LMFDB - Embedded newform 4650.2.a.bh.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 186)
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)

$f(q)$

$=$

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +5.00000 q^{11} -1.00000 q^{12} +7.00000 q^{13} +2.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +7.00000 q^{19} -2.00000 q^{21} +5.00000 q^{22} -4.00000 q^{23} -1.00000 q^{24} +7.00000 q^{26} -1.00000 q^{27} +2.00000 q^{28} -8.00000 q^{29} -1.00000 q^{31} +1.00000 q^{32} -5.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} +6.00000 q^{37} +7.00000 q^{38} -7.00000 q^{39} -2.00000 q^{41} -2.00000 q^{42} +10.0000 q^{43} +5.00000 q^{44} -4.00000 q^{46} +1.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{51} +7.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} +2.00000 q^{56} -7.00000 q^{57} -8.00000 q^{58} -10.0000 q^{59} +1.00000 q^{61} -1.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} -5.00000 q^{66} +3.00000 q^{67} +1.00000 q^{68} +4.00000 q^{69} +3.00000 q^{71} +1.00000 q^{72} -14.0000 q^{73} +6.00000 q^{74} +7.00000 q^{76} +10.0000 q^{77} -7.00000 q^{78} -11.0000 q^{79} +1.00000 q^{81} -2.00000 q^{82} -7.00000 q^{83} -2.00000 q^{84} +10.0000 q^{86} +8.00000 q^{87} +5.00000 q^{88} -6.00000 q^{89} +14.0000 q^{91} -4.00000 q^{92} +1.00000 q^{93} +1.00000 q^{94} -1.00000 q^{96} +3.00000 q^{97} -3.00000 q^{98} +5.00000 q^{99} +O(q^{100})\)

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	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	−1.00000	−0.288675
$13$	7.00000	1.94145	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	7.00000	1.94145	0.970725	+	0.240192i	$0.0772105\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000	0.242536	0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000	0.242536	0.121268	+	0.992620i	$0.461304\pi$
$18$	1.00000	0.235702
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	0	0
$21$	−2.00000	−0.436436
$22$	5.00000	1.06600
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	7.00000	1.37281
$27$	−1.00000	−0.192450
$28$	2.00000	0.377964
$29$	−8.00000	−1.48556	−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000	−1.48556	−0.742781	+	0.669534i	$0.766494\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−5.00000	−0.870388
$34$	1.00000	0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	7.00000	1.13555
$39$	−7.00000	−1.12090
$40$	0	0
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	−2.00000	−0.308607
$43$	10.0000	1.52499	0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000	1.52499	0.762493	+	0.646997i	$0.223975\pi$
$44$	5.00000	0.753778
$45$	0	0
$46$	−4.00000	−0.589768
$47$	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
$52$	7.00000	0.970725
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	2.00000	0.267261
$57$	−7.00000	−0.927173
$58$	−8.00000	−1.05045
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	0	0
$61$	1.00000	0.128037	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000	0.128037	0.0640184	+	0.997949i	$0.479608\pi$
$62$	−1.00000	−0.127000
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	−5.00000	−0.615457
$67$	3.00000	0.366508	0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000	0.366508	0.183254	+	0.983066i	$0.441337\pi$
$68$	1.00000	0.121268
$69$	4.00000	0.481543
$70$	0	0
$71$	3.00000	0.356034	0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000	0.356034	0.178017	+	0.984027i	$0.443032\pi$
$72$	1.00000	0.117851
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	6.00000	0.697486
$75$	0	0
$76$	7.00000	0.802955
$77$	10.0000	1.13961
$78$	−7.00000	−0.792594
$79$	−11.0000	−1.23760	−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000	−1.23760	−0.618798	+	0.785550i	$0.712380\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	−7.00000	−0.768350	−0.384175	−	0.923260i	$-0.625514\pi$
$83$	−7.00000	−0.768350	−0.384175	+	0.923260i	$0.625514\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	10.0000	1.07833
$87$	8.00000	0.857690
$88$	5.00000	0.533002
$89$	−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
$91$	14.0000	1.46760
$92$	−4.00000	−0.417029
$93$	1.00000	0.103695
$94$	1.00000	0.103142
$95$	0	0
$96$	−1.00000	−0.102062
$97$	3.00000	0.304604	0.152302	−	0.988334i	$-0.451331\pi$
$97$	3.00000	0.304604	0.152302	+	0.988334i	$0.451331\pi$
$98$	−3.00000	−0.303046
$99$	5.00000	0.502519
$100$	0	0
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	−1.00000	−0.0990148
$103$	−10.0000	−0.985329	−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000	−0.985329	−0.492665	+	0.870219i	$0.663977\pi$
$104$	7.00000	0.686406
$105$	0	0
$106$	−6.00000	−0.582772
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	−1.00000	−0.0962250
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	0	0
$111$	−6.00000	−0.569495
$112$	2.00000	0.188982
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−7.00000	−0.655610
$115$	0	0
$116$	−8.00000	−0.742781
$117$	7.00000	0.647150
$118$	−10.0000	−0.920575
$119$	2.00000	0.183340
$120$	0	0
$121$	14.0000	1.27273
$122$	1.00000	0.0905357
$123$	2.00000	0.180334
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	2.00000	0.178174
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	1.00000	0.0883883
$129$	−10.0000	−0.880451
$130$	0	0
$131$	10.0000	0.873704	0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000	0.873704	0.436852	+	0.899533i	$0.356093\pi$
$132$	−5.00000	−0.435194
$133$	14.0000	1.21395
$134$	3.00000	0.259161
$135$	0	0
$136$	1.00000	0.0857493
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	4.00000	0.340503
$139$	−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
$141$	−1.00000	−0.0842152
$142$	3.00000	0.251754
$143$	35.0000	2.92685
$144$	1.00000	0.0833333
$145$	0	0
$146$	−14.0000	−1.15865
$147$	3.00000	0.247436
$148$	6.00000	0.493197
$149$	15.0000	1.22885	0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000	1.22885	0.614424	+	0.788976i	$0.289388\pi$
$150$	0	0
$151$	−1.00000	−0.0813788	−0.0406894	−	0.999172i	$-0.512955\pi$
$151$	−1.00000	−0.0813788	−0.0406894	+	0.999172i	$0.512955\pi$
$152$	7.00000	0.567775
$153$	1.00000	0.0808452
$154$	10.0000	0.805823
$155$	0	0
$156$	−7.00000	−0.560449
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	−11.0000	−0.875113
$159$	6.00000	0.475831
$160$	0	0
$161$	−8.00000	−0.630488
$162$	1.00000	0.0785674
$163$	9.00000	0.704934	0.352467	−	0.935824i	$-0.385343\pi$
$163$	9.00000	0.704934	0.352467	+	0.935824i	$0.385343\pi$
$164$	−2.00000	−0.156174
$165$	0	0
$166$	−7.00000	−0.543305
$167$	−10.0000	−0.773823	−0.386912	−	0.922117i	$-0.626458\pi$
$167$	−10.0000	−0.773823	−0.386912	+	0.922117i	$0.626458\pi$
$168$	−2.00000	−0.154303
$169$	36.0000	2.76923
$170$	0	0
$171$	7.00000	0.535303
$172$	10.0000	0.762493
$173$	−1.00000	−0.0760286	−0.0380143	−	0.999277i	$-0.512103\pi$
$173$	−1.00000	−0.0760286	−0.0380143	+	0.999277i	$0.512103\pi$
$174$	8.00000	0.606478
$175$	0	0
$176$	5.00000	0.376889
$177$	10.0000	0.751646
$178$	−6.00000	−0.449719
$179$	19.0000	1.42013	0.710063	−	0.704138i	$-0.248666\pi$
$179$	19.0000	1.42013	0.710063	+	0.704138i	$0.248666\pi$
$180$	0	0
$181$	18.0000	1.33793	0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000	1.33793	0.668965	+	0.743294i	$0.266738\pi$
$182$	14.0000	1.03775
$183$	−1.00000	−0.0739221
$184$	−4.00000	−0.294884
$185$	0	0
$186$	1.00000	0.0733236
$187$	5.00000	0.365636
$188$	1.00000	0.0729325
$189$	−2.00000	−0.145479
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−1.00000	−0.0721688
$193$	−19.0000	−1.36765	−0.683825	−	0.729646i	$-0.739685\pi$
$193$	−19.0000	−1.36765	−0.683825	+	0.729646i	$0.739685\pi$
$194$	3.00000	0.215387
$195$	0	0
$196$	−3.00000	−0.214286
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	5.00000	0.355335
$199$	−11.0000	−0.779769	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000	−0.779769	−0.389885	+	0.920864i	$0.627485\pi$
$200$	0	0
$201$	−3.00000	−0.211604
$202$	6.00000	0.422159
$203$	−16.0000	−1.12298
$204$	−1.00000	−0.0700140
$205$	0	0
$206$	−10.0000	−0.696733
$207$	−4.00000	−0.278019
$208$	7.00000	0.485363
$209$	35.0000	2.42100
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	−6.00000	−0.412082
$213$	−3.00000	−0.205557
$214$	−8.00000	−0.546869
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−2.00000	−0.135769
$218$	−6.00000	−0.406371
$219$	14.0000	0.946032
$220$	0	0
$221$	7.00000	0.470871
$222$	−6.00000	−0.402694
$223$	5.00000	0.334825	0.167412	−	0.985887i	$-0.446459\pi$
$223$	5.00000	0.334825	0.167412	+	0.985887i	$0.446459\pi$
$224$	2.00000	0.133631
$225$	0	0
$226$	−6.00000	−0.399114
$227$	−22.0000	−1.46019	−0.730096	−	0.683345i	$-0.760525\pi$
$227$	−22.0000	−1.46019	−0.730096	+	0.683345i	$0.760525\pi$
$228$	−7.00000	−0.463586
$229$	13.0000	0.859064	0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000	0.859064	0.429532	+	0.903052i	$0.358679\pi$
$230$	0	0
$231$	−10.0000	−0.657952
$232$	−8.00000	−0.525226
$233$	−20.0000	−1.31024	−0.655122	−	0.755523i	$-0.727383\pi$
$233$	−20.0000	−1.31024	−0.655122	+	0.755523i	$0.727383\pi$
$234$	7.00000	0.457604
$235$	0	0
$236$	−10.0000	−0.650945
$237$	11.0000	0.714527
$238$	2.00000	0.129641
$239$	−4.00000	−0.258738	−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000	−0.258738	−0.129369	+	0.991596i	$0.541295\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	14.0000	0.899954
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	0	0
$246$	2.00000	0.127515
$247$	49.0000	3.11780
$248$	−1.00000	−0.0635001
$249$	7.00000	0.443607
$250$	0	0
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	2.00000	0.125988
$253$	−20.0000	−1.25739
$254$	−4.00000	−0.250982
$255$	0	0
$256$	1.00000	0.0625000
$257$	12.0000	0.748539	0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000	0.748539	0.374270	+	0.927320i	$0.377893\pi$
$258$	−10.0000	−0.622573
$259$	12.0000	0.745644
$260$	0	0
$261$	−8.00000	−0.495188
$262$	10.0000	0.617802
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	−5.00000	−0.307729
$265$	0	0
$266$	14.0000	0.858395
$267$	6.00000	0.367194
$268$	3.00000	0.183254
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	−19.0000	−1.15417	−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000	−1.15417	−0.577084	+	0.816685i	$0.695809\pi$
$272$	1.00000	0.0606339
$273$	−14.0000	−0.847319
$274$	18.0000	1.08742
$275$	0	0
$276$	4.00000	0.240772
$277$	7.00000	0.420589	0.210295	−	0.977638i	$-0.432558\pi$
$277$	7.00000	0.420589	0.210295	+	0.977638i	$0.432558\pi$
$278$	−8.00000	−0.479808
$279$	−1.00000	−0.0598684
$280$	0	0
$281$	−30.0000	−1.78965	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000	−1.78965	−0.894825	+	0.446417i	$0.852700\pi$
$282$	−1.00000	−0.0595491
$283$	−5.00000	−0.297219	−0.148610	−	0.988896i	$-0.547480\pi$
$283$	−5.00000	−0.297219	−0.148610	+	0.988896i	$0.547480\pi$
$284$	3.00000	0.178017
$285$	0	0
$286$	35.0000	2.06959
$287$	−4.00000	−0.236113
$288$	1.00000	0.0589256
$289$	−16.0000	−0.941176
$290$	0	0
$291$	−3.00000	−0.175863
$292$	−14.0000	−0.819288
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	3.00000	0.174964
$295$	0	0
$296$	6.00000	0.348743
$297$	−5.00000	−0.290129
$298$	15.0000	0.868927
$299$	−28.0000	−1.61928
$300$	0	0
$301$	20.0000	1.15278
$302$	−1.00000	−0.0575435
$303$	−6.00000	−0.344691
$304$	7.00000	0.401478
$305$	0	0
$306$	1.00000	0.0571662
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	10.0000	0.569803
$309$	10.0000	0.568880
$310$	0	0
$311$	21.0000	1.19080	0.595400	−	0.803429i	$-0.296993\pi$
$311$	21.0000	1.19080	0.595400	+	0.803429i	$0.296993\pi$
$312$	−7.00000	−0.396297
$313$	−2.00000	−0.113047	−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000	−0.113047	−0.0565233	+	0.998401i	$0.518002\pi$
$314$	4.00000	0.225733
$315$	0	0
$316$	−11.0000	−0.618798
$317$	−5.00000	−0.280828	−0.140414	−	0.990093i	$-0.544843\pi$
$317$	−5.00000	−0.280828	−0.140414	+	0.990093i	$0.544843\pi$
$318$	6.00000	0.336463
$319$	−40.0000	−2.23957
$320$	0	0
$321$	8.00000	0.446516
$322$	−8.00000	−0.445823
$323$	7.00000	0.389490
$324$	1.00000	0.0555556
$325$	0	0
$326$	9.00000	0.498464
$327$	6.00000	0.331801
$328$	−2.00000	−0.110432
$329$	2.00000	0.110264
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	−7.00000	−0.384175
$333$	6.00000	0.328798
$334$	−10.0000	−0.547176
$335$	0	0
$336$	−2.00000	−0.109109
$337$	8.00000	0.435788	0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000	0.435788	0.217894	+	0.975972i	$0.430081\pi$
$338$	36.0000	1.95814
$339$	6.00000	0.325875
$340$	0	0
$341$	−5.00000	−0.270765
$342$	7.00000	0.378517
$343$	−20.0000	−1.07990
$344$	10.0000	0.539164
$345$	0	0
$346$	−1.00000	−0.0537603
$347$	−17.0000	−0.912608	−0.456304	−	0.889824i	$-0.650827\pi$
$347$	−17.0000	−0.912608	−0.456304	+	0.889824i	$0.650827\pi$
$348$	8.00000	0.428845
$349$	24.0000	1.28469	0.642345	−	0.766415i	$-0.277962\pi$
$349$	24.0000	1.28469	0.642345	+	0.766415i	$0.277962\pi$
$350$	0	0
$351$	−7.00000	−0.373632
$352$	5.00000	0.266501
$353$	11.0000	0.585471	0.292735	−	0.956193i	$-0.405434\pi$
$353$	11.0000	0.585471	0.292735	+	0.956193i	$0.405434\pi$
$354$	10.0000	0.531494
$355$	0	0
$356$	−6.00000	−0.317999
$357$	−2.00000	−0.105851
$358$	19.0000	1.00418
$359$	−17.0000	−0.897226	−0.448613	−	0.893726i	$-0.648082\pi$
$359$	−17.0000	−0.897226	−0.448613	+	0.893726i	$0.648082\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	18.0000	0.946059
$363$	−14.0000	−0.734809
$364$	14.0000	0.733799
$365$	0	0
$366$	−1.00000	−0.0522708
$367$	11.0000	0.574195	0.287098	−	0.957901i	$-0.407310\pi$
$367$	11.0000	0.574195	0.287098	+	0.957901i	$0.407310\pi$
$368$	−4.00000	−0.208514
$369$	−2.00000	−0.104116
$370$	0	0
$371$	−12.0000	−0.623009
$372$	1.00000	0.0518476
$373$	32.0000	1.65690	0.828449	−	0.560065i	$-0.189224\pi$
$373$	32.0000	1.65690	0.828449	+	0.560065i	$0.189224\pi$
$374$	5.00000	0.258544
$375$	0	0
$376$	1.00000	0.0515711
$377$	−56.0000	−2.88415
$378$	−2.00000	−0.102869
$379$	1.00000	0.0513665	0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000	0.0513665	0.0256833	+	0.999670i	$0.491824\pi$
$380$	0	0
$381$	4.00000	0.204926
$382$	0	0
$383$	10.0000	0.510976	0.255488	−	0.966812i	$-0.417764\pi$
$383$	10.0000	0.510976	0.255488	+	0.966812i	$0.417764\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−19.0000	−0.967075
$387$	10.0000	0.508329
$388$	3.00000	0.152302
$389$	−34.0000	−1.72387	−0.861934	−	0.507020i	$-0.830747\pi$
$389$	−34.0000	−1.72387	−0.861934	+	0.507020i	$0.830747\pi$
$390$	0	0
$391$	−4.00000	−0.202289
$392$	−3.00000	−0.151523
$393$	−10.0000	−0.504433
$394$	2.00000	0.100759
$395$	0	0
$396$	5.00000	0.251259
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	−11.0000	−0.551380
$399$	−14.0000	−0.700877
$400$	0	0
$401$	−23.0000	−1.14857	−0.574283	−	0.818657i	$-0.694719\pi$
$401$	−23.0000	−1.14857	−0.574283	+	0.818657i	$0.694719\pi$
$402$	−3.00000	−0.149626
$403$	−7.00000	−0.348695
$404$	6.00000	0.298511
$405$	0	0
$406$	−16.0000	−0.794067
$407$	30.0000	1.48704
$408$	−1.00000	−0.0495074
$409$	−30.0000	−1.48340	−0.741702	−	0.670729i	$-0.765981\pi$
$409$	−30.0000	−1.48340	−0.741702	+	0.670729i	$0.765981\pi$
$410$	0	0
$411$	−18.0000	−0.887875
$412$	−10.0000	−0.492665
$413$	−20.0000	−0.984136
$414$	−4.00000	−0.196589
$415$	0	0
$416$	7.00000	0.343203
$417$	8.00000	0.391762
$418$	35.0000	1.71191
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	0	0
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	0	0
$423$	1.00000	0.0486217
$424$	−6.00000	−0.291386
$425$	0	0
$426$	−3.00000	−0.145350
$427$	2.00000	0.0967868
$428$	−8.00000	−0.386695
$429$	−35.0000	−1.68982
$430$	0	0
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	−1.00000	−0.0481125
$433$	−28.0000	−1.34559	−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000	−1.34559	−0.672797	+	0.739827i	$0.734907\pi$
$434$	−2.00000	−0.0960031
$435$	0	0
$436$	−6.00000	−0.287348
$437$	−28.0000	−1.33942
$438$	14.0000	0.668946
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	7.00000	0.332956
$443$	14.0000	0.665160	0.332580	−	0.943075i	$-0.392081\pi$
$443$	14.0000	0.665160	0.332580	+	0.943075i	$0.392081\pi$
$444$	−6.00000	−0.284747
$445$	0	0
$446$	5.00000	0.236757
$447$	−15.0000	−0.709476
$448$	2.00000	0.0944911
$449$	−11.0000	−0.519122	−0.259561	−	0.965727i	$-0.583578\pi$
$449$	−11.0000	−0.519122	−0.259561	+	0.965727i	$0.583578\pi$
$450$	0	0
$451$	−10.0000	−0.470882
$452$	−6.00000	−0.282216
$453$	1.00000	0.0469841
$454$	−22.0000	−1.03251
$455$	0	0
$456$	−7.00000	−0.327805
$457$	42.0000	1.96468	0.982339	−	0.187112i	$-0.0599128\pi$
$457$	42.0000	1.96468	0.982339	+	0.187112i	$0.0599128\pi$
$458$	13.0000	0.607450
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	−34.0000	−1.58354	−0.791769	−	0.610821i	$-0.790840\pi$
$461$	−34.0000	−1.58354	−0.791769	+	0.610821i	$0.790840\pi$
$462$	−10.0000	−0.465242
$463$	−33.0000	−1.53364	−0.766820	−	0.641862i	$-0.778162\pi$
$463$	−33.0000	−1.53364	−0.766820	+	0.641862i	$0.778162\pi$
$464$	−8.00000	−0.371391
$465$	0	0
$466$	−20.0000	−0.926482
$467$	−24.0000	−1.11059	−0.555294	−	0.831654i	$-0.687394\pi$
$467$	−24.0000	−1.11059	−0.555294	+	0.831654i	$0.687394\pi$
$468$	7.00000	0.323575
$469$	6.00000	0.277054
$470$	0	0
$471$	−4.00000	−0.184310
$472$	−10.0000	−0.460287
$473$	50.0000	2.29900
$474$	11.0000	0.505247
$475$	0	0
$476$	2.00000	0.0916698
$477$	−6.00000	−0.274721
$478$	−4.00000	−0.182956
$479$	29.0000	1.32504	0.662522	−	0.749043i	$-0.269486\pi$
$479$	29.0000	1.32504	0.662522	+	0.749043i	$0.269486\pi$
$480$	0	0
$481$	42.0000	1.91504
$482$	−14.0000	−0.637683
$483$	8.00000	0.364013
$484$	14.0000	0.636364
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	27.0000	1.22349	0.611743	−	0.791056i	$-0.290469\pi$
$487$	27.0000	1.22349	0.611743	+	0.791056i	$0.290469\pi$
$488$	1.00000	0.0452679
$489$	−9.00000	−0.406994
$490$	0	0
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	2.00000	0.0901670
$493$	−8.00000	−0.360302
$494$	49.0000	2.20461
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	6.00000	0.269137
$498$	7.00000	0.313678
$499$	−24.0000	−1.07439	−0.537194	−	0.843459i	$-0.680516\pi$
$499$	−24.0000	−1.07439	−0.537194	+	0.843459i	$0.680516\pi$
$500$	0	0
$501$	10.0000	0.446767
$502$	20.0000	0.892644
$503$	33.0000	1.47140	0.735699	−	0.677309i	$-0.236854\pi$
$503$	33.0000	1.47140	0.735699	+	0.677309i	$0.236854\pi$
$504$	2.00000	0.0890871
$505$	0	0
$506$	−20.0000	−0.889108
$507$	−36.0000	−1.59882
$508$	−4.00000	−0.177471
$509$	40.0000	1.77297	0.886484	−	0.462758i	$-0.153140\pi$
$509$	40.0000	1.77297	0.886484	+	0.462758i	$0.153140\pi$
$510$	0	0
$511$	−28.0000	−1.23865
$512$	1.00000	0.0441942
$513$	−7.00000	−0.309058
$514$	12.0000	0.529297
$515$	0	0
$516$	−10.0000	−0.440225
$517$	5.00000	0.219900
$518$	12.0000	0.527250
$519$	1.00000	0.0438951
$520$	0	0
$521$	12.0000	0.525730	0.262865	−	0.964833i	$-0.415333\pi$
$521$	12.0000	0.525730	0.262865	+	0.964833i	$0.415333\pi$
$522$	−8.00000	−0.350150
$523$	−30.0000	−1.31181	−0.655904	−	0.754844i	$-0.727712\pi$
$523$	−30.0000	−1.31181	−0.655904	+	0.754844i	$0.727712\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	−12.0000	−0.523225
$527$	−1.00000	−0.0435607
$528$	−5.00000	−0.217597
$529$	−7.00000	−0.304348
$530$	0	0
$531$	−10.0000	−0.433963
$532$	14.0000	0.606977
$533$	−14.0000	−0.606407
$534$	6.00000	0.259645
$535$	0	0
$536$	3.00000	0.129580
$537$	−19.0000	−0.819911
$538$	6.00000	0.258678
$539$	−15.0000	−0.646096
$540$	0	0
$541$	44.0000	1.89171	0.945854	−	0.324593i	$-0.105227\pi$
$541$	44.0000	1.89171	0.945854	+	0.324593i	$0.105227\pi$
$542$	−19.0000	−0.816120
$543$	−18.0000	−0.772454
$544$	1.00000	0.0428746
$545$	0	0
$546$	−14.0000	−0.599145
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	18.0000	0.768922
$549$	1.00000	0.0426790
$550$	0	0
$551$	−56.0000	−2.38568
$552$	4.00000	0.170251
$553$	−22.0000	−0.935535
$554$	7.00000	0.297402
$555$	0	0
$556$	−8.00000	−0.339276
$557$	24.0000	1.01691	0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000	1.01691	0.508456	+	0.861088i	$0.330216\pi$
$558$	−1.00000	−0.0423334
$559$	70.0000	2.96068
$560$	0	0
$561$	−5.00000	−0.211100
$562$	−30.0000	−1.26547
$563$	24.0000	1.01148	0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000	1.01148	0.505740	+	0.862686i	$0.331220\pi$
$564$	−1.00000	−0.0421076
$565$	0	0
$566$	−5.00000	−0.210166
$567$	2.00000	0.0839921
$568$	3.00000	0.125877
$569$	26.0000	1.08998	0.544988	−	0.838444i	$-0.316534\pi$
$569$	26.0000	1.08998	0.544988	+	0.838444i	$0.316534\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	35.0000	1.46342
$573$	0	0
$574$	−4.00000	−0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	−27.0000	−1.12402	−0.562012	−	0.827129i	$-0.689973\pi$
$577$	−27.0000	−1.12402	−0.562012	+	0.827129i	$0.689973\pi$
$578$	−16.0000	−0.665512
$579$	19.0000	0.789613
$580$	0	0
$581$	−14.0000	−0.580818
$582$	−3.00000	−0.124354
$583$	−30.0000	−1.24247
$584$	−14.0000	−0.579324
$585$	0	0
$586$	6.00000	0.247858
$587$	17.0000	0.701665	0.350833	−	0.936438i	$-0.385899\pi$
$587$	17.0000	0.701665	0.350833	+	0.936438i	$0.385899\pi$
$588$	3.00000	0.123718
$589$	−7.00000	−0.288430
$590$	0	0
$591$	−2.00000	−0.0822690
$592$	6.00000	0.246598
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	−5.00000	−0.205152
$595$	0	0
$596$	15.0000	0.614424
$597$	11.0000	0.450200
$598$	−28.0000	−1.14501
$599$	−39.0000	−1.59350	−0.796748	−	0.604311i	$-0.793448\pi$
$599$	−39.0000	−1.59350	−0.796748	+	0.604311i	$0.793448\pi$
$600$	0	0
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	20.0000	0.815139
$603$	3.00000	0.122169
$604$	−1.00000	−0.0406894
$605$	0	0
$606$	−6.00000	−0.243733
$607$	−10.0000	−0.405887	−0.202944	−	0.979190i	$-0.565051\pi$
$607$	−10.0000	−0.405887	−0.202944	+	0.979190i	$0.565051\pi$
$608$	7.00000	0.283887
$609$	16.0000	0.648353
$610$	0	0
$611$	7.00000	0.283190
$612$	1.00000	0.0404226
$613$	−5.00000	−0.201948	−0.100974	−	0.994889i	$-0.532196\pi$
$613$	−5.00000	−0.201948	−0.100974	+	0.994889i	$0.532196\pi$
$614$	−16.0000	−0.645707
$615$	0	0
$616$	10.0000	0.402911
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	10.0000	0.402259
$619$	−8.00000	−0.321547	−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000	−0.321547	−0.160774	+	0.986991i	$0.551399\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	21.0000	0.842023
$623$	−12.0000	−0.480770
$624$	−7.00000	−0.280224
$625$	0	0
$626$	−2.00000	−0.0799361
$627$	−35.0000	−1.39777
$628$	4.00000	0.159617
$629$	6.00000	0.239236
$630$	0	0
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	−11.0000	−0.437557
$633$	0	0
$634$	−5.00000	−0.198575
$635$	0	0
$636$	6.00000	0.237915
$637$	−21.0000	−0.832050
$638$	−40.0000	−1.58362
$639$	3.00000	0.118678
$640$	0	0
$641$	23.0000	0.908445	0.454223	−	0.890888i	$-0.349917\pi$
$641$	23.0000	0.908445	0.454223	+	0.890888i	$0.349917\pi$
$642$	8.00000	0.315735
$643$	32.0000	1.26196	0.630978	−	0.775800i	$-0.282654\pi$
$643$	32.0000	1.26196	0.630978	+	0.775800i	$0.282654\pi$
$644$	−8.00000	−0.315244
$645$	0	0
$646$	7.00000	0.275411
$647$	−14.0000	−0.550397	−0.275198	−	0.961387i	$-0.588744\pi$
$647$	−14.0000	−0.550397	−0.275198	+	0.961387i	$0.588744\pi$
$648$	1.00000	0.0392837
$649$	−50.0000	−1.96267
$650$	0	0
$651$	2.00000	0.0783862
$652$	9.00000	0.352467
$653$	−27.0000	−1.05659	−0.528296	−	0.849060i	$-0.677169\pi$
$653$	−27.0000	−1.05659	−0.528296	+	0.849060i	$0.677169\pi$
$654$	6.00000	0.234619
$655$	0	0
$656$	−2.00000	−0.0780869
$657$	−14.0000	−0.546192
$658$	2.00000	0.0779681
$659$	−26.0000	−1.01282	−0.506408	−	0.862294i	$-0.669027\pi$
$659$	−26.0000	−1.01282	−0.506408	+	0.862294i	$0.669027\pi$
$660$	0	0
$661$	4.00000	0.155582	0.0777910	−	0.996970i	$-0.475213\pi$
$661$	4.00000	0.155582	0.0777910	+	0.996970i	$0.475213\pi$
$662$	0	0
$663$	−7.00000	−0.271857
$664$	−7.00000	−0.271653
$665$	0	0
$666$	6.00000	0.232495
$667$	32.0000	1.23904
$668$	−10.0000	−0.386912
$669$	−5.00000	−0.193311
$670$	0	0
$671$	5.00000	0.193023
$672$	−2.00000	−0.0771517
$673$	−8.00000	−0.308377	−0.154189	−	0.988041i	$-0.549276\pi$
$673$	−8.00000	−0.308377	−0.154189	+	0.988041i	$0.549276\pi$
$674$	8.00000	0.308148
$675$	0	0
$676$	36.0000	1.38462
$677$	−36.0000	−1.38359	−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000	−1.38359	−0.691796	+	0.722093i	$0.743180\pi$
$678$	6.00000	0.230429
$679$	6.00000	0.230259
$680$	0	0
$681$	22.0000	0.843042
$682$	−5.00000	−0.191460
$683$	−16.0000	−0.612223	−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000	−0.612223	−0.306111	+	0.951996i	$0.599028\pi$
$684$	7.00000	0.267652
$685$	0	0
$686$	−20.0000	−0.763604
$687$	−13.0000	−0.495981
$688$	10.0000	0.381246
$689$	−42.0000	−1.60007
$690$	0	0
$691$	13.0000	0.494543	0.247272	−	0.968946i	$-0.420466\pi$
$691$	13.0000	0.494543	0.247272	+	0.968946i	$0.420466\pi$
$692$	−1.00000	−0.0380143
$693$	10.0000	0.379869
$694$	−17.0000	−0.645311
$695$	0	0
$696$	8.00000	0.303239
$697$	−2.00000	−0.0757554
$698$	24.0000	0.908413
$699$	20.0000	0.756469
$700$	0	0
$701$	35.0000	1.32193	0.660966	−	0.750416i	$-0.270147\pi$
$701$	35.0000	1.32193	0.660966	+	0.750416i	$0.270147\pi$
$702$	−7.00000	−0.264198
$703$	42.0000	1.58406
$704$	5.00000	0.188445
$705$	0	0
$706$	11.0000	0.413990
$707$	12.0000	0.451306
$708$	10.0000	0.375823
$709$	−21.0000	−0.788672	−0.394336	−	0.918966i	$-0.629025\pi$
$709$	−21.0000	−0.788672	−0.394336	+	0.918966i	$0.629025\pi$
$710$	0	0
$711$	−11.0000	−0.412532
$712$	−6.00000	−0.224860
$713$	4.00000	0.149801
$714$	−2.00000	−0.0748481
$715$	0	0
$716$	19.0000	0.710063
$717$	4.00000	0.149383
$718$	−17.0000	−0.634434
$719$	−12.0000	−0.447524	−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000	−0.447524	−0.223762	+	0.974644i	$0.571834\pi$
$720$	0	0
$721$	−20.0000	−0.744839
$722$	30.0000	1.11648
$723$	14.0000	0.520666
$724$	18.0000	0.668965
$725$	0	0
$726$	−14.0000	−0.519589
$727$	−4.00000	−0.148352	−0.0741759	−	0.997245i	$-0.523633\pi$
$727$	−4.00000	−0.148352	−0.0741759	+	0.997245i	$0.523633\pi$
$728$	14.0000	0.518875
$729$	1.00000	0.0370370
$730$	0	0
$731$	10.0000	0.369863
$732$	−1.00000	−0.0369611
$733$	30.0000	1.10808	0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000	1.10808	0.554038	+	0.832492i	$0.313086\pi$
$734$	11.0000	0.406017
$735$	0	0
$736$	−4.00000	−0.147442
$737$	15.0000	0.552532
$738$	−2.00000	−0.0736210
$739$	−16.0000	−0.588570	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000	−0.588570	−0.294285	+	0.955718i	$0.595081\pi$
$740$	0	0
$741$	−49.0000	−1.80006
$742$	−12.0000	−0.440534
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	1.00000	0.0366618
$745$	0	0
$746$	32.0000	1.17160
$747$	−7.00000	−0.256117
$748$	5.00000	0.182818
$749$	−16.0000	−0.584627
$750$	0	0
$751$	−38.0000	−1.38664	−0.693320	−	0.720630i	$-0.743853\pi$
$751$	−38.0000	−1.38664	−0.693320	+	0.720630i	$0.743853\pi$
$752$	1.00000	0.0364662
$753$	−20.0000	−0.728841
$754$	−56.0000	−2.03940
$755$	0	0
$756$	−2.00000	−0.0727393
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	1.00000	0.0363216
$759$	20.0000	0.725954
$760$	0	0
$761$	1.00000	0.0362500	0.0181250	−	0.999836i	$-0.494230\pi$
$761$	1.00000	0.0362500	0.0181250	+	0.999836i	$0.494230\pi$
$762$	4.00000	0.144905
$763$	−12.0000	−0.434429
$764$	0	0
$765$	0	0
$766$	10.0000	0.361315
$767$	−70.0000	−2.52755
$768$	−1.00000	−0.0360844
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	0	0
$771$	−12.0000	−0.432169
$772$	−19.0000	−0.683825
$773$	16.0000	0.575480	0.287740	−	0.957709i	$-0.407096\pi$
$773$	16.0000	0.575480	0.287740	+	0.957709i	$0.407096\pi$
$774$	10.0000	0.359443
$775$	0	0
$776$	3.00000	0.107694
$777$	−12.0000	−0.430498
$778$	−34.0000	−1.21896
$779$	−14.0000	−0.501602
$780$	0	0
$781$	15.0000	0.536742
$782$	−4.00000	−0.143040
$783$	8.00000	0.285897
$784$	−3.00000	−0.107143
$785$	0	0
$786$	−10.0000	−0.356688
$787$	−40.0000	−1.42585	−0.712923	−	0.701242i	$-0.752629\pi$
$787$	−40.0000	−1.42585	−0.712923	+	0.701242i	$0.752629\pi$
$788$	2.00000	0.0712470
$789$	12.0000	0.427211
$790$	0	0
$791$	−12.0000	−0.426671
$792$	5.00000	0.177667
$793$	7.00000	0.248577
$794$	22.0000	0.780751
$795$	0	0
$796$	−11.0000	−0.389885
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	−14.0000	−0.495595
$799$	1.00000	0.0353775
$800$	0	0
$801$	−6.00000	−0.212000
$802$	−23.0000	−0.812158
$803$	−70.0000	−2.47025
$804$	−3.00000	−0.105802
$805$	0	0
$806$	−7.00000	−0.246564
$807$	−6.00000	−0.211210
$808$	6.00000	0.211079
$809$	−29.0000	−1.01959	−0.509793	−	0.860297i	$-0.670278\pi$
$809$	−29.0000	−1.01959	−0.509793	+	0.860297i	$0.670278\pi$
$810$	0	0
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	−16.0000	−0.561490
$813$	19.0000	0.666359
$814$	30.0000	1.05150
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	70.0000	2.44899
$818$	−30.0000	−1.04893
$819$	14.0000	0.489200
$820$	0	0
$821$	−10.0000	−0.349002	−0.174501	−	0.984657i	$-0.555831\pi$
$821$	−10.0000	−0.349002	−0.174501	+	0.984657i	$0.555831\pi$
$822$	−18.0000	−0.627822
$823$	−43.0000	−1.49889	−0.749443	−	0.662069i	$-0.769679\pi$
$823$	−43.0000	−1.49889	−0.749443	+	0.662069i	$0.769679\pi$
$824$	−10.0000	−0.348367
$825$	0	0
$826$	−20.0000	−0.695889
$827$	−27.0000	−0.938882	−0.469441	−	0.882964i	$-0.655545\pi$
$827$	−27.0000	−0.938882	−0.469441	+	0.882964i	$0.655545\pi$
$828$	−4.00000	−0.139010
$829$	26.0000	0.903017	0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000	0.903017	0.451509	+	0.892267i	$0.350886\pi$
$830$	0	0
$831$	−7.00000	−0.242827
$832$	7.00000	0.242681
$833$	−3.00000	−0.103944
$834$	8.00000	0.277017
$835$	0	0
$836$	35.0000	1.21050
$837$	1.00000	0.0345651
$838$	−4.00000	−0.138178
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	2.00000	0.0689246
$843$	30.0000	1.03325
$844$	0	0
$845$	0	0
$846$	1.00000	0.0343807
$847$	28.0000	0.962091
$848$	−6.00000	−0.206041
$849$	5.00000	0.171600
$850$	0	0
$851$	−24.0000	−0.822709
$852$	−3.00000	−0.102778
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	2.00000	0.0684386
$855$	0	0
$856$	−8.00000	−0.273434
$857$	8.00000	0.273275	0.136637	−	0.990621i	$-0.456370\pi$
$857$	8.00000	0.273275	0.136637	+	0.990621i	$0.456370\pi$
$858$	−35.0000	−1.19488
$859$	−26.0000	−0.887109	−0.443554	−	0.896248i	$-0.646283\pi$
$859$	−26.0000	−0.887109	−0.443554	+	0.896248i	$0.646283\pi$
$860$	0	0
$861$	4.00000	0.136320
$862$	24.0000	0.817443
$863$	−10.0000	−0.340404	−0.170202	−	0.985409i	$-0.554442\pi$
$863$	−10.0000	−0.340404	−0.170202	+	0.985409i	$0.554442\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−28.0000	−0.951479
$867$	16.0000	0.543388
$868$	−2.00000	−0.0678844
$869$	−55.0000	−1.86575
$870$	0	0
$871$	21.0000	0.711558
$872$	−6.00000	−0.203186
$873$	3.00000	0.101535
$874$	−28.0000	−0.947114
$875$	0	0
$876$	14.0000	0.473016
$877$	−28.0000	−0.945493	−0.472746	−	0.881199i	$-0.656737\pi$
$877$	−28.0000	−0.945493	−0.472746	+	0.881199i	$0.656737\pi$
$878$	32.0000	1.07995
$879$	−6.00000	−0.202375
$880$	0	0
$881$	51.0000	1.71823	0.859117	−	0.511780i	$-0.171014\pi$
$881$	51.0000	1.71823	0.859117	+	0.511780i	$0.171014\pi$
$882$	−3.00000	−0.101015
$883$	46.0000	1.54802	0.774012	−	0.633171i	$-0.218247\pi$
$883$	46.0000	1.54802	0.774012	+	0.633171i	$0.218247\pi$
$884$	7.00000	0.235435
$885$	0	0
$886$	14.0000	0.470339
$887$	−16.0000	−0.537227	−0.268614	−	0.963248i	$-0.586566\pi$
$887$	−16.0000	−0.537227	−0.268614	+	0.963248i	$0.586566\pi$
$888$	−6.00000	−0.201347
$889$	−8.00000	−0.268311
$890$	0	0
$891$	5.00000	0.167506
$892$	5.00000	0.167412
$893$	7.00000	0.234246
$894$	−15.0000	−0.501675
$895$	0	0
$896$	2.00000	0.0668153
$897$	28.0000	0.934893
$898$	−11.0000	−0.367075
$899$	8.00000	0.266815
$900$	0	0
$901$	−6.00000	−0.199889
$902$	−10.0000	−0.332964
$903$	−20.0000	−0.665558
$904$	−6.00000	−0.199557
$905$	0	0
$906$	1.00000	0.0332228
$907$	1.00000	0.0332045	0.0166022	−	0.999862i	$-0.494715\pi$
$907$	1.00000	0.0332045	0.0166022	+	0.999862i	$0.494715\pi$
$908$	−22.0000	−0.730096
$909$	6.00000	0.199007
$910$	0	0
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	−7.00000	−0.231793
$913$	−35.0000	−1.15833
$914$	42.0000	1.38924
$915$	0	0
$916$	13.0000	0.429532
$917$	20.0000	0.660458
$918$	−1.00000	−0.0330049
$919$	28.0000	0.923635	0.461817	−	0.886975i	$-0.347198\pi$
$919$	28.0000	0.923635	0.461817	+	0.886975i	$0.347198\pi$
$920$	0	0
$921$	16.0000	0.527218
$922$	−34.0000	−1.11973
$923$	21.0000	0.691223
$924$	−10.0000	−0.328976
$925$	0	0
$926$	−33.0000	−1.08445
$927$	−10.0000	−0.328443
$928$	−8.00000	−0.262613
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	0	0
$931$	−21.0000	−0.688247
$932$	−20.0000	−0.655122
$933$	−21.0000	−0.687509
$934$	−24.0000	−0.785304
$935$	0	0
$936$	7.00000	0.228802
$937$	−1.00000	−0.0326686	−0.0163343	−	0.999867i	$-0.505200\pi$
$937$	−1.00000	−0.0326686	−0.0163343	+	0.999867i	$0.505200\pi$
$938$	6.00000	0.195907
$939$	2.00000	0.0652675
$940$	0	0
$941$	−48.0000	−1.56476	−0.782378	−	0.622804i	$-0.785993\pi$
$941$	−48.0000	−1.56476	−0.782378	+	0.622804i	$0.785993\pi$
$942$	−4.00000	−0.130327
$943$	8.00000	0.260516
$944$	−10.0000	−0.325472
$945$	0	0
$946$	50.0000	1.62564
$947$	5.00000	0.162478	0.0812391	−	0.996695i	$-0.474112\pi$
$947$	5.00000	0.162478	0.0812391	+	0.996695i	$0.474112\pi$
$948$	11.0000	0.357263
$949$	−98.0000	−3.18121
$950$	0	0
$951$	5.00000	0.162136
$952$	2.00000	0.0648204
$953$	5.00000	0.161966	0.0809829	−	0.996715i	$-0.474194\pi$
$953$	5.00000	0.161966	0.0809829	+	0.996715i	$0.474194\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	−4.00000	−0.129369
$957$	40.0000	1.29302
$958$	29.0000	0.936947
$959$	36.0000	1.16250
$960$	0	0
$961$	1.00000	0.0322581
$962$	42.0000	1.35413
$963$	−8.00000	−0.257796
$964$	−14.0000	−0.450910
$965$	0	0
$966$	8.00000	0.257396
$967$	−33.0000	−1.06121	−0.530604	−	0.847620i	$-0.678035\pi$
$967$	−33.0000	−1.06121	−0.530604	+	0.847620i	$0.678035\pi$
$968$	14.0000	0.449977
$969$	−7.00000	−0.224872
$970$	0	0
$971$	34.0000	1.09111	0.545556	−	0.838074i	$-0.316319\pi$
$971$	34.0000	1.09111	0.545556	+	0.838074i	$0.316319\pi$
$972$	−1.00000	−0.0320750
$973$	−16.0000	−0.512936
$974$	27.0000	0.865136
$975$	0	0
$976$	1.00000	0.0320092
$977$	22.0000	0.703842	0.351921	−	0.936030i	$-0.385529\pi$
$977$	22.0000	0.703842	0.351921	+	0.936030i	$0.385529\pi$
$978$	−9.00000	−0.287788
$979$	−30.0000	−0.958804
$980$	0	0
$981$	−6.00000	−0.191565
$982$	−20.0000	−0.638226
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	2.00000	0.0637577
$985$	0	0
$986$	−8.00000	−0.254772
$987$	−2.00000	−0.0636607
$988$	49.0000	1.55890
$989$	−40.0000	−1.27193
$990$	0	0
$991$	−20.0000	−0.635321	−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000	−0.635321	−0.317660	+	0.948205i	$0.602897\pi$
$992$	−1.00000	−0.0317500
$993$	0	0
$994$	6.00000	0.190308
$995$	0	0
$996$	7.00000	0.221803
$997$	42.0000	1.33015	0.665077	−	0.746775i	$-0.268399\pi$
$997$	42.0000	1.33015	0.665077	+	0.746775i	$0.268399\pi$
$998$	−24.0000	−0.759707
$999$	−6.00000	−0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4650.2.a.bh.1.1		1
5.2	odd	4		4650.2.d.k.3349.2		2
5.3	odd	4		4650.2.d.k.3349.1		2
5.4	even	2		186.2.a.b.1.1	✓	1
15.14	odd	2		558.2.a.f.1.1		1
20.19	odd	2		1488.2.a.h.1.1		1
35.34	odd	2		9114.2.a.b.1.1		1
40.19	odd	2		5952.2.a.s.1.1		1
40.29	even	2		5952.2.a.b.1.1		1
60.59	even	2		4464.2.a.c.1.1		1
155.154	odd	2		5766.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.a.b.1.1	✓	1	5.4	even	2
558.2.a.f.1.1		1	15.14	odd	2
1488.2.a.h.1.1		1	20.19	odd	2
4464.2.a.c.1.1		1	60.59	even	2
4650.2.a.bh.1.1		1	1.1	even	1	trivial
4650.2.d.k.3349.1		2	5.3	odd	4
4650.2.d.k.3349.2		2	5.2	odd	4
5766.2.a.c.1.1		1	155.154	odd	2
5952.2.a.b.1.1		1	40.29	even	2
5952.2.a.s.1.1		1	40.19	odd	2
9114.2.a.b.1.1		1	35.34	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:	\( N \)	\(=\)	\( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4650.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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