LMFDB - Embedded newform 1470.4.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,4,Mod(1,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, 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("1470.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1470.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:	$86.7328077084$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +33.0000 q^{11} +12.0000 q^{12} -37.0000 q^{13} +15.0000 q^{15} +16.0000 q^{16} +60.0000 q^{17} -18.0000 q^{18} +119.000 q^{19} +20.0000 q^{20} -66.0000 q^{22} +75.0000 q^{23} -24.0000 q^{24} +25.0000 q^{25} +74.0000 q^{26} +27.0000 q^{27} -144.000 q^{29} -30.0000 q^{30} -46.0000 q^{31} -32.0000 q^{32} +99.0000 q^{33} -120.000 q^{34} +36.0000 q^{36} -199.000 q^{37} -238.000 q^{38} -111.000 q^{39} -40.0000 q^{40} -135.000 q^{41} +260.000 q^{43} +132.000 q^{44} +45.0000 q^{45} -150.000 q^{46} +183.000 q^{47} +48.0000 q^{48} -50.0000 q^{50} +180.000 q^{51} -148.000 q^{52} +411.000 q^{53} -54.0000 q^{54} +165.000 q^{55} +357.000 q^{57} +288.000 q^{58} +492.000 q^{59} +60.0000 q^{60} -460.000 q^{61} +92.0000 q^{62} +64.0000 q^{64} -185.000 q^{65} -198.000 q^{66} +980.000 q^{67} +240.000 q^{68} +225.000 q^{69} -306.000 q^{71} -72.0000 q^{72} -934.000 q^{73} +398.000 q^{74} +75.0000 q^{75} +476.000 q^{76} +222.000 q^{78} -604.000 q^{79} +80.0000 q^{80} +81.0000 q^{81} +270.000 q^{82} +108.000 q^{83} +300.000 q^{85} -520.000 q^{86} -432.000 q^{87} -264.000 q^{88} -546.000 q^{89} -90.0000 q^{90} +300.000 q^{92} -138.000 q^{93} -366.000 q^{94} +595.000 q^{95} -96.0000 q^{96} +1808.00 q^{97} +297.000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−6.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−10.0000	−0.316228
$11$	33.0000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	33.0000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	12.0000	0.288675
$13$	−37.0000	−0.789381	−0.394691	−	0.918814i	$-0.629148\pi$
$13$	−37.0000	−0.789381	−0.394691	+	0.918814i	$0.629148\pi$
$14$	0	0
$15$	15.0000	0.258199
$16$	16.0000	0.250000
$17$	60.0000	0.856008	0.428004	−	0.903777i	$-0.359217\pi$
$17$	60.0000	0.856008	0.428004	+	0.903777i	$0.359217\pi$
$18$	−18.0000	−0.235702
$19$	119.000	1.43687	0.718433	−	0.695596i	$-0.244859\pi$
$19$	119.000	1.43687	0.718433	+	0.695596i	$0.244859\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−66.0000	−0.639602
$23$	75.0000	0.679938	0.339969	−	0.940437i	$-0.389583\pi$
$23$	75.0000	0.679938	0.339969	+	0.940437i	$0.389583\pi$
$24$	−24.0000	−0.204124
$25$	25.0000	0.200000
$26$	74.0000	0.558177
$27$	27.0000	0.192450
$28$	0	0
$29$	−144.000	−0.922073	−0.461037	−	0.887381i	$-0.652522\pi$
$29$	−144.000	−0.922073	−0.461037	+	0.887381i	$0.652522\pi$
$30$	−30.0000	−0.182574
$31$	−46.0000	−0.266511	−0.133256	−	0.991082i	$-0.542543\pi$
$31$	−46.0000	−0.266511	−0.133256	+	0.991082i	$0.542543\pi$
$32$	−32.0000	−0.176777
$33$	99.0000	0.522233
$34$	−120.000	−0.605289
$35$	0	0
$36$	36.0000	0.166667
$37$	−199.000	−0.884200	−0.442100	−	0.896966i	$-0.645766\pi$
$37$	−199.000	−0.884200	−0.442100	+	0.896966i	$0.645766\pi$
$38$	−238.000	−1.01602
$39$	−111.000	−0.455749
$40$	−40.0000	−0.158114
$41$	−135.000	−0.514231	−0.257115	−	0.966381i	$-0.582772\pi$
$41$	−135.000	−0.514231	−0.257115	+	0.966381i	$0.582772\pi$
$42$	0	0
$43$	260.000	0.922084	0.461042	−	0.887378i	$-0.347476\pi$
$43$	260.000	0.922084	0.461042	+	0.887378i	$0.347476\pi$
$44$	132.000	0.452267
$45$	45.0000	0.149071
$46$	−150.000	−0.480789
$47$	183.000	0.567942	0.283971	−	0.958833i	$-0.408348\pi$
$47$	183.000	0.567942	0.283971	+	0.958833i	$0.408348\pi$
$48$	48.0000	0.144338
$49$	0	0
$50$	−50.0000	−0.141421
$51$	180.000	0.494217
$52$	−148.000	−0.394691
$53$	411.000	1.06519	0.532596	−	0.846370i	$-0.321216\pi$
$53$	411.000	1.06519	0.532596	+	0.846370i	$0.321216\pi$
$54$	−54.0000	−0.136083
$55$	165.000	0.404520
$56$	0	0
$57$	357.000	0.829576
$58$	288.000	0.652004
$59$	492.000	1.08564	0.542822	−	0.839848i	$-0.317356\pi$
$59$	492.000	1.08564	0.542822	+	0.839848i	$0.317356\pi$
$60$	60.0000	0.129099
$61$	−460.000	−0.965524	−0.482762	−	0.875752i	$-0.660366\pi$
$61$	−460.000	−0.965524	−0.482762	+	0.875752i	$0.660366\pi$
$62$	92.0000	0.188452
$63$	0	0
$64$	64.0000	0.125000
$65$	−185.000	−0.353022
$66$	−198.000	−0.369274
$67$	980.000	1.78696	0.893478	−	0.449107i	$-0.148258\pi$
$67$	980.000	1.78696	0.893478	+	0.449107i	$0.148258\pi$
$68$	240.000	0.428004
$69$	225.000	0.392563
$70$	0	0
$71$	−306.000	−0.511486	−0.255743	−	0.966745i	$-0.582320\pi$
$71$	−306.000	−0.511486	−0.255743	+	0.966745i	$0.582320\pi$
$72$	−72.0000	−0.117851
$73$	−934.000	−1.49749	−0.748743	−	0.662861i	$-0.769342\pi$
$73$	−934.000	−1.49749	−0.748743	+	0.662861i	$0.769342\pi$
$74$	398.000	0.625224
$75$	75.0000	0.115470
$76$	476.000	0.718433
$77$	0	0
$78$	222.000	0.322263
$79$	−604.000	−0.860194	−0.430097	−	0.902783i	$-0.641521\pi$
$79$	−604.000	−0.860194	−0.430097	+	0.902783i	$0.641521\pi$
$80$	80.0000	0.111803
$81$	81.0000	0.111111
$82$	270.000	0.363616
$83$	108.000	0.142826	0.0714129	−	0.997447i	$-0.477249\pi$
$83$	108.000	0.142826	0.0714129	+	0.997447i	$0.477249\pi$
$84$	0	0
$85$	300.000	0.382818
$86$	−520.000	−0.652012
$87$	−432.000	−0.532359
$88$	−264.000	−0.319801
$89$	−546.000	−0.650291	−0.325145	−	0.945664i	$-0.605413\pi$
$89$	−546.000	−0.650291	−0.325145	+	0.945664i	$0.605413\pi$
$90$	−90.0000	−0.105409
$91$	0	0
$92$	300.000	0.339969
$93$	−138.000	−0.153870
$94$	−366.000	−0.401596
$95$	595.000	0.642586
$96$	−96.0000	−0.102062
$97$	1808.00	1.89252	0.946261	−	0.323405i	$-0.104828\pi$
$97$	1808.00	1.89252	0.946261	+	0.323405i	$0.104828\pi$
$98$	0	0
$99$	297.000	0.301511
$100$	100.000	0.100000
$101$	312.000	0.307378	0.153689	−	0.988119i	$-0.450885\pi$
$101$	312.000	0.307378	0.153689	+	0.988119i	$0.450885\pi$
$102$	−360.000	−0.349464
$103$	584.000	0.558672	0.279336	−	0.960193i	$-0.409886\pi$
$103$	584.000	0.558672	0.279336	+	0.960193i	$0.409886\pi$
$104$	296.000	0.279088
$105$	0	0
$106$	−822.000	−0.753205
$107$	−1086.00	−0.981192	−0.490596	−	0.871387i	$-0.663221\pi$
$107$	−1086.00	−0.981192	−0.490596	+	0.871387i	$0.663221\pi$
$108$	108.000	0.0962250
$109$	1286.00	1.13006	0.565030	−	0.825071i	$-0.308865\pi$
$109$	1286.00	1.13006	0.565030	+	0.825071i	$0.308865\pi$
$110$	−330.000	−0.286039
$111$	−597.000	−0.510493
$112$	0	0
$113$	90.0000	0.0749247	0.0374623	−	0.999298i	$-0.488073\pi$
$113$	90.0000	0.0749247	0.0374623	+	0.999298i	$0.488073\pi$
$114$	−714.000	−0.586598
$115$	375.000	0.304078
$116$	−576.000	−0.461037
$117$	−333.000	−0.263127
$118$	−984.000	−0.767666
$119$	0	0
$120$	−120.000	−0.0912871
$121$	−242.000	−0.181818
$122$	920.000	0.682729
$123$	−405.000	−0.296891
$124$	−184.000	−0.133256
$125$	125.000	0.0894427
$126$	0	0
$127$	2375.00	1.65943	0.829713	−	0.558190i	$-0.188504\pi$
$127$	2375.00	1.65943	0.829713	+	0.558190i	$0.188504\pi$
$128$	−128.000	−0.0883883
$129$	780.000	0.532366
$130$	370.000	0.249624
$131$	1821.00	1.21452	0.607258	−	0.794505i	$-0.292270\pi$
$131$	1821.00	1.21452	0.607258	+	0.794505i	$0.292270\pi$
$132$	396.000	0.261116
$133$	0	0
$134$	−1960.00	−1.26357
$135$	135.000	0.0860663
$136$	−480.000	−0.302645
$137$	−354.000	−0.220761	−0.110381	−	0.993889i	$-0.535207\pi$
$137$	−354.000	−0.220761	−0.110381	+	0.993889i	$0.535207\pi$
$138$	−450.000	−0.277584
$139$	908.000	0.554069	0.277034	−	0.960860i	$-0.410648\pi$
$139$	908.000	0.554069	0.277034	+	0.960860i	$0.410648\pi$
$140$	0	0
$141$	549.000	0.327902
$142$	612.000	0.361675
$143$	−1221.00	−0.714022
$144$	144.000	0.0833333
$145$	−720.000	−0.412364
$146$	1868.00	1.05888
$147$	0	0
$148$	−796.000	−0.442100
$149$	−2868.00	−1.57688	−0.788442	−	0.615109i	$-0.789112\pi$
$149$	−2868.00	−1.57688	−0.788442	+	0.615109i	$0.789112\pi$
$150$	−150.000	−0.0816497
$151$	−406.000	−0.218807	−0.109403	−	0.993997i	$-0.534894\pi$
$151$	−406.000	−0.218807	−0.109403	+	0.993997i	$0.534894\pi$
$152$	−952.000	−0.508009
$153$	540.000	0.285336
$154$	0	0
$155$	−230.000	−0.119187
$156$	−444.000	−0.227875
$157$	−1573.00	−0.799612	−0.399806	−	0.916600i	$-0.630922\pi$
$157$	−1573.00	−0.799612	−0.399806	+	0.916600i	$0.630922\pi$
$158$	1208.00	0.608249
$159$	1233.00	0.614989
$160$	−160.000	−0.0790569
$161$	0	0
$162$	−162.000	−0.0785674
$163$	3392.00	1.62995	0.814975	−	0.579496i	$-0.196750\pi$
$163$	3392.00	1.62995	0.814975	+	0.579496i	$0.196750\pi$
$164$	−540.000	−0.257115
$165$	495.000	0.233550
$166$	−216.000	−0.100993
$167$	−4023.00	−1.86413	−0.932063	−	0.362296i	$-0.881993\pi$
$167$	−4023.00	−1.86413	−0.932063	+	0.362296i	$0.881993\pi$
$168$	0	0
$169$	−828.000	−0.376878
$170$	−600.000	−0.270694
$171$	1071.00	0.478956
$172$	1040.00	0.461042
$173$	2199.00	0.966398	0.483199	−	0.875511i	$-0.339475\pi$
$173$	2199.00	0.966398	0.483199	+	0.875511i	$0.339475\pi$
$174$	864.000	0.376435
$175$	0	0
$176$	528.000	0.226134
$177$	1476.00	0.626796
$178$	1092.00	0.459825
$179$	1923.00	0.802971	0.401485	−	0.915865i	$-0.368494\pi$
$179$	1923.00	0.802971	0.401485	+	0.915865i	$0.368494\pi$
$180$	180.000	0.0745356
$181$	−52.0000	−0.0213543	−0.0106772	−	0.999943i	$-0.503399\pi$
$181$	−52.0000	−0.0213543	−0.0106772	+	0.999943i	$0.503399\pi$
$182$	0	0
$183$	−1380.00	−0.557446
$184$	−600.000	−0.240394
$185$	−995.000	−0.395426
$186$	276.000	0.108803
$187$	1980.00	0.774288
$188$	732.000	0.283971
$189$	0	0
$190$	−1190.00	−0.454377
$191$	570.000	0.215936	0.107968	−	0.994154i	$-0.465566\pi$
$191$	570.000	0.215936	0.107968	+	0.994154i	$0.465566\pi$
$192$	192.000	0.0721688
$193$	1538.00	0.573615	0.286807	−	0.957988i	$-0.407406\pi$
$193$	1538.00	0.573615	0.286807	+	0.957988i	$0.407406\pi$
$194$	−3616.00	−1.33821
$195$	−555.000	−0.203817
$196$	0	0
$197$	−4383.00	−1.58516	−0.792578	−	0.609770i	$-0.791262\pi$
$197$	−4383.00	−1.58516	−0.792578	+	0.609770i	$0.791262\pi$
$198$	−594.000	−0.213201
$199$	−100.000	−0.0356222	−0.0178111	−	0.999841i	$-0.505670\pi$
$199$	−100.000	−0.0356222	−0.0178111	+	0.999841i	$0.505670\pi$
$200$	−200.000	−0.0707107
$201$	2940.00	1.03170
$202$	−624.000	−0.217349
$203$	0	0
$204$	720.000	0.247108
$205$	−675.000	−0.229971
$206$	−1168.00	−0.395041
$207$	675.000	0.226646
$208$	−592.000	−0.197345
$209$	3927.00	1.29970
$210$	0	0
$211$	−2881.00	−0.939982	−0.469991	−	0.882671i	$-0.655743\pi$
$211$	−2881.00	−0.939982	−0.469991	+	0.882671i	$0.655743\pi$
$212$	1644.00	0.532596
$213$	−918.000	−0.295307
$214$	2172.00	0.693808
$215$	1300.00	0.412369
$216$	−216.000	−0.0680414
$217$	0	0
$218$	−2572.00	−0.799073
$219$	−2802.00	−0.864574
$220$	660.000	0.202260
$221$	−2220.00	−0.675717
$222$	1194.00	0.360973
$223$	4988.00	1.49785	0.748926	−	0.662653i	$-0.230570\pi$
$223$	4988.00	1.49785	0.748926	+	0.662653i	$0.230570\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	−180.000	−0.0529797
$227$	276.000	0.0806994	0.0403497	−	0.999186i	$-0.487153\pi$
$227$	276.000	0.0806994	0.0403497	+	0.999186i	$0.487153\pi$
$228$	1428.00	0.414788
$229$	1034.00	0.298378	0.149189	−	0.988809i	$-0.452334\pi$
$229$	1034.00	0.298378	0.149189	+	0.988809i	$0.452334\pi$
$230$	−750.000	−0.215015
$231$	0	0
$232$	1152.00	0.326002
$233$	−3102.00	−0.872184	−0.436092	−	0.899902i	$-0.643638\pi$
$233$	−3102.00	−0.872184	−0.436092	+	0.899902i	$0.643638\pi$
$234$	666.000	0.186059
$235$	915.000	0.253992
$236$	1968.00	0.542822
$237$	−1812.00	−0.496633
$238$	0	0
$239$	−2826.00	−0.764848	−0.382424	−	0.923987i	$-0.624911\pi$
$239$	−2826.00	−0.764848	−0.382424	+	0.923987i	$0.624911\pi$
$240$	240.000	0.0645497
$241$	6839.00	1.82796	0.913981	−	0.405758i	$-0.132992\pi$
$241$	6839.00	1.82796	0.913981	+	0.405758i	$0.132992\pi$
$242$	484.000	0.128565
$243$	243.000	0.0641500
$244$	−1840.00	−0.482762
$245$	0	0
$246$	810.000	0.209934
$247$	−4403.00	−1.13424
$248$	368.000	0.0942259
$249$	324.000	0.0824605
$250$	−250.000	−0.0632456
$251$	3627.00	0.912088	0.456044	−	0.889957i	$-0.349266\pi$
$251$	3627.00	0.912088	0.456044	+	0.889957i	$0.349266\pi$
$252$	0	0
$253$	2475.00	0.615027
$254$	−4750.00	−1.17339
$255$	900.000	0.221020
$256$	256.000	0.0625000
$257$	7392.00	1.79416	0.897082	−	0.441864i	$-0.145682\pi$
$257$	7392.00	1.79416	0.897082	+	0.441864i	$0.145682\pi$
$258$	−1560.00	−0.376439
$259$	0	0
$260$	−740.000	−0.176511
$261$	−1296.00	−0.307358
$262$	−3642.00	−0.858792
$263$	−6888.00	−1.61495	−0.807476	−	0.589901i	$-0.799167\pi$
$263$	−6888.00	−1.61495	−0.807476	+	0.589901i	$0.799167\pi$
$264$	−792.000	−0.184637
$265$	2055.00	0.476368
$266$	0	0
$267$	−1638.00	−0.375446
$268$	3920.00	0.893478
$269$	−1056.00	−0.239351	−0.119676	−	0.992813i	$-0.538185\pi$
$269$	−1056.00	−0.239351	−0.119676	+	0.992813i	$0.538185\pi$
$270$	−270.000	−0.0608581
$271$	5336.00	1.19608	0.598042	−	0.801465i	$-0.295945\pi$
$271$	5336.00	1.19608	0.598042	+	0.801465i	$0.295945\pi$
$272$	960.000	0.214002
$273$	0	0
$274$	708.000	0.156102
$275$	825.000	0.180907
$276$	900.000	0.196281
$277$	7766.00	1.68453	0.842263	−	0.539067i	$-0.181223\pi$
$277$	7766.00	1.68453	0.842263	+	0.539067i	$0.181223\pi$
$278$	−1816.00	−0.391786
$279$	−414.000	−0.0888370
$280$	0	0
$281$	8091.00	1.71768	0.858841	−	0.512242i	$-0.171185\pi$
$281$	8091.00	1.71768	0.858841	+	0.512242i	$0.171185\pi$
$282$	−1098.00	−0.231862
$283$	602.000	0.126449	0.0632247	−	0.997999i	$-0.479862\pi$
$283$	602.000	0.126449	0.0632247	+	0.997999i	$0.479862\pi$
$284$	−1224.00	−0.255743
$285$	1785.00	0.370997
$286$	2442.00	0.504890
$287$	0	0
$288$	−288.000	−0.0589256
$289$	−1313.00	−0.267250
$290$	1440.00	0.291585
$291$	5424.00	1.09265
$292$	−3736.00	−0.748743
$293$	9189.00	1.83217	0.916087	−	0.400979i	$-0.131330\pi$
$293$	9189.00	1.83217	0.916087	+	0.400979i	$0.131330\pi$
$294$	0	0
$295$	2460.00	0.485514
$296$	1592.00	0.312612
$297$	891.000	0.174078
$298$	5736.00	1.11503
$299$	−2775.00	−0.536730
$300$	300.000	0.0577350
$301$	0	0
$302$	812.000	0.154720
$303$	936.000	0.177465
$304$	1904.00	0.359217
$305$	−2300.00	−0.431795
$306$	−1080.00	−0.201763
$307$	4976.00	0.925066	0.462533	−	0.886602i	$-0.346941\pi$
$307$	4976.00	0.925066	0.462533	+	0.886602i	$0.346941\pi$
$308$	0	0
$309$	1752.00	0.322550
$310$	460.000	0.0842782
$311$	9744.00	1.77663	0.888314	−	0.459236i	$-0.151877\pi$
$311$	9744.00	1.77663	0.888314	+	0.459236i	$0.151877\pi$
$312$	888.000	0.161132
$313$	−1888.00	−0.340946	−0.170473	−	0.985362i	$-0.554530\pi$
$313$	−1888.00	−0.340946	−0.170473	+	0.985362i	$0.554530\pi$
$314$	3146.00	0.565411
$315$	0	0
$316$	−2416.00	−0.430097
$317$	−5982.00	−1.05988	−0.529941	−	0.848035i	$-0.677786\pi$
$317$	−5982.00	−1.05988	−0.529941	+	0.848035i	$0.677786\pi$
$318$	−2466.00	−0.434863
$319$	−4752.00	−0.834047
$320$	320.000	0.0559017
$321$	−3258.00	−0.566492
$322$	0	0
$323$	7140.00	1.22997
$324$	324.000	0.0555556
$325$	−925.000	−0.157876
$326$	−6784.00	−1.15255
$327$	3858.00	0.652440
$328$	1080.00	0.181808
$329$	0	0
$330$	−990.000	−0.165145
$331$	2945.00	0.489039	0.244519	−	0.969644i	$-0.421370\pi$
$331$	2945.00	0.489039	0.244519	+	0.969644i	$0.421370\pi$
$332$	432.000	0.0714129
$333$	−1791.00	−0.294733
$334$	8046.00	1.31814
$335$	4900.00	0.799151
$336$	0	0
$337$	6896.00	1.11469	0.557343	−	0.830282i	$-0.311821\pi$
$337$	6896.00	1.11469	0.557343	+	0.830282i	$0.311821\pi$
$338$	1656.00	0.266493
$339$	270.000	0.0432578
$340$	1200.00	0.191409
$341$	−1518.00	−0.241068
$342$	−2142.00	−0.338673
$343$	0	0
$344$	−2080.00	−0.326006
$345$	1125.00	0.175559
$346$	−4398.00	−0.683347
$347$	1914.00	0.296106	0.148053	−	0.988979i	$-0.452699\pi$
$347$	1914.00	0.296106	0.148053	+	0.988979i	$0.452699\pi$
$348$	−1728.00	−0.266180
$349$	1124.00	0.172396	0.0861982	−	0.996278i	$-0.472528\pi$
$349$	1124.00	0.172396	0.0861982	+	0.996278i	$0.472528\pi$
$350$	0	0
$351$	−999.000	−0.151916
$352$	−1056.00	−0.159901
$353$	9312.00	1.40404	0.702022	−	0.712155i	$-0.252281\pi$
$353$	9312.00	1.40404	0.702022	+	0.712155i	$0.252281\pi$
$354$	−2952.00	−0.443212
$355$	−1530.00	−0.228744
$356$	−2184.00	−0.325145
$357$	0	0
$358$	−3846.00	−0.567786
$359$	5700.00	0.837979	0.418990	−	0.907991i	$-0.362384\pi$
$359$	5700.00	0.837979	0.418990	+	0.907991i	$0.362384\pi$
$360$	−360.000	−0.0527046
$361$	7302.00	1.06459
$362$	104.000	0.0150998
$363$	−726.000	−0.104973
$364$	0	0
$365$	−4670.00	−0.669696
$366$	2760.00	0.394174
$367$	2297.00	0.326710	0.163355	−	0.986567i	$-0.447768\pi$
$367$	2297.00	0.326710	0.163355	+	0.986567i	$0.447768\pi$
$368$	1200.00	0.169985
$369$	−1215.00	−0.171410
$370$	1990.00	0.279609
$371$	0	0
$372$	−552.000	−0.0769351
$373$	3314.00	0.460033	0.230017	−	0.973187i	$-0.426122\pi$
$373$	3314.00	0.460033	0.230017	+	0.973187i	$0.426122\pi$
$374$	−3960.00	−0.547505
$375$	375.000	0.0516398
$376$	−1464.00	−0.200798
$377$	5328.00	0.727867
$378$	0	0
$379$	−12313.0	−1.66880	−0.834401	−	0.551157i	$-0.814186\pi$
$379$	−12313.0	−1.66880	−0.834401	+	0.551157i	$0.814186\pi$
$380$	2380.00	0.321293
$381$	7125.00	0.958070
$382$	−1140.00	−0.152690
$383$	−9681.00	−1.29158	−0.645791	−	0.763514i	$-0.723472\pi$
$383$	−9681.00	−1.29158	−0.645791	+	0.763514i	$0.723472\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	−3076.00	−0.405607
$387$	2340.00	0.307361
$388$	7232.00	0.946261
$389$	−10614.0	−1.38342	−0.691711	−	0.722174i	$-0.743143\pi$
$389$	−10614.0	−1.38342	−0.691711	+	0.722174i	$0.743143\pi$
$390$	1110.00	0.144121
$391$	4500.00	0.582033
$392$	0	0
$393$	5463.00	0.701201
$394$	8766.00	1.12087
$395$	−3020.00	−0.384690
$396$	1188.00	0.150756
$397$	5642.00	0.713259	0.356630	−	0.934246i	$-0.383926\pi$
$397$	5642.00	0.713259	0.356630	+	0.934246i	$0.383926\pi$
$398$	200.000	0.0251887
$399$	0	0
$400$	400.000	0.0500000
$401$	−5721.00	−0.712452	−0.356226	−	0.934400i	$-0.615937\pi$
$401$	−5721.00	−0.712452	−0.356226	+	0.934400i	$0.615937\pi$
$402$	−5880.00	−0.729522
$403$	1702.00	0.210379
$404$	1248.00	0.153689
$405$	405.000	0.0496904
$406$	0	0
$407$	−6567.00	−0.799789
$408$	−1440.00	−0.174732
$409$	−2710.00	−0.327631	−0.163815	−	0.986491i	$-0.552380\pi$
$409$	−2710.00	−0.327631	−0.163815	+	0.986491i	$0.552380\pi$
$410$	1350.00	0.162614
$411$	−1062.00	−0.127456
$412$	2336.00	0.279336
$413$	0	0
$414$	−1350.00	−0.160263
$415$	540.000	0.0638736
$416$	1184.00	0.139544
$417$	2724.00	0.319892
$418$	−7854.00	−0.919023
$419$	−7875.00	−0.918184	−0.459092	−	0.888389i	$-0.651825\pi$
$419$	−7875.00	−0.918184	−0.459092	+	0.888389i	$0.651825\pi$
$420$	0	0
$421$	−5542.00	−0.641569	−0.320785	−	0.947152i	$-0.603947\pi$
$421$	−5542.00	−0.641569	−0.320785	+	0.947152i	$0.603947\pi$
$422$	5762.00	0.664668
$423$	1647.00	0.189314
$424$	−3288.00	−0.376602
$425$	1500.00	0.171202
$426$	1836.00	0.208813
$427$	0	0
$428$	−4344.00	−0.490596
$429$	−3663.00	−0.412241
$430$	−2600.00	−0.291589
$431$	−5268.00	−0.588749	−0.294374	−	0.955690i	$-0.595111\pi$
$431$	−5268.00	−0.588749	−0.294374	+	0.955690i	$0.595111\pi$
$432$	432.000	0.0481125
$433$	−11152.0	−1.23772	−0.618858	−	0.785503i	$-0.712404\pi$
$433$	−11152.0	−1.23772	−0.618858	+	0.785503i	$0.712404\pi$
$434$	0	0
$435$	−2160.00	−0.238078
$436$	5144.00	0.565030
$437$	8925.00	0.976981
$438$	5604.00	0.611346
$439$	14960.0	1.62643	0.813214	−	0.581965i	$-0.197716\pi$
$439$	14960.0	1.62643	0.813214	+	0.581965i	$0.197716\pi$
$440$	−1320.00	−0.143019
$441$	0	0
$442$	4440.00	0.477804
$443$	5916.00	0.634487	0.317243	−	0.948344i	$-0.397243\pi$
$443$	5916.00	0.634487	0.317243	+	0.948344i	$0.397243\pi$
$444$	−2388.00	−0.255247
$445$	−2730.00	−0.290819
$446$	−9976.00	−1.05914
$447$	−8604.00	−0.910414
$448$	0	0
$449$	−1017.00	−0.106894	−0.0534468	−	0.998571i	$-0.517021\pi$
$449$	−1017.00	−0.106894	−0.0534468	+	0.998571i	$0.517021\pi$
$450$	−450.000	−0.0471405
$451$	−4455.00	−0.465139
$452$	360.000	0.0374623
$453$	−1218.00	−0.126328
$454$	−552.000	−0.0570631
$455$	0	0
$456$	−2856.00	−0.293299
$457$	−8902.00	−0.911199	−0.455600	−	0.890185i	$-0.650575\pi$
$457$	−8902.00	−0.911199	−0.455600	+	0.890185i	$0.650575\pi$
$458$	−2068.00	−0.210985
$459$	1620.00	0.164739
$460$	1500.00	0.152039
$461$	−9180.00	−0.927452	−0.463726	−	0.885979i	$-0.653488\pi$
$461$	−9180.00	−0.927452	−0.463726	+	0.885979i	$0.653488\pi$
$462$	0	0
$463$	15779.0	1.58383	0.791914	−	0.610633i	$-0.209085\pi$
$463$	15779.0	1.58383	0.791914	+	0.610633i	$0.209085\pi$
$464$	−2304.00	−0.230518
$465$	−690.000	−0.0688129
$466$	6204.00	0.616727
$467$	−13668.0	−1.35435	−0.677173	−	0.735824i	$-0.736795\pi$
$467$	−13668.0	−1.35435	−0.677173	+	0.735824i	$0.736795\pi$
$468$	−1332.00	−0.131564
$469$	0	0
$470$	−1830.00	−0.179599
$471$	−4719.00	−0.461656
$472$	−3936.00	−0.383833
$473$	8580.00	0.834057
$474$	3624.00	0.351173
$475$	2975.00	0.287373
$476$	0	0
$477$	3699.00	0.355064
$478$	5652.00	0.540829
$479$	−11442.0	−1.09144	−0.545719	−	0.837969i	$-0.683743\pi$
$479$	−11442.0	−1.09144	−0.545719	+	0.837969i	$0.683743\pi$
$480$	−480.000	−0.0456435
$481$	7363.00	0.697971
$482$	−13678.0	−1.29256
$483$	0	0
$484$	−968.000	−0.0909091
$485$	9040.00	0.846361
$486$	−486.000	−0.0453609
$487$	−13408.0	−1.24759	−0.623793	−	0.781590i	$-0.714409\pi$
$487$	−13408.0	−1.24759	−0.623793	+	0.781590i	$0.714409\pi$
$488$	3680.00	0.341364
$489$	10176.0	0.941052
$490$	0	0
$491$	−11628.0	−1.06877	−0.534383	−	0.845242i	$-0.679456\pi$
$491$	−11628.0	−1.06877	−0.534383	+	0.845242i	$0.679456\pi$
$492$	−1620.00	−0.148446
$493$	−8640.00	−0.789302
$494$	8806.00	0.802026
$495$	1485.00	0.134840
$496$	−736.000	−0.0666278
$497$	0	0
$498$	−648.000	−0.0583084
$499$	13328.0	1.19568	0.597839	−	0.801616i	$-0.296026\pi$
$499$	13328.0	1.19568	0.597839	+	0.801616i	$0.296026\pi$
$500$	500.000	0.0447214
$501$	−12069.0	−1.07625
$502$	−7254.00	−0.644944
$503$	2844.00	0.252103	0.126051	−	0.992024i	$-0.459770\pi$
$503$	2844.00	0.252103	0.126051	+	0.992024i	$0.459770\pi$
$504$	0	0
$505$	1560.00	0.137464
$506$	−4950.00	−0.434890
$507$	−2484.00	−0.217590
$508$	9500.00	0.829713
$509$	−402.000	−0.0350066	−0.0175033	−	0.999847i	$-0.505572\pi$
$509$	−402.000	−0.0350066	−0.0175033	+	0.999847i	$0.505572\pi$
$510$	−1800.00	−0.156285
$511$	0	0
$512$	−512.000	−0.0441942
$513$	3213.00	0.276525
$514$	−14784.0	−1.26867
$515$	2920.00	0.249846
$516$	3120.00	0.266183
$517$	6039.00	0.513723
$518$	0	0
$519$	6597.00	0.557950
$520$	1480.00	0.124812
$521$	9987.00	0.839805	0.419903	−	0.907569i	$-0.362064\pi$
$521$	9987.00	0.839805	0.419903	+	0.907569i	$0.362064\pi$
$522$	2592.00	0.217335
$523$	11438.0	0.956307	0.478154	−	0.878276i	$-0.341306\pi$
$523$	11438.0	0.956307	0.478154	+	0.878276i	$0.341306\pi$
$524$	7284.00	0.607258
$525$	0	0
$526$	13776.0	1.14194
$527$	−2760.00	−0.228136
$528$	1584.00	0.130558
$529$	−6542.00	−0.537684
$530$	−4110.00	−0.336843
$531$	4428.00	0.361881
$532$	0	0
$533$	4995.00	0.405924
$534$	3276.00	0.265480
$535$	−5430.00	−0.438803
$536$	−7840.00	−0.631784
$537$	5769.00	0.463595
$538$	2112.00	0.169247
$539$	0	0
$540$	540.000	0.0430331
$541$	8786.00	0.698225	0.349112	−	0.937081i	$-0.386483\pi$
$541$	8786.00	0.698225	0.349112	+	0.937081i	$0.386483\pi$
$542$	−10672.0	−0.845760
$543$	−156.000	−0.0123289
$544$	−1920.00	−0.151322
$545$	6430.00	0.505378
$546$	0	0
$547$	15956.0	1.24722	0.623610	−	0.781736i	$-0.285665\pi$
$547$	15956.0	1.24722	0.623610	+	0.781736i	$0.285665\pi$
$548$	−1416.00	−0.110381
$549$	−4140.00	−0.321841
$550$	−1650.00	−0.127920
$551$	−17136.0	−1.32490
$552$	−1800.00	−0.138792
$553$	0	0
$554$	−15532.0	−1.19114
$555$	−2985.00	−0.228299
$556$	3632.00	0.277034
$557$	−21999.0	−1.67348	−0.836739	−	0.547601i	$-0.815541\pi$
$557$	−21999.0	−1.67348	−0.836739	+	0.547601i	$0.815541\pi$
$558$	828.000	0.0628173
$559$	−9620.00	−0.727876
$560$	0	0
$561$	5940.00	0.447036
$562$	−16182.0	−1.21458
$563$	21282.0	1.59312	0.796562	−	0.604556i	$-0.206650\pi$
$563$	21282.0	1.59312	0.796562	+	0.604556i	$0.206650\pi$
$564$	2196.00	0.163951
$565$	450.000	0.0335073
$566$	−1204.00	−0.0894132
$567$	0	0
$568$	2448.00	0.180838
$569$	−20949.0	−1.54346	−0.771729	−	0.635951i	$-0.780608\pi$
$569$	−20949.0	−1.54346	−0.771729	+	0.635951i	$0.780608\pi$
$570$	−3570.00	−0.262335
$571$	−304.000	−0.0222802	−0.0111401	−	0.999938i	$-0.503546\pi$
$571$	−304.000	−0.0222802	−0.0111401	+	0.999938i	$0.503546\pi$
$572$	−4884.00	−0.357011
$573$	1710.00	0.124671
$574$	0	0
$575$	1875.00	0.135988
$576$	576.000	0.0416667
$577$	6146.00	0.443434	0.221717	−	0.975111i	$-0.428834\pi$
$577$	6146.00	0.443434	0.221717	+	0.975111i	$0.428834\pi$
$578$	2626.00	0.188974
$579$	4614.00	0.331177
$580$	−2880.00	−0.206182
$581$	0	0
$582$	−10848.0	−0.772619
$583$	13563.0	0.963503
$584$	7472.00	0.529441
$585$	−1665.00	−0.117674
$586$	−18378.0	−1.29554
$587$	−16578.0	−1.16567	−0.582834	−	0.812591i	$-0.698056\pi$
$587$	−16578.0	−1.16567	−0.582834	+	0.812591i	$0.698056\pi$
$588$	0	0
$589$	−5474.00	−0.382941
$590$	−4920.00	−0.343310
$591$	−13149.0	−0.915191
$592$	−3184.00	−0.221050
$593$	−24828.0	−1.71933	−0.859666	−	0.510857i	$-0.829328\pi$
$593$	−24828.0	−1.71933	−0.859666	+	0.510857i	$0.829328\pi$
$594$	−1782.00	−0.123091
$595$	0	0
$596$	−11472.0	−0.788442
$597$	−300.000	−0.0205665
$598$	5550.00	0.379526
$599$	−27822.0	−1.89779	−0.948895	−	0.315592i	$-0.897797\pi$
$599$	−27822.0	−1.89779	−0.948895	+	0.315592i	$0.897797\pi$
$600$	−600.000	−0.0408248
$601$	−27514.0	−1.86742	−0.933710	−	0.358030i	$-0.883449\pi$
$601$	−27514.0	−1.86742	−0.933710	+	0.358030i	$0.883449\pi$
$602$	0	0
$603$	8820.00	0.595652
$604$	−1624.00	−0.109403
$605$	−1210.00	−0.0813116
$606$	−1872.00	−0.125486
$607$	−27709.0	−1.85284	−0.926420	−	0.376492i	$-0.877130\pi$
$607$	−27709.0	−1.85284	−0.926420	+	0.376492i	$0.877130\pi$
$608$	−3808.00	−0.254005
$609$	0	0
$610$	4600.00	0.305326
$611$	−6771.00	−0.448323
$612$	2160.00	0.142668
$613$	21077.0	1.38873	0.694365	−	0.719623i	$-0.255685\pi$
$613$	21077.0	1.38873	0.694365	+	0.719623i	$0.255685\pi$
$614$	−9952.00	−0.654121
$615$	−2025.00	−0.132774
$616$	0	0
$617$	2448.00	0.159729	0.0798645	−	0.996806i	$-0.474551\pi$
$617$	2448.00	0.159729	0.0798645	+	0.996806i	$0.474551\pi$
$618$	−3504.00	−0.228077
$619$	−13681.0	−0.888345	−0.444173	−	0.895941i	$-0.646502\pi$
$619$	−13681.0	−0.888345	−0.444173	+	0.895941i	$0.646502\pi$
$620$	−920.000	−0.0595937
$621$	2025.00	0.130854
$622$	−19488.0	−1.25627
$623$	0	0
$624$	−1776.00	−0.113937
$625$	625.000	0.0400000
$626$	3776.00	0.241085
$627$	11781.0	0.750379
$628$	−6292.00	−0.399806
$629$	−11940.0	−0.756882
$630$	0	0
$631$	8378.00	0.528562	0.264281	−	0.964446i	$-0.414865\pi$
$631$	8378.00	0.528562	0.264281	+	0.964446i	$0.414865\pi$
$632$	4832.00	0.304124
$633$	−8643.00	−0.542699
$634$	11964.0	0.749450
$635$	11875.0	0.742118
$636$	4932.00	0.307495
$637$	0	0
$638$	9504.00	0.589760
$639$	−2754.00	−0.170495
$640$	−640.000	−0.0395285
$641$	−12855.0	−0.792109	−0.396055	−	0.918227i	$-0.629621\pi$
$641$	−12855.0	−0.792109	−0.396055	+	0.918227i	$0.629621\pi$
$642$	6516.00	0.400570
$643$	11798.0	0.723589	0.361794	−	0.932258i	$-0.382164\pi$
$643$	11798.0	0.723589	0.361794	+	0.932258i	$0.382164\pi$
$644$	0	0
$645$	3900.00	0.238081
$646$	−14280.0	−0.869720
$647$	7539.00	0.458097	0.229048	−	0.973415i	$-0.426439\pi$
$647$	7539.00	0.458097	0.229048	+	0.973415i	$0.426439\pi$
$648$	−648.000	−0.0392837
$649$	16236.0	0.982001
$650$	1850.00	0.111635
$651$	0	0
$652$	13568.0	0.814975
$653$	4809.00	0.288194	0.144097	−	0.989564i	$-0.453972\pi$
$653$	4809.00	0.288194	0.144097	+	0.989564i	$0.453972\pi$
$654$	−7716.00	−0.461345
$655$	9105.00	0.543148
$656$	−2160.00	−0.128558
$657$	−8406.00	−0.499162
$658$	0	0
$659$	15444.0	0.912918	0.456459	−	0.889745i	$-0.349118\pi$
$659$	15444.0	0.912918	0.456459	+	0.889745i	$0.349118\pi$
$660$	1980.00	0.116775
$661$	6824.00	0.401547	0.200774	−	0.979638i	$-0.435654\pi$
$661$	6824.00	0.401547	0.200774	+	0.979638i	$0.435654\pi$
$662$	−5890.00	−0.345803
$663$	−6660.00	−0.390125
$664$	−864.000	−0.0504965
$665$	0	0
$666$	3582.00	0.208408
$667$	−10800.0	−0.626953
$668$	−16092.0	−0.932063
$669$	14964.0	0.864786
$670$	−9800.00	−0.565085
$671$	−15180.0	−0.873349
$672$	0	0
$673$	−3868.00	−0.221546	−0.110773	−	0.993846i	$-0.535333\pi$
$673$	−3868.00	−0.221546	−0.110773	+	0.993846i	$0.535333\pi$
$674$	−13792.0	−0.788202
$675$	675.000	0.0384900
$676$	−3312.00	−0.188439
$677$	7509.00	0.426284	0.213142	−	0.977021i	$-0.431630\pi$
$677$	7509.00	0.426284	0.213142	+	0.977021i	$0.431630\pi$
$678$	−540.000	−0.0305879
$679$	0	0
$680$	−2400.00	−0.135347
$681$	828.000	0.0465918
$682$	3036.00	0.170461
$683$	−4116.00	−0.230592	−0.115296	−	0.993331i	$-0.536782\pi$
$683$	−4116.00	−0.230592	−0.115296	+	0.993331i	$0.536782\pi$
$684$	4284.00	0.239478
$685$	−1770.00	−0.0987273
$686$	0	0
$687$	3102.00	0.172269
$688$	4160.00	0.230521
$689$	−15207.0	−0.840843
$690$	−2250.00	−0.124139
$691$	−532.000	−0.0292883	−0.0146442	−	0.999893i	$-0.504662\pi$
$691$	−532.000	−0.0292883	−0.0146442	+	0.999893i	$0.504662\pi$
$692$	8796.00	0.483199
$693$	0	0
$694$	−3828.00	−0.209379
$695$	4540.00	0.247787
$696$	3456.00	0.188217
$697$	−8100.00	−0.440186
$698$	−2248.00	−0.121903
$699$	−9306.00	−0.503555
$700$	0	0
$701$	5670.00	0.305496	0.152748	−	0.988265i	$-0.451188\pi$
$701$	5670.00	0.305496	0.152748	+	0.988265i	$0.451188\pi$
$702$	1998.00	0.107421
$703$	−23681.0	−1.27048
$704$	2112.00	0.113067
$705$	2745.00	0.146642
$706$	−18624.0	−0.992809
$707$	0	0
$708$	5904.00	0.313398
$709$	−21700.0	−1.14945	−0.574725	−	0.818346i	$-0.694891\pi$
$709$	−21700.0	−1.14945	−0.574725	+	0.818346i	$0.694891\pi$
$710$	3060.00	0.161746
$711$	−5436.00	−0.286731
$712$	4368.00	0.229913
$713$	−3450.00	−0.181211
$714$	0	0
$715$	−6105.00	−0.319320
$716$	7692.00	0.401485
$717$	−8478.00	−0.441585
$718$	−11400.0	−0.592541
$719$	−1482.00	−0.0768696	−0.0384348	−	0.999261i	$-0.512237\pi$
$719$	−1482.00	−0.0768696	−0.0384348	+	0.999261i	$0.512237\pi$
$720$	720.000	0.0372678
$721$	0	0
$722$	−14604.0	−0.752776
$723$	20517.0	1.05537
$724$	−208.000	−0.0106772
$725$	−3600.00	−0.184415
$726$	1452.00	0.0742270
$727$	−3061.00	−0.156157	−0.0780785	−	0.996947i	$-0.524878\pi$
$727$	−3061.00	−0.156157	−0.0780785	+	0.996947i	$0.524878\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	9340.00	0.473546
$731$	15600.0	0.789312
$732$	−5520.00	−0.278723
$733$	15785.0	0.795406	0.397703	−	0.917514i	$-0.369808\pi$
$733$	15785.0	0.795406	0.397703	+	0.917514i	$0.369808\pi$
$734$	−4594.00	−0.231019
$735$	0	0
$736$	−2400.00	−0.120197
$737$	32340.0	1.61636
$738$	2430.00	0.121205
$739$	−12385.0	−0.616495	−0.308247	−	0.951306i	$-0.599742\pi$
$739$	−12385.0	−0.616495	−0.308247	+	0.951306i	$0.599742\pi$
$740$	−3980.00	−0.197713
$741$	−13209.0	−0.654851
$742$	0	0
$743$	22581.0	1.11496	0.557481	−	0.830190i	$-0.311768\pi$
$743$	22581.0	1.11496	0.557481	+	0.830190i	$0.311768\pi$
$744$	1104.00	0.0544013
$745$	−14340.0	−0.705204
$746$	−6628.00	−0.325293
$747$	972.000	0.0476086
$748$	7920.00	0.387144
$749$	0	0
$750$	−750.000	−0.0365148
$751$	−23902.0	−1.16138	−0.580690	−	0.814125i	$-0.697217\pi$
$751$	−23902.0	−1.16138	−0.580690	+	0.814125i	$0.697217\pi$
$752$	2928.00	0.141986
$753$	10881.0	0.526595
$754$	−10656.0	−0.514680
$755$	−2030.00	−0.0978533
$756$	0	0
$757$	−31834.0	−1.52844	−0.764218	−	0.644958i	$-0.776875\pi$
$757$	−31834.0	−1.52844	−0.764218	+	0.644958i	$0.776875\pi$
$758$	24626.0	1.18002
$759$	7425.00	0.355086
$760$	−4760.00	−0.227189
$761$	19047.0	0.907297	0.453649	−	0.891181i	$-0.350122\pi$
$761$	19047.0	0.907297	0.453649	+	0.891181i	$0.350122\pi$
$762$	−14250.0	−0.677458
$763$	0	0
$764$	2280.00	0.107968
$765$	2700.00	0.127606
$766$	19362.0	0.913287
$767$	−18204.0	−0.856986
$768$	768.000	0.0360844
$769$	−28501.0	−1.33651	−0.668253	−	0.743935i	$-0.732957\pi$
$769$	−28501.0	−1.33651	−0.668253	+	0.743935i	$0.732957\pi$
$770$	0	0
$771$	22176.0	1.03586
$772$	6152.00	0.286807
$773$	−12297.0	−0.572176	−0.286088	−	0.958203i	$-0.592355\pi$
$773$	−12297.0	−0.572176	−0.286088	+	0.958203i	$0.592355\pi$
$774$	−4680.00	−0.217337
$775$	−1150.00	−0.0533022
$776$	−14464.0	−0.669107
$777$	0	0
$778$	21228.0	0.978227
$779$	−16065.0	−0.738881
$780$	−2220.00	−0.101909
$781$	−10098.0	−0.462657
$782$	−9000.00	−0.411559
$783$	−3888.00	−0.177453
$784$	0	0
$785$	−7865.00	−0.357597
$786$	−10926.0	−0.495824
$787$	−1090.00	−0.0493701	−0.0246851	−	0.999695i	$-0.507858\pi$
$787$	−1090.00	−0.0493701	−0.0246851	+	0.999695i	$0.507858\pi$
$788$	−17532.0	−0.792578
$789$	−20664.0	−0.932393
$790$	6040.00	0.272017
$791$	0	0
$792$	−2376.00	−0.106600
$793$	17020.0	0.762166
$794$	−11284.0	−0.504350
$795$	6165.00	0.275031
$796$	−400.000	−0.0178111
$797$	22194.0	0.986389	0.493194	−	0.869919i	$-0.335829\pi$
$797$	22194.0	0.986389	0.493194	+	0.869919i	$0.335829\pi$
$798$	0	0
$799$	10980.0	0.486163
$800$	−800.000	−0.0353553
$801$	−4914.00	−0.216764
$802$	11442.0	0.503779
$803$	−30822.0	−1.35453
$804$	11760.0	0.515850
$805$	0	0
$806$	−3404.00	−0.148760
$807$	−3168.00	−0.138189
$808$	−2496.00	−0.108674
$809$	−26355.0	−1.14536	−0.572678	−	0.819781i	$-0.694095\pi$
$809$	−26355.0	−1.14536	−0.572678	+	0.819781i	$0.694095\pi$
$810$	−810.000	−0.0351364
$811$	−30373.0	−1.31509	−0.657546	−	0.753414i	$-0.728406\pi$
$811$	−30373.0	−1.31509	−0.657546	+	0.753414i	$0.728406\pi$
$812$	0	0
$813$	16008.0	0.690560
$814$	13134.0	0.565536
$815$	16960.0	0.728936
$816$	2880.00	0.123554
$817$	30940.0	1.32491
$818$	5420.00	0.231670
$819$	0	0
$820$	−2700.00	−0.114985
$821$	−29238.0	−1.24289	−0.621445	−	0.783458i	$-0.713454\pi$
$821$	−29238.0	−1.24289	−0.621445	+	0.783458i	$0.713454\pi$
$822$	2124.00	0.0901253
$823$	−15400.0	−0.652260	−0.326130	−	0.945325i	$-0.605745\pi$
$823$	−15400.0	−0.652260	−0.326130	+	0.945325i	$0.605745\pi$
$824$	−4672.00	−0.197520
$825$	2475.00	0.104447
$826$	0	0
$827$	−9450.00	−0.397350	−0.198675	−	0.980065i	$-0.563664\pi$
$827$	−9450.00	−0.397350	−0.198675	+	0.980065i	$0.563664\pi$
$828$	2700.00	0.113323
$829$	32924.0	1.37937	0.689685	−	0.724109i	$-0.257749\pi$
$829$	32924.0	1.37937	0.689685	+	0.724109i	$0.257749\pi$
$830$	−1080.00	−0.0451655
$831$	23298.0	0.972562
$832$	−2368.00	−0.0986726
$833$	0	0
$834$	−5448.00	−0.226198
$835$	−20115.0	−0.833663
$836$	15708.0	0.649848
$837$	−1242.00	−0.0512901
$838$	15750.0	0.649254
$839$	23724.0	0.976214	0.488107	−	0.872784i	$-0.337688\pi$
$839$	23724.0	0.976214	0.488107	+	0.872784i	$0.337688\pi$
$840$	0	0
$841$	−3653.00	−0.149781
$842$	11084.0	0.453658
$843$	24273.0	0.991704
$844$	−11524.0	−0.469991
$845$	−4140.00	−0.168545
$846$	−3294.00	−0.133865
$847$	0	0
$848$	6576.00	0.266298
$849$	1806.00	0.0730056
$850$	−3000.00	−0.121058
$851$	−14925.0	−0.601201
$852$	−3672.00	−0.147653
$853$	−5515.00	−0.221372	−0.110686	−	0.993855i	$-0.535305\pi$
$853$	−5515.00	−0.221372	−0.110686	+	0.993855i	$0.535305\pi$
$854$	0	0
$855$	5355.00	0.214195
$856$	8688.00	0.346904
$857$	14226.0	0.567037	0.283519	−	0.958967i	$-0.408498\pi$
$857$	14226.0	0.567037	0.283519	+	0.958967i	$0.408498\pi$
$858$	7326.00	0.291498
$859$	−31060.0	−1.23371	−0.616853	−	0.787078i	$-0.711593\pi$
$859$	−31060.0	−1.23371	−0.616853	+	0.787078i	$0.711593\pi$
$860$	5200.00	0.206184
$861$	0	0
$862$	10536.0	0.416308
$863$	30063.0	1.18581	0.592906	−	0.805271i	$-0.297980\pi$
$863$	30063.0	1.18581	0.592906	+	0.805271i	$0.297980\pi$
$864$	−864.000	−0.0340207
$865$	10995.0	0.432186
$866$	22304.0	0.875197
$867$	−3939.00	−0.154297
$868$	0	0
$869$	−19932.0	−0.778075
$870$	4320.00	0.168347
$871$	−36260.0	−1.41059
$872$	−10288.0	−0.399536
$873$	16272.0	0.630841
$874$	−17850.0	−0.690830
$875$	0	0
$876$	−11208.0	−0.432287
$877$	−25021.0	−0.963397	−0.481698	−	0.876337i	$-0.659980\pi$
$877$	−25021.0	−0.963397	−0.481698	+	0.876337i	$0.659980\pi$
$878$	−29920.0	−1.15006
$879$	27567.0	1.05781
$880$	2640.00	0.101130
$881$	−1521.00	−0.0581655	−0.0290827	−	0.999577i	$-0.509259\pi$
$881$	−1521.00	−0.0581655	−0.0290827	+	0.999577i	$0.509259\pi$
$882$	0	0
$883$	−25054.0	−0.954852	−0.477426	−	0.878672i	$-0.658430\pi$
$883$	−25054.0	−0.954852	−0.477426	+	0.878672i	$0.658430\pi$
$884$	−8880.00	−0.337858
$885$	7380.00	0.280312
$886$	−11832.0	−0.448650
$887$	−32748.0	−1.23965	−0.619825	−	0.784740i	$-0.712797\pi$
$887$	−32748.0	−1.23965	−0.619825	+	0.784740i	$0.712797\pi$
$888$	4776.00	0.180487
$889$	0	0
$890$	5460.00	0.205640
$891$	2673.00	0.100504
$892$	19952.0	0.748926
$893$	21777.0	0.816058
$894$	17208.0	0.643760
$895$	9615.00	0.359099
$896$	0	0
$897$	−8325.00	−0.309881
$898$	2034.00	0.0755851
$899$	6624.00	0.245743
$900$	900.000	0.0333333
$901$	24660.0	0.911813
$902$	8910.00	0.328903
$903$	0	0
$904$	−720.000	−0.0264899
$905$	−260.000	−0.00954994
$906$	2436.00	0.0893275
$907$	15866.0	0.580840	0.290420	−	0.956899i	$-0.406205\pi$
$907$	15866.0	0.580840	0.290420	+	0.956899i	$0.406205\pi$
$908$	1104.00	0.0403497
$909$	2808.00	0.102459
$910$	0	0
$911$	8226.00	0.299165	0.149583	−	0.988749i	$-0.452207\pi$
$911$	8226.00	0.299165	0.149583	+	0.988749i	$0.452207\pi$
$912$	5712.00	0.207394
$913$	3564.00	0.129191
$914$	17804.0	0.644315
$915$	−6900.00	−0.249297
$916$	4136.00	0.149189
$917$	0	0
$918$	−3240.00	−0.116488
$919$	24452.0	0.877690	0.438845	−	0.898563i	$-0.355388\pi$
$919$	24452.0	0.877690	0.438845	+	0.898563i	$0.355388\pi$
$920$	−3000.00	−0.107508
$921$	14928.0	0.534087
$922$	18360.0	0.655807
$923$	11322.0	0.403757
$924$	0	0
$925$	−4975.00	−0.176840
$926$	−31558.0	−1.11994
$927$	5256.00	0.186224
$928$	4608.00	0.163001
$929$	111.000	0.00392012	0.00196006	−	0.999998i	$-0.499376\pi$
$929$	111.000	0.00392012	0.00196006	+	0.999998i	$0.499376\pi$
$930$	1380.00	0.0486580
$931$	0	0
$932$	−12408.0	−0.436092
$933$	29232.0	1.02574
$934$	27336.0	0.957667
$935$	9900.00	0.346272
$936$	2664.00	0.0930294
$937$	−22960.0	−0.800502	−0.400251	−	0.916406i	$-0.631077\pi$
$937$	−22960.0	−0.800502	−0.400251	+	0.916406i	$0.631077\pi$
$938$	0	0
$939$	−5664.00	−0.196845
$940$	3660.00	0.126996
$941$	−21054.0	−0.729374	−0.364687	−	0.931130i	$-0.618824\pi$
$941$	−21054.0	−0.729374	−0.364687	+	0.931130i	$0.618824\pi$
$942$	9438.00	0.326440
$943$	−10125.0	−0.349645
$944$	7872.00	0.271411
$945$	0	0
$946$	−17160.0	−0.589767
$947$	−26790.0	−0.919280	−0.459640	−	0.888105i	$-0.652022\pi$
$947$	−26790.0	−0.919280	−0.459640	+	0.888105i	$0.652022\pi$
$948$	−7248.00	−0.248317
$949$	34558.0	1.18209
$950$	−5950.00	−0.203204
$951$	−17946.0	−0.611923
$952$	0	0
$953$	−36828.0	−1.25181	−0.625906	−	0.779899i	$-0.715270\pi$
$953$	−36828.0	−1.25181	−0.625906	+	0.779899i	$0.715270\pi$
$954$	−7398.00	−0.251068
$955$	2850.00	0.0965695
$956$	−11304.0	−0.382424
$957$	−14256.0	−0.481537
$958$	22884.0	0.771763
$959$	0	0
$960$	960.000	0.0322749
$961$	−27675.0	−0.928972
$962$	−14726.0	−0.493540
$963$	−9774.00	−0.327064
$964$	27356.0	0.913981
$965$	7690.00	0.256528
$966$	0	0
$967$	25388.0	0.844284	0.422142	−	0.906530i	$-0.361278\pi$
$967$	25388.0	0.844284	0.422142	+	0.906530i	$0.361278\pi$
$968$	1936.00	0.0642824
$969$	21420.0	0.710123
$970$	−18080.0	−0.598468
$971$	−3579.00	−0.118286	−0.0591429	−	0.998250i	$-0.518837\pi$
$971$	−3579.00	−0.118286	−0.0591429	+	0.998250i	$0.518837\pi$
$972$	972.000	0.0320750
$973$	0	0
$974$	26816.0	0.882177
$975$	−2775.00	−0.0911499
$976$	−7360.00	−0.241381
$977$	−45966.0	−1.50520	−0.752601	−	0.658477i	$-0.771201\pi$
$977$	−45966.0	−1.50520	−0.752601	+	0.658477i	$0.771201\pi$
$978$	−20352.0	−0.665425
$979$	−18018.0	−0.588210
$980$	0	0
$981$	11574.0	0.376686
$982$	23256.0	0.755732
$983$	−50547.0	−1.64008	−0.820040	−	0.572306i	$-0.806049\pi$
$983$	−50547.0	−1.64008	−0.820040	+	0.572306i	$0.806049\pi$
$984$	3240.00	0.104967
$985$	−21915.0	−0.708904
$986$	17280.0	0.558121
$987$	0	0
$988$	−17612.0	−0.567118
$989$	19500.0	0.626960
$990$	−2970.00	−0.0953463
$991$	−41698.0	−1.33661	−0.668305	−	0.743887i	$-0.732980\pi$
$991$	−41698.0	−1.33661	−0.668305	+	0.743887i	$0.732980\pi$
$992$	1472.00	0.0471130
$993$	8835.00	0.282347
$994$	0	0
$995$	−500.000	−0.0159307
$996$	1296.00	0.0412303
$997$	−6382.00	−0.202728	−0.101364	−	0.994849i	$-0.532321\pi$
$997$	−6382.00	−0.202728	−0.101364	+	0.994849i	$0.532321\pi$
$998$	−26656.0	−0.845472
$999$	−5373.00	−0.170164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.4.a.o.1.1		1
7.2	even	3		210.4.i.f.151.1	yes	2
7.4	even	3		210.4.i.f.121.1	✓	2
7.6	odd	2		1470.4.a.e.1.1		1
21.2	odd	6		630.4.k.e.361.1		2
21.11	odd	6		630.4.k.e.541.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.i.f.121.1	✓	2	7.4	even	3
210.4.i.f.151.1	yes	2	7.2	even	3
630.4.k.e.361.1		2	21.2	odd	6
630.4.k.e.541.1		2	21.11	odd	6
1470.4.a.e.1.1		1	7.6	odd	2
1470.4.a.o.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1470.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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