LMFDB - Embedded newform 1815.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, 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("1815.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.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:	$14.4928479669$
Analytic rank:	$0$
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	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +4.00000 q^{13} +2.00000 q^{14} -1.00000 q^{15} -1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} -6.00000 q^{19} +1.00000 q^{20} -2.00000 q^{21} +4.00000 q^{23} +3.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} +2.00000 q^{28} +6.00000 q^{29} +1.00000 q^{30} +8.00000 q^{31} -5.00000 q^{32} +6.00000 q^{34} +2.00000 q^{35} -1.00000 q^{36} -6.00000 q^{37} +6.00000 q^{38} +4.00000 q^{39} -3.00000 q^{40} -6.00000 q^{41} +2.00000 q^{42} -6.00000 q^{43} -1.00000 q^{45} -4.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} -6.00000 q^{51} -4.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} -6.00000 q^{56} -6.00000 q^{57} -6.00000 q^{58} +1.00000 q^{60} +4.00000 q^{61} -8.00000 q^{62} -2.00000 q^{63} +7.00000 q^{64} -4.00000 q^{65} +12.0000 q^{67} +6.00000 q^{68} +4.00000 q^{69} -2.00000 q^{70} +8.00000 q^{71} +3.00000 q^{72} +16.0000 q^{73} +6.00000 q^{74} +1.00000 q^{75} +6.00000 q^{76} -4.00000 q^{78} +2.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} +2.00000 q^{84} +6.00000 q^{85} +6.00000 q^{86} +6.00000 q^{87} +10.0000 q^{89} +1.00000 q^{90} -8.00000 q^{91} -4.00000 q^{92} +8.00000 q^{93} -8.00000 q^{94} +6.00000 q^{95} -5.00000 q^{96} -6.00000 q^{97} +3.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.00000	−0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−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	$0.623376\pi$
$8$	3.00000	1.06066
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	2.00000	0.534522
$15$	−1.00000	−0.258199
$16$	−1.00000	−0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−1.00000	−0.235702
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	1.00000	0.223607
$21$	−2.00000	−0.436436
$22$	0	0
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	3.00000	0.612372
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	1.00000	0.192450
$28$	2.00000	0.377964
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	1.00000	0.182574
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	6.00000	1.02899
$35$	2.00000	0.338062
$36$	−1.00000	−0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	6.00000	0.973329
$39$	4.00000	0.640513
$40$	−3.00000	−0.474342
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	2.00000	0.308607
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−4.00000	−0.589768
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	−1.00000	−0.141421
$51$	−6.00000	−0.840168
$52$	−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
$56$	−6.00000	−0.801784
$57$	−6.00000	−0.794719
$58$	−6.00000	−0.787839
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	1.00000	0.129099
$61$	4.00000	0.512148	0.256074	−	0.966657i	$-0.417571\pi$
$61$	4.00000	0.512148	0.256074	+	0.966657i	$0.417571\pi$
$62$	−8.00000	−1.01600
$63$	−2.00000	−0.251976
$64$	7.00000	0.875000
$65$	−4.00000	−0.496139
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	6.00000	0.727607
$69$	4.00000	0.481543
$70$	−2.00000	−0.239046
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	3.00000	0.353553
$73$	16.0000	1.87266	0.936329	−	0.351123i	$-0.114200\pi$
$73$	16.0000	1.87266	0.936329	+	0.351123i	$0.114200\pi$
$74$	6.00000	0.697486
$75$	1.00000	0.115470
$76$	6.00000	0.688247
$77$	0	0
$78$	−4.00000	−0.452911
$79$	2.00000	0.225018	0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000	0.225018	0.112509	+	0.993651i	$0.464111\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	2.00000	0.218218
$85$	6.00000	0.650791
$86$	6.00000	0.646997
$87$	6.00000	0.643268
$88$	0	0
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	1.00000	0.105409
$91$	−8.00000	−0.838628
$92$	−4.00000	−0.417029
$93$	8.00000	0.829561
$94$	−8.00000	−0.825137
$95$	6.00000	0.615587
$96$	−5.00000	−0.510310
$97$	−6.00000	−0.609208	−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000	−0.609208	−0.304604	+	0.952479i	$0.598524\pi$
$98$	3.00000	0.303046
$99$	0	0
$100$	−1.00000	−0.100000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	6.00000	0.594089
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	12.0000	1.17670
$105$	2.00000	0.195180
$106$	−6.00000	−0.582772
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	−1.00000	−0.0962250
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	−6.00000	−0.569495
$112$	2.00000	0.188982
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	6.00000	0.561951
$115$	−4.00000	−0.373002
$116$	−6.00000	−0.557086
$117$	4.00000	0.369800
$118$	0	0
$119$	12.0000	1.10004
$120$	−3.00000	−0.273861
$121$	0	0
$122$	−4.00000	−0.362143
$123$	−6.00000	−0.541002
$124$	−8.00000	−0.718421
$125$	−1.00000	−0.0894427
$126$	2.00000	0.178174
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	3.00000	0.265165
$129$	−6.00000	−0.528271
$130$	4.00000	0.350823
$131$	16.0000	1.39793	0.698963	−	0.715158i	$-0.253645\pi$
$131$	16.0000	1.39793	0.698963	+	0.715158i	$0.253645\pi$
$132$	0	0
$133$	12.0000	1.04053
$134$	−12.0000	−1.03664
$135$	−1.00000	−0.0860663
$136$	−18.0000	−1.54349
$137$	14.0000	1.19610	0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000	1.19610	0.598050	+	0.801459i	$0.295942\pi$
$138$	−4.00000	−0.340503
$139$	−22.0000	−1.86602	−0.933008	−	0.359856i	$-0.882826\pi$
$139$	−22.0000	−1.86602	−0.933008	+	0.359856i	$0.882826\pi$
$140$	−2.00000	−0.169031
$141$	8.00000	0.673722
$142$	−8.00000	−0.671345
$143$	0	0
$144$	−1.00000	−0.0833333
$145$	−6.00000	−0.498273
$146$	−16.0000	−1.32417
$147$	−3.00000	−0.247436
$148$	6.00000	0.493197
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	−1.00000	−0.0816497
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	−18.0000	−1.45999
$153$	−6.00000	−0.485071
$154$	0	0
$155$	−8.00000	−0.642575
$156$	−4.00000	−0.320256
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	−2.00000	−0.159111
$159$	6.00000	0.475831
$160$	5.00000	0.395285
$161$	−8.00000	−0.630488
$162$	−1.00000	−0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	−6.00000	−0.462910
$169$	3.00000	0.230769
$170$	−6.00000	−0.460179
$171$	−6.00000	−0.458831
$172$	6.00000	0.457496
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	−6.00000	−0.454859
$175$	−2.00000	−0.151186
$176$	0	0
$177$	0	0
$178$	−10.0000	−0.749532
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	1.00000	0.0745356
$181$	−26.0000	−1.93256	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−26.0000	−1.93256	−0.966282	+	0.257485i	$0.917106\pi$
$182$	8.00000	0.592999
$183$	4.00000	0.295689
$184$	12.0000	0.884652
$185$	6.00000	0.441129
$186$	−8.00000	−0.586588
$187$	0	0
$188$	−8.00000	−0.583460
$189$	−2.00000	−0.145479
$190$	−6.00000	−0.435286
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	7.00000	0.505181
$193$	20.0000	1.43963	0.719816	−	0.694165i	$-0.244226\pi$
$193$	20.0000	1.43963	0.719816	+	0.694165i	$0.244226\pi$
$194$	6.00000	0.430775
$195$	−4.00000	−0.286446
$196$	3.00000	0.214286
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	0	0
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	3.00000	0.212132
$201$	12.0000	0.846415
$202$	−14.0000	−0.985037
$203$	−12.0000	−0.842235
$204$	6.00000	0.420084
$205$	6.00000	0.419058
$206$	8.00000	0.557386
$207$	4.00000	0.278019
$208$	−4.00000	−0.277350
$209$	0	0
$210$	−2.00000	−0.138013
$211$	−22.0000	−1.51454	−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000	−1.51454	−0.757271	+	0.653101i	$0.773468\pi$
$212$	−6.00000	−0.412082
$213$	8.00000	0.548151
$214$	−8.00000	−0.546869
$215$	6.00000	0.409197
$216$	3.00000	0.204124
$217$	−16.0000	−1.08615
$218$	0	0
$219$	16.0000	1.08118
$220$	0	0
$221$	−24.0000	−1.61441
$222$	6.00000	0.402694
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	10.0000	0.668153
$225$	1.00000	0.0666667
$226$	−6.00000	−0.399114
$227$	16.0000	1.06196	0.530979	−	0.847385i	$-0.321824\pi$
$227$	16.0000	1.06196	0.530979	+	0.847385i	$0.321824\pi$
$228$	6.00000	0.397360
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	4.00000	0.263752
$231$	0	0
$232$	18.0000	1.18176
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	−4.00000	−0.261488
$235$	−8.00000	−0.521862
$236$	0	0
$237$	2.00000	0.129914
$238$	−12.0000	−0.777844
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	1.00000	0.0645497
$241$	20.0000	1.28831	0.644157	−	0.764894i	$-0.277208\pi$
$241$	20.0000	1.28831	0.644157	+	0.764894i	$0.277208\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−4.00000	−0.256074
$245$	3.00000	0.191663
$246$	6.00000	0.382546
$247$	−24.0000	−1.52708
$248$	24.0000	1.52400
$249$	0	0
$250$	1.00000	0.0632456
$251$	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
$253$	0	0
$254$	2.00000	0.125491
$255$	6.00000	0.375735
$256$	−17.0000	−1.06250
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	6.00000	0.373544
$259$	12.0000	0.745644
$260$	4.00000	0.248069
$261$	6.00000	0.371391
$262$	−16.0000	−0.988483
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	0	0
$265$	−6.00000	−0.368577
$266$	−12.0000	−0.735767
$267$	10.0000	0.611990
$268$	−12.0000	−0.733017
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	1.00000	0.0608581
$271$	14.0000	0.850439	0.425220	−	0.905090i	$-0.360197\pi$
$271$	14.0000	0.850439	0.425220	+	0.905090i	$0.360197\pi$
$272$	6.00000	0.363803
$273$	−8.00000	−0.484182
$274$	−14.0000	−0.845771
$275$	0	0
$276$	−4.00000	−0.240772
$277$	4.00000	0.240337	0.120168	−	0.992754i	$-0.461657\pi$
$277$	4.00000	0.240337	0.120168	+	0.992754i	$0.461657\pi$
$278$	22.0000	1.31947
$279$	8.00000	0.478947
$280$	6.00000	0.358569
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	−8.00000	−0.476393
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	−8.00000	−0.474713
$285$	6.00000	0.355409
$286$	0	0
$287$	12.0000	0.708338
$288$	−5.00000	−0.294628
$289$	19.0000	1.11765
$290$	6.00000	0.352332
$291$	−6.00000	−0.351726
$292$	−16.0000	−0.936329
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	3.00000	0.174964
$295$	0	0
$296$	−18.0000	−1.04623
$297$	0	0
$298$	6.00000	0.347571
$299$	16.0000	0.925304
$300$	−1.00000	−0.0577350
$301$	12.0000	0.691669
$302$	−2.00000	−0.115087
$303$	14.0000	0.804279
$304$	6.00000	0.344124
$305$	−4.00000	−0.229039
$306$	6.00000	0.342997
$307$	14.0000	0.799022	0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000	0.799022	0.399511	+	0.916728i	$0.369180\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	8.00000	0.454369
$311$	−28.0000	−1.58773	−0.793867	−	0.608091i	$-0.791935\pi$
$311$	−28.0000	−1.58773	−0.793867	+	0.608091i	$0.791935\pi$
$312$	12.0000	0.679366
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	−18.0000	−1.01580
$315$	2.00000	0.112687
$316$	−2.00000	−0.112509
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	−6.00000	−0.336463
$319$	0	0
$320$	−7.00000	−0.391312
$321$	8.00000	0.446516
$322$	8.00000	0.445823
$323$	36.0000	2.00309
$324$	−1.00000	−0.0555556
$325$	4.00000	0.221880
$326$	4.00000	0.221540
$327$	0	0
$328$	−18.0000	−0.993884
$329$	−16.0000	−0.882109
$330$	0	0
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	0	0
$333$	−6.00000	−0.328798
$334$	0	0
$335$	−12.0000	−0.655630
$336$	2.00000	0.109109
$337$	−8.00000	−0.435788	−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000	−0.435788	−0.217894	+	0.975972i	$0.569919\pi$
$338$	−3.00000	−0.163178
$339$	6.00000	0.325875
$340$	−6.00000	−0.325396
$341$	0	0
$342$	6.00000	0.324443
$343$	20.0000	1.07990
$344$	−18.0000	−0.970495
$345$	−4.00000	−0.215353
$346$	−18.0000	−0.967686
$347$	−8.00000	−0.429463	−0.214731	−	0.976673i	$-0.568888\pi$
$347$	−8.00000	−0.429463	−0.214731	+	0.976673i	$0.568888\pi$
$348$	−6.00000	−0.321634
$349$	36.0000	1.92704	0.963518	−	0.267644i	$-0.0862451\pi$
$349$	36.0000	1.92704	0.963518	+	0.267644i	$0.0862451\pi$
$350$	2.00000	0.106904
$351$	4.00000	0.213504
$352$	0	0
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	0	0
$355$	−8.00000	−0.424596
$356$	−10.0000	−0.529999
$357$	12.0000	0.635107
$358$	−12.0000	−0.634220
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	−3.00000	−0.158114
$361$	17.0000	0.894737
$362$	26.0000	1.36653
$363$	0	0
$364$	8.00000	0.419314
$365$	−16.0000	−0.837478
$366$	−4.00000	−0.209083
$367$	24.0000	1.25279	0.626395	−	0.779506i	$-0.284530\pi$
$367$	24.0000	1.25279	0.626395	+	0.779506i	$0.284530\pi$
$368$	−4.00000	−0.208514
$369$	−6.00000	−0.312348
$370$	−6.00000	−0.311925
$371$	−12.0000	−0.623009
$372$	−8.00000	−0.414781
$373$	24.0000	1.24267	0.621336	−	0.783544i	$-0.286590\pi$
$373$	24.0000	1.24267	0.621336	+	0.783544i	$0.286590\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	24.0000	1.23771
$377$	24.0000	1.23606
$378$	2.00000	0.102869
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	−6.00000	−0.307794
$381$	−2.00000	−0.102463
$382$	0	0
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	−20.0000	−1.01797
$387$	−6.00000	−0.304997
$388$	6.00000	0.304604
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	4.00000	0.202548
$391$	−24.0000	−1.21373
$392$	−9.00000	−0.454569
$393$	16.0000	0.807093
$394$	−18.0000	−0.906827
$395$	−2.00000	−0.100631
$396$	0	0
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	−16.0000	−0.802008
$399$	12.0000	0.600751
$400$	−1.00000	−0.0500000
$401$	−10.0000	−0.499376	−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000	−0.499376	−0.249688	+	0.968326i	$0.580328\pi$
$402$	−12.0000	−0.598506
$403$	32.0000	1.59403
$404$	−14.0000	−0.696526
$405$	−1.00000	−0.0496904
$406$	12.0000	0.595550
$407$	0	0
$408$	−18.0000	−0.891133
$409$	−4.00000	−0.197787	−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	−4.00000	−0.197787	−0.0988936	+	0.995098i	$0.531530\pi$
$410$	−6.00000	−0.296319
$411$	14.0000	0.690569
$412$	8.00000	0.394132
$413$	0	0
$414$	−4.00000	−0.196589
$415$	0	0
$416$	−20.0000	−0.980581
$417$	−22.0000	−1.07734
$418$	0	0
$419$	−28.0000	−1.36789	−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000	−1.36789	−0.683945	+	0.729534i	$0.739737\pi$
$420$	−2.00000	−0.0975900
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	22.0000	1.07094
$423$	8.00000	0.388973
$424$	18.0000	0.874157
$425$	−6.00000	−0.291043
$426$	−8.00000	−0.387601
$427$	−8.00000	−0.387147
$428$	−8.00000	−0.386695
$429$	0	0
$430$	−6.00000	−0.289346
$431$	−12.0000	−0.578020	−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000	−0.578020	−0.289010	+	0.957326i	$0.593326\pi$
$432$	−1.00000	−0.0481125
$433$	18.0000	0.865025	0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000	0.865025	0.432512	+	0.901628i	$0.357627\pi$
$434$	16.0000	0.768025
$435$	−6.00000	−0.287678
$436$	0	0
$437$	−24.0000	−1.14808
$438$	−16.0000	−0.764510
$439$	−26.0000	−1.24091	−0.620456	−	0.784241i	$-0.713053\pi$
$439$	−26.0000	−1.24091	−0.620456	+	0.784241i	$0.713053\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	24.0000	1.14156
$443$	16.0000	0.760183	0.380091	−	0.924949i	$-0.375893\pi$
$443$	16.0000	0.760183	0.380091	+	0.924949i	$0.375893\pi$
$444$	6.00000	0.284747
$445$	−10.0000	−0.474045
$446$	16.0000	0.757622
$447$	−6.00000	−0.283790
$448$	−14.0000	−0.661438
$449$	−30.0000	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	−6.00000	−0.282216
$453$	2.00000	0.0939682
$454$	−16.0000	−0.750917
$455$	8.00000	0.375046
$456$	−18.0000	−0.842927
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	22.0000	1.02799
$459$	−6.00000	−0.280056
$460$	4.00000	0.186501
$461$	−22.0000	−1.02464	−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000	−1.02464	−0.512321	+	0.858794i	$0.671214\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	−6.00000	−0.278543
$465$	−8.00000	−0.370991
$466$	−6.00000	−0.277945
$467$	16.0000	0.740392	0.370196	−	0.928954i	$-0.379291\pi$
$467$	16.0000	0.740392	0.370196	+	0.928954i	$0.379291\pi$
$468$	−4.00000	−0.184900
$469$	−24.0000	−1.10822
$470$	8.00000	0.369012
$471$	18.0000	0.829396
$472$	0	0
$473$	0	0
$474$	−2.00000	−0.0918630
$475$	−6.00000	−0.275299
$476$	−12.0000	−0.550019
$477$	6.00000	0.274721
$478$	12.0000	0.548867
$479$	28.0000	1.27935	0.639676	−	0.768644i	$-0.279068\pi$
$479$	28.0000	1.27935	0.639676	+	0.768644i	$0.279068\pi$
$480$	5.00000	0.228218
$481$	−24.0000	−1.09431
$482$	−20.0000	−0.910975
$483$	−8.00000	−0.364013
$484$	0	0
$485$	6.00000	0.272446
$486$	−1.00000	−0.0453609
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	12.0000	0.543214
$489$	−4.00000	−0.180886
$490$	−3.00000	−0.135526
$491$	−36.0000	−1.62466	−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000	−1.62466	−0.812329	+	0.583200i	$0.801800\pi$
$492$	6.00000	0.270501
$493$	−36.0000	−1.62136
$494$	24.0000	1.07981
$495$	0	0
$496$	−8.00000	−0.359211
$497$	−16.0000	−0.717698
$498$	0	0
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	−20.0000	−0.892644
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	−6.00000	−0.267261
$505$	−14.0000	−0.622992
$506$	0	0
$507$	3.00000	0.133235
$508$	2.00000	0.0887357
$509$	14.0000	0.620539	0.310270	−	0.950649i	$-0.399581\pi$
$509$	14.0000	0.620539	0.310270	+	0.950649i	$0.399581\pi$
$510$	−6.00000	−0.265684
$511$	−32.0000	−1.41560
$512$	11.0000	0.486136
$513$	−6.00000	−0.264906
$514$	−18.0000	−0.793946
$515$	8.00000	0.352522
$516$	6.00000	0.264135
$517$	0	0
$518$	−12.0000	−0.527250
$519$	18.0000	0.790112
$520$	−12.0000	−0.526235
$521$	−10.0000	−0.438108	−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000	−0.438108	−0.219054	+	0.975713i	$0.570297\pi$
$522$	−6.00000	−0.262613
$523$	−14.0000	−0.612177	−0.306089	−	0.952003i	$-0.599020\pi$
$523$	−14.0000	−0.612177	−0.306089	+	0.952003i	$0.599020\pi$
$524$	−16.0000	−0.698963
$525$	−2.00000	−0.0872872
$526$	24.0000	1.04645
$527$	−48.0000	−2.09091
$528$	0	0
$529$	−7.00000	−0.304348
$530$	6.00000	0.260623
$531$	0	0
$532$	−12.0000	−0.520266
$533$	−24.0000	−1.03956
$534$	−10.0000	−0.432742
$535$	−8.00000	−0.345870
$536$	36.0000	1.55496
$537$	12.0000	0.517838
$538$	−6.00000	−0.258678
$539$	0	0
$540$	1.00000	0.0430331
$541$	32.0000	1.37579	0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000	1.37579	0.687894	+	0.725811i	$0.258536\pi$
$542$	−14.0000	−0.601351
$543$	−26.0000	−1.11577
$544$	30.0000	1.28624
$545$	0	0
$546$	8.00000	0.342368
$547$	34.0000	1.45374	0.726868	−	0.686778i	$-0.240975\pi$
$547$	34.0000	1.45374	0.726868	+	0.686778i	$0.240975\pi$
$548$	−14.0000	−0.598050
$549$	4.00000	0.170716
$550$	0	0
$551$	−36.0000	−1.53365
$552$	12.0000	0.510754
$553$	−4.00000	−0.170097
$554$	−4.00000	−0.169944
$555$	6.00000	0.254686
$556$	22.0000	0.933008
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	−8.00000	−0.338667
$559$	−24.0000	−1.01509
$560$	−2.00000	−0.0845154
$561$	0	0
$562$	22.0000	0.928014
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	−8.00000	−0.336861
$565$	−6.00000	−0.252422
$566$	14.0000	0.588464
$567$	−2.00000	−0.0839921
$568$	24.0000	1.00702
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	−6.00000	−0.251312
$571$	−26.0000	−1.08807	−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000	−1.08807	−0.544033	+	0.839064i	$0.683103\pi$
$572$	0	0
$573$	0	0
$574$	−12.0000	−0.500870
$575$	4.00000	0.166812
$576$	7.00000	0.291667
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	−19.0000	−0.790296
$579$	20.0000	0.831172
$580$	6.00000	0.249136
$581$	0	0
$582$	6.00000	0.248708
$583$	0	0
$584$	48.0000	1.98625
$585$	−4.00000	−0.165380
$586$	18.0000	0.743573
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	3.00000	0.123718
$589$	−48.0000	−1.97781
$590$	0	0
$591$	18.0000	0.740421
$592$	6.00000	0.246598
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	0	0
$595$	−12.0000	−0.491952
$596$	6.00000	0.245770
$597$	16.0000	0.654836
$598$	−16.0000	−0.654289
$599$	−4.00000	−0.163436	−0.0817178	−	0.996656i	$-0.526041\pi$
$599$	−4.00000	−0.163436	−0.0817178	+	0.996656i	$0.526041\pi$
$600$	3.00000	0.122474
$601$	24.0000	0.978980	0.489490	−	0.872009i	$-0.337183\pi$
$601$	24.0000	0.978980	0.489490	+	0.872009i	$0.337183\pi$
$602$	−12.0000	−0.489083
$603$	12.0000	0.488678
$604$	−2.00000	−0.0813788
$605$	0	0
$606$	−14.0000	−0.568711
$607$	−42.0000	−1.70473	−0.852364	−	0.522949i	$-0.824832\pi$
$607$	−42.0000	−1.70473	−0.852364	+	0.522949i	$0.824832\pi$
$608$	30.0000	1.21666
$609$	−12.0000	−0.486265
$610$	4.00000	0.161955
$611$	32.0000	1.29458
$612$	6.00000	0.242536
$613$	8.00000	0.323117	0.161558	−	0.986863i	$-0.448348\pi$
$613$	8.00000	0.323117	0.161558	+	0.986863i	$0.448348\pi$
$614$	−14.0000	−0.564994
$615$	6.00000	0.241943
$616$	0	0
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	8.00000	0.321807
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	8.00000	0.321288
$621$	4.00000	0.160514
$622$	28.0000	1.12270
$623$	−20.0000	−0.801283
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	26.0000	1.03917
$627$	0	0
$628$	−18.0000	−0.718278
$629$	36.0000	1.43541
$630$	−2.00000	−0.0796819
$631$	16.0000	0.636950	0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000	0.636950	0.318475	+	0.947931i	$0.396829\pi$
$632$	6.00000	0.238667
$633$	−22.0000	−0.874421
$634$	30.0000	1.19145
$635$	2.00000	0.0793676
$636$	−6.00000	−0.237915
$637$	−12.0000	−0.475457
$638$	0	0
$639$	8.00000	0.316475
$640$	−3.00000	−0.118585
$641$	−38.0000	−1.50091	−0.750455	−	0.660922i	$-0.770166\pi$
$641$	−38.0000	−1.50091	−0.750455	+	0.660922i	$0.770166\pi$
$642$	−8.00000	−0.315735
$643$	12.0000	0.473234	0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000	0.473234	0.236617	+	0.971603i	$0.423961\pi$
$644$	8.00000	0.315244
$645$	6.00000	0.236250
$646$	−36.0000	−1.41640
$647$	−20.0000	−0.786281	−0.393141	−	0.919478i	$-0.628611\pi$
$647$	−20.0000	−0.786281	−0.393141	+	0.919478i	$0.628611\pi$
$648$	3.00000	0.117851
$649$	0	0
$650$	−4.00000	−0.156893
$651$	−16.0000	−0.627089
$652$	4.00000	0.156652
$653$	−10.0000	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$654$	0	0
$655$	−16.0000	−0.625172
$656$	6.00000	0.234261
$657$	16.0000	0.624219
$658$	16.0000	0.623745
$659$	40.0000	1.55818	0.779089	−	0.626913i	$-0.215682\pi$
$659$	40.0000	1.55818	0.779089	+	0.626913i	$0.215682\pi$
$660$	0	0
$661$	10.0000	0.388955	0.194477	−	0.980907i	$-0.437699\pi$
$661$	10.0000	0.388955	0.194477	+	0.980907i	$0.437699\pi$
$662$	28.0000	1.08825
$663$	−24.0000	−0.932083
$664$	0	0
$665$	−12.0000	−0.465340
$666$	6.00000	0.232495
$667$	24.0000	0.929284
$668$	0	0
$669$	−16.0000	−0.618596
$670$	12.0000	0.463600
$671$	0	0
$672$	10.0000	0.385758
$673$	4.00000	0.154189	0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000	0.154189	0.0770943	+	0.997024i	$0.475436\pi$
$674$	8.00000	0.308148
$675$	1.00000	0.0384900
$676$	−3.00000	−0.115385
$677$	2.00000	0.0768662	0.0384331	−	0.999261i	$-0.487763\pi$
$677$	2.00000	0.0768662	0.0384331	+	0.999261i	$0.487763\pi$
$678$	−6.00000	−0.230429
$679$	12.0000	0.460518
$680$	18.0000	0.690268
$681$	16.0000	0.613121
$682$	0	0
$683$	28.0000	1.07139	0.535695	−	0.844411i	$-0.320050\pi$
$683$	28.0000	1.07139	0.535695	+	0.844411i	$0.320050\pi$
$684$	6.00000	0.229416
$685$	−14.0000	−0.534913
$686$	−20.0000	−0.763604
$687$	−22.0000	−0.839352
$688$	6.00000	0.228748
$689$	24.0000	0.914327
$690$	4.00000	0.152277
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	−18.0000	−0.684257
$693$	0	0
$694$	8.00000	0.303676
$695$	22.0000	0.834508
$696$	18.0000	0.682288
$697$	36.0000	1.36360
$698$	−36.0000	−1.36262
$699$	6.00000	0.226941
$700$	2.00000	0.0755929
$701$	−14.0000	−0.528773	−0.264386	−	0.964417i	$-0.585169\pi$
$701$	−14.0000	−0.528773	−0.264386	+	0.964417i	$0.585169\pi$
$702$	−4.00000	−0.150970
$703$	36.0000	1.35777
$704$	0	0
$705$	−8.00000	−0.301297
$706$	−18.0000	−0.677439
$707$	−28.0000	−1.05305
$708$	0	0
$709$	−6.00000	−0.225335	−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000	−0.225335	−0.112667	+	0.993633i	$0.535939\pi$
$710$	8.00000	0.300235
$711$	2.00000	0.0750059
$712$	30.0000	1.12430
$713$	32.0000	1.19841
$714$	−12.0000	−0.449089
$715$	0	0
$716$	−12.0000	−0.448461
$717$	−12.0000	−0.448148
$718$	−8.00000	−0.298557
$719$	−40.0000	−1.49175	−0.745874	−	0.666087i	$-0.767968\pi$
$719$	−40.0000	−1.49175	−0.745874	+	0.666087i	$0.767968\pi$
$720$	1.00000	0.0372678
$721$	16.0000	0.595871
$722$	−17.0000	−0.632674
$723$	20.0000	0.743808
$724$	26.0000	0.966282
$725$	6.00000	0.222834
$726$	0	0
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	−24.0000	−0.889499
$729$	1.00000	0.0370370
$730$	16.0000	0.592187
$731$	36.0000	1.33151
$732$	−4.00000	−0.147844
$733$	−44.0000	−1.62518	−0.812589	−	0.582838i	$-0.801942\pi$
$733$	−44.0000	−1.62518	−0.812589	+	0.582838i	$0.801942\pi$
$734$	−24.0000	−0.885856
$735$	3.00000	0.110657
$736$	−20.0000	−0.737210
$737$	0	0
$738$	6.00000	0.220863
$739$	−34.0000	−1.25071	−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000	−1.25071	−0.625355	+	0.780340i	$0.715046\pi$
$740$	−6.00000	−0.220564
$741$	−24.0000	−0.881662
$742$	12.0000	0.440534
$743$	−20.0000	−0.733729	−0.366864	−	0.930274i	$-0.619569\pi$
$743$	−20.0000	−0.733729	−0.366864	+	0.930274i	$0.619569\pi$
$744$	24.0000	0.879883
$745$	6.00000	0.219823
$746$	−24.0000	−0.878702
$747$	0	0
$748$	0	0
$749$	−16.0000	−0.584627
$750$	1.00000	0.0365148
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	−8.00000	−0.291730
$753$	20.0000	0.728841
$754$	−24.0000	−0.874028
$755$	−2.00000	−0.0727875
$756$	2.00000	0.0727393
$757$	10.0000	0.363456	0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000	0.363456	0.181728	+	0.983349i	$0.441831\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	18.0000	0.652929
$761$	−50.0000	−1.81250	−0.906249	−	0.422744i	$-0.861067\pi$
$761$	−50.0000	−1.81250	−0.906249	+	0.422744i	$0.861067\pi$
$762$	2.00000	0.0724524
$763$	0	0
$764$	0	0
$765$	6.00000	0.216930
$766$	−36.0000	−1.30073
$767$	0	0
$768$	−17.0000	−0.613435
$769$	40.0000	1.44244	0.721218	−	0.692708i	$-0.243582\pi$
$769$	40.0000	1.44244	0.721218	+	0.692708i	$0.243582\pi$
$770$	0	0
$771$	18.0000	0.648254
$772$	−20.0000	−0.719816
$773$	54.0000	1.94225	0.971123	−	0.238581i	$-0.0766824\pi$
$773$	54.0000	1.94225	0.971123	+	0.238581i	$0.0766824\pi$
$774$	6.00000	0.215666
$775$	8.00000	0.287368
$776$	−18.0000	−0.646162
$777$	12.0000	0.430498
$778$	6.00000	0.215110
$779$	36.0000	1.28983
$780$	4.00000	0.143223
$781$	0	0
$782$	24.0000	0.858238
$783$	6.00000	0.214423
$784$	3.00000	0.107143
$785$	−18.0000	−0.642448
$786$	−16.0000	−0.570701
$787$	−22.0000	−0.784215	−0.392108	−	0.919919i	$-0.628254\pi$
$787$	−22.0000	−0.784215	−0.392108	+	0.919919i	$0.628254\pi$
$788$	−18.0000	−0.641223
$789$	−24.0000	−0.854423
$790$	2.00000	0.0711568
$791$	−12.0000	−0.426671
$792$	0	0
$793$	16.0000	0.568177
$794$	−14.0000	−0.496841
$795$	−6.00000	−0.212798
$796$	−16.0000	−0.567105
$797$	26.0000	0.920967	0.460484	−	0.887668i	$-0.347676\pi$
$797$	26.0000	0.920967	0.460484	+	0.887668i	$0.347676\pi$
$798$	−12.0000	−0.424795
$799$	−48.0000	−1.69812
$800$	−5.00000	−0.176777
$801$	10.0000	0.353333
$802$	10.0000	0.353112
$803$	0	0
$804$	−12.0000	−0.423207
$805$	8.00000	0.281963
$806$	−32.0000	−1.12715
$807$	6.00000	0.211210
$808$	42.0000	1.47755
$809$	46.0000	1.61727	0.808637	−	0.588308i	$-0.200206\pi$
$809$	46.0000	1.61727	0.808637	+	0.588308i	$0.200206\pi$
$810$	1.00000	0.0351364
$811$	50.0000	1.75574	0.877869	−	0.478901i	$-0.158965\pi$
$811$	50.0000	1.75574	0.877869	+	0.478901i	$0.158965\pi$
$812$	12.0000	0.421117
$813$	14.0000	0.491001
$814$	0	0
$815$	4.00000	0.140114
$816$	6.00000	0.210042
$817$	36.0000	1.25948
$818$	4.00000	0.139857
$819$	−8.00000	−0.279543
$820$	−6.00000	−0.209529
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	−14.0000	−0.488306
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	−24.0000	−0.836080
$825$	0	0
$826$	0	0
$827$	8.00000	0.278187	0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000	0.278187	0.139094	+	0.990279i	$0.455581\pi$
$828$	−4.00000	−0.139010
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	0	0
$831$	4.00000	0.138758
$832$	28.0000	0.970725
$833$	18.0000	0.623663
$834$	22.0000	0.761798
$835$	0	0
$836$	0	0
$837$	8.00000	0.276520
$838$	28.0000	0.967244
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	6.00000	0.207020
$841$	7.00000	0.241379
$842$	6.00000	0.206774
$843$	−22.0000	−0.757720
$844$	22.0000	0.757271
$845$	−3.00000	−0.103203
$846$	−8.00000	−0.275046
$847$	0	0
$848$	−6.00000	−0.206041
$849$	−14.0000	−0.480479
$850$	6.00000	0.205798
$851$	−24.0000	−0.822709
$852$	−8.00000	−0.274075
$853$	24.0000	0.821744	0.410872	−	0.911693i	$-0.365224\pi$
$853$	24.0000	0.821744	0.410872	+	0.911693i	$0.365224\pi$
$854$	8.00000	0.273754
$855$	6.00000	0.205196
$856$	24.0000	0.820303
$857$	−22.0000	−0.751506	−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000	−0.751506	−0.375753	+	0.926720i	$0.622616\pi$
$858$	0	0
$859$	−36.0000	−1.22830	−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000	−1.22830	−0.614152	+	0.789188i	$0.710502\pi$
$860$	−6.00000	−0.204598
$861$	12.0000	0.408959
$862$	12.0000	0.408722
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	−5.00000	−0.170103
$865$	−18.0000	−0.612018
$866$	−18.0000	−0.611665
$867$	19.0000	0.645274
$868$	16.0000	0.543075
$869$	0	0
$870$	6.00000	0.203419
$871$	48.0000	1.62642
$872$	0	0
$873$	−6.00000	−0.203069
$874$	24.0000	0.811812
$875$	2.00000	0.0676123
$876$	−16.0000	−0.540590
$877$	−32.0000	−1.08056	−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000	−1.08056	−0.540282	+	0.841484i	$0.681682\pi$
$878$	26.0000	0.877457
$879$	−18.0000	−0.607125
$880$	0	0
$881$	46.0000	1.54978	0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000	1.54978	0.774890	+	0.632096i	$0.217805\pi$
$882$	3.00000	0.101015
$883$	−52.0000	−1.74994	−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000	−1.74994	−0.874970	+	0.484178i	$0.839119\pi$
$884$	24.0000	0.807207
$885$	0	0
$886$	−16.0000	−0.537531
$887$	12.0000	0.402921	0.201460	−	0.979497i	$-0.435431\pi$
$887$	12.0000	0.402921	0.201460	+	0.979497i	$0.435431\pi$
$888$	−18.0000	−0.604040
$889$	4.00000	0.134156
$890$	10.0000	0.335201
$891$	0	0
$892$	16.0000	0.535720
$893$	−48.0000	−1.60626
$894$	6.00000	0.200670
$895$	−12.0000	−0.401116
$896$	−6.00000	−0.200446
$897$	16.0000	0.534224
$898$	30.0000	1.00111
$899$	48.0000	1.60089
$900$	−1.00000	−0.0333333
$901$	−36.0000	−1.19933
$902$	0	0
$903$	12.0000	0.399335
$904$	18.0000	0.598671
$905$	26.0000	0.864269
$906$	−2.00000	−0.0664455
$907$	20.0000	0.664089	0.332045	−	0.943264i	$-0.392262\pi$
$907$	20.0000	0.664089	0.332045	+	0.943264i	$0.392262\pi$
$908$	−16.0000	−0.530979
$909$	14.0000	0.464351
$910$	−8.00000	−0.265197
$911$	32.0000	1.06021	0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000	1.06021	0.530104	+	0.847933i	$0.322153\pi$
$912$	6.00000	0.198680
$913$	0	0
$914$	−8.00000	−0.264616
$915$	−4.00000	−0.132236
$916$	22.0000	0.726900
$917$	−32.0000	−1.05673
$918$	6.00000	0.198030
$919$	22.0000	0.725713	0.362857	−	0.931845i	$-0.381802\pi$
$919$	22.0000	0.725713	0.362857	+	0.931845i	$0.381802\pi$
$920$	−12.0000	−0.395628
$921$	14.0000	0.461316
$922$	22.0000	0.724531
$923$	32.0000	1.05329
$924$	0	0
$925$	−6.00000	−0.197279
$926$	8.00000	0.262896
$927$	−8.00000	−0.262754
$928$	−30.0000	−0.984798
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	8.00000	0.262330
$931$	18.0000	0.589926
$932$	−6.00000	−0.196537
$933$	−28.0000	−0.916679
$934$	−16.0000	−0.523536
$935$	0	0
$936$	12.0000	0.392232
$937$	−20.0000	−0.653372	−0.326686	−	0.945133i	$-0.605932\pi$
$937$	−20.0000	−0.653372	−0.326686	+	0.945133i	$0.605932\pi$
$938$	24.0000	0.783628
$939$	−26.0000	−0.848478
$940$	8.00000	0.260931
$941$	38.0000	1.23876	0.619382	−	0.785090i	$-0.287383\pi$
$941$	38.0000	1.23876	0.619382	+	0.785090i	$0.287383\pi$
$942$	−18.0000	−0.586472
$943$	−24.0000	−0.781548
$944$	0	0
$945$	2.00000	0.0650600
$946$	0	0
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	−2.00000	−0.0649570
$949$	64.0000	2.07753
$950$	6.00000	0.194666
$951$	−30.0000	−0.972817
$952$	36.0000	1.16677
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	12.0000	0.388108
$957$	0	0
$958$	−28.0000	−0.904639
$959$	−28.0000	−0.904167
$960$	−7.00000	−0.225924
$961$	33.0000	1.06452
$962$	24.0000	0.773791
$963$	8.00000	0.257796
$964$	−20.0000	−0.644157
$965$	−20.0000	−0.643823
$966$	8.00000	0.257396
$967$	46.0000	1.47926	0.739630	−	0.673014i	$-0.235000\pi$
$967$	46.0000	1.47926	0.739630	+	0.673014i	$0.235000\pi$
$968$	0	0
$969$	36.0000	1.15649
$970$	−6.00000	−0.192648
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	−1.00000	−0.0320750
$973$	44.0000	1.41058
$974$	16.0000	0.512673
$975$	4.00000	0.128103
$976$	−4.00000	−0.128037
$977$	30.0000	0.959785	0.479893	−	0.877327i	$-0.340676\pi$
$977$	30.0000	0.959785	0.479893	+	0.877327i	$0.340676\pi$
$978$	4.00000	0.127906
$979$	0	0
$980$	−3.00000	−0.0958315
$981$	0	0
$982$	36.0000	1.14881
$983$	−4.00000	−0.127580	−0.0637901	−	0.997963i	$-0.520319\pi$
$983$	−4.00000	−0.127580	−0.0637901	+	0.997963i	$0.520319\pi$
$984$	−18.0000	−0.573819
$985$	−18.0000	−0.573528
$986$	36.0000	1.14647
$987$	−16.0000	−0.509286
$988$	24.0000	0.763542
$989$	−24.0000	−0.763156
$990$	0	0
$991$	−32.0000	−1.01651	−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000	−1.01651	−0.508257	+	0.861206i	$0.669710\pi$
$992$	−40.0000	−1.27000
$993$	−28.0000	−0.888553
$994$	16.0000	0.507489
$995$	−16.0000	−0.507234
$996$	0	0
$997$	24.0000	0.760088	0.380044	−	0.924968i	$-0.375909\pi$
$997$	24.0000	0.760088	0.380044	+	0.924968i	$0.375909\pi$
$998$	4.00000	0.126618
$999$	−6.00000	−0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.a.a.1.1	✓	1
3.2	odd	2		5445.2.a.j.1.1		1
5.4	even	2		9075.2.a.n.1.1		1
11.10	odd	2		1815.2.a.e.1.1	yes	1
33.32	even	2		5445.2.a.e.1.1		1
55.54	odd	2		9075.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.a.a.1.1	✓	1	1.1	even	1	trivial
1815.2.a.e.1.1	yes	1	11.10	odd	2
5445.2.a.e.1.1		1	33.32	even	2
5445.2.a.j.1.1		1	3.2	odd	2
9075.2.a.d.1.1		1	55.54	odd	2
9075.2.a.n.1.1		1	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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