LMFDB - Embedded newform 194.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [194,2,Mod(1,194)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(194, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("194.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 194 = 2 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	194.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:	$1.54909779921$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	194.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} -4.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} -4.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} +4.00000 q^{10} +4.00000 q^{11} -4.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} -3.00000 q^{18} -6.00000 q^{19} +4.00000 q^{20} +4.00000 q^{22} -4.00000 q^{23} +11.0000 q^{25} -4.00000 q^{26} -4.00000 q^{28} +1.00000 q^{32} +6.00000 q^{34} -16.0000 q^{35} -3.00000 q^{36} -8.00000 q^{37} -6.00000 q^{38} +4.00000 q^{40} -2.00000 q^{41} -8.00000 q^{43} +4.00000 q^{44} -12.0000 q^{45} -4.00000 q^{46} +9.00000 q^{49} +11.0000 q^{50} -4.00000 q^{52} +6.00000 q^{53} +16.0000 q^{55} -4.00000 q^{56} +6.00000 q^{59} +10.0000 q^{61} +12.0000 q^{63} +1.00000 q^{64} -16.0000 q^{65} +6.00000 q^{67} +6.00000 q^{68} -16.0000 q^{70} -3.00000 q^{72} -10.0000 q^{73} -8.00000 q^{74} -6.00000 q^{76} -16.0000 q^{77} +8.00000 q^{79} +4.00000 q^{80} +9.00000 q^{81} -2.00000 q^{82} -2.00000 q^{83} +24.0000 q^{85} -8.00000 q^{86} +4.00000 q^{88} +14.0000 q^{89} -12.0000 q^{90} +16.0000 q^{91} -4.00000 q^{92} -24.0000 q^{95} -1.00000 q^{97} +9.00000 q^{98} -12.0000 q^{99} +O(q^{100})\)

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		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	4.00000	1.78885	0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000	1.78885	0.894427	+	0.447214i	$0.147584\pi$
$6$	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
$9$	−3.00000	−1.00000
$10$	4.00000	1.26491
$11$	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
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−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	$0.240633\pi$
$18$	−3.00000	−0.707107
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	4.00000	0.894427
$21$	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
$25$	11.0000	2.20000
$26$	−4.00000	−0.784465
$27$	0	0
$28$	−4.00000	−0.755929
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	6.00000	1.02899
$35$	−16.0000	−2.70449
$36$	−3.00000	−0.500000
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	−6.00000	−0.973329
$39$	0	0
$40$	4.00000	0.632456
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	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
$45$	−12.0000	−1.78885
$46$	−4.00000	−0.589768
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	11.0000	1.55563
$51$	0	0
$52$	−4.00000	−0.554700
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	16.0000	2.15744
$56$	−4.00000	−0.534522
$57$	0	0
$58$	0	0
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	0	0
$63$	12.0000	1.51186
$64$	1.00000	0.125000
$65$	−16.0000	−1.98456
$66$	0	0
$67$	6.00000	0.733017	0.366508	−	0.930415i	$-0.380553\pi$
$67$	6.00000	0.733017	0.366508	+	0.930415i	$0.380553\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	−16.0000	−1.91237
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	−3.00000	−0.353553
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	−6.00000	−0.688247
$77$	−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	$0.351411\pi$
$80$	4.00000	0.447214
$81$	9.00000	1.00000
$82$	−2.00000	−0.220863
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	0	0
$85$	24.0000	2.60317
$86$	−8.00000	−0.862662
$87$	0	0
$88$	4.00000	0.426401
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	−12.0000	−1.26491
$91$	16.0000	1.67726
$92$	−4.00000	−0.417029
$93$	0	0
$94$	0	0
$95$	−24.0000	−2.46235
$96$	0	0
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	9.00000	0.909137
$99$	−12.0000	−1.20605
$100$	11.0000	1.10000
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	6.00000	0.582772
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	0	0
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	16.0000	1.52554
$111$	0	0
$112$	−4.00000	−0.377964
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	−16.0000	−1.49201
$116$	0	0
$117$	12.0000	1.10940
$118$	6.00000	0.552345
$119$	−24.0000	−2.20008
$120$	0	0
$121$	5.00000	0.454545
$122$	10.0000	0.905357
$123$	0	0
$124$	0	0
$125$	24.0000	2.14663
$126$	12.0000	1.06904
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−16.0000	−1.40329
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	24.0000	2.08106
$134$	6.00000	0.518321
$135$	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
$139$	−22.0000	−1.86602	−0.933008	−	0.359856i	$-0.882826\pi$
$139$	−22.0000	−1.86602	−0.933008	+	0.359856i	$0.882826\pi$
$140$	−16.0000	−1.35225
$141$	0	0
$142$	0	0
$143$	−16.0000	−1.33799
$144$	−3.00000	−0.250000
$145$	0	0
$146$	−10.0000	−0.827606
$147$	0	0
$148$	−8.00000	−0.657596
$149$	4.00000	0.327693	0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000	0.327693	0.163846	+	0.986486i	$0.447610\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−6.00000	−0.486664
$153$	−18.0000	−1.45521
$154$	−16.0000	−1.28932
$155$	0	0
$156$	0	0
$157$	−16.0000	−1.27694	−0.638470	−	0.769647i	$-0.720432\pi$
$157$	−16.0000	−1.27694	−0.638470	+	0.769647i	$0.720432\pi$
$158$	8.00000	0.636446
$159$	0	0
$160$	4.00000	0.316228
$161$	16.0000	1.26098
$162$	9.00000	0.707107
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−2.00000	−0.156174
$165$	0	0
$166$	−2.00000	−0.155230
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	24.0000	1.84072
$171$	18.0000	1.37649
$172$	−8.00000	−0.609994
$173$	−20.0000	−1.52057	−0.760286	−	0.649589i	$-0.774941\pi$
$173$	−20.0000	−1.52057	−0.760286	+	0.649589i	$0.774941\pi$
$174$	0	0
$175$	−44.0000	−3.32609
$176$	4.00000	0.301511
$177$	0	0
$178$	14.0000	1.04934
$179$	18.0000	1.34538	0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000	1.34538	0.672692	+	0.739923i	$0.265138\pi$
$180$	−12.0000	−0.894427
$181$	16.0000	1.18927	0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000	1.18927	0.594635	+	0.803996i	$0.297296\pi$
$182$	16.0000	1.18600
$183$	0	0
$184$	−4.00000	−0.294884
$185$	−32.0000	−2.35269
$186$	0	0
$187$	24.0000	1.75505
$188$	0	0
$189$	0	0
$190$	−24.0000	−1.74114
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	0	0
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−1.00000	−0.0717958
$195$	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	$0.568565\pi$
$198$	−12.0000	−0.852803
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	11.0000	0.777817
$201$	0	0
$202$	−2.00000	−0.140720
$203$	0	0
$204$	0	0
$205$	−8.00000	−0.558744
$206$	0	0
$207$	12.0000	0.834058
$208$	−4.00000	−0.277350
$209$	−24.0000	−1.66011
$210$	0	0
$211$	26.0000	1.78991	0.894957	−	0.446153i	$-0.147206\pi$
$211$	26.0000	1.78991	0.894957	+	0.446153i	$0.147206\pi$
$212$	6.00000	0.412082
$213$	0	0
$214$	18.0000	1.23045
$215$	−32.0000	−2.18238
$216$	0	0
$217$	0	0
$218$	−10.0000	−0.677285
$219$	0	0
$220$	16.0000	1.07872
$221$	−24.0000	−1.61441
$222$	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
$225$	−33.0000	−2.20000
$226$	6.00000	0.399114
$227$	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
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	−16.0000	−1.05501
$231$	0	0
$232$	0	0
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	12.0000	0.784465
$235$	0	0
$236$	6.00000	0.390567
$237$	0	0
$238$	−24.0000	−1.55569
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	10.0000	0.640184
$245$	36.0000	2.29996
$246$	0	0
$247$	24.0000	1.52708
$248$	0	0
$249$	0	0
$250$	24.0000	1.51789
$251$	2.00000	0.126239	0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000	0.126239	0.0631194	+	0.998006i	$0.479895\pi$
$252$	12.0000	0.755929
$253$	−16.0000	−1.00591
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	0	0
$259$	32.0000	1.98838
$260$	−16.0000	−0.992278
$261$	0	0
$262$	6.00000	0.370681
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	0	0
$265$	24.0000	1.47431
$266$	24.0000	1.47153
$267$	0	0
$268$	6.00000	0.366508
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	−12.0000	−0.728948	−0.364474	−	0.931214i	$-0.618751\pi$
$271$	−12.0000	−0.728948	−0.364474	+	0.931214i	$0.618751\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	−2.00000	−0.120824
$275$	44.0000	2.65330
$276$	0	0
$277$	−32.0000	−1.92269	−0.961347	−	0.275340i	$-0.911209\pi$
$277$	−32.0000	−1.92269	−0.961347	+	0.275340i	$0.911209\pi$
$278$	−22.0000	−1.31947
$279$	0	0
$280$	−16.0000	−0.956183
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	0	0
$285$	0	0
$286$	−16.0000	−0.946100
$287$	8.00000	0.472225
$288$	−3.00000	−0.176777
$289$	19.0000	1.11765
$290$	0	0
$291$	0	0
$292$	−10.0000	−0.585206
$293$	26.0000	1.51894	0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000	1.51894	0.759468	+	0.650545i	$0.225459\pi$
$294$	0	0
$295$	24.0000	1.39733
$296$	−8.00000	−0.464991
$297$	0	0
$298$	4.00000	0.231714
$299$	16.0000	0.925304
$300$	0	0
$301$	32.0000	1.84445
$302$	8.00000	0.460348
$303$	0	0
$304$	−6.00000	−0.344124
$305$	40.0000	2.29039
$306$	−18.0000	−1.02899
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	−16.0000	−0.911685
$309$	0	0
$310$	0	0
$311$	−16.0000	−0.907277	−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000	−0.907277	−0.453638	+	0.891186i	$0.649874\pi$
$312$	0	0
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	−16.0000	−0.902932
$315$	48.0000	2.70449
$316$	8.00000	0.450035
$317$	−8.00000	−0.449325	−0.224662	−	0.974437i	$-0.572128\pi$
$317$	−8.00000	−0.449325	−0.224662	+	0.974437i	$0.572128\pi$
$318$	0	0
$319$	0	0
$320$	4.00000	0.223607
$321$	0	0
$322$	16.0000	0.891645
$323$	−36.0000	−2.00309
$324$	9.00000	0.500000
$325$	−44.0000	−2.44068
$326$	4.00000	0.221540
$327$	0	0
$328$	−2.00000	−0.110432
$329$	0	0
$330$	0	0
$331$	6.00000	0.329790	0.164895	−	0.986311i	$-0.447272\pi$
$331$	6.00000	0.329790	0.164895	+	0.986311i	$0.447272\pi$
$332$	−2.00000	−0.109764
$333$	24.0000	1.31519
$334$	−8.00000	−0.437741
$335$	24.0000	1.31126
$336$	0	0
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	3.00000	0.163178
$339$	0	0
$340$	24.0000	1.30158
$341$	0	0
$342$	18.0000	0.973329
$343$	−8.00000	−0.431959
$344$	−8.00000	−0.431331
$345$	0	0
$346$	−20.0000	−1.07521
$347$	−18.0000	−0.966291	−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000	−0.966291	−0.483145	+	0.875540i	$0.660506\pi$
$348$	0	0
$349$	−24.0000	−1.28469	−0.642345	−	0.766415i	$-0.722038\pi$
$349$	−24.0000	−1.28469	−0.642345	+	0.766415i	$0.722038\pi$
$350$	−44.0000	−2.35190
$351$	0	0
$352$	4.00000	0.213201
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	0	0
$355$	0	0
$356$	14.0000	0.741999
$357$	0	0
$358$	18.0000	0.951330
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	−12.0000	−0.632456
$361$	17.0000	0.894737
$362$	16.0000	0.840941
$363$	0	0
$364$	16.0000	0.838628
$365$	−40.0000	−2.09370
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	−4.00000	−0.208514
$369$	6.00000	0.312348
$370$	−32.0000	−1.66360
$371$	−24.0000	−1.24602
$372$	0	0
$373$	−28.0000	−1.44979	−0.724893	−	0.688862i	$-0.758111\pi$
$373$	−28.0000	−1.44979	−0.724893	+	0.688862i	$0.758111\pi$
$374$	24.0000	1.24101
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	−24.0000	−1.23117
$381$	0	0
$382$	−8.00000	−0.409316
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	0	0
$385$	−64.0000	−3.26174
$386$	−2.00000	−0.101797
$387$	24.0000	1.21999
$388$	−1.00000	−0.0507673
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	0	0
$391$	−24.0000	−1.21373
$392$	9.00000	0.454569
$393$	0	0
$394$	−6.00000	−0.302276
$395$	32.0000	1.61009
$396$	−12.0000	−0.603023
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−8.00000	−0.401004
$399$	0	0
$400$	11.0000	0.550000
$401$	14.0000	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$402$	0	0
$403$	0	0
$404$	−2.00000	−0.0995037
$405$	36.0000	1.78885
$406$	0	0
$407$	−32.0000	−1.58618
$408$	0	0
$409$	−2.00000	−0.0988936	−0.0494468	−	0.998777i	$-0.515746\pi$
$409$	−2.00000	−0.0988936	−0.0494468	+	0.998777i	$0.515746\pi$
$410$	−8.00000	−0.395092
$411$	0	0
$412$	0	0
$413$	−24.0000	−1.18096
$414$	12.0000	0.589768
$415$	−8.00000	−0.392705
$416$	−4.00000	−0.196116
$417$	0	0
$418$	−24.0000	−1.17388
$419$	24.0000	1.17248	0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000	1.17248	0.586238	+	0.810139i	$0.300608\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	26.0000	1.26566
$423$	0	0
$424$	6.00000	0.291386
$425$	66.0000	3.20147
$426$	0	0
$427$	−40.0000	−1.93574
$428$	18.0000	0.870063
$429$	0	0
$430$	−32.0000	−1.54318
$431$	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
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	0	0
$435$	0	0
$436$	−10.0000	−0.478913
$437$	24.0000	1.14808
$438$	0	0
$439$	−40.0000	−1.90910	−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000	−1.90910	−0.954548	+	0.298057i	$0.903661\pi$
$440$	16.0000	0.762770
$441$	−27.0000	−1.28571
$442$	−24.0000	−1.14156
$443$	6.00000	0.285069	0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000	0.285069	0.142534	+	0.989790i	$0.454475\pi$
$444$	0	0
$445$	56.0000	2.65465
$446$	−16.0000	−0.757622
$447$	0	0
$448$	−4.00000	−0.188982
$449$	26.0000	1.22702	0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000	1.22702	0.613508	+	0.789689i	$0.289758\pi$
$450$	−33.0000	−1.55563
$451$	−8.00000	−0.376705
$452$	6.00000	0.282216
$453$	0	0
$454$	4.00000	0.187729
$455$	64.0000	3.00037
$456$	0	0
$457$	−34.0000	−1.59045	−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000	−1.59045	−0.795226	+	0.606313i	$0.792648\pi$
$458$	2.00000	0.0934539
$459$	0	0
$460$	−16.0000	−0.746004
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	0	0
$465$	0	0
$466$	10.0000	0.463241
$467$	−16.0000	−0.740392	−0.370196	−	0.928954i	$-0.620709\pi$
$467$	−16.0000	−0.740392	−0.370196	+	0.928954i	$0.620709\pi$
$468$	12.0000	0.554700
$469$	−24.0000	−1.10822
$470$	0	0
$471$	0	0
$472$	6.00000	0.276172
$473$	−32.0000	−1.47136
$474$	0	0
$475$	−66.0000	−3.02829
$476$	−24.0000	−1.10004
$477$	−18.0000	−0.824163
$478$	−8.00000	−0.365911
$479$	−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
$481$	32.0000	1.45907
$482$	−14.0000	−0.637683
$483$	0	0
$484$	5.00000	0.227273
$485$	−4.00000	−0.181631
$486$	0	0
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	10.0000	0.452679
$489$	0	0
$490$	36.0000	1.62631
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	0	0
$493$	0	0
$494$	24.0000	1.07981
$495$	−48.0000	−2.15744
$496$	0	0
$497$	0	0
$498$	0	0
$499$	22.0000	0.984855	0.492428	−	0.870353i	$-0.336110\pi$
$499$	22.0000	0.984855	0.492428	+	0.870353i	$0.336110\pi$
$500$	24.0000	1.07331
$501$	0	0
$502$	2.00000	0.0892644
$503$	8.00000	0.356702	0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000	0.356702	0.178351	+	0.983967i	$0.442924\pi$
$504$	12.0000	0.534522
$505$	−8.00000	−0.355995
$506$	−16.0000	−0.711287
$507$	0	0
$508$	8.00000	0.354943
$509$	14.0000	0.620539	0.310270	−	0.950649i	$-0.399581\pi$
$509$	14.0000	0.620539	0.310270	+	0.950649i	$0.399581\pi$
$510$	0	0
$511$	40.0000	1.76950
$512$	1.00000	0.0441942
$513$	0	0
$514$	−6.00000	−0.264649
$515$	0	0
$516$	0	0
$517$	0	0
$518$	32.0000	1.40600
$519$	0	0
$520$	−16.0000	−0.701646
$521$	22.0000	0.963837	0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000	0.963837	0.481919	+	0.876216i	$0.339940\pi$
$522$	0	0
$523$	−2.00000	−0.0874539	−0.0437269	−	0.999044i	$-0.513923\pi$
$523$	−2.00000	−0.0874539	−0.0437269	+	0.999044i	$0.513923\pi$
$524$	6.00000	0.262111
$525$	0	0
$526$	24.0000	1.04645
$527$	0	0
$528$	0	0
$529$	−7.00000	−0.304348
$530$	24.0000	1.04249
$531$	−18.0000	−0.781133
$532$	24.0000	1.04053
$533$	8.00000	0.346518
$534$	0	0
$535$	72.0000	3.11283
$536$	6.00000	0.259161
$537$	0	0
$538$	−6.00000	−0.258678
$539$	36.0000	1.55063
$540$	0	0
$541$	32.0000	1.37579	0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000	1.37579	0.687894	+	0.725811i	$0.258536\pi$
$542$	−12.0000	−0.515444
$543$	0	0
$544$	6.00000	0.257248
$545$	−40.0000	−1.71341
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−2.00000	−0.0854358
$549$	−30.0000	−1.28037
$550$	44.0000	1.87617
$551$	0	0
$552$	0	0
$553$	−32.0000	−1.36078
$554$	−32.0000	−1.35955
$555$	0	0
$556$	−22.0000	−0.933008
$557$	34.0000	1.44063	0.720313	−	0.693649i	$-0.243998\pi$
$557$	34.0000	1.44063	0.720313	+	0.693649i	$0.243998\pi$
$558$	0	0
$559$	32.0000	1.35346
$560$	−16.0000	−0.676123
$561$	0	0
$562$	−6.00000	−0.253095
$563$	42.0000	1.77009	0.885044	−	0.465506i	$-0.154128\pi$
$563$	42.0000	1.77009	0.885044	+	0.465506i	$0.154128\pi$
$564$	0	0
$565$	24.0000	1.00969
$566$	−28.0000	−1.17693
$567$	−36.0000	−1.51186
$568$	0	0
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	−16.0000	−0.668994
$573$	0	0
$574$	8.00000	0.333914
$575$	−44.0000	−1.83493
$576$	−3.00000	−0.125000
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	19.0000	0.790296
$579$	0	0
$580$	0	0
$581$	8.00000	0.331896
$582$	0	0
$583$	24.0000	0.993978
$584$	−10.0000	−0.413803
$585$	48.0000	1.98456
$586$	26.0000	1.07405
$587$	−22.0000	−0.908037	−0.454019	−	0.890992i	$-0.650010\pi$
$587$	−22.0000	−0.908037	−0.454019	+	0.890992i	$0.650010\pi$
$588$	0	0
$589$	0	0
$590$	24.0000	0.988064
$591$	0	0
$592$	−8.00000	−0.328798
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	0	0
$595$	−96.0000	−3.93562
$596$	4.00000	0.163846
$597$	0	0
$598$	16.0000	0.654289
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	0	0
$601$	−6.00000	−0.244745	−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000	−0.244745	−0.122373	+	0.992484i	$0.539050\pi$
$602$	32.0000	1.30422
$603$	−18.0000	−0.733017
$604$	8.00000	0.325515
$605$	20.0000	0.813116
$606$	0	0
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	−6.00000	−0.243332
$609$	0	0
$610$	40.0000	1.61955
$611$	0	0
$612$	−18.0000	−0.727607
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	0	0
$615$	0	0
$616$	−16.0000	−0.644658
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	0	0
$619$	−6.00000	−0.241160	−0.120580	−	0.992704i	$-0.538475\pi$
$619$	−6.00000	−0.241160	−0.120580	+	0.992704i	$0.538475\pi$
$620$	0	0
$621$	0	0
$622$	−16.0000	−0.641542
$623$	−56.0000	−2.24359
$624$	0	0
$625$	41.0000	1.64000
$626$	−14.0000	−0.559553
$627$	0	0
$628$	−16.0000	−0.638470
$629$	−48.0000	−1.91389
$630$	48.0000	1.91237
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	8.00000	0.318223
$633$	0	0
$634$	−8.00000	−0.317721
$635$	32.0000	1.26988
$636$	0	0
$637$	−36.0000	−1.42637
$638$	0	0
$639$	0	0
$640$	4.00000	0.158114
$641$	−26.0000	−1.02694	−0.513469	−	0.858108i	$-0.671640\pi$
$641$	−26.0000	−1.02694	−0.513469	+	0.858108i	$0.671640\pi$
$642$	0	0
$643$	16.0000	0.630978	0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000	0.630978	0.315489	+	0.948929i	$0.397831\pi$
$644$	16.0000	0.630488
$645$	0	0
$646$	−36.0000	−1.41640
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	9.00000	0.353553
$649$	24.0000	0.942082
$650$	−44.0000	−1.72582
$651$	0	0
$652$	4.00000	0.156652
$653$	24.0000	0.939193	0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000	0.939193	0.469596	+	0.882881i	$0.344399\pi$
$654$	0	0
$655$	24.0000	0.937758
$656$	−2.00000	−0.0780869
$657$	30.0000	1.17041
$658$	0	0
$659$	30.0000	1.16863	0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000	1.16863	0.584317	+	0.811525i	$0.301362\pi$
$660$	0	0
$661$	6.00000	0.233373	0.116686	−	0.993169i	$-0.462773\pi$
$661$	6.00000	0.233373	0.116686	+	0.993169i	$0.462773\pi$
$662$	6.00000	0.233197
$663$	0	0
$664$	−2.00000	−0.0776151
$665$	96.0000	3.72272
$666$	24.0000	0.929981
$667$	0	0
$668$	−8.00000	−0.309529
$669$	0	0
$670$	24.0000	0.927201
$671$	40.0000	1.54418
$672$	0	0
$673$	14.0000	0.539660	0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000	0.539660	0.269830	+	0.962908i	$0.413032\pi$
$674$	2.00000	0.0770371
$675$	0	0
$676$	3.00000	0.115385
$677$	34.0000	1.30673	0.653363	−	0.757045i	$-0.273358\pi$
$677$	34.0000	1.30673	0.653363	+	0.757045i	$0.273358\pi$
$678$	0	0
$679$	4.00000	0.153506
$680$	24.0000	0.920358
$681$	0	0
$682$	0	0
$683$	−40.0000	−1.53056	−0.765279	−	0.643699i	$-0.777399\pi$
$683$	−40.0000	−1.53056	−0.765279	+	0.643699i	$0.777399\pi$
$684$	18.0000	0.688247
$685$	−8.00000	−0.305664
$686$	−8.00000	−0.305441
$687$	0	0
$688$	−8.00000	−0.304997
$689$	−24.0000	−0.914327
$690$	0	0
$691$	16.0000	0.608669	0.304334	−	0.952565i	$-0.401566\pi$
$691$	16.0000	0.608669	0.304334	+	0.952565i	$0.401566\pi$
$692$	−20.0000	−0.760286
$693$	48.0000	1.82337
$694$	−18.0000	−0.683271
$695$	−88.0000	−3.33803
$696$	0	0
$697$	−12.0000	−0.454532
$698$	−24.0000	−0.908413
$699$	0	0
$700$	−44.0000	−1.66304
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	0	0
$703$	48.0000	1.81035
$704$	4.00000	0.150756
$705$	0	0
$706$	18.0000	0.677439
$707$	8.00000	0.300871
$708$	0	0
$709$	−4.00000	−0.150223	−0.0751116	−	0.997175i	$-0.523931\pi$
$709$	−4.00000	−0.150223	−0.0751116	+	0.997175i	$0.523931\pi$
$710$	0	0
$711$	−24.0000	−0.900070
$712$	14.0000	0.524672
$713$	0	0
$714$	0	0
$715$	−64.0000	−2.39346
$716$	18.0000	0.672692
$717$	0	0
$718$	0	0
$719$	48.0000	1.79010	0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000	1.79010	0.895049	+	0.445968i	$0.147140\pi$
$720$	−12.0000	−0.447214
$721$	0	0
$722$	17.0000	0.632674
$723$	0	0
$724$	16.0000	0.594635
$725$	0	0
$726$	0	0
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	16.0000	0.592999
$729$	−27.0000	−1.00000
$730$	−40.0000	−1.48047
$731$	−48.0000	−1.77534
$732$	0	0
$733$	26.0000	0.960332	0.480166	−	0.877178i	$-0.340576\pi$
$733$	26.0000	0.960332	0.480166	+	0.877178i	$0.340576\pi$
$734$	0	0
$735$	0	0
$736$	−4.00000	−0.147442
$737$	24.0000	0.884051
$738$	6.00000	0.220863
$739$	−2.00000	−0.0735712	−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000	−0.0735712	−0.0367856	+	0.999323i	$0.511712\pi$
$740$	−32.0000	−1.17634
$741$	0	0
$742$	−24.0000	−0.881068
$743$	−40.0000	−1.46746	−0.733729	−	0.679442i	$-0.762222\pi$
$743$	−40.0000	−1.46746	−0.733729	+	0.679442i	$0.762222\pi$
$744$	0	0
$745$	16.0000	0.586195
$746$	−28.0000	−1.02515
$747$	6.00000	0.219529
$748$	24.0000	0.877527
$749$	−72.0000	−2.63082
$750$	0	0
$751$	48.0000	1.75154	0.875772	−	0.482724i	$-0.160353\pi$
$751$	48.0000	1.75154	0.875772	+	0.482724i	$0.160353\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	32.0000	1.16460
$756$	0	0
$757$	−32.0000	−1.16306	−0.581530	−	0.813525i	$-0.697546\pi$
$757$	−32.0000	−1.16306	−0.581530	+	0.813525i	$0.697546\pi$
$758$	28.0000	1.01701
$759$	0	0
$760$	−24.0000	−0.870572
$761$	38.0000	1.37750	0.688749	−	0.724999i	$-0.258160\pi$
$761$	38.0000	1.37750	0.688749	+	0.724999i	$0.258160\pi$
$762$	0	0
$763$	40.0000	1.44810
$764$	−8.00000	−0.289430
$765$	−72.0000	−2.60317
$766$	−12.0000	−0.433578
$767$	−24.0000	−0.866590
$768$	0	0
$769$	−34.0000	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$770$	−64.0000	−2.30640
$771$	0	0
$772$	−2.00000	−0.0719816
$773$	26.0000	0.935155	0.467578	−	0.883952i	$-0.345127\pi$
$773$	26.0000	0.935155	0.467578	+	0.883952i	$0.345127\pi$
$774$	24.0000	0.862662
$775$	0	0
$776$	−1.00000	−0.0358979
$777$	0	0
$778$	−18.0000	−0.645331
$779$	12.0000	0.429945
$780$	0	0
$781$	0	0
$782$	−24.0000	−0.858238
$783$	0	0
$784$	9.00000	0.321429
$785$	−64.0000	−2.28426
$786$	0	0
$787$	24.0000	0.855508	0.427754	−	0.903895i	$-0.359305\pi$
$787$	24.0000	0.855508	0.427754	+	0.903895i	$0.359305\pi$
$788$	−6.00000	−0.213741
$789$	0	0
$790$	32.0000	1.13851
$791$	−24.0000	−0.853342
$792$	−12.0000	−0.426401
$793$	−40.0000	−1.42044
$794$	−2.00000	−0.0709773
$795$	0	0
$796$	−8.00000	−0.283552
$797$	28.0000	0.991811	0.495905	−	0.868377i	$-0.334836\pi$
$797$	28.0000	0.991811	0.495905	+	0.868377i	$0.334836\pi$
$798$	0	0
$799$	0	0
$800$	11.0000	0.388909
$801$	−42.0000	−1.48400
$802$	14.0000	0.494357
$803$	−40.0000	−1.41157
$804$	0	0
$805$	64.0000	2.25570
$806$	0	0
$807$	0	0
$808$	−2.00000	−0.0703598
$809$	34.0000	1.19538	0.597688	−	0.801729i	$-0.296086\pi$
$809$	34.0000	1.19538	0.597688	+	0.801729i	$0.296086\pi$
$810$	36.0000	1.26491
$811$	−40.0000	−1.40459	−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000	−1.40459	−0.702295	+	0.711886i	$0.747841\pi$
$812$	0	0
$813$	0	0
$814$	−32.0000	−1.12160
$815$	16.0000	0.560456
$816$	0	0
$817$	48.0000	1.67931
$818$	−2.00000	−0.0699284
$819$	−48.0000	−1.67726
$820$	−8.00000	−0.279372
$821$	40.0000	1.39601	0.698005	−	0.716093i	$-0.254071\pi$
$821$	40.0000	1.39601	0.698005	+	0.716093i	$0.254071\pi$
$822$	0	0
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	0	0
$825$	0	0
$826$	−24.0000	−0.835067
$827$	−30.0000	−1.04320	−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000	−1.04320	−0.521601	+	0.853189i	$0.674665\pi$
$828$	12.0000	0.417029
$829$	10.0000	0.347314	0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000	0.347314	0.173657	+	0.984806i	$0.444442\pi$
$830$	−8.00000	−0.277684
$831$	0	0
$832$	−4.00000	−0.138675
$833$	54.0000	1.87099
$834$	0	0
$835$	−32.0000	−1.10741
$836$	−24.0000	−0.830057
$837$	0	0
$838$	24.0000	0.829066
$839$	−56.0000	−1.93333	−0.966667	−	0.256036i	$-0.917584\pi$
$839$	−56.0000	−1.93333	−0.966667	+	0.256036i	$0.917584\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	−10.0000	−0.344623
$843$	0	0
$844$	26.0000	0.894957
$845$	12.0000	0.412813
$846$	0	0
$847$	−20.0000	−0.687208
$848$	6.00000	0.206041
$849$	0	0
$850$	66.0000	2.26378
$851$	32.0000	1.09695
$852$	0	0
$853$	20.0000	0.684787	0.342393	−	0.939557i	$-0.388762\pi$
$853$	20.0000	0.684787	0.342393	+	0.939557i	$0.388762\pi$
$854$	−40.0000	−1.36877
$855$	72.0000	2.46235
$856$	18.0000	0.615227
$857$	38.0000	1.29806	0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000	1.29806	0.649028	+	0.760765i	$0.275176\pi$
$858$	0	0
$859$	54.0000	1.84246	0.921228	−	0.389023i	$-0.127187\pi$
$859$	54.0000	1.84246	0.921228	+	0.389023i	$0.127187\pi$
$860$	−32.0000	−1.09119
$861$	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
$865$	−80.0000	−2.72008
$866$	−2.00000	−0.0679628
$867$	0	0
$868$	0	0
$869$	32.0000	1.08553
$870$	0	0
$871$	−24.0000	−0.813209
$872$	−10.0000	−0.338643
$873$	3.00000	0.101535
$874$	24.0000	0.811812
$875$	−96.0000	−3.24539
$876$	0	0
$877$	30.0000	1.01303	0.506514	−	0.862232i	$-0.330934\pi$
$877$	30.0000	1.01303	0.506514	+	0.862232i	$0.330934\pi$
$878$	−40.0000	−1.34993
$879$	0	0
$880$	16.0000	0.539360
$881$	−2.00000	−0.0673817	−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000	−0.0673817	−0.0336909	+	0.999432i	$0.510726\pi$
$882$	−27.0000	−0.909137
$883$	58.0000	1.95186	0.975928	−	0.218094i	$-0.0699840\pi$
$883$	58.0000	1.95186	0.975928	+	0.218094i	$0.0699840\pi$
$884$	−24.0000	−0.807207
$885$	0	0
$886$	6.00000	0.201574
$887$	−4.00000	−0.134307	−0.0671534	−	0.997743i	$-0.521392\pi$
$887$	−4.00000	−0.134307	−0.0671534	+	0.997743i	$0.521392\pi$
$888$	0	0
$889$	−32.0000	−1.07325
$890$	56.0000	1.87712
$891$	36.0000	1.20605
$892$	−16.0000	−0.535720
$893$	0	0
$894$	0	0
$895$	72.0000	2.40669
$896$	−4.00000	−0.133631
$897$	0	0
$898$	26.0000	0.867631
$899$	0	0
$900$	−33.0000	−1.10000
$901$	36.0000	1.19933
$902$	−8.00000	−0.266371
$903$	0	0
$904$	6.00000	0.199557
$905$	64.0000	2.12743
$906$	0	0
$907$	−18.0000	−0.597680	−0.298840	−	0.954303i	$-0.596600\pi$
$907$	−18.0000	−0.597680	−0.298840	+	0.954303i	$0.596600\pi$
$908$	4.00000	0.132745
$909$	6.00000	0.199007
$910$	64.0000	2.12158
$911$	−28.0000	−0.927681	−0.463841	−	0.885919i	$-0.653529\pi$
$911$	−28.0000	−0.927681	−0.463841	+	0.885919i	$0.653529\pi$
$912$	0	0
$913$	−8.00000	−0.264761
$914$	−34.0000	−1.12462
$915$	0	0
$916$	2.00000	0.0660819
$917$	−24.0000	−0.792550
$918$	0	0
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	−16.0000	−0.527504
$921$	0	0
$922$	−6.00000	−0.197599
$923$	0	0
$924$	0	0
$925$	−88.0000	−2.89342
$926$	16.0000	0.525793
$927$	0	0
$928$	0	0
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	−54.0000	−1.76978
$932$	10.0000	0.327561
$933$	0	0
$934$	−16.0000	−0.523536
$935$	96.0000	3.13954
$936$	12.0000	0.392232
$937$	58.0000	1.89478	0.947389	−	0.320085i	$-0.103712\pi$
$937$	58.0000	1.89478	0.947389	+	0.320085i	$0.103712\pi$
$938$	−24.0000	−0.783628
$939$	0	0
$940$	0	0
$941$	−44.0000	−1.43436	−0.717180	−	0.696888i	$-0.754567\pi$
$941$	−44.0000	−1.43436	−0.717180	+	0.696888i	$0.754567\pi$
$942$	0	0
$943$	8.00000	0.260516
$944$	6.00000	0.195283
$945$	0	0
$946$	−32.0000	−1.04041
$947$	26.0000	0.844886	0.422443	−	0.906389i	$-0.361173\pi$
$947$	26.0000	0.844886	0.422443	+	0.906389i	$0.361173\pi$
$948$	0	0
$949$	40.0000	1.29845
$950$	−66.0000	−2.14132
$951$	0	0
$952$	−24.0000	−0.777844
$953$	54.0000	1.74923	0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000	1.74923	0.874616	+	0.484817i	$0.161114\pi$
$954$	−18.0000	−0.582772
$955$	−32.0000	−1.03550
$956$	−8.00000	−0.258738
$957$	0	0
$958$	−24.0000	−0.775405
$959$	8.00000	0.258333
$960$	0	0
$961$	−31.0000	−1.00000
$962$	32.0000	1.03172
$963$	−54.0000	−1.74013
$964$	−14.0000	−0.450910
$965$	−8.00000	−0.257529
$966$	0	0
$967$	16.0000	0.514525	0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000	0.514525	0.257263	+	0.966342i	$0.417179\pi$
$968$	5.00000	0.160706
$969$	0	0
$970$	−4.00000	−0.128432
$971$	−40.0000	−1.28366	−0.641831	−	0.766846i	$-0.721825\pi$
$971$	−40.0000	−1.28366	−0.641831	+	0.766846i	$0.721825\pi$
$972$	0	0
$973$	88.0000	2.82115
$974$	16.0000	0.512673
$975$	0	0
$976$	10.0000	0.320092
$977$	−34.0000	−1.08776	−0.543878	−	0.839164i	$-0.683045\pi$
$977$	−34.0000	−1.08776	−0.543878	+	0.839164i	$0.683045\pi$
$978$	0	0
$979$	56.0000	1.78977
$980$	36.0000	1.14998
$981$	30.0000	0.957826
$982$	−20.0000	−0.638226
$983$	−8.00000	−0.255160	−0.127580	−	0.991828i	$-0.540721\pi$
$983$	−8.00000	−0.255160	−0.127580	+	0.991828i	$0.540721\pi$
$984$	0	0
$985$	−24.0000	−0.764704
$986$	0	0
$987$	0	0
$988$	24.0000	0.763542
$989$	32.0000	1.01754
$990$	−48.0000	−1.52554
$991$	−20.0000	−0.635321	−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000	−0.635321	−0.317660	+	0.948205i	$0.602897\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	−32.0000	−1.01447
$996$	0	0
$997$	26.0000	0.823428	0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000	0.823428	0.411714	+	0.911313i	$0.364930\pi$
$998$	22.0000	0.696398
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	194.2.a.a.1.1	✓	1
3.2	odd	2		1746.2.a.a.1.1		1
4.3	odd	2		1552.2.a.b.1.1		1
5.4	even	2		4850.2.a.e.1.1		1
7.6	odd	2		9506.2.a.d.1.1		1
8.3	odd	2		6208.2.a.b.1.1		1
8.5	even	2		6208.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
194.2.a.a.1.1	✓	1	1.1	even	1	trivial
1552.2.a.b.1.1		1	4.3	odd	2
1746.2.a.a.1.1		1	3.2	odd	2
4850.2.a.e.1.1		1	5.4	even	2
6208.2.a.a.1.1		1	8.5	even	2
6208.2.a.b.1.1		1	8.3	odd	2
9506.2.a.d.1.1		1	7.6	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:	\( N \)	\(=\)	\( 194 = 2 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	194.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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