LMFDB - Embedded newform 4650.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4650,2,Mod(1,4650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4650, 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("4650.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4650.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:	$37.1304369399$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4650.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} +2.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} +2.00000 q^{21} -2.00000 q^{22} -2.00000 q^{23} +1.00000 q^{24} +4.00000 q^{26} -1.00000 q^{27} -2.00000 q^{28} +3.00000 q^{29} -1.00000 q^{31} -1.00000 q^{32} -2.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} +4.00000 q^{37} -4.00000 q^{38} +4.00000 q^{39} -8.00000 q^{41} -2.00000 q^{42} +13.0000 q^{43} +2.00000 q^{44} +2.00000 q^{46} +1.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{51} -4.00000 q^{52} +6.00000 q^{53} +1.00000 q^{54} +2.00000 q^{56} -4.00000 q^{57} -3.00000 q^{58} -12.0000 q^{61} +1.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +2.00000 q^{66} -2.00000 q^{67} -1.00000 q^{68} +2.00000 q^{69} +5.00000 q^{71} -1.00000 q^{72} -2.00000 q^{73} -4.00000 q^{74} +4.00000 q^{76} -4.00000 q^{77} -4.00000 q^{78} -3.00000 q^{79} +1.00000 q^{81} +8.00000 q^{82} -12.0000 q^{83} +2.00000 q^{84} -13.0000 q^{86} -3.00000 q^{87} -2.00000 q^{88} +15.0000 q^{89} +8.00000 q^{91} -2.00000 q^{92} +1.00000 q^{93} -1.00000 q^{94} +1.00000 q^{96} +1.00000 q^{97} +3.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.00000	−0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536	−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000	−0.242536	−0.121268	+	0.992620i	$0.538696\pi$
$18$	−1.00000	−0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	−2.00000	−0.426401
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	4.00000	0.784465
$27$	−1.00000	−0.192450
$28$	−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
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	1.00000	0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	−4.00000	−0.648886
$39$	4.00000	0.640513
$40$	0	0
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	−2.00000	−0.308607
$43$	13.0000	1.98248	0.991241	−	0.132068i	$-0.0421616\pi$
$43$	13.0000	1.98248	0.991241	+	0.132068i	$0.0421616\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	2.00000	0.294884
$47$	1.00000	0.145865	0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000	0.145865	0.0729325	+	0.997337i	$0.476764\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	0	0
$51$	1.00000	0.140028
$52$	−4.00000	−0.554700
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	2.00000	0.267261
$57$	−4.00000	−0.529813
$58$	−3.00000	−0.393919
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−12.0000	−1.53644	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000	−1.53644	−0.768221	+	0.640184i	$0.778858\pi$
$62$	1.00000	0.127000
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	2.00000	0.246183
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	−1.00000	−0.121268
$69$	2.00000	0.240772
$70$	0	0
$71$	5.00000	0.593391	0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000	0.593391	0.296695	+	0.954972i	$0.404115\pi$
$72$	−1.00000	−0.117851
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	4.00000	0.458831
$77$	−4.00000	−0.455842
$78$	−4.00000	−0.452911
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	8.00000	0.883452
$83$	−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
$86$	−13.0000	−1.40183
$87$	−3.00000	−0.321634
$88$	−2.00000	−0.213201
$89$	15.0000	1.59000	0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000	1.59000	0.794998	+	0.606612i	$0.207472\pi$
$90$	0	0
$91$	8.00000	0.838628
$92$	−2.00000	−0.208514
$93$	1.00000	0.103695
$94$	−1.00000	−0.103142
$95$	0	0
$96$	1.00000	0.102062
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	3.00000	0.303046
$99$	2.00000	0.201008
$100$	0	0
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	−1.00000	−0.0990148
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	4.00000	0.392232
$105$	0	0
$106$	−6.00000	−0.582772
$107$	1.00000	0.0966736	0.0483368	−	0.998831i	$-0.484608\pi$
$107$	1.00000	0.0966736	0.0483368	+	0.998831i	$0.484608\pi$
$108$	−1.00000	−0.0962250
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	0	0
$111$	−4.00000	−0.379663
$112$	−2.00000	−0.188982
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	4.00000	0.374634
$115$	0	0
$116$	3.00000	0.278543
$117$	−4.00000	−0.369800
$118$	0	0
$119$	2.00000	0.183340
$120$	0	0
$121$	−7.00000	−0.636364
$122$	12.0000	1.08643
$123$	8.00000	0.721336
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	2.00000	0.178174
$127$	−11.0000	−0.976092	−0.488046	−	0.872818i	$-0.662290\pi$
$127$	−11.0000	−0.976092	−0.488046	+	0.872818i	$0.662290\pi$
$128$	−1.00000	−0.0883883
$129$	−13.0000	−1.14459
$130$	0	0
$131$	−11.0000	−0.961074	−0.480537	−	0.876974i	$-0.659558\pi$
$131$	−11.0000	−0.961074	−0.480537	+	0.876974i	$0.659558\pi$
$132$	−2.00000	−0.174078
$133$	−8.00000	−0.693688
$134$	2.00000	0.172774
$135$	0	0
$136$	1.00000	0.0857493
$137$	−17.0000	−1.45241	−0.726204	−	0.687479i	$-0.758717\pi$
$137$	−17.0000	−1.45241	−0.726204	+	0.687479i	$0.758717\pi$
$138$	−2.00000	−0.170251
$139$	−5.00000	−0.424094	−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000	−0.424094	−0.212047	+	0.977259i	$0.568013\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−5.00000	−0.419591
$143$	−8.00000	−0.668994
$144$	1.00000	0.0833333
$145$	0	0
$146$	2.00000	0.165521
$147$	3.00000	0.247436
$148$	4.00000	0.328798
$149$	16.0000	1.31077	0.655386	−	0.755295i	$-0.272506\pi$
$149$	16.0000	1.31077	0.655386	+	0.755295i	$0.272506\pi$
$150$	0	0
$151$	−17.0000	−1.38344	−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000	−1.38344	−0.691720	+	0.722166i	$0.743147\pi$
$152$	−4.00000	−0.324443
$153$	−1.00000	−0.0808452
$154$	4.00000	0.322329
$155$	0	0
$156$	4.00000	0.320256
$157$	7.00000	0.558661	0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000	0.558661	0.279330	+	0.960195i	$0.409888\pi$
$158$	3.00000	0.238667
$159$	−6.00000	−0.475831
$160$	0	0
$161$	4.00000	0.315244
$162$	−1.00000	−0.0785674
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	−8.00000	−0.624695
$165$	0	0
$166$	12.0000	0.931381
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	−2.00000	−0.154303
$169$	3.00000	0.230769
$170$	0	0
$171$	4.00000	0.305888
$172$	13.0000	0.991241
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	3.00000	0.227429
$175$	0	0
$176$	2.00000	0.150756
$177$	0	0
$178$	−15.0000	−1.12430
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	0	0
$181$	−16.0000	−1.18927	−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000	−1.18927	−0.594635	+	0.803996i	$0.702704\pi$
$182$	−8.00000	−0.592999
$183$	12.0000	0.887066
$184$	2.00000	0.147442
$185$	0	0
$186$	−1.00000	−0.0733236
$187$	−2.00000	−0.146254
$188$	1.00000	0.0729325
$189$	2.00000	0.145479
$190$	0	0
$191$	−5.00000	−0.361787	−0.180894	−	0.983503i	$-0.557899\pi$
$191$	−5.00000	−0.361787	−0.180894	+	0.983503i	$0.557899\pi$
$192$	−1.00000	−0.0721688
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−1.00000	−0.0717958
$195$	0	0
$196$	−3.00000	−0.214286
$197$	13.0000	0.926212	0.463106	−	0.886303i	$-0.346735\pi$
$197$	13.0000	0.926212	0.463106	+	0.886303i	$0.346735\pi$
$198$	−2.00000	−0.142134
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	0	0
$201$	2.00000	0.141069
$202$	−10.0000	−0.703598
$203$	−6.00000	−0.421117
$204$	1.00000	0.0700140
$205$	0	0
$206$	4.00000	0.278693
$207$	−2.00000	−0.139010
$208$	−4.00000	−0.277350
$209$	8.00000	0.553372
$210$	0	0
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	6.00000	0.412082
$213$	−5.00000	−0.342594
$214$	−1.00000	−0.0683586
$215$	0	0
$216$	1.00000	0.0680414
$217$	2.00000	0.135769
$218$	−11.0000	−0.745014
$219$	2.00000	0.135147
$220$	0	0
$221$	4.00000	0.269069
$222$	4.00000	0.268462
$223$	−15.0000	−1.00447	−0.502237	−	0.864730i	$-0.667490\pi$
$223$	−15.0000	−1.00447	−0.502237	+	0.864730i	$0.667490\pi$
$224$	2.00000	0.133631
$225$	0	0
$226$	2.00000	0.133038
$227$	−5.00000	−0.331862	−0.165931	−	0.986137i	$-0.553063\pi$
$227$	−5.00000	−0.331862	−0.165931	+	0.986137i	$0.553063\pi$
$228$	−4.00000	−0.264906
$229$	−4.00000	−0.264327	−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000	−0.264327	−0.132164	+	0.991228i	$0.542192\pi$
$230$	0	0
$231$	4.00000	0.263181
$232$	−3.00000	−0.196960
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	4.00000	0.261488
$235$	0	0
$236$	0	0
$237$	3.00000	0.194871
$238$	−2.00000	−0.129641
$239$	30.0000	1.94054	0.970269	−	0.242028i	$-0.0778125\pi$
$239$	30.0000	1.94054	0.970269	+	0.242028i	$0.0778125\pi$
$240$	0	0
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	7.00000	0.449977
$243$	−1.00000	−0.0641500
$244$	−12.0000	−0.768221
$245$	0	0
$246$	−8.00000	−0.510061
$247$	−16.0000	−1.01806
$248$	1.00000	0.0635001
$249$	12.0000	0.760469
$250$	0	0
$251$	−22.0000	−1.38863	−0.694314	−	0.719672i	$-0.744292\pi$
$251$	−22.0000	−1.38863	−0.694314	+	0.719672i	$0.744292\pi$
$252$	−2.00000	−0.125988
$253$	−4.00000	−0.251478
$254$	11.0000	0.690201
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	13.0000	0.809345
$259$	−8.00000	−0.497096
$260$	0	0
$261$	3.00000	0.185695
$262$	11.0000	0.679582
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	2.00000	0.123091
$265$	0	0
$266$	8.00000	0.490511
$267$	−15.0000	−0.917985
$268$	−2.00000	−0.122169
$269$	1.00000	0.0609711	0.0304855	−	0.999535i	$-0.490295\pi$
$269$	1.00000	0.0609711	0.0304855	+	0.999535i	$0.490295\pi$
$270$	0	0
$271$	−21.0000	−1.27566	−0.637830	−	0.770178i	$-0.720168\pi$
$271$	−21.0000	−1.27566	−0.637830	+	0.770178i	$0.720168\pi$
$272$	−1.00000	−0.0606339
$273$	−8.00000	−0.484182
$274$	17.0000	1.02701
$275$	0	0
$276$	2.00000	0.120386
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	5.00000	0.299880
$279$	−1.00000	−0.0598684
$280$	0	0
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	1.00000	0.0595491
$283$	−6.00000	−0.356663	−0.178331	−	0.983970i	$-0.557070\pi$
$283$	−6.00000	−0.356663	−0.178331	+	0.983970i	$0.557070\pi$
$284$	5.00000	0.296695
$285$	0	0
$286$	8.00000	0.473050
$287$	16.0000	0.944450
$288$	−1.00000	−0.0589256
$289$	−16.0000	−0.941176
$290$	0	0
$291$	−1.00000	−0.0586210
$292$	−2.00000	−0.117041
$293$	−10.0000	−0.584206	−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000	−0.584206	−0.292103	+	0.956387i	$0.594355\pi$
$294$	−3.00000	−0.174964
$295$	0	0
$296$	−4.00000	−0.232495
$297$	−2.00000	−0.116052
$298$	−16.0000	−0.926855
$299$	8.00000	0.462652
$300$	0	0
$301$	−26.0000	−1.49862
$302$	17.0000	0.978240
$303$	−10.0000	−0.574485
$304$	4.00000	0.229416
$305$	0	0
$306$	1.00000	0.0571662
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	−4.00000	−0.227921
$309$	4.00000	0.227552
$310$	0	0
$311$	−25.0000	−1.41762	−0.708810	−	0.705399i	$-0.750768\pi$
$311$	−25.0000	−1.41762	−0.708810	+	0.705399i	$0.750768\pi$
$312$	−4.00000	−0.226455
$313$	20.0000	1.13047	0.565233	−	0.824931i	$-0.308786\pi$
$313$	20.0000	1.13047	0.565233	+	0.824931i	$0.308786\pi$
$314$	−7.00000	−0.395033
$315$	0	0
$316$	−3.00000	−0.168763
$317$	−14.0000	−0.786318	−0.393159	−	0.919470i	$-0.628618\pi$
$317$	−14.0000	−0.786318	−0.393159	+	0.919470i	$0.628618\pi$
$318$	6.00000	0.336463
$319$	6.00000	0.335936
$320$	0	0
$321$	−1.00000	−0.0558146
$322$	−4.00000	−0.222911
$323$	−4.00000	−0.222566
$324$	1.00000	0.0555556
$325$	0	0
$326$	16.0000	0.886158
$327$	−11.0000	−0.608301
$328$	8.00000	0.441726
$329$	−2.00000	−0.110264
$330$	0	0
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	−12.0000	−0.658586
$333$	4.00000	0.219199
$334$	−8.00000	−0.437741
$335$	0	0
$336$	2.00000	0.109109
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	−3.00000	−0.163178
$339$	2.00000	0.108625
$340$	0	0
$341$	−2.00000	−0.108306
$342$	−4.00000	−0.216295
$343$	20.0000	1.07990
$344$	−13.0000	−0.700913
$345$	0	0
$346$	−18.0000	−0.967686
$347$	−14.0000	−0.751559	−0.375780	−	0.926709i	$-0.622625\pi$
$347$	−14.0000	−0.751559	−0.375780	+	0.926709i	$0.622625\pi$
$348$	−3.00000	−0.160817
$349$	−5.00000	−0.267644	−0.133822	−	0.991005i	$-0.542725\pi$
$349$	−5.00000	−0.267644	−0.133822	+	0.991005i	$0.542725\pi$
$350$	0	0
$351$	4.00000	0.213504
$352$	−2.00000	−0.106600
$353$	−10.0000	−0.532246	−0.266123	−	0.963939i	$-0.585743\pi$
$353$	−10.0000	−0.532246	−0.266123	+	0.963939i	$0.585743\pi$
$354$	0	0
$355$	0	0
$356$	15.0000	0.794998
$357$	−2.00000	−0.105851
$358$	−6.00000	−0.317110
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	16.0000	0.840941
$363$	7.00000	0.367405
$364$	8.00000	0.419314
$365$	0	0
$366$	−12.0000	−0.627250
$367$	3.00000	0.156599	0.0782994	−	0.996930i	$-0.475051\pi$
$367$	3.00000	0.156599	0.0782994	+	0.996930i	$0.475051\pi$
$368$	−2.00000	−0.104257
$369$	−8.00000	−0.416463
$370$	0	0
$371$	−12.0000	−0.623009
$372$	1.00000	0.0518476
$373$	7.00000	0.362446	0.181223	−	0.983442i	$-0.441994\pi$
$373$	7.00000	0.362446	0.181223	+	0.983442i	$0.441994\pi$
$374$	2.00000	0.103418
$375$	0	0
$376$	−1.00000	−0.0515711
$377$	−12.0000	−0.618031
$378$	−2.00000	−0.102869
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	0	0
$381$	11.0000	0.563547
$382$	5.00000	0.255822
$383$	−26.0000	−1.32854	−0.664269	−	0.747494i	$-0.731257\pi$
$383$	−26.0000	−1.32854	−0.664269	+	0.747494i	$0.731257\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	10.0000	0.508987
$387$	13.0000	0.660827
$388$	1.00000	0.0507673
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	2.00000	0.101144
$392$	3.00000	0.151523
$393$	11.0000	0.554877
$394$	−13.0000	−0.654931
$395$	0	0
$396$	2.00000	0.100504
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	8.00000	0.401004
$399$	8.00000	0.400501
$400$	0	0
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	−2.00000	−0.0997509
$403$	4.00000	0.199254
$404$	10.0000	0.497519
$405$	0	0
$406$	6.00000	0.297775
$407$	8.00000	0.396545
$408$	−1.00000	−0.0495074
$409$	−20.0000	−0.988936	−0.494468	−	0.869196i	$-0.664637\pi$
$409$	−20.0000	−0.988936	−0.494468	+	0.869196i	$0.664637\pi$
$410$	0	0
$411$	17.0000	0.838548
$412$	−4.00000	−0.197066
$413$	0	0
$414$	2.00000	0.0982946
$415$	0	0
$416$	4.00000	0.196116
$417$	5.00000	0.244851
$418$	−8.00000	−0.391293
$419$	−9.00000	−0.439679	−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000	−0.439679	−0.219839	+	0.975536i	$0.570553\pi$
$420$	0	0
$421$	17.0000	0.828529	0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000	0.828529	0.414265	+	0.910156i	$0.364039\pi$
$422$	8.00000	0.389434
$423$	1.00000	0.0486217
$424$	−6.00000	−0.291386
$425$	0	0
$426$	5.00000	0.242251
$427$	24.0000	1.16144
$428$	1.00000	0.0483368
$429$	8.00000	0.386244
$430$	0	0
$431$	−16.0000	−0.770693	−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000	−0.770693	−0.385346	+	0.922772i	$0.625918\pi$
$432$	−1.00000	−0.0481125
$433$	−38.0000	−1.82616	−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000	−1.82616	−0.913082	+	0.407777i	$0.866304\pi$
$434$	−2.00000	−0.0960031
$435$	0	0
$436$	11.0000	0.526804
$437$	−8.00000	−0.382692
$438$	−2.00000	−0.0955637
$439$	−30.0000	−1.43182	−0.715911	−	0.698192i	$-0.753988\pi$
$439$	−30.0000	−1.43182	−0.715911	+	0.698192i	$0.753988\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	−4.00000	−0.190261
$443$	17.0000	0.807694	0.403847	−	0.914826i	$-0.367673\pi$
$443$	17.0000	0.807694	0.403847	+	0.914826i	$0.367673\pi$
$444$	−4.00000	−0.189832
$445$	0	0
$446$	15.0000	0.710271
$447$	−16.0000	−0.756774
$448$	−2.00000	−0.0944911
$449$	35.0000	1.65175	0.825876	−	0.563852i	$-0.190681\pi$
$449$	35.0000	1.65175	0.825876	+	0.563852i	$0.190681\pi$
$450$	0	0
$451$	−16.0000	−0.753411
$452$	−2.00000	−0.0940721
$453$	17.0000	0.798730
$454$	5.00000	0.234662
$455$	0	0
$456$	4.00000	0.187317
$457$	0	0		−	1.00000i	$-0.5\pi$
$457$	0	0			1.00000i	$0.5\pi$
$458$	4.00000	0.186908
$459$	1.00000	0.0466760
$460$	0	0
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	−4.00000	−0.186097
$463$	−35.0000	−1.62659	−0.813294	−	0.581853i	$-0.802328\pi$
$463$	−35.0000	−1.62659	−0.813294	+	0.581853i	$0.802328\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	−14.0000	−0.648537
$467$	−3.00000	−0.138823	−0.0694117	−	0.997588i	$-0.522112\pi$
$467$	−3.00000	−0.138823	−0.0694117	+	0.997588i	$0.522112\pi$
$468$	−4.00000	−0.184900
$469$	4.00000	0.184703
$470$	0	0
$471$	−7.00000	−0.322543
$472$	0	0
$473$	26.0000	1.19548
$474$	−3.00000	−0.137795
$475$	0	0
$476$	2.00000	0.0916698
$477$	6.00000	0.274721
$478$	−30.0000	−1.37217
$479$	23.0000	1.05090	0.525448	−	0.850825i	$-0.323898\pi$
$479$	23.0000	1.05090	0.525448	+	0.850825i	$0.323898\pi$
$480$	0	0
$481$	−16.0000	−0.729537
$482$	−4.00000	−0.182195
$483$	−4.00000	−0.182006
$484$	−7.00000	−0.318182
$485$	0	0
$486$	1.00000	0.0453609
$487$	11.0000	0.498458	0.249229	−	0.968445i	$-0.419823\pi$
$487$	11.0000	0.498458	0.249229	+	0.968445i	$0.419823\pi$
$488$	12.0000	0.543214
$489$	16.0000	0.723545
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	8.00000	0.360668
$493$	−3.00000	−0.135113
$494$	16.0000	0.719874
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	−10.0000	−0.448561
$498$	−12.0000	−0.537733
$499$	−35.0000	−1.56682	−0.783408	−	0.621508i	$-0.786520\pi$
$499$	−35.0000	−1.56682	−0.783408	+	0.621508i	$0.786520\pi$
$500$	0	0
$501$	−8.00000	−0.357414
$502$	22.0000	0.981908
$503$	9.00000	0.401290	0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000	0.401290	0.200645	+	0.979664i	$0.435696\pi$
$504$	2.00000	0.0890871
$505$	0	0
$506$	4.00000	0.177822
$507$	−3.00000	−0.133235
$508$	−11.0000	−0.488046
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	0	0
$511$	4.00000	0.176950
$512$	−1.00000	−0.0441942
$513$	−4.00000	−0.176604
$514$	6.00000	0.264649
$515$	0	0
$516$	−13.0000	−0.572293
$517$	2.00000	0.0879599
$518$	8.00000	0.351500
$519$	−18.0000	−0.790112
$520$	0	0
$521$	−16.0000	−0.700973	−0.350486	−	0.936568i	$-0.613984\pi$
$521$	−16.0000	−0.700973	−0.350486	+	0.936568i	$0.613984\pi$
$522$	−3.00000	−0.131306
$523$	−15.0000	−0.655904	−0.327952	−	0.944694i	$-0.606358\pi$
$523$	−15.0000	−0.655904	−0.327952	+	0.944694i	$0.606358\pi$
$524$	−11.0000	−0.480537
$525$	0	0
$526$	−8.00000	−0.348817
$527$	1.00000	0.0435607
$528$	−2.00000	−0.0870388
$529$	−19.0000	−0.826087
$530$	0	0
$531$	0	0
$532$	−8.00000	−0.346844
$533$	32.0000	1.38607
$534$	15.0000	0.649113
$535$	0	0
$536$	2.00000	0.0863868
$537$	−6.00000	−0.258919
$538$	−1.00000	−0.0431131
$539$	−6.00000	−0.258438
$540$	0	0
$541$	35.0000	1.50477	0.752384	−	0.658725i	$-0.228904\pi$
$541$	35.0000	1.50477	0.752384	+	0.658725i	$0.228904\pi$
$542$	21.0000	0.902027
$543$	16.0000	0.686626
$544$	1.00000	0.0428746
$545$	0	0
$546$	8.00000	0.342368
$547$	−24.0000	−1.02617	−0.513083	−	0.858339i	$-0.671497\pi$
$547$	−24.0000	−1.02617	−0.513083	+	0.858339i	$0.671497\pi$
$548$	−17.0000	−0.726204
$549$	−12.0000	−0.512148
$550$	0	0
$551$	12.0000	0.511217
$552$	−2.00000	−0.0851257
$553$	6.00000	0.255146
$554$	0	0
$555$	0	0
$556$	−5.00000	−0.212047
$557$	11.0000	0.466085	0.233042	−	0.972467i	$-0.425132\pi$
$557$	11.0000	0.466085	0.233042	+	0.972467i	$0.425132\pi$
$558$	1.00000	0.0423334
$559$	−52.0000	−2.19937
$560$	0	0
$561$	2.00000	0.0844401
$562$	22.0000	0.928014
$563$	−13.0000	−0.547885	−0.273942	−	0.961746i	$-0.588328\pi$
$563$	−13.0000	−0.547885	−0.273942	+	0.961746i	$0.588328\pi$
$564$	−1.00000	−0.0421076
$565$	0	0
$566$	6.00000	0.252199
$567$	−2.00000	−0.0839921
$568$	−5.00000	−0.209795
$569$	−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	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	−8.00000	−0.334497
$573$	5.00000	0.208878
$574$	−16.0000	−0.667827
$575$	0	0
$576$	1.00000	0.0416667
$577$	−3.00000	−0.124892	−0.0624458	−	0.998048i	$-0.519890\pi$
$577$	−3.00000	−0.124892	−0.0624458	+	0.998048i	$0.519890\pi$
$578$	16.0000	0.665512
$579$	10.0000	0.415586
$580$	0	0
$581$	24.0000	0.995688
$582$	1.00000	0.0414513
$583$	12.0000	0.496989
$584$	2.00000	0.0827606
$585$	0	0
$586$	10.0000	0.413096
$587$	−18.0000	−0.742940	−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000	−0.742940	−0.371470	+	0.928445i	$0.621146\pi$
$588$	3.00000	0.123718
$589$	−4.00000	−0.164817
$590$	0	0
$591$	−13.0000	−0.534749
$592$	4.00000	0.164399
$593$	−22.0000	−0.903432	−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000	−0.903432	−0.451716	+	0.892162i	$0.649188\pi$
$594$	2.00000	0.0820610
$595$	0	0
$596$	16.0000	0.655386
$597$	8.00000	0.327418
$598$	−8.00000	−0.327144
$599$	−15.0000	−0.612883	−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000	−0.612883	−0.306442	+	0.951889i	$0.599138\pi$
$600$	0	0
$601$	30.0000	1.22373	0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000	1.22373	0.611863	+	0.790964i	$0.290420\pi$
$602$	26.0000	1.05968
$603$	−2.00000	−0.0814463
$604$	−17.0000	−0.691720
$605$	0	0
$606$	10.0000	0.406222
$607$	12.0000	0.487065	0.243532	−	0.969893i	$-0.421694\pi$
$607$	12.0000	0.487065	0.243532	+	0.969893i	$0.421694\pi$
$608$	−4.00000	−0.162221
$609$	6.00000	0.243132
$610$	0	0
$611$	−4.00000	−0.161823
$612$	−1.00000	−0.0404226
$613$	24.0000	0.969351	0.484675	−	0.874694i	$-0.338938\pi$
$613$	24.0000	0.969351	0.484675	+	0.874694i	$0.338938\pi$
$614$	20.0000	0.807134
$615$	0	0
$616$	4.00000	0.161165
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	−4.00000	−0.160904
$619$	11.0000	0.442127	0.221064	−	0.975259i	$-0.429047\pi$
$619$	11.0000	0.442127	0.221064	+	0.975259i	$0.429047\pi$
$620$	0	0
$621$	2.00000	0.0802572
$622$	25.0000	1.00241
$623$	−30.0000	−1.20192
$624$	4.00000	0.160128
$625$	0	0
$626$	−20.0000	−0.799361
$627$	−8.00000	−0.319489
$628$	7.00000	0.279330
$629$	−4.00000	−0.159490
$630$	0	0
$631$	−25.0000	−0.995234	−0.497617	−	0.867397i	$-0.665792\pi$
$631$	−25.0000	−0.995234	−0.497617	+	0.867397i	$0.665792\pi$
$632$	3.00000	0.119334
$633$	8.00000	0.317971
$634$	14.0000	0.556011
$635$	0	0
$636$	−6.00000	−0.237915
$637$	12.0000	0.475457
$638$	−6.00000	−0.237542
$639$	5.00000	0.197797
$640$	0	0
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	1.00000	0.0394669
$643$	−35.0000	−1.38027	−0.690133	−	0.723683i	$-0.742448\pi$
$643$	−35.0000	−1.38027	−0.690133	+	0.723683i	$0.742448\pi$
$644$	4.00000	0.157622
$645$	0	0
$646$	4.00000	0.157378
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	−16.0000	−0.626608
$653$	−24.0000	−0.939193	−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000	−0.939193	−0.469596	+	0.882881i	$0.655601\pi$
$654$	11.0000	0.430134
$655$	0	0
$656$	−8.00000	−0.312348
$657$	−2.00000	−0.0780274
$658$	2.00000	0.0779681
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	33.0000	1.28355	0.641776	−	0.766892i	$-0.278198\pi$
$661$	33.0000	1.28355	0.641776	+	0.766892i	$0.278198\pi$
$662$	−4.00000	−0.155464
$663$	−4.00000	−0.155347
$664$	12.0000	0.465690
$665$	0	0
$666$	−4.00000	−0.154997
$667$	−6.00000	−0.232321
$668$	8.00000	0.309529
$669$	15.0000	0.579934
$670$	0	0
$671$	−24.0000	−0.926510
$672$	−2.00000	−0.0771517
$673$	42.0000	1.61898	0.809491	−	0.587133i	$-0.199743\pi$
$673$	42.0000	1.61898	0.809491	+	0.587133i	$0.199743\pi$
$674$	−18.0000	−0.693334
$675$	0	0
$676$	3.00000	0.115385
$677$	−25.0000	−0.960828	−0.480414	−	0.877042i	$-0.659514\pi$
$677$	−25.0000	−0.960828	−0.480414	+	0.877042i	$0.659514\pi$
$678$	−2.00000	−0.0768095
$679$	−2.00000	−0.0767530
$680$	0	0
$681$	5.00000	0.191600
$682$	2.00000	0.0765840
$683$	−9.00000	−0.344375	−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000	−0.344375	−0.172188	+	0.985064i	$0.555084\pi$
$684$	4.00000	0.152944
$685$	0	0
$686$	−20.0000	−0.763604
$687$	4.00000	0.152610
$688$	13.0000	0.495620
$689$	−24.0000	−0.914327
$690$	0	0
$691$	−2.00000	−0.0760836	−0.0380418	−	0.999276i	$-0.512112\pi$
$691$	−2.00000	−0.0760836	−0.0380418	+	0.999276i	$0.512112\pi$
$692$	18.0000	0.684257
$693$	−4.00000	−0.151947
$694$	14.0000	0.531433
$695$	0	0
$696$	3.00000	0.113715
$697$	8.00000	0.303022
$698$	5.00000	0.189253
$699$	−14.0000	−0.529529
$700$	0	0
$701$	42.0000	1.58632	0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000	1.58632	0.793159	+	0.609015i	$0.208435\pi$
$702$	−4.00000	−0.150970
$703$	16.0000	0.603451
$704$	2.00000	0.0753778
$705$	0	0
$706$	10.0000	0.376355
$707$	−20.0000	−0.752177
$708$	0	0
$709$	−30.0000	−1.12667	−0.563337	−	0.826227i	$-0.690483\pi$
$709$	−30.0000	−1.12667	−0.563337	+	0.826227i	$0.690483\pi$
$710$	0	0
$711$	−3.00000	−0.112509
$712$	−15.0000	−0.562149
$713$	2.00000	0.0749006
$714$	2.00000	0.0748481
$715$	0	0
$716$	6.00000	0.224231
$717$	−30.0000	−1.12037
$718$	−8.00000	−0.298557
$719$	−6.00000	−0.223762	−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000	−0.223762	−0.111881	+	0.993722i	$0.535688\pi$
$720$	0	0
$721$	8.00000	0.297936
$722$	3.00000	0.111648
$723$	−4.00000	−0.148762
$724$	−16.0000	−0.594635
$725$	0	0
$726$	−7.00000	−0.259794
$727$	30.0000	1.11264	0.556319	−	0.830969i	$-0.312213\pi$
$727$	30.0000	1.11264	0.556319	+	0.830969i	$0.312213\pi$
$728$	−8.00000	−0.296500
$729$	1.00000	0.0370370
$730$	0	0
$731$	−13.0000	−0.480822
$732$	12.0000	0.443533
$733$	−5.00000	−0.184679	−0.0923396	−	0.995728i	$-0.529435\pi$
$733$	−5.00000	−0.184679	−0.0923396	+	0.995728i	$0.529435\pi$
$734$	−3.00000	−0.110732
$735$	0	0
$736$	2.00000	0.0737210
$737$	−4.00000	−0.147342
$738$	8.00000	0.294484
$739$	−21.0000	−0.772497	−0.386249	−	0.922395i	$-0.626229\pi$
$739$	−21.0000	−0.772497	−0.386249	+	0.922395i	$0.626229\pi$
$740$	0	0
$741$	16.0000	0.587775
$742$	12.0000	0.440534
$743$	−2.00000	−0.0733729	−0.0366864	−	0.999327i	$-0.511680\pi$
$743$	−2.00000	−0.0733729	−0.0366864	+	0.999327i	$0.511680\pi$
$744$	−1.00000	−0.0366618
$745$	0	0
$746$	−7.00000	−0.256288
$747$	−12.0000	−0.439057
$748$	−2.00000	−0.0731272
$749$	−2.00000	−0.0730784
$750$	0	0
$751$	36.0000	1.31366	0.656829	−	0.754039i	$-0.271897\pi$
$751$	36.0000	1.31366	0.656829	+	0.754039i	$0.271897\pi$
$752$	1.00000	0.0364662
$753$	22.0000	0.801725
$754$	12.0000	0.437014
$755$	0	0
$756$	2.00000	0.0727393
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	28.0000	1.01701
$759$	4.00000	0.145191
$760$	0	0
$761$	11.0000	0.398750	0.199375	−	0.979923i	$-0.436109\pi$
$761$	11.0000	0.398750	0.199375	+	0.979923i	$0.436109\pi$
$762$	−11.0000	−0.398488
$763$	−22.0000	−0.796453
$764$	−5.00000	−0.180894
$765$	0	0
$766$	26.0000	0.939418
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	1.00000	0.0360609	0.0180305	−	0.999837i	$-0.494260\pi$
$769$	1.00000	0.0360609	0.0180305	+	0.999837i	$0.494260\pi$
$770$	0	0
$771$	6.00000	0.216085
$772$	−10.0000	−0.359908
$773$	51.0000	1.83434	0.917171	−	0.398493i	$-0.130467\pi$
$773$	51.0000	1.83434	0.917171	+	0.398493i	$0.130467\pi$
$774$	−13.0000	−0.467275
$775$	0	0
$776$	−1.00000	−0.0358979
$777$	8.00000	0.286998
$778$	−6.00000	−0.215110
$779$	−32.0000	−1.14652
$780$	0	0
$781$	10.0000	0.357828
$782$	−2.00000	−0.0715199
$783$	−3.00000	−0.107211
$784$	−3.00000	−0.107143
$785$	0	0
$786$	−11.0000	−0.392357
$787$	44.0000	1.56843	0.784215	−	0.620489i	$-0.213066\pi$
$787$	44.0000	1.56843	0.784215	+	0.620489i	$0.213066\pi$
$788$	13.0000	0.463106
$789$	−8.00000	−0.284808
$790$	0	0
$791$	4.00000	0.142224
$792$	−2.00000	−0.0710669
$793$	48.0000	1.70453
$794$	14.0000	0.496841
$795$	0	0
$796$	−8.00000	−0.283552
$797$	−22.0000	−0.779280	−0.389640	−	0.920967i	$-0.627401\pi$
$797$	−22.0000	−0.779280	−0.389640	+	0.920967i	$0.627401\pi$
$798$	−8.00000	−0.283197
$799$	−1.00000	−0.0353775
$800$	0	0
$801$	15.0000	0.529999
$802$	30.0000	1.05934
$803$	−4.00000	−0.141157
$804$	2.00000	0.0705346
$805$	0	0
$806$	−4.00000	−0.140894
$807$	−1.00000	−0.0352017
$808$	−10.0000	−0.351799
$809$	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
$811$	−12.0000	−0.421377	−0.210688	−	0.977553i	$-0.567571\pi$
$811$	−12.0000	−0.421377	−0.210688	+	0.977553i	$0.567571\pi$
$812$	−6.00000	−0.210559
$813$	21.0000	0.736502
$814$	−8.00000	−0.280400
$815$	0	0
$816$	1.00000	0.0350070
$817$	52.0000	1.81925
$818$	20.0000	0.699284
$819$	8.00000	0.279543
$820$	0	0
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	−17.0000	−0.592943
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	0	0
$827$	6.00000	0.208640	0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000	0.208640	0.104320	+	0.994544i	$0.466733\pi$
$828$	−2.00000	−0.0695048
$829$	−16.0000	−0.555703	−0.277851	−	0.960624i	$-0.589622\pi$
$829$	−16.0000	−0.555703	−0.277851	+	0.960624i	$0.589622\pi$
$830$	0	0
$831$	0	0
$832$	−4.00000	−0.138675
$833$	3.00000	0.103944
$834$	−5.00000	−0.173136
$835$	0	0
$836$	8.00000	0.276686
$837$	1.00000	0.0345651
$838$	9.00000	0.310900
$839$	7.00000	0.241667	0.120833	−	0.992673i	$-0.461443\pi$
$839$	7.00000	0.241667	0.120833	+	0.992673i	$0.461443\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−17.0000	−0.585859
$843$	22.0000	0.757720
$844$	−8.00000	−0.275371
$845$	0	0
$846$	−1.00000	−0.0343807
$847$	14.0000	0.481046
$848$	6.00000	0.206041
$849$	6.00000	0.205919
$850$	0	0
$851$	−8.00000	−0.274236
$852$	−5.00000	−0.171297
$853$	21.0000	0.719026	0.359513	−	0.933140i	$-0.382943\pi$
$853$	21.0000	0.719026	0.359513	+	0.933140i	$0.382943\pi$
$854$	−24.0000	−0.821263
$855$	0	0
$856$	−1.00000	−0.0341793
$857$	−32.0000	−1.09310	−0.546550	−	0.837427i	$-0.684059\pi$
$857$	−32.0000	−1.09310	−0.546550	+	0.837427i	$0.684059\pi$
$858$	−8.00000	−0.273115
$859$	−21.0000	−0.716511	−0.358255	−	0.933624i	$-0.616628\pi$
$859$	−21.0000	−0.716511	−0.358255	+	0.933624i	$0.616628\pi$
$860$	0	0
$861$	−16.0000	−0.545279
$862$	16.0000	0.544962
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	38.0000	1.29129
$867$	16.0000	0.543388
$868$	2.00000	0.0678844
$869$	−6.00000	−0.203536
$870$	0	0
$871$	8.00000	0.271070
$872$	−11.0000	−0.372507
$873$	1.00000	0.0338449
$874$	8.00000	0.270604
$875$	0	0
$876$	2.00000	0.0675737
$877$	−47.0000	−1.58708	−0.793539	−	0.608520i	$-0.791764\pi$
$877$	−47.0000	−1.58708	−0.793539	+	0.608520i	$0.791764\pi$
$878$	30.0000	1.01245
$879$	10.0000	0.337292
$880$	0	0
$881$	−5.00000	−0.168454	−0.0842271	−	0.996447i	$-0.526842\pi$
$881$	−5.00000	−0.168454	−0.0842271	+	0.996447i	$0.526842\pi$
$882$	3.00000	0.101015
$883$	−8.00000	−0.269221	−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000	−0.269221	−0.134611	+	0.990899i	$0.542978\pi$
$884$	4.00000	0.134535
$885$	0	0
$886$	−17.0000	−0.571126
$887$	7.00000	0.235037	0.117518	−	0.993071i	$-0.462506\pi$
$887$	7.00000	0.235037	0.117518	+	0.993071i	$0.462506\pi$
$888$	4.00000	0.134231
$889$	22.0000	0.737856
$890$	0	0
$891$	2.00000	0.0670025
$892$	−15.0000	−0.502237
$893$	4.00000	0.133855
$894$	16.0000	0.535120
$895$	0	0
$896$	2.00000	0.0668153
$897$	−8.00000	−0.267112
$898$	−35.0000	−1.16797
$899$	−3.00000	−0.100056
$900$	0	0
$901$	−6.00000	−0.199889
$902$	16.0000	0.532742
$903$	26.0000	0.865226
$904$	2.00000	0.0665190
$905$	0	0
$906$	−17.0000	−0.564787
$907$	−24.0000	−0.796907	−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000	−0.796907	−0.398453	+	0.917189i	$0.630453\pi$
$908$	−5.00000	−0.165931
$909$	10.0000	0.331679
$910$	0	0
$911$	40.0000	1.32526	0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000	1.32526	0.662630	+	0.748947i	$0.269440\pi$
$912$	−4.00000	−0.132453
$913$	−24.0000	−0.794284
$914$	0	0
$915$	0	0
$916$	−4.00000	−0.132164
$917$	22.0000	0.726504
$918$	−1.00000	−0.0330049
$919$	38.0000	1.25350	0.626752	−	0.779219i	$-0.284384\pi$
$919$	38.0000	1.25350	0.626752	+	0.779219i	$0.284384\pi$
$920$	0	0
$921$	20.0000	0.659022
$922$	18.0000	0.592798
$923$	−20.0000	−0.658308
$924$	4.00000	0.131590
$925$	0	0
$926$	35.0000	1.15017
$927$	−4.00000	−0.131377
$928$	−3.00000	−0.0984798
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	0	0
$931$	−12.0000	−0.393284
$932$	14.0000	0.458585
$933$	25.0000	0.818463
$934$	3.00000	0.0981630
$935$	0	0
$936$	4.00000	0.130744
$937$	22.0000	0.718709	0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000	0.718709	0.359354	+	0.933201i	$0.382997\pi$
$938$	−4.00000	−0.130605
$939$	−20.0000	−0.652675
$940$	0	0
$941$	21.0000	0.684580	0.342290	−	0.939594i	$-0.388797\pi$
$941$	21.0000	0.684580	0.342290	+	0.939594i	$0.388797\pi$
$942$	7.00000	0.228072
$943$	16.0000	0.521032
$944$	0	0
$945$	0	0
$946$	−26.0000	−0.845333
$947$	48.0000	1.55979	0.779895	−	0.625910i	$-0.215272\pi$
$947$	48.0000	1.55979	0.779895	+	0.625910i	$0.215272\pi$
$948$	3.00000	0.0974355
$949$	8.00000	0.259691
$950$	0	0
$951$	14.0000	0.453981
$952$	−2.00000	−0.0648204
$953$	14.0000	0.453504	0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000	0.453504	0.226752	+	0.973952i	$0.427189\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	30.0000	0.970269
$957$	−6.00000	−0.193952
$958$	−23.0000	−0.743096
$959$	34.0000	1.09792
$960$	0	0
$961$	1.00000	0.0322581
$962$	16.0000	0.515861
$963$	1.00000	0.0322245
$964$	4.00000	0.128831
$965$	0	0
$966$	4.00000	0.128698
$967$	40.0000	1.28631	0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000	1.28631	0.643157	+	0.765735i	$0.277624\pi$
$968$	7.00000	0.224989
$969$	4.00000	0.128499
$970$	0	0
$971$	27.0000	0.866471	0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000	0.866471	0.433236	+	0.901281i	$0.357372\pi$
$972$	−1.00000	−0.0320750
$973$	10.0000	0.320585
$974$	−11.0000	−0.352463
$975$	0	0
$976$	−12.0000	−0.384111
$977$	−62.0000	−1.98356	−0.991778	−	0.127971i	$-0.959153\pi$
$977$	−62.0000	−1.98356	−0.991778	+	0.127971i	$0.959153\pi$
$978$	−16.0000	−0.511624
$979$	30.0000	0.958804
$980$	0	0
$981$	11.0000	0.351203
$982$	0	0
$983$	52.0000	1.65854	0.829271	−	0.558846i	$-0.188756\pi$
$983$	52.0000	1.65854	0.829271	+	0.558846i	$0.188756\pi$
$984$	−8.00000	−0.255031
$985$	0	0
$986$	3.00000	0.0955395
$987$	2.00000	0.0636607
$988$	−16.0000	−0.509028
$989$	−26.0000	−0.826752
$990$	0	0
$991$	37.0000	1.17534	0.587672	−	0.809099i	$-0.300045\pi$
$991$	37.0000	1.17534	0.587672	+	0.809099i	$0.300045\pi$
$992$	1.00000	0.0317500
$993$	−4.00000	−0.126936
$994$	10.0000	0.317181
$995$	0	0
$996$	12.0000	0.380235
$997$	−6.00000	−0.190022	−0.0950110	−	0.995476i	$-0.530289\pi$
$997$	−6.00000	−0.190022	−0.0950110	+	0.995476i	$0.530289\pi$
$998$	35.0000	1.10791
$999$	−4.00000	−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4650.2.a.e.1.1	✓	1
5.2	odd	4		4650.2.d.w.3349.1		2
5.3	odd	4		4650.2.d.w.3349.2		2
5.4	even	2		4650.2.a.bt.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4650.2.a.e.1.1	✓	1	1.1	even	1	trivial
4650.2.a.bt.1.1	yes	1	5.4	even	2
4650.2.d.w.3349.1		2	5.2	odd	4
4650.2.d.w.3349.2		2	5.3	odd	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:	\( N \)	\(=\)	\( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4650.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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