LMFDB - Embedded newform 3200.2.a.br.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3200,2,Mod(1,3200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3200.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3200 = 2^{7} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3200.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:	$25.5521286468$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 640)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	3200.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.806063 q^{3} -2.15633 q^{7} -2.35026 q^{9} +O(q^{10})$	$q-0.806063 q^{3} -2.15633 q^{7} -2.35026 q^{9} +0.387873 q^{11} -0.962389 q^{13} +1.61213 q^{17} -6.31265 q^{19} +1.73813 q^{21} +6.15633 q^{23} +4.31265 q^{27} -2.00000 q^{29} -9.92478 q^{31} -0.312650 q^{33} +6.57452 q^{37} +0.775746 q^{39} +4.57452 q^{41} -11.5066 q^{43} +4.54420 q^{47} -2.35026 q^{49} -1.29948 q^{51} +8.96239 q^{53} +5.08840 q^{57} +6.31265 q^{59} -0.261865 q^{61} +5.06793 q^{63} -9.89446 q^{67} -4.96239 q^{69} +10.7005 q^{71} +13.0884 q^{73} -0.836381 q^{77} +1.92478 q^{79} +3.57452 q^{81} -2.88129 q^{83} +1.61213 q^{87} +10.6253 q^{89} +2.07522 q^{91} +8.00000 q^{93} +9.61213 q^{97} -0.911603 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{3} + 4 q^{7} + 3 q^{9}+O(q^{10}) $ 3 * q - 2 * q^3 + 4 * q^7 + 3 * q^9	$ 3 q - 2 q^{3} + 4 q^{7} + 3 q^{9} + 2 q^{11} + 8 q^{13} + 4 q^{17} + 2 q^{19} - 4 q^{21} + 8 q^{23} - 8 q^{27} - 6 q^{29} - 8 q^{31} + 20 q^{33} + 8 q^{37} + 4 q^{39} + 2 q^{41} - 14 q^{43} + 4 q^{47} + 3 q^{49} - 24 q^{51} + 16 q^{53} - 4 q^{57} - 2 q^{59} - 10 q^{61} + 24 q^{63} - 10 q^{67} - 4 q^{69} + 12 q^{71} + 20 q^{73} - 16 q^{79} - q^{81} - 30 q^{83} + 4 q^{87} - 10 q^{89} + 28 q^{91} + 24 q^{93} + 28 q^{97} - 22 q^{99}+O(q^{100}) $ 3 * q - 2 * q^3 + 4 * q^7 + 3 * q^9 + 2 * q^11 + 8 * q^13 + 4 * q^17 + 2 * q^19 - 4 * q^21 + 8 * q^23 - 8 * q^27 - 6 * q^29 - 8 * q^31 + 20 * q^33 + 8 * q^37 + 4 * q^39 + 2 * q^41 - 14 * q^43 + 4 * q^47 + 3 * q^49 - 24 * q^51 + 16 * q^53 - 4 * q^57 - 2 * q^59 - 10 * q^61 + 24 * q^63 - 10 * q^67 - 4 * q^69 + 12 * q^71 + 20 * q^73 - 16 * q^79 - q^81 - 30 * q^83 + 4 * q^87 - 10 * q^89 + 28 * q^91 + 24 * q^93 + 28 * q^97 - 22 * 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
$3$	−0.806063	−0.465381	−0.232690	−	0.972551i	$-0.574753\pi$
$3$	−0.806063	−0.465381	−0.232690	+	0.972551i	$0.574753\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−2.15633	−0.815014	−0.407507	−	0.913202i	$-0.633602\pi$
$7$	−2.15633	−0.815014	−0.407507	+	0.913202i	$0.633602\pi$
$8$	0	0
$9$	−2.35026	−0.783421
$10$	0	0
$11$	0.387873	0.116948	0.0584741	−	0.998289i	$-0.481377\pi$
$11$	0.387873	0.116948	0.0584741	+	0.998289i	$0.481377\pi$
$12$	0	0
$13$	−0.962389	−0.266919	−0.133459	−	0.991054i	$-0.542609\pi$
$13$	−0.962389	−0.266919	−0.133459	+	0.991054i	$0.542609\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	1.61213	0.390998	0.195499	−	0.980704i	$-0.437367\pi$
$17$	1.61213	0.390998	0.195499	+	0.980704i	$0.437367\pi$
$18$	0	0
$19$	−6.31265	−1.44822	−0.724111	−	0.689684i	$-0.757750\pi$
$19$	−6.31265	−1.44822	−0.724111	+	0.689684i	$0.757750\pi$
$20$	0	0
$21$	1.73813	0.379292
$22$	0	0
$23$	6.15633	1.28368	0.641841	−	0.766838i	$-0.278171\pi$
$23$	6.15633	1.28368	0.641841	+	0.766838i	$0.278171\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	4.31265	0.829970
$28$	0	0
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	−9.92478	−1.78254	−0.891271	−	0.453470i	$-0.850186\pi$
$31$	−9.92478	−1.78254	−0.891271	+	0.453470i	$0.850186\pi$
$32$	0	0
$33$	−0.312650	−0.0544254
$34$	0	0
$35$	0	0
$36$	0	0
$37$	6.57452	1.08084	0.540422	−	0.841394i	$-0.318265\pi$
$37$	6.57452	1.08084	0.540422	+	0.841394i	$0.318265\pi$
$38$	0	0
$39$	0.775746	0.124219
$40$	0	0
$41$	4.57452	0.714419	0.357210	−	0.934024i	$-0.383728\pi$
$41$	4.57452	0.714419	0.357210	+	0.934024i	$0.383728\pi$
$42$	0	0
$43$	−11.5066	−1.75474	−0.877369	−	0.479816i	$-0.840703\pi$
$43$	−11.5066	−1.75474	−0.877369	+	0.479816i	$0.840703\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	4.54420	0.662839	0.331420	−	0.943483i	$-0.392472\pi$
$47$	4.54420	0.662839	0.331420	+	0.943483i	$0.392472\pi$
$48$	0	0
$49$	−2.35026	−0.335752
$50$	0	0
$51$	−1.29948	−0.181963
$52$	0	0
$53$	8.96239	1.23108	0.615539	−	0.788106i	$-0.288938\pi$
$53$	8.96239	1.23108	0.615539	+	0.788106i	$0.288938\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	5.08840	0.673975
$58$	0	0
$59$	6.31265	0.821837	0.410919	−	0.911672i	$-0.365208\pi$
$59$	6.31265	0.821837	0.410919	+	0.911672i	$0.365208\pi$
$60$	0	0
$61$	−0.261865	−0.0335284	−0.0167642	−	0.999859i	$-0.505336\pi$
$61$	−0.261865	−0.0335284	−0.0167642	+	0.999859i	$0.505336\pi$
$62$	0	0
$63$	5.06793	0.638499
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−9.89446	−1.20880	−0.604400	−	0.796681i	$-0.706587\pi$
$67$	−9.89446	−1.20880	−0.604400	+	0.796681i	$0.706587\pi$
$68$	0	0
$69$	−4.96239	−0.597401
$70$	0	0
$71$	10.7005	1.26992	0.634959	−	0.772546i	$-0.281017\pi$
$71$	10.7005	1.26992	0.634959	+	0.772546i	$0.281017\pi$
$72$	0	0
$73$	13.0884	1.53188	0.765940	−	0.642911i	$-0.222274\pi$
$73$	13.0884	1.53188	0.765940	+	0.642911i	$0.222274\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−0.836381	−0.0953144
$78$	0	0
$79$	1.92478	0.216554	0.108277	−	0.994121i	$-0.465467\pi$
$79$	1.92478	0.216554	0.108277	+	0.994121i	$0.465467\pi$
$80$	0	0
$81$	3.57452	0.397168
$82$	0	0
$83$	−2.88129	−0.316262	−0.158131	−	0.987418i	$-0.550547\pi$
$83$	−2.88129	−0.316262	−0.158131	+	0.987418i	$0.550547\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	1.61213	0.172838
$88$	0	0
$89$	10.6253	1.12628	0.563140	−	0.826362i	$-0.309593\pi$
$89$	10.6253	1.12628	0.563140	+	0.826362i	$0.309593\pi$
$90$	0	0
$91$	2.07522	0.217542
$92$	0	0
$93$	8.00000	0.829561
$94$	0	0
$95$	0	0
$96$	0	0
$97$	9.61213	0.975964	0.487982	−	0.872854i	$-0.337733\pi$
$97$	9.61213	0.975964	0.487982	+	0.872854i	$0.337733\pi$
$98$	0	0
$99$	−0.911603	−0.0916196
$100$	0	0
$101$	−11.4010	−1.13445	−0.567223	−	0.823564i	$-0.691982\pi$
$101$	−11.4010	−1.13445	−0.567223	+	0.823564i	$0.691982\pi$
$102$	0	0
$103$	10.9321	1.07717	0.538585	−	0.842572i	$-0.318959\pi$
$103$	10.9321	1.07717	0.538585	+	0.842572i	$0.318959\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−11.0435	−1.06761	−0.533807	−	0.845606i	$-0.679239\pi$
$107$	−11.0435	−1.06761	−0.533807	+	0.845606i	$0.679239\pi$
$108$	0	0
$109$	5.03761	0.482516	0.241258	−	0.970461i	$-0.422440\pi$
$109$	5.03761	0.482516	0.241258	+	0.970461i	$0.422440\pi$
$110$	0	0
$111$	−5.29948	−0.503004
$112$	0	0
$113$	19.8496	1.86729	0.933645	−	0.358201i	$-0.116610\pi$
$113$	19.8496	1.86729	0.933645	+	0.358201i	$0.116610\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	2.26187	0.209110
$118$	0	0
$119$	−3.47627	−0.318669
$120$	0	0
$121$	−10.8496	−0.986323
$122$	0	0
$123$	−3.68735	−0.332477
$124$	0	0
$125$	0	0
$126$	0	0
$127$	11.7685	1.04428	0.522141	−	0.852859i	$-0.325134\pi$
$127$	11.7685	1.04428	0.522141	+	0.852859i	$0.325134\pi$
$128$	0	0
$129$	9.27504	0.816622
$130$	0	0
$131$	−15.0884	−1.31828	−0.659140	−	0.752021i	$-0.729079\pi$
$131$	−15.0884	−1.31828	−0.659140	+	0.752021i	$0.729079\pi$
$132$	0	0
$133$	13.6121	1.18032
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−18.5501	−1.58484	−0.792420	−	0.609976i	$-0.791179\pi$
$137$	−18.5501	−1.58484	−0.792420	+	0.609976i	$0.791179\pi$
$138$	0	0
$139$	7.61213	0.645652	0.322826	−	0.946458i	$-0.395367\pi$
$139$	7.61213	0.645652	0.322826	+	0.946458i	$0.395367\pi$
$140$	0	0
$141$	−3.66291	−0.308473
$142$	0	0
$143$	−0.373285	−0.0312156
$144$	0	0
$145$	0	0
$146$	0	0
$147$	1.89446	0.156252
$148$	0	0
$149$	13.6629	1.11931	0.559655	−	0.828726i	$-0.310934\pi$
$149$	13.6629	1.11931	0.559655	+	0.828726i	$0.310934\pi$
$150$	0	0
$151$	15.2243	1.23893	0.619466	−	0.785023i	$-0.287349\pi$
$151$	15.2243	1.23893	0.619466	+	0.785023i	$0.287349\pi$
$152$	0	0
$153$	−3.78892	−0.306316
$154$	0	0
$155$	0	0
$156$	0	0
$157$	1.42548	0.113766	0.0568830	−	0.998381i	$-0.481884\pi$
$157$	1.42548	0.113766	0.0568830	+	0.998381i	$0.481884\pi$
$158$	0	0
$159$	−7.22425	−0.572921
$160$	0	0
$161$	−13.2750	−1.04622
$162$	0	0
$163$	−8.80606	−0.689744	−0.344872	−	0.938650i	$-0.612078\pi$
$163$	−8.80606	−0.689744	−0.344872	+	0.938650i	$0.612078\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	10.4690	0.810114	0.405057	−	0.914292i	$-0.367252\pi$
$167$	10.4690	0.810114	0.405057	+	0.914292i	$0.367252\pi$
$168$	0	0
$169$	−12.0738	−0.928754
$170$	0	0
$171$	14.8364	1.13457
$172$	0	0
$173$	19.9756	1.51871	0.759357	−	0.650674i	$-0.225514\pi$
$173$	19.9756	1.51871	0.759357	+	0.650674i	$0.225514\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−5.08840	−0.382467
$178$	0	0
$179$	12.2374	0.914668	0.457334	−	0.889295i	$-0.348804\pi$
$179$	12.2374	0.914668	0.457334	+	0.889295i	$0.348804\pi$
$180$	0	0
$181$	13.8496	1.02943	0.514715	−	0.857362i	$-0.327898\pi$
$181$	13.8496	1.02943	0.514715	+	0.857362i	$0.327898\pi$
$182$	0	0
$183$	0.211080	0.0156035
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0.625301	0.0457265
$188$	0	0
$189$	−9.29948	−0.676437
$190$	0	0
$191$	3.84955	0.278544	0.139272	−	0.990254i	$-0.455524\pi$
$191$	3.84955	0.278544	0.139272	+	0.990254i	$0.455524\pi$
$192$	0	0
$193$	9.61213	0.691896	0.345948	−	0.938254i	$-0.387557\pi$
$193$	9.61213	0.691896	0.345948	+	0.938254i	$0.387557\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−9.58769	−0.683095	−0.341547	−	0.939865i	$-0.610951\pi$
$197$	−9.58769	−0.683095	−0.341547	+	0.939865i	$0.610951\pi$
$198$	0	0
$199$	5.29948	0.375670	0.187835	−	0.982201i	$-0.439853\pi$
$199$	5.29948	0.375670	0.187835	+	0.982201i	$0.439853\pi$
$200$	0	0
$201$	7.97556	0.562553
$202$	0	0
$203$	4.31265	0.302689
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−14.4690	−1.00566
$208$	0	0
$209$	−2.44851	−0.169367
$210$	0	0
$211$	−15.0884	−1.03873	−0.519364	−	0.854553i	$-0.673831\pi$
$211$	−15.0884	−1.03873	−0.519364	+	0.854553i	$0.673831\pi$
$212$	0	0
$213$	−8.62530	−0.590996
$214$	0	0
$215$	0	0
$216$	0	0
$217$	21.4010	1.45280
$218$	0	0
$219$	−10.5501	−0.712908
$220$	0	0
$221$	−1.55149	−0.104365
$222$	0	0
$223$	22.5296	1.50869	0.754347	−	0.656476i	$-0.227954\pi$
$223$	22.5296	1.50869	0.754347	+	0.656476i	$0.227954\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	2.35756	0.156476	0.0782382	−	0.996935i	$-0.475071\pi$
$227$	2.35756	0.156476	0.0782382	+	0.996935i	$0.475071\pi$
$228$	0	0
$229$	−3.55149	−0.234689	−0.117345	−	0.993091i	$-0.537438\pi$
$229$	−3.55149	−0.234689	−0.117345	+	0.993091i	$0.537438\pi$
$230$	0	0
$231$	0.674176	0.0443575
$232$	0	0
$233$	13.0884	0.857449	0.428725	−	0.903435i	$-0.358963\pi$
$233$	13.0884	0.857449	0.428725	+	0.903435i	$0.358963\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−1.55149	−0.100780
$238$	0	0
$239$	−15.3258	−0.991345	−0.495673	−	0.868509i	$-0.665078\pi$
$239$	−15.3258	−0.991345	−0.495673	+	0.868509i	$0.665078\pi$
$240$	0	0
$241$	2.12601	0.136948	0.0684741	−	0.997653i	$-0.478187\pi$
$241$	2.12601	0.136948	0.0684741	+	0.997653i	$0.478187\pi$
$242$	0	0
$243$	−15.8192	−1.01480
$244$	0	0
$245$	0	0
$246$	0	0
$247$	6.07522	0.386557
$248$	0	0
$249$	2.32250	0.147182
$250$	0	0
$251$	26.6859	1.68440	0.842201	−	0.539164i	$-0.181260\pi$
$251$	26.6859	1.68440	0.842201	+	0.539164i	$0.181260\pi$
$252$	0	0
$253$	2.38787	0.150124
$254$	0	0
$255$	0	0
$256$	0	0
$257$	5.40105	0.336908	0.168454	−	0.985710i	$-0.446123\pi$
$257$	5.40105	0.336908	0.168454	+	0.985710i	$0.446123\pi$
$258$	0	0
$259$	−14.1768	−0.880903
$260$	0	0
$261$	4.70052	0.290955
$262$	0	0
$263$	−14.4690	−0.892195	−0.446098	−	0.894984i	$-0.647187\pi$
$263$	−14.4690	−0.892195	−0.446098	+	0.894984i	$0.647187\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−8.56467	−0.524149
$268$	0	0
$269$	28.1114	1.71398	0.856992	−	0.515330i	$-0.172331\pi$
$269$	28.1114	1.71398	0.856992	+	0.515330i	$0.172331\pi$
$270$	0	0
$271$	−24.8773	−1.51119	−0.755595	−	0.655039i	$-0.772652\pi$
$271$	−24.8773	−1.51119	−0.755595	+	0.655039i	$0.772652\pi$
$272$	0	0
$273$	−1.67276	−0.101240
$274$	0	0
$275$	0	0
$276$	0	0
$277$	19.9756	1.20022	0.600108	−	0.799919i	$-0.295124\pi$
$277$	19.9756	1.20022	0.600108	+	0.799919i	$0.295124\pi$
$278$	0	0
$279$	23.3258	1.39648
$280$	0	0
$281$	−14.4993	−0.864955	−0.432478	−	0.901645i	$-0.642361\pi$
$281$	−14.4993	−0.864955	−0.432478	+	0.901645i	$0.642361\pi$
$282$	0	0
$283$	−8.80606	−0.523466	−0.261733	−	0.965140i	$-0.584294\pi$
$283$	−8.80606	−0.523466	−0.261733	+	0.965140i	$0.584294\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−9.86414	−0.582262
$288$	0	0
$289$	−14.4010	−0.847120
$290$	0	0
$291$	−7.74798	−0.454195
$292$	0	0
$293$	−3.35026	−0.195724	−0.0978622	−	0.995200i	$-0.531200\pi$
$293$	−3.35026	−0.195724	−0.0978622	+	0.995200i	$0.531200\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	1.67276	0.0970634
$298$	0	0
$299$	−5.92478	−0.342639
$300$	0	0
$301$	24.8119	1.43014
$302$	0	0
$303$	9.18997	0.527950
$304$	0	0
$305$	0	0
$306$	0	0
$307$	1.95509	0.111583	0.0557916	−	0.998442i	$-0.482232\pi$
$307$	1.95509	0.111583	0.0557916	+	0.998442i	$0.482232\pi$
$308$	0	0
$309$	−8.81194	−0.501294
$310$	0	0
$311$	8.77575	0.497627	0.248813	−	0.968551i	$-0.419959\pi$
$311$	8.77575	0.497627	0.248813	+	0.968551i	$0.419959\pi$
$312$	0	0
$313$	−18.5501	−1.04851	−0.524256	−	0.851561i	$-0.675657\pi$
$313$	−18.5501	−1.04851	−0.524256	+	0.851561i	$0.675657\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	9.58769	0.538498	0.269249	−	0.963071i	$-0.413224\pi$
$317$	9.58769	0.538498	0.269249	+	0.963071i	$0.413224\pi$
$318$	0	0
$319$	−0.775746	−0.0434335
$320$	0	0
$321$	8.90175	0.496847
$322$	0	0
$323$	−10.1768	−0.566252
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−4.06063	−0.224554
$328$	0	0
$329$	−9.79877	−0.540224
$330$	0	0
$331$	23.0884	1.26905	0.634527	−	0.772901i	$-0.281195\pi$
$331$	23.0884	1.26905	0.634527	+	0.772901i	$0.281195\pi$
$332$	0	0
$333$	−15.4518	−0.846755
$334$	0	0
$335$	0	0
$336$	0	0
$337$	4.77575	0.260151	0.130076	−	0.991504i	$-0.458478\pi$
$337$	4.77575	0.260151	0.130076	+	0.991504i	$0.458478\pi$
$338$	0	0
$339$	−16.0000	−0.869001
$340$	0	0
$341$	−3.84955	−0.208465
$342$	0	0
$343$	20.1622	1.08866
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−1.89446	−0.101700	−0.0508500	−	0.998706i	$-0.516193\pi$
$347$	−1.89446	−0.101700	−0.0508500	+	0.998706i	$0.516193\pi$
$348$	0	0
$349$	−31.4010	−1.68086	−0.840430	−	0.541921i	$-0.817697\pi$
$349$	−31.4010	−1.68086	−0.840430	+	0.541921i	$0.817697\pi$
$350$	0	0
$351$	−4.15045	−0.221534
$352$	0	0
$353$	−12.7757	−0.679984	−0.339992	−	0.940428i	$-0.610424\pi$
$353$	−12.7757	−0.679984	−0.339992	+	0.940428i	$0.610424\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	2.80209	0.148303
$358$	0	0
$359$	16.4749	0.869510	0.434755	−	0.900549i	$-0.356835\pi$
$359$	16.4749	0.869510	0.434755	+	0.900549i	$0.356835\pi$
$360$	0	0
$361$	20.8496	1.09734
$362$	0	0
$363$	8.74543	0.459016
$364$	0	0
$365$	0	0
$366$	0	0
$367$	10.0957	0.526991	0.263495	−	0.964661i	$-0.415125\pi$
$367$	10.0957	0.526991	0.263495	+	0.964661i	$0.415125\pi$
$368$	0	0
$369$	−10.7513	−0.559691
$370$	0	0
$371$	−19.3258	−1.00335
$372$	0	0
$373$	6.82653	0.353464	0.176732	−	0.984259i	$-0.443447\pi$
$373$	6.82653	0.353464	0.176732	+	0.984259i	$0.443447\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	1.92478	0.0991311
$378$	0	0
$379$	19.4617	0.999679	0.499840	−	0.866118i	$-0.333392\pi$
$379$	19.4617	0.999679	0.499840	+	0.866118i	$0.333392\pi$
$380$	0	0
$381$	−9.48612	−0.485989
$382$	0	0
$383$	5.90431	0.301696	0.150848	−	0.988557i	$-0.451800\pi$
$383$	5.90431	0.301696	0.150848	+	0.988557i	$0.451800\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	27.0435	1.37470
$388$	0	0
$389$	−14.1866	−0.719291	−0.359646	−	0.933089i	$-0.617102\pi$
$389$	−14.1866	−0.719291	−0.359646	+	0.933089i	$0.617102\pi$
$390$	0	0
$391$	9.92478	0.501918
$392$	0	0
$393$	12.1622	0.613502
$394$	0	0
$395$	0	0
$396$	0	0
$397$	28.1866	1.41465	0.707324	−	0.706890i	$-0.249902\pi$
$397$	28.1866	1.41465	0.707324	+	0.706890i	$0.249902\pi$
$398$	0	0
$399$	−10.9722	−0.549299
$400$	0	0
$401$	6.62530	0.330852	0.165426	−	0.986222i	$-0.447100\pi$
$401$	6.62530	0.330852	0.165426	+	0.986222i	$0.447100\pi$
$402$	0	0
$403$	9.55149	0.475794
$404$	0	0
$405$	0	0
$406$	0	0
$407$	2.55008	0.126403
$408$	0	0
$409$	12.6761	0.626792	0.313396	−	0.949623i	$-0.398533\pi$
$409$	12.6761	0.626792	0.313396	+	0.949623i	$0.398533\pi$
$410$	0	0
$411$	14.9525	0.737554
$412$	0	0
$413$	−13.6121	−0.669809
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−6.13586	−0.300474
$418$	0	0
$419$	14.8364	0.724805	0.362402	−	0.932022i	$-0.381957\pi$
$419$	14.8364	0.724805	0.362402	+	0.932022i	$0.381957\pi$
$420$	0	0
$421$	−0.261865	−0.0127625	−0.00638126	−	0.999980i	$-0.502031\pi$
$421$	−0.261865	−0.0127625	−0.00638126	+	0.999980i	$0.502031\pi$
$422$	0	0
$423$	−10.6801	−0.519282
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0.564666	0.0273261
$428$	0	0
$429$	0.300891	0.0145272
$430$	0	0
$431$	−4.52373	−0.217900	−0.108950	−	0.994047i	$-0.534749\pi$
$431$	−4.52373	−0.217900	−0.108950	+	0.994047i	$0.534749\pi$
$432$	0	0
$433$	−15.6385	−0.751537	−0.375769	−	0.926714i	$-0.622621\pi$
$433$	−15.6385	−0.751537	−0.375769	+	0.926714i	$0.622621\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−38.8627	−1.85906
$438$	0	0
$439$	10.3272	0.492892	0.246446	−	0.969156i	$-0.420737\pi$
$439$	10.3272	0.492892	0.246446	+	0.969156i	$0.420737\pi$
$440$	0	0
$441$	5.52373	0.263035
$442$	0	0
$443$	15.1939	0.721886	0.360943	−	0.932588i	$-0.382455\pi$
$443$	15.1939	0.721886	0.360943	+	0.932588i	$0.382455\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−11.0132	−0.520905
$448$	0	0
$449$	24.6761	1.16454	0.582268	−	0.812997i	$-0.302165\pi$
$449$	24.6761	1.16454	0.582268	+	0.812997i	$0.302165\pi$
$450$	0	0
$451$	1.77433	0.0835500
$452$	0	0
$453$	−12.2717	−0.576575
$454$	0	0
$455$	0	0
$456$	0	0
$457$	8.37328	0.391686	0.195843	−	0.980635i	$-0.437256\pi$
$457$	8.37328	0.391686	0.195843	+	0.980635i	$0.437256\pi$
$458$	0	0
$459$	6.95254	0.324517
$460$	0	0
$461$	−8.29806	−0.386479	−0.193240	−	0.981152i	$-0.561899\pi$
$461$	−8.29806	−0.386479	−0.193240	+	0.981152i	$0.561899\pi$
$462$	0	0
$463$	−39.4676	−1.83421	−0.917107	−	0.398642i	$-0.869482\pi$
$463$	−39.4676	−1.83421	−0.917107	+	0.398642i	$0.869482\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−2.41819	−0.111901	−0.0559503	−	0.998434i	$-0.517819\pi$
$467$	−2.41819	−0.111901	−0.0559503	+	0.998434i	$0.517819\pi$
$468$	0	0
$469$	21.3357	0.985190
$470$	0	0
$471$	−1.14903	−0.0529446
$472$	0	0
$473$	−4.46310	−0.205213
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−21.0640	−0.964452
$478$	0	0
$479$	6.44851	0.294640	0.147320	−	0.989089i	$-0.452935\pi$
$479$	6.44851	0.294640	0.147320	+	0.989089i	$0.452935\pi$
$480$	0	0
$481$	−6.32724	−0.288497
$482$	0	0
$483$	10.7005	0.486891
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−12.3331	−0.558867	−0.279433	−	0.960165i	$-0.590147\pi$
$487$	−12.3331	−0.558867	−0.279433	+	0.960165i	$0.590147\pi$
$488$	0	0
$489$	7.09825	0.320994
$490$	0	0
$491$	−14.3127	−0.645921	−0.322960	−	0.946412i	$-0.604678\pi$
$491$	−14.3127	−0.645921	−0.322960	+	0.946412i	$0.604678\pi$
$492$	0	0
$493$	−3.22425	−0.145213
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−23.0738	−1.03500
$498$	0	0
$499$	−14.0606	−0.629440	−0.314720	−	0.949184i	$-0.601911\pi$
$499$	−14.0606	−0.629440	−0.314720	+	0.949184i	$0.601911\pi$
$500$	0	0
$501$	−8.43866	−0.377011
$502$	0	0
$503$	−31.8700	−1.42101	−0.710507	−	0.703690i	$-0.751534\pi$
$503$	−31.8700	−1.42101	−0.710507	+	0.703690i	$0.751534\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	9.73226	0.432225
$508$	0	0
$509$	−26.0000	−1.15243	−0.576215	−	0.817298i	$-0.695471\pi$
$509$	−26.0000	−1.15243	−0.576215	+	0.817298i	$0.695471\pi$
$510$	0	0
$511$	−28.2228	−1.24850
$512$	0	0
$513$	−27.2243	−1.20198
$514$	0	0
$515$	0	0
$516$	0	0
$517$	1.76257	0.0775178
$518$	0	0
$519$	−16.1016	−0.706780
$520$	0	0
$521$	−19.4010	−0.849975	−0.424988	−	0.905199i	$-0.639722\pi$
$521$	−19.4010	−0.849975	−0.424988	+	0.905199i	$0.639722\pi$
$522$	0	0
$523$	−7.75860	−0.339260	−0.169630	−	0.985508i	$-0.554257\pi$
$523$	−7.75860	−0.339260	−0.169630	+	0.985508i	$0.554257\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−16.0000	−0.696971
$528$	0	0
$529$	14.9003	0.647841
$530$	0	0
$531$	−14.8364	−0.643844
$532$	0	0
$533$	−4.40246	−0.190692
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−9.86414	−0.425669
$538$	0	0
$539$	−0.911603	−0.0392655
$540$	0	0
$541$	−25.8496	−1.11136	−0.555680	−	0.831397i	$-0.687542\pi$
$541$	−25.8496	−1.11136	−0.555680	+	0.831397i	$0.687542\pi$
$542$	0	0
$543$	−11.1636	−0.479077
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−38.2677	−1.63621	−0.818105	−	0.575068i	$-0.804975\pi$
$547$	−38.2677	−1.63621	−0.818105	+	0.575068i	$0.804975\pi$
$548$	0	0
$549$	0.615452	0.0262668
$550$	0	0
$551$	12.6253	0.537856
$552$	0	0
$553$	−4.15045	−0.176495
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−37.5271	−1.59007	−0.795036	−	0.606562i	$-0.792548\pi$
$557$	−37.5271	−1.59007	−0.795036	+	0.606562i	$0.792548\pi$
$558$	0	0
$559$	11.0738	0.468372
$560$	0	0
$561$	−0.504032	−0.0212802
$562$	0	0
$563$	43.6688	1.84042	0.920210	−	0.391425i	$-0.128018\pi$
$563$	43.6688	1.84042	0.920210	+	0.391425i	$0.128018\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−7.70782	−0.323698
$568$	0	0
$569$	−8.42407	−0.353155	−0.176578	−	0.984287i	$-0.556503\pi$
$569$	−8.42407	−0.353155	−0.176578	+	0.984287i	$0.556503\pi$
$570$	0	0
$571$	−24.8627	−1.04047	−0.520236	−	0.854022i	$-0.674156\pi$
$571$	−24.8627	−1.04047	−0.520236	+	0.854022i	$0.674156\pi$
$572$	0	0
$573$	−3.10299	−0.129629
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−14.0263	−0.583924	−0.291962	−	0.956430i	$-0.594308\pi$
$577$	−14.0263	−0.583924	−0.291962	+	0.956430i	$0.594308\pi$
$578$	0	0
$579$	−7.74798	−0.321995
$580$	0	0
$581$	6.21299	0.257758
$582$	0	0
$583$	3.47627	0.143972
$584$	0	0
$585$	0	0
$586$	0	0
$587$	34.5804	1.42729	0.713643	−	0.700510i	$-0.247044\pi$
$587$	34.5804	1.42729	0.713643	+	0.700510i	$0.247044\pi$
$588$	0	0
$589$	62.6516	2.58152
$590$	0	0
$591$	7.72829	0.317899
$592$	0	0
$593$	−8.00000	−0.328521	−0.164260	−	0.986417i	$-0.552524\pi$
$593$	−8.00000	−0.328521	−0.164260	+	0.986417i	$0.552524\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−4.27171	−0.174830
$598$	0	0
$599$	−42.3996	−1.73240	−0.866201	−	0.499696i	$-0.833445\pi$
$599$	−42.3996	−1.73240	−0.866201	+	0.499696i	$0.833445\pi$
$600$	0	0
$601$	2.75131	0.112228	0.0561141	−	0.998424i	$-0.482129\pi$
$601$	2.75131	0.112228	0.0561141	+	0.998424i	$0.482129\pi$
$602$	0	0
$603$	23.2546	0.946999
$604$	0	0
$605$	0	0
$606$	0	0
$607$	37.7948	1.53404	0.767022	−	0.641621i	$-0.221738\pi$
$607$	37.7948	1.53404	0.767022	+	0.641621i	$0.221738\pi$
$608$	0	0
$609$	−3.47627	−0.140866
$610$	0	0
$611$	−4.37328	−0.176924
$612$	0	0
$613$	−18.7659	−0.757947	−0.378974	−	0.925407i	$-0.623723\pi$
$613$	−18.7659	−0.757947	−0.378974	+	0.925407i	$0.623723\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−18.6107	−0.749239	−0.374620	−	0.927179i	$-0.622227\pi$
$617$	−18.6107	−0.749239	−0.374620	+	0.927179i	$0.622227\pi$
$618$	0	0
$619$	19.2097	0.772102	0.386051	−	0.922478i	$-0.373839\pi$
$619$	19.2097	0.772102	0.386051	+	0.922478i	$0.373839\pi$
$620$	0	0
$621$	26.5501	1.06542
$622$	0	0
$623$	−22.9116	−0.917934
$624$	0	0
$625$	0	0
$626$	0	0
$627$	1.97365	0.0788201
$628$	0	0
$629$	10.5990	0.422608
$630$	0	0
$631$	26.0263	1.03609	0.518046	−	0.855353i	$-0.326659\pi$
$631$	26.0263	1.03609	0.518046	+	0.855353i	$0.326659\pi$
$632$	0	0
$633$	12.1622	0.483404
$634$	0	0
$635$	0	0
$636$	0	0
$637$	2.26187	0.0896184
$638$	0	0
$639$	−25.1490	−0.994880
$640$	0	0
$641$	11.1735	0.441325	0.220663	−	0.975350i	$-0.429178\pi$
$641$	11.1735	0.441325	0.220663	+	0.975350i	$0.429178\pi$
$642$	0	0
$643$	35.1451	1.38599	0.692993	−	0.720944i	$-0.256292\pi$
$643$	35.1451	1.38599	0.692993	+	0.720944i	$0.256292\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−6.93207	−0.272528	−0.136264	−	0.990673i	$-0.543510\pi$
$647$	−6.93207	−0.272528	−0.136264	+	0.990673i	$0.543510\pi$
$648$	0	0
$649$	2.44851	0.0961123
$650$	0	0
$651$	−17.2506	−0.676104
$652$	0	0
$653$	−29.7381	−1.16374	−0.581872	−	0.813281i	$-0.697679\pi$
$653$	−29.7381	−1.16374	−0.581872	+	0.813281i	$0.697679\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−30.7612	−1.20011
$658$	0	0
$659$	24.3879	0.950017	0.475008	−	0.879981i	$-0.342445\pi$
$659$	24.3879	0.950017	0.475008	+	0.879981i	$0.342445\pi$
$660$	0	0
$661$	−34.1378	−1.32781	−0.663903	−	0.747819i	$-0.731101\pi$
$661$	−34.1378	−1.32781	−0.663903	+	0.747819i	$0.731101\pi$
$662$	0	0
$663$	1.25060	0.0485693
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−12.3127	−0.476748
$668$	0	0
$669$	−18.1603	−0.702118
$670$	0	0
$671$	−0.101570	−0.00392108
$672$	0	0
$673$	23.6385	0.911196	0.455598	−	0.890186i	$-0.349425\pi$
$673$	23.6385	0.911196	0.455598	+	0.890186i	$0.349425\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	2.88717	0.110963	0.0554814	−	0.998460i	$-0.482331\pi$
$677$	2.88717	0.110963	0.0554814	+	0.998460i	$0.482331\pi$
$678$	0	0
$679$	−20.7269	−0.795424
$680$	0	0
$681$	−1.90034	−0.0728212
$682$	0	0
$683$	13.7440	0.525900	0.262950	−	0.964809i	$-0.415305\pi$
$683$	13.7440	0.525900	0.262950	+	0.964809i	$0.415305\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	2.86273	0.109220
$688$	0	0
$689$	−8.62530	−0.328598
$690$	0	0
$691$	31.5633	1.20072	0.600361	−	0.799729i	$-0.295023\pi$
$691$	31.5633	1.20072	0.600361	+	0.799729i	$0.295023\pi$
$692$	0	0
$693$	1.96571	0.0746713
$694$	0	0
$695$	0	0
$696$	0	0
$697$	7.37470	0.279337
$698$	0	0
$699$	−10.5501	−0.399041
$700$	0	0
$701$	−23.8397	−0.900413	−0.450207	−	0.892924i	$-0.648650\pi$
$701$	−23.8397	−0.900413	−0.450207	+	0.892924i	$0.648650\pi$
$702$	0	0
$703$	−41.5026	−1.56530
$704$	0	0
$705$	0	0
$706$	0	0
$707$	24.5844	0.924590
$708$	0	0
$709$	−21.8496	−0.820577	−0.410289	−	0.911956i	$-0.634572\pi$
$709$	−21.8496	−0.820577	−0.410289	+	0.911956i	$0.634572\pi$
$710$	0	0
$711$	−4.52373	−0.169653
$712$	0	0
$713$	−61.1002	−2.28822
$714$	0	0
$715$	0	0
$716$	0	0
$717$	12.3536	0.461353
$718$	0	0
$719$	33.9248	1.26518	0.632590	−	0.774487i	$-0.281992\pi$
$719$	33.9248	1.26518	0.632590	+	0.774487i	$0.281992\pi$
$720$	0	0
$721$	−23.5731	−0.877908
$722$	0	0
$723$	−1.71370	−0.0637331
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−2.78163	−0.103165	−0.0515824	−	0.998669i	$-0.516426\pi$
$727$	−2.78163	−0.103165	−0.0515824	+	0.998669i	$0.516426\pi$
$728$	0	0
$729$	2.02776	0.0751023
$730$	0	0
$731$	−18.5501	−0.686099
$732$	0	0
$733$	4.90175	0.181050	0.0905252	−	0.995894i	$-0.471145\pi$
$733$	4.90175	0.181050	0.0905252	+	0.995894i	$0.471145\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−3.83780	−0.141367
$738$	0	0
$739$	−25.9102	−0.953122	−0.476561	−	0.879141i	$-0.658117\pi$
$739$	−25.9102	−0.953122	−0.476561	+	0.879141i	$0.658117\pi$
$740$	0	0
$741$	−4.89701	−0.179896
$742$	0	0
$743$	−9.06793	−0.332670	−0.166335	−	0.986069i	$-0.553193\pi$
$743$	−9.06793	−0.332670	−0.166335	+	0.986069i	$0.553193\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	6.77178	0.247766
$748$	0	0
$749$	23.8134	0.870121
$750$	0	0
$751$	11.8496	0.432396	0.216198	−	0.976349i	$-0.430634\pi$
$751$	11.8496	0.432396	0.216198	+	0.976349i	$0.430634\pi$
$752$	0	0
$753$	−21.5106	−0.783888
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−2.05079	−0.0745371	−0.0372685	−	0.999305i	$-0.511866\pi$
$757$	−2.05079	−0.0745371	−0.0372685	+	0.999305i	$0.511866\pi$
$758$	0	0
$759$	−1.92478	−0.0698650
$760$	0	0
$761$	25.0738	0.908925	0.454462	−	0.890766i	$-0.349831\pi$
$761$	25.0738	0.908925	0.454462	+	0.890766i	$0.349831\pi$
$762$	0	0
$763$	−10.8627	−0.393257
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−6.07522	−0.219364
$768$	0	0
$769$	−14.7466	−0.531775	−0.265887	−	0.964004i	$-0.585665\pi$
$769$	−14.7466	−0.531775	−0.265887	+	0.964004i	$0.585665\pi$
$770$	0	0
$771$	−4.35359	−0.156791
$772$	0	0
$773$	−10.8872	−0.391584	−0.195792	−	0.980645i	$-0.562728\pi$
$773$	−10.8872	−0.391584	−0.195792	+	0.980645i	$0.562728\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	11.4274	0.409955
$778$	0	0
$779$	−28.8773	−1.03464
$780$	0	0
$781$	4.15045	0.148515
$782$	0	0
$783$	−8.62530	−0.308243
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−36.8178	−1.31241	−0.656207	−	0.754581i	$-0.727840\pi$
$787$	−36.8178	−1.31241	−0.656207	+	0.754581i	$0.727840\pi$
$788$	0	0
$789$	11.6629	0.415211
$790$	0	0
$791$	−42.8021	−1.52187
$792$	0	0
$793$	0.252016	0.00894935
$794$	0	0
$795$	0	0
$796$	0	0
$797$	12.8119	0.453822	0.226911	−	0.973915i	$-0.427137\pi$
$797$	12.8119	0.453822	0.226911	+	0.973915i	$0.427137\pi$
$798$	0	0
$799$	7.32582	0.259169
$800$	0	0
$801$	−24.9722	−0.882351
$802$	0	0
$803$	5.07664	0.179151
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−22.6596	−0.797655
$808$	0	0
$809$	16.2981	0.573009	0.286505	−	0.958079i	$-0.407507\pi$
$809$	16.2981	0.573009	0.286505	+	0.958079i	$0.407507\pi$
$810$	0	0
$811$	−2.21108	−0.0776415	−0.0388208	−	0.999246i	$-0.512360\pi$
$811$	−2.21108	−0.0776415	−0.0388208	+	0.999246i	$0.512360\pi$
$812$	0	0
$813$	20.0527	0.703279
$814$	0	0
$815$	0	0
$816$	0	0
$817$	72.6371	2.54125
$818$	0	0
$819$	−4.87732	−0.170427
$820$	0	0
$821$	50.6615	1.76810	0.884049	−	0.467394i	$-0.154807\pi$
$821$	50.6615	1.76810	0.884049	+	0.467394i	$0.154807\pi$
$822$	0	0
$823$	−0.917483	−0.0319814	−0.0159907	−	0.999872i	$-0.505090\pi$
$823$	−0.917483	−0.0319814	−0.0159907	+	0.999872i	$0.505090\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−10.5198	−0.365808	−0.182904	−	0.983131i	$-0.558550\pi$
$827$	−10.5198	−0.365808	−0.182904	+	0.983131i	$0.558550\pi$
$828$	0	0
$829$	−38.6907	−1.34378	−0.671891	−	0.740650i	$-0.734518\pi$
$829$	−38.6907	−1.34378	−0.671891	+	0.740650i	$0.734518\pi$
$830$	0	0
$831$	−16.1016	−0.558557
$832$	0	0
$833$	−3.78892	−0.131278
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−42.8021	−1.47946
$838$	0	0
$839$	10.0263	0.346148	0.173074	−	0.984909i	$-0.444630\pi$
$839$	10.0263	0.346148	0.173074	+	0.984909i	$0.444630\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	0	0
$843$	11.6873	0.402534
$844$	0	0
$845$	0	0
$846$	0	0
$847$	23.3952	0.803867
$848$	0	0
$849$	7.09825	0.243611
$850$	0	0
$851$	40.4749	1.38746
$852$	0	0
$853$	−49.5388	−1.69618	−0.848088	−	0.529855i	$-0.822246\pi$
$853$	−49.5388	−1.69618	−0.848088	+	0.529855i	$0.822246\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−43.4763	−1.48512	−0.742561	−	0.669779i	$-0.766389\pi$
$857$	−43.4763	−1.48512	−0.742561	+	0.669779i	$0.766389\pi$
$858$	0	0
$859$	23.5633	0.803968	0.401984	−	0.915647i	$-0.368321\pi$
$859$	23.5633	0.803968	0.401984	+	0.915647i	$0.368321\pi$
$860$	0	0
$861$	7.95112	0.270974
$862$	0	0
$863$	13.3317	0.453816	0.226908	−	0.973916i	$-0.427138\pi$
$863$	13.3317	0.453816	0.226908	+	0.973916i	$0.427138\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	11.6082	0.394234
$868$	0	0
$869$	0.746569	0.0253256
$870$	0	0
$871$	9.52232	0.322651
$872$	0	0
$873$	−22.5910	−0.764590
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−13.6483	−0.460871	−0.230436	−	0.973088i	$-0.574015\pi$
$877$	−13.6483	−0.460871	−0.230436	+	0.973088i	$0.574015\pi$
$878$	0	0
$879$	2.70052	0.0910864
$880$	0	0
$881$	16.3028	0.549255	0.274628	−	0.961551i	$-0.411445\pi$
$881$	16.3028	0.549255	0.274628	+	0.961551i	$0.411445\pi$
$882$	0	0
$883$	−13.5818	−0.457064	−0.228532	−	0.973536i	$-0.573393\pi$
$883$	−13.5818	−0.457064	−0.228532	+	0.973536i	$0.573393\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−37.0797	−1.24501	−0.622507	−	0.782614i	$-0.713886\pi$
$887$	−37.0797	−1.24501	−0.622507	+	0.782614i	$0.713886\pi$
$888$	0	0
$889$	−25.3766	−0.851104
$890$	0	0
$891$	1.38646	0.0464481
$892$	0	0
$893$	−28.6859	−0.959938
$894$	0	0
$895$	0	0
$896$	0	0
$897$	4.77575	0.159458
$898$	0	0
$899$	19.8496	0.662020
$900$	0	0
$901$	14.4485	0.481350
$902$	0	0
$903$	−20.0000	−0.665558
$904$	0	0
$905$	0	0
$906$	0	0
$907$	35.7294	1.18638	0.593188	−	0.805064i	$-0.297869\pi$
$907$	35.7294	1.18638	0.593188	+	0.805064i	$0.297869\pi$
$908$	0	0
$909$	26.7954	0.888749
$910$	0	0
$911$	20.5237	0.679982	0.339991	−	0.940429i	$-0.389576\pi$
$911$	20.5237	0.679982	0.339991	+	0.940429i	$0.389576\pi$
$912$	0	0
$913$	−1.11757	−0.0369863
$914$	0	0
$915$	0	0
$916$	0	0
$917$	32.5355	1.07442
$918$	0	0
$919$	20.9986	0.692679	0.346340	−	0.938109i	$-0.387424\pi$
$919$	20.9986	0.692679	0.346340	+	0.938109i	$0.387424\pi$
$920$	0	0
$921$	−1.57593	−0.0519287
$922$	0	0
$923$	−10.2981	−0.338965
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−25.6932	−0.843876
$928$	0	0
$929$	−31.5271	−1.03437	−0.517185	−	0.855874i	$-0.673020\pi$
$929$	−31.5271	−1.03437	−0.517185	+	0.855874i	$0.673020\pi$
$930$	0	0
$931$	14.8364	0.486243
$932$	0	0
$933$	−7.07381	−0.231586
$934$	0	0
$935$	0	0
$936$	0	0
$937$	17.8641	0.583596	0.291798	−	0.956480i	$-0.405746\pi$
$937$	17.8641	0.583596	0.291798	+	0.956480i	$0.405746\pi$
$938$	0	0
$939$	14.9525	0.487958
$940$	0	0
$941$	45.5487	1.48484	0.742422	−	0.669933i	$-0.233677\pi$
$941$	45.5487	1.48484	0.742422	+	0.669933i	$0.233677\pi$
$942$	0	0
$943$	28.1622	0.917088
$944$	0	0
$945$	0	0
$946$	0	0
$947$	43.2057	1.40400	0.701998	−	0.712179i	$-0.252291\pi$
$947$	43.2057	1.40400	0.701998	+	0.712179i	$0.252291\pi$
$948$	0	0
$949$	−12.5961	−0.408887
$950$	0	0
$951$	−7.72829	−0.250607
$952$	0	0
$953$	−10.9722	−0.355426	−0.177713	−	0.984082i	$-0.556870\pi$
$953$	−10.9722	−0.355426	−0.177713	+	0.984082i	$0.556870\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0.625301	0.0202131
$958$	0	0
$959$	40.0000	1.29167
$960$	0	0
$961$	67.5012	2.17746
$962$	0	0
$963$	25.9551	0.836391
$964$	0	0
$965$	0	0
$966$	0	0
$967$	44.1417	1.41950	0.709751	−	0.704452i	$-0.248807\pi$
$967$	44.1417	1.41950	0.709751	+	0.704452i	$0.248807\pi$
$968$	0	0
$969$	8.20314	0.263523
$970$	0	0
$971$	20.1886	0.647881	0.323941	−	0.946077i	$-0.394992\pi$
$971$	20.1886	0.647881	0.323941	+	0.946077i	$0.394992\pi$
$972$	0	0
$973$	−16.4142	−0.526216
$974$	0	0
$975$	0	0
$976$	0	0
$977$	1.73340	0.0554562	0.0277281	−	0.999616i	$-0.491173\pi$
$977$	1.73340	0.0554562	0.0277281	+	0.999616i	$0.491173\pi$
$978$	0	0
$979$	4.12127	0.131716
$980$	0	0
$981$	−11.8397	−0.378013
$982$	0	0
$983$	14.0059	0.446718	0.223359	−	0.974736i	$-0.428298\pi$
$983$	14.0059	0.446718	0.223359	+	0.974736i	$0.428298\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	7.89843	0.251410
$988$	0	0
$989$	−70.8383	−2.25253
$990$	0	0
$991$	42.8021	1.35965	0.679827	−	0.733373i	$-0.262055\pi$
$991$	42.8021	1.35965	0.679827	+	0.733373i	$0.262055\pi$
$992$	0	0
$993$	−18.6107	−0.590593
$994$	0	0
$995$	0	0
$996$	0	0
$997$	42.8872	1.35825	0.679125	−	0.734023i	$-0.262359\pi$
$997$	42.8872	1.35825	0.679125	+	0.734023i	$0.262359\pi$
$998$	0	0
$999$	28.3536	0.897068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3200.2.a.br.1.2		3
4.3	odd	2		3200.2.a.bs.1.2		3
5.2	odd	4		640.2.c.b.129.4	yes	6
5.3	odd	4		640.2.c.b.129.3	yes	6
5.4	even	2		3200.2.a.bt.1.2		3
8.3	odd	2		3200.2.a.bp.1.2		3
8.5	even	2		3200.2.a.bu.1.2		3
20.3	even	4		640.2.c.a.129.4	yes	6
20.7	even	4		640.2.c.a.129.3	✓	6
20.19	odd	2		3200.2.a.bq.1.2		3
40.3	even	4		640.2.c.d.129.3	yes	6
40.13	odd	4		640.2.c.c.129.4	yes	6
40.19	odd	2		3200.2.a.bv.1.2		3
40.27	even	4		640.2.c.d.129.4	yes	6
40.29	even	2		3200.2.a.bo.1.2		3
40.37	odd	4		640.2.c.c.129.3	yes	6
80.3	even	4		1280.2.f.i.129.3		6
80.13	odd	4		1280.2.f.k.129.3		6
80.27	even	4		1280.2.f.i.129.4		6
80.37	odd	4		1280.2.f.k.129.4		6
80.43	even	4		1280.2.f.l.129.4		6
80.53	odd	4		1280.2.f.j.129.4		6
80.67	even	4		1280.2.f.l.129.3		6
80.77	odd	4		1280.2.f.j.129.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.c.a.129.3	✓	6	20.7	even	4
640.2.c.a.129.4	yes	6	20.3	even	4
640.2.c.b.129.3	yes	6	5.3	odd	4
640.2.c.b.129.4	yes	6	5.2	odd	4
640.2.c.c.129.3	yes	6	40.37	odd	4
640.2.c.c.129.4	yes	6	40.13	odd	4
640.2.c.d.129.3	yes	6	40.3	even	4
640.2.c.d.129.4	yes	6	40.27	even	4
1280.2.f.i.129.3		6	80.3	even	4
1280.2.f.i.129.4		6	80.27	even	4
1280.2.f.j.129.3		6	80.77	odd	4
1280.2.f.j.129.4		6	80.53	odd	4
1280.2.f.k.129.3		6	80.13	odd	4
1280.2.f.k.129.4		6	80.37	odd	4
1280.2.f.l.129.3		6	80.67	even	4
1280.2.f.l.129.4		6	80.43	even	4
3200.2.a.bo.1.2		3	40.29	even	2
3200.2.a.bp.1.2		3	8.3	odd	2
3200.2.a.bq.1.2		3	20.19	odd	2
3200.2.a.br.1.2		3	1.1	even	1	trivial
3200.2.a.bs.1.2		3	4.3	odd	2
3200.2.a.bt.1.2		3	5.4	even	2
3200.2.a.bu.1.2		3	8.5	even	2
3200.2.a.bv.1.2		3	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3200 = 2^{7} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3200.a (trivial)

\(f(q)\)	\(=\)	\(q-0.806063 q^{3} -2.15633 q^{7} -2.35026 q^{9} +O(q^{10})\)	\(q-0.806063 q^{3} -2.15633 q^{7} -2.35026 q^{9} +0.387873 q^{11} -0.962389 q^{13} +1.61213 q^{17} -6.31265 q^{19} +1.73813 q^{21} +6.15633 q^{23} +4.31265 q^{27} -2.00000 q^{29} -9.92478 q^{31} -0.312650 q^{33} +6.57452 q^{37} +0.775746 q^{39} +4.57452 q^{41} -11.5066 q^{43} +4.54420 q^{47} -2.35026 q^{49} -1.29948 q^{51} +8.96239 q^{53} +5.08840 q^{57} +6.31265 q^{59} -0.261865 q^{61} +5.06793 q^{63} -9.89446 q^{67} -4.96239 q^{69} +10.7005 q^{71} +13.0884 q^{73} -0.836381 q^{77} +1.92478 q^{79} +3.57452 q^{81} -2.88129 q^{83} +1.61213 q^{87} +10.6253 q^{89} +2.07522 q^{91} +8.00000 q^{93} +9.61213 q^{97} -0.911603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{3} + 4 q^{7} + 3 q^{9}+O(q^{10}) \) 3 * q - 2 * q^3 + 4 * q^7 + 3 * q^9	\( 3 q - 2 q^{3} + 4 q^{7} + 3 q^{9} + 2 q^{11} + 8 q^{13} + 4 q^{17} + 2 q^{19} - 4 q^{21} + 8 q^{23} - 8 q^{27} - 6 q^{29} - 8 q^{31} + 20 q^{33} + 8 q^{37} + 4 q^{39} + 2 q^{41} - 14 q^{43} + 4 q^{47} + 3 q^{49} - 24 q^{51} + 16 q^{53} - 4 q^{57} - 2 q^{59} - 10 q^{61} + 24 q^{63} - 10 q^{67} - 4 q^{69} + 12 q^{71} + 20 q^{73} - 16 q^{79} - q^{81} - 30 q^{83} + 4 q^{87} - 10 q^{89} + 28 q^{91} + 24 q^{93} + 28 q^{97} - 22 q^{99}+O(q^{100}) \) 3 * q - 2 * q^3 + 4 * q^7 + 3 * q^9 + 2 * q^11 + 8 * q^13 + 4 * q^17 + 2 * q^19 - 4 * q^21 + 8 * q^23 - 8 * q^27 - 6 * q^29 - 8 * q^31 + 20 * q^33 + 8 * q^37 + 4 * q^39 + 2 * q^41 - 14 * q^43 + 4 * q^47 + 3 * q^49 - 24 * q^51 + 16 * q^53 - 4 * q^57 - 2 * q^59 - 10 * q^61 + 24 * q^63 - 10 * q^67 - 4 * q^69 + 12 * q^71 + 20 * q^73 - 16 * q^79 - q^81 - 30 * q^83 + 4 * q^87 - 10 * q^89 + 28 * q^91 + 24 * q^93 + 28 * q^97 - 22 * q^99

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