LMFDB - Embedded newform 153.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(1,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("153.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.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:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	153.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -7.00000 q^{4} +20.0000 q^{5} -2.00000 q^{7} -15.0000 q^{8} +O(q^{10})$

\(q+1.00000 q^{2} -7.00000 q^{4} +20.0000 q^{5} -2.00000 q^{7} -15.0000 q^{8} +20.0000 q^{10} +48.0000 q^{11} -14.0000 q^{13} -2.00000 q^{14} +41.0000 q^{16} +17.0000 q^{17} +92.0000 q^{19} -140.000 q^{20} +48.0000 q^{22} +122.000 q^{23} +275.000 q^{25} -14.0000 q^{26} +14.0000 q^{28} +36.0000 q^{29} -182.000 q^{31} +161.000 q^{32} +17.0000 q^{34} -40.0000 q^{35} +76.0000 q^{37} +92.0000 q^{38} -300.000 q^{40} -294.000 q^{41} -428.000 q^{43} -336.000 q^{44} +122.000 q^{46} +12.0000 q^{47} -339.000 q^{49} +275.000 q^{50} +98.0000 q^{52} +234.000 q^{53} +960.000 q^{55} +30.0000 q^{56} +36.0000 q^{58} +540.000 q^{59} -820.000 q^{61} -182.000 q^{62} -167.000 q^{64} -280.000 q^{65} +700.000 q^{67} -119.000 q^{68} -40.0000 q^{70} -794.000 q^{71} -1038.00 q^{73} +76.0000 q^{74} -644.000 q^{76} -96.0000 q^{77} +858.000 q^{79} +820.000 q^{80} -294.000 q^{82} -1052.00 q^{83} +340.000 q^{85} -428.000 q^{86} -720.000 q^{88} -1102.00 q^{89} +28.0000 q^{91} -854.000 q^{92} +12.0000 q^{94} +1840.00 q^{95} +710.000 q^{97} -339.000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.353553	0.176777	−	0.984251i	$-0.443433\pi$
$2$	1.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	0	0
$3$	0	0
$4$	−7.00000	−0.875000
$5$	20.0000	1.78885	0.894427	−	0.447214i	$-0.147584\pi$
$5$	20.0000	1.78885	0.894427	+	0.447214i	$0.147584\pi$
$6$	0	0
$7$	−2.00000	−0.107990	−0.0539949	−	0.998541i	$-0.517195\pi$
$7$	−2.00000	−0.107990	−0.0539949	+	0.998541i	$0.517195\pi$
$8$	−15.0000	−0.662913
$9$	0	0
$10$	20.0000	0.632456
$11$	48.0000	1.31569	0.657843	−	0.753155i	$-0.271469\pi$
$11$	48.0000	1.31569	0.657843	+	0.753155i	$0.271469\pi$
$12$	0	0
$13$	−14.0000	−0.298685	−0.149342	−	0.988786i	$-0.547716\pi$
$13$	−14.0000	−0.298685	−0.149342	+	0.988786i	$0.547716\pi$
$14$	−2.00000	−0.0381802
$15$	0	0
$16$	41.0000	0.640625
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	0	0
$19$	92.0000	1.11086	0.555428	−	0.831565i	$-0.312555\pi$
$19$	92.0000	1.11086	0.555428	+	0.831565i	$0.312555\pi$
$20$	−140.000	−1.56525
$21$	0	0
$22$	48.0000	0.465165
$23$	122.000	1.10603	0.553016	−	0.833170i	$-0.313477\pi$
$23$	122.000	1.10603	0.553016	+	0.833170i	$0.313477\pi$
$24$	0	0
$25$	275.000	2.20000
$26$	−14.0000	−0.105601
$27$	0	0
$28$	14.0000	0.0944911
$29$	36.0000	0.230518	0.115259	−	0.993335i	$-0.463230\pi$
$29$	36.0000	0.230518	0.115259	+	0.993335i	$0.463230\pi$
$30$	0	0
$31$	−182.000	−1.05446	−0.527228	−	0.849724i	$-0.676769\pi$
$31$	−182.000	−1.05446	−0.527228	+	0.849724i	$0.676769\pi$
$32$	161.000	0.889408
$33$	0	0
$34$	17.0000	0.0857493
$35$	−40.0000	−0.193178
$36$	0	0
$37$	76.0000	0.337684	0.168842	−	0.985643i	$-0.445997\pi$
$37$	76.0000	0.337684	0.168842	+	0.985643i	$0.445997\pi$
$38$	92.0000	0.392747
$39$	0	0
$40$	−300.000	−1.18585
$41$	−294.000	−1.11988	−0.559940	−	0.828533i	$-0.689176\pi$
$41$	−294.000	−1.11988	−0.559940	+	0.828533i	$0.689176\pi$
$42$	0	0
$43$	−428.000	−1.51789	−0.758946	−	0.651153i	$-0.774286\pi$
$43$	−428.000	−1.51789	−0.758946	+	0.651153i	$0.774286\pi$
$44$	−336.000	−1.15123
$45$	0	0
$46$	122.000	0.391042
$47$	12.0000	0.0372421	0.0186211	−	0.999827i	$-0.494072\pi$
$47$	12.0000	0.0372421	0.0186211	+	0.999827i	$0.494072\pi$
$48$	0	0
$49$	−339.000	−0.988338
$50$	275.000	0.777817
$51$	0	0
$52$	98.0000	0.261349
$53$	234.000	0.606460	0.303230	−	0.952917i	$-0.401935\pi$
$53$	234.000	0.606460	0.303230	+	0.952917i	$0.401935\pi$
$54$	0	0
$55$	960.000	2.35357
$56$	30.0000	0.0715878
$57$	0	0
$58$	36.0000	0.0815005
$59$	540.000	1.19156	0.595780	−	0.803148i	$-0.296843\pi$
$59$	540.000	1.19156	0.595780	+	0.803148i	$0.296843\pi$
$60$	0	0
$61$	−820.000	−1.72115	−0.860576	−	0.509322i	$-0.829896\pi$
$61$	−820.000	−1.72115	−0.860576	+	0.509322i	$0.829896\pi$
$62$	−182.000	−0.372807
$63$	0	0
$64$	−167.000	−0.326172
$65$	−280.000	−0.534303
$66$	0	0
$67$	700.000	1.27640	0.638199	−	0.769872i	$-0.279680\pi$
$67$	700.000	1.27640	0.638199	+	0.769872i	$0.279680\pi$
$68$	−119.000	−0.212219
$69$	0	0
$70$	−40.0000	−0.0682988
$71$	−794.000	−1.32719	−0.663595	−	0.748092i	$-0.730970\pi$
$71$	−794.000	−1.32719	−0.663595	+	0.748092i	$0.730970\pi$
$72$	0	0
$73$	−1038.00	−1.66423	−0.832114	−	0.554604i	$-0.812870\pi$
$73$	−1038.00	−1.66423	−0.832114	+	0.554604i	$0.812870\pi$
$74$	76.0000	0.119389
$75$	0	0
$76$	−644.000	−0.971998
$77$	−96.0000	−0.142081
$78$	0	0
$79$	858.000	1.22193	0.610965	−	0.791657i	$-0.290781\pi$
$79$	858.000	1.22193	0.610965	+	0.791657i	$0.290781\pi$
$80$	820.000	1.14598
$81$	0	0
$82$	−294.000	−0.395937
$83$	−1052.00	−1.39123	−0.695614	−	0.718415i	$-0.744868\pi$
$83$	−1052.00	−1.39123	−0.695614	+	0.718415i	$0.744868\pi$
$84$	0	0
$85$	340.000	0.433861
$86$	−428.000	−0.536656
$87$	0	0
$88$	−720.000	−0.872185
$89$	−1102.00	−1.31249	−0.656246	−	0.754547i	$-0.727857\pi$
$89$	−1102.00	−1.31249	−0.656246	+	0.754547i	$0.727857\pi$
$90$	0	0
$91$	28.0000	0.0322549
$92$	−854.000	−0.967779
$93$	0	0
$94$	12.0000	0.0131671
$95$	1840.00	1.98716
$96$	0	0
$97$	710.000	0.743192	0.371596	−	0.928395i	$-0.378811\pi$
$97$	710.000	0.743192	0.371596	+	0.928395i	$0.378811\pi$
$98$	−339.000	−0.349430
$99$	0	0
$100$	−1925.00	−1.92500
$101$	1210.00	1.19207	0.596037	−	0.802957i	$-0.296741\pi$
$101$	1210.00	1.19207	0.596037	+	0.802957i	$0.296741\pi$
$102$	0	0
$103$	644.000	0.616070	0.308035	−	0.951375i	$-0.400329\pi$
$103$	644.000	0.616070	0.308035	+	0.951375i	$0.400329\pi$
$104$	210.000	0.198002
$105$	0	0
$106$	234.000	0.214416
$107$	256.000	0.231294	0.115647	−	0.993290i	$-0.463106\pi$
$107$	256.000	0.231294	0.115647	+	0.993290i	$0.463106\pi$
$108$	0	0
$109$	−1248.00	−1.09667	−0.548334	−	0.836260i	$-0.684738\pi$
$109$	−1248.00	−1.09667	−0.548334	+	0.836260i	$0.684738\pi$
$110$	960.000	0.832113
$111$	0	0
$112$	−82.0000	−0.0691810
$113$	350.000	0.291374	0.145687	−	0.989331i	$-0.453461\pi$
$113$	350.000	0.291374	0.145687	+	0.989331i	$0.453461\pi$
$114$	0	0
$115$	2440.00	1.97853
$116$	−252.000	−0.201704
$117$	0	0
$118$	540.000	0.421280
$119$	−34.0000	−0.0261914
$120$	0	0
$121$	973.000	0.731029
$122$	−820.000	−0.608519
$123$	0	0
$124$	1274.00	0.922650
$125$	3000.00	2.14663
$126$	0	0
$127$	−328.000	−0.229176	−0.114588	−	0.993413i	$-0.536555\pi$
$127$	−328.000	−0.229176	−0.114588	+	0.993413i	$0.536555\pi$
$128$	−1455.00	−1.00473
$129$	0	0
$130$	−280.000	−0.188905
$131$	1952.00	1.30189	0.650943	−	0.759127i	$-0.274374\pi$
$131$	1952.00	1.30189	0.650943	+	0.759127i	$0.274374\pi$
$132$	0	0
$133$	−184.000	−0.119961
$134$	700.000	0.451275
$135$	0	0
$136$	−255.000	−0.160780
$137$	−2634.00	−1.64261	−0.821306	−	0.570488i	$-0.806754\pi$
$137$	−2634.00	−1.64261	−0.821306	+	0.570488i	$0.806754\pi$
$138$	0	0
$139$	1864.00	1.13743	0.568714	−	0.822536i	$-0.307441\pi$
$139$	1864.00	1.13743	0.568714	+	0.822536i	$0.307441\pi$
$140$	280.000	0.169031
$141$	0	0
$142$	−794.000	−0.469232
$143$	−672.000	−0.392975
$144$	0	0
$145$	720.000	0.412364
$146$	−1038.00	−0.588394
$147$	0	0
$148$	−532.000	−0.295474
$149$	286.000	0.157249	0.0786243	−	0.996904i	$-0.474947\pi$
$149$	286.000	0.157249	0.0786243	+	0.996904i	$0.474947\pi$
$150$	0	0
$151$	−1624.00	−0.875227	−0.437613	−	0.899163i	$-0.644176\pi$
$151$	−1624.00	−0.875227	−0.437613	+	0.899163i	$0.644176\pi$
$152$	−1380.00	−0.736400
$153$	0	0
$154$	−96.0000	−0.0502331
$155$	−3640.00	−1.88627
$156$	0	0
$157$	2542.00	1.29219	0.646095	−	0.763257i	$-0.276401\pi$
$157$	2542.00	1.29219	0.646095	+	0.763257i	$0.276401\pi$
$158$	858.000	0.432018
$159$	0	0
$160$	3220.00	1.59102
$161$	−244.000	−0.119440
$162$	0	0
$163$	684.000	0.328681	0.164341	−	0.986404i	$-0.447450\pi$
$163$	684.000	0.328681	0.164341	+	0.986404i	$0.447450\pi$
$164$	2058.00	0.979895
$165$	0	0
$166$	−1052.00	−0.491874
$167$	−542.000	−0.251145	−0.125573	−	0.992084i	$-0.540077\pi$
$167$	−542.000	−0.251145	−0.125573	+	0.992084i	$0.540077\pi$
$168$	0	0
$169$	−2001.00	−0.910787
$170$	340.000	0.153393
$171$	0	0
$172$	2996.00	1.32816
$173$	836.000	0.367398	0.183699	−	0.982983i	$-0.441193\pi$
$173$	836.000	0.367398	0.183699	+	0.982983i	$0.441193\pi$
$174$	0	0
$175$	−550.000	−0.237578
$176$	1968.00	0.842861
$177$	0	0
$178$	−1102.00	−0.464036
$179$	3444.00	1.43808	0.719041	−	0.694968i	$-0.244581\pi$
$179$	3444.00	1.43808	0.719041	+	0.694968i	$0.244581\pi$
$180$	0	0
$181$	−3284.00	−1.34861	−0.674303	−	0.738454i	$-0.735556\pi$
$181$	−3284.00	−1.34861	−0.674303	+	0.738454i	$0.735556\pi$
$182$	28.0000	0.0114038
$183$	0	0
$184$	−1830.00	−0.733203
$185$	1520.00	0.604068
$186$	0	0
$187$	816.000	0.319101
$188$	−84.0000	−0.0325869
$189$	0	0
$190$	1840.00	0.702566
$191$	340.000	0.128804	0.0644019	−	0.997924i	$-0.479486\pi$
$191$	340.000	0.128804	0.0644019	+	0.997924i	$0.479486\pi$
$192$	0	0
$193$	−1498.00	−0.558696	−0.279348	−	0.960190i	$-0.590118\pi$
$193$	−1498.00	−0.558696	−0.279348	+	0.960190i	$0.590118\pi$
$194$	710.000	0.262758
$195$	0	0
$196$	2373.00	0.864796
$197$	1176.00	0.425312	0.212656	−	0.977127i	$-0.431789\pi$
$197$	1176.00	0.425312	0.212656	+	0.977127i	$0.431789\pi$
$198$	0	0
$199$	−2450.00	−0.872743	−0.436372	−	0.899767i	$-0.643737\pi$
$199$	−2450.00	−0.872743	−0.436372	+	0.899767i	$0.643737\pi$
$200$	−4125.00	−1.45841
$201$	0	0
$202$	1210.00	0.421462
$203$	−72.0000	−0.0248936
$204$	0	0
$205$	−5880.00	−2.00330
$206$	644.000	0.217814
$207$	0	0
$208$	−574.000	−0.191345
$209$	4416.00	1.46154
$210$	0	0
$211$	1064.00	0.347151	0.173575	−	0.984821i	$-0.444468\pi$
$211$	1064.00	0.347151	0.173575	+	0.984821i	$0.444468\pi$
$212$	−1638.00	−0.530652
$213$	0	0
$214$	256.000	0.0817748
$215$	−8560.00	−2.71529
$216$	0	0
$217$	364.000	0.113871
$218$	−1248.00	−0.387730
$219$	0	0
$220$	−6720.00	−2.05937
$221$	−238.000	−0.0724417
$222$	0	0
$223$	−2244.00	−0.673854	−0.336927	−	0.941531i	$-0.609387\pi$
$223$	−2244.00	−0.673854	−0.336927	+	0.941531i	$0.609387\pi$
$224$	−322.000	−0.0960470
$225$	0	0
$226$	350.000	0.103016
$227$	−516.000	−0.150873	−0.0754364	−	0.997151i	$-0.524035\pi$
$227$	−516.000	−0.150873	−0.0754364	+	0.997151i	$0.524035\pi$
$228$	0	0
$229$	−2922.00	−0.843193	−0.421596	−	0.906784i	$-0.638530\pi$
$229$	−2922.00	−0.843193	−0.421596	+	0.906784i	$0.638530\pi$
$230$	2440.00	0.699517
$231$	0	0
$232$	−540.000	−0.152814
$233$	−3114.00	−0.875558	−0.437779	−	0.899083i	$-0.644235\pi$
$233$	−3114.00	−0.875558	−0.437779	+	0.899083i	$0.644235\pi$
$234$	0	0
$235$	240.000	0.0666207
$236$	−3780.00	−1.04261
$237$	0	0
$238$	−34.0000	−0.00926005
$239$	−4124.00	−1.11615	−0.558074	−	0.829791i	$-0.688459\pi$
$239$	−4124.00	−1.11615	−0.558074	+	0.829791i	$0.688459\pi$
$240$	0	0
$241$	−2034.00	−0.543658	−0.271829	−	0.962346i	$-0.587628\pi$
$241$	−2034.00	−0.543658	−0.271829	+	0.962346i	$0.587628\pi$
$242$	973.000	0.258458
$243$	0	0
$244$	5740.00	1.50601
$245$	−6780.00	−1.76799
$246$	0	0
$247$	−1288.00	−0.331795
$248$	2730.00	0.699013
$249$	0	0
$250$	3000.00	0.758947
$251$	−996.000	−0.250466	−0.125233	−	0.992127i	$-0.539968\pi$
$251$	−996.000	−0.250466	−0.125233	+	0.992127i	$0.539968\pi$
$252$	0	0
$253$	5856.00	1.45519
$254$	−328.000	−0.0810258
$255$	0	0
$256$	−119.000	−0.0290527
$257$	3246.00	0.787860	0.393930	−	0.919141i	$-0.371115\pi$
$257$	3246.00	0.787860	0.393930	+	0.919141i	$0.371115\pi$
$258$	0	0
$259$	−152.000	−0.0364665
$260$	1960.00	0.467516
$261$	0	0
$262$	1952.00	0.460286
$263$	−932.000	−0.218516	−0.109258	−	0.994013i	$-0.534847\pi$
$263$	−932.000	−0.218516	−0.109258	+	0.994013i	$0.534847\pi$
$264$	0	0
$265$	4680.00	1.08487
$266$	−184.000	−0.0424126
$267$	0	0
$268$	−4900.00	−1.11685
$269$	3884.00	0.880341	0.440170	−	0.897914i	$-0.354918\pi$
$269$	3884.00	0.880341	0.440170	+	0.897914i	$0.354918\pi$
$270$	0	0
$271$	−1936.00	−0.433962	−0.216981	−	0.976176i	$-0.569621\pi$
$271$	−1936.00	−0.433962	−0.216981	+	0.976176i	$0.569621\pi$
$272$	697.000	0.155374
$273$	0	0
$274$	−2634.00	−0.580751
$275$	13200.0	2.89451
$276$	0	0
$277$	872.000	0.189146	0.0945729	−	0.995518i	$-0.469851\pi$
$277$	872.000	0.189146	0.0945729	+	0.995518i	$0.469851\pi$
$278$	1864.00	0.402141
$279$	0	0
$280$	600.000	0.128060
$281$	−3198.00	−0.678921	−0.339460	−	0.940620i	$-0.610244\pi$
$281$	−3198.00	−0.678921	−0.339460	+	0.940620i	$0.610244\pi$
$282$	0	0
$283$	−1936.00	−0.406655	−0.203327	−	0.979111i	$-0.565176\pi$
$283$	−1936.00	−0.406655	−0.203327	+	0.979111i	$0.565176\pi$
$284$	5558.00	1.16129
$285$	0	0
$286$	−672.000	−0.138938
$287$	588.000	0.120936
$288$	0	0
$289$	289.000	0.0588235
$290$	720.000	0.145793
$291$	0	0
$292$	7266.00	1.45620
$293$	5718.00	1.14010	0.570050	−	0.821610i	$-0.306924\pi$
$293$	5718.00	1.14010	0.570050	+	0.821610i	$0.306924\pi$
$294$	0	0
$295$	10800.0	2.13153
$296$	−1140.00	−0.223855
$297$	0	0
$298$	286.000	0.0555958
$299$	−1708.00	−0.330355
$300$	0	0
$301$	856.000	0.163917
$302$	−1624.00	−0.309439
$303$	0	0
$304$	3772.00	0.711642
$305$	−16400.0	−3.07889
$306$	0	0
$307$	684.000	0.127159	0.0635797	−	0.997977i	$-0.479748\pi$
$307$	684.000	0.127159	0.0635797	+	0.997977i	$0.479748\pi$
$308$	672.000	0.124321
$309$	0	0
$310$	−3640.00	−0.666897
$311$	290.000	0.0528759	0.0264379	−	0.999650i	$-0.491584\pi$
$311$	290.000	0.0528759	0.0264379	+	0.999650i	$0.491584\pi$
$312$	0	0
$313$	−11050.0	−1.99547	−0.997736	−	0.0672478i	$-0.978578\pi$
$313$	−11050.0	−1.99547	−0.997736	+	0.0672478i	$0.978578\pi$
$314$	2542.00	0.456858
$315$	0	0
$316$	−6006.00	−1.06919
$317$	−992.000	−0.175761	−0.0878806	−	0.996131i	$-0.528009\pi$
$317$	−992.000	−0.175761	−0.0878806	+	0.996131i	$0.528009\pi$
$318$	0	0
$319$	1728.00	0.303290
$320$	−3340.00	−0.583474
$321$	0	0
$322$	−244.000	−0.0422285
$323$	1564.00	0.269422
$324$	0	0
$325$	−3850.00	−0.657106
$326$	684.000	0.116206
$327$	0	0
$328$	4410.00	0.742383
$329$	−24.0000	−0.00402177
$330$	0	0
$331$	2860.00	0.474924	0.237462	−	0.971397i	$-0.423684\pi$
$331$	2860.00	0.474924	0.237462	+	0.971397i	$0.423684\pi$
$332$	7364.00	1.21733
$333$	0	0
$334$	−542.000	−0.0887932
$335$	14000.0	2.28329
$336$	0	0
$337$	6298.00	1.01802	0.509012	−	0.860760i	$-0.330011\pi$
$337$	6298.00	1.01802	0.509012	+	0.860760i	$0.330011\pi$
$338$	−2001.00	−0.322012
$339$	0	0
$340$	−2380.00	−0.379628
$341$	−8736.00	−1.38733
$342$	0	0
$343$	1364.00	0.214720
$344$	6420.00	1.00623
$345$	0	0
$346$	836.000	0.129895
$347$	3508.00	0.542707	0.271353	−	0.962480i	$-0.412529\pi$
$347$	3508.00	0.542707	0.271353	+	0.962480i	$0.412529\pi$
$348$	0	0
$349$	−2406.00	−0.369026	−0.184513	−	0.982830i	$-0.559071\pi$
$349$	−2406.00	−0.369026	−0.184513	+	0.982830i	$0.559071\pi$
$350$	−550.000	−0.0839964
$351$	0	0
$352$	7728.00	1.17018
$353$	1842.00	0.277733	0.138867	−	0.990311i	$-0.455654\pi$
$353$	1842.00	0.277733	0.138867	+	0.990311i	$0.455654\pi$
$354$	0	0
$355$	−15880.0	−2.37415
$356$	7714.00	1.14843
$357$	0	0
$358$	3444.00	0.508439
$359$	−3264.00	−0.479853	−0.239927	−	0.970791i	$-0.577123\pi$
$359$	−3264.00	−0.479853	−0.239927	+	0.970791i	$0.577123\pi$
$360$	0	0
$361$	1605.00	0.233999
$362$	−3284.00	−0.476804
$363$	0	0
$364$	−196.000	−0.0282231
$365$	−20760.0	−2.97706
$366$	0	0
$367$	7354.00	1.04598	0.522991	−	0.852338i	$-0.324816\pi$
$367$	7354.00	1.04598	0.522991	+	0.852338i	$0.324816\pi$
$368$	5002.00	0.708552
$369$	0	0
$370$	1520.00	0.213570
$371$	−468.000	−0.0654915
$372$	0	0
$373$	11322.0	1.57166	0.785832	−	0.618440i	$-0.212235\pi$
$373$	11322.0	1.57166	0.785832	+	0.618440i	$0.212235\pi$
$374$	816.000	0.112819
$375$	0	0
$376$	−180.000	−0.0246883
$377$	−504.000	−0.0688523
$378$	0	0
$379$	12796.0	1.73426	0.867132	−	0.498078i	$-0.165961\pi$
$379$	12796.0	1.73426	0.867132	+	0.498078i	$0.165961\pi$
$380$	−12880.0	−1.73876
$381$	0	0
$382$	340.000	0.0455390
$383$	420.000	0.0560339	0.0280170	−	0.999607i	$-0.491081\pi$
$383$	420.000	0.0560339	0.0280170	+	0.999607i	$0.491081\pi$
$384$	0	0
$385$	−1920.00	−0.254162
$386$	−1498.00	−0.197529
$387$	0	0
$388$	−4970.00	−0.650293
$389$	−6426.00	−0.837561	−0.418780	−	0.908088i	$-0.637542\pi$
$389$	−6426.00	−0.837561	−0.418780	+	0.908088i	$0.637542\pi$
$390$	0	0
$391$	2074.00	0.268252
$392$	5085.00	0.655182
$393$	0	0
$394$	1176.00	0.150371
$395$	17160.0	2.18586
$396$	0	0
$397$	−13212.0	−1.67026	−0.835128	−	0.550056i	$-0.814606\pi$
$397$	−13212.0	−1.67026	−0.835128	+	0.550056i	$0.814606\pi$
$398$	−2450.00	−0.308561
$399$	0	0
$400$	11275.0	1.40938
$401$	6242.00	0.777333	0.388667	−	0.921378i	$-0.372936\pi$
$401$	6242.00	0.777333	0.388667	+	0.921378i	$0.372936\pi$
$402$	0	0
$403$	2548.00	0.314950
$404$	−8470.00	−1.04306
$405$	0	0
$406$	−72.0000	−0.00880123
$407$	3648.00	0.444287
$408$	0	0
$409$	−5194.00	−0.627938	−0.313969	−	0.949433i	$-0.601659\pi$
$409$	−5194.00	−0.627938	−0.313969	+	0.949433i	$0.601659\pi$
$410$	−5880.00	−0.708274
$411$	0	0
$412$	−4508.00	−0.539061
$413$	−1080.00	−0.128676
$414$	0	0
$415$	−21040.0	−2.48871
$416$	−2254.00	−0.265653
$417$	0	0
$418$	4416.00	0.516731
$419$	−15956.0	−1.86039	−0.930193	−	0.367071i	$-0.880361\pi$
$419$	−15956.0	−1.86039	−0.930193	+	0.367071i	$0.880361\pi$
$420$	0	0
$421$	−15254.0	−1.76588	−0.882939	−	0.469488i	$-0.844438\pi$
$421$	−15254.0	−1.76588	−0.882939	+	0.469488i	$0.844438\pi$
$422$	1064.00	0.122736
$423$	0	0
$424$	−3510.00	−0.402030
$425$	4675.00	0.533578
$426$	0	0
$427$	1640.00	0.185867
$428$	−1792.00	−0.202382
$429$	0	0
$430$	−8560.00	−0.960000
$431$	5538.00	0.618924	0.309462	−	0.950912i	$-0.399851\pi$
$431$	5538.00	0.618924	0.309462	+	0.950912i	$0.399851\pi$
$432$	0	0
$433$	11342.0	1.25880	0.629402	−	0.777080i	$-0.283300\pi$
$433$	11342.0	1.25880	0.629402	+	0.777080i	$0.283300\pi$
$434$	364.000	0.0402594
$435$	0	0
$436$	8736.00	0.959584
$437$	11224.0	1.22864
$438$	0	0
$439$	982.000	0.106762	0.0533808	−	0.998574i	$-0.483000\pi$
$439$	982.000	0.106762	0.0533808	+	0.998574i	$0.483000\pi$
$440$	−14400.0	−1.56021
$441$	0	0
$442$	−238.000	−0.0256120
$443$	2492.00	0.267265	0.133633	−	0.991031i	$-0.457336\pi$
$443$	2492.00	0.267265	0.133633	+	0.991031i	$0.457336\pi$
$444$	0	0
$445$	−22040.0	−2.34786
$446$	−2244.00	−0.238243
$447$	0	0
$448$	334.000	0.0352233
$449$	5498.00	0.577877	0.288938	−	0.957348i	$-0.406698\pi$
$449$	5498.00	0.577877	0.288938	+	0.957348i	$0.406698\pi$
$450$	0	0
$451$	−14112.0	−1.47341
$452$	−2450.00	−0.254952
$453$	0	0
$454$	−516.000	−0.0533416
$455$	560.000	0.0576994
$456$	0	0
$457$	4998.00	0.511590	0.255795	−	0.966731i	$-0.417663\pi$
$457$	4998.00	0.511590	0.255795	+	0.966731i	$0.417663\pi$
$458$	−2922.00	−0.298114
$459$	0	0
$460$	−17080.0	−1.73122
$461$	7586.00	0.766411	0.383205	−	0.923663i	$-0.374820\pi$
$461$	7586.00	0.766411	0.383205	+	0.923663i	$0.374820\pi$
$462$	0	0
$463$	5900.00	0.592217	0.296108	−	0.955154i	$-0.404311\pi$
$463$	5900.00	0.592217	0.296108	+	0.955154i	$0.404311\pi$
$464$	1476.00	0.147676
$465$	0	0
$466$	−3114.00	−0.309556
$467$	19404.0	1.92272	0.961360	−	0.275295i	$-0.0887755\pi$
$467$	19404.0	1.92272	0.961360	+	0.275295i	$0.0887755\pi$
$468$	0	0
$469$	−1400.00	−0.137838
$470$	240.000	0.0235540
$471$	0	0
$472$	−8100.00	−0.789900
$473$	−20544.0	−1.99707
$474$	0	0
$475$	25300.0	2.44388
$476$	238.000	0.0229175
$477$	0	0
$478$	−4124.00	−0.394618
$479$	−2586.00	−0.246675	−0.123338	−	0.992365i	$-0.539360\pi$
$479$	−2586.00	−0.246675	−0.123338	+	0.992365i	$0.539360\pi$
$480$	0	0
$481$	−1064.00	−0.100861
$482$	−2034.00	−0.192212
$483$	0	0
$484$	−6811.00	−0.639651
$485$	14200.0	1.32946
$486$	0	0
$487$	10106.0	0.940342	0.470171	−	0.882575i	$-0.344192\pi$
$487$	10106.0	0.940342	0.470171	+	0.882575i	$0.344192\pi$
$488$	12300.0	1.14097
$489$	0	0
$490$	−6780.00	−0.625080
$491$	76.0000	0.00698540	0.00349270	−	0.999994i	$-0.498888\pi$
$491$	76.0000	0.00698540	0.00349270	+	0.999994i	$0.498888\pi$
$492$	0	0
$493$	612.000	0.0559089
$494$	−1288.00	−0.117307
$495$	0	0
$496$	−7462.00	−0.675511
$497$	1588.00	0.143323
$498$	0	0
$499$	8096.00	0.726306	0.363153	−	0.931730i	$-0.381700\pi$
$499$	8096.00	0.726306	0.363153	+	0.931730i	$0.381700\pi$
$500$	−21000.0	−1.87830
$501$	0	0
$502$	−996.000	−0.0885531
$503$	−15942.0	−1.41316	−0.706579	−	0.707634i	$-0.749763\pi$
$503$	−15942.0	−1.41316	−0.706579	+	0.707634i	$0.749763\pi$
$504$	0	0
$505$	24200.0	2.13245
$506$	5856.00	0.514488
$507$	0	0
$508$	2296.00	0.200529
$509$	13742.0	1.19667	0.598333	−	0.801247i	$-0.295830\pi$
$509$	13742.0	1.19667	0.598333	+	0.801247i	$0.295830\pi$
$510$	0	0
$511$	2076.00	0.179720
$512$	11521.0	0.994455
$513$	0	0
$514$	3246.00	0.278550
$515$	12880.0	1.10206
$516$	0	0
$517$	576.000	0.0489989
$518$	−152.000	−0.0128929
$519$	0	0
$520$	4200.00	0.354197
$521$	−11942.0	−1.00420	−0.502100	−	0.864809i	$-0.667439\pi$
$521$	−11942.0	−1.00420	−0.502100	+	0.864809i	$0.667439\pi$
$522$	0	0
$523$	−6012.00	−0.502651	−0.251325	−	0.967903i	$-0.580866\pi$
$523$	−6012.00	−0.502651	−0.251325	+	0.967903i	$0.580866\pi$
$524$	−13664.0	−1.13915
$525$	0	0
$526$	−932.000	−0.0772569
$527$	−3094.00	−0.255743
$528$	0	0
$529$	2717.00	0.223309
$530$	4680.00	0.383559
$531$	0	0
$532$	1288.00	0.104966
$533$	4116.00	0.334491
$534$	0	0
$535$	5120.00	0.413751
$536$	−10500.0	−0.846140
$537$	0	0
$538$	3884.00	0.311247
$539$	−16272.0	−1.30034
$540$	0	0
$541$	6420.00	0.510198	0.255099	−	0.966915i	$-0.417892\pi$
$541$	6420.00	0.510198	0.255099	+	0.966915i	$0.417892\pi$
$542$	−1936.00	−0.153429
$543$	0	0
$544$	2737.00	0.215713
$545$	−24960.0	−1.96178
$546$	0	0
$547$	1576.00	0.123190	0.0615950	−	0.998101i	$-0.480381\pi$
$547$	1576.00	0.123190	0.0615950	+	0.998101i	$0.480381\pi$
$548$	18438.0	1.43729
$549$	0	0
$550$	13200.0	1.02336
$551$	3312.00	0.256072
$552$	0	0
$553$	−1716.00	−0.131956
$554$	872.000	0.0668732
$555$	0	0
$556$	−13048.0	−0.995249
$557$	−15318.0	−1.16525	−0.582625	−	0.812741i	$-0.697974\pi$
$557$	−15318.0	−1.16525	−0.582625	+	0.812741i	$0.697974\pi$
$558$	0	0
$559$	5992.00	0.453371
$560$	−1640.00	−0.123755
$561$	0	0
$562$	−3198.00	−0.240035
$563$	−13220.0	−0.989621	−0.494810	−	0.869001i	$-0.664763\pi$
$563$	−13220.0	−0.989621	−0.494810	+	0.869001i	$0.664763\pi$
$564$	0	0
$565$	7000.00	0.521225
$566$	−1936.00	−0.143774
$567$	0	0
$568$	11910.0	0.879811
$569$	−2794.00	−0.205853	−0.102927	−	0.994689i	$-0.532821\pi$
$569$	−2794.00	−0.205853	−0.102927	+	0.994689i	$0.532821\pi$
$570$	0	0
$571$	−14756.0	−1.08147	−0.540735	−	0.841193i	$-0.681854\pi$
$571$	−14756.0	−1.08147	−0.540735	+	0.841193i	$0.681854\pi$
$572$	4704.00	0.343853
$573$	0	0
$574$	588.000	0.0427572
$575$	33550.0	2.43327
$576$	0	0
$577$	−2846.00	−0.205339	−0.102669	−	0.994716i	$-0.532738\pi$
$577$	−2846.00	−0.205339	−0.102669	+	0.994716i	$0.532738\pi$
$578$	289.000	0.0207973
$579$	0	0
$580$	−5040.00	−0.360818
$581$	2104.00	0.150239
$582$	0	0
$583$	11232.0	0.797911
$584$	15570.0	1.10324
$585$	0	0
$586$	5718.00	0.403086
$587$	16820.0	1.18268	0.591342	−	0.806421i	$-0.298598\pi$
$587$	16820.0	1.18268	0.591342	+	0.806421i	$0.298598\pi$
$588$	0	0
$589$	−16744.0	−1.17135
$590$	10800.0	0.753608
$591$	0	0
$592$	3116.00	0.216329
$593$	−13314.0	−0.921991	−0.460995	−	0.887403i	$-0.652508\pi$
$593$	−13314.0	−0.921991	−0.460995	+	0.887403i	$0.652508\pi$
$594$	0	0
$595$	−680.000	−0.0468526
$596$	−2002.00	−0.137592
$597$	0	0
$598$	−1708.00	−0.116798
$599$	−2880.00	−0.196450	−0.0982250	−	0.995164i	$-0.531317\pi$
$599$	−2880.00	−0.196450	−0.0982250	+	0.995164i	$0.531317\pi$
$600$	0	0
$601$	−24854.0	−1.68688	−0.843441	−	0.537222i	$-0.819474\pi$
$601$	−24854.0	−1.68688	−0.843441	+	0.537222i	$0.819474\pi$
$602$	856.000	0.0579534
$603$	0	0
$604$	11368.0	0.765823
$605$	19460.0	1.30770
$606$	0	0
$607$	6122.00	0.409365	0.204682	−	0.978828i	$-0.434384\pi$
$607$	6122.00	0.409365	0.204682	+	0.978828i	$0.434384\pi$
$608$	14812.0	0.988003
$609$	0	0
$610$	−16400.0	−1.08855
$611$	−168.000	−0.0111237
$612$	0	0
$613$	17398.0	1.14633	0.573164	−	0.819441i	$-0.305716\pi$
$613$	17398.0	1.14633	0.573164	+	0.819441i	$0.305716\pi$
$614$	684.000	0.0449576
$615$	0	0
$616$	1440.00	0.0941871
$617$	−2922.00	−0.190657	−0.0953284	−	0.995446i	$-0.530390\pi$
$617$	−2922.00	−0.190657	−0.0953284	+	0.995446i	$0.530390\pi$
$618$	0	0
$619$	9660.00	0.627251	0.313625	−	0.949547i	$-0.398456\pi$
$619$	9660.00	0.627251	0.313625	+	0.949547i	$0.398456\pi$
$620$	25480.0	1.65049
$621$	0	0
$622$	290.000	0.0186944
$623$	2204.00	0.141736
$624$	0	0
$625$	25625.0	1.64000
$626$	−11050.0	−0.705506
$627$	0	0
$628$	−17794.0	−1.13067
$629$	1292.00	0.0819005
$630$	0	0
$631$	2788.00	0.175893	0.0879465	−	0.996125i	$-0.471970\pi$
$631$	2788.00	0.175893	0.0879465	+	0.996125i	$0.471970\pi$
$632$	−12870.0	−0.810033
$633$	0	0
$634$	−992.000	−0.0621409
$635$	−6560.00	−0.409962
$636$	0	0
$637$	4746.00	0.295202
$638$	1728.00	0.107229
$639$	0	0
$640$	−29100.0	−1.79731
$641$	16290.0	1.00377	0.501885	−	0.864934i	$-0.332640\pi$
$641$	16290.0	1.00377	0.501885	+	0.864934i	$0.332640\pi$
$642$	0	0
$643$	−16588.0	−1.01737	−0.508683	−	0.860954i	$-0.669868\pi$
$643$	−16588.0	−1.01737	−0.508683	+	0.860954i	$0.669868\pi$
$644$	1708.00	0.104510
$645$	0	0
$646$	1564.00	0.0952550
$647$	−22364.0	−1.35892	−0.679459	−	0.733714i	$-0.737785\pi$
$647$	−22364.0	−1.35892	−0.679459	+	0.733714i	$0.737785\pi$
$648$	0	0
$649$	25920.0	1.56772
$650$	−3850.00	−0.232322
$651$	0	0
$652$	−4788.00	−0.287596
$653$	19356.0	1.15997	0.579984	−	0.814628i	$-0.303059\pi$
$653$	19356.0	1.15997	0.579984	+	0.814628i	$0.303059\pi$
$654$	0	0
$655$	39040.0	2.32888
$656$	−12054.0	−0.717423
$657$	0	0
$658$	−24.0000	−0.00142191
$659$	4220.00	0.249450	0.124725	−	0.992191i	$-0.460195\pi$
$659$	4220.00	0.249450	0.124725	+	0.992191i	$0.460195\pi$
$660$	0	0
$661$	−12070.0	−0.710240	−0.355120	−	0.934821i	$-0.615560\pi$
$661$	−12070.0	−0.710240	−0.355120	+	0.934821i	$0.615560\pi$
$662$	2860.00	0.167911
$663$	0	0
$664$	15780.0	0.922263
$665$	−3680.00	−0.214593
$666$	0	0
$667$	4392.00	0.254961
$668$	3794.00	0.219752
$669$	0	0
$670$	14000.0	0.807264
$671$	−39360.0	−2.26449
$672$	0	0
$673$	−5914.00	−0.338734	−0.169367	−	0.985553i	$-0.554172\pi$
$673$	−5914.00	−0.338734	−0.169367	+	0.985553i	$0.554172\pi$
$674$	6298.00	0.359926
$675$	0	0
$676$	14007.0	0.796939
$677$	27624.0	1.56821	0.784104	−	0.620630i	$-0.213123\pi$
$677$	27624.0	1.56821	0.784104	+	0.620630i	$0.213123\pi$
$678$	0	0
$679$	−1420.00	−0.0802571
$680$	−5100.00	−0.287612
$681$	0	0
$682$	−8736.00	−0.490497
$683$	−29132.0	−1.63207	−0.816036	−	0.578001i	$-0.803833\pi$
$683$	−29132.0	−1.63207	−0.816036	+	0.578001i	$0.803833\pi$
$684$	0	0
$685$	−52680.0	−2.93839
$686$	1364.00	0.0759151
$687$	0	0
$688$	−17548.0	−0.972400
$689$	−3276.00	−0.181140
$690$	0	0
$691$	−20336.0	−1.11956	−0.559781	−	0.828640i	$-0.689115\pi$
$691$	−20336.0	−1.11956	−0.559781	+	0.828640i	$0.689115\pi$
$692$	−5852.00	−0.321473
$693$	0	0
$694$	3508.00	0.191876
$695$	37280.0	2.03469
$696$	0	0
$697$	−4998.00	−0.271611
$698$	−2406.00	−0.130471
$699$	0	0
$700$	3850.00	0.207880
$701$	−17142.0	−0.923601	−0.461801	−	0.886984i	$-0.652796\pi$
$701$	−17142.0	−0.923601	−0.461801	+	0.886984i	$0.652796\pi$
$702$	0	0
$703$	6992.00	0.375118
$704$	−8016.00	−0.429140
$705$	0	0
$706$	1842.00	0.0981935
$707$	−2420.00	−0.128732
$708$	0	0
$709$	22784.0	1.20687	0.603435	−	0.797412i	$-0.293798\pi$
$709$	22784.0	1.20687	0.603435	+	0.797412i	$0.293798\pi$
$710$	−15880.0	−0.839388
$711$	0	0
$712$	16530.0	0.870067
$713$	−22204.0	−1.16626
$714$	0	0
$715$	−13440.0	−0.702976
$716$	−24108.0	−1.25832
$717$	0	0
$718$	−3264.00	−0.169654
$719$	−58.0000	−0.00300839	−0.00150420	−	0.999999i	$-0.500479\pi$
$719$	−58.0000	−0.00300839	−0.00150420	+	0.999999i	$0.500479\pi$
$720$	0	0
$721$	−1288.00	−0.0665293
$722$	1605.00	0.0827312
$723$	0	0
$724$	22988.0	1.18003
$725$	9900.00	0.507140
$726$	0	0
$727$	712.000	0.0363227	0.0181614	−	0.999835i	$-0.494219\pi$
$727$	712.000	0.0363227	0.0181614	+	0.999835i	$0.494219\pi$
$728$	−420.000	−0.0213822
$729$	0	0
$730$	−20760.0	−1.05255
$731$	−7276.00	−0.368143
$732$	0	0
$733$	23050.0	1.16149	0.580744	−	0.814086i	$-0.302762\pi$
$733$	23050.0	1.16149	0.580744	+	0.814086i	$0.302762\pi$
$734$	7354.00	0.369811
$735$	0	0
$736$	19642.0	0.983714
$737$	33600.0	1.67934
$738$	0	0
$739$	−38708.0	−1.92679	−0.963394	−	0.268088i	$-0.913608\pi$
$739$	−38708.0	−1.92679	−0.963394	+	0.268088i	$0.913608\pi$
$740$	−10640.0	−0.528560
$741$	0	0
$742$	−468.000	−0.0231547
$743$	11034.0	0.544816	0.272408	−	0.962182i	$-0.412180\pi$
$743$	11034.0	0.544816	0.272408	+	0.962182i	$0.412180\pi$
$744$	0	0
$745$	5720.00	0.281295
$746$	11322.0	0.555667
$747$	0	0
$748$	−5712.00	−0.279213
$749$	−512.000	−0.0249774
$750$	0	0
$751$	7502.00	0.364516	0.182258	−	0.983251i	$-0.441659\pi$
$751$	7502.00	0.364516	0.182258	+	0.983251i	$0.441659\pi$
$752$	492.000	0.0238582
$753$	0	0
$754$	−504.000	−0.0243430
$755$	−32480.0	−1.56565
$756$	0	0
$757$	−20954.0	−1.00606	−0.503029	−	0.864269i	$-0.667781\pi$
$757$	−20954.0	−1.00606	−0.503029	+	0.864269i	$0.667781\pi$
$758$	12796.0	0.613155
$759$	0	0
$760$	−27600.0	−1.31731
$761$	−8186.00	−0.389937	−0.194969	−	0.980809i	$-0.562461\pi$
$761$	−8186.00	−0.389937	−0.194969	+	0.980809i	$0.562461\pi$
$762$	0	0
$763$	2496.00	0.118429
$764$	−2380.00	−0.112703
$765$	0	0
$766$	420.000	0.0198110
$767$	−7560.00	−0.355901
$768$	0	0
$769$	−5798.00	−0.271887	−0.135944	−	0.990717i	$-0.543407\pi$
$769$	−5798.00	−0.271887	−0.135944	+	0.990717i	$0.543407\pi$
$770$	−1920.00	−0.0898597
$771$	0	0
$772$	10486.0	0.488859
$773$	39950.0	1.85886	0.929432	−	0.368994i	$-0.120298\pi$
$773$	39950.0	1.85886	0.929432	+	0.368994i	$0.120298\pi$
$774$	0	0
$775$	−50050.0	−2.31981
$776$	−10650.0	−0.492671
$777$	0	0
$778$	−6426.00	−0.296122
$779$	−27048.0	−1.24402
$780$	0	0
$781$	−38112.0	−1.74616
$782$	2074.00	0.0948415
$783$	0	0
$784$	−13899.0	−0.633154
$785$	50840.0	2.31154
$786$	0	0
$787$	20656.0	0.935587	0.467793	−	0.883838i	$-0.345049\pi$
$787$	20656.0	0.935587	0.467793	+	0.883838i	$0.345049\pi$
$788$	−8232.00	−0.372148
$789$	0	0
$790$	17160.0	0.772817
$791$	−700.000	−0.0314654
$792$	0	0
$793$	11480.0	0.514082
$794$	−13212.0	−0.590524
$795$	0	0
$796$	17150.0	0.763650
$797$	3722.00	0.165420	0.0827102	−	0.996574i	$-0.473642\pi$
$797$	3722.00	0.165420	0.0827102	+	0.996574i	$0.473642\pi$
$798$	0	0
$799$	204.000	0.00903254
$800$	44275.0	1.95670
$801$	0	0
$802$	6242.00	0.274829
$803$	−49824.0	−2.18960
$804$	0	0
$805$	−4880.00	−0.213661
$806$	2548.00	0.111352
$807$	0	0
$808$	−18150.0	−0.790241
$809$	−6518.00	−0.283264	−0.141632	−	0.989919i	$-0.545235\pi$
$809$	−6518.00	−0.283264	−0.141632	+	0.989919i	$0.545235\pi$
$810$	0	0
$811$	−33068.0	−1.43178	−0.715891	−	0.698212i	$-0.753979\pi$
$811$	−33068.0	−1.43178	−0.715891	+	0.698212i	$0.753979\pi$
$812$	504.000	0.0217819
$813$	0	0
$814$	3648.00	0.157079
$815$	13680.0	0.587963
$816$	0	0
$817$	−39376.0	−1.68616
$818$	−5194.00	−0.222010
$819$	0	0
$820$	41160.0	1.75289
$821$	5328.00	0.226490	0.113245	−	0.993567i	$-0.463875\pi$
$821$	5328.00	0.226490	0.113245	+	0.993567i	$0.463875\pi$
$822$	0	0
$823$	25874.0	1.09588	0.547941	−	0.836517i	$-0.315412\pi$
$823$	25874.0	1.09588	0.547941	+	0.836517i	$0.315412\pi$
$824$	−9660.00	−0.408401
$825$	0	0
$826$	−1080.00	−0.0454940
$827$	−29184.0	−1.22712	−0.613559	−	0.789649i	$-0.710263\pi$
$827$	−29184.0	−1.22712	−0.613559	+	0.789649i	$0.710263\pi$
$828$	0	0
$829$	−9394.00	−0.393567	−0.196784	−	0.980447i	$-0.563050\pi$
$829$	−9394.00	−0.393567	−0.196784	+	0.980447i	$0.563050\pi$
$830$	−21040.0	−0.879890
$831$	0	0
$832$	2338.00	0.0974226
$833$	−5763.00	−0.239707
$834$	0	0
$835$	−10840.0	−0.449262
$836$	−30912.0	−1.27884
$837$	0	0
$838$	−15956.0	−0.657746
$839$	32062.0	1.31931	0.659656	−	0.751567i	$-0.270702\pi$
$839$	32062.0	1.31931	0.659656	+	0.751567i	$0.270702\pi$
$840$	0	0
$841$	−23093.0	−0.946861
$842$	−15254.0	−0.624332
$843$	0	0
$844$	−7448.00	−0.303757
$845$	−40020.0	−1.62927
$846$	0	0
$847$	−1946.00	−0.0789437
$848$	9594.00	0.388513
$849$	0	0
$850$	4675.00	0.188648
$851$	9272.00	0.373490
$852$	0	0
$853$	9152.00	0.367361	0.183680	−	0.982986i	$-0.441199\pi$
$853$	9152.00	0.367361	0.183680	+	0.982986i	$0.441199\pi$
$854$	1640.00	0.0657139
$855$	0	0
$856$	−3840.00	−0.153328
$857$	19706.0	0.785466	0.392733	−	0.919653i	$-0.371530\pi$
$857$	19706.0	0.785466	0.392733	+	0.919653i	$0.371530\pi$
$858$	0	0
$859$	28684.0	1.13933	0.569666	−	0.821877i	$-0.307073\pi$
$859$	28684.0	1.13933	0.569666	+	0.821877i	$0.307073\pi$
$860$	59920.0	2.37588
$861$	0	0
$862$	5538.00	0.218823
$863$	6320.00	0.249288	0.124644	−	0.992202i	$-0.460221\pi$
$863$	6320.00	0.249288	0.124644	+	0.992202i	$0.460221\pi$
$864$	0	0
$865$	16720.0	0.657222
$866$	11342.0	0.445054
$867$	0	0
$868$	−2548.00	−0.0996368
$869$	41184.0	1.60768
$870$	0	0
$871$	−9800.00	−0.381240
$872$	18720.0	0.726994
$873$	0	0
$874$	11224.0	0.434391
$875$	−6000.00	−0.231814
$876$	0	0
$877$	49272.0	1.89715	0.948573	−	0.316558i	$-0.102527\pi$
$877$	49272.0	1.89715	0.948573	+	0.316558i	$0.102527\pi$
$878$	982.000	0.0377459
$879$	0	0
$880$	39360.0	1.50776
$881$	16462.0	0.629533	0.314767	−	0.949169i	$-0.398074\pi$
$881$	16462.0	0.629533	0.314767	+	0.949169i	$0.398074\pi$
$882$	0	0
$883$	21300.0	0.811780	0.405890	−	0.913922i	$-0.366962\pi$
$883$	21300.0	0.811780	0.405890	+	0.913922i	$0.366962\pi$
$884$	1666.00	0.0633865
$885$	0	0
$886$	2492.00	0.0944925
$887$	16590.0	0.628002	0.314001	−	0.949423i	$-0.398330\pi$
$887$	16590.0	0.628002	0.314001	+	0.949423i	$0.398330\pi$
$888$	0	0
$889$	656.000	0.0247486
$890$	−22040.0	−0.830093
$891$	0	0
$892$	15708.0	0.589622
$893$	1104.00	0.0413706
$894$	0	0
$895$	68880.0	2.57252
$896$	2910.00	0.108500
$897$	0	0
$898$	5498.00	0.204310
$899$	−6552.00	−0.243072
$900$	0	0
$901$	3978.00	0.147088
$902$	−14112.0	−0.520929
$903$	0	0
$904$	−5250.00	−0.193155
$905$	−65680.0	−2.41246
$906$	0	0
$907$	−36184.0	−1.32466	−0.662332	−	0.749211i	$-0.730433\pi$
$907$	−36184.0	−1.32466	−0.662332	+	0.749211i	$0.730433\pi$
$908$	3612.00	0.132014
$909$	0	0
$910$	560.000	0.0203998
$911$	−15626.0	−0.568290	−0.284145	−	0.958781i	$-0.591710\pi$
$911$	−15626.0	−0.568290	−0.284145	+	0.958781i	$0.591710\pi$
$912$	0	0
$913$	−50496.0	−1.83042
$914$	4998.00	0.180874
$915$	0	0
$916$	20454.0	0.737794
$917$	−3904.00	−0.140590
$918$	0	0
$919$	36672.0	1.31632	0.658160	−	0.752878i	$-0.271335\pi$
$919$	36672.0	1.31632	0.658160	+	0.752878i	$0.271335\pi$
$920$	−36600.0	−1.31159
$921$	0	0
$922$	7586.00	0.270967
$923$	11116.0	0.396411
$924$	0	0
$925$	20900.0	0.742906
$926$	5900.00	0.209380
$927$	0	0
$928$	5796.00	0.205025
$929$	15810.0	0.558352	0.279176	−	0.960240i	$-0.409939\pi$
$929$	15810.0	0.558352	0.279176	+	0.960240i	$0.409939\pi$
$930$	0	0
$931$	−31188.0	−1.09790
$932$	21798.0	0.766113
$933$	0	0
$934$	19404.0	0.679784
$935$	16320.0	0.570825
$936$	0	0
$937$	48646.0	1.69605	0.848023	−	0.529959i	$-0.177793\pi$
$937$	48646.0	1.69605	0.848023	+	0.529959i	$0.177793\pi$
$938$	−1400.00	−0.0487331
$939$	0	0
$940$	−1680.00	−0.0582931
$941$	−43872.0	−1.51986	−0.759929	−	0.650006i	$-0.774766\pi$
$941$	−43872.0	−1.51986	−0.759929	+	0.650006i	$0.774766\pi$
$942$	0	0
$943$	−35868.0	−1.23862
$944$	22140.0	0.763343
$945$	0	0
$946$	−20544.0	−0.706071
$947$	−38552.0	−1.32288	−0.661442	−	0.749996i	$-0.730055\pi$
$947$	−38552.0	−1.32288	−0.661442	+	0.749996i	$0.730055\pi$
$948$	0	0
$949$	14532.0	0.497080
$950$	25300.0	0.864043
$951$	0	0
$952$	510.000	0.0173626
$953$	52954.0	1.79995	0.899973	−	0.435946i	$-0.143586\pi$
$953$	52954.0	1.79995	0.899973	+	0.435946i	$0.143586\pi$
$954$	0	0
$955$	6800.00	0.230411
$956$	28868.0	0.976630
$957$	0	0
$958$	−2586.00	−0.0872128
$959$	5268.00	0.177385
$960$	0	0
$961$	3333.00	0.111879
$962$	−1064.00	−0.0356598
$963$	0	0
$964$	14238.0	0.475700
$965$	−29960.0	−0.999426
$966$	0	0
$967$	−46428.0	−1.54398	−0.771988	−	0.635638i	$-0.780737\pi$
$967$	−46428.0	−1.54398	−0.771988	+	0.635638i	$0.780737\pi$
$968$	−14595.0	−0.484609
$969$	0	0
$970$	14200.0	0.470036
$971$	40980.0	1.35439	0.677194	−	0.735804i	$-0.263196\pi$
$971$	40980.0	1.35439	0.677194	+	0.735804i	$0.263196\pi$
$972$	0	0
$973$	−3728.00	−0.122831
$974$	10106.0	0.332461
$975$	0	0
$976$	−33620.0	−1.10261
$977$	10206.0	0.334206	0.167103	−	0.985939i	$-0.446559\pi$
$977$	10206.0	0.334206	0.167103	+	0.985939i	$0.446559\pi$
$978$	0	0
$979$	−52896.0	−1.72683
$980$	47460.0	1.54699
$981$	0	0
$982$	76.0000	0.00246971
$983$	44934.0	1.45796	0.728979	−	0.684536i	$-0.239995\pi$
$983$	44934.0	1.45796	0.728979	+	0.684536i	$0.239995\pi$
$984$	0	0
$985$	23520.0	0.760822
$986$	612.000	0.0197668
$987$	0	0
$988$	9016.00	0.290321
$989$	−52216.0	−1.67884
$990$	0	0
$991$	20526.0	0.657951	0.328976	−	0.944338i	$-0.393297\pi$
$991$	20526.0	0.657951	0.328976	+	0.944338i	$0.393297\pi$
$992$	−29302.0	−0.937842
$993$	0	0
$994$	1588.00	0.0506723
$995$	−49000.0	−1.56121
$996$	0	0
$997$	29260.0	0.929462	0.464731	−	0.885452i	$-0.346151\pi$
$997$	29260.0	0.929462	0.464731	+	0.885452i	$0.346151\pi$
$998$	8096.00	0.256788
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.a.c.1.1		1
3.2	odd	2		51.4.a.b.1.1	✓	1
4.3	odd	2		2448.4.a.r.1.1		1
12.11	even	2		816.4.a.a.1.1		1
15.14	odd	2		1275.4.a.e.1.1		1
21.20	even	2		2499.4.a.d.1.1		1
51.50	odd	2		867.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.a.b.1.1	✓	1	3.2	odd	2
153.4.a.c.1.1		1	1.1	even	1	trivial
816.4.a.a.1.1		1	12.11	even	2
867.4.a.c.1.1		1	51.50	odd	2
1275.4.a.e.1.1		1	15.14	odd	2
2448.4.a.r.1.1		1	4.3	odd	2
2499.4.a.d.1.1		1	21.20	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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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