LMFDB - Embedded newform 1850.2.a.f.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1850,2,Mod(1,1850)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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

Newform invariants

comment:select newform

sage:traces = [1,-1,2,1,0,-2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$14.7723243739$
Analytic rank:	$1$
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)

$f(q)$

$=$

\(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{12} -2.00000 q^{13} +2.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} +2.00000 q^{19} -4.00000 q^{21} -2.00000 q^{24} +2.00000 q^{26} -4.00000 q^{27} -2.00000 q^{28} +6.00000 q^{29} -10.0000 q^{31} -1.00000 q^{32} +6.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} -2.00000 q^{38} -4.00000 q^{39} -6.00000 q^{41} +4.00000 q^{42} +4.00000 q^{43} +6.00000 q^{47} +2.00000 q^{48} -3.00000 q^{49} -12.0000 q^{51} -2.00000 q^{52} -6.00000 q^{53} +4.00000 q^{54} +2.00000 q^{56} +4.00000 q^{57} -6.00000 q^{58} -6.00000 q^{59} -10.0000 q^{61} +10.0000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -2.00000 q^{67} -6.00000 q^{68} -1.00000 q^{72} -2.00000 q^{73} +1.00000 q^{74} +2.00000 q^{76} +4.00000 q^{78} -10.0000 q^{79} -11.0000 q^{81} +6.00000 q^{82} +6.00000 q^{83} -4.00000 q^{84} -4.00000 q^{86} +12.0000 q^{87} -6.00000 q^{89} +4.00000 q^{91} -20.0000 q^{93} -6.00000 q^{94} -2.00000 q^{96} -2.00000 q^{97} +3.00000 q^{98} +O(q^{100})\)

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
$3$	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
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	2.00000	0.577350
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	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
$19$	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
$21$	−4.00000	−0.872872
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−2.00000	−0.408248
$25$	0	0
$26$	2.00000	0.392232
$27$	−4.00000	−0.769800
$28$	−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	$0.311919\pi$
$30$	0	0
$31$	−10.0000	−1.79605	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000	−1.79605	−0.898027	+	0.439941i	$0.854999\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	6.00000	1.02899
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−2.00000	−0.324443
$39$	−4.00000	−0.640513
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	4.00000	0.617213
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	2.00000	0.288675
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−12.0000	−1.68034
$52$	−2.00000	−0.277350
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	2.00000	0.267261
$57$	4.00000	0.529813
$58$	−6.00000	−0.787839
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	10.0000	1.27000
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	−1.00000	−0.117851
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	2.00000	0.229416
$77$	0	0
$78$	4.00000	0.452911
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	6.00000	0.662589
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	−4.00000	−0.431331
$87$	12.0000	1.28654
$88$	0	0
$89$	−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
$92$	0	0
$93$	−20.0000	−2.07390
$94$	−6.00000	−0.618853
$95$	0	0
$96$	−2.00000	−0.204124
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	3.00000	0.303046
$99$	0	0
$100$	0	0
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	12.0000	1.18818
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	6.00000	0.582772
$107$	−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
$109$	14.0000	1.34096	0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	−2.00000	−0.188982
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−4.00000	−0.374634
$115$	0	0
$116$	6.00000	0.557086
$117$	−2.00000	−0.184900
$118$	6.00000	0.552345
$119$	12.0000	1.10004
$120$	0	0
$121$	−11.0000	−1.00000
$122$	10.0000	0.905357
$123$	−12.0000	−1.08200
$124$	−10.0000	−0.898027
$125$	0	0
$126$	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	$0.528283\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	2.00000	0.172774
$135$	0	0
$136$	6.00000	0.514496
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	12.0000	1.01058
$142$	0	0
$143$	0	0
$144$	1.00000	0.0833333
$145$	0	0
$146$	2.00000	0.165521
$147$	−6.00000	−0.494872
$148$	−1.00000	−0.0821995
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	−2.00000	−0.162221
$153$	−6.00000	−0.485071
$154$	0	0
$155$	0	0
$156$	−4.00000	−0.320256
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	10.0000	0.795557
$159$	−12.0000	−0.951662
$160$	0	0
$161$	0	0
$162$	11.0000	0.864242
$163$	16.0000	1.25322	0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000	1.25322	0.626608	+	0.779334i	$0.284443\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	−6.00000	−0.465690
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	4.00000	0.308607
$169$	−9.00000	−0.692308
$170$	0	0
$171$	2.00000	0.152944
$172$	4.00000	0.304997
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	−12.0000	−0.909718
$175$	0	0
$176$	0	0
$177$	−12.0000	−0.901975
$178$	6.00000	0.449719
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	0	0
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	−4.00000	−0.296500
$183$	−20.0000	−1.47844
$184$	0	0
$185$	0	0
$186$	20.0000	1.46647
$187$	0	0
$188$	6.00000	0.437595
$189$	8.00000	0.581914
$190$	0	0
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	2.00000	0.144338
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	−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
$199$	−22.0000	−1.55954	−0.779769	−	0.626067i	$-0.784664\pi$
$199$	−22.0000	−1.55954	−0.779769	+	0.626067i	$0.784664\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	−18.0000	−1.26648
$203$	−12.0000	−0.842235
$204$	−12.0000	−0.840168
$205$	0	0
$206$	−4.00000	−0.278693
$207$	0	0
$208$	−2.00000	−0.138675
$209$	0	0
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	6.00000	0.410152
$215$	0	0
$216$	4.00000	0.272166
$217$	20.0000	1.35769
$218$	−14.0000	−0.948200
$219$	−4.00000	−0.270295
$220$	0	0
$221$	12.0000	0.807207
$222$	2.00000	0.134231
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	2.00000	0.133631
$225$	0	0
$226$	6.00000	0.399114
$227$	−24.0000	−1.59294	−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−24.0000	−1.59294	−0.796468	+	0.604681i	$0.793301\pi$
$228$	4.00000	0.264906
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	0	0
$232$	−6.00000	−0.393919
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−6.00000	−0.390567
$237$	−20.0000	−1.29914
$238$	−12.0000	−0.777844
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	11.0000	0.707107
$243$	−10.0000	−0.641500
$244$	−10.0000	−0.640184
$245$	0	0
$246$	12.0000	0.765092
$247$	−4.00000	−0.254514
$248$	10.0000	0.635001
$249$	12.0000	0.760469
$250$	0	0
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	−2.00000	−0.125988
$253$	0	0
$254$	2.00000	0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	−8.00000	−0.498058
$259$	2.00000	0.124274
$260$	0	0
$261$	6.00000	0.371391
$262$	6.00000	0.370681
$263$	6.00000	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$264$	0	0
$265$	0	0
$266$	4.00000	0.245256
$267$	−12.0000	−0.734388
$268$	−2.00000	−0.122169
$269$	−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
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−6.00000	−0.363803
$273$	8.00000	0.484182
$274$	−6.00000	−0.362473
$275$	0	0
$276$	0	0
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	4.00000	0.239904
$279$	−10.0000	−0.598684
$280$	0	0
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	−12.0000	−0.714590
$283$	16.0000	0.951101	0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000	0.951101	0.475551	+	0.879688i	$0.342249\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	12.0000	0.708338
$288$	−1.00000	−0.0589256
$289$	19.0000	1.11765
$290$	0	0
$291$	−4.00000	−0.234484
$292$	−2.00000	−0.117041
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	6.00000	0.349927
$295$	0	0
$296$	1.00000	0.0581238
$297$	0	0
$298$	−18.0000	−1.04271
$299$	0	0
$300$	0	0
$301$	−8.00000	−0.461112
$302$	−20.0000	−1.15087
$303$	36.0000	2.06815
$304$	2.00000	0.114708
$305$	0	0
$306$	6.00000	0.342997
$307$	−26.0000	−1.48390	−0.741949	−	0.670456i	$-0.766098\pi$
$307$	−26.0000	−1.48390	−0.741949	+	0.670456i	$0.766098\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	0	0
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	4.00000	0.226455
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−10.0000	−0.562544
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	12.0000	0.672927
$319$	0	0
$320$	0	0
$321$	−12.0000	−0.669775
$322$	0	0
$323$	−12.0000	−0.667698
$324$	−11.0000	−0.611111
$325$	0	0
$326$	−16.0000	−0.886158
$327$	28.0000	1.54840
$328$	6.00000	0.331295
$329$	−12.0000	−0.661581
$330$	0	0
$331$	−10.0000	−0.549650	−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000	−0.549650	−0.274825	+	0.961494i	$0.588620\pi$
$332$	6.00000	0.329293
$333$	−1.00000	−0.0547997
$334$	12.0000	0.656611
$335$	0	0
$336$	−4.00000	−0.218218
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	9.00000	0.489535
$339$	−12.0000	−0.651751
$340$	0	0
$341$	0	0
$342$	−2.00000	−0.108148
$343$	20.0000	1.07990
$344$	−4.00000	−0.215666
$345$	0	0
$346$	−18.0000	−0.967686
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	12.0000	0.643268
$349$	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
$351$	8.00000	0.427008
$352$	0	0
$353$	30.0000	1.59674	0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000	1.59674	0.798369	+	0.602168i	$0.205696\pi$
$354$	12.0000	0.637793
$355$	0	0
$356$	−6.00000	−0.317999
$357$	24.0000	1.27021
$358$	−6.00000	−0.317110
$359$	36.0000	1.90001	0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000	1.90001	0.950004	+	0.312239i	$0.101079\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	22.0000	1.15629
$363$	−22.0000	−1.15470
$364$	4.00000	0.209657
$365$	0	0
$366$	20.0000	1.04542
$367$	−2.00000	−0.104399	−0.0521996	−	0.998637i	$-0.516623\pi$
$367$	−2.00000	−0.104399	−0.0521996	+	0.998637i	$0.516623\pi$
$368$	0	0
$369$	−6.00000	−0.312348
$370$	0	0
$371$	12.0000	0.623009
$372$	−20.0000	−1.03695
$373$	34.0000	1.76045	0.880227	−	0.474554i	$-0.157390\pi$
$373$	34.0000	1.76045	0.880227	+	0.474554i	$0.157390\pi$
$374$	0	0
$375$	0	0
$376$	−6.00000	−0.309426
$377$	−12.0000	−0.618031
$378$	−8.00000	−0.411476
$379$	−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
$381$	−4.00000	−0.204926
$382$	6.00000	0.306987
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	2.00000	0.101797
$387$	4.00000	0.203331
$388$	−2.00000	−0.101535
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	0	0
$392$	3.00000	0.151523
$393$	−12.0000	−0.605320
$394$	−18.0000	−0.906827
$395$	0	0
$396$	0	0
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	22.0000	1.10276
$399$	−8.00000	−0.400501
$400$	0	0
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	4.00000	0.199502
$403$	20.0000	0.996271
$404$	18.0000	0.895533
$405$	0	0
$406$	12.0000	0.595550
$407$	0	0
$408$	12.0000	0.594089
$409$	2.00000	0.0988936	0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000	0.0988936	0.0494468	+	0.998777i	$0.484254\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	4.00000	0.197066
$413$	12.0000	0.590481
$414$	0	0
$415$	0	0
$416$	2.00000	0.0980581
$417$	−8.00000	−0.391762
$418$	0	0
$419$	24.0000	1.17248	0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000	1.17248	0.586238	+	0.810139i	$0.300608\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−20.0000	−0.973585
$423$	6.00000	0.291730
$424$	6.00000	0.291386
$425$	0	0
$426$	0	0
$427$	20.0000	0.967868
$428$	−6.00000	−0.290021
$429$	0	0
$430$	0	0
$431$	30.0000	1.44505	0.722525	−	0.691345i	$-0.242982\pi$
$431$	30.0000	1.44505	0.722525	+	0.691345i	$0.242982\pi$
$432$	−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	$0.515303\pi$
$434$	−20.0000	−0.960031
$435$	0	0
$436$	14.0000	0.670478
$437$	0	0
$438$	4.00000	0.191127
$439$	−22.0000	−1.05000	−0.525001	−	0.851101i	$-0.675935\pi$
$439$	−22.0000	−1.05000	−0.525001	+	0.851101i	$0.675935\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	−12.0000	−0.570782
$443$	−6.00000	−0.285069	−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000	−0.285069	−0.142534	+	0.989790i	$0.545525\pi$
$444$	−2.00000	−0.0949158
$445$	0	0
$446$	14.0000	0.662919
$447$	36.0000	1.70274
$448$	−2.00000	−0.0944911
$449$	−30.0000	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$450$	0	0
$451$	0	0
$452$	−6.00000	−0.282216
$453$	40.0000	1.87936
$454$	24.0000	1.12638
$455$	0	0
$456$	−4.00000	−0.187317
$457$	−26.0000	−1.21623	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000	−1.21623	−0.608114	+	0.793849i	$0.708074\pi$
$458$	10.0000	0.467269
$459$	24.0000	1.12022
$460$	0	0
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	40.0000	1.85896	0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000	1.85896	0.929479	+	0.368875i	$0.120257\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	18.0000	0.833834
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	−2.00000	−0.0924500
$469$	4.00000	0.184703
$470$	0	0
$471$	20.0000	0.921551
$472$	6.00000	0.276172
$473$	0	0
$474$	20.0000	0.918630
$475$	0	0
$476$	12.0000	0.550019
$477$	−6.00000	−0.274721
$478$	−6.00000	−0.274434
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	22.0000	1.00207
$483$	0	0
$484$	−11.0000	−0.500000
$485$	0	0
$486$	10.0000	0.453609
$487$	−20.0000	−0.906287	−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000	−0.906287	−0.453143	+	0.891438i	$0.649697\pi$
$488$	10.0000	0.452679
$489$	32.0000	1.44709
$490$	0	0
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	−12.0000	−0.541002
$493$	−36.0000	−1.62136
$494$	4.00000	0.179969
$495$	0	0
$496$	−10.0000	−0.449013
$497$	0	0
$498$	−12.0000	−0.537733
$499$	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
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	2.00000	0.0890871
$505$	0	0
$506$	0	0
$507$	−18.0000	−0.799408
$508$	−2.00000	−0.0887357
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	0	0
$511$	4.00000	0.176950
$512$	−1.00000	−0.0441942
$513$	−8.00000	−0.353209
$514$	6.00000	0.264649
$515$	0	0
$516$	8.00000	0.352180
$517$	0	0
$518$	−2.00000	−0.0878750
$519$	36.0000	1.58022
$520$	0	0
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	−6.00000	−0.262613
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−6.00000	−0.262111
$525$	0	0
$526$	−6.00000	−0.261612
$527$	60.0000	2.61364
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	−6.00000	−0.260378
$532$	−4.00000	−0.173422
$533$	12.0000	0.519778
$534$	12.0000	0.519291
$535$	0	0
$536$	2.00000	0.0863868
$537$	12.0000	0.517838
$538$	6.00000	0.258678
$539$	0	0
$540$	0	0
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	16.0000	0.687259
$543$	−44.0000	−1.88822
$544$	6.00000	0.257248
$545$	0	0
$546$	−8.00000	−0.342368
$547$	−44.0000	−1.88130	−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000	−1.88130	−0.940652	+	0.339372i	$0.889785\pi$
$548$	6.00000	0.256307
$549$	−10.0000	−0.426790
$550$	0	0
$551$	12.0000	0.511217
$552$	0	0
$553$	20.0000	0.850487
$554$	26.0000	1.10463
$555$	0	0
$556$	−4.00000	−0.169638
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	10.0000	0.423334
$559$	−8.00000	−0.338364
$560$	0	0
$561$	0	0
$562$	−18.0000	−0.759284
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	12.0000	0.505291
$565$	0	0
$566$	−16.0000	−0.672530
$567$	22.0000	0.923913
$568$	0	0
$569$	−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
$571$	−28.0000	−1.17176	−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000	−1.17176	−0.585882	+	0.810397i	$0.699252\pi$
$572$	0	0
$573$	−12.0000	−0.501307
$574$	−12.0000	−0.500870
$575$	0	0
$576$	1.00000	0.0416667
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	−19.0000	−0.790296
$579$	−4.00000	−0.166234
$580$	0	0
$581$	−12.0000	−0.497844
$582$	4.00000	0.165805
$583$	0	0
$584$	2.00000	0.0827606
$585$	0	0
$586$	6.00000	0.247858
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	−6.00000	−0.247436
$589$	−20.0000	−0.824086
$590$	0	0
$591$	36.0000	1.48084
$592$	−1.00000	−0.0410997
$593$	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
$595$	0	0
$596$	18.0000	0.737309
$597$	−44.0000	−1.80080
$598$	0	0
$599$	−36.0000	−1.47092	−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000	−1.47092	−0.735460	+	0.677568i	$0.763034\pi$
$600$	0	0
$601$	38.0000	1.55005	0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000	1.55005	0.775026	+	0.631929i	$0.217737\pi$
$602$	8.00000	0.326056
$603$	−2.00000	−0.0814463
$604$	20.0000	0.813788
$605$	0	0
$606$	−36.0000	−1.46240
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	−2.00000	−0.0811107
$609$	−24.0000	−0.972529
$610$	0	0
$611$	−12.0000	−0.485468
$612$	−6.00000	−0.242536
$613$	34.0000	1.37325	0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000	1.37325	0.686624	+	0.727013i	$0.259092\pi$
$614$	26.0000	1.04927
$615$	0	0
$616$	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	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	0	0
$621$	0	0
$622$	18.0000	0.721734
$623$	12.0000	0.480770
$624$	−4.00000	−0.160128
$625$	0	0
$626$	−22.0000	−0.879297
$627$	0	0
$628$	10.0000	0.399043
$629$	6.00000	0.239236
$630$	0	0
$631$	14.0000	0.557331	0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000	0.557331	0.278666	+	0.960388i	$0.410108\pi$
$632$	10.0000	0.397779
$633$	40.0000	1.58986
$634$	−18.0000	−0.714871
$635$	0	0
$636$	−12.0000	−0.475831
$637$	6.00000	0.237729
$638$	0	0
$639$	0	0
$640$	0	0
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	12.0000	0.473602
$643$	−32.0000	−1.26196	−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000	−1.26196	−0.630978	+	0.775800i	$0.717346\pi$
$644$	0	0
$645$	0	0
$646$	12.0000	0.472134
$647$	−48.0000	−1.88707	−0.943537	−	0.331266i	$-0.892524\pi$
$647$	−48.0000	−1.88707	−0.943537	+	0.331266i	$0.892524\pi$
$648$	11.0000	0.432121
$649$	0	0
$650$	0	0
$651$	40.0000	1.56772
$652$	16.0000	0.626608
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	−28.0000	−1.09489
$655$	0	0
$656$	−6.00000	−0.234261
$657$	−2.00000	−0.0780274
$658$	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
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	10.0000	0.388661
$663$	24.0000	0.932083
$664$	−6.00000	−0.232845
$665$	0	0
$666$	1.00000	0.0387492
$667$	0	0
$668$	−12.0000	−0.464294
$669$	−28.0000	−1.08254
$670$	0	0
$671$	0	0
$672$	4.00000	0.154303
$673$	−26.0000	−1.00223	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501113	+	0.865382i	$0.667076\pi$
$674$	2.00000	0.0770371
$675$	0	0
$676$	−9.00000	−0.346154
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	12.0000	0.460857
$679$	4.00000	0.153506
$680$	0	0
$681$	−48.0000	−1.83936
$682$	0	0
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	2.00000	0.0764719
$685$	0	0
$686$	−20.0000	−0.763604
$687$	−20.0000	−0.763048
$688$	4.00000	0.152499
$689$	12.0000	0.457164
$690$	0	0
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	18.0000	0.684257
$693$	0	0
$694$	−12.0000	−0.455514
$695$	0	0
$696$	−12.0000	−0.454859
$697$	36.0000	1.36360
$698$	−26.0000	−0.984115
$699$	−36.0000	−1.36165
$700$	0	0
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	−8.00000	−0.301941
$703$	−2.00000	−0.0754314
$704$	0	0
$705$	0	0
$706$	−30.0000	−1.12906
$707$	−36.0000	−1.35392
$708$	−12.0000	−0.450988
$709$	38.0000	1.42712	0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000	1.42712	0.713560	+	0.700594i	$0.247082\pi$
$710$	0	0
$711$	−10.0000	−0.375029
$712$	6.00000	0.224860
$713$	0	0
$714$	−24.0000	−0.898177
$715$	0	0
$716$	6.00000	0.224231
$717$	12.0000	0.448148
$718$	−36.0000	−1.34351
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	0	0
$721$	−8.00000	−0.297936
$722$	15.0000	0.558242
$723$	−44.0000	−1.63638
$724$	−22.0000	−0.817624
$725$	0	0
$726$	22.0000	0.816497
$727$	−32.0000	−1.18681	−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000	−1.18681	−0.593407	+	0.804902i	$0.702218\pi$
$728$	−4.00000	−0.148250
$729$	13.0000	0.481481
$730$	0	0
$731$	−24.0000	−0.887672
$732$	−20.0000	−0.739221
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	2.00000	0.0738213
$735$	0	0
$736$	0	0
$737$	0	0
$738$	6.00000	0.220863
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	0	0
$741$	−8.00000	−0.293887
$742$	−12.0000	−0.440534
$743$	−18.0000	−0.660356	−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000	−0.660356	−0.330178	+	0.943919i	$0.607109\pi$
$744$	20.0000	0.733236
$745$	0	0
$746$	−34.0000	−1.24483
$747$	6.00000	0.219529
$748$	0	0
$749$	12.0000	0.438470
$750$	0	0
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	6.00000	0.218797
$753$	36.0000	1.31191
$754$	12.0000	0.437014
$755$	0	0
$756$	8.00000	0.290957
$757$	10.0000	0.363456	0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000	0.363456	0.181728	+	0.983349i	$0.441831\pi$
$758$	16.0000	0.581146
$759$	0	0
$760$	0	0
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	4.00000	0.144905
$763$	−28.0000	−1.01367
$764$	−6.00000	−0.217072
$765$	0	0
$766$	0	0
$767$	12.0000	0.433295
$768$	2.00000	0.0721688
$769$	26.0000	0.937584	0.468792	−	0.883309i	$-0.344689\pi$
$769$	26.0000	0.937584	0.468792	+	0.883309i	$0.344689\pi$
$770$	0	0
$771$	−12.0000	−0.432169
$772$	−2.00000	−0.0719816
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	−4.00000	−0.143777
$775$	0	0
$776$	2.00000	0.0717958
$777$	4.00000	0.143499
$778$	−6.00000	−0.215110
$779$	−12.0000	−0.429945
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−24.0000	−0.857690
$784$	−3.00000	−0.107143
$785$	0	0
$786$	12.0000	0.428026
$787$	10.0000	0.356462	0.178231	−	0.983989i	$-0.442963\pi$
$787$	10.0000	0.356462	0.178231	+	0.983989i	$0.442963\pi$
$788$	18.0000	0.641223
$789$	12.0000	0.427211
$790$	0	0
$791$	12.0000	0.426671
$792$	0	0
$793$	20.0000	0.710221
$794$	14.0000	0.496841
$795$	0	0
$796$	−22.0000	−0.779769
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	8.00000	0.283197
$799$	−36.0000	−1.27359
$800$	0	0
$801$	−6.00000	−0.212000
$802$	6.00000	0.211867
$803$	0	0
$804$	−4.00000	−0.141069
$805$	0	0
$806$	−20.0000	−0.704470
$807$	−12.0000	−0.422420
$808$	−18.0000	−0.633238
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	0	0
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	−12.0000	−0.421117
$813$	−32.0000	−1.12229
$814$	0	0
$815$	0	0
$816$	−12.0000	−0.420084
$817$	8.00000	0.279885
$818$	−2.00000	−0.0699284
$819$	4.00000	0.139771
$820$	0	0
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	−12.0000	−0.418548
$823$	34.0000	1.18517	0.592583	−	0.805510i	$-0.298108\pi$
$823$	34.0000	1.18517	0.592583	+	0.805510i	$0.298108\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	−12.0000	−0.417533
$827$	−24.0000	−0.834562	−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000	−0.834562	−0.417281	+	0.908778i	$0.637017\pi$
$828$	0	0
$829$	−34.0000	−1.18087	−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000	−1.18087	−0.590434	+	0.807086i	$0.701044\pi$
$830$	0	0
$831$	−52.0000	−1.80386
$832$	−2.00000	−0.0693375
$833$	18.0000	0.623663
$834$	8.00000	0.277017
$835$	0	0
$836$	0	0
$837$	40.0000	1.38260
$838$	−24.0000	−0.829066
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	10.0000	0.344623
$843$	36.0000	1.23991
$844$	20.0000	0.688428
$845$	0	0
$846$	−6.00000	−0.206284
$847$	22.0000	0.755929
$848$	−6.00000	−0.206041
$849$	32.0000	1.09824
$850$	0	0
$851$	0	0
$852$	0	0
$853$	10.0000	0.342393	0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000	0.342393	0.171197	+	0.985237i	$0.445237\pi$
$854$	−20.0000	−0.684386
$855$	0	0
$856$	6.00000	0.205076
$857$	−42.0000	−1.43469	−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000	−1.43469	−0.717346	+	0.696717i	$0.754643\pi$
$858$	0	0
$859$	50.0000	1.70598	0.852989	−	0.521929i	$-0.174787\pi$
$859$	50.0000	1.70598	0.852989	+	0.521929i	$0.174787\pi$
$860$	0	0
$861$	24.0000	0.817918
$862$	−30.0000	−1.02180
$863$	−54.0000	−1.83818	−0.919091	−	0.394046i	$-0.871075\pi$
$863$	−54.0000	−1.83818	−0.919091	+	0.394046i	$0.871075\pi$
$864$	4.00000	0.136083
$865$	0	0
$866$	2.00000	0.0679628
$867$	38.0000	1.29055
$868$	20.0000	0.678844
$869$	0	0
$870$	0	0
$871$	4.00000	0.135535
$872$	−14.0000	−0.474100
$873$	−2.00000	−0.0676897
$874$	0	0
$875$	0	0
$876$	−4.00000	−0.135147
$877$	10.0000	0.337676	0.168838	−	0.985644i	$-0.445999\pi$
$877$	10.0000	0.337676	0.168838	+	0.985644i	$0.445999\pi$
$878$	22.0000	0.742464
$879$	−12.0000	−0.404750
$880$	0	0
$881$	−42.0000	−1.41502	−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000	−1.41502	−0.707508	+	0.706705i	$0.750181\pi$
$882$	3.00000	0.101015
$883$	−56.0000	−1.88455	−0.942275	−	0.334840i	$-0.891318\pi$
$883$	−56.0000	−1.88455	−0.942275	+	0.334840i	$0.891318\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	6.00000	0.201574
$887$	42.0000	1.41022	0.705111	−	0.709097i	$-0.250897\pi$
$887$	42.0000	1.41022	0.705111	+	0.709097i	$0.250897\pi$
$888$	2.00000	0.0671156
$889$	4.00000	0.134156
$890$	0	0
$891$	0	0
$892$	−14.0000	−0.468755
$893$	12.0000	0.401565
$894$	−36.0000	−1.20402
$895$	0	0
$896$	2.00000	0.0668153
$897$	0	0
$898$	30.0000	1.00111
$899$	−60.0000	−2.00111
$900$	0	0
$901$	36.0000	1.19933
$902$	0	0
$903$	−16.0000	−0.532447
$904$	6.00000	0.199557
$905$	0	0
$906$	−40.0000	−1.32891
$907$	−8.00000	−0.265636	−0.132818	−	0.991140i	$-0.542403\pi$
$907$	−8.00000	−0.265636	−0.132818	+	0.991140i	$0.542403\pi$
$908$	−24.0000	−0.796468
$909$	18.0000	0.597022
$910$	0	0
$911$	−30.0000	−0.993944	−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000	−0.993944	−0.496972	+	0.867766i	$0.665555\pi$
$912$	4.00000	0.132453
$913$	0	0
$914$	26.0000	0.860004
$915$	0	0
$916$	−10.0000	−0.330409
$917$	12.0000	0.396275
$918$	−24.0000	−0.792118
$919$	−46.0000	−1.51740	−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000	−1.51740	−0.758700	+	0.651440i	$0.774165\pi$
$920$	0	0
$921$	−52.0000	−1.71346
$922$	−6.00000	−0.197599
$923$	0	0
$924$	0	0
$925$	0	0
$926$	−40.0000	−1.31448
$927$	4.00000	0.131377
$928$	−6.00000	−0.196960
$929$	−30.0000	−0.984268	−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000	−0.984268	−0.492134	+	0.870519i	$0.663783\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	−18.0000	−0.589610
$933$	−36.0000	−1.17859
$934$	0	0
$935$	0	0
$936$	2.00000	0.0653720
$937$	−26.0000	−0.849383	−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000	−0.849383	−0.424691	+	0.905338i	$0.639617\pi$
$938$	−4.00000	−0.130605
$939$	44.0000	1.43589
$940$	0	0
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	−20.0000	−0.651635
$943$	0	0
$944$	−6.00000	−0.195283
$945$	0	0
$946$	0	0
$947$	−48.0000	−1.55979	−0.779895	−	0.625910i	$-0.784728\pi$
$947$	−48.0000	−1.55979	−0.779895	+	0.625910i	$0.784728\pi$
$948$	−20.0000	−0.649570
$949$	4.00000	0.129845
$950$	0	0
$951$	36.0000	1.16738
$952$	−12.0000	−0.388922
$953$	−42.0000	−1.36051	−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000	−1.36051	−0.680257	+	0.732974i	$0.738132\pi$
$954$	6.00000	0.194257
$955$	0	0
$956$	6.00000	0.194054
$957$	0	0
$958$	18.0000	0.581554
$959$	−12.0000	−0.387500
$960$	0	0
$961$	69.0000	2.22581
$962$	−2.00000	−0.0644826
$963$	−6.00000	−0.193347
$964$	−22.0000	−0.708572
$965$	0	0
$966$	0	0
$967$	4.00000	0.128631	0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000	0.128631	0.0643157	+	0.997930i	$0.479514\pi$
$968$	11.0000	0.353553
$969$	−24.0000	−0.770991
$970$	0	0
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	−10.0000	−0.320750
$973$	8.00000	0.256468
$974$	20.0000	0.640841
$975$	0	0
$976$	−10.0000	−0.320092
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	−32.0000	−1.02325
$979$	0	0
$980$	0	0
$981$	14.0000	0.446986
$982$	−36.0000	−1.14881
$983$	−18.0000	−0.574111	−0.287055	−	0.957914i	$-0.592676\pi$
$983$	−18.0000	−0.574111	−0.287055	+	0.957914i	$0.592676\pi$
$984$	12.0000	0.382546
$985$	0	0
$986$	36.0000	1.14647
$987$	−24.0000	−0.763928
$988$	−4.00000	−0.127257
$989$	0	0
$990$	0	0
$991$	−34.0000	−1.08005	−0.540023	−	0.841650i	$-0.681584\pi$
$991$	−34.0000	−1.08005	−0.540023	+	0.841650i	$0.681584\pi$
$992$	10.0000	0.317500
$993$	−20.0000	−0.634681
$994$	0	0
$995$	0	0
$996$	12.0000	0.380235
$997$	10.0000	0.316703	0.158352	−	0.987383i	$-0.449382\pi$
$997$	10.0000	0.316703	0.158352	+	0.987383i	$0.449382\pi$
$998$	−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.f.1.1		1
5.2	odd	4		1850.2.b.b.149.1		2
5.3	odd	4		1850.2.b.b.149.2		2
5.4	even	2		370.2.a.d.1.1	✓	1
15.14	odd	2		3330.2.a.d.1.1		1
20.19	odd	2		2960.2.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.a.d.1.1	✓	1	5.4	even	2
1850.2.a.f.1.1		1	1.1	even	1	trivial
1850.2.b.b.149.1		2	5.2	odd	4
1850.2.b.b.149.2		2	5.3	odd	4
2960.2.a.m.1.1		1	20.19	odd	2
3330.2.a.d.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 $\F_{q}$
Belyi maps

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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