LMFDB - Embedded newform 935.1.h.b.934.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [935,1,Mod(934,935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(935, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("935.934");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 935 = 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	935.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:	$0.466625786812$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{7}$
Projective field:	Galois closure of 7.1.817400375.1
Artin image:	$D_{14}$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{14} - \cdots)$

Embedding invariants

Embedding label			934.1
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	935.934

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.80194 q^{2} +0.445042 q^{3} +2.24698 q^{4} -1.00000 q^{5} -0.801938 q^{6} -2.24698 q^{8} -0.801938 q^{9} +O(q^{10})$	\(q-1.80194 q^{2} +0.445042 q^{3} +2.24698 q^{4} -1.00000 q^{5} -0.801938 q^{6} -2.24698 q^{8} -0.801938 q^{9} +1.80194 q^{10} -1.00000 q^{11} +1.00000 q^{12} +1.24698 q^{13} -0.445042 q^{15} +1.80194 q^{16} +1.00000 q^{17} +1.44504 q^{18} -2.24698 q^{20} +1.80194 q^{22} +1.80194 q^{23} -1.00000 q^{24} +1.00000 q^{25} -2.24698 q^{26} -0.801938 q^{27} +1.80194 q^{29} +0.801938 q^{30} -1.00000 q^{32} -0.445042 q^{33} -1.80194 q^{34} -1.80194 q^{36} -1.24698 q^{37} +0.554958 q^{39} +2.24698 q^{40} +0.445042 q^{41} -0.445042 q^{43} -2.24698 q^{44} +0.801938 q^{45} -3.24698 q^{46} +0.801938 q^{48} +1.00000 q^{49} -1.80194 q^{50} +0.445042 q^{51} +2.80194 q^{52} +1.44504 q^{54} +1.00000 q^{55} -3.24698 q^{58} +1.24698 q^{59} -1.00000 q^{60} -1.24698 q^{61} -1.24698 q^{65} +0.801938 q^{66} +2.24698 q^{68} +0.801938 q^{69} +1.80194 q^{72} +2.24698 q^{74} +0.445042 q^{75} -1.00000 q^{78} +0.445042 q^{79} -1.80194 q^{80} +0.445042 q^{81} -0.801938 q^{82} +1.24698 q^{83} -1.00000 q^{85} +0.801938 q^{86} +0.801938 q^{87} +2.24698 q^{88} -0.445042 q^{89} -1.44504 q^{90} +4.04892 q^{92} -0.445042 q^{96} +1.80194 q^{97} -1.80194 q^{98} +0.801938 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q - q^2 + q^3 + 2 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9	$ 3 q - q^{2} + q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} - 3 q^{11} + 3 q^{12} - q^{13} - q^{15} + q^{16} + 3 q^{17} + 4 q^{18} - 2 q^{20} + q^{22} + q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} + 2 q^{27} + q^{29} - 2 q^{30} - 3 q^{32} - q^{33} - q^{34} - q^{36} + q^{37} + 2 q^{39} + 2 q^{40} + q^{41} - q^{43} - 2 q^{44} - 2 q^{45} - 5 q^{46} - 2 q^{48} + 3 q^{49} - q^{50} + q^{51} + 4 q^{52} + 4 q^{54} + 3 q^{55} - 5 q^{58} - q^{59} - 3 q^{60} + q^{61} + q^{65} - 2 q^{66} + 2 q^{68} - 2 q^{69} + q^{72} + 2 q^{74} + q^{75} - 3 q^{78} + q^{79} - q^{80} + q^{81} + 2 q^{82} - q^{83} - 3 q^{85} - 2 q^{86} - 2 q^{87} + 2 q^{88} - q^{89} - 4 q^{90} + 3 q^{92} - q^{96} + q^{97} - q^{98} - 2 q^{99}+O(q^{100}) $ 3 * q - q^2 + q^3 + 2 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 - 3 * q^11 + 3 * q^12 - q^13 - q^15 + q^16 + 3 * q^17 + 4 * q^18 - 2 * q^20 + q^22 + q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 + 2 * q^27 + q^29 - 2 * q^30 - 3 * q^32 - q^33 - q^34 - q^36 + q^37 + 2 * q^39 + 2 * q^40 + q^41 - q^43 - 2 * q^44 - 2 * q^45 - 5 * q^46 - 2 * q^48 + 3 * q^49 - q^50 + q^51 + 4 * q^52 + 4 * q^54 + 3 * q^55 - 5 * q^58 - q^59 - 3 * q^60 + q^61 + q^65 - 2 * q^66 + 2 * q^68 - 2 * q^69 + q^72 + 2 * q^74 + q^75 - 3 * q^78 + q^79 - q^80 + q^81 + 2 * q^82 - q^83 - 3 * q^85 - 2 * q^86 - 2 * q^87 + 2 * q^88 - q^89 - 4 * q^90 + 3 * q^92 - q^96 + q^97 - q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/935\mathbb{Z}\right)^\times$.

$n$	$496$	$562$	$596$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$2$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$3$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$3$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$4$	2.24698	2.24698
$5$	−1.00000	−1.00000
$5$	−1.00000	−1.00000
$6$	−0.801938	−0.801938
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	−2.24698	−2.24698
$9$	−0.801938	−0.801938
$10$	1.80194	1.80194
$11$	−1.00000	−1.00000
$11$	−1.00000	−1.00000
$12$	1.00000	1.00000
$13$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$13$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$14$	0	0
$15$	−0.445042	−0.445042
$16$	1.80194	1.80194
$17$	1.00000	1.00000
$17$	1.00000	1.00000
$18$	1.44504	1.44504
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−2.24698	−2.24698
$21$	0	0
$22$	1.80194	1.80194
$23$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$23$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$24$	−1.00000	−1.00000
$25$	1.00000	1.00000
$26$	−2.24698	−2.24698
$27$	−0.801938	−0.801938
$28$	0	0
$29$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$29$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$30$	0.801938	0.801938
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	−1.00000	−1.00000
$33$	−0.445042	−0.445042
$34$	−1.80194	−1.80194
$35$	0	0
$36$	−1.80194	−1.80194
$37$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$37$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$38$	0	0
$39$	0.554958	0.554958
$40$	2.24698	2.24698
$41$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$41$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$42$	0	0
$43$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$43$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$44$	−2.24698	−2.24698
$45$	0.801938	0.801938
$46$	−3.24698	−3.24698
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0.801938	0.801938
$49$	1.00000	1.00000
$50$	−1.80194	−1.80194
$51$	0.445042	0.445042
$52$	2.80194	2.80194
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	1.44504	1.44504
$55$	1.00000	1.00000
$56$	0	0
$57$	0	0
$58$	−3.24698	−3.24698
$59$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$59$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$60$	−1.00000	−1.00000
$61$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$61$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−1.24698	−1.24698
$66$	0.801938	0.801938
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	2.24698	2.24698
$69$	0.801938	0.801938
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	1.80194	1.80194
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	2.24698	2.24698
$75$	0.445042	0.445042
$76$	0	0
$77$	0	0
$78$	−1.00000	−1.00000
$79$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$79$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$80$	−1.80194	−1.80194
$81$	0.445042	0.445042
$82$	−0.801938	−0.801938
$83$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$83$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$84$	0	0
$85$	−1.00000	−1.00000
$86$	0.801938	0.801938
$87$	0.801938	0.801938
$88$	2.24698	2.24698
$89$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$89$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$90$	−1.44504	−1.44504
$91$	0	0
$92$	4.04892	4.04892
$93$	0	0
$94$	0	0
$95$	0	0
$96$	−0.445042	−0.445042
$97$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$97$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$98$	−1.80194	−1.80194
$99$	0.801938	0.801938
$100$	2.24698	2.24698
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	−0.801938	−0.801938
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	−2.80194	−2.80194
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	−1.80194	−1.80194
$109$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$109$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$110$	−1.80194	−1.80194
$111$	−0.554958	−0.554958
$112$	0	0
$113$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$113$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$114$	0	0
$115$	−1.80194	−1.80194
$116$	4.04892	4.04892
$117$	−1.00000	−1.00000
$118$	−2.24698	−2.24698
$119$	0	0
$120$	1.00000	1.00000
$121$	1.00000	1.00000
$122$	2.24698	2.24698
$123$	0.198062	0.198062
$124$	0	0
$125$	−1.00000	−1.00000
$126$	0	0
$127$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$127$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$128$	1.00000	1.00000
$129$	−0.198062	−0.198062
$130$	2.24698	2.24698
$131$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$131$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$132$	−1.00000	−1.00000
$133$	0	0
$134$	0	0
$135$	0.801938	0.801938
$136$	−2.24698	−2.24698
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	−1.44504	−1.44504
$139$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$139$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−1.24698	−1.24698
$144$	−1.44504	−1.44504
$145$	−1.80194	−1.80194
$146$	0	0
$147$	0.445042	0.445042
$148$	−2.80194	−2.80194
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	−0.801938	−0.801938
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	−0.801938	−0.801938
$154$	0	0
$155$	0	0
$156$	1.24698	1.24698
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	−0.801938	−0.801938
$159$	0	0
$160$	1.00000	1.00000
$161$	0	0
$162$	−0.801938	−0.801938
$163$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$163$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$164$	1.00000	1.00000
$165$	0.445042	0.445042
$166$	−2.24698	−2.24698
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	0.554958	0.554958
$170$	1.80194	1.80194
$171$	0	0
$172$	−1.00000	−1.00000
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	−1.44504	−1.44504
$175$	0	0
$176$	−1.80194	−1.80194
$177$	0.554958	0.554958
$178$	0.801938	0.801938
$179$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$179$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$180$	1.80194	1.80194
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	−0.554958	−0.554958
$184$	−4.04892	−4.04892
$185$	1.24698	1.24698
$186$	0	0
$187$	−1.00000	−1.00000
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$191$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	−3.24698	−3.24698
$195$	−0.554958	−0.554958
$196$	2.24698	2.24698
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	−1.44504	−1.44504
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−2.24698	−2.24698
$201$	0	0
$202$	0	0
$203$	0	0
$204$	1.00000	1.00000
$205$	−0.445042	−0.445042
$206$	0	0
$207$	−1.44504	−1.44504
$208$	2.24698	2.24698
$209$	0	0
$210$	0	0
$211$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$211$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0.445042	0.445042
$216$	1.80194	1.80194
$217$	0	0
$218$	−0.801938	−0.801938
$219$	0	0
$220$	2.24698	2.24698
$221$	1.24698	1.24698
$222$	1.00000	1.00000
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	−0.801938	−0.801938
$226$	2.24698	2.24698
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$229$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$230$	3.24698	3.24698
$231$	0	0
$232$	−4.04892	−4.04892
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	1.80194	1.80194
$235$	0	0
$236$	2.80194	2.80194
$237$	0.198062	0.198062
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	−0.801938	−0.801938
$241$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$241$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$242$	−1.80194	−1.80194
$243$	1.00000	1.00000
$244$	−2.80194	−2.80194
$245$	−1.00000	−1.00000
$246$	−0.356896	−0.356896
$247$	0	0
$248$	0	0
$249$	0.554958	0.554958
$250$	1.80194	1.80194
$251$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$251$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$252$	0	0
$253$	−1.80194	−1.80194
$254$	3.24698	3.24698
$255$	−0.445042	−0.445042
$256$	−1.80194	−1.80194
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0.356896	0.356896
$259$	0	0
$260$	−2.80194	−2.80194
$261$	−1.44504	−1.44504
$262$	2.24698	2.24698
$263$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$263$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$264$	1.00000	1.00000
$265$	0	0
$266$	0	0
$267$	−0.198062	−0.198062
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	−1.44504	−1.44504
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	1.80194	1.80194
$273$	0	0
$274$	0	0
$275$	−1.00000	−1.00000
$276$	1.80194	1.80194
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	2.24698	2.24698
$279$	0	0
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	2.24698	2.24698
$287$	0	0
$288$	0.801938	0.801938
$289$	1.00000	1.00000
$290$	3.24698	3.24698
$291$	0.801938	0.801938
$292$	0	0
$293$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$293$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$294$	−0.801938	−0.801938
$295$	−1.24698	−1.24698
$296$	2.80194	2.80194
$297$	0.801938	0.801938
$298$	0	0
$299$	2.24698	2.24698
$300$	1.00000	1.00000
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	1.24698	1.24698
$306$	1.44504	1.44504
$307$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$307$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	−1.24698	−1.24698
$313$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$313$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$314$	0	0
$315$	0	0
$316$	1.00000	1.00000
$317$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$317$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$318$	0	0
$319$	−1.80194	−1.80194
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	1.00000	1.00000
$325$	1.24698	1.24698
$326$	−3.24698	−3.24698
$327$	0.198062	0.198062
$328$	−1.00000	−1.00000
$329$	0	0
$330$	−0.801938	−0.801938
$331$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$331$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$332$	2.80194	2.80194
$333$	1.00000	1.00000
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	−1.00000	−1.00000
$339$	−0.554958	−0.554958
$340$	−2.24698	−2.24698
$341$	0	0
$342$	0	0
$343$	0	0
$344$	1.00000	1.00000
$345$	−0.801938	−0.801938
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	1.80194	1.80194
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	−1.00000	−1.00000
$352$	1.00000	1.00000
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	−1.00000	−1.00000
$355$	0	0
$356$	−1.00000	−1.00000
$357$	0	0
$358$	3.24698	3.24698
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	−1.80194	−1.80194
$361$	1.00000	1.00000
$362$	0	0
$363$	0.445042	0.445042
$364$	0	0
$365$	0	0
$366$	1.00000	1.00000
$367$	−2.00000	−2.00000	−1.00000			$\pi$
$367$	−2.00000	−2.00000	−1.00000			$\pi$
$368$	3.24698	3.24698
$369$	−0.356896	−0.356896
$370$	−2.24698	−2.24698
$371$	0	0
$372$	0	0
$373$	2.00000	2.00000	1.00000			$0$
$373$	2.00000	2.00000	1.00000			$0$
$374$	1.80194	1.80194
$375$	−0.445042	−0.445042
$376$	0	0
$377$	2.24698	2.24698
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	−0.801938	−0.801938
$382$	3.24698	3.24698
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0.445042	0.445042
$385$	0	0
$386$	0	0
$387$	0.356896	0.356896
$388$	4.04892	4.04892
$389$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$389$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$390$	1.00000	1.00000
$391$	1.80194	1.80194
$392$	−2.24698	−2.24698
$393$	−0.554958	−0.554958
$394$	0	0
$395$	−0.445042	−0.445042
$396$	1.80194	1.80194
$397$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$397$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$398$	0	0
$399$	0	0
$400$	1.80194	1.80194
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−0.445042	−0.445042
$406$	0	0
$407$	1.24698	1.24698
$408$	−1.00000	−1.00000
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0.801938	0.801938
$411$	0	0
$412$	0	0
$413$	0	0
$414$	2.60388	2.60388
$415$	−1.24698	−1.24698
$416$	−1.24698	−1.24698
$417$	−0.554958	−0.554958
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$421$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$422$	−3.24698	−3.24698
$423$	0	0
$424$	0	0
$425$	1.00000	1.00000
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−0.554958	−0.554958
$430$	−0.801938	−0.801938
$431$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$431$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$432$	−1.44504	−1.44504
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	−0.801938	−0.801938
$436$	1.00000	1.00000
$437$	0	0
$438$	0	0
$439$	−2.00000	−2.00000	−1.00000			$\pi$
$439$	−2.00000	−2.00000	−1.00000			$\pi$
$440$	−2.24698	−2.24698
$441$	−0.801938	−0.801938
$442$	−2.24698	−2.24698
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	−1.24698	−1.24698
$445$	0.445042	0.445042
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	1.44504	1.44504
$451$	−0.445042	−0.445042
$452$	−2.80194	−2.80194
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$457$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$458$	0.801938	0.801938
$459$	−0.801938	−0.801938
$460$	−4.04892	−4.04892
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	3.24698	3.24698
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	−2.24698	−2.24698
$469$	0	0
$470$	0	0
$471$	0	0
$472$	−2.80194	−2.80194
$473$	0.445042	0.445042
$474$	−0.356896	−0.356896
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$479$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$480$	0.445042	0.445042
$481$	−1.55496	−1.55496
$482$	−3.24698	−3.24698
$483$	0	0
$484$	2.24698	2.24698
$485$	−1.80194	−1.80194
$486$	−1.80194	−1.80194
$487$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$487$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$488$	2.80194	2.80194
$489$	0.801938	0.801938
$490$	1.80194	1.80194
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0.445042	0.445042
$493$	1.80194	1.80194
$494$	0	0
$495$	−0.801938	−0.801938
$496$	0	0
$497$	0	0
$498$	−1.00000	−1.00000
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	−2.24698	−2.24698
$501$	0	0
$502$	0.801938	0.801938
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	3.24698	3.24698
$507$	0.246980	0.246980
$508$	−4.04892	−4.04892
$509$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$509$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$510$	0.801938	0.801938
$511$	0	0
$512$	2.24698	2.24698
$513$	0	0
$514$	0	0
$515$	0	0
$516$	−0.445042	−0.445042
$517$	0	0
$518$	0	0
$519$	0	0
$520$	2.80194	2.80194
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	2.60388	2.60388
$523$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$523$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$524$	−2.80194	−2.80194
$525$	0	0
$526$	0.801938	0.801938
$527$	0	0
$528$	−0.801938	−0.801938
$529$	2.24698	2.24698
$530$	0	0
$531$	−1.00000	−1.00000
$532$	0	0
$533$	0.554958	0.554958
$534$	0.356896	0.356896
$535$	0	0
$536$	0	0
$537$	−0.801938	−0.801938
$538$	0	0
$539$	−1.00000	−1.00000
$540$	1.80194	1.80194
$541$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$541$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$542$	0	0
$543$	0	0
$544$	−1.00000	−1.00000
$545$	−0.445042	−0.445042
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	1.00000	1.00000
$550$	1.80194	1.80194
$551$	0	0
$552$	−1.80194	−1.80194
$553$	0	0
$554$	0	0
$555$	0.554958	0.554958
$556$	−2.80194	−2.80194
$557$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$557$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$558$	0	0
$559$	−0.554958	−0.554958
$560$	0	0
$561$	−0.445042	−0.445042
$562$	0	0
$563$	2.00000	2.00000	1.00000			$0$
$563$	2.00000	2.00000	1.00000			$0$
$564$	0	0
$565$	1.24698	1.24698
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$571$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$572$	−2.80194	−2.80194
$573$	−0.801938	−0.801938
$574$	0	0
$575$	1.80194	1.80194
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	−1.80194	−1.80194
$579$	0	0
$580$	−4.04892	−4.04892
$581$	0	0
$582$	−1.44504	−1.44504
$583$	0	0
$584$	0	0
$585$	1.00000	1.00000
$586$	0.801938	0.801938
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	1.00000	1.00000
$589$	0	0
$590$	2.24698	2.24698
$591$	0	0
$592$	−2.24698	−2.24698
$593$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$593$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$594$	−1.44504	−1.44504
$595$	0	0
$596$	0	0
$597$	0	0
$598$	−4.04892	−4.04892
$599$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$599$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$600$	−1.00000	−1.00000
$601$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$601$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	−1.00000	−1.00000
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	0	0
$610$	−2.24698	−2.24698
$611$	0	0
$612$	−1.80194	−1.80194
$613$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$613$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$614$	3.24698	3.24698
$615$	−0.198062	−0.198062
$616$	0	0
$617$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$617$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	−1.44504	−1.44504
$622$	0	0
$623$	0	0
$624$	1.00000	1.00000
$625$	1.00000	1.00000
$626$	−0.801938	−0.801938
$627$	0	0
$628$	0	0
$629$	−1.24698	−1.24698
$630$	0	0
$631$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$631$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$632$	−1.00000	−1.00000
$633$	0.801938	0.801938
$634$	−0.801938	−0.801938
$635$	1.80194	1.80194
$636$	0	0
$637$	1.24698	1.24698
$638$	3.24698	3.24698
$639$	0	0
$640$	−1.00000	−1.00000
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$643$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$644$	0	0
$645$	0.198062	0.198062
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	−1.00000	−1.00000
$649$	−1.24698	−1.24698
$650$	−2.24698	−2.24698
$651$	0	0
$652$	4.04892	4.04892
$653$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$653$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$654$	−0.356896	−0.356896
$655$	1.24698	1.24698
$656$	0.801938	0.801938
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	1.00000	1.00000
$661$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$661$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$662$	0.801938	0.801938
$663$	0.554958	0.554958
$664$	−2.80194	−2.80194
$665$	0	0
$666$	−1.80194	−1.80194
$667$	3.24698	3.24698
$668$	0	0
$669$	0	0
$670$	0	0
$671$	1.24698	1.24698
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	−0.801938	−0.801938
$676$	1.24698	1.24698
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	1.00000	1.00000
$679$	0	0
$680$	2.24698	2.24698
$681$	0	0
$682$	0	0
$683$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$683$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−0.198062	−0.198062
$688$	−0.801938	−0.801938
$689$	0	0
$690$	1.44504	1.44504
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	1.24698	1.24698
$696$	−1.80194	−1.80194
$697$	0.445042	0.445042
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	1.80194	1.80194
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	1.24698	1.24698
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	−0.356896	−0.356896
$712$	1.00000	1.00000
$713$	0	0
$714$	0	0
$715$	1.24698	1.24698
$716$	−4.04892	−4.04892
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	1.44504	1.44504
$721$	0	0
$722$	−1.80194	−1.80194
$723$	0.801938	0.801938
$724$	0	0
$725$	1.80194	1.80194
$726$	−0.801938	−0.801938
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	−0.445042	−0.445042
$732$	−1.24698	−1.24698
$733$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$733$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$734$	3.60388	3.60388
$735$	−0.445042	−0.445042
$736$	−1.80194	−1.80194
$737$	0	0
$738$	0.643104	0.643104
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	2.80194	2.80194
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	−3.60388	−3.60388
$747$	−1.00000	−1.00000
$748$	−2.24698	−2.24698
$749$	0	0
$750$	0.801938	0.801938
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	−0.198062	−0.198062
$754$	−4.04892	−4.04892
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	−0.801938	−0.801938
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	1.44504	1.44504
$763$	0	0
$764$	−4.04892	−4.04892
$765$	0.801938	0.801938
$766$	0	0
$767$	1.55496	1.55496
$768$	−0.801938	−0.801938
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	−0.643104	−0.643104
$775$	0	0
$776$	−4.04892	−4.04892
$777$	0	0
$778$	0.801938	0.801938
$779$	0	0
$780$	−1.24698	−1.24698
$781$	0	0
$782$	−3.24698	−3.24698
$783$	−1.44504	−1.44504
$784$	1.80194	1.80194
$785$	0	0
$786$	1.00000	1.00000
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	−0.198062	−0.198062
$790$	0.801938	0.801938
$791$	0	0
$792$	−1.80194	−1.80194
$793$	−1.55496	−1.55496
$794$	−0.801938	−0.801938
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−1.00000
$801$	0.356896	0.356896
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−2.00000	−2.00000	−1.00000			$\pi$
$809$	−2.00000	−2.00000	−1.00000			$\pi$
$810$	0.801938	0.801938
$811$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$811$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$812$	0	0
$813$	0	0
$814$	−2.24698	−2.24698
$815$	−1.80194	−1.80194
$816$	0.801938	0.801938
$817$	0	0
$818$	0	0
$819$	0	0
$820$	−1.00000	−1.00000
$821$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$821$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$822$	0	0
$823$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$823$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$824$	0	0
$825$	−0.445042	−0.445042
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	−3.24698	−3.24698
$829$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$829$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$830$	2.24698	2.24698
$831$	0	0
$832$	0	0
$833$	1.00000	1.00000
$834$	1.00000	1.00000
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	2.24698	2.24698
$842$	3.24698	3.24698
$843$	0	0
$844$	4.04892	4.04892
$845$	−0.554958	−0.554958
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	−1.80194	−1.80194
$851$	−2.24698	−2.24698
$852$	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			$\pi$
$858$	1.00000	1.00000
$859$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$859$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$860$	1.00000	1.00000
$861$	0	0
$862$	2.24698	2.24698
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0.801938	0.801938
$865$	0	0
$866$	0	0
$867$	0.445042	0.445042
$868$	0	0
$869$	−0.445042	−0.445042
$870$	1.44504	1.44504
$871$	0	0
$872$	−1.00000	−1.00000
$873$	−1.44504	−1.44504
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	3.60388	3.60388
$879$	−0.198062	−0.198062
$880$	1.80194	1.80194
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	1.44504	1.44504
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	2.80194	2.80194
$885$	−0.554958	−0.554958
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	1.24698	1.24698
$889$	0	0
$890$	−0.801938	−0.801938
$891$	−0.445042	−0.445042
$892$	0	0
$893$	0	0
$894$	0	0
$895$	1.80194	1.80194
$896$	0	0
$897$	1.00000	1.00000
$898$	0	0
$899$	0	0
$900$	−1.80194	−1.80194
$901$	0	0
$902$	0.801938	0.801938
$903$	0	0
$904$	2.80194	2.80194
$905$	0	0
$906$	0	0
$907$	−2.00000	−2.00000	−1.00000			$\pi$
$907$	−2.00000	−2.00000	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	−1.24698	−1.24698
$914$	0.801938	0.801938
$915$	0.554958	0.554958
$916$	−1.00000	−1.00000
$917$	0	0
$918$	1.44504	1.44504
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	4.04892	4.04892
$921$	−0.801938	−0.801938
$922$	0	0
$923$	0	0
$924$	0	0
$925$	−1.24698	−1.24698
$926$	0	0
$927$	0	0
$928$	−1.80194	−1.80194
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	1.00000	1.00000
$936$	2.24698	2.24698
$937$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$937$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$938$	0	0
$939$	0.198062	0.198062
$940$	0	0
$941$	−2.00000	−2.00000	−1.00000			$\pi$
$941$	−2.00000	−2.00000	−1.00000			$\pi$
$942$	0	0
$943$	0.801938	0.801938
$944$	2.24698	2.24698
$945$	0	0
$946$	−0.801938	−0.801938
$947$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$947$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$948$	0.445042	0.445042
$949$	0	0
$950$	0	0
$951$	0.198062	0.198062
$952$	0	0
$953$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$953$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$954$	0	0
$955$	1.80194	1.80194
$956$	0	0
$957$	−0.801938	−0.801938
$958$	−3.24698	−3.24698
$959$	0	0
$960$	0	0
$961$	1.00000	1.00000
$962$	2.80194	2.80194
$963$	0	0
$964$	4.04892	4.04892
$965$	0	0
$966$	0	0
$967$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$967$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$968$	−2.24698	−2.24698
$969$	0	0
$970$	3.24698	3.24698
$971$	2.00000	2.00000	1.00000			$0$
$971$	2.00000	2.00000	1.00000			$0$
$972$	2.24698	2.24698
$973$	0	0
$974$	2.24698	2.24698
$975$	0.554958	0.554958
$976$	−2.24698	−2.24698
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	−1.44504	−1.44504
$979$	0.445042	0.445042
$980$	−2.24698	−2.24698
$981$	−0.356896	−0.356896
$982$	0	0
$983$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$983$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$984$	−0.445042	−0.445042
$985$	0	0
$986$	−3.24698	−3.24698
$987$	0	0
$988$	0	0
$989$	−0.801938	−0.801938
$990$	1.44504	1.44504
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	−0.198062	−0.198062
$994$	0	0
$995$	0	0
$996$	1.24698	1.24698
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	1.00000	1.00000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	935.1.h.b.934.1	yes	3
5.4	even	2		935.1.h.c.934.3	yes	3
11.10	odd	2		935.1.h.d.934.3	yes	3
17.16	even	2		935.1.h.a.934.1	✓	3
55.54	odd	2		935.1.h.a.934.1	✓	3
85.84	even	2		935.1.h.d.934.3	yes	3
187.186	odd	2		935.1.h.c.934.3	yes	3
935.934	odd	2	CM	935.1.h.b.934.1	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
935.1.h.a.934.1	✓	3	17.16	even	2
935.1.h.a.934.1	✓	3	55.54	odd	2
935.1.h.b.934.1	yes	3	1.1	even	1	trivial
935.1.h.b.934.1	yes	3	935.934	odd	2	CM
935.1.h.c.934.3	yes	3	5.4	even	2
935.1.h.c.934.3	yes	3	187.186	odd	2
935.1.h.d.934.3	yes	3	11.10	odd	2
935.1.h.d.934.3	yes	3	85.84	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:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	935.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.80194 q^{2} +0.445042 q^{3} +2.24698 q^{4} -1.00000 q^{5} -0.801938 q^{6} -2.24698 q^{8} -0.801938 q^{9} +O(q^{10})\)	\(q-1.80194 q^{2} +0.445042 q^{3} +2.24698 q^{4} -1.00000 q^{5} -0.801938 q^{6} -2.24698 q^{8} -0.801938 q^{9} +1.80194 q^{10} -1.00000 q^{11} +1.00000 q^{12} +1.24698 q^{13} -0.445042 q^{15} +1.80194 q^{16} +1.00000 q^{17} +1.44504 q^{18} -2.24698 q^{20} +1.80194 q^{22} +1.80194 q^{23} -1.00000 q^{24} +1.00000 q^{25} -2.24698 q^{26} -0.801938 q^{27} +1.80194 q^{29} +0.801938 q^{30} -1.00000 q^{32} -0.445042 q^{33} -1.80194 q^{34} -1.80194 q^{36} -1.24698 q^{37} +0.554958 q^{39} +2.24698 q^{40} +0.445042 q^{41} -0.445042 q^{43} -2.24698 q^{44} +0.801938 q^{45} -3.24698 q^{46} +0.801938 q^{48} +1.00000 q^{49} -1.80194 q^{50} +0.445042 q^{51} +2.80194 q^{52} +1.44504 q^{54} +1.00000 q^{55} -3.24698 q^{58} +1.24698 q^{59} -1.00000 q^{60} -1.24698 q^{61} -1.24698 q^{65} +0.801938 q^{66} +2.24698 q^{68} +0.801938 q^{69} +1.80194 q^{72} +2.24698 q^{74} +0.445042 q^{75} -1.00000 q^{78} +0.445042 q^{79} -1.80194 q^{80} +0.445042 q^{81} -0.801938 q^{82} +1.24698 q^{83} -1.00000 q^{85} +0.801938 q^{86} +0.801938 q^{87} +2.24698 q^{88} -0.445042 q^{89} -1.44504 q^{90} +4.04892 q^{92} -0.445042 q^{96} +1.80194 q^{97} -1.80194 q^{98} +0.801938 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q - q^2 + q^3 + 2 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9	\( 3 q - q^{2} + q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} - 3 q^{11} + 3 q^{12} - q^{13} - q^{15} + q^{16} + 3 q^{17} + 4 q^{18} - 2 q^{20} + q^{22} + q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} + 2 q^{27} + q^{29} - 2 q^{30} - 3 q^{32} - q^{33} - q^{34} - q^{36} + q^{37} + 2 q^{39} + 2 q^{40} + q^{41} - q^{43} - 2 q^{44} - 2 q^{45} - 5 q^{46} - 2 q^{48} + 3 q^{49} - q^{50} + q^{51} + 4 q^{52} + 4 q^{54} + 3 q^{55} - 5 q^{58} - q^{59} - 3 q^{60} + q^{61} + q^{65} - 2 q^{66} + 2 q^{68} - 2 q^{69} + q^{72} + 2 q^{74} + q^{75} - 3 q^{78} + q^{79} - q^{80} + q^{81} + 2 q^{82} - q^{83} - 3 q^{85} - 2 q^{86} - 2 q^{87} + 2 q^{88} - q^{89} - 4 q^{90} + 3 q^{92} - q^{96} + q^{97} - q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q - q^2 + q^3 + 2 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 - 3 * q^11 + 3 * q^12 - q^13 - q^15 + q^16 + 3 * q^17 + 4 * q^18 - 2 * q^20 + q^22 + q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 + 2 * q^27 + q^29 - 2 * q^30 - 3 * q^32 - q^33 - q^34 - q^36 + q^37 + 2 * q^39 + 2 * q^40 + q^41 - q^43 - 2 * q^44 - 2 * q^45 - 5 * q^46 - 2 * q^48 + 3 * q^49 - q^50 + q^51 + 4 * q^52 + 4 * q^54 + 3 * q^55 - 5 * q^58 - q^59 - 3 * q^60 + q^61 + q^65 - 2 * q^66 + 2 * q^68 - 2 * q^69 + q^72 + 2 * q^74 + q^75 - 3 * q^78 + q^79 - q^80 + q^81 + 2 * q^82 - q^83 - 3 * q^85 - 2 * q^86 - 2 * q^87 + 2 * q^88 - q^89 - 4 * q^90 + 3 * q^92 - q^96 + q^97 - q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more