4.50000	+	7.79423i	−0.169360	+	0.293340i
$707$	−41.5692	−	24.0000i	−1.56337	−	0.902613i
$708$		0			0
$709$	−26.0000	−	45.0333i	−0.976450	−	1.69126i	−0.675063	−	0.737760i	$-0.735884\pi$
$709$	−26.0000	−	45.0333i	−0.976450	−	1.69126i	−0.301388	−	0.953502i	$-0.597450\pi$
$710$		0			0
$711$		0			0
$712$			9.00000i			0.337289i
$713$	−41.5692	+	24.0000i	−1.55678	+	0.898807i
$714$		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	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$		0			0
$721$	−32.0000			−1.19174
$722$	−2.59808	+	1.50000i	−0.0966904	+	0.0558242i
$723$		0			0
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$		0			0
$726$		0			0
$727$	12.1244	−	7.00000i	0.449667	−	0.259616i	−0.258022	−	0.966139i	$-0.583071\pi$
$727$	12.1244	−	7.00000i	0.449667	−	0.259616i	0.707690	+	0.706523i	$0.249737\pi$
$728$		−	16.0000i		−	0.592999i
$729$		0			0
$730$		0			0
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$		0			0
$733$	−3.46410	−	2.00000i	−0.127950	−	0.0738717i	0.434659	−	0.900595i	$-0.356869\pi$
$733$	−3.46410	−	2.00000i	−0.127950	−	0.0738717i	−0.562609	+	0.826723i	$0.690202\pi$
$734$	13.0000	−	22.5167i	0.479839	−	0.831105i
$735$		0			0
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$			12.0000i			0.442026i
$738$		0			0
$739$	25.0000			0.919640			0.459820	−	0.888012i	$-0.347914\pi$
$739$	25.0000			0.919640			0.459820	+	0.888012i	$0.347914\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$743$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$744$		0			0
$745$		0			0
$746$	8.00000			0.292901
$747$		0			0
$748$			9.00000i			0.329073i
$749$	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	$-0.0463382\pi$
$752$	10.3923	+	6.00000i	0.378968	+	0.218797i
$753$		0			0
$754$	−12.0000	−	20.7846i	−0.437014	−	0.756931i
$755$		0			0
$756$		0			0
$757$			20.0000i			0.726912i	0.931611	+	0.363456i	$0.118403\pi$
$757$			20.0000i			0.726912i	−0.931611	+	0.363456i	$0.881597\pi$
$758$	−25.1147	+	14.5000i	−0.912208	+	0.526664i
$759$		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
$763$	6.92820	−	4.00000i	0.250818	−	0.144810i
$764$	6.00000			0.217072
$765$		0			0
$766$	−18.0000			−0.650366
$767$	−31.1769	+	18.0000i	−1.12573	+	0.649942i
$768$		0			0
$769$	2.50000	−	4.33013i	0.0901523	−	0.156148i	−0.817423	−	0.576038i	$-0.804598\pi$
$769$	2.50000	−	4.33013i	0.0901523	−	0.156148i	0.907575	+	0.419890i	$0.137931\pi$
$770$		0			0
$771$		0			0
$772$	4.33013	−	2.50000i	0.155845	−	0.0899770i
$773$		−	42.0000i		−	1.51064i	−0.655359	−	0.755318i	$-0.727483\pi$
$773$		−	42.0000i		−	1.51064i	0.655359	−	0.755318i	$-0.272517\pi$
$774$		0			0
$775$		0			0
$776$	3.50000	+	6.06218i	0.125643	+	0.217620i
$777$		0			0
$778$	5.19615	+	3.00000i	0.186291	+	0.107555i
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$			18.0000i			0.643679i
$783$		0			0
$784$	−9.00000			−0.321429
$785$		0			0
$786$		0			0
$787$	3.46410	+	2.00000i	0.123482	+	0.0712923i	0.560469	−	0.828176i	$-0.310621\pi$
$787$	3.46410	+	2.00000i	0.123482	+	0.0712923i	−0.436987	+	0.899468i	$0.643954\pi$
$788$	15.5885	+	9.00000i	0.555316	+	0.320612i
$789$		0			0
$790$		0			0
$791$	12.0000			0.426671
$792$		0			0
$793$			32.0000i			1.13635i
$794$	7.00000	+	12.1244i	0.248421	+	0.430277i
$795$		0			0
$796$	−1.00000	+	1.73205i	−0.0354441	+	0.0613909i
$797$	10.3923	+	6.00000i	0.368114	+	0.212531i	0.672634	−	0.739975i	$-0.265163\pi$
$797$	10.3923	+	6.00000i	0.368114	+	0.212531i	−0.304520	+	0.952506i	$0.598496\pi$
$798$		0			0
$799$	−18.0000	−	31.1769i	−0.636794	−	1.10296i
$800$		0			0
$801$		0			0
$802$			15.0000i			0.529668i
$803$	36.3731	−	21.0000i	1.28358	−	0.741074i
$804$		0			0
$805$		0			0
$806$	16.0000	−	27.7128i	0.563576	−	0.976142i
$807$		0			0
$808$	10.3923	−	6.00000i	0.365600	−	0.211079i
$809$	45.0000			1.58212			0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000			1.58212			0.791058	+	0.611741i	$0.209531\pi$
$810$		0			0
$811$	5.00000			0.175574			0.0877869	−	0.996139i	$-0.472021\pi$
$811$	5.00000			0.175574			0.0877869	+	0.996139i	$0.472021\pi$
$812$	−20.7846	+	12.0000i	−0.729397	+	0.421117i
$813$		0			0
$814$	−12.0000	+	20.7846i	−0.420600	+	0.728500i
$815$		0			0
$816$		0			0
$817$	3.46410	−	2.00000i	0.121194	−	0.0699711i
$818$			22.0000i			0.769212i
$819$		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
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.245295	−	0.969448i	$-0.578885\pi$
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.962215	+	0.272292i	$0.912218\pi$
$824$	4.00000	−	6.92820i	0.139347	−	0.241355i
$825$		0			0
$826$	18.0000	+	31.1769i	0.626300	+	1.08478i
$827$		−	15.0000i		−	0.521601i	−0.965393	−	0.260801i	$-0.916014\pi$
$827$		−	15.0000i		−	0.521601i	0.965393	−	0.260801i	$-0.0839865\pi$
$828$		0			0
$829$	−20.0000			−0.694629			−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000			−0.694629			−0.347314	+	0.937749i	$0.612906\pi$
$830$		0			0
$831$		0			0
$832$	3.46410	+	2.00000i	0.120096	+	0.0693375i
$833$	23.3827	+	13.5000i	0.810162	+	0.467747i
$834$		0			0
$835$		0			0
$836$	12.0000			0.415029
$837$		0			0
$838$			9.00000i			0.310900i
$839$	−24.0000	−	41.5692i	−0.828572	−	1.43513i	−0.899158	−	0.437623i	$-0.855820\pi$
$839$	−24.0000	−	41.5692i	−0.828572	−	1.43513i	0.0705865	−	0.997506i	$-0.477513\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−27.7128	−	16.0000i	−0.955047	−	0.551396i
$843$		0			0
$844$	11.5000	+	19.9186i	0.395846	+	0.685626i
$845$		0			0
$846$		0			0
$847$			8.00000i			0.274883i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−24.0000	+	41.5692i	−0.822709	+	1.42497i
$852$		0			0
$853$	39.8372	−	23.0000i	1.36400	−	0.787505i	0.373845	−	0.927491i	$-0.378039\pi$
$853$	39.8372	−	23.0000i	1.36400	−	0.787505i	0.990153	+	0.139986i	$0.0447058\pi$
$854$	32.0000			1.09502
$855$		0			0
$856$	−12.0000			−0.410152
$857$	23.3827	−	13.5000i	0.798737	−	0.461151i	−0.0442921	−	0.999019i	$-0.514103\pi$
$857$	23.3827	−	13.5000i	0.798737	−	0.461151i	0.843029	+	0.537867i	$0.180770\pi$
$858$		0			0
$859$	−8.00000	+	13.8564i	−0.272956	+	0.472774i	−0.969618	−	0.244626i	$-0.921335\pi$
$859$	−8.00000	+	13.8564i	−0.272956	+	0.472774i	0.696661	+	0.717400i	$0.254668\pi$
$860$		0			0
$861$		0			0
$862$	−5.19615	+	3.00000i	−0.176982	+	0.102180i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$		0			0
$865$		0			0
$866$	3.50000	+	6.06218i	0.118935	+	0.206001i
$867$		0			0
$868$	−27.7128	−	16.0000i	−0.940634	−	0.543075i
$869$	−12.0000	+	20.7846i	−0.407072	+	0.705070i
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$			2.00000i			0.0677285i
$873$		0			0
$874$	24.0000			0.811812
$875$		0			0
$876$		0			0
$877$	13.8564	+	8.00000i	0.467898	+	0.270141i	0.715359	−	0.698757i	$-0.246263\pi$
$877$	13.8564	+	8.00000i	0.467898	+	0.270141i	−0.247462	+	0.968898i	$0.579596\pi$
$878$	12.1244	+	7.00000i	0.409177	+	0.236239i
$879$		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
$883$			13.0000i			0.437485i	0.975783	+	0.218742i	$0.0701954\pi$
$883$			13.0000i			0.437485i	−0.975783	+	0.218742i	$0.929805\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$		0			0
$886$	4.50000	−	7.79423i	0.151180	−	0.261852i
$887$	25.9808	+	15.0000i	0.872349	+	0.503651i	0.868128	−	0.496340i	$-0.165323\pi$
$887$	25.9808	+	15.0000i	0.872349	+	0.503651i	0.00422062	+	0.999991i	$0.498657\pi$
$888$		0			0
$889$	32.0000	+	55.4256i	1.07325	+	1.85892i
$890$		0			0
$891$		0			0
$892$			2.00000i			0.0669650i
$893$	−41.5692	+	24.0000i	−1.39106	+	0.803129i
$894$		0			0
$895$		0			0
$896$	2.00000	−	3.46410i	0.0668153	−	0.115728i
$897$		0			0
$898$	15.5885	−	9.00000i	0.520194	−	0.300334i
$899$	−48.0000			−1.60089
$900$		0			0
$901$		0			0
$902$	−15.5885	+	9.00000i	−0.519039	+	0.299667i
$903$		0			0
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$		0			0
$906$		0			0
$907$	14.7224	−	8.50000i	0.488850	−	0.282238i	−0.235247	−	0.971936i	$-0.575590\pi$
$907$	14.7224	−	8.50000i	0.488850	−	0.282238i	0.724097	+	0.689698i	$0.242257\pi$
$908$		−	27.0000i		−	0.896026i
$909$		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
$913$	−23.3827	−	13.5000i	−0.773854	−	0.446785i
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$		0			0
$916$	−4.00000	−	6.92820i	−0.132164	−	0.228914i
$917$			48.0000i			1.58510i
$918$		0			0
$919$	46.0000			1.51740			0.758700	−	0.651440i	$-0.225835\pi$
$919$	46.0000			1.51740			0.758700	+	0.651440i	$0.225835\pi$
$920$		0			0
$921$		0			0
$922$	−5.19615	−	3.00000i	−0.171126	−	0.0987997i
$923$	−20.7846	−	12.0000i	−0.684134	−	0.394985i
$924$		0			0
$925$		0			0
$926$	14.0000			0.460069
$927$		0			0
$928$		−	6.00000i		−	0.196960i
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	−0.972166	−	0.234294i	$-0.924722\pi$
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	0.283178	−	0.959067i	$-0.408611\pi$
$930$		0			0
$931$	18.0000	−	31.1769i	0.589926	−	1.02178i
$932$	12.9904	+	7.50000i	0.425514	+	0.245671i
$933$		0			0
$934$	−4.50000	−	7.79423i	−0.147244	−	0.255035i
$935$		0			0
$936$		0			0
$937$		−	37.0000i		−	1.20874i	−0.796705	−	0.604369i	$-0.793425\pi$
$937$		−	37.0000i		−	1.20874i	0.796705	−	0.604369i	$-0.206575\pi$
$938$	−13.8564	+	8.00000i	−0.452428	+	0.261209i
$939$		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
$943$	−31.1769	+	18.0000i	−1.01526	+	0.586161i
$944$	−9.00000			−0.292925
$945$		0			0
$946$	3.00000			0.0975384
$947$	7.79423	−	4.50000i	0.253278	−	0.146230i	−0.367986	−	0.929831i	$-0.619953\pi$
$947$	7.79423	−	4.50000i	0.253278	−	0.146230i	0.621264	+	0.783601i	$0.286619\pi$
$948$		0			0
$949$	−28.0000	+	48.4974i	−0.908918	+	1.57429i
$950$		0			0
$951$		0			0
$952$	−10.3923	+	6.00000i	−0.336817	+	0.194461i
$953$		−	27.0000i		−	0.874616i	−0.899312	−	0.437308i	$-0.855932\pi$
$953$		−	27.0000i		−	0.874616i	0.899312	−	0.437308i	$-0.144068\pi$
$954$		0			0
$955$		0			0
$956$	9.00000	+	15.5885i	0.291081	+	0.504167i
$957$		0			0
$958$	10.3923	+	6.00000i	0.335760	+	0.193851i
$959$	36.0000	−	62.3538i	1.16250	−	2.01351i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		−	32.0000i		−	1.03172i
$963$		0			0
$964$	−26.0000			−0.837404
$965$		0			0
$966$		0			0
$967$	24.2487	+	14.0000i	0.779786	+	0.450210i	0.836354	−	0.548189i	$-0.184683\pi$
$967$	24.2487	+	14.0000i	0.779786	+	0.450210i	−0.0565684	+	0.998399i	$0.518016\pi$
$968$	−1.73205	−	1.00000i	−0.0556702	−	0.0321412i
$969$		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
$973$			44.0000i			1.41058i
$974$	1.00000	+	1.73205i	0.0320421	+	0.0554985i
$975$		0			0
$976$	−4.00000	+	6.92820i	−0.128037	+	0.221766i
$977$	−46.7654	−	27.0000i	−1.49616	−	0.863807i	−0.496167	−	0.868227i	$-0.665259\pi$
$977$	−46.7654	−	27.0000i	−1.49616	−	0.863807i	−0.999990	+	0.00442082i	$0.998593\pi$
$978$		0			0
$979$	−13.5000	−	23.3827i	−0.431462	−	0.747314i
$980$		0			0
$981$		0			0
$982$			15.0000i			0.478669i
$983$	46.7654	−	27.0000i	1.49158	−	0.861166i	0.491630	−	0.870804i	$-0.336401\pi$
$983$	46.7654	−	27.0000i	1.49158	−	0.861166i	0.999954	+	0.00963785i	$0.00306787\pi$
$984$		0			0
$985$		0			0
$986$	−9.00000	+	15.5885i	−0.286618	+	0.496438i
$987$		0			0
$988$	−13.8564	+	8.00000i	−0.440831	+	0.254514i
$989$	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	$0.581789\pi$
$992$	6.92820	−	4.00000i	0.219971	−	0.127000i
$993$		0			0
$994$	−12.0000	+	20.7846i	−0.380617	+	0.659248i
$995$		0			0
$996$		0			0
$997$	−8.66025	+	5.00000i	−0.274273	+	0.158352i	−0.630828	−	0.775923i	$-0.717285\pi$
$997$	−8.66025	+	5.00000i	−0.274273	+	0.158352i	0.356555	+	0.934274i	$0.383951\pi$
$998$		−	11.0000i		−	0.348199i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(1.50000 + 2.59808i) q^{11} +(-3.46410 - 2.00000i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.00000i q^{17} +4.00000 q^{19} +(2.59808 + 1.50000i) q^{22} +(5.19615 + 3.00000i) q^{23} -4.00000 q^{26} +4.00000i q^{28} +(3.00000 + 5.19615i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.50000 + 2.59808i) q^{34} +8.00000i q^{37} +(3.46410 - 2.00000i) q^{38} +(-3.00000 + 5.19615i) q^{41} +(0.866025 - 0.500000i) q^{43} +3.00000 q^{44} +6.00000 q^{46} +(-10.3923 + 6.00000i) q^{47} +(4.50000 - 7.79423i) q^{49} +(-3.46410 + 2.00000i) q^{52} +(2.00000 + 3.46410i) q^{56} +(5.19615 + 3.00000i) q^{58} +(4.50000 - 7.79423i) q^{59} +(-4.00000 - 6.92820i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(3.46410 + 2.00000i) q^{67} +(2.59808 + 1.50000i) q^{68} +6.00000 q^{71} -14.0000i q^{73} +(4.00000 + 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-10.3923 - 6.00000i) q^{77} +(4.00000 + 6.92820i) q^{79} +6.00000i q^{82} +(-7.79423 + 4.50000i) q^{83} +(0.500000 - 0.866025i) q^{86} +(2.59808 - 1.50000i) q^{88} -9.00000 q^{89} +16.0000 q^{91} +(5.19615 - 3.00000i) q^{92} +(-6.00000 + 10.3923i) q^{94} +(-6.06218 + 3.50000i) q^{97} -9.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} + 6 q^{11} - 8 q^{14} - 2 q^{16} + 16 q^{19} - 16 q^{26} + 12 q^{29} - 16 q^{31} + 6 q^{34} - 12 q^{41} + 12 q^{44} + 24 q^{46} + 18 q^{49} + 8 q^{56} + 18 q^{59} - 16 q^{61} - 4 q^{64} + 24 q^{71} + 16 q^{74} + 8 q^{76} + 16 q^{79} + 2 q^{86} - 36 q^{89} + 64 q^{91} - 24 q^{94}+O(q^{100}) \) 4 * q + 2 * q^4 + 6 * q^11 - 8 * q^14 - 2 * q^16 + 16 * q^19 - 16 * q^26 + 12 * q^29 - 16 * q^31 + 6 * q^34 - 12 * q^41 + 12 * q^44 + 24 * q^46 + 18 * q^49 + 8 * q^56 + 18 * q^59 - 16 * q^61 - 4 * q^64 + 24 * q^71 + 16 * q^74 + 8 * q^76 + 16 * q^79 + 2 * q^86 - 36 * q^89 + 64 * q^91 - 24 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more