LMFDB - Embedded newform 4025.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} -2.00000 q^{6} +1.00000 q^{7} -2.00000 q^{9} -5.00000 q^{11} +2.00000 q^{12} -3.00000 q^{13} -2.00000 q^{14} -4.00000 q^{16} +5.00000 q^{17} +4.00000 q^{18} +1.00000 q^{21} +10.0000 q^{22} +1.00000 q^{23} +6.00000 q^{26} -5.00000 q^{27} +2.00000 q^{28} +3.00000 q^{29} +6.00000 q^{31} +8.00000 q^{32} -5.00000 q^{33} -10.0000 q^{34} -4.00000 q^{36} +4.00000 q^{37} -3.00000 q^{39} -2.00000 q^{42} +2.00000 q^{43} -10.0000 q^{44} -2.00000 q^{46} +9.00000 q^{47} -4.00000 q^{48} +1.00000 q^{49} +5.00000 q^{51} -6.00000 q^{52} +6.00000 q^{53} +10.0000 q^{54} -6.00000 q^{58} -6.00000 q^{59} +10.0000 q^{61} -12.0000 q^{62} -2.00000 q^{63} -8.00000 q^{64} +10.0000 q^{66} -4.00000 q^{67} +10.0000 q^{68} +1.00000 q^{69} -8.00000 q^{71} -10.0000 q^{73} -8.00000 q^{74} -5.00000 q^{77} +6.00000 q^{78} -15.0000 q^{79} +1.00000 q^{81} -12.0000 q^{83} +2.00000 q^{84} -4.00000 q^{86} +3.00000 q^{87} -10.0000 q^{89} -3.00000 q^{91} +2.00000 q^{92} +6.00000 q^{93} -18.0000 q^{94} +8.00000 q^{96} -7.00000 q^{97} -2.00000 q^{98} +10.0000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	2.00000	1.00000
$5$	0	0
$5$	0	0
$6$	−2.00000	−0.816497
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	2.00000	0.577350
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	−4.00000	−1.00000
$17$	5.00000	1.21268	0.606339	−	0.795206i	$-0.292637\pi$
$17$	5.00000	1.21268	0.606339	+	0.795206i	$0.292637\pi$
$18$	4.00000	0.942809
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	10.0000	2.13201
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	0	0
$26$	6.00000	1.17670
$27$	−5.00000	−0.962250
$28$	2.00000	0.377964
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	8.00000	1.41421
$33$	−5.00000	−0.870388
$34$	−10.0000	−1.71499
$35$	0	0
$36$	−4.00000	−0.666667
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	0	0
$39$	−3.00000	−0.480384
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	−2.00000	−0.308607
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	−10.0000	−1.50756
$45$	0	0
$46$	−2.00000	−0.294884
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	−4.00000	−0.577350
$49$	1.00000	0.142857
$50$	0	0
$51$	5.00000	0.700140
$52$	−6.00000	−0.832050
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	10.0000	1.36083
$55$	0	0
$56$	0	0
$57$	0	0
$58$	−6.00000	−0.787839
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	−12.0000	−1.52400
$63$	−2.00000	−0.251976
$64$	−8.00000	−1.00000
$65$	0	0
$66$	10.0000	1.23091
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	10.0000	1.21268
$69$	1.00000	0.120386
$70$	0	0
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	0	0
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	0	0
$77$	−5.00000	−0.569803
$78$	6.00000	0.679366
$79$	−15.0000	−1.68763	−0.843816	−	0.536633i	$-0.819696\pi$
$79$	−15.0000	−1.68763	−0.843816	+	0.536633i	$0.819696\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	−4.00000	−0.431331
$87$	3.00000	0.321634
$88$	0	0
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	2.00000	0.208514
$93$	6.00000	0.622171
$94$	−18.0000	−1.85656
$95$	0	0
$96$	8.00000	0.816497
$97$	−7.00000	−0.710742	−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000	−0.710742	−0.355371	+	0.934725i	$0.615646\pi$
$98$	−2.00000	−0.202031
$99$	10.0000	1.00504
$100$	0	0
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	−10.0000	−0.990148
$103$	−1.00000	−0.0985329	−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000	−0.0985329	−0.0492665	+	0.998786i	$0.515688\pi$
$104$	0	0
$105$	0	0
$106$	−12.0000	−1.16554
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	−10.0000	−0.962250
$109$	−17.0000	−1.62830	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	−17.0000	−1.62830	−0.814152	+	0.580651i	$0.802798\pi$
$110$	0	0
$111$	4.00000	0.379663
$112$	−4.00000	−0.377964
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	0	0
$115$	0	0
$116$	6.00000	0.557086
$117$	6.00000	0.554700
$118$	12.0000	1.10469
$119$	5.00000	0.458349
$120$	0	0
$121$	14.0000	1.27273
$122$	−20.0000	−1.81071
$123$	0	0
$124$	12.0000	1.07763
$125$	0	0
$126$	4.00000	0.356348
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	0	0
$129$	2.00000	0.176090
$130$	0	0
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	−10.0000	−0.870388
$133$	0	0
$134$	8.00000	0.691095
$135$	0	0
$136$	0	0
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	−2.00000	−0.170251
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	0	0
$141$	9.00000	0.757937
$142$	16.0000	1.34269
$143$	15.0000	1.25436
$144$	8.00000	0.666667
$145$	0	0
$146$	20.0000	1.65521
$147$	1.00000	0.0824786
$148$	8.00000	0.657596
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	0	0
$151$	−9.00000	−0.732410	−0.366205	−	0.930534i	$-0.619343\pi$
$151$	−9.00000	−0.732410	−0.366205	+	0.930534i	$0.619343\pi$
$152$	0	0
$153$	−10.0000	−0.808452
$154$	10.0000	0.805823
$155$	0	0
$156$	−6.00000	−0.480384
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	30.0000	2.38667
$159$	6.00000	0.475831
$160$	0	0
$161$	1.00000	0.0788110
$162$	−2.00000	−0.157135
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	0	0
$165$	0	0
$166$	24.0000	1.86276
$167$	1.00000	0.0773823	0.0386912	−	0.999251i	$-0.487681\pi$
$167$	1.00000	0.0773823	0.0386912	+	0.999251i	$0.487681\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	0	0
$171$	0	0
$172$	4.00000	0.304997
$173$	3.00000	0.228086	0.114043	−	0.993476i	$-0.463620\pi$
$173$	3.00000	0.228086	0.114043	+	0.993476i	$0.463620\pi$
$174$	−6.00000	−0.454859
$175$	0	0
$176$	20.0000	1.50756
$177$	−6.00000	−0.450988
$178$	20.0000	1.49906
$179$	8.00000	0.597948	0.298974	−	0.954261i	$-0.403356\pi$
$179$	8.00000	0.597948	0.298974	+	0.954261i	$0.403356\pi$
$180$	0	0
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	6.00000	0.444750
$183$	10.0000	0.739221
$184$	0	0
$185$	0	0
$186$	−12.0000	−0.879883
$187$	−25.0000	−1.82818
$188$	18.0000	1.31278
$189$	−5.00000	−0.363696
$190$	0	0
$191$	27.0000	1.95365	0.976826	−	0.214036i	$-0.0686611\pi$
$191$	27.0000	1.95365	0.976826	+	0.214036i	$0.0686611\pi$
$192$	−8.00000	−0.577350
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	2.00000	0.142857
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	−20.0000	−1.42134
$199$	−22.0000	−1.55954	−0.779769	−	0.626067i	$-0.784664\pi$
$199$	−22.0000	−1.55954	−0.779769	+	0.626067i	$0.784664\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	−20.0000	−1.40720
$203$	3.00000	0.210559
$204$	10.0000	0.700140
$205$	0	0
$206$	2.00000	0.139347
$207$	−2.00000	−0.139010
$208$	12.0000	0.832050
$209$	0	0
$210$	0	0
$211$	−17.0000	−1.17033	−0.585164	−	0.810915i	$-0.698970\pi$
$211$	−17.0000	−1.17033	−0.585164	+	0.810915i	$0.698970\pi$
$212$	12.0000	0.824163
$213$	−8.00000	−0.548151
$214$	−12.0000	−0.820303
$215$	0	0
$216$	0	0
$217$	6.00000	0.407307
$218$	34.0000	2.30277
$219$	−10.0000	−0.675737
$220$	0	0
$221$	−15.0000	−1.00901
$222$	−8.00000	−0.536925
$223$	−15.0000	−1.00447	−0.502237	−	0.864730i	$-0.667490\pi$
$223$	−15.0000	−1.00447	−0.502237	+	0.864730i	$0.667490\pi$
$224$	8.00000	0.534522
$225$	0	0
$226$	36.0000	2.39468
$227$	3.00000	0.199117	0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000	0.199117	0.0995585	+	0.995032i	$0.468257\pi$
$228$	0	0
$229$	−8.00000	−0.528655	−0.264327	−	0.964433i	$-0.585150\pi$
$229$	−8.00000	−0.528655	−0.264327	+	0.964433i	$0.585150\pi$
$230$	0	0
$231$	−5.00000	−0.328976
$232$	0	0
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	−12.0000	−0.784465
$235$	0	0
$236$	−12.0000	−0.781133
$237$	−15.0000	−0.974355
$238$	−10.0000	−0.648204
$239$	7.00000	0.452792	0.226396	−	0.974035i	$-0.427306\pi$
$239$	7.00000	0.452792	0.226396	+	0.974035i	$0.427306\pi$
$240$	0	0
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	−28.0000	−1.79991
$243$	16.0000	1.02640
$244$	20.0000	1.28037
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−12.0000	−0.760469
$250$	0	0
$251$	−20.0000	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$252$	−4.00000	−0.251976
$253$	−5.00000	−0.314347
$254$	8.00000	0.501965
$255$	0	0
$256$	16.0000	1.00000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	−4.00000	−0.249029
$259$	4.00000	0.248548
$260$	0	0
$261$	−6.00000	−0.371391
$262$	40.0000	2.47121
$263$	28.0000	1.72655	0.863277	−	0.504730i	$-0.168408\pi$
$263$	28.0000	1.72655	0.863277	+	0.504730i	$0.168408\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−10.0000	−0.611990
$268$	−8.00000	−0.488678
$269$	2.00000	0.121942	0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000	0.121942	0.0609711	+	0.998140i	$0.480580\pi$
$270$	0	0
$271$	−18.0000	−1.09342	−0.546711	−	0.837321i	$-0.684120\pi$
$271$	−18.0000	−1.09342	−0.546711	+	0.837321i	$0.684120\pi$
$272$	−20.0000	−1.21268
$273$	−3.00000	−0.181568
$274$	−12.0000	−0.724947
$275$	0	0
$276$	2.00000	0.120386
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	16.0000	0.959616
$279$	−12.0000	−0.718421
$280$	0	0
$281$	−3.00000	−0.178965	−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000	−0.178965	−0.0894825	+	0.995988i	$0.528521\pi$
$282$	−18.0000	−1.07188
$283$	25.0000	1.48610	0.743048	−	0.669238i	$-0.233379\pi$
$283$	25.0000	1.48610	0.743048	+	0.669238i	$0.233379\pi$
$284$	−16.0000	−0.949425
$285$	0	0
$286$	−30.0000	−1.77394
$287$	0	0
$288$	−16.0000	−0.942809
$289$	8.00000	0.470588
$290$	0	0
$291$	−7.00000	−0.410347
$292$	−20.0000	−1.17041
$293$	9.00000	0.525786	0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000	0.525786	0.262893	+	0.964825i	$0.415323\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	0	0
$297$	25.0000	1.45065
$298$	4.00000	0.231714
$299$	−3.00000	−0.173494
$300$	0	0
$301$	2.00000	0.115278
$302$	18.0000	1.03578
$303$	10.0000	0.574485
$304$	0	0
$305$	0	0
$306$	20.0000	1.14332
$307$	−17.0000	−0.970241	−0.485121	−	0.874447i	$-0.661224\pi$
$307$	−17.0000	−0.970241	−0.485121	+	0.874447i	$0.661224\pi$
$308$	−10.0000	−0.569803
$309$	−1.00000	−0.0568880
$310$	0	0
$311$	−20.0000	−1.13410	−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000	−1.13410	−0.567048	+	0.823685i	$0.691915\pi$
$312$	0	0
$313$	15.0000	0.847850	0.423925	−	0.905697i	$-0.360652\pi$
$313$	15.0000	0.847850	0.423925	+	0.905697i	$0.360652\pi$
$314$	4.00000	0.225733
$315$	0	0
$316$	−30.0000	−1.68763
$317$	20.0000	1.12331	0.561656	−	0.827371i	$-0.310164\pi$
$317$	20.0000	1.12331	0.561656	+	0.827371i	$0.310164\pi$
$318$	−12.0000	−0.672927
$319$	−15.0000	−0.839839
$320$	0	0
$321$	6.00000	0.334887
$322$	−2.00000	−0.111456
$323$	0	0
$324$	2.00000	0.111111
$325$	0	0
$326$	16.0000	0.886158
$327$	−17.0000	−0.940102
$328$	0	0
$329$	9.00000	0.496186
$330$	0	0
$331$	24.0000	1.31916	0.659580	−	0.751635i	$-0.270734\pi$
$331$	24.0000	1.31916	0.659580	+	0.751635i	$0.270734\pi$
$332$	−24.0000	−1.31717
$333$	−8.00000	−0.438397
$334$	−2.00000	−0.109435
$335$	0	0
$336$	−4.00000	−0.218218
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	8.00000	0.435143
$339$	−18.0000	−0.977626
$340$	0	0
$341$	−30.0000	−1.62459
$342$	0	0
$343$	1.00000	0.0539949
$344$	0	0
$345$	0	0
$346$	−6.00000	−0.322562
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	6.00000	0.321634
$349$	28.0000	1.49881	0.749403	−	0.662114i	$-0.230341\pi$
$349$	28.0000	1.49881	0.749403	+	0.662114i	$0.230341\pi$
$350$	0	0
$351$	15.0000	0.800641
$352$	−40.0000	−2.13201
$353$	−21.0000	−1.11772	−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000	−1.11772	−0.558859	+	0.829263i	$0.688761\pi$
$354$	12.0000	0.637793
$355$	0	0
$356$	−20.0000	−1.06000
$357$	5.00000	0.264628
$358$	−16.0000	−0.845626
$359$	32.0000	1.68890	0.844448	−	0.535638i	$-0.179929\pi$
$359$	32.0000	1.68890	0.844448	+	0.535638i	$0.179929\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	28.0000	1.47165
$363$	14.0000	0.734809
$364$	−6.00000	−0.314485
$365$	0	0
$366$	−20.0000	−1.04542
$367$	23.0000	1.20059	0.600295	−	0.799779i	$-0.295050\pi$
$367$	23.0000	1.20059	0.600295	+	0.799779i	$0.295050\pi$
$368$	−4.00000	−0.208514
$369$	0	0
$370$	0	0
$371$	6.00000	0.311504
$372$	12.0000	0.622171
$373$	−26.0000	−1.34623	−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000	−1.34623	−0.673114	+	0.739538i	$0.735044\pi$
$374$	50.0000	2.58544
$375$	0	0
$376$	0	0
$377$	−9.00000	−0.463524
$378$	10.0000	0.514344
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	−4.00000	−0.204926
$382$	−54.0000	−2.76288
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	0	0
$386$	12.0000	0.610784
$387$	−4.00000	−0.203331
$388$	−14.0000	−0.710742
$389$	31.0000	1.57176	0.785881	−	0.618378i	$-0.212210\pi$
$389$	31.0000	1.57176	0.785881	+	0.618378i	$0.212210\pi$
$390$	0	0
$391$	5.00000	0.252861
$392$	0	0
$393$	−20.0000	−1.00887
$394$	−24.0000	−1.20910
$395$	0	0
$396$	20.0000	1.00504
$397$	−5.00000	−0.250943	−0.125471	−	0.992097i	$-0.540044\pi$
$397$	−5.00000	−0.250943	−0.125471	+	0.992097i	$0.540044\pi$
$398$	44.0000	2.20552
$399$	0	0
$400$	0	0
$401$	3.00000	0.149813	0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000	0.149813	0.0749064	+	0.997191i	$0.476134\pi$
$402$	8.00000	0.399004
$403$	−18.0000	−0.896644
$404$	20.0000	0.995037
$405$	0	0
$406$	−6.00000	−0.297775
$407$	−20.0000	−0.991363
$408$	0	0
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	0	0
$411$	6.00000	0.295958
$412$	−2.00000	−0.0985329
$413$	−6.00000	−0.295241
$414$	4.00000	0.196589
$415$	0	0
$416$	−24.0000	−1.17670
$417$	−8.00000	−0.391762
$418$	0	0
$419$	−18.0000	−0.879358	−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000	−0.879358	−0.439679	+	0.898155i	$0.644908\pi$
$420$	0	0
$421$	−37.0000	−1.80327	−0.901635	−	0.432498i	$-0.857632\pi$
$421$	−37.0000	−1.80327	−0.901635	+	0.432498i	$0.857632\pi$
$422$	34.0000	1.65509
$423$	−18.0000	−0.875190
$424$	0	0
$425$	0	0
$426$	16.0000	0.775203
$427$	10.0000	0.483934
$428$	12.0000	0.580042
$429$	15.0000	0.724207
$430$	0	0
$431$	−33.0000	−1.58955	−0.794777	−	0.606902i	$-0.792412\pi$
$431$	−33.0000	−1.58955	−0.794777	+	0.606902i	$0.792412\pi$
$432$	20.0000	0.962250
$433$	−34.0000	−1.63394	−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000	−1.63394	−0.816968	+	0.576683i	$0.804347\pi$
$434$	−12.0000	−0.576018
$435$	0	0
$436$	−34.0000	−1.62830
$437$	0	0
$438$	20.0000	0.955637
$439$	−6.00000	−0.286364	−0.143182	−	0.989696i	$-0.545733\pi$
$439$	−6.00000	−0.286364	−0.143182	+	0.989696i	$0.545733\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	30.0000	1.42695
$443$	6.00000	0.285069	0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000	0.285069	0.142534	+	0.989790i	$0.454475\pi$
$444$	8.00000	0.379663
$445$	0	0
$446$	30.0000	1.42054
$447$	−2.00000	−0.0945968
$448$	−8.00000	−0.377964
$449$	−9.00000	−0.424736	−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000	−0.424736	−0.212368	+	0.977190i	$0.568118\pi$
$450$	0	0
$451$	0	0
$452$	−36.0000	−1.69330
$453$	−9.00000	−0.422857
$454$	−6.00000	−0.281594
$455$	0	0
$456$	0	0
$457$	0	0		−	1.00000i	$-0.5\pi$
$457$	0	0			1.00000i	$0.5\pi$
$458$	16.0000	0.747631
$459$	−25.0000	−1.16690
$460$	0	0
$461$	32.0000	1.49039	0.745194	−	0.666847i	$-0.232357\pi$
$461$	32.0000	1.49039	0.745194	+	0.666847i	$0.232357\pi$
$462$	10.0000	0.465242
$463$	10.0000	0.464739	0.232370	−	0.972628i	$-0.425352\pi$
$463$	10.0000	0.464739	0.232370	+	0.972628i	$0.425352\pi$
$464$	−12.0000	−0.557086
$465$	0	0
$466$	36.0000	1.66767
$467$	21.0000	0.971764	0.485882	−	0.874024i	$-0.338498\pi$
$467$	21.0000	0.971764	0.485882	+	0.874024i	$0.338498\pi$
$468$	12.0000	0.554700
$469$	−4.00000	−0.184703
$470$	0	0
$471$	−2.00000	−0.0921551
$472$	0	0
$473$	−10.0000	−0.459800
$474$	30.0000	1.37795
$475$	0	0
$476$	10.0000	0.458349
$477$	−12.0000	−0.549442
$478$	−14.0000	−0.640345
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	0	0
$481$	−12.0000	−0.547153
$482$	−4.00000	−0.182195
$483$	1.00000	0.0455016
$484$	28.0000	1.27273
$485$	0	0
$486$	−32.0000	−1.45155
$487$	−10.0000	−0.453143	−0.226572	−	0.973995i	$-0.572752\pi$
$487$	−10.0000	−0.453143	−0.226572	+	0.973995i	$0.572752\pi$
$488$	0	0
$489$	−8.00000	−0.361773
$490$	0	0
$491$	−41.0000	−1.85030	−0.925152	−	0.379597i	$-0.876063\pi$
$491$	−41.0000	−1.85030	−0.925152	+	0.379597i	$0.876063\pi$
$492$	0	0
$493$	15.0000	0.675566
$494$	0	0
$495$	0	0
$496$	−24.0000	−1.07763
$497$	−8.00000	−0.358849
$498$	24.0000	1.07547
$499$	25.0000	1.11915	0.559577	−	0.828778i	$-0.310964\pi$
$499$	25.0000	1.11915	0.559577	+	0.828778i	$0.310964\pi$
$500$	0	0
$501$	1.00000	0.0446767
$502$	40.0000	1.78529
$503$	−39.0000	−1.73892	−0.869462	−	0.494000i	$-0.835534\pi$
$503$	−39.0000	−1.73892	−0.869462	+	0.494000i	$0.835534\pi$
$504$	0	0
$505$	0	0
$506$	10.0000	0.444554
$507$	−4.00000	−0.177646
$508$	−8.00000	−0.354943
$509$	36.0000	1.59567	0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000	1.59567	0.797836	+	0.602875i	$0.205978\pi$
$510$	0	0
$511$	−10.0000	−0.442374
$512$	−32.0000	−1.41421
$513$	0	0
$514$	4.00000	0.176432
$515$	0	0
$516$	4.00000	0.176090
$517$	−45.0000	−1.97910
$518$	−8.00000	−0.351500
$519$	3.00000	0.131685
$520$	0	0
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	12.0000	0.525226
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−40.0000	−1.74741
$525$	0	0
$526$	−56.0000	−2.44172
$527$	30.0000	1.30682
$528$	20.0000	0.870388
$529$	1.00000	0.0434783
$530$	0	0
$531$	12.0000	0.520756
$532$	0	0
$533$	0	0
$534$	20.0000	0.865485
$535$	0	0
$536$	0	0
$537$	8.00000	0.345225
$538$	−4.00000	−0.172452
$539$	−5.00000	−0.215365
$540$	0	0
$541$	−9.00000	−0.386940	−0.193470	−	0.981106i	$-0.561974\pi$
$541$	−9.00000	−0.386940	−0.193470	+	0.981106i	$0.561974\pi$
$542$	36.0000	1.54633
$543$	−14.0000	−0.600798
$544$	40.0000	1.71499
$545$	0	0
$546$	6.00000	0.256776
$547$	38.0000	1.62476	0.812381	−	0.583127i	$-0.198171\pi$
$547$	38.0000	1.62476	0.812381	+	0.583127i	$0.198171\pi$
$548$	12.0000	0.512615
$549$	−20.0000	−0.853579
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−15.0000	−0.637865
$554$	−16.0000	−0.679775
$555$	0	0
$556$	−16.0000	−0.678551
$557$	14.0000	0.593199	0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000	0.593199	0.296600	+	0.955002i	$0.404147\pi$
$558$	24.0000	1.01600
$559$	−6.00000	−0.253773
$560$	0	0
$561$	−25.0000	−1.05550
$562$	6.00000	0.253095
$563$	−20.0000	−0.842900	−0.421450	−	0.906852i	$-0.638479\pi$
$563$	−20.0000	−0.842900	−0.421450	+	0.906852i	$0.638479\pi$
$564$	18.0000	0.757937
$565$	0	0
$566$	−50.0000	−2.10166
$567$	1.00000	0.0419961
$568$	0	0
$569$	−2.00000	−0.0838444	−0.0419222	−	0.999121i	$-0.513348\pi$
$569$	−2.00000	−0.0838444	−0.0419222	+	0.999121i	$0.513348\pi$
$570$	0	0
$571$	8.00000	0.334790	0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000	0.334790	0.167395	+	0.985890i	$0.446465\pi$
$572$	30.0000	1.25436
$573$	27.0000	1.12794
$574$	0	0
$575$	0	0
$576$	16.0000	0.666667
$577$	−23.0000	−0.957503	−0.478751	−	0.877951i	$-0.658910\pi$
$577$	−23.0000	−0.957503	−0.478751	+	0.877951i	$0.658910\pi$
$578$	−16.0000	−0.665512
$579$	−6.00000	−0.249351
$580$	0	0
$581$	−12.0000	−0.497844
$582$	14.0000	0.580319
$583$	−30.0000	−1.24247
$584$	0	0
$585$	0	0
$586$	−18.0000	−0.743573
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	2.00000	0.0824786
$589$	0	0
$590$	0	0
$591$	12.0000	0.493614
$592$	−16.0000	−0.657596
$593$	−27.0000	−1.10876	−0.554379	−	0.832265i	$-0.687044\pi$
$593$	−27.0000	−1.10876	−0.554379	+	0.832265i	$0.687044\pi$
$594$	−50.0000	−2.05152
$595$	0	0
$596$	−4.00000	−0.163846
$597$	−22.0000	−0.900400
$598$	6.00000	0.245358
$599$	−43.0000	−1.75693	−0.878466	−	0.477805i	$-0.841433\pi$
$599$	−43.0000	−1.75693	−0.878466	+	0.477805i	$0.841433\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	−4.00000	−0.163028
$603$	8.00000	0.325785
$604$	−18.0000	−0.732410
$605$	0	0
$606$	−20.0000	−0.812444
$607$	−33.0000	−1.33943	−0.669714	−	0.742619i	$-0.733583\pi$
$607$	−33.0000	−1.33943	−0.669714	+	0.742619i	$0.733583\pi$
$608$	0	0
$609$	3.00000	0.121566
$610$	0	0
$611$	−27.0000	−1.09230
$612$	−20.0000	−0.808452
$613$	−24.0000	−0.969351	−0.484675	−	0.874694i	$-0.661062\pi$
$613$	−24.0000	−0.969351	−0.484675	+	0.874694i	$0.661062\pi$
$614$	34.0000	1.37213
$615$	0	0
$616$	0	0
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	2.00000	0.0804518
$619$	−10.0000	−0.401934	−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000	−0.401934	−0.200967	+	0.979598i	$0.564408\pi$
$620$	0	0
$621$	−5.00000	−0.200643
$622$	40.0000	1.60385
$623$	−10.0000	−0.400642
$624$	12.0000	0.480384
$625$	0	0
$626$	−30.0000	−1.19904
$627$	0	0
$628$	−4.00000	−0.159617
$629$	20.0000	0.797452
$630$	0	0
$631$	35.0000	1.39333	0.696664	−	0.717398i	$-0.254667\pi$
$631$	35.0000	1.39333	0.696664	+	0.717398i	$0.254667\pi$
$632$	0	0
$633$	−17.0000	−0.675689
$634$	−40.0000	−1.58860
$635$	0	0
$636$	12.0000	0.475831
$637$	−3.00000	−0.118864
$638$	30.0000	1.18771
$639$	16.0000	0.632950
$640$	0	0
$641$	26.0000	1.02694	0.513469	−	0.858108i	$-0.328360\pi$
$641$	26.0000	1.02694	0.513469	+	0.858108i	$0.328360\pi$
$642$	−12.0000	−0.473602
$643$	31.0000	1.22252	0.611260	−	0.791430i	$-0.290663\pi$
$643$	31.0000	1.22252	0.611260	+	0.791430i	$0.290663\pi$
$644$	2.00000	0.0788110
$645$	0	0
$646$	0	0
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	0	0
$649$	30.0000	1.17760
$650$	0	0
$651$	6.00000	0.235159
$652$	−16.0000	−0.626608
$653$	36.0000	1.40879	0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000	1.40879	0.704394	+	0.709809i	$0.251219\pi$
$654$	34.0000	1.32951
$655$	0	0
$656$	0	0
$657$	20.0000	0.780274
$658$	−18.0000	−0.701713
$659$	−21.0000	−0.818044	−0.409022	−	0.912525i	$-0.634130\pi$
$659$	−21.0000	−0.818044	−0.409022	+	0.912525i	$0.634130\pi$
$660$	0	0
$661$	40.0000	1.55582	0.777910	−	0.628376i	$-0.216280\pi$
$661$	40.0000	1.55582	0.777910	+	0.628376i	$0.216280\pi$
$662$	−48.0000	−1.86557
$663$	−15.0000	−0.582552
$664$	0	0
$665$	0	0
$666$	16.0000	0.619987
$667$	3.00000	0.116160
$668$	2.00000	0.0773823
$669$	−15.0000	−0.579934
$670$	0	0
$671$	−50.0000	−1.93023
$672$	8.00000	0.308607
$673$	−44.0000	−1.69608	−0.848038	−	0.529936i	$-0.822216\pi$
$673$	−44.0000	−1.69608	−0.848038	+	0.529936i	$0.822216\pi$
$674$	4.00000	0.154074
$675$	0	0
$676$	−8.00000	−0.307692
$677$	39.0000	1.49889	0.749446	−	0.662066i	$-0.230320\pi$
$677$	39.0000	1.49889	0.749446	+	0.662066i	$0.230320\pi$
$678$	36.0000	1.38257
$679$	−7.00000	−0.268635
$680$	0	0
$681$	3.00000	0.114960
$682$	60.0000	2.29752
$683$	44.0000	1.68361	0.841807	−	0.539779i	$-0.181492\pi$
$683$	44.0000	1.68361	0.841807	+	0.539779i	$0.181492\pi$
$684$	0	0
$685$	0	0
$686$	−2.00000	−0.0763604
$687$	−8.00000	−0.305219
$688$	−8.00000	−0.304997
$689$	−18.0000	−0.685745
$690$	0	0
$691$	26.0000	0.989087	0.494543	−	0.869153i	$-0.335335\pi$
$691$	26.0000	0.989087	0.494543	+	0.869153i	$0.335335\pi$
$692$	6.00000	0.228086
$693$	10.0000	0.379869
$694$	24.0000	0.911028
$695$	0	0
$696$	0	0
$697$	0	0
$698$	−56.0000	−2.11963
$699$	−18.0000	−0.680823
$700$	0	0
$701$	45.0000	1.69963	0.849813	−	0.527084i	$-0.176715\pi$
$701$	45.0000	1.69963	0.849813	+	0.527084i	$0.176715\pi$
$702$	−30.0000	−1.13228
$703$	0	0
$704$	40.0000	1.50756
$705$	0	0
$706$	42.0000	1.58069
$707$	10.0000	0.376089
$708$	−12.0000	−0.450988
$709$	−51.0000	−1.91535	−0.957673	−	0.287860i	$-0.907056\pi$
$709$	−51.0000	−1.91535	−0.957673	+	0.287860i	$0.907056\pi$
$710$	0	0
$711$	30.0000	1.12509
$712$	0	0
$713$	6.00000	0.224702
$714$	−10.0000	−0.374241
$715$	0	0
$716$	16.0000	0.597948
$717$	7.00000	0.261420
$718$	−64.0000	−2.38846
$719$	26.0000	0.969636	0.484818	−	0.874615i	$-0.338886\pi$
$719$	26.0000	0.969636	0.484818	+	0.874615i	$0.338886\pi$
$720$	0	0
$721$	−1.00000	−0.0372419
$722$	38.0000	1.41421
$723$	2.00000	0.0743808
$724$	−28.0000	−1.04061
$725$	0	0
$726$	−28.0000	−1.03918
$727$	−16.0000	−0.593407	−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000	−0.593407	−0.296704	+	0.954970i	$0.595887\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	10.0000	0.369863
$732$	20.0000	0.739221
$733$	−29.0000	−1.07114	−0.535570	−	0.844491i	$-0.679903\pi$
$733$	−29.0000	−1.07114	−0.535570	+	0.844491i	$0.679903\pi$
$734$	−46.0000	−1.69789
$735$	0	0
$736$	8.00000	0.294884
$737$	20.0000	0.736709
$738$	0	0
$739$	−43.0000	−1.58178	−0.790890	−	0.611958i	$-0.790382\pi$
$739$	−43.0000	−1.58178	−0.790890	+	0.611958i	$0.790382\pi$
$740$	0	0
$741$	0	0
$742$	−12.0000	−0.440534
$743$	30.0000	1.10059	0.550297	−	0.834969i	$-0.314515\pi$
$743$	30.0000	1.10059	0.550297	+	0.834969i	$0.314515\pi$
$744$	0	0
$745$	0	0
$746$	52.0000	1.90386
$747$	24.0000	0.878114
$748$	−50.0000	−1.82818
$749$	6.00000	0.219235
$750$	0	0
$751$	53.0000	1.93400	0.966999	−	0.254781i	$-0.0820034\pi$
$751$	53.0000	1.93400	0.966999	+	0.254781i	$0.0820034\pi$
$752$	−36.0000	−1.31278
$753$	−20.0000	−0.728841
$754$	18.0000	0.655521
$755$	0	0
$756$	−10.0000	−0.363696
$757$	−8.00000	−0.290765	−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000	−0.290765	−0.145382	+	0.989376i	$0.546441\pi$
$758$	40.0000	1.45287
$759$	−5.00000	−0.181489
$760$	0	0
$761$	−36.0000	−1.30500	−0.652499	−	0.757789i	$-0.726280\pi$
$761$	−36.0000	−1.30500	−0.652499	+	0.757789i	$0.726280\pi$
$762$	8.00000	0.289809
$763$	−17.0000	−0.615441
$764$	54.0000	1.95365
$765$	0	0
$766$	32.0000	1.15621
$767$	18.0000	0.649942
$768$	16.0000	0.577350
$769$	−16.0000	−0.576975	−0.288487	−	0.957484i	$-0.593152\pi$
$769$	−16.0000	−0.576975	−0.288487	+	0.957484i	$0.593152\pi$
$770$	0	0
$771$	−2.00000	−0.0720282
$772$	−12.0000	−0.431889
$773$	15.0000	0.539513	0.269756	−	0.962929i	$-0.413057\pi$
$773$	15.0000	0.539513	0.269756	+	0.962929i	$0.413057\pi$
$774$	8.00000	0.287554
$775$	0	0
$776$	0	0
$777$	4.00000	0.143499
$778$	−62.0000	−2.22281
$779$	0	0
$780$	0	0
$781$	40.0000	1.43131
$782$	−10.0000	−0.357599
$783$	−15.0000	−0.536056
$784$	−4.00000	−0.142857
$785$	0	0
$786$	40.0000	1.42675
$787$	−37.0000	−1.31891	−0.659454	−	0.751745i	$-0.729212\pi$
$787$	−37.0000	−1.31891	−0.659454	+	0.751745i	$0.729212\pi$
$788$	24.0000	0.854965
$789$	28.0000	0.996826
$790$	0	0
$791$	−18.0000	−0.640006
$792$	0	0
$793$	−30.0000	−1.06533
$794$	10.0000	0.354887
$795$	0	0
$796$	−44.0000	−1.55954
$797$	−51.0000	−1.80651	−0.903256	−	0.429101i	$-0.858830\pi$
$797$	−51.0000	−1.80651	−0.903256	+	0.429101i	$0.858830\pi$
$798$	0	0
$799$	45.0000	1.59199
$800$	0	0
$801$	20.0000	0.706665
$802$	−6.00000	−0.211867
$803$	50.0000	1.76446
$804$	−8.00000	−0.282138
$805$	0	0
$806$	36.0000	1.26805
$807$	2.00000	0.0704033
$808$	0	0
$809$	9.00000	0.316423	0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000	0.316423	0.158212	+	0.987405i	$0.449427\pi$
$810$	0	0
$811$	22.0000	0.772524	0.386262	−	0.922389i	$-0.373766\pi$
$811$	22.0000	0.772524	0.386262	+	0.922389i	$0.373766\pi$
$812$	6.00000	0.210559
$813$	−18.0000	−0.631288
$814$	40.0000	1.40200
$815$	0	0
$816$	−20.0000	−0.700140
$817$	0	0
$818$	12.0000	0.419570
$819$	6.00000	0.209657
$820$	0	0
$821$	−19.0000	−0.663105	−0.331552	−	0.943437i	$-0.607572\pi$
$821$	−19.0000	−0.663105	−0.331552	+	0.943437i	$0.607572\pi$
$822$	−12.0000	−0.418548
$823$	−42.0000	−1.46403	−0.732014	−	0.681290i	$-0.761419\pi$
$823$	−42.0000	−1.46403	−0.732014	+	0.681290i	$0.761419\pi$
$824$	0	0
$825$	0	0
$826$	12.0000	0.417533
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	−4.00000	−0.139010
$829$	16.0000	0.555703	0.277851	−	0.960624i	$-0.410378\pi$
$829$	16.0000	0.555703	0.277851	+	0.960624i	$0.410378\pi$
$830$	0	0
$831$	8.00000	0.277517
$832$	24.0000	0.832050
$833$	5.00000	0.173240
$834$	16.0000	0.554035
$835$	0	0
$836$	0	0
$837$	−30.0000	−1.03695
$838$	36.0000	1.24360
$839$	36.0000	1.24286	0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000	1.24286	0.621429	+	0.783470i	$0.286552\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	74.0000	2.55021
$843$	−3.00000	−0.103325
$844$	−34.0000	−1.17033
$845$	0	0
$846$	36.0000	1.23771
$847$	14.0000	0.481046
$848$	−24.0000	−0.824163
$849$	25.0000	0.857998
$850$	0	0
$851$	4.00000	0.137118
$852$	−16.0000	−0.548151
$853$	2.00000	0.0684787	0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000	0.0684787	0.0342393	+	0.999414i	$0.489099\pi$
$854$	−20.0000	−0.684386
$855$	0	0
$856$	0	0
$857$	−46.0000	−1.57133	−0.785665	−	0.618652i	$-0.787679\pi$
$857$	−46.0000	−1.57133	−0.785665	+	0.618652i	$0.787679\pi$
$858$	−30.0000	−1.02418
$859$	40.0000	1.36478	0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000	1.36478	0.682391	+	0.730987i	$0.260940\pi$
$860$	0	0
$861$	0	0
$862$	66.0000	2.24797
$863$	−30.0000	−1.02121	−0.510606	−	0.859815i	$-0.670579\pi$
$863$	−30.0000	−1.02121	−0.510606	+	0.859815i	$0.670579\pi$
$864$	−40.0000	−1.36083
$865$	0	0
$866$	68.0000	2.31073
$867$	8.00000	0.271694
$868$	12.0000	0.407307
$869$	75.0000	2.54420
$870$	0	0
$871$	12.0000	0.406604
$872$	0	0
$873$	14.0000	0.473828
$874$	0	0
$875$	0	0
$876$	−20.0000	−0.675737
$877$	−8.00000	−0.270141	−0.135070	−	0.990836i	$-0.543126\pi$
$877$	−8.00000	−0.270141	−0.135070	+	0.990836i	$0.543126\pi$
$878$	12.0000	0.404980
$879$	9.00000	0.303562
$880$	0	0
$881$	−34.0000	−1.14549	−0.572745	−	0.819734i	$-0.694121\pi$
$881$	−34.0000	−1.14549	−0.572745	+	0.819734i	$0.694121\pi$
$882$	4.00000	0.134687
$883$	48.0000	1.61533	0.807664	−	0.589643i	$-0.200731\pi$
$883$	48.0000	1.61533	0.807664	+	0.589643i	$0.200731\pi$
$884$	−30.0000	−1.00901
$885$	0	0
$886$	−12.0000	−0.403148
$887$	16.0000	0.537227	0.268614	−	0.963248i	$-0.413434\pi$
$887$	16.0000	0.537227	0.268614	+	0.963248i	$0.413434\pi$
$888$	0	0
$889$	−4.00000	−0.134156
$890$	0	0
$891$	−5.00000	−0.167506
$892$	−30.0000	−1.00447
$893$	0	0
$894$	4.00000	0.133780
$895$	0	0
$896$	0	0
$897$	−3.00000	−0.100167
$898$	18.0000	0.600668
$899$	18.0000	0.600334
$900$	0	0
$901$	30.0000	0.999445
$902$	0	0
$903$	2.00000	0.0665558
$904$	0	0
$905$	0	0
$906$	18.0000	0.598010
$907$	−4.00000	−0.132818	−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000	−0.132818	−0.0664089	+	0.997792i	$0.521154\pi$
$908$	6.00000	0.199117
$909$	−20.0000	−0.663358
$910$	0	0
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	0	0
$913$	60.0000	1.98571
$914$	0	0
$915$	0	0
$916$	−16.0000	−0.528655
$917$	−20.0000	−0.660458
$918$	50.0000	1.65025
$919$	37.0000	1.22052	0.610259	−	0.792202i	$-0.291065\pi$
$919$	37.0000	1.22052	0.610259	+	0.792202i	$0.291065\pi$
$920$	0	0
$921$	−17.0000	−0.560169
$922$	−64.0000	−2.10773
$923$	24.0000	0.789970
$924$	−10.0000	−0.328976
$925$	0	0
$926$	−20.0000	−0.657241
$927$	2.00000	0.0656886
$928$	24.0000	0.787839
$929$	−14.0000	−0.459325	−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000	−0.459325	−0.229663	+	0.973270i	$0.573762\pi$
$930$	0	0
$931$	0	0
$932$	−36.0000	−1.17922
$933$	−20.0000	−0.654771
$934$	−42.0000	−1.37428
$935$	0	0
$936$	0	0
$937$	−3.00000	−0.0980057	−0.0490029	−	0.998799i	$-0.515604\pi$
$937$	−3.00000	−0.0980057	−0.0490029	+	0.998799i	$0.515604\pi$
$938$	8.00000	0.261209
$939$	15.0000	0.489506
$940$	0	0
$941$	20.0000	0.651981	0.325991	−	0.945373i	$-0.394302\pi$
$941$	20.0000	0.651981	0.325991	+	0.945373i	$0.394302\pi$
$942$	4.00000	0.130327
$943$	0	0
$944$	24.0000	0.781133
$945$	0	0
$946$	20.0000	0.650256
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	−30.0000	−0.974355
$949$	30.0000	0.973841
$950$	0	0
$951$	20.0000	0.648544
$952$	0	0
$953$	−50.0000	−1.61966	−0.809829	−	0.586665i	$-0.800440\pi$
$953$	−50.0000	−1.61966	−0.809829	+	0.586665i	$0.800440\pi$
$954$	24.0000	0.777029
$955$	0	0
$956$	14.0000	0.452792
$957$	−15.0000	−0.484881
$958$	36.0000	1.16311
$959$	6.00000	0.193750
$960$	0	0
$961$	5.00000	0.161290
$962$	24.0000	0.773791
$963$	−12.0000	−0.386695
$964$	4.00000	0.128831
$965$	0	0
$966$	−2.00000	−0.0643489
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	32.0000	1.02640
$973$	−8.00000	−0.256468
$974$	20.0000	0.640841
$975$	0	0
$976$	−40.0000	−1.28037
$977$	48.0000	1.53566	0.767828	−	0.640656i	$-0.221338\pi$
$977$	48.0000	1.53566	0.767828	+	0.640656i	$0.221338\pi$
$978$	16.0000	0.511624
$979$	50.0000	1.59801
$980$	0	0
$981$	34.0000	1.08554
$982$	82.0000	2.61673
$983$	13.0000	0.414636	0.207318	−	0.978274i	$-0.433527\pi$
$983$	13.0000	0.414636	0.207318	+	0.978274i	$0.433527\pi$
$984$	0	0
$985$	0	0
$986$	−30.0000	−0.955395
$987$	9.00000	0.286473
$988$	0	0
$989$	2.00000	0.0635963
$990$	0	0
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	48.0000	1.52400
$993$	24.0000	0.761617
$994$	16.0000	0.507489
$995$	0	0
$996$	−24.0000	−0.760469
$997$	51.0000	1.61519	0.807593	−	0.589740i	$-0.200770\pi$
$997$	51.0000	1.61519	0.807593	+	0.589740i	$0.200770\pi$
$998$	−50.0000	−1.58272
$999$	−20.0000	−0.632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.b.1.1		1
5.4	even	2		805.2.a.c.1.1	✓	1
15.14	odd	2		7245.2.a.d.1.1		1
35.34	odd	2		5635.2.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.c.1.1	✓	1	5.4	even	2
4025.2.a.b.1.1		1	1.1	even	1	trivial
5635.2.a.k.1.1		1	35.34	odd	2
7245.2.a.d.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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