LMFDB - Embedded newform 1815.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,4,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, 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("1815.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1815.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:	$107.088466660$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +3.00000 q^{3} -7.00000 q^{4} +5.00000 q^{5} -3.00000 q^{6} +24.0000 q^{7} +15.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +3.00000 q^{3} -7.00000 q^{4} +5.00000 q^{5} -3.00000 q^{6} +24.0000 q^{7} +15.0000 q^{8} +9.00000 q^{9} -5.00000 q^{10} -21.0000 q^{12} -22.0000 q^{13} -24.0000 q^{14} +15.0000 q^{15} +41.0000 q^{16} +14.0000 q^{17} -9.00000 q^{18} +20.0000 q^{19} -35.0000 q^{20} +72.0000 q^{21} -168.000 q^{23} +45.0000 q^{24} +25.0000 q^{25} +22.0000 q^{26} +27.0000 q^{27} -168.000 q^{28} -230.000 q^{29} -15.0000 q^{30} -288.000 q^{31} -161.000 q^{32} -14.0000 q^{34} +120.000 q^{35} -63.0000 q^{36} -34.0000 q^{37} -20.0000 q^{38} -66.0000 q^{39} +75.0000 q^{40} -122.000 q^{41} -72.0000 q^{42} +188.000 q^{43} +45.0000 q^{45} +168.000 q^{46} +256.000 q^{47} +123.000 q^{48} +233.000 q^{49} -25.0000 q^{50} +42.0000 q^{51} +154.000 q^{52} -338.000 q^{53} -27.0000 q^{54} +360.000 q^{56} +60.0000 q^{57} +230.000 q^{58} +100.000 q^{59} -105.000 q^{60} -742.000 q^{61} +288.000 q^{62} +216.000 q^{63} -167.000 q^{64} -110.000 q^{65} -84.0000 q^{67} -98.0000 q^{68} -504.000 q^{69} -120.000 q^{70} -328.000 q^{71} +135.000 q^{72} +38.0000 q^{73} +34.0000 q^{74} +75.0000 q^{75} -140.000 q^{76} +66.0000 q^{78} +240.000 q^{79} +205.000 q^{80} +81.0000 q^{81} +122.000 q^{82} -1212.00 q^{83} -504.000 q^{84} +70.0000 q^{85} -188.000 q^{86} -690.000 q^{87} +330.000 q^{89} -45.0000 q^{90} -528.000 q^{91} +1176.00 q^{92} -864.000 q^{93} -256.000 q^{94} +100.000 q^{95} -483.000 q^{96} +866.000 q^{97} -233.000 q^{98} +O(q^{100})\)

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	$-0.556567\pi$
$2$	−1.00000	−0.353553	−0.176777	+	0.984251i	$0.556567\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.00000	−0.875000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−3.00000	−0.204124
$7$	24.0000	1.29588	0.647939	−	0.761692i	$-0.275631\pi$
$7$	24.0000	1.29588	0.647939	+	0.761692i	$0.275631\pi$
$8$	15.0000	0.662913
$9$	9.00000	0.333333
$10$	−5.00000	−0.158114
$11$	0	0
$11$	0	0
$12$	−21.0000	−0.505181
$13$	−22.0000	−0.469362	−0.234681	−	0.972072i	$-0.575405\pi$
$13$	−22.0000	−0.469362	−0.234681	+	0.972072i	$0.575405\pi$
$14$	−24.0000	−0.458162
$15$	15.0000	0.258199
$16$	41.0000	0.640625
$17$	14.0000	0.199735	0.0998676	−	0.995001i	$-0.468158\pi$
$17$	14.0000	0.199735	0.0998676	+	0.995001i	$0.468158\pi$
$18$	−9.00000	−0.117851
$19$	20.0000	0.241490	0.120745	−	0.992684i	$-0.461472\pi$
$19$	20.0000	0.241490	0.120745	+	0.992684i	$0.461472\pi$
$20$	−35.0000	−0.391312
$21$	72.0000	0.748176
$22$	0	0
$23$	−168.000	−1.52306	−0.761531	−	0.648129i	$-0.775552\pi$
$23$	−168.000	−1.52306	−0.761531	+	0.648129i	$0.775552\pi$
$24$	45.0000	0.382733
$25$	25.0000	0.200000
$26$	22.0000	0.165944
$27$	27.0000	0.192450
$28$	−168.000	−1.13389
$29$	−230.000	−1.47276	−0.736378	−	0.676570i	$-0.763465\pi$
$29$	−230.000	−1.47276	−0.736378	+	0.676570i	$0.763465\pi$
$30$	−15.0000	−0.0912871
$31$	−288.000	−1.66859	−0.834296	−	0.551317i	$-0.814125\pi$
$31$	−288.000	−1.66859	−0.834296	+	0.551317i	$0.814125\pi$
$32$	−161.000	−0.889408
$33$	0	0
$34$	−14.0000	−0.0706171
$35$	120.000	0.579534
$36$	−63.0000	−0.291667
$37$	−34.0000	−0.151069	−0.0755347	−	0.997143i	$-0.524066\pi$
$37$	−34.0000	−0.151069	−0.0755347	+	0.997143i	$0.524066\pi$
$38$	−20.0000	−0.0853797
$39$	−66.0000	−0.270986
$40$	75.0000	0.296464
$41$	−122.000	−0.464712	−0.232356	−	0.972631i	$-0.574643\pi$
$41$	−122.000	−0.464712	−0.232356	+	0.972631i	$0.574643\pi$
$42$	−72.0000	−0.264520
$43$	188.000	0.666738	0.333369	−	0.942796i	$-0.391815\pi$
$43$	188.000	0.666738	0.333369	+	0.942796i	$0.391815\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	168.000	0.538484
$47$	256.000	0.794499	0.397249	−	0.917711i	$-0.369965\pi$
$47$	256.000	0.794499	0.397249	+	0.917711i	$0.369965\pi$
$48$	123.000	0.369865
$49$	233.000	0.679300
$50$	−25.0000	−0.0707107
$51$	42.0000	0.115317
$52$	154.000	0.410691
$53$	−338.000	−0.875998	−0.437999	−	0.898976i	$-0.644313\pi$
$53$	−338.000	−0.875998	−0.437999	+	0.898976i	$0.644313\pi$
$54$	−27.0000	−0.0680414
$55$	0	0
$56$	360.000	0.859054
$57$	60.0000	0.139424
$58$	230.000	0.520698
$59$	100.000	0.220659	0.110330	−	0.993895i	$-0.464809\pi$
$59$	100.000	0.220659	0.110330	+	0.993895i	$0.464809\pi$
$60$	−105.000	−0.225924
$61$	−742.000	−1.55743	−0.778716	−	0.627376i	$-0.784129\pi$
$61$	−742.000	−1.55743	−0.778716	+	0.627376i	$0.784129\pi$
$62$	288.000	0.589936
$63$	216.000	0.431959
$64$	−167.000	−0.326172
$65$	−110.000	−0.209905
$66$	0	0
$67$	−84.0000	−0.153168	−0.0765838	−	0.997063i	$-0.524401\pi$
$67$	−84.0000	−0.153168	−0.0765838	+	0.997063i	$0.524401\pi$
$68$	−98.0000	−0.174768
$69$	−504.000	−0.879340
$70$	−120.000	−0.204896
$71$	−328.000	−0.548260	−0.274130	−	0.961693i	$-0.588390\pi$
$71$	−328.000	−0.548260	−0.274130	+	0.961693i	$0.588390\pi$
$72$	135.000	0.220971
$73$	38.0000	0.0609255	0.0304628	−	0.999536i	$-0.490302\pi$
$73$	38.0000	0.0609255	0.0304628	+	0.999536i	$0.490302\pi$
$74$	34.0000	0.0534111
$75$	75.0000	0.115470
$76$	−140.000	−0.211304
$77$	0	0
$78$	66.0000	0.0958081
$79$	240.000	0.341799	0.170899	−	0.985288i	$-0.445333\pi$
$79$	240.000	0.341799	0.170899	+	0.985288i	$0.445333\pi$
$80$	205.000	0.286496
$81$	81.0000	0.111111
$82$	122.000	0.164301
$83$	−1212.00	−1.60282	−0.801411	−	0.598114i	$-0.795917\pi$
$83$	−1212.00	−1.60282	−0.801411	+	0.598114i	$0.795917\pi$
$84$	−504.000	−0.654654
$85$	70.0000	0.0893243
$86$	−188.000	−0.235727
$87$	−690.000	−0.850296
$88$	0	0
$89$	330.000	0.393033	0.196516	−	0.980501i	$-0.437037\pi$
$89$	330.000	0.393033	0.196516	+	0.980501i	$0.437037\pi$
$90$	−45.0000	−0.0527046
$91$	−528.000	−0.608236
$92$	1176.00	1.33268
$93$	−864.000	−0.963362
$94$	−256.000	−0.280898
$95$	100.000	0.107998
$96$	−483.000	−0.513500
$97$	866.000	0.906484	0.453242	−	0.891387i	$-0.350267\pi$
$97$	866.000	0.906484	0.453242	+	0.891387i	$0.350267\pi$
$98$	−233.000	−0.240169
$99$	0	0
$100$	−175.000	−0.175000
$101$	1218.00	1.19996	0.599978	−	0.800017i	$-0.295176\pi$
$101$	1218.00	1.19996	0.599978	+	0.800017i	$0.295176\pi$
$102$	−42.0000	−0.0407708
$103$	−88.0000	−0.0841835	−0.0420917	−	0.999114i	$-0.513402\pi$
$103$	−88.0000	−0.0841835	−0.0420917	+	0.999114i	$0.513402\pi$
$104$	−330.000	−0.311146
$105$	360.000	0.334594
$106$	338.000	0.309712
$107$	−36.0000	−0.0325257	−0.0162629	−	0.999868i	$-0.505177\pi$
$107$	−36.0000	−0.0325257	−0.0162629	+	0.999868i	$0.505177\pi$
$108$	−189.000	−0.168394
$109$	970.000	0.852378	0.426189	−	0.904634i	$-0.359856\pi$
$109$	970.000	0.852378	0.426189	+	0.904634i	$0.359856\pi$
$110$	0	0
$111$	−102.000	−0.0872199
$112$	984.000	0.830172
$113$	1042.00	0.867461	0.433731	−	0.901043i	$-0.357197\pi$
$113$	1042.00	0.867461	0.433731	+	0.901043i	$0.357197\pi$
$114$	−60.0000	−0.0492940
$115$	−840.000	−0.681134
$116$	1610.00	1.28866
$117$	−198.000	−0.156454
$118$	−100.000	−0.0780148
$119$	336.000	0.258833
$120$	225.000	0.171163
$121$	0	0
$122$	742.000	0.550635
$123$	−366.000	−0.268302
$124$	2016.00	1.46002
$125$	125.000	0.0894427
$126$	−216.000	−0.152721
$127$	−1936.00	−1.35269	−0.676347	−	0.736583i	$-0.736438\pi$
$127$	−1936.00	−1.35269	−0.676347	+	0.736583i	$0.736438\pi$
$128$	1455.00	1.00473
$129$	564.000	0.384941
$130$	110.000	0.0742126
$131$	−732.000	−0.488207	−0.244104	−	0.969749i	$-0.578494\pi$
$131$	−732.000	−0.488207	−0.244104	+	0.969749i	$0.578494\pi$
$132$	0	0
$133$	480.000	0.312942
$134$	84.0000	0.0541529
$135$	135.000	0.0860663
$136$	210.000	0.132407
$137$	−2214.00	−1.38069	−0.690346	−	0.723479i	$-0.742542\pi$
$137$	−2214.00	−1.38069	−0.690346	+	0.723479i	$0.742542\pi$
$138$	504.000	0.310894
$139$	−20.0000	−0.0122042	−0.00610208	−	0.999981i	$-0.501942\pi$
$139$	−20.0000	−0.0122042	−0.00610208	+	0.999981i	$0.501942\pi$
$140$	−840.000	−0.507093
$141$	768.000	0.458704
$142$	328.000	0.193839
$143$	0	0
$144$	369.000	0.213542
$145$	−1150.00	−0.658637
$146$	−38.0000	−0.0215404
$147$	699.000	0.392194
$148$	238.000	0.132186
$149$	1330.00	0.731261	0.365630	−	0.930760i	$-0.380853\pi$
$149$	1330.00	0.731261	0.365630	+	0.930760i	$0.380853\pi$
$150$	−75.0000	−0.0408248
$151$	1208.00	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	1208.00	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	300.000	0.160087
$153$	126.000	0.0665784
$154$	0	0
$155$	−1440.00	−0.746217
$156$	462.000	0.237113
$157$	−3514.00	−1.78629	−0.893146	−	0.449768i	$-0.851507\pi$
$157$	−3514.00	−1.78629	−0.893146	+	0.449768i	$0.851507\pi$
$158$	−240.000	−0.120844
$159$	−1014.00	−0.505757
$160$	−805.000	−0.397755
$161$	−4032.00	−1.97370
$162$	−81.0000	−0.0392837
$163$	−2068.00	−0.993732	−0.496866	−	0.867827i	$-0.665516\pi$
$163$	−2068.00	−0.993732	−0.496866	+	0.867827i	$0.665516\pi$
$164$	854.000	0.406623
$165$	0	0
$166$	1212.00	0.566683
$167$	24.0000	0.0111208	0.00556041	−	0.999985i	$-0.498230\pi$
$167$	24.0000	0.0111208	0.00556041	+	0.999985i	$0.498230\pi$
$168$	1080.00	0.495975
$169$	−1713.00	−0.779700
$170$	−70.0000	−0.0315809
$171$	180.000	0.0804967
$172$	−1316.00	−0.583396
$173$	618.000	0.271593	0.135797	−	0.990737i	$-0.456641\pi$
$173$	618.000	0.271593	0.135797	+	0.990737i	$0.456641\pi$
$174$	690.000	0.300625
$175$	600.000	0.259176
$176$	0	0
$177$	300.000	0.127398
$178$	−330.000	−0.138958
$179$	3340.00	1.39466	0.697328	−	0.716752i	$-0.254372\pi$
$179$	3340.00	1.39466	0.697328	+	0.716752i	$0.254372\pi$
$180$	−315.000	−0.130437
$181$	−178.000	−0.0730974	−0.0365487	−	0.999332i	$-0.511636\pi$
$181$	−178.000	−0.0730974	−0.0365487	+	0.999332i	$0.511636\pi$
$182$	528.000	0.215044
$183$	−2226.00	−0.899184
$184$	−2520.00	−1.00966
$185$	−170.000	−0.0675603
$186$	864.000	0.340600
$187$	0	0
$188$	−1792.00	−0.695186
$189$	648.000	0.249392
$190$	−100.000	−0.0381830
$191$	−1888.00	−0.715240	−0.357620	−	0.933867i	$-0.616412\pi$
$191$	−1888.00	−0.715240	−0.357620	+	0.933867i	$0.616412\pi$
$192$	−501.000	−0.188315
$193$	−1922.00	−0.716832	−0.358416	−	0.933562i	$-0.616683\pi$
$193$	−1922.00	−0.716832	−0.358416	+	0.933562i	$0.616683\pi$
$194$	−866.000	−0.320491
$195$	−330.000	−0.121189
$196$	−1631.00	−0.594388
$197$	−2526.00	−0.913554	−0.456777	−	0.889581i	$-0.650996\pi$
$197$	−2526.00	−0.913554	−0.456777	+	0.889581i	$0.650996\pi$
$198$	0	0
$199$	−1160.00	−0.413217	−0.206609	−	0.978424i	$-0.566243\pi$
$199$	−1160.00	−0.413217	−0.206609	+	0.978424i	$0.566243\pi$
$200$	375.000	0.132583
$201$	−252.000	−0.0884314
$202$	−1218.00	−0.424248
$203$	−5520.00	−1.90851
$204$	−294.000	−0.100903
$205$	−610.000	−0.207826
$206$	88.0000	0.0297634
$207$	−1512.00	−0.507687
$208$	−902.000	−0.300685
$209$	0	0
$210$	−360.000	−0.118297
$211$	4468.00	1.45777	0.728886	−	0.684635i	$-0.240039\pi$
$211$	4468.00	1.45777	0.728886	+	0.684635i	$0.240039\pi$
$212$	2366.00	0.766498
$213$	−984.000	−0.316538
$214$	36.0000	0.0114996
$215$	940.000	0.298174
$216$	405.000	0.127578
$217$	−6912.00	−2.16229
$218$	−970.000	−0.301361
$219$	114.000	0.0351754
$220$	0	0
$221$	−308.000	−0.0937481
$222$	102.000	0.0308369
$223$	6032.00	1.81136	0.905678	−	0.423965i	$-0.139362\pi$
$223$	6032.00	1.81136	0.905678	+	0.423965i	$0.139362\pi$
$224$	−3864.00	−1.15256
$225$	225.000	0.0666667
$226$	−1042.00	−0.306694
$227$	−2636.00	−0.770738	−0.385369	−	0.922763i	$-0.625926\pi$
$227$	−2636.00	−0.770738	−0.385369	+	0.922763i	$0.625926\pi$
$228$	−420.000	−0.121996
$229$	4830.00	1.39378	0.696889	−	0.717179i	$-0.254567\pi$
$229$	4830.00	1.39378	0.696889	+	0.717179i	$0.254567\pi$
$230$	840.000	0.240817
$231$	0	0
$232$	−3450.00	−0.976309
$233$	−2682.00	−0.754093	−0.377046	−	0.926194i	$-0.623060\pi$
$233$	−2682.00	−0.754093	−0.377046	+	0.926194i	$0.623060\pi$
$234$	198.000	0.0553148
$235$	1280.00	0.355311
$236$	−700.000	−0.193077
$237$	720.000	0.197338
$238$	−336.000	−0.0915111
$239$	−2320.00	−0.627901	−0.313950	−	0.949439i	$-0.601653\pi$
$239$	−2320.00	−0.627901	−0.313950	+	0.949439i	$0.601653\pi$
$240$	615.000	0.165409
$241$	−2002.00	−0.535104	−0.267552	−	0.963543i	$-0.586215\pi$
$241$	−2002.00	−0.535104	−0.267552	+	0.963543i	$0.586215\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	5194.00	1.36275
$245$	1165.00	0.303792
$246$	366.000	0.0948590
$247$	−440.000	−0.113346
$248$	−4320.00	−1.10613
$249$	−3636.00	−0.925390
$250$	−125.000	−0.0316228
$251$	132.000	0.0331943	0.0165971	−	0.999862i	$-0.494717\pi$
$251$	132.000	0.0331943	0.0165971	+	0.999862i	$0.494717\pi$
$252$	−1512.00	−0.377964
$253$	0	0
$254$	1936.00	0.478250
$255$	210.000	0.0515714
$256$	−119.000	−0.0290527
$257$	−7614.00	−1.84805	−0.924024	−	0.382335i	$-0.875120\pi$
$257$	−7614.00	−1.84805	−0.924024	+	0.382335i	$0.875120\pi$
$258$	−564.000	−0.136097
$259$	−816.000	−0.195767
$260$	770.000	0.183667
$261$	−2070.00	−0.490919
$262$	732.000	0.172607
$263$	4888.00	1.14603	0.573017	−	0.819543i	$-0.305773\pi$
$263$	4888.00	1.14603	0.573017	+	0.819543i	$0.305773\pi$
$264$	0	0
$265$	−1690.00	−0.391758
$266$	−480.000	−0.110642
$267$	990.000	0.226918
$268$	588.000	0.134022
$269$	1270.00	0.287856	0.143928	−	0.989588i	$-0.454027\pi$
$269$	1270.00	0.287856	0.143928	+	0.989588i	$0.454027\pi$
$270$	−135.000	−0.0304290
$271$	−1072.00	−0.240293	−0.120146	−	0.992756i	$-0.538336\pi$
$271$	−1072.00	−0.240293	−0.120146	+	0.992756i	$0.538336\pi$
$272$	574.000	0.127955
$273$	−1584.00	−0.351165
$274$	2214.00	0.488148
$275$	0	0
$276$	3528.00	0.769423
$277$	5394.00	1.17001	0.585007	−	0.811028i	$-0.301092\pi$
$277$	5394.00	1.17001	0.585007	+	0.811028i	$0.301092\pi$
$278$	20.0000	0.00431482
$279$	−2592.00	−0.556197
$280$	1800.00	0.384181
$281$	−2442.00	−0.518425	−0.259213	−	0.965820i	$-0.583463\pi$
$281$	−2442.00	−0.518425	−0.259213	+	0.965820i	$0.583463\pi$
$282$	−768.000	−0.162176
$283$	−2772.00	−0.582255	−0.291128	−	0.956684i	$-0.594030\pi$
$283$	−2772.00	−0.582255	−0.291128	+	0.956684i	$0.594030\pi$
$284$	2296.00	0.479727
$285$	300.000	0.0623525
$286$	0	0
$287$	−2928.00	−0.602210
$288$	−1449.00	−0.296469
$289$	−4717.00	−0.960106
$290$	1150.00	0.232863
$291$	2598.00	0.523359
$292$	−266.000	−0.0533098
$293$	−4542.00	−0.905619	−0.452810	−	0.891607i	$-0.649578\pi$
$293$	−4542.00	−0.905619	−0.452810	+	0.891607i	$0.649578\pi$
$294$	−699.000	−0.138662
$295$	500.000	0.0986818
$296$	−510.000	−0.100146
$297$	0	0
$298$	−1330.00	−0.258540
$299$	3696.00	0.714867
$300$	−525.000	−0.101036
$301$	4512.00	0.864011
$302$	−1208.00	−0.230174
$303$	3654.00	0.692795
$304$	820.000	0.154705
$305$	−3710.00	−0.696505
$306$	−126.000	−0.0235390
$307$	−5116.00	−0.951093	−0.475546	−	0.879691i	$-0.657750\pi$
$307$	−5116.00	−0.951093	−0.475546	+	0.879691i	$0.657750\pi$
$308$	0	0
$309$	−264.000	−0.0486034
$310$	1440.00	0.263827
$311$	−2808.00	−0.511984	−0.255992	−	0.966679i	$-0.582402\pi$
$311$	−2808.00	−0.511984	−0.255992	+	0.966679i	$0.582402\pi$
$312$	−990.000	−0.179640
$313$	−7318.00	−1.32153	−0.660763	−	0.750594i	$-0.729767\pi$
$313$	−7318.00	−1.32153	−0.660763	+	0.750594i	$0.729767\pi$
$314$	3514.00	0.631549
$315$	1080.00	0.193178
$316$	−1680.00	−0.299074
$317$	2246.00	0.397943	0.198971	−	0.980005i	$-0.436240\pi$
$317$	2246.00	0.397943	0.198971	+	0.980005i	$0.436240\pi$
$318$	1014.00	0.178812
$319$	0	0
$320$	−835.000	−0.145868
$321$	−108.000	−0.0187787
$322$	4032.00	0.697809
$323$	280.000	0.0482341
$324$	−567.000	−0.0972222
$325$	−550.000	−0.0938723
$326$	2068.00	0.351337
$327$	2910.00	0.492120
$328$	−1830.00	−0.308064
$329$	6144.00	1.02957
$330$	0	0
$331$	1332.00	0.221188	0.110594	−	0.993866i	$-0.464725\pi$
$331$	1332.00	0.221188	0.110594	+	0.993866i	$0.464725\pi$
$332$	8484.00	1.40247
$333$	−306.000	−0.0503564
$334$	−24.0000	−0.00393180
$335$	−420.000	−0.0684987
$336$	2952.00	0.479300
$337$	11534.0	1.86438	0.932191	−	0.361966i	$-0.117894\pi$
$337$	11534.0	1.86438	0.932191	+	0.361966i	$0.117894\pi$
$338$	1713.00	0.275665
$339$	3126.00	0.500829
$340$	−490.000	−0.0781588
$341$	0	0
$342$	−180.000	−0.0284599
$343$	−2640.00	−0.415588
$344$	2820.00	0.441989
$345$	−2520.00	−0.393253
$346$	−618.000	−0.0960228
$347$	−11956.0	−1.84966	−0.924830	−	0.380382i	$-0.875793\pi$
$347$	−11956.0	−1.84966	−0.924830	+	0.380382i	$0.875793\pi$
$348$	4830.00	0.744009
$349$	−4870.00	−0.746949	−0.373474	−	0.927640i	$-0.621834\pi$
$349$	−4870.00	−0.746949	−0.373474	+	0.927640i	$0.621834\pi$
$350$	−600.000	−0.0916324
$351$	−594.000	−0.0903287
$352$	0	0
$353$	10722.0	1.61664	0.808321	−	0.588742i	$-0.200377\pi$
$353$	10722.0	1.61664	0.808321	+	0.588742i	$0.200377\pi$
$354$	−300.000	−0.0450419
$355$	−1640.00	−0.245189
$356$	−2310.00	−0.343904
$357$	1008.00	0.149437
$358$	−3340.00	−0.493085
$359$	−120.000	−0.0176417	−0.00882083	−	0.999961i	$-0.502808\pi$
$359$	−120.000	−0.0176417	−0.00882083	+	0.999961i	$0.502808\pi$
$360$	675.000	0.0988212
$361$	−6459.00	−0.941682
$362$	178.000	0.0258438
$363$	0	0
$364$	3696.00	0.532206
$365$	190.000	0.0272467
$366$	2226.00	0.317910
$367$	3936.00	0.559830	0.279915	−	0.960025i	$-0.409694\pi$
$367$	3936.00	0.559830	0.279915	+	0.960025i	$0.409694\pi$
$368$	−6888.00	−0.975711
$369$	−1098.00	−0.154904
$370$	170.000	0.0238862
$371$	−8112.00	−1.13519
$372$	6048.00	0.842941
$373$	−3022.00	−0.419499	−0.209750	−	0.977755i	$-0.567265\pi$
$373$	−3022.00	−0.419499	−0.209750	+	0.977755i	$0.567265\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	3840.00	0.526683
$377$	5060.00	0.691255
$378$	−648.000	−0.0881733
$379$	−13340.0	−1.80799	−0.903997	−	0.427539i	$-0.859381\pi$
$379$	−13340.0	−1.80799	−0.903997	+	0.427539i	$0.859381\pi$
$380$	−700.000	−0.0944980
$381$	−5808.00	−0.780979
$382$	1888.00	0.252876
$383$	−1008.00	−0.134481	−0.0672407	−	0.997737i	$-0.521420\pi$
$383$	−1008.00	−0.134481	−0.0672407	+	0.997737i	$0.521420\pi$
$384$	4365.00	0.580079
$385$	0	0
$386$	1922.00	0.253438
$387$	1692.00	0.222246
$388$	−6062.00	−0.793174
$389$	9630.00	1.25517	0.627584	−	0.778549i	$-0.284044\pi$
$389$	9630.00	1.25517	0.627584	+	0.778549i	$0.284044\pi$
$390$	330.000	0.0428467
$391$	−2352.00	−0.304209
$392$	3495.00	0.450317
$393$	−2196.00	−0.281867
$394$	2526.00	0.322990
$395$	1200.00	0.152857
$396$	0	0
$397$	7126.00	0.900866	0.450433	−	0.892810i	$-0.351270\pi$
$397$	7126.00	0.900866	0.450433	+	0.892810i	$0.351270\pi$
$398$	1160.00	0.146094
$399$	1440.00	0.180677
$400$	1025.00	0.128125
$401$	−8718.00	−1.08568	−0.542838	−	0.839837i	$-0.682650\pi$
$401$	−8718.00	−1.08568	−0.542838	+	0.839837i	$0.682650\pi$
$402$	252.000	0.0312652
$403$	6336.00	0.783173
$404$	−8526.00	−1.04996
$405$	405.000	0.0496904
$406$	5520.00	0.674761
$407$	0	0
$408$	630.000	0.0764452
$409$	10870.0	1.31415	0.657074	−	0.753826i	$-0.271794\pi$
$409$	10870.0	1.31415	0.657074	+	0.753826i	$0.271794\pi$
$410$	610.000	0.0734774
$411$	−6642.00	−0.797143
$412$	616.000	0.0736605
$413$	2400.00	0.285947
$414$	1512.00	0.179495
$415$	−6060.00	−0.716804
$416$	3542.00	0.417454
$417$	−60.0000	−0.00704607
$418$	0	0
$419$	−9700.00	−1.13097	−0.565484	−	0.824759i	$-0.691311\pi$
$419$	−9700.00	−1.13097	−0.565484	+	0.824759i	$0.691311\pi$
$420$	−2520.00	−0.292770
$421$	862.000	0.0997893	0.0498947	−	0.998754i	$-0.484111\pi$
$421$	862.000	0.0997893	0.0498947	+	0.998754i	$0.484111\pi$
$422$	−4468.00	−0.515400
$423$	2304.00	0.264833
$424$	−5070.00	−0.580710
$425$	350.000	0.0399470
$426$	984.000	0.111913
$427$	−17808.0	−2.01824
$428$	252.000	0.0284600
$429$	0	0
$430$	−940.000	−0.105421
$431$	−15792.0	−1.76490	−0.882452	−	0.470402i	$-0.844109\pi$
$431$	−15792.0	−1.76490	−0.882452	+	0.470402i	$0.844109\pi$
$432$	1107.00	0.123288
$433$	11602.0	1.28766	0.643830	−	0.765169i	$-0.277345\pi$
$433$	11602.0	1.28766	0.643830	+	0.765169i	$0.277345\pi$
$434$	6912.00	0.764485
$435$	−3450.00	−0.380264
$436$	−6790.00	−0.745830
$437$	−3360.00	−0.367805
$438$	−114.000	−0.0124364
$439$	440.000	0.0478361	0.0239181	−	0.999714i	$-0.492386\pi$
$439$	440.000	0.0478361	0.0239181	+	0.999714i	$0.492386\pi$
$440$	0	0
$441$	2097.00	0.226433
$442$	308.000	0.0331449
$443$	−10188.0	−1.09266	−0.546328	−	0.837571i	$-0.683975\pi$
$443$	−10188.0	−1.09266	−0.546328	+	0.837571i	$0.683975\pi$
$444$	714.000	0.0763174
$445$	1650.00	0.175770
$446$	−6032.00	−0.640411
$447$	3990.00	0.422194
$448$	−4008.00	−0.422679
$449$	−13310.0	−1.39897	−0.699485	−	0.714647i	$-0.746587\pi$
$449$	−13310.0	−1.39897	−0.699485	+	0.714647i	$0.746587\pi$
$450$	−225.000	−0.0235702
$451$	0	0
$452$	−7294.00	−0.759029
$453$	3624.00	0.375873
$454$	2636.00	0.272497
$455$	−2640.00	−0.272011
$456$	900.000	0.0924262
$457$	−3226.00	−0.330210	−0.165105	−	0.986276i	$-0.552796\pi$
$457$	−3226.00	−0.330210	−0.165105	+	0.986276i	$0.552796\pi$
$458$	−4830.00	−0.492775
$459$	378.000	0.0384391
$460$	5880.00	0.595992
$461$	−6582.00	−0.664977	−0.332488	−	0.943107i	$-0.607888\pi$
$461$	−6582.00	−0.664977	−0.332488	+	0.943107i	$0.607888\pi$
$462$	0	0
$463$	15072.0	1.51286	0.756431	−	0.654073i	$-0.226941\pi$
$463$	15072.0	1.51286	0.756431	+	0.654073i	$0.226941\pi$
$464$	−9430.00	−0.943484
$465$	−4320.00	−0.430828
$466$	2682.00	0.266612
$467$	476.000	0.0471663	0.0235831	−	0.999722i	$-0.492493\pi$
$467$	476.000	0.0471663	0.0235831	+	0.999722i	$0.492493\pi$
$468$	1386.00	0.136897
$469$	−2016.00	−0.198487
$470$	−1280.00	−0.125621
$471$	−10542.0	−1.03132
$472$	1500.00	0.146278
$473$	0	0
$474$	−720.000	−0.0697694
$475$	500.000	0.0482980
$476$	−2352.00	−0.226478
$477$	−3042.00	−0.291999
$478$	2320.00	0.221997
$479$	19680.0	1.87725	0.938624	−	0.344941i	$-0.112101\pi$
$479$	19680.0	1.87725	0.938624	+	0.344941i	$0.112101\pi$
$480$	−2415.00	−0.229644
$481$	748.000	0.0709062
$482$	2002.00	0.189188
$483$	−12096.0	−1.13952
$484$	0	0
$485$	4330.00	0.405392
$486$	−243.000	−0.0226805
$487$	−5944.00	−0.553077	−0.276538	−	0.961003i	$-0.589187\pi$
$487$	−5944.00	−0.553077	−0.276538	+	0.961003i	$0.589187\pi$
$488$	−11130.0	−1.03244
$489$	−6204.00	−0.573731
$490$	−1165.00	−0.107407
$491$	−10772.0	−0.990089	−0.495044	−	0.868868i	$-0.664848\pi$
$491$	−10772.0	−0.990089	−0.495044	+	0.868868i	$0.664848\pi$
$492$	2562.00	0.234764
$493$	−3220.00	−0.294161
$494$	440.000	0.0400740
$495$	0	0
$496$	−11808.0	−1.06894
$497$	−7872.00	−0.710478
$498$	3636.00	0.327175
$499$	8140.00	0.730253	0.365127	−	0.930958i	$-0.381026\pi$
$499$	8140.00	0.730253	0.365127	+	0.930958i	$0.381026\pi$
$500$	−875.000	−0.0782624
$501$	72.0000	0.00642060
$502$	−132.000	−0.0117360
$503$	13768.0	1.22045	0.610223	−	0.792229i	$-0.291080\pi$
$503$	13768.0	1.22045	0.610223	+	0.792229i	$0.291080\pi$
$504$	3240.00	0.286351
$505$	6090.00	0.536637
$506$	0	0
$507$	−5139.00	−0.450160
$508$	13552.0	1.18361
$509$	22150.0	1.92884	0.964422	−	0.264368i	$-0.0851633\pi$
$509$	22150.0	1.92884	0.964422	+	0.264368i	$0.0851633\pi$
$510$	−210.000	−0.0182332
$511$	912.000	0.0789521
$512$	−11521.0	−0.994455
$513$	540.000	0.0464748
$514$	7614.00	0.653384
$515$	−440.000	−0.0376480
$516$	−3948.00	−0.336824
$517$	0	0
$518$	816.000	0.0692143
$519$	1854.00	0.156805
$520$	−1650.00	−0.139149
$521$	1562.00	0.131348	0.0656741	−	0.997841i	$-0.479080\pi$
$521$	1562.00	0.131348	0.0656741	+	0.997841i	$0.479080\pi$
$522$	2070.00	0.173566
$523$	668.000	0.0558501	0.0279250	−	0.999610i	$-0.491110\pi$
$523$	668.000	0.0558501	0.0279250	+	0.999610i	$0.491110\pi$
$524$	5124.00	0.427181
$525$	1800.00	0.149635
$526$	−4888.00	−0.405184
$527$	−4032.00	−0.333276
$528$	0	0
$529$	16057.0	1.31972
$530$	1690.00	0.138507
$531$	900.000	0.0735531
$532$	−3360.00	−0.273824
$533$	2684.00	0.218118
$534$	−990.000	−0.0802275
$535$	−180.000	−0.0145459
$536$	−1260.00	−0.101537
$537$	10020.0	0.805205
$538$	−1270.00	−0.101772
$539$	0	0
$540$	−945.000	−0.0753080
$541$	6138.00	0.487788	0.243894	−	0.969802i	$-0.421575\pi$
$541$	6138.00	0.487788	0.243894	+	0.969802i	$0.421575\pi$
$542$	1072.00	0.0849564
$543$	−534.000	−0.0422028
$544$	−2254.00	−0.177646
$545$	4850.00	0.381195
$546$	1584.00	0.124156
$547$	10484.0	0.819494	0.409747	−	0.912199i	$-0.365617\pi$
$547$	10484.0	0.819494	0.409747	+	0.912199i	$0.365617\pi$
$548$	15498.0	1.20811
$549$	−6678.00	−0.519144
$550$	0	0
$551$	−4600.00	−0.355656
$552$	−7560.00	−0.582926
$553$	5760.00	0.442930
$554$	−5394.00	−0.413663
$555$	−510.000	−0.0390059
$556$	140.000	0.0106786
$557$	−3606.00	−0.274311	−0.137155	−	0.990550i	$-0.543796\pi$
$557$	−3606.00	−0.274311	−0.137155	+	0.990550i	$0.543796\pi$
$558$	2592.00	0.196645
$559$	−4136.00	−0.312941
$560$	4920.00	0.371264
$561$	0	0
$562$	2442.00	0.183291
$563$	−12252.0	−0.917159	−0.458579	−	0.888654i	$-0.651641\pi$
$563$	−12252.0	−0.917159	−0.458579	+	0.888654i	$0.651641\pi$
$564$	−5376.00	−0.401366
$565$	5210.00	0.387940
$566$	2772.00	0.205858
$567$	1944.00	0.143986
$568$	−4920.00	−0.363448
$569$	14550.0	1.07200	0.536000	−	0.844218i	$-0.319935\pi$
$569$	14550.0	1.07200	0.536000	+	0.844218i	$0.319935\pi$
$570$	−300.000	−0.0220449
$571$	25468.0	1.86655	0.933277	−	0.359157i	$-0.116936\pi$
$571$	25468.0	1.86655	0.933277	+	0.359157i	$0.116936\pi$
$572$	0	0
$573$	−5664.00	−0.412944
$574$	2928.00	0.212914
$575$	−4200.00	−0.304612
$576$	−1503.00	−0.108724
$577$	12866.0	0.928282	0.464141	−	0.885761i	$-0.346363\pi$
$577$	12866.0	0.928282	0.464141	+	0.885761i	$0.346363\pi$
$578$	4717.00	0.339449
$579$	−5766.00	−0.413863
$580$	8050.00	0.576307
$581$	−29088.0	−2.07706
$582$	−2598.00	−0.185035
$583$	0	0
$584$	570.000	0.0403883
$585$	−990.000	−0.0699683
$586$	4542.00	0.320185
$587$	−14844.0	−1.04374	−0.521872	−	0.853024i	$-0.674766\pi$
$587$	−14844.0	−1.04374	−0.521872	+	0.853024i	$0.674766\pi$
$588$	−4893.00	−0.343170
$589$	−5760.00	−0.402948
$590$	−500.000	−0.0348893
$591$	−7578.00	−0.527440
$592$	−1394.00	−0.0967788
$593$	−20402.0	−1.41283	−0.706416	−	0.707797i	$-0.749689\pi$
$593$	−20402.0	−1.41283	−0.706416	+	0.707797i	$0.749689\pi$
$594$	0	0
$595$	1680.00	0.115753
$596$	−9310.00	−0.639853
$597$	−3480.00	−0.238571
$598$	−3696.00	−0.252744
$599$	10760.0	0.733959	0.366980	−	0.930229i	$-0.380392\pi$
$599$	10760.0	0.733959	0.366980	+	0.930229i	$0.380392\pi$
$600$	1125.00	0.0765466
$601$	−14282.0	−0.969343	−0.484671	−	0.874696i	$-0.661061\pi$
$601$	−14282.0	−0.969343	−0.484671	+	0.874696i	$0.661061\pi$
$602$	−4512.00	−0.305474
$603$	−756.000	−0.0510559
$604$	−8456.00	−0.569652
$605$	0	0
$606$	−3654.00	−0.244940
$607$	−11056.0	−0.739290	−0.369645	−	0.929173i	$-0.620521\pi$
$607$	−11056.0	−0.739290	−0.369645	+	0.929173i	$0.620521\pi$
$608$	−3220.00	−0.214783
$609$	−16560.0	−1.10188
$610$	3710.00	0.246252
$611$	−5632.00	−0.372907
$612$	−882.000	−0.0582561
$613$	16418.0	1.08176	0.540878	−	0.841101i	$-0.318092\pi$
$613$	16418.0	1.08176	0.540878	+	0.841101i	$0.318092\pi$
$614$	5116.00	0.336262
$615$	−1830.00	−0.119988
$616$	0	0
$617$	−10374.0	−0.676891	−0.338445	−	0.940986i	$-0.609901\pi$
$617$	−10374.0	−0.676891	−0.338445	+	0.940986i	$0.609901\pi$
$618$	264.000	0.0171839
$619$	−5260.00	−0.341546	−0.170773	−	0.985310i	$-0.554627\pi$
$619$	−5260.00	−0.341546	−0.170773	+	0.985310i	$0.554627\pi$
$620$	10080.0	0.652940
$621$	−4536.00	−0.293113
$622$	2808.00	0.181014
$623$	7920.00	0.509323
$624$	−2706.00	−0.173600
$625$	625.000	0.0400000
$626$	7318.00	0.467230
$627$	0	0
$628$	24598.0	1.56300
$629$	−476.000	−0.0301739
$630$	−1080.00	−0.0682988
$631$	21352.0	1.34708	0.673542	−	0.739149i	$-0.264772\pi$
$631$	21352.0	1.34708	0.673542	+	0.739149i	$0.264772\pi$
$632$	3600.00	0.226583
$633$	13404.0	0.841645
$634$	−2246.00	−0.140694
$635$	−9680.00	−0.604943
$636$	7098.00	0.442538
$637$	−5126.00	−0.318838
$638$	0	0
$639$	−2952.00	−0.182753
$640$	7275.00	0.449328
$641$	−29118.0	−1.79422	−0.897108	−	0.441812i	$-0.854336\pi$
$641$	−29118.0	−1.79422	−0.897108	+	0.441812i	$0.854336\pi$
$642$	108.000	0.00663928
$643$	5772.00	0.354005	0.177003	−	0.984210i	$-0.443360\pi$
$643$	5772.00	0.354005	0.177003	+	0.984210i	$0.443360\pi$
$644$	28224.0	1.72699
$645$	2820.00	0.172151
$646$	−280.000	−0.0170533
$647$	−14264.0	−0.866732	−0.433366	−	0.901218i	$-0.642674\pi$
$647$	−14264.0	−0.866732	−0.433366	+	0.901218i	$0.642674\pi$
$648$	1215.00	0.0736570
$649$	0	0
$650$	550.000	0.0331889
$651$	−20736.0	−1.24840
$652$	14476.0	0.869515
$653$	6902.00	0.413623	0.206812	−	0.978381i	$-0.433691\pi$
$653$	6902.00	0.413623	0.206812	+	0.978381i	$0.433691\pi$
$654$	−2910.00	−0.173991
$655$	−3660.00	−0.218333
$656$	−5002.00	−0.297706
$657$	342.000	0.0203085
$658$	−6144.00	−0.364009
$659$	−20140.0	−1.19051	−0.595253	−	0.803539i	$-0.702948\pi$
$659$	−20140.0	−1.19051	−0.595253	+	0.803539i	$0.702948\pi$
$660$	0	0
$661$	−3218.00	−0.189358	−0.0946790	−	0.995508i	$-0.530182\pi$
$661$	−3218.00	−0.189358	−0.0946790	+	0.995508i	$0.530182\pi$
$662$	−1332.00	−0.0782019
$663$	−924.000	−0.0541255
$664$	−18180.0	−1.06253
$665$	2400.00	0.139952
$666$	306.000	0.0178037
$667$	38640.0	2.24310
$668$	−168.000	−0.00973071
$669$	18096.0	1.04579
$670$	420.000	0.0242179
$671$	0	0
$672$	−11592.0	−0.665433
$673$	7518.00	0.430606	0.215303	−	0.976547i	$-0.430926\pi$
$673$	7518.00	0.430606	0.215303	+	0.976547i	$0.430926\pi$
$674$	−11534.0	−0.659159
$675$	675.000	0.0384900
$676$	11991.0	0.682237
$677$	18114.0	1.02833	0.514164	−	0.857692i	$-0.328102\pi$
$677$	18114.0	1.02833	0.514164	+	0.857692i	$0.328102\pi$
$678$	−3126.00	−0.177070
$679$	20784.0	1.17469
$680$	1050.00	0.0592142
$681$	−7908.00	−0.444986
$682$	0	0
$683$	−23868.0	−1.33716	−0.668582	−	0.743638i	$-0.733099\pi$
$683$	−23868.0	−1.33716	−0.668582	+	0.743638i	$0.733099\pi$
$684$	−1260.00	−0.0704347
$685$	−11070.0	−0.617464
$686$	2640.00	0.146932
$687$	14490.0	0.804699
$688$	7708.00	0.427129
$689$	7436.00	0.411160
$690$	2520.00	0.139036
$691$	172.000	0.00946916	0.00473458	−	0.999989i	$-0.498493\pi$
$691$	172.000	0.00946916	0.00473458	+	0.999989i	$0.498493\pi$
$692$	−4326.00	−0.237644
$693$	0	0
$694$	11956.0	0.653953
$695$	−100.000	−0.00545787
$696$	−10350.0	−0.563672
$697$	−1708.00	−0.0928194
$698$	4870.00	0.264086
$699$	−8046.00	−0.435376
$700$	−4200.00	−0.226779
$701$	22138.0	1.19278	0.596391	−	0.802694i	$-0.296601\pi$
$701$	22138.0	1.19278	0.596391	+	0.802694i	$0.296601\pi$
$702$	594.000	0.0319360
$703$	−680.000	−0.0364818
$704$	0	0
$705$	3840.00	0.205139
$706$	−10722.0	−0.571569
$707$	29232.0	1.55500
$708$	−2100.00	−0.111473
$709$	3070.00	0.162618	0.0813091	−	0.996689i	$-0.474090\pi$
$709$	3070.00	0.162618	0.0813091	+	0.996689i	$0.474090\pi$
$710$	1640.00	0.0866875
$711$	2160.00	0.113933
$712$	4950.00	0.260546
$713$	48384.0	2.54137
$714$	−1008.00	−0.0528340
$715$	0	0
$716$	−23380.0	−1.22032
$717$	−6960.00	−0.362519
$718$	120.000	0.00623727
$719$	15600.0	0.809154	0.404577	−	0.914504i	$-0.367419\pi$
$719$	15600.0	0.809154	0.404577	+	0.914504i	$0.367419\pi$
$720$	1845.00	0.0954987
$721$	−2112.00	−0.109092
$722$	6459.00	0.332935
$723$	−6006.00	−0.308943
$724$	1246.00	0.0639603
$725$	−5750.00	−0.294551
$726$	0	0
$727$	20696.0	1.05581	0.527904	−	0.849304i	$-0.322978\pi$
$727$	20696.0	1.05581	0.527904	+	0.849304i	$0.322978\pi$
$728$	−7920.00	−0.403207
$729$	729.000	0.0370370
$730$	−190.000	−0.00963317
$731$	2632.00	0.133171
$732$	15582.0	0.786786
$733$	30778.0	1.55090	0.775451	−	0.631408i	$-0.217522\pi$
$733$	30778.0	1.55090	0.775451	+	0.631408i	$0.217522\pi$
$734$	−3936.00	−0.197930
$735$	3495.00	0.175395
$736$	27048.0	1.35462
$737$	0	0
$738$	1098.00	0.0547669
$739$	−11740.0	−0.584388	−0.292194	−	0.956359i	$-0.594385\pi$
$739$	−11740.0	−0.584388	−0.292194	+	0.956359i	$0.594385\pi$
$740$	1190.00	0.0591152
$741$	−1320.00	−0.0654405
$742$	8112.00	0.401349
$743$	−2632.00	−0.129958	−0.0649789	−	0.997887i	$-0.520698\pi$
$743$	−2632.00	−0.129958	−0.0649789	+	0.997887i	$0.520698\pi$
$744$	−12960.0	−0.638625
$745$	6650.00	0.327030
$746$	3022.00	0.148315
$747$	−10908.0	−0.534274
$748$	0	0
$749$	−864.000	−0.0421494
$750$	−375.000	−0.0182574
$751$	−20528.0	−0.997440	−0.498720	−	0.866763i	$-0.666196\pi$
$751$	−20528.0	−0.997440	−0.498720	+	0.866763i	$0.666196\pi$
$752$	10496.0	0.508976
$753$	396.000	0.0191647
$754$	−5060.00	−0.244396
$755$	6040.00	0.291150
$756$	−4536.00	−0.218218
$757$	21646.0	1.03928	0.519642	−	0.854384i	$-0.326066\pi$
$757$	21646.0	1.03928	0.519642	+	0.854384i	$0.326066\pi$
$758$	13340.0	0.639222
$759$	0	0
$760$	1500.00	0.0715931
$761$	−18282.0	−0.870857	−0.435428	−	0.900223i	$-0.643403\pi$
$761$	−18282.0	−0.870857	−0.435428	+	0.900223i	$0.643403\pi$
$762$	5808.00	0.276118
$763$	23280.0	1.10458
$764$	13216.0	0.625835
$765$	630.000	0.0297748
$766$	1008.00	0.0475464
$767$	−2200.00	−0.103569
$768$	−357.000	−0.0167736
$769$	24190.0	1.13435	0.567174	−	0.823598i	$-0.308037\pi$
$769$	24190.0	1.13435	0.567174	+	0.823598i	$0.308037\pi$
$770$	0	0
$771$	−22842.0	−1.06697
$772$	13454.0	0.627228
$773$	−25698.0	−1.19572	−0.597861	−	0.801600i	$-0.703982\pi$
$773$	−25698.0	−1.19572	−0.597861	+	0.801600i	$0.703982\pi$
$774$	−1692.00	−0.0785758
$775$	−7200.00	−0.333718
$776$	12990.0	0.600920
$777$	−2448.00	−0.113026
$778$	−9630.00	−0.443769
$779$	−2440.00	−0.112223
$780$	2310.00	0.106040
$781$	0	0
$782$	2352.00	0.107554
$783$	−6210.00	−0.283432
$784$	9553.00	0.435177
$785$	−17570.0	−0.798854
$786$	2196.00	0.0996549
$787$	−33436.0	−1.51444	−0.757220	−	0.653160i	$-0.773443\pi$
$787$	−33436.0	−1.51444	−0.757220	+	0.653160i	$0.773443\pi$
$788$	17682.0	0.799359
$789$	14664.0	0.661663
$790$	−1200.00	−0.0540431
$791$	25008.0	1.12412
$792$	0	0
$793$	16324.0	0.730999
$794$	−7126.00	−0.318504
$795$	−5070.00	−0.226182
$796$	8120.00	0.361565
$797$	−37594.0	−1.67083	−0.835413	−	0.549623i	$-0.814771\pi$
$797$	−37594.0	−1.67083	−0.835413	+	0.549623i	$0.814771\pi$
$798$	−1440.00	−0.0638790
$799$	3584.00	0.158689
$800$	−4025.00	−0.177882
$801$	2970.00	0.131011
$802$	8718.00	0.383844
$803$	0	0
$804$	1764.00	0.0773775
$805$	−20160.0	−0.882667
$806$	−6336.00	−0.276893
$807$	3810.00	0.166194
$808$	18270.0	0.795466
$809$	−4730.00	−0.205560	−0.102780	−	0.994704i	$-0.532774\pi$
$809$	−4730.00	−0.205560	−0.102780	+	0.994704i	$0.532774\pi$
$810$	−405.000	−0.0175682
$811$	8748.00	0.378772	0.189386	−	0.981903i	$-0.439350\pi$
$811$	8748.00	0.378772	0.189386	+	0.981903i	$0.439350\pi$
$812$	38640.0	1.66995
$813$	−3216.00	−0.138733
$814$	0	0
$815$	−10340.0	−0.444410
$816$	1722.00	0.0738751
$817$	3760.00	0.161011
$818$	−10870.0	−0.464622
$819$	−4752.00	−0.202745
$820$	4270.00	0.181847
$821$	−44142.0	−1.87645	−0.938226	−	0.346024i	$-0.887532\pi$
$821$	−44142.0	−1.87645	−0.938226	+	0.346024i	$0.887532\pi$
$822$	6642.00	0.281833
$823$	3992.00	0.169079	0.0845397	−	0.996420i	$-0.473058\pi$
$823$	3992.00	0.169079	0.0845397	+	0.996420i	$0.473058\pi$
$824$	−1320.00	−0.0558063
$825$	0	0
$826$	−2400.00	−0.101098
$827$	14444.0	0.607336	0.303668	−	0.952778i	$-0.401789\pi$
$827$	14444.0	0.607336	0.303668	+	0.952778i	$0.401789\pi$
$828$	10584.0	0.444226
$829$	42150.0	1.76590	0.882949	−	0.469468i	$-0.155554\pi$
$829$	42150.0	1.76590	0.882949	+	0.469468i	$0.155554\pi$
$830$	6060.00	0.253429
$831$	16182.0	0.675508
$832$	3674.00	0.153093
$833$	3262.00	0.135680
$834$	60.0000	0.00249116
$835$	120.000	0.00497338
$836$	0	0
$837$	−7776.00	−0.321121
$838$	9700.00	0.399858
$839$	13400.0	0.551394	0.275697	−	0.961245i	$-0.411091\pi$
$839$	13400.0	0.551394	0.275697	+	0.961245i	$0.411091\pi$
$840$	5400.00	0.221807
$841$	28511.0	1.16901
$842$	−862.000	−0.0352809
$843$	−7326.00	−0.299313
$844$	−31276.0	−1.27555
$845$	−8565.00	−0.348692
$846$	−2304.00	−0.0936326
$847$	0	0
$848$	−13858.0	−0.561186
$849$	−8316.00	−0.336165
$850$	−350.000	−0.0141234
$851$	5712.00	0.230088
$852$	6888.00	0.276971
$853$	8658.00	0.347531	0.173766	−	0.984787i	$-0.444406\pi$
$853$	8658.00	0.347531	0.173766	+	0.984787i	$0.444406\pi$
$854$	17808.0	0.713556
$855$	900.000	0.0359992
$856$	−540.000	−0.0215617
$857$	−42826.0	−1.70701	−0.853505	−	0.521084i	$-0.825528\pi$
$857$	−42826.0	−1.70701	−0.853505	+	0.521084i	$0.825528\pi$
$858$	0	0
$859$	−35900.0	−1.42595	−0.712976	−	0.701189i	$-0.752653\pi$
$859$	−35900.0	−1.42595	−0.712976	+	0.701189i	$0.752653\pi$
$860$	−6580.00	−0.260902
$861$	−8784.00	−0.347686
$862$	15792.0	0.623988
$863$	−3088.00	−0.121804	−0.0609019	−	0.998144i	$-0.519398\pi$
$863$	−3088.00	−0.121804	−0.0609019	+	0.998144i	$0.519398\pi$
$864$	−4347.00	−0.171167
$865$	3090.00	0.121460
$866$	−11602.0	−0.455256
$867$	−14151.0	−0.554317
$868$	48384.0	1.89200
$869$	0	0
$870$	3450.00	0.134444
$871$	1848.00	0.0718910
$872$	14550.0	0.565052
$873$	7794.00	0.302161
$874$	3360.00	0.130039
$875$	3000.00	0.115907
$876$	−798.000	−0.0307784
$877$	35274.0	1.35817	0.679087	−	0.734058i	$-0.262376\pi$
$877$	35274.0	1.35817	0.679087	+	0.734058i	$0.262376\pi$
$878$	−440.000	−0.0169126
$879$	−13626.0	−0.522860
$880$	0	0
$881$	25042.0	0.957646	0.478823	−	0.877911i	$-0.341064\pi$
$881$	25042.0	0.957646	0.478823	+	0.877911i	$0.341064\pi$
$882$	−2097.00	−0.0800563
$883$	12572.0	0.479141	0.239570	−	0.970879i	$-0.422993\pi$
$883$	12572.0	0.479141	0.239570	+	0.970879i	$0.422993\pi$
$884$	2156.00	0.0820296
$885$	1500.00	0.0569740
$886$	10188.0	0.386312
$887$	21864.0	0.827645	0.413823	−	0.910358i	$-0.364193\pi$
$887$	21864.0	0.827645	0.413823	+	0.910358i	$0.364193\pi$
$888$	−1530.00	−0.0578192
$889$	−46464.0	−1.75293
$890$	−1650.00	−0.0621440
$891$	0	0
$892$	−42224.0	−1.58494
$893$	5120.00	0.191864
$894$	−3990.00	−0.149268
$895$	16700.0	0.623709
$896$	34920.0	1.30200
$897$	11088.0	0.412729
$898$	13310.0	0.494611
$899$	66240.0	2.45743
$900$	−1575.00	−0.0583333
$901$	−4732.00	−0.174968
$902$	0	0
$903$	13536.0	0.498837
$904$	15630.0	0.575051
$905$	−890.000	−0.0326902
$906$	−3624.00	−0.132891
$907$	31236.0	1.14352	0.571761	−	0.820420i	$-0.306260\pi$
$907$	31236.0	1.14352	0.571761	+	0.820420i	$0.306260\pi$
$908$	18452.0	0.674396
$909$	10962.0	0.399985
$910$	2640.00	0.0961705
$911$	8272.00	0.300838	0.150419	−	0.988622i	$-0.451938\pi$
$911$	8272.00	0.300838	0.150419	+	0.988622i	$0.451938\pi$
$912$	2460.00	0.0893188
$913$	0	0
$914$	3226.00	0.116747
$915$	−11130.0	−0.402127
$916$	−33810.0	−1.21956
$917$	−17568.0	−0.632657
$918$	−378.000	−0.0135903
$919$	−20200.0	−0.725067	−0.362533	−	0.931971i	$-0.618088\pi$
$919$	−20200.0	−0.725067	−0.362533	+	0.931971i	$0.618088\pi$
$920$	−12600.0	−0.451532
$921$	−15348.0	−0.549114
$922$	6582.00	0.235105
$923$	7216.00	0.257332
$924$	0	0
$925$	−850.000	−0.0302139
$926$	−15072.0	−0.534878
$927$	−792.000	−0.0280612
$928$	37030.0	1.30988
$929$	31010.0	1.09516	0.547581	−	0.836753i	$-0.315549\pi$
$929$	31010.0	1.09516	0.547581	+	0.836753i	$0.315549\pi$
$930$	4320.00	0.152321
$931$	4660.00	0.164044
$932$	18774.0	0.659831
$933$	−8424.00	−0.295594
$934$	−476.000	−0.0166758
$935$	0	0
$936$	−2970.00	−0.103715
$937$	39174.0	1.36580	0.682902	−	0.730510i	$-0.260717\pi$
$937$	39174.0	1.36580	0.682902	+	0.730510i	$0.260717\pi$
$938$	2016.00	0.0701756
$939$	−21954.0	−0.762984
$940$	−8960.00	−0.310897
$941$	4138.00	0.143353	0.0716764	−	0.997428i	$-0.477165\pi$
$941$	4138.00	0.143353	0.0716764	+	0.997428i	$0.477165\pi$
$942$	10542.0	0.364625
$943$	20496.0	0.707785
$944$	4100.00	0.141360
$945$	3240.00	0.111531
$946$	0	0
$947$	23676.0	0.812425	0.406213	−	0.913779i	$-0.366849\pi$
$947$	23676.0	0.812425	0.406213	+	0.913779i	$0.366849\pi$
$948$	−5040.00	−0.172670
$949$	−836.000	−0.0285961
$950$	−500.000	−0.0170759
$951$	6738.00	0.229752
$952$	5040.00	0.171583
$953$	−18922.0	−0.643173	−0.321586	−	0.946880i	$-0.604216\pi$
$953$	−18922.0	−0.643173	−0.321586	+	0.946880i	$0.604216\pi$
$954$	3042.00	0.103237
$955$	−9440.00	−0.319865
$956$	16240.0	0.549413
$957$	0	0
$958$	−19680.0	−0.663708
$959$	−53136.0	−1.78921
$960$	−2505.00	−0.0842172
$961$	53153.0	1.78420
$962$	−748.000	−0.0250691
$963$	−324.000	−0.0108419
$964$	14014.0	0.468216
$965$	−9610.00	−0.320577
$966$	12096.0	0.402880
$967$	−39656.0	−1.31877	−0.659385	−	0.751805i	$-0.729183\pi$
$967$	−39656.0	−1.31877	−0.659385	+	0.751805i	$0.729183\pi$
$968$	0	0
$969$	840.000	0.0278480
$970$	−4330.00	−0.143328
$971$	−33228.0	−1.09818	−0.549092	−	0.835762i	$-0.685026\pi$
$971$	−33228.0	−1.09818	−0.549092	+	0.835762i	$0.685026\pi$
$972$	−1701.00	−0.0561313
$973$	−480.000	−0.0158151
$974$	5944.00	0.195542
$975$	−1650.00	−0.0541972
$976$	−30422.0	−0.997730
$977$	−974.000	−0.0318946	−0.0159473	−	0.999873i	$-0.505076\pi$
$977$	−974.000	−0.0318946	−0.0159473	+	0.999873i	$0.505076\pi$
$978$	6204.00	0.202845
$979$	0	0
$980$	−8155.00	−0.265818
$981$	8730.00	0.284126
$982$	10772.0	0.350049
$983$	−13608.0	−0.441534	−0.220767	−	0.975327i	$-0.570856\pi$
$983$	−13608.0	−0.441534	−0.220767	+	0.975327i	$0.570856\pi$
$984$	−5490.00	−0.177861
$985$	−12630.0	−0.408554
$986$	3220.00	0.104002
$987$	18432.0	0.594425
$988$	3080.00	0.0991780
$989$	−31584.0	−1.01548
$990$	0	0
$991$	13472.0	0.431839	0.215919	−	0.976411i	$-0.430725\pi$
$991$	13472.0	0.431839	0.215919	+	0.976411i	$0.430725\pi$
$992$	46368.0	1.48406
$993$	3996.00	0.127703
$994$	7872.00	0.251192
$995$	−5800.00	−0.184796
$996$	25452.0	0.809716
$997$	3234.00	0.102730	0.0513650	−	0.998680i	$-0.483643\pi$
$997$	3234.00	0.102730	0.0513650	+	0.998680i	$0.483643\pi$
$998$	−8140.00	−0.258184
$999$	−918.000	−0.0290733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.e.1.1		1
11.10	odd	2		15.4.a.a.1.1	✓	1
33.32	even	2		45.4.a.c.1.1		1
44.43	even	2		240.4.a.e.1.1		1
55.32	even	4		75.4.b.b.49.2		2
55.43	even	4		75.4.b.b.49.1		2
55.54	odd	2		75.4.a.b.1.1		1
77.76	even	2		735.4.a.e.1.1		1
88.21	odd	2		960.4.a.b.1.1		1
88.43	even	2		960.4.a.ba.1.1		1
99.32	even	6		405.4.e.i.136.1		2
99.43	odd	6		405.4.e.g.271.1		2
99.65	even	6		405.4.e.i.271.1		2
99.76	odd	6		405.4.e.g.136.1		2
132.131	odd	2		720.4.a.n.1.1		1
165.32	odd	4		225.4.b.e.199.1		2
165.98	odd	4		225.4.b.e.199.2		2
165.164	even	2		225.4.a.f.1.1		1
220.43	odd	4		1200.4.f.b.49.1		2
220.87	odd	4		1200.4.f.b.49.2		2
220.219	even	2		1200.4.a.t.1.1		1
231.230	odd	2		2205.4.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.4.a.a.1.1	✓	1	11.10	odd	2
45.4.a.c.1.1		1	33.32	even	2
75.4.a.b.1.1		1	55.54	odd	2
75.4.b.b.49.1		2	55.43	even	4
75.4.b.b.49.2		2	55.32	even	4
225.4.a.f.1.1		1	165.164	even	2
225.4.b.e.199.1		2	165.32	odd	4
225.4.b.e.199.2		2	165.98	odd	4
240.4.a.e.1.1		1	44.43	even	2
405.4.e.g.136.1		2	99.76	odd	6
405.4.e.g.271.1		2	99.43	odd	6
405.4.e.i.136.1		2	99.32	even	6
405.4.e.i.271.1		2	99.65	even	6
720.4.a.n.1.1		1	132.131	odd	2
735.4.a.e.1.1		1	77.76	even	2
960.4.a.b.1.1		1	88.21	odd	2
960.4.a.ba.1.1		1	88.43	even	2
1200.4.a.t.1.1		1	220.219	even	2
1200.4.f.b.49.1		2	220.43	odd	4
1200.4.f.b.49.2		2	220.87	odd	4
1815.4.a.e.1.1		1	1.1	even	1	trivial
2205.4.a.l.1.1		1	231.230	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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