LMFDB - Embedded newform 2925.2.a.bq.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2925,2,Mod(1,2925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2925, 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("2925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2925 = 3^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2925.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:	$23.3562425912$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.1509051136.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 13x^{4} + 43x^{2} - 19 $ x^6 - 13x^4 + 43x^2 - 19
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.721444$ of defining polynomial
Character	$\chi$	$=$	2925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.721444 q^{2} -1.47952 q^{4} +2.55352 q^{7} +2.51028 q^{8} +O(q^{10})$	$q-0.721444 q^{2} -1.47952 q^{4} +2.55352 q^{7} +2.51028 q^{8} -3.95317 q^{11} +1.00000 q^{13} -1.84222 q^{14} +1.14801 q^{16} +5.07395 q^{17} -0.479518 q^{19} +2.85199 q^{22} -4.67461 q^{23} -0.721444 q^{26} -3.77798 q^{28} +6.51684 q^{29} +3.92599 q^{31} -5.84878 q^{32} -3.66057 q^{34} +5.58657 q^{37} +0.345946 q^{38} -4.67461 q^{41} -4.47952 q^{43} +5.84878 q^{44} +3.37247 q^{46} +0.721444 q^{47} -0.479518 q^{49} -1.47952 q^{52} -11.1914 q^{53} +6.41005 q^{56} -4.70153 q^{58} +2.16433 q^{59} +8.85199 q^{61} -2.83239 q^{62} +1.92355 q^{64} +5.92599 q^{67} -7.50700 q^{68} +11.9367 q^{71} -7.43855 q^{73} -4.03040 q^{74} +0.709456 q^{76} -10.0945 q^{77} +13.4386 q^{79} +3.37247 q^{82} +10.8693 q^{83} +3.23172 q^{86} -9.92355 q^{88} -18.0542 q^{89} +2.55352 q^{91} +6.91617 q^{92} -0.520482 q^{94} -1.10705 q^{97} +0.345946 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 14 q^{4} + 6 q^{7}+O(q^{10}) $ 6 * q + 14 * q^4 + 6 * q^7	$ 6 q + 14 q^{4} + 6 q^{7} + 6 q^{13} + 34 q^{16} + 20 q^{19} - 10 q^{22} + 18 q^{28} + 10 q^{31} + 6 q^{34} - 8 q^{37} - 4 q^{43} + 16 q^{46} + 20 q^{49} + 14 q^{52} - 46 q^{58} + 26 q^{61} + 70 q^{64} + 22 q^{67} + 24 q^{73} + 100 q^{76} + 12 q^{79} + 16 q^{82} - 118 q^{88} + 6 q^{91} - 26 q^{94} + 12 q^{97}+O(q^{100}) $ 6 * q + 14 * q^4 + 6 * q^7 + 6 * q^13 + 34 * q^16 + 20 * q^19 - 10 * q^22 + 18 * q^28 + 10 * q^31 + 6 * q^34 - 8 * q^37 - 4 * q^43 + 16 * q^46 + 20 * q^49 + 14 * q^52 - 46 * q^58 + 26 * q^61 + 70 * q^64 + 22 * q^67 + 24 * q^73 + 100 * q^76 + 12 * q^79 + 16 * q^82 - 118 * q^88 + 6 * q^91 - 26 * q^94 + 12 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.721444	−0.510138	−0.255069	−	0.966923i	$-0.582098\pi$
$2$	−0.721444	−0.510138	−0.255069	+	0.966923i	$0.582098\pi$
$3$	0	0
$3$	0	0
$4$	−1.47952	−0.739759
$5$	0	0
$5$	0	0
$6$	0	0
$7$	2.55352	0.965141	0.482571	−	0.875857i	$-0.339703\pi$
$7$	2.55352	0.965141	0.482571	+	0.875857i	$0.339703\pi$
$8$	2.51028	0.887517
$9$	0	0
$10$	0	0
$11$	−3.95317	−1.19192	−0.595962	−	0.803012i	$-0.703229\pi$
$11$	−3.95317	−1.19192	−0.595962	+	0.803012i	$0.703229\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.84222	−0.492355
$15$	0	0
$16$	1.14801	0.287003
$17$	5.07395	1.23061	0.615307	−	0.788288i	$-0.289032\pi$
$17$	5.07395	1.23061	0.615307	+	0.788288i	$0.289032\pi$
$18$	0	0
$19$	−0.479518	−0.110009	−0.0550045	−	0.998486i	$-0.517517\pi$
$19$	−0.479518	−0.110009	−0.0550045	+	0.998486i	$0.517517\pi$
$20$	0	0
$21$	0	0
$22$	2.85199	0.608046
$23$	−4.67461	−0.974724	−0.487362	−	0.873200i	$-0.662041\pi$
$23$	−4.67461	−0.974724	−0.487362	+	0.873200i	$0.662041\pi$
$24$	0	0
$25$	0	0
$26$	−0.721444	−0.141487
$27$	0	0
$28$	−3.77798	−0.713972
$29$	6.51684	1.21015	0.605073	−	0.796170i	$-0.293144\pi$
$29$	6.51684	1.21015	0.605073	+	0.796170i	$0.293144\pi$
$30$	0	0
$31$	3.92599	0.705129	0.352565	−	0.935787i	$-0.385310\pi$
$31$	3.92599	0.705129	0.352565	+	0.935787i	$0.385310\pi$
$32$	−5.84878	−1.03393
$33$	0	0
$34$	−3.66057	−0.627783
$35$	0	0
$36$	0	0
$37$	5.58657	0.918426	0.459213	−	0.888326i	$-0.348132\pi$
$37$	5.58657	0.918426	0.459213	+	0.888326i	$0.348132\pi$
$38$	0.345946	0.0561198
$39$	0	0
$40$	0	0
$41$	−4.67461	−0.730052	−0.365026	−	0.930997i	$-0.618940\pi$
$41$	−4.67461	−0.730052	−0.365026	+	0.930997i	$0.618940\pi$
$42$	0	0
$43$	−4.47952	−0.683120	−0.341560	−	0.939860i	$-0.610955\pi$
$43$	−4.47952	−0.683120	−0.341560	+	0.939860i	$0.610955\pi$
$44$	5.84878	0.881737
$45$	0	0
$46$	3.37247	0.497244
$47$	0.721444	0.105233	0.0526167	−	0.998615i	$-0.483244\pi$
$47$	0.721444	0.105233	0.0526167	+	0.998615i	$0.483244\pi$
$48$	0	0
$49$	−0.479518	−0.0685026
$50$	0	0
$51$	0	0
$52$	−1.47952	−0.205172
$53$	−11.1914	−1.53726	−0.768632	−	0.639692i	$-0.779062\pi$
$53$	−11.1914	−1.53726	−0.768632	+	0.639692i	$0.779062\pi$
$54$	0	0
$55$	0	0
$56$	6.41005	0.856580
$57$	0	0
$58$	−4.70153	−0.617342
$59$	2.16433	0.281772	0.140886	−	0.990026i	$-0.455005\pi$
$59$	2.16433	0.281772	0.140886	+	0.990026i	$0.455005\pi$
$60$	0	0
$61$	8.85199	1.13338	0.566691	−	0.823931i	$-0.308224\pi$
$61$	8.85199	1.13338	0.566691	+	0.823931i	$0.308224\pi$
$62$	−2.83239	−0.359713
$63$	0	0
$64$	1.92355	0.240444
$65$	0	0
$66$	0	0
$67$	5.92599	0.723975	0.361988	−	0.932183i	$-0.382098\pi$
$67$	5.92599	0.723975	0.361988	+	0.932183i	$0.382098\pi$
$68$	−7.50700	−0.910357
$69$	0	0
$70$	0	0
$71$	11.9367	1.41663	0.708315	−	0.705897i	$-0.249456\pi$
$71$	11.9367	1.41663	0.708315	+	0.705897i	$0.249456\pi$
$72$	0	0
$73$	−7.43855	−0.870617	−0.435308	−	0.900281i	$-0.643361\pi$
$73$	−7.43855	−0.870617	−0.435308	+	0.900281i	$0.643361\pi$
$74$	−4.03040	−0.468524
$75$	0	0
$76$	0.709456	0.0813802
$77$	−10.0945	−1.15038
$78$	0	0
$79$	13.4386	1.51196	0.755978	−	0.654597i	$-0.227162\pi$
$79$	13.4386	1.51196	0.755978	+	0.654597i	$0.227162\pi$
$80$	0	0
$81$	0	0
$82$	3.37247	0.372427
$83$	10.8693	1.19306	0.596532	−	0.802589i	$-0.296545\pi$
$83$	10.8693	1.19306	0.596532	+	0.802589i	$0.296545\pi$
$84$	0	0
$85$	0	0
$86$	3.23172	0.348486
$87$	0	0
$88$	−9.92355	−1.05785
$89$	−18.0542	−1.91374	−0.956872	−	0.290509i	$-0.906175\pi$
$89$	−18.0542	−1.91374	−0.956872	+	0.290509i	$0.906175\pi$
$90$	0	0
$91$	2.55352	0.267682
$92$	6.91617	0.721061
$93$	0	0
$94$	−0.520482	−0.0536836
$95$	0	0
$96$	0	0
$97$	−1.10705	−0.112404	−0.0562018	−	0.998419i	$-0.517899\pi$
$97$	−1.10705	−0.112404	−0.0562018	+	0.998419i	$0.517899\pi$
$98$	0.345946	0.0349458
$99$	0	0
$100$	0	0
$101$	−12.6343	−1.25716	−0.628582	−	0.777744i	$-0.716364\pi$
$101$	−12.6343	−1.25716	−0.628582	+	0.777744i	$0.716364\pi$
$102$	0	0
$103$	−1.52048	−0.149818	−0.0749088	−	0.997190i	$-0.523867\pi$
$103$	−1.52048	−0.149818	−0.0749088	+	0.997190i	$0.523867\pi$
$104$	2.51028	0.246153
$105$	0	0
$106$	8.07401	0.784217
$107$	7.90633	0.764334	0.382167	−	0.924093i	$-0.375178\pi$
$107$	7.90633	0.764334	0.382167	+	0.924093i	$0.375178\pi$
$108$	0	0
$109$	17.4386	1.67031	0.835155	−	0.550014i	$-0.185378\pi$
$109$	17.4386	1.67031	0.835155	+	0.550014i	$0.185378\pi$
$110$	0	0
$111$	0	0
$112$	2.93147	0.276998
$113$	−8.70501	−0.818898	−0.409449	−	0.912333i	$-0.634279\pi$
$113$	−8.70501	−0.818898	−0.409449	+	0.912333i	$0.634279\pi$
$114$	0	0
$115$	0	0
$116$	−9.64178	−0.895217
$117$	0	0
$118$	−1.56145	−0.143743
$119$	12.9564	1.18772
$120$	0	0
$121$	4.62753	0.420684
$122$	−6.38622	−0.578181
$123$	0	0
$124$	−5.80858	−0.521626
$125$	0	0
$126$	0	0
$127$	12.5456	1.11324	0.556621	−	0.830767i	$-0.312098\pi$
$127$	12.5456	1.11324	0.556621	+	0.830767i	$0.312098\pi$
$128$	10.3098	0.911269
$129$	0	0
$130$	0	0
$131$	−8.35906	−0.730335	−0.365167	−	0.930942i	$-0.618988\pi$
$131$	−8.35906	−0.730335	−0.365167	+	0.930942i	$0.618988\pi$
$132$	0	0
$133$	−1.22446	−0.106174
$134$	−4.27527	−0.369327
$135$	0	0
$136$	12.7370	1.09219
$137$	−8.70501	−0.743719	−0.371859	−	0.928289i	$-0.621280\pi$
$137$	−8.70501	−0.743719	−0.371859	+	0.928289i	$0.621280\pi$
$138$	0	0
$139$	13.1731	1.11733	0.558665	−	0.829393i	$-0.311314\pi$
$139$	13.1731	1.11733	0.558665	+	0.829393i	$0.311314\pi$
$140$	0	0
$141$	0	0
$142$	−8.61168	−0.722677
$143$	−3.95317	−0.330580
$144$	0	0
$145$	0	0
$146$	5.36650	0.444135
$147$	0	0
$148$	−8.26542	−0.679414
$149$	5.02056	0.411300	0.205650	−	0.978626i	$-0.434069\pi$
$149$	5.02056	0.411300	0.205650	+	0.978626i	$0.434069\pi$
$150$	0	0
$151$	13.3645	1.08759	0.543796	−	0.839218i	$-0.316987\pi$
$151$	13.3645	1.08759	0.543796	+	0.839218i	$0.316987\pi$
$152$	−1.20372	−0.0976349
$153$	0	0
$154$	7.28262	0.586850
$155$	0	0
$156$	0	0
$157$	4.43855	0.354235	0.177118	−	0.984190i	$-0.443323\pi$
$157$	4.43855	0.354235	0.177118	+	0.984190i	$0.443323\pi$
$158$	−9.69517	−0.771306
$159$	0	0
$160$	0	0
$161$	−11.9367	−0.940746
$162$	0	0
$163$	−5.73458	−0.449167	−0.224583	−	0.974455i	$-0.572102\pi$
$163$	−5.73458	−0.449167	−0.224583	+	0.974455i	$0.572102\pi$
$164$	6.91617	0.540062
$165$	0	0
$166$	−7.84162	−0.608628
$167$	9.00328	0.696694	0.348347	−	0.937366i	$-0.386743\pi$
$167$	9.00328	0.696694	0.348347	+	0.937366i	$0.386743\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	0	0
$172$	6.62753	0.505344
$173$	12.6343	0.960571	0.480285	−	0.877112i	$-0.340533\pi$
$173$	12.6343	0.960571	0.480285	+	0.877112i	$0.340533\pi$
$174$	0	0
$175$	0	0
$176$	−4.53828	−0.342085
$177$	0	0
$178$	13.0251	0.976274
$179$	0.345946	0.0258572	0.0129286	−	0.999916i	$-0.495885\pi$
$179$	0.345946	0.0258572	0.0129286	+	0.999916i	$0.495885\pi$
$180$	0	0
$181$	23.4637	1.74404	0.872021	−	0.489469i	$-0.162809\pi$
$181$	23.4637	1.74404	0.872021	+	0.489469i	$0.162809\pi$
$182$	−1.84222	−0.136555
$183$	0	0
$184$	−11.7346	−0.865084
$185$	0	0
$186$	0	0
$187$	−20.0582	−1.46680
$188$	−1.06739	−0.0778474
$189$	0	0
$190$	0	0
$191$	16.6113	1.20195	0.600977	−	0.799266i	$-0.294778\pi$
$191$	16.6113	1.20195	0.600977	+	0.799266i	$0.294778\pi$
$192$	0	0
$193$	15.6526	1.12670	0.563351	−	0.826218i	$-0.309512\pi$
$193$	15.6526	1.12670	0.563351	+	0.826218i	$0.309512\pi$
$194$	0.798673	0.0573413
$195$	0	0
$196$	0.709456	0.0506754
$197$	−14.0238	−0.999157	−0.499578	−	0.866269i	$-0.666512\pi$
$197$	−14.0238	−0.999157	−0.499578	+	0.866269i	$0.666512\pi$
$198$	0	0
$199$	21.1731	1.50092	0.750462	−	0.660914i	$-0.229831\pi$
$199$	21.1731	1.50092	0.750462	+	0.660914i	$0.229831\pi$
$200$	0	0
$201$	0	0
$202$	9.11497	0.641327
$203$	16.6409	1.16796
$204$	0	0
$205$	0	0
$206$	1.09694	0.0764276
$207$	0	0
$208$	1.14801	0.0796002
$209$	1.89562	0.131122
$210$	0	0
$211$	9.37247	0.645228	0.322614	−	0.946531i	$-0.395439\pi$
$211$	9.37247	0.645228	0.322614	+	0.946531i	$0.395439\pi$
$212$	16.5579	1.13720
$213$	0	0
$214$	−5.70398	−0.389916
$215$	0	0
$216$	0	0
$217$	10.0251	0.680549
$218$	−12.5809	−0.852089
$219$	0	0
$220$	0	0
$221$	5.07395	0.341311
$222$	0	0
$223$	2.26542	0.151704	0.0758520	−	0.997119i	$-0.475832\pi$
$223$	2.26542	0.151704	0.0758520	+	0.997119i	$0.475832\pi$
$224$	−14.9350	−0.997887
$225$	0	0
$226$	6.28018	0.417751
$227$	26.3361	1.74799	0.873993	−	0.485939i	$-0.161522\pi$
$227$	26.3361	1.74799	0.873993	+	0.485939i	$0.161522\pi$
$228$	0	0
$229$	−18.1322	−1.19821	−0.599104	−	0.800671i	$-0.704476\pi$
$229$	−18.1322	−1.19821	−0.599104	+	0.800671i	$0.704476\pi$
$230$	0	0
$231$	0	0
$232$	16.3591	1.07403
$233$	15.1685	0.993718	0.496859	−	0.867831i	$-0.334487\pi$
$233$	15.1685	0.993718	0.496859	+	0.867831i	$0.334487\pi$
$234$	0	0
$235$	0	0
$236$	−3.20217	−0.208443
$237$	0	0
$238$	−9.34735	−0.605899
$239$	−0.0772283	−0.00499548	−0.00249774	−	0.999997i	$-0.500795\pi$
$239$	−0.0772283	−0.00499548	−0.00249774	+	0.999997i	$0.500795\pi$
$240$	0	0
$241$	9.73458	0.627059	0.313530	−	0.949578i	$-0.398489\pi$
$241$	9.73458	0.627059	0.313530	+	0.949578i	$0.398489\pi$
$242$	−3.33850	−0.214607
$243$	0	0
$244$	−13.0967	−0.838429
$245$	0	0
$246$	0	0
$247$	−0.479518	−0.0305110
$248$	9.85534	0.625815
$249$	0	0
$250$	0	0
$251$	19.0444	1.20207	0.601036	−	0.799222i	$-0.294755\pi$
$251$	19.0444	1.20207	0.601036	+	0.799222i	$0.294755\pi$
$252$	0	0
$253$	18.4795	1.16180
$254$	−9.05095	−0.567907
$255$	0	0
$256$	−11.2851	−0.705317
$257$	14.0772	0.878113	0.439057	−	0.898459i	$-0.355313\pi$
$257$	14.0772	0.878113	0.439057	+	0.898459i	$0.355313\pi$
$258$	0	0
$259$	14.2654	0.886410
$260$	0	0
$261$	0	0
$262$	6.03060	0.372571
$263$	−17.0641	−1.05222	−0.526108	−	0.850418i	$-0.676349\pi$
$263$	−17.0641	−1.05222	−0.526108	+	0.850418i	$0.676349\pi$
$264$	0	0
$265$	0	0
$266$	0.883380	0.0541635
$267$	0	0
$268$	−8.76762	−0.535567
$269$	26.6582	1.62538	0.812689	−	0.582698i	$-0.198003\pi$
$269$	26.6582	1.62538	0.812689	+	0.582698i	$0.198003\pi$
$270$	0	0
$271$	6.33943	0.385093	0.192546	−	0.981288i	$-0.438325\pi$
$271$	6.33943	0.385093	0.192546	+	0.981288i	$0.438325\pi$
$272$	5.82494	0.353189
$273$	0	0
$274$	6.28018	0.379399
$275$	0	0
$276$	0	0
$277$	−14.5969	−0.877045	−0.438522	−	0.898720i	$-0.644498\pi$
$277$	−14.5969	−0.877045	−0.438522	+	0.898720i	$0.644498\pi$
$278$	−9.50368	−0.569993
$279$	0	0
$280$	0	0
$281$	16.6113	0.990949	0.495475	−	0.868622i	$-0.334994\pi$
$281$	16.6113	0.990949	0.495475	+	0.868622i	$0.334994\pi$
$282$	0	0
$283$	−28.8771	−1.71657	−0.858283	−	0.513177i	$-0.828469\pi$
$283$	−28.8771	−1.71657	−0.858283	+	0.513177i	$0.828469\pi$
$284$	−17.6606	−1.04796
$285$	0	0
$286$	2.85199	0.168642
$287$	−11.9367	−0.704603
$288$	0	0
$289$	8.74494	0.514408
$290$	0	0
$291$	0	0
$292$	11.0055	0.644047
$293$	15.0140	0.877127	0.438563	−	0.898700i	$-0.355487\pi$
$293$	15.0140	0.877127	0.438563	+	0.898700i	$0.355487\pi$
$294$	0	0
$295$	0	0
$296$	14.0238	0.815119
$297$	0	0
$298$	−3.62205	−0.209820
$299$	−4.67461	−0.270340
$300$	0	0
$301$	−11.4386	−0.659307
$302$	−9.64178	−0.554822
$303$	0	0
$304$	−0.550492	−0.0315729
$305$	0	0
$306$	0	0
$307$	−4.84162	−0.276326	−0.138163	−	0.990410i	$-0.544120\pi$
$307$	−4.84162	−0.276326	−0.138163	+	0.990410i	$0.544120\pi$
$308$	14.9350	0.851001
$309$	0	0
$310$	0	0
$311$	−13.7256	−0.778305	−0.389153	−	0.921173i	$-0.627232\pi$
$311$	−13.7256	−0.778305	−0.389153	+	0.921173i	$0.627232\pi$
$312$	0	0
$313$	13.6936	0.774009	0.387004	−	0.922078i	$-0.373510\pi$
$313$	13.6936	0.774009	0.387004	+	0.922078i	$0.373510\pi$
$314$	−3.20217	−0.180709
$315$	0	0
$316$	−19.8826	−1.11848
$317$	9.00328	0.505674	0.252837	−	0.967509i	$-0.418636\pi$
$317$	9.00328	0.505674	0.252837	+	0.967509i	$0.418636\pi$
$318$	0	0
$319$	−25.7621	−1.44240
$320$	0	0
$321$	0	0
$322$	8.61168	0.479910
$323$	−2.43305	−0.135379
$324$	0	0
$325$	0	0
$326$	4.13718	0.229137
$327$	0	0
$328$	−11.7346	−0.647934
$329$	1.84222	0.101565
$330$	0	0
$331$	12.4795	0.685936	0.342968	−	0.939347i	$-0.388568\pi$
$331$	12.4795	0.685936	0.342968	+	0.939347i	$0.388568\pi$
$332$	−16.0814	−0.882581
$333$	0	0
$334$	−6.49536	−0.355410
$335$	0	0
$336$	0	0
$337$	−28.7187	−1.56441	−0.782204	−	0.623022i	$-0.785905\pi$
$337$	−28.7187	−1.56441	−0.782204	+	0.623022i	$0.785905\pi$
$338$	−0.721444	−0.0392414
$339$	0	0
$340$	0	0
$341$	−15.5201	−0.840461
$342$	0	0
$343$	−19.0991	−1.03126
$344$	−11.2448	−0.606281
$345$	0	0
$346$	−9.11497	−0.490024
$347$	−5.66477	−0.304101	−0.152050	−	0.988373i	$-0.548588\pi$
$347$	−5.66477	−0.304101	−0.152050	+	0.988373i	$0.548588\pi$
$348$	0	0
$349$	9.58657	0.513157	0.256579	−	0.966523i	$-0.417405\pi$
$349$	9.58657	0.513157	0.256579	+	0.966523i	$0.417405\pi$
$350$	0	0
$351$	0	0
$352$	23.1212	1.23236
$353$	13.3319	0.709588	0.354794	−	0.934945i	$-0.384551\pi$
$353$	13.3319	0.709588	0.354794	+	0.934945i	$0.384551\pi$
$354$	0	0
$355$	0	0
$356$	26.7116	1.41571
$357$	0	0
$358$	−0.249580	−0.0131907
$359$	−25.2391	−1.33207	−0.666035	−	0.745921i	$-0.732010\pi$
$359$	−25.2391	−1.33207	−0.666035	+	0.745921i	$0.732010\pi$
$360$	0	0
$361$	−18.7701	−0.987898
$362$	−16.9277	−0.889702
$363$	0	0
$364$	−3.77798	−0.198020
$365$	0	0
$366$	0	0
$367$	−9.25506	−0.483110	−0.241555	−	0.970387i	$-0.577657\pi$
$367$	−9.25506	−0.483110	−0.241555	+	0.970387i	$0.577657\pi$
$368$	−5.36650	−0.279748
$369$	0	0
$370$	0	0
$371$	−28.5776	−1.48368
$372$	0	0
$373$	27.3315	1.41517	0.707586	−	0.706627i	$-0.249784\pi$
$373$	27.3315	1.41517	0.707586	+	0.706627i	$0.249784\pi$
$374$	14.4708	0.748270
$375$	0	0
$376$	1.81103	0.0933965
$377$	6.51684	0.335634
$378$	0	0
$379$	4.00792	0.205873	0.102937	−	0.994688i	$-0.467176\pi$
$379$	4.00792	0.205873	0.102937	+	0.994688i	$0.467176\pi$
$380$	0	0
$381$	0	0
$382$	−11.9842	−0.613163
$383$	−2.58751	−0.132215	−0.0661077	−	0.997812i	$-0.521058\pi$
$383$	−2.58751	−0.132215	−0.0661077	+	0.997812i	$0.521058\pi$
$384$	0	0
$385$	0	0
$386$	−11.2925	−0.574774
$387$	0	0
$388$	1.63790	0.0831516
$389$	−27.4035	−1.38941	−0.694705	−	0.719295i	$-0.744465\pi$
$389$	−27.4035	−1.38941	−0.694705	+	0.719295i	$0.744465\pi$
$390$	0	0
$391$	−23.7187	−1.19951
$392$	−1.20372	−0.0607973
$393$	0	0
$394$	10.1174	0.509708
$395$	0	0
$396$	0	0
$397$	−1.93392	−0.0970605	−0.0485303	−	0.998822i	$-0.515454\pi$
$397$	−1.93392	−0.0970605	−0.0485303	+	0.998822i	$0.515454\pi$
$398$	−15.2752	−0.765678
$399$	0	0
$400$	0	0
$401$	−0.990162	−0.0494463	−0.0247232	−	0.999694i	$-0.507870\pi$
$401$	−0.990162	−0.0494463	−0.0247232	+	0.999694i	$0.507870\pi$
$402$	0	0
$403$	3.92599	0.195568
$404$	18.6927	0.929998
$405$	0	0
$406$	−12.0055	−0.595822
$407$	−22.0846	−1.09469
$408$	0	0
$409$	−35.7187	−1.76618	−0.883089	−	0.469206i	$-0.844540\pi$
$409$	−35.7187	−1.76618	−0.883089	+	0.469206i	$0.844540\pi$
$410$	0	0
$411$	0	0
$412$	2.24958	0.110829
$413$	5.52667	0.271950
$414$	0	0
$415$	0	0
$416$	−5.84878	−0.286760
$417$	0	0
$418$	−1.36758	−0.0668906
$419$	−15.4667	−0.755599	−0.377799	−	0.925887i	$-0.623319\pi$
$419$	−15.4667	−0.755599	−0.377799	+	0.925887i	$0.623319\pi$
$420$	0	0
$421$	−27.7040	−1.35021	−0.675105	−	0.737722i	$-0.735902\pi$
$421$	−27.7040	−1.35021	−0.675105	+	0.737722i	$0.735902\pi$
$422$	−6.76172	−0.329155
$423$	0	0
$424$	−28.0936	−1.36435
$425$	0	0
$426$	0	0
$427$	22.6038	1.09387
$428$	−11.6976	−0.565423
$429$	0	0
$430$	0	0
$431$	33.5210	1.61465	0.807324	−	0.590109i	$-0.200915\pi$
$431$	33.5210	1.61465	0.807324	+	0.590109i	$0.200915\pi$
$432$	0	0
$433$	−21.2392	−1.02069	−0.510346	−	0.859969i	$-0.670483\pi$
$433$	−21.2392	−1.02069	−0.510346	+	0.859969i	$0.670483\pi$
$434$	−7.23256	−0.347174
$435$	0	0
$436$	−25.8007	−1.23563
$437$	2.24156	0.107228
$438$	0	0
$439$	23.2905	1.11160	0.555799	−	0.831317i	$-0.312413\pi$
$439$	23.2905	1.11160	0.555799	+	0.831317i	$0.312413\pi$
$440$	0	0
$441$	0	0
$442$	−3.66057	−0.174116
$443$	−0.452727	−0.0215097	−0.0107549	−	0.999942i	$-0.503423\pi$
$443$	−0.452727	−0.0215097	−0.0107549	+	0.999942i	$0.503423\pi$
$444$	0	0
$445$	0	0
$446$	−1.63438	−0.0773900
$447$	0	0
$448$	4.91183	0.232062
$449$	4.48312	0.211572	0.105786	−	0.994389i	$-0.466264\pi$
$449$	4.48312	0.211572	0.105786	+	0.994389i	$0.466264\pi$
$450$	0	0
$451$	18.4795	0.870167
$452$	12.8792	0.605787
$453$	0	0
$454$	−19.0000	−0.891714
$455$	0	0
$456$	0	0
$457$	−23.5866	−1.10333	−0.551666	−	0.834065i	$-0.686008\pi$
$457$	−23.5866	−1.10333	−0.551666	+	0.834065i	$0.686008\pi$
$458$	13.0813	0.611251
$459$	0	0
$460$	0	0
$461$	−5.66477	−0.263835	−0.131917	−	0.991261i	$-0.542113\pi$
$461$	−5.66477	−0.263835	−0.131917	+	0.991261i	$0.542113\pi$
$462$	0	0
$463$	−9.84407	−0.457493	−0.228746	−	0.973486i	$-0.573463\pi$
$463$	−9.84407	−0.457493	−0.228746	+	0.973486i	$0.573463\pi$
$464$	7.48140	0.347315
$465$	0	0
$466$	−10.9432	−0.506934
$467$	17.3623	0.803433	0.401717	−	0.915764i	$-0.368414\pi$
$467$	17.3623	0.803433	0.401717	+	0.915764i	$0.368414\pi$
$468$	0	0
$469$	15.1322	0.698739
$470$	0	0
$471$	0	0
$472$	5.43308	0.250078
$473$	17.7083	0.814228
$474$	0	0
$475$	0	0
$476$	−19.1693	−0.878623
$477$	0	0
$478$	0.0557159	0.00254839
$479$	37.9745	1.73510	0.867550	−	0.497350i	$-0.165693\pi$
$479$	37.9745	1.73510	0.867550	+	0.497350i	$0.165693\pi$
$480$	0	0
$481$	5.58657	0.254725
$482$	−7.02295	−0.319887
$483$	0	0
$484$	−6.84651	−0.311205
$485$	0	0
$486$	0	0
$487$	−28.1242	−1.27443	−0.637216	−	0.770686i	$-0.719914\pi$
$487$	−28.1242	−1.27443	−0.637216	+	0.770686i	$0.719914\pi$
$488$	22.2210	1.00590
$489$	0	0
$490$	0	0
$491$	−2.08710	−0.0941897	−0.0470949	−	0.998890i	$-0.514996\pi$
$491$	−2.08710	−0.0941897	−0.0470949	+	0.998890i	$0.514996\pi$
$492$	0	0
$493$	33.0661	1.48922
$494$	0.345946	0.0155648
$495$	0	0
$496$	4.50708	0.202374
$497$	30.4807	1.36725
$498$	0	0
$499$	19.5945	0.877170	0.438585	−	0.898690i	$-0.355480\pi$
$499$	19.5945	0.877170	0.438585	+	0.898690i	$0.355480\pi$
$500$	0	0
$501$	0	0
$502$	−13.7395	−0.613222
$503$	30.6352	1.36595	0.682977	−	0.730439i	$-0.260685\pi$
$503$	30.6352	1.36595	0.682977	+	0.730439i	$0.260685\pi$
$504$	0	0
$505$	0	0
$506$	−13.3319	−0.592677
$507$	0	0
$508$	−18.5614	−0.823531
$509$	21.1315	0.936637	0.468319	−	0.883560i	$-0.344860\pi$
$509$	21.1315	0.936637	0.468319	+	0.883560i	$0.344860\pi$
$510$	0	0
$511$	−18.9945	−0.840268
$512$	−12.4781	−0.551460
$513$	0	0
$514$	−10.1559	−0.447959
$515$	0	0
$516$	0	0
$517$	−2.85199	−0.125430
$518$	−10.2917	−0.452192
$519$	0	0
$520$	0	0
$521$	9.34922	0.409597	0.204798	−	0.978804i	$-0.434346\pi$
$521$	9.34922	0.409597	0.204798	+	0.978804i	$0.434346\pi$
$522$	0	0
$523$	11.5560	0.505307	0.252654	−	0.967557i	$-0.418697\pi$
$523$	11.5560	0.505307	0.252654	+	0.967557i	$0.418697\pi$
$524$	12.3674	0.540272
$525$	0	0
$526$	12.3108	0.536775
$527$	19.9203	0.867742
$528$	0	0
$529$	−1.14801	−0.0499135
$530$	0	0
$531$	0	0
$532$	1.81161	0.0785434
$533$	−4.67461	−0.202480
$534$	0	0
$535$	0	0
$536$	14.8759	0.642541
$537$	0	0
$538$	−19.2324	−0.829167
$539$	1.89562	0.0816499
$540$	0	0
$541$	−14.7755	−0.635250	−0.317625	−	0.948216i	$-0.602885\pi$
$541$	−14.7755	−0.635250	−0.317625	+	0.948216i	$0.602885\pi$
$542$	−4.57355	−0.196451
$543$	0	0
$544$	−29.6764	−1.27237
$545$	0	0
$546$	0	0
$547$	−24.2654	−1.03751	−0.518757	−	0.854922i	$-0.673605\pi$
$547$	−24.2654	−1.03751	−0.518757	+	0.854922i	$0.673605\pi$
$548$	12.8792	0.550173
$549$	0	0
$550$	0	0
$551$	−3.12494	−0.133127
$552$	0	0
$553$	34.3157	1.45925
$554$	10.5309	0.447414
$555$	0	0
$556$	−19.4899	−0.826555
$557$	19.8431	0.840778	0.420389	−	0.907344i	$-0.361894\pi$
$557$	19.8431	0.840778	0.420389	+	0.907344i	$0.361894\pi$
$558$	0	0
$559$	−4.47952	−0.189463
$560$	0	0
$561$	0	0
$562$	−11.9842	−0.505521
$563$	−30.7420	−1.29562	−0.647809	−	0.761802i	$-0.724315\pi$
$563$	−30.7420	−1.29562	−0.647809	+	0.761802i	$0.724315\pi$
$564$	0	0
$565$	0	0
$566$	20.8332	0.875686
$567$	0	0
$568$	29.9645	1.25728
$569$	−39.3936	−1.65146	−0.825732	−	0.564062i	$-0.809238\pi$
$569$	−39.3936	−1.65146	−0.825732	+	0.564062i	$0.809238\pi$
$570$	0	0
$571$	−11.2905	−0.472495	−0.236247	−	0.971693i	$-0.575918\pi$
$571$	−11.2905	−0.472495	−0.236247	+	0.971693i	$0.575918\pi$
$572$	5.84878	0.244550
$573$	0	0
$574$	8.61168	0.359445
$575$	0	0
$576$	0	0
$577$	−30.0661	−1.25167	−0.625834	−	0.779957i	$-0.715241\pi$
$577$	−30.0661	−1.25167	−0.625834	+	0.779957i	$0.715241\pi$
$578$	−6.30899	−0.262419
$579$	0	0
$580$	0	0
$581$	27.7551	1.15148
$582$	0	0
$583$	44.2417	1.83230
$584$	−18.6728	−0.772688
$585$	0	0
$586$	−10.8318	−0.447456
$587$	3.30895	0.136575	0.0682875	−	0.997666i	$-0.478246\pi$
$587$	3.30895	0.136575	0.0682875	+	0.997666i	$0.478246\pi$
$588$	0	0
$589$	−1.88259	−0.0775706
$590$	0	0
$591$	0	0
$592$	6.41343	0.263591
$593$	−38.1956	−1.56850	−0.784252	−	0.620443i	$-0.786953\pi$
$593$	−38.1956	−1.56850	−0.784252	+	0.620443i	$0.786953\pi$
$594$	0	0
$595$	0	0
$596$	−7.42801	−0.304263
$597$	0	0
$598$	3.37247	0.137911
$599$	−36.4067	−1.48754	−0.743769	−	0.668436i	$-0.766964\pi$
$599$	−36.4067	−1.48754	−0.743769	+	0.668436i	$0.766964\pi$
$600$	0	0
$601$	−4.30639	−0.175661	−0.0878306	−	0.996135i	$-0.527993\pi$
$601$	−4.30639	−0.175661	−0.0878306	+	0.996135i	$0.527993\pi$
$602$	8.25228	0.336338
$603$	0	0
$604$	−19.7731	−0.804556
$605$	0	0
$606$	0	0
$607$	31.0251	1.25927	0.629635	−	0.776891i	$-0.283204\pi$
$607$	31.0251	1.25927	0.629635	+	0.776891i	$0.283204\pi$
$608$	2.80460	0.113741
$609$	0	0
$610$	0	0
$611$	0.721444	0.0291865
$612$	0	0
$613$	31.3872	1.26772	0.633859	−	0.773449i	$-0.281470\pi$
$613$	31.3872	1.26772	0.633859	+	0.773449i	$0.281470\pi$
$614$	3.49296	0.140964
$615$	0	0
$616$	−25.3400	−1.02098
$617$	−4.32867	−0.174266	−0.0871328	−	0.996197i	$-0.527770\pi$
$617$	−4.32867	−0.174266	−0.0871328	+	0.996197i	$0.527770\pi$
$618$	0	0
$619$	12.4134	0.498938	0.249469	−	0.968383i	$-0.419744\pi$
$619$	12.4134	0.498938	0.249469	+	0.968383i	$0.419744\pi$
$620$	0	0
$621$	0	0
$622$	9.90223	0.397043
$623$	−46.1019	−1.84703
$624$	0	0
$625$	0	0
$626$	−9.87918	−0.394851
$627$	0	0
$628$	−6.56692	−0.262049
$629$	28.3459	1.13023
$630$	0	0
$631$	38.7597	1.54300	0.771500	−	0.636230i	$-0.219507\pi$
$631$	38.7597	1.54300	0.771500	+	0.636230i	$0.219507\pi$
$632$	33.7345	1.34189
$633$	0	0
$634$	−6.49536	−0.257964
$635$	0	0
$636$	0	0
$637$	−0.479518	−0.0189992
$638$	18.5859	0.735825
$639$	0	0
$640$	0	0
$641$	−46.9540	−1.85457	−0.927285	−	0.374356i	$-0.877864\pi$
$641$	−46.9540	−1.85457	−0.927285	+	0.374356i	$0.877864\pi$
$642$	0	0
$643$	48.6117	1.91706	0.958529	−	0.284996i	$-0.0919921\pi$
$643$	48.6117	1.91706	0.958529	+	0.284996i	$0.0919921\pi$
$644$	17.6606	0.695925
$645$	0	0
$646$	1.75531	0.0690617
$647$	−47.0073	−1.84805	−0.924025	−	0.382333i	$-0.875121\pi$
$647$	−47.0073	−1.84805	−0.924025	+	0.382333i	$0.875121\pi$
$648$	0	0
$649$	−8.55597	−0.335851
$650$	0	0
$651$	0	0
$652$	8.48441	0.332275
$653$	6.56451	0.256889	0.128445	−	0.991717i	$-0.459002\pi$
$653$	6.56451	0.256889	0.128445	+	0.991717i	$0.459002\pi$
$654$	0	0
$655$	0	0
$656$	−5.36650	−0.209527
$657$	0	0
$658$	−1.32906	−0.0518123
$659$	43.6212	1.69924	0.849620	−	0.527396i	$-0.176831\pi$
$659$	43.6212	1.69924	0.849620	+	0.527396i	$0.176831\pi$
$660$	0	0
$661$	−32.5456	−1.26588	−0.632939	−	0.774202i	$-0.718151\pi$
$661$	−32.5456	−1.26588	−0.632939	+	0.774202i	$0.718151\pi$
$662$	−9.00328	−0.349922
$663$	0	0
$664$	27.2851	1.05887
$665$	0	0
$666$	0	0
$667$	−30.4637	−1.17956
$668$	−13.3205	−0.515386
$669$	0	0
$670$	0	0
$671$	−34.9934	−1.35090
$672$	0	0
$673$	11.4134	0.439956	0.219978	−	0.975505i	$-0.429402\pi$
$673$	11.4134	0.439956	0.219978	+	0.975505i	$0.429402\pi$
$674$	20.7190	0.798065
$675$	0	0
$676$	−1.47952	−0.0569045
$677$	−0.691891	−0.0265915	−0.0132958	−	0.999912i	$-0.504232\pi$
$677$	−0.691891	−0.0265915	−0.0132958	+	0.999912i	$0.504232\pi$
$678$	0	0
$679$	−2.82687	−0.108485
$680$	0	0
$681$	0	0
$682$	11.1969	0.428751
$683$	−43.7461	−1.67390	−0.836948	−	0.547282i	$-0.815663\pi$
$683$	−43.7461	−1.67390	−0.836948	+	0.547282i	$0.815663\pi$
$684$	0	0
$685$	0	0
$686$	13.7790	0.526083
$687$	0	0
$688$	−5.14253	−0.196057
$689$	−11.1914	−0.426360
$690$	0	0
$691$	−5.06364	−0.192630	−0.0963149	−	0.995351i	$-0.530706\pi$
$691$	−5.06364	−0.192630	−0.0963149	+	0.995351i	$0.530706\pi$
$692$	−18.6927	−0.710591
$693$	0	0
$694$	4.08682	0.155133
$695$	0	0
$696$	0	0
$697$	−23.7187	−0.898411
$698$	−6.91617	−0.261781
$699$	0	0
$700$	0	0
$701$	28.7929	1.08749	0.543747	−	0.839249i	$-0.317005\pi$
$701$	28.7929	1.08749	0.543747	+	0.839249i	$0.317005\pi$
$702$	0	0
$703$	−2.67886	−0.101035
$704$	−7.60411	−0.286591
$705$	0	0
$706$	−9.61825	−0.361988
$707$	−32.2621	−1.21334
$708$	0	0
$709$	13.8007	0.518295	0.259147	−	0.965838i	$-0.416558\pi$
$709$	13.8007	0.518295	0.259147	+	0.965838i	$0.416558\pi$
$710$	0	0
$711$	0	0
$712$	−45.3211	−1.69848
$713$	−18.3525	−0.687306
$714$	0	0
$715$	0	0
$716$	−0.511833	−0.0191281
$717$	0	0
$718$	18.2086	0.679540
$719$	−17.7560	−0.662186	−0.331093	−	0.943598i	$-0.607417\pi$
$719$	−17.7560	−0.662186	−0.331093	+	0.943598i	$0.607417\pi$
$720$	0	0
$721$	−3.88259	−0.144595
$722$	13.5416	0.503964
$723$	0	0
$724$	−34.7149	−1.29017
$725$	0	0
$726$	0	0
$727$	−5.52048	−0.204743	−0.102372	−	0.994746i	$-0.532643\pi$
$727$	−5.52048	−0.204743	−0.102372	+	0.994746i	$0.532643\pi$
$728$	6.41005	0.237572
$729$	0	0
$730$	0	0
$731$	−22.7288	−0.840657
$732$	0	0
$733$	−51.5401	−1.90368	−0.951839	−	0.306598i	$-0.900809\pi$
$733$	−51.5401	−1.90368	−0.951839	+	0.306598i	$0.900809\pi$
$734$	6.67701	0.246453
$735$	0	0
$736$	27.3408	1.00779
$737$	−23.4264	−0.862924
$738$	0	0
$739$	15.5432	0.571764	0.285882	−	0.958265i	$-0.407713\pi$
$739$	15.5432	0.571764	0.285882	+	0.958265i	$0.407713\pi$
$740$	0	0
$741$	0	0
$742$	20.6172	0.756880
$743$	46.6319	1.71076	0.855378	−	0.518004i	$-0.173325\pi$
$743$	46.6319	1.71076	0.855378	+	0.518004i	$0.173325\pi$
$744$	0	0
$745$	0	0
$746$	−19.7182	−0.721933
$747$	0	0
$748$	29.6764	1.08508
$749$	20.1890	0.737690
$750$	0	0
$751$	−15.2905	−0.557960	−0.278980	−	0.960297i	$-0.589996\pi$
$751$	−15.2905	−0.557960	−0.278980	+	0.960297i	$0.589996\pi$
$752$	0.828226	0.0302023
$753$	0	0
$754$	−4.70153	−0.171220
$755$	0	0
$756$	0	0
$757$	−25.6630	−0.932738	−0.466369	−	0.884590i	$-0.654438\pi$
$757$	−25.6630	−0.932738	−0.466369	+	0.884590i	$0.654438\pi$
$758$	−2.89149	−0.105024
$759$	0	0
$760$	0	0
$761$	42.9178	1.55577	0.777885	−	0.628406i	$-0.216292\pi$
$761$	42.9178	1.55577	0.777885	+	0.628406i	$0.216292\pi$
$762$	0	0
$763$	44.5298	1.61209
$764$	−24.5768	−0.889157
$765$	0	0
$766$	1.86674	0.0674481
$767$	2.16433	0.0781495
$768$	0	0
$769$	−13.8520	−0.499516	−0.249758	−	0.968308i	$-0.580351\pi$
$769$	−13.8520	−0.499516	−0.249758	+	0.968308i	$0.580351\pi$
$770$	0	0
$771$	0	0
$772$	−23.1584	−0.833488
$773$	−20.1413	−0.724433	−0.362217	−	0.932094i	$-0.617980\pi$
$773$	−20.1413	−0.724433	−0.362217	+	0.932094i	$0.617980\pi$
$774$	0	0
$775$	0	0
$776$	−2.77900	−0.0997601
$777$	0	0
$778$	19.7701	0.708791
$779$	2.24156	0.0803123
$780$	0	0
$781$	−47.1879	−1.68852
$782$	17.1117	0.611915
$783$	0	0
$784$	−0.550492	−0.0196604
$785$	0	0
$786$	0	0
$787$	−7.77798	−0.277255	−0.138628	−	0.990345i	$-0.544269\pi$
$787$	−7.77798	−0.277255	−0.138628	+	0.990345i	$0.544269\pi$
$788$	20.7485	0.739135
$789$	0	0
$790$	0	0
$791$	−22.2284	−0.790352
$792$	0	0
$793$	8.85199	0.314343
$794$	1.39521	0.0495143
$795$	0	0
$796$	−31.3260	−1.11032
$797$	−38.9408	−1.37936	−0.689678	−	0.724116i	$-0.742248\pi$
$797$	−38.9408	−1.37936	−0.689678	+	0.724116i	$0.742248\pi$
$798$	0	0
$799$	3.66057	0.129502
$800$	0	0
$801$	0	0
$802$	0.714346	0.0252244
$803$	29.4058	1.03771
$804$	0	0
$805$	0	0
$806$	−2.83239	−0.0997666
$807$	0	0
$808$	−31.7157	−1.11575
$809$	−9.30155	−0.327025	−0.163512	−	0.986541i	$-0.552282\pi$
$809$	−9.30155	−0.327025	−0.163512	+	0.986541i	$0.552282\pi$
$810$	0	0
$811$	−12.2575	−0.430419	−0.215210	−	0.976568i	$-0.569043\pi$
$811$	−12.2575	−0.430419	−0.215210	+	0.976568i	$0.569043\pi$
$812$	−24.6205	−0.864010
$813$	0	0
$814$	15.9328	0.558445
$815$	0	0
$816$	0	0
$817$	2.14801	0.0751494
$818$	25.7691	0.900995
$819$	0	0
$820$	0	0
$821$	−17.7083	−0.618023	−0.309012	−	0.951058i	$-0.599998\pi$
$821$	−17.7083	−0.618023	−0.309012	+	0.951058i	$0.599998\pi$
$822$	0	0
$823$	−50.5150	−1.76084	−0.880421	−	0.474192i	$-0.842740\pi$
$823$	−50.5150	−1.76084	−0.880421	+	0.474192i	$0.842740\pi$
$824$	−3.81683	−0.132966
$825$	0	0
$826$	−3.98719	−0.138732
$827$	−57.2695	−1.99146	−0.995728	−	0.0923360i	$-0.970567\pi$
$827$	−57.2695	−1.99146	−0.995728	+	0.0923360i	$0.970567\pi$
$828$	0	0
$829$	47.4943	1.64954	0.824772	−	0.565465i	$-0.191303\pi$
$829$	47.4943	1.64954	0.824772	+	0.565465i	$0.191303\pi$
$830$	0	0
$831$	0	0
$832$	1.92355	0.0666871
$833$	−2.43305	−0.0843002
$834$	0	0
$835$	0	0
$836$	−2.80460	−0.0969990
$837$	0	0
$838$	11.1584	0.385460
$839$	19.6886	0.679726	0.339863	−	0.940475i	$-0.389619\pi$
$839$	19.6886	0.679726	0.339863	+	0.940475i	$0.389619\pi$
$840$	0	0
$841$	13.4692	0.464453
$842$	19.9869	0.688793
$843$	0	0
$844$	−13.8667	−0.477313
$845$	0	0
$846$	0	0
$847$	11.8165	0.406020
$848$	−12.8479	−0.441199
$849$	0	0
$850$	0	0
$851$	−26.1150	−0.895211
$852$	0	0
$853$	53.7542	1.84051	0.920255	−	0.391320i	$-0.127981\pi$
$853$	53.7542	1.84051	0.920255	+	0.391320i	$0.127981\pi$
$854$	−16.3074	−0.558026
$855$	0	0
$856$	19.8471	0.678360
$857$	28.7396	0.981725	0.490862	−	0.871237i	$-0.336682\pi$
$857$	28.7396	0.981725	0.490862	+	0.871237i	$0.336682\pi$
$858$	0	0
$859$	−21.8667	−0.746084	−0.373042	−	0.927815i	$-0.621685\pi$
$859$	−21.8667	−0.746084	−0.373042	+	0.927815i	$0.621685\pi$
$860$	0	0
$861$	0	0
$862$	−24.1835	−0.823693
$863$	7.53084	0.256353	0.128176	−	0.991751i	$-0.459088\pi$
$863$	7.53084	0.256353	0.128176	+	0.991751i	$0.459088\pi$
$864$	0	0
$865$	0	0
$866$	15.3229	0.520694
$867$	0	0
$868$	−14.8323	−0.503443
$869$	−53.1248	−1.80214
$870$	0	0
$871$	5.92599	0.200795
$872$	43.7756	1.48243
$873$	0	0
$874$	−1.61716	−0.0547013
$875$	0	0
$876$	0	0
$877$	11.2392	0.379521	0.189761	−	0.981830i	$-0.439229\pi$
$877$	11.2392	0.379521	0.189761	+	0.981830i	$0.439229\pi$
$878$	−16.8028	−0.567068
$879$	0	0
$880$	0	0
$881$	2.53412	0.0853765	0.0426883	−	0.999088i	$-0.486408\pi$
$881$	2.53412	0.0853765	0.0426883	+	0.999088i	$0.486408\pi$
$882$	0	0
$883$	−44.1982	−1.48739	−0.743695	−	0.668519i	$-0.766928\pi$
$883$	−44.1982	−1.48739	−0.743695	+	0.668519i	$0.766928\pi$
$884$	−7.50700	−0.252488
$885$	0	0
$886$	0.326617	0.0109729
$887$	37.8496	1.27087	0.635433	−	0.772156i	$-0.280822\pi$
$887$	37.8496	1.27087	0.635433	+	0.772156i	$0.280822\pi$
$888$	0	0
$889$	32.0355	1.07444
$890$	0	0
$891$	0	0
$892$	−3.35174	−0.112224
$893$	−0.345946	−0.0115766
$894$	0	0
$895$	0	0
$896$	26.3264	0.879503
$897$	0	0
$898$	−3.23432	−0.107931
$899$	25.5851	0.853310
$900$	0	0
$901$	−56.7848	−1.89178
$902$	−13.3319	−0.443905
$903$	0	0
$904$	−21.8520	−0.726786
$905$	0	0
$906$	0	0
$907$	−3.70398	−0.122989	−0.0614943	−	0.998107i	$-0.519587\pi$
$907$	−3.70398	−0.122989	−0.0614943	+	0.998107i	$0.519587\pi$
$908$	−38.9647	−1.29309
$909$	0	0
$910$	0	0
$911$	22.6812	0.751461	0.375730	−	0.926729i	$-0.377392\pi$
$911$	22.6812	0.751461	0.375730	+	0.926729i	$0.377392\pi$
$912$	0	0
$913$	−42.9683	−1.42204
$914$	17.0164	0.562852
$915$	0	0
$916$	26.8269	0.886385
$917$	−21.3451	−0.704876
$918$	0	0
$919$	−29.9022	−0.986384	−0.493192	−	0.869921i	$-0.664170\pi$
$919$	−29.9022	−0.986384	−0.493192	+	0.869921i	$0.664170\pi$
$920$	0	0
$921$	0	0
$922$	4.08682	0.134592
$923$	11.9367	0.392902
$924$	0	0
$925$	0	0
$926$	7.10195	0.233384
$927$	0	0
$928$	−38.1156	−1.25120
$929$	8.55055	0.280534	0.140267	−	0.990114i	$-0.455204\pi$
$929$	8.55055	0.280534	0.140267	+	0.990114i	$0.455204\pi$
$930$	0	0
$931$	0.229938	0.00753590
$932$	−22.4420	−0.735112
$933$	0	0
$934$	−12.5260	−0.409862
$935$	0	0
$936$	0	0
$937$	−42.3211	−1.38257	−0.691286	−	0.722582i	$-0.742955\pi$
$937$	−42.3211	−1.38257	−0.691286	+	0.722582i	$0.742955\pi$
$938$	−10.9170	−0.356453
$939$	0	0
$940$	0	0
$941$	27.7017	0.903050	0.451525	−	0.892258i	$-0.350880\pi$
$941$	27.7017	0.903050	0.451525	+	0.892258i	$0.350880\pi$
$942$	0	0
$943$	21.8520	0.711599
$944$	2.48468	0.0808693
$945$	0	0
$946$	−12.7755	−0.415369
$947$	13.4092	0.435739	0.217870	−	0.975978i	$-0.430089\pi$
$947$	13.4092	0.435739	0.217870	+	0.975978i	$0.430089\pi$
$948$	0	0
$949$	−7.43855	−0.241466
$950$	0	0
$951$	0	0
$952$	32.5243	1.05412
$953$	−24.0707	−0.779725	−0.389863	−	0.920873i	$-0.627478\pi$
$953$	−24.0707	−0.779725	−0.389863	+	0.920873i	$0.627478\pi$
$954$	0	0
$955$	0	0
$956$	0.114261	0.00369546
$957$	0	0
$958$	−27.3965	−0.885141
$959$	−22.2284	−0.717794
$960$	0	0
$961$	−15.5866	−0.502792
$962$	−4.03040	−0.129945
$963$	0	0
$964$	−14.4025	−0.463873
$965$	0	0
$966$	0	0
$967$	33.3951	1.07392	0.536958	−	0.843609i	$-0.319573\pi$
$967$	33.3951	1.07392	0.536958	+	0.843609i	$0.319573\pi$
$968$	11.6164	0.373365
$969$	0	0
$970$	0	0
$971$	−35.3575	−1.13467	−0.567337	−	0.823485i	$-0.692026\pi$
$971$	−35.3575	−1.13467	−0.567337	+	0.823485i	$0.692026\pi$
$972$	0	0
$973$	33.6379	1.07838
$974$	20.2901	0.650136
$975$	0	0
$976$	10.1622	0.325283
$977$	−28.0477	−0.897324	−0.448662	−	0.893701i	$-0.648099\pi$
$977$	−28.0477	−0.897324	−0.448662	+	0.893701i	$0.648099\pi$
$978$	0	0
$979$	71.3714	2.28104
$980$	0	0
$981$	0	0
$982$	1.50573	0.0480498
$983$	−0.529955	−0.0169029	−0.00845147	−	0.999964i	$-0.502690\pi$
$983$	−0.529955	−0.0169029	−0.00845147	+	0.999964i	$0.502690\pi$
$984$	0	0
$985$	0	0
$986$	−23.8553	−0.759709
$987$	0	0
$988$	0.709456	0.0225708
$989$	20.9400	0.665853
$990$	0	0
$991$	5.53633	0.175867	0.0879336	−	0.996126i	$-0.471974\pi$
$991$	5.53633	0.175867	0.0879336	+	0.996126i	$0.471974\pi$
$992$	−22.9623	−0.729053
$993$	0	0
$994$	−21.9901	−0.697485
$995$	0	0
$996$	0	0
$997$	25.4123	0.804817	0.402408	−	0.915460i	$-0.368173\pi$
$997$	25.4123	0.804817	0.402408	+	0.915460i	$0.368173\pi$
$998$	−14.1363	−0.447478
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2925.2.a.bq.1.3	yes	6
3.2	odd	2	inner	2925.2.a.bq.1.4	yes	6
5.2	odd	4		2925.2.c.z.2224.6		12
5.3	odd	4		2925.2.c.z.2224.7		12
5.4	even	2		2925.2.a.bp.1.4	yes	6
15.2	even	4		2925.2.c.z.2224.8		12
15.8	even	4		2925.2.c.z.2224.5		12
15.14	odd	2		2925.2.a.bp.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2925.2.a.bp.1.3	✓	6	15.14	odd	2
2925.2.a.bp.1.4	yes	6	5.4	even	2
2925.2.a.bq.1.3	yes	6	1.1	even	1	trivial
2925.2.a.bq.1.4	yes	6	3.2	odd	2	inner
2925.2.c.z.2224.5		12	15.8	even	4
2925.2.c.z.2224.6		12	5.2	odd	4
2925.2.c.z.2224.7		12	5.3	odd	4
2925.2.c.z.2224.8		12	15.2	even	4

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:	\( N \)	\(=\)	\( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2925.a (trivial)

\(f(q)\)	\(=\)	\(q-0.721444 q^{2} -1.47952 q^{4} +2.55352 q^{7} +2.51028 q^{8} +O(q^{10})\)	\(q-0.721444 q^{2} -1.47952 q^{4} +2.55352 q^{7} +2.51028 q^{8} -3.95317 q^{11} +1.00000 q^{13} -1.84222 q^{14} +1.14801 q^{16} +5.07395 q^{17} -0.479518 q^{19} +2.85199 q^{22} -4.67461 q^{23} -0.721444 q^{26} -3.77798 q^{28} +6.51684 q^{29} +3.92599 q^{31} -5.84878 q^{32} -3.66057 q^{34} +5.58657 q^{37} +0.345946 q^{38} -4.67461 q^{41} -4.47952 q^{43} +5.84878 q^{44} +3.37247 q^{46} +0.721444 q^{47} -0.479518 q^{49} -1.47952 q^{52} -11.1914 q^{53} +6.41005 q^{56} -4.70153 q^{58} +2.16433 q^{59} +8.85199 q^{61} -2.83239 q^{62} +1.92355 q^{64} +5.92599 q^{67} -7.50700 q^{68} +11.9367 q^{71} -7.43855 q^{73} -4.03040 q^{74} +0.709456 q^{76} -10.0945 q^{77} +13.4386 q^{79} +3.37247 q^{82} +10.8693 q^{83} +3.23172 q^{86} -9.92355 q^{88} -18.0542 q^{89} +2.55352 q^{91} +6.91617 q^{92} -0.520482 q^{94} -1.10705 q^{97} +0.345946 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 14 q^{4} + 6 q^{7}+O(q^{10}) \) 6 * q + 14 * q^4 + 6 * q^7	\( 6 q + 14 q^{4} + 6 q^{7} + 6 q^{13} + 34 q^{16} + 20 q^{19} - 10 q^{22} + 18 q^{28} + 10 q^{31} + 6 q^{34} - 8 q^{37} - 4 q^{43} + 16 q^{46} + 20 q^{49} + 14 q^{52} - 46 q^{58} + 26 q^{61} + 70 q^{64} + 22 q^{67} + 24 q^{73} + 100 q^{76} + 12 q^{79} + 16 q^{82} - 118 q^{88} + 6 q^{91} - 26 q^{94} + 12 q^{97}+O(q^{100}) \) 6 * q + 14 * q^4 + 6 * q^7 + 6 * q^13 + 34 * q^16 + 20 * q^19 - 10 * q^22 + 18 * q^28 + 10 * q^31 + 6 * q^34 - 8 * q^37 - 4 * q^43 + 16 * q^46 + 20 * q^49 + 14 * q^52 - 46 * q^58 + 26 * q^61 + 70 * q^64 + 22 * q^67 + 24 * q^73 + 100 * q^76 + 12 * q^79 + 16 * q^82 - 118 * q^88 + 6 * q^91 - 26 * q^94 + 12 * q^97

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