LMFDB - Embedded newform 9800.2.a.cg.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9800,2,Mod(1,9800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9800, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9800.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9800.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:	$78.2533939809$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.363328$ of defining polynomial
Character	$\chi$	$=$	9800.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.363328 q^{3} -2.86799 q^{9} +O(q^{10})$	$q-0.363328 q^{3} -2.86799 q^{9} +5.14134 q^{11} +4.64600 q^{13} -3.86799 q^{17} +0.778008 q^{19} +5.00933 q^{23} +2.13201 q^{27} +9.42401 q^{29} -4.72666 q^{31} -1.86799 q^{33} +6.00000 q^{37} -1.68802 q^{39} +1.00933 q^{41} -7.00933 q^{43} +11.4240 q^{47} +1.40535 q^{51} +7.55602 q^{53} -0.282672 q^{57} -12.5140 q^{59} -11.5047 q^{61} -11.7360 q^{67} -1.82003 q^{69} +2.72666 q^{71} -5.00933 q^{73} +5.68802 q^{79} +7.82936 q^{81} +4.67531 q^{83} -3.42401 q^{87} +2.82936 q^{89} +1.71733 q^{93} +1.58532 q^{97} -14.7453 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{3} + 4 q^{9}+O(q^{10}) $ 3 * q + q^3 + 4 * q^9	$ 3 q + q^{3} + 4 q^{9} + 7 q^{11} - 5 q^{13} + q^{17} - 4 q^{19} - 6 q^{23} + 19 q^{27} + 3 q^{29} - 10 q^{31} + 7 q^{33} + 18 q^{37} - 5 q^{39} - 18 q^{41} + 9 q^{47} + 21 q^{51} + 10 q^{53} + 16 q^{57} - 6 q^{59} - 24 q^{61} - 10 q^{67} - 18 q^{69} + 4 q^{71} + 6 q^{73} + 17 q^{79} + 15 q^{81} + 12 q^{83} + 15 q^{87} + 22 q^{93} + 9 q^{97} + 2 q^{99}+O(q^{100}) $ 3 * q + q^3 + 4 * q^9 + 7 * q^11 - 5 * q^13 + q^17 - 4 * q^19 - 6 * q^23 + 19 * q^27 + 3 * q^29 - 10 * q^31 + 7 * q^33 + 18 * q^37 - 5 * q^39 - 18 * q^41 + 9 * q^47 + 21 * q^51 + 10 * q^53 + 16 * q^57 - 6 * q^59 - 24 * q^61 - 10 * q^67 - 18 * q^69 + 4 * q^71 + 6 * q^73 + 17 * q^79 + 15 * q^81 + 12 * q^83 + 15 * q^87 + 22 * q^93 + 9 * q^97 + 2 * q^99

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 $

$2$	0	0
$2$	0	0
$3$	−0.363328	−0.209768	−0.104884	−	0.994484i	$-0.533447\pi$
$3$	−0.363328	−0.209768	−0.104884	+	0.994484i	$0.533447\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−2.86799	−0.955998
$10$	0	0
$11$	5.14134	1.55017	0.775086	−	0.631856i	$-0.217707\pi$
$11$	5.14134	1.55017	0.775086	+	0.631856i	$0.217707\pi$
$12$	0	0
$13$	4.64600	1.28857	0.644284	−	0.764786i	$-0.277155\pi$
$13$	4.64600	1.28857	0.644284	+	0.764786i	$0.277155\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−3.86799	−0.938126	−0.469063	−	0.883165i	$-0.655408\pi$
$17$	−3.86799	−0.938126	−0.469063	+	0.883165i	$0.655408\pi$
$18$	0	0
$19$	0.778008	0.178487	0.0892436	−	0.996010i	$-0.471555\pi$
$19$	0.778008	0.178487	0.0892436	+	0.996010i	$0.471555\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	5.00933	1.04452	0.522259	−	0.852787i	$-0.325090\pi$
$23$	5.00933	1.04452	0.522259	+	0.852787i	$0.325090\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	2.13201	0.410305
$28$	0	0
$29$	9.42401	1.74999	0.874997	−	0.484128i	$-0.160863\pi$
$29$	9.42401	1.74999	0.874997	+	0.484128i	$0.160863\pi$
$30$	0	0
$31$	−4.72666	−0.848933	−0.424466	−	0.905444i	$-0.639538\pi$
$31$	−4.72666	−0.848933	−0.424466	+	0.905444i	$0.639538\pi$
$32$	0	0
$33$	−1.86799	−0.325176
$34$	0	0
$35$	0	0
$36$	0	0
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	0	0
$39$	−1.68802	−0.270300
$40$	0	0
$41$	1.00933	0.157631	0.0788153	−	0.996889i	$-0.474886\pi$
$41$	1.00933	0.157631	0.0788153	+	0.996889i	$0.474886\pi$
$42$	0	0
$43$	−7.00933	−1.06891	−0.534456	−	0.845196i	$-0.679484\pi$
$43$	−7.00933	−1.06891	−0.534456	+	0.845196i	$0.679484\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	11.4240	1.66636	0.833181	−	0.553000i	$-0.186517\pi$
$47$	11.4240	1.66636	0.833181	+	0.553000i	$0.186517\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	1.40535	0.196788
$52$	0	0
$53$	7.55602	1.03790	0.518949	−	0.854805i	$-0.326323\pi$
$53$	7.55602	1.03790	0.518949	+	0.854805i	$0.326323\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−0.282672	−0.0374409
$58$	0	0
$59$	−12.5140	−1.62918	−0.814592	−	0.580035i	$-0.803039\pi$
$59$	−12.5140	−1.62918	−0.814592	+	0.580035i	$0.803039\pi$
$60$	0	0
$61$	−11.5047	−1.47302	−0.736511	−	0.676426i	$-0.763528\pi$
$61$	−11.5047	−1.47302	−0.736511	+	0.676426i	$0.763528\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−11.7360	−1.43378	−0.716889	−	0.697187i	$-0.754435\pi$
$67$	−11.7360	−1.43378	−0.716889	+	0.697187i	$0.754435\pi$
$68$	0	0
$69$	−1.82003	−0.219106
$70$	0	0
$71$	2.72666	0.323595	0.161797	−	0.986824i	$-0.448271\pi$
$71$	2.72666	0.323595	0.161797	+	0.986824i	$0.448271\pi$
$72$	0	0
$73$	−5.00933	−0.586298	−0.293149	−	0.956067i	$-0.594703\pi$
$73$	−5.00933	−0.586298	−0.293149	+	0.956067i	$0.594703\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	5.68802	0.639953	0.319976	−	0.947426i	$-0.396325\pi$
$79$	5.68802	0.639953	0.319976	+	0.947426i	$0.396325\pi$
$80$	0	0
$81$	7.82936	0.869929
$82$	0	0
$83$	4.67531	0.513181	0.256591	−	0.966520i	$-0.417401\pi$
$83$	4.67531	0.513181	0.256591	+	0.966520i	$0.417401\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−3.42401	−0.367092
$88$	0	0
$89$	2.82936	0.299911	0.149956	−	0.988693i	$-0.452087\pi$
$89$	2.82936	0.299911	0.149956	+	0.988693i	$0.452087\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	1.71733	0.178079
$94$	0	0
$95$	0	0
$96$	0	0
$97$	1.58532	0.160965	0.0804824	−	0.996756i	$-0.474354\pi$
$97$	1.58532	0.160965	0.0804824	+	0.996756i	$0.474354\pi$
$98$	0	0
$99$	−14.7453	−1.48196
$100$	0	0
$101$	9.06068	0.901571	0.450786	−	0.892632i	$-0.351144\pi$
$101$	9.06068	0.901571	0.450786	+	0.892632i	$0.351144\pi$
$102$	0	0
$103$	−5.14134	−0.506591	−0.253295	−	0.967389i	$-0.581514\pi$
$103$	−5.14134	−0.506591	−0.253295	+	0.967389i	$0.581514\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	−3.97070	−0.380324	−0.190162	−	0.981753i	$-0.560901\pi$
$109$	−3.97070	−0.380324	−0.190162	+	0.981753i	$0.560901\pi$
$110$	0	0
$111$	−2.17997	−0.206914
$112$	0	0
$113$	4.54669	0.427716	0.213858	−	0.976865i	$-0.431397\pi$
$113$	4.54669	0.427716	0.213858	+	0.976865i	$0.431397\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−13.3247	−1.23187
$118$	0	0
$119$	0	0
$120$	0	0
$121$	15.4333	1.40303
$122$	0	0
$123$	−0.366718	−0.0330658
$124$	0	0
$125$	0	0
$126$	0	0
$127$	16.1214	1.43054	0.715270	−	0.698849i	$-0.246304\pi$
$127$	16.1214	1.43054	0.715270	+	0.698849i	$0.246304\pi$
$128$	0	0
$129$	2.54669	0.224223
$130$	0	0
$131$	−0.0513514	−0.00448659	−0.00224330	−	0.999997i	$-0.500714\pi$
$131$	−0.0513514	−0.00448659	−0.00224330	+	0.999997i	$0.500714\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−14.0187	−1.19769	−0.598847	−	0.800863i	$-0.704374\pi$
$137$	−14.0187	−1.19769	−0.598847	+	0.800863i	$0.704374\pi$
$138$	0	0
$139$	−12.6167	−1.07013	−0.535067	−	0.844810i	$-0.679714\pi$
$139$	−12.6167	−1.07013	−0.535067	+	0.844810i	$0.679714\pi$
$140$	0	0
$141$	−4.15066	−0.349549
$142$	0	0
$143$	23.8867	1.99750
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−11.4533	−0.938292	−0.469146	−	0.883121i	$-0.655438\pi$
$149$	−11.4533	−0.938292	−0.469146	+	0.883121i	$0.655438\pi$
$150$	0	0
$151$	5.86799	0.477530	0.238765	−	0.971077i	$-0.423257\pi$
$151$	5.86799	0.477530	0.238765	+	0.971077i	$0.423257\pi$
$152$	0	0
$153$	11.0934	0.896846
$154$	0	0
$155$	0	0
$156$	0	0
$157$	5.78734	0.461880	0.230940	−	0.972968i	$-0.425820\pi$
$157$	5.78734	0.461880	0.230940	+	0.972968i	$0.425820\pi$
$158$	0	0
$159$	−2.74531	−0.217718
$160$	0	0
$161$	0	0
$162$	0	0
$163$	3.27334	0.256388	0.128194	−	0.991749i	$-0.459082\pi$
$163$	3.27334	0.256388	0.128194	+	0.991749i	$0.459082\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	24.8773	1.92506	0.962532	−	0.271166i	$-0.0874094\pi$
$167$	24.8773	1.92506	0.962532	+	0.271166i	$0.0874094\pi$
$168$	0	0
$169$	8.58532	0.660409
$170$	0	0
$171$	−2.23132	−0.170633
$172$	0	0
$173$	−6.62734	−0.503868	−0.251934	−	0.967744i	$-0.581067\pi$
$173$	−6.62734	−0.503868	−0.251934	+	0.967744i	$0.581067\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	4.54669	0.341750
$178$	0	0
$179$	−10.0187	−0.748830	−0.374415	−	0.927261i	$-0.622156\pi$
$179$	−10.0187	−0.748830	−0.374415	+	0.927261i	$0.622156\pi$
$180$	0	0
$181$	−1.78734	−0.132852	−0.0664258	−	0.997791i	$-0.521160\pi$
$181$	−1.78734	−0.132852	−0.0664258	+	0.997791i	$0.521160\pi$
$182$	0	0
$183$	4.17997	0.308992
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−19.8867	−1.45426
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−8.59465	−0.621887	−0.310943	−	0.950428i	$-0.600645\pi$
$191$	−8.59465	−0.621887	−0.310943	+	0.950428i	$0.600645\pi$
$192$	0	0
$193$	−5.17064	−0.372191	−0.186095	−	0.982532i	$-0.559583\pi$
$193$	−5.17064	−0.372191	−0.186095	+	0.982532i	$0.559583\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	23.9160	1.70394	0.851971	−	0.523590i	$-0.175407\pi$
$197$	23.9160	1.70394	0.851971	+	0.523590i	$0.175407\pi$
$198$	0	0
$199$	15.3107	1.08534	0.542672	−	0.839945i	$-0.317413\pi$
$199$	15.3107	1.08534	0.542672	+	0.839945i	$0.317413\pi$
$200$	0	0
$201$	4.26401	0.300760
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−14.3667	−0.998556
$208$	0	0
$209$	4.00000	0.276686
$210$	0	0
$211$	−1.03863	−0.0715025	−0.0357512	−	0.999361i	$-0.511382\pi$
$211$	−1.03863	−0.0715025	−0.0357512	+	0.999361i	$0.511382\pi$
$212$	0	0
$213$	−0.990671	−0.0678797
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	1.82003	0.122986
$220$	0	0
$221$	−17.9707	−1.20884
$222$	0	0
$223$	9.86799	0.660810	0.330405	−	0.943839i	$-0.392815\pi$
$223$	9.86799	0.660810	0.330405	+	0.943839i	$0.392815\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	21.6553	1.43731	0.718657	−	0.695364i	$-0.244757\pi$
$227$	21.6553	1.43731	0.718657	+	0.695364i	$0.244757\pi$
$228$	0	0
$229$	−20.2313	−1.33692	−0.668462	−	0.743747i	$-0.733047\pi$
$229$	−20.2313	−1.33692	−0.668462	+	0.743747i	$0.733047\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−5.45331	−0.357258	−0.178629	−	0.983916i	$-0.557166\pi$
$233$	−5.45331	−0.357258	−0.178629	+	0.983916i	$0.557166\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−2.06662	−0.134241
$238$	0	0
$239$	−11.5853	−0.749392	−0.374696	−	0.927148i	$-0.622253\pi$
$239$	−11.5853	−0.749392	−0.374696	+	0.927148i	$0.622253\pi$
$240$	0	0
$241$	5.00933	0.322679	0.161340	−	0.986899i	$-0.448419\pi$
$241$	5.00933	0.322679	0.161340	+	0.986899i	$0.448419\pi$
$242$	0	0
$243$	−9.24065	−0.592788
$244$	0	0
$245$	0	0
$246$	0	0
$247$	3.61462	0.229993
$248$	0	0
$249$	−1.69867	−0.107649
$250$	0	0
$251$	23.4206	1.47830	0.739148	−	0.673543i	$-0.235228\pi$
$251$	23.4206	1.47830	0.739148	+	0.673543i	$0.235228\pi$
$252$	0	0
$253$	25.7546	1.61918
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−13.0093	−0.811500	−0.405750	−	0.913984i	$-0.632990\pi$
$257$	−13.0093	−0.811500	−0.405750	+	0.913984i	$0.632990\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−27.0280	−1.67299
$262$	0	0
$263$	6.01866	0.371126	0.185563	−	0.982632i	$-0.440589\pi$
$263$	6.01866	0.371126	0.185563	+	0.982632i	$0.440589\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−1.02799	−0.0629117
$268$	0	0
$269$	−3.24065	−0.197586	−0.0987929	−	0.995108i	$-0.531498\pi$
$269$	−3.24065	−0.197586	−0.0987929	+	0.995108i	$0.531498\pi$
$270$	0	0
$271$	29.1307	1.76956	0.884782	−	0.466006i	$-0.154307\pi$
$271$	29.1307	1.76956	0.884782	+	0.466006i	$0.154307\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−4.44398	−0.267013	−0.133507	−	0.991048i	$-0.542624\pi$
$277$	−4.44398	−0.267013	−0.133507	+	0.991048i	$0.542624\pi$
$278$	0	0
$279$	13.5560	0.811577
$280$	0	0
$281$	−24.6974	−1.47332	−0.736660	−	0.676263i	$-0.763598\pi$
$281$	−24.6974	−1.47332	−0.736660	+	0.676263i	$0.763598\pi$
$282$	0	0
$283$	−7.73937	−0.460058	−0.230029	−	0.973184i	$-0.573882\pi$
$283$	−7.73937	−0.460058	−0.230029	+	0.973184i	$0.573882\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−2.03863	−0.119920
$290$	0	0
$291$	−0.575992	−0.0337652
$292$	0	0
$293$	−25.1086	−1.46686	−0.733431	−	0.679764i	$-0.762082\pi$
$293$	−25.1086	−1.46686	−0.733431	+	0.679764i	$0.762082\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	10.9614	0.636043
$298$	0	0
$299$	23.2733	1.34593
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−3.29200	−0.189121
$304$	0	0
$305$	0	0
$306$	0	0
$307$	33.9193	1.93588	0.967940	−	0.251183i	$-0.0808196\pi$
$307$	33.9193	1.93588	0.967940	+	0.251183i	$0.0808196\pi$
$308$	0	0
$309$	1.86799	0.106266
$310$	0	0
$311$	−0.565344	−0.0320577	−0.0160289	−	0.999872i	$-0.505102\pi$
$311$	−0.565344	−0.0320577	−0.0160289	+	0.999872i	$0.505102\pi$
$312$	0	0
$313$	27.3400	1.54535	0.772673	−	0.634804i	$-0.218919\pi$
$313$	27.3400	1.54535	0.772673	+	0.634804i	$0.218919\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	22.7267	1.27646	0.638228	−	0.769847i	$-0.279668\pi$
$317$	22.7267	1.27646	0.638228	+	0.769847i	$0.279668\pi$
$318$	0	0
$319$	48.4520	2.71279
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−3.00933	−0.167444
$324$	0	0
$325$	0	0
$326$	0	0
$327$	1.44267	0.0797796
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0.462642	0.0254291	0.0127145	−	0.999919i	$-0.495953\pi$
$331$	0.462642	0.0254291	0.0127145	+	0.999919i	$0.495953\pi$
$332$	0	0
$333$	−17.2080	−0.942990
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−10.5653	−0.575531	−0.287765	−	0.957701i	$-0.592912\pi$
$337$	−10.5653	−0.575531	−0.287765	+	0.957701i	$0.592912\pi$
$338$	0	0
$339$	−1.65194	−0.0897211
$340$	0	0
$341$	−24.3013	−1.31599
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	31.8760	1.71119	0.855597	−	0.517643i	$-0.173190\pi$
$347$	31.8760	1.71119	0.855597	+	0.517643i	$0.173190\pi$
$348$	0	0
$349$	9.62602	0.515269	0.257635	−	0.966242i	$-0.417057\pi$
$349$	9.62602	0.515269	0.257635	+	0.966242i	$0.417057\pi$
$350$	0	0
$351$	9.90531	0.528706
$352$	0	0
$353$	26.2534	1.39733	0.698663	−	0.715451i	$-0.253779\pi$
$353$	26.2534	1.39733	0.698663	+	0.715451i	$0.253779\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−4.56534	−0.240950	−0.120475	−	0.992716i	$-0.538442\pi$
$359$	−4.56534	−0.240950	−0.120475	+	0.992716i	$0.538442\pi$
$360$	0	0
$361$	−18.3947	−0.968142
$362$	0	0
$363$	−5.60737	−0.294310
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−3.79073	−0.197874	−0.0989371	−	0.995094i	$-0.531544\pi$
$367$	−3.79073	−0.197874	−0.0989371	+	0.995094i	$0.531544\pi$
$368$	0	0
$369$	−2.89475	−0.150695
$370$	0	0
$371$	0	0
$372$	0	0
$373$	20.7453	1.07415	0.537076	−	0.843534i	$-0.319529\pi$
$373$	20.7453	1.07415	0.537076	+	0.843534i	$0.319529\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	43.7839	2.25499
$378$	0	0
$379$	3.00933	0.154579	0.0772894	−	0.997009i	$-0.475373\pi$
$379$	3.00933	0.154579	0.0772894	+	0.997009i	$0.475373\pi$
$380$	0	0
$381$	−5.85735	−0.300081
$382$	0	0
$383$	−7.00933	−0.358160	−0.179080	−	0.983835i	$-0.557312\pi$
$383$	−7.00933	−0.358160	−0.179080	+	0.983835i	$0.557312\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	20.1027	1.02188
$388$	0	0
$389$	−19.7653	−1.00214	−0.501070	−	0.865407i	$-0.667060\pi$
$389$	−19.7653	−1.00214	−0.501070	+	0.865407i	$0.667060\pi$
$390$	0	0
$391$	−19.3760	−0.979889
$392$	0	0
$393$	0.0186574	0.000941142 0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	9.37266	0.470400	0.235200	−	0.971947i	$-0.424425\pi$
$397$	9.37266	0.470400	0.235200	+	0.971947i	$0.424425\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−16.1507	−0.806526	−0.403263	−	0.915084i	$-0.632124\pi$
$401$	−16.1507	−0.806526	−0.403263	+	0.915084i	$0.632124\pi$
$402$	0	0
$403$	−21.9600	−1.09391
$404$	0	0
$405$	0	0
$406$	0	0
$407$	30.8480	1.52908
$408$	0	0
$409$	−15.2920	−0.756141	−0.378070	−	0.925777i	$-0.623412\pi$
$409$	−15.2920	−0.756141	−0.378070	+	0.925777i	$0.623412\pi$
$410$	0	0
$411$	5.09337	0.251238
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	4.58400	0.224480
$418$	0	0
$419$	33.1820	1.62105	0.810524	−	0.585705i	$-0.199182\pi$
$419$	33.1820	1.62105	0.810524	+	0.585705i	$0.199182\pi$
$420$	0	0
$421$	27.8094	1.35535	0.677673	−	0.735363i	$-0.262988\pi$
$421$	27.8094	1.35535	0.677673	+	0.735363i	$0.262988\pi$
$422$	0	0
$423$	−32.7640	−1.59304
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−8.67869	−0.419011
$430$	0	0
$431$	−21.5454	−1.03780	−0.518902	−	0.854834i	$-0.673659\pi$
$431$	−21.5454	−1.03780	−0.518902	+	0.854834i	$0.673659\pi$
$432$	0	0
$433$	36.0187	1.73095	0.865473	−	0.500955i	$-0.167018\pi$
$433$	36.0187	1.73095	0.865473	+	0.500955i	$0.167018\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	3.89730	0.186433
$438$	0	0
$439$	21.1893	1.01131	0.505655	−	0.862736i	$-0.331251\pi$
$439$	21.1893	1.01131	0.505655	+	0.862736i	$0.331251\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−11.1120	−0.527949	−0.263974	−	0.964530i	$-0.585033\pi$
$443$	−11.1120	−0.527949	−0.263974	+	0.964530i	$0.585033\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	4.16131	0.196823
$448$	0	0
$449$	0.961367	0.0453697	0.0226848	−	0.999743i	$-0.492779\pi$
$449$	0.961367	0.0453697	0.0226848	+	0.999743i	$0.492779\pi$
$450$	0	0
$451$	5.18930	0.244355
$452$	0	0
$453$	−2.13201	−0.100170
$454$	0	0
$455$	0	0
$456$	0	0
$457$	28.2241	1.32027	0.660133	−	0.751149i	$-0.270500\pi$
$457$	28.2241	1.32027	0.660133	+	0.751149i	$0.270500\pi$
$458$	0	0
$459$	−8.24659	−0.384918
$460$	0	0
$461$	−26.0887	−1.21507	−0.607535	−	0.794293i	$-0.707842\pi$
$461$	−26.0887	−1.21507	−0.607535	+	0.794293i	$0.707842\pi$
$462$	0	0
$463$	−2.90663	−0.135082	−0.0675412	−	0.997716i	$-0.521515\pi$
$463$	−2.90663	−0.135082	−0.0675412	+	0.997716i	$0.521515\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−12.2020	−0.564642	−0.282321	−	0.959320i	$-0.591104\pi$
$467$	−12.2020	−0.564642	−0.282321	+	0.959320i	$0.591104\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−2.10270	−0.0968874
$472$	0	0
$473$	−36.0373	−1.65700
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−21.6706	−0.992228
$478$	0	0
$479$	17.6519	0.806538	0.403269	−	0.915082i	$-0.367874\pi$
$479$	17.6519	0.806538	0.403269	+	0.915082i	$0.367874\pi$
$480$	0	0
$481$	27.8760	1.27104
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−1.57467	−0.0713553	−0.0356776	−	0.999363i	$-0.511359\pi$
$487$	−1.57467	−0.0713553	−0.0356776	+	0.999363i	$0.511359\pi$
$488$	0	0
$489$	−1.18930	−0.0537819
$490$	0	0
$491$	−3.26270	−0.147243	−0.0736217	−	0.997286i	$-0.523456\pi$
$491$	−3.26270	−0.147243	−0.0736217	+	0.997286i	$0.523456\pi$
$492$	0	0
$493$	−36.4520	−1.64172
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	42.5293	1.90387	0.951936	−	0.306298i	$-0.0990905\pi$
$499$	42.5293	1.90387	0.951936	+	0.306298i	$0.0990905\pi$
$500$	0	0
$501$	−9.03863	−0.403816
$502$	0	0
$503$	18.6974	0.833674	0.416837	−	0.908981i	$-0.363139\pi$
$503$	18.6974	0.833674	0.416837	+	0.908981i	$0.363139\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−3.11929	−0.138533
$508$	0	0
$509$	−20.2313	−0.896738	−0.448369	−	0.893849i	$-0.647995\pi$
$509$	−20.2313	−0.896738	−0.448369	+	0.893849i	$0.647995\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	1.65872	0.0732342
$514$	0	0
$515$	0	0
$516$	0	0
$517$	58.7347	2.58315
$518$	0	0
$519$	2.40790	0.105695
$520$	0	0
$521$	−21.8387	−0.956770	−0.478385	−	0.878150i	$-0.658778\pi$
$521$	−21.8387	−0.956770	−0.478385	+	0.878150i	$0.658778\pi$
$522$	0	0
$523$	20.4554	0.894451	0.447226	−	0.894421i	$-0.352412\pi$
$523$	20.4554	0.894451	0.447226	+	0.894421i	$0.352412\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	18.2827	0.796406
$528$	0	0
$529$	2.09337	0.0910163
$530$	0	0
$531$	35.8900	1.55750
$532$	0	0
$533$	4.68934	0.203118
$534$	0	0
$535$	0	0
$536$	0	0
$537$	3.64006	0.157080
$538$	0	0
$539$	0	0
$540$	0	0
$541$	27.3400	1.17544	0.587718	−	0.809066i	$-0.300026\pi$
$541$	27.3400	1.17544	0.587718	+	0.809066i	$0.300026\pi$
$542$	0	0
$543$	0.649390	0.0278680
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−22.6867	−0.970013	−0.485007	−	0.874510i	$-0.661183\pi$
$547$	−22.6867	−0.970013	−0.485007	+	0.874510i	$0.661183\pi$
$548$	0	0
$549$	32.9953	1.40820
$550$	0	0
$551$	7.33195	0.312352
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−12.7453	−0.540036	−0.270018	−	0.962855i	$-0.587030\pi$
$557$	−12.7453	−0.540036	−0.270018	+	0.962855i	$0.587030\pi$
$558$	0	0
$559$	−32.5653	−1.37737
$560$	0	0
$561$	7.22538	0.305056
$562$	0	0
$563$	5.20333	0.219294	0.109647	−	0.993971i	$-0.465028\pi$
$563$	5.20333	0.219294	0.109647	+	0.993971i	$0.465028\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−7.37605	−0.309220	−0.154610	−	0.987976i	$-0.549412\pi$
$569$	−7.37605	−0.309220	−0.154610	+	0.987976i	$0.549412\pi$
$570$	0	0
$571$	15.8973	0.665281	0.332641	−	0.943054i	$-0.392060\pi$
$571$	15.8973	0.665281	0.332641	+	0.943054i	$0.392060\pi$
$572$	0	0
$573$	3.12268	0.130452
$574$	0	0
$575$	0	0
$576$	0	0
$577$	19.9707	0.831391	0.415695	−	0.909504i	$-0.363538\pi$
$577$	19.9707	0.831391	0.415695	+	0.909504i	$0.363538\pi$
$578$	0	0
$579$	1.87864	0.0780736
$580$	0	0
$581$	0	0
$582$	0	0
$583$	38.8480	1.60892
$584$	0	0
$585$	0	0
$586$	0	0
$587$	13.8060	0.569834	0.284917	−	0.958552i	$-0.408034\pi$
$587$	13.8060	0.569834	0.284917	+	0.958552i	$0.408034\pi$
$588$	0	0
$589$	−3.67738	−0.151524
$590$	0	0
$591$	−8.68934	−0.357432
$592$	0	0
$593$	−20.0666	−0.824037	−0.412019	−	0.911175i	$-0.635176\pi$
$593$	−20.0666	−0.824037	−0.412019	+	0.911175i	$0.635176\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−5.56279	−0.227670
$598$	0	0
$599$	46.0267	1.88060	0.940299	−	0.340349i	$-0.110545\pi$
$599$	46.0267	1.88060	0.940299	+	0.340349i	$0.110545\pi$
$600$	0	0
$601$	1.37605	0.0561301	0.0280651	−	0.999606i	$-0.491065\pi$
$601$	1.37605	0.0561301	0.0280651	+	0.999606i	$0.491065\pi$
$602$	0	0
$603$	33.6587	1.37069
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−18.7933	−0.762796	−0.381398	−	0.924411i	$-0.624557\pi$
$607$	−18.7933	−0.762796	−0.381398	+	0.924411i	$0.624557\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	53.0759	2.14722
$612$	0	0
$613$	24.8480	1.00360	0.501801	−	0.864983i	$-0.332671\pi$
$613$	24.8480	1.00360	0.501801	+	0.864983i	$0.332671\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	43.1680	1.73788	0.868939	−	0.494919i	$-0.164802\pi$
$617$	43.1680	1.73788	0.868939	+	0.494919i	$0.164802\pi$
$618$	0	0
$619$	−31.9486	−1.28412	−0.642062	−	0.766652i	$-0.721921\pi$
$619$	−31.9486	−1.28412	−0.642062	+	0.766652i	$0.721921\pi$
$620$	0	0
$621$	10.6799	0.428571
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−1.45331	−0.0580397
$628$	0	0
$629$	−23.2080	−0.925362
$630$	0	0
$631$	−8.59465	−0.342148	−0.171074	−	0.985258i	$-0.554724\pi$
$631$	−8.59465	−0.342148	−0.171074	+	0.985258i	$0.554724\pi$
$632$	0	0
$633$	0.377365	0.0149989
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−7.82003	−0.309356
$640$	0	0
$641$	33.2266	1.31237	0.656186	−	0.754599i	$-0.272169\pi$
$641$	33.2266	1.31237	0.656186	+	0.754599i	$0.272169\pi$
$642$	0	0
$643$	−17.4940	−0.689897	−0.344948	−	0.938622i	$-0.612104\pi$
$643$	−17.4940	−0.689897	−0.344948	+	0.938622i	$0.612104\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−9.91595	−0.389836	−0.194918	−	0.980820i	$-0.562444\pi$
$647$	−9.91595	−0.389836	−0.194918	+	0.980820i	$0.562444\pi$
$648$	0	0
$649$	−64.3386	−2.52551
$650$	0	0
$651$	0	0
$652$	0	0
$653$	14.6240	0.572280	0.286140	−	0.958188i	$-0.407628\pi$
$653$	14.6240	0.572280	0.286140	+	0.958188i	$0.407628\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	14.3667	0.560499
$658$	0	0
$659$	20.2534	0.788959	0.394480	−	0.918905i	$-0.370925\pi$
$659$	20.2534	0.788959	0.394480	+	0.918905i	$0.370925\pi$
$660$	0	0
$661$	12.4299	0.483469	0.241734	−	0.970342i	$-0.422284\pi$
$661$	12.4299	0.483469	0.241734	+	0.970342i	$0.422284\pi$
$662$	0	0
$663$	6.52926	0.253575
$664$	0	0
$665$	0	0
$666$	0	0
$667$	47.2080	1.82790
$668$	0	0
$669$	−3.58532	−0.138616
$670$	0	0
$671$	−59.1493	−2.28344
$672$	0	0
$673$	−47.6774	−1.83783	−0.918914	−	0.394458i	$-0.870932\pi$
$673$	−47.6774	−1.83783	−0.918914	+	0.394458i	$0.870932\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−6.00339	−0.230729	−0.115364	−	0.993323i	$-0.536804\pi$
$677$	−6.00339	−0.230729	−0.115364	+	0.993323i	$0.536804\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−7.86799	−0.301502
$682$	0	0
$683$	−28.5653	−1.09302	−0.546511	−	0.837452i	$-0.684044\pi$
$683$	−28.5653	−1.09302	−0.546511	+	0.837452i	$0.684044\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	7.35061	0.280443
$688$	0	0
$689$	35.1053	1.33740
$690$	0	0
$691$	−47.8247	−1.81934	−0.909668	−	0.415337i	$-0.863664\pi$
$691$	−47.8247	−1.81934	−0.909668	+	0.415337i	$0.863664\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−3.90408	−0.147877
$698$	0	0
$699$	1.98134	0.0749413
$700$	0	0
$701$	−4.80005	−0.181296	−0.0906478	−	0.995883i	$-0.528894\pi$
$701$	−4.80005	−0.181296	−0.0906478	+	0.995883i	$0.528894\pi$
$702$	0	0
$703$	4.66805	0.176059
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	11.7653	0.441855	0.220927	−	0.975290i	$-0.429092\pi$
$709$	11.7653	0.441855	0.220927	+	0.975290i	$0.429092\pi$
$710$	0	0
$711$	−16.3132	−0.611793
$712$	0	0
$713$	−23.6774	−0.886725
$714$	0	0
$715$	0	0
$716$	0	0
$717$	4.20927	0.157198
$718$	0	0
$719$	40.7640	1.52024	0.760120	−	0.649783i	$-0.225140\pi$
$719$	40.7640	1.52024	0.760120	+	0.649783i	$0.225140\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−1.82003	−0.0676877
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−22.1214	−0.820436	−0.410218	−	0.911988i	$-0.634547\pi$
$727$	−22.1214	−0.820436	−0.410218	+	0.911988i	$0.634547\pi$
$728$	0	0
$729$	−20.1307	−0.745581
$730$	0	0
$731$	27.1120	1.00277
$732$	0	0
$733$	−13.0500	−0.482014	−0.241007	−	0.970523i	$-0.577478\pi$
$733$	−13.0500	−0.482014	−0.241007	+	0.970523i	$0.577478\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−60.3386	−2.22260
$738$	0	0
$739$	−34.5734	−1.27180	−0.635901	−	0.771771i	$-0.719371\pi$
$739$	−34.5734	−1.27180	−0.635901	+	0.771771i	$0.719371\pi$
$740$	0	0
$741$	−1.31330	−0.0482451
$742$	0	0
$743$	−3.55602	−0.130458	−0.0652288	−	0.997870i	$-0.520778\pi$
$743$	−3.55602	−0.130458	−0.0652288	+	0.997870i	$0.520778\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−13.4087	−0.490600
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−23.6226	−0.862002	−0.431001	−	0.902351i	$-0.641839\pi$
$751$	−23.6226	−0.862002	−0.431001	+	0.902351i	$0.641839\pi$
$752$	0	0
$753$	−8.50937	−0.310099
$754$	0	0
$755$	0	0
$756$	0	0
$757$	15.1893	0.552064	0.276032	−	0.961148i	$-0.410980\pi$
$757$	15.1893	0.552064	0.276032	+	0.961148i	$0.410980\pi$
$758$	0	0
$759$	−9.35739	−0.339652
$760$	0	0
$761$	−34.4626	−1.24927	−0.624635	−	0.780917i	$-0.714752\pi$
$761$	−34.4626	−1.24927	−0.624635	+	0.780917i	$0.714752\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−58.1400	−2.09931
$768$	0	0
$769$	−40.3854	−1.45633	−0.728167	−	0.685400i	$-0.759627\pi$
$769$	−40.3854	−1.45633	−0.728167	+	0.685400i	$0.759627\pi$
$770$	0	0
$771$	4.72666	0.170226
$772$	0	0
$773$	10.7674	0.387275	0.193638	−	0.981073i	$-0.437971\pi$
$773$	10.7674	0.387275	0.193638	+	0.981073i	$0.437971\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0.785266	0.0281351
$780$	0	0
$781$	14.0187	0.501627
$782$	0	0
$783$	20.0921	0.718031
$784$	0	0
$785$	0	0
$786$	0	0
$787$	9.19269	0.327684	0.163842	−	0.986487i	$-0.447611\pi$
$787$	9.19269	0.327684	0.163842	+	0.986487i	$0.447611\pi$
$788$	0	0
$789$	−2.18675	−0.0778503
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−53.4507	−1.89809
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−21.1086	−0.747706	−0.373853	−	0.927488i	$-0.621964\pi$
$797$	−21.1086	−0.747706	−0.373853	+	0.927488i	$0.621964\pi$
$798$	0	0
$799$	−44.1880	−1.56326
$800$	0	0
$801$	−8.11458	−0.286715
$802$	0	0
$803$	−25.7546	−0.908862
$804$	0	0
$805$	0	0
$806$	0	0
$807$	1.17742	0.0414471
$808$	0	0
$809$	−27.8280	−0.978382	−0.489191	−	0.872177i	$-0.662708\pi$
$809$	−27.8280	−0.978382	−0.489191	+	0.872177i	$0.662708\pi$
$810$	0	0
$811$	11.0607	0.388393	0.194197	−	0.980963i	$-0.437790\pi$
$811$	11.0607	0.388393	0.194197	+	0.980963i	$0.437790\pi$
$812$	0	0
$813$	−10.5840	−0.371197
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−5.45331	−0.190787
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−17.8867	−0.624248	−0.312124	−	0.950041i	$-0.601041\pi$
$821$	−17.8867	−0.624248	−0.312124	+	0.950041i	$0.601041\pi$
$822$	0	0
$823$	52.8667	1.84282	0.921408	−	0.388596i	$-0.127040\pi$
$823$	52.8667	1.84282	0.921408	+	0.388596i	$0.127040\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	36.3013	1.26232	0.631160	−	0.775652i	$-0.282579\pi$
$827$	36.3013	1.26232	0.631160	+	0.775652i	$0.282579\pi$
$828$	0	0
$829$	0.759350	0.0263733	0.0131867	−	0.999913i	$-0.495802\pi$
$829$	0.759350	0.0263733	0.0131867	+	0.999913i	$0.495802\pi$
$830$	0	0
$831$	1.61462	0.0560107
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−10.0773	−0.348321
$838$	0	0
$839$	43.3107	1.49525	0.747625	−	0.664121i	$-0.231194\pi$
$839$	43.3107	1.49525	0.747625	+	0.664121i	$0.231194\pi$
$840$	0	0
$841$	59.8119	2.06248
$842$	0	0
$843$	8.97325	0.309055
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	2.81193	0.0965053
$850$	0	0
$851$	30.0560	1.03031
$852$	0	0
$853$	40.3713	1.38229	0.691144	−	0.722717i	$-0.257107\pi$
$853$	40.3713	1.38229	0.691144	+	0.722717i	$0.257107\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−13.4720	−0.460194	−0.230097	−	0.973168i	$-0.573904\pi$
$857$	−13.4720	−0.460194	−0.230097	+	0.973168i	$0.573904\pi$
$858$	0	0
$859$	34.7313	1.18502	0.592508	−	0.805565i	$-0.298138\pi$
$859$	34.7313	1.18502	0.592508	+	0.805565i	$0.298138\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−14.2454	−0.484918	−0.242459	−	0.970162i	$-0.577954\pi$
$863$	−14.2454	−0.484918	−0.242459	+	0.970162i	$0.577954\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0.740693	0.0251553
$868$	0	0
$869$	29.2440	0.992036
$870$	0	0
$871$	−54.5254	−1.84752
$872$	0	0
$873$	−4.54669	−0.153882
$874$	0	0
$875$	0	0
$876$	0	0
$877$	19.7546	0.667067	0.333533	−	0.942738i	$-0.391759\pi$
$877$	19.7546	0.667067	0.333533	+	0.942738i	$0.391759\pi$
$878$	0	0
$879$	9.12268	0.307700
$880$	0	0
$881$	9.53058	0.321093	0.160547	−	0.987028i	$-0.448674\pi$
$881$	9.53058	0.321093	0.160547	+	0.987028i	$0.448674\pi$
$882$	0	0
$883$	51.1867	1.72257	0.861284	−	0.508124i	$-0.169661\pi$
$883$	51.1867	1.72257	0.861284	+	0.508124i	$0.169661\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−24.4626	−0.821375	−0.410688	−	0.911776i	$-0.634711\pi$
$887$	−24.4626	−0.821375	−0.410688	+	0.911776i	$0.634711\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	40.2534	1.34854
$892$	0	0
$893$	8.88797	0.297425
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−8.45586	−0.282333
$898$	0	0
$899$	−44.5441	−1.48563
$900$	0	0
$901$	−29.2266	−0.973680
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−8.09592	−0.268821	−0.134410	−	0.990926i	$-0.542914\pi$
$907$	−8.09592	−0.268821	−0.134410	+	0.990926i	$0.542914\pi$
$908$	0	0
$909$	−25.9860	−0.861900
$910$	0	0
$911$	−59.5093	−1.97163	−0.985815	−	0.167834i	$-0.946323\pi$
$911$	−59.5093	−1.97163	−0.985815	+	0.167834i	$0.946323\pi$
$912$	0	0
$913$	24.0373	0.795519
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	51.7067	1.70565	0.852823	−	0.522200i	$-0.174889\pi$
$919$	51.7067	1.70565	0.852823	+	0.522200i	$0.174889\pi$
$920$	0	0
$921$	−12.3239	−0.406085
$922$	0	0
$923$	12.6680	0.416974
$924$	0	0
$925$	0	0
$926$	0	0
$927$	14.7453	0.484300
$928$	0	0
$929$	3.76142	0.123408	0.0617041	−	0.998094i	$-0.480346\pi$
$929$	3.76142	0.123408	0.0617041	+	0.998094i	$0.480346\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0.205406	0.00672468
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−21.1014	−0.689352	−0.344676	−	0.938722i	$-0.612011\pi$
$937$	−21.1014	−0.689352	−0.344676	+	0.938722i	$0.612011\pi$
$938$	0	0
$939$	−9.93338	−0.324164
$940$	0	0
$941$	1.72873	0.0563549	0.0281775	−	0.999603i	$-0.491030\pi$
$941$	1.72873	0.0563549	0.0281775	+	0.999603i	$0.491030\pi$
$942$	0	0
$943$	5.05606	0.164648
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−24.7267	−0.803508	−0.401754	−	0.915748i	$-0.631599\pi$
$947$	−24.7267	−0.803508	−0.401754	+	0.915748i	$0.631599\pi$
$948$	0	0
$949$	−23.2733	−0.755485
$950$	0	0
$951$	−8.25724	−0.267759
$952$	0	0
$953$	1.18930	0.0385251	0.0192626	−	0.999814i	$-0.493868\pi$
$953$	1.18930	0.0385251	0.0192626	+	0.999814i	$0.493868\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−17.6040	−0.569056
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−8.65872	−0.279314
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−23.3293	−0.750220	−0.375110	−	0.926980i	$-0.622395\pi$
$967$	−23.3293	−0.750220	−0.375110	+	0.926980i	$0.622395\pi$
$968$	0	0
$969$	1.09337	0.0351242
$970$	0	0
$971$	4.61670	0.148157	0.0740784	−	0.997252i	$-0.476398\pi$
$971$	4.61670	0.148157	0.0740784	+	0.997252i	$0.476398\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−19.1120	−0.611448	−0.305724	−	0.952120i	$-0.598898\pi$
$977$	−19.1120	−0.611448	−0.305724	+	0.952120i	$0.598898\pi$
$978$	0	0
$979$	14.5467	0.464914
$980$	0	0
$981$	11.3879	0.363588
$982$	0	0
$983$	52.6506	1.67929	0.839647	−	0.543132i	$-0.182762\pi$
$983$	52.6506	1.67929	0.839647	+	0.543132i	$0.182762\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−35.1120	−1.11650
$990$	0	0
$991$	52.4227	1.66526	0.832631	−	0.553828i	$-0.186834\pi$
$991$	52.4227	1.66526	0.832631	+	0.553828i	$0.186834\pi$
$992$	0	0
$993$	−0.168091	−0.00533420
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−19.7580	−0.625743	−0.312872	−	0.949795i	$-0.601291\pi$
$997$	−19.7580	−0.625743	−0.312872	+	0.949795i	$0.601291\pi$
$998$	0	0
$999$	12.7920	0.404722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.cg.1.2		3
5.2	odd	4		1960.2.g.c.1569.4		6
5.3	odd	4		1960.2.g.c.1569.3		6
5.4	even	2		9800.2.a.cd.1.2		3
7.6	odd	2		1400.2.a.s.1.2		3
28.27	even	2		2800.2.a.br.1.2		3
35.13	even	4		280.2.g.b.169.4	yes	6
35.27	even	4		280.2.g.b.169.3	✓	6
35.34	odd	2		1400.2.a.t.1.2		3
105.62	odd	4		2520.2.t.g.1009.5		6
105.83	odd	4		2520.2.t.g.1009.6		6
140.27	odd	4		560.2.g.f.449.4		6
140.83	odd	4		560.2.g.f.449.3		6
140.139	even	2		2800.2.a.bq.1.2		3
280.13	even	4		2240.2.g.l.449.3		6
280.27	odd	4		2240.2.g.m.449.3		6
280.83	odd	4		2240.2.g.m.449.4		6
280.237	even	4		2240.2.g.l.449.4		6
420.83	even	4		5040.2.t.y.1009.6		6
420.167	even	4		5040.2.t.y.1009.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.g.b.169.3	✓	6	35.27	even	4
280.2.g.b.169.4	yes	6	35.13	even	4
560.2.g.f.449.3		6	140.83	odd	4
560.2.g.f.449.4		6	140.27	odd	4
1400.2.a.s.1.2		3	7.6	odd	2
1400.2.a.t.1.2		3	35.34	odd	2
1960.2.g.c.1569.3		6	5.3	odd	4
1960.2.g.c.1569.4		6	5.2	odd	4
2240.2.g.l.449.3		6	280.13	even	4
2240.2.g.l.449.4		6	280.237	even	4
2240.2.g.m.449.3		6	280.27	odd	4
2240.2.g.m.449.4		6	280.83	odd	4
2520.2.t.g.1009.5		6	105.62	odd	4
2520.2.t.g.1009.6		6	105.83	odd	4
2800.2.a.bq.1.2		3	140.139	even	2
2800.2.a.br.1.2		3	28.27	even	2
5040.2.t.y.1009.5		6	420.167	even	4
5040.2.t.y.1009.6		6	420.83	even	4
9800.2.a.cd.1.2		3	5.4	even	2
9800.2.a.cg.1.2		3	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:	\( N \)	\(=\)	\( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9800.a (trivial)

\(f(q)\)	\(=\)	\(q-0.363328 q^{3} -2.86799 q^{9} +O(q^{10})\)	\(q-0.363328 q^{3} -2.86799 q^{9} +5.14134 q^{11} +4.64600 q^{13} -3.86799 q^{17} +0.778008 q^{19} +5.00933 q^{23} +2.13201 q^{27} +9.42401 q^{29} -4.72666 q^{31} -1.86799 q^{33} +6.00000 q^{37} -1.68802 q^{39} +1.00933 q^{41} -7.00933 q^{43} +11.4240 q^{47} +1.40535 q^{51} +7.55602 q^{53} -0.282672 q^{57} -12.5140 q^{59} -11.5047 q^{61} -11.7360 q^{67} -1.82003 q^{69} +2.72666 q^{71} -5.00933 q^{73} +5.68802 q^{79} +7.82936 q^{81} +4.67531 q^{83} -3.42401 q^{87} +2.82936 q^{89} +1.71733 q^{93} +1.58532 q^{97} -14.7453 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{3} + 4 q^{9}+O(q^{10}) \) 3 * q + q^3 + 4 * q^9	\( 3 q + q^{3} + 4 q^{9} + 7 q^{11} - 5 q^{13} + q^{17} - 4 q^{19} - 6 q^{23} + 19 q^{27} + 3 q^{29} - 10 q^{31} + 7 q^{33} + 18 q^{37} - 5 q^{39} - 18 q^{41} + 9 q^{47} + 21 q^{51} + 10 q^{53} + 16 q^{57} - 6 q^{59} - 24 q^{61} - 10 q^{67} - 18 q^{69} + 4 q^{71} + 6 q^{73} + 17 q^{79} + 15 q^{81} + 12 q^{83} + 15 q^{87} + 22 q^{93} + 9 q^{97} + 2 q^{99}+O(q^{100}) \) 3 * q + q^3 + 4 * q^9 + 7 * q^11 - 5 * q^13 + q^17 - 4 * q^19 - 6 * q^23 + 19 * q^27 + 3 * q^29 - 10 * q^31 + 7 * q^33 + 18 * q^37 - 5 * q^39 - 18 * q^41 + 9 * q^47 + 21 * q^51 + 10 * q^53 + 16 * q^57 - 6 * q^59 - 24 * q^61 - 10 * q^67 - 18 * q^69 + 4 * q^71 + 6 * q^73 + 17 * q^79 + 15 * q^81 + 12 * q^83 + 15 * q^87 + 22 * q^93 + 9 * q^97 + 2 * q^99

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