LMFDB - Embedded newform 2832.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2832,2,Mod(1,2832)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2832, 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("2832.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2832 = 2^{4} \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2832.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:	$22.6136338524$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	2832.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} -2.23607 q^{5} +2.38197 q^{7} +1.00000 q^{9} +O(q^{10})$	$q+1.00000 q^{3} -2.23607 q^{5} +2.38197 q^{7} +1.00000 q^{9} -2.23607 q^{11} -6.23607 q^{13} -2.23607 q^{15} +1.85410 q^{17} -3.09017 q^{19} +2.38197 q^{21} +4.61803 q^{23} +1.00000 q^{27} +6.38197 q^{29} +10.5623 q^{31} -2.23607 q^{33} -5.32624 q^{35} -0.145898 q^{37} -6.23607 q^{39} +8.09017 q^{41} +8.70820 q^{43} -2.23607 q^{45} +10.8541 q^{47} -1.32624 q^{49} +1.85410 q^{51} +6.23607 q^{53} +5.00000 q^{55} -3.09017 q^{57} +1.00000 q^{59} -3.14590 q^{61} +2.38197 q^{63} +13.9443 q^{65} -10.7082 q^{67} +4.61803 q^{69} +7.94427 q^{71} +0.854102 q^{73} -5.32624 q^{77} +3.00000 q^{79} +1.00000 q^{81} +1.61803 q^{83} -4.14590 q^{85} +6.38197 q^{87} -13.7984 q^{89} -14.8541 q^{91} +10.5623 q^{93} +6.90983 q^{95} +3.00000 q^{97} -2.23607 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 7 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 7 * q^7 + 2 * q^9	$ 2 q + 2 q^{3} + 7 q^{7} + 2 q^{9} - 8 q^{13} - 3 q^{17} + 5 q^{19} + 7 q^{21} + 7 q^{23} + 2 q^{27} + 15 q^{29} + q^{31} + 5 q^{35} - 7 q^{37} - 8 q^{39} + 5 q^{41} + 4 q^{43} + 15 q^{47} + 13 q^{49} - 3 q^{51} + 8 q^{53} + 10 q^{55} + 5 q^{57} + 2 q^{59} - 13 q^{61} + 7 q^{63} + 10 q^{65} - 8 q^{67} + 7 q^{69} - 2 q^{71} - 5 q^{73} + 5 q^{77} + 6 q^{79} + 2 q^{81} + q^{83} - 15 q^{85} + 15 q^{87} - 3 q^{89} - 23 q^{91} + q^{93} + 25 q^{95} + 6 q^{97}+O(q^{100}) $ 2 * q + 2 * q^3 + 7 * q^7 + 2 * q^9 - 8 * q^13 - 3 * q^17 + 5 * q^19 + 7 * q^21 + 7 * q^23 + 2 * q^27 + 15 * q^29 + q^31 + 5 * q^35 - 7 * q^37 - 8 * q^39 + 5 * q^41 + 4 * q^43 + 15 * q^47 + 13 * q^49 - 3 * q^51 + 8 * q^53 + 10 * q^55 + 5 * q^57 + 2 * q^59 - 13 * q^61 + 7 * q^63 + 10 * q^65 - 8 * q^67 + 7 * q^69 - 2 * q^71 - 5 * q^73 + 5 * q^77 + 6 * q^79 + 2 * q^81 + q^83 - 15 * q^85 + 15 * q^87 - 3 * q^89 - 23 * q^91 + q^93 + 25 * q^95 + 6 * q^97

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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0	0
$5$	−2.23607	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	−2.23607	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$6$	0	0
$7$	2.38197	0.900299	0.450149	−	0.892953i	$-0.351371\pi$
$7$	2.38197	0.900299	0.450149	+	0.892953i	$0.351371\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.23607	−0.674200	−0.337100	−	0.941469i	$-0.609446\pi$
$11$	−2.23607	−0.674200	−0.337100	+	0.941469i	$0.609446\pi$
$12$	0	0
$13$	−6.23607	−1.72957	−0.864787	−	0.502139i	$-0.832547\pi$
$13$	−6.23607	−1.72957	−0.864787	+	0.502139i	$0.832547\pi$
$14$	0	0
$15$	−2.23607	−0.577350
$16$	0	0
$17$	1.85410	0.449686	0.224843	−	0.974395i	$-0.427813\pi$
$17$	1.85410	0.449686	0.224843	+	0.974395i	$0.427813\pi$
$18$	0	0
$19$	−3.09017	−0.708934	−0.354467	−	0.935069i	$-0.615338\pi$
$19$	−3.09017	−0.708934	−0.354467	+	0.935069i	$0.615338\pi$
$20$	0	0
$21$	2.38197	0.519788
$22$	0	0
$23$	4.61803	0.962927	0.481463	−	0.876466i	$-0.340105\pi$
$23$	4.61803	0.962927	0.481463	+	0.876466i	$0.340105\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	1.00000	0.192450
$28$	0	0
$29$	6.38197	1.18510	0.592551	−	0.805533i	$-0.298121\pi$
$29$	6.38197	1.18510	0.592551	+	0.805533i	$0.298121\pi$
$30$	0	0
$31$	10.5623	1.89705	0.948523	−	0.316708i	$-0.102578\pi$
$31$	10.5623	1.89705	0.948523	+	0.316708i	$0.102578\pi$
$32$	0	0
$33$	−2.23607	−0.389249
$34$	0	0
$35$	−5.32624	−0.900299
$36$	0	0
$37$	−0.145898	−0.0239855	−0.0119927	−	0.999928i	$-0.503818\pi$
$37$	−0.145898	−0.0239855	−0.0119927	+	0.999928i	$0.503818\pi$
$38$	0	0
$39$	−6.23607	−0.998570
$40$	0	0
$41$	8.09017	1.26347	0.631736	−	0.775183i	$-0.282343\pi$
$41$	8.09017	1.26347	0.631736	+	0.775183i	$0.282343\pi$
$42$	0	0
$43$	8.70820	1.32799	0.663994	−	0.747738i	$-0.268860\pi$
$43$	8.70820	1.32799	0.663994	+	0.747738i	$0.268860\pi$
$44$	0	0
$45$	−2.23607	−0.333333
$46$	0	0
$47$	10.8541	1.58323	0.791617	−	0.611018i	$-0.209240\pi$
$47$	10.8541	1.58323	0.791617	+	0.611018i	$0.209240\pi$
$48$	0	0
$49$	−1.32624	−0.189463
$50$	0	0
$51$	1.85410	0.259626
$52$	0	0
$53$	6.23607	0.856590	0.428295	−	0.903639i	$-0.359114\pi$
$53$	6.23607	0.856590	0.428295	+	0.903639i	$0.359114\pi$
$54$	0	0
$55$	5.00000	0.674200
$56$	0	0
$57$	−3.09017	−0.409303
$58$	0	0
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0	0
$61$	−3.14590	−0.402791	−0.201395	−	0.979510i	$-0.564548\pi$
$61$	−3.14590	−0.402791	−0.201395	+	0.979510i	$0.564548\pi$
$62$	0	0
$63$	2.38197	0.300100
$64$	0	0
$65$	13.9443	1.72957
$66$	0	0
$67$	−10.7082	−1.30822	−0.654108	−	0.756401i	$-0.726956\pi$
$67$	−10.7082	−1.30822	−0.654108	+	0.756401i	$0.726956\pi$
$68$	0	0
$69$	4.61803	0.555946
$70$	0	0
$71$	7.94427	0.942812	0.471406	−	0.881916i	$-0.343747\pi$
$71$	7.94427	0.942812	0.471406	+	0.881916i	$0.343747\pi$
$72$	0	0
$73$	0.854102	0.0999651	0.0499825	−	0.998750i	$-0.484083\pi$
$73$	0.854102	0.0999651	0.0499825	+	0.998750i	$0.484083\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−5.32624	−0.606981
$78$	0	0
$79$	3.00000	0.337526	0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000	0.337526	0.168763	+	0.985657i	$0.446023\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	1.61803	0.177602	0.0888012	−	0.996049i	$-0.471696\pi$
$83$	1.61803	0.177602	0.0888012	+	0.996049i	$0.471696\pi$
$84$	0	0
$85$	−4.14590	−0.449686
$86$	0	0
$87$	6.38197	0.684219
$88$	0	0
$89$	−13.7984	−1.46262	−0.731312	−	0.682043i	$-0.761092\pi$
$89$	−13.7984	−1.46262	−0.731312	+	0.682043i	$0.761092\pi$
$90$	0	0
$91$	−14.8541	−1.55713
$92$	0	0
$93$	10.5623	1.09526
$94$	0	0
$95$	6.90983	0.708934
$96$	0	0
$97$	3.00000	0.304604	0.152302	−	0.988334i	$-0.451331\pi$
$97$	3.00000	0.304604	0.152302	+	0.988334i	$0.451331\pi$
$98$	0	0
$99$	−2.23607	−0.224733
$100$	0	0
$101$	3.70820	0.368980	0.184490	−	0.982834i	$-0.440937\pi$
$101$	3.70820	0.368980	0.184490	+	0.982834i	$0.440937\pi$
$102$	0	0
$103$	3.23607	0.318859	0.159430	−	0.987209i	$-0.449034\pi$
$103$	3.23607	0.318859	0.159430	+	0.987209i	$0.449034\pi$
$104$	0	0
$105$	−5.32624	−0.519788
$106$	0	0
$107$	−0.909830	−0.0879566	−0.0439783	−	0.999032i	$-0.514003\pi$
$107$	−0.909830	−0.0879566	−0.0439783	+	0.999032i	$0.514003\pi$
$108$	0	0
$109$	−4.14590	−0.397105	−0.198553	−	0.980090i	$-0.563624\pi$
$109$	−4.14590	−0.397105	−0.198553	+	0.980090i	$0.563624\pi$
$110$	0	0
$111$	−0.145898	−0.0138480
$112$	0	0
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	0	0
$115$	−10.3262	−0.962927
$116$	0	0
$117$	−6.23607	−0.576525
$118$	0	0
$119$	4.41641	0.404851
$120$	0	0
$121$	−6.00000	−0.545455
$122$	0	0
$123$	8.09017	0.729466
$124$	0	0
$125$	11.1803	1.00000
$126$	0	0
$127$	−15.9443	−1.41483	−0.707413	−	0.706801i	$-0.750138\pi$
$127$	−15.9443	−1.41483	−0.707413	+	0.706801i	$0.750138\pi$
$128$	0	0
$129$	8.70820	0.766715
$130$	0	0
$131$	20.6525	1.80442	0.902208	−	0.431302i	$-0.141946\pi$
$131$	20.6525	1.80442	0.902208	+	0.431302i	$0.141946\pi$
$132$	0	0
$133$	−7.36068	−0.638252
$134$	0	0
$135$	−2.23607	−0.192450
$136$	0	0
$137$	12.2361	1.04540	0.522699	−	0.852517i	$-0.324925\pi$
$137$	12.2361	1.04540	0.522699	+	0.852517i	$0.324925\pi$
$138$	0	0
$139$	−11.7639	−0.997804	−0.498902	−	0.866658i	$-0.666263\pi$
$139$	−11.7639	−0.997804	−0.498902	+	0.866658i	$0.666263\pi$
$140$	0	0
$141$	10.8541	0.914080
$142$	0	0
$143$	13.9443	1.16608
$144$	0	0
$145$	−14.2705	−1.18510
$146$	0	0
$147$	−1.32624	−0.109386
$148$	0	0
$149$	19.0902	1.56393	0.781964	−	0.623324i	$-0.214218\pi$
$149$	19.0902	1.56393	0.781964	+	0.623324i	$0.214218\pi$
$150$	0	0
$151$	−2.56231	−0.208517	−0.104259	−	0.994550i	$-0.533247\pi$
$151$	−2.56231	−0.208517	−0.104259	+	0.994550i	$0.533247\pi$
$152$	0	0
$153$	1.85410	0.149895
$154$	0	0
$155$	−23.6180	−1.89705
$156$	0	0
$157$	9.00000	0.718278	0.359139	−	0.933284i	$-0.383070\pi$
$157$	9.00000	0.718278	0.359139	+	0.933284i	$0.383070\pi$
$158$	0	0
$159$	6.23607	0.494552
$160$	0	0
$161$	11.0000	0.866921
$162$	0	0
$163$	18.5623	1.45391	0.726956	−	0.686684i	$-0.240934\pi$
$163$	18.5623	1.45391	0.726956	+	0.686684i	$0.240934\pi$
$164$	0	0
$165$	5.00000	0.389249
$166$	0	0
$167$	−7.03444	−0.544341	−0.272171	−	0.962249i	$-0.587742\pi$
$167$	−7.03444	−0.544341	−0.272171	+	0.962249i	$0.587742\pi$
$168$	0	0
$169$	25.8885	1.99143
$170$	0	0
$171$	−3.09017	−0.236311
$172$	0	0
$173$	12.3820	0.941383	0.470692	−	0.882298i	$-0.344004\pi$
$173$	12.3820	0.941383	0.470692	+	0.882298i	$0.344004\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	1.00000	0.0751646
$178$	0	0
$179$	0.527864	0.0394544	0.0197272	−	0.999805i	$-0.493720\pi$
$179$	0.527864	0.0394544	0.0197272	+	0.999805i	$0.493720\pi$
$180$	0	0
$181$	22.2705	1.65535	0.827677	−	0.561205i	$-0.189662\pi$
$181$	22.2705	1.65535	0.827677	+	0.561205i	$0.189662\pi$
$182$	0	0
$183$	−3.14590	−0.232551
$184$	0	0
$185$	0.326238	0.0239855
$186$	0	0
$187$	−4.14590	−0.303178
$188$	0	0
$189$	2.38197	0.173263
$190$	0	0
$191$	−16.4164	−1.18785	−0.593925	−	0.804521i	$-0.702422\pi$
$191$	−16.4164	−1.18785	−0.593925	+	0.804521i	$0.702422\pi$
$192$	0	0
$193$	8.00000	0.575853	0.287926	−	0.957653i	$-0.407034\pi$
$193$	8.00000	0.575853	0.287926	+	0.957653i	$0.407034\pi$
$194$	0	0
$195$	13.9443	0.998570
$196$	0	0
$197$	−20.6525	−1.47143	−0.735714	−	0.677292i	$-0.763153\pi$
$197$	−20.6525	−1.47143	−0.735714	+	0.677292i	$0.763153\pi$
$198$	0	0
$199$	16.5623	1.17407	0.587035	−	0.809561i	$-0.300295\pi$
$199$	16.5623	1.17407	0.587035	+	0.809561i	$0.300295\pi$
$200$	0	0
$201$	−10.7082	−0.755298
$202$	0	0
$203$	15.2016	1.06694
$204$	0	0
$205$	−18.0902	−1.26347
$206$	0	0
$207$	4.61803	0.320976
$208$	0	0
$209$	6.90983	0.477963
$210$	0	0
$211$	2.14590	0.147730	0.0738649	−	0.997268i	$-0.476467\pi$
$211$	2.14590	0.147730	0.0738649	+	0.997268i	$0.476467\pi$
$212$	0	0
$213$	7.94427	0.544333
$214$	0	0
$215$	−19.4721	−1.32799
$216$	0	0
$217$	25.1591	1.70791
$218$	0	0
$219$	0.854102	0.0577149
$220$	0	0
$221$	−11.5623	−0.777765
$222$	0	0
$223$	9.52786	0.638033	0.319016	−	0.947749i	$-0.396647\pi$
$223$	9.52786	0.638033	0.319016	+	0.947749i	$0.396647\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	22.1459	1.46987	0.734937	−	0.678135i	$-0.237211\pi$
$227$	22.1459	1.46987	0.734937	+	0.678135i	$0.237211\pi$
$228$	0	0
$229$	−9.14590	−0.604378	−0.302189	−	0.953248i	$-0.597717\pi$
$229$	−9.14590	−0.604378	−0.302189	+	0.953248i	$0.597717\pi$
$230$	0	0
$231$	−5.32624	−0.350441
$232$	0	0
$233$	−8.29180	−0.543214	−0.271607	−	0.962408i	$-0.587555\pi$
$233$	−8.29180	−0.543214	−0.271607	+	0.962408i	$0.587555\pi$
$234$	0	0
$235$	−24.2705	−1.58323
$236$	0	0
$237$	3.00000	0.194871
$238$	0	0
$239$	1.47214	0.0952246	0.0476123	−	0.998866i	$-0.484839\pi$
$239$	1.47214	0.0952246	0.0476123	+	0.998866i	$0.484839\pi$
$240$	0	0
$241$	−23.4164	−1.50838	−0.754192	−	0.656654i	$-0.771971\pi$
$241$	−23.4164	−1.50838	−0.754192	+	0.656654i	$0.771971\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	0	0
$245$	2.96556	0.189463
$246$	0	0
$247$	19.2705	1.22615
$248$	0	0
$249$	1.61803	0.102539
$250$	0	0
$251$	−15.1803	−0.958175	−0.479087	−	0.877767i	$-0.659032\pi$
$251$	−15.1803	−0.958175	−0.479087	+	0.877767i	$0.659032\pi$
$252$	0	0
$253$	−10.3262	−0.649205
$254$	0	0
$255$	−4.14590	−0.259626
$256$	0	0
$257$	−19.4164	−1.21116	−0.605581	−	0.795784i	$-0.707059\pi$
$257$	−19.4164	−1.21116	−0.605581	+	0.795784i	$0.707059\pi$
$258$	0	0
$259$	−0.347524	−0.0215941
$260$	0	0
$261$	6.38197	0.395034
$262$	0	0
$263$	−1.61803	−0.0997722	−0.0498861	−	0.998755i	$-0.515886\pi$
$263$	−1.61803	−0.0997722	−0.0498861	+	0.998755i	$0.515886\pi$
$264$	0	0
$265$	−13.9443	−0.856590
$266$	0	0
$267$	−13.7984	−0.844447
$268$	0	0
$269$	−11.4721	−0.699468	−0.349734	−	0.936849i	$-0.613728\pi$
$269$	−11.4721	−0.699468	−0.349734	+	0.936849i	$0.613728\pi$
$270$	0	0
$271$	7.76393	0.471625	0.235813	−	0.971799i	$-0.424225\pi$
$271$	7.76393	0.471625	0.235813	+	0.971799i	$0.424225\pi$
$272$	0	0
$273$	−14.8541	−0.899011
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−5.47214	−0.328789	−0.164394	−	0.986395i	$-0.552567\pi$
$277$	−5.47214	−0.328789	−0.164394	+	0.986395i	$0.552567\pi$
$278$	0	0
$279$	10.5623	0.632349
$280$	0	0
$281$	9.70820	0.579143	0.289571	−	0.957156i	$-0.406487\pi$
$281$	9.70820	0.579143	0.289571	+	0.957156i	$0.406487\pi$
$282$	0	0
$283$	23.2705	1.38329	0.691644	−	0.722238i	$-0.256887\pi$
$283$	23.2705	1.38329	0.691644	+	0.722238i	$0.256887\pi$
$284$	0	0
$285$	6.90983	0.409303
$286$	0	0
$287$	19.2705	1.13750
$288$	0	0
$289$	−13.5623	−0.797783
$290$	0	0
$291$	3.00000	0.175863
$292$	0	0
$293$	19.3820	1.13231	0.566153	−	0.824300i	$-0.308431\pi$
$293$	19.3820	1.13231	0.566153	+	0.824300i	$0.308431\pi$
$294$	0	0
$295$	−2.23607	−0.130189
$296$	0	0
$297$	−2.23607	−0.129750
$298$	0	0
$299$	−28.7984	−1.66545
$300$	0	0
$301$	20.7426	1.19559
$302$	0	0
$303$	3.70820	0.213031
$304$	0	0
$305$	7.03444	0.402791
$306$	0	0
$307$	25.8885	1.47754	0.738769	−	0.673959i	$-0.235408\pi$
$307$	25.8885	1.47754	0.738769	+	0.673959i	$0.235408\pi$
$308$	0	0
$309$	3.23607	0.184093
$310$	0	0
$311$	−27.4508	−1.55659	−0.778297	−	0.627896i	$-0.783916\pi$
$311$	−27.4508	−1.55659	−0.778297	+	0.627896i	$0.783916\pi$
$312$	0	0
$313$	−20.7984	−1.17559	−0.587797	−	0.809009i	$-0.700005\pi$
$313$	−20.7984	−1.17559	−0.587797	+	0.809009i	$0.700005\pi$
$314$	0	0
$315$	−5.32624	−0.300100
$316$	0	0
$317$	−29.1803	−1.63893	−0.819466	−	0.573128i	$-0.805730\pi$
$317$	−29.1803	−1.63893	−0.819466	+	0.573128i	$0.805730\pi$
$318$	0	0
$319$	−14.2705	−0.798995
$320$	0	0
$321$	−0.909830	−0.0507818
$322$	0	0
$323$	−5.72949	−0.318797
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−4.14590	−0.229269
$328$	0	0
$329$	25.8541	1.42538
$330$	0	0
$331$	11.1246	0.611464	0.305732	−	0.952118i	$-0.401099\pi$
$331$	11.1246	0.611464	0.305732	+	0.952118i	$0.401099\pi$
$332$	0	0
$333$	−0.145898	−0.00799516
$334$	0	0
$335$	23.9443	1.30822
$336$	0	0
$337$	−14.9098	−0.812190	−0.406095	−	0.913831i	$-0.633110\pi$
$337$	−14.9098	−0.812190	−0.406095	+	0.913831i	$0.633110\pi$
$338$	0	0
$339$	−9.00000	−0.488813
$340$	0	0
$341$	−23.6180	−1.27899
$342$	0	0
$343$	−19.8328	−1.07087
$344$	0	0
$345$	−10.3262	−0.555946
$346$	0	0
$347$	−31.0344	−1.66602	−0.833008	−	0.553261i	$-0.813383\pi$
$347$	−31.0344	−1.66602	−0.833008	+	0.553261i	$0.813383\pi$
$348$	0	0
$349$	−27.0000	−1.44528	−0.722638	−	0.691226i	$-0.757071\pi$
$349$	−27.0000	−1.44528	−0.722638	+	0.691226i	$0.757071\pi$
$350$	0	0
$351$	−6.23607	−0.332857
$352$	0	0
$353$	−16.0344	−0.853427	−0.426714	−	0.904387i	$-0.640329\pi$
$353$	−16.0344	−0.853427	−0.426714	+	0.904387i	$0.640329\pi$
$354$	0	0
$355$	−17.7639	−0.942812
$356$	0	0
$357$	4.41641	0.233741
$358$	0	0
$359$	21.8885	1.15523	0.577617	−	0.816308i	$-0.303983\pi$
$359$	21.8885	1.15523	0.577617	+	0.816308i	$0.303983\pi$
$360$	0	0
$361$	−9.45085	−0.497413
$362$	0	0
$363$	−6.00000	−0.314918
$364$	0	0
$365$	−1.90983	−0.0999651
$366$	0	0
$367$	−29.8328	−1.55726	−0.778630	−	0.627483i	$-0.784085\pi$
$367$	−29.8328	−1.55726	−0.778630	+	0.627483i	$0.784085\pi$
$368$	0	0
$369$	8.09017	0.421157
$370$	0	0
$371$	14.8541	0.771187
$372$	0	0
$373$	34.3262	1.77735	0.888673	−	0.458542i	$-0.151628\pi$
$373$	34.3262	1.77735	0.888673	+	0.458542i	$0.151628\pi$
$374$	0	0
$375$	11.1803	0.577350
$376$	0	0
$377$	−39.7984	−2.04972
$378$	0	0
$379$	−22.4164	−1.15145	−0.575727	−	0.817642i	$-0.695281\pi$
$379$	−22.4164	−1.15145	−0.575727	+	0.817642i	$0.695281\pi$
$380$	0	0
$381$	−15.9443	−0.816850
$382$	0	0
$383$	18.2361	0.931820	0.465910	−	0.884832i	$-0.345727\pi$
$383$	18.2361	0.931820	0.465910	+	0.884832i	$0.345727\pi$
$384$	0	0
$385$	11.9098	0.606981
$386$	0	0
$387$	8.70820	0.442663
$388$	0	0
$389$	32.4721	1.64640	0.823201	−	0.567750i	$-0.192186\pi$
$389$	32.4721	1.64640	0.823201	+	0.567750i	$0.192186\pi$
$390$	0	0
$391$	8.56231	0.433014
$392$	0	0
$393$	20.6525	1.04178
$394$	0	0
$395$	−6.70820	−0.337526
$396$	0	0
$397$	3.00000	0.150566	0.0752828	−	0.997162i	$-0.476014\pi$
$397$	3.00000	0.150566	0.0752828	+	0.997162i	$0.476014\pi$
$398$	0	0
$399$	−7.36068	−0.368495
$400$	0	0
$401$	−17.0902	−0.853442	−0.426721	−	0.904383i	$-0.640331\pi$
$401$	−17.0902	−0.853442	−0.426721	+	0.904383i	$0.640331\pi$
$402$	0	0
$403$	−65.8673	−3.28108
$404$	0	0
$405$	−2.23607	−0.111111
$406$	0	0
$407$	0.326238	0.0161710
$408$	0	0
$409$	−10.5836	−0.523325	−0.261662	−	0.965159i	$-0.584271\pi$
$409$	−10.5836	−0.523325	−0.261662	+	0.965159i	$0.584271\pi$
$410$	0	0
$411$	12.2361	0.603561
$412$	0	0
$413$	2.38197	0.117209
$414$	0	0
$415$	−3.61803	−0.177602
$416$	0	0
$417$	−11.7639	−0.576082
$418$	0	0
$419$	31.3050	1.52935	0.764673	−	0.644418i	$-0.222900\pi$
$419$	31.3050	1.52935	0.764673	+	0.644418i	$0.222900\pi$
$420$	0	0
$421$	1.00000	0.0487370	0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000	0.0487370	0.0243685	+	0.999703i	$0.492242\pi$
$422$	0	0
$423$	10.8541	0.527744
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−7.49342	−0.362632
$428$	0	0
$429$	13.9443	0.673236
$430$	0	0
$431$	−12.3820	−0.596418	−0.298209	−	0.954501i	$-0.596389\pi$
$431$	−12.3820	−0.596418	−0.298209	+	0.954501i	$0.596389\pi$
$432$	0	0
$433$	3.67376	0.176550	0.0882749	−	0.996096i	$-0.471865\pi$
$433$	3.67376	0.176550	0.0882749	+	0.996096i	$0.471865\pi$
$434$	0	0
$435$	−14.2705	−0.684219
$436$	0	0
$437$	−14.2705	−0.682651
$438$	0	0
$439$	34.6180	1.65223	0.826114	−	0.563503i	$-0.190547\pi$
$439$	34.6180	1.65223	0.826114	+	0.563503i	$0.190547\pi$
$440$	0	0
$441$	−1.32624	−0.0631542
$442$	0	0
$443$	−3.38197	−0.160682	−0.0803410	−	0.996767i	$-0.525601\pi$
$443$	−3.38197	−0.160682	−0.0803410	+	0.996767i	$0.525601\pi$
$444$	0	0
$445$	30.8541	1.46262
$446$	0	0
$447$	19.0902	0.902934
$448$	0	0
$449$	6.88854	0.325090	0.162545	−	0.986701i	$-0.448030\pi$
$449$	6.88854	0.325090	0.162545	+	0.986701i	$0.448030\pi$
$450$	0	0
$451$	−18.0902	−0.851833
$452$	0	0
$453$	−2.56231	−0.120388
$454$	0	0
$455$	33.2148	1.55713
$456$	0	0
$457$	33.6869	1.57581	0.787904	−	0.615798i	$-0.211166\pi$
$457$	33.6869	1.57581	0.787904	+	0.615798i	$0.211166\pi$
$458$	0	0
$459$	1.85410	0.0865421
$460$	0	0
$461$	23.7426	1.10581	0.552903	−	0.833246i	$-0.313520\pi$
$461$	23.7426	1.10581	0.552903	+	0.833246i	$0.313520\pi$
$462$	0	0
$463$	−4.14590	−0.192676	−0.0963381	−	0.995349i	$-0.530713\pi$
$463$	−4.14590	−0.192676	−0.0963381	+	0.995349i	$0.530713\pi$
$464$	0	0
$465$	−23.6180	−1.09526
$466$	0	0
$467$	−14.8328	−0.686381	−0.343190	−	0.939266i	$-0.611508\pi$
$467$	−14.8328	−0.686381	−0.343190	+	0.939266i	$0.611508\pi$
$468$	0	0
$469$	−25.5066	−1.17778
$470$	0	0
$471$	9.00000	0.414698
$472$	0	0
$473$	−19.4721	−0.895330
$474$	0	0
$475$	0	0
$476$	0	0
$477$	6.23607	0.285530
$478$	0	0
$479$	14.9098	0.681248	0.340624	−	0.940200i	$-0.389362\pi$
$479$	14.9098	0.681248	0.340624	+	0.940200i	$0.389362\pi$
$480$	0	0
$481$	0.909830	0.0414847
$482$	0	0
$483$	11.0000	0.500517
$484$	0	0
$485$	−6.70820	−0.304604
$486$	0	0
$487$	5.74265	0.260224	0.130112	−	0.991499i	$-0.458466\pi$
$487$	5.74265	0.260224	0.130112	+	0.991499i	$0.458466\pi$
$488$	0	0
$489$	18.5623	0.839416
$490$	0	0
$491$	11.5066	0.519285	0.259642	−	0.965705i	$-0.416395\pi$
$491$	11.5066	0.519285	0.259642	+	0.965705i	$0.416395\pi$
$492$	0	0
$493$	11.8328	0.532923
$494$	0	0
$495$	5.00000	0.224733
$496$	0	0
$497$	18.9230	0.848812
$498$	0	0
$499$	14.4164	0.645367	0.322684	−	0.946507i	$-0.395415\pi$
$499$	14.4164	0.645367	0.322684	+	0.946507i	$0.395415\pi$
$500$	0	0
$501$	−7.03444	−0.314276
$502$	0	0
$503$	−3.79837	−0.169361	−0.0846806	−	0.996408i	$-0.526987\pi$
$503$	−3.79837	−0.169361	−0.0846806	+	0.996408i	$0.526987\pi$
$504$	0	0
$505$	−8.29180	−0.368980
$506$	0	0
$507$	25.8885	1.14975
$508$	0	0
$509$	34.9230	1.54793	0.773967	−	0.633226i	$-0.218270\pi$
$509$	34.9230	1.54793	0.773967	+	0.633226i	$0.218270\pi$
$510$	0	0
$511$	2.03444	0.0899984
$512$	0	0
$513$	−3.09017	−0.136434
$514$	0	0
$515$	−7.23607	−0.318859
$516$	0	0
$517$	−24.2705	−1.06742
$518$	0	0
$519$	12.3820	0.543508
$520$	0	0
$521$	23.5066	1.02984	0.514921	−	0.857238i	$-0.327821\pi$
$521$	23.5066	1.02984	0.514921	+	0.857238i	$0.327821\pi$
$522$	0	0
$523$	−14.0557	−0.614614	−0.307307	−	0.951610i	$-0.599428\pi$
$523$	−14.0557	−0.614614	−0.307307	+	0.951610i	$0.599428\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	19.5836	0.853075
$528$	0	0
$529$	−1.67376	−0.0727723
$530$	0	0
$531$	1.00000	0.0433963
$532$	0	0
$533$	−50.4508	−2.18527
$534$	0	0
$535$	2.03444	0.0879566
$536$	0	0
$537$	0.527864	0.0227790
$538$	0	0
$539$	2.96556	0.127736
$540$	0	0
$541$	−26.1246	−1.12318	−0.561592	−	0.827414i	$-0.689811\pi$
$541$	−26.1246	−1.12318	−0.561592	+	0.827414i	$0.689811\pi$
$542$	0	0
$543$	22.2705	0.955719
$544$	0	0
$545$	9.27051	0.397105
$546$	0	0
$547$	−12.4377	−0.531797	−0.265899	−	0.964001i	$-0.585669\pi$
$547$	−12.4377	−0.531797	−0.265899	+	0.964001i	$0.585669\pi$
$548$	0	0
$549$	−3.14590	−0.134264
$550$	0	0
$551$	−19.7214	−0.840158
$552$	0	0
$553$	7.14590	0.303874
$554$	0	0
$555$	0.326238	0.0138480
$556$	0	0
$557$	−25.4164	−1.07693	−0.538464	−	0.842649i	$-0.680995\pi$
$557$	−25.4164	−1.07693	−0.538464	+	0.842649i	$0.680995\pi$
$558$	0	0
$559$	−54.3050	−2.29685
$560$	0	0
$561$	−4.14590	−0.175040
$562$	0	0
$563$	20.5967	0.868049	0.434025	−	0.900901i	$-0.357093\pi$
$563$	20.5967	0.868049	0.434025	+	0.900901i	$0.357093\pi$
$564$	0	0
$565$	20.1246	0.846649
$566$	0	0
$567$	2.38197	0.100033
$568$	0	0
$569$	−11.5066	−0.482381	−0.241190	−	0.970478i	$-0.577538\pi$
$569$	−11.5066	−0.482381	−0.241190	+	0.970478i	$0.577538\pi$
$570$	0	0
$571$	−1.58359	−0.0662713	−0.0331356	−	0.999451i	$-0.510549\pi$
$571$	−1.58359	−0.0662713	−0.0331356	+	0.999451i	$0.510549\pi$
$572$	0	0
$573$	−16.4164	−0.685805
$574$	0	0
$575$	0	0
$576$	0	0
$577$	12.5279	0.521542	0.260771	−	0.965401i	$-0.416023\pi$
$577$	12.5279	0.521542	0.260771	+	0.965401i	$0.416023\pi$
$578$	0	0
$579$	8.00000	0.332469
$580$	0	0
$581$	3.85410	0.159895
$582$	0	0
$583$	−13.9443	−0.577513
$584$	0	0
$585$	13.9443	0.576525
$586$	0	0
$587$	15.3607	0.634003	0.317002	−	0.948425i	$-0.397324\pi$
$587$	15.3607	0.634003	0.317002	+	0.948425i	$0.397324\pi$
$588$	0	0
$589$	−32.6393	−1.34488
$590$	0	0
$591$	−20.6525	−0.849529
$592$	0	0
$593$	16.0902	0.660744	0.330372	−	0.943851i	$-0.392826\pi$
$593$	16.0902	0.660744	0.330372	+	0.943851i	$0.392826\pi$
$594$	0	0
$595$	−9.87539	−0.404851
$596$	0	0
$597$	16.5623	0.677850
$598$	0	0
$599$	−2.65248	−0.108377	−0.0541886	−	0.998531i	$-0.517257\pi$
$599$	−2.65248	−0.108377	−0.0541886	+	0.998531i	$0.517257\pi$
$600$	0	0
$601$	23.3820	0.953770	0.476885	−	0.878966i	$-0.341766\pi$
$601$	23.3820	0.953770	0.476885	+	0.878966i	$0.341766\pi$
$602$	0	0
$603$	−10.7082	−0.436072
$604$	0	0
$605$	13.4164	0.545455
$606$	0	0
$607$	13.6525	0.554137	0.277068	−	0.960850i	$-0.410637\pi$
$607$	13.6525	0.554137	0.277068	+	0.960850i	$0.410637\pi$
$608$	0	0
$609$	15.2016	0.616001
$610$	0	0
$611$	−67.6869	−2.73832
$612$	0	0
$613$	−38.6525	−1.56116	−0.780579	−	0.625057i	$-0.785076\pi$
$613$	−38.6525	−1.56116	−0.780579	+	0.625057i	$0.785076\pi$
$614$	0	0
$615$	−18.0902	−0.729466
$616$	0	0
$617$	22.1459	0.891560	0.445780	−	0.895142i	$-0.352926\pi$
$617$	22.1459	0.891560	0.445780	+	0.895142i	$0.352926\pi$
$618$	0	0
$619$	−12.1246	−0.487329	−0.243665	−	0.969860i	$-0.578350\pi$
$619$	−12.1246	−0.487329	−0.243665	+	0.969860i	$0.578350\pi$
$620$	0	0
$621$	4.61803	0.185315
$622$	0	0
$623$	−32.8673	−1.31680
$624$	0	0
$625$	−25.0000	−1.00000
$626$	0	0
$627$	6.90983	0.275952
$628$	0	0
$629$	−0.270510	−0.0107859
$630$	0	0
$631$	40.4164	1.60895	0.804476	−	0.593985i	$-0.202446\pi$
$631$	40.4164	1.60895	0.804476	+	0.593985i	$0.202446\pi$
$632$	0	0
$633$	2.14590	0.0852918
$634$	0	0
$635$	35.6525	1.41483
$636$	0	0
$637$	8.27051	0.327690
$638$	0	0
$639$	7.94427	0.314271
$640$	0	0
$641$	−27.9443	−1.10373	−0.551866	−	0.833933i	$-0.686084\pi$
$641$	−27.9443	−1.10373	−0.551866	+	0.833933i	$0.686084\pi$
$642$	0	0
$643$	19.8541	0.782969	0.391485	−	0.920185i	$-0.371962\pi$
$643$	19.8541	0.782969	0.391485	+	0.920185i	$0.371962\pi$
$644$	0	0
$645$	−19.4721	−0.766715
$646$	0	0
$647$	−44.9443	−1.76694	−0.883471	−	0.468486i	$-0.844800\pi$
$647$	−44.9443	−1.76694	−0.883471	+	0.468486i	$0.844800\pi$
$648$	0	0
$649$	−2.23607	−0.0877733
$650$	0	0
$651$	25.1591	0.986061
$652$	0	0
$653$	40.0902	1.56885	0.784425	−	0.620224i	$-0.212958\pi$
$653$	40.0902	1.56885	0.784425	+	0.620224i	$0.212958\pi$
$654$	0	0
$655$	−46.1803	−1.80442
$656$	0	0
$657$	0.854102	0.0333217
$658$	0	0
$659$	−1.85410	−0.0722256	−0.0361128	−	0.999348i	$-0.511498\pi$
$659$	−1.85410	−0.0722256	−0.0361128	+	0.999348i	$0.511498\pi$
$660$	0	0
$661$	30.7426	1.19575	0.597875	−	0.801589i	$-0.296012\pi$
$661$	30.7426	1.19575	0.597875	+	0.801589i	$0.296012\pi$
$662$	0	0
$663$	−11.5623	−0.449043
$664$	0	0
$665$	16.4590	0.638252
$666$	0	0
$667$	29.4721	1.14117
$668$	0	0
$669$	9.52786	0.368369
$670$	0	0
$671$	7.03444	0.271562
$672$	0	0
$673$	−8.47214	−0.326577	−0.163288	−	0.986578i	$-0.552210\pi$
$673$	−8.47214	−0.326577	−0.163288	+	0.986578i	$0.552210\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−27.8197	−1.06920	−0.534598	−	0.845106i	$-0.679537\pi$
$677$	−27.8197	−1.06920	−0.534598	+	0.845106i	$0.679537\pi$
$678$	0	0
$679$	7.14590	0.274234
$680$	0	0
$681$	22.1459	0.848633
$682$	0	0
$683$	−39.0000	−1.49229	−0.746147	−	0.665782i	$-0.768098\pi$
$683$	−39.0000	−1.49229	−0.746147	+	0.665782i	$0.768098\pi$
$684$	0	0
$685$	−27.3607	−1.04540
$686$	0	0
$687$	−9.14590	−0.348938
$688$	0	0
$689$	−38.8885	−1.48154
$690$	0	0
$691$	−35.1246	−1.33620	−0.668102	−	0.744070i	$-0.732893\pi$
$691$	−35.1246	−1.33620	−0.668102	+	0.744070i	$0.732893\pi$
$692$	0	0
$693$	−5.32624	−0.202327
$694$	0	0
$695$	26.3050	0.997804
$696$	0	0
$697$	15.0000	0.568166
$698$	0	0
$699$	−8.29180	−0.313625
$700$	0	0
$701$	18.2016	0.687466	0.343733	−	0.939067i	$-0.388308\pi$
$701$	18.2016	0.687466	0.343733	+	0.939067i	$0.388308\pi$
$702$	0	0
$703$	0.450850	0.0170041
$704$	0	0
$705$	−24.2705	−0.914080
$706$	0	0
$707$	8.83282	0.332192
$708$	0	0
$709$	−27.7082	−1.04060	−0.520302	−	0.853983i	$-0.674181\pi$
$709$	−27.7082	−1.04060	−0.520302	+	0.853983i	$0.674181\pi$
$710$	0	0
$711$	3.00000	0.112509
$712$	0	0
$713$	48.7771	1.82672
$714$	0	0
$715$	−31.1803	−1.16608
$716$	0	0
$717$	1.47214	0.0549779
$718$	0	0
$719$	−14.6180	−0.545161	−0.272580	−	0.962133i	$-0.587877\pi$
$719$	−14.6180	−0.545161	−0.272580	+	0.962133i	$0.587877\pi$
$720$	0	0
$721$	7.70820	0.287069
$722$	0	0
$723$	−23.4164	−0.870866
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−26.0000	−0.964287	−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000	−0.964287	−0.482143	+	0.876092i	$0.660142\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	16.1459	0.597178
$732$	0	0
$733$	20.5279	0.758214	0.379107	−	0.925353i	$-0.376231\pi$
$733$	20.5279	0.758214	0.379107	+	0.925353i	$0.376231\pi$
$734$	0	0
$735$	2.96556	0.109386
$736$	0	0
$737$	23.9443	0.881999
$738$	0	0
$739$	−48.1033	−1.76951	−0.884755	−	0.466057i	$-0.845674\pi$
$739$	−48.1033	−1.76951	−0.884755	+	0.466057i	$0.845674\pi$
$740$	0	0
$741$	19.2705	0.707920
$742$	0	0
$743$	24.6180	0.903148	0.451574	−	0.892234i	$-0.350863\pi$
$743$	24.6180	0.903148	0.451574	+	0.892234i	$0.350863\pi$
$744$	0	0
$745$	−42.6869	−1.56393
$746$	0	0
$747$	1.61803	0.0592008
$748$	0	0
$749$	−2.16718	−0.0791872
$750$	0	0
$751$	4.87539	0.177905	0.0889527	−	0.996036i	$-0.471648\pi$
$751$	4.87539	0.177905	0.0889527	+	0.996036i	$0.471648\pi$
$752$	0	0
$753$	−15.1803	−0.553202
$754$	0	0
$755$	5.72949	0.208517
$756$	0	0
$757$	−41.3820	−1.50405	−0.752027	−	0.659133i	$-0.770924\pi$
$757$	−41.3820	−1.50405	−0.752027	+	0.659133i	$0.770924\pi$
$758$	0	0
$759$	−10.3262	−0.374819
$760$	0	0
$761$	30.7082	1.11317	0.556586	−	0.830790i	$-0.312111\pi$
$761$	30.7082	1.11317	0.556586	+	0.830790i	$0.312111\pi$
$762$	0	0
$763$	−9.87539	−0.357513
$764$	0	0
$765$	−4.14590	−0.149895
$766$	0	0
$767$	−6.23607	−0.225171
$768$	0	0
$769$	10.9787	0.395903	0.197951	−	0.980212i	$-0.436571\pi$
$769$	10.9787	0.395903	0.197951	+	0.980212i	$0.436571\pi$
$770$	0	0
$771$	−19.4164	−0.699265
$772$	0	0
$773$	28.6525	1.03056	0.515279	−	0.857023i	$-0.327688\pi$
$773$	28.6525	1.03056	0.515279	+	0.857023i	$0.327688\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−0.347524	−0.0124674
$778$	0	0
$779$	−25.0000	−0.895718
$780$	0	0
$781$	−17.7639	−0.635643
$782$	0	0
$783$	6.38197	0.228073
$784$	0	0
$785$	−20.1246	−0.718278
$786$	0	0
$787$	4.29180	0.152986	0.0764930	−	0.997070i	$-0.475628\pi$
$787$	4.29180	0.152986	0.0764930	+	0.997070i	$0.475628\pi$
$788$	0	0
$789$	−1.61803	−0.0576035
$790$	0	0
$791$	−21.4377	−0.762237
$792$	0	0
$793$	19.6180	0.696657
$794$	0	0
$795$	−13.9443	−0.494552
$796$	0	0
$797$	−1.23607	−0.0437838	−0.0218919	−	0.999760i	$-0.506969\pi$
$797$	−1.23607	−0.0437838	−0.0218919	+	0.999760i	$0.506969\pi$
$798$	0	0
$799$	20.1246	0.711958
$800$	0	0
$801$	−13.7984	−0.487542
$802$	0	0
$803$	−1.90983	−0.0673964
$804$	0	0
$805$	−24.5967	−0.866921
$806$	0	0
$807$	−11.4721	−0.403838
$808$	0	0
$809$	7.67376	0.269795	0.134898	−	0.990860i	$-0.456929\pi$
$809$	7.67376	0.269795	0.134898	+	0.990860i	$0.456929\pi$
$810$	0	0
$811$	−14.6525	−0.514518	−0.257259	−	0.966342i	$-0.582819\pi$
$811$	−14.6525	−0.514518	−0.257259	+	0.966342i	$0.582819\pi$
$812$	0	0
$813$	7.76393	0.272293
$814$	0	0
$815$	−41.5066	−1.45391
$816$	0	0
$817$	−26.9098	−0.941456
$818$	0	0
$819$	−14.8541	−0.519044
$820$	0	0
$821$	−40.9230	−1.42822	−0.714111	−	0.700032i	$-0.753169\pi$
$821$	−40.9230	−1.42822	−0.714111	+	0.700032i	$0.753169\pi$
$822$	0	0
$823$	−11.2918	−0.393607	−0.196804	−	0.980443i	$-0.563056\pi$
$823$	−11.2918	−0.393607	−0.196804	+	0.980443i	$0.563056\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	2.81966	0.0980492	0.0490246	−	0.998798i	$-0.484389\pi$
$827$	2.81966	0.0980492	0.0490246	+	0.998798i	$0.484389\pi$
$828$	0	0
$829$	−45.6869	−1.58677	−0.793386	−	0.608719i	$-0.791684\pi$
$829$	−45.6869	−1.58677	−0.793386	+	0.608719i	$0.791684\pi$
$830$	0	0
$831$	−5.47214	−0.189826
$832$	0	0
$833$	−2.45898	−0.0851986
$834$	0	0
$835$	15.7295	0.544341
$836$	0	0
$837$	10.5623	0.365087
$838$	0	0
$839$	24.8197	0.856870	0.428435	−	0.903573i	$-0.359065\pi$
$839$	24.8197	0.856870	0.428435	+	0.903573i	$0.359065\pi$
$840$	0	0
$841$	11.7295	0.404465
$842$	0	0
$843$	9.70820	0.334368
$844$	0	0
$845$	−57.8885	−1.99143
$846$	0	0
$847$	−14.2918	−0.491072
$848$	0	0
$849$	23.2705	0.798642
$850$	0	0
$851$	−0.673762	−0.0230963
$852$	0	0
$853$	−3.96556	−0.135778	−0.0678891	−	0.997693i	$-0.521626\pi$
$853$	−3.96556	−0.135778	−0.0678891	+	0.997693i	$0.521626\pi$
$854$	0	0
$855$	6.90983	0.236311
$856$	0	0
$857$	−28.7771	−0.983007	−0.491503	−	0.870876i	$-0.663552\pi$
$857$	−28.7771	−0.983007	−0.491503	+	0.870876i	$0.663552\pi$
$858$	0	0
$859$	−15.5279	−0.529804	−0.264902	−	0.964275i	$-0.585340\pi$
$859$	−15.5279	−0.529804	−0.264902	+	0.964275i	$0.585340\pi$
$860$	0	0
$861$	19.2705	0.656737
$862$	0	0
$863$	−19.2016	−0.653631	−0.326815	−	0.945088i	$-0.605976\pi$
$863$	−19.2016	−0.653631	−0.326815	+	0.945088i	$0.605976\pi$
$864$	0	0
$865$	−27.6869	−0.941383
$866$	0	0
$867$	−13.5623	−0.460600
$868$	0	0
$869$	−6.70820	−0.227560
$870$	0	0
$871$	66.7771	2.26266
$872$	0	0
$873$	3.00000	0.101535
$874$	0	0
$875$	26.6312	0.900299
$876$	0	0
$877$	−16.1115	−0.544045	−0.272023	−	0.962291i	$-0.587693\pi$
$877$	−16.1115	−0.544045	−0.272023	+	0.962291i	$0.587693\pi$
$878$	0	0
$879$	19.3820	0.653737
$880$	0	0
$881$	−15.7082	−0.529223	−0.264611	−	0.964355i	$-0.585244\pi$
$881$	−15.7082	−0.529223	−0.264611	+	0.964355i	$0.585244\pi$
$882$	0	0
$883$	23.4164	0.788025	0.394012	−	0.919105i	$-0.371087\pi$
$883$	23.4164	0.788025	0.394012	+	0.919105i	$0.371087\pi$
$884$	0	0
$885$	−2.23607	−0.0751646
$886$	0	0
$887$	22.5279	0.756412	0.378206	−	0.925722i	$-0.376541\pi$
$887$	22.5279	0.756412	0.378206	+	0.925722i	$0.376541\pi$
$888$	0	0
$889$	−37.9787	−1.27377
$890$	0	0
$891$	−2.23607	−0.0749111
$892$	0	0
$893$	−33.5410	−1.12241
$894$	0	0
$895$	−1.18034	−0.0394544
$896$	0	0
$897$	−28.7984	−0.961550
$898$	0	0
$899$	67.4083	2.24819
$900$	0	0
$901$	11.5623	0.385196
$902$	0	0
$903$	20.7426	0.690272
$904$	0	0
$905$	−49.7984	−1.65535
$906$	0	0
$907$	19.9443	0.662239	0.331119	−	0.943589i	$-0.392574\pi$
$907$	19.9443	0.662239	0.331119	+	0.943589i	$0.392574\pi$
$908$	0	0
$909$	3.70820	0.122993
$910$	0	0
$911$	45.1033	1.49434	0.747170	−	0.664633i	$-0.231412\pi$
$911$	45.1033	1.49434	0.747170	+	0.664633i	$0.231412\pi$
$912$	0	0
$913$	−3.61803	−0.119739
$914$	0	0
$915$	7.03444	0.232551
$916$	0	0
$917$	49.1935	1.62451
$918$	0	0
$919$	13.5967	0.448515	0.224258	−	0.974530i	$-0.428004\pi$
$919$	13.5967	0.448515	0.224258	+	0.974530i	$0.428004\pi$
$920$	0	0
$921$	25.8885	0.853057
$922$	0	0
$923$	−49.5410	−1.63066
$924$	0	0
$925$	0	0
$926$	0	0
$927$	3.23607	0.106286
$928$	0	0
$929$	−48.7082	−1.59806	−0.799032	−	0.601288i	$-0.794654\pi$
$929$	−48.7082	−1.59806	−0.799032	+	0.601288i	$0.794654\pi$
$930$	0	0
$931$	4.09830	0.134316
$932$	0	0
$933$	−27.4508	−0.898700
$934$	0	0
$935$	9.27051	0.303178
$936$	0	0
$937$	51.7214	1.68966	0.844832	−	0.535032i	$-0.179701\pi$
$937$	51.7214	1.68966	0.844832	+	0.535032i	$0.179701\pi$
$938$	0	0
$939$	−20.7984	−0.678729
$940$	0	0
$941$	40.3050	1.31390	0.656952	−	0.753932i	$-0.271845\pi$
$941$	40.3050	1.31390	0.656952	+	0.753932i	$0.271845\pi$
$942$	0	0
$943$	37.3607	1.21663
$944$	0	0
$945$	−5.32624	−0.173263
$946$	0	0
$947$	−25.0344	−0.813510	−0.406755	−	0.913537i	$-0.633340\pi$
$947$	−25.0344	−0.813510	−0.406755	+	0.913537i	$0.633340\pi$
$948$	0	0
$949$	−5.32624	−0.172897
$950$	0	0
$951$	−29.1803	−0.946237
$952$	0	0
$953$	4.94427	0.160161	0.0800803	−	0.996788i	$-0.474482\pi$
$953$	4.94427	0.160161	0.0800803	+	0.996788i	$0.474482\pi$
$954$	0	0
$955$	36.7082	1.18785
$956$	0	0
$957$	−14.2705	−0.461300
$958$	0	0
$959$	29.1459	0.941170
$960$	0	0
$961$	80.5623	2.59878
$962$	0	0
$963$	−0.909830	−0.0293189
$964$	0	0
$965$	−17.8885	−0.575853
$966$	0	0
$967$	−15.2705	−0.491066	−0.245533	−	0.969388i	$-0.578963\pi$
$967$	−15.2705	−0.491066	−0.245533	+	0.969388i	$0.578963\pi$
$968$	0	0
$969$	−5.72949	−0.184058
$970$	0	0
$971$	−46.7984	−1.50183	−0.750916	−	0.660398i	$-0.770388\pi$
$971$	−46.7984	−1.50183	−0.750916	+	0.660398i	$0.770388\pi$
$972$	0	0
$973$	−28.0213	−0.898321
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−20.8885	−0.668284	−0.334142	−	0.942523i	$-0.608446\pi$
$977$	−20.8885	−0.668284	−0.334142	+	0.942523i	$0.608446\pi$
$978$	0	0
$979$	30.8541	0.986101
$980$	0	0
$981$	−4.14590	−0.132368
$982$	0	0
$983$	9.40325	0.299917	0.149959	−	0.988692i	$-0.452086\pi$
$983$	9.40325	0.299917	0.149959	+	0.988692i	$0.452086\pi$
$984$	0	0
$985$	46.1803	1.47143
$986$	0	0
$987$	25.8541	0.822945
$988$	0	0
$989$	40.2148	1.27876
$990$	0	0
$991$	−23.7426	−0.754210	−0.377105	−	0.926171i	$-0.623080\pi$
$991$	−23.7426	−0.754210	−0.377105	+	0.926171i	$0.623080\pi$
$992$	0	0
$993$	11.1246	0.353029
$994$	0	0
$995$	−37.0344	−1.17407
$996$	0	0
$997$	53.2148	1.68533	0.842665	−	0.538439i	$-0.180986\pi$
$997$	53.2148	1.68533	0.842665	+	0.538439i	$0.180986\pi$
$998$	0	0
$999$	−0.145898	−0.00461601

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2832.2.a.o.1.1		2
3.2	odd	2		8496.2.a.bb.1.2		2
4.3	odd	2		177.2.a.b.1.2	✓	2
12.11	even	2		531.2.a.b.1.1		2
20.19	odd	2		4425.2.a.t.1.1		2
28.27	even	2		8673.2.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.a.b.1.2	✓	2	4.3	odd	2
531.2.a.b.1.1		2	12.11	even	2
2832.2.a.o.1.1		2	1.1	even	1	trivial
4425.2.a.t.1.1		2	20.19	odd	2
8496.2.a.bb.1.2		2	3.2	odd	2
8673.2.a.k.1.2		2	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2832 = 2^{4} \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2832.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} -2.23607 q^{5} +2.38197 q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} -2.23607 q^{5} +2.38197 q^{7} +1.00000 q^{9} -2.23607 q^{11} -6.23607 q^{13} -2.23607 q^{15} +1.85410 q^{17} -3.09017 q^{19} +2.38197 q^{21} +4.61803 q^{23} +1.00000 q^{27} +6.38197 q^{29} +10.5623 q^{31} -2.23607 q^{33} -5.32624 q^{35} -0.145898 q^{37} -6.23607 q^{39} +8.09017 q^{41} +8.70820 q^{43} -2.23607 q^{45} +10.8541 q^{47} -1.32624 q^{49} +1.85410 q^{51} +6.23607 q^{53} +5.00000 q^{55} -3.09017 q^{57} +1.00000 q^{59} -3.14590 q^{61} +2.38197 q^{63} +13.9443 q^{65} -10.7082 q^{67} +4.61803 q^{69} +7.94427 q^{71} +0.854102 q^{73} -5.32624 q^{77} +3.00000 q^{79} +1.00000 q^{81} +1.61803 q^{83} -4.14590 q^{85} +6.38197 q^{87} -13.7984 q^{89} -14.8541 q^{91} +10.5623 q^{93} +6.90983 q^{95} +3.00000 q^{97} -2.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 7 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 7 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} + 7 q^{7} + 2 q^{9} - 8 q^{13} - 3 q^{17} + 5 q^{19} + 7 q^{21} + 7 q^{23} + 2 q^{27} + 15 q^{29} + q^{31} + 5 q^{35} - 7 q^{37} - 8 q^{39} + 5 q^{41} + 4 q^{43} + 15 q^{47} + 13 q^{49} - 3 q^{51} + 8 q^{53} + 10 q^{55} + 5 q^{57} + 2 q^{59} - 13 q^{61} + 7 q^{63} + 10 q^{65} - 8 q^{67} + 7 q^{69} - 2 q^{71} - 5 q^{73} + 5 q^{77} + 6 q^{79} + 2 q^{81} + q^{83} - 15 q^{85} + 15 q^{87} - 3 q^{89} - 23 q^{91} + q^{93} + 25 q^{95} + 6 q^{97}+O(q^{100}) \) 2 * q + 2 * q^3 + 7 * q^7 + 2 * q^9 - 8 * q^13 - 3 * q^17 + 5 * q^19 + 7 * q^21 + 7 * q^23 + 2 * q^27 + 15 * q^29 + q^31 + 5 * q^35 - 7 * q^37 - 8 * q^39 + 5 * q^41 + 4 * q^43 + 15 * q^47 + 13 * q^49 - 3 * q^51 + 8 * q^53 + 10 * q^55 + 5 * q^57 + 2 * q^59 - 13 * q^61 + 7 * q^63 + 10 * q^65 - 8 * q^67 + 7 * q^69 - 2 * q^71 - 5 * q^73 + 5 * q^77 + 6 * q^79 + 2 * q^81 + q^83 - 15 * q^85 + 15 * q^87 - 3 * q^89 - 23 * q^91 + q^93 + 25 * q^95 + 6 * q^97

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