LMFDB - Embedded newform 1225.4.a.i.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1225,4,Mod(1,1225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1225.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1225, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1225 = 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1225.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,1,-7,-7,0,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$72.2773397570$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1225.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+1.00000 q^{2} -7.00000 q^{3} -7.00000 q^{4} -7.00000 q^{6} -15.0000 q^{8} +22.0000 q^{9} -43.0000 q^{11} +49.0000 q^{12} +28.0000 q^{13} +41.0000 q^{16} -91.0000 q^{17} +22.0000 q^{18} +35.0000 q^{19} -43.0000 q^{22} +162.000 q^{23} +105.000 q^{24} +28.0000 q^{26} +35.0000 q^{27} +160.000 q^{29} -42.0000 q^{31} +161.000 q^{32} +301.000 q^{33} -91.0000 q^{34} -154.000 q^{36} -314.000 q^{37} +35.0000 q^{38} -196.000 q^{39} +203.000 q^{41} +92.0000 q^{43} +301.000 q^{44} +162.000 q^{46} -196.000 q^{47} -287.000 q^{48} +637.000 q^{51} -196.000 q^{52} +82.0000 q^{53} +35.0000 q^{54} -245.000 q^{57} +160.000 q^{58} +280.000 q^{59} +518.000 q^{61} -42.0000 q^{62} -167.000 q^{64} +301.000 q^{66} +141.000 q^{67} +637.000 q^{68} -1134.00 q^{69} +412.000 q^{71} -330.000 q^{72} +763.000 q^{73} -314.000 q^{74} -245.000 q^{76} -196.000 q^{78} +510.000 q^{79} -839.000 q^{81} +203.000 q^{82} -777.000 q^{83} +92.0000 q^{86} -1120.00 q^{87} +645.000 q^{88} +945.000 q^{89} -1134.00 q^{92} +294.000 q^{93} -196.000 q^{94} -1127.00 q^{96} -1246.00 q^{97} -946.000 q^{99} +O(q^{100})\)

Coefficient data

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

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

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

$2$	1.00000	0.353553	0.176777	−	0.984251i	$-0.443433\pi$
$2$	1.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	−7.00000	−1.34715	−0.673575	−	0.739119i	$-0.735242\pi$
$3$	−7.00000	−1.34715	−0.673575	+	0.739119i	$0.735242\pi$
$4$	−7.00000	−0.875000
$5$	0	0
$5$	0	0
$6$	−7.00000	−0.476290
$7$	0	0
$7$	0	0
$8$	−15.0000	−0.662913
$9$	22.0000	0.814815
$10$	0	0
$11$	−43.0000	−1.17864	−0.589318	−	0.807901i	$-0.700603\pi$
$11$	−43.0000	−1.17864	−0.589318	+	0.807901i	$0.700603\pi$
$12$	49.0000	1.17876
$13$	28.0000	0.597369	0.298685	−	0.954352i	$-0.403452\pi$
$13$	28.0000	0.597369	0.298685	+	0.954352i	$0.403452\pi$
$14$	0	0
$15$	0	0
$16$	41.0000	0.640625
$17$	−91.0000	−1.29828	−0.649139	−	0.760669i	$-0.724871\pi$
$17$	−91.0000	−1.29828	−0.649139	+	0.760669i	$0.724871\pi$
$18$	22.0000	0.288081
$19$	35.0000	0.422608	0.211304	−	0.977420i	$-0.432229\pi$
$19$	35.0000	0.422608	0.211304	+	0.977420i	$0.432229\pi$
$20$	0	0
$21$	0	0
$22$	−43.0000	−0.416710
$23$	162.000	1.46867	0.734333	−	0.678789i	$-0.237495\pi$
$23$	162.000	1.46867	0.734333	+	0.678789i	$0.237495\pi$
$24$	105.000	0.893043
$25$	0	0
$26$	28.0000	0.211202
$27$	35.0000	0.249472
$28$	0	0
$29$	160.000	1.02453	0.512263	−	0.858829i	$-0.328807\pi$
$29$	160.000	1.02453	0.512263	+	0.858829i	$0.328807\pi$
$30$	0	0
$31$	−42.0000	−0.243336	−0.121668	−	0.992571i	$-0.538824\pi$
$31$	−42.0000	−0.243336	−0.121668	+	0.992571i	$0.538824\pi$
$32$	161.000	0.889408
$33$	301.000	1.58780
$34$	−91.0000	−0.459011
$35$	0	0
$36$	−154.000	−0.712963
$37$	−314.000	−1.39517	−0.697585	−	0.716502i	$-0.745742\pi$
$37$	−314.000	−1.39517	−0.697585	+	0.716502i	$0.745742\pi$
$38$	35.0000	0.149414
$39$	−196.000	−0.804747
$40$	0	0
$41$	203.000	0.773251	0.386625	−	0.922237i	$-0.373641\pi$
$41$	203.000	0.773251	0.386625	+	0.922237i	$0.373641\pi$
$42$	0	0
$43$	92.0000	0.326276	0.163138	−	0.986603i	$-0.447838\pi$
$43$	92.0000	0.326276	0.163138	+	0.986603i	$0.447838\pi$
$44$	301.000	1.03131
$45$	0	0
$46$	162.000	0.519252
$47$	−196.000	−0.608288	−0.304144	−	0.952626i	$-0.598370\pi$
$47$	−196.000	−0.608288	−0.304144	+	0.952626i	$0.598370\pi$
$48$	−287.000	−0.863018
$49$	0	0
$50$	0	0
$51$	637.000	1.74898
$52$	−196.000	−0.522698
$53$	82.0000	0.212520	0.106260	−	0.994338i	$-0.466112\pi$
$53$	82.0000	0.212520	0.106260	+	0.994338i	$0.466112\pi$
$54$	35.0000	0.0882018
$55$	0	0
$56$	0	0
$57$	−245.000	−0.569317
$58$	160.000	0.362225
$59$	280.000	0.617846	0.308923	−	0.951087i	$-0.400032\pi$
$59$	280.000	0.617846	0.308923	+	0.951087i	$0.400032\pi$
$60$	0	0
$61$	518.000	1.08726	0.543632	−	0.839324i	$-0.317049\pi$
$61$	518.000	1.08726	0.543632	+	0.839324i	$0.317049\pi$
$62$	−42.0000	−0.0860323
$63$	0	0
$64$	−167.000	−0.326172
$65$	0	0
$66$	301.000	0.561372
$67$	141.000	0.257103	0.128551	−	0.991703i	$-0.458967\pi$
$67$	141.000	0.257103	0.128551	+	0.991703i	$0.458967\pi$
$68$	637.000	1.13599
$69$	−1134.00	−1.97852
$70$	0	0
$71$	412.000	0.688668	0.344334	−	0.938847i	$-0.388105\pi$
$71$	412.000	0.688668	0.344334	+	0.938847i	$0.388105\pi$
$72$	−330.000	−0.540151
$73$	763.000	1.22332	0.611660	−	0.791121i	$-0.290502\pi$
$73$	763.000	1.22332	0.611660	+	0.791121i	$0.290502\pi$
$74$	−314.000	−0.493267
$75$	0	0
$76$	−245.000	−0.369782
$77$	0	0
$78$	−196.000	−0.284521
$79$	510.000	0.726323	0.363161	−	0.931726i	$-0.381697\pi$
$79$	510.000	0.726323	0.363161	+	0.931726i	$0.381697\pi$
$80$	0	0
$81$	−839.000	−1.15089
$82$	203.000	0.273385
$83$	−777.000	−1.02755	−0.513776	−	0.857924i	$-0.671754\pi$
$83$	−777.000	−1.02755	−0.513776	+	0.857924i	$0.671754\pi$
$84$	0	0
$85$	0	0
$86$	92.0000	0.115356
$87$	−1120.00	−1.38019
$88$	645.000	0.781332
$89$	945.000	1.12550	0.562752	−	0.826626i	$-0.309743\pi$
$89$	945.000	1.12550	0.562752	+	0.826626i	$0.309743\pi$
$90$	0	0
$91$	0	0
$92$	−1134.00	−1.28508
$93$	294.000	0.327811
$94$	−196.000	−0.215062
$95$	0	0
$96$	−1127.00	−1.19817
$97$	−1246.00	−1.30425	−0.652124	−	0.758112i	$-0.726122\pi$
$97$	−1246.00	−1.30425	−0.652124	+	0.758112i	$0.726122\pi$
$98$	0	0
$99$	−946.000	−0.960369
$100$	0	0
$101$	−1302.00	−1.28271	−0.641356	−	0.767244i	$-0.721628\pi$
$101$	−1302.00	−1.28271	−0.641356	+	0.767244i	$0.721628\pi$
$102$	637.000	0.618357
$103$	−532.000	−0.508927	−0.254464	−	0.967082i	$-0.581899\pi$
$103$	−532.000	−0.508927	−0.254464	+	0.967082i	$0.581899\pi$
$104$	−420.000	−0.396004
$105$	0	0
$106$	82.0000	0.0751372
$107$	−1269.00	−1.14653	−0.573266	−	0.819370i	$-0.694324\pi$
$107$	−1269.00	−1.14653	−0.573266	+	0.819370i	$0.694324\pi$
$108$	−245.000	−0.218288
$109$	1070.00	0.940251	0.470126	−	0.882599i	$-0.344209\pi$
$109$	1070.00	0.940251	0.470126	+	0.882599i	$0.344209\pi$
$110$	0	0
$111$	2198.00	1.87950
$112$	0	0
$113$	−503.000	−0.418746	−0.209373	−	0.977836i	$-0.567142\pi$
$113$	−503.000	−0.418746	−0.209373	+	0.977836i	$0.567142\pi$
$114$	−245.000	−0.201284
$115$	0	0
$116$	−1120.00	−0.896460
$117$	616.000	0.486745
$118$	280.000	0.218441
$119$	0	0
$120$	0	0
$121$	518.000	0.389181
$122$	518.000	0.384406
$123$	−1421.00	−1.04169
$124$	294.000	0.212919
$125$	0	0
$126$	0	0
$127$	−874.000	−0.610669	−0.305334	−	0.952245i	$-0.598768\pi$
$127$	−874.000	−0.610669	−0.305334	+	0.952245i	$0.598768\pi$
$128$	−1455.00	−1.00473
$129$	−644.000	−0.439543
$130$	0	0
$131$	−1092.00	−0.728309	−0.364155	−	0.931339i	$-0.618642\pi$
$131$	−1092.00	−0.728309	−0.364155	+	0.931339i	$0.618642\pi$
$132$	−2107.00	−1.38932
$133$	0	0
$134$	141.000	0.0908996
$135$	0	0
$136$	1365.00	0.860645
$137$	411.000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	411.000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	−1134.00	−0.699511
$139$	595.000	0.363074	0.181537	−	0.983384i	$-0.441893\pi$
$139$	595.000	0.363074	0.181537	+	0.983384i	$0.441893\pi$
$140$	0	0
$141$	1372.00	0.819456
$142$	412.000	0.243481
$143$	−1204.00	−0.704081
$144$	902.000	0.521991
$145$	0	0
$146$	763.000	0.432509
$147$	0	0
$148$	2198.00	1.22077
$149$	−3200.00	−1.75942	−0.879712	−	0.475507i	$-0.842265\pi$
$149$	−3200.00	−1.75942	−0.879712	+	0.475507i	$0.842265\pi$
$150$	0	0
$151$	202.000	0.108864	0.0544322	−	0.998517i	$-0.482665\pi$
$151$	202.000	0.108864	0.0544322	+	0.998517i	$0.482665\pi$
$152$	−525.000	−0.280152
$153$	−2002.00	−1.05786
$154$	0	0
$155$	0	0
$156$	1372.00	0.704153
$157$	−406.000	−0.206384	−0.103192	−	0.994661i	$-0.532906\pi$
$157$	−406.000	−0.206384	−0.103192	+	0.994661i	$0.532906\pi$
$158$	510.000	0.256794
$159$	−574.000	−0.286297
$160$	0	0
$161$	0	0
$162$	−839.000	−0.406902
$163$	−3803.00	−1.82745	−0.913724	−	0.406336i	$-0.866806\pi$
$163$	−3803.00	−1.82745	−0.913724	+	0.406336i	$0.866806\pi$
$164$	−1421.00	−0.676594
$165$	0	0
$166$	−777.000	−0.363295
$167$	−4116.00	−1.90722	−0.953610	−	0.301046i	$-0.902664\pi$
$167$	−4116.00	−1.90722	−0.953610	+	0.301046i	$0.902664\pi$
$168$	0	0
$169$	−1413.00	−0.643150
$170$	0	0
$171$	770.000	0.344347
$172$	−644.000	−0.285492
$173$	−1512.00	−0.664481	−0.332241	−	0.943195i	$-0.607805\pi$
$173$	−1512.00	−0.664481	−0.332241	+	0.943195i	$0.607805\pi$
$174$	−1120.00	−0.487971
$175$	0	0
$176$	−1763.00	−0.755063
$177$	−1960.00	−0.832331
$178$	945.000	0.397926
$179$	2585.00	1.07940	0.539698	−	0.841859i	$-0.318538\pi$
$179$	2585.00	1.07940	0.539698	+	0.841859i	$0.318538\pi$
$180$	0	0
$181$	2758.00	1.13260	0.566300	−	0.824199i	$-0.308374\pi$
$181$	2758.00	1.13260	0.566300	+	0.824199i	$0.308374\pi$
$182$	0	0
$183$	−3626.00	−1.46471
$184$	−2430.00	−0.973598
$185$	0	0
$186$	294.000	0.115899
$187$	3913.00	1.53020
$188$	1372.00	0.532252
$189$	0	0
$190$	0	0
$191$	−2378.00	−0.900869	−0.450435	−	0.892809i	$-0.648731\pi$
$191$	−2378.00	−0.900869	−0.450435	+	0.892809i	$0.648731\pi$
$192$	1169.00	0.439403
$193$	3067.00	1.14387	0.571937	−	0.820298i	$-0.306192\pi$
$193$	3067.00	1.14387	0.571937	+	0.820298i	$0.306192\pi$
$194$	−1246.00	−0.461122
$195$	0	0
$196$	0	0
$197$	2346.00	0.848455	0.424227	−	0.905556i	$-0.360546\pi$
$197$	2346.00	0.848455	0.424227	+	0.905556i	$0.360546\pi$
$198$	−946.000	−0.339542
$199$	−4900.00	−1.74549	−0.872743	−	0.488180i	$-0.837661\pi$
$199$	−4900.00	−1.74549	−0.872743	+	0.488180i	$0.837661\pi$
$200$	0	0
$201$	−987.000	−0.346356
$202$	−1302.00	−0.453507
$203$	0	0
$204$	−4459.00	−1.53036
$205$	0	0
$206$	−532.000	−0.179933
$207$	3564.00	1.19669
$208$	1148.00	0.382690
$209$	−1505.00	−0.498101
$210$	0	0
$211$	4307.00	1.40524	0.702621	−	0.711564i	$-0.252013\pi$
$211$	4307.00	1.40524	0.702621	+	0.711564i	$0.252013\pi$
$212$	−574.000	−0.185955
$213$	−2884.00	−0.927739
$214$	−1269.00	−0.405360
$215$	0	0
$216$	−525.000	−0.165378
$217$	0	0
$218$	1070.00	0.332429
$219$	−5341.00	−1.64800
$220$	0	0
$221$	−2548.00	−0.775552
$222$	2198.00	0.664505
$223$	−2212.00	−0.664244	−0.332122	−	0.943236i	$-0.607765\pi$
$223$	−2212.00	−0.664244	−0.332122	+	0.943236i	$0.607765\pi$
$224$	0	0
$225$	0	0
$226$	−503.000	−0.148049
$227$	−476.000	−0.139177	−0.0695886	−	0.997576i	$-0.522169\pi$
$227$	−476.000	−0.139177	−0.0695886	+	0.997576i	$0.522169\pi$
$228$	1715.00	0.498152
$229$	2940.00	0.848387	0.424194	−	0.905572i	$-0.360558\pi$
$229$	2940.00	0.848387	0.424194	+	0.905572i	$0.360558\pi$
$230$	0	0
$231$	0	0
$232$	−2400.00	−0.679171
$233$	1002.00	0.281730	0.140865	−	0.990029i	$-0.455012\pi$
$233$	1002.00	0.281730	0.140865	+	0.990029i	$0.455012\pi$
$234$	616.000	0.172091
$235$	0	0
$236$	−1960.00	−0.540615
$237$	−3570.00	−0.978466
$238$	0	0
$239$	2480.00	0.671204	0.335602	−	0.942004i	$-0.391060\pi$
$239$	2480.00	0.671204	0.335602	+	0.942004i	$0.391060\pi$
$240$	0	0
$241$	−1897.00	−0.507039	−0.253520	−	0.967330i	$-0.581588\pi$
$241$	−1897.00	−0.507039	−0.253520	+	0.967330i	$0.581588\pi$
$242$	518.000	0.137596
$243$	4928.00	1.30095
$244$	−3626.00	−0.951356
$245$	0	0
$246$	−1421.00	−0.368291
$247$	980.000	0.252453
$248$	630.000	0.161311
$249$	5439.00	1.38427
$250$	0	0
$251$	2373.00	0.596743	0.298371	−	0.954450i	$-0.403557\pi$
$251$	2373.00	0.596743	0.298371	+	0.954450i	$0.403557\pi$
$252$	0	0
$253$	−6966.00	−1.73102
$254$	−874.000	−0.215904
$255$	0	0
$256$	−119.000	−0.0290527
$257$	4494.00	1.09077	0.545385	−	0.838185i	$-0.316383\pi$
$257$	4494.00	1.09077	0.545385	+	0.838185i	$0.316383\pi$
$258$	−644.000	−0.155402
$259$	0	0
$260$	0	0
$261$	3520.00	0.834799
$262$	−1092.00	−0.257496
$263$	722.000	0.169279	0.0846396	−	0.996412i	$-0.473026\pi$
$263$	722.000	0.169279	0.0846396	+	0.996412i	$0.473026\pi$
$264$	−4515.00	−1.05257
$265$	0	0
$266$	0	0
$267$	−6615.00	−1.51622
$268$	−987.000	−0.224965
$269$	6160.00	1.39621	0.698107	−	0.715993i	$-0.254026\pi$
$269$	6160.00	1.39621	0.698107	+	0.715993i	$0.254026\pi$
$270$	0	0
$271$	7238.00	1.62243	0.811213	−	0.584751i	$-0.198808\pi$
$271$	7238.00	1.62243	0.811213	+	0.584751i	$0.198808\pi$
$272$	−3731.00	−0.831710
$273$	0	0
$274$	411.000	0.0906183
$275$	0	0
$276$	7938.00	1.73120
$277$	1776.00	0.385233	0.192616	−	0.981274i	$-0.438303\pi$
$277$	1776.00	0.385233	0.192616	+	0.981274i	$0.438303\pi$
$278$	595.000	0.128366
$279$	−924.000	−0.198274
$280$	0	0
$281$	4542.00	0.964246	0.482123	−	0.876104i	$-0.339866\pi$
$281$	4542.00	0.964246	0.482123	+	0.876104i	$0.339866\pi$
$282$	1372.00	0.289721
$283$	−7077.00	−1.48652	−0.743258	−	0.669005i	$-0.766720\pi$
$283$	−7077.00	−1.48652	−0.743258	+	0.669005i	$0.766720\pi$
$284$	−2884.00	−0.602584
$285$	0	0
$286$	−1204.00	−0.248930
$287$	0	0
$288$	3542.00	0.724703
$289$	3368.00	0.685528
$290$	0	0
$291$	8722.00	1.75702
$292$	−5341.00	−1.07041
$293$	4158.00	0.829054	0.414527	−	0.910037i	$-0.363947\pi$
$293$	4158.00	0.829054	0.414527	+	0.910037i	$0.363947\pi$
$294$	0	0
$295$	0	0
$296$	4710.00	0.924876
$297$	−1505.00	−0.294037
$298$	−3200.00	−0.622050
$299$	4536.00	0.877337
$300$	0	0
$301$	0	0
$302$	202.000	0.0384894
$303$	9114.00	1.72801
$304$	1435.00	0.270733
$305$	0	0
$306$	−2002.00	−0.374009
$307$	2569.00	0.477591	0.238796	−	0.971070i	$-0.423247\pi$
$307$	2569.00	0.477591	0.238796	+	0.971070i	$0.423247\pi$
$308$	0	0
$309$	3724.00	0.685602
$310$	0	0
$311$	−2982.00	−0.543710	−0.271855	−	0.962338i	$-0.587637\pi$
$311$	−2982.00	−0.543710	−0.271855	+	0.962338i	$0.587637\pi$
$312$	2940.00	0.533477
$313$	−2422.00	−0.437379	−0.218689	−	0.975795i	$-0.570178\pi$
$313$	−2422.00	−0.437379	−0.218689	+	0.975795i	$0.570178\pi$
$314$	−406.000	−0.0729679
$315$	0	0
$316$	−3570.00	−0.635532
$317$	−9484.00	−1.68036	−0.840181	−	0.542307i	$-0.817551\pi$
$317$	−9484.00	−1.68036	−0.840181	+	0.542307i	$0.817551\pi$
$318$	−574.000	−0.101221
$319$	−6880.00	−1.20754
$320$	0	0
$321$	8883.00	1.54455
$322$	0	0
$323$	−3185.00	−0.548663
$324$	5873.00	1.00703
$325$	0	0
$326$	−3803.00	−0.646100
$327$	−7490.00	−1.26666
$328$	−3045.00	−0.512598
$329$	0	0
$330$	0	0
$331$	−183.000	−0.0303885	−0.0151942	−	0.999885i	$-0.504837\pi$
$331$	−183.000	−0.0303885	−0.0151942	+	0.999885i	$0.504837\pi$
$332$	5439.00	0.899108
$333$	−6908.00	−1.13681
$334$	−4116.00	−0.674304
$335$	0	0
$336$	0	0
$337$	2861.00	0.462459	0.231229	−	0.972899i	$-0.425725\pi$
$337$	2861.00	0.462459	0.231229	+	0.972899i	$0.425725\pi$
$338$	−1413.00	−0.227388
$339$	3521.00	0.564113
$340$	0	0
$341$	1806.00	0.286805
$342$	770.000	0.121745
$343$	0	0
$344$	−1380.00	−0.216292
$345$	0	0
$346$	−1512.00	−0.234930
$347$	−629.000	−0.0973098	−0.0486549	−	0.998816i	$-0.515493\pi$
$347$	−629.000	−0.0973098	−0.0486549	+	0.998816i	$0.515493\pi$
$348$	7840.00	1.20767
$349$	−5950.00	−0.912597	−0.456298	−	0.889827i	$-0.650825\pi$
$349$	−5950.00	−0.912597	−0.456298	+	0.889827i	$0.650825\pi$
$350$	0	0
$351$	980.000	0.149027
$352$	−6923.00	−1.04829
$353$	11718.0	1.76682	0.883408	−	0.468604i	$-0.155243\pi$
$353$	11718.0	1.76682	0.883408	+	0.468604i	$0.155243\pi$
$354$	−1960.00	−0.294274
$355$	0	0
$356$	−6615.00	−0.984815
$357$	0	0
$358$	2585.00	0.381624
$359$	8070.00	1.18640	0.593201	−	0.805054i	$-0.297864\pi$
$359$	8070.00	1.18640	0.593201	+	0.805054i	$0.297864\pi$
$360$	0	0
$361$	−5634.00	−0.821403
$362$	2758.00	0.400434
$363$	−3626.00	−0.524286
$364$	0	0
$365$	0	0
$366$	−3626.00	−0.517853
$367$	−8316.00	−1.18281	−0.591406	−	0.806374i	$-0.701427\pi$
$367$	−8316.00	−1.18281	−0.591406	+	0.806374i	$0.701427\pi$
$368$	6642.00	0.940865
$369$	4466.00	0.630056
$370$	0	0
$371$	0	0
$372$	−2058.00	−0.286834
$373$	12062.0	1.67439	0.837194	−	0.546906i	$-0.184195\pi$
$373$	12062.0	1.67439	0.837194	+	0.546906i	$0.184195\pi$
$374$	3913.00	0.541006
$375$	0	0
$376$	2940.00	0.403242
$377$	4480.00	0.612021
$378$	0	0
$379$	1735.00	0.235148	0.117574	−	0.993064i	$-0.462488\pi$
$379$	1735.00	0.235148	0.117574	+	0.993064i	$0.462488\pi$
$380$	0	0
$381$	6118.00	0.822663
$382$	−2378.00	−0.318505
$383$	−7602.00	−1.01421	−0.507107	−	0.861883i	$-0.669285\pi$
$383$	−7602.00	−1.01421	−0.507107	+	0.861883i	$0.669285\pi$
$384$	10185.0	1.35352
$385$	0	0
$386$	3067.00	0.404420
$387$	2024.00	0.265855
$388$	8722.00	1.14122
$389$	3030.00	0.394928	0.197464	−	0.980310i	$-0.436729\pi$
$389$	3030.00	0.394928	0.197464	+	0.980310i	$0.436729\pi$
$390$	0	0
$391$	−14742.0	−1.90674
$392$	0	0
$393$	7644.00	0.981142
$394$	2346.00	0.299974
$395$	0	0
$396$	6622.00	0.840323
$397$	1204.00	0.152209	0.0761046	−	0.997100i	$-0.475752\pi$
$397$	1204.00	0.152209	0.0761046	+	0.997100i	$0.475752\pi$
$398$	−4900.00	−0.617123
$399$	0	0
$400$	0	0
$401$	1077.00	0.134122	0.0670609	−	0.997749i	$-0.478638\pi$
$401$	1077.00	0.134122	0.0670609	+	0.997749i	$0.478638\pi$
$402$	−987.000	−0.122455
$403$	−1176.00	−0.145362
$404$	9114.00	1.12237
$405$	0	0
$406$	0	0
$407$	13502.0	1.64440
$408$	−9555.00	−1.15942
$409$	3955.00	0.478147	0.239074	−	0.971001i	$-0.423156\pi$
$409$	3955.00	0.478147	0.239074	+	0.971001i	$0.423156\pi$
$410$	0	0
$411$	−2877.00	−0.345285
$412$	3724.00	0.445311
$413$	0	0
$414$	3564.00	0.423094
$415$	0	0
$416$	4508.00	0.531305
$417$	−4165.00	−0.489115
$418$	−1505.00	−0.176105
$419$	−6265.00	−0.730466	−0.365233	−	0.930916i	$-0.619011\pi$
$419$	−6265.00	−0.730466	−0.365233	+	0.930916i	$0.619011\pi$
$420$	0	0
$421$	−3788.00	−0.438517	−0.219259	−	0.975667i	$-0.570364\pi$
$421$	−3788.00	−0.438517	−0.219259	+	0.975667i	$0.570364\pi$
$422$	4307.00	0.496828
$423$	−4312.00	−0.495642
$424$	−1230.00	−0.140882
$425$	0	0
$426$	−2884.00	−0.328005
$427$	0	0
$428$	8883.00	1.00321
$429$	8428.00	0.948503
$430$	0	0
$431$	−15258.0	−1.70523	−0.852613	−	0.522544i	$-0.824983\pi$
$431$	−15258.0	−1.70523	−0.852613	+	0.522544i	$0.824983\pi$
$432$	1435.00	0.159818
$433$	13573.0	1.50641	0.753206	−	0.657784i	$-0.228506\pi$
$433$	13573.0	1.50641	0.753206	+	0.657784i	$0.228506\pi$
$434$	0	0
$435$	0	0
$436$	−7490.00	−0.822720
$437$	5670.00	0.620670
$438$	−5341.00	−0.582655
$439$	8120.00	0.882794	0.441397	−	0.897312i	$-0.354483\pi$
$439$	8120.00	0.882794	0.441397	+	0.897312i	$0.354483\pi$
$440$	0	0
$441$	0	0
$442$	−2548.00	−0.274199
$443$	−6183.00	−0.663122	−0.331561	−	0.943434i	$-0.607575\pi$
$443$	−6183.00	−0.663122	−0.331561	+	0.943434i	$0.607575\pi$
$444$	−15386.0	−1.64457
$445$	0	0
$446$	−2212.00	−0.234846
$447$	22400.0	2.37021
$448$	0	0
$449$	−1975.00	−0.207586	−0.103793	−	0.994599i	$-0.533098\pi$
$449$	−1975.00	−0.207586	−0.103793	+	0.994599i	$0.533098\pi$
$450$	0	0
$451$	−8729.00	−0.911380
$452$	3521.00	0.366402
$453$	−1414.00	−0.146657
$454$	−476.000	−0.0492066
$455$	0	0
$456$	3675.00	0.377407
$457$	11831.0	1.21101	0.605504	−	0.795842i	$-0.292971\pi$
$457$	11831.0	1.21101	0.605504	+	0.795842i	$0.292971\pi$
$458$	2940.00	0.299950
$459$	−3185.00	−0.323885
$460$	0	0
$461$	−1932.00	−0.195189	−0.0975946	−	0.995226i	$-0.531115\pi$
$461$	−1932.00	−0.195189	−0.0975946	+	0.995226i	$0.531115\pi$
$462$	0	0
$463$	−9228.00	−0.926267	−0.463133	−	0.886289i	$-0.653275\pi$
$463$	−9228.00	−0.926267	−0.463133	+	0.886289i	$0.653275\pi$
$464$	6560.00	0.656337
$465$	0	0
$466$	1002.00	0.0996068
$467$	−13916.0	−1.37892	−0.689460	−	0.724324i	$-0.742152\pi$
$467$	−13916.0	−1.37892	−0.689460	+	0.724324i	$0.742152\pi$
$468$	−4312.00	−0.425902
$469$	0	0
$470$	0	0
$471$	2842.00	0.278031
$472$	−4200.00	−0.409578
$473$	−3956.00	−0.384560
$474$	−3570.00	−0.345940
$475$	0	0
$476$	0	0
$477$	1804.00	0.173165
$478$	2480.00	0.237307
$479$	−2310.00	−0.220348	−0.110174	−	0.993912i	$-0.535141\pi$
$479$	−2310.00	−0.220348	−0.110174	+	0.993912i	$0.535141\pi$
$480$	0	0
$481$	−8792.00	−0.833432
$482$	−1897.00	−0.179266
$483$	0	0
$484$	−3626.00	−0.340533
$485$	0	0
$486$	4928.00	0.459956
$487$	−17114.0	−1.59242	−0.796211	−	0.605019i	$-0.793165\pi$
$487$	−17114.0	−1.59242	−0.796211	+	0.605019i	$0.793165\pi$
$488$	−7770.00	−0.720761
$489$	26621.0	2.46185
$490$	0	0
$491$	−17228.0	−1.58348	−0.791740	−	0.610858i	$-0.790825\pi$
$491$	−17228.0	−1.58348	−0.791740	+	0.610858i	$0.790825\pi$
$492$	9947.00	0.911474
$493$	−14560.0	−1.33012
$494$	980.000	0.0892556
$495$	0	0
$496$	−1722.00	−0.155887
$497$	0	0
$498$	5439.00	0.489412
$499$	−12500.0	−1.12140	−0.560698	−	0.828020i	$-0.689467\pi$
$499$	−12500.0	−1.12140	−0.560698	+	0.828020i	$0.689467\pi$
$500$	0	0
$501$	28812.0	2.56931
$502$	2373.00	0.210980
$503$	868.000	0.0769428	0.0384714	−	0.999260i	$-0.487751\pi$
$503$	868.000	0.0769428	0.0384714	+	0.999260i	$0.487751\pi$
$504$	0	0
$505$	0	0
$506$	−6966.00	−0.612009
$507$	9891.00	0.866420
$508$	6118.00	0.534335
$509$	−13370.0	−1.16427	−0.582136	−	0.813091i	$-0.697783\pi$
$509$	−13370.0	−1.16427	−0.582136	+	0.813091i	$0.697783\pi$
$510$	0	0
$511$	0	0
$512$	11521.0	0.994455
$513$	1225.00	0.105429
$514$	4494.00	0.385646
$515$	0	0
$516$	4508.00	0.384600
$517$	8428.00	0.716950
$518$	0	0
$519$	10584.0	0.895156
$520$	0	0
$521$	−21637.0	−1.81945	−0.909726	−	0.415210i	$-0.863708\pi$
$521$	−21637.0	−1.81945	−0.909726	+	0.415210i	$0.863708\pi$
$522$	3520.00	0.295146
$523$	−287.000	−0.0239955	−0.0119977	−	0.999928i	$-0.503819\pi$
$523$	−287.000	−0.0239955	−0.0119977	+	0.999928i	$0.503819\pi$
$524$	7644.00	0.637270
$525$	0	0
$526$	722.000	0.0598492
$527$	3822.00	0.315918
$528$	12341.0	1.01718
$529$	14077.0	1.15698
$530$	0	0
$531$	6160.00	0.503430
$532$	0	0
$533$	5684.00	0.461916
$534$	−6615.00	−0.536066
$535$	0	0
$536$	−2115.00	−0.170437
$537$	−18095.0	−1.45411
$538$	6160.00	0.493637
$539$	0	0
$540$	0	0
$541$	−5328.00	−0.423417	−0.211709	−	0.977333i	$-0.567903\pi$
$541$	−5328.00	−0.423417	−0.211709	+	0.977333i	$0.567903\pi$
$542$	7238.00	0.573614
$543$	−19306.0	−1.52578
$544$	−14651.0	−1.15470
$545$	0	0
$546$	0	0
$547$	71.0000	0.00554980	0.00277490	−	0.999996i	$-0.499117\pi$
$547$	71.0000	0.00554980	0.00277490	+	0.999996i	$0.499117\pi$
$548$	−2877.00	−0.224269
$549$	11396.0	0.885919
$550$	0	0
$551$	5600.00	0.432973
$552$	17010.0	1.31158
$553$	0	0
$554$	1776.00	0.136200
$555$	0	0
$556$	−4165.00	−0.317689
$557$	−18444.0	−1.40305	−0.701524	−	0.712646i	$-0.747497\pi$
$557$	−18444.0	−1.40305	−0.701524	+	0.712646i	$0.747497\pi$
$558$	−924.000	−0.0701004
$559$	2576.00	0.194907
$560$	0	0
$561$	−27391.0	−2.06141
$562$	4542.00	0.340912
$563$	−672.000	−0.0503045	−0.0251522	−	0.999684i	$-0.508007\pi$
$563$	−672.000	−0.0503045	−0.0251522	+	0.999684i	$0.508007\pi$
$564$	−9604.00	−0.717024
$565$	0	0
$566$	−7077.00	−0.525563
$567$	0	0
$568$	−6180.00	−0.456526
$569$	−10935.0	−0.805657	−0.402829	−	0.915275i	$-0.631973\pi$
$569$	−10935.0	−0.805657	−0.402829	+	0.915275i	$0.631973\pi$
$570$	0	0
$571$	−13588.0	−0.995867	−0.497934	−	0.867215i	$-0.665908\pi$
$571$	−13588.0	−0.995867	−0.497934	+	0.867215i	$0.665908\pi$
$572$	8428.00	0.616071
$573$	16646.0	1.21361
$574$	0	0
$575$	0	0
$576$	−3674.00	−0.265770
$577$	−8701.00	−0.627777	−0.313889	−	0.949460i	$-0.601632\pi$
$577$	−8701.00	−0.627777	−0.313889	+	0.949460i	$0.601632\pi$
$578$	3368.00	0.242371
$579$	−21469.0	−1.54097
$580$	0	0
$581$	0	0
$582$	8722.00	0.621200
$583$	−3526.00	−0.250484
$584$	−11445.0	−0.810955
$585$	0	0
$586$	4158.00	0.293115
$587$	−11361.0	−0.798839	−0.399420	−	0.916768i	$-0.630788\pi$
$587$	−11361.0	−0.798839	−0.399420	+	0.916768i	$0.630788\pi$
$588$	0	0
$589$	−1470.00	−0.102836
$590$	0	0
$591$	−16422.0	−1.14300
$592$	−12874.0	−0.893781
$593$	−11417.0	−0.790624	−0.395312	−	0.918547i	$-0.629364\pi$
$593$	−11417.0	−0.790624	−0.395312	+	0.918547i	$0.629364\pi$
$594$	−1505.00	−0.103958
$595$	0	0
$596$	22400.0	1.53950
$597$	34300.0	2.35143
$598$	4536.00	0.310185
$599$	−21050.0	−1.43586	−0.717930	−	0.696116i	$-0.754910\pi$
$599$	−21050.0	−1.43586	−0.717930	+	0.696116i	$0.754910\pi$
$600$	0	0
$601$	−7427.00	−0.504083	−0.252041	−	0.967716i	$-0.581102\pi$
$601$	−7427.00	−0.504083	−0.252041	+	0.967716i	$0.581102\pi$
$602$	0	0
$603$	3102.00	0.209491
$604$	−1414.00	−0.0952564
$605$	0	0
$606$	9114.00	0.610942
$607$	4144.00	0.277100	0.138550	−	0.990355i	$-0.455756\pi$
$607$	4144.00	0.277100	0.138550	+	0.990355i	$0.455756\pi$
$608$	5635.00	0.375871
$609$	0	0
$610$	0	0
$611$	−5488.00	−0.363373
$612$	14014.0	0.925625
$613$	30122.0	1.98469	0.992346	−	0.123489i	$-0.0394084\pi$
$613$	30122.0	1.98469	0.992346	+	0.123489i	$0.0394084\pi$
$614$	2569.00	0.168854
$615$	0	0
$616$	0	0
$617$	−11934.0	−0.778679	−0.389339	−	0.921094i	$-0.627297\pi$
$617$	−11934.0	−0.778679	−0.389339	+	0.921094i	$0.627297\pi$
$618$	3724.00	0.242397
$619$	−8540.00	−0.554526	−0.277263	−	0.960794i	$-0.589427\pi$
$619$	−8540.00	−0.554526	−0.277263	+	0.960794i	$0.589427\pi$
$620$	0	0
$621$	5670.00	0.366392
$622$	−2982.00	−0.192230
$623$	0	0
$624$	−8036.00	−0.515541
$625$	0	0
$626$	−2422.00	−0.154637
$627$	10535.0	0.671017
$628$	2842.00	0.180586
$629$	28574.0	1.81132
$630$	0	0
$631$	−3158.00	−0.199236	−0.0996181	−	0.995026i	$-0.531762\pi$
$631$	−3158.00	−0.199236	−0.0996181	+	0.995026i	$0.531762\pi$
$632$	−7650.00	−0.481488
$633$	−30149.0	−1.89307
$634$	−9484.00	−0.594097
$635$	0	0
$636$	4018.00	0.250510
$637$	0	0
$638$	−6880.00	−0.426931
$639$	9064.00	0.561137
$640$	0	0
$641$	−4278.00	−0.263605	−0.131803	−	0.991276i	$-0.542076\pi$
$641$	−4278.00	−0.263605	−0.131803	+	0.991276i	$0.542076\pi$
$642$	8883.00	0.546081
$643$	11508.0	0.705803	0.352901	−	0.935661i	$-0.385195\pi$
$643$	11508.0	0.705803	0.352901	+	0.935661i	$0.385195\pi$
$644$	0	0
$645$	0	0
$646$	−3185.00	−0.193982
$647$	8204.00	0.498505	0.249252	−	0.968439i	$-0.419815\pi$
$647$	8204.00	0.498505	0.249252	+	0.968439i	$0.419815\pi$
$648$	12585.0	0.762941
$649$	−12040.0	−0.728215
$650$	0	0
$651$	0	0
$652$	26621.0	1.59902
$653$	−5518.00	−0.330683	−0.165342	−	0.986236i	$-0.552873\pi$
$653$	−5518.00	−0.330683	−0.165342	+	0.986236i	$0.552873\pi$
$654$	−7490.00	−0.447832
$655$	0	0
$656$	8323.00	0.495364
$657$	16786.0	0.996780
$658$	0	0
$659$	13295.0	0.785887	0.392944	−	0.919563i	$-0.371457\pi$
$659$	13295.0	0.785887	0.392944	+	0.919563i	$0.371457\pi$
$660$	0	0
$661$	9968.00	0.586551	0.293276	−	0.956028i	$-0.405255\pi$
$661$	9968.00	0.586551	0.293276	+	0.956028i	$0.405255\pi$
$662$	−183.000	−0.0107440
$663$	17836.0	1.04479
$664$	11655.0	0.681177
$665$	0	0
$666$	−6908.00	−0.401921
$667$	25920.0	1.50469
$668$	28812.0	1.66882
$669$	15484.0	0.894837
$670$	0	0
$671$	−22274.0	−1.28149
$672$	0	0
$673$	−15738.0	−0.901419	−0.450710	−	0.892671i	$-0.648829\pi$
$673$	−15738.0	−0.901419	−0.450710	+	0.892671i	$0.648829\pi$
$674$	2861.00	0.163504
$675$	0	0
$676$	9891.00	0.562756
$677$	19824.0	1.12540	0.562702	−	0.826660i	$-0.309762\pi$
$677$	19824.0	1.12540	0.562702	+	0.826660i	$0.309762\pi$
$678$	3521.00	0.199444
$679$	0	0
$680$	0	0
$681$	3332.00	0.187493
$682$	1806.00	0.101401
$683$	−11073.0	−0.620346	−0.310173	−	0.950680i	$-0.600387\pi$
$683$	−11073.0	−0.620346	−0.310173	+	0.950680i	$0.600387\pi$
$684$	−5390.00	−0.301304
$685$	0	0
$686$	0	0
$687$	−20580.0	−1.14291
$688$	3772.00	0.209021
$689$	2296.00	0.126953
$690$	0	0
$691$	6503.00	0.358011	0.179006	−	0.983848i	$-0.442712\pi$
$691$	6503.00	0.358011	0.179006	+	0.983848i	$0.442712\pi$
$692$	10584.0	0.581421
$693$	0	0
$694$	−629.000	−0.0344042
$695$	0	0
$696$	16800.0	0.914946
$697$	−18473.0	−1.00389
$698$	−5950.00	−0.322652
$699$	−7014.00	−0.379533
$700$	0	0
$701$	−10148.0	−0.546768	−0.273384	−	0.961905i	$-0.588143\pi$
$701$	−10148.0	−0.546768	−0.273384	+	0.961905i	$0.588143\pi$
$702$	980.000	0.0526891
$703$	−10990.0	−0.589610
$704$	7181.00	0.384438
$705$	0	0
$706$	11718.0	0.624664
$707$	0	0
$708$	13720.0	0.728290
$709$	−9980.00	−0.528641	−0.264321	−	0.964435i	$-0.585148\pi$
$709$	−9980.00	−0.528641	−0.264321	+	0.964435i	$0.585148\pi$
$710$	0	0
$711$	11220.0	0.591818
$712$	−14175.0	−0.746110
$713$	−6804.00	−0.357380
$714$	0	0
$715$	0	0
$716$	−18095.0	−0.944472
$717$	−17360.0	−0.904214
$718$	8070.00	0.419456
$719$	27510.0	1.42691	0.713456	−	0.700700i	$-0.247129\pi$
$719$	27510.0	1.42691	0.713456	+	0.700700i	$0.247129\pi$
$720$	0	0
$721$	0	0
$722$	−5634.00	−0.290410
$723$	13279.0	0.683059
$724$	−19306.0	−0.991025
$725$	0	0
$726$	−3626.00	−0.185363
$727$	17024.0	0.868480	0.434240	−	0.900797i	$-0.357017\pi$
$727$	17024.0	0.868480	0.434240	+	0.900797i	$0.357017\pi$
$728$	0	0
$729$	−11843.0	−0.601687
$730$	0	0
$731$	−8372.00	−0.423597
$732$	25382.0	1.28162
$733$	34748.0	1.75095	0.875475	−	0.483263i	$-0.160549\pi$
$733$	34748.0	1.75095	0.875475	+	0.483263i	$0.160549\pi$
$734$	−8316.00	−0.418187
$735$	0	0
$736$	26082.0	1.30624
$737$	−6063.00	−0.303030
$738$	4466.00	0.222758
$739$	−12020.0	−0.598326	−0.299163	−	0.954202i	$-0.596707\pi$
$739$	−12020.0	−0.598326	−0.299163	+	0.954202i	$0.596707\pi$
$740$	0	0
$741$	−6860.00	−0.340092
$742$	0	0
$743$	28642.0	1.41423	0.707115	−	0.707098i	$-0.249996\pi$
$743$	28642.0	1.41423	0.707115	+	0.707098i	$0.249996\pi$
$744$	−4410.00	−0.217310
$745$	0	0
$746$	12062.0	0.591986
$747$	−17094.0	−0.837265
$748$	−27391.0	−1.33892
$749$	0	0
$750$	0	0
$751$	8752.00	0.425253	0.212627	−	0.977134i	$-0.431798\pi$
$751$	8752.00	0.425253	0.212627	+	0.977134i	$0.431798\pi$
$752$	−8036.00	−0.389685
$753$	−16611.0	−0.803902
$754$	4480.00	0.216382
$755$	0	0
$756$	0	0
$757$	10256.0	0.492418	0.246209	−	0.969217i	$-0.420815\pi$
$757$	10256.0	0.492418	0.246209	+	0.969217i	$0.420815\pi$
$758$	1735.00	0.0831373
$759$	48762.0	2.33195
$760$	0	0
$761$	−33957.0	−1.61753	−0.808765	−	0.588132i	$-0.799864\pi$
$761$	−33957.0	−1.61753	−0.808765	+	0.588132i	$0.799864\pi$
$762$	6118.00	0.290855
$763$	0	0
$764$	16646.0	0.788261
$765$	0	0
$766$	−7602.00	−0.358579
$767$	7840.00	0.369082
$768$	833.000	0.0391384
$769$	−27965.0	−1.31137	−0.655685	−	0.755034i	$-0.727620\pi$
$769$	−27965.0	−1.31137	−0.655685	+	0.755034i	$0.727620\pi$
$770$	0	0
$771$	−31458.0	−1.46943
$772$	−21469.0	−1.00089
$773$	−9912.00	−0.461203	−0.230601	−	0.973048i	$-0.574069\pi$
$773$	−9912.00	−0.461203	−0.230601	+	0.973048i	$0.574069\pi$
$774$	2024.00	0.0939938
$775$	0	0
$776$	18690.0	0.864603
$777$	0	0
$778$	3030.00	0.139628
$779$	7105.00	0.326782
$780$	0	0
$781$	−17716.0	−0.811688
$782$	−14742.0	−0.674134
$783$	5600.00	0.255591
$784$	0	0
$785$	0	0
$786$	7644.00	0.346886
$787$	25564.0	1.15789	0.578944	−	0.815367i	$-0.303465\pi$
$787$	25564.0	1.15789	0.578944	+	0.815367i	$0.303465\pi$
$788$	−16422.0	−0.742398
$789$	−5054.00	−0.228045
$790$	0	0
$791$	0	0
$792$	14190.0	0.636641
$793$	14504.0	0.649498
$794$	1204.00	0.0538141
$795$	0	0
$796$	34300.0	1.52730
$797$	−12446.0	−0.553149	−0.276575	−	0.960992i	$-0.589199\pi$
$797$	−12446.0	−0.553149	−0.276575	+	0.960992i	$0.589199\pi$
$798$	0	0
$799$	17836.0	0.789728
$800$	0	0
$801$	20790.0	0.917077
$802$	1077.00	0.0474192
$803$	−32809.0	−1.44185
$804$	6909.00	0.303062
$805$	0	0
$806$	−1176.00	−0.0513931
$807$	−43120.0	−1.88091
$808$	19530.0	0.850325
$809$	33970.0	1.47629	0.738147	−	0.674640i	$-0.235701\pi$
$809$	33970.0	1.47629	0.738147	+	0.674640i	$0.235701\pi$
$810$	0	0
$811$	−18732.0	−0.811060	−0.405530	−	0.914082i	$-0.632913\pi$
$811$	−18732.0	−0.811060	−0.405530	+	0.914082i	$0.632913\pi$
$812$	0	0
$813$	−50666.0	−2.18565
$814$	13502.0	0.581382
$815$	0	0
$816$	26117.0	1.12044
$817$	3220.00	0.137887
$818$	3955.00	0.169051
$819$	0	0
$820$	0	0
$821$	6162.00	0.261943	0.130972	−	0.991386i	$-0.458190\pi$
$821$	6162.00	0.261943	0.130972	+	0.991386i	$0.458190\pi$
$822$	−2877.00	−0.122077
$823$	−25388.0	−1.07530	−0.537649	−	0.843169i	$-0.680687\pi$
$823$	−25388.0	−1.07530	−0.537649	+	0.843169i	$0.680687\pi$
$824$	7980.00	0.337374
$825$	0	0
$826$	0	0
$827$	25201.0	1.05964	0.529821	−	0.848109i	$-0.322259\pi$
$827$	25201.0	1.05964	0.529821	+	0.848109i	$0.322259\pi$
$828$	−24948.0	−1.04710
$829$	19740.0	0.827019	0.413509	−	0.910500i	$-0.364303\pi$
$829$	19740.0	0.827019	0.413509	+	0.910500i	$0.364303\pi$
$830$	0	0
$831$	−12432.0	−0.518967
$832$	−4676.00	−0.194845
$833$	0	0
$834$	−4165.00	−0.172928
$835$	0	0
$836$	10535.0	0.435838
$837$	−1470.00	−0.0607057
$838$	−6265.00	−0.258259
$839$	−29680.0	−1.22130	−0.610648	−	0.791902i	$-0.709091\pi$
$839$	−29680.0	−1.22130	−0.610648	+	0.791902i	$0.709091\pi$
$840$	0	0
$841$	1211.00	0.0496535
$842$	−3788.00	−0.155039
$843$	−31794.0	−1.29898
$844$	−30149.0	−1.22959
$845$	0	0
$846$	−4312.00	−0.175236
$847$	0	0
$848$	3362.00	0.136146
$849$	49539.0	2.00256
$850$	0	0
$851$	−50868.0	−2.04904
$852$	20188.0	0.811772
$853$	1218.00	0.0488904	0.0244452	−	0.999701i	$-0.492218\pi$
$853$	1218.00	0.0488904	0.0244452	+	0.999701i	$0.492218\pi$
$854$	0	0
$855$	0	0
$856$	19035.0	0.760050
$857$	−38731.0	−1.54379	−0.771894	−	0.635752i	$-0.780690\pi$
$857$	−38731.0	−1.54379	−0.771894	+	0.635752i	$0.780690\pi$
$858$	8428.00	0.335346
$859$	23555.0	0.935607	0.467803	−	0.883833i	$-0.345046\pi$
$859$	23555.0	0.935607	0.467803	+	0.883833i	$0.345046\pi$
$860$	0	0
$861$	0	0
$862$	−15258.0	−0.602888
$863$	24872.0	0.981058	0.490529	−	0.871425i	$-0.336804\pi$
$863$	24872.0	0.981058	0.490529	+	0.871425i	$0.336804\pi$
$864$	5635.00	0.221883
$865$	0	0
$866$	13573.0	0.532597
$867$	−23576.0	−0.923510
$868$	0	0
$869$	−21930.0	−0.856069
$870$	0	0
$871$	3948.00	0.153585
$872$	−16050.0	−0.623305
$873$	−27412.0	−1.06272
$874$	5670.00	0.219440
$875$	0	0
$876$	37387.0	1.44200
$877$	−17124.0	−0.659335	−0.329667	−	0.944097i	$-0.606937\pi$
$877$	−17124.0	−0.659335	−0.329667	+	0.944097i	$0.606937\pi$
$878$	8120.00	0.312115
$879$	−29106.0	−1.11686
$880$	0	0
$881$	658.000	0.0251630	0.0125815	−	0.999921i	$-0.495995\pi$
$881$	658.000	0.0251630	0.0125815	+	0.999921i	$0.495995\pi$
$882$	0	0
$883$	33727.0	1.28540	0.642698	−	0.766120i	$-0.277815\pi$
$883$	33727.0	1.28540	0.642698	+	0.766120i	$0.277815\pi$
$884$	17836.0	0.678608
$885$	0	0
$886$	−6183.00	−0.234449
$887$	−36036.0	−1.36412	−0.682058	−	0.731298i	$-0.738915\pi$
$887$	−36036.0	−1.36412	−0.682058	+	0.731298i	$0.738915\pi$
$888$	−32970.0	−1.24595
$889$	0	0
$890$	0	0
$891$	36077.0	1.35648
$892$	15484.0	0.581214
$893$	−6860.00	−0.257067
$894$	22400.0	0.837996
$895$	0	0
$896$	0	0
$897$	−31752.0	−1.18190
$898$	−1975.00	−0.0733927
$899$	−6720.00	−0.249304
$900$	0	0
$901$	−7462.00	−0.275910
$902$	−8729.00	−0.322222
$903$	0	0
$904$	7545.00	0.277592
$905$	0	0
$906$	−1414.00	−0.0518510
$907$	39156.0	1.43347	0.716733	−	0.697348i	$-0.245637\pi$
$907$	39156.0	1.43347	0.716733	+	0.697348i	$0.245637\pi$
$908$	3332.00	0.121780
$909$	−28644.0	−1.04517
$910$	0	0
$911$	43532.0	1.58318	0.791591	−	0.611051i	$-0.209253\pi$
$911$	43532.0	1.58318	0.791591	+	0.611051i	$0.209253\pi$
$912$	−10045.0	−0.364718
$913$	33411.0	1.21111
$914$	11831.0	0.428156
$915$	0	0
$916$	−20580.0	−0.742339
$917$	0	0
$918$	−3185.00	−0.114511
$919$	−28610.0	−1.02694	−0.513469	−	0.858108i	$-0.671640\pi$
$919$	−28610.0	−1.02694	−0.513469	+	0.858108i	$0.671640\pi$
$920$	0	0
$921$	−17983.0	−0.643388
$922$	−1932.00	−0.0690098
$923$	11536.0	0.411389
$924$	0	0
$925$	0	0
$926$	−9228.00	−0.327485
$927$	−11704.0	−0.414682
$928$	25760.0	0.911221
$929$	24290.0	0.857835	0.428918	−	0.903344i	$-0.358895\pi$
$929$	24290.0	0.857835	0.428918	+	0.903344i	$0.358895\pi$
$930$	0	0
$931$	0	0
$932$	−7014.00	−0.246514
$933$	20874.0	0.732459
$934$	−13916.0	−0.487522
$935$	0	0
$936$	−9240.00	−0.322670
$937$	−34461.0	−1.20149	−0.600743	−	0.799442i	$-0.705128\pi$
$937$	−34461.0	−1.20149	−0.600743	+	0.799442i	$0.705128\pi$
$938$	0	0
$939$	16954.0	0.589215
$940$	0	0
$941$	40628.0	1.40748	0.703738	−	0.710460i	$-0.251513\pi$
$941$	40628.0	1.40748	0.703738	+	0.710460i	$0.251513\pi$
$942$	2842.00	0.0982987
$943$	32886.0	1.13565
$944$	11480.0	0.395807
$945$	0	0
$946$	−3956.00	−0.135963
$947$	−20904.0	−0.717306	−0.358653	−	0.933471i	$-0.616764\pi$
$947$	−20904.0	−0.717306	−0.358653	+	0.933471i	$0.616764\pi$
$948$	24990.0	0.856158
$949$	21364.0	0.730774
$950$	0	0
$951$	66388.0	2.26370
$952$	0	0
$953$	1807.00	0.0614213	0.0307106	−	0.999528i	$-0.490223\pi$
$953$	1807.00	0.0614213	0.0307106	+	0.999528i	$0.490223\pi$
$954$	1804.00	0.0612229
$955$	0	0
$956$	−17360.0	−0.587304
$957$	48160.0	1.62674
$958$	−2310.00	−0.0779047
$959$	0	0
$960$	0	0
$961$	−28027.0	−0.940787
$962$	−8792.00	−0.294663
$963$	−27918.0	−0.934211
$964$	13279.0	0.443660
$965$	0	0
$966$	0	0
$967$	−57584.0	−1.91497	−0.957485	−	0.288482i	$-0.906849\pi$
$967$	−57584.0	−1.91497	−0.957485	+	0.288482i	$0.906849\pi$
$968$	−7770.00	−0.257993
$969$	22295.0	0.739132
$970$	0	0
$971$	−27237.0	−0.900182	−0.450091	−	0.892983i	$-0.648608\pi$
$971$	−27237.0	−0.900182	−0.450091	+	0.892983i	$0.648608\pi$
$972$	−34496.0	−1.13833
$973$	0	0
$974$	−17114.0	−0.563006
$975$	0	0
$976$	21238.0	0.696528
$977$	−13649.0	−0.446950	−0.223475	−	0.974710i	$-0.571740\pi$
$977$	−13649.0	−0.446950	−0.223475	+	0.974710i	$0.571740\pi$
$978$	26621.0	0.870394
$979$	−40635.0	−1.32656
$980$	0	0
$981$	23540.0	0.766131
$982$	−17228.0	−0.559845
$983$	−16002.0	−0.519211	−0.259606	−	0.965715i	$-0.583593\pi$
$983$	−16002.0	−0.519211	−0.259606	+	0.965715i	$0.583593\pi$
$984$	21315.0	0.690546
$985$	0	0
$986$	−14560.0	−0.470269
$987$	0	0
$988$	−6860.00	−0.220896
$989$	14904.0	0.479191
$990$	0	0
$991$	37022.0	1.18672	0.593362	−	0.804936i	$-0.297800\pi$
$991$	37022.0	1.18672	0.593362	+	0.804936i	$0.297800\pi$
$992$	−6762.00	−0.216425
$993$	1281.00	0.0409379
$994$	0	0
$995$	0	0
$996$	−38073.0	−1.21123
$997$	−18396.0	−0.584360	−0.292180	−	0.956363i	$-0.594381\pi$
$997$	−18396.0	−0.584360	−0.292180	+	0.956363i	$0.594381\pi$
$998$	−12500.0	−0.396474
$999$	−10990.0	−0.348056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1225.4.a.i.1.1		1
5.4	even	2		1225.4.a.h.1.1		1
7.6	odd	2		25.4.a.b.1.1	yes	1
21.20	even	2		225.4.a.c.1.1		1
28.27	even	2		400.4.a.c.1.1		1
35.13	even	4		25.4.b.b.24.1		2
35.27	even	4		25.4.b.b.24.2		2
35.34	odd	2		25.4.a.a.1.1	✓	1
56.13	odd	2		1600.4.a.i.1.1		1
56.27	even	2		1600.4.a.bs.1.1		1
105.62	odd	4		225.4.b.f.199.1		2
105.83	odd	4		225.4.b.f.199.2		2
105.104	even	2		225.4.a.e.1.1		1
140.27	odd	4		400.4.c.e.49.2		2
140.83	odd	4		400.4.c.e.49.1		2
140.139	even	2		400.4.a.s.1.1		1
280.69	odd	2		1600.4.a.bt.1.1		1
280.139	even	2		1600.4.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.a.a.1.1	✓	1	35.34	odd	2
25.4.a.b.1.1	yes	1	7.6	odd	2
25.4.b.b.24.1		2	35.13	even	4
25.4.b.b.24.2		2	35.27	even	4
225.4.a.c.1.1		1	21.20	even	2
225.4.a.e.1.1		1	105.104	even	2
225.4.b.f.199.1		2	105.62	odd	4
225.4.b.f.199.2		2	105.83	odd	4
400.4.a.c.1.1		1	28.27	even	2
400.4.a.s.1.1		1	140.139	even	2
400.4.c.e.49.1		2	140.83	odd	4
400.4.c.e.49.2		2	140.27	odd	4
1225.4.a.h.1.1		1	5.4	even	2
1225.4.a.i.1.1		1	1.1	even	1	trivial
1600.4.a.h.1.1		1	280.139	even	2
1600.4.a.i.1.1		1	56.13	odd	2
1600.4.a.bs.1.1		1	56.27	even	2
1600.4.a.bt.1.1		1	280.69	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1225 = 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1225.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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