LMFDB - Embedded newform 1925.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, 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("1925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.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:	$15.3712023891$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -2.00000 q^{3} -1.00000 q^{4} +2.00000 q^{6} -1.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -2.00000 q^{3} -1.00000 q^{4} +2.00000 q^{6} -1.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +1.00000 q^{11} +2.00000 q^{12} -2.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} +2.00000 q^{21} -1.00000 q^{22} -6.00000 q^{23} -6.00000 q^{24} +2.00000 q^{26} +4.00000 q^{27} +1.00000 q^{28} +10.0000 q^{29} +8.00000 q^{31} -5.00000 q^{32} -2.00000 q^{33} +2.00000 q^{34} -1.00000 q^{36} -4.00000 q^{37} +4.00000 q^{39} +2.00000 q^{41} -2.00000 q^{42} +8.00000 q^{43} -1.00000 q^{44} +6.00000 q^{46} -6.00000 q^{47} +2.00000 q^{48} +1.00000 q^{49} +4.00000 q^{51} +2.00000 q^{52} +12.0000 q^{53} -4.00000 q^{54} -3.00000 q^{56} -10.0000 q^{58} +4.00000 q^{59} -2.00000 q^{61} -8.00000 q^{62} -1.00000 q^{63} +7.00000 q^{64} +2.00000 q^{66} +2.00000 q^{67} +2.00000 q^{68} +12.0000 q^{69} -8.00000 q^{71} +3.00000 q^{72} +6.00000 q^{73} +4.00000 q^{74} -1.00000 q^{77} -4.00000 q^{78} -8.00000 q^{79} -11.0000 q^{81} -2.00000 q^{82} -16.0000 q^{83} -2.00000 q^{84} -8.00000 q^{86} -20.0000 q^{87} +3.00000 q^{88} -6.00000 q^{89} +2.00000 q^{91} +6.00000 q^{92} -16.0000 q^{93} +6.00000 q^{94} +10.0000 q^{96} -8.00000 q^{97} -1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	2.00000	0.816497
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.00000	1.06066
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.00000	0.577350
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	−1.00000	−0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−1.00000	−0.235702
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	−1.00000	−0.213201
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	−6.00000	−1.22474
$25$	0	0
$26$	2.00000	0.392232
$27$	4.00000	0.769800
$28$	1.00000	0.188982
$29$	10.0000	1.85695	0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000	1.85695	0.928477	+	0.371391i	$0.121119\pi$
$30$	0	0
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	−5.00000	−0.883883
$33$	−2.00000	−0.348155
$34$	2.00000	0.342997
$35$	0	0
$36$	−1.00000	−0.166667
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	0	0
$39$	4.00000	0.640513
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	−2.00000	−0.308607
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	6.00000	0.884652
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	2.00000	0.288675
$49$	1.00000	0.142857
$50$	0	0
$51$	4.00000	0.560112
$52$	2.00000	0.277350
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	−4.00000	−0.544331
$55$	0	0
$56$	−3.00000	−0.400892
$57$	0	0
$58$	−10.0000	−1.31306
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−8.00000	−1.01600
$63$	−1.00000	−0.125988
$64$	7.00000	0.875000
$65$	0	0
$66$	2.00000	0.246183
$67$	2.00000	0.244339	0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000	0.244339	0.122169	+	0.992509i	$0.461015\pi$
$68$	2.00000	0.242536
$69$	12.0000	1.44463
$70$	0	0
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	3.00000	0.353553
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	0	0
$77$	−1.00000	−0.113961
$78$	−4.00000	−0.452911
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	−2.00000	−0.220863
$83$	−16.0000	−1.75623	−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000	−1.75623	−0.878114	+	0.478451i	$0.841198\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	−8.00000	−0.862662
$87$	−20.0000	−2.14423
$88$	3.00000	0.319801
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	6.00000	0.625543
$93$	−16.0000	−1.65912
$94$	6.00000	0.618853
$95$	0	0
$96$	10.0000	1.02062
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	−1.00000	−0.101015
$99$	1.00000	0.100504
$100$	0	0
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	−4.00000	−0.396059
$103$	2.00000	0.197066	0.0985329	−	0.995134i	$-0.468585\pi$
$103$	2.00000	0.197066	0.0985329	+	0.995134i	$0.468585\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	−12.0000	−1.16554
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	−4.00000	−0.384900
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	1.00000	0.0944911
$113$	12.0000	1.12887	0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000	1.12887	0.564433	+	0.825479i	$0.309095\pi$
$114$	0	0
$115$	0	0
$116$	−10.0000	−0.928477
$117$	−2.00000	−0.184900
$118$	−4.00000	−0.368230
$119$	2.00000	0.183340
$120$	0	0
$121$	1.00000	0.0909091
$122$	2.00000	0.181071
$123$	−4.00000	−0.360668
$124$	−8.00000	−0.718421
$125$	0	0
$126$	1.00000	0.0890871
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	3.00000	0.265165
$129$	−16.0000	−1.40872
$130$	0	0
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	2.00000	0.174078
$133$	0	0
$134$	−2.00000	−0.172774
$135$	0	0
$136$	−6.00000	−0.514496
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	−12.0000	−1.02151
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	12.0000	1.01058
$142$	8.00000	0.671345
$143$	−2.00000	−0.167248
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−6.00000	−0.496564
$147$	−2.00000	−0.164957
$148$	4.00000	0.328798
$149$	22.0000	1.80231	0.901155	−	0.433497i	$-0.142720\pi$
$149$	22.0000	1.80231	0.901155	+	0.433497i	$0.142720\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	0	0
$153$	−2.00000	−0.161690
$154$	1.00000	0.0805823
$155$	0	0
$156$	−4.00000	−0.320256
$157$	−12.0000	−0.957704	−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000	−0.957704	−0.478852	+	0.877896i	$0.658947\pi$
$158$	8.00000	0.636446
$159$	−24.0000	−1.90332
$160$	0	0
$161$	6.00000	0.472866
$162$	11.0000	0.864242
$163$	−14.0000	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$164$	−2.00000	−0.156174
$165$	0	0
$166$	16.0000	1.24184
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	6.00000	0.462910
$169$	−9.00000	−0.692308
$170$	0	0
$171$	0	0
$172$	−8.00000	−0.609994
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	20.0000	1.51620
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	−8.00000	−0.601317
$178$	6.00000	0.449719
$179$	−20.0000	−1.49487	−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000	−1.49487	−0.747435	+	0.664335i	$0.768715\pi$
$180$	0	0
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	−2.00000	−0.148250
$183$	4.00000	0.295689
$184$	−18.0000	−1.32698
$185$	0	0
$186$	16.0000	1.17318
$187$	−2.00000	−0.146254
$188$	6.00000	0.437595
$189$	−4.00000	−0.290957
$190$	0	0
$191$	−24.0000	−1.73658	−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000	−1.73658	−0.868290	+	0.496058i	$0.834780\pi$
$192$	−14.0000	−1.01036
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	8.00000	0.574367
$195$	0	0
$196$	−1.00000	−0.0714286
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	−1.00000	−0.0710669
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	6.00000	0.422159
$203$	−10.0000	−0.701862
$204$	−4.00000	−0.280056
$205$	0	0
$206$	−2.00000	−0.139347
$207$	−6.00000	−0.417029
$208$	2.00000	0.138675
$209$	0	0
$210$	0	0
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	−12.0000	−0.824163
$213$	16.0000	1.09630
$214$	−4.00000	−0.273434
$215$	0	0
$216$	12.0000	0.816497
$217$	−8.00000	−0.543075
$218$	10.0000	0.677285
$219$	−12.0000	−0.810885
$220$	0	0
$221$	4.00000	0.269069
$222$	−8.00000	−0.536925
$223$	−18.0000	−1.20537	−0.602685	−	0.797980i	$-0.705902\pi$
$223$	−18.0000	−1.20537	−0.602685	+	0.797980i	$0.705902\pi$
$224$	5.00000	0.334077
$225$	0	0
$226$	−12.0000	−0.798228
$227$	8.00000	0.530979	0.265489	−	0.964114i	$-0.414466\pi$
$227$	8.00000	0.530979	0.265489	+	0.964114i	$0.414466\pi$
$228$	0	0
$229$	26.0000	1.71813	0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000	1.71813	0.859064	+	0.511868i	$0.171046\pi$
$230$	0	0
$231$	2.00000	0.131590
$232$	30.0000	1.96960
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−4.00000	−0.260378
$237$	16.0000	1.03931
$238$	−2.00000	−0.129641
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−1.00000	−0.0642824
$243$	10.0000	0.641500
$244$	2.00000	0.128037
$245$	0	0
$246$	4.00000	0.255031
$247$	0	0
$248$	24.0000	1.52400
$249$	32.0000	2.02792
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	1.00000	0.0629941
$253$	−6.00000	−0.377217
$254$	4.00000	0.250982
$255$	0	0
$256$	−17.0000	−1.06250
$257$	28.0000	1.74659	0.873296	−	0.487190i	$-0.161978\pi$
$257$	28.0000	1.74659	0.873296	+	0.487190i	$0.161978\pi$
$258$	16.0000	0.996116
$259$	4.00000	0.248548
$260$	0	0
$261$	10.0000	0.618984
$262$	20.0000	1.23560
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	−6.00000	−0.369274
$265$	0	0
$266$	0	0
$267$	12.0000	0.734388
$268$	−2.00000	−0.122169
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	−32.0000	−1.94386	−0.971931	−	0.235267i	$-0.924404\pi$
$271$	−32.0000	−1.94386	−0.971931	+	0.235267i	$0.924404\pi$
$272$	2.00000	0.121268
$273$	−4.00000	−0.242091
$274$	12.0000	0.724947
$275$	0	0
$276$	−12.0000	−0.722315
$277$	14.0000	0.841178	0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000	0.841178	0.420589	+	0.907251i	$0.361823\pi$
$278$	4.00000	0.239904
$279$	8.00000	0.478947
$280$	0	0
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	−12.0000	−0.714590
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	8.00000	0.474713
$285$	0	0
$286$	2.00000	0.118262
$287$	−2.00000	−0.118056
$288$	−5.00000	−0.294628
$289$	−13.0000	−0.764706
$290$	0	0
$291$	16.0000	0.937937
$292$	−6.00000	−0.351123
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	2.00000	0.116642
$295$	0	0
$296$	−12.0000	−0.697486
$297$	4.00000	0.232104
$298$	−22.0000	−1.27443
$299$	12.0000	0.693978
$300$	0	0
$301$	−8.00000	−0.461112
$302$	−20.0000	−1.15087
$303$	12.0000	0.689382
$304$	0	0
$305$	0	0
$306$	2.00000	0.114332
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	1.00000	0.0569803
$309$	−4.00000	−0.227552
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	12.0000	0.679366
$313$	−12.0000	−0.678280	−0.339140	−	0.940736i	$-0.610136\pi$
$313$	−12.0000	−0.678280	−0.339140	+	0.940736i	$0.610136\pi$
$314$	12.0000	0.677199
$315$	0	0
$316$	8.00000	0.450035
$317$	24.0000	1.34797	0.673987	−	0.738743i	$-0.264580\pi$
$317$	24.0000	1.34797	0.673987	+	0.738743i	$0.264580\pi$
$318$	24.0000	1.34585
$319$	10.0000	0.559893
$320$	0	0
$321$	−8.00000	−0.446516
$322$	−6.00000	−0.334367
$323$	0	0
$324$	11.0000	0.611111
$325$	0	0
$326$	14.0000	0.775388
$327$	20.0000	1.10600
$328$	6.00000	0.331295
$329$	6.00000	0.330791
$330$	0	0
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	16.0000	0.878114
$333$	−4.00000	−0.219199
$334$	−12.0000	−0.656611
$335$	0	0
$336$	−2.00000	−0.109109
$337$	6.00000	0.326841	0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000	0.326841	0.163420	+	0.986557i	$0.447747\pi$
$338$	9.00000	0.489535
$339$	−24.0000	−1.30350
$340$	0	0
$341$	8.00000	0.433224
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	24.0000	1.29399
$345$	0	0
$346$	6.00000	0.322562
$347$	−36.0000	−1.93258	−0.966291	−	0.257454i	$-0.917117\pi$
$347$	−36.0000	−1.93258	−0.966291	+	0.257454i	$0.917117\pi$
$348$	20.0000	1.07211
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	0	0
$351$	−8.00000	−0.427008
$352$	−5.00000	−0.266501
$353$	−4.00000	−0.212899	−0.106449	−	0.994318i	$-0.533948\pi$
$353$	−4.00000	−0.212899	−0.106449	+	0.994318i	$0.533948\pi$
$354$	8.00000	0.425195
$355$	0	0
$356$	6.00000	0.317999
$357$	−4.00000	−0.211702
$358$	20.0000	1.05703
$359$	−8.00000	−0.422224	−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000	−0.422224	−0.211112	+	0.977462i	$0.567708\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	6.00000	0.315353
$363$	−2.00000	−0.104973
$364$	−2.00000	−0.104828
$365$	0	0
$366$	−4.00000	−0.209083
$367$	−6.00000	−0.313197	−0.156599	−	0.987662i	$-0.550053\pi$
$367$	−6.00000	−0.313197	−0.156599	+	0.987662i	$0.550053\pi$
$368$	6.00000	0.312772
$369$	2.00000	0.104116
$370$	0	0
$371$	−12.0000	−0.623009
$372$	16.0000	0.829561
$373$	−30.0000	−1.55334	−0.776671	−	0.629907i	$-0.783093\pi$
$373$	−30.0000	−1.55334	−0.776671	+	0.629907i	$0.783093\pi$
$374$	2.00000	0.103418
$375$	0	0
$376$	−18.0000	−0.928279
$377$	−20.0000	−1.03005
$378$	4.00000	0.205738
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	0	0
$381$	8.00000	0.409852
$382$	24.0000	1.22795
$383$	34.0000	1.73732	0.868659	−	0.495410i	$-0.164982\pi$
$383$	34.0000	1.73732	0.868659	+	0.495410i	$0.164982\pi$
$384$	−6.00000	−0.306186
$385$	0	0
$386$	2.00000	0.101797
$387$	8.00000	0.406663
$388$	8.00000	0.406138
$389$	26.0000	1.31825	0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000	1.31825	0.659126	+	0.752032i	$0.270926\pi$
$390$	0	0
$391$	12.0000	0.606866
$392$	3.00000	0.151523
$393$	40.0000	2.01773
$394$	−2.00000	−0.100759
$395$	0	0
$396$	−1.00000	−0.0502519
$397$	4.00000	0.200754	0.100377	−	0.994949i	$-0.467995\pi$
$397$	4.00000	0.200754	0.100377	+	0.994949i	$0.467995\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	0	0
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	4.00000	0.199502
$403$	−16.0000	−0.797017
$404$	6.00000	0.298511
$405$	0	0
$406$	10.0000	0.496292
$407$	−4.00000	−0.198273
$408$	12.0000	0.594089
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	0	0
$411$	24.0000	1.18383
$412$	−2.00000	−0.0985329
$413$	−4.00000	−0.196827
$414$	6.00000	0.294884
$415$	0	0
$416$	10.0000	0.490290
$417$	8.00000	0.391762
$418$	0	0
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	−8.00000	−0.389434
$423$	−6.00000	−0.291730
$424$	36.0000	1.74831
$425$	0	0
$426$	−16.0000	−0.775203
$427$	2.00000	0.0967868
$428$	−4.00000	−0.193347
$429$	4.00000	0.193122
$430$	0	0
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	−4.00000	−0.192450
$433$	8.00000	0.384455	0.192228	−	0.981350i	$-0.438429\pi$
$433$	8.00000	0.384455	0.192228	+	0.981350i	$0.438429\pi$
$434$	8.00000	0.384012
$435$	0	0
$436$	10.0000	0.478913
$437$	0	0
$438$	12.0000	0.573382
$439$	24.0000	1.14546	0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000	1.14546	0.572729	+	0.819745i	$0.305885\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−4.00000	−0.190261
$443$	26.0000	1.23530	0.617649	−	0.786454i	$-0.288085\pi$
$443$	26.0000	1.23530	0.617649	+	0.786454i	$0.288085\pi$
$444$	−8.00000	−0.379663
$445$	0	0
$446$	18.0000	0.852325
$447$	−44.0000	−2.08113
$448$	−7.00000	−0.330719
$449$	34.0000	1.60456	0.802280	−	0.596948i	$-0.203620\pi$
$449$	34.0000	1.60456	0.802280	+	0.596948i	$0.203620\pi$
$450$	0	0
$451$	2.00000	0.0941763
$452$	−12.0000	−0.564433
$453$	−40.0000	−1.87936
$454$	−8.00000	−0.375459
$455$	0	0
$456$	0	0
$457$	−14.0000	−0.654892	−0.327446	−	0.944870i	$-0.606188\pi$
$457$	−14.0000	−0.654892	−0.327446	+	0.944870i	$0.606188\pi$
$458$	−26.0000	−1.21490
$459$	−8.00000	−0.373408
$460$	0	0
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	−2.00000	−0.0930484
$463$	−6.00000	−0.278844	−0.139422	−	0.990233i	$-0.544524\pi$
$463$	−6.00000	−0.278844	−0.139422	+	0.990233i	$0.544524\pi$
$464$	−10.0000	−0.464238
$465$	0	0
$466$	−10.0000	−0.463241
$467$	30.0000	1.38823	0.694117	−	0.719862i	$-0.255795\pi$
$467$	30.0000	1.38823	0.694117	+	0.719862i	$0.255795\pi$
$468$	2.00000	0.0924500
$469$	−2.00000	−0.0923514
$470$	0	0
$471$	24.0000	1.10586
$472$	12.0000	0.552345
$473$	8.00000	0.367840
$474$	−16.0000	−0.734904
$475$	0	0
$476$	−2.00000	−0.0916698
$477$	12.0000	0.549442
$478$	0	0
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	0	0
$481$	8.00000	0.364769
$482$	14.0000	0.637683
$483$	−12.0000	−0.546019
$484$	−1.00000	−0.0454545
$485$	0	0
$486$	−10.0000	−0.453609
$487$	30.0000	1.35943	0.679715	−	0.733476i	$-0.262104\pi$
$487$	30.0000	1.35943	0.679715	+	0.733476i	$0.262104\pi$
$488$	−6.00000	−0.271607
$489$	28.0000	1.26620
$490$	0	0
$491$	4.00000	0.180517	0.0902587	−	0.995918i	$-0.471231\pi$
$491$	4.00000	0.180517	0.0902587	+	0.995918i	$0.471231\pi$
$492$	4.00000	0.180334
$493$	−20.0000	−0.900755
$494$	0	0
$495$	0	0
$496$	−8.00000	−0.359211
$497$	8.00000	0.358849
$498$	−32.0000	−1.43395
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	0	0
$501$	−24.0000	−1.07224
$502$	−12.0000	−0.535586
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	6.00000	0.266733
$507$	18.0000	0.799408
$508$	4.00000	0.177471
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	0	0
$511$	−6.00000	−0.265424
$512$	11.0000	0.486136
$513$	0	0
$514$	−28.0000	−1.23503
$515$	0	0
$516$	16.0000	0.704361
$517$	−6.00000	−0.263880
$518$	−4.00000	−0.175750
$519$	12.0000	0.526742
$520$	0	0
$521$	−10.0000	−0.438108	−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000	−0.438108	−0.219054	+	0.975713i	$0.570297\pi$
$522$	−10.0000	−0.437688
$523$	−28.0000	−1.22435	−0.612177	−	0.790721i	$-0.709706\pi$
$523$	−28.0000	−1.22435	−0.612177	+	0.790721i	$0.709706\pi$
$524$	20.0000	0.873704
$525$	0	0
$526$	12.0000	0.523225
$527$	−16.0000	−0.696971
$528$	2.00000	0.0870388
$529$	13.0000	0.565217
$530$	0	0
$531$	4.00000	0.173585
$532$	0	0
$533$	−4.00000	−0.173259
$534$	−12.0000	−0.519291
$535$	0	0
$536$	6.00000	0.259161
$537$	40.0000	1.72613
$538$	14.0000	0.603583
$539$	1.00000	0.0430730
$540$	0	0
$541$	6.00000	0.257960	0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000	0.257960	0.128980	+	0.991647i	$0.458830\pi$
$542$	32.0000	1.37452
$543$	12.0000	0.514969
$544$	10.0000	0.428746
$545$	0	0
$546$	4.00000	0.171184
$547$	−40.0000	−1.71028	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−40.0000	−1.71028	−0.855138	+	0.518400i	$0.826528\pi$
$548$	12.0000	0.512615
$549$	−2.00000	−0.0853579
$550$	0	0
$551$	0	0
$552$	36.0000	1.53226
$553$	8.00000	0.340195
$554$	−14.0000	−0.594803
$555$	0	0
$556$	4.00000	0.169638
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	−8.00000	−0.338667
$559$	−16.0000	−0.676728
$560$	0	0
$561$	4.00000	0.168880
$562$	−22.0000	−0.928014
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	−12.0000	−0.505291
$565$	0	0
$566$	16.0000	0.672530
$567$	11.0000	0.461957
$568$	−24.0000	−1.00702
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	2.00000	0.0836242
$573$	48.0000	2.00523
$574$	2.00000	0.0834784
$575$	0	0
$576$	7.00000	0.291667
$577$	−16.0000	−0.666089	−0.333044	−	0.942911i	$-0.608076\pi$
$577$	−16.0000	−0.666089	−0.333044	+	0.942911i	$0.608076\pi$
$578$	13.0000	0.540729
$579$	4.00000	0.166234
$580$	0	0
$581$	16.0000	0.663792
$582$	−16.0000	−0.663221
$583$	12.0000	0.496989
$584$	18.0000	0.744845
$585$	0	0
$586$	18.0000	0.743573
$587$	−18.0000	−0.742940	−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000	−0.742940	−0.371470	+	0.928445i	$0.621146\pi$
$588$	2.00000	0.0824786
$589$	0	0
$590$	0	0
$591$	−4.00000	−0.164538
$592$	4.00000	0.164399
$593$	14.0000	0.574911	0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000	0.574911	0.287456	+	0.957794i	$0.407191\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	−22.0000	−0.901155
$597$	32.0000	1.30967
$598$	−12.0000	−0.490716
$599$	16.0000	0.653742	0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000	0.653742	0.326871	+	0.945069i	$0.394006\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	8.00000	0.326056
$603$	2.00000	0.0814463
$604$	−20.0000	−0.813788
$605$	0	0
$606$	−12.0000	−0.487467
$607$	12.0000	0.487065	0.243532	−	0.969893i	$-0.421694\pi$
$607$	12.0000	0.487065	0.243532	+	0.969893i	$0.421694\pi$
$608$	0	0
$609$	20.0000	0.810441
$610$	0	0
$611$	12.0000	0.485468
$612$	2.00000	0.0808452
$613$	34.0000	1.37325	0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000	1.37325	0.686624	+	0.727013i	$0.259092\pi$
$614$	−4.00000	−0.161427
$615$	0	0
$616$	−3.00000	−0.120873
$617$	28.0000	1.12724	0.563619	−	0.826035i	$-0.309409\pi$
$617$	28.0000	1.12724	0.563619	+	0.826035i	$0.309409\pi$
$618$	4.00000	0.160904
$619$	−44.0000	−1.76851	−0.884255	−	0.467005i	$-0.845333\pi$
$619$	−44.0000	−1.76851	−0.884255	+	0.467005i	$0.845333\pi$
$620$	0	0
$621$	−24.0000	−0.963087
$622$	0	0
$623$	6.00000	0.240385
$624$	−4.00000	−0.160128
$625$	0	0
$626$	12.0000	0.479616
$627$	0	0
$628$	12.0000	0.478852
$629$	8.00000	0.318981
$630$	0	0
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	−24.0000	−0.954669
$633$	−16.0000	−0.635943
$634$	−24.0000	−0.953162
$635$	0	0
$636$	24.0000	0.951662
$637$	−2.00000	−0.0792429
$638$	−10.0000	−0.395904
$639$	−8.00000	−0.316475
$640$	0	0
$641$	46.0000	1.81689	0.908445	−	0.418004i	$-0.137270\pi$
$641$	46.0000	1.81689	0.908445	+	0.418004i	$0.137270\pi$
$642$	8.00000	0.315735
$643$	−26.0000	−1.02534	−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000	−1.02534	−0.512670	+	0.858586i	$0.671344\pi$
$644$	−6.00000	−0.236433
$645$	0	0
$646$	0	0
$647$	−2.00000	−0.0786281	−0.0393141	−	0.999227i	$-0.512517\pi$
$647$	−2.00000	−0.0786281	−0.0393141	+	0.999227i	$0.512517\pi$
$648$	−33.0000	−1.29636
$649$	4.00000	0.157014
$650$	0	0
$651$	16.0000	0.627089
$652$	14.0000	0.548282
$653$	20.0000	0.782660	0.391330	−	0.920250i	$-0.372015\pi$
$653$	20.0000	0.782660	0.391330	+	0.920250i	$0.372015\pi$
$654$	−20.0000	−0.782062
$655$	0	0
$656$	−2.00000	−0.0780869
$657$	6.00000	0.234082
$658$	−6.00000	−0.233904
$659$	−24.0000	−0.934907	−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000	−0.934907	−0.467454	+	0.884018i	$0.654829\pi$
$660$	0	0
$661$	−42.0000	−1.63361	−0.816805	−	0.576913i	$-0.804257\pi$
$661$	−42.0000	−1.63361	−0.816805	+	0.576913i	$0.804257\pi$
$662$	12.0000	0.466393
$663$	−8.00000	−0.310694
$664$	−48.0000	−1.86276
$665$	0	0
$666$	4.00000	0.154997
$667$	−60.0000	−2.32321
$668$	−12.0000	−0.464294
$669$	36.0000	1.39184
$670$	0	0
$671$	−2.00000	−0.0772091
$672$	−10.0000	−0.385758
$673$	6.00000	0.231283	0.115642	−	0.993291i	$-0.463108\pi$
$673$	6.00000	0.231283	0.115642	+	0.993291i	$0.463108\pi$
$674$	−6.00000	−0.231111
$675$	0	0
$676$	9.00000	0.346154
$677$	38.0000	1.46046	0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000	1.46046	0.730229	+	0.683202i	$0.239413\pi$
$678$	24.0000	0.921714
$679$	8.00000	0.307012
$680$	0	0
$681$	−16.0000	−0.613121
$682$	−8.00000	−0.306336
$683$	−26.0000	−0.994862	−0.497431	−	0.867503i	$-0.665723\pi$
$683$	−26.0000	−0.994862	−0.497431	+	0.867503i	$0.665723\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	0.0381802
$687$	−52.0000	−1.98392
$688$	−8.00000	−0.304997
$689$	−24.0000	−0.914327
$690$	0	0
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	6.00000	0.228086
$693$	−1.00000	−0.0379869
$694$	36.0000	1.36654
$695$	0	0
$696$	−60.0000	−2.27429
$697$	−4.00000	−0.151511
$698$	2.00000	0.0757011
$699$	−20.0000	−0.756469
$700$	0	0
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	8.00000	0.301941
$703$	0	0
$704$	7.00000	0.263822
$705$	0	0
$706$	4.00000	0.150542
$707$	6.00000	0.225653
$708$	8.00000	0.300658
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	0	0
$711$	−8.00000	−0.300023
$712$	−18.0000	−0.674579
$713$	−48.0000	−1.79761
$714$	4.00000	0.149696
$715$	0	0
$716$	20.0000	0.747435
$717$	0	0
$718$	8.00000	0.298557
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	0	0
$721$	−2.00000	−0.0744839
$722$	19.0000	0.707107
$723$	28.0000	1.04133
$724$	6.00000	0.222988
$725$	0	0
$726$	2.00000	0.0742270
$727$	38.0000	1.40934	0.704671	−	0.709534i	$-0.251095\pi$
$727$	38.0000	1.40934	0.704671	+	0.709534i	$0.251095\pi$
$728$	6.00000	0.222375
$729$	13.0000	0.481481
$730$	0	0
$731$	−16.0000	−0.591781
$732$	−4.00000	−0.147844
$733$	10.0000	0.369358	0.184679	−	0.982799i	$-0.440875\pi$
$733$	10.0000	0.369358	0.184679	+	0.982799i	$0.440875\pi$
$734$	6.00000	0.221464
$735$	0	0
$736$	30.0000	1.10581
$737$	2.00000	0.0736709
$738$	−2.00000	−0.0736210
$739$	16.0000	0.588570	0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000	0.588570	0.294285	+	0.955718i	$0.404919\pi$
$740$	0	0
$741$	0	0
$742$	12.0000	0.440534
$743$	4.00000	0.146746	0.0733729	−	0.997305i	$-0.476624\pi$
$743$	4.00000	0.146746	0.0733729	+	0.997305i	$0.476624\pi$
$744$	−48.0000	−1.75977
$745$	0	0
$746$	30.0000	1.09838
$747$	−16.0000	−0.585409
$748$	2.00000	0.0731272
$749$	−4.00000	−0.146157
$750$	0	0
$751$	24.0000	0.875772	0.437886	−	0.899030i	$-0.355727\pi$
$751$	24.0000	0.875772	0.437886	+	0.899030i	$0.355727\pi$
$752$	6.00000	0.218797
$753$	−24.0000	−0.874609
$754$	20.0000	0.728357
$755$	0	0
$756$	4.00000	0.145479
$757$	−16.0000	−0.581530	−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000	−0.581530	−0.290765	+	0.956795i	$0.593910\pi$
$758$	4.00000	0.145287
$759$	12.0000	0.435572
$760$	0	0
$761$	−34.0000	−1.23250	−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000	−1.23250	−0.616250	+	0.787551i	$0.711349\pi$
$762$	−8.00000	−0.289809
$763$	10.0000	0.362024
$764$	24.0000	0.868290
$765$	0	0
$766$	−34.0000	−1.22847
$767$	−8.00000	−0.288863
$768$	34.0000	1.22687
$769$	−6.00000	−0.216366	−0.108183	−	0.994131i	$-0.534503\pi$
$769$	−6.00000	−0.216366	−0.108183	+	0.994131i	$0.534503\pi$
$770$	0	0
$771$	−56.0000	−2.01679
$772$	2.00000	0.0719816
$773$	24.0000	0.863220	0.431610	−	0.902060i	$-0.357946\pi$
$773$	24.0000	0.863220	0.431610	+	0.902060i	$0.357946\pi$
$774$	−8.00000	−0.287554
$775$	0	0
$776$	−24.0000	−0.861550
$777$	−8.00000	−0.286998
$778$	−26.0000	−0.932145
$779$	0	0
$780$	0	0
$781$	−8.00000	−0.286263
$782$	−12.0000	−0.429119
$783$	40.0000	1.42948
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	−40.0000	−1.42675
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	−2.00000	−0.0712470
$789$	24.0000	0.854423
$790$	0	0
$791$	−12.0000	−0.426671
$792$	3.00000	0.106600
$793$	4.00000	0.142044
$794$	−4.00000	−0.141955
$795$	0	0
$796$	16.0000	0.567105
$797$	−4.00000	−0.141687	−0.0708436	−	0.997487i	$-0.522569\pi$
$797$	−4.00000	−0.141687	−0.0708436	+	0.997487i	$0.522569\pi$
$798$	0	0
$799$	12.0000	0.424529
$800$	0	0
$801$	−6.00000	−0.212000
$802$	−30.0000	−1.05934
$803$	6.00000	0.211735
$804$	4.00000	0.141069
$805$	0	0
$806$	16.0000	0.563576
$807$	28.0000	0.985647
$808$	−18.0000	−0.633238
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	0	0
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	10.0000	0.350931
$813$	64.0000	2.24458
$814$	4.00000	0.140200
$815$	0	0
$816$	−4.00000	−0.140028
$817$	0	0
$818$	10.0000	0.349642
$819$	2.00000	0.0698857
$820$	0	0
$821$	−38.0000	−1.32621	−0.663105	−	0.748527i	$-0.730762\pi$
$821$	−38.0000	−1.32621	−0.663105	+	0.748527i	$0.730762\pi$
$822$	−24.0000	−0.837096
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	6.00000	0.209020
$825$	0	0
$826$	4.00000	0.139178
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	6.00000	0.208514
$829$	54.0000	1.87550	0.937749	−	0.347314i	$-0.112906\pi$
$829$	54.0000	1.87550	0.937749	+	0.347314i	$0.112906\pi$
$830$	0	0
$831$	−28.0000	−0.971309
$832$	−14.0000	−0.485363
$833$	−2.00000	−0.0692959
$834$	−8.00000	−0.277017
$835$	0	0
$836$	0	0
$837$	32.0000	1.10608
$838$	12.0000	0.414533
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	6.00000	0.206774
$843$	−44.0000	−1.51544
$844$	−8.00000	−0.275371
$845$	0	0
$846$	6.00000	0.206284
$847$	−1.00000	−0.0343604
$848$	−12.0000	−0.412082
$849$	32.0000	1.09824
$850$	0	0
$851$	24.0000	0.822709
$852$	−16.0000	−0.548151
$853$	−30.0000	−1.02718	−0.513590	−	0.858036i	$-0.671685\pi$
$853$	−30.0000	−1.02718	−0.513590	+	0.858036i	$0.671685\pi$
$854$	−2.00000	−0.0684386
$855$	0	0
$856$	12.0000	0.410152
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	−4.00000	−0.136558
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	0	0
$861$	4.00000	0.136320
$862$	−16.0000	−0.544962
$863$	6.00000	0.204242	0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000	0.204242	0.102121	+	0.994772i	$0.467437\pi$
$864$	−20.0000	−0.680414
$865$	0	0
$866$	−8.00000	−0.271851
$867$	26.0000	0.883006
$868$	8.00000	0.271538
$869$	−8.00000	−0.271381
$870$	0	0
$871$	−4.00000	−0.135535
$872$	−30.0000	−1.01593
$873$	−8.00000	−0.270759
$874$	0	0
$875$	0	0
$876$	12.0000	0.405442
$877$	−22.0000	−0.742887	−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000	−0.742887	−0.371444	+	0.928456i	$0.621137\pi$
$878$	−24.0000	−0.809961
$879$	36.0000	1.21425
$880$	0	0
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	−1.00000	−0.0336718
$883$	−30.0000	−1.00958	−0.504790	−	0.863242i	$-0.668430\pi$
$883$	−30.0000	−1.00958	−0.504790	+	0.863242i	$0.668430\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	−26.0000	−0.873487
$887$	−52.0000	−1.74599	−0.872995	−	0.487730i	$-0.837825\pi$
$887$	−52.0000	−1.74599	−0.872995	+	0.487730i	$0.837825\pi$
$888$	24.0000	0.805387
$889$	4.00000	0.134156
$890$	0	0
$891$	−11.0000	−0.368514
$892$	18.0000	0.602685
$893$	0	0
$894$	44.0000	1.47158
$895$	0	0
$896$	−3.00000	−0.100223
$897$	−24.0000	−0.801337
$898$	−34.0000	−1.13459
$899$	80.0000	2.66815
$900$	0	0
$901$	−24.0000	−0.799556
$902$	−2.00000	−0.0665927
$903$	16.0000	0.532447
$904$	36.0000	1.19734
$905$	0	0
$906$	40.0000	1.32891
$907$	−14.0000	−0.464862	−0.232431	−	0.972613i	$-0.574668\pi$
$907$	−14.0000	−0.464862	−0.232431	+	0.972613i	$0.574668\pi$
$908$	−8.00000	−0.265489
$909$	−6.00000	−0.199007
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	−16.0000	−0.529523
$914$	14.0000	0.463079
$915$	0	0
$916$	−26.0000	−0.859064
$917$	20.0000	0.660458
$918$	8.00000	0.264039
$919$	52.0000	1.71532	0.857661	−	0.514216i	$-0.171917\pi$
$919$	52.0000	1.71532	0.857661	+	0.514216i	$0.171917\pi$
$920$	0	0
$921$	−8.00000	−0.263609
$922$	30.0000	0.987997
$923$	16.0000	0.526646
$924$	−2.00000	−0.0657952
$925$	0	0
$926$	6.00000	0.197172
$927$	2.00000	0.0656886
$928$	−50.0000	−1.64133
$929$	−50.0000	−1.64045	−0.820223	−	0.572043i	$-0.806151\pi$
$929$	−50.0000	−1.64045	−0.820223	+	0.572043i	$0.806151\pi$
$930$	0	0
$931$	0	0
$932$	−10.0000	−0.327561
$933$	0	0
$934$	−30.0000	−0.981630
$935$	0	0
$936$	−6.00000	−0.196116
$937$	−46.0000	−1.50275	−0.751377	−	0.659873i	$-0.770610\pi$
$937$	−46.0000	−1.50275	−0.751377	+	0.659873i	$0.770610\pi$
$938$	2.00000	0.0653023
$939$	24.0000	0.783210
$940$	0	0
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	−24.0000	−0.781962
$943$	−12.0000	−0.390774
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−8.00000	−0.260102
$947$	−6.00000	−0.194974	−0.0974869	−	0.995237i	$-0.531080\pi$
$947$	−6.00000	−0.194974	−0.0974869	+	0.995237i	$0.531080\pi$
$948$	−16.0000	−0.519656
$949$	−12.0000	−0.389536
$950$	0	0
$951$	−48.0000	−1.55651
$952$	6.00000	0.194461
$953$	−54.0000	−1.74923	−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000	−1.74923	−0.874616	+	0.484817i	$0.838886\pi$
$954$	−12.0000	−0.388514
$955$	0	0
$956$	0	0
$957$	−20.0000	−0.646508
$958$	36.0000	1.16311
$959$	12.0000	0.387500
$960$	0	0
$961$	33.0000	1.06452
$962$	−8.00000	−0.257930
$963$	4.00000	0.128898
$964$	14.0000	0.450910
$965$	0	0
$966$	12.0000	0.386094
$967$	−44.0000	−1.41494	−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000	−1.41494	−0.707472	+	0.706741i	$0.750165\pi$
$968$	3.00000	0.0964237
$969$	0	0
$970$	0	0
$971$	4.00000	0.128366	0.0641831	−	0.997938i	$-0.479556\pi$
$971$	4.00000	0.128366	0.0641831	+	0.997938i	$0.479556\pi$
$972$	−10.0000	−0.320750
$973$	4.00000	0.128234
$974$	−30.0000	−0.961262
$975$	0	0
$976$	2.00000	0.0640184
$977$	60.0000	1.91957	0.959785	−	0.280736i	$-0.0905785\pi$
$977$	60.0000	1.91957	0.959785	+	0.280736i	$0.0905785\pi$
$978$	−28.0000	−0.895341
$979$	−6.00000	−0.191761
$980$	0	0
$981$	−10.0000	−0.319275
$982$	−4.00000	−0.127645
$983$	−6.00000	−0.191370	−0.0956851	−	0.995412i	$-0.530504\pi$
$983$	−6.00000	−0.191370	−0.0956851	+	0.995412i	$0.530504\pi$
$984$	−12.0000	−0.382546
$985$	0	0
$986$	20.0000	0.636930
$987$	−12.0000	−0.381964
$988$	0	0
$989$	−48.0000	−1.52631
$990$	0	0
$991$	−32.0000	−1.01651	−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000	−1.01651	−0.508257	+	0.861206i	$0.669710\pi$
$992$	−40.0000	−1.27000
$993$	24.0000	0.761617
$994$	−8.00000	−0.253745
$995$	0	0
$996$	−32.0000	−1.01396
$997$	−46.0000	−1.45683	−0.728417	−	0.685134i	$-0.759744\pi$
$997$	−46.0000	−1.45683	−0.728417	+	0.685134i	$0.759744\pi$
$998$	20.0000	0.633089
$999$	−16.0000	−0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.a.b.1.1		1
5.2	odd	4		385.2.b.b.309.1	✓	2
5.3	odd	4		385.2.b.b.309.2	yes	2
5.4	even	2		1925.2.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.b.b.309.1	✓	2	5.2	odd	4
385.2.b.b.309.2	yes	2	5.3	odd	4
1925.2.a.b.1.1		1	1.1	even	1	trivial
1925.2.a.l.1.1		1	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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