LMFDB - Embedded newform 2175.1.h.e.1826.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2175,1,Mod(1826,2175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2175, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2175.1826");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2175.h (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:	yes
Analytic conductor:	$1.08546640248$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{9}$
Projective field:	Galois closure of 9.1.895152515625.1
Artin image:	$D_9$
Artin field:	Galois closure of 9.1.895152515625.1

Embedding invariants

Embedding label			1826.2
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	2175.1826

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.347296 q^{2} +1.00000 q^{3} -0.879385 q^{4} +0.347296 q^{6} -1.87939 q^{7} -0.652704 q^{8} +1.00000 q^{9} +O(q^{10})$	$q+0.347296 q^{2} +1.00000 q^{3} -0.879385 q^{4} +0.347296 q^{6} -1.87939 q^{7} -0.652704 q^{8} +1.00000 q^{9} +1.53209 q^{11} -0.879385 q^{12} +0.347296 q^{13} -0.652704 q^{14} +0.652704 q^{16} +1.53209 q^{17} +0.347296 q^{18} -1.87939 q^{21} +0.532089 q^{22} -0.652704 q^{24} +0.120615 q^{26} +1.00000 q^{27} +1.65270 q^{28} +1.00000 q^{29} +0.879385 q^{32} +1.53209 q^{33} +0.532089 q^{34} -0.879385 q^{36} +0.347296 q^{39} -1.00000 q^{41} -0.652704 q^{42} -1.34730 q^{44} -1.87939 q^{47} +0.652704 q^{48} +2.53209 q^{49} +1.53209 q^{51} -0.305407 q^{52} +0.347296 q^{54} +1.22668 q^{56} +0.347296 q^{58} -1.87939 q^{63} -0.347296 q^{64} +0.532089 q^{66} +1.53209 q^{67} -1.34730 q^{68} -0.652704 q^{72} -2.87939 q^{77} +0.120615 q^{78} +1.00000 q^{81} -0.347296 q^{82} +1.65270 q^{84} +1.00000 q^{87} -1.00000 q^{88} +0.347296 q^{89} -0.652704 q^{91} -0.652704 q^{94} +0.879385 q^{96} +0.879385 q^{98} +1.53209 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} + 3 q^{4} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^3 + 3 * q^4 - 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{3} + 3 q^{4} - 3 q^{8} + 3 q^{9} + 3 q^{12} - 3 q^{14} + 3 q^{16} - 3 q^{22} - 3 q^{24} + 6 q^{26} + 3 q^{27} + 6 q^{28} + 3 q^{29} - 3 q^{32} - 3 q^{34} + 3 q^{36} - 3 q^{41} - 3 q^{42} - 3 q^{44} + 3 q^{48} + 3 q^{49} - 3 q^{52} - 3 q^{56} - 3 q^{66} - 3 q^{68} - 3 q^{72} - 3 q^{77} + 6 q^{78} + 3 q^{81} + 6 q^{84} + 3 q^{87} - 3 q^{88} - 3 q^{91} - 3 q^{94} - 3 q^{96} - 3 q^{98}+O(q^{100}) $ 3 * q + 3 * q^3 + 3 * q^4 - 3 * q^8 + 3 * q^9 + 3 * q^12 - 3 * q^14 + 3 * q^16 - 3 * q^22 - 3 * q^24 + 6 * q^26 + 3 * q^27 + 6 * q^28 + 3 * q^29 - 3 * q^32 - 3 * q^34 + 3 * q^36 - 3 * q^41 - 3 * q^42 - 3 * q^44 + 3 * q^48 + 3 * q^49 - 3 * q^52 - 3 * q^56 - 3 * q^66 - 3 * q^68 - 3 * q^72 - 3 * q^77 + 6 * q^78 + 3 * q^81 + 6 * q^84 + 3 * q^87 - 3 * q^88 - 3 * q^91 - 3 * q^94 - 3 * q^96 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2175\mathbb{Z}\right)^\times$.

$n$	$901$	$1451$	$2002$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$2$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$3$	1.00000	1.00000
$3$	1.00000	1.00000
$4$	−0.879385	−0.879385
$5$	0	0
$5$	0	0
$6$	0.347296	0.347296
$7$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$7$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$8$	−0.652704	−0.652704
$9$	1.00000	1.00000
$10$	0	0
$11$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$11$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$12$	−0.879385	−0.879385
$13$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$13$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$14$	−0.652704	−0.652704
$15$	0	0
$16$	0.652704	0.652704
$17$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$17$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$18$	0.347296	0.347296
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	−1.87939	−1.87939
$22$	0.532089	0.532089
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	−0.652704	−0.652704
$25$	0	0
$26$	0.120615	0.120615
$27$	1.00000	1.00000
$28$	1.65270	1.65270
$29$	1.00000	1.00000
$29$	1.00000	1.00000
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0.879385	0.879385
$33$	1.53209	1.53209
$34$	0.532089	0.532089
$35$	0	0
$36$	−0.879385	−0.879385
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0.347296	0.347296
$40$	0	0
$41$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$41$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$42$	−0.652704	−0.652704
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	−1.34730	−1.34730
$45$	0	0
$46$	0	0
$47$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$47$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$48$	0.652704	0.652704
$49$	2.53209	2.53209
$50$	0	0
$51$	1.53209	1.53209
$52$	−0.305407	−0.305407
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0.347296	0.347296
$55$	0	0
$56$	1.22668	1.22668
$57$	0	0
$58$	0.347296	0.347296
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	−1.87939	−1.87939
$64$	−0.347296	−0.347296
$65$	0	0
$66$	0.532089	0.532089
$67$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$67$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$68$	−1.34730	−1.34730
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−0.652704	−0.652704
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−2.87939	−2.87939
$78$	0.120615	0.120615
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	1.00000	1.00000
$82$	−0.347296	−0.347296
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	1.65270	1.65270
$85$	0	0
$86$	0	0
$87$	1.00000	1.00000
$88$	−1.00000	−1.00000
$89$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$89$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$90$	0	0
$91$	−0.652704	−0.652704
$92$	0	0
$93$	0	0
$94$	−0.652704	−0.652704
$95$	0	0
$96$	0.879385	0.879385
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0.879385	0.879385
$99$	1.53209	1.53209
$100$	0	0
$101$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$101$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$102$	0.532089	0.532089
$103$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$103$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$104$	−0.226682	−0.226682
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	−0.879385	−0.879385
$109$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$109$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$110$	0	0
$111$	0	0
$112$	−1.22668	−1.22668
$113$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$113$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$114$	0	0
$115$	0	0
$116$	−0.879385	−0.879385
$117$	0.347296	0.347296
$118$	0	0
$119$	−2.87939	−2.87939
$120$	0	0
$121$	1.34730	1.34730
$122$	0	0
$123$	−1.00000	−1.00000
$124$	0	0
$125$	0	0
$126$	−0.652704	−0.652704
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−1.00000	−1.00000
$129$	0	0
$130$	0	0
$131$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$131$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$132$	−1.34730	−1.34730
$133$	0	0
$134$	0.532089	0.532089
$135$	0	0
$136$	−1.00000	−1.00000
$137$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$137$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$138$	0	0
$139$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$139$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$140$	0	0
$141$	−1.87939	−1.87939
$142$	0	0
$143$	0.532089	0.532089
$144$	0.652704	0.652704
$145$	0	0
$146$	0	0
$147$	2.53209	2.53209
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$151$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$152$	0	0
$153$	1.53209	1.53209
$154$	−1.00000	−1.00000
$155$	0	0
$156$	−0.305407	−0.305407
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0.347296	0.347296
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0.879385	0.879385
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	1.22668	1.22668
$169$	−0.879385	−0.879385
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0.347296	0.347296
$175$	0	0
$176$	1.00000	1.00000
$177$	0	0
$178$	0.120615	0.120615
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$181$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$182$	−0.226682	−0.226682
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	2.34730	2.34730
$188$	1.65270	1.65270
$189$	−1.87939	−1.87939
$190$	0	0
$191$	2.00000	2.00000	1.00000			$0$
$191$	2.00000	2.00000	1.00000			$0$
$192$	−0.347296	−0.347296
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	−2.22668	−2.22668
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0.532089	0.532089
$199$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$199$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$200$	0	0
$201$	1.53209	1.53209
$202$	0.120615	0.120615
$203$	−1.87939	−1.87939
$204$	−1.34730	−1.34730
$205$	0	0
$206$	−0.347296	−0.347296
$207$	0	0
$208$	0.226682	0.226682
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	−0.652704	−0.652704
$217$	0	0
$218$	0.120615	0.120615
$219$	0	0
$220$	0	0
$221$	0.532089	0.532089
$222$	0	0
$223$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$223$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$224$	−1.65270	−1.65270
$225$	0	0
$226$	−0.652704	−0.652704
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	−2.87939	−2.87939
$232$	−0.652704	−0.652704
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0.120615	0.120615
$235$	0	0
$236$	0	0
$237$	0	0
$238$	−1.00000	−1.00000
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$241$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$242$	0.467911	0.467911
$243$	1.00000	1.00000
$244$	0	0
$245$	0	0
$246$	−0.347296	−0.347296
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$251$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$252$	1.65270	1.65270
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	1.00000	1.00000
$262$	−0.652704	−0.652704
$263$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$263$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$264$	−1.00000	−1.00000
$265$	0	0
$266$	0	0
$267$	0.347296	0.347296
$268$	−1.34730	−1.34730
$269$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$269$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	1.00000	1.00000
$273$	−0.652704	−0.652704
$274$	−0.347296	−0.347296
$275$	0	0
$276$	0	0
$277$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$277$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$278$	−0.652704	−0.652704
$279$	0	0
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	−0.652704	−0.652704
$283$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$283$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$284$	0	0
$285$	0	0
$286$	0.184793	0.184793
$287$	1.87939	1.87939
$288$	0.879385	0.879385
$289$	1.34730	1.34730
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$293$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$294$	0.879385	0.879385
$295$	0	0
$296$	0	0
$297$	1.53209	1.53209
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	−0.347296	−0.347296
$303$	0.347296	0.347296
$304$	0	0
$305$	0	0
$306$	0.532089	0.532089
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	2.53209	2.53209
$309$	−1.00000	−1.00000
$310$	0	0
$311$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$311$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$312$	−0.226682	−0.226682
$313$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$313$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$317$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$318$	0	0
$319$	1.53209	1.53209
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−0.879385	−0.879385
$325$	0	0
$326$	0	0
$327$	0.347296	0.347296
$328$	0.652704	0.652704
$329$	3.53209	3.53209
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	−1.22668	−1.22668
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	−0.305407	−0.305407
$339$	−1.87939	−1.87939
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−2.87939	−2.87939
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	−0.879385	−0.879385
$349$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$349$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$350$	0	0
$351$	0.347296	0.347296
$352$	1.34730	1.34730
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	−0.305407	−0.305407
$357$	−2.87939	−2.87939
$358$	0	0
$359$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$359$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$360$	0	0
$361$	1.00000	1.00000
$362$	0.532089	0.532089
$363$	1.34730	1.34730
$364$	0.573978	0.573978
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	−1.00000	−1.00000
$370$	0	0
$371$	0	0
$372$	0	0
$373$	2.00000	2.00000	1.00000			$0$
$373$	2.00000	2.00000	1.00000			$0$
$374$	0.815207	0.815207
$375$	0	0
$376$	1.22668	1.22668
$377$	0.347296	0.347296
$378$	−0.652704	−0.652704
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	0	0
$382$	0.694593	0.694593
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	−1.00000	−1.00000
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$389$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$390$	0	0
$391$	0	0
$392$	−1.65270	−1.65270
$393$	−1.87939	−1.87939
$394$	0	0
$395$	0	0
$396$	−1.34730	−1.34730
$397$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$397$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$398$	0.120615	0.120615
$399$	0	0
$400$	0	0
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0.532089	0.532089
$403$	0	0
$404$	−0.305407	−0.305407
$405$	0	0
$406$	−0.652704	−0.652704
$407$	0	0
$408$	−1.00000	−1.00000
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	−1.00000	−1.00000
$412$	0.879385	0.879385
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0.305407	0.305407
$417$	−1.87939	−1.87939
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	−1.87939	−1.87939
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0.532089	0.532089
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0.652704	0.652704
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	−0.305407	−0.305407
$437$	0	0
$438$	0	0
$439$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$439$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$440$	0	0
$441$	2.53209	2.53209
$442$	0.184793	0.184793
$443$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$443$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$444$	0	0
$445$	0	0
$446$	0.532089	0.532089
$447$	0	0
$448$	0.652704	0.652704
$449$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$449$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$450$	0	0
$451$	−1.53209	−1.53209
$452$	1.65270	1.65270
$453$	−1.00000	−1.00000
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$457$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$458$	0	0
$459$	1.53209	1.53209
$460$	0	0
$461$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$461$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$462$	−1.00000	−1.00000
$463$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$463$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$464$	0.652704	0.652704
$465$	0	0
$466$	0	0
$467$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$467$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$468$	−0.305407	−0.305407
$469$	−2.87939	−2.87939
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	2.53209	2.53209
$477$	0	0
$478$	0	0
$479$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$479$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$480$	0	0
$481$	0	0
$482$	−0.652704	−0.652704
$483$	0	0
$484$	−1.18479	−1.18479
$485$	0	0
$486$	0.347296	0.347296
$487$	2.00000	2.00000	1.00000			$0$
$487$	2.00000	2.00000	1.00000			$0$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$491$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$492$	0.879385	0.879385
$493$	1.53209	1.53209
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$499$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$500$	0	0
$501$	0	0
$502$	0.120615	0.120615
$503$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$503$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$504$	1.22668	1.22668
$505$	0	0
$506$	0	0
$507$	−0.879385	−0.879385
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	1.00000
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−2.87939	−2.87939
$518$	0	0
$519$	0	0
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0.347296	0.347296
$523$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$523$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$524$	1.65270	1.65270
$525$	0	0
$526$	−0.347296	−0.347296
$527$	0	0
$528$	1.00000	1.00000
$529$	1.00000	1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	−0.347296	−0.347296
$534$	0.120615	0.120615
$535$	0	0
$536$	−1.00000	−1.00000
$537$	0	0
$538$	0.532089	0.532089
$539$	3.87939	3.87939
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	1.53209	1.53209
$544$	1.34730	1.34730
$545$	0	0
$546$	−0.226682	−0.226682
$547$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$547$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$548$	0.879385	0.879385
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0.532089	0.532089
$555$	0	0
$556$	1.65270	1.65270
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	2.34730	2.34730
$562$	0	0
$563$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$563$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$564$	1.65270	1.65270
$565$	0	0
$566$	−0.347296	−0.347296
$567$	−1.87939	−1.87939
$568$	0	0
$569$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$569$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$570$	0	0
$571$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$572$	−0.467911	−0.467911
$573$	2.00000	2.00000
$574$	0.652704	0.652704
$575$	0	0
$576$	−0.347296	−0.347296
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0.467911	0.467911
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0.120615	0.120615
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	−2.22668	−2.22668
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0.532089	0.532089
$595$	0	0
$596$	0	0
$597$	0.347296	0.347296
$598$	0	0
$599$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$599$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	1.53209	1.53209
$604$	0.879385	0.879385
$605$	0	0
$606$	0.120615	0.120615
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	−1.87939	−1.87939
$610$	0	0
$611$	−0.652704	−0.652704
$612$	−1.34730	−1.34730
$613$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$613$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$614$	0	0
$615$	0	0
$616$	1.87939	1.87939
$617$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$617$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$618$	−0.347296	−0.347296
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	−0.652704	−0.652704
$623$	−0.652704	−0.652704
$624$	0.226682	0.226682
$625$	0	0
$626$	−0.652704	−0.652704
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$631$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$632$	0	0
$633$	0	0
$634$	0.120615	0.120615
$635$	0	0
$636$	0	0
$637$	0.879385	0.879385
$638$	0.532089	0.532089
$639$	0	0
$640$	0	0
$641$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$641$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$642$	0	0
$643$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$643$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	−0.652704	−0.652704
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$653$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$654$	0.120615	0.120615
$655$	0	0
$656$	−0.652704	−0.652704
$657$	0	0
$658$	1.22668	1.22668
$659$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$659$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$660$	0	0
$661$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$661$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$662$	0	0
$663$	0.532089	0.532089
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	1.53209	1.53209
$670$	0	0
$671$	0	0
$672$	−1.65270	−1.65270
$673$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$673$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$674$	0	0
$675$	0	0
$676$	0.773318	0.773318
$677$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$677$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$678$	−0.652704	−0.652704
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	−1.00000	−1.00000
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$691$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$692$	0	0
$693$	−2.87939	−2.87939
$694$	0	0
$695$	0	0
$696$	−0.652704	−0.652704
$697$	−1.53209	−1.53209
$698$	−0.347296	−0.347296
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0.120615	0.120615
$703$	0	0
$704$	−0.532089	−0.532089
$705$	0	0
$706$	0	0
$707$	−0.652704	−0.652704
$708$	0	0
$709$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$709$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$710$	0	0
$711$	0	0
$712$	−0.226682	−0.226682
$713$	0	0
$714$	−1.00000	−1.00000
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−0.347296	−0.347296
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	1.87939	1.87939
$722$	0.347296	0.347296
$723$	−1.87939	−1.87939
$724$	−1.34730	−1.34730
$725$	0	0
$726$	0.467911	0.467911
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0.426022	0.426022
$729$	1.00000	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	2.34730	2.34730
$738$	−0.347296	−0.347296
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$743$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$744$	0	0
$745$	0	0
$746$	0.694593	0.694593
$747$	0	0
$748$	−2.06418	−2.06418
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	−1.22668	−1.22668
$753$	0.347296	0.347296
$754$	0.120615	0.120615
$755$	0	0
$756$	1.65270	1.65270
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	−0.652704	−0.652704
$764$	−1.75877	−1.75877
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	2.00000	2.00000	1.00000			$0$
$773$	2.00000	2.00000	1.00000			$0$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0.120615	0.120615
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	1.00000	1.00000
$784$	1.65270	1.65270
$785$	0	0
$786$	−0.652704	−0.652704
$787$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$787$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$788$	0	0
$789$	−1.00000	−1.00000
$790$	0	0
$791$	3.53209	3.53209
$792$	−1.00000	−1.00000
$793$	0	0
$794$	−0.347296	−0.347296
$795$	0	0
$796$	−0.305407	−0.305407
$797$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$797$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$798$	0	0
$799$	−2.87939	−2.87939
$800$	0	0
$801$	0.347296	0.347296
$802$	0	0
$803$	0	0
$804$	−1.34730	−1.34730
$805$	0	0
$806$	0	0
$807$	1.53209	1.53209
$808$	−0.226682	−0.226682
$809$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$809$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$810$	0	0
$811$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$811$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$812$	1.65270	1.65270
$813$	0	0
$814$	0	0
$815$	0	0
$816$	1.00000	1.00000
$817$	0	0
$818$	0	0
$819$	−0.652704	−0.652704
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	−0.347296	−0.347296
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0.652704	0.652704
$825$	0	0
$826$	0	0
$827$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$827$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	1.53209	1.53209
$832$	−0.120615	−0.120615
$833$	3.87939	3.87939
$834$	−0.652704	−0.652704
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$839$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	−0.652704	−0.652704
$847$	−2.53209	−2.53209
$848$	0	0
$849$	−1.00000	−1.00000
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0.184793	0.184793
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	1.87939	1.87939
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0.879385	0.879385
$865$	0	0
$866$	0	0
$867$	1.34730	1.34730
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0.532089	0.532089
$872$	−0.226682	−0.226682
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$877$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$878$	0.532089	0.532089
$879$	0.347296	0.347296
$880$	0	0
$881$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$881$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$882$	0.879385	0.879385
$883$	2.00000	2.00000	1.00000			$0$
$883$	2.00000	2.00000	1.00000			$0$
$884$	−0.467911	−0.467911
$885$	0	0
$886$	0.120615	0.120615
$887$	−1.87939	−1.87939	−0.939693	−	0.342020i	$-0.888889\pi$
$887$	−1.87939	−1.87939	−0.939693	+	0.342020i	$0.888889\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	1.53209	1.53209
$892$	−1.34730	−1.34730
$893$	0	0
$894$	0	0
$895$	0	0
$896$	1.87939	1.87939
$897$	0	0
$898$	−0.652704	−0.652704
$899$	0	0
$900$	0	0
$901$	0	0
$902$	−0.532089	−0.532089
$903$	0	0
$904$	1.22668	1.22668
$905$	0	0
$906$	−0.347296	−0.347296
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	0.347296	0.347296
$910$	0	0
$911$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$911$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$912$	0	0
$913$	0	0
$914$	−0.652704	−0.652704
$915$	0	0
$916$	0	0
$917$	3.53209	3.53209
$918$	0.532089	0.532089
$919$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$919$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$920$	0	0
$921$	0	0
$922$	−0.347296	−0.347296
$923$	0	0
$924$	2.53209	2.53209
$925$	0	0
$926$	0.120615	0.120615
$927$	−1.00000	−1.00000
$928$	0.879385	0.879385
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−1.87939	−1.87939
$934$	−0.347296	−0.347296
$935$	0	0
$936$	−0.226682	−0.226682
$937$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$937$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$938$	−1.00000	−1.00000
$939$	−1.87939	−1.87939
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	1.53209	1.53209	0.766044	−	0.642788i	$-0.222222\pi$
$947$	1.53209	1.53209	0.766044	+	0.642788i	$0.222222\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0.347296	0.347296
$952$	1.87939	1.87939
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	1.53209	1.53209
$958$	−0.347296	−0.347296
$959$	1.87939	1.87939
$960$	0	0
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	1.65270	1.65270
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	−0.879385	−0.879385
$969$	0	0
$970$	0	0
$971$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$971$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$972$	−0.879385	−0.879385
$973$	3.53209	3.53209
$974$	0.694593	0.694593
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0.532089	0.532089
$980$	0	0
$981$	0.347296	0.347296
$982$	−0.347296	−0.347296
$983$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$983$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$984$	0.652704	0.652704
$985$	0	0
$986$	0.532089	0.532089
$987$	3.53209	3.53209
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0.347296	0.347296	0.173648	−	0.984808i	$-0.444444\pi$
$991$	0.347296	0.347296	0.173648	+	0.984808i	$0.444444\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0.120615	0.120615
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2175.1.h.e.1826.2	yes	3
3.2	odd	2		2175.1.h.d.1826.2	yes	3
5.2	odd	4		2175.1.b.d.2174.4		6
5.3	odd	4		2175.1.b.d.2174.3		6
5.4	even	2		2175.1.h.c.1826.2	✓	3
15.2	even	4		2175.1.b.c.2174.3		6
15.8	even	4		2175.1.b.c.2174.4		6
15.14	odd	2		2175.1.h.f.1826.2	yes	3
29.28	even	2		2175.1.h.d.1826.2	yes	3
87.86	odd	2	CM	2175.1.h.e.1826.2	yes	3
145.28	odd	4		2175.1.b.c.2174.4		6
145.57	odd	4		2175.1.b.c.2174.3		6
145.144	even	2		2175.1.h.f.1826.2	yes	3
435.173	even	4		2175.1.b.d.2174.3		6
435.347	even	4		2175.1.b.d.2174.4		6
435.434	odd	2		2175.1.h.c.1826.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2175.1.b.c.2174.3		6	15.2	even	4
2175.1.b.c.2174.3		6	145.57	odd	4
2175.1.b.c.2174.4		6	15.8	even	4
2175.1.b.c.2174.4		6	145.28	odd	4
2175.1.b.d.2174.3		6	5.3	odd	4
2175.1.b.d.2174.3		6	435.173	even	4
2175.1.b.d.2174.4		6	5.2	odd	4
2175.1.b.d.2174.4		6	435.347	even	4
2175.1.h.c.1826.2	✓	3	5.4	even	2
2175.1.h.c.1826.2	✓	3	435.434	odd	2
2175.1.h.d.1826.2	yes	3	3.2	odd	2
2175.1.h.d.1826.2	yes	3	29.28	even	2
2175.1.h.e.1826.2	yes	3	1.1	even	1	trivial
2175.1.h.e.1826.2	yes	3	87.86	odd	2	CM
2175.1.h.f.1826.2	yes	3	15.14	odd	2
2175.1.h.f.1826.2	yes	3	145.144	even	2

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:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2175.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.347296 q^{2} +1.00000 q^{3} -0.879385 q^{4} +0.347296 q^{6} -1.87939 q^{7} -0.652704 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.347296 q^{2} +1.00000 q^{3} -0.879385 q^{4} +0.347296 q^{6} -1.87939 q^{7} -0.652704 q^{8} +1.00000 q^{9} +1.53209 q^{11} -0.879385 q^{12} +0.347296 q^{13} -0.652704 q^{14} +0.652704 q^{16} +1.53209 q^{17} +0.347296 q^{18} -1.87939 q^{21} +0.532089 q^{22} -0.652704 q^{24} +0.120615 q^{26} +1.00000 q^{27} +1.65270 q^{28} +1.00000 q^{29} +0.879385 q^{32} +1.53209 q^{33} +0.532089 q^{34} -0.879385 q^{36} +0.347296 q^{39} -1.00000 q^{41} -0.652704 q^{42} -1.34730 q^{44} -1.87939 q^{47} +0.652704 q^{48} +2.53209 q^{49} +1.53209 q^{51} -0.305407 q^{52} +0.347296 q^{54} +1.22668 q^{56} +0.347296 q^{58} -1.87939 q^{63} -0.347296 q^{64} +0.532089 q^{66} +1.53209 q^{67} -1.34730 q^{68} -0.652704 q^{72} -2.87939 q^{77} +0.120615 q^{78} +1.00000 q^{81} -0.347296 q^{82} +1.65270 q^{84} +1.00000 q^{87} -1.00000 q^{88} +0.347296 q^{89} -0.652704 q^{91} -0.652704 q^{94} +0.879385 q^{96} +0.879385 q^{98} +1.53209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} + 3 q^{4} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^3 + 3 * q^4 - 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{3} + 3 q^{4} - 3 q^{8} + 3 q^{9} + 3 q^{12} - 3 q^{14} + 3 q^{16} - 3 q^{22} - 3 q^{24} + 6 q^{26} + 3 q^{27} + 6 q^{28} + 3 q^{29} - 3 q^{32} - 3 q^{34} + 3 q^{36} - 3 q^{41} - 3 q^{42} - 3 q^{44} + 3 q^{48} + 3 q^{49} - 3 q^{52} - 3 q^{56} - 3 q^{66} - 3 q^{68} - 3 q^{72} - 3 q^{77} + 6 q^{78} + 3 q^{81} + 6 q^{84} + 3 q^{87} - 3 q^{88} - 3 q^{91} - 3 q^{94} - 3 q^{96} - 3 q^{98}+O(q^{100}) \) 3 * q + 3 * q^3 + 3 * q^4 - 3 * q^8 + 3 * q^9 + 3 * q^12 - 3 * q^14 + 3 * q^16 - 3 * q^22 - 3 * q^24 + 6 * q^26 + 3 * q^27 + 6 * q^28 + 3 * q^29 - 3 * q^32 - 3 * q^34 + 3 * q^36 - 3 * q^41 - 3 * q^42 - 3 * q^44 + 3 * q^48 + 3 * q^49 - 3 * q^52 - 3 * q^56 - 3 * q^66 - 3 * q^68 - 3 * q^72 - 3 * q^77 + 6 * q^78 + 3 * q^81 + 6 * q^84 + 3 * q^87 - 3 * q^88 - 3 * q^91 - 3 * q^94 - 3 * q^96 - 3 * q^98

Introduction

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Database

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