LMFDB - Embedded newform 1850.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(1,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, 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("1850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.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:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 370)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.00000 q^{11} +2.00000 q^{12} +4.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} +1.00000 q^{18} +2.00000 q^{19} +2.00000 q^{21} +3.00000 q^{22} -6.00000 q^{23} +2.00000 q^{24} +4.00000 q^{26} -4.00000 q^{27} +1.00000 q^{28} +3.00000 q^{29} +5.00000 q^{31} +1.00000 q^{32} +6.00000 q^{33} -3.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} +2.00000 q^{38} +8.00000 q^{39} +3.00000 q^{41} +2.00000 q^{42} +1.00000 q^{43} +3.00000 q^{44} -6.00000 q^{46} -12.0000 q^{47} +2.00000 q^{48} -6.00000 q^{49} -6.00000 q^{51} +4.00000 q^{52} -3.00000 q^{53} -4.00000 q^{54} +1.00000 q^{56} +4.00000 q^{57} +3.00000 q^{58} -1.00000 q^{61} +5.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.00000 q^{66} +4.00000 q^{67} -3.00000 q^{68} -12.0000 q^{69} +6.00000 q^{71} +1.00000 q^{72} +16.0000 q^{73} -1.00000 q^{74} +2.00000 q^{76} +3.00000 q^{77} +8.00000 q^{78} +8.00000 q^{79} -11.0000 q^{81} +3.00000 q^{82} +12.0000 q^{83} +2.00000 q^{84} +1.00000 q^{86} +6.00000 q^{87} +3.00000 q^{88} -6.00000 q^{89} +4.00000 q^{91} -6.00000 q^{92} +10.0000 q^{93} -12.0000 q^{94} +2.00000 q^{96} -17.0000 q^{97} -6.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	2.00000	0.816497
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	2.00000	0.577350
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	1.00000	0.235702
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	3.00000	0.639602
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	2.00000	0.408248
$25$	0	0
$26$	4.00000	0.784465
$27$	−4.00000	−0.769800
$28$	1.00000	0.188982
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	1.00000	0.176777
$33$	6.00000	1.04447
$34$	−3.00000	−0.514496
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	2.00000	0.324443
$39$	8.00000	1.28103
$40$	0	0
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	2.00000	0.308607
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	−6.00000	−0.884652
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	2.00000	0.288675
$49$	−6.00000	−0.857143
$50$	0	0
$51$	−6.00000	−0.840168
$52$	4.00000	0.554700
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	−4.00000	−0.544331
$55$	0	0
$56$	1.00000	0.133631
$57$	4.00000	0.529813
$58$	3.00000	0.393919
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−1.00000	−0.128037	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000	−0.128037	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	5.00000	0.635001
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	6.00000	0.738549
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−3.00000	−0.363803
$69$	−12.0000	−1.44463
$70$	0	0
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	1.00000	0.117851
$73$	16.0000	1.87266	0.936329	−	0.351123i	$-0.114200\pi$
$73$	16.0000	1.87266	0.936329	+	0.351123i	$0.114200\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	2.00000	0.229416
$77$	3.00000	0.341882
$78$	8.00000	0.905822
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	3.00000	0.331295
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	1.00000	0.107833
$87$	6.00000	0.643268
$88$	3.00000	0.319801
$89$	−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
$91$	4.00000	0.419314
$92$	−6.00000	−0.625543
$93$	10.0000	1.03695
$94$	−12.0000	−1.23771
$95$	0	0
$96$	2.00000	0.204124
$97$	−17.0000	−1.72609	−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000	−1.72609	−0.863044	+	0.505128i	$0.831445\pi$
$98$	−6.00000	−0.606092
$99$	3.00000	0.301511
$100$	0	0
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	−6.00000	−0.594089
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	4.00000	0.392232
$105$	0	0
$106$	−3.00000	−0.291386
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	−4.00000	−0.384900
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	1.00000	0.0944911
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	4.00000	0.374634
$115$	0	0
$116$	3.00000	0.278543
$117$	4.00000	0.369800
$118$	0	0
$119$	−3.00000	−0.275010
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−1.00000	−0.0905357
$123$	6.00000	0.541002
$124$	5.00000	0.449013
$125$	0	0
$126$	1.00000	0.0890871
$127$	−20.0000	−1.77471	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000	−1.77471	−0.887357	+	0.461084i	$0.847461\pi$
$128$	1.00000	0.0883883
$129$	2.00000	0.176090
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	6.00000	0.522233
$133$	2.00000	0.173422
$134$	4.00000	0.345547
$135$	0	0
$136$	−3.00000	−0.257248
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	−12.0000	−1.02151
$139$	−13.0000	−1.10265	−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000	−1.10265	−0.551323	+	0.834292i	$0.685877\pi$
$140$	0	0
$141$	−24.0000	−2.02116
$142$	6.00000	0.503509
$143$	12.0000	1.00349
$144$	1.00000	0.0833333
$145$	0	0
$146$	16.0000	1.32417
$147$	−12.0000	−0.989743
$148$	−1.00000	−0.0821995
$149$	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
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	2.00000	0.162221
$153$	−3.00000	−0.242536
$154$	3.00000	0.241747
$155$	0	0
$156$	8.00000	0.640513
$157$	13.0000	1.03751	0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000	1.03751	0.518756	+	0.854922i	$0.326395\pi$
$158$	8.00000	0.636446
$159$	−6.00000	−0.475831
$160$	0	0
$161$	−6.00000	−0.472866
$162$	−11.0000	−0.864242
$163$	−11.0000	−0.861586	−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000	−0.861586	−0.430793	+	0.902451i	$0.641766\pi$
$164$	3.00000	0.234261
$165$	0	0
$166$	12.0000	0.931381
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	2.00000	0.154303
$169$	3.00000	0.230769
$170$	0	0
$171$	2.00000	0.152944
$172$	1.00000	0.0762493
$173$	−15.0000	−1.14043	−0.570214	−	0.821496i	$-0.693140\pi$
$173$	−15.0000	−1.14043	−0.570214	+	0.821496i	$0.693140\pi$
$174$	6.00000	0.454859
$175$	0	0
$176$	3.00000	0.226134
$177$	0	0
$178$	−6.00000	−0.449719
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	4.00000	0.296500
$183$	−2.00000	−0.147844
$184$	−6.00000	−0.442326
$185$	0	0
$186$	10.0000	0.733236
$187$	−9.00000	−0.658145
$188$	−12.0000	−0.875190
$189$	−4.00000	−0.290957
$190$	0	0
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	2.00000	0.144338
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	−17.0000	−1.22053
$195$	0	0
$196$	−6.00000	−0.428571
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	3.00000	0.213201
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	8.00000	0.564276
$202$	−6.00000	−0.422159
$203$	3.00000	0.210559
$204$	−6.00000	−0.420084
$205$	0	0
$206$	4.00000	0.278693
$207$	−6.00000	−0.417029
$208$	4.00000	0.277350
$209$	6.00000	0.415029
$210$	0	0
$211$	5.00000	0.344214	0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000	0.344214	0.172107	+	0.985078i	$0.444942\pi$
$212$	−3.00000	−0.206041
$213$	12.0000	0.822226
$214$	−6.00000	−0.410152
$215$	0	0
$216$	−4.00000	−0.272166
$217$	5.00000	0.339422
$218$	11.0000	0.745014
$219$	32.0000	2.16236
$220$	0	0
$221$	−12.0000	−0.807207
$222$	−2.00000	−0.134231
$223$	−17.0000	−1.13840	−0.569202	−	0.822198i	$-0.692748\pi$
$223$	−17.0000	−1.13840	−0.569202	+	0.822198i	$0.692748\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−9.00000	−0.598671
$227$	27.0000	1.79205	0.896026	−	0.444001i	$-0.146441\pi$
$227$	27.0000	1.79205	0.896026	+	0.444001i	$0.146441\pi$
$228$	4.00000	0.264906
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	6.00000	0.394771
$232$	3.00000	0.196960
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	4.00000	0.261488
$235$	0	0
$236$	0	0
$237$	16.0000	1.03931
$238$	−3.00000	−0.194461
$239$	−9.00000	−0.582162	−0.291081	−	0.956698i	$-0.594015\pi$
$239$	−9.00000	−0.582162	−0.291081	+	0.956698i	$0.594015\pi$
$240$	0	0
$241$	−28.0000	−1.80364	−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000	−1.80364	−0.901819	+	0.432113i	$0.857768\pi$
$242$	−2.00000	−0.128565
$243$	−10.0000	−0.641500
$244$	−1.00000	−0.0640184
$245$	0	0
$246$	6.00000	0.382546
$247$	8.00000	0.509028
$248$	5.00000	0.317500
$249$	24.0000	1.52094
$250$	0	0
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	1.00000	0.0629941
$253$	−18.0000	−1.13165
$254$	−20.0000	−1.25491
$255$	0	0
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	2.00000	0.124515
$259$	−1.00000	−0.0621370
$260$	0	0
$261$	3.00000	0.185695
$262$	0	0
$263$	−9.00000	−0.554964	−0.277482	−	0.960731i	$-0.589500\pi$
$263$	−9.00000	−0.554964	−0.277482	+	0.960731i	$0.589500\pi$
$264$	6.00000	0.369274
$265$	0	0
$266$	2.00000	0.122628
$267$	−12.0000	−0.734388
$268$	4.00000	0.244339
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	0	0
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	−3.00000	−0.181902
$273$	8.00000	0.484182
$274$	−12.0000	−0.724947
$275$	0	0
$276$	−12.0000	−0.722315
$277$	28.0000	1.68236	0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000	1.68236	0.841178	+	0.540758i	$0.181862\pi$
$278$	−13.0000	−0.779688
$279$	5.00000	0.299342
$280$	0	0
$281$	24.0000	1.43172	0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000	1.43172	0.715860	+	0.698244i	$0.246035\pi$
$282$	−24.0000	−1.42918
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	12.0000	0.709575
$287$	3.00000	0.177084
$288$	1.00000	0.0589256
$289$	−8.00000	−0.470588
$290$	0	0
$291$	−34.0000	−1.99312
$292$	16.0000	0.936329
$293$	−21.0000	−1.22683	−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000	−1.22683	−0.613417	+	0.789760i	$0.710205\pi$
$294$	−12.0000	−0.699854
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	−12.0000	−0.696311
$298$	6.00000	0.347571
$299$	−24.0000	−1.38796
$300$	0	0
$301$	1.00000	0.0576390
$302$	8.00000	0.460348
$303$	−12.0000	−0.689382
$304$	2.00000	0.114708
$305$	0	0
$306$	−3.00000	−0.171499
$307$	34.0000	1.94048	0.970241	−	0.242140i	$-0.0778494\pi$
$307$	34.0000	1.94048	0.970241	+	0.242140i	$0.0778494\pi$
$308$	3.00000	0.170941
$309$	8.00000	0.455104
$310$	0	0
$311$	−9.00000	−0.510343	−0.255172	−	0.966896i	$-0.582132\pi$
$311$	−9.00000	−0.510343	−0.255172	+	0.966896i	$0.582132\pi$
$312$	8.00000	0.452911
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	13.0000	0.733632
$315$	0	0
$316$	8.00000	0.450035
$317$	21.0000	1.17948	0.589739	−	0.807594i	$-0.299231\pi$
$317$	21.0000	1.17948	0.589739	+	0.807594i	$0.299231\pi$
$318$	−6.00000	−0.336463
$319$	9.00000	0.503903
$320$	0	0
$321$	−12.0000	−0.669775
$322$	−6.00000	−0.334367
$323$	−6.00000	−0.333849
$324$	−11.0000	−0.611111
$325$	0	0
$326$	−11.0000	−0.609234
$327$	22.0000	1.21660
$328$	3.00000	0.165647
$329$	−12.0000	−0.661581
$330$	0	0
$331$	26.0000	1.42909	0.714545	−	0.699590i	$-0.246634\pi$
$331$	26.0000	1.42909	0.714545	+	0.699590i	$0.246634\pi$
$332$	12.0000	0.658586
$333$	−1.00000	−0.0547997
$334$	−12.0000	−0.656611
$335$	0	0
$336$	2.00000	0.109109
$337$	4.00000	0.217894	0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000	0.217894	0.108947	+	0.994048i	$0.465252\pi$
$338$	3.00000	0.163178
$339$	−18.0000	−0.977626
$340$	0	0
$341$	15.0000	0.812296
$342$	2.00000	0.108148
$343$	−13.0000	−0.701934
$344$	1.00000	0.0539164
$345$	0	0
$346$	−15.0000	−0.806405
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	6.00000	0.321634
$349$	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
$351$	−16.0000	−0.854017
$352$	3.00000	0.159901
$353$	21.0000	1.11772	0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000	1.11772	0.558859	+	0.829263i	$0.311239\pi$
$354$	0	0
$355$	0	0
$356$	−6.00000	−0.317999
$357$	−6.00000	−0.317554
$358$	0	0
$359$	−36.0000	−1.90001	−0.950004	−	0.312239i	$-0.898921\pi$
$359$	−36.0000	−1.90001	−0.950004	+	0.312239i	$0.898921\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	2.00000	0.105118
$363$	−4.00000	−0.209946
$364$	4.00000	0.209657
$365$	0	0
$366$	−2.00000	−0.104542
$367$	−35.0000	−1.82699	−0.913493	−	0.406855i	$-0.866625\pi$
$367$	−35.0000	−1.82699	−0.913493	+	0.406855i	$0.866625\pi$
$368$	−6.00000	−0.312772
$369$	3.00000	0.156174
$370$	0	0
$371$	−3.00000	−0.155752
$372$	10.0000	0.518476
$373$	22.0000	1.13912	0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000	1.13912	0.569558	+	0.821951i	$0.307114\pi$
$374$	−9.00000	−0.465379
$375$	0	0
$376$	−12.0000	−0.618853
$377$	12.0000	0.618031
$378$	−4.00000	−0.205738
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	0	0
$381$	−40.0000	−2.04926
$382$	3.00000	0.153493
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	2.00000	0.102062
$385$	0	0
$386$	−14.0000	−0.712581
$387$	1.00000	0.0508329
$388$	−17.0000	−0.863044
$389$	9.00000	0.456318	0.228159	−	0.973624i	$-0.426729\pi$
$389$	9.00000	0.456318	0.228159	+	0.973624i	$0.426729\pi$
$390$	0	0
$391$	18.0000	0.910299
$392$	−6.00000	−0.303046
$393$	0	0
$394$	6.00000	0.302276
$395$	0	0
$396$	3.00000	0.150756
$397$	34.0000	1.70641	0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000	1.70641	0.853206	+	0.521575i	$0.174655\pi$
$398$	−16.0000	−0.802008
$399$	4.00000	0.200250
$400$	0	0
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	8.00000	0.399004
$403$	20.0000	0.996271
$404$	−6.00000	−0.298511
$405$	0	0
$406$	3.00000	0.148888
$407$	−3.00000	−0.148704
$408$	−6.00000	−0.297044
$409$	32.0000	1.58230	0.791149	−	0.611623i	$-0.209483\pi$
$409$	32.0000	1.58230	0.791149	+	0.611623i	$0.209483\pi$
$410$	0	0
$411$	−24.0000	−1.18383
$412$	4.00000	0.197066
$413$	0	0
$414$	−6.00000	−0.294884
$415$	0	0
$416$	4.00000	0.196116
$417$	−26.0000	−1.27323
$418$	6.00000	0.293470
$419$	−36.0000	−1.75872	−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000	−1.75872	−0.879358	+	0.476162i	$0.842028\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	5.00000	0.243396
$423$	−12.0000	−0.583460
$424$	−3.00000	−0.145693
$425$	0	0
$426$	12.0000	0.581402
$427$	−1.00000	−0.0483934
$428$	−6.00000	−0.290021
$429$	24.0000	1.15873
$430$	0	0
$431$	15.0000	0.722525	0.361262	−	0.932464i	$-0.382346\pi$
$431$	15.0000	0.722525	0.361262	+	0.932464i	$0.382346\pi$
$432$	−4.00000	−0.192450
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	5.00000	0.240008
$435$	0	0
$436$	11.0000	0.526804
$437$	−12.0000	−0.574038
$438$	32.0000	1.52902
$439$	35.0000	1.67046	0.835229	−	0.549902i	$-0.185335\pi$
$439$	35.0000	1.67046	0.835229	+	0.549902i	$0.185335\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	−12.0000	−0.570782
$443$	−30.0000	−1.42534	−0.712672	−	0.701498i	$-0.752515\pi$
$443$	−30.0000	−1.42534	−0.712672	+	0.701498i	$0.752515\pi$
$444$	−2.00000	−0.0949158
$445$	0	0
$446$	−17.0000	−0.804973
$447$	12.0000	0.567581
$448$	1.00000	0.0472456
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	0	0
$451$	9.00000	0.423793
$452$	−9.00000	−0.423324
$453$	16.0000	0.751746
$454$	27.0000	1.26717
$455$	0	0
$456$	4.00000	0.187317
$457$	−17.0000	−0.795226	−0.397613	−	0.917553i	$-0.630161\pi$
$457$	−17.0000	−0.795226	−0.397613	+	0.917553i	$0.630161\pi$
$458$	14.0000	0.654177
$459$	12.0000	0.560112
$460$	0	0
$461$	33.0000	1.53696	0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000	1.53696	0.768482	+	0.639872i	$0.221013\pi$
$462$	6.00000	0.279145
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	0	0
$467$	−27.0000	−1.24941	−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000	−1.24941	−0.624705	+	0.780860i	$0.714781\pi$
$468$	4.00000	0.184900
$469$	4.00000	0.184703
$470$	0	0
$471$	26.0000	1.19802
$472$	0	0
$473$	3.00000	0.137940
$474$	16.0000	0.734904
$475$	0	0
$476$	−3.00000	−0.137505
$477$	−3.00000	−0.137361
$478$	−9.00000	−0.411650
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	−28.0000	−1.27537
$483$	−12.0000	−0.546019
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	−10.0000	−0.453609
$487$	−2.00000	−0.0906287	−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000	−0.0906287	−0.0453143	+	0.998973i	$0.514429\pi$
$488$	−1.00000	−0.0452679
$489$	−22.0000	−0.994874
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	6.00000	0.270501
$493$	−9.00000	−0.405340
$494$	8.00000	0.359937
$495$	0	0
$496$	5.00000	0.224507
$497$	6.00000	0.269137
$498$	24.0000	1.07547
$499$	14.0000	0.626726	0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000	0.626726	0.313363	+	0.949633i	$0.398544\pi$
$500$	0	0
$501$	−24.0000	−1.07224
$502$	18.0000	0.803379
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	1.00000	0.0445435
$505$	0	0
$506$	−18.0000	−0.800198
$507$	6.00000	0.266469
$508$	−20.0000	−0.887357
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	16.0000	0.707798
$512$	1.00000	0.0441942
$513$	−8.00000	−0.353209
$514$	−18.0000	−0.793946
$515$	0	0
$516$	2.00000	0.0880451
$517$	−36.0000	−1.58328
$518$	−1.00000	−0.0439375
$519$	−30.0000	−1.31685
$520$	0	0
$521$	−39.0000	−1.70862	−0.854311	−	0.519763i	$-0.826020\pi$
$521$	−39.0000	−1.70862	−0.854311	+	0.519763i	$0.826020\pi$
$522$	3.00000	0.131306
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	0	0
$525$	0	0
$526$	−9.00000	−0.392419
$527$	−15.0000	−0.653410
$528$	6.00000	0.261116
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	2.00000	0.0867110
$533$	12.0000	0.519778
$534$	−12.0000	−0.519291
$535$	0	0
$536$	4.00000	0.172774
$537$	0	0
$538$	−18.0000	−0.776035
$539$	−18.0000	−0.775315
$540$	0	0
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	2.00000	0.0859074
$543$	4.00000	0.171656
$544$	−3.00000	−0.128624
$545$	0	0
$546$	8.00000	0.342368
$547$	1.00000	0.0427569	0.0213785	−	0.999771i	$-0.493195\pi$
$547$	1.00000	0.0427569	0.0213785	+	0.999771i	$0.493195\pi$
$548$	−12.0000	−0.512615
$549$	−1.00000	−0.0426790
$550$	0	0
$551$	6.00000	0.255609
$552$	−12.0000	−0.510754
$553$	8.00000	0.340195
$554$	28.0000	1.18961
$555$	0	0
$556$	−13.0000	−0.551323
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	5.00000	0.211667
$559$	4.00000	0.169182
$560$	0	0
$561$	−18.0000	−0.759961
$562$	24.0000	1.01238
$563$	3.00000	0.126435	0.0632175	−	0.998000i	$-0.479864\pi$
$563$	3.00000	0.126435	0.0632175	+	0.998000i	$0.479864\pi$
$564$	−24.0000	−1.01058
$565$	0	0
$566$	4.00000	0.168133
$567$	−11.0000	−0.461957
$568$	6.00000	0.251754
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	−31.0000	−1.29731	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	−31.0000	−1.29731	−0.648655	+	0.761083i	$0.724668\pi$
$572$	12.0000	0.501745
$573$	6.00000	0.250654
$574$	3.00000	0.125218
$575$	0	0
$576$	1.00000	0.0416667
$577$	34.0000	1.41544	0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000	1.41544	0.707719	+	0.706494i	$0.249724\pi$
$578$	−8.00000	−0.332756
$579$	−28.0000	−1.16364
$580$	0	0
$581$	12.0000	0.497844
$582$	−34.0000	−1.40935
$583$	−9.00000	−0.372742
$584$	16.0000	0.662085
$585$	0	0
$586$	−21.0000	−0.867502
$587$	−27.0000	−1.11441	−0.557205	−	0.830375i	$-0.688126\pi$
$587$	−27.0000	−1.11441	−0.557205	+	0.830375i	$0.688126\pi$
$588$	−12.0000	−0.494872
$589$	10.0000	0.412043
$590$	0	0
$591$	12.0000	0.493614
$592$	−1.00000	−0.0410997
$593$	36.0000	1.47834	0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000	1.47834	0.739171	+	0.673517i	$0.235217\pi$
$594$	−12.0000	−0.492366
$595$	0	0
$596$	6.00000	0.245770
$597$	−32.0000	−1.30967
$598$	−24.0000	−0.981433
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	0	0
$601$	−19.0000	−0.775026	−0.387513	−	0.921864i	$-0.626666\pi$
$601$	−19.0000	−0.775026	−0.387513	+	0.921864i	$0.626666\pi$
$602$	1.00000	0.0407570
$603$	4.00000	0.162893
$604$	8.00000	0.325515
$605$	0	0
$606$	−12.0000	−0.487467
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	2.00000	0.0811107
$609$	6.00000	0.243132
$610$	0	0
$611$	−48.0000	−1.94187
$612$	−3.00000	−0.121268
$613$	−29.0000	−1.17130	−0.585649	−	0.810564i	$-0.699160\pi$
$613$	−29.0000	−1.17130	−0.585649	+	0.810564i	$0.699160\pi$
$614$	34.0000	1.37213
$615$	0	0
$616$	3.00000	0.120873
$617$	0	0		−	1.00000i	$-0.5\pi$
$617$	0	0			1.00000i	$0.5\pi$
$618$	8.00000	0.321807
$619$	35.0000	1.40677	0.703384	−	0.710810i	$-0.251671\pi$
$619$	35.0000	1.40677	0.703384	+	0.710810i	$0.251671\pi$
$620$	0	0
$621$	24.0000	0.963087
$622$	−9.00000	−0.360867
$623$	−6.00000	−0.240385
$624$	8.00000	0.320256
$625$	0	0
$626$	−26.0000	−1.03917
$627$	12.0000	0.479234
$628$	13.0000	0.518756
$629$	3.00000	0.119618
$630$	0	0
$631$	−7.00000	−0.278666	−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000	−0.278666	−0.139333	+	0.990246i	$0.544496\pi$
$632$	8.00000	0.318223
$633$	10.0000	0.397464
$634$	21.0000	0.834017
$635$	0	0
$636$	−6.00000	−0.237915
$637$	−24.0000	−0.950915
$638$	9.00000	0.356313
$639$	6.00000	0.237356
$640$	0	0
$641$	15.0000	0.592464	0.296232	−	0.955116i	$-0.404270\pi$
$641$	15.0000	0.592464	0.296232	+	0.955116i	$0.404270\pi$
$642$	−12.0000	−0.473602
$643$	13.0000	0.512670	0.256335	−	0.966588i	$-0.417485\pi$
$643$	13.0000	0.512670	0.256335	+	0.966588i	$0.417485\pi$
$644$	−6.00000	−0.236433
$645$	0	0
$646$	−6.00000	−0.236067
$647$	48.0000	1.88707	0.943537	−	0.331266i	$-0.107476\pi$
$647$	48.0000	1.88707	0.943537	+	0.331266i	$0.107476\pi$
$648$	−11.0000	−0.432121
$649$	0	0
$650$	0	0
$651$	10.0000	0.391931
$652$	−11.0000	−0.430793
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	22.0000	0.860268
$655$	0	0
$656$	3.00000	0.117130
$657$	16.0000	0.624219
$658$	−12.0000	−0.467809
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	5.00000	0.194477	0.0972387	−	0.995261i	$-0.468999\pi$
$661$	5.00000	0.194477	0.0972387	+	0.995261i	$0.468999\pi$
$662$	26.0000	1.01052
$663$	−24.0000	−0.932083
$664$	12.0000	0.465690
$665$	0	0
$666$	−1.00000	−0.0387492
$667$	−18.0000	−0.696963
$668$	−12.0000	−0.464294
$669$	−34.0000	−1.31452
$670$	0	0
$671$	−3.00000	−0.115814
$672$	2.00000	0.0771517
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	4.00000	0.154074
$675$	0	0
$676$	3.00000	0.115385
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	−18.0000	−0.691286
$679$	−17.0000	−0.652400
$680$	0	0
$681$	54.0000	2.06928
$682$	15.0000	0.574380
$683$	15.0000	0.573959	0.286980	−	0.957937i	$-0.407349\pi$
$683$	15.0000	0.573959	0.286980	+	0.957937i	$0.407349\pi$
$684$	2.00000	0.0764719
$685$	0	0
$686$	−13.0000	−0.496342
$687$	28.0000	1.06827
$688$	1.00000	0.0381246
$689$	−12.0000	−0.457164
$690$	0	0
$691$	−19.0000	−0.722794	−0.361397	−	0.932412i	$-0.617700\pi$
$691$	−19.0000	−0.722794	−0.361397	+	0.932412i	$0.617700\pi$
$692$	−15.0000	−0.570214
$693$	3.00000	0.113961
$694$	12.0000	0.455514
$695$	0	0
$696$	6.00000	0.227429
$697$	−9.00000	−0.340899
$698$	26.0000	0.984115
$699$	0	0
$700$	0	0
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	−16.0000	−0.603881
$703$	−2.00000	−0.0754314
$704$	3.00000	0.113067
$705$	0	0
$706$	21.0000	0.790345
$707$	−6.00000	−0.225653
$708$	0	0
$709$	35.0000	1.31445	0.657226	−	0.753693i	$-0.271730\pi$
$709$	35.0000	1.31445	0.657226	+	0.753693i	$0.271730\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	−6.00000	−0.224860
$713$	−30.0000	−1.12351
$714$	−6.00000	−0.224544
$715$	0	0
$716$	0	0
$717$	−18.0000	−0.672222
$718$	−36.0000	−1.34351
$719$	−42.0000	−1.56634	−0.783168	−	0.621810i	$-0.786397\pi$
$719$	−42.0000	−1.56634	−0.783168	+	0.621810i	$0.786397\pi$
$720$	0	0
$721$	4.00000	0.148968
$722$	−15.0000	−0.558242
$723$	−56.0000	−2.08266
$724$	2.00000	0.0743294
$725$	0	0
$726$	−4.00000	−0.148454
$727$	28.0000	1.03846	0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000	1.03846	0.519231	+	0.854634i	$0.326218\pi$
$728$	4.00000	0.148250
$729$	13.0000	0.481481
$730$	0	0
$731$	−3.00000	−0.110959
$732$	−2.00000	−0.0739221
$733$	31.0000	1.14501	0.572506	−	0.819901i	$-0.305971\pi$
$733$	31.0000	1.14501	0.572506	+	0.819901i	$0.305971\pi$
$734$	−35.0000	−1.29187
$735$	0	0
$736$	−6.00000	−0.221163
$737$	12.0000	0.442026
$738$	3.00000	0.110432
$739$	11.0000	0.404642	0.202321	−	0.979319i	$-0.435152\pi$
$739$	11.0000	0.404642	0.202321	+	0.979319i	$0.435152\pi$
$740$	0	0
$741$	16.0000	0.587775
$742$	−3.00000	−0.110133
$743$	51.0000	1.87101	0.935504	−	0.353315i	$-0.114946\pi$
$743$	51.0000	1.87101	0.935504	+	0.353315i	$0.114946\pi$
$744$	10.0000	0.366618
$745$	0	0
$746$	22.0000	0.805477
$747$	12.0000	0.439057
$748$	−9.00000	−0.329073
$749$	−6.00000	−0.219235
$750$	0	0
$751$	14.0000	0.510867	0.255434	−	0.966827i	$-0.417782\pi$
$751$	14.0000	0.510867	0.255434	+	0.966827i	$0.417782\pi$
$752$	−12.0000	−0.437595
$753$	36.0000	1.31191
$754$	12.0000	0.437014
$755$	0	0
$756$	−4.00000	−0.145479
$757$	34.0000	1.23575	0.617876	−	0.786276i	$-0.287994\pi$
$757$	34.0000	1.23575	0.617876	+	0.786276i	$0.287994\pi$
$758$	−16.0000	−0.581146
$759$	−36.0000	−1.30672
$760$	0	0
$761$	27.0000	0.978749	0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000	0.978749	0.489375	+	0.872074i	$0.337225\pi$
$762$	−40.0000	−1.44905
$763$	11.0000	0.398227
$764$	3.00000	0.108536
$765$	0	0
$766$	24.0000	0.867155
$767$	0	0
$768$	2.00000	0.0721688
$769$	−40.0000	−1.44244	−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000	−1.44244	−0.721218	+	0.692708i	$0.756418\pi$
$770$	0	0
$771$	−36.0000	−1.29651
$772$	−14.0000	−0.503871
$773$	39.0000	1.40273	0.701366	−	0.712801i	$-0.252574\pi$
$773$	39.0000	1.40273	0.701366	+	0.712801i	$0.252574\pi$
$774$	1.00000	0.0359443
$775$	0	0
$776$	−17.0000	−0.610264
$777$	−2.00000	−0.0717496
$778$	9.00000	0.322666
$779$	6.00000	0.214972
$780$	0	0
$781$	18.0000	0.644091
$782$	18.0000	0.643679
$783$	−12.0000	−0.428845
$784$	−6.00000	−0.214286
$785$	0	0
$786$	0	0
$787$	22.0000	0.784215	0.392108	−	0.919919i	$-0.371746\pi$
$787$	22.0000	0.784215	0.392108	+	0.919919i	$0.371746\pi$
$788$	6.00000	0.213741
$789$	−18.0000	−0.640817
$790$	0	0
$791$	−9.00000	−0.320003
$792$	3.00000	0.106600
$793$	−4.00000	−0.142044
$794$	34.0000	1.20661
$795$	0	0
$796$	−16.0000	−0.567105
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	4.00000	0.141598
$799$	36.0000	1.27359
$800$	0	0
$801$	−6.00000	−0.212000
$802$	6.00000	0.211867
$803$	48.0000	1.69388
$804$	8.00000	0.282138
$805$	0	0
$806$	20.0000	0.704470
$807$	−36.0000	−1.26726
$808$	−6.00000	−0.211079
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	0	0
$811$	−16.0000	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$812$	3.00000	0.105279
$813$	4.00000	0.140286
$814$	−3.00000	−0.105150
$815$	0	0
$816$	−6.00000	−0.210042
$817$	2.00000	0.0699711
$818$	32.0000	1.11885
$819$	4.00000	0.139771
$820$	0	0
$821$	36.0000	1.25641	0.628204	−	0.778048i	$-0.283790\pi$
$821$	36.0000	1.25641	0.628204	+	0.778048i	$0.283790\pi$
$822$	−24.0000	−0.837096
$823$	40.0000	1.39431	0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000	1.39431	0.697156	+	0.716919i	$0.254448\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	0	0
$827$	3.00000	0.104320	0.0521601	−	0.998639i	$-0.483389\pi$
$827$	3.00000	0.104320	0.0521601	+	0.998639i	$0.483389\pi$
$828$	−6.00000	−0.208514
$829$	47.0000	1.63238	0.816189	−	0.577785i	$-0.196083\pi$
$829$	47.0000	1.63238	0.816189	+	0.577785i	$0.196083\pi$
$830$	0	0
$831$	56.0000	1.94262
$832$	4.00000	0.138675
$833$	18.0000	0.623663
$834$	−26.0000	−0.900306
$835$	0	0
$836$	6.00000	0.207514
$837$	−20.0000	−0.691301
$838$	−36.0000	−1.24360
$839$	−48.0000	−1.65714	−0.828572	−	0.559883i	$-0.810846\pi$
$839$	−48.0000	−1.65714	−0.828572	+	0.559883i	$0.810846\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−10.0000	−0.344623
$843$	48.0000	1.65321
$844$	5.00000	0.172107
$845$	0	0
$846$	−12.0000	−0.412568
$847$	−2.00000	−0.0687208
$848$	−3.00000	−0.103020
$849$	8.00000	0.274559
$850$	0	0
$851$	6.00000	0.205677
$852$	12.0000	0.411113
$853$	10.0000	0.342393	0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000	0.342393	0.171197	+	0.985237i	$0.445237\pi$
$854$	−1.00000	−0.0342193
$855$	0	0
$856$	−6.00000	−0.205076
$857$	15.0000	0.512390	0.256195	−	0.966625i	$-0.417531\pi$
$857$	15.0000	0.512390	0.256195	+	0.966625i	$0.417531\pi$
$858$	24.0000	0.819346
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	0	0
$861$	6.00000	0.204479
$862$	15.0000	0.510902
$863$	−39.0000	−1.32758	−0.663788	−	0.747921i	$-0.731052\pi$
$863$	−39.0000	−1.32758	−0.663788	+	0.747921i	$0.731052\pi$
$864$	−4.00000	−0.136083
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	−16.0000	−0.543388
$868$	5.00000	0.169711
$869$	24.0000	0.814144
$870$	0	0
$871$	16.0000	0.542139
$872$	11.0000	0.372507
$873$	−17.0000	−0.575363
$874$	−12.0000	−0.405906
$875$	0	0
$876$	32.0000	1.08118
$877$	13.0000	0.438979	0.219489	−	0.975615i	$-0.429561\pi$
$877$	13.0000	0.438979	0.219489	+	0.975615i	$0.429561\pi$
$878$	35.0000	1.18119
$879$	−42.0000	−1.41662
$880$	0	0
$881$	15.0000	0.505363	0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000	0.505363	0.252681	+	0.967550i	$0.418688\pi$
$882$	−6.00000	−0.202031
$883$	−29.0000	−0.975928	−0.487964	−	0.872864i	$-0.662260\pi$
$883$	−29.0000	−0.975928	−0.487964	+	0.872864i	$0.662260\pi$
$884$	−12.0000	−0.403604
$885$	0	0
$886$	−30.0000	−1.00787
$887$	−33.0000	−1.10803	−0.554016	−	0.832506i	$-0.686905\pi$
$887$	−33.0000	−1.10803	−0.554016	+	0.832506i	$0.686905\pi$
$888$	−2.00000	−0.0671156
$889$	−20.0000	−0.670778
$890$	0	0
$891$	−33.0000	−1.10554
$892$	−17.0000	−0.569202
$893$	−24.0000	−0.803129
$894$	12.0000	0.401340
$895$	0	0
$896$	1.00000	0.0334077
$897$	−48.0000	−1.60267
$898$	6.00000	0.200223
$899$	15.0000	0.500278
$900$	0	0
$901$	9.00000	0.299833
$902$	9.00000	0.299667
$903$	2.00000	0.0665558
$904$	−9.00000	−0.299336
$905$	0	0
$906$	16.0000	0.531564
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	27.0000	0.896026
$909$	−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	$0.630149\pi$
$912$	4.00000	0.132453
$913$	36.0000	1.19143
$914$	−17.0000	−0.562310
$915$	0	0
$916$	14.0000	0.462573
$917$	0	0
$918$	12.0000	0.396059
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	68.0000	2.24068
$922$	33.0000	1.08680
$923$	24.0000	0.789970
$924$	6.00000	0.197386
$925$	0	0
$926$	4.00000	0.131448
$927$	4.00000	0.131377
$928$	3.00000	0.0984798
$929$	45.0000	1.47640	0.738201	−	0.674581i	$-0.235676\pi$
$929$	45.0000	1.47640	0.738201	+	0.674581i	$0.235676\pi$
$930$	0	0
$931$	−12.0000	−0.393284
$932$	0	0
$933$	−18.0000	−0.589294
$934$	−27.0000	−0.883467
$935$	0	0
$936$	4.00000	0.130744
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	4.00000	0.130605
$939$	−52.0000	−1.69696
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	26.0000	0.847126
$943$	−18.0000	−0.586161
$944$	0	0
$945$	0	0
$946$	3.00000	0.0975384
$947$	−33.0000	−1.07236	−0.536178	−	0.844105i	$-0.680132\pi$
$947$	−33.0000	−1.07236	−0.536178	+	0.844105i	$0.680132\pi$
$948$	16.0000	0.519656
$949$	64.0000	2.07753
$950$	0	0
$951$	42.0000	1.36194
$952$	−3.00000	−0.0972306
$953$	60.0000	1.94359	0.971795	−	0.235826i	$-0.0757795\pi$
$953$	60.0000	1.94359	0.971795	+	0.235826i	$0.0757795\pi$
$954$	−3.00000	−0.0971286
$955$	0	0
$956$	−9.00000	−0.291081
$957$	18.0000	0.581857
$958$	24.0000	0.775405
$959$	−12.0000	−0.387500
$960$	0	0
$961$	−6.00000	−0.193548
$962$	−4.00000	−0.128965
$963$	−6.00000	−0.193347
$964$	−28.0000	−0.901819
$965$	0	0
$966$	−12.0000	−0.386094
$967$	40.0000	1.28631	0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000	1.28631	0.643157	+	0.765735i	$0.277624\pi$
$968$	−2.00000	−0.0642824
$969$	−12.0000	−0.385496
$970$	0	0
$971$	57.0000	1.82922	0.914609	−	0.404341i	$-0.132499\pi$
$971$	57.0000	1.82922	0.914609	+	0.404341i	$0.132499\pi$
$972$	−10.0000	−0.320750
$973$	−13.0000	−0.416761
$974$	−2.00000	−0.0640841
$975$	0	0
$976$	−1.00000	−0.0320092
$977$	45.0000	1.43968	0.719839	−	0.694141i	$-0.244216\pi$
$977$	45.0000	1.43968	0.719839	+	0.694141i	$0.244216\pi$
$978$	−22.0000	−0.703482
$979$	−18.0000	−0.575282
$980$	0	0
$981$	11.0000	0.351203
$982$	−12.0000	−0.382935
$983$	−51.0000	−1.62665	−0.813324	−	0.581811i	$-0.802344\pi$
$983$	−51.0000	−1.62665	−0.813324	+	0.581811i	$0.802344\pi$
$984$	6.00000	0.191273
$985$	0	0
$986$	−9.00000	−0.286618
$987$	−24.0000	−0.763928
$988$	8.00000	0.254514
$989$	−6.00000	−0.190789
$990$	0	0
$991$	47.0000	1.49300	0.746502	−	0.665383i	$-0.231732\pi$
$991$	47.0000	1.49300	0.746502	+	0.665383i	$0.231732\pi$
$992$	5.00000	0.158750
$993$	52.0000	1.65017
$994$	6.00000	0.190308
$995$	0	0
$996$	24.0000	0.760469
$997$	28.0000	0.886769	0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000	0.886769	0.443384	+	0.896332i	$0.353778\pi$
$998$	14.0000	0.443162
$999$	4.00000	0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.a.o.1.1		1
5.2	odd	4		1850.2.b.g.149.2		2
5.3	odd	4		1850.2.b.g.149.1		2
5.4	even	2		370.2.a.a.1.1	✓	1
15.14	odd	2		3330.2.a.v.1.1		1
20.19	odd	2		2960.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.a.a.1.1	✓	1	5.4	even	2
1850.2.a.o.1.1		1	1.1	even	1	trivial
1850.2.b.g.149.1		2	5.3	odd	4
1850.2.b.g.149.2		2	5.2	odd	4
2960.2.a.j.1.1		1	20.19	odd	2
3330.2.a.v.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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