LMFDB - Embedded newform 935.1.h.c.934.2

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			934.2
Root			$-1.24698$ 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)

$f(q)$	$=$	$q+0.445042 q^{2} +1.24698 q^{3} -0.801938 q^{4} +1.00000 q^{5} +0.554958 q^{6} -0.801938 q^{8} +0.554958 q^{9} +O(q^{10})$	\(q+0.445042 q^{2} +1.24698 q^{3} -0.801938 q^{4} +1.00000 q^{5} +0.554958 q^{6} -0.801938 q^{8} +0.554958 q^{9} +0.445042 q^{10} -1.00000 q^{11} -1.00000 q^{12} +1.80194 q^{13} +1.24698 q^{15} +0.445042 q^{16} -1.00000 q^{17} +0.246980 q^{18} -0.801938 q^{20} -0.445042 q^{22} -0.445042 q^{23} -1.00000 q^{24} +1.00000 q^{25} +0.801938 q^{26} -0.554958 q^{27} +0.445042 q^{29} +0.554958 q^{30} +1.00000 q^{32} -1.24698 q^{33} -0.445042 q^{34} -0.445042 q^{36} -1.80194 q^{37} +2.24698 q^{39} -0.801938 q^{40} -1.24698 q^{41} -1.24698 q^{43} +0.801938 q^{44} +0.554958 q^{45} -0.198062 q^{46} +0.554958 q^{48} +1.00000 q^{49} +0.445042 q^{50} -1.24698 q^{51} -1.44504 q^{52} -0.246980 q^{54} -1.00000 q^{55} +0.198062 q^{58} -1.80194 q^{59} -1.00000 q^{60} +1.80194 q^{61} +1.80194 q^{65} -0.554958 q^{66} +0.801938 q^{68} -0.554958 q^{69} -0.445042 q^{72} -0.801938 q^{74} +1.24698 q^{75} +1.00000 q^{78} -1.24698 q^{79} +0.445042 q^{80} -1.24698 q^{81} -0.554958 q^{82} +1.80194 q^{83} -1.00000 q^{85} -0.554958 q^{86} +0.554958 q^{87} +0.801938 q^{88} +1.24698 q^{89} +0.246980 q^{90} +0.356896 q^{92} +1.24698 q^{96} -0.445042 q^{97} +0.445042 q^{98} -0.554958 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$2$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$3$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$3$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$4$	−0.801938	−0.801938
$5$	1.00000	1.00000
$5$	1.00000	1.00000
$6$	0.554958	0.554958
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	−0.801938	−0.801938
$9$	0.554958	0.554958
$10$	0.445042	0.445042
$11$	−1.00000	−1.00000
$11$	−1.00000	−1.00000
$12$	−1.00000	−1.00000
$13$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$13$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$14$	0	0
$15$	1.24698	1.24698
$16$	0.445042	0.445042
$17$	−1.00000	−1.00000
$17$	−1.00000	−1.00000
$18$	0.246980	0.246980
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−0.801938	−0.801938
$21$	0	0
$22$	−0.445042	−0.445042
$23$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$23$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$24$	−1.00000	−1.00000
$25$	1.00000	1.00000
$26$	0.801938	0.801938
$27$	−0.554958	−0.554958
$28$	0	0
$29$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$29$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$30$	0.554958	0.554958
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	1.00000	1.00000
$33$	−1.24698	−1.24698
$34$	−0.445042	−0.445042
$35$	0	0
$36$	−0.445042	−0.445042
$37$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$37$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$38$	0	0
$39$	2.24698	2.24698
$40$	−0.801938	−0.801938
$41$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$41$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$42$	0	0
$43$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$43$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$44$	0.801938	0.801938
$45$	0.554958	0.554958
$46$	−0.198062	−0.198062
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0.554958	0.554958
$49$	1.00000	1.00000
$50$	0.445042	0.445042
$51$	−1.24698	−1.24698
$52$	−1.44504	−1.44504
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	−0.246980	−0.246980
$55$	−1.00000	−1.00000
$56$	0	0
$57$	0	0
$58$	0.198062	0.198062
$59$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$59$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$60$	−1.00000	−1.00000
$61$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$61$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	1.80194	1.80194
$66$	−0.554958	−0.554958
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0.801938	0.801938
$69$	−0.554958	−0.554958
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−0.445042	−0.445042
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	−0.801938	−0.801938
$75$	1.24698	1.24698
$76$	0	0
$77$	0	0
$78$	1.00000	1.00000
$79$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$79$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$80$	0.445042	0.445042
$81$	−1.24698	−1.24698
$82$	−0.554958	−0.554958
$83$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$83$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$84$	0	0
$85$	−1.00000	−1.00000
$86$	−0.554958	−0.554958
$87$	0.554958	0.554958
$88$	0.801938	0.801938
$89$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$89$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$90$	0.246980	0.246980
$91$	0	0
$92$	0.356896	0.356896
$93$	0	0
$94$	0	0
$95$	0	0
$96$	1.24698	1.24698
$97$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$97$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$98$	0.445042	0.445042
$99$	−0.554958	−0.554958
$100$	−0.801938	−0.801938
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	−0.554958	−0.554958
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	−1.44504	−1.44504
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0.445042	0.445042
$109$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$109$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$110$	−0.445042	−0.445042
$111$	−2.24698	−2.24698
$112$	0	0
$113$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$113$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$114$	0	0
$115$	−0.445042	−0.445042
$116$	−0.356896	−0.356896
$117$	1.00000	1.00000
$118$	−0.801938	−0.801938
$119$	0	0
$120$	−1.00000	−1.00000
$121$	1.00000	1.00000
$122$	0.801938	0.801938
$123$	−1.55496	−1.55496
$124$	0	0
$125$	1.00000	1.00000
$126$	0	0
$127$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$127$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$128$	−1.00000	−1.00000
$129$	−1.55496	−1.55496
$130$	0.801938	0.801938
$131$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$131$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$132$	1.00000	1.00000
$133$	0	0
$134$	0	0
$135$	−0.554958	−0.554958
$136$	0.801938	0.801938
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	−0.246980	−0.246980
$139$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$139$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−1.80194	−1.80194
$144$	0.246980	0.246980
$145$	0.445042	0.445042
$146$	0	0
$147$	1.24698	1.24698
$148$	1.44504	1.44504
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0.554958	0.554958
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	−0.554958	−0.554958
$154$	0	0
$155$	0	0
$156$	−1.80194	−1.80194
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	−0.554958	−0.554958
$159$	0	0
$160$	1.00000	1.00000
$161$	0	0
$162$	−0.554958	−0.554958
$163$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$163$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$164$	1.00000	1.00000
$165$	−1.24698	−1.24698
$166$	0.801938	0.801938
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	2.24698	2.24698
$170$	−0.445042	−0.445042
$171$	0	0
$172$	1.00000	1.00000
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0.246980	0.246980
$175$	0	0
$176$	−0.445042	−0.445042
$177$	−2.24698	−2.24698
$178$	0.554958	0.554958
$179$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$179$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$180$	−0.445042	−0.445042
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	2.24698	2.24698
$184$	0.356896	0.356896
$185$	−1.80194	−1.80194
$186$	0	0
$187$	1.00000	1.00000
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$191$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	−0.198062	−0.198062
$195$	2.24698	2.24698
$196$	−0.801938	−0.801938
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	−0.246980	−0.246980
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−0.801938	−0.801938
$201$	0	0
$202$	0	0
$203$	0	0
$204$	1.00000	1.00000
$205$	−1.24698	−1.24698
$206$	0	0
$207$	−0.246980	−0.246980
$208$	0.801938	0.801938
$209$	0	0
$210$	0	0
$211$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$211$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	−1.24698	−1.24698
$216$	0.445042	0.445042
$217$	0	0
$218$	−0.554958	−0.554958
$219$	0	0
$220$	0.801938	0.801938
$221$	−1.80194	−1.80194
$222$	−1.00000	−1.00000
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	0.554958	0.554958
$226$	−0.801938	−0.801938
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$229$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$230$	−0.198062	−0.198062
$231$	0	0
$232$	−0.356896	−0.356896
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0.445042	0.445042
$235$	0	0
$236$	1.44504	1.44504
$237$	−1.55496	−1.55496
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0.554958	0.554958
$241$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$241$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$242$	0.445042	0.445042
$243$	−1.00000	−1.00000
$244$	−1.44504	−1.44504
$245$	1.00000	1.00000
$246$	−0.692021	−0.692021
$247$	0	0
$248$	0	0
$249$	2.24698	2.24698
$250$	0.445042	0.445042
$251$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$251$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$252$	0	0
$253$	0.445042	0.445042
$254$	0.198062	0.198062
$255$	−1.24698	−1.24698
$256$	−0.445042	−0.445042
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	−0.692021	−0.692021
$259$	0	0
$260$	−1.44504	−1.44504
$261$	0.246980	0.246980
$262$	0.801938	0.801938
$263$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$263$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$264$	1.00000	1.00000
$265$	0	0
$266$	0	0
$267$	1.55496	1.55496
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	−0.246980	−0.246980
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	−0.445042	−0.445042
$273$	0	0
$274$	0	0
$275$	−1.00000	−1.00000
$276$	0.445042	0.445042
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0.801938	0.801938
$279$	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
$286$	−0.801938	−0.801938
$287$	0	0
$288$	0.554958	0.554958
$289$	1.00000	1.00000
$290$	0.198062	0.198062
$291$	−0.554958	−0.554958
$292$	0	0
$293$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$293$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$294$	0.554958	0.554958
$295$	−1.80194	−1.80194
$296$	1.44504	1.44504
$297$	0.554958	0.554958
$298$	0	0
$299$	−0.801938	−0.801938
$300$	−1.00000	−1.00000
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	1.80194	1.80194
$306$	−0.246980	−0.246980
$307$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$307$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	−1.80194	−1.80194
$313$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$313$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$314$	0	0
$315$	0	0
$316$	1.00000	1.00000
$317$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$317$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$318$	0	0
$319$	−0.445042	−0.445042
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	1.00000	1.00000
$325$	1.80194	1.80194
$326$	−0.198062	−0.198062
$327$	−1.55496	−1.55496
$328$	1.00000	1.00000
$329$	0	0
$330$	−0.554958	−0.554958
$331$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$331$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$332$	−1.44504	−1.44504
$333$	−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
$339$	−2.24698	−2.24698
$340$	0.801938	0.801938
$341$	0	0
$342$	0	0
$343$	0	0
$344$	1.00000	1.00000
$345$	−0.554958	−0.554958
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	−0.445042	−0.445042
$349$	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
$358$	−0.198062	−0.198062
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	−0.445042	−0.445042
$361$	1.00000	1.00000
$362$	0	0
$363$	1.24698	1.24698
$364$	0	0
$365$	0	0
$366$	1.00000	1.00000
$367$	2.00000	2.00000	1.00000			$0$
$367$	2.00000	2.00000	1.00000			$0$
$368$	−0.198062	−0.198062
$369$	−0.692021	−0.692021
$370$	−0.801938	−0.801938
$371$	0	0
$372$	0	0
$373$	−2.00000	−2.00000	−1.00000			$\pi$
$373$	−2.00000	−2.00000	−1.00000			$\pi$
$374$	0.445042	0.445042
$375$	1.24698	1.24698
$376$	0	0
$377$	0.801938	0.801938
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	0.554958	0.554958
$382$	−0.198062	−0.198062
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	−1.24698	−1.24698
$385$	0	0
$386$	0	0
$387$	−0.692021	−0.692021
$388$	0.356896	0.356896
$389$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$389$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$390$	1.00000	1.00000
$391$	0.445042	0.445042
$392$	−0.801938	−0.801938
$393$	2.24698	2.24698
$394$	0	0
$395$	−1.24698	−1.24698
$396$	0.445042	0.445042
$397$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$397$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$398$	0	0
$399$	0	0
$400$	0.445042	0.445042
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−1.24698	−1.24698
$406$	0	0
$407$	1.80194	1.80194
$408$	1.00000	1.00000
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	−0.554958	−0.554958
$411$	0	0
$412$	0	0
$413$	0	0
$414$	−0.109916	−0.109916
$415$	1.80194	1.80194
$416$	1.80194	1.80194
$417$	2.24698	2.24698
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$421$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$422$	0.198062	0.198062
$423$	0	0
$424$	0	0
$425$	−1.00000	−1.00000
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−2.24698	−2.24698
$430$	−0.554958	−0.554958
$431$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$431$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$432$	−0.246980	−0.246980
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0.554958	0.554958
$436$	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			$\pi$
$440$	0.801938	0.801938
$441$	0.554958	0.554958
$442$	−0.801938	−0.801938
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	1.80194	1.80194
$445$	1.24698	1.24698
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0.246980	0.246980
$451$	1.24698	1.24698
$452$	1.44504	1.44504
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$457$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$458$	0.554958	0.554958
$459$	0.554958	0.554958
$460$	0.356896	0.356896
$461$	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			$\pi$
$464$	0.198062	0.198062
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	−0.801938	−0.801938
$469$	0	0
$470$	0	0
$471$	0	0
$472$	1.44504	1.44504
$473$	1.24698	1.24698
$474$	−0.692021	−0.692021
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$479$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$480$	1.24698	1.24698
$481$	−3.24698	−3.24698
$482$	0.198062	0.198062
$483$	0	0
$484$	−0.801938	−0.801938
$485$	−0.445042	−0.445042
$486$	−0.445042	−0.445042
$487$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$487$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$488$	−1.44504	−1.44504
$489$	−0.554958	−0.554958
$490$	0.445042	0.445042
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	1.24698	1.24698
$493$	−0.445042	−0.445042
$494$	0	0
$495$	−0.554958	−0.554958
$496$	0	0
$497$	0	0
$498$	1.00000	1.00000
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	−0.801938	−0.801938
$501$	0	0
$502$	0.554958	0.554958
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0.198062	0.198062
$507$	2.80194	2.80194
$508$	−0.356896	−0.356896
$509$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$509$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$510$	−0.554958	−0.554958
$511$	0	0
$512$	0.801938	0.801938
$513$	0	0
$514$	0	0
$515$	0	0
$516$	1.24698	1.24698
$517$	0	0
$518$	0	0
$519$	0	0
$520$	−1.44504	−1.44504
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0.109916	0.109916
$523$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$523$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$524$	−1.44504	−1.44504
$525$	0	0
$526$	−0.554958	−0.554958
$527$	0	0
$528$	−0.554958	−0.554958
$529$	−0.801938	−0.801938
$530$	0	0
$531$	−1.00000	−1.00000
$532$	0	0
$533$	−2.24698	−2.24698
$534$	0.692021	0.692021
$535$	0	0
$536$	0	0
$537$	−0.554958	−0.554958
$538$	0	0
$539$	−1.00000	−1.00000
$540$	0.445042	0.445042
$541$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$541$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$542$	0	0
$543$	0	0
$544$	−1.00000	−1.00000
$545$	−1.24698	−1.24698
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	1.00000	1.00000
$550$	−0.445042	−0.445042
$551$	0	0
$552$	0.445042	0.445042
$553$	0	0
$554$	0	0
$555$	−2.24698	−2.24698
$556$	−1.44504	−1.44504
$557$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$557$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$558$	0	0
$559$	−2.24698	−2.24698
$560$	0	0
$561$	1.24698	1.24698
$562$	0	0
$563$	−2.00000	−2.00000	−1.00000			$\pi$
$563$	−2.00000	−2.00000	−1.00000			$\pi$
$564$	0	0
$565$	−1.80194	−1.80194
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$571$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$572$	1.44504	1.44504
$573$	−0.554958	−0.554958
$574$	0	0
$575$	−0.445042	−0.445042
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0.445042	0.445042
$579$	0	0
$580$	−0.356896	−0.356896
$581$	0	0
$582$	−0.246980	−0.246980
$583$	0	0
$584$	0	0
$585$	1.00000	1.00000
$586$	−0.554958	−0.554958
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	−1.00000	−1.00000
$589$	0	0
$590$	−0.801938	−0.801938
$591$	0	0
$592$	−0.801938	−0.801938
$593$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$593$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$594$	0.246980	0.246980
$595$	0	0
$596$	0	0
$597$	0	0
$598$	−0.356896	−0.356896
$599$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$599$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$600$	−1.00000	−1.00000
$601$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$601$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$602$	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
$610$	0.801938	0.801938
$611$	0	0
$612$	0.445042	0.445042
$613$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$613$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$614$	0.198062	0.198062
$615$	−1.55496	−1.55496
$616$	0	0
$617$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$617$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0.246980	0.246980
$622$	0	0
$623$	0	0
$624$	1.00000	1.00000
$625$	1.00000	1.00000
$626$	0.554958	0.554958
$627$	0	0
$628$	0	0
$629$	1.80194	1.80194
$630$	0	0
$631$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$631$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$632$	1.00000	1.00000
$633$	0.554958	0.554958
$634$	0.554958	0.554958
$635$	0.445042	0.445042
$636$	0	0
$637$	1.80194	1.80194
$638$	−0.198062	−0.198062
$639$	0	0
$640$	−1.00000	−1.00000
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$643$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$644$	0	0
$645$	−1.55496	−1.55496
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	1.00000	1.00000
$649$	1.80194	1.80194
$650$	0.801938	0.801938
$651$	0	0
$652$	0.356896	0.356896
$653$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$653$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$654$	−0.692021	−0.692021
$655$	1.80194	1.80194
$656$	−0.554958	−0.554958
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	1.00000	1.00000
$661$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$661$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$662$	0.554958	0.554958
$663$	−2.24698	−2.24698
$664$	−1.44504	−1.44504
$665$	0	0
$666$	−0.445042	−0.445042
$667$	−0.198062	−0.198062
$668$	0	0
$669$	0	0
$670$	0	0
$671$	−1.80194	−1.80194
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	−0.554958	−0.554958
$676$	−1.80194	−1.80194
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	−1.00000	−1.00000
$679$	0	0
$680$	0.801938	0.801938
$681$	0	0
$682$	0	0
$683$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$683$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	1.55496	1.55496
$688$	−0.554958	−0.554958
$689$	0	0
$690$	−0.246980	−0.246980
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	1.80194	1.80194
$696$	−0.445042	−0.445042
$697$	1.24698	1.24698
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	−0.445042	−0.445042
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	1.80194	1.80194
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	−0.692021	−0.692021
$712$	−1.00000	−1.00000
$713$	0	0
$714$	0	0
$715$	−1.80194	−1.80194
$716$	0.356896	0.356896
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0.246980	0.246980
$721$	0	0
$722$	0.445042	0.445042
$723$	0.554958	0.554958
$724$	0	0
$725$	0.445042	0.445042
$726$	0.554958	0.554958
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	1.24698	1.24698
$732$	−1.80194	−1.80194
$733$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$733$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$734$	0.890084	0.890084
$735$	1.24698	1.24698
$736$	−0.445042	−0.445042
$737$	0	0
$738$	−0.307979	−0.307979
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	1.44504	1.44504
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	−0.890084	−0.890084
$747$	1.00000	1.00000
$748$	−0.801938	−0.801938
$749$	0	0
$750$	0.554958	0.554958
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	1.55496	1.55496
$754$	0.356896	0.356896
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0.554958	0.554958
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0.246980	0.246980
$763$	0	0
$764$	0.356896	0.356896
$765$	−0.554958	−0.554958
$766$	0	0
$767$	−3.24698	−3.24698
$768$	−0.554958	−0.554958
$769$	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			$\pi$
$774$	−0.307979	−0.307979
$775$	0	0
$776$	0.356896	0.356896
$777$	0	0
$778$	0.554958	0.554958
$779$	0	0
$780$	−1.80194	−1.80194
$781$	0	0
$782$	0.198062	0.198062
$783$	−0.246980	−0.246980
$784$	0.445042	0.445042
$785$	0	0
$786$	1.00000	1.00000
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	−1.55496	−1.55496
$790$	−0.554958	−0.554958
$791$	0	0
$792$	0.445042	0.445042
$793$	3.24698	3.24698
$794$	0.554958	0.554958
$795$	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
$801$	0.692021	0.692021
$802$	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			$\pi$
$810$	−0.554958	−0.554958
$811$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$811$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$812$	0	0
$813$	0	0
$814$	0.801938	0.801938
$815$	−0.445042	−0.445042
$816$	−0.554958	−0.554958
$817$	0	0
$818$	0	0
$819$	0	0
$820$	1.00000	1.00000
$821$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$821$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$822$	0	0
$823$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$823$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$824$	0	0
$825$	−1.24698	−1.24698
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0.198062	0.198062
$829$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$829$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$830$	0.801938	0.801938
$831$	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
$841$	−0.801938	−0.801938
$842$	−0.198062	−0.198062
$843$	0	0
$844$	−0.356896	−0.356896
$845$	2.24698	2.24698
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	−0.445042	−0.445042
$851$	0.801938	0.801938
$852$	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
$859$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$859$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$860$	1.00000	1.00000
$861$	0	0
$862$	0.801938	0.801938
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	−0.554958	−0.554958
$865$	0	0
$866$	0	0
$867$	1.24698	1.24698
$868$	0	0
$869$	1.24698	1.24698
$870$	0.246980	0.246980
$871$	0	0
$872$	1.00000	1.00000
$873$	−0.246980	−0.246980
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	−0.890084	−0.890084
$879$	−1.55496	−1.55496
$880$	−0.445042	−0.445042
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0.246980	0.246980
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	1.44504	1.44504
$885$	−2.24698	−2.24698
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	1.80194	1.80194
$889$	0	0
$890$	0.554958	0.554958
$891$	1.24698	1.24698
$892$	0	0
$893$	0	0
$894$	0	0
$895$	−0.445042	−0.445042
$896$	0	0
$897$	−1.00000	−1.00000
$898$	0	0
$899$	0	0
$900$	−0.445042	−0.445042
$901$	0	0
$902$	0.554958	0.554958
$903$	0	0
$904$	1.44504	1.44504
$905$	0	0
$906$	0	0
$907$	2.00000	2.00000	1.00000			$0$
$907$	2.00000	2.00000	1.00000			$0$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	−1.80194	−1.80194
$914$	−0.554958	−0.554958
$915$	2.24698	2.24698
$916$	−1.00000	−1.00000
$917$	0	0
$918$	0.246980	0.246980
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0.356896	0.356896
$921$	0.554958	0.554958
$922$	0	0
$923$	0	0
$924$	0	0
$925$	−1.80194	−1.80194
$926$	0	0
$927$	0	0
$928$	0.445042	0.445042
$929$	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
$936$	−0.801938	−0.801938
$937$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$937$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$938$	0	0
$939$	1.55496	1.55496
$940$	0	0
$941$	−2.00000	−2.00000	−1.00000			$\pi$
$941$	−2.00000	−2.00000	−1.00000			$\pi$
$942$	0	0
$943$	0.554958	0.554958
$944$	−0.801938	−0.801938
$945$	0	0
$946$	0.554958	0.554958
$947$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$947$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$948$	1.24698	1.24698
$949$	0	0
$950$	0	0
$951$	1.55496	1.55496
$952$	0	0
$953$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$953$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$954$	0	0
$955$	−0.445042	−0.445042
$956$	0	0
$957$	−0.554958	−0.554958
$958$	0.198062	0.198062
$959$	0	0
$960$	0	0
$961$	1.00000	1.00000
$962$	−1.44504	−1.44504
$963$	0	0
$964$	−0.356896	−0.356896
$965$	0	0
$966$	0	0
$967$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$967$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$968$	−0.801938	−0.801938
$969$	0	0
$970$	−0.198062	−0.198062
$971$	2.00000	2.00000	1.00000			$0$
$971$	2.00000	2.00000	1.00000			$0$
$972$	0.801938	0.801938
$973$	0	0
$974$	−0.801938	−0.801938
$975$	2.24698	2.24698
$976$	0.801938	0.801938
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	−0.246980	−0.246980
$979$	−1.24698	−1.24698
$980$	−0.801938	−0.801938
$981$	−0.692021	−0.692021
$982$	0	0
$983$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$983$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$984$	1.24698	1.24698
$985$	0	0
$986$	−0.198062	−0.198062
$987$	0	0
$988$	0	0
$989$	0.554958	0.554958
$990$	−0.246980	−0.246980
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	1.55496	1.55496
$994$	0	0
$995$	0	0
$996$	−1.80194	−1.80194
$997$	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.c.934.2	yes	3
5.4	even	2		935.1.h.b.934.2	yes	3
11.10	odd	2		935.1.h.a.934.2	✓	3
17.16	even	2		935.1.h.d.934.2	yes	3
55.54	odd	2		935.1.h.d.934.2	yes	3
85.84	even	2		935.1.h.a.934.2	✓	3
187.186	odd	2		935.1.h.b.934.2	yes	3
935.934	odd	2	CM	935.1.h.c.934.2	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
935.1.h.a.934.2	✓	3	11.10	odd	2
935.1.h.a.934.2	✓	3	85.84	even	2
935.1.h.b.934.2	yes	3	5.4	even	2
935.1.h.b.934.2	yes	3	187.186	odd	2
935.1.h.c.934.2	yes	3	1.1	even	1	trivial
935.1.h.c.934.2	yes	3	935.934	odd	2	CM
935.1.h.d.934.2	yes	3	17.16	even	2
935.1.h.d.934.2	yes	3	55.54	odd	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)

\(f(q)\)	\(=\)	\(q+0.445042 q^{2} +1.24698 q^{3} -0.801938 q^{4} +1.00000 q^{5} +0.554958 q^{6} -0.801938 q^{8} +0.554958 q^{9} +O(q^{10})\)	\(q+0.445042 q^{2} +1.24698 q^{3} -0.801938 q^{4} +1.00000 q^{5} +0.554958 q^{6} -0.801938 q^{8} +0.554958 q^{9} +0.445042 q^{10} -1.00000 q^{11} -1.00000 q^{12} +1.80194 q^{13} +1.24698 q^{15} +0.445042 q^{16} -1.00000 q^{17} +0.246980 q^{18} -0.801938 q^{20} -0.445042 q^{22} -0.445042 q^{23} -1.00000 q^{24} +1.00000 q^{25} +0.801938 q^{26} -0.554958 q^{27} +0.445042 q^{29} +0.554958 q^{30} +1.00000 q^{32} -1.24698 q^{33} -0.445042 q^{34} -0.445042 q^{36} -1.80194 q^{37} +2.24698 q^{39} -0.801938 q^{40} -1.24698 q^{41} -1.24698 q^{43} +0.801938 q^{44} +0.554958 q^{45} -0.198062 q^{46} +0.554958 q^{48} +1.00000 q^{49} +0.445042 q^{50} -1.24698 q^{51} -1.44504 q^{52} -0.246980 q^{54} -1.00000 q^{55} +0.198062 q^{58} -1.80194 q^{59} -1.00000 q^{60} +1.80194 q^{61} +1.80194 q^{65} -0.554958 q^{66} +0.801938 q^{68} -0.554958 q^{69} -0.445042 q^{72} -0.801938 q^{74} +1.24698 q^{75} +1.00000 q^{78} -1.24698 q^{79} +0.445042 q^{80} -1.24698 q^{81} -0.554958 q^{82} +1.80194 q^{83} -1.00000 q^{85} -0.554958 q^{86} +0.554958 q^{87} +0.801938 q^{88} +1.24698 q^{89} +0.246980 q^{90} +0.356896 q^{92} +1.24698 q^{96} -0.445042 q^{97} +0.445042 q^{98} -0.554958 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - q^{3} + 2 q^{4} + 3 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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

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