LMFDB - Embedded newform 151.1.b.a.150.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,1,Mod(150,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("151.150");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	151.b (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:	$0.0753588169076$
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 7.1.3442951.1
Artin image:	$D_7$
Artin field:	Galois closure of 7.1.3442951.1

Embedding invariants

Embedding label			150.3
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	151.150

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.24698 q^{2} +0.554958 q^{4} -1.80194 q^{5} -0.554958 q^{8} +1.00000 q^{9} +O(q^{10})$	$q+1.24698 q^{2} +0.554958 q^{4} -1.80194 q^{5} -0.554958 q^{8} +1.00000 q^{9} -2.24698 q^{10} -0.445042 q^{11} -1.24698 q^{16} -0.445042 q^{17} +1.24698 q^{18} +1.24698 q^{19} -1.00000 q^{20} -0.554958 q^{22} +2.24698 q^{25} +1.24698 q^{29} -1.80194 q^{31} -1.00000 q^{32} -0.554958 q^{34} +0.554958 q^{36} -0.445042 q^{37} +1.55496 q^{38} +1.00000 q^{40} -1.80194 q^{43} -0.246980 q^{44} -1.80194 q^{45} +1.24698 q^{47} +1.00000 q^{49} +2.80194 q^{50} +0.801938 q^{55} +1.55496 q^{58} -1.80194 q^{59} -2.24698 q^{62} -0.246980 q^{68} -0.554958 q^{72} -0.554958 q^{74} +0.692021 q^{76} +2.24698 q^{80} +1.00000 q^{81} +0.801938 q^{85} -2.24698 q^{86} +0.246980 q^{88} -2.24698 q^{90} +1.55496 q^{94} -2.24698 q^{95} +1.24698 q^{97} +1.24698 q^{98} -0.445042 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 2 q^{4} - q^{5} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - q^2 + 2 * q^4 - q^5 - 2 * q^8 + 3 * q^9	$ 3 q - q^{2} + 2 q^{4} - q^{5} - 2 q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + q^{16} - q^{17} - q^{18} - q^{19} - 3 q^{20} - 2 q^{22} + 2 q^{25} - q^{29} - q^{31} - 3 q^{32} - 2 q^{34} + 2 q^{36} - q^{37} + 5 q^{38} + 3 q^{40} - q^{43} + 4 q^{44} - q^{45} - q^{47} + 3 q^{49} + 4 q^{50} - 2 q^{55} + 5 q^{58} - q^{59} - 2 q^{62} + 4 q^{68} - 2 q^{72} - 2 q^{74} - 3 q^{76} + 2 q^{80} + 3 q^{81} - 2 q^{85} - 2 q^{86} - 4 q^{88} - 2 q^{90} + 5 q^{94} - 2 q^{95} - q^{97} - q^{98} - q^{99}+O(q^{100}) $ 3 * q - q^2 + 2 * q^4 - q^5 - 2 * q^8 + 3 * q^9 - 2 * q^10 - q^11 + q^16 - q^17 - q^18 - q^19 - 3 * q^20 - 2 * q^22 + 2 * q^25 - q^29 - q^31 - 3 * q^32 - 2 * q^34 + 2 * q^36 - q^37 + 5 * q^38 + 3 * q^40 - q^43 + 4 * q^44 - q^45 - q^47 + 3 * q^49 + 4 * q^50 - 2 * q^55 + 5 * q^58 - q^59 - 2 * q^62 + 4 * q^68 - 2 * q^72 - 2 * q^74 - 3 * q^76 + 2 * q^80 + 3 * q^81 - 2 * q^85 - 2 * q^86 - 4 * q^88 - 2 * q^90 + 5 * q^94 - 2 * q^95 - q^97 - q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$-1$

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 $

$2$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$2$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	0.554958	0.554958
$5$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$5$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$6$	0	0
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	−0.554958	−0.554958
$9$	1.00000	1.00000
$10$	−2.24698	−2.24698
$11$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$11$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	−1.24698	−1.24698
$17$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$17$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$18$	1.24698	1.24698
$19$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$19$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$20$	−1.00000	−1.00000
$21$	0	0
$22$	−0.554958	−0.554958
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	2.24698	2.24698
$26$	0	0
$27$	0	0
$28$	0	0
$29$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$29$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$30$	0	0
$31$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$31$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$32$	−1.00000	−1.00000
$33$	0	0
$34$	−0.554958	−0.554958
$35$	0	0
$36$	0.554958	0.554958
$37$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$37$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$38$	1.55496	1.55496
$39$	0	0
$40$	1.00000	1.00000
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$43$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$44$	−0.246980	−0.246980
$45$	−1.80194	−1.80194
$46$	0	0
$47$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$47$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$48$	0	0
$49$	1.00000	1.00000
$50$	2.80194	2.80194
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0.801938	0.801938
$56$	0	0
$57$	0	0
$58$	1.55496	1.55496
$59$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$59$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	−2.24698	−2.24698
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	−0.246980	−0.246980
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−0.554958	−0.554958
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	−0.554958	−0.554958
$75$	0	0
$76$	0.692021	0.692021
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	2.24698	2.24698
$81$	1.00000	1.00000
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0.801938	0.801938
$86$	−2.24698	−2.24698
$87$	0	0
$88$	0.246980	0.246980
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	−2.24698	−2.24698
$91$	0	0
$92$	0	0
$93$	0	0
$94$	1.55496	1.55496
$95$	−2.24698	−2.24698
$96$	0	0
$97$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$97$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$98$	1.24698	1.24698
$99$	−0.445042	−0.445042
$100$	1.24698	1.24698
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$103$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	1.00000	1.00000
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	0.692021	0.692021
$117$	0	0
$118$	−2.24698	−2.24698
$119$	0	0
$120$	0	0
$121$	−0.801938	−0.801938
$122$	0	0
$123$	0	0
$124$	−1.00000	−1.00000
$125$	−2.24698	−2.24698
$126$	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	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0.246980	0.246980
$137$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$137$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$138$	0	0
$139$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$139$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	−1.24698	−1.24698
$145$	−2.24698	−2.24698
$146$	0	0
$147$	0	0
$148$	−0.246980	−0.246980
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	1.00000	1.00000
$151$	1.00000	1.00000
$152$	−0.692021	−0.692021
$153$	−0.445042	−0.445042
$154$	0	0
$155$	3.24698	3.24698
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	1.80194	1.80194
$161$	0	0
$162$	1.24698	1.24698
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	2.00000	2.00000	1.00000			$0$
$167$	2.00000	2.00000	1.00000			$0$
$168$	0	0
$169$	1.00000	1.00000
$170$	1.00000	1.00000
$171$	1.24698	1.24698
$172$	−1.00000	−1.00000
$173$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$173$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$174$	0	0
$175$	0	0
$176$	0.554958	0.554958
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	−1.00000	−1.00000
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0.801938	0.801938
$186$	0	0
$187$	0.198062	0.198062
$188$	0.692021	0.692021
$189$	0	0
$190$	−2.80194	−2.80194
$191$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$191$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$192$	0	0
$193$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$193$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$194$	1.55496	1.55496
$195$	0	0
$196$	0.554958	0.554958
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	−0.554958	−0.554958
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−1.24698	−1.24698
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	−0.554958	−0.554958
$207$	0	0
$208$	0	0
$209$	−0.554958	−0.554958
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	3.24698	3.24698
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0.445042	0.445042
$221$	0	0
$222$	0	0
$223$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$223$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$224$	0	0
$225$	2.24698	2.24698
$226$	0	0
$227$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$227$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$228$	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	0
$231$	0	0
$232$	−0.692021	−0.692021
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	−2.24698	−2.24698
$236$	−1.00000	−1.00000
$237$	0	0
$238$	0	0
$239$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$239$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$240$	0	0
$241$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$241$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$242$	−1.00000	−1.00000
$243$	0	0
$244$	0	0
$245$	−1.80194	−1.80194
$246$	0	0
$247$	0	0
$248$	1.00000	1.00000
$249$	0	0
$250$	−2.80194	−2.80194
$251$	2.00000	2.00000	1.00000			$0$
$251$	2.00000	2.00000	1.00000			$0$
$252$	0	0
$253$	0	0
$254$	−2.24698	−2.24698
$255$	0	0
$256$	1.24698	1.24698
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	1.24698	1.24698
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$269$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0.554958	0.554958
$273$	0	0
$274$	−2.24698	−2.24698
$275$	−1.00000	−1.00000
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	1.55496	1.55496
$279$	−1.80194	−1.80194
$280$	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	0
$287$	0	0
$288$	−1.00000	−1.00000
$289$	−0.801938	−0.801938
$290$	−2.80194	−2.80194
$291$	0	0
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	3.24698	3.24698
$296$	0.246980	0.246980
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	1.24698	1.24698
$303$	0	0
$304$	−1.55496	−1.55496
$305$	0	0
$306$	−0.554958	−0.554958
$307$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$307$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$308$	0	0
$309$	0	0
$310$	4.04892	4.04892
$311$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$311$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$312$	0	0
$313$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$313$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	−0.554958	−0.554958
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−0.554958	−0.554958
$324$	0.554958	0.554958
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$331$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$332$	0	0
$333$	−0.445042	−0.445042
$334$	2.49396	2.49396
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	1.24698	1.24698
$339$	0	0
$340$	0.445042	0.445042
$341$	0.801938	0.801938
$342$	1.55496	1.55496
$343$	0	0
$344$	1.00000	1.00000
$345$	0	0
$346$	1.55496	1.55496
$347$	2.00000	2.00000	1.00000			$0$
$347$	2.00000	2.00000	1.00000			$0$
$348$	0	0
$349$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$349$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$350$	0	0
$351$	0	0
$352$	0.445042	0.445042
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	1.00000	1.00000
$361$	0.554958	0.554958
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	1.00000	1.00000
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0.246980	0.246980
$375$	0	0
$376$	−0.692021	−0.692021
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	−1.24698	−1.24698
$381$	0	0
$382$	1.55496	1.55496
$383$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$383$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$384$	0	0
$385$	0	0
$386$	−2.24698	−2.24698
$387$	−1.80194	−1.80194
$388$	0.692021	0.692021
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	−0.554958	−0.554958
$393$	0	0
$394$	0	0
$395$	0	0
$396$	−0.246980	−0.246980
$397$	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
$400$	−2.80194	−2.80194
$401$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$401$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−1.80194	−1.80194
$406$	0	0
$407$	0.198062	0.198062
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	−0.246980	−0.246980
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	−0.692021	−0.692021
$419$	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
$423$	1.24698	1.24698
$424$	0	0
$425$	−1.00000	−1.00000
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	4.04892	4.04892
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$439$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$440$	−0.445042	−0.445042
$441$	1.00000	1.00000
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	−0.554958	−0.554958
$447$	0	0
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	2.80194	2.80194
$451$	0	0
$452$	0	0
$453$	0	0
$454$	−0.554958	−0.554958
$455$	0	0
$456$	0	0
$457$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$457$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$458$	1.55496	1.55496
$459$	0	0
$460$	0	0
$461$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$461$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$462$	0	0
$463$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$463$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$464$	−1.55496	−1.55496
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	0	0
$470$	−2.80194	−2.80194
$471$	0	0
$472$	1.00000	1.00000
$473$	0.801938	0.801938
$474$	0	0
$475$	2.80194	2.80194
$476$	0	0
$477$	0	0
$478$	−0.554958	−0.554958
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	−0.554958	−0.554958
$483$	0	0
$484$	−0.445042	−0.445042
$485$	−2.24698	−2.24698
$486$	0	0
$487$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$487$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$488$	0	0
$489$	0	0
$490$	−2.24698	−2.24698
$491$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$491$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$492$	0	0
$493$	−0.554958	−0.554958
$494$	0	0
$495$	0.801938	0.801938
$496$	2.24698	2.24698
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	−1.24698	−1.24698
$501$	0	0
$502$	2.49396	2.49396
$503$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$503$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	−1.00000	−1.00000
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	0.554958	0.554958
$513$	0	0
$514$	0	0
$515$	0.801938	0.801938
$516$	0	0
$517$	−0.554958	−0.554958
$518$	0	0
$519$	0	0
$520$	0	0
$521$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$521$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$522$	1.55496	1.55496
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0.801938	0.801938
$528$	0	0
$529$	1.00000	1.00000
$530$	0	0
$531$	−1.80194	−1.80194
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	−0.554958	−0.554958
$539$	−0.445042	−0.445042
$540$	0	0
$541$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$541$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$542$	0	0
$543$	0	0
$544$	0.445042	0.445042
$545$	0	0
$546$	0	0
$547$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$547$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$548$	−1.00000	−1.00000
$549$	0	0
$550$	−1.24698	−1.24698
$551$	1.55496	1.55496
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0.692021	0.692021
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	−2.24698	−2.24698
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$563$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$569$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$570$	0	0
$571$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$571$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$577$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$578$	−1.00000	−1.00000
$579$	0	0
$580$	−1.24698	−1.24698
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	−2.24698	−2.24698
$590$	4.04892	4.04892
$591$	0	0
$592$	0.554958	0.554958
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$601$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$602$	0	0
$603$	0	0
$604$	0.554958	0.554958
$605$	1.44504	1.44504
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	−1.24698	−1.24698
$609$	0	0
$610$	0	0
$611$	0	0
$612$	−0.246980	−0.246980
$613$	2.00000	2.00000	1.00000			$0$
$613$	2.00000	2.00000	1.00000			$0$
$614$	−0.554958	−0.554958
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	1.80194	1.80194
$621$	0	0
$622$	−2.24698	−2.24698
$623$	0	0
$624$	0	0
$625$	1.80194	1.80194
$626$	−2.24698	−2.24698
$627$	0	0
$628$	0	0
$629$	0.198062	0.198062
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	3.24698	3.24698
$636$	0	0
$637$	0	0
$638$	−0.692021	−0.692021
$639$	0	0
$640$	−1.80194	−1.80194
$641$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$641$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$642$	0	0
$643$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$643$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$644$	0	0
$645$	0	0
$646$	−0.692021	−0.692021
$647$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$647$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$648$	−0.554958	−0.554958
$649$	0.801938	0.801938
$650$	0	0
$651$	0	0
$652$	0	0
$653$	2.00000	2.00000	1.00000			$0$
$653$	2.00000	2.00000	1.00000			$0$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$659$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	−0.554958	−0.554958
$663$	0	0
$664$	0	0
$665$	0	0
$666$	−0.554958	−0.554958
$667$	0	0
$668$	1.10992	1.10992
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$673$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$674$	0	0
$675$	0	0
$676$	0.554958	0.554958
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	−0.445042	−0.445042
$681$	0	0
$682$	1.00000	1.00000
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0.692021	0.692021
$685$	3.24698	3.24698
$686$	0	0
$687$	0	0
$688$	2.24698	2.24698
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0.692021	0.692021
$693$	0	0
$694$	2.49396	2.49396
$695$	−2.24698	−2.24698
$696$	0	0
$697$	0	0
$698$	−0.554958	−0.554958
$699$	0	0
$700$	0	0
$701$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$701$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$702$	0	0
$703$	−0.554958	−0.554958
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$709$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	2.24698	2.24698
$721$	0	0
$722$	0.692021	0.692021
$723$	0	0
$724$	0	0
$725$	2.80194	2.80194
$726$	0	0
$727$	2.00000	2.00000	1.00000			$0$
$727$	2.00000	2.00000	1.00000			$0$
$728$	0	0
$729$	1.00000	1.00000
$730$	0	0
$731$	0.801938	0.801938
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0.445042	0.445042
$741$	0	0
$742$	0	0
$743$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$743$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0.109916	0.109916
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	−1.55496	−1.55496
$753$	0	0
$754$	0	0
$755$	−1.80194	−1.80194
$756$	0	0
$757$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$757$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$758$	0	0
$759$	0	0
$760$	1.24698	1.24698
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	0.692021	0.692021
$765$	0.801938	0.801938
$766$	−2.24698	−2.24698
$767$	0	0
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	−1.00000	−1.00000
$773$	2.00000	2.00000	1.00000			$0$
$773$	2.00000	2.00000	1.00000			$0$
$774$	−2.24698	−2.24698
$775$	−4.04892	−4.04892
$776$	−0.692021	−0.692021
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−1.24698	−1.24698
$785$	0	0
$786$	0	0
$787$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$787$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0.246980	0.246980
$793$	0	0
$794$	1.55496	1.55496
$795$	0	0
$796$	0	0
$797$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$797$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$798$	0	0
$799$	−0.554958	−0.554958
$800$	−2.24698	−2.24698
$801$	0	0
$802$	1.55496	1.55496
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	−2.24698	−2.24698
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0.246980	0.246980
$815$	0	0
$816$	0	0
$817$	−2.24698	−2.24698
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$823$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$824$	0.246980	0.246980
$825$	0	0
$826$	0	0
$827$	2.00000	2.00000	1.00000			$0$
$827$	2.00000	2.00000	1.00000			$0$
$828$	0	0
$829$	2.00000	2.00000	1.00000			$0$
$829$	2.00000	2.00000	1.00000			$0$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−0.445042	−0.445042
$834$	0	0
$835$	−3.60388	−3.60388
$836$	−0.307979	−0.307979
$837$	0	0
$838$	0	0
$839$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$839$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$840$	0	0
$841$	0.554958	0.554958
$842$	0	0
$843$	0	0
$844$	0	0
$845$	−1.80194	−1.80194
$846$	1.55496	1.55496
$847$	0	0
$848$	0	0
$849$	0	0
$850$	−1.24698	−1.24698
$851$	0	0
$852$	0	0
$853$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$853$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$854$	0	0
$855$	−2.24698	−2.24698
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	1.80194	1.80194
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	−2.24698	−2.24698
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	1.24698	1.24698
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	−0.554958	−0.554958
$879$	0	0
$880$	−1.00000	−1.00000
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	1.24698	1.24698
$883$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$883$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−0.445042	−0.445042
$892$	−0.246980	−0.246980
$893$	1.55496	1.55496
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	−2.24698	−2.24698
$900$	1.24698	1.24698
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$907$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$908$	−0.246980	−0.246980
$909$	0	0
$910$	0	0
$911$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$911$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$912$	0	0
$913$	0	0
$914$	−2.24698	−2.24698
$915$	0	0
$916$	0.692021	0.692021
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	−0.554958	−0.554958
$923$	0	0
$924$	0	0
$925$	−1.00000	−1.00000
$926$	−0.554958	−0.554958
$927$	−0.445042	−0.445042
$928$	−1.24698	−1.24698
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	1.24698	1.24698
$932$	0	0
$933$	0	0
$934$	0	0
$935$	−0.356896	−0.356896
$936$	0	0
$937$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$937$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$938$	0	0
$939$	0	0
$940$	−1.24698	−1.24698
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	2.24698	2.24698
$945$	0	0
$946$	1.00000	1.00000
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	0	0
$950$	3.49396	3.49396
$951$	0	0
$952$	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
$955$	−2.24698	−2.24698
$956$	−0.246980	−0.246980
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	2.24698	2.24698
$962$	0	0
$963$	0	0
$964$	−0.246980	−0.246980
$965$	3.24698	3.24698
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	0.445042	0.445042
$969$	0	0
$970$	−2.80194	−2.80194
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	1.55496	1.55496
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	−1.00000	−1.00000
$981$	0	0
$982$	−2.24698	−2.24698
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	−0.692021	−0.692021
$987$	0	0
$988$	0	0
$989$	0	0
$990$	1.00000	1.00000
$991$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$991$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$992$	1.80194	1.80194
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$997$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.1.b.a.150.3	✓	3
3.2	odd	2		1359.1.d.b.1207.1		3
4.3	odd	2		2416.1.e.a.2113.1		3
5.2	odd	4		3775.1.c.c.3774.5		6
5.3	odd	4		3775.1.c.c.3774.2		6
5.4	even	2		3775.1.d.d.301.1		3
151.150	odd	2	CM	151.1.b.a.150.3	✓	3
453.452	even	2		1359.1.d.b.1207.1		3
604.603	even	2		2416.1.e.a.2113.1		3
755.452	even	4		3775.1.c.c.3774.5		6
755.603	even	4		3775.1.c.c.3774.2		6
755.754	odd	2		3775.1.d.d.301.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.1.b.a.150.3	✓	3	1.1	even	1	trivial
151.1.b.a.150.3	✓	3	151.150	odd	2	CM
1359.1.d.b.1207.1		3	3.2	odd	2
1359.1.d.b.1207.1		3	453.452	even	2
2416.1.e.a.2113.1		3	4.3	odd	2
2416.1.e.a.2113.1		3	604.603	even	2
3775.1.c.c.3774.2		6	5.3	odd	4
3775.1.c.c.3774.2		6	755.603	even	4
3775.1.c.c.3774.5		6	5.2	odd	4
3775.1.c.c.3774.5		6	755.452	even	4
3775.1.d.d.301.1		3	5.4	even	2
3775.1.d.d.301.1		3	755.754	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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	151.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.24698 q^{2} +0.554958 q^{4} -1.80194 q^{5} -0.554958 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.24698 q^{2} +0.554958 q^{4} -1.80194 q^{5} -0.554958 q^{8} +1.00000 q^{9} -2.24698 q^{10} -0.445042 q^{11} -1.24698 q^{16} -0.445042 q^{17} +1.24698 q^{18} +1.24698 q^{19} -1.00000 q^{20} -0.554958 q^{22} +2.24698 q^{25} +1.24698 q^{29} -1.80194 q^{31} -1.00000 q^{32} -0.554958 q^{34} +0.554958 q^{36} -0.445042 q^{37} +1.55496 q^{38} +1.00000 q^{40} -1.80194 q^{43} -0.246980 q^{44} -1.80194 q^{45} +1.24698 q^{47} +1.00000 q^{49} +2.80194 q^{50} +0.801938 q^{55} +1.55496 q^{58} -1.80194 q^{59} -2.24698 q^{62} -0.246980 q^{68} -0.554958 q^{72} -0.554958 q^{74} +0.692021 q^{76} +2.24698 q^{80} +1.00000 q^{81} +0.801938 q^{85} -2.24698 q^{86} +0.246980 q^{88} -2.24698 q^{90} +1.55496 q^{94} -2.24698 q^{95} +1.24698 q^{97} +1.24698 q^{98} -0.445042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 2 q^{4} - q^{5} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - q^2 + 2 * q^4 - q^5 - 2 * q^8 + 3 * q^9	\( 3 q - q^{2} + 2 q^{4} - q^{5} - 2 q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + q^{16} - q^{17} - q^{18} - q^{19} - 3 q^{20} - 2 q^{22} + 2 q^{25} - q^{29} - q^{31} - 3 q^{32} - 2 q^{34} + 2 q^{36} - q^{37} + 5 q^{38} + 3 q^{40} - q^{43} + 4 q^{44} - q^{45} - q^{47} + 3 q^{49} + 4 q^{50} - 2 q^{55} + 5 q^{58} - q^{59} - 2 q^{62} + 4 q^{68} - 2 q^{72} - 2 q^{74} - 3 q^{76} + 2 q^{80} + 3 q^{81} - 2 q^{85} - 2 q^{86} - 4 q^{88} - 2 q^{90} + 5 q^{94} - 2 q^{95} - q^{97} - q^{98} - q^{99}+O(q^{100}) \) 3 * q - q^2 + 2 * q^4 - q^5 - 2 * q^8 + 3 * q^9 - 2 * q^10 - q^11 + q^16 - q^17 - q^18 - q^19 - 3 * q^20 - 2 * q^22 + 2 * q^25 - q^29 - q^31 - 3 * q^32 - 2 * q^34 + 2 * q^36 - q^37 + 5 * q^38 + 3 * q^40 - q^43 + 4 * q^44 - q^45 - q^47 + 3 * q^49 + 4 * q^50 - 2 * q^55 + 5 * q^58 - q^59 - 2 * q^62 + 4 * q^68 - 2 * q^72 - 2 * q^74 - 3 * q^76 + 2 * q^80 + 3 * q^81 - 2 * q^85 - 2 * q^86 - 4 * q^88 - 2 * q^90 + 5 * q^94 - 2 * q^95 - q^97 - q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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