LMFDB - Embedded newform 9800.2.a.cy.1.3

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:	$6$
Coefficient field:	6.6.239575536.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 12x^{4} + 8x^{3} + 35x^{2} - 15x - 8 $ x^6 - x^5 - 12x^4 + 8x^3 + 35x^2 - 15x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 280)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.319986$ 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)

$f(q)$	$=$	$q-0.319986 q^{3} -2.89761 q^{9} +O(q^{10})$	$q-0.319986 q^{3} -2.89761 q^{9} +4.16603 q^{11} -2.89761 q^{13} +4.30274 q^{17} -1.95888 q^{19} -2.57762 q^{23} +1.88715 q^{27} -5.96541 q^{29} -9.43018 q^{31} -1.33307 q^{33} -6.32942 q^{37} +0.927195 q^{39} +7.19271 q^{41} -4.73966 q^{43} +4.43546 q^{47} -1.37682 q^{51} +7.35975 q^{53} +0.626816 q^{57} +3.22069 q^{59} +11.9000 q^{61} +11.6824 q^{67} +0.824804 q^{69} +7.58808 q^{71} +9.90676 q^{73} -12.8327 q^{79} +8.08896 q^{81} +5.75180 q^{83} +1.90885 q^{87} +3.01815 q^{89} +3.01753 q^{93} -0.414281 q^{97} -12.0715 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 7 q^{9}+O(q^{10}) $ 6 * q + q^3 + 7 * q^9	$ 6 q + q^{3} + 7 q^{9} + q^{11} + 7 q^{13} + 4 q^{17} + 5 q^{19} + 6 q^{23} + 7 q^{27} - 3 q^{29} + 2 q^{31} + 16 q^{33} + 9 q^{37} + 10 q^{39} - 6 q^{41} - 3 q^{43} + 27 q^{47} - 5 q^{53} - 26 q^{57} + 24 q^{59} - 9 q^{61} + 17 q^{67} - 15 q^{69} + 4 q^{71} + 18 q^{73} - 22 q^{79} - 6 q^{81} + 9 q^{83} + 39 q^{87} - 15 q^{89} + 10 q^{93} + 12 q^{97} + 11 q^{99}+O(q^{100}) $ 6 * q + q^3 + 7 * q^9 + q^11 + 7 * q^13 + 4 * q^17 + 5 * q^19 + 6 * q^23 + 7 * q^27 - 3 * q^29 + 2 * q^31 + 16 * q^33 + 9 * q^37 + 10 * q^39 - 6 * q^41 - 3 * q^43 + 27 * q^47 - 5 * q^53 - 26 * q^57 + 24 * q^59 - 9 * q^61 + 17 * q^67 - 15 * q^69 + 4 * q^71 + 18 * q^73 - 22 * q^79 - 6 * q^81 + 9 * q^83 + 39 * q^87 - 15 * q^89 + 10 * q^93 + 12 * q^97 + 11 * 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
$3$	−0.319986	−0.184744	−0.0923721	−	0.995725i	$-0.529445\pi$
$3$	−0.319986	−0.184744	−0.0923721	+	0.995725i	$0.529445\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−2.89761	−0.965870
$10$	0	0
$11$	4.16603	1.25610	0.628052	−	0.778171i	$-0.283853\pi$
$11$	4.16603	1.25610	0.628052	+	0.778171i	$0.283853\pi$
$12$	0	0
$13$	−2.89761	−0.803652	−0.401826	−	0.915716i	$-0.631624\pi$
$13$	−2.89761	−0.803652	−0.401826	+	0.915716i	$0.631624\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	4.30274	1.04357	0.521784	−	0.853078i	$-0.325267\pi$
$17$	4.30274	1.04357	0.521784	+	0.853078i	$0.325267\pi$
$18$	0	0
$19$	−1.95888	−0.449399	−0.224700	−	0.974428i	$-0.572140\pi$
$19$	−1.95888	−0.449399	−0.224700	+	0.974428i	$0.572140\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−2.57762	−0.537471	−0.268736	−	0.963214i	$-0.586606\pi$
$23$	−2.57762	−0.537471	−0.268736	+	0.963214i	$0.586606\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	1.88715	0.363183
$28$	0	0
$29$	−5.96541	−1.10775	−0.553874	−	0.832600i	$-0.686851\pi$
$29$	−5.96541	−1.10775	−0.553874	+	0.832600i	$0.686851\pi$
$30$	0	0
$31$	−9.43018	−1.69371	−0.846856	−	0.531823i	$-0.821507\pi$
$31$	−9.43018	−1.69371	−0.846856	+	0.531823i	$0.821507\pi$
$32$	0	0
$33$	−1.33307	−0.232058
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−6.32942	−1.04055	−0.520275	−	0.853999i	$-0.674171\pi$
$37$	−6.32942	−1.04055	−0.520275	+	0.853999i	$0.674171\pi$
$38$	0	0
$39$	0.927195	0.148470
$40$	0	0
$41$	7.19271	1.12331	0.561656	−	0.827371i	$-0.310164\pi$
$41$	7.19271	1.12331	0.561656	+	0.827371i	$0.310164\pi$
$42$	0	0
$43$	−4.73966	−0.722792	−0.361396	−	0.932412i	$-0.617700\pi$
$43$	−4.73966	−0.722792	−0.361396	+	0.932412i	$0.617700\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	4.43546	0.646979	0.323489	−	0.946232i	$-0.395144\pi$
$47$	4.43546	0.646979	0.323489	+	0.946232i	$0.395144\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−1.37682	−0.192793
$52$	0	0
$53$	7.35975	1.01094	0.505470	−	0.862844i	$-0.331319\pi$
$53$	7.35975	1.01094	0.505470	+	0.862844i	$0.331319\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0.626816	0.0830239
$58$	0	0
$59$	3.22069	0.419297	0.209649	−	0.977777i	$-0.432768\pi$
$59$	3.22069	0.419297	0.209649	+	0.977777i	$0.432768\pi$
$60$	0	0
$61$	11.9000	1.52363	0.761817	−	0.647792i	$-0.224307\pi$
$61$	11.9000	1.52363	0.761817	+	0.647792i	$0.224307\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	11.6824	1.42723	0.713614	−	0.700539i	$-0.247057\pi$
$67$	11.6824	1.42723	0.713614	+	0.700539i	$0.247057\pi$
$68$	0	0
$69$	0.824804	0.0992947
$70$	0	0
$71$	7.58808	0.900539	0.450270	−	0.892893i	$-0.351328\pi$
$71$	7.58808	0.900539	0.450270	+	0.892893i	$0.351328\pi$
$72$	0	0
$73$	9.90676	1.15950	0.579749	−	0.814795i	$-0.303150\pi$
$73$	9.90676	1.15950	0.579749	+	0.814795i	$0.303150\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−12.8327	−1.44379	−0.721895	−	0.692003i	$-0.756729\pi$
$79$	−12.8327	−1.44379	−0.721895	+	0.692003i	$0.756729\pi$
$80$	0	0
$81$	8.08896	0.898774
$82$	0	0
$83$	5.75180	0.631342	0.315671	−	0.948869i	$-0.397770\pi$
$83$	5.75180	0.631342	0.315671	+	0.948869i	$0.397770\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	1.90885	0.204650
$88$	0	0
$89$	3.01815	0.319923	0.159961	−	0.987123i	$-0.448863\pi$
$89$	3.01815	0.319923	0.159961	+	0.987123i	$0.448863\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	3.01753	0.312903
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−0.414281	−0.0420639	−0.0210320	−	0.999779i	$-0.506695\pi$
$97$	−0.414281	−0.0420639	−0.0210320	+	0.999779i	$0.506695\pi$
$98$	0	0
$99$	−12.0715	−1.21323
$100$	0	0
$101$	−15.9987	−1.59193	−0.795965	−	0.605342i	$-0.793036\pi$
$101$	−15.9987	−1.59193	−0.795965	+	0.605342i	$0.793036\pi$
$102$	0	0
$103$	2.59341	0.255536	0.127768	−	0.991804i	$-0.459219\pi$
$103$	2.59341	0.255536	0.127768	+	0.991804i	$0.459219\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	19.7357	1.90793	0.953963	−	0.299925i	$-0.0969615\pi$
$107$	19.7357	1.90793	0.953963	+	0.299925i	$0.0969615\pi$
$108$	0	0
$109$	−9.38469	−0.898891	−0.449445	−	0.893308i	$-0.648378\pi$
$109$	−9.38469	−0.898891	−0.449445	+	0.893308i	$0.648378\pi$
$110$	0	0
$111$	2.02533	0.192236
$112$	0	0
$113$	2.61401	0.245906	0.122953	−	0.992413i	$-0.460764\pi$
$113$	2.61401	0.245906	0.122953	+	0.992413i	$0.460764\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	8.39614	0.776223
$118$	0	0
$119$	0	0
$120$	0	0
$121$	6.35577	0.577797
$122$	0	0
$123$	−2.30157	−0.207525
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−20.3587	−1.80655	−0.903273	−	0.429067i	$-0.858843\pi$
$127$	−20.3587	−1.80655	−0.903273	+	0.429067i	$0.858843\pi$
$128$	0	0
$129$	1.51663	0.133532
$130$	0	0
$131$	3.65075	0.318968	0.159484	−	0.987201i	$-0.449017\pi$
$131$	3.65075	0.318968	0.159484	+	0.987201i	$0.449017\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−10.6716	−0.911740	−0.455870	−	0.890046i	$-0.650672\pi$
$137$	−10.6716	−0.911740	−0.455870	+	0.890046i	$0.650672\pi$
$138$	0	0
$139$	−12.0047	−1.01823	−0.509113	−	0.860699i	$-0.670027\pi$
$139$	−12.0047	−1.01823	−0.509113	+	0.860699i	$0.670027\pi$
$140$	0	0
$141$	−1.41929	−0.119526
$142$	0	0
$143$	−12.0715	−1.00947
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	13.4250	1.09982	0.549910	−	0.835224i	$-0.314662\pi$
$149$	13.4250	1.09982	0.549910	+	0.835224i	$0.314662\pi$
$150$	0	0
$151$	−6.57453	−0.535028	−0.267514	−	0.963554i	$-0.586202\pi$
$151$	−6.57453	−0.535028	−0.267514	+	0.963554i	$0.586202\pi$
$152$	0	0
$153$	−12.4676	−1.00795
$154$	0	0
$155$	0	0
$156$	0	0
$157$	2.95052	0.235478	0.117739	−	0.993045i	$-0.462435\pi$
$157$	2.95052	0.235478	0.117739	+	0.993045i	$0.462435\pi$
$158$	0	0
$159$	−2.35502	−0.186765
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−5.34161	−0.418387	−0.209194	−	0.977874i	$-0.567084\pi$
$163$	−5.34161	−0.418387	−0.209194	+	0.977874i	$0.567084\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	1.56009	0.120724	0.0603618	−	0.998177i	$-0.480775\pi$
$167$	1.56009	0.120724	0.0603618	+	0.998177i	$0.480775\pi$
$168$	0	0
$169$	−4.60386	−0.354143
$170$	0	0
$171$	5.67608	0.434061
$172$	0	0
$173$	15.7156	1.19484	0.597418	−	0.801930i	$-0.296193\pi$
$173$	15.7156	1.19484	0.597418	+	0.801930i	$0.296193\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−1.03058	−0.0774628
$178$	0	0
$179$	11.0717	0.827535	0.413767	−	0.910383i	$-0.364213\pi$
$179$	11.0717	0.827535	0.413767	+	0.910383i	$0.364213\pi$
$180$	0	0
$181$	−14.8950	−1.10713	−0.553567	−	0.832805i	$-0.686734\pi$
$181$	−14.8950	−1.10713	−0.553567	+	0.832805i	$0.686734\pi$
$182$	0	0
$183$	−3.80783	−0.281483
$184$	0	0
$185$	0	0
$186$	0	0
$187$	17.9253	1.31083
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−1.01354	−0.0733375	−0.0366688	−	0.999327i	$-0.511675\pi$
$191$	−1.01354	−0.0733375	−0.0366688	+	0.999327i	$0.511675\pi$
$192$	0	0
$193$	−7.54257	−0.542926	−0.271463	−	0.962449i	$-0.587507\pi$
$193$	−7.54257	−0.542926	−0.271463	+	0.962449i	$0.587507\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−9.26180	−0.659876	−0.329938	−	0.944003i	$-0.607028\pi$
$197$	−9.26180	−0.659876	−0.329938	+	0.944003i	$0.607028\pi$
$198$	0	0
$199$	16.0992	1.14124	0.570622	−	0.821213i	$-0.306702\pi$
$199$	16.0992	1.14124	0.570622	+	0.821213i	$0.306702\pi$
$200$	0	0
$201$	−3.73820	−0.263672
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	7.46894	0.519127
$208$	0	0
$209$	−8.16076	−0.564492
$210$	0	0
$211$	3.20349	0.220537	0.110269	−	0.993902i	$-0.464829\pi$
$211$	3.20349	0.220537	0.110269	+	0.993902i	$0.464829\pi$
$212$	0	0
$213$	−2.42808	−0.166369
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−3.17003	−0.214211
$220$	0	0
$221$	−12.4676	−0.838665
$222$	0	0
$223$	18.7564	1.25602	0.628010	−	0.778206i	$-0.283870\pi$
$223$	18.7564	1.25602	0.628010	+	0.778206i	$0.283870\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	6.75938	0.448636	0.224318	−	0.974516i	$-0.427985\pi$
$227$	6.75938	0.448636	0.224318	+	0.974516i	$0.427985\pi$
$228$	0	0
$229$	−0.163154	−0.0107815	−0.00539076	−	0.999985i	$-0.501716\pi$
$229$	−0.163154	−0.0107815	−0.00539076	+	0.999985i	$0.501716\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	27.3516	1.79186	0.895931	−	0.444193i	$-0.146510\pi$
$233$	27.3516	1.79186	0.895931	+	0.444193i	$0.146510\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	4.10628	0.266732
$238$	0	0
$239$	19.3226	1.24988	0.624938	−	0.780674i	$-0.285124\pi$
$239$	19.3226	1.24988	0.624938	+	0.780674i	$0.285124\pi$
$240$	0	0
$241$	24.3519	1.56865	0.784323	−	0.620353i	$-0.213011\pi$
$241$	24.3519	1.56865	0.784323	+	0.620353i	$0.213011\pi$
$242$	0	0
$243$	−8.24982	−0.529226
$244$	0	0
$245$	0	0
$246$	0	0
$247$	5.67608	0.361160
$248$	0	0
$249$	−1.84050	−0.116637
$250$	0	0
$251$	8.53106	0.538476	0.269238	−	0.963074i	$-0.413228\pi$
$251$	8.53106	0.538476	0.269238	+	0.963074i	$0.413228\pi$
$252$	0	0
$253$	−10.7384	−0.675120
$254$	0	0
$255$	0	0
$256$	0	0
$257$	21.9333	1.36816	0.684080	−	0.729407i	$-0.260204\pi$
$257$	21.9333	1.36816	0.684080	+	0.729407i	$0.260204\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	17.2854	1.06994
$262$	0	0
$263$	−10.8432	−0.668622	−0.334311	−	0.942463i	$-0.608504\pi$
$263$	−10.8432	−0.668622	−0.334311	+	0.942463i	$0.608504\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−0.965765	−0.0591039
$268$	0	0
$269$	−19.1669	−1.16862	−0.584312	−	0.811529i	$-0.698636\pi$
$269$	−19.1669	−1.16862	−0.584312	+	0.811529i	$0.698636\pi$
$270$	0	0
$271$	−11.9137	−0.723703	−0.361851	−	0.932236i	$-0.617855\pi$
$271$	−11.9137	−0.723703	−0.361851	+	0.932236i	$0.617855\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	9.39149	0.564280	0.282140	−	0.959373i	$-0.408956\pi$
$277$	9.39149	0.564280	0.282140	+	0.959373i	$0.408956\pi$
$278$	0	0
$279$	27.3250	1.63590
$280$	0	0
$281$	1.15248	0.0687513	0.0343756	−	0.999409i	$-0.489056\pi$
$281$	1.15248	0.0687513	0.0343756	+	0.999409i	$0.489056\pi$
$282$	0	0
$283$	21.0762	1.25285	0.626424	−	0.779483i	$-0.284518\pi$
$283$	21.0762	1.25285	0.626424	+	0.779483i	$0.284518\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	1.51355	0.0890321
$290$	0	0
$291$	0.132564	0.00777106
$292$	0	0
$293$	9.92590	0.579877	0.289939	−	0.957045i	$-0.406365\pi$
$293$	9.92590	0.579877	0.289939	+	0.957045i	$0.406365\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	7.86193	0.456196
$298$	0	0
$299$	7.46894	0.431940
$300$	0	0
$301$	0	0
$302$	0	0
$303$	5.11937	0.294100
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−2.94680	−0.168183	−0.0840915	−	0.996458i	$-0.526799\pi$
$307$	−2.94680	−0.168183	−0.0840915	+	0.996458i	$0.526799\pi$
$308$	0	0
$309$	−0.829856	−0.0472088
$310$	0	0
$311$	21.0825	1.19548	0.597740	−	0.801690i	$-0.296066\pi$
$311$	21.0825	1.19548	0.597740	+	0.801690i	$0.296066\pi$
$312$	0	0
$313$	12.7810	0.722423	0.361211	−	0.932484i	$-0.382363\pi$
$313$	12.7810	0.722423	0.361211	+	0.932484i	$0.382363\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	7.10773	0.399210	0.199605	−	0.979876i	$-0.436034\pi$
$317$	7.10773	0.399210	0.199605	+	0.979876i	$0.436034\pi$
$318$	0	0
$319$	−24.8520	−1.39145
$320$	0	0
$321$	−6.31517	−0.352478
$322$	0	0
$323$	−8.42857	−0.468978
$324$	0	0
$325$	0	0
$326$	0	0
$327$	3.00297	0.166065
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−5.41204	−0.297473	−0.148736	−	0.988877i	$-0.547521\pi$
$331$	−5.41204	−0.297473	−0.148736	+	0.988877i	$0.547521\pi$
$332$	0	0
$333$	18.3402	1.00504
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−16.9764	−0.924765	−0.462382	−	0.886681i	$-0.653005\pi$
$337$	−16.9764	−0.924765	−0.462382	+	0.886681i	$0.653005\pi$
$338$	0	0
$339$	−0.836448	−0.0454296
$340$	0	0
$341$	−39.2864	−2.12748
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	15.8683	0.851855	0.425928	−	0.904757i	$-0.359948\pi$
$347$	15.8683	0.851855	0.425928	+	0.904757i	$0.359948\pi$
$348$	0	0
$349$	−19.1130	−1.02309	−0.511547	−	0.859255i	$-0.670927\pi$
$349$	−19.1130	−1.02309	−0.511547	+	0.859255i	$0.670927\pi$
$350$	0	0
$351$	−5.46823	−0.291873
$352$	0	0
$353$	26.1090	1.38964	0.694820	−	0.719184i	$-0.255484\pi$
$353$	26.1090	1.38964	0.694820	+	0.719184i	$0.255484\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	23.0133	1.21460	0.607298	−	0.794474i	$-0.292253\pi$
$359$	23.0133	1.21460	0.607298	+	0.794474i	$0.292253\pi$
$360$	0	0
$361$	−15.1628	−0.798041
$362$	0	0
$363$	−2.03376	−0.106745
$364$	0	0
$365$	0	0
$366$	0	0
$367$	32.6624	1.70496	0.852482	−	0.522756i	$-0.175096\pi$
$367$	32.6624	1.70496	0.852482	+	0.522756i	$0.175096\pi$
$368$	0	0
$369$	−20.8417	−1.08497
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−24.1480	−1.25034	−0.625169	−	0.780489i	$-0.714970\pi$
$373$	−24.1480	−1.25034	−0.625169	+	0.780489i	$0.714970\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	17.2854	0.890244
$378$	0	0
$379$	30.6614	1.57497	0.787484	−	0.616335i	$-0.211383\pi$
$379$	30.6614	1.57497	0.787484	+	0.616335i	$0.211383\pi$
$380$	0	0
$381$	6.51452	0.333749
$382$	0	0
$383$	31.9748	1.63384	0.816919	−	0.576753i	$-0.195680\pi$
$383$	31.9748	1.63384	0.816919	+	0.576753i	$0.195680\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	13.7337	0.698123
$388$	0	0
$389$	13.4488	0.681883	0.340942	−	0.940084i	$-0.389254\pi$
$389$	13.4488	0.681883	0.340942	+	0.940084i	$0.389254\pi$
$390$	0	0
$391$	−11.0908	−0.560887
$392$	0	0
$393$	−1.16819	−0.0589275
$394$	0	0
$395$	0	0
$396$	0	0
$397$	11.9998	0.602251	0.301125	−	0.953585i	$-0.402638\pi$
$397$	11.9998	0.602251	0.301125	+	0.953585i	$0.402638\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−32.8936	−1.64263	−0.821315	−	0.570476i	$-0.806759\pi$
$401$	−32.8936	−1.64263	−0.821315	+	0.570476i	$0.806759\pi$
$402$	0	0
$403$	27.3250	1.36115
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−26.3685	−1.30704
$408$	0	0
$409$	−20.4024	−1.00883	−0.504416	−	0.863461i	$-0.668292\pi$
$409$	−20.4024	−1.00883	−0.504416	+	0.863461i	$0.668292\pi$
$410$	0	0
$411$	3.41478	0.168439
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	3.84135	0.188111
$418$	0	0
$419$	28.0820	1.37190	0.685949	−	0.727650i	$-0.259387\pi$
$419$	28.0820	1.37190	0.685949	+	0.727650i	$0.259387\pi$
$420$	0	0
$421$	−14.4438	−0.703949	−0.351974	−	0.936010i	$-0.614490\pi$
$421$	−14.4438	−0.703949	−0.351974	+	0.936010i	$0.614490\pi$
$422$	0	0
$423$	−12.8522	−0.624897
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	3.86272	0.186494
$430$	0	0
$431$	−13.3456	−0.642835	−0.321417	−	0.946938i	$-0.604159\pi$
$431$	−13.3456	−0.642835	−0.321417	+	0.946938i	$0.604159\pi$
$432$	0	0
$433$	−2.96912	−0.142687	−0.0713434	−	0.997452i	$-0.522729\pi$
$433$	−2.96912	−0.142687	−0.0713434	+	0.997452i	$0.522729\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	5.04927	0.241539
$438$	0	0
$439$	28.5380	1.36205	0.681023	−	0.732262i	$-0.261536\pi$
$439$	28.5380	1.36205	0.681023	+	0.732262i	$0.261536\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−6.95266	−0.330331	−0.165165	−	0.986266i	$-0.552816\pi$
$443$	−6.95266	−0.330331	−0.165165	+	0.986266i	$0.552816\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−4.29582	−0.203185
$448$	0	0
$449$	5.33832	0.251931	0.125965	−	0.992035i	$-0.459797\pi$
$449$	5.33832	0.251931	0.125965	+	0.992035i	$0.459797\pi$
$450$	0	0
$451$	29.9650	1.41100
$452$	0	0
$453$	2.10376	0.0988433
$454$	0	0
$455$	0	0
$456$	0	0
$457$	4.78096	0.223644	0.111822	−	0.993728i	$-0.464331\pi$
$457$	4.78096	0.223644	0.111822	+	0.993728i	$0.464331\pi$
$458$	0	0
$459$	8.11993	0.379006
$460$	0	0
$461$	1.39398	0.0649242	0.0324621	−	0.999473i	$-0.489665\pi$
$461$	1.39398	0.0649242	0.0324621	+	0.999473i	$0.489665\pi$
$462$	0	0
$463$	27.4620	1.27627	0.638135	−	0.769925i	$-0.279706\pi$
$463$	27.4620	1.27627	0.638135	+	0.769925i	$0.279706\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	39.2446	1.81602	0.908012	−	0.418945i	$-0.137600\pi$
$467$	39.2446	1.81602	0.908012	+	0.418945i	$0.137600\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−0.944128	−0.0435031
$472$	0	0
$473$	−19.7456	−0.907902
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−21.3257	−0.976436
$478$	0	0
$479$	9.28135	0.424076	0.212038	−	0.977261i	$-0.431990\pi$
$479$	9.28135	0.424076	0.212038	+	0.977261i	$0.431990\pi$
$480$	0	0
$481$	18.3402	0.836240
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−11.9601	−0.541965	−0.270983	−	0.962584i	$-0.587349\pi$
$487$	−11.9601	−0.541965	−0.270983	+	0.962584i	$0.587349\pi$
$488$	0	0
$489$	1.70924	0.0772946
$490$	0	0
$491$	−38.6956	−1.74631	−0.873153	−	0.487446i	$-0.837928\pi$
$491$	−38.6956	−1.74631	−0.873153	+	0.487446i	$0.837928\pi$
$492$	0	0
$493$	−25.6676	−1.15601
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−28.2882	−1.26635	−0.633177	−	0.774007i	$-0.718249\pi$
$499$	−28.2882	−1.26635	−0.633177	+	0.774007i	$0.718249\pi$
$500$	0	0
$501$	−0.499208	−0.0223030
$502$	0	0
$503$	−8.88492	−0.396159	−0.198079	−	0.980186i	$-0.563470\pi$
$503$	−8.88492	−0.396159	−0.198079	+	0.980186i	$0.563470\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	1.47317	0.0654259
$508$	0	0
$509$	−2.16317	−0.0958807	−0.0479404	−	0.998850i	$-0.515266\pi$
$509$	−2.16317	−0.0958807	−0.0479404	+	0.998850i	$0.515266\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−3.69672	−0.163214
$514$	0	0
$515$	0	0
$516$	0	0
$517$	18.4783	0.812673
$518$	0	0
$519$	−5.02878	−0.220739
$520$	0	0
$521$	−29.7025	−1.30129	−0.650646	−	0.759381i	$-0.725502\pi$
$521$	−29.7025	−1.30129	−0.650646	+	0.759381i	$0.725502\pi$
$522$	0	0
$523$	−11.9601	−0.522980	−0.261490	−	0.965206i	$-0.584214\pi$
$523$	−11.9601	−0.522980	−0.261490	+	0.965206i	$0.584214\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−40.5756	−1.76750
$528$	0	0
$529$	−16.3559	−0.711124
$530$	0	0
$531$	−9.33229	−0.404987
$532$	0	0
$533$	−20.8417	−0.902752
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−3.54278	−0.152882
$538$	0	0
$539$	0	0
$540$	0	0
$541$	10.9682	0.471558	0.235779	−	0.971807i	$-0.424236\pi$
$541$	10.9682	0.471558	0.235779	+	0.971807i	$0.424236\pi$
$542$	0	0
$543$	4.76618	0.204537
$544$	0	0
$545$	0	0
$546$	0	0
$547$	30.4206	1.30069	0.650346	−	0.759638i	$-0.274624\pi$
$547$	30.4206	1.30069	0.650346	+	0.759638i	$0.274624\pi$
$548$	0	0
$549$	−34.4814	−1.47163
$550$	0	0
$551$	11.6855	0.497821
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	38.1740	1.61748	0.808742	−	0.588164i	$-0.200149\pi$
$557$	38.1740	1.61748	0.808742	+	0.588164i	$0.200149\pi$
$558$	0	0
$559$	13.7337	0.580873
$560$	0	0
$561$	−5.73586	−0.242168
$562$	0	0
$563$	18.8585	0.794792	0.397396	−	0.917647i	$-0.369914\pi$
$563$	18.8585	0.794792	0.397396	+	0.917647i	$0.369914\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	43.5494	1.82569	0.912844	−	0.408309i	$-0.133881\pi$
$569$	43.5494	1.82569	0.912844	+	0.408309i	$0.133881\pi$
$570$	0	0
$571$	14.4287	0.603824	0.301912	−	0.953336i	$-0.402375\pi$
$571$	14.4287	0.603824	0.301912	+	0.953336i	$0.402375\pi$
$572$	0	0
$573$	0.324320	0.0135487
$574$	0	0
$575$	0	0
$576$	0	0
$577$	34.5072	1.43655	0.718276	−	0.695758i	$-0.244931\pi$
$577$	34.5072	1.43655	0.718276	+	0.695758i	$0.244931\pi$
$578$	0	0
$579$	2.41352	0.100302
$580$	0	0
$581$	0	0
$582$	0	0
$583$	30.6609	1.26985
$584$	0	0
$585$	0	0
$586$	0	0
$587$	9.37071	0.386771	0.193385	−	0.981123i	$-0.438053\pi$
$587$	9.37071	0.386771	0.193385	+	0.981123i	$0.438053\pi$
$588$	0	0
$589$	18.4726	0.761152
$590$	0	0
$591$	2.96365	0.121908
$592$	0	0
$593$	−40.9347	−1.68099	−0.840494	−	0.541821i	$-0.817735\pi$
$593$	−40.9347	−1.68099	−0.840494	+	0.541821i	$0.817735\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−5.15153	−0.210838
$598$	0	0
$599$	35.6448	1.45641	0.728203	−	0.685362i	$-0.240356\pi$
$599$	35.6448	1.45641	0.728203	+	0.685362i	$0.240356\pi$
$600$	0	0
$601$	−15.3323	−0.625417	−0.312708	−	0.949849i	$-0.601236\pi$
$601$	−15.3323	−0.625417	−0.312708	+	0.949849i	$0.601236\pi$
$602$	0	0
$603$	−33.8509	−1.37852
$604$	0	0
$605$	0	0
$606$	0	0
$607$	22.4053	0.909403	0.454701	−	0.890644i	$-0.349746\pi$
$607$	22.4053	0.909403	0.454701	+	0.890644i	$0.349746\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−12.8522	−0.519946
$612$	0	0
$613$	28.1930	1.13871	0.569353	−	0.822093i	$-0.307194\pi$
$613$	28.1930	1.13871	0.569353	+	0.822093i	$0.307194\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−31.0381	−1.24955	−0.624773	−	0.780807i	$-0.714808\pi$
$617$	−31.0381	−1.24955	−0.624773	+	0.780807i	$0.714808\pi$
$618$	0	0
$619$	30.0462	1.20766	0.603829	−	0.797114i	$-0.293641\pi$
$619$	30.0462	1.20766	0.603829	+	0.797114i	$0.293641\pi$
$620$	0	0
$621$	−4.86437	−0.195200
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	2.61133	0.104287
$628$	0	0
$629$	−27.2338	−1.08588
$630$	0	0
$631$	26.4263	1.05201	0.526007	−	0.850480i	$-0.323688\pi$
$631$	26.4263	1.05201	0.526007	+	0.850480i	$0.323688\pi$
$632$	0	0
$633$	−1.02507	−0.0407430
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−21.9873	−0.869803
$640$	0	0
$641$	7.00977	0.276869	0.138435	−	0.990372i	$-0.455793\pi$
$641$	7.00977	0.276869	0.138435	+	0.990372i	$0.455793\pi$
$642$	0	0
$643$	−32.0207	−1.26277	−0.631386	−	0.775469i	$-0.717514\pi$
$643$	−32.0207	−1.26277	−0.631386	+	0.775469i	$0.717514\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	27.5411	1.08275	0.541377	−	0.840780i	$-0.317903\pi$
$647$	27.5411	1.08275	0.541377	+	0.840780i	$0.317903\pi$
$648$	0	0
$649$	13.4175	0.526681
$650$	0	0
$651$	0	0
$652$	0	0
$653$	11.7793	0.460960	0.230480	−	0.973077i	$-0.425970\pi$
$653$	11.7793	0.460960	0.230480	+	0.973077i	$0.425970\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−28.7059	−1.11992
$658$	0	0
$659$	−7.11635	−0.277214	−0.138607	−	0.990347i	$-0.544262\pi$
$659$	−7.11635	−0.277214	−0.138607	+	0.990347i	$0.544262\pi$
$660$	0	0
$661$	−29.9047	−1.16316	−0.581579	−	0.813490i	$-0.697565\pi$
$661$	−29.9047	−1.16316	−0.581579	+	0.813490i	$0.697565\pi$
$662$	0	0
$663$	3.98948	0.154938
$664$	0	0
$665$	0	0
$666$	0	0
$667$	15.3766	0.595383
$668$	0	0
$669$	−6.00178	−0.232042
$670$	0	0
$671$	49.5756	1.91384
$672$	0	0
$673$	−10.8573	−0.418520	−0.209260	−	0.977860i	$-0.567105\pi$
$673$	−10.8573	−0.418520	−0.209260	+	0.977860i	$0.567105\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	21.3099	0.819005	0.409503	−	0.912309i	$-0.365702\pi$
$677$	21.3099	0.819005	0.409503	+	0.912309i	$0.365702\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−2.16291	−0.0828829
$682$	0	0
$683$	−17.7566	−0.679438	−0.339719	−	0.940527i	$-0.610332\pi$
$683$	−17.7566	−0.679438	−0.339719	+	0.940527i	$0.610332\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0.0522070	0.00199182
$688$	0	0
$689$	−21.3257	−0.812444
$690$	0	0
$691$	19.5734	0.744609	0.372304	−	0.928111i	$-0.378568\pi$
$691$	19.5734	0.744609	0.372304	+	0.928111i	$0.378568\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	30.9483	1.17225
$698$	0	0
$699$	−8.75213	−0.331036
$700$	0	0
$701$	−4.10176	−0.154921	−0.0774607	−	0.996995i	$-0.524681\pi$
$701$	−4.10176	−0.154921	−0.0774607	+	0.996995i	$0.524681\pi$
$702$	0	0
$703$	12.3986	0.467622
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	13.7479	0.516312	0.258156	−	0.966103i	$-0.416885\pi$
$709$	13.7479	0.516312	0.258156	+	0.966103i	$0.416885\pi$
$710$	0	0
$711$	37.1841	1.39451
$712$	0	0
$713$	24.3075	0.910321
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−6.18298	−0.230907
$718$	0	0
$719$	−15.1859	−0.566340	−0.283170	−	0.959070i	$-0.591386\pi$
$719$	−15.1859	−0.566340	−0.283170	+	0.959070i	$0.591386\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−7.79228	−0.289798
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−2.68973	−0.0997565	−0.0498783	−	0.998755i	$-0.515883\pi$
$727$	−2.68973	−0.0997565	−0.0498783	+	0.998755i	$0.515883\pi$
$728$	0	0
$729$	−21.6271	−0.801002
$730$	0	0
$731$	−20.3935	−0.754282
$732$	0	0
$733$	32.8630	1.21382	0.606911	−	0.794770i	$-0.292408\pi$
$733$	32.8630	1.21382	0.606911	+	0.794770i	$0.292408\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	48.6691	1.79275
$738$	0	0
$739$	27.1963	1.00043	0.500216	−	0.865901i	$-0.333254\pi$
$739$	27.1963	1.00043	0.500216	+	0.865901i	$0.333254\pi$
$740$	0	0
$741$	−1.81627	−0.0667223
$742$	0	0
$743$	23.8026	0.873233	0.436617	−	0.899648i	$-0.356177\pi$
$743$	23.8026	0.873233	0.436617	+	0.899648i	$0.356177\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−16.6665	−0.609794
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−25.4543	−0.928840	−0.464420	−	0.885615i	$-0.653737\pi$
$751$	−25.4543	−0.928840	−0.464420	+	0.885615i	$0.653737\pi$
$752$	0	0
$753$	−2.72982	−0.0994803
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−21.9982	−0.799537	−0.399769	−	0.916616i	$-0.630909\pi$
$757$	−21.9982	−0.799537	−0.399769	+	0.916616i	$0.630909\pi$
$758$	0	0
$759$	3.43615	0.124725
$760$	0	0
$761$	−4.77983	−0.173269	−0.0866343	−	0.996240i	$-0.527611\pi$
$761$	−4.77983	−0.173269	−0.0866343	+	0.996240i	$0.527611\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−9.33229	−0.336969
$768$	0	0
$769$	−0.775623	−0.0279697	−0.0139848	−	0.999902i	$-0.504452\pi$
$769$	−0.775623	−0.0279697	−0.0139848	+	0.999902i	$0.504452\pi$
$770$	0	0
$771$	−7.01835	−0.252760
$772$	0	0
$773$	−2.25550	−0.0811246	−0.0405623	−	0.999177i	$-0.512915\pi$
$773$	−2.25550	−0.0811246	−0.0405623	+	0.999177i	$0.512915\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−14.0897	−0.504815
$780$	0	0
$781$	31.6121	1.13117
$782$	0	0
$783$	−11.2576	−0.402315
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−44.0436	−1.56999	−0.784993	−	0.619504i	$-0.787334\pi$
$787$	−44.0436	−1.56999	−0.784993	+	0.619504i	$0.787334\pi$
$788$	0	0
$789$	3.46969	0.123524
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−34.4814	−1.22447
$794$	0	0
$795$	0	0
$796$	0	0
$797$	1.05089	0.0372245	0.0186122	−	0.999827i	$-0.494075\pi$
$797$	1.05089	0.0372245	0.0186122	+	0.999827i	$0.494075\pi$
$798$	0	0
$799$	19.0846	0.675166
$800$	0	0
$801$	−8.74540	−0.309004
$802$	0	0
$803$	41.2718	1.45645
$804$	0	0
$805$	0	0
$806$	0	0
$807$	6.13314	0.215897
$808$	0	0
$809$	14.5501	0.511555	0.255777	−	0.966736i	$-0.417669\pi$
$809$	14.5501	0.511555	0.255777	+	0.966736i	$0.417669\pi$
$810$	0	0
$811$	−13.0148	−0.457010	−0.228505	−	0.973543i	$-0.573384\pi$
$811$	−13.0148	−0.457010	−0.228505	+	0.973543i	$0.573384\pi$
$812$	0	0
$813$	3.81221	0.133700
$814$	0	0
$815$	0	0
$816$	0	0
$817$	9.28445	0.324822
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−3.51532	−0.122685	−0.0613427	−	0.998117i	$-0.519538\pi$
$821$	−3.51532	−0.122685	−0.0613427	+	0.998117i	$0.519538\pi$
$822$	0	0
$823$	41.2284	1.43713	0.718567	−	0.695458i	$-0.244799\pi$
$823$	41.2284	1.43713	0.718567	+	0.695458i	$0.244799\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−6.21314	−0.216052	−0.108026	−	0.994148i	$-0.534453\pi$
$827$	−6.21314	−0.216052	−0.108026	+	0.994148i	$0.534453\pi$
$828$	0	0
$829$	7.53879	0.261833	0.130917	−	0.991393i	$-0.458208\pi$
$829$	7.53879	0.261833	0.130917	+	0.991393i	$0.458208\pi$
$830$	0	0
$831$	−3.00515	−0.104247
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−17.7962	−0.615127
$838$	0	0
$839$	−16.2861	−0.562259	−0.281129	−	0.959670i	$-0.590709\pi$
$839$	−16.2861	−0.562259	−0.281129	+	0.959670i	$0.590709\pi$
$840$	0	0
$841$	6.58608	0.227106
$842$	0	0
$843$	−0.368778	−0.0127014
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−6.74408	−0.231456
$850$	0	0
$851$	16.3149	0.559266
$852$	0	0
$853$	30.0261	1.02808	0.514038	−	0.857768i	$-0.328149\pi$
$853$	30.0261	1.02808	0.514038	+	0.857768i	$0.328149\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−22.2140	−0.758815	−0.379407	−	0.925230i	$-0.623872\pi$
$857$	−22.2140	−0.758815	−0.379407	+	0.925230i	$0.623872\pi$
$858$	0	0
$859$	−25.4485	−0.868291	−0.434146	−	0.900843i	$-0.642950\pi$
$859$	−25.4485	−0.868291	−0.434146	+	0.900843i	$0.642950\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	8.55988	0.291382	0.145691	−	0.989330i	$-0.453460\pi$
$863$	8.55988	0.291382	0.145691	+	0.989330i	$0.453460\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−0.484314	−0.0164482
$868$	0	0
$869$	−53.4613	−1.81355
$870$	0	0
$871$	−33.8509	−1.14700
$872$	0	0
$873$	1.20043	0.0406282
$874$	0	0
$875$	0	0
$876$	0	0
$877$	42.6895	1.44152	0.720760	−	0.693184i	$-0.243793\pi$
$877$	42.6895	1.44152	0.720760	+	0.693184i	$0.243793\pi$
$878$	0	0
$879$	−3.17615	−0.107129
$880$	0	0
$881$	20.0315	0.674879	0.337439	−	0.941347i	$-0.390439\pi$
$881$	20.0315	0.674879	0.337439	+	0.941347i	$0.390439\pi$
$882$	0	0
$883$	−13.5719	−0.456730	−0.228365	−	0.973576i	$-0.573338\pi$
$883$	−13.5719	−0.456730	−0.228365	+	0.973576i	$0.573338\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−29.1571	−0.979000	−0.489500	−	0.872003i	$-0.662821\pi$
$887$	−29.1571	−0.979000	−0.489500	+	0.872003i	$0.662821\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	33.6988	1.12895
$892$	0	0
$893$	−8.68856	−0.290752
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−2.38996	−0.0797984
$898$	0	0
$899$	56.2549	1.87621
$900$	0	0
$901$	31.6671	1.05498
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−47.9742	−1.59296	−0.796479	−	0.604666i	$-0.793307\pi$
$907$	−47.9742	−1.59296	−0.796479	+	0.604666i	$0.793307\pi$
$908$	0	0
$909$	46.3580	1.53760
$910$	0	0
$911$	42.2832	1.40091	0.700453	−	0.713699i	$-0.252981\pi$
$911$	42.2832	1.40091	0.700453	+	0.713699i	$0.252981\pi$
$912$	0	0
$913$	23.9621	0.793031
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−37.9642	−1.25232	−0.626162	−	0.779693i	$-0.715375\pi$
$919$	−37.9642	−1.25232	−0.626162	+	0.779693i	$0.715375\pi$
$920$	0	0
$921$	0.942937	0.0310708
$922$	0	0
$923$	−21.9873	−0.723720
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−7.51469	−0.246815
$928$	0	0
$929$	2.52762	0.0829286	0.0414643	−	0.999140i	$-0.486798\pi$
$929$	2.52762	0.0829286	0.0414643	+	0.999140i	$0.486798\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−6.74611	−0.220858
$934$	0	0
$935$	0	0
$936$	0	0
$937$	1.05740	0.0345438	0.0172719	−	0.999851i	$-0.494502\pi$
$937$	1.05740	0.0345438	0.0172719	+	0.999851i	$0.494502\pi$
$938$	0	0
$939$	−4.08973	−0.133463
$940$	0	0
$941$	10.6758	0.348022	0.174011	−	0.984744i	$-0.444327\pi$
$941$	10.6758	0.348022	0.174011	+	0.984744i	$0.444327\pi$
$942$	0	0
$943$	−18.5401	−0.603748
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−29.2566	−0.950712	−0.475356	−	0.879793i	$-0.657681\pi$
$947$	−29.2566	−0.950712	−0.475356	+	0.879793i	$0.657681\pi$
$948$	0	0
$949$	−28.7059	−0.931834
$950$	0	0
$951$	−2.27438	−0.0737517
$952$	0	0
$953$	−6.31630	−0.204605	−0.102302	−	0.994753i	$-0.532621\pi$
$953$	−6.31630	−0.204605	−0.102302	+	0.994753i	$0.532621\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	7.95231	0.257062
$958$	0	0
$959$	0	0
$960$	0	0
$961$	57.9284	1.86866
$962$	0	0
$963$	−57.1864	−1.84281
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−54.2185	−1.74355	−0.871775	−	0.489906i	$-0.837031\pi$
$967$	−54.2185	−1.74355	−0.871775	+	0.489906i	$0.837031\pi$
$968$	0	0
$969$	2.69703	0.0866410
$970$	0	0
$971$	14.4079	0.462372	0.231186	−	0.972910i	$-0.425739\pi$
$971$	14.4079	0.462372	0.231186	+	0.972910i	$0.425739\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−24.3238	−0.778187	−0.389093	−	0.921198i	$-0.627212\pi$
$977$	−24.3238	−0.778187	−0.389093	+	0.921198i	$0.627212\pi$
$978$	0	0
$979$	12.5737	0.401856
$980$	0	0
$981$	27.1932	0.868211
$982$	0	0
$983$	−22.2385	−0.709297	−0.354649	−	0.935000i	$-0.615400\pi$
$983$	−22.2385	−0.709297	−0.354649	+	0.935000i	$0.615400\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	12.2171	0.388480
$990$	0	0
$991$	−12.2655	−0.389626	−0.194813	−	0.980840i	$-0.562410\pi$
$991$	−12.2655	−0.389626	−0.194813	+	0.980840i	$0.562410\pi$
$992$	0	0
$993$	1.73178	0.0549563
$994$	0	0
$995$	0	0
$996$	0	0
$997$	4.82783	0.152899	0.0764495	−	0.997073i	$-0.475642\pi$
$997$	4.82783	0.152899	0.0764495	+	0.997073i	$0.475642\pi$
$998$	0	0
$999$	−11.9446	−0.377910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.cy.1.3		6
5.2	odd	4		1960.2.g.e.1569.7		12
5.3	odd	4		1960.2.g.e.1569.6		12
5.4	even	2		9800.2.a.cw.1.4		6
7.3	odd	6		1400.2.q.o.401.3		12
7.5	odd	6		1400.2.q.o.1201.3		12
7.6	odd	2		9800.2.a.cv.1.4		6
35.3	even	12		280.2.bg.a.9.7	yes	24
35.12	even	12		280.2.bg.a.249.7	yes	24
35.13	even	4		1960.2.g.f.1569.7		12
35.17	even	12		280.2.bg.a.9.6	✓	24
35.19	odd	6		1400.2.q.n.1201.4		12
35.24	odd	6		1400.2.q.n.401.4		12
35.27	even	4		1960.2.g.f.1569.6		12
35.33	even	12		280.2.bg.a.249.6	yes	24
35.34	odd	2		9800.2.a.cx.1.3		6
140.3	odd	12		560.2.bw.f.289.6		24
140.47	odd	12		560.2.bw.f.529.6		24
140.87	odd	12		560.2.bw.f.289.7		24
140.103	odd	12		560.2.bw.f.529.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bg.a.9.6	✓	24	35.17	even	12
280.2.bg.a.9.7	yes	24	35.3	even	12
280.2.bg.a.249.6	yes	24	35.33	even	12
280.2.bg.a.249.7	yes	24	35.12	even	12
560.2.bw.f.289.6		24	140.3	odd	12
560.2.bw.f.289.7		24	140.87	odd	12
560.2.bw.f.529.6		24	140.47	odd	12
560.2.bw.f.529.7		24	140.103	odd	12
1400.2.q.n.401.4		12	35.24	odd	6
1400.2.q.n.1201.4		12	35.19	odd	6
1400.2.q.o.401.3		12	7.3	odd	6
1400.2.q.o.1201.3		12	7.5	odd	6
1960.2.g.e.1569.6		12	5.3	odd	4
1960.2.g.e.1569.7		12	5.2	odd	4
1960.2.g.f.1569.6		12	35.27	even	4
1960.2.g.f.1569.7		12	35.13	even	4
9800.2.a.cv.1.4		6	7.6	odd	2
9800.2.a.cw.1.4		6	5.4	even	2
9800.2.a.cx.1.3		6	35.34	odd	2
9800.2.a.cy.1.3		6	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)

\(f(q)\)	\(=\)	\(q-0.319986 q^{3} -2.89761 q^{9} +O(q^{10})\)	\(q-0.319986 q^{3} -2.89761 q^{9} +4.16603 q^{11} -2.89761 q^{13} +4.30274 q^{17} -1.95888 q^{19} -2.57762 q^{23} +1.88715 q^{27} -5.96541 q^{29} -9.43018 q^{31} -1.33307 q^{33} -6.32942 q^{37} +0.927195 q^{39} +7.19271 q^{41} -4.73966 q^{43} +4.43546 q^{47} -1.37682 q^{51} +7.35975 q^{53} +0.626816 q^{57} +3.22069 q^{59} +11.9000 q^{61} +11.6824 q^{67} +0.824804 q^{69} +7.58808 q^{71} +9.90676 q^{73} -12.8327 q^{79} +8.08896 q^{81} +5.75180 q^{83} +1.90885 q^{87} +3.01815 q^{89} +3.01753 q^{93} -0.414281 q^{97} -12.0715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 7 q^{9}+O(q^{10}) \) 6 * q + q^3 + 7 * q^9	\( 6 q + q^{3} + 7 q^{9} + q^{11} + 7 q^{13} + 4 q^{17} + 5 q^{19} + 6 q^{23} + 7 q^{27} - 3 q^{29} + 2 q^{31} + 16 q^{33} + 9 q^{37} + 10 q^{39} - 6 q^{41} - 3 q^{43} + 27 q^{47} - 5 q^{53} - 26 q^{57} + 24 q^{59} - 9 q^{61} + 17 q^{67} - 15 q^{69} + 4 q^{71} + 18 q^{73} - 22 q^{79} - 6 q^{81} + 9 q^{83} + 39 q^{87} - 15 q^{89} + 10 q^{93} + 12 q^{97} + 11 q^{99}+O(q^{100}) \) 6 * q + q^3 + 7 * q^9 + q^11 + 7 * q^13 + 4 * q^17 + 5 * q^19 + 6 * q^23 + 7 * q^27 - 3 * q^29 + 2 * q^31 + 16 * q^33 + 9 * q^37 + 10 * q^39 - 6 * q^41 - 3 * q^43 + 27 * q^47 - 5 * q^53 - 26 * q^57 + 24 * q^59 - 9 * q^61 + 17 * q^67 - 15 * q^69 + 4 * q^71 + 18 * q^73 - 22 * q^79 - 6 * q^81 + 9 * q^83 + 39 * q^87 - 15 * q^89 + 10 * q^93 + 12 * q^97 + 11 * q^99

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