LMFDB - Embedded newform 3584.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3584,2,Mod(1,3584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3584, 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("3584.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3584 = 2^{9} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3584.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:	$28.6183840844$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.18857984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 9x^{4} + 16x^{3} + 6x^{2} - 12x + 2 $ x^6 - 2x^5 - 9x^4 + 16x^3 + 6x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.194171$ of defining polynomial
Character	$\chi$	$=$	3584.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.01685 q^{3} -1.29145 q^{5} -1.00000 q^{7} -1.96601 q^{9} +O(q^{10})$	$q-1.01685 q^{3} -1.29145 q^{5} -1.00000 q^{7} -1.96601 q^{9} -3.99188 q^{11} -0.534938 q^{13} +1.31322 q^{15} -6.47379 q^{17} +3.19046 q^{19} +1.01685 q^{21} -2.28447 q^{23} -3.33215 q^{25} +5.04971 q^{27} +6.09287 q^{29} -5.70453 q^{31} +4.05916 q^{33} +1.29145 q^{35} -6.44008 q^{37} +0.543954 q^{39} -4.27923 q^{41} +5.11578 q^{43} +2.53901 q^{45} -7.83993 q^{47} +1.00000 q^{49} +6.58291 q^{51} -13.5814 q^{53} +5.15533 q^{55} -3.24424 q^{57} +9.71935 q^{59} +2.06814 q^{61} +1.96601 q^{63} +0.690848 q^{65} +9.06175 q^{67} +2.32298 q^{69} +16.4535 q^{71} +8.18408 q^{73} +3.38831 q^{75} +3.99188 q^{77} -0.960761 q^{79} +0.763200 q^{81} -5.40599 q^{83} +8.36061 q^{85} -6.19556 q^{87} +4.97125 q^{89} +0.534938 q^{91} +5.80068 q^{93} -4.12034 q^{95} +6.97532 q^{97} +7.84806 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{3} - 6 q^{7} + 10 q^{9}+O(q^{10}) $ 6 * q + 4 * q^3 - 6 * q^7 + 10 * q^9	$ 6 q + 4 q^{3} - 6 q^{7} + 10 q^{9} + 8 q^{11} + 8 q^{15} + 20 q^{19} - 4 q^{21} + 2 q^{25} + 16 q^{27} - 4 q^{29} + 8 q^{31} + 4 q^{33} - 20 q^{37} - 4 q^{41} + 24 q^{43} - 8 q^{47} + 6 q^{49} + 24 q^{51} - 4 q^{53} - 16 q^{55} - 4 q^{57} + 12 q^{59} + 8 q^{61} - 10 q^{63} - 8 q^{65} + 16 q^{67} + 40 q^{69} + 8 q^{71} + 16 q^{73} + 28 q^{75} - 8 q^{77} + 24 q^{79} + 10 q^{81} + 12 q^{83} + 8 q^{87} + 16 q^{89} - 24 q^{93} + 16 q^{95} + 16 q^{97} + 40 q^{99}+O(q^{100}) $ 6 * q + 4 * q^3 - 6 * q^7 + 10 * q^9 + 8 * q^11 + 8 * q^15 + 20 * q^19 - 4 * q^21 + 2 * q^25 + 16 * q^27 - 4 * q^29 + 8 * q^31 + 4 * q^33 - 20 * q^37 - 4 * q^41 + 24 * q^43 - 8 * q^47 + 6 * q^49 + 24 * q^51 - 4 * q^53 - 16 * q^55 - 4 * q^57 + 12 * q^59 + 8 * q^61 - 10 * q^63 - 8 * q^65 + 16 * q^67 + 40 * q^69 + 8 * q^71 + 16 * q^73 + 28 * q^75 - 8 * q^77 + 24 * q^79 + 10 * q^81 + 12 * q^83 + 8 * q^87 + 16 * q^89 - 24 * q^93 + 16 * q^95 + 16 * q^97 + 40 * 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
$3$	−1.01685	−0.587081	−0.293541	−	0.955947i	$-0.594834\pi$
$3$	−1.01685	−0.587081	−0.293541	+	0.955947i	$0.594834\pi$
$4$	0	0
$5$	−1.29145	−0.577556	−0.288778	−	0.957396i	$-0.593249\pi$
$5$	−1.29145	−0.577556	−0.288778	+	0.957396i	$0.593249\pi$
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	−1.96601	−0.655335
$10$	0	0
$11$	−3.99188	−1.20360	−0.601798	−	0.798648i	$-0.705549\pi$
$11$	−3.99188	−1.20360	−0.601798	+	0.798648i	$0.705549\pi$
$12$	0	0
$13$	−0.534938	−0.148365	−0.0741825	−	0.997245i	$-0.523635\pi$
$13$	−0.534938	−0.148365	−0.0741825	+	0.997245i	$0.523635\pi$
$14$	0	0
$15$	1.31322	0.339072
$16$	0	0
$17$	−6.47379	−1.57013	−0.785063	−	0.619416i	$-0.787369\pi$
$17$	−6.47379	−1.57013	−0.785063	+	0.619416i	$0.787369\pi$
$18$	0	0
$19$	3.19046	0.731942	0.365971	−	0.930626i	$-0.380737\pi$
$19$	3.19046	0.731942	0.365971	+	0.930626i	$0.380737\pi$
$20$	0	0
$21$	1.01685	0.221896
$22$	0	0
$23$	−2.28447	−0.476346	−0.238173	−	0.971223i	$-0.576548\pi$
$23$	−2.28447	−0.476346	−0.238173	+	0.971223i	$0.576548\pi$
$24$	0	0
$25$	−3.33215	−0.666429
$26$	0	0
$27$	5.04971	0.971817
$28$	0	0
$29$	6.09287	1.13142	0.565709	−	0.824605i	$-0.308603\pi$
$29$	6.09287	1.13142	0.565709	+	0.824605i	$0.308603\pi$
$30$	0	0
$31$	−5.70453	−1.02456	−0.512282	−	0.858818i	$-0.671200\pi$
$31$	−5.70453	−1.02456	−0.512282	+	0.858818i	$0.671200\pi$
$32$	0	0
$33$	4.05916	0.706609
$34$	0	0
$35$	1.29145	0.218296
$36$	0	0
$37$	−6.44008	−1.05874	−0.529372	−	0.848390i	$-0.677572\pi$
$37$	−6.44008	−1.05874	−0.529372	+	0.848390i	$0.677572\pi$
$38$	0	0
$39$	0.543954	0.0871024
$40$	0	0
$41$	−4.27923	−0.668303	−0.334152	−	0.942519i	$-0.608450\pi$
$41$	−4.27923	−0.668303	−0.334152	+	0.942519i	$0.608450\pi$
$42$	0	0
$43$	5.11578	0.780149	0.390074	−	0.920783i	$-0.372449\pi$
$43$	5.11578	0.780149	0.390074	+	0.920783i	$0.372449\pi$
$44$	0	0
$45$	2.53901	0.378493
$46$	0	0
$47$	−7.83993	−1.14357	−0.571786	−	0.820403i	$-0.693749\pi$
$47$	−7.83993	−1.14357	−0.571786	+	0.820403i	$0.693749\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	6.58291	0.921792
$52$	0	0
$53$	−13.5814	−1.86556	−0.932778	−	0.360452i	$-0.882622\pi$
$53$	−13.5814	−1.86556	−0.932778	+	0.360452i	$0.882622\pi$
$54$	0	0
$55$	5.15533	0.695144
$56$	0	0
$57$	−3.24424	−0.429710
$58$	0	0
$59$	9.71935	1.26535	0.632676	−	0.774417i	$-0.281957\pi$
$59$	9.71935	1.26535	0.632676	+	0.774417i	$0.281957\pi$
$60$	0	0
$61$	2.06814	0.264798	0.132399	−	0.991196i	$-0.457732\pi$
$61$	2.06814	0.264798	0.132399	+	0.991196i	$0.457732\pi$
$62$	0	0
$63$	1.96601	0.247694
$64$	0	0
$65$	0.690848	0.0856891
$66$	0	0
$67$	9.06175	1.10707	0.553535	−	0.832826i	$-0.313279\pi$
$67$	9.06175	1.10707	0.553535	+	0.832826i	$0.313279\pi$
$68$	0	0
$69$	2.32298	0.279654
$70$	0	0
$71$	16.4535	1.95267	0.976334	−	0.216266i	$-0.0693880\pi$
$71$	16.4535	1.95267	0.976334	+	0.216266i	$0.0693880\pi$
$72$	0	0
$73$	8.18408	0.957874	0.478937	−	0.877849i	$-0.341022\pi$
$73$	8.18408	0.957874	0.478937	+	0.877849i	$0.341022\pi$
$74$	0	0
$75$	3.38831	0.391248
$76$	0	0
$77$	3.99188	0.454917
$78$	0	0
$79$	−0.960761	−0.108094	−0.0540470	−	0.998538i	$-0.517212\pi$
$79$	−0.960761	−0.108094	−0.0540470	+	0.998538i	$0.517212\pi$
$80$	0	0
$81$	0.763200	0.0848000
$82$	0	0
$83$	−5.40599	−0.593384	−0.296692	−	0.954973i	$-0.595884\pi$
$83$	−5.40599	−0.593384	−0.296692	+	0.954973i	$0.595884\pi$
$84$	0	0
$85$	8.36061	0.906835
$86$	0	0
$87$	−6.19556	−0.664234
$88$	0	0
$89$	4.97125	0.526952	0.263476	−	0.964666i	$-0.415131\pi$
$89$	4.97125	0.526952	0.263476	+	0.964666i	$0.415131\pi$
$90$	0	0
$91$	0.534938	0.0560767
$92$	0	0
$93$	5.80068	0.601502
$94$	0	0
$95$	−4.12034	−0.422738
$96$	0	0
$97$	6.97532	0.708237	0.354118	−	0.935201i	$-0.384781\pi$
$97$	6.97532	0.708237	0.354118	+	0.935201i	$0.384781\pi$
$98$	0	0
$99$	7.84806	0.788759
$100$	0	0
$101$	−6.19179	−0.616106	−0.308053	−	0.951369i	$-0.599677\pi$
$101$	−6.19179	−0.616106	−0.308053	+	0.951369i	$0.599677\pi$
$102$	0	0
$103$	−9.38281	−0.924516	−0.462258	−	0.886745i	$-0.652961\pi$
$103$	−9.38281	−0.924516	−0.462258	+	0.886745i	$0.652961\pi$
$104$	0	0
$105$	−1.31322	−0.128157
$106$	0	0
$107$	−2.14532	−0.207396	−0.103698	−	0.994609i	$-0.533067\pi$
$107$	−2.14532	−0.207396	−0.103698	+	0.994609i	$0.533067\pi$
$108$	0	0
$109$	−8.50343	−0.814481	−0.407241	−	0.913321i	$-0.633509\pi$
$109$	−8.50343	−0.814481	−0.407241	+	0.913321i	$0.633509\pi$
$110$	0	0
$111$	6.54863	0.621569
$112$	0	0
$113$	−13.0194	−1.22476	−0.612382	−	0.790562i	$-0.709788\pi$
$113$	−13.0194	−1.22476	−0.612382	+	0.790562i	$0.709788\pi$
$114$	0	0
$115$	2.95029	0.275116
$116$	0	0
$117$	1.05169	0.0972289
$118$	0	0
$119$	6.47379	0.593452
$120$	0	0
$121$	4.93509	0.448644
$122$	0	0
$123$	4.35135	0.392348
$124$	0	0
$125$	10.7606	0.962456
$126$	0	0
$127$	2.47162	0.219321	0.109660	−	0.993969i	$-0.465024\pi$
$127$	2.47162	0.219321	0.109660	+	0.993969i	$0.465024\pi$
$128$	0	0
$129$	−5.20200	−0.458011
$130$	0	0
$131$	3.65319	0.319181	0.159590	−	0.987183i	$-0.448983\pi$
$131$	3.65319	0.319181	0.159590	+	0.987183i	$0.448983\pi$
$132$	0	0
$133$	−3.19046	−0.276648
$134$	0	0
$135$	−6.52147	−0.561279
$136$	0	0
$137$	−13.4016	−1.14498	−0.572490	−	0.819912i	$-0.694022\pi$
$137$	−13.4016	−1.14498	−0.572490	+	0.819912i	$0.694022\pi$
$138$	0	0
$139$	16.3563	1.38732	0.693661	−	0.720302i	$-0.255997\pi$
$139$	16.3563	1.38732	0.693661	+	0.720302i	$0.255997\pi$
$140$	0	0
$141$	7.97207	0.671370
$142$	0	0
$143$	2.13541	0.178572
$144$	0	0
$145$	−7.86866	−0.653457
$146$	0	0
$147$	−1.01685	−0.0838688
$148$	0	0
$149$	1.92053	0.157336	0.0786678	−	0.996901i	$-0.474933\pi$
$149$	1.92053	0.157336	0.0786678	+	0.996901i	$0.474933\pi$
$150$	0	0
$151$	4.47078	0.363827	0.181913	−	0.983315i	$-0.441771\pi$
$151$	4.47078	0.363827	0.181913	+	0.983315i	$0.441771\pi$
$152$	0	0
$153$	12.7275	1.02896
$154$	0	0
$155$	7.36714	0.591743
$156$	0	0
$157$	4.92407	0.392984	0.196492	−	0.980505i	$-0.437045\pi$
$157$	4.92407	0.392984	0.196492	+	0.980505i	$0.437045\pi$
$158$	0	0
$159$	13.8104	1.09523
$160$	0	0
$161$	2.28447	0.180042
$162$	0	0
$163$	11.7644	0.921458	0.460729	−	0.887541i	$-0.347588\pi$
$163$	11.7644	0.921458	0.460729	+	0.887541i	$0.347588\pi$
$164$	0	0
$165$	−5.24222	−0.408106
$166$	0	0
$167$	−11.5691	−0.895245	−0.447623	−	0.894223i	$-0.647729\pi$
$167$	−11.5691	−0.895245	−0.447623	+	0.894223i	$0.647729\pi$
$168$	0	0
$169$	−12.7138	−0.977988
$170$	0	0
$171$	−6.27247	−0.479668
$172$	0	0
$173$	25.6008	1.94640	0.973198	−	0.229968i	$-0.0738622\pi$
$173$	25.6008	1.94640	0.973198	+	0.229968i	$0.0738622\pi$
$174$	0	0
$175$	3.33215	0.251887
$176$	0	0
$177$	−9.88316	−0.742864
$178$	0	0
$179$	10.2520	0.766267	0.383134	−	0.923693i	$-0.374845\pi$
$179$	10.2520	0.766267	0.383134	+	0.923693i	$0.374845\pi$
$180$	0	0
$181$	−26.2524	−1.95133	−0.975664	−	0.219270i	$-0.929632\pi$
$181$	−26.2524	−1.95133	−0.975664	+	0.219270i	$0.929632\pi$
$182$	0	0
$183$	−2.10300	−0.155458
$184$	0	0
$185$	8.31708	0.611484
$186$	0	0
$187$	25.8426	1.88980
$188$	0	0
$189$	−5.04971	−0.367312
$190$	0	0
$191$	−8.18715	−0.592401	−0.296201	−	0.955126i	$-0.595720\pi$
$191$	−8.18715	−0.592401	−0.296201	+	0.955126i	$0.595720\pi$
$192$	0	0
$193$	25.3226	1.82276	0.911382	−	0.411561i	$-0.135016\pi$
$193$	25.3226	1.82276	0.911382	+	0.411561i	$0.135016\pi$
$194$	0	0
$195$	−0.702492	−0.0503065
$196$	0	0
$197$	−20.8467	−1.48526	−0.742632	−	0.669699i	$-0.766423\pi$
$197$	−20.8467	−1.48526	−0.742632	+	0.669699i	$0.766423\pi$
$198$	0	0
$199$	20.2055	1.43233	0.716164	−	0.697932i	$-0.245896\pi$
$199$	20.2055	1.43233	0.716164	+	0.697932i	$0.245896\pi$
$200$	0	0
$201$	−9.21449	−0.649940
$202$	0	0
$203$	−6.09287	−0.427636
$204$	0	0
$205$	5.52643	0.385982
$206$	0	0
$207$	4.49129	0.312166
$208$	0	0
$209$	−12.7359	−0.880963
$210$	0	0
$211$	−0.231640	−0.0159468	−0.00797339	−	0.999968i	$-0.502538\pi$
$211$	−0.231640	−0.0159468	−0.00797339	+	0.999968i	$0.502538\pi$
$212$	0	0
$213$	−16.7308	−1.14638
$214$	0	0
$215$	−6.60679	−0.450580
$216$	0	0
$217$	5.70453	0.387249
$218$	0	0
$219$	−8.32202	−0.562350
$220$	0	0
$221$	3.46308	0.232952
$222$	0	0
$223$	22.3886	1.49925	0.749625	−	0.661863i	$-0.230234\pi$
$223$	22.3886	1.49925	0.749625	+	0.661863i	$0.230234\pi$
$224$	0	0
$225$	6.55102	0.436735
$226$	0	0
$227$	17.1167	1.13608	0.568038	−	0.823002i	$-0.307703\pi$
$227$	17.1167	1.13608	0.568038	+	0.823002i	$0.307703\pi$
$228$	0	0
$229$	15.0638	0.995445	0.497723	−	0.867336i	$-0.334170\pi$
$229$	15.0638	0.995445	0.497723	+	0.867336i	$0.334170\pi$
$230$	0	0
$231$	−4.05916	−0.267073
$232$	0	0
$233$	11.8566	0.776752	0.388376	−	0.921501i	$-0.373036\pi$
$233$	11.8566	0.776752	0.388376	+	0.921501i	$0.373036\pi$
$234$	0	0
$235$	10.1249	0.660477
$236$	0	0
$237$	0.976955	0.0634600
$238$	0	0
$239$	−8.55444	−0.553341	−0.276670	−	0.960965i	$-0.589231\pi$
$239$	−8.55444	−0.553341	−0.276670	+	0.960965i	$0.589231\pi$
$240$	0	0
$241$	−14.3170	−0.922236	−0.461118	−	0.887339i	$-0.652552\pi$
$241$	−14.3170	−0.922236	−0.461118	+	0.887339i	$0.652552\pi$
$242$	0	0
$243$	−15.9252	−1.02160
$244$	0	0
$245$	−1.29145	−0.0825080
$246$	0	0
$247$	−1.70670	−0.108595
$248$	0	0
$249$	5.49710	0.348365
$250$	0	0
$251$	−0.346212	−0.0218527	−0.0109264	−	0.999940i	$-0.503478\pi$
$251$	−0.346212	−0.0218527	−0.0109264	+	0.999940i	$0.503478\pi$
$252$	0	0
$253$	9.11934	0.573328
$254$	0	0
$255$	−8.50153	−0.532386
$256$	0	0
$257$	21.7703	1.35799	0.678996	−	0.734142i	$-0.262415\pi$
$257$	21.7703	1.35799	0.678996	+	0.734142i	$0.262415\pi$
$258$	0	0
$259$	6.44008	0.400167
$260$	0	0
$261$	−11.9786	−0.741458
$262$	0	0
$263$	−16.0380	−0.988946	−0.494473	−	0.869193i	$-0.664639\pi$
$263$	−16.0380	−0.988946	−0.494473	+	0.869193i	$0.664639\pi$
$264$	0	0
$265$	17.5398	1.07746
$266$	0	0
$267$	−5.05504	−0.309363
$268$	0	0
$269$	−6.98157	−0.425674	−0.212837	−	0.977088i	$-0.568270\pi$
$269$	−6.98157	−0.425674	−0.212837	+	0.977088i	$0.568270\pi$
$270$	0	0
$271$	3.13231	0.190275	0.0951373	−	0.995464i	$-0.469671\pi$
$271$	3.13231	0.190275	0.0951373	+	0.995464i	$0.469671\pi$
$272$	0	0
$273$	−0.543954	−0.0329216
$274$	0	0
$275$	13.3015	0.802112
$276$	0	0
$277$	−2.07134	−0.124454	−0.0622272	−	0.998062i	$-0.519820\pi$
$277$	−2.07134	−0.124454	−0.0622272	+	0.998062i	$0.519820\pi$
$278$	0	0
$279$	11.2151	0.671433
$280$	0	0
$281$	10.1923	0.608024	0.304012	−	0.952668i	$-0.401674\pi$
$281$	10.1923	0.608024	0.304012	+	0.952668i	$0.401674\pi$
$282$	0	0
$283$	−14.8446	−0.882421	−0.441210	−	0.897404i	$-0.645451\pi$
$283$	−14.8446	−0.882421	−0.441210	+	0.897404i	$0.645451\pi$
$284$	0	0
$285$	4.18978	0.248181
$286$	0	0
$287$	4.27923	0.252595
$288$	0	0
$289$	24.9100	1.46529
$290$	0	0
$291$	−7.09289	−0.415792
$292$	0	0
$293$	10.2362	0.598007	0.299004	−	0.954252i	$-0.403346\pi$
$293$	10.2362	0.598007	0.299004	+	0.954252i	$0.403346\pi$
$294$	0	0
$295$	−12.5521	−0.730811
$296$	0	0
$297$	−20.1578	−1.16967
$298$	0	0
$299$	1.22205	0.0706730
$300$	0	0
$301$	−5.11578	−0.294869
$302$	0	0
$303$	6.29615	0.361705
$304$	0	0
$305$	−2.67091	−0.152936
$306$	0	0
$307$	19.6132	1.11938	0.559691	−	0.828701i	$-0.310920\pi$
$307$	19.6132	1.11938	0.559691	+	0.828701i	$0.310920\pi$
$308$	0	0
$309$	9.54096	0.542766
$310$	0	0
$311$	−9.88322	−0.560426	−0.280213	−	0.959938i	$-0.590405\pi$
$311$	−9.88322	−0.560426	−0.280213	+	0.959938i	$0.590405\pi$
$312$	0	0
$313$	0.573015	0.0323887	0.0161944	−	0.999869i	$-0.494845\pi$
$313$	0.573015	0.0323887	0.0161944	+	0.999869i	$0.494845\pi$
$314$	0	0
$315$	−2.53901	−0.143057
$316$	0	0
$317$	−19.7491	−1.10922	−0.554611	−	0.832110i	$-0.687133\pi$
$317$	−19.7491	−1.10922	−0.554611	+	0.832110i	$0.687133\pi$
$318$	0	0
$319$	−24.3220	−1.36177
$320$	0	0
$321$	2.18148	0.121758
$322$	0	0
$323$	−20.6544	−1.14924
$324$	0	0
$325$	1.78249	0.0988748
$326$	0	0
$327$	8.64676	0.478167
$328$	0	0
$329$	7.83993	0.432230
$330$	0	0
$331$	22.8436	1.25560	0.627799	−	0.778376i	$-0.283956\pi$
$331$	22.8436	1.25560	0.627799	+	0.778376i	$0.283956\pi$
$332$	0	0
$333$	12.6612	0.693832
$334$	0	0
$335$	−11.7028	−0.639395
$336$	0	0
$337$	−2.69392	−0.146747	−0.0733736	−	0.997305i	$-0.523377\pi$
$337$	−2.69392	−0.146747	−0.0733736	+	0.997305i	$0.523377\pi$
$338$	0	0
$339$	13.2389	0.719036
$340$	0	0
$341$	22.7718	1.23316
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	−3.00002	−0.161516
$346$	0	0
$347$	6.08073	0.326431	0.163215	−	0.986590i	$-0.447813\pi$
$347$	6.08073	0.326431	0.163215	+	0.986590i	$0.447813\pi$
$348$	0	0
$349$	−17.0896	−0.914787	−0.457394	−	0.889264i	$-0.651217\pi$
$349$	−17.0896	−0.914787	−0.457394	+	0.889264i	$0.651217\pi$
$350$	0	0
$351$	−2.70128	−0.144184
$352$	0	0
$353$	28.3967	1.51140	0.755702	−	0.654916i	$-0.227296\pi$
$353$	28.3967	1.51140	0.755702	+	0.654916i	$0.227296\pi$
$354$	0	0
$355$	−21.2489	−1.12778
$356$	0	0
$357$	−6.58291	−0.348404
$358$	0	0
$359$	−5.18843	−0.273835	−0.136917	−	0.990582i	$-0.543719\pi$
$359$	−5.18843	−0.273835	−0.136917	+	0.990582i	$0.543719\pi$
$360$	0	0
$361$	−8.82095	−0.464260
$362$	0	0
$363$	−5.01826	−0.263391
$364$	0	0
$365$	−10.5694	−0.553226
$366$	0	0
$367$	20.9256	1.09231	0.546153	−	0.837685i	$-0.316092\pi$
$367$	20.9256	1.09231	0.546153	+	0.837685i	$0.316092\pi$
$368$	0	0
$369$	8.41299	0.437963
$370$	0	0
$371$	13.5814	0.705114
$372$	0	0
$373$	−5.93536	−0.307321	−0.153661	−	0.988124i	$-0.549106\pi$
$373$	−5.93536	−0.307321	−0.153661	+	0.988124i	$0.549106\pi$
$374$	0	0
$375$	−10.9420	−0.565040
$376$	0	0
$377$	−3.25931	−0.167863
$378$	0	0
$379$	6.04243	0.310379	0.155189	−	0.987885i	$-0.450401\pi$
$379$	6.04243	0.310379	0.155189	+	0.987885i	$0.450401\pi$
$380$	0	0
$381$	−2.51328	−0.128759
$382$	0	0
$383$	−3.53306	−0.180531	−0.0902653	−	0.995918i	$-0.528772\pi$
$383$	−3.53306	−0.180531	−0.0902653	+	0.995918i	$0.528772\pi$
$384$	0	0
$385$	−5.15533	−0.262740
$386$	0	0
$387$	−10.0577	−0.511259
$388$	0	0
$389$	−2.75123	−0.139493	−0.0697466	−	0.997565i	$-0.522219\pi$
$389$	−2.75123	−0.139493	−0.0697466	+	0.997565i	$0.522219\pi$
$390$	0	0
$391$	14.7892	0.747922
$392$	0	0
$393$	−3.71477	−0.187385
$394$	0	0
$395$	1.24078	0.0624304
$396$	0	0
$397$	27.5791	1.38416	0.692079	−	0.721822i	$-0.256695\pi$
$397$	27.5791	1.38416	0.692079	+	0.721822i	$0.256695\pi$
$398$	0	0
$399$	3.24424	0.162415
$400$	0	0
$401$	−1.51409	−0.0756099	−0.0378050	−	0.999285i	$-0.512037\pi$
$401$	−1.51409	−0.0756099	−0.0378050	+	0.999285i	$0.512037\pi$
$402$	0	0
$403$	3.05157	0.152009
$404$	0	0
$405$	−0.985638	−0.0489767
$406$	0	0
$407$	25.7080	1.27430
$408$	0	0
$409$	−3.50489	−0.173306	−0.0866529	−	0.996239i	$-0.527617\pi$
$409$	−3.50489	−0.173306	−0.0866529	+	0.996239i	$0.527617\pi$
$410$	0	0
$411$	13.6275	0.672196
$412$	0	0
$413$	−9.71935	−0.478258
$414$	0	0
$415$	6.98159	0.342713
$416$	0	0
$417$	−16.6320	−0.814471
$418$	0	0
$419$	0.0423241	0.00206767	0.00103383	−	0.999999i	$-0.499671\pi$
$419$	0.0423241	0.00206767	0.00103383	+	0.999999i	$0.499671\pi$
$420$	0	0
$421$	25.8137	1.25808	0.629041	−	0.777372i	$-0.283448\pi$
$421$	25.8137	1.25808	0.629041	+	0.777372i	$0.283448\pi$
$422$	0	0
$423$	15.4134	0.749423
$424$	0	0
$425$	21.5716	1.04638
$426$	0	0
$427$	−2.06814	−0.100084
$428$	0	0
$429$	−2.17140	−0.104836
$430$	0	0
$431$	−33.0398	−1.59147	−0.795735	−	0.605645i	$-0.792915\pi$
$431$	−33.0398	−1.59147	−0.795735	+	0.605645i	$0.792915\pi$
$432$	0	0
$433$	−10.7807	−0.518086	−0.259043	−	0.965866i	$-0.583407\pi$
$433$	−10.7807	−0.518086	−0.259043	+	0.965866i	$0.583407\pi$
$434$	0	0
$435$	8.00129	0.383632
$436$	0	0
$437$	−7.28853	−0.348657
$438$	0	0
$439$	−23.5740	−1.12513	−0.562564	−	0.826754i	$-0.690185\pi$
$439$	−23.5740	−1.12513	−0.562564	+	0.826754i	$0.690185\pi$
$440$	0	0
$441$	−1.96601	−0.0936193
$442$	0	0
$443$	−35.7764	−1.69979	−0.849893	−	0.526955i	$-0.823334\pi$
$443$	−35.7764	−1.69979	−0.849893	+	0.526955i	$0.823334\pi$
$444$	0	0
$445$	−6.42014	−0.304344
$446$	0	0
$447$	−1.95290	−0.0923688
$448$	0	0
$449$	−12.9320	−0.610300	−0.305150	−	0.952304i	$-0.598707\pi$
$449$	−12.9320	−0.610300	−0.305150	+	0.952304i	$0.598707\pi$
$450$	0	0
$451$	17.0822	0.804367
$452$	0	0
$453$	−4.54613	−0.213596
$454$	0	0
$455$	−0.690848	−0.0323875
$456$	0	0
$457$	−30.5150	−1.42743	−0.713715	−	0.700436i	$-0.752989\pi$
$457$	−30.5150	−1.42743	−0.713715	+	0.700436i	$0.752989\pi$
$458$	0	0
$459$	−32.6908	−1.52587
$460$	0	0
$461$	19.6155	0.913585	0.456793	−	0.889573i	$-0.348998\pi$
$461$	19.6155	0.913585	0.456793	+	0.889573i	$0.348998\pi$
$462$	0	0
$463$	−15.3254	−0.712231	−0.356116	−	0.934442i	$-0.615899\pi$
$463$	−15.3254	−0.712231	−0.356116	+	0.934442i	$0.615899\pi$
$464$	0	0
$465$	−7.49131	−0.347401
$466$	0	0
$467$	−30.2233	−1.39857	−0.699283	−	0.714845i	$-0.746497\pi$
$467$	−30.2233	−1.39857	−0.699283	+	0.714845i	$0.746497\pi$
$468$	0	0
$469$	−9.06175	−0.418433
$470$	0	0
$471$	−5.00706	−0.230713
$472$	0	0
$473$	−20.4216	−0.938984
$474$	0	0
$475$	−10.6311	−0.487788
$476$	0	0
$477$	26.7012	1.22256
$478$	0	0
$479$	18.2121	0.832131	0.416066	−	0.909335i	$-0.363409\pi$
$479$	18.2121	0.832131	0.416066	+	0.909335i	$0.363409\pi$
$480$	0	0
$481$	3.44505	0.157081
$482$	0	0
$483$	−2.32298	−0.105699
$484$	0	0
$485$	−9.00831	−0.409046
$486$	0	0
$487$	−33.1641	−1.50281	−0.751404	−	0.659843i	$-0.770623\pi$
$487$	−33.1641	−1.50281	−0.751404	+	0.659843i	$0.770623\pi$
$488$	0	0
$489$	−11.9627	−0.540971
$490$	0	0
$491$	38.1547	1.72190	0.860950	−	0.508690i	$-0.169870\pi$
$491$	38.1547	1.72190	0.860950	+	0.508690i	$0.169870\pi$
$492$	0	0
$493$	−39.4440	−1.77647
$494$	0	0
$495$	−10.1354	−0.455553
$496$	0	0
$497$	−16.4535	−0.738039
$498$	0	0
$499$	1.44819	0.0648298	0.0324149	−	0.999474i	$-0.489680\pi$
$499$	1.44819	0.0648298	0.0324149	+	0.999474i	$0.489680\pi$
$500$	0	0
$501$	11.7641	0.525582
$502$	0	0
$503$	−14.4905	−0.646098	−0.323049	−	0.946382i	$-0.604708\pi$
$503$	−14.4905	−0.646098	−0.323049	+	0.946382i	$0.604708\pi$
$504$	0	0
$505$	7.99642	0.355836
$506$	0	0
$507$	12.9281	0.574158
$508$	0	0
$509$	29.1421	1.29170	0.645850	−	0.763464i	$-0.276503\pi$
$509$	29.1421	1.29170	0.645850	+	0.763464i	$0.276503\pi$
$510$	0	0
$511$	−8.18408	−0.362042
$512$	0	0
$513$	16.1109	0.711314
$514$	0	0
$515$	12.1175	0.533960
$516$	0	0
$517$	31.2961	1.37640
$518$	0	0
$519$	−26.0323	−1.14269
$520$	0	0
$521$	1.25214	0.0548573	0.0274287	−	0.999624i	$-0.491268\pi$
$521$	1.25214	0.0548573	0.0274287	+	0.999624i	$0.491268\pi$
$522$	0	0
$523$	34.3401	1.50159	0.750795	−	0.660536i	$-0.229671\pi$
$523$	34.3401	1.50159	0.750795	+	0.660536i	$0.229671\pi$
$524$	0	0
$525$	−3.38831	−0.147878
$526$	0	0
$527$	36.9299	1.60869
$528$	0	0
$529$	−17.7812	−0.773095
$530$	0	0
$531$	−19.1083	−0.829229
$532$	0	0
$533$	2.28912	0.0991529
$534$	0	0
$535$	2.77058	0.119783
$536$	0	0
$537$	−10.4247	−0.449861
$538$	0	0
$539$	−3.99188	−0.171942
$540$	0	0
$541$	−37.9611	−1.63207	−0.816037	−	0.578000i	$-0.803833\pi$
$541$	−37.9611	−1.63207	−0.816037	+	0.578000i	$0.803833\pi$
$542$	0	0
$543$	26.6949	1.14559
$544$	0	0
$545$	10.9818	0.470409
$546$	0	0
$547$	−9.82521	−0.420096	−0.210048	−	0.977691i	$-0.567362\pi$
$547$	−9.82521	−0.420096	−0.210048	+	0.977691i	$0.567362\pi$
$548$	0	0
$549$	−4.06598	−0.173532
$550$	0	0
$551$	19.4391	0.828132
$552$	0	0
$553$	0.960761	0.0408557
$554$	0	0
$555$	−8.45726	−0.358991
$556$	0	0
$557$	−32.5759	−1.38028	−0.690142	−	0.723674i	$-0.742452\pi$
$557$	−32.5759	−1.38028	−0.690142	+	0.723674i	$0.742452\pi$
$558$	0	0
$559$	−2.73662	−0.115747
$560$	0	0
$561$	−26.2782	−1.10946
$562$	0	0
$563$	−40.1157	−1.69067	−0.845337	−	0.534234i	$-0.820600\pi$
$563$	−40.1157	−1.69067	−0.845337	+	0.534234i	$0.820600\pi$
$564$	0	0
$565$	16.8140	0.707369
$566$	0	0
$567$	−0.763200	−0.0320514
$568$	0	0
$569$	0.461975	0.0193670	0.00968351	−	0.999953i	$-0.496918\pi$
$569$	0.461975	0.0193670	0.00968351	+	0.999953i	$0.496918\pi$
$570$	0	0
$571$	−41.6492	−1.74296	−0.871482	−	0.490428i	$-0.836841\pi$
$571$	−41.6492	−1.74296	−0.871482	+	0.490428i	$0.836841\pi$
$572$	0	0
$573$	8.32514	0.347788
$574$	0	0
$575$	7.61220	0.317451
$576$	0	0
$577$	−12.1029	−0.503851	−0.251925	−	0.967747i	$-0.581064\pi$
$577$	−12.1029	−0.503851	−0.251925	+	0.967747i	$0.581064\pi$
$578$	0	0
$579$	−25.7495	−1.07011
$580$	0	0
$581$	5.40599	0.224278
$582$	0	0
$583$	54.2155	2.24538
$584$	0	0
$585$	−1.35821	−0.0561551
$586$	0	0
$587$	−14.2165	−0.586779	−0.293389	−	0.955993i	$-0.594783\pi$
$587$	−14.2165	−0.586779	−0.293389	+	0.955993i	$0.594783\pi$
$588$	0	0
$589$	−18.2001	−0.749921
$590$	0	0
$591$	21.1980	0.871971
$592$	0	0
$593$	−12.7044	−0.521705	−0.260853	−	0.965379i	$-0.584004\pi$
$593$	−12.7044	−0.521705	−0.260853	+	0.965379i	$0.584004\pi$
$594$	0	0
$595$	−8.36061	−0.342752
$596$	0	0
$597$	−20.5460	−0.840894
$598$	0	0
$599$	14.0608	0.574510	0.287255	−	0.957854i	$-0.407257\pi$
$599$	14.0608	0.574510	0.287255	+	0.957854i	$0.407257\pi$
$600$	0	0
$601$	26.0142	1.06114	0.530570	−	0.847641i	$-0.321978\pi$
$601$	26.0142	1.06114	0.530570	+	0.847641i	$0.321978\pi$
$602$	0	0
$603$	−17.8155	−0.725502
$604$	0	0
$605$	−6.37344	−0.259117
$606$	0	0
$607$	−28.0201	−1.13730	−0.568650	−	0.822579i	$-0.692534\pi$
$607$	−28.0201	−1.13730	−0.568650	+	0.822579i	$0.692534\pi$
$608$	0	0
$609$	6.19556	0.251057
$610$	0	0
$611$	4.19388	0.169666
$612$	0	0
$613$	−18.1315	−0.732323	−0.366161	−	0.930551i	$-0.619328\pi$
$613$	−18.1315	−0.732323	−0.366161	+	0.930551i	$0.619328\pi$
$614$	0	0
$615$	−5.61957	−0.226603
$616$	0	0
$617$	24.2692	0.977042	0.488521	−	0.872552i	$-0.337537\pi$
$617$	24.2692	0.977042	0.488521	+	0.872552i	$0.337537\pi$
$618$	0	0
$619$	−34.4384	−1.38420	−0.692099	−	0.721803i	$-0.743314\pi$
$619$	−34.4384	−1.38420	−0.692099	+	0.721803i	$0.743314\pi$
$620$	0	0
$621$	−11.5359	−0.462921
$622$	0	0
$623$	−4.97125	−0.199169
$624$	0	0
$625$	2.76392	0.110557
$626$	0	0
$627$	12.9506	0.517197
$628$	0	0
$629$	41.6918	1.66236
$630$	0	0
$631$	45.3042	1.80353	0.901766	−	0.432224i	$-0.142271\pi$
$631$	45.3042	1.80353	0.901766	+	0.432224i	$0.142271\pi$
$632$	0	0
$633$	0.235545	0.00936206
$634$	0	0
$635$	−3.19199	−0.126670
$636$	0	0
$637$	−0.534938	−0.0211950
$638$	0	0
$639$	−32.3476	−1.27965
$640$	0	0
$641$	46.2702	1.82756	0.913782	−	0.406204i	$-0.133148\pi$
$641$	46.2702	1.82756	0.913782	+	0.406204i	$0.133148\pi$
$642$	0	0
$643$	−20.9674	−0.826872	−0.413436	−	0.910533i	$-0.635671\pi$
$643$	−20.9674	−0.826872	−0.413436	+	0.910533i	$0.635671\pi$
$644$	0	0
$645$	6.71815	0.264527
$646$	0	0
$647$	44.7211	1.75817	0.879083	−	0.476668i	$-0.158156\pi$
$647$	44.7211	1.75817	0.879083	+	0.476668i	$0.158156\pi$
$648$	0	0
$649$	−38.7984	−1.52297
$650$	0	0
$651$	−5.80068	−0.227346
$652$	0	0
$653$	−2.23312	−0.0873886	−0.0436943	−	0.999045i	$-0.513913\pi$
$653$	−2.23312	−0.0873886	−0.0436943	+	0.999045i	$0.513913\pi$
$654$	0	0
$655$	−4.71793	−0.184345
$656$	0	0
$657$	−16.0899	−0.627729
$658$	0	0
$659$	−45.3644	−1.76715	−0.883573	−	0.468294i	$-0.844869\pi$
$659$	−45.3644	−1.76715	−0.883573	+	0.468294i	$0.844869\pi$
$660$	0	0
$661$	36.0951	1.40394	0.701969	−	0.712208i	$-0.252305\pi$
$661$	36.0951	1.40394	0.701969	+	0.712208i	$0.252305\pi$
$662$	0	0
$663$	−3.52145	−0.136762
$664$	0	0
$665$	4.12034	0.159780
$666$	0	0
$667$	−13.9190	−0.538946
$668$	0	0
$669$	−22.7659	−0.880181
$670$	0	0
$671$	−8.25576	−0.318710
$672$	0	0
$673$	9.23324	0.355915	0.177958	−	0.984038i	$-0.443051\pi$
$673$	9.23324	0.355915	0.177958	+	0.984038i	$0.443051\pi$
$674$	0	0
$675$	−16.8264	−0.647647
$676$	0	0
$677$	42.4578	1.63179	0.815893	−	0.578202i	$-0.196246\pi$
$677$	42.4578	1.63179	0.815893	+	0.578202i	$0.196246\pi$
$678$	0	0
$679$	−6.97532	−0.267688
$680$	0	0
$681$	−17.4052	−0.666969
$682$	0	0
$683$	−29.5156	−1.12938	−0.564692	−	0.825302i	$-0.691005\pi$
$683$	−29.5156	−1.12938	−0.564692	+	0.825302i	$0.691005\pi$
$684$	0	0
$685$	17.3076	0.661289
$686$	0	0
$687$	−15.3177	−0.584407
$688$	0	0
$689$	7.26523	0.276783
$690$	0	0
$691$	−21.1911	−0.806147	−0.403073	−	0.915168i	$-0.632058\pi$
$691$	−21.1911	−0.806147	−0.403073	+	0.915168i	$0.632058\pi$
$692$	0	0
$693$	−7.84806	−0.298123
$694$	0	0
$695$	−21.1234	−0.801256
$696$	0	0
$697$	27.7028	1.04932
$698$	0	0
$699$	−12.0564	−0.456017
$700$	0	0
$701$	10.3625	0.391386	0.195693	−	0.980665i	$-0.437304\pi$
$701$	10.3625	0.391386	0.195693	+	0.980665i	$0.437304\pi$
$702$	0	0
$703$	−20.5468	−0.774939
$704$	0	0
$705$	−10.2956	−0.387754
$706$	0	0
$707$	6.19179	0.232866
$708$	0	0
$709$	14.9196	0.560318	0.280159	−	0.959954i	$-0.409613\pi$
$709$	14.9196	0.560318	0.280159	+	0.959954i	$0.409613\pi$
$710$	0	0
$711$	1.88886	0.0708379
$712$	0	0
$713$	13.0318	0.488046
$714$	0	0
$715$	−2.75778	−0.103135
$716$	0	0
$717$	8.69863	0.324856
$718$	0	0
$719$	19.3570	0.721896	0.360948	−	0.932586i	$-0.382453\pi$
$719$	19.3570	0.721896	0.360948	+	0.932586i	$0.382453\pi$
$720$	0	0
$721$	9.38281	0.349434
$722$	0	0
$723$	14.5583	0.541428
$724$	0	0
$725$	−20.3023	−0.754010
$726$	0	0
$727$	11.1685	0.414216	0.207108	−	0.978318i	$-0.433595\pi$
$727$	11.1685	0.414216	0.207108	+	0.978318i	$0.433595\pi$
$728$	0	0
$729$	13.9040	0.514963
$730$	0	0
$731$	−33.1185	−1.22493
$732$	0	0
$733$	−27.4759	−1.01484	−0.507422	−	0.861698i	$-0.669401\pi$
$733$	−27.4759	−1.01484	−0.507422	+	0.861698i	$0.669401\pi$
$734$	0	0
$735$	1.31322	0.0484389
$736$	0	0
$737$	−36.1734	−1.33246
$738$	0	0
$739$	47.1619	1.73488	0.867440	−	0.497542i	$-0.165764\pi$
$739$	47.1619	1.73488	0.867440	+	0.497542i	$0.165764\pi$
$740$	0	0
$741$	1.73547	0.0637539
$742$	0	0
$743$	−47.0796	−1.72718	−0.863591	−	0.504193i	$-0.831790\pi$
$743$	−47.0796	−1.72718	−0.863591	+	0.504193i	$0.831790\pi$
$744$	0	0
$745$	−2.48027	−0.0908701
$746$	0	0
$747$	10.6282	0.388866
$748$	0	0
$749$	2.14532	0.0783882
$750$	0	0
$751$	−44.5767	−1.62663	−0.813313	−	0.581827i	$-0.802338\pi$
$751$	−44.5767	−1.62663	−0.813313	+	0.581827i	$0.802338\pi$
$752$	0	0
$753$	0.352047	0.0128293
$754$	0	0
$755$	−5.77381	−0.210130
$756$	0	0
$757$	28.9656	1.05277	0.526386	−	0.850246i	$-0.323547\pi$
$757$	28.9656	1.05277	0.526386	+	0.850246i	$0.323547\pi$
$758$	0	0
$759$	−9.27304	−0.336590
$760$	0	0
$761$	−9.89164	−0.358572	−0.179286	−	0.983797i	$-0.557379\pi$
$761$	−9.89164	−0.358572	−0.179286	+	0.983797i	$0.557379\pi$
$762$	0	0
$763$	8.50343	0.307845
$764$	0	0
$765$	−16.4370	−0.594281
$766$	0	0
$767$	−5.19925	−0.187734
$768$	0	0
$769$	−22.1642	−0.799260	−0.399630	−	0.916677i	$-0.630861\pi$
$769$	−22.1642	−0.799260	−0.399630	+	0.916677i	$0.630861\pi$
$770$	0	0
$771$	−22.1372	−0.797252
$772$	0	0
$773$	−40.6860	−1.46337	−0.731686	−	0.681641i	$-0.761266\pi$
$773$	−40.6860	−1.46337	−0.731686	+	0.681641i	$0.761266\pi$
$774$	0	0
$775$	19.0083	0.682799
$776$	0	0
$777$	−6.54863	−0.234931
$778$	0	0
$779$	−13.6527	−0.489159
$780$	0	0
$781$	−65.6803	−2.35022
$782$	0	0
$783$	30.7672	1.09953
$784$	0	0
$785$	−6.35921	−0.226970
$786$	0	0
$787$	50.6622	1.80591	0.902955	−	0.429734i	$-0.141393\pi$
$787$	50.6622	1.80591	0.902955	+	0.429734i	$0.141393\pi$
$788$	0	0
$789$	16.3083	0.580592
$790$	0	0
$791$	13.0194	0.462917
$792$	0	0
$793$	−1.10633	−0.0392868
$794$	0	0
$795$	−17.8355	−0.632558
$796$	0	0
$797$	4.92249	0.174364	0.0871818	−	0.996192i	$-0.472214\pi$
$797$	4.92249	0.174364	0.0871818	+	0.996192i	$0.472214\pi$
$798$	0	0
$799$	50.7541	1.79555
$800$	0	0
$801$	−9.77351	−0.345330
$802$	0	0
$803$	−32.6698	−1.15289
$804$	0	0
$805$	−2.95029	−0.103984
$806$	0	0
$807$	7.09924	0.249905
$808$	0	0
$809$	22.1155	0.777538	0.388769	−	0.921335i	$-0.372900\pi$
$809$	22.1155	0.777538	0.388769	+	0.921335i	$0.372900\pi$
$810$	0	0
$811$	46.3318	1.62693	0.813464	−	0.581615i	$-0.197579\pi$
$811$	46.3318	1.62693	0.813464	+	0.581615i	$0.197579\pi$
$812$	0	0
$813$	−3.18511	−0.111707
$814$	0	0
$815$	−15.1932	−0.532194
$816$	0	0
$817$	16.3217	0.571024
$818$	0	0
$819$	−1.05169	−0.0367491
$820$	0	0
$821$	−41.9810	−1.46515	−0.732573	−	0.680689i	$-0.761681\pi$
$821$	−41.9810	−1.46515	−0.732573	+	0.680689i	$0.761681\pi$
$822$	0	0
$823$	33.7030	1.17481	0.587406	−	0.809292i	$-0.300149\pi$
$823$	33.7030	1.17481	0.587406	+	0.809292i	$0.300149\pi$
$824$	0	0
$825$	−13.5257	−0.470905
$826$	0	0
$827$	7.51764	0.261414	0.130707	−	0.991421i	$-0.458275\pi$
$827$	7.51764	0.261414	0.130707	+	0.991421i	$0.458275\pi$
$828$	0	0
$829$	12.0080	0.417055	0.208528	−	0.978016i	$-0.433133\pi$
$829$	12.0080	0.417055	0.208528	+	0.978016i	$0.433133\pi$
$830$	0	0
$831$	2.10625	0.0730649
$832$	0	0
$833$	−6.47379	−0.224304
$834$	0	0
$835$	14.9410	0.517054
$836$	0	0
$837$	−28.8062	−0.995688
$838$	0	0
$839$	−0.308970	−0.0106668	−0.00533341	−	0.999986i	$-0.501698\pi$
$839$	−0.308970	−0.0106668	−0.00533341	+	0.999986i	$0.501698\pi$
$840$	0	0
$841$	8.12306	0.280105
$842$	0	0
$843$	−10.3641	−0.356959
$844$	0	0
$845$	16.4193	0.564843
$846$	0	0
$847$	−4.93509	−0.169572
$848$	0	0
$849$	15.0948	0.518053
$850$	0	0
$851$	14.7122	0.504328
$852$	0	0
$853$	48.4197	1.65786	0.828929	−	0.559354i	$-0.188951\pi$
$853$	48.4197	1.65786	0.828929	+	0.559354i	$0.188951\pi$
$854$	0	0
$855$	8.10061	0.277035
$856$	0	0
$857$	8.09941	0.276671	0.138335	−	0.990385i	$-0.455825\pi$
$857$	8.09941	0.276671	0.138335	+	0.990385i	$0.455825\pi$
$858$	0	0
$859$	40.2757	1.37419	0.687094	−	0.726568i	$-0.258886\pi$
$859$	40.2757	1.37419	0.687094	+	0.726568i	$0.258886\pi$
$860$	0	0
$861$	−4.35135	−0.148294
$862$	0	0
$863$	2.93426	0.0998835	0.0499417	−	0.998752i	$-0.484096\pi$
$863$	2.93426	0.0998835	0.0499417	+	0.998752i	$0.484096\pi$
$864$	0	0
$865$	−33.0623	−1.12415
$866$	0	0
$867$	−25.3299	−0.860247
$868$	0	0
$869$	3.83524	0.130102
$870$	0	0
$871$	−4.84748	−0.164250
$872$	0	0
$873$	−13.7135	−0.464132
$874$	0	0
$875$	−10.7606	−0.363774
$876$	0	0
$877$	−54.3937	−1.83674	−0.918372	−	0.395719i	$-0.870495\pi$
$877$	−54.3937	−1.83674	−0.918372	+	0.395719i	$0.870495\pi$
$878$	0	0
$879$	−10.4088	−0.351079
$880$	0	0
$881$	27.0359	0.910862	0.455431	−	0.890271i	$-0.349485\pi$
$881$	27.0359	0.910862	0.455431	+	0.890271i	$0.349485\pi$
$882$	0	0
$883$	−13.3882	−0.450549	−0.225274	−	0.974295i	$-0.572328\pi$
$883$	−13.3882	−0.450549	−0.225274	+	0.974295i	$0.572328\pi$
$884$	0	0
$885$	12.7637	0.429046
$886$	0	0
$887$	−12.6712	−0.425457	−0.212729	−	0.977111i	$-0.568235\pi$
$887$	−12.6712	−0.425457	−0.212729	+	0.977111i	$0.568235\pi$
$888$	0	0
$889$	−2.47162	−0.0828955
$890$	0	0
$891$	−3.04660	−0.102065
$892$	0	0
$893$	−25.0130	−0.837029
$894$	0	0
$895$	−13.2399	−0.442562
$896$	0	0
$897$	−1.24265	−0.0414908
$898$	0	0
$899$	−34.7569	−1.15921
$900$	0	0
$901$	87.9235	2.92916
$902$	0	0
$903$	5.20200	0.173112
$904$	0	0
$905$	33.9038	1.12700
$906$	0	0
$907$	−22.0547	−0.732313	−0.366157	−	0.930553i	$-0.619327\pi$
$907$	−22.0547	−0.732313	−0.366157	+	0.930553i	$0.619327\pi$
$908$	0	0
$909$	12.1731	0.403756
$910$	0	0
$911$	43.3934	1.43769	0.718844	−	0.695171i	$-0.244672\pi$
$911$	43.3934	1.43769	0.718844	+	0.695171i	$0.244672\pi$
$912$	0	0
$913$	21.5800	0.714195
$914$	0	0
$915$	2.71593	0.0897857
$916$	0	0
$917$	−3.65319	−0.120639
$918$	0	0
$919$	−52.4028	−1.72861	−0.864304	−	0.502970i	$-0.832241\pi$
$919$	−52.4028	−1.72861	−0.864304	+	0.502970i	$0.832241\pi$
$920$	0	0
$921$	−19.9437	−0.657168
$922$	0	0
$923$	−8.80159	−0.289708
$924$	0	0
$925$	21.4593	0.705577
$926$	0	0
$927$	18.4467	0.605868
$928$	0	0
$929$	−8.43753	−0.276826	−0.138413	−	0.990375i	$-0.544200\pi$
$929$	−8.43753	−0.276826	−0.138413	+	0.990375i	$0.544200\pi$
$930$	0	0
$931$	3.19046	0.104563
$932$	0	0
$933$	10.0498	0.329016
$934$	0	0
$935$	−33.3745	−1.09146
$936$	0	0
$937$	−35.8332	−1.17062	−0.585310	−	0.810810i	$-0.699027\pi$
$937$	−35.8332	−1.17062	−0.585310	+	0.810810i	$0.699027\pi$
$938$	0	0
$939$	−0.582673	−0.0190148
$940$	0	0
$941$	−21.7906	−0.710352	−0.355176	−	0.934800i	$-0.615579\pi$
$941$	−21.7906	−0.710352	−0.355176	+	0.934800i	$0.615579\pi$
$942$	0	0
$943$	9.77578	0.318343
$944$	0	0
$945$	6.52147	0.212143
$946$	0	0
$947$	−11.1570	−0.362555	−0.181277	−	0.983432i	$-0.558023\pi$
$947$	−11.1570	−0.362555	−0.181277	+	0.983432i	$0.558023\pi$
$948$	0	0
$949$	−4.37797	−0.142115
$950$	0	0
$951$	20.0820	0.651203
$952$	0	0
$953$	−49.6642	−1.60878	−0.804391	−	0.594101i	$-0.797508\pi$
$953$	−49.6642	−1.60878	−0.804391	+	0.594101i	$0.797508\pi$
$954$	0	0
$955$	10.5733	0.342145
$956$	0	0
$957$	24.7319	0.799470
$958$	0	0
$959$	13.4016	0.432761
$960$	0	0
$961$	1.54163	0.0497299
$962$	0	0
$963$	4.21771	0.135914
$964$	0	0
$965$	−32.7030	−1.05275
$966$	0	0
$967$	−15.8683	−0.510291	−0.255145	−	0.966903i	$-0.582123\pi$
$967$	−15.8683	−0.510291	−0.255145	+	0.966903i	$0.582123\pi$
$968$	0	0
$969$	21.0025	0.674698
$970$	0	0
$971$	−1.01819	−0.0326752	−0.0163376	−	0.999867i	$-0.505201\pi$
$971$	−1.01819	−0.0326752	−0.0163376	+	0.999867i	$0.505201\pi$
$972$	0	0
$973$	−16.3563	−0.524358
$974$	0	0
$975$	−1.81253	−0.0580476
$976$	0	0
$977$	34.8975	1.11647	0.558235	−	0.829683i	$-0.311479\pi$
$977$	34.8975	1.11647	0.558235	+	0.829683i	$0.311479\pi$
$978$	0	0
$979$	−19.8446	−0.634237
$980$	0	0
$981$	16.7178	0.533758
$982$	0	0
$983$	−56.4029	−1.79897	−0.899487	−	0.436947i	$-0.856060\pi$
$983$	−56.4029	−1.79897	−0.899487	+	0.436947i	$0.856060\pi$
$984$	0	0
$985$	26.9225	0.857823
$986$	0	0
$987$	−7.97207	−0.253754
$988$	0	0
$989$	−11.6869	−0.371620
$990$	0	0
$991$	24.2515	0.770374	0.385187	−	0.922839i	$-0.374137\pi$
$991$	24.2515	0.770374	0.385187	+	0.922839i	$0.374137\pi$
$992$	0	0
$993$	−23.2286	−0.737138
$994$	0	0
$995$	−26.0945	−0.827250
$996$	0	0
$997$	34.7021	1.09902	0.549512	−	0.835486i	$-0.314813\pi$
$997$	34.7021	1.09902	0.549512	+	0.835486i	$0.314813\pi$
$998$	0	0
$999$	−32.5205	−1.02890

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3584.2.a.k.1.2	yes	6
4.3	odd	2		3584.2.a.f.1.5	yes	6
8.3	odd	2		3584.2.a.l.1.2	yes	6
8.5	even	2		3584.2.a.e.1.5	✓	6
16.3	odd	4		3584.2.b.i.1793.8		12
16.5	even	4		3584.2.b.k.1793.8		12
16.11	odd	4		3584.2.b.i.1793.5		12
16.13	even	4		3584.2.b.k.1793.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3584.2.a.e.1.5	✓	6	8.5	even	2
3584.2.a.f.1.5	yes	6	4.3	odd	2
3584.2.a.k.1.2	yes	6	1.1	even	1	trivial
3584.2.a.l.1.2	yes	6	8.3	odd	2
3584.2.b.i.1793.5		12	16.11	odd	4
3584.2.b.i.1793.8		12	16.3	odd	4
3584.2.b.k.1793.5		12	16.13	even	4
3584.2.b.k.1793.8		12	16.5	even	4

Overview	Random
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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:	\( N \)	\(=\)	\( 3584 = 2^{9} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3584.a (trivial)

\(f(q)\)	\(=\)	\(q-1.01685 q^{3} -1.29145 q^{5} -1.00000 q^{7} -1.96601 q^{9} +O(q^{10})\)	\(q-1.01685 q^{3} -1.29145 q^{5} -1.00000 q^{7} -1.96601 q^{9} -3.99188 q^{11} -0.534938 q^{13} +1.31322 q^{15} -6.47379 q^{17} +3.19046 q^{19} +1.01685 q^{21} -2.28447 q^{23} -3.33215 q^{25} +5.04971 q^{27} +6.09287 q^{29} -5.70453 q^{31} +4.05916 q^{33} +1.29145 q^{35} -6.44008 q^{37} +0.543954 q^{39} -4.27923 q^{41} +5.11578 q^{43} +2.53901 q^{45} -7.83993 q^{47} +1.00000 q^{49} +6.58291 q^{51} -13.5814 q^{53} +5.15533 q^{55} -3.24424 q^{57} +9.71935 q^{59} +2.06814 q^{61} +1.96601 q^{63} +0.690848 q^{65} +9.06175 q^{67} +2.32298 q^{69} +16.4535 q^{71} +8.18408 q^{73} +3.38831 q^{75} +3.99188 q^{77} -0.960761 q^{79} +0.763200 q^{81} -5.40599 q^{83} +8.36061 q^{85} -6.19556 q^{87} +4.97125 q^{89} +0.534938 q^{91} +5.80068 q^{93} -4.12034 q^{95} +6.97532 q^{97} +7.84806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{3} - 6 q^{7} + 10 q^{9}+O(q^{10}) \) 6 * q + 4 * q^3 - 6 * q^7 + 10 * q^9	\( 6 q + 4 q^{3} - 6 q^{7} + 10 q^{9} + 8 q^{11} + 8 q^{15} + 20 q^{19} - 4 q^{21} + 2 q^{25} + 16 q^{27} - 4 q^{29} + 8 q^{31} + 4 q^{33} - 20 q^{37} - 4 q^{41} + 24 q^{43} - 8 q^{47} + 6 q^{49} + 24 q^{51} - 4 q^{53} - 16 q^{55} - 4 q^{57} + 12 q^{59} + 8 q^{61} - 10 q^{63} - 8 q^{65} + 16 q^{67} + 40 q^{69} + 8 q^{71} + 16 q^{73} + 28 q^{75} - 8 q^{77} + 24 q^{79} + 10 q^{81} + 12 q^{83} + 8 q^{87} + 16 q^{89} - 24 q^{93} + 16 q^{95} + 16 q^{97} + 40 q^{99}+O(q^{100}) \) 6 * q + 4 * q^3 - 6 * q^7 + 10 * q^9 + 8 * q^11 + 8 * q^15 + 20 * q^19 - 4 * q^21 + 2 * q^25 + 16 * q^27 - 4 * q^29 + 8 * q^31 + 4 * q^33 - 20 * q^37 - 4 * q^41 + 24 * q^43 - 8 * q^47 + 6 * q^49 + 24 * q^51 - 4 * q^53 - 16 * q^55 - 4 * q^57 + 12 * q^59 + 8 * q^61 - 10 * q^63 - 8 * q^65 + 16 * q^67 + 40 * q^69 + 8 * q^71 + 16 * q^73 + 28 * q^75 - 8 * q^77 + 24 * q^79 + 10 * q^81 + 12 * q^83 + 8 * q^87 + 16 * q^89 - 24 * q^93 + 16 * q^95 + 16 * q^97 + 40 * q^99

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