LMFDB - Embedded newform 1386.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,4,Mod(1,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1386.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1386.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:	$81.7766472680$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1386.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +4.00000 q^{4} -3.00000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +O(q^{10})$

\(q-2.00000 q^{2} +4.00000 q^{4} -3.00000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +6.00000 q^{10} +11.0000 q^{11} -16.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} -6.00000 q^{17} +14.0000 q^{19} -12.0000 q^{20} -22.0000 q^{22} +51.0000 q^{23} -116.000 q^{25} +32.0000 q^{26} +28.0000 q^{28} -54.0000 q^{29} +95.0000 q^{31} -32.0000 q^{32} +12.0000 q^{34} -21.0000 q^{35} -193.000 q^{37} -28.0000 q^{38} +24.0000 q^{40} -102.000 q^{41} +284.000 q^{43} +44.0000 q^{44} -102.000 q^{46} +72.0000 q^{47} +49.0000 q^{49} +232.000 q^{50} -64.0000 q^{52} +102.000 q^{53} -33.0000 q^{55} -56.0000 q^{56} +108.000 q^{58} +63.0000 q^{59} -790.000 q^{61} -190.000 q^{62} +64.0000 q^{64} +48.0000 q^{65} -433.000 q^{67} -24.0000 q^{68} +42.0000 q^{70} -135.000 q^{71} -238.000 q^{73} +386.000 q^{74} +56.0000 q^{76} +77.0000 q^{77} +770.000 q^{79} -48.0000 q^{80} +204.000 q^{82} +1008.00 q^{83} +18.0000 q^{85} -568.000 q^{86} -88.0000 q^{88} +639.000 q^{89} -112.000 q^{91} +204.000 q^{92} -144.000 q^{94} -42.0000 q^{95} +11.0000 q^{97} -98.0000 q^{98} +O(q^{100})\)

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	−0.707107
$2$	−2.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	−3.00000	−0.268328	−0.134164	−	0.990959i	$-0.542835\pi$
$5$	−3.00000	−0.268328	−0.134164	+	0.990959i	$0.542835\pi$
$6$	0	0
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	0	0
$10$	6.00000	0.189737
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	0	0
$13$	−16.0000	−0.341354	−0.170677	−	0.985327i	$-0.554595\pi$
$13$	−16.0000	−0.341354	−0.170677	+	0.985327i	$0.554595\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−6.00000	−0.0856008	−0.0428004	−	0.999084i	$-0.513628\pi$
$17$	−6.00000	−0.0856008	−0.0428004	+	0.999084i	$0.513628\pi$
$18$	0	0
$19$	14.0000	0.169043	0.0845216	−	0.996422i	$-0.473064\pi$
$19$	14.0000	0.169043	0.0845216	+	0.996422i	$0.473064\pi$
$20$	−12.0000	−0.134164
$21$	0	0
$22$	−22.0000	−0.213201
$23$	51.0000	0.462358	0.231179	−	0.972911i	$-0.425742\pi$
$23$	51.0000	0.462358	0.231179	+	0.972911i	$0.425742\pi$
$24$	0	0
$25$	−116.000	−0.928000
$26$	32.0000	0.241374
$27$	0	0
$28$	28.0000	0.188982
$29$	−54.0000	−0.345778	−0.172889	−	0.984941i	$-0.555310\pi$
$29$	−54.0000	−0.345778	−0.172889	+	0.984941i	$0.555310\pi$
$30$	0	0
$31$	95.0000	0.550403	0.275202	−	0.961387i	$-0.411255\pi$
$31$	95.0000	0.550403	0.275202	+	0.961387i	$0.411255\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	12.0000	0.0605289
$35$	−21.0000	−0.101419
$36$	0	0
$37$	−193.000	−0.857541	−0.428770	−	0.903414i	$-0.641053\pi$
$37$	−193.000	−0.857541	−0.428770	+	0.903414i	$0.641053\pi$
$38$	−28.0000	−0.119532
$39$	0	0
$40$	24.0000	0.0948683
$41$	−102.000	−0.388530	−0.194265	−	0.980949i	$-0.562232\pi$
$41$	−102.000	−0.388530	−0.194265	+	0.980949i	$0.562232\pi$
$42$	0	0
$43$	284.000	1.00720	0.503600	−	0.863937i	$-0.332009\pi$
$43$	284.000	1.00720	0.503600	+	0.863937i	$0.332009\pi$
$44$	44.0000	0.150756
$45$	0	0
$46$	−102.000	−0.326937
$47$	72.0000	0.223453	0.111726	−	0.993739i	$-0.464362\pi$
$47$	72.0000	0.223453	0.111726	+	0.993739i	$0.464362\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	232.000	0.656195
$51$	0	0
$52$	−64.0000	−0.170677
$53$	102.000	0.264354	0.132177	−	0.991226i	$-0.457803\pi$
$53$	102.000	0.264354	0.132177	+	0.991226i	$0.457803\pi$
$54$	0	0
$55$	−33.0000	−0.0809040
$56$	−56.0000	−0.133631
$57$	0	0
$58$	108.000	0.244502
$59$	63.0000	0.139015	0.0695076	−	0.997581i	$-0.477857\pi$
$59$	63.0000	0.139015	0.0695076	+	0.997581i	$0.477857\pi$
$60$	0	0
$61$	−790.000	−1.65818	−0.829091	−	0.559113i	$-0.811142\pi$
$61$	−790.000	−1.65818	−0.829091	+	0.559113i	$0.811142\pi$
$62$	−190.000	−0.389194
$63$	0	0
$64$	64.0000	0.125000
$65$	48.0000	0.0915949
$66$	0	0
$67$	−433.000	−0.789543	−0.394771	−	0.918779i	$-0.629176\pi$
$67$	−433.000	−0.789543	−0.394771	+	0.918779i	$0.629176\pi$
$68$	−24.0000	−0.0428004
$69$	0	0
$70$	42.0000	0.0717137
$71$	−135.000	−0.225656	−0.112828	−	0.993615i	$-0.535991\pi$
$71$	−135.000	−0.225656	−0.112828	+	0.993615i	$0.535991\pi$
$72$	0	0
$73$	−238.000	−0.381586	−0.190793	−	0.981630i	$-0.561106\pi$
$73$	−238.000	−0.381586	−0.190793	+	0.981630i	$0.561106\pi$
$74$	386.000	0.606373
$75$	0	0
$76$	56.0000	0.0845216
$77$	77.0000	0.113961
$78$	0	0
$79$	770.000	1.09660	0.548302	−	0.836280i	$-0.315274\pi$
$79$	770.000	1.09660	0.548302	+	0.836280i	$0.315274\pi$
$80$	−48.0000	−0.0670820
$81$	0	0
$82$	204.000	0.274732
$83$	1008.00	1.33304	0.666520	−	0.745487i	$-0.267783\pi$
$83$	1008.00	1.33304	0.666520	+	0.745487i	$0.267783\pi$
$84$	0	0
$85$	18.0000	0.0229691
$86$	−568.000	−0.712198
$87$	0	0
$88$	−88.0000	−0.106600
$89$	639.000	0.761055	0.380527	−	0.924770i	$-0.375742\pi$
$89$	639.000	0.761055	0.380527	+	0.924770i	$0.375742\pi$
$90$	0	0
$91$	−112.000	−0.129020
$92$	204.000	0.231179
$93$	0	0
$94$	−144.000	−0.158005
$95$	−42.0000	−0.0453590
$96$	0	0
$97$	11.0000	0.0115142	0.00575712	−	0.999983i	$-0.498167\pi$
$97$	11.0000	0.0115142	0.00575712	+	0.999983i	$0.498167\pi$
$98$	−98.0000	−0.101015
$99$	0	0
$100$	−464.000	−0.464000
$101$	−1692.00	−1.66693	−0.833467	−	0.552570i	$-0.813647\pi$
$101$	−1692.00	−1.66693	−0.833467	+	0.552570i	$0.813647\pi$
$102$	0	0
$103$	−532.000	−0.508927	−0.254464	−	0.967082i	$-0.581899\pi$
$103$	−532.000	−0.508927	−0.254464	+	0.967082i	$0.581899\pi$
$104$	128.000	0.120687
$105$	0	0
$106$	−204.000	−0.186927
$107$	−1350.00	−1.21971	−0.609857	−	0.792511i	$-0.708773\pi$
$107$	−1350.00	−1.21971	−0.609857	+	0.792511i	$0.708773\pi$
$108$	0	0
$109$	1616.00	1.42004	0.710022	−	0.704180i	$-0.248685\pi$
$109$	1616.00	1.42004	0.710022	+	0.704180i	$0.248685\pi$
$110$	66.0000	0.0572078
$111$	0	0
$112$	112.000	0.0944911
$113$	−597.000	−0.497000	−0.248500	−	0.968632i	$-0.579938\pi$
$113$	−597.000	−0.497000	−0.248500	+	0.968632i	$0.579938\pi$
$114$	0	0
$115$	−153.000	−0.124064
$116$	−216.000	−0.172889
$117$	0	0
$118$	−126.000	−0.0982986
$119$	−42.0000	−0.0323541
$120$	0	0
$121$	121.000	0.0909091
$122$	1580.00	1.17251
$123$	0	0
$124$	380.000	0.275202
$125$	723.000	0.517337
$126$	0	0
$127$	302.000	0.211009	0.105505	−	0.994419i	$-0.466354\pi$
$127$	302.000	0.211009	0.105505	+	0.994419i	$0.466354\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	−96.0000	−0.0647674
$131$	462.000	0.308131	0.154065	−	0.988061i	$-0.450763\pi$
$131$	462.000	0.308131	0.154065	+	0.988061i	$0.450763\pi$
$132$	0	0
$133$	98.0000	0.0638923
$134$	866.000	0.558291
$135$	0	0
$136$	48.0000	0.0302645
$137$	−3021.00	−1.88395	−0.941976	−	0.335680i	$-0.891034\pi$
$137$	−3021.00	−1.88395	−0.941976	+	0.335680i	$0.891034\pi$
$138$	0	0
$139$	−1594.00	−0.972671	−0.486336	−	0.873772i	$-0.661667\pi$
$139$	−1594.00	−0.972671	−0.486336	+	0.873772i	$0.661667\pi$
$140$	−84.0000	−0.0507093
$141$	0	0
$142$	270.000	0.159563
$143$	−176.000	−0.102922
$144$	0	0
$145$	162.000	0.0927818
$146$	476.000	0.269822
$147$	0	0
$148$	−772.000	−0.428770
$149$	−2814.00	−1.54719	−0.773597	−	0.633678i	$-0.781544\pi$
$149$	−2814.00	−1.54719	−0.773597	+	0.633678i	$0.781544\pi$
$150$	0	0
$151$	2450.00	1.32039	0.660193	−	0.751096i	$-0.270475\pi$
$151$	2450.00	1.32039	0.660193	+	0.751096i	$0.270475\pi$
$152$	−112.000	−0.0597658
$153$	0	0
$154$	−154.000	−0.0805823
$155$	−285.000	−0.147689
$156$	0	0
$157$	3899.00	1.98200	0.991000	−	0.133860i	$-0.0427373\pi$
$157$	3899.00	1.98200	0.991000	+	0.133860i	$0.0427373\pi$
$158$	−1540.00	−0.775417
$159$	0	0
$160$	96.0000	0.0474342
$161$	357.000	0.174755
$162$	0	0
$163$	−124.000	−0.0595855	−0.0297927	−	0.999556i	$-0.509485\pi$
$163$	−124.000	−0.0595855	−0.0297927	+	0.999556i	$0.509485\pi$
$164$	−408.000	−0.194265
$165$	0	0
$166$	−2016.00	−0.942602
$167$	30.0000	0.0139010	0.00695051	−	0.999976i	$-0.497788\pi$
$167$	30.0000	0.0139010	0.00695051	+	0.999976i	$0.497788\pi$
$168$	0	0
$169$	−1941.00	−0.883477
$170$	−36.0000	−0.0162416
$171$	0	0
$172$	1136.00	0.503600
$173$	−2268.00	−0.996722	−0.498361	−	0.866970i	$-0.666065\pi$
$173$	−2268.00	−0.996722	−0.498361	+	0.866970i	$0.666065\pi$
$174$	0	0
$175$	−812.000	−0.350751
$176$	176.000	0.0753778
$177$	0	0
$178$	−1278.00	−0.538147
$179$	−1731.00	−0.722799	−0.361399	−	0.932411i	$-0.617701\pi$
$179$	−1731.00	−0.722799	−0.361399	+	0.932411i	$0.617701\pi$
$180$	0	0
$181$	785.000	0.322368	0.161184	−	0.986924i	$-0.448469\pi$
$181$	785.000	0.322368	0.161184	+	0.986924i	$0.448469\pi$
$182$	224.000	0.0912307
$183$	0	0
$184$	−408.000	−0.163468
$185$	579.000	0.230102
$186$	0	0
$187$	−66.0000	−0.0258096
$188$	288.000	0.111726
$189$	0	0
$190$	84.0000	0.0320737
$191$	−51.0000	−0.0193206	−0.00966029	−	0.999953i	$-0.503075\pi$
$191$	−51.0000	−0.0193206	−0.00966029	+	0.999953i	$0.503075\pi$
$192$	0	0
$193$	1226.00	0.457251	0.228625	−	0.973514i	$-0.426577\pi$
$193$	1226.00	0.457251	0.228625	+	0.973514i	$0.426577\pi$
$194$	−22.0000	−0.00814179
$195$	0	0
$196$	196.000	0.0714286
$197$	−2754.00	−0.996012	−0.498006	−	0.867174i	$-0.665934\pi$
$197$	−2754.00	−0.996012	−0.498006	+	0.867174i	$0.665934\pi$
$198$	0	0
$199$	−1744.00	−0.621251	−0.310625	−	0.950532i	$-0.600538\pi$
$199$	−1744.00	−0.621251	−0.310625	+	0.950532i	$0.600538\pi$
$200$	928.000	0.328098
$201$	0	0
$202$	3384.00	1.17870
$203$	−378.000	−0.130692
$204$	0	0
$205$	306.000	0.104253
$206$	1064.00	0.359866
$207$	0	0
$208$	−256.000	−0.0853385
$209$	154.000	0.0509684
$210$	0	0
$211$	−4210.00	−1.37359	−0.686797	−	0.726849i	$-0.740984\pi$
$211$	−4210.00	−1.37359	−0.686797	+	0.726849i	$0.740984\pi$
$212$	408.000	0.132177
$213$	0	0
$214$	2700.00	0.862468
$215$	−852.000	−0.270260
$216$	0	0
$217$	665.000	0.208033
$218$	−3232.00	−1.00412
$219$	0	0
$220$	−132.000	−0.0404520
$221$	96.0000	0.0292202
$222$	0	0
$223$	−5497.00	−1.65070	−0.825351	−	0.564621i	$-0.809022\pi$
$223$	−5497.00	−1.65070	−0.825351	+	0.564621i	$0.809022\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	1194.00	0.351432
$227$	3732.00	1.09120	0.545598	−	0.838047i	$-0.316303\pi$
$227$	3732.00	1.09120	0.545598	+	0.838047i	$0.316303\pi$
$228$	0	0
$229$	−3883.00	−1.12051	−0.560253	−	0.828322i	$-0.689296\pi$
$229$	−3883.00	−1.12051	−0.560253	+	0.828322i	$0.689296\pi$
$230$	306.000	0.0877263
$231$	0	0
$232$	432.000	0.122251
$233$	222.000	0.0624193	0.0312097	−	0.999513i	$-0.490064\pi$
$233$	222.000	0.0624193	0.0312097	+	0.999513i	$0.490064\pi$
$234$	0	0
$235$	−216.000	−0.0599587
$236$	252.000	0.0695076
$237$	0	0
$238$	84.0000	0.0228778
$239$	2304.00	0.623571	0.311785	−	0.950153i	$-0.399073\pi$
$239$	2304.00	0.623571	0.311785	+	0.950153i	$0.399073\pi$
$240$	0	0
$241$	−1276.00	−0.341056	−0.170528	−	0.985353i	$-0.554547\pi$
$241$	−1276.00	−0.341056	−0.170528	+	0.985353i	$0.554547\pi$
$242$	−242.000	−0.0642824
$243$	0	0
$244$	−3160.00	−0.829091
$245$	−147.000	−0.0383326
$246$	0	0
$247$	−224.000	−0.0577036
$248$	−760.000	−0.194597
$249$	0	0
$250$	−1446.00	−0.365812
$251$	255.000	0.0641253	0.0320627	−	0.999486i	$-0.489792\pi$
$251$	255.000	0.0641253	0.0320627	+	0.999486i	$0.489792\pi$
$252$	0	0
$253$	561.000	0.139406
$254$	−604.000	−0.149206
$255$	0	0
$256$	256.000	0.0625000
$257$	−2370.00	−0.575239	−0.287620	−	0.957745i	$-0.592864\pi$
$257$	−2370.00	−0.575239	−0.287620	+	0.957745i	$0.592864\pi$
$258$	0	0
$259$	−1351.00	−0.324120
$260$	192.000	0.0457974
$261$	0	0
$262$	−924.000	−0.217881
$263$	−2466.00	−0.578175	−0.289088	−	0.957303i	$-0.593352\pi$
$263$	−2466.00	−0.578175	−0.289088	+	0.957303i	$0.593352\pi$
$264$	0	0
$265$	−306.000	−0.0709337
$266$	−196.000	−0.0451787
$267$	0	0
$268$	−1732.00	−0.394771
$269$	−6774.00	−1.53538	−0.767692	−	0.640820i	$-0.778595\pi$
$269$	−6774.00	−1.53538	−0.767692	+	0.640820i	$0.778595\pi$
$270$	0	0
$271$	−4876.00	−1.09297	−0.546487	−	0.837468i	$-0.684035\pi$
$271$	−4876.00	−1.09297	−0.546487	+	0.837468i	$0.684035\pi$
$272$	−96.0000	−0.0214002
$273$	0	0
$274$	6042.00	1.33216
$275$	−1276.00	−0.279803
$276$	0	0
$277$	−3268.00	−0.708863	−0.354432	−	0.935082i	$-0.615326\pi$
$277$	−3268.00	−0.708863	−0.354432	+	0.935082i	$0.615326\pi$
$278$	3188.00	0.687782
$279$	0	0
$280$	168.000	0.0358569
$281$	−5928.00	−1.25849	−0.629243	−	0.777208i	$-0.716635\pi$
$281$	−5928.00	−1.25849	−0.629243	+	0.777208i	$0.716635\pi$
$282$	0	0
$283$	2672.00	0.561251	0.280625	−	0.959817i	$-0.409458\pi$
$283$	2672.00	0.561251	0.280625	+	0.959817i	$0.409458\pi$
$284$	−540.000	−0.112828
$285$	0	0
$286$	352.000	0.0727769
$287$	−714.000	−0.146850
$288$	0	0
$289$	−4877.00	−0.992673
$290$	−324.000	−0.0656067
$291$	0	0
$292$	−952.000	−0.190793
$293$	−5322.00	−1.06114	−0.530571	−	0.847641i	$-0.678022\pi$
$293$	−5322.00	−1.06114	−0.530571	+	0.847641i	$0.678022\pi$
$294$	0	0
$295$	−189.000	−0.0373017
$296$	1544.00	0.303186
$297$	0	0
$298$	5628.00	1.09403
$299$	−816.000	−0.157828
$300$	0	0
$301$	1988.00	0.380686
$302$	−4900.00	−0.933653
$303$	0	0
$304$	224.000	0.0422608
$305$	2370.00	0.444937
$306$	0	0
$307$	2816.00	0.523510	0.261755	−	0.965134i	$-0.415699\pi$
$307$	2816.00	0.523510	0.261755	+	0.965134i	$0.415699\pi$
$308$	308.000	0.0569803
$309$	0	0
$310$	570.000	0.104432
$311$	−8760.00	−1.59722	−0.798608	−	0.601852i	$-0.794430\pi$
$311$	−8760.00	−1.59722	−0.798608	+	0.601852i	$0.794430\pi$
$312$	0	0
$313$	1337.00	0.241443	0.120722	−	0.992686i	$-0.461479\pi$
$313$	1337.00	0.241443	0.120722	+	0.992686i	$0.461479\pi$
$314$	−7798.00	−1.40149
$315$	0	0
$316$	3080.00	0.548302
$317$	−4269.00	−0.756375	−0.378188	−	0.925729i	$-0.623453\pi$
$317$	−4269.00	−0.756375	−0.378188	+	0.925729i	$0.623453\pi$
$318$	0	0
$319$	−594.000	−0.104256
$320$	−192.000	−0.0335410
$321$	0	0
$322$	−714.000	−0.123570
$323$	−84.0000	−0.0144702
$324$	0	0
$325$	1856.00	0.316776
$326$	248.000	0.0421333
$327$	0	0
$328$	816.000	0.137366
$329$	504.000	0.0844572
$330$	0	0
$331$	−4843.00	−0.804216	−0.402108	−	0.915592i	$-0.631722\pi$
$331$	−4843.00	−0.804216	−0.402108	+	0.915592i	$0.631722\pi$
$332$	4032.00	0.666520
$333$	0	0
$334$	−60.0000	−0.00982950
$335$	1299.00	0.211857
$336$	0	0
$337$	−3790.00	−0.612624	−0.306312	−	0.951931i	$-0.599095\pi$
$337$	−3790.00	−0.612624	−0.306312	+	0.951931i	$0.599095\pi$
$338$	3882.00	0.624713
$339$	0	0
$340$	72.0000	0.0114846
$341$	1045.00	0.165953
$342$	0	0
$343$	343.000	0.0539949
$344$	−2272.00	−0.356099
$345$	0	0
$346$	4536.00	0.704789
$347$	−1722.00	−0.266403	−0.133201	−	0.991089i	$-0.542526\pi$
$347$	−1722.00	−0.266403	−0.133201	+	0.991089i	$0.542526\pi$
$348$	0	0
$349$	−3166.00	−0.485593	−0.242797	−	0.970077i	$-0.578065\pi$
$349$	−3166.00	−0.485593	−0.242797	+	0.970077i	$0.578065\pi$
$350$	1624.00	0.248018
$351$	0	0
$352$	−352.000	−0.0533002
$353$	4167.00	0.628292	0.314146	−	0.949375i	$-0.398282\pi$
$353$	4167.00	0.628292	0.314146	+	0.949375i	$0.398282\pi$
$354$	0	0
$355$	405.000	0.0605498
$356$	2556.00	0.380527
$357$	0	0
$358$	3462.00	0.511096
$359$	−1380.00	−0.202879	−0.101440	−	0.994842i	$-0.532345\pi$
$359$	−1380.00	−0.202879	−0.101440	+	0.994842i	$0.532345\pi$
$360$	0	0
$361$	−6663.00	−0.971424
$362$	−1570.00	−0.227949
$363$	0	0
$364$	−448.000	−0.0645098
$365$	714.000	0.102390
$366$	0	0
$367$	755.000	0.107386	0.0536930	−	0.998557i	$-0.482901\pi$
$367$	755.000	0.107386	0.0536930	+	0.998557i	$0.482901\pi$
$368$	816.000	0.115590
$369$	0	0
$370$	−1158.00	−0.162707
$371$	714.000	0.0999165
$372$	0	0
$373$	−8596.00	−1.19325	−0.596627	−	0.802518i	$-0.703493\pi$
$373$	−8596.00	−1.19325	−0.596627	+	0.802518i	$0.703493\pi$
$374$	132.000	0.0182502
$375$	0	0
$376$	−576.000	−0.0790025
$377$	864.000	0.118033
$378$	0	0
$379$	−11287.0	−1.52975	−0.764874	−	0.644180i	$-0.777199\pi$
$379$	−11287.0	−1.52975	−0.764874	+	0.644180i	$0.777199\pi$
$380$	−168.000	−0.0226795
$381$	0	0
$382$	102.000	0.0136617
$383$	1185.00	0.158096	0.0790479	−	0.996871i	$-0.474812\pi$
$383$	1185.00	0.158096	0.0790479	+	0.996871i	$0.474812\pi$
$384$	0	0
$385$	−231.000	−0.0305788
$386$	−2452.00	−0.323325
$387$	0	0
$388$	44.0000	0.00575712
$389$	11643.0	1.51754	0.758771	−	0.651358i	$-0.225800\pi$
$389$	11643.0	1.51754	0.758771	+	0.651358i	$0.225800\pi$
$390$	0	0
$391$	−306.000	−0.0395782
$392$	−392.000	−0.0505076
$393$	0	0
$394$	5508.00	0.704287
$395$	−2310.00	−0.294250
$396$	0	0
$397$	−3382.00	−0.427551	−0.213775	−	0.976883i	$-0.568576\pi$
$397$	−3382.00	−0.427551	−0.213775	+	0.976883i	$0.568576\pi$
$398$	3488.00	0.439291
$399$	0	0
$400$	−1856.00	−0.232000
$401$	7566.00	0.942214	0.471107	−	0.882076i	$-0.343854\pi$
$401$	7566.00	0.942214	0.471107	+	0.882076i	$0.343854\pi$
$402$	0	0
$403$	−1520.00	−0.187882
$404$	−6768.00	−0.833467
$405$	0	0
$406$	756.000	0.0924129
$407$	−2123.00	−0.258558
$408$	0	0
$409$	86.0000	0.0103971	0.00519857	−	0.999986i	$-0.498345\pi$
$409$	86.0000	0.0103971	0.00519857	+	0.999986i	$0.498345\pi$
$410$	−612.000	−0.0737184
$411$	0	0
$412$	−2128.00	−0.254464
$413$	441.000	0.0525428
$414$	0	0
$415$	−3024.00	−0.357692
$416$	512.000	0.0603434
$417$	0	0
$418$	−308.000	−0.0360401
$419$	12672.0	1.47749	0.738744	−	0.673986i	$-0.235419\pi$
$419$	12672.0	1.47749	0.738744	+	0.673986i	$0.235419\pi$
$420$	0	0
$421$	12398.0	1.43525	0.717627	−	0.696428i	$-0.245229\pi$
$421$	12398.0	1.43525	0.717627	+	0.696428i	$0.245229\pi$
$422$	8420.00	0.971278
$423$	0	0
$424$	−816.000	−0.0934634
$425$	696.000	0.0794376
$426$	0	0
$427$	−5530.00	−0.626734
$428$	−5400.00	−0.609857
$429$	0	0
$430$	1704.00	0.191103
$431$	−12372.0	−1.38269	−0.691344	−	0.722526i	$-0.742981\pi$
$431$	−12372.0	−1.38269	−0.691344	+	0.722526i	$0.742981\pi$
$432$	0	0
$433$	−14929.0	−1.65691	−0.828455	−	0.560056i	$-0.810780\pi$
$433$	−14929.0	−1.65691	−0.828455	+	0.560056i	$0.810780\pi$
$434$	−1330.00	−0.147101
$435$	0	0
$436$	6464.00	0.710022
$437$	714.000	0.0781585
$438$	0	0
$439$	9146.00	0.994339	0.497169	−	0.867653i	$-0.334373\pi$
$439$	9146.00	0.994339	0.497169	+	0.867653i	$0.334373\pi$
$440$	264.000	0.0286039
$441$	0	0
$442$	−192.000	−0.0206618
$443$	11253.0	1.20688	0.603438	−	0.797410i	$-0.293797\pi$
$443$	11253.0	1.20688	0.603438	+	0.797410i	$0.293797\pi$
$444$	0	0
$445$	−1917.00	−0.204212
$446$	10994.0	1.16722
$447$	0	0
$448$	448.000	0.0472456
$449$	−6711.00	−0.705371	−0.352686	−	0.935742i	$-0.614731\pi$
$449$	−6711.00	−0.705371	−0.352686	+	0.935742i	$0.614731\pi$
$450$	0	0
$451$	−1122.00	−0.117146
$452$	−2388.00	−0.248500
$453$	0	0
$454$	−7464.00	−0.771592
$455$	336.000	0.0346196
$456$	0	0
$457$	16952.0	1.73519	0.867594	−	0.497273i	$-0.165665\pi$
$457$	16952.0	1.73519	0.867594	+	0.497273i	$0.165665\pi$
$458$	7766.00	0.792317
$459$	0	0
$460$	−612.000	−0.0620318
$461$	5850.00	0.591023	0.295512	−	0.955339i	$-0.404510\pi$
$461$	5850.00	0.591023	0.295512	+	0.955339i	$0.404510\pi$
$462$	0	0
$463$	−4957.00	−0.497562	−0.248781	−	0.968560i	$-0.580030\pi$
$463$	−4957.00	−0.497562	−0.248781	+	0.968560i	$0.580030\pi$
$464$	−864.000	−0.0864444
$465$	0	0
$466$	−444.000	−0.0441371
$467$	−3753.00	−0.371880	−0.185940	−	0.982561i	$-0.559533\pi$
$467$	−3753.00	−0.371880	−0.185940	+	0.982561i	$0.559533\pi$
$468$	0	0
$469$	−3031.00	−0.298419
$470$	432.000	0.0423972
$471$	0	0
$472$	−504.000	−0.0491493
$473$	3124.00	0.303682
$474$	0	0
$475$	−1624.00	−0.156872
$476$	−168.000	−0.0161770
$477$	0	0
$478$	−4608.00	−0.440931
$479$	16272.0	1.55216	0.776082	−	0.630632i	$-0.217204\pi$
$479$	16272.0	1.55216	0.776082	+	0.630632i	$0.217204\pi$
$480$	0	0
$481$	3088.00	0.292725
$482$	2552.00	0.241163
$483$	0	0
$484$	484.000	0.0454545
$485$	−33.0000	−0.00308959
$486$	0	0
$487$	10613.0	0.987517	0.493759	−	0.869599i	$-0.335623\pi$
$487$	10613.0	0.987517	0.493759	+	0.869599i	$0.335623\pi$
$488$	6320.00	0.586256
$489$	0	0
$490$	294.000	0.0271052
$491$	−11562.0	−1.06270	−0.531350	−	0.847152i	$-0.678315\pi$
$491$	−11562.0	−1.06270	−0.531350	+	0.847152i	$0.678315\pi$
$492$	0	0
$493$	324.000	0.0295988
$494$	448.000	0.0408026
$495$	0	0
$496$	1520.00	0.137601
$497$	−945.000	−0.0852898
$498$	0	0
$499$	−9604.00	−0.861591	−0.430796	−	0.902449i	$-0.641767\pi$
$499$	−9604.00	−0.861591	−0.430796	+	0.902449i	$0.641767\pi$
$500$	2892.00	0.258668
$501$	0	0
$502$	−510.000	−0.0453435
$503$	15852.0	1.40518	0.702590	−	0.711595i	$-0.252027\pi$
$503$	15852.0	1.40518	0.702590	+	0.711595i	$0.252027\pi$
$504$	0	0
$505$	5076.00	0.447285
$506$	−1122.00	−0.0985751
$507$	0	0
$508$	1208.00	0.105505
$509$	−15669.0	−1.36447	−0.682236	−	0.731132i	$-0.738992\pi$
$509$	−15669.0	−1.36447	−0.682236	+	0.731132i	$0.738992\pi$
$510$	0	0
$511$	−1666.00	−0.144226
$512$	−512.000	−0.0441942
$513$	0	0
$514$	4740.00	0.406756
$515$	1596.00	0.136560
$516$	0	0
$517$	792.000	0.0673735
$518$	2702.00	0.229187
$519$	0	0
$520$	−384.000	−0.0323837
$521$	2817.00	0.236881	0.118441	−	0.992961i	$-0.462211\pi$
$521$	2817.00	0.236881	0.118441	+	0.992961i	$0.462211\pi$
$522$	0	0
$523$	−12364.0	−1.03373	−0.516864	−	0.856067i	$-0.672901\pi$
$523$	−12364.0	−1.03373	−0.516864	+	0.856067i	$0.672901\pi$
$524$	1848.00	0.154065
$525$	0	0
$526$	4932.00	0.408832
$527$	−570.000	−0.0471150
$528$	0	0
$529$	−9566.00	−0.786225
$530$	612.000	0.0501577
$531$	0	0
$532$	392.000	0.0319462
$533$	1632.00	0.132626
$534$	0	0
$535$	4050.00	0.327284
$536$	3464.00	0.279146
$537$	0	0
$538$	13548.0	1.08568
$539$	539.000	0.0430730
$540$	0	0
$541$	2372.00	0.188503	0.0942516	−	0.995548i	$-0.469954\pi$
$541$	2372.00	0.188503	0.0942516	+	0.995548i	$0.469954\pi$
$542$	9752.00	0.772849
$543$	0	0
$544$	192.000	0.0151322
$545$	−4848.00	−0.381038
$546$	0	0
$547$	−12832.0	−1.00303	−0.501514	−	0.865149i	$-0.667224\pi$
$547$	−12832.0	−1.00303	−0.501514	+	0.865149i	$0.667224\pi$
$548$	−12084.0	−0.941976
$549$	0	0
$550$	2552.00	0.197850
$551$	−756.000	−0.0584513
$552$	0	0
$553$	5390.00	0.414478
$554$	6536.00	0.501242
$555$	0	0
$556$	−6376.00	−0.486336
$557$	14166.0	1.07762	0.538809	−	0.842428i	$-0.318875\pi$
$557$	14166.0	1.07762	0.538809	+	0.842428i	$0.318875\pi$
$558$	0	0
$559$	−4544.00	−0.343812
$560$	−336.000	−0.0253546
$561$	0	0
$562$	11856.0	0.889885
$563$	18540.0	1.38786	0.693932	−	0.720040i	$-0.255877\pi$
$563$	18540.0	1.38786	0.693932	+	0.720040i	$0.255877\pi$
$564$	0	0
$565$	1791.00	0.133359
$566$	−5344.00	−0.396864
$567$	0	0
$568$	1080.00	0.0797813
$569$	21894.0	1.61308	0.806541	−	0.591177i	$-0.201337\pi$
$569$	21894.0	1.61308	0.806541	+	0.591177i	$0.201337\pi$
$570$	0	0
$571$	23204.0	1.70063	0.850313	−	0.526278i	$-0.176413\pi$
$571$	23204.0	1.70063	0.850313	+	0.526278i	$0.176413\pi$
$572$	−704.000	−0.0514610
$573$	0	0
$574$	1428.00	0.103839
$575$	−5916.00	−0.429068
$576$	0	0
$577$	18479.0	1.33326	0.666630	−	0.745389i	$-0.267736\pi$
$577$	18479.0	1.33326	0.666630	+	0.745389i	$0.267736\pi$
$578$	9754.00	0.701925
$579$	0	0
$580$	648.000	0.0463909
$581$	7056.00	0.503842
$582$	0	0
$583$	1122.00	0.0797058
$584$	1904.00	0.134911
$585$	0	0
$586$	10644.0	0.750341
$587$	1116.00	0.0784706	0.0392353	−	0.999230i	$-0.487508\pi$
$587$	1116.00	0.0784706	0.0392353	+	0.999230i	$0.487508\pi$
$588$	0	0
$589$	1330.00	0.0930419
$590$	378.000	0.0263763
$591$	0	0
$592$	−3088.00	−0.214385
$593$	3654.00	0.253038	0.126519	−	0.991964i	$-0.459619\pi$
$593$	3654.00	0.253038	0.126519	+	0.991964i	$0.459619\pi$
$594$	0	0
$595$	126.000	0.00868151
$596$	−11256.0	−0.773597
$597$	0	0
$598$	1632.00	0.111601
$599$	−10248.0	−0.699035	−0.349517	−	0.936930i	$-0.613654\pi$
$599$	−10248.0	−0.699035	−0.349517	+	0.936930i	$0.613654\pi$
$600$	0	0
$601$	18848.0	1.27924	0.639622	−	0.768689i	$-0.279091\pi$
$601$	18848.0	1.27924	0.639622	+	0.768689i	$0.279091\pi$
$602$	−3976.00	−0.269185
$603$	0	0
$604$	9800.00	0.660193
$605$	−363.000	−0.0243935
$606$	0	0
$607$	−13198.0	−0.882521	−0.441261	−	0.897379i	$-0.645469\pi$
$607$	−13198.0	−0.882521	−0.441261	+	0.897379i	$0.645469\pi$
$608$	−448.000	−0.0298829
$609$	0	0
$610$	−4740.00	−0.314618
$611$	−1152.00	−0.0762765
$612$	0	0
$613$	1712.00	0.112801	0.0564005	−	0.998408i	$-0.482038\pi$
$613$	1712.00	0.112801	0.0564005	+	0.998408i	$0.482038\pi$
$614$	−5632.00	−0.370178
$615$	0	0
$616$	−616.000	−0.0402911
$617$	−20994.0	−1.36983	−0.684916	−	0.728622i	$-0.740161\pi$
$617$	−20994.0	−1.36983	−0.684916	+	0.728622i	$0.740161\pi$
$618$	0	0
$619$	25691.0	1.66819	0.834094	−	0.551622i	$-0.185991\pi$
$619$	25691.0	1.66819	0.834094	+	0.551622i	$0.185991\pi$
$620$	−1140.00	−0.0738444
$621$	0	0
$622$	17520.0	1.12940
$623$	4473.00	0.287652
$624$	0	0
$625$	12331.0	0.789184
$626$	−2674.00	−0.170726
$627$	0	0
$628$	15596.0	0.991000
$629$	1158.00	0.0734062
$630$	0	0
$631$	25445.0	1.60531	0.802654	−	0.596445i	$-0.203421\pi$
$631$	25445.0	1.60531	0.802654	+	0.596445i	$0.203421\pi$
$632$	−6160.00	−0.387708
$633$	0	0
$634$	8538.00	0.534838
$635$	−906.000	−0.0566197
$636$	0	0
$637$	−784.000	−0.0487649
$638$	1188.00	0.0737200
$639$	0	0
$640$	384.000	0.0237171
$641$	−19095.0	−1.17661	−0.588305	−	0.808639i	$-0.700205\pi$
$641$	−19095.0	−1.17661	−0.588305	+	0.808639i	$0.700205\pi$
$642$	0	0
$643$	−24391.0	−1.49594	−0.747968	−	0.663735i	$-0.768970\pi$
$643$	−24391.0	−1.49594	−0.747968	+	0.663735i	$0.768970\pi$
$644$	1428.00	0.0873775
$645$	0	0
$646$	168.000	0.0102320
$647$	5691.00	0.345806	0.172903	−	0.984939i	$-0.444685\pi$
$647$	5691.00	0.345806	0.172903	+	0.984939i	$0.444685\pi$
$648$	0	0
$649$	693.000	0.0419147
$650$	−3712.00	−0.223995
$651$	0	0
$652$	−496.000	−0.0297927
$653$	25749.0	1.54309	0.771544	−	0.636176i	$-0.219485\pi$
$653$	25749.0	1.54309	0.771544	+	0.636176i	$0.219485\pi$
$654$	0	0
$655$	−1386.00	−0.0826802
$656$	−1632.00	−0.0971325
$657$	0	0
$658$	−1008.00	−0.0597203
$659$	9030.00	0.533777	0.266888	−	0.963727i	$-0.414005\pi$
$659$	9030.00	0.533777	0.266888	+	0.963727i	$0.414005\pi$
$660$	0	0
$661$	28895.0	1.70028	0.850140	−	0.526557i	$-0.176517\pi$
$661$	28895.0	1.70028	0.850140	+	0.526557i	$0.176517\pi$
$662$	9686.00	0.568666
$663$	0	0
$664$	−8064.00	−0.471301
$665$	−294.000	−0.0171441
$666$	0	0
$667$	−2754.00	−0.159873
$668$	120.000	0.00695051
$669$	0	0
$670$	−2598.00	−0.149805
$671$	−8690.00	−0.499961
$672$	0	0
$673$	16856.0	0.965455	0.482727	−	0.875771i	$-0.339646\pi$
$673$	16856.0	0.965455	0.482727	+	0.875771i	$0.339646\pi$
$674$	7580.00	0.433191
$675$	0	0
$676$	−7764.00	−0.441739
$677$	19470.0	1.10531	0.552654	−	0.833411i	$-0.313615\pi$
$677$	19470.0	1.10531	0.552654	+	0.833411i	$0.313615\pi$
$678$	0	0
$679$	77.0000	0.00435197
$680$	−144.000	−0.00812081
$681$	0	0
$682$	−2090.00	−0.117346
$683$	14820.0	0.830266	0.415133	−	0.909761i	$-0.363735\pi$
$683$	14820.0	0.830266	0.415133	+	0.909761i	$0.363735\pi$
$684$	0	0
$685$	9063.00	0.505517
$686$	−686.000	−0.0381802
$687$	0	0
$688$	4544.00	0.251800
$689$	−1632.00	−0.0902384
$690$	0	0
$691$	−18451.0	−1.01579	−0.507894	−	0.861420i	$-0.669576\pi$
$691$	−18451.0	−1.01579	−0.507894	+	0.861420i	$0.669576\pi$
$692$	−9072.00	−0.498361
$693$	0	0
$694$	3444.00	0.188375
$695$	4782.00	0.260995
$696$	0	0
$697$	612.000	0.0332585
$698$	6332.00	0.343366
$699$	0	0
$700$	−3248.00	−0.175376
$701$	−6288.00	−0.338794	−0.169397	−	0.985548i	$-0.554182\pi$
$701$	−6288.00	−0.338794	−0.169397	+	0.985548i	$0.554182\pi$
$702$	0	0
$703$	−2702.00	−0.144961
$704$	704.000	0.0376889
$705$	0	0
$706$	−8334.00	−0.444269
$707$	−11844.0	−0.630042
$708$	0	0
$709$	−17629.0	−0.933810	−0.466905	−	0.884308i	$-0.654631\pi$
$709$	−17629.0	−0.933810	−0.466905	+	0.884308i	$0.654631\pi$
$710$	−810.000	−0.0428152
$711$	0	0
$712$	−5112.00	−0.269073
$713$	4845.00	0.254483
$714$	0	0
$715$	528.000	0.0276169
$716$	−6924.00	−0.361399
$717$	0	0
$718$	2760.00	0.143457
$719$	−2067.00	−0.107213	−0.0536065	−	0.998562i	$-0.517072\pi$
$719$	−2067.00	−0.107213	−0.0536065	+	0.998562i	$0.517072\pi$
$720$	0	0
$721$	−3724.00	−0.192356
$722$	13326.0	0.686901
$723$	0	0
$724$	3140.00	0.161184
$725$	6264.00	0.320882
$726$	0	0
$727$	11315.0	0.577235	0.288618	−	0.957444i	$-0.406804\pi$
$727$	11315.0	0.577235	0.288618	+	0.957444i	$0.406804\pi$
$728$	896.000	0.0456153
$729$	0	0
$730$	−1428.00	−0.0724009
$731$	−1704.00	−0.0862171
$732$	0	0
$733$	−23644.0	−1.19142	−0.595710	−	0.803199i	$-0.703129\pi$
$733$	−23644.0	−1.19142	−0.595710	+	0.803199i	$0.703129\pi$
$734$	−1510.00	−0.0759334
$735$	0	0
$736$	−1632.00	−0.0817341
$737$	−4763.00	−0.238056
$738$	0	0
$739$	−862.000	−0.0429082	−0.0214541	−	0.999770i	$-0.506830\pi$
$739$	−862.000	−0.0429082	−0.0214541	+	0.999770i	$0.506830\pi$
$740$	2316.00	0.115051
$741$	0	0
$742$	−1428.00	−0.0706517
$743$	−9072.00	−0.447940	−0.223970	−	0.974596i	$-0.571902\pi$
$743$	−9072.00	−0.447940	−0.223970	+	0.974596i	$0.571902\pi$
$744$	0	0
$745$	8442.00	0.415156
$746$	17192.0	0.843759
$747$	0	0
$748$	−264.000	−0.0129048
$749$	−9450.00	−0.461009
$750$	0	0
$751$	9407.00	0.457079	0.228539	−	0.973535i	$-0.426605\pi$
$751$	9407.00	0.457079	0.228539	+	0.973535i	$0.426605\pi$
$752$	1152.00	0.0558632
$753$	0	0
$754$	−1728.00	−0.0834616
$755$	−7350.00	−0.354297
$756$	0	0
$757$	−15946.0	−0.765611	−0.382805	−	0.923829i	$-0.625042\pi$
$757$	−15946.0	−0.765611	−0.382805	+	0.923829i	$0.625042\pi$
$758$	22574.0	1.08169
$759$	0	0
$760$	336.000	0.0160368
$761$	8220.00	0.391557	0.195778	−	0.980648i	$-0.437277\pi$
$761$	8220.00	0.391557	0.195778	+	0.980648i	$0.437277\pi$
$762$	0	0
$763$	11312.0	0.536726
$764$	−204.000	−0.00966029
$765$	0	0
$766$	−2370.00	−0.111791
$767$	−1008.00	−0.0474534
$768$	0	0
$769$	14372.0	0.673950	0.336975	−	0.941514i	$-0.390596\pi$
$769$	14372.0	0.673950	0.336975	+	0.941514i	$0.390596\pi$
$770$	462.000	0.0216225
$771$	0	0
$772$	4904.00	0.228625
$773$	−14082.0	−0.655232	−0.327616	−	0.944811i	$-0.606245\pi$
$773$	−14082.0	−0.655232	−0.327616	+	0.944811i	$0.606245\pi$
$774$	0	0
$775$	−11020.0	−0.510774
$776$	−88.0000	−0.00407090
$777$	0	0
$778$	−23286.0	−1.07306
$779$	−1428.00	−0.0656783
$780$	0	0
$781$	−1485.00	−0.0680377
$782$	612.000	0.0279860
$783$	0	0
$784$	784.000	0.0357143
$785$	−11697.0	−0.531827
$786$	0	0
$787$	−12742.0	−0.577132	−0.288566	−	0.957460i	$-0.593179\pi$
$787$	−12742.0	−0.577132	−0.288566	+	0.957460i	$0.593179\pi$
$788$	−11016.0	−0.498006
$789$	0	0
$790$	4620.00	0.208066
$791$	−4179.00	−0.187848
$792$	0	0
$793$	12640.0	0.566027
$794$	6764.00	0.302324
$795$	0	0
$796$	−6976.00	−0.310625
$797$	−7131.00	−0.316930	−0.158465	−	0.987365i	$-0.550654\pi$
$797$	−7131.00	−0.316930	−0.158465	+	0.987365i	$0.550654\pi$
$798$	0	0
$799$	−432.000	−0.0191277
$800$	3712.00	0.164049
$801$	0	0
$802$	−15132.0	−0.666246
$803$	−2618.00	−0.115053
$804$	0	0
$805$	−1071.00	−0.0468917
$806$	3040.00	0.132853
$807$	0	0
$808$	13536.0	0.589350
$809$	−21966.0	−0.954615	−0.477307	−	0.878736i	$-0.658387\pi$
$809$	−21966.0	−0.954615	−0.477307	+	0.878736i	$0.658387\pi$
$810$	0	0
$811$	−10978.0	−0.475326	−0.237663	−	0.971348i	$-0.576381\pi$
$811$	−10978.0	−0.475326	−0.237663	+	0.971348i	$0.576381\pi$
$812$	−1512.00	−0.0653458
$813$	0	0
$814$	4246.00	0.182828
$815$	372.000	0.0159885
$816$	0	0
$817$	3976.00	0.170260
$818$	−172.000	−0.00735188
$819$	0	0
$820$	1224.00	0.0521267
$821$	27534.0	1.17045	0.585227	−	0.810869i	$-0.301005\pi$
$821$	27534.0	1.17045	0.585227	+	0.810869i	$0.301005\pi$
$822$	0	0
$823$	−19591.0	−0.829768	−0.414884	−	0.909874i	$-0.636178\pi$
$823$	−19591.0	−0.829768	−0.414884	+	0.909874i	$0.636178\pi$
$824$	4256.00	0.179933
$825$	0	0
$826$	−882.000	−0.0371534
$827$	−12744.0	−0.535855	−0.267928	−	0.963439i	$-0.586339\pi$
$827$	−12744.0	−0.535855	−0.267928	+	0.963439i	$0.586339\pi$
$828$	0	0
$829$	23567.0	0.987353	0.493677	−	0.869646i	$-0.335653\pi$
$829$	23567.0	0.987353	0.493677	+	0.869646i	$0.335653\pi$
$830$	6048.00	0.252927
$831$	0	0
$832$	−1024.00	−0.0426692
$833$	−294.000	−0.0122287
$834$	0	0
$835$	−90.0000	−0.00373003
$836$	616.000	0.0254842
$837$	0	0
$838$	−25344.0	−1.04474
$839$	−30219.0	−1.24348	−0.621738	−	0.783226i	$-0.713573\pi$
$839$	−30219.0	−1.24348	−0.621738	+	0.783226i	$0.713573\pi$
$840$	0	0
$841$	−21473.0	−0.880438
$842$	−24796.0	−1.01488
$843$	0	0
$844$	−16840.0	−0.686797
$845$	5823.00	0.237062
$846$	0	0
$847$	847.000	0.0343604
$848$	1632.00	0.0660886
$849$	0	0
$850$	−1392.00	−0.0561708
$851$	−9843.00	−0.396491
$852$	0	0
$853$	8654.00	0.347371	0.173685	−	0.984801i	$-0.444432\pi$
$853$	8654.00	0.347371	0.173685	+	0.984801i	$0.444432\pi$
$854$	11060.0	0.443168
$855$	0	0
$856$	10800.0	0.431234
$857$	43284.0	1.72527	0.862633	−	0.505830i	$-0.168814\pi$
$857$	43284.0	1.72527	0.862633	+	0.505830i	$0.168814\pi$
$858$	0	0
$859$	−21931.0	−0.871101	−0.435551	−	0.900164i	$-0.643446\pi$
$859$	−21931.0	−0.871101	−0.435551	+	0.900164i	$0.643446\pi$
$860$	−3408.00	−0.135130
$861$	0	0
$862$	24744.0	0.977708
$863$	22404.0	0.883709	0.441855	−	0.897087i	$-0.354321\pi$
$863$	22404.0	0.883709	0.441855	+	0.897087i	$0.354321\pi$
$864$	0	0
$865$	6804.00	0.267448
$866$	29858.0	1.17161
$867$	0	0
$868$	2660.00	0.104016
$869$	8470.00	0.330639
$870$	0	0
$871$	6928.00	0.269514
$872$	−12928.0	−0.502061
$873$	0	0
$874$	−1428.00	−0.0552664
$875$	5061.00	0.195535
$876$	0	0
$877$	4826.00	0.185818	0.0929090	−	0.995675i	$-0.470383\pi$
$877$	4826.00	0.185818	0.0929090	+	0.995675i	$0.470383\pi$
$878$	−18292.0	−0.703104
$879$	0	0
$880$	−528.000	−0.0202260
$881$	−40203.0	−1.53743	−0.768714	−	0.639593i	$-0.779103\pi$
$881$	−40203.0	−1.53743	−0.768714	+	0.639593i	$0.779103\pi$
$882$	0	0
$883$	−41716.0	−1.58987	−0.794935	−	0.606695i	$-0.792495\pi$
$883$	−41716.0	−1.58987	−0.794935	+	0.606695i	$0.792495\pi$
$884$	384.000	0.0146101
$885$	0	0
$886$	−22506.0	−0.853390
$887$	44358.0	1.67914	0.839569	−	0.543253i	$-0.182807\pi$
$887$	44358.0	1.67914	0.839569	+	0.543253i	$0.182807\pi$
$888$	0	0
$889$	2114.00	0.0797540
$890$	3834.00	0.144400
$891$	0	0
$892$	−21988.0	−0.825351
$893$	1008.00	0.0377732
$894$	0	0
$895$	5193.00	0.193947
$896$	−896.000	−0.0334077
$897$	0	0
$898$	13422.0	0.498773
$899$	−5130.00	−0.190317
$900$	0	0
$901$	−612.000	−0.0226289
$902$	2244.00	0.0828348
$903$	0	0
$904$	4776.00	0.175716
$905$	−2355.00	−0.0865004
$906$	0	0
$907$	29384.0	1.07572	0.537861	−	0.843034i	$-0.319233\pi$
$907$	29384.0	1.07572	0.537861	+	0.843034i	$0.319233\pi$
$908$	14928.0	0.545598
$909$	0	0
$910$	−672.000	−0.0244798
$911$	−5160.00	−0.187660	−0.0938301	−	0.995588i	$-0.529911\pi$
$911$	−5160.00	−0.187660	−0.0938301	+	0.995588i	$0.529911\pi$
$912$	0	0
$913$	11088.0	0.401927
$914$	−33904.0	−1.22696
$915$	0	0
$916$	−15532.0	−0.560253
$917$	3234.00	0.116462
$918$	0	0
$919$	10436.0	0.374594	0.187297	−	0.982303i	$-0.440027\pi$
$919$	10436.0	0.374594	0.187297	+	0.982303i	$0.440027\pi$
$920$	1224.00	0.0438631
$921$	0	0
$922$	−11700.0	−0.417916
$923$	2160.00	0.0770285
$924$	0	0
$925$	22388.0	0.795798
$926$	9914.00	0.351830
$927$	0	0
$928$	1728.00	0.0611254
$929$	−40626.0	−1.43476	−0.717382	−	0.696680i	$-0.754660\pi$
$929$	−40626.0	−1.43476	−0.717382	+	0.696680i	$0.754660\pi$
$930$	0	0
$931$	686.000	0.0241490
$932$	888.000	0.0312097
$933$	0	0
$934$	7506.00	0.262959
$935$	198.000	0.00692545
$936$	0	0
$937$	−2608.00	−0.0909281	−0.0454641	−	0.998966i	$-0.514477\pi$
$937$	−2608.00	−0.0909281	−0.0454641	+	0.998966i	$0.514477\pi$
$938$	6062.00	0.211014
$939$	0	0
$940$	−864.000	−0.0299793
$941$	57150.0	1.97985	0.989924	−	0.141600i	$-0.0452248\pi$
$941$	57150.0	1.97985	0.989924	+	0.141600i	$0.0452248\pi$
$942$	0	0
$943$	−5202.00	−0.179640
$944$	1008.00	0.0347538
$945$	0	0
$946$	−6248.00	−0.214736
$947$	657.000	0.0225445	0.0112722	−	0.999936i	$-0.496412\pi$
$947$	657.000	0.0225445	0.0112722	+	0.999936i	$0.496412\pi$
$948$	0	0
$949$	3808.00	0.130256
$950$	3248.00	0.110925
$951$	0	0
$952$	336.000	0.0114389
$953$	−5508.00	−0.187221	−0.0936105	−	0.995609i	$-0.529841\pi$
$953$	−5508.00	−0.187221	−0.0936105	+	0.995609i	$0.529841\pi$
$954$	0	0
$955$	153.000	0.00518426
$956$	9216.00	0.311785
$957$	0	0
$958$	−32544.0	−1.09755
$959$	−21147.0	−0.712067
$960$	0	0
$961$	−20766.0	−0.697056
$962$	−6176.00	−0.206988
$963$	0	0
$964$	−5104.00	−0.170528
$965$	−3678.00	−0.122693
$966$	0	0
$967$	−1690.00	−0.0562014	−0.0281007	−	0.999605i	$-0.508946\pi$
$967$	−1690.00	−0.0562014	−0.0281007	+	0.999605i	$0.508946\pi$
$968$	−968.000	−0.0321412
$969$	0	0
$970$	66.0000	0.00218467
$971$	−7263.00	−0.240042	−0.120021	−	0.992771i	$-0.538296\pi$
$971$	−7263.00	−0.240042	−0.120021	+	0.992771i	$0.538296\pi$
$972$	0	0
$973$	−11158.0	−0.367635
$974$	−21226.0	−0.698280
$975$	0	0
$976$	−12640.0	−0.414546
$977$	−1569.00	−0.0513785	−0.0256892	−	0.999670i	$-0.508178\pi$
$977$	−1569.00	−0.0513785	−0.0256892	+	0.999670i	$0.508178\pi$
$978$	0	0
$979$	7029.00	0.229467
$980$	−588.000	−0.0191663
$981$	0	0
$982$	23124.0	0.751442
$983$	9261.00	0.300488	0.150244	−	0.988649i	$-0.451994\pi$
$983$	9261.00	0.300488	0.150244	+	0.988649i	$0.451994\pi$
$984$	0	0
$985$	8262.00	0.267258
$986$	−648.000	−0.0209295
$987$	0	0
$988$	−896.000	−0.0288518
$989$	14484.0	0.465687
$990$	0	0
$991$	19400.0	0.621858	0.310929	−	0.950433i	$-0.399360\pi$
$991$	19400.0	0.621858	0.310929	+	0.950433i	$0.399360\pi$
$992$	−3040.00	−0.0972985
$993$	0	0
$994$	1890.00	0.0603090
$995$	5232.00	0.166699
$996$	0	0
$997$	−20740.0	−0.658819	−0.329409	−	0.944187i	$-0.606850\pi$
$997$	−20740.0	−0.658819	−0.329409	+	0.944187i	$0.606850\pi$
$998$	19208.0	0.609237
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.4.a.b.1.1		1
3.2	odd	2		154.4.a.e.1.1	✓	1
12.11	even	2		1232.4.a.b.1.1		1
21.20	even	2		1078.4.a.e.1.1		1
33.32	even	2		1694.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.4.a.e.1.1	✓	1	3.2	odd	2
1078.4.a.e.1.1		1	21.20	even	2
1232.4.a.b.1.1		1	12.11	even	2
1386.4.a.b.1.1		1	1.1	even	1	trivial
1694.4.a.d.1.1		1	33.32	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1386.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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