LMFDB - Embedded newform 3200.2.a.bv.1.1

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			1.1
Root			$2.17009$ 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)

$f(q)$	$=$	$q-1.70928 q^{3} +2.63090 q^{7} -0.0783777 q^{9} +O(q^{10})$	$q-1.70928 q^{3} +2.63090 q^{7} -0.0783777 q^{9} +5.41855 q^{11} +6.34017 q^{13} +3.41855 q^{17} +3.26180 q^{19} -4.49693 q^{21} +1.36910 q^{23} +5.26180 q^{27} +2.00000 q^{29} -4.68035 q^{31} -9.26180 q^{33} -5.75872 q^{37} -10.8371 q^{39} -7.75872 q^{41} +4.44748 q^{43} +4.78765 q^{47} -0.0783777 q^{49} -5.84324 q^{51} +1.65983 q^{53} -5.57531 q^{57} -3.26180 q^{59} -2.49693 q^{61} -0.206204 q^{63} +7.86603 q^{67} -2.34017 q^{69} -6.15676 q^{71} -13.5753 q^{73} +14.2557 q^{77} +12.6803 q^{79} -8.75872 q^{81} +14.9711 q^{83} -3.41855 q^{87} -8.52359 q^{89} +16.6803 q^{91} +8.00000 q^{93} -4.58145 q^{97} -0.424694 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.70928	−0.986851	−0.493425	−	0.869788i	$-0.664255\pi$
$3$	−1.70928	−0.986851	−0.493425	+	0.869788i	$0.664255\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	2.63090	0.994386	0.497193	−	0.867640i	$-0.334364\pi$
$7$	2.63090	0.994386	0.497193	+	0.867640i	$0.334364\pi$
$8$	0	0
$9$	−0.0783777	−0.0261259
$10$	0	0
$11$	5.41855	1.63375	0.816877	−	0.576812i	$-0.195703\pi$
$11$	5.41855	1.63375	0.816877	+	0.576812i	$0.195703\pi$
$12$	0	0
$13$	6.34017	1.75845	0.879224	−	0.476409i	$-0.158062\pi$
$13$	6.34017	1.75845	0.879224	+	0.476409i	$0.158062\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	3.41855	0.829120	0.414560	−	0.910022i	$-0.363935\pi$
$17$	3.41855	0.829120	0.414560	+	0.910022i	$0.363935\pi$
$18$	0	0
$19$	3.26180	0.748307	0.374154	−	0.927367i	$-0.377933\pi$
$19$	3.26180	0.748307	0.374154	+	0.927367i	$0.377933\pi$
$20$	0	0
$21$	−4.49693	−0.981310
$22$	0	0
$23$	1.36910	0.285478	0.142739	−	0.989760i	$-0.454409\pi$
$23$	1.36910	0.285478	0.142739	+	0.989760i	$0.454409\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	5.26180	1.01263
$28$	0	0
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	−4.68035	−0.840615	−0.420307	−	0.907382i	$-0.638078\pi$
$31$	−4.68035	−0.840615	−0.420307	+	0.907382i	$0.638078\pi$
$32$	0	0
$33$	−9.26180	−1.61227
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−5.75872	−0.946728	−0.473364	−	0.880867i	$-0.656961\pi$
$37$	−5.75872	−0.946728	−0.473364	+	0.880867i	$0.656961\pi$
$38$	0	0
$39$	−10.8371	−1.73533
$40$	0	0
$41$	−7.75872	−1.21171	−0.605855	−	0.795575i	$-0.707169\pi$
$41$	−7.75872	−1.21171	−0.605855	+	0.795575i	$0.707169\pi$
$42$	0	0
$43$	4.44748	0.678234	0.339117	−	0.940744i	$-0.389872\pi$
$43$	4.44748	0.678234	0.339117	+	0.940744i	$0.389872\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	4.78765	0.698351	0.349175	−	0.937057i	$-0.386462\pi$
$47$	4.78765	0.698351	0.349175	+	0.937057i	$0.386462\pi$
$48$	0	0
$49$	−0.0783777	−0.0111968
$50$	0	0
$51$	−5.84324	−0.818218
$52$	0	0
$53$	1.65983	0.227995	0.113997	−	0.993481i	$-0.463634\pi$
$53$	1.65983	0.227995	0.113997	+	0.993481i	$0.463634\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−5.57531	−0.738467
$58$	0	0
$59$	−3.26180	−0.424650	−0.212325	−	0.977199i	$-0.568103\pi$
$59$	−3.26180	−0.424650	−0.212325	+	0.977199i	$0.568103\pi$
$60$	0	0
$61$	−2.49693	−0.319699	−0.159849	−	0.987141i	$-0.551101\pi$
$61$	−2.49693	−0.319699	−0.159849	+	0.987141i	$0.551101\pi$
$62$	0	0
$63$	−0.206204	−0.0259792
$64$	0	0
$65$	0	0
$66$	0	0
$67$	7.86603	0.960989	0.480494	−	0.876998i	$-0.340457\pi$
$67$	7.86603	0.960989	0.480494	+	0.876998i	$0.340457\pi$
$68$	0	0
$69$	−2.34017	−0.281724
$70$	0	0
$71$	−6.15676	−0.730672	−0.365336	−	0.930876i	$-0.619046\pi$
$71$	−6.15676	−0.730672	−0.365336	+	0.930876i	$0.619046\pi$
$72$	0	0
$73$	−13.5753	−1.58887	−0.794435	−	0.607350i	$-0.792233\pi$
$73$	−13.5753	−1.58887	−0.794435	+	0.607350i	$0.792233\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	14.2557	1.62458
$78$	0	0
$79$	12.6803	1.42665	0.713325	−	0.700833i	$-0.247188\pi$
$79$	12.6803	1.42665	0.713325	+	0.700833i	$0.247188\pi$
$80$	0	0
$81$	−8.75872	−0.973192
$82$	0	0
$83$	14.9711	1.64329	0.821644	−	0.570001i	$-0.193057\pi$
$83$	14.9711	1.64329	0.821644	+	0.570001i	$0.193057\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−3.41855	−0.366507
$88$	0	0
$89$	−8.52359	−0.903499	−0.451749	−	0.892145i	$-0.649200\pi$
$89$	−8.52359	−0.903499	−0.451749	+	0.892145i	$0.649200\pi$
$90$	0	0
$91$	16.6803	1.74858
$92$	0	0
$93$	8.00000	0.829561
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−4.58145	−0.465176	−0.232588	−	0.972575i	$-0.574719\pi$
$97$	−4.58145	−0.465176	−0.232588	+	0.972575i	$0.574719\pi$
$98$	0	0
$99$	−0.424694	−0.0426833
$100$	0	0
$101$	2.31351	0.230203	0.115101	−	0.993354i	$-0.463281\pi$
$101$	2.31351	0.230203	0.115101	+	0.993354i	$0.463281\pi$
$102$	0	0
$103$	16.2062	1.59684	0.798422	−	0.602098i	$-0.205668\pi$
$103$	16.2062	1.59684	0.798422	+	0.602098i	$0.205668\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−15.6514	−1.51308	−0.756540	−	0.653948i	$-0.773112\pi$
$107$	−15.6514	−1.51308	−0.756540	+	0.653948i	$0.773112\pi$
$108$	0	0
$109$	−12.3402	−1.18197	−0.590987	−	0.806681i	$-0.701262\pi$
$109$	−12.3402	−1.18197	−0.590987	+	0.806681i	$0.701262\pi$
$110$	0	0
$111$	9.84324	0.934279
$112$	0	0
$113$	9.36069	0.880580	0.440290	−	0.897856i	$-0.354876\pi$
$113$	9.36069	0.880580	0.440290	+	0.897856i	$0.354876\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−0.496928	−0.0459411
$118$	0	0
$119$	8.99386	0.824466
$120$	0	0
$121$	18.3607	1.66915
$122$	0	0
$123$	13.2618	1.19578
$124$	0	0
$125$	0	0
$126$	0	0
$127$	1.95055	0.173083	0.0865417	−	0.996248i	$-0.472418\pi$
$127$	1.95055	0.173083	0.0865417	+	0.996248i	$0.472418\pi$
$128$	0	0
$129$	−7.60197	−0.669316
$130$	0	0
$131$	−15.5753	−1.36082	−0.680410	−	0.732831i	$-0.738198\pi$
$131$	−15.5753	−1.36082	−0.680410	+	0.732831i	$0.738198\pi$
$132$	0	0
$133$	8.58145	0.744106
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−15.2039	−1.29896	−0.649480	−	0.760379i	$-0.725013\pi$
$137$	−15.2039	−1.29896	−0.649480	+	0.760379i	$0.725013\pi$
$138$	0	0
$139$	2.58145	0.218956	0.109478	−	0.993989i	$-0.465082\pi$
$139$	2.58145	0.218956	0.109478	+	0.993989i	$0.465082\pi$
$140$	0	0
$141$	−8.18342	−0.689168
$142$	0	0
$143$	34.3545	2.87287
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0.133969	0.0110496
$148$	0	0
$149$	−1.81658	−0.148820	−0.0744101	−	0.997228i	$-0.523707\pi$
$149$	−1.81658	−0.148820	−0.0744101	+	0.997228i	$0.523707\pi$
$150$	0	0
$151$	−5.16290	−0.420151	−0.210075	−	0.977685i	$-0.567371\pi$
$151$	−5.16290	−0.420151	−0.210075	+	0.977685i	$0.567371\pi$
$152$	0	0
$153$	−0.267938	−0.0216615
$154$	0	0
$155$	0	0
$156$	0	0
$157$	13.7587	1.09807	0.549033	−	0.835801i	$-0.314996\pi$
$157$	13.7587	1.09807	0.549033	+	0.835801i	$0.314996\pi$
$158$	0	0
$159$	−2.83710	−0.224997
$160$	0	0
$161$	3.60197	0.283875
$162$	0	0
$163$	6.29072	0.492728	0.246364	−	0.969177i	$-0.420764\pi$
$163$	6.29072	0.492728	0.246364	+	0.969177i	$0.420764\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−3.89269	−0.301226	−0.150613	−	0.988593i	$-0.548125\pi$
$167$	−3.89269	−0.301226	−0.150613	+	0.988593i	$0.548125\pi$
$168$	0	0
$169$	27.1978	2.09214
$170$	0	0
$171$	−0.255652	−0.0195502
$172$	0	0
$173$	−1.44521	−0.109877	−0.0549387	−	0.998490i	$-0.517496\pi$
$173$	−1.44521	−0.109877	−0.0549387	+	0.998490i	$0.517496\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	5.57531	0.419066
$178$	0	0
$179$	−11.9421	−0.892598	−0.446299	−	0.894884i	$-0.647258\pi$
$179$	−11.9421	−0.892598	−0.446299	+	0.894884i	$0.647258\pi$
$180$	0	0
$181$	15.3607	1.14175	0.570876	−	0.821037i	$-0.306604\pi$
$181$	15.3607	1.14175	0.570876	+	0.821037i	$0.306604\pi$
$182$	0	0
$183$	4.26794	0.315495
$184$	0	0
$185$	0	0
$186$	0	0
$187$	18.5236	1.35458
$188$	0	0
$189$	13.8432	1.00695
$190$	0	0
$191$	25.3607	1.83504	0.917518	−	0.397695i	$-0.130190\pi$
$191$	25.3607	1.83504	0.917518	+	0.397695i	$0.130190\pi$
$192$	0	0
$193$	−4.58145	−0.329780	−0.164890	−	0.986312i	$-0.552727\pi$
$193$	−4.58145	−0.329780	−0.164890	+	0.986312i	$0.552727\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	16.8638	1.20149	0.600747	−	0.799439i	$-0.294870\pi$
$197$	16.8638	1.20149	0.600747	+	0.799439i	$0.294870\pi$
$198$	0	0
$199$	−9.84324	−0.697769	−0.348885	−	0.937166i	$-0.613439\pi$
$199$	−9.84324	−0.697769	−0.348885	+	0.937166i	$0.613439\pi$
$200$	0	0
$201$	−13.4452	−0.948352
$202$	0	0
$203$	5.26180	0.369306
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−0.107307	−0.00745836
$208$	0	0
$209$	17.6742	1.22255
$210$	0	0
$211$	−15.5753	−1.07225	−0.536124	−	0.844139i	$-0.680112\pi$
$211$	−15.5753	−1.07225	−0.536124	+	0.844139i	$0.680112\pi$
$212$	0	0
$213$	10.5236	0.721065
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−12.3135	−0.835896
$218$	0	0
$219$	23.2039	1.56798
$220$	0	0
$221$	21.6742	1.45796
$222$	0	0
$223$	−16.9854	−1.13743	−0.568715	−	0.822535i	$-0.692559\pi$
$223$	−16.9854	−1.13743	−0.568715	+	0.822535i	$0.692559\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−19.9649	−1.32512	−0.662559	−	0.749009i	$-0.730530\pi$
$227$	−19.9649	−1.32512	−0.662559	+	0.749009i	$0.730530\pi$
$228$	0	0
$229$	23.6742	1.56444	0.782218	−	0.623005i	$-0.214088\pi$
$229$	23.6742	1.56444	0.782218	+	0.623005i	$0.214088\pi$
$230$	0	0
$231$	−24.3668	−1.60322
$232$	0	0
$233$	−13.5753	−0.889348	−0.444674	−	0.895693i	$-0.646680\pi$
$233$	−13.5753	−0.889348	−0.444674	+	0.895693i	$0.646680\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−21.6742	−1.40789
$238$	0	0
$239$	−8.36683	−0.541206	−0.270603	−	0.962691i	$-0.587223\pi$
$239$	−8.36683	−0.541206	−0.270603	+	0.962691i	$0.587223\pi$
$240$	0	0
$241$	9.91548	0.638712	0.319356	−	0.947635i	$-0.396533\pi$
$241$	9.91548	0.638712	0.319356	+	0.947635i	$0.396533\pi$
$242$	0	0
$243$	−0.814315	−0.0522383
$244$	0	0
$245$	0	0
$246$	0	0
$247$	20.6803	1.31586
$248$	0	0
$249$	−25.5897	−1.62168
$250$	0	0
$251$	−17.6163	−1.11193	−0.555967	−	0.831204i	$-0.687652\pi$
$251$	−17.6163	−1.11193	−0.555967	+	0.831204i	$0.687652\pi$
$252$	0	0
$253$	7.41855	0.466400
$254$	0	0
$255$	0	0
$256$	0	0
$257$	3.68649	0.229957	0.114978	−	0.993368i	$-0.463320\pi$
$257$	3.68649	0.229957	0.114978	+	0.993368i	$0.463320\pi$
$258$	0	0
$259$	−15.1506	−0.941413
$260$	0	0
$261$	−0.156755	−0.00970292
$262$	0	0
$263$	−0.107307	−0.00661684	−0.00330842	−	0.999995i	$-0.501053\pi$
$263$	−0.107307	−0.00661684	−0.00330842	+	0.999995i	$0.501053\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	14.5692	0.891618
$268$	0	0
$269$	3.85762	0.235203	0.117602	−	0.993061i	$-0.462479\pi$
$269$	3.85762	0.235203	0.117602	+	0.993061i	$0.462479\pi$
$270$	0	0
$271$	21.3074	1.29433	0.647165	−	0.762350i	$-0.275954\pi$
$271$	21.3074	1.29433	0.647165	+	0.762350i	$0.275954\pi$
$272$	0	0
$273$	−28.5113	−1.72558
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−1.44521	−0.0868344	−0.0434172	−	0.999057i	$-0.513824\pi$
$277$	−1.44521	−0.0868344	−0.0434172	+	0.999057i	$0.513824\pi$
$278$	0	0
$279$	0.366835	0.0219618
$280$	0	0
$281$	12.4391	0.742053	0.371026	−	0.928622i	$-0.379006\pi$
$281$	12.4391	0.742053	0.371026	+	0.928622i	$0.379006\pi$
$282$	0	0
$283$	6.29072	0.373945	0.186972	−	0.982365i	$-0.440133\pi$
$283$	6.29072	0.373945	0.186972	+	0.982365i	$0.440133\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−20.4124	−1.20491
$288$	0	0
$289$	−5.31351	−0.312559
$290$	0	0
$291$	7.83096	0.459059
$292$	0	0
$293$	−1.07838	−0.0629995	−0.0314998	−	0.999504i	$-0.510028\pi$
$293$	−1.07838	−0.0629995	−0.0314998	+	0.999504i	$0.510028\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	28.5113	1.65439
$298$	0	0
$299$	8.68035	0.501997
$300$	0	0
$301$	11.7009	0.674427
$302$	0	0
$303$	−3.95443	−0.227176
$304$	0	0
$305$	0	0
$306$	0	0
$307$	25.2267	1.43977	0.719883	−	0.694096i	$-0.244196\pi$
$307$	25.2267	1.43977	0.719883	+	0.694096i	$0.244196\pi$
$308$	0	0
$309$	−27.7009	−1.57585
$310$	0	0
$311$	−18.8371	−1.06815	−0.534077	−	0.845436i	$-0.679341\pi$
$311$	−18.8371	−1.06815	−0.534077	+	0.845436i	$0.679341\pi$
$312$	0	0
$313$	−15.2039	−0.859377	−0.429689	−	0.902977i	$-0.641377\pi$
$313$	−15.2039	−0.859377	−0.429689	+	0.902977i	$0.641377\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−16.8638	−0.947163	−0.473582	−	0.880750i	$-0.657039\pi$
$317$	−16.8638	−0.947163	−0.473582	+	0.880750i	$0.657039\pi$
$318$	0	0
$319$	10.8371	0.606761
$320$	0	0
$321$	26.7526	1.49318
$322$	0	0
$323$	11.1506	0.620437
$324$	0	0
$325$	0	0
$326$	0	0
$327$	21.0928	1.16643
$328$	0	0
$329$	12.5958	0.694430
$330$	0	0
$331$	23.5753	1.29582	0.647908	−	0.761719i	$-0.275644\pi$
$331$	23.5753	1.29582	0.647908	+	0.761719i	$0.275644\pi$
$332$	0	0
$333$	0.451356	0.0247341
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−14.8371	−0.808228	−0.404114	−	0.914709i	$-0.632420\pi$
$337$	−14.8371	−0.808228	−0.404114	+	0.914709i	$0.632420\pi$
$338$	0	0
$339$	−16.0000	−0.869001
$340$	0	0
$341$	−25.3607	−1.37336
$342$	0	0
$343$	−18.6225	−1.00552
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−0.133969	−0.00719184	−0.00359592	−	0.999994i	$-0.501145\pi$
$347$	−0.133969	−0.00719184	−0.00359592	+	0.999994i	$0.501145\pi$
$348$	0	0
$349$	22.3135	1.19441	0.597207	−	0.802087i	$-0.296277\pi$
$349$	22.3135	1.19441	0.597207	+	0.802087i	$0.296277\pi$
$350$	0	0
$351$	33.3607	1.78066
$352$	0	0
$353$	22.8371	1.21550	0.607748	−	0.794130i	$-0.292073\pi$
$353$	22.8371	1.21550	0.607748	+	0.794130i	$0.292073\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−15.3730	−0.813624
$358$	0	0
$359$	31.8843	1.68279	0.841394	−	0.540422i	$-0.181735\pi$
$359$	31.8843	1.68279	0.841394	+	0.540422i	$0.181735\pi$
$360$	0	0
$361$	−8.36069	−0.440036
$362$	0	0
$363$	−31.3835	−1.64721
$364$	0	0
$365$	0	0
$366$	0	0
$367$	30.4619	1.59010	0.795048	−	0.606547i	$-0.207446\pi$
$367$	30.4619	1.59010	0.795048	+	0.606547i	$0.207446\pi$
$368$	0	0
$369$	0.608111	0.0316570
$370$	0	0
$371$	4.36683	0.226715
$372$	0	0
$373$	10.0722	0.521521	0.260760	−	0.965404i	$-0.416027\pi$
$373$	10.0722	0.521521	0.260760	+	0.965404i	$0.416027\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	12.6803	0.653071
$378$	0	0
$379$	−14.7792	−0.759159	−0.379579	−	0.925159i	$-0.623931\pi$
$379$	−14.7792	−0.759159	−0.379579	+	0.925159i	$0.623931\pi$
$380$	0	0
$381$	−3.33403	−0.170808
$382$	0	0
$383$	−14.4619	−0.738966	−0.369483	−	0.929237i	$-0.620465\pi$
$383$	−14.4619	−0.738966	−0.369483	+	0.929237i	$0.620465\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−0.348583	−0.0177195
$388$	0	0
$389$	−3.17727	−0.161094	−0.0805471	−	0.996751i	$-0.525667\pi$
$389$	−3.17727	−0.161094	−0.0805471	+	0.996751i	$0.525667\pi$
$390$	0	0
$391$	4.68035	0.236695
$392$	0	0
$393$	26.6225	1.34293
$394$	0	0
$395$	0	0
$396$	0	0
$397$	10.8227	0.543177	0.271589	−	0.962413i	$-0.412451\pi$
$397$	10.8227	0.543177	0.271589	+	0.962413i	$0.412451\pi$
$398$	0	0
$399$	−14.6681	−0.734321
$400$	0	0
$401$	−12.5236	−0.625398	−0.312699	−	0.949852i	$-0.601233\pi$
$401$	−12.5236	−0.625398	−0.312699	+	0.949852i	$0.601233\pi$
$402$	0	0
$403$	−29.6742	−1.47818
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−31.2039	−1.54672
$408$	0	0
$409$	−13.2885	−0.657072	−0.328536	−	0.944491i	$-0.606555\pi$
$409$	−13.2885	−0.657072	−0.328536	+	0.944491i	$0.606555\pi$
$410$	0	0
$411$	25.9877	1.28188
$412$	0	0
$413$	−8.58145	−0.422266
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−4.41241	−0.216077
$418$	0	0
$419$	−0.255652	−0.0124894	−0.00624471	−	0.999981i	$-0.501988\pi$
$419$	−0.255652	−0.0124894	−0.00624471	+	0.999981i	$0.501988\pi$
$420$	0	0
$421$	−2.49693	−0.121693	−0.0608464	−	0.998147i	$-0.519380\pi$
$421$	−2.49693	−0.121693	−0.0608464	+	0.998147i	$0.519380\pi$
$422$	0	0
$423$	−0.375245	−0.0182451
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−6.56916	−0.317904
$428$	0	0
$429$	−58.7214	−2.83510
$430$	0	0
$431$	−0.993857	−0.0478724	−0.0239362	−	0.999713i	$-0.507620\pi$
$431$	−0.993857	−0.0478724	−0.0239362	+	0.999713i	$0.507620\pi$
$432$	0	0
$433$	−17.6286	−0.847178	−0.423589	−	0.905855i	$-0.639230\pi$
$433$	−17.6286	−0.847178	−0.423589	+	0.905855i	$0.639230\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	4.46573	0.213625
$438$	0	0
$439$	−40.5113	−1.93350	−0.966750	−	0.255725i	$-0.917686\pi$
$439$	−40.5113	−1.93350	−0.966750	+	0.255725i	$0.917686\pi$
$440$	0	0
$441$	0.00614307	0.000292527 0
$442$	0	0
$443$	−17.7093	−0.841393	−0.420697	−	0.907201i	$-0.638214\pi$
$443$	−17.7093	−0.841393	−0.420697	+	0.907201i	$0.638214\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	3.10504	0.146863
$448$	0	0
$449$	−1.28846	−0.0608061	−0.0304030	−	0.999538i	$-0.509679\pi$
$449$	−1.28846	−0.0608061	−0.0304030	+	0.999538i	$0.509679\pi$
$450$	0	0
$451$	−42.0410	−1.97964
$452$	0	0
$453$	8.82482	0.414626
$454$	0	0
$455$	0	0
$456$	0	0
$457$	26.3545	1.23281	0.616407	−	0.787428i	$-0.288588\pi$
$457$	26.3545	1.23281	0.616407	+	0.787428i	$0.288588\pi$
$458$	0	0
$459$	17.9877	0.839595
$460$	0	0
$461$	−41.0349	−1.91119	−0.955593	−	0.294690i	$-0.904783\pi$
$461$	−41.0349	−1.91119	−0.955593	+	0.294690i	$0.904783\pi$
$462$	0	0
$463$	28.7708	1.33709	0.668547	−	0.743670i	$-0.266917\pi$
$463$	28.7708	1.33709	0.668547	+	0.743670i	$0.266917\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−5.12783	−0.237287	−0.118644	−	0.992937i	$-0.537855\pi$
$467$	−5.12783	−0.237287	−0.118644	+	0.992937i	$0.537855\pi$
$468$	0	0
$469$	20.6947	0.955593
$470$	0	0
$471$	−23.5174	−1.08363
$472$	0	0
$473$	24.0989	1.10807
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−0.130094	−0.00595657
$478$	0	0
$479$	13.6742	0.624790	0.312395	−	0.949952i	$-0.398869\pi$
$479$	13.6742	0.624790	0.312395	+	0.949952i	$0.398869\pi$
$480$	0	0
$481$	−36.5113	−1.66477
$482$	0	0
$483$	−6.15676	−0.280142
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−8.51971	−0.386065	−0.193033	−	0.981192i	$-0.561832\pi$
$487$	−8.51971	−0.386065	−0.193033	+	0.981192i	$0.561832\pi$
$488$	0	0
$489$	−10.7526	−0.486249
$490$	0	0
$491$	−4.73820	−0.213832	−0.106916	−	0.994268i	$-0.534098\pi$
$491$	−4.73820	−0.213832	−0.106916	+	0.994268i	$0.534098\pi$
$492$	0	0
$493$	6.83710	0.307928
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−16.1978	−0.726570
$498$	0	0
$499$	11.0928	0.496580	0.248290	−	0.968686i	$-0.420131\pi$
$499$	11.0928	0.496580	0.248290	+	0.968686i	$0.420131\pi$
$500$	0	0
$501$	6.65368	0.297265
$502$	0	0
$503$	−8.42082	−0.375466	−0.187733	−	0.982220i	$-0.560114\pi$
$503$	−8.42082	−0.375466	−0.187733	+	0.982220i	$0.560114\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−46.4885	−2.06463
$508$	0	0
$509$	26.0000	1.15243	0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000	1.15243	0.576215	+	0.817298i	$0.304529\pi$
$510$	0	0
$511$	−35.7152	−1.57995
$512$	0	0
$513$	17.1629	0.757760
$514$	0	0
$515$	0	0
$516$	0	0
$517$	25.9421	1.14093
$518$	0	0
$519$	2.47027	0.108433
$520$	0	0
$521$	−10.3135	−0.451843	−0.225922	−	0.974145i	$-0.572539\pi$
$521$	−10.3135	−0.451843	−0.225922	+	0.974145i	$0.572539\pi$
$522$	0	0
$523$	16.2784	0.711806	0.355903	−	0.934523i	$-0.384173\pi$
$523$	16.2784	0.711806	0.355903	+	0.934523i	$0.384173\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−16.0000	−0.696971
$528$	0	0
$529$	−21.1256	−0.918503
$530$	0	0
$531$	0.255652	0.0110944
$532$	0	0
$533$	−49.1917	−2.13073
$534$	0	0
$535$	0	0
$536$	0	0
$537$	20.4124	0.880860
$538$	0	0
$539$	−0.424694	−0.0182929
$540$	0	0
$541$	−3.36069	−0.144487	−0.0722437	−	0.997387i	$-0.523016\pi$
$541$	−3.36069	−0.144487	−0.0722437	+	0.997387i	$0.523016\pi$
$542$	0	0
$543$	−26.2557	−1.12674
$544$	0	0
$545$	0	0
$546$	0	0
$547$	1.51148	0.0646263	0.0323132	−	0.999478i	$-0.489713\pi$
$547$	1.51148	0.0646263	0.0323132	+	0.999478i	$0.489713\pi$
$548$	0	0
$549$	0.195704	0.00835243
$550$	0	0
$551$	6.52359	0.277914
$552$	0	0
$553$	33.3607	1.41864
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−36.2290	−1.53507	−0.767536	−	0.641006i	$-0.778517\pi$
$557$	−36.2290	−1.53507	−0.767536	+	0.641006i	$0.778517\pi$
$558$	0	0
$559$	28.1978	1.19264
$560$	0	0
$561$	−31.6619	−1.33677
$562$	0	0
$563$	2.17501	0.0916656	0.0458328	−	0.998949i	$-0.485406\pi$
$563$	2.17501	0.0916656	0.0458328	+	0.998949i	$0.485406\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−23.0433	−0.967728
$568$	0	0
$569$	33.1194	1.38844	0.694219	−	0.719764i	$-0.255750\pi$
$569$	33.1194	1.38844	0.694219	+	0.719764i	$0.255750\pi$
$570$	0	0
$571$	18.4657	0.772767	0.386383	−	0.922338i	$-0.373724\pi$
$571$	18.4657	0.772767	0.386383	+	0.922338i	$0.373724\pi$
$572$	0	0
$573$	−43.3484	−1.81091
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−14.2101	−0.591573	−0.295787	−	0.955254i	$-0.595582\pi$
$577$	−14.2101	−0.591573	−0.295787	+	0.955254i	$0.595582\pi$
$578$	0	0
$579$	7.83096	0.325444
$580$	0	0
$581$	39.3874	1.63406
$582$	0	0
$583$	8.99386	0.372487
$584$	0	0
$585$	0	0
$586$	0	0
$587$	11.7503	0.484987	0.242494	−	0.970153i	$-0.422035\pi$
$587$	11.7503	0.484987	0.242494	+	0.970153i	$0.422035\pi$
$588$	0	0
$589$	−15.2663	−0.629038
$590$	0	0
$591$	−28.8248	−1.18569
$592$	0	0
$593$	8.00000	0.328521	0.164260	−	0.986417i	$-0.447476\pi$
$593$	8.00000	0.328521	0.164260	+	0.986417i	$0.447476\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	16.8248	0.688594
$598$	0	0
$599$	−20.5646	−0.840248	−0.420124	−	0.907467i	$-0.638013\pi$
$599$	−20.5646	−0.840248	−0.420124	+	0.907467i	$0.638013\pi$
$600$	0	0
$601$	−8.60811	−0.351132	−0.175566	−	0.984468i	$-0.556176\pi$
$601$	−8.60811	−0.351132	−0.175566	+	0.984468i	$0.556176\pi$
$602$	0	0
$603$	−0.616522	−0.0251067
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−0.259528	−0.0105339	−0.00526695	−	0.999986i	$-0.501677\pi$
$607$	−0.259528	−0.0105339	−0.00526695	+	0.999986i	$0.501677\pi$
$608$	0	0
$609$	−8.99386	−0.364449
$610$	0	0
$611$	30.3545	1.22801
$612$	0	0
$613$	−47.1650	−1.90498	−0.952488	−	0.304576i	$-0.901485\pi$
$613$	−47.1650	−1.90498	−0.952488	+	0.304576i	$0.901485\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−40.2967	−1.62228	−0.811142	−	0.584849i	$-0.801154\pi$
$617$	−40.2967	−1.62228	−0.811142	+	0.584849i	$0.801154\pi$
$618$	0	0
$619$	−30.6102	−1.23033	−0.615164	−	0.788399i	$-0.710910\pi$
$619$	−30.6102	−1.23033	−0.615164	+	0.788399i	$0.710910\pi$
$620$	0	0
$621$	7.20394	0.289084
$622$	0	0
$623$	−22.4247	−0.898426
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−30.2101	−1.20647
$628$	0	0
$629$	−19.6865	−0.784952
$630$	0	0
$631$	2.21008	0.0879819	0.0439909	−	0.999032i	$-0.485993\pi$
$631$	2.21008	0.0879819	0.0439909	+	0.999032i	$0.485993\pi$
$632$	0	0
$633$	26.6225	1.05815
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−0.496928	−0.0196890
$638$	0	0
$639$	0.482553	0.0190895
$640$	0	0
$641$	7.92777	0.313128	0.156564	−	0.987668i	$-0.449958\pi$
$641$	7.92777	0.313128	0.156564	+	0.987668i	$0.449958\pi$
$642$	0	0
$643$	5.18115	0.204325	0.102162	−	0.994768i	$-0.467424\pi$
$643$	5.18115	0.204325	0.102162	+	0.994768i	$0.467424\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−12.2062	−0.479875	−0.239938	−	0.970788i	$-0.577127\pi$
$647$	−12.2062	−0.479875	−0.239938	+	0.970788i	$0.577127\pi$
$648$	0	0
$649$	−17.6742	−0.693773
$650$	0	0
$651$	21.0472	0.824904
$652$	0	0
$653$	−32.4969	−1.27170	−0.635852	−	0.771811i	$-0.719351\pi$
$653$	−32.4969	−1.27170	−0.635852	+	0.771811i	$0.719351\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	1.06400	0.0415107
$658$	0	0
$659$	29.4186	1.14598	0.572992	−	0.819561i	$-0.305783\pi$
$659$	29.4186	1.14598	0.572992	+	0.819561i	$0.305783\pi$
$660$	0	0
$661$	−26.0677	−1.01392	−0.506958	−	0.861971i	$-0.669230\pi$
$661$	−26.0677	−1.01392	−0.506958	+	0.861971i	$0.669230\pi$
$662$	0	0
$663$	−37.0472	−1.43879
$664$	0	0
$665$	0	0
$666$	0	0
$667$	2.73820	0.106024
$668$	0	0
$669$	29.0328	1.12247
$670$	0	0
$671$	−13.5297	−0.522310
$672$	0	0
$673$	9.62863	0.371156	0.185578	−	0.982629i	$-0.440584\pi$
$673$	9.62863	0.371156	0.185578	+	0.982629i	$0.440584\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−19.0205	−0.731018	−0.365509	−	0.930808i	$-0.619105\pi$
$677$	−19.0205	−0.731018	−0.365509	+	0.930808i	$0.619105\pi$
$678$	0	0
$679$	−12.0533	−0.462564
$680$	0	0
$681$	34.1256	1.30769
$682$	0	0
$683$	17.4947	0.669415	0.334707	−	0.942322i	$-0.391363\pi$
$683$	17.4947	0.669415	0.334707	+	0.942322i	$0.391363\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−40.4657	−1.54386
$688$	0	0
$689$	10.5236	0.400917
$690$	0	0
$691$	−16.3090	−0.620423	−0.310211	−	0.950668i	$-0.600400\pi$
$691$	−16.3090	−0.620423	−0.310211	+	0.950668i	$0.600400\pi$
$692$	0	0
$693$	−1.11733	−0.0424437
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−26.5236	−1.00465
$698$	0	0
$699$	23.2039	0.877653
$700$	0	0
$701$	12.9672	0.489764	0.244882	−	0.969553i	$-0.421251\pi$
$701$	12.9672	0.489764	0.244882	+	0.969553i	$0.421251\pi$
$702$	0	0
$703$	−18.7838	−0.708444
$704$	0	0
$705$	0	0
$706$	0	0
$707$	6.08661	0.228911
$708$	0	0
$709$	−7.36069	−0.276437	−0.138218	−	0.990402i	$-0.544138\pi$
$709$	−7.36069	−0.276437	−0.138218	+	0.990402i	$0.544138\pi$
$710$	0	0
$711$	−0.993857	−0.0372725
$712$	0	0
$713$	−6.40787	−0.239977
$714$	0	0
$715$	0	0
$716$	0	0
$717$	14.3012	0.534089
$718$	0	0
$719$	−19.3197	−0.720502	−0.360251	−	0.932856i	$-0.617309\pi$
$719$	−19.3197	−0.720502	−0.360251	+	0.932856i	$0.617309\pi$
$720$	0	0
$721$	42.6369	1.58788
$722$	0	0
$723$	−16.9483	−0.630313
$724$	0	0
$725$	0	0
$726$	0	0
$727$	21.1545	0.784577	0.392288	−	0.919842i	$-0.371684\pi$
$727$	21.1545	0.784577	0.392288	+	0.919842i	$0.371684\pi$
$728$	0	0
$729$	27.6681	1.02474
$730$	0	0
$731$	15.2039	0.562338
$732$	0	0
$733$	22.7526	0.840386	0.420193	−	0.907435i	$-0.361962\pi$
$733$	22.7526	0.840386	0.420193	+	0.907435i	$0.361962\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	42.6225	1.57002
$738$	0	0
$739$	28.4534	1.04668	0.523338	−	0.852125i	$-0.324686\pi$
$739$	28.4534	1.04668	0.523338	+	0.852125i	$0.324686\pi$
$740$	0	0
$741$	−35.3484	−1.29856
$742$	0	0
$743$	−3.79380	−0.139181	−0.0695904	−	0.997576i	$-0.522169\pi$
$743$	−3.79380	−0.139181	−0.0695904	+	0.997576i	$0.522169\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−1.17340	−0.0429324
$748$	0	0
$749$	−41.1773	−1.50458
$750$	0	0
$751$	17.3607	0.633501	0.316750	−	0.948509i	$-0.397408\pi$
$751$	17.3607	0.633501	0.316750	+	0.948509i	$0.397408\pi$
$752$	0	0
$753$	30.1112	1.09731
$754$	0	0
$755$	0	0
$756$	0	0
$757$	4.76487	0.173182	0.0865910	−	0.996244i	$-0.472403\pi$
$757$	4.76487	0.173182	0.0865910	+	0.996244i	$0.472403\pi$
$758$	0	0
$759$	−12.6803	−0.460267
$760$	0	0
$761$	−14.1978	−0.514670	−0.257335	−	0.966322i	$-0.582844\pi$
$761$	−14.1978	−0.514670	−0.257335	+	0.966322i	$0.582844\pi$
$762$	0	0
$763$	−32.4657	−1.17534
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−20.6803	−0.746724
$768$	0	0
$769$	54.7091	1.97286	0.986430	−	0.164181i	$-0.0524981\pi$
$769$	54.7091	1.97286	0.986430	+	0.164181i	$0.0524981\pi$
$770$	0	0
$771$	−6.30122	−0.226933
$772$	0	0
$773$	11.0205	0.396381	0.198190	−	0.980164i	$-0.436494\pi$
$773$	11.0205	0.396381	0.198190	+	0.980164i	$0.436494\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	25.8966	0.929034
$778$	0	0
$779$	−25.3074	−0.906731
$780$	0	0
$781$	−33.3607	−1.19374
$782$	0	0
$783$	10.5236	0.376082
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−33.6925	−1.20101	−0.600503	−	0.799622i	$-0.705033\pi$
$787$	−33.6925	−1.20101	−0.600503	+	0.799622i	$0.705033\pi$
$788$	0	0
$789$	0.183417	0.00652984
$790$	0	0
$791$	24.6270	0.875636
$792$	0	0
$793$	−15.8310	−0.562174
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−23.7009	−0.839528	−0.419764	−	0.907633i	$-0.637887\pi$
$797$	−23.7009	−0.839528	−0.419764	+	0.907633i	$0.637887\pi$
$798$	0	0
$799$	16.3668	0.579017
$800$	0	0
$801$	0.668060	0.0236047
$802$	0	0
$803$	−73.5585	−2.59582
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−6.59374	−0.232110
$808$	0	0
$809$	−33.0349	−1.16145	−0.580723	−	0.814102i	$-0.697230\pi$
$809$	−33.0349	−1.16145	−0.580723	+	0.814102i	$0.697230\pi$
$810$	0	0
$811$	−6.26794	−0.220097	−0.110049	−	0.993926i	$-0.535101\pi$
$811$	−6.26794	−0.220097	−0.110049	+	0.993926i	$0.535101\pi$
$812$	0	0
$813$	−36.4202	−1.27731
$814$	0	0
$815$	0	0
$816$	0	0
$817$	14.5068	0.507528
$818$	0	0
$819$	−1.30737	−0.0456831
$820$	0	0
$821$	15.0616	0.525652	0.262826	−	0.964843i	$-0.415345\pi$
$821$	15.0616	0.525652	0.262826	+	0.964843i	$0.415345\pi$
$822$	0	0
$823$	33.5669	1.17007	0.585034	−	0.811009i	$-0.301081\pi$
$823$	33.5669	1.17007	0.585034	+	0.811009i	$0.301081\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−10.6576	−0.370600	−0.185300	−	0.982682i	$-0.559326\pi$
$827$	−10.6576	−0.370600	−0.185300	+	0.982682i	$0.559326\pi$
$828$	0	0
$829$	52.4846	1.82287	0.911433	−	0.411447i	$-0.134977\pi$
$829$	52.4846	1.82287	0.911433	+	0.411447i	$0.134977\pi$
$830$	0	0
$831$	2.47027	0.0856926
$832$	0	0
$833$	−0.267938	−0.00928351
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−24.6270	−0.851234
$838$	0	0
$839$	18.2101	0.628682	0.314341	−	0.949310i	$-0.398217\pi$
$839$	18.2101	0.628682	0.314341	+	0.949310i	$0.398217\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	0	0
$843$	−21.2618	−0.732295
$844$	0	0
$845$	0	0
$846$	0	0
$847$	48.3051	1.65978
$848$	0	0
$849$	−10.7526	−0.369028
$850$	0	0
$851$	−7.88428	−0.270270
$852$	0	0
$853$	19.7542	0.676371	0.338185	−	0.941080i	$-0.390187\pi$
$853$	19.7542	0.676371	0.338185	+	0.941080i	$0.390187\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	48.9939	1.67360	0.836799	−	0.547510i	$-0.184424\pi$
$857$	48.9939	1.67360	0.836799	+	0.547510i	$0.184424\pi$
$858$	0	0
$859$	−24.3090	−0.829412	−0.414706	−	0.909956i	$-0.636115\pi$
$859$	−24.3090	−0.829412	−0.414706	+	0.909956i	$0.636115\pi$
$860$	0	0
$861$	34.8904	1.18906
$862$	0	0
$863$	−44.3584	−1.50998	−0.754989	−	0.655737i	$-0.772358\pi$
$863$	−44.3584	−1.50998	−0.754989	+	0.655737i	$0.772358\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	9.08225	0.308449
$868$	0	0
$869$	68.7091	2.33080
$870$	0	0
$871$	49.8720	1.68985
$872$	0	0
$873$	0.359084	0.0121531
$874$	0	0
$875$	0	0
$876$	0	0
$877$	37.9565	1.28170	0.640850	−	0.767666i	$-0.278582\pi$
$877$	37.9565	1.28170	0.640850	+	0.767666i	$0.278582\pi$
$878$	0	0
$879$	1.84324	0.0621711
$880$	0	0
$881$	25.0661	0.844498	0.422249	−	0.906480i	$-0.361241\pi$
$881$	25.0661	0.844498	0.422249	+	0.906480i	$0.361241\pi$
$882$	0	0
$883$	21.1278	0.711008	0.355504	−	0.934675i	$-0.384309\pi$
$883$	21.1278	0.711008	0.355504	+	0.934675i	$0.384309\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	36.1894	1.21512	0.607560	−	0.794274i	$-0.292148\pi$
$887$	36.1894	1.21512	0.607560	+	0.794274i	$0.292148\pi$
$888$	0	0
$889$	5.13170	0.172112
$890$	0	0
$891$	−47.4596	−1.58996
$892$	0	0
$893$	15.6163	0.522581
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−14.8371	−0.495396
$898$	0	0
$899$	−9.36069	−0.312197
$900$	0	0
$901$	5.67420	0.189035
$902$	0	0
$903$	−20.0000	−0.665558
$904$	0	0
$905$	0	0
$906$	0	0
$907$	35.2678	1.17105	0.585523	−	0.810656i	$-0.300889\pi$
$907$	35.2678	1.17105	0.585523	+	0.810656i	$0.300889\pi$
$908$	0	0
$909$	−0.181328	−0.00601426
$910$	0	0
$911$	−15.0061	−0.497176	−0.248588	−	0.968609i	$-0.579966\pi$
$911$	−15.0061	−0.497176	−0.248588	+	0.968609i	$0.579966\pi$
$912$	0	0
$913$	81.1215	2.68473
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−40.9770	−1.35318
$918$	0	0
$919$	32.8781	1.08455	0.542275	−	0.840201i	$-0.317563\pi$
$919$	32.8781	1.08455	0.542275	+	0.840201i	$0.317563\pi$
$920$	0	0
$921$	−43.1194	−1.42083
$922$	0	0
$923$	−39.0349	−1.28485
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−1.27021	−0.0417190
$928$	0	0
$929$	−30.2290	−0.991781	−0.495890	−	0.868385i	$-0.665158\pi$
$929$	−30.2290	−0.991781	−0.495890	+	0.868385i	$0.665158\pi$
$930$	0	0
$931$	−0.255652	−0.00837866
$932$	0	0
$933$	32.1978	1.05411
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−28.4124	−0.928193	−0.464096	−	0.885785i	$-0.653621\pi$
$937$	−28.4124	−0.928193	−0.464096	+	0.885785i	$0.653621\pi$
$938$	0	0
$939$	25.9877	0.848077
$940$	0	0
$941$	42.0821	1.37184	0.685918	−	0.727679i	$-0.259401\pi$
$941$	42.0821	1.37184	0.685918	+	0.727679i	$0.259401\pi$
$942$	0	0
$943$	−10.6225	−0.345916
$944$	0	0
$945$	0	0
$946$	0	0
$947$	22.2739	0.723805	0.361902	−	0.932216i	$-0.382127\pi$
$947$	22.2739	0.723805	0.361902	+	0.932216i	$0.382127\pi$
$948$	0	0
$949$	−86.0698	−2.79394
$950$	0	0
$951$	28.8248	0.934709
$952$	0	0
$953$	−14.6681	−0.475145	−0.237573	−	0.971370i	$-0.576352\pi$
$953$	−14.6681	−0.475145	−0.237573	+	0.971370i	$0.576352\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−18.5236	−0.598783
$958$	0	0
$959$	−40.0000	−1.29167
$960$	0	0
$961$	−9.09436	−0.293367
$962$	0	0
$963$	1.22672	0.0395306
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−0.403997	−0.0129917	−0.00649584	−	0.999979i	$-0.502068\pi$
$967$	−0.403997	−0.0129917	−0.00649584	+	0.999979i	$0.502068\pi$
$968$	0	0
$969$	−19.0595	−0.612278
$970$	0	0
$971$	−46.8326	−1.50293	−0.751464	−	0.659774i	$-0.770652\pi$
$971$	−46.8326	−1.50293	−0.751464	+	0.659774i	$0.770652\pi$
$972$	0	0
$973$	6.79153	0.217726
$974$	0	0
$975$	0	0
$976$	0	0
$977$	53.6041	1.71495	0.857473	−	0.514529i	$-0.172033\pi$
$977$	53.6041	1.71495	0.857473	+	0.514529i	$0.172033\pi$
$978$	0	0
$979$	−46.1855	−1.47610
$980$	0	0
$981$	0.967195	0.0308802
$982$	0	0
$983$	−19.9916	−0.637633	−0.318816	−	0.947817i	$-0.603285\pi$
$983$	−19.9916	−0.637633	−0.318816	+	0.947817i	$0.603285\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−21.5297	−0.685299
$988$	0	0
$989$	6.08906	0.193621
$990$	0	0
$991$	−24.6270	−0.782303	−0.391152	−	0.920326i	$-0.627923\pi$
$991$	−24.6270	−0.782303	−0.391152	+	0.920326i	$0.627923\pi$
$992$	0	0
$993$	−40.2967	−1.27878
$994$	0	0
$995$	0	0
$996$	0	0
$997$	20.9795	0.664427	0.332213	−	0.943204i	$-0.392205\pi$
$997$	20.9795	0.664427	0.332213	+	0.943204i	$0.392205\pi$
$998$	0	0
$999$	−30.3012	−0.958688

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3200.2.a.bv.1.1		3
4.3	odd	2		3200.2.a.bo.1.3		3
5.2	odd	4		640.2.c.d.129.5	yes	6
5.3	odd	4		640.2.c.d.129.2	yes	6
5.4	even	2		3200.2.a.bp.1.3		3
8.3	odd	2		3200.2.a.bt.1.1		3
8.5	even	2		3200.2.a.bq.1.3		3
20.3	even	4		640.2.c.c.129.5	yes	6
20.7	even	4		640.2.c.c.129.2	yes	6
20.19	odd	2		3200.2.a.bu.1.1		3
40.3	even	4		640.2.c.b.129.2	yes	6
40.13	odd	4		640.2.c.a.129.5	yes	6
40.19	odd	2		3200.2.a.br.1.3		3
40.27	even	4		640.2.c.b.129.5	yes	6
40.29	even	2		3200.2.a.bs.1.1		3
40.37	odd	4		640.2.c.a.129.2	✓	6
80.3	even	4		1280.2.f.k.129.1		6
80.13	odd	4		1280.2.f.i.129.5		6
80.27	even	4		1280.2.f.k.129.2		6
80.37	odd	4		1280.2.f.i.129.6		6
80.43	even	4		1280.2.f.j.129.6		6
80.53	odd	4		1280.2.f.l.129.2		6
80.67	even	4		1280.2.f.j.129.5		6
80.77	odd	4		1280.2.f.l.129.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.c.a.129.2	✓	6	40.37	odd	4
640.2.c.a.129.5	yes	6	40.13	odd	4
640.2.c.b.129.2	yes	6	40.3	even	4
640.2.c.b.129.5	yes	6	40.27	even	4
640.2.c.c.129.2	yes	6	20.7	even	4
640.2.c.c.129.5	yes	6	20.3	even	4
640.2.c.d.129.2	yes	6	5.3	odd	4
640.2.c.d.129.5	yes	6	5.2	odd	4
1280.2.f.i.129.5		6	80.13	odd	4
1280.2.f.i.129.6		6	80.37	odd	4
1280.2.f.j.129.5		6	80.67	even	4
1280.2.f.j.129.6		6	80.43	even	4
1280.2.f.k.129.1		6	80.3	even	4
1280.2.f.k.129.2		6	80.27	even	4
1280.2.f.l.129.1		6	80.77	odd	4
1280.2.f.l.129.2		6	80.53	odd	4
3200.2.a.bo.1.3		3	4.3	odd	2
3200.2.a.bp.1.3		3	5.4	even	2
3200.2.a.bq.1.3		3	8.5	even	2
3200.2.a.br.1.3		3	40.19	odd	2
3200.2.a.bs.1.1		3	40.29	even	2
3200.2.a.bt.1.1		3	8.3	odd	2
3200.2.a.bu.1.1		3	20.19	odd	2
3200.2.a.bv.1.1		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.70928 q^{3} +2.63090 q^{7} -0.0783777 q^{9} +O(q^{10})\)	\(q-1.70928 q^{3} +2.63090 q^{7} -0.0783777 q^{9} +5.41855 q^{11} +6.34017 q^{13} +3.41855 q^{17} +3.26180 q^{19} -4.49693 q^{21} +1.36910 q^{23} +5.26180 q^{27} +2.00000 q^{29} -4.68035 q^{31} -9.26180 q^{33} -5.75872 q^{37} -10.8371 q^{39} -7.75872 q^{41} +4.44748 q^{43} +4.78765 q^{47} -0.0783777 q^{49} -5.84324 q^{51} +1.65983 q^{53} -5.57531 q^{57} -3.26180 q^{59} -2.49693 q^{61} -0.206204 q^{63} +7.86603 q^{67} -2.34017 q^{69} -6.15676 q^{71} -13.5753 q^{73} +14.2557 q^{77} +12.6803 q^{79} -8.75872 q^{81} +14.9711 q^{83} -3.41855 q^{87} -8.52359 q^{89} +16.6803 q^{91} +8.00000 q^{93} -4.58145 q^{97} -0.424694 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{3} + 4 q^{7} + 3 q^{9}+O(q^{10}) \) 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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