LMFDB - Embedded newform 1710.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1710.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.a (trivial)

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:	$13.6544187456$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1710.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -4.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -4.00000 q^{7} +1.00000 q^{8} -1.00000 q^{10} +4.00000 q^{11} -6.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} -1.00000 q^{19} -1.00000 q^{20} +4.00000 q^{22} -4.00000 q^{23} +1.00000 q^{25} -6.00000 q^{26} -4.00000 q^{28} -6.00000 q^{29} -8.00000 q^{31} +1.00000 q^{32} +6.00000 q^{34} +4.00000 q^{35} +2.00000 q^{37} -1.00000 q^{38} -1.00000 q^{40} -10.0000 q^{41} -8.00000 q^{43} +4.00000 q^{44} -4.00000 q^{46} -12.0000 q^{47} +9.00000 q^{49} +1.00000 q^{50} -6.00000 q^{52} -2.00000 q^{53} -4.00000 q^{55} -4.00000 q^{56} -6.00000 q^{58} +4.00000 q^{59} -2.00000 q^{61} -8.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} -12.0000 q^{67} +6.00000 q^{68} +4.00000 q^{70} +16.0000 q^{71} -14.0000 q^{73} +2.00000 q^{74} -1.00000 q^{76} -16.0000 q^{77} +8.00000 q^{79} -1.00000 q^{80} -10.0000 q^{82} -6.00000 q^{85} -8.00000 q^{86} +4.00000 q^{88} +6.00000 q^{89} +24.0000 q^{91} -4.00000 q^{92} -12.0000 q^{94} +1.00000 q^{95} +14.0000 q^{97} +9.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	−1.00000	−0.316228
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	−4.00000	−1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	0	0
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.00000	−0.223607
$21$	0	0
$22$	4.00000	0.852803
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	−6.00000	−1.17670
$27$	0	0
$28$	−4.00000	−0.755929
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	6.00000	1.02899
$35$	4.00000	0.676123
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	−4.00000	−0.589768
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	1.00000	0.141421
$51$	0	0
$52$	−6.00000	−0.832050
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	0	0
$55$	−4.00000	−0.539360
$56$	−4.00000	−0.534522
$57$	0	0
$58$	−6.00000	−0.787839
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−8.00000	−1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	6.00000	0.744208
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	4.00000	0.478091
$71$	16.0000	1.89885	0.949425	−	0.313993i	$-0.101667\pi$
$71$	16.0000	1.89885	0.949425	+	0.313993i	$0.101667\pi$
$72$	0	0
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	−1.00000	−0.114708
$77$	−16.0000	−1.82337
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−1.00000	−0.111803
$81$	0	0
$82$	−10.0000	−1.10432
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	−6.00000	−0.650791
$86$	−8.00000	−0.862662
$87$	0	0
$88$	4.00000	0.426401
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	24.0000	2.51588
$92$	−4.00000	−0.417029
$93$	0	0
$94$	−12.0000	−1.23771
$95$	1.00000	0.102598
$96$	0	0
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	9.00000	0.909137
$99$	0	0
$100$	1.00000	0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	0	0
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	−2.00000	−0.194257
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	−4.00000	−0.381385
$111$	0	0
$112$	−4.00000	−0.377964
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	0	0
$115$	4.00000	0.373002
$116$	−6.00000	−0.557086
$117$	0	0
$118$	4.00000	0.368230
$119$	−24.0000	−2.20008
$120$	0	0
$121$	5.00000	0.454545
$122$	−2.00000	−0.181071
$123$	0	0
$124$	−8.00000	−0.718421
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	6.00000	0.526235
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	4.00000	0.346844
$134$	−12.0000	−1.03664
$135$	0	0
$136$	6.00000	0.514496
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	0	0
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	4.00000	0.338062
$141$	0	0
$142$	16.0000	1.34269
$143$	−24.0000	−2.00698
$144$	0	0
$145$	6.00000	0.498273
$146$	−14.0000	−1.15865
$147$	0	0
$148$	2.00000	0.164399
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−1.00000	−0.0811107
$153$	0	0
$154$	−16.0000	−1.28932
$155$	8.00000	0.642575
$156$	0	0
$157$	22.0000	1.75579	0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000	1.75579	0.877896	+	0.478852i	$0.158947\pi$
$158$	8.00000	0.636446
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	16.0000	1.26098
$162$	0	0
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	−10.0000	−0.780869
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	−6.00000	−0.460179
$171$	0	0
$172$	−8.00000	−0.609994
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	−4.00000	−0.302372
$176$	4.00000	0.301511
$177$	0	0
$178$	6.00000	0.449719
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	24.0000	1.77900
$183$	0	0
$184$	−4.00000	−0.294884
$185$	−2.00000	−0.147043
$186$	0	0
$187$	24.0000	1.75505
$188$	−12.0000	−0.875190
$189$	0	0
$190$	1.00000	0.0725476
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	0	0
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	9.00000	0.642857
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	−6.00000	−0.422159
$203$	24.0000	1.68447
$204$	0	0
$205$	10.0000	0.698430
$206$	8.00000	0.557386
$207$	0	0
$208$	−6.00000	−0.416025
$209$	−4.00000	−0.276686
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	−2.00000	−0.137361
$213$	0	0
$214$	12.0000	0.820303
$215$	8.00000	0.545595
$216$	0	0
$217$	32.0000	2.17230
$218$	6.00000	0.406371
$219$	0	0
$220$	−4.00000	−0.269680
$221$	−36.0000	−2.42162
$222$	0	0
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	−4.00000	−0.267261
$225$	0	0
$226$	10.0000	0.665190
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	0	0
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	4.00000	0.263752
$231$	0	0
$232$	−6.00000	−0.393919
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	0	0
$235$	12.0000	0.782794
$236$	4.00000	0.260378
$237$	0	0
$238$	−24.0000	−1.55569
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	−2.00000	−0.128037
$245$	−9.00000	−0.574989
$246$	0	0
$247$	6.00000	0.381771
$248$	−8.00000	−0.508001
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	0	0
$253$	−16.0000	−1.00591
$254$	−16.0000	−1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	0	0
$259$	−8.00000	−0.497096
$260$	6.00000	0.372104
$261$	0	0
$262$	−12.0000	−0.741362
$263$	−20.0000	−1.23325	−0.616626	−	0.787256i	$-0.711501\pi$
$263$	−20.0000	−1.23325	−0.616626	+	0.787256i	$0.711501\pi$
$264$	0	0
$265$	2.00000	0.122859
$266$	4.00000	0.245256
$267$	0	0
$268$	−12.0000	−0.733017
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	−2.00000	−0.120824
$275$	4.00000	0.241209
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	12.0000	0.719712
$279$	0	0
$280$	4.00000	0.239046
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	0	0
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	16.0000	0.949425
$285$	0	0
$286$	−24.0000	−1.41915
$287$	40.0000	2.36113
$288$	0	0
$289$	19.0000	1.11765
$290$	6.00000	0.352332
$291$	0	0
$292$	−14.0000	−0.819288
$293$	−2.00000	−0.116841	−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000	−0.116841	−0.0584206	+	0.998292i	$0.518606\pi$
$294$	0	0
$295$	−4.00000	−0.232889
$296$	2.00000	0.116248
$297$	0	0
$298$	10.0000	0.579284
$299$	24.0000	1.38796
$300$	0	0
$301$	32.0000	1.84445
$302$	8.00000	0.460348
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	2.00000	0.114520
$306$	0	0
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	−16.0000	−0.911685
$309$	0	0
$310$	8.00000	0.454369
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	0	0
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	22.0000	1.24153
$315$	0	0
$316$	8.00000	0.450035
$317$	14.0000	0.786318	0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000	0.786318	0.393159	+	0.919470i	$0.371382\pi$
$318$	0	0
$319$	−24.0000	−1.34374
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	16.0000	0.891645
$323$	−6.00000	−0.333849
$324$	0	0
$325$	−6.00000	−0.332820
$326$	−16.0000	−0.886158
$327$	0	0
$328$	−10.0000	−0.552158
$329$	48.0000	2.64633
$330$	0	0
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	12.0000	0.655630
$336$	0	0
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	23.0000	1.25104
$339$	0	0
$340$	−6.00000	−0.325396
$341$	−32.0000	−1.73290
$342$	0	0
$343$	−8.00000	−0.431959
$344$	−8.00000	−0.431331
$345$	0	0
$346$	6.00000	0.322562
$347$	−32.0000	−1.71785	−0.858925	−	0.512101i	$-0.828867\pi$
$347$	−32.0000	−1.71785	−0.858925	+	0.512101i	$0.828867\pi$
$348$	0	0
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	−4.00000	−0.213809
$351$	0	0
$352$	4.00000	0.213201
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	0	0
$355$	−16.0000	−0.849192
$356$	6.00000	0.317999
$357$	0	0
$358$	12.0000	0.634220
$359$	16.0000	0.844448	0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000	0.844448	0.422224	+	0.906492i	$0.361250\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−2.00000	−0.105118
$363$	0	0
$364$	24.0000	1.25794
$365$	14.0000	0.732793
$366$	0	0
$367$	4.00000	0.208798	0.104399	−	0.994535i	$-0.466708\pi$
$367$	4.00000	0.208798	0.104399	+	0.994535i	$0.466708\pi$
$368$	−4.00000	−0.208514
$369$	0	0
$370$	−2.00000	−0.103975
$371$	8.00000	0.415339
$372$	0	0
$373$	10.0000	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$374$	24.0000	1.24101
$375$	0	0
$376$	−12.0000	−0.618853
$377$	36.0000	1.85409
$378$	0	0
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	1.00000	0.0512989
$381$	0	0
$382$	8.00000	0.409316
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	16.0000	0.815436
$386$	−2.00000	−0.101797
$387$	0	0
$388$	14.0000	0.710742
$389$	26.0000	1.31825	0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000	1.31825	0.659126	+	0.752032i	$0.270926\pi$
$390$	0	0
$391$	−24.0000	−1.21373
$392$	9.00000	0.454569
$393$	0	0
$394$	−6.00000	−0.302276
$395$	−8.00000	−0.402524
$396$	0	0
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	−16.0000	−0.802008
$399$	0	0
$400$	1.00000	0.0500000
$401$	22.0000	1.09863	0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000	1.09863	0.549314	+	0.835616i	$0.314889\pi$
$402$	0	0
$403$	48.0000	2.39105
$404$	−6.00000	−0.298511
$405$	0	0
$406$	24.0000	1.19110
$407$	8.00000	0.396545
$408$	0	0
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	10.0000	0.493865
$411$	0	0
$412$	8.00000	0.394132
$413$	−16.0000	−0.787309
$414$	0	0
$415$	0	0
$416$	−6.00000	−0.294174
$417$	0	0
$418$	−4.00000	−0.195646
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	0	0
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	−2.00000	−0.0971286
$425$	6.00000	0.291043
$426$	0	0
$427$	8.00000	0.387147
$428$	12.0000	0.580042
$429$	0	0
$430$	8.00000	0.385794
$431$	32.0000	1.54139	0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000	1.54139	0.770693	+	0.637207i	$0.219910\pi$
$432$	0	0
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	32.0000	1.53605
$435$	0	0
$436$	6.00000	0.287348
$437$	4.00000	0.191346
$438$	0	0
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	−4.00000	−0.190693
$441$	0	0
$442$	−36.0000	−1.71235
$443$	−8.00000	−0.380091	−0.190046	−	0.981775i	$-0.560864\pi$
$443$	−8.00000	−0.380091	−0.190046	+	0.981775i	$0.560864\pi$
$444$	0	0
$445$	−6.00000	−0.284427
$446$	−16.0000	−0.757622
$447$	0	0
$448$	−4.00000	−0.188982
$449$	−10.0000	−0.471929	−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000	−0.471929	−0.235965	+	0.971762i	$0.575825\pi$
$450$	0	0
$451$	−40.0000	−1.88353
$452$	10.0000	0.470360
$453$	0	0
$454$	4.00000	0.187729
$455$	−24.0000	−1.12514
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	6.00000	0.280362
$459$	0	0
$460$	4.00000	0.186501
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	20.0000	0.929479	0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000	0.929479	0.464739	+	0.885448i	$0.346148\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−10.0000	−0.463241
$467$	8.00000	0.370196	0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000	0.370196	0.185098	+	0.982720i	$0.440740\pi$
$468$	0	0
$469$	48.0000	2.21643
$470$	12.0000	0.553519
$471$	0	0
$472$	4.00000	0.184115
$473$	−32.0000	−1.47136
$474$	0	0
$475$	−1.00000	−0.0458831
$476$	−24.0000	−1.10004
$477$	0	0
$478$	−16.0000	−0.731823
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	−12.0000	−0.547153
$482$	−22.0000	−1.00207
$483$	0	0
$484$	5.00000	0.227273
$485$	−14.0000	−0.635707
$486$	0	0
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	−2.00000	−0.0905357
$489$	0	0
$490$	−9.00000	−0.406579
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	−36.0000	−1.62136
$494$	6.00000	0.269953
$495$	0	0
$496$	−8.00000	−0.359211
$497$	−64.0000	−2.87079
$498$	0	0
$499$	−28.0000	−1.25345	−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000	−1.25345	−0.626726	+	0.779240i	$0.715605\pi$
$500$	−1.00000	−0.0447214
$501$	0	0
$502$	−4.00000	−0.178529
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	−16.0000	−0.711287
$507$	0	0
$508$	−16.0000	−0.709885
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	0	0
$511$	56.0000	2.47729
$512$	1.00000	0.0441942
$513$	0	0
$514$	18.0000	0.793946
$515$	−8.00000	−0.352522
$516$	0	0
$517$	−48.0000	−2.11104
$518$	−8.00000	−0.351500
$519$	0	0
$520$	6.00000	0.263117
$521$	14.0000	0.613351	0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000	0.613351	0.306676	+	0.951814i	$0.400783\pi$
$522$	0	0
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−20.0000	−0.872041
$527$	−48.0000	−2.09091
$528$	0	0
$529$	−7.00000	−0.304348
$530$	2.00000	0.0868744
$531$	0	0
$532$	4.00000	0.173422
$533$	60.0000	2.59889
$534$	0	0
$535$	−12.0000	−0.518805
$536$	−12.0000	−0.518321
$537$	0	0
$538$	−14.0000	−0.603583
$539$	36.0000	1.55063
$540$	0	0
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	−8.00000	−0.343629
$543$	0	0
$544$	6.00000	0.257248
$545$	−6.00000	−0.257012
$546$	0	0
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	−2.00000	−0.0854358
$549$	0	0
$550$	4.00000	0.170561
$551$	6.00000	0.255609
$552$	0	0
$553$	−32.0000	−1.36078
$554$	−2.00000	−0.0849719
$555$	0	0
$556$	12.0000	0.508913
$557$	26.0000	1.10166	0.550828	−	0.834619i	$-0.314312\pi$
$557$	26.0000	1.10166	0.550828	+	0.834619i	$0.314312\pi$
$558$	0	0
$559$	48.0000	2.03018
$560$	4.00000	0.169031
$561$	0	0
$562$	22.0000	0.928014
$563$	20.0000	0.842900	0.421450	−	0.906852i	$-0.361521\pi$
$563$	20.0000	0.842900	0.421450	+	0.906852i	$0.361521\pi$
$564$	0	0
$565$	−10.0000	−0.420703
$566$	−16.0000	−0.672530
$567$	0	0
$568$	16.0000	0.671345
$569$	−34.0000	−1.42535	−0.712677	−	0.701492i	$-0.752517\pi$
$569$	−34.0000	−1.42535	−0.712677	+	0.701492i	$0.752517\pi$
$570$	0	0
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	−24.0000	−1.00349
$573$	0	0
$574$	40.0000	1.66957
$575$	−4.00000	−0.166812
$576$	0	0
$577$	18.0000	0.749350	0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000	0.749350	0.374675	+	0.927156i	$0.377754\pi$
$578$	19.0000	0.790296
$579$	0	0
$580$	6.00000	0.249136
$581$	0	0
$582$	0	0
$583$	−8.00000	−0.331326
$584$	−14.0000	−0.579324
$585$	0	0
$586$	−2.00000	−0.0826192
$587$	−32.0000	−1.32078	−0.660391	−	0.750922i	$-0.729609\pi$
$587$	−32.0000	−1.32078	−0.660391	+	0.750922i	$0.729609\pi$
$588$	0	0
$589$	8.00000	0.329634
$590$	−4.00000	−0.164677
$591$	0	0
$592$	2.00000	0.0821995
$593$	−34.0000	−1.39621	−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000	−1.39621	−0.698106	+	0.715994i	$0.745974\pi$
$594$	0	0
$595$	24.0000	0.983904
$596$	10.0000	0.409616
$597$	0	0
$598$	24.0000	0.981433
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	32.0000	1.30422
$603$	0	0
$604$	8.00000	0.325515
$605$	−5.00000	−0.203279
$606$	0	0
$607$	24.0000	0.974130	0.487065	−	0.873366i	$-0.338067\pi$
$607$	24.0000	0.974130	0.487065	+	0.873366i	$0.338067\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	2.00000	0.0809776
$611$	72.0000	2.91281
$612$	0	0
$613$	46.0000	1.85792	0.928961	−	0.370177i	$-0.120703\pi$
$613$	46.0000	1.85792	0.928961	+	0.370177i	$0.120703\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	−16.0000	−0.644658
$617$	14.0000	0.563619	0.281809	−	0.959470i	$-0.409065\pi$
$617$	14.0000	0.563619	0.281809	+	0.959470i	$0.409065\pi$
$618$	0	0
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	8.00000	0.321288
$621$	0	0
$622$	8.00000	0.320771
$623$	−24.0000	−0.961540
$624$	0	0
$625$	1.00000	0.0400000
$626$	−6.00000	−0.239808
$627$	0	0
$628$	22.0000	0.877896
$629$	12.0000	0.478471
$630$	0	0
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	8.00000	0.318223
$633$	0	0
$634$	14.0000	0.556011
$635$	16.0000	0.634941
$636$	0	0
$637$	−54.0000	−2.13956
$638$	−24.0000	−0.950169
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	14.0000	0.552967	0.276483	−	0.961019i	$-0.410831\pi$
$641$	14.0000	0.552967	0.276483	+	0.961019i	$0.410831\pi$
$642$	0	0
$643$	−40.0000	−1.57745	−0.788723	−	0.614749i	$-0.789257\pi$
$643$	−40.0000	−1.57745	−0.788723	+	0.614749i	$0.789257\pi$
$644$	16.0000	0.630488
$645$	0	0
$646$	−6.00000	−0.236067
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	0	0
$649$	16.0000	0.628055
$650$	−6.00000	−0.235339
$651$	0	0
$652$	−16.0000	−0.626608
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	0	0
$655$	12.0000	0.468879
$656$	−10.0000	−0.390434
$657$	0	0
$658$	48.0000	1.87123
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	4.00000	0.155464
$663$	0	0
$664$	0	0
$665$	−4.00000	−0.155113
$666$	0	0
$667$	24.0000	0.929284
$668$	0	0
$669$	0	0
$670$	12.0000	0.463600
$671$	−8.00000	−0.308837
$672$	0	0
$673$	22.0000	0.848038	0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000	0.848038	0.424019	+	0.905653i	$0.360619\pi$
$674$	14.0000	0.539260
$675$	0	0
$676$	23.0000	0.884615
$677$	30.0000	1.15299	0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000	1.15299	0.576497	+	0.817099i	$0.304419\pi$
$678$	0	0
$679$	−56.0000	−2.14908
$680$	−6.00000	−0.230089
$681$	0	0
$682$	−32.0000	−1.22534
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	0	0
$685$	2.00000	0.0764161
$686$	−8.00000	−0.305441
$687$	0	0
$688$	−8.00000	−0.304997
$689$	12.0000	0.457164
$690$	0	0
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	−32.0000	−1.21470
$695$	−12.0000	−0.455186
$696$	0	0
$697$	−60.0000	−2.27266
$698$	−2.00000	−0.0757011
$699$	0	0
$700$	−4.00000	−0.151186
$701$	18.0000	0.679851	0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000	0.679851	0.339925	+	0.940452i	$0.389598\pi$
$702$	0	0
$703$	−2.00000	−0.0754314
$704$	4.00000	0.150756
$705$	0	0
$706$	−26.0000	−0.978523
$707$	24.0000	0.902613
$708$	0	0
$709$	6.00000	0.225335	0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000	0.225335	0.112667	+	0.993633i	$0.464061\pi$
$710$	−16.0000	−0.600469
$711$	0	0
$712$	6.00000	0.224860
$713$	32.0000	1.19841
$714$	0	0
$715$	24.0000	0.897549
$716$	12.0000	0.448461
$717$	0	0
$718$	16.0000	0.597115
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	0	0
$721$	−32.0000	−1.19174
$722$	1.00000	0.0372161
$723$	0	0
$724$	−2.00000	−0.0743294
$725$	−6.00000	−0.222834
$726$	0	0
$727$	28.0000	1.03846	0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000	1.03846	0.519231	+	0.854634i	$0.326218\pi$
$728$	24.0000	0.889499
$729$	0	0
$730$	14.0000	0.518163
$731$	−48.0000	−1.77534
$732$	0	0
$733$	−50.0000	−1.84679	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000	−1.84679	−0.923396	+	0.383849i	$0.874598\pi$
$734$	4.00000	0.147643
$735$	0	0
$736$	−4.00000	−0.147442
$737$	−48.0000	−1.76810
$738$	0	0
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	−2.00000	−0.0735215
$741$	0	0
$742$	8.00000	0.293689
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	0	0
$745$	−10.0000	−0.366372
$746$	10.0000	0.366126
$747$	0	0
$748$	24.0000	0.877527
$749$	−48.0000	−1.75388
$750$	0	0
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	−12.0000	−0.437595
$753$	0	0
$754$	36.0000	1.31104
$755$	−8.00000	−0.291150
$756$	0	0
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	4.00000	0.145287
$759$	0	0
$760$	1.00000	0.0362738
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	0	0
$763$	−24.0000	−0.868858
$764$	8.00000	0.289430
$765$	0	0
$766$	−24.0000	−0.867155
$767$	−24.0000	−0.866590
$768$	0	0
$769$	18.0000	0.649097	0.324548	−	0.945869i	$-0.394788\pi$
$769$	18.0000	0.649097	0.324548	+	0.945869i	$0.394788\pi$
$770$	16.0000	0.576600
$771$	0	0
$772$	−2.00000	−0.0719816
$773$	−10.0000	−0.359675	−0.179838	−	0.983696i	$-0.557557\pi$
$773$	−10.0000	−0.359675	−0.179838	+	0.983696i	$0.557557\pi$
$774$	0	0
$775$	−8.00000	−0.287368
$776$	14.0000	0.502571
$777$	0	0
$778$	26.0000	0.932145
$779$	10.0000	0.358287
$780$	0	0
$781$	64.0000	2.29010
$782$	−24.0000	−0.858238
$783$	0	0
$784$	9.00000	0.321429
$785$	−22.0000	−0.785214
$786$	0	0
$787$	−52.0000	−1.85360	−0.926800	−	0.375555i	$-0.877452\pi$
$787$	−52.0000	−1.85360	−0.926800	+	0.375555i	$0.877452\pi$
$788$	−6.00000	−0.213741
$789$	0	0
$790$	−8.00000	−0.284627
$791$	−40.0000	−1.42224
$792$	0	0
$793$	12.0000	0.426132
$794$	22.0000	0.780751
$795$	0	0
$796$	−16.0000	−0.567105
$797$	38.0000	1.34603	0.673015	−	0.739629i	$-0.264999\pi$
$797$	38.0000	1.34603	0.673015	+	0.739629i	$0.264999\pi$
$798$	0	0
$799$	−72.0000	−2.54718
$800$	1.00000	0.0353553
$801$	0	0
$802$	22.0000	0.776847
$803$	−56.0000	−1.97620
$804$	0	0
$805$	−16.0000	−0.563926
$806$	48.0000	1.69073
$807$	0	0
$808$	−6.00000	−0.211079
$809$	−42.0000	−1.47664	−0.738321	−	0.674450i	$-0.764381\pi$
$809$	−42.0000	−1.47664	−0.738321	+	0.674450i	$0.764381\pi$
$810$	0	0
$811$	28.0000	0.983213	0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000	0.983213	0.491606	+	0.870817i	$0.336410\pi$
$812$	24.0000	0.842235
$813$	0	0
$814$	8.00000	0.280400
$815$	16.0000	0.560456
$816$	0	0
$817$	8.00000	0.279885
$818$	−6.00000	−0.209785
$819$	0	0
$820$	10.0000	0.349215
$821$	−6.00000	−0.209401	−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000	−0.209401	−0.104701	+	0.994504i	$0.533388\pi$
$822$	0	0
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	−16.0000	−0.556711
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	−26.0000	−0.903017	−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000	−0.903017	−0.451509	+	0.892267i	$0.649114\pi$
$830$	0	0
$831$	0	0
$832$	−6.00000	−0.208013
$833$	54.0000	1.87099
$834$	0	0
$835$	0	0
$836$	−4.00000	−0.138343
$837$	0	0
$838$	−20.0000	−0.690889
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−26.0000	−0.896019
$843$	0	0
$844$	−20.0000	−0.688428
$845$	−23.0000	−0.791224
$846$	0	0
$847$	−20.0000	−0.687208
$848$	−2.00000	−0.0686803
$849$	0	0
$850$	6.00000	0.205798
$851$	−8.00000	−0.274236
$852$	0	0
$853$	−10.0000	−0.342393	−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000	−0.342393	−0.171197	+	0.985237i	$0.554763\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	12.0000	0.410152
$857$	−6.00000	−0.204956	−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000	−0.204956	−0.102478	+	0.994735i	$0.532677\pi$
$858$	0	0
$859$	−44.0000	−1.50126	−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000	−1.50126	−0.750630	+	0.660722i	$0.770250\pi$
$860$	8.00000	0.272798
$861$	0	0
$862$	32.0000	1.08992
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	0	0
$865$	−6.00000	−0.204006
$866$	14.0000	0.475739
$867$	0	0
$868$	32.0000	1.08615
$869$	32.0000	1.08553
$870$	0	0
$871$	72.0000	2.43963
$872$	6.00000	0.203186
$873$	0	0
$874$	4.00000	0.135302
$875$	4.00000	0.135225
$876$	0	0
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	32.0000	1.07995
$879$	0	0
$880$	−4.00000	−0.134840
$881$	14.0000	0.471672	0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000	0.471672	0.235836	+	0.971793i	$0.424217\pi$
$882$	0	0
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	−36.0000	−1.21081
$885$	0	0
$886$	−8.00000	−0.268765
$887$	8.00000	0.268614	0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000	0.268614	0.134307	+	0.990940i	$0.457119\pi$
$888$	0	0
$889$	64.0000	2.14649
$890$	−6.00000	−0.201120
$891$	0	0
$892$	−16.0000	−0.535720
$893$	12.0000	0.401565
$894$	0	0
$895$	−12.0000	−0.401116
$896$	−4.00000	−0.133631
$897$	0	0
$898$	−10.0000	−0.333704
$899$	48.0000	1.60089
$900$	0	0
$901$	−12.0000	−0.399778
$902$	−40.0000	−1.33185
$903$	0	0
$904$	10.0000	0.332595
$905$	2.00000	0.0664822
$906$	0	0
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	4.00000	0.132745
$909$	0	0
$910$	−24.0000	−0.795592
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	0	0
$913$	0	0
$914$	10.0000	0.330771
$915$	0	0
$916$	6.00000	0.198246
$917$	48.0000	1.58510
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	4.00000	0.131876
$921$	0	0
$922$	18.0000	0.592798
$923$	−96.0000	−3.15988
$924$	0	0
$925$	2.00000	0.0657596
$926$	20.0000	0.657241
$927$	0	0
$928$	−6.00000	−0.196960
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	0	0
$931$	−9.00000	−0.294963
$932$	−10.0000	−0.327561
$933$	0	0
$934$	8.00000	0.261768
$935$	−24.0000	−0.784884
$936$	0	0
$937$	−30.0000	−0.980057	−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000	−0.980057	−0.490029	+	0.871706i	$0.663014\pi$
$938$	48.0000	1.56726
$939$	0	0
$940$	12.0000	0.391397
$941$	−46.0000	−1.49956	−0.749779	−	0.661689i	$-0.769840\pi$
$941$	−46.0000	−1.49956	−0.749779	+	0.661689i	$0.769840\pi$
$942$	0	0
$943$	40.0000	1.30258
$944$	4.00000	0.130189
$945$	0	0
$946$	−32.0000	−1.04041
$947$	24.0000	0.779895	0.389948	−	0.920837i	$-0.372493\pi$
$947$	24.0000	0.779895	0.389948	+	0.920837i	$0.372493\pi$
$948$	0	0
$949$	84.0000	2.72676
$950$	−1.00000	−0.0324443
$951$	0	0
$952$	−24.0000	−0.777844
$953$	42.0000	1.36051	0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000	1.36051	0.680257	+	0.732974i	$0.261868\pi$
$954$	0	0
$955$	−8.00000	−0.258874
$956$	−16.0000	−0.517477
$957$	0	0
$958$	−24.0000	−0.775405
$959$	8.00000	0.258333
$960$	0	0
$961$	33.0000	1.06452
$962$	−12.0000	−0.386896
$963$	0	0
$964$	−22.0000	−0.708572
$965$	2.00000	0.0643823
$966$	0	0
$967$	52.0000	1.67221	0.836104	−	0.548572i	$-0.184828\pi$
$967$	52.0000	1.67221	0.836104	+	0.548572i	$0.184828\pi$
$968$	5.00000	0.160706
$969$	0	0
$970$	−14.0000	−0.449513
$971$	−28.0000	−0.898563	−0.449281	−	0.893390i	$-0.648320\pi$
$971$	−28.0000	−0.898563	−0.449281	+	0.893390i	$0.648320\pi$
$972$	0	0
$973$	−48.0000	−1.53881
$974$	−16.0000	−0.512673
$975$	0	0
$976$	−2.00000	−0.0640184
$977$	2.00000	0.0639857	0.0319928	−	0.999488i	$-0.489815\pi$
$977$	2.00000	0.0639857	0.0319928	+	0.999488i	$0.489815\pi$
$978$	0	0
$979$	24.0000	0.767043
$980$	−9.00000	−0.287494
$981$	0	0
$982$	12.0000	0.382935
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	6.00000	0.191176
$986$	−36.0000	−1.14647
$987$	0	0
$988$	6.00000	0.190885
$989$	32.0000	1.01754
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	−8.00000	−0.254000
$993$	0	0
$994$	−64.0000	−2.02996
$995$	16.0000	0.507234
$996$	0	0
$997$	46.0000	1.45683	0.728417	−	0.685134i	$-0.240256\pi$
$997$	46.0000	1.45683	0.728417	+	0.685134i	$0.240256\pi$
$998$	−28.0000	−0.886325
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.a.l.1.1		1
3.2	odd	2		570.2.a.e.1.1	✓	1
5.4	even	2		8550.2.a.r.1.1		1
12.11	even	2		4560.2.a.q.1.1		1
15.2	even	4		2850.2.d.a.799.1		2
15.8	even	4		2850.2.d.a.799.2		2
15.14	odd	2		2850.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.a.e.1.1	✓	1	3.2	odd	2
1710.2.a.l.1.1		1	1.1	even	1	trivial
2850.2.a.v.1.1		1	15.14	odd	2
2850.2.d.a.799.1		2	15.2	even	4
2850.2.d.a.799.2		2	15.8	even	4
4560.2.a.q.1.1		1	12.11	even	2
8550.2.a.r.1.1		1	5.4	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more