LMFDB - Embedded newform 1755.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1755,2,Mod(1,1755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1755, 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("1755.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1755 = 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1755.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:	$14.0137455547$
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	$\chi$	$=$	1755.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +2.00000 q^{4} -1.00000 q^{5} +O(q^{10})$

$q-2.00000 q^{2} +2.00000 q^{4} -1.00000 q^{5} +2.00000 q^{10} -5.00000 q^{11} -1.00000 q^{13} -4.00000 q^{16} +1.00000 q^{17} +4.00000 q^{19} -2.00000 q^{20} +10.0000 q^{22} -9.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} +2.00000 q^{29} +6.00000 q^{31} +8.00000 q^{32} -2.00000 q^{34} -1.00000 q^{37} -8.00000 q^{38} +2.00000 q^{41} +4.00000 q^{43} -10.0000 q^{44} +18.0000 q^{46} -2.00000 q^{47} -7.00000 q^{49} -2.00000 q^{50} -2.00000 q^{52} -2.00000 q^{53} +5.00000 q^{55} -4.00000 q^{58} +1.00000 q^{59} +1.00000 q^{61} -12.0000 q^{62} -8.00000 q^{64} +1.00000 q^{65} -3.00000 q^{67} +2.00000 q^{68} +8.00000 q^{71} +7.00000 q^{73} +2.00000 q^{74} +8.00000 q^{76} -12.0000 q^{79} +4.00000 q^{80} -4.00000 q^{82} -1.00000 q^{85} -8.00000 q^{86} +15.0000 q^{89} -18.0000 q^{92} +4.00000 q^{94} -4.00000 q^{95} -7.00000 q^{97} +14.0000 q^{98} +O(q^{100})$

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	0	0
$3$	0	0
$4$	2.00000	1.00000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	0	0
$10$	2.00000	0.632456
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	−4.00000	−1.00000
$17$	1.00000	0.242536	0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000	0.242536	0.121268	+	0.992620i	$0.461304\pi$
$18$	0	0
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	10.0000	2.13201
$23$	−9.00000	−1.87663	−0.938315	−	0.345782i	$-0.887614\pi$
$23$	−9.00000	−1.87663	−0.938315	+	0.345782i	$0.887614\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	0	0
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	8.00000	1.41421
$33$	0	0
$34$	−2.00000	−0.342997
$35$	0	0
$36$	0	0
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−8.00000	−1.29777
$39$	0	0
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−10.0000	−1.50756
$45$	0	0
$46$	18.0000	2.65396
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	−2.00000	−0.282843
$51$	0	0
$52$	−2.00000	−0.277350
$53$	−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
$55$	5.00000	0.674200
$56$	0	0
$57$	0	0
$58$	−4.00000	−0.525226
$59$	1.00000	0.130189	0.0650945	−	0.997879i	$-0.479265\pi$
$59$	1.00000	0.130189	0.0650945	+	0.997879i	$0.479265\pi$
$60$	0	0
$61$	1.00000	0.128037	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000	0.128037	0.0640184	+	0.997949i	$0.479608\pi$
$62$	−12.0000	−1.52400
$63$	0	0
$64$	−8.00000	−1.00000
$65$	1.00000	0.124035
$66$	0	0
$67$	−3.00000	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$68$	2.00000	0.242536
$69$	0	0
$70$	0	0
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	0	0
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	8.00000	0.917663
$77$	0	0
$78$	0	0
$79$	−12.0000	−1.35011	−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000	−1.35011	−0.675053	+	0.737769i	$0.735879\pi$
$80$	4.00000	0.447214
$81$	0	0
$82$	−4.00000	−0.441726
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	−1.00000	−0.108465
$86$	−8.00000	−0.862662
$87$	0	0
$88$	0	0
$89$	15.0000	1.59000	0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000	1.59000	0.794998	+	0.606612i	$0.207472\pi$
$90$	0	0
$91$	0	0
$92$	−18.0000	−1.87663
$93$	0	0
$94$	4.00000	0.412568
$95$	−4.00000	−0.410391
$96$	0	0
$97$	−7.00000	−0.710742	−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000	−0.710742	−0.355371	+	0.934725i	$0.615646\pi$
$98$	14.0000	1.41421
$99$	0	0
$100$	2.00000	0.200000
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	0	0
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	0	0
$105$	0	0
$106$	4.00000	0.388514
$107$	−15.0000	−1.45010	−0.725052	−	0.688694i	$-0.758184\pi$
$107$	−15.0000	−1.45010	−0.725052	+	0.688694i	$0.758184\pi$
$108$	0	0
$109$	14.0000	1.34096	0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	−10.0000	−0.953463
$111$	0	0
$112$	0	0
$113$	−11.0000	−1.03479	−0.517396	−	0.855746i	$-0.673099\pi$
$113$	−11.0000	−1.03479	−0.517396	+	0.855746i	$0.673099\pi$
$114$	0	0
$115$	9.00000	0.839254
$116$	4.00000	0.371391
$117$	0	0
$118$	−2.00000	−0.184115
$119$	0	0
$120$	0	0
$121$	14.0000	1.27273
$122$	−2.00000	−0.181071
$123$	0	0
$124$	12.0000	1.07763
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	0	0
$129$	0	0
$130$	−2.00000	−0.175412
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	0	0
$133$	0	0
$134$	6.00000	0.518321
$135$	0	0
$136$	0	0
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	−7.00000	−0.593732	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	−7.00000	−0.593732	−0.296866	+	0.954919i	$0.595942\pi$
$140$	0	0
$141$	0	0
$142$	−16.0000	−1.34269
$143$	5.00000	0.418121
$144$	0	0
$145$	−2.00000	−0.166091
$146$	−14.0000	−1.15865
$147$	0	0
$148$	−2.00000	−0.164399
$149$	23.0000	1.88423	0.942117	−	0.335285i	$-0.108833\pi$
$149$	23.0000	1.88423	0.942117	+	0.335285i	$0.108833\pi$
$150$	0	0
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	−6.00000	−0.481932
$156$	0	0
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	24.0000	1.90934
$159$	0	0
$160$	−8.00000	−0.632456
$161$	0	0
$162$	0	0
$163$	−7.00000	−0.548282	−0.274141	−	0.961689i	$-0.588394\pi$
$163$	−7.00000	−0.548282	−0.274141	+	0.961689i	$0.588394\pi$
$164$	4.00000	0.312348
$165$	0	0
$166$	0	0
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	2.00000	0.153393
$171$	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
$175$	0	0
$176$	20.0000	1.50756
$177$	0	0
$178$	−30.0000	−2.24860
$179$	10.0000	0.747435	0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000	0.747435	0.373718	+	0.927543i	$0.378083\pi$
$180$	0	0
$181$	26.0000	1.93256	0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000	1.93256	0.966282	+	0.257485i	$0.0828937\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	1.00000	0.0735215
$186$	0	0
$187$	−5.00000	−0.365636
$188$	−4.00000	−0.291730
$189$	0	0
$190$	8.00000	0.580381
$191$	2.00000	0.144715	0.0723575	−	0.997379i	$-0.476948\pi$
$191$	2.00000	0.144715	0.0723575	+	0.997379i	$0.476948\pi$
$192$	0	0
$193$	23.0000	1.65558	0.827788	−	0.561041i	$-0.189599\pi$
$193$	23.0000	1.65558	0.827788	+	0.561041i	$0.189599\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	−14.0000	−1.00000
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	7.00000	0.496217	0.248108	−	0.968732i	$-0.420191\pi$
$199$	7.00000	0.496217	0.248108	+	0.968732i	$0.420191\pi$
$200$	0	0
$201$	0	0
$202$	−36.0000	−2.53295
$203$	0	0
$204$	0	0
$205$	−2.00000	−0.139686
$206$	−28.0000	−1.95085
$207$	0	0
$208$	4.00000	0.277350
$209$	−20.0000	−1.38343
$210$	0	0
$211$	5.00000	0.344214	0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000	0.344214	0.172107	+	0.985078i	$0.444942\pi$
$212$	−4.00000	−0.274721
$213$	0	0
$214$	30.0000	2.05076
$215$	−4.00000	−0.272798
$216$	0	0
$217$	0	0
$218$	−28.0000	−1.89640
$219$	0	0
$220$	10.0000	0.674200
$221$	−1.00000	−0.0672673
$222$	0	0
$223$	−19.0000	−1.27233	−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000	−1.27233	−0.636167	+	0.771551i	$0.719481\pi$
$224$	0	0
$225$	0	0
$226$	22.0000	1.46342
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	0	0
$229$	−24.0000	−1.58596	−0.792982	−	0.609245i	$-0.791473\pi$
$229$	−24.0000	−1.58596	−0.792982	+	0.609245i	$0.791473\pi$
$230$	−18.0000	−1.18688
$231$	0	0
$232$	0	0
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	2.00000	0.130466
$236$	2.00000	0.130189
$237$	0	0
$238$	0	0
$239$	25.0000	1.61712	0.808558	−	0.588417i	$-0.200249\pi$
$239$	25.0000	1.61712	0.808558	+	0.588417i	$0.200249\pi$
$240$	0	0
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	−28.0000	−1.79991
$243$	0	0
$244$	2.00000	0.128037
$245$	7.00000	0.447214
$246$	0	0
$247$	−4.00000	−0.254514
$248$	0	0
$249$	0	0
$250$	2.00000	0.126491
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	0	0
$253$	45.0000	2.82913
$254$	16.0000	1.00393
$255$	0	0
$256$	16.0000	1.00000
$257$	9.00000	0.561405	0.280702	−	0.959795i	$-0.409433\pi$
$257$	9.00000	0.561405	0.280702	+	0.959795i	$0.409433\pi$
$258$	0	0
$259$	0	0
$260$	2.00000	0.124035
$261$	0	0
$262$	−36.0000	−2.22409
$263$	−1.00000	−0.0616626	−0.0308313	−	0.999525i	$-0.509815\pi$
$263$	−1.00000	−0.0616626	−0.0308313	+	0.999525i	$0.509815\pi$
$264$	0	0
$265$	2.00000	0.122859
$266$	0	0
$267$	0	0
$268$	−6.00000	−0.366508
$269$	−26.0000	−1.58525	−0.792624	−	0.609711i	$-0.791286\pi$
$269$	−26.0000	−1.58525	−0.792624	+	0.609711i	$0.791286\pi$
$270$	0	0
$271$	22.0000	1.33640	0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000	1.33640	0.668202	+	0.743980i	$0.267064\pi$
$272$	−4.00000	−0.242536
$273$	0	0
$274$	−12.0000	−0.724947
$275$	−5.00000	−0.301511
$276$	0	0
$277$	12.0000	0.721010	0.360505	−	0.932757i	$-0.382604\pi$
$277$	12.0000	0.721010	0.360505	+	0.932757i	$0.382604\pi$
$278$	14.0000	0.839664
$279$	0	0
$280$	0	0
$281$	−15.0000	−0.894825	−0.447412	−	0.894328i	$-0.647654\pi$
$281$	−15.0000	−0.894825	−0.447412	+	0.894328i	$0.647654\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	16.0000	0.949425
$285$	0	0
$286$	−10.0000	−0.591312
$287$	0	0
$288$	0	0
$289$	−16.0000	−0.941176
$290$	4.00000	0.234888
$291$	0	0
$292$	14.0000	0.819288
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	0	0
$295$	−1.00000	−0.0582223
$296$	0	0
$297$	0	0
$298$	−46.0000	−2.66471
$299$	9.00000	0.520483
$300$	0	0
$301$	0	0
$302$	−8.00000	−0.460348
$303$	0	0
$304$	−16.0000	−0.917663
$305$	−1.00000	−0.0572598
$306$	0	0
$307$	19.0000	1.08439	0.542194	−	0.840254i	$-0.317594\pi$
$307$	19.0000	1.08439	0.542194	+	0.840254i	$0.317594\pi$
$308$	0	0
$309$	0	0
$310$	12.0000	0.681554
$311$	30.0000	1.70114	0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000	1.70114	0.850572	+	0.525859i	$0.176256\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	8.00000	0.451466
$315$	0	0
$316$	−24.0000	−1.35011
$317$	−22.0000	−1.23564	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−22.0000	−1.23564	−0.617822	+	0.786318i	$0.711985\pi$
$318$	0	0
$319$	−10.0000	−0.559893
$320$	8.00000	0.447214
$321$	0	0
$322$	0	0
$323$	4.00000	0.222566
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	14.0000	0.775388
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−24.0000	−1.31916	−0.659580	−	0.751635i	$-0.729266\pi$
$331$	−24.0000	−1.31916	−0.659580	+	0.751635i	$0.729266\pi$
$332$	0	0
$333$	0	0
$334$	−36.0000	−1.96983
$335$	3.00000	0.163908
$336$	0	0
$337$	−26.0000	−1.41631	−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000	−1.41631	−0.708155	+	0.706057i	$0.750472\pi$
$338$	−2.00000	−0.108786
$339$	0	0
$340$	−2.00000	−0.108465
$341$	−30.0000	−1.62459
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	−12.0000	−0.645124
$347$	−17.0000	−0.912608	−0.456304	−	0.889824i	$-0.650827\pi$
$347$	−17.0000	−0.912608	−0.456304	+	0.889824i	$0.650827\pi$
$348$	0	0
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	0	0
$351$	0	0
$352$	−40.0000	−2.13201
$353$	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
$355$	−8.00000	−0.424596
$356$	30.0000	1.59000
$357$	0	0
$358$	−20.0000	−1.05703
$359$	−21.0000	−1.10834	−0.554169	−	0.832404i	$-0.686964\pi$
$359$	−21.0000	−1.10834	−0.554169	+	0.832404i	$0.686964\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	−52.0000	−2.73306
$363$	0	0
$364$	0	0
$365$	−7.00000	−0.366397
$366$	0	0
$367$	24.0000	1.25279	0.626395	−	0.779506i	$-0.284530\pi$
$367$	24.0000	1.25279	0.626395	+	0.779506i	$0.284530\pi$
$368$	36.0000	1.87663
$369$	0	0
$370$	−2.00000	−0.103975
$371$	0	0
$372$	0	0
$373$	−8.00000	−0.414224	−0.207112	−	0.978317i	$-0.566407\pi$
$373$	−8.00000	−0.414224	−0.207112	+	0.978317i	$0.566407\pi$
$374$	10.0000	0.517088
$375$	0	0
$376$	0	0
$377$	−2.00000	−0.103005
$378$	0	0
$379$	−8.00000	−0.410932	−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000	−0.410932	−0.205466	+	0.978664i	$0.565871\pi$
$380$	−8.00000	−0.410391
$381$	0	0
$382$	−4.00000	−0.204658
$383$	−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
$385$	0	0
$386$	−46.0000	−2.34134
$387$	0	0
$388$	−14.0000	−0.710742
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	−9.00000	−0.455150
$392$	0	0
$393$	0	0
$394$	0	0
$395$	12.0000	0.603786
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−14.0000	−0.701757
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−3.00000	−0.149813	−0.0749064	−	0.997191i	$-0.523866\pi$
$401$	−3.00000	−0.149813	−0.0749064	+	0.997191i	$0.523866\pi$
$402$	0	0
$403$	−6.00000	−0.298881
$404$	36.0000	1.79107
$405$	0	0
$406$	0	0
$407$	5.00000	0.247841
$408$	0	0
$409$	−16.0000	−0.791149	−0.395575	−	0.918434i	$-0.629455\pi$
$409$	−16.0000	−0.791149	−0.395575	+	0.918434i	$0.629455\pi$
$410$	4.00000	0.197546
$411$	0	0
$412$	28.0000	1.37946
$413$	0	0
$414$	0	0
$415$	0	0
$416$	−8.00000	−0.392232
$417$	0	0
$418$	40.0000	1.95646
$419$	−16.0000	−0.781651	−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000	−0.781651	−0.390826	+	0.920465i	$0.627810\pi$
$420$	0	0
$421$	16.0000	0.779792	0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000	0.779792	0.389896	+	0.920859i	$0.372511\pi$
$422$	−10.0000	−0.486792
$423$	0	0
$424$	0	0
$425$	1.00000	0.0485071
$426$	0	0
$427$	0	0
$428$	−30.0000	−1.45010
$429$	0	0
$430$	8.00000	0.385794
$431$	−36.0000	−1.73406	−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000	−1.73406	−0.867029	+	0.498257i	$0.833974\pi$
$432$	0	0
$433$	−8.00000	−0.384455	−0.192228	−	0.981350i	$-0.561571\pi$
$433$	−8.00000	−0.384455	−0.192228	+	0.981350i	$0.561571\pi$
$434$	0	0
$435$	0	0
$436$	28.0000	1.34096
$437$	−36.0000	−1.72211
$438$	0	0
$439$	−29.0000	−1.38409	−0.692047	−	0.721852i	$-0.743291\pi$
$439$	−29.0000	−1.38409	−0.692047	+	0.721852i	$0.743291\pi$
$440$	0	0
$441$	0	0
$442$	2.00000	0.0951303
$443$	21.0000	0.997740	0.498870	−	0.866677i	$-0.333748\pi$
$443$	21.0000	0.997740	0.498870	+	0.866677i	$0.333748\pi$
$444$	0	0
$445$	−15.0000	−0.711068
$446$	38.0000	1.79935
$447$	0	0
$448$	0	0
$449$	−23.0000	−1.08544	−0.542719	−	0.839915i	$-0.682605\pi$
$449$	−23.0000	−1.08544	−0.542719	+	0.839915i	$0.682605\pi$
$450$	0	0
$451$	−10.0000	−0.470882
$452$	−22.0000	−1.03479
$453$	0	0
$454$	−40.0000	−1.87729
$455$	0	0
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	48.0000	2.24289
$459$	0	0
$460$	18.0000	0.839254
$461$	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
$463$	−33.0000	−1.53364	−0.766820	−	0.641862i	$-0.778162\pi$
$463$	−33.0000	−1.53364	−0.766820	+	0.641862i	$0.778162\pi$
$464$	−8.00000	−0.371391
$465$	0	0
$466$	−12.0000	−0.555889
$467$	−25.0000	−1.15686	−0.578431	−	0.815731i	$-0.696335\pi$
$467$	−25.0000	−1.15686	−0.578431	+	0.815731i	$0.696335\pi$
$468$	0	0
$469$	0	0
$470$	−4.00000	−0.184506
$471$	0	0
$472$	0	0
$473$	−20.0000	−0.919601
$474$	0	0
$475$	4.00000	0.183533
$476$	0	0
$477$	0	0
$478$	−50.0000	−2.28695
$479$	−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
$481$	1.00000	0.0455961
$482$	−8.00000	−0.364390
$483$	0	0
$484$	28.0000	1.27273
$485$	7.00000	0.317854
$486$	0	0
$487$	−1.00000	−0.0453143	−0.0226572	−	0.999743i	$-0.507213\pi$
$487$	−1.00000	−0.0453143	−0.0226572	+	0.999743i	$0.507213\pi$
$488$	0	0
$489$	0	0
$490$	−14.0000	−0.632456
$491$	−16.0000	−0.722070	−0.361035	−	0.932552i	$-0.617576\pi$
$491$	−16.0000	−0.722070	−0.361035	+	0.932552i	$0.617576\pi$
$492$	0	0
$493$	2.00000	0.0900755
$494$	8.00000	0.359937
$495$	0	0
$496$	−24.0000	−1.07763
$497$	0	0
$498$	0	0
$499$	−8.00000	−0.358129	−0.179065	−	0.983837i	$-0.557307\pi$
$499$	−8.00000	−0.358129	−0.179065	+	0.983837i	$0.557307\pi$
$500$	−2.00000	−0.0894427
$501$	0	0
$502$	−24.0000	−1.07117
$503$	8.00000	0.356702	0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000	0.356702	0.178351	+	0.983967i	$0.442924\pi$
$504$	0	0
$505$	−18.0000	−0.800989
$506$	−90.0000	−4.00099
$507$	0	0
$508$	−16.0000	−0.709885
$509$	43.0000	1.90594	0.952971	−	0.303062i	$-0.0980090\pi$
$509$	43.0000	1.90594	0.952971	+	0.303062i	$0.0980090\pi$
$510$	0	0
$511$	0	0
$512$	−32.0000	−1.41421
$513$	0	0
$514$	−18.0000	−0.793946
$515$	−14.0000	−0.616914
$516$	0	0
$517$	10.0000	0.439799
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−28.0000	−1.22670	−0.613351	−	0.789810i	$-0.710179\pi$
$521$	−28.0000	−1.22670	−0.613351	+	0.789810i	$0.710179\pi$
$522$	0	0
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	36.0000	1.57267
$525$	0	0
$526$	2.00000	0.0872041
$527$	6.00000	0.261364
$528$	0	0
$529$	58.0000	2.52174
$530$	−4.00000	−0.173749
$531$	0	0
$532$	0	0
$533$	−2.00000	−0.0866296
$534$	0	0
$535$	15.0000	0.648507
$536$	0	0
$537$	0	0
$538$	52.0000	2.24188
$539$	35.0000	1.50756
$540$	0	0
$541$	6.00000	0.257960	0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000	0.257960	0.128980	+	0.991647i	$0.458830\pi$
$542$	−44.0000	−1.88996
$543$	0	0
$544$	8.00000	0.342997
$545$	−14.0000	−0.599694
$546$	0	0
$547$	−2.00000	−0.0855138	−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000	−0.0855138	−0.0427569	+	0.999086i	$0.513614\pi$
$548$	12.0000	0.512615
$549$	0	0
$550$	10.0000	0.426401
$551$	8.00000	0.340811
$552$	0	0
$553$	0	0
$554$	−24.0000	−1.01966
$555$	0	0
$556$	−14.0000	−0.593732
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	0	0
$559$	−4.00000	−0.169182
$560$	0	0
$561$	0	0
$562$	30.0000	1.26547
$563$	3.00000	0.126435	0.0632175	−	0.998000i	$-0.479864\pi$
$563$	3.00000	0.126435	0.0632175	+	0.998000i	$0.479864\pi$
$564$	0	0
$565$	11.0000	0.462773
$566$	0	0
$567$	0	0
$568$	0	0
$569$	36.0000	1.50920	0.754599	−	0.656186i	$-0.227831\pi$
$569$	36.0000	1.50920	0.754599	+	0.656186i	$0.227831\pi$
$570$	0	0
$571$	−31.0000	−1.29731	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	−31.0000	−1.29731	−0.648655	+	0.761083i	$0.724668\pi$
$572$	10.0000	0.418121
$573$	0	0
$574$	0	0
$575$	−9.00000	−0.375326
$576$	0	0
$577$	17.0000	0.707719	0.353860	−	0.935299i	$-0.384869\pi$
$577$	17.0000	0.707719	0.353860	+	0.935299i	$0.384869\pi$
$578$	32.0000	1.33102
$579$	0	0
$580$	−4.00000	−0.166091
$581$	0	0
$582$	0	0
$583$	10.0000	0.414158
$584$	0	0
$585$	0	0
$586$	−48.0000	−1.98286
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	0	0
$589$	24.0000	0.988903
$590$	2.00000	0.0823387
$591$	0	0
$592$	4.00000	0.164399
$593$	−4.00000	−0.164260	−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000	−0.164260	−0.0821302	+	0.996622i	$0.526172\pi$
$594$	0	0
$595$	0	0
$596$	46.0000	1.88423
$597$	0	0
$598$	−18.0000	−0.736075
$599$	−40.0000	−1.63436	−0.817178	−	0.576386i	$-0.804463\pi$
$599$	−40.0000	−1.63436	−0.817178	+	0.576386i	$0.804463\pi$
$600$	0	0
$601$	14.0000	0.571072	0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000	0.571072	0.285536	+	0.958368i	$0.407828\pi$
$602$	0	0
$603$	0	0
$604$	8.00000	0.325515
$605$	−14.0000	−0.569181
$606$	0	0
$607$	−2.00000	−0.0811775	−0.0405887	−	0.999176i	$-0.512923\pi$
$607$	−2.00000	−0.0811775	−0.0405887	+	0.999176i	$0.512923\pi$
$608$	32.0000	1.29777
$609$	0	0
$610$	2.00000	0.0809776
$611$	2.00000	0.0809113
$612$	0	0
$613$	25.0000	1.00974	0.504870	−	0.863195i	$-0.331540\pi$
$613$	25.0000	1.00974	0.504870	+	0.863195i	$0.331540\pi$
$614$	−38.0000	−1.53356
$615$	0	0
$616$	0	0
$617$	−24.0000	−0.966204	−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000	−0.966204	−0.483102	+	0.875564i	$0.660490\pi$
$618$	0	0
$619$	14.0000	0.562708	0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000	0.562708	0.281354	+	0.959604i	$0.409217\pi$
$620$	−12.0000	−0.481932
$621$	0	0
$622$	−60.0000	−2.40578
$623$	0	0
$624$	0	0
$625$	1.00000	0.0400000
$626$	−28.0000	−1.11911
$627$	0	0
$628$	−8.00000	−0.319235
$629$	−1.00000	−0.0398726
$630$	0	0
$631$	46.0000	1.83123	0.915616	−	0.402055i	$-0.131704\pi$
$631$	46.0000	1.83123	0.915616	+	0.402055i	$0.131704\pi$
$632$	0	0
$633$	0	0
$634$	44.0000	1.74746
$635$	8.00000	0.317470
$636$	0	0
$637$	7.00000	0.277350
$638$	20.0000	0.791808
$639$	0	0
$640$	0	0
$641$	24.0000	0.947943	0.473972	−	0.880540i	$-0.342820\pi$
$641$	24.0000	0.947943	0.473972	+	0.880540i	$0.342820\pi$
$642$	0	0
$643$	33.0000	1.30139	0.650696	−	0.759338i	$-0.274477\pi$
$643$	33.0000	1.30139	0.650696	+	0.759338i	$0.274477\pi$
$644$	0	0
$645$	0	0
$646$	−8.00000	−0.314756
$647$	16.0000	0.629025	0.314512	−	0.949253i	$-0.398159\pi$
$647$	16.0000	0.629025	0.314512	+	0.949253i	$0.398159\pi$
$648$	0	0
$649$	−5.00000	−0.196267
$650$	2.00000	0.0784465
$651$	0	0
$652$	−14.0000	−0.548282
$653$	−49.0000	−1.91752	−0.958759	−	0.284220i	$-0.908265\pi$
$653$	−49.0000	−1.91752	−0.958759	+	0.284220i	$0.908265\pi$
$654$	0	0
$655$	−18.0000	−0.703318
$656$	−8.00000	−0.312348
$657$	0	0
$658$	0	0
$659$	10.0000	0.389545	0.194772	−	0.980848i	$-0.437603\pi$
$659$	10.0000	0.389545	0.194772	+	0.980848i	$0.437603\pi$
$660$	0	0
$661$	46.0000	1.78919	0.894596	−	0.446875i	$-0.147463\pi$
$661$	46.0000	1.78919	0.894596	+	0.446875i	$0.147463\pi$
$662$	48.0000	1.86557
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−18.0000	−0.696963
$668$	36.0000	1.39288
$669$	0	0
$670$	−6.00000	−0.231800
$671$	−5.00000	−0.193023
$672$	0	0
$673$	18.0000	0.693849	0.346925	−	0.937893i	$-0.387226\pi$
$673$	18.0000	0.693849	0.346925	+	0.937893i	$0.387226\pi$
$674$	52.0000	2.00297
$675$	0	0
$676$	2.00000	0.0769231
$677$	9.00000	0.345898	0.172949	−	0.984931i	$-0.444670\pi$
$677$	9.00000	0.345898	0.172949	+	0.984931i	$0.444670\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	60.0000	2.29752
$683$	30.0000	1.14792	0.573959	−	0.818884i	$-0.305407\pi$
$683$	30.0000	1.14792	0.573959	+	0.818884i	$0.305407\pi$
$684$	0	0
$685$	−6.00000	−0.229248
$686$	0	0
$687$	0	0
$688$	−16.0000	−0.609994
$689$	2.00000	0.0761939
$690$	0	0
$691$	−26.0000	−0.989087	−0.494543	−	0.869153i	$-0.664665\pi$
$691$	−26.0000	−0.989087	−0.494543	+	0.869153i	$0.664665\pi$
$692$	12.0000	0.456172
$693$	0	0
$694$	34.0000	1.29062
$695$	7.00000	0.265525
$696$	0	0
$697$	2.00000	0.0757554
$698$	−20.0000	−0.757011
$699$	0	0
$700$	0	0
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	0	0
$703$	−4.00000	−0.150863
$704$	40.0000	1.50756
$705$	0	0
$706$	−36.0000	−1.35488
$707$	0	0
$708$	0	0
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	16.0000	0.600469
$711$	0	0
$712$	0	0
$713$	−54.0000	−2.02232
$714$	0	0
$715$	−5.00000	−0.186989
$716$	20.0000	0.747435
$717$	0	0
$718$	42.0000	1.56743
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	6.00000	0.223297
$723$	0	0
$724$	52.0000	1.93256
$725$	2.00000	0.0742781
$726$	0	0
$727$	2.00000	0.0741759	0.0370879	−	0.999312i	$-0.488192\pi$
$727$	2.00000	0.0741759	0.0370879	+	0.999312i	$0.488192\pi$
$728$	0	0
$729$	0	0
$730$	14.0000	0.518163
$731$	4.00000	0.147945
$732$	0	0
$733$	−13.0000	−0.480166	−0.240083	−	0.970752i	$-0.577175\pi$
$733$	−13.0000	−0.480166	−0.240083	+	0.970752i	$0.577175\pi$
$734$	−48.0000	−1.77171
$735$	0	0
$736$	−72.0000	−2.65396
$737$	15.0000	0.552532
$738$	0	0
$739$	−50.0000	−1.83928	−0.919640	−	0.392763i	$-0.871519\pi$
$739$	−50.0000	−1.83928	−0.919640	+	0.392763i	$0.871519\pi$
$740$	2.00000	0.0735215
$741$	0	0
$742$	0	0
$743$	−44.0000	−1.61420	−0.807102	−	0.590412i	$-0.798965\pi$
$743$	−44.0000	−1.61420	−0.807102	+	0.590412i	$0.798965\pi$
$744$	0	0
$745$	−23.0000	−0.842655
$746$	16.0000	0.585802
$747$	0	0
$748$	−10.0000	−0.365636
$749$	0	0
$750$	0	0
$751$	37.0000	1.35015	0.675075	−	0.737749i	$-0.264111\pi$
$751$	37.0000	1.35015	0.675075	+	0.737749i	$0.264111\pi$
$752$	8.00000	0.291730
$753$	0	0
$754$	4.00000	0.145671
$755$	−4.00000	−0.145575
$756$	0	0
$757$	28.0000	1.01768	0.508839	−	0.860862i	$-0.330075\pi$
$757$	28.0000	1.01768	0.508839	+	0.860862i	$0.330075\pi$
$758$	16.0000	0.581146
$759$	0	0
$760$	0	0
$761$	39.0000	1.41375	0.706874	−	0.707339i	$-0.250105\pi$
$761$	39.0000	1.41375	0.706874	+	0.707339i	$0.250105\pi$
$762$	0	0
$763$	0	0
$764$	4.00000	0.144715
$765$	0	0
$766$	48.0000	1.73431
$767$	−1.00000	−0.0361079
$768$	0	0
$769$	−16.0000	−0.576975	−0.288487	−	0.957484i	$-0.593152\pi$
$769$	−16.0000	−0.576975	−0.288487	+	0.957484i	$0.593152\pi$
$770$	0	0
$771$	0	0
$772$	46.0000	1.65558
$773$	36.0000	1.29483	0.647415	−	0.762138i	$-0.275850\pi$
$773$	36.0000	1.29483	0.647415	+	0.762138i	$0.275850\pi$
$774$	0	0
$775$	6.00000	0.215526
$776$	0	0
$777$	0	0
$778$	12.0000	0.430221
$779$	8.00000	0.286630
$780$	0	0
$781$	−40.0000	−1.43131
$782$	18.0000	0.643679
$783$	0	0
$784$	28.0000	1.00000
$785$	4.00000	0.142766
$786$	0	0
$787$	37.0000	1.31891	0.659454	−	0.751745i	$-0.270788\pi$
$787$	37.0000	1.31891	0.659454	+	0.751745i	$0.270788\pi$
$788$	0	0
$789$	0	0
$790$	−24.0000	−0.853882
$791$	0	0
$792$	0	0
$793$	−1.00000	−0.0355110
$794$	4.00000	0.141955
$795$	0	0
$796$	14.0000	0.496217
$797$	2.00000	0.0708436	0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000	0.0708436	0.0354218	+	0.999372i	$0.488723\pi$
$798$	0	0
$799$	−2.00000	−0.0707549
$800$	8.00000	0.282843
$801$	0	0
$802$	6.00000	0.211867
$803$	−35.0000	−1.23512
$804$	0	0
$805$	0	0
$806$	12.0000	0.422682
$807$	0	0
$808$	0	0
$809$	−22.0000	−0.773479	−0.386739	−	0.922189i	$-0.626399\pi$
$809$	−22.0000	−0.773479	−0.386739	+	0.922189i	$0.626399\pi$
$810$	0	0
$811$	−6.00000	−0.210688	−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000	−0.210688	−0.105344	+	0.994436i	$0.533594\pi$
$812$	0	0
$813$	0	0
$814$	−10.0000	−0.350500
$815$	7.00000	0.245199
$816$	0	0
$817$	16.0000	0.559769
$818$	32.0000	1.11885
$819$	0	0
$820$	−4.00000	−0.139686
$821$	33.0000	1.15171	0.575854	−	0.817553i	$-0.304670\pi$
$821$	33.0000	1.15171	0.575854	+	0.817553i	$0.304670\pi$
$822$	0	0
$823$	−34.0000	−1.18517	−0.592583	−	0.805510i	$-0.701892\pi$
$823$	−34.0000	−1.18517	−0.592583	+	0.805510i	$0.701892\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−26.0000	−0.904109	−0.452054	−	0.891990i	$-0.649309\pi$
$827$	−26.0000	−0.904109	−0.452054	+	0.891990i	$0.649309\pi$
$828$	0	0
$829$	3.00000	0.104194	0.0520972	−	0.998642i	$-0.483409\pi$
$829$	3.00000	0.104194	0.0520972	+	0.998642i	$0.483409\pi$
$830$	0	0
$831$	0	0
$832$	8.00000	0.277350
$833$	−7.00000	−0.242536
$834$	0	0
$835$	−18.0000	−0.622916
$836$	−40.0000	−1.38343
$837$	0	0
$838$	32.0000	1.10542
$839$	−13.0000	−0.448810	−0.224405	−	0.974496i	$-0.572044\pi$
$839$	−13.0000	−0.448810	−0.224405	+	0.974496i	$0.572044\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−32.0000	−1.10279
$843$	0	0
$844$	10.0000	0.344214
$845$	−1.00000	−0.0344010
$846$	0	0
$847$	0	0
$848$	8.00000	0.274721
$849$	0	0
$850$	−2.00000	−0.0685994
$851$	9.00000	0.308516
$852$	0	0
$853$	33.0000	1.12990	0.564949	−	0.825126i	$-0.308896\pi$
$853$	33.0000	1.12990	0.564949	+	0.825126i	$0.308896\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−5.00000	−0.170797	−0.0853984	−	0.996347i	$-0.527216\pi$
$857$	−5.00000	−0.170797	−0.0853984	+	0.996347i	$0.527216\pi$
$858$	0	0
$859$	7.00000	0.238837	0.119418	−	0.992844i	$-0.461897\pi$
$859$	7.00000	0.238837	0.119418	+	0.992844i	$0.461897\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	72.0000	2.45233
$863$	−28.0000	−0.953131	−0.476566	−	0.879139i	$-0.658119\pi$
$863$	−28.0000	−0.953131	−0.476566	+	0.879139i	$0.658119\pi$
$864$	0	0
$865$	−6.00000	−0.204006
$866$	16.0000	0.543702
$867$	0	0
$868$	0	0
$869$	60.0000	2.03536
$870$	0	0
$871$	3.00000	0.101651
$872$	0	0
$873$	0	0
$874$	72.0000	2.43544
$875$	0	0
$876$	0	0
$877$	−9.00000	−0.303908	−0.151954	−	0.988388i	$-0.548557\pi$
$877$	−9.00000	−0.303908	−0.151954	+	0.988388i	$0.548557\pi$
$878$	58.0000	1.95741
$879$	0	0
$880$	−20.0000	−0.674200
$881$	−20.0000	−0.673817	−0.336909	−	0.941537i	$-0.609381\pi$
$881$	−20.0000	−0.673817	−0.336909	+	0.941537i	$0.609381\pi$
$882$	0	0
$883$	50.0000	1.68263	0.841317	−	0.540542i	$-0.181781\pi$
$883$	50.0000	1.68263	0.841317	+	0.540542i	$0.181781\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	−42.0000	−1.41102
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	0	0
$889$	0	0
$890$	30.0000	1.00560
$891$	0	0
$892$	−38.0000	−1.27233
$893$	−8.00000	−0.267710
$894$	0	0
$895$	−10.0000	−0.334263
$896$	0	0
$897$	0	0
$898$	46.0000	1.53504
$899$	12.0000	0.400222
$900$	0	0
$901$	−2.00000	−0.0666297
$902$	20.0000	0.665927
$903$	0	0
$904$	0	0
$905$	−26.0000	−0.864269
$906$	0	0
$907$	42.0000	1.39459	0.697294	−	0.716786i	$-0.254387\pi$
$907$	42.0000	1.39459	0.697294	+	0.716786i	$0.254387\pi$
$908$	40.0000	1.32745
$909$	0	0
$910$	0	0
$911$	34.0000	1.12647	0.563235	−	0.826297i	$-0.309557\pi$
$911$	34.0000	1.12647	0.563235	+	0.826297i	$0.309557\pi$
$912$	0	0
$913$	0	0
$914$	−20.0000	−0.661541
$915$	0	0
$916$	−48.0000	−1.58596
$917$	0	0
$918$	0	0
$919$	−56.0000	−1.84727	−0.923635	−	0.383274i	$-0.874797\pi$
$919$	−56.0000	−1.84727	−0.923635	+	0.383274i	$0.874797\pi$
$920$	0	0
$921$	0	0
$922$	−36.0000	−1.18560
$923$	−8.00000	−0.263323
$924$	0	0
$925$	−1.00000	−0.0328798
$926$	66.0000	2.16889
$927$	0	0
$928$	16.0000	0.525226
$929$	23.0000	0.754606	0.377303	−	0.926090i	$-0.376852\pi$
$929$	23.0000	0.754606	0.377303	+	0.926090i	$0.376852\pi$
$930$	0	0
$931$	−28.0000	−0.917663
$932$	12.0000	0.393073
$933$	0	0
$934$	50.0000	1.63605
$935$	5.00000	0.163517
$936$	0	0
$937$	−54.0000	−1.76410	−0.882052	−	0.471153i	$-0.843838\pi$
$937$	−54.0000	−1.76410	−0.882052	+	0.471153i	$0.843838\pi$
$938$	0	0
$939$	0	0
$940$	4.00000	0.130466
$941$	11.0000	0.358590	0.179295	−	0.983795i	$-0.442618\pi$
$941$	11.0000	0.358590	0.179295	+	0.983795i	$0.442618\pi$
$942$	0	0
$943$	−18.0000	−0.586161
$944$	−4.00000	−0.130189
$945$	0	0
$946$	40.0000	1.30051
$947$	18.0000	0.584921	0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000	0.584921	0.292461	+	0.956278i	$0.405526\pi$
$948$	0	0
$949$	−7.00000	−0.227230
$950$	−8.00000	−0.259554
$951$	0	0
$952$	0	0
$953$	−11.0000	−0.356325	−0.178162	−	0.984001i	$-0.557015\pi$
$953$	−11.0000	−0.356325	−0.178162	+	0.984001i	$0.557015\pi$
$954$	0	0
$955$	−2.00000	−0.0647185
$956$	50.0000	1.61712
$957$	0	0
$958$	48.0000	1.55081
$959$	0	0
$960$	0	0
$961$	5.00000	0.161290
$962$	−2.00000	−0.0644826
$963$	0	0
$964$	8.00000	0.257663
$965$	−23.0000	−0.740396
$966$	0	0
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	0	0
$969$	0	0
$970$	−14.0000	−0.449513
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	0	0
$973$	0	0
$974$	2.00000	0.0640841
$975$	0	0
$976$	−4.00000	−0.128037
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	0	0
$979$	−75.0000	−2.39701
$980$	14.0000	0.447214
$981$	0	0
$982$	32.0000	1.02116
$983$	−48.0000	−1.53096	−0.765481	−	0.643458i	$-0.777499\pi$
$983$	−48.0000	−1.53096	−0.765481	+	0.643458i	$0.777499\pi$
$984$	0	0
$985$	0	0
$986$	−4.00000	−0.127386
$987$	0	0
$988$	−8.00000	−0.254514
$989$	−36.0000	−1.14473
$990$	0	0
$991$	47.0000	1.49300	0.746502	−	0.665383i	$-0.231732\pi$
$991$	47.0000	1.49300	0.746502	+	0.665383i	$0.231732\pi$
$992$	48.0000	1.52400
$993$	0	0
$994$	0	0
$995$	−7.00000	−0.221915
$996$	0	0
$997$	−48.0000	−1.52018	−0.760088	−	0.649821i	$-0.774844\pi$
$997$	−48.0000	−1.52018	−0.760088	+	0.649821i	$0.774844\pi$
$998$	16.0000	0.506471
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1755.2.a.a.1.1	✓	1
3.2	odd	2		1755.2.a.f.1.1	yes	1
5.4	even	2		8775.2.a.q.1.1		1
15.14	odd	2		8775.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1755.2.a.a.1.1	✓	1	1.1	even	1	trivial
1755.2.a.f.1.1	yes	1	3.2	odd	2
8775.2.a.a.1.1		1	15.14	odd	2
8775.2.a.q.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:	\( N \)	\(=\)	\( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1755.a (trivial)

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