LMFDB - Embedded newform 1150.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.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:	$9.18279623245$
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	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} -3.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +6.00000 q^{9} +3.00000 q^{11} -3.00000 q^{12} +6.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} -5.00000 q^{17} +6.00000 q^{18} -1.00000 q^{19} +12.0000 q^{21} +3.00000 q^{22} -1.00000 q^{23} -3.00000 q^{24} +6.00000 q^{26} -9.00000 q^{27} -4.00000 q^{28} -8.00000 q^{29} -8.00000 q^{31} +1.00000 q^{32} -9.00000 q^{33} -5.00000 q^{34} +6.00000 q^{36} -2.00000 q^{37} -1.00000 q^{38} -18.0000 q^{39} -7.00000 q^{41} +12.0000 q^{42} -4.00000 q^{43} +3.00000 q^{44} -1.00000 q^{46} -10.0000 q^{47} -3.00000 q^{48} +9.00000 q^{49} +15.0000 q^{51} +6.00000 q^{52} +12.0000 q^{53} -9.00000 q^{54} -4.00000 q^{56} +3.00000 q^{57} -8.00000 q^{58} +4.00000 q^{59} -8.00000 q^{61} -8.00000 q^{62} -24.0000 q^{63} +1.00000 q^{64} -9.00000 q^{66} -3.00000 q^{67} -5.00000 q^{68} +3.00000 q^{69} +4.00000 q^{71} +6.00000 q^{72} +7.00000 q^{73} -2.00000 q^{74} -1.00000 q^{76} -12.0000 q^{77} -18.0000 q^{78} -6.00000 q^{79} +9.00000 q^{81} -7.00000 q^{82} -11.0000 q^{83} +12.0000 q^{84} -4.00000 q^{86} +24.0000 q^{87} +3.00000 q^{88} -3.00000 q^{89} -24.0000 q^{91} -1.00000 q^{92} +24.0000 q^{93} -10.0000 q^{94} -3.00000 q^{96} +14.0000 q^{97} +9.00000 q^{98} +18.0000 q^{99} +O(q^{100})\)

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
$3$	−3.00000	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−3.00000	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−3.00000	−1.22474
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	1.00000	0.353553
$9$	6.00000	2.00000
$10$	0	0
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	−3.00000	−0.866025
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	−4.00000	−1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	−5.00000	−1.21268	−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000	−1.21268	−0.606339	+	0.795206i	$0.707363\pi$
$18$	6.00000	1.41421
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	0	0
$21$	12.0000	2.61861
$22$	3.00000	0.639602
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.00000	−0.612372
$25$	0	0
$26$	6.00000	1.17670
$27$	−9.00000	−1.73205
$28$	−4.00000	−0.755929
$29$	−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
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	−9.00000	−1.56670
$34$	−5.00000	−0.857493
$35$	0	0
$36$	6.00000	1.00000
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−1.00000	−0.162221
$39$	−18.0000	−2.88231
$40$	0	0
$41$	−7.00000	−1.09322	−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000	−1.09322	−0.546608	+	0.837389i	$0.684081\pi$
$42$	12.0000	1.85164
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	−1.00000	−0.147442
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	−3.00000	−0.433013
$49$	9.00000	1.28571
$50$	0	0
$51$	15.0000	2.10042
$52$	6.00000	0.832050
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	−9.00000	−1.22474
$55$	0	0
$56$	−4.00000	−0.534522
$57$	3.00000	0.397360
$58$	−8.00000	−1.05045
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	−8.00000	−1.01600
$63$	−24.0000	−3.02372
$64$	1.00000	0.125000
$65$	0	0
$66$	−9.00000	−1.10782
$67$	−3.00000	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$68$	−5.00000	−0.606339
$69$	3.00000	0.361158
$70$	0	0
$71$	4.00000	0.474713	0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000	0.474713	0.237356	+	0.971423i	$0.423719\pi$
$72$	6.00000	0.707107
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−1.00000	−0.114708
$77$	−12.0000	−1.36753
$78$	−18.0000	−2.03810
$79$	−6.00000	−0.675053	−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000	−0.675053	−0.337526	+	0.941316i	$0.609590\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	−7.00000	−0.773021
$83$	−11.0000	−1.20741	−0.603703	−	0.797209i	$-0.706309\pi$
$83$	−11.0000	−1.20741	−0.603703	+	0.797209i	$0.706309\pi$
$84$	12.0000	1.30931
$85$	0	0
$86$	−4.00000	−0.431331
$87$	24.0000	2.57307
$88$	3.00000	0.319801
$89$	−3.00000	−0.317999	−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000	−0.317999	−0.159000	+	0.987279i	$0.550827\pi$
$90$	0	0
$91$	−24.0000	−2.51588
$92$	−1.00000	−0.104257
$93$	24.0000	2.48868
$94$	−10.0000	−1.03142
$95$	0	0
$96$	−3.00000	−0.306186
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	9.00000	0.909137
$99$	18.0000	1.80907
$100$	0	0
$101$	4.00000	0.398015	0.199007	−	0.979998i	$-0.436228\pi$
$101$	4.00000	0.398015	0.199007	+	0.979998i	$0.436228\pi$
$102$	15.0000	1.48522
$103$	−10.0000	−0.985329	−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000	−0.985329	−0.492665	+	0.870219i	$0.663977\pi$
$104$	6.00000	0.588348
$105$	0	0
$106$	12.0000	1.16554
$107$	−5.00000	−0.483368	−0.241684	−	0.970355i	$-0.577700\pi$
$107$	−5.00000	−0.483368	−0.241684	+	0.970355i	$0.577700\pi$
$108$	−9.00000	−0.866025
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	6.00000	0.569495
$112$	−4.00000	−0.377964
$113$	−15.0000	−1.41108	−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000	−1.41108	−0.705541	+	0.708669i	$0.749296\pi$
$114$	3.00000	0.280976
$115$	0	0
$116$	−8.00000	−0.742781
$117$	36.0000	3.32820
$118$	4.00000	0.368230
$119$	20.0000	1.83340
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−8.00000	−0.724286
$123$	21.0000	1.89351
$124$	−8.00000	−0.718421
$125$	0	0
$126$	−24.0000	−2.13809
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000	0.0883883
$129$	12.0000	1.05654
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	−9.00000	−0.783349
$133$	4.00000	0.346844
$134$	−3.00000	−0.259161
$135$	0	0
$136$	−5.00000	−0.428746
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	3.00000	0.255377
$139$	−19.0000	−1.61156	−0.805779	−	0.592216i	$-0.798253\pi$
$139$	−19.0000	−1.61156	−0.805779	+	0.592216i	$0.798253\pi$
$140$	0	0
$141$	30.0000	2.52646
$142$	4.00000	0.335673
$143$	18.0000	1.50524
$144$	6.00000	0.500000
$145$	0	0
$146$	7.00000	0.579324
$147$	−27.0000	−2.22692
$148$	−2.00000	−0.164399
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	−1.00000	−0.0811107
$153$	−30.0000	−2.42536
$154$	−12.0000	−0.966988
$155$	0	0
$156$	−18.0000	−1.44115
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−6.00000	−0.477334
$159$	−36.0000	−2.85499
$160$	0	0
$161$	4.00000	0.315244
$162$	9.00000	0.707107
$163$	−5.00000	−0.391630	−0.195815	−	0.980641i	$-0.562735\pi$
$163$	−5.00000	−0.391630	−0.195815	+	0.980641i	$0.562735\pi$
$164$	−7.00000	−0.546608
$165$	0	0
$166$	−11.0000	−0.853766
$167$	−22.0000	−1.70241	−0.851206	−	0.524832i	$-0.824128\pi$
$167$	−22.0000	−1.70241	−0.851206	+	0.524832i	$0.824128\pi$
$168$	12.0000	0.925820
$169$	23.0000	1.76923
$170$	0	0
$171$	−6.00000	−0.458831
$172$	−4.00000	−0.304997
$173$	−4.00000	−0.304114	−0.152057	−	0.988372i	$-0.548590\pi$
$173$	−4.00000	−0.304114	−0.152057	+	0.988372i	$0.548590\pi$
$174$	24.0000	1.81944
$175$	0	0
$176$	3.00000	0.226134
$177$	−12.0000	−0.901975
$178$	−3.00000	−0.224860
$179$	−3.00000	−0.224231	−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000	−0.224231	−0.112115	+	0.993695i	$0.535763\pi$
$180$	0	0
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	−24.0000	−1.77900
$183$	24.0000	1.77413
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	24.0000	1.75977
$187$	−15.0000	−1.09691
$188$	−10.0000	−0.729325
$189$	36.0000	2.61861
$190$	0	0
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	−3.00000	−0.216506
$193$	9.00000	0.647834	0.323917	−	0.946085i	$-0.395000\pi$
$193$	9.00000	0.647834	0.323917	+	0.946085i	$0.395000\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	9.00000	0.642857
$197$	8.00000	0.569976	0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000	0.569976	0.284988	+	0.958531i	$0.408010\pi$
$198$	18.0000	1.27920
$199$	18.0000	1.27599	0.637993	−	0.770042i	$-0.279765\pi$
$199$	18.0000	1.27599	0.637993	+	0.770042i	$0.279765\pi$
$200$	0	0
$201$	9.00000	0.634811
$202$	4.00000	0.281439
$203$	32.0000	2.24596
$204$	15.0000	1.05021
$205$	0	0
$206$	−10.0000	−0.696733
$207$	−6.00000	−0.417029
$208$	6.00000	0.416025
$209$	−3.00000	−0.207514
$210$	0	0
$211$	−1.00000	−0.0688428	−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000	−0.0688428	−0.0344214	+	0.999407i	$0.510959\pi$
$212$	12.0000	0.824163
$213$	−12.0000	−0.822226
$214$	−5.00000	−0.341793
$215$	0	0
$216$	−9.00000	−0.612372
$217$	32.0000	2.17230
$218$	−10.0000	−0.677285
$219$	−21.0000	−1.41905
$220$	0	0
$221$	−30.0000	−2.01802
$222$	6.00000	0.402694
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	−4.00000	−0.267261
$225$	0	0
$226$	−15.0000	−0.997785
$227$	8.00000	0.530979	0.265489	−	0.964114i	$-0.414466\pi$
$227$	8.00000	0.530979	0.265489	+	0.964114i	$0.414466\pi$
$228$	3.00000	0.198680
$229$	−30.0000	−1.98246	−0.991228	−	0.132164i	$-0.957808\pi$
$229$	−30.0000	−1.98246	−0.991228	+	0.132164i	$0.957808\pi$
$230$	0	0
$231$	36.0000	2.36863
$232$	−8.00000	−0.525226
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	36.0000	2.35339
$235$	0	0
$236$	4.00000	0.260378
$237$	18.0000	1.16923
$238$	20.0000	1.29641
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	23.0000	1.48156	0.740780	−	0.671748i	$-0.234456\pi$
$241$	23.0000	1.48156	0.740780	+	0.671748i	$0.234456\pi$
$242$	−2.00000	−0.128565
$243$	0	0
$244$	−8.00000	−0.512148
$245$	0	0
$246$	21.0000	1.33891
$247$	−6.00000	−0.381771
$248$	−8.00000	−0.508001
$249$	33.0000	2.09129
$250$	0	0
$251$	−7.00000	−0.441836	−0.220918	−	0.975292i	$-0.570905\pi$
$251$	−7.00000	−0.441836	−0.220918	+	0.975292i	$0.570905\pi$
$252$	−24.0000	−1.51186
$253$	−3.00000	−0.188608
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	12.0000	0.747087
$259$	8.00000	0.497096
$260$	0	0
$261$	−48.0000	−2.97113
$262$	12.0000	0.741362
$263$	4.00000	0.246651	0.123325	−	0.992366i	$-0.460644\pi$
$263$	4.00000	0.246651	0.123325	+	0.992366i	$0.460644\pi$
$264$	−9.00000	−0.553912
$265$	0	0
$266$	4.00000	0.245256
$267$	9.00000	0.550791
$268$	−3.00000	−0.183254
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	10.0000	0.607457	0.303728	−	0.952759i	$-0.401768\pi$
$271$	10.0000	0.607457	0.303728	+	0.952759i	$0.401768\pi$
$272$	−5.00000	−0.303170
$273$	72.0000	4.35764
$274$	3.00000	0.181237
$275$	0	0
$276$	3.00000	0.180579
$277$	28.0000	1.68236	0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000	1.68236	0.841178	+	0.540758i	$0.181862\pi$
$278$	−19.0000	−1.13954
$279$	−48.0000	−2.87368
$280$	0	0
$281$	−30.0000	−1.78965	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000	−1.78965	−0.894825	+	0.446417i	$0.852700\pi$
$282$	30.0000	1.78647
$283$	33.0000	1.96165	0.980823	−	0.194900i	$-0.0624381\pi$
$283$	33.0000	1.96165	0.980823	+	0.194900i	$0.0624381\pi$
$284$	4.00000	0.237356
$285$	0	0
$286$	18.0000	1.06436
$287$	28.0000	1.65279
$288$	6.00000	0.353553
$289$	8.00000	0.470588
$290$	0	0
$291$	−42.0000	−2.46208
$292$	7.00000	0.409644
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	−27.0000	−1.57467
$295$	0	0
$296$	−2.00000	−0.116248
$297$	−27.0000	−1.56670
$298$	6.00000	0.347571
$299$	−6.00000	−0.346989
$300$	0	0
$301$	16.0000	0.922225
$302$	20.0000	1.15087
$303$	−12.0000	−0.689382
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	−30.0000	−1.71499
$307$	9.00000	0.513657	0.256829	−	0.966457i	$-0.417322\pi$
$307$	9.00000	0.513657	0.256829	+	0.966457i	$0.417322\pi$
$308$	−12.0000	−0.683763
$309$	30.0000	1.70664
$310$	0	0
$311$	2.00000	0.113410	0.0567048	−	0.998391i	$-0.481941\pi$
$311$	2.00000	0.113410	0.0567048	+	0.998391i	$0.481941\pi$
$312$	−18.0000	−1.01905
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	−14.0000	−0.790066
$315$	0	0
$316$	−6.00000	−0.337526
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	−36.0000	−2.01878
$319$	−24.0000	−1.34374
$320$	0	0
$321$	15.0000	0.837218
$322$	4.00000	0.222911
$323$	5.00000	0.278207
$324$	9.00000	0.500000
$325$	0	0
$326$	−5.00000	−0.276924
$327$	30.0000	1.65900
$328$	−7.00000	−0.386510
$329$	40.0000	2.20527
$330$	0	0
$331$	25.0000	1.37412	0.687062	−	0.726599i	$-0.258900\pi$
$331$	25.0000	1.37412	0.687062	+	0.726599i	$0.258900\pi$
$332$	−11.0000	−0.603703
$333$	−12.0000	−0.657596
$334$	−22.0000	−1.20379
$335$	0	0
$336$	12.0000	0.654654
$337$	−3.00000	−0.163420	−0.0817102	−	0.996656i	$-0.526038\pi$
$337$	−3.00000	−0.163420	−0.0817102	+	0.996656i	$0.526038\pi$
$338$	23.0000	1.25104
$339$	45.0000	2.44406
$340$	0	0
$341$	−24.0000	−1.29967
$342$	−6.00000	−0.324443
$343$	−8.00000	−0.431959
$344$	−4.00000	−0.215666
$345$	0	0
$346$	−4.00000	−0.215041
$347$	−7.00000	−0.375780	−0.187890	−	0.982190i	$-0.560165\pi$
$347$	−7.00000	−0.375780	−0.187890	+	0.982190i	$0.560165\pi$
$348$	24.0000	1.28654
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	0	0
$351$	−54.0000	−2.88231
$352$	3.00000	0.159901
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	−12.0000	−0.637793
$355$	0	0
$356$	−3.00000	−0.159000
$357$	−60.0000	−3.17554
$358$	−3.00000	−0.158555
$359$	−20.0000	−1.05556	−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000	−1.05556	−0.527780	+	0.849381i	$0.676975\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	−22.0000	−1.15629
$363$	6.00000	0.314918
$364$	−24.0000	−1.25794
$365$	0	0
$366$	24.0000	1.25450
$367$	−2.00000	−0.104399	−0.0521996	−	0.998637i	$-0.516623\pi$
$367$	−2.00000	−0.104399	−0.0521996	+	0.998637i	$0.516623\pi$
$368$	−1.00000	−0.0521286
$369$	−42.0000	−2.18643
$370$	0	0
$371$	−48.0000	−2.49204
$372$	24.0000	1.24434
$373$	12.0000	0.621336	0.310668	−	0.950518i	$-0.399447\pi$
$373$	12.0000	0.621336	0.310668	+	0.950518i	$0.399447\pi$
$374$	−15.0000	−0.775632
$375$	0	0
$376$	−10.0000	−0.515711
$377$	−48.0000	−2.47213
$378$	36.0000	1.85164
$379$	5.00000	0.256833	0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000	0.256833	0.128416	+	0.991720i	$0.459011\pi$
$380$	0	0
$381$	−24.0000	−1.22956
$382$	12.0000	0.613973
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	−3.00000	−0.153093
$385$	0	0
$386$	9.00000	0.458088
$387$	−24.0000	−1.21999
$388$	14.0000	0.710742
$389$	−36.0000	−1.82527	−0.912636	−	0.408773i	$-0.865957\pi$
$389$	−36.0000	−1.82527	−0.912636	+	0.408773i	$0.865957\pi$
$390$	0	0
$391$	5.00000	0.252861
$392$	9.00000	0.454569
$393$	−36.0000	−1.81596
$394$	8.00000	0.403034
$395$	0	0
$396$	18.0000	0.904534
$397$	12.0000	0.602263	0.301131	−	0.953583i	$-0.402636\pi$
$397$	12.0000	0.602263	0.301131	+	0.953583i	$0.402636\pi$
$398$	18.0000	0.902258
$399$	−12.0000	−0.600751
$400$	0	0
$401$	−5.00000	−0.249688	−0.124844	−	0.992176i	$-0.539843\pi$
$401$	−5.00000	−0.249688	−0.124844	+	0.992176i	$0.539843\pi$
$402$	9.00000	0.448879
$403$	−48.0000	−2.39105
$404$	4.00000	0.199007
$405$	0	0
$406$	32.0000	1.58813
$407$	−6.00000	−0.297409
$408$	15.0000	0.742611
$409$	21.0000	1.03838	0.519192	−	0.854658i	$-0.326233\pi$
$409$	21.0000	1.03838	0.519192	+	0.854658i	$0.326233\pi$
$410$	0	0
$411$	−9.00000	−0.443937
$412$	−10.0000	−0.492665
$413$	−16.0000	−0.787309
$414$	−6.00000	−0.294884
$415$	0	0
$416$	6.00000	0.294174
$417$	57.0000	2.79130
$418$	−3.00000	−0.146735
$419$	3.00000	0.146560	0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000	0.146560	0.0732798	+	0.997311i	$0.476653\pi$
$420$	0	0
$421$	−14.0000	−0.682318	−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000	−0.682318	−0.341159	+	0.940006i	$0.610819\pi$
$422$	−1.00000	−0.0486792
$423$	−60.0000	−2.91730
$424$	12.0000	0.582772
$425$	0	0
$426$	−12.0000	−0.581402
$427$	32.0000	1.54859
$428$	−5.00000	−0.241684
$429$	−54.0000	−2.60714
$430$	0	0
$431$	−4.00000	−0.192673	−0.0963366	−	0.995349i	$-0.530713\pi$
$431$	−4.00000	−0.192673	−0.0963366	+	0.995349i	$0.530713\pi$
$432$	−9.00000	−0.433013
$433$	−29.0000	−1.39365	−0.696826	−	0.717241i	$-0.745405\pi$
$433$	−29.0000	−1.39365	−0.696826	+	0.717241i	$0.745405\pi$
$434$	32.0000	1.53605
$435$	0	0
$436$	−10.0000	−0.478913
$437$	1.00000	0.0478365
$438$	−21.0000	−1.00342
$439$	−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
$441$	54.0000	2.57143
$442$	−30.0000	−1.42695
$443$	39.0000	1.85295	0.926473	−	0.376361i	$-0.122825\pi$
$443$	39.0000	1.85295	0.926473	+	0.376361i	$0.122825\pi$
$444$	6.00000	0.284747
$445$	0	0
$446$	0	0
$447$	−18.0000	−0.851371
$448$	−4.00000	−0.188982
$449$	5.00000	0.235965	0.117982	−	0.993016i	$-0.462357\pi$
$449$	5.00000	0.235965	0.117982	+	0.993016i	$0.462357\pi$
$450$	0	0
$451$	−21.0000	−0.988851
$452$	−15.0000	−0.705541
$453$	−60.0000	−2.81905
$454$	8.00000	0.375459
$455$	0	0
$456$	3.00000	0.140488
$457$	7.00000	0.327446	0.163723	−	0.986506i	$-0.447650\pi$
$457$	7.00000	0.327446	0.163723	+	0.986506i	$0.447650\pi$
$458$	−30.0000	−1.40181
$459$	45.0000	2.10042
$460$	0	0
$461$	−24.0000	−1.11779	−0.558896	−	0.829238i	$-0.688775\pi$
$461$	−24.0000	−1.11779	−0.558896	+	0.829238i	$0.688775\pi$
$462$	36.0000	1.67487
$463$	−26.0000	−1.20832	−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000	−1.20832	−0.604161	+	0.796862i	$0.706492\pi$
$464$	−8.00000	−0.371391
$465$	0	0
$466$	14.0000	0.648537
$467$	−28.0000	−1.29569	−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000	−1.29569	−0.647843	+	0.761774i	$0.724329\pi$
$468$	36.0000	1.66410
$469$	12.0000	0.554109
$470$	0	0
$471$	42.0000	1.93526
$472$	4.00000	0.184115
$473$	−12.0000	−0.551761
$474$	18.0000	0.826767
$475$	0	0
$476$	20.0000	0.916698
$477$	72.0000	3.29665
$478$	−6.00000	−0.274434
$479$	−4.00000	−0.182765	−0.0913823	−	0.995816i	$-0.529129\pi$
$479$	−4.00000	−0.182765	−0.0913823	+	0.995816i	$0.529129\pi$
$480$	0	0
$481$	−12.0000	−0.547153
$482$	23.0000	1.04762
$483$	−12.0000	−0.546019
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	0	0
$487$	30.0000	1.35943	0.679715	−	0.733476i	$-0.262104\pi$
$487$	30.0000	1.35943	0.679715	+	0.733476i	$0.262104\pi$
$488$	−8.00000	−0.362143
$489$	15.0000	0.678323
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	21.0000	0.946753
$493$	40.0000	1.80151
$494$	−6.00000	−0.269953
$495$	0	0
$496$	−8.00000	−0.359211
$497$	−16.0000	−0.717698
$498$	33.0000	1.47877
$499$	−12.0000	−0.537194	−0.268597	−	0.963253i	$-0.586560\pi$
$499$	−12.0000	−0.537194	−0.268597	+	0.963253i	$0.586560\pi$
$500$	0	0
$501$	66.0000	2.94866
$502$	−7.00000	−0.312425
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	−24.0000	−1.06904
$505$	0	0
$506$	−3.00000	−0.133366
$507$	−69.0000	−3.06440
$508$	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
$511$	−28.0000	−1.23865
$512$	1.00000	0.0441942
$513$	9.00000	0.397360
$514$	−2.00000	−0.0882162
$515$	0	0
$516$	12.0000	0.528271
$517$	−30.0000	−1.31940
$518$	8.00000	0.351500
$519$	12.0000	0.526742
$520$	0	0
$521$	31.0000	1.35813	0.679067	−	0.734076i	$-0.262384\pi$
$521$	31.0000	1.35813	0.679067	+	0.734076i	$0.262384\pi$
$522$	−48.0000	−2.10090
$523$	−37.0000	−1.61790	−0.808949	−	0.587879i	$-0.799963\pi$
$523$	−37.0000	−1.61790	−0.808949	+	0.587879i	$0.799963\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	4.00000	0.174408
$527$	40.0000	1.74243
$528$	−9.00000	−0.391675
$529$	1.00000	0.0434783
$530$	0	0
$531$	24.0000	1.04151
$532$	4.00000	0.173422
$533$	−42.0000	−1.81922
$534$	9.00000	0.389468
$535$	0	0
$536$	−3.00000	−0.129580
$537$	9.00000	0.388379
$538$	−6.00000	−0.258678
$539$	27.0000	1.16297
$540$	0	0
$541$	16.0000	0.687894	0.343947	−	0.938989i	$-0.388236\pi$
$541$	16.0000	0.687894	0.343947	+	0.938989i	$0.388236\pi$
$542$	10.0000	0.429537
$543$	66.0000	2.83233
$544$	−5.00000	−0.214373
$545$	0	0
$546$	72.0000	3.08132
$547$	17.0000	0.726868	0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000	0.726868	0.363434	+	0.931620i	$0.381604\pi$
$548$	3.00000	0.128154
$549$	−48.0000	−2.04859
$550$	0	0
$551$	8.00000	0.340811
$552$	3.00000	0.127688
$553$	24.0000	1.02058
$554$	28.0000	1.18961
$555$	0	0
$556$	−19.0000	−0.805779
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	−48.0000	−2.03200
$559$	−24.0000	−1.01509
$560$	0	0
$561$	45.0000	1.89990
$562$	−30.0000	−1.26547
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	30.0000	1.26323
$565$	0	0
$566$	33.0000	1.38709
$567$	−36.0000	−1.51186
$568$	4.00000	0.167836
$569$	−9.00000	−0.377300	−0.188650	−	0.982044i	$-0.560411\pi$
$569$	−9.00000	−0.377300	−0.188650	+	0.982044i	$0.560411\pi$
$570$	0	0
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	18.0000	0.752618
$573$	−36.0000	−1.50392
$574$	28.0000	1.16870
$575$	0	0
$576$	6.00000	0.250000
$577$	−17.0000	−0.707719	−0.353860	−	0.935299i	$-0.615131\pi$
$577$	−17.0000	−0.707719	−0.353860	+	0.935299i	$0.615131\pi$
$578$	8.00000	0.332756
$579$	−27.0000	−1.12208
$580$	0	0
$581$	44.0000	1.82543
$582$	−42.0000	−1.74096
$583$	36.0000	1.49097
$584$	7.00000	0.289662
$585$	0	0
$586$	−24.0000	−0.991431
$587$	−17.0000	−0.701665	−0.350833	−	0.936438i	$-0.614101\pi$
$587$	−17.0000	−0.701665	−0.350833	+	0.936438i	$0.614101\pi$
$588$	−27.0000	−1.11346
$589$	8.00000	0.329634
$590$	0	0
$591$	−24.0000	−0.987228
$592$	−2.00000	−0.0821995
$593$	35.0000	1.43728	0.718639	−	0.695383i	$-0.244765\pi$
$593$	35.0000	1.43728	0.718639	+	0.695383i	$0.244765\pi$
$594$	−27.0000	−1.10782
$595$	0	0
$596$	6.00000	0.245770
$597$	−54.0000	−2.21007
$598$	−6.00000	−0.245358
$599$	−20.0000	−0.817178	−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000	−0.817178	−0.408589	+	0.912719i	$0.633979\pi$
$600$	0	0
$601$	31.0000	1.26452	0.632258	−	0.774758i	$-0.282128\pi$
$601$	31.0000	1.26452	0.632258	+	0.774758i	$0.282128\pi$
$602$	16.0000	0.652111
$603$	−18.0000	−0.733017
$604$	20.0000	0.813788
$605$	0	0
$606$	−12.0000	−0.487467
$607$	−10.0000	−0.405887	−0.202944	−	0.979190i	$-0.565051\pi$
$607$	−10.0000	−0.405887	−0.202944	+	0.979190i	$0.565051\pi$
$608$	−1.00000	−0.0405554
$609$	−96.0000	−3.89012
$610$	0	0
$611$	−60.0000	−2.42734
$612$	−30.0000	−1.21268
$613$	8.00000	0.323117	0.161558	−	0.986863i	$-0.448348\pi$
$613$	8.00000	0.323117	0.161558	+	0.986863i	$0.448348\pi$
$614$	9.00000	0.363210
$615$	0	0
$616$	−12.0000	−0.483494
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	30.0000	1.20678
$619$	28.0000	1.12542	0.562708	−	0.826656i	$-0.309760\pi$
$619$	28.0000	1.12542	0.562708	+	0.826656i	$0.309760\pi$
$620$	0	0
$621$	9.00000	0.361158
$622$	2.00000	0.0801927
$623$	12.0000	0.480770
$624$	−18.0000	−0.720577
$625$	0	0
$626$	10.0000	0.399680
$627$	9.00000	0.359425
$628$	−14.0000	−0.558661
$629$	10.0000	0.398726
$630$	0	0
$631$	30.0000	1.19428	0.597141	−	0.802137i	$-0.296303\pi$
$631$	30.0000	1.19428	0.597141	+	0.802137i	$0.296303\pi$
$632$	−6.00000	−0.238667
$633$	3.00000	0.119239
$634$	−12.0000	−0.476581
$635$	0	0
$636$	−36.0000	−1.42749
$637$	54.0000	2.13956
$638$	−24.0000	−0.950169
$639$	24.0000	0.949425
$640$	0	0
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	15.0000	0.592003
$643$	−32.0000	−1.26196	−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000	−1.26196	−0.630978	+	0.775800i	$0.717346\pi$
$644$	4.00000	0.157622
$645$	0	0
$646$	5.00000	0.196722
$647$	−28.0000	−1.10079	−0.550397	−	0.834903i	$-0.685524\pi$
$647$	−28.0000	−1.10079	−0.550397	+	0.834903i	$0.685524\pi$
$648$	9.00000	0.353553
$649$	12.0000	0.471041
$650$	0	0
$651$	−96.0000	−3.76254
$652$	−5.00000	−0.195815
$653$	−14.0000	−0.547862	−0.273931	−	0.961749i	$-0.588324\pi$
$653$	−14.0000	−0.547862	−0.273931	+	0.961749i	$0.588324\pi$
$654$	30.0000	1.17309
$655$	0	0
$656$	−7.00000	−0.273304
$657$	42.0000	1.63858
$658$	40.0000	1.55936
$659$	5.00000	0.194772	0.0973862	−	0.995247i	$-0.468952\pi$
$659$	5.00000	0.194772	0.0973862	+	0.995247i	$0.468952\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	25.0000	0.971653
$663$	90.0000	3.49531
$664$	−11.0000	−0.426883
$665$	0	0
$666$	−12.0000	−0.464991
$667$	8.00000	0.309761
$668$	−22.0000	−0.851206
$669$	0	0
$670$	0	0
$671$	−24.0000	−0.926510
$672$	12.0000	0.462910
$673$	−34.0000	−1.31060	−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000	−1.31060	−0.655302	+	0.755367i	$0.727459\pi$
$674$	−3.00000	−0.115556
$675$	0	0
$676$	23.0000	0.884615
$677$	−42.0000	−1.61419	−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000	−1.61419	−0.807096	+	0.590421i	$0.798962\pi$
$678$	45.0000	1.72821
$679$	−56.0000	−2.14908
$680$	0	0
$681$	−24.0000	−0.919682
$682$	−24.0000	−0.919007
$683$	−35.0000	−1.33924	−0.669619	−	0.742705i	$-0.733543\pi$
$683$	−35.0000	−1.33924	−0.669619	+	0.742705i	$0.733543\pi$
$684$	−6.00000	−0.229416
$685$	0	0
$686$	−8.00000	−0.305441
$687$	90.0000	3.43371
$688$	−4.00000	−0.152499
$689$	72.0000	2.74298
$690$	0	0
$691$	29.0000	1.10321	0.551606	−	0.834105i	$-0.314015\pi$
$691$	29.0000	1.10321	0.551606	+	0.834105i	$0.314015\pi$
$692$	−4.00000	−0.152057
$693$	−72.0000	−2.73505
$694$	−7.00000	−0.265716
$695$	0	0
$696$	24.0000	0.909718
$697$	35.0000	1.32572
$698$	26.0000	0.984115
$699$	−42.0000	−1.58859
$700$	0	0
$701$	−8.00000	−0.302156	−0.151078	−	0.988522i	$-0.548274\pi$
$701$	−8.00000	−0.302156	−0.151078	+	0.988522i	$0.548274\pi$
$702$	−54.0000	−2.03810
$703$	2.00000	0.0754314
$704$	3.00000	0.113067
$705$	0	0
$706$	−18.0000	−0.677439
$707$	−16.0000	−0.601742
$708$	−12.0000	−0.450988
$709$	16.0000	0.600893	0.300446	−	0.953799i	$-0.402864\pi$
$709$	16.0000	0.600893	0.300446	+	0.953799i	$0.402864\pi$
$710$	0	0
$711$	−36.0000	−1.35011
$712$	−3.00000	−0.112430
$713$	8.00000	0.299602
$714$	−60.0000	−2.24544
$715$	0	0
$716$	−3.00000	−0.112115
$717$	18.0000	0.672222
$718$	−20.0000	−0.746393
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	0	0
$721$	40.0000	1.48968
$722$	−18.0000	−0.669891
$723$	−69.0000	−2.56614
$724$	−22.0000	−0.817624
$725$	0	0
$726$	6.00000	0.222681
$727$	28.0000	1.03846	0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000	1.03846	0.519231	+	0.854634i	$0.326218\pi$
$728$	−24.0000	−0.889499
$729$	−27.0000	−1.00000
$730$	0	0
$731$	20.0000	0.739727
$732$	24.0000	0.887066
$733$	−38.0000	−1.40356	−0.701781	−	0.712393i	$-0.747612\pi$
$733$	−38.0000	−1.40356	−0.701781	+	0.712393i	$0.747612\pi$
$734$	−2.00000	−0.0738213
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−9.00000	−0.331519
$738$	−42.0000	−1.54604
$739$	−4.00000	−0.147142	−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000	−0.147142	−0.0735712	+	0.997290i	$0.523440\pi$
$740$	0	0
$741$	18.0000	0.661247
$742$	−48.0000	−1.76214
$743$	−26.0000	−0.953847	−0.476924	−	0.878945i	$-0.658248\pi$
$743$	−26.0000	−0.953847	−0.476924	+	0.878945i	$0.658248\pi$
$744$	24.0000	0.879883
$745$	0	0
$746$	12.0000	0.439351
$747$	−66.0000	−2.41481
$748$	−15.0000	−0.548454
$749$	20.0000	0.730784
$750$	0	0
$751$	24.0000	0.875772	0.437886	−	0.899030i	$-0.355727\pi$
$751$	24.0000	0.875772	0.437886	+	0.899030i	$0.355727\pi$
$752$	−10.0000	−0.364662
$753$	21.0000	0.765283
$754$	−48.0000	−1.74806
$755$	0	0
$756$	36.0000	1.30931
$757$	−16.0000	−0.581530	−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000	−0.581530	−0.290765	+	0.956795i	$0.593910\pi$
$758$	5.00000	0.181608
$759$	9.00000	0.326679
$760$	0	0
$761$	−15.0000	−0.543750	−0.271875	−	0.962333i	$-0.587644\pi$
$761$	−15.0000	−0.543750	−0.271875	+	0.962333i	$0.587644\pi$
$762$	−24.0000	−0.869428
$763$	40.0000	1.44810
$764$	12.0000	0.434145
$765$	0	0
$766$	6.00000	0.216789
$767$	24.0000	0.866590
$768$	−3.00000	−0.108253
$769$	−21.0000	−0.757279	−0.378640	−	0.925544i	$-0.623608\pi$
$769$	−21.0000	−0.757279	−0.378640	+	0.925544i	$0.623608\pi$
$770$	0	0
$771$	6.00000	0.216085
$772$	9.00000	0.323917
$773$	−4.00000	−0.143870	−0.0719350	−	0.997409i	$-0.522917\pi$
$773$	−4.00000	−0.143870	−0.0719350	+	0.997409i	$0.522917\pi$
$774$	−24.0000	−0.862662
$775$	0	0
$776$	14.0000	0.502571
$777$	−24.0000	−0.860995
$778$	−36.0000	−1.29066
$779$	7.00000	0.250801
$780$	0	0
$781$	12.0000	0.429394
$782$	5.00000	0.178800
$783$	72.0000	2.57307
$784$	9.00000	0.321429
$785$	0	0
$786$	−36.0000	−1.28408
$787$	52.0000	1.85360	0.926800	−	0.375555i	$-0.122548\pi$
$787$	52.0000	1.85360	0.926800	+	0.375555i	$0.122548\pi$
$788$	8.00000	0.284988
$789$	−12.0000	−0.427211
$790$	0	0
$791$	60.0000	2.13335
$792$	18.0000	0.639602
$793$	−48.0000	−1.70453
$794$	12.0000	0.425864
$795$	0	0
$796$	18.0000	0.637993
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	−12.0000	−0.424795
$799$	50.0000	1.76887
$800$	0	0
$801$	−18.0000	−0.635999
$802$	−5.00000	−0.176556
$803$	21.0000	0.741074
$804$	9.00000	0.317406
$805$	0	0
$806$	−48.0000	−1.69073
$807$	18.0000	0.633630
$808$	4.00000	0.140720
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	0	0
$811$	4.00000	0.140459	0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000	0.140459	0.0702295	+	0.997531i	$0.477627\pi$
$812$	32.0000	1.12298
$813$	−30.0000	−1.05215
$814$	−6.00000	−0.210300
$815$	0	0
$816$	15.0000	0.525105
$817$	4.00000	0.139942
$818$	21.0000	0.734248
$819$	−144.000	−5.03177
$820$	0	0
$821$	16.0000	0.558404	0.279202	−	0.960232i	$-0.409930\pi$
$821$	16.0000	0.558404	0.279202	+	0.960232i	$0.409930\pi$
$822$	−9.00000	−0.313911
$823$	26.0000	0.906303	0.453152	−	0.891434i	$-0.350300\pi$
$823$	26.0000	0.906303	0.453152	+	0.891434i	$0.350300\pi$
$824$	−10.0000	−0.348367
$825$	0	0
$826$	−16.0000	−0.556711
$827$	17.0000	0.591148	0.295574	−	0.955320i	$-0.404489\pi$
$827$	17.0000	0.591148	0.295574	+	0.955320i	$0.404489\pi$
$828$	−6.00000	−0.208514
$829$	24.0000	0.833554	0.416777	−	0.909009i	$-0.363160\pi$
$829$	24.0000	0.833554	0.416777	+	0.909009i	$0.363160\pi$
$830$	0	0
$831$	−84.0000	−2.91393
$832$	6.00000	0.208013
$833$	−45.0000	−1.55916
$834$	57.0000	1.97375
$835$	0	0
$836$	−3.00000	−0.103757
$837$	72.0000	2.48868
$838$	3.00000	0.103633
$839$	26.0000	0.897620	0.448810	−	0.893627i	$-0.351848\pi$
$839$	26.0000	0.897620	0.448810	+	0.893627i	$0.351848\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	−14.0000	−0.482472
$843$	90.0000	3.09976
$844$	−1.00000	−0.0344214
$845$	0	0
$846$	−60.0000	−2.06284
$847$	8.00000	0.274883
$848$	12.0000	0.412082
$849$	−99.0000	−3.39767
$850$	0	0
$851$	2.00000	0.0685591
$852$	−12.0000	−0.411113
$853$	−12.0000	−0.410872	−0.205436	−	0.978671i	$-0.565861\pi$
$853$	−12.0000	−0.410872	−0.205436	+	0.978671i	$0.565861\pi$
$854$	32.0000	1.09502
$855$	0	0
$856$	−5.00000	−0.170896
$857$	21.0000	0.717346	0.358673	−	0.933463i	$-0.383229\pi$
$857$	21.0000	0.717346	0.358673	+	0.933463i	$0.383229\pi$
$858$	−54.0000	−1.84353
$859$	−11.0000	−0.375315	−0.187658	−	0.982235i	$-0.560090\pi$
$859$	−11.0000	−0.375315	−0.187658	+	0.982235i	$0.560090\pi$
$860$	0	0
$861$	−84.0000	−2.86271
$862$	−4.00000	−0.136241
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	−9.00000	−0.306186
$865$	0	0
$866$	−29.0000	−0.985460
$867$	−24.0000	−0.815083
$868$	32.0000	1.08615
$869$	−18.0000	−0.610608
$870$	0	0
$871$	−18.0000	−0.609907
$872$	−10.0000	−0.338643
$873$	84.0000	2.84297
$874$	1.00000	0.0338255
$875$	0	0
$876$	−21.0000	−0.709524
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	−6.00000	−0.202490
$879$	72.0000	2.42850
$880$	0	0
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	54.0000	1.81827
$883$	37.0000	1.24515	0.622575	−	0.782560i	$-0.286087\pi$
$883$	37.0000	1.24515	0.622575	+	0.782560i	$0.286087\pi$
$884$	−30.0000	−1.00901
$885$	0	0
$886$	39.0000	1.31023
$887$	−12.0000	−0.402921	−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000	−0.402921	−0.201460	+	0.979497i	$0.564569\pi$
$888$	6.00000	0.201347
$889$	−32.0000	−1.07325
$890$	0	0
$891$	27.0000	0.904534
$892$	0	0
$893$	10.0000	0.334637
$894$	−18.0000	−0.602010
$895$	0	0
$896$	−4.00000	−0.133631
$897$	18.0000	0.601003
$898$	5.00000	0.166852
$899$	64.0000	2.13452
$900$	0	0
$901$	−60.0000	−1.99889
$902$	−21.0000	−0.699224
$903$	−48.0000	−1.59734
$904$	−15.0000	−0.498893
$905$	0	0
$906$	−60.0000	−1.99337
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	8.00000	0.265489
$909$	24.0000	0.796030
$910$	0	0
$911$	−10.0000	−0.331315	−0.165657	−	0.986183i	$-0.552975\pi$
$911$	−10.0000	−0.331315	−0.165657	+	0.986183i	$0.552975\pi$
$912$	3.00000	0.0993399
$913$	−33.0000	−1.09214
$914$	7.00000	0.231539
$915$	0	0
$916$	−30.0000	−0.991228
$917$	−48.0000	−1.58510
$918$	45.0000	1.48522
$919$	52.0000	1.71532	0.857661	−	0.514216i	$-0.171917\pi$
$919$	52.0000	1.71532	0.857661	+	0.514216i	$0.171917\pi$
$920$	0	0
$921$	−27.0000	−0.889680
$922$	−24.0000	−0.790398
$923$	24.0000	0.789970
$924$	36.0000	1.18431
$925$	0	0
$926$	−26.0000	−0.854413
$927$	−60.0000	−1.97066
$928$	−8.00000	−0.262613
$929$	−22.0000	−0.721797	−0.360898	−	0.932605i	$-0.617530\pi$
$929$	−22.0000	−0.721797	−0.360898	+	0.932605i	$0.617530\pi$
$930$	0	0
$931$	−9.00000	−0.294963
$932$	14.0000	0.458585
$933$	−6.00000	−0.196431
$934$	−28.0000	−0.916188
$935$	0	0
$936$	36.0000	1.17670
$937$	9.00000	0.294017	0.147009	−	0.989135i	$-0.453036\pi$
$937$	9.00000	0.294017	0.147009	+	0.989135i	$0.453036\pi$
$938$	12.0000	0.391814
$939$	−30.0000	−0.979013
$940$	0	0
$941$	4.00000	0.130396	0.0651981	−	0.997872i	$-0.479232\pi$
$941$	4.00000	0.130396	0.0651981	+	0.997872i	$0.479232\pi$
$942$	42.0000	1.36843
$943$	7.00000	0.227951
$944$	4.00000	0.130189
$945$	0	0
$946$	−12.0000	−0.390154
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	18.0000	0.584613
$949$	42.0000	1.36338
$950$	0	0
$951$	36.0000	1.16738
$952$	20.0000	0.648204
$953$	27.0000	0.874616	0.437308	−	0.899312i	$-0.355932\pi$
$953$	27.0000	0.874616	0.437308	+	0.899312i	$0.355932\pi$
$954$	72.0000	2.33109
$955$	0	0
$956$	−6.00000	−0.194054
$957$	72.0000	2.32743
$958$	−4.00000	−0.129234
$959$	−12.0000	−0.387500
$960$	0	0
$961$	33.0000	1.06452
$962$	−12.0000	−0.386896
$963$	−30.0000	−0.966736
$964$	23.0000	0.740780
$965$	0	0
$966$	−12.0000	−0.386094
$967$	28.0000	0.900419	0.450210	−	0.892923i	$-0.351349\pi$
$967$	28.0000	0.900419	0.450210	+	0.892923i	$0.351349\pi$
$968$	−2.00000	−0.0642824
$969$	−15.0000	−0.481869
$970$	0	0
$971$	15.0000	0.481373	0.240686	−	0.970603i	$-0.422627\pi$
$971$	15.0000	0.481373	0.240686	+	0.970603i	$0.422627\pi$
$972$	0	0
$973$	76.0000	2.43645
$974$	30.0000	0.961262
$975$	0	0
$976$	−8.00000	−0.256074
$977$	−17.0000	−0.543878	−0.271939	−	0.962314i	$-0.587665\pi$
$977$	−17.0000	−0.543878	−0.271939	+	0.962314i	$0.587665\pi$
$978$	15.0000	0.479647
$979$	−9.00000	−0.287641
$980$	0	0
$981$	−60.0000	−1.91565
$982$	0	0
$983$	−42.0000	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$984$	21.0000	0.669456
$985$	0	0
$986$	40.0000	1.27386
$987$	−120.000	−3.81964
$988$	−6.00000	−0.190885
$989$	4.00000	0.127193
$990$	0	0
$991$	2.00000	0.0635321	0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000	0.0635321	0.0317660	+	0.999495i	$0.489887\pi$
$992$	−8.00000	−0.254000
$993$	−75.0000	−2.38005
$994$	−16.0000	−0.507489
$995$	0	0
$996$	33.0000	1.04565
$997$	−22.0000	−0.696747	−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000	−0.696747	−0.348373	+	0.937356i	$0.613266\pi$
$998$	−12.0000	−0.379853
$999$	18.0000	0.569495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.e.1.1	yes	1
4.3	odd	2		9200.2.a.bl.1.1		1
5.2	odd	4		1150.2.b.a.599.2		2
5.3	odd	4		1150.2.b.a.599.1		2
5.4	even	2		1150.2.a.d.1.1	✓	1
20.19	odd	2		9200.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.2.a.d.1.1	✓	1	5.4	even	2
1150.2.a.e.1.1	yes	1	1.1	even	1	trivial
1150.2.b.a.599.1		2	5.3	odd	4
1150.2.b.a.599.2		2	5.2	odd	4
9200.2.a.a.1.1		1	20.19	odd	2
9200.2.a.bl.1.1		1	4.3	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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