LMFDB - Embedded newform 1890.2.g.l.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(379,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1890.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.g (of order $2$, degree $1$, 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1890.379
Dual form			1890.2.g.l.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +(1.00000 + 2.00000i) q^{10} -2.00000i q^{13} +1.00000 q^{14} +1.00000 q^{16} -8.00000i q^{17} -4.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} +4.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +2.00000 q^{26} +1.00000i q^{28} -7.00000 q^{29} +1.00000 q^{31} +1.00000i q^{32} +8.00000 q^{34} +(-1.00000 - 2.00000i) q^{35} -7.00000i q^{37} -4.00000i q^{38} +(-1.00000 - 2.00000i) q^{40} -9.00000 q^{41} +2.00000i q^{43} -4.00000 q^{46} -7.00000i q^{47} -1.00000 q^{49} +(4.00000 + 3.00000i) q^{50} +2.00000i q^{52} +6.00000i q^{53} -1.00000 q^{56} -7.00000i q^{58} -1.00000 q^{59} +3.00000 q^{61} +1.00000i q^{62} -1.00000 q^{64} +(-2.00000 - 4.00000i) q^{65} +4.00000i q^{67} +8.00000i q^{68} +(2.00000 - 1.00000i) q^{70} -3.00000 q^{71} -13.0000i q^{73} +7.00000 q^{74} +4.00000 q^{76} +16.0000 q^{79} +(2.00000 - 1.00000i) q^{80} -9.00000i q^{82} +6.00000i q^{83} +(-8.00000 - 16.0000i) q^{85} -2.00000 q^{86} -10.0000 q^{89} -2.00000 q^{91} -4.00000i q^{92} +7.00000 q^{94} +(-8.00000 + 4.00000i) q^{95} -6.00000i q^{97} -1.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 4 q^{5}+O(q^{10}) $ 2 * q - 2 * q^4 + 4 * q^5	$ 2 q - 2 q^{4} + 4 q^{5} + 2 q^{10} + 2 q^{14} + 2 q^{16} - 8 q^{19} - 4 q^{20} + 6 q^{25} + 4 q^{26} - 14 q^{29} + 2 q^{31} + 16 q^{34} - 2 q^{35} - 2 q^{40} - 18 q^{41} - 8 q^{46} - 2 q^{49} + 8 q^{50} - 2 q^{56} - 2 q^{59} + 6 q^{61} - 2 q^{64} - 4 q^{65} + 4 q^{70} - 6 q^{71} + 14 q^{74} + 8 q^{76} + 32 q^{79} + 4 q^{80} - 16 q^{85} - 4 q^{86} - 20 q^{89} - 4 q^{91} + 14 q^{94} - 16 q^{95}+O(q^{100}) $ 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^10 + 2 * q^14 + 2 * q^16 - 8 * q^19 - 4 * q^20 + 6 * q^25 + 4 * q^26 - 14 * q^29 + 2 * q^31 + 16 * q^34 - 2 * q^35 - 2 * q^40 - 18 * q^41 - 8 * q^46 - 2 * q^49 + 8 * q^50 - 2 * q^56 - 2 * q^59 + 6 * q^61 - 2 * q^64 - 4 * q^65 + 4 * q^70 - 6 * q^71 + 14 * q^74 + 8 * q^76 + 32 * q^79 + 4 * q^80 - 16 * q^85 - 4 * q^86 - 20 * q^89 - 4 * q^91 + 14 * q^94 - 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	1.00000			0.250000
$17$		−	8.00000i		−	1.94029i	−0.242536	−	0.970143i	$-0.577979\pi$
$17$		−	8.00000i		−	1.94029i	0.242536	−	0.970143i	$-0.422021\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	−2.00000	+	1.00000i	−0.447214	+	0.223607i
$21$		0			0
$22$		0			0
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$	2.00000			0.392232
$27$		0			0
$28$			1.00000i			0.188982i
$29$	−7.00000			−1.29987			−0.649934	−	0.759991i	$-0.725203\pi$
$29$	−7.00000			−1.29987			−0.649934	+	0.759991i	$0.725203\pi$
$30$		0			0
$31$	1.00000			0.179605			0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000			0.179605			0.0898027	+	0.995960i	$0.471376\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	8.00000			1.37199
$35$	−1.00000	−	2.00000i	−0.169031	−	0.338062i
$36$		0			0
$37$		−	7.00000i		−	1.15079i	−0.817875	−	0.575396i	$-0.804848\pi$
$37$		−	7.00000i		−	1.15079i	0.817875	−	0.575396i	$-0.195152\pi$
$38$		−	4.00000i		−	0.648886i
$39$		0			0
$40$	−1.00000	−	2.00000i	−0.158114	−	0.316228i
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$		0			0
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$		0			0
$45$		0			0
$46$	−4.00000			−0.589768
$47$		−	7.00000i		−	1.02105i	−0.859861	−	0.510527i	$-0.829450\pi$
$47$		−	7.00000i		−	1.02105i	0.859861	−	0.510527i	$-0.170550\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	4.00000	+	3.00000i	0.565685	+	0.424264i
$51$		0			0
$52$			2.00000i			0.277350i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		0			0
$55$		0			0
$56$	−1.00000			−0.133631
$57$		0			0
$58$		−	7.00000i		−	0.919145i
$59$	−1.00000			−0.130189			−0.0650945	−	0.997879i	$-0.520735\pi$
$59$	−1.00000			−0.130189			−0.0650945	+	0.997879i	$0.520735\pi$
$60$		0			0
$61$	3.00000			0.384111			0.192055	−	0.981384i	$-0.438485\pi$
$61$	3.00000			0.384111			0.192055	+	0.981384i	$0.438485\pi$
$62$			1.00000i			0.127000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.00000	−	4.00000i	−0.248069	−	0.496139i
$66$		0			0
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$			8.00000i			0.970143i
$69$		0			0
$70$	2.00000	−	1.00000i	0.239046	−	0.119523i
$71$	−3.00000			−0.356034			−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000			−0.356034			−0.178017	+	0.984027i	$0.556968\pi$
$72$		0			0
$73$		−	13.0000i		−	1.52153i	−0.649025	−	0.760767i	$-0.724823\pi$
$73$		−	13.0000i		−	1.52153i	0.649025	−	0.760767i	$-0.275177\pi$
$74$	7.00000			0.813733
$75$		0			0
$76$	4.00000			0.458831
$77$		0			0
$78$		0			0
$79$	16.0000			1.80014			0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000			1.80014			0.900070	+	0.435745i	$0.143515\pi$
$80$	2.00000	−	1.00000i	0.223607	−	0.111803i
$81$		0			0
$82$		−	9.00000i		−	0.993884i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		0			0
$85$	−8.00000	−	16.0000i	−0.867722	−	1.73544i
$86$	−2.00000			−0.215666
$87$		0			0
$88$		0			0
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$	−2.00000			−0.209657
$92$		−	4.00000i		−	0.417029i
$93$		0			0
$94$	7.00000			0.721995
$95$	−8.00000	+	4.00000i	−0.820783	+	0.410391i
$96$		0			0
$97$		−	6.00000i		−	0.609208i	−0.952479	−	0.304604i	$-0.901476\pi$
$97$		−	6.00000i		−	0.609208i	0.952479	−	0.304604i	$-0.0985241\pi$
$98$		−	1.00000i		−	0.101015i
$99$		0			0
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		0			0
$103$		−	14.0000i		−	1.37946i	−0.724066	−	0.689730i	$-0.757729\pi$
$103$		−	14.0000i		−	1.37946i	0.724066	−	0.689730i	$-0.242271\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	−6.00000			−0.582772
$107$		−	7.00000i		−	0.676716i	−0.941018	−	0.338358i	$-0.890129\pi$
$107$		−	7.00000i		−	0.676716i	0.941018	−	0.338358i	$-0.109871\pi$
$108$		0			0
$109$	16.0000			1.53252			0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000			1.53252			0.766261	+	0.642529i	$0.222115\pi$
$110$		0			0
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$			1.00000i			0.0940721i	0.998893	+	0.0470360i	$0.0149776\pi$
$113$			1.00000i			0.0940721i	−0.998893	+	0.0470360i	$0.985022\pi$
$114$		0			0
$115$	4.00000	+	8.00000i	0.373002	+	0.746004i
$116$	7.00000			0.649934
$117$		0			0
$118$		−	1.00000i		−	0.0920575i
$119$	−8.00000			−0.733359
$120$		0			0
$121$	−11.0000			−1.00000
$122$			3.00000i			0.271607i
$123$		0			0
$124$	−1.00000			−0.0898027
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$		−	13.0000i		−	1.15356i	−0.816898	−	0.576782i	$-0.804308\pi$
$127$		−	13.0000i		−	1.15356i	0.816898	−	0.576782i	$-0.195692\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	4.00000	−	2.00000i	0.350823	−	0.175412i
$131$	13.0000			1.13582			0.567908	−	0.823092i	$-0.307753\pi$
$131$	13.0000			1.13582			0.567908	+	0.823092i	$0.307753\pi$
$132$		0			0
$133$			4.00000i			0.346844i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	−8.00000			−0.685994
$137$			19.0000i			1.62328i	0.584158	+	0.811640i	$0.301425\pi$
$137$			19.0000i			1.62328i	−0.584158	+	0.811640i	$0.698575\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$	1.00000	+	2.00000i	0.0845154	+	0.169031i
$141$		0			0
$142$		−	3.00000i		−	0.251754i
$143$		0			0
$144$		0			0
$145$	−14.0000	+	7.00000i	−1.16264	+	0.581318i
$146$	13.0000			1.07589
$147$		0			0
$148$			7.00000i			0.575396i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$		0			0
$151$	18.0000			1.46482			0.732410	−	0.680864i	$-0.238396\pi$
$151$	18.0000			1.46482			0.732410	+	0.680864i	$0.238396\pi$
$152$			4.00000i			0.324443i
$153$		0			0
$154$		0			0
$155$	2.00000	−	1.00000i	0.160644	−	0.0803219i
$156$		0			0
$157$			6.00000i			0.478852i	0.970915	+	0.239426i	$0.0769593\pi$
$157$			6.00000i			0.478852i	−0.970915	+	0.239426i	$0.923041\pi$
$158$			16.0000i			1.27289i
$159$		0			0
$160$	1.00000	+	2.00000i	0.0790569	+	0.158114i
$161$	4.00000			0.315244
$162$		0			0
$163$		−	6.00000i		−	0.469956i	−0.972001	−	0.234978i	$-0.924498\pi$
$163$		−	6.00000i		−	0.469956i	0.972001	−	0.234978i	$-0.0755019\pi$
$164$	9.00000			0.702782
$165$		0			0
$166$	−6.00000			−0.465690
$167$		−	15.0000i		−	1.16073i	−0.814355	−	0.580367i	$-0.802909\pi$
$167$		−	15.0000i		−	1.16073i	0.814355	−	0.580367i	$-0.197091\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	16.0000	−	8.00000i	1.22714	−	0.613572i
$171$		0			0
$172$		−	2.00000i		−	0.152499i
$173$			9.00000i			0.684257i	0.939653	+	0.342129i	$0.111148\pi$
$173$			9.00000i			0.684257i	−0.939653	+	0.342129i	$0.888852\pi$
$174$		0			0
$175$	−4.00000	−	3.00000i	−0.302372	−	0.226779i
$176$		0			0
$177$		0			0
$178$		−	10.0000i		−	0.749532i
$179$	16.0000			1.19590			0.597948	−	0.801535i	$-0.295983\pi$
$179$	16.0000			1.19590			0.597948	+	0.801535i	$0.295983\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$		−	2.00000i		−	0.148250i
$183$		0			0
$184$	4.00000			0.294884
$185$	−7.00000	−	14.0000i	−0.514650	−	1.02930i
$186$		0			0
$187$		0			0
$188$			7.00000i			0.510527i
$189$		0			0
$190$	−4.00000	−	8.00000i	−0.290191	−	0.580381i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$			26.0000i			1.87152i	0.352636	+	0.935760i	$0.385285\pi$
$193$			26.0000i			1.87152i	−0.352636	+	0.935760i	$0.614715\pi$
$194$	6.00000			0.430775
$195$		0			0
$196$	1.00000			0.0714286
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−4.00000	−	3.00000i	−0.282843	−	0.212132i
$201$		0			0
$202$		−	6.00000i		−	0.422159i
$203$			7.00000i			0.491304i
$204$		0			0
$205$	−18.0000	+	9.00000i	−1.25717	+	0.628587i
$206$	14.0000			0.975426
$207$		0			0
$208$		−	2.00000i		−	0.138675i
$209$		0			0
$210$		0			0
$211$	−3.00000			−0.206529			−0.103264	−	0.994654i	$-0.532929\pi$
$211$	−3.00000			−0.206529			−0.103264	+	0.994654i	$0.532929\pi$
$212$		−	6.00000i		−	0.412082i
$213$		0			0
$214$	7.00000			0.478510
$215$	2.00000	+	4.00000i	0.136399	+	0.272798i
$216$		0			0
$217$		−	1.00000i		−	0.0678844i
$218$			16.0000i			1.08366i
$219$		0			0
$220$		0			0
$221$	−16.0000			−1.07628
$222$		0			0
$223$			28.0000i			1.87502i	0.347960	+	0.937509i	$0.386874\pi$
$223$			28.0000i			1.87502i	−0.347960	+	0.937509i	$0.613126\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−1.00000			−0.0665190
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	−8.00000	+	4.00000i	−0.527504	+	0.263752i
$231$		0			0
$232$			7.00000i			0.459573i
$233$		−	7.00000i		−	0.458585i	−0.973358	−	0.229293i	$-0.926359\pi$
$233$		−	7.00000i		−	0.458585i	0.973358	−	0.229293i	$-0.0736413\pi$
$234$		0			0
$235$	−7.00000	−	14.0000i	−0.456630	−	0.913259i
$236$	1.00000			0.0650945
$237$		0			0
$238$		−	8.00000i		−	0.518563i
$239$	5.00000			0.323423			0.161712	−	0.986838i	$-0.448299\pi$
$239$	5.00000			0.323423			0.161712	+	0.986838i	$0.448299\pi$
$240$		0			0
$241$	30.0000			1.93247			0.966235	−	0.257663i	$-0.0829523\pi$
$241$	30.0000			1.93247			0.966235	+	0.257663i	$0.0829523\pi$
$242$		−	11.0000i		−	0.707107i
$243$		0			0
$244$	−3.00000			−0.192055
$245$	−2.00000	+	1.00000i	−0.127775	+	0.0638877i
$246$		0			0
$247$			8.00000i			0.509028i
$248$		−	1.00000i		−	0.0635001i
$249$		0			0
$250$	11.0000	+	2.00000i	0.695701	+	0.126491i
$251$	−20.0000			−1.26239			−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000			−1.26239			−0.631194	+	0.775625i	$0.717435\pi$
$252$		0			0
$253$		0			0
$254$	13.0000			0.815693
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	24.0000i		−	1.49708i	−0.663090	−	0.748539i	$-0.730755\pi$
$257$		−	24.0000i		−	1.49708i	0.663090	−	0.748539i	$-0.269245\pi$
$258$		0			0
$259$	−7.00000			−0.434959
$260$	2.00000	+	4.00000i	0.124035	+	0.248069i
$261$		0			0
$262$			13.0000i			0.803143i
$263$			12.0000i			0.739952i	0.929041	+	0.369976i	$0.120634\pi$
$263$			12.0000i			0.739952i	−0.929041	+	0.369976i	$0.879366\pi$
$264$		0			0
$265$	6.00000	+	12.0000i	0.368577	+	0.737154i
$266$	−4.00000			−0.245256
$267$		0			0
$268$		−	4.00000i		−	0.244339i
$269$	−4.00000			−0.243884			−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000			−0.243884			−0.121942	+	0.992537i	$0.538912\pi$
$270$		0			0
$271$	−21.0000			−1.27566			−0.637830	−	0.770178i	$-0.720168\pi$
$271$	−21.0000			−1.27566			−0.637830	+	0.770178i	$0.720168\pi$
$272$		−	8.00000i		−	0.485071i
$273$		0			0
$274$	−19.0000			−1.14783
$275$		0			0
$276$		0			0
$277$		−	10.0000i		−	0.600842i	−0.953807	−	0.300421i	$-0.902873\pi$
$277$		−	10.0000i		−	0.600842i	0.953807	−	0.300421i	$-0.0971271\pi$
$278$			14.0000i			0.839664i
$279$		0			0
$280$	−2.00000	+	1.00000i	−0.119523	+	0.0597614i
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$		0			0
$283$		−	7.00000i		−	0.416107i	−0.978117	−	0.208053i	$-0.933287\pi$
$283$		−	7.00000i		−	0.416107i	0.978117	−	0.208053i	$-0.0667128\pi$
$284$	3.00000			0.178017
$285$		0			0
$286$		0			0
$287$			9.00000i			0.531253i
$288$		0			0
$289$	−47.0000			−2.76471
$290$	−7.00000	−	14.0000i	−0.411054	−	0.822108i
$291$		0			0
$292$			13.0000i			0.760767i
$293$			15.0000i			0.876309i	0.898900	+	0.438155i	$0.144368\pi$
$293$			15.0000i			0.876309i	−0.898900	+	0.438155i	$0.855632\pi$
$294$		0			0
$295$	−2.00000	+	1.00000i	−0.116445	+	0.0582223i
$296$	−7.00000			−0.406867
$297$		0			0
$298$			6.00000i			0.347571i
$299$	8.00000			0.462652
$300$		0			0
$301$	2.00000			0.115278
$302$			18.0000i			1.03578i
$303$		0			0
$304$	−4.00000			−0.229416
$305$	6.00000	−	3.00000i	0.343559	−	0.171780i
$306$		0			0
$307$			28.0000i			1.59804i	0.601302	+	0.799022i	$0.294649\pi$
$307$			28.0000i			1.59804i	−0.601302	+	0.799022i	$0.705351\pi$
$308$		0			0
$309$		0			0
$310$	1.00000	+	2.00000i	0.0567962	+	0.113592i
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$		0			0
$313$		−	10.0000i		−	0.565233i	−0.959233	−	0.282617i	$-0.908798\pi$
$313$		−	10.0000i		−	0.565233i	0.959233	−	0.282617i	$-0.0912024\pi$
$314$	−6.00000			−0.338600
$315$		0			0
$316$	−16.0000			−0.900070
$317$			10.0000i			0.561656i	0.959758	+	0.280828i	$0.0906090\pi$
$317$			10.0000i			0.561656i	−0.959758	+	0.280828i	$0.909391\pi$
$318$		0			0
$319$		0			0
$320$	−2.00000	+	1.00000i	−0.111803	+	0.0559017i
$321$		0			0
$322$			4.00000i			0.222911i
$323$			32.0000i			1.78053i
$324$		0			0
$325$	−8.00000	−	6.00000i	−0.443760	−	0.332820i
$326$	6.00000			0.332309
$327$		0			0
$328$			9.00000i			0.496942i
$329$	−7.00000			−0.385922
$330$		0			0
$331$	−7.00000			−0.384755			−0.192377	−	0.981321i	$-0.561620\pi$
$331$	−7.00000			−0.384755			−0.192377	+	0.981321i	$0.561620\pi$
$332$		−	6.00000i		−	0.329293i
$333$		0			0
$334$	15.0000			0.820763
$335$	4.00000	+	8.00000i	0.218543	+	0.437087i
$336$		0			0
$337$		−	4.00000i		−	0.217894i	−0.994048	−	0.108947i	$-0.965252\pi$
$337$		−	4.00000i		−	0.217894i	0.994048	−	0.108947i	$-0.0347479\pi$
$338$			9.00000i			0.489535i
$339$		0			0
$340$	8.00000	+	16.0000i	0.433861	+	0.867722i
$341$		0			0
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	2.00000			0.107833
$345$		0			0
$346$	−9.00000			−0.483843
$347$			3.00000i			0.161048i	0.996753	+	0.0805242i	$0.0256594\pi$
$347$			3.00000i			0.161048i	−0.996753	+	0.0805242i	$0.974341\pi$
$348$		0			0
$349$	30.0000			1.60586			0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000			1.60586			0.802932	+	0.596071i	$0.203272\pi$
$350$	3.00000	−	4.00000i	0.160357	−	0.213809i
$351$		0			0
$352$		0			0
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$	−6.00000	+	3.00000i	−0.318447	+	0.159223i
$356$	10.0000			0.529999
$357$		0			0
$358$			16.0000i			0.845626i
$359$	−20.0000			−1.05556			−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000			−1.05556			−0.527780	+	0.849381i	$0.676975\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$			5.00000i			0.262794i
$363$		0			0
$364$	2.00000			0.104828
$365$	−13.0000	−	26.0000i	−0.680451	−	1.36090i
$366$		0			0
$367$			14.0000i			0.730794i	0.930852	+	0.365397i	$0.119067\pi$
$367$			14.0000i			0.730794i	−0.930852	+	0.365397i	$0.880933\pi$
$368$			4.00000i			0.208514i
$369$		0			0
$370$	14.0000	−	7.00000i	0.727825	−	0.363913i
$371$	6.00000			0.311504
$372$		0			0
$373$		−	13.0000i		−	0.673114i	−0.941663	−	0.336557i	$-0.890737\pi$
$373$		−	13.0000i		−	0.673114i	0.941663	−	0.336557i	$-0.109263\pi$
$374$		0			0
$375$		0			0
$376$	−7.00000			−0.360997
$377$			14.0000i			0.721037i
$378$		0			0
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$	8.00000	−	4.00000i	0.410391	−	0.205196i
$381$		0			0
$382$			8.00000i			0.409316i
$383$		−	24.0000i		−	1.22634i	−0.789950	−	0.613171i	$-0.789894\pi$
$383$		−	24.0000i		−	1.22634i	0.789950	−	0.613171i	$-0.210106\pi$
$384$		0			0
$385$		0			0
$386$	−26.0000			−1.32337
$387$		0			0
$388$			6.00000i			0.304604i
$389$	−27.0000			−1.36895			−0.684477	−	0.729034i	$-0.739969\pi$
$389$	−27.0000			−1.36895			−0.684477	+	0.729034i	$0.739969\pi$
$390$		0			0
$391$	32.0000			1.61831
$392$			1.00000i			0.0505076i
$393$		0			0
$394$	8.00000			0.403034
$395$	32.0000	−	16.0000i	1.61009	−	0.805047i
$396$		0			0
$397$			14.0000i			0.702640i	0.936255	+	0.351320i	$0.114267\pi$
$397$			14.0000i			0.702640i	−0.936255	+	0.351320i	$0.885733\pi$
$398$		0			0
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−36.0000			−1.79775			−0.898877	−	0.438201i	$-0.855616\pi$
$401$	−36.0000			−1.79775			−0.898877	+	0.438201i	$0.855616\pi$
$402$		0			0
$403$		−	2.00000i		−	0.0996271i
$404$	6.00000			0.298511
$405$		0			0
$406$	−7.00000			−0.347404
$407$		0			0
$408$		0			0
$409$	32.0000			1.58230			0.791149	−	0.611623i	$-0.209483\pi$
$409$	32.0000			1.58230			0.791149	+	0.611623i	$0.209483\pi$
$410$	−9.00000	−	18.0000i	−0.444478	−	0.888957i
$411$		0			0
$412$			14.0000i			0.689730i
$413$			1.00000i			0.0492068i
$414$		0			0
$415$	6.00000	+	12.0000i	0.294528	+	0.589057i
$416$	2.00000			0.0980581
$417$		0			0
$418$		0			0
$419$	35.0000			1.70986			0.854931	−	0.518742i	$-0.173599\pi$
$419$	35.0000			1.70986			0.854931	+	0.518742i	$0.173599\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$		−	3.00000i		−	0.146038i
$423$		0			0
$424$	6.00000			0.291386
$425$	−32.0000	−	24.0000i	−1.55223	−	1.16417i
$426$		0			0
$427$		−	3.00000i		−	0.145180i
$428$			7.00000i			0.338358i
$429$		0			0
$430$	−4.00000	+	2.00000i	−0.192897	+	0.0964486i
$431$	−5.00000			−0.240842			−0.120421	−	0.992723i	$-0.538424\pi$
$431$	−5.00000			−0.240842			−0.120421	+	0.992723i	$0.538424\pi$
$432$		0			0
$433$			7.00000i			0.336399i	0.985753	+	0.168199i	$0.0537952\pi$
$433$			7.00000i			0.336399i	−0.985753	+	0.168199i	$0.946205\pi$
$434$	1.00000			0.0480015
$435$		0			0
$436$	−16.0000			−0.766261
$437$		−	16.0000i		−	0.765384i
$438$		0			0
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$		0			0
$441$		0			0
$442$		−	16.0000i		−	0.761042i
$443$			39.0000i			1.85295i	0.376361	+	0.926473i	$0.377175\pi$
$443$			39.0000i			1.85295i	−0.376361	+	0.926473i	$0.622825\pi$
$444$		0			0
$445$	−20.0000	+	10.0000i	−0.948091	+	0.474045i
$446$	−28.0000			−1.32584
$447$		0			0
$448$			1.00000i			0.0472456i
$449$	−28.0000			−1.32140			−0.660701	−	0.750649i	$-0.729741\pi$
$449$	−28.0000			−1.32140			−0.660701	+	0.750649i	$0.729741\pi$
$450$		0			0
$451$		0			0
$452$		−	1.00000i		−	0.0470360i
$453$		0			0
$454$	12.0000			0.563188
$455$	−4.00000	+	2.00000i	−0.187523	+	0.0937614i
$456$		0			0
$457$		−	8.00000i		−	0.374224i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$		−	8.00000i		−	0.374224i	0.982339	−	0.187112i	$-0.0599128\pi$
$458$		−	10.0000i		−	0.467269i
$459$		0			0
$460$	−4.00000	−	8.00000i	−0.186501	−	0.373002i
$461$	−16.0000			−0.745194			−0.372597	−	0.927993i	$-0.621533\pi$
$461$	−16.0000			−0.745194			−0.372597	+	0.927993i	$0.621533\pi$
$462$		0			0
$463$			19.0000i			0.883005i	0.897260	+	0.441502i	$0.145554\pi$
$463$			19.0000i			0.883005i	−0.897260	+	0.441502i	$0.854446\pi$
$464$	−7.00000			−0.324967
$465$		0			0
$466$	7.00000			0.324269
$467$		−	2.00000i		−	0.0925490i	−0.998929	−	0.0462745i	$-0.985265\pi$
$467$		−	2.00000i		−	0.0925490i	0.998929	−	0.0462745i	$-0.0147349\pi$
$468$		0			0
$469$	4.00000			0.184703
$470$	14.0000	−	7.00000i	0.645772	−	0.322886i
$471$		0			0
$472$			1.00000i			0.0460287i
$473$		0			0
$474$		0			0
$475$	−12.0000	+	16.0000i	−0.550598	+	0.734130i
$476$	8.00000			0.366679
$477$		0			0
$478$			5.00000i			0.228695i
$479$	−24.0000			−1.09659			−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000			−1.09659			−0.548294	+	0.836286i	$0.684723\pi$
$480$		0			0
$481$	−14.0000			−0.638345
$482$			30.0000i			1.36646i
$483$		0			0
$484$	11.0000			0.500000
$485$	−6.00000	−	12.0000i	−0.272446	−	0.544892i
$486$		0			0
$487$			17.0000i			0.770344i	0.922845	+	0.385172i	$0.125858\pi$
$487$			17.0000i			0.770344i	−0.922845	+	0.385172i	$0.874142\pi$
$488$		−	3.00000i		−	0.135804i
$489$		0			0
$490$	−1.00000	−	2.00000i	−0.0451754	−	0.0903508i
$491$	6.00000			0.270776			0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000			0.270776			0.135388	+	0.990793i	$0.456772\pi$
$492$		0			0
$493$			56.0000i			2.52211i
$494$	−8.00000			−0.359937
$495$		0			0
$496$	1.00000			0.0449013
$497$			3.00000i			0.134568i
$498$		0			0
$499$	−37.0000			−1.65635			−0.828174	−	0.560471i	$-0.810620\pi$
$499$	−37.0000			−1.65635			−0.828174	+	0.560471i	$0.810620\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$		0			0
$502$		−	20.0000i		−	0.892644i
$503$			8.00000i			0.356702i	0.983967	+	0.178351i	$0.0570763\pi$
$503$			8.00000i			0.356702i	−0.983967	+	0.178351i	$0.942924\pi$
$504$		0			0
$505$	−12.0000	+	6.00000i	−0.533993	+	0.266996i
$506$		0			0
$507$		0			0
$508$			13.0000i			0.576782i
$509$	44.0000			1.95027			0.975133	−	0.221621i	$-0.0711348\pi$
$509$	44.0000			1.95027			0.975133	+	0.221621i	$0.0711348\pi$
$510$		0			0
$511$	−13.0000			−0.575086
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	24.0000			1.05859
$515$	−14.0000	−	28.0000i	−0.616914	−	1.23383i
$516$		0			0
$517$		0			0
$518$		−	7.00000i		−	0.307562i
$519$		0			0
$520$	−4.00000	+	2.00000i	−0.175412	+	0.0877058i
$521$	30.0000			1.31432			0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000			1.31432			0.657162	+	0.753749i	$0.271757\pi$
$522$		0			0
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	−13.0000			−0.567908
$525$		0			0
$526$	−12.0000			−0.523225
$527$		−	8.00000i		−	0.348485i
$528$		0			0
$529$	7.00000			0.304348
$530$	−12.0000	+	6.00000i	−0.521247	+	0.260623i
$531$		0			0
$532$		−	4.00000i		−	0.173422i
$533$			18.0000i			0.779667i
$534$		0			0
$535$	−7.00000	−	14.0000i	−0.302636	−	0.605273i
$536$	4.00000			0.172774
$537$		0			0
$538$		−	4.00000i		−	0.172452i
$539$		0			0
$540$		0			0
$541$	8.00000			0.343947			0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000			0.343947			0.171973	+	0.985102i	$0.444986\pi$
$542$		−	21.0000i		−	0.902027i
$543$		0			0
$544$	8.00000			0.342997
$545$	32.0000	−	16.0000i	1.37073	−	0.685365i
$546$		0			0
$547$		−	28.0000i		−	1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$		−	28.0000i		−	1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$		−	19.0000i		−	0.811640i
$549$		0			0
$550$		0			0
$551$	28.0000			1.19284
$552$		0			0
$553$		−	16.0000i		−	0.680389i
$554$	10.0000			0.424859
$555$		0			0
$556$	−14.0000			−0.593732
$557$		−	16.0000i		−	0.677942i	−0.940797	−	0.338971i	$-0.889921\pi$
$557$		−	16.0000i		−	0.677942i	0.940797	−	0.338971i	$-0.110079\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$	−1.00000	−	2.00000i	−0.0422577	−	0.0845154i
$561$		0			0
$562$		0			0
$563$			34.0000i			1.43293i	0.697623	+	0.716465i	$0.254241\pi$
$563$			34.0000i			1.43293i	−0.697623	+	0.716465i	$0.745759\pi$
$564$		0			0
$565$	1.00000	+	2.00000i	0.0420703	+	0.0841406i
$566$	7.00000			0.294232
$567$		0			0
$568$			3.00000i			0.125877i
$569$	36.0000			1.50920			0.754599	−	0.656186i	$-0.227831\pi$
$569$	36.0000			1.50920			0.754599	+	0.656186i	$0.227831\pi$
$570$		0			0
$571$	23.0000			0.962520			0.481260	−	0.876578i	$-0.340179\pi$
$571$	23.0000			0.962520			0.481260	+	0.876578i	$0.340179\pi$
$572$		0			0
$573$		0			0
$574$	−9.00000			−0.375653
$575$	16.0000	+	12.0000i	0.667246	+	0.500435i
$576$		0			0
$577$		−	17.0000i		−	0.707719i	−0.935299	−	0.353860i	$-0.884869\pi$
$577$		−	17.0000i		−	0.707719i	0.935299	−	0.353860i	$-0.115131\pi$
$578$		−	47.0000i		−	1.95494i
$579$		0			0
$580$	14.0000	−	7.00000i	0.581318	−	0.290659i
$581$	6.00000			0.248922
$582$		0			0
$583$		0			0
$584$	−13.0000			−0.537944
$585$		0			0
$586$	−15.0000			−0.619644
$587$		−	2.00000i		−	0.0825488i	−0.999148	−	0.0412744i	$-0.986858\pi$
$587$		−	2.00000i		−	0.0825488i	0.999148	−	0.0412744i	$-0.0131418\pi$
$588$		0			0
$589$	−4.00000			−0.164817
$590$	−1.00000	−	2.00000i	−0.0411693	−	0.0823387i
$591$		0			0
$592$		−	7.00000i		−	0.287698i
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$		0			0
$595$	−16.0000	+	8.00000i	−0.655936	+	0.327968i
$596$	−6.00000			−0.245770
$597$		0			0
$598$			8.00000i			0.327144i
$599$	15.0000			0.612883			0.306442	−	0.951889i	$-0.400862\pi$
$599$	15.0000			0.612883			0.306442	+	0.951889i	$0.400862\pi$
$600$		0			0
$601$	44.0000			1.79480			0.897399	−	0.441221i	$-0.145454\pi$
$601$	44.0000			1.79480			0.897399	+	0.441221i	$0.145454\pi$
$602$			2.00000i			0.0815139i
$603$		0			0
$604$	−18.0000			−0.732410
$605$	−22.0000	+	11.0000i	−0.894427	+	0.447214i
$606$		0			0
$607$			34.0000i			1.38002i	0.723801	+	0.690009i	$0.242393\pi$
$607$			34.0000i			1.38002i	−0.723801	+	0.690009i	$0.757607\pi$
$608$		−	4.00000i		−	0.162221i
$609$		0			0
$610$	3.00000	+	6.00000i	0.121466	+	0.242933i
$611$	−14.0000			−0.566379
$612$		0			0
$613$		−	6.00000i		−	0.242338i	−0.992632	−	0.121169i	$-0.961336\pi$
$613$		−	6.00000i		−	0.242338i	0.992632	−	0.121169i	$-0.0386643\pi$
$614$	−28.0000			−1.12999
$615$		0			0
$616$		0			0
$617$		−	13.0000i		−	0.523360i	−0.965155	−	0.261680i	$-0.915723\pi$
$617$		−	13.0000i		−	0.523360i	0.965155	−	0.261680i	$-0.0842766\pi$
$618$		0			0
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$	−2.00000	+	1.00000i	−0.0803219	+	0.0401610i
$621$		0			0
$622$			18.0000i			0.721734i
$623$			10.0000i			0.400642i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	10.0000			0.399680
$627$		0			0
$628$		−	6.00000i		−	0.239426i
$629$	−56.0000			−2.23287
$630$		0			0
$631$	12.0000			0.477712			0.238856	−	0.971055i	$-0.423228\pi$
$631$	12.0000			0.477712			0.238856	+	0.971055i	$0.423228\pi$
$632$		−	16.0000i		−	0.636446i
$633$		0			0
$634$	−10.0000			−0.397151
$635$	−13.0000	−	26.0000i	−0.515889	−	1.03178i
$636$		0			0
$637$			2.00000i			0.0792429i
$638$		0			0
$639$		0			0
$640$	−1.00000	−	2.00000i	−0.0395285	−	0.0790569i
$641$	−22.0000			−0.868948			−0.434474	−	0.900684i	$-0.643066\pi$
$641$	−22.0000			−0.868948			−0.434474	+	0.900684i	$0.643066\pi$
$642$		0			0
$643$		−	47.0000i		−	1.85350i	−0.375680	−	0.926750i	$-0.622591\pi$
$643$		−	47.0000i		−	1.85350i	0.375680	−	0.926750i	$-0.377409\pi$
$644$	−4.00000			−0.157622
$645$		0			0
$646$	−32.0000			−1.25902
$647$			45.0000i			1.76913i	0.466415	+	0.884566i	$0.345546\pi$
$647$			45.0000i			1.76913i	−0.466415	+	0.884566i	$0.654454\pi$
$648$		0			0
$649$		0			0
$650$	6.00000	−	8.00000i	0.235339	−	0.313786i
$651$		0			0
$652$			6.00000i			0.234978i
$653$		−	18.0000i		−	0.704394i	−0.935926	−	0.352197i	$-0.885435\pi$
$653$		−	18.0000i		−	0.704394i	0.935926	−	0.352197i	$-0.114565\pi$
$654$		0			0
$655$	26.0000	−	13.0000i	1.01590	−	0.507952i
$656$	−9.00000			−0.351391
$657$		0			0
$658$		−	7.00000i		−	0.272888i
$659$	42.0000			1.63609			0.818044	−	0.575156i	$-0.195059\pi$
$659$	42.0000			1.63609			0.818044	+	0.575156i	$0.195059\pi$
$660$		0			0
$661$	−17.0000			−0.661223			−0.330612	−	0.943767i	$-0.607255\pi$
$661$	−17.0000			−0.661223			−0.330612	+	0.943767i	$0.607255\pi$
$662$		−	7.00000i		−	0.272063i
$663$		0			0
$664$	6.00000			0.232845
$665$	4.00000	+	8.00000i	0.155113	+	0.310227i
$666$		0			0
$667$		−	28.0000i		−	1.08416i
$668$			15.0000i			0.580367i
$669$		0			0
$670$	−8.00000	+	4.00000i	−0.309067	+	0.154533i
$671$		0			0
$672$		0			0
$673$			20.0000i			0.770943i	0.922720	+	0.385472i	$0.125961\pi$
$673$			20.0000i			0.770943i	−0.922720	+	0.385472i	$0.874039\pi$
$674$	4.00000			0.154074
$675$		0			0
$676$	−9.00000			−0.346154
$677$		−	35.0000i		−	1.34516i	−0.740025	−	0.672580i	$-0.765186\pi$
$677$		−	35.0000i		−	1.34516i	0.740025	−	0.672580i	$-0.234814\pi$
$678$		0			0
$679$	−6.00000			−0.230259
$680$	−16.0000	+	8.00000i	−0.613572	+	0.306786i
$681$		0			0
$682$		0			0
$683$			47.0000i			1.79841i	0.437533	+	0.899203i	$0.355852\pi$
$683$			47.0000i			1.79841i	−0.437533	+	0.899203i	$0.644148\pi$
$684$		0			0
$685$	19.0000	+	38.0000i	0.725953	+	1.45191i
$686$	−1.00000			−0.0381802
$687$		0			0
$688$			2.00000i			0.0762493i
$689$	12.0000			0.457164
$690$		0			0
$691$	34.0000			1.29342			0.646710	−	0.762736i	$-0.276144\pi$
$691$	34.0000			1.29342			0.646710	+	0.762736i	$0.276144\pi$
$692$		−	9.00000i		−	0.342129i
$693$		0			0
$694$	−3.00000			−0.113878
$695$	28.0000	−	14.0000i	1.06210	−	0.531050i
$696$		0			0
$697$			72.0000i			2.72719i
$698$			30.0000i			1.13552i
$699$		0			0
$700$	4.00000	+	3.00000i	0.151186	+	0.113389i
$701$	31.0000			1.17085			0.585427	−	0.810725i	$-0.300927\pi$
$701$	31.0000			1.17085			0.585427	+	0.810725i	$0.300927\pi$
$702$		0			0
$703$			28.0000i			1.05604i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			6.00000i			0.225653i
$708$		0			0
$709$	24.0000			0.901339			0.450669	−	0.892691i	$-0.351185\pi$
$709$	24.0000			0.901339			0.450669	+	0.892691i	$0.351185\pi$
$710$	−3.00000	−	6.00000i	−0.112588	−	0.225176i
$711$		0			0
$712$			10.0000i			0.374766i
$713$			4.00000i			0.149801i
$714$		0			0
$715$		0			0
$716$	−16.0000			−0.597948
$717$		0			0
$718$		−	20.0000i		−	0.746393i
$719$	−34.0000			−1.26799			−0.633993	−	0.773339i	$-0.718585\pi$
$719$	−34.0000			−1.26799			−0.633993	+	0.773339i	$0.718585\pi$
$720$		0			0
$721$	−14.0000			−0.521387
$722$		−	3.00000i		−	0.111648i
$723$		0			0
$724$	−5.00000			−0.185824
$725$	−21.0000	+	28.0000i	−0.779920	+	1.03989i
$726$		0			0
$727$			26.0000i			0.964287i	0.876092	+	0.482143i	$0.160142\pi$
$727$			26.0000i			0.964287i	−0.876092	+	0.482143i	$0.839858\pi$
$728$			2.00000i			0.0741249i
$729$		0			0
$730$	26.0000	−	13.0000i	0.962303	−	0.481152i
$731$	16.0000			0.591781
$732$		0			0
$733$			8.00000i			0.295487i	0.989026	+	0.147743i	$0.0472010\pi$
$733$			8.00000i			0.295487i	−0.989026	+	0.147743i	$0.952799\pi$
$734$	−14.0000			−0.516749
$735$		0			0
$736$	−4.00000			−0.147442
$737$		0			0
$738$		0			0
$739$	23.0000			0.846069			0.423034	−	0.906114i	$-0.360965\pi$
$739$	23.0000			0.846069			0.423034	+	0.906114i	$0.360965\pi$
$740$	7.00000	+	14.0000i	0.257325	+	0.514650i
$741$		0			0
$742$			6.00000i			0.220267i
$743$		−	18.0000i		−	0.660356i	−0.943919	−	0.330178i	$-0.892891\pi$
$743$		−	18.0000i		−	0.660356i	0.943919	−	0.330178i	$-0.107109\pi$
$744$		0			0
$745$	12.0000	−	6.00000i	0.439646	−	0.219823i
$746$	13.0000			0.475964
$747$		0			0
$748$		0			0
$749$	−7.00000			−0.255774
$750$		0			0
$751$	10.0000			0.364905			0.182453	−	0.983215i	$-0.441596\pi$
$751$	10.0000			0.364905			0.182453	+	0.983215i	$0.441596\pi$
$752$		−	7.00000i		−	0.255264i
$753$		0			0
$754$	−14.0000			−0.509850
$755$	36.0000	−	18.0000i	1.31017	−	0.655087i
$756$		0			0
$757$		−	21.0000i		−	0.763258i	−0.924316	−	0.381629i	$-0.875363\pi$
$757$		−	21.0000i		−	0.763258i	0.924316	−	0.381629i	$-0.124637\pi$
$758$		−	19.0000i		−	0.690111i
$759$		0			0
$760$	4.00000	+	8.00000i	0.145095	+	0.290191i
$761$	29.0000			1.05125			0.525625	−	0.850717i	$-0.323832\pi$
$761$	29.0000			1.05125			0.525625	+	0.850717i	$0.323832\pi$
$762$		0			0
$763$		−	16.0000i		−	0.579239i
$764$	−8.00000			−0.289430
$765$		0			0
$766$	24.0000			0.867155
$767$			2.00000i			0.0722158i
$768$		0			0
$769$	−4.00000			−0.144244			−0.0721218	−	0.997396i	$-0.522977\pi$
$769$	−4.00000			−0.144244			−0.0721218	+	0.997396i	$0.522977\pi$
$770$		0			0
$771$		0			0
$772$		−	26.0000i		−	0.935760i
$773$			21.0000i			0.755318i	0.925945	+	0.377659i	$0.123271\pi$
$773$			21.0000i			0.755318i	−0.925945	+	0.377659i	$0.876729\pi$
$774$		0			0
$775$	3.00000	−	4.00000i	0.107763	−	0.143684i
$776$	−6.00000			−0.215387
$777$		0			0
$778$		−	27.0000i		−	0.967997i
$779$	36.0000			1.28983
$780$		0			0
$781$		0			0
$782$			32.0000i			1.14432i
$783$		0			0
$784$	−1.00000			−0.0357143
$785$	6.00000	+	12.0000i	0.214149	+	0.428298i
$786$		0			0
$787$		−	39.0000i		−	1.39020i	−0.718913	−	0.695100i	$-0.755360\pi$
$787$		−	39.0000i		−	1.39020i	0.718913	−	0.695100i	$-0.244640\pi$
$788$			8.00000i			0.284988i
$789$		0			0
$790$	16.0000	+	32.0000i	0.569254	+	1.13851i
$791$	1.00000			0.0355559
$792$		0			0
$793$		−	6.00000i		−	0.213066i
$794$	−14.0000			−0.496841
$795$		0			0
$796$		0			0
$797$		−	5.00000i		−	0.177109i	−0.996071	−	0.0885545i	$-0.971775\pi$
$797$		−	5.00000i		−	0.177109i	0.996071	−	0.0885545i	$-0.0282248\pi$
$798$		0			0
$799$	−56.0000			−1.98114
$800$	4.00000	+	3.00000i	0.141421	+	0.106066i
$801$		0			0
$802$		−	36.0000i		−	1.27120i
$803$		0			0
$804$		0			0
$805$	8.00000	−	4.00000i	0.281963	−	0.140981i
$806$	2.00000			0.0704470
$807$		0			0
$808$			6.00000i			0.211079i
$809$	−26.0000			−0.914111			−0.457056	−	0.889438i	$-0.651096\pi$
$809$	−26.0000			−0.914111			−0.457056	+	0.889438i	$0.651096\pi$
$810$		0			0
$811$	30.0000			1.05344			0.526721	−	0.850038i	$-0.323421\pi$
$811$	30.0000			1.05344			0.526721	+	0.850038i	$0.323421\pi$
$812$		−	7.00000i		−	0.245652i
$813$		0			0
$814$		0			0
$815$	−6.00000	−	12.0000i	−0.210171	−	0.420342i
$816$		0			0
$817$		−	8.00000i		−	0.279885i
$818$			32.0000i			1.11885i
$819$		0			0
$820$	18.0000	−	9.00000i	0.628587	−	0.314294i
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$		0			0
$823$		−	15.0000i		−	0.522867i	−0.965221	−	0.261434i	$-0.915805\pi$
$823$		−	15.0000i		−	0.522867i	0.965221	−	0.261434i	$-0.0841952\pi$
$824$	−14.0000			−0.487713
$825$		0			0
$826$	−1.00000			−0.0347945
$827$			17.0000i			0.591148i	0.955320	+	0.295574i	$0.0955109\pi$
$827$			17.0000i			0.591148i	−0.955320	+	0.295574i	$0.904489\pi$
$828$		0			0
$829$	−10.0000			−0.347314			−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000			−0.347314			−0.173657	+	0.984806i	$0.555558\pi$
$830$	−12.0000	+	6.00000i	−0.416526	+	0.208263i
$831$		0			0
$832$			2.00000i			0.0693375i
$833$			8.00000i			0.277184i
$834$		0			0
$835$	−15.0000	−	30.0000i	−0.519096	−	1.03819i
$836$		0			0
$837$		0			0
$838$			35.0000i			1.20905i
$839$	32.0000			1.10476			0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000			1.10476			0.552381	+	0.833592i	$0.313719\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$		−	20.0000i		−	0.689246i
$843$		0			0
$844$	3.00000			0.103264
$845$	18.0000	−	9.00000i	0.619219	−	0.309609i
$846$		0			0
$847$			11.0000i			0.377964i
$848$			6.00000i			0.206041i
$849$		0			0
$850$	24.0000	−	32.0000i	0.823193	−	1.09759i
$851$	28.0000			0.959828
$852$		0			0
$853$		−	4.00000i		−	0.136957i	−0.997653	−	0.0684787i	$-0.978185\pi$
$853$		−	4.00000i		−	0.136957i	0.997653	−	0.0684787i	$-0.0218145\pi$
$854$	3.00000			0.102658
$855$		0			0
$856$	−7.00000			−0.239255
$857$			32.0000i			1.09310i	0.837427	+	0.546550i	$0.184059\pi$
$857$			32.0000i			1.09310i	−0.837427	+	0.546550i	$0.815941\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$	−2.00000	−	4.00000i	−0.0681994	−	0.136399i
$861$		0			0
$862$		−	5.00000i		−	0.170301i
$863$			14.0000i			0.476566i	0.971196	+	0.238283i	$0.0765845\pi$
$863$			14.0000i			0.476566i	−0.971196	+	0.238283i	$0.923415\pi$
$864$		0			0
$865$	9.00000	+	18.0000i	0.306009	+	0.612018i
$866$	−7.00000			−0.237870
$867$		0			0
$868$			1.00000i			0.0339422i
$869$		0			0
$870$		0			0
$871$	8.00000			0.271070
$872$		−	16.0000i		−	0.541828i
$873$		0			0
$874$	16.0000			0.541208
$875$	−11.0000	−	2.00000i	−0.371868	−	0.0676123i
$876$		0			0
$877$			23.0000i			0.776655i	0.921521	+	0.388327i	$0.126947\pi$
$877$			23.0000i			0.776655i	−0.921521	+	0.388327i	$0.873053\pi$
$878$		−	8.00000i		−	0.269987i
$879$		0			0
$880$		0			0
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$		0			0
$883$		−	2.00000i		−	0.0673054i	−0.999434	−	0.0336527i	$-0.989286\pi$
$883$		−	2.00000i		−	0.0673054i	0.999434	−	0.0336527i	$-0.0107140\pi$
$884$	16.0000			0.538138
$885$		0			0
$886$	−39.0000			−1.31023
$887$			45.0000i			1.51095i	0.655176	+	0.755476i	$0.272594\pi$
$887$			45.0000i			1.51095i	−0.655176	+	0.755476i	$0.727406\pi$
$888$		0			0
$889$	−13.0000			−0.436006
$890$	−10.0000	−	20.0000i	−0.335201	−	0.670402i
$891$		0			0
$892$		−	28.0000i		−	0.937509i
$893$			28.0000i			0.936984i
$894$		0			0
$895$	32.0000	−	16.0000i	1.06964	−	0.534821i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$		−	28.0000i		−	0.934372i
$899$	−7.00000			−0.233463
$900$		0			0
$901$	48.0000			1.59911
$902$		0			0
$903$		0			0
$904$	1.00000			0.0332595
$905$	10.0000	−	5.00000i	0.332411	−	0.166206i
$906$		0			0
$907$		−	44.0000i		−	1.46100i	−0.682915	−	0.730498i	$-0.739288\pi$
$907$		−	44.0000i		−	1.46100i	0.682915	−	0.730498i	$-0.260712\pi$
$908$			12.0000i			0.398234i
$909$		0			0
$910$	−2.00000	−	4.00000i	−0.0662994	−	0.132599i
$911$	−23.0000			−0.762024			−0.381012	−	0.924570i	$-0.624424\pi$
$911$	−23.0000			−0.762024			−0.381012	+	0.924570i	$0.624424\pi$
$912$		0			0
$913$		0			0
$914$	8.00000			0.264616
$915$		0			0
$916$	10.0000			0.330409
$917$		−	13.0000i		−	0.429298i
$918$		0			0
$919$	−38.0000			−1.25350			−0.626752	−	0.779219i	$-0.715616\pi$
$919$	−38.0000			−1.25350			−0.626752	+	0.779219i	$0.715616\pi$
$920$	8.00000	−	4.00000i	0.263752	−	0.131876i
$921$		0			0
$922$		−	16.0000i		−	0.526932i
$923$			6.00000i			0.197492i
$924$		0			0
$925$	−28.0000	−	21.0000i	−0.920634	−	0.690476i
$926$	−19.0000			−0.624379
$927$		0			0
$928$		−	7.00000i		−	0.229786i
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$		0			0
$931$	4.00000			0.131095
$932$			7.00000i			0.229293i
$933$		0			0
$934$	2.00000			0.0654420
$935$		0			0
$936$		0			0
$937$		−	19.0000i		−	0.620703i	−0.950622	−	0.310351i	$-0.899553\pi$
$937$		−	19.0000i		−	0.620703i	0.950622	−	0.310351i	$-0.100447\pi$
$938$			4.00000i			0.130605i
$939$		0			0
$940$	7.00000	+	14.0000i	0.228315	+	0.456630i
$941$	−20.0000			−0.651981			−0.325991	−	0.945373i	$-0.605698\pi$
$941$	−20.0000			−0.651981			−0.325991	+	0.945373i	$0.605698\pi$
$942$		0			0
$943$		−	36.0000i		−	1.17232i
$944$	−1.00000			−0.0325472
$945$		0			0
$946$		0			0
$947$			36.0000i			1.16984i	0.811090	+	0.584921i	$0.198875\pi$
$947$			36.0000i			1.16984i	−0.811090	+	0.584921i	$0.801125\pi$
$948$		0			0
$949$	−26.0000			−0.843996
$950$	−16.0000	−	12.0000i	−0.519109	−	0.389331i
$951$		0			0
$952$			8.00000i			0.259281i
$953$		−	54.0000i		−	1.74923i	−0.484817	−	0.874616i	$-0.661114\pi$
$953$		−	54.0000i		−	1.74923i	0.484817	−	0.874616i	$-0.338886\pi$
$954$		0			0
$955$	16.0000	−	8.00000i	0.517748	−	0.258874i
$956$	−5.00000			−0.161712
$957$		0			0
$958$		−	24.0000i		−	0.775405i
$959$	19.0000			0.613542
$960$		0			0
$961$	−30.0000			−0.967742
$962$		−	14.0000i		−	0.451378i
$963$		0			0
$964$	−30.0000			−0.966235
$965$	26.0000	+	52.0000i	0.836970	+	1.67394i
$966$		0			0
$967$			1.00000i			0.0321578i	0.999871	+	0.0160789i	$0.00511830\pi$
$967$			1.00000i			0.0321578i	−0.999871	+	0.0160789i	$0.994882\pi$
$968$			11.0000i			0.353553i
$969$		0			0
$970$	12.0000	−	6.00000i	0.385297	−	0.192648i
$971$	51.0000			1.63667			0.818334	−	0.574743i	$-0.194898\pi$
$971$	51.0000			1.63667			0.818334	+	0.574743i	$0.194898\pi$
$972$		0			0
$973$		−	14.0000i		−	0.448819i
$974$	−17.0000			−0.544715
$975$		0			0
$976$	3.00000			0.0960277
$977$		−	18.0000i		−	0.575871i	−0.957650	−	0.287936i	$-0.907031\pi$
$977$		−	18.0000i		−	0.575871i	0.957650	−	0.287936i	$-0.0929689\pi$
$978$		0			0
$979$		0			0
$980$	2.00000	−	1.00000i	0.0638877	−	0.0319438i
$981$		0			0
$982$			6.00000i			0.191468i
$983$		−	28.0000i		−	0.893061i	−0.894768	−	0.446531i	$-0.852659\pi$
$983$		−	28.0000i		−	0.893061i	0.894768	−	0.446531i	$-0.147341\pi$
$984$		0			0
$985$	−8.00000	−	16.0000i	−0.254901	−	0.509802i
$986$	−56.0000			−1.78340
$987$		0			0
$988$		−	8.00000i		−	0.254514i
$989$	−8.00000			−0.254385
$990$		0			0
$991$	46.0000			1.46124			0.730619	−	0.682785i	$-0.239232\pi$
$991$	46.0000			1.46124			0.730619	+	0.682785i	$0.239232\pi$
$992$			1.00000i			0.0317500i
$993$		0			0
$994$	−3.00000			−0.0951542
$995$		0			0
$996$		0			0
$997$		−	40.0000i		−	1.26681i	−0.773819	−	0.633406i	$-0.781656\pi$
$997$		−	40.0000i		−	1.26681i	0.773819	−	0.633406i	$-0.218344\pi$
$998$		−	37.0000i		−	1.17121i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.g.l.379.2	yes	2
3.2	odd	2		1890.2.g.b.379.1	✓	2
5.2	odd	4		9450.2.a.bm.1.1		1
5.3	odd	4		9450.2.a.cn.1.1		1
5.4	even	2	inner	1890.2.g.l.379.1	yes	2
15.2	even	4		9450.2.a.dm.1.1		1
15.8	even	4		9450.2.a.o.1.1		1
15.14	odd	2		1890.2.g.b.379.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.g.b.379.1	✓	2	3.2	odd	2
1890.2.g.b.379.2	yes	2	15.14	odd	2
1890.2.g.l.379.1	yes	2	5.4	even	2	inner
1890.2.g.l.379.2	yes	2	1.1	even	1	trivial
9450.2.a.o.1.1		1	15.8	even	4
9450.2.a.bm.1.1		1	5.2	odd	4
9450.2.a.cn.1.1		1	5.3	odd	4
9450.2.a.dm.1.1		1	15.2	even	4

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +(1.00000 + 2.00000i) q^{10} -2.00000i q^{13} +1.00000 q^{14} +1.00000 q^{16} -8.00000i q^{17} -4.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} +4.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +2.00000 q^{26} +1.00000i q^{28} -7.00000 q^{29} +1.00000 q^{31} +1.00000i q^{32} +8.00000 q^{34} +(-1.00000 - 2.00000i) q^{35} -7.00000i q^{37} -4.00000i q^{38} +(-1.00000 - 2.00000i) q^{40} -9.00000 q^{41} +2.00000i q^{43} -4.00000 q^{46} -7.00000i q^{47} -1.00000 q^{49} +(4.00000 + 3.00000i) q^{50} +2.00000i q^{52} +6.00000i q^{53} -1.00000 q^{56} -7.00000i q^{58} -1.00000 q^{59} +3.00000 q^{61} +1.00000i q^{62} -1.00000 q^{64} +(-2.00000 - 4.00000i) q^{65} +4.00000i q^{67} +8.00000i q^{68} +(2.00000 - 1.00000i) q^{70} -3.00000 q^{71} -13.0000i q^{73} +7.00000 q^{74} +4.00000 q^{76} +16.0000 q^{79} +(2.00000 - 1.00000i) q^{80} -9.00000i q^{82} +6.00000i q^{83} +(-8.00000 - 16.0000i) q^{85} -2.00000 q^{86} -10.0000 q^{89} -2.00000 q^{91} -4.00000i q^{92} +7.00000 q^{94} +(-8.00000 + 4.00000i) q^{95} -6.00000i q^{97} -1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 4 q^{5}+O(q^{10}) \) 2 * q - 2 * q^4 + 4 * q^5	\( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{10} + 2 q^{14} + 2 q^{16} - 8 q^{19} - 4 q^{20} + 6 q^{25} + 4 q^{26} - 14 q^{29} + 2 q^{31} + 16 q^{34} - 2 q^{35} - 2 q^{40} - 18 q^{41} - 8 q^{46} - 2 q^{49} + 8 q^{50} - 2 q^{56} - 2 q^{59} + 6 q^{61} - 2 q^{64} - 4 q^{65} + 4 q^{70} - 6 q^{71} + 14 q^{74} + 8 q^{76} + 32 q^{79} + 4 q^{80} - 16 q^{85} - 4 q^{86} - 20 q^{89} - 4 q^{91} + 14 q^{94} - 16 q^{95}+O(q^{100}) \) 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^10 + 2 * q^14 + 2 * q^16 - 8 * q^19 - 4 * q^20 + 6 * q^25 + 4 * q^26 - 14 * q^29 + 2 * q^31 + 16 * q^34 - 2 * q^35 - 2 * q^40 - 18 * q^41 - 8 * q^46 - 2 * q^49 + 8 * q^50 - 2 * q^56 - 2 * q^59 + 6 * q^61 - 2 * q^64 - 4 * q^65 + 4 * q^70 - 6 * q^71 + 14 * q^74 + 8 * q^76 + 32 * q^79 + 4 * q^80 - 16 * q^85 - 4 * q^86 - 20 * q^89 - 4 * q^91 + 14 * q^94 - 16 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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