LMFDB - Embedded newform 147.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, 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("147.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.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:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} +18.0000 q^{5} -9.00000 q^{6} +21.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-3.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} +18.0000 q^{5} -9.00000 q^{6} +21.0000 q^{8} +9.00000 q^{9} -54.0000 q^{10} -36.0000 q^{11} +3.00000 q^{12} +34.0000 q^{13} +54.0000 q^{15} -71.0000 q^{16} -42.0000 q^{17} -27.0000 q^{18} +124.000 q^{19} +18.0000 q^{20} +108.000 q^{22} +63.0000 q^{24} +199.000 q^{25} -102.000 q^{26} +27.0000 q^{27} +102.000 q^{29} -162.000 q^{30} +160.000 q^{31} +45.0000 q^{32} -108.000 q^{33} +126.000 q^{34} +9.00000 q^{36} +398.000 q^{37} -372.000 q^{38} +102.000 q^{39} +378.000 q^{40} +318.000 q^{41} -268.000 q^{43} -36.0000 q^{44} +162.000 q^{45} -240.000 q^{47} -213.000 q^{48} -597.000 q^{50} -126.000 q^{51} +34.0000 q^{52} -498.000 q^{53} -81.0000 q^{54} -648.000 q^{55} +372.000 q^{57} -306.000 q^{58} +132.000 q^{59} +54.0000 q^{60} -398.000 q^{61} -480.000 q^{62} +433.000 q^{64} +612.000 q^{65} +324.000 q^{66} +92.0000 q^{67} -42.0000 q^{68} -720.000 q^{71} +189.000 q^{72} +502.000 q^{73} -1194.00 q^{74} +597.000 q^{75} +124.000 q^{76} -306.000 q^{78} -1024.00 q^{79} -1278.00 q^{80} +81.0000 q^{81} -954.000 q^{82} +204.000 q^{83} -756.000 q^{85} +804.000 q^{86} +306.000 q^{87} -756.000 q^{88} -354.000 q^{89} -486.000 q^{90} +480.000 q^{93} +720.000 q^{94} +2232.00 q^{95} +135.000 q^{96} +286.000 q^{97} -324.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.00000	−1.06066	−0.530330	−	0.847791i	$-0.677932\pi$
$2$	−3.00000	−1.06066	−0.530330	+	0.847791i	$0.677932\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	1.00000	0.125000
$5$	18.0000	1.60997	0.804984	−	0.593296i	$-0.202174\pi$
$5$	18.0000	1.60997	0.804984	+	0.593296i	$0.202174\pi$
$6$	−9.00000	−0.612372
$7$	0	0
$7$	0	0
$8$	21.0000	0.928078
$9$	9.00000	0.333333
$10$	−54.0000	−1.70763
$11$	−36.0000	−0.986764	−0.493382	−	0.869813i	$-0.664240\pi$
$11$	−36.0000	−0.986764	−0.493382	+	0.869813i	$0.664240\pi$
$12$	3.00000	0.0721688
$13$	34.0000	0.725377	0.362689	−	0.931910i	$-0.381859\pi$
$13$	34.0000	0.725377	0.362689	+	0.931910i	$0.381859\pi$
$14$	0	0
$15$	54.0000	0.929516
$16$	−71.0000	−1.10938
$17$	−42.0000	−0.599206	−0.299603	−	0.954064i	$-0.596854\pi$
$17$	−42.0000	−0.599206	−0.299603	+	0.954064i	$0.596854\pi$
$18$	−27.0000	−0.353553
$19$	124.000	1.49724	0.748620	−	0.663000i	$-0.230717\pi$
$19$	124.000	1.49724	0.748620	+	0.663000i	$0.230717\pi$
$20$	18.0000	0.201246
$21$	0	0
$22$	108.000	1.04662
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	63.0000	0.535826
$25$	199.000	1.59200
$26$	−102.000	−0.769379
$27$	27.0000	0.192450
$28$	0	0
$29$	102.000	0.653135	0.326568	−	0.945174i	$-0.394108\pi$
$29$	102.000	0.653135	0.326568	+	0.945174i	$0.394108\pi$
$30$	−162.000	−0.985901
$31$	160.000	0.926995	0.463498	−	0.886098i	$-0.346594\pi$
$31$	160.000	0.926995	0.463498	+	0.886098i	$0.346594\pi$
$32$	45.0000	0.248592
$33$	−108.000	−0.569709
$34$	126.000	0.635554
$35$	0	0
$36$	9.00000	0.0416667
$37$	398.000	1.76840	0.884200	−	0.467109i	$-0.154704\pi$
$37$	398.000	1.76840	0.884200	+	0.467109i	$0.154704\pi$
$38$	−372.000	−1.58806
$39$	102.000	0.418797
$40$	378.000	1.49418
$41$	318.000	1.21130	0.605649	−	0.795732i	$-0.292913\pi$
$41$	318.000	1.21130	0.605649	+	0.795732i	$0.292913\pi$
$42$	0	0
$43$	−268.000	−0.950456	−0.475228	−	0.879863i	$-0.657634\pi$
$43$	−268.000	−0.950456	−0.475228	+	0.879863i	$0.657634\pi$
$44$	−36.0000	−0.123346
$45$	162.000	0.536656
$46$	0	0
$47$	−240.000	−0.744843	−0.372421	−	0.928064i	$-0.621472\pi$
$47$	−240.000	−0.744843	−0.372421	+	0.928064i	$0.621472\pi$
$48$	−213.000	−0.640498
$49$	0	0
$50$	−597.000	−1.68857
$51$	−126.000	−0.345952
$52$	34.0000	0.0906721
$53$	−498.000	−1.29067	−0.645335	−	0.763899i	$-0.723282\pi$
$53$	−498.000	−1.29067	−0.645335	+	0.763899i	$0.723282\pi$
$54$	−81.0000	−0.204124
$55$	−648.000	−1.58866
$56$	0	0
$57$	372.000	0.864432
$58$	−306.000	−0.692755
$59$	132.000	0.291270	0.145635	−	0.989338i	$-0.453477\pi$
$59$	132.000	0.291270	0.145635	+	0.989338i	$0.453477\pi$
$60$	54.0000	0.116190
$61$	−398.000	−0.835388	−0.417694	−	0.908588i	$-0.637162\pi$
$61$	−398.000	−0.835388	−0.417694	+	0.908588i	$0.637162\pi$
$62$	−480.000	−0.983227
$63$	0	0
$64$	433.000	0.845703
$65$	612.000	1.16783
$66$	324.000	0.604267
$67$	92.0000	0.167755	0.0838775	−	0.996476i	$-0.473270\pi$
$67$	92.0000	0.167755	0.0838775	+	0.996476i	$0.473270\pi$
$68$	−42.0000	−0.0749007
$69$	0	0
$70$	0	0
$71$	−720.000	−1.20350	−0.601748	−	0.798686i	$-0.705529\pi$
$71$	−720.000	−1.20350	−0.601748	+	0.798686i	$0.705529\pi$
$72$	189.000	0.309359
$73$	502.000	0.804858	0.402429	−	0.915451i	$-0.368166\pi$
$73$	502.000	0.804858	0.402429	+	0.915451i	$0.368166\pi$
$74$	−1194.00	−1.87567
$75$	597.000	0.919142
$76$	124.000	0.187155
$77$	0	0
$78$	−306.000	−0.444201
$79$	−1024.00	−1.45834	−0.729171	−	0.684332i	$-0.760094\pi$
$79$	−1024.00	−1.45834	−0.729171	+	0.684332i	$0.760094\pi$
$80$	−1278.00	−1.78606
$81$	81.0000	0.111111
$82$	−954.000	−1.28478
$83$	204.000	0.269782	0.134891	−	0.990860i	$-0.456932\pi$
$83$	204.000	0.269782	0.134891	+	0.990860i	$0.456932\pi$
$84$	0	0
$85$	−756.000	−0.964703
$86$	804.000	1.00811
$87$	306.000	0.377088
$88$	−756.000	−0.915794
$89$	−354.000	−0.421617	−0.210809	−	0.977527i	$-0.567610\pi$
$89$	−354.000	−0.421617	−0.210809	+	0.977527i	$0.567610\pi$
$90$	−486.000	−0.569210
$91$	0	0
$92$	0	0
$93$	480.000	0.535201
$94$	720.000	0.790025
$95$	2232.00	2.41051
$96$	135.000	0.143525
$97$	286.000	0.299370	0.149685	−	0.988734i	$-0.452174\pi$
$97$	286.000	0.299370	0.149685	+	0.988734i	$0.452174\pi$
$98$	0	0
$99$	−324.000	−0.328921
$100$	199.000	0.199000
$101$	−414.000	−0.407867	−0.203933	−	0.978985i	$-0.565373\pi$
$101$	−414.000	−0.407867	−0.203933	+	0.978985i	$0.565373\pi$
$102$	378.000	0.366937
$103$	−56.0000	−0.0535713	−0.0267857	−	0.999641i	$-0.508527\pi$
$103$	−56.0000	−0.0535713	−0.0267857	+	0.999641i	$0.508527\pi$
$104$	714.000	0.673206
$105$	0	0
$106$	1494.00	1.36896
$107$	12.0000	0.0108419	0.00542095	−	0.999985i	$-0.498274\pi$
$107$	12.0000	0.0108419	0.00542095	+	0.999985i	$0.498274\pi$
$108$	27.0000	0.0240563
$109$	1478.00	1.29878	0.649389	−	0.760457i	$-0.275025\pi$
$109$	1478.00	1.29878	0.649389	+	0.760457i	$0.275025\pi$
$110$	1944.00	1.68503
$111$	1194.00	1.02099
$112$	0	0
$113$	402.000	0.334664	0.167332	−	0.985901i	$-0.446485\pi$
$113$	402.000	0.334664	0.167332	+	0.985901i	$0.446485\pi$
$114$	−1116.00	−0.916868
$115$	0	0
$116$	102.000	0.0816419
$117$	306.000	0.241792
$118$	−396.000	−0.308939
$119$	0	0
$120$	1134.00	0.862663
$121$	−35.0000	−0.0262960
$122$	1194.00	0.886063
$123$	954.000	0.699344
$124$	160.000	0.115874
$125$	1332.00	0.953102
$126$	0	0
$127$	1280.00	0.894344	0.447172	−	0.894448i	$-0.352431\pi$
$127$	1280.00	0.894344	0.447172	+	0.894448i	$0.352431\pi$
$128$	−1659.00	−1.14560
$129$	−804.000	−0.548746
$130$	−1836.00	−1.23868
$131$	−1764.00	−1.17650	−0.588250	−	0.808679i	$-0.700183\pi$
$131$	−1764.00	−1.17650	−0.588250	+	0.808679i	$0.700183\pi$
$132$	−108.000	−0.0712136
$133$	0	0
$134$	−276.000	−0.177931
$135$	486.000	0.309839
$136$	−882.000	−0.556109
$137$	−2358.00	−1.47049	−0.735246	−	0.677800i	$-0.762934\pi$
$137$	−2358.00	−1.47049	−0.735246	+	0.677800i	$0.762934\pi$
$138$	0	0
$139$	52.0000	0.0317308	0.0158654	−	0.999874i	$-0.494950\pi$
$139$	52.0000	0.0317308	0.0158654	+	0.999874i	$0.494950\pi$
$140$	0	0
$141$	−720.000	−0.430035
$142$	2160.00	1.27650
$143$	−1224.00	−0.715776
$144$	−639.000	−0.369792
$145$	1836.00	1.05153
$146$	−1506.00	−0.853681
$147$	0	0
$148$	398.000	0.221050
$149$	−1746.00	−0.959986	−0.479993	−	0.877272i	$-0.659361\pi$
$149$	−1746.00	−0.959986	−0.479993	+	0.877272i	$0.659361\pi$
$150$	−1791.00	−0.974897
$151$	−232.000	−0.125032	−0.0625162	−	0.998044i	$-0.519913\pi$
$151$	−232.000	−0.125032	−0.0625162	+	0.998044i	$0.519913\pi$
$152$	2604.00	1.38955
$153$	−378.000	−0.199735
$154$	0	0
$155$	2880.00	1.49243
$156$	102.000	0.0523496
$157$	−1694.00	−0.861120	−0.430560	−	0.902562i	$-0.641684\pi$
$157$	−1694.00	−0.861120	−0.430560	+	0.902562i	$0.641684\pi$
$158$	3072.00	1.54681
$159$	−1494.00	−0.745169
$160$	810.000	0.400226
$161$	0	0
$162$	−243.000	−0.117851
$163$	−2932.00	−1.40891	−0.704454	−	0.709750i	$-0.748808\pi$
$163$	−2932.00	−1.40891	−0.704454	+	0.709750i	$0.748808\pi$
$164$	318.000	0.151412
$165$	−1944.00	−0.917213
$166$	−612.000	−0.286147
$167$	−1176.00	−0.544920	−0.272460	−	0.962167i	$-0.587837\pi$
$167$	−1176.00	−0.544920	−0.272460	+	0.962167i	$0.587837\pi$
$168$	0	0
$169$	−1041.00	−0.473828
$170$	2268.00	1.02322
$171$	1116.00	0.499080
$172$	−268.000	−0.118807
$173$	−870.000	−0.382340	−0.191170	−	0.981557i	$-0.561228\pi$
$173$	−870.000	−0.382340	−0.191170	+	0.981557i	$0.561228\pi$
$174$	−918.000	−0.399962
$175$	0	0
$176$	2556.00	1.09469
$177$	396.000	0.168165
$178$	1062.00	0.447193
$179$	−2316.00	−0.967072	−0.483536	−	0.875324i	$-0.660648\pi$
$179$	−2316.00	−0.967072	−0.483536	+	0.875324i	$0.660648\pi$
$180$	162.000	0.0670820
$181$	106.000	0.0435299	0.0217650	−	0.999763i	$-0.493071\pi$
$181$	106.000	0.0435299	0.0217650	+	0.999763i	$0.493071\pi$
$182$	0	0
$183$	−1194.00	−0.482312
$184$	0	0
$185$	7164.00	2.84707
$186$	−1440.00	−0.567666
$187$	1512.00	0.591275
$188$	−240.000	−0.0931053
$189$	0	0
$190$	−6696.00	−2.55673
$191$	−1128.00	−0.427326	−0.213663	−	0.976907i	$-0.568539\pi$
$191$	−1128.00	−0.427326	−0.213663	+	0.976907i	$0.568539\pi$
$192$	1299.00	0.488267
$193$	4034.00	1.50453	0.752263	−	0.658862i	$-0.228962\pi$
$193$	4034.00	1.50453	0.752263	+	0.658862i	$0.228962\pi$
$194$	−858.000	−0.317530
$195$	1836.00	0.674250
$196$	0	0
$197$	−1314.00	−0.475221	−0.237611	−	0.971360i	$-0.576364\pi$
$197$	−1314.00	−0.475221	−0.237611	+	0.971360i	$0.576364\pi$
$198$	972.000	0.348874
$199$	−5096.00	−1.81531	−0.907653	−	0.419722i	$-0.862128\pi$
$199$	−5096.00	−1.81531	−0.907653	+	0.419722i	$0.862128\pi$
$200$	4179.00	1.47750
$201$	276.000	0.0968534
$202$	1242.00	0.432608
$203$	0	0
$204$	−126.000	−0.0432439
$205$	5724.00	1.95015
$206$	168.000	0.0568209
$207$	0	0
$208$	−2414.00	−0.804715
$209$	−4464.00	−1.47742
$210$	0	0
$211$	−3076.00	−1.00360	−0.501802	−	0.864982i	$-0.667330\pi$
$211$	−3076.00	−1.00360	−0.501802	+	0.864982i	$0.667330\pi$
$212$	−498.000	−0.161334
$213$	−2160.00	−0.694839
$214$	−36.0000	−0.0114996
$215$	−4824.00	−1.53020
$216$	567.000	0.178609
$217$	0	0
$218$	−4434.00	−1.37756
$219$	1506.00	0.464685
$220$	−648.000	−0.198583
$221$	−1428.00	−0.434650
$222$	−3582.00	−1.08292
$223$	1888.00	0.566950	0.283475	−	0.958980i	$-0.408513\pi$
$223$	1888.00	0.566950	0.283475	+	0.958980i	$0.408513\pi$
$224$	0	0
$225$	1791.00	0.530667
$226$	−1206.00	−0.354964
$227$	4716.00	1.37891	0.689454	−	0.724330i	$-0.257851\pi$
$227$	4716.00	1.37891	0.689454	+	0.724330i	$0.257851\pi$
$228$	372.000	0.108054
$229$	1690.00	0.487678	0.243839	−	0.969816i	$-0.421593\pi$
$229$	1690.00	0.487678	0.243839	+	0.969816i	$0.421593\pi$
$230$	0	0
$231$	0	0
$232$	2142.00	0.606160
$233$	138.000	0.0388012	0.0194006	−	0.999812i	$-0.493824\pi$
$233$	138.000	0.0388012	0.0194006	+	0.999812i	$0.493824\pi$
$234$	−918.000	−0.256460
$235$	−4320.00	−1.19917
$236$	132.000	0.0364088
$237$	−3072.00	−0.841974
$238$	0	0
$239$	1896.00	0.513147	0.256573	−	0.966525i	$-0.417406\pi$
$239$	1896.00	0.513147	0.256573	+	0.966525i	$0.417406\pi$
$240$	−3834.00	−1.03118
$241$	3598.00	0.961691	0.480846	−	0.876805i	$-0.340330\pi$
$241$	3598.00	0.961691	0.480846	+	0.876805i	$0.340330\pi$
$242$	105.000	0.0278911
$243$	243.000	0.0641500
$244$	−398.000	−0.104424
$245$	0	0
$246$	−2862.00	−0.741766
$247$	4216.00	1.08606
$248$	3360.00	0.860323
$249$	612.000	0.155759
$250$	−3996.00	−1.01092
$251$	3060.00	0.769504	0.384752	−	0.923020i	$-0.374287\pi$
$251$	3060.00	0.769504	0.384752	+	0.923020i	$0.374287\pi$
$252$	0	0
$253$	0	0
$254$	−3840.00	−0.948595
$255$	−2268.00	−0.556971
$256$	1513.00	0.369385
$257$	6822.00	1.65582	0.827908	−	0.560864i	$-0.189531\pi$
$257$	6822.00	1.65582	0.827908	+	0.560864i	$0.189531\pi$
$258$	2412.00	0.582033
$259$	0	0
$260$	612.000	0.145979
$261$	918.000	0.217712
$262$	5292.00	1.24787
$263$	2592.00	0.607717	0.303858	−	0.952717i	$-0.401725\pi$
$263$	2592.00	0.607717	0.303858	+	0.952717i	$0.401725\pi$
$264$	−2268.00	−0.528734
$265$	−8964.00	−2.07794
$266$	0	0
$267$	−1062.00	−0.243421
$268$	92.0000	0.0209694
$269$	−8214.00	−1.86177	−0.930886	−	0.365311i	$-0.880963\pi$
$269$	−8214.00	−1.86177	−0.930886	+	0.365311i	$0.880963\pi$
$270$	−1458.00	−0.328634
$271$	5344.00	1.19788	0.598939	−	0.800795i	$-0.295589\pi$
$271$	5344.00	1.19788	0.598939	+	0.800795i	$0.295589\pi$
$272$	2982.00	0.664744
$273$	0	0
$274$	7074.00	1.55969
$275$	−7164.00	−1.57093
$276$	0	0
$277$	−6514.00	−1.41295	−0.706477	−	0.707736i	$-0.749717\pi$
$277$	−6514.00	−1.41295	−0.706477	+	0.707736i	$0.749717\pi$
$278$	−156.000	−0.0336556
$279$	1440.00	0.308998
$280$	0	0
$281$	6618.00	1.40497	0.702485	−	0.711698i	$-0.252074\pi$
$281$	6618.00	1.40497	0.702485	+	0.711698i	$0.252074\pi$
$282$	2160.00	0.456121
$283$	−3260.00	−0.684759	−0.342380	−	0.939562i	$-0.611233\pi$
$283$	−3260.00	−0.684759	−0.342380	+	0.939562i	$0.611233\pi$
$284$	−720.000	−0.150437
$285$	6696.00	1.39171
$286$	3672.00	0.759195
$287$	0	0
$288$	405.000	0.0828641
$289$	−3149.00	−0.640953
$290$	−5508.00	−1.11531
$291$	858.000	0.172841
$292$	502.000	0.100607
$293$	−5118.00	−1.02047	−0.510233	−	0.860036i	$-0.670441\pi$
$293$	−5118.00	−1.02047	−0.510233	+	0.860036i	$0.670441\pi$
$294$	0	0
$295$	2376.00	0.468936
$296$	8358.00	1.64121
$297$	−972.000	−0.189903
$298$	5238.00	1.01822
$299$	0	0
$300$	597.000	0.114893
$301$	0	0
$302$	696.000	0.132617
$303$	−1242.00	−0.235482
$304$	−8804.00	−1.66100
$305$	−7164.00	−1.34495
$306$	1134.00	0.211851
$307$	−452.000	−0.0840293	−0.0420147	−	0.999117i	$-0.513378\pi$
$307$	−452.000	−0.0840293	−0.0420147	+	0.999117i	$0.513378\pi$
$308$	0	0
$309$	−168.000	−0.0309294
$310$	−8640.00	−1.58296
$311$	−5016.00	−0.914570	−0.457285	−	0.889320i	$-0.651178\pi$
$311$	−5016.00	−0.914570	−0.457285	+	0.889320i	$0.651178\pi$
$312$	2142.00	0.388676
$313$	−5402.00	−0.975524	−0.487762	−	0.872977i	$-0.662187\pi$
$313$	−5402.00	−0.975524	−0.487762	+	0.872977i	$0.662187\pi$
$314$	5082.00	0.913356
$315$	0	0
$316$	−1024.00	−0.182293
$317$	10086.0	1.78702	0.893511	−	0.449041i	$-0.148234\pi$
$317$	10086.0	1.78702	0.893511	+	0.449041i	$0.148234\pi$
$318$	4482.00	0.790371
$319$	−3672.00	−0.644491
$320$	7794.00	1.36156
$321$	36.0000	0.00625958
$322$	0	0
$323$	−5208.00	−0.897154
$324$	81.0000	0.0138889
$325$	6766.00	1.15480
$326$	8796.00	1.49437
$327$	4434.00	0.749849
$328$	6678.00	1.12418
$329$	0	0
$330$	5832.00	0.972852
$331$	−8044.00	−1.33577	−0.667883	−	0.744267i	$-0.732799\pi$
$331$	−8044.00	−1.33577	−0.667883	+	0.744267i	$0.732799\pi$
$332$	204.000	0.0337228
$333$	3582.00	0.589467
$334$	3528.00	0.577975
$335$	1656.00	0.270080
$336$	0	0
$337$	4178.00	0.675342	0.337671	−	0.941264i	$-0.390361\pi$
$337$	4178.00	0.675342	0.337671	+	0.941264i	$0.390361\pi$
$338$	3123.00	0.502570
$339$	1206.00	0.193218
$340$	−756.000	−0.120588
$341$	−5760.00	−0.914726
$342$	−3348.00	−0.529354
$343$	0	0
$344$	−5628.00	−0.882097
$345$	0	0
$346$	2610.00	0.405533
$347$	156.000	0.0241341	0.0120670	−	0.999927i	$-0.496159\pi$
$347$	156.000	0.0241341	0.0120670	+	0.999927i	$0.496159\pi$
$348$	306.000	0.0471360
$349$	12418.0	1.90464	0.952321	−	0.305097i	$-0.0986888\pi$
$349$	12418.0	1.90464	0.952321	+	0.305097i	$0.0986888\pi$
$350$	0	0
$351$	918.000	0.139599
$352$	−1620.00	−0.245302
$353$	7830.00	1.18059	0.590296	−	0.807187i	$-0.299011\pi$
$353$	7830.00	1.18059	0.590296	+	0.807187i	$0.299011\pi$
$354$	−1188.00	−0.178366
$355$	−12960.0	−1.93759
$356$	−354.000	−0.0527021
$357$	0	0
$358$	6948.00	1.02574
$359$	−9312.00	−1.36899	−0.684497	−	0.729016i	$-0.739978\pi$
$359$	−9312.00	−1.36899	−0.684497	+	0.729016i	$0.739978\pi$
$360$	3402.00	0.498059
$361$	8517.00	1.24173
$362$	−318.000	−0.0461705
$363$	−105.000	−0.0151820
$364$	0	0
$365$	9036.00	1.29580
$366$	3582.00	0.511569
$367$	3760.00	0.534797	0.267398	−	0.963586i	$-0.413836\pi$
$367$	3760.00	0.534797	0.267398	+	0.963586i	$0.413836\pi$
$368$	0	0
$369$	2862.00	0.403766
$370$	−21492.0	−3.01977
$371$	0	0
$372$	480.000	0.0669001
$373$	5870.00	0.814845	0.407422	−	0.913240i	$-0.366428\pi$
$373$	5870.00	0.814845	0.407422	+	0.913240i	$0.366428\pi$
$374$	−4536.00	−0.627142
$375$	3996.00	0.550273
$376$	−5040.00	−0.691272
$377$	3468.00	0.473769
$378$	0	0
$379$	−1852.00	−0.251005	−0.125502	−	0.992093i	$-0.540054\pi$
$379$	−1852.00	−0.251005	−0.125502	+	0.992093i	$0.540054\pi$
$380$	2232.00	0.301314
$381$	3840.00	0.516350
$382$	3384.00	0.453247
$383$	−2160.00	−0.288175	−0.144087	−	0.989565i	$-0.546025\pi$
$383$	−2160.00	−0.288175	−0.144087	+	0.989565i	$0.546025\pi$
$384$	−4977.00	−0.661410
$385$	0	0
$386$	−12102.0	−1.59579
$387$	−2412.00	−0.316819
$388$	286.000	0.0374213
$389$	−6786.00	−0.884483	−0.442241	−	0.896896i	$-0.645817\pi$
$389$	−6786.00	−0.884483	−0.442241	+	0.896896i	$0.645817\pi$
$390$	−5508.00	−0.715150
$391$	0	0
$392$	0	0
$393$	−5292.00	−0.679252
$394$	3942.00	0.504048
$395$	−18432.0	−2.34788
$396$	−324.000	−0.0411152
$397$	6514.00	0.823497	0.411748	−	0.911298i	$-0.364918\pi$
$397$	6514.00	0.823497	0.411748	+	0.911298i	$0.364918\pi$
$398$	15288.0	1.92542
$399$	0	0
$400$	−14129.0	−1.76612
$401$	3330.00	0.414694	0.207347	−	0.978267i	$-0.433517\pi$
$401$	3330.00	0.414694	0.207347	+	0.978267i	$0.433517\pi$
$402$	−828.000	−0.102729
$403$	5440.00	0.672421
$404$	−414.000	−0.0509833
$405$	1458.00	0.178885
$406$	0	0
$407$	−14328.0	−1.74499
$408$	−2646.00	−0.321070
$409$	5398.00	0.652601	0.326301	−	0.945266i	$-0.394198\pi$
$409$	5398.00	0.652601	0.326301	+	0.945266i	$0.394198\pi$
$410$	−17172.0	−2.06845
$411$	−7074.00	−0.848990
$412$	−56.0000	−0.00669641
$413$	0	0
$414$	0	0
$415$	3672.00	0.434341
$416$	1530.00	0.180323
$417$	156.000	0.0183198
$418$	13392.0	1.56704
$419$	−13092.0	−1.52646	−0.763229	−	0.646128i	$-0.776387\pi$
$419$	−13092.0	−1.52646	−0.763229	+	0.646128i	$0.776387\pi$
$420$	0	0
$421$	−322.000	−0.0372763	−0.0186381	−	0.999826i	$-0.505933\pi$
$421$	−322.000	−0.0372763	−0.0186381	+	0.999826i	$0.505933\pi$
$422$	9228.00	1.06448
$423$	−2160.00	−0.248281
$424$	−10458.0	−1.19784
$425$	−8358.00	−0.953935
$426$	6480.00	0.736988
$427$	0	0
$428$	12.0000	0.00135524
$429$	−3672.00	−0.413254
$430$	14472.0	1.62303
$431$	2616.00	0.292363	0.146181	−	0.989258i	$-0.453302\pi$
$431$	2616.00	0.292363	0.146181	+	0.989258i	$0.453302\pi$
$432$	−1917.00	−0.213499
$433$	−4322.00	−0.479681	−0.239841	−	0.970812i	$-0.577095\pi$
$433$	−4322.00	−0.479681	−0.239841	+	0.970812i	$0.577095\pi$
$434$	0	0
$435$	5508.00	0.607100
$436$	1478.00	0.162347
$437$	0	0
$438$	−4518.00	−0.492873
$439$	9016.00	0.980205	0.490103	−	0.871665i	$-0.336959\pi$
$439$	9016.00	0.980205	0.490103	+	0.871665i	$0.336959\pi$
$440$	−13608.0	−1.47440
$441$	0	0
$442$	4284.00	0.461016
$443$	−5268.00	−0.564989	−0.282495	−	0.959269i	$-0.591162\pi$
$443$	−5268.00	−0.564989	−0.282495	+	0.959269i	$0.591162\pi$
$444$	1194.00	0.127623
$445$	−6372.00	−0.678790
$446$	−5664.00	−0.601341
$447$	−5238.00	−0.554248
$448$	0	0
$449$	−5310.00	−0.558117	−0.279058	−	0.960274i	$-0.590022\pi$
$449$	−5310.00	−0.558117	−0.279058	+	0.960274i	$0.590022\pi$
$450$	−5373.00	−0.562857
$451$	−11448.0	−1.19527
$452$	402.000	0.0418329
$453$	−696.000	−0.0721875
$454$	−14148.0	−1.46255
$455$	0	0
$456$	7812.00	0.802260
$457$	15770.0	1.61420	0.807100	−	0.590415i	$-0.201036\pi$
$457$	15770.0	1.61420	0.807100	+	0.590415i	$0.201036\pi$
$458$	−5070.00	−0.517261
$459$	−1134.00	−0.115317
$460$	0	0
$461$	5370.00	0.542529	0.271264	−	0.962505i	$-0.412558\pi$
$461$	5370.00	0.542529	0.271264	+	0.962505i	$0.412558\pi$
$462$	0	0
$463$	−3328.00	−0.334050	−0.167025	−	0.985953i	$-0.553416\pi$
$463$	−3328.00	−0.334050	−0.167025	+	0.985953i	$0.553416\pi$
$464$	−7242.00	−0.724572
$465$	8640.00	0.861657
$466$	−414.000	−0.0411549
$467$	−4548.00	−0.450656	−0.225328	−	0.974283i	$-0.572345\pi$
$467$	−4548.00	−0.450656	−0.225328	+	0.974283i	$0.572345\pi$
$468$	306.000	0.0302240
$469$	0	0
$470$	12960.0	1.27192
$471$	−5082.00	−0.497168
$472$	2772.00	0.270321
$473$	9648.00	0.937876
$474$	9216.00	0.893048
$475$	24676.0	2.38361
$476$	0	0
$477$	−4482.00	−0.430224
$478$	−5688.00	−0.544274
$479$	8064.00	0.769214	0.384607	−	0.923080i	$-0.374337\pi$
$479$	8064.00	0.769214	0.384607	+	0.923080i	$0.374337\pi$
$480$	2430.00	0.231070
$481$	13532.0	1.28276
$482$	−10794.0	−1.02003
$483$	0	0
$484$	−35.0000	−0.00328700
$485$	5148.00	0.481977
$486$	−729.000	−0.0680414
$487$	16616.0	1.54608	0.773042	−	0.634355i	$-0.218734\pi$
$487$	16616.0	1.54608	0.773042	+	0.634355i	$0.218734\pi$
$488$	−8358.00	−0.775305
$489$	−8796.00	−0.813433
$490$	0	0
$491$	−7140.00	−0.656260	−0.328130	−	0.944633i	$-0.606418\pi$
$491$	−7140.00	−0.656260	−0.328130	+	0.944633i	$0.606418\pi$
$492$	954.000	0.0874180
$493$	−4284.00	−0.391362
$494$	−12648.0	−1.15194
$495$	−5832.00	−0.529553
$496$	−11360.0	−1.02839
$497$	0	0
$498$	−1836.00	−0.165207
$499$	−9124.00	−0.818530	−0.409265	−	0.912416i	$-0.634215\pi$
$499$	−9124.00	−0.818530	−0.409265	+	0.912416i	$0.634215\pi$
$500$	1332.00	0.119138
$501$	−3528.00	−0.314610
$502$	−9180.00	−0.816182
$503$	6552.00	0.580794	0.290397	−	0.956906i	$-0.406213\pi$
$503$	6552.00	0.580794	0.290397	+	0.956906i	$0.406213\pi$
$504$	0	0
$505$	−7452.00	−0.656653
$506$	0	0
$507$	−3123.00	−0.273565
$508$	1280.00	0.111793
$509$	−2790.00	−0.242956	−0.121478	−	0.992594i	$-0.538763\pi$
$509$	−2790.00	−0.242956	−0.121478	+	0.992594i	$0.538763\pi$
$510$	6804.00	0.590757
$511$	0	0
$512$	8733.00	0.753804
$513$	3348.00	0.288144
$514$	−20466.0	−1.75626
$515$	−1008.00	−0.0862481
$516$	−804.000	−0.0685933
$517$	8640.00	0.734984
$518$	0	0
$519$	−2610.00	−0.220744
$520$	12852.0	1.08384
$521$	14862.0	1.24974	0.624871	−	0.780728i	$-0.285151\pi$
$521$	14862.0	1.24974	0.624871	+	0.780728i	$0.285151\pi$
$522$	−2754.00	−0.230918
$523$	−17660.0	−1.47652	−0.738258	−	0.674518i	$-0.764351\pi$
$523$	−17660.0	−1.47652	−0.738258	+	0.674518i	$0.764351\pi$
$524$	−1764.00	−0.147062
$525$	0	0
$526$	−7776.00	−0.644581
$527$	−6720.00	−0.555461
$528$	7668.00	0.632021
$529$	−12167.0	−1.00000
$530$	26892.0	2.20399
$531$	1188.00	0.0970900
$532$	0	0
$533$	10812.0	0.878649
$534$	3186.00	0.258187
$535$	216.000	0.0174551
$536$	1932.00	0.155690
$537$	−6948.00	−0.558340
$538$	24642.0	1.97471
$539$	0	0
$540$	486.000	0.0387298
$541$	−19834.0	−1.57621	−0.788106	−	0.615540i	$-0.788938\pi$
$541$	−19834.0	−1.57621	−0.788106	+	0.615540i	$0.788938\pi$
$542$	−16032.0	−1.27054
$543$	318.000	0.0251320
$544$	−1890.00	−0.148958
$545$	26604.0	2.09099
$546$	0	0
$547$	20972.0	1.63930	0.819651	−	0.572863i	$-0.194167\pi$
$547$	20972.0	1.63930	0.819651	+	0.572863i	$0.194167\pi$
$548$	−2358.00	−0.183812
$549$	−3582.00	−0.278463
$550$	21492.0	1.66622
$551$	12648.0	0.977900
$552$	0	0
$553$	0	0
$554$	19542.0	1.49866
$555$	21492.0	1.64376
$556$	52.0000	0.00396635
$557$	21174.0	1.61072	0.805360	−	0.592786i	$-0.201972\pi$
$557$	21174.0	1.61072	0.805360	+	0.592786i	$0.201972\pi$
$558$	−4320.00	−0.327742
$559$	−9112.00	−0.689439
$560$	0	0
$561$	4536.00	0.341373
$562$	−19854.0	−1.49020
$563$	17772.0	1.33037	0.665187	−	0.746677i	$-0.268352\pi$
$563$	17772.0	1.33037	0.665187	+	0.746677i	$0.268352\pi$
$564$	−720.000	−0.0537544
$565$	7236.00	0.538798
$566$	9780.00	0.726297
$567$	0	0
$568$	−15120.0	−1.11694
$569$	8250.00	0.607835	0.303917	−	0.952698i	$-0.401705\pi$
$569$	8250.00	0.607835	0.303917	+	0.952698i	$0.401705\pi$
$570$	−20088.0	−1.47613
$571$	20756.0	1.52121	0.760606	−	0.649214i	$-0.224902\pi$
$571$	20756.0	1.52121	0.760606	+	0.649214i	$0.224902\pi$
$572$	−1224.00	−0.0894720
$573$	−3384.00	−0.246717
$574$	0	0
$575$	0	0
$576$	3897.00	0.281901
$577$	−2.00000	−0.000144300 0	−7.21500e−5	−	1.00000i	$-0.500023\pi$
$577$	−2.00000	−0.000144300 0	−7.21500e−5		1.00000i	$0.500023\pi$
$578$	9447.00	0.679833
$579$	12102.0	0.868639
$580$	1836.00	0.131441
$581$	0	0
$582$	−2574.00	−0.183326
$583$	17928.0	1.27359
$584$	10542.0	0.746971
$585$	5508.00	0.389278
$586$	15354.0	1.08237
$587$	−26364.0	−1.85376	−0.926881	−	0.375354i	$-0.877521\pi$
$587$	−26364.0	−1.85376	−0.926881	+	0.375354i	$0.877521\pi$
$588$	0	0
$589$	19840.0	1.38793
$590$	−7128.00	−0.497382
$591$	−3942.00	−0.274369
$592$	−28258.0	−1.96182
$593$	−2298.00	−0.159136	−0.0795679	−	0.996829i	$-0.525354\pi$
$593$	−2298.00	−0.159136	−0.0795679	+	0.996829i	$0.525354\pi$
$594$	2916.00	0.201422
$595$	0	0
$596$	−1746.00	−0.119998
$597$	−15288.0	−1.04807
$598$	0	0
$599$	3072.00	0.209547	0.104773	−	0.994496i	$-0.466588\pi$
$599$	3072.00	0.209547	0.104773	+	0.994496i	$0.466588\pi$
$600$	12537.0	0.853035
$601$	−24554.0	−1.66652	−0.833260	−	0.552881i	$-0.813528\pi$
$601$	−24554.0	−1.66652	−0.833260	+	0.552881i	$0.813528\pi$
$602$	0	0
$603$	828.000	0.0559184
$604$	−232.000	−0.0156290
$605$	−630.000	−0.0423358
$606$	3726.00	0.249766
$607$	−16832.0	−1.12552	−0.562759	−	0.826621i	$-0.690260\pi$
$607$	−16832.0	−1.12552	−0.562759	+	0.826621i	$0.690260\pi$
$608$	5580.00	0.372202
$609$	0	0
$610$	21492.0	1.42653
$611$	−8160.00	−0.540292
$612$	−378.000	−0.0249669
$613$	−2482.00	−0.163535	−0.0817676	−	0.996651i	$-0.526057\pi$
$613$	−2482.00	−0.163535	−0.0817676	+	0.996651i	$0.526057\pi$
$614$	1356.00	0.0891266
$615$	17172.0	1.12592
$616$	0	0
$617$	−15798.0	−1.03080	−0.515400	−	0.856950i	$-0.672357\pi$
$617$	−15798.0	−1.03080	−0.515400	+	0.856950i	$0.672357\pi$
$618$	504.000	0.0328056
$619$	15460.0	1.00386	0.501930	−	0.864908i	$-0.332623\pi$
$619$	15460.0	1.00386	0.501930	+	0.864908i	$0.332623\pi$
$620$	2880.00	0.186554
$621$	0	0
$622$	15048.0	0.970048
$623$	0	0
$624$	−7242.00	−0.464603
$625$	−899.000	−0.0575360
$626$	16206.0	1.03470
$627$	−13392.0	−0.852990
$628$	−1694.00	−0.107640
$629$	−16716.0	−1.05964
$630$	0	0
$631$	−7720.00	−0.487050	−0.243525	−	0.969895i	$-0.578304\pi$
$631$	−7720.00	−0.487050	−0.243525	+	0.969895i	$0.578304\pi$
$632$	−21504.0	−1.35345
$633$	−9228.00	−0.579431
$634$	−30258.0	−1.89542
$635$	23040.0	1.43987
$636$	−1494.00	−0.0931462
$637$	0	0
$638$	11016.0	0.683586
$639$	−6480.00	−0.401166
$640$	−29862.0	−1.84437
$641$	−17262.0	−1.06366	−0.531832	−	0.846850i	$-0.678496\pi$
$641$	−17262.0	−1.06366	−0.531832	+	0.846850i	$0.678496\pi$
$642$	−108.000	−0.00663928
$643$	12220.0	0.749471	0.374735	−	0.927132i	$-0.377734\pi$
$643$	12220.0	0.749471	0.374735	+	0.927132i	$0.377734\pi$
$644$	0	0
$645$	−14472.0	−0.883464
$646$	15624.0	0.951576
$647$	−13560.0	−0.823955	−0.411977	−	0.911194i	$-0.635162\pi$
$647$	−13560.0	−0.823955	−0.411977	+	0.911194i	$0.635162\pi$
$648$	1701.00	0.103120
$649$	−4752.00	−0.287415
$650$	−20298.0	−1.22485
$651$	0	0
$652$	−2932.00	−0.176113
$653$	23094.0	1.38398	0.691989	−	0.721908i	$-0.256735\pi$
$653$	23094.0	1.38398	0.691989	+	0.721908i	$0.256735\pi$
$654$	−13302.0	−0.795335
$655$	−31752.0	−1.89413
$656$	−22578.0	−1.34378
$657$	4518.00	0.268286
$658$	0	0
$659$	22548.0	1.33285	0.666423	−	0.745574i	$-0.267825\pi$
$659$	22548.0	1.33285	0.666423	+	0.745574i	$0.267825\pi$
$660$	−1944.00	−0.114652
$661$	−17462.0	−1.02752	−0.513762	−	0.857933i	$-0.671748\pi$
$661$	−17462.0	−1.02752	−0.513762	+	0.857933i	$0.671748\pi$
$662$	24132.0	1.41679
$663$	−4284.00	−0.250945
$664$	4284.00	0.250379
$665$	0	0
$666$	−10746.0	−0.625224
$667$	0	0
$668$	−1176.00	−0.0681150
$669$	5664.00	0.327329
$670$	−4968.00	−0.286464
$671$	14328.0	0.824331
$672$	0	0
$673$	−22462.0	−1.28655	−0.643274	−	0.765636i	$-0.722424\pi$
$673$	−22462.0	−1.28655	−0.643274	+	0.765636i	$0.722424\pi$
$674$	−12534.0	−0.716308
$675$	5373.00	0.306381
$676$	−1041.00	−0.0592285
$677$	25554.0	1.45069	0.725347	−	0.688383i	$-0.241679\pi$
$677$	25554.0	1.45069	0.725347	+	0.688383i	$0.241679\pi$
$678$	−3618.00	−0.204939
$679$	0	0
$680$	−15876.0	−0.895319
$681$	14148.0	0.796112
$682$	17280.0	0.970213
$683$	9276.00	0.519672	0.259836	−	0.965653i	$-0.416331\pi$
$683$	9276.00	0.519672	0.259836	+	0.965653i	$0.416331\pi$
$684$	1116.00	0.0623850
$685$	−42444.0	−2.36745
$686$	0	0
$687$	5070.00	0.281561
$688$	19028.0	1.05441
$689$	−16932.0	−0.936223
$690$	0	0
$691$	−27380.0	−1.50736	−0.753679	−	0.657243i	$-0.771723\pi$
$691$	−27380.0	−1.50736	−0.753679	+	0.657243i	$0.771723\pi$
$692$	−870.000	−0.0477925
$693$	0	0
$694$	−468.000	−0.0255980
$695$	936.000	0.0510856
$696$	6426.00	0.349967
$697$	−13356.0	−0.725817
$698$	−37254.0	−2.02018
$699$	414.000	0.0224019
$700$	0	0
$701$	25830.0	1.39171	0.695853	−	0.718184i	$-0.255027\pi$
$701$	25830.0	1.39171	0.695853	+	0.718184i	$0.255027\pi$
$702$	−2754.00	−0.148067
$703$	49352.0	2.64772
$704$	−15588.0	−0.834510
$705$	−12960.0	−0.692343
$706$	−23490.0	−1.25221
$707$	0	0
$708$	396.000	0.0210206
$709$	−6226.00	−0.329792	−0.164896	−	0.986311i	$-0.552729\pi$
$709$	−6226.00	−0.329792	−0.164896	+	0.986311i	$0.552729\pi$
$710$	38880.0	2.05513
$711$	−9216.00	−0.486114
$712$	−7434.00	−0.391293
$713$	0	0
$714$	0	0
$715$	−22032.0	−1.15238
$716$	−2316.00	−0.120884
$717$	5688.00	0.296265
$718$	27936.0	1.45204
$719$	15072.0	0.781767	0.390884	−	0.920440i	$-0.372169\pi$
$719$	15072.0	0.781767	0.390884	+	0.920440i	$0.372169\pi$
$720$	−11502.0	−0.595353
$721$	0	0
$722$	−25551.0	−1.31705
$723$	10794.0	0.555233
$724$	106.000	0.00544124
$725$	20298.0	1.03979
$726$	315.000	0.0161030
$727$	32920.0	1.67942	0.839708	−	0.543038i	$-0.182726\pi$
$727$	32920.0	1.67942	0.839708	+	0.543038i	$0.182726\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−27108.0	−1.37440
$731$	11256.0	0.569519
$732$	−1194.00	−0.0602889
$733$	6946.00	0.350009	0.175004	−	0.984568i	$-0.444006\pi$
$733$	6946.00	0.350009	0.175004	+	0.984568i	$0.444006\pi$
$734$	−11280.0	−0.567238
$735$	0	0
$736$	0	0
$737$	−3312.00	−0.165535
$738$	−8586.00	−0.428259
$739$	−2356.00	−0.117276	−0.0586379	−	0.998279i	$-0.518676\pi$
$739$	−2356.00	−0.117276	−0.0586379	+	0.998279i	$0.518676\pi$
$740$	7164.00	0.355884
$741$	12648.0	0.627039
$742$	0	0
$743$	−23520.0	−1.16133	−0.580663	−	0.814144i	$-0.697207\pi$
$743$	−23520.0	−1.16133	−0.580663	+	0.814144i	$0.697207\pi$
$744$	10080.0	0.496708
$745$	−31428.0	−1.54555
$746$	−17610.0	−0.864273
$747$	1836.00	0.0899273
$748$	1512.00	0.0739094
$749$	0	0
$750$	−11988.0	−0.583653
$751$	3008.00	0.146156	0.0730782	−	0.997326i	$-0.476718\pi$
$751$	3008.00	0.146156	0.0730782	+	0.997326i	$0.476718\pi$
$752$	17040.0	0.826310
$753$	9180.00	0.444273
$754$	−10404.0	−0.502508
$755$	−4176.00	−0.201298
$756$	0	0
$757$	−20770.0	−0.997224	−0.498612	−	0.866825i	$-0.666157\pi$
$757$	−20770.0	−0.997224	−0.498612	+	0.866825i	$0.666157\pi$
$758$	5556.00	0.266231
$759$	0	0
$760$	46872.0	2.23714
$761$	−11538.0	−0.549609	−0.274804	−	0.961500i	$-0.588613\pi$
$761$	−11538.0	−0.549609	−0.274804	+	0.961500i	$0.588613\pi$
$762$	−11520.0	−0.547671
$763$	0	0
$764$	−1128.00	−0.0534157
$765$	−6804.00	−0.321568
$766$	6480.00	0.305655
$767$	4488.00	0.211281
$768$	4539.00	0.213264
$769$	−8498.00	−0.398499	−0.199249	−	0.979949i	$-0.563850\pi$
$769$	−8498.00	−0.398499	−0.199249	+	0.979949i	$0.563850\pi$
$770$	0	0
$771$	20466.0	0.955986
$772$	4034.00	0.188066
$773$	32322.0	1.50393	0.751967	−	0.659200i	$-0.229105\pi$
$773$	32322.0	1.50393	0.751967	+	0.659200i	$0.229105\pi$
$774$	7236.00	0.336037
$775$	31840.0	1.47578
$776$	6006.00	0.277839
$777$	0	0
$778$	20358.0	0.938136
$779$	39432.0	1.81360
$780$	1836.00	0.0842812
$781$	25920.0	1.18757
$782$	0	0
$783$	2754.00	0.125696
$784$	0	0
$785$	−30492.0	−1.38638
$786$	15876.0	0.720456
$787$	−26228.0	−1.18796	−0.593982	−	0.804479i	$-0.702445\pi$
$787$	−26228.0	−1.18796	−0.593982	+	0.804479i	$0.702445\pi$
$788$	−1314.00	−0.0594027
$789$	7776.00	0.350866
$790$	55296.0	2.49031
$791$	0	0
$792$	−6804.00	−0.305265
$793$	−13532.0	−0.605972
$794$	−19542.0	−0.873450
$795$	−26892.0	−1.19970
$796$	−5096.00	−0.226913
$797$	43338.0	1.92611	0.963056	−	0.269302i	$-0.0867931\pi$
$797$	43338.0	1.92611	0.963056	+	0.269302i	$0.0867931\pi$
$798$	0	0
$799$	10080.0	0.446314
$800$	8955.00	0.395759
$801$	−3186.00	−0.140539
$802$	−9990.00	−0.439849
$803$	−18072.0	−0.794206
$804$	276.000	0.0121067
$805$	0	0
$806$	−16320.0	−0.713210
$807$	−24642.0	−1.07489
$808$	−8694.00	−0.378532
$809$	−28902.0	−1.25604	−0.628022	−	0.778195i	$-0.716135\pi$
$809$	−28902.0	−1.25604	−0.628022	+	0.778195i	$0.716135\pi$
$810$	−4374.00	−0.189737
$811$	−27164.0	−1.17615	−0.588075	−	0.808807i	$-0.700114\pi$
$811$	−27164.0	−1.17615	−0.588075	+	0.808807i	$0.700114\pi$
$812$	0	0
$813$	16032.0	0.691595
$814$	42984.0	1.85085
$815$	−52776.0	−2.26830
$816$	8946.00	0.383790
$817$	−33232.0	−1.42306
$818$	−16194.0	−0.692188
$819$	0	0
$820$	5724.00	0.243769
$821$	−17202.0	−0.731247	−0.365624	−	0.930763i	$-0.619144\pi$
$821$	−17202.0	−0.731247	−0.365624	+	0.930763i	$0.619144\pi$
$822$	21222.0	0.900489
$823$	−5992.00	−0.253789	−0.126894	−	0.991916i	$-0.540501\pi$
$823$	−5992.00	−0.253789	−0.126894	+	0.991916i	$0.540501\pi$
$824$	−1176.00	−0.0497183
$825$	−21492.0	−0.906976
$826$	0	0
$827$	25884.0	1.08836	0.544181	−	0.838968i	$-0.316841\pi$
$827$	25884.0	1.08836	0.544181	+	0.838968i	$0.316841\pi$
$828$	0	0
$829$	1474.00	0.0617541	0.0308770	−	0.999523i	$-0.490170\pi$
$829$	1474.00	0.0617541	0.0308770	+	0.999523i	$0.490170\pi$
$830$	−11016.0	−0.460688
$831$	−19542.0	−0.815770
$832$	14722.0	0.613454
$833$	0	0
$834$	−468.000	−0.0194311
$835$	−21168.0	−0.877304
$836$	−4464.00	−0.184678
$837$	4320.00	0.178400
$838$	39276.0	1.61905
$839$	−33528.0	−1.37964	−0.689818	−	0.723983i	$-0.742310\pi$
$839$	−33528.0	−1.37964	−0.689818	+	0.723983i	$0.742310\pi$
$840$	0	0
$841$	−13985.0	−0.573414
$842$	966.000	0.0395375
$843$	19854.0	0.811160
$844$	−3076.00	−0.125451
$845$	−18738.0	−0.762848
$846$	6480.00	0.263342
$847$	0	0
$848$	35358.0	1.43184
$849$	−9780.00	−0.395346
$850$	25074.0	1.01180
$851$	0	0
$852$	−2160.00	−0.0868549
$853$	−1190.00	−0.0477665	−0.0238832	−	0.999715i	$-0.507603\pi$
$853$	−1190.00	−0.0477665	−0.0238832	+	0.999715i	$0.507603\pi$
$854$	0	0
$855$	20088.0	0.803503
$856$	252.000	0.0100621
$857$	−34578.0	−1.37825	−0.689126	−	0.724642i	$-0.742005\pi$
$857$	−34578.0	−1.37825	−0.689126	+	0.724642i	$0.742005\pi$
$858$	11016.0	0.438322
$859$	44404.0	1.76373	0.881865	−	0.471501i	$-0.156288\pi$
$859$	44404.0	1.76373	0.881865	+	0.471501i	$0.156288\pi$
$860$	−4824.00	−0.191276
$861$	0	0
$862$	−7848.00	−0.310097
$863$	−38328.0	−1.51182	−0.755910	−	0.654676i	$-0.772805\pi$
$863$	−38328.0	−1.51182	−0.755910	+	0.654676i	$0.772805\pi$
$864$	1215.00	0.0478416
$865$	−15660.0	−0.615556
$866$	12966.0	0.508779
$867$	−9447.00	−0.370054
$868$	0	0
$869$	36864.0	1.43904
$870$	−16524.0	−0.643927
$871$	3128.00	0.121686
$872$	31038.0	1.20537
$873$	2574.00	0.0997900
$874$	0	0
$875$	0	0
$876$	1506.00	0.0580856
$877$	−38842.0	−1.49555	−0.747777	−	0.663950i	$-0.768879\pi$
$877$	−38842.0	−1.49555	−0.747777	+	0.663950i	$0.768879\pi$
$878$	−27048.0	−1.03966
$879$	−15354.0	−0.589167
$880$	46008.0	1.76242
$881$	35046.0	1.34022	0.670108	−	0.742264i	$-0.266248\pi$
$881$	35046.0	1.34022	0.670108	+	0.742264i	$0.266248\pi$
$882$	0	0
$883$	14204.0	0.541339	0.270670	−	0.962672i	$-0.412755\pi$
$883$	14204.0	0.541339	0.270670	+	0.962672i	$0.412755\pi$
$884$	−1428.00	−0.0543313
$885$	7128.00	0.270740
$886$	15804.0	0.599262
$887$	26136.0	0.989359	0.494679	−	0.869076i	$-0.335286\pi$
$887$	26136.0	0.989359	0.494679	+	0.869076i	$0.335286\pi$
$888$	25074.0	0.947554
$889$	0	0
$890$	19116.0	0.719966
$891$	−2916.00	−0.109640
$892$	1888.00	0.0708687
$893$	−29760.0	−1.11521
$894$	15714.0	0.587869
$895$	−41688.0	−1.55696
$896$	0	0
$897$	0	0
$898$	15930.0	0.591972
$899$	16320.0	0.605453
$900$	1791.00	0.0663333
$901$	20916.0	0.773377
$902$	34344.0	1.26777
$903$	0	0
$904$	8442.00	0.310594
$905$	1908.00	0.0700818
$906$	2088.00	0.0765664
$907$	−9052.00	−0.331386	−0.165693	−	0.986177i	$-0.552986\pi$
$907$	−9052.00	−0.331386	−0.165693	+	0.986177i	$0.552986\pi$
$908$	4716.00	0.172363
$909$	−3726.00	−0.135956
$910$	0	0
$911$	5016.00	0.182423	0.0912116	−	0.995832i	$-0.470926\pi$
$911$	5016.00	0.182423	0.0912116	+	0.995832i	$0.470926\pi$
$912$	−26412.0	−0.958979
$913$	−7344.00	−0.266211
$914$	−47310.0	−1.71212
$915$	−21492.0	−0.776507
$916$	1690.00	0.0609598
$917$	0	0
$918$	3402.00	0.122312
$919$	44552.0	1.59917	0.799584	−	0.600555i	$-0.205054\pi$
$919$	44552.0	1.59917	0.799584	+	0.600555i	$0.205054\pi$
$920$	0	0
$921$	−1356.00	−0.0485144
$922$	−16110.0	−0.575439
$923$	−24480.0	−0.872989
$924$	0	0
$925$	79202.0	2.81529
$926$	9984.00	0.354314
$927$	−504.000	−0.0178571
$928$	4590.00	0.162364
$929$	−24234.0	−0.855858	−0.427929	−	0.903812i	$-0.640757\pi$
$929$	−24234.0	−0.855858	−0.427929	+	0.903812i	$0.640757\pi$
$930$	−25920.0	−0.913925
$931$	0	0
$932$	138.000	0.00485015
$933$	−15048.0	−0.528027
$934$	13644.0	0.477993
$935$	27216.0	0.951934
$936$	6426.00	0.224402
$937$	13894.0	0.484415	0.242208	−	0.970224i	$-0.422128\pi$
$937$	13894.0	0.484415	0.242208	+	0.970224i	$0.422128\pi$
$938$	0	0
$939$	−16206.0	−0.563219
$940$	−4320.00	−0.149897
$941$	−46758.0	−1.61984	−0.809919	−	0.586542i	$-0.800489\pi$
$941$	−46758.0	−1.61984	−0.809919	+	0.586542i	$0.800489\pi$
$942$	15246.0	0.527326
$943$	0	0
$944$	−9372.00	−0.323128
$945$	0	0
$946$	−28944.0	−0.994768
$947$	13812.0	0.473949	0.236974	−	0.971516i	$-0.423844\pi$
$947$	13812.0	0.473949	0.236974	+	0.971516i	$0.423844\pi$
$948$	−3072.00	−0.105247
$949$	17068.0	0.583826
$950$	−74028.0	−2.52820
$951$	30258.0	1.03174
$952$	0	0
$953$	−58518.0	−1.98907	−0.994535	−	0.104402i	$-0.966707\pi$
$953$	−58518.0	−1.98907	−0.994535	+	0.104402i	$0.966707\pi$
$954$	13446.0	0.456321
$955$	−20304.0	−0.687981
$956$	1896.00	0.0641433
$957$	−11016.0	−0.372097
$958$	−24192.0	−0.815875
$959$	0	0
$960$	23382.0	0.786095
$961$	−4191.00	−0.140680
$962$	−40596.0	−1.36057
$963$	108.000	0.00361397
$964$	3598.00	0.120211
$965$	72612.0	2.42224
$966$	0	0
$967$	19640.0	0.653133	0.326567	−	0.945174i	$-0.394108\pi$
$967$	19640.0	0.653133	0.326567	+	0.945174i	$0.394108\pi$
$968$	−735.000	−0.0244047
$969$	−15624.0	−0.517972
$970$	−15444.0	−0.511213
$971$	58308.0	1.92708	0.963539	−	0.267568i	$-0.0862200\pi$
$971$	58308.0	1.92708	0.963539	+	0.267568i	$0.0862200\pi$
$972$	243.000	0.00801875
$973$	0	0
$974$	−49848.0	−1.63987
$975$	20298.0	0.666724
$976$	28258.0	0.926759
$977$	−23550.0	−0.771168	−0.385584	−	0.922673i	$-0.626000\pi$
$977$	−23550.0	−0.771168	−0.385584	+	0.922673i	$0.626000\pi$
$978$	26388.0	0.862776
$979$	12744.0	0.416037
$980$	0	0
$981$	13302.0	0.432926
$982$	21420.0	0.696069
$983$	−15768.0	−0.511619	−0.255809	−	0.966727i	$-0.582342\pi$
$983$	−15768.0	−0.511619	−0.255809	+	0.966727i	$0.582342\pi$
$984$	20034.0	0.649045
$985$	−23652.0	−0.765092
$986$	12852.0	0.415102
$987$	0	0
$988$	4216.00	0.135758
$989$	0	0
$990$	17496.0	0.561676
$991$	35264.0	1.13037	0.565186	−	0.824964i	$-0.308805\pi$
$991$	35264.0	1.13037	0.565186	+	0.824964i	$0.308805\pi$
$992$	7200.00	0.230444
$993$	−24132.0	−0.771204
$994$	0	0
$995$	−91728.0	−2.92259
$996$	612.000	0.0194698
$997$	29338.0	0.931940	0.465970	−	0.884801i	$-0.345706\pi$
$997$	29338.0	0.931940	0.465970	+	0.884801i	$0.345706\pi$
$998$	27372.0	0.868182
$999$	10746.0	0.340329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.a.c.1.1		1
3.2	odd	2		441.4.a.j.1.1		1
4.3	odd	2		2352.4.a.r.1.1		1
7.2	even	3		147.4.e.g.67.1		2
7.3	odd	6		147.4.e.i.79.1		2
7.4	even	3		147.4.e.g.79.1		2
7.5	odd	6		147.4.e.i.67.1		2
7.6	odd	2		21.4.a.a.1.1	✓	1
21.2	odd	6		441.4.e.d.361.1		2
21.5	even	6		441.4.e.b.361.1		2
21.11	odd	6		441.4.e.d.226.1		2
21.17	even	6		441.4.e.b.226.1		2
21.20	even	2		63.4.a.c.1.1		1
28.27	even	2		336.4.a.f.1.1		1
35.13	even	4		525.4.d.c.274.2		2
35.27	even	4		525.4.d.c.274.1		2
35.34	odd	2		525.4.a.g.1.1		1
56.13	odd	2		1344.4.a.ba.1.1		1
56.27	even	2		1344.4.a.n.1.1		1
84.83	odd	2		1008.4.a.v.1.1		1
105.104	even	2		1575.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.a.1.1	✓	1	7.6	odd	2
63.4.a.c.1.1		1	21.20	even	2
147.4.a.c.1.1		1	1.1	even	1	trivial
147.4.e.g.67.1		2	7.2	even	3
147.4.e.g.79.1		2	7.4	even	3
147.4.e.i.67.1		2	7.5	odd	6
147.4.e.i.79.1		2	7.3	odd	6
336.4.a.f.1.1		1	28.27	even	2
441.4.a.j.1.1		1	3.2	odd	2
441.4.e.b.226.1		2	21.17	even	6
441.4.e.b.361.1		2	21.5	even	6
441.4.e.d.226.1		2	21.11	odd	6
441.4.e.d.361.1		2	21.2	odd	6
525.4.a.g.1.1		1	35.34	odd	2
525.4.d.c.274.1		2	35.27	even	4
525.4.d.c.274.2		2	35.13	even	4
1008.4.a.v.1.1		1	84.83	odd	2
1344.4.a.n.1.1		1	56.27	even	2
1344.4.a.ba.1.1		1	56.13	odd	2
1575.4.a.b.1.1		1	105.104	even	2
2352.4.a.r.1.1		1	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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